Properties

Label 287.2.h.c.78.6
Level $287$
Weight $2$
Character 287.78
Analytic conductor $2.292$
Analytic rank $0$
Dimension $40$
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] = [287,2,Mod(57,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.57");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.h (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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 78.6
Character \(\chi\) \(=\) 287.78
Dual form 287.2.h.c.92.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.539909 - 0.392267i) q^{2} -3.00502 q^{3} +(-0.480406 + 1.47854i) q^{4} +(0.818883 - 2.52026i) q^{5} +(-1.62244 + 1.17877i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.733059 + 2.25612i) q^{8} +6.03012 q^{9} +O(q^{10})\) \(q+(0.539909 - 0.392267i) q^{2} -3.00502 q^{3} +(-0.480406 + 1.47854i) q^{4} +(0.818883 - 2.52026i) q^{5} +(-1.62244 + 1.17877i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.733059 + 2.25612i) q^{8} +6.03012 q^{9} +(-0.546493 - 1.68193i) q^{10} +(2.02711 + 6.23880i) q^{11} +(1.44363 - 4.44303i) q^{12} +(-1.47260 + 1.06991i) q^{13} -0.667364 q^{14} +(-2.46076 + 7.57343i) q^{15} +(-1.23465 - 0.897025i) q^{16} +(0.796013 + 2.44988i) q^{17} +(3.25572 - 2.36542i) q^{18} +(6.38527 + 4.63917i) q^{19} +(3.33290 + 2.42150i) q^{20} +(2.43111 + 1.76630i) q^{21} +(3.54173 + 2.57322i) q^{22} +(-1.42319 + 1.03401i) q^{23} +(-2.20285 - 6.77969i) q^{24} +(-1.63607 - 1.18868i) q^{25} +(-0.375381 + 1.15530i) q^{26} -9.10557 q^{27} +(1.25772 - 0.913786i) q^{28} +(1.57183 - 4.83761i) q^{29} +(1.64222 + 5.05424i) q^{30} +(-1.21893 - 3.75148i) q^{31} -5.76293 q^{32} +(-6.09150 - 18.7477i) q^{33} +(1.39078 + 1.01046i) q^{34} +(-2.14386 + 1.55761i) q^{35} +(-2.89690 + 8.91576i) q^{36} +(-0.577897 + 1.77858i) q^{37} +5.26725 q^{38} +(4.42518 - 3.21508i) q^{39} +6.28632 q^{40} +(-0.0811299 + 6.40261i) q^{41} +2.00544 q^{42} +(1.58062 - 1.14839i) q^{43} -10.1981 q^{44} +(4.93797 - 15.1975i) q^{45} +(-0.362785 + 1.11654i) q^{46} +(-7.28213 + 5.29078i) q^{47} +(3.71014 + 2.69557i) q^{48} +(0.309017 + 0.951057i) q^{49} -1.34961 q^{50} +(-2.39203 - 7.36191i) q^{51} +(-0.874449 - 2.69128i) q^{52} +(1.85984 - 5.72399i) q^{53} +(-4.91618 + 3.57181i) q^{54} +17.3834 q^{55} +(0.733059 - 2.25612i) q^{56} +(-19.1878 - 13.9408i) q^{57} +(-1.04899 - 3.22845i) q^{58} +(0.469012 - 0.340757i) q^{59} +(-10.0154 - 7.27664i) q^{60} +(1.76169 + 1.27994i) q^{61} +(-2.12969 - 1.54731i) q^{62} +(-4.87847 - 3.54442i) q^{63} +(-0.642160 + 0.466556i) q^{64} +(1.49056 + 4.58746i) q^{65} +(-10.6430 - 7.73256i) q^{66} +(-2.15980 + 6.64718i) q^{67} -4.00464 q^{68} +(4.27670 - 3.10720i) q^{69} +(-0.546493 + 