Properties

Label 450.2.w.a.113.5
Level $450$
Weight $2$
Character 450.113
Analytic conductor $3.593$
Analytic rank $0$
Dimension $480$
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] = [450,2,Mod(23,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([50, 33]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.w (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(30\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 113.5
Character \(\chi\) \(=\) 450.113
Dual form 450.2.w.a.227.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.777146 + 0.629320i) q^{2} +(-0.942695 + 1.45304i) q^{3} +(0.207912 - 0.978148i) q^{4} +(1.99402 - 1.01188i) q^{5} +(-0.181816 - 1.72248i) q^{6} +(-1.72082 - 0.461093i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.22265 - 2.73955i) q^{9} +O(q^{10})\) \(q+(-0.777146 + 0.629320i) q^{2} +(-0.942695 + 1.45304i) q^{3} +(0.207912 - 0.978148i) q^{4} +(1.99402 - 1.01188i) q^{5} +(-0.181816 - 1.72248i) q^{6} +(-1.72082 - 0.461093i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.22265 - 2.73955i) q^{9} +(-0.912847 + 2.04125i) q^{10} +(-4.41688 - 0.464233i) q^{11} +(1.22529 + 1.22420i) q^{12} +(-1.01486 + 1.25325i) q^{13} +(1.62750 - 0.724612i) q^{14} +(-0.409451 + 3.85128i) q^{15} +(-0.913545 - 0.406737i) q^{16} +(-5.47158 + 2.78791i) q^{17} +(2.67423 + 1.35959i) q^{18} +(-3.58379 - 1.16445i) q^{19} +(-0.575186 - 2.16082i) q^{20} +(2.29220 - 2.06575i) q^{21} +(3.72471 - 2.41886i) q^{22} +(-1.64865 + 4.29489i) q^{23} +(-1.72264 - 0.180281i) q^{24} +(2.95221 - 4.03540i) q^{25} -1.61264i q^{26} +(5.13326 + 0.805997i) q^{27} +(-0.808796 + 1.58735i) q^{28} +(-3.83350 + 4.25753i) q^{29} +(-2.10549 - 3.25068i) q^{30} +(-4.81814 - 5.35108i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.83832 - 5.98028i) q^{33} +(2.49773 - 5.60999i) q^{34} +(-3.89792 + 0.821834i) q^{35} +(-2.93389 + 0.626350i) q^{36} +(1.49361 - 9.43029i) q^{37} +(3.51794 - 1.35041i) q^{38} +(-0.864319 - 2.65607i) q^{39} +(1.80685 + 1.31730i) q^{40} +(10.2542 - 1.07776i) q^{41} +(-0.481351 + 3.04792i) q^{42} +(-1.25356 + 4.67836i) q^{43} +(-1.37241 + 4.22384i) q^{44} +(-5.21008 - 4.22553i) q^{45} +(-1.42162 - 4.37529i) q^{46} +(-4.88436 + 0.255978i) q^{47} +(1.45220 - 0.943990i) q^{48} +(-3.31356 - 1.91308i) q^{49} +(0.245265 + 4.99398i) q^{50} +(1.10709 - 10.5786i) q^{51} +(1.01486 + 1.25325i) q^{52} +(-0.446914 - 0.227714i) q^{53} +(-4.49652 + 2.60409i) q^{54} +(-9.27709 + 3.54366i) q^{55} +(-0.370400 - 1.74260i) q^{56} +(5.07041 - 4.10968i) q^{57} +(0.299836 - 5.72122i) q^{58} +(0.344792 + 3.28048i) q^{59} +(3.68199 + 1.20123i) q^{60} +(1.05258 - 10.0146i) q^{61} +(7.11194 + 1.12642i) q^{62} +(0.840779 + 5.27803i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-0.755518 + 3.52593i) q^{65} +(0.00342721 + 7.69240i) q^{66} +(11.1234 + 0.582955i) q^{67} +(1.58938 + 5.93166i) q^{68} +(-4.68647 - 6.44433i) q^{69} +(2.51205 - 3.09172i) q^{70} +(-3.66720 + 1.19154i) q^{71} +(1.88588 - 2.33312i) q^{72} +(1.95852 + 12.3656i) q^{73} +(4.77392 + 8.26867i) q^{74} +(3.08057 + 8.09383i) q^{75} +(-1.88411 + 3.26338i) q^{76} +(7.38661 + 2.83545i) q^{77} +(2.34322 + 1.52022i) q^{78} +(0.600522 + 0.540713i) q^{79} +(-2.23319 + 0.113357i) q^{80} +(-6.01025 + 6.69903i) q^{81} +(-7.29077 + 7.29077i) q^{82} +(-4.97216 + 7.65646i) q^{83} +(-1.54404 - 2.67160i) q^{84} +(-8.08941 + 11.0957i) q^{85} +(-1.96998 - 4.42466i) q^{86} +(-2.57254 - 9.58378i) q^{87} +(-1.59159 - 4.14623i) q^{88} +(7.69318 + 5.58942i) q^{89} +(6.70820 + 0.00504793i) q^{90} +(2.32427 - 1.68868i) q^{91} +(3.85826 + 2.50558i) q^{92} +(12.3174 - 1.95651i) q^{93} +(3.63477 - 3.27276i) q^{94} +(-8.32442 + 1.30444i) q^{95} +(-0.534499 + 1.64752i) q^{96} +(0.188306 + 3.59310i) q^{97} +(3.77906 - 0.598544i) q^{98} +(4.12852 + 12.6679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 480 q - 4 q^{3} + 4 q^{12} + 8 q^{15} - 60 q^{16} + 8 q^{18} + 12 q^{20} + 24 q^{23} - 48 q^{25} + 8 q^{27} + 24 q^{30} - 16 q^{33} + 24 q^{37} - 36 q^{38} + 40 q^{39} - 44 q^{42} + 12 q^{45} - 48 q^{47} - 8 q^{48} - 48 q^{50} + 24 q^{55} + 28 q^{57} - 12 q^{58} - 60 q^{59} - 24 q^{60} + 20 q^{63} + 24 q^{65} + 12 q^{67} - 144 q^{68} - 140 q^{69} + 16 q^{72} - 168 q^{75} - 432 q^{77} - 76 q^{78} + 40 q^{81} + 48 q^{82} - 60 q^{83} - 60 q^{84} + 24 q^{85} - 44 q^{87} - 52 q^{90} + 24 q^{92} - 72 q^{93} - 60 q^{95} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.777146 + 0.629320i −0.549525 + 0.444997i
\(3\) −0.942695 + 1.45304i −0.544265 + 0.838913i
\(4\) 0.207912 0.978148i 0.103956 0.489074i
\(5\) 1.99402 1.01188i 0.891751 0.452525i
\(6\) −0.181816 1.72248i −0.0742261 0.703200i
\(7\) −1.72082 0.461093i −0.650409 0.174277i −0.0814955 0.996674i \(-0.525970\pi\)
−0.568914 + 0.822397i \(0.692636\pi\)
\(8\) 0.453990 + 0.891007i 0.160510 + 0.315018i
\(9\) −1.22265 2.73955i −0.407551 0.913183i
\(10\) −0.912847 + 2.04125i −0.288668 + 0.645501i
\(11\) −4.41688 0.464233i −1.33174 0.139972i −0.588229 0.808695i \(-0.700174\pi\)
−0.743511 + 0.668723i \(0.766841\pi\)
\(12\) 1.22529 + 1.22420i 0.353711 + 0.353396i
\(13\) −1.01486 + 1.25325i −0.281473 + 0.347590i −0.898200 0.439587i \(-0.855125\pi\)
0.616727 + 0.787177i \(0.288458\pi\)
\(14\) 1.62750 0.724612i 0.434969 0.193661i
\(15\) −0.409451 + 3.85128i −0.105720 + 0.994396i
\(16\) −0.913545 0.406737i −0.228386 0.101684i
\(17\) −5.47158 + 2.78791i −1.32705 + 0.676168i −0.966523 0.256580i \(-0.917404\pi\)
−0.360531 + 0.932747i \(0.617404\pi\)
\(18\) 2.67423 + 1.35959i 0.630323 + 0.320458i
\(19\) −3.58379 1.16445i −0.822179 0.267142i −0.132431 0.991192i \(-0.542278\pi\)
−0.689747 + 0.724050i \(0.742278\pi\)
\(20\) −0.575186 2.16082i −0.128616 0.483175i
\(21\) 2.29220 2.06575i 0.500198 0.450784i
\(22\) 3.72471 2.41886i 0.794112 0.515702i
\(23\) −1.64865 + 4.29489i −0.343768 + 0.895546i 0.647306 + 0.762230i \(0.275896\pi\)
−0.991074 + 0.133316i \(0.957438\pi\)
\(24\) −1.72264 0.180281i −0.351633 0.0367997i
\(25\) 2.95221 4.03540i 0.590441 0.807081i
\(26\) 1.61264i 0.316264i
\(27\) 5.13326 + 0.805997i 0.987897 + 0.155114i
\(28\) −0.808796 + 1.58735i −0.152848 + 0.299981i
\(29\) −3.83350 + 4.25753i −0.711863 + 0.790604i −0.985217 0.171310i \(-0.945200\pi\)
0.273355 + 0.961913i \(0.411867\pi\)
\(30\) −2.10549 3.25068i −0.384407 0.593491i
\(31\) −4.81814 5.35108i −0.865363 0.961083i 0.134191 0.990956i \(-0.457157\pi\)
−0.999554 + 0.0298724i \(0.990490\pi\)
\(32\) 0.965926 0.258819i 0.170753 0.0457532i
\(33\) 4.83832 5.98028i 0.842244 1.04103i
\(34\) 2.49773 5.60999i 0.428357 0.962106i
\(35\) −3.89792 + 0.821834i −0.658868 + 0.138915i
\(36\) −2.93389 + 0.626350i −0.488981 + 0.104392i
\(37\) 1.49361 9.43029i 0.245548 1.55033i −0.489311 0.872110i \(-0.662752\pi\)
0.734859 0.678220i \(-0.237248\pi\)
\(38\) 3.51794 1.35041i 0.570685 0.219066i
\(39\) −0.864319 2.65607i −0.138402 0.425312i
\(40\) 1.80685 + 1.31730i 0.285689 + 0.208283i
\(41\) 10.2542 1.07776i 1.60144 0.168318i 0.738725 0.674007i \(-0.235428\pi\)
0.862716 + 0.505689i \(0.168761\pi\)
\(42\) −0.481351 + 3.04792i −0.0742741 + 0.470304i
\(43\) −1.25356 + 4.67836i −0.191166 + 0.713443i 0.802060 + 0.597244i \(0.203738\pi\)
−0.993226 + 0.116199i \(0.962929\pi\)
\(44\) −1.37241 + 4.22384i −0.206899 + 0.636768i
\(45\) −5.21008 4.22553i −0.776672 0.629905i
\(46\) −1.42162 4.37529i −0.209606 0.645101i
\(47\) −4.88436 + 0.255978i −0.712457 + 0.0373383i −0.405121 0.914263i \(-0.632771\pi\)
−0.307336 + 0.951601i \(0.599437\pi\)
\(48\) 1.45220 0.943990i 0.209607 0.136253i
\(49\) −3.31356 1.91308i −0.473365 0.273298i
\(50\) 0.245265 + 4.99398i 0.0346857 + 0.706256i
\(51\) 1.10709 10.5786i 0.155023 1.48130i
\(52\) 1.01486 + 1.25325i 0.140736 + 0.173795i
\(53\) −0.446914 0.227714i −0.0613883 0.0312789i 0.423027 0.906117i \(-0.360968\pi\)
−0.484415 + 0.874838i \(0.660968\pi\)
\(54\) −4.49652 + 2.60409i −0.611899 + 0.354372i
\(55\) −9.27709 + 3.54366i −1.25092 + 0.477826i
\(56\) −0.370400 1.74260i −0.0494968 0.232864i
\(57\) 5.07041 4.10968i 0.671593 0.544341i
\(58\) 0.299836 5.72122i 0.0393705 0.751233i
