Properties

Label 1110.2.d.i.889.5
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(889,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.5
Root \(-1.75233 - 1.75233i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.i.889.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.38900 + 1.75233i) q^{5} -1.00000 q^{6} +2.50466i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.38900 + 1.75233i) q^{5} -1.00000 q^{6} +2.50466i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.75233 + 1.38900i) q^{10} -3.77801 q^{11} -1.00000i q^{12} -1.36333i q^{13} -2.50466 q^{14} +(-1.75233 + 1.38900i) q^{15} +1.00000 q^{16} +0.221992i q^{17} -1.00000i q^{18} -6.14134 q^{19} +(-1.38900 - 1.75233i) q^{20} -2.50466 q^{21} -3.77801i q^{22} +0.867993i q^{23} +1.00000 q^{24} +(-1.14134 + 4.86799i) q^{25} +1.36333 q^{26} -1.00000i q^{27} -2.50466i q^{28} -0.646000 q^{29} +(-1.38900 - 1.75233i) q^{30} +3.86799 q^{31} +1.00000i q^{32} -3.77801i q^{33} -0.221992 q^{34} +(-4.38900 + 3.47899i) q^{35} +1.00000 q^{36} +1.00000i q^{37} -6.14134i q^{38} +1.36333 q^{39} +(1.75233 - 1.38900i) q^{40} -0.910015 q^{41} -2.50466i q^{42} +4.59465i q^{43} +3.77801 q^{44} +(-1.38900 - 1.75233i) q^{45} -0.867993 q^{46} -0.778008i q^{47} +1.00000i q^{48} +0.726656 q^{49} +(-4.86799 - 1.14134i) q^{50} -0.221992 q^{51} +1.36333i q^{52} -2.27334i q^{53} +1.00000 q^{54} +(-5.24767 - 6.62032i) q^{55} +2.50466 q^{56} -6.14134i q^{57} -0.646000i q^{58} -7.78734 q^{59} +(1.75233 - 1.38900i) q^{60} +9.42401 q^{61} +3.86799i q^{62} -2.50466i q^{63} -1.00000 q^{64} +(2.38900 - 1.89367i) q^{65} +3.77801 q^{66} +10.7267i q^{67} -0.221992i q^{68} -0.867993 q^{69} +(-3.47899 - 4.38900i) q^{70} -11.2406 q^{71} +1.00000i q^{72} -2.86799i q^{73} -1.00000 q^{74} +(-4.86799 - 1.14134i) q^{75} +6.14134 q^{76} -9.46264i q^{77} +1.36333i q^{78} +0.495336 q^{79} +(1.38900 + 1.75233i) q^{80} +1.00000 q^{81} -0.910015i q^{82} -1.08066i q^{83} +2.50466 q^{84} +(-0.389004 + 0.308348i) q^{85} -4.59465 q^{86} -0.646000i q^{87} +3.77801i q^{88} +0.0899847 q^{89} +(1.75233 - 1.38900i) q^{90} +3.41468 q^{91} -0.867993i q^{92} +3.86799i q^{93} +0.778008 q^{94} +(-8.53034 - 10.7617i) q^{95} -1.00000 q^{96} +4.46603i q^{97} +0.726656i q^{98} +3.77801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} - 10 q^{11} + 6 q^{14} + 6 q^{16} - 20 q^{19} - 2 q^{20} + 6 q^{21} + 6 q^{24} + 10 q^{25} + 4 q^{26} + 34 q^{29} - 2 q^{30} - 2 q^{31} - 14 q^{34} - 20 q^{35} + 6 q^{36} + 4 q^{39} - 18 q^{41} + 10 q^{44} - 2 q^{45} + 20 q^{46} - 4 q^{49} - 4 q^{50} - 14 q^{51} + 6 q^{54} - 42 q^{55} - 6 q^{56} + 8 q^{59} + 6 q^{61} - 6 q^{64} + 8 q^{65} + 10 q^{66} + 20 q^{69} - 2 q^{70} + 4 q^{71} - 6 q^{74} - 4 q^{75} + 20 q^{76} + 24 q^{79} + 2 q^{80} + 6 q^{81} - 6 q^{84} + 4 q^{85} + 6 q^{86} - 12 q^{89} + 12 q^{91} - 8 q^{94} - 28 q^{95} - 6 q^{96} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.38900 + 1.75233i 0.621181 + 0.783667i
\(6\) −1.00000 −0.408248
\(7\) 2.50466i 0.946674i 0.880881 + 0.473337i \(0.156951\pi\)
−0.880881 + 0.473337i \(0.843049\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.75233 + 1.38900i −0.554136 + 0.439242i
\(11\) −3.77801 −1.13911 −0.569556 0.821952i \(-0.692885\pi\)
−0.569556 + 0.821952i \(0.692885\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.36333i 0.378119i −0.981966 0.189060i \(-0.939456\pi\)
0.981966 0.189060i \(-0.0605439\pi\)
\(14\) −2.50466 −0.669400
\(15\) −1.75233 + 1.38900i −0.452450 + 0.358639i
\(16\) 1.00000 0.250000
\(17\) 0.221992i 0.0538410i 0.999638 + 0.0269205i \(0.00857010\pi\)
−0.999638 + 0.0269205i \(0.991430\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.14134 −1.40892 −0.704460 0.709744i \(-0.748811\pi\)
−0.704460 + 0.709744i \(0.748811\pi\)
\(20\) −1.38900 1.75233i −0.310591 0.391833i
\(21\) −2.50466 −0.546563
\(22\) 3.77801i 0.805474i
\(23\) 0.867993i 0.180989i 0.995897 + 0.0904945i \(0.0288447\pi\)
−0.995897 + 0.0904945i \(0.971155\pi\)
\(24\) 1.00000 0.204124
\(25\) −1.14134 + 4.86799i −0.228267 + 0.973599i
\(26\) 1.36333 0.267371
\(27\) 1.00000i 0.192450i
\(28\) 2.50466i 0.473337i
\(29\) −0.646000 −0.119959 −0.0599796 0.998200i \(-0.519104\pi\)
−0.0599796 + 0.998200i \(0.519104\pi\)
\(30\) −1.38900 1.75233i −0.253596 0.319931i
\(31\) 3.86799 0.694712 0.347356 0.937733i \(-0.387080\pi\)
0.347356 + 0.937733i \(0.387080\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.77801i 0.657667i
\(34\) −0.221992 −0.0380713
\(35\) −4.38900 + 3.47899i −0.741877 + 0.588056i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 6.14134i 0.996256i
\(39\) 1.36333 0.218307
\(40\) 1.75233 1.38900i 0.277068 0.219621i
\(41\) −0.910015 −0.142121 −0.0710603 0.997472i \(-0.522638\pi\)
−0.0710603 + 0.997472i \(0.522638\pi\)
\(42\) 2.50466i 0.386478i
\(43\) 4.59465i 0.700677i 0.936623 + 0.350339i \(0.113934\pi\)
−0.936623 + 0.350339i \(0.886066\pi\)
\(44\) 3.77801 0.569556
\(45\) −1.38900 1.75233i −0.207060 0.261222i
\(46\) −0.867993 −0.127979
\(47\) 0.778008i 0.113484i −0.998389 0.0567421i \(-0.981929\pi\)
0.998389 0.0567421i \(-0.0180713\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0.726656 0.103808
\(50\) −4.86799 1.14134i −0.688438 0.161409i
\(51\) −0.221992 −0.0310851
\(52\) 1.36333i 0.189060i
\(53\) 2.27334i 0.312268i −0.987736 0.156134i \(-0.950097\pi\)
0.987736 0.156134i \(-0.0499031\pi\)
\(54\) 1.00000 0.136083
\(55\) −5.24767 6.62032i −0.707595 0.892684i
\(56\) 2.50466 0.334700
\(57\) 6.14134i 0.813440i
\(58\) 0.646000i 0.0848240i
\(59\) −7.78734 −1.01382 −0.506912 0.861998i \(-0.669213\pi\)
−0.506912 + 0.861998i \(0.669213\pi\)
\(60\) 1.75233 1.38900i 0.226225 0.179320i
\(61\) 9.42401 1.20662 0.603310 0.797507i \(-0.293848\pi\)
0.603310 + 0.797507i \(0.293848\pi\)
\(62\) 3.86799i 0.491236i
\(63\) 2.50466i 0.315558i
\(64\) −1.00000 −0.125000
\(65\) 2.38900 1.89367i 0.296319 0.234881i
\(66\) 3.77801 0.465041
