Properties

Label 225.2.h.e.91.4
Level $225$
Weight $2$
Character 225.91
Analytic conductor $1.797$
Analytic rank $0$
Dimension $16$
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] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: 16.0.1130304400000000000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.4
Root \(1.13937 - 0.289499i\) of defining polynomial
Character \(\chi\) \(=\) 225.91
Dual form 225.2.h.e.136.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.64259 + 1.19341i) q^{2} +(0.655837 + 2.01846i) q^{4} +(2.23130 + 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 + 0.236224i) q^{8} +O(q^{10})\) \(q+(1.64259 + 1.19341i) q^{2} +(0.655837 + 2.01846i) q^{4} +(2.23130 + 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 + 0.236224i) q^{8} +(3.49087 + 2.90266i) q^{10} +(-2.78196 - 2.02121i) q^{11} +(-3.99517 + 2.90266i) q^{13} +(-0.828357 - 0.601837i) q^{14} +(3.02602 - 2.19853i) q^{16} +(0.363841 - 1.11979i) q^{17} +(-1.83504 + 5.64767i) q^{19} +(1.16868 + 4.59953i) q^{20} +(-2.15748 - 6.64004i) q^{22} +(-2.40939 - 1.75052i) q^{23} +(4.95737 + 0.651513i) q^{25} -10.0265 q^{26} +(-0.330738 - 1.01791i) q^{28} +(-1.55064 - 4.77239i) q^{29} +(1.10061 - 3.38734i) q^{31} +8.09103 q^{32} +(1.93401 - 1.40514i) q^{34} +(-1.12524 - 0.0736248i) q^{35} +(1.21435 - 0.882274i) q^{37} +(-9.75420 + 7.08684i) q^{38} +(-0.205748 + 0.515879i) q^{40} +(7.10690 - 5.16346i) q^{41} -10.2500 q^{43} +(2.25522 - 6.94085i) q^{44} +(-1.86854 - 5.75078i) q^{46} +(-0.881597 - 2.71328i) q^{47} -6.74568 q^{49} +(7.36541 + 6.98635i) q^{50} +(-8.47909 - 6.16042i) q^{52} +(4.09875 + 12.6147i) q^{53} +(-5.91229 - 4.91607i) q^{55} +(0.0387069 - 0.119127i) q^{56} +(3.14835 - 9.68964i) q^{58} +(7.68621 - 5.58436i) q^{59} +(6.86106 + 4.98485i) q^{61} +(5.85034 - 4.25052i) q^{62} +(7.23820 + 5.25886i) q^{64} +(-9.33819 + 5.89343i) q^{65} +(-2.99836 + 9.22800i) q^{67} +2.49886 q^{68} +(-1.76045 - 1.46381i) q^{70} +(4.23839 + 13.0444i) q^{71} +(10.0633 + 7.31141i) q^{73} +3.04759 q^{74} -12.6031 q^{76} +(1.40294 + 1.01930i) q^{77} +(-4.54026 - 13.9735i) q^{79} +(7.07292 - 4.46380i) q^{80} +17.8359 q^{82} +(0.110065 - 0.338746i) q^{83} +(0.975319 - 2.44546i) q^{85} +(-16.8365 - 12.2324i) q^{86} +(0.690983 - 0.502029i) q^{88} +(-5.26703 - 3.82672i) q^{89} +(2.01476 - 1.46381i) q^{91} +(1.95319 - 6.01131i) q^{92} +(1.78995 - 5.50891i) q^{94} +(-4.91904 + 12.3337i) q^{95} +(3.39322 + 10.4433i) q^{97} +(-11.0804 - 8.05038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.64259 + 1.19341i 1.16149 + 0.843869i 0.989965 0.141311i \(-0.0451317\pi\)
0.171521 + 0.985180i \(0.445132\pi\)
\(3\) 0 0
\(4\) 0.655837 + 2.01846i 0.327919 + 1.00923i
\(5\) 2.23130 + 0.145994i 0.997866 + 0.0652906i
\(6\) 0 0
\(7\) −0.504300 −0.190607 −0.0953037 0.995448i \(-0.530382\pi\)
−0.0953037 + 0.995448i \(0.530382\pi\)
\(8\) −0.0767537 + 0.236224i −0.0271365 + 0.0835177i
\(9\) 0 0
\(10\) 3.49087 + 2.90266i 1.10391 + 0.917903i
\(11\) −2.78196 2.02121i −0.838792 0.609418i 0.0832413 0.996529i \(-0.473473\pi\)
−0.922033 + 0.387112i \(0.873473\pi\)
\(12\) 0 0
\(13\) −3.99517 + 2.90266i −1.10806 + 0.805054i −0.982357 0.187014i \(-0.940119\pi\)
−0.125705 + 0.992068i \(0.540119\pi\)
\(14\) −0.828357 0.601837i −0.221388 0.160848i
\(15\) 0 0
\(16\) 3.02602 2.19853i 0.756505 0.549633i
\(17\) 0.363841 1.11979i 0.0882443 0.271588i −0.897190 0.441645i \(-0.854395\pi\)
0.985434 + 0.170057i \(0.0543951\pi\)
\(18\) 0 0
\(19\) −1.83504 + 5.64767i −0.420987 + 1.29566i 0.485799 + 0.874071i \(0.338529\pi\)
−0.906785 + 0.421593i \(0.861471\pi\)
\(20\) 1.16868 + 4.59953i 0.261326 + 1.02849i
\(21\) 0 0
\(22\) −2.15748 6.64004i −0.459976 1.41566i
\(23\) −2.40939 1.75052i −0.502392 0.365009i 0.307538 0.951536i \(-0.400495\pi\)
−0.809930 + 0.586527i \(0.800495\pi\)
\(24\) 0 0
\(25\) 4.95737 + 0.651513i 0.991474 + 0.130303i
\(26\) −10.0265 −1.96636
\(27\) 0 0
\(28\) −0.330738 1.01791i −0.0625037 0.192367i
\(29\) −1.55064 4.77239i −0.287947 0.886211i −0.985500 0.169677i \(-0.945728\pi\)
0.697552 0.716534i \(-0.254272\pi\)
\(30\) 0 0
\(31\) 1.10061 3.38734i 0.197676 0.608383i −0.802259 0.596976i \(-0.796369\pi\)
0.999935 0.0114076i \(-0.00363122\pi\)
\(32\) 8.09103 1.43031
\(33\) 0 0
\(34\) 1.93401 1.40514i 0.331680 0.240979i
\(35\) −1.12524 0.0736248i −0.190201 0.0124449i
\(36\) 0 0
\(37\) 1.21435 0.882274i 0.199637 0.145045i −0.483475 0.875358i \(-0.660626\pi\)
0.683113 + 0.730313i \(0.260626\pi\)
\(38\) −9.75420 + 7.08684i −1.58234 + 1.14964i
\(39\) 0 0
\(40\) −0.205748 + 0.515879i −0.0325316 + 0.0815677i
\(41\) 7.10690 5.16346i 1.10991 0.806397i 0.127261 0.991869i \(-0.459381\pi\)
0.982650 + 0.185472i \(0.0593814\pi\)
\(42\) 0 0
\(43\) −10.2500 −1.56311 −0.781554 0.623838i \(-0.785573\pi\)
−0.781554 + 0.623838i \(0.785573\pi\)
\(44\) 2.25522 6.94085i 0.339987 1.04637i
\(45\) 0 0
\(46\) −1.86854 5.75078i −0.275501 0.847906i
\(47\) −0.881597 2.71328i −0.128594 0.395772i 0.865945 0.500140i \(-0.166718\pi\)
−0.994539 + 0.104368i \(0.966718\pi\)
\(48\) 0 0
\(49\) −6.74568 −0.963669
\(50\) 7.36541 + 6.98635i 1.04163 + 0.988020i
\(51\) 0 0
\(52\) −8.47909 6.16042i −1.17584 0.854297i
\(53\) 4.09875 + 12.6147i 0.563007 + 1.73276i 0.673800 + 0.738914i \(0.264661\pi\)
−0.110793 + 0.993844i \(0.535339\pi\)
\(54\) 0 0
\(55\) −5.91229 4.91607i −0.797213 0.662883i
\(56\) 0.0387069 0.119127i 0.00517242 0.0159191i
\(57\) 0 0
\(58\) 3.14835 9.68964i 0.413399 1.27231i
\(59\) 7.68621 5.58436i 1.00066 0.727022i 0.0384302 0.999261i \(-0.487764\pi\)
0.962230 + 0.272239i \(0.0877643\pi\)
\(60\) 0 0
\(61\) 6.86106 + 4.98485i 0.878469 + 0.638245i 0.932846 0.360276i \(-0.117317\pi\)
−0.0543773 + 0.998520i \(0.517317\pi\)
\(62\) 5.85034 4.25052i 0.742994 0.539817i
\(63\) 0 0
\(64\) 7.23820 + 5.25886i 0.904775 + 0.657357i
\(65\) −9.33819 + 5.89343i −1.15826 + 0.730990i
\(66\) 0 0
\(67\) −2.99836 + 9.22800i −0.366308 + 1.12738i 0.582850 + 0.812579i \(0.301937\pi\)
−0.949158 + 0.314800i \(0.898063\pi\)
\(68\) 2.49886 0.303032
\(69\) 0 0
\(70\) −1.76045 1.46381i −0.210414 0.174959i
\(71\) 4.23839 + 13.0444i 0.503004 + 1.54809i 0.804100 + 0.594494i \(0.202647\pi\)
