Properties

Label 630.2.i.i.151.8
Level $630$
Weight $2$
Character 630.151
Analytic conductor $5.031$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(121,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + 243 x^{7} - 315 x^{6} + 54 x^{5} + 405 x^{4} - 972 x^{3} + 1458 x^{2} - 2187 x + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.8
Root \(0.748691 - 1.56188i\) of defining polynomial
Character \(\chi\) \(=\) 630.151
Dual form 630.2.i.i.121.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.72697 + 0.132553i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.72697 - 0.132553i) q^{6} +(1.01860 - 2.44181i) q^{7} -1.00000 q^{8} +(2.96486 + 0.457832i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.72697 + 0.132553i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.72697 - 0.132553i) q^{6} +(1.01860 - 2.44181i) q^{7} -1.00000 q^{8} +(2.96486 + 0.457832i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.91301 + 5.04548i) q^{11} +(1.72697 + 0.132553i) q^{12} +(-0.511531 - 0.885998i) q^{13} +(-1.01860 + 2.44181i) q^{14} +(0.978280 - 1.42932i) q^{15} +1.00000 q^{16} +(-2.17561 + 3.76827i) q^{17} +(-2.96486 - 0.457832i) q^{18} +(-0.704732 - 1.22063i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.08276 - 4.08193i) q^{21} +(-2.91301 - 5.04548i) q^{22} +(3.30138 - 5.71815i) q^{23} +(-1.72697 - 0.132553i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.511531 + 0.885998i) q^{26} +(5.05954 + 1.18366i) q^{27} +(1.01860 - 2.44181i) q^{28} +(2.77093 - 4.79939i) q^{29} +(-0.978280 + 1.42932i) q^{30} -3.82602 q^{31} -1.00000 q^{32} +(4.36189 + 9.09953i) q^{33} +(2.17561 - 3.76827i) q^{34} +(-1.60537 - 2.10304i) q^{35} +(2.96486 + 0.457832i) q^{36} +(-3.85479 - 6.67670i) q^{37} +(0.704732 + 1.22063i) q^{38} +(-0.765957 - 1.59790i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(5.46652 + 9.46829i) q^{41} +(-2.08276 + 4.08193i) q^{42} +(-0.340159 + 0.589173i) q^{43} +(2.91301 + 5.04548i) q^{44} +(1.87892 - 2.33873i) q^{45} +(-3.30138 + 5.71815i) q^{46} +3.58765 q^{47} +(1.72697 + 0.132553i) q^{48} +(-4.92492 - 4.97445i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.25672 + 6.21931i) q^{51} +(-0.511531 - 0.885998i) q^{52} +(-3.17645 + 5.50177i) q^{53} +(-5.05954 - 1.18366i) q^{54} +5.82602 q^{55} +(-1.01860 + 2.44181i) q^{56} +(-1.05525 - 2.20141i) q^{57} +(-2.77093 + 4.79939i) q^{58} -8.56197 q^{59} +(0.978280 - 1.42932i) q^{60} +1.43754 q^{61} +3.82602 q^{62} +(4.13794 - 6.77329i) q^{63} +1.00000 q^{64} -1.02306 q^{65} +(-4.36189 - 9.09953i) q^{66} +13.9015 q^{67} +(-2.17561 + 3.76827i) q^{68} +(6.45934 - 9.43747i) q^{69} +(1.60537 + 2.10304i) q^{70} -10.4573 q^{71} +(-2.96486 - 0.457832i) q^{72} +(-0.343505 + 0.594968i) q^{73} +(3.85479 + 6.67670i) q^{74} +(-0.748691 - 1.56188i) q^{75} +(-0.704732 - 1.22063i) q^{76} +(15.2873 - 1.97372i) q^{77} +(0.765957 + 1.59790i) q^{78} +5.35025 q^{79} +(0.500000 - 0.866025i) q^{80} +(8.58078 + 2.71481i) q^{81} +(-5.46652 - 9.46829i) q^{82} +(-6.94521 + 12.0295i) q^{83} +(2.08276 - 4.08193i) q^{84} +(2.17561 + 3.76827i) q^{85} +(0.340159 - 0.589173i) q^{86} +(5.42149 - 7.92112i) q^{87} +(-2.91301 - 5.04548i) q^{88} +(-1.81945 - 3.15139i) q^{89} +(-1.87892 + 2.33873i) q^{90} +(-2.68449 + 0.346589i) q^{91} +(3.30138 - 5.71815i) q^{92} +(-6.60743 - 0.507152i) q^{93} -3.58765 q^{94} -1.40946 q^{95} +(-1.72697 - 0.132553i) q^{96} +(5.46600 - 9.46739i) q^{97} +(4.92492 + 4.97445i) q^{98} +(6.32669 + 16.2928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.72697 + 0.132553i 0.997067 + 0.0765297i
\(4\) 1.00000 0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.72697 0.132553i −0.705033 0.0541147i
\(7\) 1.01860 2.44181i 0.384994 0.922919i
\(8\) −1.00000 −0.353553
\(9\) 2.96486 + 0.457832i 0.988286 + 0.152611i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 2.91301 + 5.04548i 0.878306 + 1.52127i 0.853199 + 0.521585i \(0.174659\pi\)
0.0251068 + 0.999685i \(0.492007\pi\)
\(12\) 1.72697 + 0.132553i 0.498534 + 0.0382648i
\(13\) −0.511531 0.885998i −0.141873 0.245732i 0.786329 0.617808i \(-0.211979\pi\)
−0.928202 + 0.372077i \(0.878646\pi\)
\(14\) −1.01860 + 2.44181i −0.272232 + 0.652602i
\(15\) 0.978280 1.42932i 0.252591 0.369050i
\(16\) 1.00000 0.250000
\(17\) −2.17561 + 3.76827i −0.527664 + 0.913940i 0.471816 + 0.881697i \(0.343598\pi\)
−0.999480 + 0.0322433i \(0.989735\pi\)
\(18\) −2.96486 0.457832i −0.698824 0.107912i
\(19\) −0.704732 1.22063i −0.161677 0.280032i 0.773794 0.633438i \(-0.218357\pi\)
−0.935470 + 0.353406i \(0.885023\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 2.08276 4.08193i 0.454495 0.890749i
\(22\) −2.91301 5.04548i −0.621056 1.07570i
\(23\) 3.30138 5.71815i 0.688384 1.19232i −0.283976 0.958831i \(-0.591654\pi\)
0.972360 0.233485i \(-0.0750131\pi\)
\(24\) −1.72697 0.132553i −0.352517 0.0270573i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.511531 + 0.885998i 0.100319 + 0.173758i
\(27\) 5.05954 + 1.18366i 0.973709 + 0.227796i
\(28\) 1.01860 2.44181i 0.192497 0.461460i
\(29\) 2.77093 4.79939i 0.514549 0.891225i −0.485309 0.874343i \(-0.661293\pi\)
0.999857 0.0168819i \(-0.00537394\pi\)
\(30\) −0.978280 + 1.42932i −0.178609 + 0.260958i
\(31\) −3.82602 −0.687174 −0.343587 0.939121i \(-0.611642\pi\)
−0.343587 + 0.939121i \(0.611642\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.36189 + 9.09953i 0.759308 + 1.58403i
\(34\) 2.17561 3.76827i 0.373114 0.646253i
\(35\) −1.60537 2.10304i −0.271358 0.355478i
\(36\) 2.96486 + 0.457832i 0.494143 + 0.0763053i
\(37\) −3.85479 6.67670i −0.633724 1.09764i −0.986784 0.162042i \(-0.948192\pi\)
0.353060 0.935601i \(-0.385141\pi\)
\(38\) 0.704732 + 1.22063i 0.114323 + 0.198012i
\(39\) −0.765957 1.59790i −0.122651 0.255868i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 5.46652 + 9.46829i 0.853727 + 1.47870i 0.877821 + 0.478988i \(0.158996\pi\)
−0.0240946 + 0.999710i \(0.507670\pi\)
\(42\) −2.08276 + 4.08193i −0.321377 + 0.629855i
\(43\) −0.340159 + 0.589173i −0.0518737 + 0.0898480i −0.890796 0.454403i \(-0.849853\pi\)
0.838923 + 0.544251i \(0.183186\pi\)
\(44\) 2.91301 + 5.04548i 0.439153 + 0.760635i
\(45\) 1.87892 2.33873i 0.280093 0.348637i
\(46\) −3.30138 + 5.71815i −0.486761 + 0.843095i
\(47\) 3.58765 0.523312 0.261656 0.965161i \(-0.415731\pi\)
0.261656 + 0.965161i \(0.415731\pi\)
\(48\) 1.72697 + 0.132553i 0.249267 + 0.0191324i
\(49\) −4.92492 4.97445i −0.703560 0.710636i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −4.25672 + 6.21931i −0.596060 + 0.870878i
\(52\) −0.511531 0.885998i −0.0709366 0.122866i
\(53\) −3.17645 + 5.50177i −0.436319 + 0.755726i −0.997402 0.0720329i \(-0.977051\pi\)
0.561083 + 0.827759i \(0.310385\pi\)
\(54\) −5.05954 1.18366i −0.688516 0.161076i
\(55\) 5.82602 0.785581
\(56\) −1.01860 + 2.44181i −0.136116 + 0.326301i
\(57\) −1.05525 2.20141i −0.139772 0.291584i
\(58\) −2.77093 + 4.79939i −0.363841 + 0.630191i
\(59\) −8.56197 −1.11467 −0.557337 0.830286i \(-0.688177\pi\)
−0.557337 + 0.830286i \(0.688177\pi\)
\(60\) 0.978280 1.42932i 0.126295 0.184525i
\(61\) 1.43754 0.184058 0.0920291 0.995756i \(-0.470665\pi\)
0.0920291 + 0.995756i \(0.470665\pi\)
\(62\) 3.82602 0.485905
\(63\) 4.13794 6.77329i 0.521331 0.853354i
\(64\) 1.00000 0.125000
\(65\) −1.02306 −0.126895
\(66\) −4.36189 9.09953i −0.536912 1.12008i
\(67\) 13.9015 1.69833 0.849166 0.528126i \(-0.177105\pi\)
0.849166 + 0.528126i \(0.177105\pi\)
\(68\) −2.17561 + 3.76827i −0.263832 + 0.456970i
\(69\) 6.45934 9.43747i 0.777613 1.13614i
\(70\) 1.60537 + 2.10304i 0.191879 + 0.251361i
