Properties

Label 1470.2.d.f.1469.2
Level $1470$
Weight $2$
Character 1470.1469
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(1469,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.1469");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1469.2
Root \(-1.72286 - 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 1470.1469
Dual form 1470.2.d.f.1469.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.707107 - 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 - 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +(1.41421 + 1.73205i) q^{10} +4.68556i q^{11} +(-0.707107 - 1.58114i) q^{12} +1.04456 q^{13} +(1.73861 - 3.46081i) q^{15} +1.00000 q^{16} -3.16228i q^{17} +(-2.00000 + 2.23607i) q^{18} -1.43023i q^{19} +(1.41421 + 1.73205i) q^{20} +4.68556i q^{22} +4.47723 q^{23} +(-0.707107 - 1.58114i) q^{24} +(-1.00000 + 4.89898i) q^{25} +1.04456 q^{26} +(4.94975 + 1.58114i) q^{27} +6.92163i q^{29} +(1.73861 - 3.46081i) q^{30} +6.62638i q^{31} +1.00000 q^{32} +(7.40852 - 3.31319i) q^{33} -3.16228i q^{34} +(-2.00000 + 2.23607i) q^{36} +2.66291i q^{37} -1.43023i q^{38} +(-0.738613 - 1.65159i) q^{39} +(1.41421 + 1.73205i) q^{40} -1.04456 q^{41} +6.92163i q^{43} +4.68556i q^{44} +(-6.70141 - 0.301824i) q^{45} +4.47723 q^{46} -11.2189i q^{47} +(-0.707107 - 1.58114i) q^{48} +(-1.00000 + 4.89898i) q^{50} +(-5.00000 + 2.23607i) q^{51} +1.04456 q^{52} +5.00000 q^{53} +(4.94975 + 1.58114i) q^{54} +(-8.11562 + 6.62638i) q^{55} +(-2.26139 + 1.01132i) q^{57} +6.92163i q^{58} +10.5744 q^{59} +(1.73861 - 3.46081i) q^{60} +3.46410i q^{61} +6.62638i q^{62} +1.00000 q^{64} +(1.47723 + 1.80922i) q^{65} +(7.40852 - 3.31319i) q^{66} -14.2701i q^{67} -3.16228i q^{68} +(-3.16588 - 7.07912i) q^{69} -6.92163i q^{71} +(-2.00000 + 2.23607i) q^{72} -3.50333 q^{73} +2.66291i q^{74} +(8.45307 - 1.88296i) q^{75} -1.43023i q^{76} +(-0.738613 - 1.65159i) q^{78} +11.4772 q^{79} +(1.41421 + 1.73205i) q^{80} +(-1.00000 - 8.94427i) q^{81} -1.04456 q^{82} -4.06775i q^{83} +(5.47723 - 4.47214i) q^{85} +6.92163i q^{86} +(10.9441 - 4.89433i) q^{87} +4.68556i q^{88} +4.91754 q^{89} +(-6.70141 - 0.301824i) q^{90} +4.47723 q^{92} +(10.4772 - 4.68556i) q^{93} -11.2189i q^{94} +(2.47723 - 2.02265i) q^{95} +(-0.707107 - 1.58114i) q^{96} -11.9886 q^{97} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9} - 8 q^{15} + 8 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} - 8 q^{30} + 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} - 8 q^{50} - 40 q^{51} + 40 q^{53} - 40 q^{57}+ \cdots - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.707107 1.58114i −0.408248 0.912871i
\(4\) 1.00000 0.500000
\(5\) 1.41421 + 1.73205i 0.632456 + 0.774597i
\(6\) −0.707107 1.58114i −0.288675 0.645497i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 + 2.23607i −0.666667 + 0.745356i
\(10\) 1.41421 + 1.73205i 0.447214 + 0.547723i
\(11\) 4.68556i 1.41275i 0.707838 + 0.706374i \(0.249670\pi\)
−0.707838 + 0.706374i \(0.750330\pi\)
\(12\) −0.707107 1.58114i −0.204124 0.456435i
\(13\) 1.04456 0.289708 0.144854 0.989453i \(-0.453729\pi\)
0.144854 + 0.989453i \(0.453729\pi\)
\(14\) 0 0
\(15\) 1.73861 3.46081i 0.448908 0.893578i
\(16\) 1.00000 0.250000
\(17\) 3.16228i 0.766965i −0.923548 0.383482i \(-0.874725\pi\)
0.923548 0.383482i \(-0.125275\pi\)
\(18\) −2.00000 + 2.23607i −0.471405 + 0.527046i
\(19\) 1.43023i 0.328117i −0.986451 0.164058i \(-0.947541\pi\)
0.986451 0.164058i \(-0.0524585\pi\)
\(20\) 1.41421 + 1.73205i 0.316228 + 0.387298i
\(21\) 0 0
\(22\) 4.68556i 0.998964i
\(23\) 4.47723 0.933566 0.466783 0.884372i \(-0.345413\pi\)
0.466783 + 0.884372i \(0.345413\pi\)
\(24\) −0.707107 1.58114i −0.144338 0.322749i
\(25\) −1.00000 + 4.89898i −0.200000 + 0.979796i
\(26\) 1.04456 0.204854
\(27\) 4.94975 + 1.58114i 0.952579 + 0.304290i
\(28\) 0 0
\(29\) 6.92163i 1.28531i 0.766154 + 0.642657i \(0.222168\pi\)
−0.766154 + 0.642657i \(0.777832\pi\)
\(30\) 1.73861 3.46081i 0.317426 0.631855i
\(31\) 6.62638i 1.19013i 0.803677 + 0.595066i \(0.202874\pi\)
−0.803677 + 0.595066i \(0.797126\pi\)
\(32\) 1.00000 0.176777
\(33\) 7.40852 3.31319i 1.28966 0.576752i
\(34\) 3.16228i 0.542326i
\(35\) 0 0
\(36\) −2.00000 + 2.23607i −0.333333 + 0.372678i
\(37\) 2.66291i 0.437780i 0.975750 + 0.218890i \(0.0702436\pi\)
−0.975750 + 0.218890i \(0.929756\pi\)
\(38\) 1.43023i 0.232013i
\(39\) −0.738613 1.65159i −0.118273 0.264466i
\(40\) 1.41421 + 1.73205i 0.223607 + 0.273861i
\(41\) −1.04456 −0.163132 −0.0815661 0.996668i \(-0.525992\pi\)
−0.0815661 + 0.996668i \(0.525992\pi\)
\(42\) 0 0
\(43\) 6.92163i 1.05554i 0.849388 + 0.527769i \(0.176971\pi\)
−0.849388 + 0.527769i \(0.823029\pi\)
\(44\) 4.68556i 0.706374i
\(45\) −6.70141 0.301824i −0.998987 0.0449933i
\(46\) 4.47723 0.660131
\(47\) 11.2189i 1.63644i −0.574904 0.818221i \(-0.694960\pi\)
0.574904 0.818221i \(-0.305040\pi\)
\(48\) −0.707107 1.58114i −0.102062 0.228218i
\(49\) 0 0
\(50\) −1.00000 + 4.89898i −0.141421 + 0.692820i
\(51\) −5.00000 + 2.23607i −0.700140 + 0.313112i
\(52\) 1.04456 0.144854
\(53\) 5.00000 0.686803 0.343401 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) 4.94975 + 1.58114i 0.673575 + 0.215166i
\(55\) −8.11562 + 6.62638i −1.09431 + 0.893501i
\(56\) 0 0
\(57\) −2.26139 + 1.01132i −0.299528 + 0.133953i
\(58\) 6.92163i 0.908854i
\(59\) 10.5744 1.37667 0.688334 0.725394i \(-0.258342\pi\)
0.688334 + 0.725394i \(0.258342\pi\)
\(60\) 1.73861 3.46081i 0.224454 0.446789i
\(61\) 3.46410i 0.443533i 0.975100 + 0.221766i \(0.0711822\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(62\) 6.62638i 0.841551i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.47723 + 1.80922i 0.183227 + 0.224407i
\(66\) 7.40852 3.31319i 0.911925 0.407825i
\(67\) 14.2701i 1.74337i −0.490067 0.871685i \(-0.663028\pi\)
0.490067 0.871685i \(-0.336972\pi\)
\(68\) 3.16228i 0.383482i
\(69\) −3.16588 7.07912i −0.381127 0.852225i
\(70\) 0 0
\(71\) 6.92163i 0.821446i −0.911760 0.410723i \(-0.865276\pi\)
0.911760 0.410723i \(-0.134724\pi\)
\(72\) −2.00000 + 2.23607i −0.235702 + 0.263523i
\(73\) −3.50333 −0.410033 −0.205017 0.978758i \(-0.565725\pi\)
−0.205017 + 0.978758i \(0.565725\pi\)
