Properties

Label 567.2.s.f.458.3
Level $567$
Weight $2$
Character 567.458
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(26,567)]
 
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([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.s (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: \(\Z[a_1, \ldots, a_{5}]\)
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 458.3
Root \(1.65604 + 0.956115i\) of defining polynomial
Character \(\chi\) \(=\) 567.458
Dual form 567.2.s.f.26.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.568650 - 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} -3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} +2.34338i q^{8} +O(q^{10})\) \(q+(-0.568650 - 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} -3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} +2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} -2.34338i q^{11} +(1.36834 + 0.790014i) q^{13} +(0.373387 - 1.69665i) q^{14} +(-0.799494 + 1.38476i) q^{16} +(0.568650 - 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} +(2.59808 + 4.50000i) q^{20} +(-0.769355 + 1.33256i) q^{22} +9.39331i q^{23} +5.96986 q^{25} +(-0.518739 - 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +(3.16673 - 1.82831i) q^{29} +(6.33821 - 3.65936i) q^{31} +(4.96812 - 2.86834i) q^{32} +(-0.646726 + 0.373387i) q^{34} +(-2.64799 - 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} -2.92155 q^{38} -7.76146i q^{40} +(4.82277 - 8.35327i) q^{41} +(1.08392 + 1.87740i) q^{43} +(-3.18386 + 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} +(-2.79334 + 4.83821i) q^{47} +(-5.72162 + 4.03275i) q^{49} +(-3.39476 - 1.95997i) q^{50} -2.47883i q^{52} +(8.70349 + 5.02496i) q^{53} +7.76146i q^{55} +(-5.91015 + 1.87352i) q^{56} -2.40101 q^{58} +(1.08739 + 1.88341i) q^{59} +(-3.46986 - 2.00333i) q^{61} -4.80563 q^{62} -0.568850 q^{64} +(-4.53206 - 2.61659i) q^{65} +(5.38341 + 9.32435i) q^{67} -1.78425 q^{68} +(-1.23669 + 5.61945i) q^{70} +6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} -3.39331i q^{74} +(-6.04521 - 3.49020i) q^{76} +(5.91015 - 1.87352i) q^{77} +(-0.616587 + 1.06796i) q^{79} +(2.64799 - 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +(-0.518739 - 0.898482i) q^{83} +(-1.88341 + 3.26217i) q^{85} -1.42345i q^{86} +5.49143 q^{88} +(3.73538 + 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +(12.7623 - 7.36834i) q^{92} +(3.17686 - 1.83416i) q^{94} +(-12.7623 + 7.36834i) q^{95} +(-11.7367 + 6.77618i) q^{97} +(4.57759 - 0.414758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.568650 0.328310i −0.402096 0.232150i 0.285292 0.958441i \(-0.407909\pi\)
−0.687388 + 0.726290i \(0.741243\pi\)
\(3\) 0 0
\(4\) −0.784425 1.35866i −0.392212 0.679332i
\(5\) −3.31208 −1.48121 −0.740603 0.671943i \(-0.765460\pi\)
−0.740603 + 0.671943i \(0.765460\pi\)
\(6\) 0 0
\(7\) 0.799494 + 2.52206i 0.302180 + 0.953251i
\(8\) 2.34338i 0.828510i
\(9\) 0 0
\(10\) 1.88341 + 1.08739i 0.595588 + 0.343863i
\(11\) 2.34338i 0.706556i −0.935518 0.353278i \(-0.885067\pi\)
0.935518 0.353278i \(-0.114933\pi\)
\(12\) 0 0
\(13\) 1.36834 + 0.790014i 0.379510 + 0.219110i 0.677605 0.735426i \(-0.263018\pi\)
−0.298095 + 0.954536i \(0.596351\pi\)
\(14\) 0.373387 1.69665i 0.0997919 0.453450i
\(15\) 0 0
\(16\) −0.799494 + 1.38476i −0.199874 + 0.346191i
\(17\) 0.568650 0.984931i 0.137918 0.238881i −0.788790 0.614662i \(-0.789292\pi\)
0.926708 + 0.375781i \(0.122626\pi\)
\(18\) 0 0
\(19\) 3.85327 2.22469i 0.884002 0.510379i 0.0120260 0.999928i \(-0.496172\pi\)
0.871976 + 0.489549i \(0.162839\pi\)
\(20\) 2.59808 + 4.50000i 0.580948 + 1.00623i
\(21\) 0 0
\(22\) −0.769355 + 1.33256i −0.164027 + 0.284103i
\(23\) 9.39331i 1.95864i 0.202317 + 0.979320i \(0.435153\pi\)
−0.202317 + 0.979320i \(0.564847\pi\)
\(24\) 0 0
\(25\) 5.96986 1.19397
\(26\) −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
\(31\) 6.33821 3.65936i 1.13838 0.657241i 0.192347 0.981327i \(-0.438390\pi\)
0.946028 + 0.324086i \(0.105057\pi\)
\(32\) 4.96812 2.86834i 0.878247 0.507056i
\(33\) 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 0.996401 0.0847630i \(-0.0270133\pi\)
−0.571607 + 0.820527i \(0.693680\pi\)
\(38\) −2.92155 −0.473938
\(39\) 0 0
\(40\) 7.76146i 1.22719i
\(41\) 4.82277 8.35327i 0.753189 1.30456i −0.193080 0.981183i \(-0.561848\pi\)
0.946269 0.323379i \(-0.104819\pi\)
\(42\) 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
\(47\) −2.79334 + 4.83821i −0.407450 + 0.705725i −0.994603 0.103751i \(-0.966915\pi\)
0.587153 + 0.809476i \(0.300249\pi\)
\(48\) 0 0
\(49\) −5.72162 + 4.03275i −0.817374 + 0.576107i
\(50\) −3.39476 1.95997i −0.480092 0.277181i
\(51\) 0 0
\(52\) 2.47883i 0.343751i
\(53\) 8.70349 + 5.02496i 1.19552 + 0.690232i 0.959552 0.281530i \(-0.0908418\pi\)
0.235964 + 0.971762i \(0.424175\pi\)
\(54\) 0 0
\(55\) 7.76146i 1.04655i
\(56\) −5.91015 + 1.87352i −0.789778 + 0.250359i
\(57\) 0 0
\(58\) −2.40101 −0.315268
\(59\) 1.08739 + 1.88341i 0.141566 + 0.245200i 0.928087 0.372365i \(-0.121453\pi\)
−0.786521 + 0.617564i \(0.788120\pi\)
