Properties

Label 1155.2.l.d.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.d.1121.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +3.82843 q^{4} -1.00000i q^{5} +(2.41421 - 3.41421i) q^{6} +1.00000i q^{7} +4.41421 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+2.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +3.82843 q^{4} -1.00000i q^{5} +(2.41421 - 3.41421i) q^{6} +1.00000i q^{7} +4.41421 q^{8} +(-1.00000 - 2.82843i) q^{9} -2.41421i q^{10} +(1.41421 - 3.00000i) q^{11} +(3.82843 - 5.41421i) q^{12} +2.41421i q^{14} +(-1.41421 - 1.00000i) q^{15} +3.00000 q^{16} -1.17157 q^{17} +(-2.41421 - 6.82843i) q^{18} +4.82843i q^{19} -3.82843i q^{20} +(1.41421 + 1.00000i) q^{21} +(3.41421 - 7.24264i) q^{22} +4.82843i q^{23} +(4.41421 - 6.24264i) q^{24} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +3.82843i q^{28} +5.65685 q^{29} +(-3.41421 - 2.41421i) q^{30} -4.82843 q^{31} -1.58579 q^{32} +(-2.82843 - 5.00000i) q^{33} -2.82843 q^{34} +1.00000 q^{35} +(-3.82843 - 10.8284i) q^{36} +6.00000 q^{37} +11.6569i q^{38} -4.41421i q^{40} +3.65685 q^{41} +(3.41421 + 2.41421i) q^{42} +1.65685i q^{43} +(5.41421 - 11.4853i) q^{44} +(-2.82843 + 1.00000i) q^{45} +11.6569i q^{46} -5.17157i q^{47} +(3.00000 - 4.24264i) q^{48} -1.00000 q^{49} -2.41421 q^{50} +(-1.17157 + 1.65685i) q^{51} +4.82843i q^{53} +(-12.0711 - 3.41421i) q^{54} +(-3.00000 - 1.41421i) q^{55} +4.41421i q^{56} +(6.82843 + 4.82843i) q^{57} +13.6569 q^{58} +11.6569i q^{59} +(-5.41421 - 3.82843i) q^{60} +10.8284i q^{61} -11.6569 q^{62} +(2.82843 - 1.00000i) q^{63} -9.82843 q^{64} +(-6.82843 - 12.0711i) q^{66} +10.4853 q^{67} -4.48528 q^{68} +(6.82843 + 4.82843i) q^{69} +2.41421 q^{70} -11.6569i q^{71} +(-4.41421 - 12.4853i) q^{72} -12.0000i q^{73} +14.4853 q^{74} +(-1.00000 + 1.41421i) q^{75} +18.4853i q^{76} +(3.00000 + 1.41421i) q^{77} +4.00000i q^{79} -3.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} +8.82843 q^{82} -12.0000 q^{83} +(5.41421 + 3.82843i) q^{84} +1.17157i q^{85} +4.00000i q^{86} +(5.65685 - 8.00000i) q^{87} +(6.24264 - 13.2426i) q^{88} +3.65685i q^{89} +(-6.82843 + 2.41421i) q^{90} +18.4853i q^{92} +(-4.82843 + 6.82843i) q^{93} -12.4853i q^{94} +4.82843 q^{95} +(-1.58579 + 2.24264i) q^{96} -10.8284 q^{97} -2.41421 q^{98} +(-9.89949 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 12 q^{16} - 16 q^{17} - 4 q^{18} + 8 q^{22} + 12 q^{24} - 4 q^{25} - 20 q^{27} - 8 q^{30} - 8 q^{31} - 12 q^{32} + 4 q^{35} - 4 q^{36} + 24 q^{37} - 8 q^{41} + 8 q^{42} + 16 q^{44} + 12 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 20 q^{54} - 12 q^{55} + 16 q^{57} + 32 q^{58} - 16 q^{60} - 24 q^{62} - 28 q^{64} - 16 q^{66} + 8 q^{67} + 16 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{72} + 24 q^{74} - 4 q^{75} + 12 q^{77} - 28 q^{81} + 24 q^{82} - 48 q^{83} + 16 q^{84} + 8 q^{88} - 16 q^{90} - 8 q^{93} + 8 q^{95} - 12 q^{96} - 32 q^{97} - 4 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.41421 1.70711 0.853553 0.521005i \(-0.174443\pi\)
0.853553 + 0.521005i \(0.174443\pi\)
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 3.82843 1.91421
\(5\) 1.00000i 0.447214i
\(6\) 2.41421 3.41421i 0.985599 1.39385i
\(7\) 1.00000i 0.377964i
\(8\) 4.41421 1.56066
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 2.41421i 0.763441i
\(11\) 1.41421 3.00000i 0.426401 0.904534i
\(12\) 3.82843 5.41421i 1.10517 1.56295i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 2.41421i 0.645226i
\(15\) −1.41421 1.00000i −0.365148 0.258199i
\(16\) 3.00000 0.750000
\(17\) −1.17157 −0.284148 −0.142074 0.989856i \(-0.545377\pi\)
−0.142074 + 0.989856i \(0.545377\pi\)
\(18\) −2.41421 6.82843i −0.569036 1.60948i
\(19\) 4.82843i 1.10772i 0.832611 + 0.553859i \(0.186845\pi\)
−0.832611 + 0.553859i \(0.813155\pi\)
\(20\) 3.82843i 0.856062i
\(21\) 1.41421 + 1.00000i 0.308607 + 0.218218i
\(22\) 3.41421 7.24264i 0.727913 1.54414i
\(23\) 4.82843i 1.00680i 0.864054 + 0.503398i \(0.167917\pi\)
−0.864054 + 0.503398i \(0.832083\pi\)
\(24\) 4.41421 6.24264i 0.901048 1.27427i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 3.82843i 0.723505i
\(29\) 5.65685 1.05045 0.525226 0.850963i \(-0.323981\pi\)
0.525226 + 0.850963i \(0.323981\pi\)
\(30\) −3.41421 2.41421i −0.623347 0.440773i
\(31\) −4.82843 −0.867211 −0.433606 0.901103i \(-0.642759\pi\)
−0.433606 + 0.901103i \(0.642759\pi\)
\(32\) −1.58579 −0.280330
\(33\) −2.82843 5.00000i −0.492366 0.870388i
\(34\) −2.82843 −0.485071
\(35\) 1.00000 0.169031
\(36\) −3.82843 10.8284i −0.638071 1.80474i
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 11.6569i 1.89099i
\(39\) 0 0
\(40\) 4.41421i 0.697948i
\(41\) 3.65685 0.571105 0.285552 0.958363i \(-0.407823\pi\)
0.285552 + 0.958363i \(0.407823\pi\)
\(42\) 3.41421 + 2.41421i 0.526825 + 0.372521i
\(43\) 1.65685i 0.252668i 0.991988 + 0.126334i \(0.0403211\pi\)
−0.991988 + 0.126334i \(0.959679\pi\)
\(44\) 5.41421 11.4853i 0.816223 1.73147i
\(45\) −2.82843 + 1.00000i −0.421637 + 0.149071i
\(46\) 11.6569i 1.71871i
\(47\) 5.17157i 0.754351i −0.926142 0.377176i \(-0.876895\pi\)
0.926142 0.377176i \(-0.123105\pi\)
\(48\) 3.00000 4.24264i 0.433013 0.612372i
\(49\) −1.00000 −0.142857
\(50\) −2.41421 −0.341421
\(51\) −1.17157 + 1.65685i −0.164053 + 0.232006i
\(52\) 0 0
\(53\) 4.82843i 0.663235i 0.943414 + 0.331618i \(0.107594\pi\)
−0.943414 + 0.331618i \(0.892406\pi\)
\(54\) −12.0711 3.41421i −1.64266 0.464616i
\(55\) −3.00000 1.41421i −0.404520 0.190693i
\(56\) 4.41421i 0.589874i
\(57\) 6.82843 + 4.82843i 0.904447 + 0.639541i
\(58\) 13.6569 1.79323
\(59\) 11.6569i 1.51759i 0.651328 + 0.758797i \(0.274212\pi\)
−0.651328 + 0.758797i \(0.725788\pi\)
\(60\) −5.41421 3.82843i −0.698972 0.494248i
\(61\) 10.8284i 1.38644i 0.720727 + 0.693219i \(0.243808\pi\)
−0.720727 + 0.693219i \(0.756192\pi\)
\(62\) −11.6569 −1.48042
\(63\) 2.82843 1.00000i 0.356348 0.125988i
\(64\) −9.82843 −1.22855
\(65\) 0 0
\(66\) −6.82843 12.0711i −0.840521 1.48585i
