Properties

Label 300.3.c.e.151.4
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 151.4
Root \(-2.65095 - 1.53053i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.e.151.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.534079 + 1.92737i) q^{2} +1.73205i q^{3} +(-3.42952 - 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-0.534079 + 1.92737i) q^{2} +1.73205i q^{3} +(-3.42952 - 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} -3.00000 q^{9} +14.5382i q^{11} +(3.56583 - 5.94010i) q^{12} +22.4802 q^{13} +(23.0738 + 6.39379i) q^{14} +(7.52322 + 14.1209i) q^{16} +12.6890 q^{17} +(1.60224 - 5.78211i) q^{18} -8.76336i q^{19} +20.7355 q^{21} +(-28.0205 - 7.76455i) q^{22} +4.99653i q^{23} +(9.54435 + 10.0452i) q^{24} +(-12.0062 + 43.3278i) q^{26} -5.19615i q^{27} +(-24.6464 + 41.0570i) q^{28} +2.74712 q^{29} -16.3466i q^{31} +(-31.2343 + 6.95833i) q^{32} -25.1809 q^{33} +(-6.77695 + 24.4565i) q^{34} +(10.2886 + 6.17621i) q^{36} +32.4872 q^{37} +(16.8902 + 4.68032i) q^{38} +38.9369i q^{39} +42.7586 q^{41} +(-11.0744 + 39.9650i) q^{42} +16.5435i q^{43} +(29.9303 - 49.8591i) q^{44} +(-9.63018 - 2.66854i) q^{46} -48.5912i q^{47} +(-24.4582 + 13.0306i) q^{48} -94.3200 q^{49} +21.9781i q^{51} +(-77.0964 - 46.2809i) q^{52} +94.1066 q^{53} +(10.0149 + 2.77515i) q^{54} +(-65.9689 - 69.4305i) q^{56} +15.1786 q^{57} +(-1.46718 + 5.29471i) q^{58} +43.2650i q^{59} +56.7678 q^{61} +(31.5060 + 8.73038i) q^{62} +35.9149i q^{63} +(3.27028 - 63.9164i) q^{64} +(13.4486 - 48.5330i) q^{66} +61.1106i q^{67} +(-43.5173 - 26.1234i) q^{68} -8.65425 q^{69} +39.6643i q^{71} +(-17.3987 + 16.5313i) q^{72} -99.5452 q^{73} +(-17.3507 + 62.6149i) q^{74} +(-18.0414 + 30.0541i) q^{76} +174.046 q^{77} +(-75.0459 - 20.7954i) q^{78} -10.7780i q^{79} +9.00000 q^{81} +(-22.8365 + 82.4118i) q^{82} -140.263i q^{83} +(-71.1127 - 42.6889i) q^{84} +(-31.8855 - 8.83554i) q^{86} +4.75815i q^{87} +(80.1118 + 84.3156i) q^{88} +54.8723 q^{89} -269.125i q^{91} +(10.2865 - 17.1357i) q^{92} +28.3132 q^{93} +(93.6533 + 25.9515i) q^{94} +(-12.0522 - 54.0994i) q^{96} +14.1601 q^{97} +(50.3743 - 181.790i) q^{98} -43.6146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.534079 + 1.92737i −0.267039 + 0.963686i
\(3\) 1.73205i 0.577350i
\(4\) −3.42952 2.05874i −0.857380 0.514684i
\(5\) 0 0
\(6\) −3.33830 0.925051i −0.556384 0.154175i
\(7\) 11.9716i 1.71023i −0.518436 0.855117i \(-0.673485\pi\)
0.518436 0.855117i \(-0.326515\pi\)
\(8\) 5.79958 5.51043i 0.724948 0.688804i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 14.5382i 1.32166i 0.750537 + 0.660828i \(0.229795\pi\)
−0.750537 + 0.660828i \(0.770205\pi\)
\(12\) 3.56583 5.94010i 0.297153 0.495009i
\(13\) 22.4802 1.72925 0.864625 0.502418i \(-0.167556\pi\)
0.864625 + 0.502418i \(0.167556\pi\)
\(14\) 23.0738 + 6.39379i 1.64813 + 0.456699i
\(15\) 0 0
\(16\) 7.52322 + 14.1209i 0.470201 + 0.882559i
\(17\) 12.6890 0.746414 0.373207 0.927748i \(-0.378258\pi\)
0.373207 + 0.927748i \(0.378258\pi\)
\(18\) 1.60224 5.78211i 0.0890131 0.321229i
\(19\) 8.76336i 0.461229i −0.973045 0.230615i \(-0.925926\pi\)
0.973045 0.230615i \(-0.0740737\pi\)
\(20\) 0 0
\(21\) 20.7355 0.987404
\(22\) −28.0205 7.76455i −1.27366 0.352934i
\(23\) 4.99653i 0.217241i 0.994083 + 0.108620i \(0.0346433\pi\)
−0.994083 + 0.108620i \(0.965357\pi\)
\(24\) 9.54435 + 10.0452i 0.397681 + 0.418549i
\(25\) 0 0
\(26\) −12.0062 + 43.3278i −0.461778 + 1.66645i
\(27\) 5.19615i 0.192450i
\(28\) −24.6464 + 41.0570i −0.880229 + 1.46632i
\(29\) 2.74712 0.0947282 0.0473641 0.998878i \(-0.484918\pi\)
0.0473641 + 0.998878i \(0.484918\pi\)
\(30\) 0 0
\(31\) 16.3466i 0.527310i −0.964617 0.263655i \(-0.915072\pi\)
0.964617 0.263655i \(-0.0849281\pi\)
\(32\) −31.2343 + 6.95833i −0.976072 + 0.217448i
\(33\) −25.1809 −0.763058
\(34\) −6.77695 + 24.4565i −0.199322 + 0.719309i
\(35\) 0 0
\(36\) 10.2886 + 6.17621i 0.285793 + 0.171561i
\(37\) 32.4872 0.878032 0.439016 0.898479i \(-0.355327\pi\)
0.439016 + 0.898479i \(0.355327\pi\)
\(38\) 16.8902 + 4.68032i 0.444480 + 0.123166i
\(39\) 38.9369i 0.998383i
\(40\) 0 0
\(41\) 42.7586 1.04289 0.521447 0.853284i \(-0.325393\pi\)
0.521447 + 0.853284i \(0.325393\pi\)
\(42\) −11.0744 + 39.9650i −0.263676 + 0.951547i
\(43\) 16.5435i 0.384733i 0.981323 + 0.192367i \(0.0616163\pi\)
−0.981323 + 0.192367i \(0.938384\pi\)
\(44\) 29.9303 49.8591i 0.680235 1.13316i
\(45\) 0 0
\(46\) −9.63018 2.66854i −0.209352 0.0580118i
\(47\) 48.5912i 1.03386i −0.856029 0.516928i \(-0.827076\pi\)
0.856029 0.516928i \(-0.172924\pi\)
\(48\) −24.4582 + 13.0306i −0.509546 + 0.271471i
\(49\) −94.3200 −1.92490
\(50\) 0 0
\(51\) 21.9781i 0.430943i
\(52\) −77.0964 46.2809i −1.48262 0.890017i
\(53\) 94.1066 1.77560 0.887798 0.460233i \(-0.152234\pi\)
0.887798 + 0.460233i \(0.152234\pi\)
\(54\) 10.0149 + 2.77515i 0.185461 + 0.0513917i
\(55\) 0 0
\(56\) −65.9689 69.4305i −1.17802 1.23983i
\(57\) 15.1786 0.266291
\(58\) −1.46718 + 5.29471i −0.0252961 + 0.0912882i
\(59\) 43.2650i 0.733305i 0.930358 + 0.366653i \(0.119496\pi\)
−0.930358 + 0.366653i \(0.880504\pi\)
\(60\) 0 0
\(61\) 56.7678 0.930620 0.465310 0.885148i \(-0.345943\pi\)
0.465310 + 0.885148i \(0.345943\pi\)
\(62\) 31.5060 + 8.73038i 0.508161 + 0.140813i
\(63\) 35.9149i 0.570078i
\(64\) 3.27028 63.9164i 0.0510981 0.998694i
\(65\) 0 0
\(66\) 13.4486 48.5330i 0.203767 0.735348i
\(67\) 61.1106i 0.912098i 0.889955 + 0.456049i \(0.150736\pi\)
−0.889955 + 0.456049i \(0.849264\pi\)
\(68\) −43.5173 26.1234i −0.639961 0.384167i
\(69\) −8.65425 −0.125424
\(70\) 0 0
\(71\) 39.6643i 0.558652i 0.960196 + 0.279326i \(0.0901110\pi\)
−0.960196 + 0.279326i \(0.909889\pi\)
\(72\) −17.3987 + 16.5313i −0.241649 + 0.229601i
\(73\) −99.5452 −1.36363 −0.681817 0.731523i \(-0.738810\pi\)
−0.681817 + 0.731523i \(0.738810\pi\)
\(74\) −17.3507 + 62.6149i −0.234469 + 0.846147i
\(75\) 0 0
\(76\) −18.0414 + 30.0541i −0.237387 + 0.395449i
\(77\) 174.046 2.26034
\(78\) −75.0459 20.7954i −0.962127 0.266607i
