Properties

Label 405.2.j.b.109.2
Level $405$
Weight $2$
Character 405.109
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,2,Mod(109,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.j (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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.2
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 405.109
Dual form 405.2.j.b.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.686141 - 0.396143i) q^{2} +(-0.686141 + 1.18843i) q^{4} +(-2.18614 - 0.469882i) q^{5} +(3.00000 - 1.73205i) q^{7} +2.67181i q^{8} +O(q^{10})\) \(q+(0.686141 - 0.396143i) q^{2} +(-0.686141 + 1.18843i) q^{4} +(-2.18614 - 0.469882i) q^{5} +(3.00000 - 1.73205i) q^{7} +2.67181i q^{8} +(-1.68614 + 0.543620i) q^{10} +(2.18614 + 3.78651i) q^{11} +(5.05842 + 2.92048i) q^{13} +(1.37228 - 2.37686i) q^{14} +(-0.313859 - 0.543620i) q^{16} +0.792287i q^{17} +0.372281 q^{19} +(2.05842 - 2.27567i) q^{20} +(3.00000 + 1.73205i) q^{22} +(1.37228 + 0.792287i) q^{23} +(4.55842 + 2.05446i) q^{25} +4.62772 q^{26} +4.75372i q^{28} +(-2.87228 - 4.97494i) q^{29} +(-3.18614 + 5.51856i) q^{31} +(-5.05842 - 2.92048i) q^{32} +(0.313859 + 0.543620i) q^{34} +(-7.37228 + 2.37686i) q^{35} -2.37686i q^{37} +(0.255437 - 0.147477i) q^{38} +(1.25544 - 5.84096i) q^{40} +(-2.18614 + 3.78651i) q^{41} +(3.00000 - 1.73205i) q^{43} -6.00000 q^{44} +1.25544 q^{46} +(1.62772 - 0.939764i) q^{47} +(2.50000 - 4.33013i) q^{49} +(3.94158 - 0.396143i) q^{50} +(-6.94158 + 4.00772i) q^{52} -11.9769i q^{53} +(-3.00000 - 9.30506i) q^{55} +(4.62772 + 8.01544i) q^{56} +(-3.94158 - 2.27567i) q^{58} +(0.813859 - 1.40965i) q^{59} +(-4.68614 - 8.11663i) q^{61} +5.04868i q^{62} -3.37228 q^{64} +(-9.68614 - 8.76144i) q^{65} +(-10.1168 - 5.84096i) q^{67} +(-0.941578 - 0.543620i) q^{68} +(-4.11684 + 4.55134i) q^{70} +13.1168 q^{71} +2.37686i q^{73} +(-0.941578 - 1.63086i) q^{74} +(-0.255437 + 0.442430i) q^{76} +(13.1168 + 7.57301i) q^{77} +(3.37228 + 5.84096i) q^{79} +(0.430703 + 1.33591i) q^{80} +3.46410i q^{82} +(-10.3723 + 5.98844i) q^{83} +(0.372281 - 1.73205i) q^{85} +(1.37228 - 2.37686i) q^{86} +(-10.1168 + 5.84096i) q^{88} +3.00000 q^{89} +20.2337 q^{91} +(-1.88316 + 1.08724i) q^{92} +(0.744563 - 1.28962i) q^{94} +(-0.813859 - 0.174928i) q^{95} +(-1.11684 + 0.644810i) q^{97} -3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + 12 q^{7} - q^{10} + 3 q^{11} + 3 q^{13} - 6 q^{14} - 7 q^{16} - 10 q^{19} - 9 q^{20} + 12 q^{22} - 6 q^{23} + q^{25} + 30 q^{26} - 7 q^{31} - 3 q^{32} + 7 q^{34} - 18 q^{35} + 24 q^{38} + 28 q^{40} - 3 q^{41} + 12 q^{43} - 24 q^{44} + 28 q^{46} + 18 q^{47} + 10 q^{49} + 33 q^{50} - 45 q^{52} - 12 q^{55} + 30 q^{56} - 33 q^{58} + 9 q^{59} - 13 q^{61} - 2 q^{64} - 33 q^{65} - 6 q^{67} - 21 q^{68} + 18 q^{70} + 18 q^{71} - 21 q^{74} - 24 q^{76} + 18 q^{77} + 2 q^{79} - 27 q^{80} - 30 q^{83} - 10 q^{85} - 6 q^{86} - 6 q^{88} + 12 q^{89} + 12 q^{91} - 42 q^{92} - 20 q^{94} - 9 q^{95} + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.686141 0.396143i 0.485175 0.280116i −0.237396 0.971413i \(-0.576294\pi\)
0.722570 + 0.691297i \(0.242960\pi\)
\(3\) 0 0
\(4\) −0.686141 + 1.18843i −0.343070 + 0.594215i
\(5\) −2.18614 0.469882i −0.977672 0.210138i
\(6\) 0 0
\(7\) 3.00000 1.73205i 1.13389 0.654654i 0.188982 0.981981i \(-0.439481\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 2.67181i 0.944629i
\(9\) 0 0
\(10\) −1.68614 + 0.543620i −0.533204 + 0.171908i
\(11\) 2.18614 + 3.78651i 0.659146 + 1.14167i 0.980837 + 0.194830i \(0.0624155\pi\)
−0.321691 + 0.946845i \(0.604251\pi\)
\(12\) 0 0
\(13\) 5.05842 + 2.92048i 1.40295 + 0.809996i 0.994695 0.102870i \(-0.0328027\pi\)
0.408259 + 0.912866i \(0.366136\pi\)
\(14\) 1.37228 2.37686i 0.366758 0.635243i
\(15\) 0 0
\(16\) −0.313859 0.543620i −0.0784648 0.135905i
\(17\) 0.792287i 0.192158i 0.995374 + 0.0960789i \(0.0306301\pi\)
−0.995374 + 0.0960789i \(0.969370\pi\)
\(18\) 0 0
\(19\) 0.372281 0.0854072 0.0427036 0.999088i \(-0.486403\pi\)
0.0427036 + 0.999088i \(0.486403\pi\)
\(20\) 2.05842 2.27567i 0.460277 0.508856i
\(21\) 0 0
\(22\) 3.00000 + 1.73205i 0.639602 + 0.369274i
\(23\) 1.37228 + 0.792287i 0.286140 + 0.165203i 0.636200 0.771524i \(-0.280505\pi\)
−0.350060 + 0.936727i \(0.613839\pi\)
\(24\) 0 0
\(25\) 4.55842 + 2.05446i 0.911684 + 0.410891i
\(26\) 4.62772 0.907570
\(27\) 0 0
\(28\) 4.75372i 0.898369i
\(29\) −2.87228 4.97494i −0.533369 0.923823i −0.999240 0.0389701i \(-0.987592\pi\)
0.465871 0.884853i \(-0.345741\pi\)
\(30\) 0 0
\(31\) −3.18614 + 5.51856i −0.572248 + 0.991162i 0.424087 + 0.905621i \(0.360595\pi\)
−0.996335 + 0.0855407i \(0.972738\pi\)
\(32\) −5.05842 2.92048i −0.894211 0.516273i
\(33\) 0 0
\(34\) 0.313859 + 0.543620i 0.0538264 + 0.0932301i
\(35\) −7.37228 + 2.37686i −1.24614 + 0.401763i
\(36\) 0 0
\(37\) 2.37686i 0.390754i −0.980728 0.195377i \(-0.937407\pi\)
0.980728 0.195377i \(-0.0625930\pi\)
\(38\) 0.255437 0.147477i 0.0414374 0.0239239i
\(39\) 0 0
\(40\) 1.25544 5.84096i 0.198502 0.923537i
\(41\) −2.18614 + 3.78651i −0.341418 + 0.591353i −0.984696 0.174279i \(-0.944240\pi\)
0.643278 + 0.765632i \(0.277574\pi\)
\(42\) 0 0
\(43\) 3.00000 1.73205i 0.457496 0.264135i −0.253495 0.967337i \(-0.581580\pi\)
0.710991 + 0.703201i \(0.248247\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 1.25544 0.185104
\(47\) 1.62772 0.939764i 0.237427 0.137079i −0.376566 0.926390i \(-0.622895\pi\)
0.613994 + 0.789311i \(0.289562\pi\)
\(48\) 0 0
\(49\) 2.50000 4.33013i 0.357143 0.618590i
\(50\) 3.94158 0.396143i 0.557423 0.0560232i
\(51\) 0 0
\(52\) −6.94158 + 4.00772i −0.962624 + 0.555771i
\(53\) 11.9769i 1.64515i −0.568656 0.822575i \(-0.692536\pi\)
0.568656 0.822575i \(-0.307464\pi\)
\(54\) 0 0
\(55\) −3.00000 9.30506i −0.404520 1.25469i
\(56\) 4.62772 + 8.01544i 0.618405 + 1.07111i
\(57\) 0 0
\(58\) −3.94158 2.27567i −0.517555 0.298810i
\(59\) 0.813859 1.40965i 0.105955 0.183520i −0.808173 0.588946i \(-0.799543\pi\)
0.914128 + 0.405425i \(0.132877\pi\)
\(60\) 0 0