\(67\) 10.7267i 1.31047i 0.755425 + 0.655235i \(0.227430\pi\)
−0.755425 + 0.655235i \(0.772570\pi\)
\(68\) 0.221992i 0.0269205i
\(69\) −0.867993 −0.104494
\(70\) −3.47899 4.38900i −0.415819 0.524586i
\(71\) −11.2406 −1.33402 −0.667010 0.745049i \(-0.732426\pi\)
−0.667010 + 0.745049i \(0.732426\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 2.86799i 0.335673i −0.985815 0.167837i \(-0.946322\pi\)
0.985815 0.167837i \(-0.0536781\pi\)
\(74\) −1.00000 −0.116248
\(75\) −4.86799 1.14134i −0.562107 0.131790i
\(76\) 6.14134 0.704460
\(77\) 9.46264i 1.07837i
\(78\) 1.36333i 0.154367i
\(79\) 0.495336 0.0557296 0.0278648 0.999612i \(-0.491129\pi\)
0.0278648 + 0.999612i \(0.491129\pi\)
\(80\) 1.38900 + 1.75233i 0.155295 + 0.195917i
\(81\) 1.00000 0.111111
\(82\) 0.910015i 0.100494i
\(83\) 1.08066i 0.118617i −0.998240 0.0593087i \(-0.981110\pi\)
0.998240 0.0593087i \(-0.0188896\pi\)
\(84\) 2.50466 0.273281
\(85\) −0.389004 + 0.308348i −0.0421934 + 0.0334450i
\(86\) −4.59465 −0.495454
\(87\) 0.646000i 0.0692585i
\(88\) 3.77801i 0.402737i
\(89\) 0.0899847 0.00953836 0.00476918 0.999989i \(-0.498482\pi\)
0.00476918 + 0.999989i \(0.498482\pi\)
\(90\) 1.75233 1.38900i 0.184712 0.146414i
\(91\) 3.41468 0.357956
\(92\) 0.867993i 0.0904945i
\(93\) 3.86799i 0.401092i
\(94\) 0.778008 0.0802454
\(95\) −8.53034 10.7617i −0.875194 1.10412i
\(96\) −1.00000 −0.102062
\(97\) 4.46603i 0.453457i 0.973958 + 0.226728i \(0.0728030\pi\)
−0.973958 + 0.226728i \(0.927197\pi\)
\(98\) 0.726656i 0.0734034i
\(99\) 3.77801 0.379704
\(100\) 1.14134 4.86799i 0.114134 0.486799i
\(101\) −6.56534 −0.653276 −0.326638 0.945149i \(-0.605916\pi\)
−0.326638 + 0.945149i \(0.605916\pi\)
\(102\) 0.221992i 0.0219805i
\(103\) 16.9580i 1.67092i −0.549552 0.835460i \(-0.685202\pi\)
0.549552 0.835460i \(-0.314798\pi\)
\(104\) −1.36333 −0.133685
\(105\) −3.47899 4.38900i −0.339515 0.428323i
\(106\) 2.27334 0.220807
\(107\) 15.8260i 1.52995i 0.644057 + 0.764977i \(0.277250\pi\)
−0.644057 + 0.764977i \(0.722750\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −0.948649 −0.0908641 −0.0454320 0.998967i \(-0.514466\pi\)
−0.0454320 + 0.998967i \(0.514466\pi\)
\(110\) 6.62032 5.24767i 0.631223 0.500345i
\(111\) −1.00000 −0.0949158
\(112\) 2.50466i 0.236669i
\(113\) 0.311977i 0.0293483i 0.999892 + 0.0146742i \(0.00467110\pi\)
−0.999892 + 0.0146742i \(0.995329\pi\)
\(114\) 6.14134 0.575189
\(115\) −1.52101 + 1.20565i −0.141835 + 0.112427i
\(116\) 0.646000 0.0599796
\(117\) 1.36333i 0.126040i
\(118\) 7.78734i 0.716882i
\(119\) −0.556016 −0.0509699
\(120\) 1.38900 + 1.75233i 0.126798 + 0.159965i
\(121\) 3.27334 0.297577
\(122\) 9.42401i 0.853210i
\(123\) 0.910015i 0.0820533i
\(124\) −3.86799 −0.347356
\(125\) −10.1157 + 4.76166i −0.904772 + 0.425896i
\(126\) 2.50466 0.223133
\(127\) 3.09931i 0.275020i −0.990500 0.137510i \(-0.956090\pi\)
0.990500 0.137510i \(-0.0439099\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.59465 −0.404536
\(130\) 1.89367 + 2.38900i 0.166086 + 0.209530i
\(131\) −11.3434 −0.991073 −0.495537 0.868587i \(-0.665029\pi\)
−0.495537 + 0.868587i \(0.665029\pi\)
\(132\) 3.77801i 0.328833i
\(133\) 15.3820i 1.33379i
\(134\) −10.7267 −0.926642
\(135\) 1.75233 1.38900i 0.150817 0.119546i
\(136\) 0.221992 0.0190357
\(137\) 10.4953i 0.896677i 0.893864 + 0.448339i \(0.147984\pi\)
−0.893864 + 0.448339i \(0.852016\pi\)
\(138\) 0.867993i 0.0738884i
\(139\) 18.8773 1.60115 0.800577 0.599230i \(-0.204527\pi\)
0.800577 + 0.599230i \(0.204527\pi\)
\(140\) 4.38900 3.47899i 0.370939 0.294028i
\(141\) 0.778008 0.0655201
\(142\) 11.2406i 0.943294i
\(143\) 5.15066i 0.430720i
\(144\) −1.00000 −0.0833333
\(145\) −0.897297 1.13201i −0.0745165 0.0940081i
\(146\) 2.86799 0.237357
\(147\) 0.726656i 0.0599336i
\(148\) 1.00000i 0.0821995i
\(149\) 17.0280 1.39499 0.697493 0.716591i \(-0.254299\pi\)
0.697493 + 0.716591i \(0.254299\pi\)
\(150\) 1.14134 4.86799i 0.0931897 0.397470i
\(151\) 22.3727 1.82066 0.910331 0.413882i \(-0.135827\pi\)
0.910331 + 0.413882i \(0.135827\pi\)
\(152\) 6.14134i 0.498128i
\(153\) 0.221992i 0.0179470i
\(154\) 9.46264 0.762521
\(155\) 5.37266 + 6.77801i 0.431542 + 0.544423i
\(156\) −1.36333 −0.109154
\(157\) 16.9800i 1.35515i 0.735452 + 0.677577i \(0.236970\pi\)
−0.735452 + 0.677577i \(0.763030\pi\)
\(158\) 0.495336i 0.0394068i
\(159\) 2.27334 0.180288
\(160\) −1.75233 + 1.38900i −0.138534 + 0.109810i
\(161\) −2.17403 −0.171338
\(162\) 1.00000i 0.0785674i
\(163\) 7.00000i 0.548282i −0.961689 0.274141i \(-0.911606\pi\)
0.961689 0.274141i \(-0.0883936\pi\)
\(164\) 0.910015 0.0710603
\(165\) 6.62032 5.24767i 0.515392 0.408530i
\(166\) 1.08066 0.0838752
\(167\) 23.4333i 1.81333i 0.421856 + 0.906663i \(0.361379\pi\)
−0.421856 + 0.906663i \(0.638621\pi\)
\(168\) 2.50466i 0.193239i
\(169\) 11.1413 0.857026
\(170\) −0.308348 0.389004i −0.0236492 0.0298352i
\(171\) 6.14134 0.469640
\(172\) 4.59465i 0.350339i
\(173\) 7.28267i 0.553691i 0.960914 + 0.276846i \(0.0892891\pi\)
−0.960914 + 0.276846i \(0.910711\pi\)
\(174\) 0.646000 0.0489732
\(175\) −12.1927 2.85866i −0.921681 0.216095i
\(176\) −3.77801 −0.284778
\(177\) 7.78734i 0.585332i
\(178\) 0.0899847i 0.00674464i
\(179\) −1.82003 −0.136035 −0.0680177 0.997684i \(-0.521667\pi\)
−0.0680177 + 0.997684i \(0.521667\pi\)
\(180\) 1.38900 + 1.75233i 0.103530 + 0.130611i
\(181\) 0.212663 0.0158071 0.00790357 0.999969i \(-0.497484\pi\)
0.00790357 + 0.999969i \(0.497484\pi\)
\(182\) 3.41468i 0.253113i
\(183\) 9.42401i 0.696643i
\(184\) 0.867993 0.0639893
\(185\) −1.75233 + 1.38900i −0.128834 + 0.102122i
\(186\) −3.86799 −0.283615
\(187\) 0.838688i 0.0613309i
\(188\) 0.778008i 0.0567421i
\(189\) 2.50466 0.182188
\(190\) 10.7617 8.53034i 0.780733 0.618856i
\(191\) −2.00933 −0.145390 −0.0726950 0.997354i \(-0.523160\pi\)
−0.0726950 + 0.997354i \(0.523160\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 6.00000i 0.431889i 0.976406 + 0.215945i \(0.0692831\pi\)
