Properties

Label 418.2.f.h.229.4
Level $418$
Weight $2$
Character 418.229
Analytic conductor $3.338$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), degree \(4\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + 7288 x^{12} + 5704 x^{11} + 24392 x^{10} + 10376 x^{9} + 48880 x^{8} + 21224 x^{7} + \cdots + 1936 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 229.4
Root \(0.488718 + 1.50412i\) of defining polynomial
Character \(\chi\) \(=\) 418.229
Dual form 418.2.f.h.115.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(1.27948 - 0.929596i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.804188 + 2.47504i) q^{5} +(0.488718 + 1.50412i) q^{6} +(1.25444 + 0.911401i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.154132 + 0.474370i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(1.27948 - 0.929596i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.804188 + 2.47504i) q^{5} +(0.488718 + 1.50412i) q^{6} +(1.25444 + 0.911401i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.154132 + 0.474370i) q^{9} -2.60241 q^{10} +(-1.72947 + 2.83001i) q^{11} -1.58152 q^{12} +(0.710450 - 2.18654i) q^{13} +(-1.25444 + 0.911401i) q^{14} +(3.32973 + 2.41919i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.0656020 + 0.201902i) q^{17} +(-0.403523 - 0.293177i) q^{18} +(0.809017 - 0.587785i) q^{19} +(0.804188 - 2.47504i) q^{20} +2.45226 q^{21} +(-2.15706 - 2.51934i) q^{22} -2.47068 q^{23} +(0.488718 - 1.50412i) q^{24} +(-1.43400 + 1.04186i) q^{25} +(1.85998 + 1.35136i) q^{26} +(1.70992 + 5.26258i) q^{27} +(-0.479152 - 1.47468i) q^{28} +(3.79183 + 2.75492i) q^{29} +(-3.32973 + 2.41919i) q^{30} +(1.22033 - 3.75578i) q^{31} -1.00000 q^{32} +(0.417951 + 5.22864i) q^{33} -0.212293 q^{34} +(-1.24695 + 3.83771i) q^{35} +(0.403523 - 0.293177i) q^{36} +(2.14343 + 1.55729i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.12359 - 3.45806i) q^{39} +(2.10539 + 1.52966i) q^{40} +(6.10649 - 4.43662i) q^{41} +(-0.757790 + 2.33224i) q^{42} +5.85824 q^{43} +(3.06260 - 1.27297i) q^{44} -1.29803 q^{45} +(0.763482 - 2.34975i) q^{46} +(-10.1002 + 7.33820i) q^{47} +(1.27948 + 0.929596i) q^{48} +(-1.42016 - 4.37081i) q^{49} +(-0.547738 - 1.68577i) q^{50} +(0.271624 + 0.197346i) q^{51} +(-1.85998 + 1.35136i) q^{52} +(2.31354 - 7.12033i) q^{53} -5.53341 q^{54} +(-8.39519 - 2.00463i) q^{55} +1.55057 q^{56} +(0.488718 - 1.50412i) q^{57} +(-3.79183 + 2.75492i) q^{58} +(-3.38431 - 2.45884i) q^{59} +(-1.27184 - 3.91433i) q^{60} +(-4.02292 - 12.3813i) q^{61} +(3.19486 + 2.32120i) q^{62} +(-0.625690 + 0.454590i) q^{63} +(0.309017 - 0.951057i) q^{64} +5.98310 q^{65} +(-5.10189 - 1.21825i) q^{66} -8.97065 q^{67} +(0.0656020 - 0.201902i) q^{68} +(-3.16118 + 2.29673i) q^{69} +(-3.26455 - 2.37183i) q^{70} +(2.10796 + 6.48762i) q^{71} +(0.154132 + 0.474370i) q^{72} +(6.83808 + 4.96816i) q^{73} +(-2.14343 + 1.55729i) q^{74} +(-0.866261 + 2.66608i) q^{75} -1.00000 q^{76} +(-4.74877 + 1.97383i) q^{77} +3.63602 q^{78} +(2.77538 - 8.54173i) q^{79} +(-2.10539 + 1.52966i) q^{80} +(5.86931 + 4.26431i) q^{81} +(2.33247 + 7.17861i) q^{82} +(-5.03599 - 15.4992i) q^{83} +(-1.98392 - 1.44140i) q^{84} +(-0.446959 + 0.324735i) q^{85} +(-1.81030 + 5.57152i) q^{86} +7.41253 q^{87} +(0.264271 + 3.30608i) q^{88} -3.58951 q^{89} +(0.401114 - 1.23450i) q^{90} +(2.88403 - 2.09537i) q^{91} +(1.99882 + 1.45223i) q^{92} +(-1.92998 - 5.93986i) q^{93} +(-3.85792 - 11.8735i) q^{94} +(2.10539 + 1.52966i) q^{95} +(-1.27948 + 0.929596i) q^{96} +(-0.460238 + 1.41647i) q^{97} +4.59574 q^{98} +(-1.07590 - 1.25660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) 1.27948 0.929596i 0.738708 0.536703i −0.153598 0.988133i \(-0.549086\pi\)
0.892306 + 0.451431i \(0.149086\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.804188 + 2.47504i 0.359644 + 1.10687i 0.953268 + 0.302127i \(0.0976967\pi\)
−0.593624 + 0.804743i \(0.702303\pi\)
\(6\) 0.488718 + 1.50412i 0.199518 + 0.614054i
\(7\) 1.25444 + 0.911401i 0.474132 + 0.344477i 0.799049 0.601265i \(-0.205337\pi\)
−0.324917 + 0.945742i \(0.605337\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) −0.154132 + 0.474370i −0.0513774 + 0.158123i
\(10\) −2.60241 −0.822953
\(11\) −1.72947 + 2.83001i −0.521453 + 0.853280i
\(12\) −1.58152 −0.456547
\(13\) 0.710450 2.18654i 0.197043 0.606437i −0.802903 0.596109i \(-0.796713\pi\)
0.999947 0.0103276i \(-0.00328744\pi\)
\(14\) −1.25444 + 0.911401i −0.335262 + 0.243582i
\(15\) 3.32973 + 2.41919i 0.859732 + 0.624632i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 0.0656020 + 0.201902i 0.0159108 + 0.0489685i 0.958697 0.284430i \(-0.0918044\pi\)
−0.942786 + 0.333399i \(0.891804\pi\)
\(18\) −0.403523 0.293177i −0.0951113 0.0691024i
\(19\) 0.809017 0.587785i 0.185601 0.134847i
\(20\) 0.804188 2.47504i 0.179822 0.553435i
\(21\) 2.45226 0.535127
\(22\) −2.15706 2.51934i −0.459888 0.537125i
\(23\) −2.47068 −0.515172 −0.257586 0.966255i \(-0.582927\pi\)
−0.257586 + 0.966255i \(0.582927\pi\)
\(24\) 0.488718 1.50412i 0.0997591 0.307027i
\(25\) −1.43400 + 1.04186i −0.286799 + 0.208372i
\(26\) 1.85998 + 1.35136i 0.364772 + 0.265023i
\(27\) 1.70992 + 5.26258i 0.329074 + 1.01278i
\(28\) −0.479152 1.47468i −0.0905511 0.278688i
\(29\) 3.79183 + 2.75492i 0.704125 + 0.511577i 0.881273 0.472608i \(-0.156687\pi\)
−0.177148 + 0.984184i \(0.556687\pi\)
\(30\) −3.32973 + 2.41919i −0.607922 + 0.441681i
\(31\) 1.22033 3.75578i 0.219177 0.674558i −0.779653 0.626211i \(-0.784605\pi\)
0.998831 0.0483468i \(-0.0153953\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.417951 + 5.22864i 0.0727559 + 0.910190i
\(34\) −0.212293 −0.0364079
\(35\) −1.24695 + 3.83771i −0.210773 + 0.648691i
\(36\) 0.403523 0.293177i 0.0672539 0.0488628i
\(37\) 2.14343 + 1.55729i 0.352377 + 0.256017i 0.749866 0.661590i \(-0.230118\pi\)
−0.397488 + 0.917607i \(0.630118\pi\)
\(38\) 0.309017 + 0.951057i 0.0501292 + 0.154282i
\(39\) −1.12359 3.45806i −0.179919 0.553733i
\(40\) 2.10539 + 1.52966i 0.332892 + 0.241860i
\(41\) 6.10649 4.43662i 0.953673 0.692884i 0.00200054 0.999998i \(-0.499363\pi\)
0.951673 + 0.307114i \(0.0993632\pi\)
\(42\) −0.757790 + 2.33224i −0.116929 + 0.359872i
\(43\) 5.85824 0.893374 0.446687 0.894690i \(-0.352604\pi\)
0.446687 + 0.894690i \(0.352604\pi\)
\(44\) 3.06260 1.27297i 0.461705 0.191908i
\(45\) −1.29803 −0.193499
\(46\) 0.763482 2.34975i 0.112569 0.346452i
\(47\) −10.1002 + 7.33820i −1.47326 + 1.07039i −0.493608 + 0.869684i \(0.664322\pi\)
−0.979652 + 0.200702i \(0.935678\pi\)
\(48\) 1.27948 + 0.929596i 0.184677 + 0.134176i
\(49\) −1.42016 4.37081i −0.202880 0.624401i
\(50\) −0.547738 1.68577i −0.0774619 0.238403i
\(51\) 0.271624 + 0.197346i 0.0380350 + 0.0276340i
\(52\) −1.85998 + 1.35136i −0.257933 + 0.187399i
\(53\) 2.31354 7.12033i 0.317789 0.978053i −0.656803 0.754062i \(-0.728092\pi\)
0.974591 0.223990i \(-0.0719084\pi\)
\(54\) −5.53341 −0.753001
\(55\) −8.39519 2.00463i −1.13201 0.270304i
\(56\) 1.55057 0.207203
\(57\) 0.488718 1.50412i 0.0647323 0.199225i
\(58\) −3.79183 + 2.75492i −0.497891 + 0.361739i
\(59\) −3.38431 2.45884i −0.440599 0.320114i 0.345274 0.938502i \(-0.387786\pi\)
−0.785873 + 0.618388i \(0.787786\pi\)
\(60\) −1.27184 3.91433i −0.164194 0.505338i
\(61\) −4.02292 12.3813i −0.515082 1.58526i −0.783132 0.621856i \(-0.786379\pi\)
0.268050 0.963405i \(-0.413621\pi\)
\(62\) 3.19486 + 2.32120i 0.405747 + 0.294793i
\(63\) −0.625690 + 0.454590i −0.0788295 + 0.0572730i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 5.98310 0.742112
\(66\) −5.10189 1.21825i −0.627999 0.149956i
