Properties

Label 475.2.e.f.201.2
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 201.2
Root \(1.20634 + 2.08945i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.f.26.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.08504 + 1.87935i) q^{2} +(0.706345 - 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} -1.76171 q^{7} +1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +O(q^{10})\) \(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 \(0.445038\pi\)
−0.939053 + 0.343771i \(0.888295\pi\)
\(3\) 0.706345 1.22342i 0.407808 0.706345i −0.586836 0.809706i \(-0.699627\pi\)
0.994644 + 0.103361i \(0.0329598\pi\)
\(4\) −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 \(-0.608038\pi\)
−0.332931 + 0.942951i \(0.608038\pi\)
\(8\) 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 0.988163 0.153407i \(-0.0490245\pi\)
−0.626936 + 0.779071i \(0.715691\pi\)
\(14\) 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 \(0.338377\pi\)
−0.999874 + 0.0158451i \(0.994956\pi\)
\(18\) −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 0.957790 0.287470i \(-0.0928143\pi\)
−0.727851 + 0.685735i \(0.759481\pi\)
\(24\) 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 \(-0.396019\pi\)
0.320887 + 0.947118i \(0.396019\pi\)
\(38\) −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 −0.941576 0.336800i \(-0.890655\pi\)
0.762465 + 0.647029i \(0.223989\pi\)
\(44\) −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 \(0.0108066\pi\)
−0.470316 + 0.882498i \(0.655860\pi\)
\(48\) −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 \(-0.906460\pi\)
0.227720 0.973727i \(-0.426873\pi\)
\(54\) −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 \(-0.873596\pi\)
0.126152 0.992011i \(-0.459737\pi\)
\(68\) 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 \(-0.653049\pi\)
0.999085 0.0427676i \(-0.0136175\pi\)
\(74\) −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 \(-0.375699\pi\)
0.380654 + 0.924718i \(0.375699\pi\)
\(84\) 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 −0.992960 0.118452i \(-0.962207\pi\)
0.599062 + 0.800703i \(0.295540\pi\)
\(98\) 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 \(-0.377383\pi\)
0.375756 + 0.926718i \(0.377383\pi\)
\(104\) 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 \(-0.399257\pi\)
0.311236 + 0.950333i \(0.399257\pi\)
\(108\) −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 \(-0.296590\pi\)
0.596417 + 0.802674i \(0.296590\pi\)
\(114\) 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 \(0.0691208\pi\)
−0.301675 + 0.953411i \(0.597546\pi\)
\(128\) 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 \(-0.761082\pi\)
−0.225040 0.974350i \(-0.572251\pi\)
\(138\) −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 −0.890394 0.455191i \(-0.849571\pi\)
0.839404 + 0.543508i \(0.182904\pi\)
\(158\) −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 \(-0.401922\pi\)
0.303268 + 0.952905i \(0.401922\pi\)
\(164\) 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 0.702569 0.711616i \(-0.252036\pi\)
−0.967562 + 0.252635i \(0.918703\pi\)
\(168\) −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 −0.978846 0.204600i \(-0.934411\pi\)
0.666611 + 0.745405i \(0.267744\pi\)
\(174\) −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 −0.671802 0.740730i \(-0.734480\pi\)
0.977393 + 0.211433i \(0.0678130\pi\)
\(194\) −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 \(-0.467387\pi\)
0.102279 + 0.994756i \(0.467387\pi\)
\(198\) −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 \(0.360737\pi\)
−0.996296 + 0.0859855i \(0.972596\pi\)
\(224\) −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 \(-0.389174\pi\)
0.341178 + 0.939999i \(0.389174\pi\)
\(228\) −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 −0.881859 0.471512i \(-0.843708\pi\)
0.849271 + 0.527957i \(0.177042\pi\)
\(234\) −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 0.524021 0.851705i \(-0.324431\pi\)
−0.999609 + 0.0279628i \(0.991098\pi\)
\(258\) −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 −0.962181 0.272412i \(-0.912179\pi\)
0.717006 + 0.697067i \(0.245512\pi\)
\(264\) 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 \(-0.792106\pi\)
−0.794194 + 0.607665i \(0.792106\pi\)
\(278\) 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 \(-0.632942\pi\)
0.994393 0.105751i \(-0.0337245\pi\)
\(284\) 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 \(-0.308817\pi\)
0.565152 + 0.824987i \(0.308817\pi\)
\(294\) −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 \(0.463147\pi\)
−0.917986 + 0.396612i \(0.870186\pi\)
\(308\) 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 \(-0.962659\pi\)
