Properties

Label 864.2.v.a.109.6
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
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] = [864,2,Mod(109,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.6
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.a.325.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18499 + 0.771885i) q^{2} +(0.808388 - 1.82935i) q^{4} +(-0.796479 + 0.329912i) q^{5} +(3.41414 - 3.41414i) q^{7} +(0.454114 + 2.79173i) q^{8} +O(q^{10})\) \(q+(-1.18499 + 0.771885i) q^{2} +(0.808388 - 1.82935i) q^{4} +(-0.796479 + 0.329912i) q^{5} +(3.41414 - 3.41414i) q^{7} +(0.454114 + 2.79173i) q^{8} +(0.689163 - 1.00573i) q^{10} +(-0.811278 - 1.95860i) q^{11} +(-3.44869 - 1.42849i) q^{13} +(-1.41039 + 6.68103i) q^{14} +(-2.69302 - 2.95764i) q^{16} -5.12913i q^{17} +(1.84398 + 0.763801i) q^{19} +(-0.0403403 + 1.72373i) q^{20} +(2.47316 + 1.69470i) q^{22} +(-0.655049 - 0.655049i) q^{23} +(-3.01000 + 3.01000i) q^{25} +(5.18928 - 0.969242i) q^{26} +(-3.48569 - 9.00559i) q^{28} +(-3.09893 + 7.48148i) q^{29} -7.46197 q^{31} +(5.47415 + 1.42607i) q^{32} +(3.95910 + 6.07796i) q^{34} +(-1.59292 + 3.84565i) q^{35} +(1.04147 - 0.431390i) q^{37} +(-2.77466 + 0.518245i) q^{38} +(-1.28272 - 2.07374i) q^{40} +(-7.85358 - 7.85358i) q^{41} +(1.55013 + 3.74235i) q^{43} +(-4.23878 - 0.0991997i) q^{44} +(1.28185 + 0.270602i) q^{46} -8.53070i q^{47} -16.3127i q^{49} +(1.24344 - 5.89018i) q^{50} +(-5.40108 + 5.15406i) q^{52} +(2.21888 + 5.35684i) q^{53} +(1.29233 + 1.29233i) q^{55} +(11.0818 + 7.98095i) q^{56} +(-2.10265 - 11.2575i) q^{58} +(-3.55676 + 1.47326i) q^{59} +(5.53850 - 13.3711i) q^{61} +(8.84233 - 5.75978i) q^{62} +(-7.58756 + 2.53553i) q^{64} +3.21808 q^{65} +(1.49796 - 3.61639i) q^{67} +(-9.38296 - 4.14633i) q^{68} +(-1.08081 - 5.78660i) q^{70} +(3.65387 - 3.65387i) q^{71} +(-1.36736 - 1.36736i) q^{73} +(-0.901143 + 1.31508i) q^{74} +(2.88791 - 2.75583i) q^{76} +(-9.45673 - 3.91711i) q^{77} +9.69095i q^{79} +(3.12069 + 1.46724i) q^{80} +(15.3684 + 3.24433i) q^{82} +(-1.86485 - 0.772448i) q^{83} +(1.69216 + 4.08525i) q^{85} +(-4.72555 - 3.23811i) q^{86} +(5.09947 - 3.15430i) q^{88} +(9.11861 - 9.11861i) q^{89} +(-16.6514 + 6.89722i) q^{91} +(-1.72785 + 0.668777i) q^{92} +(6.58472 + 10.1088i) q^{94} -1.72068 q^{95} +15.7002 q^{97} +(12.5915 + 19.3303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18499 + 0.771885i −0.837912 + 0.545805i
\(3\) 0 0
\(4\) 0.808388 1.82935i 0.404194 0.914673i
\(5\) −0.796479 + 0.329912i −0.356196 + 0.147541i −0.553604 0.832780i \(-0.686748\pi\)
0.197408 + 0.980321i \(0.436748\pi\)
\(6\) 0 0
\(7\) 3.41414 3.41414i 1.29042 1.29042i 0.355897 0.934525i \(-0.384175\pi\)
0.934525 0.355897i \(-0.115825\pi\)
\(8\) 0.454114 + 2.79173i 0.160554 + 0.987027i
\(9\) 0 0
\(10\) 0.689163 1.00573i 0.217932 0.318040i
\(11\) −0.811278 1.95860i −0.244609 0.590539i 0.753120 0.657883i \(-0.228548\pi\)
−0.997730 + 0.0673433i \(0.978548\pi\)
\(12\) 0 0
\(13\) −3.44869 1.42849i −0.956493 0.396193i −0.150826 0.988560i \(-0.548193\pi\)
−0.805668 + 0.592368i \(0.798193\pi\)
\(14\) −1.41039 + 6.68103i −0.376942 + 1.78558i
\(15\) 0 0
\(16\) −2.69302 2.95764i −0.673254 0.739411i
\(17\) 5.12913i 1.24400i −0.783018 0.621999i \(-0.786321\pi\)
0.783018 0.621999i \(-0.213679\pi\)
\(18\) 0 0
\(19\) 1.84398 + 0.763801i 0.423038 + 0.175228i 0.584038 0.811726i \(-0.301472\pi\)
−0.161000 + 0.986954i \(0.551472\pi\)
\(20\) −0.0403403 + 1.72373i −0.00902037 + 0.385438i
\(21\) 0 0
\(22\) 2.47316 + 1.69470i 0.527280 + 0.361311i
\(23\) −0.655049 0.655049i −0.136587 0.136587i 0.635508 0.772095i \(-0.280791\pi\)
−0.772095 + 0.635508i \(0.780791\pi\)
\(24\) 0 0
\(25\) −3.01000 + 3.01000i −0.602000 + 0.602000i
\(26\) 5.18928 0.969242i 1.01770 0.190084i
\(27\) 0 0
\(28\) −3.48569 9.00559i −0.658734 1.70190i
\(29\) −3.09893 + 7.48148i −0.575457 + 1.38928i 0.321394 + 0.946945i \(0.395848\pi\)
−0.896852 + 0.442331i \(0.854152\pi\)
\(30\) 0 0
\(31\) −7.46197 −1.34021 −0.670104 0.742267i \(-0.733751\pi\)
−0.670104 + 0.742267i \(0.733751\pi\)
\(32\) 5.47415 + 1.42607i 0.967702 + 0.252096i
\(33\) 0 0
\(34\) 3.95910 + 6.07796i 0.678980 + 1.04236i
\(35\) −1.59292 + 3.84565i −0.269253 + 0.650034i
\(36\) 0 0
\(37\) 1.04147 0.431390i 0.171216 0.0709201i −0.295429 0.955365i \(-0.595463\pi\)
0.466645 + 0.884445i \(0.345463\pi\)
\(38\) −2.77466 + 0.518245i −0.450109 + 0.0840704i
\(39\) 0 0
\(40\) −1.28272 2.07374i −0.202816 0.327887i
\(41\) −7.85358 7.85358i −1.22652 1.22652i −0.965270 0.261253i \(-0.915864\pi\)
−0.261253 0.965270i \(-0.584136\pi\)
\(42\) 0 0
\(43\) 1.55013 + 3.74235i 0.236393 + 0.570703i 0.996905 0.0786213i \(-0.0250518\pi\)
−0.760512 + 0.649324i \(0.775052\pi\)
\(44\) −4.23878 0.0991997i −0.639020 0.0149549i
\(45\) 0 0
\(46\) 1.28185 + 0.270602i 0.188998 + 0.0398981i
\(47\) 8.53070i 1.24433i −0.782886 0.622165i \(-0.786253\pi\)
0.782886 0.622165i \(-0.213747\pi\)
\(48\) 0 0
\(49\) 16.3127i 2.33038i
\(50\) 1.24344 5.89018i 0.175849 0.832997i
\(51\) 0 0
\(52\) −5.40108 + 5.15406i −0.748996 + 0.714740i
\(53\) 2.21888 + 5.35684i 0.304786 + 0.735818i 0.999858 + 0.0168778i \(0.00537263\pi\)
−0.695072 + 0.718940i \(0.744627\pi\)
\(54\) 0 0
\(55\) 1.29233 + 1.29233i 0.174258 + 0.174258i
\(56\) 11.0818 + 7.98095i 1.48086 + 1.06650i
\(57\) 0 0
\(58\) −2.10265 11.2575i −0.276091 1.47818i
\(59\) −3.55676 + 1.47326i −0.463050 + 0.191802i −0.601997 0.798498i \(-0.705628\pi\)
0.138947 + 0.990300i \(0.455628\pi\)
\(60\) 0 0
\(61\) 5.53850 13.3711i 0.709132 1.71200i 0.00697220 0.999976i \(-0.497781\pi\)
0.702160 0.712020i \(-0.252219\pi\)
\(62\) 8.84233 5.75978i 1.12298 0.731492i
\(63\) 0 0
\(64\) −7.58756 + 2.53553i −0.948445 + 0.316942i
\(65\) 3.21808 0.399154
\(66\) 0 0
\(67\) 1.49796 3.61639i 0.183005 0.441813i −0.805578 0.592489i \(-0.798145\pi\)
0.988583 + 0.150677i \(0.0481453\pi\)
\(68\) −9.38296 4.14633i −1.13785 0.502817i
\(69\) 0 0
\(70\) −1.08081 5.78660i −0.129181 0.691631i
\(71\) 3.65387 3.65387i 0.433635 0.433635i −0.456228 0.889863i \(-0.650800\pi\)
0.889863 + 0.456228i \(0.150800\pi\)
\(72\) 0 0
\(73\) −1.36736 1.36736i −0.160038 0.160038i 0.622546 0.782583i \(-0.286098\pi\)
