Properties

Label 225.2.q.a.121.12
Level $225$
Weight $2$
Character 225.121
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 121.12
Character \(\chi\) \(=\) 225.121
Dual form 225.2.q.a.106.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.745950 + 0.158557i) q^{2} +(1.13811 + 1.30565i) q^{3} +(-1.29579 + 0.576923i) q^{4} +(-1.26382 + 1.84465i) q^{5} +(-1.05599 - 0.793494i) q^{6} +(-0.476660 - 0.825599i) q^{7} +(2.10906 - 1.53232i) q^{8} +(-0.409434 + 2.97193i) q^{9} +O(q^{10})\) \(q+(-0.745950 + 0.158557i) q^{2} +(1.13811 + 1.30565i) q^{3} +(-1.29579 + 0.576923i) q^{4} +(-1.26382 + 1.84465i) q^{5} +(-1.05599 - 0.793494i) q^{6} +(-0.476660 - 0.825599i) q^{7} +(2.10906 - 1.53232i) q^{8} +(-0.409434 + 2.97193i) q^{9} +(0.650268 - 1.57641i) q^{10} +(-2.83092 + 0.601732i) q^{11} +(-2.22800 - 1.03525i) q^{12} +(-1.91095 - 0.406185i) q^{13} +(0.486468 + 0.540278i) q^{14} +(-3.84683 + 0.449300i) q^{15} +(0.567924 - 0.630744i) q^{16} +(-5.51944 + 4.01011i) q^{17} +(-0.165802 - 2.28183i) q^{18} +(3.77403 - 2.74200i) q^{19} +(0.573428 - 3.11941i) q^{20} +(0.535453 - 1.56197i) q^{21} +(2.01632 - 0.897723i) q^{22} +(5.89471 + 6.54674i) q^{23} +(4.40100 + 1.00975i) q^{24} +(-1.80550 - 4.66264i) q^{25} +1.48988 q^{26} +(-4.34627 + 2.84779i) q^{27} +(1.09396 + 0.794807i) q^{28} +(-0.0975850 + 0.928459i) q^{29} +(2.79831 - 0.945095i) q^{30} +(0.277775 + 2.64285i) q^{31} +(-2.93057 + 5.07590i) q^{32} +(-4.00754 - 3.01136i) q^{33} +(3.48139 - 3.86648i) q^{34} +(2.12536 + 0.164140i) q^{35} +(-1.18403 - 4.08721i) q^{36} +(0.799338 + 2.46011i) q^{37} +(-2.38048 + 2.64379i) q^{38} +(-1.64453 - 2.95731i) q^{39} +(0.161121 + 5.82706i) q^{40} +(5.30176 + 1.12692i) q^{41} +(-0.151761 + 1.25005i) q^{42} +(4.43871 + 7.68807i) q^{43} +(3.32113 - 2.41294i) q^{44} +(-4.96473 - 4.51126i) q^{45} +(-5.43519 - 3.94889i) q^{46} +(0.419452 - 3.99082i) q^{47} +(1.46989 + 0.0236566i) q^{48} +(3.04559 - 5.27512i) q^{49} +(2.08610 + 3.19182i) q^{50} +(-11.5175 - 2.64252i) q^{51} +(2.71053 - 0.576140i) q^{52} +(4.30252 + 3.12596i) q^{53} +(2.79057 - 2.81344i) q^{54} +(2.46781 - 5.98256i) q^{55} +(-2.27038 - 1.01084i) q^{56} +(7.87533 + 1.80688i) q^{57} +(-0.0744198 - 0.708057i) q^{58} +(-4.69343 - 0.997620i) q^{59} +(4.72548 - 2.80152i) q^{60} +(10.9896 - 2.33592i) q^{61} +(-0.626247 - 1.92739i) q^{62} +(2.64878 - 1.07857i) q^{63} +(0.856686 - 2.63661i) q^{64} +(3.16438 - 3.01170i) q^{65} +(3.46689 + 1.61090i) q^{66} +(-0.387024 - 3.68228i) q^{67} +(4.83851 - 8.38055i) q^{68} +(-1.83894 + 15.1473i) q^{69} +(-1.61144 + 0.214549i) q^{70} +(-0.125408 - 0.0911140i) q^{71} +(3.69042 + 6.89535i) q^{72} +(-3.09917 + 9.53828i) q^{73} +(-0.986332 - 1.70838i) q^{74} +(4.03292 - 7.66391i) q^{75} +(-3.30843 + 5.73038i) q^{76} +(1.84618 + 2.05039i) q^{77} +(1.69564 + 1.94525i) q^{78} +(-0.442202 + 4.20727i) q^{79} +(0.445747 + 1.84477i) q^{80} +(-8.66473 - 2.43362i) q^{81} -4.13353 q^{82} +(-3.01510 - 1.34241i) q^{83} +(0.207301 + 2.33290i) q^{84} +(-0.421657 - 15.2495i) q^{85} +(-4.53005 - 5.03113i) q^{86} +(-1.32330 + 0.929272i) q^{87} +(-5.04853 + 5.60696i) q^{88} +(5.32122 - 16.3770i) q^{89} +(4.41873 + 2.57798i) q^{90} +(0.575527 + 1.77129i) q^{91} +(-11.4153 - 5.08241i) q^{92} +(-3.13449 + 3.37051i) q^{93} +(0.319881 + 3.04346i) q^{94} +(0.288317 + 10.4272i) q^{95} +(-9.96263 + 1.95061i) q^{96} +(0.203049 - 1.93189i) q^{97} +(-1.43545 + 4.41787i) q^{98} +(-0.629227 - 8.65968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.745950 + 0.158557i −0.527466 + 0.112116i −0.463945 0.885864i \(-0.653566\pi\)
−0.0635213 + 0.997980i \(0.520233\pi\)
\(3\) 1.13811 + 1.30565i 0.657085 + 0.753816i
\(4\) −1.29579 + 0.576923i −0.647895 + 0.288461i
\(5\) −1.26382 + 1.84465i −0.565200 + 0.824954i
\(6\) −1.05599 0.793494i −0.431105 0.323943i
\(7\) −0.476660 0.825599i −0.180161 0.312047i 0.761775 0.647842i \(-0.224328\pi\)
−0.941935 + 0.335795i \(0.890995\pi\)
\(8\) 2.10906 1.53232i 0.745664 0.541757i
\(9\) −0.409434 + 2.97193i −0.136478 + 0.990643i
\(10\) 0.650268 1.57641i 0.205633 0.498504i
\(11\) −2.83092 + 0.601732i −0.853556 + 0.181429i −0.613856 0.789418i \(-0.710382\pi\)
−0.239700 + 0.970847i \(0.577049\pi\)
\(12\) −2.22800 1.03525i −0.643169 0.298850i
\(13\) −1.91095 0.406185i −0.530002 0.112655i −0.0648650 0.997894i \(-0.520662\pi\)
−0.465137 + 0.885239i \(0.653995\pi\)
\(14\) 0.486468 + 0.540278i 0.130014 + 0.144395i
\(15\) −3.84683 + 0.449300i −0.993248 + 0.116009i
\(16\) 0.567924 0.630744i 0.141981 0.157686i
\(17\) −5.51944 + 4.01011i −1.33866 + 0.972594i −0.339168 + 0.940726i \(0.610146\pi\)
−0.999492 + 0.0318678i \(0.989854\pi\)
\(18\) −0.165802 2.28183i −0.0390798 0.537832i
\(19\) 3.77403 2.74200i 0.865823 0.629057i −0.0636402 0.997973i \(-0.520271\pi\)
0.929463 + 0.368916i \(0.120271\pi\)
\(20\) 0.573428 3.11941i 0.128222 0.697522i
\(21\) 0.535453 1.56197i 0.116845 0.340849i
\(22\) 2.01632 0.897723i 0.429881 0.191395i
\(23\) 5.89471 + 6.54674i 1.22913 + 1.36509i 0.908500 + 0.417885i \(0.137229\pi\)
0.320632 + 0.947204i \(0.396105\pi\)
\(24\) 4.40100 + 1.00975i 0.898350 + 0.206113i
\(25\) −1.80550 4.66264i −0.361099 0.932527i
\(26\) 1.48988 0.292189
\(27\) −4.34627 + 2.84779i −0.836441 + 0.548058i
\(28\) 1.09396 + 0.794807i 0.206739 + 0.150204i
\(29\) −0.0975850 + 0.928459i −0.0181211 + 0.172411i −0.999839 0.0179298i \(-0.994292\pi\)
0.981718 + 0.190340i \(0.0609591\pi\)
\(30\) 2.79831 0.945095i 0.510898 0.172550i
\(31\) 0.277775 + 2.64285i 0.0498898 + 0.474670i 0.990733 + 0.135826i \(0.0433689\pi\)
−0.940843 + 0.338843i \(0.889964\pi\)
\(32\) −2.93057 + 5.07590i −0.518057 + 0.897300i
\(33\) −4.00754 3.01136i −0.697623 0.524210i
\(34\) 3.48139 3.86648i 0.597054 0.663096i
\(35\) 2.12536 + 0.164140i 0.359251 + 0.0277447i
\(36\) −1.18403 4.08721i −0.197339 0.681201i
\(37\) 0.799338 + 2.46011i 0.131410 + 0.404439i 0.995014 0.0997312i \(-0.0317983\pi\)
−0.863604 + 0.504171i \(0.831798\pi\)
\(38\) −2.38048 + 2.64379i −0.386164 + 0.428879i
\(39\) −1.64453 2.95731i −0.263335 0.473549i
\(40\) 0.161121 + 5.82706i 0.0254755 + 0.921339i
\(41\) 5.30176 + 1.12692i 0.827996 + 0.175996i 0.602369 0.798218i \(-0.294224\pi\)
0.225627 + 0.974214i \(0.427557\pi\)
\(42\) −0.151761 + 1.25005i −0.0234172 + 0.192887i
\(43\) 4.43871 + 7.68807i 0.676897 + 1.17242i 0.975911 + 0.218171i \(0.0700090\pi\)
−0.299014 + 0.954249i \(0.596658\pi\)
\(44\) 3.32113 2.41294i 0.500679 0.363765i
\(45\) −4.96473 4.51126i −0.740098 0.672499i
\(46\) −5.43519 3.94889i −0.801374 0.582233i
\(47\) 0.419452 3.99082i 0.0611834 0.582121i −0.920385 0.391012i \(-0.872125\pi\)
0.981569 0.191109i \(-0.0612084\pi\)
\(48\) 1.46989 + 0.0236566i 0.212160 + 0.00341453i
\(49\) 3.04559 5.27512i 0.435084 0.753588i
\(50\) 2.08610 + 3.19182i 0.295019 + 0.451392i
\(51\) −11.5175 2.64252i −1.61277 0.370027i
\(52\) 2.71053 0.576140i 0.375883 0.0798963i
\(53\) 4.30252 + 3.12596i 0.590996 + 0.429384i 0.842672 0.538428i \(-0.180982\pi\)
−0.251675 + 0.967812i \(0.580982\pi\)
\(54\) 2.79057 2.81344i 0.379748 0.382861i
\(55\) 2.46781 5.98256i 0.332759 0.806688i
\(56\) −2.27038 1.01084i −0.303393 0.135079i
\(57\) 7.87533 + 1.80688i 1.04311 + 0.239327i
\(58\) −0.0744198 0.708057i −0.00977179 0.0929724i
\(59\) −4.69343 0.997620i −0.611033 0.129879i −0.108007 0.994150i \(-0.534447\pi\)
−0.503026 + 0.864271i \(0.667780\pi\)
\(60\) 4.72548 2.80152i 0.610057 0.361675i
\(61\) 10.9896 2.33592i 1.40708 0.299084i 0.559095 0.829104i \(-0.311149\pi\)
0.847985 + 0.530020i \(0.177815\pi\)
\(62\) −0.626247 1.92739i −0.0795334 0.244779i
\(63\) 2.64878 1.07857i 0.333715 0.135887i
\(64\) 0.856686 2.63661i 0.107086 0.329576i
\(65\) 3.16438 3.01170i 0.392493 0.373555i
\(66\) 3.46689 + 1.61090i 0.426745 + 0.198288i
\(67\) −0.387024 3.68228i −0.0472824 0.449862i −0.992393 0.123111i \(-0.960713\pi\)
0.945110 0.326751i \(-0.105954\pi\)
\(68\) 4.83851 8.38055i 0.586756 1.01629i
\(69\) −1.83894 + 15.1473i −0.221382 + 1.82352i
\(70\) −1.61144 + 0.214549i −0.192604 + 0.0256436i