\(74\) 2.66291i 0.309557i
\(75\) 8.45307 1.88296i 0.976077 0.217426i
\(76\) 1.43023i 0.164058i
\(77\) 0 0
\(78\) −0.738613 1.65159i −0.0836314 0.187006i
\(79\) 11.4772 1.29129 0.645644 0.763638i \(-0.276589\pi\)
0.645644 + 0.763638i \(0.276589\pi\)
\(80\) 1.41421 + 1.73205i 0.158114 + 0.193649i
\(81\) −1.00000 8.94427i −0.111111 0.993808i
\(82\) −1.04456 −0.115352
\(83\) 4.06775i 0.446494i −0.974762 0.223247i \(-0.928334\pi\)
0.974762 0.223247i \(-0.0716656\pi\)
\(84\) 0 0
\(85\) 5.47723 4.47214i 0.594089 0.485071i
\(86\) 6.92163i 0.746378i
\(87\) 10.9441 4.89433i 1.17333 0.524727i
\(88\) 4.68556i 0.499482i
\(89\) 4.91754 0.521258 0.260629 0.965439i \(-0.416070\pi\)
0.260629 + 0.965439i \(0.416070\pi\)
\(90\) −6.70141 0.301824i −0.706391 0.0318150i
\(91\) 0 0
\(92\) 4.47723 0.466783
\(93\) 10.4772 4.68556i 1.08644 0.485870i
\(94\) 11.2189i 1.15714i
\(95\) 2.47723 2.02265i 0.254158 0.207519i
\(96\) −0.707107 1.58114i −0.0721688 0.161374i
\(97\) −11.9886 −1.21726 −0.608629 0.793455i \(-0.708280\pi\)
−0.608629 + 0.793455i \(0.708280\pi\)
\(98\) 0 0
\(99\) −10.4772 9.37112i −1.05300 0.941833i
\(100\) −1.00000 + 4.89898i −0.100000 + 0.489898i
\(101\) −11.3137 −1.12576 −0.562878 0.826540i \(-0.690306\pi\)
−0.562878 + 0.826540i \(0.690306\pi\)
\(102\) −5.00000 + 2.23607i −0.495074 + 0.221404i
\(103\) 4.91754 0.484540 0.242270 0.970209i \(-0.422108\pi\)
0.242270 + 0.970209i \(0.422108\pi\)
\(104\) 1.04456 0.102427
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) −5.47723 −0.529503 −0.264752 0.964317i \(-0.585290\pi\)
−0.264752 + 0.964317i \(0.585290\pi\)
\(108\) 4.94975 + 1.58114i 0.476290 + 0.152145i
\(109\) −20.4317 −1.95700 −0.978500 0.206248i \(-0.933875\pi\)
−0.978500 + 0.206248i \(0.933875\pi\)
\(110\) −8.11562 + 6.62638i −0.773794 + 0.631800i
\(111\) 4.21043 1.88296i 0.399637 0.178723i
\(112\) 0 0
\(113\) 17.4772 1.64412 0.822060 0.569402i \(-0.192825\pi\)
0.822060 + 0.569402i \(0.192825\pi\)
\(114\) −2.26139 + 1.01132i −0.211798 + 0.0947191i
\(115\) 6.33175 + 7.75478i 0.590439 + 0.723137i
\(116\) 6.92163i 0.642657i
\(117\) −2.08911 + 2.33570i −0.193139 + 0.215935i
\(118\) 10.5744 0.973452
\(119\) 0 0
\(120\) 1.73861 3.46081i 0.158713 0.315928i
\(121\) −10.9545 −0.995859
\(122\) 3.46410i 0.313625i
\(123\) 0.738613 + 1.65159i 0.0665985 + 0.148919i
\(124\) 6.62638i 0.595066i
\(125\) −9.89949 + 5.19615i −0.885438 + 0.464758i
\(126\) 0 0
\(127\) 8.73085i 0.774738i −0.921925 0.387369i \(-0.873384\pi\)
0.921925 0.387369i \(-0.126616\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.9441 4.89433i 0.963570 0.430922i
\(130\) 1.47723 + 1.80922i 0.129561 + 0.158679i
\(131\) 13.7725 1.20331 0.601654 0.798757i \(-0.294509\pi\)
0.601654 + 0.798757i \(0.294509\pi\)
\(132\) 7.40852 3.31319i 0.644829 0.288376i
\(133\) 0 0
\(134\) 14.2701i 1.23275i
\(135\) 4.26139 + 10.8093i 0.366762 + 0.930315i
\(136\) 3.16228i 0.271163i
\(137\) −3.47723 −0.297079 −0.148540 0.988906i \(-0.547457\pi\)
−0.148540 + 0.988906i \(0.547457\pi\)
\(138\) −3.16588 7.07912i −0.269497 0.602614i
\(139\) 20.1810i 1.71173i 0.517202 + 0.855863i \(0.326974\pi\)
−0.517202 + 0.855863i \(0.673026\pi\)
\(140\) 0 0
\(141\) −17.7386 + 7.93295i −1.49386 + 0.668075i
\(142\) 6.92163i 0.580850i
\(143\) 4.89433i 0.409284i
\(144\) −2.00000 + 2.23607i −0.166667 + 0.186339i
\(145\) −11.9886 + 9.78866i −0.995600 + 0.812904i
\(146\) −3.50333 −0.289937
\(147\) 0 0
\(148\) 2.66291i 0.218890i
\(149\) 2.44949i 0.200670i −0.994954 0.100335i \(-0.968009\pi\)
0.994954 0.100335i \(-0.0319915\pi\)
\(150\) 8.45307 1.88296i 0.690191 0.153743i
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 1.43023i 0.116007i
\(153\) 7.07107 + 6.32456i 0.571662 + 0.511310i
\(154\) 0 0
\(155\) −11.4772 + 9.37112i −0.921873 + 0.752706i
\(156\) −0.738613 1.65159i −0.0591364 0.132233i
\(157\) −14.4474 −1.15303 −0.576513 0.817088i \(-0.695587\pi\)
−0.576513 + 0.817088i \(0.695587\pi\)
\(158\) 11.4772 0.913079
\(159\) −3.53553 7.90569i −0.280386 0.626962i
\(160\) 1.41421 + 1.73205i 0.111803 + 0.136931i
\(161\) 0 0
\(162\) −1.00000 8.94427i −0.0785674 0.702728i
\(163\) 14.6969i 1.15115i 0.817748 + 0.575577i \(0.195222\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(164\) −1.04456 −0.0815661
\(165\) 16.2158 + 8.14637i 1.26240 + 0.634194i
\(166\) 4.06775i 0.315719i
\(167\) 4.29068i 0.332023i −0.986124 0.166011i \(-0.946911\pi\)
0.986124 0.166011i \(-0.0530889\pi\)
\(168\) 0 0
\(169\) −11.9089 −0.916069
\(170\) 5.47723 4.47214i 0.420084 0.342997i
\(171\) 3.19808 + 2.86045i 0.244564 + 0.218744i
\(172\) 6.92163i 0.527769i
\(173\) 1.12840i 0.0857909i 0.999080 + 0.0428954i \(0.0136582\pi\)
−0.999080 + 0.0428954i \(0.986342\pi\)
\(174\) 10.9441 4.89433i 0.829666 0.371038i
\(175\) 0 0
\(176\) 4.68556i 0.353187i
\(177\) −7.47723 16.7196i −0.562023 1.25672i
\(178\) 4.91754 0.368585
\(179\) 19.3825i 1.44872i −0.689424 0.724358i \(-0.742136\pi\)
0.689424 0.724358i \(-0.257864\pi\)
\(180\) −6.70141 0.301824i −0.499494 0.0224966i
\(181\) 3.16228i 0.235050i 0.993070 + 0.117525i \(0.0374961\pi\)
−0.993070 + 0.117525i \(0.962504\pi\)
\(182\) 0 0
\(183\) 5.47723 2.44949i 0.404888 0.181071i
\(184\) 4.47723 0.330065
\(185\) −4.61230 + 3.76593i −0.339103 + 0.276876i
\(186\) 10.4772 4.68556i 0.768227 0.343562i
\(187\) 14.8170 1.08353
\(188\) 11.2189i 0.818221i
\(189\) 0 0
\(190\) 2.47723 2.02265i 0.179717 0.146738i
\(191\) 16.2927i 1.17890i −0.807804 0.589451i \(-0.799344\pi\)
0.807804 0.589451i \(-0.200656\pi\)
\(192\) −0.707107 1.58114i −0.0510310 0.114109i
\(193\) 7.34847i 0.528954i −0.964392 0.264477i \(-0.914801\pi\)
0.964392 0.264477i \(-0.0851994\pi\)
\(194\) −11.9886 −0.860732
\(195\) 1.81608 3.61501i 0.130052 0.258877i
\(196\) 0 0
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) −10.4772 9.37112i −0.744584 0.665976i
\(199\) 15.5096i 1.09944i −0.835348 0.549722i \(-0.814734\pi\)
0.835348 0.549722i \(-0.185266\pi\)
\(200\) −1.00000 + 4.89898i −0.0707107 + 0.346410i
\(201\) −22.5630 + 10.0905i −1.59147 + 0.711728i
\(202\) −11.3137 −0.796030
\(203\) 0 0
\(204\) −5.00000 + 2.23607i −0.350070 + 0.156556i
\(205\) −1.47723 1.80922i −0.103174 0.126362i