\(79\) 10.7780i 0.136430i −0.997671 0.0682151i \(-0.978270\pi\)
0.997671 0.0682151i \(-0.0217304\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −22.8365 + 82.4118i −0.278494 + 1.00502i
\(83\) 140.263i 1.68991i −0.534837 0.844955i \(-0.679627\pi\)
0.534837 0.844955i \(-0.320373\pi\)
\(84\) −71.1127 42.6889i −0.846580 0.508201i
\(85\) 0 0
\(86\) −31.8855 8.83554i −0.370762 0.102739i
\(87\) 4.75815i 0.0546913i
\(88\) 80.1118 + 84.3156i 0.910362 + 0.958131i
\(89\) 54.8723 0.616543 0.308271 0.951298i \(-0.400249\pi\)
0.308271 + 0.951298i \(0.400249\pi\)
\(90\) 0 0
\(91\) 269.125i 2.95742i
\(92\) 10.2865 17.1357i 0.111810 0.186258i
\(93\) 28.3132 0.304443
\(94\) 93.6533 + 25.9515i 0.996312 + 0.276080i
\(95\) 0 0
\(96\) −12.0522 54.0994i −0.125544 0.563535i
\(97\) 14.1601 0.145980 0.0729902 0.997333i \(-0.476746\pi\)
0.0729902 + 0.997333i \(0.476746\pi\)
\(98\) 50.3743 181.790i 0.514023 1.85500i
\(99\) 43.6146i 0.440552i
\(100\) 0 0
\(101\) −163.410 −1.61792 −0.808962 0.587861i \(-0.799970\pi\)
−0.808962 + 0.587861i \(0.799970\pi\)
\(102\) −42.3599 11.7380i −0.415293 0.115079i
\(103\) 169.591i 1.64651i −0.567672 0.823255i \(-0.692156\pi\)
0.567672 0.823255i \(-0.307844\pi\)
\(104\) 130.376 123.876i 1.25362 1.19111i
\(105\) 0 0
\(106\) −50.2603 + 181.378i −0.474154 + 1.71112i
\(107\) 8.14840i 0.0761532i −0.999275 0.0380766i \(-0.987877\pi\)
0.999275 0.0380766i \(-0.0121231\pi\)
\(108\) −10.6975 + 17.8203i −0.0990510 + 0.165003i
\(109\) −25.2322 −0.231488 −0.115744 0.993279i \(-0.536925\pi\)
−0.115744 + 0.993279i \(0.536925\pi\)
\(110\) 0 0
\(111\) 56.2695i 0.506932i
\(112\) 169.051 90.0652i 1.50938 0.804153i
\(113\) 97.8142 0.865613 0.432806 0.901487i \(-0.357523\pi\)
0.432806 + 0.901487i \(0.357523\pi\)
\(114\) −8.10655 + 29.2548i −0.0711101 + 0.256621i
\(115\) 0 0
\(116\) −9.42129 5.65559i −0.0812180 0.0487551i
\(117\) −67.4407 −0.576417
\(118\) −83.3877 23.1069i −0.706676 0.195821i
\(119\) 151.909i 1.27654i
\(120\) 0 0
\(121\) −90.3597 −0.746774
\(122\) −30.3185 + 109.413i −0.248512 + 0.896825i
\(123\) 74.0601i 0.602115i
\(124\) −33.6534 + 56.0611i −0.271398 + 0.452105i
\(125\) 0 0
\(126\) −69.2213 19.1814i −0.549376 0.152233i
\(127\) 167.563i 1.31939i 0.751533 + 0.659695i \(0.229315\pi\)
−0.751533 + 0.659695i \(0.770685\pi\)
\(128\) 121.444 + 40.4394i 0.948782 + 0.315933i
\(129\) −28.6542 −0.222126
\(130\) 0 0
\(131\) 82.0465i 0.626309i 0.949702 + 0.313155i \(0.101386\pi\)
−0.949702 + 0.313155i \(0.898614\pi\)
\(132\) 86.3585 + 51.8409i 0.654231 + 0.392734i
\(133\) −104.912 −0.788810
\(134\) −117.783 32.6378i −0.878976 0.243566i
\(135\) 0 0
\(136\) 73.5911 69.9221i 0.541111 0.514133i
\(137\) −254.459 −1.85737 −0.928683 0.370874i \(-0.879058\pi\)
−0.928683 + 0.370874i \(0.879058\pi\)
\(138\) 4.62205 16.6800i 0.0334931 0.120869i
\(139\) 78.9483i 0.567974i −0.958828 0.283987i \(-0.908343\pi\)
0.958828 0.283987i \(-0.0916572\pi\)
\(140\) 0 0
\(141\) 84.1624 0.596897
\(142\) −76.4478 21.1838i −0.538365 0.149182i
\(143\) 326.823i 2.28547i
\(144\) −22.5696 42.3628i −0.156734 0.294186i
\(145\) 0 0
\(146\) 53.1650 191.861i 0.364144 1.31411i
\(147\) 163.367i 1.11134i
\(148\) −111.415 66.8825i −0.752807 0.451909i
\(149\) −32.3433 −0.217069 −0.108534 0.994093i \(-0.534616\pi\)
−0.108534 + 0.994093i \(0.534616\pi\)
\(150\) 0 0
\(151\) 38.7953i 0.256922i 0.991715 + 0.128461i \(0.0410038\pi\)
−0.991715 + 0.128461i \(0.958996\pi\)
\(152\) −48.2899 50.8238i −0.317697 0.334367i
\(153\) −38.0671 −0.248805
\(154\) −92.9543 + 335.452i −0.603600 + 2.17826i
\(155\) 0 0
\(156\) 80.1608 133.535i 0.513851 0.855993i
\(157\) 44.2021 0.281542 0.140771 0.990042i \(-0.455042\pi\)
0.140771 + 0.990042i \(0.455042\pi\)
\(158\) 20.7732 + 5.75629i 0.131476 + 0.0364322i
\(159\) 162.997i 1.02514i
\(160\) 0 0
\(161\) 59.8167 0.371532
\(162\) −4.80671 + 17.3463i −0.0296710 + 0.107076i
\(163\) 52.9366i 0.324764i −0.986728 0.162382i \(-0.948082\pi\)
0.986728 0.162382i \(-0.0519177\pi\)
\(164\) −146.642 88.0287i −0.894156 0.536760i
\(165\) 0 0
\(166\) 270.338 + 74.9112i 1.62854 + 0.451272i
\(167\) 179.273i 1.07349i −0.843744 0.536745i \(-0.819654\pi\)
0.843744 0.536745i \(-0.180346\pi\)
\(168\) 120.257 114.261i 0.715816 0.680128i
\(169\) 336.361 1.99030
\(170\) 0 0
\(171\) 26.2901i 0.153743i
\(172\) 34.0587 56.7364i 0.198016 0.329863i
\(173\) −177.276 −1.02471 −0.512357 0.858772i \(-0.671228\pi\)
−0.512357 + 0.858772i \(0.671228\pi\)
\(174\) −9.17071 2.54122i −0.0527053 0.0146047i
\(175\) 0 0
\(176\) −205.293 + 109.374i −1.16644 + 0.621444i
\(177\) −74.9372 −0.423374
\(178\) −29.3061 + 105.759i −0.164641 + 0.594154i
\(179\) 102.849i 0.574573i 0.957845 + 0.287286i \(0.0927532\pi\)
−0.957845 + 0.287286i \(0.907247\pi\)
\(180\) 0 0
\(181\) −115.413 −0.637640 −0.318820 0.947815i \(-0.603286\pi\)
−0.318820 + 0.947815i \(0.603286\pi\)
\(182\) 518.704 + 143.734i 2.85002 + 0.789747i
\(183\) 98.3247i 0.537294i
\(184\) 27.5331 + 28.9778i 0.149636 + 0.157488i
\(185\) 0 0
\(186\) −15.1215 + 54.5700i −0.0812982 + 0.293387i
\(187\) 184.476i 0.986503i
\(188\) −100.036 + 166.645i −0.532109 + 0.886407i
\(189\) −62.2064 −0.329135
\(190\) 0 0
\(191\) 191.305i 1.00160i 0.865563 + 0.500799i \(0.166960\pi\)
−0.865563 + 0.500799i \(0.833040\pi\)
\(192\) 110.706 + 5.66429i 0.576596 + 0.0295015i
\(193\) 160.332 0.830734 0.415367 0.909654i \(-0.363653\pi\)
0.415367 + 0.909654i \(0.363653\pi\)
\(194\) −7.56261 + 27.2918i −0.0389825 + 0.140679i
\(195\) 0 0
\(196\) 323.472 + 194.180i 1.65037 + 0.990714i
\(197\) −355.081 −1.80244 −0.901220 0.433362i \(-0.857327\pi\)
−0.901220 + 0.433362i \(0.857327\pi\)
\(198\) 84.0616 + 23.2936i 0.424554 + 0.117645i
\(199\) 88.2032i 0.443232i 0.975134 + 0.221616i \(0.0711332\pi\)
−0.975134 + 0.221616i \(0.928867\pi\)
\(200\) 0 0
\(201\) −105.847 −0.526600
\(202\) 87.2740 314.952i 0.432049 1.55917i
\(203\) 32.8875i 0.162007i
\(204\) 45.2470 75.3742i 0.221799 0.369482i
\(205\) 0 0
\(206\) 326.864 + 90.5747i 1.58672 + 0.439683i