\(71\) −0.125408 0.0911140i −0.0148832 0.0108132i 0.580319 0.814389i \(-0.302928\pi\)
−0.595202 + 0.803576i \(0.702928\pi\)
\(72\) 3.69042 + 6.89535i 0.434921 + 0.812625i
\(73\) −3.09917 + 9.53828i −0.362731 + 1.11637i 0.588659 + 0.808381i \(0.299656\pi\)
−0.951390 + 0.307989i \(0.900344\pi\)
\(74\) −0.986332 1.70838i −0.114659 0.198595i
\(75\) 4.03292 7.66391i 0.465682 0.884952i
\(76\) −3.30843 + 5.73038i −0.379503 + 0.657319i
\(77\) 1.84618 + 2.05039i 0.210391 + 0.233663i
\(78\) 1.69564 + 1.94525i 0.191993 + 0.220257i
\(79\) −0.442202 + 4.20727i −0.0497516 + 0.473355i 0.941073 + 0.338203i \(0.109819\pi\)
−0.990825 + 0.135152i \(0.956848\pi\)
\(80\) 0.445747 + 1.84477i 0.0498361 + 0.206252i
\(81\) −8.66473 2.43362i −0.962748 0.270402i
\(82\) −4.13353 −0.456472
\(83\) −3.01510 1.34241i −0.330950 0.147348i 0.234534 0.972108i \(-0.424644\pi\)
−0.565483 + 0.824760i \(0.691310\pi\)
\(84\) 0.207301 + 2.33290i 0.0226184 + 0.254540i
\(85\) −0.421657 15.2495i −0.0457351 1.65404i
\(86\) −4.53005 5.03113i −0.488488 0.542520i
\(87\) −1.32330 + 0.929272i −0.141873 + 0.0996285i
\(88\) −5.04853 + 5.60696i −0.538176 + 0.597704i
\(89\) 5.32122 16.3770i 0.564048 1.73596i −0.106716 0.994290i \(-0.534034\pi\)
0.670764 0.741671i \(-0.265966\pi\)
\(90\) 4.41873 + 2.57798i 0.465775 + 0.271743i
\(91\) 0.575527 + 1.77129i 0.0603317 + 0.185682i
\(92\) −11.4153 5.08241i −1.19012 0.529877i
\(93\) −3.13449 + 3.37051i −0.325032 + 0.349506i
\(94\) 0.319881 + 3.04346i 0.0329932 + 0.313909i
\(95\) 0.288317 + 10.4272i 0.0295807 + 1.06981i
\(96\) −9.96263 + 1.95061i −1.01681 + 0.199083i
\(97\) 0.203049 1.93189i 0.0206165 0.196153i −0.979366 0.202096i \(-0.935225\pi\)
0.999982 + 0.00594233i \(0.00189151\pi\)
\(98\) −1.43545 + 4.41787i −0.145003 + 0.446272i
\(99\) −0.629227 8.65968i −0.0632397 0.870330i
\(100\) 5.02952 + 5.00017i 0.502952 + 0.500017i
\(101\) 3.61804 + 6.26663i 0.360009 + 0.623553i 0.987962 0.154698i \(-0.0494404\pi\)
−0.627953 + 0.778251i \(0.716107\pi\)
\(102\) 9.01046 + 0.145016i 0.892168 + 0.0143587i
\(103\) −16.2100 + 7.21716i −1.59722 + 0.711128i −0.996117 0.0880440i \(-0.971938\pi\)
−0.601103 + 0.799172i \(0.705272\pi\)
\(104\) −4.65271 + 2.07152i −0.456235 + 0.203129i
\(105\) 2.20457 + 2.96178i 0.215144 + 0.289040i
\(106\) −3.70510 1.64962i −0.359872 0.160225i
\(107\) 1.19151 0.115188 0.0575940 0.998340i \(-0.481657\pi\)
0.0575940 + 0.998340i \(0.481657\pi\)
\(108\) 3.98890 6.19760i 0.383832 0.596365i
\(109\) 0.597453 + 1.83877i 0.0572256 + 0.176122i 0.975584 0.219628i \(-0.0704845\pi\)
−0.918358 + 0.395751i \(0.870484\pi\)
\(110\) −0.892285 + 4.85398i −0.0850761 + 0.462808i
\(111\) −2.30231 + 3.84352i −0.218525 + 0.364810i
\(112\) −0.791448 0.168227i −0.0747848 0.0158960i
\(113\) −7.86072 1.67085i −0.739475 0.157180i −0.177251 0.984166i \(-0.556721\pi\)
−0.562223 + 0.826985i \(0.690054\pi\)
\(114\) −6.16109 0.0991575i −0.577039 0.00928695i
\(115\) −19.5263 + 2.59977i −1.82084 + 0.242430i
\(116\) −0.409200 1.25939i −0.0379932 0.116931i
\(117\) 1.98956 5.51290i 0.183935 0.509668i
\(118\) 3.65924 0.336861
\(119\) 5.94163 + 2.64539i 0.544669 + 0.242502i
\(120\) −7.42472 + 6.84217i −0.677781 + 0.624602i
\(121\) −2.39695 + 1.06719i −0.217904 + 0.0970172i
\(122\) −7.82735 + 3.48496i −0.708655 + 0.315513i
\(123\) 4.56260 + 8.20479i 0.411395 + 0.739801i
\(124\) −1.88466 3.26432i −0.169247 0.293145i
\(125\) 10.8828 + 2.56224i 0.973385 + 0.229174i
\(126\) −1.80484 + 1.22454i −0.160788 + 0.109091i
\(127\) −4.50280 + 13.8582i −0.399559 + 1.22972i 0.525794 + 0.850612i \(0.323768\pi\)
−0.925354 + 0.379105i \(0.876232\pi\)
\(128\) 1.00432 9.55546i 0.0887701 0.844591i
\(129\) −4.98620 + 14.5452i −0.439010 + 1.28064i
\(130\) −1.88294 + 2.74831i −0.165145 + 0.241042i
\(131\) −1.41875 13.4985i −0.123956 1.17937i −0.862820 0.505511i \(-0.831304\pi\)
0.738864 0.673855i \(-0.235363\pi\)
\(132\) 6.93025 + 1.59005i 0.603201 + 0.138396i
\(133\) −4.06272 1.80884i −0.352282 0.156846i
\(134\) 0.872550 + 2.68543i 0.0753768 + 0.231986i
\(135\) 0.239738 11.6165i 0.0206334 0.999787i
\(136\) −5.49604 + 16.9151i −0.471282 + 1.45046i
\(137\) −5.85192 + 6.49921i −0.499963 + 0.555265i −0.939318 0.343048i \(-0.888541\pi\)
0.439355 + 0.898314i \(0.355207\pi\)
\(138\) −1.02995 11.5907i −0.0876749 0.986665i
\(139\) 12.6640 + 14.0648i 1.07415 + 1.19296i 0.980329 + 0.197373i \(0.0632409\pi\)
0.0938192 + 0.995589i \(0.470092\pi\)
\(140\) −2.84872 + 1.01348i −0.240760 + 0.0856545i
\(141\) 5.68799 3.99432i 0.479015 0.336382i
\(142\) 0.107995 + 0.0480823i 0.00906271 + 0.00403498i
\(143\) 5.65417 0.472825
\(144\) 1.64200 + 1.94608i 0.136833 + 0.162173i
\(145\) −1.58936 1.35342i −0.131989 0.112395i
\(146\) 0.799472 7.60647i 0.0661648 0.629516i
\(147\) 10.3536 2.02717i 0.853955 0.167198i
\(148\) −2.45507 2.72663i −0.201805 0.224127i
\(149\) 3.03989 5.26524i 0.249037 0.431345i −0.714222 0.699919i \(-0.753219\pi\)
0.963259 + 0.268574i \(0.0865525\pi\)
\(150\) −1.79319 + 6.35634i −0.146414 + 0.518993i
\(151\) 4.71367 + 8.16432i 0.383593 + 0.664403i 0.991573 0.129550i \(-0.0413532\pi\)
−0.607980 + 0.793952i \(0.708020\pi\)
\(152\) 3.75804 11.5660i 0.304817 0.938130i
\(153\) −9.65791 18.0453i −0.780795 1.45887i
\(154\) −1.70226 1.23676i −0.137172 0.0996612i
\(155\) −5.22620 2.82770i −0.419778 0.227126i
\(156\) 3.83710 + 2.88329i 0.307214 + 0.230848i
\(157\) 10.2999 17.8399i 0.822020 1.42378i −0.0821548 0.996620i \(-0.526180\pi\)
0.904175 0.427162i \(-0.140486\pi\)
\(158\) −0.337230 3.20853i −0.0268285 0.255257i
\(159\) 0.815311 + 9.17525i 0.0646583 + 0.727645i
\(160\) −5.65955 11.8209i −0.447426 0.934527i
\(161\) 2.59521 7.98723i 0.204531 0.629482i
\(162\) 6.84932 + 0.441508i 0.538133 + 0.0346881i
\(163\) −3.22118 9.91378i −0.252302 0.776507i −0.994349 0.106159i \(-0.966145\pi\)
0.742047 0.670348i \(-0.233855\pi\)
\(164\) −7.52012 + 1.59845i −0.587223 + 0.124818i
\(165\) 10.6197 3.58669i 0.826746 0.279224i
\(166\) 2.46196 + 0.523305i 0.191085 + 0.0406164i
\(167\) 1.61643 + 15.3793i 0.125083 + 1.19009i 0.859408 + 0.511291i \(0.170832\pi\)
−0.734325 + 0.678799i \(0.762501\pi\)
\(168\) −1.26413 4.11476i −0.0975300 0.317461i
\(169\) −8.38935 3.73518i −0.645334 0.287321i
\(170\) 2.73245 + 11.3085i 0.209569 + 0.867324i
\(171\) 6.60380 + 12.3388i 0.505005 + 0.943574i
\(172\) −10.1871 7.40133i −0.776756 0.564346i
\(173\) 14.5479 3.09226i 1.10606 0.235100i 0.381539 0.924353i \(-0.375394\pi\)
0.724521 + 0.689253i \(0.242061\pi\)
\(174\) 0.839775 0.903009i 0.0636632 0.0684569i
\(175\) −2.98886 + 3.71311i −0.225937 + 0.280685i
\(176\) −1.22821 + 2.12733i −0.0925800 + 0.160353i
\(177\) −4.03908 7.26337i −0.303596 0.545948i
\(178\) −1.37268 + 13.0601i −0.102886 + 0.978899i
\(179\) −21.5801 15.6788i −1.61297 1.17189i −0.852954 0.521987i \(-0.825191\pi\)
−0.760016 0.649904i \(-0.774809\pi\)
\(180\) 9.03589 + 2.98138i 0.673496 + 0.222219i
\(181\) 16.0289 11.6457i 1.19142 0.865617i 0.198007 0.980201i \(-0.436553\pi\)
0.993414 + 0.114583i \(0.0365533\pi\)
\(182\) −0.710164 1.23004i −0.0526409 0.0911767i
\(183\) 15.5573 + 11.6901i 1.15003 + 0.864156i
\(184\) 22.4640 + 4.77486i 1.65607 + 0.352008i
\(185\) −5.54827 1.63464i −0.407917 0.120181i
\(186\) 1.80376 3.01123i 0.132258 0.220794i
\(187\) 13.2121 14.6735i 0.966165 1.07303i
\(188\) 1.75888 + 5.41326i 0.128279 + 0.394803i
\(189\) 4.42283 + 2.23085i 0.321713 + 0.162271i
\(190\) −1.86837 7.73244i −0.135546 0.560970i
\(191\) −8.03506 + 8.92383i −0.581396 + 0.645706i −0.960049 0.279833i \(-0.909721\pi\)
0.378652 + 0.925539i \(0.376388\pi\)
\(192\) 4.41748 1.88221i 0.318804 0.135837i
\(193\) 12.6897 21.9792i 0.913424 1.58210i 0.104232 0.994553i \(-0.466762\pi\)
0.809192 0.587544i \(-0.199905\pi\)
\(194\) 0.154848 + 1.47328i 0.0111175 + 0.105776i
\(195\) 7.53361 + 0.703937i 0.539493 + 0.0504100i
\(196\) −0.903110 + 8.59252i −0.0645078 + 0.613751i
\(197\) −1.37622 0.999883i −0.0980516 0.0712387i 0.537679 0.843150i \(-0.319301\pi\)
−0.635731 + 0.771911i \(0.719301\pi\)