\(67\) −8.97065 −1.09594 −0.547970 0.836498i \(-0.684599\pi\)
−0.547970 + 0.836498i \(0.684599\pi\)
\(68\) 0.0656020 0.201902i 0.00795541 0.0244842i
\(69\) −3.16118 + 2.29673i −0.380562 + 0.276494i
\(70\) −3.26455 2.37183i −0.390188 0.283488i
\(71\) 2.10796 + 6.48762i 0.250168 + 0.769939i 0.994743 + 0.102400i \(0.0326523\pi\)
−0.744575 + 0.667539i \(0.767348\pi\)
\(72\) 0.154132 + 0.474370i 0.0181646 + 0.0559050i
\(73\) 6.83808 + 4.96816i 0.800337 + 0.581479i 0.911013 0.412378i \(-0.135302\pi\)
−0.110676 + 0.993857i \(0.535302\pi\)
\(74\) −2.14343 + 1.55729i −0.249168 + 0.181031i
\(75\) −0.866261 + 2.66608i −0.100027 + 0.307852i
\(76\) −1.00000 −0.114708
\(77\) −4.74877 + 1.97383i −0.541173 + 0.224939i
\(78\) 3.63602 0.411699
\(79\) 2.77538 8.54173i 0.312254 0.961020i −0.664616 0.747185i \(-0.731405\pi\)
0.976870 0.213834i \(-0.0685953\pi\)
\(80\) −2.10539 + 1.52966i −0.235390 + 0.171021i
\(81\) 5.86931 + 4.26431i 0.652146 + 0.473812i
\(82\) 2.33247 + 7.17861i 0.257578 + 0.792745i
\(83\) −5.03599 15.4992i −0.552772 1.70126i −0.701757 0.712417i \(-0.747601\pi\)
0.148985 0.988839i \(-0.452399\pi\)
\(84\) −1.98392 1.44140i −0.216463 0.157270i
\(85\) −0.446959 + 0.324735i −0.0484795 + 0.0352224i
\(86\) −1.81030 + 5.57152i −0.195209 + 0.600792i
\(87\) 7.41253 0.794707
\(88\) 0.264271 + 3.30608i 0.0281714 + 0.352429i
\(89\) −3.58951 −0.380487 −0.190244 0.981737i \(-0.560928\pi\)
−0.190244 + 0.981737i \(0.560928\pi\)
\(90\) 0.401114 1.23450i 0.0422812 0.130128i
\(91\) 2.88403 2.09537i 0.302328 0.219654i
\(92\) 1.99882 + 1.45223i 0.208391 + 0.151405i
\(93\) −1.92998 5.93986i −0.200129 0.615935i
\(94\) −3.85792 11.8735i −0.397914 1.22465i
\(95\) 2.10539 + 1.52966i 0.216009 + 0.156939i
\(96\) −1.27948 + 0.929596i −0.130586 + 0.0948765i
\(97\) −0.460238 + 1.41647i −0.0467301 + 0.143820i −0.971699 0.236222i \(-0.924091\pi\)
0.924969 + 0.380043i \(0.124091\pi\)
\(98\) 4.59574 0.464240
\(99\) −1.07590 1.25660i −0.108133 0.126293i
\(100\) 1.77252 0.177252
\(101\) −0.776576 + 2.39005i −0.0772722 + 0.237819i −0.982230 0.187683i \(-0.939902\pi\)
0.904958 + 0.425502i \(0.139902\pi\)
\(102\) −0.271624 + 0.197346i −0.0268948 + 0.0195402i
\(103\) −5.47964 3.98119i −0.539925 0.392278i 0.284132 0.958785i \(-0.408294\pi\)
−0.824057 + 0.566507i \(0.808294\pi\)
\(104\) −0.710450 2.18654i −0.0696653 0.214408i
\(105\) 1.97208 + 6.06943i 0.192455 + 0.592316i
\(106\) 6.05692 + 4.40061i 0.588300 + 0.427425i
\(107\) 10.6272 7.72110i 1.02737 0.746427i 0.0595887 0.998223i \(-0.481021\pi\)
0.967780 + 0.251796i \(0.0810211\pi\)
\(108\) 1.70992 5.26258i 0.164537 0.506392i
\(109\) −2.72603 −0.261106 −0.130553 0.991441i \(-0.541675\pi\)
−0.130553 + 0.991441i \(0.541675\pi\)
\(110\) 4.50077 7.36483i 0.429132 0.702209i
\(111\) 4.19012 0.397709
\(112\) −0.479152 + 1.47468i −0.0452756 + 0.139344i
\(113\) 7.16377 5.20479i 0.673911 0.489625i −0.197421 0.980319i \(-0.563257\pi\)
0.871332 + 0.490694i \(0.163257\pi\)
\(114\) 1.27948 + 0.929596i 0.119834 + 0.0870647i
\(115\) −1.98689 6.11502i −0.185278 0.570228i
\(116\) −1.44835 4.45756i −0.134476 0.413874i
\(117\) 0.927725 + 0.674032i 0.0857682 + 0.0623143i
\(118\) 3.38431 2.45884i 0.311551 0.226355i
\(119\) −0.101720 + 0.313063i −0.00932469 + 0.0286984i
\(120\) 4.11577 0.375716
\(121\) −5.01790 9.78880i −0.456173 0.889891i
\(122\) 13.0184 1.17864
\(123\) 3.68886 11.3531i 0.332613 1.02368i
\(124\) −3.19486 + 2.32120i −0.286907 + 0.208450i
\(125\) 6.79511 + 4.93694i 0.607773 + 0.441573i
\(126\) −0.238992 0.735542i −0.0212911 0.0655273i
\(127\) −2.85928 8.79997i −0.253720 0.780871i −0.994079 0.108659i \(-0.965344\pi\)
0.740359 0.672212i \(-0.234656\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 7.49550 5.44580i 0.659942 0.479476i
\(130\) −1.84888 + 5.69026i −0.162157 + 0.499069i
\(131\) 12.1117 1.05821 0.529103 0.848558i \(-0.322528\pi\)
0.529103 + 0.848558i \(0.322528\pi\)
\(132\) 2.73519 4.47573i 0.238068 0.389562i
\(133\) 1.55057 0.134451
\(134\) 2.77208 8.53159i 0.239471 0.737017i
\(135\) −11.6500 + 8.46421i −1.00267 + 0.728483i
\(136\) 0.171748 + 0.124782i 0.0147273 + 0.0107000i
\(137\) −3.01282 9.27249i −0.257402 0.792203i −0.993347 0.115161i \(-0.963262\pi\)
0.735945 0.677042i \(-0.236738\pi\)
\(138\) −1.20746 3.71619i −0.102786 0.316343i
\(139\) −10.2880 7.47470i −0.872621 0.633996i 0.0586683 0.998278i \(-0.481315\pi\)
−0.931289 + 0.364282i \(0.881315\pi\)
\(140\) 3.26455 2.37183i 0.275905 0.200457i
\(141\) −6.10139 + 18.7782i −0.513830 + 1.58141i
\(142\) −6.82149 −0.572447
\(143\) 4.95923 + 5.79212i 0.414711 + 0.484361i
\(144\) −0.498782 −0.0415652
\(145\) −3.76919 + 11.6004i −0.313014 + 0.963359i
\(146\) −6.83808 + 4.96816i −0.565924 + 0.411168i
\(147\) −5.88016 4.27218i −0.484987 0.352364i
\(148\) −0.818716 2.51975i −0.0672980 0.207122i
\(149\) 4.19154 + 12.9002i 0.343384 + 1.05683i 0.962443 + 0.271483i \(0.0875141\pi\)
−0.619059 + 0.785344i \(0.712486\pi\)
\(150\) −2.26790 1.64773i −0.185173 0.134536i
\(151\) −8.77937 + 6.37859i −0.714455 + 0.519082i −0.884608 0.466336i \(-0.845574\pi\)
0.170153 + 0.985418i \(0.445574\pi\)
\(152\) 0.309017 0.951057i 0.0250646 0.0771409i
\(153\) −0.105888 −0.00856051
\(154\) −0.409770 5.12630i −0.0330202 0.413089i
\(155\) 10.2771 0.825474
\(156\) −1.12359 + 3.45806i −0.0899594 + 0.276867i
\(157\) −4.18545 + 3.04091i −0.334035 + 0.242691i −0.742141 0.670244i \(-0.766190\pi\)
0.408106 + 0.912935i \(0.366190\pi\)
\(158\) 7.26603 + 5.27908i 0.578054 + 0.419981i
\(159\) −3.65891 11.2610i −0.290171 0.893054i
\(160\) −0.804188 2.47504i −0.0635766 0.195669i
\(161\) −3.09931 2.25178i −0.244260 0.177465i
\(162\) −5.86931 + 4.26431i −0.461137 + 0.335036i
\(163\) −0.370823 + 1.14128i −0.0290451 + 0.0893916i −0.964528 0.263980i \(-0.914965\pi\)
0.935483 + 0.353371i \(0.114965\pi\)
\(164\) −7.54804 −0.589403
\(165\) −12.6050 + 5.23925i −0.981295 + 0.407875i
\(166\) 16.2968 1.26488
\(167\) −2.41844 + 7.44320i −0.187145 + 0.575972i −0.999979 0.00652332i \(-0.997924\pi\)
0.812834 + 0.582495i \(0.197924\pi\)
\(168\) 1.98392 1.44140i 0.153063 0.111207i
\(169\) 6.24101 + 4.53436i 0.480077 + 0.348797i
\(170\) −0.170723 0.525432i −0.0130939 0.0402988i
\(171\) 0.154132 + 0.474370i 0.0117868 + 0.0362760i
\(172\) −4.73942 3.44339i −0.361377 0.262556i
\(173\) −3.97941 + 2.89121i −0.302549 + 0.219815i −0.728693 0.684841i \(-0.759872\pi\)
0.426144 + 0.904655i \(0.359872\pi\)
\(174\) −2.29060 + 7.04974i −0.173650 + 0.534439i
\(175\) −2.74841 −0.207760
\(176\) −3.22593 0.770298i −0.243164 0.0580634i
\(177\) −6.61589 −0.497280
\(178\) 1.10922 3.41383i 0.0831395 0.255877i
\(179\) −7.71402 + 5.60457i −0.576573 + 0.418905i −0.837487 0.546457i \(-0.815976\pi\)
0.260914 + 0.965362i \(0.415976\pi\)
\(180\) 1.05013 + 0.762965i 0.0782722 + 0.0568680i
\(181\) 5.97446 + 18.3875i 0.444078 + 1.36673i 0.883491 + 0.468447i \(0.155186\pi\)
−0.439413 + 0.898285i \(0.644814\pi\)
\(182\) 1.10160 + 3.39038i 0.0816560 + 0.251311i
\(183\) −16.6568 12.1019i −1.23131 0.894599i
\(184\) −1.99882 + 1.45223i −0.147355 + 0.107060i
\(185\) −2.13063 + 6.55741i −0.156647 + 0.482110i
\(186\) 6.24554 0.457945
\(187\) −0.684841 0.163529i −0.0500806 0.0119584i
\(188\) 12.4845 0.910525
\(189\) −2.65134 + 8.15999i −0.192857 + 0.593552i
\(190\) −2.10539 + 1.52966i −0.152741 + 0.110973i
\(191\) 1.69016 + 1.22798i 0.122296 + 0.0888533i 0.647252 0.762276i \(-0.275918\pi\)
−0.524956 + 0.851129i \(0.675918\pi\)
\(192\) −0.488718 1.50412i −0.0352702 0.108550i
\(193\) −2.33862 7.19752i −0.168337 0.518089i 0.830929 0.556378i \(-0.187809\pi\)
−0.999267 + 0.0382889i \(0.987809\pi\)