\(71\) −10.4573 −1.24105 −0.620525 0.784187i \(-0.713080\pi\)
−0.620525 + 0.784187i \(0.713080\pi\)
\(72\) −2.96486 0.457832i −0.349412 0.0539560i
\(73\) −0.343505 + 0.594968i −0.0402042 + 0.0696357i −0.885427 0.464778i \(-0.846134\pi\)
0.845223 + 0.534414i \(0.179468\pi\)
\(74\) 3.85479 + 6.67670i 0.448111 + 0.776150i
\(75\) −0.748691 1.56188i −0.0864514 0.180350i
\(76\) −0.704732 1.22063i −0.0808383 0.140016i
\(77\) 15.2873 1.97372i 1.74215 0.224926i
\(78\) 0.765957 + 1.59790i 0.0867276 + 0.180926i
\(79\) 5.35025 0.601950 0.300975 0.953632i \(-0.402688\pi\)
0.300975 + 0.953632i \(0.402688\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 8.58078 + 2.71481i 0.953420 + 0.301646i
\(82\) −5.46652 9.46829i −0.603676 1.04560i
\(83\) −6.94521 + 12.0295i −0.762336 + 1.32040i 0.179308 + 0.983793i \(0.442614\pi\)
−0.941644 + 0.336611i \(0.890719\pi\)
\(84\) 2.08276 4.08193i 0.227248 0.445375i
\(85\) 2.17561 + 3.76827i 0.235978 + 0.408726i
\(86\) 0.340159 0.589173i 0.0366803 0.0635321i
\(87\) 5.42149 7.92112i 0.581245 0.849233i
\(88\) −2.91301 5.04548i −0.310528 0.537850i
\(89\) −1.81945 3.15139i −0.192862 0.334046i 0.753336 0.657636i \(-0.228444\pi\)
−0.946197 + 0.323590i \(0.895110\pi\)
\(90\) −1.87892 + 2.33873i −0.198056 + 0.246524i
\(91\) −2.68449 + 0.346589i −0.281411 + 0.0363324i
\(92\) 3.30138 5.71815i 0.344192 0.596158i
\(93\) −6.60743 0.507152i −0.685158 0.0525892i
\(94\) −3.58765 −0.370038
\(95\) −1.40946 −0.144608
\(96\) −1.72697 0.132553i −0.176258 0.0135287i
\(97\) 5.46600 9.46739i 0.554988 0.961268i −0.442916 0.896563i \(-0.646056\pi\)
0.997904 0.0647051i \(-0.0206107\pi\)
\(98\) 4.92492 + 4.97445i 0.497492 + 0.502496i
\(99\) 6.32669 + 16.2928i 0.635856 + 1.63749i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 3.93224 + 6.81084i 0.391273 + 0.677704i 0.992618 0.121285i \(-0.0387016\pi\)
−0.601345 + 0.798989i \(0.705368\pi\)
\(102\) 4.25672 6.21931i 0.421478 0.615804i
\(103\) −1.72295 + 2.98424i −0.169768 + 0.294046i −0.938338 0.345719i \(-0.887635\pi\)
0.768570 + 0.639765i \(0.220968\pi\)
\(104\) 0.511531 + 0.885998i 0.0501597 + 0.0868792i
\(105\) −2.49367 3.84469i −0.243357 0.375203i
\(106\) 3.17645 5.50177i 0.308524 0.534379i
\(107\) −9.49393 16.4440i −0.917813 1.58970i −0.802729 0.596343i \(-0.796620\pi\)
−0.115084 0.993356i \(-0.536714\pi\)
\(108\) 5.05954 + 1.18366i 0.486854 + 0.113898i
\(109\) −5.82204 + 10.0841i −0.557651 + 0.965879i 0.440041 + 0.897977i \(0.354964\pi\)
−0.997692 + 0.0679016i \(0.978370\pi\)
\(110\) −5.82602 −0.555489
\(111\) −5.77210 12.0414i −0.547863 1.14292i
\(112\) 1.01860 2.44181i 0.0962484 0.230730i
\(113\) −8.66188 15.0028i −0.814841 1.41135i −0.909442 0.415831i \(-0.863491\pi\)
0.0946006 0.995515i \(-0.469843\pi\)
\(114\) 1.05525 + 2.20141i 0.0988334 + 0.206181i
\(115\) −3.30138 5.71815i −0.307855 0.533220i
\(116\) 2.77093 4.79939i 0.257274 0.445612i
\(117\) −1.11098 2.86105i −0.102710 0.264505i
\(118\) 8.56197 0.788194
\(119\) 6.98535 + 9.15080i 0.640346 + 0.838852i
\(120\) −0.978280 + 1.42932i −0.0893044 + 0.130479i
\(121\) −11.4713 + 19.8688i −1.04284 + 1.80626i
\(122\) −1.43754 −0.130149
\(123\) 8.18547 + 17.0761i 0.738059 + 1.53970i
\(124\) −3.82602 −0.343587
\(125\) −1.00000 −0.0894427
\(126\) −4.13794 + 6.77329i −0.368637 + 0.603413i
\(127\) −14.9902 −1.33016 −0.665081 0.746771i \(-0.731603\pi\)
−0.665081 + 0.746771i \(0.731603\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.665541 + 0.972395i −0.0585977 + 0.0856146i
\(130\) 1.02306 0.0897285
\(131\) −8.91663 + 15.4441i −0.779050 + 1.34935i 0.153440 + 0.988158i \(0.450965\pi\)
−0.932490 + 0.361196i \(0.882369\pi\)
\(132\) 4.36189 + 9.09953i 0.379654 + 0.792013i
\(133\) −3.69839 + 0.477492i −0.320691 + 0.0414038i
\(134\) −13.9015 −1.20090
\(135\) 3.55485 3.78986i 0.305953 0.326179i
\(136\) 2.17561 3.76827i 0.186557 0.323127i
\(137\) 3.36590 + 5.82991i 0.287568 + 0.498083i 0.973229 0.229839i \(-0.0738199\pi\)
−0.685661 + 0.727921i \(0.740487\pi\)
\(138\) −6.45934 + 9.43747i −0.549856 + 0.803371i
\(139\) 2.84986 + 4.93611i 0.241722 + 0.418675i 0.961205 0.275835i \(-0.0889543\pi\)
−0.719483 + 0.694510i \(0.755621\pi\)
\(140\) −1.60537 2.10304i −0.135679 0.177739i
\(141\) 6.19576 + 0.475555i 0.521778 + 0.0400489i
\(142\) 10.4573 0.877555
\(143\) 2.98019 5.16184i 0.249216 0.431655i
\(144\) 2.96486 + 0.457832i 0.247072 + 0.0381526i
\(145\) −2.77093 4.79939i −0.230113 0.398568i
\(146\) 0.343505 0.594968i 0.0284287 0.0492399i
\(147\) −7.84581 9.24355i −0.647112 0.762395i
\(148\) −3.85479 6.67670i −0.316862 0.548821i
\(149\) −8.48240 + 14.6920i −0.694906 + 1.20361i 0.275307 + 0.961356i \(0.411221\pi\)
−0.970213 + 0.242255i \(0.922113\pi\)
\(150\) 0.748691 + 1.56188i 0.0611304 + 0.127527i
\(151\) −0.349942 0.606118i −0.0284779 0.0493251i 0.851435 0.524460i \(-0.175733\pi\)
−0.879913 + 0.475135i \(0.842399\pi\)
\(152\) 0.704732 + 1.22063i 0.0571613 + 0.0990062i
\(153\) −8.17562 + 10.1763i −0.660960 + 0.822708i
\(154\) −15.2873 + 1.97372i −1.23189 + 0.159047i
\(155\) −1.91301 + 3.31343i −0.153657 + 0.266141i
\(156\) −0.765957 1.59790i −0.0613257 0.127934i
\(157\) −16.0589 −1.28164 −0.640820 0.767691i \(-0.721405\pi\)
−0.640820 + 0.767691i \(0.721405\pi\)
\(158\) −5.35025 −0.425643
\(159\) −6.21491 + 9.08035i −0.492875 + 0.720119i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −10.5999 13.8858i −0.835388 1.09436i
\(162\) −8.58078 2.71481i −0.674170 0.213296i
\(163\) −2.52702 4.37693i −0.197932 0.342827i 0.749926 0.661522i \(-0.230089\pi\)
−0.947858 + 0.318694i \(0.896756\pi\)
\(164\) 5.46652 + 9.46829i 0.426863 + 0.739349i
\(165\) 10.0614 + 0.772259i 0.783277 + 0.0601202i
\(166\) 6.94521 12.0295i 0.539053 0.933667i
\(167\) −2.71733 4.70655i −0.210273 0.364204i 0.741527 0.670923i \(-0.234102\pi\)
−0.951800 + 0.306720i \(0.900769\pi\)
\(168\) −2.08276 + 4.08193i −0.160688 + 0.314927i
\(169\) 5.97667 10.3519i 0.459744 0.796300i
\(170\) −2.17561 3.76827i −0.166862 0.289013i
\(171\) −1.53059 3.94165i −0.117047 0.301425i
\(172\) −0.340159 + 0.589173i −0.0259369 + 0.0449240i
\(173\) 6.77920 0.515413 0.257707 0.966223i \(-0.417033\pi\)
0.257707 + 0.966223i \(0.417033\pi\)
\(174\) −5.42149 + 7.92112i −0.411002 + 0.600498i
\(175\) −2.62397 + 0.338776i −0.198354 + 0.0256091i
\(176\) 2.91301 + 5.04548i 0.219576 + 0.380318i
\(177\) −14.7863 1.13492i −1.11141 0.0853057i
\(178\) 1.81945 + 3.15139i 0.136374 + 0.236206i
\(179\) 3.25481 5.63749i 0.243276 0.421366i −0.718370 0.695662i \(-0.755111\pi\)
0.961645 + 0.274296i \(0.0884447\pi\)
\(180\) 1.87892 2.33873i 0.140047 0.174318i
\(181\) 0.658355 0.0489352 0.0244676 0.999701i \(-0.492211\pi\)
0.0244676 + 0.999701i \(0.492211\pi\)
\(182\) 2.68449 0.346589i 0.198987 0.0256909i
\(183\) 2.48259 + 0.190551i 0.183519 + 0.0140859i
\(184\) −3.30138 + 5.71815i −0.243381 + 0.421548i
\(185\) −7.70959 −0.566820
\(186\) 6.60743 + 0.507152i 0.484480 + 0.0371862i
\(187\) −25.3503 −1.85380
\(188\) 3.58765 0.261656
\(189\) 8.04392 11.1488i 0.585109 0.810954i
\(190\) 1.40946 0.102253
\(191\) −26.3284 −1.90506 −0.952529 0.304449i \(-0.901528\pi\)
−0.952529 + 0.304449i \(0.901528\pi\)
\(192\) 1.72697 + 0.132553i 0.124633 + 0.00956621i
\(193\) 1.94965 0.140339 0.0701695 0.997535i \(-0.477646\pi\)
0.0701695 + 0.997535i \(0.477646\pi\)
\(194\) −5.46600 + 9.46739i −0.392436 + 0.679719i
\(195\) −1.76680 0.135610i −0.126523 0.00971125i
\(196\) −4.92492 4.97445i −0.351780 0.355318i
\(197\) 12.1983 0.869095 0.434548 0.900649i \(-0.356908\pi\)
0.434548 + 0.900649i \(0.356908\pi\)
