Properties

Label 567.2.i.f.215.4
Level $567$
Weight $2$
Character 567.215
Analytic conductor $4.528$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(215,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.i (of order \(6\), degree \(2\), not 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.4
Root \(1.65604 + 0.956115i\) of defining polynomial
Character \(\chi\) \(=\) 567.215
Dual form 567.2.i.f.269.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.656620i q^{2} +1.56885 q^{4} +(-1.65604 - 2.86834i) q^{5} +(1.78442 + 1.95341i) q^{7} +2.34338i q^{8} +O(q^{10})\) \(q+0.656620i q^{2} +1.56885 q^{4} +(-1.65604 - 2.86834i) q^{5} +(1.78442 + 1.95341i) q^{7} +2.34338i q^{8} +(1.88341 - 1.08739i) q^{10} +(2.02943 + 1.17169i) q^{11} +(-1.36834 - 0.790014i) q^{13} +(-1.28265 + 1.17169i) q^{14} +1.59899 q^{16} +(-0.568650 - 0.984931i) q^{17} +(3.85327 + 2.22469i) q^{19} +(-2.59808 - 4.50000i) q^{20} +(-0.769355 + 1.33256i) q^{22} +(8.13484 - 4.69665i) q^{23} +(-2.98493 + 5.17005i) q^{25} +(0.518739 - 0.898482i) q^{26} +(2.79949 + 3.06461i) q^{28} +(3.16673 - 1.82831i) q^{29} -7.31873i q^{31} +5.73669i q^{32} +(0.646726 - 0.373387i) q^{34} +(2.64799 - 8.35327i) q^{35} +(2.58392 - 4.47548i) q^{37} +(-1.46078 + 2.53014i) q^{38} +(6.72162 - 3.88073i) q^{40} +(-4.82277 + 8.35327i) q^{41} +(1.08392 + 1.87740i) q^{43} +(3.18386 + 1.83821i) q^{44} +(3.08392 + 5.34150i) q^{46} -5.58668 q^{47} +(-0.631656 + 6.97144i) q^{49} +(-3.39476 - 1.95997i) q^{50} +(-2.14673 - 1.23941i) q^{52} +(-8.70349 + 5.02496i) q^{53} -7.76146i q^{55} +(-4.57759 + 4.18158i) q^{56} +(1.20051 + 2.07934i) q^{58} +2.17478 q^{59} -4.00665i q^{61} +4.80563 q^{62} -0.568850 q^{64} +5.23317i q^{65} -10.7668 q^{67} +(-0.892126 - 1.54521i) q^{68} +(5.48493 + 1.73872i) q^{70} +6.39331i q^{71} +(-9.25176 + 5.34150i) q^{73} +(2.93869 + 1.69665i) q^{74} +(6.04521 + 3.49020i) q^{76} +(1.33256 + 6.05510i) q^{77} +1.23317 q^{79} +(-2.64799 - 4.58645i) q^{80} +(-5.48493 - 3.16673i) q^{82} +(0.518739 + 0.898482i) q^{83} +(-1.88341 + 3.26217i) q^{85} +(-1.23274 + 0.711723i) q^{86} +(-2.74571 + 4.75572i) q^{88} +(-3.73538 + 6.46986i) q^{89} +(-0.898482 - 4.08266i) q^{91} +(12.7623 - 7.36834i) q^{92} -3.66833i q^{94} -14.7367i q^{95} +(11.7367 - 6.77618i) q^{97} +(-4.57759 - 0.414758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.656620i 0.464301i 0.972680 + 0.232150i \(0.0745761\pi\)
−0.972680 + 0.232150i \(0.925424\pi\)
\(3\) 0 0
\(4\) 1.56885 0.784425
\(5\) −1.65604 2.86834i −0.740603 1.28276i −0.952221 0.305410i \(-0.901207\pi\)
0.211618 0.977352i \(-0.432127\pi\)
\(6\) 0 0
\(7\) 1.78442 + 1.95341i 0.674449 + 0.738321i
\(8\) 2.34338i 0.828510i
\(9\) 0 0
\(10\) 1.88341 1.08739i 0.595588 0.343863i
\(11\) 2.02943 + 1.17169i 0.611895 + 0.353278i 0.773707 0.633544i \(-0.218400\pi\)
−0.161812 + 0.986822i \(0.551734\pi\)
\(12\) 0 0
\(13\) −1.36834 0.790014i −0.379510 0.219110i 0.298095 0.954536i \(-0.403649\pi\)
−0.677605 + 0.735426i \(0.736982\pi\)
\(14\) −1.28265 + 1.17169i −0.342803 + 0.313147i
\(15\) 0 0
\(16\) 1.59899 0.399747
\(17\) −0.568650 0.984931i −0.137918 0.238881i 0.788790 0.614662i \(-0.210708\pi\)
−0.926708 + 0.375781i \(0.877374\pi\)
\(18\) 0 0
\(19\) 3.85327 + 2.22469i 0.884002 + 0.510379i 0.871976 0.489549i \(-0.162839\pi\)
0.0120260 + 0.999928i \(0.496172\pi\)
\(20\) −2.59808 4.50000i −0.580948 1.00623i
\(21\) 0 0
\(22\) −0.769355 + 1.33256i −0.164027 + 0.284103i
\(23\) 8.13484 4.69665i 1.69623 0.979320i 0.746957 0.664872i \(-0.231514\pi\)
0.949275 0.314448i \(-0.101819\pi\)
\(24\) 0 0
\(25\) −2.98493 + 5.17005i −0.596986 + 1.03401i
\(26\) 0.518739 0.898482i 0.101733 0.176207i
\(27\) 0 0
\(28\) 2.79949 + 3.06461i 0.529055 + 0.579158i
\(29\) 3.16673 1.82831i 0.588046 0.339509i −0.176278 0.984340i \(-0.556406\pi\)
0.764325 + 0.644832i \(0.223073\pi\)
\(30\) 0 0
\(31\) 7.31873i 1.31448i −0.753680 0.657241i \(-0.771723\pi\)
0.753680 0.657241i \(-0.228277\pi\)
\(32\) 5.73669i 1.01411i
\(33\) 0 0
\(34\) 0.646726 0.373387i 0.110913 0.0640354i
\(35\) 2.64799 8.35327i 0.447592 1.41196i
\(36\) 0 0
\(37\) 2.58392 4.47548i 0.424794 0.735764i −0.571607 0.820527i \(-0.693680\pi\)
0.996401 + 0.0847630i \(0.0270133\pi\)
\(38\) −1.46078 + 2.53014i −0.236969 + 0.410443i
\(39\) 0 0
\(40\) 6.72162 3.88073i 1.06278 0.613597i
\(41\) −4.82277 + 8.35327i −0.753189 + 1.30456i 0.193080 + 0.981183i \(0.438152\pi\)
−0.946269 + 0.323379i \(0.895181\pi\)
\(42\) 0 0
\(43\) 1.08392 + 1.87740i 0.165296 + 0.286301i 0.936760 0.349971i \(-0.113809\pi\)
−0.771464 + 0.636273i \(0.780475\pi\)
\(44\) 3.18386 + 1.83821i 0.479986 + 0.277120i
\(45\) 0 0
\(46\) 3.08392 + 5.34150i 0.454699 + 0.787562i
\(47\) −5.58668 −0.814901 −0.407450 0.913227i \(-0.633582\pi\)
−0.407450 + 0.913227i \(0.633582\pi\)
\(48\) 0 0
\(49\) −0.631656 + 6.97144i −0.0902366 + 0.995920i
\(50\) −3.39476 1.95997i −0.480092 0.277181i
\(51\) 0 0
\(52\) −2.14673 1.23941i −0.297697 0.171876i
\(53\) −8.70349 + 5.02496i −1.19552 + 0.690232i −0.959552 0.281530i \(-0.909158\pi\)
−0.235964 + 0.971762i \(0.575825\pi\)
\(54\) 0 0
\(55\) 7.76146i 1.04655i
\(56\) −4.57759 + 4.18158i −0.611706 + 0.558788i
\(57\) 0 0
\(58\) 1.20051 + 2.07934i 0.157634 + 0.273030i
\(59\) 2.17478 0.283132 0.141566 0.989929i \(-0.454786\pi\)
0.141566 + 0.989929i \(0.454786\pi\)
\(60\) 0 0
\(61\) 4.00665i 0.512999i −0.966544 0.256500i \(-0.917431\pi\)
0.966544 0.256500i \(-0.0825692\pi\)
\(62\) 4.80563 0.610315
\(63\) 0 0
\(64\) −0.568850 −0.0711062
\(65\) 5.23317i 0.649095i
\(66\) 0 0
\(67\) −10.7668 −1.31538 −0.657689 0.753290i \(-0.728466\pi\)
−0.657689 + 0.753290i \(0.728466\pi\)
\(68\) −0.892126 1.54521i −0.108186 0.187384i
\(69\) 0 0
\(70\) 5.48493 + 1.73872i 0.655575 + 0.207817i
\(71\) 6.39331i 0.758746i 0.925244 + 0.379373i \(0.123860\pi\)
−0.925244 + 0.379373i \(0.876140\pi\)
\(72\) 0 0
\(73\) −9.25176 + 5.34150i −1.08284 + 0.625176i −0.931660 0.363331i \(-0.881639\pi\)
−0.151176 + 0.988507i \(0.548306\pi\)
