Properties

Label 675.2.u.b.49.1
Level $675$
Weight $2$
Character 675.49
Analytic conductor $5.390$
Analytic rank $0$
Dimension $24$
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] = [675,2,Mod(49,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\), degree \(6\), not 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 675.49
Dual form 675.2.u.b.124.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36054 - 1.62143i) q^{2} +(1.42389 + 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.957561 + 0.168844i) q^{7} +(0.880031 - 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +O(q^{10})\) \(q+(-1.36054 - 1.62143i) q^{2} +(1.42389 + 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.957561 + 0.168844i) q^{7} +(0.880031 - 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(-3.02185 + 3.05303i) q^{12} +(-0.973200 + 1.15981i) q^{13} +(1.57657 + 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(-1.01731 - 0.587342i) q^{17} +(3.11830 - 5.53146i) q^{18} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(-0.229414 - 0.630310i) q^{22} +(-2.12988 - 0.375556i) q^{23} +(1.75413 + 0.144396i) q^{24} +3.20463 q^{26} +(-1.26740 + 5.03922i) q^{27} -2.41147i q^{28} +(3.37436 - 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(-2.72885 - 7.49746i) q^{32} +(0.317135 + 0.448003i) q^{33} +(0.431752 + 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(3.86823 + 2.23332i) q^{37} +(4.50341 - 12.3730i) q^{38} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(0.940269 + 3.43842i) q^{42} +(-1.91223 + 5.25381i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(2.43845 - 0.429965i) q^{47} +(2.81139 + 3.97153i) q^{48} +(-5.68943 + 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(-2.41362 - 2.87645i) q^{52} +10.8920i q^{53} +(9.89507 - 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(-0.883963 + 10.7384i) q^{57} +(-9.18189 - 1.61901i) q^{58} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(15.8985 - 9.17898i) q^{62} +(-1.48436 - 2.51109i) q^{63} +(-5.63455 + 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(-0.550580 + 0.656156i) q^{67} +(1.87265 - 2.23174i) q^{68} +(-2.66237 - 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(2.35530 + 1.93547i) q^{72} +(13.1998 - 7.62091i) q^{73} +(-1.64171 - 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(-0.303453 - 0.0535070i) q^{77} +(4.56306 + 3.16030i) q^{78} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} -12.3721i q^{82} +(-3.01141 - 3.58886i) q^{83} +(2.37811 - 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(7.59698 - 0.703969i) q^{87} +(0.317135 - 0.0559194i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(1.83453 - 5.04032i) q^{92} +(-10.5678 + 10.6769i) q^{93} +(-4.01476 - 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(-1.89804 + 5.21481i) q^{97} +(11.0983 + 6.40762i) q^{98} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36054 1.62143i −0.962046 1.14652i −0.989153 0.146889i \(-0.953074\pi\)
0.0271067 0.999633i \(-0.491371\pi\)
\(3\) 1.42389 + 0.986166i 0.822086 + 0.569363i
\(4\) −0.430663 + 2.44241i −0.215332 + 1.22121i
\(5\) 0 0
\(6\) −0.338267 3.65046i −0.138097 1.49029i
\(7\) −0.957561 + 0.168844i −0.361924 + 0.0638170i −0.351653 0.936130i \(-0.614380\pi\)
−0.0102706 + 0.999947i \(0.503269\pi\)
\(8\) 0.880031 0.508086i 0.311138 0.179636i
\(9\) 1.05495 + 2.80839i 0.351651 + 0.936131i
\(10\) 0 0
\(11\) 0.297791 + 0.108387i 0.0897872 + 0.0326799i 0.386523 0.922280i \(-0.373676\pi\)
−0.296736 + 0.954960i \(0.595898\pi\)
\(12\) −3.02185 + 3.05303i −0.872332 + 0.881335i
\(13\) −0.973200 + 1.15981i −0.269917 + 0.321675i −0.883928 0.467623i \(-0.845111\pi\)
0.614011 + 0.789297i \(0.289555\pi\)
\(14\) 1.57657 + 1.32290i 0.421355 + 0.353559i
\(15\) 0 0
\(16\) 2.63991 + 0.960847i 0.659977 + 0.240212i
\(17\) −1.01731 0.587342i −0.246733 0.142451i 0.371534 0.928419i \(-0.378832\pi\)
−0.618267 + 0.785968i \(0.712165\pi\)
\(18\) 3.11830 5.53146i 0.734991 1.30378i
\(19\) 3.11040 + 5.38737i 0.713575 + 1.23595i 0.963507 + 0.267685i \(0.0862586\pi\)
−0.249931 + 0.968264i \(0.580408\pi\)
\(20\) 0 0
\(21\) −1.52997 0.703898i −0.333868 0.153603i
\(22\) −0.229414 0.630310i −0.0489113 0.134383i
\(23\) −2.12988 0.375556i −0.444112 0.0783089i −0.0528796 0.998601i \(-0.516840\pi\)
−0.391232 + 0.920292i \(0.627951\pi\)
\(24\) 1.75413 + 0.144396i 0.358060 + 0.0294747i
\(25\) 0 0
\(26\) 3.20463 0.628480
\(27\) −1.26740 + 5.03922i −0.243912 + 0.969797i
\(28\) 2.41147i 0.455726i
\(29\) 3.37436 2.83142i 0.626602 0.525782i −0.273269 0.961938i \(-0.588105\pi\)
0.899871 + 0.436156i \(0.143660\pi\)
\(30\) 0 0
\(31\) −1.50609 + 8.54146i −0.270502 + 1.53409i 0.482395 + 0.875954i \(0.339767\pi\)
−0.752897 + 0.658138i \(0.771344\pi\)
\(32\) −2.72885 7.49746i −0.482398 1.32538i
\(33\) 0.317135 + 0.448003i 0.0552061 + 0.0779872i
\(34\) 0.431752 + 2.44859i 0.0740449 + 0.419930i
\(35\) 0 0
\(36\) −7.31359 + 1.36716i −1.21893 + 0.227859i
\(37\) 3.86823 + 2.23332i 0.635933 + 0.367156i 0.783046 0.621964i \(-0.213665\pi\)
−0.147113 + 0.989120i \(0.546998\pi\)
\(38\) 4.50341 12.3730i 0.730550 2.00717i
\(39\) −2.52950 + 0.691717i −0.405045 + 0.110763i
\(40\) 0 0
\(41\) 4.47767 + 3.75721i 0.699295 + 0.586778i 0.921573 0.388205i \(-0.126905\pi\)
−0.222278 + 0.974983i \(0.571349\pi\)
\(42\) 0.940269 + 3.43842i 0.145087 + 0.530560i
\(43\) −1.91223 + 5.25381i −0.291613 + 0.801199i 0.704219 + 0.709983i \(0.251298\pi\)