\(59\) 0.344792 + 3.28048i 0.0448881 + 0.427082i 0.993770 + 0.111450i \(0.0355496\pi\)
−0.948882 + 0.315631i \(0.897784\pi\)
\(60\) 3.68199 + 1.20123i 0.475343 + 0.155078i
\(61\) 1.05258 10.0146i 0.134769 1.28224i −0.692904 0.721030i \(-0.743669\pi\)
0.827673 0.561211i \(-0.189664\pi\)
\(62\) 7.11194 + 1.12642i 0.903218 + 0.143056i
\(63\) 0.840779 + 5.27803i 0.105928 + 0.664969i
\(64\) −0.587785 + 0.809017i −0.0734732 + 0.101127i
\(65\) −0.755518 + 3.52593i −0.0937104 + 0.437337i
\(66\) 0.00342721 + 7.69240i 0.000421860 + 0.946869i
\(67\) 11.1234 + 0.582955i 1.35894 + 0.0712192i 0.717826 0.696223i \(-0.245137\pi\)
0.641118 + 0.767442i \(0.278471\pi\)
\(68\) 1.58938 + 5.93166i 0.192741 + 0.719319i
\(69\) −4.68647 6.44433i −0.564184 0.775806i
\(70\) 2.51205 3.09172i 0.300248 0.369532i
\(71\) −3.66720 + 1.19154i −0.435216 + 0.141410i −0.518427 0.855122i \(-0.673482\pi\)
0.0832113 + 0.996532i \(0.473482\pi\)
\(72\) 1.88588 2.33312i 0.222253 0.274961i
\(73\) 1.95852 + 12.3656i 0.229227 + 1.44728i 0.786827 + 0.617174i \(0.211723\pi\)
−0.557599 + 0.830110i \(0.688277\pi\)
\(74\) 4.77392 + 8.26867i 0.554957 + 0.961213i
\(75\) 3.08057 + 8.09383i 0.355714 + 0.934595i
\(76\) −1.88411 + 3.26338i −0.216123 + 0.374335i
\(77\) 7.38661 + 2.83545i 0.841783 + 0.323130i
\(78\) 2.34322 + 1.52022i 0.265318 + 0.172131i
\(79\) 0.600522 + 0.540713i 0.0675641 + 0.0608349i 0.702221 0.711959i \(-0.252192\pi\)
−0.634657 + 0.772794i \(0.718859\pi\)
\(80\) −2.23319 + 0.113357i −0.249679 + 0.0126736i
\(81\) −6.01025 + 6.69903i −0.667805 + 0.744336i
\(82\) −7.29077 + 7.29077i −0.805131 + 0.805131i
\(83\) −4.97216 + 7.65646i −0.545766 + 0.840405i −0.998691 0.0511428i \(-0.983714\pi\)
0.452926 + 0.891548i \(0.350380\pi\)
\(84\) −1.54404 2.67160i −0.168468 0.291496i
\(85\) −8.08941 + 11.0957i −0.877419 + 1.20350i
\(86\) −1.96998 4.42466i −0.212429 0.477123i
\(87\) −2.57254 9.58378i −0.275806 1.02749i
\(88\) −1.59159 4.14623i −0.169664 0.441989i
\(89\) 7.69318 + 5.58942i 0.815476 + 0.592478i 0.915413 0.402516i \(-0.131864\pi\)
−0.0999374 + 0.994994i \(0.531864\pi\)
\(90\) 6.70820 + 0.00504793i 0.707107 + 0.000532099i
\(91\) 2.32427 1.68868i 0.243649 0.177022i
\(92\) 3.85826 + 2.50558i 0.402251 + 0.261225i
\(93\) 12.3174 1.95651i 1.27725 0.202880i
\(94\) 3.63477 3.27276i 0.374898 0.337559i
\(95\) −8.32442 + 1.30444i −0.854068 + 0.133833i
\(96\) −0.534499 + 1.64752i −0.0545521 + 0.168149i
\(97\) 0.188306 + 3.59310i 0.0191196 + 0.364824i 0.991388 + 0.130957i \(0.0418048\pi\)
−0.972268 + 0.233867i \(0.924862\pi\)
\(98\) 3.77906 0.598544i 0.381743 0.0604621i
\(99\) 4.12852 + 12.6679i 0.414932 + 1.27317i
\(100\) −3.33342 3.72670i −0.333342 0.372670i
\(101\) −8.64843 + 4.99317i −0.860550 + 0.496839i −0.864197 0.503154i \(-0.832173\pi\)
0.00364612 + 0.999993i \(0.498839\pi\)
\(102\) 5.79695 + 8.91781i 0.573983 + 0.882995i
\(103\) −0.425874 0.655788i −0.0419626 0.0646167i 0.817067 0.576543i \(-0.195599\pi\)
−0.859029 + 0.511926i \(0.828932\pi\)
\(104\) −1.57740 0.335286i −0.154676 0.0328775i
\(105\) 2.48039 6.43857i 0.242061 0.628340i
\(106\) 0.490622 0.104285i 0.0476534 0.0101290i
\(107\) −7.65071 7.65071i −0.739622 0.739622i 0.232883 0.972505i \(-0.425184\pi\)
−0.972505 + 0.232883i \(0.925184\pi\)
\(108\) 1.85565 4.85351i 0.178560 0.467029i
\(109\) 4.48694 + 6.17575i 0.429771 + 0.591529i 0.967901 0.251333i \(-0.0808689\pi\)
−0.538129 + 0.842862i \(0.680869\pi\)
\(110\) 4.97955 8.59220i 0.474782 0.819234i
\(111\) 12.2946 + 11.0602i 1.16695 + 1.04978i
\(112\) 1.38451 + 1.12115i 0.130823 + 0.105939i
\(113\) −15.3266 12.4113i −1.44181 1.16755i −0.955955 0.293512i \(-0.905176\pi\)
−0.485852 0.874041i \(-0.661491\pi\)
\(114\) −1.35414 + 6.38474i −0.126827 + 0.597985i
\(115\) 1.05846 + 10.2323i 0.0987018 + 0.954168i
\(116\) 3.36746 + 4.63492i 0.312661 + 0.430341i
\(117\) 4.67417 + 1.24798i 0.432127 + 0.115376i
\(118\) −2.33242 2.33242i −0.214717 0.214717i
\(119\) 10.7011 2.27459i 0.980969 0.208511i
\(120\) −3.61740 + 1.38362i −0.330222 + 0.126307i
\(121\) 8.53371 + 1.81390i 0.775792 + 0.164900i
\(122\) 5.48440 + 8.44523i 0.496534 + 0.764595i
\(123\) −8.10058 + 15.9158i −0.730405 + 1.43508i
\(124\) −6.23590 + 3.60030i −0.560000 + 0.323316i
\(125\) 1.80342 11.0339i 0.161303 0.986905i
\(126\) −3.97498 3.57268i −0.354119 0.318280i
\(127\) 2.62929 0.416438i 0.233311 0.0369529i −0.0386838 0.999252i \(-0.512317\pi\)
0.271995 + 0.962299i \(0.412317\pi\)
\(128\) −0.0523360 0.998630i −0.00462589 0.0882672i
\(129\) −5.61611 6.23174i −0.494471 0.548674i
\(130\) −1.63179 3.21562i −0.143117 0.282029i
\(131\) 13.2808 11.9581i 1.16035 1.04478i 0.162029 0.986786i \(-0.448196\pi\)
0.998317 0.0579942i \(-0.0184705\pi\)
\(132\) −4.84365 5.97596i −0.421586 0.520141i
\(133\) 5.63015 + 3.65627i 0.488196 + 0.317038i
\(134\) −9.01140 + 6.54716i −0.778466 + 0.565589i
\(135\) 11.0514 3.58706i 0.951151 0.308725i
\(136\) −4.96809 3.60953i −0.426011 0.309515i
\(137\) 0.760998 + 1.98247i 0.0650165 + 0.169374i 0.962240 0.272204i \(-0.0877524\pi\)
−0.897223 + 0.441577i \(0.854419\pi\)
\(138\) 7.69762 + 2.05889i 0.655265 + 0.175265i
\(139\) −0.849556 1.90813i −0.0720584 0.161846i 0.873925 0.486061i \(-0.161567\pi\)
−0.945983 + 0.324215i \(0.894900\pi\)
\(140\) −0.00654732 + 3.98361i −0.000553350 + 0.336676i
\(141\) 4.23251 7.33848i 0.356442 0.618011i
\(142\) 2.10008 3.23384i 0.176235 0.271378i
\(143\) 5.06434 5.06434i 0.423501 0.423501i
\(144\) 0.00267319 + 3.00000i 0.000222766 + 0.250000i
\(145\) −3.33596 + 12.3686i −0.277036 + 1.02716i
\(146\) −9.30398 8.37734i −0.770003 0.693314i
\(147\) 5.90346 3.01128i 0.486909 0.248366i
\(148\) −8.91367 3.42164i −0.732699 0.281257i
\(149\) −3.03610 + 5.25868i −0.248727 + 0.430808i −0.963173 0.268883i \(-0.913346\pi\)
0.714446 + 0.699691i \(0.246679\pi\)
\(150\) −7.48767 4.35142i −0.611365 0.355292i
\(151\) 2.54734 + 4.41212i 0.207299 + 0.359053i 0.950863 0.309612i \(-0.100199\pi\)
−0.743564 + 0.668665i \(0.766866\pi\)
\(152\) −0.589480 3.72183i −0.0478132 0.301880i
\(153\) 14.3275 + 11.5810i 1.15831 + 0.936270i
\(154\) −7.52489 + 2.44498i −0.606373 + 0.197022i
\(155\) −15.0221 5.79479i −1.20660 0.465448i
\(156\) −2.77773 + 0.293203i −0.222397 + 0.0234750i
\(157\) −5.28424 19.7211i −0.421728 1.57391i −0.770965 0.636877i \(-0.780226\pi\)
0.349237 0.937035i \(-0.386441\pi\)
\(158\) −0.806975 0.0422918i −0.0641995 0.00336455i
\(159\) 0.752181 0.434719i 0.0596518 0.0344754i
\(160\) 1.66418 1.49349i 0.131565 0.118071i
\(161\) 4.81738 6.63055i 0.379663 0.522561i
\(162\) 0.455006 8.98849i 0.0357486 0.706203i
\(163\) −16.3097 2.58320i −1.27747 0.202332i −0.519416 0.854522i \(-0.673850\pi\)
−0.758055 + 0.652190i \(0.773850\pi\)
\(164\) 1.07776 10.2542i 0.0841591 0.800721i
\(165\) 3.59639 16.8206i 0.279978 1.30948i
\(166\) −0.954270 9.07927i −0.0740657 0.704688i
\(167\) 0.131976 2.51824i 0.0102126 0.194868i −0.988759 0.149520i \(-0.952227\pi\)
0.998971 0.0453475i \(-0.0144395\pi\)
\(168\) 2.88124 + 1.10453i 0.222292 + 0.0852163i
\(169\) 2.16216 + 10.1722i 0.166320 + 0.782474i
\(170\) −0.696111 13.7138i −0.0533893 1.05180i
\(171\) 1.19168 + 11.2417i 0.0911299 + 0.859673i
\(172\) 4.31549 + 2.19885i 0.329053 + 0.167661i
\(173\) 10.6512 + 13.1532i 0.809799 + 1.00002i 0.999834 + 0.0182415i \(0.00580678\pi\)
−0.190034 + 0.981777i \(0.560860\pi\)
\(174\) 8.03051 + 5.82904i 0.608791 + 0.441899i
\(175\) −6.94092 + 5.58297i −0.524684 + 0.422033i
\(176\) 3.84620 + 2.22061i 0.289918 + 0.167384i
\(177\) −5.09170 2.59149i −0.382715 0.194789i
\(178\) −9.49626 + 0.497678i −0.711775 + 0.0373025i
\(179\) 0.186994 + 0.575509i 0.0139766 + 0.0430155i 0.957802 0.287430i \(-0.0928009\pi\)
−0.943825 + 0.330446i \(0.892801\pi\)
\(180\) −5.21643 + 4.21769i −0.388810 + 0.314368i
\(181\) 1.80091 5.54262i 0.133860 0.411980i −0.861551 0.507672i \(-0.830506\pi\)
0.995411 + 0.0956917i \(0.0305063\pi\)
\(182\) −0.743574 + 2.77506i −0.0551174 + 0.205701i
\(183\) 13.5594 + 10.9702i 1.00234 + 0.810939i
\(184\) −4.57525 + 0.480878i −0.337292 + 0.0354508i
\(185\) −6.56401 20.3155i −0.482596 1.49363i
\(186\) −8.34113 + 9.27207i −0.611601 + 0.679861i