\(198\) 1.84242 + 6.35992i 0.130935 + 0.451980i
\(199\) −6.51877 −0.462104 −0.231052 0.972941i \(-0.574217\pi\)
−0.231052 + 0.972941i \(0.574217\pi\)
\(200\) −10.9525 7.06717i −0.774461 0.499724i
\(201\) 4.36729 4.69614i 0.308045 0.331240i
\(202\) −3.69249 4.10093i −0.259803 0.288540i
\(203\) 0.813050 0.361993i 0.0570649 0.0254069i
\(204\) 16.4488 3.22055i 1.15164 0.225484i
\(205\) −8.77928 + 8.35568i −0.613172 + 0.583586i
\(206\) 10.9475 7.95384i 0.762750 0.554170i
\(207\) −21.8699 + 14.8382i −1.52007 + 1.03133i
\(208\) −1.34147 + 0.974638i −0.0930145 + 0.0675790i
\(209\) −9.03406 + 10.0333i −0.624899 + 0.694020i
\(210\) −2.11411 1.85979i −0.145887 0.128338i
\(211\) 5.33924 + 5.92982i 0.367568 + 0.408226i 0.898348 0.439284i \(-0.144768\pi\)
−0.530780 + 0.847510i \(0.678101\pi\)
\(212\) −7.37860 1.56837i −0.506764 0.107716i
\(213\) −0.0237643 0.267436i −0.00162830 0.0183244i
\(214\) −0.888810 + 0.188922i −0.0607578 + 0.0129145i
\(215\) −19.7916 1.52849i −1.34977 0.104242i
\(216\) −4.80281 + 12.6660i −0.326790 + 0.861814i
\(217\) 2.04953 1.48907i 0.139131 0.101085i
\(218\) −0.737219 1.27690i −0.0499307 0.0864826i
\(219\) −15.9808 + 6.80913i −1.07988 + 0.460118i
\(220\) 0.253717 + 9.17587i 0.0171056 + 0.618637i
\(221\) 12.1762 5.42120i 0.819061 0.364669i
\(222\) 1.10799 3.23212i 0.0743634 0.216925i
\(223\) 9.23109 1.96213i 0.618160 0.131394i 0.111821 0.993728i \(-0.464332\pi\)
0.506339 + 0.862335i \(0.330998\pi\)
\(224\) 5.58754 0.373333
\(225\) 14.5963 3.45676i 0.973084 0.230451i
\(226\) 6.12863 0.407670
\(227\) 23.0879 4.90748i 1.53240 0.325721i 0.636955 0.770901i \(-0.280194\pi\)
0.895441 + 0.445180i \(0.146860\pi\)
\(228\) −11.2472 + 2.20212i −0.744864 + 0.145839i
\(229\) −14.3491 + 6.38865i −0.948218 + 0.422174i −0.821783 0.569801i \(-0.807020\pi\)
−0.126435 + 0.991975i \(0.540354\pi\)
\(230\) 14.1535 5.03533i 0.933252 0.332020i
\(231\) −0.575941 + 4.74401i −0.0378941 + 0.312133i
\(232\) 1.21688 + 2.10770i 0.0798923 + 0.138378i
\(233\) −1.52687 + 1.10933i −0.100028 + 0.0726749i −0.636675 0.771132i \(-0.719691\pi\)
0.536647 + 0.843807i \(0.319691\pi\)
\(234\) −0.610006 + 4.42781i −0.0398773 + 0.289455i
\(235\) 6.83157 + 5.81744i 0.445643 + 0.379488i
\(236\) 6.65725 1.41504i 0.433350 0.0921115i
\(237\) −5.99649 + 4.21095i −0.389514 + 0.273531i
\(238\) −4.85160 1.03124i −0.314483 0.0668454i
\(239\) −0.959065 1.06515i −0.0620368 0.0688988i 0.711328 0.702861i \(-0.248094\pi\)
−0.773364 + 0.633962i \(0.781428\pi\)
\(240\) −1.90132 + 2.68153i −0.122729 + 0.173092i
\(241\) 7.32923 8.13993i 0.472117 0.524339i −0.459306 0.888278i \(-0.651902\pi\)
0.931423 + 0.363939i \(0.118568\pi\)
\(242\) 1.61879 1.17612i 0.104060 0.0756039i
\(243\) −6.68392 14.0828i −0.428774 0.903412i
\(244\) −12.8926 + 9.36704i −0.825366 + 0.599663i
\(245\) 5.88167 + 12.2849i 0.375766 + 0.784852i
\(246\) −4.70439 5.39694i −0.299941 0.344096i
\(247\) −8.32575 + 3.70686i −0.529755 + 0.235862i
\(248\) 4.63553 + 5.14828i 0.294356 + 0.326916i
\(249\) −1.67879 5.46446i −0.106389 0.346296i
\(250\) −8.52427 0.185768i −0.539122 0.0117490i
\(251\) 9.34568 0.589894 0.294947 0.955514i \(-0.404698\pi\)
0.294947 + 0.955514i \(0.404698\pi\)
\(252\) −2.81001 + 2.92575i −0.177014 + 0.184305i
\(253\) −20.6269 14.9863i −1.29680 0.942180i
\(254\) 1.16156 11.0515i 0.0728825 0.693431i
\(255\) 19.4306 17.9061i 1.21679 1.12132i
\(256\) 1.34548 + 12.8013i 0.0840922 + 0.800084i
\(257\) −3.12162 + 5.40681i −0.194722 + 0.337268i −0.946809 0.321795i \(-0.895714\pi\)
0.752088 + 0.659063i \(0.229047\pi\)
\(258\) 1.41321 11.6406i 0.0879828 0.724712i
\(259\) 1.65005 1.83257i 0.102529 0.113870i
\(260\) −2.36285 + 5.72813i −0.146538 + 0.355243i
\(261\) −2.71936 0.670159i −0.168324 0.0414818i
\(262\) 3.19858 + 9.84422i 0.197609 + 0.608178i
\(263\) 1.24587 1.38368i 0.0768239 0.0853216i −0.703507 0.710688i \(-0.748384\pi\)
0.780331 + 0.625366i \(0.215050\pi\)
\(264\) −13.0665 0.210294i −0.804187 0.0129427i
\(265\) −11.2039 + 3.98599i −0.688253 + 0.244857i
\(266\) 3.31739 + 0.705133i 0.203402 + 0.0432345i
\(267\) 27.4387 11.6911i 1.67922 0.715486i
\(268\) 2.62589 + 4.54818i 0.160402 + 0.277824i
\(269\) 3.89397 2.82914i 0.237420 0.172496i −0.462713 0.886508i \(-0.653124\pi\)
0.700133 + 0.714012i \(0.253124\pi\)
\(270\) 1.66304 + 8.70332i 0.101209 + 0.529667i
\(271\) 18.4402 + 13.3976i 1.12016 + 0.813846i 0.984234 0.176873i \(-0.0565982\pi\)
0.135929 + 0.990719i \(0.456598\pi\)
\(272\) −0.605273 + 5.75879i −0.0367001 + 0.349178i
\(273\) −1.65767 + 2.76735i −0.100327 + 0.167488i
\(274\) 3.33474 5.77595i 0.201459 0.348938i
\(275\) 7.91688 + 12.1132i 0.477406 + 0.730451i
\(276\) −6.35594 20.6886i −0.382583 1.24531i
\(277\) −7.64077 + 1.62410i −0.459089 + 0.0975825i −0.431650 0.902041i \(-0.642069\pi\)
−0.0274391 + 0.999623i \(0.508735\pi\)
\(278\) −11.6768 8.48368i −0.700327 0.508817i
\(279\) −7.96809 0.256546i −0.477037 0.0153590i
\(280\) 4.73402 2.91055i 0.282912 0.173938i
\(281\) −1.44142 0.641761i −0.0859878 0.0382842i 0.363292 0.931675i \(-0.381653\pi\)
−0.449280 + 0.893391i \(0.648319\pi\)
\(282\) −3.60963 + 3.88143i −0.214950 + 0.231136i
\(283\) 0.811572 + 7.72159i 0.0482429 + 0.459001i 0.991801 + 0.127793i \(0.0407894\pi\)
−0.943558 + 0.331208i \(0.892544\pi\)
\(284\) 0.215068 + 0.0457141i 0.0127619 + 0.00271263i
\(285\) −13.2861 + 12.2437i −0.787001 + 0.725253i
\(286\) −4.21773 + 0.896506i −0.249399 + 0.0530115i
\(287\) −1.59675 4.91429i −0.0942532 0.290081i
\(288\) −13.8853 10.7877i −0.818201 0.635671i
\(289\) 9.12995 28.0991i 0.537056 1.65289i
\(290\) 1.40017 + 0.757581i 0.0822210 + 0.0444867i
\(291\) 2.75345 1.93358i 0.161410 0.113348i
\(292\) −1.48697 14.1476i −0.0870184 0.827925i
\(293\) 5.25540 9.10262i 0.307024 0.531781i −0.670686 0.741741i \(-0.734000\pi\)
0.977710 + 0.209961i \(0.0673336\pi\)
\(294\) −7.40188 + 3.15380i −0.431687 + 0.183934i
\(295\) 7.77194 7.39694i 0.452500 0.430667i
\(296\) 5.45552 + 3.96367i 0.317096 + 0.230383i
\(297\) 10.5904 10.6772i 0.614515 0.619552i
\(298\) −1.43276 + 4.40960i −0.0829978 + 0.255441i
\(299\) −8.60531 14.9048i −0.497658 0.861969i
\(300\) −0.804332 + 12.2575i −0.0464381 + 0.707687i
\(301\) 4.23151 7.32919i 0.243900 0.422447i
\(302\) −4.81067 5.34279i −0.276823 0.307443i
\(303\) −4.06431 + 11.8560i −0.233488 + 0.681108i
\(304\) 0.413868 3.93769i 0.0237370 0.225842i
\(305\) −9.58002 + 23.2243i −0.548550 + 1.32982i
\(306\) 10.0655 + 11.9295i 0.575407 + 0.681966i
\(307\) 3.00205 0.171336 0.0856680 0.996324i \(-0.472698\pi\)
0.0856680 + 0.996324i \(0.472698\pi\)
\(308\) −3.57517 1.59177i −0.203714 0.0906995i
\(309\) −27.8718 12.9507i −1.58557 0.736738i
\(310\) 4.34683 + 1.28067i 0.246883 + 0.0727373i
\(311\) −9.37603 10.4131i −0.531666 0.590475i 0.416149 0.909297i \(-0.363380\pi\)
−0.947815 + 0.318822i \(0.896713\pi\)
\(312\) −7.99994 3.71719i −0.452908 0.210445i
\(313\) −3.71665 + 4.12776i −0.210077 + 0.233315i −0.838970 0.544178i \(-0.816842\pi\)
0.628893 + 0.777492i \(0.283508\pi\)
\(314\) −4.85456 + 14.9408i −0.273959 + 0.843158i
\(315\) −1.35801 + 6.24921i −0.0765150 + 0.352103i
\(316\) −1.85427 5.70685i −0.104311 0.321036i
\(317\) 4.15158 + 1.84840i 0.233176 + 0.103817i 0.519999 0.854167i \(-0.325932\pi\)
−0.286823 + 0.957984i \(0.592599\pi\)
\(318\) −2.06298 6.71500i −0.115686 0.376559i
\(319\) −0.282427 2.68712i −0.0158129 0.150450i
\(320\) 3.78093 + 4.91250i 0.211360 + 0.274617i
\(321\) 1.35607 + 1.55570i 0.0756884 + 0.0868307i
\(322\) −0.669468 + 6.36956i −0.0373080 + 0.354962i
\(323\) −9.83485 + 30.2685i −0.547226 + 1.68419i
\(324\) 12.6317 1.84542i 0.701760 0.102523i
\(325\) 1.55632 + 9.64343i 0.0863290 + 0.534921i
\(326\) 3.97473 + 6.88444i 0.220140 + 0.381294i
\(327\) −1.72082 + 2.87278i −0.0951617 + 0.158865i
\(328\) 12.9085 5.74724i 0.712754 0.317338i
\(329\) −3.49476 + 1.55597i −0.192672 + 0.0857832i
\(330\) −7.35310 + 4.35932i −0.404775 + 0.239973i
\(331\) 5.29985 + 2.35964i 0.291306 + 0.129698i 0.547187 0.837011i \(-0.315699\pi\)