1.68193i) q^{70} +(2.46698 + 7.59258i) q^{71} +(4.42044 + 13.6047i) q^{72} +6.71184 q^{73} +(0.385667 + 1.18696i) q^{74} +(4.91642 + 3.57199i) q^{75} +(-9.92670 + 7.21217i) q^{76} +(2.02711 - 6.23880i) q^{77} +(1.12802 - 3.47170i) q^{78} +8.80808 q^{79} +(-3.27177 + 2.37708i) q^{80} +9.27202 q^{81} +(2.46773 + 3.48865i) q^{82} -7.12960 q^{83} +(-3.77946 + 2.74594i) q^{84} +6.82617 q^{85} +(0.402916 - 1.24005i) q^{86} +(-4.72339 + 14.5371i) q^{87} +(-12.5895 + 9.14682i) q^{88} +(-14.3145 - 10.4001i) q^{89} +(-3.29542 - 10.1423i) q^{90} +1.82023 q^{91} +(-0.845108 - 2.60097i) q^{92} +(3.66291 + 11.2733i) q^{93} +(-1.85629 + 5.71307i) q^{94} +(16.9207 - 12.2936i) q^{95} +17.3177 q^{96} +(-0.00934027 + 0.0287464i) q^{97} +(0.539909 + 0.392267i) q^{98} +(12.2237 + 37.6208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.539909 0.392267i 0.381773 0.277375i −0.380303 0.924862i \(-0.624180\pi\)
0.762076 + 0.647488i \(0.224180\pi\)
\(3\) −3.00502 −1.73495 −0.867473 0.497483i \(-0.834258\pi\)
−0.867473 + 0.497483i \(0.834258\pi\)
\(4\) −0.480406 + 1.47854i −0.240203 + 0.739268i
\(5\) 0.818883 2.52026i 0.366216 1.12710i −0.583001 0.812472i \(-0.698122\pi\)
0.949216 0.314624i \(-0.101878\pi\)
\(6\) −1.62244 + 1.17877i −0.662356 + 0.481230i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) 0.733059 + 2.25612i 0.259176 + 0.797660i
\(9\) 6.03012 2.01004
\(10\) −0.546493 1.68193i −0.172816 0.531874i
\(11\) 2.02711 + 6.23880i 0.611197 + 1.88107i 0.446674 + 0.894697i \(0.352608\pi\)
0.164523 + 0.986373i \(0.447392\pi\)
\(12\) 1.44363 4.44303i 0.416739 1.28259i
\(13\) −1.47260 + 1.06991i −0.408425 + 0.296738i −0.772964 0.634450i \(-0.781227\pi\)
0.364539 + 0.931188i \(0.381227\pi\)
\(14\) −0.667364 −0.178361
\(15\) −2.46076 + 7.57343i −0.635365 + 1.95545i
\(16\) −1.23465 0.897025i −0.308662 0.224256i
\(17\) 0.796013 + 2.44988i 0.193061 + 0.594182i 0.999994 + 0.00353805i \(0.00112620\pi\)
−0.806932 + 0.590644i \(0.798874\pi\)
\(18\) 3.25572 2.36542i 0.767380 0.557534i
\(19\) 6.38527 + 4.63917i 1.46488 + 1.06430i 0.982058 + 0.188580i \(0.0603886\pi\)
0.482823 + 0.875718i \(0.339611\pi\)
\(20\) 3.33290 + 2.42150i 0.745260 + 0.541463i
\(21\) 2.43111 + 1.76630i 0.530512 + 0.385439i
\(22\) 3.54173 + 2.57322i 0.755099 + 0.548612i
\(23\) −1.42319 + 1.03401i −0.296755 + 0.215605i −0.726192 0.687492i \(-0.758712\pi\)
0.429438 + 0.903097i \(0.358712\pi\)
\(24\) −2.20285 6.77969i −0.449656 1.38390i
\(25\) −1.63607 1.18868i −0.327214 0.237735i
\(26\) −0.375381 + 1.15530i −0.0736182 + 0.226574i
\(27\) −9.10557 −1.75237
\(28\) 1.25772 0.913786i 0.237686 0.172689i
\(29\) 1.57183 4.83761i 0.291882 0.898321i −0.692369 0.721544i \(-0.743433\pi\)
0.984251 0.176777i \(-0.0565672\pi\)
