Properties

Label 297.2.n.b.91.6
Level $297$
Weight $2$
Character 297.91
Analytic conductor $2.372$
Analytic rank $0$
Dimension $72$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), not 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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 91.6
Character \(\chi\) \(=\) 297.91
Dual form 297.2.n.b.235.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.606887 + 0.270203i) q^{2} +(-1.04296 - 1.15832i) q^{4} +(-1.02009 + 0.454172i) q^{5} +(3.81922 - 0.811800i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(2.09587 - 2.57048i) q^{11} +(-0.279928 - 2.66333i) q^{13} +(2.53719 + 0.539295i) q^{14} +(-0.161688 + 1.53836i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(1.58999 + 0.707907i) q^{20} +(1.96651 - 0.993678i) q^{22} +(1.05719 - 1.83110i) q^{23} +(-2.51135 + 2.78914i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(1.05937 - 0.225177i) q^{29} +(0.0449642 + 0.427806i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(0.356392 - 3.39084i) q^{38} +(1.76638 + 1.96176i) q^{40} +(-2.85529 - 0.606910i) q^{41} +(1.11628 + 1.93346i) q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-8.58861 + 9.53861i) q^{47} +(7.53259 - 3.35373i) q^{49} +(-2.27774 + 1.01411i) q^{50} +(-2.79305 + 3.10200i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +(-4.61537 - 7.99405i) q^{56} +(0.703764 + 0.149590i) q^{58} +(1.58943 + 1.76524i) q^{59} +(0.426942 - 4.06208i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(-0.903682 - 8.59796i) q^{68} +(-2.83308 + 0.602190i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-3.86988 + 4.29793i) q^{74} +(-3.99983 + 6.92792i) q^{76} +(5.91786 - 11.5186i) q^{77} +(4.12439 + 1.83630i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.0503831 - 0.479363i) q^{83} +(-6.05809 - 1.28769i) q^{85} +(0.155030 + 1.47502i) q^{86} +(-7.31058 - 2.83448i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(-3.22362 + 0.685201i) q^{92} +(-7.78968 + 3.46819i) q^{94} +(3.83471 + 4.25888i) q^{95} +(7.32266 + 3.26026i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.606887 + 0.270203i 0.429134 + 0.191063i 0.609926 0.792459i \(-0.291199\pi\)
−0.180792 + 0.983521i \(0.557866\pi\)
\(3\) 0 0
\(4\) −1.04296 1.15832i −0.521480 0.579162i
\(5\) −1.02009 + 0.454172i −0.456196 + 0.203112i −0.621952 0.783055i \(-0.713660\pi\)
0.165756 + 0.986167i \(0.446994\pi\)
\(6\) 0 0
\(7\) 3.81922 0.811800i 1.44353 0.306832i 0.581440 0.813589i \(-0.302489\pi\)
0.862089 + 0.506758i \(0.169156\pi\)
\(8\) −0.730548 2.24840i −0.258288 0.794928i
\(9\) 0 0
\(10\) −0.741796 −0.234576
\(11\) 2.09587 2.57048i 0.631928 0.775027i
\(12\) 0 0
\(13\) −0.279928 2.66333i −0.0776380 0.738676i −0.962217 0.272285i \(-0.912221\pi\)
0.884579 0.466391i \(-0.154446\pi\)
\(14\) 2.53719 + 0.539295i 0.678091 + 0.144133i
\(15\) 0 0
\(16\) −0.161688 + 1.53836i −0.0404221 + 0.384590i
\(17\) 4.48727 + 3.26019i 1.08832 + 0.790713i 0.979115 0.203306i \(-0.0651688\pi\)
0.109207 + 0.994019i \(0.465169\pi\)
\(18\) 0 0
\(19\) −1.58598 4.88115i −0.363849 1.11981i −0.950699 0.310116i \(-0.899632\pi\)
0.586850 0.809696i \(-0.300368\pi\)
\(20\) 1.58999 + 0.707907i 0.355532 + 0.158293i
\(21\) 0 0
\(22\) 1.96651 0.993678i 0.419260 0.211853i
\(23\) 1.05719 1.83110i 0.220439 0.381812i −0.734502 0.678606i \(-0.762584\pi\)
0.954941 + 0.296795i \(0.0959176\pi\)
\(24\) 0 0
\(25\) −2.51135 + 2.78914i −0.502270 + 0.557827i
\(26\) 0.549758 1.69198i 0.107816 0.331825i
\(27\) 0 0
\(28\) −4.92362 3.57722i −0.930476 0.676030i
\(29\) 1.05937 0.225177i 0.196721 0.0418143i −0.108497 0.994097i \(-0.534604\pi\)
0.305218 + 0.952282i \(0.401271\pi\)
\(30\) 0 0
\(31\) 0.0449642 + 0.427806i 0.00807581 + 0.0768362i 0.997817 0.0660323i \(-0.0210340\pi\)
−0.989742 + 0.142869i \(0.954367\pi\)
\(32\) −2.87790 + 4.98467i −0.508746 + 0.881173i
\(33\) 0 0
\(34\) 1.84235 + 3.19104i 0.315960 + 0.547259i
\(35\) −3.52724 + 2.56269i −0.596212 + 0.433173i
\(36\) 0 0
\(37\) −2.69024 + 8.27970i −0.442273 + 1.36118i 0.443175 + 0.896435i \(0.353852\pi\)
−0.885447 + 0.464740i \(0.846148\pi\)
\(38\) 0.356392 3.39084i 0.0578144 0.550067i
\(39\) 0 0
\(40\) 1.76638 + 1.96176i 0.279289 + 0.310182i
\(41\) −2.85529 0.606910i −0.445921 0.0947834i −0.0205221 0.999789i \(-0.506533\pi\)
−0.425399 + 0.905006i \(0.639866\pi\)
\(42\) 0 0
\(43\) 1.11628 + 1.93346i 0.170232 + 0.294850i 0.938501 0.345277i \(-0.112215\pi\)
−0.768269 + 0.640127i \(0.778882\pi\)
\(44\) −5.16335 + 0.253209i −0.778404 + 0.0381728i
\(45\) 0 0
\(46\) 1.13637 0.825618i 0.167548 0.121731i
\(47\) −8.58861 + 9.53861i −1.25278 + 1.39135i −0.365044 + 0.930990i \(0.618946\pi\)
−0.887733 + 0.460359i \(0.847721\pi\)
\(48\) 0 0
\(49\) 7.53259 3.35373i 1.07608 0.479104i
\(50\) −2.27774 + 1.01411i −0.322121 + 0.143418i
\(51\) 0 0
\(52\) −2.79305 + 3.10200i −0.387326 + 0.430169i
\(53\) 4.56381 3.31581i 0.626888 0.455461i −0.228433 0.973560i \(-0.573360\pi\)
0.855321 + 0.518099i \(0.173360\pi\)
\(54\) 0 0
\(55\) −0.970527 + 3.57399i −0.130866 + 0.481917i
\(56\) −4.61537 7.99405i −0.616755 1.06825i
\(57\) 0 0
\(58\) 0.703764 + 0.149590i 0.0924087 + 0.0196421i
\(59\) 1.58943 + 1.76524i 0.206927 + 0.229815i 0.837671 0.546176i \(-0.183917\pi\)
−0.630744 + 0.775991i \(0.717250\pi\)
\(60\) 0 0
\(61\) 0.426942 4.06208i 0.0546643 0.520096i −0.932589 0.360940i \(-0.882456\pi\)
0.987253 0.159156i \(-0.0508773\pi\)
\(62\) −0.0883065 + 0.271779i −0.0112149 + 0.0345160i
\(63\) 0 0
\(64\) −0.590604 + 0.429099i −0.0738255 + 0.0536374i
\(65\) 1.49516 + 2.58969i 0.185452 + 0.321212i
\(66\) 0 0
\(67\) 4.87584 8.44521i 0.595679 1.03175i −0.397772 0.917484i \(-0.630216\pi\)
0.993451 0.114262i \(-0.0364503\pi\)
\(68\) −0.903682 8.59796i −0.109587 1.04266i
\(69\) 0 0
\(70\) −2.83308 + 0.602190i −0.338618 + 0.0719754i
\(71\) 5.11062 + 3.71308i 0.606519 + 0.440662i 0.848187 0.529697i \(-0.177694\pi\)
−0.241668 + 0.970359i \(0.577694\pi\)
\(72\) 0 0
\(73\) −3.60705 + 11.1014i −0.422174 + 1.29932i 0.483501 + 0.875344i \(0.339365\pi\)
−0.905675 + 0.423973i \(0.860635\pi\)
\(74\) −3.86988 + 4.29793i −0.449864 + 0.499625i
\(75\) 0 0
\(76\) −3.99983 + 6.92792i −0.458812 + 0.794686i
\(77\) 5.91786 11.5186i 0.674403 1.31267i
\(78\) 0 0
\(79\) 4.12439 + 1.83630i 0.464030 + 0.206600i 0.625416 0.780292i \(-0.284929\pi\)
−0.161385 + 0.986891i \(0.551596\pi\)
\(80\) −0.533744 1.64269i −0.0596744 0.183659i