\(67\) 10.4853 1.28098 0.640490 0.767966i \(-0.278731\pi\)
0.640490 + 0.767966i \(0.278731\pi\)
\(68\) −4.48528 −0.543920
\(69\) 6.82843 + 4.82843i 0.822046 + 0.581274i
\(70\) 2.41421 0.288554
\(71\) 11.6569i 1.38341i −0.722178 0.691707i \(-0.756859\pi\)
0.722178 0.691707i \(-0.243141\pi\)
\(72\) −4.41421 12.4853i −0.520220 1.47140i
\(73\) 12.0000i 1.40449i −0.711934 0.702247i \(-0.752180\pi\)
0.711934 0.702247i \(-0.247820\pi\)
\(74\) 14.4853 1.68388
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 18.4853i 2.12041i
\(77\) 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
\(82\) 8.82843 0.974937
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 5.41421 + 3.82843i 0.590739 + 0.417716i
\(85\) 1.17157i 0.127075i
\(86\) 4.00000i 0.431331i
\(87\) 5.65685 8.00000i 0.606478 0.857690i
\(88\) 6.24264 13.2426i 0.665468 1.41167i
\(89\) 3.65685i 0.387626i 0.981039 + 0.193813i \(0.0620855\pi\)
−0.981039 + 0.193813i \(0.937915\pi\)
\(90\) −6.82843 + 2.41421i −0.719779 + 0.254480i
\(91\) 0 0
\(92\) 18.4853i 1.92722i
\(93\) −4.82843 + 6.82843i −0.500685 + 0.708075i
\(94\) 12.4853i 1.28776i
\(95\) 4.82843 0.495386
\(96\) −1.58579 + 2.24264i −0.161849 + 0.228889i
\(97\) −10.8284 −1.09946 −0.549730 0.835342i \(-0.685269\pi\)
−0.549730 + 0.835342i \(0.685269\pi\)
\(98\) −2.41421 −0.243872
\(99\) −9.89949 1.00000i −0.994937 0.100504i
\(100\) −3.82843 −0.382843
\(101\) −13.3137 −1.32476 −0.662382 0.749166i \(-0.730454\pi\)
−0.662382 + 0.749166i \(0.730454\pi\)
\(102\) −2.82843 + 4.00000i −0.280056 + 0.396059i
\(103\) −13.3137 −1.31184 −0.655919 0.754831i \(-0.727719\pi\)
−0.655919 + 0.754831i \(0.727719\pi\)
\(104\) 0 0
\(105\) 1.00000 1.41421i 0.0975900 0.138013i
\(106\) 11.6569i 1.13221i
\(107\) 13.3137 1.28708 0.643542 0.765410i \(-0.277464\pi\)
0.643542 + 0.765410i \(0.277464\pi\)
\(108\) −19.1421 5.41421i −1.84195 0.520983i
\(109\) 1.65685i 0.158698i 0.996847 + 0.0793489i \(0.0252841\pi\)
−0.996847 + 0.0793489i \(0.974716\pi\)
\(110\) −7.24264 3.41421i −0.690559 0.325532i
\(111\) 6.00000 8.48528i 0.569495 0.805387i
\(112\) 3.00000i 0.283473i
\(113\) 8.82843i 0.830509i −0.909705 0.415254i \(-0.863693\pi\)
0.909705 0.415254i \(-0.136307\pi\)
\(114\) 16.4853 + 11.6569i 1.54399 + 1.09176i
\(115\) 4.82843 0.450253
\(116\) 21.6569 2.01079
\(117\) 0 0
\(118\) 28.1421i 2.59069i
\(119\) 1.17157i 0.107398i
\(120\) −6.24264 4.41421i −0.569873 0.402961i
\(121\) −7.00000 8.48528i −0.636364 0.771389i
\(122\) 26.1421i 2.36680i
\(123\) 3.65685 5.17157i 0.329727 0.466305i
\(124\) −18.4853 −1.66003
\(125\) 1.00000i 0.0894427i
\(126\) 6.82843 2.41421i 0.608325 0.215075i
\(127\) 2.34315i 0.207921i 0.994581 + 0.103960i \(0.0331515\pi\)
−0.994581 + 0.103960i \(0.966849\pi\)
\(128\) −20.5563 −1.81694
\(129\) 2.34315 + 1.65685i 0.206302 + 0.145878i
\(130\) 0 0
\(131\) 6.34315 0.554203 0.277102 0.960841i \(-0.410626\pi\)
0.277102 + 0.960841i \(0.410626\pi\)
\(132\) −10.8284 19.1421i −0.942494 1.66611i
\(133\) −4.82843 −0.418678
\(134\) 25.3137 2.18677
\(135\) −1.41421 + 5.00000i −0.121716 + 0.430331i
\(136\) −5.17157 −0.443459
\(137\) 7.17157i 0.612709i 0.951918 + 0.306354i \(0.0991093\pi\)
−0.951918 + 0.306354i \(0.900891\pi\)
\(138\) 16.4853 + 11.6569i 1.40332 + 0.992297i
\(139\) 10.4853i 0.889350i −0.895692 0.444675i \(-0.853319\pi\)
0.895692 0.444675i \(-0.146681\pi\)
\(140\) 3.82843 0.323561
\(141\) −7.31371 5.17157i −0.615925 0.435525i
\(142\) 28.1421i 2.36164i
\(143\) 0 0
\(144\) −3.00000 8.48528i −0.250000 0.707107i
\(145\) 5.65685i 0.469776i
\(146\) 28.9706i 2.39762i
\(147\) −1.00000 + 1.41421i −0.0824786 + 0.116642i
\(148\) 22.9706 1.88817
\(149\) 15.3137 1.25455 0.627274 0.778799i \(-0.284171\pi\)
0.627274 + 0.778799i \(0.284171\pi\)
\(150\) −2.41421 + 3.41421i −0.197120 + 0.278769i
\(151\) 19.3137i 1.57173i 0.618400 + 0.785864i \(0.287781\pi\)
−0.618400 + 0.785864i \(0.712219\pi\)
\(152\) 21.3137i 1.72877i
\(153\) 1.17157 + 3.31371i 0.0947161 + 0.267897i
\(154\) 7.24264 + 3.41421i 0.583629 + 0.275125i
\(155\) 4.82843i 0.387829i
\(156\) 0 0
\(157\) −13.1716 −1.05121 −0.525603 0.850730i \(-0.676160\pi\)
−0.525603 + 0.850730i \(0.676160\pi\)
\(158\) 9.65685i 0.768258i
\(159\) 6.82843 + 4.82843i 0.541529 + 0.382919i
\(160\) 1.58579i 0.125367i
\(161\) −4.82843 −0.380533
\(162\) −16.8995 + 13.6569i −1.32775 + 1.07298i
\(163\) −18.4853 −1.44788 −0.723939 0.689863i \(-0.757671\pi\)
−0.723939 + 0.689863i \(0.757671\pi\)
\(164\) 14.0000 1.09322
\(165\) −5.00000 + 2.82843i −0.389249 + 0.220193i
\(166\) −28.9706 −2.24855
\(167\) 13.6569 1.05680 0.528400 0.848996i \(-0.322792\pi\)
0.528400 + 0.848996i \(0.322792\pi\)
\(168\) 6.24264 + 4.41421i 0.481630 + 0.340564i
\(169\) 13.0000 1.00000
\(170\) 2.82843i 0.216930i
\(171\) 13.6569 4.82843i 1.04437 0.369239i
\(172\) 6.34315i 0.483660i
\(173\) 18.1421 1.37932 0.689661 0.724133i \(-0.257760\pi\)
0.689661 + 0.724133i \(0.257760\pi\)
\(174\) 13.6569 19.3137i 1.03532 1.46417i
\(175\) 1.00000i 0.0755929i
\(176\) 4.24264 9.00000i 0.319801 0.678401i
\(177\) 16.4853 + 11.6569i 1.23911 + 0.876183i
\(178\) 8.82843i 0.661719i
\(179\) 0.343146i 0.0256479i 0.999918 + 0.0128240i \(0.00408210\pi\)
−0.999918 + 0.0128240i \(0.995918\pi\)
\(180\) −10.8284 + 3.82843i −0.807103 + 0.285354i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 15.3137 + 10.8284i 1.13202 + 0.800460i
\(184\) 21.3137i 1.57127i
\(185\) 6.00000i 0.441129i
\(186\) −11.6569 + 16.4853i −0.854722 + 1.20876i
\(187\) −1.65685 + 3.51472i −0.121161 + 0.257022i
\(188\) 19.7990i 1.44399i
\(189\) 1.41421 5.00000i 0.102869 0.363696i
\(190\) 11.6569 0.845677
\(191\) 6.00000i 0.434145i −0.976156 0.217072i \(-0.930349\pi\)
0.976156 0.217072i \(-0.0696508\pi\)
\(192\) −9.82843 + 13.8995i −0.709306 + 1.00311i
\(193\) 5.51472i 0.396958i 0.980105 + 0.198479i \(0.0636002\pi\)
−0.980105 + 0.198479i \(0.936400\pi\)
\(194\) −26.1421 −1.87690
\(195\) 0 0
\(196\) −3.82843 −0.273459
\(197\) −9.17157 −0.653448 −0.326724 0.945120i \(-0.605945\pi\)