\(61\) −4.68614 8.11663i −0.599999 1.03923i −0.992820 0.119614i \(-0.961834\pi\)
0.392822 0.919615i \(-0.371499\pi\)
\(62\) 5.04868i 0.641182i
\(63\) 0 0
\(64\) −3.37228 −0.421535
\(65\) −9.68614 8.76144i −1.20142 1.08672i
\(66\) 0 0
\(67\) −10.1168 5.84096i −1.23597 0.713587i −0.267701 0.963502i \(-0.586264\pi\)
−0.968268 + 0.249915i \(0.919597\pi\)
\(68\) −0.941578 0.543620i −0.114183 0.0659236i
\(69\) 0 0
\(70\) −4.11684 + 4.55134i −0.492057 + 0.543989i
\(71\) 13.1168 1.55668 0.778341 0.627841i \(-0.216061\pi\)
0.778341 + 0.627841i \(0.216061\pi\)
\(72\) 0 0
\(73\) 2.37686i 0.278191i 0.990279 + 0.139095i \(0.0444194\pi\)
−0.990279 + 0.139095i \(0.955581\pi\)
\(74\) −0.941578 1.63086i −0.109456 0.189584i
\(75\) 0 0
\(76\) −0.255437 + 0.442430i −0.0293007 + 0.0507503i
\(77\) 13.1168 + 7.57301i 1.49480 + 0.863025i
\(78\) 0 0
\(79\) 3.37228 + 5.84096i 0.379411 + 0.657160i 0.990977 0.134034i \(-0.0427932\pi\)
−0.611565 + 0.791194i \(0.709460\pi\)
\(80\) 0.430703 + 1.33591i 0.0481541 + 0.149359i
\(81\) 0 0
\(82\) 3.46410i 0.382546i
\(83\) −10.3723 + 5.98844i −1.13851 + 0.657317i −0.946060 0.323991i \(-0.894975\pi\)
−0.192446 + 0.981308i \(0.561642\pi\)
\(84\) 0 0
\(85\) 0.372281 1.73205i 0.0403796 0.187867i
\(86\) 1.37228 2.37686i 0.147977 0.256304i
\(87\) 0 0
\(88\) −10.1168 + 5.84096i −1.07846 + 0.622649i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 20.2337 2.12107
\(92\) −1.88316 + 1.08724i −0.196333 + 0.113353i
\(93\) 0 0
\(94\) 0.744563 1.28962i 0.0767958 0.133014i
\(95\) −0.813859 0.174928i −0.0835002 0.0179473i
\(96\) 0 0
\(97\) −1.11684 + 0.644810i −0.113398 + 0.0654706i −0.555626 0.831432i \(-0.687522\pi\)
0.442228 + 0.896903i \(0.354188\pi\)
\(98\) 3.96143i 0.400165i
\(99\) 0 0
\(100\) −5.56930 + 4.00772i −0.556930 + 0.400772i
\(101\) 8.18614 + 14.1788i 0.814551 + 1.41084i 0.909650 + 0.415377i \(0.136350\pi\)
−0.0950981 + 0.995468i \(0.530316\pi\)
\(102\) 0 0
\(103\) −6.00000 3.46410i −0.591198 0.341328i 0.174373 0.984680i \(-0.444210\pi\)
−0.765571 + 0.643352i \(0.777543\pi\)
\(104\) −7.80298 + 13.5152i −0.765146 + 1.32527i
\(105\) 0 0
\(106\) −4.74456 8.21782i −0.460833 0.798186i
\(107\) 13.2665i 1.28252i −0.767323 0.641260i \(-0.778412\pi\)
0.767323 0.641260i \(-0.221588\pi\)
\(108\) 0 0
\(109\) −9.74456 −0.933360 −0.466680 0.884426i \(-0.654550\pi\)
−0.466680 + 0.884426i \(0.654550\pi\)
\(110\) −5.74456 5.19615i −0.547723 0.495434i
\(111\) 0 0
\(112\) −1.88316 1.08724i −0.177942 0.102735i
\(113\) 5.31386 + 3.06796i 0.499886 + 0.288609i 0.728666 0.684869i \(-0.240140\pi\)
−0.228781 + 0.973478i \(0.573474\pi\)
\(114\) 0 0
\(115\) −2.62772 2.37686i −0.245036 0.221643i
\(116\) 7.88316 0.731933
\(117\) 0 0
\(118\) 1.28962i 0.118719i
\(119\) 1.37228 + 2.37686i 0.125797 + 0.217886i
\(120\) 0 0
\(121\) −4.05842 + 7.02939i −0.368947 + 0.639036i
\(122\) −6.43070 3.71277i −0.582209 0.336138i
\(123\) 0 0
\(124\) −4.37228 7.57301i −0.392642 0.680077i
\(125\) −9.00000 6.63325i −0.804984 0.593296i
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 7.80298 4.50506i 0.689693 0.398194i
\(129\) 0 0
\(130\) −10.1168 2.17448i −0.887306 0.190715i
\(131\) −2.18614 + 3.78651i −0.191004 + 0.330829i −0.945583 0.325380i \(-0.894508\pi\)
0.754579 + 0.656209i \(0.227841\pi\)
\(132\) 0 0
\(133\) 1.11684 0.644810i 0.0968427 0.0559121i
\(134\) −9.25544 −0.799548
\(135\) 0 0
\(136\) −2.11684 −0.181518
\(137\) −12.4307 + 7.17687i −1.06203 + 0.613161i −0.925992 0.377543i \(-0.876769\pi\)
−0.136034 + 0.990704i \(0.543436\pi\)
\(138\) 0 0
\(139\) 5.55842 9.62747i 0.471459 0.816591i −0.528008 0.849240i \(-0.677061\pi\)
0.999467 + 0.0326483i \(0.0103941\pi\)
\(140\) 2.23369 10.3923i 0.188781 0.878310i
\(141\) 0 0
\(142\) 9.00000 5.19615i 0.755263 0.436051i
\(143\) 25.5383i 2.13562i
\(144\) 0 0
\(145\) 3.94158 + 12.2255i 0.327330 + 1.01528i
\(146\) 0.941578 + 1.63086i 0.0779256 + 0.134971i
\(147\) 0 0
\(148\) 2.82473 + 1.63086i 0.232192 + 0.134056i
\(149\) 5.31386 9.20387i 0.435328 0.754011i −0.561994 0.827141i \(-0.689966\pi\)
0.997322 + 0.0731305i \(0.0232990\pi\)
\(150\) 0 0
\(151\) −0.441578 0.764836i −0.0359351 0.0622414i 0.847499 0.530798i \(-0.178108\pi\)
−0.883434 + 0.468556i \(0.844774\pi\)
\(152\) 0.994667i 0.0806781i
\(153\) 0 0
\(154\) 12.0000 0.966988
\(155\) 9.55842 10.5672i 0.767751 0.848781i
\(156\) 0 0
\(157\) 9.94158 + 5.73977i 0.793424 + 0.458084i 0.841167 0.540776i \(-0.181869\pi\)
−0.0477424 + 0.998860i \(0.515203\pi\)
\(158\) 4.62772 + 2.67181i 0.368162 + 0.212558i
\(159\) 0 0
\(160\) 9.68614 + 8.76144i 0.765757 + 0.692653i
\(161\) 5.48913 0.432604
\(162\) 0 0
\(163\) 15.1460i 1.18633i −0.805082 0.593164i \(-0.797878\pi\)
0.805082 0.593164i \(-0.202122\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −4.74456 + 8.21782i −0.368249 + 0.637827i
\(167\) −11.7446 6.78073i −0.908822 0.524708i −0.0287697 0.999586i \(-0.509159\pi\)
−0.880052 + 0.474878i \(0.842492\pi\)
\(168\) 0 0
\(169\) 10.5584 + 18.2877i 0.812186 + 1.40675i
\(170\) −0.430703 1.33591i −0.0330334 0.102459i
\(171\) 0 0
\(172\) 4.75372i 0.362468i
\(173\) 9.68614 5.59230i 0.736424 0.425174i −0.0843439 0.996437i \(-0.526879\pi\)
0.820768 + 0.571262i \(0.193546\pi\)
\(174\) 0 0
\(175\) 17.2337 1.73205i 1.30274 0.130931i
\(176\) 1.37228 2.37686i 0.103440 0.179163i
\(177\) 0 0
\(178\) 2.05842 1.18843i 0.154285 0.0890766i
\(179\) 4.88316 0.364984 0.182492 0.983207i \(-0.441584\pi\)
0.182492 + 0.983207i \(0.441584\pi\)
\(180\) 0 0
\(181\) −13.8614 −1.03031 −0.515155 0.857097i \(-0.672266\pi\)
−0.515155 + 0.857097i \(0.672266\pi\)
\(182\) 13.8832 8.01544i 1.02909 0.594144i
\(183\) 0 0
\(184\) −2.11684 + 3.66648i −0.156056 + 0.270297i
\(185\) −1.11684 + 5.19615i −0.0821120 + 0.382029i
\(186\) 0 0
\(187\) −3.00000 + 1.73205i −0.219382 + 0.126660i
\(188\) 2.57924i 0.188110i
\(189\) 0 0
\(190\) −0.627719 + 0.202380i −0.0455395 + 0.0146822i
\(191\) −3.81386 6.60580i −0.275961 0.477979i 0.694416 0.719574i \(-0.255663\pi\)
−0.970377 + 0.241595i \(0.922329\pi\)
\(192\) 0 0
\(193\) 9.94158 + 5.73977i 0.715610 + 0.413158i 0.813135 0.582075i \(-0.197759\pi\)
