Properties

Label 525.2.j.b.218.1
Level $525$
Weight $2$
Character 525.218
Analytic conductor $4.192$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(218,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.218");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.1
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.79963 - 1.79963i) q^{2} +(-0.491204 + 1.66094i) q^{3} +4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 - 0.707107i) q^{7} +(4.45829 - 4.45829i) q^{8} +(-2.51744 - 1.63172i) q^{9} +O(q^{10})\) \(q+(-1.79963 - 1.79963i) q^{2} +(-0.491204 + 1.66094i) q^{3} +4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 - 0.707107i) q^{7} +(4.45829 - 4.45829i) q^{8} +(-2.51744 - 1.63172i) q^{9} -1.56870i q^{11} +(-7.43658 - 2.19929i) q^{12} +(-2.21881 - 2.21881i) q^{13} -2.54506 q^{14} -7.09187 q^{16} +(3.60725 + 3.60725i) q^{17} +(1.59396 + 7.46695i) q^{18} +1.68040i q^{19} +(0.827127 + 1.52180i) q^{21} +(-2.82308 + 2.82308i) q^{22} +(0.995850 - 0.995850i) q^{23} +(5.21502 + 9.59488i) q^{24} +7.98606i q^{26} +(3.94676 - 3.37980i) q^{27} +(3.16595 + 3.16595i) q^{28} +8.91955 q^{29} +2.74834 q^{31} +(3.84616 + 3.84616i) q^{32} +(2.60552 + 0.770553i) q^{33} -12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(-0.440360 + 0.440360i) q^{37} +(3.02410 - 3.02410i) q^{38} +(4.77519 - 2.59542i) q^{39} +6.44292i q^{41} +(1.25015 - 4.22719i) q^{42} +(5.47734 + 5.47734i) q^{43} +7.02360 q^{44} -3.58432 q^{46} +(3.69358 + 3.69358i) q^{47} +(3.48356 - 11.7792i) q^{48} -1.00000i q^{49} +(-7.76331 + 4.21952i) q^{51} +(9.93435 - 9.93435i) q^{52} +(2.83358 - 2.83358i) q^{53} +(-13.1851 - 1.02033i) q^{54} -6.30497i q^{56} +(-2.79104 - 0.825420i) q^{57} +(-16.0519 - 16.0519i) q^{58} -5.54871 q^{59} +7.40665 q^{61} +(-4.94599 - 4.94599i) q^{62} +(-2.93390 + 0.626296i) q^{63} +0.340400i q^{64} +(-3.30226 - 6.07568i) q^{66} +(3.75240 - 3.75240i) q^{67} +(-16.1509 + 16.1509i) q^{68} +(1.16488 + 2.14321i) q^{69} -3.61943i q^{71} +(-18.4981 + 3.94878i) q^{72} +(5.89737 + 5.89737i) q^{73} +1.58497 q^{74} -7.52372 q^{76} +(-1.10924 - 1.10924i) q^{77} +(-13.2644 - 3.92279i) q^{78} -17.0572i q^{79} +(3.67497 + 8.21551i) q^{81} +(11.5949 - 11.5949i) q^{82} +(3.21312 - 3.21312i) q^{83} +(-6.81359 + 3.70333i) q^{84} -19.7144i q^{86} +(-4.38132 + 14.8148i) q^{87} +(-6.99372 - 6.99372i) q^{88} +9.40273 q^{89} -3.13787 q^{91} +(4.45876 + 4.45876i) q^{92} +(-1.35000 + 4.56482i) q^{93} -13.2941i q^{94} +(-8.27749 + 4.49899i) q^{96} +(-4.39640 + 4.39640i) q^{97} +(-1.79963 + 1.79963i) q^{98} +(-2.55968 + 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79963 1.79963i −1.27253 1.27253i −0.944756 0.327775i \(-0.893701\pi\)
−0.327775 0.944756i \(-0.606299\pi\)
\(3\) −0.491204 + 1.66094i −0.283597 + 0.958944i
\(4\) 4.47734i 2.23867i
\(5\) 0 0
\(6\) 3.87306 2.10509i 1.58117 0.859399i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 4.45829 4.45829i 1.57624 1.57624i
\(9\) −2.51744 1.63172i −0.839146 0.543907i
\(10\) 0 0
\(11\) 1.56870i 0.472981i −0.971634 0.236491i \(-0.924003\pi\)
0.971634 0.236491i \(-0.0759973\pi\)
\(12\) −7.43658 2.19929i −2.14676 0.634880i
\(13\) −2.21881 2.21881i −0.615386 0.615386i 0.328958 0.944345i \(-0.393303\pi\)
−0.944345 + 0.328958i \(0.893303\pi\)
\(14\) −2.54506 −0.680196
\(15\) 0 0
\(16\) −7.09187 −1.77297
\(17\) 3.60725 + 3.60725i 0.874886 + 0.874886i 0.993000 0.118114i \(-0.0376849\pi\)
−0.118114 + 0.993000i \(0.537685\pi\)
\(18\) 1.59396 + 7.46695i 0.375700 + 1.75998i
\(19\) 1.68040i 0.385510i 0.981247 + 0.192755i \(0.0617423\pi\)
−0.981247 + 0.192755i \(0.938258\pi\)
\(20\) 0 0
\(21\) 0.827127 + 1.52180i 0.180494 + 0.332083i
\(22\) −2.82308 + 2.82308i −0.601883 + 0.601883i
\(23\) 0.995850 0.995850i 0.207649 0.207649i −0.595618 0.803268i \(-0.703093\pi\)
0.803268 + 0.595618i \(0.203093\pi\)
\(24\) 5.21502 + 9.59488i 1.06451 + 1.95855i
\(25\) 0 0
\(26\) 7.98606i 1.56620i
\(27\) 3.94676 3.37980i 0.759555 0.650443i
\(28\) 3.16595 + 3.16595i 0.598309 + 0.598309i
\(29\) 8.91955 1.65632 0.828159 0.560493i \(-0.189388\pi\)
0.828159 + 0.560493i \(0.189388\pi\)
\(30\) 0 0
\(31\) 2.74834 0.493616 0.246808 0.969064i \(-0.420618\pi\)
0.246808 + 0.969064i \(0.420618\pi\)
\(32\) 3.84616 + 3.84616i 0.679912 + 0.679912i
\(33\) 2.60552 + 0.770553i 0.453562 + 0.134136i
\(34\) 12.9834i 2.22664i
\(35\) 0 0
\(36\) 7.30576 11.2714i 1.21763 1.87857i
\(37\) −0.440360 + 0.440360i −0.0723947 + 0.0723947i −0.742377 0.669982i \(-0.766302\pi\)
0.669982 + 0.742377i \(0.266302\pi\)
\(38\) 3.02410 3.02410i 0.490574 0.490574i
\(39\) 4.77519 2.59542i 0.764643 0.415599i
\(40\) 0 0
\(41\) 6.44292i 1.00622i 0.864224 + 0.503108i \(0.167810\pi\)
−0.864224 + 0.503108i \(0.832190\pi\)
\(42\) 1.25015 4.22719i 0.192902 0.652270i
\(43\) 5.47734 + 5.47734i 0.835286 + 0.835286i 0.988234 0.152948i \(-0.0488768\pi\)
−0.152948 + 0.988234i \(0.548877\pi\)
\(44\) 7.02360 1.05885
\(45\) 0 0
\(46\) −3.58432 −0.528480
\(47\) 3.69358 + 3.69358i 0.538763 + 0.538763i 0.923166 0.384402i \(-0.125592\pi\)
−0.384402 + 0.923166i \(0.625592\pi\)
\(48\) 3.48356 11.7792i 0.502808 1.70018i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −7.76331 + 4.21952i −1.08708 + 0.590851i
\(52\) 9.93435 9.93435i 1.37765 1.37765i
\(53\) 2.83358 2.83358i 0.389222 0.389222i −0.485188 0.874410i \(-0.661249\pi\)
0.874410 + 0.485188i \(0.161249\pi\)
\(54\) −13.1851 1.02033i −1.79427 0.138849i
\(55\) 0 0
\(56\) 6.30497i 0.842537i
\(57\) −2.79104 0.825420i −0.369683 0.109330i
\(58\) −16.0519 16.0519i −2.10772 2.10772i
\(59\) −5.54871 −0.722381 −0.361191 0.932492i \(-0.617630\pi\)
−0.361191 + 0.932492i \(0.617630\pi\)
\(60\) 0 0
\(61\) 7.40665 0.948325 0.474162 0.880437i \(-0.342751\pi\)
0.474162 + 0.880437i \(0.342751\pi\)
\(62\) −4.94599 4.94599i −0.628141 0.628141i
\(63\) −2.93390 + 0.626296i −0.369636 + 0.0789058i
\(64\) 0.340400i 0.0425500i
\(65\) 0 0
\(66\) −3.30226 6.07568i −0.406480 0.747864i
\(67\) 3.75240 3.75240i 0.458429 0.458429i −0.439711 0.898139i \(-0.644919\pi\)
0.898139 + 0.439711i \(0.144919\pi\)
\(68\) −16.1509 + 16.1509i −1.95858 + 1.95858i
\(69\) 1.16488 + 2.14321i 0.140235 + 0.258012i
\(70\) 0 0
\(71\) 3.61943i 0.429548i −0.976664 0.214774i \(-0.931099\pi\)
0.976664 0.214774i \(-0.0689015\pi\)
\(72\) −18.4981 + 3.94878i −2.18003 + 0.465368i
\(73\) 5.89737 + 5.89737i 0.690235 + 0.690235i 0.962284 0.272049i \(-0.0877011\pi\)
−0.272049 + 0.962284i \(0.587701\pi\)
\(74\) 1.58497 0.184249
\(75\) 0 0