\(194\) −1.20492 0.875424i −0.0865081 0.0628518i
\(195\) 7.65525 5.56186i 0.548204 0.398293i
\(196\) −1.42016 + 4.37081i −0.101440 + 0.312201i
\(197\) 1.65699 0.118055 0.0590277 0.998256i \(-0.481200\pi\)
0.0590277 + 0.998256i \(0.481200\pi\)
\(198\) 1.52757 0.634935i 0.108560 0.0451229i
\(199\) −3.68327 −0.261100 −0.130550 0.991442i \(-0.541674\pi\)
−0.130550 + 0.991442i \(0.541674\pi\)
\(200\) −0.547738 + 1.68577i −0.0387309 + 0.119202i
\(201\) −11.4778 + 8.33908i −0.809579 + 0.588194i
\(202\) −2.03310 1.47713i −0.143049 0.103931i
\(203\) 2.24576 + 6.91175i 0.157622 + 0.485110i
\(204\) −0.103751 0.319313i −0.00726403 0.0223564i
\(205\) 15.8916 + 11.5459i 1.10992 + 0.806400i
\(206\) 5.47964 3.98119i 0.381784 0.277383i
\(207\) 0.380811 1.17202i 0.0264682 0.0814607i
\(208\) 2.29906 0.159411
\(209\) 0.264271 + 3.30608i 0.0182800 + 0.228686i
\(210\) −6.38177 −0.440384
\(211\) −0.645508 + 1.98667i −0.0444386 + 0.136768i −0.970814 0.239833i \(-0.922907\pi\)
0.926376 + 0.376601i \(0.122907\pi\)
\(212\) −6.05692 + 4.40061i −0.415991 + 0.302235i
\(213\) 8.72796 + 6.34123i 0.598030 + 0.434494i
\(214\) 4.05923 + 12.4930i 0.277483 + 0.854005i
\(215\) 4.71113 + 14.4994i 0.321296 + 0.988848i
\(216\) 4.47662 + 3.25246i 0.304595 + 0.221302i
\(217\) 4.95384 3.59918i 0.336289 0.244328i
\(218\) 0.842389 2.59261i 0.0570538 0.175593i
\(219\) 13.3676 0.903297
\(220\) 5.61356 + 6.55635i 0.378466 + 0.442029i
\(221\) 0.488074 0.0328314
\(222\) −1.29482 + 3.98504i −0.0869026 + 0.267459i
\(223\) −18.7493 + 13.6222i −1.25555 + 0.912209i −0.998530 0.0541981i \(-0.982740\pi\)
−0.257017 + 0.966407i \(0.582740\pi\)
\(224\) −1.25444 0.911401i −0.0838155 0.0608955i
\(225\) −0.273202 0.840829i −0.0182135 0.0560553i
\(226\) 2.73632 + 8.42152i 0.182017 + 0.560191i
\(227\) −7.45948 5.41963i −0.495103 0.359714i 0.312040 0.950069i \(-0.398988\pi\)
−0.807143 + 0.590355i \(0.798988\pi\)
\(228\) −1.27948 + 0.929596i −0.0847356 + 0.0615640i
\(229\) −5.03217 + 15.4874i −0.332535 + 1.02344i 0.635388 + 0.772193i \(0.280840\pi\)
−0.967923 + 0.251245i \(0.919160\pi\)
\(230\) 6.42971 0.423962
\(231\) −4.24110 + 6.93992i −0.279044 + 0.456613i
\(232\) 4.68696 0.307714
\(233\) −4.84624 + 14.9152i −0.317488 + 0.977128i 0.657230 + 0.753690i \(0.271728\pi\)
−0.974718 + 0.223438i \(0.928272\pi\)
\(234\) −0.927725 + 0.674032i −0.0606473 + 0.0440628i
\(235\) −26.2847 19.0970i −1.71463 1.24575i
\(236\) 1.29269 + 3.97849i 0.0841470 + 0.258978i
\(237\) −4.38932 13.5089i −0.285117 0.877501i
\(238\) −0.266307 0.193484i −0.0172621 0.0125417i
\(239\) 19.3770 14.0782i 1.25339 0.910644i 0.254981 0.966946i \(-0.417931\pi\)
0.998414 + 0.0563017i \(0.0179309\pi\)
\(240\) −1.27184 + 3.91433i −0.0820971 + 0.252669i
\(241\) −3.80838 −0.245320 −0.122660 0.992449i \(-0.539142\pi\)
−0.122660 + 0.992449i \(0.539142\pi\)
\(242\) 10.8603 1.74740i 0.698128 0.112327i
\(243\) −5.12647 −0.328863
\(244\) −4.02292 + 12.3813i −0.257541 + 0.792630i
\(245\) 9.67583 7.02990i 0.618166 0.449124i
\(246\) 9.65756 + 7.01663i 0.615743 + 0.447364i
\(247\) −0.710450 2.18654i −0.0452048 0.139126i
\(248\) −1.22033 3.75578i −0.0774909 0.238492i
\(249\) −20.8514 15.1494i −1.32141 0.960057i
\(250\) −6.79511 + 4.93694i −0.429761 + 0.312239i
\(251\) 1.43218 4.40778i 0.0903981 0.278217i −0.895629 0.444802i \(-0.853274\pi\)
0.986027 + 0.166585i \(0.0532741\pi\)
\(252\) 0.773395 0.0487193
\(253\) 4.27295 6.99204i 0.268638 0.439586i
\(254\) 9.25283 0.580574
\(255\) −0.270003 + 0.830983i −0.0169082 + 0.0520381i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 20.7952 + 15.1086i 1.29717 + 0.942449i 0.999924 0.0123525i \(-0.00393203\pi\)
0.297245 + 0.954801i \(0.403932\pi\)
\(258\) 2.86303 + 8.81149i 0.178244 + 0.548580i
\(259\) 1.26947 + 3.90704i 0.0788813 + 0.242772i
\(260\) −4.84043 3.51678i −0.300190 0.218101i
\(261\) −1.89130 + 1.37411i −0.117068 + 0.0850551i
\(262\) −3.74273 + 11.5189i −0.231227 + 0.711642i
\(263\) −21.8725 −1.34872 −0.674358 0.738405i \(-0.735579\pi\)
−0.674358 + 0.738405i \(0.735579\pi\)
\(264\) 3.41145 + 3.98440i 0.209960 + 0.245223i
\(265\) 19.4836 1.19687
\(266\) −0.479152 + 1.47468i −0.0293787 + 0.0904183i
\(267\) −4.59270 + 3.33680i −0.281069 + 0.204209i
\(268\) 7.25741 + 5.27281i 0.443317 + 0.322088i
\(269\) −6.36520 19.5901i −0.388093 1.19443i −0.934211 0.356720i \(-0.883895\pi\)
0.546118 0.837708i \(-0.316105\pi\)
\(270\) −4.44990 13.6954i −0.270812 0.833474i
\(271\) 17.9197 + 13.0194i 1.08854 + 0.790872i 0.979152 0.203127i \(-0.0651103\pi\)
0.109390 + 0.993999i \(0.465110\pi\)
\(272\) −0.171748 + 0.124782i −0.0104138 + 0.00756605i
\(273\) 1.74221 5.36196i 0.105443 0.324521i
\(274\) 9.74968 0.588999
\(275\) −0.468425 5.86009i −0.0282471 0.353376i
\(276\) 3.90744 0.235200
\(277\) −2.71751 + 8.36362i −0.163279 + 0.502521i −0.998905 0.0467770i \(-0.985105\pi\)
0.835626 + 0.549298i \(0.185105\pi\)
\(278\) 10.2880 7.47470i 0.617036 0.448303i
\(279\) 1.59354 + 1.15777i 0.0954026 + 0.0693141i
\(280\) 1.24695 + 3.83771i 0.0745193 + 0.229347i
\(281\) 5.28386 + 16.2621i 0.315209 + 0.970113i 0.975668 + 0.219252i \(0.0703615\pi\)
−0.660459 + 0.750862i \(0.729638\pi\)
\(282\) −15.9737 11.6055i −0.951217 0.691100i
\(283\) 19.4980 14.1661i 1.15904 0.842090i 0.169381 0.985551i \(-0.445823\pi\)
0.989656 + 0.143461i \(0.0458231\pi\)
\(284\) 2.10796 6.48762i 0.125084 0.384970i
\(285\) 4.11577 0.243797
\(286\) −7.04112 + 2.92664i −0.416350 + 0.173056i
\(287\) 11.7037 0.690850
\(288\) 0.154132 0.474370i 0.00908232 0.0279525i
\(289\) 13.7168 9.96586i 0.806872 0.586227i
\(290\) −9.86788 7.16943i −0.579462 0.421003i
\(291\) 0.727877 + 2.24018i 0.0426689 + 0.131321i
\(292\) −2.61192 8.03865i −0.152851 0.470426i
\(293\) 2.06559 + 1.50074i 0.120673 + 0.0876740i 0.646485 0.762927i \(-0.276238\pi\)
−0.525812 + 0.850601i \(0.676238\pi\)
\(294\) 5.88016 4.27218i 0.342938 0.249159i
\(295\) 3.36411 10.3537i 0.195866 0.602813i
\(296\) 2.64942 0.153994
\(297\) −17.8504 4.26237i −1.03579 0.247328i
\(298\) −13.5641 −0.785747
\(299\) −1.75529 + 5.40223i −0.101511 + 0.312419i
\(300\) 2.26790 1.64773i 0.130937 0.0951315i
\(301\) 7.34879 + 5.33921i 0.423577 + 0.307747i
\(302\) −3.35342 10.3208i −0.192968 0.593894i
\(303\) 1.22817 + 3.77993i 0.0705567 + 0.217151i
\(304\) 0.809017 + 0.587785i 0.0464003 + 0.0337118i
\(305\) 27.4089 19.9137i 1.56943 1.14026i
\(306\) 0.0327211 0.100705i 0.00187054 0.00575693i
\(307\) −18.9304 −1.08041 −0.540207 0.841532i \(-0.681654\pi\)
−0.540207 + 0.841532i \(0.681654\pi\)
\(308\) 5.00203 + 1.19440i 0.285017 + 0.0680572i
\(309\) −10.7120 −0.609383
\(310\) −3.17579 + 9.77407i −0.180373 + 0.555130i
\(311\) −13.6085 + 9.88713i −0.771666 + 0.560648i −0.902466 0.430761i \(-0.858245\pi\)
0.130801 + 0.991409i \(0.458245\pi\)
\(312\) −2.94160 2.13720i −0.166536 0.120995i
\(313\) −7.62692 23.4733i −0.431099 1.32679i −0.897032 0.441966i \(-0.854281\pi\)
0.465932 0.884820i \(-0.345719\pi\)
\(314\) −1.59870 4.92029i −0.0902199 0.277668i
\(315\) −1.62830 1.18303i −0.0917443 0.0666561i
\(316\) −7.26603 + 5.27908i −0.408746 + 0.296971i
\(317\) 7.24916 22.3106i 0.407154 1.25309i −0.511930 0.859027i \(-0.671069\pi\)
0.919084 0.394063i \(-0.128931\pi\)
\(318\) 11.8405 0.663982
\(319\) −14.3543 + 5.96636i −0.803686 + 0.334052i
\(320\) 2.60241 0.145479
\(321\) 6.41976 19.7580i 0.358316 1.10278i
\(322\) 3.09931 2.25178i 0.172718 0.125487i
\(323\) 0.171748 + 0.124782i 0.00955633 + 0.00694308i
\(324\) −2.24188 6.89979i −0.124549 0.383322i
\(325\) 1.25928 + 3.87568i 0.0698525 + 0.214984i
\(326\) −0.970827 0.705347i −0.0537691 0.0390655i