−0.326724 + 0.945120i \(0.605945\pi\)
\(198\) −23.8995 2.41421i −1.69846 0.171571i
\(199\) 2.48528 0.176177 0.0880885 0.996113i \(-0.471924\pi\)
0.0880885 + 0.996113i \(0.471924\pi\)
\(200\) −4.41421 −0.312132
\(201\) 10.4853 14.8284i 0.739575 1.04592i
\(202\) −32.1421 −2.26151
\(203\) 5.65685i 0.397033i
\(204\) −4.48528 + 6.34315i −0.314033 + 0.444109i
\(205\) 3.65685i 0.255406i
\(206\) −32.1421 −2.23945
\(207\) 13.6569 4.82843i 0.949217 0.335599i
\(208\) 0 0
\(209\) 14.4853 + 6.82843i 1.00197 + 0.472332i
\(210\) 2.41421 3.41421i 0.166597 0.235603i
\(211\) 16.9706i 1.16830i −0.811645 0.584151i \(-0.801428\pi\)
0.811645 0.584151i \(-0.198572\pi\)
\(212\) 18.4853i 1.26957i
\(213\) −16.4853 11.6569i −1.12955 0.798714i
\(214\) 32.1421 2.19719
\(215\) 1.65685 0.112997
\(216\) −22.0711 6.24264i −1.50175 0.424758i
\(217\) 4.82843i 0.327775i
\(218\) 4.00000i 0.270914i
\(219\) −16.9706 12.0000i −1.14676 0.810885i
\(220\) −11.4853 5.41421i −0.774338 0.365026i
\(221\) 0 0
\(222\) 14.4853 20.4853i 0.972188 1.37488i
\(223\) 18.9706 1.27036 0.635181 0.772363i \(-0.280925\pi\)
0.635181 + 0.772363i \(0.280925\pi\)
\(224\) 1.58579i 0.105955i
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 21.3137i 1.41777i
\(227\) −25.6569 −1.70291 −0.851453 0.524432i \(-0.824278\pi\)
−0.851453 + 0.524432i \(0.824278\pi\)
\(228\) 26.1421 + 18.4853i 1.73131 + 1.22422i
\(229\) 13.3137 0.879795 0.439897 0.898048i \(-0.355015\pi\)
0.439897 + 0.898048i \(0.355015\pi\)
\(230\) 11.6569 0.768630
\(231\) 5.00000 2.82843i 0.328976 0.186097i
\(232\) 24.9706 1.63940
\(233\) −27.7990 −1.82117 −0.910586 0.413319i \(-0.864369\pi\)
−0.910586 + 0.413319i \(0.864369\pi\)
\(234\) 0 0
\(235\) −5.17157 −0.337356
\(236\) 44.6274i 2.90500i
\(237\) 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
\(241\) 17.1716i 1.10612i −0.833142 0.553059i \(-0.813460\pi\)
0.833142 0.553059i \(-0.186540\pi\)
\(242\) −16.8995 20.4853i −1.08634 1.31684i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 41.4558i 2.65394i
\(245\) 1.00000i 0.0638877i
\(246\) 8.82843 12.4853i 0.562880 0.796032i
\(247\) 0 0
\(248\) −21.3137 −1.35342
\(249\) −12.0000 + 16.9706i −0.760469 + 1.07547i
\(250\) 2.41421i 0.152688i
\(251\) 24.6274i 1.55447i −0.629211 0.777234i \(-0.716622\pi\)
0.629211 0.777234i \(-0.283378\pi\)
\(252\) 10.8284 3.82843i 0.682127 0.241168i
\(253\) 14.4853 + 6.82843i 0.910682 + 0.429300i
\(254\) 5.65685i 0.354943i
\(255\) 1.65685 + 1.17157i 0.103756 + 0.0733667i
\(256\) −29.9706 −1.87316
\(257\) 9.31371i 0.580973i −0.956879 0.290487i \(-0.906183\pi\)
0.956879 0.290487i \(-0.0938172\pi\)
\(258\) 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
\(262\) 15.3137 0.946084
\(263\) −5.31371 −0.327657 −0.163829 0.986489i \(-0.552384\pi\)
−0.163829 + 0.986489i \(0.552384\pi\)
\(264\) −12.4853 22.0711i −0.768416 1.35838i
\(265\) 4.82843 0.296608
\(266\) −11.6569 −0.714728
\(267\) 5.17157 + 3.65685i 0.316495 + 0.223796i
\(268\) 40.1421 2.45207
\(269\) 5.31371i 0.323983i −0.986792 0.161991i \(-0.948208\pi\)
0.986792 0.161991i \(-0.0517916\pi\)
\(270\) −3.41421 + 12.0711i −0.207782 + 0.734622i
\(271\) 14.4853i 0.879918i 0.898018 + 0.439959i \(0.145007\pi\)
−0.898018 + 0.439959i \(0.854993\pi\)
\(272\) −3.51472 −0.213111
\(273\) 0 0
\(274\) 17.3137i 1.04596i
\(275\) −1.41421 + 3.00000i −0.0852803 + 0.180907i
\(276\) 26.1421 + 18.4853i 1.57357 + 1.11268i
\(277\) 0.828427i 0.0497754i −0.999690 0.0248877i \(-0.992077\pi\)
0.999690 0.0248877i \(-0.00792281\pi\)
\(278\) 25.3137i 1.51822i
\(279\) 4.82843 + 13.6569i 0.289070 + 0.817614i
\(280\) 4.41421 0.263800
\(281\) −4.97056 −0.296519 −0.148259 0.988948i \(-0.547367\pi\)
−0.148259 + 0.988948i \(0.547367\pi\)
\(282\) −17.6569 12.4853i −1.05145 0.743488i
\(283\) 4.97056i 0.295469i −0.989027 0.147735i \(-0.952802\pi\)
0.989027 0.147735i \(-0.0471982\pi\)
\(284\) 44.6274i 2.64815i
\(285\) 4.82843 6.82843i 0.286011 0.404481i
\(286\) 0 0
\(287\) 3.65685i 0.215857i
\(288\) 1.58579 + 4.48528i 0.0934434 + 0.264298i
\(289\) −15.6274 −0.919260
\(290\) 13.6569i 0.801958i
\(291\) −10.8284 + 15.3137i −0.634774 + 0.897705i
\(292\) 45.9411i 2.68850i
\(293\) 13.1716 0.769492 0.384746 0.923023i \(-0.374289\pi\)
0.384746 + 0.923023i \(0.374289\pi\)
\(294\) −2.41421 + 3.41421i −0.140800 + 0.199121i
\(295\) 11.6569 0.678688
\(296\) 26.4853 1.53943
\(297\) −11.3137 + 13.0000i −0.656488 + 0.754337i
\(298\) 36.9706 2.14165
\(299\) 0 0
\(300\) −3.82843 + 5.41421i −0.221034 + 0.312590i
\(301\) −1.65685 −0.0954995
\(302\) 46.6274i 2.68311i
\(303\) −13.3137 + 18.8284i −0.764853 + 1.08166i
\(304\) 14.4853i 0.830788i
\(305\) 10.8284 0.620034
\(306\) 2.82843 + 8.00000i 0.161690 + 0.457330i
\(307\) 24.9706i 1.42515i 0.701598 + 0.712573i \(0.252470\pi\)
−0.701598 + 0.712573i \(0.747530\pi\)
\(308\) 11.4853 + 5.41421i 0.654435 + 0.308503i
\(309\) −13.3137 + 18.8284i −0.757390 + 1.07111i
\(310\) 11.6569i 0.662065i
\(311\) 20.6274i 1.16967i −0.811151 0.584837i \(-0.801159\pi\)
0.811151 0.584837i \(-0.198841\pi\)
\(312\) 0 0
\(313\) 18.8284 1.06425 0.532123 0.846667i \(-0.321394\pi\)
0.532123 + 0.846667i \(0.321394\pi\)
\(314\) −31.7990 −1.79452
\(315\) −1.00000 2.82843i −0.0563436 0.159364i
\(316\) 15.3137i 0.861463i
\(317\) 23.1716i 1.30145i −0.759316 0.650723i \(-0.774466\pi\)
0.759316 0.650723i \(-0.225534\pi\)
\(318\) 16.4853 + 11.6569i 0.924449 + 0.653684i
\(319\) 8.00000 16.9706i 0.447914 0.950169i
\(320\) 9.82843i 0.549426i
\(321\) 13.3137 18.8284i 0.743099 1.05090i
\(322\) −11.6569 −0.649611
\(323\) 5.65685i 0.314756i
\(324\) −26.7990 + 21.6569i −1.48883 + 1.20316i
\(325\) 0 0
\(326\) −44.6274 −2.47168
\(327\) 2.34315 + 1.65685i 0.129576 + 0.0916242i
\(328\) 16.1421 0.891300
\(329\) 5.17157 0.285118
\(330\) −12.0711 + 6.82843i −0.664490 + 0.375893i
\(331\) −21.6569 −1.19037 −0.595184 0.803589i \(-0.702921\pi\)
−0.595184 + 0.803589i \(0.702921\pi\)
\(332\) −45.9411 −2.52135