−0.782583 + 0.622546i \(0.786098\pi\)
\(74\) −0.901143 + 1.31508i −0.104756 + 0.152875i
\(75\) 0 0
\(76\) 2.88791 2.75583i 0.331266 0.316115i
\(77\) −9.45673 3.91711i −1.07769 0.446396i
\(78\) 0 0
\(79\) 9.69095i 1.09032i 0.838333 + 0.545158i \(0.183530\pi\)
−0.838333 + 0.545158i \(0.816470\pi\)
\(80\) 3.12069 + 1.46724i 0.348904 + 0.164043i
\(81\) 0 0
\(82\) 15.3684 + 3.24433i 1.69716 + 0.358277i
\(83\) −1.86485 0.772448i −0.204694 0.0847871i 0.277981 0.960587i \(-0.410335\pi\)
−0.482675 + 0.875799i \(0.660335\pi\)
\(84\) 0 0
\(85\) 1.69216 + 4.08525i 0.183541 + 0.443107i
\(86\) −4.72555 3.23811i −0.509569 0.349175i
\(87\) 0 0
\(88\) 5.09947 3.15430i 0.543605 0.336249i
\(89\) 9.11861 9.11861i 0.966571 0.966571i −0.0328878 0.999459i \(-0.510470\pi\)
0.999459 + 0.0328878i \(0.0104704\pi\)
\(90\) 0 0
\(91\) −16.6514 + 6.89722i −1.74554 + 0.723025i
\(92\) −1.72785 + 0.668777i −0.180140 + 0.0697249i
\(93\) 0 0
\(94\) 6.58472 + 10.1088i 0.679162 + 1.04264i
\(95\) −1.72068 −0.176538
\(96\) 0 0
\(97\) 15.7002 1.59412 0.797059 0.603901i \(-0.206388\pi\)
0.797059 + 0.603901i \(0.206388\pi\)
\(98\) 12.5915 + 19.3303i 1.27193 + 1.95265i
\(99\) 0 0
\(100\) 3.07308 + 7.93958i 0.307308 + 0.793958i
\(101\) 3.71071 1.53702i 0.369229 0.152940i −0.190351 0.981716i \(-0.560963\pi\)
0.559580 + 0.828776i \(0.310963\pi\)
\(102\) 0 0
\(103\) −2.42846 + 2.42846i −0.239283 + 0.239283i −0.816553 0.577270i \(-0.804118\pi\)
0.577270 + 0.816553i \(0.304118\pi\)
\(104\) 2.42187 10.2765i 0.237484 1.00770i
\(105\) 0 0
\(106\) −6.76420 4.63507i −0.656997 0.450198i
\(107\) −0.754155 1.82069i −0.0729069 0.176013i 0.883225 0.468950i \(-0.155367\pi\)
−0.956132 + 0.292937i \(0.905367\pi\)
\(108\) 0 0
\(109\) 0.496041 + 0.205467i 0.0475121 + 0.0196802i 0.406313 0.913734i \(-0.366814\pi\)
−0.358801 + 0.933414i \(0.616814\pi\)
\(110\) −2.52893 0.533865i −0.241124 0.0509020i
\(111\) 0 0
\(112\) −19.2921 0.903478i −1.82293 0.0853706i
\(113\) 5.54357i 0.521495i −0.965407 0.260747i \(-0.916031\pi\)
0.965407 0.260747i \(-0.0839690\pi\)
\(114\) 0 0
\(115\) 0.737841 + 0.305624i 0.0688040 + 0.0284996i
\(116\) 11.1811 + 11.7170i 1.03814 + 1.08789i
\(117\) 0 0
\(118\) 3.07753 4.49120i 0.283309 0.413448i
\(119\) −17.5116 17.5116i −1.60528 1.60528i
\(120\) 0 0
\(121\) 4.60024 4.60024i 0.418204 0.418204i
\(122\) 3.75791 + 20.1197i 0.340225 + 1.82155i
\(123\) 0 0
\(124\) −6.03217 + 13.6505i −0.541705 + 1.22585i
\(125\) 3.05393 7.37283i 0.273151 0.659446i
\(126\) 0 0
\(127\) −16.3887 −1.45426 −0.727131 0.686499i \(-0.759147\pi\)
−0.727131 + 0.686499i \(0.759147\pi\)
\(128\) 7.03402 8.86130i 0.621725 0.783235i
\(129\) 0 0
\(130\) −3.81339 + 2.48399i −0.334456 + 0.217860i
\(131\) 6.49987 15.6921i 0.567896 1.37102i −0.335429 0.942066i \(-0.608881\pi\)
0.903325 0.428957i \(-0.141119\pi\)
\(132\) 0 0
\(133\) 8.90332 3.68787i 0.772016 0.319779i
\(134\) 1.01638 + 5.44163i 0.0878015 + 0.470085i
\(135\) 0 0
\(136\) 14.3192 2.32921i 1.22786 0.199728i
\(137\) 1.13040 + 1.13040i 0.0965770 + 0.0965770i 0.753745 0.657168i \(-0.228246\pi\)
−0.657168 + 0.753745i \(0.728246\pi\)
\(138\) 0 0
\(139\) 5.78620 + 13.9691i 0.490779 + 1.18485i 0.954324 + 0.298772i \(0.0965770\pi\)
−0.463546 + 0.886073i \(0.653423\pi\)
\(140\) 5.74733 + 6.02279i 0.485738 + 0.509018i
\(141\) 0 0
\(142\) −1.50942 + 7.15016i −0.126668 + 0.600028i
\(143\) 7.91349i 0.661759i
\(144\) 0 0
\(145\) 6.98122i 0.579759i
\(146\) 2.67575 + 0.564860i 0.221447 + 0.0467482i
\(147\) 0 0
\(148\) 0.0527486 2.25394i 0.00433591 0.185272i
\(149\) −4.69891 11.3442i −0.384950 0.929352i −0.990992 0.133919i \(-0.957244\pi\)
0.606042 0.795432i \(-0.292756\pi\)
\(150\) 0 0
\(151\) 6.45669 + 6.45669i 0.525438 + 0.525438i 0.919209 0.393771i \(-0.128830\pi\)
−0.393771 + 0.919209i \(0.628830\pi\)
\(152\) −1.29495 + 5.49475i −0.105034 + 0.445683i
\(153\) 0 0
\(154\) 14.2297 2.65778i 1.14666 0.214170i
\(155\) 5.94330 2.46179i 0.477377 0.197736i
\(156\) 0 0
\(157\) −4.69075 + 11.3245i −0.374362 + 0.903791i 0.618638 + 0.785676i \(0.287685\pi\)
−0.993000 + 0.118114i \(0.962315\pi\)
\(158\) −7.48029 11.4836i −0.595100 0.913590i
\(159\) 0 0
\(160\) −4.83052 + 0.670153i −0.381886 + 0.0529802i
\(161\) −4.47285 −0.352510
\(162\) 0 0
\(163\) −1.67653 + 4.04751i −0.131316 + 0.317026i −0.975838 0.218496i \(-0.929885\pi\)
0.844522 + 0.535522i \(0.179885\pi\)
\(164\) −20.7157 + 8.01818i −1.61762 + 0.626114i
\(165\) 0 0
\(166\) 2.80607 0.524111i 0.217793 0.0406789i
\(167\) −13.1383 + 13.1383i −1.01667 + 1.01667i −0.0168127 + 0.999859i \(0.505352\pi\)
−0.999859 + 0.0168127i \(0.994648\pi\)
\(168\) 0 0
\(169\) 0.660455 + 0.660455i 0.0508042 + 0.0508042i
\(170\) −5.15853 3.53481i −0.395641 0.271107i
\(171\) 0 0
\(172\) 8.09916 + 0.189544i 0.617555 + 0.0144526i
\(173\) −0.199667 0.0827046i −0.0151804 0.00628791i 0.375080 0.926992i \(-0.377615\pi\)
−0.390261 + 0.920704i \(0.627615\pi\)
\(174\) 0 0
\(175\) 20.5531i 1.55367i
\(176\) −3.60805 + 7.67401i −0.271967 + 0.578450i
\(177\) 0 0
\(178\) −3.76692 + 17.8440i −0.282343 + 1.33746i
\(179\) 19.2636 + 7.97926i 1.43983 + 0.596398i 0.959757 0.280831i \(-0.0906099\pi\)
0.480074 + 0.877228i \(0.340610\pi\)
\(180\) 0 0
\(181\) −7.70588 18.6036i −0.572773 1.38280i −0.899185 0.437569i \(-0.855839\pi\)
0.326411 0.945228i \(-0.394161\pi\)
\(182\) 14.4078 21.0260i 1.06798 1.55855i
\(183\) 0 0
\(184\) 1.53126 2.12619i 0.112886 0.156745i
\(185\) −0.687186 + 0.687186i −0.0505229 + 0.0505229i
\(186\) 0 0
\(187\) −10.0459 + 4.16115i −0.734629 + 0.304293i
\(188\) −15.6056 6.89612i −1.13816 0.502951i
\(189\) 0 0
\(190\) 2.03898 1.32816i 0.147923 0.0963552i
\(191\) −4.18542 −0.302846 −0.151423 0.988469i \(-0.548386\pi\)
−0.151423 + 0.988469i \(0.548386\pi\)
\(192\) 0 0
\(193\) 12.7503 0.917788 0.458894 0.888491i \(-0.348246\pi\)
0.458894 + 0.888491i \(0.348246\pi\)
\(194\) −18.6046 + 12.1188i −1.33573 + 0.870077i
\(195\) 0 0
\(196\) −29.8415 13.1870i −2.13154 0.941926i
\(197\) −23.7046 + 9.81875i −1.68888 + 0.699557i −0.999687 0.0250215i \(-0.992035\pi\)
−0.689193 + 0.724578i \(0.742035\pi\)
\(198\) 0 0
\(199\) 1.70090 1.70090i 0.120574 0.120574i −0.644245 0.764819i \(-0.722828\pi\)