−0.301096 + 0.953594i \(0.597353\pi\)
\(72\) 0 0
\(73\) 10.0633 + 7.31141i 1.17782 + 0.855736i 0.991924 0.126833i \(-0.0404813\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(74\) 3.04759 0.354275
\(75\) 0 0
\(76\) −12.6031 −1.44567
\(77\) 1.40294 + 1.01930i 0.159880 + 0.116159i
\(78\) 0 0
\(79\) −4.54026 13.9735i −0.510819 1.57214i −0.790763 0.612123i \(-0.790316\pi\)
0.279943 0.960016i \(-0.409684\pi\)
\(80\) 7.07292 4.46380i 0.790777 0.499068i
\(81\) 0 0
\(82\) 17.8359 1.96964
\(83\) 0.110065 0.338746i 0.0120812 0.0371823i −0.944834 0.327549i \(-0.893777\pi\)
0.956915 + 0.290367i \(0.0937773\pi\)
\(84\) 0 0
\(85\) 0.975319 2.44546i 0.105788 0.265247i
\(86\) −16.8365 12.2324i −1.81553 1.31906i
\(87\) 0 0
\(88\) 0.690983 0.502029i 0.0736590 0.0535164i
\(89\) −5.26703 3.82672i −0.558304 0.405632i 0.272534 0.962146i \(-0.412138\pi\)
−0.830838 + 0.556515i \(0.812138\pi\)
\(90\) 0 0
\(91\) 2.01476 1.46381i 0.211205 0.153449i
\(92\) 1.95319 6.01131i 0.203634 0.626722i
\(93\) 0 0
\(94\) 1.78995 5.50891i 0.184620 0.568201i
\(95\) −4.91904 + 12.3337i −0.504683 + 1.26541i
\(96\) 0 0
\(97\) 3.39322 + 10.4433i 0.344530 + 1.06035i 0.961835 + 0.273629i \(0.0882242\pi\)
−0.617306 + 0.786723i \(0.711776\pi\)
\(98\) −11.0804 8.05038i −1.11929 0.813211i
\(99\) 0 0
\(100\) 1.93618 + 10.4335i 0.193618 + 1.04335i
\(101\) −8.10395 −0.806373 −0.403187 0.915118i \(-0.632097\pi\)
−0.403187 + 0.915118i \(0.632097\pi\)
\(102\) 0 0
\(103\) 1.66863 + 5.13553i 0.164415 + 0.506019i 0.998993 0.0448722i \(-0.0142881\pi\)
−0.834577 + 0.550891i \(0.814288\pi\)
\(104\) −0.379033 1.16654i −0.0371673 0.114389i
\(105\) 0 0
\(106\) −8.32192 + 25.6122i −0.808296 + 2.48768i
\(107\) −10.6007 −1.02481 −0.512403 0.858745i \(-0.671245\pi\)
−0.512403 + 0.858745i \(0.671245\pi\)
\(108\) 0 0
\(109\) 2.26426 1.64508i 0.216876 0.157570i −0.474043 0.880502i \(-0.657206\pi\)
0.690920 + 0.722932i \(0.257206\pi\)
\(110\) −3.84457 15.1309i −0.366565 1.44267i
\(111\) 0 0
\(112\) −1.52602 + 1.10872i −0.144195 + 0.104764i
\(113\) −5.77531 + 4.19601i −0.543296 + 0.394728i −0.825308 0.564683i \(-0.808998\pi\)
0.282012 + 0.959411i \(0.408998\pi\)
\(114\) 0 0
\(115\) −5.12049 4.25769i −0.477488 0.397032i
\(116\) 8.61591 6.25982i 0.799967 0.581210i
\(117\) 0 0
\(118\) 19.2897 1.77576
\(119\) −0.183485 + 0.564708i −0.0168200 + 0.0517667i
\(120\) 0 0
\(121\) 0.254807 + 0.784215i 0.0231643 + 0.0712923i
\(122\) 5.32093 + 16.3761i 0.481734 + 1.48263i
\(123\) 0 0
\(124\) 7.55902 0.678820
\(125\) 10.9663 + 2.17747i 0.980851 + 0.194759i
\(126\) 0 0
\(127\) 3.66227 + 2.66079i 0.324974 + 0.236107i 0.738295 0.674478i \(-0.235631\pi\)
−0.413321 + 0.910585i \(0.635631\pi\)
\(128\) 0.612881 + 1.88625i 0.0541715 + 0.166723i
\(129\) 0 0
\(130\) −22.3721 1.46381i −1.96216 0.128385i
\(131\) 2.99410 9.21489i 0.261596 0.805109i −0.730863 0.682525i \(-0.760882\pi\)
0.992458 0.122584i \(-0.0391180\pi\)
\(132\) 0 0
\(133\) 0.925409 2.84812i 0.0802431 0.246963i
\(134\) −15.9379 + 11.5795i −1.37682 + 1.00032i
\(135\) 0 0
\(136\) 0.236594 + 0.171896i 0.0202878 + 0.0147399i
\(137\) 3.22362 2.34210i 0.275412 0.200099i −0.441502 0.897260i \(-0.645554\pi\)
0.716914 + 0.697162i \(0.245554\pi\)
\(138\) 0 0
\(139\) −4.01391 2.91628i −0.340456 0.247356i 0.404398 0.914583i \(-0.367481\pi\)
−0.744854 + 0.667227i \(0.767481\pi\)
\(140\) −0.589367 2.31954i −0.0498106 0.196037i
\(141\) 0 0
\(142\) −8.60542 + 26.4848i −0.722151 + 2.22255i
\(143\) 16.9813 1.42005
\(144\) 0 0
\(145\) −2.76321 10.8750i −0.229472 0.903120i
\(146\) 7.80435 + 24.0193i 0.645892 + 1.98785i
\(147\) 0 0
\(148\) 2.57725 + 1.87248i 0.211849 + 0.153917i
\(149\) −5.62123 −0.460509 −0.230254 0.973130i \(-0.573956\pi\)
−0.230254 + 0.973130i \(0.573956\pi\)
\(150\) 0 0
\(151\) −2.35414 −0.191577 −0.0957886 0.995402i \(-0.530537\pi\)
−0.0957886 + 0.995402i \(0.530537\pi\)
\(152\) −1.19327 0.866959i −0.0967867 0.0703196i
\(153\) 0 0
\(154\) 1.08802 + 3.34857i 0.0876748 + 0.269835i
\(155\) 2.95032 7.39747i 0.236976 0.594179i
\(156\) 0 0
\(157\) 20.7688 1.65753 0.828767 0.559594i \(-0.189043\pi\)
0.828767 + 0.559594i \(0.189043\pi\)
\(158\) 9.21833 28.3711i 0.733371 2.25708i
\(159\) 0 0
\(160\) 18.0535 + 1.18124i 1.42725 + 0.0933855i
\(161\) 1.21505 + 0.882787i 0.0957595 + 0.0695734i
\(162\) 0 0
\(163\) 5.65797 4.11075i 0.443166 0.321979i −0.343725 0.939070i \(-0.611689\pi\)
0.786892 + 0.617091i \(0.211689\pi\)
\(164\) 15.0832 + 10.9586i 1.17780 + 0.855722i
\(165\) 0 0
\(166\) 0.585056 0.425068i 0.0454092 0.0329917i
\(167\) −4.59910 + 14.1546i −0.355889 + 1.09531i 0.599603 + 0.800297i \(0.295325\pi\)
−0.955492 + 0.295016i \(0.904675\pi\)
\(168\) 0 0
\(169\) 3.51874 10.8296i 0.270672 0.833043i
\(170\) 4.52049 2.85293i 0.346706 0.218810i
\(171\) 0 0
\(172\) −6.72232 20.6892i −0.512572 1.57753i
\(173\) −1.26528 0.919283i −0.0961978 0.0698918i 0.538647 0.842532i \(-0.318936\pi\)
−0.634844 + 0.772640i \(0.718936\pi\)
\(174\) 0 0
\(175\) −2.50000 0.328558i −0.188982 0.0248366i
\(176\) −12.8620 −0.969506
\(177\) 0 0
\(178\) −4.08472 12.5715i −0.306162 0.942271i
\(179\) 3.69979 + 11.3868i 0.276535 + 0.851089i 0.988809 + 0.149187i \(0.0476655\pi\)
−0.712274 + 0.701902i \(0.752334\pi\)
\(180\) 0 0
\(181\) −0.257789 + 0.793394i −0.0191613 + 0.0589725i −0.960180 0.279382i \(-0.909870\pi\)
0.941019 + 0.338355i \(0.109870\pi\)
\(182\) 5.05636 0.374803
\(183\) 0 0
\(184\) 0.598444 0.434795i 0.0441179 0.0320535i
\(185\) 2.83837 1.79133i 0.208681 0.131701i
\(186\) 0 0
\(187\) −3.27551 + 2.37980i −0.239529 + 0.174028i
\(188\) 4.89845 3.55893i 0.357256 0.259562i
\(189\) 0 0
\(190\) −22.7992 + 14.3888i −1.65403 + 1.04387i
\(191\) 21.4128 15.5573i 1.54938 1.12569i 0.605287 0.796007i \(-0.293058\pi\)
0.944092 0.329683i \(-0.106942\pi\)
\(192\) 0 0
\(193\) −3.97684 −0.286259 −0.143130 0.989704i \(-0.545717\pi\)
−0.143130 + 0.989704i \(0.545717\pi\)
\(194\) −6.88944 + 21.2035i −0.494633 + 1.52232i
\(195\) 0 0
\(196\) −4.42407 13.6159i −0.316005 0.972563i
\(197\) −7.21923 22.2185i −0.514349 1.58300i −0.784464 0.620174i \(-0.787062\pi\)
0.270115 0.962828i \(-0.412938\pi\)
\(198\) 0 0