\(207\) 14.9896i 0.0724135i
\(208\) 169.124 + 317.442i 0.813095 + 1.52617i
\(209\) 127.404 0.609586
\(210\) 0 0
\(211\) 190.584i 0.903243i −0.892210 0.451622i \(-0.850846\pi\)
0.892210 0.451622i \(-0.149154\pi\)
\(212\) −322.741 193.741i −1.52236 0.913871i
\(213\) −68.7006 −0.322538
\(214\) 15.7050 + 4.35188i 0.0733878 + 0.0203359i
\(215\) 0 0
\(216\) −28.6330 30.1355i −0.132560 0.139516i
\(217\) −195.696 −0.901824
\(218\) 13.4760 48.6318i 0.0618164 0.223082i
\(219\) 172.417i 0.787294i
\(220\) 0 0
\(221\) 285.253 1.29074
\(222\) −108.452 30.0523i −0.488523 0.135371i
\(223\) 79.2869i 0.355547i −0.984071 0.177773i \(-0.943111\pi\)
0.984071 0.177773i \(-0.0568894\pi\)
\(224\) 83.3026 + 373.926i 0.371887 + 1.66931i
\(225\) 0 0
\(226\) −52.2405 + 188.524i −0.231153 + 0.834178i
\(227\) 353.645i 1.55791i 0.627082 + 0.778953i \(0.284249\pi\)
−0.627082 + 0.778953i \(0.715751\pi\)
\(228\) −52.0552 31.2487i −0.228312 0.137056i
\(229\) −22.7911 −0.0995244 −0.0497622 0.998761i \(-0.515846\pi\)
−0.0497622 + 0.998761i \(0.515846\pi\)
\(230\) 0 0
\(231\) 301.457i 1.30501i
\(232\) 15.9321 15.1378i 0.0686730 0.0652491i
\(233\) −189.710 −0.814205 −0.407103 0.913382i \(-0.633461\pi\)
−0.407103 + 0.913382i \(0.633461\pi\)
\(234\) 36.0187 129.983i 0.153926 0.555484i
\(235\) 0 0
\(236\) 89.0712 148.378i 0.377420 0.628721i
\(237\) 18.6680 0.0787680
\(238\) 292.784 + 81.1311i 1.23019 + 0.340887i
\(239\) 267.778i 1.12041i 0.828355 + 0.560204i \(0.189277\pi\)
−0.828355 + 0.560204i \(0.810723\pi\)
\(240\) 0 0
\(241\) −301.663 −1.25171 −0.625857 0.779938i \(-0.715251\pi\)
−0.625857 + 0.779938i \(0.715251\pi\)
\(242\) 48.2592 174.157i 0.199418 0.719656i
\(243\) 15.5885i 0.0641500i
\(244\) −194.686 116.870i −0.797895 0.478975i
\(245\) 0 0
\(246\) −142.741 39.5539i −0.580249 0.160788i
\(247\) 197.002i 0.797580i
\(248\) −90.0769 94.8035i −0.363213 0.382272i
\(249\) 242.942 0.975670
\(250\) 0 0
\(251\) 63.1891i 0.251749i 0.992046 + 0.125875i \(0.0401737\pi\)
−0.992046 + 0.125875i \(0.959826\pi\)
\(252\) 73.9393 123.171i 0.293410 0.488773i
\(253\) −72.6407 −0.287117
\(254\) −322.955 89.4916i −1.27148 0.352329i
\(255\) 0 0
\(256\) −142.802 + 212.470i −0.557822 + 0.829961i
\(257\) 150.719 0.586456 0.293228 0.956043i \(-0.405271\pi\)
0.293228 + 0.956043i \(0.405271\pi\)
\(258\) 15.3036 55.2273i 0.0593163 0.214059i
\(259\) 388.925i 1.50164i
\(260\) 0 0
\(261\) −8.24135 −0.0315761
\(262\) −158.134 43.8193i −0.603565 0.167249i
\(263\) 203.755i 0.774735i 0.921925 + 0.387368i \(0.126616\pi\)
−0.921925 + 0.387368i \(0.873384\pi\)
\(264\) −146.039 + 138.758i −0.553177 + 0.525598i
\(265\) 0 0
\(266\) 56.0311 202.204i 0.210643 0.760165i
\(267\) 95.0416i 0.355961i
\(268\) 125.810 209.580i 0.469442 0.782014i
\(269\) 76.3986 0.284010 0.142005 0.989866i \(-0.454645\pi\)
0.142005 + 0.989866i \(0.454645\pi\)
\(270\) 0 0
\(271\) 169.216i 0.624414i 0.950014 + 0.312207i \(0.101068\pi\)
−0.950014 + 0.312207i \(0.898932\pi\)
\(272\) 95.4624 + 179.181i 0.350965 + 0.658755i
\(273\) 466.139 1.70747
\(274\) 135.901 490.437i 0.495990 1.78992i
\(275\) 0 0
\(276\) 29.6799 + 17.8168i 0.107536 + 0.0645537i
\(277\) −273.891 −0.988774 −0.494387 0.869242i \(-0.664607\pi\)
−0.494387 + 0.869242i \(0.664607\pi\)
\(278\) 152.163 + 42.1646i 0.547348 + 0.151671i
\(279\) 49.0399i 0.175770i
\(280\) 0 0
\(281\) −311.672 −1.10915 −0.554577 0.832133i \(-0.687120\pi\)
−0.554577 + 0.832133i \(0.687120\pi\)
\(282\) −44.9494 + 162.212i −0.159395 + 0.575221i
\(283\) 264.566i 0.934861i −0.884030 0.467431i \(-0.845180\pi\)
0.884030 0.467431i \(-0.154820\pi\)
\(284\) 81.6583 136.029i 0.287529 0.478977i
\(285\) 0 0
\(286\) −629.909 174.549i −2.20248 0.610311i
\(287\) 511.891i 1.78359i
\(288\) 93.7029 20.8750i 0.325357 0.0724826i
\(289\) −127.988 −0.442866
\(290\) 0 0
\(291\) 24.5260i 0.0842818i
\(292\) 341.392 + 204.937i 1.16915 + 0.701840i
\(293\) 121.281 0.413927 0.206964 0.978349i \(-0.433642\pi\)
0.206964 + 0.978349i \(0.433642\pi\)
\(294\) 314.869 + 87.2508i 1.07098 + 0.296772i
\(295\) 0 0
\(296\) 188.412 179.018i 0.636527 0.604792i
\(297\) 75.5428 0.254353
\(298\) 17.2739 62.3375i 0.0579659 0.209186i
\(299\) 112.323i 0.375663i
\(300\) 0 0
\(301\) 198.053 0.657984
\(302\) −74.7729 20.7197i −0.247592 0.0686083i
\(303\) 283.035i 0.934109i
\(304\) 123.747 65.9286i 0.407062 0.216870i
\(305\) 0 0
\(306\) 20.3308 73.3695i 0.0664407 0.239770i
\(307\) 161.768i 0.526932i 0.964669 + 0.263466i \(0.0848656\pi\)
−0.964669 + 0.263466i \(0.915134\pi\)
\(308\) −596.895 358.315i −1.93797 1.16336i
\(309\) 293.739 0.950613
\(310\) 0 0
\(311\) 26.3813i 0.0848273i −0.999100 0.0424137i \(-0.986495\pi\)
0.999100 0.0424137i \(-0.0135047\pi\)
\(312\) 214.559 + 225.818i 0.687690 + 0.723775i
\(313\) 5.39902 0.0172493 0.00862463 0.999963i \(-0.497255\pi\)
0.00862463 + 0.999963i \(0.497255\pi\)
\(314\) −23.6074 + 85.1938i −0.0751827 + 0.271318i
\(315\) 0 0
\(316\) −22.1890 + 36.9633i −0.0702184 + 0.116972i
\(317\) 270.157 0.852231 0.426116 0.904669i \(-0.359882\pi\)
0.426116 + 0.904669i \(0.359882\pi\)
\(318\) −314.157 87.0535i −0.987914 0.273753i
\(319\) 39.9382i 0.125198i
\(320\) 0 0
\(321\) 14.1134 0.0439671
\(322\) −31.9468 + 115.289i −0.0992137 + 0.358040i
\(323\) 111.199i 0.344268i
\(324\) −30.8657 18.5286i −0.0952644 0.0571871i
\(325\) 0 0
\(326\) 102.028 + 28.2723i 0.312971 + 0.0867248i
\(327\) 43.7034i 0.133650i
\(328\) 247.982 235.619i 0.756043 0.718349i
\(329\) −581.716 −1.76813
\(330\) 0 0
\(331\) 480.728i 1.45235i −0.687510 0.726174i \(-0.741296\pi\)
0.687510 0.726174i \(-0.258704\pi\)
\(332\) −288.763 + 481.033i −0.869770 + 1.44890i
\(333\) −97.4616 −0.292677
\(334\) 345.526 + 95.7459i 1.03451 + 0.286664i
\(335\) 0 0
\(336\) 155.997 + 292.805i 0.464278 + 0.871442i
\(337\) 568.382 1.68659 0.843297 0.537448i \(-0.180612\pi\)
0.843297 + 0.537448i \(0.180612\pi\)
\(338\) −179.643 + 648.293i −0.531489 + 1.91803i
\(339\) 169.419i 0.499762i
\(340\) 0 0
\(341\) 237.651 0.696923