0.764819 + 0.644245i \(0.222828\pi\)
\(200\) −9.77000 7.03623i −0.690843 0.497537i
\(201\) 0 0
\(202\) −3.21073 + 4.68559i −0.225906 + 0.329677i
\(203\) 14.9626 + 36.1230i 1.05017 + 2.53534i
\(204\) 0 0
\(205\) 8.84620 + 3.66422i 0.617846 + 0.255920i
\(206\) 1.00320 4.75218i 0.0698964 0.331100i
\(207\) 0 0
\(208\) 5.06239 + 14.0469i 0.351014 + 0.973980i
\(209\) 4.23127i 0.292683i
\(210\) 0 0
\(211\) 3.62230 + 1.50041i 0.249370 + 0.103292i 0.503867 0.863781i \(-0.331910\pi\)
−0.254498 + 0.967073i \(0.581910\pi\)
\(212\) 11.5932 + 0.271315i 0.796226 + 0.0186340i
\(213\) 0 0
\(214\) 2.29903 + 1.57537i 0.157158 + 0.107690i
\(215\) −2.46929 2.46929i −0.168404 0.168404i
\(216\) 0 0
\(217\) −25.4762 + 25.4762i −1.72944 + 1.72944i
\(218\) −0.746399 + 0.139411i −0.0505525 + 0.00944209i
\(219\) 0 0
\(220\) 3.40883 1.31942i 0.229823 0.0889550i
\(221\) −7.32693 + 17.6888i −0.492863 + 1.18988i
\(222\) 0 0
\(223\) 21.0777 1.41147 0.705735 0.708476i \(-0.250617\pi\)
0.705735 + 0.708476i \(0.250617\pi\)
\(224\) 23.5583 13.8207i 1.57406 0.923434i
\(225\) 0 0
\(226\) 4.27899 + 6.56905i 0.284634 + 0.436967i
\(227\) −4.27989 + 10.3326i −0.284066 + 0.685796i −0.999922 0.0124513i \(-0.996037\pi\)
0.715856 + 0.698248i \(0.246037\pi\)
\(228\) 0 0
\(229\) −12.2828 + 5.08771i −0.811671 + 0.336205i −0.749621 0.661868i \(-0.769764\pi\)
−0.0620505 + 0.998073i \(0.519764\pi\)
\(230\) −1.11024 + 0.207368i −0.0732070 + 0.0136734i
\(231\) 0 0
\(232\) −22.2936 5.25394i −1.46365 0.344938i
\(233\) 20.3969 + 20.3969i 1.33624 + 1.33624i 0.899667 + 0.436577i \(0.143809\pi\)
0.436577 + 0.899667i \(0.356191\pi\)
\(234\) 0 0
\(235\) 2.81438 + 6.79452i 0.183590 + 0.443226i
\(236\) −0.180144 + 7.69751i −0.0117264 + 0.501065i
\(237\) 0 0
\(238\) 34.2679 + 7.23407i 2.22126 + 0.468915i
\(239\) 14.5221i 0.939359i −0.882837 0.469680i \(-0.844369\pi\)
0.882837 0.469680i \(-0.155631\pi\)
\(240\) 0 0
\(241\) 7.44892i 0.479827i −0.970794 0.239914i \(-0.922881\pi\)
0.970794 0.239914i \(-0.0771191\pi\)
\(242\) −1.90037 + 9.00208i −0.122161 + 0.578676i
\(243\) 0 0
\(244\) −19.9831 20.9409i −1.27929 1.34060i
\(245\) 5.38175 + 12.9927i 0.343827 + 0.830072i
\(246\) 0 0
\(247\) −5.26822 5.26822i −0.335209 0.335209i
\(248\) −3.38859 20.8318i −0.215175 1.32282i
\(249\) 0 0
\(250\) 2.07211 + 11.0940i 0.131052 + 0.701645i
\(251\) 15.2305 6.30867i 0.961339 0.398200i 0.153858 0.988093i \(-0.450830\pi\)
0.807481 + 0.589893i \(0.200830\pi\)
\(252\) 0 0
\(253\) −0.751550 + 1.81440i −0.0472496 + 0.114071i
\(254\) 19.4204 12.6502i 1.21854 0.793743i
\(255\) 0 0
\(256\) −1.49533 + 15.9300i −0.0934579 + 0.995623i
\(257\) 20.4112 1.27321 0.636606 0.771189i \(-0.280338\pi\)
0.636606 + 0.771189i \(0.280338\pi\)
\(258\) 0 0
\(259\) 2.08289 5.02854i 0.129424 0.312458i
\(260\) 2.60146 5.88699i 0.161336 0.365095i
\(261\) 0 0
\(262\) 4.41021 + 23.6120i 0.272464 + 1.45876i
\(263\) −12.7243 + 12.7243i −0.784617 + 0.784617i −0.980606 0.195989i \(-0.937208\pi\)
0.195989 + 0.980606i \(0.437208\pi\)
\(264\) 0 0
\(265\) −3.53457 3.53457i −0.217127 0.217127i
\(266\) −7.70370 + 11.2424i −0.472344 + 0.689317i
\(267\) 0 0
\(268\) −5.40470 5.66373i −0.330145 0.345968i
\(269\) 9.30185 + 3.85295i 0.567144 + 0.234919i 0.647783 0.761825i \(-0.275696\pi\)
−0.0806395 + 0.996743i \(0.525696\pi\)
\(270\) 0 0
\(271\) 16.5614i 1.00603i 0.864277 + 0.503016i \(0.167776\pi\)
−0.864277 + 0.503016i \(0.832224\pi\)
\(272\) −15.1702 + 13.8128i −0.919826 + 0.837526i
\(273\) 0 0
\(274\) −2.21206 0.466973i −0.133635 0.0282109i
\(275\) 8.33732 + 3.45343i 0.502759 + 0.208250i
\(276\) 0 0
\(277\) −8.16236 19.7057i −0.490428 1.18400i −0.954503 0.298203i \(-0.903613\pi\)
0.464074 0.885796i \(-0.346387\pi\)
\(278\) −17.6391 12.0869i −1.05792 0.724927i
\(279\) 0 0
\(280\) −11.4594 2.70065i −0.684831 0.161395i
\(281\) 5.12450 5.12450i 0.305702 0.305702i −0.537538 0.843240i \(-0.680645\pi\)
0.843240 + 0.537538i \(0.180645\pi\)
\(282\) 0 0
\(283\) −8.24987 + 3.41721i −0.490404 + 0.203132i −0.614161 0.789181i \(-0.710506\pi\)
0.123757 + 0.992312i \(0.460506\pi\)
\(284\) −3.73045 9.63795i −0.221362 0.571907i
\(285\) 0 0
\(286\) −6.10830 9.37738i −0.361191 0.554496i
\(287\) −53.6264 −3.16547
\(288\) 0 0
\(289\) −9.30801 −0.547530
\(290\) 5.38870 + 8.27265i 0.316435 + 0.485787i
\(291\) 0 0
\(292\) −3.60674 + 1.39602i −0.211068 + 0.0816958i
\(293\) −7.39341 + 3.06245i −0.431928 + 0.178910i −0.588045 0.808828i \(-0.700102\pi\)
0.156117 + 0.987739i \(0.450102\pi\)
\(294\) 0 0
\(295\) 2.34684 2.34684i 0.136638 0.136638i
\(296\) 1.67727 + 2.71160i 0.0974895 + 0.157609i
\(297\) 0 0
\(298\) 14.3246 + 9.81569i 0.829799 + 0.568608i
\(299\) 1.32333 + 3.19479i 0.0765299 + 0.184759i
\(300\) 0 0
\(301\) 18.0693 + 7.48453i 1.04149 + 0.431401i
\(302\) −12.6349 2.66728i −0.727058 0.153484i
\(303\) 0 0
\(304\) −2.70681 7.51076i −0.155246 0.430772i
\(305\) 12.4770i 0.714432i
\(306\) 0 0
\(307\) 23.7724 + 9.84685i 1.35676 + 0.561989i 0.938167 0.346183i \(-0.112522\pi\)
0.418596 + 0.908173i \(0.362522\pi\)
\(308\) −14.8105 + 14.1331i −0.843904 + 0.805308i
\(309\) 0 0
\(310\) −5.14251 + 7.50473i −0.292075 + 0.426240i
\(311\) 1.72058 + 1.72058i 0.0975652 + 0.0975652i 0.754205 0.656639i \(-0.228023\pi\)
−0.656639 + 0.754205i \(0.728023\pi\)
\(312\) 0 0
\(313\) 6.18203 6.18203i 0.349429 0.349429i −0.510468 0.859897i \(-0.670528\pi\)
0.859897 + 0.510468i \(0.170528\pi\)
\(314\) −3.18271 17.0401i −0.179610 0.961626i
\(315\) 0 0
\(316\) 17.7281 + 7.83405i 0.997284 + 0.440700i
\(317\) −3.77605 + 9.11619i −0.212084 + 0.512016i −0.993743 0.111690i \(-0.964374\pi\)
0.781659 + 0.623706i \(0.214374\pi\)
\(318\) 0 0
\(319\) 17.1673 0.961185
\(320\) 5.20683 4.52273i 0.291070 0.252828i
\(321\) 0 0
\(322\) 5.30027 3.45253i 0.295373 0.192402i
\(323\) 3.91764 9.45801i 0.217983 0.526258i
\(324\) 0 0
\(325\) 14.6803 6.08078i 0.814316 0.337301i
\(326\) −1.13754 6.09034i −0.0630025 0.337313i
\(327\) 0 0
\(328\) 18.3587 25.4915i 1.01369 1.40753i
\(329\) −29.1250 29.1250i −1.60571 1.60571i
\(330\) 0 0
\(331\) −9.97778 24.0885i −0.548428 1.32402i −0.918647 0.395079i \(-0.870717\pi\)
0.370219 0.928944i \(-0.379283\pi\)
\(332\) −2.92060 + 2.78702i −0.160289 + 0.152958i
