Properties

Label 1155.2.l.a.1121.3
Level $1155$
Weight $2$
Character 1155.1121
Analytic conductor $9.223$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(1121,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.1121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.l (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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1121.3
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1155.1121
Dual form 1155.2.l.a.1121.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.414214 q^{2} +(1.00000 - 1.41421i) q^{3} -1.82843 q^{4} +1.00000i q^{5} +(0.414214 - 0.585786i) q^{6} +1.00000i q^{7} -1.58579 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+0.414214 q^{2} +(1.00000 - 1.41421i) q^{3} -1.82843 q^{4} +1.00000i q^{5} +(0.414214 - 0.585786i) q^{6} +1.00000i q^{7} -1.58579 q^{8} +(-1.00000 - 2.82843i) q^{9} +0.414214i q^{10} +(1.41421 + 3.00000i) q^{11} +(-1.82843 + 2.58579i) q^{12} +0.414214i q^{14} +(1.41421 + 1.00000i) q^{15} +3.00000 q^{16} +6.82843 q^{17} +(-0.414214 - 1.17157i) q^{18} -0.828427i q^{19} -1.82843i q^{20} +(1.41421 + 1.00000i) q^{21} +(0.585786 + 1.24264i) q^{22} +0.828427i q^{23} +(-1.58579 + 2.24264i) q^{24} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} -1.82843i q^{28} +5.65685 q^{29} +(0.585786 + 0.414214i) q^{30} +0.828427 q^{31} +4.41421 q^{32} +(5.65685 + 1.00000i) q^{33} +2.82843 q^{34} -1.00000 q^{35} +(1.82843 + 5.17157i) q^{36} +6.00000 q^{37} -0.343146i q^{38} -1.58579i q^{40} +7.65685 q^{41} +(0.585786 + 0.414214i) q^{42} -9.65685i q^{43} +(-2.58579 - 5.48528i) q^{44} +(2.82843 - 1.00000i) q^{45} +0.343146i q^{46} +10.8284i q^{47} +(3.00000 - 4.24264i) q^{48} -1.00000 q^{49} -0.414214 q^{50} +(6.82843 - 9.65685i) q^{51} +0.828427i q^{53} +(-2.07107 - 0.585786i) q^{54} +(-3.00000 + 1.41421i) q^{55} -1.58579i q^{56} +(-1.17157 - 0.828427i) q^{57} +2.34315 q^{58} -0.343146i q^{59} +(-2.58579 - 1.82843i) q^{60} +5.17157i q^{61} +0.343146 q^{62} +(2.82843 - 1.00000i) q^{63} -4.17157 q^{64} +(2.34315 + 0.414214i) q^{66} -6.48528 q^{67} -12.4853 q^{68} +(1.17157 + 0.828427i) q^{69} -0.414214 q^{70} +0.343146i q^{71} +(1.58579 + 4.48528i) q^{72} -12.0000i q^{73} +2.48528 q^{74} +(-1.00000 + 1.41421i) q^{75} +1.51472i q^{76} +(-3.00000 + 1.41421i) q^{77} +4.00000i q^{79} +3.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} +3.17157 q^{82} +12.0000 q^{83} +(-2.58579 - 1.82843i) q^{84} +6.82843i q^{85} -4.00000i q^{86} +(5.65685 - 8.00000i) q^{87} +(-2.24264 - 4.75736i) q^{88} +7.65685i q^{89} +(1.17157 - 0.414214i) q^{90} -1.51472i q^{92} +(0.828427 - 1.17157i) q^{93} +4.48528i q^{94} +0.828427 q^{95} +(4.41421 - 6.24264i) q^{96} -5.17157 q^{97} -0.414214 q^{98} +(7.07107 - 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 12 q^{8} - 4 q^{9} + 4 q^{12} + 12 q^{16} + 16 q^{17} + 4 q^{18} + 8 q^{22} - 12 q^{24} - 4 q^{25} - 20 q^{27} + 8 q^{30} - 8 q^{31} + 12 q^{32} - 4 q^{35} - 4 q^{36} + 24 q^{37} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 12 q^{48} - 4 q^{49} + 4 q^{50} + 16 q^{51} + 20 q^{54} - 12 q^{55} - 16 q^{57} + 32 q^{58} - 16 q^{60} + 24 q^{62} - 28 q^{64} + 32 q^{66} + 8 q^{67} - 16 q^{68} + 16 q^{69} + 4 q^{70} + 12 q^{72} - 24 q^{74} - 4 q^{75} - 12 q^{77} - 28 q^{81} + 24 q^{82} + 48 q^{83} - 16 q^{84} + 8 q^{88} + 16 q^{90} - 8 q^{93} - 8 q^{95} + 12 q^{96} - 32 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.414214 0.292893 0.146447 0.989219i \(-0.453216\pi\)
0.146447 + 0.989219i \(0.453216\pi\)
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) −1.82843 −0.914214
\(5\) 1.00000i 0.447214i
\(6\) 0.414214 0.585786i 0.169102 0.239146i
\(7\) 1.00000i 0.377964i
\(8\) −1.58579 −0.560660
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0.414214i 0.130986i
\(11\) 1.41421 + 3.00000i 0.426401 + 0.904534i
\(12\) −1.82843 + 2.58579i −0.527821 + 0.746452i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.414214i 0.110703i
\(15\) 1.41421 + 1.00000i 0.365148 + 0.258199i
\(16\) 3.00000 0.750000
\(17\) 6.82843 1.65614 0.828068 0.560627i \(-0.189440\pi\)
0.828068 + 0.560627i \(0.189440\pi\)
\(18\) −0.414214 1.17157i −0.0976311 0.276142i
\(19\) 0.828427i 0.190054i −0.995475 0.0950271i \(-0.969706\pi\)
0.995475 0.0950271i \(-0.0302938\pi\)
\(20\) 1.82843i 0.408849i
\(21\) 1.41421 + 1.00000i 0.308607 + 0.218218i
\(22\) 0.585786 + 1.24264i 0.124890 + 0.264932i
\(23\) 0.828427i 0.172739i 0.996263 + 0.0863695i \(0.0275266\pi\)
−0.996263 + 0.0863695i \(0.972473\pi\)
\(24\) −1.58579 + 2.24264i −0.323697 + 0.457777i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 1.82843i 0.345540i
\(29\) 5.65685 1.05045 0.525226 0.850963i \(-0.323981\pi\)
0.525226 + 0.850963i \(0.323981\pi\)
\(30\) 0.585786 + 0.414214i 0.106949 + 0.0756247i
\(31\) 0.828427 0.148790 0.0743950 0.997229i \(-0.476297\pi\)
0.0743950 + 0.997229i \(0.476297\pi\)
\(32\) 4.41421 0.780330
\(33\) 5.65685 + 1.00000i 0.984732 + 0.174078i
\(34\) 2.82843 0.485071
\(35\) −1.00000 −0.169031
\(36\) 1.82843 + 5.17157i 0.304738 + 0.861929i
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0.343146i 0.0556656i
\(39\) 0 0
\(40\) 1.58579i 0.250735i
\(41\) 7.65685 1.19580 0.597900 0.801571i \(-0.296002\pi\)
0.597900 + 0.801571i \(0.296002\pi\)
\(42\) 0.585786 + 0.414214i 0.0903888 + 0.0639145i
\(43\) 9.65685i 1.47266i −0.676625 0.736328i \(-0.736558\pi\)
0.676625 0.736328i \(-0.263442\pi\)
\(44\) −2.58579 5.48528i −0.389822 0.826937i
\(45\) 2.82843 1.00000i 0.421637 0.149071i
\(46\) 0.343146i 0.0505941i
\(47\) 10.8284i 1.57949i 0.613436 + 0.789744i \(0.289787\pi\)
−0.613436 + 0.789744i \(0.710213\pi\)
\(48\) 3.00000 4.24264i 0.433013 0.612372i
\(49\) −1.00000 −0.142857
\(50\) −0.414214 −0.0585786
\(51\) 6.82843 9.65685i 0.956171 1.35223i
\(52\) 0 0
\(53\) 0.828427i 0.113793i 0.998380 + 0.0568966i \(0.0181205\pi\)
−0.998380 + 0.0568966i \(0.981879\pi\)
\(54\) −2.07107 0.585786i −0.281837 0.0797154i
\(55\) −3.00000 + 1.41421i −0.404520 + 0.190693i
\(56\) 1.58579i 0.211910i
\(57\) −1.17157 0.828427i −0.155179 0.109728i
\(58\) 2.34315 0.307670
\(59\) 0.343146i 0.0446738i −0.999751 0.0223369i \(-0.992889\pi\)