−0.976406 + 0.215945i \(0.930717\pi\)
\(194\) −4.46603 −0.320642
\(195\) 1.89367 + 2.38900i 0.135608 + 0.171080i
\(196\) −0.726656 −0.0519040
\(197\) 2.76529i 0.197019i 0.995136 + 0.0985094i \(0.0314074\pi\)
−0.995136 + 0.0985094i \(0.968593\pi\)
\(198\) 3.77801i 0.268491i
\(199\) −1.98134 −0.140454 −0.0702268 0.997531i \(-0.522372\pi\)
−0.0702268 + 0.997531i \(0.522372\pi\)
\(200\) 4.86799 + 1.14134i 0.344219 + 0.0807047i
\(201\) −10.7267 −0.756600
\(202\) 6.56534i 0.461936i
\(203\) 1.61801i 0.113562i
\(204\) 0.221992 0.0155426
\(205\) −1.26401 1.59465i −0.0882826 0.111375i
\(206\) 16.9580 1.18152
\(207\) 0.867993i 0.0603297i
\(208\) 1.36333i 0.0945298i
\(209\) 23.2020 1.60492
\(210\) 4.38900 3.47899i 0.302870 0.240073i
\(211\) −20.9473 −1.44207 −0.721037 0.692897i \(-0.756334\pi\)
−0.721037 + 0.692897i \(0.756334\pi\)
\(212\) 2.27334i 0.156134i
\(213\) 11.2406i 0.770197i
\(214\) −15.8260 −1.08184
\(215\) −8.05135 + 6.38199i −0.549098 + 0.435248i
\(216\) −1.00000 −0.0680414
\(217\) 9.68802i 0.657666i
\(218\) 0.948649i 0.0642506i
\(219\) 2.86799 0.193801
\(220\) 5.24767 + 6.62032i 0.353798 + 0.446342i
\(221\) 0.302648 0.0203583
\(222\) 1.00000i 0.0671156i
\(223\) 20.1507i 1.34939i 0.738097 + 0.674694i \(0.235724\pi\)
−0.738097 + 0.674694i \(0.764276\pi\)
\(224\) −2.50466 −0.167350
\(225\) 1.14134 4.86799i 0.0760891 0.324533i
\(226\) −0.311977 −0.0207524
\(227\) 28.4520i 1.88843i 0.329337 + 0.944213i \(0.393175\pi\)
−0.329337 + 0.944213i \(0.606825\pi\)
\(228\) 6.14134i 0.406720i
\(229\) −18.6940 −1.23533 −0.617666 0.786441i \(-0.711922\pi\)
−0.617666 + 0.786441i \(0.711922\pi\)
\(230\) −1.20565 1.52101i −0.0794979 0.100293i
\(231\) 9.46264 0.622596
\(232\) 0.646000i 0.0424120i
\(233\) 9.00933i 0.590221i −0.955463 0.295110i \(-0.904644\pi\)
0.955463 0.295110i \(-0.0953564\pi\)
\(234\) −1.36333 −0.0891236
\(235\) 1.36333 1.08066i 0.0889337 0.0704942i
\(236\) 7.78734 0.506912
\(237\) 0.495336i 0.0321755i
\(238\) 0.556016i 0.0360411i
\(239\) −16.1693 −1.04591 −0.522953 0.852361i \(-0.675170\pi\)
−0.522953 + 0.852361i \(0.675170\pi\)
\(240\) −1.75233 + 1.38900i −0.113113 + 0.0896598i
\(241\) 10.3527 0.666875 0.333437 0.942772i \(-0.391791\pi\)
0.333437 + 0.942772i \(0.391791\pi\)
\(242\) 3.27334i 0.210418i
\(243\) 1.00000i 0.0641500i
\(244\) −9.42401 −0.603310
\(245\) 1.00933 + 1.27334i 0.0644836 + 0.0813509i
\(246\) 0.910015 0.0580205
\(247\) 8.37266i 0.532739i
\(248\) 3.86799i 0.245618i
\(249\) 1.08066 0.0684838
\(250\) −4.76166 10.1157i −0.301154 0.639771i
\(251\) 8.38538 0.529280 0.264640 0.964347i \(-0.414747\pi\)
0.264640 + 0.964347i \(0.414747\pi\)
\(252\) 2.50466i 0.157779i
\(253\) 3.27928i 0.206167i
\(254\) 3.09931 0.194468
\(255\) −0.308348 0.389004i −0.0193095 0.0243604i
\(256\) 1.00000 0.0625000
\(257\) 6.55263i 0.408742i 0.978894 + 0.204371i \(0.0655148\pi\)
−0.978894 + 0.204371i \(0.934485\pi\)
\(258\) 4.59465i 0.286050i
\(259\) −2.50466 −0.155632
\(260\) −2.38900 + 1.89367i −0.148160 + 0.117440i
\(261\) 0.646000 0.0399864
\(262\) 11.3434i 0.700795i
\(263\) 15.4754i 0.954252i 0.878835 + 0.477126i \(0.158321\pi\)
−0.878835 + 0.477126i \(0.841679\pi\)
\(264\) −3.77801 −0.232520
\(265\) 3.98365 3.15768i 0.244714 0.193975i
\(266\) 15.3820 0.943130
\(267\) 0.0899847i 0.00550698i
\(268\) 10.7267i 0.655235i
\(269\) 3.31198 0.201935 0.100967 0.994890i \(-0.467806\pi\)
0.100967 + 0.994890i \(0.467806\pi\)
\(270\) 1.38900 + 1.75233i 0.0845321 + 0.106644i
\(271\) 32.1986 1.95593 0.977964 0.208775i \(-0.0669477\pi\)
0.977964 + 0.208775i \(0.0669477\pi\)
\(272\) 0.221992i 0.0134602i
\(273\) 3.41468i 0.206666i
\(274\) −10.4953 −0.634046
\(275\) 4.31198 18.3913i 0.260022 1.10904i
\(276\) 0.867993 0.0522470
\(277\) 20.6553i 1.24106i 0.784183 + 0.620529i \(0.213082\pi\)
−0.784183 + 0.620529i \(0.786918\pi\)
\(278\) 18.8773i 1.13219i
\(279\) −3.86799 −0.231571
\(280\) 3.47899 + 4.38900i 0.207909 + 0.262293i
\(281\) −9.80731 −0.585055 −0.292528 0.956257i \(-0.594496\pi\)
−0.292528 + 0.956257i \(0.594496\pi\)
\(282\) 0.778008i 0.0463297i
\(283\) 18.6040i 1.10589i 0.833217 + 0.552946i \(0.186496\pi\)
−0.833217 + 0.552946i \(0.813504\pi\)
\(284\) 11.2406 0.667010
\(285\) 10.7617 8.53034i 0.637466 0.505294i
\(286\) −5.15066 −0.304565
\(287\) 2.27928i 0.134542i
\(288\) 1.00000i 0.0589256i
\(289\) 16.9507 0.997101
\(290\) 1.13201 0.897297i 0.0664738 0.0526911i
\(291\) −4.46603 −0.261803
\(292\) 2.86799i 0.167837i
\(293\) 27.8480i 1.62690i −0.581636 0.813449i \(-0.697587\pi\)
0.581636 0.813449i \(-0.302413\pi\)
\(294\) −0.726656 −0.0423795
\(295\) −10.8166 13.6460i −0.629769 0.794501i
\(296\) 1.00000 0.0581238
\(297\) 3.77801i 0.219222i
\(298\) 17.0280i 0.986405i
\(299\) 1.18336 0.0684354
\(300\) 4.86799 + 1.14134i 0.281054 + 0.0658951i
\(301\) −11.5081 −0.663313
\(302\) 22.3727i 1.28740i
\(303\) 6.56534i 0.377169i
\(304\) −6.14134 −0.352230
\(305\) 13.0900 + 16.5140i 0.749530 + 0.945588i
\(306\) 0.221992 0.0126904
\(307\) 6.05135i 0.345369i 0.984977 + 0.172684i \(0.0552441\pi\)
−0.984977 + 0.172684i \(0.944756\pi\)
\(308\) 9.46264i 0.539184i
\(309\) 16.9580 0.964706
\(310\) −6.77801 + 5.37266i −0.384965 + 0.305146i
\(311\) −28.3306 −1.60648 −0.803241 0.595654i \(-0.796893\pi\)
−0.803241 + 0.595654i \(0.796893\pi\)
\(312\) 1.36333i 0.0771833i
\(313\) 1.50466i 0.0850487i −0.999095 0.0425243i \(-0.986460\pi\)
0.999095 0.0425243i \(-0.0135400\pi\)
\(314\) −16.9800 −0.958238
\(315\) 4.38900 3.47899i 0.247292 0.196019i
\(316\) −0.495336 −0.0278648
\(317\) 20.0480i 1.12601i −0.826455 0.563003i \(-0.809646\pi\)
0.826455 0.563003i \(-0.190354\pi\)
\(318\) 2.27334i 0.127483i
\(319\) 2.44059 0.136647
\(320\) −1.38900 1.75233i −0.0776477 0.0979583i
\(321\) −15.8260 −0.883320
\(322\) 2.17403i 0.121154i
\(323\) 1.36333i 0.0758576i
\(324\) −1.00000 −0.0555556
\(325\) 6.63667 + 1.55602i 0.368136 + 0.0863122i
