Properties

Label 475.2.e.h.201.5
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.5
Root \(1.20634 + 2.08945i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.h.26.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.08504 - 1.87935i) q^{2} +(-0.706345 + 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} +1.76171 q^{7} -1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +O(q^{10})\) \(q+(1.08504 - 1.87935i) q^{2} +(-0.706345 + 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} +1.76171 q^{7} -1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +1.83810 q^{11} +3.82736 q^{12} +(-1.30242 - 2.25586i) q^{13} +(1.91153 - 3.31086i) q^{14} +(1.03919 - 1.79993i) q^{16} +(2.11787 - 3.66826i) q^{17} +2.17944 q^{18} +(4.01936 + 1.68664i) q^{19} +(-1.24437 + 2.15532i) q^{21} +(1.99442 - 3.45443i) q^{22} +(-1.10274 - 1.91001i) q^{23} +(1.08720 - 1.88308i) q^{24} -5.65274 q^{26} -5.65684 q^{27} +(-2.38647 - 4.13349i) q^{28} +(3.56413 + 6.17325i) q^{29} +0.303952 q^{31} +(-3.79432 - 6.57195i) q^{32} +(-1.29833 + 2.24878i) q^{33} +(-4.59597 - 7.96045i) q^{34} +(1.36047 - 2.35641i) q^{36} -3.90376 q^{37} +(7.53097 - 5.72370i) q^{38} +3.67984 q^{39} +(-4.11981 + 7.13572i) q^{41} +(2.70039 + 4.67722i) q^{42} +(1.17451 - 2.03431i) q^{43} +(-2.48996 - 4.31273i) q^{44} -4.78610 q^{46} +(-3.62738 - 6.28281i) q^{47} +(1.46805 + 2.54274i) q^{48} -3.89639 q^{49} +(2.99190 + 5.18211i) q^{51} +(-3.52862 + 6.11176i) q^{52} +(5.31020 + 9.19753i) q^{53} +(-6.13792 + 10.6312i) q^{54} -2.71160 q^{56} +(-4.90253 + 3.72603i) q^{57} +15.4689 q^{58} +(6.02692 - 10.4389i) q^{59} +(-5.26716 - 9.12299i) q^{61} +(0.329801 - 0.571231i) q^{62} +(0.884649 + 1.53226i) q^{63} -12.3112 q^{64} +(2.81749 + 4.88004i) q^{66} +(6.51579 + 11.2857i) q^{67} -11.4758 q^{68} +3.11567 q^{69} +(-5.91294 + 10.2415i) q^{71} +(-0.772911 - 1.33872i) q^{72} +(-4.58454 + 7.94066i) q^{73} +(-4.23574 + 7.33652i) q^{74} +(-1.48740 - 11.7154i) q^{76} +3.23819 q^{77} +(3.99278 - 6.91571i) q^{78} +(-3.94192 + 6.82761i) q^{79} +(2.48922 - 4.31145i) q^{81} +(8.94034 + 15.4851i) q^{82} -6.93584 q^{83} +6.74269 q^{84} +(-2.54879 - 4.41463i) q^{86} -10.0700 q^{87} -2.82918 q^{88} +(6.23646 + 10.8019i) q^{89} +(-2.29449 - 3.97417i) q^{91} +(-2.98764 + 5.17474i) q^{92} +(-0.214695 + 0.371862i) q^{93} -15.7435 q^{94} +10.7204 q^{96} +(3.87944 - 6.71939i) q^{97} +(-4.22775 + 7.32268i) q^{98} +(0.923009 + 1.59870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{6} - 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{6} - 4 q^{7} - 12 q^{8} - 7 q^{9} - 2 q^{11} - 14 q^{12} + 5 q^{13} + 6 q^{14} + 6 q^{16} - 3 q^{17} - 14 q^{18} - 6 q^{19} - 3 q^{21} + 9 q^{22} - 6 q^{23} - 11 q^{24} + 38 q^{26} - 36 q^{27} - 4 q^{28} - 3 q^{29} - 6 q^{31} - 6 q^{32} - 18 q^{33} + q^{34} - 13 q^{36} + 12 q^{37} + 18 q^{38} + 16 q^{39} - 11 q^{41} - 11 q^{42} + 13 q^{43} - 21 q^{44} - 24 q^{46} - 6 q^{47} - 19 q^{48} + 8 q^{49} + 17 q^{51} - q^{52} + 18 q^{53} - 18 q^{54} + 8 q^{56} + 20 q^{57} - 10 q^{58} - 4 q^{59} - 25 q^{61} - 21 q^{62} + 43 q^{63} - 44 q^{64} - 34 q^{66} + 6 q^{67} + 2 q^{68} + 26 q^{69} - 18 q^{71} + 13 q^{72} + q^{73} + 6 q^{74} + 24 q^{76} + 22 q^{77} + 72 q^{78} - 3 q^{79} - 2 q^{81} + 31 q^{82} + 46 q^{83} + 74 q^{84} - 9 q^{86} - 22 q^{87} - 22 q^{88} - 12 q^{89} + 11 q^{91} + 28 q^{92} - 13 q^{93} + 16 q^{94} - 26 q^{96} + 3 q^{97} - 22 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08504 1.87935i 0.767241 1.32890i −0.171812 0.985130i \(-0.554962\pi\)
0.939053 0.343771i \(-0.111705\pi\)
\(3\) −0.706345 + 1.22342i −0.407808 + 0.706345i −0.994644 0.103361i \(-0.967040\pi\)
0.586836 + 0.809706i \(0.300373\pi\)
\(4\) −1.35464 2.34630i −0.677319 1.17315i
\(5\) 0 0
\(6\) 1.53283 + 2.65494i 0.625775 + 1.08387i
\(7\) 1.76171 0.665862 0.332931 0.942951i \(-0.391962\pi\)
0.332931 + 0.942951i \(0.391962\pi\)
\(8\) −1.53919 −0.544185
\(9\) 0.502155 + 0.869757i 0.167385 + 0.289919i
\(10\) 0 0
\(11\) 1.83810 0.554208 0.277104 0.960840i \(-0.410625\pi\)
0.277104 + 0.960840i \(0.410625\pi\)
\(12\) 3.82736 1.10486
\(13\) −1.30242 2.25586i −0.361227 0.625664i 0.626936 0.779071i \(-0.284309\pi\)
−0.988163 + 0.153407i \(0.950975\pi\)
\(14\) 1.91153 3.31086i 0.510877 0.884865i
\(15\) 0 0
\(16\) 1.03919 1.79993i 0.259797 0.449982i
\(17\) 2.11787 3.66826i 0.513659 0.889684i −0.486215 0.873839i \(-0.661623\pi\)
0.999874 0.0158451i \(-0.00504385\pi\)
\(18\) 2.17944 0.513698
\(19\) 4.01936 + 1.68664i 0.922104 + 0.386943i
\(20\) 0 0
\(21\) −1.24437 + 2.15532i −0.271544 + 0.470328i
\(22\) 1.99442 3.45443i 0.425211 0.736487i
\(23\) −1.10274 1.91001i −0.229938 0.398264i 0.727851 0.685735i \(-0.240519\pi\)
−0.957790 + 0.287470i \(0.907186\pi\)
\(24\) 1.08720 1.88308i 0.221923 0.384382i
\(25\) 0 0
\(26\) −5.65274 −1.10859
\(27\) −5.65684 −1.08866
\(28\) −2.38647 4.13349i −0.451001 0.781157i
\(29\) 3.56413 + 6.17325i 0.661842 + 1.14634i 0.980131 + 0.198351i \(0.0635585\pi\)
−0.318289 + 0.947994i \(0.603108\pi\)
\(30\) 0 0
\(31\) 0.303952 0.0545913 0.0272957 0.999627i \(-0.491310\pi\)
0.0272957 + 0.999627i \(0.491310\pi\)
\(32\) −3.79432 6.57195i −0.670747 1.16177i
\(33\) −1.29833 + 2.24878i −0.226010 + 0.391462i
\(34\) −4.59597 7.96045i −0.788202 1.36521i
\(35\) 0 0
\(36\) 1.36047 2.35641i 0.226746 0.392735i
\(37\) −3.90376 −0.641774 −0.320887 0.947118i \(-0.603981\pi\)
−0.320887 + 0.947118i \(0.603981\pi\)
\(38\) 7.53097 5.72370i 1.22168 0.928506i
\(39\) 3.67984 0.589246
\(40\) 0 0
\(41\) −4.11981 + 7.13572i −0.643406 + 1.11441i 0.341261 + 0.939969i \(0.389146\pi\)
−0.984667 + 0.174444i \(0.944187\pi\)
\(42\) 2.70039 + 4.67722i 0.416680 + 0.721711i
\(43\) 1.17451 2.03431i 0.179111 0.310229i −0.762465 0.647029i \(-0.776011\pi\)
0.941576 + 0.336800i \(0.109345\pi\)
\(44\) −2.48996 4.31273i −0.375375 0.650169i
\(45\) 0 0
\(46\) −4.78610 −0.705672
\(47\) −3.62738 6.28281i −0.529108 0.916441i −0.999424 0.0339433i \(-0.989193\pi\)
0.470316 0.882498i \(-0.344140\pi\)
\(48\) 1.46805 + 2.54274i 0.211895 + 0.367013i
\(49\) −3.89639 −0.556627
\(50\) 0 0
\(51\) 2.99190 + 5.18211i 0.418949 + 0.725641i
\(52\) −3.52862 + 6.11176i −0.489332 + 0.847548i
\(53\) 5.31020 + 9.19753i 0.729412 + 1.26338i 0.957132 + 0.289652i \(0.0935395\pi\)
−0.227720 + 0.973727i \(0.573127\pi\)
\(54\) −6.13792 + 10.6312i −0.835265 + 1.44672i
\(55\) 0 0
\(56\) −2.71160 −0.362353
\(57\) −4.90253 + 3.72603i −0.649356 + 0.493525i
\(58\) 15.4689 2.03117