\(198\) −6.32669 16.2928i −0.449618 1.15788i
\(199\) −7.38959 + 12.7992i −0.523834 + 0.907308i 0.475781 + 0.879564i \(0.342166\pi\)
−0.999615 + 0.0277439i \(0.991168\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 24.0074 + 1.84268i 1.69335 + 0.129973i
\(202\) −3.93224 6.81084i −0.276672 0.479209i
\(203\) −8.89676 11.6547i −0.624430 0.818003i
\(204\) −4.25672 + 6.21931i −0.298030 + 0.435439i
\(205\) 10.9330 0.763596
\(206\) 1.72295 2.98424i 0.120044 0.207922i
\(207\) 12.4061 15.4420i 0.862281 1.07330i
\(208\) −0.511531 0.885998i −0.0354683 0.0614329i
\(209\) 4.10578 7.11142i 0.284003 0.491907i
\(210\) 2.49367 + 3.84469i 0.172080 + 0.265308i
\(211\) 3.23465 + 5.60257i 0.222682 + 0.385697i 0.955622 0.294597i \(-0.0951854\pi\)
−0.732939 + 0.680294i \(0.761852\pi\)
\(212\) −3.17645 + 5.50177i −0.218159 + 0.377863i
\(213\) −18.0594 1.38615i −1.23741 0.0949771i
\(214\) 9.49393 + 16.4440i 0.648992 + 1.12409i
\(215\) 0.340159 + 0.589173i 0.0231986 + 0.0401812i
\(216\) −5.05954 1.18366i −0.344258 0.0805381i
\(217\) −3.89718 + 9.34244i −0.264558 + 0.634206i
\(218\) 5.82204 10.0841i 0.394318 0.682980i
\(219\) −0.672088 + 0.981959i −0.0454155 + 0.0663547i
\(220\) 5.82602 0.392790
\(221\) 4.45157 0.299445
\(222\) 5.77210 + 12.0414i 0.387398 + 0.808168i
\(223\) −10.4900 + 18.1692i −0.702461 + 1.21670i 0.265139 + 0.964210i \(0.414582\pi\)
−0.967600 + 0.252488i \(0.918751\pi\)
\(224\) −1.01860 + 2.44181i −0.0680579 + 0.163151i
\(225\) −1.08594 2.79656i −0.0723957 0.186437i
\(226\) 8.66188 + 15.0028i 0.576180 + 0.997973i
\(227\) 6.66332 + 11.5412i 0.442260 + 0.766017i 0.997857 0.0654349i \(-0.0208435\pi\)
−0.555597 + 0.831452i \(0.687510\pi\)
\(228\) −1.05525 2.20141i −0.0698858 0.145792i
\(229\) −1.56726 + 2.71458i −0.103568 + 0.179385i −0.913152 0.407619i \(-0.866359\pi\)
0.809584 + 0.587003i \(0.199693\pi\)
\(230\) 3.30138 + 5.71815i 0.217686 + 0.377044i
\(231\) 26.6624 1.38217i 1.75426 0.0909398i
\(232\) −2.77093 + 4.79939i −0.181921 + 0.315096i
\(233\) 2.18283 + 3.78077i 0.143002 + 0.247686i 0.928626 0.371018i \(-0.120991\pi\)
−0.785624 + 0.618704i \(0.787658\pi\)
\(234\) 1.11098 + 2.86105i 0.0726270 + 0.187033i
\(235\) 1.79382 3.10699i 0.117016 0.202678i
\(236\) −8.56197 −0.557337
\(237\) 9.23972 + 0.709193i 0.600184 + 0.0460670i
\(238\) −6.98535 9.15080i −0.452793 0.593158i
\(239\) −6.38171 11.0535i −0.412799 0.714988i 0.582396 0.812905i \(-0.302115\pi\)
−0.995195 + 0.0979170i \(0.968782\pi\)
\(240\) 0.978280 1.42932i 0.0631477 0.0922625i
\(241\) 1.11443 + 1.93025i 0.0717866 + 0.124338i 0.899684 0.436541i \(-0.143797\pi\)
−0.827898 + 0.560879i \(0.810463\pi\)
\(242\) 11.4713 19.8688i 0.737401 1.27722i
\(243\) 14.4589 + 5.82581i 0.927539 + 0.373726i
\(244\) 1.43754 0.0920291
\(245\) −6.77046 + 1.77788i −0.432549 + 0.113584i
\(246\) −8.18547 17.0761i −0.521886 1.08873i
\(247\) −0.720984 + 1.24878i −0.0458751 + 0.0794580i
\(248\) 3.82602 0.242953
\(249\) −13.5887 + 19.8539i −0.861150 + 1.25819i
\(250\) 1.00000 0.0632456
\(251\) −11.5316 −0.727866 −0.363933 0.931425i \(-0.618566\pi\)
−0.363933 + 0.931425i \(0.618566\pi\)
\(252\) 4.13794 6.77329i 0.260666 0.426677i
\(253\) 38.4678 2.41845
\(254\) 14.9902 0.940567
\(255\) 3.25772 + 6.79608i 0.204007 + 0.425587i
\(256\) 1.00000 0.0625000
\(257\) −0.824882 + 1.42874i −0.0514547 + 0.0891222i −0.890606 0.454777i \(-0.849719\pi\)
0.839151 + 0.543899i \(0.183052\pi\)
\(258\) 0.665541 0.972395i 0.0414348 0.0605387i
\(259\) −20.2297 + 2.61182i −1.25702 + 0.162291i
\(260\) −1.02306 −0.0634476
\(261\) 10.4127 12.9609i 0.644532 0.802260i
\(262\) 8.91663 15.4441i 0.550871 0.954137i
\(263\) −12.0516 20.8740i −0.743133 1.28714i −0.951062 0.309000i \(-0.900006\pi\)
0.207929 0.978144i \(-0.433328\pi\)
\(264\) −4.36189 9.09953i −0.268456 0.560038i
\(265\) 3.17645 + 5.50177i 0.195128 + 0.337971i
\(266\) 3.69839 0.477492i 0.226763 0.0292769i
\(267\) −2.72442 5.68353i −0.166732 0.347826i
\(268\) 13.9015 0.849166
\(269\) 13.5646 23.4946i 0.827048 1.43249i −0.0732967 0.997310i \(-0.523352\pi\)
0.900344 0.435178i \(-0.143315\pi\)
\(270\) −3.55485 + 3.78986i −0.216341 + 0.230643i
\(271\) 6.05548 + 10.4884i 0.367844 + 0.637125i 0.989228 0.146381i \(-0.0467626\pi\)
−0.621384 + 0.783506i \(0.713429\pi\)
\(272\) −2.17561 + 3.76827i −0.131916 + 0.228485i
\(273\) −4.68197 + 0.242711i −0.283366 + 0.0146896i
\(274\) −3.36590 5.82991i −0.203341 0.352198i
\(275\) 2.91301 5.04548i 0.175661 0.304254i
\(276\) 6.45934 9.43747i 0.388807 0.568069i
\(277\) 4.20274 + 7.27936i 0.252518 + 0.437375i 0.964219 0.265109i \(-0.0854079\pi\)
−0.711700 + 0.702483i \(0.752075\pi\)
\(278\) −2.84986 4.93611i −0.170924 0.296048i
\(279\) −11.3436 1.75167i −0.679124 0.104870i
\(280\) 1.60537 + 2.10304i 0.0959395 + 0.125681i
\(281\) 5.02907 8.71060i 0.300009 0.519631i −0.676129 0.736784i \(-0.736344\pi\)
0.976138 + 0.217153i \(0.0696770\pi\)
\(282\) −6.19576 0.475555i −0.368952 0.0283189i
\(283\) −3.85272 −0.229021 −0.114510 0.993422i \(-0.536530\pi\)
−0.114510 + 0.993422i \(0.536530\pi\)
\(284\) −10.4573 −0.620525
\(285\) −2.43410 0.186829i −0.144184 0.0110668i
\(286\) −2.98019 + 5.16184i −0.176222 + 0.305226i
\(287\) 28.6880 3.70385i 1.69340 0.218631i
\(288\) −2.96486 0.457832i −0.174706 0.0269780i
\(289\) −0.966581 1.67417i −0.0568577 0.0984804i
\(290\) 2.77093 + 4.79939i 0.162715 + 0.281830i
\(291\) 10.6946 15.6254i 0.626926 0.915976i
\(292\) −0.343505 + 0.594968i −0.0201021 + 0.0348179i
\(293\) 10.2567 + 17.7651i 0.599202 + 1.03785i 0.992939 + 0.118625i \(0.0378487\pi\)
−0.393737 + 0.919223i \(0.628818\pi\)
\(294\) 7.84581 + 9.24355i 0.457577 + 0.539095i
\(295\) −4.28099 + 7.41489i −0.249249 + 0.431711i
\(296\) 3.85479 + 6.67670i 0.224055 + 0.388075i
\(297\) 8.76634 + 28.9758i 0.508675 + 1.68135i
\(298\) 8.48240 14.6920i 0.491372 0.851082i
\(299\) −6.75503 −0.390653
\(300\) −0.748691 1.56188i −0.0432257 0.0901750i
\(301\) 1.09217 + 1.43073i 0.0629513 + 0.0824662i
\(302\) 0.349942 + 0.606118i 0.0201369 + 0.0348781i
\(303\) 5.88807 + 12.2834i 0.338261 + 0.705661i
\(304\) −0.704732 1.22063i −0.0404191 0.0700080i
\(305\) 0.718771 1.24495i 0.0411567 0.0712855i
\(306\) 8.17562 10.1763i 0.467369 0.581742i
\(307\) −12.4997 −0.713395 −0.356697 0.934220i \(-0.616097\pi\)
−0.356697 + 0.934220i \(0.616097\pi\)
\(308\) 15.2873 1.97372i 0.871076 0.112463i
\(309\) −3.37106 + 4.92532i −0.191773 + 0.280191i
\(310\) 1.91301 3.31343i 0.108652 0.188190i
\(311\) −8.85431 −0.502082 −0.251041 0.967976i \(-0.580773\pi\)
−0.251041 + 0.967976i \(0.580773\pi\)
\(312\) 0.765957 + 1.59790i 0.0433638 + 0.0904631i
\(313\) 16.1005 0.910053 0.455026 0.890478i \(-0.349630\pi\)
0.455026 + 0.890478i \(0.349630\pi\)
\(314\) 16.0589 0.906256
\(315\) −3.79687 6.97020i −0.213930 0.392727i
\(316\) 5.35025 0.300975
\(317\) 29.9648 1.68299 0.841495 0.540265i \(-0.181676\pi\)
0.841495 + 0.540265i \(0.181676\pi\)
\(318\) 6.21491 9.08035i 0.348515 0.509201i
\(319\) 32.2870 1.80773
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −14.2160 29.6567i −0.793462 1.65528i
\(322\) 10.5999 + 13.8858i 0.590709 + 0.773828i
\(323\) 6.13289 0.341243
\(324\) 8.58078 + 2.71481i 0.476710 + 0.150823i
\(325\) −0.511531 + 0.885998i −0.0283746 + 0.0491463i
\(326\) 2.52702 + 4.37693i 0.139959 + 0.242416i
\(327\) −11.3912 + 16.6432i −0.629934 + 0.920370i
\(328\) −5.46652 9.46829i −0.301838 0.522799i
\(329\) 3.65437 8.76037i 0.201472 0.482975i
\(330\) −10.0614 0.772259i −0.553860 0.0425114i
\(331\) 14.8295 0.815104 0.407552 0.913182i \(-0.366383\pi\)
0.407552 + 0.913182i \(0.366383\pi\)