\(206\) 4.91754 0.342621
\(207\) −8.95445 + 10.0114i −0.622377 + 0.695839i
\(208\) 1.04456 0.0724269
\(209\) 6.70141 0.463546
\(210\) 0 0
\(211\) 24.4772 1.68508 0.842541 0.538632i \(-0.181059\pi\)
0.842541 + 0.538632i \(0.181059\pi\)
\(212\) 5.00000 0.343401
\(213\) −10.9441 + 4.89433i −0.749874 + 0.335354i
\(214\) −5.47723 −0.374415
\(215\) −11.9886 + 9.78866i −0.817616 + 0.667581i
\(216\) 4.94975 + 1.58114i 0.336788 + 0.107583i
\(217\) 0 0
\(218\) −20.4317 −1.38381
\(219\) 2.47723 + 5.53924i 0.167395 + 0.374307i
\(220\) −8.11562 + 6.62638i −0.547155 + 0.446750i
\(221\) 3.30318i 0.222196i
\(222\) 4.21043 1.88296i 0.282586 0.126376i
\(223\) −21.8881 −1.46574 −0.732868 0.680371i \(-0.761819\pi\)
−0.732868 + 0.680371i \(0.761819\pi\)
\(224\) 0 0
\(225\) −8.95445 12.0340i −0.596963 0.802268i
\(226\) 17.4772 1.16257
\(227\) 10.3923i 0.689761i −0.938647 0.344881i \(-0.887919\pi\)
0.938647 0.344881i \(-0.112081\pi\)
\(228\) −2.26139 + 1.01132i −0.149764 + 0.0669765i
\(229\) 13.5546i 0.895712i −0.894106 0.447856i \(-0.852188\pi\)
0.894106 0.447856i \(-0.147812\pi\)
\(230\) 6.33175 + 7.75478i 0.417503 + 0.511335i
\(231\) 0 0
\(232\) 6.92163i 0.454427i
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) −2.08911 + 2.33570i −0.136570 + 0.152689i
\(235\) 19.4317 15.8659i 1.26758 1.03498i
\(236\) 10.5744 0.688334
\(237\) −8.11562 18.1471i −0.527166 1.17878i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 1.73861 3.46081i 0.112227 0.223395i
\(241\) 21.3094i 1.37266i 0.727292 + 0.686328i \(0.240779\pi\)
−0.727292 + 0.686328i \(0.759221\pi\)
\(242\) −10.9545 −0.704179
\(243\) −13.4350 + 7.90569i −0.861858 + 0.507151i
\(244\) 3.46410i 0.221766i
\(245\) 0 0
\(246\) 0.738613 + 1.65159i 0.0470922 + 0.105301i
\(247\) 1.49395i 0.0950579i
\(248\) 6.62638i 0.420776i
\(249\) −6.43168 + 2.87633i −0.407591 + 0.182280i
\(250\) −9.89949 + 5.19615i −0.626099 + 0.328634i
\(251\) −8.85494 −0.558919 −0.279459 0.960158i \(-0.590155\pi\)
−0.279459 + 0.960158i \(0.590155\pi\)
\(252\) 0 0
\(253\) 20.9783i 1.31889i
\(254\) 8.73085i 0.547822i
\(255\) −10.9441 5.49798i −0.685343 0.344297i
\(256\) 1.00000 0.0625000
\(257\) 10.9960i 0.685909i −0.939352 0.342954i \(-0.888572\pi\)
0.939352 0.342954i \(-0.111428\pi\)
\(258\) 10.9441 4.89433i 0.681347 0.304708i
\(259\) 0 0
\(260\) 1.47723 + 1.80922i 0.0916136 + 0.112203i
\(261\) −15.4772 13.8433i −0.958016 0.856876i
\(262\) 13.7725 0.850867
\(263\) −2.00000 −0.123325 −0.0616626 0.998097i \(-0.519640\pi\)
−0.0616626 + 0.998097i \(0.519640\pi\)
\(264\) 7.40852 3.31319i 0.455963 0.203913i
\(265\) 7.07107 + 8.66025i 0.434372 + 0.531995i
\(266\) 0 0
\(267\) −3.47723 7.77531i −0.212803 0.475841i
\(268\) 14.2701i 0.871685i
\(269\) −17.5810 −1.07194 −0.535968 0.844239i \(-0.680053\pi\)
−0.535968 + 0.844239i \(0.680053\pi\)
\(270\) 4.26139 + 10.8093i 0.259340 + 0.657832i
\(271\) 6.32456i 0.384189i −0.981376 0.192095i \(-0.938472\pi\)
0.981376 0.192095i \(-0.0615281\pi\)
\(272\) 3.16228i 0.191741i
\(273\) 0 0
\(274\) −3.47723 −0.210067
\(275\) −22.9545 4.68556i −1.38421 0.282550i
\(276\) −3.16588 7.07912i −0.190563 0.426113i
\(277\) 9.79796i 0.588702i 0.955697 + 0.294351i \(0.0951035\pi\)
−0.955697 + 0.294351i \(0.904896\pi\)
\(278\) 20.1810i 1.21037i
\(279\) −14.8170 13.2528i −0.887073 0.793422i
\(280\) 0 0
\(281\) 1.80922i 0.107929i −0.998543 0.0539646i \(-0.982814\pi\)
0.998543 0.0539646i \(-0.0171858\pi\)
\(282\) −17.7386 + 7.93295i −1.05632 + 0.472400i
\(283\) −9.22460 −0.548345 −0.274173 0.961680i \(-0.588404\pi\)
−0.274173 + 0.961680i \(0.588404\pi\)
\(284\) 6.92163i 0.410723i
\(285\) −4.94975 2.48661i −0.293198 0.147294i
\(286\) 4.89433i 0.289408i
\(287\) 0 0
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) 7.00000 0.411765
\(290\) −11.9886 + 9.78866i −0.703995 + 0.574810i
\(291\) 8.47723 + 18.9557i 0.496944 + 1.11120i
\(292\) −3.50333 −0.205017
\(293\) 8.05661i 0.470672i 0.971914 + 0.235336i \(0.0756190\pi\)
−0.971914 + 0.235336i \(0.924381\pi\)
\(294\) 0 0
\(295\) 14.9545 + 18.3154i 0.870682 + 1.06636i
\(296\) 2.66291i 0.154779i
\(297\) −7.40852 + 23.1923i −0.429886 + 1.34576i
\(298\) 2.44949i 0.141895i
\(299\) 4.67671 0.270461
\(300\) 8.45307 1.88296i 0.488038 0.108713i
\(301\) 0 0
\(302\) −2.00000 −0.115087
\(303\) 8.00000 + 17.8885i 0.459588 + 1.02767i
\(304\) 1.43023i 0.0820291i
\(305\) −6.00000 + 4.89898i −0.343559 + 0.280515i
\(306\) 7.07107 + 6.32456i 0.404226 + 0.361551i
\(307\) 11.9886 0.684226 0.342113 0.939659i \(-0.388857\pi\)
0.342113 + 0.939659i \(0.388857\pi\)
\(308\) 0 0
\(309\) −3.47723 7.77531i −0.197812 0.442322i
\(310\) −11.4772 + 9.37112i −0.651863 + 0.532244i
\(311\) −17.5810 −0.996930 −0.498465 0.866910i \(-0.666103\pi\)
−0.498465 + 0.866910i \(0.666103\pi\)
\(312\) −0.738613 1.65159i −0.0418157 0.0935028i
\(313\) −23.2379 −1.31348 −0.656742 0.754115i \(-0.728066\pi\)
−0.656742 + 0.754115i \(0.728066\pi\)
\(314\) −14.4474 −0.815313
\(315\) 0 0
\(316\) 11.4772 0.645644
\(317\) −9.90890 −0.556539 −0.278270 0.960503i \(-0.589761\pi\)
−0.278270 + 0.960503i \(0.589761\pi\)
\(318\) −3.53553 7.90569i −0.198263 0.443329i
\(319\) −32.4317 −1.81583
\(320\) 1.41421 + 1.73205i 0.0790569 + 0.0968246i
\(321\) 3.87298 + 8.66025i 0.216169 + 0.483368i
\(322\) 0 0
\(323\) −4.52277 −0.251654
\(324\) −1.00000 8.94427i −0.0555556 0.496904i
\(325\) −1.04456 + 5.11726i −0.0579416 + 0.283854i
\(326\) 14.6969i 0.813988i
\(327\) 14.4474 + 32.3053i 0.798942 + 1.78649i
\(328\) −1.04456 −0.0576760
\(329\) 0 0
\(330\) 16.2158 + 8.14637i 0.892653 + 0.448443i
\(331\) 21.4317 1.17799 0.588996 0.808136i \(-0.299523\pi\)
0.588996 + 0.808136i \(0.299523\pi\)
\(332\) 4.06775i 0.223247i
\(333\) −5.95445 5.32582i −0.326302 0.291853i
\(334\) 4.29068i 0.234776i
\(335\) 24.7165 20.1810i 1.35041 1.10260i
\(336\) 0 0
\(337\) 17.1464i 0.934025i 0.884251 + 0.467013i \(0.154670\pi\)
−0.884251 + 0.467013i \(0.845330\pi\)
\(338\) −11.9089 −0.647759
\(339\) −12.3583 27.6339i −0.671209 1.50087i
\(340\) 5.47723 4.47214i 0.297044 0.242536i
\(341\) −31.0483 −1.68136
\(342\) 3.19808 + 2.86045i 0.172933 + 0.154676i
\(343\) 0 0
\(344\) 6.92163i 0.373189i