−0.0975245 + 0.995233i \(0.531092\pi\)
\(194\) −0.510875 + 0.884861i −0.0366787 + 0.0635293i
\(195\) 0 0
\(196\) 3.43070 + 5.94215i 0.245050 + 0.424439i
\(197\) 6.43087i 0.458181i 0.973405 + 0.229090i \(0.0735751\pi\)
−0.973405 + 0.229090i \(0.926425\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −5.48913 + 12.1793i −0.388140 + 0.861204i
\(201\) 0 0
\(202\) 11.2337 + 6.48577i 0.790400 + 0.456337i
\(203\) −17.2337 9.94987i −1.20957 0.698344i
\(204\) 0 0
\(205\) 6.55842 7.25061i 0.458060 0.506404i
\(206\) −5.48913 −0.382445
\(207\) 0 0
\(208\) 3.66648i 0.254225i
\(209\) 0.813859 + 1.40965i 0.0562958 + 0.0975072i
\(210\) 0 0
\(211\) 0.930703 1.61203i 0.0640723 0.110976i −0.832210 0.554461i \(-0.812925\pi\)
0.896282 + 0.443484i \(0.146258\pi\)
\(212\) 14.2337 + 8.21782i 0.977574 + 0.564402i
\(213\) 0 0
\(214\) −5.25544 9.10268i −0.359254 0.622247i
\(215\) −7.37228 + 2.37686i −0.502785 + 0.162101i
\(216\) 0 0
\(217\) 22.0742i 1.49850i
\(218\) −6.68614 + 3.86025i −0.452843 + 0.261449i
\(219\) 0 0
\(220\) 13.1168 + 2.81929i 0.884337 + 0.190077i
\(221\) −2.31386 + 4.00772i −0.155647 + 0.269589i
\(222\) 0 0
\(223\) 16.1168 9.30506i 1.07926 0.623113i 0.148566 0.988902i \(-0.452534\pi\)
0.930698 + 0.365789i \(0.119201\pi\)
\(224\) −20.2337 −1.35192
\(225\) 0 0
\(226\) 4.86141 0.323376
\(227\) 11.7446 6.78073i 0.779514 0.450053i −0.0567440 0.998389i \(-0.518072\pi\)
0.836258 + 0.548336i \(0.184739\pi\)
\(228\) 0 0
\(229\) −8.80298 + 15.2472i −0.581718 + 1.00756i 0.413558 + 0.910478i \(0.364286\pi\)
−0.995276 + 0.0970868i \(0.969048\pi\)
\(230\) −2.74456 0.589907i −0.180971 0.0388973i
\(231\) 0 0
\(232\) 13.2921 7.67420i 0.872670 0.503836i
\(233\) 6.13592i 0.401977i −0.979594 0.200989i \(-0.935585\pi\)
0.979594 0.200989i \(-0.0644154\pi\)
\(234\) 0 0
\(235\) −4.00000 + 1.28962i −0.260931 + 0.0841256i
\(236\) 1.11684 + 1.93443i 0.0727004 + 0.125921i
\(237\) 0 0
\(238\) 1.88316 + 1.08724i 0.122067 + 0.0704753i
\(239\) 11.4891 19.8997i 0.743170 1.28721i −0.207875 0.978155i \(-0.566655\pi\)
0.951045 0.309052i \(-0.100012\pi\)
\(240\) 0 0
\(241\) 0.755437 + 1.30846i 0.0486620 + 0.0842851i 0.889330 0.457265i \(-0.151171\pi\)
−0.840668 + 0.541550i \(0.817838\pi\)
\(242\) 6.43087i 0.413392i
\(243\) 0 0
\(244\) 12.8614 0.823367
\(245\) −7.50000 + 8.29156i −0.479157 + 0.529728i
\(246\) 0 0
\(247\) 1.88316 + 1.08724i 0.119822 + 0.0691795i
\(248\) −14.7446 8.51278i −0.936281 0.540562i
\(249\) 0 0
\(250\) −8.80298 0.986051i −0.556750 0.0623633i
\(251\) −20.2337 −1.27714 −0.638570 0.769564i \(-0.720474\pi\)
−0.638570 + 0.769564i \(0.720474\pi\)
\(252\) 0 0
\(253\) 6.92820i 0.435572i
\(254\) −4.11684 7.13058i −0.258314 0.447413i
\(255\) 0 0
\(256\) 6.94158 12.0232i 0.433849 0.751448i
\(257\) −5.56930 3.21543i −0.347403 0.200573i 0.316138 0.948713i \(-0.397614\pi\)
−0.663541 + 0.748140i \(0.730947\pi\)
\(258\) 0 0
\(259\) −4.11684 7.13058i −0.255808 0.443073i
\(260\) 17.0584 5.49972i 1.05792 0.341078i
\(261\) 0 0
\(262\) 3.46410i 0.214013i
\(263\) 22.9783 13.2665i 1.41690 0.818047i 0.420874 0.907119i \(-0.361723\pi\)
0.996025 + 0.0890715i \(0.0283900\pi\)
\(264\) 0 0
\(265\) −5.62772 + 26.1831i −0.345708 + 1.60842i
\(266\) 0.510875 0.884861i 0.0313237 0.0542543i
\(267\) 0 0
\(268\) 13.8832 8.01544i 0.848049 0.489621i
\(269\) 29.2337 1.78241 0.891205 0.453601i \(-0.149861\pi\)
0.891205 + 0.453601i \(0.149861\pi\)
\(270\) 0 0
\(271\) 5.25544 0.319245 0.159623 0.987178i \(-0.448972\pi\)
0.159623 + 0.987178i \(0.448972\pi\)
\(272\) 0.430703 0.248667i 0.0261152 0.0150776i
\(273\) 0 0
\(274\) −5.68614 + 9.84868i −0.343512 + 0.594981i
\(275\) 2.18614 + 21.7518i 0.131829 + 1.31168i
\(276\) 0 0
\(277\) −19.1168 + 11.0371i −1.14862 + 0.663156i −0.948551 0.316626i \(-0.897450\pi\)
−0.200069 + 0.979782i \(0.564117\pi\)
\(278\) 8.80773i 0.528253i
\(279\) 0 0
\(280\) −6.35053 19.6974i −0.379517 1.17714i
\(281\) 0.686141 + 1.18843i 0.0409317 + 0.0708958i 0.885765 0.464133i \(-0.153634\pi\)
−0.844834 + 0.535029i \(0.820301\pi\)
\(282\) 0 0
\(283\) −24.0000 13.8564i −1.42665 0.823678i −0.429797 0.902926i \(-0.641415\pi\)
−0.996855 + 0.0792477i \(0.974748\pi\)
\(284\) −9.00000 + 15.5885i −0.534052 + 0.925005i
\(285\) 0 0
\(286\) 10.1168 + 17.5229i 0.598222 + 1.03615i
\(287\) 15.1460i 0.894042i
\(288\) 0 0
\(289\) 16.3723 0.963075
\(290\) 7.54755 + 6.82701i 0.443207 + 0.400896i
\(291\) 0 0
\(292\) −2.82473 1.63086i −0.165305 0.0954389i
\(293\) −0.686141 0.396143i −0.0400848 0.0231430i 0.479824 0.877365i \(-0.340701\pi\)
−0.519908 + 0.854222i \(0.674034\pi\)
\(294\) 0 0
\(295\) −2.44158 + 2.69927i −0.142154 + 0.157157i
\(296\) 6.35053 0.369117
\(297\) 0 0
\(298\) 8.42020i 0.487769i
\(299\) 4.62772 + 8.01544i 0.267628 + 0.463545i
\(300\) 0 0
\(301\) 6.00000 10.3923i 0.345834 0.599002i
\(302\) −0.605969 0.349857i −0.0348696 0.0201320i
\(303\) 0 0
\(304\) −0.116844 0.202380i −0.00670146 0.0116073i
\(305\) 6.43070 + 19.9460i 0.368221 + 1.14211i
\(306\) 0 0
\(307\) 15.1460i 0.864429i −0.901771 0.432215i \(-0.857732\pi\)
0.901771 0.432215i \(-0.142268\pi\)
\(308\) −18.0000 + 10.3923i −1.02565 + 0.592157i
\(309\) 0 0
\(310\) 2.37228 11.0371i 0.134737 0.626866i
\(311\) 7.93070 13.7364i 0.449709 0.778919i −0.548658 0.836047i \(-0.684861\pi\)
0.998367 + 0.0571282i \(0.0181944\pi\)
\(312\) 0 0
\(313\) −21.1753 + 12.2255i −1.19690 + 0.691029i −0.959862 0.280472i \(-0.909509\pi\)
−0.237035 + 0.971501i \(0.576176\pi\)
\(314\) 9.09509 0.513266
\(315\) 0 0
\(316\) −9.25544 −0.520659
\(317\) −25.5475 + 14.7499i −1.43489 + 0.828436i −0.997488 0.0708288i \(-0.977436\pi\)
−0.437405 + 0.899265i \(0.644102\pi\)
\(318\) 0 0
\(319\) 12.5584 21.7518i 0.703137 1.21787i
\(320\) 7.37228 + 1.58457i 0.412123 + 0.0885804i
\(321\) 0 0
\(322\) 3.76631 2.17448i 0.209888 0.121179i
\(323\) 0.294954i 0.0164117i
\(324\) 0 0
\(325\) 17.0584 + 23.7051i 0.946231 + 1.31492i
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) 0 0
\(328\) −10.1168 5.84096i −0.558609 0.322513i
\(329\) 3.25544 5.63858i 0.179478 0.310865i
