Properties

Label 585.2.j.h.451.5
Level $585$
Weight $2$
Character 585.451
Analytic conductor $4.671$
Analytic rank $0$
Dimension $10$
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] = [585,2,Mod(406,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.j (of order \(3\), degree \(2\), 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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.5
Root \(-1.06141 - 1.83842i\) of defining polynomial
Character \(\chi\) \(=\) 585.451
Dual form 585.2.j.h.406.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.06141 - 1.83842i) q^{2} +(-1.25320 - 2.17061i) q^{4} +1.00000 q^{5} +(-0.733534 - 1.27052i) q^{7} -1.07500 q^{8} +O(q^{10})\) \(q+(1.06141 - 1.83842i) q^{2} +(-1.25320 - 2.17061i) q^{4} +1.00000 q^{5} +(-0.733534 - 1.27052i) q^{7} -1.07500 q^{8} +(1.06141 - 1.83842i) q^{10} +(-0.172120 + 0.298120i) q^{11} +(1.76679 - 3.14300i) q^{13} -3.11433 q^{14} +(1.36538 - 2.36491i) q^{16} +(-2.56781 - 4.44758i) q^{17} +(-0.253200 - 0.438555i) q^{19} +(-1.25320 - 2.17061i) q^{20} +(0.365380 + 0.632857i) q^{22} +(-0.537500 + 0.930977i) q^{23} +1.00000 q^{25} +(-3.90288 - 6.58413i) q^{26} +(-1.83853 + 3.18442i) q^{28} +(-4.02423 + 6.97018i) q^{29} +9.17129 q^{31} +(-3.97347 - 6.88225i) q^{32} -10.9021 q^{34} +(-0.733534 - 1.27052i) q^{35} +(-1.36538 + 2.36491i) q^{37} -1.07500 q^{38} -1.07500 q^{40} +(-3.06357 + 5.30625i) q^{41} +(2.93744 + 5.08780i) q^{43} +0.862801 q^{44} +(1.14102 + 1.97630i) q^{46} +4.26369 q^{47} +(2.42386 - 4.19824i) q^{49} +(1.06141 - 1.83842i) q^{50} +(-9.03636 + 0.103818i) q^{52} -4.07866 q^{53} +(-0.172120 + 0.298120i) q^{55} +(0.788548 + 1.36581i) q^{56} +(8.54276 + 14.7965i) q^{58} +(2.53063 + 4.38318i) q^{59} +(2.58565 + 4.47847i) q^{61} +(9.73454 - 16.8607i) q^{62} -11.4085 q^{64} +(1.76679 - 3.14300i) q^{65} +(-0.598595 + 1.03680i) q^{67} +(-6.43597 + 11.1474i) q^{68} -3.11433 q^{70} +(-0.222886 - 0.386049i) q^{71} -7.52634 q^{73} +(2.89847 + 5.02029i) q^{74} +(-0.634620 + 1.09919i) q^{76} +0.505022 q^{77} +0.834915 q^{79} +(1.36538 - 2.36491i) q^{80} +(6.50342 + 11.2643i) q^{82} +15.2506 q^{83} +(-2.56781 - 4.44758i) q^{85} +12.4714 q^{86} +(0.185028 - 0.320479i) q^{88} +(-5.97494 + 10.3489i) q^{89} +(-5.28924 + 0.0607674i) q^{91} +2.69438 q^{92} +(4.52554 - 7.83847i) q^{94} +(-0.253200 - 0.438555i) q^{95} +(0.700282 + 1.21292i) q^{97} +(-5.14543 - 8.91215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06141 1.83842i 0.750533 1.29996i −0.197031 0.980397i \(-0.563130\pi\)
0.947565 0.319564i \(-0.103537\pi\)
\(3\) 0 0
\(4\) −1.25320 2.17061i −0.626600 1.08530i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.733534 1.27052i −0.277250 0.480210i 0.693451 0.720504i \(-0.256090\pi\)
−0.970700 + 0.240294i \(0.922756\pi\)
\(8\) −1.07500 −0.380070
\(9\) 0 0
\(10\) 1.06141 1.83842i 0.335649 0.581360i
\(11\) −0.172120 + 0.298120i −0.0518960 + 0.0898865i −0.890806 0.454383i \(-0.849860\pi\)
0.838910 + 0.544269i \(0.183193\pi\)
\(12\) 0 0
\(13\) 1.76679 3.14300i 0.490018 0.871712i
\(14\) −3.11433 −0.832340
\(15\) 0 0
\(16\) 1.36538 2.36491i 0.341345 0.591227i
\(17\) −2.56781 4.44758i −0.622786 1.07870i −0.988964 0.148153i \(-0.952667\pi\)
0.366178 0.930545i \(-0.380666\pi\)
\(18\) 0 0
\(19\) −0.253200 0.438555i −0.0580880 0.100611i 0.835519 0.549461i \(-0.185167\pi\)
−0.893607 + 0.448850i \(0.851834\pi\)
\(20\) −1.25320 2.17061i −0.280224 0.485362i
\(21\) 0 0
\(22\) 0.365380 + 0.632857i 0.0778993 + 0.134926i
\(23\) −0.537500 + 0.930977i −0.112076 + 0.194122i −0.916607 0.399789i \(-0.869083\pi\)
0.804531 + 0.593911i \(0.202417\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.90288 6.58413i −0.765418 1.29125i
\(27\) 0 0
\(28\) −1.83853 + 3.18442i −0.347449 + 0.601800i
\(29\) −4.02423 + 6.97018i −0.747281 + 1.29433i 0.201840 + 0.979419i \(0.435308\pi\)
−0.949121 + 0.314911i \(0.898025\pi\)
\(30\) 0 0
\(31\) 9.17129 1.64721 0.823607 0.567162i \(-0.191959\pi\)
0.823607 + 0.567162i \(0.191959\pi\)
\(32\) −3.97347 6.88225i −0.702416 1.21662i
\(33\) 0 0
\(34\) −10.9021 −1.86969
\(35\) −0.733534 1.27052i −0.123990 0.214757i
\(36\) 0 0
\(37\) −1.36538 + 2.36491i −0.224467 + 0.388788i −0.956159 0.292847i \(-0.905397\pi\)
0.731692 + 0.681635i \(0.238731\pi\)
\(38\) −1.07500 −0.174388
\(39\) 0 0
\(40\) −1.07500 −0.169972
\(41\) −3.06357 + 5.30625i −0.478449 + 0.828697i −0.999695 0.0247092i \(-0.992134\pi\)
0.521246 + 0.853406i \(0.325467\pi\)
\(42\) 0 0
\(43\) 2.93744 + 5.08780i 0.447956 + 0.775882i 0.998253 0.0590868i \(-0.0188189\pi\)
−0.550297 + 0.834969i \(0.685486\pi\)
\(44\) 0.862801 0.130072
\(45\) 0 0
\(46\) 1.14102 + 1.97630i 0.168234 + 0.291390i
\(47\) 4.26369 0.621924 0.310962 0.950422i \(-0.399349\pi\)
0.310962 + 0.950422i \(0.399349\pi\)
\(48\) 0 0
\(49\) 2.42386 4.19824i 0.346265 0.599749i
\(50\) 1.06141 1.83842i 0.150107 0.259992i
\(51\) 0 0
\(52\) −9.03636 + 0.103818i −1.25312 + 0.0143969i
\(53\) −4.07866 −0.560248 −0.280124 0.959964i \(-0.590376\pi\)
−0.280124 + 0.959964i \(0.590376\pi\)
\(54\) 0 0
\(55\) −0.172120 + 0.298120i −0.0232086 + 0.0401985i
\(56\) 0.788548 + 1.36581i 0.105374 + 0.182513i
\(57\) 0 0
\(58\) 8.54276 + 14.7965i 1.12172 + 1.94287i
\(59\) 2.53063 + 4.38318i 0.329460 + 0.570642i 0.982405 0.186764i \(-0.0597999\pi\)
−0.652945 + 0.757406i \(0.726467\pi\)
\(60\) 0 0
\(61\) 2.58565 + 4.47847i 0.331058 + 0.573410i 0.982720 0.185100i \(-0.0592610\pi\)
−0.651661 + 0.758510i \(0.725928\pi\)
\(62\) 9.73454 16.8607i 1.23629 2.14131i
\(63\) 0 0
\(64\) −11.4085 −1.42606
\(65\) 1.76679 3.14300i 0.219143 0.389842i
\(66\) 0 0
\(67\) −0.598595 + 1.03680i −0.0731300 + 0.126665i −0.900272 0.435329i \(-0.856632\pi\)
0.827142 + 0.561994i \(0.189965\pi\)
\(68\) −6.43597 + 11.1474i −0.780476 + 1.35182i
\(69\) 0 0
\(70\) −3.11433 −0.372234
\(71\) −0.222886 0.386049i −0.0264517 0.0458156i 0.852497 0.522733i \(-0.175087\pi\)