−0.255881 + 0.966708i \(0.582365\pi\)
\(332\) 4.68140 0.256925
\(333\) −7.63855 + 1.36832i −0.418590 + 0.0749837i
\(334\) −3.64427 11.2159i −0.199406 0.613708i
\(335\) 7.28167 + 3.93983i 0.397840 + 0.215256i
\(336\) −0.681105 1.22481i −0.0371573 0.0668190i
\(337\) −4.80717 1.02179i −0.261863 0.0556607i 0.0751092 0.997175i \(-0.476069\pi\)
−0.336972 + 0.941515i \(0.609403\pi\)
\(338\) 6.85027 + 1.45607i 0.372605 + 0.0791997i
\(339\) −6.76479 12.1649i −0.367413 0.660709i
\(340\) 9.34418 + 19.5169i 0.506759 + 1.05845i
\(341\) −2.37664 7.31456i −0.128702 0.396106i
\(342\) −6.88250 8.15707i −0.372163 0.441084i
\(343\) −12.4801 −0.673861
\(344\) 21.1421 + 9.41305i 1.13990 + 0.507518i
\(345\) −25.6174 22.5357i −1.37920 1.21328i
\(346\) −10.3617 + 4.61334i −0.557050 + 0.248015i
\(347\) 9.10712 4.05475i 0.488896 0.217670i −0.147457 0.989068i \(-0.547109\pi\)
0.636353 + 0.771398i \(0.280442\pi\)
\(348\) 1.17860 1.96759i 0.0631798 0.105474i
\(349\) 7.15701 + 12.3963i 0.383106 + 0.663559i 0.991504 0.130073i \(-0.0415210\pi\)
−0.608398 + 0.793632i \(0.708188\pi\)
\(350\) 1.64080 3.24370i 0.0877046 0.173383i
\(351\) 9.46224 3.67660i 0.505057 0.196242i
\(352\) 5.24190 16.1329i 0.279394 0.859887i
\(353\) −2.64975 + 25.2107i −0.141032 + 1.34183i 0.663614 + 0.748075i \(0.269022\pi\)
−0.804646 + 0.593755i \(0.797645\pi\)
\(354\) 4.16460 + 4.77769i 0.221346 + 0.253931i
\(355\) 0.326567 0.116182i 0.0173324 0.00616628i
\(356\) 2.55310 + 24.2911i 0.135314 + 1.28743i
\(357\) 3.30826 + 10.7684i 0.175092 + 0.569925i
\(358\) 18.5836 + 8.27396i 0.982175 + 0.437293i
\(359\) 6.35182 + 19.5489i 0.335236 + 1.03175i 0.966606 + 0.256269i \(0.0824933\pi\)
−0.631369 + 0.775482i \(0.717507\pi\)
\(360\) −17.3836 1.90696i −0.916195 0.100505i
\(361\) 0.853463 2.62669i 0.0449191 0.138247i
\(362\) −10.1103 + 11.2286i −0.531384 + 0.590162i
\(363\) −4.12135 1.91500i −0.216315 0.100511i
\(364\) −1.76766 1.96319i −0.0926506 0.102899i
\(365\) −13.6780 17.7716i −0.715940 0.930209i
\(366\) −13.4585 6.25351i −0.703486 0.326876i
\(367\) 26.2996 + 11.7093i 1.37283 + 0.611221i 0.954810 0.297218i \(-0.0960588\pi\)
0.418016 + 0.908440i \(0.362725\pi\)
\(368\) 7.47706 0.389769
\(369\) −5.51986 + 15.2951i −0.287353 + 0.796229i
\(370\) 4.39792 + 0.339648i 0.228637 + 0.0176575i
\(371\) 0.529954 5.04218i 0.0275138 0.261777i
\(372\) 2.11712 6.17584i 0.109767 0.320202i
\(373\) 7.64527 + 8.49093i 0.395857 + 0.439644i 0.907818 0.419365i \(-0.137747\pi\)
−0.511961 + 0.859009i \(0.671081\pi\)
\(374\) −7.52898 + 13.0406i −0.389314 + 0.674312i
\(375\) 9.04036 + 17.1252i 0.466842 + 0.884341i
\(376\) −5.23057 9.05960i −0.269746 0.467213i
\(377\) 0.563606 1.73460i 0.0290272 0.0893365i
\(378\) −3.65292 0.962835i −0.187886 0.0495229i
\(379\) 2.90335 + 2.10941i 0.149135 + 0.108353i 0.659851 0.751397i \(-0.270620\pi\)
−0.510716 + 0.859750i \(0.670620\pi\)
\(380\) −6.38928 13.3451i −0.327763 0.684590i
\(381\) −23.2186 + 9.89301i −1.18953 + 0.506834i
\(382\) 4.57882 7.93074i 0.234273 0.405772i
\(383\) −0.535221 5.09229i −0.0273485 0.260204i −0.999650 0.0264718i \(-0.991573\pi\)
0.972301 0.233732i \(-0.0750939\pi\)
\(384\) 13.6191 9.56383i 0.694996 0.488052i
\(385\) −6.11550 + 0.814228i −0.311675 + 0.0414969i
\(386\) −5.98093 + 18.4074i −0.304421 + 0.936912i
\(387\) −24.6658 + 10.0438i −1.25383 + 0.510554i
\(388\) 0.851440 + 2.62046i 0.0432253 + 0.133034i
\(389\) −30.2263 + 6.42479i −1.53253 + 0.325750i −0.895491 0.445080i \(-0.853175\pi\)
−0.637041 + 0.770830i \(0.719842\pi\)
\(390\) −5.73131 + 0.669401i −0.290216 + 0.0338964i
\(391\) −58.7886 12.4959i −2.97307 0.631945i
\(392\) −1.65984 15.7923i −0.0838346 0.797633i
\(393\) 16.0096 17.2150i 0.807575 0.868384i
\(394\) 1.18513 + 0.527653i 0.0597059 + 0.0265828i
\(395\) −7.20209 6.13296i −0.362376 0.308583i
\(396\) 5.81131 + 10.8581i 0.292029 + 0.545640i
\(397\) −5.15821 3.74766i −0.258883 0.188090i 0.450771 0.892639i \(-0.351149\pi\)
−0.709654 + 0.704550i \(0.751149\pi\)
\(398\) 4.86268 1.03359i 0.243744 0.0518094i
\(399\) −2.26209 7.36313i −0.113246 0.368618i
\(400\) −3.96631 1.50922i −0.198316 0.0754610i
\(401\) 8.96136 15.5215i 0.447509 0.775108i −0.550714 0.834694i \(-0.685645\pi\)
0.998223 + 0.0595856i \(0.0189779\pi\)
\(402\) −2.51318 + 4.19555i −0.125346 + 0.209255i
\(403\) 0.542672 5.16318i 0.0270324 0.257196i
\(404\) −8.30359 6.03291i −0.413119 0.300149i
\(405\) 15.4399 12.9078i 0.767214 0.641392i
\(406\) −0.549098 + 0.398943i −0.0272513 + 0.0197992i
\(407\) −3.74319 6.48340i −0.185543 0.321370i
\(408\) −28.3402 + 12.0752i −1.40305 + 0.597813i
\(409\) 37.5919 + 7.99041i 1.85880 + 0.395101i 0.994217 0.107387i \(-0.0342483\pi\)
0.864585 + 0.502487i \(0.167582\pi\)
\(410\) 5.22406 7.62493i 0.257998 0.376569i
\(411\) −15.1458 0.243758i −0.747086 0.0120237i
\(412\) 16.8410 18.7038i 0.829697 0.921472i
\(413\) 1.41354 + 4.35042i 0.0695556 + 0.214070i
\(414\) 13.9612 14.5362i 0.686155 0.714414i
\(415\) 6.28683 3.86524i 0.308608 0.189737i
\(416\) 7.66193 8.50943i 0.375657 0.417209i
\(417\) −3.95072 + 32.5420i −0.193468 + 1.59359i
\(418\) 5.14810 8.91677i 0.251802 0.436134i
\(419\) −0.552525 5.25693i −0.0269926 0.256818i −0.999694 0.0247553i \(-0.992119\pi\)
0.972701 0.232062i \(-0.0745473\pi\)
\(420\) −4.56538 2.56598i −0.222768 0.125207i
\(421\) 2.83193 26.9440i 0.138020 1.31317i −0.677964 0.735095i \(-0.737137\pi\)
0.815984 0.578075i \(-0.196196\pi\)
\(422\) −4.92301 3.57678i −0.239649 0.174115i
\(423\) 11.6887 + 2.88056i 0.568324 + 0.140058i
\(424\) 13.8642 0.673306
\(425\) 28.6630 + 18.4949i 1.39036 + 0.897135i
\(426\) 0.0601306 + 0.195726i 0.00291334 + 0.00948294i
\(427\) −7.16686 7.95960i −0.346829 0.385192i
\(428\) −1.54395 + 0.687412i −0.0746298 + 0.0332273i
\(429\) 6.43504 + 7.38236i 0.310687 + 0.356424i
\(430\) 15.0059 1.99791i 0.723647 0.0963476i
\(431\) −28.0178 + 20.3561i −1.34957 + 0.980518i −0.350535 + 0.936550i \(0.614000\pi\)
−0.999033 + 0.0439685i \(0.986000\pi\)
\(432\) −0.672127 + 4.35871i −0.0323377 + 0.209709i
\(433\) −7.43160 + 5.39937i −0.357140 + 0.259477i −0.751858 0.659325i \(-0.770842\pi\)
0.394718 + 0.918802i \(0.370842\pi\)
\(434\) −1.29274 + 1.43574i −0.0620537 + 0.0689176i
\(435\) −0.0417631 3.61547i −0.00200239 0.173349i
\(436\) −1.83500 2.03798i −0.0878806 0.0976013i
\(437\) 40.1980 + 8.54434i 1.92293 + 0.408731i
\(438\) 10.8413 7.61313i 0.518015 0.363769i
\(439\) −7.02176 + 1.49252i −0.335130 + 0.0712342i −0.372403 0.928071i \(-0.621466\pi\)
0.0372730 + 0.999305i \(0.488133\pi\)
\(440\) −3.96245 16.3990i −0.188902 0.781792i
\(441\) 14.4303 + 11.2111i 0.687158 + 0.533862i
\(442\) −8.22328 + 5.97456i −0.391141 + 0.284181i
\(443\) 12.6804 + 21.9630i 0.602462 + 1.04349i 0.992447 + 0.122673i \(0.0391468\pi\)
−0.389985 + 0.920821i \(0.627520\pi\)
\(444\) 0.765893 6.30864i 0.0363477 0.299395i
\(445\) 23.4848 + 30.5135i 1.11329 + 1.44648i
\(446\) −6.57482 + 2.92730i −0.311327 + 0.138612i
\(447\) 10.3343 2.02337i 0.488793 0.0957022i
\(448\) −2.58513 + 0.549486i −0.122136 + 0.0259608i
\(449\) −7.13943 −0.336930 −0.168465 0.985708i \(-0.553881\pi\)
−0.168465 + 0.985708i \(0.553881\pi\)
\(450\) −10.3400 + 4.89290i −0.487432 + 0.230654i
\(451\) −15.6870 −0.738672
\(452\) 11.1498 2.36996i 0.524442 0.111474i
\(453\) −5.29507 + 15.4462i −0.248784 + 0.725728i
\(454\) −16.4443 + 7.32147i −0.771768 + 0.343613i
\(455\) −3.99478 1.17695i −0.187278 0.0551764i
\(456\) 19.3782 8.25670i 0.907468 0.386655i
\(457\) −17.8907 30.9875i −0.836890 1.44954i −0.892482 0.451082i \(-0.851038\pi\)
0.0555925 0.998454i \(-0.482295\pi\)
\(458\) 9.69078 7.04076i 0.452820 0.328993i
\(459\) 12.5690 33.1472i 0.586672 1.54718i
\(460\) 23.8022 14.6340i 1.10978 0.682311i
\(461\) 14.9012 3.16735i 0.694018 0.147518i 0.152621 0.988285i \(-0.451229\pi\)
0.541397 + 0.840767i \(0.317895\pi\)
\(462\) −0.322571 3.63012i −0.0150074 0.168888i
\(463\) 24.3097 + 5.16720i 1.12977 + 0.240140i 0.734621 0.678477i \(-0.237360\pi\)
0.395148 + 0.918617i \(0.370693\pi\)
\(464\) 0.530199 + 0.588846i 0.0246139 + 0.0273365i