\(332\) −6.94521 + 12.0295i −0.381168 + 0.660202i
\(333\) −8.37212 21.5603i −0.458789 1.18150i
\(334\) 2.71733 + 4.70655i 0.148685 + 0.257531i
\(335\) 6.95073 12.0390i 0.379759 0.657761i
\(336\) 2.08276 4.08193i 0.113624 0.222687i
\(337\) 3.36028 + 5.82017i 0.183046 + 0.317045i 0.942916 0.333030i \(-0.108071\pi\)
−0.759870 + 0.650075i \(0.774738\pi\)
\(338\) −5.97667 + 10.3519i −0.325088 + 0.563069i
\(339\) −12.9701 27.0576i −0.704442 1.46957i
\(340\) 2.17561 + 3.76827i 0.117989 + 0.204363i
\(341\) −11.1452 19.3041i −0.603549 1.04538i
\(342\) 1.53059 + 3.94165i 0.0827646 + 0.213140i
\(343\) −17.1632 + 6.95877i −0.926726 + 0.375738i
\(344\) 0.340159 0.589173i 0.0183401 0.0317661i
\(345\) −4.94342 10.3127i −0.266145 0.555217i
\(346\) −6.77920 −0.364452
\(347\) −28.5813 −1.53432 −0.767162 0.641453i \(-0.778332\pi\)
−0.767162 + 0.641453i \(0.778332\pi\)
\(348\) 5.42149 7.92112i 0.290623 0.424616i
\(349\) 9.49935 16.4534i 0.508489 0.880728i −0.491463 0.870898i \(-0.663538\pi\)
0.999952 0.00982963i \(-0.00312892\pi\)
\(350\) 2.62397 0.338776i 0.140257 0.0181083i
\(351\) −1.53939 5.08822i −0.0821665 0.271589i
\(352\) −2.91301 5.04548i −0.155264 0.268925i
\(353\) −1.85105 3.20612i −0.0985216 0.170644i 0.812551 0.582890i \(-0.198078\pi\)
−0.911073 + 0.412245i \(0.864745\pi\)
\(354\) 14.7863 + 1.13492i 0.785882 + 0.0603202i
\(355\) −5.22863 + 9.05626i −0.277507 + 0.480656i
\(356\) −1.81945 3.15139i −0.0964309 0.167023i
\(357\) 10.8505 + 16.7291i 0.574271 + 0.885397i
\(358\) −3.25481 + 5.63749i −0.172022 + 0.297951i
\(359\) 9.64730 + 16.7096i 0.509165 + 0.881899i 0.999944 + 0.0106151i \(0.00337897\pi\)
−0.490779 + 0.871284i \(0.663288\pi\)
\(360\) −1.87892 + 2.33873i −0.0990280 + 0.123262i
\(361\) 8.50671 14.7340i 0.447721 0.775476i
\(362\) −0.658355 −0.0346024
\(363\) −22.4442 + 32.7923i −1.17802 + 1.72115i
\(364\) −2.68449 + 0.346589i −0.140705 + 0.0181662i
\(365\) 0.343505 + 0.594968i 0.0179799 + 0.0311420i
\(366\) −2.48259 0.190551i −0.129767 0.00996025i
\(367\) −6.31895 10.9448i −0.329847 0.571311i 0.652634 0.757673i \(-0.273664\pi\)
−0.982481 + 0.186362i \(0.940330\pi\)
\(368\) 3.30138 5.71815i 0.172096 0.298079i
\(369\) 11.8726 + 30.5749i 0.618062 + 1.59166i
\(370\) 7.70959 0.400802
\(371\) 10.1988 + 13.3604i 0.529494 + 0.693637i
\(372\) −6.60743 0.507152i −0.342579 0.0262946i
\(373\) 13.1929 22.8507i 0.683100 1.18316i −0.290930 0.956744i \(-0.593965\pi\)
0.974030 0.226420i \(-0.0727021\pi\)
\(374\) 25.3503 1.31083
\(375\) −1.72697 0.132553i −0.0891804 0.00684502i
\(376\) −3.58765 −0.185019
\(377\) −5.66967 −0.292003
\(378\) −8.04392 + 11.1488i −0.413735 + 0.573431i
\(379\) −1.42816 −0.0733594 −0.0366797 0.999327i \(-0.511678\pi\)
−0.0366797 + 0.999327i \(0.511678\pi\)
\(380\) −1.40946 −0.0723039
\(381\) −25.8876 1.98700i −1.32626 0.101797i
\(382\) 26.3284 1.34708
\(383\) −12.3309 + 21.3577i −0.630078 + 1.09133i 0.357457 + 0.933930i \(0.383644\pi\)
−0.987535 + 0.157398i \(0.949690\pi\)
\(384\) −1.72697 0.132553i −0.0881291 0.00676433i
\(385\) 5.93437 14.2261i 0.302444 0.725027i
\(386\) −1.94965 −0.0992346
\(387\) −1.27827 + 1.59108i −0.0649779 + 0.0808790i
\(388\) 5.46600 9.46739i 0.277494 0.480634i
\(389\) 2.86604 + 4.96412i 0.145314 + 0.251691i 0.929490 0.368847i \(-0.120247\pi\)
−0.784176 + 0.620538i \(0.786914\pi\)
\(390\) 1.76680 + 0.135610i 0.0894653 + 0.00686689i
\(391\) 14.3650 + 24.8810i 0.726471 + 1.25828i
\(392\) 4.92492 + 4.97445i 0.248746 + 0.251248i
\(393\) −17.4459 + 25.4895i −0.880030 + 1.28578i
\(394\) −12.1983 −0.614543
\(395\) 2.67512 4.63345i 0.134600 0.233134i
\(396\) 6.32669 + 16.2928i 0.317928 + 0.818745i
\(397\) −16.2946 28.2231i −0.817804 1.41648i −0.907297 0.420491i \(-0.861858\pi\)
0.0894925 0.995987i \(-0.471475\pi\)
\(398\) 7.38959 12.7992i 0.370407 0.641564i
\(399\) −6.45031 + 0.334381i −0.322919 + 0.0167400i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 13.8103 23.9201i 0.689653 1.19451i −0.282298 0.959327i \(-0.591097\pi\)
0.971950 0.235187i \(-0.0755701\pi\)
\(402\) −24.0074 1.84268i −1.19738 0.0919047i
\(403\) 1.95713 + 3.38985i 0.0974915 + 0.168860i
\(404\) 3.93224 + 6.81084i 0.195636 + 0.338852i
\(405\) 6.64149 6.07377i 0.330018 0.301808i
\(406\) 8.89676 + 11.6547i 0.441539 + 0.578415i
\(407\) 22.4581 38.8986i 1.11321 1.92813i
\(408\) 4.25672 6.21931i 0.210739 0.307902i
\(409\) 20.5087 1.01409 0.507046 0.861919i \(-0.330737\pi\)
0.507046 + 0.861919i \(0.330737\pi\)
\(410\) −10.9330 −0.539944
\(411\) 5.04004 + 10.5142i 0.248607 + 0.518629i
\(412\) −1.72295 + 2.98424i −0.0848838 + 0.147023i
\(413\) −8.72121 + 20.9068i −0.429143 + 1.02875i
\(414\) −12.4061 + 15.4420i −0.609725 + 0.758935i
\(415\) 6.94521 + 12.0295i 0.340927 + 0.590503i
\(416\) 0.511531 + 0.885998i 0.0250799 + 0.0434396i
\(417\) 4.26734 + 8.90228i 0.208972 + 0.435946i
\(418\) −4.10578 + 7.11142i −0.200820 + 0.347831i
\(419\) −13.3504 23.1236i −0.652209 1.12966i −0.982586 0.185810i \(-0.940509\pi\)
0.330376 0.943849i \(-0.392824\pi\)
\(420\) −2.49367 3.84469i −0.121679 0.187601i
\(421\) 5.78804 10.0252i 0.282092 0.488597i −0.689808 0.723992i \(-0.742305\pi\)
0.971900 + 0.235395i \(0.0756384\pi\)
\(422\) −3.23465 5.60257i −0.157460 0.272729i
\(423\) 10.6369 + 1.64254i 0.517182 + 0.0798630i
\(424\) 3.17645 5.50177i 0.154262 0.267190i
\(425\) 4.35123 0.211065
\(426\) 18.0594 + 1.38615i 0.874981 + 0.0671590i
\(427\) 1.46428 3.51021i 0.0708613 0.169871i
\(428\) −9.49393 16.4440i −0.458907 0.794850i
\(429\) 5.83092 8.51932i 0.281520 0.411317i
\(430\) −0.340159 0.589173i −0.0164039 0.0284124i
\(431\) −0.486659 + 0.842918i −0.0234415 + 0.0406019i −0.877508 0.479562i \(-0.840796\pi\)
0.854067 + 0.520164i \(0.174129\pi\)
\(432\) 5.05954 + 1.18366i 0.243427 + 0.0569491i
\(433\) 22.4006 1.07650 0.538252 0.842784i \(-0.319085\pi\)
0.538252 + 0.842784i \(0.319085\pi\)
\(434\) 3.89718 9.34244i 0.187070 0.448451i
\(435\) −4.14914 8.65571i −0.198936 0.415009i
\(436\) −5.82204 + 10.0841i −0.278825 + 0.482940i
\(437\) −9.30634 −0.445182
\(438\) 0.672088 0.981959i 0.0321136 0.0469198i
\(439\) −10.2877 −0.491004 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(440\) −5.82602 −0.277745
\(441\) −12.3242 17.0033i −0.586868 0.809683i
\(442\) −4.45157 −0.211740
\(443\) 2.76392 0.131318 0.0656589 0.997842i \(-0.479085\pi\)
0.0656589 + 0.997842i \(0.479085\pi\)
\(444\) −5.77210 12.0414i −0.273932 0.571461i
\(445\) −3.63891 −0.172501
\(446\) 10.4900 18.1692i 0.496715 0.860335i
\(447\) −16.5963 + 24.2482i −0.784980 + 1.14690i
\(448\) 1.01860 2.44181i 0.0481242 0.115365i
\(449\) −7.23588 −0.341482 −0.170741 0.985316i \(-0.554616\pi\)
−0.170741 + 0.985316i \(0.554616\pi\)
\(450\) 1.08594 + 2.79656i 0.0511915 + 0.131831i
\(451\) −31.8481 + 55.1624i −1.49967 + 2.59750i
\(452\) −8.66188 15.0028i −0.407421 0.705673i
\(453\) −0.523997 1.09313i −0.0246195 0.0513599i
\(454\) −6.66332 11.5412i −0.312725 0.541656i
\(455\) −1.04209 + 2.49813i −0.0488539 + 0.117114i
\(456\) 1.05525 + 2.20141i 0.0494167 + 0.103090i
\(457\) −16.9550 −0.793119 −0.396560 0.918009i \(-0.629796\pi\)
−0.396560 + 0.918009i \(0.629796\pi\)
\(458\) 1.56726 2.71458i 0.0732334 0.126844i
\(459\) −15.4680 + 16.4905i −0.721983 + 0.769712i
\(460\) −3.30138 5.71815i −0.153927 0.266610i
\(461\) −13.3292 + 23.0868i −0.620801 + 1.07526i 0.368536 + 0.929613i \(0.379859\pi\)
−0.989337 + 0.145645i \(0.953474\pi\)
\(462\) −26.6624 + 1.38217i −1.24045 + 0.0643042i
\(463\) 10.2503 + 17.7540i 0.476372 + 0.825100i 0.999633 0.0270722i \(-0.00861839\pi\)
−0.523262 + 0.852172i \(0.675285\pi\)
