Properties

Label 630.2.p.a.433.3
Level $630$
Weight $2$
Character 630.433
Analytic conductor $5.031$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [630,2,Mod(307,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.307"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 433.3
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 630.433
Dual form 630.2.p.a.307.3

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.158513 + 2.23044i) q^{5} +(-0.941740 + 2.47247i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.46508 + 1.68925i) q^{10} -2.82843 q^{11} +(-4.23671 + 4.23671i) q^{13} +(1.08239 + 2.41421i) q^{14} -1.00000 q^{16} +(3.69552 + 3.69552i) q^{17} +1.39942 q^{19} +(2.23044 + 0.158513i) q^{20} +(-2.00000 + 2.00000i) q^{22} +(-0.414214 - 0.414214i) q^{23} +(-4.94975 - 0.707107i) q^{25} +5.99162i q^{26} +(2.47247 + 0.941740i) q^{28} -0.828427i q^{29} -1.53073i q^{31} +(-0.707107 + 0.707107i) q^{32} +5.22625 q^{34} +(-5.36543 - 2.49242i) q^{35} +(2.58579 - 2.58579i) q^{37} +(0.989538 - 0.989538i) q^{38} +(1.68925 - 1.46508i) q^{40} +3.69552i q^{41} +(4.00000 + 4.00000i) q^{43} +2.82843i q^{44} -0.585786 q^{46} +(-1.08239 - 1.08239i) q^{47} +(-5.22625 - 4.65685i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(4.23671 + 4.23671i) q^{52} +(8.24264 + 8.24264i) q^{53} +(0.448342 - 6.30864i) q^{55} +(2.41421 - 1.08239i) q^{56} +(-0.585786 - 0.585786i) q^{58} +9.23880 q^{59} +6.43996i q^{61} +(-1.08239 - 1.08239i) q^{62} +1.00000i q^{64} +(-8.77817 - 10.1213i) q^{65} +(10.4853 - 10.4853i) q^{67} +(3.69552 - 3.69552i) q^{68} +(-5.55634 + 2.03153i) q^{70} +0.585786 q^{71} +(4.14386 - 4.14386i) q^{73} -3.65685i q^{74} -1.39942i q^{76} +(2.66364 - 6.99321i) q^{77} -5.07107i q^{79} +(0.158513 - 2.23044i) q^{80} +(2.61313 + 2.61313i) q^{82} +(-5.31911 + 5.31911i) q^{83} +(-8.82843 + 7.65685i) q^{85} +5.65685 q^{86} +(2.00000 + 2.00000i) q^{88} -11.3492 q^{89} +(-6.48528 - 14.4650i) q^{91} +(-0.414214 + 0.414214i) q^{92} -1.53073 q^{94} +(-0.221825 + 3.12132i) q^{95} +(-4.59220 - 4.59220i) q^{97} +(-6.98841 + 0.402625i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{7} - 8 q^{16} - 16 q^{22} + 8 q^{23} + 8 q^{28} + 8 q^{35} + 32 q^{37} + 32 q^{43} - 16 q^{46} - 32 q^{50} + 32 q^{53} + 8 q^{56} - 16 q^{58} - 8 q^{65} + 16 q^{67} - 24 q^{70} + 16 q^{71} + 16 q^{77}+ \cdots - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) −0.158513 + 2.23044i −0.0708890 + 0.997484i
\(6\) 0 0
\(7\) −0.941740 + 2.47247i −0.355944 + 0.934507i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) 1.46508 + 1.68925i 0.463298 + 0.534187i
\(11\) −2.82843 −0.852803 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) −4.23671 + 4.23671i −1.17505 + 1.17505i −0.194064 + 0.980989i \(0.562167\pi\)
−0.980989 + 0.194064i \(0.937833\pi\)
\(14\) 1.08239 + 2.41421i 0.289281 + 0.645226i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.69552 + 3.69552i 0.896295 + 0.896295i 0.995106 0.0988114i \(-0.0315040\pi\)
−0.0988114 + 0.995106i \(0.531504\pi\)
\(18\) 0 0
\(19\) 1.39942 0.321048 0.160524 0.987032i \(-0.448682\pi\)
0.160524 + 0.987032i \(0.448682\pi\)
\(20\) 2.23044 + 0.158513i 0.498742 + 0.0354445i
\(21\) 0 0
\(22\) −2.00000 + 2.00000i −0.426401 + 0.426401i
\(23\) −0.414214 0.414214i −0.0863695 0.0863695i 0.662602 0.748972i \(-0.269452\pi\)
−0.748972 + 0.662602i \(0.769452\pi\)
\(24\) 0 0
\(25\) −4.94975 0.707107i −0.989949 0.141421i
\(26\) 5.99162i 1.17505i
\(27\) 0 0
\(28\) 2.47247 + 0.941740i 0.467254 + 0.177972i
\(29\) 0.828427i 0.153835i −0.997037 0.0769175i \(-0.975492\pi\)
0.997037 0.0769175i \(-0.0245078\pi\)
\(30\) 0 0
\(31\) 1.53073i 0.274928i −0.990507 0.137464i \(-0.956105\pi\)
0.990507 0.137464i \(-0.0438951\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 5.22625 0.896295
\(35\) −5.36543 2.49242i −0.906924 0.421295i
\(36\) 0 0
\(37\) 2.58579 2.58579i 0.425101 0.425101i −0.461855 0.886956i \(-0.652816\pi\)
0.886956 + 0.461855i \(0.152816\pi\)
\(38\) 0.989538 0.989538i 0.160524 0.160524i
\(39\) 0 0
\(40\) 1.68925 1.46508i 0.267093 0.231649i
\(41\) 3.69552i 0.577143i 0.957458 + 0.288571i \(0.0931803\pi\)
−0.957458 + 0.288571i \(0.906820\pi\)
\(42\) 0 0
\(43\) 4.00000 + 4.00000i 0.609994 + 0.609994i 0.942944 0.332950i \(-0.108044\pi\)
−0.332950 + 0.942944i \(0.608044\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0 0
\(46\) −0.585786 −0.0863695
\(47\) −1.08239 1.08239i −0.157883 0.157883i 0.623745 0.781628i \(-0.285610\pi\)
−0.781628 + 0.623745i \(0.785610\pi\)
\(48\) 0 0
\(49\) −5.22625 4.65685i −0.746607 0.665265i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 4.23671 + 4.23671i 0.587527 + 0.587527i
\(53\) 8.24264 + 8.24264i 1.13221 + 1.13221i 0.989808 + 0.142405i \(0.0454837\pi\)
0.142405 + 0.989808i \(0.454516\pi\)
\(54\) 0 0
\(55\) 0.448342 6.30864i 0.0604544 0.850657i
\(56\) 2.41421 1.08239i 0.322613 0.144641i
\(57\) 0 0
\(58\) −0.585786 0.585786i −0.0769175 0.0769175i
\(59\) 9.23880 1.20279 0.601394 0.798952i \(-0.294612\pi\)
0.601394 + 0.798952i \(0.294612\pi\)
\(60\) 0 0
\(61\) 6.43996i 0.824552i 0.911059 + 0.412276i \(0.135266\pi\)
−0.911059 + 0.412276i \(0.864734\pi\)
\(62\) −1.08239 1.08239i −0.137464 0.137464i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −8.77817 10.1213i −1.08880 1.25540i
\(66\) 0 0
\(67\) 10.4853 10.4853i 1.28098 1.28098i 0.340871 0.940110i \(-0.389278\pi\)
0.940110 0.340871i \(-0.110722\pi\)
\(68\) 3.69552 3.69552i 0.448147 0.448147i
\(69\) 0 0
\(70\) −5.55634 + 2.03153i −0.664109 + 0.242814i
\(71\) 0.585786 0.0695201 0.0347600 0.999396i \(-0.488933\pi\)
0.0347600 + 0.999396i \(0.488933\pi\)
\(72\) 0 0
\(73\) 4.14386 4.14386i 0.485002 0.485002i −0.421723 0.906725i \(-0.638574\pi\)
0.906725 + 0.421723i \(0.138574\pi\)
\(74\) 3.65685i 0.425101i
\(75\) 0 0
\(76\) 1.39942i 0.160524i
\(77\) 2.66364 6.99321i 0.303550 0.796950i
\(78\) 0 0
\(79\) 5.07107i 0.570540i −0.958447 0.285270i \(-0.907917\pi\)