\(465\) −2.25598 10.0418i −0.104619 0.465677i
\(466\) 0.963075 1.06960i 0.0446136 0.0495484i
\(467\) −21.1648 + 15.3771i −0.979389 + 0.711568i −0.957572 0.288194i \(-0.906945\pi\)
−0.0218169 + 0.999762i \(0.506945\pi\)
\(468\) 0.602466 + 8.29139i 0.0278490 + 0.383270i
\(469\) −2.85561 + 2.07472i −0.131860 + 0.0958018i
\(470\) −6.01840 3.25633i −0.277608 0.150203i
\(471\) 35.0150 6.85568i 1.61341 0.315893i
\(472\) −11.4274 + 5.08780i −0.525988 + 0.234185i
\(473\) −17.1918 19.0934i −0.790480 0.877917i
\(474\) 3.80540 4.09194i 0.174788 0.187949i
\(475\) −19.5989 12.6463i −0.899261 0.580251i
\(476\) −9.22529 −0.422841
\(477\) −11.0517 + 11.5069i −0.506024 + 0.526865i
\(478\) 0.884301 + 0.642482i 0.0404470 + 0.0293865i
\(479\) 1.00563 9.56794i 0.0459484 0.437170i −0.947229 0.320558i \(-0.896130\pi\)
0.993177 0.116613i \(-0.0372036\pi\)
\(480\) 8.99282 20.8428i 0.410464 0.951341i
\(481\) −0.528235 5.02583i −0.0240855 0.229158i
\(482\) −4.17660 + 7.23408i −0.190239 + 0.329503i
\(483\) 13.3821 5.70188i 0.608908 0.259445i
\(484\) 2.49025 2.76571i 0.113193 0.125714i
\(485\) 3.30704 + 2.81612i 0.150165 + 0.127873i
\(486\) 7.21879 + 9.44528i 0.327451 + 0.428447i
\(487\) 12.1864 + 37.5059i 0.552219 + 1.69956i 0.703177 + 0.711015i \(0.251764\pi\)
−0.150958 + 0.988540i \(0.548236\pi\)
\(488\) 19.5984 21.7662i 0.887178 0.985311i
\(489\) 9.27786 15.4887i 0.419560 0.700421i
\(490\) −6.33528 8.23133i −0.286199 0.371854i
\(491\) −9.52590 2.02479i −0.429898 0.0913776i −0.0121194 0.999927i \(-0.503858\pi\)
−0.417778 + 0.908549i \(0.637191\pi\)
\(492\) −10.6457 7.99943i −0.479945 0.360642i
\(493\) −3.18461 5.51590i −0.143427 0.248424i
\(494\) 5.62284 4.08523i 0.252984 0.183803i
\(495\) 16.7693 + 9.78361i 0.753726 + 0.439740i
\(496\) 1.82471 + 1.32573i 0.0819321 + 0.0595272i
\(497\) −0.0154468 + 0.146967i −0.000692886 + 0.00659237i
\(498\) 2.11871 + 3.81003i 0.0949419 + 0.170731i
\(499\) −4.37718 + 7.58149i −0.195949 + 0.339394i −0.947211 0.320610i \(-0.896112\pi\)
0.751262 + 0.660004i \(0.229445\pi\)
\(500\) −15.5800 + 2.95840i −0.696759 + 0.132304i
\(501\) −18.2403 + 19.6138i −0.814918 + 0.876280i
\(502\) −6.97140 + 1.48182i −0.311149 + 0.0661368i
\(503\) −16.1674 11.7463i −0.720867 0.523741i 0.165794 0.986160i \(-0.446981\pi\)
−0.886661 + 0.462420i \(0.846981\pi\)
\(504\) 3.93372 6.33355i 0.175222 0.282119i
\(505\) −16.1323 1.24589i −0.717880 0.0554414i
\(506\) 17.7628 + 7.90850i 0.789652 + 0.351576i
\(507\) −4.67113 15.2046i −0.207452 0.675258i
\(508\) −2.16043 20.5551i −0.0958535 0.911985i
\(509\) 32.6145 + 6.93243i 1.44561 + 0.307274i 0.862888 0.505395i \(-0.168653\pi\)
0.582725 + 0.812670i \(0.301987\pi\)
\(510\) −11.6551 + 16.4379i −0.516098 + 0.727882i
\(511\) 9.35204 1.98784i 0.413710 0.0879368i
\(512\) 2.90473 + 8.93985i 0.128372 + 0.395089i
\(513\) −8.59435 + 22.6651i −0.379450 + 1.00069i
\(514\) 1.47129 4.52816i 0.0648958 0.199729i
\(515\) 7.17344 39.0231i 0.316100 1.71956i
\(516\) −1.93041 21.7242i −0.0849815 0.956355i
\(517\) 1.21397 + 11.5501i 0.0533902 + 0.507974i
\(518\) −0.940290 + 1.62863i −0.0413140 + 0.0715579i
\(519\) 20.5945 + 15.4752i 0.903998 + 0.679285i
\(520\) 2.05897 11.2007i 0.0902918 0.491182i
\(521\) −18.9750 13.7861i −0.831308 0.603981i 0.0886210 0.996065i \(-0.471754\pi\)
−0.919929 + 0.392085i \(0.871754\pi\)
\(522\) 2.13476 + 0.0687322i 0.0934361 + 0.00300833i
\(523\) 6.59815 20.3070i 0.288517 0.887963i −0.696806 0.717260i \(-0.745396\pi\)
0.985322 0.170703i \(-0.0546040\pi\)
\(524\) 9.62597 + 16.6727i 0.420512 + 0.728349i
\(525\) −8.24965 + 0.323504i −0.360044 + 0.0141189i
\(526\) −0.709968 + 1.22970i −0.0309561 + 0.0536175i
\(527\) −12.1313 13.4731i −0.528446 0.586899i
\(528\) −4.17537 + 0.817507i −0.181710 + 0.0355774i
\(529\) −5.70803 + 54.3082i −0.248175 + 2.36123i
\(530\) 7.72558 4.74981i 0.335578 0.206318i
\(531\) 4.88651 13.5401i 0.212056 0.587590i
\(532\) 6.30799 0.273486
\(533\) −9.67366 4.30699i −0.419013 0.186557i
\(534\) −18.6142 + 13.0716i −0.805515 + 0.565663i
\(535\) −1.50587 + 2.19793i −0.0651042 + 0.0950249i
\(536\) −6.45869 7.17310i −0.278973 0.309831i
\(537\) −4.08934 46.0201i −0.176468 1.98592i
\(538\) −2.45613 + 2.72781i −0.105891 + 0.117604i
\(539\) −5.44763 + 16.7661i −0.234646 + 0.722167i
\(540\) 6.39116 + 15.1908i 0.275032 + 0.653709i
\(541\) 10.3808 + 31.9488i 0.446305 + 1.37358i 0.881047 + 0.473029i \(0.156840\pi\)
−0.434742 + 0.900555i \(0.643160\pi\)
\(542\) −15.8797 7.07012i −0.682093 0.303687i
\(543\) 33.4478 + 7.67411i 1.43538 + 0.329328i
\(544\) −4.17979 39.7680i −0.179207 1.70504i
\(545\) −4.14697 1.22179i −0.177637 0.0523357i
\(546\) 0.797759 2.32714i 0.0341409 0.0995924i
\(547\) −3.47767 + 33.0878i −0.148694 + 1.41473i 0.624729 + 0.780842i \(0.285210\pi\)
−0.773423 + 0.633890i \(0.781457\pi\)
\(548\) 3.83331 11.7977i 0.163751 0.503974i
\(549\) 2.44266 + 33.6169i 0.104250 + 1.43473i
\(550\) −7.82621 7.78053i −0.333711 0.331763i
\(551\) 2.17754 + 3.77161i 0.0927664 + 0.160676i
\(552\) 19.3321 + 34.7643i 0.822827 + 1.47967i
\(553\) 3.68430 1.64036i 0.156672 0.0697550i
\(554\) 5.44212 2.42299i 0.231214 0.102943i
\(555\) −4.18025 9.10449i −0.177442 0.386464i
\(556\) −24.5242 10.9189i −1.04006 0.463064i
\(557\) 29.7702 1.26140 0.630702 0.776025i \(-0.282767\pi\)
0.630702 + 0.776025i \(0.282767\pi\)
\(558\) 5.98447 1.07202i 0.253343 0.0453823i
\(559\) −5.35937 16.4945i −0.226677 0.697641i
\(560\) 1.31057 1.24734i 0.0553818 0.0527096i
\(561\) 34.1952 + 0.550343i 1.44372 + 0.0232355i
\(562\) 1.17698 + 0.250175i 0.0496479 + 0.0105530i
\(563\) −23.2130 4.93408i −0.978312 0.207947i −0.309109 0.951027i \(-0.600031\pi\)
−0.669203 + 0.743080i \(0.733364\pi\)
\(564\) −5.06603 + 8.45733i −0.213318 + 0.356118i
\(565\) 13.0167 12.3887i 0.547617 0.521195i
\(566\) −1.82970 5.63124i −0.0769080 0.236699i
\(567\) 2.12094 + 8.31360i 0.0890709 + 0.349138i
\(568\) −0.404108 −0.0169560
\(569\) 26.6550 + 11.8676i 1.11744 + 0.497515i 0.880517 0.474014i \(-0.157195\pi\)
0.236920 + 0.971529i \(0.423862\pi\)
\(570\) 7.96945 11.2398i 0.333804 0.470782i
\(571\) −2.43726 + 1.08514i −0.101996 + 0.0454116i −0.457100 0.889415i \(-0.651112\pi\)
0.355104 + 0.934827i \(0.384445\pi\)
\(572\) −7.32662 + 3.26202i −0.306341 + 0.136392i
\(573\) −20.7961 0.334696i −0.868771 0.0139821i
\(574\) 1.97029 + 3.41264i 0.0822382 + 0.142441i
\(575\) 19.8822 39.3050i 0.829145 1.63913i
\(576\) 7.48506 + 3.62553i 0.311877 + 0.151064i
\(577\) −10.1294 + 31.1750i −0.421692 + 1.29783i 0.484435 + 0.874827i \(0.339025\pi\)
−0.906127 + 0.423007i \(0.860975\pi\)
\(578\) −2.35519 + 22.4081i −0.0979630 + 0.932055i
\(579\) 43.1393 8.44636i 1.79281 0.351019i
\(580\) 2.84029 + 0.836813i 0.117937 + 0.0347468i
\(581\) 0.328885 + 3.12913i 0.0136445 + 0.129818i
\(582\) −1.74736 + 1.87893i −0.0724303 + 0.0778841i
\(583\) −14.0611 6.26040i −0.582351 0.259279i
\(584\) 8.07935 + 24.8657i 0.334326 + 1.02895i
\(585\) 7.65494 + 10.6374i 0.316493 + 0.439802i
\(586\) −2.47698 + 7.62337i −0.102323 + 0.314919i
\(587\) −2.85518 + 3.17100i −0.117846 + 0.130881i −0.799181 0.601091i \(-0.794733\pi\)
0.681335 + 0.731972i \(0.261400\pi\)
\(588\) −12.2466 + 8.60004i −0.505043 + 0.354660i
\(589\) 8.29501 + 9.21254i 0.341790 + 0.379596i
\(590\) −4.62464 + 6.75004i −0.190394 + 0.277895i
\(591\) −0.260788 2.93483i −0.0107274 0.120723i
\(592\) 2.00566 + 0.892978i 0.0824322 + 0.0367012i
\(593\) −7.81313 −0.320847 −0.160423 0.987048i \(-0.551286\pi\)
−0.160423 + 0.987048i \(0.551286\pi\)
\(594\) −6.20695 + 9.64380i −0.254674 + 0.395690i
\(595\) −12.3890 + 7.61695i −0.507900 + 0.312265i
\(596\) −0.901418 + 8.57642i −0.0369235 + 0.351304i
\(597\) −7.41905 8.51123i −0.303642 0.348341i
\(598\) 8.78239 + 9.75383i 0.359139 + 0.398864i
\(599\) 22.2102 38.4691i 0.907483 1.57181i 0.0899331 0.995948i \(-0.471335\pi\)
0.817550 0.575858i \(-0.195332\pi\)
\(600\) −3.23790 22.3433i −0.132187 0.912163i
\(601\) −7.98356 13.8279i −0.325656 0.564053i 0.655989 0.754771i \(-0.272252\pi\)