\(60\) 0 0
\(61\) −3.46986 2.00333i −0.444270 0.256500i 0.261137 0.965302i \(-0.415903\pi\)
−0.705407 + 0.708802i \(0.749236\pi\)
\(62\) −4.80563 −0.610315
\(63\) 0 0
\(64\) −0.568850 −0.0711062
\(65\) −4.53206 2.61659i −0.562133 0.324548i
\(66\) 0 0
\(67\) 5.38341 + 9.32435i 0.657689 + 1.13915i 0.981213 + 0.192930i \(0.0617990\pi\)
−0.323524 + 0.946220i \(0.604868\pi\)
\(68\) −1.78425 −0.216372
\(69\) 0 0
\(70\) −1.23669 + 5.61945i −0.147812 + 0.671653i
\(71\) 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 −0.151176 0.988507i \(-0.548306\pi\)
−0.931660 + 0.363331i \(0.881639\pi\)
\(74\) 3.39331i 0.394464i
\(75\) 0 0
\(76\) −6.04521 3.49020i −0.693433 0.400354i
\(77\) 5.91015 1.87352i 0.673525 0.213507i
\(78\) 0 0
\(79\) −0.616587 + 1.06796i −0.0693714 + 0.120155i −0.898625 0.438718i \(-0.855433\pi\)
0.829253 + 0.558873i \(0.188766\pi\)
\(80\) 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 0.836151 0.548499i \(-0.184801\pi\)
−0.893090 + 0.449878i \(0.851467\pi\)
\(84\) 0 0
\(85\) −1.88341 + 3.26217i −0.204285 + 0.353832i
\(86\) 1.42345i 0.153494i
\(87\) 0 0
\(88\) 5.49143 0.585388
\(89\) 3.73538 + 6.46986i 0.395949 + 0.685804i 0.993222 0.116234i \(-0.0370823\pi\)
−0.597273 + 0.802038i \(0.703749\pi\)
\(90\) 0 0
\(91\) −0.898482 + 4.08266i −0.0941866 + 0.427979i
\(92\) 12.7623 7.36834i 1.33057 0.768203i
\(93\) 0 0
\(94\) 3.17686 1.83416i 0.327669 0.189180i
\(95\) −12.7623 + 7.36834i −1.30939 + 0.755976i
\(96\) 0 0
\(97\) −11.7367 + 6.77618i −1.19168 + 0.688017i −0.958687 0.284462i \(-0.908185\pi\)
−0.232993 + 0.972478i \(0.574852\pi\)
\(98\) 4.57759 0.414758i 0.462407 0.0418969i
\(99\) 0 0
\(100\) −4.68291 8.11103i −0.468291 0.811103i
\(101\) 13.7044 1.36364 0.681819 0.731521i \(-0.261189\pi\)
0.681819 + 0.731521i \(0.261189\pi\)
\(102\) 0 0
\(103\) 4.89211i 0.482033i 0.970521 + 0.241017i \(0.0774809\pi\)
−0.970521 + 0.241017i \(0.922519\pi\)
\(104\) −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 \(-0.628827\pi\)
0.599180 + 0.800614i \(0.295493\pi\)
\(108\) 0 0
\(109\) −2.16784 + 3.75481i −0.207641 + 0.359645i −0.950971 0.309280i \(-0.899912\pi\)
0.743330 + 0.668925i \(0.233245\pi\)
\(110\) 2.54817 4.41355i 0.242958 0.420816i
\(111\) 0 0
\(112\) −4.13166 0.909265i −0.390405 0.0859174i
\(113\) −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
\(115\) 31.1114i 2.90115i
\(116\) −4.96812 2.86834i −0.461278 0.266319i
\(117\) 0 0
\(118\) 1.42800i 0.131458i
\(119\) 2.93869 + 0.646726i 0.269389 + 0.0592852i
\(120\) 0 0
\(121\) 5.50857 0.500779
\(122\) 1.31542 + 2.27838i 0.119093 + 0.206275i
\(123\) 0 0
\(124\) −9.94369 5.74099i −0.892970 0.515556i
\(125\) −3.21226 −0.287313
\(126\) 0 0
\(127\) −17.7065 −1.57120 −0.785601 0.618733i \(-0.787646\pi\)
−0.785601 + 0.618733i \(0.787646\pi\)
\(128\) −9.61276 5.54993i −0.849656 0.490549i
\(129\) 0 0
\(130\) 1.71810 + 2.97584i 0.150688 + 0.260999i
\(131\) 13.6046 1.18864 0.594318 0.804230i \(-0.297422\pi\)
0.594318 + 0.804230i \(0.297422\pi\)
\(132\) 0 0
\(133\) 8.69148 + 7.93958i 0.753647 + 0.688449i
\(134\) 7.06972i 0.610731i
\(135\) 0 0
\(136\) 2.30807 + 1.33256i 0.197915 + 0.114266i
\(137\) 10.1601i 0.868039i 0.900904 + 0.434019i \(0.142905\pi\)
−0.900904 + 0.434019i \(0.857095\pi\)
\(138\) 0 0
\(139\) −3.33821 1.92731i −0.283143 0.163473i 0.351703 0.936112i \(-0.385603\pi\)
−0.634845 + 0.772639i \(0.718936\pi\)
\(140\) −9.27214 + 10.1502i −0.783639 + 0.857852i
\(141\) 0 0
\(142\) 2.09899 3.63555i 0.176143 0.305089i
\(143\) 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
\(149\) 5.08007i 0.416175i −0.978110 0.208088i \(-0.933276\pi\)
0.978110 0.208088i \(-0.0667239\pi\)
\(150\) 0 0
\(151\) 18.3055 1.48968 0.744842 0.667241i \(-0.232525\pi\)
0.744842 + 0.667241i \(0.232525\pi\)
\(152\) 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
\(157\) −2.86834 + 1.65604i −0.228919 + 0.132166i −0.610073 0.792345i \(-0.708860\pi\)
0.381154 + 0.924511i \(0.375527\pi\)
\(158\) 0.701244 0.404864i 0.0557880 0.0322092i
\(159\) 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 0.907434 0.420194i \(-0.138038\pi\)
−0.817616 + 0.575764i \(0.804705\pi\)
\(164\) −15.1324 −1.18164
\(165\) 0 0
\(166\) 0.681229i 0.0528737i
\(167\) 1.33256 2.30807i 0.103117 0.178604i −0.809850 0.586636i \(-0.800452\pi\)
0.912967 + 0.408033i \(0.133785\pi\)
\(168\) 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
\(173\) 1.28265 2.22162i 0.0975182 0.168907i −0.813139 0.582070i \(-0.802243\pi\)
0.910657 + 0.413164i \(0.135576\pi\)
\(174\) 0 0
\(175\) 4.77287 + 15.0564i 0.360795 + 1.13815i
\(176\) 3.24503 + 1.87352i 0.244603 + 0.141222i
\(177\) 0 0
\(178\) 4.90545i 0.367679i
\(179\) −11.9828 6.91827i −0.895636 0.517096i −0.0198545 0.999803i \(-0.506320\pi\)
−0.875782 + 0.482707i \(0.839654\pi\)
\(180\) 0 0
\(181\) 4.74008i 0.352328i −0.984361 0.176164i \(-0.943631\pi\)
0.984361 0.176164i \(-0.0563688\pi\)
\(182\) 1.85130 2.02662i 0.137228 0.150223i
\(183\) 0 0
\(184\) −22.0121 −1.62275
\(185\) −8.55814 14.8231i −0.629207 1.08982i
\(186\) 0 0