\(327\) −3.48790 + 2.53411i −0.192881 + 0.140136i
\(328\) 2.33247 7.17861i 0.128789 0.396372i
\(329\) −19.3580 −1.06724
\(330\) −1.08768 13.6071i −0.0598747 0.749044i
\(331\) 16.6549 0.915436 0.457718 0.889097i \(-0.348667\pi\)
0.457718 + 0.889097i \(0.348667\pi\)
\(332\) −5.03599 + 15.4992i −0.276386 + 0.850628i
\(333\) −1.06910 + 0.776748i −0.0585865 + 0.0425656i
\(334\) −6.33156 4.60015i −0.346448 0.251709i
\(335\) −7.21409 22.2027i −0.394148 1.21306i
\(336\) 0.757790 + 2.33224i 0.0413408 + 0.127234i
\(337\) 18.1247 + 13.1684i 0.987317 + 0.717328i 0.959332 0.282281i \(-0.0910909\pi\)
0.0279850 + 0.999608i \(0.491091\pi\)
\(338\) −6.24101 + 4.53436i −0.339466 + 0.246637i
\(339\) 4.32755 13.3188i 0.235040 0.723380i
\(340\) 0.552471 0.0299620
\(341\) 8.51838 + 9.94903i 0.461296 + 0.538770i
\(342\) −0.498782 −0.0269710
\(343\) 5.55612 17.1000i 0.300002 0.923312i
\(344\) 4.73942 3.44339i 0.255532 0.185655i
\(345\) −8.22668 5.97703i −0.442910 0.321793i
\(346\) −1.52000 4.67808i −0.0817157 0.251495i
\(347\) −3.11524 9.58771i −0.167235 0.514695i 0.831959 0.554837i \(-0.187219\pi\)
−0.999194 + 0.0401412i \(0.987219\pi\)
\(348\) −5.99687 4.35698i −0.321466 0.233559i
\(349\) −20.7205 + 15.0543i −1.10914 + 0.805839i −0.982528 0.186113i \(-0.940411\pi\)
−0.126614 + 0.991952i \(0.540411\pi\)
\(350\) 0.849305 2.61389i 0.0453973 0.139718i
\(351\) 12.7217 0.679032
\(352\) 1.72947 2.83001i 0.0921808 0.150840i
\(353\) −6.10891 −0.325144 −0.162572 0.986697i \(-0.551979\pi\)
−0.162572 + 0.986697i \(0.551979\pi\)
\(354\) 2.04442 6.29208i 0.108660 0.334420i
\(355\) −14.3619 + 10.4345i −0.762251 + 0.553808i
\(356\) 2.90397 + 2.10986i 0.153910 + 0.111822i
\(357\) 0.160873 + 0.495117i 0.00851431 + 0.0262043i
\(358\) −2.94650 9.06838i −0.155727 0.479279i
\(359\) 20.8917 + 15.1787i 1.10262 + 0.801102i 0.981486 0.191534i \(-0.0613463\pi\)
0.121136 + 0.992636i \(0.461346\pi\)
\(360\) −1.05013 + 0.762965i −0.0553468 + 0.0402118i
\(361\) 0.309017 0.951057i 0.0162641 0.0500556i
\(362\) −19.3338 −1.01616
\(363\) −15.5199 7.85995i −0.814586 0.412541i
\(364\) −3.56485 −0.186849
\(365\) −6.79727 + 20.9198i −0.355785 + 1.09499i
\(366\) 16.6568 12.1019i 0.870667 0.632577i
\(367\) 19.7237 + 14.3301i 1.02957 + 0.748026i 0.968223 0.250090i \(-0.0804602\pi\)
0.0613474 + 0.998116i \(0.480460\pi\)
\(368\) −0.763482 2.34975i −0.0397992 0.122489i
\(369\) 1.16339 + 3.58056i 0.0605639 + 0.186397i
\(370\) −5.57807 4.05270i −0.289990 0.210690i
\(371\) 9.39166 6.82344i 0.487591 0.354255i
\(372\) −1.92998 + 5.93986i −0.100065 + 0.307967i
\(373\) 4.33069 0.224234 0.112117 0.993695i \(-0.464237\pi\)
0.112117 + 0.993695i \(0.464237\pi\)
\(374\) 0.367153 0.600790i 0.0189850 0.0310661i
\(375\) 13.2836 0.685960
\(376\) −3.85792 + 11.8735i −0.198957 + 0.612327i
\(377\) 8.71765 6.33374i 0.448982 0.326204i
\(378\) −6.94130 5.04315i −0.357022 0.259392i
\(379\) −0.762790 2.34763i −0.0391819 0.120589i 0.929552 0.368690i \(-0.120194\pi\)
−0.968734 + 0.248101i \(0.920194\pi\)
\(380\) −0.804188 2.47504i −0.0412540 0.126967i
\(381\) −11.8388 8.60140i −0.606521 0.440663i
\(382\) −1.69016 + 1.22798i −0.0864764 + 0.0628287i
\(383\) −6.62480 + 20.3890i −0.338512 + 1.04183i 0.626455 + 0.779458i \(0.284505\pi\)
−0.964966 + 0.262374i \(0.915495\pi\)
\(384\) 1.58152 0.0807068
\(385\) −8.70420 10.1661i −0.443607 0.518110i
\(386\) 7.56792 0.385197
\(387\) −0.902943 + 2.77897i −0.0458992 + 0.141263i
\(388\) 1.20492 0.875424i 0.0611705 0.0444429i
\(389\) 4.77449 + 3.46887i 0.242076 + 0.175879i 0.702208 0.711972i \(-0.252198\pi\)
−0.460132 + 0.887851i \(0.652198\pi\)
\(390\) 2.92405 + 8.99929i 0.148065 + 0.455697i
\(391\) −0.162081 0.498835i −0.00819681 0.0252272i
\(392\) −3.71803 2.70131i −0.187789 0.136437i
\(393\) 15.4967 11.2590i 0.781705 0.567942i
\(394\) −0.512037 + 1.57589i −0.0257961 + 0.0793921i
\(395\) 23.3730 1.17602
\(396\) 0.131814 + 1.64901i 0.00662388 + 0.0828660i
\(397\) 11.4881 0.576571 0.288286 0.957544i \(-0.406915\pi\)
0.288286 + 0.957544i \(0.406915\pi\)
\(398\) 1.13819 3.50300i 0.0570525 0.175589i
\(399\) 1.98392 1.44140i 0.0993202 0.0721603i
\(400\) −1.43400 1.04186i −0.0716999 0.0520930i
\(401\) 8.68180 + 26.7198i 0.433549 + 1.33433i 0.894567 + 0.446935i \(0.147484\pi\)
−0.461018 + 0.887391i \(0.652516\pi\)
\(402\) −4.38412 13.4929i −0.218660 0.672966i
\(403\) −7.34518 5.33659i −0.365889 0.265834i
\(404\) 2.03310 1.47713i 0.101151 0.0734902i
\(405\) −5.83428 + 17.9561i −0.289908 + 0.892244i
\(406\) −7.26744 −0.360677
\(407\) −8.11413 + 3.37264i −0.402202 + 0.167175i
\(408\) 0.335746 0.0166219
\(409\) 9.44920 29.0816i 0.467233 1.43799i −0.388920 0.921272i \(-0.627152\pi\)
0.856153 0.516723i \(-0.172848\pi\)
\(410\) −15.8916 + 11.5459i −0.784828 + 0.570211i
\(411\) −12.4745 9.06326i −0.615322 0.447058i
\(412\) 2.09303 + 6.44170i 0.103116 + 0.317360i
\(413\) −2.00440 6.16892i −0.0986303 0.303553i
\(414\) 0.996976 + 0.724345i 0.0489987 + 0.0355996i
\(415\) 34.3111 24.9285i 1.68427 1.22369i
\(416\) −0.710450 + 2.18654i −0.0348327 + 0.107204i
\(417\) −20.1118 −0.984879
\(418\) −3.22593 0.770298i −0.157786 0.0376765i
\(419\) −29.3802 −1.43532 −0.717658 0.696395i \(-0.754786\pi\)
−0.717658 + 0.696395i \(0.754786\pi\)
\(420\) 1.97208 6.06943i 0.0962275 0.296158i
\(421\) 10.6786 7.75846i 0.520444 0.378124i −0.296327 0.955086i \(-0.595762\pi\)
0.816771 + 0.576962i \(0.195762\pi\)
\(422\) −1.68996 1.22783i −0.0822660 0.0597698i
\(423\) −1.92426 5.92227i −0.0935608 0.287950i
\(424\) −2.31354 7.12033i −0.112355 0.345794i
\(425\) −0.304427 0.221179i −0.0147669 0.0107288i
\(426\) −8.72796 + 6.34123i −0.422871 + 0.307234i
\(427\) 6.23781 19.1980i 0.301869 0.929057i
\(428\) −13.1359 −0.634949
\(429\) 11.7296 + 2.80082i 0.566309 + 0.135225i
\(430\) −15.2455 −0.735205
\(431\) −10.4157 + 32.0562i −0.501706 + 1.54409i 0.304532 + 0.952502i \(0.401500\pi\)
−0.806238 + 0.591591i \(0.798500\pi\)
\(432\) −4.47662 + 3.25246i −0.215382 + 0.156484i
\(433\) 29.3735 + 21.3411i 1.41160 + 1.02559i 0.993088 + 0.117374i \(0.0374477\pi\)
0.418510 + 0.908212i \(0.362552\pi\)
\(434\) 1.89220 + 5.82359i 0.0908285 + 0.279541i
\(435\) 5.96107 + 18.3463i 0.285811 + 0.879637i
\(436\) 2.20540 + 1.60232i 0.105620 + 0.0767371i
\(437\) −1.99882 + 1.45223i −0.0956166 + 0.0694695i
\(438\) −4.13081 + 12.7133i −0.197378 + 0.607466i
\(439\) −15.5926 −0.744196 −0.372098 0.928194i \(-0.621361\pi\)
−0.372098 + 0.928194i \(0.621361\pi\)
\(440\) −7.97014 + 3.31279i −0.379962 + 0.157931i
\(441\) 2.29227 0.109156
\(442\) −0.150823 + 0.464186i −0.00717392 + 0.0220791i
\(443\) 5.79119 4.20755i 0.275148 0.199907i −0.441650 0.897187i \(-0.645607\pi\)
0.716798 + 0.697281i \(0.245607\pi\)
\(444\) −3.38988 2.46289i −0.160877 0.116884i
\(445\) −2.88664 8.88416i −0.136840 0.421150i
\(446\) −7.16160 22.0412i −0.339112 1.04368i
\(447\) 17.3550 + 12.6091i 0.820863 + 0.596392i
\(448\) 1.25444 0.911401i 0.0592665 0.0430596i
\(449\) 4.49288 13.8277i 0.212032 0.652567i −0.787319 0.616546i \(-0.788532\pi\)
0.999351 0.0360215i \(-0.0114685\pi\)
\(450\) 0.884100 0.0416769
\(451\) 1.99473 + 24.9544i 0.0939280 + 1.17506i
\(452\) −8.85491 −0.416500
\(453\) −5.30352 + 16.3225i −0.249181 + 0.766900i
\(454\) 7.45948 5.41963i 0.350091 0.254356i
\(455\) 7.50541 + 5.45300i 0.351859 + 0.255640i
\(456\) −0.488718 1.50412i −0.0228863 0.0704368i
\(457\) −0.893475 2.74983i −0.0417950 0.128632i 0.927982 0.372626i \(-0.121542\pi\)
−0.969777 + 0.243994i \(0.921542\pi\)
\(458\) −13.1744 9.57176i −0.615599 0.447259i
\(459\) −0.950353 + 0.690472i −0.0443587 + 0.0322285i