\(74\) 2.93869 + 1.69665i 0.341616 + 0.197232i
\(75\) 0 0
\(76\) 6.04521 + 3.49020i 0.693433 + 0.400354i
\(77\) 1.33256 + 6.05510i 0.151860 + 0.690043i
\(78\) 0 0
\(79\) 1.23317 0.138743 0.0693714 0.997591i \(-0.477901\pi\)
0.0693714 + 0.997591i \(0.477901\pi\)
\(80\) −2.64799 4.58645i −0.296054 0.512780i
\(81\) 0 0
\(82\) −5.48493 3.16673i −0.605709 0.349706i
\(83\) 0.518739 + 0.898482i 0.0569390 + 0.0986213i 0.893090 0.449878i \(-0.148533\pi\)
−0.836151 + 0.548499i \(0.815199\pi\)
\(84\) 0 0
\(85\) −1.88341 + 3.26217i −0.204285 + 0.353832i
\(86\) −1.23274 + 0.711723i −0.132930 + 0.0767471i
\(87\) 0 0
\(88\) −2.74571 + 4.75572i −0.292694 + 0.506961i
\(89\) −3.73538 + 6.46986i −0.395949 + 0.685804i −0.993222 0.116234i \(-0.962918\pi\)
0.597273 + 0.802038i \(0.296251\pi\)
\(90\) 0 0
\(91\) −0.898482 4.08266i −0.0941866 0.427979i
\(92\) 12.7623 7.36834i 1.33057 0.768203i
\(93\) 0 0
\(94\) 3.66833i 0.378359i
\(95\) 14.7367i 1.51195i
\(96\) 0 0
\(97\) 11.7367 6.77618i 1.19168 0.688017i 0.232993 0.972478i \(-0.425148\pi\)
0.958687 + 0.284462i \(0.0918149\pi\)
\(98\) −4.57759 0.414758i −0.462407 0.0418969i
\(99\) 0 0
\(100\) −4.68291 + 8.11103i −0.468291 + 0.811103i
\(101\) 6.85219 11.8683i 0.681819 1.18094i −0.292607 0.956233i \(-0.594523\pi\)
0.974425 0.224711i \(-0.0721440\pi\)
\(102\) 0 0
\(103\) −4.23669 + 2.44605i −0.417453 + 0.241017i −0.693987 0.719987i \(-0.744148\pi\)
0.276534 + 0.961004i \(0.410814\pi\)
\(104\) 1.85130 3.20655i 0.181535 0.314428i
\(105\) 0 0
\(106\) −3.29949 5.71489i −0.320475 0.555079i
\(107\) −2.12487 1.22679i −0.205419 0.118599i 0.393762 0.919213i \(-0.371173\pi\)
−0.599180 + 0.800614i \(0.704507\pi\)
\(108\) 0 0
\(109\) −2.16784 3.75481i −0.207641 0.359645i 0.743330 0.668925i \(-0.233245\pi\)
−0.950971 + 0.309280i \(0.899912\pi\)
\(110\) 5.09633 0.485916
\(111\) 0 0
\(112\) 2.85327 + 3.12349i 0.269609 + 0.295142i
\(113\) −6.20086 3.58007i −0.583328 0.336784i 0.179127 0.983826i \(-0.442673\pi\)
−0.762455 + 0.647042i \(0.776006\pi\)
\(114\) 0 0
\(115\) −26.9432 15.5557i −2.51247 1.45058i
\(116\) 4.96812 2.86834i 0.461278 0.266319i
\(117\) 0 0
\(118\) 1.42800i 0.131458i
\(119\) 0.909265 2.86834i 0.0833522 0.262941i
\(120\) 0 0
\(121\) −2.75429 4.77056i −0.250390 0.433688i
\(122\) 2.63085 0.238186
\(123\) 0 0
\(124\) 11.4820i 1.03111i
\(125\) 3.21226 0.287313
\(126\) 0 0
\(127\) −17.7065 −1.57120 −0.785601 0.618733i \(-0.787646\pi\)
−0.785601 + 0.618733i \(0.787646\pi\)
\(128\) 11.0999i 0.981098i
\(129\) 0 0
\(130\) −3.43621 −0.301375
\(131\) 6.80228 + 11.7819i 0.594318 + 1.02939i 0.993643 + 0.112579i \(0.0359113\pi\)
−0.399325 + 0.916810i \(0.630755\pi\)
\(132\) 0 0
\(133\) 2.53014 + 11.4968i 0.219391 + 0.996902i
\(134\) 7.06972i 0.610731i
\(135\) 0 0
\(136\) 2.30807 1.33256i 0.197915 0.114266i
\(137\) −8.79893 5.08007i −0.751744 0.434019i 0.0745799 0.997215i \(-0.476238\pi\)
−0.826324 + 0.563196i \(0.809572\pi\)
\(138\) 0 0
\(139\) 3.33821 + 1.92731i 0.283143 + 0.163473i 0.634845 0.772639i \(-0.281064\pi\)
−0.351703 + 0.936112i \(0.614397\pi\)
\(140\) 4.15429 13.1050i 0.351102 1.10758i
\(141\) 0 0
\(142\) −4.19798 −0.352286
\(143\) −1.85130 3.20655i −0.154814 0.268145i
\(144\) 0 0
\(145\) −10.4884 6.05551i −0.871018 0.502882i
\(146\) −3.50734 6.07489i −0.290270 0.502762i
\(147\) 0 0
\(148\) 4.05378 7.02135i 0.333219 0.577152i
\(149\) −4.39947 + 2.54003i −0.360418 + 0.208088i −0.669264 0.743024i \(-0.733391\pi\)
0.308846 + 0.951112i \(0.400057\pi\)
\(150\) 0 0
\(151\) −9.15277 + 15.8531i −0.744842 + 1.29010i 0.205427 + 0.978672i \(0.434142\pi\)
−0.950269 + 0.311431i \(0.899192\pi\)
\(152\) −5.21329 + 9.02968i −0.422854 + 0.732404i
\(153\) 0 0
\(154\) −3.97590 + 0.874988i −0.320387 + 0.0705085i
\(155\) −20.9926 + 12.1201i −1.68617 + 0.973510i
\(156\) 0 0
\(157\) 3.31208i 0.264333i 0.991228 + 0.132166i \(0.0421933\pi\)
−0.991228 + 0.132166i \(0.957807\pi\)
\(158\) 0.809727i 0.0644184i
\(159\) 0 0
\(160\) 16.4548 9.50018i 1.30087 0.751055i
\(161\) 23.6905 + 7.50989i 1.86708 + 0.591863i
\(162\) 0 0
\(163\) 1.14673 1.98619i 0.0898185 0.155570i −0.817616 0.575764i \(-0.804705\pi\)
0.907434 + 0.420194i \(0.138038\pi\)
\(164\) −7.56619 + 13.1050i −0.590820 + 1.02333i
\(165\) 0 0
\(166\) −0.589962 + 0.340615i −0.0457899 + 0.0264368i
\(167\) −1.33256 + 2.30807i −0.103117 + 0.178604i −0.912967 0.408033i \(-0.866215\pi\)
0.809850 + 0.586636i \(0.199548\pi\)
\(168\) 0 0
\(169\) −5.25176 9.09631i −0.403981 0.699716i
\(170\) −2.14201 1.23669i −0.164284 0.0948496i
\(171\) 0 0
\(172\) 1.70051 + 2.94536i 0.129662 + 0.224582i
\(173\) 2.56530 0.195036 0.0975182 0.995234i \(-0.468910\pi\)
0.0975182 + 0.995234i \(0.468910\pi\)
\(174\) 0 0
\(175\) −15.4256 + 3.39476i −1.16607 + 0.256620i
\(176\) 3.24503 + 1.87352i 0.244603 + 0.141222i
\(177\) 0 0
\(178\) −4.24824 2.45272i −0.318419 0.183839i
\(179\) 11.9828 6.91827i 0.895636 0.517096i 0.0198545 0.999803i \(-0.493680\pi\)
0.875782 + 0.482707i \(0.160346\pi\)
\(180\) 0 0
\(181\) 4.74008i 0.352328i 0.984361 + 0.176164i \(0.0563688\pi\)
−0.984361 + 0.176164i \(0.943631\pi\)
\(182\) 2.68076 0.589962i 0.198711 0.0437309i
\(183\) 0 0
\(184\) 11.0060 + 19.0630i 0.811376 + 1.40534i
\(185\) −17.1163 −1.25841
\(186\) 0 0
\(187\) 2.66513i 0.194893i
\(188\) −8.76466 −0.639228
\(189\) 0 0
\(190\) 9.67641 0.702001
\(191\) 8.34338i 0.603706i −0.953355 0.301853i \(-0.902395\pi\)
0.953355 0.301853i \(-0.0976051\pi\)
\(192\) 0 0
\(193\) −17.8442 −1.28446 −0.642229 0.766513i \(-0.721990\pi\)
−0.642229 + 0.766513i \(0.721990\pi\)
\(194\) 4.44938 + 7.70655i 0.319447 + 0.553298i
\(195\) 0 0
\(196\) −0.990974 + 10.9371i −0.0707838 + 0.781225i
\(197\) 15.1102i 1.07656i −0.842767 0.538279i \(-0.819075\pi\)
0.842767 0.538279i \(-0.180925\pi\)
\(198\) 0 0
\(199\) −7.50000 + 4.33013i −0.531661 + 0.306955i −0.741693 0.670740i \(-0.765977\pi\)
0.210032 + 0.977695i \(0.432643\pi\)
\(200\) −12.1154 6.99483i −0.856688 0.494609i
\(201\) 0 0
\(202\) 7.79300 + 4.49929i 0.548313 + 0.316569i