−0.878948 + 0.476917i \(0.841754\pi\)
\(72\) 0 0
\(73\) −7.52634 −0.880892 −0.440446 0.897779i \(-0.645180\pi\)
−0.440446 + 0.897779i \(0.645180\pi\)
\(74\) 2.89847 + 5.02029i 0.336940 + 0.583597i
\(75\) 0 0
\(76\) −0.634620 + 1.09919i −0.0727959 + 0.126086i
\(77\) 0.505022 0.0575526
\(78\) 0 0
\(79\) 0.834915 0.0939352 0.0469676 0.998896i \(-0.485044\pi\)
0.0469676 + 0.998896i \(0.485044\pi\)
\(80\) 1.36538 2.36491i 0.152654 0.264405i
\(81\) 0 0
\(82\) 6.50342 + 11.2643i 0.718183 + 1.24393i
\(83\) 15.2506 1.67397 0.836985 0.547226i \(-0.184316\pi\)
0.836985 + 0.547226i \(0.184316\pi\)
\(84\) 0 0
\(85\) −2.56781 4.44758i −0.278518 0.482408i
\(86\) 12.4714 1.34482
\(87\) 0 0
\(88\) 0.185028 0.320479i 0.0197241 0.0341631i
\(89\) −5.97494 + 10.3489i −0.633343 + 1.09698i 0.353521 + 0.935427i \(0.384984\pi\)
−0.986864 + 0.161555i \(0.948349\pi\)
\(90\) 0 0
\(91\) −5.28924 + 0.0607674i −0.554463 + 0.00637016i
\(92\) 2.69438 0.280908
\(93\) 0 0
\(94\) 4.52554 7.83847i 0.466774 0.808477i
\(95\) −0.253200 0.438555i −0.0259778 0.0449948i
\(96\) 0 0
\(97\) 0.700282 + 1.21292i 0.0711029 + 0.123154i 0.899385 0.437158i \(-0.144015\pi\)
−0.828282 + 0.560311i \(0.810681\pi\)
\(98\) −5.14543 8.91215i −0.519767 0.900263i
\(99\) 0 0
\(100\) −1.25320 2.17061i −0.125320 0.217061i
\(101\) −5.04700 + 8.74167i −0.502196 + 0.869828i 0.497801 + 0.867291i \(0.334141\pi\)
−0.999997 + 0.00253716i \(0.999192\pi\)
\(102\) 0 0
\(103\) 15.5592 1.53309 0.766545 0.642190i \(-0.221974\pi\)
0.766545 + 0.642190i \(0.221974\pi\)
\(104\) −1.89929 + 3.37873i −0.186241 + 0.331311i
\(105\) 0 0
\(106\) −4.32915 + 7.49831i −0.420484 + 0.728300i
\(107\) −1.05685 + 1.83051i −0.102169 + 0.176962i −0.912578 0.408902i \(-0.865912\pi\)
0.810409 + 0.585865i \(0.199245\pi\)
\(108\) 0 0
\(109\) 4.12514 0.395117 0.197558 0.980291i \(-0.436699\pi\)
0.197558 + 0.980291i \(0.436699\pi\)
\(110\) 0.365380 + 0.632857i 0.0348376 + 0.0603405i
\(111\) 0 0
\(112\) −4.00621 −0.378551
\(113\) 5.69573 + 9.86529i 0.535809 + 0.928049i 0.999124 + 0.0418549i \(0.0133267\pi\)
−0.463314 + 0.886194i \(0.653340\pi\)
\(114\) 0 0
\(115\) −0.537500 + 0.930977i −0.0501221 + 0.0868140i
\(116\) 20.1727 1.87299
\(117\) 0 0
\(118\) 10.7442 0.989083
\(119\) −3.76716 + 6.52490i −0.345335 + 0.598137i
\(120\) 0 0
\(121\) 5.44075 + 9.42365i 0.494614 + 0.856696i
\(122\) 10.9778 0.993881
\(123\) 0 0
\(124\) −11.4935 19.9073i −1.03214 1.78773i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.5067 18.1982i 0.932322 1.61483i 0.152980 0.988229i \(-0.451113\pi\)
0.779342 0.626599i \(-0.215554\pi\)
\(128\) −4.16216 + 7.20907i −0.367886 + 0.637198i
\(129\) 0 0
\(130\) −3.90288 6.58413i −0.342305 0.577466i
\(131\) −13.4726 −1.17711 −0.588555 0.808457i \(-0.700303\pi\)
−0.588555 + 0.808457i \(0.700303\pi\)
\(132\) 0 0
\(133\) −0.371461 + 0.643390i −0.0322098 + 0.0557889i
\(134\) 1.27071 + 2.20094i 0.109773 + 0.190132i
\(135\) 0 0
\(136\) 2.76040 + 4.78115i 0.236702 + 0.409980i
\(137\) −5.10101 8.83521i −0.435809 0.754843i 0.561553 0.827441i \(-0.310204\pi\)
−0.997361 + 0.0725982i \(0.976871\pi\)
\(138\) 0 0
\(139\) −6.07601 10.5240i −0.515360 0.892630i −0.999841 0.0178282i \(-0.994325\pi\)
0.484481 0.874802i \(-0.339009\pi\)
\(140\) −1.83853 + 3.18442i −0.155384 + 0.269133i
\(141\) 0 0
\(142\) −0.946296 −0.0794114
\(143\) 0.632893 + 1.06769i 0.0529252 + 0.0892844i
\(144\) 0 0
\(145\) −4.02423 + 6.97018i −0.334194 + 0.578842i
\(146\) −7.98857 + 13.8366i −0.661138 + 1.14513i
\(147\) 0 0
\(148\) 6.84438 0.562604
\(149\) −0.333643 0.577886i −0.0273331 0.0473423i 0.852035 0.523484i \(-0.175368\pi\)
−0.879368 + 0.476142i \(0.842035\pi\)
\(150\) 0 0
\(151\) −15.9198 −1.29553 −0.647767 0.761839i \(-0.724297\pi\)
−0.647767 + 0.761839i \(0.724297\pi\)
\(152\) 0.272190 + 0.471446i 0.0220775 + 0.0382393i
\(153\) 0 0
\(154\) 0.536037 0.928444i 0.0431951 0.0748161i
\(155\) 9.17129 0.736656
\(156\) 0 0
\(157\) 17.4611 1.39355 0.696774 0.717290i \(-0.254618\pi\)
0.696774 + 0.717290i \(0.254618\pi\)
\(158\) 0.886190 1.53493i 0.0705015 0.122112i
\(159\) 0 0
\(160\) −3.97347 6.88225i −0.314130 0.544089i
\(161\) 1.57710 0.124293
\(162\) 0 0
\(163\) −7.27927 12.6081i −0.570156 0.987539i −0.996549 0.0830015i \(-0.973549\pi\)
0.426393 0.904538i \(-0.359784\pi\)
\(164\) 15.3570 1.19918
\(165\) 0 0
\(166\) 16.1872 28.0370i 1.25637 2.17610i
\(167\) −7.76055 + 13.4417i −0.600530 + 1.04015i 0.392211 + 0.919875i \(0.371710\pi\)
−0.992741 + 0.120273i \(0.961623\pi\)
\(168\) 0 0
\(169\) −6.75694 11.1060i −0.519765 0.854309i
\(170\) −10.9021 −0.836149
\(171\) 0 0
\(172\) 7.36240 12.7521i 0.561378 0.972335i
\(173\) 4.16295 + 7.21044i 0.316503 + 0.548199i 0.979756 0.200196i \(-0.0641579\pi\)
−0.663253 + 0.748395i \(0.730825\pi\)
\(174\) 0 0
\(175\) −0.733534 1.27052i −0.0554499 0.0960421i
\(176\) 0.470017 + 0.814094i 0.0354289 + 0.0613646i
\(177\) 0 0
\(178\) 12.6838 + 21.9689i 0.950689 + 1.64664i
\(179\) 12.6313 21.8781i 0.944111 1.63525i 0.186589 0.982438i \(-0.440257\pi\)
0.757522 0.652810i \(-0.226410\pi\)
\(180\) 0 0
\(181\) −21.6041 −1.60582 −0.802909 0.596102i \(-0.796716\pi\)
−0.802909 + 0.596102i \(0.796716\pi\)
\(182\) −5.50235 + 9.78836i −0.407862 + 0.725561i
\(183\) 0 0
\(184\) 0.577812 1.00080i 0.0425968 0.0737799i
\(185\) −1.36538 + 2.36491i −0.100385 + 0.173871i
\(186\) 0 0
\(187\) 1.76788 0.129280
\(188\) −5.34326 9.25480i −0.389697 0.674975i
\(189\) 0 0
\(190\) −1.07500 −0.0779886
\(191\) −4.65724 8.06657i −0.336986 0.583676i 0.646878 0.762593i \(-0.276074\pi\)
−0.983864 + 0.178917i \(0.942741\pi\)
\(192\) 0 0
\(193\) 3.80004 6.58186i 0.273533 0.473772i −0.696231 0.717818i \(-0.745141\pi\)
0.969764 + 0.244045i \(0.0784745\pi\)
\(194\) 2.97316 0.213460
\(195\) 0 0
\(196\) −12.1503 −0.867879
\(197\) −5.47163 + 9.47715i −0.389838 + 0.675219i −0.992427 0.122832i \(-0.960802\pi\)
0.602590 + 0.798051i \(0.294136\pi\)
