Properties

Label 300.3.c.g.151.2
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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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: 8.0.4069419264.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.2
Root \(0.151747 - 0.0876113i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.g.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33290 + 1.49110i) q^{2} +1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} +6.56834i q^{7} +(6.52255 + 4.63210i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.33290 + 1.49110i) q^{2} +1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} +6.56834i q^{7} +(6.52255 + 4.63210i) q^{8} -3.00000 q^{9} +2.26696i q^{11} +(6.88486 - 0.773791i) q^{12} +14.8772 q^{13} +(-9.79404 - 8.75495i) q^{14} +(-15.6008 + 3.55163i) q^{16} -26.8250 q^{17} +(3.99870 - 4.47330i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(-3.38027 - 3.02164i) q^{22} +36.4610i q^{23} +(-8.02303 + 11.2974i) q^{24} +(-19.8298 + 22.1834i) q^{26} -5.19615i q^{27} +(26.1090 - 2.93440i) q^{28} -35.2510 q^{29} -23.8330i q^{31} +(15.4985 - 27.9963i) q^{32} -3.92650 q^{33} +(35.7550 - 39.9987i) q^{34} +(1.34025 + 11.9249i) q^{36} -54.7495 q^{37} +(-16.2053 - 14.4860i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(15.1640 - 16.9638i) q^{42} -56.2515i q^{43} +(9.01112 - 1.01276i) q^{44} +(-54.3670 - 48.5989i) q^{46} +51.4177i q^{47} +(-6.15160 - 27.0214i) q^{48} +5.85689 q^{49} -46.4622i q^{51} +(-6.64636 - 59.1364i) q^{52} -30.6465 q^{53} +(7.74797 + 6.92596i) q^{54} +(-30.4252 + 42.8423i) q^{56} -18.8240 q^{57} +(46.9861 - 52.5627i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(35.5374 + 31.7671i) q^{62} -19.7050i q^{63} +(21.0873 + 60.4262i) q^{64} +(5.23363 - 5.85479i) q^{66} +111.444i q^{67} +(11.9840 + 106.629i) q^{68} -63.1524 q^{69} -31.3190i q^{71} +(-19.5676 - 13.8963i) q^{72} -110.909 q^{73} +(72.9757 - 81.6369i) q^{74} +(43.2002 - 4.85528i) q^{76} -14.8902 q^{77} +(-38.4227 - 34.3463i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(31.7628 - 35.5326i) q^{82} +142.416i q^{83} +(5.08253 + 45.2221i) q^{84} +(83.8765 + 74.9776i) q^{86} -61.0565i q^{87} +(-10.5008 + 14.7864i) q^{88} +7.14798 q^{89} +97.7185i q^{91} +(144.932 - 16.2889i) q^{92} +41.2800 q^{93} +(-76.6689 - 68.5347i) q^{94} +(48.4911 + 26.8443i) q^{96} +126.308 q^{97} +(-7.80665 + 8.73319i) q^{98} -6.80089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} + 8 q^{13} + 22 q^{14} + 40 q^{16} - 6 q^{18} + 24 q^{21} + 4 q^{22} - 36 q^{24} - 66 q^{26} + 104 q^{28} - 32 q^{29} + 112 q^{32} + 124 q^{34} + 24 q^{36} - 176 q^{37} - 170 q^{38} - 16 q^{41} + 54 q^{42} + 40 q^{44} - 76 q^{46} + 24 q^{48} + 16 q^{49} + 56 q^{52} - 304 q^{53} + 18 q^{54} - 172 q^{56} + 72 q^{57} - 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} - 108 q^{66} + 88 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} - 108 q^{74} + 120 q^{76} - 384 q^{77} + 150 q^{78} + 72 q^{81} + 320 q^{82} - 144 q^{84} + 214 q^{86} - 200 q^{88} + 128 q^{89} + 312 q^{92} + 72 q^{93} + 12 q^{94} + 96 q^{96} + 216 q^{97} + 60 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33290 + 1.49110i −0.666451 + 0.745549i
\(3\) 1.73205i 0.577350i
\(4\) −0.446749 3.97497i −0.111687 0.993743i
\(5\) 0 0
\(6\) −2.58266 2.30865i −0.430443 0.384775i
\(7\) 6.56834i 0.938335i 0.883109 + 0.469167i \(0.155446\pi\)
−0.883109 + 0.469167i \(0.844554\pi\)
\(8\) 6.52255 + 4.63210i 0.815319 + 0.579013i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 2.26696i 0.206088i 0.994677 + 0.103044i \(0.0328582\pi\)
−0.994677 + 0.103044i \(0.967142\pi\)
\(12\) 6.88486 0.773791i 0.573738 0.0644826i
\(13\) 14.8772 1.14440 0.572200 0.820114i \(-0.306090\pi\)
0.572200 + 0.820114i \(0.306090\pi\)
\(14\) −9.79404 8.75495i −0.699575 0.625354i
\(15\) 0 0
\(16\) −15.6008 + 3.55163i −0.975052 + 0.221977i
\(17\) −26.8250 −1.57794 −0.788969 0.614432i \(-0.789385\pi\)
−0.788969 + 0.614432i \(0.789385\pi\)
\(18\) 3.99870 4.47330i 0.222150 0.248516i
\(19\) 10.8680i 0.572002i 0.958229 + 0.286001i \(0.0923260\pi\)
−0.958229 + 0.286001i \(0.907674\pi\)
\(20\) 0 0
\(21\) −11.3767 −0.541748
\(22\) −3.38027 3.02164i −0.153648 0.137347i
\(23\) 36.4610i 1.58526i 0.609702 + 0.792631i \(0.291289\pi\)
−0.609702 + 0.792631i \(0.708711\pi\)
\(24\) −8.02303 + 11.2974i −0.334293 + 0.470724i
\(25\) 0 0
\(26\) −19.8298 + 22.1834i −0.762685 + 0.853206i
\(27\) 5.19615i 0.192450i
\(28\) 26.1090 2.93440i 0.932464 0.104800i
\(29\) −35.2510 −1.21555 −0.607775 0.794109i \(-0.707938\pi\)
−0.607775 + 0.794109i \(0.707938\pi\)
\(30\) 0 0
\(31\) 23.8330i 0.768808i −0.923165 0.384404i \(-0.874407\pi\)
0.923165 0.384404i \(-0.125593\pi\)
\(32\) 15.4985 27.9963i 0.484329 0.874886i
\(33\) −3.92650 −0.118985
\(34\) 35.7550 39.9987i 1.05162 1.17643i
\(35\) 0 0
\(36\) 1.34025 + 11.9249i 0.0372290 + 0.331248i
\(37\) −54.7495 −1.47972 −0.739858 0.672763i \(-0.765107\pi\)
−0.739858 + 0.672763i \(0.765107\pi\)
\(38\) −16.2053 14.4860i −0.426455 0.381211i
\(39\) 25.7680i 0.660719i
\(40\) 0 0
\(41\) −23.8298 −0.581215 −0.290608 0.956842i \(-0.593857\pi\)
−0.290608 + 0.956842i \(0.593857\pi\)
\(42\) 15.1640 16.9638i 0.361048 0.403900i
\(43\) 56.2515i 1.30817i −0.756420 0.654087i \(-0.773053\pi\)
0.756420 0.654087i \(-0.226947\pi\)
\(44\) 9.01112 1.01276i 0.204798 0.0230173i
\(45\) 0 0
\(46\) −54.3670 48.5989i −1.18189 1.05650i
\(47\) 51.4177i 1.09399i 0.837135 + 0.546997i \(0.184229\pi\)
−0.837135 + 0.546997i \(0.815771\pi\)
\(48\) −6.15160 27.0214i −0.128158 0.562947i
\(49\) 5.85689 0.119528
\(50\) 0 0
\(51\) 46.4622i 0.911023i
\(52\) −6.64636 59.1364i −0.127815 1.13724i
\(53\) −30.6465 −0.578236 −0.289118 0.957293i \(-0.593362\pi\)
−0.289118 + 0.957293i \(0.593362\pi\)
\(54\) 7.74797 + 6.92596i 0.143481 + 0.128258i
\(55\) 0 0
\(56\) −30.4252 + 42.8423i −0.543308 + 0.765042i
\(57\) −18.8240 −0.330245
\(58\) 46.9861 52.5627i 0.810105 0.906253i
\(59\) 6.92483i 0.117370i −0.998277 0.0586850i \(-0.981309\pi\)
0.998277 0.0586850i \(-0.0186908\pi\)
\(60\) 0 0