0.999751 0.0223369i \(-0.00711064\pi\)
\(60\) −2.58579 1.82843i −0.333824 0.236049i
\(61\) 5.17157i 0.662152i 0.943604 + 0.331076i \(0.107412\pi\)
−0.943604 + 0.331076i \(0.892588\pi\)
\(62\) 0.343146 0.0435796
\(63\) 2.82843 1.00000i 0.356348 0.125988i
\(64\) −4.17157 −0.521447
\(65\) 0 0
\(66\) 2.34315 + 0.414214i 0.288421 + 0.0509862i
\(67\) −6.48528 −0.792303 −0.396152 0.918185i \(-0.629655\pi\)
−0.396152 + 0.918185i \(0.629655\pi\)
\(68\) −12.4853 −1.51406
\(69\) 1.17157 + 0.828427i 0.141041 + 0.0997309i
\(70\) −0.414214 −0.0495080
\(71\) 0.343146i 0.0407239i 0.999793 + 0.0203620i \(0.00648186\pi\)
−0.999793 + 0.0203620i \(0.993518\pi\)
\(72\) 1.58579 + 4.48528i 0.186887 + 0.528595i
\(73\) 12.0000i 1.40449i −0.711934 0.702247i \(-0.752180\pi\)
0.711934 0.702247i \(-0.247820\pi\)
\(74\) 2.48528 0.288908
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 1.51472i 0.173750i
\(77\) −3.00000 + 1.41421i −0.341882 + 0.161165i
\(78\) 0 0
\(79\) 4.00000i 0.450035i 0.974355 + 0.225018i \(0.0722440\pi\)
−0.974355 + 0.225018i \(0.927756\pi\)
\(80\) 3.00000i 0.335410i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 3.17157 0.350242
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −2.58579 1.82843i −0.282132 0.199498i
\(85\) 6.82843i 0.740647i
\(86\) 4.00000i 0.431331i
\(87\) 5.65685 8.00000i 0.606478 0.857690i
\(88\) −2.24264 4.75736i −0.239066 0.507136i
\(89\) 7.65685i 0.811625i 0.913956 + 0.405812i \(0.133011\pi\)
−0.913956 + 0.405812i \(0.866989\pi\)
\(90\) 1.17157 0.414214i 0.123495 0.0436619i
\(91\) 0 0
\(92\) 1.51472i 0.157920i
\(93\) 0.828427 1.17157i 0.0859039 0.121486i
\(94\) 4.48528i 0.462621i
\(95\) 0.828427 0.0849948
\(96\) 4.41421 6.24264i 0.450524 0.637137i
\(97\) −5.17157 −0.525094 −0.262547 0.964919i \(-0.584562\pi\)
−0.262547 + 0.964919i \(0.584562\pi\)
\(98\) −0.414214 −0.0418419
\(99\) 7.07107 7.00000i 0.710669 0.703526i
\(100\) 1.82843 0.182843
\(101\) −9.31371 −0.926749 −0.463374 0.886163i \(-0.653361\pi\)
−0.463374 + 0.886163i \(0.653361\pi\)
\(102\) 2.82843 4.00000i 0.280056 0.396059i
\(103\) 9.31371 0.917707 0.458853 0.888512i \(-0.348260\pi\)
0.458853 + 0.888512i \(0.348260\pi\)
\(104\) 0 0
\(105\) −1.00000 + 1.41421i −0.0975900 + 0.138013i
\(106\) 0.343146i 0.0333293i
\(107\) 9.31371 0.900390 0.450195 0.892930i \(-0.351354\pi\)
0.450195 + 0.892930i \(0.351354\pi\)
\(108\) 9.14214 + 2.58579i 0.879702 + 0.248817i
\(109\) 9.65685i 0.924959i −0.886630 0.462479i \(-0.846960\pi\)
0.886630 0.462479i \(-0.153040\pi\)
\(110\) −1.24264 + 0.585786i −0.118481 + 0.0558525i
\(111\) 6.00000 8.48528i 0.569495 0.805387i
\(112\) 3.00000i 0.283473i
\(113\) 3.17157i 0.298356i 0.988810 + 0.149178i \(0.0476628\pi\)
−0.988810 + 0.149178i \(0.952337\pi\)
\(114\) −0.485281 0.343146i −0.0454508 0.0321385i
\(115\) −0.828427 −0.0772512
\(116\) −10.3431 −0.960337
\(117\) 0 0
\(118\) 0.142136i 0.0130846i
\(119\) 6.82843i 0.625961i
\(120\) −2.24264 1.58579i −0.204724 0.144762i
\(121\) −7.00000 + 8.48528i −0.636364 + 0.771389i
\(122\) 2.14214i 0.193940i
\(123\) 7.65685 10.8284i 0.690395 0.976366i
\(124\) −1.51472 −0.136026
\(125\) 1.00000i 0.0894427i
\(126\) 1.17157 0.414214i 0.104372 0.0369011i
\(127\) 13.6569i 1.21185i 0.795522 + 0.605925i \(0.207197\pi\)
−0.795522 + 0.605925i \(0.792803\pi\)
\(128\) −10.5563 −0.933058
\(129\) −13.6569 9.65685i −1.20242 0.850239i
\(130\) 0 0
\(131\) −17.6569 −1.54269 −0.771343 0.636419i \(-0.780415\pi\)
−0.771343 + 0.636419i \(0.780415\pi\)
\(132\) −10.3431 1.82843i −0.900255 0.159144i
\(133\) 0.828427 0.0718337
\(134\) −2.68629 −0.232060
\(135\) 1.41421 5.00000i 0.121716 0.430331i
\(136\) −10.8284 −0.928530
\(137\) 12.8284i 1.09601i −0.836476 0.548003i \(-0.815388\pi\)
0.836476 0.548003i \(-0.184612\pi\)
\(138\) 0.485281 + 0.343146i 0.0413099 + 0.0292105i
\(139\) 6.48528i 0.550074i 0.961434 + 0.275037i \(0.0886902\pi\)
−0.961434 + 0.275037i \(0.911310\pi\)
\(140\) 1.82843 0.154530
\(141\) 15.3137 + 10.8284i 1.28965 + 0.911918i
\(142\) 0.142136i 0.0119278i
\(143\) 0 0
\(144\) −3.00000 8.48528i −0.250000 0.707107i
\(145\) 5.65685i 0.469776i
\(146\) 4.97056i 0.411367i
\(147\) −1.00000 + 1.41421i −0.0824786 + 0.116642i
\(148\) −10.9706 −0.901775
\(149\) 7.31371 0.599162 0.299581 0.954071i \(-0.403153\pi\)
0.299581 + 0.954071i \(0.403153\pi\)
\(150\) −0.414214 + 0.585786i −0.0338204 + 0.0478293i
\(151\) 3.31371i 0.269666i −0.990868 0.134833i \(-0.956950\pi\)
0.990868 0.134833i \(-0.0430498\pi\)
\(152\) 1.31371i 0.106556i
\(153\) −6.82843 19.3137i −0.552046 1.56142i
\(154\) −1.24264 + 0.585786i −0.100135 + 0.0472040i
\(155\) 0.828427i 0.0665409i
\(156\) 0 0
\(157\) −18.8284 −1.50267 −0.751336 0.659920i \(-0.770590\pi\)
−0.751336 + 0.659920i \(0.770590\pi\)
\(158\) 1.65685i 0.131812i
\(159\) 1.17157 + 0.828427i 0.0929118 + 0.0656985i
\(160\) 4.41421i 0.348974i
\(161\) −0.828427 −0.0652892
\(162\) −2.89949 + 2.34315i −0.227806 + 0.184095i
\(163\) −1.51472 −0.118642 −0.0593210 0.998239i \(-0.518894\pi\)
−0.0593210 + 0.998239i \(0.518894\pi\)
\(164\) −14.0000 −1.09322
\(165\) −1.00000 + 5.65685i −0.0778499 + 0.440386i
\(166\) 4.97056 0.385790
\(167\) −2.34315 −0.181318 −0.0906590 0.995882i \(-0.528897\pi\)
−0.0906590 + 0.995882i \(0.528897\pi\)
\(168\) −2.24264 1.58579i −0.173023 0.122346i
\(169\) 13.0000 1.00000
\(170\) 2.82843i 0.216930i
\(171\) −2.34315 + 0.828427i −0.179185 + 0.0633514i
\(172\) 17.6569i 1.34632i
\(173\) 10.1421 0.771092 0.385546 0.922689i \(-0.374013\pi\)
0.385546 + 0.922689i \(0.374013\pi\)
\(174\) 2.34315 3.31371i 0.177633 0.251212i
\(175\) 1.00000i 0.0755929i
\(176\) 4.24264 + 9.00000i 0.319801 + 0.678401i
\(177\) −0.485281 0.343146i −0.0364760 0.0257924i
\(178\) 3.17157i 0.237719i
\(179\) 11.6569i 0.871274i −0.900122 0.435637i \(-0.856523\pi\)
0.900122 0.435637i \(-0.143477\pi\)
\(180\) −5.17157 + 1.82843i −0.385466 + 0.136283i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 7.31371 + 5.17157i 0.540645 + 0.382294i
\(184\) 1.31371i 0.0968479i
\(185\) 6.00000i 0.441129i
\(186\) 0.343146 0.485281i 0.0251607 0.0355826i
\(187\) 9.65685 + 20.4853i 0.706179 + 1.49803i
\(188\) 19.7990i 1.44399i
\(189\) 1.41421 5.00000i 0.102869 0.363696i
\(190\) 0.343146 0.0248944