\(342\) −50.6707 14.0410i −0.148160 0.0410554i
\(343\) 542.554i 1.58179i
\(344\) 91.1620 + 95.9455i 0.265006 + 0.278911i
\(345\) 0 0
\(346\) 94.6791 341.676i 0.273639 0.987503i
\(347\) 370.184i 1.06681i 0.845859 + 0.533406i \(0.179088\pi\)
−0.845859 + 0.533406i \(0.820912\pi\)
\(348\) 9.79576 16.3182i 0.0281487 0.0468913i
\(349\) −488.570 −1.39991 −0.699957 0.714185i \(-0.746797\pi\)
−0.699957 + 0.714185i \(0.746797\pi\)
\(350\) 0 0
\(351\) 116.811i 0.332794i
\(352\) −101.162 454.091i −0.287391 1.29003i
\(353\) −649.728 −1.84059 −0.920295 0.391226i \(-0.872051\pi\)
−0.920295 + 0.391226i \(0.872051\pi\)
\(354\) 40.0224 144.432i 0.113058 0.407999i
\(355\) 0 0
\(356\) −188.186 112.968i −0.528612 0.317325i
\(357\) 263.113 0.737012
\(358\) −198.227 54.9292i −0.553708 0.153434i
\(359\) 405.910i 1.13067i −0.824862 0.565334i \(-0.808747\pi\)
0.824862 0.565334i \(-0.191253\pi\)
\(360\) 0 0
\(361\) 284.204 0.787268
\(362\) 61.6395 222.443i 0.170275 0.614484i
\(363\) 156.508i 0.431150i
\(364\) −554.058 + 922.970i −1.52214 + 2.53563i
\(365\) 0 0
\(366\) −189.508 52.5131i −0.517782 0.143479i
\(367\) 46.2347i 0.125980i 0.998014 + 0.0629900i \(0.0200636\pi\)
−0.998014 + 0.0629900i \(0.979936\pi\)
\(368\) −70.5558 + 37.5900i −0.191728 + 0.102147i
\(369\) −128.276 −0.347631
\(370\) 0 0
\(371\) 1126.61i 3.03668i
\(372\) −97.1006 58.2893i −0.261023 0.156692i
\(373\) 138.262 0.370676 0.185338 0.982675i \(-0.440662\pi\)
0.185338 + 0.982675i \(0.440662\pi\)
\(374\) −355.554 98.5247i −0.950679 0.263435i
\(375\) 0 0
\(376\) −267.759 281.809i −0.712124 0.749491i
\(377\) 61.7559 0.163809
\(378\) 33.2231 119.895i 0.0878919 0.317182i
\(379\) 254.516i 0.671546i −0.941943 0.335773i \(-0.891002\pi\)
0.941943 0.335773i \(-0.108998\pi\)
\(380\) 0 0
\(381\) −290.227 −0.761750
\(382\) −368.716 102.172i −0.965226 0.267466i
\(383\) 62.7205i 0.163761i −0.996642 0.0818805i \(-0.973907\pi\)
0.996642 0.0818805i \(-0.0260926\pi\)
\(384\) −70.0431 + 210.347i −0.182404 + 0.547779i
\(385\) 0 0
\(386\) −85.6298 + 309.019i −0.221839 + 0.800567i
\(387\) 49.6306i 0.128244i
\(388\) −48.5623 29.1519i −0.125161 0.0751338i
\(389\) 110.130 0.283112 0.141556 0.989930i \(-0.454790\pi\)
0.141556 + 0.989930i \(0.454790\pi\)
\(390\) 0 0
\(391\) 63.4012i 0.162152i
\(392\) −547.016 + 519.744i −1.39545 + 1.32588i
\(393\) −142.109 −0.361600
\(394\) 189.641 684.372i 0.481322 1.73698i
\(395\) 0 0
\(396\) −89.7910 + 149.577i −0.226745 + 0.377720i
\(397\) 292.953 0.737916 0.368958 0.929446i \(-0.379715\pi\)
0.368958 + 0.929446i \(0.379715\pi\)
\(398\) −170.000 47.1074i −0.427136 0.118360i
\(399\) 181.712i 0.455419i
\(400\) 0 0
\(401\) 518.103 1.29203 0.646014 0.763325i \(-0.276435\pi\)
0.646014 + 0.763325i \(0.276435\pi\)
\(402\) 56.5304 204.006i 0.140623 0.507477i
\(403\) 367.476i 0.911851i
\(404\) 560.419 + 336.419i 1.38718 + 0.832720i
\(405\) 0 0
\(406\) 63.3864 + 17.5645i 0.156124 + 0.0432623i
\(407\) 472.306i 1.16046i
\(408\) 121.109 + 127.464i 0.296835 + 0.312411i
\(409\) −181.984 −0.444948 −0.222474 0.974939i \(-0.571413\pi\)
−0.222474 + 0.974939i \(0.571413\pi\)
\(410\) 0 0
\(411\) 440.736i 1.07235i
\(412\) −349.142 + 581.614i −0.847432 + 1.41168i
\(413\) 517.953 1.25412
\(414\) 28.8905 + 8.00563i 0.0697839 + 0.0193373i
\(415\) 0 0
\(416\) −702.155 + 156.425i −1.68787 + 0.376022i
\(417\) 136.743 0.327920
\(418\) −68.0435 + 245.554i −0.162784 + 0.587450i
\(419\) 163.347i 0.389849i 0.980818 + 0.194925i \(0.0624462\pi\)
−0.980818 + 0.194925i \(0.937554\pi\)
\(420\) 0 0
\(421\) −467.206 −1.10975 −0.554876 0.831933i \(-0.687234\pi\)
−0.554876 + 0.831933i \(0.687234\pi\)
\(422\) 367.327 + 101.787i 0.870442 + 0.241201i
\(423\) 145.774i 0.344619i
\(424\) 545.779 518.568i 1.28721 1.22304i
\(425\) 0 0
\(426\) 36.6915 132.411i 0.0861303 0.310825i
\(427\) 679.603i 1.59158i
\(428\) −16.7754 + 27.9451i −0.0391948 + 0.0652923i
\(429\) −566.073 −1.31952
\(430\) 0 0
\(431\) 685.527i 1.59055i 0.606248 + 0.795275i \(0.292674\pi\)
−0.606248 + 0.795275i \(0.707326\pi\)
\(432\) 73.3746 39.0918i 0.169849 0.0904902i
\(433\) 592.777 1.36900 0.684500 0.729013i \(-0.260021\pi\)
0.684500 + 0.729013i \(0.260021\pi\)
\(434\) 104.517 377.178i 0.240822 0.869074i
\(435\) 0 0
\(436\) 86.5343 + 51.9464i 0.198473 + 0.119143i
\(437\) 43.7864 0.100198
\(438\) 332.312 + 92.0844i 0.758704 + 0.210238i
\(439\) 464.439i 1.05795i 0.848638 + 0.528974i \(0.177423\pi\)
−0.848638 + 0.528974i \(0.822577\pi\)
\(440\) 0 0
\(441\) 282.960 0.641633
\(442\) −152.347 + 549.788i −0.344677 + 1.24386i
\(443\) 54.2868i 0.122544i −0.998121 0.0612718i \(-0.980484\pi\)
0.998121 0.0612718i \(-0.0195156\pi\)
\(444\) 115.844 192.977i 0.260910 0.434633i
\(445\) 0 0
\(446\) 152.815 + 42.3454i 0.342635 + 0.0949449i
\(447\) 56.0202i 0.125325i
\(448\) −765.184 39.1506i −1.70800 0.0873897i
\(449\) −428.051 −0.953343 −0.476671 0.879082i \(-0.658157\pi\)
−0.476671 + 0.879082i \(0.658157\pi\)
\(450\) 0 0
\(451\) 621.634i 1.37835i
\(452\) −335.456 201.374i −0.742159 0.445517i
\(453\) −67.1954 −0.148334
\(454\) −681.605 188.874i −1.50133 0.416022i
\(455\) 0 0
\(456\) 88.0294 83.6405i 0.193047 0.183422i
\(457\) −66.5848 −0.145700 −0.0728498 0.997343i \(-0.523209\pi\)
−0.0728498 + 0.997343i \(0.523209\pi\)
\(458\) 12.1722 43.9269i 0.0265769 0.0959103i
\(459\) 65.9342i 0.143648i
\(460\) 0 0
\(461\) −238.626 −0.517627 −0.258814 0.965927i \(-0.583332\pi\)
−0.258814 + 0.965927i \(0.583332\pi\)
\(462\) −581.019 161.002i −1.25762 0.348488i
\(463\) 386.958i 0.835762i 0.908502 + 0.417881i \(0.137227\pi\)
−0.908502 + 0.417881i \(0.862773\pi\)
\(464\) 20.6672 + 38.7919i 0.0445413 + 0.0836032i
\(465\) 0 0
\(466\) 101.320 365.641i 0.217425 0.784638i
\(467\) 235.964i 0.505276i −0.967561 0.252638i \(-0.918702\pi\)
0.967561 0.252638i \(-0.0812981\pi\)
\(468\) 231.289 + 138.843i 0.494208 + 0.296672i
\(469\) 731.593 1.55990
\(470\) 0 0
\(471\) 76.5602i 0.162548i
\(472\) 238.409 + 250.919i 0.505104 + 0.531608i
\(473\) −240.513 −0.508485