\(199\) −4.43506 −0.314393 −0.157197 0.987567i \(-0.550246\pi\)
−0.157197 + 0.987567i \(0.550246\pi\)
\(200\) −0.534399 + 1.12104i −0.0377877 + 0.0792697i
\(201\) 0 0
\(202\) −13.3115 9.67135i −0.936592 0.680474i
\(203\) 0.781989 + 2.40671i 0.0548849 + 0.168918i
\(204\) 0 0
\(205\) 16.6114 10.4837i 1.16019 0.732210i
\(206\) −3.38792 + 10.4269i −0.236047 + 0.726479i
\(207\) 0 0
\(208\) −5.70788 + 17.5670i −0.395770 + 1.21806i
\(209\) 16.5201 12.0026i 1.14272 0.830235i
\(210\) 0 0
\(211\) 5.09234 + 3.69980i 0.350571 + 0.254705i 0.749109 0.662447i \(-0.230482\pi\)
−0.398538 + 0.917152i \(0.630482\pi\)
\(212\) −22.7741 + 16.5463i −1.56413 + 1.13641i
\(213\) 0 0
\(214\) −17.4126 12.6510i −1.19030 0.864803i
\(215\) −22.8708 1.49644i −1.55977 0.102056i
\(216\) 0 0
\(217\) −0.555038 + 1.70823i −0.0376784 + 0.115962i
\(218\) 5.68250 0.384868
\(219\) 0 0
\(220\) 6.04539 15.1578i 0.407580 1.02194i
\(221\) 1.79676 + 5.52985i 0.120863 + 0.371978i
\(222\) 0 0
\(223\) −19.7640 14.3594i −1.32350 0.961577i −0.999882 0.0153877i \(-0.995102\pi\)
−0.323615 0.946189i \(-0.604898\pi\)
\(224\) −4.08030 −0.272627
\(225\) 0 0
\(226\) −14.4940 −0.964129
\(227\) −10.8784 7.90360i −0.722023 0.524581i 0.165007 0.986292i \(-0.447235\pi\)
−0.887030 + 0.461712i \(0.847235\pi\)
\(228\) 0 0
\(229\) 4.68153 + 14.4083i 0.309364 + 0.952126i 0.978012 + 0.208547i \(0.0668733\pi\)
−0.668648 + 0.743579i \(0.733127\pi\)
\(230\) −3.32969 13.1045i −0.219553 0.864085i
\(231\) 0 0
\(232\) 1.24637 0.0818281
\(233\) −0.986111 + 3.03494i −0.0646023 + 0.198825i −0.978148 0.207911i \(-0.933333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(234\) 0 0
\(235\) −1.57098 6.18283i −0.102480 0.403324i
\(236\) 16.3127 + 11.8519i 1.06187 + 0.771491i
\(237\) 0 0
\(238\) −0.975319 + 0.708611i −0.0632206 + 0.0459324i
\(239\) −18.2944 13.2917i −1.18337 0.859767i −0.190820 0.981625i \(-0.561115\pi\)
−0.992548 + 0.121858i \(0.961115\pi\)
\(240\) 0 0
\(241\) 15.5019 11.2628i 0.998567 0.725501i 0.0367866 0.999323i \(-0.488288\pi\)
0.961780 + 0.273822i \(0.0882878\pi\)
\(242\) −0.517348 + 1.59223i −0.0332564 + 0.102353i
\(243\) 0 0
\(244\) −5.56198 + 17.1180i −0.356069 + 1.09587i
\(245\) −15.0516 0.984831i −0.961613 0.0629185i
\(246\) 0 0
\(247\) −9.06198 27.8899i −0.576600 1.77459i
\(248\) 0.715693 + 0.519981i 0.0454465 + 0.0330188i
\(249\) 0 0
\(250\) 15.4144 + 16.6639i 0.974895 + 1.05392i
\(251\) 21.1160 1.33283 0.666414 0.745582i \(-0.267828\pi\)
0.666414 + 0.745582i \(0.267828\pi\)
\(252\) 0 0
\(253\) 3.16464 + 9.73975i 0.198959 + 0.612333i
\(254\) 2.84018 + 8.74119i 0.178209 + 0.548471i
\(255\) 0 0
\(256\) 4.28513 13.1883i 0.267820 0.824267i
\(257\) −18.4143 −1.14865 −0.574325 0.818627i \(-0.694735\pi\)
−0.574325 + 0.818627i \(0.694735\pi\)
\(258\) 0 0
\(259\) −0.612394 + 0.444931i −0.0380523 + 0.0276466i
\(260\) −18.0200 14.9836i −1.11755 0.929245i
\(261\) 0 0
\(262\) 15.9152 11.5631i 0.983246 0.714370i
\(263\) 0.481568 0.349879i 0.0296947 0.0215745i −0.572839 0.819668i \(-0.694158\pi\)
0.602534 + 0.798093i \(0.294158\pi\)
\(264\) 0 0
\(265\) 7.30387 + 28.7455i 0.448673 + 1.76582i
\(266\) 4.91904 3.57389i 0.301606 0.219129i
\(267\) 0 0
\(268\) −20.5928 −1.25790
\(269\) 2.41478 7.43193i 0.147232 0.453133i −0.850059 0.526687i \(-0.823434\pi\)
0.997291 + 0.0735538i \(0.0234341\pi\)
\(270\) 0 0
\(271\) −6.51138 20.0400i −0.395538 1.21734i −0.928542 0.371228i \(-0.878937\pi\)
0.533003 0.846113i \(-0.321063\pi\)
\(272\) −1.36090 4.18841i −0.0825166 0.253960i
\(273\) 0 0
\(274\) 8.09017 0.488745
\(275\) −12.4743 11.8324i −0.752232 0.713519i
\(276\) 0 0
\(277\) −16.1304 11.7194i −0.969184 0.704153i −0.0139182 0.999903i \(-0.504430\pi\)
−0.955265 + 0.295750i \(0.904430\pi\)
\(278\) −3.11289 9.58050i −0.186699 0.574600i
\(279\) 0 0
\(280\) 0.103758 0.260158i 0.00620075 0.0155474i
\(281\) −3.17758 + 9.77960i −0.189559 + 0.583402i −0.999997 0.00242215i \(-0.999229\pi\)
0.810438 + 0.585824i \(0.199229\pi\)
\(282\) 0 0
\(283\) −2.98891 + 9.19891i −0.177672 + 0.546819i −0.999745 0.0225631i \(-0.992817\pi\)
0.822073 + 0.569382i \(0.192817\pi\)
\(284\) −23.5499 + 17.1100i −1.39743 + 1.01529i
\(285\) 0 0
\(286\) 27.8933 + 20.2657i 1.64937 + 1.19833i
\(287\) −3.58400 + 2.60393i −0.211557 + 0.153705i
\(288\) 0 0
\(289\) 12.6317 + 9.17750i 0.743044 + 0.539853i
\(290\) 8.43954 21.1608i 0.495587 1.24261i
\(291\) 0 0
\(292\) −8.15791 + 25.1075i −0.477405 + 1.46930i
\(293\) 11.0903 0.647900 0.323950 0.946074i \(-0.394989\pi\)
0.323950 + 0.946074i \(0.394989\pi\)
\(294\) 0 0
\(295\) 17.9655 11.3382i 1.04599 0.660137i
\(296\) 0.115208 + 0.354575i 0.00669636 + 0.0206093i
\(297\) 0 0
\(298\) −9.23337 6.70844i −0.534875 0.388609i
\(299\) 14.7071 0.850533
\(300\) 0 0
\(301\) 5.16906 0.297940
\(302\) −3.86689 2.80946i −0.222514 0.161666i
\(303\) 0 0
\(304\) 6.86372 + 21.1243i 0.393661 + 1.21156i
\(305\) 14.5813 + 12.1244i 0.834923 + 0.694239i
\(306\) 0 0
\(307\) 2.14760 0.122570 0.0612850 0.998120i \(-0.480480\pi\)
0.0612850 + 0.998120i \(0.480480\pi\)
\(308\) −1.13731 + 3.50027i −0.0648040 + 0.199446i
\(309\) 0 0
\(310\) 13.6744 8.63006i 0.776654 0.490154i
\(311\) 8.93231 + 6.48970i 0.506505 + 0.367997i 0.811496 0.584358i \(-0.198654\pi\)
−0.304991 + 0.952355i \(0.598654\pi\)
\(312\) 0 0
\(313\) 9.40884 6.83592i 0.531819 0.386389i −0.289219 0.957263i \(-0.593396\pi\)
0.821038 + 0.570874i \(0.193396\pi\)
\(314\) 34.1147 + 24.7858i 1.92520 + 1.39874i
\(315\) 0 0
\(316\) 25.2272 18.3287i 1.41914 1.03107i
\(317\) 3.25520 10.0185i 0.182830 0.562694i −0.817074 0.576533i \(-0.804405\pi\)
0.999904 + 0.0138389i \(0.00440520\pi\)
\(318\) 0 0
\(319\) −5.33218 + 16.4108i −0.298545 + 0.918826i
\(320\) 15.3828 + 12.7908i 0.859925 + 0.715028i
\(321\) 0 0
\(322\) 0.942305 + 2.90012i 0.0525126 + 0.161617i
\(323\) 5.65652 + 4.10970i 0.314737 + 0.228670i
\(324\) 0 0
\(325\) −21.6967 + 11.7867i −1.20352 + 0.653807i
\(326\) 14.1995 0.786440
\(327\) 0 0
\(328\) 0.674251 + 2.07513i 0.0372293 + 0.114580i
\(329\) 0.444589 + 1.36830i 0.0245110 + 0.0754370i
\(330\) 0 0
\(331\) −7.22593 + 22.2391i −0.397173 + 1.22237i 0.530083 + 0.847945i \(0.322161\pi\)
−0.927256 + 0.374427i \(0.877839\pi\)
