Properties

Label 28.3.g.a.11.3
Level $28$
Weight $3$
Character 28.11
Analytic conductor $0.763$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [28,3,Mod(11,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("28.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.g (of order \(6\), 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: \(0.762944740209\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.3
Root \(2.79733 - 1.03769i\) of defining polynomial
Character \(\chi\) \(=\) 28.11
Dual form 28.3.g.a.23.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.371518 - 1.96519i) q^{2} +(3.95004 + 2.28056i) q^{3} +(-3.72395 + 1.46021i) q^{4} +(-2.62655 - 4.54932i) q^{5} +(3.01422 - 8.60985i) q^{6} +(-5.86799 + 3.81663i) q^{7} +(4.25310 + 6.77577i) q^{8} +(5.90188 + 10.2224i) q^{9} +O(q^{10})\) \(q+(-0.371518 - 1.96519i) q^{2} +(3.95004 + 2.28056i) q^{3} +(-3.72395 + 1.46021i) q^{4} +(-2.62655 - 4.54932i) q^{5} +(3.01422 - 8.60985i) q^{6} +(-5.86799 + 3.81663i) q^{7} +(4.25310 + 6.77577i) q^{8} +(5.90188 + 10.2224i) q^{9} +(-7.96447 + 6.85183i) q^{10} +(1.91795 + 1.10733i) q^{11} +(-18.0398 - 2.72479i) q^{12} -3.29755 q^{13} +(9.68047 + 10.1138i) q^{14} -23.9600i q^{15} +(11.7356 - 10.8755i) q^{16} +(6.69943 - 11.6038i) q^{17} +(17.8962 - 15.3961i) q^{18} +(-6.72474 + 3.88253i) q^{19} +(16.4241 + 13.1061i) q^{20} +(-31.8829 + 1.69356i) q^{21} +(1.46356 - 4.18053i) q^{22} +(3.66033 - 2.11329i) q^{23} +(1.34740 + 36.4640i) q^{24} +(-1.29755 + 2.24743i) q^{25} +(1.22510 + 6.48032i) q^{26} +12.7883i q^{27} +(16.2790 - 22.7814i) q^{28} +39.4113 q^{29} +(-47.0860 + 8.90158i) q^{30} +(-17.2001 - 9.93050i) q^{31} +(-25.7324 - 19.0222i) q^{32} +(5.05066 + 8.74799i) q^{33} +(-25.2926 - 8.85465i) q^{34} +(32.7757 + 16.6708i) q^{35} +(-36.9051 - 29.4495i) q^{36} +(12.8704 + 22.2922i) q^{37} +(10.1283 + 11.7730i) q^{38} +(-13.0255 - 7.52026i) q^{39} +(19.6542 - 37.1457i) q^{40} -55.0188 q^{41} +(15.1732 + 62.0267i) q^{42} +78.2646i q^{43} +(-8.75928 - 1.32303i) q^{44} +(31.0032 - 53.6991i) q^{45} +(-5.51290 - 6.40812i) q^{46} +(18.3993 - 10.6228i) q^{47} +(71.1582 - 16.1950i) q^{48} +(19.8667 - 44.7919i) q^{49} +(4.89869 + 1.71498i) q^{50} +(52.9261 - 30.5569i) q^{51} +(12.2799 - 4.81512i) q^{52} +(-24.0346 + 41.6292i) q^{53} +(25.1314 - 4.75108i) q^{54} -11.6338i q^{55} +(-50.8178 - 23.5277i) q^{56} -35.4173 q^{57} +(-14.6420 - 77.4507i) q^{58} +(-66.7995 - 38.5667i) q^{59} +(34.9866 + 89.2258i) q^{60} +(23.7371 + 41.1138i) q^{61} +(-13.1252 + 37.4909i) q^{62} +(-73.6472 - 37.4594i) q^{63} +(-27.8222 + 57.6361i) q^{64} +(8.66119 + 15.0016i) q^{65} +(15.3151 - 13.1755i) q^{66} +(45.2217 + 26.1088i) q^{67} +(-8.00443 + 52.9944i) q^{68} +19.2779 q^{69} +(20.5845 - 70.6039i) q^{70} -90.1012i q^{71} +(-44.1631 + 83.4666i) q^{72} +(-20.7976 + 36.0224i) q^{73} +(39.0269 - 33.5748i) q^{74} +(-10.2508 + 5.91828i) q^{75} +(19.3733 - 24.2779i) q^{76} +(-15.4808 + 0.822311i) q^{77} +(-9.93954 + 28.3914i) q^{78} +(-114.033 + 65.8371i) q^{79} +(-80.3002 - 24.8239i) q^{80} +(23.9525 - 41.4870i) q^{81} +(20.4405 + 108.122i) q^{82} -11.8366i q^{83} +(116.257 - 52.8623i) q^{84} -70.3856 q^{85} +(153.805 - 29.0768i) q^{86} +(155.676 + 89.8797i) q^{87} +(0.654232 + 17.7052i) q^{88} +(-15.5569 - 26.9453i) q^{89} +(-117.047 - 40.9770i) q^{90} +(19.3500 - 12.5855i) q^{91} +(-10.5450 + 13.2146i) q^{92} +(-45.2941 - 78.4517i) q^{93} +(-27.7116 - 32.2115i) q^{94} +(35.3257 + 20.3953i) q^{95} +(-58.2627 - 133.823i) q^{96} +140.501 q^{97} +(-95.4055 - 22.4007i) q^{98} +26.1413i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9} - 2 q^{10} - 24 q^{12} - 24 q^{13} + 2 q^{14} + 16 q^{16} - 2 q^{17} + 56 q^{18} + 152 q^{20} - 78 q^{21} + 44 q^{22} - 44 q^{24} + 56 q^{26} + 8 q^{28} + 72 q^{29} - 74 q^{30} - 112 q^{32} - 14 q^{33} - 316 q^{34} - 160 q^{36} + 86 q^{37} - 2 q^{38} - 148 q^{40} + 8 q^{41} + 68 q^{42} + 64 q^{44} + 156 q^{45} + 162 q^{46} + 512 q^{48} + 108 q^{49} + 208 q^{50} - 64 q^{52} - 74 q^{53} + 182 q^{54} + 16 q^{56} - 220 q^{57} - 176 q^{58} - 232 q^{60} + 86 q^{61} - 532 q^{62} - 160 q^{64} - 140 q^{65} + 102 q^{66} - 68 q^{68} - 300 q^{69} + 90 q^{70} + 152 q^{72} - 234 q^{73} + 290 q^{74} + 576 q^{76} - 262 q^{77} + 64 q^{78} + 146 q^{81} + 272 q^{82} - 28 q^{84} + 268 q^{85} - 16 q^{86} - 188 q^{88} + 6 q^{89} - 640 q^{90} - 448 q^{92} + 162 q^{93} + 102 q^{94} - 320 q^{96} + 744 q^{97} - 190 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.371518 1.96519i −0.185759 0.982595i
\(3\) 3.95004 + 2.28056i 1.31668 + 0.760186i 0.983193 0.182569i \(-0.0584413\pi\)
0.333487 + 0.942755i \(0.391775\pi\)
\(4\) −3.72395 + 1.46021i −0.930987 + 0.365052i
\(5\) −2.62655 4.54932i −0.525310 0.909864i −0.999565 0.0294768i \(-0.990616\pi\)
0.474255 0.880388i \(-0.342717\pi\)
\(6\) 3.01422 8.60985i 0.502369 1.43498i
\(7\) −5.86799 + 3.81663i −0.838285 + 0.545233i
\(8\) 4.25310 + 6.77577i 0.531638 + 0.846972i
\(9\) 5.90188 + 10.2224i 0.655765 + 1.13582i
\(10\) −7.96447 + 6.85183i −0.796447 + 0.685183i
\(11\) 1.91795 + 1.10733i 0.174359 + 0.100666i 0.584640 0.811293i \(-0.301236\pi\)
−0.410281 + 0.911959i \(0.634569\pi\)
\(12\) −18.0398 2.72479i −1.50332 0.227066i
\(13\) −3.29755 −0.253658 −0.126829 0.991925i \(-0.540480\pi\)
−0.126829 + 0.991925i \(0.540480\pi\)
\(14\) 9.68047 + 10.1138i 0.691462 + 0.722412i
\(15\) 23.9600i 1.59733i
\(16\) 11.7356 10.8755i 0.733474 0.679718i
\(17\) 6.69943 11.6038i 0.394084 0.682574i −0.598900 0.800824i \(-0.704395\pi\)
0.992984 + 0.118250i \(0.0377285\pi\)
\(18\) 17.8962 15.3961i 0.994235 0.855340i
\(19\) −6.72474 + 3.88253i −0.353934 + 0.204344i −0.666416 0.745580i \(-0.732173\pi\)
0.312483 + 0.949923i \(0.398839\pi\)
\(20\) 16.4241 + 13.1061i 0.821205 + 0.655306i
\(21\) −31.8829 + 1.69356i −1.51823 + 0.0806456i
\(22\) 1.46356 4.18053i 0.0665254 0.190024i
\(23\) 3.66033 2.11329i 0.159145 0.0918823i −0.418313 0.908303i \(-0.637378\pi\)
0.577457 + 0.816421i \(0.304045\pi\)
\(24\) 1.34740 + 36.4640i 0.0561416 + 1.51933i
\(25\) −1.29755 + 2.24743i −0.0519021 + 0.0898971i
\(26\) 1.22510 + 6.48032i 0.0471193 + 0.249243i
\(27\) 12.7883i 0.473640i
\(28\) 16.2790 22.7814i 0.581394 0.813623i
\(29\) 39.4113 1.35901 0.679505 0.733671i \(-0.262195\pi\)
0.679505 + 0.733671i \(0.262195\pi\)
\(30\) −47.0860 + 8.90158i −1.56953 + 0.296719i
\(31\) −17.2001 9.93050i −0.554843 0.320339i 0.196230 0.980558i \(-0.437130\pi\)
−0.751073 + 0.660219i \(0.770463\pi\)
\(32\) −25.7324 19.0222i −0.804137 0.594444i
\(33\) 5.05066 + 8.74799i 0.153050 + 0.265091i
\(34\) −25.2926 8.85465i −0.743899 0.260431i
\(35\) 32.7757 + 16.6708i 0.936448 + 0.476309i
\(36\) −36.9051 29.4495i −1.02514 0.818043i
\(37\) 12.8704 + 22.2922i 0.347850 + 0.602493i 0.985867 0.167529i \(-0.0535787\pi\)
−0.638018 + 0.770022i \(0.720245\pi\)
\(38\) 10.1283 + 11.7730i 0.266533 + 0.309815i
\(39\) −13.0255 7.52026i −0.333986 0.192827i
\(40\) 19.6542 37.1457i 0.491354 0.928642i
\(41\) −55.0188 −1.34192 −0.670961 0.741493i \(-0.734118\pi\)
−0.670961 + 0.741493i \(0.734118\pi\)
\(42\) 15.1732 + 62.0267i 0.361267 + 1.47683i
\(43\) 78.2646i 1.82011i 0.414490 + 0.910054i \(0.363960\pi\)
−0.414490 + 0.910054i \(0.636040\pi\)
\(44\) −8.75928 1.32303i −0.199075 0.0300688i
\(45\) 31.0032 53.6991i 0.688960 1.19331i
\(46\) −5.51290 6.40812i −0.119846 0.139307i
\(47\) 18.3993 10.6228i 0.391474 0.226018i −0.291324 0.956624i \(-0.594096\pi\)
0.682799 + 0.730607i \(0.260763\pi\)
\(48\) 71.1582 16.1950i 1.48246 0.337395i
\(49\) 19.8667 44.7919i 0.405442 0.914121i
\(50\) 4.89869 + 1.71498i 0.0979737 + 0.0342995i
\(51\) 52.9261 30.5569i 1.03777 0.599154i
\(52\) 12.2799 4.81512i 0.236152 0.0925984i
\(53\) −24.0346 + 41.6292i −0.453484 + 0.785457i −0.998600 0.0529038i \(-0.983152\pi\)
0.545116 + 0.838361i \(0.316486\pi\)
\(54\) 25.1314 4.75108i 0.465396 0.0879829i
\(55\) 11.6338i 0.211524i