\(333\) −6.00000 16.9706i −0.328798 0.929981i
\(334\) 32.9706 1.80407
\(335\) 10.4853i 0.572872i
\(336\) 4.24264 + 3.00000i 0.231455 + 0.163663i
\(337\) 14.4853i 0.789064i 0.918882 + 0.394532i \(0.129093\pi\)
−0.918882 + 0.394532i \(0.870907\pi\)
\(338\) 31.3848 1.70711
\(339\) −12.4853 8.82843i −0.678107 0.479494i
\(340\) 4.48528i 0.243249i
\(341\) −6.82843 + 14.4853i −0.369780 + 0.784422i
\(342\) 32.9706 11.6569i 1.78284 0.630330i
\(343\) 1.00000i 0.0539949i
\(344\) 7.31371i 0.394329i
\(345\) 4.82843 6.82843i 0.259954 0.367630i
\(346\) 43.7990 2.35465
\(347\) −23.6569 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(348\) 21.6569 30.6274i 1.16093 1.64180i
\(349\) 15.5147i 0.830484i −0.909711 0.415242i \(-0.863697\pi\)
0.909711 0.415242i \(-0.136303\pi\)
\(350\) 2.41421i 0.129045i
\(351\) 0 0
\(352\) −2.24264 + 4.75736i −0.119533 + 0.253568i
\(353\) 11.6569i 0.620432i −0.950666 0.310216i \(-0.899599\pi\)
0.950666 0.310216i \(-0.100401\pi\)
\(354\) 39.7990 + 28.1421i 2.11529 + 1.49574i
\(355\) −11.6569 −0.618682
\(356\) 14.0000i 0.741999i
\(357\) −1.65685 1.17157i −0.0876900 0.0620062i
\(358\) 0.828427i 0.0437837i
\(359\) 8.48528 0.447836 0.223918 0.974608i \(-0.428115\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(360\) −12.4853 + 4.41421i −0.658032 + 0.232649i
\(361\) −4.31371 −0.227037
\(362\) −4.82843 −0.253776
\(363\) −19.0000 + 1.41421i −0.997241 + 0.0742270i
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 36.9706 + 26.1421i 1.93248 + 1.36647i
\(367\) −18.0000 −0.939592 −0.469796 0.882775i \(-0.655673\pi\)
−0.469796 + 0.882775i \(0.655673\pi\)
\(368\) 14.4853i 0.755097i
\(369\) −3.65685 10.3431i −0.190368 0.538443i
\(370\) 14.4853i 0.753054i
\(371\) −4.82843 −0.250679
\(372\) −18.4853 + 26.1421i −0.958417 + 1.35541i
\(373\) 24.1421i 1.25003i −0.780612 0.625016i \(-0.785092\pi\)
0.780612 0.625016i \(-0.214908\pi\)
\(374\) −4.00000 + 8.48528i −0.206835 + 0.438763i
\(375\) 1.41421 + 1.00000i 0.0730297 + 0.0516398i
\(376\) 22.8284i 1.17729i
\(377\) 0 0
\(378\) 3.41421 12.0711i 0.175608 0.620869i
\(379\) 29.9411 1.53797 0.768986 0.639265i \(-0.220761\pi\)
0.768986 + 0.639265i \(0.220761\pi\)
\(380\) 18.4853 0.948275
\(381\) 3.31371 + 2.34315i 0.169766 + 0.120043i
\(382\) 14.4853i 0.741131i
\(383\) 15.7990i 0.807291i −0.914916 0.403645i \(-0.867743\pi\)
0.914916 0.403645i \(-0.132257\pi\)
\(384\) −20.5563 + 29.0711i −1.04901 + 1.48353i
\(385\) 1.41421 3.00000i 0.0720750 0.152894i
\(386\) 13.3137i 0.677650i
\(387\) 4.68629 1.65685i 0.238218 0.0842226i
\(388\) −41.4558 −2.10460
\(389\) 34.6274i 1.75568i −0.478954 0.877840i \(-0.658984\pi\)
0.478954 0.877840i \(-0.341016\pi\)
\(390\) 0 0
\(391\) 5.65685i 0.286079i
\(392\) −4.41421 −0.222951
\(393\) 6.34315 8.97056i 0.319969 0.452505i
\(394\) −22.1421 −1.11550
\(395\) 4.00000 0.201262
\(396\) −37.8995 3.82843i −1.90452 0.192386i
\(397\) 3.51472 0.176399 0.0881993 0.996103i \(-0.471889\pi\)
0.0881993 + 0.996103i \(0.471889\pi\)
\(398\) 6.00000 0.300753
\(399\) −4.82843 + 6.82843i −0.241724 + 0.341849i
\(400\) −3.00000 −0.150000
\(401\) 27.3137i 1.36398i −0.731361 0.681991i \(-0.761114\pi\)
0.731361 0.681991i \(-0.238886\pi\)
\(402\) 25.3137 35.7990i 1.26253 1.78549i
\(403\) 0 0
\(404\) −50.9706 −2.53588
\(405\) 5.65685 + 7.00000i 0.281091 + 0.347833i
\(406\) 13.6569i 0.677778i
\(407\) 8.48528 18.0000i 0.420600 0.892227i
\(408\) −5.17157 + 7.31371i −0.256031 + 0.362083i
\(409\) 13.4558i 0.665349i 0.943042 + 0.332674i \(0.107951\pi\)
−0.943042 + 0.332674i \(0.892049\pi\)
\(410\) 8.82843i 0.436005i
\(411\) 10.1421 + 7.17157i 0.500275 + 0.353748i
\(412\) −50.9706 −2.51114
\(413\) −11.6569 −0.573596
\(414\) 32.9706 11.6569i 1.62041 0.572903i
\(415\) 12.0000i 0.589057i
\(416\) 0 0
\(417\) −14.8284 10.4853i −0.726151 0.513466i
\(418\) 34.9706 + 16.4853i 1.71047 + 0.806321i
\(419\) 2.68629i 0.131234i 0.997845 + 0.0656170i \(0.0209015\pi\)
−0.997845 + 0.0656170i \(0.979098\pi\)
\(420\) 3.82843 5.41421i 0.186808 0.264187i
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 40.9706i 1.99442i
\(423\) −14.6274 + 5.17157i −0.711209 + 0.251450i
\(424\) 21.3137i 1.03509i
\(425\) 1.17157 0.0568296
\(426\) −39.7990 28.1421i −1.92827 1.36349i
\(427\) −10.8284 −0.524024
\(428\) 50.9706 2.46376
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) −10.1421 −0.488529 −0.244265 0.969709i \(-0.578547\pi\)
−0.244265 + 0.969709i \(0.578547\pi\)
\(432\) −15.0000 4.24264i −0.721688 0.204124i
\(433\) −29.1716 −1.40190 −0.700948 0.713212i \(-0.747240\pi\)
−0.700948 + 0.713212i \(0.747240\pi\)
\(434\) 11.6569i 0.559547i
\(435\) −8.00000 5.65685i −0.383571 0.271225i
\(436\) 6.34315i 0.303782i
\(437\) −23.3137 −1.11525
\(438\) −40.9706 28.9706i −1.95765 1.38427i
\(439\) 31.4558i 1.50131i 0.660697 + 0.750653i \(0.270261\pi\)
−0.660697 + 0.750653i \(0.729739\pi\)
\(440\) −13.2426 6.24264i −0.631318 0.297606i
\(441\) 1.00000 + 2.82843i 0.0476190 + 0.134687i
\(442\) 0 0
\(443\) 1.79899i 0.0854726i 0.999086 + 0.0427363i \(0.0136075\pi\)
−0.999086 + 0.0427363i \(0.986392\pi\)
\(444\) 22.9706 32.4853i 1.09013 1.54168i
\(445\) 3.65685 0.173352
\(446\) 45.7990 2.16865
\(447\) 15.3137 21.6569i 0.724314 1.02433i
\(448\) 9.82843i 0.464350i
\(449\) 17.6569i 0.833278i −0.909072 0.416639i \(-0.863208\pi\)
0.909072 0.416639i \(-0.136792\pi\)
\(450\) 2.41421 + 6.82843i 0.113807 + 0.321895i
\(451\) 5.17157 10.9706i 0.243520 0.516584i
\(452\) 33.7990i 1.58977i
\(453\) 27.3137 + 19.3137i 1.28331 + 0.907437i
\(454\) −61.9411 −2.90704
\(455\) 0 0
\(456\) 30.1421 + 21.3137i 1.41153 + 0.998106i
\(457\) 9.51472i 0.445080i −0.974924 0.222540i \(-0.928565\pi\)
0.974924 0.222540i \(-0.0714348\pi\)
\(458\) 32.1421 1.50190
\(459\) 5.85786 + 1.65685i 0.273422 + 0.0773353i
\(460\) 18.4853 0.861881
\(461\) 23.6569 1.10181 0.550905 0.834568i \(-0.314283\pi\)
0.550905 + 0.834568i \(0.314283\pi\)
\(462\) 12.0711 6.82843i 0.561597 0.317687i
\(463\) 11.4558 0.532398 0.266199 0.963918i \(-0.414232\pi\)