\(474\) −9.97018 + 35.9802i −0.0210341 + 0.0759076i
\(475\) 0 0
\(476\) −312.740 + 520.974i −0.657016 + 1.09448i
\(477\) −282.320 −0.591866
\(478\) −516.107 143.014i −1.07972 0.299193i
\(479\) 529.496i 1.10542i 0.833374 + 0.552710i \(0.186406\pi\)
−0.833374 + 0.552710i \(0.813594\pi\)
\(480\) 0 0
\(481\) 730.320 1.51834
\(482\) 161.112 581.417i 0.334257 1.20626i
\(483\) 103.606i 0.214504i
\(484\) 309.890 + 186.027i 0.640270 + 0.384353i
\(485\) 0 0
\(486\) −30.0447 8.32546i −0.0618205 0.0171306i
\(487\) 880.801i 1.80863i −0.426869 0.904314i \(-0.640383\pi\)
0.426869 0.904314i \(-0.359617\pi\)
\(488\) 329.230 312.815i 0.674651 0.641015i
\(489\) 91.6888 0.187503
\(490\) 0 0
\(491\) 86.4466i 0.176062i 0.996118 + 0.0880312i \(0.0280575\pi\)
−0.996118 + 0.0880312i \(0.971942\pi\)
\(492\) 152.470 253.991i 0.309899 0.516241i
\(493\) 34.8583 0.0707065
\(494\) 379.697 + 105.215i 0.768617 + 0.212985i
\(495\) 0 0
\(496\) 230.830 122.979i 0.465383 0.247942i
\(497\) 474.846 0.955425
\(498\) −129.750 + 468.239i −0.260542 + 0.940239i
\(499\) 874.536i 1.75258i 0.481786 + 0.876289i \(0.339988\pi\)
−0.481786 + 0.876289i \(0.660012\pi\)
\(500\) 0 0
\(501\) 310.510 0.619780
\(502\) −121.789 33.7479i −0.242607 0.0672269i
\(503\) 17.5479i 0.0348865i 0.999848 + 0.0174433i \(0.00555265\pi\)
−0.999848 + 0.0174433i \(0.994447\pi\)
\(504\) 197.907 + 208.291i 0.392672 + 0.413277i
\(505\) 0 0
\(506\) 38.7958 140.006i 0.0766716 0.276691i
\(507\) 582.595i 1.14910i
\(508\) 344.967 574.659i 0.679069 1.13122i
\(509\) 609.132 1.19672 0.598362 0.801226i \(-0.295819\pi\)
0.598362 + 0.801226i \(0.295819\pi\)
\(510\) 0 0
\(511\) 1191.72i 2.33213i
\(512\) −333.241 388.709i −0.650861 0.759197i
\(513\) −45.5357 −0.0887636
\(514\) −80.4959 + 290.492i −0.156607 + 0.565159i
\(515\) 0 0
\(516\) 98.2703 + 58.9915i 0.190446 + 0.114325i
\(517\) 706.430 1.36640
\(518\) 749.602 + 207.716i 1.44711 + 0.400997i
\(519\) 307.050i 0.591619i
\(520\) 0 0
\(521\) 433.724 0.832484 0.416242 0.909254i \(-0.363347\pi\)
0.416242 + 0.909254i \(0.363347\pi\)
\(522\) 4.40153 15.8841i 0.00843205 0.0304294i
\(523\) 473.223i 0.904823i −0.891809 0.452412i \(-0.850564\pi\)
0.891809 0.452412i \(-0.149436\pi\)
\(524\) 168.912 281.380i 0.322351 0.536985i
\(525\) 0 0
\(526\) −392.712 108.821i −0.746601 0.206885i
\(527\) 207.423i 0.393592i
\(528\) −189.442 355.579i −0.358791 0.673444i
\(529\) 504.035 0.952807
\(530\) 0 0
\(531\) 129.795i 0.244435i
\(532\) 359.797 + 215.985i 0.676310 + 0.405988i
\(533\) 961.224 1.80342
\(534\) −183.181 50.7597i −0.343035 0.0950556i
\(535\) 0 0
\(536\) 336.746 + 354.416i 0.628257 + 0.661223i
\(537\) −178.139 −0.331730
\(538\) −40.8029 + 147.249i −0.0758418 + 0.273696i
\(539\) 1371.24i 2.54405i
\(540\) 0 0
\(541\) 294.889 0.545081 0.272540 0.962144i \(-0.412136\pi\)
0.272540 + 0.962144i \(0.412136\pi\)
\(542\) −326.142 90.3747i −0.601739 0.166743i
\(543\) 199.901i 0.368141i
\(544\) −396.333 + 88.2946i −0.728554 + 0.162306i
\(545\) 0 0
\(546\) −248.955 + 898.422i −0.455961 + 1.64546i
\(547\) 966.695i 1.76727i 0.468179 + 0.883634i \(0.344910\pi\)
−0.468179 + 0.883634i \(0.655090\pi\)
\(548\) 872.673 + 523.864i 1.59247 + 0.955956i
\(549\) −170.303 −0.310207
\(550\) 0 0
\(551\) 24.0740i 0.0436914i
\(552\) −50.1910 + 47.6887i −0.0909258 + 0.0863925i
\(553\) −129.030 −0.233327
\(554\) 146.279 527.889i 0.264042 0.952868i
\(555\) 0 0
\(556\) −162.534 + 270.755i −0.292327 + 0.486969i
\(557\) 74.2603 0.133322 0.0666609 0.997776i \(-0.478765\pi\)
0.0666609 + 0.997776i \(0.478765\pi\)
\(558\) −94.5180 26.1911i −0.169387 0.0469375i
\(559\) 371.903i 0.665300i
\(560\) 0 0
\(561\) −319.522 −0.569558
\(562\) 166.457 600.708i 0.296187 1.06887i
\(563\) 663.688i 1.17884i −0.807826 0.589421i \(-0.799356\pi\)
0.807826 0.589421i \(-0.200644\pi\)
\(564\) −288.637 173.268i −0.511767 0.307213i
\(565\) 0 0
\(566\) 509.916 + 141.299i 0.900912 + 0.249645i
\(567\) 107.745i 0.190026i
\(568\) 218.567 + 230.036i 0.384802 + 0.404993i
\(569\) −667.450 −1.17302 −0.586511 0.809941i \(-0.699499\pi\)
−0.586511 + 0.809941i \(0.699499\pi\)
\(570\) 0 0
\(571\) 185.898i 0.325565i 0.986662 + 0.162782i \(0.0520469\pi\)
−0.986662 + 0.162782i \(0.947953\pi\)
\(572\) 672.841 1120.84i 1.17630 1.95952i
\(573\) −331.350 −0.578273
\(574\) 986.603 + 273.390i 1.71882 + 0.476289i
\(575\) 0 0
\(576\) −9.81084 + 191.749i −0.0170327 + 0.332898i
\(577\) −664.331 −1.15135 −0.575676 0.817678i \(-0.695261\pi\)
−0.575676 + 0.817678i \(0.695261\pi\)
\(578\) 68.3557 246.681i 0.118263 0.426783i
\(579\) 277.703i 0.479625i
\(580\) 0 0
\(581\) −1679.17 −2.89014
\(582\) −47.2707 13.0988i −0.0812212 0.0225066i
\(583\) 1368.14i 2.34673i
\(584\) −577.321 + 548.537i −0.988563 + 0.939276i
\(585\) 0 0
\(586\) −64.7734 + 233.753i −0.110535 + 0.398896i
\(587\) 763.083i 1.29997i −0.759946 0.649986i \(-0.774775\pi\)
0.759946 0.649986i \(-0.225225\pi\)
\(588\) −336.329 + 560.270i −0.571989 + 0.952841i
\(589\) −143.251 −0.243211
\(590\) 0 0
\(591\) 615.018i 1.04064i
\(592\) 244.408 + 458.750i 0.412852 + 0.774915i
\(593\) 286.193 0.482618 0.241309 0.970448i \(-0.422423\pi\)
0.241309 + 0.970448i \(0.422423\pi\)
\(594\) −40.3458 + 145.599i −0.0679222 + 0.245116i
\(595\) 0 0
\(596\) 110.922 + 66.5862i 0.186111 + 0.111722i
\(597\) −152.772 −0.255900
\(598\) −216.489 59.9895i −0.362021 0.100317i
\(599\) 604.151i 1.00860i 0.863529 + 0.504300i \(0.168249\pi\)
−0.863529 + 0.504300i \(0.831751\pi\)
\(600\) 0 0
\(601\) 275.562 0.458505 0.229253 0.973367i \(-0.426372\pi\)
0.229253 + 0.973367i \(0.426372\pi\)
\(602\) −105.776 + 381.722i −0.175707 + 0.634089i
\(603\) 183.332i 0.304033i
\(604\) 79.8692 133.049i 0.132234 0.220280i
\(605\) 0 0
\(606\) 545.514 + 151.163i 0.900188 + 0.249444i
\(607\) 52.1487i 0.0859121i −0.999077 0.0429561i \(-0.986322\pi\)
0.999077 0.0429561i \(-0.0136775\pi\)
\(608\) 60.9784 + 273.717i 0.100293 + 0.450193i
\(609\) 56.9628 0.0935349
\(610\) 0 0
\(611\) 1092.34i 1.78779i
\(612\) 130.552 + 78.3702i 0.213320 + 0.128056i