−0.995831 + 0.0912158i \(0.970925\pi\)
\(44\) −0.392973 + 0.680649i −0.0592429 + 0.102612i
\(45\) 0 0
\(46\) 2.28885 + 3.96441i 0.337473 + 0.584521i
\(47\) 2.43845 0.429965i 0.355685 0.0627168i 0.00704911 0.999975i \(-0.497756\pi\)
0.348636 + 0.937258i \(0.386645\pi\)
\(48\) 2.81139 + 3.97153i 0.405790 + 0.573241i
\(49\) −5.68943 + 2.07078i −0.812776 + 0.295826i
\(50\) 0 0
\(51\) −0.869320 1.83955i −0.121729 0.257588i
\(52\) −2.41362 2.87645i −0.334710 0.398891i
\(53\) 10.8920i 1.49613i 0.663628 + 0.748063i \(0.269016\pi\)
−0.663628 + 0.748063i \(0.730984\pi\)
\(54\) 9.89507 4.80105i 1.34655 0.653340i
\(55\) 0 0
\(56\) −0.756896 + 0.635111i −0.101145 + 0.0848703i
\(57\) −0.883963 + 10.7384i −0.117084 + 1.42234i
\(58\) −9.18189 1.61901i −1.20564 0.212587i
\(59\) −1.62023 + 0.589715i −0.210936 + 0.0767743i −0.445327 0.895368i \(-0.646913\pi\)
0.234391 + 0.972142i \(0.424690\pi\)
\(60\) 0 0
\(61\) 0.176214 + 0.999361i 0.0225619 + 0.127955i 0.994008 0.109304i \(-0.0348621\pi\)
−0.971446 + 0.237259i \(0.923751\pi\)
\(62\) 15.8985 9.17898i 2.01911 1.16573i
\(63\) −1.48436 2.51109i −0.187012 0.316367i
\(64\) −5.63455 + 9.75933i −0.704319 + 1.21992i
\(65\) 0 0
\(66\) 0.294929 1.12374i 0.0363033 0.138322i
\(67\) −0.550580 + 0.656156i −0.0672641 + 0.0801622i −0.798627 0.601826i \(-0.794440\pi\)
0.731363 + 0.681988i \(0.238884\pi\)
\(68\) 1.87265 2.23174i 0.227092 0.270638i
\(69\) −2.66237 2.63517i −0.320512 0.317238i
\(70\) 0 0
\(71\) 4.79788 8.31018i 0.569404 0.986237i −0.427221 0.904147i \(-0.640507\pi\)
0.996625 0.0820894i \(-0.0261593\pi\)
\(72\) 2.35530 + 1.93547i 0.277574 + 0.228097i
\(73\) 13.1998 7.62091i 1.54492 0.891960i 0.546404 0.837522i \(-0.315996\pi\)
0.998517 0.0544385i \(-0.0173369\pi\)
\(74\) −1.64171 9.31057i −0.190844 1.08233i
\(75\) 0 0
\(76\) −14.4977 + 5.27674i −1.66300 + 0.605284i
\(77\) −0.303453 0.0535070i −0.0345817 0.00609768i
\(78\) 4.56306 + 3.16030i 0.516664 + 0.357833i
\(79\) 8.59024 7.20807i 0.966478 0.810971i −0.0155168 0.999880i \(-0.504939\pi\)
0.981995 + 0.188908i \(0.0604949\pi\)
\(80\) 0 0
\(81\) −6.77415 + 5.92544i −0.752684 + 0.658382i
\(82\) 12.3721i 1.36626i
\(83\) −3.01141 3.58886i −0.330546 0.393929i 0.575017 0.818141i \(-0.304995\pi\)
−0.905563 + 0.424212i \(0.860551\pi\)
\(84\) 2.37811 3.43369i 0.259474 0.374646i
\(85\) 0 0
\(86\) 11.1203 4.04747i 1.19914 0.436450i
\(87\) 7.59698 0.703969i 0.814482 0.0754734i
\(88\) 0.317135 0.0559194i 0.0338067 0.00596103i
\(89\) −7.74976 13.4230i −0.821473 1.42283i −0.904586 0.426292i \(-0.859820\pi\)
0.0831130 0.996540i \(-0.473514\pi\)
\(90\) 0 0
\(91\) 0.736071 1.27491i 0.0771612 0.133647i
\(92\) 1.83453 5.04032i 0.191263 0.525490i
\(93\) −10.5678 + 10.6769i −1.09583 + 1.10714i
\(94\) −4.01476 3.36879i −0.414091 0.347464i
\(95\) 0 0
\(96\) 3.50815 13.3667i 0.358049 1.36423i
\(97\) −1.89804 + 5.21481i −0.192716 + 0.529484i −0.997987 0.0634241i \(-0.979798\pi\)
0.805270 + 0.592908i \(0.202020\pi\)
\(98\) 11.0983 + 6.40762i 1.12110 + 0.647267i
\(99\) 0.00976156 + 0.950656i 0.000981074 + 0.0955445i
\(100\) 0 0
\(101\) −1.76063 9.98501i −0.175189 0.993546i −0.937926 0.346836i \(-0.887256\pi\)
0.762737 0.646709i \(-0.223855\pi\)
\(102\) −1.79995 + 3.91231i −0.178221 + 0.387377i
\(103\) −3.37002 9.25906i −0.332058 0.912323i −0.987576 0.157143i \(-0.949772\pi\)
0.655518 0.755180i \(-0.272451\pi\)
\(104\) −0.267160 + 1.51514i −0.0261972 + 0.148572i
\(105\) 0 0
\(106\) 17.6605 14.8189i 1.71534 1.43934i
\(107\) 5.17080i 0.499880i 0.968261 + 0.249940i \(0.0804109\pi\)
−0.968261 + 0.249940i \(0.919589\pi\)
\(108\) −11.7620 5.26573i −1.13180 0.506695i
\(109\) 7.31065 0.700234 0.350117 0.936706i \(-0.386142\pi\)
0.350117 + 0.936706i \(0.386142\pi\)
\(110\) 0 0
\(111\) 3.30552 + 6.99473i 0.313746 + 0.663911i
\(112\) −2.69010 0.474338i −0.254191 0.0448207i
\(113\) 3.54868 + 9.74991i 0.333832 + 0.917195i 0.987105 + 0.160073i \(0.0511729\pi\)
−0.653274 + 0.757122i \(0.726605\pi\)
\(114\) 18.6142 13.1768i 1.74338 1.23412i
\(115\) 0 0
\(116\) 5.46229 + 9.46096i 0.507161 + 0.878428i
\(117\) −4.28390 1.50958i −0.396046 0.139561i
\(118\) 3.16056 + 1.82475i 0.290953 + 0.167982i
\(119\) 1.07330 + 0.390650i 0.0983894 + 0.0358108i
\(120\) 0 0
\(121\) −8.34956 7.00611i −0.759051 0.636919i
\(122\) 1.38064 1.64539i 0.124998 0.148966i
\(123\) 2.67050 + 9.76560i 0.240790 + 0.880535i
\(124\) −20.2132 7.35699i −1.81520 0.660677i
\(125\) 0 0
\(126\) −2.05201 + 5.82321i −0.182808 + 0.518773i
\(127\) 4.52709 2.61372i 0.401714 0.231930i −0.285509 0.958376i \(-0.592163\pi\)
0.687223 + 0.726446i \(0.258829\pi\)
\(128\) 7.77522 1.37098i 0.687239 0.121179i
\(129\) −7.90395 + 5.59510i −0.695904 + 0.492621i
\(130\) 0 0
\(131\) −1.25622 + 7.12440i −0.109757 + 0.622461i 0.879457 + 0.475979i \(0.157906\pi\)
−0.989213 + 0.146482i \(0.953205\pi\)
\(132\) −1.23079 + 0.581636i −0.107126 + 0.0506249i
\(133\) −3.88802 4.63357i −0.337134 0.401781i
\(134\) 1.81300 0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) 7.23092 + 8.61748i 0.617779 + 0.736241i 0.980687 0.195584i \(-0.0626603\pi\)
−0.362907 + 0.931825i \(0.618216\pi\)
\(138\) −0.650482 + 7.90210i −0.0553727 + 0.672671i
\(139\) −1.62885 + 9.23766i −0.138157 + 0.783528i 0.834452 + 0.551081i \(0.185784\pi\)
−0.972609 + 0.232447i \(0.925327\pi\)
\(140\) 0 0
\(141\) 3.89612 + 1.79249i 0.328112 + 0.150955i
\(142\) −20.0021 + 3.52690i −1.67854 + 0.295971i
\(143\) −0.415518 + 0.239900i −0.0347474 + 0.0200614i