\(330\) 0 0
\(331\) −4.55842 7.89542i −0.250554 0.433971i 0.713125 0.701037i \(-0.247279\pi\)
−0.963678 + 0.267066i \(0.913946\pi\)
\(332\) 16.4356i 0.902023i
\(333\) 0 0
\(334\) −10.7446 −0.587916
\(335\) 19.3723 + 17.5229i 1.05842 + 0.957378i
\(336\) 0 0
\(337\) −6.00000 3.46410i −0.326841 0.188702i 0.327597 0.944818i \(-0.393761\pi\)
−0.654438 + 0.756116i \(0.727095\pi\)
\(338\) 14.4891 + 8.36530i 0.788105 + 0.455012i
\(339\) 0 0
\(340\) 1.80298 + 1.63086i 0.0977806 + 0.0884459i
\(341\) −27.8614 −1.50878
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) 4.62772 + 8.01544i 0.249510 + 0.432164i
\(345\) 0 0
\(346\) 4.43070 7.67420i 0.238196 0.412568i
\(347\) 2.48913 + 1.43710i 0.133623 + 0.0771474i 0.565321 0.824871i \(-0.308752\pi\)
−0.431698 + 0.902018i \(0.642085\pi\)
\(348\) 0 0
\(349\) −13.3030 23.0414i −0.712092 1.23338i −0.964070 0.265647i \(-0.914414\pi\)
0.251978 0.967733i \(-0.418919\pi\)
\(350\) 11.1386 8.01544i 0.595383 0.428443i
\(351\) 0 0
\(352\) 25.5383i 1.36120i
\(353\) 1.62772 0.939764i 0.0866347 0.0500186i −0.456057 0.889951i \(-0.650739\pi\)
0.542692 + 0.839932i \(0.317405\pi\)
\(354\) 0 0
\(355\) −28.6753 6.16337i −1.52193 0.327118i
\(356\) −2.05842 + 3.56529i −0.109096 + 0.188960i
\(357\) 0 0
\(358\) 3.35053 1.93443i 0.177081 0.102238i
\(359\) 10.8832 0.574391 0.287196 0.957872i \(-0.407277\pi\)
0.287196 + 0.957872i \(0.407277\pi\)
\(360\) 0 0
\(361\) −18.8614 −0.992706
\(362\) −9.51087 + 5.49111i −0.499880 + 0.288606i
\(363\) 0 0
\(364\) −13.8832 + 24.0463i −0.727675 + 1.26037i
\(365\) 1.11684 5.19615i 0.0584583 0.271979i
\(366\) 0 0
\(367\) −14.2337 + 8.21782i −0.742992 + 0.428967i −0.823156 0.567815i \(-0.807789\pi\)
0.0801639 + 0.996782i \(0.474456\pi\)
\(368\) 0.994667i 0.0518506i
\(369\) 0 0
\(370\) 1.29211 + 4.00772i 0.0671736 + 0.208352i
\(371\) −20.7446 35.9306i −1.07700 1.86543i
\(372\) 0 0
\(373\) 7.11684 + 4.10891i 0.368496 + 0.212751i 0.672801 0.739823i \(-0.265091\pi\)
−0.304305 + 0.952575i \(0.598424\pi\)
\(374\) −1.37228 + 2.37686i −0.0709590 + 0.122905i
\(375\) 0 0
\(376\) 2.51087 + 4.34896i 0.129488 + 0.224281i
\(377\) 33.5538i 1.72811i
\(378\) 0 0
\(379\) 1.48913 0.0764912 0.0382456 0.999268i \(-0.487823\pi\)
0.0382456 + 0.999268i \(0.487823\pi\)
\(380\) 0.766312 0.847190i 0.0393110 0.0434599i
\(381\) 0 0
\(382\) −5.23369 3.02167i −0.267779 0.154602i
\(383\) 9.60597 + 5.54601i 0.490842 + 0.283388i 0.724924 0.688829i \(-0.241875\pi\)
−0.234082 + 0.972217i \(0.575208\pi\)
\(384\) 0 0
\(385\) −25.1168 22.7190i −1.28007 1.15787i
\(386\) 9.09509 0.462928
\(387\) 0 0
\(388\) 1.76972i 0.0898440i
\(389\) −0.255437 0.442430i −0.0129512 0.0224321i 0.859477 0.511174i \(-0.170789\pi\)
−0.872428 + 0.488742i \(0.837456\pi\)
\(390\) 0 0
\(391\) −0.627719 + 1.08724i −0.0317451 + 0.0549841i
\(392\) 11.5693 + 6.67954i 0.584338 + 0.337368i
\(393\) 0 0
\(394\) 2.54755 + 4.41248i 0.128344 + 0.222298i
\(395\) −4.62772 14.3537i −0.232846 0.722215i
\(396\) 0 0
\(397\) 17.5229i 0.879449i 0.898133 + 0.439724i \(0.144924\pi\)
−0.898133 + 0.439724i \(0.855076\pi\)
\(398\) −10.9783 + 6.33830i −0.550290 + 0.317710i
\(399\) 0 0
\(400\) −0.313859 3.12286i −0.0156930 0.156143i
\(401\) −12.6861 + 21.9730i −0.633516 + 1.09728i 0.353312 + 0.935506i \(0.385055\pi\)
−0.986828 + 0.161776i \(0.948278\pi\)
\(402\) 0 0
\(403\) −32.2337 + 18.6101i −1.60567 + 0.927037i
\(404\) −22.4674 −1.11779
\(405\) 0 0
\(406\) −15.7663 −0.782469
\(407\) 9.00000 5.19615i 0.446113 0.257564i
\(408\) 0 0
\(409\) 11.4307 19.7986i 0.565212 0.978976i −0.431818 0.901961i \(-0.642128\pi\)
0.997030 0.0770150i \(-0.0245389\pi\)
\(410\) 1.62772 7.57301i 0.0803873 0.374004i
\(411\) 0 0
\(412\) 8.23369 4.75372i 0.405645 0.234199i
\(413\) 5.63858i 0.277457i
\(414\) 0 0
\(415\) 25.4891 8.21782i 1.25121 0.403397i
\(416\) −17.0584 29.5461i −0.836358 1.44861i
\(417\) 0 0
\(418\) 1.11684 + 0.644810i 0.0546266 + 0.0315387i
\(419\) −8.74456 + 15.1460i −0.427200 + 0.739932i −0.996623 0.0821127i \(-0.973833\pi\)
0.569423 + 0.822045i \(0.307167\pi\)
\(420\) 0 0
\(421\) 10.8723 + 18.8313i 0.529883 + 0.917784i 0.999392 + 0.0348563i \(0.0110973\pi\)
−0.469510 + 0.882927i \(0.655569\pi\)
\(422\) 1.47477i 0.0717906i
\(423\) 0 0
\(424\) 32.0000 1.55406
\(425\) −1.62772 + 3.61158i −0.0789560 + 0.175187i
\(426\) 0 0
\(427\) −28.1168 16.2333i −1.36067 0.785583i
\(428\) 15.7663 + 9.10268i 0.762093 + 0.439995i
\(429\) 0 0
\(430\) −4.11684 + 4.55134i −0.198532 + 0.219485i
\(431\) −33.3505 −1.60644 −0.803219 0.595683i \(-0.796881\pi\)
−0.803219 + 0.595683i \(0.796881\pi\)
\(432\) 0 0
\(433\) 12.7692i 0.613647i 0.951766 + 0.306823i \(0.0992661\pi\)
−0.951766 + 0.306823i \(0.900734\pi\)
\(434\) 8.74456 + 15.1460i 0.419752 + 0.727033i
\(435\) 0 0
\(436\) 6.68614 11.5807i 0.320208 0.554617i
\(437\) 0.510875 + 0.294954i 0.0244385 + 0.0141095i
\(438\) 0 0
\(439\) 15.9307 + 27.5928i 0.760331 + 1.31693i 0.942680 + 0.333698i \(0.108297\pi\)
−0.182349 + 0.983234i \(0.558370\pi\)
\(440\) 24.8614 8.01544i 1.18522 0.382121i
\(441\) 0 0
\(442\) 3.66648i 0.174397i
\(443\) −18.6060 + 10.7422i −0.883996 + 0.510375i −0.871974 0.489552i \(-0.837160\pi\)
−0.0120223 + 0.999928i \(0.503827\pi\)
\(444\) 0 0
\(445\) −6.55842 1.40965i −0.310899 0.0668236i
\(446\) 7.37228 12.7692i 0.349088 0.604638i
\(447\) 0 0
\(448\) −10.1168 + 5.84096i −0.477976 + 0.275960i
\(449\) 10.8832 0.513608 0.256804 0.966464i \(-0.417331\pi\)
0.256804 + 0.966464i \(0.417331\pi\)
\(450\) 0 0
\(451\) −19.1168 −0.900177
\(452\) −7.29211 + 4.21010i −0.342992 + 0.198027i
\(453\) 0 0
\(454\) 5.37228 9.30506i 0.252134 0.436708i
\(455\) −44.2337 9.50744i −2.07371 0.445716i
\(456\) 0 0
\(457\) 18.1753 10.4935i 0.850203 0.490865i −0.0105163 0.999945i \(-0.503348\pi\)
0.860719 + 0.509080i \(0.170014\pi\)
\(458\) 13.9490i 0.651793i
\(459\) 0 0
\(460\) 4.62772 1.49200i 0.215768 0.0695649i
\(461\) −12.0475 20.8670i −0.561110 0.971871i −0.997400 0.0720652i \(-0.977041\pi\)
0.436290 0.899806i \(-0.356292\pi\)
\(462\) 0 0