\(76\) −7.52372 −0.863030
\(77\) −1.10924 1.10924i −0.126410 0.126410i
\(78\) −13.2644 3.92279i −1.50189 0.444168i
\(79\) 17.0572i 1.91909i −0.281558 0.959544i \(-0.590851\pi\)
0.281558 0.959544i \(-0.409149\pi\)
\(80\) 0 0
\(81\) 3.67497 + 8.21551i 0.408330 + 0.912834i
\(82\) 11.5949 11.5949i 1.28044 1.28044i
\(83\) 3.21312 3.21312i 0.352686 0.352686i −0.508422 0.861108i \(-0.669771\pi\)
0.861108 + 0.508422i \(0.169771\pi\)
\(84\) −6.81359 + 3.70333i −0.743423 + 0.404066i
\(85\) 0 0
\(86\) 19.7144i 2.12585i
\(87\) −4.38132 + 14.8148i −0.469727 + 1.58832i
\(88\) −6.99372 6.99372i −0.745533 0.745533i
\(89\) 9.40273 0.996688 0.498344 0.866979i \(-0.333942\pi\)
0.498344 + 0.866979i \(0.333942\pi\)
\(90\) 0 0
\(91\) −3.13787 −0.328938
\(92\) 4.45876 + 4.45876i 0.464858 + 0.464858i
\(93\) −1.35000 + 4.56482i −0.139988 + 0.473350i
\(94\) 13.2941i 1.37119i
\(95\) 0 0
\(96\) −8.27749 + 4.49899i −0.844818 + 0.459176i
\(97\) −4.39640 + 4.39640i −0.446386 + 0.446386i −0.894151 0.447765i \(-0.852220\pi\)
0.447765 + 0.894151i \(0.352220\pi\)
\(98\) −1.79963 + 1.79963i −0.181790 + 0.181790i
\(99\) −2.55968 + 3.94911i −0.257258 + 0.396900i
\(100\) 0 0
\(101\) 1.01132i 0.100630i 0.998733 + 0.0503152i \(0.0160226\pi\)
−0.998733 + 0.0503152i \(0.983977\pi\)
\(102\) 21.5647 + 6.37751i 2.13522 + 0.631468i
\(103\) 4.03058 + 4.03058i 0.397145 + 0.397145i 0.877225 0.480080i \(-0.159392\pi\)
−0.480080 + 0.877225i \(0.659392\pi\)
\(104\) −19.7842 −1.94000
\(105\) 0 0
\(106\) −10.1988 −0.990593
\(107\) 2.81760 + 2.81760i 0.272388 + 0.272388i 0.830061 0.557673i \(-0.188306\pi\)
−0.557673 + 0.830061i \(0.688306\pi\)
\(108\) 15.1325 + 17.6710i 1.45613 + 1.70039i
\(109\) 6.42246i 0.615160i 0.951522 + 0.307580i \(0.0995192\pi\)
−0.951522 + 0.307580i \(0.900481\pi\)
\(110\) 0 0
\(111\) −0.515104 0.947718i −0.0488915 0.0899534i
\(112\) −5.01471 + 5.01471i −0.473845 + 0.473845i
\(113\) 3.29246 3.29246i 0.309729 0.309729i −0.535075 0.844804i \(-0.679717\pi\)
0.844804 + 0.535075i \(0.179717\pi\)
\(114\) 3.53739 + 6.50830i 0.331307 + 0.609558i
\(115\) 0 0
\(116\) 39.9358i 3.70795i
\(117\) 1.96523 + 9.20618i 0.181686 + 0.851112i
\(118\) 9.98563 + 9.98563i 0.919252 + 0.919252i
\(119\) 5.10142 0.467646
\(120\) 0 0
\(121\) 8.53918 0.776289
\(122\) −13.3292 13.3292i −1.20677 1.20677i
\(123\) −10.7013 3.16479i −0.964904 0.285360i
\(124\) 12.3052i 1.10504i
\(125\) 0 0
\(126\) 6.40703 + 4.15283i 0.570784 + 0.369963i
\(127\) −14.2818 + 14.2818i −1.26730 + 1.26730i −0.319826 + 0.947476i \(0.603624\pi\)
−0.947476 + 0.319826i \(0.896376\pi\)
\(128\) 8.30492 8.30492i 0.734058 0.734058i
\(129\) −11.7880 + 6.40703i −1.03788 + 0.564108i
\(130\) 0 0
\(131\) 4.89729i 0.427878i −0.976847 0.213939i \(-0.931371\pi\)
0.976847 0.213939i \(-0.0686294\pi\)
\(132\) −3.45002 + 11.6658i −0.300286 + 1.01538i
\(133\) 1.18822 + 1.18822i 0.103032 + 0.103032i
\(134\) −13.5059 −1.16673
\(135\) 0 0
\(136\) 32.1643 2.75807
\(137\) −4.55880 4.55880i −0.389485 0.389485i 0.485019 0.874504i \(-0.338813\pi\)
−0.874504 + 0.485019i \(0.838813\pi\)
\(138\) 1.76064 5.95334i 0.149875 0.506782i
\(139\) 10.2045i 0.865536i 0.901505 + 0.432768i \(0.142463\pi\)
−0.901505 + 0.432768i \(0.857537\pi\)
\(140\) 0 0
\(141\) −7.94911 + 4.32050i −0.669435 + 0.363852i
\(142\) −6.51364 + 6.51364i −0.546613 + 0.546613i
\(143\) −3.48065 + 3.48065i −0.291066 + 0.291066i
\(144\) 17.8533 + 11.5720i 1.48778 + 0.964329i
\(145\) 0 0
\(146\) 21.2262i 1.75669i
\(147\) 1.66094 + 0.491204i 0.136992 + 0.0405139i
\(148\) −1.97164 1.97164i −0.162068 0.162068i
\(149\) 0.923124 0.0756253 0.0378126 0.999285i \(-0.487961\pi\)
0.0378126 + 0.999285i \(0.487961\pi\)
\(150\) 0 0
\(151\) −13.7310 −1.11741 −0.558705 0.829366i \(-0.688702\pi\)
−0.558705 + 0.829366i \(0.688702\pi\)
\(152\) 7.49171 + 7.49171i 0.607658 + 0.607658i
\(153\) −3.19499 14.9670i −0.258300 1.21001i
\(154\) 3.99244i 0.321720i
\(155\) 0 0
\(156\) 11.6205 + 21.3801i 0.930389 + 1.71178i
\(157\) 13.7211 13.7211i 1.09506 1.09506i 0.100086 0.994979i \(-0.468088\pi\)
0.994979 0.100086i \(-0.0319118\pi\)
\(158\) −30.6967 + 30.6967i −2.44210 + 2.44210i
\(159\) 3.31453 + 6.09826i 0.262859 + 0.483624i
\(160\) 0 0
\(161\) 1.40834i 0.110993i
\(162\) 8.17128 21.3985i 0.641997 1.68122i
\(163\) −6.60566 6.60566i −0.517395 0.517395i 0.399387 0.916782i \(-0.369223\pi\)
−0.916782 + 0.399387i \(0.869223\pi\)
\(164\) −28.8471 −2.25258
\(165\) 0 0
\(166\) −11.5649 −0.897607
\(167\) −3.11442 3.11442i −0.241001 0.241001i 0.576263 0.817264i \(-0.304510\pi\)
−0.817264 + 0.576263i \(0.804510\pi\)
\(168\) 10.4722 + 3.09703i 0.807946 + 0.238941i
\(169\) 3.15379i 0.242599i
\(170\) 0 0
\(171\) 2.74195 4.23030i 0.209682 0.323499i
\(172\) −24.5239 + 24.5239i −1.86993 + 1.86993i
\(173\) 8.12870 8.12870i 0.618013 0.618013i −0.327008 0.945022i \(-0.606040\pi\)
0.945022 + 0.327008i \(0.106040\pi\)
\(174\) 34.5460 18.7764i 2.61892 1.42344i
\(175\) 0 0
\(176\) 11.1250i 0.838580i
\(177\) 2.72555 9.21608i 0.204865 0.692723i
\(178\) −16.9214 16.9214i −1.26832 1.26832i
\(179\) −16.5980 −1.24059 −0.620297 0.784367i \(-0.712988\pi\)
−0.620297 + 0.784367i \(0.712988\pi\)
\(180\) 0 0
\(181\) 11.6532 0.866174 0.433087 0.901352i \(-0.357424\pi\)
0.433087 + 0.901352i \(0.357424\pi\)
\(182\) 5.64700 + 5.64700i 0.418583 + 0.418583i
\(183\) −3.63818 + 12.3020i −0.268942 + 0.909390i
\(184\) 8.87958i 0.654611i
\(185\) 0 0
\(186\) 10.6445 5.78550i 0.780491 0.424213i
\(187\) 5.65869 5.65869i 0.413805 0.413805i
\(188\) −16.5374 + 16.5374i −1.20611 + 1.20611i
\(189\) 0.400905 5.18066i 0.0291615 0.376838i
\(190\) 0 0
\(191\) 12.8543i 0.930108i 0.885282 + 0.465054i \(0.153965\pi\)
−0.885282 + 0.465054i \(0.846035\pi\)
\(192\) −0.565384 0.167206i −0.0408031 0.0120671i
\(193\) 8.06158 + 8.06158i 0.580285 + 0.580285i 0.934982 0.354696i \(-0.115416\pi\)
−0.354696 + 0.934982i \(0.615416\pi\)
\(194\) 15.8238 1.13608
\(195\) 0 0
\(196\) 4.47734 0.319810
\(197\) −18.7512 18.7512i −1.33597 1.33597i −0.899929 0.436036i \(-0.856382\pi\)
−0.436036 0.899929i \(-0.643618\pi\)
\(198\) 11.7134 2.50045i 0.832436 0.177699i
\(199\) 4.20728i 0.298246i 0.988819 + 0.149123i \(0.0476451\pi\)
−0.988819 + 0.149123i \(0.952355\pi\)
\(200\) 0 0
\(201\) 4.38931 + 8.07570i 0.309598 + 0.569616i
\(202\) 1.82001 1.82001i 0.128055 0.128055i
\(203\) 6.30707 6.30707i 0.442670 0.442670i
\(204\) −18.8922 34.7590i −1.32272 2.43361i
\(205\) 0 0
\(206\) 14.5071i 1.01076i
\(207\) −4.13194 + 0.882040i −0.287190 + 0.0613060i