\(187\) −2.30807 1.33256i −0.168783 0.0974466i
\(188\) 8.76466 0.639228
\(189\) 0 0
\(190\) 9.67641 0.702001
\(191\) 7.22558 + 4.17169i 0.522825 + 0.301853i 0.738090 0.674703i \(-0.235728\pi\)
−0.215265 + 0.976556i \(0.569062\pi\)
\(192\) 0 0
\(193\) 8.92212 + 15.4536i 0.642229 + 1.11237i 0.984934 + 0.172930i \(0.0553233\pi\)
−0.342706 + 0.939443i \(0.611343\pi\)
\(194\) 8.89876 0.638893
\(195\) 0 0
\(196\) 9.96733 + 4.61036i 0.711952 + 0.329312i
\(197\) 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 0.210032 0.977695i \(-0.432643\pi\)
−0.741693 + 0.670740i \(0.765977\pi\)
\(200\) 13.9897i 0.989218i
\(201\) 0 0
\(202\) −7.79300 4.49929i −0.548313 0.316569i
\(203\) 7.14290 + 6.52496i 0.501333 + 0.457963i
\(204\) 0 0
\(205\) −15.9734 + 27.6667i −1.11563 + 1.93233i
\(206\) 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 \(-0.000697506\pi\)
\(212\) 15.7668i 1.08287i
\(213\) 0 0
\(214\) −1.61107 −0.110131
\(215\) −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
\(220\) 10.5452 6.08828i 0.710958 0.410472i
\(221\) 1.55622 0.898482i 0.104683 0.0604385i
\(222\) 0 0
\(223\) 9.16531 5.29159i 0.613754 0.354351i −0.160679 0.987007i \(-0.551368\pi\)
0.774433 + 0.632655i \(0.218035\pi\)
\(224\) 11.2061 + 10.2367i 0.748741 + 0.683967i
\(225\) 0 0
\(226\) 2.35075 + 4.07161i 0.156369 + 0.270839i
\(227\) 6.72398 0.446286 0.223143 0.974786i \(-0.428368\pi\)
0.223143 + 0.974786i \(0.428368\pi\)
\(228\) 0 0
\(229\) 12.2630i 0.810364i −0.914236 0.405182i \(-0.867208\pi\)
0.914236 0.405182i \(-0.132792\pi\)
\(230\) −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 \(-0.607664\pi\)
0.651045 + 0.759039i \(0.274331\pi\)
\(234\) 0 0
\(235\) 9.25176 16.0245i 0.603518 1.04532i
\(236\) 1.70595 2.95479i 0.111048 0.192341i
\(237\) 0 0
\(238\) −1.45876 1.33256i −0.0945574 0.0863772i
\(239\) 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
\(241\) 4.58806i 0.295543i 0.989022 + 0.147771i \(0.0472100\pi\)
−0.989022 + 0.147771i \(0.952790\pi\)
\(242\) −3.13245 1.80852i −0.201361 0.116256i
\(243\) 0 0
\(244\) 6.28583i 0.402409i
\(245\) 18.9504 13.3568i 1.21070 0.853334i
\(246\) 0 0
\(247\) 7.03014 0.447317
\(248\) 8.57528 + 14.8528i 0.544531 + 0.943155i
\(249\) 0 0
\(250\) 1.82665 + 1.05462i 0.115527 + 0.0666998i
\(251\) 13.8042 0.871314 0.435657 0.900113i \(-0.356516\pi\)
0.435657 + 0.900113i \(0.356516\pi\)
\(252\) 0 0
\(253\) 22.0121 1.38389
\(254\) 10.0688 + 5.81324i 0.631774 + 0.364755i
\(255\) 0 0
\(256\) 4.21305 + 7.29721i 0.263315 + 0.456076i
\(257\) −8.96430 −0.559178 −0.279589 0.960120i \(-0.590198\pi\)
−0.279589 + 0.960120i \(0.590198\pi\)
\(258\) 0 0
\(259\) −9.22162 + 10.0949i −0.573003 + 0.627268i
\(260\) 8.21006i 0.509166i
\(261\) 0 0
\(262\) −7.73623 4.46652i −0.477946 0.275942i
\(263\) 28.5534i 1.76068i −0.474343 0.880340i \(-0.657314\pi\)
0.474343 0.880340i \(-0.342686\pi\)
\(264\) 0 0
\(265\) −28.8266 16.6431i −1.77081 1.02238i
\(266\) −2.33576 7.36834i −0.143215 0.451782i
\(267\) 0 0
\(268\) 8.44577 14.6285i 0.515907 0.893578i
\(269\) −11.9657 + 20.7251i −0.729559 + 1.26363i 0.227510 + 0.973776i \(0.426941\pi\)
−0.957070 + 0.289858i \(0.906392\pi\)
\(270\) 0 0
\(271\) 12.6467 7.30159i 0.768234 0.443540i −0.0640103 0.997949i \(-0.520389\pi\)
0.832244 + 0.554409i \(0.187056\pi\)
\(272\) 0.909265 + 1.57489i 0.0551323 + 0.0954919i
\(273\) 0 0
\(274\) 3.33568 5.77756i 0.201516 0.349035i
\(275\) 13.9897i 0.843608i
\(276\) 0 0
\(277\) 22.3830 1.34486 0.672431 0.740160i \(-0.265250\pi\)
0.672431 + 0.740160i \(0.265250\pi\)
\(278\) 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
\(283\) 12.9849 7.49685i 0.771874 0.445642i −0.0616687 0.998097i \(-0.519642\pi\)
0.833543 + 0.552455i \(0.186309\pi\)
\(284\) 8.68635 5.01507i 0.515440 0.297590i
\(285\) 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
\(290\) 7.95234 0.466977
\(291\) 0 0
\(292\) 16.7600i 0.980807i
\(293\) −8.16762 + 14.1467i −0.477157 + 0.826461i −0.999657 0.0261787i \(-0.991666\pi\)
0.522500 + 0.852639i \(0.324999\pi\)
\(294\) 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
\(299\) −7.42084 + 12.8533i −0.429158 + 0.743324i
\(300\) 0 0
\(301\) −3.86834 + 4.23469i −0.222968 + 0.244083i
\(302\) −10.4094 6.00989i −0.598996 0.345831i
\(303\) 0 0
\(304\) 7.11450i 0.408045i
\(305\) 11.4925 + 6.63517i 0.658056 + 0.379929i
\(306\) 0 0
\(307\) 3.17340i 0.181115i −0.995891 0.0905577i \(-0.971135\pi\)
0.995891 0.0905577i \(-0.0288650\pi\)
\(308\) −7.18155 6.56028i −0.409207 0.373806i
\(309\) 0 0
\(310\) 15.9166 0.904003
\(311\) −12.5671 21.7668i −0.712614 1.23428i −0.963873 0.266364i \(-0.914178\pi\)
0.251259 0.967920i \(-0.419155\pi\)
\(312\) 0 0
\(313\) 16.1463 + 9.32205i 0.912641 + 0.526914i 0.881280 0.472594i \(-0.156682\pi\)
0.0313612 + 0.999508i \(0.490016\pi\)
\(314\) 2.17478 0.122730
\(315\) 0 0
\(316\) 1.93466 0.108833
\(317\) 6.91924 + 3.99483i 0.388623 + 0.224372i 0.681563 0.731759i \(-0.261300\pi\)
−0.292940 + 0.956131i \(0.594634\pi\)
\(318\) 0 0
\(319\) −4.28442 7.42084i −0.239882 0.415487i
\(320\) 1.88407 0.105323
\(321\) 0 0