0.958447 0.285270i \(-0.0920832\pi\)
\(80\) 0.158513 2.23044i 0.0177223 0.249371i
\(81\) 0 0
\(82\) 2.61313 + 2.61313i 0.288571 + 0.288571i
\(83\) −5.31911 + 5.31911i −0.583848 + 0.583848i −0.935958 0.352111i \(-0.885464\pi\)
0.352111 + 0.935958i \(0.385464\pi\)
\(84\) 0 0
\(85\) −8.82843 + 7.65685i −0.957577 + 0.830502i
\(86\) 5.65685 0.609994
\(87\) 0 0
\(88\) 2.00000 + 2.00000i 0.213201 + 0.213201i
\(89\) −11.3492 −1.20301 −0.601506 0.798869i \(-0.705432\pi\)
−0.601506 + 0.798869i \(0.705432\pi\)
\(90\) 0 0
\(91\) −6.48528 14.4650i −0.679842 1.51635i
\(92\) −0.414214 + 0.414214i −0.0431847 + 0.0431847i
\(93\) 0 0
\(94\) −1.53073 −0.157883
\(95\) −0.221825 + 3.12132i −0.0227588 + 0.320241i
\(96\) 0 0
\(97\) −4.59220 4.59220i −0.466267 0.466267i 0.434436 0.900703i \(-0.356948\pi\)
−0.900703 + 0.434436i \(0.856948\pi\)
\(98\) −6.98841 + 0.402625i −0.705936 + 0.0406713i
\(99\) 0 0
\(100\) −0.707107 + 4.94975i −0.0707107 + 0.494975i
\(101\) 2.74444i 0.273082i −0.990634 0.136541i \(-0.956401\pi\)
0.990634 0.136541i \(-0.0435986\pi\)
\(102\) 0 0
\(103\) −10.0042 + 10.0042i −0.985739 + 0.985739i −0.999900 0.0141603i \(-0.995492\pi\)
0.0141603 + 0.999900i \(0.495492\pi\)
\(104\) 5.99162 0.587527
\(105\) 0 0
\(106\) 11.6569 1.13221
\(107\) 3.65685 3.65685i 0.353521 0.353521i −0.507897 0.861418i \(-0.669577\pi\)
0.861418 + 0.507897i \(0.169577\pi\)
\(108\) 0 0
\(109\) 12.1421i 1.16301i 0.813544 + 0.581503i \(0.197535\pi\)
−0.813544 + 0.581503i \(0.802465\pi\)
\(110\) −4.14386 4.77791i −0.395102 0.455556i
\(111\) 0 0
\(112\) 0.941740 2.47247i 0.0889861 0.233627i
\(113\) −1.17157 1.17157i −0.110212 0.110212i 0.649850 0.760062i \(-0.274832\pi\)
−0.760062 + 0.649850i \(0.774832\pi\)
\(114\) 0 0
\(115\) 0.989538 0.858221i 0.0922749 0.0800296i
\(116\) −0.828427 −0.0769175
\(117\) 0 0
\(118\) 6.53281 6.53281i 0.601394 0.601394i
\(119\) −12.6173 + 5.65685i −1.15662 + 0.518563i
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) 4.55374 + 4.55374i 0.412276 + 0.412276i
\(123\) 0 0
\(124\) −1.53073 −0.137464
\(125\) 2.36176 10.9280i 0.211242 0.977434i
\(126\) 0 0
\(127\) 3.58579 3.58579i 0.318187 0.318187i −0.529883 0.848071i \(-0.677764\pi\)
0.848071 + 0.529883i \(0.177764\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −13.3640 0.949747i −1.17210 0.0832984i
\(131\) 14.6508i 1.28004i −0.768357 0.640021i \(-0.778926\pi\)
0.768357 0.640021i \(-0.221074\pi\)
\(132\) 0 0
\(133\) −1.31789 + 3.46002i −0.114275 + 0.300022i
\(134\) 14.8284i 1.28098i
\(135\) 0 0
\(136\) 5.22625i 0.448147i
\(137\) 8.17157 8.17157i 0.698145 0.698145i −0.265866 0.964010i \(-0.585658\pi\)
0.964010 + 0.265866i \(0.0856577\pi\)
\(138\) 0 0
\(139\) −8.60474 −0.729845 −0.364922 0.931038i \(-0.618905\pi\)
−0.364922 + 0.931038i \(0.618905\pi\)
\(140\) −2.49242 + 5.36543i −0.210648 + 0.453462i
\(141\) 0 0
\(142\) 0.414214 0.414214i 0.0347600 0.0347600i
\(143\) 11.9832 11.9832i 1.00209 1.00209i
\(144\) 0 0
\(145\) 1.84776 + 0.131316i 0.153448 + 0.0109052i
\(146\) 5.86030i 0.485002i
\(147\) 0 0
\(148\) −2.58579 2.58579i −0.212550 0.212550i
\(149\) 17.3137i 1.41839i 0.705010 + 0.709197i \(0.250942\pi\)
−0.705010 + 0.709197i \(0.749058\pi\)
\(150\) 0 0
\(151\) −8.82843 −0.718447 −0.359224 0.933252i \(-0.616958\pi\)
−0.359224 + 0.933252i \(0.616958\pi\)
\(152\) −0.989538 0.989538i −0.0802621 0.0802621i
\(153\) 0 0
\(154\) −3.06147 6.82843i −0.246700 0.550250i
\(155\) 3.41421 + 0.242641i 0.274236 + 0.0194894i
\(156\) 0 0
\(157\) 10.2283 + 10.2283i 0.816310 + 0.816310i 0.985571 0.169261i \(-0.0541382\pi\)
−0.169261 + 0.985571i \(0.554138\pi\)
\(158\) −3.58579 3.58579i −0.285270 0.285270i
\(159\) 0 0
\(160\) −1.46508 1.68925i −0.115824 0.133547i
\(161\) 1.41421 0.634051i 0.111456 0.0499702i
\(162\) 0 0
\(163\) 13.6569 + 13.6569i 1.06969 + 1.06969i 0.997383 + 0.0723048i \(0.0230354\pi\)
0.0723048 + 0.997383i \(0.476965\pi\)
\(164\) 3.69552 0.288571
\(165\) 0 0
\(166\) 7.52235i 0.583848i
\(167\) 1.71644 + 1.71644i 0.132822 + 0.132822i 0.770392 0.637570i \(-0.220060\pi\)
−0.637570 + 0.770392i \(0.720060\pi\)
\(168\) 0 0
\(169\) 22.8995i 1.76150i
\(170\) −0.828427 + 11.6569i −0.0635375 + 0.894040i
\(171\) 0 0
\(172\) 4.00000 4.00000i 0.304997 0.304997i
\(173\) −13.2898 + 13.2898i −1.01040 + 1.01040i −0.0104595 + 0.999945i \(0.503329\pi\)
−0.999945 + 0.0104595i \(0.996671\pi\)
\(174\) 0 0
\(175\) 6.40968 11.5722i 0.484526 0.874777i
\(176\) 2.82843 0.213201
\(177\) 0 0
\(178\) −8.02509 + 8.02509i −0.601506 + 0.601506i
\(179\) 13.6569i 1.02076i −0.859949 0.510381i \(-0.829505\pi\)
0.859949 0.510381i \(-0.170495\pi\)
\(180\) 0 0
\(181\) 8.79045i 0.653389i 0.945130 + 0.326695i \(0.105935\pi\)
−0.945130 + 0.326695i \(0.894065\pi\)
\(182\) −14.8141 5.64255i −1.09810 0.418253i
\(183\) 0 0
\(184\) 0.585786i 0.0431847i
\(185\) 5.35757 + 6.17733i 0.393896 + 0.454166i
\(186\) 0 0
\(187\) −10.4525 10.4525i −0.764363 0.764363i
\(188\) −1.08239 + 1.08239i −0.0789416 + 0.0789416i
\(189\) 0 0
\(190\) 2.05025 + 2.36396i 0.148741 + 0.171500i
\(191\) −1.75736 −0.127158 −0.0635790 0.997977i \(-0.520251\pi\)
−0.0635790 + 0.997977i \(0.520251\pi\)
\(192\) 0 0
\(193\) 8.24264 + 8.24264i 0.593318 + 0.593318i 0.938526 0.345208i \(-0.112192\pi\)
−0.345208 + 0.938526i \(0.612192\pi\)
\(194\) −6.49435 −0.466267
\(195\) 0 0
\(196\) −4.65685 + 5.22625i −0.332632 + 0.373304i
\(197\) −0.585786 + 0.585786i −0.0417356 + 0.0417356i −0.727667 0.685931i \(-0.759395\pi\)
0.685931 + 0.727667i \(0.259395\pi\)
\(198\) 0 0
\(199\) 28.0334 1.98724 0.993618 0.112798i \(-0.0359814\pi\)
0.993618 + 0.112798i \(0.0359814\pi\)
\(200\) 3.00000 + 4.00000i 0.212132 + 0.282843i
\(201\) 0 0
\(202\) −1.94061 1.94061i −0.136541 0.136541i
\(203\) 2.04826 + 0.780163i 0.143760 + 0.0547567i
\(204\) 0 0
\(205\) −8.24264 0.585786i −0.575691 0.0409131i
\(206\) 14.1480i 0.985739i
\(207\) 0 0
\(208\) 4.23671 4.23671i 0.293763 0.293763i