\(30\) 1.64222 + 5.05424i 0.299827 + 0.922773i
\(31\) −1.21893 3.75148i −0.218927 0.673787i −0.998851 0.0479135i \(-0.984743\pi\)
0.779925 0.625873i \(-0.215257\pi\)
\(32\) −5.76293 −1.01875
\(33\) −6.09150 18.7477i −1.06039 3.26356i
\(34\) 1.39078 + 1.01046i 0.238517 + 0.173292i
\(35\) −2.14386 + 1.55761i −0.362379 + 0.263284i
\(36\) −2.89690 + 8.91576i −0.482817 + 1.48596i
\(37\) −0.577897 + 1.77858i −0.0950056 + 0.292397i −0.987255 0.159145i \(-0.949126\pi\)
0.892250 + 0.451543i \(0.149126\pi\)
\(38\) 5.26725 0.854462
\(39\) 4.42518 3.21508i 0.708596 0.514825i
\(40\) 6.28632 0.993954
\(41\) −0.0811299 + 6.40261i −0.0126704 + 0.999920i
\(42\) 2.00544 0.309446
\(43\) 1.58062 1.14839i 0.241042 0.175127i −0.460705 0.887553i \(-0.652404\pi\)
0.701747 + 0.712426i \(0.252404\pi\)
\(44\) −10.1981 −1.53743
\(45\) 4.93797 15.1975i 0.736108 2.26551i
\(46\) −0.362785 + 1.11654i −0.0534897 + 0.164624i
\(47\) −7.28213 + 5.29078i −1.06221 + 0.771739i −0.974496 0.224407i \(-0.927956\pi\)
−0.0877120 + 0.996146i \(0.527956\pi\)
\(48\) 3.71014 + 2.69557i 0.535512 + 0.389073i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) −1.34961 −0.190863
\(51\) −2.39203 7.36191i −0.334951 1.03087i
\(52\) −0.874449 2.69128i −0.121264 0.373213i
\(53\) 1.85984 5.72399i 0.255468 0.786251i −0.738269 0.674507i \(-0.764356\pi\)
0.993737 0.111744i \(-0.0356436\pi\)
\(54\) −4.91618 + 3.57181i −0.669007 + 0.486062i
\(55\) 17.3834 2.34398
\(56\) 0.733059 2.25612i 0.0979592 0.301487i
\(57\) −19.1878 13.9408i −2.54149 1.84650i
\(58\) −1.04899 3.22845i −0.137739 0.423916i
\(59\) 0.469012 0.340757i 0.0610602 0.0443628i −0.556836 0.830622i \(-0.687985\pi\)
0.617897 + 0.786259i \(0.287985\pi\)
\(60\) −10.0154 7.27664i −1.29299 0.939410i
\(61\) 1.76169 + 1.27994i 0.225561 + 0.163880i 0.694827 0.719177i \(-0.255481\pi\)
−0.469265 + 0.883057i \(0.655481\pi\)
\(62\) −2.12969 1.54731i −0.270471 0.196509i
\(63\) −4.87847 3.54442i −0.614630 0.446555i
\(64\) −0.642160 + 0.466556i −0.0802700 + 0.0583195i
\(65\) 1.49056 + 4.58746i 0.184881 + 0.569005i
\(66\) −10.6430 7.73256i −1.31006 0.951813i
\(67\) −2.15980 + 6.64718i −0.263861 + 0.812082i 0.728092 + 0.685479i \(0.240407\pi\)
−0.991954 + 0.126603i \(0.959593\pi\)
\(68\) −4.00464 −0.485634
\(69\) 4.27670 3.10720i 0.514854 0.374063i
\(70\) −0.546493 + 1.68193i −0.0653184 + 0.201029i
\(71\) 2.46698 + 7.59258i 0.292776 + 0.901073i 0.983959 + 0.178393i \(0.0570899\pi\)
−0.691183 + 0.722680i \(0.742910\pi\)
\(72\) 4.42044 + 13.6047i 0.520954 + 1.60333i
\(73\) 6.71184 0.785561 0.392781 0.919632i \(-0.371513\pi\)
0.392781 + 0.919632i \(0.371513\pi\)
\(74\) 0.385667 + 1.18696i 0.0448329 + 0.137982i