\(59\) 6.02692 10.4389i 0.784638 1.35903i −0.144578 0.989493i \(-0.546182\pi\)
0.929215 0.369539i \(-0.120484\pi\)
\(60\) 0 0
\(61\) −5.26716 9.12299i −0.674390 1.16808i −0.976647 0.214852i \(-0.931073\pi\)
0.302256 0.953227i \(-0.402260\pi\)
\(62\) 0.329801 0.571231i 0.0418847 0.0725464i
\(63\) 0.884649 + 1.53226i 0.111455 + 0.193046i
\(64\) −12.3112 −1.53891
\(65\) 0 0
\(66\) 2.81749 + 4.88004i 0.346809 + 0.600691i
\(67\) 6.51579 + 11.2857i 0.796031 + 1.37877i 0.922183 + 0.386755i \(0.126404\pi\)
−0.126152 + 0.992011i \(0.540263\pi\)
\(68\) −11.4758 −1.39164
\(69\) 3.11567 0.375083
\(70\) 0 0
\(71\) −5.91294 + 10.2415i −0.701737 + 1.21544i 0.266119 + 0.963940i \(0.414259\pi\)
−0.967856 + 0.251504i \(0.919075\pi\)
\(72\) −0.772911 1.33872i −0.0910884 0.157770i
\(73\) −4.58454 + 7.94066i −0.536580 + 0.929384i 0.462505 + 0.886617i \(0.346951\pi\)
−0.999085 + 0.0427676i \(0.986382\pi\)
\(74\) −4.23574 + 7.33652i −0.492395 + 0.852854i
\(75\) 0 0
\(76\) −1.48740 11.7154i −0.170616 1.34385i
\(77\) 3.23819 0.369026
\(78\) 3.99278 6.91571i 0.452094 0.783049i
\(79\) −3.94192 + 6.82761i −0.443501 + 0.768167i −0.997946 0.0640536i \(-0.979597\pi\)
0.554445 + 0.832220i \(0.312930\pi\)
\(80\) 0 0
\(81\) 2.48922 4.31145i 0.276580 0.479050i
\(82\) 8.94034 + 15.4851i 0.987296 + 1.71005i
\(83\) −6.93584 −0.761307 −0.380654 0.924718i \(-0.624301\pi\)
−0.380654 + 0.924718i \(0.624301\pi\)
\(84\) 6.74269 0.735688
\(85\) 0 0
\(86\) −2.54879 4.41463i −0.274843 0.476041i
\(87\) −10.0700 −1.07962
\(88\) −2.82918 −0.301592
\(89\) 6.23646 + 10.8019i 0.661063 + 1.14500i 0.980337 + 0.197333i \(0.0632279\pi\)
−0.319273 + 0.947663i \(0.603439\pi\)
\(90\) 0 0
\(91\) −2.29449 3.97417i −0.240528 0.416606i
\(92\) −2.98764 + 5.17474i −0.311483 + 0.539504i
\(93\) −0.214695 + 0.371862i −0.0222628 + 0.0385603i
\(94\) −15.7435 −1.62381
\(95\) 0 0
\(96\) 10.7204 1.09414
\(97\) 3.87944 6.71939i 0.393898 0.682251i −0.599062 0.800703i \(-0.704460\pi\)
0.992960 + 0.118452i \(0.0377931\pi\)
\(98\) −4.22775 + 7.32268i −0.427067 + 0.739703i
\(99\) 0.923009 + 1.59870i 0.0927659 + 0.160675i
\(100\) 0 0
\(101\) −1.43509 2.48565i −0.142797 0.247331i 0.785752 0.618542i \(-0.212276\pi\)
−0.928549 + 0.371210i \(0.878943\pi\)
\(102\) 12.9853 1.28574
\(103\) −7.62702 −0.751513 −0.375756 0.926718i \(-0.622617\pi\)
−0.375756 + 0.926718i \(0.622617\pi\)
\(104\) 2.00468 + 3.47220i 0.196575 + 0.340477i
\(105\) 0 0
\(106\) 23.0472 2.23854
\(107\) −6.43891 −0.622473 −0.311236 0.950333i \(-0.600743\pi\)
−0.311236 + 0.950333i \(0.600743\pi\)
\(108\) 7.66297 + 13.2727i 0.737370 + 1.27716i
\(109\) 5.35464 9.27450i 0.512881 0.888336i −0.487007 0.873398i \(-0.661911\pi\)
0.999888 0.0149384i \(-0.00475523\pi\)
\(110\) 0 0
\(111\) 2.75740 4.77595i 0.261721 0.453313i
\(112\) 1.83075 3.17094i 0.172989 0.299626i
\(113\) −12.6800 −1.19283 −0.596417 0.802674i \(-0.703410\pi\)
−0.596417 + 0.802674i \(0.703410\pi\)
\(114\) 1.68305 + 13.2565i 0.157632 + 1.24158i
\(115\) 0 0
\(116\) 9.65621 16.7250i 0.896556 1.55288i
\(117\) 1.30804 2.26558i 0.120928 0.209453i
\(118\) −13.0789 22.6534i −1.20401 2.08541i
\(119\) 3.73107 6.46240i 0.342027 0.592407i
\(120\) 0 0
\(121\) −7.62139 −0.692854
\(122\) −22.8604 −2.06968
\(123\) −5.82001 10.0806i −0.524773 0.908933i
\(124\) −0.411744 0.713162i −0.0369757 0.0640438i
\(125\) 0 0
\(126\) 3.83953 0.342052
\(127\) −7.60506 13.1724i −0.674840 1.16886i −0.976516 0.215447i \(-0.930879\pi\)
0.301675 0.953411i \(-0.402454\pi\)
\(128\) −5.76959 + 9.99323i −0.509965 + 0.883285i
\(129\) 1.65922 + 2.87385i 0.146086 + 0.253028i
\(130\) 0 0
\(131\) 3.52804 6.11075i 0.308246 0.533898i −0.669733 0.742602i \(-0.733591\pi\)
0.977979 + 0.208704i \(0.0669246\pi\)
\(132\) 7.03507 0.612324
\(133\) 7.08093 + 2.97137i 0.613994 + 0.257651i
\(134\) 28.2797 2.44299
\(135\) 0 0
\(136\) −3.25981 + 5.64615i −0.279526 + 0.484153i
\(137\) 11.1936 + 19.3878i 0.956331 + 1.65641i 0.731291 + 0.682065i \(0.238918\pi\)
0.225040 + 0.974350i \(0.427749\pi\)
\(138\) 3.38064 5.85543i 0.287779 0.498448i
\(139\) −9.38099 16.2484i −0.795685 1.37817i −0.922403 0.386229i \(-0.873777\pi\)
0.126717 0.991939i \(-0.459556\pi\)
\(140\) 0 0
\(141\) 10.2487 0.863098
\(142\) 12.8316 + 22.2250i 1.07680 + 1.86508i
\(143\) −2.39398 4.14650i −0.200195 0.346748i
\(144\) 2.08733 0.173944
\(145\) 0 0
\(146\) 9.94886 + 17.2319i 0.823373 + 1.42612i
\(147\) 2.75219 4.76694i 0.226997 0.393171i
\(148\) 5.28818 + 9.15939i 0.434685 + 0.752897i
\(149\) −9.07030 + 15.7102i −0.743068 + 1.28703i 0.208024 + 0.978124i \(0.433297\pi\)
−0.951092 + 0.308907i \(0.900037\pi\)
\(150\) 0 0
\(151\) 2.71348 0.220820 0.110410 0.993886i \(-0.464784\pi\)
0.110410 + 0.993886i \(0.464784\pi\)
\(152\) −6.18655 2.59606i −0.501795 0.210569i
\(153\) 4.25400 0.343915
\(154\) 3.51358 6.08569i 0.283132 0.490399i
\(155\) 0 0
\(156\) −4.98485 8.63401i −0.399107 0.691274i
\(157\) 0.638899 1.10660i 0.0509897 0.0883167i −0.839404 0.543508i \(-0.817096\pi\)
0.890394 + 0.455191i \(0.150429\pi\)
\(158\) 8.55432 + 14.8165i 0.680545 + 1.17874i
\(159\) −15.0033 −1.18984
\(160\) 0 0
\(161\) −1.94271 3.36488i −0.153107 0.265189i
\(162\) −5.40182 9.35622i −0.424407 0.735094i
\(163\) −7.74374 −0.606537 −0.303268 0.952905i \(-0.598078\pi\)
−0.303268 + 0.952905i \(0.598078\pi\)
\(164\) 22.3234 1.74316
\(165\) 0 0
\(166\) −7.52568 + 13.0349i −0.584106 + 1.01170i
\(167\) 3.42446 + 5.93135i 0.264993 + 0.458981i 0.967562 0.252635i \(-0.0812970\pi\)
−0.702569 + 0.711616i \(0.747964\pi\)
\(168\) 1.91532 3.31744i 0.147770 0.255946i
\(169\) 3.10739 5.38215i 0.239030 0.414012i
\(170\) 0 0
\(171\) 0.551367 + 4.34282i 0.0421641 + 0.332104i
\(172\) −6.36413 −0.485261
\(173\) 4.10680 7.11319i 0.312234 0.540806i −0.666611 0.745405i \(-0.732256\pi\)
0.978846 + 0.204600i \(0.0655893\pi\)
\(174\) −10.9264 + 18.9251i −0.828328 + 1.43471i
\(175\) 0 0
\(176\) 1.91013 3.30844i 0.143982 0.249383i
\(177\) 8.51416 + 14.7470i 0.639963 + 1.10845i
\(178\) 27.0673 2.02878
\(179\) 4.46213 0.333515 0.166758 0.985998i \(-0.446670\pi\)
0.166758 + 0.985998i \(0.446670\pi\)
\(180\) 0 0
\(181\) −3.77070 6.53105i −0.280274 0.485449i 0.691178 0.722685i \(-0.257092\pi\)
−0.971452 + 0.237235i \(0.923759\pi\)
\(182\) −9.95847 −0.738171
\(183\) 14.8817 1.10009
\(184\) 1.69733 + 2.93986i 0.125129 + 0.216730i
\(185\) 0 0
\(186\) 0.465906 + 0.806972i 0.0341619 + 0.0591701i
\(187\) 3.89286 6.74263i 0.284674 0.493070i
\(188\) −9.82757 + 17.0219i −0.716749 + 1.24145i