\(198\) 0 0
\(199\) 7.09839 + 12.2948i 0.503192 + 0.871554i 0.999993 + 0.00368935i \(0.00117436\pi\)
−0.496802 + 0.867864i \(0.665492\pi\)
\(200\) −1.07500 −0.0760139
\(201\) 0 0
\(202\) 10.7139 + 18.5571i 0.753829 + 1.30567i
\(203\) 11.8076 0.828734
\(204\) 0 0
\(205\) −3.06357 + 5.30625i −0.213969 + 0.370605i
\(206\) 16.5147 28.6043i 1.15064 1.99296i
\(207\) 0 0
\(208\) −5.02058 8.46968i −0.348115 0.587267i
\(209\) 0.174322 0.0120581
\(210\) 0 0
\(211\) −5.16489 + 8.94586i −0.355566 + 0.615858i −0.987215 0.159396i \(-0.949045\pi\)
0.631649 + 0.775255i \(0.282379\pi\)
\(212\) 5.11138 + 8.85317i 0.351051 + 0.608038i
\(213\) 0 0
\(214\) 2.24351 + 3.88586i 0.153363 + 0.265632i
\(215\) 2.93744 + 5.08780i 0.200332 + 0.346985i
\(216\) 0 0
\(217\) −6.72745 11.6523i −0.456689 0.791009i
\(218\) 4.37848 7.58375i 0.296548 0.513637i
\(219\) 0 0
\(220\) 0.862801 0.0581700
\(221\) −18.5155 + 0.212723i −1.24549 + 0.0143093i
\(222\) 0 0
\(223\) −12.2531 + 21.2229i −0.820526 + 1.42119i 0.0847654 + 0.996401i \(0.472986\pi\)
−0.905291 + 0.424791i \(0.860347\pi\)
\(224\) −5.82934 + 10.0967i −0.389489 + 0.674615i
\(225\) 0 0
\(226\) 24.1821 1.60857
\(227\) −1.50262 2.60261i −0.0997323 0.172741i 0.811842 0.583878i \(-0.198465\pi\)
−0.911574 + 0.411136i \(0.865132\pi\)
\(228\) 0 0
\(229\) −21.9741 −1.45209 −0.726046 0.687646i \(-0.758644\pi\)
−0.726046 + 0.687646i \(0.758644\pi\)
\(230\) 1.14102 + 1.97630i 0.0752366 + 0.130314i
\(231\) 0 0
\(232\) 4.32605 7.49293i 0.284019 0.491935i
\(233\) 7.22372 0.473242 0.236621 0.971602i \(-0.423960\pi\)
0.236621 + 0.971602i \(0.423960\pi\)
\(234\) 0 0
\(235\) 4.26369 0.278133
\(236\) 6.34278 10.9860i 0.412880 0.715128i
\(237\) 0 0
\(238\) 7.99702 + 13.8513i 0.518370 + 0.897843i
\(239\) 0.492963 0.0318871 0.0159436 0.999873i \(-0.494925\pi\)
0.0159436 + 0.999873i \(0.494925\pi\)
\(240\) 0 0
\(241\) 13.1384 + 22.7564i 0.846320 + 1.46587i 0.884470 + 0.466597i \(0.154520\pi\)
−0.0381504 + 0.999272i \(0.512147\pi\)
\(242\) 23.0996 1.48490
\(243\) 0 0
\(244\) 6.48066 11.2248i 0.414882 0.718597i
\(245\) 2.42386 4.19824i 0.154855 0.268216i
\(246\) 0 0
\(247\) −1.82573 + 0.0209756i −0.116168 + 0.00133465i
\(248\) −9.85914 −0.626056
\(249\) 0 0
\(250\) 1.06141 1.83842i 0.0671297 0.116272i
\(251\) 10.7771 + 18.6665i 0.680246 + 1.17822i 0.974906 + 0.222619i \(0.0714605\pi\)
−0.294659 + 0.955602i \(0.595206\pi\)
\(252\) 0 0
\(253\) −0.185028 0.320479i −0.0116326 0.0201483i
\(254\) −22.3040 38.6316i −1.39948 2.42396i
\(255\) 0 0
\(256\) −2.57290 4.45640i −0.160806 0.278525i
\(257\) −6.40603 + 11.0956i −0.399597 + 0.692122i −0.993676 0.112284i \(-0.964183\pi\)
0.594079 + 0.804407i \(0.297517\pi\)
\(258\) 0 0
\(259\) 4.00621 0.248934
\(260\) −9.03636 + 0.103818i −0.560411 + 0.00643850i
\(261\) 0 0
\(262\) −14.3000 + 24.7684i −0.883460 + 1.53020i
\(263\) 12.2190 21.1639i 0.753454 1.30502i −0.192685 0.981261i \(-0.561720\pi\)
0.946139 0.323760i \(-0.104947\pi\)
\(264\) 0 0
\(265\) −4.07866 −0.250550
\(266\) 0.788548 + 1.36581i 0.0483490 + 0.0837429i
\(267\) 0 0
\(268\) 3.00064 0.183293
\(269\) −11.9134 20.6346i −0.726372 1.25811i −0.958407 0.285405i \(-0.907872\pi\)
0.232035 0.972707i \(-0.425461\pi\)
\(270\) 0 0
\(271\) −10.3877 + 17.9920i −0.631007 + 1.09294i 0.356339 + 0.934357i \(0.384025\pi\)
−0.987346 + 0.158579i \(0.949309\pi\)
\(272\) −14.0242 −0.850340
\(273\) 0 0
\(274\) −21.6571 −1.30836
\(275\) −0.172120 + 0.298120i −0.0103792 + 0.0179773i
\(276\) 0 0
\(277\) −0.234055 0.405396i −0.0140630 0.0243579i 0.858908 0.512129i \(-0.171143\pi\)
−0.872971 + 0.487772i \(0.837810\pi\)
\(278\) −25.7966 −1.54718
\(279\) 0 0
\(280\) 0.788548 + 1.36581i 0.0471248 + 0.0816225i
\(281\) −24.5123 −1.46228 −0.731141 0.682226i \(-0.761012\pi\)
−0.731141 + 0.682226i \(0.761012\pi\)
\(282\) 0 0
\(283\) −11.4475 + 19.8276i −0.680481 + 1.17863i 0.294354 + 0.955697i \(0.404896\pi\)
−0.974834 + 0.222930i \(0.928438\pi\)
\(284\) −0.558641 + 0.967594i −0.0331492 + 0.0574162i
\(285\) 0 0
\(286\) 2.63462 0.0302688i 0.155788 0.00178983i
\(287\) 8.98891 0.530599
\(288\) 0 0
\(289\) −4.68733 + 8.11870i −0.275726 + 0.477571i
\(290\) 8.54276 + 14.7965i 0.501648 + 0.868880i
\(291\) 0 0
\(292\) 9.43201 + 16.3367i 0.551967 + 0.956034i
\(293\) −9.62021 16.6627i −0.562019 0.973445i −0.997320 0.0731601i \(-0.976692\pi\)
0.435302 0.900285i \(-0.356642\pi\)
\(294\) 0 0
\(295\) 2.53063 + 4.38318i 0.147339 + 0.255199i
\(296\) 1.46778 2.54227i 0.0853131 0.147767i
\(297\) 0 0
\(298\) −1.41653 −0.0820575
\(299\) 1.97642 + 3.33420i 0.114299 + 0.192822i
\(300\) 0 0
\(301\) 4.30943 7.46414i 0.248391 0.430226i
\(302\) −16.8975 + 29.2673i −0.972341 + 1.68414i
\(303\) 0 0
\(304\) −1.38286 −0.0793122
\(305\) 2.58565 + 4.47847i 0.148054 + 0.256437i
\(306\) 0 0
\(307\) −16.4739 −0.940216 −0.470108 0.882609i \(-0.655785\pi\)
−0.470108 + 0.882609i \(0.655785\pi\)
\(308\) −0.632893 1.09620i −0.0360624 0.0624620i
\(309\) 0 0
\(310\) 9.73454 16.8607i 0.552885 0.957625i
\(311\) 9.54562 0.541283 0.270641 0.962680i \(-0.412764\pi\)
0.270641 + 0.962680i \(0.412764\pi\)
\(312\) 0 0
\(313\) 21.9067 1.23824 0.619120 0.785297i \(-0.287490\pi\)
0.619120 + 0.785297i \(0.287490\pi\)
\(314\) 18.5335 32.1009i 1.04590 1.81156i
\(315\) 0 0
\(316\) −1.04631 1.81227i −0.0588598 0.101948i
\(317\) −27.1321 −1.52389 −0.761945 0.647642i \(-0.775755\pi\)
−0.761945 + 0.647642i \(0.775755\pi\)
\(318\) 0 0
\(319\) −1.38530 2.39941i −0.0775618 0.134341i
\(320\) −11.4085 −0.637752
\(321\) 0 0
\(322\) 1.67395 2.89937i 0.0932857 0.161576i
\(323\) −1.30034 + 2.25225i −0.0723528 + 0.125319i
\(324\) 0 0
\(325\) 1.76679 3.14300i 0.0980036 0.174342i
\(326\) −30.9053 −1.71168
\(327\) 0 0
\(328\) 3.29333 5.70422i 0.181844 0.314963i
\(329\) −3.12756 5.41710i −0.172428 0.298654i
\(330\) 0 0
\(331\) −0.568970 0.985485i −0.0312734 0.0541672i 0.849965 0.526839i \(-0.176623\pi\)