\(56\) −50.8178 23.5277i −0.907461 0.420137i
\(57\) −35.4173 −0.621356
\(58\) −14.6420 77.4507i −0.252449 1.33536i
\(59\) −66.7995 38.5667i −1.13220 0.653673i −0.187710 0.982225i \(-0.560106\pi\)
−0.944486 + 0.328551i \(0.893440\pi\)
\(60\) 34.9866 + 89.2258i 0.583110 + 1.48710i
\(61\) 23.7371 + 41.1138i 0.389133 + 0.673997i 0.992333 0.123592i \(-0.0394415\pi\)
−0.603200 + 0.797590i \(0.706108\pi\)
\(62\) −13.1252 + 37.4909i −0.211696 + 0.604692i
\(63\) −73.6472 37.4594i −1.16900 0.594594i
\(64\) −27.8222 + 57.6361i −0.434722 + 0.900565i
\(65\) 8.66119 + 15.0016i 0.133249 + 0.230794i
\(66\) 15.3151 13.1755i 0.232046 0.199629i
\(67\) 45.2217 + 26.1088i 0.674951 + 0.389683i 0.797950 0.602724i \(-0.205918\pi\)
−0.122999 + 0.992407i \(0.539251\pi\)
\(68\) −8.00443 + 52.9944i −0.117712 + 0.779329i
\(69\) 19.2779 0.279390
\(70\) 20.5845 70.6039i 0.294065 1.00863i
\(71\) 90.1012i 1.26903i −0.772910 0.634515i \(-0.781200\pi\)
0.772910 0.634515i \(-0.218800\pi\)
\(72\) −44.1631 + 83.4666i −0.613376 + 1.15926i
\(73\) −20.7976 + 36.0224i −0.284898 + 0.493458i −0.972584 0.232550i \(-0.925293\pi\)
0.687686 + 0.726008i \(0.258626\pi\)
\(74\) 39.0269 33.5748i 0.527391 0.453714i
\(75\) −10.2508 + 5.91828i −0.136677 + 0.0789105i
\(76\) 19.3733 24.2779i 0.254911 0.319445i
\(77\) −15.4808 + 0.822311i −0.201049 + 0.0106794i
\(78\) −9.93954 + 28.3914i −0.127430 + 0.363993i
\(79\) −114.033 + 65.8371i −1.44346 + 0.833381i −0.998079 0.0619609i \(-0.980265\pi\)
−0.445380 + 0.895342i \(0.646931\pi\)
\(80\) −80.3002 24.8239i −1.00375 0.310299i
\(81\) 23.9525 41.4870i 0.295710 0.512185i
\(82\) 20.4405 + 108.122i 0.249274 + 1.31857i
\(83\) 11.8366i 0.142609i −0.997455 0.0713046i \(-0.977284\pi\)
0.997455 0.0713046i \(-0.0227162\pi\)
\(84\) 116.257 52.8623i 1.38401 0.629314i
\(85\) −70.3856 −0.828066
\(86\) 153.805 29.0768i 1.78843 0.338102i
\(87\) 155.676 + 89.8797i 1.78938 + 1.03310i
\(88\) 0.654232 + 17.7052i 0.00743445 + 0.201195i
\(89\) −15.5569 26.9453i −0.174796 0.302756i 0.765295 0.643680i \(-0.222593\pi\)
−0.940091 + 0.340924i \(0.889260\pi\)
\(90\) −117.047 40.9770i −1.30052 0.455300i
\(91\) 19.3500 12.5855i 0.212637 0.138303i
\(92\) −10.5450 + 13.2146i −0.114620 + 0.143637i
\(93\) −45.2941 78.4517i −0.487034 0.843567i
\(94\) −27.7116 32.2115i −0.294804 0.342676i
\(95\) 35.3257 + 20.3953i 0.371850 + 0.214688i
\(96\) −58.2627 133.823i −0.606904 1.39399i
\(97\) 140.501 1.44846 0.724230 0.689559i \(-0.242196\pi\)
0.724230 + 0.689559i \(0.242196\pi\)
\(98\) −95.4055 22.4007i −0.973525 0.228579i
\(99\) 26.1413i 0.264054i
\(100\) 1.55031 10.2640i 0.0155031 0.102640i
\(101\) 21.1388 36.6135i 0.209295 0.362509i −0.742198 0.670181i \(-0.766216\pi\)
0.951493 + 0.307672i \(0.0995498\pi\)
\(102\) −79.7131 92.6574i −0.781501 0.908406i
\(103\) 83.8778 48.4268i 0.814347 0.470164i −0.0341161 0.999418i \(-0.510862\pi\)
0.848463 + 0.529254i \(0.177528\pi\)
\(104\) −14.0248 22.3435i −0.134854 0.214841i
\(105\) 91.4465 + 140.597i 0.870919 + 1.33902i
\(106\) 90.7387 + 31.7666i 0.856025 + 0.299685i
\(107\) −2.26178 + 1.30584i −0.0211382 + 0.0122041i −0.510532 0.859859i \(-0.670551\pi\)
0.489394 + 0.872063i \(0.337218\pi\)
\(108\) −18.6736 47.6229i −0.172903 0.440952i
\(109\) −3.86724 + 6.69825i −0.0354793 + 0.0614519i −0.883220 0.468959i \(-0.844629\pi\)
0.847741 + 0.530411i \(0.177962\pi\)
\(110\) −22.8627 + 4.32218i −0.207843 + 0.0392926i
\(111\) 117.407i 1.05772i
\(112\) −27.3566 + 108.608i −0.244255 + 0.969711i
\(113\) 34.5495 0.305748 0.152874 0.988246i \(-0.451147\pi\)
0.152874 + 0.988246i \(0.451147\pi\)
\(114\) 13.1582 + 69.6018i 0.115423 + 0.610542i
\(115\) −19.2281 11.1013i −0.167201 0.0965335i
\(116\) −146.766 + 57.5487i −1.26522 + 0.496110i
\(117\) −19.4618 33.7088i −0.166340 0.288109i
\(118\) −50.9737 + 145.602i −0.431981 + 1.23392i
\(119\) 4.97505 + 93.6600i 0.0418071 + 0.787059i
\(120\) 162.348 101.904i 1.35290 0.849203i
\(121\) −58.0476 100.541i −0.479733 0.830921i
\(122\) 71.9778 61.9225i 0.589982 0.507561i
\(123\) −217.327 125.474i −1.76688 1.02011i
\(124\) 78.5530 + 11.8649i 0.633492 + 0.0956845i
\(125\) −117.695 −0.941562
\(126\) −46.2536 + 158.648i −0.367092 + 1.25911i
\(127\) 53.4789i 0.421093i −0.977584 0.210547i \(-0.932476\pi\)
0.977584 0.210547i \(-0.0675244\pi\)
\(128\) 123.602 + 33.2631i 0.965644 + 0.259868i
\(129\) −178.487 + 309.148i −1.38362 + 2.39650i
\(130\) 26.2633 22.5943i 0.202025 0.173802i
\(131\) −112.200 + 64.7790i −0.856492 + 0.494496i −0.862836 0.505484i \(-0.831314\pi\)
0.00634380 + 0.999980i \(0.497981\pi\)
\(132\) −31.5823 25.2021i −0.239260 0.190925i
\(133\) 24.6425 48.4485i 0.185282 0.364274i
\(134\) 34.5080 98.5692i 0.257522 0.735591i
\(135\) 58.1780 33.5891i 0.430948 0.248808i
\(136\) 107.118 3.95816i 0.787631 0.0291041i
\(137\) 81.4651 141.102i 0.594636 1.02994i −0.398962 0.916967i \(-0.630630\pi\)
0.993598 0.112972i \(-0.0360372\pi\)
\(138\) −7.16211 37.8848i −0.0518993 0.274528i
\(139\) 249.241i 1.79310i −0.442941 0.896551i \(-0.646065\pi\)
0.442941 0.896551i \(-0.353935\pi\)
\(140\) −146.398 14.2219i −1.04570 0.101585i
\(141\) 96.9039 0.687262
\(142\) −177.066 + 33.4743i −1.24694 + 0.235734i
\(143\) −6.32454 3.65148i −0.0442276 0.0255348i
\(144\) 180.435 + 55.7795i 1.25302 + 0.387357i
\(145\) −103.516 179.295i −0.713902 1.23651i
\(146\) 78.5176 + 27.4882i 0.537792 + 0.188275i
\(147\) 180.625 131.623i 1.22874 0.895394i
\(148\) −80.4802 64.2216i −0.543785 0.433930i
\(149\) 87.6130 + 151.750i 0.588006 + 1.01846i 0.994493 + 0.104800i \(0.0334204\pi\)
−0.406487 + 0.913657i \(0.633246\pi\)
\(150\) 15.4389 + 17.9460i 0.102926 + 0.119640i
\(151\) 69.0086 + 39.8421i 0.457011 + 0.263855i 0.710787 0.703408i \(-0.248339\pi\)
−0.253776 + 0.967263i \(0.581673\pi\)
\(152\) −54.9081 29.0525i −0.361238 0.191135i
\(153\) 158.157 1.03371
\(154\) 7.36740 + 30.1172i 0.0478402 + 0.195566i
\(155\) 104.332i 0.673109i
\(156\) 59.4873 + 8.98514i 0.381329 + 0.0575971i
\(157\) −53.6734 + 92.9650i −0.341869 + 0.592134i −0.984780 0.173807i \(-0.944393\pi\)
0.642911 + 0.765941i \(0.277726\pi\)
\(158\) 171.748 + 199.637i 1.08701 + 1.26353i
\(159\) −189.876 + 109.625i −1.19419 + 0.689464i
\(160\) −18.9507 + 167.028i −0.118442 + 1.04392i
\(161\) −13.4131 + 26.3709i −0.0833114 + 0.163795i
\(162\) −90.4287 31.6581i −0.558202 0.195420i
\(163\) 72.7579 42.0068i 0.446367 0.257710i −0.259928 0.965628i \(-0.583699\pi\)
0.706295 + 0.707918i \(0.250365\pi\)
\(164\) 204.887 80.3390i 1.24931 0.489872i
\(165\) 26.5316 45.9541i 0.160798 0.278510i
\(166\) −23.2611 + 4.39750i −0.140127 + 0.0264910i
\(167\) 6.08656i 0.0364465i 0.999834 + 0.0182232i \(0.00580095\pi\)
−0.999834 + 0.0182232i \(0.994199\pi\)
\(168\) −147.076 208.828i −0.875454 1.24302i
\(169\) −158.126 −0.935658
\(170\) 26.1496 + 138.321i 0.153821 + 0.813654i
\(171\) −79.3772 45.8284i −0.464194 0.268003i
\(172\) −114.283 291.453i −0.664434 1.69450i
\(173\) 69.7755 + 120.855i 0.403327 + 0.698582i 0.994125 0.108237i \(-0.0345205\pi\)
−0.590798 + 0.806819i \(0.701187\pi\)
\(174\) 118.794 339.325i 0.682725 1.95015i
\(175\) −0.963572 18.1402i −0.00550612 0.103658i
\(176\) 34.5510 7.86349i 0.196313 0.0446789i
\(177\) −175.907 304.680i −0.993826 1.72136i
\(178\) −47.1730 + 40.5829i −0.265017 + 0.227994i
\(179\) 134.840 + 77.8496i 0.753293 + 0.434914i 0.826883 0.562374i \(-0.190112\pi\)
−0.0735892 + 0.997289i \(0.523445\pi\)
\(180\) −37.0424 + 245.244i −0.205791 + 1.36247i
\(181\) 97.1269 0.536613 0.268306 0.963334i \(-0.413536\pi\)
0.268306 + 0.963334i \(0.413536\pi\)
\(182\) −31.9219 33.3507i −0.175395 0.183246i
\(183\) 216.535i 1.18325i
\(184\) 29.8870 + 15.8135i 0.162429 + 0.0859430i
\(185\) 67.6097 117.103i 0.365458 0.632992i
\(186\) −137.345 + 118.158i −0.738414 + 0.635257i
\(187\) 25.6984 14.8370i 0.137424 0.0793420i
\(188\) −53.0064 + 66.4257i −0.281949 + 0.353328i