\(191\) 6.00000i 0.434145i 0.976156 + 0.217072i \(0.0696508\pi\)
−0.976156 + 0.217072i \(0.930349\pi\)
\(192\) −4.17157 + 5.89949i −0.301057 + 0.425759i
\(193\) 22.4853i 1.61853i 0.587447 + 0.809263i \(0.300133\pi\)
−0.587447 + 0.809263i \(0.699867\pi\)
\(194\) −2.14214 −0.153796
\(195\) 0 0
\(196\) 1.82843 0.130602
\(197\) 14.8284 1.05648 0.528241 0.849095i \(-0.322852\pi\)
0.528241 + 0.849095i \(0.322852\pi\)
\(198\) 2.92893 2.89949i 0.208150 0.206058i
\(199\) −14.4853 −1.02683 −0.513417 0.858139i \(-0.671621\pi\)
−0.513417 + 0.858139i \(0.671621\pi\)
\(200\) 1.58579 0.112132
\(201\) −6.48528 + 9.17157i −0.457436 + 0.646913i
\(202\) −3.85786 −0.271438
\(203\) 5.65685i 0.397033i
\(204\) −12.4853 + 17.6569i −0.874145 + 1.23623i
\(205\) 7.65685i 0.534778i
\(206\) 3.85786 0.268790
\(207\) 2.34315 0.828427i 0.162860 0.0575797i
\(208\) 0 0
\(209\) 2.48528 1.17157i 0.171911 0.0810394i
\(210\) −0.414214 + 0.585786i −0.0285835 + 0.0404231i
\(211\) 16.9706i 1.16830i 0.811645 + 0.584151i \(0.198572\pi\)
−0.811645 + 0.584151i \(0.801428\pi\)
\(212\) 1.51472i 0.104031i
\(213\) 0.485281 + 0.343146i 0.0332509 + 0.0235120i
\(214\) 3.85786 0.263718
\(215\) 9.65685 0.658592
\(216\) 7.92893 + 2.24264i 0.539496 + 0.152592i
\(217\) 0.828427i 0.0562373i
\(218\) 4.00000i 0.270914i
\(219\) −16.9706 12.0000i −1.14676 0.810885i
\(220\) 5.48528 2.58579i 0.369818 0.174334i
\(221\) 0 0
\(222\) 2.48528 3.51472i 0.166801 0.235892i
\(223\) −14.9706 −1.00250 −0.501252 0.865302i \(-0.667127\pi\)
−0.501252 + 0.865302i \(0.667127\pi\)
\(224\) 4.41421i 0.294937i
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 1.31371i 0.0873866i
\(227\) 14.3431 0.951988 0.475994 0.879449i \(-0.342088\pi\)
0.475994 + 0.879449i \(0.342088\pi\)
\(228\) 2.14214 + 1.51472i 0.141866 + 0.100315i
\(229\) −9.31371 −0.615467 −0.307734 0.951473i \(-0.599571\pi\)
−0.307734 + 0.951473i \(0.599571\pi\)
\(230\) −0.343146 −0.0226264
\(231\) −1.00000 + 5.65685i −0.0657952 + 0.372194i
\(232\) −8.97056 −0.588946
\(233\) −11.7990 −0.772978 −0.386489 0.922294i \(-0.626312\pi\)
−0.386489 + 0.922294i \(0.626312\pi\)
\(234\) 0 0
\(235\) −10.8284 −0.706369
\(236\) 0.627417i 0.0408414i
\(237\) 5.65685 + 4.00000i 0.367452 + 0.259828i
\(238\) 2.82843i 0.183340i
\(239\) −2.82843 −0.182956 −0.0914779 0.995807i \(-0.529159\pi\)
−0.0914779 + 0.995807i \(0.529159\pi\)
\(240\) 4.24264 + 3.00000i 0.273861 + 0.193649i
\(241\) 22.8284i 1.47051i −0.677792 0.735254i \(-0.737063\pi\)
0.677792 0.735254i \(-0.262937\pi\)
\(242\) −2.89949 + 3.51472i −0.186387 + 0.225935i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 9.45584i 0.605348i
\(245\) 1.00000i 0.0638877i
\(246\) 3.17157 4.48528i 0.202212 0.285971i
\(247\) 0 0
\(248\) −1.31371 −0.0834206
\(249\) 12.0000 16.9706i 0.760469 1.07547i
\(250\) 0.414214i 0.0261972i
\(251\) 20.6274i 1.30199i −0.759082 0.650996i \(-0.774352\pi\)
0.759082 0.650996i \(-0.225648\pi\)
\(252\) −5.17157 + 1.82843i −0.325778 + 0.115180i
\(253\) −2.48528 + 1.17157i −0.156248 + 0.0736562i
\(254\) 5.65685i 0.354943i
\(255\) 9.65685 + 6.82843i 0.604736 + 0.427613i
\(256\) 3.97056 0.248160
\(257\) 13.3137i 0.830486i −0.909710 0.415243i \(-0.863696\pi\)
0.909710 0.415243i \(-0.136304\pi\)
\(258\) −5.65685 4.00000i −0.352180 0.249029i
\(259\) 6.00000i 0.372822i
\(260\) 0 0
\(261\) −5.65685 16.0000i −0.350150 0.990375i
\(262\) −7.31371 −0.451842
\(263\) −17.3137 −1.06761 −0.533805 0.845608i \(-0.679238\pi\)
−0.533805 + 0.845608i \(0.679238\pi\)
\(264\) −8.97056 1.58579i −0.552100 0.0975984i
\(265\) −0.828427 −0.0508899
\(266\) 0.343146 0.0210396
\(267\) 10.8284 + 7.65685i 0.662689 + 0.468592i
\(268\) 11.8579 0.724334
\(269\) 17.3137i 1.05564i −0.849358 0.527818i \(-0.823010\pi\)
0.849358 0.527818i \(-0.176990\pi\)
\(270\) 0.585786 2.07107i 0.0356498 0.126041i
\(271\) 2.48528i 0.150970i −0.997147 0.0754850i \(-0.975949\pi\)
0.997147 0.0754850i \(-0.0240505\pi\)
\(272\) 20.4853 1.24210
\(273\) 0 0
\(274\) 5.31371i 0.321013i
\(275\) −1.41421 3.00000i −0.0852803 0.180907i
\(276\) −2.14214 1.51472i −0.128941 0.0911753i
\(277\) 4.82843i 0.290112i 0.989423 + 0.145056i \(0.0463362\pi\)
−0.989423 + 0.145056i \(0.953664\pi\)
\(278\) 2.68629i 0.161113i
\(279\) −0.828427 2.34315i −0.0495966 0.140280i
\(280\) 1.58579 0.0947689
\(281\) −28.9706 −1.72824 −0.864119 0.503287i \(-0.832124\pi\)
−0.864119 + 0.503287i \(0.832124\pi\)
\(282\) 6.34315 + 4.48528i 0.377729 + 0.267095i
\(283\) 28.9706i 1.72212i 0.508502 + 0.861061i \(0.330199\pi\)
−0.508502 + 0.861061i \(0.669801\pi\)
\(284\) 0.627417i 0.0372303i
\(285\) 0.828427 1.17157i 0.0490718 0.0693980i
\(286\) 0 0
\(287\) 7.65685i 0.451970i
\(288\) −4.41421 12.4853i −0.260110 0.735702i
\(289\) 29.6274 1.74279
\(290\) 2.34315i 0.137594i
\(291\) −5.17157 + 7.31371i −0.303163 + 0.428737i
\(292\) 21.9411i 1.28401i
\(293\) −18.8284 −1.09997 −0.549984 0.835175i \(-0.685366\pi\)
−0.549984 + 0.835175i \(0.685366\pi\)
\(294\) −0.414214 + 0.585786i −0.0241574 + 0.0341638i
\(295\) 0.343146 0.0199787
\(296\) −9.51472 −0.553032
\(297\) −2.82843 17.0000i −0.164122 0.986440i
\(298\) 3.02944 0.175491
\(299\) 0 0
\(300\) 1.82843 2.58579i 0.105564 0.149290i
\(301\) 9.65685 0.556612
\(302\) 1.37258i 0.0789833i
\(303\) −9.31371 + 13.1716i −0.535059 + 0.756687i
\(304\) 2.48528i 0.142541i
\(305\) −5.17157 −0.296123
\(306\) −2.82843 8.00000i −0.161690 0.457330i
\(307\) 8.97056i 0.511977i −0.966680 0.255989i \(-0.917599\pi\)
0.966680 0.255989i \(-0.0824009\pi\)
\(308\) 5.48528 2.58579i 0.312553 0.147339i
\(309\) 9.31371 13.1716i 0.529838 0.749305i
\(310\) 0.343146i 0.0194894i
\(311\) 24.6274i 1.39649i −0.715858 0.698246i \(-0.753964\pi\)
0.715858 0.698246i \(-0.246036\pi\)
\(312\) 0 0
\(313\) 13.1716 0.744501 0.372251 0.928132i \(-0.378586\pi\)
0.372251 + 0.928132i \(0.378586\pi\)
\(314\) −7.79899 −0.440122
\(315\) 1.00000 + 2.82843i 0.0563436 + 0.159364i
\(316\) 7.31371i 0.411428i
\(317\) 28.8284i 1.61917i 0.587006 + 0.809583i \(0.300307\pi\)
−0.587006 + 0.809583i \(0.699693\pi\)
\(318\) 0.485281 + 0.343146i 0.0272132 + 0.0192427i
\(319\) 8.00000 + 16.9706i 0.447914 + 0.950169i
\(320\) 4.17157i 0.233198i
\(321\) 9.31371 13.1716i 0.519841 0.735166i