\(460\) −1.98689 + 6.11502i −0.0926392 + 0.285114i
\(461\) −22.8907 −1.06612 −0.533062 0.846076i \(-0.678959\pi\)
−0.533062 + 0.846076i \(0.678959\pi\)
\(462\) −5.28968 6.17807i −0.246098 0.287430i
\(463\) −39.1694 −1.82036 −0.910178 0.414218i \(-0.864055\pi\)
−0.910178 + 0.414218i \(0.864055\pi\)
\(464\) −1.44835 + 4.45756i −0.0672379 + 0.206937i
\(465\) 13.1493 9.55352i 0.609784 0.443034i
\(466\) −12.6876 9.21810i −0.587743 0.427020i
\(467\) −8.56679 26.3659i −0.396424 1.22007i −0.927847 0.372960i \(-0.878343\pi\)
0.531424 0.847106i \(-0.321657\pi\)
\(468\) −0.354359 1.09061i −0.0163803 0.0504133i
\(469\) −11.2531 8.17585i −0.519620 0.377526i
\(470\) 26.2847 19.0970i 1.21242 0.880878i
\(471\) −2.52838 + 7.78156i −0.116502 + 0.358555i
\(472\) −4.18323 −0.192549
\(473\) −10.1316 + 16.5789i −0.465853 + 0.762298i
\(474\) 14.2041 0.652418
\(475\) −0.547738 + 1.68577i −0.0251320 + 0.0773482i
\(476\) 0.266307 0.193484i 0.0122062 0.00886830i
\(477\) 3.02108 + 2.19494i 0.138326 + 0.100500i
\(478\) 7.40136 + 22.7790i 0.338530 + 1.04189i
\(479\) 5.20943 + 16.0330i 0.238025 + 0.732565i 0.996706 + 0.0811029i \(0.0258442\pi\)
−0.758681 + 0.651463i \(0.774156\pi\)
\(480\) −3.32973 2.41919i −0.151981 0.110420i
\(481\) 4.92787 3.58031i 0.224692 0.163248i
\(482\) 1.17686 3.62199i 0.0536043 0.164977i
\(483\) −6.05874 −0.275682
\(484\) −1.69415 + 10.8688i −0.0770067 + 0.494034i
\(485\) −3.87592 −0.175997
\(486\) 1.58417 4.87556i 0.0718593 0.221160i
\(487\) 22.2862 16.1918i 1.00988 0.733723i 0.0456980 0.998955i \(-0.485449\pi\)
0.964184 + 0.265233i \(0.0854488\pi\)
\(488\) −10.5321 7.65205i −0.476768 0.346392i
\(489\) 0.586465 + 1.80495i 0.0265209 + 0.0816228i
\(490\) 3.69584 + 11.3746i 0.166961 + 0.513853i
\(491\) −16.2475 11.8045i −0.733239 0.532729i 0.157347 0.987543i \(-0.449706\pi\)
−0.890587 + 0.454814i \(0.849706\pi\)
\(492\) −9.65756 + 7.01663i −0.435396 + 0.316334i
\(493\) −0.307474 + 0.946307i −0.0138479 + 0.0426195i
\(494\) 2.29906 0.103440
\(495\) 2.24490 3.67345i 0.100901 0.165109i
\(496\) 3.94906 0.177318
\(497\) −3.26853 + 10.0595i −0.146614 + 0.451230i
\(498\) 20.8514 15.1494i 0.934375 0.678863i
\(499\) 13.4352 + 9.76122i 0.601441 + 0.436972i 0.846390 0.532564i \(-0.178771\pi\)
−0.244949 + 0.969536i \(0.578771\pi\)
\(500\) −2.59550 7.98813i −0.116074 0.357240i
\(501\) 3.82482 + 11.7716i 0.170881 + 0.525916i
\(502\) 3.74948 + 2.72416i 0.167348 + 0.121585i
\(503\) −18.5466 + 13.4749i −0.826954 + 0.600817i −0.918696 0.394966i \(-0.870757\pi\)
0.0917419 + 0.995783i \(0.470757\pi\)
\(504\) −0.238992 + 0.735542i −0.0106456 + 0.0327637i
\(505\) −6.53998 −0.291025
\(506\) 5.32941 + 6.22448i 0.236921 + 0.276712i
\(507\) 12.2004 0.541837
\(508\) −2.85928 + 8.79997i −0.126860 + 0.390435i
\(509\) 28.8493 20.9603i 1.27872 0.929048i 0.279211 0.960230i \(-0.409927\pi\)
0.999514 + 0.0311824i \(0.00992727\pi\)
\(510\) −0.706876 0.513575i −0.0313010 0.0227415i
\(511\) 4.04995 + 12.4645i 0.179159 + 0.551396i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) 4.47662 + 3.25246i 0.197648 + 0.143599i
\(514\) −20.7952 + 15.1086i −0.917237 + 0.666412i
\(515\) 5.44693 16.7639i 0.240020 0.738706i
\(516\) −9.26495 −0.407867
\(517\) −3.29929 41.2747i −0.145102 1.81526i
\(518\) −4.10810 −0.180500
\(519\) −2.40392 + 7.39849i −0.105520 + 0.324758i
\(520\) 4.84043 3.51678i 0.212267 0.154221i
\(521\) −13.2413 9.62034i −0.580110 0.421475i 0.258653 0.965970i \(-0.416721\pi\)
−0.838764 + 0.544495i \(0.816721\pi\)
\(522\) −0.722411 2.22335i −0.0316191 0.0973134i
\(523\) −10.9362 33.6580i −0.478205 1.47176i −0.841586 0.540123i \(-0.818378\pi\)
0.363381 0.931640i \(-0.381622\pi\)
\(524\) −9.79859 7.11909i −0.428053 0.310999i
\(525\) −3.51653 + 2.55491i −0.153474 + 0.111505i
\(526\) 6.75897 20.8020i 0.294705 0.907009i
\(527\) 0.838356 0.0365194
\(528\) −4.84358 + 2.01323i −0.210790 + 0.0876148i
\(529\) −16.8957 −0.734598
\(530\) −6.02076 + 18.5300i −0.261525 + 0.804892i
\(531\) 1.68803 1.22643i 0.0732543 0.0532224i
\(532\) −1.25444 0.911401i −0.0543867 0.0395142i
\(533\) −5.36250 16.5041i −0.232276 0.714871i
\(534\) −1.75426 5.39905i −0.0759141 0.233640i
\(535\) 27.6563 + 20.0935i 1.19568 + 0.868716i
\(536\) −7.25741 + 5.27281i −0.313472 + 0.227751i
\(537\) −4.65995 + 14.3419i −0.201092 + 0.618897i
\(538\) 20.5982 0.888053
\(539\) 14.8256 + 3.54009i 0.638582 + 0.152483i
\(540\) 14.4002 0.619685
\(541\) 11.3076 34.8012i 0.486151 1.49622i −0.344156 0.938913i \(-0.611835\pi\)
0.830307 0.557307i \(-0.188165\pi\)
\(542\) −17.9197 + 13.0194i −0.769716 + 0.559231i
\(543\) 24.7372 + 17.9726i 1.06157 + 0.771278i
\(544\) −0.0656020 0.201902i −0.00281266 0.00865649i
\(545\) −2.19224 6.74701i −0.0939051 0.289010i
\(546\) 4.56116 + 3.31387i 0.195199 + 0.141821i
\(547\) −11.5303 + 8.37727i −0.493001 + 0.358186i −0.806337 0.591456i \(-0.798553\pi\)
0.313336 + 0.949642i \(0.398553\pi\)
\(548\) −3.01282 + 9.27249i −0.128701 + 0.396101i
\(549\) 6.49337 0.277130
\(550\) 5.71802 + 1.36537i 0.243817 + 0.0582195i
\(551\) 4.68696 0.199671
\(552\) −1.20746 + 3.71619i −0.0513931 + 0.158172i
\(553\) 11.2665 8.18557i 0.479099 0.348086i
\(554\) −7.11452 5.16900i −0.302267 0.219610i
\(555\) 3.36964 + 10.3707i 0.143033 + 0.440212i
\(556\) 3.92968 + 12.0943i 0.166656 + 0.512913i
\(557\) −26.5043 19.2565i −1.12302 0.815924i −0.138359 0.990382i \(-0.544183\pi\)
−0.984665 + 0.174458i \(0.944183\pi\)
\(558\) −1.59354 + 1.15777i −0.0674598 + 0.0490124i
\(559\) 4.16199 12.8093i 0.176033 0.541775i
\(560\) −4.03521 −0.170519
\(561\) −1.02826 + 0.427395i −0.0434130 + 0.0180446i
\(562\) −17.0989 −0.721275
\(563\) 3.11500 9.58698i 0.131282 0.404043i −0.863712 0.503986i \(-0.831866\pi\)
0.994993 + 0.0999433i \(0.0318661\pi\)
\(564\) 15.9737 11.6055i 0.672612 0.488681i
\(565\) 18.6430 + 13.5450i 0.784319 + 0.569841i
\(566\) 7.44758 + 22.9213i 0.313045 + 0.963454i
\(567\) 3.47618 + 10.6986i 0.145986 + 0.449299i
\(568\) 5.51870 + 4.00957i 0.231560 + 0.168238i
\(569\) −33.0609 + 24.0201i −1.38598 + 1.00698i −0.389692 + 0.920945i \(0.627418\pi\)
−0.996292 + 0.0860311i \(0.972582\pi\)
\(570\) −1.27184 + 3.91433i −0.0532716 + 0.163953i
\(571\) −28.0002 −1.17177 −0.585886 0.810393i \(-0.699253\pi\)
−0.585886 + 0.810393i \(0.699253\pi\)
\(572\) −0.607575 7.60088i −0.0254040 0.317809i
\(573\) 3.30405 0.138029
\(574\) −3.61665 + 11.1309i −0.150956 + 0.464595i
\(575\) 3.54295 2.57410i 0.147751 0.107347i
\(576\) 0.403523 + 0.293177i 0.0168135 + 0.0122157i
\(577\) −8.73832 26.8938i −0.363781 1.11960i −0.950741 0.309987i \(-0.899675\pi\)
0.586960 0.809616i \(-0.300325\pi\)
\(578\) 5.23936 + 16.1251i 0.217929 + 0.670716i
\(579\) −9.68300 7.03511i −0.402412 0.292369i
\(580\) 9.86788 7.16943i 0.409741 0.297694i
\(581\) 7.80864 24.0325i 0.323957 0.997037i
\(582\) −2.35546 −0.0976370
\(583\) 16.1494 + 18.8617i 0.668841 + 0.781172i
\(584\) 8.45234 0.349760
\(585\) −0.922187 + 2.83820i −0.0381278 + 0.117345i
\(586\) −2.06559 + 1.50074i −0.0853286 + 0.0619949i
\(587\) 10.3272 + 7.50317i 0.426250 + 0.309689i 0.780148 0.625595i \(-0.215144\pi\)
−0.353897 + 0.935284i \(0.615144\pi\)
\(588\) 2.24602 + 6.91254i 0.0926243 + 0.285068i
\(589\) −1.22033 3.75578i −0.0502827 0.154754i
\(590\) 8.80734 + 6.39891i 0.362593 + 0.263439i
\(591\) 2.12008 1.54033i 0.0872085 0.0633607i
\(592\) −0.818716 + 2.51975i −0.0336490 + 0.103561i
\(593\) −25.1426 −1.03248 −0.516242 0.856443i \(-0.672669\pi\)
−0.516242 + 0.856443i \(0.672669\pi\)
\(594\) 9.56984 15.6596i 0.392655 0.642521i
\(595\) −0.856644 −0.0351190
\(596\) 4.19154 12.9002i 0.171692 0.528414i