\(189\) −9.96570 −0.724898
\(190\) 0 0
\(191\) −13.7765 −0.996834 −0.498417 0.866938i \(-0.666085\pi\)
−0.498417 + 0.866938i \(0.666085\pi\)
\(192\) 8.69598 15.0619i 0.627578 1.08700i
\(193\) −4.24539 + 7.35324i −0.305590 + 0.529297i −0.977393 0.211433i \(-0.932187\pi\)
0.671802 + 0.740730i \(0.265520\pi\)
\(194\) −8.41872 14.5817i −0.604429 1.04690i
\(195\) 0 0
\(196\) 5.27820 + 9.14211i 0.377014 + 0.653008i
\(197\) −2.87111 −0.204558 −0.102279 0.994756i \(-0.532613\pi\)
−0.102279 + 0.994756i \(0.532613\pi\)
\(198\) 4.00602 0.284695
\(199\) −11.4245 19.7879i −0.809865 1.40273i −0.912957 0.408055i \(-0.866207\pi\)
0.103092 0.994672i \(-0.467126\pi\)
\(200\) 0 0
\(201\) −18.4096 −1.29851
\(202\) −6.22854 −0.438238
\(203\) 6.27895 + 10.8755i 0.440696 + 0.763308i
\(204\) 8.10587 14.0398i 0.567524 0.982981i
\(205\) 0 0
\(206\) −8.27565 + 14.3338i −0.576592 + 0.998686i
\(207\) 1.10750 1.91824i 0.0769763 0.133327i
\(208\) −5.41386 −0.375383
\(209\) 7.38797 + 3.10022i 0.511037 + 0.214447i
\(210\) 0 0
\(211\) 7.04497 12.2022i 0.484995 0.840037i −0.514856 0.857277i \(-0.672155\pi\)
0.999851 + 0.0172400i \(0.00548794\pi\)
\(212\) 14.3868 24.9187i 0.988089 1.71142i
\(213\) −8.35315 14.4681i −0.572348 0.991337i
\(214\) −6.98650 + 12.1010i −0.477587 + 0.827205i
\(215\) 0 0
\(216\) 8.70695 0.592433
\(217\) 0.535473 0.0363503
\(218\) −11.6200 20.1265i −0.787008 1.36314i
\(219\) −6.47654 11.2177i −0.437644 0.758021i
\(220\) 0 0
\(221\) −11.0335 −0.742191
\(222\) −5.98379 10.3642i −0.401606 0.695602i
\(223\) 8.55095 14.8107i 0.572614 0.991796i −0.423683 0.905811i \(-0.639263\pi\)
0.996296 0.0859855i \(-0.0274039\pi\)
\(224\) −6.68448 11.5779i −0.446625 0.773578i
\(225\) 0 0
\(226\) −13.7584 + 23.8302i −0.915192 + 1.58516i
\(227\) −10.2807 −0.682356 −0.341178 0.939999i \(-0.610826\pi\)
−0.341178 + 0.939999i \(0.610826\pi\)
\(228\) 15.3835 + 6.45540i 1.01880 + 0.427519i
\(229\) 12.8863 0.851553 0.425777 0.904828i \(-0.360001\pi\)
0.425777 + 0.904828i \(0.360001\pi\)
\(230\) 0 0
\(231\) −2.28728 + 3.96168i −0.150492 + 0.260659i
\(232\) −5.48587 9.50180i −0.360165 0.623824i
\(233\) 0.497436 0.861584i 0.0325881 0.0564442i −0.849271 0.527957i \(-0.822958\pi\)
0.881859 + 0.471512i \(0.156292\pi\)
\(234\) −2.83855 4.91651i −0.185562 0.321403i
\(235\) 0 0
\(236\) −32.6571 −2.12580
\(237\) −5.56871 9.64530i −0.361727 0.626529i
\(238\) −8.09674 14.0240i −0.524834 0.909039i
\(239\) −0.764329 −0.0494404 −0.0247202 0.999694i \(-0.507869\pi\)
−0.0247202 + 0.999694i \(0.507869\pi\)
\(240\) 0 0
\(241\) 6.27892 + 10.8754i 0.404461 + 0.700547i 0.994259 0.107004i \(-0.0341258\pi\)
−0.589798 + 0.807551i \(0.700793\pi\)
\(242\) −8.26954 + 14.3233i −0.531586 + 0.920735i
\(243\) −4.96878 8.60617i −0.318747 0.552086i
\(244\) −14.2702 + 24.7167i −0.913555 + 1.58232i
\(245\) 0 0
\(246\) −25.2599 −1.61051
\(247\) −1.43007 11.2638i −0.0909929 0.716701i
\(248\) −0.467839 −0.0297078
\(249\) 4.89909 8.48548i 0.310467 0.537745i
\(250\) 0 0
\(251\) 4.96004 + 8.59105i 0.313075 + 0.542262i 0.979026 0.203733i \(-0.0653075\pi\)
−0.665951 + 0.745995i \(0.731974\pi\)
\(252\) 2.39676 4.15131i 0.150982 0.261508i
\(253\) −2.02695 3.51078i −0.127433 0.220721i
\(254\) −33.0073 −2.07106
\(255\) 0 0
\(256\) 0.209275 + 0.362476i 0.0130797 + 0.0226547i
\(257\) 7.62426 + 13.2056i 0.475588 + 0.823743i 0.999609 0.0279628i \(-0.00890199\pi\)
−0.524021 + 0.851705i \(0.675569\pi\)
\(258\) 7.20128 0.448332
\(259\) −6.87727 −0.427333
\(260\) 0 0
\(261\) −3.57949 + 6.19985i −0.221565 + 0.383761i
\(262\) −7.65615 13.2608i −0.472999 0.819258i
\(263\) 3.97607 6.88675i 0.245175 0.424655i −0.717006 0.697067i \(-0.754488\pi\)
0.962181 + 0.272412i \(0.0878213\pi\)
\(264\) 1.99838 3.46129i 0.122992 0.213028i
\(265\) 0 0
\(266\) 13.2674 10.0835i 0.813474 0.618257i
\(267\) −17.6204 −1.07835
\(268\) 17.6531 30.5760i 1.07833 1.86773i
\(269\) −10.1217 + 17.5312i −0.617128 + 1.06890i 0.372879 + 0.927880i \(0.378371\pi\)
−0.990007 + 0.141018i \(0.954963\pi\)
\(270\) 0 0
\(271\) 2.41486 4.18265i 0.146692 0.254078i −0.783311 0.621630i \(-0.786471\pi\)
0.930003 + 0.367552i \(0.119804\pi\)
\(272\) −4.40174 7.62403i −0.266895 0.462275i
\(273\) 6.48280 0.392357
\(274\) 48.5820 2.93495
\(275\) 0 0
\(276\) −4.22060 7.31030i −0.254050 0.440028i
\(277\) 26.4360 1.58839 0.794194 0.607665i \(-0.207894\pi\)
0.794194 + 0.607665i \(0.207894\pi\)
\(278\) −40.7151 −2.44193
\(279\) 0.152631 + 0.264364i 0.00913776 + 0.0158271i
\(280\) 0 0
\(281\) −2.64587 4.58278i −0.157839 0.273386i 0.776250 0.630425i \(-0.217119\pi\)
−0.934089 + 0.357040i \(0.883786\pi\)
\(282\) 11.1203 19.2609i 0.662204 1.14697i
\(283\) −9.90480 + 17.1556i −0.588779 + 1.01980i 0.405614 + 0.914045i \(0.367058\pi\)
−0.994393 + 0.105751i \(0.966275\pi\)
\(284\) 32.0396 1.90120
\(285\) 0 0
\(286\) −10.3903 −0.614391
\(287\) −7.25790 + 12.5710i −0.428420 + 0.742045i
\(288\) 3.81067 6.60027i 0.224546 0.388925i
\(289\) −0.470765 0.815389i −0.0276921 0.0479641i
\(290\) 0 0
\(291\) 5.48045 + 9.49241i 0.321269 + 0.556455i
\(292\) 24.8416 1.45374
\(293\) −19.3477 −1.13030 −0.565152 0.824987i \(-0.691183\pi\)
−0.565152 + 0.824987i \(0.691183\pi\)
\(294\) −5.97250 10.3447i −0.348323 0.603314i
\(295\) 0 0
\(296\) 6.00862 0.349244
\(297\) −10.3978 −0.603344
\(298\) 19.6833 + 34.0925i 1.14022 + 1.97493i
\(299\) −2.87248 + 4.97528i −0.166120 + 0.287728i
\(300\) 0 0
\(301\) 2.06914 3.58385i 0.119263 0.206570i
\(302\) 2.94424 5.09958i 0.169422 0.293448i
\(303\) 4.05467 0.232935
\(304\) 7.21271 5.48181i 0.413677 0.314403i
\(305\) 0 0
\(306\) 4.61577 7.99475i 0.263866 0.457029i
\(307\) 14.0604 24.3533i 0.802469 1.38992i −0.115517 0.993305i \(-0.536853\pi\)
0.917986 0.396612i \(-0.129814\pi\)
\(308\) −4.38657 7.59777i −0.249948 0.432923i
\(309\) 5.38731 9.33109i 0.306473 0.530827i
\(310\) 0 0
\(311\) 2.75320 0.156120 0.0780598 0.996949i \(-0.475127\pi\)
0.0780598 + 0.996949i \(0.475127\pi\)
\(312\) −5.66397 −0.320659
\(313\) 10.5784 + 18.3223i 0.597924 + 1.03564i 0.993127 + 0.117041i \(0.0373410\pi\)
−0.395203 + 0.918594i \(0.629326\pi\)
\(314\) −1.38647 2.40143i −0.0782428 0.135520i
\(315\) 0 0
\(316\) 21.3595 1.20157
\(317\) 15.9665 + 27.6548i 0.896768 + 1.55325i 0.831602 + 0.555373i \(0.187424\pi\)
0.0651661 + 0.997874i \(0.479242\pi\)
\(318\) −16.2793 + 28.1965i −0.912895 + 1.58118i
\(319\) 6.55122 + 11.3470i 0.366798 + 0.635313i
\(320\) 0 0
\(321\) 4.54809 7.87752i 0.253850 0.439680i
\(322\) −8.43170 −0.469880