−0.881239 + 0.472672i \(0.843290\pi\)
\(332\) −19.1120 33.1030i −1.04891 1.81676i
\(333\) 0 0
\(334\) 16.4743 + 28.5344i 0.901435 + 1.56133i
\(335\) −0.598595 + 1.03680i −0.0327047 + 0.0566463i
\(336\) 0 0
\(337\) −26.9676 −1.46902 −0.734510 0.678598i \(-0.762588\pi\)
−0.734510 + 0.678598i \(0.762588\pi\)
\(338\) −27.5895 + 0.634028i −1.50067 + 0.0344866i
\(339\) 0 0
\(340\) −6.43597 + 11.1474i −0.349039 + 0.604554i
\(341\) −1.57856 + 2.73414i −0.0854837 + 0.148062i
\(342\) 0 0
\(343\) −17.3814 −0.938507
\(344\) −3.15775 5.46938i −0.170254 0.294889i
\(345\) 0 0
\(346\) 17.6744 0.950184
\(347\) 3.26695 + 5.65853i 0.175379 + 0.303766i 0.940292 0.340368i \(-0.110552\pi\)
−0.764913 + 0.644133i \(0.777218\pi\)
\(348\) 0 0
\(349\) 0.528839 0.915976i 0.0283081 0.0490311i −0.851524 0.524315i \(-0.824321\pi\)
0.879832 + 0.475284i \(0.157655\pi\)
\(350\) −3.11433 −0.166468
\(351\) 0 0
\(352\) 2.73564 0.145810
\(353\) 12.2843 21.2771i 0.653828 1.13246i −0.328358 0.944553i \(-0.606495\pi\)
0.982186 0.187910i \(-0.0601715\pi\)
\(354\) 0 0
\(355\) −0.222886 0.386049i −0.0118295 0.0204894i
\(356\) 29.9512 1.58741
\(357\) 0 0
\(358\) −26.8142 46.4435i −1.41717 2.45462i
\(359\) 7.44704 0.393040 0.196520 0.980500i \(-0.437036\pi\)
0.196520 + 0.980500i \(0.437036\pi\)
\(360\) 0 0
\(361\) 9.37178 16.2324i 0.493252 0.854337i
\(362\) −22.9309 + 39.7174i −1.20522 + 2.08750i
\(363\) 0 0
\(364\) 6.76037 + 11.4047i 0.354340 + 0.597768i
\(365\) −7.52634 −0.393947
\(366\) 0 0
\(367\) 0.0222907 0.0386086i 0.00116356 0.00201535i −0.865443 0.501007i \(-0.832963\pi\)
0.866607 + 0.498992i \(0.166296\pi\)
\(368\) 1.46778 + 2.54227i 0.0765135 + 0.132525i
\(369\) 0 0
\(370\) 2.89847 + 5.02029i 0.150684 + 0.260993i
\(371\) 2.99184 + 5.18201i 0.155328 + 0.269037i
\(372\) 0 0
\(373\) 1.67118 + 2.89457i 0.0865304 + 0.149875i 0.906042 0.423187i \(-0.139089\pi\)
−0.819512 + 0.573062i \(0.805755\pi\)
\(374\) 1.87646 3.25012i 0.0970292 0.168060i
\(375\) 0 0
\(376\) −4.58347 −0.236374
\(377\) 14.7973 + 24.9630i 0.762101 + 1.28566i
\(378\) 0 0
\(379\) 13.1095 22.7064i 0.673391 1.16635i −0.303545 0.952817i \(-0.598170\pi\)
0.976936 0.213530i \(-0.0684962\pi\)
\(380\) −0.634620 + 1.09919i −0.0325553 + 0.0563875i
\(381\) 0 0
\(382\) −19.7730 −1.01168
\(383\) −6.44955 11.1710i −0.329557 0.570809i 0.652867 0.757472i \(-0.273566\pi\)
−0.982424 + 0.186663i \(0.940233\pi\)
\(384\) 0 0
\(385\) 0.505022 0.0257383
\(386\) −8.06682 13.9721i −0.410591 0.711164i
\(387\) 0 0
\(388\) 1.75519 3.04007i 0.0891061 0.154336i
\(389\) 5.08578 0.257859 0.128930 0.991654i \(-0.458846\pi\)
0.128930 + 0.991654i \(0.458846\pi\)
\(390\) 0 0
\(391\) 5.52080 0.279199
\(392\) −2.60564 + 4.51311i −0.131605 + 0.227946i
\(393\) 0 0
\(394\) 11.6153 + 20.1184i 0.585172 + 1.01355i
\(395\) 0.834915 0.0420091
\(396\) 0 0
\(397\) 5.53209 + 9.58187i 0.277648 + 0.480900i 0.970800 0.239891i \(-0.0771119\pi\)
−0.693152 + 0.720791i \(0.743779\pi\)
\(398\) 30.1373 1.51065
\(399\) 0 0
\(400\) 1.36538 2.36491i 0.0682690 0.118245i
\(401\) 11.5476 20.0011i 0.576662 0.998807i −0.419197 0.907895i \(-0.637688\pi\)
0.995859 0.0909120i \(-0.0289782\pi\)
\(402\) 0 0
\(403\) 16.2037 28.8254i 0.807164 1.43590i
\(404\) 25.2996 1.25870
\(405\) 0 0
\(406\) 12.5328 21.7074i 0.621992 1.07732i
\(407\) −0.470017 0.814094i −0.0232979 0.0403531i
\(408\) 0 0
\(409\) −7.21057 12.4891i −0.356540 0.617545i 0.630840 0.775913i \(-0.282710\pi\)
−0.987380 + 0.158367i \(0.949377\pi\)
\(410\) 6.50342 + 11.2643i 0.321181 + 0.556302i
\(411\) 0 0
\(412\) −19.4987 33.7728i −0.960634 1.66387i
\(413\) 3.71261 6.43043i 0.182686 0.316421i
\(414\) 0 0
\(415\) 15.2506 0.748622
\(416\) −28.6512 + 0.329170i −1.40474 + 0.0161389i
\(417\) 0 0
\(418\) 0.185028 0.320479i 0.00905003 0.0156751i
\(419\) 7.58423 13.1363i 0.370514 0.641749i −0.619131 0.785288i \(-0.712515\pi\)
0.989645 + 0.143539i \(0.0458483\pi\)
\(420\) 0 0
\(421\) 10.7707 0.524932 0.262466 0.964941i \(-0.415464\pi\)
0.262466 + 0.964941i \(0.415464\pi\)
\(422\) 10.9642 + 18.9905i 0.533728 + 0.924444i
\(423\) 0 0
\(424\) 4.38456 0.212933
\(425\) −2.56781 4.44758i −0.124557 0.215740i
\(426\) 0 0
\(427\) 3.79332 6.57022i 0.183572 0.317955i
\(428\) 5.29776 0.256077
\(429\) 0 0
\(430\) 12.4714 0.601423
\(431\) 20.6570 35.7789i 0.995010 1.72341i 0.411100 0.911590i \(-0.365145\pi\)
0.583910 0.811818i \(-0.301522\pi\)
\(432\) 0 0
\(433\) −9.22620 15.9802i −0.443383 0.767962i 0.554555 0.832147i \(-0.312888\pi\)
−0.997938 + 0.0641854i \(0.979555\pi\)
\(434\) −28.5625 −1.37104
\(435\) 0 0
\(436\) −5.16963 8.95405i −0.247580 0.428821i
\(437\) 0.544379 0.0260412
\(438\) 0 0
\(439\) −3.94070 + 6.82548i −0.188079 + 0.325763i −0.944610 0.328196i \(-0.893559\pi\)
0.756531 + 0.653958i \(0.226893\pi\)
\(440\) 0.185028 0.320479i 0.00882088 0.0152782i
\(441\) 0 0
\(442\) −19.2616 + 34.2652i −0.916180 + 1.62983i
\(443\) 38.2769 1.81859 0.909294 0.416154i \(-0.136622\pi\)
0.909294 + 0.416154i \(0.136622\pi\)
\(444\) 0 0
\(445\) −5.97494 + 10.3489i −0.283239 + 0.490585i
\(446\) 26.0111 + 45.0526i 1.23166 + 2.13330i
\(447\) 0 0
\(448\) 8.36848 + 14.4946i 0.395374 + 0.684807i
\(449\) −6.27219 10.8638i −0.296003 0.512692i 0.679215 0.733940i \(-0.262320\pi\)
−0.975218 + 0.221247i \(0.928987\pi\)
\(450\) 0 0
\(451\) −1.05460 1.82662i −0.0496591 0.0860121i
\(452\) 14.2758 24.7264i 0.671476 1.16303i
\(453\) 0 0
\(454\) −6.37960 −0.299410
\(455\) −5.28924 + 0.0607674i −0.247963 + 0.00284882i
\(456\) 0 0
\(457\) 10.1343 17.5532i 0.474064 0.821103i −0.525495 0.850797i \(-0.676120\pi\)
0.999559 + 0.0296935i \(0.00945313\pi\)
\(458\) −23.3237 + 40.3977i −1.08984 + 1.88766i
\(459\) 0 0
\(460\) 2.69438 0.125626
\(461\) −6.25006 10.8254i −0.291094 0.504190i 0.682975 0.730442i \(-0.260686\pi\)
−0.974069 + 0.226252i \(0.927353\pi\)
\(462\) 0 0
\(463\) −15.0923 −0.701400 −0.350700 0.936488i \(-0.614056\pi\)