0.266199 + 0.963918i \(0.414232\pi\)
\(464\) 16.9706 0.787839
\(465\) 6.82843 + 4.82843i 0.316661 + 0.223913i
\(466\) −67.1127 −3.10894
\(467\) 6.82843i 0.315982i −0.987441 0.157991i \(-0.949498\pi\)
0.987441 0.157991i \(-0.0505017\pi\)
\(468\) 0 0
\(469\) 10.4853i 0.484165i
\(470\) −12.4853 −0.575903
\(471\) −13.1716 + 18.6274i −0.606914 + 0.858306i
\(472\) 51.4558i 2.36845i
\(473\) 4.97056 + 2.34315i 0.228547 + 0.107738i
\(474\) 13.6569 + 9.65685i 0.627280 + 0.443554i
\(475\) 4.82843i 0.221543i
\(476\) 4.48528i 0.205583i
\(477\) 13.6569 4.82843i 0.625304 0.221078i
\(478\) −6.82843 −0.312325
\(479\) 11.3137 0.516937 0.258468 0.966020i \(-0.416782\pi\)
0.258468 + 0.966020i \(0.416782\pi\)
\(480\) 2.24264 + 1.58579i 0.102362 + 0.0723809i
\(481\) 0 0
\(482\) 41.4558i 1.88826i
\(483\) −4.82843 + 6.82843i −0.219701 + 0.310704i
\(484\) −26.7990 32.4853i −1.21814 1.47660i
\(485\) 10.8284i 0.491694i
\(486\) 2.41421 + 37.5563i 0.109511 + 1.70359i
\(487\) 9.51472 0.431153 0.215577 0.976487i \(-0.430837\pi\)
0.215577 + 0.976487i \(0.430837\pi\)
\(488\) 47.7990i 2.16376i
\(489\) −18.4853 + 26.1421i −0.835933 + 1.18219i
\(490\) 2.41421i 0.109063i
\(491\) −10.1421 −0.457708 −0.228854 0.973461i \(-0.573498\pi\)
−0.228854 + 0.973461i \(0.573498\pi\)
\(492\) 14.0000 19.7990i 0.631169 0.892607i
\(493\) −6.62742 −0.298484
\(494\) 0 0
\(495\) −1.00000 + 9.89949i −0.0449467 + 0.444949i
\(496\) −14.4853 −0.650408
\(497\) 11.6569 0.522881
\(498\) −28.9706 + 40.9706i −1.29820 + 1.83593i
\(499\) 36.0000 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 3.82843i 0.171212i
\(501\) 13.6569 19.3137i 0.610143 0.862873i
\(502\) 59.4558i 2.65364i
\(503\) −14.3431 −0.639529 −0.319765 0.947497i \(-0.603604\pi\)
−0.319765 + 0.947497i \(0.603604\pi\)
\(504\) 12.4853 4.41421i 0.556139 0.196625i
\(505\) 13.3137i 0.592452i
\(506\) 34.9706 + 16.4853i 1.55463 + 0.732860i
\(507\) 13.0000 18.3848i 0.577350 0.816497i
\(508\) 8.97056i 0.398004i
\(509\) 22.9706i 1.01815i 0.860721 + 0.509076i \(0.170013\pi\)
−0.860721 + 0.509076i \(0.829987\pi\)
\(510\) 4.00000 + 2.82843i 0.177123 + 0.125245i
\(511\) 12.0000 0.530849
\(512\) −31.2426 −1.38074
\(513\) 6.82843 24.1421i 0.301482 1.06590i
\(514\) 22.4853i 0.991783i
\(515\) 13.3137i 0.586672i
\(516\) 8.97056 + 6.34315i 0.394907 + 0.279241i
\(517\) −15.5147 7.31371i −0.682337 0.321657i
\(518\) 14.4853i 0.636447i
\(519\) 18.1421 25.6569i 0.796351 1.12621i
\(520\) 0 0
\(521\) 13.3137i 0.583284i −0.956528 0.291642i \(-0.905798\pi\)
0.956528 0.291642i \(-0.0942016\pi\)
\(522\) −13.6569 38.6274i −0.597744 1.69068i
\(523\) 20.9706i 0.916979i 0.888700 + 0.458489i \(0.151609\pi\)
−0.888700 + 0.458489i \(0.848391\pi\)
\(524\) 24.2843 1.06086
\(525\) −1.41421 1.00000i −0.0617213 0.0436436i
\(526\) −12.8284 −0.559346
\(527\) 5.65685 0.246416
\(528\) −8.48528 15.0000i −0.369274 0.652791i
\(529\) −0.313708 −0.0136395
\(530\) 11.6569 0.506341
\(531\) 32.9706 11.6569i 1.43080 0.505864i
\(532\) −18.4853 −0.801439
\(533\) 0 0
\(534\) 12.4853 + 8.82843i 0.540291 + 0.382043i
\(535\) 13.3137i 0.575602i
\(536\) 46.2843 1.99918
\(537\) 0.485281 + 0.343146i 0.0209414 + 0.0148078i
\(538\) 12.8284i 0.553073i
\(539\) −1.41421 + 3.00000i −0.0609145 + 0.129219i
\(540\) −5.41421 + 19.1421i −0.232991 + 0.823746i
\(541\) 4.97056i 0.213701i 0.994275 + 0.106851i \(0.0340767\pi\)
−0.994275 + 0.106851i \(0.965923\pi\)
\(542\) 34.9706i 1.50211i
\(543\) −2.00000 + 2.82843i −0.0858282 + 0.121379i
\(544\) 1.85786 0.0796553
\(545\) 1.65685 0.0709718
\(546\) 0 0
\(547\) 24.2843i 1.03832i 0.854677 + 0.519160i \(0.173755\pi\)
−0.854677 + 0.519160i \(0.826245\pi\)
\(548\) 27.4558i 1.17286i
\(549\) 30.6274 10.8284i 1.30715 0.462146i
\(550\) −3.41421 + 7.24264i −0.145583 + 0.308827i
\(551\) 27.3137i 1.16360i
\(552\) 30.1421 + 21.3137i 1.28293 + 0.907172i
\(553\) −4.00000 −0.170097
\(554\) 2.00000i 0.0849719i
\(555\) −8.48528 6.00000i −0.360180 0.254686i
\(556\) 40.1421i 1.70241i
\(557\) −27.5147 −1.16584 −0.582918 0.812531i \(-0.698089\pi\)
−0.582918 + 0.812531i \(0.698089\pi\)
\(558\) 11.6569 + 32.9706i 0.493474 + 1.39576i
\(559\) 0 0
\(560\) 3.00000 0.126773
\(561\) 3.31371 + 5.85786i 0.139905 + 0.247319i
\(562\) −12.0000 −0.506189
\(563\) −40.9706 −1.72670 −0.863352 0.504603i \(-0.831639\pi\)
−0.863352 + 0.504603i \(0.831639\pi\)
\(564\) −28.0000 19.7990i −1.17901 0.833688i
\(565\) −8.82843 −0.371415
\(566\) 12.0000i 0.504398i
\(567\) −5.65685 7.00000i −0.237566 0.293972i
\(568\) 51.4558i 2.15904i
\(569\) 0.686292 0.0287708 0.0143854 0.999897i \(-0.495421\pi\)
0.0143854 + 0.999897i \(0.495421\pi\)
\(570\) 11.6569 16.4853i 0.488252 0.690492i
\(571\) 28.9706i 1.21238i 0.795320 + 0.606190i \(0.207303\pi\)
−0.795320 + 0.606190i \(0.792697\pi\)
\(572\) 0 0
\(573\) −8.48528 6.00000i −0.354478 0.250654i
\(574\) 8.82843i 0.368491i
\(575\) 4.82843i 0.201359i
\(576\) 9.82843 + 27.7990i 0.409518 + 1.15829i
\(577\) −3.51472 −0.146320 −0.0731598 0.997320i \(-0.523308\pi\)
−0.0731598 + 0.997320i \(0.523308\pi\)
\(578\) −37.7279 −1.56927
\(579\) 7.79899 + 5.51472i 0.324115 + 0.229184i
\(580\) 21.6569i 0.899252i
\(581\) 12.0000i 0.497844i
\(582\) −26.1421 + 36.9706i −1.08363 + 1.53248i
\(583\) 14.4853 + 6.82843i 0.599919 + 0.282805i
\(584\) 52.9706i 2.19194i
\(585\) 0 0
\(586\) 31.7990 1.31360
\(587\) 13.4558i 0.555382i 0.960670 + 0.277691i \(0.0895692\pi\)
−0.960670 + 0.277691i \(0.910431\pi\)
\(588\) −3.82843 + 5.41421i −0.157882 + 0.223278i
\(589\) 23.3137i 0.960625i
\(590\) 28.1421 1.15859
\(591\) −9.17157 + 12.9706i −0.377268 + 0.533538i
\(592\) 18.0000 0.739795
\(593\) −22.8284 −0.937451 −0.468726 0.883344i \(-0.655287\pi\)
−0.468726 + 0.883344i \(0.655287\pi\)
\(594\) −27.3137 + 31.3848i −1.12070 + 1.28773i
\(595\) −1.17157 −0.0480298
\(596\) 58.6274 2.40147
\(597\) 2.48528 3.51472i 0.101716 0.143848i
\(598\) 0 0
\(599\) 27.9411i 1.14164i 0.821074 + 0.570822i \(0.193375\pi\)
−0.821074 + 0.570822i \(0.806625\pi\)