\(208\) 15.7355 + 15.7355i 1.09106 + 1.09106i
\(209\) 2.63605 0.182339
\(210\) 0 0
\(211\) −21.5211 −1.48158 −0.740788 0.671739i \(-0.765548\pi\)
−0.740788 + 0.671739i \(0.765548\pi\)
\(212\) 12.6869 + 12.6869i 0.871338 + 0.871338i
\(213\) 6.01166 + 1.77788i 0.411912 + 0.121818i
\(214\) 10.1413i 0.693244i
\(215\) 0 0
\(216\) 2.52769 32.6639i 0.171988 2.22250i
\(217\) 1.94337 1.94337i 0.131924 0.131924i
\(218\) 11.5581 11.5581i 0.782810 0.782810i
\(219\) −12.6920 + 6.89836i −0.857645 + 0.466148i
\(220\) 0 0
\(221\) 16.0076i 1.07679i
\(222\) −0.778544 + 2.63254i −0.0522525 + 0.176684i
\(223\) −12.4001 12.4001i −0.830375 0.830375i 0.157193 0.987568i \(-0.449756\pi\)
−0.987568 + 0.157193i \(0.949756\pi\)
\(224\) 5.43929 0.363428
\(225\) 0 0
\(226\) −11.8504 −0.788279
\(227\) −8.70556 8.70556i −0.577809 0.577809i 0.356490 0.934299i \(-0.383973\pi\)
−0.934299 + 0.356490i \(0.883973\pi\)
\(228\) 3.69568 12.4964i 0.244753 0.827597i
\(229\) 4.46342i 0.294951i 0.989066 + 0.147476i \(0.0471148\pi\)
−0.989066 + 0.147476i \(0.952885\pi\)
\(230\) 0 0
\(231\) 2.38724 1.29752i 0.157069 0.0853703i
\(232\) 39.7659 39.7659i 2.61076 2.61076i
\(233\) −5.64161 + 5.64161i −0.369594 + 0.369594i −0.867329 0.497735i \(-0.834165\pi\)
0.497735 + 0.867329i \(0.334165\pi\)
\(234\) 13.0310 20.1044i 0.851865 1.31427i
\(235\) 0 0
\(236\) 24.8435i 1.61717i
\(237\) 28.3310 + 8.37859i 1.84030 + 0.544248i
\(238\) −9.18066 9.18066i −0.595094 0.595094i
\(239\) −11.8594 −0.767124 −0.383562 0.923515i \(-0.625303\pi\)
−0.383562 + 0.923515i \(0.625303\pi\)
\(240\) 0 0
\(241\) −18.0723 −1.16414 −0.582071 0.813138i \(-0.697757\pi\)
−0.582071 + 0.813138i \(0.697757\pi\)
\(242\) −15.3674 15.3674i −0.987851 0.987851i
\(243\) −15.4506 + 2.06841i −0.991158 + 0.132689i
\(244\) 33.1621i 2.12298i
\(245\) 0 0
\(246\) 13.5629 + 24.9538i 0.864741 + 1.59100i
\(247\) 3.72849 3.72849i 0.237238 0.237238i
\(248\) 12.2529 12.2529i 0.778059 0.778059i
\(249\) 3.75850 + 6.91510i 0.238185 + 0.438226i
\(250\) 0 0
\(251\) 3.19253i 0.201511i −0.994911 0.100755i \(-0.967874\pi\)
0.994911 0.100755i \(-0.0321259\pi\)
\(252\) −2.80414 13.1360i −0.176644 0.827493i
\(253\) −1.56219 1.56219i −0.0982141 0.0982141i
\(254\) 51.4038 3.22536
\(255\) 0 0
\(256\) −29.2108 −1.82567
\(257\) 11.8118 + 11.8118i 0.736799 + 0.736799i 0.971957 0.235158i \(-0.0755607\pi\)
−0.235158 + 0.971957i \(0.575561\pi\)
\(258\) 32.7443 + 9.68378i 2.03857 + 0.602886i
\(259\) 0.622763i 0.0386966i
\(260\) 0 0
\(261\) −22.4544 14.5542i −1.38989 0.900883i
\(262\) −8.81331 + 8.81331i −0.544488 + 0.544488i
\(263\) 13.1502 13.1502i 0.810874 0.810874i −0.173891 0.984765i \(-0.555634\pi\)
0.984765 + 0.173891i \(0.0556339\pi\)
\(264\) 15.0515 8.18080i 0.926356 0.503493i
\(265\) 0 0
\(266\) 4.27672i 0.262223i
\(267\) −4.61866 + 15.6174i −0.282658 + 0.955767i
\(268\) 16.8008 + 16.8008i 1.02627 + 1.02627i
\(269\) 29.3405 1.78892 0.894461 0.447146i \(-0.147559\pi\)
0.894461 + 0.447146i \(0.147559\pi\)
\(270\) 0 0
\(271\) 3.18366 0.193394 0.0966968 0.995314i \(-0.469172\pi\)
0.0966968 + 0.995314i \(0.469172\pi\)
\(272\) −25.5821 25.5821i −1.55114 1.55114i
\(273\) 1.54133 5.21181i 0.0932858 0.315433i
\(274\) 16.4083i 0.991263i
\(275\) 0 0
\(276\) −9.59588 + 5.21556i −0.577604 + 0.313940i
\(277\) −16.8636 + 16.8636i −1.01324 + 1.01324i −0.0133247 + 0.999911i \(0.504242\pi\)
−0.999911 + 0.0133247i \(0.995758\pi\)
\(278\) 18.3644 18.3644i 1.10142 1.10142i
\(279\) −6.91877 4.48452i −0.414216 0.268481i
\(280\) 0 0
\(281\) 24.8052i 1.47975i −0.672742 0.739877i \(-0.734884\pi\)
0.672742 0.739877i \(-0.265116\pi\)
\(282\) 22.0808 + 6.53014i 1.31489 + 0.388864i
\(283\) −5.41918 5.41918i −0.322137 0.322137i 0.527449 0.849586i \(-0.323148\pi\)
−0.849586 + 0.527449i \(0.823148\pi\)
\(284\) 16.2054 0.961615
\(285\) 0 0
\(286\) 12.5277 0.740781
\(287\) 4.55583 + 4.55583i 0.268922 + 0.268922i
\(288\) −3.40661 15.9583i −0.200736 0.940354i
\(289\) 9.02446i 0.530850i
\(290\) 0 0
\(291\) −5.14262 9.46168i −0.301466 0.554653i
\(292\) −26.4045 + 26.4045i −1.54521 + 1.54521i
\(293\) 8.60739 8.60739i 0.502849 0.502849i −0.409473 0.912322i \(-0.634288\pi\)
0.912322 + 0.409473i \(0.134288\pi\)
\(294\) −2.10509 3.87306i −0.122771 0.225882i
\(295\) 0 0
\(296\) 3.92650i 0.228223i
\(297\) −5.30190 6.19129i −0.307647 0.359255i
\(298\) −1.66128 1.66128i −0.0962355 0.0962355i
\(299\) −4.41920 −0.255569
\(300\) 0 0
\(301\) 7.74612 0.446479
\(302\) 24.7107 + 24.7107i 1.42194 + 1.42194i
\(303\) −1.67975 0.496766i −0.0964989 0.0285385i
\(304\) 11.9172i 0.683497i
\(305\) 0 0
\(306\) −21.1853 + 32.6849i −1.21108 + 1.86847i
\(307\) 11.8525 11.8525i 0.676457 0.676457i −0.282740 0.959197i \(-0.591243\pi\)
0.959197 + 0.282740i \(0.0912434\pi\)
\(308\) 4.96644 4.96644i 0.282989 0.282989i
\(309\) −8.67440 + 4.71471i −0.493469 + 0.268211i
\(310\) 0 0
\(311\) 29.2800i 1.66032i 0.557528 + 0.830158i \(0.311750\pi\)
−0.557528 + 0.830158i \(0.688250\pi\)
\(312\) 9.71807 32.8603i 0.550177 1.86035i
\(313\) −1.22577 1.22577i −0.0692848 0.0692848i 0.671615 0.740900i \(-0.265601\pi\)
−0.740900 + 0.671615i \(0.765601\pi\)
\(314\) −49.3859 −2.78701
\(315\) 0 0
\(316\) 76.3710 4.29620
\(317\) −4.30159 4.30159i −0.241601 0.241601i 0.575911 0.817512i \(-0.304647\pi\)
−0.817512 + 0.575911i \(0.804647\pi\)
\(318\) 5.00968 16.9395i 0.280929 0.949922i
\(319\) 13.9921i 0.783408i
\(320\) 0 0
\(321\) −6.06388 + 3.29585i −0.338453 + 0.183956i
\(322\) −2.53450 + 2.53450i −0.141242 + 0.141242i
\(323\) −6.06162 + 6.06162i −0.337278 + 0.337278i
\(324\) −36.7836 + 16.4541i −2.04353 + 0.914116i
\(325\) 0 0
\(326\) 23.7755i 1.31680i
\(327\) −10.6673 3.15474i −0.589904 0.174458i
\(328\) 28.7244 + 28.7244i 1.58604 + 1.58604i
\(329\) 5.22351 0.287981
\(330\) 0 0
\(331\) 33.2602 1.82815 0.914074 0.405548i \(-0.132919\pi\)
0.914074 + 0.405548i \(0.132919\pi\)
\(332\) 14.3862 + 14.3862i 0.789547 + 0.789547i
\(333\) 1.82712 0.390034i 0.100126 0.0213737i
\(334\) 11.2096i 0.613363i
\(335\) 0 0
\(336\) −5.86588 10.7924i −0.320010 0.588772i
\(337\) −10.3056 + 10.3056i −0.561383 + 0.561383i −0.929700 0.368317i \(-0.879934\pi\)
0.368317 + 0.929700i \(0.379934\pi\)
\(338\) −5.67565 + 5.67565i −0.308715 + 0.308715i
\(339\) 3.85131 + 7.08585i 0.209174 + 0.384851i
\(340\) 0 0
\(341\) 4.31132i 0.233471i
\(342\) −12.5475 + 2.67849i −0.678489 + 0.144836i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 48.8391 2.63323
\(345\) 0 0
\(346\) −29.2573 −1.57288