\(332\) 0.755931 0.0414871
\(333\) 0 0
\(334\) −24.4467 + 17.7615i −1.33766 + 0.971868i
\(335\) −8.03746 + 20.1527i −0.439133 + 1.10106i
\(336\) 0 0
\(337\) −3.37793 + 2.45421i −0.184008 + 0.133689i −0.675976 0.736924i \(-0.736278\pi\)
0.491968 + 0.870613i \(0.336278\pi\)
\(338\) 18.7040 13.5892i 1.01736 0.739157i
\(339\) 0 0
\(340\) 5.57571 + 0.364820i 0.302385 + 0.0197851i
\(341\) −9.90837 + 7.19885i −0.536568 + 0.389840i
\(342\) 0 0
\(343\) 6.93194 0.374290
\(344\) 0.786724 2.42129i 0.0424173 0.130547i
\(345\) 0 0
\(346\) −0.981261 3.02001i −0.0527529 0.162357i
\(347\) 2.58175 + 7.94582i 0.138596 + 0.426554i 0.996132 0.0878696i \(-0.0280059\pi\)
−0.857536 + 0.514424i \(0.828006\pi\)
\(348\) 0 0
\(349\) 8.84117 0.473257 0.236628 0.971600i \(-0.423958\pi\)
0.236628 + 0.971600i \(0.423958\pi\)
\(350\) −3.71437 3.52321i −0.198541 0.188324i
\(351\) 0 0
\(352\) −22.5089 16.3537i −1.19973 0.871653i
\(353\) 2.87823 + 8.85828i 0.153193 + 0.471479i 0.997973 0.0636341i \(-0.0202691\pi\)
−0.844781 + 0.535113i \(0.820269\pi\)
\(354\) 0 0
\(355\) 7.55269 + 29.7247i 0.400855 + 1.57763i
\(356\) 4.26977 13.1410i 0.226297 0.696471i
\(357\) 0 0
\(358\) −7.51188 + 23.1192i −0.397015 + 1.22189i
\(359\) 5.70869 4.14761i 0.301293 0.218902i −0.426858 0.904319i \(-0.640380\pi\)
0.728152 + 0.685416i \(0.240380\pi\)
\(360\) 0 0
\(361\) −13.1574 9.55944i −0.692497 0.503128i
\(362\) −1.37029 + 0.995572i −0.0720207 + 0.0523261i
\(363\) 0 0
\(364\) 4.27600 + 3.10670i 0.224123 + 0.162835i
\(365\) 21.3868 + 17.7831i 1.11944 + 0.930811i
\(366\) 0 0
\(367\) 1.03134 3.17412i 0.0538353 0.165688i −0.920524 0.390686i \(-0.872238\pi\)
0.974359 + 0.224998i \(0.0722377\pi\)
\(368\) −11.1394 −0.580683
\(369\) 0 0
\(370\) 6.80008 + 0.444931i 0.353519 + 0.0231308i
\(371\) −2.06700 6.36157i −0.107313 0.330276i
\(372\) 0 0
\(373\) −13.6425 9.91184i −0.706381 0.513216i 0.175623 0.984457i \(-0.443806\pi\)
−0.882004 + 0.471242i \(0.843806\pi\)
\(374\) −8.22041 −0.425067
\(375\) 0 0
\(376\) 0.708606 0.0365436
\(377\) 20.0477 + 14.5655i 1.03251 + 0.750163i
\(378\) 0 0
\(379\) −0.605237 1.86273i −0.0310889 0.0956819i 0.934308 0.356467i \(-0.116019\pi\)
−0.965397 + 0.260785i \(0.916019\pi\)
\(380\) −28.1212 1.83998i −1.44259 0.0943887i
\(381\) 0 0
\(382\) 53.7388 2.74952
\(383\) 4.58432 14.1091i 0.234248 0.720940i −0.762973 0.646431i \(-0.776261\pi\)
0.997220 0.0745092i \(-0.0237390\pi\)
\(384\) 0 0
\(385\) 2.98156 + 2.47917i 0.151955 + 0.126350i
\(386\) −6.53231 4.74600i −0.332486 0.241565i
\(387\) 0 0
\(388\) −18.8539 + 13.6982i −0.957162 + 0.695419i
\(389\) −24.1901 17.5751i −1.22649 0.891094i −0.229863 0.973223i \(-0.573828\pi\)
−0.996622 + 0.0821294i \(0.973828\pi\)
\(390\) 0 0
\(391\) −2.83684 + 2.06109i −0.143465 + 0.104234i
\(392\) 0.517756 1.59349i 0.0261506 0.0804834i
\(393\) 0 0
\(394\) 14.6576 45.1114i 0.738438 2.27268i
\(395\) −8.09062 31.8418i −0.407083 1.60214i
\(396\) 0 0
\(397\) 0.858602 + 2.64251i 0.0430920 + 0.132624i 0.970288 0.241953i \(-0.0777880\pi\)
−0.927196 + 0.374577i \(0.877788\pi\)
\(398\) −7.28499 5.29285i −0.365163 0.265307i
\(399\) 0 0
\(400\) 16.4335 8.92745i 0.821674 0.446373i
\(401\) −8.54941 −0.426937 −0.213469 0.976950i \(-0.568476\pi\)
−0.213469 + 0.976950i \(0.568476\pi\)
\(402\) 0 0
\(403\) 5.43516 + 16.7277i 0.270745 + 0.833266i
\(404\) −5.31487 16.3575i −0.264425 0.813816i
\(405\) 0 0
\(406\) −1.58771 + 4.88648i −0.0787969 + 0.242512i
\(407\) −5.16152 −0.255847
\(408\) 0 0
\(409\) −5.03563 + 3.65860i −0.248996 + 0.180906i −0.705282 0.708927i \(-0.749180\pi\)
0.456286 + 0.889833i \(0.349180\pi\)
\(410\) 39.7971 + 2.60393i 1.96544 + 0.128599i
\(411\) 0 0
\(412\) −9.27150 + 6.73614i −0.456774 + 0.331866i
\(413\) −3.87615 + 2.81619i −0.190733 + 0.138576i
\(414\) 0 0
\(415\) 0.295044 0.739775i 0.0144831 0.0363141i
\(416\) −32.3251 + 23.4855i −1.58487 + 1.15147i
\(417\) 0 0
\(418\) 41.4598 2.02786
\(419\) −11.5879 + 35.6639i −0.566106 + 1.74229i 0.0985382 + 0.995133i \(0.468583\pi\)
−0.664644 + 0.747160i \(0.731417\pi\)
\(420\) 0 0
\(421\) 2.92653 + 9.00692i 0.142630 + 0.438970i 0.996699 0.0811902i \(-0.0258721\pi\)
−0.854069 + 0.520161i \(0.825872\pi\)
\(422\) 3.94924 + 12.1545i 0.192246 + 0.591672i
\(423\) 0 0
\(424\) −3.29448 −0.159994
\(425\) 2.53325 5.31415i 0.122881 0.257774i
\(426\) 0 0
\(427\) −3.46003 2.51386i −0.167443 0.121654i
\(428\) −6.95232 21.3970i −0.336053 1.03427i
\(429\) 0 0
\(430\) −35.7814 29.7523i −1.72553 1.43478i
\(431\) 3.05401 9.39927i 0.147106 0.452747i −0.850170 0.526509i \(-0.823501\pi\)
0.997276 + 0.0737623i \(0.0235006\pi\)
\(432\) 0 0
\(433\) 7.50377 23.0942i 0.360608 1.10984i −0.592077 0.805881i \(-0.701692\pi\)
0.952686 0.303957i \(-0.0983080\pi\)
\(434\) −2.95032 + 2.14354i −0.141620 + 0.102893i
\(435\) 0 0
\(436\) 4.80551 + 3.49141i 0.230142 + 0.167208i
\(437\) 14.3077 10.3951i 0.684429 0.497267i
\(438\) 0 0
\(439\) 1.42111 + 1.03250i 0.0678258 + 0.0492784i 0.621182 0.783667i \(-0.286653\pi\)
−0.553356 + 0.832945i \(0.686653\pi\)
\(440\) 1.61508 1.01930i 0.0769960 0.0485930i
\(441\) 0 0
\(442\) −3.64805 + 11.2276i −0.173520 + 0.534040i
\(443\) −37.3529 −1.77469 −0.887346 0.461105i \(-0.847453\pi\)
−0.887346 + 0.461105i \(0.847453\pi\)
\(444\) 0 0
\(445\) −11.1936 9.30751i −0.530629 0.441218i
\(446\) −15.3275 47.1732i −0.725779 2.23372i
\(447\) 0 0
\(448\) −3.65022 2.65204i −0.172457 0.125297i
\(449\) −12.9452 −0.610923 −0.305461 0.952204i \(-0.598811\pi\)
−0.305461 + 0.952204i \(0.598811\pi\)
\(450\) 0 0
\(451\) −30.2075 −1.42242
\(452\) −12.2571 8.90534i −0.576528 0.418872i
\(453\) 0 0
\(454\) −8.43646 25.9648i −0.395943 1.21859i
\(455\) 4.70925 2.97206i 0.220773 0.139332i
\(456\) 0 0
\(457\) −22.2891 −1.04264 −0.521320 0.853361i \(-0.674560\pi\)
−0.521320 + 0.853361i \(0.674560\pi\)
\(458\) −9.50516 + 29.2539i −0.444147 + 1.36694i
\(459\) 0 0
\(460\) 5.23577 13.1279i 0.244119 0.612089i
\(461\) −0.434539 0.315711i −0.0202385 0.0147041i 0.577620 0.816306i \(-0.303982\pi\)
−0.597859 + 0.801602i \(0.703982\pi\)
\(462\) 0 0
\(463\) 18.0822 13.1375i 0.840349 0.610550i −0.0821189 0.996623i \(-0.526169\pi\)
0.922468 + 0.386073i \(0.126169\pi\)