\(209\) −3.95815 −0.273791
\(210\) 0 0
\(211\) −10.3431 −0.712052 −0.356026 0.934476i \(-0.615868\pi\)
−0.356026 + 0.934476i \(0.615868\pi\)
\(212\) 8.24264 8.24264i 0.566107 0.566107i
\(213\) 0 0
\(214\) 5.17157i 0.353521i
\(215\) −9.55582 + 8.28772i −0.651702 + 0.565218i
\(216\) 0 0
\(217\) 3.78470 + 1.44155i 0.256922 + 0.0978590i
\(218\) 8.58579 + 8.58579i 0.581503 + 0.581503i
\(219\) 0 0
\(220\) −6.30864 0.448342i −0.425329 0.0302272i
\(221\) −31.3137 −2.10639
\(222\) 0 0
\(223\) 6.75699 6.75699i 0.452481 0.452481i −0.443696 0.896177i \(-0.646333\pi\)
0.896177 + 0.443696i \(0.146333\pi\)
\(224\) −1.08239 2.41421i −0.0723204 0.161306i
\(225\) 0 0
\(226\) −1.65685 −0.110212
\(227\) 8.38057 + 8.38057i 0.556238 + 0.556238i 0.928234 0.371996i \(-0.121327\pi\)
−0.371996 + 0.928234i \(0.621327\pi\)
\(228\) 0 0
\(229\) 7.70806 0.509363 0.254682 0.967025i \(-0.418029\pi\)
0.254682 + 0.967025i \(0.418029\pi\)
\(230\) 0.0928546 1.30656i 0.00612265 0.0861522i
\(231\) 0 0
\(232\) −0.585786 + 0.585786i −0.0384588 + 0.0384588i
\(233\) −3.00000 3.00000i −0.196537 0.196537i 0.601977 0.798513i \(-0.294380\pi\)
−0.798513 + 0.601977i \(0.794380\pi\)
\(234\) 0 0
\(235\) 2.58579 2.24264i 0.168678 0.146294i
\(236\) 9.23880i 0.601394i
\(237\) 0 0
\(238\) −4.92177 + 12.9218i −0.319031 + 0.837594i
\(239\) 6.48528i 0.419498i −0.977755 0.209749i \(-0.932735\pi\)
0.977755 0.209749i \(-0.0672647\pi\)
\(240\) 0 0
\(241\) 6.75699i 0.435256i 0.976032 + 0.217628i \(0.0698319\pi\)
−0.976032 + 0.217628i \(0.930168\pi\)
\(242\) −2.12132 + 2.12132i −0.136364 + 0.136364i
\(243\) 0 0
\(244\) 6.43996 0.412276
\(245\) 11.2153 10.9187i 0.716517 0.697569i
\(246\) 0 0
\(247\) −5.92893 + 5.92893i −0.377249 + 0.377249i
\(248\) −1.08239 + 1.08239i −0.0687320 + 0.0687320i
\(249\) 0 0
\(250\) −6.05728 9.39731i −0.383096 0.594338i
\(251\) 14.0936i 0.889582i −0.895634 0.444791i \(-0.853278\pi\)
0.895634 0.444791i \(-0.146722\pi\)
\(252\) 0 0
\(253\) 1.17157 + 1.17157i 0.0736562 + 0.0736562i
\(254\) 5.07107i 0.318187i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 7.83938 + 7.83938i 0.489007 + 0.489007i 0.907993 0.418986i \(-0.137614\pi\)
−0.418986 + 0.907993i \(0.637614\pi\)
\(258\) 0 0
\(259\) 3.95815 + 8.82843i 0.245948 + 0.548572i
\(260\) −10.1213 + 8.77817i −0.627698 + 0.544399i
\(261\) 0 0
\(262\) −10.3596 10.3596i −0.640021 0.640021i
\(263\) 19.4142 + 19.4142i 1.19713 + 1.19713i 0.975022 + 0.222110i \(0.0712944\pi\)
0.222110 + 0.975022i \(0.428706\pi\)
\(264\) 0 0
\(265\) −19.6913 + 17.0782i −1.20963 + 1.04910i
\(266\) 1.51472 + 3.37849i 0.0928734 + 0.207149i
\(267\) 0 0
\(268\) −10.4853 10.4853i −0.640490 0.640490i
\(269\) 26.8966 1.63992 0.819958 0.572424i \(-0.193997\pi\)
0.819958 + 0.572424i \(0.193997\pi\)
\(270\) 0 0
\(271\) 18.7402i 1.13839i −0.822203 0.569194i \(-0.807255\pi\)
0.822203 0.569194i \(-0.192745\pi\)
\(272\) −3.69552 3.69552i −0.224074 0.224074i
\(273\) 0 0
\(274\) 11.5563i 0.698145i
\(275\) 14.0000 + 2.00000i 0.844232 + 0.120605i
\(276\) 0 0
\(277\) −1.75736 + 1.75736i −0.105589 + 0.105589i −0.757928 0.652338i \(-0.773788\pi\)
0.652338 + 0.757928i \(0.273788\pi\)
\(278\) −6.08447 + 6.08447i −0.364922 + 0.364922i
\(279\) 0 0
\(280\) 2.03153 + 5.55634i 0.121407 + 0.332055i
\(281\) 5.65685 0.337460 0.168730 0.985662i \(-0.446033\pi\)
0.168730 + 0.985662i \(0.446033\pi\)
\(282\) 0 0
\(283\) 3.15432 3.15432i 0.187505 0.187505i −0.607112 0.794617i \(-0.707672\pi\)
0.794617 + 0.607112i \(0.207672\pi\)
\(284\) 0.585786i 0.0347600i
\(285\) 0 0
\(286\) 16.9469i 1.00209i
\(287\) −9.13707 3.48022i −0.539344 0.205431i
\(288\) 0 0
\(289\) 10.3137i 0.606689i
\(290\) 1.39942 1.21371i 0.0821766 0.0712714i
\(291\) 0 0
\(292\) −4.14386 4.14386i −0.242501 0.242501i
\(293\) 2.38896 2.38896i 0.139564 0.139564i −0.633873 0.773437i \(-0.718536\pi\)
0.773437 + 0.633873i \(0.218536\pi\)
\(294\) 0 0
\(295\) −1.46447 + 20.6066i −0.0852645 + 1.19976i
\(296\) −3.65685 −0.212550
\(297\) 0 0
\(298\) 12.2426 + 12.2426i 0.709197 + 0.709197i
\(299\) 3.50981 0.202977
\(300\) 0 0
\(301\) −13.6569 + 6.12293i −0.787168 + 0.352920i
\(302\) −6.24264 + 6.24264i −0.359224 + 0.359224i
\(303\) 0 0
\(304\) −1.39942 −0.0802621
\(305\) −14.3640 1.02082i −0.822478 0.0584517i
\(306\) 0 0
\(307\) 23.1626 + 23.1626i 1.32196 + 1.32196i 0.912186 + 0.409776i \(0.134393\pi\)
0.409776 + 0.912186i \(0.365607\pi\)
\(308\) −6.99321 2.66364i −0.398475 0.151775i
\(309\) 0 0
\(310\) 2.58579 2.24264i 0.146863 0.127373i
\(311\) 3.43289i 0.194661i 0.995252 + 0.0973305i \(0.0310304\pi\)
−0.995252 + 0.0973305i \(0.968970\pi\)
\(312\) 0 0
\(313\) −6.75699 + 6.75699i −0.381927 + 0.381927i −0.871796 0.489869i \(-0.837045\pi\)
0.489869 + 0.871796i \(0.337045\pi\)
\(314\) 14.4650 0.816310
\(315\) 0 0
\(316\) −5.07107 −0.285270
\(317\) −21.8995 + 21.8995i −1.23000 + 1.23000i −0.266035 + 0.963963i \(0.585714\pi\)
−0.963963 + 0.266035i \(0.914286\pi\)
\(318\) 0 0
\(319\) 2.34315i 0.131191i
\(320\) −2.23044 0.158513i −0.124686 0.00886113i
\(321\) 0 0
\(322\) 0.551658 1.44834i 0.0307427 0.0807129i
\(323\) 5.17157 + 5.17157i 0.287754 + 0.287754i
\(324\) 0 0
\(325\) 23.9665 17.9749i 1.32942 0.997066i
\(326\) 19.3137 1.06969
\(327\) 0 0
\(328\) 2.61313 2.61313i 0.144286 0.144286i
\(329\) 3.69552 1.65685i 0.203741 0.0913453i
\(330\) 0 0
\(331\) 23.3137 1.28144 0.640719 0.767776i \(-0.278637\pi\)
0.640719 + 0.767776i \(0.278637\pi\)
\(332\) 5.31911 + 5.31911i 0.291924 + 0.291924i
\(333\) 0 0
\(334\) 2.42742 0.132822
\(335\) 21.7248 + 25.0489i 1.18695 + 1.36857i
\(336\) 0 0
\(337\) 3.75736 3.75736i 0.204676 0.204676i −0.597324 0.802000i \(-0.703769\pi\)
0.802000 + 0.597324i \(0.203769\pi\)
\(338\) −16.1924 16.1924i −0.880750 0.880750i
\(339\) 0 0
\(340\) 7.65685 + 8.82843i 0.415251 + 0.478789i
\(341\) 4.32957i 0.234459i
\(342\) 0 0
\(343\) 16.4357 8.53622i 0.887445 0.460913i
\(344\) 5.65685i 0.304997i
\(345\) 0 0
\(346\) 18.7946i 1.01040i