\(326\) 7.00000 0.387694
\(327\) 0.948649i 0.0524604i
\(328\) 0.910015i 0.0502472i
\(329\) 1.94865 0.107432
\(330\) 5.24767 + 6.62032i 0.288875 + 0.364437i
\(331\) 21.5747 1.18585 0.592926 0.805257i \(-0.297973\pi\)
0.592926 + 0.805257i \(0.297973\pi\)
\(332\) 1.08066i 0.0593087i
\(333\) 1.00000i 0.0547997i
\(334\) −23.4333 −1.28222
\(335\) −18.7967 + 14.8994i −1.02697 + 0.814039i
\(336\) −2.50466 −0.136641
\(337\) 12.4427i 0.677795i 0.940823 + 0.338898i \(0.110054\pi\)
−0.940823 + 0.338898i \(0.889946\pi\)
\(338\) 11.1413i 0.606009i
\(339\) −0.311977 −0.0169443
\(340\) 0.389004 0.308348i 0.0210967 0.0167225i
\(341\) −14.6133 −0.791355
\(342\) 6.14134i 0.332085i
\(343\) 19.3527i 1.04495i
\(344\) 4.59465 0.247727
\(345\) −1.20565 1.52101i −0.0649098 0.0818885i
\(346\) −7.28267 −0.391519
\(347\) 12.0700i 0.647952i −0.946065 0.323976i \(-0.894980\pi\)
0.946065 0.323976i \(-0.105020\pi\)
\(348\) 0.646000i 0.0346293i
\(349\) 19.3434 1.03543 0.517713 0.855554i \(-0.326784\pi\)
0.517713 + 0.855554i \(0.326784\pi\)
\(350\) 2.85866 12.1927i 0.152802 0.651727i
\(351\) −1.36333 −0.0727691
\(352\) 3.77801i 0.201368i
\(353\) 5.48262i 0.291810i −0.989299 0.145905i \(-0.953391\pi\)
0.989299 0.145905i \(-0.0466094\pi\)
\(354\) 7.78734 0.413892
\(355\) −15.6133 19.6974i −0.828668 1.04543i
\(356\) −0.0899847 −0.00476918
\(357\) 0.556016i 0.0294275i
\(358\) 1.82003i 0.0961916i
\(359\) 1.60737 0.0848336 0.0424168 0.999100i \(-0.486494\pi\)
0.0424168 + 0.999100i \(0.486494\pi\)
\(360\) −1.75233 + 1.38900i −0.0923560 + 0.0732069i
\(361\) 18.7160 0.985053
\(362\) 0.212663i 0.0111773i
\(363\) 3.27334i 0.171806i
\(364\) −3.41468 −0.178978
\(365\) 5.02568 3.98365i 0.263056 0.208514i
\(366\) −9.42401 −0.492601
\(367\) 7.51399i 0.392227i −0.980581 0.196114i \(-0.937168\pi\)
0.980581 0.196114i \(-0.0628321\pi\)
\(368\) 0.867993i 0.0452472i
\(369\) 0.910015 0.0473735
\(370\) −1.38900 1.75233i −0.0722109 0.0910994i
\(371\) 5.69396 0.295616
\(372\) 3.86799i 0.200546i
\(373\) 12.5140i 0.647950i 0.946066 + 0.323975i \(0.105019\pi\)
−0.946066 + 0.323975i \(0.894981\pi\)
\(374\) 0.838688 0.0433675
\(375\) −4.76166 10.1157i −0.245891 0.522370i
\(376\) −0.778008 −0.0401227
\(377\) 0.880711i 0.0453589i
\(378\) 2.50466i 0.128826i
\(379\) −37.6260 −1.93272 −0.966360 0.257195i \(-0.917202\pi\)
−0.966360 + 0.257195i \(0.917202\pi\)
\(380\) 8.53034 + 10.7617i 0.437597 + 0.552062i
\(381\) 3.09931 0.158783
\(382\) 2.00933i 0.102806i
\(383\) 14.2440i 0.727836i −0.931431 0.363918i \(-0.881439\pi\)
0.931431 0.363918i \(-0.118561\pi\)
\(384\) 1.00000 0.0510310
\(385\) 16.5817 13.1436i 0.845081 0.669862i
\(386\) −6.00000 −0.305392
\(387\) 4.59465i 0.233559i
\(388\) 4.46603i 0.226728i
\(389\) −0.697352 −0.0353571 −0.0176786 0.999844i \(-0.505628\pi\)
−0.0176786 + 0.999844i \(0.505628\pi\)
\(390\) −2.38900 + 1.89367i −0.120972 + 0.0958896i
\(391\) −0.192688 −0.00974463
\(392\) 0.726656i 0.0367017i
\(393\) 11.3434i 0.572196i
\(394\) −2.76529 −0.139313
\(395\) 0.688023 + 0.867993i 0.0346182 + 0.0436734i
\(396\) −3.77801 −0.189852
\(397\) 28.4040i 1.42556i −0.701389 0.712779i \(-0.747436\pi\)
0.701389 0.712779i \(-0.252564\pi\)
\(398\) 1.98134i 0.0993157i
\(399\) 15.3820 0.770062
\(400\) −1.14134 + 4.86799i −0.0570668 + 0.243400i
\(401\) 22.7580 1.13648 0.568241 0.822862i \(-0.307624\pi\)
0.568241 + 0.822862i \(0.307624\pi\)
\(402\) 10.7267i 0.534997i
\(403\) 5.27334i 0.262684i
\(404\) 6.56534 0.326638
\(405\) 1.38900 + 1.75233i 0.0690202 + 0.0870741i
\(406\) 1.61801 0.0803007
\(407\) 3.77801i 0.187269i
\(408\) 0.221992i 0.0109902i
\(409\) 16.3527 0.808588 0.404294 0.914629i \(-0.367517\pi\)
0.404294 + 0.914629i \(0.367517\pi\)
\(410\) 1.59465 1.26401i 0.0787541 0.0624252i
\(411\) −10.4953 −0.517697
\(412\) 16.9580i 0.835460i
\(413\) 19.5047i 0.959762i
\(414\) 0.867993 0.0426595
\(415\) 1.89367 1.50104i 0.0929565 0.0736829i
\(416\) 1.36333 0.0668427
\(417\) 18.8773i 0.924426i
\(418\) 23.2020i 1.13485i
\(419\) −11.2020 −0.547254 −0.273627 0.961836i \(-0.588223\pi\)
−0.273627 + 0.961836i \(0.588223\pi\)
\(420\) 3.47899 + 4.38900i 0.169757 + 0.214161i
\(421\) 13.8200 0.673547 0.336774 0.941586i \(-0.390664\pi\)
0.336774 + 0.941586i \(0.390664\pi\)
\(422\) 20.9473i 1.01970i
\(423\) 0.778008i 0.0378280i
\(424\) −2.27334 −0.110403
\(425\) −1.08066 0.253368i −0.0524195 0.0122901i
\(426\) 11.2406 0.544611
\(427\) 23.6040i 1.14228i
\(428\) 15.8260i 0.764977i
\(429\) −5.15066 −0.248676
\(430\) −6.38199 8.05135i −0.307767 0.388271i
\(431\) 36.1493 1.74125 0.870626 0.491945i \(-0.163714\pi\)
0.870626 + 0.491945i \(0.163714\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 19.4147i 0.933010i −0.884519 0.466505i \(-0.845513\pi\)
0.884519 0.466505i \(-0.154487\pi\)
\(434\) −9.68802 −0.465040
\(435\) 1.13201 0.897297i 0.0542756 0.0430221i
\(436\) 0.948649 0.0454320
\(437\) 5.33063i 0.254999i
\(438\) 2.86799i 0.137038i
\(439\) 24.2207 1.15599 0.577995 0.816040i \(-0.303835\pi\)
0.577995 + 0.816040i \(0.303835\pi\)
\(440\) −6.62032 + 5.24767i −0.315612 + 0.250173i
\(441\) −0.726656 −0.0346027
\(442\) 0.302648i 0.0143955i
\(443\) 22.0373i 1.04702i −0.852018 0.523512i \(-0.824621\pi\)
0.852018 0.523512i \(-0.175379\pi\)
\(444\) 1.00000 0.0474579
\(445\) 0.124989 + 0.157683i 0.00592505 + 0.00747490i
\(446\) −20.1507 −0.954162
\(447\) 17.0280i 0.805396i
\(448\) 2.50466i 0.118334i
\(449\) −1.63328 −0.0770794 −0.0385397 0.999257i \(-0.512271\pi\)
−0.0385397 + 0.999257i \(0.512271\pi\)
\(450\) 4.86799 + 1.14134i 0.229479 + 0.0538031i
\(451\) 3.43804 0.161891
\(452\) 0.311977i 0.0146742i
\(453\) 22.3727i 1.05116i
\(454\) −28.4520 −1.33532
\(455\) 4.74300 + 5.98365i 0.222355 + 0.280518i
\(456\) −6.14134 −0.287594
\(457\) 14.2279i 0.665555i −0.943005 0.332777i \(-0.892014\pi\)
0.943005 0.332777i \(-0.107986\pi\)
\(458\) 18.6940i 0.873512i
\(459\) 0.221992 0.0103617