\(189\) −48.8081 75.0415i −0.258244 0.397045i
\(190\) 26.9565 76.9991i 0.141877 0.405258i
\(191\) −36.6730 + 21.1732i −0.192005 + 0.110854i −0.592921 0.805261i \(-0.702025\pi\)
0.400916 + 0.916115i \(0.368692\pi\)
\(192\) −241.341 + 164.215i −1.25699 + 0.855286i
\(193\) −139.401 + 241.450i −0.722287 + 1.25104i 0.237794 + 0.971316i \(0.423576\pi\)
−0.960081 + 0.279722i \(0.909758\pi\)
\(194\) −52.1985 276.110i −0.269065 1.42325i
\(195\) 79.0094i 0.405176i
\(196\) −8.57683 + 195.812i −0.0437593 + 0.999042i
\(197\) 63.5394 0.322535 0.161268 0.986911i \(-0.448442\pi\)
0.161268 + 0.986911i \(0.448442\pi\)
\(198\) 51.3727 9.71198i 0.259458 0.0490504i
\(199\) 116.351 + 67.1755i 0.584680 + 0.337565i 0.762991 0.646409i \(-0.223730\pi\)
−0.178311 + 0.983974i \(0.557063\pi\)
\(200\) −20.7467 + 0.766619i −0.103733 + 0.00383310i
\(201\) 119.085 + 206.261i 0.592463 + 1.02618i
\(202\) −79.8059 27.9392i −0.395079 0.138313i
\(203\) −231.265 + 150.418i −1.13924 + 0.740977i
\(204\) −152.474 + 191.075i −0.747424 + 0.936644i
\(205\) 144.510 + 250.298i 0.704926 + 1.22097i
\(206\) −126.330 146.844i −0.613253 0.712837i
\(207\) 43.2057 + 24.9448i 0.208723 + 0.120506i
\(208\) −38.6987 + 35.8625i −0.186051 + 0.172416i
\(209\) −17.1970 −0.0822821
\(210\) 242.326 231.944i 1.15393 1.10450i
\(211\) 239.385i 1.13453i −0.823536 0.567264i \(-0.808002\pi\)
0.823536 0.567264i \(-0.191998\pi\)
\(212\) 28.7164 190.121i 0.135455 0.896796i
\(213\) 205.481 355.903i 0.964699 1.67091i
\(214\) 3.40652 + 3.95969i 0.0159183 + 0.0185032i
\(215\) 356.051 205.566i 1.65605 0.956122i
\(216\) −86.6504 + 54.3899i −0.401159 + 0.251805i
\(217\) 138.831 7.37446i 0.639775 0.0339837i
\(218\) 14.6001 + 5.11134i 0.0669729 + 0.0234465i
\(219\) −164.302 + 94.8600i −0.750239 + 0.433151i
\(220\) 16.9878 + 43.3238i 0.0772174 + 0.196926i
\(221\) −22.0917 + 38.2640i −0.0999626 + 0.173140i
\(222\) 230.727 43.6189i 1.03931 0.196481i
\(223\) 1.49794i 0.00671723i −0.999994 0.00335862i \(-0.998931\pi\)
0.999994 0.00335862i \(-0.00106908\pi\)
\(224\) 223.598 + 13.4111i 0.998206 + 0.0598711i
\(225\) −30.6320 −0.136142
\(226\) −12.8358 67.8963i −0.0567954 0.300426i
\(227\) −12.8691 7.42998i −0.0566921 0.0327312i 0.471386 0.881927i \(-0.343754\pi\)
−0.528078 + 0.849196i \(0.677087\pi\)
\(228\) 131.892 51.7167i 0.578475 0.226828i
\(229\) −134.196 232.435i −0.586010 1.01500i −0.994749 0.102348i \(-0.967364\pi\)
0.408738 0.912652i \(-0.365969\pi\)
\(230\) −14.6727 + 41.9112i −0.0637942 + 0.182223i
\(231\) −63.0251 32.0567i −0.272836 0.138773i
\(232\) 167.620 + 267.042i 0.722501 + 1.15104i
\(233\) −41.2942 71.5236i −0.177228 0.306968i 0.763702 0.645569i \(-0.223380\pi\)
−0.940930 + 0.338601i \(0.890046\pi\)
\(234\) −59.0137 + 50.7695i −0.252195 + 0.216964i
\(235\) −96.6534 55.8029i −0.411291 0.237459i
\(236\) 305.074 + 46.0792i 1.29268 + 0.195251i
\(237\) −600.581 −2.53410
\(238\) 182.211 44.5733i 0.765594 0.187283i
\(239\) 205.327i 0.859111i −0.903041 0.429555i \(-0.858670\pi\)
0.903041 0.429555i \(-0.141330\pi\)
\(240\) −260.577 281.185i −1.08574 1.17160i
\(241\) 7.72782 13.3850i 0.0320656 0.0555393i −0.849547 0.527513i \(-0.823125\pi\)
0.881613 + 0.471973i \(0.156458\pi\)
\(242\) −176.017 + 151.428i −0.727345 + 0.625734i
\(243\) 288.902 166.797i 1.18890 0.686409i
\(244\) −148.430 118.445i −0.608322 0.485429i
\(245\) −255.954 + 27.2685i −1.04471 + 0.111300i
\(246\) −165.839 + 473.704i −0.674141 + 1.92562i
\(247\) 22.1752 12.8028i 0.0897780 0.0518334i
\(248\) −5.86713 158.780i −0.0236578 0.640240i
\(249\) 26.9940 46.7549i 0.108410 0.187771i
\(250\) 43.7260 + 231.294i 0.174904 + 0.925174i
\(251\) 410.701i 1.63626i 0.575034 + 0.818129i \(0.304989\pi\)
−0.575034 + 0.818129i \(0.695011\pi\)
\(252\) 328.957 + 31.9567i 1.30538 + 0.126812i
\(253\) 9.36045 0.0369978
\(254\) −105.096 + 19.8684i −0.413764 + 0.0782220i
\(255\) −278.026 160.518i −1.09030 0.629484i
\(256\) 19.4476 255.260i 0.0759674 0.997110i
\(257\) 172.787 + 299.275i 0.672322 + 1.16450i 0.977244 + 0.212118i \(0.0680362\pi\)
−0.304922 + 0.952377i \(0.598630\pi\)
\(258\) 673.847 + 235.907i 2.61181 + 0.914366i
\(259\) −160.605 81.6890i −0.620096 0.315402i
\(260\) −54.1593 43.2181i −0.208305 0.166224i
\(261\) 232.601 + 402.876i 0.891190 + 1.54359i
\(262\) 168.988 + 196.429i 0.644991 + 0.749728i
\(263\) −262.276 151.425i −0.997245 0.575760i −0.0898132 0.995959i \(-0.528627\pi\)
−0.907432 + 0.420199i \(0.861960\pi\)
\(264\) −37.7935 + 71.4282i −0.143157 + 0.270562i
\(265\) 252.513 0.952879
\(266\) −104.366 30.4277i −0.392352 0.114390i
\(267\) 141.913i 0.531510i
\(268\) −206.528 31.1945i −0.770625 0.116398i
\(269\) 177.668 307.730i 0.660476 1.14398i −0.320014 0.947413i \(-0.603688\pi\)
0.980491 0.196566i \(-0.0629790\pi\)
\(270\) −87.6231 101.852i −0.324530 0.377229i
\(271\) −413.381 + 238.666i −1.52539 + 0.880685i −0.525844 + 0.850581i \(0.676251\pi\)
−0.999547 + 0.0301040i \(0.990416\pi\)
\(272\) −47.5748 209.036i −0.174907 0.768516i
\(273\) 105.135 5.58459i 0.385111 0.0204564i
\(274\) −307.558 107.673i −1.12247 0.392966i
\(275\) −4.97728 + 2.87364i −0.0180992 + 0.0104496i
\(276\) −71.7900 + 28.1498i −0.260109 + 0.101992i
\(277\) −44.4671 + 77.0192i −0.160531 + 0.278048i −0.935059 0.354492i \(-0.884654\pi\)
0.774528 + 0.632539i \(0.217987\pi\)
\(278\) −489.806 + 92.5976i −1.76189 + 0.333085i
\(279\) 234.434i 0.840267i
\(280\) 26.4408 + 292.983i 0.0944313 + 1.04637i
\(281\) −195.954 −0.697347 −0.348673 0.937244i \(-0.613368\pi\)
−0.348673 + 0.937244i \(0.613368\pi\)
\(282\) −36.0016 190.435i −0.127665 0.675300i
\(283\) 319.080 + 184.221i 1.12749 + 0.650957i 0.943303 0.331934i \(-0.107701\pi\)
0.184189 + 0.982891i \(0.441034\pi\)
\(284\) 131.567 + 335.532i 0.463263 + 1.18145i
\(285\) 93.0254 + 161.125i 0.326405 + 0.565350i
\(286\) −4.82616 + 13.7855i −0.0168747 + 0.0482011i
\(287\) 322.850 209.986i 1.12491 0.731660i
\(288\) 42.5823 375.312i 0.147855 1.30317i
\(289\) 54.7352 + 94.8041i 0.189395 + 0.328042i
\(290\) −313.890 + 270.040i −1.08238 + 0.931171i
\(291\) 554.983 + 320.419i 1.90716 + 1.10110i
\(292\) 24.8487 164.514i 0.0850985 0.563405i
\(293\) −307.799 −1.05051 −0.525254 0.850946i \(-0.676030\pi\)
−0.525254 + 0.850946i \(0.676030\pi\)
\(294\) −325.769 306.061i −1.10806 1.04103i
\(295\) 405.190i 1.37353i
\(296\) −96.3079 + 182.018i −0.325365 + 0.614927i
\(297\) −14.1608 + 24.5273i −0.0476796 + 0.0825835i
\(298\) 265.668 228.554i 0.891504 0.766960i
\(299\) −12.0701 + 6.96869i −0.0403683 + 0.0233067i
\(300\) 29.5314 37.0077i 0.0984380 0.123359i
\(301\) −298.707 459.256i −0.992383 1.52577i
\(302\) 52.6594 150.417i 0.174369 0.498070i
\(303\) 166.998 96.4164i 0.551149 0.318206i
\(304\) −36.6943 + 118.699i −0.120705 + 0.390456i
\(305\) 124.693 215.975i 0.408831 0.708116i
\(306\) −58.7582 310.809i −0.192020 1.01571i
\(307\) 192.082i 0.625675i 0.949807 + 0.312838i \(0.101280\pi\)
−0.949807 + 0.312838i \(0.898720\pi\)
\(308\) 56.4489 25.6674i 0.183276 0.0833358i
\(309\) 441.761 1.42965
\(310\) 205.032 38.7612i 0.661394 0.125036i
\(311\) −441.033 254.630i −1.41811 0.818747i −0.421978 0.906606i \(-0.638664\pi\)
−0.996133 + 0.0878588i \(0.971998\pi\)
\(312\) −4.44311 120.242i −0.0142407 0.385391i
\(313\) −160.504 278.002i −0.512794 0.888185i −0.999890 0.0148364i \(-0.995277\pi\)
0.487096 0.873348i \(-0.338056\pi\)
\(314\) 202.635 + 70.9402i 0.645333 + 0.225924i
\(315\) 23.0232 + 433.434i 0.0730895 + 1.37598i
\(316\) 328.518 411.686i 1.03961 1.30280i
\(317\) −48.8820 84.6662i −0.154202 0.267086i 0.778566 0.627563i \(-0.215947\pi\)
−0.932768 + 0.360477i \(0.882614\pi\)
\(318\) 285.976 + 332.414i 0.899295 + 1.04533i
\(319\) 75.5889 + 43.6413i 0.236956 + 0.136807i
\(320\) 335.282 24.8122i 1.04776 0.0775380i
\(321\) −11.9122 −0.0371096
\(322\) 56.8071 + 16.5621i 0.176420 + 0.0514350i
\(323\) 104.043i 0.322114i
\(324\) −28.6183 + 189.471i −0.0883281 + 0.584788i