\(600\) −4.41421 + 6.24264i −0.180210 + 0.254855i
\(601\) 45.4558i 1.85418i 0.374836 + 0.927091i \(0.377699\pi\)
−0.374836 + 0.927091i \(0.622301\pi\)
\(602\) −4.00000 −0.163028
\(603\) −10.4853 29.6569i −0.426994 1.20772i
\(604\) 73.9411i 3.00862i
\(605\) −8.48528 + 7.00000i −0.344976 + 0.284590i
\(606\) −32.1421 + 45.4558i −1.30569 + 1.84652i
\(607\) 36.0000i 1.46119i 0.682808 + 0.730597i \(0.260758\pi\)
−0.682808 + 0.730597i \(0.739242\pi\)
\(608\) 7.65685i 0.310526i
\(609\) 8.00000 + 5.65685i 0.324176 + 0.229227i
\(610\) 26.1421 1.05846
\(611\) 0 0
\(612\) 4.48528 + 12.6863i 0.181307 + 0.512813i
\(613\) 33.7990i 1.36513i −0.730826 0.682564i \(-0.760865\pi\)
0.730826 0.682564i \(-0.239135\pi\)
\(614\) 60.2843i 2.43288i
\(615\) −5.17157 3.65685i −0.208538 0.147459i
\(616\) 13.2426 + 6.24264i 0.533561 + 0.251523i
\(617\) 31.4558i 1.26636i 0.774003 + 0.633182i \(0.218252\pi\)
−0.774003 + 0.633182i \(0.781748\pi\)
\(618\) −32.1421 + 45.4558i −1.29295 + 1.82850i
\(619\) 17.7990 0.715402 0.357701 0.933836i \(-0.383561\pi\)
0.357701 + 0.933836i \(0.383561\pi\)
\(620\) 18.4853i 0.742387i
\(621\) 6.82843 24.1421i 0.274015 0.968791i
\(622\) 49.7990i 1.99676i
\(623\) −3.65685 −0.146509
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 45.4558 1.81678
\(627\) 24.1421 13.6569i 0.964144 0.545402i
\(628\) −50.4264 −2.01223
\(629\) −7.02944 −0.280282
\(630\) −2.41421 6.82843i −0.0961846 0.272051i
\(631\) −0.970563 −0.0386375 −0.0193187 0.999813i \(-0.506150\pi\)
−0.0193187 + 0.999813i \(0.506150\pi\)
\(632\) 17.6569i 0.702352i
\(633\) −24.0000 16.9706i −0.953914 0.674519i
\(634\) 55.9411i 2.22171i
\(635\) 2.34315 0.0929849
\(636\) 26.1421 + 18.4853i 1.03660 + 0.732989i
\(637\) 0 0
\(638\) 19.3137 40.9706i 0.764637 1.62204i
\(639\) −32.9706 + 11.6569i −1.30430 + 0.461138i
\(640\) 20.5563i 0.812561i
\(641\) 39.3137i 1.55280i 0.630242 + 0.776399i \(0.282956\pi\)
−0.630242 + 0.776399i \(0.717044\pi\)
\(642\) 32.1421 45.4558i 1.26855 1.79400i
\(643\) 22.9706 0.905871 0.452935 0.891543i \(-0.350377\pi\)
0.452935 + 0.891543i \(0.350377\pi\)
\(644\) −18.4853 −0.728422
\(645\) 1.65685 2.34315i 0.0652386 0.0922613i
\(646\) 13.6569i 0.537322i
\(647\) 43.7990i 1.72192i −0.508676 0.860958i \(-0.669865\pi\)
0.508676 0.860958i \(-0.330135\pi\)
\(648\) −30.8995 + 24.9706i −1.21385 + 0.980936i
\(649\) 34.9706 + 16.4853i 1.37271 + 0.647104i
\(650\) 0 0
\(651\) −6.82843 4.82843i −0.267627 0.189241i
\(652\) −70.7696 −2.77155
\(653\) 9.51472i 0.372340i −0.982518 0.186170i \(-0.940393\pi\)
0.982518 0.186170i \(-0.0596075\pi\)
\(654\) 5.65685 + 4.00000i 0.221201 + 0.156412i
\(655\) 6.34315i 0.247847i
\(656\) 10.9706 0.428329
\(657\) −33.9411 + 12.0000i −1.32417 + 0.468165i
\(658\) 12.4853 0.486727
\(659\) 27.5147 1.07182 0.535911 0.844275i \(-0.319968\pi\)
0.535911 + 0.844275i \(0.319968\pi\)
\(660\) −19.1421 + 10.8284i −0.745107 + 0.421496i
\(661\) −13.0294 −0.506786 −0.253393 0.967363i \(-0.581547\pi\)
−0.253393 + 0.967363i \(0.581547\pi\)
\(662\) −52.2843 −2.03209
\(663\) 0 0
\(664\) −52.9706 −2.05566
\(665\) 4.82843i 0.187238i
\(666\) −14.4853 40.9706i −0.561293 1.58758i
\(667\) 27.3137i 1.05759i
\(668\) 52.2843 2.02294
\(669\) 18.9706 26.8284i 0.733444 1.03725i
\(670\) 25.3137i 0.977954i
\(671\) 32.4853 + 15.3137i 1.25408 + 0.591179i
\(672\) −2.24264 1.58579i −0.0865117 0.0611730i
\(673\) 42.4853i 1.63769i −0.574017 0.818844i \(-0.694616\pi\)
0.574017 0.818844i \(-0.305384\pi\)
\(674\) 34.9706i 1.34702i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) 49.7696 1.91421
\(677\) 32.7696 1.25944 0.629718 0.776824i \(-0.283170\pi\)
0.629718 + 0.776824i \(0.283170\pi\)
\(678\) −30.1421 21.3137i −1.15760 0.818548i
\(679\) 10.8284i 0.415557i
\(680\) 5.17157i 0.198321i
\(681\) −25.6569 + 36.2843i −0.983173 + 1.39042i
\(682\) −16.4853 + 34.9706i −0.631254 + 1.33909i
\(683\) 1.79899i 0.0688364i −0.999408 0.0344182i \(-0.989042\pi\)
0.999408 0.0344182i \(-0.0109578\pi\)
\(684\) 52.2843 18.4853i 1.99914 0.706802i
\(685\) 7.17157 0.274012
\(686\) 2.41421i 0.0921751i
\(687\) 13.3137 18.8284i 0.507950 0.718349i
\(688\) 4.97056i 0.189501i
\(689\) 0 0
\(690\) 11.6569 16.4853i 0.443769 0.627584i
\(691\) −22.4853 −0.855380 −0.427690 0.903925i \(-0.640673\pi\)
−0.427690 + 0.903925i \(0.640673\pi\)
\(692\) 69.4558 2.64032
\(693\) 1.00000 9.89949i 0.0379869 0.376051i
\(694\) −57.1127 −2.16797
\(695\) −10.4853 −0.397729
\(696\) 24.9706 35.3137i 0.946507 1.33856i
\(697\) −4.28427 −0.162278
\(698\) 37.4558i 1.41772i
\(699\) −27.7990 + 39.3137i −1.05145 + 1.48698i
\(700\) 3.82843i 0.144701i
\(701\) 47.5980 1.79775 0.898875 0.438204i \(-0.144385\pi\)
0.898875 + 0.438204i \(0.144385\pi\)
\(702\) 0 0
\(703\) 28.9706i 1.09265i
\(704\) −13.8995 + 29.4853i −0.523857 + 1.11127i
\(705\) −5.17157 + 7.31371i −0.194773 + 0.275450i
\(706\) 28.1421i 1.05914i
\(707\) 13.3137i 0.500714i
\(708\) 63.1127 + 44.6274i 2.37192 + 1.67720i
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) −28.1421 −1.05616
\(711\) 11.3137 4.00000i 0.424297 0.150012i
\(712\) 16.1421i 0.604952i
\(713\) 23.3137i 0.873105i
\(714\) −4.00000 2.82843i −0.149696 0.105851i
\(715\) 0 0
\(716\) 1.31371i 0.0490956i
\(717\) −2.82843 + 4.00000i −0.105630 + 0.149383i
\(718\) 20.4853 0.764504
\(719\) 29.3137i 1.09322i −0.837388 0.546608i \(-0.815919\pi\)
0.837388 0.546608i \(-0.184081\pi\)
\(720\) −8.48528 + 3.00000i −0.316228 + 0.111803i
\(721\) 13.3137i 0.495828i
\(722\) −10.4142 −0.387577
\(723\) −24.2843 17.1716i −0.903142 0.638618i
\(724\) −7.65685 −0.284565
\(725\) −5.65685 −0.210090
\(726\) −45.8701 + 3.41421i −1.70240 + 0.126713i
\(727\) 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
\(730\) −28.9706 −1.07225
\(731\) 1.94113i 0.0717951i
\(732\) 58.6274 + 41.4558i 2.16693 + 1.53225i
\(733\) 37.9411i 1.40139i −0.713462 0.700694i \(-0.752874\pi\)
0.713462 0.700694i \(-0.247126\pi\)
\(734\) −43.4558 −1.60398
\(735\) 1.41421 + 1.00000i 0.0521641 + 0.0368856i
\(736\) 7.65685i 0.282235i