\(187\) 25.4616 9.77378i 1.86194 0.714730i
\(188\) −0.765131 + 4.83084i −0.0558029 + 0.352326i
\(189\) −8.46179 3.75389i −0.615504 0.273055i
\(190\) 5.64838 6.25247i 0.409777 0.453602i
\(191\) −2.88947 + 6.48985i −0.209075 + 0.469589i −0.987394 0.158279i \(-0.949406\pi\)
0.778320 + 0.627868i \(0.216072\pi\)
\(192\) −0.621432 1.61673i −0.0448480 0.116678i
\(193\) −17.4128 + 4.66574i −1.25340 + 0.335847i −0.823649 0.567101i \(-0.808065\pi\)
−0.429750 + 0.902948i \(0.641398\pi\)
\(194\) −2.40755 2.67386i −0.172852 0.191972i
\(195\) −4.41109 4.42167i −0.315885 0.316642i
\(196\) −2.56020 + 2.84340i −0.182872 + 0.203100i
\(197\) −9.29176 + 18.2361i −0.662010 + 1.29927i 0.278804 + 0.960348i \(0.410062\pi\)
−0.940815 + 0.338921i \(0.889938\pi\)
\(198\) −11.1806 7.24661i −0.794571 0.514994i
\(199\) 12.5222i 0.887672i 0.896108 + 0.443836i \(0.146383\pi\)
−0.896108 + 0.443836i \(0.853617\pi\)
\(200\) 4.93584 + 0.798401i 0.349017 + 0.0564555i
\(201\) −11.3331 + 15.6132i −0.799373 + 1.10127i
\(202\) 3.57878 9.32305i 0.251802 0.655968i
\(203\) 8.55988 5.55885i 0.600786 0.390155i
\(204\) −10.1172 3.28231i −0.708348 0.229807i
\(205\) 19.3565 12.5251i 1.35192 0.874791i
\(206\) 0.743667 + 0.241632i 0.0518138 + 0.0168353i
\(207\) 13.7818 0.734587i 0.957900 0.0510573i
\(208\) 1.43687 0.732121i 0.0996289 0.0507635i
\(209\) 15.2886 + 6.80693i 1.05754 + 0.470846i
\(210\) 2.12430 + 6.56467i 0.146591 + 0.453005i
\(211\) −8.42725 + 3.75205i −0.580156 + 0.258302i −0.675765 0.737117i \(-0.736187\pi\)
0.0956095 + 0.995419i \(0.469520\pi\)
\(212\) −0.315656 + 0.389803i −0.0216794 + 0.0267718i
\(213\) 1.72569 6.45185i 0.118242 0.442073i
\(214\) 10.7605 + 1.13097i 0.735570 + 0.0773115i
\(215\) 2.23430 + 10.5972i 0.152378 + 0.722721i
\(216\) 1.61230 + 4.93968i 0.109703 + 0.336103i
\(217\) 5.82381 + 11.4299i 0.395346 + 0.775910i
\(218\) −7.37353 1.97573i −0.499399 0.133813i
\(219\) −19.8140 8.81119i −1.33891 0.595405i
\(220\) 1.53740 + 9.81113i 0.103652 + 0.661466i
\(221\) 2.05896 9.68663i 0.138500 0.651593i
\(222\) −16.5151 0.858140i −1.10842 0.0575946i
\(223\) −7.69934 + 6.23480i −0.515586 + 0.417513i −0.851481 0.524386i \(-0.824295\pi\)
0.335894 + 0.941900i \(0.390961\pi\)
\(224\) −1.78153 −0.119033
\(225\) −14.6647 3.15382i −0.977647 0.210255i
\(226\) 19.7217 1.31187
\(227\) 9.31843 7.54591i 0.618486 0.500840i −0.268108 0.963389i \(-0.586398\pi\)
0.886594 + 0.462549i \(0.153065\pi\)
\(228\) −2.96568 5.81406i −0.196407 0.385046i
\(229\) 5.00704 23.5563i 0.330875 1.55664i −0.427005 0.904249i \(-0.640431\pi\)
0.757880 0.652394i \(-0.226235\pi\)
\(230\) −7.26198 7.28589i −0.478841 0.480417i
\(231\) −11.0834 + 8.06008i −0.729231 + 0.530314i
\(232\) −5.53386 1.48279i −0.363316 0.0973501i
\(233\) −6.16382 12.0972i −0.403805 0.792512i 0.596141 0.802880i \(-0.296700\pi\)
−0.999946 + 0.0103674i \(0.996700\pi\)
\(234\) −4.41789 + 1.97169i −0.288807 + 0.128893i
\(235\) −9.48047 + 5.45280i −0.618438 + 0.355701i
\(236\) 3.28048 + 0.344792i 0.213541 + 0.0224440i
\(237\) −1.35179 + 0.362856i −0.0878080 + 0.0235700i
\(238\) −6.88487 + 8.50211i −0.446280 + 0.551110i
\(239\) 12.7456 5.67472i 0.824446 0.367067i 0.0492491 0.998787i \(-0.484317\pi\)
0.775197 + 0.631719i \(0.217651\pi\)
\(240\) 1.94051 3.35178i 0.125259 0.216356i
\(241\) 7.42090 + 3.30400i 0.478022 + 0.212829i 0.631580 0.775310i \(-0.282407\pi\)
−0.153558 + 0.988140i \(0.549073\pi\)
\(242\) −7.77346 + 3.96078i −0.499697 + 0.254608i
\(243\) −4.06812 15.0483i −0.260970 0.965347i
\(244\) −9.57693 3.11173i −0.613100 0.199208i
\(245\) −8.54309 0.461806i −0.545798 0.0295037i
\(246\) −3.72081 17.4668i −0.237230 1.11364i
\(247\) 5.09641 3.30965i 0.324277 0.210588i
\(248\) 2.58046 6.72233i 0.163860 0.426869i
\(249\) −6.43791 14.4425i −0.407986 0.915254i
\(250\) 5.54236 + 9.70990i 0.350530 + 0.614108i
\(251\) 27.4754i 1.73423i −0.498105 0.867117i \(-0.665971\pi\)
0.498105 0.867117i \(-0.334029\pi\)
\(252\) 5.33750 + 0.274958i 0.336231 + 0.0173207i
\(253\) 9.27573 18.2047i 0.583160 1.14452i
\(254\) −1.78127 + 1.97830i −0.111767 + 0.124129i
\(255\) −8.49668 22.2141i −0.532083 1.39110i
\(256\) 0.669131 + 0.743145i 0.0418207 + 0.0464466i
\(257\) −28.3696 + 7.60160i −1.76964 + 0.474175i −0.988634 0.150344i \(-0.951962\pi\)
−0.781010 + 0.624518i \(0.785295\pi\)
\(258\) 8.28630 + 1.30864i 0.515882 + 0.0814722i
\(259\) −6.91848 + 15.5392i −0.429893 + 0.965556i
\(260\) 3.29179 + 1.47209i 0.204148 + 0.0912951i
\(261\) 16.3507 + 5.29657i 1.01209 + 0.327850i
\(262\) −2.79565 + 17.6510i −0.172716 + 1.09048i
\(263\) 24.1460 9.26877i 1.48890 0.571537i 0.528202 0.849119i \(-0.322866\pi\)
0.960702 + 0.277582i \(0.0895330\pi\)
\(264\) 7.52502 + 1.59599i 0.463133 + 0.0982263i
\(265\) −1.12157 0.00184338i −0.0688976 0.000113238i
\(266\) −6.67641 + 0.701719i −0.409357 + 0.0430252i
\(267\) −15.3740 + 5.90938i −0.940872 + 0.361648i
\(268\) 2.88291 10.7592i 0.176102 0.657220i
\(269\) −3.61270 + 11.1188i −0.220270 + 0.677922i 0.778467 + 0.627685i \(0.215998\pi\)
−0.998737 + 0.0502368i \(0.984002\pi\)
\(270\) −6.33112 + 9.74253i −0.385300 + 0.592911i
\(271\) −1.90257 5.85550i −0.115573 0.355696i 0.876493 0.481414i \(-0.159877\pi\)
−0.992066 + 0.125718i \(0.959877\pi\)
\(272\) 6.13249 0.321390i 0.371837 0.0194871i
\(273\) 0.262643 + 4.96916i 0.0158959 + 0.300747i
\(274\) −1.83901 1.06176i −0.111099 0.0641430i
\(275\) −14.9129 + 16.4534i −0.899283 + 0.992176i
\(276\) −7.27788 + 3.24421i −0.438077 + 0.195278i
\(277\) 2.03081 + 2.50784i 0.122019 + 0.150681i 0.834495 0.551015i \(-0.185759\pi\)
−0.712476 + 0.701697i \(0.752426\pi\)
\(278\) 1.86106 + 0.948256i 0.111619 + 0.0568726i
\(279\) −8.76865 + 19.7420i −0.524965 + 1.18192i
\(280\) −2.50188 3.09996i −0.149516 0.185258i
\(281\) 2.16201 + 10.1715i 0.128975 + 0.606779i 0.994395 + 0.105731i \(0.0337184\pi\)
−0.865420 + 0.501047i \(0.832948\pi\)
\(282\) 1.32897 + 8.36668i 0.0791392 + 0.498228i
\(283\) −0.0288926 + 0.551303i −0.00171749 + 0.0327716i −0.999354 0.0359431i \(-0.988556\pi\)
0.997636 + 0.0687147i \(0.0218898\pi\)
\(284\) 0.403053 + 3.83479i 0.0239168 + 0.227553i
\(285\) 5.95199 13.3254i 0.352566 0.789329i
\(286\) −0.748638 + 7.12282i −0.0442679 + 0.421181i
\(287\) −18.1426 2.87351i −1.07093 0.169618i
\(288\) −1.89004 2.32975i −0.111372 0.137282i
\(289\) 12.1734 16.7553i 0.716084 0.985605i
\(290\) −5.19130 11.7116i −0.304843 0.687729i
\(291\) −5.39843 3.11358i −0.316462 0.182521i
\(292\) 12.5026 + 0.655233i 0.731658 + 0.0383446i
\(293\) −3.25087 12.1324i −0.189918 0.708784i −0.993524 0.113622i \(-0.963755\pi\)
0.803606 0.595162i \(-0.202912\pi\)
\(294\) −2.69279 + 6.05537i −0.157047 + 0.353156i
\(295\) 4.00696 + 6.19244i 0.233294 + 0.360538i
\(296\) 9.08053 2.95044i 0.527795 0.171491i
\(297\) −22.2988 5.94302i −1.29391 0.344849i
\(298\) −0.949902 5.99745i −0.0550264 0.347423i
\(299\) −3.70942 6.42491i −0.214521 0.371562i
\(300\) 8.55745 1.33045i 0.494064 0.0768136i
\(301\) 4.31431 7.47261i 0.248673 0.430714i
\(302\) −4.75629 1.82577i −0.273694 0.105061i
\(303\) 0.897551 17.2735i 0.0515630 0.992339i
\(304\) 2.80034 + 2.52143i 0.160610 + 0.144614i
\(305\) −8.03471 21.0344i −0.460066 1.20443i
\(306\) −18.4227 + 0.0164158i −1.05316 + 0.000938428i
\(307\) −18.6930 + 18.6930i −1.06686 + 1.06686i −0.0692654 + 0.997598i \(0.522066\pi\)
−0.997598 + 0.0692654i \(0.977934\pi\)
\(308\) 4.30926 6.63567i 0.245543 0.378103i
\(309\) 1.35436 0.000603408i 0.0770466 3.43267e-5i
\(310\) 15.3211 4.95031i 0.870182 0.281159i
\(311\) 11.0688 + 24.8609i 0.627654 + 1.40973i 0.894970 + 0.446125i \(0.147196\pi\)
−0.267316 + 0.963609i \(0.586137\pi\)
\(312\) 1.97419 1.97595i 0.111766 0.111866i
\(313\) 7.19521 + 18.7442i 0.406697 + 1.05948i 0.972079 + 0.234653i \(0.0753954\pi\)
−0.565382 + 0.824829i \(0.691271\pi\)
\(314\) 16.5175 + 12.0007i 0.932136 + 0.677236i
\(315\) 7.01725 + 9.67371i 0.395377 + 0.545052i
\(316\) 0.653753 0.474979i 0.0367765 0.0267197i
\(317\) −21.4634 13.9385i −1.20551 0.782865i −0.224055 0.974577i \(-0.571929\pi\)
−0.981451 + 0.191712i \(0.938596\pi\)
\(318\) −0.310977 + 0.811202i −0.0174387 + 0.0454900i
\(319\) 18.9086 17.0254i 1.05868 0.953238i