\(597\) −4.71267 + 3.42395i −0.192877 + 0.140133i
\(598\) −4.59541 3.33876i −0.187920 0.136532i
\(599\) 14.6543 + 45.1012i 0.598757 + 1.84278i 0.535060 + 0.844814i \(0.320289\pi\)
0.0636963 + 0.997969i \(0.479711\pi\)
\(600\) 0.866261 + 2.66608i 0.0353650 + 0.108842i
\(601\) 19.2860 + 14.0121i 0.786692 + 0.571565i 0.906980 0.421174i \(-0.138382\pi\)
−0.120288 + 0.992739i \(0.538382\pi\)
\(602\) −7.34879 + 5.33921i −0.299514 + 0.217610i
\(603\) 1.38267 4.25541i 0.0563065 0.173294i
\(604\) 10.8519 0.441557
\(605\) 20.1923 20.2915i 0.820934 0.824968i
\(606\) −3.97445 −0.161451
\(607\) −0.906405 + 2.78963i −0.0367899 + 0.113228i −0.967765 0.251855i \(-0.918959\pi\)
0.930975 + 0.365083i \(0.118959\pi\)
\(608\) −0.809017 + 0.587785i −0.0328100 + 0.0238378i
\(609\) 9.29854 + 6.75579i 0.376796 + 0.273758i
\(610\) 10.4693 + 32.2211i 0.423889 + 1.30460i
\(611\) 8.86960 + 27.2978i 0.358826 + 1.10435i
\(612\) 0.0856650 + 0.0622392i 0.00346280 + 0.00251587i
\(613\) −4.94153 + 3.59023i −0.199587 + 0.145008i −0.683090 0.730335i \(-0.739364\pi\)
0.483503 + 0.875343i \(0.339364\pi\)
\(614\) 5.84982 18.0039i 0.236079 0.726577i
\(615\) 31.0660 1.25270
\(616\) −2.68165 + 4.38812i −0.108047 + 0.176802i
\(617\) −21.6728 −0.872513 −0.436257 0.899822i \(-0.643696\pi\)
−0.436257 + 0.899822i \(0.643696\pi\)
\(618\) 3.31018 10.1877i 0.133155 0.409809i
\(619\) −6.57355 + 4.77596i −0.264213 + 0.191962i −0.712002 0.702177i \(-0.752212\pi\)
0.447789 + 0.894139i \(0.352212\pi\)
\(620\) −8.31432 6.04071i −0.333911 0.242601i
\(621\) −4.22465 13.0022i −0.169530 0.521758i
\(622\) −5.19797 15.9977i −0.208420 0.641450i
\(623\) −4.50281 3.27148i −0.180401 0.131069i
\(624\) 2.94160 2.13720i 0.117758 0.0855565i
\(625\) −9.49324 + 29.2172i −0.379730 + 1.16869i
\(626\) 24.6812 0.986461
\(627\) 3.41145 + 3.98440i 0.136240 + 0.159121i
\(628\) 5.17350 0.206445
\(629\) −0.173807 + 0.534924i −0.00693015 + 0.0213288i
\(630\) 1.62830 1.18303i 0.0648730 0.0471330i
\(631\) 35.0530 + 25.4675i 1.39544 + 1.01384i 0.995244 + 0.0974129i \(0.0310567\pi\)
0.400192 + 0.916431i \(0.368943\pi\)
\(632\) −2.77538 8.54173i −0.110399 0.339772i
\(633\) 1.02089 + 3.14196i 0.0405766 + 0.124882i
\(634\) 18.9786 + 13.7887i 0.753735 + 0.547620i
\(635\) 19.4808 14.1536i 0.773073 0.561670i
\(636\) −3.65891 + 11.2610i −0.145085 + 0.446527i
\(637\) −10.5659 −0.418636
\(638\) −1.23863 15.4954i −0.0490377 0.613471i
\(639\) −3.40244 −0.134598
\(640\) −0.804188 + 2.47504i −0.0317883 + 0.0978344i
\(641\) −29.8500 + 21.6873i −1.17900 + 0.856597i −0.992059 0.125774i \(-0.959859\pi\)
−0.186945 + 0.982370i \(0.559859\pi\)
\(642\) 16.8072 + 12.2111i 0.663325 + 0.481934i
\(643\) 8.23856 + 25.3557i 0.324897 + 0.999930i 0.971487 + 0.237092i \(0.0761944\pi\)
−0.646590 + 0.762838i \(0.723806\pi\)
\(644\) 1.18383 + 3.64345i 0.0466494 + 0.143572i
\(645\) 19.5063 + 14.1722i 0.768062 + 0.558029i
\(646\) −0.171748 + 0.124782i −0.00675735 + 0.00490950i
\(647\) 4.54738 13.9954i 0.178776 0.550216i −0.821010 0.570914i \(-0.806589\pi\)
0.999786 + 0.0206984i \(0.00658898\pi\)
\(648\) 7.25487 0.284998
\(649\) 12.8116 5.32514i 0.502899 0.209030i
\(650\) −4.07513 −0.159840
\(651\) 2.99256 9.21015i 0.117288 0.360974i
\(652\) 0.970827 0.705347i 0.0380205 0.0276235i
\(653\) −29.4101 21.3677i −1.15091 0.836183i −0.162305 0.986741i \(-0.551893\pi\)
−0.988601 + 0.150558i \(0.951893\pi\)
\(654\) −1.33226 4.10027i −0.0520954 0.160333i
\(655\) 9.74010 + 29.9769i 0.380577 + 1.17130i
\(656\) 6.10649 + 4.43662i 0.238418 + 0.173221i
\(657\) −3.41071 + 2.47803i −0.133065 + 0.0966771i
\(658\) 5.98196 18.4106i 0.233201 0.717720i
\(659\) 12.1432 0.473030 0.236515 0.971628i \(-0.423995\pi\)
0.236515 + 0.971628i \(0.423995\pi\)
\(660\) 13.2772 + 3.17037i 0.516814 + 0.123406i
\(661\) −6.74774 −0.262457 −0.131228 0.991352i \(-0.541892\pi\)
−0.131228 + 0.991352i \(0.541892\pi\)
\(662\) −5.14665 + 15.8397i −0.200030 + 0.615629i
\(663\) 0.624481 0.453712i 0.0242528 0.0176207i
\(664\) −13.1844 9.57902i −0.511654 0.371738i
\(665\) 1.24695 + 3.83771i 0.0483545 + 0.148820i
\(666\) −0.408361 1.25681i −0.0158237 0.0487002i
\(667\) −9.36839 6.80653i −0.362745 0.263550i
\(668\) 6.33156 4.60015i 0.244976 0.177985i
\(669\) −11.3262 + 34.8586i −0.437898 + 1.34771i
\(670\) 23.3453 0.901907
\(671\) 41.9966 + 10.0281i 1.62126 + 0.387130i
\(672\) −2.45226 −0.0945980
\(673\) −2.72016 + 8.37178i −0.104854 + 0.322709i −0.989696 0.143183i \(-0.954266\pi\)
0.884842 + 0.465891i \(0.154266\pi\)
\(674\) −18.1247 + 13.1684i −0.698138 + 0.507227i
\(675\) −7.93489 5.76504i −0.305414 0.221896i
\(676\) −2.38385 7.33674i −0.0916866 0.282182i
\(677\) −1.97991 6.09352i −0.0760939 0.234193i 0.905773 0.423762i \(-0.139291\pi\)
−0.981867 + 0.189569i \(0.939291\pi\)
\(678\) 11.3297 + 8.23149i 0.435114 + 0.316129i
\(679\) −1.86831 + 1.35740i −0.0716990 + 0.0520924i
\(680\) −0.170723 + 0.525432i −0.00654693 + 0.0201494i
\(681\) −14.5823 −0.558796
\(682\) −12.0944 + 5.02704i −0.463119 + 0.192495i
\(683\) −33.6400 −1.28720 −0.643600 0.765362i \(-0.722560\pi\)
−0.643600 + 0.765362i \(0.722560\pi\)
\(684\) 0.154132 0.474370i 0.00589339 0.0181380i
\(685\) 20.5269 14.9137i 0.784292 0.569821i
\(686\) 14.5461 + 10.5684i 0.555373 + 0.403502i
\(687\) 7.95850 + 24.4937i 0.303636 + 0.934494i
\(688\) 1.81030 + 5.57152i 0.0690169 + 0.212412i
\(689\) −13.9252 10.1173i −0.530509 0.385437i
\(690\) 8.22668 5.97703i 0.313184 0.227542i
\(691\) −7.28286 + 22.4143i −0.277053 + 0.852682i 0.711616 + 0.702569i \(0.247964\pi\)
−0.988669 + 0.150113i \(0.952036\pi\)
\(692\) 4.91882 0.186986
\(693\) −0.204386 2.55691i −0.00776397 0.0971288i
\(694\) 10.0811 0.382674
\(695\) 10.2266 31.4743i 0.387918 1.19389i
\(696\) 5.99687 4.35698i 0.227311 0.165151i
\(697\) 1.29636 + 0.941862i 0.0491032 + 0.0356756i
\(698\) −7.91453 24.3584i −0.299569 0.921979i
\(699\) 7.66445 + 23.5888i 0.289896 + 0.892209i
\(700\) 2.22351 + 1.61547i 0.0840408 + 0.0610592i
\(701\) −39.5136 + 28.7083i −1.49241 + 1.08430i −0.519120 + 0.854701i \(0.673740\pi\)
−0.973286 + 0.229596i \(0.926260\pi\)
\(702\) −3.93121 + 12.0990i −0.148374 + 0.456648i
\(703\) 2.64942 0.0999248
\(704\) 2.15706 + 2.51934i 0.0812974 + 0.0949512i
\(705\) −51.3833 −1.93521
\(706\) 1.88776 5.80992i 0.0710467 0.218659i
\(707\) −3.15246 + 2.29040i −0.118560 + 0.0861392i
\(708\) 5.35236 + 3.88872i 0.201154 + 0.146147i
\(709\) 1.40048 + 4.31022i 0.0525960 + 0.161874i 0.973904 0.226959i \(-0.0728783\pi\)
−0.921308 + 0.388833i \(0.872878\pi\)
\(710\) −5.48576 16.8834i −0.205877 0.633624i
\(711\) 3.62416 + 2.63311i 0.135917 + 0.0987493i
\(712\) −2.90397 + 2.10986i −0.108831 + 0.0790704i
\(713\) −3.01504 + 9.27933i −0.112914 + 0.347513i
\(714\) −0.520596 −0.0194828
\(715\) −10.3476 + 16.9322i −0.386977 + 0.633229i
\(716\) 9.53506 0.356342
\(717\) 11.7054 36.0256i 0.437147 1.34540i
\(718\) −20.8917 + 15.1787i −0.779671 + 0.566464i
\(719\) −33.9454 24.6628i −1.26595 0.919766i −0.266916 0.963720i \(-0.586005\pi\)
−0.999034 + 0.0439532i \(0.986005\pi\)
\(720\) −0.401114 1.23450i −0.0149487 0.0460072i
\(721\) −3.24539 9.98829i −0.120865 0.371983i
\(722\) 0.809017 + 0.587785i 0.0301085 + 0.0218751i
\(723\) −4.87275 + 3.54026i −0.181220 + 0.131664i
\(724\) 5.97446 18.3875i 0.222039 0.683366i
\(725\) −8.30772 −0.308541
\(726\) 12.2712 12.3315i 0.455426 0.457664i
\(727\) −25.2797 −0.937572 −0.468786 0.883312i \(-0.655308\pi\)
−0.468786 + 0.883312i \(0.655308\pi\)
\(728\) 1.10160 3.39038i 0.0408280 0.125656i
\(729\) −24.1672 + 17.5585i −0.895080 + 0.650314i
\(730\) −17.7955 12.9292i −0.658640 0.478530i
\(731\) 0.384312 + 1.18279i 0.0142143 + 0.0437471i