\(144\) 0.0865360 + 8.42754i 0.00721133 + 0.702295i
\(145\) 0 0
\(146\) −30.3156 11.0340i −2.50894 0.913179i
\(147\) −10.1433 2.66215i −0.836605 0.219570i
\(148\) −7.12060 + 8.48600i −0.585310 + 0.697545i
\(149\) −14.5941 12.2459i −1.19560 1.00322i −0.999745 0.0225899i \(-0.992809\pi\)
−0.195851 0.980634i \(-0.562747\pi\)
\(150\) 0 0
\(151\) −3.77193 1.37287i −0.306955 0.111723i 0.183950 0.982936i \(-0.441112\pi\)
−0.490905 + 0.871213i \(0.663334\pi\)
\(152\) 5.47450 + 3.16070i 0.444041 + 0.256367i
\(153\) 0.576279 3.47661i 0.0465894 0.281068i
\(154\) 0.326102 + 0.564825i 0.0262780 + 0.0455149i
\(155\) 0 0
\(156\) −0.600093 6.47599i −0.0480459 0.518494i
\(157\) −2.48851 6.83713i −0.198605 0.545662i 0.799911 0.600118i \(-0.204880\pi\)
−0.998516 + 0.0544560i \(0.982658\pi\)
\(158\) −23.3747 4.12159i −1.85959 0.327896i
\(159\) −10.7413 + 15.5090i −0.851839 + 1.22994i
\(160\) 0 0
\(161\) 2.10290 0.165732
\(162\) 18.8242 + 2.92200i 1.47897 + 0.229574i
\(163\) 12.4492i 0.975094i −0.873097 0.487547i \(-0.837892\pi\)
0.873097 0.487547i \(-0.162108\pi\)
\(164\) −11.1050 + 9.31823i −0.867157 + 0.727632i
\(165\) 0 0
\(166\) −1.72194 + 9.76558i −0.133648 + 0.757956i
\(167\) 0.797553 + 2.19126i 0.0617165 + 0.169565i 0.966718 0.255843i \(-0.0823530\pi\)
−0.905002 + 0.425408i \(0.860131\pi\)
\(168\) −1.70407 + 0.157906i −0.131472 + 0.0121827i
\(169\) 1.85937 + 10.5450i 0.143029 + 0.811157i
\(170\) 0 0
\(171\) −11.8485 + 14.4187i −0.906081 + 1.10262i
\(172\) −12.0085 6.93308i −0.915636 0.528643i
\(173\) 1.22521 3.36623i 0.0931509 0.255930i −0.884363 0.466799i \(-0.845407\pi\)
0.977514 + 0.210869i \(0.0676294\pi\)
\(174\) −11.4774 11.3602i −0.870101 0.861213i
\(175\) 0 0
\(176\) 0.681996 + 0.572262i 0.0514074 + 0.0431359i
\(177\) −2.88859 0.758123i −0.217120 0.0569840i
\(178\) −11.2205 + 30.8281i −0.841014 + 2.31067i
\(179\) −9.99785 + 17.3168i −0.747275 + 1.29432i 0.201850 + 0.979416i \(0.435305\pi\)
−0.949124 + 0.314901i \(0.898029\pi\)
\(180\) 0 0
\(181\) −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i \(-0.284470\pi\)
−0.988241 + 0.152907i \(0.951136\pi\)
\(182\) −3.06863 + 0.541082i −0.227462 + 0.0401077i
\(183\) −0.734626 + 1.59676i −0.0543051 + 0.118036i
\(184\) −2.06518 + 0.751664i −0.152247 + 0.0554134i
\(185\) 0 0
\(186\) 31.6897 + 2.60862i 2.32360 + 0.191274i
\(187\) −0.239284 0.285168i −0.0174982 0.0208535i
\(188\) 6.14088i 0.447869i
\(189\) 0.362776 5.03935i 0.0263881 0.366559i
\(190\) 0 0
\(191\) −13.6023 + 11.4137i −0.984227 + 0.825864i −0.984722 0.174135i \(-0.944287\pi\)
0.000494763 1.00000i \(0.499843\pi\)
\(192\) −17.6473 + 8.33965i −1.27359 + 0.601862i
\(193\) −10.4235 1.83795i −0.750303 0.132299i −0.214596 0.976703i \(-0.568844\pi\)
−0.535706 + 0.844404i \(0.679955\pi\)
\(194\) 11.0378 4.01743i 0.792467 0.288434i
\(195\) 0 0
\(196\) −2.60748 14.7878i −0.186249 1.05627i
\(197\) 12.2620 7.07945i 0.873628 0.504390i 0.00507615 0.999987i \(-0.498384\pi\)
0.868552 + 0.495597i \(0.165051\pi\)
\(198\) 1.52814 1.30923i 0.108600 0.0930431i
\(199\) 3.77010 6.53000i 0.267255 0.462899i −0.700897 0.713263i \(-0.747217\pi\)
0.968152 + 0.250363i \(0.0805501\pi\)
\(200\) 0 0
\(201\) −1.43105 + 0.391333i −0.100938 + 0.0276025i
\(202\) −13.7946 + 16.4397i −0.970582 + 1.15669i
\(203\) −2.75308 + 3.28100i −0.193229 + 0.230281i
\(204\) 4.86732 1.33101i 0.340780 0.0931896i
\(205\) 0 0
\(206\) −10.4278 + 18.0616i −0.726543 + 1.25841i
\(207\) −1.19222 6.37775i −0.0828648 0.443284i
\(208\) −3.68356 + 2.12670i −0.255409 + 0.147460i
\(209\) 0.342328 + 1.94144i 0.0236793 + 0.134292i
\(210\) 0 0
\(211\) −4.89922 + 1.78317i −0.337276 + 0.122758i −0.505106 0.863058i \(-0.668546\pi\)
0.167829 + 0.985816i \(0.446324\pi\)
\(212\) −26.6027 4.69077i −1.82708 0.322163i
\(213\) 15.0269 7.10131i 1.02963 0.486573i
\(214\) 8.38408 7.03508i 0.573124 0.480908i
\(215\) 0 0
\(216\) 1.44500 + 5.07862i 0.0983199 + 0.345556i
\(217\) 8.43326i 0.572487i
\(218\) −9.94643 11.8537i −0.673657 0.802833i
\(219\) 26.3106 + 2.16583i 1.77791 + 0.146353i
\(220\) 0 0
\(221\) 1.67125 0.608285i 0.112420 0.0409177i
\(222\) 6.84416 14.8763i 0.459350 0.998430i
\(223\) 17.4250 3.07250i 1.16686 0.205750i 0.443537 0.896256i \(-0.353723\pi\)
0.723326 + 0.690506i \(0.242612\pi\)
\(224\) 3.87894 + 6.71853i 0.259173 + 0.448901i
\(225\) 0 0
\(226\) 10.9807 19.0191i 0.730423 1.26513i
\(227\) −5.39434 + 14.8208i −0.358035 + 0.983692i 0.621676 + 0.783275i \(0.286452\pi\)
−0.979711 + 0.200418i \(0.935770\pi\)
\(228\) −25.8470 6.78365i −1.71176 0.449258i
\(229\) 1.35350 + 1.13572i 0.0894415 + 0.0750504i 0.686412 0.727213i \(-0.259185\pi\)
−0.596971 + 0.802263i \(0.703629\pi\)
\(230\) 0 0
\(231\) −0.379318 0.375443i −0.0249573 0.0247024i
\(232\) 1.53093 4.20620i 0.100511 0.276151i
\(233\) −12.0364 6.94920i −0.788529 0.455257i 0.0509157 0.998703i \(-0.483786\pi\)
−0.839444 + 0.543446i \(0.817119\pi\)
\(234\) 3.38073 + 8.99987i 0.221005 + 0.588340i
\(235\) 0 0
\(236\) −0.742554 4.21123i −0.0483362 0.274128i
\(237\) 19.3400 1.79212i 1.25627 0.116411i
\(238\) −0.826858 2.27177i −0.0535973 0.147257i
\(239\) 3.44391 19.5314i 0.222768 1.26338i −0.644138 0.764909i \(-0.722784\pi\)
0.866906 0.498471i \(-0.166105\pi\)
\(240\) 0 0
\(241\) 14.8419 12.4538i 0.956050 0.802221i −0.0242563 0.999706i \(-0.507722\pi\)
0.980306 + 0.197485i \(0.0632773\pi\)
\(242\) 23.0703i 1.48301i
\(243\) −15.4892 + 1.75676i −0.993629 + 0.112696i
\(244\) −2.51674 −0.161118