\(325\) 4.27875 7.41101i 0.0131654 0.0228031i
\(326\) −109.582 127.377i −0.336142 0.390726i
\(327\) −30.5515 + 17.6389i −0.0934297 + 0.0539416i
\(328\) −234.001 372.795i −0.713417 1.13657i
\(329\) −67.4234 + 132.558i −0.204934 + 0.402912i
\(330\) −100.166 35.0669i −0.303532 0.106263i
\(331\) 264.468 152.690i 0.798996 0.461300i −0.0441241 0.999026i \(-0.514050\pi\)
0.843120 + 0.537726i \(0.180716\pi\)
\(332\) 17.2839 + 44.0788i 0.0520598 + 0.132767i
\(333\) −151.920 + 263.132i −0.456215 + 0.790187i
\(334\) 11.9612 2.26127i 0.0358121 0.00677026i
\(335\) 274.304i 0.818818i
\(336\) −355.745 + 366.616i −1.05877 + 1.09112i
\(337\) 385.052 1.14259 0.571293 0.820746i \(-0.306442\pi\)
0.571293 + 0.820746i \(0.306442\pi\)
\(338\) 58.7468 + 310.748i 0.173807 + 0.919373i
\(339\) 136.472 + 78.7921i 0.402572 + 0.232425i
\(340\) 262.112 102.778i 0.770919 0.302287i
\(341\) −21.9927 38.0924i −0.0644946 0.111708i
\(342\) −60.5715 + 173.017i −0.177110 + 0.505899i
\(343\) 54.3769 + 338.662i 0.158533 + 0.987354i
\(344\) −530.303 + 332.868i −1.54158 + 0.967638i
\(345\) −50.6345 87.7015i −0.146767 0.254207i
\(346\) 211.580 182.022i 0.611502 0.526075i
\(347\) −351.494 202.935i −1.01295 0.584827i −0.100897 0.994897i \(-0.532171\pi\)
−0.912054 + 0.410070i \(0.865504\pi\)
\(348\) −710.973 107.388i −2.04303 0.308585i
\(349\) 597.434 1.71185 0.855923 0.517103i \(-0.172990\pi\)
0.855923 + 0.517103i \(0.172990\pi\)
\(350\) −35.2909 + 8.63301i −0.100831 + 0.0246657i
\(351\) 42.1700i 0.120142i
\(352\) −28.2896 64.9779i −0.0803682 0.184596i
\(353\) −254.527 + 440.853i −0.721039 + 1.24888i 0.239544 + 0.970885i \(0.423002\pi\)
−0.960584 + 0.277991i \(0.910331\pi\)
\(354\) −533.402 + 458.886i −1.50679 + 1.29629i
\(355\) −409.899 + 236.656i −1.15465 + 0.666635i
\(356\) 97.2787 + 77.6266i 0.273255 + 0.218052i
\(357\) −193.945 + 381.307i −0.543264 + 1.06809i
\(358\) 102.894 293.908i 0.287413 0.820972i
\(359\) 462.550 267.054i 1.28844 0.743882i 0.310065 0.950715i \(-0.399649\pi\)
0.978376 + 0.206834i \(0.0663159\pi\)
\(360\) 495.713 18.3173i 1.37698 0.0508814i
\(361\) −150.352 + 260.417i −0.416487 + 0.721377i
\(362\) −36.0844 190.873i −0.0996807 0.527273i
\(363\) 529.524i 1.45874i
\(364\) −53.6809 + 75.1230i −0.147475 + 0.206382i
\(365\) 218.503 0.598640
\(366\) 425.533 80.4468i 1.16266 0.219800i
\(367\) −279.779 161.530i −0.762341 0.440138i 0.0677948 0.997699i \(-0.478404\pi\)
−0.830136 + 0.557562i \(0.811737\pi\)
\(368\) 19.9730 64.6086i 0.0542745 0.175567i
\(369\) −324.714 562.422i −0.879985 1.52418i
\(370\) −255.249 89.3599i −0.689862 0.241513i
\(371\) −17.8483 336.011i −0.0481086 0.905691i
\(372\) 283.229 + 226.011i 0.761368 + 0.607557i
\(373\) −4.10428 7.10883i −0.0110034 0.0190585i 0.860471 0.509499i \(-0.170169\pi\)
−0.871475 + 0.490440i \(0.836836\pi\)
\(374\) −38.7049 44.9900i −0.103489 0.120294i
\(375\) −464.901 268.411i −1.23974 0.715762i
\(376\) 150.232 + 79.4894i 0.399553 + 0.211408i
\(377\) −129.961 −0.344724
\(378\) −129.338 + 123.797i −0.342163 + 0.327504i
\(379\) 51.9349i 0.137031i −0.997650 0.0685157i \(-0.978174\pi\)
0.997650 0.0685157i \(-0.0218263\pi\)
\(380\) −161.333 24.3682i −0.424560 0.0641268i
\(381\) 121.962 211.244i 0.320109 0.554445i
\(382\) 55.2340 + 64.2032i 0.144592 + 0.168071i
\(383\) −94.1005 + 54.3289i −0.245693 + 0.141851i −0.617791 0.786343i \(-0.711972\pi\)
0.372097 + 0.928194i \(0.378639\pi\)
\(384\) 412.376 + 413.273i 1.07390 + 1.07623i
\(385\) 44.4021 + 68.2673i 0.115330 + 0.177318i
\(386\) 526.286 + 184.247i 1.36344 + 0.477324i
\(387\) −800.049 + 461.909i −2.06731 + 1.19356i
\(388\) −523.217 + 205.160i −1.34850 + 0.528763i
\(389\) 51.3814 88.9951i 0.132086 0.228779i −0.792395 0.610009i \(-0.791166\pi\)
0.924480 + 0.381230i \(0.124499\pi\)
\(390\) 155.268 29.3534i 0.398124 0.0752652i
\(391\) 56.6315i 0.144837i
\(392\) 387.995 55.8927i 0.989783 0.142584i
\(393\) −590.929 −1.50364
\(394\) −23.6061 124.867i −0.0599139 0.316921i
\(395\) 599.028 + 345.849i 1.51653 + 0.875567i
\(396\) −38.1718 97.3489i −0.0963934 0.245831i
\(397\) 195.656 + 338.887i 0.492837 + 0.853619i 0.999966 0.00825158i \(-0.00262659\pi\)
−0.507129 + 0.861870i \(0.669293\pi\)
\(398\) 88.7859 253.609i 0.223080 0.637210i
\(399\) 207.828 135.175i 0.520873 0.338784i
\(400\) 9.21433 + 40.4864i 0.0230358 + 0.101216i
\(401\) −110.175 190.829i −0.274751 0.475883i 0.695321 0.718699i \(-0.255262\pi\)
−0.970072 + 0.242816i \(0.921929\pi\)
\(402\) 361.101 310.655i 0.898260 0.772773i
\(403\) 56.7183 + 32.7463i 0.140740 + 0.0812564i
\(404\) −25.2565 + 167.214i −0.0625160 + 0.413895i
\(405\) −251.650 −0.621359
\(406\) 381.520 + 398.597i 0.939704 + 0.981766i
\(407\) 57.0072i 0.140067i
\(408\) 432.147 + 228.653i 1.05918 + 0.560425i
\(409\) −267.662 + 463.605i −0.654431 + 1.13351i 0.327605 + 0.944815i \(0.393759\pi\)
−0.982036 + 0.188694i \(0.939575\pi\)
\(410\) 438.196 376.980i 1.06877 0.919463i
\(411\) 643.581 371.572i 1.56589 0.904068i
\(412\) −241.643 + 302.818i −0.586512 + 0.734995i
\(413\) 539.174 28.6399i 1.30551 0.0693461i
\(414\) 32.9696 94.1748i 0.0796367 0.227475i
\(415\) −53.8484 + 31.0894i −0.129755 + 0.0749141i
\(416\) 84.8539 + 62.7267i 0.203976 + 0.150785i
\(417\) 568.408 984.512i 1.36309 2.36094i
\(418\) 6.38899 + 33.7953i 0.0152847 + 0.0808500i
\(419\) 550.175i 1.31307i 0.754297 + 0.656534i \(0.227978\pi\)
−0.754297 + 0.656534i \(0.772022\pi\)
\(420\) −545.843 390.045i −1.29963 0.928680i
\(421\) −470.081 −1.11658 −0.558291 0.829645i \(-0.688543\pi\)
−0.558291 + 0.829645i \(0.688543\pi\)
\(422\) −470.438 + 88.9360i −1.11478 + 0.210749i
\(423\) 217.181 + 125.389i 0.513430 + 0.296429i
\(424\) −384.292 + 14.2001i −0.906349 + 0.0334909i
\(425\) 17.3857 + 30.1130i 0.0409076 + 0.0708540i
\(426\) −775.758 271.585i −1.82103 0.637522i
\(427\) −296.205 150.660i −0.693689 0.352834i
\(428\) 6.51596 8.16556i 0.0152242 0.0190784i
\(429\) −16.6548 28.8470i −0.0388224 0.0672424i
\(430\) −536.256 623.336i −1.24711 1.44962i
\(431\) 534.589 + 308.645i 1.24035 + 0.716114i 0.969165 0.246415i \(-0.0792525\pi\)
0.271181 + 0.962528i \(0.412586\pi\)
\(432\) 139.079 + 150.078i 0.321941 + 0.347402i
\(433\) 189.923 0.438621 0.219310 0.975655i \(-0.429619\pi\)
0.219310 + 0.975655i \(0.429619\pi\)
\(434\) −66.0706 270.090i −0.152236 0.622327i
\(435\) 944.295i 2.17079i
\(436\) 4.62055 30.5909i 0.0105976 0.0701627i
\(437\) −16.4098 + 28.4227i −0.0375511 + 0.0650404i
\(438\) 247.459 + 287.643i 0.564976 + 0.656720i
\(439\) 78.0565 45.0659i 0.177805 0.102656i −0.408456 0.912778i \(-0.633933\pi\)
0.586261 + 0.810122i \(0.300599\pi\)
\(440\) 78.8282 49.4799i 0.179155 0.112454i
\(441\) 575.130 61.2725i 1.30415 0.138940i
\(442\) 83.4035 + 29.1987i 0.188696 + 0.0660604i
\(443\) −199.870 + 115.395i −0.451174 + 0.260486i −0.708326 0.705886i \(-0.750549\pi\)
0.257152 + 0.966371i \(0.417216\pi\)
\(444\) −171.439 437.218i −0.386123 0.984725i
\(445\) −81.7218 + 141.546i −0.183645 + 0.318082i
\(446\) −2.94374 + 0.556514i −0.00660032 + 0.00124779i
\(447\) 799.225i 1.78798i
\(448\) −56.7154 444.396i −0.126597 0.991954i
\(449\) 176.049 0.392091 0.196045 0.980595i \(-0.437190\pi\)
0.196045 + 0.980595i \(0.437190\pi\)
\(450\) 11.3804 + 60.1977i 0.0252897 + 0.133773i
\(451\) −105.523 60.9240i −0.233976 0.135086i
\(452\) −128.661 + 50.4495i −0.284647 + 0.111614i
\(453\) 181.725 + 314.756i 0.401158 + 0.694826i
\(454\) −9.82022 + 28.0506i −0.0216304 + 0.0617855i
\(455\) −108.079 54.9728i −0.237537 0.120819i
\(456\) −150.634 239.980i −0.330337 0.526271i
\(457\) 22.3534 + 38.7173i 0.0489134 + 0.0847205i 0.889445 0.457041i \(-0.151091\pi\)
−0.840532 + 0.541762i \(0.817757\pi\)
\(458\) −406.923 + 350.075i −0.888477 + 0.764357i
\(459\) 148.392 + 85.6742i 0.323294 + 0.186654i
\(460\) 87.8147 + 13.2638i 0.190902 + 0.0288343i
\(461\) 291.131 0.631520 0.315760 0.948839i \(-0.397740\pi\)