−0.350700 + 0.936488i \(0.614056\pi\)
\(464\) 10.9892 + 19.0339i 0.510162 + 0.883626i
\(465\) 0 0
\(466\) 7.66736 13.2803i 0.355184 0.615196i
\(467\) 14.8821 0.688662 0.344331 0.938848i \(-0.388106\pi\)
0.344331 + 0.938848i \(0.388106\pi\)
\(468\) 0 0
\(469\) 1.75636 0.0811011
\(470\) 4.52554 7.83847i 0.208748 0.361562i
\(471\) 0 0
\(472\) −2.72043 4.71192i −0.125218 0.216884i
\(473\) −2.02236 −0.0929884
\(474\) 0 0
\(475\) −0.253200 0.438555i −0.0116176 0.0201223i
\(476\) 18.8840 0.865546
\(477\) 0 0
\(478\) 0.523238 0.906275i 0.0239324 0.0414521i
\(479\) −0.152080 + 0.263411i −0.00694873 + 0.0120355i −0.869479 0.493970i \(-0.835545\pi\)
0.862530 + 0.506006i \(0.168879\pi\)
\(480\) 0 0
\(481\) 5.02058 + 8.46968i 0.228919 + 0.386184i
\(482\) 55.7812 2.54076
\(483\) 0 0
\(484\) 13.6367 23.6194i 0.619850 1.07361i
\(485\) 0.700282 + 1.21292i 0.0317982 + 0.0550761i
\(486\) 0 0
\(487\) −20.8582 36.1274i −0.945174 1.63709i −0.755402 0.655261i \(-0.772559\pi\)
−0.189772 0.981828i \(-0.560775\pi\)
\(488\) −2.77957 4.81435i −0.125825 0.217936i
\(489\) 0 0
\(490\) −5.14543 8.91215i −0.232447 0.402610i
\(491\) −20.2798 + 35.1256i −0.915213 + 1.58520i −0.108624 + 0.994083i \(0.534644\pi\)
−0.806589 + 0.591112i \(0.798689\pi\)
\(492\) 0 0
\(493\) 41.3339 1.86159
\(494\) −1.89929 + 3.37873i −0.0854532 + 0.152016i
\(495\) 0 0
\(496\) 12.5223 21.6893i 0.562268 0.973877i
\(497\) −0.326988 + 0.566361i −0.0146674 + 0.0254047i
\(498\) 0 0
\(499\) 21.7238 0.972493 0.486246 0.873822i \(-0.338366\pi\)
0.486246 + 0.873822i \(0.338366\pi\)
\(500\) −1.25320 2.17061i −0.0560448 0.0970724i
\(501\) 0 0
\(502\) 45.7560 2.04219
\(503\) −12.2136 21.1545i −0.544575 0.943232i −0.998634 0.0522601i \(-0.983358\pi\)
0.454058 0.890972i \(-0.349976\pi\)
\(504\) 0 0
\(505\) −5.04700 + 8.74167i −0.224589 + 0.388999i
\(506\) −0.785567 −0.0349227
\(507\) 0 0
\(508\) −52.6681 −2.33677
\(509\) −15.7512 + 27.2819i −0.698161 + 1.20925i 0.270942 + 0.962596i \(0.412665\pi\)
−0.969103 + 0.246655i \(0.920669\pi\)
\(510\) 0 0
\(511\) 5.52083 + 9.56235i 0.244227 + 0.423013i
\(512\) −27.5723 −1.21854
\(513\) 0 0
\(514\) 13.5989 + 23.5540i 0.599821 + 1.03892i
\(515\) 15.5592 0.685619
\(516\) 0 0
\(517\) −0.733865 + 1.27109i −0.0322753 + 0.0559025i
\(518\) 4.25225 7.36511i 0.186833 0.323604i
\(519\) 0 0
\(520\) −1.89929 + 3.37873i −0.0832895 + 0.148167i
\(521\) −38.2684 −1.67657 −0.838284 0.545235i \(-0.816441\pi\)
−0.838284 + 0.545235i \(0.816441\pi\)
\(522\) 0 0
\(523\) −7.50085 + 12.9919i −0.327989 + 0.568094i −0.982113 0.188294i \(-0.939704\pi\)
0.654123 + 0.756388i \(0.273038\pi\)
\(524\) 16.8839 + 29.2438i 0.737577 + 1.27752i
\(525\) 0 0
\(526\) −25.9388 44.9273i −1.13098 1.95892i
\(527\) −23.5502 40.7901i −1.02586 1.77684i
\(528\) 0 0
\(529\) 10.9222 + 18.9178i 0.474878 + 0.822512i
\(530\) −4.32915 + 7.49831i −0.188046 + 0.325706i
\(531\) 0 0
\(532\) 1.86206 0.0807305
\(533\) 11.2649 + 19.0038i 0.487937 + 0.823146i
\(534\) 0 0
\(535\) −1.05685 + 1.83051i −0.0456915 + 0.0791400i
\(536\) 0.643489 1.11456i 0.0277945 0.0481415i
\(537\) 0 0
\(538\) −50.5801 −2.18066
\(539\) 0.834386 + 1.44520i 0.0359396 + 0.0622491i
\(540\) 0 0
\(541\) −11.9341 −0.513089 −0.256544 0.966532i \(-0.582584\pi\)
−0.256544 + 0.966532i \(0.582584\pi\)
\(542\) 22.0513 + 38.1939i 0.947183 + 1.64057i
\(543\) 0 0
\(544\) −20.4062 + 35.3447i −0.874911 + 1.51539i
\(545\) 4.12514 0.176702
\(546\) 0 0
\(547\) 23.5978 1.00897 0.504484 0.863421i \(-0.331683\pi\)
0.504484 + 0.863421i \(0.331683\pi\)
\(548\) −12.7852 + 22.1446i −0.546155 + 0.945969i
\(549\) 0 0
\(550\) 0.365380 + 0.632857i 0.0155799 + 0.0269851i
\(551\) 4.07574 0.173632
\(552\) 0 0
\(553\) −0.612438 1.06077i −0.0260435 0.0451087i
\(554\) −0.993719 −0.0422191
\(555\) 0 0
\(556\) −15.2289 + 26.3772i −0.645849 + 1.11864i
\(557\) −7.33970 + 12.7127i −0.310993 + 0.538656i −0.978578 0.205878i \(-0.933995\pi\)
0.667585 + 0.744534i \(0.267328\pi\)
\(558\) 0 0
\(559\) 21.1808 0.243344i 0.895852 0.0102923i
\(560\) −4.00621 −0.169293
\(561\) 0 0
\(562\) −26.0177 + 45.0640i −1.09749 + 1.90091i
\(563\) 15.2670 + 26.4431i 0.643425 + 1.11445i 0.984663 + 0.174468i \(0.0558206\pi\)
−0.341237 + 0.939977i \(0.610846\pi\)
\(564\) 0 0
\(565\) 5.69573 + 9.86529i 0.239621 + 0.415036i
\(566\) 24.3010 + 42.0905i 1.02145 + 1.76920i
\(567\) 0 0
\(568\) 0.239602 + 0.415003i 0.0100535 + 0.0174131i
\(569\) 9.56420 16.5657i 0.400952 0.694469i −0.592889 0.805284i \(-0.702013\pi\)
0.993841 + 0.110815i \(0.0353460\pi\)
\(570\) 0 0
\(571\) −25.5461 −1.06907 −0.534535 0.845146i \(-0.679513\pi\)
−0.534535 + 0.845146i \(0.679513\pi\)
\(572\) 1.52438 2.71179i 0.0637377 0.113385i
\(573\) 0 0
\(574\) 9.54096 16.5254i 0.398232 0.689758i
\(575\) −0.537500 + 0.930977i −0.0224153 + 0.0388244i
\(576\) 0 0
\(577\) 28.2497 1.17605 0.588025 0.808843i \(-0.299906\pi\)
0.588025 + 0.808843i \(0.299906\pi\)
\(578\) 9.95041 + 17.2346i 0.413882 + 0.716865i
\(579\) 0 0
\(580\) 20.1727 0.837625
\(581\) −11.1868 19.3761i −0.464108 0.803858i
\(582\) 0 0
\(583\) 0.702018 1.21593i 0.0290746 0.0503587i
\(584\) 8.09081 0.334800
\(585\) 0 0
\(586\) −40.8441 −1.68725
\(587\) −0.397524 + 0.688532i −0.0164076 + 0.0284188i −0.874113 0.485723i \(-0.838556\pi\)
0.857705 + 0.514142i \(0.171890\pi\)
\(588\) 0 0
\(589\) −2.32217 4.02212i −0.0956833 0.165728i
\(590\) 10.7442 0.442332
\(591\) 0 0
\(592\) 3.72853 + 6.45800i 0.153241 + 0.265422i
\(593\) −36.0924 −1.48214 −0.741068 0.671430i \(-0.765680\pi\)
−0.741068 + 0.671430i \(0.765680\pi\)
\(594\) 0 0
\(595\) −3.76716 + 6.52490i −0.154438 + 0.267495i
\(596\) −0.836242 + 1.44841i −0.0342538 + 0.0593294i
\(597\) 0 0
\(598\) 8.22747 0.0945244i 0.336446 0.00386539i
\(599\) −2.37758 −0.0971454 −0.0485727 0.998820i \(-0.515467\pi\)
−0.0485727 + 0.998820i \(0.515467\pi\)
\(600\) 0 0
\(601\) −14.0688 + 24.3679i −0.573880 + 0.993989i 0.422283 + 0.906464i \(0.361229\pi\)