\(347\) 19.2241 + 19.2241i 1.03200 + 1.03200i 0.999471 + 0.0325323i \(0.0103572\pi\)
0.0325323 + 0.999471i \(0.489643\pi\)
\(348\) −66.3310 19.6166i −3.55571 1.05156i
\(349\) 30.1301i 1.61283i −0.591353 0.806413i \(-0.701406\pi\)
0.591353 0.806413i \(-0.298594\pi\)
\(350\) 0 0
\(351\) −16.2562 1.25799i −0.867694 0.0671463i
\(352\) 6.03348 6.03348i 0.321586 0.321586i
\(353\) −17.0339 + 17.0339i −0.906625 + 0.906625i −0.995998 0.0893729i \(-0.971514\pi\)
0.0893729 + 0.995998i \(0.471514\pi\)
\(354\) −21.4905 + 11.6805i −1.14221 + 0.620814i
\(355\) 0 0
\(356\) 42.0992i 2.23125i
\(357\) −2.50584 + 8.47314i −0.132623 + 0.448446i
\(358\) 29.8703 + 29.8703i 1.57869 + 1.57869i
\(359\) −0.737982 −0.0389492 −0.0194746 0.999810i \(-0.506199\pi\)
−0.0194746 + 0.999810i \(0.506199\pi\)
\(360\) 0 0
\(361\) 16.1763 0.851382
\(362\) −20.9714 20.9714i −1.10223 1.10223i
\(363\) −4.19448 + 14.1831i −0.220153 + 0.744417i
\(364\) 14.0493i 0.736383i
\(365\) 0 0
\(366\) 28.6864 15.5917i 1.49946 0.814990i
\(367\) −23.2923 + 23.2923i −1.21585 + 1.21585i −0.246776 + 0.969073i \(0.579371\pi\)
−0.969073 + 0.246776i \(0.920629\pi\)
\(368\) −7.06244 + 7.06244i −0.368155 + 0.368155i
\(369\) 10.5131 16.2196i 0.547288 0.844361i
\(370\) 0 0
\(371\) 4.00728i 0.208048i
\(372\) −20.4382 6.04438i −1.05967 0.313387i
\(373\) 5.28110 + 5.28110i 0.273445 + 0.273445i 0.830485 0.557040i \(-0.188063\pi\)
−0.557040 + 0.830485i \(0.688063\pi\)
\(374\) −20.3671 −1.05316
\(375\) 0 0
\(376\) 32.9341 1.69844
\(377\) −19.7908 19.7908i −1.01928 1.01928i
\(378\) −10.0448 + 8.60180i −0.516647 + 0.442429i
\(379\) 3.38353i 0.173800i −0.996217 0.0869000i \(-0.972304\pi\)
0.996217 0.0869000i \(-0.0276961\pi\)
\(380\) 0 0
\(381\) −16.7059 30.7364i −0.855868 1.57467i
\(382\) 23.1331 23.1331i 1.18359 1.18359i
\(383\) 2.86741 2.86741i 0.146518 0.146518i −0.630043 0.776561i \(-0.716963\pi\)
0.776561 + 0.630043i \(0.216963\pi\)
\(384\) 9.71455 + 17.8734i 0.495744 + 0.912097i
\(385\) 0 0
\(386\) 29.0157i 1.47686i
\(387\) −4.85136 22.7263i −0.246609 1.15524i
\(388\) −19.6841 19.6841i −0.999311 0.999311i
\(389\) 10.2102 0.517675 0.258838 0.965921i \(-0.416661\pi\)
0.258838 + 0.965921i \(0.416661\pi\)
\(390\) 0 0
\(391\) 7.18455 0.363339
\(392\) −4.45829 4.45829i −0.225178 0.225178i
\(393\) 8.13410 + 2.40557i 0.410311 + 0.121345i
\(394\) 67.4903i 3.40011i
\(395\) 0 0
\(396\) −17.6815 11.4606i −0.888528 0.575915i
\(397\) 24.0534 24.0534i 1.20721 1.20721i 0.235280 0.971928i \(-0.424399\pi\)
0.971928 0.235280i \(-0.0756009\pi\)
\(398\) 7.57156 7.57156i 0.379528 0.379528i
\(399\) −2.55723 + 1.38991i −0.128021 + 0.0695823i
\(400\) 0 0
\(401\) 20.0912i 1.00331i 0.865068 + 0.501654i \(0.167275\pi\)
−0.865068 + 0.501654i \(0.832725\pi\)
\(402\) 6.63414 22.4324i 0.330881 1.11883i
\(403\) −6.09803 6.09803i −0.303765 0.303765i
\(404\) −4.52803 −0.225278
\(405\) 0 0
\(406\) −22.7008 −1.12662
\(407\) 0.690793 + 0.690793i 0.0342413 + 0.0342413i
\(408\) −15.7992 + 53.4229i −0.782179 + 2.64483i
\(409\) 33.5102i 1.65697i 0.560008 + 0.828487i \(0.310798\pi\)
−0.560008 + 0.828487i \(0.689202\pi\)
\(410\) 0 0
\(411\) 9.81120 5.33259i 0.483951 0.263037i
\(412\) −18.0463 + 18.0463i −0.889077 + 0.889077i
\(413\) −3.92353 + 3.92353i −0.193064 + 0.193064i
\(414\) 9.02331 + 5.84862i 0.443471 + 0.287444i
\(415\) 0 0
\(416\) 17.0678i 0.836817i
\(417\) −16.9491 5.01251i −0.830000 0.245463i
\(418\) −4.74391 4.74391i −0.232032 0.232032i
\(419\) −25.8773 −1.26419 −0.632093 0.774892i \(-0.717804\pi\)
−0.632093 + 0.774892i \(0.717804\pi\)
\(420\) 0 0
\(421\) 10.4030 0.507013 0.253507 0.967334i \(-0.418416\pi\)
0.253507 + 0.967334i \(0.418416\pi\)
\(422\) 38.7301 + 38.7301i 1.88535 + 1.88535i
\(423\) −3.27146 15.3252i −0.159064 0.745138i
\(424\) 25.2658i 1.22702i
\(425\) 0 0
\(426\) −7.61923 14.0183i −0.369153 0.679188i
\(427\) 5.23730 5.23730i 0.253450 0.253450i
\(428\) −12.6154 + 12.6154i −0.609786 + 0.609786i
\(429\) −4.07143 7.49085i −0.196571 0.361662i
\(430\) 0 0
\(431\) 0.449005i 0.0216278i −0.999942 0.0108139i \(-0.996558\pi\)
0.999942 0.0108139i \(-0.00344224\pi\)
\(432\) −27.9899 + 23.9691i −1.34667 + 1.15321i
\(433\) 17.7813 + 17.7813i 0.854517 + 0.854517i 0.990686 0.136169i \(-0.0434790\pi\)
−0.136169 + 0.990686i \(0.543479\pi\)
\(434\) −6.99469 −0.335756
\(435\) 0 0
\(436\) −28.7555 −1.37714
\(437\) 1.67343 + 1.67343i 0.0800509 + 0.0800509i
\(438\) 35.2554 + 10.4264i 1.68457 + 0.498192i
\(439\) 29.5293i 1.40936i −0.709526 0.704679i \(-0.751091\pi\)
0.709526 0.704679i \(-0.248909\pi\)
\(440\) 0 0
\(441\) −1.63172 + 2.51744i −0.0777010 + 0.119878i
\(442\) −28.8077 + 28.8077i −1.37024 + 1.37024i
\(443\) −15.5643 + 15.5643i −0.739483 + 0.739483i −0.972478 0.232995i \(-0.925147\pi\)
0.232995 + 0.972478i \(0.425147\pi\)
\(444\) 4.24325 2.30630i 0.201376 0.109452i
\(445\) 0 0
\(446\) 44.6313i 2.11336i
\(447\) −0.453443 + 1.53325i −0.0214471 + 0.0725204i
\(448\) 0.240699 + 0.240699i 0.0113720 + 0.0113720i
\(449\) −16.3214 −0.770252 −0.385126 0.922864i \(-0.625842\pi\)
−0.385126 + 0.922864i \(0.625842\pi\)
\(450\) 0 0
\(451\) 10.1070 0.475921
\(452\) 14.7415 + 14.7415i 0.693380 + 0.693380i
\(453\) 6.74471 22.8063i 0.316894 1.07153i
\(454\) 31.3336i 1.47056i
\(455\) 0 0
\(456\) −16.1232 + 8.76332i −0.755040 + 0.410380i
\(457\) 20.6299 20.6299i 0.965028 0.965028i −0.0343811 0.999409i \(-0.510946\pi\)
0.999409 + 0.0343811i \(0.0109460\pi\)
\(458\) 8.03251 8.03251i 0.375335 0.375335i
\(459\) 26.4287 + 2.04518i 1.23359 + 0.0954609i
\(460\) 0 0
\(461\) 15.2893i 0.712094i 0.934468 + 0.356047i \(0.115876\pi\)
−0.934468 + 0.356047i \(0.884124\pi\)
\(462\) −6.63120 1.96110i −0.308511 0.0912388i
\(463\) −0.492195 0.492195i −0.0228743 0.0228743i 0.695577 0.718451i \(-0.255149\pi\)
−0.718451 + 0.695577i \(0.755149\pi\)
\(464\) −63.2563 −2.93660
\(465\) 0 0
\(466\) 20.3056 0.940640
\(467\) −9.00044 9.00044i −0.416491 0.416491i 0.467501 0.883992i \(-0.345154\pi\)
−0.883992 + 0.467501i \(0.845154\pi\)
\(468\) −41.2192 + 8.79901i −1.90536 + 0.406734i
\(469\) 5.30669i 0.245040i
\(470\) 0 0
\(471\) 16.0501 + 29.5298i 0.739548 + 1.36066i
\(472\) −24.7378 + 24.7378i −1.13865 + 1.13865i
\(473\) 8.59230 8.59230i 0.395075 0.395075i
\(474\) −35.9070 66.0637i −1.64926 3.03441i
\(475\) 0 0
\(476\) 22.8408i 1.04690i
\(477\) −11.7570 + 2.50974i −0.538314 + 0.114913i
\(478\) 21.3426 + 21.3426i 0.976188 + 0.976188i
\(479\) 22.7572 1.03980 0.519901 0.854226i \(-0.325969\pi\)