\(320\) −0.353427 + 2.20796i −0.0197572 + 0.123429i
\(321\) 18.3291 3.90450i 1.02303 0.217928i
\(322\) 0.428936 + 8.18458i 0.0239037 + 0.456109i
\(323\) 22.8554 3.61994i 1.27171 0.201419i
\(324\) 5.30303 + 7.27171i 0.294613 + 0.403984i
\(325\) 2.06129 + 7.79525i 0.114340 + 0.432403i
\(326\) 14.3006 8.25648i 0.792039 0.457284i
\(327\) −13.2034 + 0.697861i −0.730151 + 0.0385918i
\(328\) 5.61562 + 8.64729i 0.310070 + 0.477467i
\(329\) 8.52314 + 1.81165i 0.469896 + 0.0998795i
\(330\) 7.79061 + 15.3353i 0.428859 + 0.844181i
\(331\) −13.0882 + 2.78198i −0.719392 + 0.152911i −0.553040 0.833155i \(-0.686532\pi\)
−0.166352 + 0.986066i \(0.553199\pi\)
\(332\) 6.45538 + 6.45538i 0.354285 + 0.354285i
\(333\) −27.6609 + 7.43814i −1.51581 + 0.407607i
\(334\) 1.48222 + 2.04010i 0.0811034 + 0.111629i
\(335\) 22.7702 10.0931i 1.24407 0.551447i
\(336\) −2.93424 + 0.954839i −0.160076 + 0.0520907i
\(337\) 7.30368 + 5.91440i 0.397857 + 0.322178i 0.807282 0.590166i \(-0.200938\pi\)
−0.409426 + 0.912343i \(0.634271\pi\)
\(338\) −8.08186 6.54456i −0.439595 0.355977i
\(339\) 32.4824 10.5702i 1.76420 0.574093i
\(340\) 9.17137 + 10.2196i 0.497387 + 0.554234i
\(341\) 18.7970 + 25.8718i 1.01791 + 1.40104i
\(342\) −8.00073 7.98649i −0.432630 0.431860i
\(343\) 13.6380 + 13.6380i 0.736385 + 0.736385i
\(344\) −4.73755 + 1.00700i −0.255432 + 0.0542937i
\(345\) −15.8658 8.10797i −0.854184 0.436518i
\(346\) −16.5551 3.51891i −0.890010 0.189178i
\(347\) 1.45122 + 2.23468i 0.0779056 + 0.119964i 0.875476 0.483262i \(-0.160548\pi\)
−0.797570 + 0.603226i \(0.793882\pi\)
\(348\) −9.90921 + 0.523747i −0.531190 + 0.0280758i
\(349\) −18.0069 + 10.3963i −0.963885 + 0.556499i −0.897367 0.441286i \(-0.854522\pi\)
−0.0665185 + 0.997785i \(0.521189\pi\)
\(350\) 1.88063 8.70684i 0.100524 0.465400i
\(351\) −6.21968 + 5.61530i −0.331982 + 0.299722i
\(352\) −4.38653 + 0.694759i −0.233803 + 0.0370308i
\(353\) −0.120441 2.29815i −0.00641043 0.122318i −0.999960 0.00892146i \(-0.997160\pi\)
0.993550 0.113397i \(-0.0361732\pi\)
\(354\) 5.58787 1.19034i 0.296992 0.0632659i
\(355\) −6.10675 + 6.08671i −0.324113 + 0.323049i
\(356\) 7.06678 6.36296i 0.374539 0.337236i
\(357\) −6.78281 + 17.6934i −0.358984 + 0.936433i
\(358\) −0.507501 0.329575i −0.0268223 0.0174186i
\(359\) 10.0128 7.27470i 0.528453 0.383944i −0.291326 0.956624i \(-0.594096\pi\)
0.819779 + 0.572680i \(0.194096\pi\)
\(360\) 1.39965 6.56056i 0.0737681 0.345772i
\(361\) −3.88367 2.82165i −0.204404 0.148508i
\(362\) 2.08852 + 5.44078i 0.109770 + 0.285961i
\(363\) −10.6804 + 10.6899i −0.560573 + 0.561073i
\(364\) −1.16853 2.62457i −0.0612478 0.137565i
\(365\) 16.4178 + 22.6754i 0.859347 + 1.18689i
\(366\) −17.4414 + 0.00777068i −0.911675 + 0.000406180i
\(367\) 8.20418 12.6333i 0.428255 0.659454i −0.557007 0.830508i \(-0.688050\pi\)
0.985262 + 0.171053i \(0.0547170\pi\)
\(368\) 3.25301 3.25301i 0.169575 0.169575i
\(369\) −15.4899 26.7742i −0.806374 1.39381i
\(370\) 17.8862 + 11.6572i 0.929857 + 0.606031i
\(371\) 0.664061 + 0.597924i 0.0344763 + 0.0310426i
\(372\) 0.647174 12.4550i 0.0335544 0.645761i
\(373\) −5.89789 2.26399i −0.305381 0.117225i 0.200852 0.979622i \(-0.435629\pi\)
−0.506233 + 0.862397i \(0.668962\pi\)
\(374\) −13.6365 + 23.6191i −0.705128 + 1.22132i
\(375\) 14.3327 + 13.0221i 0.740136 + 0.672457i
\(376\) −2.44553 4.23578i −0.126119 0.218444i
\(377\) −1.44528 9.12516i −0.0744358 0.469969i
\(378\) 8.93844 2.40786i 0.459744 0.123847i
\(379\) 25.8903 8.41226i 1.32989 0.432109i 0.444012 0.896021i \(-0.353555\pi\)
0.885881 + 0.463912i \(0.153555\pi\)
\(380\) −0.454812 + 8.41372i −0.0233314 + 0.431615i
\(381\) −1.87351 + 4.21303i −0.0959830 + 0.215840i
\(382\) −1.83866 6.86196i −0.0940739 0.351089i
\(383\) −12.3573 0.647621i −0.631431 0.0330919i −0.266064 0.963955i \(-0.585723\pi\)
−0.365367 + 0.930864i \(0.619057\pi\)
\(384\) 1.50039 + 0.865357i 0.0765662 + 0.0441601i
\(385\) 17.5982 1.82040i 0.896885 0.0927763i
\(386\) 10.5960 14.5842i 0.539323 0.742315i
\(387\) 14.3492 2.28581i 0.729413 0.116194i
\(388\) 3.55373 + 0.562856i 0.180413 + 0.0285747i
\(389\) 2.02983 19.3126i 0.102917 0.979187i −0.814205 0.580578i \(-0.802827\pi\)
0.917121 0.398609i \(-0.130507\pi\)
\(390\) 6.21071 + 0.660295i 0.314491 + 0.0334354i
\(391\) −2.95302 28.0961i −0.149341 1.42088i
\(392\) 0.200246 3.82092i 0.0101140 0.192986i
\(393\) 4.85582 + 30.5703i 0.244944 + 1.54207i
\(394\) −4.25530 20.0196i −0.214379 1.00857i
\(395\) 1.74459 + 0.470535i 0.0877797 + 0.0236752i
\(396\) 13.2494 1.40451i 0.665807 0.0705791i
\(397\) 0.471353 + 0.240166i 0.0236565 + 0.0120536i 0.465779 0.884901i \(-0.345774\pi\)
−0.442122 + 0.896955i \(0.645774\pi\)
\(398\) −7.88045 9.73154i −0.395011 0.487798i
\(399\) −10.6202 + 4.73410i −0.531676 + 0.237001i
\(400\) −4.33832 + 2.48575i −0.216916 + 0.124288i
\(401\) 22.3782 + 12.9200i 1.11751 + 0.645196i 0.940765 0.339060i \(-0.110109\pi\)
0.176748 + 0.984256i \(0.443442\pi\)
\(402\) −1.01829 19.2659i −0.0507877 0.960896i
\(403\) 11.5960 0.607722i 0.577639 0.0302728i
\(404\) 3.08595 + 9.49757i 0.153532 + 0.472522i
\(405\) −5.20594 + 19.4396i −0.258685 + 0.965962i
\(406\) −3.15398 + 9.70695i −0.156529 + 0.481748i
\(407\) −10.9750 + 40.9591i −0.544008 + 2.03027i
\(408\) 9.92819 3.81615i 0.491519 0.188928i
\(409\) 22.0052 2.31284i 1.08809 0.114362i 0.456541 0.889702i \(-0.349088\pi\)
0.631544 + 0.775340i \(0.282421\pi\)
\(410\) −7.16055 + 21.9153i −0.353635 + 1.08232i
\(411\) −3.59800 0.763102i −0.177476 0.0376411i
\(412\) −0.730002 + 0.280222i −0.0359646 + 0.0138055i
\(413\) 0.919279 5.80410i 0.0452347 0.285601i
\(414\) −10.2482 + 9.24404i −0.503670 + 0.454320i
\(415\) −2.16718 + 20.2983i −0.106382 + 0.996406i
\(416\) −0.655918 + 1.47322i −0.0321590 + 0.0722303i
\(417\) 3.57347 + 0.564350i 0.174993 + 0.0276363i
\(418\) −16.1652 + 4.33146i −0.790668 + 0.211859i
\(419\) −6.93008 7.69663i −0.338557 0.376005i 0.549693 0.835367i \(-0.314745\pi\)
−0.888249 + 0.459362i \(0.848078\pi\)
\(420\) −5.78217 3.76484i −0.282141 0.183705i
\(421\) −21.4538 + 23.8269i −1.04560 + 1.16125i −0.0589679 + 0.998260i \(0.518781\pi\)
−0.986627 + 0.162991i \(0.947886\pi\)
\(422\) 4.18796 8.21933i 0.203867 0.400111i
\(423\) 6.67313 + 13.0680i 0.324459 + 0.635386i
\(424\) 0.501583i 0.0243590i
\(425\) −4.90290 + 30.3105i −0.237826 + 1.47028i
\(426\) 2.71917 + 6.10004i 0.131744 + 0.295548i
\(427\) −6.42897 + 16.7480i −0.311120 + 0.810494i
\(428\) −9.07419 + 5.89285i −0.438618 + 0.284842i
\(429\) 2.58456 + 12.1328i 0.124784 + 0.585778i
\(430\) −8.40539 6.82946i −0.405344 0.329346i
\(431\) −6.30829 2.04969i −0.303860 0.0987300i 0.153119 0.988208i \(-0.451068\pi\)
−0.456978 + 0.889478i \(0.651068\pi\)
\(432\) −4.36164 2.82420i −0.209849 0.135879i
\(433\) 14.4935 7.38481i 0.696513 0.354891i −0.0696196 0.997574i \(-0.522179\pi\)
0.766133 + 0.642682i \(0.222179\pi\)
\(434\) −11.7190 5.21764i −0.562530 0.250455i
\(435\) −14.8273 16.5071i −0.710915 0.791456i
\(436\) 6.97368 3.10488i 0.333979 0.148697i
\(437\) 10.9096 13.4722i 0.521877 0.644464i
\(438\) 20.9434 5.62178i 1.00072 0.268619i
\(439\) −7.06808 0.742885i −0.337341 0.0354560i −0.0656563 0.997842i \(-0.520914\pi\)
−0.271685 + 0.962386i \(0.587581\pi\)
\(440\) −7.36913 6.65716i −0.351309 0.317368i
\(441\) −1.18966 + 11.4167i −0.0566503 + 0.543652i
\(442\) 4.49588 + 8.82367i 0.213847 + 0.419699i
\(443\) 6.51485 + 1.74565i 0.309530 + 0.0829383i 0.410240 0.911978i \(-0.365445\pi\)
−0.100710 + 0.994916i \(0.532112\pi\)
\(444\) 13.3747 9.72636i 0.634733 0.461593i
\(445\) 20.9961 + 3.36085i 0.995313 + 0.159319i
\(446\) 2.05982 9.69071i 0.0975355 0.458868i
\(447\) −4.77896 9.36892i −0.226037 0.443135i
\(448\) 1.38451 1.12115i 0.0654117 0.0529694i
\(449\) −6.11578 −0.288622 −0.144311 0.989532i \(-0.546097\pi\)
−0.144311 + 0.989532i \(0.546097\pi\)
\(450\) 13.3814 6.77781i 0.630804 0.319509i
\(451\) −45.7920 −2.15626
\(452\) −15.3266 + 12.4113i −0.720904 + 0.583776i
\(453\) −8.81234 0.457898i −0.414040 0.0215139i
\(454\) −2.49298 + 11.7286i −0.117001 + 0.550448i
\(455\) 2.92589 5.71913i 0.137168 0.268117i