−0.981645 + 0.190718i \(0.938919\pi\)
\(602\) −1.99440 + 6.13814i −0.0812858 + 0.250172i
\(603\) 11.1019 + 0.357445i 0.452106 + 0.0145563i
\(604\) −10.8181 7.85982i −0.440183 0.319811i
\(605\) 1.06073 5.77028i 0.0431246 0.234595i
\(606\) 1.15193 9.48839i 0.0467938 0.385439i
\(607\) −5.79724 + 10.0411i −0.235303 + 0.407557i −0.959361 0.282183i \(-0.908942\pi\)
0.724058 + 0.689739i \(0.242275\pi\)
\(608\) 2.85802 + 27.1922i 0.115908 + 1.10279i
\(609\) 1.39797 + 0.649571i 0.0566487 + 0.0263219i
\(610\) 3.46385 18.8431i 0.140247 0.762936i
\(611\) −2.42257 + 7.45589i −0.0980065 + 0.301633i
\(612\) 22.9253 + 17.8110i 0.926702 + 0.719967i
\(613\) 0.0509077 + 0.156678i 0.00205614 + 0.00632816i 0.952079 0.305851i \(-0.0989410\pi\)
−0.950023 + 0.312179i \(0.898941\pi\)
\(614\) −2.23938 + 0.475994i −0.0903739 + 0.0192096i
\(615\) −20.9013 1.95301i −0.842823 0.0787530i
\(616\) 7.03554 + 1.49545i 0.283470 + 0.0602534i
\(617\) −3.76370 35.8092i −0.151521 1.44162i −0.760965 0.648794i \(-0.775274\pi\)
0.609444 0.792829i \(-0.291393\pi\)
\(618\) 22.8443 + 5.24131i 0.918934 + 0.210836i
\(619\) −43.6439 19.4315i −1.75420 0.781019i −0.990840 0.135043i \(-0.956883\pi\)
−0.763358 0.645976i \(-0.776451\pi\)
\(620\) 8.40342 + 0.648990i 0.337489 + 0.0260641i
\(621\) −44.2638 11.6670i −1.77624 0.468181i
\(622\) 8.64512 + 6.28105i 0.346638 + 0.251847i
\(623\) −16.0573 + 3.41308i −0.643321 + 0.136742i
\(624\) −2.79927 0.642252i −0.112061 0.0257107i
\(625\) −18.4804 + 16.8367i −0.739215 + 0.673470i
\(626\) 2.11795 3.66840i 0.0846503 0.146619i
\(627\) −23.3817 0.376309i −0.933776 0.0150283i
\(628\) −3.05423 + 29.0590i −0.121877 + 1.15958i
\(629\) −14.2772 10.3730i −0.569269 0.413598i
\(630\) 0.0221514 4.87692i 0.000882534 0.194301i
\(631\) −12.6855 + 9.21654i −0.505001 + 0.366905i −0.810924 0.585152i \(-0.801035\pi\)
0.305923 + 0.952056i \(0.401035\pi\)
\(632\) 5.51425 + 9.55096i 0.219345 + 0.379917i
\(633\) −1.66565 + 13.7199i −0.0662037 + 0.545318i
\(634\) −3.38994 0.720555i −0.134632 0.0286169i
\(635\) −19.8728 25.8205i −0.788629 1.02465i
\(636\) −6.34988 11.4188i −0.251789 0.452786i
\(637\) −7.96265 + 8.84341i −0.315492 + 0.350389i
\(638\) 0.636737 + 1.95967i 0.0252087 + 0.0775843i
\(639\) 0.322131 0.335398i 0.0127433 0.0132681i
\(640\) 16.3572 + 13.9290i 0.646576 + 0.550594i
\(641\) −24.8019 + 27.5453i −0.979616 + 1.08797i 0.0164943 + 0.999864i \(0.494749\pi\)
−0.996111 + 0.0881103i \(0.971917\pi\)
\(642\) −1.25823 0.945460i −0.0496582 0.0373143i
\(643\) 3.29095 5.70009i 0.129782 0.224790i −0.793810 0.608166i \(-0.791905\pi\)
0.923592 + 0.383376i \(0.125239\pi\)
\(644\) 1.24517 + 11.8470i 0.0490666 + 0.466838i
\(645\) −20.5292 27.5804i −0.808337 1.08598i
\(646\) 2.53703 24.1382i 0.0998180 0.949705i
\(647\) 2.22736 + 1.61827i 0.0875666 + 0.0636209i 0.630707 0.776021i \(-0.282765\pi\)
−0.543141 + 0.839642i \(0.682765\pi\)
\(648\) −22.0035 + 8.14449i −0.864378 + 0.319946i
\(649\) 13.8871 0.545115
\(650\) −2.68996 6.94675i −0.105509 0.272474i
\(651\) 4.27678 + 0.981246i 0.167620 + 0.0384581i
\(652\) 9.89346 + 10.9878i 0.387458 + 0.430316i
\(653\) 5.91127 2.63187i 0.231326 0.102993i −0.287801 0.957690i \(-0.592924\pi\)
0.519126 + 0.854697i \(0.326257\pi\)
\(654\) 0.828150 2.41579i 0.0323832 0.0944650i
\(655\) 26.6930 + 14.4426i 1.04298 + 0.564319i
\(656\) 3.72180 2.70405i 0.145312 0.105575i
\(657\) −27.0782 13.1158i −1.05642 0.511697i
\(658\) 2.36020 1.71479i 0.0920103 0.0668494i
\(659\) 6.54526 7.26924i 0.254967 0.283170i −0.602049 0.798459i \(-0.705649\pi\)
0.857016 + 0.515289i \(0.172316\pi\)
\(660\) −11.6917 + 10.7744i −0.455099 + 0.419392i
\(661\) −0.222630 0.247256i −0.00865932 0.00961714i 0.738800 0.673925i \(-0.235393\pi\)
−0.747459 + 0.664308i \(0.768726\pi\)
\(662\) −4.32756 0.919851i −0.168195 0.0357510i
\(663\) 20.9360 + 9.72796i 0.813087 + 0.377803i
\(664\) −8.41601 + 1.78888i −0.326604 + 0.0694219i
\(665\) 8.47125 5.20826i 0.328501 0.201967i
\(666\) 5.48102 2.23184i 0.212385 0.0864821i
\(667\) −6.65361 + 4.83413i −0.257629 + 0.187178i
\(668\) −10.9673 18.9958i −0.424336 0.734971i
\(669\) 13.0678 + 9.81945i 0.505230 + 0.379642i
\(670\) −6.05644 1.78436i −0.233981 0.0689360i
\(671\) −29.7053 + 13.2256i −1.14676 + 0.510570i
\(672\) 6.35921 + 7.29536i 0.245312 + 0.281425i
\(673\) 6.03084 1.28189i 0.232472 0.0494134i −0.0902026 0.995923i \(-0.528751\pi\)
0.322674 + 0.946510i \(0.395418\pi\)
\(674\) 3.74792 0.144364
\(675\) 21.1254 + 15.1234i 0.813117 + 0.582101i
\(676\) 13.0257 0.500990
\(677\) 14.2930 3.03808i 0.549326 0.116763i 0.0751165 0.997175i \(-0.476067\pi\)
0.474210 + 0.880412i \(0.342734\pi\)
\(678\) 6.97502 + 8.00183i 0.267874 + 0.307309i
\(679\) −1.69175 + 0.753215i −0.0649233 + 0.0289057i
\(680\) −24.2564 31.5160i −0.930192 1.20858i
\(681\) 32.6839 + 24.5594i 1.25245 + 0.941119i
\(682\) 2.93263 + 5.07946i 0.112296 + 0.194503i
\(683\) 16.7839 12.1942i 0.642217 0.466598i −0.218394 0.975861i \(-0.570082\pi\)
0.860611 + 0.509263i \(0.170082\pi\)
\(684\) −15.6757 12.1786i −0.599375 0.465662i
\(685\) −4.59300 19.0086i −0.175490 0.726282i
\(686\) 9.30951 1.97880i 0.355439 0.0755509i
\(687\) −24.6722 11.4640i −0.941301 0.437378i
\(688\) 7.37005 + 1.56655i 0.280981 + 0.0597243i
\(689\) −6.95218 7.72118i −0.264857 0.294153i
\(690\) 22.6825 + 12.7487i 0.863508 + 0.485335i
\(691\) 17.5081 19.4447i 0.666040 0.739713i −0.311550 0.950230i \(-0.600848\pi\)
0.977590 + 0.210517i \(0.0675148\pi\)
\(692\) −17.0671 + 12.4000i −0.648793 + 0.471376i
\(693\) −6.84949 + 4.64721i −0.260191 + 0.176533i
\(694\) −6.15055 + 4.46863i −0.233472 + 0.169627i
\(695\) −41.9498 + 5.58527i −1.59125 + 0.211861i
\(696\) −1.36698 + 3.98761i −0.0518152 + 0.151150i
\(697\) −33.7818 + 15.0406i −1.27958 + 0.569705i
\(698\) −7.30429 8.11223i −0.276471 0.307053i
\(699\) −3.18614 0.731013i −0.120511 0.0276495i
\(700\) 1.73076 6.53575i 0.0654166 0.247028i
\(701\) −24.6481 −0.930945 −0.465472 0.885062i \(-0.654116\pi\)
−0.465472 + 0.885062i \(0.654116\pi\)
\(702\) −6.47541 + 4.24286i −0.244399 + 0.160136i
\(703\) 9.76234 + 7.09275i 0.368193 + 0.267508i
\(704\) −0.838683 + 7.97954i −0.0316091 + 0.300740i
\(705\) 0.179512 + 15.5405i 0.00676080 + 0.585289i
\(706\) −2.02074 19.2260i −0.0760515 0.723582i
\(707\) 3.44915 5.97411i 0.129719 0.224679i
\(708\) 9.42420 + 7.08156i 0.354183 + 0.266141i
\(709\) −18.3812 + 20.4144i −0.690321 + 0.766680i −0.981804 0.189897i \(-0.939185\pi\)
0.291483 + 0.956576i \(0.405851\pi\)
\(710\) −0.225181 + 0.138445i −0.00845091 + 0.00519575i
\(711\) −12.3227 3.03679i −0.462136 0.113889i
\(712\) −13.8721 42.6938i −0.519878 1.60002i
\(713\) −15.6646 + 17.3973i −0.586645 + 0.651535i
\(714\) −4.17520 7.50815i −0.156253 0.280985i
\(715\) −7.14588 + 10.4300i −0.267241 + 0.390059i
\(716\) 37.0087 + 7.86644i 1.38308 + 0.293983i
\(717\) 0.299194 2.46445i 0.0111736 0.0920367i
\(718\) −7.83774 13.5754i −0.292502 0.506628i
\(719\) 29.6588 21.5483i 1.10609 0.803618i 0.124042 0.992277i \(-0.460414\pi\)
0.982043 + 0.188659i \(0.0604141\pi\)
\(720\) −5.66504 + 0.569417i −0.211124 + 0.0212209i
\(721\) 13.6851 + 9.94284i 0.509661 + 0.370291i
\(722\) −0.220162 + 2.09470i −0.00819358 + 0.0779567i
\(723\) 18.9693 + 0.305295i 0.705476 + 0.0113540i
\(724\) −14.0514 + 24.3378i −0.522218 + 0.904508i
\(725\) 4.50526 1.22133i 0.167321 0.0453589i
\(726\) 3.37796 + 0.775023i 0.125368 + 0.0287638i
\(727\) −9.30118 + 1.97703i −0.344962 + 0.0733239i −0.377135 0.926158i \(-0.623091\pi\)
0.0321730 + 0.999482i \(0.489757\pi\)
\(728\) 3.92800 + 2.85386i 0.145581 + 0.105771i
\(729\) 10.7802 24.7546i 0.399266 0.916835i
\(730\) 13.0209 + 11.0880i 0.481925 + 0.410385i
\(731\) −55.3291 24.6341i −2.04642 0.911126i
\(732\) −26.9032 6.17256i −0.994372 0.228144i
\(733\) −1.05311 10.0197i −0.0388976 0.370086i −0.996604 0.0823398i \(-0.973761\pi\)
0.957707 0.287746i \(-0.0929059\pi\)
\(734\) −21.4747 4.56460i −0.792647 0.168482i
\(735\) −9.34577 + 21.6609i −0.344724 + 0.798974i
\(736\) −50.5054 + 10.7353i −1.86166 + 0.395707i