\(61\) 107.426 1.76107 0.880537 0.473977i \(-0.157182\pi\)
0.880537 + 0.473977i \(0.157182\pi\)
\(62\) 35.5374 + 31.7671i 0.573184 + 0.512372i
\(63\) 19.7050i 0.312778i
\(64\) 21.0873 + 60.4262i 0.329489 + 0.944160i
\(65\) 0 0
\(66\) 5.23363 5.85479i 0.0792975 0.0887090i
\(67\) 111.444i 1.66334i 0.555271 + 0.831670i \(0.312615\pi\)
−0.555271 + 0.831670i \(0.687385\pi\)
\(68\) 11.9840 + 106.629i 0.176235 + 1.56807i
\(69\) −63.1524 −0.915251
\(70\) 0 0
\(71\) 31.3190i 0.441113i −0.975374 0.220556i \(-0.929213\pi\)
0.975374 0.220556i \(-0.0707873\pi\)
\(72\) −19.5676 13.8963i −0.271773 0.193004i
\(73\) −110.909 −1.51930 −0.759652 0.650330i \(-0.774631\pi\)
−0.759652 + 0.650330i \(0.774631\pi\)
\(74\) 72.9757 81.6369i 0.986158 1.10320i
\(75\) 0 0
\(76\) 43.2002 4.85528i 0.568423 0.0638853i
\(77\) −14.8902 −0.193379
\(78\) −38.4227 34.3463i −0.492599 0.440337i
\(79\) 59.0065i 0.746917i 0.927647 + 0.373459i \(0.121828\pi\)
−0.927647 + 0.373459i \(0.878172\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 31.7628 35.5326i 0.387351 0.433325i
\(83\) 142.416i 1.71586i 0.513767 + 0.857930i \(0.328249\pi\)
−0.513767 + 0.857930i \(0.671751\pi\)
\(84\) 5.08253 + 45.2221i 0.0605063 + 0.538358i
\(85\) 0 0
\(86\) 83.8765 + 74.9776i 0.975308 + 0.871833i
\(87\) 61.0565i 0.701799i
\(88\) −10.5008 + 14.7864i −0.119327 + 0.168027i
\(89\) 7.14798 0.0803144 0.0401572 0.999193i \(-0.487214\pi\)
0.0401572 + 0.999193i \(0.487214\pi\)
\(90\) 0 0
\(91\) 97.7185i 1.07383i
\(92\) 144.932 16.2889i 1.57534 0.177053i
\(93\) 41.2800 0.443871
\(94\) −76.6689 68.5347i −0.815626 0.729093i
\(95\) 0 0
\(96\) 48.4911 + 26.8443i 0.505116 + 0.279628i
\(97\) 126.308 1.30214 0.651070 0.759017i \(-0.274320\pi\)
0.651070 + 0.759017i \(0.274320\pi\)
\(98\) −7.80665 + 8.73319i −0.0796597 + 0.0891142i
\(99\) 6.80089i 0.0686959i
\(100\) 0 0
\(101\) 86.7133 0.858547 0.429274 0.903174i \(-0.358770\pi\)
0.429274 + 0.903174i \(0.358770\pi\)
\(102\) 69.2797 + 61.9295i 0.679213 + 0.607152i
\(103\) 21.9281i 0.212895i −0.994318 0.106447i \(-0.966052\pi\)
0.994318 0.106447i \(-0.0339475\pi\)
\(104\) 97.0372 + 68.9126i 0.933050 + 0.662622i
\(105\) 0 0
\(106\) 40.8488 45.6970i 0.385366 0.431104i
\(107\) 7.17725i 0.0670771i 0.999437 + 0.0335385i \(0.0106777\pi\)
−0.999437 + 0.0335385i \(0.989322\pi\)
\(108\) −20.6546 + 2.32137i −0.191246 + 0.0214942i
\(109\) 25.4256 0.233262 0.116631 0.993175i \(-0.462790\pi\)
0.116631 + 0.993175i \(0.462790\pi\)
\(110\) 0 0
\(111\) 94.8289i 0.854315i
\(112\) −23.3283 102.472i −0.208288 0.914925i
\(113\) 78.3588 0.693441 0.346720 0.937968i \(-0.387295\pi\)
0.346720 + 0.937968i \(0.387295\pi\)
\(114\) 25.0905 28.0684i 0.220092 0.246214i
\(115\) 0 0
\(116\) 15.7483 + 140.122i 0.135761 + 1.20795i
\(117\) −44.6316 −0.381466
\(118\) 10.3256 + 9.23012i 0.0875052 + 0.0782214i
\(119\) 176.196i 1.48063i
\(120\) 0 0
\(121\) 115.861 0.957528
\(122\) −143.188 + 160.182i −1.17367 + 1.31297i
\(123\) 41.2745i 0.335565i
\(124\) −94.7357 + 10.6474i −0.763997 + 0.0858659i
\(125\) 0 0
\(126\) 29.3821 + 26.2649i 0.233192 + 0.208451i
\(127\) 71.6077i 0.563840i −0.959438 0.281920i \(-0.909029\pi\)
0.959438 0.281920i \(-0.0909713\pi\)
\(128\) −118.209 49.0990i −0.923505 0.383586i
\(129\) 97.4304 0.755274
\(130\) 0 0
\(131\) 103.978i 0.793728i 0.917877 + 0.396864i \(0.129902\pi\)
−0.917877 + 0.396864i \(0.870098\pi\)
\(132\) 1.75416 + 15.6077i 0.0132891 + 0.118240i
\(133\) −71.3850 −0.536729
\(134\) −166.174 148.543i −1.24010 1.10853i
\(135\) 0 0
\(136\) −174.967 124.256i −1.28652 0.913647i
\(137\) −7.16645 −0.0523099 −0.0261549 0.999658i \(-0.508326\pi\)
−0.0261549 + 0.999658i \(0.508326\pi\)
\(138\) 84.1758 94.1664i 0.609970 0.682365i
\(139\) 146.909i 1.05690i 0.848965 + 0.528449i \(0.177226\pi\)
−0.848965 + 0.528449i \(0.822774\pi\)
\(140\) 0 0
\(141\) −89.0581 −0.631618
\(142\) 46.6997 + 41.7451i 0.328871 + 0.293980i
\(143\) 33.7261i 0.235847i
\(144\) 46.8025 10.6549i 0.325017 0.0739922i
\(145\) 0 0
\(146\) 147.831 165.376i 1.01254 1.13272i
\(147\) 10.1444i 0.0690097i
\(148\) 24.4593 + 217.628i 0.165265 + 1.47046i
\(149\) 79.6054 0.534265 0.267132 0.963660i \(-0.413924\pi\)
0.267132 + 0.963660i \(0.413924\pi\)
\(150\) 0 0
\(151\) 182.722i 1.21008i 0.796196 + 0.605039i \(0.206842\pi\)
−0.796196 + 0.605039i \(0.793158\pi\)
\(152\) −50.3418 + 70.8873i −0.331196 + 0.466364i
\(153\) 80.4749 0.525980
\(154\) 19.8472 22.2027i 0.128878 0.144174i
\(155\) 0 0
\(156\) 102.427 11.5118i 0.656585 0.0737938i
\(157\) 212.182 1.35148 0.675739 0.737141i \(-0.263825\pi\)
0.675739 + 0.737141i \(0.263825\pi\)
\(158\) −87.9844 78.6498i −0.556864 0.497783i
\(159\) 53.0813i 0.333845i
\(160\) 0 0
\(161\) −239.488 −1.48751
\(162\) −11.9961 + 13.4199i −0.0740501 + 0.0828388i
\(163\) 243.400i 1.49325i −0.665244 0.746626i \(-0.731673\pi\)
0.665244 0.746626i \(-0.268327\pi\)
\(164\) 10.6459 + 94.7229i 0.0649143 + 0.577579i
\(165\) 0 0
\(166\) −212.357 189.827i −1.27926 1.14354i
\(167\) 211.395i 1.26584i −0.774218 0.632919i \(-0.781857\pi\)
0.774218 0.632919i \(-0.218143\pi\)
\(168\) −74.2051 52.6980i −0.441697 0.313679i
\(169\) 52.3307 0.309649
\(170\) 0 0
\(171\) 32.6041i 0.190667i
\(172\) −223.598 + 25.1303i −1.29999 + 0.146106i
\(173\) −22.3138 −0.128982 −0.0644909 0.997918i \(-0.520542\pi\)
−0.0644909 + 0.997918i \(0.520542\pi\)
\(174\) 91.0412 + 81.3823i 0.523225 + 0.467714i
\(175\) 0 0
\(176\) −8.05141 35.3665i −0.0457467 0.200946i
\(177\) 11.9942 0.0677636
\(178\) −9.52755 + 10.6583i −0.0535255 + 0.0598783i
\(179\) 94.5219i 0.528055i 0.964515 + 0.264028i \(0.0850510\pi\)
−0.964515 + 0.264028i \(0.914949\pi\)
\(180\) 0 0
\(181\) −80.6179 −0.445403 −0.222702 0.974887i \(-0.571488\pi\)
−0.222702 + 0.974887i \(0.571488\pi\)
\(182\) −145.708 130.249i −0.800592 0.715654i
\(183\) 186.067i 1.01676i
\(184\) −168.891 + 237.819i −0.917887 + 1.29249i
\(185\) 0 0
\(186\) −55.0222 + 61.5526i −0.295818 + 0.330928i
\(187\) 60.8112i 0.325194i
\(188\) 204.384 22.9708i 1.08715 0.122185i
\(189\) 34.1301 0.180583
\(190\) 0 0
\(191\) 330.540i 1.73058i −0.501275 0.865288i \(-0.667135\pi\)
0.501275 0.865288i \(-0.332865\pi\)