\(456\) 5.96367 + 2.65201i 0.279275 + 0.124192i
\(457\) −9.98351 2.67507i −0.467009 0.125135i 0.0176383 0.999844i \(-0.494385\pi\)
−0.484647 + 0.874710i \(0.661052\pi\)
\(458\) 10.9332 + 21.4577i 0.510877 + 1.00265i
\(459\) −30.3341 + 9.90100i −1.41588 + 0.462139i
\(460\) 10.2288 + 1.09209i 0.476919 + 0.0509189i
\(461\) −29.9945 3.15255i −1.39698 0.146829i −0.624083 0.781358i \(-0.714527\pi\)
−0.772899 + 0.634529i \(0.781194\pi\)
\(462\) 3.54101 13.2388i 0.164743 0.615926i
\(463\) −13.3879 + 16.5327i −0.622188 + 0.768338i −0.986646 0.162882i \(-0.947921\pi\)
0.364458 + 0.931220i \(0.381254\pi\)
\(464\) 5.23377 2.33022i 0.242972 0.108178i
\(465\) 22.5813 16.3650i 1.04718 0.758908i
\(466\) 12.4032 + 5.52225i 0.574566 + 0.255813i
\(467\) −22.6390 + 11.5352i −1.04761 + 0.533784i −0.891060 0.453886i \(-0.850037\pi\)
−0.156550 + 0.987670i \(0.550037\pi\)
\(468\) 2.19252 4.31256i 0.101349 0.199348i
\(469\) −18.8727 6.13210i −0.871458 0.283154i
\(470\) 3.93615 10.2039i 0.181561 0.470670i
\(471\) 33.6369 + 10.9127i 1.54991 + 0.502832i
\(472\) −2.76639 + 1.79652i −0.127334 + 0.0826914i
\(473\) 7.70868 20.0818i 0.354446 0.923362i
\(474\) 0.822183 1.13270i 0.0377641 0.0520266i
\(475\) −15.2791 + 11.0244i −0.701054 + 0.505833i
\(476\) 10.9402i 0.501442i
\(477\) −0.0774134 + 1.50276i −0.00354452 + 0.0688065i
\(478\) −6.33400 + 12.4312i −0.289710 + 0.568588i
\(479\) 26.1685 29.0631i 1.19567 1.32792i 0.264041 0.964512i \(-0.414945\pi\)
0.931628 0.363413i \(-0.118389\pi\)
\(480\) 0.601285 + 3.82602i 0.0274448 + 0.174633i
\(481\) 10.3027 + 11.4423i 0.469764 + 0.521725i
\(482\) −7.84639 + 2.10244i −0.357393 + 0.0957633i
\(483\) 5.09314 + 13.2504i 0.231746 + 0.602916i
\(484\) 3.54852 7.97010i 0.161296 0.362277i
\(485\) 4.01126 + 6.97416i 0.182142 + 0.316680i
\(486\) 12.6317 + 9.13455i 0.572986 + 0.414352i
\(487\) 0.135676 0.856626i 0.00614808 0.0388174i −0.984424 0.175813i \(-0.943745\pi\)
0.990572 + 0.136996i \(0.0437446\pi\)
\(488\) 9.40095 3.60869i 0.425561 0.163358i
\(489\) 19.1285 21.2634i 0.865022 0.961565i
\(490\) 6.92986 5.01745i 0.313059 0.226665i
\(491\) −22.3097 + 2.34485i −1.00682 + 0.105821i −0.593560 0.804790i \(-0.702278\pi\)
−0.413264 + 0.910611i \(0.635611\pi\)
\(492\) 13.8838 + 11.2326i 0.625930 + 0.506407i
\(493\) 9.10569 33.9829i 0.410099 1.53051i
\(494\) −1.87783 + 5.77935i −0.0844874 + 0.260025i
\(495\) 21.0507 + 21.0824i 0.946157 + 0.947582i
\(496\) 2.22511 + 6.84817i 0.0999102 + 0.307492i
\(497\) 6.86000 0.359518i 0.307713 0.0161266i
\(498\) 14.0921 + 7.17239i 0.631483 + 0.321403i
\(499\) 4.53023 + 2.61553i 0.202801 + 0.117087i 0.597961 0.801525i \(-0.295978\pi\)
−0.395160 + 0.918612i \(0.629311\pi\)
\(500\) −10.4179 4.05809i −0.465901 0.181483i
\(501\) 3.53470 + 2.56570i 0.157919 + 0.114627i
\(502\) 17.2908 + 21.3524i 0.771728 + 0.953005i
\(503\) −28.2480 14.3931i −1.25951 0.641755i −0.308595 0.951193i \(-0.599859\pi\)
−0.950919 + 0.309439i \(0.899859\pi\)
\(504\) −4.32105 + 3.14532i −0.192475 + 0.140103i
\(505\) −12.1926 + 18.7076i −0.542565 + 0.832478i
\(506\) 4.24796 + 19.9851i 0.188845 + 0.888445i
\(507\) −16.8188 6.44754i −0.746949 0.286345i
\(508\) 0.139321 2.65841i 0.00618139 0.117948i
\(509\) −0.919620 8.74960i −0.0407615 0.387819i −0.995815 0.0913873i \(-0.970870\pi\)
0.955054 0.296432i \(-0.0957968\pi\)
\(510\) 20.5829 + 11.9165i 0.911428 + 0.527670i
\(511\) 2.33143 22.1821i 0.103136 0.981276i
\(512\) −0.987688 0.156434i −0.0436501 0.00691349i
\(513\) −17.4580 8.86593i −0.770790 0.391440i
\(514\) 17.2634 23.7611i 0.761458 1.04806i
\(515\) −1.51278 0.876721i −0.0666609 0.0386329i
\(516\) −7.26322 + 4.19774i −0.319745 + 0.184795i
\(517\) 21.6925 + 1.13685i 0.954034 + 0.0499988i
\(518\) −4.40244 16.4301i −0.193432 0.721898i
\(519\) −29.1530 + 3.07724i −1.27967 + 0.135076i
\(520\) −3.48462 + 0.927566i −0.152811 + 0.0406764i
\(521\) 5.72149 1.85902i 0.250663 0.0814454i −0.180990 0.983485i \(-0.557930\pi\)
0.431654 + 0.902039i \(0.357930\pi\)
\(522\) −16.0402 + 6.17364i −0.702058 + 0.270213i
\(523\) −4.01761 25.3662i −0.175678 1.10919i −0.905124 0.425148i \(-0.860222\pi\)
0.729446 0.684038i \(-0.239778\pi\)
\(524\) −8.93552 15.4768i −0.390350 0.676106i
\(525\) −1.56911 15.3485i −0.0684814 0.669862i
\(526\) −12.9319 + 22.3987i −0.563858 + 0.976631i
\(527\) 41.2812 + 15.8464i 1.79824 + 0.690278i
\(528\) −6.85243 + 3.49533i −0.298214 + 0.152115i
\(529\) 1.36433 + 1.22844i 0.0593185 + 0.0534106i
\(530\) 0.872785 0.704395i 0.0379114 0.0305970i
\(531\) 8.56546 4.95545i 0.371709 0.215048i
\(532\) 4.74694 4.74694i 0.205806 0.205806i
\(533\) −9.05594 + 13.9449i −0.392256 + 0.604022i
\(534\) 8.22893 14.2676i 0.356101 0.617420i
\(535\) −22.9972 7.51406i −0.994257 0.324861i
\(536\) 4.53052 + 10.1757i 0.195689 + 0.439524i
\(537\) −1.01252 0.270819i −0.0436933 0.0116867i
\(538\) −4.18966 10.9144i −0.180629 0.470555i
\(539\) 13.7475 + 9.98812i 0.592146 + 0.430219i
\(540\) −1.21096 11.5557i −0.0521116 0.497277i
\(541\) 32.4543 23.5795i 1.39532 1.01376i 0.400063 0.916487i \(-0.368988\pi\)
0.995258 0.0972727i \(-0.0310119\pi\)
\(542\) 5.16356 + 3.35325i 0.221794 + 0.144035i
\(543\) 6.35595 + 7.84180i 0.272760 + 0.336524i
\(544\) −4.56358 + 4.10907i −0.195662 + 0.176175i
\(545\) 15.1961 + 7.77431i 0.650931 + 0.333015i
\(546\) −3.33131 3.69648i −0.142567 0.158195i
\(547\) −0.680011 12.9754i −0.0290752 0.554787i −0.973867 0.227117i \(-0.927070\pi\)
0.944792 0.327670i \(-0.106263\pi\)
\(548\) 2.09737 0.332190i 0.0895951 0.0141905i
\(549\) −28.7225 + 9.36080i −1.22585 + 0.399509i
\(550\) 1.23506 22.1717i 0.0526633 0.945404i
\(551\) 18.6961 10.7942i 0.796482 0.459849i
\(552\) 3.61433 7.10134i 0.153836 0.302253i
\(553\) −0.784073 1.20737i −0.0333422 0.0513425i
\(554\) −3.15647 0.670928i −0.134105 0.0285050i
\(555\) 35.7071 + 9.61355i 1.51568 + 0.408073i
\(556\) −2.04307 + 0.434268i −0.0866455 + 0.0184171i
\(557\) −17.6792 17.6792i −0.749090 0.749090i 0.225218 0.974308i \(-0.427690\pi\)
−0.974308 + 0.225218i \(0.927690\pi\)
\(558\) −5.60954 20.8607i −0.237471 0.883105i
\(559\) −4.59097 6.31892i −0.194177 0.267262i
\(560\) 3.89519 + 0.834643i 0.164602 + 0.0352701i
\(561\) −9.80081 + 46.2104i −0.413790 + 1.95100i
\(562\) −8.08131 6.54411i −0.340889 0.276047i
\(563\) −28.7851 23.3097i −1.21315 0.982387i −0.999986 0.00536975i \(-0.998291\pi\)
−0.213161 0.977017i \(-0.568376\pi\)
\(564\) −6.29813 5.66578i −0.265199 0.238572i
\(565\) −43.1202 9.23959i −1.81408 0.388712i
\(566\) −0.324493 0.446626i −0.0136394 0.0187731i
\(567\) 13.4314 8.75655i 0.564067 0.367740i
\(568\) −2.72655 2.72655i −0.114403 0.114403i
\(569\) −15.8854 + 3.37656i −0.665953 + 0.141553i −0.528471 0.848952i \(-0.677234\pi\)
−0.137482 + 0.990504i \(0.543901\pi\)
\(570\) 3.76038 + 14.1015i 0.157505 + 0.590647i
\(571\) −4.15317 0.882783i −0.173805 0.0369433i 0.120187 0.992751i \(-0.461651\pi\)
−0.293992 + 0.955808i \(0.594984\pi\)
\(572\) −3.90073 6.00660i −0.163098 0.251149i
\(573\) −6.70613 10.3165i −0.280152 0.430976i
\(574\) 15.9078 9.18440i 0.663981 0.383349i
\(575\) 12.4644 + 19.3324i 0.519803 + 0.806216i
\(576\) 2.93500 + 0.621120i 0.122292 + 0.0258800i
\(577\) 18.6359 2.95163i 0.775822 0.122878i 0.244047 0.969763i \(-0.421525\pi\)
0.531776 + 0.846885i \(0.321525\pi\)
\(578\) 1.08391 + 20.6823i 0.0450848 + 0.860270i
\(579\) 9.63543 29.6998i 0.400435 1.23428i
\(580\) 11.4047 + 5.83464i 0.473556 + 0.242270i
\(581\) 12.0865 10.8828i 0.501434 0.451493i
\(582\) 6.15481 0.977637i 0.255125 0.0405244i
\(583\) 1.86825 + 1.21326i 0.0773751 + 0.0502480i
\(584\) −10.1287 + 7.35892i −0.419128 + 0.304514i
\(585\) 10.5832 2.24120i 0.437561 0.0926623i
\(586\) 10.1616 + 7.38283i 0.419771 + 0.304982i
\(587\) −2.35761 6.14179i −0.0973091 0.253499i 0.876282 0.481799i \(-0.160017\pi\)
−0.973591 + 0.228300i \(0.926683\pi\)
\(588\) −1.71808 6.40054i −0.0708522 0.263954i
\(589\) 11.0362 + 24.7876i 0.454738 + 1.02136i
\(590\) −7.01102 2.29077i −0.288639 0.0943093i
\(591\) −17.7385 30.6924i −0.729664 1.26252i
\(592\) −5.20012 + 8.00749i −0.213724 + 0.329106i
\(593\) −26.8990 + 26.8990i −1.10461 + 1.10461i −0.110763 + 0.993847i \(0.535330\pi\)