\(464\) −15.1845 11.0322i −0.704925 0.512158i
\(465\) 0 0
\(466\) −5.24171 + 3.80832i −0.242817 + 0.176417i
\(467\) −11.5807 + 35.6417i −0.535890 + 1.64930i 0.205827 + 0.978588i \(0.434012\pi\)
−0.741717 + 0.670712i \(0.765988\pi\)
\(468\) 0 0
\(469\) 1.51207 4.65367i 0.0698209 0.214887i
\(470\) 4.79819 12.0307i 0.221324 0.554934i
\(471\) 0 0
\(472\) 0.729213 + 2.24429i 0.0335647 + 0.103302i
\(473\) 28.5150 + 20.7174i 1.31112 + 0.952585i
\(474\) 0 0
\(475\) −12.7765 + 26.8020i −0.586226 + 1.22976i
\(476\) −1.26018 −0.0577601
\(477\) 0 0
\(478\) −14.1878 43.6656i −0.648935 1.99722i
\(479\) 5.75361 + 17.7078i 0.262889 + 0.809089i 0.992172 + 0.124877i \(0.0398538\pi\)
−0.729283 + 0.684212i \(0.760146\pi\)
\(480\) 0 0
\(481\) −2.29058 + 7.04968i −0.104441 + 0.321438i
\(482\) 38.9045 1.77205
\(483\) 0 0
\(484\) −1.41579 + 1.02864i −0.0643543 + 0.0467561i
\(485\) 6.04663 + 23.7974i 0.274563 + 1.08058i
\(486\) 0 0
\(487\) 1.44904 1.05279i 0.0656622 0.0477064i −0.554470 0.832204i \(-0.687079\pi\)
0.620132 + 0.784497i \(0.287079\pi\)
\(488\) −1.70415 + 1.23814i −0.0771433 + 0.0560479i
\(489\) 0 0
\(490\) −23.5483 19.5804i −1.06381 0.884555i
\(491\) −22.0663 + 16.0321i −0.995839 + 0.723519i −0.961192 0.275880i \(-0.911031\pi\)
−0.0346469 + 0.999400i \(0.511031\pi\)
\(492\) 0 0
\(493\) −5.90825 −0.266094
\(494\) 18.3990 56.6264i 0.827811 2.54774i
\(495\) 0 0
\(496\) −4.11669 12.6699i −0.184845 0.568894i
\(497\) −2.13742 6.57829i −0.0958763 0.295077i
\(498\) 0 0
\(499\) 10.5722 0.473275 0.236637 0.971598i \(-0.423955\pi\)
0.236637 + 0.971598i \(0.423955\pi\)
\(500\) 2.79695 + 23.5630i 0.125083 + 1.05377i
\(501\) 0 0
\(502\) 34.6849 + 25.2000i 1.54806 + 1.12473i
\(503\) −8.37251 25.7679i −0.373312 1.14894i −0.944610 0.328194i \(-0.893560\pi\)
0.571299 0.820742i \(-0.306440\pi\)
\(504\) 0 0
\(505\) −18.0823 1.18313i −0.804653 0.0526486i
\(506\) −6.42533 + 19.7751i −0.285641 + 0.879112i
\(507\) 0 0
\(508\) −2.96885 + 9.13719i −0.131721 + 0.405397i
\(509\) 22.7355 16.5183i 1.00773 0.732161i 0.0440004 0.999032i \(-0.485990\pi\)
0.963732 + 0.266871i \(0.0859897\pi\)
\(510\) 0 0
\(511\) −5.07492 3.68714i −0.224501 0.163110i
\(512\) 25.9868 18.8805i 1.14847 0.834410i
\(513\) 0 0
\(514\) −30.2471 21.9758i −1.33414 0.969311i
\(515\) 2.97346 + 11.7025i 0.131026 + 0.515674i
\(516\) 0 0
\(517\) −3.03154 + 9.33011i −0.133327 + 0.410338i
\(518\) −1.53690 −0.0675274
\(519\) 0 0
\(520\) −0.675427 2.65824i −0.0296194 0.116572i
\(521\) −10.2133 31.4332i −0.447452 1.37711i −0.879772 0.475395i \(-0.842305\pi\)
0.432321 0.901720i \(-0.357695\pi\)
\(522\) 0 0
\(523\) 32.9601 + 23.9469i 1.44125 + 1.04713i 0.987780 + 0.155852i \(0.0498122\pi\)
0.453465 + 0.891274i \(0.350188\pi\)
\(524\) 20.5635 0.898321
\(525\) 0 0
\(526\) 1.20857 0.0526961
\(527\) −3.39265 2.46490i −0.147786 0.107373i
\(528\) 0 0
\(529\) −4.36657 13.4389i −0.189851 0.584301i
\(530\) −22.3079 + 55.9335i −0.968993 + 2.42960i
\(531\) 0 0
\(532\) 6.35572 0.275555
\(533\) −13.4055 + 41.2579i −0.580656 + 1.78708i
\(534\) 0 0
\(535\) −23.6533 1.54764i −1.02262 0.0669102i
\(536\) −1.94974 1.41657i −0.0842158 0.0611863i
\(537\) 0 0
\(538\) 12.8359 9.32579i 0.553393 0.402063i
\(539\) 18.7662 + 13.6344i 0.808317 + 0.587277i
\(540\) 0 0
\(541\) −36.5725 + 26.5715i −1.57238 + 1.14240i −0.647538 + 0.762033i \(0.724201\pi\)
−0.924837 + 0.380364i \(0.875799\pi\)
\(542\) 13.2204 40.6882i 0.567865 1.74771i
\(543\) 0 0
\(544\) 2.94385 9.06022i 0.126216 0.388454i
\(545\) 5.29240 3.34009i 0.226702 0.143074i
\(546\) 0 0
\(547\) 0.753668 + 2.31955i 0.0322245 + 0.0991768i 0.965875 0.259008i \(-0.0833957\pi\)
−0.933651 + 0.358185i \(0.883396\pi\)
\(548\) 6.84159 + 4.97071i 0.292258 + 0.212338i
\(549\) 0 0
\(550\) −6.36936 34.3228i −0.271590 1.46353i
\(551\) 29.7984 1.26945
\(552\) 0 0
\(553\) 2.28965 + 7.04682i 0.0973659 + 0.299661i
\(554\) −12.5096 38.5005i −0.531480 1.63573i
\(555\) 0 0
\(556\) 3.25392 10.0145i 0.137997 0.424710i
\(557\) −7.91914 −0.335545 −0.167772 0.985826i \(-0.553657\pi\)
−0.167772 + 0.985826i \(0.553657\pi\)
\(558\) 0 0
\(559\) 40.9505 29.7523i 1.73202 1.25839i
\(560\) −3.56687 + 2.25109i −0.150728 + 0.0951260i
\(561\) 0 0
\(562\) −16.8906 + 12.2717i −0.712485 + 0.517651i
\(563\) 19.4577 14.1369i 0.820045 0.595797i −0.0966805 0.995315i \(-0.530822\pi\)
0.916725 + 0.399518i \(0.130822\pi\)
\(564\) 0 0
\(565\) −13.4990 + 8.51939i −0.567909 + 0.358413i
\(566\) −15.8876 + 11.5430i −0.667807 + 0.485190i
\(567\) 0 0
\(568\) −3.40671 −0.142942
\(569\) 4.52263 13.9192i 0.189598 0.583524i −0.810399 0.585879i \(-0.800749\pi\)
0.999997 + 0.00235460i \(0.000749494\pi\)
\(570\) 0 0
\(571\) 6.53259 + 20.1052i 0.273380 + 0.841378i 0.989643 + 0.143548i \(0.0458511\pi\)
−0.716263 + 0.697830i \(0.754149\pi\)
\(572\) 11.1370 + 34.2761i 0.465660 + 1.43315i
\(573\) 0 0
\(574\) −8.99461 −0.375428
\(575\) −10.8037 10.2477i −0.450547 0.427360i
\(576\) 0 0
\(577\) 3.19476 + 2.32113i 0.132999 + 0.0966298i 0.652296 0.757964i \(-0.273806\pi\)
−0.519296 + 0.854594i \(0.673806\pi\)
\(578\) 9.79625 + 30.1497i 0.407470 + 1.25406i
\(579\) 0 0
\(580\) 20.1385 12.7096i 0.836207 0.527739i
\(581\) −0.0555059 + 0.170830i −0.00230277 + 0.00708721i
\(582\) 0 0
\(583\) 14.0943 43.3779i 0.583728 1.79653i
\(584\) −2.49952 + 1.81601i −0.103431 + 0.0751471i
\(585\) 0 0
\(586\) 18.2168 + 13.2353i 0.752528 + 0.546743i
\(587\) 16.4014 11.9164i 0.676960 0.491840i −0.195388 0.980726i \(-0.562596\pi\)
0.872348 + 0.488886i \(0.162596\pi\)
\(588\) 0 0
\(589\) 17.1109 + 12.4318i 0.705041 + 0.512243i
\(590\) 43.0411 + 2.81619i 1.77198 + 0.115941i
\(591\) 0 0
\(592\) 1.73493 5.33956i 0.0713051 0.219455i
\(593\) −30.2561 −1.24247 −0.621234 0.783625i \(-0.713368\pi\)
−0.621234 + 0.783625i \(0.713368\pi\)
\(594\) 0 0
\(595\) −0.491853 + 1.23324i −0.0201640 + 0.0505580i
\(596\) −3.68661 11.3462i −0.151009 0.464759i
\(597\) 0 0
\(598\) 24.1577 + 17.5516i 0.987883 + 0.717739i
\(599\) 1.02686 0.0419563 0.0209781 0.999780i \(-0.493322\pi\)
0.0209781 + 0.999780i \(0.493322\pi\)
\(600\) 0 0
\(601\) −16.9840 −0.692791 −0.346396 0.938089i \(-0.612594\pi\)