0.519901 + 0.854226i \(0.325969\pi\)
\(480\) 0 0
\(481\) 1.95415 0.0891015
\(482\) 32.5235 + 32.5235i 1.48141 + 1.48141i
\(483\) 2.33917 + 0.691785i 0.106436 + 0.0314773i
\(484\) 38.2328i 1.73785i
\(485\) 0 0
\(486\) 31.5278 + 24.0830i 1.43013 + 1.09243i
\(487\) 11.4919 11.4919i 0.520746 0.520746i −0.397051 0.917797i \(-0.629966\pi\)
0.917797 + 0.397051i \(0.129966\pi\)
\(488\) 33.0210 33.0210i 1.49479 1.49479i
\(489\) 14.2163 7.72687i 0.642884 0.349421i
\(490\) 0 0
\(491\) 0.301729i 0.0136168i 0.999977 + 0.00680841i \(0.00216720\pi\)
−0.999977 + 0.00680841i \(0.997833\pi\)
\(492\) 14.1698 47.9133i 0.638826 2.16010i
\(493\) 32.1750 + 32.1750i 1.44909 + 1.44909i
\(494\) −13.4198 −0.603785
\(495\) 0 0
\(496\) −19.4909 −0.875165
\(497\) −2.55933 2.55933i −0.114801 0.114801i
\(498\) 5.68071 19.2085i 0.254559 0.860754i
\(499\) 20.2207i 0.905202i −0.891713 0.452601i \(-0.850496\pi\)
0.891713 0.452601i \(-0.149504\pi\)
\(500\) 0 0
\(501\) 6.70268 3.64305i 0.299454 0.162759i
\(502\) −5.74537 + 5.74537i −0.256428 + 0.256428i
\(503\) −23.8859 + 23.8859i −1.06502 + 1.06502i −0.0672882 + 0.997734i \(0.521435\pi\)
−0.997734 + 0.0672882i \(0.978565\pi\)
\(504\) −10.2880 + 15.8724i −0.458262 + 0.707012i
\(505\) 0 0
\(506\) 5.62273i 0.249961i
\(507\) 5.23825 + 1.54915i 0.232639 + 0.0688004i
\(508\) −63.9443 63.9443i −2.83707 2.83707i
\(509\) 11.7721 0.521788 0.260894 0.965368i \(-0.415983\pi\)
0.260894 + 0.965368i \(0.415983\pi\)
\(510\) 0 0
\(511\) 8.34014 0.368946
\(512\) 35.9587 + 35.9587i 1.58917 + 1.58917i
\(513\) 5.67942 + 6.63215i 0.250752 + 0.292816i
\(514\) 42.5137i 1.87520i
\(515\) 0 0
\(516\) −28.6864 52.7789i −1.26285 2.32346i
\(517\) 5.79412 5.79412i 0.254825 0.254825i
\(518\) 1.12074 1.12074i 0.0492426 0.0492426i
\(519\) 9.50842 + 17.4941i 0.417373 + 0.767907i
\(520\) 0 0
\(521\) 29.7872i 1.30500i −0.757789 0.652500i \(-0.773720\pi\)
0.757789 0.652500i \(-0.226280\pi\)
\(522\) 14.2174 + 66.6018i 0.622279 + 2.91508i
\(523\) −17.4673 17.4673i −0.763792 0.763792i 0.213214 0.977006i \(-0.431607\pi\)
−0.977006 + 0.213214i \(0.931607\pi\)
\(524\) 21.9268 0.957877
\(525\) 0 0
\(526\) −47.3309 −2.06373
\(527\) 9.91393 + 9.91393i 0.431858 + 0.431858i
\(528\) −18.4780 5.46466i −0.804151 0.237819i
\(529\) 21.0166i 0.913764i
\(530\) 0 0
\(531\) 13.9685 + 9.05395i 0.606183 + 0.392908i
\(532\) −5.32007 + 5.32007i −0.230654 + 0.230654i
\(533\) 14.2956 14.2956i 0.619211 0.619211i
\(534\) 36.4174 19.7936i 1.57593 0.856553i
\(535\) 0 0
\(536\) 33.4586i 1.44519i
\(537\) 8.15302 27.5683i 0.351829 1.18966i
\(538\) −52.8021 52.8021i −2.27646 2.27646i
\(539\) −1.56870 −0.0675687
\(540\) 0 0
\(541\) −23.1117 −0.993650 −0.496825 0.867851i \(-0.665501\pi\)
−0.496825 + 0.867851i \(0.665501\pi\)
\(542\) −5.72941 5.72941i −0.246099 0.246099i
\(543\) −5.72409 + 19.3552i −0.245644 + 0.830612i
\(544\) 27.7481i 1.18969i
\(545\) 0 0
\(546\) −12.1532 + 6.60549i −0.520107 + 0.282689i
\(547\) 25.6689 25.6689i 1.09752 1.09752i 0.102823 0.994700i \(-0.467213\pi\)
0.994700 0.102823i \(-0.0327874\pi\)
\(548\) 20.4113 20.4113i 0.871928 0.871928i
\(549\) −18.6458 12.0856i −0.795783 0.515801i
\(550\) 0 0
\(551\) 14.9884i 0.638528i
\(552\) 14.7484 + 4.36169i 0.627735 + 0.185646i
\(553\) −12.0613 12.0613i −0.512898 0.512898i
\(554\) 60.6965 2.57875
\(555\) 0 0
\(556\) −45.6891 −1.93765
\(557\) −10.5779 10.5779i −0.448199 0.448199i 0.446556 0.894756i \(-0.352650\pi\)
−0.894756 + 0.446556i \(0.852650\pi\)
\(558\) 4.38074 + 20.5217i 0.185452 + 0.868753i
\(559\) 24.3063i 1.02805i
\(560\) 0 0
\(561\) 6.61917 + 12.1783i 0.279462 + 0.514169i
\(562\) −44.6402 + 44.6402i −1.88303 + 1.88303i
\(563\) −10.9216 + 10.9216i −0.460291 + 0.460291i −0.898751 0.438460i \(-0.855524\pi\)
0.438460 + 0.898751i \(0.355524\pi\)
\(564\) −19.3444 35.5908i −0.814544 1.49864i
\(565\) 0 0
\(566\) 19.5050i 0.819858i
\(567\) 8.40784 + 3.21064i 0.353096 + 0.134834i
\(568\) −16.1365 16.1365i −0.677072 0.677072i
\(569\) −42.0710 −1.76371 −0.881854 0.471523i \(-0.843705\pi\)
−0.881854 + 0.471523i \(0.843705\pi\)
\(570\) 0 0
\(571\) 10.8342 0.453399 0.226699 0.973965i \(-0.427207\pi\)
0.226699 + 0.973965i \(0.427207\pi\)
\(572\) −15.5840 15.5840i −0.651601 0.651601i
\(573\) −21.3503 6.31411i −0.891921 0.263776i
\(574\) 16.3976i 0.684424i
\(575\) 0 0
\(576\) 0.555438 0.856936i 0.0231433 0.0357057i
\(577\) −14.6975 + 14.6975i −0.611865 + 0.611865i −0.943432 0.331567i \(-0.892423\pi\)
0.331567 + 0.943432i \(0.392423\pi\)
\(578\) 16.2407 16.2407i 0.675523 0.675523i
\(579\) −17.3497 + 9.42991i −0.721028 + 0.391894i
\(580\) 0 0
\(581\) 4.54404i 0.188519i
\(582\) −7.77271 + 26.2823i −0.322189 + 1.08944i
\(583\) −4.44503 4.44503i −0.184094 0.184094i
\(584\) 52.5844 2.17596
\(585\) 0 0
\(586\) −30.9802 −1.27978
\(587\) 4.89737 + 4.89737i 0.202136 + 0.202136i 0.800915 0.598779i \(-0.204347\pi\)
−0.598779 + 0.800915i \(0.704347\pi\)
\(588\) −2.19929 + 7.43658i −0.0906971 + 0.306680i
\(589\) 4.61831i 0.190294i
\(590\) 0 0
\(591\) 40.3552 21.9339i 1.65999 0.902240i
\(592\) 3.12297 3.12297i 0.128353 0.128353i
\(593\) −22.5635 + 22.5635i −0.926573 + 0.926573i −0.997483 0.0709102i \(-0.977410\pi\)
0.0709102 + 0.997483i \(0.477410\pi\)
\(594\) −1.60059 + 20.6835i −0.0656729 + 0.848654i
\(595\) 0 0
\(596\) 4.13314i 0.169300i
\(597\) −6.98804 2.06664i −0.286002 0.0845818i
\(598\) 7.95292 + 7.95292i 0.325219 + 0.325219i
\(599\) −6.81971 −0.278646 −0.139323 0.990247i \(-0.544493\pi\)
−0.139323 + 0.990247i \(0.544493\pi\)
\(600\) 0 0
\(601\) −8.46733 −0.345390 −0.172695 0.984975i \(-0.555247\pi\)
−0.172695 + 0.984975i \(0.555247\pi\)
\(602\) −13.9402 13.9402i −0.568158 0.568158i
\(603\) −15.5693 + 3.32356i −0.634031 + 0.135346i
\(604\) 61.4782i 2.50151i
\(605\) 0 0
\(606\) 2.12893 + 3.91692i 0.0864817 + 0.159114i
\(607\) −6.30295 + 6.30295i −0.255829 + 0.255829i −0.823355 0.567526i \(-0.807900\pi\)
0.567526 + 0.823355i \(0.307900\pi\)
\(608\) −6.46309 + 6.46309i −0.262113 + 0.262113i
\(609\) 7.37760 + 13.5737i 0.298956 + 0.550035i
\(610\) 0 0
\(611\) 16.3907i 0.663095i
\(612\) 67.0125 14.3051i 2.70882 0.578248i
\(613\) 5.24728 + 5.24728i 0.211935 + 0.211935i 0.805089 0.593154i \(-0.202117\pi\)
−0.593154 + 0.805089i \(0.702117\pi\)
\(614\) −42.6601 −1.72162
\(615\) 0 0
\(616\) −9.89062 −0.398504
\(617\) −2.10719 2.10719i −0.0848323 0.0848323i 0.663417 0.748250i \(-0.269105\pi\)
−0.748250 + 0.663417i \(0.769105\pi\)
\(618\) 24.0954 + 7.12596i 0.969261 + 0.286648i