\(347\) 5.31371 5.31371i 0.285255 0.285255i −0.549946 0.835200i \(-0.685352\pi\)
0.835200 + 0.549946i \(0.185352\pi\)
\(348\) 0 0
\(349\) 2.66752 0.142789 0.0713945 0.997448i \(-0.477255\pi\)
0.0713945 + 0.997448i \(0.477255\pi\)
\(350\) −3.65046 12.7151i −0.195125 0.679651i
\(351\) 0 0
\(352\) 2.00000 2.00000i 0.106600 0.106600i
\(353\) −8.47343 + 8.47343i −0.450995 + 0.450995i −0.895685 0.444690i \(-0.853314\pi\)
0.444690 + 0.895685i \(0.353314\pi\)
\(354\) 0 0
\(355\) −0.0928546 + 1.30656i −0.00492821 + 0.0693452i
\(356\) 11.3492i 0.601506i
\(357\) 0 0
\(358\) −9.65685 9.65685i −0.510381 0.510381i
\(359\) 16.9706i 0.895672i −0.894116 0.447836i \(-0.852195\pi\)
0.894116 0.447836i \(-0.147805\pi\)
\(360\) 0 0
\(361\) −17.0416 −0.896928
\(362\) 6.21579 + 6.21579i 0.326695 + 0.326695i
\(363\) 0 0
\(364\) −14.4650 + 6.48528i −0.758174 + 0.339921i
\(365\) 8.58579 + 9.89949i 0.449401 + 0.518163i
\(366\) 0 0
\(367\) 3.06147 + 3.06147i 0.159807 + 0.159807i 0.782481 0.622674i \(-0.213954\pi\)
−0.622674 + 0.782481i \(0.713954\pi\)
\(368\) 0.414214 + 0.414214i 0.0215924 + 0.0215924i
\(369\) 0 0
\(370\) 8.15640 + 0.579658i 0.424031 + 0.0301350i
\(371\) −28.1421 + 12.6173i −1.46107 + 0.655057i
\(372\) 0 0
\(373\) −15.0711 15.0711i −0.780350 0.780350i 0.199539 0.979890i \(-0.436055\pi\)
−0.979890 + 0.199539i \(0.936055\pi\)
\(374\) −14.7821 −0.764363
\(375\) 0 0
\(376\) 1.53073i 0.0789416i
\(377\) 3.50981 + 3.50981i 0.180764 + 0.180764i
\(378\) 0 0
\(379\) 6.14214i 0.315500i −0.987479 0.157750i \(-0.949576\pi\)
0.987479 0.157750i \(-0.0504241\pi\)
\(380\) 3.12132 + 0.221825i 0.160120 + 0.0113794i
\(381\) 0 0
\(382\) −1.24264 + 1.24264i −0.0635790 + 0.0635790i
\(383\) 10.6382 10.6382i 0.543587 0.543587i −0.380991 0.924579i \(-0.624417\pi\)
0.924579 + 0.380991i \(0.124417\pi\)
\(384\) 0 0
\(385\) 15.1757 + 7.04961i 0.773427 + 0.359282i
\(386\) 11.6569 0.593318
\(387\) 0 0
\(388\) −4.59220 + 4.59220i −0.233134 + 0.233134i
\(389\) 0.142136i 0.00720656i 0.999994 + 0.00360328i \(0.00114696\pi\)
−0.999994 + 0.00360328i \(0.998853\pi\)
\(390\) 0 0
\(391\) 3.06147i 0.154825i
\(392\) 0.402625 + 6.98841i 0.0203356 + 0.352968i
\(393\) 0 0
\(394\) 0.828427i 0.0417356i
\(395\) 11.3107 + 0.803828i 0.569104 + 0.0404450i
\(396\) 0 0
\(397\) 1.12085 + 1.12085i 0.0562540 + 0.0562540i 0.734674 0.678420i \(-0.237335\pi\)
−0.678420 + 0.734674i \(0.737335\pi\)
\(398\) 19.8226 19.8226i 0.993618 0.993618i
\(399\) 0 0
\(400\) 4.94975 + 0.707107i 0.247487 + 0.0353553i
\(401\) 19.7574 0.986635 0.493318 0.869849i \(-0.335784\pi\)
0.493318 + 0.869849i \(0.335784\pi\)
\(402\) 0 0
\(403\) 6.48528 + 6.48528i 0.323055 + 0.323055i
\(404\) −2.74444 −0.136541
\(405\) 0 0
\(406\) 2.00000 0.896683i 0.0992583 0.0445016i
\(407\) −7.31371 + 7.31371i −0.362527 + 0.362527i
\(408\) 0 0
\(409\) −24.9719 −1.23478 −0.617392 0.786656i \(-0.711811\pi\)
−0.617392 + 0.786656i \(0.711811\pi\)
\(410\) −6.24264 + 5.41421i −0.308302 + 0.267389i
\(411\) 0 0
\(412\) 10.0042 + 10.0042i 0.492870 + 0.492870i
\(413\) −8.70054 + 22.8427i −0.428126 + 1.12401i
\(414\) 0 0
\(415\) −11.0208 12.7071i −0.540991 0.623767i
\(416\) 5.99162i 0.293763i
\(417\) 0 0
\(418\) −2.79884 + 2.79884i −0.136895 + 0.136895i
\(419\) −11.5893 −0.566174 −0.283087 0.959094i \(-0.591358\pi\)
−0.283087 + 0.959094i \(0.591358\pi\)
\(420\) 0 0
\(421\) 17.7990 0.867470 0.433735 0.901041i \(-0.357195\pi\)
0.433735 + 0.901041i \(0.357195\pi\)
\(422\) −7.31371 + 7.31371i −0.356026 + 0.356026i
\(423\) 0 0
\(424\) 11.6569i 0.566107i
\(425\) −15.6788 20.9050i −0.760531 1.01404i
\(426\) 0 0
\(427\) −15.9226 6.06477i −0.770550 0.293495i
\(428\) −3.65685 3.65685i −0.176761 0.176761i
\(429\) 0 0
\(430\) −0.896683 + 12.6173i −0.0432419 + 0.608460i
\(431\) −5.65685 −0.272481 −0.136241 0.990676i \(-0.543502\pi\)
−0.136241 + 0.990676i \(0.543502\pi\)
\(432\) 0 0
\(433\) −10.4525 + 10.4525i −0.502315 + 0.502315i −0.912157 0.409841i \(-0.865584\pi\)
0.409841 + 0.912157i \(0.365584\pi\)
\(434\) 3.69552 1.65685i 0.177391 0.0795315i
\(435\) 0 0
\(436\) 12.1421 0.581503
\(437\) −0.579658 0.579658i −0.0277288 0.0277288i
\(438\) 0 0
\(439\) −13.8854 −0.662713 −0.331357 0.943506i \(-0.607506\pi\)
−0.331357 + 0.943506i \(0.607506\pi\)
\(440\) −4.77791 + 4.14386i −0.227778 + 0.197551i
\(441\) 0 0
\(442\) −22.1421 + 22.1421i −1.05319 + 1.05319i
\(443\) 4.14214 + 4.14214i 0.196799 + 0.196799i 0.798626 0.601827i \(-0.205560\pi\)
−0.601827 + 0.798626i \(0.705560\pi\)
\(444\) 0 0
\(445\) 1.79899 25.3137i 0.0852803 1.19998i
\(446\) 9.55582i 0.452481i
\(447\) 0 0
\(448\) −2.47247 0.941740i −0.116813 0.0444930i
\(449\) 25.6569i 1.21082i 0.795913 + 0.605411i \(0.206991\pi\)
−0.795913 + 0.605411i \(0.793009\pi\)
\(450\) 0 0
\(451\) 10.4525i 0.492189i
\(452\) −1.17157 + 1.17157i −0.0551062 + 0.0551062i
\(453\) 0 0
\(454\) 11.8519 0.556238
\(455\) 33.2915 12.1722i 1.56073 0.570639i
\(456\) 0 0
\(457\) −1.65685 + 1.65685i −0.0775044 + 0.0775044i −0.744796 0.667292i \(-0.767453\pi\)
0.667292 + 0.744796i \(0.267453\pi\)
\(458\) 5.45042 5.45042i 0.254682 0.254682i
\(459\) 0 0
\(460\) −0.858221 0.989538i −0.0400148 0.0461374i
\(461\) 34.0250i 1.58470i 0.610064 + 0.792352i \(0.291144\pi\)
−0.610064 + 0.792352i \(0.708856\pi\)
\(462\) 0 0
\(463\) −12.9706 12.9706i −0.602793 0.602793i 0.338260 0.941053i \(-0.390162\pi\)
−0.941053 + 0.338260i \(0.890162\pi\)
\(464\) 0.828427i 0.0384588i
\(465\) 0 0
\(466\) −4.24264 −0.196537
\(467\) −17.4337 17.4337i −0.806734 0.806734i 0.177404 0.984138i \(-0.443230\pi\)
−0.984138 + 0.177404i \(0.943230\pi\)
\(468\) 0 0
\(469\) 16.0502 + 35.7990i 0.741128 + 1.65304i
\(470\) 0.242641 3.41421i 0.0111922 0.157486i
\(471\) 0 0
\(472\) −6.53281 6.53281i −0.300697 0.300697i
\(473\) −11.3137 11.3137i −0.520205 0.520205i
\(474\) 0 0
\(475\) −6.92676 0.989538i −0.317822 0.0454031i
\(476\) 5.65685 + 12.6173i 0.259281 + 0.578312i
\(477\) 0 0