\(464\) 2.77093 4.79939i 0.128637 0.222806i
\(465\) −3.74292 + 5.46863i −0.173574 + 0.253601i
\(466\) −2.18283 3.78077i −0.101118 0.175141i
\(467\) 18.4234 + 31.9103i 0.852533 + 1.47663i 0.878915 + 0.476979i \(0.158268\pi\)
−0.0263814 + 0.999652i \(0.508398\pi\)
\(468\) −1.11098 2.86105i −0.0513551 0.132252i
\(469\) 14.1600 33.9448i 0.653847 1.56742i
\(470\) −1.79382 + 3.10699i −0.0827429 + 0.143315i
\(471\) −27.7332 2.12866i −1.27788 0.0980835i
\(472\) 8.56197 0.394097
\(473\) −3.96355 −0.182244
\(474\) −9.23972 0.709193i −0.424394 0.0325743i
\(475\) −0.704732 + 1.22063i −0.0323353 + 0.0560064i
\(476\) 6.98535 + 9.15080i 0.320173 + 0.419426i
\(477\) −11.9366 + 14.8577i −0.546540 + 0.680287i
\(478\) 6.38171 + 11.0535i 0.291893 + 0.505573i
\(479\) −6.28715 10.8897i −0.287267 0.497562i 0.685889 0.727706i \(-0.259414\pi\)
−0.973157 + 0.230144i \(0.926080\pi\)
\(480\) −0.978280 + 1.42932i −0.0446522 + 0.0652394i
\(481\) −3.94369 + 6.83068i −0.179817 + 0.311452i
\(482\) −1.11443 1.93025i −0.0507608 0.0879203i
\(483\) −16.4651 25.3855i −0.749188 1.15508i
\(484\) −11.4713 + 19.8688i −0.521421 + 0.903128i
\(485\) −5.46600 9.46739i −0.248198 0.429892i
\(486\) −14.4589 5.82581i −0.655869 0.264264i
\(487\) −9.47787 + 16.4161i −0.429483 + 0.743887i −0.996827 0.0795942i \(-0.974638\pi\)
0.567344 + 0.823481i \(0.307971\pi\)
\(488\) −1.43754 −0.0650744
\(489\) −3.78392 7.89379i −0.171115 0.356970i
\(490\) 6.77046 1.77788i 0.305858 0.0803163i
\(491\) −2.38354 4.12842i −0.107568 0.186313i 0.807217 0.590255i \(-0.200973\pi\)
−0.914784 + 0.403942i \(0.867640\pi\)
\(492\) 8.18547 + 17.0761i 0.369029 + 0.769848i
\(493\) 12.0569 + 20.8832i 0.543017 + 0.940534i
\(494\) 0.720984 1.24878i 0.0324386 0.0561853i
\(495\) 17.2733 + 2.66734i 0.776379 + 0.119888i
\(496\) −3.82602 −0.171793
\(497\) −10.6517 + 25.5347i −0.477796 + 1.14539i
\(498\) 13.5887 19.8539i 0.608925 0.889675i
\(499\) 8.30616 14.3867i 0.371835 0.644037i −0.618013 0.786168i \(-0.712062\pi\)
0.989848 + 0.142131i \(0.0453955\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −4.06888 8.48826i −0.181784 0.379228i
\(502\) 11.5316 0.514679
\(503\) −11.3485 −0.506007 −0.253003 0.967465i \(-0.581418\pi\)
−0.253003 + 0.967465i \(0.581418\pi\)
\(504\) −4.13794 + 6.77329i −0.184318 + 0.301706i
\(505\) 7.86448 0.349965
\(506\) −38.4678 −1.71010
\(507\) 11.6937 17.0852i 0.519336 0.758781i
\(508\) −14.9902 −0.665081
\(509\) −20.2856 + 35.1357i −0.899145 + 1.55736i −0.0705548 + 0.997508i \(0.522477\pi\)
−0.828590 + 0.559856i \(0.810856\pi\)
\(510\) −3.25772 6.79608i −0.144254 0.300936i
\(511\) 1.10291 + 1.44481i 0.0487898 + 0.0639145i
\(512\) −1.00000 −0.0441942
\(513\) −2.12080 7.01000i −0.0936356 0.309499i
\(514\) 0.824882 1.42874i 0.0363840 0.0630189i
\(515\) 1.72295 + 2.98424i 0.0759224 + 0.131501i
\(516\) −0.665541 + 0.972395i −0.0292988 + 0.0428073i
\(517\) 10.4509 + 18.1014i 0.459628 + 0.796099i
\(518\) 20.2297 2.61182i 0.888844 0.114757i
\(519\) 11.7075 + 0.898606i 0.513902 + 0.0394444i
\(520\) 1.02306 0.0448642
\(521\) 10.5287 18.2362i 0.461270 0.798943i −0.537754 0.843102i \(-0.680727\pi\)
0.999025 + 0.0441581i \(0.0140605\pi\)
\(522\) −10.4127 + 12.9609i −0.455753 + 0.567283i
\(523\) −18.9366 32.7991i −0.828039 1.43421i −0.899574 0.436768i \(-0.856123\pi\)
0.0715346 0.997438i \(-0.477210\pi\)
\(524\) −8.91663 + 15.4441i −0.389525 + 0.674677i
\(525\) −4.57643 + 0.237240i −0.199732 + 0.0103540i
\(526\) 12.0516 + 20.8740i 0.525474 + 0.910148i
\(527\) 8.32394 14.4175i 0.362597 0.628036i
\(528\) 4.36189 + 9.09953i 0.189827 + 0.396006i
\(529\) −10.2982 17.8369i −0.447746 0.775520i
\(530\) −3.17645 5.50177i −0.137976 0.238982i
\(531\) −25.3851 3.91994i −1.10162 0.170111i
\(532\) −3.69839 + 0.477492i −0.160346 + 0.0207019i
\(533\) 5.59259 9.68665i 0.242242 0.419575i
\(534\) 2.72442 + 5.68353i 0.117897 + 0.245950i
\(535\) −18.9879 −0.820917
\(536\) −13.9015 −0.600451
\(537\) 6.36823 9.30435i 0.274809 0.401512i
\(538\) −13.5646 + 23.4946i −0.584811 + 1.01292i
\(539\) 10.7522 39.3392i 0.463129 1.69446i
\(540\) 3.55485 3.78986i 0.152977 0.163090i
\(541\) 7.55055 + 13.0779i 0.324624 + 0.562265i 0.981436 0.191789i \(-0.0614290\pi\)
−0.656812 + 0.754054i \(0.728096\pi\)
\(542\) −6.05548 10.4884i −0.260105 0.450515i
\(543\) 1.13696 + 0.0872672i 0.0487917 + 0.00374499i
\(544\) 2.17561 3.76827i 0.0932786 0.161563i
\(545\) 5.82204 + 10.0841i 0.249389 + 0.431954i
\(546\) 4.68197 0.242711i 0.200370 0.0103871i
\(547\) 7.20802 12.4847i 0.308193 0.533805i −0.669774 0.742565i \(-0.733609\pi\)
0.977967 + 0.208759i \(0.0669425\pi\)
\(548\) 3.36590 + 5.82991i 0.143784 + 0.249041i
\(549\) 4.26211 + 0.658152i 0.181902 + 0.0280892i
\(550\) −2.91301 + 5.04548i −0.124211 + 0.215140i
\(551\) −7.81105 −0.332762
\(552\) −6.45934 + 9.43747i −0.274928 + 0.401686i
\(553\) 5.44975 13.0643i 0.231747 0.555551i
\(554\) −4.20274 7.27936i −0.178557 0.309270i
\(555\) −13.3142 1.02193i −0.565158 0.0433786i
\(556\) 2.84986 + 4.93611i 0.120861 + 0.209338i
\(557\) −5.40895 + 9.36858i −0.229185 + 0.396960i −0.957567 0.288212i \(-0.906939\pi\)
0.728382 + 0.685171i \(0.240273\pi\)
\(558\) 11.3436 + 1.75167i 0.480214 + 0.0741542i
\(559\) 0.696007 0.0294380
\(560\) −1.60537 2.10304i −0.0678395 0.0888696i
\(561\) −43.7793 3.36027i −1.84836 0.141871i
\(562\) −5.02907 + 8.71060i −0.212138 + 0.367434i
\(563\) 17.5941 0.741501 0.370751 0.928732i \(-0.379100\pi\)
0.370751 + 0.928732i \(0.379100\pi\)
\(564\) 6.19576 + 0.475555i 0.260889 + 0.0200245i
\(565\) −17.3238 −0.728816
\(566\) 3.85272 0.161942
\(567\) 15.3694 18.1874i 0.645455 0.763798i
\(568\) 10.4573 0.438777
\(569\) 34.2289 1.43495 0.717474 0.696585i \(-0.245298\pi\)
0.717474 + 0.696585i \(0.245298\pi\)
\(570\) 2.43410 + 0.186829i 0.101953 + 0.00782541i
\(571\) 36.2409 1.51663 0.758316 0.651887i \(-0.226022\pi\)
0.758316 + 0.651887i \(0.226022\pi\)
\(572\) 2.98019 5.16184i 0.124608 0.215827i
\(573\) −45.4684 3.48992i −1.89947 0.145793i
\(574\) −28.6880 + 3.70385i −1.19741 + 0.154596i
\(575\) −6.60275 −0.275354
\(576\) 2.96486 + 0.457832i 0.123536 + 0.0190763i
\(577\) −19.6210 + 33.9846i −0.816835 + 1.41480i 0.0911681 + 0.995836i \(0.470940\pi\)
−0.908003 + 0.418964i \(0.862393\pi\)
\(578\) 0.966581 + 1.67417i 0.0402045 + 0.0696362i
\(579\) 3.36699 + 0.258433i 0.139927 + 0.0107401i
\(580\) −2.77093 4.79939i −0.115057 0.199284i
\(581\) 22.2993 + 29.2121i 0.925132 + 1.21192i
\(582\) −10.6946 + 15.6254i −0.443304 + 0.647693i
\(583\) −37.0121 −1.53289
\(584\) 0.343505 0.594968i 0.0142143 0.0246199i
\(585\) −3.03324 0.468390i −0.125409 0.0193655i
\(586\) −10.2567 17.7651i −0.423700 0.733869i
\(587\) 3.09277 5.35683i 0.127652 0.221100i −0.795114 0.606460i \(-0.792589\pi\)
0.922767 + 0.385359i \(0.125923\pi\)
\(588\) −7.84581 9.24355i −0.323556 0.381198i
\(589\) 2.69632 + 4.67016i 0.111100 + 0.192431i
\(590\) 4.28099 7.41489i 0.176245 0.305266i
\(591\) 21.0662 + 1.61693i 0.866546 + 0.0665116i
\(592\) −3.85479 6.67670i −0.158431 0.274411i
\(593\) −7.85509 13.6054i −0.322570 0.558707i 0.658448 0.752626i \(-0.271213\pi\)
−0.981018 + 0.193919i \(0.937880\pi\)
\(594\) −8.76634 28.9758i −0.359687 1.18889i
\(595\) 11.4175 1.47409i 0.468072 0.0604318i
\(596\) −8.48240 + 14.6920i −0.347453 + 0.601806i
\(597\) −14.4582 + 21.1243i −0.591734 + 0.864558i
\(598\) 6.75503 0.276234
\(599\) 18.0983 0.739475 0.369737 0.929136i \(-0.379448\pi\)
0.369737 + 0.929136i \(0.379448\pi\)
\(600\) 0.748691 + 1.56188i 0.0305652 + 0.0637634i
\(601\) 8.44466 14.6266i 0.344465 0.596630i −0.640792 0.767715i \(-0.721394\pi\)