\(619\) 21.0734i 0.847012i −0.905893 0.423506i \(-0.860799\pi\)
0.905893 0.423506i \(-0.139201\pi\)
\(620\) 0 0
\(621\) 0.564612 7.29616i 0.0226571 0.292785i
\(622\) 52.6932 52.6932i 2.11280 2.11280i
\(623\) 6.64874 6.64874i 0.266376 0.266376i
\(624\) −33.8650 + 18.4063i −1.35569 + 0.736844i
\(625\) 0 0
\(626\) 4.41188i 0.176334i
\(627\) −1.29484 + 4.37831i −0.0517108 + 0.174853i
\(628\) 61.4341 + 61.4341i 2.45149 + 2.45149i
\(629\) −3.17697 −0.126674
\(630\) 0 0
\(631\) −11.6376 −0.463287 −0.231643 0.972801i \(-0.574410\pi\)
−0.231643 + 0.972801i \(0.574410\pi\)
\(632\) −76.0461 76.0461i −3.02495 3.02495i
\(633\) 10.5713 35.7453i 0.420170 1.42075i
\(634\) 15.4825i 0.614890i
\(635\) 0 0
\(636\) −27.3040 + 14.8403i −1.08267 + 0.588455i
\(637\) −2.21881 + 2.21881i −0.0879123 + 0.0879123i
\(638\) −25.1806 + 25.1806i −0.996910 + 0.996910i
\(639\) −5.90591 + 9.11170i −0.233634 + 0.360453i
\(640\) 0 0
\(641\) 36.1036i 1.42601i −0.701161 0.713003i \(-0.747335\pi\)
0.701161 0.713003i \(-0.252665\pi\)
\(642\) 16.8441 + 4.98144i 0.664782 + 0.196602i
\(643\) 21.0115 + 21.0115i 0.828614 + 0.828614i 0.987325 0.158711i \(-0.0507337\pi\)
−0.158711 + 0.987325i \(0.550734\pi\)
\(644\) 6.30563 0.248477
\(645\) 0 0
\(646\) 21.8173 0.858392
\(647\) 18.9025 + 18.9025i 0.743133 + 0.743133i 0.973180 0.230046i \(-0.0738878\pi\)
−0.230046 + 0.973180i \(0.573888\pi\)
\(648\) 53.0112 + 20.2430i 2.08248 + 0.795221i
\(649\) 8.70428i 0.341673i
\(650\) 0 0
\(651\) 2.27322 + 4.18241i 0.0890947 + 0.163921i
\(652\) 29.5757 29.5757i 1.15828 1.15828i
\(653\) 12.2864 12.2864i 0.480803 0.480803i −0.424585 0.905388i \(-0.639580\pi\)
0.905388 + 0.424585i \(0.139580\pi\)
\(654\) 13.5199 + 24.8746i 0.528668 + 0.972674i
\(655\) 0 0
\(656\) 45.6924i 1.78399i
\(657\) −5.22339 24.4691i −0.203784 0.954631i
\(658\) −9.40038 9.40038i −0.366465 0.366465i
\(659\) −0.708622 −0.0276040 −0.0138020 0.999905i \(-0.504393\pi\)
−0.0138020 + 0.999905i \(0.504393\pi\)
\(660\) 0 0
\(661\) 17.4206 0.677582 0.338791 0.940862i \(-0.389982\pi\)
0.338791 + 0.940862i \(0.389982\pi\)
\(662\) −59.8561 59.8561i −2.32637 2.32637i
\(663\) 26.5876 + 7.86299i 1.03258 + 0.305373i
\(664\) 28.6500i 1.11184i
\(665\) 0 0
\(666\) −3.99006 2.58623i −0.154612 0.100214i
\(667\) 8.88253 8.88253i 0.343933 0.343933i
\(668\) 13.9443 13.9443i 0.539522 0.539522i
\(669\) 26.6869 14.5049i 1.03177 0.560791i
\(670\) 0 0
\(671\) 11.6188i 0.448540i
\(672\) −2.67181 + 9.03434i −0.103067 + 0.348507i
\(673\) 8.20389 + 8.20389i 0.316237 + 0.316237i 0.847320 0.531083i \(-0.178215\pi\)
−0.531083 + 0.847320i \(0.678215\pi\)
\(674\) 37.0926 1.42875
\(675\) 0 0
\(676\) 14.1206 0.543099
\(677\) 32.8605 + 32.8605i 1.26293 + 1.26293i 0.949666 + 0.313264i \(0.101422\pi\)
0.313264 + 0.949666i \(0.398578\pi\)
\(678\) 5.82098 19.6828i 0.223554 0.755915i
\(679\) 6.21744i 0.238604i
\(680\) 0 0
\(681\) 18.7356 10.1832i 0.717951 0.390221i
\(682\) −7.75878 + 7.75878i −0.297099 + 0.297099i
\(683\) −28.4978 + 28.4978i −1.09044 + 1.09044i −0.0949562 + 0.995481i \(0.530271\pi\)
−0.995481 + 0.0949562i \(0.969729\pi\)
\(684\) 18.9405 + 12.2766i 0.724208 + 0.469408i
\(685\) 0 0
\(686\) 2.54506i 0.0971709i
\(687\) −7.41347 2.19245i −0.282842 0.0836473i
\(688\) −38.8446 38.8446i −1.48093 1.48093i
\(689\) −12.5743 −0.479043
\(690\) 0 0
\(691\) 5.79939 0.220619 0.110310 0.993897i \(-0.464816\pi\)
0.110310 + 0.993897i \(0.464816\pi\)
\(692\) 36.3949 + 36.3949i 1.38353 + 1.38353i
\(693\) 0.982471 + 4.60241i 0.0373210 + 0.174831i
\(694\) 69.1925i 2.62651i
\(695\) 0 0
\(696\) 46.5156 + 85.5820i 1.76317 + 3.24398i
\(697\) −23.2412 + 23.2412i −0.880324 + 0.880324i
\(698\) −54.2230 + 54.2230i −2.05237 + 2.05237i
\(699\) −6.59919 12.1416i −0.249604 0.459236i
\(700\) 0 0
\(701\) 4.92775i 0.186118i 0.995661 + 0.0930592i \(0.0296646\pi\)
−0.995661 + 0.0930592i \(0.970335\pi\)
\(702\) 26.9913 + 31.5191i 1.01872 + 1.18961i
\(703\) −0.739981 0.739981i −0.0279089 0.0279089i
\(704\) 0.533986 0.0201254
\(705\) 0 0
\(706\) 61.3096 2.30742
\(707\) 0.715113 + 0.715113i 0.0268946 + 0.0268946i
\(708\) 41.2635 + 12.2032i 1.55078 + 0.458625i
\(709\) 17.1922i 0.645666i 0.946456 + 0.322833i \(0.104635\pi\)
−0.946456 + 0.322833i \(0.895365\pi\)
\(710\) 0 0
\(711\) −27.8326 + 42.9405i −1.04381 + 1.61039i
\(712\) 41.9201 41.9201i 1.57102 1.57102i
\(713\) 2.73693 2.73693i 0.102499 0.102499i
\(714\) 19.7581 10.7389i 0.739428 0.401895i
\(715\) 0 0
\(716\) 74.3149i 2.77728i
\(717\) 5.82541 19.6978i 0.217554 0.735628i
\(718\) 1.32809 + 1.32809i 0.0495640 + 0.0495640i
\(719\) −12.2556 −0.457059 −0.228529 0.973537i \(-0.573392\pi\)
−0.228529 + 0.973537i \(0.573392\pi\)
\(720\) 0 0
\(721\) 5.70011 0.212283
\(722\) −29.1113 29.1113i −1.08341 1.08341i
\(723\) 8.87721 30.0170i 0.330147 1.11635i
\(724\) 52.1752i 1.93908i
\(725\) 0 0
\(726\) 33.0728 17.9757i 1.22745 0.667142i
\(727\) −5.83842 + 5.83842i −0.216535 + 0.216535i −0.807037 0.590501i \(-0.798930\pi\)
0.590501 + 0.807037i \(0.298930\pi\)
\(728\) −13.9895 + 13.9895i −0.518486 + 0.518486i
\(729\) 4.15390 26.6786i 0.153848 0.988094i
\(730\) 0 0
\(731\) 39.5162i 1.46156i
\(732\) −55.0802 16.2894i −2.03582 0.602072i
\(733\) −13.5940 13.5940i −0.502105 0.502105i 0.409987 0.912091i \(-0.365533\pi\)
−0.912091 + 0.409987i \(0.865533\pi\)
\(734\) 83.8351 3.09441
\(735\) 0 0
\(736\) 7.66040 0.282366
\(737\) −5.88639 5.88639i −0.216828 0.216828i
\(738\) −48.1090 + 10.2698i −1.77092 + 0.378035i
\(739\) 15.1801i 0.558411i 0.960231 + 0.279205i \(0.0900710\pi\)
−0.960231 + 0.279205i \(0.909929\pi\)
\(740\) 0 0
\(741\) 4.36134 + 8.02424i 0.160218 + 0.294778i
\(742\) −7.21162 + 7.21162i −0.264747 + 0.264747i
\(743\) −34.4215 + 34.4215i −1.26280 + 1.26280i −0.313073 + 0.949729i \(0.601358\pi\)
−0.949729 + 0.313073i \(0.898642\pi\)
\(744\) 14.3326 + 26.3700i 0.525459 + 0.966770i
\(745\) 0 0
\(746\) 19.0080i 0.695934i
\(747\) −13.3317 + 2.84591i −0.487783 + 0.104126i
\(748\) 25.3359 + 25.3359i 0.926371 + 0.926371i
\(749\) 3.98469 0.145597
\(750\) 0 0
\(751\) −22.2515 −0.811970 −0.405985 0.913880i \(-0.633071\pi\)
−0.405985 + 0.913880i \(0.633071\pi\)
\(752\) −26.1944 26.1944i −0.955210 0.955210i
\(753\) 5.30260 + 1.56818i 0.193237 + 0.0571478i
\(754\) 71.2321i 2.59412i
\(755\) 0 0
\(756\) 23.1956 + 1.79498i 0.843615 + 0.0652830i
\(757\) 1.88407 1.88407i 0.0684777 0.0684777i −0.672038 0.740516i \(-0.734581\pi\)
0.740516 + 0.672038i \(0.234581\pi\)
\(758\) −6.08909 + 6.08909i −0.221166 + 0.221166i