\(322\) 15.9372 + 3.50734i 0.888145 + 0.195456i
\(323\) 5.06028i 0.281561i
\(324\) 0 0
\(325\) 8.16882 + 4.71627i 0.453125 + 0.261612i
\(326\) 1.50593i 0.0834056i
\(327\) 0 0
\(328\) 19.5749 + 11.3016i 1.08084 + 0.624025i
\(329\) −14.4355 3.17686i −0.795856 0.175146i
\(330\) 0 0
\(331\) 4.46733 7.73765i 0.245547 0.425299i −0.716738 0.697342i \(-0.754366\pi\)
0.962285 + 0.272043i \(0.0876992\pi\)
\(332\) −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 \(0.203554\pi\)
\(338\) 6.89682i 0.375138i
\(339\) 0 0
\(340\) 5.90958 0.320492
\(341\) −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
\(346\) −1.45876 + 0.842215i −0.0784234 + 0.0452778i
\(347\) 2.27460 1.31324i 0.122107 0.0704985i −0.437702 0.899120i \(-0.644208\pi\)
0.559809 + 0.828621i \(0.310874\pi\)
\(348\) 0 0
\(349\) −28.1387 + 16.2459i −1.50623 + 0.869622i −0.506255 + 0.862384i \(0.668971\pi\)
−0.999974 + 0.00723825i \(0.997696\pi\)
\(350\) 2.22907 10.1288i 0.119149 0.541407i
\(351\) 0 0
\(352\) −6.72162 11.6422i −0.358263 0.620531i
\(353\) −23.3842 −1.24461 −0.622307 0.782773i \(-0.713805\pi\)
−0.622307 + 0.782773i \(0.713805\pi\)
\(354\) 0 0
\(355\) 21.1751i 1.12386i
\(356\) 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 \(-0.857180\pi\)
−0.0748455 + 0.997195i \(0.523846\pi\)
\(360\) 0 0
\(361\) 0.398482 0.690192i 0.0209728 0.0363259i
\(362\) −1.55622 + 2.69545i −0.0817930 + 0.141670i
\(363\) 0 0
\(364\) 6.25176 1.98181i 0.327681 0.103875i
\(365\) 30.6425 + 17.6915i 1.60390 + 0.926014i
\(366\) 0 0
\(367\) 15.5229i 0.810289i −0.914253 0.405145i \(-0.867221\pi\)
0.914253 0.405145i \(-0.132779\pi\)
\(368\) −13.0075 7.50989i −0.678064 0.391480i
\(369\) 0 0
\(370\) 11.2389i 0.584283i
\(371\) −5.71489 + 25.9682i −0.296702 + 1.34820i
\(372\) 0 0
\(373\) −23.3528 −1.20916 −0.604582 0.796543i \(-0.706660\pi\)
−0.604582 + 0.796543i \(0.706660\pi\)
\(374\) 0.874988 + 1.51552i 0.0452445 + 0.0783659i
\(375\) 0 0
\(376\) −11.3378 6.54585i −0.584700 0.337577i
\(377\) 5.77756 0.297559
\(378\) 0 0
\(379\) 2.53871 0.130405 0.0652024 0.997872i \(-0.479231\pi\)
0.0652024 + 0.997872i \(0.479231\pi\)
\(380\) 20.0222 + 11.5598i 1.02712 + 0.593006i
\(381\) 0 0
\(382\) −2.73922 4.74446i −0.140151 0.242748i
\(383\) −16.2041 −0.827993 −0.413996 0.910278i \(-0.635867\pi\)
−0.413996 + 0.910278i \(0.635867\pi\)
\(384\) 0 0
\(385\) −19.5749 + 6.20524i −0.997629 + 0.316248i
\(386\) 11.7169i 0.596374i
\(387\) 0 0
\(388\) 18.4131 + 10.6308i 0.934783 + 0.539697i
\(389\) 22.3330i 1.13233i 0.824292 + 0.566165i \(0.191573\pi\)
−0.824292 + 0.566165i \(0.808427\pi\)
\(390\) 0 0
\(391\) 9.25176 + 5.34150i 0.467881 + 0.270131i
\(392\) −9.45027 13.4079i −0.477311 0.677202i
\(393\) 0 0
\(394\) −4.96083 + 8.59242i −0.249923 + 0.432880i
\(395\) 2.04218 3.53717i 0.102753 0.177974i
\(396\) 0 0
\(397\) 28.3116 16.3457i 1.42092 0.820367i 0.424540 0.905409i \(-0.360436\pi\)
0.996377 + 0.0850420i \(0.0271025\pi\)
\(398\) 2.84325 + 4.92465i 0.142519 + 0.246851i
\(399\) 0 0
\(400\) −4.77287 + 8.26685i −0.238643 + 0.413343i
\(401\) 28.9270i 1.44454i 0.691609 + 0.722272i \(0.256902\pi\)
−0.691609 + 0.722272i \(0.743098\pi\)
\(402\) 0 0
\(403\) 11.5638 0.576033
\(404\) −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
\(409\) −0.910038 + 0.525411i −0.0449985 + 0.0259799i −0.522330 0.852743i \(-0.674937\pi\)
0.477332 + 0.878723i \(0.341604\pi\)
\(410\) 18.1665 10.4884i 0.897180 0.517987i
\(411\) 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
\(416\) 9.06412 0.444405
\(417\) 0 0
\(418\) 6.84631i 0.334864i
\(419\) 1.56060 2.70304i 0.0762402 0.132052i −0.825385 0.564571i \(-0.809042\pi\)
0.901625 + 0.432519i \(0.142375\pi\)
\(420\) 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
\(425\) 3.39476 5.87990i 0.164670 0.285217i
\(426\) 0 0
\(427\) 2.27838 10.3529i 0.110259 0.501010i
\(428\) −3.33360 1.92465i −0.161136 0.0930316i
\(429\) 0 0
\(430\) 4.71457i 0.227357i
\(431\) 23.6279 + 13.6416i 1.13811 + 0.657090i 0.945963 0.324275i \(-0.105120\pi\)
0.192151 + 0.981365i \(0.438454\pi\)
\(432\) 0 0
\(433\) 12.8711i 0.618547i −0.950973 0.309274i \(-0.899914\pi\)
0.950973 0.309274i \(-0.100086\pi\)
\(434\) −3.84207 12.1201i −0.184425 0.581783i
\(435\) 0 0
\(436\) 6.80202 0.325758
\(437\) 20.8972 + 36.1950i 0.999648 + 1.73144i
\(438\) 0 0
\(439\) −15.9734 9.22223i −0.762368 0.440153i 0.0677776 0.997700i \(-0.478409\pi\)
−0.830145 + 0.557547i \(0.811743\pi\)
\(440\) −18.1880 −0.867081
\(441\) 0 0
\(442\) −1.17992 −0.0561233
\(443\) 2.48550 + 1.43500i 0.118090 + 0.0681790i 0.557881 0.829921i \(-0.311614\pi\)
−0.439792 + 0.898100i \(0.644948\pi\)
\(444\) 0 0
\(445\) −12.3719 21.4287i −0.586482 1.01582i
\(446\) −6.94914 −0.329051
\(447\) 0 0
\(448\) −0.454792 1.43468i −0.0214869 0.0677820i
\(449\) 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
\(452\) 11.2332i 0.528364i
\(453\) 0 0
\(454\) −3.82359 2.20755i −0.179450 0.103605i
\(455\) 2.97584 13.5221i 0.139510 0.633926i
\(456\) 0 0
\(457\) −3.07788 + 5.33104i −0.143977 + 0.249375i −0.928991 0.370103i \(-0.879322\pi\)