\(478\) −4.58579 4.58579i −0.209749 0.209749i
\(479\) 11.0866 0.506558 0.253279 0.967393i \(-0.418491\pi\)
0.253279 + 0.967393i \(0.418491\pi\)
\(480\) 0 0
\(481\) 21.9105i 0.999032i
\(482\) 4.77791 + 4.77791i 0.217628 + 0.217628i
\(483\) 0 0
\(484\) 3.00000i 0.136364i
\(485\) 10.9706 9.51472i 0.498148 0.432041i
\(486\) 0 0
\(487\) 1.10051 1.10051i 0.0498686 0.0498686i −0.681733 0.731601i \(-0.738773\pi\)
0.731601 + 0.681733i \(0.238773\pi\)
\(488\) 4.55374 4.55374i 0.206138 0.206138i
\(489\) 0 0
\(490\) 0.209720 15.6511i 0.00947418 0.707043i
\(491\) −25.1716 −1.13598 −0.567989 0.823036i \(-0.692278\pi\)
−0.567989 + 0.823036i \(0.692278\pi\)
\(492\) 0 0
\(493\) 3.06147 3.06147i 0.137882 0.137882i
\(494\) 8.38478i 0.377249i
\(495\) 0 0
\(496\) 1.53073i 0.0687320i
\(497\) −0.551658 + 1.44834i −0.0247453 + 0.0649670i
\(498\) 0 0
\(499\) 7.51472i 0.336405i −0.985752 0.168203i \(-0.946204\pi\)
0.985752 0.168203i \(-0.0537963\pi\)
\(500\) −10.9280 2.36176i −0.488717 0.105621i
\(501\) 0 0
\(502\) −9.96570 9.96570i −0.444791 0.444791i
\(503\) −18.1062 + 18.1062i −0.807314 + 0.807314i −0.984227 0.176912i \(-0.943389\pi\)
0.176912 + 0.984227i \(0.443389\pi\)
\(504\) 0 0
\(505\) 6.12132 + 0.435029i 0.272395 + 0.0193585i
\(506\) 1.65685 0.0736562
\(507\) 0 0
\(508\) −3.58579 3.58579i −0.159094 0.159094i
\(509\) −14.4650 −0.641152 −0.320576 0.947223i \(-0.603876\pi\)
−0.320576 + 0.947223i \(0.603876\pi\)
\(510\) 0 0
\(511\) 6.34315 + 14.1480i 0.280604 + 0.625872i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 11.0866 0.489007
\(515\) −20.7279 23.8995i −0.913381 1.05314i
\(516\) 0 0
\(517\) 3.06147 + 3.06147i 0.134643 + 0.134643i
\(518\) 9.04148 + 3.44381i 0.397260 + 0.151312i
\(519\) 0 0
\(520\) −0.949747 + 13.3640i −0.0416492 + 0.586048i
\(521\) 36.6925i 1.60753i −0.594947 0.803765i \(-0.702827\pi\)
0.594947 0.803765i \(-0.297173\pi\)
\(522\) 0 0
\(523\) 1.75490 1.75490i 0.0767366 0.0767366i −0.667697 0.744433i \(-0.732720\pi\)
0.744433 + 0.667697i \(0.232720\pi\)
\(524\) −14.6508 −0.640021
\(525\) 0 0
\(526\) 27.4558 1.19713
\(527\) 5.65685 5.65685i 0.246416 0.246416i
\(528\) 0 0
\(529\) 22.6569i 0.985081i
\(530\) −1.84776 + 25.9999i −0.0802615 + 1.12937i
\(531\) 0 0
\(532\) 3.46002 + 1.31789i 0.150011 + 0.0571377i
\(533\) −15.6569 15.6569i −0.678174 0.678174i
\(534\) 0 0
\(535\) 7.57675 + 8.73606i 0.327571 + 0.377693i
\(536\) −14.8284 −0.640490
\(537\) 0 0
\(538\) 19.0188 19.0188i 0.819958 0.819958i
\(539\) 14.7821 + 13.1716i 0.636709 + 0.567340i
\(540\) 0 0
\(541\) 10.9706 0.471661 0.235831 0.971794i \(-0.424219\pi\)
0.235831 + 0.971794i \(0.424219\pi\)
\(542\) −13.2513 13.2513i −0.569194 0.569194i
\(543\) 0 0
\(544\) −5.22625 −0.224074
\(545\) −27.0823 1.92468i −1.16008 0.0824443i
\(546\) 0 0
\(547\) −30.6274 + 30.6274i −1.30953 + 1.30953i −0.387783 + 0.921751i \(0.626759\pi\)
−0.921751 + 0.387783i \(0.873241\pi\)
\(548\) −8.17157 8.17157i −0.349072 0.349072i
\(549\) 0 0
\(550\) 11.3137 8.48528i 0.482418 0.361814i
\(551\) 1.15932i 0.0493885i
\(552\) 0 0
\(553\) 12.5381 + 4.77563i 0.533173 + 0.203080i
\(554\) 2.48528i 0.105589i
\(555\) 0 0
\(556\) 8.60474i 0.364922i
\(557\) 26.7279 26.7279i 1.13250 1.13250i 0.142738 0.989761i \(-0.454409\pi\)
0.989761 0.142738i \(-0.0455906\pi\)
\(558\) 0 0
\(559\) −33.8937 −1.43355
\(560\) 5.36543 + 2.49242i 0.226731 + 0.105324i
\(561\) 0 0
\(562\) 4.00000 4.00000i 0.168730 0.168730i
\(563\) −3.54827 + 3.54827i −0.149542 + 0.149542i −0.777913 0.628372i \(-0.783722\pi\)
0.628372 + 0.777913i \(0.283722\pi\)
\(564\) 0 0
\(565\) 2.79884 2.42742i 0.117748 0.102122i
\(566\) 4.46088i 0.187505i
\(567\) 0 0
\(568\) −0.414214 0.414214i −0.0173800 0.0173800i
\(569\) 1.41421i 0.0592869i 0.999561 + 0.0296435i \(0.00943719\pi\)
−0.999561 + 0.0296435i \(0.990563\pi\)
\(570\) 0 0
\(571\) −25.4558 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(572\) −11.9832 11.9832i −0.501044 0.501044i
\(573\) 0 0
\(574\) −8.92177 + 4.00000i −0.372387 + 0.166957i
\(575\) 1.75736 + 2.34315i 0.0732869 + 0.0977159i
\(576\) 0 0
\(577\) −26.3170 26.3170i −1.09559 1.09559i −0.994920 0.100670i \(-0.967901\pi\)
−0.100670 0.994920i \(-0.532099\pi\)
\(578\) 7.29289 + 7.29289i 0.303344 + 0.303344i
\(579\) 0 0
\(580\) 0.131316 1.84776i 0.00545261 0.0767240i
\(581\) −8.14214 18.1606i −0.337793 0.753427i
\(582\) 0 0
\(583\) −23.3137 23.3137i −0.965555 0.965555i
\(584\) −5.86030 −0.242501
\(585\) 0 0
\(586\) 3.37849i 0.139564i
\(587\) −16.0886 16.0886i −0.664049 0.664049i 0.292283 0.956332i \(-0.405585\pi\)
−0.956332 + 0.292283i \(0.905585\pi\)
\(588\) 0 0
\(589\) 2.14214i 0.0882652i
\(590\) 13.5355 + 15.6066i 0.557249 + 0.642514i
\(591\) 0 0
\(592\) −2.58579 + 2.58579i −0.106275 + 0.106275i
\(593\) 22.8841 22.8841i 0.939737 0.939737i −0.0585480 0.998285i \(-0.518647\pi\)
0.998285 + 0.0585480i \(0.0186471\pi\)
\(594\) 0 0
\(595\) −10.6173 29.0388i −0.435266 1.19048i
\(596\) 17.3137 0.709197
\(597\) 0 0
\(598\) 2.48181 2.48181i 0.101489 0.101489i
\(599\) 18.5269i 0.756989i 0.925604 + 0.378495i \(0.123558\pi\)
−0.925604 + 0.378495i \(0.876442\pi\)
\(600\) 0 0
\(601\) 16.5754i 0.676126i −0.941123 0.338063i \(-0.890228\pi\)
0.941123 0.338063i \(-0.109772\pi\)
\(602\) −5.32729 + 13.9864i −0.217124 + 0.570044i
\(603\) 0 0
\(604\) 8.82843i 0.359224i
\(605\) 0.475538 6.69133i 0.0193334 0.272041i
\(606\) 0 0
\(607\) −21.5391 21.5391i −0.874243 0.874243i 0.118688 0.992932i \(-0.462131\pi\)
−0.992932 + 0.118688i \(0.962131\pi\)
\(608\) −0.989538 + 0.989538i −0.0401311 + 0.0401311i
\(609\) 0 0
\(610\) −10.8787 + 9.43503i −0.440465 + 0.382013i
\(611\) 9.17157 0.371042
\(612\) 0 0
\(613\) 19.8995 + 19.8995i 0.803733 + 0.803733i 0.983677 0.179944i \(-0.0575916\pi\)
−0.179944 + 0.983677i \(0.557592\pi\)
\(614\) 32.7569 1.32196
\(615\) 0 0
\(616\) −6.82843 + 3.06147i −0.275125 + 0.123350i
\(617\) 28.4853 28.4853i 1.14677 1.14677i 0.159591 0.987183i \(-0.448982\pi\)