\(322\) −0.343146 −0.0191228
\(323\) 5.65685i 0.314756i
\(324\) 12.7990 10.3431i 0.711055 0.574619i
\(325\) 0 0
\(326\) −0.627417 −0.0347494
\(327\) −13.6569 9.65685i −0.755226 0.534025i
\(328\) −12.1421 −0.670437
\(329\) −10.8284 −0.596991
\(330\) −0.414214 + 2.34315i −0.0228017 + 0.128986i
\(331\) −10.3431 −0.568511 −0.284255 0.958749i \(-0.591746\pi\)
−0.284255 + 0.958749i \(0.591746\pi\)
\(332\) −21.9411 −1.20418
\(333\) −6.00000 16.9706i −0.328798 0.929981i
\(334\) −0.970563 −0.0531068
\(335\) 6.48528i 0.354329i
\(336\) 4.24264 + 3.00000i 0.231455 + 0.163663i
\(337\) 2.48528i 0.135382i −0.997706 0.0676910i \(-0.978437\pi\)
0.997706 0.0676910i \(-0.0215632\pi\)
\(338\) 5.38478 0.292893
\(339\) 4.48528 + 3.17157i 0.243607 + 0.172256i
\(340\) 12.4853i 0.677109i
\(341\) 1.17157 + 2.48528i 0.0634442 + 0.134586i
\(342\) −0.970563 + 0.343146i −0.0524820 + 0.0185552i
\(343\) 1.00000i 0.0539949i
\(344\) 15.3137i 0.825660i
\(345\) −0.828427 + 1.17157i −0.0446010 + 0.0630754i
\(346\) 4.20101 0.225848
\(347\) 12.3431 0.662615 0.331307 0.943523i \(-0.392510\pi\)
0.331307 + 0.943523i \(0.392510\pi\)
\(348\) −10.3431 + 14.6274i −0.554451 + 0.784112i
\(349\) 32.4853i 1.73890i −0.494023 0.869449i \(-0.664474\pi\)
0.494023 0.869449i \(-0.335526\pi\)
\(350\) 0.414214i 0.0221406i
\(351\) 0 0
\(352\) 6.24264 + 13.2426i 0.332734 + 0.705835i
\(353\) 0.343146i 0.0182638i 0.999958 + 0.00913190i \(0.00290682\pi\)
−0.999958 + 0.00913190i \(0.997093\pi\)
\(354\) −0.201010 0.142136i −0.0106836 0.00755442i
\(355\) −0.343146 −0.0182123
\(356\) 14.0000i 0.741999i
\(357\) 9.65685 + 6.82843i 0.511095 + 0.361399i
\(358\) 4.82843i 0.255190i
\(359\) 8.48528 0.447836 0.223918 0.974608i \(-0.428115\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(360\) −4.48528 + 1.58579i −0.236395 + 0.0835783i
\(361\) 18.3137 0.963879
\(362\) −0.828427 −0.0435412
\(363\) 5.00000 + 18.3848i 0.262432 + 0.964951i
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 3.02944 + 2.14214i 0.158351 + 0.111971i
\(367\) −18.0000 −0.939592 −0.469796 0.882775i \(-0.655673\pi\)
−0.469796 + 0.882775i \(0.655673\pi\)
\(368\) 2.48528i 0.129554i
\(369\) −7.65685 21.6569i −0.398600 1.12741i
\(370\) 2.48528i 0.129204i
\(371\) −0.828427 −0.0430098
\(372\) −1.51472 + 2.14214i −0.0785345 + 0.111065i
\(373\) 4.14214i 0.214472i 0.994234 + 0.107236i \(0.0342000\pi\)
−0.994234 + 0.107236i \(0.965800\pi\)
\(374\) 4.00000 + 8.48528i 0.206835 + 0.438763i
\(375\) −1.41421 1.00000i −0.0730297 0.0516398i
\(376\) 17.1716i 0.885556i
\(377\) 0 0
\(378\) 0.585786 2.07107i 0.0301296 0.106524i
\(379\) −37.9411 −1.94890 −0.974452 0.224594i \(-0.927894\pi\)
−0.974452 + 0.224594i \(0.927894\pi\)
\(380\) −1.51472 −0.0777034
\(381\) 19.3137 + 13.6569i 0.989471 + 0.699662i
\(382\) 2.48528i 0.127158i
\(383\) 23.7990i 1.21607i −0.793910 0.608036i \(-0.791958\pi\)
0.793910 0.608036i \(-0.208042\pi\)
\(384\) −10.5563 + 14.9289i −0.538701 + 0.761839i
\(385\) −1.41421 3.00000i −0.0720750 0.152894i
\(386\) 9.31371i 0.474055i
\(387\) −27.3137 + 9.65685i −1.38843 + 0.490885i
\(388\) 9.45584 0.480048
\(389\) 10.6274i 0.538831i −0.963024 0.269416i \(-0.913169\pi\)
0.963024 0.269416i \(-0.0868306\pi\)
\(390\) 0 0
\(391\) 5.65685i 0.286079i
\(392\) 1.58579 0.0800943
\(393\) −17.6569 + 24.9706i −0.890670 + 1.25960i
\(394\) 6.14214 0.309436
\(395\) −4.00000 −0.201262
\(396\) −12.9289 + 12.7990i −0.649703 + 0.643173i
\(397\) 20.4853 1.02813 0.514063 0.857752i \(-0.328140\pi\)
0.514063 + 0.857752i \(0.328140\pi\)
\(398\) −6.00000 −0.300753
\(399\) 0.828427 1.17157i 0.0414732 0.0586520i
\(400\) −3.00000 −0.150000
\(401\) 4.68629i 0.234022i 0.993131 + 0.117011i \(0.0373313\pi\)
−0.993131 + 0.117011i \(0.962669\pi\)
\(402\) −2.68629 + 3.79899i −0.133980 + 0.189476i
\(403\) 0 0
\(404\) 17.0294 0.847246
\(405\) −5.65685 7.00000i −0.281091 0.347833i
\(406\) 2.34315i 0.116288i
\(407\) 8.48528 + 18.0000i 0.420600 + 0.892227i
\(408\) −10.8284 + 15.3137i −0.536087 + 0.758142i
\(409\) 37.4558i 1.85207i −0.377435 0.926036i \(-0.623194\pi\)
0.377435 0.926036i \(-0.376806\pi\)
\(410\) 3.17157i 0.156633i
\(411\) −18.1421 12.8284i −0.894886 0.632780i
\(412\) −17.0294 −0.838980
\(413\) 0.343146 0.0168851
\(414\) 0.970563 0.343146i 0.0477006 0.0168647i
\(415\) 12.0000i 0.589057i
\(416\) 0 0
\(417\) 9.17157 + 6.48528i 0.449134 + 0.317586i
\(418\) 1.02944 0.485281i 0.0503514 0.0237359i
\(419\) 25.3137i 1.23666i −0.785920 0.618328i \(-0.787810\pi\)
0.785920 0.618328i \(-0.212190\pi\)
\(420\) 1.82843 2.58579i 0.0892181 0.126173i
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 7.02944i 0.342188i
\(423\) 30.6274 10.8284i 1.48916 0.526496i
\(424\) 1.31371i 0.0637993i
\(425\) −6.82843 −0.331227
\(426\) 0.201010 + 0.142136i 0.00973897 + 0.00688649i
\(427\) −5.17157 −0.250270
\(428\) −17.0294 −0.823149
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) −18.1421 −0.873876 −0.436938 0.899492i \(-0.643937\pi\)
−0.436938 + 0.899492i \(0.643937\pi\)
\(432\) −15.0000 4.24264i −0.721688 0.204124i
\(433\) −34.8284 −1.67375 −0.836874 0.547396i \(-0.815619\pi\)
−0.836874 + 0.547396i \(0.815619\pi\)
\(434\) 0.343146i 0.0164715i
\(435\) 8.00000 + 5.65685i 0.383571 + 0.271225i
\(436\) 17.6569i 0.845610i
\(437\) 0.686292 0.0328298
\(438\) −7.02944 4.97056i −0.335880 0.237503i
\(439\) 19.4558i 0.928577i −0.885684 0.464288i \(-0.846310\pi\)
0.885684 0.464288i \(-0.153690\pi\)
\(440\) 4.75736 2.24264i 0.226798 0.106914i
\(441\) 1.00000 + 2.82843i 0.0476190 + 0.134687i
\(442\) 0 0
\(443\) 37.7990i 1.79588i 0.440114 + 0.897942i \(0.354938\pi\)
−0.440114 + 0.897942i \(0.645062\pi\)
\(444\) −10.9706 + 15.5147i −0.520640 + 0.736296i
\(445\) −7.65685 −0.362970
\(446\) −6.20101 −0.293626
\(447\) 7.31371 10.3431i 0.345927 0.489214i
\(448\) 4.17157i 0.197088i
\(449\) 6.34315i 0.299352i 0.988735 + 0.149676i \(0.0478230\pi\)
−0.988735 + 0.149676i \(0.952177\pi\)
\(450\) 0.414214 + 1.17157i 0.0195262 + 0.0552285i
\(451\) 10.8284 + 22.9706i 0.509891 + 1.08164i
\(452\) 5.79899i 0.272762i
\(453\) −4.68629 3.31371i −0.220181 0.155692i
\(454\) 5.94113 0.278831
\(455\) 0 0
\(456\) 1.85786 + 1.31371i 0.0870025 + 0.0615200i