\(463\) 12.0000 + 6.92820i 0.557687 + 0.321981i 0.752217 0.658916i \(-0.228985\pi\)
−0.194529 + 0.980897i \(0.562318\pi\)
\(464\) −1.80298 + 3.12286i −0.0837015 + 0.144975i
\(465\) 0 0
\(466\) −2.43070 4.21010i −0.112600 0.195029i
\(467\) 18.3152i 0.847525i 0.905773 + 0.423763i \(0.139291\pi\)
−0.905773 + 0.423763i \(0.860709\pi\)
\(468\) 0 0
\(469\) −40.4674 −1.86861
\(470\) −2.23369 + 2.46943i −0.103032 + 0.113907i
\(471\) 0 0
\(472\) 3.76631 + 2.17448i 0.173359 + 0.100089i
\(473\) 13.1168 + 7.57301i 0.603113 + 0.348208i
\(474\) 0 0
\(475\) 1.69702 + 0.764836i 0.0778644 + 0.0350931i
\(476\) −3.76631 −0.172629
\(477\) 0 0
\(478\) 18.2054i 0.832694i
\(479\) 9.30298 + 16.1132i 0.425064 + 0.736233i 0.996426 0.0844652i \(-0.0269182\pi\)
−0.571362 + 0.820698i \(0.693585\pi\)
\(480\) 0 0
\(481\) 6.94158 12.0232i 0.316509 0.548209i
\(482\) 1.03667 + 0.598523i 0.0472191 + 0.0272620i
\(483\) 0 0
\(484\) −5.56930 9.64630i −0.253150 0.438468i
\(485\) 2.74456 0.884861i 0.124624 0.0401795i
\(486\) 0 0
\(487\) 9.50744i 0.430823i −0.976523 0.215412i \(-0.930891\pi\)
0.976523 0.215412i \(-0.0691093\pi\)
\(488\) 21.6861 12.5205i 0.981685 0.566776i
\(489\) 0 0
\(490\) −1.86141 + 8.66025i −0.0840898 + 0.391230i
\(491\) 15.8139 27.3904i 0.713669 1.23611i −0.249801 0.968297i \(-0.580365\pi\)
0.963470 0.267815i \(-0.0863015\pi\)
\(492\) 0 0
\(493\) 3.94158 2.27567i 0.177520 0.102491i
\(494\) 1.72281 0.0775130
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 39.3505 22.7190i 1.76511 1.01909i
\(498\) 0 0
\(499\) −12.1861 + 21.1070i −0.545527 + 0.944880i 0.453047 + 0.891487i \(0.350337\pi\)
−0.998574 + 0.0533931i \(0.982996\pi\)
\(500\) 14.0584 6.14453i 0.628712 0.274792i
\(501\) 0 0
\(502\) −13.8832 + 8.01544i −0.619636 + 0.357747i
\(503\) 3.16915i 0.141305i 0.997501 + 0.0706527i \(0.0225082\pi\)
−0.997501 + 0.0706527i \(0.977492\pi\)
\(504\) 0 0
\(505\) −11.2337 34.8434i −0.499893 1.55051i
\(506\) 2.74456 + 4.75372i 0.122011 + 0.211329i
\(507\) 0 0
\(508\) 12.3505 + 7.13058i 0.547966 + 0.316368i
\(509\) 0.255437 0.442430i 0.0113221 0.0196104i −0.860309 0.509773i \(-0.829729\pi\)
0.871631 + 0.490163i \(0.163063\pi\)
\(510\) 0 0
\(511\) 4.11684 + 7.13058i 0.182118 + 0.315438i
\(512\) 7.02078i 0.310277i
\(513\) 0 0
\(514\) −5.09509 −0.224735
\(515\) 11.4891 + 10.3923i 0.506271 + 0.457940i
\(516\) 0 0
\(517\) 7.11684 + 4.10891i 0.312998 + 0.180710i
\(518\) −5.64947 3.26172i −0.248223 0.143312i
\(519\) 0 0
\(520\) 23.4090 25.8796i 1.02655 1.13489i
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 4.75372i 0.207866i 0.994584 + 0.103933i \(0.0331427\pi\)
−0.994584 + 0.103933i \(0.966857\pi\)
\(524\) −3.00000 5.19615i −0.131056 0.226995i
\(525\) 0 0
\(526\) 10.5109 18.2054i 0.458296 0.793792i
\(527\) −4.37228 2.52434i −0.190460 0.109962i
\(528\) 0 0
\(529\) −10.2446 17.7441i −0.445416 0.771483i
\(530\) 6.51087 + 20.1947i 0.282814 + 0.877202i
\(531\) 0 0
\(532\) 1.76972i 0.0767272i
\(533\) −22.1168 + 12.7692i −0.957987 + 0.553094i
\(534\) 0 0
\(535\) −6.23369 + 29.0024i −0.269506 + 1.25388i
\(536\) 15.6060 27.0303i 0.674075 1.16753i
\(537\) 0 0
\(538\) 20.0584 11.5807i 0.864780 0.499281i
\(539\) 21.8614 0.941637
\(540\) 0 0
\(541\) 19.2337 0.826921 0.413460 0.910522i \(-0.364320\pi\)
0.413460 + 0.910522i \(0.364320\pi\)
\(542\) 3.60597 2.08191i 0.154890 0.0894256i
\(543\) 0 0
\(544\) 2.31386 4.00772i 0.0992059 0.171830i
\(545\) 21.3030 + 4.57879i 0.912520 + 0.196134i
\(546\) 0 0
\(547\) −6.00000 + 3.46410i −0.256541 + 0.148114i −0.622756 0.782416i \(-0.713987\pi\)
0.366214 + 0.930531i \(0.380654\pi\)
\(548\) 19.6974i 0.841430i
\(549\) 0 0
\(550\) 10.1168 + 14.0588i 0.431384 + 0.599469i
\(551\) −1.06930 1.85208i −0.0455536 0.0789011i
\(552\) 0 0
\(553\) 20.2337 + 11.6819i 0.860424 + 0.496766i
\(554\) −8.74456 + 15.1460i −0.371521 + 0.643493i
\(555\) 0 0
\(556\) 7.62772 + 13.2116i 0.323487 + 0.560296i
\(557\) 25.0410i 1.06102i 0.847678 + 0.530511i \(0.178000\pi\)
−0.847678 + 0.530511i \(0.822000\pi\)
\(558\) 0 0
\(559\) 20.2337 0.855794
\(560\) 3.60597 + 3.26172i 0.152380 + 0.137833i
\(561\) 0 0
\(562\) 0.941578 + 0.543620i 0.0397181 + 0.0229312i
\(563\) −27.8614 16.0858i −1.17422 0.677935i −0.219548 0.975602i \(-0.570458\pi\)
−0.954670 + 0.297666i \(0.903792\pi\)
\(564\) 0 0
\(565\) −10.1753 9.20387i −0.428077 0.387210i
\(566\) −21.9565 −0.922901
\(567\) 0 0
\(568\) 35.0458i 1.47049i
\(569\) 10.2446 + 17.7441i 0.429474 + 0.743871i 0.996827 0.0796038i \(-0.0253655\pi\)
−0.567352 + 0.823475i \(0.692032\pi\)
\(570\) 0 0
\(571\) −2.06930 + 3.58413i −0.0865974 + 0.149991i −0.906071 0.423126i \(-0.860933\pi\)
0.819473 + 0.573117i \(0.194266\pi\)
\(572\) −30.3505 17.5229i −1.26902 0.732669i
\(573\) 0 0
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) 4.62772 + 6.43087i 0.192989 + 0.268186i
\(576\) 0 0
\(577\) 18.4077i 0.766325i 0.923681 + 0.383162i \(0.125165\pi\)
−0.923681 + 0.383162i \(0.874835\pi\)
\(578\) 11.2337 6.48577i 0.467260 0.269773i
\(579\) 0 0
\(580\) −17.2337 3.70415i −0.715590 0.153807i
\(581\) −20.7446 + 35.9306i −0.860629 + 1.49065i
\(582\) 0 0
\(583\) 45.3505 26.1831i 1.87823 1.08439i
\(584\) −6.35053 −0.262787
\(585\) 0 0
\(586\) −0.627719 −0.0259308
\(587\) −14.4891 + 8.36530i −0.598030 + 0.345273i −0.768266 0.640130i \(-0.778880\pi\)
0.170236 + 0.985403i \(0.445547\pi\)
\(588\) 0 0
\(589\) −1.18614 + 2.05446i −0.0488741 + 0.0846524i
\(590\) −0.605969 + 2.81929i −0.0249474 + 0.116068i
\(591\) 0 0
\(592\) −1.29211 + 0.746000i −0.0531054 + 0.0306604i
\(593\) 1.67715i 0.0688722i 0.999407 + 0.0344361i \(0.0109635\pi\)
−0.999407 + 0.0344361i \(0.989036\pi\)
\(594\) 0 0
\(595\) −1.88316 5.84096i −0.0772019 0.239456i
\(596\) 7.29211 + 12.6303i 0.298696 + 0.517357i
\(597\) 0 0
\(598\) 6.35053 + 3.66648i 0.259693 + 0.149934i
\(599\) 0.813859 1.40965i 0.0332534 0.0575966i −0.848920 0.528522i \(-0.822746\pi\)
0.882173 + 0.470925i \(0.156080\pi\)
\(600\) 0 0
\(601\) 8.98913 + 15.5696i 0.366674 + 0.635098i 0.989043 0.147626i \(-0.0471631\pi\)
−0.622369 + 0.782724i \(0.713830\pi\)
\(602\) 9.50744i 0.387494i