\(81\) 0 0
\(82\) −1.56885 1.13983i −0.173250 0.125874i
\(83\) 0.0503831 0.479363i 0.00553026 0.0526169i −0.991409 0.130800i \(-0.958245\pi\)
0.996939 + 0.0781834i \(0.0249120\pi\)
\(84\) 0 0
\(85\) −6.05809 1.28769i −0.657092 0.139669i
\(86\) 0.155030 + 1.47502i 0.0167174 + 0.159055i
\(87\) 0 0
\(88\) −7.31058 2.83448i −0.779310 0.302157i
\(89\) −16.0830 −1.70480 −0.852399 0.522891i \(-0.824853\pi\)
−0.852399 + 0.522891i \(0.824853\pi\)
\(90\) 0 0
\(91\) −3.23120 9.94461i −0.338722 1.04248i
\(92\) −3.22362 + 0.685201i −0.336085 + 0.0714371i
\(93\) 0 0
\(94\) −7.78968 + 3.46819i −0.803444 + 0.357716i
\(95\) 3.83471 + 4.25888i 0.393433 + 0.436952i
\(96\) 0 0
\(97\) 7.32266 + 3.26026i 0.743504 + 0.331029i 0.743289 0.668971i \(-0.233265\pi\)
0.000215058 1.00000i \(0.499932\pi\)
\(98\) 5.47762 0.553323
\(99\) 0 0
\(100\) 5.84996 0.584996
\(101\) −1.60904 0.716391i −0.160106 0.0712836i 0.325119 0.945673i \(-0.394596\pi\)
−0.485225 + 0.874389i \(0.661262\pi\)
\(102\) 0 0
\(103\) 1.79840 + 1.99732i 0.177202 + 0.196802i 0.825202 0.564838i \(-0.191061\pi\)
−0.648001 + 0.761640i \(0.724395\pi\)
\(104\) −5.78373 + 2.57508i −0.567141 + 0.252507i
\(105\) 0 0
\(106\) 3.66566 0.779160i 0.356041 0.0756787i
\(107\) 3.17558 + 9.77342i 0.306995 + 0.944833i 0.978925 + 0.204219i \(0.0654653\pi\)
−0.671931 + 0.740614i \(0.734535\pi\)
\(108\) 0 0
\(109\) 2.36284 0.226319 0.113160 0.993577i \(-0.463903\pi\)
0.113160 + 0.993577i \(0.463903\pi\)
\(110\) −1.55470 + 1.90677i −0.148235 + 0.181803i
\(111\) 0 0
\(112\) 0.631319 + 6.00659i 0.0596540 + 0.567570i
\(113\) 1.49895 + 0.318611i 0.141009 + 0.0299724i 0.277875 0.960617i \(-0.410370\pi\)
−0.136866 + 0.990590i \(0.543703\pi\)
\(114\) 0 0
\(115\) −0.246788 + 2.34803i −0.0230131 + 0.218955i
\(116\) −1.36571 0.992247i −0.126803 0.0921279i
\(117\) 0 0
\(118\) 0.487631 + 1.50077i 0.0448901 + 0.138157i
\(119\) 19.7845 + 8.80862i 1.81364 + 0.807485i
\(120\) 0 0
\(121\) −2.21469 10.7747i −0.201335 0.979522i
\(122\) 1.35669 2.34986i 0.122829 0.212746i
\(123\) 0 0
\(124\) 0.448642 0.498267i 0.0402892 0.0447457i
\(125\) 3.02032 9.29560i 0.270146 0.831424i
\(126\) 0 0
\(127\) 6.19006 + 4.49734i 0.549279 + 0.399074i 0.827519 0.561437i \(-0.189751\pi\)
−0.278241 + 0.960511i \(0.589751\pi\)
\(128\) 10.7857 2.29256i 0.953328 0.202636i
\(129\) 0 0
\(130\) 0.207649 + 1.97565i 0.0182120 + 0.173276i
\(131\) −2.67956 + 4.64113i −0.234114 + 0.405498i −0.959015 0.283356i \(-0.908552\pi\)
0.724901 + 0.688853i \(0.241886\pi\)
\(132\) 0 0
\(133\) −10.0197 17.3547i −0.868820 1.50484i
\(134\) 5.24101 3.80782i 0.452754 0.328945i
\(135\) 0 0
\(136\) 4.05203 12.4709i 0.347459 1.06937i
\(137\) 1.74889 16.6395i 0.149417 1.42161i −0.620869 0.783914i \(-0.713220\pi\)
0.770287 0.637698i \(-0.220113\pi\)
\(138\) 0 0
\(139\) 9.19393 + 10.2109i 0.779819 + 0.866077i 0.993848 0.110751i \(-0.0353255\pi\)
−0.214029 + 0.976827i \(0.568659\pi\)
\(140\) 6.64718 + 1.41290i 0.561790 + 0.119412i
\(141\) 0 0
\(142\) 2.09828 + 3.63433i 0.176084 + 0.304986i
\(143\) −7.43273 4.86244i −0.621556 0.406618i
\(144\) 0 0
\(145\) −0.978384 + 0.710837i −0.0812503 + 0.0590318i
\(146\) −5.18870 + 5.76264i −0.429420 + 0.476919i
\(147\) 0 0
\(148\) 12.3964 5.51923i 1.01898 0.453678i
\(149\) −5.07900 + 2.26132i −0.416088 + 0.185254i −0.604093 0.796914i \(-0.706464\pi\)
0.188005 + 0.982168i \(0.439798\pi\)
\(150\) 0 0
\(151\) −0.109676 + 0.121807i −0.00892527 + 0.00991252i −0.747591 0.664159i \(-0.768790\pi\)
0.738666 + 0.674072i \(0.235456\pi\)
\(152\) −9.81611 + 7.13182i −0.796192 + 0.578467i
\(153\) 0 0
\(154\) 6.70385 5.39148i 0.540211 0.434458i
\(155\) −0.240165 0.415978i −0.0192905 0.0334121i
\(156\) 0 0
\(157\) −23.3318 4.95932i −1.86208 0.395797i −0.867294 0.497797i \(-0.834142\pi\)
−0.994784 + 0.102000i \(0.967476\pi\)
\(158\) 2.00687 + 2.22885i 0.159658 + 0.177318i
\(159\) 0 0
\(160\) 0.671811 6.39185i 0.0531113 0.505320i
\(161\) 2.55114 7.85161i 0.201058 0.618794i
\(162\) 0 0
\(163\) 3.39466 2.46636i 0.265890 0.193180i −0.446850 0.894609i \(-0.647454\pi\)
0.712740 + 0.701429i \(0.247454\pi\)
\(164\) 2.27495 + 3.94033i 0.177644 + 0.307688i
\(165\) 0 0
\(166\) 0.160102 0.277306i 0.0124264 0.0215231i
\(167\) 1.65577 + 15.7536i 0.128128 + 1.21905i 0.849909 + 0.526930i \(0.176657\pi\)
−0.721781 + 0.692121i \(0.756676\pi\)
\(168\) 0 0
\(169\) 5.70093 1.21177i 0.438533 0.0932131i
\(170\) −3.32864 2.41840i −0.255295 0.185482i
\(171\) 0 0
\(172\) 1.07533 3.30954i 0.0819935 0.252350i
\(173\) 1.74167 1.93432i 0.132417 0.147064i −0.673290 0.739379i \(-0.735119\pi\)
0.805706 + 0.592315i \(0.201786\pi\)
\(174\) 0 0
\(175\) −7.32717 + 12.6910i −0.553882 + 0.959352i
\(176\) 3.61544 + 3.63981i 0.272524 + 0.274361i
\(177\) 0 0
\(178\) −9.76059 4.34569i −0.731587 0.325724i
\(179\) −2.34483 7.21663i −0.175261 0.539396i 0.824385 0.566030i \(-0.191521\pi\)
−0.999645 + 0.0266334i \(0.991521\pi\)
\(180\) 0 0
\(181\) 1.94179 + 1.41080i 0.144332 + 0.104864i 0.657608 0.753360i \(-0.271568\pi\)
−0.513276 + 0.858224i \(0.671568\pi\)
\(182\) 0.726095 6.90833i 0.0538218 0.512080i
\(183\) 0 0
\(184\) −4.88937 1.03927i −0.360449 0.0766159i
\(185\) −1.01613 9.66784i −0.0747074 0.710794i
\(186\) 0 0
\(187\) 17.7850 4.70149i 1.30056 0.343807i
\(188\) 20.0064 1.45911
\(189\) 0 0
\(190\) 1.17647 + 3.62081i 0.0853504 + 0.262681i
\(191\) −16.1573 + 3.43433i −1.16910 + 0.248500i −0.751251 0.660017i \(-0.770549\pi\)
−0.417849 + 0.908517i \(0.637216\pi\)
\(192\) 0 0
\(193\) −7.43166 + 3.30879i −0.534942 + 0.238172i −0.656384 0.754427i \(-0.727915\pi\)
0.121442 + 0.992599i \(0.461248\pi\)
\(194\) 3.56310 + 3.95722i 0.255815 + 0.284112i
\(195\) 0 0
\(196\) −11.7409 5.22738i −0.838635 0.373384i
\(197\) 22.9072 1.63207 0.816035 0.578003i \(-0.196168\pi\)
0.816035 + 0.578003i \(0.196168\pi\)
\(198\) 0 0
\(199\) 9.27177 0.657259 0.328629 0.944459i \(-0.393413\pi\)
0.328629 + 0.944459i \(0.393413\pi\)
\(200\) 8.10574 + 3.60891i 0.573162 + 0.255188i
\(201\) 0 0
\(202\) −0.782935 0.869537i −0.0550871 0.0611804i
\(203\) 3.86318 1.72000i 0.271142 0.120720i
\(204\) 0 0
\(205\) 3.18828 0.677690i 0.222679 0.0473319i
\(206\) 0.551741 + 1.69808i 0.0384416 + 0.118311i
\(207\) 0 0
\(208\) 4.14243 0.287226
\(209\) −15.8709 6.15351i −1.09781 0.425647i
\(210\) 0 0
\(211\) −0.440125 4.18751i −0.0302995 0.288280i −0.999171 0.0407153i \(-0.987036\pi\)
0.968871 0.247565i \(-0.0796303\pi\)