−0.993847 + 0.110763i \(0.964670\pi\)
\(594\) 21.0695 9.41452i 0.864493 0.386282i
\(595\) 19.0366 15.3638i 0.780424 0.629854i
\(596\) 4.51253 + 4.06310i 0.184840 + 0.166431i
\(597\) −18.1952 11.8046i −0.744680 0.483129i
\(598\) 6.92609 + 2.65868i 0.283229 + 0.108721i
\(599\) 2.90008 5.02308i 0.118494 0.205237i −0.800677 0.599096i \(-0.795527\pi\)
0.919171 + 0.393859i \(0.128860\pi\)
\(600\) −5.81311 + 6.41933i −0.237319 + 0.262068i
\(601\) −14.9330 25.8647i −0.609129 1.05504i −0.991384 0.130985i \(-0.958186\pi\)
0.382256 0.924057i \(-0.375147\pi\)
\(602\) 1.34981 + 8.52239i 0.0550143 + 0.347347i
\(603\) −12.0031 31.1859i −0.488802 1.26999i
\(604\) 4.84532 1.57434i 0.197153 0.0640590i
\(605\) 18.8518 5.01813i 0.766435 0.204016i
\(606\) 10.1731 + 13.9889i 0.413253 + 0.568261i
\(607\) 0.434832 + 1.62282i 0.0176493 + 0.0658681i 0.974189 0.225735i \(-0.0724782\pi\)
−0.956540 + 0.291603i \(0.905812\pi\)
\(608\) −3.76306 0.197214i −0.152612 0.00799807i
\(609\) 0.00787617 + 17.6782i 0.000319159 + 0.716355i
\(610\) 19.4815 + 11.2904i 0.788784 + 0.457135i
\(611\) 4.63615 6.38112i 0.187559 0.258152i
\(612\) 14.3068 11.6065i 0.578318 0.469166i
\(613\) −25.2998 4.00710i −1.02185 0.161845i −0.377048 0.926194i \(-0.623061\pi\)
−0.644803 + 0.764349i \(0.723061\pi\)
\(614\) 2.76330 26.2910i 0.111518 1.06102i
\(615\) −0.0478413 + 39.9332i −0.00192915 + 1.61026i
\(616\) 0.827043 + 7.86879i 0.0333225 + 0.317043i
\(617\) −1.68692 + 32.1883i −0.0679128 + 1.29585i 0.725947 + 0.687751i \(0.241402\pi\)
−0.793859 + 0.608102i \(0.791931\pi\)
\(618\) −1.05215 + 0.852793i −0.0423238 + 0.0343044i
\(619\) −9.59072 45.1208i −0.385484 1.81356i −0.559518 0.828818i \(-0.689014\pi\)
0.174034 0.984740i \(-0.444320\pi\)
\(620\) −8.79143 + 13.4890i −0.353072 + 0.541732i
\(621\) −11.9246 + 20.7180i −0.478519 + 0.831384i
\(622\) −24.2476 12.3548i −0.972239 0.495380i
\(623\) −10.6614 13.1657i −0.427138 0.527471i
\(624\) −0.290728 + 2.77799i −0.0116384 + 0.111209i
\(625\) −7.56895 23.8267i −0.302758 0.953068i
\(626\) −17.3878 10.0389i −0.694957 0.401233i
\(627\) −24.3033 + 15.7981i −0.970579 + 0.630916i
\(628\) −20.3888 + 1.06853i −0.813600 + 0.0426390i
\(629\) 18.1184 + 55.7627i 0.722427 + 2.22340i
\(630\) −11.5413 3.10179i −0.459816 0.123578i
\(631\) −2.12428 + 6.53788i −0.0845664 + 0.260269i −0.984394 0.175976i \(-0.943692\pi\)
0.899828 + 0.436245i \(0.143692\pi\)
\(632\) −0.209147 + 0.780548i −0.00831943 + 0.0310485i
\(633\) 2.49244 15.7822i 0.0990657 0.627285i
\(634\) 25.4520 2.67511i 1.01083 0.106242i
\(635\) 4.82146 3.49090i 0.191334 0.138532i
\(636\) −0.268832 0.826127i −0.0106599 0.0327581i
\(637\) 5.76039 2.21121i 0.228235 0.0876111i
\(638\) −3.98032 + 25.1308i −0.157582 + 0.994936i
\(639\) 7.74800 + 8.58962i 0.306506 + 0.339800i
\(640\) −1.11485 1.93833i −0.0440683 0.0766191i
\(641\) −18.6920 + 41.9830i −0.738291 + 1.65823i 0.0144360 + 0.999896i \(0.495405\pi\)
−0.752727 + 0.658333i \(0.771262\pi\)
\(642\) −11.7872 + 14.5692i −0.465203 + 0.575001i
\(643\) −30.5588 + 8.18821i −1.20512 + 0.322911i −0.804846 0.593484i \(-0.797752\pi\)
−0.400275 + 0.916395i \(0.631085\pi\)
\(644\) −5.48407 6.09068i −0.216103 0.240006i
\(645\) −17.5044 6.74337i −0.689234 0.265520i
\(646\) −15.4839 + 17.1966i −0.609205 + 0.676591i
\(647\) 20.9851 41.1857i 0.825011 1.61918i 0.0404024 0.999183i \(-0.487136\pi\)
0.784608 0.619992i \(-0.212864\pi\)
\(648\) −8.69747 2.31388i −0.341669 0.0908976i
\(649\) 14.6495i 0.575045i
\(650\) −6.50763 4.76083i −0.255250 0.186735i
\(651\) −22.0981 2.31265i −0.866094 0.0906401i
\(652\) −5.91772 + 15.4162i −0.231756 + 0.603744i
\(653\) 5.81646 3.77725i 0.227616 0.147815i −0.425793 0.904820i \(-0.640005\pi\)
0.653409 + 0.757005i \(0.273338\pi\)
\(654\) 9.82181 8.85153i 0.384063 0.346122i
\(655\) 14.3820 37.2831i 0.561951 1.45677i
\(656\) −9.80607 3.18618i −0.382863 0.124400i
\(657\) 31.4816 20.4843i 1.22821 0.799168i
\(658\) −7.76383 + 3.95587i −0.302666 + 0.154216i
\(659\) −1.76342 0.785125i −0.0686931 0.0305841i 0.372103 0.928192i \(-0.378637\pi\)
−0.440796 + 0.897607i \(0.645304\pi\)
\(660\) −15.7053 7.01499i −0.611327 0.273058i
\(661\) 2.23309 0.994234i 0.0868570 0.0386712i −0.362848 0.931848i \(-0.618196\pi\)
0.449705 + 0.893177i \(0.351529\pi\)
\(662\) 8.42067 10.3987i 0.327279 0.404156i
\(663\) 12.1341 + 12.1233i 0.471249 + 0.470829i
\(664\) −9.07927 0.954270i −0.352344 0.0370328i
\(665\) 14.9263 + 1.59363i 0.578818 + 0.0617982i
\(666\) 16.8156 23.1881i 0.651590 0.898520i
\(667\) −11.9655 23.4836i −0.463306 0.909290i
\(668\) −2.43578 0.652664i −0.0942430 0.0252523i
\(669\) −1.80129 17.0650i −0.0696418 0.659770i
\(670\) −11.3440 + 22.1736i −0.438255 + 0.856640i
\(671\) −9.29824 + 43.7448i −0.358954 + 1.68875i
\(672\) 1.67944 2.58863i 0.0647856 0.0998585i
\(673\) 8.70175 7.04654i 0.335428 0.271624i −0.446777 0.894645i \(-0.647428\pi\)
0.782205 + 0.623021i \(0.214095\pi\)
\(674\) −9.39808 −0.362000
\(675\) 18.4070 18.3353i 0.708485 0.705726i
\(676\) 10.3994 0.399977
\(677\) 8.16567 6.61243i 0.313832 0.254136i −0.459442 0.888208i \(-0.651951\pi\)
0.773275 + 0.634071i \(0.218617\pi\)
\(678\) −18.5915 + 28.6564i −0.714004 + 1.10054i
\(679\) 1.33271 6.26991i 0.0511447 0.240617i
\(680\) −13.5589 2.17036i −0.519959 0.0832296i
\(681\) 2.18008 + 20.6535i 0.0835408 + 0.791446i
\(682\) −30.8897 8.27687i −1.18283 0.316938i
\(683\) −10.1617 19.9435i −0.388827 0.763115i 0.610762 0.791815i \(-0.290863\pi\)
−0.999588 + 0.0286996i \(0.990863\pi\)
\(684\) 11.2438 + 1.17164i 0.429917 + 0.0447988i
\(685\) 3.52346 + 3.18304i 0.134624 + 0.121618i
\(686\) −19.1814 2.01605i −0.732351 0.0769732i
\(687\) 29.5081 + 29.4818i 1.12580 + 1.12480i
\(688\) 3.04804 3.76402i 0.116206 0.143502i
\(689\) 0.738940 0.328997i 0.0281514 0.0125338i
\(690\) 17.4325 3.68358i 0.663645 0.140231i
\(691\) −45.5290 20.2708i −1.73201 0.771139i −0.995506 0.0947009i \(-0.969811\pi\)
−0.736500 0.676438i \(-0.763523\pi\)
\(692\) 15.0803 7.68379i 0.573266 0.292094i
\(693\) −1.26339 23.7028i −0.0479922 0.900393i
\(694\) −2.53414 0.823392i −0.0961947 0.0312555i
\(695\) −3.62483 2.94521i −0.137498 0.111718i
\(696\) 7.37130 6.64310i 0.279408 0.251806i
\(697\) −53.1022 + 34.4849i −2.01139 + 1.30621i
\(698\) 7.45138 19.4115i 0.282039 0.734736i
\(699\) 23.3883 + 2.44767i 0.884626 + 0.0925795i
\(700\) 4.01787 + 7.95001i 0.151861 + 0.300482i
\(701\) 15.7690i 0.595586i 0.954631 + 0.297793i \(0.0962505\pi\)
−0.954631 + 0.297793i \(0.903750\pi\)
\(702\) 1.29978 8.27808i 0.0490570 0.312436i
\(703\) −16.3339 + 32.0570i −0.616043 + 1.20905i
\(704\) 2.97175 3.30046i 0.112002 0.124391i
\(705\) 1.01406 18.9158i 0.0381918 0.712412i
\(706\) 1.53988 + 1.71020i 0.0579540 + 0.0643644i
\(707\) 17.1847 4.60463i 0.646298 0.173175i
\(708\) −3.59349 + 4.44163i −0.135051 + 0.166927i
\(709\) −20.1326 + 45.2185i −0.756095 + 1.69822i −0.0410309 + 0.999158i \(0.513064\pi\)
−0.715064 + 0.699059i \(0.753602\pi\)
\(710\) 0.915346 8.57337i 0.0343523 0.321753i
\(711\) 0.747079 2.30626i 0.0280177 0.0864916i
\(712\) −1.48758 + 9.39222i −0.0557495 + 0.351988i
\(713\) 30.9257 11.8713i 1.15818 0.444583i
\(714\) −5.86357 18.0189i −0.219439 0.674340i
\(715\) 4.97388 15.2229i 0.186013 0.569303i
\(716\) 0.601811 0.0632529i 0.0224907 0.00236387i
\(717\) −3.76965 + 23.8694i −0.140780 + 0.891421i
\(718\) −3.20326 + 11.9547i −0.119545 + 0.446147i
\(719\) 9.20118 28.3183i 0.343146 1.05610i −0.619422 0.785058i \(-0.712633\pi\)
0.962569 0.271038i \(-0.0873668\pi\)
\(720\) 3.04096 + 5.97934i 0.113330 + 0.222837i
\(721\) 0.430474 + 1.32486i 0.0160317 + 0.0493405i
\(722\) 4.79390 0.251238i 0.178411 0.00935010i
\(723\) −11.7965 + 7.66820i −0.438716 + 0.285184i
\(724\) −5.04707 2.91393i −0.187573 0.108295i
\(725\) 5.86357 + 28.0388i 0.217768 + 1.04134i
\(726\) 1.57284 15.0290i 0.0583735 0.557777i
\(727\) 8.55823 + 10.5685i 0.317407 + 0.391965i 0.910732 0.412998i \(-0.135518\pi\)
−0.593325 + 0.804963i \(0.702185\pi\)
\(728\) 2.55982 + 1.30429i 0.0948732 + 0.0483403i
\(729\) 25.7007 + 8.27479i 0.951879 + 0.306474i
\(730\) −27.0291 7.29007i −1.00039 0.269818i