0.985256 + 0.171084i \(0.0547271\pi\)
\(602\) −1.09217 1.43073i −0.0445133 0.0583124i
\(603\) 41.2158 + 6.36452i 1.67844 + 0.259183i
\(604\) −0.349942 0.606118i −0.0142389 0.0246626i
\(605\) 11.4713 + 19.8688i 0.466373 + 0.807782i
\(606\) −5.88807 12.2834i −0.239186 0.498977i
\(607\) 19.0270 32.9558i 0.772283 1.33763i −0.164026 0.986456i \(-0.552448\pi\)
0.936309 0.351178i \(-0.114219\pi\)
\(608\) 0.704732 + 1.22063i 0.0285806 + 0.0495031i
\(609\) −13.8196 21.3067i −0.559998 0.863392i
\(610\) −0.718771 + 1.24495i −0.0291022 + 0.0504064i
\(611\) −1.83519 3.17865i −0.0742440 0.128594i
\(612\) −8.17562 + 10.1763i −0.330480 + 0.411354i
\(613\) −1.64068 + 2.84174i −0.0662665 + 0.114777i −0.897255 0.441512i \(-0.854442\pi\)
0.830989 + 0.556289i \(0.187775\pi\)
\(614\) 12.4997 0.504446
\(615\) 18.8810 + 1.44921i 0.761357 + 0.0584378i
\(616\) −15.2873 + 1.97372i −0.615944 + 0.0795233i
\(617\) 14.2783 + 24.7307i 0.574821 + 0.995619i 0.996061 + 0.0886700i \(0.0282616\pi\)
−0.421240 + 0.906949i \(0.638405\pi\)
\(618\) 3.37106 4.92532i 0.135604 0.198125i
\(619\) 11.1760 + 19.3574i 0.449202 + 0.778041i 0.998334 0.0576943i \(-0.0183749\pi\)
−0.549132 + 0.835736i \(0.685042\pi\)
\(620\) −1.91301 + 3.31343i −0.0768284 + 0.133071i
\(621\) 23.4718 25.0235i 0.941891 1.00416i
\(622\) 8.85431 0.355026
\(623\) −9.54839 + 1.23277i −0.382548 + 0.0493901i
\(624\) −0.765957 1.59790i −0.0306628 0.0639671i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −16.1005 −0.643504
\(627\) 8.03321 11.7370i 0.320815 0.468730i
\(628\) −16.0589 −0.640820
\(629\) 33.5462 1.33757
\(630\) 3.79687 + 6.97020i 0.151271 + 0.277700i
\(631\) 15.2841 0.608449 0.304224 0.952600i \(-0.401603\pi\)
0.304224 + 0.952600i \(0.401603\pi\)
\(632\) −5.35025 −0.212821
\(633\) 4.84350 + 10.1042i 0.192512 + 0.401608i
\(634\) −29.9648 −1.19005
\(635\) −7.49508 + 12.9819i −0.297433 + 0.515170i
\(636\) −6.21491 + 9.08035i −0.246437 + 0.360059i
\(637\) −1.88811 + 6.90805i −0.0748095 + 0.273707i
\(638\) −32.2870 −1.27825
\(639\) −31.0043 4.78767i −1.22651 0.189397i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −12.3144 21.3291i −0.486389 0.842451i 0.513489 0.858096i \(-0.328353\pi\)
−0.999878 + 0.0156459i \(0.995020\pi\)
\(642\) 14.2160 + 29.6567i 0.561063 + 1.17046i
\(643\) 2.35267 + 4.07495i 0.0927804 + 0.160700i 0.908680 0.417493i \(-0.137091\pi\)
−0.815900 + 0.578193i \(0.803758\pi\)
\(644\) −10.5999 13.8858i −0.417694 0.547179i
\(645\) 0.509348 + 1.06257i 0.0200556 + 0.0418388i
\(646\) −6.13289 −0.241295
\(647\) −14.0604 + 24.3532i −0.552769 + 0.957425i 0.445304 + 0.895380i \(0.353096\pi\)
−0.998073 + 0.0620453i \(0.980238\pi\)
\(648\) −8.58078 2.71481i −0.337085 0.106648i
\(649\) −24.9411 43.1993i −0.979025 1.69572i
\(650\) 0.511531 0.885998i 0.0200639 0.0347517i
\(651\) −7.96868 + 15.6175i −0.312317 + 0.612099i
\(652\) −2.52702 4.37693i −0.0989658 0.171414i
\(653\) 6.73216 11.6604i 0.263450 0.456309i −0.703706 0.710491i \(-0.748473\pi\)
0.967156 + 0.254182i \(0.0818063\pi\)
\(654\) 11.3912 16.6432i 0.445430 0.650800i
\(655\) 8.91663 + 15.4441i 0.348402 + 0.603449i
\(656\) 5.46652 + 9.46829i 0.213432 + 0.369675i
\(657\) −1.29084 + 1.60673i −0.0503604 + 0.0626844i
\(658\) −3.65437 + 8.76037i −0.142462 + 0.341515i
\(659\) 20.7279 35.9017i 0.807443 1.39853i −0.107186 0.994239i \(-0.534184\pi\)
0.914629 0.404294i \(-0.132483\pi\)
\(660\) 10.0614 + 0.772259i 0.391638 + 0.0300601i
\(661\) 38.7067 1.50551 0.752757 0.658298i \(-0.228723\pi\)
0.752757 + 0.658298i \(0.228723\pi\)
\(662\) −14.8295 −0.576365
\(663\) 7.68774 + 0.590071i 0.298567 + 0.0229165i
\(664\) 6.94521 12.0295i 0.269526 0.466833i
\(665\) −1.43568 + 3.44165i −0.0556731 + 0.133461i
\(666\) 8.37212 + 21.5603i 0.324413 + 0.835445i
\(667\) −18.2958 31.6892i −0.708415 1.22701i
\(668\) −2.71733 4.70655i −0.105137 0.182102i
\(669\) −20.5243 + 29.9872i −0.793514 + 1.15937i
\(670\) −6.95073 + 12.0390i −0.268530 + 0.465108i
\(671\) 4.18757 + 7.25309i 0.161659 + 0.280002i
\(672\) −2.08276 + 4.08193i −0.0803442 + 0.157464i
\(673\) −20.7404 + 35.9234i −0.799482 + 1.38474i 0.120471 + 0.992717i \(0.461559\pi\)
−0.919954 + 0.392027i \(0.871774\pi\)
\(674\) −3.36028 5.82017i −0.129433 0.224184i
\(675\) −1.50469 4.97352i −0.0579154 0.191431i
\(676\) 5.97667 10.3519i 0.229872 0.398150i
\(677\) 17.9170 0.688605 0.344303 0.938859i \(-0.388115\pi\)
0.344303 + 0.938859i \(0.388115\pi\)
\(678\) 12.9701 + 27.0576i 0.498115 + 1.03914i
\(679\) −17.5500 22.9904i −0.673506 0.882292i
\(680\) −2.17561 3.76827i −0.0834309 0.144507i
\(681\) 9.97754 + 20.8146i 0.382340 + 0.797617i
\(682\) 11.1452 + 19.3041i 0.426773 + 0.739193i
\(683\) 9.20678 15.9466i 0.352288 0.610180i −0.634362 0.773036i \(-0.718737\pi\)
0.986650 + 0.162856i \(0.0520705\pi\)
\(684\) −1.53059 3.94165i −0.0585234 0.150713i
\(685\) 6.73180 0.257209
\(686\) 17.1632 6.95877i 0.655294 0.265687i
\(687\) −3.06645 + 4.48026i −0.116992 + 0.170932i
\(688\) −0.340159 + 0.589173i −0.0129684 + 0.0224620i
\(689\) 6.49941 0.247608
\(690\) 4.94342 + 10.3127i 0.188193 + 0.392597i
\(691\) 18.9163 0.719611 0.359806 0.933027i \(-0.382843\pi\)
0.359806 + 0.933027i \(0.382843\pi\)
\(692\) 6.77920 0.257707
\(693\) 46.2284 + 1.14723i 1.75607 + 0.0435795i
\(694\) 28.5813 1.08493
\(695\) 5.69973 0.216203
\(696\) −5.42149 + 7.92112i −0.205501 + 0.300249i
\(697\) −47.5721 −1.80192
\(698\) −9.49935 + 16.4534i −0.359556 + 0.622769i
\(699\) 3.26853 + 6.81862i 0.123627 + 0.257904i
\(700\) −2.62397 + 0.338776i −0.0991768 + 0.0128045i
\(701\) 22.1110 0.835120 0.417560 0.908649i \(-0.362885\pi\)
0.417560 + 0.908649i \(0.362885\pi\)
\(702\) 1.53939 + 5.08822i 0.0581005 + 0.192043i
\(703\) −5.43319 + 9.41056i −0.204917 + 0.354926i
\(704\) 2.91301 + 5.04548i 0.109788 + 0.190159i
\(705\) 3.50972 5.12791i 0.132184 0.193128i
\(706\) 1.85105 + 3.20612i 0.0696653 + 0.120664i
\(707\) 20.6362 2.66430i 0.776104 0.100201i
\(708\) −14.7863 1.13492i −0.555703 0.0426528i
\(709\) 26.0880 0.979757 0.489878 0.871791i \(-0.337041\pi\)
0.489878 + 0.871791i \(0.337041\pi\)
\(710\) 5.22863 9.05626i 0.196227 0.339875i
\(711\) 15.8627 + 2.44951i 0.594899 + 0.0918638i
\(712\) 1.81945 + 3.15139i 0.0681869 + 0.118103i
\(713\) −12.6311 + 21.8778i −0.473040 + 0.819329i
\(714\) −10.8505 16.7291i −0.406071 0.626070i
\(715\) −2.98019 5.16184i −0.111453 0.193042i
\(716\) 3.25481 5.63749i 0.121638 0.210683i
\(717\) −9.55586 19.9349i −0.356870 0.744483i
\(718\) −9.64730 16.7096i −0.360034 0.623597i
\(719\) −22.4710 38.9208i −0.838025 1.45150i −0.891543 0.452935i \(-0.850377\pi\)
0.0535184 0.998567i \(-0.482956\pi\)
\(720\) 1.87892 2.33873i 0.0700233 0.0871592i
\(721\) 5.53197 + 7.24687i 0.206021 + 0.269888i
\(722\) −8.50671 + 14.7340i −0.316587 + 0.548345i
\(723\) 1.66872 + 3.48120i 0.0620605 + 0.129467i
\(724\) 0.658355 0.0244676
\(725\) −5.54186 −0.205820
\(726\) 22.4442 32.7923i 0.832983 1.21704i
\(727\) 18.3077 31.7099i 0.678996 1.17606i −0.296287 0.955099i \(-0.595749\pi\)
0.975283 0.220957i \(-0.0709181\pi\)
\(728\) 2.68449 0.346589i 0.0994937 0.0128454i
\(729\) 24.1979 + 11.9776i 0.896218 + 0.443614i
\(730\) −0.343505 0.594968i −0.0127137 0.0220207i
\(731\) −1.48011 2.56362i −0.0547438 0.0948190i
\(732\) 2.48259 + 0.190551i 0.0917593 + 0.00704296i
\(733\) 8.00977 13.8733i 0.295848 0.512423i −0.679334 0.733829i \(-0.737731\pi\)
0.975182 + 0.221406i \(0.0710646\pi\)
\(734\) 6.31895 + 10.9448i 0.233237 + 0.403978i
\(735\) −11.9281 + 2.17290i −0.439973 + 0.0801485i
\(736\) −3.30138 + 5.71815i −0.121690 + 0.210774i