\(245\) 0 0
\(246\) 12.2009 17.6165i 0.777901 1.12319i
\(247\) −9.27540 1.63550i −0.590179 0.104065i
\(248\) 3.01439 + 8.28198i 0.191414 + 0.525906i
\(249\) −0.748720 8.07992i −0.0474482 0.512044i
\(250\) 0 0
\(251\) 2.73786 + 4.74212i 0.172812 + 0.299320i 0.939402 0.342818i \(-0.111381\pi\)
−0.766590 + 0.642137i \(0.778048\pi\)
\(252\) 6.77237 2.54399i 0.426619 0.160256i
\(253\) −0.593554 0.342689i −0.0373164 0.0215447i
\(254\) −10.3972 3.78428i −0.652380 0.237447i
\(255\) 0 0
\(256\) 4.46383 + 3.74560i 0.278989 + 0.234100i
\(257\) 7.43395 8.85943i 0.463717 0.552636i −0.482615 0.875833i \(-0.660313\pi\)
0.946332 + 0.323196i \(0.104757\pi\)
\(258\) 19.8257 + 5.20333i 1.23429 + 0.323945i
\(259\) −4.08115 1.48542i −0.253590 0.0922993i
\(260\) 0 0
\(261\) 11.5115 + 6.48951i 0.712546 + 0.401691i
\(262\) 13.2608 7.65614i 0.819257 0.472998i
\(263\) 6.37952 1.12488i 0.393378 0.0693632i 0.0265395 0.999648i \(-0.491551\pi\)
0.366839 + 0.930285i \(0.380440\pi\)
\(264\) 0.506712 + 0.233124i 0.0311860 + 0.0143478i
\(265\) 0 0
\(266\) −2.22318 + 12.6083i −0.136312 + 0.773064i
\(267\) 2.20245 26.7554i 0.134788 1.63741i
\(268\) −1.36549 1.62733i −0.0834106 0.0994048i
\(269\) 13.8387 0.843758 0.421879 0.906652i \(-0.361371\pi\)
0.421879 + 0.906652i \(0.361371\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) −2.12125 2.52800i −0.128619 0.153283i
\(273\) 2.30536 1.08945i 0.139527 0.0659366i
\(274\) 4.13466 23.4488i 0.249784 1.41660i
\(275\) 0 0
\(276\) 7.58277 5.36774i 0.456429 0.323100i
\(277\) −12.2832 + 2.16586i −0.738026 + 0.130134i −0.530010 0.847991i \(-0.677812\pi\)
−0.208016 + 0.978125i \(0.566701\pi\)
\(278\) 17.1943 9.92713i 1.03125 0.595390i
\(279\) −25.5766 + 4.78114i −1.53123 + 0.286239i
\(280\) 0 0
\(281\) −9.16752 3.33670i −0.546888 0.199051i 0.0537751 0.998553i \(-0.482875\pi\)
−0.600663 + 0.799502i \(0.705097\pi\)
\(282\) −2.39442 8.75602i −0.142585 0.521414i
\(283\) 17.0797 20.3547i 1.01528 1.20996i 0.0377246 0.999288i \(-0.487989\pi\)
0.977556 0.210676i \(-0.0675665\pi\)
\(284\) 18.2306 + 15.2973i 1.08179 + 0.907728i
\(285\) 0 0
\(286\) 0.954309 + 0.347340i 0.0564295 + 0.0205386i
\(287\) −4.92202 2.84173i −0.290538 0.167742i
\(288\) 18.1770 15.5732i 1.07109 0.917657i
\(289\) −7.81006 13.5274i −0.459415 0.795730i
\(290\) 0 0
\(291\) −7.84527 + 5.55356i −0.459898 + 0.325556i
\(292\) 12.9287 + 35.5214i 0.756598 + 2.07873i
\(293\) −12.0712 2.12849i −0.705210 0.124347i −0.190469 0.981693i \(-0.561001\pi\)
−0.514741 + 0.857346i \(0.672112\pi\)
\(294\) 9.48386 + 20.0686i 0.553110 + 1.17042i
\(295\) 0 0
\(296\) 4.53888 0.263817
\(297\) −0.923606 + 1.36326i −0.0535930 + 0.0791044i
\(298\) 40.3243i 2.33592i
\(299\) 2.50838 2.10478i 0.145063 0.121723i
\(300\) 0 0
\(301\) 0.944004 5.35371i 0.0544115 0.308583i
\(302\) 2.90585 + 7.98375i 0.167213 + 0.459413i
\(303\) 7.33993 15.9539i 0.421668 0.916526i
\(304\) 3.03473 + 17.2108i 0.174053 + 0.987106i
\(305\) 0 0
\(306\) −6.42113 + 3.79567i −0.367071 + 0.216984i
\(307\) 22.9271 + 13.2370i 1.30852 + 0.755475i 0.981849 0.189663i \(-0.0607396\pi\)
0.326671 + 0.945138i \(0.394073\pi\)
\(308\) 0.261372 0.718114i 0.0148931 0.0409184i
\(309\) 4.33242 16.5073i 0.246463 0.939070i
\(310\) 0 0
\(311\) −13.5280 11.3513i −0.767100 0.643673i 0.172865 0.984946i \(-0.444698\pi\)
−0.939964 + 0.341272i \(0.889142\pi\)
\(312\) −1.87459 + 1.89394i −0.106128 + 0.107223i
\(313\) −3.29954 + 9.06541i −0.186501 + 0.512407i −0.997342 0.0728589i \(-0.976788\pi\)
0.810841 + 0.585266i \(0.199010\pi\)
\(314\) −7.70019 + 13.3371i −0.434547 + 0.752657i
\(315\) 0 0
\(316\) 13.9056 + 24.0852i 0.782250 + 1.35490i
\(317\) 3.65412 0.644320i 0.205236 0.0361886i −0.0700850 0.997541i \(-0.522327\pi\)
0.275321 + 0.961352i \(0.411216\pi\)
\(318\) 39.7606 3.68439i 2.22967 0.206610i
\(319\) 1.31174 0.477435i 0.0734434 0.0267312i
\(320\) 0 0
\(321\) −5.09927 + 7.36268i −0.284614 + 0.410945i
\(322\) −2.86108 3.40971i −0.159442 0.190016i
\(323\) 7.30748i 0.406599i
\(324\) −11.5550 19.0972i −0.641944 1.06095i
\(325\) 0 0
\(326\) −20.1854 + 16.9376i −1.11797 + 0.938085i
\(327\) 10.4096 + 7.20952i 0.575652 + 0.398687i
\(328\) 5.84948 + 1.03142i 0.322983 + 0.0569507i
\(329\) −2.26237 + 0.823435i −0.124728 + 0.0453974i
\(330\) 0 0
\(331\) −0.245329 1.39133i −0.0134845 0.0764745i 0.977323 0.211755i \(-0.0679177\pi\)
−0.990807 + 0.135280i \(0.956807\pi\)
\(332\) 10.0624 5.80953i 0.552246 0.318839i
\(333\) −2.19126 + 13.2196i −0.120080 + 0.724427i
\(334\) 2.46786 4.27446i 0.135035 0.233888i
\(335\) 0 0
\(336\) −3.36265 3.32830i −0.183447 0.181573i
\(337\) 8.34986 9.95097i 0.454846 0.542064i −0.489073 0.872243i \(-0.662665\pi\)
0.943918 + 0.330179i \(0.107109\pi\)
\(338\) 14.5683 17.3618i 0.792409 0.944356i
\(339\) −4.56209 + 17.3824i −0.247779 + 0.944084i
\(340\) 0 0
\(341\) −1.37428 + 2.38033i −0.0744215 + 0.128902i
\(342\) 39.4992 0.405587i 2.13587 0.0219316i
\(343\) 10.9928 6.34669i 0.593555 0.342689i
\(344\) 0.986567 + 5.59510i 0.0531921 + 0.301667i
\(345\) 0 0
\(346\) −7.12504 + 2.59330i −0.383045 + 0.139417i
\(347\) −4.72753 0.833591i −0.253787 0.0447495i 0.0453070 0.998973i \(-0.485573\pi\)
−0.299094 + 0.954224i \(0.596684\pi\)
\(348\) −1.55236 + 18.8581i −0.0832152 + 1.01090i
\(349\) 17.2954 14.5126i 0.925803 0.776841i −0.0492565 0.998786i \(-0.515685\pi\)
0.975059 + 0.221946i \(0.0712407\pi\)
\(350\) 0 0
\(351\) −4.61112 6.37412i −0.246123 0.340225i
\(352\) 2.52845i 0.134767i