\(731\) −6.18387 29.0928i −0.228719 1.07604i
\(732\) 13.5496 10.9823i 0.500808 0.405916i
\(733\) −0.380822 + 7.26652i −0.0140660 + 0.268395i 0.982539 + 0.186059i \(0.0595715\pi\)
−0.996605 + 0.0823362i \(0.973762\pi\)
\(734\) 1.57457 + 14.9810i 0.0581183 + 0.552959i
\(735\) 8.72456 11.9781i 0.321810 0.441820i
\(736\) −0.480878 + 4.57525i −0.0177254 + 0.168646i
\(737\) −48.8603 7.73871i −1.79979 0.285059i
\(738\) 28.8875 + 11.0593i 1.06336 + 0.407100i
\(739\) 3.81435 5.25000i 0.140313 0.193124i −0.733077 0.680146i \(-0.761917\pi\)
0.873390 + 0.487021i \(0.161917\pi\)
\(740\) −21.2363 + 2.19674i −0.780662 + 0.0807538i
\(741\) 0.00468934 + 10.5253i 0.000172267 + 0.386656i
\(742\) −0.892358 0.0467665i −0.0327595 0.00171685i
\(743\) −0.0768573 0.286835i −0.00281962 0.0105230i 0.964502 0.264077i \(-0.0850672\pi\)
−0.967321 + 0.253554i \(0.918401\pi\)
\(744\) 7.33523 + 10.0866i 0.268923 + 0.369794i
\(745\) −0.732895 + 13.5581i −0.0268512 + 0.496729i
\(746\) 6.00830 1.95221i 0.219979 0.0714757i
\(747\) 27.0545 + 4.26030i 0.989871 + 0.155876i
\(748\) −4.26644 26.9373i −0.155997 0.984924i
\(749\) 9.63782 + 16.6932i 0.352158 + 0.609956i
\(750\) −19.3336 1.10021i −0.705965 0.0401739i
\(751\) −15.8560 + 27.4635i −0.578595 + 1.00216i 0.417046 + 0.908886i \(0.363065\pi\)
−0.995641 + 0.0932706i \(0.970268\pi\)
\(752\) 4.56620 + 1.75280i 0.166512 + 0.0639180i
\(753\) 39.9229 + 25.9009i 1.45487 + 0.943883i
\(754\) 6.86584 + 6.18203i 0.250039 + 0.225136i
\(755\) 9.54395 + 6.22024i 0.347340 + 0.226378i
\(756\) −5.43116 + 7.49640i −0.197529 + 0.272641i
\(757\) 19.2640 19.2640i 0.700162 0.700162i −0.264283 0.964445i \(-0.585135\pi\)
0.964445 + 0.264283i \(0.0851352\pi\)
\(758\) −14.8265 + 22.8308i −0.538523 + 0.829253i
\(759\) 17.7079 + 30.6395i 0.642756 + 1.11214i
\(760\) −4.94147 6.82491i −0.179246 0.247566i
\(761\) −12.8807 28.9305i −0.466925 1.04873i −0.981531 0.191304i \(-0.938728\pi\)
0.514605 0.857427i \(-0.327938\pi\)
\(762\) −1.19535 4.45318i −0.0433031 0.161322i
\(763\) −4.87364 12.6963i −0.176438 0.459635i
\(764\) 5.74728 + 4.17564i 0.207929 + 0.151069i
\(765\) 40.2878 + 8.59512i 1.45661 + 0.310757i
\(766\) 10.0110 7.27343i 0.361713 0.262800i
\(767\) −4.46118 2.89713i −0.161084 0.104609i
\(768\) −1.71061 + 0.271715i −0.0617262 + 0.00980466i
\(769\) −19.2126 + 17.2991i −0.692823 + 0.623821i −0.938398 0.345557i \(-0.887690\pi\)
0.245575 + 0.969378i \(0.421023\pi\)
\(770\) −12.5307 + 12.4896i −0.451576 + 0.450094i
\(771\) 15.6984 48.3881i 0.565364 1.74265i
\(772\) 0.943462 + 18.0023i 0.0339559 + 0.647918i
\(773\) −11.9486 + 1.89247i −0.429762 + 0.0680675i −0.367568 0.929997i \(-0.619810\pi\)
−0.0621934 + 0.998064i \(0.519810\pi\)
\(774\) −9.71296 + 10.8067i −0.349125 + 0.388438i
\(775\) −35.8179 + 3.64562i −1.28662 + 0.130954i
\(776\) −3.11599 + 1.79902i −0.111857 + 0.0645809i
\(777\) −16.0570 24.7015i −0.576042 0.886162i
\(778\) 10.5763 + 16.2861i 0.379180 + 0.583885i
\(779\) −38.0040 8.07801i −1.36164 0.289425i
\(780\) −5.24216 + 3.39538i −0.187700 + 0.121574i
\(781\) 16.7507 3.56048i 0.599388 0.127404i
\(782\) 19.9764 + 19.9764i 0.714355 + 0.714355i
\(783\) −23.1099 + 18.7652i −0.825880 + 0.670614i
\(784\) 2.24896 + 3.09543i 0.0803201 + 0.110551i
\(785\) −30.4922 33.9771i −1.08831 1.21270i
\(786\) −23.0122 20.7017i −0.820818 0.738406i
\(787\) 19.7158 + 15.9656i 0.702794 + 0.569111i 0.912710 0.408608i \(-0.133986\pi\)
−0.209916 + 0.977719i \(0.567319\pi\)
\(788\) 15.9057 + 12.8802i 0.566618 + 0.458839i
\(789\) −9.29439 + 43.8227i −0.330889 + 1.56013i
\(790\) −1.65192 + 0.732230i −0.0587725 + 0.0260516i
\(791\) 20.6517 + 28.4246i 0.734288 + 1.01066i
\(792\) −9.41283 + 9.42962i −0.334470 + 0.335067i
\(793\) 11.4826 + 11.4826i 0.407760 + 0.407760i
\(794\) −0.517452 + 0.109988i −0.0183637 + 0.00390332i
\(795\) 1.05998 1.62795i 0.0375936 0.0577375i
\(796\) 12.2485 + 2.60350i 0.434137 + 0.0922787i
\(797\) 3.01141 + 4.63716i 0.106669 + 0.164257i 0.887974 0.459893i \(-0.152112\pi\)
−0.781305 + 0.624150i \(0.785446\pi\)
\(798\) 5.27420 10.3626i 0.186705 0.366832i
\(799\) 26.0115 15.0178i 0.920222 0.531290i
\(800\) 1.80717 4.66199i 0.0638933 0.164826i
\(801\) 5.90641 27.9098i 0.208693 0.986143i
\(802\) −25.5219 + 4.04228i −0.901211 + 0.142738i
\(803\) −2.91003 55.5266i −0.102693 1.95949i
\(804\) 12.9158 + 14.3316i 0.455505 + 0.505436i
\(805\) 2.89663 18.0960i 0.102093 0.637802i
\(806\) −8.62935 + 7.76990i −0.303956 + 0.273683i
\(807\) −12.7503 15.7310i −0.448832 0.553757i
\(808\) −8.37525 5.43895i −0.294640 0.191342i
\(809\) −19.1502 + 13.9134i −0.673285 + 0.489170i −0.871123 0.491065i \(-0.836608\pi\)
0.197838 + 0.980235i \(0.436608\pi\)
\(810\) −8.18796 18.3836i −0.287696 0.645934i
\(811\) −24.9996 18.1633i −0.877854 0.637798i 0.0548286 0.998496i \(-0.482539\pi\)
−0.932683 + 0.360697i \(0.882539\pi\)
\(812\) −3.65768 9.52858i −0.128359 0.334388i
\(813\) 10.3018 + 2.75545i 0.361301 + 0.0966377i
\(814\) −17.2472 38.7380i −0.604516 1.35776i
\(815\) −35.1356 + 11.3524i −1.23075 + 0.397659i
\(816\) −5.31407 + 9.21372i −0.186030 + 0.322545i
\(817\) 9.94020 15.3066i 0.347763 0.535509i
\(818\) −15.6457 + 15.6457i −0.547040 + 0.547040i
\(819\) −7.46798 4.30277i −0.260952 0.150351i
\(820\) −8.22695 21.5377i −0.287297 0.752128i
\(821\) 24.2611 + 21.8448i 0.846720 + 0.762390i 0.973293 0.229567i \(-0.0737312\pi\)
−0.126573 + 0.991957i \(0.540398\pi\)
\(822\) 3.27640 1.67125i 0.114278 0.0582915i
\(823\) 37.8660 + 14.5354i 1.31992 + 0.506672i 0.913435 0.406984i \(-0.133419\pi\)
0.406489 + 0.913655i \(0.366753\pi\)
\(824\) 0.390969 0.677178i 0.0136201 0.0235906i
\(825\) −9.84909 37.1796i −0.342901 1.29443i
\(826\) 2.93822 + 5.08915i 0.102234 + 0.177074i
\(827\) 4.31393 + 27.2371i 0.150010 + 0.947126i 0.941761 + 0.336282i \(0.109170\pi\)
−0.791751 + 0.610844i \(0.790830\pi\)
\(828\) 2.14686 13.6333i 0.0746085 0.473791i
\(829\) −10.9199 + 3.54809i −0.379264 + 0.123230i −0.492444 0.870344i \(-0.663896\pi\)
0.113180 + 0.993575i \(0.463896\pi\)
\(830\) −11.0899 17.1386i −0.384937 0.594890i
\(831\) −5.55842 + 0.586718i −0.192820 + 0.0203530i
\(832\) −0.417381 1.55769i −0.0144701 0.0540030i
\(833\) 23.4639 + 1.22969i 0.812976 + 0.0426063i
\(834\) −3.13226 + 1.81027i −0.108461 + 0.0626847i
\(835\) −2.28499 5.15496i −0.0790755 0.178395i
\(836\) 9.83687 13.5393i 0.340215 0.468266i
\(837\) −20.4198 31.3519i −0.705812 1.08368i
\(838\) 10.2293 + 1.62017i 0.353366 + 0.0559677i
\(839\) −3.23331 + 30.7628i −0.111626 + 1.06205i 0.785071 + 0.619406i \(0.212627\pi\)
−0.896697 + 0.442645i \(0.854040\pi\)
\(840\) 6.86288 0.713006i 0.236792 0.0246010i
\(841\) −0.399536 3.80133i −0.0137771 0.131080i
\(842\) 1.67801 32.0183i 0.0578280 1.10342i
\(843\) −16.8177 6.44710i −0.579231 0.222050i
\(844\) 1.91794 + 9.02319i 0.0660181 + 0.310591i
\(845\) 14.6044 + 18.0956i 0.502405 + 0.622508i
\(846\) −13.4099 5.95617i −0.461043 0.204778i
\(847\) −13.8486 7.05623i −0.475844 0.242455i
\(848\) 0.315656 + 0.389803i 0.0108397 + 0.0133859i
\(849\) −0.773829 0.561693i −0.0265577 0.0192773i
\(850\) −15.2648 26.6412i −0.523577 0.913786i
\(851\) 38.0396 + 21.9622i 1.30398 + 0.752853i
\(852\) −5.95207 3.02939i −0.203914 0.103785i
\(853\) 13.1107 0.687103i 0.448902 0.0235259i 0.173454 0.984842i \(-0.444507\pi\)
0.275448 + 0.961316i \(0.411174\pi\)
\(854\) −5.54363 17.0616i −0.189699 0.583834i
\(855\) 13.7514 + 21.2103i 0.470289 + 0.725376i
\(856\) 3.34348 10.2902i 0.114278 0.351711i
\(857\) −12.2906 + 45.8693i −0.419840 + 1.56686i 0.355099 + 0.934829i \(0.384447\pi\)
−0.774939 + 0.632036i \(0.782219\pi\)
\(858\) −9.64400 7.80245i −0.329241 0.266371i
\(859\) 15.4288 1.62164i 0.526425 0.0553295i 0.162411 0.986723i \(-0.448073\pi\)
0.364014 + 0.931394i \(0.381406\pi\)
\(860\) 10.8301 + 0.0178000i 0.369305 + 0.000606976i
\(861\) 21.2783 23.6531i 0.725163 0.806097i
\(862\) 6.19237 2.37703i 0.210913 0.0809620i
\(863\) −6.44707 + 40.7052i −0.219461 + 1.38562i 0.594217 + 0.804305i \(0.297462\pi\)
−0.813678 + 0.581316i \(0.802538\pi\)
\(864\) 5.16696 0.550052i 0.175783 0.0187132i
\(865\) 34.5482 + 15.4499i 1.17467 + 0.525314i
\(866\) −6.61615 + 14.8601i −0.224826 + 0.504968i