\(737\) 40.4951 + 70.1395i 1.49166 + 2.58362i
\(738\) −11.8726 30.5749i −0.437036 1.12548i
\(739\) 12.3189 21.3369i 0.453158 0.784892i −0.545423 0.838161i \(-0.683631\pi\)
0.998580 + 0.0532692i \(0.0169641\pi\)
\(740\) −7.70959 −0.283410
\(741\) −1.41065 + 2.06104i −0.0518215 + 0.0757142i
\(742\) −10.1988 13.3604i −0.374409 0.490475i
\(743\) 2.42125 + 4.19374i 0.0888272 + 0.153853i 0.907016 0.421097i \(-0.138355\pi\)
−0.818188 + 0.574950i \(0.805021\pi\)
\(744\) 6.60743 + 0.507152i 0.242240 + 0.0185931i
\(745\) 8.48240 + 14.6920i 0.310771 + 0.538272i
\(746\) −13.1929 + 22.8507i −0.483025 + 0.836624i
\(747\) −26.0990 + 32.4859i −0.954914 + 1.18860i
\(748\) −25.3503 −0.926900
\(749\) −49.8236 + 6.43263i −1.82052 + 0.235043i
\(750\) 1.72697 + 0.132553i 0.0630601 + 0.00484016i
\(751\) 13.7116 23.7492i 0.500344 0.866621i −0.499656 0.866224i \(-0.666540\pi\)
1.00000 0.000397064i \(-0.000126389\pi\)
\(752\) 3.58765 0.130828
\(753\) −19.9147 1.52855i −0.725732 0.0557034i
\(754\) 5.66967 0.206477
\(755\) −0.699884 −0.0254714
\(756\) 8.04392 11.1488i 0.292555 0.405477i
\(757\) 26.1378 0.949996 0.474998 0.879987i \(-0.342449\pi\)
0.474998 + 0.879987i \(0.342449\pi\)
\(758\) 1.42816 0.0518729
\(759\) 66.4327 + 5.09903i 2.41136 + 0.185083i
\(760\) 1.40946 0.0511266
\(761\) −21.8943 + 37.9220i −0.793668 + 1.37467i 0.130014 + 0.991512i \(0.458498\pi\)
−0.923682 + 0.383161i \(0.874835\pi\)
\(762\) 25.8876 + 1.98700i 0.937808 + 0.0719813i
\(763\) 18.6931 + 24.4880i 0.676736 + 0.886524i
\(764\) −26.3284 −0.952529
\(765\) 4.72515 + 12.1685i 0.170838 + 0.439952i
\(766\) 12.3309 21.3577i 0.445532 0.771685i
\(767\) 4.37972 + 7.58589i 0.158142 + 0.273911i
\(768\) 1.72697 + 0.132553i 0.0623167 + 0.00478311i
\(769\) −15.7683 27.3116i −0.568621 0.984881i −0.996703 0.0811407i \(-0.974144\pi\)
0.428081 0.903740i \(-0.359190\pi\)
\(770\) −5.93437 + 14.2261i −0.213860 + 0.512672i
\(771\) −1.61393 + 2.35805i −0.0581243 + 0.0849230i
\(772\) 1.94965 0.0701695
\(773\) 16.6378 28.8174i 0.598418 1.03649i −0.394636 0.918837i \(-0.629129\pi\)
0.993055 0.117654i \(-0.0375372\pi\)
\(774\) 1.27827 1.59108i 0.0459463 0.0571901i
\(775\) 1.91301 + 3.31343i 0.0687174 + 0.119022i
\(776\) −5.46600 + 9.46739i −0.196218 + 0.339860i
\(777\) −35.2824 + 1.82902i −1.26575 + 0.0656158i
\(778\) −2.86604 4.96412i −0.102752 0.177972i
\(779\) 7.70486 13.3452i 0.276055 0.478141i
\(780\) −1.76680 0.135610i −0.0632615 0.00485563i
\(781\) −30.4621 52.7620i −1.09002 1.88797i
\(782\) −14.3650 24.8810i −0.513692 0.889741i
\(783\) 19.7005 21.0029i 0.704038 0.750581i
\(784\) −4.92492 4.97445i −0.175890 0.177659i
\(785\) −8.02945 + 13.9074i −0.286583 + 0.496377i
\(786\) 17.4459 25.4895i 0.622276 0.909181i
\(787\) −27.2886 −0.972733 −0.486367 0.873755i \(-0.661678\pi\)
−0.486367 + 0.873755i \(0.661678\pi\)
\(788\) 12.1983 0.434548
\(789\) −18.0458 37.6462i −0.642449 1.34024i
\(790\) −2.67512 + 4.63345i −0.0951766 + 0.164851i
\(791\) −45.4571 + 5.86887i −1.61627 + 0.208673i
\(792\) −6.32669 16.2928i −0.224809 0.578940i
\(793\) −0.735347 1.27366i −0.0261129 0.0452289i
\(794\) 16.2946 + 28.2231i 0.578275 + 1.00160i
\(795\) 4.75636 + 9.92245i 0.168691 + 0.351913i
\(796\) −7.38959 + 12.7992i −0.261917 + 0.453654i
\(797\) −25.0977 43.4705i −0.889006 1.53980i −0.841052 0.540954i \(-0.818063\pi\)
−0.0479541 0.998850i \(-0.515270\pi\)
\(798\) 6.45031 0.334381i 0.228339 0.0118370i
\(799\) −7.80533 + 13.5192i −0.276133 + 0.478276i
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −3.95162 10.1764i −0.139624 0.359566i
\(802\) −13.8103 + 23.9201i −0.487658 + 0.844649i
\(803\) −4.00253 −0.141246
\(804\) 24.0074 + 1.84268i 0.846676 + 0.0649864i
\(805\) −17.3254 + 2.23685i −0.610641 + 0.0788387i
\(806\) −1.95713 3.38985i −0.0689369 0.119402i
\(807\) 26.5399 38.7764i 0.934250 1.36499i
\(808\) −3.93224 6.81084i −0.138336 0.239605i
\(809\) −8.05657 + 13.9544i −0.283254 + 0.490610i −0.972184 0.234218i \(-0.924747\pi\)
0.688930 + 0.724827i \(0.258081\pi\)
\(810\) −6.64149 + 6.07377i −0.233358 + 0.213410i
\(811\) −0.973184 −0.0341731 −0.0170866 0.999854i \(-0.505439\pi\)
−0.0170866 + 0.999854i \(0.505439\pi\)
\(812\) −8.89676 11.6547i −0.312215 0.409002i
\(813\) 9.06737 + 18.9158i 0.318007 + 0.663408i
\(814\) −22.4581 + 38.8986i −0.787156 + 1.36339i
\(815\) −5.05404 −0.177035
\(816\) −4.25672 + 6.21931i −0.149015 + 0.217719i
\(817\) 0.958883 0.0335471
\(818\) −20.5087 −0.717072
\(819\) −8.11780 0.201456i −0.283659 0.00703943i
\(820\) 10.9330 0.381798
\(821\) −25.7714 −0.899427 −0.449714 0.893173i \(-0.648474\pi\)
−0.449714 + 0.893173i \(0.648474\pi\)
\(822\) −5.04004 10.5142i −0.175791 0.366726i
\(823\) −26.4275 −0.921204 −0.460602 0.887607i \(-0.652367\pi\)
−0.460602 + 0.887607i \(0.652367\pi\)
\(824\) 1.72295 2.98424i 0.0600219 0.103961i
\(825\) 5.69948 8.32727i 0.198430 0.289918i
\(826\) 8.72121 20.9068i 0.303450 0.727439i
\(827\) −47.8905 −1.66531 −0.832657 0.553789i \(-0.813182\pi\)
−0.832657 + 0.553789i \(0.813182\pi\)
\(828\) 12.4061 15.4420i 0.431141 0.536648i
\(829\) −5.63061 + 9.75251i −0.195559 + 0.338719i −0.947084 0.320987i \(-0.895986\pi\)
0.751524 + 0.659705i \(0.229319\pi\)
\(830\) −6.94521 12.0295i −0.241072 0.417548i
\(831\) 6.29311 + 13.1283i 0.218306 + 0.455417i
\(832\) −0.511531 0.885998i −0.0177341 0.0307164i
\(833\) 29.4598 7.73595i 1.02072 0.268035i
\(834\) −4.26734 8.90228i −0.147766 0.308261i
\(835\) −5.43465 −0.188074
\(836\) 4.10578 7.11142i 0.142001 0.245954i
\(837\) −19.3579 4.52872i −0.669107 0.156536i
\(838\) 13.3504 + 23.1236i 0.461182 + 0.798790i
\(839\) 6.94107 12.0223i 0.239632 0.415055i −0.720977 0.692959i \(-0.756306\pi\)
0.960609 + 0.277904i \(0.0896398\pi\)
\(840\) 2.49367 + 3.84469i 0.0860398 + 0.132654i
\(841\) −0.856114 1.48283i −0.0295212 0.0511322i
\(842\) −5.78804 + 10.0252i −0.199469 + 0.345490i
\(843\) 9.83967 14.3763i 0.338896 0.495147i
\(844\) 3.23465 + 5.60257i 0.111341 + 0.192849i
\(845\) −5.97667 10.3519i −0.205604 0.356116i
\(846\) −10.6369 1.64254i −0.365703 0.0564716i
\(847\) 36.8314 + 48.2490i 1.26554 + 1.65786i
\(848\) −3.17645 + 5.50177i −0.109080 + 0.188932i
\(849\) −6.65354 0.510691i −0.228349 0.0175269i
\(850\) −4.35123 −0.149246
\(851\) −50.9045 −1.74498
\(852\) −18.0594 1.38615i −0.618705 0.0474886i
\(853\) 27.2825 47.2546i 0.934134 1.61797i 0.157964 0.987445i \(-0.449507\pi\)
0.776170 0.630523i \(-0.217160\pi\)
\(854\) −1.46428 + 3.51021i −0.0501065 + 0.120117i
\(855\) −4.17886 0.645297i −0.142914 0.0220687i
\(856\) 9.49393 + 16.4440i 0.324496 + 0.562044i
\(857\) 11.3133 + 19.5953i 0.386456 + 0.669361i 0.991970 0.126473i \(-0.0403658\pi\)
−0.605514 + 0.795835i \(0.707033\pi\)
\(858\) −5.83092 + 8.51932i −0.199064 + 0.290845i
\(859\) 22.2546 38.5462i 0.759319 1.31518i −0.183880 0.982949i \(-0.558866\pi\)
0.943199 0.332230i \(-0.107801\pi\)
\(860\) 0.340159 + 0.589173i 0.0115993 + 0.0200906i
\(861\) 50.0343 2.59375i 1.70516 0.0883949i
\(862\) 0.486659 0.842918i 0.0165757 0.0287099i
\(863\) 15.6344 + 27.0795i 0.532200 + 0.921797i 0.999293 + 0.0375894i \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(864\) −5.05954 1.18366i −0.172129 0.0402691i
\(865\) 3.38960 5.87096i 0.115250 0.199619i
\(866\) −22.4006 −0.761203
\(867\) −1.44734 3.01936i −0.0491543 0.102543i
\(868\) −3.89718 + 9.34244i −0.132279 + 0.317103i
\(869\) 15.5853 + 26.9946i 0.528696 + 0.915728i
\(870\) 4.14914 + 8.65571i 0.140669 + 0.293456i
\(871\) −7.11102 12.3167i −0.240948 0.417334i
\(872\) 5.82204 10.0841i 0.197159 0.341490i
\(873\) 20.5404 25.5670i 0.695187 0.865311i