\(603\) 0 0
\(604\) 1.21194 0.0493131
\(605\) 12.1753 13.4603i 0.494995 0.547238i
\(606\) 0 0
\(607\) 37.4674 + 21.6318i 1.52075 + 0.878008i 0.999700 + 0.0244837i \(0.00779419\pi\)
0.521054 + 0.853524i \(0.325539\pi\)
\(608\) −1.88316 1.08724i −0.0763721 0.0440934i
\(609\) 0 0
\(610\) 12.3139 + 11.1383i 0.498574 + 0.450977i
\(611\) 10.9783 0.444132
\(612\) 0 0
\(613\) 30.2921i 1.22348i 0.791057 + 0.611742i \(0.209531\pi\)
−0.791057 + 0.611742i \(0.790469\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 0 0
\(616\) −20.2337 + 35.0458i −0.815239 + 1.41203i
\(617\) −17.9198 10.3460i −0.721425 0.416515i 0.0938519 0.995586i \(-0.470082\pi\)
−0.815277 + 0.579071i \(0.803415\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 6.00000 + 18.6101i 0.240966 + 0.747401i
\(621\) 0 0
\(622\) 12.5668i 0.503882i
\(623\) 9.00000 5.19615i 0.360577 0.208179i
\(624\) 0 0
\(625\) 16.5584 + 18.7302i 0.662337 + 0.749206i
\(626\) −9.68614 + 16.7769i −0.387136 + 0.670539i
\(627\) 0 0
\(628\) −13.6426 + 7.87658i −0.544401 + 0.314310i
\(629\) 1.88316 0.0750863
\(630\) 0 0
\(631\) 6.37228 0.253677 0.126838 0.991923i \(-0.459517\pi\)
0.126838 + 0.991923i \(0.459517\pi\)
\(632\) −15.6060 + 9.01011i −0.620772 + 0.358403i
\(633\) 0 0
\(634\) −11.6861 + 20.2410i −0.464116 + 0.803872i
\(635\) −4.88316 + 22.7190i −0.193782 + 0.901578i
\(636\) 0 0
\(637\) 25.2921 14.6024i 1.00211 0.578568i
\(638\) 19.8997i 0.787839i
\(639\) 0 0
\(640\) −19.1753 + 6.18220i −0.757969 + 0.244373i
\(641\) −3.98913 6.90937i −0.157561 0.272904i 0.776428 0.630206i \(-0.217030\pi\)
−0.933989 + 0.357303i \(0.883696\pi\)
\(642\) 0 0
\(643\) −1.11684 0.644810i −0.0440440 0.0254288i 0.477816 0.878460i \(-0.341428\pi\)
−0.521860 + 0.853031i \(0.674762\pi\)
\(644\) −3.76631 + 6.52344i −0.148413 + 0.257060i
\(645\) 0 0
\(646\) 0.116844 + 0.202380i 0.00459716 + 0.00796252i
\(647\) 28.7075i 1.12861i 0.825567 + 0.564304i \(0.190855\pi\)
−0.825567 + 0.564304i \(0.809145\pi\)
\(648\) 0 0
\(649\) 7.11684 0.279361
\(650\) 21.0951 + 9.50744i 0.827418 + 0.372913i
\(651\) 0 0
\(652\) 18.0000 + 10.3923i 0.704934 + 0.406994i
\(653\) 5.48913 + 3.16915i 0.214806 + 0.124018i 0.603543 0.797330i \(-0.293755\pi\)
−0.388737 + 0.921349i \(0.627089\pi\)
\(654\) 0 0
\(655\) 6.55842 7.25061i 0.256259 0.283305i
\(656\) 2.74456 0.107157
\(657\) 0 0
\(658\) 5.15848i 0.201099i
\(659\) 10.6277 + 18.4077i 0.413997 + 0.717064i 0.995323 0.0966070i \(-0.0307990\pi\)
−0.581325 + 0.813671i \(0.697466\pi\)
\(660\) 0 0
\(661\) 7.61684 13.1928i 0.296261 0.513139i −0.679017 0.734123i \(-0.737594\pi\)
0.975277 + 0.220984i \(0.0709269\pi\)
\(662\) −6.25544 3.61158i −0.243124 0.140368i
\(663\) 0 0
\(664\) −16.0000 27.7128i −0.620920 1.07547i
\(665\) −2.74456 + 0.884861i −0.106430 + 0.0343134i
\(666\) 0 0
\(667\) 9.10268i 0.352457i
\(668\) 16.1168 9.30506i 0.623579 0.360024i
\(669\) 0 0
\(670\) 20.2337 + 4.34896i 0.781696 + 0.168015i
\(671\) 20.4891 35.4882i 0.790974 1.37001i
\(672\) 0 0
\(673\) 9.17527 5.29734i 0.353681 0.204198i −0.312625 0.949877i \(-0.601208\pi\)
0.666305 + 0.745679i \(0.267875\pi\)
\(674\) −5.48913 −0.211433
\(675\) 0 0
\(676\) −28.9783 −1.11455
\(677\) 22.9783 13.2665i 0.883126 0.509873i 0.0114381 0.999935i \(-0.496359\pi\)
0.871688 + 0.490062i \(0.163026\pi\)
\(678\) 0 0
\(679\) −2.23369 + 3.86886i −0.0857211 + 0.148473i
\(680\) 4.62772 + 0.994667i 0.177465 + 0.0381437i
\(681\) 0 0
\(682\) −19.1168 + 11.0371i −0.732022 + 0.422633i
\(683\) 27.1229i 1.03783i −0.854826 0.518915i \(-0.826336\pi\)
0.854826 0.518915i \(-0.173664\pi\)
\(684\) 0 0
\(685\) 30.5475 9.84868i 1.16716 0.376299i
\(686\) 2.74456 + 4.75372i 0.104788 + 0.181498i
\(687\) 0 0
\(688\) −1.88316 1.08724i −0.0717947 0.0414507i
\(689\) 34.9783 60.5841i 1.33257 2.30807i
\(690\) 0 0
\(691\) −22.8614 39.5971i −0.869689 1.50635i −0.862315 0.506373i \(-0.830986\pi\)
−0.00737407 0.999973i \(-0.502347\pi\)
\(692\) 15.3484i 0.583459i
\(693\) 0 0
\(694\) 2.27719 0.0864408
\(695\) −16.6753 + 18.4352i −0.632529 + 0.699287i
\(696\) 0 0
\(697\) −3.00000 1.73205i −0.113633 0.0656061i
\(698\) −18.2554 10.5398i −0.690978 0.398937i
\(699\) 0 0
\(700\) −9.76631 + 21.6695i −0.369132 + 0.819029i
\(701\) 17.2337 0.650907 0.325454 0.945558i \(-0.394483\pi\)
0.325454 + 0.945558i \(0.394483\pi\)
\(702\) 0 0
\(703\) 0.884861i 0.0333732i
\(704\) −7.37228 12.7692i −0.277853 0.481256i
\(705\) 0 0
\(706\) 0.744563 1.28962i 0.0280220 0.0485355i
\(707\) 49.1168 + 28.3576i 1.84723 + 1.06650i
\(708\) 0 0
\(709\) 26.1753 + 45.3369i 0.983033 + 1.70266i 0.650372 + 0.759616i \(0.274613\pi\)
0.332661 + 0.943046i \(0.392053\pi\)
\(710\) −22.1168 + 7.13058i −0.830030 + 0.267606i
\(711\) 0 0
\(712\) 8.01544i 0.300391i
\(713\) −8.74456 + 5.04868i −0.327486 + 0.189074i
\(714\) 0 0
\(715\) 12.0000 55.8304i 0.448775 2.08794i
\(716\) −3.35053 + 5.80329i −0.125215 + 0.216879i
\(717\) 0 0
\(718\) 7.46738 4.31129i 0.278680 0.160896i
\(719\) −10.8832 −0.405873 −0.202937 0.979192i \(-0.565049\pi\)
−0.202937 + 0.979192i \(0.565049\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) −12.9416 + 7.47182i −0.481636 + 0.278072i
\(723\) 0 0
\(724\) 9.51087 16.4733i 0.353469 0.612226i
\(725\) −2.87228 28.5788i −0.106674 1.06139i
\(726\) 0 0
\(727\) 42.3505 24.4511i 1.57069 0.906841i 0.574610 0.818427i \(-0.305154\pi\)
0.996084 0.0884137i \(-0.0281798\pi\)
\(728\) 54.0607i 2.00362i
\(729\) 0 0
\(730\) −1.29211 4.00772i −0.0478231 0.148332i
\(731\) 1.37228 + 2.37686i 0.0507557 + 0.0879114i
\(732\) 0 0
\(733\) −14.2337 8.21782i −0.525733 0.303532i 0.213544 0.976933i \(-0.431499\pi\)
−0.739277 + 0.673401i \(0.764833\pi\)
\(734\) −6.51087 + 11.2772i −0.240321 + 0.416248i
\(735\) 0 0
\(736\) −4.62772 8.01544i −0.170580 0.295453i
\(737\) 51.0767i 1.88143i
\(738\) 0 0
\(739\) −5.62772 −0.207019 −0.103509 0.994628i \(-0.533007\pi\)
−0.103509 + 0.994628i \(0.533007\pi\)
\(740\) −5.40895 4.89258i −0.198837 0.179855i
\(741\) 0 0
\(742\) −28.4674 16.4356i −1.04507 0.603372i
\(743\) 8.13859 + 4.69882i 0.298576 + 0.172383i 0.641803 0.766870i \(-0.278187\pi\)