\(203\) 9.22223 + 2.92345i 0.647274 + 0.205186i
\(204\) 0 0
\(205\) 31.9468 2.23126
\(206\) −1.60613 2.78190i −0.111904 0.193824i
\(207\) 0 0
\(208\) −2.18797 1.26322i −0.151708 0.0875887i
\(209\) 5.21329 + 9.02968i 0.360611 + 0.624596i
\(210\) 0 0
\(211\) 7.29047 12.6275i 0.501897 0.869310i −0.498101 0.867119i \(-0.665969\pi\)
0.999998 0.00219128i \(-0.000697506\pi\)
\(212\) −13.6545 + 7.88341i −0.937793 + 0.541435i
\(213\) 0 0
\(214\) 0.805537 1.39523i 0.0550654 0.0953760i
\(215\) 3.59002 6.21810i 0.244838 0.424071i
\(216\) 0 0
\(217\) 14.2965 13.0597i 0.970510 0.886552i
\(218\) 2.46548 1.42345i 0.166984 0.0964080i
\(219\) 0 0
\(220\) 12.1766i 0.820943i
\(221\) 1.79696i 0.120877i
\(222\) 0 0
\(223\) −9.16531 + 5.29159i −0.613754 + 0.354351i −0.774433 0.632655i \(-0.781965\pi\)
0.160679 + 0.987007i \(0.448632\pi\)
\(224\) −11.2061 + 10.2367i −0.748741 + 0.683967i
\(225\) 0 0
\(226\) 2.35075 4.07161i 0.156369 0.270839i
\(227\) 3.36199 5.82314i 0.223143 0.386495i −0.732618 0.680640i \(-0.761702\pi\)
0.955761 + 0.294145i \(0.0950350\pi\)
\(228\) 0 0
\(229\) 10.6201 6.13152i 0.701796 0.405182i −0.106220 0.994343i \(-0.533875\pi\)
0.808016 + 0.589161i \(0.200541\pi\)
\(230\) 10.2142 17.6915i 0.673503 1.16654i
\(231\) 0 0
\(232\) 4.28442 + 7.42084i 0.281286 + 0.487202i
\(233\) −4.87268 2.81324i −0.319220 0.184302i 0.331825 0.943341i \(-0.392336\pi\)
−0.651045 + 0.759039i \(0.725669\pi\)
\(234\) 0 0
\(235\) 9.25176 + 16.0245i 0.603518 + 1.04532i
\(236\) 3.41190 0.222096
\(237\) 0 0
\(238\) 1.88341 + 0.597042i 0.122084 + 0.0387005i
\(239\) 13.8213 + 7.97976i 0.894028 + 0.516168i 0.875258 0.483656i \(-0.160692\pi\)
0.0187704 + 0.999824i \(0.494025\pi\)
\(240\) 0 0
\(241\) 3.97338 + 2.29403i 0.255948 + 0.147771i 0.622485 0.782632i \(-0.286123\pi\)
−0.366537 + 0.930403i \(0.619457\pi\)
\(242\) 3.13245 1.80852i 0.201361 0.116256i
\(243\) 0 0
\(244\) 6.28583i 0.402409i
\(245\) 21.0425 9.73317i 1.34436 0.621830i
\(246\) 0 0
\(247\) −3.51507 6.08828i −0.223659 0.387388i
\(248\) 17.1506 1.08906
\(249\) 0 0
\(250\) 2.10923i 0.133400i
\(251\) −13.8042 −0.871314 −0.435657 0.900113i \(-0.643484\pi\)
−0.435657 + 0.900113i \(0.643484\pi\)
\(252\) 0 0
\(253\) 22.0121 1.38389
\(254\) 11.6265i 0.729510i
\(255\) 0 0
\(256\) −8.42609 −0.526631
\(257\) −4.48215 7.76331i −0.279589 0.484262i 0.691694 0.722191i \(-0.256865\pi\)
−0.971283 + 0.237929i \(0.923531\pi\)
\(258\) 0 0
\(259\) 13.3533 2.93869i 0.829732 0.182601i
\(260\) 8.21006i 0.509166i
\(261\) 0 0
\(262\) −7.73623 + 4.46652i −0.477946 + 0.275942i
\(263\) 24.7280 + 14.2767i 1.52479 + 0.880340i 0.999568 + 0.0293774i \(0.00935247\pi\)
0.525226 + 0.850963i \(0.323981\pi\)
\(264\) 0 0
\(265\) 28.8266 + 16.6431i 1.77081 + 1.02238i
\(266\) −7.54905 + 1.66134i −0.462862 + 0.101863i
\(267\) 0 0
\(268\) −16.8915 −1.03181
\(269\) 11.9657 + 20.7251i 0.729559 + 1.26363i 0.957070 + 0.289858i \(0.0936081\pi\)
−0.227510 + 0.973776i \(0.573059\pi\)
\(270\) 0 0
\(271\) 12.6467 + 7.30159i 0.768234 + 0.443540i 0.832244 0.554409i \(-0.187056\pi\)
−0.0640103 + 0.997949i \(0.520389\pi\)
\(272\) −0.909265 1.57489i −0.0551323 0.0954919i
\(273\) 0 0
\(274\) 3.33568 5.77756i 0.201516 0.349035i
\(275\) −12.1154 + 6.99483i −0.730586 + 0.421804i
\(276\) 0 0
\(277\) −11.1915 + 19.3842i −0.672431 + 1.16468i 0.304782 + 0.952422i \(0.401416\pi\)
−0.977213 + 0.212262i \(0.931917\pi\)
\(278\) −1.26551 + 2.19193i −0.0759005 + 0.131463i
\(279\) 0 0
\(280\) 19.5749 + 6.20524i 1.16982 + 0.370834i
\(281\) −10.0517 + 5.80335i −0.599634 + 0.346199i −0.768897 0.639372i \(-0.779194\pi\)
0.169264 + 0.985571i \(0.445861\pi\)
\(282\) 0 0
\(283\) 14.9937i 0.891283i −0.895211 0.445642i \(-0.852976\pi\)
0.895211 0.445642i \(-0.147024\pi\)
\(284\) 10.0301i 0.595179i
\(285\) 0 0
\(286\) 2.10549 1.21560i 0.124500 0.0718801i
\(287\) −24.9233 + 5.48493i −1.47117 + 0.323765i
\(288\) 0 0
\(289\) 7.85327 13.6023i 0.461957 0.800134i
\(290\) 3.97617 6.88693i 0.233489 0.404414i
\(291\) 0 0
\(292\) −14.5146 + 8.38002i −0.849404 + 0.490403i
\(293\) 8.16762 14.1467i 0.477157 0.826461i −0.522500 0.852639i \(-0.675001\pi\)
0.999657 + 0.0261787i \(0.00833389\pi\)
\(294\) 0 0
\(295\) −3.60152 6.23801i −0.209688 0.363191i
\(296\) 10.4877 + 6.05510i 0.609588 + 0.351946i
\(297\) 0 0
\(298\) −1.66784 2.88878i −0.0966153 0.167343i
\(299\) −14.8417 −0.858317
\(300\) 0 0
\(301\) −1.73317 + 5.46743i −0.0998985 + 0.315137i
\(302\) −10.4094 6.00989i −0.598996 0.345831i
\(303\) 0 0
\(304\) 6.16134 + 3.55725i 0.353377 + 0.204022i
\(305\) −11.4925 + 6.63517i −0.658056 + 0.379929i
\(306\) 0 0
\(307\) 3.17340i 0.181115i 0.995891 + 0.0905577i \(0.0288650\pi\)
−0.995891 + 0.0905577i \(0.971135\pi\)
\(308\) 2.09059 + 9.49955i 0.119122 + 0.541287i
\(309\) 0 0
\(310\) −7.95831 13.7842i −0.452001 0.782889i
\(311\) −25.1342 −1.42523 −0.712614 0.701556i \(-0.752489\pi\)
−0.712614 + 0.701556i \(0.752489\pi\)
\(312\) 0 0
\(313\) 18.6441i 1.05383i 0.849919 + 0.526914i \(0.176651\pi\)
−0.849919 + 0.526914i \(0.823349\pi\)
\(314\) −2.17478 −0.122730
\(315\) 0 0
\(316\) 1.93466 0.108833
\(317\) 7.98965i 0.448744i −0.974504 0.224372i \(-0.927967\pi\)
0.974504 0.224372i \(-0.0720330\pi\)
\(318\) 0 0
\(319\) 8.56885 0.479763
\(320\) 0.942037 + 1.63166i 0.0526615 + 0.0912124i
\(321\) 0 0
\(322\) −4.93115 + 15.5557i −0.274802 + 0.866884i
\(323\) 5.06028i 0.281561i
\(324\) 0 0
\(325\) 8.16882 4.71627i 0.453125 0.261612i
\(326\) 1.30417 + 0.752963i 0.0722313 + 0.0417028i
\(327\) 0 0
\(328\) −19.5749 11.3016i −1.08084 0.624025i
\(329\) −9.96901 10.9131i −0.549609 0.601659i
\(330\) 0 0
\(331\) −8.93466 −0.491094 −0.245547 0.969385i \(-0.578967\pi\)
−0.245547 + 0.969385i \(0.578967\pi\)
\(332\) 0.813824 + 1.40958i 0.0446644 + 0.0773610i
\(333\) 0 0
\(334\) −1.51552 0.874988i −0.0829258 0.0478772i
\(335\) 17.8303 + 30.8830i 0.974173 + 1.68732i
\(336\) 0 0
\(337\) −2.12263 + 3.67650i −0.115627 + 0.200272i −0.918030 0.396510i \(-0.870221\pi\)