−0.346396 + 0.938089i \(0.612594\pi\)
\(602\) 8.49065 + 6.16882i 0.346053 + 0.251422i
\(603\) 0 0
\(604\) −1.54393 4.75173i −0.0628217 0.193345i
\(605\) 0.454059 + 1.78702i 0.0184601 + 0.0726526i
\(606\) 0 0
\(607\) 10.7660 0.436977 0.218488 0.975840i \(-0.429887\pi\)
0.218488 + 0.975840i \(0.429887\pi\)
\(608\) −14.8473 + 45.6954i −0.602139 + 1.85319i
\(609\) 0 0
\(610\) 9.48175 + 37.3168i 0.383905 + 1.51091i
\(611\) 11.3979 + 8.28103i 0.461108 + 0.335015i
\(612\) 0 0
\(613\) 4.08204 2.96577i 0.164872 0.119786i −0.502290 0.864699i \(-0.667509\pi\)
0.667162 + 0.744913i \(0.267509\pi\)
\(614\) 3.52763 + 2.56297i 0.142363 + 0.103433i
\(615\) 0 0
\(616\) −0.348462 + 0.253173i −0.0140400 + 0.0102006i
\(617\) 9.60737 29.5684i 0.386778 1.19038i −0.548404 0.836213i \(-0.684764\pi\)
0.935182 0.354167i \(-0.115236\pi\)
\(618\) 0 0
\(619\) −10.7533 + 33.0951i −0.432210 + 1.33021i 0.463708 + 0.885988i \(0.346519\pi\)
−0.895919 + 0.444218i \(0.853481\pi\)
\(620\) 16.8664 + 1.10357i 0.677372 + 0.0443206i
\(621\) 0 0
\(622\) 6.92724 + 21.3198i 0.277757 + 0.854848i
\(623\) 2.65616 + 1.92981i 0.106417 + 0.0773163i
\(624\) 0 0
\(625\) 24.1511 + 6.45958i 0.966042 + 0.258383i
\(626\) 23.6129 0.943763
\(627\) 0 0
\(628\) 13.6210 + 41.9211i 0.543536 + 1.67283i
\(629\) −0.546130 1.68082i −0.0217756 0.0670186i
\(630\) 0 0
\(631\) −2.86250 + 8.80987i −0.113954 + 0.350715i −0.991727 0.128361i \(-0.959028\pi\)
0.877773 + 0.479076i \(0.159028\pi\)
\(632\) 3.64935 0.145163
\(633\) 0 0
\(634\) 17.3031 12.5715i 0.687195 0.499277i
\(635\) 7.78315 + 6.47169i 0.308865 + 0.256821i
\(636\) 0 0
\(637\) 26.9502 19.5804i 1.06780 0.775806i
\(638\) −28.3434 + 20.5927i −1.12213 + 0.815272i
\(639\) 0 0
\(640\) 1.09214 + 4.29827i 0.0431705 + 0.169904i
\(641\) −35.3179 + 25.6600i −1.39497 + 1.01351i −0.399674 + 0.916657i \(0.630877\pi\)
−0.995299 + 0.0968498i \(0.969123\pi\)
\(642\) 0 0
\(643\) −35.4133 −1.39656 −0.698281 0.715824i \(-0.746051\pi\)
−0.698281 + 0.715824i \(0.746051\pi\)
\(644\) −0.984994 + 3.03150i −0.0388142 + 0.119458i
\(645\) 0 0
\(646\) 4.38678 + 13.5011i 0.172595 + 0.531194i
\(647\) −10.2984 31.6951i −0.404870 1.24606i −0.921004 0.389554i \(-0.872629\pi\)
0.516134 0.856508i \(-0.327371\pi\)
\(648\) 0 0
\(649\) −32.6699 −1.28240
\(650\) −49.7051 6.53240i −1.94960 0.256222i
\(651\) 0 0
\(652\) 12.0081 + 8.72439i 0.470273 + 0.341674i
\(653\) −5.78030 17.7899i −0.226201 0.696174i −0.998168 0.0605113i \(-0.980727\pi\)
0.771967 0.635663i \(-0.219273\pi\)
\(654\) 0 0
\(655\) 8.02604 20.1240i 0.313603 0.786311i
\(656\) 10.1536 31.2495i 0.396430 1.22009i
\(657\) 0 0
\(658\) −0.902672 + 2.77814i −0.0351898 + 0.108303i
\(659\) 20.9712 15.2365i 0.816921 0.593528i −0.0989077 0.995097i \(-0.531535\pi\)
0.915829 + 0.401569i \(0.131535\pi\)
\(660\) 0 0
\(661\) −18.6395 13.5424i −0.724992 0.526738i 0.162983 0.986629i \(-0.447888\pi\)
−0.887975 + 0.459891i \(0.847888\pi\)
\(662\) −38.4097 + 27.9063i −1.49283 + 1.08461i
\(663\) 0 0
\(664\) 0.0715720 + 0.0520001i 0.00277753 + 0.00201800i
\(665\) 2.48067 6.21989i 0.0961963 0.241197i
\(666\) 0 0
\(667\) −4.61807 + 14.2130i −0.178813 + 0.550328i
\(668\) −31.5867 −1.22213
\(669\) 0 0
\(670\) −37.2527 + 23.5106i −1.43920 + 0.908292i
\(671\) −9.01174 27.7353i −0.347894 1.07071i
\(672\) 0 0
\(673\) 4.97293 + 3.61304i 0.191692 + 0.139273i 0.679492 0.733683i \(-0.262200\pi\)
−0.487800 + 0.872956i \(0.662200\pi\)
\(674\) −8.47744 −0.326539
\(675\) 0 0
\(676\) 24.1668 0.929491
\(677\) 28.7547 + 20.8915i 1.10513 + 0.802925i 0.981890 0.189452i \(-0.0606711\pi\)
0.123241 + 0.992377i \(0.460671\pi\)
\(678\) 0 0
\(679\) −1.71120 5.26653i −0.0656698 0.202111i
\(680\) 0.502816 + 0.418091i 0.0192821 + 0.0160331i
\(681\) 0 0
\(682\) −24.8666 −0.952191
\(683\) 5.23883 16.1235i 0.200458 0.616947i −0.799411 0.600784i \(-0.794855\pi\)
0.999869 0.0161627i \(-0.00514496\pi\)
\(684\) 0 0
\(685\) 7.53478 4.75528i 0.287889 0.181690i
\(686\) 11.3863 + 8.27266i 0.434732 + 0.315852i
\(687\) 0 0
\(688\) −31.0167 + 22.5349i −1.18250 + 0.859136i
\(689\) −52.9914 38.5005i −2.01881 1.46675i
\(690\) 0 0
\(691\) 12.9241 9.38990i 0.491656 0.357209i −0.314165 0.949368i \(-0.601725\pi\)
0.805821 + 0.592160i \(0.201725\pi\)
\(692\) 1.02571 3.15683i 0.0389918 0.120004i
\(693\) 0 0
\(694\) −5.24187 + 16.1328i −0.198979 + 0.612394i
\(695\) −8.53047 7.09309i −0.323579 0.269056i
\(696\) 0 0
\(697\) −3.19620 9.83689i −0.121065 0.372599i
\(698\) 14.5224 + 10.5512i 0.549681 + 0.399367i
\(699\) 0 0
\(700\) −0.976413 5.26163i −0.0369049 0.198871i
\(701\) −19.5403 −0.738026 −0.369013 0.929424i \(-0.620304\pi\)
−0.369013 + 0.929424i \(0.620304\pi\)
\(702\) 0 0
\(703\) 2.75442 + 8.47723i 0.103885 + 0.319725i
\(704\) −9.50710 29.2598i −0.358312 1.10277i
\(705\) 0 0
\(706\) −5.84382 + 17.9854i −0.219935 + 0.676891i
\(707\) 4.08682 0.153701
\(708\) 0 0
\(709\) 10.6571 7.74285i 0.400236 0.290789i −0.369401 0.929270i \(-0.620437\pi\)
0.769637 + 0.638481i \(0.220437\pi\)
\(710\) −23.0679 + 57.8390i −0.865722 + 2.17066i
\(711\) 0 0
\(712\) 1.30823 0.950482i 0.0490278 0.0356208i
\(713\) −8.58141 + 6.23476i −0.321376 + 0.233493i
\(714\) 0 0
\(715\) 37.8903 + 2.47917i 1.41702 + 0.0927157i
\(716\) −20.5573 + 14.9358i −0.768263 + 0.558175i
\(717\) 0 0
\(718\) 14.3268 0.534673
\(719\) 2.58348 7.95114i 0.0963476 0.296527i −0.891255 0.453503i \(-0.850174\pi\)
0.987603 + 0.156975i \(0.0501743\pi\)
\(720\) 0 0
\(721\) −0.841492 2.58984i −0.0313388 0.0964509i
\(722\) −10.2039 31.4045i −0.379751 1.16875i
\(723\) 0 0
\(724\) −1.77050 −0.0658002
\(725\) −4.57784 24.6688i −0.170017 0.916175i
\(726\) 0 0
\(727\) 0.213756 + 0.155303i 0.00792778 + 0.00575987i 0.591742 0.806127i \(-0.298440\pi\)
−0.583814 + 0.811887i \(0.698440\pi\)
\(728\) 0.191146 + 0.588288i 0.00708436 + 0.0218034i
\(729\) 0 0
\(730\) 13.9071 + 54.7336i 0.514726 + 2.02578i
\(731\) −3.72936 + 11.4778i −0.137935 + 0.424522i
\(732\) 0 0
\(733\) 5.55648 17.1011i 0.205233 0.631643i −0.794470 0.607303i \(-0.792251\pi\)
0.999704 0.0243402i \(-0.00774850\pi\)
\(734\) 5.48210 3.98298i 0.202348 0.147014i
\(735\) 0 0
\(736\) −19.4944 14.1635i −0.718574 0.522074i
\(737\) 26.9930 19.6116i 0.994301 0.722402i