\(345\) 7.78416 15.4948i 0.419085 0.834214i
\(346\) 1.12840i 0.0606633i
\(347\) −17.4772 −0.938227 −0.469113 0.883138i \(-0.655426\pi\)
−0.469113 + 0.883138i \(0.655426\pi\)
\(348\) 10.9441 4.89433i 0.586663 0.262364i
\(349\) 11.7436i 0.628623i −0.949320 0.314311i \(-0.898226\pi\)
0.949320 0.314311i \(-0.101774\pi\)
\(350\) 0 0
\(351\) 5.17029 + 1.65159i 0.275970 + 0.0881553i
\(352\) 4.68556i 0.249741i
\(353\) 0.603648i 0.0321289i −0.999871 0.0160645i \(-0.994886\pi\)
0.999871 0.0160645i \(-0.00511370\pi\)
\(354\) −7.47723 16.7196i −0.397410 0.888636i
\(355\) 11.9886 9.78866i 0.636289 0.519528i
\(356\) 4.91754 0.260629
\(357\) 0 0
\(358\) 19.3825i 1.02440i
\(359\) 11.3938i 0.601340i 0.953728 + 0.300670i \(0.0972102\pi\)
−0.953728 + 0.300670i \(0.902790\pi\)
\(360\) −6.70141 0.301824i −0.353195 0.0159075i
\(361\) 16.9545 0.892340
\(362\) 3.16228i 0.166206i
\(363\) 7.74597 + 17.3205i 0.406558 + 0.909091i
\(364\) 0 0
\(365\) −4.95445 6.06794i −0.259328 0.317610i
\(366\) 5.47723 2.44949i 0.286299 0.128037i
\(367\) −0.369657 −0.0192960 −0.00964798 0.999953i \(-0.503071\pi\)
−0.00964798 + 0.999953i \(0.503071\pi\)
\(368\) 4.47723 0.233392
\(369\) 2.08911 2.33570i 0.108755 0.121592i
\(370\) −4.61230 + 3.76593i −0.239782 + 0.195781i
\(371\) 0 0
\(372\) 10.4772 4.68556i 0.543219 0.242935i
\(373\) 23.2144i 1.20199i −0.799251 0.600997i \(-0.794770\pi\)
0.799251 0.600997i \(-0.205230\pi\)
\(374\) 14.8170 0.766171
\(375\) 15.2158 + 11.9782i 0.785743 + 0.618554i
\(376\) 11.2189i 0.578570i
\(377\) 7.23003i 0.372365i
\(378\) 0 0
\(379\) −20.4772 −1.05184 −0.525922 0.850533i \(-0.676280\pi\)
−0.525922 + 0.850533i \(0.676280\pi\)
\(380\) 2.47723 2.02265i 0.127079 0.103760i
\(381\) −13.8047 + 6.17364i −0.707235 + 0.316285i
\(382\) 16.2927i 0.833609i
\(383\) 18.1471i 0.927273i 0.886026 + 0.463636i \(0.153456\pi\)
−0.886026 + 0.463636i \(0.846544\pi\)
\(384\) −0.707107 1.58114i −0.0360844 0.0806872i
\(385\) 0 0
\(386\) 7.34847i 0.374027i
\(387\) −15.4772 13.8433i −0.786752 0.703692i
\(388\) −11.9886 −0.608629
\(389\) 7.34847i 0.372582i −0.982495 0.186291i \(-0.940353\pi\)
0.982495 0.186291i \(-0.0596468\pi\)
\(390\) 1.81608 3.61501i 0.0919607 0.183053i
\(391\) 14.1582i 0.716012i
\(392\) 0 0
\(393\) −9.73861 21.7762i −0.491248 1.09846i
\(394\) 9.00000 0.453413
\(395\) 16.2312 + 19.8791i 0.816683 + 1.00023i
\(396\) −10.4772 9.37112i −0.526500 0.470916i
\(397\) −14.8815 −0.746879 −0.373439 0.927655i \(-0.621822\pi\)
−0.373439 + 0.927655i \(0.621822\pi\)
\(398\) 15.5096i 0.777424i
\(399\) 0 0
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) 0.955537i 0.0477173i −0.999715 0.0238586i \(-0.992405\pi\)
0.999715 0.0238586i \(-0.00759516\pi\)
\(402\) −22.5630 + 10.0905i −1.12534 + 0.503267i
\(403\) 6.92163i 0.344791i
\(404\) −11.3137 −0.562878
\(405\) 14.0777 14.3812i 0.699528 0.714606i
\(406\) 0 0
\(407\) −12.4772 −0.618473
\(408\) −5.00000 + 2.23607i −0.247537 + 0.110702i
\(409\) 15.5096i 0.766899i −0.923562 0.383449i \(-0.874736\pi\)
0.923562 0.383449i \(-0.125264\pi\)
\(410\) −1.47723 1.80922i −0.0729550 0.0893512i
\(411\) 2.45877 + 5.49798i 0.121282 + 0.271195i
\(412\) 4.91754 0.242270
\(413\) 0 0
\(414\) −8.95445 + 10.0114i −0.440087 + 0.492033i
\(415\) 7.04555 5.75267i 0.345852 0.282387i
\(416\) 1.04456 0.0512136
\(417\) 31.9089 14.2701i 1.56259 0.698810i
\(418\) 6.70141 0.327777
\(419\) 8.85494 0.432592 0.216296 0.976328i \(-0.430602\pi\)
0.216296 + 0.976328i \(0.430602\pi\)
\(420\) 0 0
\(421\) 18.9545 0.923783 0.461892 0.886936i \(-0.347171\pi\)
0.461892 + 0.886936i \(0.347171\pi\)
\(422\) 24.4772 1.19153
\(423\) 25.0862 + 22.4378i 1.21973 + 1.09096i
\(424\) 5.00000 0.242821
\(425\) 15.4919 + 3.16228i 0.751469 + 0.153393i
\(426\) −10.9441 + 4.89433i −0.530241 + 0.237131i
\(427\) 0 0
\(428\) −5.47723 −0.264752
\(429\) 7.73861 3.46081i 0.373624 0.167090i
\(430\) −11.9886 + 9.78866i −0.578142 + 0.472051i
\(431\) 7.66374i 0.369149i −0.982818 0.184575i \(-0.940909\pi\)
0.982818 0.184575i \(-0.0590908\pi\)
\(432\) 4.94975 + 1.58114i 0.238145 + 0.0760726i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 23.9545 + 12.0340i 1.14853 + 0.576987i
\(436\) −20.4317 −0.978500
\(437\) 6.40345i 0.306318i
\(438\) 2.47723 + 5.53924i 0.118366 + 0.264675i
\(439\) 8.88319i 0.423971i −0.977273 0.211986i \(-0.932007\pi\)
0.977273 0.211986i \(-0.0679930\pi\)
\(440\) −8.11562 + 6.62638i −0.386897 + 0.315900i
\(441\) 0 0
\(442\) 3.30318i 0.157116i
\(443\) −15.0455 −0.714836 −0.357418 0.933945i \(-0.616343\pi\)
−0.357418 + 0.933945i \(0.616343\pi\)
\(444\) 4.21043 1.88296i 0.199818 0.0893615i
\(445\) 6.95445 + 8.51743i 0.329673 + 0.403765i
\(446\) −21.8881 −1.03643
\(447\) −3.87298 + 1.73205i −0.183186 + 0.0819232i
\(448\) 0 0
\(449\) 25.8773i 1.22122i −0.791930 0.610612i \(-0.790923\pi\)
0.791930 0.610612i \(-0.209077\pi\)
\(450\) −8.95445 12.0340i −0.422117 0.567289i
\(451\) 4.89433i 0.230465i
\(452\) 17.4772 0.822060
\(453\) 1.41421 + 3.16228i 0.0664455 + 0.148577i
\(454\) 10.3923i 0.487735i
\(455\) 0 0
\(456\) −2.26139 + 1.01132i −0.105899 + 0.0473595i
\(457\) 11.0785i 0.518230i 0.965846 + 0.259115i \(0.0834308\pi\)
−0.965846 + 0.259115i \(0.916569\pi\)
\(458\) 13.5546i 0.633364i
\(459\) 5.00000 15.6525i 0.233380 0.730595i
\(460\) 6.33175 + 7.75478i 0.295220 + 0.361569i
\(461\) 31.7876 1.48050 0.740248 0.672334i \(-0.234708\pi\)
0.740248 + 0.672334i \(0.234708\pi\)
\(462\) 0 0
\(463\) 22.5741i 1.04911i −0.851377 0.524554i \(-0.824232\pi\)
0.851377 0.524554i \(-0.175768\pi\)
\(464\) 6.92163i 0.321328i
\(465\) 22.9327 + 11.5207i 1.06348 + 0.534260i
\(466\) −4.00000 −0.185296
\(467\) 28.0146i 1.29636i −0.761486 0.648181i \(-0.775530\pi\)
0.761486 0.648181i \(-0.224470\pi\)
\(468\) −2.08911 + 2.33570i −0.0965693 + 0.107968i
\(469\) 0 0
\(470\) 19.4317 15.8659i 0.896316 0.731839i
\(471\) 10.2158 + 22.8433i 0.470721 + 1.05256i
\(472\) 10.5744 0.486726
\(473\) −32.4317 −1.49121
\(474\) −8.11562 18.1471i −0.372763 0.833523i
\(475\) 7.00665 + 1.43023i 0.321487 + 0.0656233i
\(476\) 0 0
\(477\) −10.0000 + 11.1803i −0.457869 + 0.511913i
\(478\) 0 0
\(479\) 42.3620 1.93557 0.967784 0.251780i \(-0.0810161\pi\)