\(613\) −898.128 −1.46513 −0.732567 0.680695i \(-0.761678\pi\)
−0.732567 + 0.680695i \(0.761678\pi\)
\(614\) −311.787 86.3968i −0.507796 0.140711i
\(615\) 0 0
\(616\) 1009.39 959.070i 1.63863 1.55693i
\(617\) −636.868 −1.03220 −0.516101 0.856528i \(-0.672617\pi\)
−0.516101 + 0.856528i \(0.672617\pi\)
\(618\) −156.880 + 566.145i −0.253851 + 0.916092i
\(619\) 190.559i 0.307849i −0.988083 0.153925i \(-0.950809\pi\)
0.988083 0.153925i \(-0.0491913\pi\)
\(620\) 0 0
\(621\) 25.9628 0.0418080
\(622\) 50.8466 + 14.0897i 0.0817469 + 0.0226522i
\(623\) 656.911i 1.05443i
\(624\) −549.826 + 292.931i −0.881132 + 0.469441i
\(625\) 0 0
\(626\) −2.88350 + 10.4059i −0.00460623 + 0.0166229i
\(627\) 220.669i 0.351945i
\(628\) −151.592 91.0004i −0.241388 0.144905i
\(629\) 412.231 0.655376
\(630\) 0 0
\(631\) 578.160i 0.916261i 0.888885 + 0.458130i \(0.151481\pi\)
−0.888885 + 0.458130i \(0.848519\pi\)
\(632\) −59.3913 62.5078i −0.0939736 0.0989047i
\(633\) 330.102 0.521488
\(634\) −144.285 + 520.693i −0.227579 + 0.821283i
\(635\) 0 0
\(636\) 335.569 559.003i 0.527624 0.878936i
\(637\) −2120.34 −3.32863
\(638\) −76.9757 21.3301i −0.120652 0.0334328i
\(639\) 118.993i 0.186217i
\(640\) 0 0
\(641\) −35.3085 −0.0550834 −0.0275417 0.999621i \(-0.508768\pi\)
−0.0275417 + 0.999621i \(0.508768\pi\)
\(642\) −7.53768 + 27.2018i −0.0117409 + 0.0423704i
\(643\) 1045.67i 1.62623i 0.582100 + 0.813117i \(0.302231\pi\)
−0.582100 + 0.813117i \(0.697769\pi\)
\(644\) −205.143 123.147i −0.318544 0.191222i
\(645\) 0 0
\(646\) 214.321 + 59.3888i 0.331766 + 0.0919331i
\(647\) 2.71164i 0.00419110i 0.999998 + 0.00209555i \(0.000667035\pi\)
−0.999998 + 0.00209555i \(0.999333\pi\)
\(648\) 52.1962 49.5939i 0.0805497 0.0765338i
\(649\) −628.996 −0.969177
\(650\) 0 0
\(651\) 338.955i 0.520668i
\(652\) −108.982 + 181.547i −0.167151 + 0.278446i
\(653\) −206.765 −0.316639 −0.158319 0.987388i \(-0.550608\pi\)
−0.158319 + 0.987388i \(0.550608\pi\)
\(654\) 84.2327 + 23.3411i 0.128796 + 0.0356897i
\(655\) 0 0
\(656\) 321.682 + 603.792i 0.490370 + 0.920415i
\(657\) 298.636 0.454544
\(658\) 310.682 1121.18i 0.472161 1.70393i
\(659\) 708.330i 1.07486i −0.843309 0.537428i \(-0.819396\pi\)
0.843309 0.537428i \(-0.180604\pi\)
\(660\) 0 0
\(661\) 1229.66 1.86031 0.930155 0.367167i \(-0.119672\pi\)
0.930155 + 0.367167i \(0.119672\pi\)
\(662\) 926.540 + 256.746i 1.39961 + 0.387834i
\(663\) 494.072i 0.745207i
\(664\) −772.907 813.464i −1.16402 1.22510i
\(665\) 0 0
\(666\) 52.0521 187.845i 0.0781564 0.282049i
\(667\) 13.7261i 0.0205788i
\(668\) −369.076 + 614.820i −0.552508 + 0.920390i
\(669\) 137.329 0.205275
\(670\) 0 0
\(671\) 825.303i 1.22996i
\(672\) −647.658 + 144.284i −0.963777 + 0.214709i
\(673\) −753.492 −1.11960 −0.559801 0.828627i \(-0.689122\pi\)
−0.559801 + 0.828627i \(0.689122\pi\)
\(674\) −303.561 + 1095.48i −0.450387 + 1.62535i
\(675\) 0 0
\(676\) −1153.56 692.479i −1.70645 1.02438i
\(677\) 332.246 0.490762 0.245381 0.969427i \(-0.421087\pi\)
0.245381 + 0.969427i \(0.421087\pi\)
\(678\) −326.534 90.4832i −0.481613 0.133456i
\(679\) 169.520i 0.249661i
\(680\) 0 0
\(681\) −612.531 −0.899458
\(682\) −126.924 + 458.041i −0.186106 + 0.671615i
\(683\) 1120.62i 1.64074i 0.571835 + 0.820368i \(0.306232\pi\)
−0.571835 + 0.820368i \(0.693768\pi\)
\(684\) 54.1243 90.1623i 0.0791291 0.131816i
\(685\) 0 0
\(686\) −1045.70 289.767i −1.52435 0.422400i
\(687\) 39.4753i 0.0574605i
\(688\) −233.610 + 124.461i −0.339550 + 0.180902i
\(689\) 2115.54 3.07045
\(690\) 0 0
\(691\) 331.115i 0.479182i 0.970874 + 0.239591i \(0.0770134\pi\)
−0.970874 + 0.239591i \(0.922987\pi\)
\(692\) 607.970 + 364.964i 0.878570 + 0.527404i
\(693\) −522.139 −0.753447
\(694\) −713.482 197.707i −1.02807 0.284881i
\(695\) 0 0
\(696\) 26.2194 + 27.5953i 0.0376716 + 0.0396484i
\(697\) 542.566 0.778431
\(698\) 260.935 941.655i 0.373832 1.34908i
\(699\) 328.587i 0.470081i
\(700\) 0 0
\(701\) −564.971 −0.805949 −0.402975 0.915211i \(-0.632024\pi\)
−0.402975 + 0.915211i \(0.632024\pi\)
\(702\) 225.138 + 62.3861i 0.320709 + 0.0888691i
\(703\) 284.697i 0.404974i
\(704\) 929.230 + 47.5440i 1.31993 + 0.0675341i
\(705\) 0 0
\(706\) 347.006 1252.27i 0.491510 1.77375i
\(707\) 1956.29i 2.76703i
\(708\) 256.999 + 154.276i 0.362992 + 0.217904i
\(709\) 1.56083 0.00220146 0.00110073 0.999999i \(-0.499650\pi\)
0.00110073 + 0.999999i \(0.499650\pi\)
\(710\) 0 0
\(711\) 32.3339i 0.0454767i
\(712\) 318.236 302.370i 0.446961 0.424677i
\(713\) 81.6765 0.114553
\(714\) −140.523 + 507.117i −0.196811 + 0.710248i
\(715\) 0 0
\(716\) 211.738 352.721i 0.295723 0.492627i
\(717\) −463.804 −0.646868
\(718\) 782.339 + 216.788i 1.08961 + 0.301933i
\(719\) 75.0325i 0.104357i 0.998638 + 0.0521784i \(0.0166164\pi\)
−0.998638 + 0.0521784i \(0.983384\pi\)
\(720\) 0 0
\(721\) −2030.28 −2.81592
\(722\) −151.787 + 547.766i −0.210231 + 0.758678i
\(723\) 522.496i 0.722678i
\(724\) 395.810 + 237.604i 0.546699 + 0.328183i
\(725\) 0 0
\(726\) 301.648 + 83.5874i 0.415493 + 0.115134i
\(727\) 1229.26i 1.69087i −0.534082 0.845433i \(-0.679343\pi\)
0.534082 0.845433i \(-0.320657\pi\)
\(728\) −1483.00 1560.81i −2.03708 2.14397i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 209.922i 0.287170i
\(732\) 202.425 337.207i 0.276536 0.460665i
\(733\) −691.736 −0.943705 −0.471852 0.881678i \(-0.656414\pi\)
−0.471852 + 0.881678i \(0.656414\pi\)
\(734\) −89.1114 24.6930i −0.121405 0.0336416i
\(735\) 0 0
\(736\) −34.7676 156.063i −0.0472385 0.212042i
\(737\) −888.438 −1.20548
\(738\) 68.5094 247.235i 0.0928312 0.335007i
\(739\) 71.4311i 0.0966591i 0.998831 + 0.0483296i \(0.0153898\pi\)
−0.998831 + 0.0483296i \(0.984610\pi\)
\(740\) 0 0
\(741\) 341.218 0.460483
\(742\) 2171.40 + 601.698i 2.92641 + 0.810914i
\(743\) 1006.92i 1.35521i −0.735426 0.677605i \(-0.763018\pi\)
0.735426 0.677605i \(-0.236982\pi\)
\(744\) 164.205 156.018i 0.220705 0.209701i
\(745\) 0 0
\(746\) −73.8428 + 266.482i −0.0989850 + 0.357215i
\(747\) 420.788i 0.563303i