\(192\) −104.661 + 36.5242i −0.545111 + 0.190230i
\(193\) 103.609 0.536836 0.268418 0.963303i \(-0.413499\pi\)
0.268418 + 0.963303i \(0.413499\pi\)
\(194\) −168.356 + 188.337i −0.867812 + 0.970810i
\(195\) 0 0
\(196\) −2.61656 23.2810i −0.0133498 0.118780i
\(197\) −160.633 −0.815394 −0.407697 0.913117i \(-0.633668\pi\)
−0.407697 + 0.913117i \(0.633668\pi\)
\(198\) 10.1408 + 9.06492i 0.0512162 + 0.0457824i
\(199\) 27.5518i 0.138451i −0.997601 0.0692255i \(-0.977947\pi\)
0.997601 0.0692255i \(-0.0220528\pi\)
\(200\) 0 0
\(201\) −193.026 −0.960329
\(202\) −115.580 + 129.298i −0.572179 + 0.640089i
\(203\) 231.540i 1.14059i
\(204\) −184.686 + 20.7569i −0.905324 + 0.101750i
\(205\) 0 0
\(206\) 32.6970 + 29.2280i 0.158723 + 0.141884i
\(207\) 109.383i 0.528421i
\(208\) −232.097 + 52.8382i −1.11585 + 0.254030i
\(209\) −24.6374 −0.117883
\(210\) 0 0
\(211\) 269.808i 1.27871i 0.768911 + 0.639355i \(0.220799\pi\)
−0.768911 + 0.639355i \(0.779201\pi\)
\(212\) 13.6913 + 121.819i 0.0645816 + 0.574618i
\(213\) 54.2461 0.254677
\(214\) −10.7020 9.56656i −0.0500093 0.0447036i
\(215\) 0 0
\(216\) 24.0691 33.8922i 0.111431 0.156908i
\(217\) 156.544 0.721399
\(218\) −33.8898 + 37.9120i −0.155458 + 0.173908i
\(219\) 192.100i 0.877170i
\(220\) 0 0
\(221\) −399.080 −1.80579
\(222\) 141.399 + 126.398i 0.636934 + 0.569359i
\(223\) 41.3345i 0.185356i 0.995696 + 0.0926782i \(0.0295428\pi\)
−0.995696 + 0.0926782i \(0.970457\pi\)
\(224\) 183.890 + 101.800i 0.820935 + 0.454463i
\(225\) 0 0
\(226\) −104.445 + 116.841i −0.462144 + 0.516994i
\(227\) 149.837i 0.660076i −0.943968 0.330038i \(-0.892939\pi\)
0.943968 0.330038i \(-0.107061\pi\)
\(228\) 8.40959 + 74.8249i 0.0368842 + 0.328179i
\(229\) −61.6770 −0.269332 −0.134666 0.990891i \(-0.542996\pi\)
−0.134666 + 0.990891i \(0.542996\pi\)
\(230\) 0 0
\(231\) 25.7906i 0.111648i
\(232\) −229.926 163.286i −0.991061 0.703819i
\(233\) 405.585 1.74071 0.870355 0.492425i \(-0.163890\pi\)
0.870355 + 0.492425i \(0.163890\pi\)
\(234\) 59.4895 66.5501i 0.254228 0.284402i
\(235\) 0 0
\(236\) −27.5260 + 3.09366i −0.116636 + 0.0131087i
\(237\) −102.202 −0.431233
\(238\) 262.725 + 234.851i 1.10389 + 0.986770i
\(239\) 267.769i 1.12037i −0.828367 0.560185i \(-0.810730\pi\)
0.828367 0.560185i \(-0.189270\pi\)
\(240\) 0 0
\(241\) −89.5377 −0.371526 −0.185763 0.982595i \(-0.559476\pi\)
−0.185763 + 0.982595i \(0.559476\pi\)
\(242\) −154.431 + 172.760i −0.638145 + 0.713884i
\(243\) 15.5885i 0.0641500i
\(244\) −47.9922 427.014i −0.196689 1.75006i
\(245\) 0 0
\(246\) 61.5443 + 55.0148i 0.250180 + 0.223637i
\(247\) 161.686i 0.654598i
\(248\) 110.397 155.452i 0.445149 0.626823i
\(249\) −246.672 −0.990652
\(250\) 0 0
\(251\) 227.844i 0.907745i 0.891067 + 0.453873i \(0.149958\pi\)
−0.891067 + 0.453873i \(0.850042\pi\)
\(252\) −78.3270 + 8.80319i −0.310821 + 0.0349333i
\(253\) −82.6559 −0.326703
\(254\) 106.774 + 95.4460i 0.420371 + 0.375772i
\(255\) 0 0
\(256\) 230.772 110.817i 0.901453 0.432878i
\(257\) 442.129 1.72035 0.860173 0.510003i \(-0.170356\pi\)
0.860173 + 0.510003i \(0.170356\pi\)
\(258\) −129.865 + 145.278i −0.503353 + 0.563094i
\(259\) 359.614i 1.38847i
\(260\) 0 0
\(261\) 105.753 0.405184
\(262\) −155.042 138.593i −0.591763 0.528981i
\(263\) 34.1556i 0.129869i −0.997890 0.0649346i \(-0.979316\pi\)
0.997890 0.0649346i \(-0.0206839\pi\)
\(264\) −25.6108 18.1879i −0.0970105 0.0688937i
\(265\) 0 0
\(266\) 95.1491 106.442i 0.357703 0.400158i
\(267\) 12.3807i 0.0463695i
\(268\) 442.986 49.7873i 1.65293 0.185774i
\(269\) −9.96085 −0.0370292 −0.0185146 0.999829i \(-0.505894\pi\)
−0.0185146 + 0.999829i \(0.505894\pi\)
\(270\) 0 0
\(271\) 56.5791i 0.208779i −0.994536 0.104390i \(-0.966711\pi\)
0.994536 0.104390i \(-0.0332889\pi\)
\(272\) 418.492 95.2723i 1.53857 0.350266i
\(273\) −169.253 −0.619976
\(274\) 9.55218 10.6859i 0.0348620 0.0389996i
\(275\) 0 0
\(276\) 28.2132 + 251.029i 0.102222 + 0.909525i
\(277\) −103.794 −0.374708 −0.187354 0.982292i \(-0.559991\pi\)
−0.187354 + 0.982292i \(0.559991\pi\)
\(278\) −219.056 195.815i −0.787969 0.704370i
\(279\) 71.4991i 0.256269i
\(280\) 0 0
\(281\) 393.069 1.39882 0.699411 0.714720i \(-0.253446\pi\)
0.699411 + 0.714720i \(0.253446\pi\)
\(282\) 118.706 132.794i 0.420942 0.470902i
\(283\) 114.027i 0.402923i 0.979496 + 0.201462i \(0.0645692\pi\)
−0.979496 + 0.201462i \(0.935431\pi\)
\(284\) −124.492 + 13.9917i −0.438353 + 0.0492666i
\(285\) 0 0
\(286\) −50.2889 44.9535i −0.175835 0.157180i
\(287\) 156.522i 0.545374i
\(288\) −46.4956 + 83.9890i −0.161443 + 0.291629i
\(289\) 430.579 1.48989
\(290\) 0 0
\(291\) 218.771i 0.751791i
\(292\) 49.5485 + 440.861i 0.169687 + 1.50980i
\(293\) −126.796 −0.432750 −0.216375 0.976310i \(-0.569423\pi\)
−0.216375 + 0.976310i \(0.569423\pi\)
\(294\) −15.1263 13.5215i −0.0514501 0.0459915i
\(295\) 0 0
\(296\) −357.106 253.605i −1.20644 0.856775i
\(297\) 11.7795 0.0396616
\(298\) −106.106 + 118.700i −0.356061 + 0.398321i
\(299\) 542.438i 1.81417i
\(300\) 0 0
\(301\) 369.479 1.22750
\(302\) −272.456 243.550i −0.902172 0.806457i
\(303\) 150.192i 0.495683i
\(304\) −38.5992 169.550i −0.126971 0.557732i
\(305\) 0 0
\(306\) −107.265 + 119.996i −0.350539 + 0.392144i
\(307\) 408.420i 1.33036i 0.746683 + 0.665180i \(0.231645\pi\)
−0.746683 + 0.665180i \(0.768355\pi\)
\(308\) 6.65217 + 59.1881i 0.0215980 + 0.192169i
\(309\) 37.9806 0.122915
\(310\) 0 0
\(311\) 472.495i 1.51928i −0.650345 0.759639i \(-0.725376\pi\)
0.650345 0.759639i \(-0.274624\pi\)
\(312\) −119.360 + 168.073i −0.382565 + 0.538697i
\(313\) −54.6519 −0.174607 −0.0873033 0.996182i \(-0.527825\pi\)
−0.0873033 + 0.996182i \(0.527825\pi\)
\(314\) −282.818 + 316.384i −0.900693 + 1.00759i
\(315\) 0 0
\(316\) 234.549 26.3611i 0.742244 0.0834211i
\(317\) 63.3734 0.199916 0.0999581 0.994992i \(-0.468129\pi\)
0.0999581 + 0.994992i \(0.468129\pi\)
\(318\) 79.1495 + 70.7522i 0.248898 + 0.222491i
\(319\) 79.9127i 0.250510i
\(320\) 0 0
\(321\) −12.4314 −0.0387270
\(322\) 319.215 357.101i 0.991349 1.10901i
\(323\) 291.535i 0.902584i
\(324\) −4.02074 35.7748i −0.0124097 0.110416i
\(325\) 0 0
\(326\) 362.933 + 324.428i 1.11329 + 0.995179i