\(212\) −8.60065 1.82812i −0.590695 0.125556i
\(213\) 0 0
\(214\) −0.713596 + 6.78942i −0.0487804 + 0.464115i
\(215\) −2.01683 1.46531i −0.137547 0.0999334i
\(216\) 0 0
\(217\) 0.519021 + 1.59738i 0.0352335 + 0.108437i
\(218\) 1.43398 + 0.638448i 0.0971212 + 0.0432412i
\(219\) 0 0
\(220\) 5.15206 2.60334i 0.347352 0.175517i
\(221\) 7.42687 12.8637i 0.499585 0.865307i
\(222\) 0 0
\(223\) −4.58961 + 5.09728i −0.307343 + 0.341339i −0.876953 0.480576i \(-0.840428\pi\)
0.569610 + 0.821915i \(0.307094\pi\)
\(224\) −6.94477 + 21.3738i −0.464017 + 1.42810i
\(225\) 0 0
\(226\) 0.823601 + 0.598381i 0.0547851 + 0.0398037i
\(227\) 27.5152 5.84854i 1.82625 0.388181i 0.838585 0.544771i \(-0.183383\pi\)
0.987664 + 0.156590i \(0.0500502\pi\)
\(228\) 0 0
\(229\) 1.46703 + 13.9578i 0.0969438 + 0.922358i 0.929600 + 0.368569i \(0.120152\pi\)
−0.832657 + 0.553789i \(0.813181\pi\)
\(230\) −0.784218 + 1.35831i −0.0517098 + 0.0895640i
\(231\) 0 0
\(232\) −1.28021 2.21739i −0.0840499 0.145579i
\(233\) −11.7385 + 8.52854i −0.769017 + 0.558723i −0.901663 0.432440i \(-0.857653\pi\)
0.132646 + 0.991163i \(0.457653\pi\)
\(234\) 0 0
\(235\) 4.42895 13.6309i 0.288913 0.889182i
\(236\) 0.387010 3.68216i 0.0251922 0.239688i
\(237\) 0 0
\(238\) 9.62682 + 10.6917i 0.624014 + 0.693038i
\(239\) −24.5986 5.22859i −1.59115 0.338209i −0.674617 0.738168i \(-0.735691\pi\)
−0.916533 + 0.399959i \(0.869024\pi\)
\(240\) 0 0
\(241\) −8.87110 15.3652i −0.571438 0.989759i −0.996419 0.0845570i \(-0.973053\pi\)
0.424981 0.905202i \(-0.360281\pi\)
\(242\) 1.56731 7.13747i 0.100750 0.458814i
\(243\) 0 0
\(244\) −5.15048 + 3.74205i −0.329726 + 0.239560i
\(245\) −6.16073 + 6.84218i −0.393594 + 0.437131i
\(246\) 0 0
\(247\) −12.5562 + 5.59036i −0.798929 + 0.355706i
\(248\) 0.929029 0.413630i 0.0589934 0.0262655i
\(249\) 0 0
\(250\) 4.34470 4.82528i 0.274783 0.305177i
\(251\) −17.6993 + 12.8593i −1.11717 + 0.811670i −0.983777 0.179394i \(-0.942586\pi\)
−0.133390 + 0.991064i \(0.542586\pi\)
\(252\) 0 0
\(253\) −2.49108 6.55523i −0.156613 0.412124i
\(254\) 2.54147 + 4.40195i 0.159466 + 0.276203i
\(255\) 0 0
\(256\) 8.59329 + 1.82656i 0.537081 + 0.114160i
\(257\) −3.45520 3.83739i −0.215530 0.239370i 0.625679 0.780081i \(-0.284822\pi\)
−0.841209 + 0.540711i \(0.818155\pi\)
\(258\) 0 0
\(259\) −3.55315 + 33.8059i −0.220782 + 2.10060i
\(260\) 1.44031 4.43283i 0.0893244 0.274912i
\(261\) 0 0
\(262\) −2.88024 + 2.09262i −0.177942 + 0.129282i
\(263\) −13.9491 24.1605i −0.860135 1.48980i −0.871798 0.489866i \(-0.837046\pi\)
0.0116625 0.999932i \(-0.496288\pi\)
\(264\) 0 0
\(265\) −3.14954 + 5.45516i −0.193475 + 0.335108i
\(266\) −1.39155 13.2397i −0.0853212 0.811777i
\(267\) 0 0
\(268\) −14.8676 + 3.16020i −0.908183 + 0.193040i
\(269\) 2.44290 + 1.77487i 0.148946 + 0.108216i 0.659763 0.751474i \(-0.270657\pi\)
−0.510816 + 0.859690i \(0.670657\pi\)
\(270\) 0 0
\(271\) −7.84125 + 24.1329i −0.476322 + 1.46597i 0.367845 + 0.929887i \(0.380096\pi\)
−0.844167 + 0.536081i \(0.819904\pi\)
\(272\) −5.74089 + 6.37590i −0.348093 + 0.386596i
\(273\) 0 0
\(274\) 5.55744 9.62577i 0.335737 0.581514i
\(275\) 1.90595 + 12.3010i 0.114933 + 0.741779i
\(276\) 0 0
\(277\) −9.65105 4.29692i −0.579875 0.258177i 0.0957707 0.995403i \(-0.469468\pi\)
−0.675646 + 0.737226i \(0.736135\pi\)
\(278\) 2.82066 + 8.68109i 0.169172 + 0.520657i
\(279\) 0 0
\(280\) 8.33875 + 6.05845i 0.498335 + 0.362062i
\(281\) −2.35926 + 22.4469i −0.140742 + 1.33907i 0.665019 + 0.746827i \(0.268424\pi\)
−0.805761 + 0.592241i \(0.798243\pi\)
\(282\) 0 0
\(283\) 5.74880 + 1.22195i 0.341731 + 0.0726371i 0.375580 0.926790i \(-0.377443\pi\)
−0.0338497 + 0.999427i \(0.510777\pi\)
\(284\) −1.02922 9.79234i −0.0610728 0.581069i
\(285\) 0 0
\(286\) −3.19697 4.95930i −0.189041 0.293250i
\(287\) −11.3977 −0.672782
\(288\) 0 0
\(289\) 4.25344 + 13.0907i 0.250202 + 0.770044i
\(290\) −0.785839 + 0.167035i −0.0461461 + 0.00980865i
\(291\) 0 0
\(292\) 16.6210 7.40014i 0.972670 0.433061i
\(293\) −4.74689 5.27195i −0.277316 0.307991i 0.588356 0.808602i \(-0.299775\pi\)
−0.865672 + 0.500611i \(0.833109\pi\)
\(294\) 0 0
\(295\) −2.42308 1.07883i −0.141077 0.0628117i
\(296\) 20.5814 1.19627
\(297\) 0 0
\(298\) −3.69339 −0.213953
\(299\) −5.17278 2.30307i −0.299150 0.133190i
\(300\) 0 0
\(301\) 5.83291 + 6.47811i 0.336204 + 0.373392i
\(302\) −0.0994733 + 0.0442884i −0.00572405 + 0.00254851i
\(303\) 0 0
\(304\) 7.76540 1.65059i 0.445376 0.0946676i
\(305\) 1.40936 + 4.33757i 0.0806999 + 0.248369i
\(306\) 0 0
\(307\) −18.5370 −1.05796 −0.528981 0.848633i \(-0.677426\pi\)
−0.528981 + 0.848633i \(0.677426\pi\)
\(308\) −19.5144 + 5.15867i −1.11194 + 0.293942i
\(309\) 0 0
\(310\) −0.0333543 0.317345i −0.00189440 0.0180240i
\(311\) 6.72598 + 1.42965i 0.381395 + 0.0810680i 0.394620 0.918845i \(-0.370876\pi\)
−0.0132247 + 0.999913i \(0.504210\pi\)
\(312\) 0 0
\(313\) 2.64727 25.1871i 0.149632 1.42366i −0.619715 0.784827i \(-0.712752\pi\)
0.769348 0.638830i \(-0.220581\pi\)
\(314\) −12.8197 9.31407i −0.723459 0.525624i
\(315\) 0 0
\(316\) −2.17455 6.69256i −0.122328 0.376486i
\(317\) −10.0301 4.46567i −0.563344 0.250817i 0.105248 0.994446i \(-0.466436\pi\)
−0.668593 + 0.743629i \(0.733103\pi\)
\(318\) 0 0
\(319\) 1.64149 3.19503i 0.0919060 0.178888i
\(320\) 0.407582 0.705953i 0.0227845 0.0394640i
\(321\) 0 0
\(322\) 3.66979 4.07571i 0.204509 0.227131i
\(323\) 8.79675 27.0736i 0.489464 1.50642i
\(324\) 0 0
\(325\) 8.13140 + 5.90780i 0.451049 + 0.327706i
\(326\) 2.72659 0.579555i 0.151012 0.0320986i
\(327\) 0 0
\(328\) 0.721351 + 6.86319i 0.0398299 + 0.378956i
\(329\) −25.0583 + 43.4023i −1.38151 + 2.39284i
\(330\) 0 0
\(331\) 1.85513 + 3.21317i 0.101967 + 0.176612i 0.912495 0.409088i \(-0.134153\pi\)
−0.810528 + 0.585700i \(0.800820\pi\)
\(332\) −0.607805 + 0.441596i −0.0333576 + 0.0242357i
\(333\) 0 0
\(334\) −3.25182 + 10.0081i −0.177931 + 0.547617i
\(335\) −1.13821 + 10.8293i −0.0621869 + 0.591668i
\(336\) 0 0
\(337\) −21.5428 23.9257i −1.17351 1.30331i −0.943976 0.330013i \(-0.892947\pi\)
−0.229533 0.973301i \(-0.573720\pi\)
\(338\) 3.78725 + 0.805004i 0.205999 + 0.0437864i
\(339\) 0 0
\(340\) 4.82678 + 8.36023i 0.261769 + 0.453397i
\(341\) 1.19390 + 0.781045i 0.0646535 + 0.0422960i
\(342\) 0 0
\(343\) 3.93417 2.85834i 0.212425 0.154336i
\(344\) 3.53168 3.92233i 0.190416 0.211478i
\(345\) 0 0
\(346\) 1.57966 0.703310i 0.0849230 0.0378102i