\(738\) 0 0
\(739\) 30.3496 + 22.0502i 1.11643 + 0.811132i 0.983664 0.180016i \(-0.0576150\pi\)
0.132763 + 0.991148i \(0.457615\pi\)
\(740\) 5.47724 + 4.55432i 0.201347 + 0.167420i
\(741\) 0 0
\(742\) 4.19674 12.9162i 0.154067 0.474170i
\(743\) 18.6523 0.684285 0.342142 0.939648i \(-0.388847\pi\)
0.342142 + 0.939648i \(0.388847\pi\)
\(744\) 0 0
\(745\) −12.5426 0.820667i −0.459526 0.0300669i
\(746\) −10.5801 32.5622i −0.387365 1.19219i
\(747\) 0 0
\(748\) −6.95173 5.05073i −0.254180 0.184673i
\(749\) 5.34592 0.195336
\(750\) 0 0
\(751\) 51.3728 1.87462 0.937310 0.348496i \(-0.113307\pi\)
0.937310 + 0.348496i \(0.113307\pi\)
\(752\) −8.63296 6.27221i −0.314812 0.228724i
\(753\) 0 0
\(754\) 15.5475 + 47.8504i 0.566208 + 1.74261i
\(755\) −5.25278 0.343691i −0.191168 0.0125082i
\(756\) 0 0
\(757\) −33.8427 −1.23003 −0.615016 0.788514i \(-0.710851\pi\)
−0.615016 + 0.788514i \(0.710851\pi\)
\(758\) 1.22884 3.78199i 0.0446336 0.137368i
\(759\) 0 0
\(760\) −2.53596 2.10865i −0.0919889 0.0764888i
\(761\) −8.76122 6.36540i −0.317594 0.230746i 0.417554 0.908652i \(-0.362887\pi\)
−0.735148 + 0.677906i \(0.762887\pi\)
\(762\) 0 0
\(763\) −1.14186 + 0.829613i −0.0413382 + 0.0300340i
\(764\) 45.4452 + 33.0179i 1.64415 + 1.19454i
\(765\) 0 0
\(766\) 24.3681 17.7044i 0.880455 0.639688i
\(767\) −14.4982 + 44.6210i −0.523501 + 1.61117i
\(768\) 0 0
\(769\) −10.2290 + 31.4815i −0.368866 + 1.13525i 0.578658 + 0.815570i \(0.303577\pi\)
−0.947524 + 0.319683i \(0.896423\pi\)
\(770\) 1.93881 + 7.63049i 0.0698700 + 0.274984i
\(771\) 0 0
\(772\) −2.60816 8.02708i −0.0938696 0.288901i
\(773\) −8.15139 5.92233i −0.293185 0.213011i 0.431463 0.902131i \(-0.357998\pi\)
−0.724648 + 0.689119i \(0.757998\pi\)
\(774\) 0 0
\(775\) 7.66304 16.0752i 0.275264 0.577439i
\(776\) −2.72739 −0.0979075
\(777\) 0 0
\(778\) −18.7600 57.7374i −0.672579 2.06999i
\(779\) 16.1201 + 49.6125i 0.577562 + 1.77755i
\(780\) 0 0
\(781\) 14.5745 44.8557i 0.521516 1.60506i
\(782\) −7.11950 −0.254593
\(783\) 0 0
\(784\) −20.4126 + 14.8306i −0.729021 + 0.529664i
\(785\) 46.3415 + 3.03213i 1.65400 + 0.108221i
\(786\) 0 0
\(787\) −5.26393 + 3.82447i −0.187639 + 0.136328i −0.677639 0.735395i \(-0.736997\pi\)
0.490000 + 0.871722i \(0.336997\pi\)
\(788\) 40.1125 29.1434i 1.42895 1.03819i
\(789\) 0 0
\(790\) 24.7108 61.9585i 0.879172 2.20439i
\(791\) 2.91249 2.11605i 0.103556 0.0752380i
\(792\) 0 0
\(793\) −41.8805 −1.48722
\(794\) −1.74327 + 5.36522i −0.0618662 + 0.190405i
\(795\) 0 0
\(796\) −2.90868 8.95199i −0.103095 0.317295i
\(797\) 5.20336 + 16.0143i 0.184312 + 0.567255i 0.999936 0.0113279i \(-0.00360587\pi\)
−0.815623 + 0.578583i \(0.803606\pi\)
\(798\) 0 0
\(799\) −3.35905 −0.118835
\(800\) 40.1102 + 5.27141i 1.41811 + 0.186372i
\(801\) 0 0
\(802\) −14.0432 10.2030i −0.495882 0.360279i
\(803\) −13.2178 40.6801i −0.466445 1.43557i
\(804\) 0 0
\(805\) 2.58226 + 2.14715i 0.0910127 + 0.0756771i
\(806\) −11.0353 + 33.9631i −0.388702 + 1.19630i
\(807\) 0 0
\(808\) 0.622008 1.91435i 0.0218822 0.0673464i
\(809\) −33.7304 + 24.5065i −1.18590 + 0.861604i −0.992824 0.119581i \(-0.961845\pi\)
−0.193072 + 0.981185i \(0.561845\pi\)
\(810\) 0 0
\(811\) 28.0451 + 20.3760i 0.984797 + 0.715497i 0.958776 0.284164i \(-0.0917162\pi\)
0.0260215 + 0.999661i \(0.491716\pi\)
\(812\) −4.34500 + 3.15683i −0.152480 + 0.110783i
\(813\) 0 0
\(814\) −8.47826 6.15982i −0.297163 0.215902i
\(815\) 13.2248 8.34628i 0.463243 0.292358i
\(816\) 0 0
\(817\) 18.8091 57.8885i 0.658047 2.02526i
\(818\) −12.6377 −0.441867
\(819\) 0 0
\(820\) 32.0552 + 26.6539i 1.11942 + 0.930795i
\(821\) −8.05430 24.7886i −0.281097 0.865128i −0.987541 0.157359i \(-0.949702\pi\)
0.706444 0.707769i \(-0.250298\pi\)
\(822\) 0 0
\(823\) 10.0510 + 7.30244i 0.350354 + 0.254547i 0.749018 0.662550i \(-0.230526\pi\)
−0.398663 + 0.917097i \(0.630526\pi\)
\(824\) −1.34121 −0.0467232
\(825\) 0 0
\(826\) −9.72781 −0.338474
\(827\) 25.5860 + 18.5893i 0.889713 + 0.646414i 0.935803 0.352523i \(-0.114676\pi\)
−0.0460905 + 0.998937i \(0.514676\pi\)
\(828\) 0 0
\(829\) −12.1998 37.5471i −0.423716 1.30406i −0.904218 0.427070i \(-0.859546\pi\)
0.480502 0.876993i \(-0.340454\pi\)
\(830\) 1.36749 0.863039i 0.0474663 0.0299565i
\(831\) 0 0
\(832\) −44.1826 −1.53176
\(833\) −2.45435 + 7.55373i −0.0850383 + 0.261721i
\(834\) 0 0
\(835\) −12.3284 + 30.9116i −0.426643 + 1.06974i
\(836\) 35.0612 + 25.4734i 1.21262 + 0.881018i
\(837\) 0 0
\(838\) −61.5958 + 44.7520i −2.12779 + 1.54593i
\(839\) 15.3954 + 11.1854i 0.531509 + 0.386164i 0.820922 0.571041i \(-0.193460\pi\)
−0.289413 + 0.957204i \(0.593460\pi\)
\(840\) 0 0
\(841\) 3.09027 2.24522i 0.106561 0.0774212i
\(842\) −5.94188 + 18.2872i −0.204771 + 0.630219i
\(843\) 0 0
\(844\) −4.12815 + 12.7051i −0.142097 + 0.437329i
\(845\) 9.43241 23.6503i 0.324485 0.813594i
\(846\) 0 0
\(847\) −0.128499 0.395479i −0.00441528 0.0135888i
\(848\) 40.1367 + 29.1610i 1.37830 + 1.00139i
\(849\) 0 0
\(850\) 10.5031 5.70576i 0.360252 0.195706i
\(851\) −4.47027 −0.153239
\(852\) 0 0
\(853\) 8.92882 + 27.4801i 0.305717 + 0.940900i 0.979409 + 0.201887i \(0.0647075\pi\)
−0.673692 + 0.739012i \(0.735292\pi\)
\(854\) −2.68334 8.25848i −0.0918221 0.282599i
\(855\) 0 0
\(856\) 0.813642 2.50413i 0.0278097 0.0855894i
\(857\) 54.7084 1.86880 0.934401 0.356222i \(-0.115935\pi\)
0.934401 + 0.356222i \(0.115935\pi\)
\(858\) 0 0
\(859\) −14.0341 + 10.1963i −0.478836 + 0.347895i −0.800875 0.598832i \(-0.795632\pi\)
0.322039 + 0.946726i \(0.395632\pi\)
\(860\) −11.9790 47.1451i −0.408480 1.60763i
\(861\) 0 0
\(862\) 16.2337 11.7945i 0.552921 0.401721i
\(863\) 25.6542 18.6388i 0.873278 0.634473i −0.0581867 0.998306i \(-0.518532\pi\)
0.931464 + 0.363832i \(0.118532\pi\)
\(864\) 0 0
\(865\) −2.68902 2.23592i −0.0914293 0.0760235i
\(866\) 39.8866 28.9793i 1.35540 0.984756i
\(867\) 0 0
\(868\) −3.81201 −0.129388
\(869\) −15.6125 + 48.0504i −0.529619 + 1.63000i
\(870\) 0 0
\(871\) −14.8068 45.5707i −0.501710 1.54410i
\(872\) 0.214816 + 0.661137i 0.00727460 + 0.0223889i
\(873\) 0 0
\(874\) 35.9073 1.21458
\(875\) −5.53027 1.09810i −0.186957 0.0371224i
\(876\) 0 0