\(748\) 379.787 632.664i 0.507737 0.845808i
\(749\) −97.5496 −0.130240
\(750\) 0 0
\(751\) 1110.14i 1.47822i −0.673587 0.739108i \(-0.735247\pi\)
0.673587 0.739108i \(-0.264753\pi\)
\(752\) 686.154 365.562i 0.912439 0.486120i
\(753\) −109.447 −0.145347
\(754\) −32.9825 + 119.026i −0.0437433 + 0.157860i
\(755\) 0 0
\(756\) 213.338 + 128.067i 0.282193 + 0.169400i
\(757\) −326.752 −0.431641 −0.215821 0.976433i \(-0.569243\pi\)
−0.215821 + 0.976433i \(0.569243\pi\)
\(758\) 490.547 + 135.932i 0.647160 + 0.179329i
\(759\) 125.817i 0.165767i
\(760\) 0 0
\(761\) 162.162 0.213091 0.106546 0.994308i \(-0.466021\pi\)
0.106546 + 0.994308i \(0.466021\pi\)
\(762\) 155.004 559.375i 0.203417 0.734088i
\(763\) 302.070i 0.395898i
\(764\) 393.847 656.085i 0.515507 0.858750i
\(765\) 0 0
\(766\) 120.886 + 33.4977i 0.157814 + 0.0437306i
\(767\) 972.608i 1.26807i
\(768\) −368.009 247.341i −0.479178 0.322059i
\(769\) −154.694 −0.201162 −0.100581 0.994929i \(-0.532070\pi\)
−0.100581 + 0.994929i \(0.532070\pi\)
\(770\) 0 0
\(771\) 261.053i 0.338590i
\(772\) −549.861 330.081i −0.712255 0.427566i
\(773\) 208.302 0.269472 0.134736 0.990882i \(-0.456981\pi\)
0.134736 + 0.990882i \(0.456981\pi\)
\(774\) 95.6566 + 26.5066i 0.123587 + 0.0342463i
\(775\) 0 0
\(776\) 82.1226 78.0283i 0.105828 0.100552i
\(777\) 673.637 0.866972
\(778\) −58.8183 + 212.262i −0.0756019 + 0.272831i
\(779\) 374.709i 0.481013i
\(780\) 0 0
\(781\) −576.648 −0.738346
\(782\) −122.198 33.8612i −0.156263 0.0433008i
\(783\) 14.2744i 0.0182304i
\(784\) −709.590 1331.89i −0.905089 1.69884i
\(785\) 0 0
\(786\) 75.8972 273.896i 0.0965613 0.348468i
\(787\) 377.158i 0.479235i −0.970867 0.239617i \(-0.922978\pi\)
0.970867 0.239617i \(-0.0770220\pi\)
\(788\) 1217.76 + 731.017i 1.54538 + 0.927687i
\(789\) −352.915 −0.447294
\(790\) 0 0
\(791\) 1171.00i 1.48040i
\(792\) −240.336 252.947i −0.303454 0.319377i
\(793\) 1276.15 1.60927
\(794\) −156.460 + 564.629i −0.197053 + 0.711119i
\(795\) 0 0
\(796\) 181.587 302.495i 0.228124 0.380018i
\(797\) −321.141 −0.402937 −0.201468 0.979495i \(-0.564571\pi\)
−0.201468 + 0.979495i \(0.564571\pi\)
\(798\) 350.227 + 97.0487i 0.438881 + 0.121615i
\(799\) 616.576i 0.771685i
\(800\) 0 0
\(801\) −164.617 −0.205514
\(802\) −276.708 + 998.577i −0.345022 + 1.24511i
\(803\) 1447.21i 1.80225i
\(804\) 363.003 + 217.910i 0.451496 + 0.271032i
\(805\) 0 0
\(806\) 708.263 + 196.261i 0.878738 + 0.243500i
\(807\) 132.326i 0.163973i
\(808\) −947.712 + 900.462i −1.17291 + 1.11443i
\(809\) −861.938 −1.06544 −0.532718 0.846293i \(-0.678829\pi\)
−0.532718 + 0.846293i \(0.678829\pi\)
\(810\) 0 0
\(811\) 1011.44i 1.24715i −0.781765 0.623574i \(-0.785680\pi\)
0.781765 0.623574i \(-0.214320\pi\)
\(812\) −67.7066 + 112.788i −0.0833825 + 0.138902i
\(813\) −293.091 −0.360506
\(814\) −910.308 252.248i −1.11832 0.309887i
\(815\) 0 0
\(816\) −310.351 + 165.346i −0.380332 + 0.202630i
\(817\) 144.977 0.177450
\(818\) 97.1935 350.750i 0.118818 0.428790i
\(819\) 807.376i 0.985807i
\(820\) 0 0
\(821\) 68.0368 0.0828707 0.0414353 0.999141i \(-0.486807\pi\)
0.0414353 + 0.999141i \(0.486807\pi\)
\(822\) 849.462 + 235.388i 1.03341 + 0.286360i
\(823\) 980.340i 1.19118i −0.803289 0.595589i \(-0.796919\pi\)
0.803289 0.595589i \(-0.203081\pi\)
\(824\) −934.517 983.554i −1.13412 1.19363i
\(825\) 0 0
\(826\) −276.628 + 998.288i −0.334900 + 1.20858i
\(827\) 1183.88i 1.43153i −0.698341 0.715766i \(-0.746078\pi\)
0.698341 0.715766i \(-0.253922\pi\)
\(828\) −30.8596 + 51.4071i −0.0372701 + 0.0620859i
\(829\) 98.7892 0.119167 0.0595833 0.998223i \(-0.481023\pi\)
0.0595833 + 0.998223i \(0.481023\pi\)
\(830\) 0 0
\(831\) 474.392i 0.570869i
\(832\) 73.5167 1436.86i 0.0883614 1.72699i
\(833\) −1196.83 −1.43677
\(834\) −73.0313 + 263.554i −0.0875675 + 0.316012i
\(835\) 0 0
\(836\) −436.933 262.290i −0.522647 0.313744i
\(837\) −84.9395 −0.101481
\(838\) −314.830 87.2401i −0.375692 0.104105i
\(839\) 407.965i 0.486251i −0.969995 0.243125i \(-0.921827\pi\)
0.969995 0.243125i \(-0.0781727\pi\)
\(840\) 0 0
\(841\) −833.453 −0.991027
\(842\) 249.525 900.479i 0.296347 1.06945i
\(843\) 539.832i 0.640370i
\(844\) −392.363 + 653.613i −0.464885 + 0.774423i
\(845\) 0 0
\(846\) −280.960 77.8546i −0.332104 0.0920267i
\(847\) 1081.75i 1.27716i
\(848\) 707.984 + 1328.87i 0.834887 + 1.56707i
\(849\) 458.241 0.539742
\(850\) 0 0
\(851\) 162.323i 0.190744i
\(852\) 235.610 + 141.436i 0.276537 + 0.166005i
\(853\) 907.020 1.06333 0.531665 0.846955i \(-0.321567\pi\)
0.531665 + 0.846955i \(0.321567\pi\)
\(854\) 1309.85 + 362.962i 1.53378 + 0.425014i
\(855\) 0 0
\(856\) −44.9012 47.2573i −0.0524546 0.0552071i
\(857\) 693.549 0.809275 0.404638 0.914477i \(-0.367398\pi\)
0.404638 + 0.914477i \(0.367398\pi\)
\(858\) 302.328 1091.03i 0.352363 1.27160i
\(859\) 397.401i 0.462632i 0.972879 + 0.231316i \(0.0743031\pi\)
−0.972879 + 0.231316i \(0.925697\pi\)
\(860\) 0 0
\(861\) 886.621 1.02976
\(862\) −1321.27 366.126i −1.53279 0.424740i
\(863\) 1193.06i 1.38246i 0.722636 + 0.691229i \(0.242930\pi\)
−0.722636 + 0.691229i \(0.757070\pi\)
\(864\) 36.1566 + 162.298i 0.0418479 + 0.187845i
\(865\) 0 0
\(866\) −316.590 + 1142.50i −0.365577 + 1.31929i
\(867\) 221.682i 0.255689i
\(868\) 671.142 + 402.886i 0.773206 + 0.464154i
\(869\) 156.693 0.180314
\(870\) 0 0
\(871\) 1373.78i 1.57724i
\(872\) −146.336 + 139.040i −0.167817 + 0.159450i
\(873\) −42.4803 −0.0486601
\(874\) −23.3854 + 84.3927i −0.0267567 + 0.0965591i
\(875\) 0 0
\(876\) −354.962 + 591.309i −0.405208 + 0.675010i
\(877\) 136.545 0.155695 0.0778477 0.996965i \(-0.475195\pi\)
0.0778477 + 0.996965i \(0.475195\pi\)
\(878\) −895.146 248.047i −1.01953 0.282514i
\(879\) 210.064i 0.238981i
\(880\) 0 0
\(881\) −836.578 −0.949578 −0.474789 0.880100i \(-0.657476\pi\)
−0.474789 + 0.880100i \(0.657476\pi\)
\(882\) −151.123 + 545.369i −0.171341 + 0.618332i
\(883\) 632.625i 0.716450i −0.933635 0.358225i \(-0.883382\pi\)
0.933635 0.358225i \(-0.116618\pi\)