\(732\) 6.36235 + 19.5813i 0.235159 + 0.723745i
\(733\) 25.0916 + 18.2301i 0.926779 + 0.673344i 0.945202 0.326486i \(-0.105865\pi\)
−0.0184232 + 0.999830i \(0.505865\pi\)
\(734\) −19.7237 + 14.3301i −0.728016 + 0.528935i
\(735\) 5.84506 17.9892i 0.215598 0.663543i
\(736\) 2.47068 0.0910704
\(737\) 15.5144 25.3870i 0.571481 0.935143i
\(738\) −3.76482 −0.138585
\(739\) −10.7093 + 32.9597i −0.393947 + 1.21244i 0.535832 + 0.844325i \(0.319998\pi\)
−0.929779 + 0.368119i \(0.880002\pi\)
\(740\) 5.57807 4.05270i 0.205054 0.148980i
\(741\) −2.94160 2.13720i −0.108063 0.0785120i
\(742\) 3.58729 + 11.0406i 0.131694 + 0.405311i
\(743\) 2.76915 + 8.52258i 0.101590 + 0.312663i 0.988915 0.148482i \(-0.0474387\pi\)
−0.887325 + 0.461145i \(0.847439\pi\)
\(744\) −5.05274 3.67103i −0.185243 0.134587i
\(745\) −28.5577 + 20.7484i −1.04627 + 0.760163i
\(746\) −1.33826 + 4.11873i −0.0489970 + 0.150797i
\(747\) 8.12855 0.297408
\(748\) 0.457929 + 0.534837i 0.0167435 + 0.0195556i
\(749\) 20.3681 0.744236
\(750\) −4.10485 + 12.6334i −0.149888 + 0.461307i
\(751\) −7.40654 + 5.38117i −0.270269 + 0.196362i −0.714662 0.699470i \(-0.753419\pi\)
0.444393 + 0.895832i \(0.353419\pi\)
\(752\) −10.1002 7.33820i −0.368315 0.267597i
\(753\) −2.26502 6.97102i −0.0825419 0.254038i
\(754\) 3.32985 + 10.2482i 0.121266 + 0.373218i
\(755\) −22.8475 16.5997i −0.831505 0.604124i
\(756\) 6.94130 5.04315i 0.252453 0.183418i
\(757\) 7.09476 21.8354i 0.257863 0.793622i −0.735389 0.677646i \(-0.763000\pi\)
0.993252 0.115976i \(-0.0369997\pi\)
\(758\) 2.46844 0.0896578
\(759\) −1.03262 12.9183i −0.0374818 0.468904i
\(760\) 2.60241 0.0943992
\(761\) 10.3237 31.7730i 0.374233 1.15177i −0.569762 0.821809i \(-0.692965\pi\)
0.943995 0.329960i \(-0.107035\pi\)
\(762\) 11.8388 8.60140i 0.428875 0.311596i
\(763\) −3.41962 2.48450i −0.123799 0.0899450i
\(764\) −0.645585 1.98691i −0.0233565 0.0718838i
\(765\) −0.0851536 0.262076i −0.00307873 0.00947537i
\(766\) −17.3440 12.6011i −0.626663 0.455297i
\(767\) −7.78074 + 5.65304i −0.280946 + 0.204119i
\(768\) −0.488718 + 1.50412i −0.0176351 + 0.0542752i
\(769\) 16.2969 0.587681 0.293841 0.955854i \(-0.405066\pi\)
0.293841 + 0.955854i \(0.405066\pi\)
\(770\) 12.3582 5.13670i 0.445360 0.185114i
\(771\) 40.6519 1.46404
\(772\) −2.33862 + 7.19752i −0.0841687 + 0.259045i
\(773\) −32.2035 + 23.3972i −1.15828 + 0.841539i −0.989559 0.144125i \(-0.953963\pi\)
−0.168720 + 0.985664i \(0.553963\pi\)
\(774\) −2.36394 1.71750i −0.0849699 0.0617343i
\(775\) 2.16305 + 6.65719i 0.0776991 + 0.239133i
\(776\) 0.460238 + 1.41647i 0.0165216 + 0.0508482i
\(777\) 5.25624 + 3.81888i 0.188566 + 0.137002i
\(778\) −4.77449 + 3.46887i −0.171174 + 0.124365i
\(779\) 2.33247 7.17861i 0.0835695 0.257200i
\(780\) −9.46241 −0.338809
\(781\) −22.0057 5.25458i −0.787425 0.188024i
\(782\) 0.524507 0.0187563
\(783\) −8.01431 + 24.6655i −0.286408 + 0.881473i
\(784\) 3.71803 2.70131i 0.132787 0.0964753i
\(785\) −10.8922 7.91368i −0.388761 0.282451i
\(786\) 5.91921 + 18.2175i 0.211131 + 0.649796i
\(787\) −11.4162 35.1355i −0.406945 1.25245i −0.919261 0.393650i \(-0.871212\pi\)
0.512316 0.858797i \(-0.328788\pi\)
\(788\) −1.34053 0.973952i −0.0477544 0.0346956i
\(789\) −27.9854 + 20.3326i −0.996307 + 0.723860i
\(790\) −7.22266 + 22.2290i −0.256971 + 0.790874i
\(791\) 13.7301 0.488187
\(792\) −1.60904 0.384211i −0.0571746 0.0136523i
\(793\) −29.9302 −1.06285
\(794\) −3.55002 + 10.9258i −0.125985 + 0.387743i
\(795\) 24.9289 18.1119i 0.884136 0.642362i
\(796\) 2.97983 + 2.16497i 0.105617 + 0.0767354i
\(797\) −15.8721 48.8493i −0.562218 1.73033i −0.676075 0.736833i \(-0.736320\pi\)
0.113856 0.993497i \(-0.463680\pi\)
\(798\) 0.757790 + 2.33224i 0.0268255 + 0.0825603i
\(799\) −2.14419 1.55784i −0.0758560 0.0551126i
\(800\) 1.43400 1.04186i 0.0506995 0.0368353i
\(801\) 0.553259 1.70276i 0.0195484 0.0601639i
\(802\) −28.0949 −0.992066
\(803\) −25.8862 + 10.7596i −0.913503 + 0.379697i
\(804\) 14.1873 0.500347
\(805\) 3.08081 9.48174i 0.108584 0.334188i
\(806\) 7.34518 5.33659i 0.258723 0.187973i
\(807\) −26.3550 19.1480i −0.927741 0.674043i
\(808\) 0.776576 + 2.39005i 0.0273198 + 0.0840818i
\(809\) 2.71886 + 8.36778i 0.0955899 + 0.294195i 0.987407 0.158201i \(-0.0505693\pi\)
−0.891817 + 0.452396i \(0.850569\pi\)
\(810\) −15.2743 11.0975i −0.536686 0.389925i
\(811\) 27.7158 20.1367i 0.973233 0.707095i 0.0170466 0.999855i \(-0.494574\pi\)
0.956186 + 0.292760i \(0.0945736\pi\)
\(812\) 2.24576 6.91175i 0.0788108 0.242555i
\(813\) 35.0306 1.22858
\(814\) −0.700165 8.75919i −0.0245408 0.307010i
\(815\) −3.12291 −0.109391
\(816\) −0.103751 + 0.319313i −0.00363202 + 0.0111782i
\(817\) 4.73942 3.44339i 0.165811 0.120469i
\(818\) 24.7383 + 17.9734i 0.864955 + 0.628427i
\(819\) 0.549458 + 1.69106i 0.0191996 + 0.0590904i
\(820\) −6.07004 18.6817i −0.211975 0.652392i
\(821\) −22.6766 16.4755i −0.791419 0.574999i 0.116965 0.993136i \(-0.462683\pi\)
−0.908384 + 0.418137i \(0.862683\pi\)
\(822\) 12.4745 9.06326i 0.435099 0.316118i
\(823\) 8.51814 26.2161i 0.296924 0.913837i −0.685645 0.727936i \(-0.740480\pi\)
0.982568 0.185901i \(-0.0595204\pi\)
\(824\) −6.77320 −0.235956
\(825\) −6.04686 7.06242i −0.210524 0.245882i
\(826\) 6.48639 0.225690
\(827\) 12.6598 38.9628i 0.440223 1.35487i −0.447415 0.894327i \(-0.647655\pi\)
0.887638 0.460542i \(-0.152345\pi\)
\(828\) −0.996976 + 0.724345i −0.0346473 + 0.0251727i
\(829\) 10.3317 + 7.50638i 0.358833 + 0.260707i 0.752565 0.658518i \(-0.228816\pi\)
−0.393732 + 0.919225i \(0.628816\pi\)
\(830\) 13.1057 + 40.3352i 0.454905 + 1.40005i
\(831\) 4.29780 + 13.2273i 0.149089 + 0.458849i
\(832\) −1.85998 1.35136i −0.0644832 0.0468498i
\(833\) 0.789311 0.573468i 0.0273480 0.0198695i
\(834\) 6.21489 19.1275i 0.215204 0.662330i
\(835\) −20.3671 −0.704831
\(836\) 1.72947 2.83001i 0.0598148 0.0978779i
\(837\) 21.8518 0.755308
\(838\) 9.07898 27.9422i 0.313628 0.965248i
\(839\) −4.26472 + 3.09850i −0.147235 + 0.106972i −0.658964 0.752174i \(-0.729005\pi\)
0.511729 + 0.859147i \(0.329005\pi\)
\(840\) 5.16296 + 3.75111i 0.178139 + 0.129426i
\(841\) −2.17314 6.68825i −0.0749360 0.230629i
\(842\) 4.07887 + 12.5535i 0.140567 + 0.432621i
\(843\) 21.8778 + 15.8951i 0.753510 + 0.547457i
\(844\) 1.68996 1.22783i 0.0581709 0.0422636i
\(845\) −6.20375 + 19.0932i −0.213416 + 0.656826i
\(846\) 6.22704 0.214090
\(847\) 2.62689 16.8527i 0.0902610 0.579067i
\(848\) 7.48676 0.257096
\(849\) 11.7785 36.2506i 0.404238 1.24412i
\(850\) 0.304427 0.221179i 0.0104418 0.00758638i
\(851\) −5.29572 3.84756i −0.181535 0.131893i
\(852\) −3.33378 10.2603i −0.114214 0.351513i
\(853\) −0.840042 2.58538i −0.0287625 0.0885219i 0.935645 0.352943i \(-0.114819\pi\)
−0.964407 + 0.264421i \(0.914819\pi\)
\(854\) 16.3308 + 11.8650i 0.558829 + 0.406013i
\(855\) −1.05013 + 0.762965i −0.0359137 + 0.0260929i
\(856\) 4.05923 12.4930i 0.138741 0.427002i
\(857\) 51.9734 1.77538 0.887689 0.460443i \(-0.152309\pi\)
0.887689 + 0.460443i \(0.152309\pi\)
\(858\) −6.28838 + 10.2900i −0.214682 + 0.351294i
\(859\) −44.7212 −1.52587 −0.762933 0.646477i \(-0.776242\pi\)
−0.762933 + 0.646477i \(0.776242\pi\)
\(860\) 4.71113 14.4994i 0.160648 0.494424i
\(861\) 14.9747 10.8798i 0.510336 0.370781i
\(862\) −27.2686 19.8118i −0.928774 0.674793i
\(863\) 12.3271 + 37.9389i 0.419619 + 1.29146i 0.908053 + 0.418854i \(0.137568\pi\)
−0.488434 + 0.872601i \(0.662432\pi\)
\(864\) −1.70992 5.26258i −0.0581726 0.179037i
\(865\) −10.3560 7.52411i −0.352116 0.255827i
\(866\) −29.3735 + 21.3411i −0.998151 + 0.725199i