−0.996162 + 0.0875246i \(0.972104\pi\)
\(602\) −9.14817 15.8451i −0.372852 0.645798i
\(603\) 0 0
\(604\) 19.9507 + 34.5556i 0.811781 + 1.40605i
\(605\) 5.44075 + 9.42365i 0.221198 + 0.383126i
\(606\) 0 0
\(607\) −4.57022 7.91586i −0.185500 0.321295i 0.758245 0.651970i \(-0.226057\pi\)
−0.943745 + 0.330675i \(0.892724\pi\)
\(608\) −2.01216 + 3.48517i −0.0816039 + 0.141342i
\(609\) 0 0
\(610\) 10.9778 0.444477
\(611\) 7.53303 13.4008i 0.304754 0.542138i
\(612\) 0 0
\(613\) 19.3652 33.5415i 0.782153 1.35473i −0.148532 0.988908i \(-0.547455\pi\)
0.930685 0.365821i \(-0.119212\pi\)
\(614\) −17.4856 + 30.2860i −0.705663 + 1.22224i
\(615\) 0 0
\(616\) −0.542898 −0.0218740
\(617\) −18.8173 32.5924i −0.757554 1.31212i −0.944095 0.329675i \(-0.893061\pi\)
0.186541 0.982447i \(-0.440272\pi\)
\(618\) 0 0
\(619\) 33.3469 1.34033 0.670163 0.742214i \(-0.266224\pi\)
0.670163 + 0.742214i \(0.266224\pi\)
\(620\) −11.4935 19.9073i −0.461589 0.799495i
\(621\) 0 0
\(622\) 10.1319 17.5489i 0.406251 0.703647i
\(623\) 17.5313 0.702376
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 23.2521 40.2738i 0.929340 1.60966i
\(627\) 0 0
\(628\) −21.8823 37.9012i −0.873197 1.51242i
\(629\) 14.0242 0.559180
\(630\) 0 0
\(631\) 18.5301 + 32.0951i 0.737673 + 1.27769i 0.953541 + 0.301265i \(0.0974088\pi\)
−0.215867 + 0.976423i \(0.569258\pi\)
\(632\) −0.897533 −0.0357019
\(633\) 0 0
\(634\) −28.7984 + 49.8803i −1.14373 + 1.98100i
\(635\) 10.5067 18.1982i 0.416947 0.722173i
\(636\) 0 0
\(637\) −8.91266 15.0356i −0.353132 0.595732i
\(638\) −5.88150 −0.232851
\(639\) 0 0
\(640\) −4.16216 + 7.20907i −0.164524 + 0.284964i
\(641\) 17.0532 + 29.5370i 0.673561 + 1.16664i 0.976887 + 0.213756i \(0.0685696\pi\)
−0.303326 + 0.952887i \(0.598097\pi\)
\(642\) 0 0
\(643\) −3.63742 6.30019i −0.143446 0.248455i 0.785346 0.619057i \(-0.212485\pi\)
−0.928792 + 0.370601i \(0.879152\pi\)
\(644\) −1.97642 3.42325i −0.0778817 0.134895i
\(645\) 0 0
\(646\) 2.76040 + 4.78115i 0.108606 + 0.188112i
\(647\) 23.3891 40.5111i 0.919521 1.59266i 0.119377 0.992849i \(-0.461910\pi\)
0.800144 0.599808i \(-0.204756\pi\)
\(648\) 0 0
\(649\) −1.74228 −0.0683907
\(650\) −3.90288 6.58413i −0.153084 0.258251i
\(651\) 0 0
\(652\) −18.2447 + 31.6008i −0.714519 + 1.23758i
\(653\) −0.899891 + 1.55866i −0.0352154 + 0.0609949i −0.883096 0.469192i \(-0.844545\pi\)
0.847881 + 0.530187i \(0.177878\pi\)
\(654\) 0 0
\(655\) −13.4726 −0.526420
\(656\) 8.36586 + 14.4901i 0.326632 + 0.565743i
\(657\) 0 0
\(658\) −13.2786 −0.517652
\(659\) 13.6361 + 23.6184i 0.531186 + 0.920041i 0.999338 + 0.0363930i \(0.0115868\pi\)
−0.468152 + 0.883648i \(0.655080\pi\)
\(660\) 0 0
\(661\) −12.0632 + 20.8941i −0.469204 + 0.812686i −0.999380 0.0352019i \(-0.988793\pi\)
0.530176 + 0.847888i \(0.322126\pi\)
\(662\) −2.41565 −0.0938870
\(663\) 0 0
\(664\) −16.3944 −0.636225
\(665\) −0.371461 + 0.643390i −0.0144046 + 0.0249496i
\(666\) 0 0
\(667\) −4.32605 7.49293i −0.167505 0.290128i
\(668\) 38.9021 1.50517
\(669\) 0 0
\(670\) 1.27071 + 2.20094i 0.0490920 + 0.0850298i
\(671\) −1.78016 −0.0687224
\(672\) 0 0
\(673\) −19.4433 + 33.6768i −0.749485 + 1.29815i 0.198584 + 0.980084i \(0.436366\pi\)
−0.948070 + 0.318063i \(0.896968\pi\)
\(674\) −28.6238 + 49.5779i −1.10255 + 1.90967i
\(675\) 0 0
\(676\) −15.6390 + 28.5847i −0.601500 + 1.09941i
\(677\) 23.0788 0.886991 0.443495 0.896277i \(-0.353738\pi\)
0.443495 + 0.896277i \(0.353738\pi\)
\(678\) 0 0
\(679\) 1.02736 1.77944i 0.0394265 0.0682887i
\(680\) 2.76040 + 4.78115i 0.105856 + 0.183349i
\(681\) 0 0
\(682\) 3.35101 + 5.80412i 0.128317 + 0.222251i
\(683\) 0.457785 + 0.792906i 0.0175166 + 0.0303397i 0.874651 0.484753i \(-0.161091\pi\)
−0.857134 + 0.515093i \(0.827757\pi\)
\(684\) 0 0
\(685\) −5.10101 8.83521i −0.194900 0.337576i
\(686\) −18.4489 + 31.9544i −0.704381 + 1.22002i
\(687\) 0 0
\(688\) 16.0429 0.611630
\(689\) −7.20612 + 12.8193i −0.274531 + 0.488375i
\(690\) 0 0
\(691\) −3.58980 + 6.21771i −0.136562 + 0.236533i −0.926193 0.377049i \(-0.876939\pi\)
0.789631 + 0.613582i \(0.210272\pi\)
\(692\) 10.4340 18.0722i 0.396641 0.687003i
\(693\) 0 0
\(694\) 13.8704 0.526512
\(695\) −6.07601 10.5240i −0.230476 0.399196i
\(696\) 0 0
\(697\) 31.4667 1.19188
\(698\) −1.12263 1.94446i −0.0424923 0.0735989i
\(699\) 0 0
\(700\) −1.83853 + 3.18442i −0.0694898 + 0.120360i
\(701\) 32.6040 1.23143 0.615717 0.787967i \(-0.288866\pi\)
0.615717 + 0.787967i \(0.288866\pi\)
\(702\) 0 0
\(703\) 1.38286 0.0521554
\(704\) 1.96362 3.40109i 0.0740066 0.128183i
\(705\) 0 0
\(706\) −26.0775 45.1675i −0.981440 1.69990i
\(707\) 14.8086 0.556934
\(708\) 0 0
\(709\) −1.75954 3.04762i −0.0660811 0.114456i 0.831092 0.556135i \(-0.187716\pi\)
−0.897173 + 0.441679i \(0.854383\pi\)
\(710\) −0.946296 −0.0355139
\(711\) 0 0
\(712\) 6.42306 11.1251i 0.240714 0.416929i
\(713\) −4.92957 + 8.53826i −0.184614 + 0.319760i
\(714\) 0 0
\(715\) 0.632893 + 1.06769i 0.0236689 + 0.0399292i
\(716\) −63.3184 −2.36632
\(717\) 0 0
\(718\) 7.90439 13.6908i 0.294989 0.510937i
\(719\) −10.7649 18.6453i −0.401462 0.695352i 0.592441 0.805614i \(-0.298164\pi\)
−0.993903 + 0.110262i \(0.964831\pi\)
\(720\) 0 0
\(721\) −11.4132 19.7682i −0.425049 0.736206i
\(722\) −19.8947 34.4586i −0.740403 1.28242i
\(723\) 0 0
\(724\) 27.0742 + 46.8939i 1.00621 + 1.74280i
\(725\) −4.02423 + 6.97018i −0.149456 + 0.258866i
\(726\) 0 0
\(727\) 51.8935 1.92462 0.962312 0.271948i \(-0.0876679\pi\)
0.962312 + 0.271948i \(0.0876679\pi\)
\(728\) 5.68593 0.0653250i 0.210734 0.00242110i
\(729\) 0 0
\(730\) −7.98857 + 13.8366i −0.295670 + 0.512116i
\(731\) 15.0856 26.1290i 0.557961 0.966417i
\(732\) 0 0
\(733\) −22.8890 −0.845423 −0.422711 0.906264i \(-0.638922\pi\)
−0.422711 + 0.906264i \(0.638922\pi\)
\(734\) −0.0473193 0.0819594i −0.00174659 0.00302518i
\(735\) 0 0
\(736\) 8.54295 0.314897
\(737\) −0.206060 0.356906i −0.00759031 0.0131468i