0.967784 + 0.251780i \(0.0810161\pi\)
\(480\) 1.73861 3.46081i 0.0793565 0.157964i
\(481\) 2.78156i 0.126828i
\(482\) 21.3094i 0.970615i
\(483\) 0 0
\(484\) −10.9545 −0.497930
\(485\) −16.9545 20.7649i −0.769862 0.942884i
\(486\) −13.4350 + 7.90569i −0.609425 + 0.358610i
\(487\) 17.0349i 0.771923i 0.922515 + 0.385962i \(0.126130\pi\)
−0.922515 + 0.385962i \(0.873870\pi\)
\(488\) 3.46410i 0.156813i
\(489\) 23.2379 10.3923i 1.05085 0.469956i
\(490\) 0 0
\(491\) 13.8433i 0.624737i 0.949961 + 0.312369i \(0.101122\pi\)
−0.949961 + 0.312369i \(0.898878\pi\)
\(492\) 0.738613 + 1.65159i 0.0332992 + 0.0744594i
\(493\) 21.8881 0.985791
\(494\) 1.49395i 0.0672161i
\(495\) 1.41421 31.3998i 0.0635642 1.41132i
\(496\) 6.62638i 0.297533i
\(497\) 0 0
\(498\) −6.43168 + 2.87633i −0.288210 + 0.128892i
\(499\) 1.90890 0.0854542 0.0427271 0.999087i \(-0.486395\pi\)
0.0427271 + 0.999087i \(0.486395\pi\)
\(500\) −9.89949 + 5.19615i −0.442719 + 0.232379i
\(501\) −6.78416 + 3.03397i −0.303094 + 0.135548i
\(502\) −8.85494 −0.395215
\(503\) 15.5096i 0.691537i 0.938320 + 0.345769i \(0.112382\pi\)
−0.938320 + 0.345769i \(0.887618\pi\)
\(504\) 0 0
\(505\) −16.0000 19.5959i −0.711991 0.872007i
\(506\) 20.9783i 0.932599i
\(507\) 8.42087 + 18.8296i 0.373984 + 0.836253i
\(508\) 8.73085i 0.387369i
\(509\) 24.7165 1.09554 0.547770 0.836629i \(-0.315477\pi\)
0.547770 + 0.836629i \(0.315477\pi\)
\(510\) −10.9441 5.49798i −0.484611 0.243454i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 2.26139 7.07926i 0.0998427 0.312557i
\(514\) 10.9960i 0.485011i
\(515\) 6.95445 + 8.51743i 0.306450 + 0.375323i
\(516\) 10.9441 4.89433i 0.481785 0.215461i
\(517\) 52.5667 2.31188
\(518\) 0 0
\(519\) 1.78416 0.797901i 0.0783160 0.0350240i
\(520\) 1.47723 + 1.80922i 0.0647806 + 0.0793397i
\(521\) 35.5962 1.55950 0.779748 0.626093i \(-0.215347\pi\)
0.779748 + 0.626093i \(0.215347\pi\)
\(522\) −15.4772 13.8433i −0.677420 0.605903i
\(523\) 16.9061 0.739254 0.369627 0.929180i \(-0.379485\pi\)
0.369627 + 0.929180i \(0.379485\pi\)
\(524\) 13.7725 0.601654
\(525\) 0 0
\(526\) −2.00000 −0.0872041
\(527\) 20.9545 0.912790
\(528\) 7.40852 3.31319i 0.322414 0.144188i
\(529\) −2.95445 −0.128454
\(530\) 7.07107 + 8.66025i 0.307148 + 0.376177i
\(531\) −21.1488 + 23.6451i −0.917779 + 1.02611i
\(532\) 0 0
\(533\) −1.09110 −0.0472607
\(534\) −3.47723 7.77531i −0.150474 0.336471i
\(535\) −7.74597 9.48683i −0.334887 0.410152i
\(536\) 14.2701i 0.616374i
\(537\) −30.6464 + 13.7055i −1.32249 + 0.591436i
\(538\) −17.5810 −0.757973
\(539\) 0 0
\(540\) 4.26139 + 10.8093i 0.183381 + 0.465157i
\(541\) 8.52277 0.366423 0.183211 0.983074i \(-0.441351\pi\)
0.183211 + 0.983074i \(0.441351\pi\)
\(542\) 6.32456i 0.271663i
\(543\) 5.00000 2.23607i 0.214571 0.0959589i
\(544\) 3.16228i 0.135582i
\(545\) −28.8948 35.3887i −1.23772 1.51589i
\(546\) 0 0
\(547\) 3.61845i 0.154714i 0.997003 + 0.0773569i \(0.0246481\pi\)
−0.997003 + 0.0773569i \(0.975352\pi\)
\(548\) −3.47723 −0.148540
\(549\) −7.74597 6.92820i −0.330590 0.295689i
\(550\) −22.9545 4.68556i −0.978781 0.199793i
\(551\) 9.89949 0.421733
\(552\) −3.16588 7.07912i −0.134749 0.301307i
\(553\) 0 0
\(554\) 9.79796i 0.416275i
\(555\) 9.21584 + 4.62977i 0.391191 + 0.196523i
\(556\) 20.1810i 0.855863i
\(557\) 27.8634 1.18061 0.590304 0.807181i \(-0.299008\pi\)
0.590304 + 0.807181i \(0.299008\pi\)
\(558\) −14.8170 13.2528i −0.627255 0.561034i
\(559\) 7.23003i 0.305798i
\(560\) 0 0
\(561\) −10.4772 23.4278i −0.442349 0.989122i
\(562\) 1.80922i 0.0763175i
\(563\) 10.3923i 0.437983i −0.975727 0.218992i \(-0.929723\pi\)
0.975727 0.218992i \(-0.0702768\pi\)
\(564\) −17.7386 + 7.93295i −0.746930 + 0.334037i
\(565\) 24.7165 + 30.2714i 1.03983 + 1.27353i
\(566\) −9.22460 −0.387739
\(567\) 0 0
\(568\) 6.92163i 0.290425i
\(569\) 7.56189i 0.317011i −0.987358 0.158505i \(-0.949332\pi\)
0.987358 0.158505i \(-0.0506676\pi\)
\(570\) −4.94975 2.48661i −0.207322 0.104153i
\(571\) 14.9545 0.625824 0.312912 0.949782i \(-0.398695\pi\)
0.312912 + 0.949782i \(0.398695\pi\)
\(572\) 4.89433i 0.204642i
\(573\) −25.7611 + 11.5207i −1.07618 + 0.481284i
\(574\) 0 0
\(575\) −4.47723 + 21.9338i −0.186713 + 0.914704i
\(576\) −2.00000 + 2.23607i −0.0833333 + 0.0931695i
\(577\) 0.674899 0.0280964 0.0140482 0.999901i \(-0.495528\pi\)
0.0140482 + 0.999901i \(0.495528\pi\)
\(578\) 7.00000 0.291162
\(579\) −11.6190 + 5.19615i −0.482867 + 0.215945i
\(580\) −11.9886 + 9.78866i −0.497800 + 0.406452i
\(581\) 0 0
\(582\) 8.47723 + 18.9557i 0.351392 + 0.785737i
\(583\) 23.4278i 0.970280i
\(584\) −3.50333 −0.144969
\(585\) −7.00000 0.315272i −0.289414 0.0130349i
\(586\) 8.05661i 0.332815i
\(587\) 21.0864i 0.870330i −0.900351 0.435165i \(-0.856690\pi\)
0.900351 0.435165i \(-0.143310\pi\)
\(588\) 0 0
\(589\) 9.47723 0.390502
\(590\) 14.9545 + 18.3154i 0.615665 + 0.754033i
\(591\) −6.36396 14.2302i −0.261778 0.585354i
\(592\) 2.66291i 0.109445i
\(593\) 1.65316i 0.0678871i −0.999424 0.0339435i \(-0.989193\pi\)
0.999424 0.0339435i \(-0.0108066\pi\)
\(594\) −7.40852 + 23.1923i −0.303975 + 0.951593i
\(595\) 0 0
\(596\) 2.44949i 0.100335i
\(597\) −24.5228 + 10.9669i −1.00365 + 0.448846i
\(598\) 4.67671 0.191245
\(599\) 23.6412i 0.965954i 0.875633 + 0.482977i \(0.160444\pi\)
−0.875633 + 0.482977i \(0.839556\pi\)
\(600\) 8.45307 1.88296i 0.345095 0.0768716i
\(601\) 4.06775i 0.165927i −0.996553 0.0829635i \(-0.973562\pi\)
0.996553 0.0829635i \(-0.0264385\pi\)
\(602\) 0 0
\(603\) 31.9089 + 28.5402i 1.29943 + 1.16225i
\(604\) −2.00000 −0.0813788
\(605\) −15.4919 18.9737i −0.629837 0.771389i
\(606\) 8.00000 + 17.8885i 0.324978 + 0.726672i
\(607\) −12.2938 −0.498992 −0.249496 0.968376i \(-0.580265\pi\)
−0.249496 + 0.968376i \(0.580265\pi\)
\(608\) 1.43023i 0.0580034i
\(609\) 0 0
\(610\) −6.00000 + 4.89898i −0.242933 + 0.198354i
\(611\) 11.7188i 0.474090i
\(612\) 7.07107 + 6.32456i 0.285831 + 0.255655i
\(613\) 5.85452i 0.236462i −0.992986 0.118231i \(-0.962278\pi\)
0.992986 0.118231i \(-0.0377223\pi\)
\(614\) 11.9886 0.483821
\(615\) −1.81608 + 3.61501i −0.0732314 + 0.145771i
\(616\) 0 0
\(617\) 14.5228 0.584665 0.292332 0.956317i \(-0.405569\pi\)
0.292332 + 0.956317i \(0.405569\pi\)