0.785014 + 0.619478i \(0.212656\pi\)
\(458\) −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 0.993363 0.115026i \(-0.0366951\pi\)
−0.596296 + 0.802764i \(0.703362\pi\)
\(462\) 0 0
\(463\) −14.7065 + 25.4725i −0.683471 + 1.18381i 0.290443 + 0.956892i \(0.406197\pi\)
−0.973915 + 0.226915i \(0.927136\pi\)
\(464\) 5.84689i 0.271435i
\(465\) 0 0
\(466\) −3.69446 −0.171143
\(467\) −13.5590 23.4849i −0.627437 1.08675i −0.988064 0.154043i \(-0.950771\pi\)
0.360627 0.932710i \(-0.382563\pi\)
\(468\) 0 0
\(469\) −19.2126 + 21.0321i −0.887155 + 0.971171i
\(470\) −10.5220 + 6.07489i −0.485345 + 0.280214i
\(471\) 0 0
\(472\) −4.41355 + 2.54817i −0.203150 + 0.117289i
\(473\) 4.39947 2.54003i 0.202288 0.116791i
\(474\) 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
\(479\) 21.5569 0.984960 0.492480 0.870324i \(-0.336090\pi\)
0.492480 + 0.870324i \(0.336090\pi\)
\(480\) 0 0
\(481\) 8.16532i 0.372307i
\(482\) 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 −0.652220 0.758029i \(-0.726162\pi\)
0.982583 + 0.185825i \(0.0594956\pi\)
\(488\) 4.69455 8.13120i 0.212512 0.368082i
\(489\) 0 0
\(490\) −15.1613 + 1.37371i −0.684920 + 0.0620580i
\(491\) 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
\(493\) 4.15867i 0.187297i
\(494\) −3.99769 2.30807i −0.179864 0.103845i
\(495\) 0 0
\(496\) 11.7026i 0.525461i
\(497\) −16.1243 + 5.11141i −0.723275 + 0.229278i
\(498\) 0 0
\(499\) 12.3055 0.550871 0.275436 0.961319i \(-0.411178\pi\)
0.275436 + 0.961319i \(0.411178\pi\)
\(500\) 2.51977 + 4.36438i 0.112688 + 0.195181i
\(501\) 0 0
\(502\) −7.84976 4.53206i −0.350352 0.202276i
\(503\) −1.78425 −0.0795559 −0.0397779 0.999209i \(-0.512665\pi\)
−0.0397779 + 0.999209i \(0.512665\pi\)
\(504\) 0 0
\(505\) −45.3900 −2.01983
\(506\) −12.5172 7.22679i −0.556456 0.321270i
\(507\) 0 0
\(508\) 13.8895 + 24.0572i 0.616245 + 1.06737i
\(509\) −39.0725 −1.73186 −0.865928 0.500168i \(-0.833272\pi\)
−0.865928 + 0.500168i \(0.833272\pi\)
\(510\) 0 0
\(511\) 6.07489 27.6040i 0.268737 1.22113i
\(512\) 16.6670i 0.736583i
\(513\) 0 0
\(514\) 5.09755 + 2.94307i 0.224843 + 0.129813i
\(515\) 16.2030i 0.713991i
\(516\) 0 0
\(517\) 11.3378 + 6.54585i 0.498634 + 0.287886i
\(518\) 8.55814 2.71293i 0.376023 0.119199i
\(519\) 0 0
\(520\) 6.13166 10.6203i 0.268891 0.465733i
\(521\) −10.1814 + 17.6347i −0.446056 + 0.772591i −0.998125 0.0612072i \(-0.980505\pi\)
0.552070 + 0.833798i \(0.313838\pi\)
\(522\) 0 0
\(523\) 1.24066 0.716293i 0.0542501 0.0313213i −0.472630 0.881261i \(-0.656695\pi\)
0.526880 + 0.849940i \(0.323362\pi\)
\(524\) −10.6718 18.4840i −0.466198 0.807478i
\(525\) 0 0
\(526\) −9.37439 + 16.2369i −0.408743 + 0.707963i
\(527\) 8.32359i 0.362581i
\(528\) 0 0
\(529\) −65.2342 −2.83627
\(530\) 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
\(535\) −7.03773 + 4.06323i −0.304267 + 0.175669i
\(536\) −21.8505 + 12.6154i −0.943797 + 0.544901i
\(537\) 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 0.953862 0.300246i \(-0.0970687\pi\)
−0.736951 + 0.675946i \(0.763735\pi\)
\(542\) −9.58875 −0.411872
\(543\) 0 0
\(544\) 6.52433i 0.279729i
\(545\) 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
\(551\) 8.13484 14.0900i 0.346556 0.600253i
\(552\) 0 0
\(553\) −3.18642 0.701244i −0.135500 0.0298199i
\(554\) −12.7281 7.34855i −0.540764 0.312210i
\(555\) 0 0
\(556\) 6.04733i 0.256464i
\(557\) −19.7970 11.4298i −0.838828 0.484297i 0.0180379 0.999837i \(-0.494258\pi\)
−0.856866 + 0.515540i \(0.827591\pi\)
\(558\) 0 0
\(559\) 3.42524i 0.144872i
\(560\) 13.6844 + 3.01156i 0.578270 + 0.127261i
\(561\) 0 0
\(562\) 7.62119 0.321481
\(563\) −10.5548 18.2814i −0.444832 0.770471i 0.553209 0.833043i \(-0.313403\pi\)
−0.998040 + 0.0625717i \(0.980070\pi\)
\(564\) 0 0
\(565\) 20.5377 + 11.8575i 0.864029 + 0.498847i
\(566\) −9.84517 −0.413824
\(567\) 0 0
\(568\) −14.9819 −0.628629
\(569\) −22.9095 13.2268i −0.960415 0.554496i −0.0641144 0.997943i \(-0.520422\pi\)
−0.896301 + 0.443447i \(0.853756\pi\)
\(570\) 0 0
\(571\) −6.01507 10.4184i −0.251723 0.435997i 0.712277 0.701898i \(-0.247664\pi\)
−0.964000 + 0.265901i \(0.914330\pi\)
\(572\) −5.80883 −0.242879
\(573\) 0 0
\(574\) −12.3719 11.3016i −0.516391 0.471718i
\(575\) 56.0767i 2.33856i
\(576\) 0 0
\(577\) −31.9055 18.4207i −1.32824 0.766862i −0.343216 0.939257i \(-0.611516\pi\)
−0.985028 + 0.172395i \(0.944850\pi\)
\(578\) 10.3132i 0.428974i
\(579\) 0 0
\(580\) 16.4548 + 9.50018i 0.683248 + 0.394473i
\(581\) 1.85130 2.02662i 0.0768049 0.0840786i
\(582\) 0 0
\(583\) 11.7754 20.3956i 0.487687 0.844699i
\(584\) 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 \(0.0356896\pi\)
−0.399963 + 0.916531i \(0.630977\pi\)
\(588\) 0 0
\(589\) 16.2819 28.2011i 0.670884 1.16200i
\(590\) 4.72966i 0.194717i
\(591\) 0 0
\(592\) −8.26331 −0.339620
\(593\) 5.29159 + 9.16531i 0.217300 + 0.376374i 0.953982 0.299865i \(-0.0969418\pi\)
−0.736682 + 0.676240i \(0.763608\pi\)
\(594\) 0 0
\(595\) −9.73317 2.14201i −0.399021 0.0878137i
\(596\) −6.90210 + 3.98493i −0.282721 + 0.163229i
\(597\) 0 0