0.802403 + 0.596782i \(0.203554\pi\)
\(338\) 5.97282 3.44841i 0.324879 0.187569i
\(339\) 0 0
\(340\) −2.95479 + 5.11785i −0.160246 + 0.277554i
\(341\) 8.57528 14.8528i 0.464377 0.804325i
\(342\) 0 0
\(343\) −14.7453 + 11.2061i −0.796169 + 0.605074i
\(344\) −4.39947 + 2.54003i −0.237203 + 0.136949i
\(345\) 0 0
\(346\) 1.68443i 0.0905556i
\(347\) 2.62648i 0.140997i 0.997512 + 0.0704985i \(0.0224590\pi\)
−0.997512 + 0.0704985i \(0.977541\pi\)
\(348\) 0 0
\(349\) 28.1387 16.2459i 1.50623 0.869622i 0.506255 0.862384i \(-0.331029\pi\)
0.999974 0.00723825i \(-0.00230403\pi\)
\(350\) −2.22907 10.1288i −0.119149 0.541407i
\(351\) 0 0
\(352\) −6.72162 + 11.6422i −0.358263 + 0.620531i
\(353\) −11.6921 + 20.2513i −0.622307 + 1.07787i 0.366748 + 0.930321i \(0.380471\pi\)
−0.989055 + 0.147548i \(0.952862\pi\)
\(354\) 0 0
\(355\) 18.3382 10.5876i 0.973291 0.561930i
\(356\) −5.86024 + 10.1502i −0.310592 + 0.537962i
\(357\) 0 0
\(358\) 4.54268 + 7.86815i 0.240088 + 0.415845i
\(359\) 18.4900 + 10.6752i 0.975865 + 0.563416i 0.901019 0.433779i \(-0.142820\pi\)
0.0748455 + 0.997195i \(0.476154\pi\)
\(360\) 0 0
\(361\) 0.398482 + 0.690192i 0.0209728 + 0.0363259i
\(362\) −3.11243 −0.163586
\(363\) 0 0
\(364\) −1.40958 6.40508i −0.0738823 0.335718i
\(365\) 30.6425 + 17.6915i 1.60390 + 0.926014i
\(366\) 0 0
\(367\) −13.4432 7.76146i −0.701731 0.405145i 0.106261 0.994338i \(-0.466112\pi\)
−0.807992 + 0.589194i \(0.799446\pi\)
\(368\) 13.0075 7.50989i 0.678064 0.391480i
\(369\) 0 0
\(370\) 11.2389i 0.584283i
\(371\) −25.3466 8.03486i −1.31593 0.417149i
\(372\) 0 0
\(373\) 11.6764 + 20.2241i 0.604582 + 1.04717i 0.992117 + 0.125311i \(0.0399930\pi\)
−0.387536 + 0.921855i \(0.626674\pi\)
\(374\) 1.74998 0.0904891
\(375\) 0 0
\(376\) 13.0917i 0.675153i
\(377\) −5.77756 −0.297559
\(378\) 0 0
\(379\) 2.53871 0.130405 0.0652024 0.997872i \(-0.479231\pi\)
0.0652024 + 0.997872i \(0.479231\pi\)
\(380\) 23.1196i 1.18601i
\(381\) 0 0
\(382\) 5.47843 0.280301
\(383\) −8.10207 14.0332i −0.413996 0.717063i 0.581326 0.813671i \(-0.302534\pi\)
−0.995323 + 0.0966078i \(0.969201\pi\)
\(384\) 0 0
\(385\) 15.1613 13.8497i 0.772693 0.705848i
\(386\) 11.7169i 0.596374i
\(387\) 0 0
\(388\) 18.4131 10.6308i 0.934783 0.539697i
\(389\) −19.3410 11.1665i −0.980626 0.566165i −0.0781671 0.996940i \(-0.524907\pi\)
−0.902459 + 0.430775i \(0.858240\pi\)
\(390\) 0 0
\(391\) −9.25176 5.34150i −0.467881 0.270131i
\(392\) −16.3367 1.48021i −0.825130 0.0747619i
\(393\) 0 0
\(394\) 9.92167 0.499847
\(395\) −2.04218 3.53717i −0.102753 0.177974i
\(396\) 0 0
\(397\) 28.3116 + 16.3457i 1.42092 + 0.820367i 0.996377 0.0850420i \(-0.0271025\pi\)
0.424540 + 0.905409i \(0.360436\pi\)
\(398\) −2.84325 4.92465i −0.142519 0.246851i
\(399\) 0 0
\(400\) −4.77287 + 8.26685i −0.238643 + 0.413343i
\(401\) 25.0515 14.4635i 1.25101 0.722272i 0.279701 0.960087i \(-0.409765\pi\)
0.971310 + 0.237815i \(0.0764313\pi\)
\(402\) 0 0
\(403\) −5.78190 + 10.0145i −0.288017 + 0.498860i
\(404\) 10.7501 18.6196i 0.534835 0.926362i
\(405\) 0 0
\(406\) −1.91959 + 6.05551i −0.0952679 + 0.300530i
\(407\) 10.4877 6.05510i 0.519858 0.300140i
\(408\) 0 0
\(409\) 1.05082i 0.0519598i 0.999662 + 0.0259799i \(0.00827059\pi\)
−0.999662 + 0.0259799i \(0.991729\pi\)
\(410\) 20.9769i 1.03597i
\(411\) 0 0
\(412\) −6.64673 + 3.83749i −0.327461 + 0.189060i
\(413\) 3.88073 + 4.24824i 0.190958 + 0.209042i
\(414\) 0 0
\(415\) 1.71810 2.97584i 0.0843384 0.146078i
\(416\) 4.53206 7.84976i 0.222203 0.384866i
\(417\) 0 0
\(418\) −5.92908 + 3.42315i −0.290001 + 0.167432i
\(419\) −1.56060 + 2.70304i −0.0762402 + 0.132052i −0.901625 0.432519i \(-0.857625\pi\)
0.825385 + 0.564571i \(0.190958\pi\)
\(420\) 0 0
\(421\) 4.35327 + 7.54009i 0.212166 + 0.367482i 0.952392 0.304876i \(-0.0986150\pi\)
−0.740226 + 0.672358i \(0.765282\pi\)
\(422\) 8.29145 + 4.78707i 0.403621 + 0.233031i
\(423\) 0 0
\(424\) −11.7754 20.3956i −0.571864 0.990497i
\(425\) 6.78952 0.329340
\(426\) 0 0
\(427\) 7.82665 7.14957i 0.378758 0.345992i
\(428\) −3.33360 1.92465i −0.161136 0.0930316i
\(429\) 0 0
\(430\) 4.08293 + 2.35728i 0.196897 + 0.113678i
\(431\) −23.6279 + 13.6416i −1.13811 + 0.657090i −0.945963 0.324275i \(-0.894880\pi\)
−0.192151 + 0.981365i \(0.561546\pi\)
\(432\) 0 0
\(433\) 12.8711i 0.618547i 0.950973 + 0.309274i \(0.100086\pi\)
−0.950973 + 0.309274i \(0.899914\pi\)
\(434\) 8.57528 + 9.38738i 0.411627 + 0.450609i
\(435\) 0 0
\(436\) −3.40101 5.89073i −0.162879 0.282115i
\(437\) 41.7944 1.99930
\(438\) 0 0
\(439\) 18.4445i 0.880306i −0.897923 0.440153i \(-0.854924\pi\)
0.897923 0.440153i \(-0.145076\pi\)
\(440\) 18.1880 0.867081
\(441\) 0 0
\(442\) −1.17992 −0.0561233
\(443\) 2.87000i 0.136358i −0.997673 0.0681790i \(-0.978281\pi\)
0.997673 0.0681790i \(-0.0217189\pi\)
\(444\) 0 0
\(445\) 24.7437 1.17296
\(446\) −3.47457 6.01813i −0.164526 0.284967i
\(447\) 0 0
\(448\) −1.01507 1.11120i −0.0479575 0.0524992i
\(449\) 1.81675i 0.0857380i −0.999081 0.0428690i \(-0.986350\pi\)
0.999081 0.0428690i \(-0.0136498\pi\)
\(450\) 0 0
\(451\) −19.5749 + 11.3016i −0.921746 + 0.532170i
\(452\) −9.72821 5.61659i −0.457577 0.264182i
\(453\) 0 0
\(454\) 3.82359 + 2.20755i 0.179450 + 0.103605i
\(455\) −10.2226 + 9.33821i −0.479241 + 0.437782i
\(456\) 0 0
\(457\) 6.15575 0.287954 0.143977 0.989581i \(-0.454011\pi\)
0.143977 + 0.989581i \(0.454011\pi\)
\(458\) 4.02608 + 6.97338i 0.188126 + 0.325844i
\(459\) 0 0
\(460\) −42.2699 24.4045i −1.97084 1.13787i
\(461\) −8.52537 14.7664i −0.397066 0.687739i 0.596296 0.802764i \(-0.296638\pi\)
−0.993363 + 0.115026i \(0.963305\pi\)
\(462\) 0 0
\(463\) −14.7065 + 25.4725i −0.683471 + 1.18381i 0.290443 + 0.956892i \(0.406197\pi\)
−0.973915 + 0.226915i \(0.927136\pi\)
\(464\) 5.06356 2.92345i 0.235070 0.135718i
\(465\) 0 0
\(466\) 1.84723 3.19950i 0.0855713 0.148214i
\(467\) 13.5590 23.4849i 0.627437 1.08675i −0.360627 0.932710i \(-0.617437\pi\)
0.988064 0.154043i \(-0.0492294\pi\)
\(468\) 0 0