0.395203 0.918594i \(-0.370674\pi\)
\(314\) −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 \(-0.812576\pi\)
−0.0651661 0.997874i \(-0.520758\pi\)
\(318\) 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 −0.708240 0.705972i \(-0.750510\pi\)
0.965510 + 0.260368i \(0.0838437\pi\)
\(338\) 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 −0.963411 0.268027i \(-0.913628\pi\)
0.713824 + 0.700325i \(0.246962\pi\)
\(348\) −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 \(-0.770756\pi\)
−0.751679 + 0.659529i \(0.770756\pi\)
\(354\) 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 0.951705 0.307014i \(-0.0993299\pi\)
−0.741735 + 0.670694i \(0.765997\pi\)
\(368\) 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 \(-0.604204\pi\)
−0.321549 + 0.946893i \(0.604204\pi\)
\(374\) −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 \(-0.540282\pi\)
0.922206 0.386698i \(-0.126384\pi\)
\(384\) −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 −0.831085 0.556145i \(-0.812280\pi\)
0.897178 + 0.441668i \(0.145613\pi\)
\(398\) 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 0.611822 0.790995i \(-0.290437\pi\)
−0.990933 + 0.134356i \(0.957103\pi\)
\(434\) 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 0.978947 0.204116i \(-0.0654321\pi\)
−0.666243 + 0.745734i \(0.732099\pi\)
\(444\) −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 \(-0.388269\pi\)
0.343848 + 0.939025i \(0.388269\pi\)
\(458\) −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 \(-0.697819\pi\)
−0.582227 + 0.813026i \(0.697819\pi\)
\(464\) 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 \(-0.745576\pi\)
−0.697212 + 0.716865i \(0.745576\pi\)
\(468\) 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 \(-0.122882\pi\)
0.926406 + 0.376527i \(0.122882\pi\)
\(488\) −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 0.761825 0.647782i \(-0.224303\pi\)
−0.941909 + 0.335869i \(0.890970\pi\)
\(504\) −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 0.970452 0.241296i \(-0.0775725\pi\)
−0.694194 + 0.719788i \(0.744239\pi\)
\(524\) −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 0.999943 0.0106584i \(-0.00339274\pi\)
−0.509202 + 0.860647i \(0.670059\pi\)
\(548\) −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 0.885684 0.464289i \(-0.153690\pi\)
−0.844928 + 0.534880i \(0.820357\pi\)
\(558\) −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 \(-0.506233\pi\)
−0.0195800 + 0.999808i \(0.506233\pi\)
\(564\) −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 \(-0.271014\pi\)
0.658919 + 0.752214i \(0.271014\pi\)
\(578\) 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 −0.806870 0.590729i \(-0.798840\pi\)
0.915021 + 0.403406i \(0.132174\pi\)
\(588\) 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 \(-0.996624\pi\)
0.490787 0.871280i \(-0.336709\pi\)
\(594\) −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 \(-0.561641\pi\)
−0.192443 + 0.981308i \(0.561641\pi\)
\(608\) 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 −0.980613 0.195953i \(-0.937220\pi\)
0.660007 + 0.751260i \(0.270553\pi\)
\(614\) −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 \(0.0380978\pi\)
−0.393018 + 0.919531i \(0.628569\pi\)
\(618\) 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 −0.596537 0.802586i \(-0.703457\pi\)
0.993328 + 0.115323i \(0.0367903\pi\)
\(644\) −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 \(-0.695949\pi\)
−0.577441 + 0.816432i \(0.695949\pi\)
\(648\) 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 \(-0.639225\pi\)
−0.423575 + 0.905861i \(0.639225\pi\)
\(654\) 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 \(-0.215557\pi\)
0.779334 + 0.626609i \(0.215557\pi\)
\(674\) 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 \(-0.497522\pi\)
0.00778566 + 0.999970i \(0.497522\pi\)
\(678\) 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 \(-0.368941\pi\)
0.400198 + 0.916429i \(0.368941\pi\)
\(684\) 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 \(0.537626\pi\)
−0.801017 + 0.598642i \(0.795707\pi\)
\(728\) −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 \(-0.288359\pi\)
0.616971 + 0.786986i \(0.288359\pi\)
\(734\) −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 −0.755005 0.655719i \(-0.772365\pi\)
0.945372 + 0.325993i \(0.105699\pi\)
\(744\) 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 −0.541743 0.840544i \(-0.682236\pi\)
0.998804 + 0.0488915i \(0.0155688\pi\)
\(758\) −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 \(0.135196\pi\)
−0.0987075 + 0.995116i \(0.531471\pi\)
\(774\) 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 <