\(759\) 3.36206 1.82735i 0.122035 0.0663286i
\(760\) 0 0
\(761\) 35.6674i 1.29294i 0.762938 + 0.646472i \(0.223756\pi\)
−0.762938 + 0.646472i \(0.776244\pi\)
\(762\) −25.2498 + 85.3786i −0.914703 + 3.09294i
\(763\) 4.54137 + 4.54137i 0.164409 + 0.164409i
\(764\) −57.5532 −2.08220
\(765\) 0 0
\(766\) −10.3206 −0.372897
\(767\) 12.3115 + 12.3115i 0.444543 + 0.444543i
\(768\) 14.3485 48.5173i 0.517755 1.75072i
\(769\) 31.7331i 1.14432i 0.820141 + 0.572162i \(0.193895\pi\)
−0.820141 + 0.572162i \(0.806105\pi\)
\(770\) 0 0
\(771\) −25.4207 + 13.8167i −0.915503 + 0.497595i
\(772\) −36.0944 + 36.0944i −1.29907 + 1.29907i
\(773\) 4.97844 4.97844i 0.179062 0.179062i −0.611885 0.790947i \(-0.709588\pi\)
0.790947 + 0.611885i \(0.209588\pi\)
\(774\) −32.1683 + 49.6296i −1.15627 + 1.78390i
\(775\) 0 0
\(776\) 39.2008i 1.40723i
\(777\) −1.03437 0.305904i −0.0371079 0.0109742i
\(778\) −18.3745 18.3745i −0.658758 0.658758i
\(779\) −10.8267 −0.387907
\(780\) 0 0
\(781\) −5.67781 −0.203168
\(782\) −12.9295 12.9295i −0.462359 0.462359i
\(783\) 35.2034 30.1463i 1.25807 1.07734i
\(784\) 7.09187i 0.253281i
\(785\) 0 0
\(786\) −10.3092 18.9675i −0.367718 0.676548i
\(787\) −18.7554 + 18.7554i −0.668557 + 0.668557i −0.957382 0.288825i \(-0.906735\pi\)
0.288825 + 0.957382i \(0.406735\pi\)
\(788\) 83.9553 83.9553i 2.99078 2.99078i
\(789\) 15.3822 + 28.3011i 0.547621 + 1.00754i
\(790\) 0 0
\(791\) 4.65625i 0.165557i
\(792\) 6.19445 + 29.0181i 0.220110 + 1.03111i
\(793\) −16.4339 16.4339i −0.583586 0.583586i
\(794\) −86.5746 −3.07242
\(795\) 0 0
\(796\) −18.8374 −0.667675
\(797\) −7.92792 7.92792i −0.280821 0.280821i 0.552615 0.833437i \(-0.313630\pi\)
−0.833437 + 0.552615i \(0.813630\pi\)
\(798\) 7.10338 + 2.10075i 0.251457 + 0.0743656i
\(799\) 26.6473i 0.942713i
\(800\) 0 0
\(801\) −23.6708 15.3426i −0.836366 0.542105i
\(802\) 36.1568 36.1568i 1.27674 1.27674i
\(803\) 9.25121 9.25121i 0.326468 0.326468i
\(804\) −36.1576 + 19.6524i −1.27518 + 0.693088i
\(805\) 0 0
\(806\) 21.9484i 0.773099i
\(807\) −14.4122 + 48.7328i −0.507333 + 1.71548i
\(808\) 4.50877 + 4.50877i 0.158618 + 0.158618i
\(809\) −33.2281 −1.16824 −0.584119 0.811668i \(-0.698560\pi\)
−0.584119 + 0.811668i \(0.698560\pi\)
\(810\) 0 0
\(811\) −49.8680 −1.75110 −0.875550 0.483127i \(-0.839501\pi\)
−0.875550 + 0.483127i \(0.839501\pi\)
\(812\) 28.2389 + 28.2389i 0.990991 + 0.990991i
\(813\) −1.56383 + 5.28787i −0.0548458 + 0.185454i
\(814\) 2.48634i 0.0871463i
\(815\) 0 0
\(816\) 55.0564 29.9243i 1.92736 1.04756i
\(817\) −9.20412 + 9.20412i −0.322011 + 0.322011i
\(818\) 60.3060 60.3060i 2.10855 2.10855i
\(819\) 7.89938 + 5.12012i 0.276027 + 0.178912i
\(820\) 0 0
\(821\) 32.4420i 1.13223i 0.824325 + 0.566116i \(0.191555\pi\)
−0.824325 + 0.566116i \(0.808445\pi\)
\(822\) −27.2532 8.05984i −0.950565 0.281119i
\(823\) 32.7235 + 32.7235i 1.14067 + 1.14067i 0.988328 + 0.152341i \(0.0486813\pi\)
0.152341 + 0.988328i \(0.451319\pi\)
\(824\) 35.9390 1.25200
\(825\) 0 0
\(826\) 14.1218 0.491361
\(827\) −36.7198 36.7198i −1.27687 1.27687i −0.942408 0.334465i \(-0.891444\pi\)
−0.334465 0.942408i \(-0.608556\pi\)
\(828\) −3.94919 18.5001i −0.137244 0.642922i
\(829\) 14.2972i 0.496562i −0.968688 0.248281i \(-0.920134\pi\)
0.968688 0.248281i \(-0.0798657\pi\)
\(830\) 0 0
\(831\) −19.7259 36.2929i −0.684285 1.25899i
\(832\) 0.755282 0.755282i 0.0261847 0.0261847i
\(833\) 3.60725 3.60725i 0.124984 0.124984i
\(834\) 21.4814 + 39.5227i 0.743841 + 1.36856i
\(835\) 0 0
\(836\) 11.8025i 0.408197i
\(837\) 10.8470 9.28883i 0.374929 0.321069i
\(838\) 46.5695 + 46.5695i 1.60872 + 1.60872i
\(839\) 33.6309 1.16107 0.580534 0.814236i \(-0.302844\pi\)
0.580534 + 0.814236i \(0.302844\pi\)
\(840\) 0 0
\(841\) 50.5583 1.74339
\(842\) −18.7216 18.7216i −0.645190 0.645190i
\(843\) 41.1999 + 12.1844i 1.41900 + 0.419654i
\(844\) 96.3574i 3.31676i
\(845\) 0 0
\(846\) −21.6923 + 33.4672i −0.745798 + 1.15062i
\(847\) 6.03811 6.03811i 0.207472 0.207472i
\(848\) −20.0953 + 20.0953i −0.690077 + 0.690077i
\(849\) 11.6629 6.33901i 0.400268 0.217554i
\(850\) 0 0
\(851\) 0.877065i 0.0300654i
\(852\) −7.96017 + 26.9162i −0.272711 + 0.922134i
\(853\) −26.5544 26.5544i −0.909206 0.909206i 0.0870025 0.996208i \(-0.472271\pi\)
−0.996208 + 0.0870025i \(0.972271\pi\)
\(854\) −18.8504 −0.645047
\(855\) 0 0
\(856\) 25.1234 0.858699
\(857\) 23.0711 + 23.0711i 0.788092 + 0.788092i 0.981181 0.193089i \(-0.0618506\pi\)
−0.193089 + 0.981181i \(0.561851\pi\)
\(858\) −6.15368 + 20.8078i −0.210083 + 0.710367i
\(859\) 17.3242i 0.591095i −0.955328 0.295548i \(-0.904498\pi\)
0.955328 0.295548i \(-0.0955021\pi\)
\(860\) 0 0
\(861\) −9.80481 + 5.32912i −0.334147 + 0.181616i
\(862\) −0.808044 + 0.808044i −0.0275221 + 0.0275221i
\(863\) −9.05228 + 9.05228i −0.308143 + 0.308143i −0.844189 0.536046i \(-0.819917\pi\)
0.536046 + 0.844189i \(0.319917\pi\)
\(864\) 28.1792 + 2.18064i 0.958674 + 0.0741868i
\(865\) 0 0
\(866\) 63.9997i 2.17480i
\(867\) −14.9891 4.43285i −0.509056 0.150548i
\(868\) 8.70111 + 8.70111i 0.295335 + 0.295335i
\(869\) −26.7577 −0.907693
\(870\) 0 0
\(871\) −16.6517 −0.564221
\(872\) 28.6332 + 28.6332i 0.969642 + 0.969642i
\(873\) 18.2413 3.89396i 0.617376 0.131790i
\(874\) 6.02310i 0.203734i
\(875\) 0 0
\(876\) −30.8863 56.8263i −1.04355 1.91998i
\(877\) −15.4630 + 15.4630i −0.522148 + 0.522148i −0.918220 0.396072i \(-0.870373\pi\)
0.396072 + 0.918220i \(0.370373\pi\)
\(878\) −53.1419 + 53.1419i −1.79345 + 1.79345i
\(879\) 10.0684 + 18.5243i 0.339597 + 0.624810i
\(880\) 0 0
\(881\) 3.93409i 0.132543i −0.997802 0.0662714i \(-0.978890\pi\)
0.997802 0.0662714i \(-0.0211103\pi\)
\(882\) 7.46695 1.59396i 0.251425 0.0536714i
\(883\) −13.5688 13.5688i −0.456625 0.456625i 0.440921 0.897546i \(-0.354652\pi\)
−0.897546 + 0.440921i \(0.854652\pi\)
\(884\) 71.6713 2.41057
\(885\) 0 0
\(886\) 56.0200 1.88203
\(887\) 4.92491 + 4.92491i 0.165362 + 0.165362i 0.784937 0.619575i \(-0.212695\pi\)
−0.619575 + 0.784937i \(0.712695\pi\)
\(888\) −6.52168 1.92872i −0.218853 0.0647235i
\(889\) 20.1975i 0.677401i
\(890\) 0 0
\(891\) 12.8877 5.76494i 0.431753 0.193133i
\(892\) 55.5196 55.5196i 1.85893 1.85893i
\(893\) −6.20669 + 6.20669i −0.207699 + 0.207699i
\(894\) 3.57532 1.94326i 0.119577 0.0649923i
\(895\) 0 0
\(896\) 11.7449i 0.392371i
\(897\) 2.17073 7.34002i 0.0724786 0.245076i
\(898\) 29.3724 + 29.3724i 0.980170 + 0.980170i
\(899\) 24.5139 0.817585
\(900\) 0 0
\(901\) 20.4428 0.681049