\(353\) 19.0950 + 22.7565i 1.01632 + 1.21121i 0.977276 + 0.211972i \(0.0679884\pi\)
0.0390490 + 0.999237i \(0.487567\pi\)
\(354\) 2.70080 + 5.71509i 0.143546 + 0.303754i
\(355\) 0 0
\(356\) 36.1220 13.1473i 1.91446 0.696807i
\(357\) 1.14302 + 1.61470i 0.0604952 + 0.0854589i
\(358\) 41.6804 7.34937i 2.20288 0.388427i
\(359\) 6.70991 + 11.6219i 0.354136 + 0.613381i 0.986970 0.160906i \(-0.0514418\pi\)
−0.632834 + 0.774288i \(0.718108\pi\)
\(360\) 0 0
\(361\) −9.84920 + 17.0593i −0.518379 + 0.897858i
\(362\) −7.04550 + 19.3573i −0.370303 + 1.01740i
\(363\) −4.97970 18.2100i −0.261366 0.955778i
\(364\) 2.79686 + 2.34685i 0.146595 + 0.123008i
\(365\) 0 0
\(366\) 3.58852 0.981314i 0.187575 0.0512941i
\(367\) −2.71905 + 7.47054i −0.141933 + 0.389959i −0.990208 0.139597i \(-0.955419\pi\)
0.848275 + 0.529556i \(0.177641\pi\)
\(368\) −5.26184 3.03793i −0.274293 0.158363i
\(369\) −5.82801 + 16.5387i −0.303394 + 0.860973i
\(370\) 0 0
\(371\) −1.83904 10.4297i −0.0954782 0.541484i
\(372\) −21.5262 30.4091i −1.11608 1.57664i
\(373\) −3.90604 10.7318i −0.202247 0.555670i 0.796557 0.604564i \(-0.206653\pi\)
−0.998804 + 0.0488939i \(0.984430\pi\)
\(374\) −0.136823 + 0.775963i −0.00707496 + 0.0401241i
\(375\) 0 0
\(376\) 1.92745 1.61733i 0.0994009 0.0834072i
\(377\) 6.66917i 0.343480i
\(378\) −8.66451 + 6.26801i −0.445654 + 0.322392i
\(379\) 24.1705 1.24155 0.620777 0.783987i \(-0.286817\pi\)
0.620777 + 0.783987i \(0.286817\pi\)
\(380\) 0 0
\(381\) 9.02366 + 0.742807i 0.462296 + 0.0380551i
\(382\) 37.0129 + 6.52637i 1.89374 + 0.333918i
\(383\) 3.22979 + 8.87378i 0.165035 + 0.453429i 0.994451 0.105202i \(-0.0335489\pi\)
−0.829416 + 0.558631i \(0.811327\pi\)
\(384\) 12.4231 + 5.71553i 0.633964 + 0.291669i
\(385\) 0 0
\(386\) 11.2015 + 19.4016i 0.570143 + 0.987516i
\(387\) −16.7721 + 0.172220i −0.852573 + 0.00875442i
\(388\) −11.9193 6.88162i −0.605111 0.349361i
\(389\) −2.39406 0.871367i −0.121384 0.0441801i 0.280614 0.959821i \(-0.409462\pi\)
−0.401998 + 0.915641i \(0.631684\pi\)
\(390\) 0 0
\(391\) 1.94617 + 1.63303i 0.0984218 + 0.0825857i
\(392\) −3.95474 + 4.71308i −0.199745 + 0.238046i
\(393\) −8.81457 + 8.90554i −0.444636 + 0.449225i
\(394\) −28.1617 10.2500i −1.41876 0.516388i
\(395\) 0 0
\(396\) −2.32610 0.385571i −0.116891 0.0193757i
\(397\) 3.18279 1.83759i 0.159740 0.0922258i −0.417999 0.908447i \(-0.637269\pi\)
0.577739 + 0.816222i \(0.303935\pi\)
\(398\) −15.7173 + 2.77138i −0.787836 + 0.138917i
\(399\) −0.966669 10.4319i −0.0483940 0.522251i
\(400\) 0 0
\(401\) 2.80420 15.9034i 0.140035 0.794177i −0.831186 0.555995i \(-0.812337\pi\)
0.971220 0.238182i \(-0.0765516\pi\)
\(402\) 2.58151 + 1.78791i 0.128754 + 0.0891731i
\(403\) −8.44078 10.0593i −0.420465 0.501091i
\(404\) 25.1458 1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) 0.909859 + 1.08433i 0.0451000 + 0.0537481i
\(408\) −1.69968 1.17717i −0.0841465 0.0582785i
\(409\) −1.59443 + 9.04248i −0.0788396 + 0.447122i 0.919677 + 0.392676i \(0.128450\pi\)
−0.998517 + 0.0544462i \(0.982661\pi\)
\(410\) 0 0
\(411\) 1.79780 + 19.4013i 0.0886792 + 0.956994i
\(412\) 24.0658 4.24345i 1.18564 0.209060i
\(413\) 1.45190 0.838253i 0.0714432 0.0412477i
\(414\) −8.71900 + 10.6103i −0.428515 + 0.521466i
\(415\) 0 0
\(416\) 11.3514 + 4.13157i 0.556548 + 0.202567i
\(417\) −11.4292 + 11.5471i −0.559689 + 0.565466i
\(418\) 2.68215 3.19646i 0.131188 0.156344i
\(419\) 5.34613 + 4.48594i 0.261176 + 0.219152i 0.763967 0.645256i \(-0.223249\pi\)
−0.502791 + 0.864408i \(0.667694\pi\)
\(420\) 0 0
\(421\) −28.9525 10.5379i −1.41106 0.513584i −0.479619 0.877477i \(-0.659225\pi\)
−0.931441 + 0.363894i \(0.881447\pi\)
\(422\) 9.55686 + 5.51765i 0.465221 + 0.268595i
\(423\) 3.77996 + 6.39454i 0.183788 + 0.310913i
\(424\) 5.53405 + 9.58526i 0.268757 + 0.465502i
\(425\) 0 0
\(426\) −31.9589 14.7034i −1.54842 0.712383i
\(427\) −0.337472 0.927196i −0.0163314 0.0448702i
\(428\) −12.6292 2.22687i −0.610457 0.107640i
\(429\) −0.828236 0.0681784i −0.0399876 0.00329169i
\(430\) 0 0
\(431\) 27.8971 1.34376 0.671879 0.740661i \(-0.265487\pi\)
0.671879 + 0.740661i \(0.265487\pi\)
\(432\) −8.18774 + 12.0853i −0.393933 + 0.581453i
\(433\) 19.1706i 0.921278i −0.887588 0.460639i \(-0.847620\pi\)
0.887588 0.460639i \(-0.152380\pi\)
\(434\) −13.6739 + 11.4738i −0.656369 + 0.550759i
\(435\) 0 0
\(436\) −3.14843 + 17.8556i −0.150782 + 0.855130i
\(437\) −4.60154 12.6426i −0.220121 0.604778i
\(438\) −32.2849 45.6075i −1.54263 2.17921i
\(439\) 4.12397 + 23.3882i 0.196826 + 1.11626i 0.909794 + 0.415060i \(0.136239\pi\)
−0.712968 + 0.701197i \(0.752649\pi\)
\(440\) 0 0
\(441\) −11.8177 13.7936i −0.562746 0.656838i
\(442\) −3.26009 1.88221i −0.155067 0.0895278i
\(443\) −7.98900 + 21.9496i −0.379569 + 1.04286i 0.591967 + 0.805962i \(0.298352\pi\)
−0.971536 + 0.236894i \(0.923871\pi\)
\(444\) −18.5076 + 5.06108i −0.878332 + 0.240188i
\(445\) 0 0
\(446\) −28.6892 24.0731i −1.35847 1.13989i
\(447\) −8.70396 31.8291i −0.411683 1.50546i
\(448\) 3.74762 10.2965i 0.177059 0.486464i
\(449\) 2.40953 4.17343i 0.113713 0.196956i −0.803552 0.595235i \(-0.797059\pi\)
0.917264 + 0.398279i \(0.130392\pi\)
\(450\) 0 0
\(451\) 0.926176 + 1.60418i 0.0436119 + 0.0755380i
\(452\) −25.3416 + 4.46841i −1.19197 + 0.210176i
\(453\) −4.01695 5.67457i −0.188733 0.266615i
\(454\) 31.3701 11.4178i 1.47227 0.535863i
\(455\) 0 0
\(456\) 4.67813 + 9.89928i 0.219074 + 0.463576i