\(75\) 4.91642 + 3.57199i 0.567699 + 0.412458i
\(76\) −9.92670 + 7.21217i −1.13867 + 0.827292i
\(77\) 2.02711 6.23880i 0.231011 0.710978i
\(78\) 1.12802 3.47170i 0.127724 0.393093i
\(79\) 8.80808 0.990986 0.495493 0.868612i \(-0.334987\pi\)
0.495493 + 0.868612i \(0.334987\pi\)
\(80\) −3.27177 + 2.37708i −0.365795 + 0.265766i
\(81\) 9.27202 1.03022
\(82\) 2.46773 + 3.48865i 0.272515 + 0.385257i
\(83\) −7.12960 −0.782576 −0.391288 0.920268i \(-0.627970\pi\)
−0.391288 + 0.920268i \(0.627970\pi\)
\(84\) −3.77946 + 2.74594i −0.412373 + 0.299607i
\(85\) 6.82617 0.740402
\(86\) 0.402916 1.24005i 0.0434475 0.133718i
\(87\) −4.72339 + 14.5371i −0.506400 + 1.55854i
\(88\) −12.5895 + 9.14682i −1.34205 + 0.975055i
\(89\) −14.3145 10.4001i −1.51734 1.10241i −0.962788 0.270257i \(-0.912891\pi\)
−0.554548 0.832152i \(-0.687109\pi\)
\(90\) −3.29542 10.1423i −0.347368 1.06909i
\(91\) 1.82023 0.190812
\(92\) −0.845108 2.60097i −0.0881086 0.271170i
\(93\) 3.66291 + 11.2733i 0.379826 + 1.16898i
\(94\) −1.85629 + 5.71307i −0.191462 + 0.589259i
\(95\) 16.9207 12.2936i 1.73603 1.26130i
\(96\) 17.3177 1.76748
\(97\) −0.00934027 + 0.0287464i −0.000948361 + 0.00291876i −0.951530 0.307557i \(-0.900488\pi\)
0.950581 + 0.310476i \(0.100488\pi\)
\(98\) 0.539909 + 0.392267i 0.0545390 + 0.0396249i
\(99\) 12.2237 + 37.6208i 1.22853 + 3.78103i
\(100\) 2.54348 1.84794i 0.254348 0.184794i
\(101\) 6.18783 + 4.49572i 0.615712 + 0.447341i 0.851421 0.524483i \(-0.175741\pi\)
−0.235709 + 0.971824i \(0.575741\pi\)
\(102\) −4.17931 3.03645i −0.413814 0.300653i
\(103\) −8.22884 5.97860i −0.810812 0.589089i 0.103254 0.994655i \(-0.467075\pi\)
−0.914066 + 0.405566i \(0.867075\pi\)
\(104\) −3.49334 2.53806i −0.342550 0.248877i
\(105\) 6.44235 4.68064i 0.628709 0.456784i
\(106\) −1.24119 3.81999i −0.120555 0.371030i
\(107\) 10.1894 + 7.40301i 0.985044 + 0.715676i 0.958830 0.283980i \(-0.0916550\pi\)
0.0262136 + 0.999656i \(0.491655\pi\)
\(108\) 4.37437 13.4629i 0.420924 1.29547i
\(109\) 6.69458 0.641225 0.320612 0.947211i \(-0.396111\pi\)
0.320612 + 0.947211i \(0.396111\pi\)
\(110\) 9.38545 6.81893i 0.894867 0.650159i
\(111\) 1.73659 5.34467i 0.164830 0.507294i
\(112\) 0.471594 + 1.45142i 0.0445614 + 0.137146i
\(113\) −0.874568 2.69164i −0.0822724 0.253209i 0.901456 0.432871i \(-0.142499\pi\)
−0.983728 + 0.179662i \(0.942499\pi\)
\(114\) −15.8282 −1.48245
\(115\) 1.44054 + 4.43353i 0.134331 + 0.413429i
\(116\) 6.39746 + 4.64803i 0.593989 + 0.431558i
\(117\) −8.87995 + 6.45166i −0.820952 + 0.596456i
\(118\) 0.119556 0.367956i 0.0110060 0.0338731i
\(119\) 0.796013 2.44988i 0.0729704 0.224580i
\(120\) −18.8905 −1.72446
\(121\) −25.9143 + 18.8278i −2.35585 + 1.71162i
\(122\) 1.45323 0.131569