\(598\) 8.43972 4.87268i 0.345126 0.199259i
\(599\) −15.7553 + 9.09634i −0.643745 + 0.371666i −0.786056 0.618156i \(-0.787880\pi\)
0.142311 + 0.989822i \(0.454547\pi\)
\(600\) 0 0
\(601\) 22.8719 13.2051i 0.932963 0.538646i 0.0452152 0.998977i \(-0.485603\pi\)
0.887747 + 0.460331i \(0.152269\pi\)
\(602\) 3.59002 1.13804i 0.146318 0.0463829i
\(603\) 0 0
\(604\) −14.3593 24.8711i −0.584272 1.01199i
\(605\) −18.2448 −0.741757
\(606\) 0 0
\(607\) 24.9776i 1.01381i −0.862003 0.506904i \(-0.830790\pi\)
0.862003 0.506904i \(-0.169210\pi\)
\(608\) 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 −0.687608 0.726082i \(-0.741339\pi\)
0.972610 + 0.232445i \(0.0746725\pi\)
\(614\) −1.04186 + 1.80455i −0.0420460 + 0.0728258i
\(615\) 0 0
\(616\) 4.39036 + 13.8497i 0.176893 + 0.558022i
\(617\) −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
\(619\) 26.5442i 1.06690i 0.845831 + 0.533452i \(0.179105\pi\)
−0.845831 + 0.533452i \(0.820895\pi\)
\(620\) 32.9343 + 19.0146i 1.32267 + 0.763645i
\(621\) 0 0
\(622\) 16.5036i 0.661734i
\(623\) −13.3310 + 14.5935i −0.534095 + 0.584675i
\(624\) 0 0
\(625\) −19.2101 −0.768403
\(626\) −6.12105 10.6020i −0.244646 0.423740i
\(627\) 0 0
\(628\) 4.50000 + 2.59808i 0.179570 + 0.103675i
\(629\) 5.87738 0.234347
\(630\) 0 0
\(631\) −8.20304 −0.326558 −0.163279 0.986580i \(-0.552207\pi\)
−0.163279 + 0.986580i \(0.552207\pi\)
\(632\) −2.50264 1.44490i −0.0995495 0.0574749i
\(633\) 0 0
\(634\) −2.62308 4.54331i −0.104176 0.180438i
\(635\) 58.6455 2.32727
\(636\) 0 0
\(637\) −11.0151 + 0.998034i −0.436433 + 0.0395436i
\(638\) 5.62648i 0.222755i
\(639\) 0 0
\(640\) 31.8382 + 18.3818i 1.25852 + 0.726604i
\(641\) 16.0499i 0.633934i −0.948437 0.316967i \(-0.897336\pi\)
0.948437 0.316967i \(-0.102664\pi\)
\(642\) 0 0
\(643\) 22.8719 + 13.2051i 0.901978 + 0.520757i 0.877841 0.478951i \(-0.158983\pi\)
0.0241366 + 0.999709i \(0.492316\pi\)
\(644\) 28.7869 + 26.2965i 1.13436 + 1.03623i
\(645\) 0 0
\(646\) −1.66134 + 2.87753i −0.0653646 + 0.113215i
\(647\) 15.8508 27.4543i 0.623158 1.07934i −0.365736 0.930719i \(-0.619183\pi\)
0.988894 0.148623i \(-0.0474840\pi\)
\(648\) 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
\(653\) 13.2901i 0.520083i −0.965597 0.260041i \(-0.916264\pi\)
0.965597 0.260041i \(-0.0837362\pi\)
\(654\) 0 0
\(655\) −45.0594 −1.76062
\(656\) 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
\(661\) −43.9880 + 25.3965i −1.71093 + 0.987809i −0.777630 + 0.628722i \(0.783578\pi\)
−0.933304 + 0.359087i \(0.883088\pi\)
\(662\) −5.08070 + 2.93334i −0.197467 + 0.114008i
\(663\) 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
\(668\) −4.18118 −0.161775
\(669\) 0 0
\(670\) 23.4155i 0.904618i
\(671\) −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
\(677\) 9.96901 17.2668i 0.383140 0.663618i −0.608369 0.793654i \(-0.708176\pi\)
0.991509 + 0.130036i \(0.0415093\pi\)
\(678\) 0 0
\(679\) −26.4734 24.1832i −1.01595 0.928065i
\(680\) −7.64450 4.41355i −0.293153 0.169252i
\(681\) 0 0
\(682\) 11.2614i 0.431222i
\(683\) −24.8234 14.3318i −0.949843 0.548392i −0.0568107 0.998385i \(-0.518093\pi\)
−0.893032 + 0.449993i \(0.851426\pi\)
\(684\) 0 0
\(685\) 33.6512i 1.28574i
\(686\) 4.70581 + 11.2134i 0.179668 + 0.428129i
\(687\) 0 0
\(688\) −3.46635 −0.132153
\(689\) 7.93958 + 13.7518i 0.302474 + 0.523900i
\(690\) 0 0
\(691\) 17.6387 + 10.1837i 0.671007 + 0.387406i 0.796458 0.604694i \(-0.206704\pi\)
−0.125451 + 0.992100i \(0.540038\pi\)
\(692\) −4.02458 −0.152991
\(693\) 0 0
\(694\) −1.72460 −0.0654650
\(695\) 11.0564 + 6.38341i 0.419393 + 0.242137i
\(696\) 0 0
\(697\) −5.48493 9.50018i −0.207757 0.359845i
\(698\) 21.3347 0.807532
\(699\) 0 0
\(700\) 16.7126 18.2953i 0.631677 0.691498i
\(701\) 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
\(704\) 1.33303i 0.0502405i
\(705\) 0 0
\(706\) 13.2974 + 7.67727i 0.500455 + 0.288938i
\(707\) 10.9566 + 34.5633i 0.412064 + 1.29989i
\(708\) 0 0
\(709\) −11.6829 + 20.2354i −0.438761 + 0.759956i −0.997594 0.0693240i \(-0.977916\pi\)
0.558833 + 0.829280i \(0.311249\pi\)
\(710\) −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
\(716\) 21.7075i 0.811246i
\(717\) 0 0
\(718\) 14.0191 0.523189
\(719\) 6.33345 + 10.9699i 0.236198 + 0.409107i 0.959620 0.281299i \(-0.0907653\pi\)
−0.723422 + 0.690406i \(0.757432\pi\)
\(720\) 0 0
\(721\) −12.3382 + 3.91121i −0.459499 + 0.145661i
\(722\) −0.453194 + 0.261652i −0.0168661 + 0.00973767i
\(723\) 0 0
\(724\) −6.44018 + 3.71824i −0.239347 + 0.138187i
\(725\) 18.9049 10.9148i 0.702111 0.405364i
\(726\) 0 0
\(727\) −2.34172 + 1.35199i −0.0868495 + 0.0501426i −0.542796 0.839865i \(-0.682634\pi\)
0.455946 + 0.890007i \(0.349301\pi\)
\(728\) −9.56723 2.10549i −0.354585 0.0780345i
\(729\) 0 0
\(730\) −11.6166 20.1205i −0.429949 0.744694i
\(731\) 2.46548 0.0911891
\(732\) 0 0
\(733\) 21.8087i 0.805524i 0.915305 + 0.402762i \(0.131950\pi\)
−0.915305 + 0.402762i \(0.868050\pi\)
\(734\) −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 0.403212 + 0.915107i \(0.367894\pi\)
−0.994112 + 0.108361i \(0.965440\pi\)