0.987183 0.159591i \(-0.0510176\pi\)
\(618\) 0 0
\(619\) −0.688444 −0.0276709 −0.0138354 0.999904i \(-0.504404\pi\)
−0.0138354 + 0.999904i \(0.504404\pi\)
\(620\) 0.242641 3.41421i 0.00974468 0.137118i
\(621\) 0 0
\(622\) 2.42742 + 2.42742i 0.0973305 + 0.0973305i
\(623\) 10.6880 28.0606i 0.428205 1.12422i
\(624\) 0 0
\(625\) 24.0000 + 7.00000i 0.960000 + 0.280000i
\(626\) 9.55582i 0.381927i
\(627\) 0 0
\(628\) 10.2283 10.2283i 0.408155 0.408155i
\(629\) 19.1116 0.762031
\(630\) 0 0
\(631\) 41.3553 1.64633 0.823165 0.567802i \(-0.192206\pi\)
0.823165 + 0.567802i \(0.192206\pi\)
\(632\) −3.58579 + 3.58579i −0.142635 + 0.142635i
\(633\) 0 0
\(634\) 30.9706i 1.23000i
\(635\) 7.42950 + 8.56628i 0.294831 + 0.339943i
\(636\) 0 0
\(637\) 41.8719 2.41237i 1.65902 0.0955818i
\(638\) 1.65685 + 1.65685i 0.0655955 + 0.0655955i
\(639\) 0 0
\(640\) −1.68925 + 1.46508i −0.0667733 + 0.0579122i
\(641\) 37.2132 1.46983 0.734917 0.678158i \(-0.237221\pi\)
0.734917 + 0.678158i \(0.237221\pi\)
\(642\) 0 0
\(643\) −20.9435 + 20.9435i −0.825930 + 0.825930i −0.986951 0.161021i \(-0.948521\pi\)
0.161021 + 0.986951i \(0.448521\pi\)
\(644\) −0.634051 1.41421i −0.0249851 0.0557278i
\(645\) 0 0
\(646\) 7.31371 0.287754
\(647\) −23.8896 23.8896i −0.939195 0.939195i 0.0590593 0.998254i \(-0.481190\pi\)
−0.998254 + 0.0590593i \(0.981190\pi\)
\(648\) 0 0
\(649\) −26.1313 −1.02574
\(650\) 4.23671 29.6570i 0.166178 1.16324i
\(651\) 0 0
\(652\) 13.6569 13.6569i 0.534844 0.534844i
\(653\) −8.72792 8.72792i −0.341550 0.341550i 0.515400 0.856950i \(-0.327643\pi\)
−0.856950 + 0.515400i \(0.827643\pi\)
\(654\) 0 0
\(655\) 32.6777 + 2.32233i 1.27682 + 0.0907410i
\(656\) 3.69552i 0.144286i
\(657\) 0 0
\(658\) 1.44155 3.78470i 0.0561976 0.147543i
\(659\) 29.6569i 1.15527i −0.816296 0.577634i \(-0.803976\pi\)
0.816296 0.577634i \(-0.196024\pi\)
\(660\) 0 0
\(661\) 47.5390i 1.84905i −0.381118 0.924526i \(-0.624461\pi\)
0.381118 0.924526i \(-0.375539\pi\)
\(662\) 16.4853 16.4853i 0.640719 0.640719i
\(663\) 0 0
\(664\) 7.52235 0.291924
\(665\) −7.50848 3.48793i −0.291166 0.135256i
\(666\) 0 0
\(667\) −0.343146 + 0.343146i −0.0132867 + 0.0132867i
\(668\) 1.71644 1.71644i 0.0664112 0.0664112i
\(669\) 0 0
\(670\) 33.0740 + 2.35049i 1.27776 + 0.0908075i
\(671\) 18.2150i 0.703181i
\(672\) 0 0
\(673\) −22.7990 22.7990i −0.878836 0.878836i 0.114578 0.993414i \(-0.463448\pi\)
−0.993414 + 0.114578i \(0.963448\pi\)
\(674\) 5.31371i 0.204676i
\(675\) 0 0
\(676\) −22.8995 −0.880750
\(677\) 22.4742 + 22.4742i 0.863754 + 0.863754i 0.991772 0.128018i \(-0.0408615\pi\)
−0.128018 + 0.991772i \(0.540862\pi\)
\(678\) 0 0
\(679\) 15.6788 7.02944i 0.601695 0.269765i
\(680\) 11.6569 + 0.828427i 0.447020 + 0.0317687i
\(681\) 0 0
\(682\) 3.06147 + 3.06147i 0.117230 + 0.117230i
\(683\) 25.3137 + 25.3137i 0.968602 + 0.968602i 0.999522 0.0309197i \(-0.00984363\pi\)
−0.0309197 + 0.999522i \(0.509844\pi\)
\(684\) 0 0
\(685\) 16.9309 + 19.5215i 0.646897 + 0.745879i
\(686\) 5.58579 17.6578i 0.213266 0.674179i
\(687\) 0 0
\(688\) −4.00000 4.00000i −0.152499 0.152499i
\(689\) −69.8434 −2.66082
\(690\) 0 0
\(691\) 25.1033i 0.954973i −0.878639 0.477487i \(-0.841548\pi\)
0.878639 0.477487i \(-0.158452\pi\)
\(692\) 13.2898 + 13.2898i 0.505202 + 0.505202i
\(693\) 0 0
\(694\) 7.51472i 0.285255i
\(695\) 1.36396 19.1924i 0.0517380 0.728009i
\(696\) 0 0
\(697\) −13.6569 + 13.6569i −0.517290 + 0.517290i
\(698\) 1.88622 1.88622i 0.0713945 0.0713945i
\(699\) 0 0
\(700\) −11.5722 6.40968i −0.437388 0.242263i
\(701\) 13.1127 0.495260 0.247630 0.968855i \(-0.420348\pi\)
0.247630 + 0.968855i \(0.420348\pi\)
\(702\) 0 0
\(703\) 3.61859 3.61859i 0.136478 0.136478i
\(704\) 2.82843i 0.106600i
\(705\) 0 0
\(706\) 11.9832i 0.450995i
\(707\) 6.78556 + 2.58455i 0.255197 + 0.0972020i
\(708\) 0 0
\(709\) 41.3137i 1.55157i 0.630998 + 0.775784i \(0.282646\pi\)
−0.630998 + 0.775784i \(0.717354\pi\)
\(710\) 0.858221 + 0.989538i 0.0322085 + 0.0371367i
\(711\) 0 0
\(712\) 8.02509 + 8.02509i 0.300753 + 0.300753i
\(713\) −0.634051 + 0.634051i −0.0237454 + 0.0237454i
\(714\) 0 0
\(715\) 24.8284 + 28.6274i 0.928531 + 1.07060i
\(716\) −13.6569 −0.510381
\(717\) 0 0
\(718\) −12.0000 12.0000i −0.447836 0.447836i
\(719\) −43.7122 −1.63019 −0.815094 0.579328i \(-0.803315\pi\)
−0.815094 + 0.579328i \(0.803315\pi\)
\(720\) 0 0
\(721\) −15.3137 34.1563i −0.570312 1.27205i
\(722\) −12.0503 + 12.0503i −0.448464 + 0.448464i
\(723\) 0 0
\(724\) 8.79045 0.326695
\(725\) −0.585786 + 4.10051i −0.0217556 + 0.152289i
\(726\) 0 0
\(727\) −22.8841 22.8841i −0.848724 0.848724i 0.141250 0.989974i \(-0.454888\pi\)
−0.989974 + 0.141250i \(0.954888\pi\)
\(728\) −5.64255 + 14.8141i −0.209127 + 0.549048i
\(729\) 0 0
\(730\) 13.0711 + 0.928932i 0.483782 + 0.0343813i
\(731\) 29.5641i 1.09347i
\(732\) 0 0
\(733\) 21.9489 21.9489i 0.810703 0.810703i −0.174037 0.984739i \(-0.555681\pi\)
0.984739 + 0.174037i \(0.0556811\pi\)
\(734\) 4.32957 0.159807
\(735\) 0 0
\(736\) 0.585786 0.0215924
\(737\) −29.6569 + 29.6569i −1.09242 + 1.09242i
\(738\) 0 0
\(739\) 9.65685i 0.355233i 0.984100 + 0.177617i \(0.0568387\pi\)
−0.984100 + 0.177617i \(0.943161\pi\)
\(740\) 6.17733 5.35757i 0.227083 0.196948i
\(741\) 0 0
\(742\) −10.9777 + 28.8213i −0.403005 + 1.05806i
\(743\) −27.0416 27.0416i −0.992061 0.992061i 0.00790753 0.999969i \(-0.497483\pi\)
−0.999969 + 0.00790753i \(0.997483\pi\)
\(744\) 0 0
\(745\) −38.6172 2.74444i −1.41483 0.100549i
\(746\) −21.3137 −0.780350
\(747\) 0 0
\(748\) −10.4525 + 10.4525i −0.382181 + 0.382181i
\(749\) 5.59767 + 12.4853i 0.204534 + 0.456202i
\(750\) 0 0
\(751\) −2.48528 −0.0906892 −0.0453446 0.998971i \(-0.514439\pi\)
−0.0453446 + 0.998971i \(0.514439\pi\)
\(752\) 1.08239 + 1.08239i 0.0394708 + 0.0394708i
\(753\) 0 0
\(754\) 4.96362 0.180764
\(755\) 1.39942 19.6913i 0.0509300 0.716640i
\(756\) 0 0
\(757\) 7.89949 7.89949i 0.287112 0.287112i −0.548825 0.835937i \(-0.684925\pi\)