\(457\) 26.4853i 1.23893i −0.785025 0.619465i \(-0.787350\pi\)
0.785025 0.619465i \(-0.212650\pi\)
\(458\) −3.85786 −0.180266
\(459\) −34.1421 9.65685i −1.59362 0.450743i
\(460\) 1.51472 0.0706241
\(461\) −12.3431 −0.574878 −0.287439 0.957799i \(-0.592804\pi\)
−0.287439 + 0.957799i \(0.592804\pi\)
\(462\) −0.414214 + 2.34315i −0.0192710 + 0.109013i
\(463\) −39.4558 −1.83367 −0.916834 0.399268i \(-0.869264\pi\)
−0.916834 + 0.399268i \(0.869264\pi\)
\(464\) 16.9706 0.787839
\(465\) 1.17157 + 0.828427i 0.0543304 + 0.0384174i
\(466\) −4.88730 −0.226400
\(467\) 1.17157i 0.0542139i 0.999633 + 0.0271070i \(0.00862947\pi\)
−0.999633 + 0.0271070i \(0.991371\pi\)
\(468\) 0 0
\(469\) 6.48528i 0.299462i
\(470\) −4.48528 −0.206891
\(471\) −18.8284 + 26.6274i −0.867568 + 1.22693i
\(472\) 0.544156i 0.0250468i
\(473\) 28.9706 13.6569i 1.33207 0.627943i
\(474\) 2.34315 + 1.65685i 0.107624 + 0.0761018i
\(475\) 0.828427i 0.0380108i
\(476\) 12.4853i 0.572262i
\(477\) 2.34315 0.828427i 0.107285 0.0379311i
\(478\) −1.17157 −0.0535865
\(479\) 11.3137 0.516937 0.258468 0.966020i \(-0.416782\pi\)
0.258468 + 0.966020i \(0.416782\pi\)
\(480\) 6.24264 + 4.41421i 0.284936 + 0.201480i
\(481\) 0 0
\(482\) 9.45584i 0.430702i
\(483\) −0.828427 + 1.17157i −0.0376947 + 0.0533084i
\(484\) 12.7990 15.5147i 0.581772 0.705214i
\(485\) 5.17157i 0.234829i
\(486\) 0.414214 + 6.44365i 0.0187891 + 0.292290i
\(487\) 26.4853 1.20016 0.600081 0.799939i \(-0.295135\pi\)
0.600081 + 0.799939i \(0.295135\pi\)
\(488\) 8.20101i 0.371242i
\(489\) −1.51472 + 2.14214i −0.0684979 + 0.0968707i
\(490\) 0.414214i 0.0187123i
\(491\) −18.1421 −0.818743 −0.409372 0.912368i \(-0.634252\pi\)
−0.409372 + 0.912368i \(0.634252\pi\)
\(492\) −14.0000 + 19.7990i −0.631169 + 0.892607i
\(493\) 38.6274 1.73969
\(494\) 0 0
\(495\) 7.00000 + 7.07107i 0.314627 + 0.317821i
\(496\) 2.48528 0.111592
\(497\) −0.343146 −0.0153922
\(498\) 4.97056 7.02944i 0.222736 0.314997i
\(499\) 36.0000 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 1.82843i 0.0817697i
\(501\) −2.34315 + 3.31371i −0.104684 + 0.148046i
\(502\) 8.54416i 0.381344i
\(503\) 25.6569 1.14398 0.571991 0.820260i \(-0.306171\pi\)
0.571991 + 0.820260i \(0.306171\pi\)
\(504\) −4.48528 + 1.58579i −0.199790 + 0.0706365i
\(505\) 9.31371i 0.414455i
\(506\) −1.02944 + 0.485281i −0.0457641 + 0.0215734i
\(507\) 13.0000 18.3848i 0.577350 0.816497i
\(508\) 24.9706i 1.10789i
\(509\) 10.9706i 0.486262i 0.969994 + 0.243131i \(0.0781744\pi\)
−0.969994 + 0.243131i \(0.921826\pi\)
\(510\) 4.00000 + 2.82843i 0.177123 + 0.125245i
\(511\) 12.0000 0.530849
\(512\) 22.7574 1.00574
\(513\) −1.17157 + 4.14214i −0.0517262 + 0.182880i
\(514\) 5.51472i 0.243244i
\(515\) 9.31371i 0.410411i
\(516\) 24.9706 + 17.6569i 1.09927 + 0.777300i
\(517\) −32.4853 + 15.3137i −1.42870 + 0.673496i
\(518\) 2.48528i 0.109197i
\(519\) 10.1421 14.3431i 0.445190 0.629594i
\(520\) 0 0
\(521\) 9.31371i 0.408041i −0.978967 0.204020i \(-0.934599\pi\)
0.978967 0.204020i \(-0.0654009\pi\)
\(522\) −2.34315 6.62742i −0.102557 0.290074i
\(523\) 12.9706i 0.567163i −0.958948 0.283582i \(-0.908477\pi\)
0.958948 0.283582i \(-0.0915227\pi\)
\(524\) 32.2843 1.41034
\(525\) −1.41421 1.00000i −0.0617213 0.0436436i
\(526\) −7.17157 −0.312695
\(527\) 5.65685 0.246416
\(528\) 16.9706 + 3.00000i 0.738549 + 0.130558i
\(529\) 22.3137 0.970161
\(530\) −0.343146 −0.0149053
\(531\) −0.970563 + 0.343146i −0.0421188 + 0.0148913i
\(532\) −1.51472 −0.0656714
\(533\) 0 0
\(534\) 4.48528 + 3.17157i 0.194097 + 0.137247i
\(535\) 9.31371i 0.402667i
\(536\) 10.2843 0.444213
\(537\) −16.4853 11.6569i −0.711392 0.503030i
\(538\) 7.17157i 0.309188i
\(539\) −1.41421 3.00000i −0.0609145 0.129219i
\(540\) −2.58579 + 9.14214i −0.111275 + 0.393415i
\(541\) 28.9706i 1.24554i −0.782404 0.622771i \(-0.786007\pi\)
0.782404 0.622771i \(-0.213993\pi\)
\(542\) 1.02944i 0.0442181i
\(543\) −2.00000 + 2.82843i −0.0858282 + 0.121379i
\(544\) 30.1421 1.29233
\(545\) 9.65685 0.413654
\(546\) 0 0
\(547\) 32.2843i 1.38038i −0.723630 0.690188i \(-0.757528\pi\)
0.723630 0.690188i \(-0.242472\pi\)
\(548\) 23.4558i 1.00198i
\(549\) 14.6274 5.17157i 0.624283 0.220717i
\(550\) −0.585786 1.24264i −0.0249780 0.0529864i
\(551\) 4.68629i 0.199643i
\(552\) −1.85786 1.31371i −0.0790760 0.0559151i
\(553\) −4.00000 −0.170097
\(554\) 2.00000i 0.0849719i
\(555\) 8.48528 + 6.00000i 0.360180 + 0.254686i
\(556\) 11.8579i 0.502885i
\(557\) 44.4853 1.88490 0.942451 0.334344i \(-0.108515\pi\)
0.942451 + 0.334344i \(0.108515\pi\)
\(558\) −0.343146 0.970563i −0.0145265 0.0410872i
\(559\) 0 0
\(560\) −3.00000 −0.126773
\(561\) 38.6274 + 6.82843i 1.63085 + 0.288296i
\(562\) −12.0000 −0.506189
\(563\) 7.02944 0.296255 0.148128 0.988968i \(-0.452675\pi\)
0.148128 + 0.988968i \(0.452675\pi\)
\(564\) −28.0000 19.7990i −1.17901 0.833688i
\(565\) −3.17157 −0.133429
\(566\) 12.0000i 0.504398i
\(567\) −5.65685 7.00000i −0.237566 0.293972i
\(568\) 0.544156i 0.0228323i
\(569\) −23.3137 −0.977362 −0.488681 0.872463i \(-0.662522\pi\)
−0.488681 + 0.872463i \(0.662522\pi\)
\(570\) 0.343146 0.485281i 0.0143728 0.0203262i
\(571\) 4.97056i 0.208012i −0.994577 0.104006i \(-0.966834\pi\)
0.994577 0.104006i \(-0.0331660\pi\)
\(572\) 0 0
\(573\) 8.48528 + 6.00000i 0.354478 + 0.250654i
\(574\) 3.17157i 0.132379i
\(575\) 0.828427i 0.0345478i
\(576\) 4.17157 + 11.7990i 0.173816 + 0.491625i
\(577\) −20.4853 −0.852813 −0.426407 0.904532i \(-0.640221\pi\)
−0.426407 + 0.904532i \(0.640221\pi\)
\(578\) 12.2721 0.510451
\(579\) 31.7990 + 22.4853i 1.32152 + 0.934456i
\(580\) 10.3431i 0.429476i
\(581\) 12.0000i 0.497844i
\(582\) −2.14214 + 3.02944i −0.0887944 + 0.125574i
\(583\) −2.48528 + 1.17157i −0.102930 + 0.0485216i
\(584\) 19.0294i 0.787444i
\(585\) 0 0
\(586\) −7.79899 −0.322173
\(587\) 37.4558i 1.54597i 0.634425 + 0.772984i \(0.281237\pi\)
−0.634425 + 0.772984i \(0.718763\pi\)
\(588\) 1.82843 2.58579i 0.0754031 0.106636i
\(589\) 0.686292i 0.0282781i
\(590\) 0.142136 0.00585163
\(591\) 14.8284 20.9706i 0.609960 0.862614i
\(592\) 18.0000 0.739795
\(593\) 17.1716 0.705152 0.352576 0.935783i \(-0.385306\pi\)
0.352576 + 0.935783i \(0.385306\pi\)