\(327\) 44.0384i 0.134674i
\(328\) −155.431 110.382i −0.473876 0.336531i
\(329\) −337.729 −1.02653
\(330\) 0 0
\(331\) 431.595i 1.30391i 0.758257 + 0.651955i \(0.226051\pi\)
−0.758257 + 0.651955i \(0.773949\pi\)
\(332\) 566.101 63.6243i 1.70512 0.191639i
\(333\) 164.249 0.493239
\(334\) 315.211 + 281.768i 0.943744 + 0.843618i
\(335\) 0 0
\(336\) 177.486 40.4058i 0.528232 0.120255i
\(337\) −486.091 −1.44241 −0.721203 0.692723i \(-0.756411\pi\)
−0.721203 + 0.692723i \(0.756411\pi\)
\(338\) −69.7517 + 78.0303i −0.206366 + 0.230859i
\(339\) 135.721i 0.400358i
\(340\) 0 0
\(341\) 54.0286 0.158442
\(342\) 48.6159 + 43.4581i 0.142152 + 0.127070i
\(343\) 360.319i 1.05049i
\(344\) 260.562 366.903i 0.757449 1.06658i
\(345\) 0 0
\(346\) 29.7422 33.2721i 0.0859600 0.0961623i
\(347\) 294.297i 0.848119i 0.905634 + 0.424060i \(0.139395\pi\)
−0.905634 + 0.424060i \(0.860605\pi\)
\(348\) −242.698 + 27.2769i −0.697408 + 0.0783819i
\(349\) 83.0428 0.237945 0.118972 0.992898i \(-0.462040\pi\)
0.118972 + 0.992898i \(0.462040\pi\)
\(350\) 0 0
\(351\) 77.3041i 0.220240i
\(352\) 63.4667 + 35.1346i 0.180303 + 0.0998143i
\(353\) −570.733 −1.61681 −0.808404 0.588628i \(-0.799668\pi\)
−0.808404 + 0.588628i \(0.799668\pi\)
\(354\) −15.9870 + 17.8845i −0.0451611 + 0.0505211i
\(355\) 0 0
\(356\) −3.19335 28.4130i −0.00897008 0.0798119i
\(357\) 305.180 0.854845
\(358\) −140.941 125.988i −0.393691 0.351923i
\(359\) 558.265i 1.55506i 0.628848 + 0.777528i \(0.283527\pi\)
−0.628848 + 0.777528i \(0.716473\pi\)
\(360\) 0 0
\(361\) 242.886 0.672814
\(362\) 107.456 120.209i 0.296839 0.332070i
\(363\) 200.677i 0.552829i
\(364\) 388.428 43.6556i 1.06711 0.119933i
\(365\) 0 0
\(366\) −277.444 248.008i −0.758042 0.677618i
\(367\) 446.467i 1.21653i −0.793734 0.608265i \(-0.791866\pi\)
0.793734 0.608265i \(-0.208134\pi\)
\(368\) −129.496 568.822i −0.351891 1.54571i
\(369\) 71.4895 0.193738
\(370\) 0 0
\(371\) 201.297i 0.542579i
\(372\) −18.4418 164.087i −0.0495747 0.441094i
\(373\) −112.924 −0.302744 −0.151372 0.988477i \(-0.548369\pi\)
−0.151372 + 0.988477i \(0.548369\pi\)
\(374\) 90.6755 + 81.0554i 0.242448 + 0.216726i
\(375\) 0 0
\(376\) −238.172 + 335.375i −0.633436 + 0.891954i
\(377\) −524.435 −1.39108
\(378\) −45.4921 + 50.8913i −0.120349 + 0.134633i
\(379\) 321.457i 0.848173i 0.905622 + 0.424086i \(0.139405\pi\)
−0.905622 + 0.424086i \(0.860595\pi\)
\(380\) 0 0
\(381\) 124.028 0.325533
\(382\) 492.868 + 440.577i 1.29023 + 1.15334i
\(383\) 89.2269i 0.232968i −0.993193 0.116484i \(-0.962838\pi\)
0.993193 0.116484i \(-0.0371624\pi\)
\(384\) 85.0419 204.743i 0.221463 0.533186i
\(385\) 0 0
\(386\) −138.101 + 154.492i −0.357775 + 0.400238i
\(387\) 168.754i 0.436058i
\(388\) −56.4278 502.069i −0.145432 1.29399i
\(389\) 260.714 0.670217 0.335108 0.942180i \(-0.391227\pi\)
0.335108 + 0.942180i \(0.391227\pi\)
\(390\) 0 0
\(391\) 978.066i 2.50145i
\(392\) 38.2018 + 27.1297i 0.0974536 + 0.0692084i
\(393\) −180.096 −0.458259
\(394\) 214.107 239.519i 0.543420 0.607916i
\(395\) 0 0
\(396\) −27.0334 + 3.03829i −0.0682661 + 0.00767245i
\(397\) 112.607 0.283644 0.141822 0.989892i \(-0.454704\pi\)
0.141822 + 0.989892i \(0.454704\pi\)
\(398\) 41.0824 + 36.7238i 0.103222 + 0.0922708i
\(399\) 123.642i 0.309881i
\(400\) 0 0
\(401\) 577.513 1.44018 0.720091 0.693880i \(-0.244100\pi\)
0.720091 + 0.693880i \(0.244100\pi\)
\(402\) 257.285 287.821i 0.640012 0.715973i
\(403\) 354.569i 0.879823i
\(404\) −38.7390 344.683i −0.0958887 0.853176i
\(405\) 0 0
\(406\) 345.250 + 308.621i 0.850368 + 0.760149i
\(407\) 124.115i 0.304951i
\(408\) 215.218 303.052i 0.527494 0.742774i
\(409\) −276.255 −0.675441 −0.337721 0.941246i \(-0.609656\pi\)
−0.337721 + 0.941246i \(0.609656\pi\)
\(410\) 0 0
\(411\) 12.4127i 0.0302011i
\(412\) −87.1638 + 9.79636i −0.211563 + 0.0237776i
\(413\) 45.4847 0.110132
\(414\) 163.101 + 145.797i 0.393964 + 0.352166i
\(415\) 0 0
\(416\) 230.575 416.507i 0.554266 1.00122i
\(417\) −254.454 −0.610200
\(418\) 32.8393 36.7369i 0.0785629 0.0878872i
\(419\) 247.520i 0.590739i −0.955383 0.295370i \(-0.904557\pi\)
0.955383 0.295370i \(-0.0954428\pi\)
\(420\) 0 0
\(421\) −77.7303 −0.184632 −0.0923162 0.995730i \(-0.529427\pi\)
−0.0923162 + 0.995730i \(0.529427\pi\)
\(422\) −402.310 359.627i −0.953342 0.852197i
\(423\) 154.253i 0.364665i
\(424\) −199.893 141.958i −0.471447 0.334806i
\(425\) 0 0
\(426\) −72.3047 + 80.8863i −0.169729 + 0.189874i
\(427\) 705.608i 1.65248i
\(428\) 28.5294 3.20643i 0.0666574 0.00749165i
\(429\) −58.4152 −0.136166
\(430\) 0 0
\(431\) 317.184i 0.735926i 0.929840 + 0.367963i \(0.119945\pi\)
−0.929840 + 0.367963i \(0.880055\pi\)
\(432\) 18.4548 + 81.0643i 0.0427194 + 0.187649i
\(433\) −82.9688 −0.191614 −0.0958069 0.995400i \(-0.530543\pi\)
−0.0958069 + 0.995400i \(0.530543\pi\)
\(434\) −208.657 + 233.422i −0.480777 + 0.537838i
\(435\) 0 0
\(436\) −11.3588 101.066i −0.0260524 0.231803i
\(437\) −396.260 −0.906773
\(438\) 286.440 + 256.051i 0.653974 + 0.584591i
\(439\) 117.621i 0.267930i −0.990986 0.133965i \(-0.957229\pi\)
0.990986 0.133965i \(-0.0427709\pi\)
\(440\) 0 0
\(441\) −17.5707 −0.0398428
\(442\) 531.934 595.068i 1.20347 1.34631i
\(443\) 35.1780i 0.0794086i −0.999211 0.0397043i \(-0.987358\pi\)
0.999211 0.0397043i \(-0.0126416\pi\)
\(444\) −376.943 + 42.3647i −0.848970 + 0.0954160i
\(445\) 0 0
\(446\) −61.6337 55.0948i −0.138192 0.123531i
\(447\) 137.881i 0.308458i
\(448\) −396.900 + 138.508i −0.885938 + 0.309171i
\(449\) −67.4253 −0.150168 −0.0750838 0.997177i \(-0.523922\pi\)
−0.0750838 + 0.997177i \(0.523922\pi\)
\(450\) 0 0
\(451\) 54.0214i 0.119781i
\(452\) −35.0067 311.474i −0.0774484 0.689102i
\(453\) −316.483 −0.698638
\(454\) 223.422 + 199.718i 0.492119 + 0.439908i
\(455\) 0 0
\(456\) −122.780 87.1946i −0.269255 0.191216i
\(457\) −204.153 −0.446724 −0.223362 0.974736i \(-0.571703\pi\)
−0.223362 + 0.974736i \(0.571703\pi\)
\(458\) 82.2094 91.9665i 0.179496 0.200800i
\(459\) 139.387i 0.303674i
\(460\) 0 0
\(461\) 125.762 0.272802 0.136401 0.990654i \(-0.456446\pi\)
0.136401 + 0.990654i \(0.456446\pi\)