0.835937 + 0.548825i \(0.184925\pi\)
\(758\) −4.34315 4.34315i −0.157750 0.157750i
\(759\) 0 0
\(760\) 2.36396 2.05025i 0.0857499 0.0743705i
\(761\) 26.3939i 0.956778i 0.878148 + 0.478389i \(0.158779\pi\)
−0.878148 + 0.478389i \(0.841221\pi\)
\(762\) 0 0
\(763\) −30.0211 11.4347i −1.08684 0.413965i
\(764\) 1.75736i 0.0635790i
\(765\) 0 0
\(766\) 15.0447i 0.543587i
\(767\) −39.1421 + 39.1421i −1.41334 + 1.41334i
\(768\) 0 0
\(769\) −17.5809 −0.633984 −0.316992 0.948428i \(-0.602673\pi\)
−0.316992 + 0.948428i \(0.602673\pi\)
\(770\) 15.7157 5.74603i 0.566354 0.207073i
\(771\) 0 0
\(772\) 8.24264 8.24264i 0.296659 0.296659i
\(773\) 14.6892 14.6892i 0.528334 0.528334i −0.391741 0.920076i \(-0.628127\pi\)
0.920076 + 0.391741i \(0.128127\pi\)
\(774\) 0 0
\(775\) −1.08239 + 7.57675i −0.0388807 + 0.272165i
\(776\) 6.49435i 0.233134i
\(777\) 0 0
\(778\) 0.100505 + 0.100505i 0.00360328 + 0.00360328i
\(779\) 5.17157i 0.185291i
\(780\) 0 0
\(781\) −1.65685 −0.0592869
\(782\) −2.16478 2.16478i −0.0774125 0.0774125i
\(783\) 0 0
\(784\) 5.22625 + 4.65685i 0.186652 + 0.166316i
\(785\) −24.4350 + 21.1924i −0.872124 + 0.756389i
\(786\) 0 0
\(787\) 24.3764 + 24.3764i 0.868923 + 0.868923i 0.992353 0.123430i \(-0.0393895\pi\)
−0.123430 + 0.992353i \(0.539389\pi\)
\(788\) 0.585786 + 0.585786i 0.0208678 + 0.0208678i
\(789\) 0 0
\(790\) 8.56628 7.42950i 0.304775 0.264330i
\(791\) 4.00000 1.79337i 0.142224 0.0637648i
\(792\) 0 0
\(793\) −27.2843 27.2843i −0.968893 0.968893i
\(794\) 1.58513 0.0562540
\(795\) 0 0
\(796\) 28.0334i 0.993618i
\(797\) −16.6683 16.6683i −0.590421 0.590421i 0.347324 0.937745i \(-0.387090\pi\)
−0.937745 + 0.347324i \(0.887090\pi\)
\(798\) 0 0
\(799\) 8.00000i 0.283020i
\(800\) 4.00000 3.00000i 0.141421 0.106066i
\(801\) 0 0
\(802\) 13.9706 13.9706i 0.493318 0.493318i
\(803\) −11.7206 + 11.7206i −0.413611 + 0.413611i
\(804\) 0 0
\(805\) 1.19004 + 3.25483i 0.0419435 + 0.114718i
\(806\) 9.17157 0.323055
\(807\) 0 0
\(808\) −1.94061 + 1.94061i −0.0682705 + 0.0682705i
\(809\) 33.8995i 1.19184i 0.803043 + 0.595921i \(0.203213\pi\)
−0.803043 + 0.595921i \(0.796787\pi\)
\(810\) 0 0
\(811\) 50.6005i 1.77682i 0.459048 + 0.888411i \(0.348191\pi\)
−0.459048 + 0.888411i \(0.651809\pi\)
\(812\) 0.780163 2.04826i 0.0273784 0.0718800i
\(813\) 0 0
\(814\) 10.3431i 0.362527i
\(815\) −32.6256 + 28.2960i −1.14283 + 0.991167i
\(816\) 0 0
\(817\) 5.59767 + 5.59767i 0.195838 + 0.195838i
\(818\) −17.6578 + 17.6578i −0.617392 + 0.617392i
\(819\) 0 0
\(820\) −0.585786 + 8.24264i −0.0204565 + 0.287845i
\(821\) 34.4853 1.20354 0.601772 0.798668i \(-0.294461\pi\)
0.601772 + 0.798668i \(0.294461\pi\)
\(822\) 0 0
\(823\) −2.34315 2.34315i −0.0816769 0.0816769i 0.665088 0.746765i \(-0.268394\pi\)
−0.746765 + 0.665088i \(0.768394\pi\)
\(824\) 14.1480 0.492870
\(825\) 0 0
\(826\) 10.0000 + 22.3044i 0.347945 + 0.776070i
\(827\) 7.51472 7.51472i 0.261312 0.261312i −0.564275 0.825587i \(-0.690844\pi\)
0.825587 + 0.564275i \(0.190844\pi\)
\(828\) 0 0
\(829\) −40.8589 −1.41909 −0.709545 0.704660i \(-0.751099\pi\)
−0.709545 + 0.704660i \(0.751099\pi\)
\(830\) −16.7782 1.19239i −0.582379 0.0413884i
\(831\) 0 0
\(832\) −4.23671 4.23671i −0.146882 0.146882i
\(833\) −2.10422 36.5232i −0.0729069 1.26545i
\(834\) 0 0
\(835\) −4.10051 + 3.55635i −0.141904 + 0.123073i
\(836\) 3.95815i 0.136895i
\(837\) 0 0
\(838\) −8.19486 + 8.19486i −0.283087 + 0.283087i
\(839\) 20.6424 0.712654 0.356327 0.934361i \(-0.384029\pi\)
0.356327 + 0.934361i \(0.384029\pi\)
\(840\) 0 0
\(841\) 28.3137 0.976335
\(842\) 12.5858 12.5858i 0.433735 0.433735i
\(843\) 0 0
\(844\) 10.3431i 0.356026i
\(845\) 51.0760 + 3.62986i 1.75707 + 0.124871i
\(846\) 0 0
\(847\) 2.82522 7.41742i 0.0970757 0.254866i
\(848\) −8.24264 8.24264i −0.283053 0.283053i
\(849\) 0 0
\(850\) −25.8686 3.69552i −0.887287 0.126755i
\(851\) −2.14214 −0.0734315
\(852\) 0 0
\(853\) 26.7268 26.7268i 0.915110 0.915110i −0.0815587 0.996669i \(-0.525990\pi\)
0.996669 + 0.0815587i \(0.0259898\pi\)
\(854\) −15.5474 + 6.97056i −0.532022 + 0.238528i
\(855\) 0 0
\(856\) −5.17157 −0.176761
\(857\) −11.4580 11.4580i −0.391397 0.391397i 0.483788 0.875185i \(-0.339261\pi\)
−0.875185 + 0.483788i \(0.839261\pi\)
\(858\) 0 0
\(859\) 40.6732 1.38775 0.693876 0.720094i \(-0.255901\pi\)
0.693876 + 0.720094i \(0.255901\pi\)
\(860\) 8.28772 + 9.55582i 0.282609 + 0.325851i
\(861\) 0 0
\(862\) −4.00000 + 4.00000i −0.136241 + 0.136241i
\(863\) 2.44365 + 2.44365i 0.0831828 + 0.0831828i 0.747474 0.664291i \(-0.231266\pi\)
−0.664291 + 0.747474i \(0.731266\pi\)
\(864\) 0 0
\(865\) −27.5355 31.7487i −0.936236 1.07949i
\(866\) 14.7821i 0.502315i
\(867\) 0 0
\(868\) 1.44155 3.78470i 0.0489295 0.128461i
\(869\) 14.3431i 0.486558i
\(870\) 0 0
\(871\) 88.8463i 3.01044i
\(872\) 8.58579 8.58579i 0.290751 0.290751i
\(873\) 0 0
\(874\) −0.819760 −0.0277288
\(875\) 24.7951 + 16.1308i 0.838228 + 0.545319i
\(876\) 0 0
\(877\) −21.5563 + 21.5563i −0.727906 + 0.727906i −0.970202 0.242296i \(-0.922099\pi\)
0.242296 + 0.970202i \(0.422099\pi\)
\(878\) −9.81845 + 9.81845i −0.331357 + 0.331357i
\(879\) 0 0
\(880\) −0.448342 + 6.30864i −0.0151136 + 0.212664i
\(881\) 13.5140i 0.455297i 0.973743 + 0.227649i \(0.0731038\pi\)
−0.973743 + 0.227649i \(0.926896\pi\)
\(882\) 0 0
\(883\) −28.8284 28.8284i −0.970154 0.970154i 0.0294135 0.999567i \(-0.490636\pi\)
−0.999567 + 0.0294135i \(0.990636\pi\)
\(884\) 31.3137i 1.05319i
\(885\) 0 0
\(886\) 5.85786 0.196799
\(887\) 32.5487 + 32.5487i 1.09288 + 1.09288i 0.995220 + 0.0976580i \(0.0311351\pi\)
0.0976580 + 0.995220i \(0.468865\pi\)
\(888\) 0 0
\(889\) 5.48888 + 12.2426i 0.184091 + 0.410605i
\(890\) −16.6274 19.1716i −0.557352 0.642633i
\(891\) 0 0
\(892\) −6.75699 6.75699i −0.226241 0.226241i
\(893\) −1.51472 1.51472i −0.0506881 0.0506881i
\(894\) 0 0
\(895\) 30.4608 + 2.16478i 1.01819 + 0.0723608i
\(896\) −2.41421 + 1.08239i −0.0806532 + 0.0361602i