\(469\) −19.2126 21.0321i −0.887155 0.971171i
\(470\) −10.5220 + 6.07489i −0.485345 + 0.280214i
\(471\) 0 0
\(472\) 5.09633i 0.234578i
\(473\) 5.08007i 0.233582i
\(474\) 0 0
\(475\) −23.0035 + 13.2811i −1.05547 + 0.609378i
\(476\) 1.42650 4.50000i 0.0653835 0.206257i
\(477\) 0 0
\(478\) −5.23967 + 9.07538i −0.239657 + 0.415098i
\(479\) 10.7784 18.6688i 0.492480 0.853000i −0.507483 0.861662i \(-0.669424\pi\)
0.999962 + 0.00866176i \(0.00275716\pi\)
\(480\) 0 0
\(481\) −7.07138 + 4.08266i −0.322427 + 0.186153i
\(482\) −1.50631 + 2.60900i −0.0686104 + 0.118837i
\(483\) 0 0
\(484\) −4.32106 7.48430i −0.196412 0.340195i
\(485\) −38.8728 22.4432i −1.76512 1.01909i
\(486\) 0 0
\(487\) 7.29047 + 12.6275i 0.330363 + 0.572205i 0.982583 0.185825i \(-0.0594956\pi\)
−0.652220 + 0.758029i \(0.726162\pi\)
\(488\) 9.38910 0.425025
\(489\) 0 0
\(490\) 6.39100 + 13.8170i 0.288716 + 0.624187i
\(491\) 0.245174 + 0.141551i 0.0110645 + 0.00638811i 0.505522 0.862814i \(-0.331300\pi\)
−0.494458 + 0.869202i \(0.664633\pi\)
\(492\) 0 0
\(493\) −3.60152 2.07934i −0.162204 0.0936486i
\(494\) 3.99769 2.30807i 0.179864 0.103845i
\(495\) 0 0
\(496\) 11.7026i 0.525461i
\(497\) −12.4888 + 11.4084i −0.560198 + 0.511736i
\(498\) 0 0
\(499\) −6.15277 10.6569i −0.275436 0.477069i 0.694809 0.719194i \(-0.255489\pi\)
−0.970245 + 0.242125i \(0.922155\pi\)
\(500\) 5.03955 0.225375
\(501\) 0 0
\(502\) 9.06412i 0.404552i
\(503\) 1.78425 0.0795559 0.0397779 0.999209i \(-0.487335\pi\)
0.0397779 + 0.999209i \(0.487335\pi\)
\(504\) 0 0
\(505\) −45.3900 −2.01983
\(506\) 14.4536i 0.642540i
\(507\) 0 0
\(508\) −27.7789 −1.23249
\(509\) −19.5362 33.8378i −0.865928 1.49983i −0.866122 0.499832i \(-0.833395\pi\)
0.000194027 1.00000i \(-0.499938\pi\)
\(510\) 0 0
\(511\) −26.9432 8.54100i −1.19190 0.377832i
\(512\) 16.6670i 0.736583i
\(513\) 0 0
\(514\) 5.09755 2.94307i 0.224843 0.129813i
\(515\) 14.0322 + 8.10152i 0.618334 + 0.356996i
\(516\) 0 0
\(517\) −11.3378 6.54585i −0.498634 0.287886i
\(518\) 1.92960 + 8.76803i 0.0847820 + 0.385245i
\(519\) 0 0
\(520\) −12.2633 −0.537782
\(521\) 10.1814 + 17.6347i 0.446056 + 0.772591i 0.998125 0.0612072i \(-0.0194950\pi\)
−0.552070 + 0.833798i \(0.686162\pi\)
\(522\) 0 0
\(523\) 1.24066 + 0.716293i 0.0542501 + 0.0313213i 0.526880 0.849940i \(-0.323362\pi\)
−0.472630 + 0.881261i \(0.656695\pi\)
\(524\) 10.6718 + 18.4840i 0.466198 + 0.807478i
\(525\) 0 0
\(526\) −9.37439 + 16.2369i −0.408743 + 0.707963i
\(527\) −7.20844 + 4.16179i −0.314005 + 0.181291i
\(528\) 0 0
\(529\) 32.6171 56.4945i 1.41814 2.45628i
\(530\) −10.9282 + 18.9282i −0.474690 + 0.822187i
\(531\) 0 0
\(532\) 3.96941 + 18.0368i 0.172096 + 0.781994i
\(533\) 13.1984 7.62010i 0.571686 0.330063i
\(534\) 0 0
\(535\) 8.12647i 0.351338i
\(536\) 25.2308i 1.08980i
\(537\) 0 0
\(538\) −13.6085 + 7.85690i −0.586706 + 0.338735i
\(539\) −9.45027 + 13.4079i −0.407052 + 0.577520i
\(540\) 0 0
\(541\) 5.04521 8.73856i 0.216910 0.375700i −0.736951 0.675946i \(-0.763735\pi\)
0.953862 + 0.300246i \(0.0970687\pi\)
\(542\) −4.79437 + 8.30410i −0.205936 + 0.356692i
\(543\) 0 0
\(544\) 5.65024 3.26217i 0.242252 0.139864i
\(545\) −7.18005 + 12.4362i −0.307559 + 0.532709i
\(546\) 0 0
\(547\) −3.65024 6.32240i −0.156073 0.270326i 0.777376 0.629036i \(-0.216550\pi\)
−0.933449 + 0.358710i \(0.883217\pi\)
\(548\) −13.8042 7.96986i −0.589686 0.340456i
\(549\) 0 0
\(550\) −4.59295 7.95521i −0.195844 0.339211i
\(551\) 16.2697 0.693112
\(552\) 0 0
\(553\) 2.20051 + 2.40890i 0.0935750 + 0.102437i
\(554\) −12.7281 7.34855i −0.540764 0.312210i
\(555\) 0 0
\(556\) 5.23714 + 3.02367i 0.222104 + 0.128232i
\(557\) 19.7970 11.4298i 0.838828 0.484297i −0.0180379 0.999837i \(-0.505742\pi\)
0.856866 + 0.515540i \(0.172409\pi\)
\(558\) 0 0
\(559\) 3.42524i 0.144872i
\(560\) 4.23410 13.3568i 0.178923 0.564427i
\(561\) 0 0
\(562\) −3.81060 6.60015i −0.160740 0.278410i
\(563\) −21.1096 −0.889663 −0.444832 0.895614i \(-0.646736\pi\)
−0.444832 + 0.895614i \(0.646736\pi\)
\(564\) 0 0
\(565\) 23.7149i 0.997694i
\(566\) 9.84517 0.413824
\(567\) 0 0
\(568\) −14.9819 −0.628629
\(569\) 26.4536i 1.10899i 0.832186 + 0.554496i \(0.187089\pi\)
−0.832186 + 0.554496i \(0.812911\pi\)
\(570\) 0 0
\(571\) 12.0301 0.503446 0.251723 0.967799i \(-0.419003\pi\)
0.251723 + 0.967799i \(0.419003\pi\)
\(572\) −2.90441 5.03059i −0.121440 0.210340i
\(573\) 0 0
\(574\) −3.60152 16.3651i −0.150324 0.683067i
\(575\) 56.0767i 2.33856i
\(576\) 0 0
\(577\) −31.9055 + 18.4207i −1.32824 + 0.766862i −0.985028 0.172395i \(-0.944850\pi\)
−0.343216 + 0.939257i \(0.611516\pi\)
\(578\) 8.93153 + 5.15662i 0.371503 + 0.214487i
\(579\) 0 0
\(580\) −16.4548 9.50018i −0.683248 0.394473i
\(581\) −0.829458 + 2.61659i −0.0344117 + 0.108554i
\(582\) 0 0
\(583\) −23.5508 −0.975374
\(584\) −12.5172 21.6804i −0.517964 0.897140i
\(585\) 0 0
\(586\) 9.28903 + 5.36302i 0.383726 + 0.221544i
\(587\) −14.3856 24.9166i −0.593758 1.02842i −0.993721 0.111887i \(-0.964310\pi\)
0.399963 0.916531i \(-0.369023\pi\)
\(588\) 0 0
\(589\) 16.2819 28.2011i 0.670884 1.16200i
\(590\) 4.09601 2.36483i 0.168630 0.0973585i
\(591\) 0 0
\(592\) 4.13166 7.15624i 0.169810 0.294120i
\(593\) −5.29159 + 9.16531i −0.217300 + 0.376374i −0.953982 0.299865i \(-0.903058\pi\)
0.736682 + 0.676240i \(0.236392\pi\)
\(594\) 0 0
\(595\) −9.73317 + 2.14201i −0.399021 + 0.0878137i
\(596\) −6.90210 + 3.98493i −0.282721 + 0.163229i
\(597\) 0 0
\(598\) 9.74535i 0.398517i
\(599\) 18.1927i 0.743333i −0.928366 0.371666i \(-0.878786\pi\)
0.928366 0.371666i \(-0.121214\pi\)
\(600\) 0 0
\(601\) −22.8719 + 13.2051i −0.932963 + 0.538646i −0.887747 0.460331i \(-0.847731\pi\)
−0.0452152 + 0.998977i \(0.514397\pi\)
\(602\) −3.59002 1.13804i −0.146318 0.0463829i
\(603\) 0 0
\(604\) −14.3593 + 24.8711i −0.584272 + 1.01199i
\(605\) −9.12241 + 15.8005i −0.370879 + 0.642381i
\(606\) 0 0
\(607\) 21.6312 12.4888i 0.877983 0.506904i 0.00799043 0.999968i \(-0.497457\pi\)
0.869993 + 0.493064i \(0.164123\pi\)