\(618\) −3.47723 7.77531i −0.139875 0.312769i
\(619\) 30.1925i 1.21354i −0.794877 0.606771i \(-0.792465\pi\)
0.794877 0.606771i \(-0.207535\pi\)
\(620\) −11.4772 + 9.37112i −0.460936 + 0.376353i
\(621\) 22.1611 + 7.07912i 0.889296 + 0.284075i
\(622\) −17.5810 −0.704936
\(623\) 0 0
\(624\) −0.738613 1.65159i −0.0295682 0.0661165i
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) −23.2379 −0.928773
\(627\) −4.73861 10.5959i −0.189242 0.423158i
\(628\) −14.4474 −0.576513
\(629\) 8.42087 0.335762
\(630\) 0 0
\(631\) 3.47723 0.138426 0.0692131 0.997602i \(-0.477951\pi\)
0.0692131 + 0.997602i \(0.477951\pi\)
\(632\) 11.4772 0.456540
\(633\) −17.3080 38.7019i −0.687932 1.53826i
\(634\) −9.90890 −0.393533
\(635\) 15.1223 12.3473i 0.600109 0.489987i
\(636\) −3.53553 7.90569i −0.140193 0.313481i
\(637\) 0 0
\(638\) −32.4317 −1.28398
\(639\) 15.4772 + 13.8433i 0.612270 + 0.547631i
\(640\) 1.41421 + 1.73205i 0.0559017 + 0.0684653i
\(641\) 16.0793i 0.635095i −0.948242 0.317547i \(-0.897141\pi\)
0.948242 0.317547i \(-0.102859\pi\)
\(642\) 3.87298 + 8.66025i 0.152854 + 0.341793i
\(643\) −26.0663 −1.02796 −0.513978 0.857803i \(-0.671829\pi\)
−0.513978 + 0.857803i \(0.671829\pi\)
\(644\) 0 0
\(645\) 23.9545 + 12.0340i 0.943206 + 0.473839i
\(646\) −4.52277 −0.177946
\(647\) 20.4039i 0.802160i −0.916043 0.401080i \(-0.868635\pi\)
0.916043 0.401080i \(-0.131365\pi\)
\(648\) −1.00000 8.94427i −0.0392837 0.351364i
\(649\) 49.5469i 1.94489i
\(650\) −1.04456 + 5.11726i −0.0409709 + 0.200715i
\(651\) 0 0
\(652\) 14.6969i 0.575577i
\(653\) 39.8634 1.55997 0.779987 0.625796i \(-0.215226\pi\)
0.779987 + 0.625796i \(0.215226\pi\)
\(654\) 14.4474 + 32.3053i 0.564937 + 1.26324i
\(655\) 19.4772 + 23.8546i 0.761038 + 0.932078i
\(656\) −1.04456 −0.0407831
\(657\) 7.00665 7.83368i 0.273356 0.305621i
\(658\) 0 0
\(659\) 34.2929i 1.33586i −0.744224 0.667930i \(-0.767181\pi\)
0.744224 0.667930i \(-0.232819\pi\)
\(660\) 16.2158 + 8.14637i 0.631201 + 0.317097i
\(661\) 0.603648i 0.0234792i −0.999931 0.0117396i \(-0.996263\pi\)
0.999931 0.0117396i \(-0.00373691\pi\)
\(662\) 21.4317 0.832966
\(663\) −5.22278 + 2.33570i −0.202836 + 0.0907110i
\(664\) 4.06775i 0.157859i
\(665\) 0 0
\(666\) −5.95445 5.32582i −0.230730 0.206371i
\(667\) 30.9897i 1.19993i
\(668\) 4.29068i 0.166011i
\(669\) 15.4772 + 34.6081i 0.598384 + 1.33803i
\(670\) 24.7165 20.1810i 0.954883 0.779659i
\(671\) −16.2312 −0.626600
\(672\) 0 0
\(673\) 14.1585i 0.545771i −0.962047 0.272885i \(-0.912022\pi\)
0.962047 0.272885i \(-0.0879780\pi\)
\(674\) 17.1464i 0.660456i
\(675\) −12.6957 + 22.6676i −0.488658 + 0.872475i
\(676\) −11.9089 −0.458035
\(677\) 32.9090i 1.26479i −0.774644 0.632397i \(-0.782071\pi\)
0.774644 0.632397i \(-0.217929\pi\)
\(678\) −12.3583 27.6339i −0.474616 1.06127i
\(679\) 0 0
\(680\) 5.47723 4.47214i 0.210042 0.171499i
\(681\) −16.4317 + 7.34847i −0.629663 + 0.281594i
\(682\) −31.0483 −1.18890
\(683\) −18.9545 −0.725272 −0.362636 0.931931i \(-0.618123\pi\)
−0.362636 + 0.931931i \(0.618123\pi\)
\(684\) 3.19808 + 2.86045i 0.122282 + 0.109372i
\(685\) −4.91754 6.02273i −0.187890 0.230117i
\(686\) 0 0
\(687\) −21.4317 + 9.58454i −0.817669 + 0.365673i
\(688\) 6.92163i 0.263885i
\(689\) 5.22278 0.198972
\(690\) 7.78416 15.4948i 0.296338 0.589878i
\(691\) 3.46410i 0.131781i 0.997827 + 0.0658903i \(0.0209887\pi\)
−0.997827 + 0.0658903i \(0.979011\pi\)
\(692\) 1.12840i 0.0428954i
\(693\) 0 0
\(694\) −17.4772 −0.663426
\(695\) −34.9545 + 28.5402i −1.32590 + 1.08259i
\(696\) 10.9441 4.89433i 0.414833 0.185519i
\(697\) 3.30318i 0.125117i
\(698\) 11.7436i 0.444503i
\(699\) 2.82843 + 6.32456i 0.106981 + 0.239217i
\(700\) 0 0
\(701\) 51.7546i 1.95474i 0.211531 + 0.977371i \(0.432155\pi\)
−0.211531 + 0.977371i \(0.567845\pi\)
\(702\) 5.17029 + 1.65159i 0.195140 + 0.0623352i
\(703\) 3.80857 0.143643
\(704\) 4.68556i 0.176594i
\(705\) −38.8265 19.5053i −1.46229 0.734612i
\(706\) 0.603648i 0.0227186i
\(707\) 0 0
\(708\) −7.47723 16.7196i −0.281011 0.628360i
\(709\) −22.4317 −0.842439 −0.421220 0.906959i \(-0.638398\pi\)
−0.421220 + 0.906959i \(0.638398\pi\)
\(710\) 11.9886 9.78866i 0.449924 0.367362i
\(711\) −22.9545 + 25.6639i −0.860859 + 0.962470i
\(712\) 4.91754 0.184293
\(713\) 29.6678i 1.11107i
\(714\) 0 0
\(715\) −8.47723 + 6.92163i −0.317030 + 0.258854i
\(716\) 19.3825i 0.724358i
\(717\) 0 0
\(718\) 11.3938i 0.425211i
\(719\) −0.803730 −0.0299741 −0.0149870 0.999888i \(-0.504771\pi\)
−0.0149870 + 0.999888i \(0.504771\pi\)
\(720\) −6.70141 0.301824i −0.249747 0.0112483i
\(721\) 0 0
\(722\) 16.9545 0.630979
\(723\) 33.6931 15.0680i 1.25306 0.560385i
\(724\) 3.16228i 0.117525i
\(725\) −33.9089 6.92163i −1.25935 0.257063i
\(726\) 7.74597 + 17.3205i 0.287480 + 0.642824i
\(727\) −15.1223 −0.560854 −0.280427 0.959875i \(-0.590476\pi\)
−0.280427 + 0.959875i \(0.590476\pi\)
\(728\) 0 0
\(729\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(730\) −4.95445 6.06794i −0.183372 0.224584i
\(731\) 21.8881 0.809561
\(732\) 5.47723 2.44949i 0.202444 0.0905357i
\(733\) −2.39435 −0.0884375 −0.0442187 0.999022i \(-0.514080\pi\)
−0.0442187 + 0.999022i \(0.514080\pi\)
\(734\) −0.369657 −0.0136443
\(735\) 0 0
\(736\) 4.47723 0.165033
\(737\) 66.8634 2.46294
\(738\) 2.08911 2.33570i 0.0769013 0.0859783i
\(739\) 6.47723 0.238269 0.119134 0.992878i \(-0.461988\pi\)
0.119134 + 0.992878i \(0.461988\pi\)
\(740\) −4.61230 + 3.76593i −0.169551 + 0.138438i
\(741\) −2.36215 + 1.05638i −0.0867756 + 0.0388072i
\(742\) 0 0
\(743\) 13.4317 0.492760 0.246380 0.969173i \(-0.420759\pi\)
0.246380 + 0.969173i \(0.420759\pi\)
\(744\) 10.4772 4.68556i 0.384114 0.171781i
\(745\) 4.24264 3.46410i 0.155438 0.126915i
\(746\) 23.2144i 0.849938i
\(747\) 9.09576 + 8.13550i 0.332797 + 0.297662i
\(748\) 14.8170 0.541764
\(749\) 0 0
\(750\) 15.2158 + 11.9782i 0.555604 + 0.437384i
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 11.2189i 0.409111i
\(753\) 6.26139 + 14.0009i 0.228178 + 0.510221i
\(754\) 7.23003i 0.263302i
\(755\) −2.82843 3.46410i −0.102937 0.126072i
\(756\) 0 0
\(757\) 48.1361i 1.74954i −0.484541 0.874768i \(-0.661014\pi\)
0.484541 0.874768i \(-0.338986\pi\)