\(740\) −13.4264 + 23.2553i −0.493566 + 0.854881i
\(741\) 0 0
\(742\) 11.7754 12.8906i 0.432288 0.473227i
\(743\) −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
\(745\) 16.8256i 0.616442i
\(746\) 13.2796 + 7.66697i 0.486200 + 0.280708i
\(747\) 0 0
\(748\) 4.18118i 0.152879i
\(749\) 4.79287 + 4.37824i 0.175128 + 0.159977i
\(750\) 0 0
\(751\) 45.8091 1.67160 0.835798 0.549037i \(-0.185005\pi\)
0.835798 + 0.549037i \(0.185005\pi\)
\(752\) −4.46652 7.73623i −0.162877 0.282111i
\(753\) 0 0
\(754\) −3.28541 1.89683i −0.119648 0.0690785i
\(755\) −60.6294 −2.20653
\(756\) 0 0
\(757\) 50.3427 1.82974 0.914868 0.403752i \(-0.132294\pi\)
0.914868 + 0.403752i \(0.132294\pi\)
\(758\) −1.44364 0.833485i −0.0524353 0.0302735i
\(759\) 0 0
\(760\) −17.2668 29.9070i −0.626334 1.08484i
\(761\) 30.3646 1.10072 0.550358 0.834929i \(-0.314491\pi\)
0.550358 + 0.834929i \(0.314491\pi\)
\(762\) 0 0
\(763\) −11.2030 2.46548i −0.405577 0.0892564i
\(764\) 13.0895i 0.473562i
\(765\) 0 0
\(766\) 9.21448 + 5.31999i 0.332933 + 0.192219i
\(767\) 3.43621i 0.124074i
\(768\) 0 0
\(769\) −35.8000 20.6692i −1.29098 0.745349i −0.312154 0.950032i \(-0.601050\pi\)
−0.978828 + 0.204683i \(0.934384\pi\)
\(770\) 13.1685 + 2.89803i 0.474560 + 0.104438i
\(771\) 0 0
\(772\) 13.9975 24.2443i 0.503780 0.872573i
\(773\) −6.99754 + 12.1201i −0.251684 + 0.435930i −0.963990 0.265940i \(-0.914318\pi\)
0.712305 + 0.701870i \(0.247651\pi\)
\(774\) 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
\(779\) 42.9166i 1.53765i
\(780\) 0 0
\(781\) 14.9819 0.536096
\(782\) −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
\(787\) −11.6799 + 6.74341i −0.416344 + 0.240377i −0.693512 0.720445i \(-0.743938\pi\)
0.277168 + 0.960822i \(0.410604\pi\)
\(788\) −20.5297 + 11.8528i −0.731340 + 0.422239i
\(789\) 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
\(794\) −21.4658 −0.761794
\(795\) 0 0
\(796\) 13.5866i 0.481566i
\(797\) 4.15867 7.20304i 0.147308 0.255145i −0.782924 0.622118i \(-0.786273\pi\)
0.930232 + 0.366973i \(0.119606\pi\)
\(798\) 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
\(803\) −12.5172 + 21.6804i −0.441721 + 0.765084i
\(804\) 0 0
\(805\) 78.4649 24.8734i 2.76552 0.876671i
\(806\) −6.57575 3.79651i −0.231621 0.133726i
\(807\) 0 0
\(808\) 32.1146i 1.12979i
\(809\) −12.5955 7.27200i −0.442833 0.255670i 0.261965 0.965077i \(-0.415629\pi\)
−0.704799 + 0.709407i \(0.748963\pi\)
\(810\) 0 0
\(811\) 41.8287i 1.46880i −0.678715 0.734401i \(-0.737463\pi\)
0.678715 0.734401i \(-0.262537\pi\)
\(812\) 3.26217 14.8231i 0.114480 0.520190i
\(813\) 0 0
\(814\) −7.95181 −0.278711
\(815\) −3.79804 6.57841i −0.133040 0.230432i
\(816\) 0 0
\(817\) 8.35327 + 4.82277i 0.292244 + 0.168727i
\(818\) 0.689991 0.0241250
\(819\) 0 0
\(820\) 50.1196 1.75025
\(821\) −40.2553 23.2414i −1.40492 0.811131i −0.410027 0.912073i \(-0.634481\pi\)
−0.994892 + 0.100942i \(0.967814\pi\)
\(822\) 0 0
\(823\) −3.86834 6.70017i −0.134842 0.233553i 0.790695 0.612210i \(-0.209719\pi\)
−0.925537 + 0.378657i \(0.876386\pi\)
\(824\) −11.4641 −0.399369
\(825\) 0 0
\(826\) 3.60152 1.14168i 0.125313 0.0397242i
\(827\) 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 0.997267 0.0738846i \(-0.0235396\pi\)
0.434647 + 0.900601i \(0.356873\pi\)
\(830\) 2.25628i 0.0783168i
\(831\) 0 0
\(832\) −0.778382 0.449399i −0.0269855 0.0155801i
\(833\) 0.718383 + 7.92862i 0.0248905 + 0.274710i
\(834\) 0 0
\(835\) −4.41355 + 7.64450i −0.152737 + 0.264549i
\(836\) −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 0.992007 0.126181i \(-0.0402721\pi\)
−0.605280 + 0.796013i \(0.706939\pi\)
\(840\) 0 0
\(841\) −7.81456 + 13.5352i −0.269468 + 0.466732i
\(842\) 5.71690i 0.197017i
\(843\) 0 0
\(844\) −22.8753 −0.787400
\(845\) 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
\(850\) −3.86086 + 2.22907i −0.132426 + 0.0764565i
\(851\) −42.0396 + 24.2715i −1.44110 + 0.832018i
\(852\) 0 0
\(853\) 41.9393 24.2136i 1.43597 0.829060i 0.438406 0.898777i \(-0.355543\pi\)
0.997567 + 0.0697173i \(0.0222097\pi\)
\(854\) −4.69455 + 5.13914i −0.160644 + 0.175858i
\(855\) 0 0
\(856\) 2.87484 + 4.97937i 0.0982600 + 0.170191i
\(857\) −49.0655 −1.67605 −0.838023 0.545636i \(-0.816288\pi\)
−0.838023 + 0.545636i \(0.816288\pi\)
\(858\) 0 0
\(859\) 12.0245i 0.410272i −0.978733 0.205136i \(-0.934236\pi\)
0.978733 0.205136i \(-0.0657636\pi\)
\(860\) −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 \(-0.953377\pi\)
−0.368252 + 0.929726i \(0.620044\pi\)
\(864\) 0 0
\(865\) −4.24824 + 7.35817i −0.144445 + 0.250185i
\(866\) −4.22572 + 7.31917i −0.143596 + 0.248715i
\(867\) 0 0
\(868\) 6.52923 29.6685i 0.221617 1.00702i
\(869\) 2.50264 + 1.44490i 0.0848961 + 0.0490148i
\(870\) 0 0
\(871\) 17.0119i 0.576426i
\(872\) −8.79893 5.08007i −0.297970 0.172033i
\(873\) 0 0
\(874\) 27.4430i 0.928275i
\(875\) −2.56818 8.10152i −0.0868203 0.273881i
\(876\) 0 0
\(877\) 13.4734 0.454964 0.227482 0.973782i \(-0.426951\pi\)
0.227482 + 0.973782i \(0.426951\pi\)
\(878\) 6.05551 + 10.4884i 0.204363 + 0.353968i