\(608\) −12.7623 + 22.1050i −0.517581 + 0.896477i
\(609\) 0 0
\(610\) −4.35679 7.54618i −0.176401 0.305536i
\(611\) 7.64450 + 4.41355i 0.309263 + 0.178553i
\(612\) 0 0
\(613\) 7.05631 + 12.2219i 0.285002 + 0.493637i 0.972610 0.232445i \(-0.0746725\pi\)
−0.687608 + 0.726082i \(0.741339\pi\)
\(614\) −2.08372 −0.0840920
\(615\) 0 0
\(616\) −14.1894 + 3.12270i −0.571707 + 0.125817i
\(617\) −12.6669 7.31324i −0.509950 0.294420i 0.222863 0.974850i \(-0.428460\pi\)
−0.732813 + 0.680430i \(0.761793\pi\)
\(618\) 0 0
\(619\) 22.9880 + 13.2721i 0.923965 + 0.533452i 0.884898 0.465785i \(-0.154228\pi\)
0.0390674 + 0.999237i \(0.487561\pi\)
\(620\) −32.9343 + 19.0146i −1.32267 + 0.763645i
\(621\) 0 0
\(622\) 16.5036i 0.661734i
\(623\) −19.3038 + 4.24824i −0.773391 + 0.170202i
\(624\) 0 0
\(625\) 9.60503 + 16.6364i 0.384201 + 0.665456i
\(626\) −12.2421 −0.489293
\(627\) 0 0
\(628\) 5.19615i 0.207349i
\(629\) −5.87738 −0.234347
\(630\) 0 0
\(631\) −8.20304 −0.326558 −0.163279 0.986580i \(-0.552207\pi\)
−0.163279 + 0.986580i \(0.552207\pi\)
\(632\) 2.88979i 0.114950i
\(633\) 0 0
\(634\) 5.24617 0.208352
\(635\) 29.3227 + 50.7885i 1.16364 + 2.01548i
\(636\) 0 0
\(637\) 6.37186 9.04031i 0.252462 0.358190i
\(638\) 5.62648i 0.222755i
\(639\) 0 0
\(640\) 31.8382 18.3818i 1.25852 0.726604i
\(641\) 13.8996 + 8.02496i 0.549003 + 0.316967i 0.748720 0.662887i \(-0.230669\pi\)
−0.199717 + 0.979854i \(0.564002\pi\)
\(642\) 0 0
\(643\) −22.8719 13.2051i −0.901978 0.520757i −0.0241366 0.999709i \(-0.507684\pi\)
−0.877841 + 0.478951i \(0.841017\pi\)
\(644\) 37.1669 + 11.7819i 1.46458 + 0.464272i
\(645\) 0 0
\(646\) 3.32268 0.130729
\(647\) −15.8508 27.4543i −0.623158 1.07934i −0.988894 0.148623i \(-0.952516\pi\)
0.365736 0.930719i \(-0.380817\pi\)
\(648\) 0 0
\(649\) 4.41355 + 2.54817i 0.173247 + 0.100024i
\(650\) 3.09680 + 5.36382i 0.121467 + 0.210386i
\(651\) 0 0
\(652\) 1.79904 3.11603i 0.0704558 0.122033i
\(653\) −11.5096 + 6.64506i −0.450405 + 0.260041i −0.708001 0.706211i \(-0.750403\pi\)
0.257596 + 0.966253i \(0.417070\pi\)
\(654\) 0 0
\(655\) 22.5297 39.0226i 0.880308 1.52474i
\(656\) −7.71155 + 13.3568i −0.301085 + 0.521495i
\(657\) 0 0
\(658\) 7.16576 6.54585i 0.279351 0.255184i
\(659\) 31.3609 18.1062i 1.22165 0.705319i 0.256379 0.966576i \(-0.417470\pi\)
0.965269 + 0.261257i \(0.0841372\pi\)
\(660\) 0 0
\(661\) 50.7930i 1.97562i 0.155674 + 0.987809i \(0.450245\pi\)
−0.155674 + 0.987809i \(0.549755\pi\)
\(662\) 5.86668i 0.228015i
\(663\) 0 0
\(664\) −2.10549 + 1.21560i −0.0817087 + 0.0471745i
\(665\) 28.7869 26.2965i 1.11631 1.01973i
\(666\) 0 0
\(667\) 17.1739 29.7460i 0.664975 1.15177i
\(668\) −2.09059 + 3.62101i −0.0808874 + 0.140101i
\(669\) 0 0
\(670\) −20.2784 + 11.7077i −0.783422 + 0.452309i
\(671\) 4.69455 8.13120i 0.181231 0.313902i
\(672\) 0 0
\(673\) −1.66432 2.88269i −0.0641550 0.111120i 0.832164 0.554530i \(-0.187102\pi\)
−0.896319 + 0.443410i \(0.853769\pi\)
\(674\) −2.41407 1.39376i −0.0929864 0.0536857i
\(675\) 0 0
\(676\) −8.23922 14.2707i −0.316893 0.548875i
\(677\) 19.9380 0.766280 0.383140 0.923690i \(-0.374843\pi\)
0.383140 + 0.923690i \(0.374843\pi\)
\(678\) 0 0
\(679\) 34.1799 + 10.8350i 1.31171 + 0.415810i
\(680\) −7.64450 4.41355i −0.293153 0.169252i
\(681\) 0 0
\(682\) 9.75267 + 5.63070i 0.373449 + 0.215611i
\(683\) 24.8234 14.3318i 0.949843 0.548392i 0.0568107 0.998385i \(-0.481907\pi\)
0.893032 + 0.449993i \(0.148574\pi\)
\(684\) 0 0
\(685\) 33.6512i 1.28574i
\(686\) −7.35817 9.68204i −0.280936 0.369662i
\(687\) 0 0
\(688\) 1.73317 + 3.00195i 0.0660766 + 0.114448i
\(689\) 15.8792 0.604948
\(690\) 0 0
\(691\) 20.3674i 0.774812i 0.921909 + 0.387406i \(0.126629\pi\)
−0.921909 + 0.387406i \(0.873371\pi\)
\(692\) 4.02458 0.152991
\(693\) 0 0
\(694\) −1.72460 −0.0654650
\(695\) 12.7668i 0.484273i
\(696\) 0 0
\(697\) 10.9699 0.415513
\(698\) 10.6674 + 18.4764i 0.403766 + 0.699343i
\(699\) 0 0
\(700\) −24.2005 + 5.32587i −0.914693 + 0.201299i
\(701\) 49.1172i 1.85513i −0.373659 0.927566i \(-0.621897\pi\)
0.373659 0.927566i \(-0.378103\pi\)
\(702\) 0 0
\(703\) 19.9131 11.4968i 0.751037 0.433611i
\(704\) −1.15444 0.666515i −0.0435095 0.0251202i
\(705\) 0 0
\(706\) −13.2974 7.67727i −0.500455 0.288938i
\(707\) 35.4110 7.79300i 1.33177 0.293086i
\(708\) 0 0
\(709\) 23.3658 0.877522 0.438761 0.898604i \(-0.355418\pi\)
0.438761 + 0.898604i \(0.355418\pi\)
\(710\) 6.95201 + 12.0412i 0.260904 + 0.451900i
\(711\) 0 0
\(712\) −15.1613 8.75340i −0.568195 0.328048i
\(713\) −34.3735 59.5367i −1.28730 2.22967i
\(714\) 0 0
\(715\) −6.13166 + 10.6203i −0.229311 + 0.397178i
\(716\) 18.7992 10.8537i 0.702559 0.405623i
\(717\) 0 0
\(718\) −7.00956 + 12.1409i −0.261594 + 0.453095i
\(719\) −6.33345 + 10.9699i −0.236198 + 0.409107i −0.959620 0.281299i \(-0.909235\pi\)
0.723422 + 0.690406i \(0.242568\pi\)
\(720\) 0 0
\(721\) −12.3382 3.91121i −0.459499 0.145661i
\(722\) −0.453194 + 0.261652i −0.0168661 + 0.00973767i
\(723\) 0 0
\(724\) 7.43648i 0.276374i
\(725\) 21.8295i 0.810728i
\(726\) 0 0
\(727\) 2.34172 1.35199i 0.0868495 0.0501426i −0.455946 0.890007i \(-0.650699\pi\)
0.542796 + 0.839865i \(0.317366\pi\)
\(728\) 9.56723 2.10549i 0.354585 0.0780345i
\(729\) 0 0
\(730\) −11.6166 + 20.1205i −0.429949 + 0.744694i
\(731\) 1.23274 2.13517i 0.0455946 0.0789721i
\(732\) 0 0
\(733\) −18.8869 + 10.9044i −0.697605 + 0.402762i −0.806455 0.591296i \(-0.798616\pi\)
0.108850 + 0.994058i \(0.465283\pi\)
\(734\) 5.09633 8.82710i 0.188109 0.325814i
\(735\) 0 0
\(736\) 26.9432 + 46.6671i 0.993141 + 1.72017i
\(737\) −21.8505 12.6154i −0.804873 0.464694i
\(738\) 0 0
\(739\) −16.0633 27.8225i −0.590899 1.02347i −0.994112 0.108361i \(-0.965440\pi\)
0.403212 0.915107i \(-0.367894\pi\)
\(740\) −26.8529 −0.987131
\(741\) 0 0
\(742\) 5.27585 16.6431i 0.193683 0.610986i
\(743\) −35.7433 20.6364i −1.31129 0.757075i −0.328983 0.944336i \(-0.606706\pi\)
−0.982310 + 0.187261i \(0.940039\pi\)
\(744\) 0 0
\(745\) 14.5714 + 8.41279i 0.533854 + 0.308221i