\(867\) 12.8703 + 33.4836i 0.437097 + 1.13716i
\(868\) 12.3909 3.32014i 0.420576 0.112693i
\(869\) −2.40142 2.66705i −0.0814626 0.0904734i
\(870\) 21.9112 + 3.49731i 0.742861 + 0.118570i
\(871\) −12.0194 + 13.3489i −0.407261 + 0.452309i
\(872\) −3.46560 + 6.80163i −0.117360 + 0.230332i
\(873\) 9.61323 4.90898i 0.325359 0.166144i
\(874\) 17.3355i 0.586383i
\(875\) −8.19103 + 18.1559i −0.276907 + 0.613781i
\(876\) −12.7382 + 17.5491i −0.430384 + 0.592928i
\(877\) 14.5521 37.9095i 0.491389 1.28011i −0.433938 0.900943i \(-0.642876\pi\)
0.925327 0.379170i \(-0.123790\pi\)
\(878\) 5.96044 3.87075i 0.201155 0.130632i
\(879\) 20.6935 + 6.71353i 0.697974 + 0.226442i
\(880\) 9.91637 + 0.536040i 0.334281 + 0.0180699i
\(881\) −31.6147 10.2722i −1.06513 0.346081i −0.276539 0.961003i \(-0.589188\pi\)
−0.788588 + 0.614922i \(0.789188\pi\)
\(882\) −6.26021 9.62110i −0.210792 0.323959i
\(883\) 27.2323 13.8755i 0.916439 0.466949i 0.0688652 0.997626i \(-0.478062\pi\)
0.847574 + 0.530677i \(0.178062\pi\)
\(884\) −9.04687 4.02793i −0.304279 0.135474i
\(885\) −12.7752 0.0153051i −0.429434 0.000514476i
\(886\) −6.16156 + 2.74330i −0.207002 + 0.0921631i
\(887\) 35.5133 43.8553i 1.19242 1.47252i 0.347456 0.937696i \(-0.387046\pi\)
0.844965 0.534821i \(-0.179621\pi\)
\(888\) −4.27306 + 15.9757i −0.143395 + 0.536111i
\(889\) −4.71655 0.495729i −0.158188 0.0166262i
\(890\) −18.4321 + 10.6014i −0.617846 + 0.355361i
\(891\) 29.6565 26.7986i 0.993529 0.897789i
\(892\) 4.49778 + 8.82738i 0.150597 + 0.295563i
\(893\) 17.8026 + 4.77020i 0.595742 + 0.159628i
\(894\) 9.61000 + 4.27352i 0.321406 + 0.142928i
\(895\) 0.955214 + 0.958359i 0.0319293 + 0.0320344i
\(896\) −0.370400 + 1.74260i −0.0123742 + 0.0582160i
\(897\) 12.8325 + 0.666790i 0.428465 + 0.0222635i
\(898\) 4.75286 3.84879i 0.158605 0.128436i
\(899\) 41.2527 1.37586
\(900\) −6.13387 + 13.6885i −0.204462 + 0.456284i
\(901\) 3.08017 0.102615
\(902\) 35.5871 28.8179i 1.18492 0.959530i
\(903\) 6.79092 + 13.3133i 0.225988 + 0.443038i
\(904\) 4.10037 19.2907i 0.136376 0.641600i
\(905\) −2.01742 12.8744i −0.0670612 0.427959i
\(906\) 7.13664 5.18993i 0.237099 0.172424i
\(907\) −22.1851 5.94447i −0.736643 0.197383i −0.129057 0.991637i \(-0.541195\pi\)
−0.607586 + 0.794254i \(0.707862\pi\)
\(908\) −5.44361 10.6837i −0.180652 0.354550i
\(909\) 24.2530 + 17.5879i 0.804423 + 0.583353i
\(910\) 1.32532 + 6.28592i 0.0439339 + 0.208376i
\(911\) 4.00879 + 0.421341i 0.132817 + 0.0139597i 0.170704 0.985322i \(-0.445396\pi\)
−0.0378865 + 0.999282i \(0.512063\pi\)
\(912\) −6.30361 + 1.69206i −0.208733 + 0.0560296i
\(913\) 25.5158 31.5094i 0.844451 1.04281i
\(914\) 9.44212 4.20390i 0.312318 0.139053i
\(915\) 38.1381 + 8.15427i 1.26081 + 0.269572i
\(916\) −22.0005 9.79526i −0.726917 0.323644i
\(917\) −28.3676 + 14.4540i −0.936781 + 0.477314i
\(918\) 17.3431 26.7844i 0.572409 0.884017i
\(919\) 8.95490 + 2.90962i 0.295395 + 0.0959796i 0.452965 0.891528i \(-0.350366\pi\)
−0.157571 + 0.987508i \(0.550366\pi\)
\(920\) −8.63653 + 5.58847i −0.284738 + 0.184246i
\(921\) −9.53986 44.7834i −0.314349 1.47566i
\(922\) 25.2940 16.4261i 0.833015 0.540966i
\(923\) 2.22840 5.80518i 0.0733487 0.191080i
\(924\) 5.57958 + 12.5169i 0.183555 + 0.411777i
\(925\) −33.6456 33.8675i −1.10626 1.11356i
\(926\) 21.2736i 0.699092i
\(927\) −1.27587 + 1.96850i −0.0419050 + 0.0646541i
\(928\) −2.60094 + 5.10464i −0.0853802 + 0.167568i
\(929\) 5.06837 5.62900i 0.166288 0.184681i −0.654242 0.756286i \(-0.727012\pi\)
0.820530 + 0.571604i \(0.193679\pi\)
\(930\) −7.25016 + 26.9289i −0.237742 + 0.883032i
\(931\) 9.64743 + 10.7146i 0.316182 + 0.351155i
\(932\) −13.1144 + 3.51398i −0.429575 + 0.115104i
\(933\) −46.5584 7.35287i −1.52425 0.240722i
\(934\) 10.3345 23.2117i 0.338156 0.759511i
\(935\) 40.8809 45.2531i 1.33695 1.47993i
\(936\) 1.01007 + 4.73129i 0.0330153 + 0.154647i
\(937\) 1.46193 9.23027i 0.0477592 0.301540i −0.952233 0.305371i \(-0.901219\pi\)
0.999993 + 0.00383116i \(0.00121950\pi\)
\(938\) 18.5259 7.11141i 0.604891 0.232196i
\(939\) −34.0189 7.21510i −1.11016 0.235456i
\(940\) 3.36254 + 10.4070i 0.109674 + 0.339439i
\(941\) 1.26808 0.133281i 0.0413384 0.00434484i −0.0838367 0.996480i \(-0.526717\pi\)
0.125175 + 0.992135i \(0.460051\pi\)
\(942\) −33.0084 + 12.6876i −1.07547 + 0.413385i
\(943\) −12.2768 + 45.8176i −0.399787 + 1.49203i
\(944\) 1.01931 3.13710i 0.0331756 0.102104i
\(945\) −20.6714 + 1.07698i −0.672441 + 0.0350342i
\(946\) 6.64712 + 20.4577i 0.216116 + 0.665138i
\(947\) 58.2562 3.05308i 1.89307 0.0992117i 0.929853 0.367930i \(-0.119933\pi\)
0.963219 + 0.268718i \(0.0866001\pi\)
\(948\) 0.0738742 + 1.39769i 0.00239932 + 0.0453948i
\(949\) −17.4849 10.0949i −0.567582 0.327694i
\(950\) 4.93624 18.1830i 0.160153 0.589934i
\(951\) 40.4867 18.0475i 1.31287 0.585229i
\(952\) 6.88487 + 8.50211i 0.223140 + 0.275555i
\(953\) −4.95140 2.52286i −0.160392 0.0817236i 0.371952 0.928252i \(-0.378689\pi\)
−0.532344 + 0.846528i \(0.678689\pi\)
\(954\) −0.885553 1.21658i −0.0286708 0.0393882i
\(955\) 0.805288 + 15.8647i 0.0260585 + 0.513368i
\(956\) −2.90075 13.6469i −0.0938169 0.441374i
\(957\) 6.91351 + 43.5247i 0.223482 + 1.40695i
\(958\) −2.04676 + 39.0546i −0.0661280 + 1.26180i
\(959\) −0.395441 3.76237i −0.0127694 0.121493i
\(960\) −2.87508 2.59498i −0.0927928 0.0837526i
\(961\) −2.17927 + 20.7343i −0.0702990 + 0.668850i
\(962\) −15.2076 2.40865i −0.490313 0.0776580i
\(963\) −11.6053 + 30.3136i −0.373977 + 0.976843i
\(964\) 4.77469 6.57180i 0.153782 0.211663i
\(965\) −30.0002 + 26.9232i −0.965741 + 0.866687i
\(966\) −12.2969 7.09231i −0.395646 0.228191i
\(967\) 54.1476 + 2.83775i 1.74127 + 0.0912560i 0.896269 0.443511i \(-0.146267\pi\)
0.845000 + 0.534767i \(0.179600\pi\)
\(968\) 2.25803 + 8.42709i 0.0725759 + 0.270857i
\(969\) −16.2858 + 36.6223i −0.523174 + 1.17648i
\(970\) −7.50632 2.89557i −0.241013 0.0929711i
\(971\) −27.0422 + 8.78655i −0.867826 + 0.281974i −0.708893 0.705316i \(-0.750805\pi\)
−0.158933 + 0.987289i \(0.550805\pi\)
\(972\) −15.5652 + 0.850513i −0.499255 + 0.0272802i
\(973\) 0.582108 + 3.67528i 0.0186615 + 0.117824i
\(974\) 0.433652 + 0.751107i 0.0138951 + 0.0240670i
\(975\) −13.2700 4.35340i −0.424979 0.139421i
\(976\) −5.03489 + 8.72069i −0.161163 + 0.279142i
\(977\) −10.4590 4.01484i −0.334613 0.128446i 0.185260 0.982690i \(-0.440687\pi\)
−0.519873 + 0.854244i \(0.674021\pi\)
\(978\) −1.48415 + 28.5628i −0.0474579 + 0.913336i
\(979\) −31.3851 28.2593i −1.00307 0.903170i
\(980\) −2.22792 + 8.26039i −0.0711684 + 0.263869i
\(981\) 11.4328 19.8430i 0.365021 0.633538i
\(982\) 15.8623 15.8623i 0.506185 0.506185i
\(983\) 12.5572 19.3364i 0.400513 0.616735i −0.579665 0.814855i \(-0.696817\pi\)
0.980178 + 0.198119i \(0.0634834\pi\)
\(984\) −17.8587 + 0.00795660i −0.569314 + 0.000253647i
\(985\) −0.0752182 + 45.7652i −0.00239665 + 1.45820i
\(986\) 14.3097 + 32.1401i 0.455713 + 1.02355i
\(987\) −10.6671 + 10.6766i −0.339538 + 0.339841i
\(988\) −2.17772 5.67316i −0.0692825 0.180487i
\(989\) −18.0263 13.0969i −0.573204 0.416457i
\(990\) −29.6270 3.13647i −0.941608 0.0996834i
\(991\) 8.74556 6.35402i 0.277812 0.201842i −0.440151 0.897924i \(-0.645075\pi\)
0.717962 + 0.696082i \(0.245075\pi\)
\(992\) −6.03893 3.92172i −0.191736 0.124515i
\(993\) 8.29584 21.6402i 0.263261 0.686731i
\(994\) −5.10497 + 4.59654i −0.161920 + 0.145793i
\(995\) 12.6709 + 24.9694i 0.401694 + 0.791583i
\(996\) −15.4654 + 3.29447i −0.490039 + 0.104389i
\(997\) −0.668977 12.7648i −0.0211867 0.404267i −0.988552 0.150881i \(-0.951789\pi\)
0.967365 0.253386i \(-0.0815443\pi\)
\(998\) −5.16666 + 0.818318i −0.163548 + 0.0259034i
\(999\) 15.2679 47.2043i 0.483054 1.49348i
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 450.2.w.a.113.5 yes 480
9.2 odd 6 inner 450.2.w.a.263.5 yes 480
25.2 odd 20 inner 450.2.w.a.77.5 480
225.2 even 60 inner 450.2.w.a.227.5 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.w.a.77.5 480 25.2 odd 20 inner
450.2.w.a.113.5 yes 480 1.1 even 1 trivial
450.2.w.a.227.5 yes 480 225.2 even 60 inner
450.2.w.a.263.5 yes 480 9.2 odd 6 inner