\(884\) −978.280 587.260i −1.10665 0.664321i
\(885\) 0 0
\(886\) 104.631 + 28.9934i 0.118093 + 0.0327239i
\(887\) 290.957i 0.328024i 0.986458 + 0.164012i \(0.0524435\pi\)
−0.986458 + 0.164012i \(0.947556\pi\)
\(888\) 310.069 + 326.339i 0.349177 + 0.367499i
\(889\) 2006.00 2.25646
\(890\) 0 0
\(891\) 130.844i 0.146851i
\(892\) −163.231 + 271.916i −0.182994 + 0.304838i
\(893\) −425.822 −0.476844
\(894\) 107.972 + 29.9192i 0.120774 + 0.0334667i
\(895\) 0 0
\(896\) 484.126 1453.88i 0.540319 1.62264i
\(897\) −194.550 −0.216889
\(898\) 228.613 825.013i 0.254580 0.918723i
\(899\) 44.9061i 0.0499511i
\(900\) 0 0
\(901\) 1194.12 1.32533
\(902\) −1198.12 332.001i −1.32829 0.368073i
\(903\) 343.038i 0.379887i
\(904\) 567.282 538.999i 0.627524 0.596237i
\(905\) 0 0
\(906\) 35.8876 129.510i 0.0396110 0.142947i
\(907\) 473.341i 0.521875i 0.965356 + 0.260938i \(0.0840317\pi\)
−0.965356 + 0.260938i \(0.915968\pi\)
\(908\) 728.061 1212.83i 0.801830 1.33572i
\(909\) 490.231 0.539308
\(910\) 0 0
\(911\) 1176.67i 1.29163i 0.763495 + 0.645813i \(0.223482\pi\)
−0.763495 + 0.645813i \(0.776518\pi\)
\(912\) 114.192 + 214.336i 0.125210 + 0.235017i
\(913\) 2039.17 2.23348
\(914\) 35.5615 128.334i 0.0389075 0.140409i
\(915\) 0 0
\(916\) 78.1625 + 46.9208i 0.0853303 + 0.0512236i
\(917\) 982.230 1.07113
\(918\) 127.080 + 35.2140i 0.138431 + 0.0383595i
\(919\) 1491.24i 1.62267i −0.584580 0.811336i \(-0.698741\pi\)
0.584580 0.811336i \(-0.301259\pi\)
\(920\) 0 0
\(921\) −280.190 −0.304224
\(922\) 127.445 459.921i 0.138227 0.498830i
\(923\) 891.663i 0.966048i
\(924\) 620.620 1033.85i 0.671667 1.11889i
\(925\) 0 0
\(926\) −745.812 206.666i −0.805412 0.223181i
\(927\) 508.772i 0.548837i
\(928\) −85.8043 + 19.1154i −0.0924615 + 0.0205984i
\(929\) −1217.24 −1.31027 −0.655134 0.755513i \(-0.727388\pi\)
−0.655134 + 0.755513i \(0.727388\pi\)
\(930\) 0 0
\(931\) 826.560i 0.887819i
\(932\) 650.613 + 390.562i 0.698083 + 0.419058i
\(933\) 45.6938 0.0489751
\(934\) 454.790 + 126.023i 0.486927 + 0.134928i
\(935\) 0 0
\(936\) −391.128 + 371.628i −0.417872 + 0.397038i
\(937\) 468.840 0.500363 0.250182 0.968199i \(-0.419510\pi\)
0.250182 + 0.968199i \(0.419510\pi\)
\(938\) −390.728 + 1410.05i −0.416555 + 1.50325i
\(939\) 9.35138i 0.00995887i
\(940\) 0 0
\(941\) 358.033 0.380481 0.190241 0.981737i \(-0.439073\pi\)
0.190241 + 0.981737i \(0.439073\pi\)
\(942\) −147.560 40.8892i −0.156645 0.0434068i
\(943\) 213.645i 0.226559i
\(944\) −610.943 + 325.492i −0.647185 + 0.344801i
\(945\) 0 0
\(946\) 128.453 463.559i 0.135785 0.490020i
\(947\) 1148.77i 1.21306i −0.795059 0.606532i \(-0.792560\pi\)
0.795059 0.606532i \(-0.207440\pi\)
\(948\) −64.0223 38.4325i −0.0675341 0.0405406i
\(949\) −2237.80 −2.35806
\(950\) 0 0
\(951\) 467.926i 0.492036i
\(952\) −837.082 881.006i −0.879288 0.925427i
\(953\) −911.785 −0.956753 −0.478376 0.878155i \(-0.658774\pi\)
−0.478376 + 0.878155i \(0.658774\pi\)
\(954\) 150.781 544.135i 0.158051 0.570372i
\(955\) 0 0
\(956\) 551.283 918.348i 0.576656 0.960615i
\(957\) −69.1750 −0.0722831
\(958\) −1020.54 282.792i −1.06528 0.295190i
\(959\) 3046.29i 3.17653i
\(960\) 0 0
\(961\) 693.788 0.721944
\(962\) −390.048 + 1407.60i −0.405455 + 1.46320i
\(963\) 24.4452i 0.0253844i
\(964\) 1034.56 + 621.045i 1.07320 + 0.644237i
\(965\) 0 0
\(966\) −199.686 55.3335i −0.206715 0.0572811i
\(967\) 311.565i 0.322197i −0.986938 0.161099i \(-0.948496\pi\)
0.986938 0.161099i \(-0.0515037\pi\)
\(968\) −524.048 + 497.921i −0.541372 + 0.514381i
\(969\) 192.602 0.198763
\(970\) 0 0
\(971\) 370.530i 0.381596i −0.981629 0.190798i \(-0.938892\pi\)
0.981629 0.190798i \(-0.0611075\pi\)
\(972\) 32.0925 53.4609i 0.0330170 0.0550010i
\(973\) −945.141 −0.971368
\(974\) 1697.63 + 470.417i 1.74295 + 0.482974i
\(975\) 0 0
\(976\) 427.077 + 801.615i 0.437578 + 0.821327i
\(977\) −1402.53 −1.43555 −0.717773 0.696278i \(-0.754838\pi\)
−0.717773 + 0.696278i \(0.754838\pi\)
\(978\) −48.9690 + 176.718i −0.0500706 + 0.180694i
\(979\) 797.746i 0.814858i
\(980\) 0 0
\(981\) 75.6966 0.0771626
\(982\) −166.615 46.1693i −0.169669 0.0470156i
\(983\) 988.944i 1.00605i 0.864273 + 0.503023i \(0.167779\pi\)
−0.864273 + 0.503023i \(0.832221\pi\)
\(984\) 408.103 + 429.518i 0.414739 + 0.436502i
\(985\) 0 0
\(986\) −18.6171 + 67.1849i −0.0188814 + 0.0681388i
\(987\) 1007.56i 1.02083i
\(988\) −405.576 + 675.624i −0.410502 + 0.683830i
\(989\) −82.6603 −0.0835797
\(990\) 0 0
\(991\) 90.1483i 0.0909670i 0.998965 + 0.0454835i \(0.0144828\pi\)
−0.998965 + 0.0454835i \(0.985517\pi\)
\(992\) 113.745 + 510.575i 0.114663 + 0.514693i
\(993\) 832.644 0.838514
\(994\) −253.605 + 915.205i −0.255136 + 0.920729i
\(995\) 0 0
\(996\) −833.174 500.153i −0.836520 0.502162i
\(997\) 655.605 0.657578 0.328789 0.944403i \(-0.393360\pi\)
0.328789 + 0.944403i \(0.393360\pi\)
\(998\) −1685.56 467.071i −1.68893 0.468007i
\(999\) 168.808i 0.168977i
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.e.151.4 yes 8
3.2 odd 2 900.3.c.t.451.5 8
4.3 odd 2 inner 300.3.c.e.151.3 8
5.2 odd 4 300.3.f.c.199.3 16
5.3 odd 4 300.3.f.c.199.14 16
5.4 even 2 300.3.c.g.151.5 yes 8
12.11 even 2 900.3.c.t.451.6 8
15.2 even 4 900.3.f.h.199.14 16
15.8 even 4 900.3.f.h.199.3 16
15.14 odd 2 900.3.c.n.451.4 8
20.3 even 4 300.3.f.c.199.4 16
20.7 even 4 300.3.f.c.199.13 16
20.19 odd 2 300.3.c.g.151.6 yes 8
60.23 odd 4 900.3.f.h.199.13 16
60.47 odd 4 900.3.f.h.199.4 16
60.59 even 2 900.3.c.n.451.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.c.e.151.3 8 4.3 odd 2 inner
300.3.c.e.151.4 yes 8 1.1 even 1 trivial
300.3.c.g.151.5 yes 8 5.4 even 2
300.3.c.g.151.6 yes 8 20.19 odd 2
300.3.f.c.199.3 16 5.2 odd 4
300.3.f.c.199.4 16 20.3 even 4
300.3.f.c.199.13 16 20.7 even 4
300.3.f.c.199.14 16 5.3 odd 4
900.3.c.n.451.3 8 60.59 even 2
900.3.c.n.451.4 8 15.14 odd 2
900.3.c.t.451.5 8 3.2 odd 2
900.3.c.t.451.6 8 12.11 even 2
900.3.f.h.199.3 16 15.8 even 4
900.3.f.h.199.4 16 60.47 odd 4
900.3.f.h.199.13 16 60.23 odd 4
900.3.f.h.199.14 16 15.2 even 4