\(333\) 0 0
\(334\) 5.42746 25.7099i 0.296977 1.40679i
\(335\) 3.37457i 0.184373i
\(336\) 0 0
\(337\) 0.646451i 0.0352144i −0.999845 0.0176072i \(-0.994395\pi\)
0.999845 0.0176072i \(-0.00560484\pi\)
\(338\) −1.29242 0.272835i −0.0702986 0.0148403i
\(339\) 0 0
\(340\) 8.84126 + 0.206911i 0.479484 + 0.0112213i
\(341\) 6.05373 + 14.6150i 0.327828 + 0.791446i
\(342\) 0 0
\(343\) −31.7947 31.7947i −1.71675 1.71675i
\(344\) −9.74371 + 6.02701i −0.525346 + 0.324955i
\(345\) 0 0
\(346\) 0.300441 0.0561157i 0.0161518 0.00301680i
\(347\) 23.1114 9.57307i 1.24069 0.513909i 0.336758 0.941591i \(-0.390670\pi\)
0.903929 + 0.427682i \(0.140670\pi\)
\(348\) 0 0
\(349\) −2.78496 + 6.72348i −0.149075 + 0.359899i −0.980723 0.195404i \(-0.937398\pi\)
0.831648 + 0.555304i \(0.187398\pi\)
\(350\) −15.8646 24.3551i −0.847999 1.30184i
\(351\) 0 0
\(352\) −1.64795 11.8786i −0.0878362 0.633131i
\(353\) 16.2559 0.865215 0.432607 0.901582i \(-0.357594\pi\)
0.432607 + 0.901582i \(0.357594\pi\)
\(354\) 0 0
\(355\) −1.70477 + 4.11569i −0.0904800 + 0.218438i
\(356\) −9.30972 24.0525i −0.493414 1.27478i
\(357\) 0 0
\(358\) −28.9862 + 5.41398i −1.53197 + 0.286138i
\(359\) 26.4226 26.4226i 1.39453 1.39453i 0.579712 0.814821i \(-0.303165\pi\)
0.814821 0.579712i \(-0.196835\pi\)
\(360\) 0 0
\(361\) −10.6182 10.6182i −0.558851 0.558851i
\(362\) 23.4912 + 16.0970i 1.23467 + 0.846040i
\(363\) 0 0
\(364\) −0.843363 + 36.0367i −0.0442042 + 1.88884i
\(365\) 1.54018 + 0.637965i 0.0806169 + 0.0333926i
\(366\) 0 0
\(367\) 1.66302i 0.0868091i −0.999058 0.0434046i \(-0.986180\pi\)
0.999058 0.0434046i \(-0.0138204\pi\)
\(368\) −0.173345 + 3.70146i −0.00903621 + 0.192952i
\(369\) 0 0
\(370\) 0.283878 1.34474i 0.0147581 0.0699094i
\(371\) 25.8645 + 10.7134i 1.34282 + 0.556214i
\(372\) 0 0
\(373\) −11.8922 28.7102i −0.615753 1.48656i −0.856593 0.515993i \(-0.827423\pi\)
0.240840 0.970565i \(-0.422577\pi\)
\(374\) 8.69234 12.6852i 0.449470 0.655936i
\(375\) 0 0
\(376\) 23.8155 3.87392i 1.22819 0.199782i
\(377\) 21.3745 21.3745i 1.10084 1.10084i
\(378\) 0 0
\(379\) 1.65256 0.684513i 0.0848863 0.0351611i −0.339836 0.940485i \(-0.610372\pi\)
0.424723 + 0.905324i \(0.360372\pi\)
\(380\) −1.39098 + 3.14771i −0.0713555 + 0.161474i
\(381\) 0 0
\(382\) 4.95966 3.23066i 0.253759 0.165295i
\(383\) 37.1405 1.89779 0.948896 0.315589i \(-0.102202\pi\)
0.948896 + 0.315589i \(0.102202\pi\)
\(384\) 0 0
\(385\) 8.82439 0.449732
\(386\) −15.1090 + 9.84177i −0.769026 + 0.500933i
\(387\) 0 0
\(388\) 12.6919 28.7212i 0.644333 1.45810i
\(389\) 14.5838 6.04079i 0.739426 0.306280i 0.0190070 0.999819i \(-0.493950\pi\)
0.720419 + 0.693539i \(0.243950\pi\)
\(390\) 0 0
\(391\) −3.35983 + 3.35983i −0.169914 + 0.169914i
\(392\) 45.5406 7.40782i 2.30015 0.374151i
\(393\) 0 0
\(394\) 20.5106 29.9323i 1.03331 1.50797i
\(395\) −3.19716 7.71863i −0.160867 0.388367i
\(396\) 0 0
\(397\) 33.5415 + 13.8933i 1.68340 + 0.697287i 0.999479 0.0322707i \(-0.0102739\pi\)
0.683920 + 0.729557i \(0.260274\pi\)
\(398\) −0.702648 + 3.32845i −0.0352206 + 0.166840i
\(399\) 0 0
\(400\) 17.0085 + 0.796531i 0.850424 + 0.0398266i
\(401\) 5.74652i 0.286968i −0.989653 0.143484i \(-0.954169\pi\)
0.989653 0.143484i \(-0.0458305\pi\)
\(402\) 0 0
\(403\) 25.7340 + 10.6594i 1.28190 + 0.530981i
\(404\) 0.187941 8.03068i 0.00935042 0.399541i
\(405\) 0 0
\(406\) −45.6133 31.2558i −2.26375 1.55120i
\(407\) −1.68984 1.68984i −0.0837622 0.0837622i
\(408\) 0 0
\(409\) 4.83666 4.83666i 0.239158 0.239158i −0.577344 0.816501i \(-0.695911\pi\)
0.816501 + 0.577344i \(0.195911\pi\)
\(410\) −13.3110 + 2.48620i −0.657383 + 0.122785i
\(411\) 0 0
\(412\) 2.47935 + 6.40563i 0.122149 + 0.315583i
\(413\) −7.11336 + 17.1732i −0.350025 + 0.845036i
\(414\) 0 0
\(415\) 1.74016 0.0854209
\(416\) −16.8415 12.7379i −0.825722 0.624525i
\(417\) 0 0
\(418\) 3.26605 + 5.01400i 0.159748 + 0.245243i
\(419\) −12.9860 + 31.3511i −0.634410 + 1.53160i 0.199615 + 0.979874i \(0.436031\pi\)
−0.834025 + 0.551727i \(0.813969\pi\)
\(420\) 0 0
\(421\) −24.2889 + 10.0608i −1.18377 + 0.490332i −0.885720 0.464219i \(-0.846335\pi\)
−0.298046 + 0.954551i \(0.596335\pi\)
\(422\) −5.45052 + 1.01804i −0.265327 + 0.0495573i
\(423\) 0 0
\(424\) −13.9472 + 8.62713i −0.677338 + 0.418970i
\(425\) 15.4387 + 15.4387i 0.748886 + 0.748886i
\(426\) 0 0
\(427\) −26.7416 64.5600i −1.29412 3.12428i
\(428\) −3.94033 0.0922150i −0.190463 0.00445738i
\(429\) 0 0
\(430\) 4.83209 + 1.02007i 0.233024 + 0.0491922i
\(431\) 6.67302i 0.321428i −0.987001 0.160714i \(-0.948620\pi\)
0.987001 0.160714i \(-0.0513797\pi\)
\(432\) 0 0
\(433\) 13.5877i 0.652981i 0.945200 + 0.326491i \(0.105866\pi\)
−0.945200 + 0.326491i \(0.894134\pi\)
\(434\) 10.5243 49.8536i 0.505181 2.39305i
\(435\) 0 0
\(436\) 0.776864 0.741334i 0.0372050 0.0355035i
\(437\) −0.707569 1.70822i −0.0338476 0.0817154i
\(438\) 0 0
\(439\) −9.87555 9.87555i −0.471334 0.471334i 0.431012 0.902346i \(-0.358157\pi\)
−0.902346 + 0.431012i \(0.858157\pi\)
\(440\) −3.02098 + 4.19471i −0.144019 + 0.199975i
\(441\) 0 0
\(442\) −4.97137 26.6165i −0.236464 1.26602i
\(443\) −16.2012 + 6.71074i −0.769741 + 0.318837i −0.732767 0.680479i \(-0.761772\pi\)
−0.0369733 + 0.999316i \(0.511772\pi\)
\(444\) 0 0
\(445\) −4.25444 + 10.2711i −0.201680 + 0.486898i
\(446\) −24.9768 + 16.2696i −1.18269 + 0.770387i
\(447\) 0 0
\(448\) −17.2483 + 34.5616i −0.814906 + 1.63288i
\(449\) −17.8762 −0.843631 −0.421816 0.906682i \(-0.638607\pi\)
−0.421816 + 0.906682i \(0.638607\pi\)
\(450\) 0 0
\(451\) −9.01057 + 21.7534i −0.424291 + 1.02433i
\(452\) −10.1411 4.48135i −0.476997 0.210785i
\(453\) 0 0
\(454\) −2.90393 15.5475i −0.136288 0.729682i
\(455\) 10.9870 10.9870i 0.515077 0.515077i
\(456\) 0 0
\(457\) −2.21164 2.21164i −0.103456 0.103456i 0.653484 0.756940i \(-0.273307\pi\)
−0.756940 + 0.653484i \(0.773307\pi\)
\(458\) 10.6278 15.5098i 0.496607 0.724724i
\(459\) 0 0
\(460\) 1.15555 1.10270i 0.0538780 0.0514139i
\(461\) −0.371943 0.154064i −0.0173231 0.00717547i 0.374005 0.927427i \(-0.377984\pi\)
−0.391328 + 0.920251i \(0.627984\pi\)
\(462\) 0 0
\(463\) 24.3117i 1.12986i 0.825138 + 0.564931i \(0.191097\pi\)
−0.825138 + 0.564931i \(0.808903\pi\)