\(460\) 1.52101 1.20565i 0.0709175 0.0562135i
\(461\) −20.8587 −0.971485 −0.485742 0.874102i \(-0.661451\pi\)
−0.485742 + 0.874102i \(0.661451\pi\)
\(462\) 9.46264i 0.440242i
\(463\) 0.0326940i 0.00151942i −1.00000 0.000759709i \(-0.999758\pi\)
1.00000 0.000759709i \(-0.000241823\pi\)
\(464\) −0.646000 −0.0299898
\(465\) −6.77801 + 5.37266i −0.314323 + 0.249151i
\(466\) 9.00933 0.417349
\(467\) 16.1834i 0.748877i 0.927252 + 0.374438i \(0.122164\pi\)
−0.927252 + 0.374438i \(0.877836\pi\)
\(468\) 1.36333i 0.0630199i
\(469\) −26.8667 −1.24059
\(470\) 1.08066 + 1.36333i 0.0498469 + 0.0628856i
\(471\) −16.9800 −0.782398
\(472\) 7.78734i 0.358441i
\(473\) 17.3586i 0.798150i
\(474\) −0.495336 −0.0227515
\(475\) 7.00933 29.8960i 0.321610 1.37172i
\(476\) 0.556016 0.0254849
\(477\) 2.27334i 0.104089i
\(478\) 16.1693i 0.739568i
\(479\) 1.15066 0.0525752 0.0262876 0.999654i \(-0.491631\pi\)
0.0262876 + 0.999654i \(0.491631\pi\)
\(480\) −1.38900 1.75233i −0.0633991 0.0799827i
\(481\) 1.36333 0.0621624
\(482\) 10.3527i 0.471552i
\(483\) 2.17403i 0.0989218i
\(484\) −3.27334 −0.148788
\(485\) −7.82597 + 6.20333i −0.355359 + 0.281679i
\(486\) −1.00000 −0.0453609
\(487\) 3.71733i 0.168448i 0.996447 + 0.0842241i \(0.0268412\pi\)
−0.996447 + 0.0842241i \(0.973159\pi\)
\(488\) 9.42401i 0.426605i
\(489\) 7.00000 0.316551
\(490\) −1.27334 + 1.00933i −0.0575238 + 0.0455968i
\(491\) 10.9966 0.496270 0.248135 0.968725i \(-0.420182\pi\)
0.248135 + 0.968725i \(0.420182\pi\)
\(492\) 0.910015i 0.0410267i
\(493\) 0.143407i 0.00645873i
\(494\) −8.37266 −0.376704
\(495\) 5.24767 + 6.62032i 0.235865 + 0.297561i
\(496\) 3.86799 0.173678
\(497\) 28.1541i 1.26288i
\(498\) 1.08066i 0.0484254i
\(499\) −29.5547 −1.32305 −0.661525 0.749923i \(-0.730090\pi\)
−0.661525 + 0.749923i \(0.730090\pi\)
\(500\) 10.1157 4.76166i 0.452386 0.212948i
\(501\) −23.4333 −1.04692
\(502\) 8.38538i 0.374258i
\(503\) 9.11203i 0.406285i −0.979149 0.203143i \(-0.934884\pi\)
0.979149 0.203143i \(-0.0651155\pi\)
\(504\) −2.50466 −0.111567
\(505\) −9.11929 11.5047i −0.405803 0.511951i
\(506\) 3.27928 0.145782
\(507\) 11.1413i 0.494804i
\(508\) 3.09931i 0.137510i
\(509\) 21.8001 0.966270 0.483135 0.875546i \(-0.339498\pi\)
0.483135 + 0.875546i \(0.339498\pi\)
\(510\) 0.389004 0.308348i 0.0172254 0.0136539i
\(511\) 7.18336 0.317773
\(512\) 1.00000i 0.0441942i
\(513\) 6.14134i 0.271147i
\(514\) −6.55263 −0.289024
\(515\) 29.7160 23.5547i 1.30944 1.03794i
\(516\) 4.59465 0.202268
\(517\) 2.93932i 0.129271i
\(518\) 2.50466i 0.110049i
\(519\) −7.28267 −0.319674
\(520\) −1.89367 2.38900i −0.0830428 0.104765i
\(521\) −11.4499 −0.501630 −0.250815 0.968035i \(-0.580699\pi\)
−0.250815 + 0.968035i \(0.580699\pi\)
\(522\) 0.646000i 0.0282747i
\(523\) 10.8294i 0.473535i 0.971566 + 0.236767i \(0.0760879\pi\)
−0.971566 + 0.236767i \(0.923912\pi\)
\(524\) 11.3434 0.495537
\(525\) 2.85866 12.1927i 0.124762 0.532133i
\(526\) −15.4754 −0.674758
\(527\) 0.858664i 0.0374040i
\(528\) 3.77801i 0.164417i
\(529\) 22.2466 0.967243
\(530\) 3.15768 + 3.98365i 0.137161 + 0.173039i
\(531\) 7.78734 0.337942
\(532\) 15.3820i 0.666894i
\(533\) 1.24065i 0.0537385i
\(534\) −0.0899847 −0.00389402
\(535\) −27.7324 + 21.9823i −1.19897 + 0.950379i
\(536\) 10.7267 0.463321
\(537\) 1.82003i 0.0785401i
\(538\) 3.31198i 0.142789i
\(539\) −2.74531 −0.118249
\(540\) −1.75233 + 1.38900i −0.0754084 + 0.0597732i
\(541\) −7.64600 −0.328727 −0.164364 0.986400i \(-0.552557\pi\)
−0.164364 + 0.986400i \(0.552557\pi\)
\(542\) 32.1986i 1.38305i
\(543\) 0.212663i 0.00912626i
\(544\) −0.221992 −0.00951783
\(545\) −1.31768 1.66235i −0.0564431 0.0712071i
\(546\) −3.41468 −0.146135
\(547\) 41.1400i 1.75902i −0.475880 0.879510i \(-0.657870\pi\)
0.475880 0.879510i \(-0.342130\pi\)
\(548\) 10.4953i 0.448339i
\(549\) −9.42401 −0.402207
\(550\) 18.3913 + 4.31198i 0.784208 + 0.183863i
\(551\) 3.96731 0.169013
\(552\) 0.867993i 0.0369442i
\(553\) 1.24065i 0.0527578i
\(554\) −20.6553 −0.877561
\(555\) −1.38900 1.75233i −0.0589599 0.0743824i
\(556\) −18.8773 −0.800577
\(557\) 17.1820i 0.728026i −0.931394 0.364013i \(-0.881406\pi\)
0.931394 0.364013i \(-0.118594\pi\)
\(558\) 3.86799i 0.163745i
\(559\) 6.26401 0.264940
\(560\) −4.38900 + 3.47899i −0.185469 + 0.147014i
\(561\) 0.838688 0.0354094
\(562\) 9.80731i 0.413697i
\(563\) 27.3140i 1.15115i −0.817749 0.575575i \(-0.804778\pi\)
0.817749 0.575575i \(-0.195222\pi\)
\(564\) −0.778008 −0.0327600
\(565\) −0.546687 + 0.433337i −0.0229993 + 0.0182306i
\(566\) −18.6040 −0.781984
\(567\) 2.50466i 0.105186i
\(568\) 11.2406i 0.471647i
\(569\) 28.1341 1.17944 0.589721 0.807607i \(-0.299238\pi\)
0.589721 + 0.807607i \(0.299238\pi\)
\(570\) 8.53034 + 10.7617i 0.357297 + 0.450756i
\(571\) −5.93800 −0.248498 −0.124249 0.992251i \(-0.539652\pi\)
−0.124249 + 0.992251i \(0.539652\pi\)
\(572\) 5.15066i 0.215360i
\(573\) 2.00933i 0.0839409i
\(574\) 2.27928 0.0951354
\(575\) −4.22538 0.990671i −0.176211 0.0413138i
\(576\) 1.00000 0.0416667
\(577\) 2.46264i 0.102521i 0.998685 + 0.0512606i \(0.0163239\pi\)
−0.998685 + 0.0512606i \(0.983676\pi\)
\(578\) 16.9507i 0.705057i
\(579\) −6.00000 −0.249351
\(580\) 0.897297 + 1.13201i 0.0372582 + 0.0470040i
\(581\) 2.70668 0.112292
\(582\) 4.46603i 0.185123i
\(583\) 8.58871i 0.355708i
\(584\) −2.86799 −0.118678
\(585\) −2.38900 + 1.89367i −0.0987732 + 0.0782935i
\(586\) 27.8480 1.15039
\(587\) 20.8187i 0.859280i 0.903000 + 0.429640i \(0.141360\pi\)
−0.903000 + 0.429640i \(0.858640\pi\)
\(588\) 0.726656i 0.0299668i
\(589\) −23.7546 −0.978793
\(590\) 13.6460 10.8166i 0.561797 0.445314i
\(591\) −2.76529 −0.113749
\(592\) 1.00000i 0.0410997i
\(593\) 25.4533i 1.04524i 0.852565 + 0.522621i \(0.175046\pi\)
−0.852565 + 0.522621i \(0.824954\pi\)
\(594\) −3.77801 −0.155014
\(595\) −0.772308 0.974324i −0.0316615 0.0399434i
\(596\) −17.0280 −0.697493
\(597\) 1.98134i 0.0810910i