\(738\) 0 0
\(739\) −12.7987 + 22.1680i −0.470807 + 0.815462i −0.999443 0.0333870i \(-0.989371\pi\)
0.528635 + 0.848849i \(0.322704\pi\)
\(740\) 6.84438 0.251604
\(741\) 0 0
\(742\) 12.7023 0.466317
\(743\) −14.0506 + 24.3364i −0.515467 + 0.892815i 0.484372 + 0.874862i \(0.339048\pi\)
−0.999839 + 0.0179525i \(0.994285\pi\)
\(744\) 0 0
\(745\) −0.333643 0.577886i −0.0122237 0.0211721i
\(746\) 7.09525 0.259776
\(747\) 0 0
\(748\) −2.21551 3.83738i −0.0810071 0.140308i
\(749\) 3.10093 0.113306
\(750\) 0 0
\(751\) −4.93493 + 8.54755i −0.180078 + 0.311905i −0.941907 0.335874i \(-0.890968\pi\)
0.761829 + 0.647778i \(0.224302\pi\)
\(752\) 5.82156 10.0832i 0.212291 0.367698i
\(753\) 0 0
\(754\) 61.5986 0.707699i 2.24329 0.0257729i
\(755\) −15.9198 −0.579380
\(756\) 0 0
\(757\) −0.930521 + 1.61171i −0.0338204 + 0.0585786i −0.882440 0.470425i \(-0.844101\pi\)
0.848620 + 0.529003i \(0.177434\pi\)
\(758\) −27.8293 48.2017i −1.01080 1.75076i
\(759\) 0 0
\(760\) 0.272190 + 0.471446i 0.00987335 + 0.0171012i
\(761\) 15.8963 + 27.5332i 0.576240 + 0.998077i 0.995906 + 0.0903983i \(0.0288140\pi\)
−0.419666 + 0.907679i \(0.637853\pi\)
\(762\) 0 0
\(763\) −3.02593 5.24106i −0.109546 0.189739i
\(764\) −11.6729 + 20.2180i −0.422310 + 0.731463i
\(765\) 0 0
\(766\) −27.3826 −0.989373
\(767\) 18.2474 0.209643i 0.658877 0.00756976i
\(768\) 0 0
\(769\) 9.66750 16.7446i 0.348619 0.603826i −0.637385 0.770545i \(-0.719984\pi\)
0.986004 + 0.166719i \(0.0533174\pi\)
\(770\) 0.536037 0.928444i 0.0193174 0.0334588i
\(771\) 0 0
\(772\) −19.0488 −0.685582
\(773\) 0.820176 + 1.42059i 0.0294997 + 0.0510949i 0.880398 0.474235i \(-0.157275\pi\)
−0.850899 + 0.525330i \(0.823942\pi\)
\(774\) 0 0
\(775\) 9.17129 0.329443
\(776\) −0.752803 1.30389i −0.0270240 0.0468070i
\(777\) 0 0
\(778\) 5.39812 9.34982i 0.193532 0.335207i
\(779\) 3.10278 0.111169
\(780\) 0 0
\(781\) 0.153452 0.00549094
\(782\) 5.85985 10.1496i 0.209548 0.362947i
\(783\) 0 0
\(784\) −6.61897 11.4644i −0.236392 0.409443i
\(785\) 17.4611 0.623214
\(786\) 0 0
\(787\) 16.1460 + 27.9657i 0.575544 + 0.996871i 0.995982 + 0.0895500i \(0.0285429\pi\)
−0.420439 + 0.907321i \(0.638124\pi\)
\(788\) 27.4282 0.977089
\(789\) 0 0
\(790\) 0.886190 1.53493i 0.0315292 0.0546102i
\(791\) 8.35602 14.4731i 0.297106 0.514602i
\(792\) 0 0
\(793\) 18.6441 0.214200i 0.662073 0.00760648i
\(794\) 23.4874 0.833535
\(795\) 0 0
\(796\) 17.7914 30.8156i 0.630600 1.09223i
\(797\) −20.5207 35.5429i −0.726880 1.25899i −0.958195 0.286115i \(-0.907636\pi\)
0.231315 0.972879i \(-0.425697\pi\)
\(798\) 0 0
\(799\) −10.9484 18.9631i −0.387325 0.670867i
\(800\) −3.97347 6.88225i −0.140483 0.243324i
\(801\) 0 0
\(802\) −24.5137 42.4589i −0.865607 1.49928i
\(803\) 1.29543 2.24375i 0.0457147 0.0791803i
\(804\) 0 0
\(805\) 1.57710 0.0555853
\(806\) −35.7945 60.3850i −1.26081 2.12697i
\(807\) 0 0
\(808\) 5.42553 9.39729i 0.190869 0.330595i
\(809\) −11.3191 + 19.6052i −0.397958 + 0.689283i −0.993474 0.114060i \(-0.963614\pi\)
0.595516 + 0.803343i \(0.296948\pi\)
\(810\) 0 0
\(811\) −6.81520 −0.239314 −0.119657 0.992815i \(-0.538180\pi\)
−0.119657 + 0.992815i \(0.538180\pi\)
\(812\) −14.7973 25.6297i −0.519285 0.899427i
\(813\) 0 0
\(814\) −1.99553 −0.0699433
\(815\) −7.27927 12.6081i −0.254982 0.441641i
\(816\) 0 0
\(817\) 1.48752 2.57646i 0.0520417 0.0901389i
\(818\) −30.6136 −1.07038
\(819\) 0 0
\(820\) 15.3570 0.536291
\(821\) −21.0056 + 36.3827i −0.733100 + 1.26977i 0.222452 + 0.974944i \(0.428594\pi\)
−0.955552 + 0.294822i \(0.904740\pi\)
\(822\) 0 0
\(823\) −16.9766 29.4043i −0.591766 1.02497i −0.993995 0.109430i \(-0.965098\pi\)
0.402228 0.915539i \(-0.368236\pi\)
\(824\) −16.7261 −0.582681
\(825\) 0 0
\(826\) −7.88123 13.6507i −0.274223 0.474968i
\(827\) 24.6063 0.855644 0.427822 0.903863i \(-0.359281\pi\)
0.427822 + 0.903863i \(0.359281\pi\)
\(828\) 0 0
\(829\) 7.42428 12.8592i 0.257856 0.446619i −0.707811 0.706401i \(-0.750317\pi\)
0.965667 + 0.259782i \(0.0836507\pi\)
\(830\) 16.1872 28.0370i 0.561866 0.973180i
\(831\) 0 0
\(832\) −20.1563 + 35.8568i −0.698793 + 1.24311i
\(833\) −24.8961 −0.862597
\(834\) 0 0
\(835\) −7.76055 + 13.4417i −0.268565 + 0.465168i
\(836\) −0.218461 0.378385i −0.00755563 0.0130867i
\(837\) 0 0
\(838\) −16.1000 27.8860i −0.556166 0.963307i
\(839\) −3.61789 6.26637i −0.124903 0.216339i 0.796792 0.604254i \(-0.206529\pi\)
−0.921695 + 0.387915i \(0.873195\pi\)
\(840\) 0 0
\(841\) −17.8889 30.9845i −0.616859 1.06843i
\(842\) 11.4322 19.8011i 0.393979 0.682391i
\(843\) 0 0
\(844\) 25.8906 0.891191
\(845\) −6.75694 11.1060i −0.232446 0.382059i
\(846\) 0 0
\(847\) 7.98195 13.8251i 0.274263 0.475037i
\(848\) −5.56893 + 9.64567i −0.191238 + 0.331234i
\(849\) 0 0
\(850\) −10.9021 −0.373937
\(851\) −1.46778 2.54227i −0.0503149 0.0871480i
\(852\) 0 0
\(853\) 36.9206 1.26414 0.632068 0.774913i \(-0.282206\pi\)
0.632068 + 0.774913i \(0.282206\pi\)
\(854\) −8.05256 13.9474i −0.275553 0.477272i
\(855\) 0 0
\(856\) 1.13611 1.96780i 0.0388314 0.0672580i
\(857\) −16.2642 −0.555573 −0.277786 0.960643i \(-0.589601\pi\)
−0.277786 + 0.960643i \(0.589601\pi\)
\(858\) 0 0
\(859\) 25.2975 0.863141 0.431571 0.902079i \(-0.357960\pi\)
0.431571 + 0.902079i \(0.357960\pi\)
\(860\) 7.36240 12.7521i 0.251056 0.434842i
\(861\) 0 0
\(862\) −43.8512 75.9524i −1.49358 2.58695i
\(863\) −55.7647 −1.89825 −0.949127 0.314894i \(-0.898031\pi\)
−0.949127 + 0.314894i \(0.898031\pi\)
\(864\) 0 0
\(865\) 4.16295 + 7.21044i 0.141544 + 0.245162i
\(866\) −39.1713 −1.33109
\(867\) 0 0
\(868\) −16.8617 + 29.2053i −0.572323 + 0.991292i
\(869\) −0.143705 + 0.248905i −0.00487486 + 0.00844351i
\(870\) 0 0
\(871\) 2.20107 + 3.71318i 0.0745804 + 0.125816i
\(872\) −4.43452 −0.150172
\(873\) 0 0
\(874\) 0.577812 1.00080i 0.0195448 0.0338525i
\(875\) −0.733534 1.27052i −0.0247980 0.0429513i
\(876\) 0 0