\(347\) 19.6618 8.75398i 1.05550 0.469939i 0.195749 0.980654i \(-0.437286\pi\)
0.859750 + 0.510715i \(0.170619\pi\)
\(348\) 0 0
\(349\) −11.2547 + 12.4997i −0.602453 + 0.669092i −0.964810 0.262948i \(-0.915305\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(350\) −7.87593 + 5.72219i −0.420986 + 0.305864i
\(351\) 0 0
\(352\) 6.78127 + 17.8448i 0.361443 + 0.951129i
\(353\) 1.56543 + 2.71140i 0.0833193 + 0.144313i 0.904674 0.426105i \(-0.140115\pi\)
−0.821355 + 0.570418i \(0.806781\pi\)
\(354\) 0 0
\(355\) −6.89965 1.46657i −0.366195 0.0778372i
\(356\) 16.7740 + 18.6294i 0.889018 + 0.987355i
\(357\) 0 0
\(358\) 0.526915 5.01326i 0.0278483 0.264959i
\(359\) −2.62315 + 8.07323i −0.138445 + 0.426089i −0.996110 0.0881197i \(-0.971914\pi\)
0.857665 + 0.514208i \(0.171914\pi\)
\(360\) 0 0
\(361\) −5.93893 + 4.31489i −0.312575 + 0.227099i
\(362\) 0.797247 + 1.38087i 0.0419024 + 0.0725770i
\(363\) 0 0
\(364\) −8.14907 + 14.1146i −0.427127 + 0.739806i
\(365\) −1.36242 12.9626i −0.0713124 0.678492i
\(366\) 0 0
\(367\) 10.7703 2.28931i 0.562208 0.119501i 0.0819628 0.996635i \(-0.473881\pi\)
0.480245 + 0.877134i \(0.340548\pi\)
\(368\) 2.64596 + 1.92241i 0.137930 + 0.100212i
\(369\) 0 0
\(370\) 1.99561 6.14185i 0.103747 0.319300i
\(371\) 14.7384 16.3687i 0.765181 0.849820i
\(372\) 0 0
\(373\) −5.50342 + 9.53220i −0.284956 + 0.493558i −0.972599 0.232491i \(-0.925312\pi\)
0.687642 + 0.726050i \(0.258646\pi\)
\(374\) 12.0638 + 1.95229i 0.623805 + 0.100950i
\(375\) 0 0
\(376\) 27.7210 + 12.3422i 1.42960 + 0.636499i
\(377\) −0.896269 2.75843i −0.0461602 0.142067i
\(378\) 0 0
\(379\) −20.5384 14.9220i −1.05499 0.766492i −0.0818315 0.996646i \(-0.526077\pi\)
−0.973154 + 0.230154i \(0.926077\pi\)
\(380\) 0.933713 8.88368i 0.0478984 0.455723i
\(381\) 0 0
\(382\) −10.7336 2.28150i −0.549179 0.116732i
\(383\) −1.26633 12.0484i −0.0647067 0.615643i −0.978038 0.208426i \(-0.933166\pi\)
0.913331 0.407217i \(-0.133501\pi\)
\(384\) 0 0
\(385\) −0.805292 + 14.4377i −0.0410415 + 0.735814i
\(386\) −5.40422 −0.275068
\(387\) 0 0
\(388\) −3.86080 11.8823i −0.196003 0.603234i
\(389\) 14.0375 2.98376i 0.711728 0.151283i 0.162200 0.986758i \(-0.448141\pi\)
0.549528 + 0.835475i \(0.314808\pi\)
\(390\) 0 0
\(391\) 10.7136 4.77002i 0.541812 0.241230i
\(392\) −13.0434 14.4862i −0.658792 0.731663i
\(393\) 0 0
\(394\) 13.9021 + 6.18960i 0.700376 + 0.311828i
\(395\) −5.04123 −0.253652
\(396\) 0 0
\(397\) −5.03882 −0.252891 −0.126446 0.991974i \(-0.540357\pi\)
−0.126446 + 0.991974i \(0.540357\pi\)
\(398\) 5.62692 + 2.50527i 0.282052 + 0.125578i
\(399\) 0 0
\(400\) −3.88464 4.31433i −0.194232 0.215717i
\(401\) 16.6267 7.40268i 0.830297 0.369672i 0.0528362 0.998603i \(-0.483174\pi\)
0.777461 + 0.628931i \(0.216507\pi\)
\(402\) 0 0
\(403\) 1.12680 0.239509i 0.0561301 0.0119308i
\(404\) 0.848352 + 2.61096i 0.0422071 + 0.129900i
\(405\) 0 0
\(406\) 2.80926 0.139421
\(407\) 15.6444 + 24.2683i 0.775464 + 1.20294i
\(408\) 0 0
\(409\) −1.71745 16.3404i −0.0849224 0.807983i −0.951232 0.308476i \(-0.900181\pi\)
0.866310 0.499507i \(-0.166486\pi\)
\(410\) 2.11804 + 0.450203i 0.104603 + 0.0222340i
\(411\) 0 0
\(412\) 0.437891 4.16626i 0.0215733 0.205257i
\(413\) 7.50342 + 5.45155i 0.369219 + 0.268253i
\(414\) 0 0
\(415\) 0.166318 + 0.511874i 0.00816423 + 0.0251269i
\(416\) 14.0814 + 6.26946i 0.690399 + 0.307386i
\(417\) 0 0
\(418\) −7.96912 8.02285i −0.389783 0.392410i
\(419\) −8.70324 + 15.0745i −0.425181 + 0.736435i −0.996437 0.0843365i \(-0.973123\pi\)
0.571256 + 0.820772i \(0.306456\pi\)
\(420\) 0 0
\(421\) 3.04364 3.38030i 0.148338 0.164746i −0.664397 0.747380i \(-0.731311\pi\)
0.812734 + 0.582634i \(0.197978\pi\)
\(422\) 0.864374 2.66027i 0.0420771 0.129500i
\(423\) 0 0
\(424\) −10.7893 7.83890i −0.523976 0.380691i
\(425\) −20.3622 + 4.32812i −0.987712 + 0.209945i
\(426\) 0 0
\(427\) −1.66701 15.8606i −0.0806723 0.767546i
\(428\) 8.00879 13.8716i 0.387120 0.670511i
\(429\) 0 0
\(430\) −0.828055 1.43423i −0.0399323 0.0691648i
\(431\) 10.1004 7.33838i 0.486520 0.353477i −0.317325 0.948317i \(-0.602784\pi\)
0.803844 + 0.594840i \(0.202784\pi\)
\(432\) 0 0
\(433\) 8.86451 27.2822i 0.426001 1.31110i −0.476031 0.879428i \(-0.657925\pi\)
0.902032 0.431668i \(-0.142075\pi\)
\(434\) −0.116631 + 1.10967i −0.00559848 + 0.0532660i
\(435\) 0 0
\(436\) −2.46435 2.73694i −0.118021 0.131075i
\(437\) −10.6146 2.25620i −0.507764 0.107929i
\(438\) 0 0
\(439\) 2.05404 + 3.55769i 0.0980338 + 0.169799i 0.910871 0.412692i \(-0.135411\pi\)
−0.812837 + 0.582491i \(0.802078\pi\)
\(440\) 8.74476 0.428841i 0.416890 0.0204442i
\(441\) 0 0
\(442\) 7.98309 5.80005i 0.379717 0.275880i
\(443\) 14.2054 15.7767i 0.674921 0.749576i −0.304255 0.952591i \(-0.598407\pi\)
0.979176 + 0.203015i \(0.0650740\pi\)
\(444\) 0 0
\(445\) 16.4061 7.30446i 0.777723 0.346265i
\(446\) −4.16267 + 1.85334i −0.197108 + 0.0877583i
\(447\) 0 0
\(448\) −1.90730 + 2.11827i −0.0901116 + 0.100079i
\(449\) 20.9494 15.2206i 0.988663 0.718306i 0.0290350 0.999578i \(-0.490757\pi\)
0.959628 + 0.281273i \(0.0907566\pi\)
\(450\) 0 0
\(451\) −7.54435 + 6.06744i −0.355249 + 0.285705i
\(452\) −1.19428 2.06856i −0.0561744 0.0972970i
\(453\) 0 0
\(454\) 18.2789 + 3.88530i 0.857872 + 0.182346i
\(455\) 7.81266 + 8.67684i 0.366263 + 0.406776i
\(456\) 0 0
\(457\) 1.07705 10.2474i 0.0503821 0.479354i −0.940018 0.341124i \(-0.889192\pi\)
0.990400 0.138229i \(-0.0441411\pi\)
\(458\) −2.88113 + 8.86721i −0.134626 + 0.414338i
\(459\) 0 0
\(460\) 2.97717 2.16304i 0.138811 0.100852i
\(461\) −12.7266 22.0432i −0.592738 1.02665i −0.993862 0.110628i \(-0.964714\pi\)
0.401124 0.916024i \(-0.368620\pi\)
\(462\) 0 0
\(463\) 19.9277 34.5158i 0.926119 1.60409i 0.136368 0.990658i \(-0.456457\pi\)
0.789751 0.613427i \(-0.210210\pi\)
\(464\) 0.175115 + 1.66611i 0.00812951 + 0.0773471i
\(465\) 0 0
\(466\) −9.42840 + 2.00407i −0.436762 + 0.0928367i
\(467\) −14.0582 10.2139i −0.650537 0.472643i 0.212917 0.977070i \(-0.431704\pi\)
−0.863454 + 0.504427i \(0.831704\pi\)
\(468\) 0 0
\(469\) 11.7661 36.2123i 0.543308 1.67213i
\(470\) 6.37099 7.07570i 0.293872 0.326378i
\(471\) 0 0
\(472\) 2.80781 4.86327i 0.129240 0.223850i
\(473\) 7.30949 + 1.18289i 0.336091 + 0.0543896i
\(474\) 0 0
\(475\) 17.5971 + 7.83475i 0.807412 + 0.359483i
\(476\) −10.4312 32.1039i −0.478112 1.47148i
\(477\) 0 0
\(478\) −13.5158 9.81979i −0.618197 0.449147i