\(594\) −1.17157 7.04163i −0.0480702 0.288922i
\(595\) −6.82843 −0.279938
\(596\) −13.3726 −0.547762
\(597\) −14.4853 + 20.4853i −0.592843 + 0.838407i
\(598\) 0 0
\(599\) 39.9411i 1.63195i 0.578087 + 0.815975i \(0.303799\pi\)
−0.578087 + 0.815975i \(0.696201\pi\)
\(600\) 1.58579 2.24264i 0.0647395 0.0915554i
\(601\) 5.45584i 0.222549i −0.993790 0.111274i \(-0.964507\pi\)
0.993790 0.111274i \(-0.0354932\pi\)
\(602\) 4.00000 0.163028
\(603\) 6.48528 + 18.3431i 0.264101 + 0.746991i
\(604\) 6.05887i 0.246532i
\(605\) −8.48528 7.00000i −0.344976 0.284590i
\(606\) −3.85786 + 5.45584i −0.156715 + 0.221629i
\(607\) 36.0000i 1.46119i 0.682808 + 0.730597i \(0.260758\pi\)
−0.682808 + 0.730597i \(0.739242\pi\)
\(608\) 3.65685i 0.148305i
\(609\) 8.00000 + 5.65685i 0.324176 + 0.229227i
\(610\) −2.14214 −0.0867325
\(611\) 0 0
\(612\) 12.4853 + 35.3137i 0.504688 + 1.42747i
\(613\) 5.79899i 0.234219i 0.993119 + 0.117109i \(0.0373628\pi\)
−0.993119 + 0.117109i \(0.962637\pi\)
\(614\) 3.71573i 0.149955i
\(615\) 10.8284 + 7.65685i 0.436644 + 0.308754i
\(616\) 4.75736 2.24264i 0.191679 0.0903586i
\(617\) 19.4558i 0.783263i 0.920122 + 0.391631i \(0.128089\pi\)
−0.920122 + 0.391631i \(0.871911\pi\)
\(618\) 3.85786 5.45584i 0.155186 0.219466i
\(619\) −21.7990 −0.876175 −0.438088 0.898932i \(-0.644344\pi\)
−0.438088 + 0.898932i \(0.644344\pi\)
\(620\) 1.51472i 0.0608326i
\(621\) 1.17157 4.14214i 0.0470136 0.166218i
\(622\) 10.2010i 0.409023i
\(623\) −7.65685 −0.306765
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 5.45584 0.218059
\(627\) 0.828427 4.68629i 0.0330842 0.187152i
\(628\) 34.4264 1.37376
\(629\) 40.9706 1.63360
\(630\) 0.414214 + 1.17157i 0.0165027 + 0.0466766i
\(631\) 32.9706 1.31254 0.656269 0.754527i \(-0.272134\pi\)
0.656269 + 0.754527i \(0.272134\pi\)
\(632\) 6.34315i 0.252317i
\(633\) 24.0000 + 16.9706i 0.953914 + 0.674519i
\(634\) 11.9411i 0.474243i
\(635\) −13.6569 −0.541956
\(636\) −2.14214 1.51472i −0.0849412 0.0600625i
\(637\) 0 0
\(638\) 3.31371 + 7.02944i 0.131191 + 0.278298i
\(639\) 0.970563 0.343146i 0.0383949 0.0135746i
\(640\) 10.5563i 0.417276i
\(641\) 16.6863i 0.659069i −0.944144 0.329534i \(-0.893108\pi\)
0.944144 0.329534i \(-0.106892\pi\)
\(642\) 3.85786 5.45584i 0.152258 0.215325i
\(643\) −10.9706 −0.432637 −0.216318 0.976323i \(-0.569405\pi\)
−0.216318 + 0.976323i \(0.569405\pi\)
\(644\) 1.51472 0.0596883
\(645\) 9.65685 13.6569i 0.380238 0.537738i
\(646\) 2.34315i 0.0921898i
\(647\) 4.20101i 0.165159i 0.996584 + 0.0825794i \(0.0263158\pi\)
−0.996584 + 0.0825794i \(0.973684\pi\)
\(648\) 11.1005 8.97056i 0.436069 0.352397i
\(649\) 1.02944 0.485281i 0.0404089 0.0190490i
\(650\) 0 0
\(651\) 1.17157 + 0.828427i 0.0459176 + 0.0324686i
\(652\) 2.76955 0.108464
\(653\) 26.4853i 1.03645i 0.855245 + 0.518225i \(0.173407\pi\)
−0.855245 + 0.518225i \(0.826593\pi\)
\(654\) −5.65685 4.00000i −0.221201 0.156412i
\(655\) 17.6569i 0.689910i
\(656\) 22.9706 0.896850
\(657\) −33.9411 + 12.0000i −1.32417 + 0.468165i
\(658\) −4.48528 −0.174854
\(659\) −44.4853 −1.73290 −0.866450 0.499263i \(-0.833604\pi\)
−0.866450 + 0.499263i \(0.833604\pi\)
\(660\) 1.82843 10.3431i 0.0711714 0.402606i
\(661\) −46.9706 −1.82694 −0.913472 0.406903i \(-0.866609\pi\)
−0.913472 + 0.406903i \(0.866609\pi\)
\(662\) −4.28427 −0.166513
\(663\) 0 0
\(664\) −19.0294 −0.738485
\(665\) 0.828427i 0.0321250i
\(666\) −2.48528 7.02944i −0.0963027 0.272385i
\(667\) 4.68629i 0.181454i
\(668\) 4.28427 0.165763
\(669\) −14.9706 + 21.1716i −0.578795 + 0.818540i
\(670\) 2.68629i 0.103780i
\(671\) −15.5147 + 7.31371i −0.598939 + 0.282343i
\(672\) 6.24264 + 4.41421i 0.240815 + 0.170282i
\(673\) 25.5147i 0.983520i −0.870731 0.491760i \(-0.836354\pi\)
0.870731 0.491760i \(-0.163646\pi\)
\(674\) 1.02944i 0.0396524i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) −23.7696 −0.914214
\(677\) 40.7696 1.56690 0.783451 0.621454i \(-0.213458\pi\)
0.783451 + 0.621454i \(0.213458\pi\)
\(678\) 1.85786 + 1.31371i 0.0713509 + 0.0504527i
\(679\) 5.17157i 0.198467i
\(680\) 10.8284i 0.415251i
\(681\) 14.3431 20.2843i 0.549631 0.777295i
\(682\) 0.485281 + 1.02944i 0.0185824 + 0.0394192i
\(683\) 37.7990i 1.44634i −0.690671 0.723169i \(-0.742685\pi\)
0.690671 0.723169i \(-0.257315\pi\)
\(684\) 4.28427 1.51472i 0.163813 0.0579167i
\(685\) 12.8284 0.490149
\(686\) 0.414214i 0.0158147i
\(687\) −9.31371 + 13.1716i −0.355340 + 0.502527i
\(688\) 28.9706i 1.10449i
\(689\) 0 0
\(690\) −0.343146 + 0.485281i −0.0130633 + 0.0184743i
\(691\) −5.51472 −0.209790 −0.104895 0.994483i \(-0.533451\pi\)
−0.104895 + 0.994483i \(0.533451\pi\)
\(692\) −18.5442 −0.704943
\(693\) 7.00000 + 7.07107i 0.265908 + 0.268608i
\(694\) 5.11270 0.194075
\(695\) −6.48528 −0.246001
\(696\) −8.97056 + 12.6863i −0.340028 + 0.480873i
\(697\) 52.2843 1.98041
\(698\) 13.4558i 0.509311i
\(699\) −11.7990 + 16.6863i −0.446279 + 0.631134i
\(700\) 1.82843i 0.0691080i
\(701\) 31.5980 1.19344 0.596720 0.802450i \(-0.296470\pi\)
0.596720 + 0.802450i \(0.296470\pi\)
\(702\) 0 0
\(703\) 4.97056i 0.187468i
\(704\) −5.89949 12.5147i −0.222346 0.471666i
\(705\) −10.8284 + 15.3137i −0.407822 + 0.576748i
\(706\) 0.142136i 0.00534934i
\(707\) 9.31371i 0.350278i
\(708\) 0.887302 + 0.627417i 0.0333468 + 0.0235798i
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) −0.142136 −0.00533425
\(711\) 11.3137 4.00000i 0.424297 0.150012i
\(712\) 12.1421i 0.455046i
\(713\) 0.686292i 0.0257018i
\(714\) 4.00000 + 2.82843i 0.149696 + 0.105851i
\(715\) 0 0
\(716\) 21.3137i 0.796531i
\(717\) −2.82843 + 4.00000i −0.105630 + 0.149383i
\(718\) 3.51472 0.131168
\(719\) 6.68629i 0.249357i 0.992197 + 0.124678i \(0.0397899\pi\)
−0.992197 + 0.124678i \(0.960210\pi\)
\(720\) 8.48528 3.00000i 0.316228 0.111803i
\(721\) 9.31371i 0.346861i
\(722\) 7.58579 0.282314
\(723\) −32.2843 22.8284i −1.20066 0.848998i
\(724\) 3.65685 0.135906
\(725\) −5.65685 −0.210090
\(726\) 2.07107 + 7.61522i 0.0768645 + 0.282627i
\(727\) 42.0000 1.55769 0.778847 0.627214i \(-0.215805\pi\)
0.778847 + 0.627214i \(0.215805\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 4.97056 0.183969
\(731\) 65.9411i 2.43892i
\(732\) −13.3726 9.45584i −0.494265 0.349498i