−0.343227 + 0.939252i \(0.611520\pi\)
\(744\) 0 0
\(745\) −15.9416 + 17.6241i −0.584054 + 0.645696i
\(746\) 6.51087 0.238380
\(747\) 0 0
\(748\) 4.75372i 0.173813i
\(749\) −22.9783 39.7995i −0.839607 1.45424i
\(750\) 0 0
\(751\) −10.8614 + 18.8125i −0.396338 + 0.686478i −0.993271 0.115813i \(-0.963053\pi\)
0.596933 + 0.802291i \(0.296386\pi\)
\(752\) −1.02175 0.589907i −0.0372594 0.0215117i
\(753\) 0 0
\(754\) −13.2921 23.0226i −0.484070 0.838434i
\(755\) 0.605969 + 1.87953i 0.0220535 + 0.0684030i
\(756\) 0 0
\(757\) 41.5692i 1.51086i −0.655230 0.755429i \(-0.727428\pi\)
0.655230 0.755429i \(-0.272572\pi\)
\(758\) 1.02175 0.589907i 0.0371116 0.0214264i
\(759\) 0 0
\(760\) 0.467376 2.17448i 0.0169535 0.0788767i
\(761\) −16.2446 + 28.1364i −0.588865 + 1.01994i 0.405517 + 0.914088i \(0.367092\pi\)
−0.994381 + 0.105856i \(0.966242\pi\)
\(762\) 0 0
\(763\) −29.2337 + 16.8781i −1.05833 + 0.611027i
\(764\) 10.4674 0.378696
\(765\) 0 0
\(766\) 8.78806 0.317526
\(767\) 8.23369 4.75372i 0.297301 0.171647i
\(768\) 0 0
\(769\) −8.24456 + 14.2800i −0.297307 + 0.514950i −0.975519 0.219916i \(-0.929422\pi\)
0.678212 + 0.734866i \(0.262755\pi\)
\(770\) −26.2337 5.63858i −0.945396 0.203200i
\(771\) 0 0
\(772\) −13.6426 + 7.87658i −0.491009 + 0.283484i
\(773\) 21.5769i 0.776067i 0.921645 + 0.388034i \(0.126846\pi\)
−0.921645 + 0.388034i \(0.873154\pi\)
\(774\) 0 0
\(775\) −25.8614 + 18.6101i −0.928969 + 0.668496i
\(776\) −1.72281 2.98400i −0.0618454 0.107119i
\(777\) 0 0
\(778\) −0.350532 0.202380i −0.0125672 0.00725566i
\(779\) −0.813859 + 1.40965i −0.0291595 + 0.0505058i
\(780\) 0 0
\(781\) 28.6753 + 49.6670i 1.02608 + 1.77723i
\(782\) 0.994667i 0.0355692i
\(783\) 0 0
\(784\) −3.13859 −0.112093
\(785\) −19.0367 17.2193i −0.679448 0.614584i
\(786\) 0 0
\(787\) −15.0000 8.66025i −0.534692 0.308705i 0.208233 0.978079i \(-0.433229\pi\)
−0.742925 + 0.669375i \(0.766562\pi\)
\(788\) −7.64264 4.41248i −0.272258 0.157188i
\(789\) 0 0
\(790\) −8.86141 8.01544i −0.315275 0.285177i
\(791\) 21.2554 0.755756
\(792\) 0 0
\(793\) 54.7431i 1.94399i
\(794\) 6.94158 + 12.0232i 0.246347 + 0.426686i
\(795\) 0 0
\(796\) 10.9783 19.0149i 0.389114 0.673965i
\(797\) 22.1970 + 12.8155i 0.786259 + 0.453947i 0.838644 0.544680i \(-0.183349\pi\)
−0.0523851 + 0.998627i \(0.516682\pi\)
\(798\) 0 0
\(799\) 0.744563 + 1.28962i 0.0263407 + 0.0456235i
\(800\) −17.0584 23.7051i −0.603106 0.838102i
\(801\) 0 0
\(802\) 20.1021i 0.709831i
\(803\) −9.00000 + 5.19615i −0.317603 + 0.183368i
\(804\) 0 0
\(805\) −12.0000 2.57924i −0.422944 0.0909063i
\(806\) −14.7446 + 25.5383i −0.519355 + 0.899549i
\(807\) 0 0
\(808\) −37.8832 + 21.8719i −1.33272 + 0.769449i
\(809\) −21.0000 −0.738321 −0.369160 0.929366i \(-0.620355\pi\)
−0.369160 + 0.929366i \(0.620355\pi\)
\(810\) 0 0
\(811\) 24.8832 0.873766 0.436883 0.899518i \(-0.356082\pi\)
0.436883 + 0.899518i \(0.356082\pi\)
\(812\) 23.6495 13.6540i 0.829934 0.479162i
\(813\) 0 0
\(814\) 4.11684 7.13058i 0.144295 0.249927i
\(815\) −7.11684 + 33.1113i −0.249292 + 1.15984i
\(816\) 0 0
\(817\) 1.11684 0.644810i 0.0390734 0.0225591i
\(818\) 18.1128i 0.633299i
\(819\) 0 0
\(820\) 4.11684 + 12.7692i 0.143766 + 0.445919i
\(821\) 20.3614 + 35.2670i 0.710618 + 1.23083i 0.964625 + 0.263624i \(0.0849179\pi\)
−0.254007 + 0.967202i \(0.581749\pi\)
\(822\) 0 0
\(823\) 3.76631 + 2.17448i 0.131285 + 0.0757977i 0.564204 0.825635i \(-0.309183\pi\)
−0.432919 + 0.901433i \(0.642516\pi\)
\(824\) 9.25544 16.0309i 0.322428 0.558462i
\(825\) 0 0
\(826\) −2.23369 3.86886i −0.0777199 0.134615i
\(827\) 22.3692i 0.777853i −0.921269 0.388926i \(-0.872846\pi\)
0.921269 0.388926i \(-0.127154\pi\)
\(828\) 0 0
\(829\) 23.3505 0.810997 0.405499 0.914096i \(-0.367098\pi\)
0.405499 + 0.914096i \(0.367098\pi\)
\(830\) 14.2337 15.7359i 0.494059 0.546202i
\(831\) 0 0
\(832\) −17.0584 9.84868i −0.591394 0.341442i
\(833\) 3.43070 + 1.98072i 0.118867 + 0.0686278i
\(834\) 0 0
\(835\) 22.4891 + 20.3422i 0.778268 + 0.703970i
\(836\) −2.23369 −0.0772537
\(837\) 0 0
\(838\) 13.8564i 0.478662i
\(839\) −22.9307 39.7171i −0.791656 1.37119i −0.924941 0.380110i \(-0.875886\pi\)
0.133285 0.991078i \(-0.457447\pi\)
\(840\) 0 0
\(841\) −2.00000 + 3.46410i −0.0689655 + 0.119452i
\(842\) 14.9198 + 8.61397i 0.514171 + 0.296857i
\(843\) 0 0
\(844\) 1.27719 + 2.21215i 0.0439626 + 0.0761454i
\(845\) −14.4891 44.9407i −0.498441 1.54601i
\(846\) 0 0
\(847\) 28.1176i 0.966131i
\(848\) −6.51087 + 3.75906i −0.223584 + 0.129086i
\(849\) 0 0
\(850\) 0.313859 + 3.12286i 0.0107653 + 0.107113i
\(851\) 1.88316 3.26172i 0.0645538 0.111810i
\(852\) 0 0
\(853\) −9.35053 + 5.39853i −0.320156 + 0.184842i −0.651462 0.758681i \(-0.725844\pi\)
0.331306 + 0.943523i \(0.392511\pi\)
\(854\) −25.7228 −0.880217
\(855\) 0 0
\(856\) 35.4456 1.21151
\(857\) −42.7812 + 24.6998i −1.46138 + 0.843728i −0.999075 0.0429939i \(-0.986310\pi\)
−0.462304 + 0.886722i \(0.652977\pi\)
\(858\) 0 0
\(859\) 24.1644 41.8540i 0.824478 1.42804i −0.0778389 0.996966i \(-0.524802\pi\)
0.902317 0.431073i \(-0.141865\pi\)
\(860\) 2.23369 10.3923i 0.0761681 0.354375i
\(861\) 0 0
\(862\) −22.8832 + 13.2116i −0.779403 + 0.449989i
\(863\) 16.7306i 0.569516i −0.958599 0.284758i \(-0.908087\pi\)
0.958599 0.284758i \(-0.0919133\pi\)
\(864\) 0 0
\(865\) −23.8030 + 7.67420i −0.809326 + 0.260931i
\(866\) 5.05842 + 8.76144i 0.171892 + 0.297726i
\(867\) 0 0
\(868\) −26.2337 15.1460i −0.890429 0.514090i
\(869\) −14.7446 + 25.5383i −0.500175 + 0.866329i
\(870\) 0 0
\(871\) −34.1168 59.0921i −1.15601 2.00226i
\(872\) 26.0357i 0.881679i
\(873\) 0 0
\(874\) 0.467376 0.0158092
\(875\) −38.4891 4.31129i −1.30117 0.145748i
\(876\) 0 0
\(877\) 0.941578 + 0.543620i 0.0317948 + 0.0183568i 0.515813 0.856701i \(-0.327490\pi\)
−0.484018 + 0.875058i \(0.660823\pi\)
\(878\) 21.8614 + 12.6217i 0.737787 + 0.425961i
\(879\) 0 0
\(880\) −4.11684 + 4.55134i −0.138779 + 0.153426i
\(881\) 10.8832 0.366663 0.183331 0.983051i \(-0.441312\pi\)
0.183331 + 0.983051i \(0.441312\pi\)
\(882\) 0 0