\(877\) −26.0784 18.9470i −0.880603 0.639796i 0.0528077 0.998605i \(-0.483183\pi\)
−0.933411 + 0.358809i \(0.883183\pi\)
\(878\) 1.10211 + 3.39194i 0.0371943 + 0.114472i
\(879\) 0 0
\(880\) −28.6988 1.87777i −0.967438 0.0632997i
\(881\) −11.5043 + 35.4065i −0.387589 + 1.19288i 0.546996 + 0.837135i \(0.315771\pi\)
−0.934585 + 0.355740i \(0.884229\pi\)
\(882\) 0 0
\(883\) 1.68169 5.17572i 0.0565935 0.174177i −0.918764 0.394807i \(-0.870811\pi\)
0.975358 + 0.220630i \(0.0708114\pi\)
\(884\) −9.98340 + 7.25336i −0.335778 + 0.243957i
\(885\) 0 0
\(886\) −61.3556 44.5774i −2.06128 1.49761i
\(887\) −38.4937 + 27.9673i −1.29249 + 0.939052i −0.999853 0.0171708i \(-0.994534\pi\)
−0.292641 + 0.956222i \(0.594534\pi\)
\(888\) 0 0
\(889\) −1.84688 1.34184i −0.0619424 0.0450038i
\(890\) −7.27886 28.6470i −0.243988 0.960250i
\(891\) 0 0
\(892\) 16.0219 49.3103i 0.536452 1.65103i
\(893\) 16.9414 0.566924
\(894\) 0 0
\(895\) 6.59293 + 25.9475i 0.220377 + 0.867328i
\(896\) −0.309076 0.951237i −0.0103255 0.0317786i
\(897\) 0 0
\(898\) −21.2637 15.4490i −0.709579 0.515539i
\(899\) −17.8723 −0.596076
\(900\) 0 0
\(901\) 15.6170 0.520279
\(902\) −49.6186 36.0500i −1.65212 1.20033i
\(903\) 0 0
\(904\) −0.547920 1.68633i −0.0182236 0.0560863i
\(905\) −0.691035 + 1.73266i −0.0229708 + 0.0575956i
\(906\) 0 0
\(907\) 21.0436 0.698742 0.349371 0.936985i \(-0.386395\pi\)
0.349371 + 0.936985i \(0.386395\pi\)
\(908\) 8.81866 27.1410i 0.292657 0.900707i
\(909\) 0 0
\(910\) 11.2822 + 0.738200i 0.374003 + 0.0244711i
\(911\) 3.57453 + 2.59705i 0.118430 + 0.0860441i 0.645423 0.763825i \(-0.276681\pi\)
−0.526994 + 0.849869i \(0.676681\pi\)
\(912\) 0 0
\(913\) −0.990875 + 0.719913i −0.0327932 + 0.0238256i
\(914\) −36.6118 26.6001i −1.21101 0.879852i
\(915\) 0 0
\(916\) −26.0122 + 18.8990i −0.859467 + 0.624439i
\(917\) −1.50992 + 4.64706i −0.0498620 + 0.153460i
\(918\) 0 0
\(919\) 13.5305 41.6425i 0.446329 1.37366i −0.434690 0.900580i \(-0.643142\pi\)
0.881019 0.473081i \(-0.156858\pi\)
\(920\) 1.39878 0.882787i 0.0461165 0.0291046i
\(921\) 0 0
\(922\) −0.336996 1.03717i −0.0110984 0.0341573i
\(923\) −54.7967 39.8121i −1.80365 1.31043i
\(924\) 0 0
\(925\) 6.59478 3.58260i 0.216835 0.117795i
\(926\) 45.3800 1.49128
\(927\) 0 0
\(928\) −12.5463 38.6135i −0.411853 1.26755i
\(929\) 0.921674 + 2.83662i 0.0302391 + 0.0930665i 0.965037 0.262114i \(-0.0844195\pi\)
−0.934798 + 0.355180i \(0.884420\pi\)
\(930\) 0 0
\(931\) 12.3786 38.0974i 0.405692 1.24859i
\(932\) −6.77263 −0.221845
\(933\) 0 0
\(934\) −61.5575 + 44.7242i −2.01422 + 1.46342i
\(935\) −7.65608 + 4.83183i −0.250381 + 0.158018i
\(936\) 0 0
\(937\) −20.5941 + 14.9625i −0.672780 + 0.488803i −0.870955 0.491363i \(-0.836499\pi\)
0.198175 + 0.980167i \(0.436499\pi\)
\(938\) 8.03746 5.83956i 0.262432 0.190668i
\(939\) 0 0
\(940\) 11.4495 7.22589i 0.373441 0.235683i
\(941\) −14.1636 + 10.2904i −0.461719 + 0.335458i −0.794205 0.607650i \(-0.792112\pi\)
0.332486 + 0.943108i \(0.392112\pi\)
\(942\) 0 0
\(943\) −26.1620 −0.851952
\(944\) 10.9812 33.7968i 0.357409 1.09999i
\(945\) 0 0
\(946\) 22.1141 + 68.0603i 0.718992 + 2.21283i
\(947\) 8.48958 + 26.1282i 0.275874 + 0.849054i 0.988987 + 0.148004i \(0.0472849\pi\)
−0.713112 + 0.701050i \(0.752715\pi\)
\(948\) 0 0
\(949\) −61.4272 −1.99401
\(950\) −52.9724 + 28.7771i −1.71865 + 0.933653i
\(951\) 0 0
\(952\) −0.119314 0.0866869i −0.00386700 0.00280954i
\(953\) 8.11556 + 24.9771i 0.262889 + 0.809088i 0.992172 + 0.124877i \(0.0398535\pi\)
−0.729284 + 0.684212i \(0.760146\pi\)
\(954\) 0 0
\(955\) 50.0497 31.5869i 1.61957 1.02213i
\(956\) 14.8305 45.6437i 0.479654 1.47622i
\(957\) 0 0
\(958\) −11.6819 + 35.9531i −0.377424 + 1.16159i
\(959\) −1.62567 + 1.18112i −0.0524956 + 0.0381403i
\(960\) 0 0
\(961\) 14.8168 + 10.7651i 0.477962 + 0.347260i
\(962\) −12.1757 + 8.84613i −0.392559 + 0.285211i
\(963\) 0 0
\(964\) 32.9003 + 23.9034i 1.05965 + 0.769878i
\(965\) −8.87350 0.580595i −0.285648 0.0186900i
\(966\) 0 0
\(967\) 4.99684 15.3787i 0.160688 0.494545i −0.838005 0.545662i \(-0.816278\pi\)
0.998693 + 0.0511170i \(0.0162781\pi\)
\(968\) −0.204808 −0.00658276
\(969\) 0 0
\(970\) −18.4680 + 46.3055i −0.592971 + 1.48678i
\(971\) 13.8119 + 42.5085i 0.443244 + 1.36416i 0.884398 + 0.466733i \(0.154569\pi\)
−0.441155 + 0.897431i \(0.645431\pi\)
\(972\) 0 0
\(973\) 2.02421 + 1.47068i 0.0648933 + 0.0471478i
\(974\) 3.63658 0.116524
\(975\) 0 0
\(976\) 31.7211 1.01537
\(977\) −18.0949 13.1467i −0.578907 0.420600i 0.259423 0.965764i \(-0.416468\pi\)
−0.838330 + 0.545164i \(0.816468\pi\)
\(978\) 0 0
\(979\) 6.91804 + 21.2915i 0.221102 + 0.680481i
\(980\) −7.88357 31.0270i −0.251831 0.991120i
\(981\) 0 0
\(982\) −55.3788 −1.76721
\(983\) 1.51247 4.65491i 0.0482404 0.148469i −0.924035 0.382308i \(-0.875129\pi\)
0.972275 + 0.233840i \(0.0751292\pi\)
\(984\) 0 0
\(985\) −12.8645 50.6300i −0.409896 1.61321i
\(986\) −9.70483 7.05097i −0.309065 0.224549i
\(987\) 0 0
\(988\) 50.3515 36.5825i 1.60189 1.16384i
\(989\) 24.6962 + 17.9428i 0.785292 + 0.570548i
\(990\) 0 0
\(991\) 10.8113 7.85485i 0.343431 0.249518i −0.402677 0.915342i \(-0.631920\pi\)
0.746108 + 0.665825i \(0.231920\pi\)
\(992\) 8.90508 27.4070i 0.282737 0.870174i
\(993\) 0 0
\(994\) 4.33971 13.3563i 0.137647 0.423635i
\(995\) −9.89593 0.647493i −0.313722 0.0205269i
\(996\) 0 0
\(997\) 13.4967 + 41.5386i 0.427445 + 1.31554i 0.900633 + 0.434580i \(0.143103\pi\)
−0.473188 + 0.880961i \(0.656897\pi\)
\(998\) 17.3657 + 12.6169i 0.549702 + 0.399382i
\(999\) 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 225.2.h.e.91.4 yes 16
3.2 odd 2 inner 225.2.h.e.91.1 16
25.6 even 5 5625.2.a.w.1.2 8
25.11 even 5 inner 225.2.h.e.136.4 yes 16
25.19 even 10 5625.2.a.v.1.7 8
75.11 odd 10 inner 225.2.h.e.136.1 yes 16
75.44 odd 10 5625.2.a.v.1.2 8
75.56 odd 10 5625.2.a.w.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.h.e.91.1 16 3.2 odd 2 inner
225.2.h.e.91.4 yes 16 1.1 even 1 trivial
225.2.h.e.136.1 yes 16 75.11 odd 10 inner
225.2.h.e.136.4 yes 16 25.11 even 5 inner
5625.2.a.v.1.2 8 75.44 odd 10
5625.2.a.v.1.7 8 25.19 even 10
5625.2.a.w.1.2 8 25.6 even 5
5625.2.a.w.1.7 8 75.56 odd 10