\(733\) 29.9411i 1.10590i 0.833214 + 0.552950i \(0.186498\pi\)
−0.833214 + 0.552950i \(0.813502\pi\)
\(734\) −7.45584 −0.275200
\(735\) −1.41421 1.00000i −0.0521641 0.0368856i
\(736\) 3.65685i 0.134793i
\(737\) −9.17157 19.4558i −0.337839 0.716665i
\(738\) −3.17157 8.97056i −0.116747 0.330211i
\(739\) 20.2843i 0.746169i 0.927797 + 0.373084i \(0.121700\pi\)
−0.927797 + 0.373084i \(0.878300\pi\)
\(740\) 10.9706i 0.403286i
\(741\) 0 0
\(742\) −0.343146 −0.0125973
\(743\) 22.6863 0.832279 0.416140 0.909301i \(-0.363383\pi\)
0.416140 + 0.909301i \(0.363383\pi\)
\(744\) −1.31371 + 1.85786i −0.0481629 + 0.0681126i
\(745\) 7.31371i 0.267954i
\(746\) 1.71573i 0.0628173i
\(747\) −12.0000 33.9411i −0.439057 1.24184i
\(748\) −17.6569 37.4558i −0.645599 1.36952i
\(749\) 9.31371i 0.340316i
\(750\) −0.585786 0.414214i −0.0213899 0.0151249i
\(751\) −29.9411 −1.09257 −0.546284 0.837600i \(-0.683958\pi\)
−0.546284 + 0.837600i \(0.683958\pi\)
\(752\) 32.4853i 1.18462i
\(753\) −29.1716 20.6274i −1.06307 0.751705i
\(754\) 0 0
\(755\) 3.31371 0.120598
\(756\) −2.58579 + 9.14214i −0.0940441 + 0.332496i
\(757\) 39.9411 1.45168 0.725842 0.687861i \(-0.241450\pi\)
0.725842 + 0.687861i \(0.241450\pi\)
\(758\) −15.7157 −0.570821
\(759\) −0.828427 + 4.68629i −0.0300700 + 0.170102i
\(760\) −1.31371 −0.0476532
\(761\) −36.3431 −1.31744 −0.658719 0.752389i \(-0.728901\pi\)
−0.658719 + 0.752389i \(0.728901\pi\)
\(762\) 8.00000 + 5.65685i 0.289809 + 0.204926i
\(763\) 9.65685 0.349602
\(764\) 10.9706i 0.396901i
\(765\) 19.3137 6.82843i 0.698289 0.246882i
\(766\) 9.85786i 0.356179i
\(767\) 0 0
\(768\) 3.97056 5.61522i 0.143275 0.202622i
\(769\) 20.4853i 0.738718i −0.929287 0.369359i \(-0.879577\pi\)
0.929287 0.369359i \(-0.120423\pi\)
\(770\) −0.585786 1.24264i −0.0211103 0.0447817i
\(771\) −18.8284 13.3137i −0.678089 0.479481i
\(772\) 41.1127i 1.47968i
\(773\) 2.68629i 0.0966192i 0.998832 + 0.0483096i \(0.0153834\pi\)
−0.998832 + 0.0483096i \(0.984617\pi\)
\(774\) −11.3137 + 4.00000i −0.406663 + 0.143777i
\(775\) −0.828427 −0.0297580
\(776\) 8.20101 0.294399
\(777\) 8.48528 + 6.00000i 0.304408 + 0.215249i
\(778\) 4.40202i 0.157820i
\(779\) 6.34315i 0.227267i
\(780\) 0 0
\(781\) −1.02944 + 0.485281i −0.0368362 + 0.0173647i
\(782\) 2.34315i 0.0837907i
\(783\) −28.2843 8.00000i −1.01080 0.285897i
\(784\) −3.00000 −0.107143
\(785\) 18.8284i 0.672015i
\(786\) −7.31371 + 10.3431i −0.260871 + 0.368928i
\(787\) 37.9411i 1.35246i −0.736693 0.676228i \(-0.763614\pi\)
0.736693 0.676228i \(-0.236386\pi\)
\(788\) −27.1127 −0.965850
\(789\) −17.3137 + 24.4853i −0.616384 + 0.871699i
\(790\) −1.65685 −0.0589482
\(791\) −3.17157 −0.112768
\(792\) −11.2132 + 11.1005i −0.398444 + 0.394439i
\(793\) 0 0
\(794\) 8.48528 0.301131
\(795\) −0.828427 + 1.17157i −0.0293813 + 0.0415514i
\(796\) 26.4853 0.938746
\(797\) 16.6274i 0.588973i 0.955656 + 0.294487i \(0.0951487\pi\)
−0.955656 + 0.294487i \(0.904851\pi\)
\(798\) 0.343146 0.485281i 0.0121472 0.0171788i
\(799\) 73.9411i 2.61585i
\(800\) −4.41421 −0.156066
\(801\) 21.6569 7.65685i 0.765207 0.270542i
\(802\) 1.94113i 0.0685435i
\(803\) 36.0000 16.9706i 1.27041 0.598878i
\(804\) 11.8579 16.7696i 0.418195 0.591417i
\(805\) 0.828427i 0.0291982i
\(806\) 0 0
\(807\) −24.4853 17.3137i −0.861923 0.609471i
\(808\) 14.7696 0.519591
\(809\) −10.6274 −0.373640 −0.186820 0.982394i \(-0.559818\pi\)
−0.186820 + 0.982394i \(0.559818\pi\)
\(810\) −2.34315 2.89949i −0.0823297 0.101878i
\(811\) 17.5147i 0.615025i 0.951544 + 0.307512i \(0.0994966\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(812\) 10.3431i 0.362973i
\(813\) −3.51472 2.48528i −0.123267 0.0871626i
\(814\) 3.51472 + 7.45584i 0.123191 + 0.261327i
\(815\) 1.51472i 0.0530583i
\(816\) 20.4853 28.9706i 0.717128 1.01417i
\(817\) −8.00000 −0.279885
\(818\) 15.5147i 0.542459i
\(819\) 0 0
\(820\) 14.0000i 0.488901i
\(821\) −6.62742 −0.231298 −0.115649 0.993290i \(-0.536895\pi\)
−0.115649 + 0.993290i \(0.536895\pi\)
\(822\) −7.51472 5.31371i −0.262106 0.185337i
\(823\) −0.142136 −0.00495454 −0.00247727 0.999997i \(-0.500789\pi\)
−0.00247727 + 0.999997i \(0.500789\pi\)
\(824\) −14.7696 −0.514522
\(825\) −5.65685 1.00000i −0.196946 0.0348155i
\(826\) 0.142136 0.00494553
\(827\) −51.2548 −1.78231 −0.891153 0.453704i \(-0.850102\pi\)
−0.891153 + 0.453704i \(0.850102\pi\)
\(828\) −4.28427 + 1.51472i −0.148889 + 0.0526401i
\(829\) −50.9706 −1.77028 −0.885140 0.465324i \(-0.845938\pi\)
−0.885140 + 0.465324i \(0.845938\pi\)
\(830\) 4.97056i 0.172531i
\(831\) 6.82843 + 4.82843i 0.236876 + 0.167496i
\(832\) 0 0
\(833\) −6.82843 −0.236591
\(834\) 3.79899 + 2.68629i 0.131548 + 0.0930187i
\(835\) 2.34315i 0.0810879i
\(836\) −4.54416 + 2.14214i −0.157163 + 0.0740873i
\(837\) −4.14214 1.17157i −0.143173 0.0404955i
\(838\) 10.4853i 0.362208i
\(839\) 51.6569i 1.78339i −0.452634 0.891696i \(-0.649516\pi\)
0.452634 0.891696i \(-0.350484\pi\)
\(840\) 1.58579 2.24264i 0.0547148 0.0773785i
\(841\) 3.00000 0.103448
\(842\) 7.45584 0.256945
\(843\) −28.9706 + 40.9706i −0.997799 + 1.41110i
\(844\) 31.0294i 1.06808i
\(845\) 13.0000i 0.447214i
\(846\) 12.6863 4.48528i 0.436164 0.154207i
\(847\) −8.48528 7.00000i −0.291558 0.240523i
\(848\) 2.48528i 0.0853449i
\(849\) 40.9706 + 28.9706i 1.40611 + 0.994267i
\(850\) −2.82843 −0.0970143
\(851\) 4.97056i 0.170389i
\(852\) −0.887302 0.627417i −0.0303985 0.0214950i
\(853\) 28.9706i 0.991933i −0.868342 0.495967i \(-0.834814\pi\)
0.868342 0.495967i \(-0.165186\pi\)
\(854\) −2.14214 −0.0733024
\(855\) −0.828427 2.34315i −0.0283316 0.0801339i
\(856\) −14.7696 −0.504813
\(857\) 23.1127 0.789515 0.394757 0.918785i \(-0.370829\pi\)
0.394757 + 0.918785i \(0.370829\pi\)
\(858\) 0 0
\(859\) −35.4558 −1.20974 −0.604869 0.796325i \(-0.706774\pi\)
−0.604869 + 0.796325i \(0.706774\pi\)
\(860\) −17.6569 −0.602094
\(861\) 10.8284 + 7.65685i 0.369032 + 0.260945i
\(862\) −7.51472 −0.255952
\(863\) 40.1421i 1.36645i 0.730206 + 0.683227i \(0.239424\pi\)
−0.730206 + 0.683227i \(0.760576\pi\)
\(864\) −22.0711 6.24264i −0.750873 0.212379i
\(865\) 10.1421i 0.344843i
\(866\) −14.4264 −0.490229
\(867\) 29.6274 41.8995i 1.00620 1.42298i
\(868\) 1.51472i 0.0514129i