\(883\) 54.9455i 1.84906i −0.381104 0.924532i \(-0.624456\pi\)
0.381104 0.924532i \(-0.375544\pi\)
\(884\) −3.17527 5.49972i −0.106796 0.184976i
\(885\) 0 0
\(886\) −8.51087 + 14.7413i −0.285928 + 0.495243i
\(887\) −37.9783 21.9268i −1.27518 0.736228i −0.299226 0.954182i \(-0.596728\pi\)
−0.975959 + 0.217954i \(0.930062\pi\)
\(888\) 0 0
\(889\) −18.0000 31.1769i −0.603701 1.04564i
\(890\) −5.05842 + 1.63086i −0.169559 + 0.0546666i
\(891\) 0 0
\(892\) 25.5383i 0.855087i
\(893\) 0.605969 0.349857i 0.0202780 0.0117075i
\(894\) 0 0
\(895\) −10.6753 2.29451i −0.356835 0.0766969i
\(896\) 15.6060 27.0303i 0.521359 0.903020i
\(897\) 0 0
\(898\) 7.46738 4.31129i 0.249190 0.143870i
\(899\) 36.6060 1.22088
\(900\) 0 0
\(901\) 9.48913 0.316129
\(902\) −13.1168 + 7.57301i −0.436743 + 0.252154i
\(903\) 0 0
\(904\) −8.19702 + 14.1976i −0.272629 + 0.472207i
\(905\) 30.3030 + 6.51322i 1.00731 + 0.216507i
\(906\) 0 0
\(907\) −15.7663 + 9.10268i −0.523512 + 0.302250i −0.738370 0.674396i \(-0.764404\pi\)
0.214858 + 0.976645i \(0.431071\pi\)
\(908\) 18.6101i 0.617599i
\(909\) 0 0
\(910\) −34.1168 + 10.9994i −1.13096 + 0.364628i
\(911\) 9.30298 + 16.1132i 0.308222 + 0.533856i 0.977973 0.208730i \(-0.0669328\pi\)
−0.669752 + 0.742585i \(0.733599\pi\)
\(912\) 0 0
\(913\) −45.3505 26.1831i −1.50088 0.866536i
\(914\) 8.31386 14.4000i 0.274998 0.476311i
\(915\) 0 0
\(916\) −12.0802 20.9235i −0.399140 0.691331i
\(917\) 15.1460i 0.500166i
\(918\) 0 0
\(919\) −55.3505 −1.82585 −0.912923 0.408132i \(-0.866180\pi\)
−0.912923 + 0.408132i \(0.866180\pi\)
\(920\) 6.35053 7.02078i 0.209371 0.231468i
\(921\) 0 0
\(922\) −16.5326 9.54511i −0.544473 0.314352i
\(923\) 66.3505 + 38.3075i 2.18395 + 1.26091i
\(924\) 0 0
\(925\) 4.88316 10.8347i 0.160557 0.356244i
\(926\) 10.9783 0.360768
\(927\) 0 0
\(928\) 33.5538i 1.10146i
\(929\) −1.75544 3.04051i −0.0575940 0.0997558i 0.835791 0.549048i \(-0.185010\pi\)
−0.893385 + 0.449292i \(0.851676\pi\)
\(930\) 0 0
\(931\) 0.930703 1.61203i 0.0305026 0.0528320i
\(932\) 7.29211 + 4.21010i 0.238861 + 0.137906i
\(933\) 0 0
\(934\) 7.25544 + 12.5668i 0.237405 + 0.411198i
\(935\) 7.37228 2.37686i 0.241099 0.0777317i
\(936\) 0 0
\(937\) 22.2766i 0.727745i −0.931449 0.363873i \(-0.881454\pi\)
0.931449 0.363873i \(-0.118546\pi\)
\(938\) −27.7663 + 16.0309i −0.906602 + 0.523427i
\(939\) 0 0
\(940\) 1.21194 5.63858i 0.0395291 0.183910i
\(941\) 3.43070 5.94215i 0.111838 0.193709i −0.804674 0.593718i \(-0.797660\pi\)
0.916511 + 0.400009i \(0.130993\pi\)
\(942\) 0 0
\(943\) −6.00000 + 3.46410i −0.195387 + 0.112807i
\(944\) −1.02175 −0.0332551
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) −37.3723 + 21.5769i −1.21444 + 0.701155i −0.963722 0.266906i \(-0.913999\pi\)
−0.250714 + 0.968061i \(0.580665\pi\)
\(948\) 0 0
\(949\) −6.94158 + 12.0232i −0.225333 + 0.390288i
\(950\) 1.46738 0.147477i 0.0476080 0.00478478i
\(951\) 0 0
\(952\) −6.35053 + 3.66648i −0.205822 + 0.118831i
\(953\) 25.0410i 0.811158i 0.914060 + 0.405579i \(0.132930\pi\)
−0.914060 + 0.405579i \(0.867070\pi\)
\(954\) 0 0
\(955\) 5.23369 + 16.2333i 0.169358 + 0.525296i
\(956\) 15.7663 + 27.3081i 0.509919 + 0.883206i
\(957\) 0 0
\(958\) 12.7663 + 7.37063i 0.412461 + 0.238134i
\(959\) −24.8614 + 43.0612i −0.802817 + 1.39052i
\(960\) 0 0
\(961\) −4.80298 8.31901i −0.154935 0.268355i
\(962\) 10.9994i 0.354636i
\(963\) 0 0
\(964\) −2.07335 −0.0667780
\(965\) −19.0367 17.2193i −0.612812 0.554309i
\(966\) 0 0
\(967\) 37.4674 + 21.6318i 1.20487 + 0.695632i 0.961634 0.274335i \(-0.0884579\pi\)
0.243236 + 0.969967i \(0.421791\pi\)
\(968\) −18.7812 10.8434i −0.603652 0.348519i
\(969\) 0 0
\(970\) 1.53262 1.69438i 0.0492096 0.0544033i
\(971\) 41.5842 1.33450 0.667251 0.744833i \(-0.267471\pi\)
0.667251 + 0.744833i \(0.267471\pi\)
\(972\) 0 0
\(973\) 38.5099i 1.23457i
\(974\) −3.76631 6.52344i −0.120680 0.209025i
\(975\) 0 0
\(976\) −2.94158 + 5.09496i −0.0941576 + 0.163086i
\(977\) −24.5109 14.1514i −0.784172 0.452742i 0.0537346 0.998555i \(-0.482888\pi\)
−0.837907 + 0.545813i \(0.816221\pi\)
\(978\) 0 0
\(979\) 6.55842 + 11.3595i 0.209608 + 0.363052i
\(980\) −4.70789 14.6024i −0.150388 0.466457i
\(981\) 0 0
\(982\) 25.0582i 0.799640i
\(983\) 43.6277 25.1885i 1.39151 0.803388i 0.398026 0.917374i \(-0.369695\pi\)
0.993482 + 0.113987i \(0.0363621\pi\)
\(984\) 0 0
\(985\) 3.02175 14.0588i 0.0962809 0.447950i
\(986\) 1.80298 3.12286i 0.0574187 0.0994522i
\(987\) 0 0
\(988\) −2.58422 + 1.49200i −0.0822150 + 0.0474668i
\(989\) 5.48913 0.174544
\(990\) 0 0
\(991\) 38.6060 1.22636 0.613180 0.789944i \(-0.289890\pi\)
0.613180 + 0.789944i \(0.289890\pi\)
\(992\) 32.2337 18.6101i 1.02342 0.590872i
\(993\) 0 0
\(994\) 18.0000 31.1769i 0.570925 0.988872i
\(995\) 34.9783 + 7.51811i 1.10889 + 0.238340i
\(996\) 0 0
\(997\) −52.2921 + 30.1909i −1.65611 + 0.956154i −0.681622 + 0.731704i \(0.738725\pi\)
−0.974486 + 0.224450i \(0.927942\pi\)
\(998\) 19.3098i 0.611242i
\(999\) 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 405.2.j.b.109.2 4
3.2 odd 2 405.2.j.d.109.1 4
5.4 even 2 405.2.j.e.109.1 4
9.2 odd 6 405.2.j.a.379.2 4
9.4 even 3 405.2.b.a.244.3 yes 4
9.5 odd 6 405.2.b.b.244.2 yes 4
9.7 even 3 405.2.j.e.379.1 4
15.14 odd 2 405.2.j.a.109.2 4
45.4 even 6 405.2.b.a.244.2 4
45.13 odd 12 2025.2.a.w.1.3 4
45.14 odd 6 405.2.b.b.244.3 yes 4
45.22 odd 12 2025.2.a.w.1.2 4
45.23 even 12 2025.2.a.x.1.2 4
45.29 odd 6 405.2.j.d.379.1 4
45.32 even 12 2025.2.a.x.1.3 4
45.34 even 6 inner 405.2.j.b.379.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
405.2.b.a.244.2 4 45.4 even 6
405.2.b.a.244.3 yes 4 9.4 even 3
405.2.b.b.244.2 yes 4 9.5 odd 6
405.2.b.b.244.3 yes 4 45.14 odd 6
405.2.j.a.109.2 4 15.14 odd 2
405.2.j.a.379.2 4 9.2 odd 6
405.2.j.b.109.2 4 1.1 even 1 trivial
405.2.j.b.379.2 4 45.34 even 6 inner
405.2.j.d.109.1 4 3.2 odd 2
405.2.j.d.379.1 4 45.29 odd 6
405.2.j.e.109.1 4 5.4 even 2
405.2.j.e.379.1 4 9.7 even 3
2025.2.a.w.1.2 4 45.22 odd 12
2025.2.a.w.1.3 4 45.13 odd 12
2025.2.a.x.1.2 4 45.23 even 12
2025.2.a.x.1.3 4 45.32 even 12