\(737\) 14.8284 31.4558i 0.546212 1.15869i
\(738\) −8.82843 24.9706i −0.324979 0.919179i
\(739\) 36.2843i 1.33474i −0.744727 0.667369i \(-0.767420\pi\)
0.744727 0.667369i \(-0.232580\pi\)
\(740\) 22.9706i 0.844415i
\(741\) 0 0
\(742\) −11.6569 −0.427937
\(743\) −45.3137 −1.66240 −0.831199 0.555974i \(-0.812345\pi\)
−0.831199 + 0.555974i \(0.812345\pi\)
\(744\) −21.3137 + 30.1421i −0.781398 + 1.10506i
\(745\) 15.3137i 0.561051i
\(746\) 58.2843i 2.13394i
\(747\) 12.0000 + 33.9411i 0.439057 + 1.24184i
\(748\) −6.34315 + 13.4558i −0.231928 + 0.491994i
\(749\) 13.3137i 0.486472i
\(750\) 3.41421 + 2.41421i 0.124669 + 0.0881546i
\(751\) 37.9411 1.38449 0.692246 0.721662i \(-0.256621\pi\)
0.692246 + 0.721662i \(0.256621\pi\)
\(752\) 15.5147i 0.565764i
\(753\) −34.8284 24.6274i −1.26922 0.897473i
\(754\) 0 0
\(755\) 19.3137 0.702898
\(756\) 5.41421 19.1421i 0.196913 0.696193i
\(757\) −27.9411 −1.01554 −0.507769 0.861493i \(-0.669530\pi\)
−0.507769 + 0.861493i \(0.669530\pi\)
\(758\) 72.2843 2.62548
\(759\) 24.1421 13.6569i 0.876304 0.495712i
\(760\) 21.3137 0.773129
\(761\) 47.6569 1.72756 0.863780 0.503869i \(-0.168091\pi\)
0.863780 + 0.503869i \(0.168091\pi\)
\(762\) 8.00000 + 5.65685i 0.289809 + 0.204926i
\(763\) −1.65685 −0.0599822
\(764\) 22.9706i 0.831046i
\(765\) 3.31371 1.17157i 0.119807 0.0423583i
\(766\) 38.1421i 1.37813i
\(767\) 0 0
\(768\) −29.9706 + 42.3848i −1.08147 + 1.52943i
\(769\) 3.51472i 0.126744i −0.997990 0.0633720i \(-0.979815\pi\)
0.997990 0.0633720i \(-0.0201855\pi\)
\(770\) 3.41421 7.24264i 0.123040 0.261007i
\(771\) −13.1716 9.31371i −0.474363 0.335425i
\(772\) 21.1127i 0.759863i
\(773\) 25.3137i 0.910471i −0.890371 0.455235i \(-0.849555\pi\)
0.890371 0.455235i \(-0.150445\pi\)
\(774\) 11.3137 4.00000i 0.406663 0.143777i
\(775\) 4.82843 0.173442
\(776\) −47.7990 −1.71588
\(777\) 8.48528 + 6.00000i 0.304408 + 0.215249i
\(778\) 83.5980i 2.99713i
\(779\) 17.6569i 0.632622i
\(780\) 0 0
\(781\) −34.9706 16.4853i −1.25135 0.589890i
\(782\) 13.6569i 0.488368i
\(783\) −28.2843 8.00000i −1.01080 0.285897i
\(784\) −3.00000 −0.107143
\(785\) 13.1716i 0.470114i
\(786\) 15.3137 21.6569i 0.546222 0.772474i
\(787\) 29.9411i 1.06729i 0.845710 + 0.533643i \(0.179177\pi\)
−0.845710 + 0.533643i \(0.820823\pi\)
\(788\) −35.1127 −1.25084
\(789\) −5.31371 + 7.51472i −0.189173 + 0.267531i
\(790\) 9.65685 0.343575
\(791\) 8.82843 0.313903
\(792\) −43.6985 4.41421i −1.55276 0.156852i
\(793\) 0 0
\(794\) 8.48528 0.301131
\(795\) 4.82843 6.82843i 0.171247 0.242179i
\(796\) 9.51472 0.337240
\(797\) 28.6274i 1.01404i 0.861936 + 0.507018i \(0.169252\pi\)
−0.861936 + 0.507018i \(0.830748\pi\)
\(798\) −11.6569 + 16.4853i −0.412648 + 0.583573i
\(799\) 6.05887i 0.214348i
\(800\) 1.58579 0.0560660
\(801\) 10.3431 3.65685i 0.365457 0.129209i
\(802\) 65.9411i 2.32846i
\(803\) −36.0000 16.9706i −1.27041 0.598878i
\(804\) 40.1421 56.7696i 1.41570 2.00211i
\(805\) 4.82843i 0.170180i
\(806\) 0 0
\(807\) −7.51472 5.31371i −0.264531 0.187051i
\(808\) −58.7696 −2.06751
\(809\) −34.6274 −1.21744 −0.608718 0.793387i \(-0.708316\pi\)
−0.608718 + 0.793387i \(0.708316\pi\)
\(810\) 13.6569 + 16.8995i 0.479853 + 0.593788i
\(811\) 34.4853i 1.21094i 0.795867 + 0.605471i \(0.207015\pi\)
−0.795867 + 0.605471i \(0.792985\pi\)
\(812\) 21.6569i 0.760007i
\(813\) 20.4853 + 14.4853i 0.718450 + 0.508021i
\(814\) 20.4853 43.4558i 0.718009 1.52313i
\(815\) 18.4853i 0.647511i
\(816\) −3.51472 + 4.97056i −0.123040 + 0.174005i
\(817\) −8.00000 −0.279885
\(818\) 32.4853i 1.13582i
\(819\) 0 0
\(820\) 14.0000i 0.488901i
\(821\) −38.6274 −1.34811 −0.674053 0.738683i \(-0.735448\pi\)
−0.674053 + 0.738683i \(0.735448\pi\)
\(822\) 24.4853 + 17.3137i 0.854022 + 0.603885i
\(823\) 28.1421 0.980973 0.490487 0.871449i \(-0.336819\pi\)
0.490487 + 0.871449i \(0.336819\pi\)
\(824\) −58.7696 −2.04733
\(825\) 2.82843 + 5.00000i 0.0984732 + 0.174078i
\(826\) −28.1421 −0.979190
\(827\) −39.2548 −1.36502 −0.682512 0.730874i \(-0.739113\pi\)
−0.682512 + 0.730874i \(0.739113\pi\)
\(828\) 52.2843 18.4853i 1.81700 0.642408i
\(829\) −17.0294 −0.591457 −0.295728 0.955272i \(-0.595562\pi\)
−0.295728 + 0.955272i \(0.595562\pi\)
\(830\) 28.9706i 1.00558i
\(831\) −1.17157 0.828427i −0.0406414 0.0287378i
\(832\) 0 0
\(833\) 1.17157 0.0405926
\(834\) −35.7990 25.3137i −1.23962 0.876542i
\(835\) 13.6569i 0.472615i
\(836\) 55.4558 + 26.1421i 1.91798 + 0.904145i
\(837\) 24.1421 + 6.82843i 0.834474 + 0.236025i
\(838\) 6.48528i 0.224030i
\(839\) 40.3431i 1.39280i 0.717654 + 0.696400i \(0.245216\pi\)
−0.717654 + 0.696400i \(0.754784\pi\)
\(840\) 4.41421 6.24264i 0.152305 0.215392i
\(841\) 3.00000 0.103448
\(842\) 43.4558 1.49759
\(843\) −4.97056 + 7.02944i −0.171195 + 0.242107i
\(844\) 64.9706i 2.23638i
\(845\) 13.0000i 0.447214i
\(846\) −35.3137 + 12.4853i −1.21411 + 0.429253i
\(847\) 8.48528 7.00000i 0.291558 0.240523i
\(848\) 14.4853i 0.497427i
\(849\) −7.02944 4.97056i −0.241250 0.170589i
\(850\) 2.82843 0.0970143
\(851\) 28.9706i 0.993098i
\(852\) −63.1127 44.6274i −2.16221 1.52891i
\(853\) 4.97056i 0.170189i 0.996373 + 0.0850944i \(0.0271192\pi\)
−0.996373 + 0.0850944i \(0.972881\pi\)
\(854\) −26.1421 −0.894565
\(855\) −4.82843 13.6569i −0.165129 0.467055i
\(856\) 58.7696 2.00870
\(857\) 39.1127 1.33606 0.668032 0.744132i \(-0.267137\pi\)
0.668032 + 0.744132i \(0.267137\pi\)
\(858\) 0 0
\(859\) 15.4558 0.527347 0.263673 0.964612i \(-0.415066\pi\)
0.263673 + 0.964612i \(0.415066\pi\)
\(860\) 6.34315 0.216299
\(861\) 5.17157 + 3.65685i 0.176247 + 0.124625i
\(862\) −24.4853 −0.833972
\(863\) 11.8579i 0.403646i −0.979422 0.201823i \(-0.935313\pi\)
0.979422 0.201823i \(-0.0646866\pi\)
\(864\) 7.92893 + 2.24264i 0.269748 + 0.0762962i
\(865\) 18.1421i 0.616851i
\(866\) −70.4264 −2.39319
\(867\) −15.6274 + 22.1005i −0.530735 + 0.750573i
\(868\) 18.4853i 0.627431i
\(869\) 12.0000 + 5.65685i 0.407072 + 0.191896i
\(870\) −19.3137 13.6569i −0.654796 0.463011i