\(758\) −20.4772 −0.743766
\(759\) 33.1696 14.8339i 1.20398 0.538436i
\(760\) 2.47723 2.02265i 0.0898584 0.0733691i
\(761\) 1.78387 0.0646653 0.0323326 0.999477i \(-0.489706\pi\)
0.0323326 + 0.999477i \(0.489706\pi\)
\(762\) −13.8047 + 6.17364i −0.500091 + 0.223648i
\(763\) 0 0
\(764\) 16.2927i 0.589451i
\(765\) −0.954451 + 21.1917i −0.0345083 + 0.766188i
\(766\) 18.1471i 0.655681i
\(767\) 11.0455 0.398832
\(768\) −0.707107 1.58114i −0.0255155 0.0570544i
\(769\) 16.1921i 0.583902i −0.956433 0.291951i \(-0.905696\pi\)
0.956433 0.291951i \(-0.0943045\pi\)
\(770\) 0 0
\(771\) −17.3861 + 7.77531i −0.626146 + 0.280021i
\(772\) 7.34847i 0.264477i
\(773\) 16.1921i 0.582390i 0.956664 + 0.291195i \(0.0940528\pi\)
−0.956664 + 0.291195i \(0.905947\pi\)
\(774\) −15.4772 13.8433i −0.556317 0.497585i
\(775\) −32.4625 6.62638i −1.16609 0.238027i
\(776\) −11.9886 −0.430366
\(777\) 0 0
\(778\) 7.34847i 0.263455i
\(779\) 1.49395i 0.0535264i
\(780\) 1.81608 3.61501i 0.0650261 0.129438i
\(781\) 32.4317 1.16050
\(782\) 14.1582i 0.506297i
\(783\) −10.9441 + 34.2603i −0.391108 + 1.22436i
\(784\) 0 0
\(785\) −20.4317 25.0236i −0.729238 0.893130i
\(786\) −9.73861 21.7762i −0.347365 0.776731i
\(787\) 50.1724 1.78845 0.894226 0.447616i \(-0.147727\pi\)
0.894226 + 0.447616i \(0.147727\pi\)
\(788\) 9.00000 0.320612
\(789\) 1.41421 + 3.16228i 0.0503473 + 0.112580i
\(790\) 16.2312 + 19.8791i 0.577482 + 0.707268i
\(791\) 0 0
\(792\) −10.4772 9.37112i −0.372292 0.332988i
\(793\) 3.61845i 0.128495i
\(794\) −14.8815 −0.528123
\(795\) 8.69306 17.3041i 0.308311 0.613712i
\(796\) 15.5096i 0.549722i
\(797\) 54.2183i 1.92051i 0.279121 + 0.960256i \(0.409957\pi\)
−0.279121 + 0.960256i \(0.590043\pi\)
\(798\) 0 0
\(799\) −35.4772 −1.25509
\(800\) −1.00000 + 4.89898i −0.0353553 + 0.173205i
\(801\) −9.83508 + 10.9960i −0.347505 + 0.388523i
\(802\) 0.955537i 0.0337412i
\(803\) 16.4150i 0.579274i
\(804\) −22.5630 + 10.0905i −0.795736 + 0.355864i
\(805\) 0 0
\(806\) 6.92163i 0.243804i
\(807\) 12.4317 + 27.7981i 0.437616 + 0.978539i
\(808\) −11.3137 −0.398015
\(809\) 8.84242i 0.310883i −0.987845 0.155441i \(-0.950320\pi\)
0.987845 0.155441i \(-0.0496800\pi\)
\(810\) 14.0777 14.3812i 0.494641 0.505303i
\(811\) 38.3280i 1.34588i −0.739697 0.672940i \(-0.765031\pi\)
0.739697 0.672940i \(-0.234969\pi\)
\(812\) 0 0
\(813\) −10.0000 + 4.47214i −0.350715 + 0.156845i
\(814\) −12.4772 −0.437327
\(815\) −25.4558 + 20.7846i −0.891679 + 0.728053i
\(816\) −5.00000 + 2.23607i −0.175035 + 0.0782780i
\(817\) 9.89949 0.346339
\(818\) 15.5096i 0.542279i
\(819\) 0 0
\(820\) −1.47723 1.80922i −0.0515870 0.0631809i
\(821\) 11.7090i 0.408648i 0.978903 + 0.204324i \(0.0654996\pi\)
−0.978903 + 0.204324i \(0.934500\pi\)
\(822\) 2.45877 + 5.49798i 0.0857594 + 0.191764i
\(823\) 3.19161i 0.111252i 0.998452 + 0.0556262i \(0.0177155\pi\)
−0.998452 + 0.0556262i \(0.982284\pi\)
\(824\) 4.91754 0.171311
\(825\) 8.82273 + 39.6074i 0.307168 + 1.37895i
\(826\) 0 0
\(827\) −3.90890 −0.135926 −0.0679629 0.997688i \(-0.521650\pi\)
−0.0679629 + 0.997688i \(0.521650\pi\)
\(828\) −8.95445 + 10.0114i −0.311189 + 0.347920i
\(829\) 50.4524i 1.75228i 0.482053 + 0.876142i \(0.339891\pi\)
−0.482053 + 0.876142i \(0.660109\pi\)
\(830\) 7.04555 5.75267i 0.244555 0.199678i
\(831\) 15.4919 6.92820i 0.537409 0.240337i
\(832\) 1.04456 0.0362135
\(833\) 0 0
\(834\) 31.9089 14.2701i 1.10491 0.494133i
\(835\) 7.43168 6.06794i 0.257184 0.209990i
\(836\) 6.70141 0.231773
\(837\) −10.4772 + 32.7989i −0.362146 + 1.13370i
\(838\) 8.85494 0.305889
\(839\) −40.1440 −1.38593 −0.692963 0.720973i \(-0.743695\pi\)
−0.692963 + 0.720973i \(0.743695\pi\)
\(840\) 0 0
\(841\) −18.9089 −0.652031
\(842\) 18.9545 0.653214
\(843\) −2.86064 + 1.27931i −0.0985255 + 0.0440619i
\(844\) 24.4772 0.842541
\(845\) −16.8417 20.6268i −0.579373 0.709584i
\(846\) 25.0862 + 22.4378i 0.862481 + 0.771426i
\(847\) 0 0
\(848\) 5.00000 0.171701
\(849\) 6.52277 + 14.5854i 0.223861 + 0.500569i
\(850\) 15.4919 + 3.16228i 0.531369 + 0.108465i
\(851\) 11.9225i 0.408697i
\(852\) −10.9441 + 4.89433i −0.374937 + 0.167677i
\(853\) 31.2891 1.07132 0.535659 0.844434i \(-0.320063\pi\)
0.535659 + 0.844434i \(0.320063\pi\)
\(854\) 0 0
\(855\) −0.431677 + 9.58454i −0.0147630 + 0.327784i
\(856\) −5.47723 −0.187208
\(857\) 15.0637i 0.514566i −0.966336 0.257283i \(-0.917173\pi\)
0.966336 0.257283i \(-0.0828273\pi\)
\(858\) 7.73861 3.46081i 0.264192 0.118150i
\(859\) 30.5733i 1.04315i −0.853207 0.521573i \(-0.825345\pi\)
0.853207 0.521573i \(-0.174655\pi\)
\(860\) −11.9886 + 9.78866i −0.408808 + 0.333790i
\(861\) 0 0
\(862\) 7.66374i 0.261028i
\(863\) −26.4772 −0.901295 −0.450648 0.892702i \(-0.648807\pi\)
−0.450648 + 0.892702i \(0.648807\pi\)
\(864\) 4.94975 + 1.58114i 0.168394 + 0.0537914i
\(865\) −1.95445 + 1.59580i −0.0664533 + 0.0542589i
\(866\) 0 0
\(867\) −4.94975 11.0680i −0.168102 0.375888i
\(868\) 0 0
\(869\) 53.7772i 1.82427i
\(870\) 23.9545 + 12.0340i 0.812132 + 0.407992i
\(871\) 14.9059i 0.505068i
\(872\) −20.4317 −0.691904
\(873\) 23.9772 26.8073i 0.811506 0.907291i
\(874\) 6.40345i 0.216600i
\(875\) 0 0
\(876\) 2.47723 + 5.53924i 0.0836977 + 0.187154i
\(877\) 55.6980i 1.88079i −0.340087 0.940394i \(-0.610457\pi\)
0.340087 0.940394i \(-0.389543\pi\)
\(878\) 8.88319i 0.299793i
\(879\) 12.7386 5.69688i 0.429663 0.192151i
\(880\) −8.11562 + 6.62638i −0.273578 + 0.223375i
\(881\) −18.7544 −0.631853 −0.315926 0.948784i \(-0.602315\pi\)
−0.315926 + 0.948784i \(0.602315\pi\)
\(882\) 0 0
\(883\) 24.3833i 0.820564i 0.911959 + 0.410282i \(0.134570\pi\)
−0.911959 + 0.410282i \(0.865430\pi\)
\(884\) 3.30318i 0.111098i
\(885\) 18.3848 36.5960i 0.617997 1.23016i
\(886\) −15.0455 −0.505465
\(887\) 3.46410i 0.116313i 0.998307 + 0.0581566i \(0.0185223\pi\)
−0.998307 + 0.0581566i \(0.981478\pi\)
\(888\) 4.21043 1.88296i 0.141293 0.0631881i
\(889\) 0 0
\(890\) 6.95445 + 8.51743i 0.233114 + 0.285505i
\(891\) 41.9089 4.68556i 1.40400 0.156972i
\(892\) −21.8881 −0.732868
\(893\) −16.0455 −0.536944
\(894\) −3.87298 + 1.73205i −0.129532 + 0.0579284i
\(895\) 33.5715 27.4110i 1.12217 0.916248i
\(896\) 0 0