\(479\) −2.28875 + 21.7760i −0.104576 + 0.994972i 0.808863 + 0.587997i \(0.200083\pi\)
−0.913439 + 0.406975i \(0.866584\pi\)
\(480\) 0 0
\(481\) 22.8047 + 4.84729i 1.03980 + 0.221017i
\(482\) −1.23203 11.7219i −0.0561172 0.533920i
\(483\) 0 0
\(484\) −10.1708 + 13.8029i −0.462310 + 0.627407i
\(485\) −8.95046 −0.406420
\(486\) 0 0
\(487\) 1.01084 + 3.11106i 0.0458057 + 0.140975i 0.971344 0.237679i \(-0.0763867\pi\)
−0.925538 + 0.378655i \(0.876387\pi\)
\(488\) −9.44506 + 2.00761i −0.427558 + 0.0908802i
\(489\) 0 0
\(490\) −5.58764 + 2.48778i −0.252424 + 0.112386i
\(491\) 4.83373 + 5.36841i 0.218143 + 0.242273i 0.842277 0.539045i \(-0.181215\pi\)
−0.624134 + 0.781318i \(0.714548\pi\)
\(492\) 0 0
\(493\) 5.48781 + 2.44333i 0.247159 + 0.110042i
\(494\) −9.13071 −0.410810
\(495\) 0 0
\(496\) −0.665390 −0.0298769
\(497\) 22.5328 + 10.0323i 1.01074 + 0.450009i
\(498\) 0 0
\(499\) 9.92622 + 11.0242i 0.444359 + 0.493511i 0.923162 0.384412i \(-0.125596\pi\)
−0.478803 + 0.877922i \(0.658929\pi\)
\(500\) −13.9174 + 6.19642i −0.622405 + 0.277112i
\(501\) 0 0
\(502\) −14.2161 + 3.02172i −0.634494 + 0.134866i
\(503\) 10.1918 + 31.3671i 0.454430 + 1.39859i 0.871803 + 0.489856i \(0.162951\pi\)
−0.417374 + 0.908735i \(0.637049\pi\)
\(504\) 0 0
\(505\) 1.96673 0.0875181
\(506\) 0.259440 4.65138i 0.0115335 0.206779i
\(507\) 0 0
\(508\) −1.24660 11.8606i −0.0553090 0.526230i
\(509\) 37.8244 + 8.03982i 1.67654 + 0.356359i 0.945410 0.325884i \(-0.105662\pi\)
0.731126 + 0.682243i \(0.238995\pi\)
\(510\) 0 0
\(511\) −4.76404 + 45.3268i −0.210749 + 2.00514i
\(512\) −13.1198 9.53213i −0.579821 0.421264i
\(513\) 0 0
\(514\) −1.06004 3.26247i −0.0467564 0.143901i
\(515\) −2.74165 1.22066i −0.120812 0.0537888i
\(516\) 0 0
\(517\) 6.51820 + 42.0685i 0.286670 + 1.85017i
\(518\) −11.2908 + 19.5563i −0.496091 + 0.859255i
\(519\) 0 0
\(520\) 4.73037 5.25361i 0.207440 0.230386i
\(521\) 5.40297 16.6286i 0.236708 0.728514i −0.760182 0.649710i \(-0.774890\pi\)
0.996890 0.0788032i \(-0.0251099\pi\)
\(522\) 0 0
\(523\) −11.7211 8.51591i −0.512530 0.372375i 0.301253 0.953544i \(-0.402595\pi\)
−0.813782 + 0.581170i \(0.802595\pi\)
\(524\) 8.17061 1.73672i 0.356935 0.0758688i
\(525\) 0 0
\(526\) −1.93726 18.4318i −0.0844683 0.803663i
\(527\) −1.19296 + 2.06627i −0.0519663 + 0.0900082i
\(528\) 0 0
\(529\) 9.26470 + 16.0469i 0.402813 + 0.697693i
\(530\) −3.38542 + 2.45965i −0.147053 + 0.106840i
\(531\) 0 0
\(532\) −9.65216 + 29.7063i −0.418474 + 1.28793i
\(533\) −0.817130 + 7.77447i −0.0353938 + 0.336750i
\(534\) 0 0
\(535\) −7.67818 8.52748i −0.331956 0.368675i
\(536\) −22.5502 4.79319i −0.974021 0.207034i
\(537\) 0 0
\(538\) 1.00299 + 1.73722i 0.0432418 + 0.0748971i
\(539\) 7.16664 26.3913i 0.308689 1.13675i
\(540\) 0 0
\(541\) −26.7771 + 19.4547i −1.15124 + 0.836422i −0.988645 0.150272i \(-0.951985\pi\)
−0.162591 + 0.986694i \(0.551985\pi\)
\(542\) −11.2795 + 12.5272i −0.484498 + 0.538089i
\(543\) 0 0
\(544\) −29.1649 + 12.9850i −1.25043 + 0.556729i
\(545\) −2.41030 + 1.07314i −0.103246 + 0.0459681i
\(546\) 0 0
\(547\) 6.16546 6.84744i 0.263616 0.292775i −0.596776 0.802408i \(-0.703552\pi\)
0.860392 + 0.509633i \(0.170219\pi\)
\(548\) −21.0980 + 15.3286i −0.901262 + 0.654805i
\(549\) 0 0
\(550\) −2.16708 + 7.98032i −0.0924046 + 0.340282i
\(551\) −2.77927 4.81383i −0.118401 0.205076i
\(552\) 0 0
\(553\) 17.2427 + 3.66504i 0.733232 + 0.155853i
\(554\) −4.69605 5.21549i −0.199516 0.221585i
\(555\) 0 0
\(556\) 2.23863 21.2991i 0.0949388 0.903283i
\(557\) −11.4496 + 35.2384i −0.485137 + 1.49310i 0.346645 + 0.937996i \(0.387321\pi\)
−0.831782 + 0.555102i \(0.812679\pi\)
\(558\) 0 0
\(559\) 4.83697 3.51427i 0.204582 0.148638i
\(560\) −3.37202 5.84052i −0.142494 0.246807i
\(561\) 0 0
\(562\) −7.49703 + 12.9852i −0.316243 + 0.547749i
\(563\) −2.82165 26.8462i −0.118918 1.13143i −0.877407 0.479746i \(-0.840729\pi\)
0.758489 0.651686i \(-0.225938\pi\)
\(564\) 0 0
\(565\) −1.67376 + 0.355768i −0.0704155 + 0.0149673i
\(566\) 3.15870 + 2.29493i 0.132770 + 0.0964630i
\(567\) 0 0
\(568\) 4.61492 14.2033i 0.193638 0.595956i
\(569\) 18.3848 20.4184i 0.770733 0.855985i −0.222159 0.975011i \(-0.571310\pi\)
0.992891 + 0.119025i \(0.0379769\pi\)
\(570\) 0 0
\(571\) 19.5052 33.7840i 0.816266 1.41381i −0.0921492 0.995745i \(-0.529374\pi\)
0.908415 0.418069i \(-0.137293\pi\)
\(572\) 2.11974 + 13.6808i 0.0886310 + 0.572024i
\(573\) 0 0
\(574\) −6.91709 3.07969i −0.288714 0.128544i
\(575\) 2.45223 + 7.54719i 0.102265 + 0.314739i
\(576\) 0 0
\(577\) 23.5957 + 17.1433i 0.982302 + 0.713684i 0.958222 0.286026i \(-0.0923344\pi\)
0.0240800 + 0.999710i \(0.492334\pi\)
\(578\) −0.955807 + 9.09390i −0.0397563 + 0.378256i
\(579\) 0 0
\(580\) 1.84379 + 0.391910i 0.0765594 + 0.0162732i
\(581\) −0.196723 1.87169i −0.00816144 0.0776509i
\(582\) 0 0
\(583\) 1.04195 18.6807i 0.0431532 0.773674i
\(584\) 27.5954 1.14191
\(585\) 0 0
\(586\) −1.45632 4.48210i −0.0601602 0.185154i
\(587\) −4.97675 + 1.05784i −0.205412 + 0.0436618i −0.309469 0.950910i \(-0.600151\pi\)
0.104056 + 0.994571i \(0.466818\pi\)
\(588\) 0 0
\(589\) 2.01687 0.897969i 0.0831037 0.0370002i
\(590\) −1.17903 1.30945i −0.0485401 0.0539092i
\(591\) 0 0
\(592\) −12.3022 5.47729i −0.505617 0.225115i
\(593\) −3.46422 −0.142258 −0.0711292 0.997467i \(-0.522660\pi\)
−0.0711292 + 0.997467i \(0.522660\pi\)
\(594\) 0 0
\(595\) −24.1825 −0.991386
\(596\) 7.91653 + 3.52466i 0.324274 + 0.144376i
\(597\) 0 0
\(598\) −2.51700 2.79541i −0.102928 0.114313i
\(599\) −22.7243 + 10.1175i −0.928489 + 0.413390i −0.814547 0.580097i \(-0.803015\pi\)
−0.113942 + 0.993487i \(0.536348\pi\)
\(600\) 0 0
\(601\) −10.8263 + 2.30119i −0.441612 + 0.0938676i −0.423351 0.905966i \(-0.639146\pi\)
−0.0182611 + 0.999833i \(0.505813\pi\)
\(602\) 1.78951 + 5.50755i 0.0729351 + 0.224471i
\(603\) 0 0
\(604\) 0.255479 0.0103953
\(605\) 7.15276 + 9.98532i 0.290801 + 0.405961i
\(606\) 0 0
\(607\) 2.92272 + 27.8078i 0.118630 + 1.12869i 0.878211 + 0.478273i \(0.158737\pi\)
−0.759582 + 0.650412i \(0.774596\pi\)
\(608\) 28.8952 + 6.14186i 1.17185 + 0.249085i
\(609\) 0 0
\(610\) −0.316703 + 3.01323i −0.0128229 + 0.122002i
\(611\) 27.8087 + 20.2042i 1.12502 + 0.817375i
\(612\) 0 0
\(613\) 3.39680 + 10.4543i 0.137196 + 0.422245i 0.995925 0.0901845i \(-0.0287457\pi\)
−0.858729 + 0.512429i \(0.828746\pi\)
\(614\) −11.2499 5.00876i −0.454008 0.202137i