\(457\) −3.14555 3.74872i −0.147142 0.175358i 0.687439 0.726242i \(-0.258735\pi\)
−0.834581 + 0.550885i \(0.814290\pi\)
\(458\) 3.73978i 0.174749i
\(459\) 4.24908 4.38203i 0.198330 0.204535i
\(460\) 0 0
\(461\) 21.4419 17.9919i 0.998650 0.837967i 0.0118535 0.999930i \(-0.496227\pi\)
0.986797 + 0.161963i \(0.0517824\pi\)
\(462\) −0.0926768 + 1.12584i −0.00431171 + 0.0523789i
\(463\) 27.0579 + 4.77104i 1.25749 + 0.221729i 0.762396 0.647111i \(-0.224023\pi\)
0.495093 + 0.868840i \(0.335134\pi\)
\(464\) 11.6285 4.23245i 0.539842 0.196486i
\(465\) 0 0
\(466\) 5.10832 + 28.9707i 0.236639 + 1.34204i
\(467\) −18.4000 + 10.6232i −0.851450 + 0.491585i −0.861140 0.508368i \(-0.830249\pi\)
0.00968963 + 0.999953i \(0.496916\pi\)
\(468\) 5.53194 9.81292i 0.255714 0.453602i
\(469\) 0.416426 0.721272i 0.0192288 0.0333052i
\(470\) 0 0
\(471\) 3.19917 12.1894i 0.147410 0.561659i
\(472\) −1.12623 + 1.34218i −0.0518387 + 0.0617790i
\(473\) −1.13889 + 1.35728i −0.0523662 + 0.0624076i
\(474\) −29.2186 28.9201i −1.34205 1.32834i
\(475\) 0 0
\(476\) −1.41636 + 2.45321i −0.0649188 + 0.112443i
\(477\) −30.5889 + 11.4905i −1.40057 + 0.526113i
\(478\) −36.3543 + 20.9892i −1.66281 + 0.960022i
\(479\) 7.23745 + 41.0456i 0.330688 + 1.87542i 0.466248 + 0.884654i \(0.345606\pi\)
−0.135560 + 0.990769i \(0.543283\pi\)
\(480\) 0 0
\(481\) −6.35480 + 2.31296i −0.289754 + 0.105462i
\(482\) −40.3859 7.12113i −1.83953 0.324358i
\(483\) 2.99431 + 2.07381i 0.136246 + 0.0943618i
\(484\) 20.7077 17.3758i 0.941258 0.789809i
\(485\) 0 0
\(486\) 23.9220 + 22.7244i 1.08513 + 1.03080i
\(487\) 4.02801i 0.182527i 0.995827 + 0.0912634i \(0.0290905\pi\)
−0.995827 + 0.0912634i \(0.970909\pi\)
\(488\) 0.662836 + 0.789937i 0.0300052 + 0.0357588i
\(489\) 12.2769 17.7263i 0.555183 0.801611i
\(490\) 0 0
\(491\) 36.2922 13.2093i 1.63784 0.596126i 0.651184 0.758920i \(-0.274273\pi\)
0.986660 + 0.162793i \(0.0520504\pi\)
\(492\) −25.0017 + 2.31677i −1.12716 + 0.104448i
\(493\) −5.09577 + 0.898521i −0.229502 + 0.0404674i
\(494\) 9.96769 + 17.2645i 0.448468 + 0.776769i
\(495\) 0 0
\(496\) −12.1830 + 21.1015i −0.547032 + 0.947487i
\(497\) −3.19114 + 8.76759i −0.143142 + 0.393280i
\(498\) −12.0823 + 12.2070i −0.541423 + 0.547011i
\(499\) 3.11922 + 2.61734i 0.139636 + 0.117168i 0.709930 0.704272i \(-0.248726\pi\)
−0.570295 + 0.821440i \(0.693171\pi\)
\(500\) 0 0
\(501\) −1.02531 + 3.90664i −0.0458076 + 0.174536i
\(502\) 3.96403 10.8911i 0.176923 0.486093i
\(503\) −2.96695 1.71297i −0.132290 0.0763775i 0.432395 0.901684i \(-0.357669\pi\)
−0.564684 + 0.825307i \(0.691002\pi\)
\(504\) −2.58213 1.45565i −0.115017 0.0648398i
\(505\) 0 0
\(506\) 0.251909 + 1.42865i 0.0111987 + 0.0635111i
\(507\) −7.75161 + 16.8487i −0.344261 + 0.748276i
\(508\) 4.43412 + 12.1827i 0.196732 + 0.540518i
\(509\) 2.12952 12.0771i 0.0943893 0.535308i −0.900543 0.434766i \(-0.856831\pi\)
0.994933 0.100542i \(-0.0320578\pi\)
\(510\) 0 0
\(511\) −11.3529 + 9.52619i −0.502222 + 0.421414i
\(512\) 28.1241i 1.24292i
\(513\) −31.0903 + 8.84601i −1.37267 + 0.390561i
\(514\) −24.4791 −1.07973
\(515\) 0 0
\(516\) −10.2616 21.7143i −0.451742 0.955920i
\(517\) 0.772750 + 0.136257i 0.0339855 + 0.00599257i
\(518\) 3.14407 + 8.63825i 0.138142 + 0.379543i
\(519\) 5.06423 3.58490i 0.222295 0.157360i
\(520\) 0 0
\(521\) −7.04117 12.1957i −0.308479 0.534302i 0.669551 0.742766i \(-0.266487\pi\)
−0.978030 + 0.208465i \(0.933153\pi\)
\(522\) −5.13962 27.4943i −0.224955 1.20339i
\(523\) 8.46897 + 4.88956i 0.370322 + 0.213806i 0.673599 0.739097i \(-0.264747\pi\)
−0.303277 + 0.952902i \(0.598081\pi\)
\(524\) −16.8597 6.13643i −0.736520 0.268071i
\(525\) 0 0
\(526\) −10.5035 8.81348i −0.457974 0.384286i
\(527\) 6.54892 7.80469i 0.285275 0.339978i
\(528\) 0.406744 + 1.48740i 0.0177013 + 0.0647309i
\(529\) −17.2176 6.26668i −0.748590 0.272464i
\(530\) 0 0
\(531\) −3.36541 3.92812i −0.146047 0.170466i
\(532\) 12.9915 7.50065i 0.563254 0.325195i
\(533\) −8.71534 + 1.53675i −0.377503 + 0.0665640i
\(534\) −46.3785 + 32.8307i −2.00699 + 1.42072i
\(535\) 0 0
\(536\) −0.151144 + 0.857180i −0.00652843 + 0.0370245i
\(537\) −31.3131 + 14.7977i −1.35126 + 0.638569i
\(538\) −18.8280 22.4384i −0.811734 0.967387i
\(539\) −1.91871 −0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) −2.64674 3.15426i −0.113687 0.135487i
\(543\) 1.38294 16.8001i 0.0593477 0.720959i
\(544\) −1.62750 + 9.22999i −0.0697783 + 0.395732i
\(545\) 0 0
\(546\) −4.90300 2.25573i −0.209829 0.0965365i
\(547\) −1.09341 + 0.192798i −0.0467508 + 0.00824343i −0.196975 0.980409i \(-0.563112\pi\)
0.150224 + 0.988652i \(0.452001\pi\)
\(548\) −24.1615 + 13.9497i −1.03213 + 0.595900i
\(549\) −2.62070 + 1.54916i −0.111849 + 0.0661164i
\(550\) 0 0
\(551\) 25.7495 + 9.37206i 1.09697 + 0.399263i
\(552\) −3.68186 0.966321i −0.156711 0.0411293i
\(553\) −7.00864 + 8.35257i −0.298038 + 0.355188i
\(554\) 20.2236 + 16.9696i 0.859216 + 0.720968i
\(555\) 0 0
\(556\) −21.8607 7.95664i −0.927100 0.337437i
\(557\) −30.3458 17.5201i −1.28579 0.742352i −0.307890 0.951422i \(-0.599623\pi\)
−0.977901 + 0.209070i \(0.932956\pi\)
\(558\) 42.5503 + 34.9657i 1.80130 + 1.48022i
\(559\) −4.23247 7.33084i −0.179014 0.310062i
\(560\) 0 0
\(561\) −0.0594925 0.642022i −0.00251178 0.0271062i
\(562\) 7.06254 + 19.4042i 0.297915 + 0.818516i
\(563\) 38.1822 + 6.73255i 1.60919 + 0.283743i 0.904724 0.425998i \(-0.140077\pi\)
0.704463 + 0.709741i \(0.251188\pi\)
\(564\) −6.05593 + 8.74396i −0.255001 + 0.368187i