\(323\) 14.6995 11.1720i 0.817904 0.621624i
\(324\) −13.4880 −0.749331
\(325\) 0 0
\(326\) −8.40230 + 14.5532i −0.465360 + 0.806028i
\(327\) 7.56444 + 13.1020i 0.418314 + 0.724542i
\(328\) 6.34117 10.9832i 0.350132 0.606447i
\(329\) −6.39038 11.0685i −0.352313 0.610224i
\(330\) 0 0
\(331\) 35.8528 1.97065 0.985324 0.170695i \(-0.0546013\pi\)
0.985324 + 0.170695i \(0.0546013\pi\)
\(332\) 9.39555 + 16.2736i 0.515648 + 0.893128i
\(333\) −1.96029 3.39532i −0.107423 0.186062i
\(334\) 14.8628 0.813254
\(335\) 0 0
\(336\) 2.58627 + 4.47956i 0.141093 + 0.244380i
\(337\) −4.72285 + 8.18021i −0.257270 + 0.445605i −0.965510 0.260368i \(-0.916156\pi\)
0.708240 + 0.705972i \(0.249490\pi\)
\(338\) −6.74330 11.6797i −0.366787 0.635294i
\(339\) 8.95646 15.5130i 0.486448 0.842552i
\(340\) 0 0
\(341\) 0.558693 0.0302549
\(342\) 8.75994 + 3.67594i 0.473683 + 0.198772i
\(343\) −19.1962 −1.03650
\(344\) −1.80779 + 3.13118i −0.0974695 + 0.168822i
\(345\) 0 0
\(346\) −8.91211 15.4362i −0.479118 0.829857i
\(347\) 4.64930 8.05283i 0.249588 0.432299i −0.713824 0.700325i \(-0.753038\pi\)
0.963411 + 0.268027i \(0.0863716\pi\)
\(348\) 13.6412 + 23.6273i 0.731246 + 1.26656i
\(349\) −22.9611 −1.22908 −0.614540 0.788886i \(-0.710658\pi\)
−0.614540 + 0.788886i \(0.710658\pi\)
\(350\) 0 0
\(351\) 7.36761 + 12.7611i 0.393254 + 0.681135i
\(352\) −6.97433 12.0799i −0.371733 0.643861i
\(353\) 28.2455 1.50336 0.751679 0.659529i \(-0.229244\pi\)
0.751679 + 0.659529i \(0.229244\pi\)
\(354\) 36.9529 1.96403
\(355\) 0 0
\(356\) 16.8963 29.2652i 0.895501 1.55105i
\(357\) 5.27084 + 9.12936i 0.278962 + 0.483177i
\(358\) 4.84160 8.38590i 0.255887 0.443209i
\(359\) 2.17756 3.77165i 0.114927 0.199060i −0.802823 0.596217i \(-0.796670\pi\)
0.917751 + 0.397157i \(0.130003\pi\)
\(360\) 0 0
\(361\) 13.3105 + 13.5585i 0.700551 + 0.713603i
\(362\) −16.3655 −0.860152
\(363\) 5.38333 9.32420i 0.282552 0.489394i
\(364\) −6.21640 + 10.7671i −0.325828 + 0.564350i
\(365\) 0 0
\(366\) 16.1473 27.9680i 0.844033 1.46191i
\(367\) −4.02245 6.96709i −0.209970 0.363679i 0.741735 0.670694i \(-0.234003\pi\)
−0.951705 + 0.307014i \(0.900670\pi\)
\(368\) −4.58384 −0.238949
\(369\) −8.27513 −0.430786
\(370\) 0 0
\(371\) 9.35501 + 16.2034i 0.485688 + 0.841236i
\(372\) 1.16333 0.0603160
\(373\) 12.4203 0.643099 0.321549 0.946893i \(-0.395796\pi\)
0.321549 + 0.946893i \(0.395796\pi\)
\(374\) −8.44784 14.6321i −0.436827 0.756607i
\(375\) 0 0
\(376\) 5.58322 + 9.67042i 0.287933 + 0.498714i
\(377\) 9.28401 16.0804i 0.478151 0.828182i
\(378\) −10.8132 + 18.7290i −0.556172 + 0.963318i
\(379\) 21.2202 1.09001 0.545005 0.838433i \(-0.316528\pi\)
0.545005 + 0.838433i \(0.316528\pi\)
\(380\) 0 0
\(381\) 21.4872 1.10082
\(382\) −14.9481 + 25.8909i −0.764812 + 1.32469i
\(383\) −15.5779 + 26.9817i −0.795993 + 1.37870i 0.126213 + 0.992003i \(0.459718\pi\)
−0.922206 + 0.386698i \(0.873616\pi\)
\(384\) −8.15064 14.1173i −0.415936 0.720422i
\(385\) 0 0
\(386\) 9.21287 + 15.9572i 0.468923 + 0.812198i
\(387\) 2.35914 0.119922
\(388\) −21.0210 −1.06718
\(389\) 10.8314 + 18.7606i 0.549176 + 0.951201i 0.998331 + 0.0577469i \(0.0183916\pi\)
−0.449155 + 0.893454i \(0.648275\pi\)
\(390\) 0 0
\(391\) −9.34189 −0.472439
\(392\) 5.99728 0.302908
\(393\) 4.98402 + 8.63258i 0.251411 + 0.435456i
\(394\) −3.11528 + 5.39582i −0.156946 + 0.271838i
\(395\) 0 0
\(396\) 2.50069 4.33132i 0.125664 0.217657i
\(397\) −1.31690 + 2.28093i −0.0660932 + 0.114477i −0.897178 0.441668i \(-0.854387\pi\)
0.831085 + 0.556145i \(0.187720\pi\)
\(398\) −49.5845 −2.48545
\(399\) −8.63682 + 6.56417i −0.432382 + 0.328619i
\(400\) 0 0
\(401\) 12.4825 21.6203i 0.623347 1.07967i −0.365511 0.930807i \(-0.619106\pi\)
0.988858 0.148862i \(-0.0475609\pi\)
\(402\) −19.9752 + 34.5980i −0.996272 + 1.72559i
\(403\) −0.395874 0.685673i −0.0197199 0.0341558i
\(404\) −3.88805 + 6.73431i −0.193438 + 0.335044i
\(405\) 0 0
\(406\) 27.2517 1.35248
\(407\) −7.17549 −0.355676
\(408\) −4.60509 7.97625i −0.227986 0.394883i
\(409\) 10.7964 + 18.6999i 0.533848 + 0.924652i 0.999218 + 0.0395357i \(0.0125879\pi\)
−0.465370 + 0.885116i \(0.654079\pi\)
\(410\) 0 0
\(411\) −31.6261 −1.56000
\(412\) 10.3319 + 17.8953i 0.509014 + 0.881638i
\(413\) 10.6177 18.3903i 0.522461 0.904928i
\(414\) −2.40336 4.16275i −0.118119 0.204588i
\(415\) 0 0
\(416\) −9.88362 + 17.1189i −0.484584 + 0.839325i
\(417\) 26.5049 1.29795
\(418\) 13.8427 10.5207i 0.677067 0.514585i
\(419\) −11.6894 −0.571067 −0.285533 0.958369i \(-0.592171\pi\)
−0.285533 + 0.958369i \(0.592171\pi\)
\(420\) 0 0
\(421\) 15.8270 27.4132i 0.771362 1.33604i −0.165454 0.986218i \(-0.552909\pi\)
0.936816 0.349821i \(-0.113758\pi\)
\(422\) −15.2882 26.4799i −0.744217 1.28902i
\(423\) 3.64301 6.30988i 0.177129 0.306797i
\(424\) −8.17340 14.1567i −0.396935 0.687512i
\(425\) 0 0
\(426\) −36.2541 −1.75652
\(427\) −9.27919 16.0720i −0.449051 0.777780i
\(428\) 8.72239 + 15.1076i 0.421613 + 0.730254i
\(429\) 6.76391 0.326564
\(430\) 0 0
\(431\) −3.01371 5.21990i −0.145165 0.251434i 0.784269 0.620421i \(-0.213038\pi\)
−0.929435 + 0.368987i \(0.879705\pi\)
\(432\) −5.87853 + 10.1819i −0.282831 + 0.489877i
\(433\) 7.88878 + 13.6638i 0.379111 + 0.656639i 0.990933 0.134356i \(-0.0428966\pi\)
−0.611822 + 0.790995i \(0.709563\pi\)
\(434\) 0.581012 1.00634i 0.0278895 0.0483060i
\(435\) 0 0
\(436\) −29.0144 −1.38954
\(437\) −1.21082 9.53695i −0.0579212 0.456214i
\(438\) −28.1093 −1.34311
\(439\) −19.6880 + 34.1007i −0.939658 + 1.62754i −0.173549 + 0.984825i \(0.555524\pi\)
−0.766109 + 0.642711i \(0.777810\pi\)
\(440\) 0 0
\(441\) −1.95659 3.38891i −0.0931710 0.161377i
\(442\) −11.9718 + 20.7357i −0.569440 + 0.986299i
\(443\) −6.58164 11.3997i −0.312703 0.541618i 0.666243 0.745734i \(-0.267901\pi\)
−0.978947 + 0.204116i \(0.934568\pi\)
\(444\) −14.9411 −0.709073
\(445\) 0 0
\(446\) −18.5563 32.1404i −0.878666 1.52189i
\(447\) −12.8135 22.1937i −0.606058 1.04972i
\(448\) −21.6888 −1.02470
\(449\) 3.54345 0.167226 0.0836129 0.996498i \(-0.473354\pi\)
0.0836129 + 0.996498i \(0.473354\pi\)
\(450\) 0 0
\(451\) −7.57262 + 13.1162i −0.356581 + 0.617616i
\(452\) 17.1768 + 29.7511i 0.807930 + 1.39937i
\(453\) −1.91665 + 3.31974i −0.0900522 + 0.155975i
\(454\) −11.1550 + 19.3211i −0.523532 + 0.906784i
\(455\) 0 0
\(456\) 7.54593 5.73506i 0.353370 0.268569i
\(457\) −14.7013 −0.687697 −0.343848 0.939025i \(-0.611731\pi\)
−0.343848 + 0.939025i \(0.611731\pi\)
\(458\) 13.9822 24.2179i 0.653347 1.13163i