\(867\) 8.28618 25.5022i 0.281413 0.866101i
\(868\) −6.12329 −0.207838
\(869\) 19.3733 + 22.6270i 0.657193 + 0.767567i
\(870\) −19.2904 −0.654007
\(871\) −6.37319 + 19.6147i −0.215947 + 0.664618i
\(872\) −2.20540 + 1.60232i −0.0746843 + 0.0542614i
\(873\) −0.600992 0.436646i −0.0203405 0.0147782i
\(874\) −0.763482 2.34975i −0.0258251 0.0794816i
\(875\) 4.02450 + 12.3861i 0.136053 + 0.418728i
\(876\) −10.8146 7.85726i −0.365391 0.265472i
\(877\) −2.42391 + 1.76108i −0.0818497 + 0.0594673i −0.627958 0.778248i \(-0.716109\pi\)
0.546108 + 0.837715i \(0.316109\pi\)
\(878\) 4.81839 14.8295i 0.162613 0.500470i
\(879\) 4.03796 0.136197
\(880\) −0.687740 8.60376i −0.0231837 0.290033i
\(881\) 20.5582 0.692625 0.346312 0.938119i \(-0.387434\pi\)
0.346312 + 0.938119i \(0.387434\pi\)
\(882\) −0.708351 + 2.18008i −0.0238514 + 0.0734072i
\(883\) 16.6620 12.1056i 0.560720 0.407387i −0.271002 0.962579i \(-0.587355\pi\)
0.831723 + 0.555192i \(0.187355\pi\)
\(884\) −0.394860 0.286883i −0.0132806 0.00964891i
\(885\) −5.32041 16.3746i −0.178844 0.550425i
\(886\) 2.21204 + 6.80795i 0.0743149 + 0.228718i
\(887\) −34.5512 25.1029i −1.16011 0.842872i −0.170322 0.985389i \(-0.554481\pi\)
−0.989792 + 0.142516i \(0.954481\pi\)
\(888\) 3.38988 2.46289i 0.113757 0.0826492i
\(889\) 4.43351 13.6449i 0.148695 0.457637i
\(890\) 9.34136 0.313123
\(891\) −22.2188 + 9.23524i −0.744358 + 0.309392i
\(892\) 23.1754 0.775971
\(893\) −3.85792 + 11.8735i −0.129100 + 0.397330i
\(894\) −17.3550 + 12.6091i −0.580438 + 0.421713i
\(895\) −20.0750 14.5854i −0.671034 0.487535i
\(896\) 0.479152 + 1.47468i 0.0160073 + 0.0492655i
\(897\) 2.77604 + 8.54376i 0.0926892 + 0.285268i
\(898\) 11.7625 + 8.54596i 0.392520 + 0.285182i
\(899\) 14.9742 10.8794i 0.499416 0.362847i
\(900\) −0.273202 + 0.840829i −0.00910673 + 0.0280276i
\(901\) 1.58938 0.0529500
\(902\) −24.3495 5.81424i −0.810748 0.193593i
\(903\) 14.3659 0.478068
\(904\) 2.73632 8.42152i 0.0910086 0.280096i
\(905\) −40.7051 + 29.5740i −1.35308 + 0.983074i
\(906\) −13.8848 10.0879i −0.461291 0.335148i
\(907\) 2.65727 + 8.17823i 0.0882331 + 0.271554i 0.985431 0.170075i \(-0.0544009\pi\)
−0.897198 + 0.441628i \(0.854401\pi\)
\(908\) 2.84927 + 8.76915i 0.0945563 + 0.291014i
\(909\) −1.01407 0.736768i −0.0336347 0.0244371i
\(910\) −7.50541 + 5.45300i −0.248802 + 0.180765i
\(911\) −9.20664 + 28.3351i −0.305030 + 0.938785i 0.674637 + 0.738150i \(0.264300\pi\)
−0.979666 + 0.200635i \(0.935700\pi\)
\(912\) 1.58152 0.0523695
\(913\) 52.5724 + 12.5534i 1.73989 + 0.415457i
\(914\) 2.89135 0.0956373
\(915\) 16.5574 50.9585i 0.547371 1.68464i
\(916\) 13.1744 9.57176i 0.435294 0.316260i
\(917\) 15.1934 + 11.0386i 0.501729 + 0.364528i
\(918\) −0.363003 1.11721i −0.0119809 0.0368733i
\(919\) 12.9936 + 39.9901i 0.428619 + 1.31915i 0.899486 + 0.436949i \(0.143941\pi\)
−0.470868 + 0.882204i \(0.656059\pi\)
\(920\) −5.20174 3.77929i −0.171496 0.124599i
\(921\) −24.2211 + 17.5976i −0.798111 + 0.579862i
\(922\) 7.07360 21.7703i 0.232957 0.716967i
\(923\) 15.6830 0.516214
\(924\) 7.51030 3.12166i 0.247071 0.102695i
\(925\) −4.69615 −0.154408
\(926\) 12.1040 37.2523i 0.397762 1.22419i
\(927\) 2.73314 1.98575i 0.0897682 0.0652204i
\(928\) −3.79183 2.75492i −0.124473 0.0904348i
\(929\) −16.8144 51.7494i −0.551663 1.69784i −0.704597 0.709608i \(-0.748872\pi\)
0.152934 0.988236i \(-0.451128\pi\)
\(930\) 5.02258 + 15.4579i 0.164697 + 0.506885i
\(931\) −3.71803 2.70131i −0.121854 0.0885318i
\(932\) 12.6876 9.21810i 0.415597 0.301949i
\(933\) −8.22072 + 25.3008i −0.269134 + 0.828310i
\(934\) 27.7227 0.907115
\(935\) −0.146002 1.82651i −0.00477478 0.0597334i
\(936\) 1.14673 0.0374821
\(937\) 10.7812 33.1812i 0.352207 1.08398i −0.605405 0.795918i \(-0.706989\pi\)
0.957611 0.288063i \(-0.0930113\pi\)
\(938\) 11.2531 8.17585i 0.367427 0.266951i
\(939\) −31.5791 22.9436i −1.03055 0.748736i
\(940\) 10.0399 + 30.8996i 0.327465 + 1.00783i
\(941\) −3.94810 12.1510i −0.128704 0.396111i 0.865854 0.500298i \(-0.166776\pi\)
−0.994558 + 0.104187i \(0.966776\pi\)
\(942\) −6.61939 4.80927i −0.215671 0.156694i
\(943\) −15.0872 + 10.9615i −0.491306 + 0.356955i
\(944\) 1.29269 3.97849i 0.0420735 0.129489i
\(945\) −22.3284 −0.726344
\(946\) −12.6366 14.7589i −0.410852 0.479853i
\(947\) 2.31945 0.0753720 0.0376860 0.999290i \(-0.488001\pi\)
0.0376860 + 0.999290i \(0.488001\pi\)
\(948\) −4.38932 + 13.5089i −0.142559 + 0.438750i
\(949\) 15.7212 11.4221i 0.510331 0.370777i
\(950\) −1.43400 1.04186i −0.0465250 0.0338024i
\(951\) −11.4647 35.2848i −0.371769 1.14419i
\(952\) 0.101720 + 0.313063i 0.00329677 + 0.0101464i
\(953\) 5.76745 + 4.19030i 0.186826 + 0.135737i 0.677267 0.735737i \(-0.263164\pi\)
−0.490441 + 0.871475i \(0.663164\pi\)
\(954\) −3.02108 + 2.19494i −0.0978111 + 0.0710639i
\(955\) −1.68008 + 5.17074i −0.0543660 + 0.167321i
\(956\) −23.9513 −0.774640
\(957\) −12.8197 + 20.9775i −0.414403 + 0.678107i
\(958\) −16.8581 −0.544660
\(959\) 4.67157 14.3776i 0.150853 0.464278i
\(960\) 3.32973 2.41919i 0.107466 0.0780789i
\(961\) 12.4628 + 9.05478i 0.402027 + 0.292090i
\(962\) 1.88228 + 5.79306i 0.0606871 + 0.186776i
\(963\) 2.02467 + 6.23129i 0.0652440 + 0.200800i
\(964\) 3.08105 + 2.23851i 0.0992339 + 0.0720976i
\(965\) 15.9334 11.5763i 0.512915 0.372655i
\(966\) 1.87225 5.76221i 0.0602388 0.185396i
\(967\) −14.9561 −0.480957 −0.240478 0.970654i \(-0.577304\pi\)
−0.240478 + 0.970654i \(0.577304\pi\)
\(968\) −9.81328 4.96986i −0.315411 0.159737i
\(969\) 0.335746 0.0107857
\(970\) 1.19773 3.68622i 0.0384567 0.118357i
\(971\) 36.1716 26.2802i 1.16080 0.843372i 0.170923 0.985284i \(-0.445325\pi\)
0.989879 + 0.141912i \(0.0453250\pi\)
\(972\) 4.14740 + 3.01326i 0.133028 + 0.0966505i
\(973\) −6.09324 18.7531i −0.195340 0.601195i
\(974\) 8.51256 + 26.1990i 0.272760 + 0.839469i
\(975\) 5.21405 + 3.78823i 0.166983 + 0.121320i
\(976\) 10.5321 7.65205i 0.337126 0.244936i
\(977\) −13.4055 + 41.2580i −0.428881 + 1.31996i 0.470348 + 0.882481i \(0.344128\pi\)
−0.899229 + 0.437478i \(0.855872\pi\)
\(978\) −1.89784 −0.0606863
\(979\) 6.20793 10.1583i 0.198406 0.324662i
\(980\) −11.9600 −0.382048
\(981\) 0.420168 1.29315i 0.0134149 0.0412870i
\(982\) 16.2475 11.8045i 0.518478 0.376697i
\(983\) −34.0915 24.7689i −1.08735 0.790007i −0.108401 0.994107i \(-0.534573\pi\)
−0.978950 + 0.204101i \(0.934573\pi\)
\(984\) −3.68886 11.3531i −0.117597 0.361925i
\(985\) 1.33253 + 4.10110i 0.0424579 + 0.130672i
\(986\) −0.804977 0.584850i −0.0256357 0.0186254i
\(987\) −24.7682 + 17.9952i −0.788381 + 0.572792i
\(988\) −0.710450 + 2.18654i −0.0226024 + 0.0695631i
\(989\) −14.4738 −0.460241
\(990\) 2.79994 + 3.27019i 0.0889880 + 0.103933i
\(991\) 55.5865 1.76576 0.882881 0.469596i \(-0.155600\pi\)
0.882881 + 0.469596i \(0.155600\pi\)
\(992\) −1.22033 + 3.75578i −0.0387454 + 0.119246i
\(993\) 21.3096 15.4823i 0.676240 0.491317i
\(994\) −8.55712 6.21711i −0.271415 0.197195i
\(995\) −2.96204 9.11622i −0.0939030 0.289004i
\(996\) 7.96454 + 24.5123i 0.252366 + 0.776703i
\(997\) 3.05604 + 2.22035i 0.0967859 + 0.0703191i 0.635126 0.772409i \(-0.280948\pi\)
−0.538340 + 0.842728i \(0.680948\pi\)
\(998\) −13.4352 + 9.76122i −0.425283 + 0.308986i
\(999\) −4.53029 + 13.9428i −0.143332 + 0.441131i
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 418.2.f.h.229.4 yes 20
11.4 even 5 4598.2.a.cc.1.3 10
11.5 even 5 inner 418.2.f.h.115.4 20
11.7 odd 10 4598.2.a.cd.1.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.115.4 20 11.5 even 5 inner
418.2.f.h.229.4 yes 20 1.1 even 1 trivial
4598.2.a.cc.1.3 10 11.4 even 5
4598.2.a.cd.1.3 10 11.7 odd 10