\(598\) 1.18336i 0.0483911i
\(599\) 27.8247 1.13688 0.568442 0.822723i \(-0.307546\pi\)
0.568442 + 0.822723i \(0.307546\pi\)
\(600\) −1.14134 + 4.86799i −0.0465949 + 0.198735i
\(601\) −10.1120 −0.412478 −0.206239 0.978502i \(-0.566122\pi\)
−0.206239 + 0.978502i \(0.566122\pi\)
\(602\) 11.5081i 0.469033i
\(603\) 10.7267i 0.436823i
\(604\) −22.3727 −0.910331
\(605\) 4.54669 + 5.73599i 0.184849 + 0.233201i
\(606\) 6.56534 0.266699
\(607\) 19.5933i 0.795269i −0.917544 0.397634i \(-0.869831\pi\)
0.917544 0.397634i \(-0.130169\pi\)
\(608\) 6.14134i 0.249064i
\(609\) 1.61801 0.0655653
\(610\) −16.5140 + 13.0900i −0.668632 + 0.529998i
\(611\) −1.06068 −0.0429105
\(612\) 0.221992i 0.00897350i
\(613\) 12.1693i 0.491514i 0.969331 + 0.245757i \(0.0790366\pi\)
−0.969331 + 0.245757i \(0.920963\pi\)
\(614\) −6.05135 −0.244213
\(615\) 1.59465 1.26401i 0.0643025 0.0509700i
\(616\) −9.46264 −0.381261
\(617\) 27.1634i 1.09356i −0.837277 0.546778i \(-0.815854\pi\)
0.837277 0.546778i \(-0.184146\pi\)
\(618\) 16.9580i 0.682150i
\(619\) −33.1273 −1.33150 −0.665749 0.746176i \(-0.731888\pi\)
−0.665749 + 0.746176i \(0.731888\pi\)
\(620\) −5.37266 6.77801i −0.215771 0.272211i
\(621\) 0.867993 0.0348313
\(622\) 28.3306i 1.13595i
\(623\) 0.225382i 0.00902972i
\(624\) 1.36333 0.0545768
\(625\) −22.3947 11.1120i −0.895788 0.444481i
\(626\) 1.50466 0.0601385
\(627\) 23.2020i 0.926599i
\(628\) 16.9800i 0.677577i
\(629\) −0.221992 −0.00885141
\(630\) 3.47899 + 4.38900i 0.138606 + 0.174862i
\(631\) −28.5547 −1.13674 −0.568372 0.822772i \(-0.692427\pi\)
−0.568372 + 0.822772i \(0.692427\pi\)
\(632\) 0.495336i 0.0197034i
\(633\) 20.9473i 0.832582i
\(634\) 20.0480 0.796206
\(635\) 5.43103 4.30496i 0.215524 0.170837i
\(636\) −2.27334 −0.0901439
\(637\) 0.990671i 0.0392518i
\(638\) 2.44059i 0.0966241i
\(639\) 11.2406 0.444673
\(640\) 1.75233 1.38900i 0.0692670 0.0549052i
\(641\) −41.2373 −1.62877 −0.814387 0.580322i \(-0.802927\pi\)
−0.814387 + 0.580322i \(0.802927\pi\)
\(642\) 15.8260i 0.624601i
\(643\) 12.7360i 0.502258i −0.967954 0.251129i \(-0.919198\pi\)
0.967954 0.251129i \(-0.0808019\pi\)
\(644\) 2.17403 0.0856688
\(645\) −6.38199 8.05135i −0.251290 0.317022i
\(646\) 1.36333 0.0536394
\(647\) 28.6040i 1.12454i −0.826954 0.562269i \(-0.809928\pi\)
0.826954 0.562269i \(-0.190072\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 29.4206 1.15486
\(650\) −1.55602 + 6.63667i −0.0610320 + 0.260312i
\(651\) −9.68802 −0.379704
\(652\) 7.00000i 0.274141i
\(653\) 25.2920i 0.989752i −0.868963 0.494876i \(-0.835213\pi\)
0.868963 0.494876i \(-0.164787\pi\)
\(654\) 0.948649 0.0370951
\(655\) −15.7560 19.8773i −0.615636 0.776671i
\(656\) −0.910015 −0.0355301
\(657\) 2.86799i 0.111891i
\(658\) 1.94865i 0.0759662i
\(659\) 28.4626 1.10875 0.554374 0.832268i \(-0.312958\pi\)
0.554374 + 0.832268i \(0.312958\pi\)
\(660\) −6.62032 + 5.24767i −0.257696 + 0.204265i
\(661\) 15.8994 0.618414 0.309207 0.950995i \(-0.399936\pi\)
0.309207 + 0.950995i \(0.399936\pi\)
\(662\) 21.5747i 0.838523i
\(663\) 0.302648i 0.0117539i
\(664\) −1.08066 −0.0419376
\(665\) 26.9543 21.3656i 1.04524 0.828524i
\(666\) 1.00000 0.0387492
\(667\) 0.560724i 0.0217113i
\(668\) 23.4333i 0.906663i
\(669\) −20.1507 −0.779070
\(670\) −14.8994 18.7967i −0.575613 0.726179i
\(671\) −35.6040 −1.37448
\(672\) 2.50466i 0.0966195i
\(673\) 27.5946i 1.06370i −0.846840 0.531848i \(-0.821498\pi\)
0.846840 0.531848i \(-0.178502\pi\)
\(674\) −12.4427 −0.479274
\(675\) 4.86799 + 1.14134i 0.187369 + 0.0439300i
\(676\) −11.1413 −0.428513
\(677\) 4.34674i 0.167059i −0.996505 0.0835294i \(-0.973381\pi\)
0.996505 0.0835294i \(-0.0266193\pi\)
\(678\) 0.311977i 0.0119814i
\(679\) −11.1859 −0.429276
\(680\) 0.308348 + 0.389004i 0.0118246 + 0.0149176i
\(681\) −28.4520 −1.09028
\(682\) 14.6133i 0.559572i
\(683\) 14.5620i 0.557198i 0.960408 + 0.278599i \(0.0898700\pi\)
−0.960408 + 0.278599i \(0.910130\pi\)
\(684\) −6.14134 −0.234820
\(685\) −18.3913 + 14.5781i −0.702696 + 0.556999i
\(686\) −19.3527 −0.738889
\(687\) 18.6940i 0.713219i
\(688\) 4.59465i 0.175169i
\(689\) −3.09931 −0.118074
\(690\) 1.52101 1.20565i 0.0579039 0.0458981i
\(691\) −43.9567 −1.67219 −0.836095 0.548585i \(-0.815167\pi\)
−0.836095 + 0.548585i \(0.815167\pi\)
\(692\) 7.28267i 0.276846i
\(693\) 9.46264i 0.359456i
\(694\) 12.0700 0.458171
\(695\) 26.2207 + 33.0793i 0.994607 + 1.25477i
\(696\) −0.646000 −0.0244866
\(697\) 0.202016i 0.00765191i
\(698\) 19.3434i 0.732157i
\(699\) 9.00933 0.340764
\(700\) 12.1927 + 2.85866i 0.460840 + 0.108047i
\(701\) −20.8667 −0.788123 −0.394062 0.919084i \(-0.628930\pi\)
−0.394062 + 0.919084i \(0.628930\pi\)
\(702\) 1.36333i 0.0514555i
\(703\) 6.14134i 0.231625i
\(704\) 3.77801 0.142389
\(705\) 1.08066 + 1.36333i 0.0406999 + 0.0513459i
\(706\) 5.48262 0.206341
\(707\) 16.4440i 0.618440i
\(708\) 7.78734i 0.292666i
\(709\) 31.6167 1.18739 0.593695 0.804690i \(-0.297669\pi\)
0.593695 + 0.804690i \(0.297669\pi\)
\(710\) 19.6974 15.6133i 0.739228 0.585957i
\(711\) −0.495336 −0.0185765
\(712\) 0.0899847i 0.00337232i
\(713\) 3.35739i 0.125735i
\(714\) 0.556016 0.0208084
\(715\) −9.02568 + 7.15429i −0.337541 + 0.267555i
\(716\) 1.82003 0.0680177
\(717\) 16.1693i 0.603854i
\(718\) 1.60737i 0.0599864i
\(719\) −16.9953 −0.633817 −0.316909 0.948456i \(-0.602645\pi\)
−0.316909 + 0.948456i \(0.602645\pi\)
\(720\) −1.38900 1.75233i −0.0517651 0.0653056i
\(721\) 42.4740 1.58182
\(722\) 18.7160i 0.696538i
\(723\) 10.3527i 0.385020i
\(724\) −0.212663 −0.00790357
\(725\) 0.737304 3.14473i 0.0273828 0.116792i
\(726\) −3.27334 −0.121485
\(727\) 1.40196i 0.0519959i 0.999662 + 0.0259979i \(0.00827633\pi\)
−0.999662 + 0.0259979i \(0.991724\pi\)
\(728\) 3.41468i 0.126556i
\(729\) −1.00000 −0.0370370
\(730\) 3.98365 + 5.02568i 0.147442 + 0.186009i
\(731\) −1.01998 −0.0377252
\(732\) 9.42401i 0.348321i
\(733\) 19.8094i 0.731676i 0.930678 + 0.365838i \(0.119218\pi\)