\(459\) −11.9805 + 20.7508i −0.559201 + 0.968564i
\(460\) 0 0
\(461\) −3.32663 + 5.76190i −0.154937 + 0.268358i −0.933036 0.359783i \(-0.882851\pi\)
0.778099 + 0.628141i \(0.216184\pi\)
\(462\) 4.96359 + 8.59719i 0.230927 + 0.399978i
\(463\) 25.0561 1.16445 0.582227 0.813026i \(-0.302181\pi\)
0.582227 + 0.813026i \(0.302181\pi\)
\(464\) 14.8152 0.687779
\(465\) 0 0
\(466\) −1.07948 1.86971i −0.0500059 0.0866127i
\(467\) 30.1338 1.39442 0.697212 0.716865i \(-0.254424\pi\)
0.697212 + 0.716865i \(0.254424\pi\)
\(468\) −7.08766 −0.327627
\(469\) 11.4789 + 19.8821i 0.530047 + 0.918068i
\(470\) 0 0
\(471\) 0.902565 + 1.56329i 0.0415880 + 0.0720326i
\(472\) −9.27656 + 16.0675i −0.426988 + 0.739566i
\(473\) 2.15886 3.73926i 0.0992646 0.171931i
\(474\) −24.1692 −1.11013
\(475\) 0 0
\(476\) −20.2170 −0.926644
\(477\) −5.33308 + 9.23717i −0.244185 + 0.422941i
\(478\) −0.829330 + 1.43644i −0.0379327 + 0.0657013i
\(479\) −2.50428 4.33754i −0.114424 0.198187i 0.803126 0.595810i \(-0.203169\pi\)
−0.917549 + 0.397622i \(0.869835\pi\)
\(480\) 0 0
\(481\) 5.08434 + 8.80634i 0.231826 + 0.401535i
\(482\) 27.2516 1.24128
\(483\) 5.48890 0.249753
\(484\) 10.3242 + 17.8821i 0.469283 + 0.812822i
\(485\) 0 0
\(486\) −21.5653 −0.978224
\(487\) −40.8880 −1.85281 −0.926406 0.376527i \(-0.877118\pi\)
−0.926406 + 0.376527i \(0.877118\pi\)
\(488\) 8.10715 + 14.0420i 0.366993 + 0.635651i
\(489\) 5.46975 9.47389i 0.247351 0.428424i
\(490\) 0 0
\(491\) 17.1773 29.7519i 0.775200 1.34269i −0.159482 0.987201i \(-0.550982\pi\)
0.934682 0.355485i \(-0.115684\pi\)
\(492\) −15.7680 + 27.3110i −0.710877 + 1.23127i
\(493\) 30.1935 1.35985
\(494\) −22.7204 9.53417i −1.02224 0.428962i
\(495\) 0 0
\(496\) 0.315863 0.547091i 0.0141827 0.0245651i
\(497\) −10.4169 + 18.0425i −0.467260 + 0.809319i
\(498\) −10.6315 18.4142i −0.476407 0.825161i
\(499\) −6.63881 + 11.4988i −0.297194 + 0.514755i −0.975493 0.220031i \(-0.929384\pi\)
0.678299 + 0.734786i \(0.262718\pi\)
\(500\) 0 0
\(501\) −9.67541 −0.432265
\(502\) 21.5274 0.960817
\(503\) 4.03885 + 6.99549i 0.180083 + 0.311913i 0.941909 0.335869i \(-0.109030\pi\)
−0.761825 + 0.647782i \(0.775697\pi\)
\(504\) −1.36164 2.35843i −0.0606523 0.105053i
\(505\) 0 0
\(506\) −8.79732 −0.391089
\(507\) 4.38977 + 7.60331i 0.194957 + 0.337675i
\(508\) −20.6042 + 35.6875i −0.914164 + 1.58338i
\(509\) −2.82539 4.89373i −0.125233 0.216911i 0.796591 0.604519i \(-0.206635\pi\)
−0.921824 + 0.387608i \(0.873301\pi\)
\(510\) 0 0
\(511\) −8.07662 + 13.9891i −0.357289 + 0.618842i
\(512\) −22.1701 −0.979789
\(513\) −22.7369 9.54108i −1.00386 0.421249i
\(514\) 33.0906 1.45956
\(515\) 0 0
\(516\) 4.49527 7.78604i 0.197893 0.342761i
\(517\) −6.66748 11.5484i −0.293235 0.507899i
\(518\) −7.46214 + 12.9248i −0.327868 + 0.567883i
\(519\) 5.80163 + 10.0487i 0.254663 + 0.441090i
\(520\) 0 0
\(521\) −33.8049 −1.48102 −0.740510 0.672045i \(-0.765416\pi\)
−0.740510 + 0.672045i \(0.765416\pi\)
\(522\) 7.76780 + 13.4542i 0.339987 + 0.588875i
\(523\) −6.31778 10.9427i −0.276257 0.478491i 0.694194 0.719788i \(-0.255761\pi\)
−0.970452 + 0.241296i \(0.922427\pi\)
\(524\) −19.1169 −0.835124
\(525\) 0 0
\(526\) −8.62841 14.9448i −0.376217 0.651626i
\(527\) 0.643730 1.11497i 0.0280413 0.0485690i
\(528\) 2.69842 + 4.67380i 0.117434 + 0.203401i
\(529\) 9.06791 15.7061i 0.394257 0.682873i
\(530\) 0 0
\(531\) 12.1058 0.525346
\(532\) −2.62036 20.6391i −0.113607 0.894819i
\(533\) 21.4629 0.929663
\(534\) −19.1189 + 33.1148i −0.827354 + 1.43302i
\(535\) 0 0
\(536\) −10.0290 17.3708i −0.433188 0.750304i
\(537\) −3.15180 + 5.45908i −0.136010 + 0.235577i
\(538\) 21.9649 + 38.0443i 0.946973 + 1.64021i
\(539\) −7.16195 −0.308487
\(540\) 0 0
\(541\) −23.0175 39.8675i −0.989599 1.71404i −0.619378 0.785093i \(-0.712615\pi\)
−0.370222 0.928943i \(-0.620718\pi\)
\(542\) −5.24045 9.07672i −0.225097 0.389879i
\(543\) 10.6537 0.457193
\(544\) −32.1435 −1.37814
\(545\) 0 0
\(546\) 7.03411 12.1834i 0.301032 0.521403i
\(547\) −11.4775 19.8796i −0.490741 0.849989i 0.509202 0.860647i \(-0.329941\pi\)
−0.999943 + 0.0106584i \(0.996607\pi\)
\(548\) 30.3265 52.5270i 1.29548 2.24384i
\(549\) 5.28985 9.16230i 0.225765 0.391037i
\(550\) 0 0
\(551\) 3.91343 + 30.8239i 0.166718 + 1.31314i
\(552\) −4.79560 −0.204114
\(553\) −6.94451 + 12.0282i −0.295311 + 0.511493i
\(554\) 28.6842 49.6826i 1.21868 2.11081i
\(555\) 0 0
\(556\) −25.4157 + 44.0213i −1.07787 + 1.86692i
\(557\) −0.961865 1.66600i −0.0407555 0.0705906i 0.844928 0.534880i \(-0.179643\pi\)
−0.885684 + 0.464289i \(0.846310\pi\)
\(558\) 0.662443 0.0280435
\(559\) −6.11883 −0.258799
\(560\) 0 0
\(561\) 5.49940 + 9.52524i 0.232185 + 0.402156i
\(562\) −11.4835 −0.484403
\(563\) 0.929173 0.0391600 0.0195800 0.999808i \(-0.493767\pi\)
0.0195800 + 0.999808i \(0.493767\pi\)
\(564\) −13.8833 24.0466i −0.584592 1.01254i
\(565\) 0 0
\(566\) 21.4943 + 37.2292i 0.903471 + 1.56486i
\(567\) 4.38527 7.59551i 0.184164 0.318982i
\(568\) 9.10114 15.7636i 0.381875 0.661427i
\(569\) 17.5587 0.736098 0.368049 0.929806i \(-0.380026\pi\)
0.368049 + 0.929806i \(0.380026\pi\)
\(570\) 0 0
\(571\) 40.0798 1.67729 0.838644 0.544680i \(-0.183349\pi\)
0.838644 + 0.544680i \(0.183349\pi\)
\(572\) −6.48596 + 11.2340i −0.271191 + 0.469717i
\(573\) 9.73097 16.8545i 0.406517 0.704108i
\(574\) 15.7503 + 27.2803i 0.657403 + 1.13866i
\(575\) 0 0
\(576\) −6.18215 10.7078i −0.257589 0.446158i
\(577\) −31.6555 −1.31784 −0.658919 0.752214i \(-0.728986\pi\)
−0.658919 + 0.752214i \(0.728986\pi\)
\(578\) −2.04320 −0.0849860
\(579\) −5.99742 10.3878i −0.249244 0.431704i
\(580\) 0 0
\(581\) −12.2189 −0.506926
\(582\) 23.7861 0.985965
\(583\) 9.76067 + 16.9060i 0.404246 + 0.700174i
\(584\) 7.05648 12.2222i 0.291999 0.505758i
\(585\) 0 0
\(586\) −20.9931 + 36.3611i −0.867217 + 1.50206i
\(587\) −2.62029 + 4.53848i −0.108151 + 0.187323i −0.915021 0.403406i \(-0.867826\pi\)
0.806870 + 0.590729i \(0.201160\pi\)
\(588\) −14.9129 −0.614998
\(589\) 1.22169 + 0.512658i 0.0503388 + 0.0211237i
\(590\) 0 0
\(591\) 2.02799 3.51259i 0.0834205 0.144489i
\(592\) −4.05674 + 7.02648i −0.166731 + 0.288787i
\(593\) 12.3988 + 21.4753i 0.509157 + 0.881886i 0.999944 + 0.0106059i \(0.00337603\pi\)
−0.490787 + 0.871280i \(0.663291\pi\)
\(594\) −11.2821 + 19.5412i −0.462910 + 0.801784i
\(595\) 0 0
\(596\) 49.1479 2.01317
\(597\) 32.2787 1.32108
\(598\) 6.23353 + 10.7968i 0.254908 + 0.441514i
\(599\) −8.60774 14.9091i −0.351703 0.609167i 0.634845 0.772639i \(-0.281064\pi\)