0.315760 + 0.948839i \(0.397740\pi\)
\(462\) −39.5825 + 135.766i −0.0856764 + 0.293866i
\(463\) 235.766i 0.509213i 0.967045 + 0.254607i \(0.0819460\pi\)
−0.967045 + 0.254607i \(0.918054\pi\)
\(464\) 462.514 428.617i 0.996798 0.923743i
\(465\) −237.935 + 412.115i −0.511688 + 0.886269i
\(466\) −125.216 + 107.723i −0.268704 + 0.231166i
\(467\) −254.414 + 146.886i −0.544784 + 0.314531i −0.747015 0.664807i \(-0.768514\pi\)
0.202232 + 0.979338i \(0.435181\pi\)
\(468\) 121.696 + 97.1114i 0.260035 + 0.207503i
\(469\) −365.008 + 19.3886i −0.778269 + 0.0413402i
\(470\) −73.7547 + 210.674i −0.156925 + 0.448243i
\(471\) −424.024 + 244.810i −0.900263 + 0.519767i
\(472\) −22.7860 616.647i −0.0482754 1.30646i
\(473\) −86.6647 + 150.108i −0.183224 + 0.317353i
\(474\) 223.127 + 1180.26i 0.470732 + 2.48999i
\(475\) 20.1511i 0.0424234i
\(476\) −155.290 341.520i −0.326240 0.717480i
\(477\) −567.398 −1.18951
\(478\) −403.508 + 76.2829i −0.844158 + 0.159588i
\(479\) 559.224 + 322.868i 1.16748 + 0.674046i 0.953086 0.302701i \(-0.0978882\pi\)
0.214396 + 0.976747i \(0.431222\pi\)
\(480\) −455.772 + 616.548i −0.949525 + 1.28448i
\(481\) −42.4409 73.5098i −0.0882348 0.152827i
\(482\) −29.1751 10.2139i −0.0605292 0.0211906i
\(483\) −113.123 + 73.5768i −0.234209 + 0.152333i
\(484\) 362.978 + 289.650i 0.749954 + 0.598449i
\(485\) −369.032 639.182i −0.760891 1.31790i
\(486\) −435.121 505.779i −0.895311 1.04070i
\(487\) −149.221 86.1527i −0.306408 0.176905i 0.338910 0.940819i \(-0.389942\pi\)
−0.645318 + 0.763914i \(0.723275\pi\)
\(488\) −177.622 + 335.699i −0.363979 + 0.687907i
\(489\) 383.195 0.783631
\(490\) 148.679 + 492.867i 0.303427 + 1.00585i
\(491\) 432.143i 0.880129i 0.897966 + 0.440064i \(0.145044\pi\)
−0.897966 + 0.440064i \(0.854956\pi\)
\(492\) 992.530 + 149.915i 2.01734 + 0.304705i
\(493\) 264.033 457.319i 0.535564 0.927625i
\(494\) −33.3985 38.8219i −0.0676083 0.0785869i
\(495\) 118.925 68.6615i 0.240253 0.138710i
\(496\) −309.852 + 70.5196i −0.624702 + 0.142177i
\(497\) 343.883 + 528.713i 0.691918 + 1.06381i
\(498\) −101.911 35.6780i −0.204641 0.0716425i
\(499\) 426.464 246.219i 0.854636 0.493425i −0.00757609 0.999971i \(-0.502412\pi\)
0.862213 + 0.506547i \(0.169078\pi\)
\(500\) 438.291 171.860i 0.876582 0.343719i
\(501\) −13.8807 + 24.0421i −0.0277061 + 0.0479883i
\(502\) 807.106 152.583i 1.60778 0.303950i
\(503\) 723.078i 1.43753i −0.695253 0.718766i \(-0.744707\pi\)
0.695253 0.718766i \(-0.255293\pi\)
\(504\) −59.4126 658.335i −0.117882 1.30622i
\(505\) −222.089 −0.439779
\(506\) −3.47758 18.3951i −0.00687268 0.0363539i
\(507\) −624.605 360.616i −1.23196 0.711274i
\(508\) 78.0903 + 199.152i 0.153721 + 0.392032i
\(509\) −232.354 402.449i −0.456491 0.790666i 0.542281 0.840197i \(-0.317561\pi\)
−0.998773 + 0.0495308i \(0.984227\pi\)
\(510\) −212.158 + 606.010i −0.415995 + 1.18825i
\(511\) −15.4444 290.756i −0.0302239 0.568994i
\(512\) −508.860 + 56.6155i −0.993868 + 0.110577i
\(513\) −49.6508 85.9978i −0.0967853 0.167637i
\(514\) 523.940 450.745i 1.01934 0.876936i
\(515\) −440.619 254.391i −0.855570 0.493964i
\(516\) 213.255 1411.88i 0.413284 2.73620i
\(517\) 47.0519 0.0910095
\(518\) −100.867 + 345.968i −0.194724 + 0.667892i
\(519\) 636.508i 1.22641i
\(520\) −64.8107 + 122.490i −0.124636 + 0.235557i
\(521\) −19.9350 + 34.5283i −0.0382629 + 0.0662732i −0.884523 0.466497i \(-0.845516\pi\)
0.846260 + 0.532770i \(0.178849\pi\)
\(522\) 705.313 606.781i 1.35117 1.16241i
\(523\) 678.225 391.574i 1.29680 0.748707i 0.316948 0.948443i \(-0.397342\pi\)
0.979850 + 0.199736i \(0.0640086\pi\)
\(524\) 323.238 405.070i 0.616866 0.773034i
\(525\) 37.5635 73.8519i 0.0715496 0.140670i
\(526\) −200.138 + 571.678i −0.380491 + 1.08684i
\(527\) −230.462 + 133.057i −0.437310 + 0.252481i
\(528\) 154.411 + 47.7344i 0.292445 + 0.0904061i
\(529\) −255.568 + 442.657i −0.483115 + 0.836780i
\(530\) −93.8132 496.236i −0.177006 0.936294i
\(531\) 910.465i 1.71462i
\(532\) −21.0226 + 216.403i −0.0395161 + 0.406772i
\(533\) 181.427 0.340389
\(534\) −278.887 + 52.7234i −0.522260 + 0.0987329i
\(535\) 11.8814 + 6.85972i 0.0222082 + 0.0128219i
\(536\) 15.4256 + 417.455i 0.0287790 + 0.778835i
\(537\) 355.081 + 615.018i 0.661231 + 1.14529i
\(538\) −670.756 234.824i −1.24676 0.436476i
\(539\) 87.7027 63.9098i 0.162714 0.118571i
\(540\) −167.605 + 210.036i −0.310379 + 0.388955i
\(541\) −139.052 240.845i −0.257027 0.445184i 0.708417 0.705794i \(-0.249410\pi\)
−0.965444 + 0.260610i \(0.916076\pi\)
\(542\) 622.602 + 723.704i 1.14871 + 1.33525i
\(543\) 383.655 + 221.503i 0.706547 + 0.407925i
\(544\) −393.121 + 171.154i −0.722650 + 0.314622i
\(545\) 40.6300 0.0745505
\(546\) −50.0345 204.536i −0.0916383 0.374609i
\(547\) 180.254i 0.329532i 0.986333 + 0.164766i \(0.0526869\pi\)
−0.986333 + 0.164766i \(0.947313\pi\)
\(548\) −97.3339 + 644.412i −0.177617 + 1.17593i
\(549\) −280.187 + 485.298i −0.510359 + 0.883967i
\(550\) 7.49640 + 8.71370i 0.0136298 + 0.0158431i
\(551\) −265.031 + 153.015i −0.480999 + 0.277705i
\(552\) 81.9911 + 130.623i 0.148535 + 0.236636i
\(553\) 417.870 821.554i 0.755642 1.48563i
\(554\) 167.878 + 58.7722i 0.303028 + 0.106087i
\(555\) 534.122 308.376i 0.962383 0.555632i
\(556\) 363.944 + 928.161i 0.654576 + 1.66935i
\(557\) −214.374 + 371.307i −0.384873 + 0.666619i −0.991752 0.128175i \(-0.959088\pi\)
0.606879 + 0.794794i \(0.292421\pi\)
\(558\) −460.708 + 87.0967i −0.825642 + 0.156087i
\(559\) 258.082i 0.461685i
\(560\) 565.945 160.810i 1.01062 0.287160i
\(561\) 135.346 0.241259
\(562\) 72.8007 + 385.088i 0.129539 + 0.685209i
\(563\) −654.562 377.912i −1.16263 0.671246i −0.210699 0.977551i \(-0.567574\pi\)
−0.951934 + 0.306305i \(0.900907\pi\)
\(564\) −360.865 + 141.500i −0.639832 + 0.250886i
\(565\) −90.7460 157.177i −0.160612 0.278189i
\(566\) 243.485 695.495i 0.430186 1.22879i
\(567\) 17.7873 + 334.863i 0.0313709 + 0.590588i
\(568\) 610.505 383.210i 1.07483 0.674665i
\(569\) −150.795 261.185i −0.265018 0.459025i 0.702550 0.711634i \(-0.252045\pi\)
−0.967568 + 0.252609i \(0.918711\pi\)
\(570\) 282.080 242.673i 0.494878 0.425743i
\(571\) −144.347 83.3386i −0.252796 0.145952i 0.368248 0.929728i \(-0.379958\pi\)
−0.621044 + 0.783776i \(0.713291\pi\)
\(572\) 28.8842 + 4.36276i 0.0504968 + 0.00762720i
\(573\) −193.146 −0.337079
\(574\) −532.608 556.448i −0.927889 0.969421i
\(575\) 10.9684i 0.0190755i
\(576\) −753.381 + 55.7531i −1.30795 + 0.0967935i
\(577\) 220.904 382.616i 0.382849 0.663113i −0.608620 0.793462i \(-0.708276\pi\)
0.991468 + 0.130349i \(0.0416098\pi\)
\(578\) 165.973 142.787i 0.287151 0.247036i
\(579\) −1101.28 + 635.826i −1.90204 + 1.09814i
\(580\) 647.295 + 516.529i 1.11603 + 0.890567i
\(581\) 45.1758 + 69.4569i 0.0777553 + 0.119547i
\(582\) 423.499 1209.69i 0.727662 2.07850i
\(583\) −92.1945 + 53.2285i −0.158138 + 0.0913011i
\(584\) −332.534 + 12.2876i −0.569407 + 0.0210404i
\(585\) −102.235 + 177.076i −0.174760 + 0.302693i
\(586\) 114.353 + 604.883i 0.195142 + 1.03222i
\(587\) 10.3386i 0.0176127i −0.999961 0.00880633i \(-0.997197\pi\)
0.999961 0.00880633i \(-0.00280318\pi\)
\(588\) −480.440 + 753.906i −0.817075 + 1.28215i
\(589\) 154.222 0.261837
\(590\) 796.276 150.536i 1.34962 0.255145i
\(591\) 250.983 + 144.905i 0.424676 + 0.245187i
\(592\) 393.481 + 121.640i 0.664664 + 0.205473i
\(593\) 41.9808 + 72.7128i 0.0707939 + 0.122619i 0.899249 0.437436i \(-0.144113\pi\)
−0.828456 + 0.560055i \(0.810780\pi\)
\(594\) 53.4618 + 18.7164i 0.0900030 + 0.0315091i
\(595\) 413.022 268.636i 0.694155 0.451489i
\(596\) −547.853 437.176i −0.919216 0.733517i
\(597\) 306.395 + 530.692i 0.513224 + 0.888931i
\(598\) 18.1791 + 21.1311i 0.0303998 + 0.0353363i
\(599\) −20.8257 12.0237i −0.0347674 0.0200730i 0.482516 0.875887i \(-0.339723\pi\)
−0.517283 + 0.855814i \(0.673057\pi\)
\(600\) −83.6985 44.2858i −0.139498 0.0738097i
\(601\) −493.245 −0.820708 −0.410354 0.911926i \(-0.634595\pi\)