−0.930678 + 0.365838i \(0.880782\pi\)
\(734\) 7.51399 0.277347
\(735\) −1.27334 + 1.00933i −0.0469680 + 0.0372297i
\(736\) −0.867993 −0.0319946
\(737\) 40.5254i 1.49277i
\(738\) 0.910015i 0.0334981i
\(739\) −18.3561 −0.675239 −0.337619 0.941283i \(-0.609622\pi\)
−0.337619 + 0.941283i \(0.609622\pi\)
\(740\) 1.75233 1.38900i 0.0644170 0.0510608i
\(741\) −8.37266 −0.307577
\(742\) 5.69396i 0.209032i
\(743\) 30.6273i 1.12361i 0.827270 + 0.561804i \(0.189893\pi\)
−0.827270 + 0.561804i \(0.810107\pi\)
\(744\) 3.86799 0.141807
\(745\) 23.6519 + 29.8387i 0.866540 + 1.09320i
\(746\) −12.5140 −0.458170
\(747\) 1.08066i 0.0395391i
\(748\) 0.838688i 0.0306655i
\(749\) −39.6387 −1.44837
\(750\) 10.1157 4.76166i 0.369372 0.173871i
\(751\) −20.6680 −0.754188 −0.377094 0.926175i \(-0.623077\pi\)
−0.377094 + 0.926175i \(0.623077\pi\)
\(752\) 0.778008i 0.0283710i
\(753\) 8.38538i 0.305580i
\(754\) −0.880711 −0.0320736
\(755\) 31.0757 + 39.2043i 1.13096 + 1.42679i
\(756\) −2.50466 −0.0910938
\(757\) 1.78866i 0.0650098i 0.999472 + 0.0325049i \(0.0103484\pi\)
−0.999472 + 0.0325049i \(0.989652\pi\)
\(758\) 37.6260i 1.36664i
\(759\) 3.27928 0.119030
\(760\) −10.7617 + 8.53034i −0.390366 + 0.309428i
\(761\) −45.5853 −1.65247 −0.826233 0.563328i \(-0.809521\pi\)
−0.826233 + 0.563328i \(0.809521\pi\)
\(762\) 3.09931i 0.112276i
\(763\) 2.37605i 0.0860187i
\(764\) 2.00933 0.0726950
\(765\) 0.389004 0.308348i 0.0140645 0.0111483i
\(766\) 14.2440 0.514658
\(767\) 10.6167i 0.383347i
\(768\) 1.00000i 0.0360844i
\(769\) 26.0887 0.940781 0.470391 0.882458i \(-0.344113\pi\)
0.470391 + 0.882458i \(0.344113\pi\)
\(770\) 13.1436 + 16.5817i 0.473664 + 0.597563i
\(771\) −6.55263 −0.235987
\(772\) 6.00000i 0.215945i
\(773\) 17.8294i 0.641277i −0.947202 0.320639i \(-0.896102\pi\)
0.947202 0.320639i \(-0.103898\pi\)
\(774\) 4.59465 0.165151
\(775\) −4.41468 + 18.8294i −0.158580 + 0.676371i
\(776\) 4.46603 0.160321
\(777\) 2.50466i 0.0898543i
\(778\) 0.697352i 0.0250013i
\(779\) 5.58871 0.200236
\(780\) −1.89367 2.38900i −0.0678042 0.0855401i
\(781\) 42.4673 1.51960
\(782\) 0.192688i 0.00689049i
\(783\) 0.646000i 0.0230862i
\(784\) 0.726656 0.0259520
\(785\) −29.7546 + 23.5853i −1.06199 + 0.841796i
\(786\) 11.3434 0.404604
\(787\) 22.1027i 0.787876i 0.919137 + 0.393938i \(0.128888\pi\)
−0.919137 + 0.393938i \(0.871112\pi\)
\(788\) 2.76529i 0.0985094i
\(789\) −15.4754 −0.550937
\(790\) −0.867993 + 0.688023i −0.0308818 + 0.0244788i
\(791\) −0.781397 −0.0277833
\(792\) 3.77801i 0.134246i
\(793\) 12.8480i 0.456246i
\(794\) 28.4040 1.00802
\(795\) 3.15768 + 3.98365i 0.111991 + 0.141286i
\(796\) 1.98134 0.0702268
\(797\) 37.6633i 1.33410i 0.745011 + 0.667052i \(0.232444\pi\)
−0.745011 + 0.667052i \(0.767556\pi\)
\(798\) 15.3820i 0.544516i
\(799\) 0.172712 0.00611010
\(800\) −4.86799 1.14134i −0.172110 0.0403523i
\(801\) −0.0899847 −0.00317945
\(802\) 22.7580i 0.803614i
\(803\) 10.8353i 0.382369i
\(804\) 10.7267 0.378300
\(805\) −3.01974 3.80962i −0.106432 0.134272i
\(806\) 5.27334 0.185746
\(807\) 3.31198i 0.116587i
\(808\) 6.56534i 0.230968i
\(809\) 31.3047 1.10062 0.550308 0.834962i \(-0.314510\pi\)
0.550308 + 0.834962i \(0.314510\pi\)
\(810\) −1.75233 + 1.38900i −0.0615707 + 0.0488046i
\(811\) 3.67738 0.129130 0.0645651 0.997913i \(-0.479434\pi\)
0.0645651 + 0.997913i \(0.479434\pi\)
\(812\) 1.61801i 0.0567812i
\(813\) 32.1986i 1.12926i
\(814\) 3.77801 0.132419
\(815\) 12.2663 9.72303i 0.429671 0.340583i
\(816\) −0.221992 −0.00777128
\(817\) 28.2173i 0.987198i
\(818\) 16.3527i 0.571758i
\(819\) −3.41468 −0.119319
\(820\) 1.26401 + 1.59465i 0.0441413 + 0.0556876i
\(821\) 9.51738 0.332159 0.166079 0.986112i \(-0.446889\pi\)
0.166079 + 0.986112i \(0.446889\pi\)
\(822\) 10.4953i 0.366067i
\(823\) 49.2580i 1.71703i 0.512792 + 0.858513i \(0.328611\pi\)
−0.512792 + 0.858513i \(0.671389\pi\)
\(824\) −16.9580 −0.590759
\(825\) 18.3913 + 4.31198i 0.640303 + 0.150124i
\(826\) 19.5047 0.678654
\(827\) 41.2487i 1.43436i −0.696890 0.717178i \(-0.745433\pi\)
0.696890 0.717178i \(-0.254567\pi\)
\(828\) 0.867993i 0.0301648i
\(829\) 19.4113 0.674182 0.337091 0.941472i \(-0.390557\pi\)
0.337091 + 0.941472i \(0.390557\pi\)
\(830\) 1.50104 + 1.89367i 0.0521017 + 0.0657302i
\(831\) −20.6553 −0.716525
\(832\) 1.36333i 0.0472649i
\(833\) 0.161312i 0.00558913i
\(834\) −18.8773 −0.653668
\(835\) −41.0630 + 32.5490i −1.42104 + 1.12640i
\(836\) −23.2020 −0.802459
\(837\) 3.86799i 0.133697i
\(838\) 11.2020i 0.386967i
\(839\) 31.8646 1.10009 0.550044 0.835136i \(-0.314611\pi\)
0.550044 + 0.835136i \(0.314611\pi\)
\(840\) −4.38900 + 3.47899i −0.151435 + 0.120037i
\(841\) −28.5827 −0.985610
\(842\) 13.8200i 0.476270i
\(843\) 9.80731i 0.337782i
\(844\) 20.9473 0.721037
\(845\) 15.4754 + 19.5233i 0.532369 + 0.671623i
\(846\) −0.778008 −0.0267485
\(847\) 8.19863i 0.281708i
\(848\) 2.27334i 0.0780669i
\(849\) −18.6040 −0.638487
\(850\) 0.253368 1.08066i 0.00869044 0.0370662i
\(851\) −0.867993 −0.0297544
\(852\) 11.2406i 0.385098i
\(853\) 51.7860i 1.77312i 0.462614 + 0.886560i \(0.346912\pi\)
−0.462614 + 0.886560i \(0.653088\pi\)
\(854\) −23.6040 −0.807711
\(855\) 8.53034 + 10.7617i 0.291731 + 0.368041i
\(856\) 15.8260 0.540921
\(857\) 50.1753i 1.71395i −0.515354 0.856977i \(-0.672340\pi\)
0.515354 0.856977i \(-0.327660\pi\)
\(858\) 5.15066i 0.175841i
\(859\) 44.5199 1.51900 0.759500 0.650507i \(-0.225444\pi\)
0.759500 + 0.650507i \(0.225444\pi\)
\(860\) 8.05135 6.38199i 0.274549 0.217624i
\(861\) 2.27928 0.0776778
\(862\) 36.1493i 1.23125i
\(863\) 9.25130i 0.314918i −0.987526 0.157459i \(-0.949670\pi\)
0.987526 0.157459i \(-0.0503302\pi\)
\(864\) 1.00000 0.0340207
\(865\) −12.7617 + 10.1157i −0.433909 + 0.343943i
\(866\) 19.4147 0.659738
\(867\) 16.9507i 0.575677i
\(868\) 9.68802i 0.328833i
\(869\) −1.87138 −0.0634823
\(870\) 0.897297 + 1.13201i 0.0304212 + 0.0383786i