\(871\) 0 0
\(872\) 7.31371i 0.247673i
\(873\) 10.8284 + 30.6274i 0.366487 + 1.03658i
\(874\) −56.2843 −1.90384
\(875\) −1.00000 −0.0338062
\(876\) −64.9706 45.9411i −2.19515 1.55221i
\(877\) 9.79899i 0.330888i −0.986219 0.165444i \(-0.947094\pi\)
0.986219 0.165444i \(-0.0529058\pi\)
\(878\) 75.9411i 2.56289i
\(879\) 13.1716 18.6274i 0.444266 0.628287i
\(880\) −9.00000 4.24264i −0.303390 0.143019i
\(881\) 35.6569i 1.20131i −0.799508 0.600655i \(-0.794907\pi\)
0.799508 0.600655i \(-0.205093\pi\)
\(882\) 2.41421 + 6.82843i 0.0812908 + 0.229925i
\(883\) −45.1127 −1.51816 −0.759082 0.650996i \(-0.774352\pi\)
−0.759082 + 0.650996i \(0.774352\pi\)
\(884\) 0 0
\(885\) 11.6569 16.4853i 0.391841 0.554147i
\(886\) 4.34315i 0.145911i
\(887\) 59.3137 1.99156 0.995780 0.0917756i \(-0.0292543\pi\)
0.995780 + 0.0917756i \(0.0292543\pi\)
\(888\) 26.4853 37.4558i 0.888788 1.25694i
\(889\) −2.34315 −0.0785866
\(890\) 8.82843 0.295930
\(891\) 7.07107 + 29.0000i 0.236890 + 0.971537i
\(892\) 72.6274 2.43175
\(893\) 24.9706 0.835608
\(894\) 36.9706 52.2843i 1.23648 1.74865i
\(895\) 0.343146 0.0114701
\(896\) 20.5563i 0.686739i
\(897\) 0 0
\(898\) 42.6274i 1.42250i
\(899\) −27.3137 −0.910963
\(900\) 3.82843 + 10.8284i 0.127614 + 0.360948i
\(901\) 5.65685i 0.188457i
\(902\) 12.4853 26.4853i 0.415714 0.881863i
\(903\) −1.65685 + 2.34315i −0.0551367 + 0.0779750i
\(904\) 38.9706i 1.29614i
\(905\) 2.00000i 0.0664822i
\(906\) 65.9411 + 46.6274i 2.19075 + 1.54909i
\(907\) −7.17157 −0.238128 −0.119064 0.992887i \(-0.537989\pi\)
−0.119064 + 0.992887i \(0.537989\pi\)
\(908\) −98.2254 −3.25972
\(909\) 13.3137 + 37.6569i 0.441588 + 1.24900i
\(910\) 0 0
\(911\) 32.6274i 1.08099i 0.841346 + 0.540497i \(0.181764\pi\)
−0.841346 + 0.540497i \(0.818236\pi\)
\(912\) 20.4853 + 14.4853i 0.678335 + 0.479656i
\(913\) −16.9706 + 36.0000i −0.561644 + 1.19143i
\(914\) 22.9706i 0.759799i
\(915\) 10.8284 15.3137i 0.357977 0.506256i
\(916\) 50.9706 1.68411
\(917\) 6.34315i 0.209469i
\(918\) 14.1421 + 4.00000i 0.466760 + 0.132020i
\(919\) 42.9117i 1.41553i −0.706450 0.707763i \(-0.749704\pi\)
0.706450 0.707763i \(-0.250296\pi\)
\(920\) 21.3137 0.702692
\(921\) 35.3137 + 24.9706i 1.16363 + 0.822808i
\(922\) 57.1127 1.88091
\(923\) 0 0
\(924\) 19.1421 10.8284i 0.629730 0.356229i
\(925\) −6.00000 −0.197279
\(926\) 27.6569 0.908861
\(927\) 13.3137 + 37.6569i 0.437280 + 1.23681i
\(928\) −8.97056 −0.294473
\(929\) 20.3431i 0.667437i −0.942673 0.333718i \(-0.891697\pi\)
0.942673 0.333718i \(-0.108303\pi\)
\(930\) 16.4853 + 11.6569i 0.540574 + 0.382243i
\(931\) 4.82843i 0.158245i
\(932\) −106.426 −3.48611
\(933\) −29.1716 20.6274i −0.955034 0.675311i
\(934\) 16.4853i 0.539415i
\(935\) 3.51472 + 1.65685i 0.114944 + 0.0541849i
\(936\) 0 0
\(937\) 20.9706i 0.685078i −0.939504 0.342539i \(-0.888713\pi\)
0.939504 0.342539i \(-0.111287\pi\)
\(938\) 25.3137i 0.826522i
\(939\) 18.8284 26.6274i 0.614442 0.868953i
\(940\) −19.7990 −0.645772
\(941\) 10.9706 0.357630 0.178815 0.983883i \(-0.442774\pi\)
0.178815 + 0.983883i \(0.442774\pi\)
\(942\) −31.7990 + 44.9706i −1.03607 + 1.46522i
\(943\) 17.6569i 0.574986i
\(944\) 34.9706i 1.13819i
\(945\) −5.00000 1.41421i −0.162650 0.0460044i
\(946\) 12.0000 + 5.65685i 0.390154 + 0.183920i
\(947\) 52.8284i 1.71669i 0.513070 + 0.858347i \(0.328508\pi\)
−0.513070 + 0.858347i \(0.671492\pi\)
\(948\) 21.6569 + 15.3137i 0.703382 + 0.497366i
\(949\) 0 0
\(950\) 11.6569i 0.378198i
\(951\) −32.7696 23.1716i −1.06263 0.751390i
\(952\) 5.17157i 0.167612i
\(953\) 42.8284 1.38735 0.693674 0.720289i \(-0.255991\pi\)
0.693674 + 0.720289i \(0.255991\pi\)
\(954\) 32.9706 11.6569i 1.06746 0.377405i
\(955\) −6.00000 −0.194155
\(956\) −10.8284 −0.350216
\(957\) −16.0000 28.2843i −0.517207 0.914301i
\(958\) 27.3137 0.882466
\(959\) −7.17157 −0.231582
\(960\) 13.8995 + 9.82843i 0.448604 + 0.317211i
\(961\) −7.68629 −0.247945
\(962\) 0 0
\(963\) −13.3137 37.6569i −0.429028 1.21348i
\(964\) 65.7401i 2.11735i
\(965\) 5.51472 0.177525
\(966\) −11.6569 + 16.4853i −0.375053 + 0.530405i
\(967\) 44.2843i 1.42409i 0.702136 + 0.712043i \(0.252230\pi\)
−0.702136 + 0.712043i \(0.747770\pi\)
\(968\) −30.8995 37.4558i −0.993147 1.20388i
\(969\) −8.00000 5.65685i −0.256997 0.181724i
\(970\) 26.1421i 0.839373i
\(971\) 26.2843i 0.843502i 0.906712 + 0.421751i \(0.138584\pi\)
−0.906712 + 0.421751i \(0.861416\pi\)
\(972\) 3.82843 + 59.5563i 0.122797 + 1.91027i
\(973\) 10.4853 0.336143
\(974\) 22.9706 0.736024
\(975\) 0 0
\(976\) 32.4853i 1.03983i
\(977\) 12.8284i 0.410418i 0.978718 + 0.205209i \(0.0657874\pi\)
−0.978718 + 0.205209i \(0.934213\pi\)
\(978\) −44.6274 + 63.1127i −1.42703 + 2.01812i
\(979\) 10.9706 + 5.17157i 0.350621 + 0.165284i
\(980\) 3.82843i 0.122295i
\(981\) 4.68629 1.65685i 0.149622 0.0528993i
\(982\) −24.4853 −0.781357
\(983\) 2.82843i 0.0902128i 0.998982 + 0.0451064i \(0.0143627\pi\)
−0.998982 + 0.0451064i \(0.985637\pi\)
\(984\) 16.1421 22.8284i 0.514592 0.727744i
\(985\) 9.17157i 0.292231i
\(986\) −16.0000 −0.509544
\(987\) 5.17157 7.31371i 0.164613 0.232798i
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) −2.41421 + 23.8995i −0.0767287 + 0.759576i
\(991\) 34.3431 1.09095 0.545473 0.838128i \(-0.316350\pi\)
0.545473 + 0.838128i \(0.316350\pi\)
\(992\) 7.65685 0.243105
\(993\) −21.6569 + 30.6274i −0.687259 + 0.971932i
\(994\) 28.1421 0.892614
\(995\) 2.48528i 0.0787887i
\(996\) −45.9411 + 64.9706i −1.45570 + 2.05867i
\(997\) 12.2843i 0.389047i 0.980898 + 0.194523i \(0.0623160\pi\)
−0.980898 + 0.194523i \(0.937684\pi\)
\(998\) 86.9117 2.75114
\(999\) −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.d.1121.3 yes 4
3.2 odd 2 1155.2.l.a.1121.2 yes 4
11.10 odd 2 1155.2.l.a.1121.1 4
33.32 even 2 inner 1155.2.l.d.1121.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.l.a.1121.1 4 11.10 odd 2
1155.2.l.a.1121.2 yes 4 3.2 odd 2
1155.2.l.d.1121.3 yes 4 1.1 even 1 trivial
1155.2.l.d.1121.4 yes 4 33.32 even 2 inner