\(746\) −13.2796 + 7.66697i −0.486200 + 0.280708i
\(747\) 0 0
\(748\) 4.18118i 0.152879i
\(749\) −1.39523 6.33987i −0.0509806 0.231654i
\(750\) 0 0
\(751\) −22.9045 39.6718i −0.835798 1.44764i −0.893379 0.449304i \(-0.851672\pi\)
0.0575810 0.998341i \(-0.481661\pi\)
\(752\) −8.93303 −0.325754
\(753\) 0 0
\(754\) 3.79366i 0.138157i
\(755\) 60.6294 2.20653
\(756\) 0 0
\(757\) 50.3427 1.82974 0.914868 0.403752i \(-0.132294\pi\)
0.914868 + 0.403752i \(0.132294\pi\)
\(758\) 1.66697i 0.0605471i
\(759\) 0 0
\(760\) 34.5337 1.25267
\(761\) 15.1823 + 26.2965i 0.550358 + 0.953248i 0.998249 + 0.0591594i \(0.0188420\pi\)
−0.447891 + 0.894088i \(0.647825\pi\)
\(762\) 0 0
\(763\) 3.46635 10.9349i 0.125490 0.395868i
\(764\) 13.0895i 0.473562i
\(765\) 0 0
\(766\) 9.21448 5.31999i 0.332933 0.192219i
\(767\) −2.97584 1.71810i −0.107452 0.0620372i
\(768\) 0 0
\(769\) 35.8000 + 20.6692i 1.29098 + 0.745349i 0.978828 0.204683i \(-0.0656163\pi\)
0.312154 + 0.950032i \(0.398950\pi\)
\(770\) 9.09402 + 9.95525i 0.327726 + 0.358762i
\(771\) 0 0
\(772\) −27.9949 −1.00756
\(773\) 6.99754 + 12.1201i 0.251684 + 0.435930i 0.963990 0.265940i \(-0.0856823\pi\)
−0.712305 + 0.701870i \(0.752349\pi\)
\(774\) 0 0
\(775\) 37.8382 + 21.8459i 1.35919 + 0.784728i
\(776\) 15.8792 + 27.5035i 0.570029 + 0.987319i
\(777\) 0 0
\(778\) 7.33216 12.6997i 0.262871 0.455305i
\(779\) −37.1669 + 21.4583i −1.33164 + 0.768824i
\(780\) 0 0
\(781\) −7.49097 + 12.9747i −0.268048 + 0.464273i
\(782\) 3.50734 6.07489i 0.125422 0.217238i
\(783\) 0 0
\(784\) −1.01001 + 11.1473i −0.0360718 + 0.398116i
\(785\) 9.50018 5.48493i 0.339076 0.195766i
\(786\) 0 0
\(787\) 13.4868i 0.480753i 0.970680 + 0.240377i \(0.0772709\pi\)
−0.970680 + 0.240377i \(0.922729\pi\)
\(788\) 23.7056i 0.844478i
\(789\) 0 0
\(790\) 2.32258 1.34094i 0.0826335 0.0477085i
\(791\) −4.07161 18.5012i −0.144770 0.657827i
\(792\) 0 0
\(793\) −3.16531 + 5.48248i −0.112403 + 0.194688i
\(794\) −10.7329 + 18.5900i −0.380897 + 0.659733i
\(795\) 0 0
\(796\) −11.7664 + 6.79332i −0.417048 + 0.240783i
\(797\) −4.15867 + 7.20304i −0.147308 + 0.255145i −0.930232 0.366973i \(-0.880394\pi\)
0.782924 + 0.622118i \(0.213727\pi\)
\(798\) 0 0
\(799\) 3.17686 + 5.50249i 0.112389 + 0.194664i
\(800\) −29.6590 17.1236i −1.04860 0.605411i
\(801\) 0 0
\(802\) 9.49702 + 16.4493i 0.335351 + 0.580846i
\(803\) −25.0343 −0.883443
\(804\) 0 0
\(805\) −17.6915 80.3893i −0.623543 2.83335i
\(806\) −6.57575 3.79651i −0.231621 0.133726i
\(807\) 0 0
\(808\) 27.8120 + 16.0573i 0.978424 + 0.564893i
\(809\) 12.5955 7.27200i 0.442833 0.255670i −0.261965 0.965077i \(-0.584371\pi\)
0.704799 + 0.709407i \(0.251037\pi\)
\(810\) 0 0
\(811\) 41.8287i 1.46880i 0.678715 + 0.734401i \(0.262537\pi\)
−0.678715 + 0.734401i \(0.737463\pi\)
\(812\) 14.4683 + 4.58645i 0.507738 + 0.160953i
\(813\) 0 0
\(814\) 3.97590 + 6.88647i 0.139355 + 0.241371i
\(815\) −7.59609 −0.266079
\(816\) 0 0
\(817\) 9.64553i 0.337454i
\(818\) −0.689991 −0.0241250
\(819\) 0 0
\(820\) 50.1196 1.75025
\(821\) 46.4828i 1.62226i 0.584865 + 0.811131i \(0.301148\pi\)
−0.584865 + 0.811131i \(0.698852\pi\)
\(822\) 0 0
\(823\) 7.73669 0.269684 0.134842 0.990867i \(-0.456947\pi\)
0.134842 + 0.990867i \(0.456947\pi\)
\(824\) −5.73203 9.92817i −0.199685 0.345864i
\(825\) 0 0
\(826\) −2.78948 + 2.54817i −0.0970585 + 0.0886620i
\(827\) 20.8898i 0.726409i 0.931709 + 0.363205i \(0.118317\pi\)
−0.931709 + 0.363205i \(0.881683\pi\)
\(828\) 0 0
\(829\) 41.2282 23.8031i 1.43191 0.826716i 0.434647 0.900601i \(-0.356873\pi\)
0.997267 + 0.0738846i \(0.0235396\pi\)
\(830\) 1.95400 + 1.12814i 0.0678243 + 0.0391584i
\(831\) 0 0
\(832\) 0.778382 + 0.449399i 0.0269855 + 0.0155801i
\(833\) 7.22558 3.34217i 0.250351 0.115799i
\(834\) 0 0
\(835\) 8.82710 0.305475
\(836\) 8.17887 + 14.1662i 0.282872 + 0.489949i
\(837\) 0 0
\(838\) −1.77487 1.02472i −0.0613118 0.0353984i
\(839\) −11.2017 19.4020i −0.386727 0.669831i 0.605280 0.796013i \(-0.293061\pi\)
−0.992007 + 0.126181i \(0.959728\pi\)
\(840\) 0 0
\(841\) −7.81456 + 13.5352i −0.269468 + 0.466732i
\(842\) −4.95098 + 2.85845i −0.170622 + 0.0985087i
\(843\) 0 0
\(844\) 11.4376 19.8106i 0.393700 0.681909i
\(845\) −17.3942 + 30.1277i −0.598380 + 1.03642i
\(846\) 0 0
\(847\) 4.40407 13.8930i 0.151326 0.477368i
\(848\) −13.9168 + 8.03486i −0.477904 + 0.275918i
\(849\) 0 0
\(850\) 4.45814i 0.152913i
\(851\) 48.5431i 1.66404i
\(852\) 0 0
\(853\) −41.9393 + 24.2136i −1.43597 + 0.829060i −0.997567 0.0697173i \(-0.977790\pi\)
−0.438406 + 0.898777i \(0.644457\pi\)
\(854\) 4.69455 + 5.13914i 0.160644 + 0.175858i
\(855\) 0 0
\(856\) 2.87484 4.97937i 0.0982600 0.170191i
\(857\) −24.5327 + 42.4920i −0.838023 + 1.45150i 0.0535230 + 0.998567i \(0.482955\pi\)
−0.891546 + 0.452931i \(0.850378\pi\)
\(858\) 0 0
\(859\) 10.4136 6.01227i 0.355306 0.205136i −0.311714 0.950176i \(-0.600903\pi\)
0.667020 + 0.745040i \(0.267570\pi\)
\(860\) 5.63221 9.75527i 0.192057 0.332652i
\(861\) 0 0
\(862\) −8.95732 15.5145i −0.305088 0.528427i
\(863\) 39.8804 + 23.0250i 1.35754 + 0.783779i 0.989292 0.145947i \(-0.0466229\pi\)
0.368252 + 0.929726i \(0.379956\pi\)
\(864\) 0 0
\(865\) −4.24824 7.35817i −0.144445 0.250185i
\(866\) −8.45145 −0.287192
\(867\) 0 0
\(868\) 22.4291 20.4887i 0.761292 0.695433i
\(869\) 2.50264 + 1.44490i 0.0848961 + 0.0490148i
\(870\) 0 0
\(871\) 14.7327 + 8.50594i 0.499199 + 0.288213i
\(872\) 8.79893 5.08007i 0.297970 0.172033i
\(873\) 0 0
\(874\) 27.4430i 0.928275i
\(875\) 5.73203 + 6.27487i 0.193778 + 0.212129i
\(876\) 0 0
\(877\) −6.73669 11.6683i −0.227482 0.394010i 0.729579 0.683896i \(-0.239716\pi\)
−0.957061 + 0.289886i \(0.906383\pi\)
\(878\) 12.1110 0.408727
\(879\) 0 0
\(880\) 12.4105i 0.418357i
\(881\) −25.5247 −0.859949 −0.429974 0.902841i \(-0.641477\pi\)
−0.429974 + 0.902841i \(0.641477\pi\)
\(882\) 0 0
\(883\) 6.45532 0.217239 0.108619 0.994083i \(-0.465357\pi\)
0.108619 + 0.994083i \(0.465357\pi\)
\(884\) 2.81917i 0.0948189i