\(462\) 38.4563 + 34.3763i 0.0832387 + 0.0744076i
\(463\) 553.629i 1.19574i 0.801592 + 0.597871i \(0.203987\pi\)
−0.801592 + 0.597871i \(0.796013\pi\)
\(464\) 549.944 125.198i 1.18523 0.269824i
\(465\) 0 0
\(466\) −540.605 + 604.768i −1.16010 + 1.29778i
\(467\) 625.772i 1.33998i 0.742369 + 0.669991i \(0.233702\pi\)
−0.742369 + 0.669991i \(0.766298\pi\)
\(468\) 19.9391 + 177.409i 0.0426049 + 0.379080i
\(469\) −732.000 −1.56077
\(470\) 0 0
\(471\) 367.510i 0.780276i
\(472\) 32.0765 45.1676i 0.0679588 0.0956940i
\(473\) 127.520 0.269598
\(474\) 136.225 152.394i 0.287395 0.321505i
\(475\) 0 0
\(476\) −700.373 + 78.7151i −1.47137 + 0.165368i
\(477\) 91.9396 0.192745
\(478\) 399.269 + 356.909i 0.835291 + 0.746672i
\(479\) 488.207i 1.01922i −0.860405 0.509610i \(-0.829790\pi\)
0.860405 0.509610i \(-0.170210\pi\)
\(480\) 0 0
\(481\) −814.519 −1.69339
\(482\) 119.345 133.509i 0.247604 0.276991i
\(483\) 414.806i 0.858812i
\(484\) −51.7607 460.544i −0.106944 0.951537i
\(485\) 0 0
\(486\) −23.2439 20.7779i −0.0478270 0.0427528i
\(487\) 609.476i 1.25149i −0.780027 0.625746i \(-0.784795\pi\)
0.780027 0.625746i \(-0.215205\pi\)
\(488\) 700.689 + 497.606i 1.43584 + 1.01968i
\(489\) 421.581 0.862129
\(490\) 0 0
\(491\) 689.074i 1.40341i 0.712468 + 0.701705i \(0.247578\pi\)
−0.712468 + 0.701705i \(0.752422\pi\)
\(492\) −164.065 + 18.4393i −0.333465 + 0.0374783i
\(493\) 945.606 1.91806
\(494\) −241.089 215.511i −0.488035 0.436257i
\(495\) 0 0
\(496\) 84.6461 + 371.815i 0.170657 + 0.749627i
\(497\) 205.714 0.413911
\(498\) 328.790 367.813i 0.660220 0.738580i
\(499\) 700.401i 1.40361i 0.712370 + 0.701804i \(0.247622\pi\)
−0.712370 + 0.701804i \(0.752378\pi\)
\(500\) 0 0
\(501\) 366.147 0.730832
\(502\) −339.738 303.694i −0.676769 0.604967i
\(503\) 943.945i 1.87663i 0.345782 + 0.938315i \(0.387614\pi\)
−0.345782 + 0.938315i \(0.612386\pi\)
\(504\) 91.2757 128.527i 0.181103 0.255014i
\(505\) 0 0
\(506\) 110.172 123.248i 0.217731 0.243573i
\(507\) 90.6395i 0.178776i
\(508\) −284.639 + 31.9906i −0.560313 + 0.0629737i
\(509\) −357.147 −0.701665 −0.350832 0.936438i \(-0.614101\pi\)
−0.350832 + 0.936438i \(0.614101\pi\)
\(510\) 0 0
\(511\) 728.489i 1.42562i
\(512\) −142.358 + 491.811i −0.278042 + 0.960569i
\(513\) 56.4720 0.110082
\(514\) −589.314 + 659.258i −1.14653 + 1.28260i
\(515\) 0 0
\(516\) −43.5269 387.283i −0.0843544 0.750549i
\(517\) −116.562 −0.225459
\(518\) 536.219 + 479.329i 1.03517 + 0.925346i
\(519\) 38.6487i 0.0744677i
\(520\) 0 0
\(521\) −88.8415 −0.170521 −0.0852605 0.996359i \(-0.527172\pi\)
−0.0852605 + 0.996359i \(0.527172\pi\)
\(522\) −140.958 + 157.688i −0.270035 + 0.302084i
\(523\) 220.427i 0.421467i 0.977544 + 0.210734i \(0.0675852\pi\)
−0.977544 + 0.210734i \(0.932415\pi\)
\(524\) 413.311 46.4522i 0.788762 0.0886492i
\(525\) 0 0
\(526\) 50.9294 + 45.5261i 0.0968239 + 0.0865514i
\(527\) 639.320i 1.21313i
\(528\) 61.2566 13.9455i 0.116016 0.0264119i
\(529\) −800.407 −1.51306
\(530\) 0 0
\(531\) 20.7745i 0.0391234i
\(532\) 31.8911 + 283.753i 0.0599457 + 0.533371i
\(533\) −354.521 −0.665142
\(534\) −18.4608 16.5022i −0.0345708 0.0309030i
\(535\) 0 0
\(536\) −516.219 + 726.897i −0.963094 + 1.35615i
\(537\) −163.717 −0.304873
\(538\) 13.2768 14.8526i 0.0246781 0.0276071i
\(539\) 13.2774i 0.0246333i
\(540\) 0 0
\(541\) −411.560 −0.760740 −0.380370 0.924834i \(-0.624203\pi\)
−0.380370 + 0.924834i \(0.624203\pi\)
\(542\) 84.3651 + 75.4144i 0.155655 + 0.139141i
\(543\) 139.634i 0.257154i
\(544\) −415.748 + 751.001i −0.764242 + 1.38052i
\(545\) 0 0
\(546\) 225.598 252.373i 0.413183 0.462222i
\(547\) 851.537i 1.55674i −0.627806 0.778370i \(-0.716047\pi\)
0.627806 0.778370i \(-0.283953\pi\)
\(548\) 3.20160 + 28.4865i 0.00584234 + 0.0519826i
\(549\) −322.277 −0.587025
\(550\) 0 0
\(551\) 383.109i 0.695297i
\(552\) −411.914 292.528i −0.746222 0.529942i
\(553\) −387.575 −0.700858
\(554\) 138.347 154.767i 0.249724 0.279363i
\(555\) 0 0
\(556\) 583.959 65.6313i 1.05029 0.118042i
\(557\) 211.553 0.379808 0.189904 0.981803i \(-0.439182\pi\)
0.189904 + 0.981803i \(0.439182\pi\)
\(558\) −106.612 95.3012i −0.191061 0.170791i
\(559\) 836.864i 1.49707i
\(560\) 0 0
\(561\) 105.328 0.187751
\(562\) −523.922 + 586.104i −0.932246 + 1.04289i
\(563\) 404.044i 0.717663i −0.933402 0.358832i \(-0.883175\pi\)
0.933402 0.358832i \(-0.116825\pi\)
\(564\) 39.7866 + 354.004i 0.0705436 + 0.627666i
\(565\) 0 0
\(566\) −170.026 151.987i −0.300399 0.268529i
\(567\) 59.1151i 0.104259i
\(568\) 145.073 204.280i 0.255410 0.359647i
\(569\) 230.465 0.405036 0.202518 0.979279i \(-0.435088\pi\)
0.202518 + 0.979279i \(0.435088\pi\)
\(570\) 0 0
\(571\) 351.234i 0.615121i −0.951529 0.307560i \(-0.900487\pi\)
0.951529 0.307560i \(-0.0995126\pi\)
\(572\) 134.060 15.0671i 0.234371 0.0263410i
\(573\) 572.512 0.999149
\(574\) 233.390 + 208.629i 0.406603 + 0.363465i
\(575\) 0 0
\(576\) −63.2618 181.279i −0.109830 0.314720i
\(577\) −638.575 −1.10672 −0.553358 0.832944i \(-0.686654\pi\)
−0.553358 + 0.832944i \(0.686654\pi\)
\(578\) −573.919 + 642.035i −0.992939 + 1.11079i
\(579\) 179.457i 0.309942i
\(580\) 0 0
\(581\) −935.439 −1.61005
\(582\) −326.209 291.600i −0.560497 0.501032i
\(583\) 69.4746i 0.119167i
\(584\) −723.410 513.742i −1.23872 0.879696i
\(585\) 0 0
\(586\) 169.006 189.065i 0.288407 0.322637i
\(587\) 105.047i 0.178956i 0.995989 + 0.0894779i \(0.0285198\pi\)
−0.995989 + 0.0894779i \(0.971480\pi\)
\(588\) 40.3238 4.53201i 0.0685779 0.00770749i
\(589\) 259.018 0.439759
\(590\) 0 0
\(591\) 278.224i 0.470768i
\(592\) 854.138 194.450i 1.44280 0.328463i
\(593\) 990.175 1.66977 0.834886 0.550422i \(-0.185533\pi\)
0.834886 + 0.550422i \(0.185533\pi\)
\(594\) −15.7009 + 17.5644i −0.0264325 + 0.0295697i
\(595\) 0 0
\(596\) −35.5636 316.429i −0.0596705 0.530922i
\(597\) 47.7210 0.0799347
\(598\) −808.828 723.016i −1.35255 1.20906i
\(599\) 78.0745i 0.130341i −0.997874 0.0651707i \(-0.979241\pi\)
0.997874 0.0651707i \(-0.0207592\pi\)
\(600\) 0 0
\(601\) −616.498 −1.02579 −0.512893 0.858452i \(-0.671426\pi\)
−0.512893 + 0.858452i \(0.671426\pi\)
\(602\) −492.479 + 550.929i −0.818071 + 0.915165i