\(615\) 0 0
\(616\) −30.2217 4.89078i −1.21767 0.197055i
\(617\) 9.31311 16.1308i 0.374932 0.649401i −0.615385 0.788227i \(-0.710999\pi\)
0.990317 + 0.138826i \(0.0443328\pi\)
\(618\) 0 0
\(619\) 1.79895 1.99793i 0.0723057 0.0803036i −0.705906 0.708305i \(-0.749460\pi\)
0.778212 + 0.628001i \(0.216127\pi\)
\(620\) −0.231355 + 0.712036i −0.00929142 + 0.0285961i
\(621\) 0 0
\(622\) 3.69561 + 2.68502i 0.148180 + 0.107659i
\(623\) −61.4246 + 13.0562i −2.46093 + 0.523086i
\(624\) 0 0
\(625\) −0.820749 7.80890i −0.0328299 0.312356i
\(626\) 8.41222 14.5704i 0.336220 0.582350i
\(627\) 0 0
\(628\) 18.5896 + 32.1981i 0.741805 + 1.28484i
\(629\) −39.0652 + 28.3826i −1.55763 + 1.13169i
\(630\) 0 0
\(631\) −12.1224 + 37.3089i −0.482585 + 1.48524i 0.352863 + 0.935675i \(0.385208\pi\)
−0.835448 + 0.549569i \(0.814792\pi\)
\(632\) 1.11566 10.6148i 0.0443784 0.422233i
\(633\) 0 0
\(634\) −4.88047 5.42031i −0.193828 0.215268i
\(635\) −8.35695 1.77633i −0.331636 0.0704913i
\(636\) 0 0
\(637\) −11.0407 19.1230i −0.437447 0.757681i
\(638\) 1.85951 1.49549i 0.0736187 0.0592069i
\(639\) 0 0
\(640\) −9.96109 + 7.23716i −0.393747 + 0.286074i
\(641\) −17.2294 + 19.1352i −0.680521 + 0.755795i −0.980149 0.198261i \(-0.936471\pi\)
0.299628 + 0.954056i \(0.403137\pi\)
\(642\) 0 0
\(643\) −12.1794 + 5.42264i −0.480310 + 0.213848i −0.632586 0.774490i \(-0.718007\pi\)
0.152276 + 0.988338i \(0.451340\pi\)
\(644\) −11.7555 + 5.23386i −0.463230 + 0.206243i
\(645\) 0 0
\(646\) 12.6540 14.0537i 0.497866 0.552936i
\(647\) 19.2955 14.0190i 0.758585 0.551145i −0.139891 0.990167i \(-0.544675\pi\)
0.898476 + 0.439022i \(0.144675\pi\)
\(648\) 0 0
\(649\) 7.86876 0.385882i 0.308876 0.0151472i
\(650\) 3.33853 + 5.78250i 0.130948 + 0.226808i
\(651\) 0 0
\(652\) −6.39733 1.35979i −0.250539 0.0532537i
\(653\) −8.51464 9.45647i −0.333204 0.370060i 0.553140 0.833088i \(-0.313430\pi\)
−0.886344 + 0.463028i \(0.846763\pi\)
\(654\) 0 0
\(655\) 0.625511 5.95134i 0.0244407 0.232538i
\(656\) 1.39531 4.29433i 0.0544778 0.167666i
\(657\) 0 0
\(658\) −26.9350 + 19.5694i −1.05004 + 0.762896i
\(659\) −13.6263 23.6015i −0.530806 0.919383i −0.999354 0.0359452i \(-0.988556\pi\)
0.468547 0.883438i \(-0.344777\pi\)
\(660\) 0 0
\(661\) −21.8220 + 37.7968i −0.848777 + 1.47012i 0.0335234 + 0.999438i \(0.489327\pi\)
−0.882300 + 0.470687i \(0.844006\pi\)
\(662\) 0.257641 + 2.45129i 0.0100135 + 0.0952723i
\(663\) 0 0
\(664\) −1.11461 + 0.236917i −0.0432551 + 0.00919415i
\(665\) 18.1030 + 13.1526i 0.702003 + 0.510035i
\(666\) 0 0
\(667\) 0.707636 2.17788i 0.0273998 0.0843278i
\(668\) 16.5209 18.3483i 0.639212 0.709917i
\(669\) 0 0
\(670\) −3.61688 + 6.26462i −0.139732 + 0.242023i
\(671\) −9.54666 9.61102i −0.368545 0.371029i
\(672\) 0 0
\(673\) −24.3795 10.8545i −0.939761 0.418408i −0.121070 0.992644i \(-0.538633\pi\)
−0.818690 + 0.574236i \(0.805299\pi\)
\(674\) −6.60922 20.3411i −0.254578 0.783510i
\(675\) 0 0
\(676\) −7.34946 5.33970i −0.282672 0.205373i
\(677\) 2.83095 26.9347i 0.108802 1.03518i −0.794817 0.606849i \(-0.792433\pi\)
0.903620 0.428336i \(-0.140900\pi\)
\(678\) 0 0
\(679\) 30.6135 + 6.50711i 1.17484 + 0.249720i
\(680\) 1.53050 + 14.5617i 0.0586918 + 0.558415i
\(681\) 0 0
\(682\) 0.513524 + 0.796603i 0.0196638 + 0.0305035i
\(683\) 16.7343 0.640322 0.320161 0.947363i \(-0.396263\pi\)
0.320161 + 0.947363i \(0.396263\pi\)
\(684\) 0 0
\(685\) 5.77319 + 17.7681i 0.220582 + 0.678883i
\(686\) 3.15993 0.671665i 0.120647 0.0256443i
\(687\) 0 0
\(688\) −3.15485 + 1.40463i −0.120278 + 0.0535510i
\(689\) −10.1086 11.2268i −0.385108 0.427706i
\(690\) 0 0
\(691\) −34.2758 15.2606i −1.30391 0.580540i −0.367039 0.930205i \(-0.619629\pi\)
−0.936875 + 0.349665i \(0.886295\pi\)
\(692\) −4.05707 −0.154226
\(693\) 0 0
\(694\) 14.2978 0.542738
\(695\) −14.0161 6.24037i −0.531661 0.236711i
\(696\) 0 0
\(697\) −10.8338 12.0322i −0.410359 0.455750i
\(698\) −10.2078 + 4.54481i −0.386371 + 0.172024i
\(699\) 0 0
\(700\) 22.3423 4.74899i 0.844458 0.179495i
\(701\) −3.15219 9.70143i −0.119056 0.366418i 0.873715 0.486438i \(-0.161704\pi\)
−0.992771 + 0.120020i \(0.961704\pi\)
\(702\) 0 0
\(703\) 44.6811 1.68518
\(704\) −0.134839 + 2.41747i −0.00508193 + 0.0911117i
\(705\) 0 0
\(706\) 0.217408 + 2.06850i 0.00818225 + 0.0778489i
\(707\) −6.72685 1.42984i −0.252989 0.0537745i
\(708\) 0 0
\(709\) 1.51542 14.4183i 0.0569128 0.541489i −0.928503 0.371325i \(-0.878904\pi\)
0.985416 0.170164i \(-0.0544297\pi\)
\(710\) −3.79104 2.75435i −0.142275 0.103369i
\(711\) 0 0
\(712\) 11.7494 + 36.1610i 0.440329 + 1.35519i
\(713\) 0.830893 + 0.369938i 0.0311172 + 0.0138543i
\(714\) 0 0
\(715\) 9.79040 + 1.58438i 0.366140 + 0.0592525i
\(716\) −5.91364 + 10.2427i −0.221003 + 0.382789i
\(717\) 0 0
\(718\) −3.77337 + 4.19075i −0.140821 + 0.156397i
\(719\) −5.94135 + 18.2856i −0.221575 + 0.681938i 0.777046 + 0.629444i \(0.216717\pi\)
−0.998621 + 0.0524943i \(0.983283\pi\)
\(720\) 0 0
\(721\) 8.48991 + 6.16828i 0.316181 + 0.229719i
\(722\) −4.77016 + 1.01393i −0.177527 + 0.0377345i
\(723\) 0 0
\(724\) −0.391054 3.72063i −0.0145334 0.138276i
\(725\) −2.03241 + 3.52023i −0.0754818 + 0.130738i
\(726\) 0 0
\(727\) −0.363414 0.629451i −0.0134783 0.0233450i 0.859208 0.511627i \(-0.170957\pi\)
−0.872686 + 0.488282i \(0.837624\pi\)
\(728\) −19.9989 + 14.5300i −0.741207 + 0.538519i
\(729\) 0 0
\(730\) 2.67570 8.23495i 0.0990320 0.304789i
\(731\) −1.29439 + 12.3153i −0.0478746 + 0.455496i
\(732\) 0 0
\(733\) −1.25521 1.39406i −0.0463624 0.0514907i 0.719518 0.694474i \(-0.244363\pi\)
−0.765880 + 0.642984i \(0.777696\pi\)
\(734\) 7.15496 + 1.52083i 0.264095 + 0.0561350i
\(735\) 0 0
\(736\) 6.08497 + 10.5395i 0.224295 + 0.388490i
\(737\) −11.4891 30.2333i −0.423206 1.11366i
\(738\) 0 0
\(739\) 42.5402 30.9073i 1.56487 1.13694i 0.632993 0.774157i \(-0.281826\pi\)
0.931873 0.362784i \(-0.118174\pi\)
\(740\) −10.1387 + 11.2602i −0.372706 + 0.413932i
\(741\) 0 0
\(742\) 13.3674 5.95157i 0.490734 0.218489i
\(743\) 30.4510 13.5577i 1.11714 0.497383i 0.236720 0.971578i \(-0.423928\pi\)
0.880420 + 0.474195i \(0.157261\pi\)
\(744\) 0 0
\(745\) 4.15399 4.61348i 0.152190 0.169025i
\(746\) −5.91558 + 4.29792i −0.216585 + 0.157358i
\(747\) 0 0
\(748\) −23.9948 15.6973i −0.877338 0.573949i
\(749\) 20.0623 + 34.7489i 0.733060 + 1.26970i
\(750\) 0 0
\(751\) 22.8535 + 4.85766i 0.833937 + 0.177259i 0.605043 0.796193i \(-0.293156\pi\)