\(565\) 0 0
\(566\) −56.2413 −2.36400
\(567\) 5.48619 6.81774i 0.230398 0.286318i
\(568\) 9.75095i 0.409141i
\(569\) 26.0213 21.8344i 1.09087 0.915347i 0.0940904 0.995564i \(-0.470006\pi\)
0.996777 + 0.0802169i \(0.0255613\pi\)
\(570\) 0 0
\(571\) 1.75191 9.93559i 0.0733153 0.415792i −0.925956 0.377631i \(-0.876739\pi\)
0.999272 0.0381610i \(-0.0121500\pi\)
\(572\) −0.406986 1.11818i −0.0170169 0.0467536i
\(573\) −30.6240 + 2.83775i −1.27934 + 0.118549i
\(574\) 2.08894 + 11.8470i 0.0871908 + 0.494484i
\(575\) 0 0
\(576\) −33.3522 5.52842i −1.38968 0.230351i
\(577\) 10.5069 + 6.06615i 0.437407 + 0.252537i 0.702497 0.711687i \(-0.252068\pi\)
−0.265090 + 0.964224i \(0.585402\pi\)
\(578\) −11.3078 + 31.0680i −0.470344 + 1.29226i
\(579\) −13.0295 12.8964i −0.541487 0.535956i
\(580\) 0 0
\(581\) 3.48957 + 2.92810i 0.144772 + 0.121478i
\(582\) 19.6785 + 5.16470i 0.815700 + 0.214084i
\(583\) −1.18055 + 3.24352i −0.0488932 + 0.134333i
\(584\) 7.74416 13.4133i 0.320456 0.555046i
\(585\) 0 0
\(586\) 12.9722 + 22.4685i 0.535877 + 0.928167i
\(587\) −31.2669 + 5.51319i −1.29052 + 0.227554i −0.776442 0.630189i \(-0.782977\pi\)
−0.514079 + 0.857743i \(0.671866\pi\)
\(588\) 10.8704 23.6276i 0.448288 0.974387i
\(589\) −50.7006 + 18.4535i −2.08908 + 0.760363i
\(590\) 0 0
\(591\) 24.4412 + 2.01195i 1.00538 + 0.0827605i
\(592\) 8.06588 + 9.61254i 0.331506 + 0.395073i
\(593\) 13.4906i 0.553993i −0.960871 0.276996i \(-0.910661\pi\)
0.960871 0.276996i \(-0.0893390\pi\)
\(594\) 3.46703 0.357210i 0.142254 0.0146565i
\(595\) 0 0
\(596\) 36.1947 30.3710i 1.48259 1.24404i
\(597\) 11.8079 5.58009i 0.483265 0.228378i
\(598\) −6.82550 1.20352i −0.279115 0.0492156i
\(599\) −39.8715 + 14.5120i −1.62911 + 0.592946i −0.985086 0.172063i \(-0.944957\pi\)
−0.644020 + 0.765009i \(0.722735\pi\)
\(600\) 0 0
\(601\) −3.43906 19.5039i −0.140282 0.795579i −0.971035 0.238938i \(-0.923201\pi\)
0.830753 0.556641i \(-0.187910\pi\)
\(602\) −9.96501 + 5.75330i −0.406144 + 0.234487i
\(603\) −2.42358 0.854034i −0.0986958 0.0347789i
\(604\) 4.97755 8.62136i 0.202533 0.350798i
\(605\) 0 0
\(606\) −35.8543 + 9.80470i −1.45648 + 0.398289i
\(607\) 23.1397 27.5769i 0.939213 1.11931i −0.0534715 0.998569i \(-0.517029\pi\)
0.992684 0.120741i \(-0.0385269\pi\)
\(608\) 31.9038 38.0215i 1.29387 1.54197i
\(609\) −7.15571 + 1.95680i −0.289964 + 0.0792934i
\(610\) 0 0
\(611\) −1.87442 + 3.24659i −0.0758310 + 0.131343i
\(612\) 8.24315 + 2.90476i 0.333209 + 0.117418i
\(613\) −22.9175 + 13.2314i −0.925627 + 0.534411i −0.885426 0.464780i \(-0.846133\pi\)
−0.0402013 + 0.999192i \(0.512800\pi\)
\(614\) −9.73045 55.1841i −0.392689 2.22705i
\(615\) 0 0
\(616\) −0.294234 + 0.107093i −0.0118550 + 0.00431488i
\(617\) 48.3705 + 8.52903i 1.94732 + 0.343366i 0.999713 + 0.0239406i \(0.00762125\pi\)
0.947611 + 0.319425i \(0.103490\pi\)
\(618\) −32.6599 + 15.4342i −1.31377 + 0.620853i
\(619\) 18.5430 15.5595i 0.745307 0.625387i −0.188950 0.981987i \(-0.560508\pi\)
0.934257 + 0.356600i \(0.116064\pi\)
\(620\) 0 0
\(621\) 4.59193 10.2570i 0.184268 0.411598i
\(622\) 37.3785i 1.49874i
\(623\) 9.68725 + 11.5448i 0.388111 + 0.462533i
\(624\) −7.34229 0.604400i −0.293927 0.0241954i
\(625\) 0 0
\(626\) 19.1881 6.98388i 0.766909 0.279132i
\(627\) −1.42714 + 3.10199i −0.0569945 + 0.123882i
\(628\) 17.7708 3.13347i 0.709132 0.125039i
\(629\) −2.62345 4.54395i −0.104604 0.181179i
\(630\) 0 0
\(631\) −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i \(-0.947917\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(632\) 3.89736 10.7079i 0.155029 0.425938i
\(633\) −8.73447 2.29240i −0.347164 0.0911147i
\(634\) −6.01629 5.04827i −0.238937 0.200492i
\(635\) 0 0
\(636\) −33.2535 32.9138i −1.31859 1.30512i
\(637\) 3.13523 8.61398i 0.124222 0.341298i
\(638\) −2.55880 1.47732i −0.101304 0.0584878i
\(639\) 28.3998 + 4.70751i 1.12348 + 0.186226i
\(640\) 0 0
\(641\) 6.60738 + 37.4723i 0.260976 + 1.48007i 0.780254 + 0.625463i \(0.215090\pi\)
−0.519278 + 0.854605i \(0.673799\pi\)
\(642\) 18.8758 1.74911i 0.744968 0.0690319i
\(643\) 16.0553 + 44.1115i 0.633158 + 1.73959i 0.672220 + 0.740352i \(0.265341\pi\)
−0.0390615 + 0.999237i \(0.512437\pi\)
\(644\) −0.905644 + 5.13616i −0.0356874 + 0.202393i
\(645\) 0 0
\(646\) −11.8485 + 9.94211i −0.466175 + 0.391167i
\(647\) 28.2333i 1.10997i −0.831862 0.554983i \(-0.812725\pi\)
0.831862 0.554983i \(-0.187275\pi\)
\(648\) −2.95083 + 8.65643i −0.115920 + 0.340057i
\(649\) −0.546406 −0.0214483
\(650\) 0 0
\(651\) 8.31660 12.0081i 0.325953 0.470634i
\(652\) 30.4060 + 5.36140i 1.19079 + 0.209969i
\(653\) 12.0758 + 33.1779i 0.472562 + 1.29835i 0.915687 + 0.401893i \(0.131647\pi\)
−0.443125 + 0.896460i \(0.646130\pi\)
\(654\) −2.47295 26.6872i −0.0967001 1.04355i
\(655\) 0 0
\(656\) 8.21052 + 14.2210i 0.320567 + 0.555239i
\(657\) 35.3277 + 29.0306i 1.37826 + 1.13259i
\(658\) 4.41318 + 2.54795i 0.172044 + 0.0993295i
\(659\) 39.1793 + 14.2601i 1.52621 + 0.555494i 0.962689 0.270609i \(-0.0872250\pi\)
0.563519 + 0.826103i \(0.309447\pi\)
\(660\) 0 0
\(661\) 0.975874 + 0.818856i 0.0379571 + 0.0318498i 0.661569 0.749884i \(-0.269891\pi\)
−0.623612 + 0.781734i \(0.714335\pi\)
\(662\) −1.92216 + 2.29075i −0.0747070 + 0.0890324i
\(663\) 2.97956 + 0.781997i 0.115716 + 0.0303702i
\(664\) −4.47359 1.62825i −0.173609 0.0631885i
\(665\) 0 0
\(666\) 24.4158 14.4328i 0.946095 0.559258i
\(667\) −8.25035 + 4.76334i −0.319455 + 0.184437i