\(603\) 334.331i 0.554446i
\(604\) 726.314 81.6306i 1.20251 0.135150i
\(605\) 0 0
\(606\) −223.951 200.191i −0.369556 0.330348i
\(607\) 226.520i 0.373179i 0.982438 + 0.186590i \(0.0597435\pi\)
−0.982438 + 0.186590i \(0.940257\pi\)
\(608\) 304.265 + 168.439i 0.500436 + 0.277037i
\(609\) 401.040 0.658522
\(610\) 0 0
\(611\) 764.951i 1.25197i
\(612\) −35.9520 319.886i −0.0587452 0.522689i
\(613\) 732.519 1.19497 0.597487 0.801879i \(-0.296166\pi\)
0.597487 + 0.801879i \(0.296166\pi\)
\(614\) −608.995 544.384i −0.991848 0.886619i
\(615\) 0 0
\(616\) −97.1220 68.9729i −0.157666 0.111969i
\(617\) 350.585 0.568209 0.284105 0.958793i \(-0.408304\pi\)
0.284105 + 0.958793i \(0.408304\pi\)
\(618\) −50.6245 + 56.6329i −0.0819166 + 0.0916390i
\(619\) 237.923i 0.384367i −0.981359 0.192184i \(-0.938443\pi\)
0.981359 0.192184i \(-0.0615569\pi\)
\(620\) 0 0
\(621\) 189.457 0.305084
\(622\) 704.537 + 629.790i 1.13270 + 1.01252i
\(623\) 46.9504i 0.0753617i
\(624\) −91.5185 402.003i −0.146664 0.644235i
\(625\) 0 0
\(626\) 72.8455 81.4913i 0.116367 0.130178i
\(627\) 42.6733i 0.0680595i
\(628\) −94.7920 843.417i −0.150943 1.34302i
\(629\) 1468.65 2.33490
\(630\) 0 0
\(631\) 200.923i 0.318419i 0.987245 + 0.159210i \(0.0508946\pi\)
−0.987245 + 0.159210i \(0.949105\pi\)
\(632\) −273.324 + 384.873i −0.432475 + 0.608976i
\(633\) −467.321 −0.738264
\(634\) −84.4705 + 94.4960i −0.133234 + 0.149047i
\(635\) 0 0
\(636\) −210.997 + 23.7140i −0.331756 + 0.0372862i
\(637\) 87.1340 0.136788
\(638\) 119.158 + 106.516i 0.186768 + 0.166953i
\(639\) 93.9570i 0.147038i
\(640\) 0 0
\(641\) 216.861 0.338316 0.169158 0.985589i \(-0.445895\pi\)
0.169158 + 0.985589i \(0.445895\pi\)
\(642\) 16.5698 18.5364i 0.0258096 0.0288729i
\(643\) 37.5349i 0.0583746i 0.999574 + 0.0291873i \(0.00929193\pi\)
−0.999574 + 0.0291873i \(0.990708\pi\)
\(644\) 106.991 + 951.960i 0.166135 + 1.47820i
\(645\) 0 0
\(646\) 434.707 + 388.587i 0.672921 + 0.601528i
\(647\) 1192.56i 1.84321i −0.388125 0.921607i \(-0.626877\pi\)
0.388125 0.921607i \(-0.373123\pi\)
\(648\) 58.7029 + 41.6889i 0.0905910 + 0.0643347i
\(649\) 15.6984 0.0241885
\(650\) 0 0
\(651\) 271.141i 0.416500i
\(652\) −967.509 + 108.739i −1.48391 + 0.166777i
\(653\) −1087.78 −1.66582 −0.832908 0.553412i \(-0.813325\pi\)
−0.832908 + 0.553412i \(0.813325\pi\)
\(654\) −65.6656 58.6988i −0.100406 0.0897535i
\(655\) 0 0
\(656\) 371.765 84.6347i 0.566715 0.129016i
\(657\) 332.727 0.506435
\(658\) 450.160 503.587i 0.684133 0.765330i
\(659\) 852.957i 1.29432i −0.762354 0.647160i \(-0.775956\pi\)
0.762354 0.647160i \(-0.224044\pi\)
\(660\) 0 0
\(661\) −504.933 −0.763892 −0.381946 0.924185i \(-0.624746\pi\)
−0.381946 + 0.924185i \(0.624746\pi\)
\(662\) −643.550 575.273i −0.972130 0.868992i
\(663\) 691.227i 1.04257i
\(664\) −659.687 + 928.917i −0.993504 + 1.39897i
\(665\) 0 0
\(666\) −218.927 + 244.911i −0.328719 + 0.367734i
\(667\) 1285.29i 1.92697i
\(668\) −840.289 + 94.4403i −1.25792 + 0.141378i
\(669\) −71.5934 −0.107016
\(670\) 0 0
\(671\) 243.530i 0.362936i
\(672\) −176.322 + 318.506i −0.262384 + 0.473967i
\(673\) −902.689 −1.34129 −0.670646 0.741778i \(-0.733983\pi\)
−0.670646 + 0.741778i \(0.733983\pi\)
\(674\) 647.911 724.810i 0.961293 1.07539i
\(675\) 0 0
\(676\) −23.3787 208.013i −0.0345838 0.307712i
\(677\) 930.750 1.37482 0.687408 0.726272i \(-0.258748\pi\)
0.687408 + 0.726272i \(0.258748\pi\)
\(678\) −202.374 180.903i −0.298487 0.266819i
\(679\) 829.632i 1.22184i
\(680\) 0 0
\(681\) 259.526 0.381095
\(682\) −72.0148 + 80.5620i −0.105594 + 0.118126i
\(683\) 64.9023i 0.0950253i 0.998871 + 0.0475127i \(0.0151294\pi\)
−0.998871 + 0.0475127i \(0.984871\pi\)
\(684\) −129.600 + 14.5658i −0.189474 + 0.0212951i
\(685\) 0 0
\(686\) −537.271 480.269i −0.783193 0.700101i
\(687\) 106.828i 0.155499i
\(688\) 199.784 + 877.570i 0.290384 + 1.27554i
\(689\) −455.934 −0.661733
\(690\) 0 0
\(691\) 348.329i 0.504094i 0.967715 + 0.252047i \(0.0811038\pi\)
−0.967715 + 0.252047i \(0.918896\pi\)
\(692\) 9.96868 + 88.6970i 0.0144056 + 0.128175i
\(693\) 44.6706 0.0644597
\(694\) −438.826 392.269i −0.632315 0.565230i
\(695\) 0 0
\(696\) 282.820 398.244i 0.406350 0.572189i
\(697\) 639.234 0.917122
\(698\) −110.688 + 123.825i −0.158579 + 0.177400i
\(699\) 702.494i 1.00500i
\(700\) 0 0
\(701\) 815.159 1.16285 0.581426 0.813600i \(-0.302495\pi\)
0.581426 + 0.813600i \(0.302495\pi\)
\(702\) 115.268 + 103.039i 0.164200 + 0.146779i
\(703\) 595.020i 0.846401i
\(704\) −136.984 + 47.8041i −0.194580 + 0.0679036i
\(705\) 0 0
\(706\) 760.731 851.020i 1.07752 1.20541i
\(707\) 569.562i 0.805605i
\(708\) −5.35838 47.6765i −0.00756833 0.0673397i
\(709\) 1300.08 1.83368 0.916839 0.399257i \(-0.130732\pi\)
0.916839 + 0.399257i \(0.130732\pi\)
\(710\) 0 0
\(711\) 177.019i 0.248972i
\(712\) 46.6230 + 33.1102i 0.0654818 + 0.0465030i
\(713\) 868.977 1.21876
\(714\) −406.774 + 455.053i −0.569712 + 0.637329i
\(715\) 0 0
\(716\) 375.722 42.2275i 0.524751 0.0589770i
\(717\) 463.789 0.646846
\(718\) −832.428 744.112i −1.15937 1.03637i
\(719\) 782.612i 1.08847i 0.838932 + 0.544237i \(0.183181\pi\)
−0.838932 + 0.544237i \(0.816819\pi\)
\(720\) 0 0
\(721\) 144.031 0.199766
\(722\) −323.743 + 362.167i −0.448397 + 0.501616i
\(723\) 155.084i 0.214500i
\(724\) 36.0160 + 320.454i 0.0497458 + 0.442616i
\(725\) 0 0
\(726\) −299.229 267.483i −0.412161 0.368433i
\(727\) 850.638i 1.17007i −0.811009 0.585033i \(-0.801081\pi\)
0.811009 0.585033i \(-0.198919\pi\)
\(728\) −452.642 + 637.373i −0.621761 + 0.875513i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1508.94i 2.06422i
\(732\) 739.610 83.1250i 1.01040 0.113559i
\(733\) 365.781 0.499019 0.249510 0.968372i \(-0.419731\pi\)
0.249510 + 0.968372i \(0.419731\pi\)
\(734\) 665.726 + 595.096i 0.906984 + 0.810758i
\(735\) 0 0
\(736\) 1020.78 + 565.093i 1.38692 + 0.767789i
\(737\) −252.639 −0.342794
\(738\) −95.2884 + 106.598i −0.129117 + 0.144442i
\(739\) 727.328i 0.984205i −0.870537 0.492103i \(-0.836228\pi\)
0.870537 0.492103i \(-0.163772\pi\)
\(740\) 0 0
\(741\) −280.048 −0.377933
\(742\) 300.153 + 268.309i 0.404519 + 0.361602i