0.228894 + 0.973451i \(0.426489\pi\)
\(752\) −13.2852 14.7547i −0.484460 0.538047i
\(753\) 0 0
\(754\) 0.201404 1.91623i 0.00733470 0.0697851i
\(755\) 0.0565572 0.174065i 0.00205833 0.00633488i
\(756\) 0 0
\(757\) 27.3472 19.8689i 0.993952 0.722148i 0.0331687 0.999450i \(-0.489440\pi\)
0.960783 + 0.277302i \(0.0894401\pi\)
\(758\) −8.43250 14.6055i −0.306282 0.530496i
\(759\) 0 0
\(760\) 6.77421 11.7333i 0.245726 0.425611i
\(761\) 2.10227 + 20.0017i 0.0762071 + 0.725062i 0.964195 + 0.265195i \(0.0854363\pi\)
−0.887988 + 0.459867i \(0.847897\pi\)
\(762\) 0 0
\(763\) 9.02421 1.91815i 0.326698 0.0694419i
\(764\) 20.8294 + 15.1335i 0.753583 + 0.547510i
\(765\) 0 0
\(766\) 2.48699 7.65417i 0.0898586 0.276556i
\(767\) 4.25651 4.72733i 0.153694 0.170694i
\(768\) 0 0
\(769\) −0.313500 + 0.542997i −0.0113051 + 0.0195810i −0.871623 0.490178i \(-0.836932\pi\)
0.860318 + 0.509759i \(0.170265\pi\)
\(770\) −4.38984 + 8.54447i −0.158199 + 0.307921i
\(771\) 0 0
\(772\) 11.5836 + 5.15733i 0.416902 + 0.185617i
\(773\) −8.88046 27.3313i −0.319408 0.983037i −0.973902 0.226970i \(-0.927118\pi\)
0.654494 0.756067i \(-0.272882\pi\)
\(774\) 0 0
\(775\) −1.30613 0.948959i −0.0469176 0.0340876i
\(776\) 1.98080 18.8460i 0.0711064 0.676533i
\(777\) 0 0
\(778\) 9.32539 + 1.98217i 0.334331 + 0.0710643i
\(779\) 1.56601 + 14.8996i 0.0561083 + 0.533834i
\(780\) 0 0
\(781\) 20.2556 5.35460i 0.724801 0.191603i
\(782\) 7.79085 0.278600
\(783\) 0 0
\(784\) 3.94131 + 12.1301i 0.140761 + 0.433218i
\(785\) 26.0528 5.53769i 0.929864 0.197649i
\(786\) 0 0
\(787\) −12.8837 + 5.73618i −0.459254 + 0.204473i −0.623305 0.781979i \(-0.714210\pi\)
0.164051 + 0.986452i \(0.447544\pi\)
\(788\) −23.8913 26.5339i −0.851091 0.945233i
\(789\) 0 0
\(790\) −3.05946 1.36216i −0.108851 0.0484634i
\(791\) 5.98345 0.212747
\(792\) 0 0
\(793\) −10.9382 −0.388426
\(794\) −3.05800 1.36151i −0.108524 0.0483181i
\(795\) 0 0
\(796\) −9.67008 10.7397i −0.342747 0.380659i
\(797\) −23.8935 + 10.6381i −0.846351 + 0.376820i −0.783642 0.621212i \(-0.786641\pi\)
−0.0627086 + 0.998032i \(0.519974\pi\)
\(798\) 0 0
\(799\) −69.6371 + 14.8018i −2.46358 + 0.523651i
\(800\) −6.67551 20.5451i −0.236015 0.726379i
\(801\) 0 0
\(802\) 12.0908 0.426939
\(803\) 20.9759 + 32.5388i 0.740223 + 1.14827i
\(804\) 0 0
\(805\) 0.963594 + 9.16798i 0.0339622 + 0.323129i
\(806\) 0.748559 + 0.159111i 0.0263669 + 0.00560445i
\(807\) 0 0
\(808\) −0.435249 + 4.14112i −0.0153120 + 0.145684i
\(809\) 12.8256 + 9.31836i 0.450925 + 0.327616i 0.789961 0.613157i \(-0.210101\pi\)
−0.339036 + 0.940773i \(0.610101\pi\)
\(810\) 0 0
\(811\) −11.2255 34.5484i −0.394179 1.21316i −0.929599 0.368573i \(-0.879846\pi\)
0.535420 0.844586i \(-0.320154\pi\)
\(812\) −6.02146 2.68093i −0.211312 0.0940820i
\(813\) 0 0
\(814\) 2.93699 + 18.9553i 0.102941 + 0.664383i
\(815\) −2.34269 + 4.05766i −0.0820608 + 0.142134i
\(816\) 0 0
\(817\) 7.66710 8.51517i 0.268238 0.297908i
\(818\) 3.37295 10.3809i 0.117932 0.362958i
\(819\) 0 0
\(820\) −4.11023 2.98626i −0.143535 0.104285i
\(821\) −15.9993 + 3.40076i −0.558379 + 0.118687i −0.478452 0.878113i \(-0.658802\pi\)
−0.0799271 + 0.996801i \(0.525469\pi\)
\(822\) 0 0
\(823\) 2.73598 + 26.0311i 0.0953703 + 0.907388i 0.932691 + 0.360676i \(0.117454\pi\)
−0.837321 + 0.546712i \(0.815879\pi\)
\(824\) 3.17696 5.50265i 0.110675 0.191694i
\(825\) 0 0
\(826\) 3.08070 + 5.33592i 0.107191 + 0.185661i
\(827\) 4.48139 3.25592i 0.155833 0.113219i −0.507136 0.861866i \(-0.669296\pi\)
0.662969 + 0.748647i \(0.269296\pi\)
\(828\) 0 0
\(829\) 5.71784 17.5977i 0.198589 0.611194i −0.801327 0.598227i \(-0.795872\pi\)
0.999916 0.0129672i \(-0.00412771\pi\)
\(830\) −0.0373740 + 0.355590i −0.00129727 + 0.0123427i
\(831\) 0 0
\(832\) 1.30816 + 1.45286i 0.0453523 + 0.0503688i
\(833\) 44.7346 + 9.50862i 1.54996 + 0.329454i
\(834\) 0 0
\(835\) −8.84388 15.3180i −0.306055 0.530103i
\(836\) 9.42492 + 24.8015i 0.325968 + 0.857776i
\(837\) 0 0
\(838\) −9.35505 + 6.79684i −0.323165 + 0.234793i
\(839\) 12.0211 13.3508i 0.415015 0.460921i −0.498999 0.866602i \(-0.666299\pi\)
0.914015 + 0.405681i \(0.132966\pi\)
\(840\) 0 0
\(841\) −25.4213 + 11.3183i −0.876595 + 0.390285i
\(842\) 2.76051 1.22906i 0.0951336 0.0423562i
\(843\) 0 0
\(844\) −4.39146 + 4.87721i −0.151160 + 0.167881i
\(845\) −5.26509 + 3.82531i −0.181125 + 0.131595i
\(846\) 0 0
\(847\) −17.2053 39.3532i −0.591182 1.35219i
\(848\) 4.36299 + 7.55692i 0.149826 + 0.259506i
\(849\) 0 0
\(850\) −13.5270 2.87526i −0.463973 0.0986206i
\(851\) 12.3169 + 13.6793i 0.422218 + 0.468921i
\(852\) 0 0
\(853\) −2.91771 + 27.7602i −0.0999006 + 0.950490i 0.823672 + 0.567067i \(0.191922\pi\)
−0.923573 + 0.383424i \(0.874745\pi\)
\(854\) 3.27389 10.0760i 0.112030 0.344794i
\(855\) 0 0
\(856\) 19.6546 14.2799i 0.671781 0.488077i
\(857\) −4.24983 7.36093i −0.145172 0.251445i 0.784265 0.620426i \(-0.213040\pi\)
−0.929437 + 0.368981i \(0.879707\pi\)
\(858\) 0 0
\(859\) −13.9259 + 24.1203i −0.475145 + 0.822974i −0.999595 0.0284667i \(-0.990938\pi\)
0.524450 + 0.851441i \(0.324271\pi\)
\(860\) 0.406165 + 3.86440i 0.0138501 + 0.131775i
\(861\) 0 0
\(862\) 8.11267 1.72440i 0.276318 0.0587333i
\(863\) 10.9978 + 7.99035i 0.374368 + 0.271995i 0.759020 0.651067i \(-0.225678\pi\)
−0.384652 + 0.923062i \(0.625678\pi\)
\(864\) 0 0
\(865\) −0.898141 + 2.76419i −0.0305377 + 0.0939854i
\(866\) 12.7515 14.1620i 0.433313 0.481243i
\(867\) 0 0
\(868\) 1.30897 2.26720i 0.0444293 0.0769538i
\(869\) 13.3643 6.75301i 0.453354 0.229080i
\(870\) 0 0
\(871\) −23.8573 10.6220i −0.808374 0.359911i
\(872\) −1.72617 5.31260i −0.0584555 0.179907i
\(873\) 0 0
\(874\) −5.83221 4.23735i −0.197278 0.143331i
\(875\) 3.98911 37.9538i 0.134856 1.28307i
\(876\) 0 0
\(877\) −35.3874 7.52182i −1.19495 0.253994i −0.432856 0.901463i \(-0.642494\pi\)
−0.762092 + 0.647469i \(0.775827\pi\)
\(878\) 0.285266 + 2.71413i 0.00962727 + 0.0915973i
\(879\) 0 0
\(880\) −5.34116 2.07089i −0.180051 0.0698098i
\(881\) −26.6423 −0.897601 −0.448800 0.893632i \(-0.648149\pi\)
−0.448800 + 0.893632i \(0.648149\pi\)
\(882\) 0 0
\(883\) −6.32757 19.4743i −0.212940 0.655361i −0.999293 0.0375844i \(-0.988034\pi\)
0.786354 0.617776i \(-0.211966\pi\)
\(884\) −22.6463 + 4.81361i −0.761676 + 0.161899i
\(885\) 0 0
\(886\) 12.8840 5.73634i 0.432847 0.192716i
\(887\) 21.4130 + 23.7815i 0.718977 + 0.798505i 0.986275 0.165109i \(-0.0527977\pi\)