\(902\) −18.1889 18.1889i −0.605624 0.605624i
\(903\) −3.80493 + 12.8658i −0.126620 + 0.428148i
\(904\) 29.3575i 0.976416i
\(905\) 0 0
\(906\) −53.1809 + 28.9049i −1.76682 + 0.960302i
\(907\) 19.0317 19.0317i 0.631938 0.631938i −0.316616 0.948554i \(-0.602547\pi\)
0.948554 + 0.316616i \(0.102547\pi\)
\(908\) 38.9777 38.9777i 1.29352 1.29352i
\(909\) 1.65020 2.54594i 0.0547336 0.0844436i
\(910\) 0 0
\(911\) 17.7669i 0.588644i 0.955706 + 0.294322i \(0.0950938\pi\)
−0.955706 + 0.294322i \(0.904906\pi\)
\(912\) 19.7937 + 5.85377i 0.655435 + 0.193838i
\(913\) −5.04043 5.04043i −0.166814 0.166814i
\(914\) −74.2525 −2.45605
\(915\) 0 0
\(916\) −19.9842 −0.660298
\(917\) −3.46291 3.46291i −0.114355 0.114355i
\(918\) −43.8814 51.2425i −1.44830 1.69125i
\(919\) 8.50470i 0.280544i −0.990113 0.140272i \(-0.955202\pi\)
0.990113 0.140272i \(-0.0447977\pi\)
\(920\) 0 0
\(921\) 13.8643 + 25.5082i 0.456843 + 0.840525i
\(922\) 27.5151 27.5151i 0.906162 0.906162i
\(923\) −8.03083 + 8.03083i −0.264338 + 0.264338i
\(924\) 5.80941 + 10.6885i 0.191116 + 0.351625i
\(925\) 0 0
\(926\) 1.77154i 0.0582164i
\(927\) −3.56995 16.7235i −0.117253 0.549273i
\(928\) 34.3060 + 34.3060i 1.12615 + 1.12615i
\(929\) 14.1589 0.464538 0.232269 0.972652i \(-0.425385\pi\)
0.232269 + 0.972652i \(0.425385\pi\)
\(930\) 0 0
\(931\) 1.68040 0.0550729
\(932\) −25.2594 25.2594i −0.827399 0.827399i
\(933\) −48.6323 14.3825i −1.59215 0.470861i
\(934\) 32.3949i 1.05999i
\(935\) 0 0
\(936\) 49.8054 + 32.2822i 1.62794 + 1.05518i
\(937\) −28.7165 + 28.7165i −0.938127 + 0.938127i −0.998194 0.0600678i \(-0.980868\pi\)
0.0600678 + 0.998194i \(0.480868\pi\)
\(938\) −9.55009 + 9.55009i −0.311821 + 0.311821i
\(939\) 2.63804 1.43383i 0.0860891 0.0467912i
\(940\) 0 0
\(941\) 17.4001i 0.567228i −0.958939 0.283614i \(-0.908467\pi\)
0.958939 0.283614i \(-0.0915335\pi\)
\(942\) 24.2586 82.0269i 0.790387 2.67258i
\(943\) 6.41619 + 6.41619i 0.208940 + 0.208940i
\(944\) 39.3508 1.28076
\(945\) 0 0
\(946\) −30.9259 −1.00549
\(947\) −8.15693 8.15693i −0.265065 0.265065i 0.562043 0.827108i \(-0.310015\pi\)
−0.827108 + 0.562043i \(0.810015\pi\)
\(948\) −37.5138 + 126.848i −1.21839 + 4.11982i
\(949\) 26.1703i 0.849522i
\(950\) 0 0
\(951\) 9.25764 5.03172i 0.300199 0.163165i
\(952\) 22.7436 22.7436i 0.737124 0.737124i
\(953\) 38.6159 38.6159i 1.25089 1.25089i 0.295569 0.955321i \(-0.404491\pi\)
0.955321 0.295569i \(-0.0955091\pi\)
\(954\) 25.6748 + 16.6416i 0.831251 + 0.538790i
\(955\) 0 0
\(956\) 53.0987i 1.71734i
\(957\) 23.2400 + 6.87298i 0.751244 + 0.222172i
\(958\) −40.9545 40.9545i −1.32318 1.32318i
\(959\) −6.44712 −0.208188
\(960\) 0 0
\(961\) −23.4466 −0.756343
\(962\) −3.51674 3.51674i −0.113384 0.113384i
\(963\) −2.49559 11.6907i −0.0804194 0.376727i
\(964\) 80.9159i 2.60613i
\(965\) 0 0
\(966\) −2.96469 5.45461i −0.0953874 0.175499i
\(967\) 18.6836 18.6836i 0.600824 0.600824i −0.339707 0.940531i \(-0.610328\pi\)
0.940531 + 0.339707i \(0.110328\pi\)
\(968\) 38.0701 38.0701i 1.22362 1.22362i
\(969\) −7.09049 13.0455i −0.227779 0.419081i
\(970\) 0 0
\(971\) 57.4980i 1.84520i −0.385761 0.922599i \(-0.626061\pi\)
0.385761 0.922599i \(-0.373939\pi\)
\(972\) −9.26098 69.1776i −0.297046 2.21887i
\(973\) 7.21569 + 7.21569i 0.231324 + 0.231324i
\(974\) −41.3622 −1.32533
\(975\) 0 0
\(976\) −52.5270 −1.68135
\(977\) −2.08515 2.08515i −0.0667100 0.0667100i 0.672965 0.739675i \(-0.265021\pi\)
−0.739675 + 0.672965i \(0.765021\pi\)
\(978\) −39.4896 11.6786i −1.26274 0.373441i
\(979\) 14.7501i 0.471415i
\(980\) 0 0
\(981\) 10.4797 16.1681i 0.334590 0.516209i
\(982\) 0.543000 0.543000i 0.0173278 0.0173278i
\(983\) 11.6041 11.6041i 0.370114 0.370114i −0.497405 0.867519i \(-0.665714\pi\)
0.867519 + 0.497405i \(0.165714\pi\)
\(984\) −61.8191 + 33.5999i −1.97072 + 1.07113i
\(985\) 0 0
\(986\) 115.806i 3.68802i
\(987\) −2.56581 + 8.67592i −0.0816706 + 0.276158i
\(988\) 16.6937 + 16.6937i 0.531097 + 0.531097i
\(989\) 10.9092 0.346893
\(990\) 0 0
\(991\) −6.34125 −0.201436 −0.100718 0.994915i \(-0.532114\pi\)
−0.100718 + 0.994915i \(0.532114\pi\)
\(992\) 10.5706 + 10.5706i 0.335615 + 0.335615i
\(993\) −16.3376 + 55.2432i −0.518457 + 1.75309i
\(994\) 9.21168i 0.292177i
\(995\) 0 0
\(996\) −30.9612 + 16.8281i −0.981044 + 0.533218i
\(997\) −1.89647 + 1.89647i −0.0600618 + 0.0600618i −0.736500 0.676438i \(-0.763523\pi\)
0.676438 + 0.736500i \(0.263523\pi\)
\(998\) −36.3897 + 36.3897i −1.15190 + 1.15190i
\(999\) −0.249668 + 3.22633i −0.00789916 + 0.102076i
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 525.2.j.b.218.1 24
3.2 odd 2 inner 525.2.j.b.218.12 24
5.2 odd 4 inner 525.2.j.b.407.12 24
5.3 odd 4 105.2.j.a.92.1 yes 24
5.4 even 2 105.2.j.a.8.12 yes 24
15.2 even 4 inner 525.2.j.b.407.1 24
15.8 even 4 105.2.j.a.92.12 yes 24
15.14 odd 2 105.2.j.a.8.1 24
35.3 even 12 735.2.y.g.422.1 48
35.4 even 6 735.2.y.j.128.1 48
35.9 even 6 735.2.y.j.263.12 48
35.13 even 4 735.2.j.h.197.1 24
35.18 odd 12 735.2.y.j.422.1 48
35.19 odd 6 735.2.y.g.263.12 48
35.23 odd 12 735.2.y.j.557.12 48
35.24 odd 6 735.2.y.g.128.1 48
35.33 even 12 735.2.y.g.557.12 48
35.34 odd 2 735.2.j.h.638.12 24
105.23 even 12 735.2.y.j.557.1 48
105.38 odd 12 735.2.y.g.422.12 48
105.44 odd 6 735.2.y.j.263.1 48
105.53 even 12 735.2.y.j.422.12 48
105.59 even 6 735.2.y.g.128.12 48
105.68 odd 12 735.2.y.g.557.1 48
105.74 odd 6 735.2.y.j.128.12 48
105.83 odd 4 735.2.j.h.197.12 24
105.89 even 6 735.2.y.g.263.1 48
105.104 even 2 735.2.j.h.638.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.j.a.8.1 24 15.14 odd 2
105.2.j.a.8.12 yes 24 5.4 even 2
105.2.j.a.92.1 yes 24 5.3 odd 4
105.2.j.a.92.12 yes 24 15.8 even 4
525.2.j.b.218.1 24 1.1 even 1 trivial
525.2.j.b.218.12 24 3.2 odd 2 inner
525.2.j.b.407.1 24 15.2 even 4 inner
525.2.j.b.407.12 24 5.2 odd 4 inner
735.2.j.h.197.1 24 35.13 even 4
735.2.j.h.197.12 24 105.83 odd 4
735.2.j.h.638.1 24 105.104 even 2
735.2.j.h.638.12 24 35.34 odd 2
735.2.y.g.128.1 48 35.24 odd 6
735.2.y.g.128.12 48 105.59 even 6
735.2.y.g.263.1 48 105.89 even 6
735.2.y.g.263.12 48 35.19 odd 6
735.2.y.g.422.1 48 35.3 even 12
735.2.y.g.422.12 48 105.38 odd 12
735.2.y.g.557.1 48 105.68 odd 12
735.2.y.g.557.12 48 35.33 even 12
735.2.y.j.128.1 48 35.4 even 6
735.2.y.j.128.12 48 105.74 odd 6
735.2.y.j.263.1 48 105.44 odd 6
735.2.y.j.263.12 48 35.9 even 6
735.2.y.j.422.1 48 35.18 odd 12
735.2.y.j.422.12 48 105.53 even 12
735.2.y.j.557.1 48 105.23 even 12
735.2.y.j.557.12 48 35.23 odd 12