\(464\) 30.4730 10.9822i 1.41468 0.509837i
\(465\) 0 0
\(466\) −39.9141 8.42600i −1.84898 0.390327i
\(467\) −18.3325 7.59355i −0.848325 0.351388i −0.0841943 0.996449i \(-0.526832\pi\)
−0.764130 + 0.645062i \(0.776832\pi\)
\(468\) 0 0
\(469\) −7.23262 17.4611i −0.333971 0.806278i
\(470\) −8.57960 5.87904i −0.395747 0.271180i
\(471\) 0 0
\(472\) −5.72812 9.26050i −0.263658 0.426249i
\(473\) 6.07217 6.07217i 0.279199 0.279199i
\(474\) 0 0
\(475\) −7.84941 + 3.25133i −0.360156 + 0.149181i
\(476\) −46.1909 + 17.8786i −2.11715 + 0.819463i
\(477\) 0 0
\(478\) 11.2094 + 17.2086i 0.512707 + 0.787101i
\(479\) 7.56363 0.345591 0.172796 0.984958i \(-0.444720\pi\)
0.172796 + 0.984958i \(0.444720\pi\)
\(480\) 0 0
\(481\) −4.20793 −0.191865
\(482\) 5.74971 + 8.82688i 0.261892 + 0.402053i
\(483\) 0 0
\(484\) −4.69665 12.1342i −0.213484 0.551555i
\(485\) −12.5049 + 5.17970i −0.567819 + 0.235198i
\(486\) 0 0
\(487\) 5.05578 5.05578i 0.229099 0.229099i −0.583217 0.812316i \(-0.698206\pi\)
0.812316 + 0.583217i \(0.198206\pi\)
\(488\) 39.8437 + 9.38999i 1.80364 + 0.425065i
\(489\) 0 0
\(490\) −16.4062 11.2421i −0.741155 0.507865i
\(491\) 8.74076 + 21.1021i 0.394465 + 0.952323i 0.988954 + 0.148220i \(0.0473543\pi\)
−0.594489 + 0.804104i \(0.702646\pi\)
\(492\) 0 0
\(493\) 38.3735 + 15.8948i 1.72826 + 0.715867i
\(494\) 10.3092 + 2.17631i 0.463834 + 0.0979170i
\(495\) 0 0
\(496\) 20.0952 + 22.0698i 0.902301 + 0.990965i
\(497\) 24.9496i 1.11914i
\(498\) 0 0
\(499\) −11.8354 4.90237i −0.529824 0.219460i 0.101702 0.994815i \(-0.467571\pi\)
−0.631526 + 0.775355i \(0.717571\pi\)
\(500\) −11.0187 11.5468i −0.492771 0.516388i
\(501\) 0 0
\(502\) −13.1783 + 19.2319i −0.588178 + 0.858360i
\(503\) 10.3156 + 10.3156i 0.459948 + 0.459948i 0.898638 0.438690i \(-0.144557\pi\)
−0.438690 + 0.898638i \(0.644557\pi\)
\(504\) 0 0
\(505\) −2.44841 + 2.44841i −0.108953 + 0.108953i
\(506\) −0.509932 2.73015i −0.0226693 0.121370i
\(507\) 0 0
\(508\) −13.2484 + 29.9806i −0.587804 + 1.33017i
\(509\) −7.07660 + 17.0844i −0.313665 + 0.757254i 0.685898 + 0.727697i \(0.259409\pi\)
−0.999563 + 0.0295564i \(0.990591\pi\)
\(510\) 0 0
\(511\) −9.33672 −0.413032
\(512\) −10.5242 20.0310i −0.465106 0.885255i
\(513\) 0 0
\(514\) −24.1870 + 15.7551i −1.06684 + 0.694926i
\(515\) 1.13304 2.73539i 0.0499276 0.120536i
\(516\) 0 0
\(517\) −16.7082 + 6.92077i −0.734826 + 0.304375i
\(518\) 1.41326 + 7.56650i 0.0620949 + 0.332453i
\(519\) 0 0
\(520\) 1.46138 + 8.98403i 0.0640857 + 0.393976i
\(521\) −16.9560 16.9560i −0.742858 0.742858i 0.230269 0.973127i \(-0.426039\pi\)
−0.973127 + 0.230269i \(0.926039\pi\)
\(522\) 0 0
\(523\) 2.21535 + 5.34834i 0.0968707 + 0.233867i 0.964885 0.262673i \(-0.0846039\pi\)
−0.868014 + 0.496539i \(0.834604\pi\)
\(524\) −23.4518 24.5758i −1.02450 1.07360i
\(525\) 0 0
\(526\) 5.25646 24.8999i 0.229192 1.08569i
\(527\) 38.2734i 1.66722i
\(528\) 0 0
\(529\) 22.1418i 0.962688i
\(530\) 6.91671 + 1.46014i 0.300443 + 0.0634245i
\(531\) 0 0
\(532\) 0.450938 19.2685i 0.0195507 0.835395i
\(533\) 15.8658 + 38.3033i 0.687222 + 1.65910i
\(534\) 0 0
\(535\) 1.20134 + 1.20134i 0.0519383 + 0.0519383i
\(536\) 10.7762 + 2.53965i 0.465463 + 0.109696i
\(537\) 0 0
\(538\) −13.9966 + 2.61426i −0.603436 + 0.112709i
\(539\) −31.9499 + 13.2341i −1.37618 + 0.570033i
\(540\) 0 0
\(541\) 13.1856 31.8329i 0.566895 1.36860i −0.337265 0.941410i \(-0.609502\pi\)
0.904160 0.427195i \(-0.140498\pi\)
\(542\) −12.7835 19.6250i −0.549097 0.842966i
\(543\) 0 0
\(544\) 7.31452 28.0776i 0.313607 1.20382i
\(545\) −0.462872 −0.0198273
\(546\) 0 0
\(547\) 8.01569 19.3516i 0.342726 0.827414i −0.654712 0.755879i \(-0.727210\pi\)
0.997438 0.0715356i \(-0.0227899\pi\)
\(548\) 2.98171 1.15410i 0.127372 0.0493005i
\(549\) 0 0
\(550\) −12.5453 + 2.34318i −0.534932 + 0.0999134i
\(551\) −11.4287 + 11.4287i −0.486880 + 0.486880i
\(552\) 0 0
\(553\) 33.0862 + 33.0862i 1.40697 + 1.40697i
\(554\) 24.8828 + 17.0506i 1.05717 + 0.724409i
\(555\) 0 0
\(556\) 30.2319 + 0.707513i 1.28212 + 0.0300052i
\(557\) 18.6004 + 7.70455i 0.788126 + 0.326452i 0.740190 0.672398i \(-0.234736\pi\)
0.0479360 + 0.998850i \(0.484736\pi\)
\(558\) 0 0
\(559\) 15.1205i 0.639531i
\(560\) 15.6638 5.64511i 0.661918 0.238549i
\(561\) 0 0
\(562\) −2.11694 + 10.0280i −0.0892979 + 0.423005i
\(563\) 25.0778 + 10.3876i 1.05690 + 0.437784i 0.842352 0.538928i \(-0.181171\pi\)
0.214553 + 0.976712i \(0.431171\pi\)
\(564\) 0 0
\(565\) 1.82889 + 4.41533i 0.0769420 + 0.185754i
\(566\) 7.13830 10.4173i 0.300045 0.437871i
\(567\) 0 0
\(568\) 11.8599 + 8.54137i 0.497631 + 0.358388i
\(569\) −19.8519 + 19.8519i −0.832235 + 0.832235i −0.987822 0.155587i \(-0.950273\pi\)
0.155587 + 0.987822i \(0.450273\pi\)
\(570\) 0 0
\(571\) −20.6373 + 8.54825i −0.863644 + 0.357733i −0.770132 0.637885i \(-0.779809\pi\)
−0.0935123 + 0.995618i \(0.529809\pi\)
\(572\) 14.4765 + 6.39717i 0.605293 + 0.267479i
\(573\) 0 0
\(574\) 63.5466 41.3934i 2.65238 1.72773i
\(575\) 3.94339 0.164451
\(576\) 0 0
\(577\) −6.90741 −0.287559 −0.143780 0.989610i \(-0.545926\pi\)
−0.143780 + 0.989610i \(0.545926\pi\)
\(578\) 11.0299 7.18471i 0.458782 0.298845i
\(579\) 0 0
\(580\) −12.7711 5.64354i −0.530290 0.234335i
\(581\) −9.00411 + 3.72962i −0.373553 + 0.154731i
\(582\) 0 0
\(583\) 8.69177 8.69177i 0.359976 0.359976i
\(584\) 3.19637 4.43825i 0.132267 0.183656i
\(585\) 0 0
\(586\) 6.39724 9.33583i 0.264268 0.385660i
\(587\) −15.4328 37.2580i −0.636978 1.53780i −0.830685 0.556743i \(-0.812051\pi\)
0.193707 0.981059i \(-0.437949\pi\)
\(588\) 0 0
\(589\) −13.7597 5.69946i −0.566959 0.234842i
\(590\) −0.969484 + 4.59246i −0.0399130 + 0.189068i
\(591\) 0 0
\(592\) −4.08059 1.91855i −0.167711 0.0788520i
\(593\) 16.1054i 0.661371i −0.943741 0.330685i \(-0.892720\pi\)
0.943741 0.330685i \(-0.107280\pi\)
\(594\) 0 0
\(595\) 19.7249 + 8.17031i 0.808641 + 0.334950i
\(596\) −24.5510 0.574564i −1.00565 0.0235351i
\(597\) 0 0
\(598\) −4.03413 2.76433i −0.164968 0.113042i
\(599\) 4.83684 + 4.83684i 0.197628 + 0.197628i 0.798982 0.601355i \(-0.205372\pi\)
−0.601355 + 0.798982i \(0.705372\pi\)
\(600\) 0 0
\(601\) 3.60693 3.60693i 0.147130 0.147130i −0.629705 0.776834i \(-0.716824\pi\)