\(743\) 481.526i 0.648083i 0.946043 + 0.324041i \(0.105042\pi\)
−0.946043 + 0.324041i \(0.894958\pi\)
\(744\) 269.251 + 191.213i 0.361896 + 0.257007i
\(745\) 0 0
\(746\) 150.516 168.380i 0.201764 0.225711i
\(747\) 427.249i 0.571953i
\(748\) −241.723 + 27.1673i −0.323159 + 0.0363200i
\(749\) −47.1426 −0.0629408
\(750\) 0 0
\(751\) 1316.30i 1.75273i −0.481647 0.876365i \(-0.659961\pi\)
0.481647 0.876365i \(-0.340039\pi\)
\(752\) −182.617 802.159i −0.242841 1.06670i
\(753\) −394.637 −0.524087
\(754\) 699.021 781.985i 0.927083 1.03711i
\(755\) 0 0
\(756\) −15.2476 135.666i −0.0201688 0.179453i
\(757\) 483.813 0.639118 0.319559 0.947566i \(-0.396465\pi\)
0.319559 + 0.947566i \(0.396465\pi\)
\(758\) −479.325 428.471i −0.632354 0.565265i
\(759\) 143.164i 0.188622i
\(760\) 0 0
\(761\) 1027.03 1.34958 0.674789 0.738011i \(-0.264235\pi\)
0.674789 + 0.738011i \(0.264235\pi\)
\(762\) −165.317 + 184.938i −0.216952 + 0.242701i
\(763\) 167.004i 0.218878i
\(764\) −1313.89 + 147.668i −1.71975 + 0.193283i
\(765\) 0 0
\(766\) 133.046 + 118.931i 0.173689 + 0.155262i
\(767\) 103.022i 0.134318i
\(768\) 191.940 + 399.709i 0.249922 + 0.520454i
\(769\) 1024.79 1.33263 0.666314 0.745671i \(-0.267871\pi\)
0.666314 + 0.745671i \(0.267871\pi\)
\(770\) 0 0
\(771\) 765.790i 0.993242i
\(772\) −46.2873 411.844i −0.0599577 0.533477i
\(773\) −1092.74 −1.41364 −0.706819 0.707395i \(-0.749870\pi\)
−0.706819 + 0.707395i \(0.749870\pi\)
\(774\) −251.629 224.933i −0.325103 0.290611i
\(775\) 0 0
\(776\) 823.848 + 585.070i 1.06166 + 0.753956i
\(777\) 622.869 0.801633
\(778\) −347.506 + 388.751i −0.446666 + 0.499679i
\(779\) 258.983i 0.332456i
\(780\) 0 0
\(781\) 70.9991 0.0909079
\(782\) 1458.39 + 1303.66i 1.86495 + 1.66709i
\(783\) 183.169i 0.233933i
\(784\) −91.3723 + 20.8015i −0.116546 + 0.0265325i
\(785\) 0 0
\(786\) 240.050 268.541i 0.305407 0.341655i
\(787\) 1385.63i 1.76064i 0.474376 + 0.880322i \(0.342674\pi\)
−0.474376 + 0.880322i \(0.657326\pi\)
\(788\) 71.7624 + 638.511i 0.0910691 + 0.810293i
\(789\) 59.1593 0.0749800
\(790\) 0 0
\(791\) 514.688i 0.650680i
\(792\) 31.5024 44.3592i 0.0397758 0.0560090i
\(793\) 1598.19 2.01537
\(794\) −150.093 + 167.907i −0.189034 + 0.211470i
\(795\) 0 0
\(796\) −109.518 + 12.3087i −0.137585 + 0.0154632i
\(797\) −98.5251 −0.123620 −0.0618100 0.998088i \(-0.519687\pi\)
−0.0618100 + 0.998088i \(0.519687\pi\)
\(798\) 184.363 + 164.803i 0.231031 + 0.206520i
\(799\) 1379.28i 1.72626i
\(800\) 0 0
\(801\) −21.4439 −0.0267715
\(802\) −769.767 + 861.128i −0.959810 + 1.07373i
\(803\) 251.427i 0.313110i
\(804\) 86.2342 + 767.274i 0.107256 + 0.954321i
\(805\) 0 0
\(806\) 528.697 + 472.605i 0.655951 + 0.586358i
\(807\) 17.2527i 0.0213788i
\(808\) 565.592 + 401.665i 0.699990 + 0.497110i
\(809\) −212.100 −0.262176 −0.131088 0.991371i \(-0.541847\pi\)
−0.131088 + 0.991371i \(0.541847\pi\)
\(810\) 0 0
\(811\) 485.409i 0.598531i −0.954170 0.299266i \(-0.903258\pi\)
0.954170 0.299266i \(-0.0967417\pi\)
\(812\) −920.367 + 103.440i −1.13346 + 0.127390i
\(813\) 97.9980 0.120539
\(814\) 185.068 + 165.433i 0.227356 + 0.203235i
\(815\) 0 0
\(816\) 165.016 + 724.849i 0.202226 + 0.888295i
\(817\) 611.343 0.748278
\(818\) 368.221 411.924i 0.450148 0.503575i
\(819\) 293.155i 0.357943i
\(820\) 0 0
\(821\) −862.231 −1.05022 −0.525110 0.851034i \(-0.675976\pi\)
−0.525110 + 0.851034i \(0.675976\pi\)
\(822\) 18.5085 + 16.5449i 0.0225164 + 0.0201276i
\(823\) 485.042i 0.589358i 0.955596 + 0.294679i \(0.0952127\pi\)
−0.955596 + 0.294679i \(0.904787\pi\)
\(824\) 101.573 143.027i 0.123269 0.173577i
\(825\) 0 0
\(826\) −60.6266 + 67.8221i −0.0733978 + 0.0821091i
\(827\) 590.547i 0.714084i −0.934088 0.357042i \(-0.883785\pi\)
0.934088 0.357042i \(-0.116215\pi\)
\(828\) −434.795 + 48.8667i −0.525115 + 0.0590178i
\(829\) −1071.30 −1.29228 −0.646139 0.763220i \(-0.723617\pi\)
−0.646139 + 0.763220i \(0.723617\pi\)
\(830\) 0 0
\(831\) 179.777i 0.216338i
\(832\) 313.719 + 898.972i 0.377067 + 1.08050i
\(833\) −157.111 −0.188608
\(834\) 339.161 379.415i 0.406668 0.454934i
\(835\) 0 0
\(836\) 11.0067 + 97.9332i 0.0131660 + 0.117145i
\(837\) −123.840 −0.147957
\(838\) 369.076 + 329.919i 0.440425 + 0.393698i
\(839\) 783.581i 0.933946i −0.884272 0.466973i \(-0.845345\pi\)
0.884272 0.466973i \(-0.154655\pi\)
\(840\) 0 0
\(841\) 401.631 0.477564
\(842\) 103.607 115.903i 0.123048 0.137653i
\(843\) 680.815i 0.807610i
\(844\) 1072.48 120.536i 1.27071 0.142816i
\(845\) 0 0
\(846\) 230.007 + 205.604i 0.271875 + 0.243031i
\(847\) 761.014i 0.898481i
\(848\) 478.111 108.845i 0.563810 0.128355i
\(849\) −197.501 −0.232628
\(850\) 0 0
\(851\) 1996.22i 2.34574i
\(852\) −24.2344 215.627i −0.0284441 0.253083i
\(853\) −104.807 −0.122868 −0.0614341 0.998111i \(-0.519567\pi\)
−0.0614341 + 0.998111i \(0.519567\pi\)
\(854\) −1052.13 940.506i −1.23200 1.10129i
\(855\) 0 0
\(856\) −33.2457 + 46.8140i −0.0388385 + 0.0546892i
\(857\) 1163.30 1.35741 0.678705 0.734411i \(-0.262542\pi\)
0.678705 + 0.734411i \(0.262542\pi\)
\(858\) 77.8617 87.1029i 0.0907480 0.101518i
\(859\) 337.818i 0.393269i 0.980477 + 0.196634i \(0.0630012\pi\)
−0.980477 + 0.196634i \(0.936999\pi\)
\(860\) 0 0
\(861\) 271.105 0.314872
\(862\) −472.953 422.775i −0.548669 0.490458i
\(863\) 199.699i 0.231400i −0.993284 0.115700i \(-0.963089\pi\)
0.993284 0.115700i \(-0.0369112\pi\)
\(864\) −145.473 80.5328i −0.168372 0.0932092i
\(865\) 0 0
\(866\) 110.589 123.715i 0.127701 0.142858i
\(867\) 745.784i 0.860189i
\(868\) −69.9356 622.256i −0.0805710 0.716885i
\(869\) −133.766 −0.153930
\(870\) 0 0
\(871\) 1657.97i 1.90352i
\(872\) 165.840 + 117.774i 0.190183 + 0.135062i
\(873\) −378.923 −0.434047
\(874\) 528.175 590.862i 0.604319 0.676044i
\(875\) 0 0
\(876\) −763.594 + 85.8205i −0.871682 + 0.0979687i
\(877\) −1032.82 −1.17767 −0.588836 0.808252i \(-0.700414\pi\)
−0.588836 + 0.808252i \(0.700414\pi\)
\(878\) 175.385 + 156.777i 0.199755 + 0.178562i
\(879\) 219.617i 0.249849i
\(880\) 0 0
\(881\) −585.412 −0.664486 −0.332243 0.943194i \(-0.607805\pi\)
−0.332243 + 0.943194i \(0.607805\pi\)
\(882\) 23.4199 26.1996i 0.0265532 0.0297047i