\(869\) −12.0000 + 5.65685i −0.407072 + 0.191896i
\(870\) 3.31371 + 2.34315i 0.112345 + 0.0794401i
\(871\) 0 0
\(872\) 15.3137i 0.518588i
\(873\) 5.17157 + 14.6274i 0.175031 + 0.495063i
\(874\) 0.284271 0.00961562
\(875\) 1.00000 0.0338062
\(876\) 31.0294 + 21.9411i 1.04839 + 0.741322i
\(877\) 29.7990i 1.00624i 0.864216 + 0.503120i \(0.167815\pi\)
−0.864216 + 0.503120i \(0.832185\pi\)
\(878\) 8.05887i 0.271974i
\(879\) −18.8284 + 26.6274i −0.635067 + 0.898120i
\(880\) −9.00000 + 4.24264i −0.303390 + 0.143019i
\(881\) 24.3431i 0.820141i 0.912054 + 0.410071i \(0.134496\pi\)
−0.912054 + 0.410071i \(0.865504\pi\)
\(882\) 0.414214 + 1.17157i 0.0139473 + 0.0394489i
\(883\) 17.1127 0.575888 0.287944 0.957647i \(-0.407028\pi\)
0.287944 + 0.957647i \(0.407028\pi\)
\(884\) 0 0
\(885\) 0.343146 0.485281i 0.0115347 0.0163126i
\(886\) 15.6569i 0.526002i
\(887\) −36.6863 −1.23181 −0.615903 0.787822i \(-0.711209\pi\)
−0.615903 + 0.787822i \(0.711209\pi\)
\(888\) −9.51472 + 13.4558i −0.319293 + 0.451549i
\(889\) −13.6569 −0.458036
\(890\) −3.17157 −0.106311
\(891\) −26.8701 13.0000i −0.900181 0.435516i
\(892\) 27.3726 0.916502
\(893\) 8.97056 0.300188
\(894\) 3.02944 4.28427i 0.101320 0.143287i
\(895\) 11.6569 0.389646
\(896\) 10.5563i 0.352663i
\(897\) 0 0
\(898\) 2.62742i 0.0876780i
\(899\) 4.68629 0.156297
\(900\) −1.82843 5.17157i −0.0609476 0.172386i
\(901\) 5.65685i 0.188457i
\(902\) 4.48528 + 9.51472i 0.149344 + 0.316805i
\(903\) 9.65685 13.6569i 0.321360 0.454472i
\(904\) 5.02944i 0.167277i
\(905\) 2.00000i 0.0664822i
\(906\) −1.94113 1.37258i −0.0644896 0.0456010i
\(907\) −12.8284 −0.425961 −0.212980 0.977056i \(-0.568317\pi\)
−0.212980 + 0.977056i \(0.568317\pi\)
\(908\) −26.2254 −0.870320
\(909\) 9.31371 + 26.3431i 0.308916 + 0.873747i
\(910\) 0 0
\(911\) 12.6274i 0.418365i 0.977877 + 0.209182i \(0.0670803\pi\)
−0.977877 + 0.209182i \(0.932920\pi\)
\(912\) −3.51472 2.48528i −0.116384 0.0822959i
\(913\) 16.9706 + 36.0000i 0.561644 + 1.19143i
\(914\) 10.9706i 0.362874i
\(915\) −5.17157 + 7.31371i −0.170967 + 0.241784i
\(916\) 17.0294 0.562668
\(917\) 17.6569i 0.583081i
\(918\) −14.1421 4.00000i −0.466760 0.132020i
\(919\) 58.9117i 1.94332i 0.236388 + 0.971659i \(0.424036\pi\)
−0.236388 + 0.971659i \(0.575964\pi\)
\(920\) 1.31371 0.0433117
\(921\) −12.6863 8.97056i −0.418028 0.295590i
\(922\) −5.11270 −0.168378
\(923\) 0 0
\(924\) 1.82843 10.3431i 0.0601508 0.340265i
\(925\) −6.00000 −0.197279
\(926\) −16.3431 −0.537069
\(927\) −9.31371 26.3431i −0.305902 0.865222i
\(928\) 24.9706 0.819699
\(929\) 31.6569i 1.03863i 0.854584 + 0.519314i \(0.173812\pi\)
−0.854584 + 0.519314i \(0.826188\pi\)
\(930\) 0.485281 + 0.343146i 0.0159130 + 0.0112522i
\(931\) 0.828427i 0.0271506i
\(932\) 21.5736 0.706667
\(933\) −34.8284 24.6274i −1.14023 0.806265i
\(934\) 0.485281i 0.0158789i
\(935\) −20.4853 + 9.65685i −0.669940 + 0.315813i
\(936\) 0 0
\(937\) 12.9706i 0.423730i 0.977299 + 0.211865i \(0.0679537\pi\)
−0.977299 + 0.211865i \(0.932046\pi\)
\(938\) 2.68629i 0.0877105i
\(939\) 13.1716 18.6274i 0.429838 0.607883i
\(940\) 19.7990 0.645772
\(941\) 22.9706 0.748819 0.374409 0.927263i \(-0.377845\pi\)
0.374409 + 0.927263i \(0.377845\pi\)
\(942\) −7.79899 + 11.0294i −0.254105 + 0.359358i
\(943\) 6.34315i 0.206561i
\(944\) 1.02944i 0.0335053i
\(945\) 5.00000 + 1.41421i 0.162650 + 0.0460044i
\(946\) 12.0000 5.65685i 0.390154 0.183920i
\(947\) 47.1716i 1.53287i −0.642322 0.766435i \(-0.722029\pi\)
0.642322 0.766435i \(-0.277971\pi\)
\(948\) −10.3431 7.31371i −0.335930 0.237538i
\(949\) 0 0
\(950\) 0.343146i 0.0111331i
\(951\) 40.7696 + 28.8284i 1.32204 + 0.934826i
\(952\) 10.8284i 0.350951i
\(953\) −37.1716 −1.20411 −0.602053 0.798456i \(-0.705650\pi\)
−0.602053 + 0.798456i \(0.705650\pi\)
\(954\) 0.970563 0.343146i 0.0314231 0.0111098i
\(955\) −6.00000 −0.194155
\(956\) 5.17157 0.167261
\(957\) 32.0000 + 5.65685i 1.03441 + 0.182860i
\(958\) 4.68629 0.151407
\(959\) 12.8284 0.414252
\(960\) −5.89949 4.17157i −0.190405 0.134637i
\(961\) −30.3137 −0.977862
\(962\) 0 0
\(963\) −9.31371 26.3431i −0.300130 0.848896i
\(964\) 41.7401i 1.34436i
\(965\) −22.4853 −0.723827
\(966\) −0.343146 + 0.485281i −0.0110405 + 0.0156137i
\(967\) 12.2843i 0.395036i −0.980299 0.197518i \(-0.936712\pi\)
0.980299 0.197518i \(-0.0632880\pi\)
\(968\) 11.1005 13.4558i 0.356784 0.432487i
\(969\) −8.00000 5.65685i −0.256997 0.181724i
\(970\) 2.14214i 0.0687798i
\(971\) 30.2843i 0.971869i 0.873995 + 0.485934i \(0.161521\pi\)
−0.873995 + 0.485934i \(0.838479\pi\)
\(972\) −1.82843 28.4437i −0.0586468 0.912331i
\(973\) −6.48528 −0.207909
\(974\) 10.9706 0.351520
\(975\) 0 0
\(976\) 15.5147i 0.496614i
\(977\) 7.17157i 0.229439i −0.993398 0.114719i \(-0.963403\pi\)
0.993398 0.114719i \(-0.0365969\pi\)
\(978\) −0.627417 + 0.887302i −0.0200626 + 0.0283728i
\(979\) −22.9706 + 10.8284i −0.734142 + 0.346078i
\(980\) 1.82843i 0.0584070i
\(981\) −27.3137 + 9.65685i −0.872060 + 0.308320i
\(982\) −7.51472 −0.239804
\(983\) 2.82843i 0.0902128i 0.998982 + 0.0451064i \(0.0143627\pi\)
−0.998982 + 0.0451064i \(0.985637\pi\)
\(984\) −12.1421 + 17.1716i −0.387077 + 0.547410i
\(985\) 14.8284i 0.472473i
\(986\) 16.0000 0.509544
\(987\) −10.8284 + 15.3137i −0.344673 + 0.487441i
\(988\) 0 0
\(989\) 8.00000 0.254385
\(990\) 2.89949 + 2.92893i 0.0921520 + 0.0930876i
\(991\) 45.6569 1.45034 0.725169 0.688571i \(-0.241762\pi\)
0.725169 + 0.688571i \(0.241762\pi\)
\(992\) 3.65685 0.116105
\(993\) −10.3431 + 14.6274i −0.328230 + 0.464187i
\(994\) −0.142136 −0.00450827
\(995\) 14.4853i 0.459214i
\(996\) −21.9411 + 31.0294i −0.695231 + 0.983205i
\(997\) 44.2843i 1.40250i −0.712917 0.701248i \(-0.752626\pi\)
0.712917 0.701248i \(-0.247374\pi\)
\(998\) 14.9117 0.472021
\(999\) −30.0000 8.48528i −0.949158 0.268462i
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 1155.2.l.a.1121.3 4
3.2 odd 2 1155.2.l.d.1121.2 yes 4
11.10 odd 2 1155.2.l.d.1121.1 yes 4
33.32 even 2 inner 1155.2.l.a.1121.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.l.a.1121.3 4 1.1 even 1 trivial
1155.2.l.a.1121.4 yes 4 33.32 even 2 inner
1155.2.l.d.1121.1 yes 4 11.10 odd 2
1155.2.l.d.1121.2 yes 4 3.2 odd 2