\(877\) −15.7171 27.2227i −0.530727 0.919246i −0.999357 0.0358518i \(-0.988586\pi\)
0.468630 0.883395i \(-0.344748\pi\)
\(878\) 8.36542 + 14.4893i 0.282319 + 0.488991i
\(879\) 0 0
\(880\) 0.470017 + 0.814094i 0.0158443 + 0.0274431i
\(881\) 15.5090 26.8624i 0.522512 0.905018i −0.477145 0.878825i \(-0.658328\pi\)
0.999657 0.0261932i \(-0.00833849\pi\)
\(882\) 0 0
\(883\) −43.7232 −1.47140 −0.735701 0.677307i \(-0.763147\pi\)
−0.735701 + 0.677307i \(0.763147\pi\)
\(884\) 23.6654 + 39.9234i 0.795954 + 1.34277i
\(885\) 0 0
\(886\) 40.6276 70.3691i 1.36491 2.36409i
\(887\) 9.12624 15.8071i 0.306429 0.530751i −0.671149 0.741322i \(-0.734199\pi\)
0.977578 + 0.210571i \(0.0675325\pi\)
\(888\) 0 0
\(889\) −30.8282 −1.03394
\(890\) 12.6838 + 21.9689i 0.425161 + 0.736401i
\(891\) 0 0
\(892\) 61.4221 2.05657
\(893\) −1.07957 1.86986i −0.0361263 0.0625726i
\(894\) 0 0
\(895\) 12.6313 21.8781i 0.422219 0.731305i
\(896\) 12.2123 0.407986
\(897\) 0 0
\(898\) −26.6296 −0.888640
\(899\) −36.9074 + 63.9255i −1.23093 + 2.13204i
\(900\) 0 0
\(901\) 10.4733 + 18.1402i 0.348915 + 0.604338i
\(902\) −4.47746 −0.149083
\(903\) 0 0
\(904\) −6.12291 10.6052i −0.203645 0.352723i
\(905\) −21.6041 −0.718144
\(906\) 0 0
\(907\) −9.08126 + 15.7292i −0.301538 + 0.522280i −0.976485 0.215587i \(-0.930833\pi\)
0.674946 + 0.737867i \(0.264167\pi\)
\(908\) −3.76616 + 6.52319i −0.124985 + 0.216480i
\(909\) 0 0
\(910\) −5.50235 + 9.78836i −0.182401 + 0.324481i
\(911\) −43.3147 −1.43508 −0.717541 0.696517i \(-0.754732\pi\)
−0.717541 + 0.696517i \(0.754732\pi\)
\(912\) 0 0
\(913\) −2.62493 + 4.54650i −0.0868723 + 0.150467i
\(914\) −21.5135 37.2624i −0.711602 1.23253i
\(915\) 0 0
\(916\) 27.5380 + 47.6972i 0.909880 + 1.57596i
\(917\) 9.88263 + 17.1172i 0.326353 + 0.565261i
\(918\) 0 0
\(919\) −2.05975 3.56759i −0.0679449 0.117684i 0.830052 0.557687i \(-0.188311\pi\)
−0.897997 + 0.440003i \(0.854978\pi\)
\(920\) 0.577812 1.00080i 0.0190499 0.0329954i
\(921\) 0 0
\(922\) −26.5356 −0.873903
\(923\) −1.60715 + 0.0184643i −0.0528999 + 0.000607760i
\(924\) 0 0
\(925\) −1.36538 + 2.36491i −0.0448934 + 0.0777577i
\(926\) −16.0192 + 27.7461i −0.526424 + 0.911793i
\(927\) 0 0
\(928\) 63.9606 2.09961
\(929\) −24.1733 41.8694i −0.793101 1.37369i −0.924038 0.382300i \(-0.875132\pi\)
0.130938 0.991391i \(-0.458201\pi\)
\(930\) 0 0
\(931\) −2.45488 −0.0804554
\(932\) −9.05277 15.6799i −0.296533 0.513611i
\(933\) 0 0
\(934\) 15.7961 27.3596i 0.516864 0.895234i
\(935\) 1.76788 0.0578160
\(936\) 0 0
\(937\) −17.7174 −0.578801 −0.289401 0.957208i \(-0.593456\pi\)
−0.289401 + 0.957208i \(0.593456\pi\)
\(938\) 1.86422 3.22893i 0.0608691 0.105428i
\(939\) 0 0
\(940\) −5.34326 9.25480i −0.174278 0.301858i
\(941\) 25.7342 0.838912 0.419456 0.907776i \(-0.362221\pi\)
0.419456 + 0.907776i \(0.362221\pi\)
\(942\) 0 0
\(943\) −3.29333 5.70422i −0.107246 0.185755i
\(944\) 13.8211 0.449839
\(945\) 0 0
\(946\) −2.14657 + 3.71796i −0.0697909 + 0.120881i
\(947\) −24.1941 + 41.9054i −0.786203 + 1.36174i 0.142075 + 0.989856i \(0.454623\pi\)
−0.928278 + 0.371888i \(0.878711\pi\)
\(948\) 0 0
\(949\) −13.2974 + 23.6553i −0.431653 + 0.767884i
\(950\) −1.07500 −0.0348776
\(951\) 0 0
\(952\) 4.04969 7.01427i 0.131251 0.227334i
\(953\) 6.91281 + 11.9733i 0.223928 + 0.387854i 0.955997 0.293376i \(-0.0947787\pi\)
−0.732069 + 0.681230i \(0.761445\pi\)
\(954\) 0 0
\(955\) −4.65724 8.06657i −0.150705 0.261028i
\(956\) −0.617781 1.07003i −0.0199805 0.0346072i
\(957\) 0 0
\(958\) 0.322840 + 0.559176i 0.0104305 + 0.0180662i
\(959\) −7.48353 + 12.9618i −0.241656 + 0.418560i
\(960\) 0 0
\(961\) 53.1126 1.71331
\(962\) 20.8998 0.240115i 0.673836 0.00774162i
\(963\) 0 0
\(964\) 32.9301 57.0366i 1.06061 1.83703i
\(965\) 3.80004 6.58186i 0.122327 0.211877i
\(966\) 0 0
\(967\) −34.8289 −1.12002 −0.560010 0.828486i \(-0.689203\pi\)
−0.560010 + 0.828486i \(0.689203\pi\)
\(968\) −5.84880 10.1304i −0.187988 0.325604i
\(969\) 0 0
\(970\) 2.97316 0.0954623
\(971\) 3.90970 + 6.77180i 0.125468 + 0.217317i 0.921916 0.387390i \(-0.126623\pi\)
−0.796448 + 0.604708i \(0.793290\pi\)
\(972\) 0 0
\(973\) −8.91391 + 15.4393i −0.285767 + 0.494963i
\(974\) −88.5566 −2.83754
\(975\) 0 0
\(976\) 14.1216 0.452020
\(977\) −2.45793 + 4.25727i −0.0786363 + 0.136202i −0.902662 0.430351i \(-0.858390\pi\)
0.824026 + 0.566553i \(0.191723\pi\)
\(978\) 0 0
\(979\) −2.05681 3.56250i −0.0657359 0.113858i
\(980\) −12.1503 −0.388127
\(981\) 0 0
\(982\) 43.0505 + 74.5656i 1.37380 + 2.37948i
\(983\) −5.23823 −0.167074 −0.0835368 0.996505i \(-0.526622\pi\)
−0.0835368 + 0.996505i \(0.526622\pi\)
\(984\) 0 0
\(985\) −5.47163 + 9.47715i −0.174341 + 0.301967i
\(986\) 43.8724 75.9892i 1.39718 2.41999i
\(987\) 0 0
\(988\) 2.33353 + 3.93665i 0.0742396 + 0.125242i
\(989\) −6.31550 −0.200821
\(990\) 0 0
\(991\) 0.889392 1.54047i 0.0282525 0.0489347i −0.851553 0.524268i \(-0.824339\pi\)
0.879806 + 0.475333i \(0.157672\pi\)
\(992\) −36.4418 63.1191i −1.15703 2.00403i
\(993\) 0 0
\(994\) 0.694140 + 1.20229i 0.0220168 + 0.0381342i
\(995\) 7.09839 + 12.2948i 0.225034 + 0.389771i
\(996\) 0 0
\(997\) −21.9585 38.0333i −0.695434 1.20453i −0.970034 0.242968i \(-0.921879\pi\)
0.274601 0.961558i \(-0.411454\pi\)
\(998\) 23.0580 39.9376i 0.729888 1.26420i
\(999\) 0 0
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 585.2.j.h.451.5 yes 10
3.2 odd 2 585.2.j.i.451.1 yes 10
13.3 even 3 inner 585.2.j.h.406.5 10
13.4 even 6 7605.2.a.cl.1.5 5
13.9 even 3 7605.2.a.co.1.1 5
39.17 odd 6 7605.2.a.cn.1.1 5
39.29 odd 6 585.2.j.i.406.1 yes 10
39.35 odd 6 7605.2.a.cm.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.j.h.406.5 10 13.3 even 3 inner
585.2.j.h.451.5 yes 10 1.1 even 1 trivial
585.2.j.i.406.1 yes 10 39.29 odd 6
585.2.j.i.451.1 yes 10 3.2 odd 2
7605.2.a.cl.1.5 5 13.4 even 6
7605.2.a.cm.1.5 5 39.35 odd 6
7605.2.a.cn.1.1 5 39.17 odd 6
7605.2.a.co.1.1 5 13.9 even 3