−0.986548 + 0.163472i \(0.947731\pi\)
\(600\) 0 0
\(601\) −1.76204 −0.0718750 −0.0359375 0.999354i \(-0.511442\pi\)
−0.0359375 + 0.999354i \(0.511442\pi\)
\(602\) −4.49021 7.77727i −0.183007 0.316978i
\(603\) −6.54387 + 11.3343i −0.266487 + 0.461569i
\(604\) −3.67578 6.36664i −0.149565 0.259055i
\(605\) 0 0
\(606\) 4.39949 7.62015i 0.178717 0.309547i
\(607\) 9.48260 0.384887 0.192443 0.981308i \(-0.438359\pi\)
0.192443 + 0.981308i \(0.438359\pi\)
\(608\) −4.16618 32.8147i −0.168961 1.33081i
\(609\) −17.7404 −0.718878
\(610\) 0 0
\(611\) −9.44877 + 16.3657i −0.382256 + 0.662087i
\(612\) −5.76262 9.98116i −0.232940 0.403464i
\(613\) 7.93785 13.7488i 0.320607 0.555307i −0.660007 0.751260i \(-0.729447\pi\)
0.980613 + 0.195953i \(0.0627799\pi\)
\(614\) −30.5123 52.8488i −1.23138 2.13280i
\(615\) 0 0
\(616\) −4.98419 −0.200819
\(617\) −14.8994 25.8066i −0.599828 1.03893i −0.992846 0.119402i \(-0.961902\pi\)
0.393018 0.919531i \(-0.371431\pi\)
\(618\) −11.6909 20.2493i −0.470278 0.814545i
\(619\) 12.8374 0.515980 0.257990 0.966148i \(-0.416940\pi\)
0.257990 + 0.966148i \(0.416940\pi\)
\(620\) 0 0
\(621\) 6.23805 + 10.8046i 0.250324 + 0.433575i
\(622\) 2.98734 5.17423i 0.119781 0.207468i
\(623\) 10.9868 + 19.0297i 0.440177 + 0.762409i
\(624\) 3.82405 6.62344i 0.153084 0.265150i
\(625\) 0 0
\(626\) 45.9119 1.83501
\(627\) −9.01134 + 6.84881i −0.359878 + 0.273515i
\(628\) −3.46190 −0.138145
\(629\) −8.26766 + 14.3200i −0.329653 + 0.570976i
\(630\) 0 0
\(631\) 9.70768 + 16.8142i 0.386456 + 0.669362i 0.991970 0.126473i \(-0.0403656\pi\)
−0.605514 + 0.795835i \(0.707032\pi\)
\(632\) 6.06737 10.5090i 0.241347 0.418025i
\(633\) 9.95235 + 17.2380i 0.395570 + 0.685148i
\(634\) 69.2973 2.75215
\(635\) 0 0
\(636\) 20.3241 + 35.2023i 0.805902 + 1.39586i
\(637\) 5.07475 + 8.78973i 0.201069 + 0.348262i
\(638\) 28.4334 1.12569
\(639\) −11.8768 −0.469841
\(640\) 0 0
\(641\) −10.1981 + 17.6637i −0.402802 + 0.697673i −0.994063 0.108807i \(-0.965297\pi\)
0.591261 + 0.806480i \(0.298630\pi\)
\(642\) −9.86975 17.0949i −0.389528 0.674682i
\(643\) −10.0616 + 17.4272i −0.396791 + 0.687263i −0.993328 0.115323i \(-0.963210\pi\)
0.596537 + 0.802586i \(0.296543\pi\)
\(644\) −5.26334 + 9.11637i −0.207405 + 0.359235i
\(645\) 0 0
\(646\) −5.04639 39.7476i −0.198547 1.56385i
\(647\) 29.3758 1.15488 0.577441 0.816432i \(-0.304051\pi\)
0.577441 + 0.816432i \(0.304051\pi\)
\(648\) −3.83138 + 6.63614i −0.150511 + 0.260692i
\(649\) 11.0781 19.1878i 0.434852 0.753186i
\(650\) 0 0
\(651\) −0.378229 + 0.655111i −0.0148240 + 0.0256758i
\(652\) 10.4900 + 18.1692i 0.410819 + 0.711559i
\(653\) 21.6479 0.847149 0.423575 0.905861i \(-0.360775\pi\)
0.423575 + 0.905861i \(0.360775\pi\)
\(654\) 32.8310 1.28379
\(655\) 0 0
\(656\) 8.56252 + 14.8307i 0.334310 + 0.579042i
\(657\) −9.20860 −0.359262
\(658\) −27.7353 −1.08124
\(659\) 15.3377 + 26.5658i 0.597474 + 1.03485i 0.993193 + 0.116483i \(0.0371621\pi\)
−0.395719 + 0.918372i \(0.629505\pi\)
\(660\) 0 0
\(661\) −10.5645 18.2982i −0.410910 0.711718i 0.584079 0.811697i \(-0.301456\pi\)
−0.994990 + 0.0999790i \(0.968122\pi\)
\(662\) 38.9018 67.3800i 1.51196 2.61880i
\(663\) 7.79343 13.4986i 0.302672 0.524243i
\(664\) 10.6756 0.414292
\(665\) 0 0
\(666\) −8.50799 −0.329678
\(667\) 7.86065 13.6150i 0.304365 0.527176i
\(668\) 9.27782 16.0696i 0.358969 0.621753i
\(669\) 12.0798 + 20.9229i 0.467033 + 0.808925i
\(670\) 0 0
\(671\) −9.68155 16.7689i −0.373752 0.647358i
\(672\) 18.8862 0.728550
\(673\) −40.4354 −1.55867 −0.779334 0.626609i \(-0.784443\pi\)
−0.779334 + 0.626609i \(0.784443\pi\)
\(674\) 10.2490 + 17.7518i 0.394776 + 0.683772i
\(675\) 0 0
\(676\) −16.8375 −0.647597
\(677\) −0.405154 −0.0155713 −0.00778566 0.999970i \(-0.502478\pi\)
−0.00778566 + 0.999970i \(0.502478\pi\)
\(678\) −19.4363 33.6646i −0.746446 1.29288i
\(679\) 6.83444 11.8376i 0.262282 0.454285i
\(680\) 0 0
\(681\) 7.26174 12.5777i 0.278270 0.481979i
\(682\) 0.606206 1.04998i 0.0232128 0.0402058i
\(683\) −20.9178 −0.800396 −0.400198 0.916429i \(-0.631059\pi\)
−0.400198 + 0.916429i \(0.631059\pi\)
\(684\) 9.44266 7.17662i 0.361049 0.274405i
\(685\) 0 0
\(686\) −20.8288 + 36.0765i −0.795245 + 1.37741i
\(687\) −9.10220 + 15.7655i −0.347271 + 0.601490i
\(688\) −2.44107 4.22806i −0.0930650 0.161193i
\(689\) 13.8323 23.9582i 0.526967 0.912733i
\(690\) 0 0
\(691\) 28.8456 1.09734 0.548669 0.836040i \(-0.315135\pi\)
0.548669 + 0.836040i \(0.315135\pi\)
\(692\) −22.2529 −0.845928
\(693\) 1.62607 + 2.81644i 0.0617694 + 0.106988i
\(694\) −10.0894 17.4753i −0.382988 0.663355i
\(695\) 0 0
\(696\) 15.4997 0.587513
\(697\) 17.4505 + 30.2251i 0.660983 + 1.14486i
\(698\) −24.9138 + 43.1520i −0.943001 + 1.63333i
\(699\) 0.702722 + 1.21715i 0.0265794 + 0.0460369i
\(700\) 0 0
\(701\) 22.6884 39.2974i 0.856928 1.48424i −0.0179163 0.999839i \(-0.505703\pi\)
0.874845 0.484404i \(-0.160963\pi\)
\(702\) 31.9767 1.20688
\(703\) −15.6906 6.58425i −0.591782 0.248330i
\(704\) −22.6293 −0.852873
\(705\) 0 0
\(706\) 30.6476 53.0833i 1.15344 1.99781i
\(707\) −2.52821 4.37898i −0.0950830 0.164689i
\(708\) 23.0672 39.9536i 0.866918 1.50155i
\(709\) 0.953671 + 1.65181i 0.0358159 + 0.0620349i 0.883378 0.468662i \(-0.155264\pi\)
−0.847562 + 0.530697i \(0.821930\pi\)
\(710\) 0 0
\(711\) −7.91782 −0.296941
\(712\) −9.59909 16.6261i −0.359741 0.623090i
\(713\) −0.335181 0.580550i −0.0125526 0.0217418i
\(714\) 22.8764 0.856126
\(715\) 0 0
\(716\) −6.04457 10.4695i −0.225896 0.391264i
\(717\) 0.539880 0.935099i 0.0201622 0.0349219i
\(718\) −4.72550 8.18481i −0.176354 0.305455i
\(719\) 9.26475 16.0470i 0.345517 0.598453i −0.639931 0.768433i \(-0.721037\pi\)
0.985448 + 0.169980i \(0.0543703\pi\)
\(720\) 0 0
\(721\) −13.4366 −0.500404
\(722\) 39.9235 10.3035i 1.48580 0.383457i
\(723\) −17.7403 −0.659770
\(724\) −10.2159 + 17.6944i −0.379670 + 0.657608i
\(725\) 0 0
\(726\) −11.6823 20.2343i −0.433571 0.750966i
\(727\) 24.7775 42.9159i 0.918948 1.59166i 0.117931 0.993022i \(-0.462374\pi\)
0.801017 0.598642i \(-0.204293\pi\)
\(728\) 3.53165 + 6.11700i 0.130892 + 0.226711i
\(729\) 28.9740 1.07311
\(730\) 0 0
\(731\) −4.97492 8.61681i −0.184004 0.318704i
\(732\) −20.1593 34.9170i −0.745110 1.29057i
\(733\) −33.4077 −1.23394 −0.616971 0.786986i \(-0.711641\pi\)
−0.616971 + 0.786986i \(0.711641\pi\)
\(734\) −17.4581 −0.644392
\(735\) 0 0
\(736\) −8.36833 + 14.4944i −0.308461 + 0.534269i
\(737\) 11.9767 + 20.7442i 0.441166 + 0.764122i