\(874\) 9.30634 0.314791
\(875\) −1.01860 + 2.44181i −0.0344349 + 0.0825484i
\(876\) −0.672088 + 0.981959i −0.0227077 + 0.0331773i
\(877\) −4.67427 + 8.09608i −0.157839 + 0.273385i −0.934089 0.357040i \(-0.883786\pi\)
0.776250 + 0.630425i \(0.217119\pi\)
\(878\) 10.2877 0.347192
\(879\) 15.3582 + 32.0394i 0.518018 + 1.08066i
\(880\) 5.82602 0.196395
\(881\) −6.87092 −0.231487 −0.115744 0.993279i \(-0.536925\pi\)
−0.115744 + 0.993279i \(0.536925\pi\)
\(882\) 12.3242 + 17.0033i 0.414978 + 0.572532i
\(883\) 2.46636 0.0829997 0.0414999 0.999139i \(-0.486786\pi\)
0.0414999 + 0.999139i \(0.486786\pi\)
\(884\) 4.45157 0.149723
\(885\) −8.37601 + 12.2378i −0.281556 + 0.411370i
\(886\) −2.76392 −0.0928556
\(887\) 10.6194 18.3933i 0.356564 0.617586i −0.630821 0.775929i \(-0.717282\pi\)
0.987384 + 0.158342i \(0.0506150\pi\)
\(888\) 5.77210 + 12.0414i 0.193699 + 0.404084i
\(889\) −15.2689 + 36.6032i −0.512104 + 1.22763i
\(890\) 3.63891 0.121976
\(891\) 11.2984 + 51.2025i 0.378510 + 1.71535i
\(892\) −10.4900 + 18.1692i −0.351230 + 0.608349i
\(893\) −2.52833 4.37919i −0.0846073 0.146544i
\(894\) 16.5963 24.2482i 0.555064 0.810981i
\(895\) −3.25481 5.63749i −0.108796 0.188441i
\(896\) −1.01860 + 2.44181i −0.0340290 + 0.0815753i
\(897\) −11.6657 0.895401i −0.389508 0.0298966i
\(898\) 7.23588 0.241464
\(899\) −10.6016 + 18.3626i −0.353585 + 0.612426i
\(900\) −1.08594 2.79656i −0.0361979 0.0932186i
\(901\) −13.8214 23.9394i −0.460459 0.797539i
\(902\) 31.8481 55.1624i 1.06042 1.83671i
\(903\) 1.69649 + 2.61561i 0.0564556 + 0.0870420i
\(904\) 8.66188 + 15.0028i 0.288090 + 0.498986i
\(905\) 0.329178 0.570152i 0.0109422 0.0189525i
\(906\) 0.523997 + 1.09313i 0.0174086 + 0.0363169i
\(907\) 6.67045 + 11.5536i 0.221489 + 0.383630i 0.955260 0.295767i \(-0.0955751\pi\)
−0.733771 + 0.679396i \(0.762242\pi\)
\(908\) 6.66332 + 11.5412i 0.221130 + 0.383009i
\(909\) 8.54032 + 21.9935i 0.283265 + 0.729478i
\(910\) 1.04209 2.49813i 0.0345449 0.0828121i
\(911\) 11.7771 20.3985i 0.390192 0.675832i −0.602283 0.798283i \(-0.705742\pi\)
0.992475 + 0.122451i \(0.0390754\pi\)
\(912\) −1.05525 2.20141i −0.0349429 0.0728959i
\(913\) −80.9259 −2.67826
\(914\) 16.9550 0.560820
\(915\) 1.40632 2.05471i 0.0464914 0.0679267i
\(916\) −1.56726 + 2.71458i −0.0517839 + 0.0896923i
\(917\) 28.6291 + 37.5040i 0.945415 + 1.23849i
\(918\) 15.4680 16.4905i 0.510519 0.544268i
\(919\) 22.9390 + 39.7315i 0.756687 + 1.31062i 0.944531 + 0.328421i \(0.106517\pi\)
−0.187845 + 0.982199i \(0.560150\pi\)
\(920\) 3.30138 + 5.71815i 0.108843 + 0.188522i
\(921\) −21.5866 1.65688i −0.711303 0.0545959i
\(922\) 13.3292 23.0868i 0.438972 0.760323i
\(923\) 5.34922 + 9.26512i 0.176072 + 0.304965i
\(924\) 26.6624 1.38217i 0.877128 0.0454699i
\(925\) −3.85479 + 6.67670i −0.126745 + 0.219529i
\(926\) −10.2503 17.7540i −0.336846 0.583434i
\(927\) −6.47459 + 8.05904i −0.212654 + 0.264693i
\(928\) −2.77093 + 4.79939i −0.0909603 + 0.157548i
\(929\) −16.1651 −0.530361 −0.265181 0.964199i \(-0.585432\pi\)
−0.265181 + 0.964199i \(0.585432\pi\)
\(930\) 3.74292 5.46863i 0.122735 0.179323i
\(931\) −2.60123 + 9.51716i −0.0852517 + 0.311912i
\(932\) 2.18283 + 3.78077i 0.0715009 + 0.123843i
\(933\) −15.2911 1.17367i −0.500609 0.0384242i
\(934\) −18.4234 31.9103i −0.602832 1.04414i
\(935\) −12.6752 + 21.9540i −0.414522 + 0.717974i
\(936\) 1.11098 + 2.86105i 0.0363135 + 0.0935165i
\(937\) −27.2402 −0.889899 −0.444950 0.895556i \(-0.646778\pi\)
−0.444950 + 0.895556i \(0.646778\pi\)
\(938\) −14.1600 + 33.9448i −0.462340 + 1.10834i
\(939\) 27.8051 + 2.13417i 0.907384 + 0.0696460i
\(940\) 1.79382 3.10699i 0.0585081 0.101339i
\(941\) 8.34601 0.272072 0.136036 0.990704i \(-0.456564\pi\)
0.136036 + 0.990704i \(0.456564\pi\)
\(942\) 27.7332 + 2.12866i 0.903598 + 0.0693555i
\(943\) 72.1881 2.35077
\(944\) −8.56197 −0.278669
\(945\) −5.63317 12.5406i −0.183247 0.407947i
\(946\) 3.96355 0.128866
\(947\) 2.29975 0.0747318 0.0373659 0.999302i \(-0.488103\pi\)
0.0373659 + 0.999302i \(0.488103\pi\)
\(948\) 9.23972 + 0.709193i 0.300092 + 0.0230335i
\(949\) 0.702853 0.0228156
\(950\) 0.704732 1.22063i 0.0228645 0.0396025i
\(951\) 51.7483 + 3.97193i 1.67805 + 0.128799i
\(952\) −6.98535 9.15080i −0.226396 0.296579i
\(953\) −12.1920 −0.394936 −0.197468 0.980309i \(-0.563272\pi\)
−0.197468 + 0.980309i \(0.563272\pi\)
\(954\) 11.9366 14.8577i 0.386462 0.481036i
\(955\) −13.1642 + 22.8011i −0.425984 + 0.737826i
\(956\) −6.38171 11.0535i −0.206399 0.357494i
\(957\) 55.7587 + 4.27975i 1.80242 + 0.138345i
\(958\) 6.28715 + 10.8897i 0.203129 + 0.351829i
\(959\) 17.6641 2.28057i 0.570402 0.0736435i
\(960\) 0.978280 1.42932i 0.0315739 0.0461312i
\(961\) −16.3616 −0.527792
\(962\) 3.94369 6.83068i 0.127150 0.220230i
\(963\) −20.6196 53.1007i −0.664458 1.71115i
\(964\) 1.11443 + 1.93025i 0.0358933 + 0.0621690i
\(965\) 0.974826 1.68845i 0.0313808 0.0543531i
\(966\) 16.4651 + 25.3855i 0.529756 + 0.816765i
\(967\) −0.714339 1.23727i −0.0229716 0.0397880i 0.854311 0.519762i \(-0.173979\pi\)
−0.877283 + 0.479974i \(0.840646\pi\)
\(968\) 11.4713 19.8688i 0.368700 0.638608i
\(969\) 10.5913 + 0.812935i 0.340242 + 0.0261152i
\(970\) 5.46600 + 9.46739i 0.175503 + 0.303980i
\(971\) 30.4968 + 52.8221i 0.978690 + 1.69514i 0.667177 + 0.744899i \(0.267502\pi\)
0.311513 + 0.950242i \(0.399164\pi\)
\(972\) 14.4589 + 5.82581i 0.463770 + 0.186863i
\(973\) 14.9559 1.93093i 0.479465 0.0619028i
\(974\) 9.47787 16.4161i 0.303690 0.526007i
\(975\) −1.00084 + 1.46229i −0.0320526 + 0.0468307i
\(976\) 1.43754 0.0460146
\(977\) −19.0633 −0.609890 −0.304945 0.952370i \(-0.598638\pi\)
−0.304945 + 0.952370i \(0.598638\pi\)
\(978\) 3.78392 + 7.89379i 0.120996 + 0.252416i
\(979\) 10.6002 18.3600i 0.338783 0.586790i
\(980\) −6.77046 + 1.77788i −0.216274 + 0.0567922i
\(981\) −21.8783 + 27.2323i −0.698522 + 0.869462i
\(982\) 2.38354 + 4.12842i 0.0760619 + 0.131743i
\(983\) −6.89478 11.9421i −0.219909 0.380894i 0.734871 0.678207i \(-0.237243\pi\)
−0.954780 + 0.297313i \(0.903909\pi\)
\(984\) −8.18547 17.0761i −0.260943 0.544365i
\(985\) 6.09917 10.5641i 0.194336 0.336599i
\(986\) −12.0569 20.8832i −0.383971 0.665058i
\(987\) 7.47221 14.6445i 0.237843 0.466140i
\(988\) −0.720984 + 1.24878i −0.0229376 + 0.0397290i
\(989\) 2.24598 + 3.89016i 0.0714182 + 0.123700i
\(990\) −17.2733 2.66734i −0.548983 0.0847735i
\(991\) −19.7167 + 34.1504i −0.626323 + 1.08482i 0.361961 + 0.932193i \(0.382107\pi\)
−0.988283 + 0.152630i \(0.951226\pi\)
\(992\) 3.82602 0.121476
\(993\) 25.6101 + 1.96570i 0.812713 + 0.0623796i
\(994\) 10.6517 25.5347i 0.337853 0.809912i
\(995\) 7.38959 + 12.7992i 0.234266 + 0.405760i
\(996\) −13.5887 + 19.8539i −0.430575 + 0.629095i
\(997\) −11.3215 19.6095i −0.358557 0.621039i 0.629163 0.777273i \(-0.283398\pi\)
−0.987720 + 0.156235i \(0.950064\pi\)
\(998\) −8.30616 + 14.3867i −0.262927 + 0.455403i
\(999\) −11.6005 38.3438i −0.367024 1.21314i
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 630.2.i.i.151.8 yes 16
3.2 odd 2 1890.2.i.i.991.6 16
7.2 even 3 630.2.l.i.331.3 yes 16
9.4 even 3 630.2.l.i.571.3 yes 16
9.5 odd 6 1890.2.l.i.361.5 16
21.2 odd 6 1890.2.l.i.1801.5 16
63.23 odd 6 1890.2.i.i.1171.6 16
63.58 even 3 inner 630.2.i.i.121.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.i.i.121.8 16 63.58 even 3 inner
630.2.i.i.151.8 yes 16 1.1 even 1 trivial
630.2.l.i.331.3 yes 16 7.2 even 3
630.2.l.i.571.3 yes 16 9.4 even 3
1890.2.i.i.991.6 16 3.2 odd 2
1890.2.i.i.1171.6 16 63.23 odd 6
1890.2.l.i.361.5 16 9.5 odd 6
1890.2.l.i.1801.5 16 21.2 odd 6