−0.410354 + 0.911926i \(0.634595\pi\)
\(602\) −791.551 + 757.639i −1.31487 + 1.25854i
\(603\) 616.363i 1.02216i
\(604\) −315.162 47.6031i −0.521792 0.0788130i
\(605\) −304.930 + 528.155i −0.504017 + 0.872983i
\(606\) −251.520 292.363i −0.415049 0.482447i
\(607\) 430.310 248.440i 0.708913 0.409291i −0.101745 0.994810i \(-0.532443\pi\)
0.810658 + 0.585519i \(0.199109\pi\)
\(608\) 246.898 + 28.0126i 0.406082 + 0.0460734i
\(609\) −1256.54 + 66.7453i −2.06329 + 0.109598i
\(610\) −470.759 164.807i −0.771735 0.270176i
\(611\) −60.6726 + 35.0293i −0.0993005 + 0.0573312i
\(612\) −588.969 + 230.942i −0.962367 + 0.377357i
\(613\) 505.351 875.294i 0.824390 1.42789i −0.0779947 0.996954i \(-0.524852\pi\)
0.902385 0.430932i \(-0.141815\pi\)
\(614\) 377.478 71.3621i 0.614785 0.116225i
\(615\) 1318.25i 2.14350i
\(616\) −71.4132 101.397i −0.115931 0.164605i
\(617\) −149.276 −0.241938 −0.120969 0.992656i \(-0.538600\pi\)
−0.120969 + 0.992656i \(0.538600\pi\)
\(618\) −164.122 868.144i −0.265570 1.40476i
\(619\) −147.508 85.1640i −0.238301 0.137583i 0.376094 0.926581i \(-0.377267\pi\)
−0.614396 + 0.788998i \(0.710600\pi\)
\(620\) −152.346 388.527i −0.245720 0.626656i
\(621\) 27.0254 + 46.8093i 0.0435191 + 0.0753773i
\(622\) −336.545 + 961.313i −0.541070 + 1.54552i
\(623\) 194.128 + 98.7399i 0.311602 + 0.158491i
\(624\) −234.648 + 53.4037i −0.376038 + 0.0855828i
\(625\) 341.572 + 591.619i 0.546514 + 0.946591i
\(626\) −486.696 + 418.705i −0.777470 + 0.668857i
\(627\) −67.9287 39.2186i −0.108339 0.0625497i
\(628\) 64.1285 424.571i 0.102115 0.676069i
\(629\) 344.898 0.548328
\(630\) 843.226 206.274i 1.33845 0.327418i
\(631\) 853.611i 1.35279i −0.736538 0.676396i \(-0.763541\pi\)
0.736538 0.676396i \(-0.236459\pi\)
\(632\) −931.092 492.651i −1.47325 0.779511i
\(633\) 545.932 945.581i 0.862451 1.49381i
\(634\) −148.225 + 127.518i −0.233793 + 0.201132i
\(635\) −243.293 + 140.465i −0.383138 + 0.221205i
\(636\) 547.012 685.495i 0.860082 1.07782i
\(637\) −65.5113 + 147.704i −0.102844 + 0.231874i
\(638\) 57.6808 164.760i 0.0904087 0.258245i
\(639\) 921.047 531.767i 1.44139 0.832185i
\(640\) −173.324 649.675i −0.270819 1.01512i
\(641\) 382.305 662.173i 0.596420 1.03303i −0.396924 0.917851i \(-0.629922\pi\)
0.993345 0.115179i \(-0.0367442\pi\)
\(642\) 4.42559 + 23.4097i 0.00689345 + 0.0364637i
\(643\) 585.159i 0.910045i 0.890480 + 0.455022i \(0.150369\pi\)
−0.890480 + 0.455022i \(0.849631\pi\)
\(644\) 11.4428 117.790i 0.0177683 0.182904i
\(645\) 1875.22 2.90732
\(646\) 204.464 38.6539i 0.316508 0.0598357i
\(647\) 318.173 + 183.697i 0.491766 + 0.283921i 0.725307 0.688426i \(-0.241698\pi\)
−0.233541 + 0.972347i \(0.575031\pi\)
\(648\) 382.979 14.1516i 0.591017 0.0218389i
\(649\) −85.4122 147.938i −0.131606 0.227948i
\(650\) −16.1537 5.65523i −0.0248518 0.00870035i
\(651\) 565.207 + 287.483i 0.868213 + 0.441602i
\(652\) −209.608 + 262.673i −0.321484 + 0.402872i
\(653\) 475.089 + 822.878i 0.727548 + 1.26015i 0.957917 + 0.287047i \(0.0926736\pi\)
−0.230368 + 0.973104i \(0.573993\pi\)
\(654\) 46.0143 + 53.4863i 0.0703582 + 0.0817834i
\(655\) 589.401 + 340.291i 0.899849 + 0.519528i
\(656\) −645.678 + 598.356i −0.984265 + 0.912128i
\(657\) −490.979 −0.747304
\(658\) 285.551 + 83.2522i 0.433968 + 0.126523i
\(659\) 351.380i 0.533202i −0.963807 0.266601i \(-0.914099\pi\)
0.963807 0.266601i \(-0.0859006\pi\)
\(660\) −31.6998 + 209.872i −0.0480300 + 0.317989i
\(661\) −130.956 + 226.822i −0.198118 + 0.343150i −0.947918 0.318514i \(-0.896816\pi\)
0.749800 + 0.661664i \(0.230150\pi\)
\(662\) −398.320 463.002i −0.601692 0.699399i
\(663\) −174.526 + 100.763i −0.263238 + 0.151980i
\(664\) 80.2019 50.3422i 0.120786 0.0758165i
\(665\) −285.133 + 15.1457i −0.428771 + 0.0227755i
\(666\) 573.546 + 200.792i 0.861180 + 0.301490i
\(667\) 144.258 83.2876i 0.216279 0.124869i
\(668\) −8.88765 22.6660i −0.0133049 0.0339312i
\(669\) 3.41615 5.91694i 0.00510635 0.00884445i
\(670\) −539.060 + 101.909i −0.804567 + 0.152103i
\(671\) 105.139i 0.156690i
\(672\) 852.637 + 562.903i 1.26881 + 0.837653i
\(673\) −420.840 −0.625319 −0.312660 0.949865i \(-0.601220\pi\)
−0.312660 + 0.949865i \(0.601220\pi\)
\(674\) −143.054 756.700i −0.212246 1.12270i
\(675\) −28.7407 16.5935i −0.0425788 0.0245829i
\(676\) 588.854 230.897i 0.871085 0.341564i
\(677\) −447.752 775.529i −0.661377 1.14554i −0.980254 0.197742i \(-0.936639\pi\)
0.318878 0.947796i \(-0.396694\pi\)
\(678\) 104.140 297.466i 0.153598 0.438740i
\(679\) −824.456 + 536.239i −1.21422 + 0.789748i
\(680\) −299.357 476.917i −0.440232 0.701349i
\(681\) −33.8890 58.6974i −0.0497635 0.0861930i
\(682\) −66.6882 + 57.3718i −0.0977833 + 0.0841229i
\(683\) 17.6165 + 10.1709i 0.0257928 + 0.0148915i 0.512841 0.858484i \(-0.328593\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(684\) 362.516 + 54.7555i 0.529994 + 0.0800518i
\(685\) −855.890 −1.24947
\(686\) 645.334 232.680i 0.940720 0.339184i
\(687\) 1224.17i 1.78191i
\(688\) 851.166 + 918.481i 1.23716 + 1.33500i
\(689\) 79.2555 137.275i 0.115030 0.199237i
\(690\) −153.539 + 132.089i −0.222520 + 0.191434i
\(691\) 267.205 154.271i 0.386694 0.223258i −0.294033 0.955795i \(-0.594998\pi\)
0.680727 + 0.732538i \(0.261664\pi\)
\(692\) −436.314 348.170i −0.630511 0.503136i
\(693\) −99.7717 153.397i −0.143971 0.221352i
\(694\) −268.220 + 766.147i −0.386484 + 1.10396i
\(695\) −1133.88 + 654.645i −1.63148 + 0.941935i
\(696\) 53.1027 + 1437.09i 0.0762969 + 2.06479i
\(697\) −368.595 + 638.425i −0.528830 + 0.915961i
\(698\) −221.958 1174.07i −0.317991 1.68205i
\(699\) 376.695i 0.538905i
\(700\) 30.0767 + 66.1460i 0.0429667 + 0.0944943i
\(701\) −1110.45 −1.58410 −0.792048 0.610458i \(-0.790985\pi\)
−0.792048 + 0.610458i \(0.790985\pi\)
\(702\) −82.8721 + 15.6669i −0.118051 + 0.0223176i
\(703\) −173.101 99.9397i −0.246231 0.142162i
\(704\) −117.184 + 79.7350i −0.166454 + 0.113260i
\(705\) −254.523 440.847i −0.361026 0.625315i
\(706\) 960.922 + 336.409i 1.36108 + 0.476499i
\(707\) 15.6978 + 295.526i 0.0222034 + 0.418001i
\(708\) 1099.97 + 877.752i 1.55363 + 1.23976i
\(709\) 282.842 + 489.897i 0.398931 + 0.690969i 0.993594 0.113006i \(-0.0360478\pi\)
−0.594663 + 0.803975i \(0.702714\pi\)
\(710\) 617.358 + 717.608i 0.869519 + 1.01072i
\(711\) −1346.02 777.125i −1.89314 1.09300i
\(712\) 116.410 220.011i 0.163497 0.309004i
\(713\) −83.9442 −0.117734
\(714\) 821.395 + 239.477i 1.15041 + 0.335402i
\(715\) 38.3632i 0.0536548i
\(716\) −615.812 93.0141i −0.860073 0.129908i
\(717\) 468.261 811.052i 0.653084 1.13117i
\(718\) −696.657 809.784i −0.970275 1.12783i
\(719\) 635.440 366.872i 0.883784 0.510253i 0.0118796 0.999929i \(-0.496219\pi\)
0.871904 + 0.489677i \(0.162885\pi\)
\(720\) −220.163 967.365i −0.305782 1.34356i
\(721\) −307.367 + 604.299i −0.426306 + 0.838140i
\(722\) 567.628 + 198.720i 0.786188 + 0.275236i
\(723\) 61.0504 35.2475i 0.0844404 0.0487517i
\(724\) −361.695 + 141.826i −0.499579 + 0.195892i
\(725\) −51.1382 + 88.5740i −0.0705355 + 0.122171i
\(726\) −1040.62 + 196.728i −1.43335 + 0.270975i
\(727\) 482.678i 0.663931i −0.943292 0.331965i \(-0.892288\pi\)
0.943292 0.331965i \(-0.107712\pi\)
\(728\) 167.574 + 77.5837i 0.230185 + 0.106571i
\(729\) 1090.42 1.49577
\(730\) −81.1780 429.401i −0.111203 0.588220i
\(731\) 908.164 + 524.329i 1.24236 + 0.717276i
\(732\) −316.187 806.366i −0.431949 1.10159i
\(733\) 539.259 + 934.023i 0.735687 + 1.27425i 0.954421 + 0.298463i \(0.0964739\pi\)
−0.218734 + 0.975785i \(0.570193\pi\)
\(734\) −213.495 + 609.831i −0.290865 + 0.830832i
\(735\) −1073.21 476.005i −1.46016 0.647626i
\(736\) −134.389 15.2475i −0.182593 0.0207167i
\(737\) 57.8220 + 100.151i 0.0784559 + 0.135890i
\(738\) −984.629 + 847.076i −1.33419 + 1.14780i
\(739\) 8.61538 + 4.97409i 0.0116582 + 0.00673084i 0.505818 0.862640i \(-0.331191\pi\)
−0.494160 + 0.869371i \(0.664524\pi\)