\(738\) −8.97887 + 15.5519i −0.330517 + 0.572472i
\(739\) 16.1610 27.9917i 0.594493 1.02969i −0.399125 0.916897i \(-0.630686\pi\)
0.993618 0.112796i \(-0.0359807\pi\)
\(740\) 0 0
\(741\) 14.7906 + 6.20658i 0.543346 + 0.228004i
\(742\) 40.6024 1.49056
\(743\) −5.18904 + 8.98768i −0.190367 + 0.329726i −0.945372 0.325993i \(-0.894301\pi\)
0.755005 + 0.655719i \(0.227635\pi\)
\(744\) 0.330455 0.572366i 0.0121151 0.0209839i
\(745\) 0 0
\(746\) 13.4766 23.3421i 0.493412 0.854615i
\(747\) −3.48286 6.03249i −0.127431 0.220717i
\(748\) −21.0936 −0.771260
\(749\) −11.3435 −0.414481
\(750\) 0 0
\(751\) −5.54684 9.60741i −0.202407 0.350580i 0.746896 0.664940i \(-0.231543\pi\)
−0.949304 + 0.314361i \(0.898210\pi\)
\(752\) −15.0781 −0.549843
\(753\) −14.0140 −0.510699
\(754\) −20.1471 34.8958i −0.733714 1.27083i
\(755\) 0 0
\(756\) 13.4999 + 23.3825i 0.490987 + 0.850414i
\(757\) −12.5754 + 21.7812i −0.457061 + 0.791653i −0.998804 0.0488915i \(-0.984431\pi\)
0.541743 + 0.840544i \(0.317764\pi\)
\(758\) 23.0249 39.8803i 0.836301 1.44852i
\(759\) 5.72691 0.207874
\(760\) 0 0
\(761\) 7.40847 0.268557 0.134278 0.990944i \(-0.457128\pi\)
0.134278 + 0.990944i \(0.457128\pi\)
\(762\) 23.3145 40.3819i 0.844596 1.46288i
\(763\) 9.43330 16.3390i 0.341508 0.591510i
\(764\) 18.6622 + 32.3239i 0.675174 + 1.16944i
\(765\) 0 0
\(766\) 33.8054 + 58.5526i 1.22144 + 2.11559i
\(767\) −31.3984 −1.13373
\(768\) −0.591282 −0.0213361
\(769\) −14.3791 24.9053i −0.518524 0.898109i −0.999768 0.0215231i \(-0.993148\pi\)
0.481245 0.876586i \(-0.340185\pi\)
\(770\) 0 0
\(771\) −21.5414 −0.775795
\(772\) 23.0039 0.827928
\(773\) −22.5882 39.1240i −0.812442 1.40719i −0.911150 0.412075i \(-0.864804\pi\)
0.0987075 0.995116i \(-0.468529\pi\)
\(774\) 2.55977 4.43365i 0.0920090 0.159364i
\(775\) 0 0
\(776\) −5.97119 + 10.3424i −0.214353 + 0.371271i
\(777\) 4.85772 8.41383i 0.174270 0.301844i
\(778\) 47.0103 1.68540
\(779\) −28.5944 + 21.7324i −1.02450 + 0.778642i
\(780\) 0 0
\(781\) −10.8686 + 18.8249i −0.388908 + 0.673608i
\(782\) −10.1363 + 17.5567i −0.362475 + 0.627825i
\(783\) −20.1617 34.9211i −0.720521 1.24798i
\(784\) −4.04909 + 7.01322i −0.144610 + 0.250472i
\(785\) 0 0
\(786\) 21.6315 0.771571
\(787\) 9.67026 0.344707 0.172354 0.985035i \(-0.444863\pi\)
0.172354 + 0.985035i \(0.444863\pi\)
\(788\) 3.88932 + 6.73649i 0.138551 + 0.239978i
\(789\) 5.61695 + 9.72884i 0.199969 + 0.346356i
\(790\) 0 0
\(791\) −22.3385 −0.794264
\(792\) −1.42069 2.46070i −0.0504819 0.0874372i
\(793\) −13.7201 + 23.7640i −0.487216 + 0.843884i
\(794\) 2.85778 + 4.94982i 0.101419 + 0.175663i
\(795\) 0 0
\(796\) −30.9522 + 53.6109i −1.09707 + 1.90019i
\(797\) 20.4295 0.723651 0.361825 0.932246i \(-0.382154\pi\)
0.361825 + 0.932246i \(0.382154\pi\)
\(798\) 2.96504 + 23.3540i 0.104961 + 0.826723i
\(799\) −30.7293 −1.08712
\(800\) 0 0
\(801\) −6.26333 + 10.8484i −0.221304 + 0.383310i
\(802\) −27.0881 46.9180i −0.956515 1.65673i
\(803\) −8.42684 + 14.5957i −0.297377 + 0.515072i
\(804\) 24.9383 + 43.1944i 0.879506 + 1.52335i
\(805\) 0 0
\(806\) −1.71816 −0.0605196
\(807\) −14.2988 24.7662i −0.503340 0.871811i
\(808\) 2.20887 + 3.82588i 0.0777079 + 0.134594i
\(809\) −32.9158 −1.15726 −0.578630 0.815590i \(-0.696412\pi\)
−0.578630 + 0.815590i \(0.696412\pi\)
\(810\) 0 0
\(811\) −9.92532 17.1912i −0.348525 0.603663i 0.637462 0.770481i \(-0.279984\pi\)
−0.985988 + 0.166818i \(0.946651\pi\)
\(812\) 17.0114 29.4646i 0.596983 1.03401i
\(813\) 3.41144 + 5.90879i 0.119645 + 0.207230i
\(814\) −7.78571 + 13.4853i −0.272889 + 0.472658i
\(815\) 0 0
\(816\) 12.4366 0.435367
\(817\) 8.15192 6.19563i 0.285200 0.216758i
\(818\) 46.8583 1.63836
\(819\) 2.30437 3.99129i 0.0805214 0.139467i
\(820\) 0 0
\(821\) 23.3799 + 40.4952i 0.815965 + 1.41329i 0.908633 + 0.417595i \(0.137127\pi\)
−0.0926686 + 0.995697i \(0.529540\pi\)
\(822\) −34.3157 + 59.4365i −1.19690 + 2.07309i
\(823\) −4.75713 8.23959i −0.165823 0.287214i 0.771124 0.636685i \(-0.219695\pi\)
−0.936947 + 0.349471i \(0.886361\pi\)
\(824\) 11.7394 0.408962
\(825\) 0 0
\(826\) −23.0412 39.9086i −0.801707 1.38860i
\(827\) 17.1130 + 29.6406i 0.595077 + 1.03070i 0.993536 + 0.113517i \(0.0362118\pi\)
−0.398459 + 0.917186i \(0.630455\pi\)
\(828\) −6.00102 −0.208550
\(829\) −26.9726 −0.936798 −0.468399 0.883517i \(-0.655169\pi\)
−0.468399 + 0.883517i \(0.655169\pi\)
\(830\) 0 0
\(831\) −18.6729 + 32.3425i −0.647757 + 1.12195i
\(832\) 16.0345 + 27.7725i 0.555895 + 0.962838i
\(833\) −8.25206 + 14.2930i −0.285917 + 0.495223i
\(834\) 28.7589 49.8119i 0.995840 1.72485i
\(835\) 0 0
\(836\) −2.73398 21.5341i −0.0945567 0.744772i
\(837\) −1.71941 −0.0594314
\(838\) −12.6836 + 21.9686i −0.438146 + 0.758891i
\(839\) 20.6632 35.7898i 0.713374 1.23560i −0.250210 0.968192i \(-0.580500\pi\)
0.963583 0.267408i \(-0.0861671\pi\)
\(840\) 0 0
\(841\) −10.9060 + 18.8898i −0.376070 + 0.651373i
\(842\) −34.3460 59.4891i −1.18364 2.05013i
\(843\) 7.47558 0.257473
\(844\) −38.1735 −1.31399
\(845\) 0 0
\(846\) −7.90565 13.6930i −0.271802 0.470774i
\(847\) −13.4267 −0.461345
\(848\) 22.0732 0.757997
\(849\) −13.9924 24.2355i −0.480218 0.831762i
\(850\) 0 0
\(851\) 4.30484 + 7.45621i 0.147568 + 0.255596i
\(852\) −22.6310 + 39.1980i −0.775325 + 1.34290i
\(853\) 15.4062 26.6843i 0.527497 0.913652i −0.471989 0.881604i \(-0.656464\pi\)
0.999486 0.0320475i \(-0.0102028\pi\)
\(854\) −40.2733 −1.37812
\(855\) 0 0
\(856\) 9.91070 0.338741
\(857\) −6.96440 + 12.0627i −0.237900 + 0.412054i −0.960111 0.279618i \(-0.909792\pi\)
0.722212 + 0.691672i \(0.243126\pi\)
\(858\) 7.33913 12.7117i 0.250554 0.433972i
\(859\) 6.09063 + 10.5493i 0.207810 + 0.359937i 0.951024 0.309116i \(-0.100033\pi\)
−0.743215 + 0.669053i \(0.766700\pi\)
\(860\) 0 0
\(861\) −10.2532 17.7590i −0.349426 0.605224i
\(862\) −13.0800 −0.445507
\(863\) −32.2800 −1.09882 −0.549412 0.835551i \(-0.685148\pi\)
−0.549412 + 0.835551i \(0.685148\pi\)
\(864\) 21.4639 + 37.1765i 0.730216 + 1.26477i
\(865\) 0 0
\(866\) 34.2387 1.16348
\(867\) 1.33009 0.0451722
\(868\) −0.725372 1.25638i −0.0246207 0.0426444i
\(869\) −7.24564 + 12.5498i −0.245792 + 0.425724i
\(870\) 0 0
\(871\) 16.9726 29.3975i 0.575096 0.996095i
\(872\) −8.24180 + 14.2752i −0.279103 + 0.483420i
\(873\) 7.79232 0.263730
\(874\) −19.2370 8.07245i −0.650703 0.273055i
\(875\) 0 0
\(876\) −17.5467 + 30.3918i −0.592849 + 1.02684i
\(877\) 14.1372 24.4863i 0.477379 0.826845i −0.522285 0.852771i \(-0.674920\pi\)