\(885\) 0 0
\(886\) 1.88450 0.0633111
\(887\) −16.5604 28.6834i −0.556043 0.963096i −0.997822 0.0659712i \(-0.978985\pi\)
0.441778 0.897124i \(-0.354348\pi\)
\(888\) 0 0
\(889\) −31.5960 34.5882i −1.05970 1.16005i
\(890\) 16.2472i 0.544608i
\(891\) 0 0
\(892\) −14.3790 + 8.30171i −0.481444 + 0.277962i
\(893\) −21.5270 12.4286i −0.720374 0.415908i
\(894\) 0 0
\(895\) −39.6880 22.9139i −1.32662 0.765926i
\(896\) −21.6826 + 19.8069i −0.724366 + 0.661701i
\(897\) 0 0
\(898\) 1.19292 0.0398082
\(899\) −13.3809 23.1764i −0.446278 0.772977i
\(900\) 0 0
\(901\) 9.89848 + 5.71489i 0.329766 + 0.190391i
\(902\) −7.42084 12.8533i −0.247087 0.427967i
\(903\) 0 0
\(904\) 8.38946 14.5310i 0.279029 0.483293i
\(905\) 13.5962 7.84976i 0.451952 0.260935i
\(906\) 0 0
\(907\) −3.10756 + 5.38245i −0.103185 + 0.178721i −0.912995 0.407970i \(-0.866237\pi\)
0.809810 + 0.586692i \(0.199570\pi\)
\(908\) 5.27446 9.13562i 0.175039 0.303176i
\(909\) 0 0
\(910\) −6.13166 6.71234i −0.203262 0.222512i
\(911\) 15.6296 9.02376i 0.517832 0.298970i −0.218215 0.975901i \(-0.570023\pi\)
0.736047 + 0.676930i \(0.236690\pi\)
\(912\) 0 0
\(913\) 2.43121i 0.0804611i
\(914\) 4.04199i 0.133697i
\(915\) 0 0
\(916\) 16.6613 9.61943i 0.550506 0.317835i
\(917\) −10.8768 + 34.3116i −0.359182 + 1.13307i
\(918\) 0 0
\(919\) 4.12913 7.15186i 0.136207 0.235918i −0.789851 0.613299i \(-0.789842\pi\)
0.926058 + 0.377381i \(0.123175\pi\)
\(920\) 36.4529 63.1382i 1.20182 2.08161i
\(921\) 0 0
\(922\) 9.69590 5.59793i 0.319318 0.184358i
\(923\) 5.05080 8.74824i 0.166249 0.287952i
\(924\) 0 0
\(925\) 15.4256 + 26.7180i 0.507192 + 0.878482i
\(926\) −16.7258 9.65662i −0.549642 0.317336i
\(927\) 0 0
\(928\) 10.4884 + 18.1665i 0.344300 + 0.596345i
\(929\) 34.7709 1.14080 0.570399 0.821368i \(-0.306789\pi\)
0.570399 + 0.821368i \(0.306789\pi\)
\(930\) 0 0
\(931\) −17.9432 + 25.4576i −0.588066 + 0.834341i
\(932\) −7.64450 4.41355i −0.250404 0.144571i
\(933\) 0 0
\(934\) 15.4207 + 8.90314i 0.504580 + 0.291320i
\(935\) −7.64450 + 4.41355i −0.250002 + 0.144339i
\(936\) 0 0
\(937\) 51.0703i 1.66839i −0.551466 0.834197i \(-0.685931\pi\)
0.551466 0.834197i \(-0.314069\pi\)
\(938\) 13.8101 12.6154i 0.450915 0.411907i
\(939\) 0 0
\(940\) 14.5146 + 25.1401i 0.473415 + 0.819978i
\(941\) −3.47744 −0.113361 −0.0566807 0.998392i \(-0.518052\pi\)
−0.0566807 + 0.998392i \(0.518052\pi\)
\(942\) 0 0
\(943\) 90.6034i 2.95045i
\(944\) 3.47744 0.113181
\(945\) 0 0
\(946\) −3.33568 −0.108452
\(947\) 14.3401i 0.465989i 0.972478 + 0.232995i \(0.0748525\pi\)
−0.972478 + 0.232995i \(0.925148\pi\)
\(948\) 0 0
\(949\) 16.8794 0.547930
\(950\) −8.72063 15.1046i −0.282935 0.490057i
\(951\) 0 0
\(952\) 6.72162 + 2.13075i 0.217849 + 0.0690581i
\(953\) 7.53697i 0.244147i 0.992521 + 0.122073i \(0.0389543\pi\)
−0.992521 + 0.122073i \(0.961046\pi\)
\(954\) 0 0
\(955\) −23.9317 + 13.8170i −0.774411 + 0.447106i
\(956\) 21.6836 + 12.5190i 0.701298 + 0.404895i
\(957\) 0 0
\(958\) 12.2583 + 7.07735i 0.396049 + 0.228659i
\(959\) −5.77756 26.2530i −0.186567 0.847752i
\(960\) 0 0
\(961\) −22.5638 −0.727864
\(962\) −2.68076 4.64321i −0.0864312 0.149703i
\(963\) 0 0
\(964\) 6.23363 + 3.59899i 0.200772 + 0.115916i
\(965\) 29.5508 + 51.1834i 0.951273 + 1.64765i
\(966\) 0 0
\(967\) 5.80807 10.0599i 0.186775 0.323503i −0.757398 0.652953i \(-0.773530\pi\)
0.944173 + 0.329450i \(0.106863\pi\)
\(968\) 11.1792 6.45434i 0.359314 0.207450i
\(969\) 0 0
\(970\) 14.7367 25.5247i 0.473167 0.819548i
\(971\) −17.7476 + 30.7397i −0.569548 + 0.986485i 0.427063 + 0.904222i \(0.359548\pi\)
−0.996611 + 0.0822636i \(0.973785\pi\)
\(972\) 0 0
\(973\) 2.19193 + 9.96004i 0.0702702 + 0.319304i
\(974\) −8.29145 + 4.78707i −0.265675 + 0.153388i
\(975\) 0 0
\(976\) 6.40659i 0.205070i
\(977\) 32.0094i 1.02407i 0.858964 + 0.512036i \(0.171109\pi\)
−0.858964 + 0.512036i \(0.828891\pi\)
\(978\) 0 0
\(979\) −15.1613 + 8.75340i −0.484559 + 0.279760i
\(980\) 33.0126 15.2699i 1.05455 0.487779i
\(981\) 0 0
\(982\) −0.0929453 + 0.160986i −0.00296600 + 0.00513727i
\(983\) 24.7324 42.8378i 0.788841 1.36631i −0.137837 0.990455i \(-0.544015\pi\)
0.926678 0.375857i \(-0.122652\pi\)
\(984\) 0 0
\(985\) −43.3413 + 25.0231i −1.38097 + 0.797302i
\(986\) 1.36534 2.36483i 0.0434811 0.0753115i
\(987\) 0 0
\(988\) −5.51462 9.55159i −0.175443 0.303877i
\(989\) 17.6350 + 10.1816i 0.560761 + 0.323756i
\(990\) 0 0
\(991\) −8.97590 15.5467i −0.285129 0.493858i 0.687511 0.726174i \(-0.258703\pi\)
−0.972640 + 0.232316i \(0.925370\pi\)
\(992\) 41.9853 1.33303
\(993\) 0 0
\(994\) −7.49097 8.20039i −0.237599 0.260101i
\(995\) 24.8406 + 14.3417i 0.787500 + 0.454663i
\(996\) 0 0
\(997\) 29.0151 + 16.7519i 0.918916 + 0.530537i 0.883289 0.468828i \(-0.155324\pi\)
0.0356272 + 0.999365i \(0.488657\pi\)
\(998\) 6.99754 4.04003i 0.221503 0.127885i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 567.2.i.f.215.4 12
3.2 odd 2 inner 567.2.i.f.215.3 12
7.3 odd 6 567.2.s.f.458.3 12
9.2 odd 6 567.2.s.f.26.3 12
9.4 even 3 189.2.p.d.26.3 12
9.5 odd 6 189.2.p.d.26.4 yes 12
9.7 even 3 567.2.s.f.26.4 12
21.17 even 6 567.2.s.f.458.4 12
63.5 even 6 1323.2.c.d.1322.6 12
63.23 odd 6 1323.2.c.d.1322.5 12
63.31 odd 6 189.2.p.d.80.4 yes 12
63.38 even 6 inner 567.2.i.f.269.3 12
63.40 odd 6 1323.2.c.d.1322.7 12
63.52 odd 6 inner 567.2.i.f.269.4 12
63.58 even 3 1323.2.c.d.1322.8 12
63.59 even 6 189.2.p.d.80.3 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.3 12 9.4 even 3
189.2.p.d.26.4 yes 12 9.5 odd 6
189.2.p.d.80.3 yes 12 63.59 even 6
189.2.p.d.80.4 yes 12 63.31 odd 6
567.2.i.f.215.3 12 3.2 odd 2 inner
567.2.i.f.215.4 12 1.1 even 1 trivial
567.2.i.f.269.3 12 63.38 even 6 inner
567.2.i.f.269.4 12 63.52 odd 6 inner
567.2.s.f.26.3 12 9.2 odd 6
567.2.s.f.26.4 12 9.7 even 3
567.2.s.f.458.3 12 7.3 odd 6
567.2.s.f.458.4 12 21.17 even 6
1323.2.c.d.1322.5 12 63.23 odd 6
1323.2.c.d.1322.6 12 63.5 even 6
1323.2.c.d.1322.7 12 63.40 odd 6
1323.2.c.d.1322.8 12 63.58 even 3