\(740\) −80.7796 + 534.812i −0.109162 + 0.722718i
\(741\) 116.790 0.157612
\(742\) −653.695 + 159.910i −0.880991 + 0.215512i
\(743\) 1171.22i 1.57634i −0.615460 0.788168i \(-0.711030\pi\)
0.615460 0.788168i \(-0.288970\pi\)
\(744\) 338.931 640.566i 0.455552 0.860976i
\(745\) 460.240 797.159i 0.617772 1.07001i
\(746\) −12.4454 + 10.7068i −0.0166828 + 0.0143522i
\(747\) 120.998 69.8580i 0.161978 0.0935181i
\(748\) −74.0343 + 92.7771i −0.0989764 + 0.124034i
\(749\) 8.28821 16.2951i 0.0110657 0.0217557i
\(750\) −354.759 + 1013.34i −0.473012 + 1.35112i
\(751\) −697.394 + 402.641i −0.928620 + 0.536139i −0.886375 0.462968i \(-0.846784\pi\)
−0.0422454 + 0.999107i \(0.513451\pi\)
\(752\) 100.398 324.766i 0.133508 0.431870i
\(753\) −936.627 + 1622.29i −1.24386 + 2.15443i
\(754\) 48.2828 + 255.398i 0.0640356 + 0.338724i
\(755\) 418.590i 0.554424i
\(756\) 291.335 + 208.181i 0.385364 + 0.275371i
\(757\) 231.613 0.305962 0.152981 0.988229i \(-0.451113\pi\)
0.152981 + 0.988229i \(0.451113\pi\)
\(758\) −102.062 + 19.2948i −0.134646 + 0.0254548i
\(759\) 36.9741 + 21.3470i 0.0487143 + 0.0281252i
\(760\) 12.0500 + 326.103i 0.0158552 + 0.429082i
\(761\) 627.730 + 1087.26i 0.824875 + 1.42873i 0.902014 + 0.431706i \(0.142088\pi\)
−0.0771390 + 0.997020i \(0.524579\pi\)
\(762\) −460.445 161.197i −0.604259 0.211544i
\(763\) −2.87184 54.0651i −0.00376388 0.0708586i
\(764\) 105.651 132.398i 0.138287 0.173296i
\(765\) −415.408 719.507i −0.543017 0.940532i
\(766\) 141.727 + 164.741i 0.185022 + 0.215067i
\(767\) 220.275 + 127.176i 0.287190 + 0.165809i
\(768\) 658.955 963.937i 0.858014 1.25513i
\(769\) 496.997 0.646291 0.323145 0.946349i \(-0.395260\pi\)
0.323145 + 0.946349i \(0.395260\pi\)
\(770\) 117.662 112.621i 0.152808 0.146261i
\(771\) 1576.20i 2.04436i
\(772\) 166.556 1102.70i 0.215746 1.42837i
\(773\) −156.922 + 271.796i −0.203003 + 0.351612i −0.949495 0.313783i \(-0.898404\pi\)
0.746491 + 0.665395i \(0.231737\pi\)
\(774\) 1204.97 + 1400.64i 1.55681 + 1.80961i
\(775\) 44.6361 25.7707i 0.0575950 0.0332525i
\(776\) 597.563 + 952.000i 0.770056 + 1.22680i
\(777\) −448.099 688.943i −0.576704 0.886671i
\(778\) −193.982 67.9108i −0.249334 0.0872890i
\(779\) 369.987 213.612i 0.474951 0.274213i
\(780\) −115.370 294.227i −0.147911 0.377214i
\(781\) 99.7717 172.810i 0.127749 0.221267i
\(782\) −111.292 + 21.0396i −0.142317 + 0.0269049i
\(783\) 504.002i 0.643681i
\(784\) −253.987 741.719i −0.323963 0.946070i
\(785\) 563.904 0.718349
\(786\) 219.541 + 1161.29i 0.279314 + 1.47746i
\(787\) −384.151 221.789i −0.488120 0.281816i 0.235674 0.971832i \(-0.424270\pi\)
−0.723794 + 0.690016i \(0.757604\pi\)
\(788\) −236.617 + 92.7808i −0.300276 + 0.117742i
\(789\) −690.666 1196.27i −0.875369 1.51618i
\(790\) 457.109 1305.69i 0.578620 1.65278i
\(791\) −202.736 + 131.863i −0.256304 + 0.166704i
\(792\) −177.128 + 111.182i −0.223646 + 0.140381i
\(793\) −78.2743 135.575i −0.0987066 0.170965i
\(794\) 593.287 510.404i 0.747213 0.642827i
\(795\) 997.436 + 575.870i 1.25464 + 0.724365i
\(796\) −531.377 80.2607i −0.667559 0.100830i
\(797\) 338.961 0.425296 0.212648 0.977129i \(-0.431791\pi\)
0.212648 + 0.977129i \(0.431791\pi\)
\(798\) −342.856 358.203i −0.429645 0.448876i
\(799\) 284.668i 0.356280i
\(800\) 76.1401 33.1493i 0.0951752 0.0414367i
\(801\) 183.630 318.056i 0.229250 0.397073i
\(802\) −334.083 + 287.412i −0.416563 + 0.358369i
\(803\) −79.7774 + 46.0595i −0.0993492 + 0.0573593i
\(804\) −744.651 594.218i −0.926183 0.739077i
\(805\) 155.200 8.24394i 0.192795 0.0102409i
\(806\) 43.2809 123.628i 0.0536984 0.153385i
\(807\) 1403.59 810.365i 1.73927 1.00417i
\(808\) 337.990 12.4892i 0.418304 0.0154569i
\(809\) 468.506 811.477i 0.579118 1.00306i −0.416463 0.909153i \(-0.636731\pi\)
0.995581 0.0939086i \(-0.0299362\pi\)
\(810\) 93.4927 + 494.541i 0.115423 + 0.610544i
\(811\) 435.479i 0.536965i 0.963285 + 0.268482i \(0.0865221\pi\)
−0.963285 + 0.268482i \(0.913478\pi\)
\(812\) 641.577 897.845i 0.790119 1.10572i
\(813\) −2177.16 −2.67794
\(814\) 112.030 21.1792i 0.137629 0.0260187i
\(815\) −382.205 220.666i −0.468963 0.270756i
\(816\) 288.797 934.199i 0.353918 1.14485i
\(817\) −303.865 526.309i −0.371927 0.644197i
\(818\) 1010.51 + 353.770i 1.23535 + 0.432482i
\(819\) 242.855 + 123.524i 0.296527 + 0.150823i
\(820\) −903.635 721.083i −1.10199 0.879370i
\(821\) 80.4273 + 139.304i 0.0979627 + 0.169676i 0.910841 0.412757i \(-0.135434\pi\)
−0.812879 + 0.582433i \(0.802101\pi\)
\(822\) −969.312 1126.71i −1.17921 1.37070i
\(823\) 1336.09 + 771.393i 1.62344 + 0.937294i 0.985990 + 0.166804i \(0.0533446\pi\)
0.637451 + 0.770491i \(0.279989\pi\)
\(824\) 684.870 + 362.372i 0.831153 + 0.439772i
\(825\) −26.2140 −0.0317745
\(826\) −256.596 1048.94i −0.310649 1.26990i
\(827\) 888.264i 1.07408i 0.843557 + 0.537040i \(0.180458\pi\)
−0.843557 + 0.537040i \(0.819542\pi\)
\(828\) −197.320 29.8039i −0.238310 0.0359950i
\(829\) −108.276 + 187.539i −0.130610 + 0.226223i −0.923912 0.382605i \(-0.875027\pi\)
0.793302 + 0.608828i \(0.208360\pi\)
\(830\) 81.1022 + 94.2720i 0.0977135 + 0.113581i
\(831\) −351.293 + 202.819i −0.422736 + 0.244067i
\(832\) 91.7452 190.058i 0.110271 0.228435i
\(833\) −386.659 530.608i −0.464177 0.636985i
\(834\) −2145.93 751.266i −2.57306 0.900799i
\(835\) 27.6897 15.9867i 0.0331613 0.0191457i
\(836\) 64.0406 25.1112i 0.0766036 0.0300373i
\(837\) 126.994 219.960i 0.151725 0.262796i
\(838\) 1081.20 204.400i 1.29021 0.243914i
\(839\) 370.077i 0.441092i −0.975377 0.220546i \(-0.929216\pi\)
0.975377 0.220546i \(-0.0707840\pi\)
\(840\) −563.723 + 1217.60i −0.671098 + 1.44952i
\(841\) 712.249 0.846908
\(842\) 174.644 + 923.800i 0.207416 + 1.09715i
\(843\) −774.028 446.885i −0.918182 0.530113i
\(844\) 349.552 + 891.458i 0.414162 + 1.05623i
\(845\) 415.327 + 719.367i 0.491511 + 0.851322i
\(846\) 165.727 473.386i 0.195895 0.559558i
\(847\) 724.353 + 368.430i 0.855198 + 0.434982i
\(848\) 170.678 + 749.931i 0.201271 + 0.884353i
\(849\) 840.253 + 1455.36i 0.989697 + 1.71421i
\(850\) 52.7186 45.3538i 0.0620219 0.0533574i
\(851\) 94.2201 + 54.3980i 0.110717 + 0.0639224i
\(852\) −245.507 + 1625.41i −0.288154 + 1.90776i
\(853\) −459.525 −0.538716 −0.269358 0.963040i \(-0.586811\pi\)
−0.269358 + 0.963040i \(0.586811\pi\)
\(854\) −186.030 + 638.073i −0.217834 + 0.747158i
\(855\) 481.483i 0.563138i
\(856\) −18.4677 9.77145i −0.0215744 0.0114152i
\(857\) 31.0889 53.8476i 0.0362764 0.0628326i −0.847317 0.531087i \(-0.821784\pi\)
0.883594 + 0.468255i \(0.155117\pi\)
\(858\) −50.5022 + 43.4470i −0.0588604 + 0.0506376i
\(859\) −1139.98 + 658.169i −1.32710 + 0.766204i −0.984851 0.173404i \(-0.944523\pi\)
−0.342254 + 0.939608i \(0.611190\pi\)
\(860\) −1025.75 + 1285.43i −1.19273 + 1.49468i
\(861\) 1754.16 93.1775i 2.03735 0.108220i
\(862\) 407.937 1165.24i 0.473244 1.35178i
\(863\) −459.711 + 265.415i −0.532690 + 0.307549i −0.742111 0.670277i \(-0.766175\pi\)
0.209421 + 0.977826i \(0.432842\pi\)
\(864\) 243.261 329.073i 0.281552 0.380871i
\(865\) 366.538 634.862i 0.423743 0.733945i
\(866\) −70.5598 373.235i −0.0814779 0.430987i
\(867\) 499.307i 0.575902i
\(868\) −506.232 + 230.185i −0.583217 + 0.265190i
\(869\) −291.613 −0.335574
\(870\) −1855.72 + 350.823i −2.13301 + 0.403245i
\(871\) −149.121 86.0950i −0.171207 0.0988462i
\(872\) −61.8336 + 2.28484i −0.0709101 + 0.00262023i
\(873\) 829.217 + 1436.25i 0.949848 + 1.64519i
\(874\) 61.9525 + 21.6889i 0.0708839 + 0.0248157i
\(875\) 690.635 449.199i 0.789297 0.513371i
\(876\) 473.338 593.170i 0.540340 0.677134i
\(877\) −563.178 975.453i −0.642165 1.11226i −0.984949 0.172847i \(-0.944703\pi\)
0.342784 0.939414i \(-0.388630\pi\)
\(878\) −117.563 136.653i −0.133898 0.155641i
\(879\) −1215.82 701.953i −1.38318 0.798581i
\(880\) −126.524 136.530i −0.143777 0.155148i
\(881\) −294.364 −0.334125 −0.167062 0.985946i \(-0.553428\pi\)
−0.167062 + 0.985946i \(0.553428\pi\)