0.999664 + 0.0259260i \(0.00825344\pi\)
\(878\) 42.7247 + 74.0014i 1.44189 + 2.49743i
\(879\) 13.6661 23.6705i 0.460948 0.798385i
\(880\) 0 0
\(881\) −43.4261 −1.46306 −0.731532 0.681807i \(-0.761194\pi\)
−0.731532 + 0.681807i \(0.761194\pi\)
\(882\) −8.49194 −0.285939
\(883\) 11.0337 + 19.1110i 0.371314 + 0.643135i 0.989768 0.142686i \(-0.0455740\pi\)
−0.618454 + 0.785821i \(0.712241\pi\)
\(884\) 14.9463 + 25.8878i 0.502700 + 0.870702i
\(885\) 0 0
\(886\) −28.5655 −0.959676
\(887\) 16.7324 + 28.9814i 0.561819 + 0.973099i 0.997338 + 0.0729195i \(0.0232316\pi\)
−0.435519 + 0.900180i \(0.643435\pi\)
\(888\) −4.24416 + 7.35109i −0.142425 + 0.246687i
\(889\) −13.3979 23.2058i −0.449351 0.778298i
\(890\) 0 0
\(891\) 4.57543 7.92487i 0.153283 0.265493i
\(892\) −46.3337 −1.55137
\(893\) −3.98288 31.3709i −0.133282 1.04979i
\(894\) −55.6129 −1.85997
\(895\) 0 0
\(896\) −10.1643 + 17.6051i −0.339566 + 0.588146i
\(897\) −4.05792 7.02853i −0.135490 0.234676i
\(898\) 3.84480 6.65938i 0.128303 0.222227i
\(899\) 1.08332 + 1.87637i 0.0361308 + 0.0625804i
\(900\) 0 0
\(901\) 44.9853 1.49868
\(902\) 16.4332 + 28.4632i 0.547167 + 0.947721i
\(903\) 2.92305 + 5.06287i 0.0972730 + 0.168482i
\(904\) 19.5169 0.649123
\(905\) 0 0
\(906\) 4.15930 + 7.20412i 0.138184 + 0.239341i
\(907\) −10.0745 + 17.4495i −0.334518 + 0.579402i −0.983392 0.181494i \(-0.941907\pi\)
0.648874 + 0.760896i \(0.275240\pi\)
\(908\) 13.9267 + 24.1217i 0.462173 + 0.800506i
\(909\) 1.44127 2.49636i 0.0478040 0.0827990i
\(910\) 0 0
\(911\) −5.36397 −0.177716 −0.0888582 0.996044i \(-0.528322\pi\)
−0.0888582 + 0.996044i \(0.528322\pi\)
\(912\) 1.61193 + 12.6963i 0.0533762 + 0.420415i
\(913\) −12.7488 −0.421922
\(914\) −15.9515 + 27.6289i −0.527630 + 0.913881i
\(915\) 0 0
\(916\) −17.4563 30.2352i −0.576773 0.999000i
\(917\) 6.21537 10.7653i 0.205250 0.355503i
\(918\) 25.9987 + 45.0310i 0.858084 + 1.48624i
\(919\) 8.22087 0.271181 0.135591 0.990765i \(-0.456707\pi\)
0.135591 + 0.990765i \(0.456707\pi\)
\(920\) 0 0
\(921\) 19.8630 + 34.4037i 0.654507 + 1.13364i
\(922\) 7.21908 + 12.5038i 0.237748 + 0.411791i
\(923\) 30.8046 1.01395
\(924\) 12.3937 0.407724
\(925\) 0 0
\(926\) 27.1869 47.0891i 0.893418 1.54745i
\(927\) −3.82994 6.63366i −0.125792 0.217878i
\(928\) 27.0469 46.8466i 0.887858 1.53781i
\(929\) −5.94771 + 10.3017i −0.195138 + 0.337989i −0.946946 0.321393i \(-0.895849\pi\)
0.751808 + 0.659382i \(0.229182\pi\)
\(930\) 0 0
\(931\) −15.6610 6.57183i −0.513268 0.215383i
\(932\) −2.69538 −0.0882901
\(933\) −1.94471 + 3.36833i −0.0636669 + 0.110274i
\(934\) 32.6964 56.6319i 1.06986 1.85305i
\(935\) 0 0
\(936\) −2.01331 + 3.48716i −0.0658072 + 0.113981i
\(937\) 18.7506 + 32.4770i 0.612555 + 1.06098i 0.990808 + 0.135274i \(0.0431914\pi\)
−0.378254 + 0.925702i \(0.623475\pi\)
\(938\) 49.8205 1.62670
\(939\) −29.8879 −0.975354
\(940\) 0 0
\(941\) −23.5916 40.8618i −0.769063 1.33206i −0.938071 0.346442i \(-0.887390\pi\)
0.169008 0.985615i \(-0.445944\pi\)
\(942\) 3.91729 0.127632
\(943\) 18.1724 0.591774
\(944\) −12.5262 21.6960i −0.407693 0.706146i
\(945\) 0 0
\(946\) −4.68492 8.11452i −0.152320 0.263826i
\(947\) −22.6206 + 39.1799i −0.735069 + 1.27318i 0.219624 + 0.975585i \(0.429517\pi\)
−0.954693 + 0.297592i \(0.903816\pi\)
\(948\) −15.0872 + 26.1318i −0.490009 + 0.848720i
\(949\) 23.8841 0.775310
\(950\) 0 0
\(951\) −45.1114 −1.46284
\(952\) −5.74282 + 9.94686i −0.186126 + 0.322379i
\(953\) 6.16935 10.6856i 0.199845 0.346141i −0.748633 0.662984i \(-0.769290\pi\)
0.948478 + 0.316843i \(0.102623\pi\)
\(954\) 11.5732 + 20.0455i 0.374698 + 0.648995i
\(955\) 0 0
\(956\) 1.03539 + 1.79335i 0.0334869 + 0.0580010i
\(957\) −18.5097 −0.598333
\(958\) −10.8690 −0.351162
\(959\) 19.7198 + 34.1557i 0.636785 + 1.10294i
\(960\) 0 0
\(961\) −30.9076 −0.997020
\(962\) 22.0669 0.711466
\(963\) −3.23333 5.60029i −0.104193 0.180467i
\(964\) 17.0113 29.4645i 0.547898 0.948987i
\(965\) 0 0
\(966\) 5.95569 10.3156i 0.191621 0.331898i
\(967\) −27.7295 + 48.0289i −0.891720 + 1.54450i −0.0539076 + 0.998546i \(0.517168\pi\)
−0.837812 + 0.545958i \(0.816166\pi\)
\(968\) 11.7308 0.377041
\(969\) 3.28511 + 25.8750i 0.105533 + 0.831226i
\(970\) 0 0
\(971\) −11.6670 + 20.2078i −0.374412 + 0.648500i −0.990239 0.139381i \(-0.955489\pi\)
0.615827 + 0.787881i \(0.288822\pi\)
\(972\) −13.4618 + 23.3165i −0.431787 + 0.747877i
\(973\) −16.5266 28.6248i −0.529817 0.917670i
\(974\) −44.3652 + 76.8428i −1.42155 + 2.46220i
\(975\) 0 0
\(976\) −21.8943 −0.700819
\(977\) −11.3809 −0.364107 −0.182054 0.983289i \(-0.558274\pi\)
−0.182054 + 0.983289i \(0.558274\pi\)
\(978\) −11.8698 20.5592i −0.379556 0.657409i
\(979\) 11.4632 + 19.8549i 0.366366 + 0.634565i
\(980\) 0 0
\(981\) 10.7554 0.343394
\(982\) −37.2762 64.5643i −1.18953 2.06033i
\(983\) 20.6632 35.7897i 0.659054 1.14151i −0.321807 0.946805i \(-0.604290\pi\)
0.980861 0.194709i \(-0.0623763\pi\)
\(984\) 8.95810 + 15.5159i 0.285574 + 0.494628i
\(985\) 0 0
\(986\) 32.7612 56.7441i 1.04333 1.80710i
\(987\) 18.0552 0.574704
\(988\) −24.4912 + 18.6138i −0.779167 + 0.592184i
\(989\) −5.18073 −0.164738
\(990\) 0 0
\(991\) 4.04937 7.01371i 0.128632 0.222798i −0.794515 0.607245i \(-0.792275\pi\)
0.923147 + 0.384447i \(0.125608\pi\)
\(992\) −1.15329 1.99756i −0.0366170 0.0634224i
\(993\) −25.3244 + 43.8632i −0.803646 + 1.39196i
\(994\) 22.6055 + 39.1539i 0.717003 + 1.24189i
\(995\) 0 0
\(996\) −26.5460 −0.841141
\(997\) −18.2128 31.5454i −0.576804 0.999054i −0.995843 0.0910857i \(-0.970966\pi\)
0.419039 0.907968i \(-0.362367\pi\)
\(998\) 14.4068 + 24.9533i 0.456039 + 0.789883i
\(999\) 22.0829 0.698673
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 475.2.e.h.201.5 yes 12
5.2 odd 4 475.2.j.d.49.12 24
5.3 odd 4 475.2.j.d.49.1 24
5.4 even 2 475.2.e.f.201.2 yes 12
19.7 even 3 inner 475.2.e.h.26.5 yes 12
19.8 odd 6 9025.2.a.by.1.5 6
19.11 even 3 9025.2.a.br.1.2 6
95.7 odd 12 475.2.j.d.349.1 24
95.49 even 6 9025.2.a.bz.1.5 6
95.64 even 6 475.2.e.f.26.2 12
95.83 odd 12 475.2.j.d.349.12 24
95.84 odd 6 9025.2.a.bs.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.2 12 95.64 even 6
475.2.e.f.201.2 yes 12 5.4 even 2
475.2.e.h.26.5 yes 12 19.7 even 3 inner
475.2.e.h.201.5 yes 12 1.1 even 1 trivial
475.2.j.d.49.1 24 5.3 odd 4
475.2.j.d.49.12 24 5.2 odd 4
475.2.j.d.349.1 24 95.7 odd 12
475.2.j.d.349.12 24 95.83 odd 12
9025.2.a.br.1.2 6 19.11 even 3
9025.2.a.bs.1.2 6 95.84 odd 6
9025.2.a.by.1.5 6 19.8 odd 6
9025.2.a.bz.1.5 6 95.49 even 6