0.776834 + 0.629705i \(0.216824\pi\)
\(602\) −27.1890 + 5.07831i −1.10814 + 0.206976i
\(603\) 0 0
\(604\) 17.0310 6.59201i 0.692983 0.268225i
\(605\) −2.14632 + 5.18167i −0.0872603 + 0.210665i
\(606\) 0 0
\(607\) 33.3188 1.35237 0.676185 0.736732i \(-0.263632\pi\)
0.676185 + 0.736732i \(0.263632\pi\)
\(608\) 9.00498 + 6.81081i 0.365200 + 0.276215i
\(609\) 0 0
\(610\) −9.63082 14.7851i −0.389941 0.598632i
\(611\) −12.1860 + 29.4197i −0.492995 + 1.19019i
\(612\) 0 0
\(613\) −31.3111 + 12.9695i −1.26464 + 0.523833i −0.911332 0.411673i \(-0.864945\pi\)
−0.353312 + 0.935505i \(0.614945\pi\)
\(614\) −35.7706 + 6.68116i −1.44358 + 0.269630i
\(615\) 0 0
\(616\) 6.64108 28.1795i 0.267577 1.13538i
\(617\) 25.1396 + 25.1396i 1.01208 + 1.01208i 0.999926 + 0.0121577i \(0.00387001\pi\)
0.0121577 + 0.999926i \(0.496130\pi\)
\(618\) 0 0
\(619\) 1.51167 + 3.64951i 0.0607593 + 0.146686i 0.951343 0.308133i \(-0.0997041\pi\)
−0.890584 + 0.454819i \(0.849704\pi\)
\(620\) 0.301018 12.8624i 0.0120892 0.516568i
\(621\) 0 0
\(622\) −3.36696 0.710776i −0.135003 0.0284995i
\(623\) 62.2644i 2.49457i
\(624\) 0 0
\(625\) 14.4041i 0.576163i
\(626\) −2.55381 + 12.0974i −0.102071 + 0.483511i
\(627\) 0 0
\(628\) 16.9244 + 17.7356i 0.675358 + 0.707726i
\(629\) −2.21266 5.34183i −0.0882244 0.212993i
\(630\) 0 0
\(631\) −25.5140 25.5140i −1.01570 1.01570i −0.999875 0.0158223i \(-0.994963\pi\)
−0.0158223 0.999875i \(-0.505037\pi\)
\(632\) −27.0546 + 4.40080i −1.07617 + 0.175054i
\(633\) 0 0
\(634\) −2.56208 13.7172i −0.101753 0.544781i
\(635\) 13.0533 5.40683i 0.518002 0.214564i
\(636\) 0 0
\(637\) −23.3025 + 56.2572i −0.923279 + 2.22899i
\(638\) −20.3430 + 13.2512i −0.805389 + 0.524619i
\(639\) 0 0
\(640\) −2.67900 + 9.37844i −0.105897 + 0.370716i
\(641\) 33.5444 1.32492 0.662461 0.749096i \(-0.269512\pi\)
0.662461 + 0.749096i \(0.269512\pi\)
\(642\) 0 0
\(643\) 10.2097 24.6483i 0.402629 0.972033i −0.584396 0.811469i \(-0.698669\pi\)
0.987025 0.160565i \(-0.0513315\pi\)
\(644\) −3.61580 + 8.18240i −0.142483 + 0.322432i
\(645\) 0 0
\(646\) 2.65815 + 14.2316i 0.104583 + 0.559934i
\(647\) −11.2919 + 11.2919i −0.443932 + 0.443932i −0.893331 0.449399i \(-0.851638\pi\)
0.449399 + 0.893331i \(0.351638\pi\)
\(648\) 0 0
\(649\) 5.77104 + 5.77104i 0.226533 + 0.226533i
\(650\) −12.7023 + 18.5371i −0.498225 + 0.727086i
\(651\) 0 0
\(652\) 6.04901 + 6.33892i 0.236897 + 0.248251i
\(653\) −18.2896 7.57581i −0.715728 0.296464i −0.00505564 0.999987i \(-0.501609\pi\)
−0.710673 + 0.703523i \(0.751609\pi\)
\(654\) 0 0
\(655\) 14.6428i 0.572141i
\(656\) −2.07828 + 44.3779i −0.0811433 + 1.73267i
\(657\) 0 0
\(658\) 56.9939 + 12.0316i 2.22185 + 0.469041i
\(659\) −32.2918 13.3757i −1.25791 0.521043i −0.348642 0.937256i \(-0.613357\pi\)
−0.909267 + 0.416213i \(0.863357\pi\)
\(660\) 0 0
\(661\) −4.02009 9.70536i −0.156363 0.377495i 0.826212 0.563360i \(-0.190491\pi\)
−0.982575 + 0.185865i \(0.940491\pi\)
\(662\) 30.4171 + 20.8429i 1.18219 + 0.810080i
\(663\) 0 0
\(664\) 1.30961 5.55695i 0.0508228 0.215652i
\(665\) −5.87463 + 5.87463i −0.227808 + 0.227808i
\(666\) 0 0
\(667\) 6.93069 2.87079i 0.268357 0.111157i
\(668\) 13.4136 + 34.6553i 0.518989 + 1.34085i
\(669\) 0 0
\(670\) −2.60478 3.99883i −0.100631 0.154488i
\(671\) −30.6819 −1.18446
\(672\) 0 0
\(673\) −4.78955 −0.184623 −0.0923117 0.995730i \(-0.529426\pi\)
−0.0923117 + 0.995730i \(0.529426\pi\)
\(674\) 0.498985 + 0.766036i 0.0192202 + 0.0295066i
\(675\) 0 0
\(676\) 1.74210 0.674296i 0.0670040 0.0259345i
\(677\) −0.657333 + 0.272276i −0.0252633 + 0.0104644i −0.395279 0.918561i \(-0.629352\pi\)
0.370016 + 0.929025i \(0.379352\pi\)
\(678\) 0 0
\(679\) 53.6028 53.6028i 2.05709 2.05709i
\(680\) −10.6365 + 6.57924i −0.407891 + 0.252302i
\(681\) 0 0
\(682\) −18.4547 12.6458i −0.706666 0.484232i
\(683\) 11.7426 + 28.3491i 0.449318 + 1.08475i 0.972578 + 0.232577i \(0.0747157\pi\)
−0.523260 + 0.852173i \(0.675284\pi\)
\(684\) 0 0
\(685\) −1.27328 0.527409i −0.0486494 0.0201513i
\(686\) 62.2181 + 13.1345i 2.37550 + 0.501476i
\(687\) 0 0
\(688\) 6.89401 14.6629i 0.262832 0.559020i
\(689\) 21.6437i 0.824559i
\(690\) 0 0
\(691\) 42.2763 + 17.5114i 1.60827 + 0.666166i 0.992554 0.121803i \(-0.0388678\pi\)
0.615714 + 0.787970i \(0.288868\pi\)
\(692\) −0.312703 + 0.298402i −0.0118872 + 0.0113435i
\(693\) 0 0
\(694\) −19.9974 + 29.1833i −0.759093 + 1.10778i
\(695\) −9.21717 9.21717i −0.349627 0.349627i
\(696\) 0 0
\(697\) −40.2821 + 40.2821i −1.52579 + 1.52579i
\(698\) −1.88961 10.1169i −0.0715229 0.382930i
\(699\) 0 0
\(700\) 37.5987 + 16.6149i 1.42110 + 0.627983i
\(701\) 9.62867 23.2457i 0.363670 0.877977i −0.631087 0.775712i \(-0.717391\pi\)
0.994757 0.102265i \(-0.0326090\pi\)
\(702\) 0 0
\(703\) 2.24994 0.0848581
\(704\) 11.1217 + 12.8040i 0.419165 + 0.482567i
\(705\) 0 0
\(706\) −19.2630 + 12.5477i −0.724974 + 0.472238i
\(707\) 7.42124 17.9165i 0.279105 0.673818i
\(708\) 0 0
\(709\) −20.1359 + 8.34057i −0.756221 + 0.313237i −0.727277 0.686344i \(-0.759214\pi\)
−0.0289438 + 0.999581i \(0.509214\pi\)
\(710\) −1.15670 6.19293i −0.0434102 0.232416i
\(711\) 0 0
\(712\) 29.5976 + 21.3159i 1.10922 + 0.798845i
\(713\) 4.88795 + 4.88795i 0.183055 + 0.183055i
\(714\) 0 0
\(715\) −2.61076 6.30293i −0.0976368 0.235716i
\(716\) 30.1693 28.7895i 1.12748 1.07591i
\(717\) 0 0
\(718\) −10.9153 + 51.7057i −0.407354 + 1.92964i
\(719\) 0.572599i 0.0213543i −0.999943 0.0106772i \(-0.996601\pi\)
0.999943 0.0106772i \(-0.00339871\pi\)
\(720\) 0 0
\(721\) 16.5822i 0.617552i
\(722\) 20.7784 + 4.38639i 0.773291 + 0.163244i
\(723\) 0 0
\(724\) −40.2618 0.942243i −1.49632 0.0350182i
\(725\) −13.1915 31.8470i −0.489919 1.18277i
\(726\) 0 0
\(727\) −10.4074 10.4074i −0.385989 0.385989i 0.487265 0.873254i \(-0.337994\pi\)
−0.873254 + 0.487265i \(0.837994\pi\)
\(728\) −26.8168 43.3540i −0.993897 1.60681i
\(729\) 0 0
\(730\) −2.31753 + 0.432864i −0.0857757 + 0.0160210i
\(731\) 19.1950 7.95083i 0.709953 0.294072i
\(732\) 0 0
\(733\) −14.5352 + 35.0911i −0.536870 + 1.29612i 0.390027 + 0.920803i \(0.372466\pi\)
−0.926897 + 0.375315i \(0.877534\pi\)
\(734\) 1.28366 + 1.97066i 0.0473808 + 0.0727384i