−0.267299 + 0.963614i \(0.586131\pi\)
\(888\) 0 0
\(889\) 27.2921 + 12.1512i 0.915348 + 0.407539i
\(890\) 11.9303 0.399906
\(891\) 0 0
\(892\) 10.6911 0.357963
\(893\) 60.1807 + 26.7942i 2.01387 + 0.896633i
\(894\) 0 0
\(895\) 5.66951 + 6.29663i 0.189511 + 0.210473i
\(896\) 39.3317 17.5116i 1.31398 0.585022i
\(897\) 0 0
\(898\) 16.8266 3.57660i 0.561510 0.119353i
\(899\) 0.143966 + 0.443082i 0.00480153 + 0.0147776i
\(900\) 0 0
\(901\) 31.2892 1.04239
\(902\) −6.21801 + 1.64374i −0.207037 + 0.0547307i
\(903\) 0 0
\(904\) −0.378689 3.60298i −0.0125950 0.119833i
\(905\) −2.62154 0.557225i −0.0871429 0.0185228i
\(906\) 0 0
\(907\) 5.12715 48.7816i 0.170244 1.61977i −0.492082 0.870549i \(-0.663764\pi\)
0.662326 0.749216i \(-0.269569\pi\)
\(908\) −35.4717 25.7717i −1.17717 0.855265i
\(909\) 0 0
\(910\) 2.39689 + 7.37687i 0.0794561 + 0.244541i
\(911\) 21.3599 + 9.51002i 0.707684 + 0.315081i 0.728829 0.684695i \(-0.240065\pi\)
−0.0211457 + 0.999776i \(0.506731\pi\)
\(912\) 0 0
\(913\) −1.12659 1.13419i −0.0372849 0.0375362i
\(914\) 3.42253 5.92800i 0.113207 0.196081i
\(915\) 0 0
\(916\) 14.6376 16.2567i 0.483641 0.537137i
\(917\) −6.46615 + 19.9008i −0.213531 + 0.657181i
\(918\) 0 0
\(919\) 6.14797 + 4.46676i 0.202803 + 0.147345i 0.684551 0.728965i \(-0.259998\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(920\) 5.45959 1.16047i 0.179997 0.0382596i
\(921\) 0 0
\(922\) −1.76748 16.8165i −0.0582090 0.553821i
\(923\) 8.45857 14.6507i 0.278417 0.482233i
\(924\) 0 0
\(925\) −16.3371 28.2967i −0.537160 0.930389i
\(926\) 21.4202 15.5627i 0.703910 0.511421i
\(927\) 0 0
\(928\) −1.92634 + 5.92866i −0.0632352 + 0.194618i
\(929\) −1.55504 + 14.7953i −0.0510193 + 0.485417i 0.938942 + 0.344076i \(0.111808\pi\)
−0.989961 + 0.141340i \(0.954859\pi\)
\(930\) 0 0
\(931\) −28.3166 31.4487i −0.928038 1.03069i
\(932\) 22.1216 + 4.70209i 0.724618 + 0.154022i
\(933\) 0 0
\(934\) −5.77192 9.99727i −0.188863 0.327121i
\(935\) −16.0069 + 12.8733i −0.523482 + 0.421003i
\(936\) 0 0
\(937\) −14.4192 + 10.4762i −0.471056 + 0.342242i −0.797853 0.602853i \(-0.794031\pi\)
0.326797 + 0.945095i \(0.394031\pi\)
\(938\) 16.9254 18.7975i 0.552633 0.613761i
\(939\) 0 0
\(940\) −20.4082 + 9.08632i −0.665643 + 0.296363i
\(941\) −38.9710 + 17.3510i −1.27042 + 0.565627i −0.927530 0.373748i \(-0.878072\pi\)
−0.342890 + 0.939376i \(0.611406\pi\)
\(942\) 0 0
\(943\) −4.12989 + 4.58671i −0.134488 + 0.149364i
\(944\) −2.97257 + 2.15970i −0.0967491 + 0.0702923i
\(945\) 0 0
\(946\) 4.11641 + 2.69293i 0.133836 + 0.0875548i
\(947\) 3.44670 + 5.96986i 0.112003 + 0.193994i 0.916578 0.399857i \(-0.130940\pi\)
−0.804575 + 0.593851i \(0.797607\pi\)
\(948\) 0 0
\(949\) 30.5764 + 6.49921i 0.992551 + 0.210973i
\(950\) 8.56249 + 9.50961i 0.277804 + 0.308533i
\(951\) 0 0
\(952\) 5.35175 50.9185i 0.173451 1.65028i
\(953\) 7.31766 22.5214i 0.237042 0.729541i −0.759802 0.650155i \(-0.774704\pi\)
0.996844 0.0793863i \(-0.0252960\pi\)
\(954\) 0 0
\(955\) 14.9220 10.8415i 0.482866 0.350822i
\(956\) 19.5989 + 33.9463i 0.633874 + 1.09790i
\(957\) 0 0
\(958\) −7.27297 + 12.5972i −0.234979 + 0.406996i
\(959\) −6.82860 64.9698i −0.220507 2.09798i
\(960\) 0 0
\(961\) 30.1416 6.40679i 0.972309 0.206671i
\(962\) 12.5301 + 9.10366i 0.403987 + 0.293514i
\(963\) 0 0
\(964\) −8.54567 + 26.3009i −0.275238 + 0.847094i
\(965\) 6.07817 6.75050i 0.195663 0.217306i
\(966\) 0 0
\(967\) 15.5700 26.9680i 0.500696 0.867231i −0.499303 0.866427i \(-0.666411\pi\)
1.00000 0.000804082i \(-0.000255947\pi\)
\(968\) −22.6080 + 12.8510i −0.726647 + 0.413046i
\(969\) 0 0
\(970\) −5.43192 2.41845i −0.174408 0.0776516i
\(971\) −4.12687 12.7012i −0.132438 0.407601i 0.862745 0.505639i \(-0.168743\pi\)
−0.995183 + 0.0980383i \(0.968743\pi\)
\(972\) 0 0
\(973\) 43.4028 + 31.5340i 1.39143 + 1.01093i
\(974\) −0.227151 + 2.16119i −0.00727838 + 0.0692491i
\(975\) 0 0
\(976\) 6.17991 + 1.31358i 0.197814 + 0.0420467i
\(977\) −0.931968 8.86709i −0.0298163 0.283683i −0.999263 0.0383817i \(-0.987780\pi\)
0.969447 0.245302i \(-0.0788870\pi\)
\(978\) 0 0
\(979\) −33.7079 + 41.3411i −1.07731 + 1.32127i
\(980\) 14.3508 0.458421
\(981\) 0 0
\(982\) 1.48297 + 4.56411i 0.0473234 + 0.145647i
\(983\) −16.4901 + 3.50509i −0.525954 + 0.111795i −0.463234 0.886236i \(-0.653311\pi\)
−0.0627203 + 0.998031i \(0.519978\pi\)
\(984\) 0 0
\(985\) −23.3673 + 10.4038i −0.744544 + 0.331492i
\(986\) 2.67029 + 2.96565i 0.0850392 + 0.0944456i
\(987\) 0 0
\(988\) 19.5710 + 8.71358i 0.622637 + 0.277216i
\(989\) 4.72049 0.150103
\(990\) 0 0
\(991\) −33.5356 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(992\) −2.26187 1.00705i −0.0718146 0.0319739i
\(993\) 0 0
\(994\) 10.9641 + 12.1769i 0.347761 + 0.386228i
\(995\) −9.45801 + 4.21098i −0.299839 + 0.133497i
\(996\) 0 0
\(997\) 3.17279 0.674397i 0.100483 0.0213584i −0.157396 0.987536i \(-0.550310\pi\)
0.257879 + 0.966177i \(0.416976\pi\)
\(998\) 3.04532 + 9.37254i 0.0963980 + 0.296682i
\(999\) 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 297.2.n.b.91.6 72
3.2 odd 2 99.2.m.b.58.4 yes 72
9.2 odd 6 99.2.m.b.25.6 yes 72
9.4 even 3 891.2.f.e.487.4 36
9.5 odd 6 891.2.f.f.487.6 36
9.7 even 3 inner 297.2.n.b.289.4 72
11.4 even 5 inner 297.2.n.b.37.4 72
33.2 even 10 1089.2.e.o.364.8 36
33.20 odd 10 1089.2.e.p.364.11 36
33.26 odd 10 99.2.m.b.4.6 72
99.2 even 30 1089.2.e.o.727.8 36
99.4 even 15 891.2.f.e.730.4 36
99.13 odd 30 9801.2.a.cn.1.8 18
99.20 odd 30 1089.2.e.p.727.11 36
99.31 even 15 9801.2.a.cp.1.11 18
99.59 odd 30 891.2.f.f.730.6 36
99.68 even 30 9801.2.a.co.1.11 18
99.70 even 15 inner 297.2.n.b.235.6 72
99.86 odd 30 9801.2.a.cm.1.8 18
99.92 odd 30 99.2.m.b.70.4 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.6 72 33.26 odd 10
99.2.m.b.25.6 yes 72 9.2 odd 6
99.2.m.b.58.4 yes 72 3.2 odd 2
99.2.m.b.70.4 yes 72 99.92 odd 30
297.2.n.b.37.4 72 11.4 even 5 inner
297.2.n.b.91.6 72 1.1 even 1 trivial
297.2.n.b.235.6 72 99.70 even 15 inner
297.2.n.b.289.4 72 9.7 even 3 inner
891.2.f.e.487.4 36 9.4 even 3
891.2.f.e.730.4 36 99.4 even 15
891.2.f.f.487.6 36 9.5 odd 6
891.2.f.f.730.6 36 99.59 odd 30
1089.2.e.o.364.8 36 33.2 even 10
1089.2.e.o.727.8 36 99.2 even 30
1089.2.e.p.364.11 36 33.20 odd 10
1089.2.e.p.727.11 36 99.20 odd 30
9801.2.a.cm.1.8 18 99.86 odd 30
9801.2.a.cn.1.8 18 99.13 odd 30
9801.2.a.co.1.11 18 99.68 even 30
9801.2.a.cp.1.11 18 99.31 even 15