\(897\) 0 0
\(898\) 18.1421 + 18.1421i 0.605411 + 0.605411i
\(899\) −1.26810 −0.0422935
\(900\) 0 0
\(901\) 60.9217i 2.02959i
\(902\) −7.39104 7.39104i −0.246095 0.246095i
\(903\) 0 0
\(904\) 1.65685i 0.0551062i
\(905\) −19.6066 1.39340i −0.651745 0.0463181i
\(906\) 0 0
\(907\) 11.1716 11.1716i 0.370946 0.370946i −0.496876 0.867822i \(-0.665520\pi\)
0.867822 + 0.496876i \(0.165520\pi\)
\(908\) 8.38057 8.38057i 0.278119 0.278119i
\(909\) 0 0
\(910\) 14.9336 32.1476i 0.495044 1.06568i
\(911\) 28.1421 0.932391 0.466195 0.884682i \(-0.345624\pi\)
0.466195 + 0.884682i \(0.345624\pi\)
\(912\) 0 0
\(913\) 15.0447 15.0447i 0.497907 0.497907i
\(914\) 2.34315i 0.0775044i
\(915\) 0 0
\(916\) 7.70806i 0.254682i
\(917\) 36.2236 + 13.7972i 1.19621 + 0.455624i
\(918\) 0 0
\(919\) 8.38478i 0.276588i −0.990391 0.138294i \(-0.955838\pi\)
0.990391 0.138294i \(-0.0441619\pi\)
\(920\) −1.30656 0.0928546i −0.0430761 0.00306132i
\(921\) 0 0
\(922\) 24.0593 + 24.0593i 0.792352 + 0.792352i
\(923\) −2.48181 + 2.48181i −0.0816898 + 0.0816898i
\(924\) 0 0
\(925\) −14.6274 + 10.9706i −0.480947 + 0.360710i
\(926\) −18.3431 −0.602793
\(927\) 0 0
\(928\) 0.585786 + 0.585786i 0.0192294 + 0.0192294i
\(929\) 33.2597 1.09121 0.545607 0.838041i \(-0.316299\pi\)
0.545607 + 0.838041i \(0.316299\pi\)
\(930\) 0 0
\(931\) −7.31371 6.51688i −0.239697 0.213582i
\(932\) −3.00000 + 3.00000i −0.0982683 + 0.0982683i
\(933\) 0 0
\(934\) −24.6549 −0.806734
\(935\) 24.9706 21.6569i 0.816625 0.708255i
\(936\) 0 0
\(937\) −17.7666 17.7666i −0.580410 0.580410i 0.354606 0.935016i \(-0.384615\pi\)
−0.935016 + 0.354606i \(0.884615\pi\)
\(938\) 36.6629 + 13.9645i 1.19709 + 0.455958i
\(939\) 0 0
\(940\) −2.24264 2.58579i −0.0731469 0.0843391i
\(941\) 23.3099i 0.759881i −0.925011 0.379940i \(-0.875944\pi\)
0.925011 0.379940i \(-0.124056\pi\)
\(942\) 0 0
\(943\) 1.53073 1.53073i 0.0498475 0.0498475i
\(944\) −9.23880 −0.300697
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) −22.9706 + 22.9706i −0.746443 + 0.746443i −0.973809 0.227366i \(-0.926989\pi\)
0.227366 + 0.973809i \(0.426989\pi\)
\(948\) 0 0
\(949\) 35.1127i 1.13981i
\(950\) −5.59767 + 4.19825i −0.181612 + 0.136209i
\(951\) 0 0
\(952\) 12.9218 + 4.92177i 0.418797 + 0.159515i
\(953\) −23.1421 23.1421i −0.749647 0.749647i 0.224766 0.974413i \(-0.427838\pi\)
−0.974413 + 0.224766i \(0.927838\pi\)
\(954\) 0 0
\(955\) 0.278564 3.91969i 0.00901411 0.126838i
\(956\) −6.48528 −0.209749
\(957\) 0 0
\(958\) 7.83938 7.83938i 0.253279 0.253279i
\(959\) 12.5085 + 27.8995i 0.403921 + 0.900922i
\(960\) 0 0
\(961\) 28.6569 0.924415
\(962\) 15.4930 + 15.4930i 0.499516 + 0.499516i
\(963\) 0 0
\(964\) 6.75699 0.217628
\(965\) −19.6913 + 17.0782i −0.633885 + 0.549766i
\(966\) 0 0
\(967\) −2.21320 + 2.21320i −0.0711718 + 0.0711718i −0.741797 0.670625i \(-0.766026\pi\)
0.670625 + 0.741797i \(0.266026\pi\)
\(968\) 2.12132 + 2.12132i 0.0681818 + 0.0681818i
\(969\) 0 0
\(970\) 1.02944 14.4853i 0.0330532 0.465094i
\(971\) 18.5320i 0.594720i 0.954765 + 0.297360i \(0.0961061\pi\)
−0.954765 + 0.297360i \(0.903894\pi\)
\(972\) 0 0
\(973\) 8.10343 21.2750i 0.259784 0.682045i
\(974\) 1.55635i 0.0498686i
\(975\) 0 0
\(976\) 6.43996i 0.206138i
\(977\) 25.8284 25.8284i 0.826325 0.826325i −0.160682 0.987006i \(-0.551369\pi\)
0.987006 + 0.160682i \(0.0513693\pi\)
\(978\) 0 0
\(979\) 32.1003 1.02593
\(980\) −10.9187 11.2153i −0.348785 0.358259i
\(981\) 0 0
\(982\) −17.7990 + 17.7990i −0.567989 + 0.567989i
\(983\) −28.7444 + 28.7444i −0.916804 + 0.916804i −0.996796 0.0799920i \(-0.974511\pi\)
0.0799920 + 0.996796i \(0.474511\pi\)
\(984\) 0 0
\(985\) −1.21371 1.39942i −0.0386720 0.0445892i
\(986\) 4.32957i 0.137882i
\(987\) 0 0
\(988\) 5.92893 + 5.92893i 0.188624 + 0.188624i
\(989\) 3.31371i 0.105370i
\(990\) 0 0
\(991\) −32.5858 −1.03512 −0.517561 0.855646i \(-0.673160\pi\)
−0.517561 + 0.855646i \(0.673160\pi\)
\(992\) 1.08239 + 1.08239i 0.0343660 + 0.0343660i
\(993\) 0 0
\(994\) 0.634051 + 1.41421i 0.0201109 + 0.0448561i
\(995\) −4.44365 + 62.5269i −0.140873 + 1.98224i
\(996\) 0 0
\(997\) −0.464273 0.464273i −0.0147037 0.0147037i 0.699717 0.714420i \(-0.253310\pi\)
−0.714420 + 0.699717i \(0.753310\pi\)
\(998\) −5.31371 5.31371i −0.168203 0.168203i
\(999\) 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 630.2.p.a.433.3 8
3.2 odd 2 70.2.g.a.13.2 yes 8
5.2 odd 4 inner 630.2.p.a.307.4 8
7.6 odd 2 inner 630.2.p.a.433.4 8
12.11 even 2 560.2.bj.c.433.1 8
15.2 even 4 70.2.g.a.27.1 yes 8
15.8 even 4 350.2.g.a.307.4 8
15.14 odd 2 350.2.g.a.293.3 8
21.2 odd 6 490.2.l.a.423.4 16
21.5 even 6 490.2.l.a.423.3 16
21.11 odd 6 490.2.l.a.313.1 16
21.17 even 6 490.2.l.a.313.2 16
21.20 even 2 70.2.g.a.13.1 8
35.27 even 4 inner 630.2.p.a.307.3 8
60.47 odd 4 560.2.bj.c.97.4 8
84.83 odd 2 560.2.bj.c.433.4 8
105.2 even 12 490.2.l.a.227.2 16
105.17 odd 12 490.2.l.a.117.4 16
105.32 even 12 490.2.l.a.117.3 16
105.47 odd 12 490.2.l.a.227.1 16
105.62 odd 4 70.2.g.a.27.2 yes 8
105.83 odd 4 350.2.g.a.307.3 8
105.104 even 2 350.2.g.a.293.4 8
420.167 even 4 560.2.bj.c.97.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.g.a.13.1 8 21.20 even 2
70.2.g.a.13.2 yes 8 3.2 odd 2
70.2.g.a.27.1 yes 8 15.2 even 4
70.2.g.a.27.2 yes 8 105.62 odd 4
350.2.g.a.293.3 8 15.14 odd 2
350.2.g.a.293.4 8 105.104 even 2
350.2.g.a.307.3 8 105.83 odd 4
350.2.g.a.307.4 8 15.8 even 4
490.2.l.a.117.3 16 105.32 even 12
490.2.l.a.117.4 16 105.17 odd 12
490.2.l.a.227.1 16 105.47 odd 12
490.2.l.a.227.2 16 105.2 even 12
490.2.l.a.313.1 16 21.11 odd 6
490.2.l.a.313.2 16 21.17 even 6
490.2.l.a.423.3 16 21.5 even 6
490.2.l.a.423.4 16 21.2 odd 6
560.2.bj.c.97.1 8 420.167 even 4
560.2.bj.c.97.4 8 60.47 odd 4
560.2.bj.c.433.1 8 12.11 even 2
560.2.bj.c.433.4 8 84.83 odd 2
630.2.p.a.307.3 8 35.27 even 4 inner
630.2.p.a.307.4 8 5.2 odd 4 inner
630.2.p.a.433.3 8 1.1 even 1 trivial
630.2.p.a.433.4 8 7.6 odd 2 inner