\(879\) 0 0
\(880\) −10.7478 6.20524i −0.362308 0.209179i
\(881\) 25.5247 0.859949 0.429974 0.902841i \(-0.358523\pi\)
0.429974 + 0.902841i \(0.358523\pi\)
\(882\) 0 0
\(883\) 6.45532 0.217239 0.108619 0.994083i \(-0.465357\pi\)
0.108619 + 0.994083i \(0.465357\pi\)
\(884\) −2.44147 1.40958i −0.0821156 0.0474094i
\(885\) 0 0
\(886\) −0.942252 1.63203i −0.0316556 0.0548291i
\(887\) −33.1208 −1.11209 −0.556043 0.831153i \(-0.687681\pi\)
−0.556043 + 0.831153i \(0.687681\pi\)
\(888\) 0 0
\(889\) −14.1563 44.6571i −0.474786 1.49775i
\(890\) 16.2472i 0.544608i
\(891\) 0 0
\(892\) −14.3790 8.30171i −0.481444 0.277962i
\(893\) 24.8572i 0.831816i
\(894\) 0 0
\(895\) 39.6880 + 22.9139i 1.32662 + 0.765926i
\(896\) 6.31193 28.6811i 0.210867 0.958169i
\(897\) 0 0
\(898\) −0.596459 + 1.03310i −0.0199041 + 0.0344749i
\(899\) 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
\(905\) 15.6995i 0.521870i
\(906\) 0 0
\(907\) 6.21512 0.206370 0.103185 0.994662i \(-0.467097\pi\)
0.103185 + 0.994662i \(0.467097\pi\)
\(908\) −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
\(913\) −2.10549 + 1.21560i −0.0696814 + 0.0402306i
\(914\) 3.50047 2.02100i 0.115785 0.0668486i
\(915\) 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 0.926058 0.377381i \(-0.123175\pi\)
−0.789851 + 0.613299i \(0.789842\pi\)
\(920\) 72.9057 2.40363
\(921\) 0 0
\(922\) 11.1959i 0.368716i
\(923\) −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
\(929\) 17.3855 30.1125i 0.570399 0.987960i −0.426126 0.904664i \(-0.640122\pi\)
0.996525 0.0832958i \(-0.0265446\pi\)
\(930\) 0 0
\(931\) −13.0753 + 28.2681i −0.428527 + 0.926450i
\(932\) −7.64450 4.41355i −0.250404 0.144571i
\(933\) 0 0
\(934\) 17.8063i 0.582639i
\(935\) 7.64450 + 4.41355i 0.250002 + 0.144339i
\(936\) 0 0
\(937\) 51.0703i 1.66839i 0.551466 + 0.834197i \(0.314069\pi\)
−0.551466 + 0.834197i \(0.685931\pi\)
\(938\) 17.8303 5.65220i 0.582179 0.184551i
\(939\) 0 0
\(940\) −29.0292 −0.946829
\(941\) −1.73872 3.01156i −0.0566807 0.0981739i 0.836293 0.548283i \(-0.184718\pi\)
−0.892974 + 0.450109i \(0.851385\pi\)
\(942\) 0 0
\(943\) 78.4649 + 45.3017i 2.55517 + 1.47523i
\(944\) −3.47744 −0.113181
\(945\) 0 0
\(946\) −3.33568 −0.108452
\(947\) −12.4189 7.17003i −0.403559 0.232995i 0.284460 0.958688i \(-0.408186\pi\)
−0.688018 + 0.725693i \(0.741519\pi\)
\(948\) 0 0
\(949\) −8.43972 14.6180i −0.273965 0.474521i
\(950\) −17.4413 −0.565869
\(951\) 0 0
\(952\) −1.51552 + 6.88647i −0.0491184 + 0.223192i
\(953\) 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
\(956\) 25.0381i 0.809789i
\(957\) 0 0
\(958\) −12.2583 7.07735i −0.396049 0.228659i
\(959\) −25.6245 + 8.12297i −0.827459 + 0.262304i
\(960\) 0 0
\(961\) 11.2819 19.5408i 0.363932 0.630349i
\(962\) 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 \(0.106863\pi\)
\(968\) 12.9087i 0.414901i
\(969\) 0 0
\(970\) −29.4734 −0.946333
\(971\) 17.7476 + 30.7397i 0.569548 + 0.986485i 0.996611 + 0.0822636i \(0.0262149\pi\)
−0.427063 + 0.904222i \(0.640452\pi\)
\(972\) 0 0
\(973\) 2.19193 9.96004i 0.0702702 0.319304i
\(974\) −8.29145 + 4.78707i −0.265675 + 0.153388i
\(975\) 0 0
\(976\) 5.54827 3.20329i 0.177596 0.102535i
\(977\) 27.7210 16.0047i 0.886873 0.512036i 0.0139546 0.999903i \(-0.495558\pi\)
0.872918 + 0.487866i \(0.162225\pi\)
\(978\) 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
\(983\) 49.4648 1.57768 0.788841 0.614598i \(-0.210682\pi\)
0.788841 + 0.614598i \(0.210682\pi\)
\(984\) 0 0
\(985\) 50.0462i 1.59460i
\(986\) −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 −0.972640 0.232316i \(-0.925370\pi\)
0.687511 + 0.726174i \(0.258703\pi\)
\(992\) 20.9926 36.3603i 0.666517 1.15444i
\(993\) 0 0
\(994\) 10.8472 + 2.38718i 0.344053 + 0.0757167i
\(995\) 24.8406 + 14.3417i 0.787500 + 0.454663i
\(996\) 0 0
\(997\) 33.5037i 1.06107i 0.847662 + 0.530537i \(0.178010\pi\)
−0.847662 + 0.530537i \(0.821990\pi\)
\(998\) −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.s.f.458.3 12
3.2 odd 2 inner 567.2.s.f.458.4 12
7.5 odd 6 567.2.i.f.215.4 12
9.2 odd 6 567.2.i.f.269.3 12
9.4 even 3 189.2.p.d.80.4 yes 12
9.5 odd 6 189.2.p.d.80.3 yes 12
9.7 even 3 567.2.i.f.269.4 12
21.5 even 6 567.2.i.f.215.3 12
63.4 even 3 1323.2.c.d.1322.7 12
63.5 even 6 189.2.p.d.26.4 yes 12
63.31 odd 6 1323.2.c.d.1322.8 12
63.32 odd 6 1323.2.c.d.1322.6 12
63.40 odd 6 189.2.p.d.26.3 12
63.47 even 6 inner 567.2.s.f.26.3 12
63.59 even 6 1323.2.c.d.1322.5 12
63.61 odd 6 inner 567.2.s.f.26.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.3 12 63.40 odd 6
189.2.p.d.26.4 yes 12 63.5 even 6
189.2.p.d.80.3 yes 12 9.5 odd 6
189.2.p.d.80.4 yes 12 9.4 even 3
567.2.i.f.215.3 12 21.5 even 6
567.2.i.f.215.4 12 7.5 odd 6
567.2.i.f.269.3 12 9.2 odd 6
567.2.i.f.269.4 12 9.7 even 3
567.2.s.f.26.3 12 63.47 even 6 inner
567.2.s.f.26.4 12 63.61 odd 6 inner
567.2.s.f.458.3 12 1.1 even 1 trivial
567.2.s.f.458.4 12 3.2 odd 2 inner
1323.2.c.d.1322.5 12 63.59 even 6
1323.2.c.d.1322.6 12 63.32 odd 6
1323.2.c.d.1322.7 12 63.4 even 3
1323.2.c.d.1322.8 12 63.31 odd 6