\(737\) 3.31138 + 10.1914i 0.121976 + 0.375404i
\(738\) 1.69241 12.2846i 0.0622984 0.452201i
\(739\) −5.85917 + 18.0327i −0.215533 + 0.663342i 0.783582 + 0.621288i \(0.213390\pi\)
−0.999115 + 0.0420544i \(0.986610\pi\)
\(740\) 8.13246 1.08277i 0.298955 0.0398034i
\(741\) −14.3154 6.65170i −0.525890 0.244356i
\(742\) 0.404151 + 3.84524i 0.0148368 + 0.141163i
\(743\) −10.9750 + 19.0092i −0.402633 + 0.697381i −0.994043 0.108990i \(-0.965238\pi\)
0.591410 + 0.806371i \(0.298572\pi\)
\(744\) −1.44612 + 11.9116i −0.0530173 + 0.436702i
\(745\) 5.87066 + 12.2619i 0.215084 + 0.449240i
\(746\) −7.04928 5.12160i −0.258092 0.187515i
\(747\) 5.22402 8.41103i 0.191137 0.307743i
\(748\) −8.65462 + 26.6362i −0.316444 + 0.973915i
\(749\) −0.567947 0.983714i −0.0207523 0.0359441i
\(750\) −9.45896 11.3411i −0.345393 0.414119i
\(751\) −6.43136 + 11.1394i −0.234684 + 0.406484i −0.959181 0.282794i \(-0.908739\pi\)
0.724497 + 0.689278i \(0.242072\pi\)
\(752\) −2.27897 2.53105i −0.0831055 0.0922980i
\(753\) 10.6364 + 12.2022i 0.387611 + 0.444672i
\(754\) −0.145390 + 1.38329i −0.00529478 + 0.0503764i
\(755\) −21.0176 1.62317i −0.764908 0.0590733i
\(756\) −7.01809 0.339085i −0.255245 0.0123324i
\(757\) −3.01935 −0.109740 −0.0548701 0.998494i \(-0.517474\pi\)
−0.0548701 + 0.998494i \(0.517474\pi\)
\(758\) −2.50021 1.11317i −0.0908118 0.0404320i
\(759\) −3.90871 43.9874i −0.141877 1.59664i
\(760\) 16.5858 + 21.5497i 0.601632 + 0.781691i
\(761\) 28.0099 + 31.1081i 1.01536 + 1.12767i 0.991781 + 0.127947i \(0.0408386\pi\)
0.0235764 + 0.999722i \(0.492495\pi\)
\(762\) 15.7513 11.0612i 0.570610 0.400703i
\(763\) 1.23331 1.36972i 0.0446486 0.0495873i
\(764\) 5.26338 16.1990i 0.190422 0.586060i
\(765\) 45.4931 + 4.99054i 1.64481 + 0.180433i
\(766\) 1.20666 + 3.71373i 0.0435985 + 0.134183i
\(767\) 8.56370 + 3.81280i 0.309217 + 0.137672i
\(768\) −15.1828 + 16.3260i −0.547861 + 0.589114i
\(769\) −4.91139 46.7288i −0.177109 1.68508i −0.616947 0.787005i \(-0.711631\pi\)
0.439837 0.898077i \(-0.355036\pi\)
\(770\) 4.43275 1.57703i 0.159745 0.0568320i
\(771\) −10.6121 + 2.07778i −0.382187 + 0.0748293i
\(772\) −3.76288 + 35.8014i −0.135429 + 1.28852i
\(773\) 8.38597 25.8093i 0.301622 0.928298i −0.679294 0.733866i \(-0.737714\pi\)
0.980916 0.194431i \(-0.0622862\pi\)
\(774\) 16.8069 11.4031i 0.604112 0.409875i
\(775\) 11.8211 6.06681i 0.424627 0.217926i
\(776\) −2.53202 4.38559i −0.0908943 0.157434i
\(777\) 4.27062 + 0.0687320i 0.153208 + 0.00246575i
\(778\) 21.5286 9.58514i 0.771837 0.343644i
\(779\) 23.0990 10.2844i 0.827609 0.368475i
\(780\) −10.1681 + 3.43416i −0.364076 + 0.122962i
\(781\) 0.409846 + 0.182475i 0.0146654 + 0.00652948i
\(782\) 45.8346 1.63904
\(783\) −2.21993 4.31324i −0.0793337 0.154143i
\(784\) −1.59758 4.91685i −0.0570565 0.175602i
\(785\) 19.8912 + 41.5463i 0.709949 + 1.48285i
\(786\) −9.21277 + 15.3800i −0.328609 + 0.548586i
\(787\) 8.70721 + 1.85077i 0.310378 + 0.0659730i 0.360467 0.932772i \(-0.382617\pi\)
−0.0500890 + 0.998745i \(0.515951\pi\)
\(788\) 2.36015 + 0.501665i 0.0840768 + 0.0178711i
\(789\) 3.22454 + 0.0518962i 0.114797 + 0.00184755i
\(790\) 6.34482 + 3.43294i 0.225738 + 0.122139i
\(791\) 2.36744 + 7.28623i 0.0841765 + 0.259069i
\(792\) −14.5965 17.2996i −0.518663 0.614713i
\(793\) −21.9495 −0.779449
\(794\) 4.44198 + 1.97770i 0.157640 + 0.0701858i
\(795\) −17.9556 10.0919i −0.636818 0.357924i
\(796\) 8.44696 3.76083i 0.299395 0.133299i
\(797\) 34.5778 15.3950i 1.22481 0.545320i 0.310590 0.950544i \(-0.399473\pi\)
0.914217 + 0.405224i \(0.132807\pi\)
\(798\) 2.85488 + 5.13386i 0.101062 + 0.181737i
\(799\) 13.6885 + 23.7091i 0.484264 + 0.838769i
\(800\) 28.9582 + 4.49968i 1.02383 + 0.159088i
\(801\) 46.4926 + 22.5196i 1.64274 + 0.795690i
\(802\) −4.22368 + 12.9992i −0.149143 + 0.459016i
\(803\) 3.03405 28.8670i 0.107069 1.01869i
\(804\) −2.94978 + 8.60480i −0.104031 + 0.303468i
\(805\) 11.4538 + 14.8817i 0.403693 + 0.524512i
\(806\) 0.413850 + 3.93752i 0.0145772 + 0.138693i
\(807\) 8.12561 + 1.86430i 0.286035 + 0.0656266i
\(808\) 17.2331 + 7.67269i 0.606260 + 0.269924i
\(809\) 5.78411 + 17.8016i 0.203358 + 0.625873i 0.999777 + 0.0211267i \(0.00672534\pi\)
−0.796418 + 0.604746i \(0.793275\pi\)
\(810\) −9.47076 + 12.0766i −0.332769 + 0.424330i
\(811\) 13.0270 40.0931i 0.457441 1.40786i −0.410804 0.911723i \(-0.634752\pi\)
0.868245 0.496135i \(-0.165248\pi\)
\(812\) −0.844700 + 0.938134i −0.0296432 + 0.0329221i
\(813\) 3.49435 + 39.3243i 0.122552 + 1.37916i
\(814\) 3.82022 + 4.24278i 0.133899 + 0.148709i
\(815\) 22.3585 + 6.58731i 0.783184 + 0.230743i
\(816\) −8.20781 + 5.76383i −0.287331 + 0.201774i
\(817\) 37.8325 + 16.8441i 1.32359 + 0.589301i
\(818\) −29.3086 −1.02475
\(819\) −5.49979 + 0.985200i −0.192178 + 0.0344257i
\(820\) 6.55552 15.8922i 0.228929 0.554979i
\(821\) 3.02671 28.7972i 0.105633 1.00503i −0.805410 0.592718i \(-0.798055\pi\)
0.911043 0.412311i \(-0.135278\pi\)
\(822\) 11.3366 2.21963i 0.395411 0.0774185i
\(823\) −8.17299 9.07702i −0.284892 0.316405i 0.583664 0.811995i \(-0.301618\pi\)
−0.868557 + 0.495590i \(0.834952\pi\)
\(824\) −23.1288 + 40.0603i −0.805731 + 1.39557i
\(825\) −6.80528 + 24.1227i −0.236929 + 0.839844i
\(826\) −1.74422 3.02107i −0.0606890 0.105116i
\(827\) 5.83473 17.9575i 0.202894 0.624442i −0.796900 0.604112i \(-0.793528\pi\)
0.999793 0.0203307i \(-0.00647191\pi\)
\(828\) 19.7783 31.8445i 0.687345 1.10667i
\(829\) −10.2118 7.41933i −0.354672 0.257684i 0.396155 0.918184i \(-0.370344\pi\)
−0.750826 + 0.660500i \(0.770344\pi\)
\(830\) −4.07680 + 3.88010i −0.141508 + 0.134680i
\(831\) −10.8165 8.12777i −0.375220 0.281949i
\(832\) −2.70804 + 4.69045i −0.0938842 + 0.162612i
\(833\) 4.34383 + 41.3288i 0.150505 + 1.43196i
\(834\) −2.21271 24.9011i −0.0766197 0.862254i
\(835\) −30.4124 16.4550i −1.05247 0.569450i
\(836\) 5.91778 18.2131i 0.204671 0.629912i
\(837\) −8.73356 10.6955i −0.301876 0.369690i
\(838\) 1.24568 + 3.83380i 0.0430312 + 0.132436i
\(839\) 43.0383 9.14808i 1.48585 0.315827i 0.607681 0.794181i \(-0.292100\pi\)
0.878167 + 0.478354i \(0.158766\pi\)
\(840\) 9.18796 + 2.86845i 0.317015 + 0.0989709i
\(841\) 27.5138 + 5.84823i 0.948751 + 0.201663i
\(842\) 2.15967 + 20.5479i 0.0744272 + 0.708127i
\(843\) −0.802571 2.61238i −0.0276420 0.0899750i
\(844\) −10.3396 4.60348i −0.355903 0.158458i
\(845\) 17.4928 10.7548i 0.601770 0.369977i
\(846\) −9.17592 0.295434i −0.315475 0.0101572i
\(847\) 2.02360 + 1.47023i 0.0695317 + 0.0505177i
\(848\) 4.41519 0.938477i 0.151618 0.0322274i
\(849\) −9.15803 + 9.84761i −0.314303 + 0.337969i
\(850\) −24.3136 9.25157i −0.833951 0.317326i
\(851\) −11.3938 + 19.7347i −0.390575 + 0.676496i
\(852\) 0.185083 + 0.332830i 0.00634085 + 0.0114026i
\(853\) 5.01106 47.6771i 0.171576 1.63243i −0.482425 0.875938i \(-0.660244\pi\)
0.654000 0.756494i \(-0.273090\pi\)
\(854\) 6.60816 + 4.80111i 0.226127 + 0.164291i
\(855\) −31.1069 3.41239i −1.06383 0.116701i
\(856\) 2.51297 1.82578i 0.0858916 0.0624039i
\(857\) −12.6888 21.9776i −0.433440 0.750741i 0.563727 0.825961i \(-0.309367\pi\)
−0.997167 + 0.0752208i \(0.976034\pi\)
\(858\) −5.97074 4.48655i −0.203838 0.153168i
\(859\) 8.22330 + 1.74792i 0.280575 + 0.0596382i 0.346050 0.938216i \(-0.387523\pi\)
−0.0654745 + 0.997854i \(0.520856\pi\)
\(860\) 26.5275 9.43761i 0.904582 0.321820i
\(861\) 4.59907 7.67777i 0.156736 0.261658i
\(862\) 17.6722 19.6270i 0.601919 0.668499i
\(863\) −9.08240 27.9528i −0.309168 0.951523i −0.978089 0.208189i \(-0.933243\pi\)
0.668920 0.743334i \(-0.266757\pi\)
\(864\) −1.71803 30.4069i −0.0584487 1.03446i
\(865\) −12.6819 + 30.7440i −0.431197 + 1.04533i
\(866\) 4.68749 5.20599i 0.159288 0.176907i
\(867\) 47.0784 20.0592i 1.59887 0.681247i
\(868\) −1.79668 + 3.11194i −0.0609833 + 0.105626i
\(869\) −1.27981 12.1765i −0.0434145 0.413061i
\(870\) 0.604410 + 2.69034i 0.0204914 + 0.0912111i
\(871\) −0.756105 + 7.19386i −0.0256197 + 0.243755i
\(872\) 4.07764 + 2.96258i 0.138086 + 0.100326i