\(735\) 0 0
\(736\) −2.65169 4.51998i −0.0977425 0.166609i
\(737\) −8.29831 −0.305672
\(738\) 0 0
\(739\) 7.77168 18.7625i 0.285886 0.690190i −0.714065 0.700079i \(-0.753148\pi\)
0.999951 + 0.00988937i \(0.00314794\pi\)
\(740\) 0.701588 + 1.81261i 0.0257909 + 0.0666330i
\(741\) 0 0
\(742\) −38.9187 + 7.26914i −1.42875 + 0.266859i
\(743\) −4.84516 + 4.84516i −0.177752 + 0.177752i −0.790375 0.612623i \(-0.790114\pi\)
0.612623 + 0.790375i \(0.290114\pi\)
\(744\) 0 0
\(745\) 7.48517 + 7.48517i 0.274235 + 0.274235i
\(746\) 36.2530 + 24.8419i 1.32732 + 0.909525i
\(747\) 0 0
\(748\) −0.508808 + 21.7413i −0.0186039 + 0.794940i
\(749\) −8.79088 3.64130i −0.321212 0.133050i
\(750\) 0 0
\(751\) 25.3393i 0.924645i 0.886712 + 0.462322i \(0.152984\pi\)
−0.886712 + 0.462322i \(0.847016\pi\)
\(752\) −25.2308 + 22.9733i −0.920072 + 0.837751i
\(753\) 0 0
\(754\) −8.82985 + 41.8271i −0.321564 + 1.52325i
\(755\) −7.27276 3.01248i −0.264683 0.109635i
\(756\) 0 0
\(757\) 9.70852 + 23.4385i 0.352862 + 0.851885i 0.996264 + 0.0863565i \(0.0275224\pi\)
−0.643402 + 0.765529i \(0.722478\pi\)
\(758\) −1.42990 + 2.08673i −0.0519362 + 0.0757933i
\(759\) 0 0
\(760\) −0.781385 4.80367i −0.0283438 0.174248i
\(761\) 26.8470 26.8470i 0.973203 0.973203i −0.0264474 0.999650i \(-0.508419\pi\)
0.999650 + 0.0264474i \(0.00841945\pi\)
\(762\) 0 0
\(763\) 2.39504 0.992060i 0.0867064 0.0359150i
\(764\) −3.38344 + 7.65658i −0.122409 + 0.277005i
\(765\) 0 0
\(766\) −44.0110 + 28.6682i −1.59018 + 1.03582i
\(767\) 14.3707 0.518895
\(768\) 0 0
\(769\) 47.9760 1.73006 0.865029 0.501722i \(-0.167300\pi\)
0.865029 + 0.501722i \(0.167300\pi\)
\(770\) −10.4568 + 6.81141i −0.376836 + 0.245466i
\(771\) 0 0
\(772\) 10.3072 23.3247i 0.370965 0.839476i
\(773\) −18.2509 + 7.55976i −0.656438 + 0.271906i −0.685939 0.727659i \(-0.740608\pi\)
0.0295005 + 0.999565i \(0.490608\pi\)
\(774\) 0 0
\(775\) 22.4605 22.4605i 0.806805 0.806805i
\(776\) 7.12971 + 43.8309i 0.255942 + 1.57344i
\(777\) 0 0
\(778\) −12.6188 + 18.4152i −0.452405 + 0.660218i
\(779\) −8.48326 20.4804i −0.303944 0.733787i
\(780\) 0 0
\(781\) −10.1208 4.19216i −0.362150 0.150007i
\(782\) 1.38796 6.57476i 0.0496332 0.235113i
\(783\) 0 0
\(784\) −48.2471 + 43.9303i −1.72311 + 1.56894i
\(785\) 10.5672i 0.377161i
\(786\) 0 0
\(787\) −15.4862 6.41459i −0.552023 0.228656i 0.0891948 0.996014i \(-0.471571\pi\)
−0.641218 + 0.767359i \(0.721571\pi\)
\(788\) −1.20060 + 51.3012i −0.0427695 + 1.82753i
\(789\) 0 0
\(790\) 9.74649 + 6.67864i 0.346765 + 0.237615i
\(791\) −18.9265 18.9265i −0.672949 0.672949i
\(792\) 0 0
\(793\) −38.2011 + 38.2011i −1.35656 + 1.35656i
\(794\) −50.4703 + 9.42673i −1.79112 + 0.334542i
\(795\) 0 0
\(796\) −1.73655 4.48654i −0.0615505 0.159021i
\(797\) 15.6239 37.7193i 0.553425 1.33609i −0.361466 0.932385i \(-0.617724\pi\)
0.914891 0.403701i \(-0.132276\pi\)
\(798\) 0 0
\(799\) −43.7551 −1.54794
\(800\) −20.7697 + 12.1847i −0.734318 + 0.430794i
\(801\) 0 0
\(802\) 4.43565 + 6.80956i 0.156628 + 0.240454i
\(803\) −1.56880 + 3.78742i −0.0553618 + 0.133655i
\(804\) 0 0
\(805\) 3.56253 1.47565i 0.125563 0.0520098i
\(806\) −38.7222 + 7.23245i −1.36393 + 0.254752i
\(807\) 0 0
\(808\) 5.97605 + 9.66132i 0.210237 + 0.339884i
\(809\) −28.6042 28.6042i −1.00567 1.00567i −0.999984 0.00568467i \(-0.998191\pi\)
−0.00568467 0.999984i \(-0.501809\pi\)
\(810\) 0 0
\(811\) 2.28061 + 5.50588i 0.0800830 + 0.193337i 0.958850 0.283914i \(-0.0916331\pi\)
−0.878767 + 0.477252i \(0.841633\pi\)
\(812\) 78.1771 + 1.82957i 2.74348 + 0.0642053i
\(813\) 0 0
\(814\) 3.30680 + 0.698077i 0.115903 + 0.0244676i
\(815\) 3.77687i 0.132298i
\(816\) 0 0
\(817\) 8.08481i 0.282852i
\(818\) −1.99804 + 9.46473i −0.0698597 + 0.330926i
\(819\) 0 0
\(820\) 13.8543 13.2207i 0.483813 0.461685i
\(821\) 11.9577 + 28.8684i 0.417326 + 1.00751i 0.983119 + 0.182967i \(0.0585701\pi\)
−0.565793 + 0.824547i \(0.691430\pi\)
\(822\) 0 0
\(823\) 23.2555 + 23.2555i 0.810636 + 0.810636i 0.984729 0.174093i \(-0.0556993\pi\)
−0.174093 + 0.984729i \(0.555699\pi\)
\(824\) −7.88241 5.67681i −0.274597 0.197761i
\(825\) 0 0
\(826\) −4.82646 25.8407i −0.167934 0.899112i
\(827\) 31.1021 12.8829i 1.08153 0.447983i 0.230482 0.973077i \(-0.425970\pi\)
0.851044 + 0.525094i \(0.175970\pi\)
\(828\) 0 0
\(829\) −10.0291 + 24.2123i −0.348324 + 0.840928i 0.648495 + 0.761219i \(0.275399\pi\)
−0.996818 + 0.0797083i \(0.974601\pi\)
\(830\) −2.06206 + 1.34320i −0.0715752 + 0.0466231i
\(831\) 0 0
\(832\) 29.7891 + 2.09451i 1.03275 + 0.0726142i
\(833\) −83.6698 −2.89899
\(834\) 0 0
\(835\) 6.12989 14.7989i 0.212133 0.512135i
\(836\) −7.74045 3.42051i −0.267709 0.118301i
\(837\) 0 0
\(838\) −8.81113 47.1744i −0.304375 1.62961i
\(839\) −13.7113 + 13.7113i −0.473368 + 0.473368i −0.903003 0.429635i \(-0.858642\pi\)
0.429635 + 0.903003i \(0.358642\pi\)
\(840\) 0 0
\(841\) −25.8631 25.8631i −0.891832 0.891832i
\(842\) 21.0162 30.6701i 0.724267 1.05696i
\(843\) 0 0
\(844\) 5.67299 5.41354i 0.195272 0.186342i
\(845\) −0.743930 0.308146i −0.0255920 0.0106005i
\(846\) 0 0
\(847\) 31.4117i 1.07932i
\(848\) 9.86816 20.9887i 0.338874 0.720755i
\(849\) 0 0
\(850\) −30.2115 6.37776i −1.03625 0.218755i
\(851\) −0.964794 0.399631i −0.0330727 0.0136992i
\(852\) 0 0
\(853\) −0.834820 2.01543i −0.0285837 0.0690071i 0.908943 0.416920i \(-0.136890\pi\)
−0.937527 + 0.347913i \(0.886890\pi\)
\(854\) 81.5213 + 55.8613i 2.78960 + 1.91153i
\(855\) 0 0
\(856\) 4.74041 2.93220i 0.162024 0.100221i
\(857\) −34.1542 + 34.1542i −1.16669 + 1.16669i −0.183705 + 0.982981i \(0.558809\pi\)
−0.982981 + 0.183705i \(0.941191\pi\)
\(858\) 0 0
\(859\) −17.2978 + 7.16498i −0.590193 + 0.244466i −0.657734 0.753251i \(-0.728485\pi\)
0.0675407 + 0.997717i \(0.478485\pi\)
\(860\) −6.51334 + 2.52105i −0.222103 + 0.0859669i
\(861\) 0 0
\(862\) 5.15080 + 7.90744i 0.175437 + 0.269329i
\(863\) −21.4602 −0.730513 −0.365256 0.930907i \(-0.619019\pi\)
−0.365256 + 0.930907i \(0.619019\pi\)
\(864\) 0 0
\(865\) 0.186315 0.00633491
\(866\) −10.4881 16.1012i −0.356400 0.547141i
\(867\) 0 0
\(868\) 26.0101 + 67.1994i 0.882840 + 2.28090i
\(869\) 18.9807 7.86205i 0.643875 0.266702i
\(870\) 0 0