\(897\) −3.30694 7.39453i −0.110415 0.246896i
\(898\) 25.8773i 0.863536i
\(899\) −45.8653 −1.52969
\(900\) −8.95445 12.0340i −0.298482 0.401134i
\(901\) 15.8114i 0.526754i
\(902\) 4.89433i 0.162963i
\(903\) 0 0
\(904\) 17.4772 0.581284
\(905\) −5.47723 + 4.47214i −0.182069 + 0.148659i
\(906\) 1.41421 + 3.16228i 0.0469841 + 0.105060i
\(907\) 9.79796i 0.325336i 0.986681 + 0.162668i \(0.0520099\pi\)
−0.986681 + 0.162668i \(0.947990\pi\)
\(908\) 10.3923i 0.344881i
\(909\) 22.6274 25.2982i 0.750504 0.839089i
\(910\) 0 0
\(911\) 24.0681i 0.797410i −0.917079 0.398705i \(-0.869460\pi\)
0.917079 0.398705i \(-0.130540\pi\)
\(912\) −2.26139 + 1.01132i −0.0748820 + 0.0334883i
\(913\) 19.0597 0.630783
\(914\) 11.0785i 0.366444i
\(915\) 11.9886 + 6.02273i 0.396331 + 0.199105i
\(916\) 13.5546i 0.447856i
\(917\) 0 0
\(918\) 5.00000 15.6525i 0.165025 0.516609i
\(919\) 0.431677 0.0142397 0.00711985 0.999975i \(-0.497734\pi\)
0.00711985 + 0.999975i \(0.497734\pi\)
\(920\) 6.33175 + 7.75478i 0.208752 + 0.255668i
\(921\) −8.47723 18.9557i −0.279334 0.624610i
\(922\) 31.7876 1.04687
\(923\) 7.23003i 0.237979i
\(924\) 0 0
\(925\) −13.0455 2.66291i −0.428935 0.0875560i
\(926\) 22.5741i 0.741831i
\(927\) −9.83508 + 10.9960i −0.323026 + 0.361154i
\(928\) 6.92163i 0.227213i
\(929\) −15.9260 −0.522515 −0.261258 0.965269i \(-0.584137\pi\)
−0.261258 + 0.965269i \(0.584137\pi\)
\(930\) 22.9327 + 11.5207i 0.751991 + 0.377779i
\(931\) 0 0
\(932\) −4.00000 −0.131024
\(933\) 12.4317 + 27.7981i 0.406995 + 0.910068i
\(934\) 28.0146i 0.916667i
\(935\) 20.9545 + 25.6639i 0.685284 + 0.839298i
\(936\) −2.08911 + 2.33570i −0.0682848 + 0.0763447i
\(937\) −53.6757 −1.75351 −0.876754 0.480938i \(-0.840296\pi\)
−0.876754 + 0.480938i \(0.840296\pi\)
\(938\) 0 0
\(939\) 16.4317 + 36.7423i 0.536228 + 1.19904i
\(940\) 19.4317 15.8659i 0.633791 0.517489i
\(941\) 20.4739 0.667430 0.333715 0.942674i \(-0.391698\pi\)
0.333715 + 0.942674i \(0.391698\pi\)
\(942\) 10.2158 + 22.8433i 0.332850 + 0.744275i
\(943\) −4.67671 −0.152295
\(944\) 10.5744 0.344167
\(945\) 0 0
\(946\) −32.4317 −1.05444
\(947\) 32.8634 1.06792 0.533958 0.845511i \(-0.320704\pi\)
0.533958 + 0.845511i \(0.320704\pi\)
\(948\) −8.11562 18.1471i −0.263583 0.589390i
\(949\) −3.65942 −0.118790
\(950\) 7.00665 + 1.43023i 0.227326 + 0.0464027i
\(951\) 7.00665 + 15.6674i 0.227206 + 0.508049i
\(952\) 0 0
\(953\) 46.9545 1.52100 0.760502 0.649336i \(-0.224953\pi\)
0.760502 + 0.649336i \(0.224953\pi\)
\(954\) −10.0000 + 11.1803i −0.323762 + 0.361977i
\(955\) 28.2199 23.0414i 0.913173 0.745603i
\(956\) 0 0
\(957\) 22.9327 + 51.2790i 0.741308 + 1.65761i
\(958\) 42.3620 1.36865
\(959\) 0 0
\(960\) 1.73861 3.46081i 0.0561135 0.111697i
\(961\) −12.9089 −0.416416
\(962\) 2.78156i 0.0896811i
\(963\) 10.9545 12.2474i 0.353002 0.394669i
\(964\) 21.3094i 0.686328i
\(965\) 12.7279 10.3923i 0.409726 0.334540i
\(966\) 0 0
\(967\) 7.23690i 0.232723i 0.993207 + 0.116361i \(0.0371231\pi\)
−0.993207 + 0.116361i \(0.962877\pi\)
\(968\) −10.9545 −0.352089
\(969\) 3.19808 + 7.15113i 0.102737 + 0.229728i
\(970\) −16.9545 20.7649i −0.544375 0.666720i
\(971\) 37.7497 1.21145 0.605723 0.795676i \(-0.292884\pi\)
0.605723 + 0.795676i \(0.292884\pi\)
\(972\) −13.4350 + 7.90569i −0.430929 + 0.253575i
\(973\) 0 0
\(974\) 17.0349i 0.545832i
\(975\) 8.82971 1.96686i 0.282777 0.0629899i
\(976\) 3.46410i 0.110883i
\(977\) 3.90890 0.125057 0.0625284 0.998043i \(-0.480084\pi\)
0.0625284 + 0.998043i \(0.480084\pi\)
\(978\) 23.2379 10.3923i 0.743066 0.332309i
\(979\) 23.0414i 0.736407i
\(980\) 0 0
\(981\) 40.8634 45.6866i 1.30467 1.45866i
\(982\) 13.8433i 0.441756i
\(983\) 52.7881i 1.68368i 0.539728 + 0.841840i \(0.318527\pi\)
−0.539728 + 0.841840i \(0.681473\pi\)
\(984\) 0.738613 + 1.65159i 0.0235461 + 0.0526507i
\(985\) 12.7279 + 15.5885i 0.405545 + 0.496690i
\(986\) 21.8881 0.697059
\(987\) 0 0
\(988\) 1.49395i 0.0475290i
\(989\) 30.9897i 0.985414i
\(990\) 1.41421 31.3998i 0.0449467 0.997953i
\(991\) 10.5228 0.334267 0.167133 0.985934i \(-0.446549\pi\)
0.167133 + 0.985934i \(0.446549\pi\)
\(992\) 6.62638i 0.210388i
\(993\) −15.1545 33.8865i −0.480913 1.07535i
\(994\) 0 0
\(995\) 26.8634 21.9338i 0.851626 0.695349i
\(996\) −6.43168 + 2.87633i −0.203795 + 0.0911401i
\(997\) −15.4919 −0.490634 −0.245317 0.969443i \(-0.578892\pi\)
−0.245317 + 0.969443i \(0.578892\pi\)
\(998\) 1.90890 0.0604252
\(999\) −4.21043 + 13.1807i −0.133212 + 0.417020i
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 1470.2.d.f.1469.2 8
3.2 odd 2 1470.2.d.e.1469.3 8
5.4 even 2 1470.2.d.e.1469.7 8
7.2 even 3 210.2.t.e.59.4 yes 8
7.3 odd 6 210.2.t.e.89.3 yes 8
7.6 odd 2 inner 1470.2.d.f.1469.7 8
15.14 odd 2 inner 1470.2.d.f.1469.6 8
21.2 odd 6 210.2.t.f.59.2 yes 8
21.17 even 6 210.2.t.f.89.1 yes 8
21.20 even 2 1470.2.d.e.1469.6 8
35.2 odd 12 1050.2.s.i.101.7 16
35.3 even 12 1050.2.s.i.551.8 16
35.9 even 6 210.2.t.f.59.1 yes 8
35.17 even 12 1050.2.s.i.551.1 16
35.23 odd 12 1050.2.s.i.101.2 16
35.24 odd 6 210.2.t.f.89.2 yes 8
35.34 odd 2 1470.2.d.e.1469.2 8
105.2 even 12 1050.2.s.i.101.1 16
105.17 odd 12 1050.2.s.i.551.7 16
105.23 even 12 1050.2.s.i.101.8 16
105.38 odd 12 1050.2.s.i.551.2 16
105.44 odd 6 210.2.t.e.59.3 8
105.59 even 6 210.2.t.e.89.4 yes 8
105.104 even 2 inner 1470.2.d.f.1469.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.e.59.3 8 105.44 odd 6
210.2.t.e.59.4 yes 8 7.2 even 3
210.2.t.e.89.3 yes 8 7.3 odd 6
210.2.t.e.89.4 yes 8 105.59 even 6
210.2.t.f.59.1 yes 8 35.9 even 6
210.2.t.f.59.2 yes 8 21.2 odd 6
210.2.t.f.89.1 yes 8 21.17 even 6
210.2.t.f.89.2 yes 8 35.24 odd 6
1050.2.s.i.101.1 16 105.2 even 12
1050.2.s.i.101.2 16 35.23 odd 12
1050.2.s.i.101.7 16 35.2 odd 12
1050.2.s.i.101.8 16 105.23 even 12
1050.2.s.i.551.1 16 35.17 even 12
1050.2.s.i.551.2 16 105.38 odd 12
1050.2.s.i.551.7 16 105.17 odd 12
1050.2.s.i.551.8 16 35.3 even 12
1470.2.d.e.1469.2 8 35.34 odd 2
1470.2.d.e.1469.3 8 3.2 odd 2
1470.2.d.e.1469.6 8 21.20 even 2
1470.2.d.e.1469.7 8 5.4 even 2
1470.2.d.f.1469.2 8 1.1 even 1 trivial
1470.2.d.f.1469.3 8 105.104 even 2 inner
1470.2.d.f.1469.6 8 15.14 odd 2 inner
1470.2.d.f.1469.7 8 7.6 odd 2 inner