\(873\) 5.65829 + 1.39443i 0.191504 + 0.0471942i
\(874\) −31.3404 −1.06011
\(875\) −3.07200 10.2061i −0.103853 0.345030i
\(876\) 16.7794 18.0429i 0.566925 0.609613i
\(877\) −30.6214 34.0085i −1.03401 1.14838i −0.988776 0.149408i \(-0.952263\pi\)
−0.0452341 0.998976i \(-0.514403\pi\)
\(878\) 5.00123 2.22669i 0.168783 0.0751472i
\(879\) 17.8660 3.49803i 0.602606 0.117986i
\(880\) −2.37193 4.95419i −0.0799579 0.167006i
\(881\) 22.8783 16.6220i 0.770789 0.560011i −0.131412 0.991328i \(-0.541951\pi\)
0.902200 + 0.431317i \(0.141951\pi\)
\(882\) −12.5419 6.07489i −0.422307 0.204552i
\(883\) 9.86953 7.17063i 0.332136 0.241311i −0.409200 0.912445i \(-0.634192\pi\)
0.741336 + 0.671134i \(0.234192\pi\)
\(884\) −12.6502 + 14.0495i −0.425472 + 0.472535i
\(885\) 18.5031 + 1.72892i 0.621975 + 0.0581170i
\(886\) −12.9413 14.3728i −0.434771 0.482862i
\(887\) −10.8668 2.30982i −0.364873 0.0775561i 0.0218271 0.999762i \(-0.493052\pi\)
−0.386700 + 0.922206i \(0.626385\pi\)
\(888\) 1.03380 + 11.6341i 0.0346920 + 0.390413i
\(889\) 13.5876 2.88814i 0.455714 0.0968651i
\(890\) −22.3566 19.0378i −0.749396 0.638150i
\(891\) 25.9936 + 1.67555i 0.870818 + 0.0561330i
\(892\) −10.8296 + 7.86813i −0.362600 + 0.263445i
\(893\) −9.35979 16.2116i −0.313214 0.542502i
\(894\) −7.38802 + 3.14790i −0.247092 + 0.105281i
\(895\) 56.1954 19.9925i 1.87841 0.668274i
\(896\) −8.36770 + 3.72554i −0.279545 + 0.124461i
\(897\) 9.66672 28.1988i 0.322762 0.941530i
\(898\) 5.32566 1.13200i 0.177719 0.0377754i
\(899\) −2.48088 −0.0827421
\(900\) −16.9194 + 12.9002i −0.563980 + 0.430005i
\(901\) −36.2829 −1.20876
\(902\) 11.7017 2.48728i 0.389624 0.0828172i
\(903\) 14.3852 2.81652i 0.478711 0.0937281i
\(904\) −19.1390 + 8.52122i −0.636553 + 0.283412i
\(905\) 1.22453 + 44.2859i 0.0407047 + 1.47211i
\(906\) 1.50076 12.3617i 0.0498593 0.410690i
\(907\) 20.6216 + 35.7176i 0.684728 + 1.18598i 0.973522 + 0.228593i \(0.0734125\pi\)
−0.288794 + 0.957391i \(0.593254\pi\)
\(908\) −27.0858 + 19.6790i −0.898874 + 0.653070i
\(909\) −20.1053 + 8.18680i −0.666852 + 0.271539i
\(910\) 3.16652 + 0.244548i 0.104969 + 0.00810670i
\(911\) 11.7894 2.50591i 0.390600 0.0830245i −0.00842543 0.999965i \(-0.502682\pi\)
0.399025 + 0.916940i \(0.369349\pi\)
\(912\) 5.61227 3.94114i 0.185841 0.130504i
\(913\) 9.34328 + 1.98598i 0.309218 + 0.0657262i
\(914\) 18.2588 + 20.2785i 0.603948 + 0.670752i
\(915\) −41.2258 + 13.9235i −1.36288 + 0.460298i
\(916\) 14.9077 16.5567i 0.492565 0.547049i
\(917\) −10.4681 + 7.60549i −0.345686 + 0.251155i
\(918\) −4.12016 + 26.7191i −0.135986 + 0.881860i
\(919\) 31.2727 22.7209i 1.03159 0.749494i 0.0629636 0.998016i \(-0.479945\pi\)
0.968626 + 0.248522i \(0.0799448\pi\)
\(920\) −37.1985 + 35.4036i −1.22640 + 1.16722i
\(921\) 3.41665 + 3.91962i 0.112582 + 0.129156i
\(922\) −10.6133 + 4.72536i −0.349532 + 0.155622i
\(923\) 0.202639 + 0.225053i 0.00666994 + 0.00740771i
\(924\) −1.99063 6.47952i −0.0654870 0.213161i
\(925\) 10.0274 8.16874i 0.329699 0.268586i
\(926\) −18.9531 −0.622839
\(927\) −14.8120 51.1299i −0.486489 1.67933i
\(928\) −4.42678 3.21625i −0.145316 0.105578i
\(929\) 4.76162 45.3038i 0.156224 1.48637i −0.582759 0.812645i \(-0.698027\pi\)
0.738983 0.673724i \(-0.235306\pi\)
\(930\) 3.27504 + 7.13297i 0.107393 + 0.233899i
\(931\) −2.97019 28.2595i −0.0973440 0.926167i
\(932\) 1.33850 2.31835i 0.0438440 0.0759401i
\(933\) 2.92499 24.0930i 0.0957597 0.788771i
\(934\) 13.3497 14.8264i 0.436816 0.485133i
\(935\) 10.3698 + 42.9165i 0.339129 + 1.40352i
\(936\) −4.25143 14.6757i −0.138962 0.479689i
\(937\) −10.9573 33.7230i −0.357958 1.10168i −0.954274 0.298932i \(-0.903370\pi\)
0.596316 0.802750i \(-0.296630\pi\)
\(938\) 1.80118 2.00041i 0.0588107 0.0653159i
\(939\) −9.61933 0.154815i −0.313915 0.00505219i
\(940\) −12.2085 3.59690i −0.398197 0.117318i
\(941\) −19.6924 4.18575i −0.641954 0.136452i −0.124578 0.992210i \(-0.539758\pi\)
−0.517376 + 0.855758i \(0.673091\pi\)
\(942\) −25.0324 + 10.6659i −0.815601 + 0.347512i
\(943\) 23.8747 + 41.3521i 0.777466 + 1.34661i
\(944\) −3.29476 + 2.39378i −0.107235 + 0.0779109i
\(945\) −9.70483 + 5.33918i −0.315698 + 0.173684i
\(946\) 15.8516 + 11.5169i 0.515380 + 0.374446i
\(947\) 2.53012 24.0725i 0.0822179 0.782251i −0.873273 0.487231i \(-0.838007\pi\)
0.955491 0.295020i \(-0.0953263\pi\)
\(948\) 5.34079 8.91602i 0.173461 0.289579i
\(949\) 9.79667 16.9683i 0.318013 0.550815i
\(950\) 16.6250 + 6.32596i 0.539385 + 0.205241i
\(951\) 2.31157 + 7.52417i 0.0749578 + 0.243988i
\(952\) 16.5848 3.52521i 0.537517 0.114253i
\(953\) −14.5798 10.5929i −0.472287 0.343137i 0.326045 0.945354i \(-0.394284\pi\)
−0.798332 + 0.602218i \(0.794284\pi\)
\(954\) 6.41955 10.3359i 0.207840 0.334637i
\(955\) −6.30648 26.1001i −0.204073 0.844578i
\(956\) 1.85726 + 0.826904i 0.0600680 + 0.0267440i
\(957\) 3.18700 3.42697i 0.103021 0.110778i
\(958\) 0.766909 + 7.29665i 0.0247777 + 0.235744i
\(959\) 8.15512 + 1.73342i 0.263343 + 0.0559752i
\(960\) −2.11090 + 10.5275i −0.0681291 + 0.339774i
\(961\) 23.4151 4.97703i 0.755325 0.160549i
\(962\) 1.19091 + 3.66526i 0.0383966 + 0.118173i
\(963\) −0.487847 + 3.54110i −0.0157206 + 0.114110i
\(964\) −4.80103 + 14.7760i −0.154631 + 0.475904i
\(965\) 24.5065 + 51.1859i 0.788891 + 1.64773i
\(966\) −9.07833 + 6.37514i −0.292091 + 0.205117i
\(967\) 3.80122 + 36.1662i 0.122239 + 1.16303i 0.867913 + 0.496715i \(0.165461\pi\)
−0.745675 + 0.666310i \(0.767873\pi\)
\(968\) −3.42002 + 5.92365i −0.109924 + 0.190393i
\(969\) −50.7132 + 21.6079i −1.62914 + 0.694147i
\(970\) −2.91340 1.57633i −0.0935436 0.0506129i
\(971\) 46.1160 + 33.5052i 1.47993 + 1.07523i 0.977578 + 0.210572i \(0.0675327\pi\)
0.502354 + 0.864662i \(0.332467\pi\)
\(972\) 16.7856 + 14.3922i 0.538400 + 0.461631i
\(973\) 5.57547 17.1595i 0.178741 0.550109i
\(974\) −15.0373 26.0453i −0.481825 0.834545i
\(975\) −10.8197 + 13.0072i −0.346507 + 0.416565i
\(976\) 4.76792 8.25828i 0.152617 0.264341i
\(977\) −10.3645 11.5109i −0.331588 0.368266i 0.554177 0.832399i \(-0.313033\pi\)
−0.885766 + 0.464132i \(0.846366\pi\)
\(978\) −4.46499 + 13.0248i −0.142775 + 0.416488i
\(979\) −5.20939 + 49.5640i −0.166493 + 1.58407i
\(980\) −14.7088 12.5254i −0.469857 0.400108i
\(981\) −5.70931 + 1.02273i −0.182284 + 0.0326533i
\(982\) 7.42689 0.237001
\(983\) −14.3663 6.39631i −0.458215 0.204011i 0.164630 0.986355i \(-0.447357\pi\)
−0.622846 + 0.782345i \(0.714024\pi\)
\(984\) 22.1951 + 10.3130i 0.707555 + 0.328767i
\(985\) 3.58374 1.27497i 0.114187 0.0406240i
\(986\) 3.25014 + 3.60964i 0.103505 + 0.114954i
\(987\) −6.00894 2.79207i −0.191267 0.0888726i
\(988\) 8.64985 9.60663i 0.275188 0.305628i
\(989\) −24.1669 + 74.3780i −0.768462 + 2.36508i
\(990\) −14.0603 4.63919i −0.446867 0.147443i
\(991\) 6.23054 + 19.1756i 0.197920 + 0.609134i 0.999930 + 0.0118242i \(0.00376384\pi\)
−0.802010 + 0.597310i \(0.796236\pi\)
\(992\) −14.2289 6.33510i −0.451767 0.201140i
\(993\) 2.95092 + 9.60526i 0.0936446 + 0.304814i
\(994\) −0.0117800 0.112079i −0.000373639 0.00355493i
\(995\) 8.23859 12.0249i 0.261181 0.381214i
\(996\) 5.32792 + 6.11226i 0.168822 + 0.193674i
\(997\) 4.26567 40.5852i 0.135095 1.28534i −0.691429 0.722444i \(-0.743019\pi\)
0.826525 0.562901i \(-0.190315\pi\)
\(998\) 2.06306 6.34944i 0.0653050 0.200988i
\(999\) −10.4800 8.41596i −0.331573 0.266269i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.2.q.a.121.12 yes 224
3.2 odd 2 675.2.r.a.496.17 224
9.2 odd 6 675.2.r.a.46.12 224
9.7 even 3 inner 225.2.q.a.196.17 yes 224
25.6 even 5 inner 225.2.q.a.31.17 224
75.56 odd 10 675.2.r.a.631.12 224
225.56 odd 30 675.2.r.a.181.17 224
225.106 even 15 inner 225.2.q.a.106.12 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.17 224 25.6 even 5 inner
225.2.q.a.106.12 yes 224 225.106 even 15 inner
225.2.q.a.121.12 yes 224 1.1 even 1 trivial
225.2.q.a.196.17 yes 224 9.7 even 3 inner
675.2.r.a.46.12 224 9.2 odd 6
675.2.r.a.181.17 224 225.56 odd 30
675.2.r.a.496.17 224 3.2 odd 2
675.2.r.a.631.12 224 75.56 odd 10