\(882\) −334.083 1107.48i −0.378779 1.25564i
\(883\) 908.203i 1.02854i 0.857628 + 0.514271i \(0.171938\pi\)
−0.857628 + 0.514271i \(0.828062\pi\)
\(884\) 26.3950 174.752i 0.0298586 0.197683i
\(885\) −924.059 + 1600.52i −1.04413 + 1.80849i
\(886\) 301.029 + 349.912i 0.339762 + 0.394934i
\(887\) 737.152 425.595i 0.831062 0.479814i −0.0231543 0.999732i \(-0.507371\pi\)
0.854216 + 0.519918i \(0.174038\pi\)
\(888\) −795.523 + 499.344i −0.895860 + 0.562325i
\(889\) 204.109 + 313.813i 0.229594 + 0.352996i
\(890\) 308.527 + 108.012i 0.346659 + 0.121362i
\(891\) 91.8796 53.0467i 0.103120 0.0595361i
\(892\) 2.18731 + 5.57826i 0.00245214 + 0.00625366i
\(893\) −82.4869 + 142.872i −0.0923706 + 0.159991i
\(894\) 1570.63 296.927i 1.75686 0.332133i
\(895\) 817.905i 0.913860i
\(896\) −852.251 + 276.558i −0.951173 + 0.308658i
\(897\) −63.5700 −0.0708696
\(898\) −65.4053 345.969i −0.0728344 0.385266i
\(899\) −677.879 391.374i −0.754037 0.435343i
\(900\) 114.072 44.7291i 0.126747 0.0496990i
\(901\) 322.037 + 557.784i 0.357422 + 0.619073i
\(902\) −80.5233 + 230.008i −0.0892720 + 0.254998i
\(903\) −132.546 2495.30i −0.146784 2.76334i
\(904\) 146.943 + 234.100i 0.162547 + 0.258960i
\(905\) −255.109 441.861i −0.281888 0.488245i
\(906\) 551.042 474.061i 0.608214 0.523246i
\(907\) −896.755 517.742i −0.988704 0.570829i −0.0838175 0.996481i \(-0.526711\pi\)
−0.904887 + 0.425653i \(0.860045\pi\)
\(908\) 58.7732 + 8.87728i 0.0647282 + 0.00977674i
\(909\) 499.034 0.548993
\(910\) −67.8786 + 232.820i −0.0745919 + 0.255846i
\(911\) 1106.93i 1.21507i 0.794293 + 0.607535i \(0.207842\pi\)
−0.794293 + 0.607535i \(0.792158\pi\)
\(912\) −415.643 + 385.180i −0.455749 + 0.422347i
\(913\) 13.1070 22.7020i 0.0143560 0.0248652i
\(914\) 67.7821 58.3129i 0.0741599 0.0637997i
\(915\) 985.088 568.741i 1.07660 0.621575i
\(916\) 839.144 + 669.621i 0.916096 + 0.731027i
\(917\) 411.154 808.350i 0.448369 0.881516i
\(918\) 113.236 323.448i 0.123350 0.352340i
\(919\) −1287.15 + 743.136i −1.40060 + 0.808635i −0.994454 0.105174i \(-0.966460\pi\)
−0.406144 + 0.913809i \(0.633127\pi\)
\(920\) −6.55889 177.500i −0.00712923 0.192935i
\(921\) −438.055 + 758.733i −0.475629 + 0.823814i
\(922\) −108.160 572.128i −0.117311 0.620529i
\(923\) 297.113i 0.321900i
\(924\) 281.512 + 27.3476i 0.304666 + 0.0295969i
\(925\) −66.8002 −0.0722165
\(926\) 463.325 87.5913i 0.500351 0.0945910i
\(927\) 990.073 + 571.619i 1.06804 + 0.616633i
\(928\) −1014.15 749.690i −1.09283 0.807855i
\(929\) −801.416 1388.09i −0.862665 1.49418i −0.869347 0.494203i \(-0.835460\pi\)
0.00668122 0.999978i \(-0.497873\pi\)
\(930\) 898.282 + 314.479i 0.965895 + 0.338149i
\(931\) 40.3079 + 378.347i 0.0432952 + 0.406387i
\(932\) 258.217 + 206.052i 0.277057 + 0.221086i
\(933\) −1161.40 2011.60i −1.24480 2.15606i
\(934\) 383.178 + 445.401i 0.410255 + 0.476875i
\(935\) −134.996 77.9401i −0.144381 0.0833584i
\(936\) 145.630 275.235i 0.155588 0.294055i
\(937\) −1446.12 −1.54335 −0.771675 0.636017i \(-0.780581\pi\)
−0.771675 + 0.636017i \(0.780581\pi\)
\(938\) 173.709 + 710.107i 0.185191 + 0.757044i
\(939\) 1464.16i 1.55927i
\(940\) 441.416 + 66.6728i 0.469591 + 0.0709285i
\(941\) 152.094 263.435i 0.161631 0.279952i −0.773823 0.633402i \(-0.781658\pi\)
0.935454 + 0.353449i \(0.114991\pi\)
\(942\) 638.632 + 742.337i 0.677953 + 0.788043i
\(943\) −201.387 + 116.271i −0.213560 + 0.123299i
\(944\) −1203.36 + 273.874i −1.27475 + 0.290121i
\(945\) −213.191 + 419.144i −0.225599 + 0.443539i
\(946\) 327.188 + 114.545i 0.345865 + 0.121083i
\(947\) 1019.53 588.627i 1.07659 0.621571i 0.146617 0.989193i \(-0.453162\pi\)
0.929975 + 0.367623i \(0.119828\pi\)
\(948\) 2236.53 876.974i 2.35921 0.925078i
\(949\) 68.5810 118.786i 0.0722666 0.125169i
\(950\) −39.6008 + 7.48652i −0.0416851 + 0.00788055i
\(951\) 445.913i 0.468889i
\(952\) −613.460 + 432.056i −0.644390 + 0.453840i
\(953\) −884.296 −0.927908 −0.463954 0.885859i \(-0.653570\pi\)
−0.463954 + 0.885859i \(0.653570\pi\)
\(954\) 210.799 + 1115.05i 0.220963 + 1.16881i
\(955\) 192.647 + 111.225i 0.201725 + 0.116466i
\(956\) 299.821 + 764.629i 0.313620 + 0.799821i
\(957\) 199.053 + 344.770i 0.207997 + 0.360261i
\(958\) 426.735 1218.93i 0.445444 1.27237i
\(959\) 60.4966 + 1138.91i 0.0630830 + 1.18760i
\(960\) 1380.96 + 666.620i 1.43850 + 0.694396i
\(961\) −283.270 490.639i −0.294766 0.510550i
\(962\) −128.693 + 110.715i −0.133777 + 0.115088i
\(963\) −26.6975 15.4138i −0.0277233 0.0160061i
\(964\) −9.23314 + 61.1292i −0.00957794 + 0.0634120i
\(965\) 1464.58 1.51770
\(966\) 186.620 + 194.973i 0.193188 + 0.201835i
\(967\) 293.782i 0.303807i 0.988395 + 0.151904i \(0.0485404\pi\)
−0.988395 + 0.151904i \(0.951460\pi\)
\(968\) 434.363 820.931i 0.448723 0.848069i
\(969\) −237.276 + 410.974i −0.244867 + 0.424122i
\(970\) −1119.01 + 962.686i −1.15362 + 0.992460i
\(971\) 456.358 263.478i 0.469988 0.271347i −0.246247 0.969207i \(-0.579197\pi\)
0.716235 + 0.697860i \(0.245864\pi\)
\(972\) −832.296 + 1043.00i −0.856271 + 1.07305i
\(973\) 951.261 + 1462.54i 0.977658 + 1.50313i
\(974\) −113.868 + 325.255i −0.116908 + 0.333937i
\(975\) 33.8025 19.5159i 0.0346692 0.0200163i
\(976\) 725.701 + 224.342i 0.743547 + 0.229859i
\(977\) −113.590 + 196.743i −0.116264 + 0.201375i −0.918284 0.395922i \(-0.870425\pi\)
0.802020 + 0.597297i \(0.203758\pi\)
\(978\) −142.364 753.052i −0.145567 0.769992i
\(979\) 68.9063i 0.0703844i
\(980\) 913.340 475.292i 0.931980 0.484992i
\(981\) −91.2959 −0.0930642
\(982\) 849.244 160.549i 0.864811 0.163492i
\(983\) −677.954 391.417i −0.689678 0.398186i 0.113813 0.993502i \(-0.463693\pi\)
−0.803491 + 0.595316i \(0.797027\pi\)
\(984\) −74.1322 2006.21i −0.0753376 2.03883i
\(985\) −166.890 289.061i −0.169431 0.293463i
\(986\) −996.812 348.973i −1.01097 0.353928i
\(987\) −568.631 + 369.846i −0.576121 + 0.374718i
\(988\) −63.8844 + 80.0575i −0.0646603 + 0.0810299i
\(989\) 165.396 + 286.474i 0.167236 + 0.289661i
\(990\) −179.116 208.202i −0.180925 0.210305i
\(991\) −1561.30 901.419i −1.57548 0.909606i −0.995478 0.0949931i \(-0.969717\pi\)
−0.580005 0.814613i \(-0.696950\pi\)
\(992\) 253.700 + 582.720i 0.255746 + 0.587419i
\(993\) 1392.88 1.40270
\(994\) 911.263 872.222i 0.916764 0.877487i
\(995\) 705.760i 0.709306i
\(996\) −32.2522 + 213.530i −0.0323817 + 0.214387i
\(997\) −687.983 + 1191.62i −0.690053 + 1.19521i 0.281767 + 0.959483i \(0.409079\pi\)
−0.971820 + 0.235724i \(0.924254\pi\)
\(998\) −642.306 746.607i −0.643593 0.748104i
\(999\) −285.079 + 164.591i −0.285365 + 0.164755i
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 28.3.g.a.11.3 yes 12
3.2 odd 2 252.3.y.c.235.4 12
4.3 odd 2 inner 28.3.g.a.11.2 12
7.2 even 3 inner 28.3.g.a.23.2 yes 12
7.3 odd 6 196.3.c.h.99.6 6
7.4 even 3 196.3.c.i.99.6 6
7.5 odd 6 196.3.g.i.79.2 12
7.6 odd 2 196.3.g.i.67.3 12
8.3 odd 2 448.3.r.h.319.6 12
8.5 even 2 448.3.r.h.319.1 12
12.11 even 2 252.3.y.c.235.5 12
21.2 odd 6 252.3.y.c.163.5 12
28.3 even 6 196.3.c.h.99.5 6
28.11 odd 6 196.3.c.i.99.5 6
28.19 even 6 196.3.g.i.79.3 12
28.23 odd 6 inner 28.3.g.a.23.3 yes 12
28.27 even 2 196.3.g.i.67.2 12
56.37 even 6 448.3.r.h.191.6 12
56.51 odd 6 448.3.r.h.191.1 12
84.23 even 6 252.3.y.c.163.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.3.g.a.11.2 12 4.3 odd 2 inner
28.3.g.a.11.3 yes 12 1.1 even 1 trivial
28.3.g.a.23.2 yes 12 7.2 even 3 inner
28.3.g.a.23.3 yes 12 28.23 odd 6 inner
196.3.c.h.99.5 6 28.3 even 6
196.3.c.h.99.6 6 7.3 odd 6
196.3.c.i.99.5 6 28.11 odd 6
196.3.c.i.99.6 6 7.4 even 3
196.3.g.i.67.2 12 28.27 even 2
196.3.g.i.67.3 12 7.6 odd 2
196.3.g.i.79.2 12 7.5 odd 6
196.3.g.i.79.3 12 28.19 even 6
252.3.y.c.163.4 12 84.23 even 6
252.3.y.c.163.5 12 21.2 odd 6
252.3.y.c.235.4 12 3.2 odd 2
252.3.y.c.235.5 12 12.11 even 2
448.3.r.h.191.1 12 56.51 odd 6
448.3.r.h.191.6 12 56.37 even 6
448.3.r.h.319.1 12 8.5 even 2
448.3.r.h.319.6 12 8.3 odd 2