\(668\) −5.69543 + 1.00426i −0.220363 + 0.0388559i
\(669\) 27.8413 + 12.8090i 1.07641 + 0.495226i
\(670\) 0 0
\(671\) −0.0558427 + 0.316700i −0.00215578 + 0.0122261i
\(672\) −1.10238 + 13.3918i −0.0425252 + 0.516598i
\(673\) −22.9043 27.2963i −0.882896 1.05219i −0.998266 0.0588715i \(-0.981250\pi\)
0.115370 0.993323i \(-0.463195\pi\)
\(674\) −27.4951 −1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) 11.5714 + 13.7902i 0.444725 + 0.530002i 0.941110 0.338100i \(-0.109784\pi\)
−0.496386 + 0.868102i \(0.665340\pi\)
\(678\) 34.3913 16.2524i 1.32079 0.624169i
\(679\) 0.936996 5.31397i 0.0359586 0.203931i
\(680\) 0 0
\(681\) −22.2968 + 15.7836i −0.854414 + 0.604828i
\(682\) 5.72929 1.01023i 0.219386 0.0386836i
\(683\) −34.4344 + 19.8807i −1.31760 + 0.760715i −0.983341 0.181768i \(-0.941818\pi\)
−0.334255 + 0.942483i \(0.608485\pi\)
\(684\) −30.1136 35.1486i −1.15142 1.34394i
\(685\) 0 0
\(686\) −25.2468 9.18909i −0.963928 0.350841i
\(687\) 0.807229 + 2.95192i 0.0307977 + 0.112623i
\(688\) −10.0962 + 12.0322i −0.384915 + 0.458724i
\(689\) −12.6327 10.6001i −0.481266 0.403830i
\(690\) 0 0
\(691\) 15.8251 + 5.75986i 0.602015 + 0.219115i 0.625006 0.780620i \(-0.285097\pi\)
−0.0229909 + 0.999736i \(0.507319\pi\)
\(692\) 7.69408 + 4.44218i 0.292485 + 0.168866i
\(693\) −0.169860 0.908663i −0.00645244 0.0345173i
\(694\) 5.08038 + 8.79948i 0.192849 + 0.334024i
\(695\) 0 0
\(696\) 6.32790 4.47944i 0.239859 0.169793i
\(697\) −2.34839 6.45216i −0.0889518 0.244393i
\(698\) −47.0622 8.29833i −1.78133 0.314097i
\(699\) −10.2854 21.7648i −0.389031 0.823220i
\(700\) 0 0
\(701\) −8.96921 −0.338762 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(702\) −4.06156 + 16.1488i −0.153294 + 0.609498i
\(703\) 27.7861i 1.04797i
\(704\) −2.73570 + 2.29552i −0.103106 + 0.0865158i
\(705\) 0 0
\(706\) 10.9186 61.9223i 0.410926 2.33048i
\(707\) 3.37181 + 9.26398i 0.126810 + 0.348408i
\(708\) 3.09566 6.72864i 0.116342 0.252878i
\(709\) −3.15026 17.8660i −0.118311 0.670973i −0.985058 0.172225i \(-0.944904\pi\)
0.866747 0.498748i \(-0.166207\pi\)
\(710\) 0 0
\(711\) 29.3054 + 16.5206i 1.09904 + 0.619572i
\(712\) −13.6401 7.87509i −0.511183 0.295131i
\(713\) 6.41560 17.6267i 0.240266 0.660125i
\(714\) 1.06299 4.05019i 0.0397814 0.151574i
\(715\) 0 0
\(716\) −37.9890 31.8766i −1.41972 1.19128i
\(717\) 24.1650 24.4144i 0.902457 0.911771i
\(718\) 9.71498 26.6917i 0.362560 0.996125i
\(719\) 15.7860 27.3421i 0.588718 1.01969i −0.405683 0.914014i \(-0.632966\pi\)
0.994401 0.105675i \(-0.0337004\pi\)
\(720\) 0 0
\(721\) 4.79034 + 8.29711i 0.178402 + 0.309001i
\(722\) 41.0606 7.24010i 1.52812 0.269449i
\(723\) 33.4148 3.09636i 1.24271 0.115155i
\(724\) 22.6814 8.25536i 0.842948 0.306808i
\(725\) 0 0
\(726\) −22.7511 + 32.8497i −0.844374 + 1.21916i
\(727\) 24.6890 + 29.4232i 0.915664 + 1.09125i 0.995530 + 0.0944407i \(0.0301063\pi\)
−0.0798662 + 0.996806i \(0.525449\pi\)
\(728\) 1.49595i 0.0554436i
\(729\) −23.7874 12.7734i −0.881014 0.473090i
\(730\) 0 0
\(731\) 5.03111 4.22160i 0.186082 0.156142i
\(732\) −3.58358 2.48193i −0.132453 0.0917346i
\(733\) 29.8695 + 5.26680i 1.10326 + 0.194534i 0.695478 0.718547i \(-0.255193\pi\)
0.407778 + 0.913081i \(0.366304\pi\)
\(734\) 15.8123 5.75521i 0.583643 0.212429i
\(735\) 0 0
\(736\) 2.99643 + 16.9936i 0.110450 + 0.626391i
\(737\) −0.235076 + 0.135721i −0.00865915 + 0.00499936i
\(738\) 34.7456 13.0519i 1.27900 0.480448i
\(739\) 5.00127 8.66245i 0.183975 0.318653i −0.759256 0.650792i \(-0.774437\pi\)
0.943230 + 0.332139i \(0.107770\pi\)
\(740\) 0 0
\(741\) −11.5943 11.4759i −0.425928 0.421577i
\(742\) −14.4089 + 17.1719i −0.528969 + 0.630400i
\(743\) 23.3163 27.7873i 0.855394 1.01942i −0.144160 0.989554i \(-0.546048\pi\)
0.999554 0.0298642i \(-0.00950748\pi\)
\(744\) −3.87523 + 14.7654i −0.142073 + 0.541324i
\(745\) 0 0
\(746\) −12.0865 + 20.9344i −0.442517 + 0.766461i
\(747\) 6.90205 12.2433i 0.252533 0.447960i
\(748\) 0.799548 0.461619i 0.0292344 0.0168785i
\(749\) −0.873058 4.95136i −0.0319008 0.180919i
\(750\) 0 0
\(751\) 13.6766 4.97788i 0.499067 0.181646i −0.0802073 0.996778i \(-0.525558\pi\)
0.579274 + 0.815133i \(0.303336\pi\)
\(752\) 6.85041 + 1.20791i 0.249809 + 0.0440480i
\(753\) −0.778089 + 9.45226i −0.0283551 + 0.344460i
\(754\) 10.8136 9.07366i 0.393807 0.330443i
\(755\) 0 0
\(756\) 12.1519 + 3.05631i 0.441962 + 0.111157i
\(757\) 45.5754i 1.65646i −0.560385 0.828232i \(-0.689347\pi\)
0.560385 0.828232i \(-0.310653\pi\)
\(758\) −32.8849 39.1907i −1.19443 1.42347i
\(759\) −0.507211 1.07330i −0.0184106 0.0389582i
\(760\) 0 0
\(761\) −20.9040 + 7.60843i −0.757769 + 0.275805i −0.691871 0.722021i \(-0.743213\pi\)
−0.0658978 + 0.997826i \(0.520991\pi\)
\(762\) −11.0726 15.6418i −0.401119 0.566643i
\(763\) −7.00040 + 1.23436i −0.253431 + 0.0446868i
\(764\) −22.0189 38.1379i −0.796616 1.37978i
\(765\) 0 0
\(766\) 9.99393 17.3100i 0.361096 0.625436i
\(767\) 0.892846 2.45307i 0.0322388 0.0885754i
\(768\) 2.66224 + 9.73542i 0.0960654 + 0.351297i
\(769\) −10.4679 8.78365i −0.377484 0.316747i 0.434230 0.900802i \(-0.357021\pi\)
−0.811714 + 0.584056i \(0.801465\pi\)
\(770\) 0 0
\(771\) 19.3220 5.28379i 0.695866 0.190291i
\(772\) 8.97807 24.6670i 0.323128 0.887786i
\(773\) −17.8869 10.3270i −0.643345 0.371436i 0.142557 0.989787i \(-0.454468\pi\)
−0.785902 + 0.618351i \(0.787801\pi\)
\(774\) 23.0983 + 26.9604i 0.830252 + 0.969072i
\(775\) 0 0
\(776\) 0.979243 + 5.55356i 0.0351528 + 0.199361i