\(871\) 14.6240 0.495514
\(872\) 0.948649i 0.0321253i
\(873\) 4.46603i 0.151152i
\(874\) 5.33063 0.180311
\(875\) −11.9264 25.3363i −0.403185 0.856524i
\(876\) −2.86799 −0.0969005
\(877\) 48.5220i 1.63847i 0.573457 + 0.819236i \(0.305602\pi\)
−0.573457 + 0.819236i \(0.694398\pi\)
\(878\) 24.2207i 0.817408i
\(879\) 27.8480 0.939290
\(880\) −5.24767 6.62032i −0.176899 0.223171i
\(881\) 42.5293 1.43285 0.716424 0.697666i \(-0.245778\pi\)
0.716424 + 0.697666i \(0.245778\pi\)
\(882\) 0.726656i 0.0244678i
\(883\) 52.0466i 1.75151i −0.482757 0.875755i \(-0.660364\pi\)
0.482757 0.875755i \(-0.339636\pi\)
\(884\) −0.302648 −0.0101792
\(885\) 13.6460 10.8166i 0.458705 0.363597i
\(886\) 22.0373 0.740358
\(887\) 34.3120i 1.15208i −0.817420 0.576042i \(-0.804597\pi\)
0.817420 0.576042i \(-0.195403\pi\)
\(888\) 1.00000i 0.0335578i
\(889\) 7.76274 0.260354
\(890\) −0.157683 + 0.124989i −0.00528555 + 0.00418964i
\(891\) −3.77801 −0.126568
\(892\) 20.1507i 0.674694i
\(893\) 4.77801i 0.159890i
\(894\) −17.0280 −0.569501
\(895\) −2.52803 3.18930i −0.0845027 0.106606i
\(896\) 2.50466 0.0836750
\(897\) 1.18336i 0.0395112i
\(898\) 1.63328i 0.0545033i
\(899\) −2.49873 −0.0833371
\(900\) −1.14134 + 4.86799i −0.0380445 + 0.162266i
\(901\) 0.504664 0.0168128
\(902\) 3.43804i 0.114474i
\(903\) 11.5081i 0.382964i
\(904\) 0.311977 0.0103762
\(905\) 0.295390 + 0.372657i 0.00981911 + 0.0123875i
\(906\) −22.3727 −0.743282
\(907\) 5.99868i 0.199183i 0.995028 + 0.0995915i \(0.0317536\pi\)
−0.995028 + 0.0995915i \(0.968246\pi\)
\(908\) 28.4520i 0.944213i
\(909\) 6.56534 0.217759
\(910\) −5.98365 + 4.74300i −0.198356 + 0.157229i
\(911\) 36.3599 1.20466 0.602329 0.798248i \(-0.294239\pi\)
0.602329 + 0.798248i \(0.294239\pi\)
\(912\) 6.14134i 0.203360i
\(913\) 4.08273i 0.135119i
\(914\) 14.2279 0.470618
\(915\) −16.5140 + 13.0900i −0.545936 + 0.432742i
\(916\) 18.6940 0.617666
\(917\) 28.4113i 0.938223i
\(918\) 0.221992i 0.00732683i
\(919\) 19.6074 0.646787 0.323394 0.946265i \(-0.395176\pi\)
0.323394 + 0.946265i \(0.395176\pi\)
\(920\) 1.20565 + 1.52101i 0.0397489 + 0.0501463i
\(921\) −6.05135 −0.199399
\(922\) 20.8587i 0.686944i
\(923\) 15.3247i 0.504418i
\(924\) −9.46264 −0.311298
\(925\) −4.86799 1.14134i −0.160059 0.0375269i
\(926\) 0.0326940 0.00107439
\(927\) 16.9580i 0.556973i
\(928\) 0.646000i 0.0212060i
\(929\) 39.0827 1.28226 0.641131 0.767431i \(-0.278465\pi\)
0.641131 + 0.767431i \(0.278465\pi\)
\(930\) −5.37266 6.77801i −0.176176 0.222260i
\(931\) −4.46264 −0.146257
\(932\) 9.00933i 0.295110i
\(933\) 28.3306i 0.927503i
\(934\) −16.1834 −0.529536
\(935\) 1.46966 1.16494i 0.0480630 0.0380976i
\(936\) 1.36333 0.0445618
\(937\) 38.0187i 1.24202i −0.783804 0.621008i \(-0.786724\pi\)
0.783804 0.621008i \(-0.213276\pi\)
\(938\) 26.8667i 0.877228i
\(939\) 1.50466 0.0491029
\(940\) −1.36333 + 1.08066i −0.0444669 + 0.0352471i
\(941\) −41.9600 −1.36786 −0.683929 0.729548i \(-0.739730\pi\)
−0.683929 + 0.729548i \(0.739730\pi\)
\(942\) 16.9800i 0.553239i
\(943\) 0.789887i 0.0257222i
\(944\) −7.78734 −0.253456
\(945\) 3.47899 + 4.38900i 0.113172 + 0.142774i
\(946\) 17.3586 0.564377
\(947\) 11.7139i 0.380652i 0.981721 + 0.190326i \(0.0609545\pi\)
−0.981721 + 0.190326i \(0.939046\pi\)
\(948\) 0.495336i 0.0160878i
\(949\) −3.91002 −0.126924
\(950\) 29.8960 + 7.00933i 0.969954 + 0.227413i
\(951\) 20.0480 0.650100
\(952\) 0.556016i 0.0180206i
\(953\) 46.6354i 1.51067i −0.655340 0.755334i \(-0.727475\pi\)
0.655340 0.755334i \(-0.272525\pi\)
\(954\) −2.27334 −0.0736022
\(955\) −2.79097 3.52101i −0.0903135 0.113937i
\(956\) 16.1693 0.522953
\(957\) 2.44059i 0.0788932i
\(958\) 1.15066i 0.0371763i
\(959\) −26.2873 −0.848861
\(960\) 1.75233 1.38900i 0.0565563 0.0448299i
\(961\) −16.0386 −0.517375
\(962\) 1.36333i 0.0439555i
\(963\) 15.8260i 0.509985i
\(964\) −10.3527 −0.333437
\(965\) −10.5140 + 8.33402i −0.338457 + 0.268282i
\(966\) 2.17403 0.0699483
\(967\) 54.6727i 1.75815i 0.476679 + 0.879077i \(0.341840\pi\)
−0.476679 + 0.879077i \(0.658160\pi\)
\(968\) 3.27334i 0.105209i
\(969\) 1.36333 0.0437964
\(970\) −6.20333 7.82597i −0.199177 0.251277i
\(971\) 26.2466 0.842293 0.421147 0.906993i \(-0.361628\pi\)
0.421147 + 0.906993i \(0.361628\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 47.2814i 1.51577i
\(974\) −3.71733 −0.119111
\(975\) −1.55602 + 6.63667i −0.0498324 + 0.212544i
\(976\) 9.42401 0.301655
\(977\) 36.3620i 1.16332i 0.813431 + 0.581662i \(0.197597\pi\)
−0.813431 + 0.581662i \(0.802403\pi\)
\(978\) 7.00000i 0.223835i
\(979\) −0.339963 −0.0108653
\(980\) −1.00933 1.27334i −0.0322418 0.0406755i
\(981\) 0.948649 0.0302880
\(982\) 10.9966i 0.350916i
\(983\) 54.6506i 1.74308i 0.490321 + 0.871542i \(0.336880\pi\)
−0.490321 + 0.871542i \(0.663120\pi\)
\(984\) −0.910015 −0.0290102
\(985\) −4.84571 + 3.84100i −0.154397 + 0.122384i
\(986\) 0.143407 0.00456701
\(987\) 1.94865i 0.0620262i
\(988\) 8.37266i 0.266370i
\(989\) −3.98812 −0.126815
\(990\) −6.62032 + 5.24767i −0.210408 + 0.166782i
\(991\) 4.05474 0.128803 0.0644015 0.997924i \(-0.479486\pi\)
0.0644015 + 0.997924i \(0.479486\pi\)
\(992\) 3.86799i 0.122809i
\(993\) 21.5747i 0.684652i
\(994\) 28.1541 0.892992
\(995\) −2.75209 3.47197i −0.0872472 0.110069i
\(996\) −1.08066 −0.0342419
\(997\) 20.7326i 0.656608i −0.944572 0.328304i \(-0.893523\pi\)
0.944572 0.328304i \(-0.106477\pi\)
\(998\) 29.5547i 0.935538i
\(999\) 1.00000 0.0316386
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 1110.2.d.i.889.5 yes 6
3.2 odd 2 3330.2.d.n.1999.2 6
5.2 odd 4 5550.2.a.cf.1.1 3
5.3 odd 4 5550.2.a.cg.1.3 3
5.4 even 2 inner 1110.2.d.i.889.2 6
15.14 odd 2 3330.2.d.n.1999.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.d.i.889.2 6 5.4 even 2 inner
1110.2.d.i.889.5 yes 6 1.1 even 1 trivial
3330.2.d.n.1999.2 6 3.2 odd 2
3330.2.d.n.1999.5 6 15.14 odd 2
5550.2.a.cf.1.1 3 5.2 odd 4
5550.2.a.cg.1.3 3 5.3 odd 4