\(883\) 536.231i 0.607283i −0.952786 0.303641i \(-0.901797\pi\)
0.952786 0.303641i \(-0.0982025\pi\)
\(884\) 178.288 + 1586.33i 0.201684 + 1.79449i
\(885\) 0 0
\(886\) 52.4539 + 46.8888i 0.0592030 + 0.0529219i
\(887\) 173.466i 0.195564i 0.995208 + 0.0977822i \(0.0311749\pi\)
−0.995208 + 0.0977822i \(0.968825\pi\)
\(888\) 439.257 618.526i 0.494659 0.696539i
\(889\) 470.344 0.529071
\(890\) 0 0
\(891\) 20.4027i 0.0228986i
\(892\) 164.303 18.4661i 0.184197 0.0207019i
\(893\) −558.810 −0.625767
\(894\) −205.594 183.781i −0.229970 0.205572i
\(895\) 0 0
\(896\) 322.499 776.435i 0.359932 0.866557i
\(897\) −939.529 −1.04741
\(898\) 89.8712 100.538i 0.100079 0.111957i
\(899\) 840.138i 0.934525i
\(900\) 0 0
\(901\) 822.092 0.912421
\(902\) 80.5512 + 72.0051i 0.0893028 + 0.0798283i
\(903\) 639.956i 0.708700i
\(904\) 511.099 + 362.966i 0.565375 + 0.401511i
\(905\) 0 0
\(906\) 421.841 471.908i 0.465608 0.520869i
\(907\) 817.237i 0.901033i −0.892768 0.450516i \(-0.851240\pi\)
0.892768 0.450516i \(-0.148760\pi\)
\(908\) −595.599 + 66.9395i −0.655946 + 0.0737220i
\(909\) −260.140 −0.286182
\(910\) 0 0
\(911\) 227.911i 0.250177i 0.992146 + 0.125088i \(0.0399215\pi\)
−0.992146 + 0.125088i \(0.960079\pi\)
\(912\) 293.670 66.8558i 0.322006 0.0733068i
\(913\) −322.853 −0.353617
\(914\) 272.115 304.412i 0.297719 0.333055i
\(915\) 0 0
\(916\) 27.5541 + 245.165i 0.0300809 + 0.267647i
\(917\) −682.966 −0.744783
\(918\) −207.839 185.789i −0.226404 0.202384i
\(919\) 669.088i 0.728061i 0.931387 + 0.364031i \(0.118600\pi\)
−0.931387 + 0.364031i \(0.881400\pi\)
\(920\) 0 0
\(921\) −707.405 −0.768083
\(922\) −167.628 + 187.523i −0.181809 + 0.203387i
\(923\) 465.939i 0.504809i
\(924\) −102.517 + 11.5219i −0.110949 + 0.0124696i
\(925\) 0 0
\(926\) −825.515 737.933i −0.891485 0.796904i
\(927\) 65.7844i 0.0709648i
\(928\) −546.339 + 986.898i −0.588727 + 1.06347i
\(929\) −1192.84 −1.28400 −0.642000 0.766705i \(-0.721895\pi\)
−0.642000 + 0.766705i \(0.721895\pi\)
\(930\) 0 0
\(931\) 63.6528i 0.0683704i
\(932\) −181.195 1612.19i −0.194415 1.72982i
\(933\) 818.386 0.877156
\(934\) −933.088 834.092i −0.999023 0.893032i
\(935\) 0 0
\(936\) −291.112 206.738i −0.311017 0.220874i
\(937\) −530.621 −0.566298 −0.283149 0.959076i \(-0.591379\pi\)
−0.283149 + 0.959076i \(0.591379\pi\)
\(938\) 975.684 1091.48i 1.04018 1.16363i
\(939\) 94.6598i 0.100809i
\(940\) 0 0
\(941\) −507.433 −0.539248 −0.269624 0.962966i \(-0.586899\pi\)
−0.269624 + 0.962966i \(0.586899\pi\)
\(942\) −547.993 489.854i −0.581734 0.520015i
\(943\) 868.860i 0.921378i
\(944\) 24.5944 + 108.033i 0.0260534 + 0.114442i
\(945\) 0 0
\(946\) −169.972 + 190.145i −0.179674 + 0.200999i
\(947\) 453.872i 0.479274i 0.970863 + 0.239637i \(0.0770284\pi\)
−0.970863 + 0.239637i \(0.922972\pi\)
\(948\) 45.6587 + 406.251i 0.0481632 + 0.428535i
\(949\) −1650.02 −1.73869
\(950\) 0 0
\(951\) 109.766i 0.115422i
\(952\) 816.155 1149.24i 0.857306 1.20719i
\(953\) 1220.52 1.28071 0.640356 0.768078i \(-0.278787\pi\)
0.640356 + 0.768078i \(0.278787\pi\)
\(954\) −122.546 + 137.091i −0.128455 + 0.143701i
\(955\) 0 0
\(956\) −1064.37 + 119.625i −1.11336 + 0.125131i
\(957\) 138.413 0.144632
\(958\) 727.964 + 650.731i 0.759879 + 0.679260i
\(959\) 47.0717i 0.0490842i
\(960\) 0 0
\(961\) 392.986 0.408935
\(962\) 1085.67 1214.53i 1.12856 1.26250i
\(963\) 21.5317i 0.0223590i
\(964\) 40.0008 + 355.910i 0.0414946 + 0.369201i
\(965\) 0 0
\(966\) 618.517 + 552.896i 0.640287 + 0.572356i
\(967\) 292.088i 0.302056i 0.988530 + 0.151028i \(0.0482583\pi\)
−0.988530 + 0.151028i \(0.951742\pi\)
\(968\) 755.708 + 536.679i 0.780690 + 0.554421i
\(969\) 504.953 0.521107
\(970\) 0 0
\(971\) 1097.69i 1.13047i −0.824928 0.565237i \(-0.808785\pi\)
0.824928 0.565237i \(-0.191215\pi\)
\(972\) 61.9637 6.96412i 0.0637487 0.00716473i
\(973\) −964.947 −0.991724
\(974\) 908.789 + 812.372i 0.933048 + 0.834057i
\(975\) 0 0
\(976\) −1675.93 + 381.536i −1.71714 + 0.390918i
\(977\) 338.550 0.346520 0.173260 0.984876i \(-0.444570\pi\)
0.173260 + 0.984876i \(0.444570\pi\)
\(978\) −561.926 + 628.619i −0.574567 + 0.642760i
\(979\) 16.2042i 0.0165518i
\(980\) 0 0
\(981\) −76.2767 −0.0777540
\(982\) −1027.48 918.468i −1.04631 0.935304i
\(983\) 346.346i 0.352336i −0.984360 0.176168i \(-0.943630\pi\)
0.984360 0.176168i \(-0.0563702\pi\)
\(984\) 191.188 269.215i 0.194296 0.273592i
\(985\) 0 0
\(986\) −1260.40 + 1409.99i −1.27830 + 1.43001i
\(987\) 584.964i 0.592669i
\(988\) 642.697 72.2329i 0.650503 0.0731102i
\(989\) 2050.99 2.07380
\(990\) 0 0
\(991\) 242.030i 0.244228i 0.992516 + 0.122114i \(0.0389673\pi\)
−0.992516 + 0.122114i \(0.961033\pi\)
\(992\) −667.238 369.377i −0.672619 0.372356i
\(993\) −747.544 −0.752813
\(994\) −274.196 + 306.740i −0.275851 + 0.308591i
\(995\) 0 0
\(996\) 110.200 + 980.516i 0.110643 + 0.984454i
\(997\) −178.452 −0.178989 −0.0894946 0.995987i \(-0.528525\pi\)
−0.0894946 + 0.995987i \(0.528525\pi\)
\(998\) −1044.37 933.565i −1.04646 0.935436i
\(999\) 284.487i 0.284772i
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.g.151.2 yes 8
3.2 odd 2 900.3.c.n.451.7 8
4.3 odd 2 inner 300.3.c.g.151.1 yes 8
5.2 odd 4 300.3.f.c.199.5 16
5.3 odd 4 300.3.f.c.199.12 16
5.4 even 2 300.3.c.e.151.7 8
12.11 even 2 900.3.c.n.451.8 8
15.2 even 4 900.3.f.h.199.12 16
15.8 even 4 900.3.f.h.199.5 16
15.14 odd 2 900.3.c.t.451.2 8
20.3 even 4 300.3.f.c.199.6 16
20.7 even 4 300.3.f.c.199.11 16
20.19 odd 2 300.3.c.e.151.8 yes 8
60.23 odd 4 900.3.f.h.199.11 16
60.47 odd 4 900.3.f.h.199.6 16
60.59 even 2 900.3.c.t.451.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.c.e.151.7 8 5.4 even 2
300.3.c.e.151.8 yes 8 20.19 odd 2
300.3.c.g.151.1 yes 8 4.3 odd 2 inner
300.3.c.g.151.2 yes 8 1.1 even 1 trivial
300.3.f.c.199.5 16 5.2 odd 4
300.3.f.c.199.6 16 20.3 even 4
300.3.f.c.199.11 16 20.7 even 4
300.3.f.c.199.12 16 5.3 odd 4
900.3.c.n.451.7 8 3.2 odd 2
900.3.c.n.451.8 8 12.11 even 2
900.3.c.t.451.1 8 60.59 even 2
900.3.c.t.451.2 8 15.14 odd 2
900.3.f.h.199.5 16 15.8 even 4
900.3.f.h.199.6 16 60.47 odd 4
900.3.f.h.199.11 16 60.23 odd 4
900.3.f.h.199.12 16 15.2 even 4