\(871\) −10.3320 + 10.3320i −0.350086 + 0.350086i
\(872\) −0.348350 + 1.47812i −0.0117966 + 0.0500555i
\(873\) 0 0
\(874\) 2.15701 + 1.47806i 0.0729620 + 0.0499961i
\(875\) −14.7453 35.5984i −0.498483 1.20344i
\(876\) 0 0
\(877\) 9.14100 + 3.78632i 0.308670 + 0.127855i 0.531641 0.846970i \(-0.321576\pi\)
−0.222971 + 0.974825i \(0.571576\pi\)
\(878\) 19.3252 + 4.07961i 0.652193 + 0.137680i
\(879\) 0 0
\(880\) 0.341988 7.30252i 0.0115284 0.246168i
\(881\) 22.2039i 0.748068i 0.927415 + 0.374034i \(0.122026\pi\)
−0.927415 + 0.374034i \(0.877974\pi\)
\(882\) 0 0
\(883\) 36.2230 + 15.0040i 1.21900 + 0.504926i 0.897091 0.441845i \(-0.145676\pi\)
0.321908 + 0.946771i \(0.395676\pi\)
\(884\) 26.4359 + 27.7029i 0.889135 + 0.931749i
\(885\) 0 0
\(886\) 14.0183 20.4576i 0.470952 0.687286i
\(887\) 6.37890 + 6.37890i 0.214183 + 0.214183i 0.806042 0.591859i \(-0.201606\pi\)
−0.591859 + 0.806042i \(0.701606\pi\)
\(888\) 0 0
\(889\) −55.9533 + 55.9533i −1.87661 + 1.87661i
\(890\) −2.88667 15.4551i −0.0967613 0.518056i
\(891\) 0 0
\(892\) 17.0390 38.5585i 0.570508 1.29103i
\(893\) 6.51576 15.7304i 0.218042 0.526399i
\(894\) 0 0
\(895\) −17.9755 −0.600856
\(896\) −6.23857 54.2688i −0.208416 1.81299i
\(897\) 0 0
\(898\) 21.1831 13.7984i 0.706889 0.460458i
\(899\) 23.1241 55.8266i 0.771233 1.86192i
\(900\) 0 0
\(901\) 27.4759 11.3809i 0.915356 0.379153i
\(902\) −6.11374 32.7327i −0.203565 1.08988i
\(903\) 0 0
\(904\) 15.4762 2.51741i 0.514729 0.0837279i
\(905\) 12.2751 + 12.2751i 0.408039 + 0.408039i
\(906\) 0 0
\(907\) −0.128881 0.311146i −0.00427941 0.0103314i 0.921725 0.387843i \(-0.126780\pi\)
−0.926005 + 0.377512i \(0.876780\pi\)
\(908\) 15.4420 + 16.1821i 0.512462 + 0.537023i
\(909\) 0 0
\(910\) −4.53875 + 21.5001i −0.150458 + 0.712721i
\(911\) 21.7326i 0.720034i 0.932946 + 0.360017i \(0.117229\pi\)
−0.932946 + 0.360017i \(0.882771\pi\)
\(912\) 0 0
\(913\) 4.27917i 0.141620i
\(914\) 4.32790 + 0.913634i 0.143154 + 0.0302203i
\(915\) 0 0
\(916\) −0.622104 + 26.5824i −0.0205549 + 0.878306i
\(917\) −31.3834 75.7663i −1.03637 2.50202i
\(918\) 0 0
\(919\) 10.6016 + 10.6016i 0.349715 + 0.349715i 0.860004 0.510288i \(-0.170461\pi\)
−0.510288 + 0.860004i \(0.670461\pi\)
\(920\) −0.518156 + 2.19864i −0.0170831 + 0.0724872i
\(921\) 0 0
\(922\) 0.559668 0.104534i 0.0184317 0.00344263i
\(923\) −17.8206 + 7.38153i −0.586572 + 0.242966i
\(924\) 0 0
\(925\) −1.83633 + 4.43330i −0.0603782 + 0.145766i
\(926\) −18.7658 28.8091i −0.616684 0.946725i
\(927\) 0 0
\(928\) −27.6332 + 36.5355i −0.907103 + 1.19934i
\(929\) 17.9213 0.587980 0.293990 0.955809i \(-0.405017\pi\)
0.293990 + 0.955809i \(0.405017\pi\)
\(930\) 0 0
\(931\) 12.4596 30.0802i 0.408348 0.985839i
\(932\) 53.8016 20.8244i 1.76233 0.682124i
\(933\) 0 0
\(934\) 27.5851 5.15228i 0.902611 0.168588i
\(935\) 6.62854 6.62854i 0.216776 0.216776i
\(936\) 0 0
\(937\) −6.04430 6.04430i −0.197459 0.197459i 0.601451 0.798910i \(-0.294589\pi\)
−0.798910 + 0.601451i \(0.794589\pi\)
\(938\) 22.0485 + 15.1084i 0.719909 + 0.493307i
\(939\) 0 0
\(940\) 14.7047 + 0.344131i 0.479613 + 0.0112243i
\(941\) 24.4987 + 10.1477i 0.798636 + 0.330806i 0.744410 0.667723i \(-0.232731\pi\)
0.0542261 + 0.998529i \(0.482731\pi\)
\(942\) 0 0
\(943\) 10.2890i 0.335055i
\(944\) 13.9358 + 6.55212i 0.453571 + 0.213253i
\(945\) 0 0
\(946\) −2.50843 + 11.8825i −0.0815560 + 0.386332i
\(947\) 41.8476 + 17.3339i 1.35987 + 0.563275i 0.939022 0.343858i \(-0.111734\pi\)
0.420844 + 0.907133i \(0.361734\pi\)
\(948\) 0 0
\(949\) 2.76233 + 6.66886i 0.0896692 + 0.216480i
\(950\) 6.79180 9.91163i 0.220355 0.321576i
\(951\) 0 0
\(952\) 40.9354 56.8399i 1.32672 1.84219i
\(953\) 3.03378 3.03378i 0.0982737 0.0982737i −0.656261 0.754534i \(-0.727863\pi\)
0.754534 + 0.656261i \(0.227863\pi\)
\(954\) 0 0
\(955\) 3.33360 1.38082i 0.107873 0.0446823i
\(956\) −26.5660 11.7395i −0.859207 0.379684i
\(957\) 0 0
\(958\) −8.96281 + 5.83825i −0.289575 + 0.188625i
\(959\) 7.71871 0.249250
\(960\) 0 0
\(961\) 24.6809 0.796159
\(962\) 4.98635 3.24804i 0.160766 0.104721i
\(963\) 0 0
\(964\) −13.6267 6.02162i −0.438885 0.193943i
\(965\) −10.1554 + 4.20649i −0.326912 + 0.135412i
\(966\) 0 0
\(967\) −6.04796 + 6.04796i −0.194489 + 0.194489i −0.797633 0.603143i \(-0.793915\pi\)
0.603143 + 0.797633i \(0.293915\pi\)
\(968\) 14.9317 + 10.7536i 0.479923 + 0.345634i
\(969\) 0 0
\(970\) 10.8200 15.7902i 0.347410 0.506994i
\(971\) 19.9364 + 48.1308i 0.639791 + 1.54459i 0.826958 + 0.562264i \(0.190070\pi\)
−0.187167 + 0.982328i \(0.559930\pi\)
\(972\) 0 0
\(973\) 67.4474 + 27.9376i 2.16226 + 0.895639i
\(974\) −2.08856 + 9.89352i −0.0669217 + 0.317009i
\(975\) 0 0
\(976\) −54.4623 + 19.6277i −1.74329 + 0.628268i
\(977\) 33.1323i 1.06000i 0.847998 + 0.529999i \(0.177808\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(978\) 0 0
\(979\) −25.2574 10.4620i −0.807231 0.334366i
\(980\) 28.1187 + 0.658058i 0.898218 + 0.0210209i
\(981\) 0 0
\(982\) −26.6461 18.2588i −0.850310 0.582662i
\(983\) −25.7915 25.7915i −0.822621 0.822621i 0.163862 0.986483i \(-0.447605\pi\)
−0.986483 + 0.163862i \(0.947605\pi\)
\(984\) 0 0
\(985\) 15.6408 15.6408i 0.498359 0.498359i
\(986\) −57.7411 + 10.7848i −1.83885 + 0.343457i
\(987\) 0 0
\(988\) −13.8962 + 5.37863i −0.442096 + 0.171117i
\(989\) 1.43601 3.46683i 0.0456624 0.110239i
\(990\) 0 0
\(991\) −4.48501 −0.142471 −0.0712356 0.997460i \(-0.522694\pi\)
−0.0712356 + 0.997460i \(0.522694\pi\)
\(992\) −40.8479 10.6413i −1.29692 0.337862i
\(993\) 0 0
\(994\) 19.2582 + 29.5650i 0.610835 + 0.937745i
\(995\) −0.793585 + 1.91588i −0.0251583 + 0.0607376i
\(996\) 0 0
\(997\) 4.06177 1.68244i 0.128638 0.0532834i −0.317436 0.948280i \(-0.602822\pi\)
0.446074 + 0.894996i \(0.352822\pi\)
\(998\) 17.8088 3.32629i 0.563728 0.105292i
\(999\) 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 864.2.v.a.109.6 128
3.2 odd 2 inner 864.2.v.a.109.27 yes 128
32.5 even 8 inner 864.2.v.a.325.6 yes 128
96.5 odd 8 inner 864.2.v.a.325.27 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.v.a.109.6 128 1.1 even 1 trivial
864.2.v.a.109.27 yes 128 3.2 odd 2 inner
864.2.v.a.325.6 yes 128 32.5 even 8 inner
864.2.v.a.325.27 yes 128 96.5 odd 8 inner