\(123\) 0.243797 19.2399i 0.0219824 1.73481i
\(124\) 6.13229 0.550696
\(125\) 6.38379 4.63810i 0.570984 0.414844i
\(126\) −4.02429 −0.358512
\(127\) 5.12587 15.7758i 0.454847 1.39988i −0.416467 0.909151i \(-0.636732\pi\)
0.871314 0.490726i \(-0.163268\pi\)
\(128\) 3.39799 10.4579i 0.300343 0.924361i
\(129\) −4.74978 + 3.45092i −0.418195 + 0.303836i
\(130\) 2.60427 + 1.89212i 0.228410 + 0.165950i
\(131\) −6.23619 19.1930i −0.544858 1.67690i −0.721326 0.692595i \(-0.756467\pi\)
0.176468 0.984306i \(-0.443533\pi\)
\(132\) 30.6456 2.66735
\(133\) −2.43896 7.50633i −0.211484 0.650882i
\(134\) 1.44137 + 4.43609i 0.124516 + 0.383220i
\(135\) −7.45640 + 22.9484i −0.641744 + 1.97509i
\(136\) −4.94370 + 3.59181i −0.423919 + 0.307995i
\(137\) 3.13572 0.267902 0.133951 0.990988i \(-0.457233\pi\)
0.133951 + 0.990988i \(0.457233\pi\)
\(138\) 1.09017 3.35521i 0.0928018 0.285615i
\(139\) −1.52131 1.10530i −0.129036 0.0937501i 0.521395 0.853315i \(-0.325412\pi\)
−0.650431 + 0.759565i \(0.725412\pi\)
\(140\) −1.27306 3.91806i −0.107593 0.331137i
\(141\) 21.8829 15.8989i 1.84287 1.33893i
\(142\) 4.31026 + 3.13159i 0.361709 + 0.262797i
\(143\) −9.66005 7.01844i −0.807814 0.586911i
\(144\) −7.44508 5.40917i −0.620424 0.450764i
\(145\) −10.9049 7.92287i −0.905602 0.657958i
\(146\) 3.62378 2.63283i 0.299906 0.217895i
\(147\) −0.928601 2.85794i −0.0765897 0.235719i
\(148\) −2.35207 1.70888i −0.193339 0.140469i
\(149\) 2.92312 8.99645i 0.239472 0.737018i −0.757025 0.653386i \(-0.773348\pi\)
0.996497 0.0836319i \(-0.0266520\pi\)
\(150\) 4.05559 0.331138
\(151\) −6.97563 + 5.06809i −0.567669 + 0.412435i −0.834258 0.551375i \(-0.814103\pi\)
0.266589 + 0.963810i \(0.414103\pi\)
\(152\) −5.78576 + 17.8067i −0.469287 + 1.44432i
\(153\) 4.80005 + 14.7730i 0.388061 + 1.19433i
\(154\) −1.35282 4.16355i −0.109013 0.335509i
\(155\) −10.4529 −0.839596
\(156\) 2.62773 + 8.08734i 0.210387 + 0.647505i
\(157\) 18.5424 + 13.4719i 1.47985 + 1.07517i 0.977605 + 0.210446i \(0.0674918\pi\)
0.502243 + 0.864726i \(0.332508\pi\)
\(158\) 4.75556 3.45512i 0.378332 0.274874i
\(159\) −5.58884 + 17.2007i −0.443224 + 1.36410i
\(160\) −4.71917 + 14.5241i −0.373083 + 1.14823i
\(161\) 1.75915 0.138641
\(162\) 5.00604 3.63710i 0.393312 0.285758i
\(163\) 15.9860 1.25212 0.626061 0.779774i \(-0.284666\pi\)
0.626061 + 0.779774i \(0.284666\pi\)
\(164\) −9.42752 3.19580i −0.736165 0.249550i
\(165\) −52.2374 −4.06667
\(166\) −3.84934 + 2.79671i −0.298766 + 0.217066i
\(167\) −11.3842 −0.880938 −0.440469 0.897768i \(-0.645188\pi\)
−0.440469 + 0.897768i \(0.645188\pi\)
\(168\) −2.20285 + 6.77969i −0.169954 + 0.523064i
\(169\) −2.99337 + 9.21265i −0.230259 + 0.708666i
\(170\) 3.68551 2.67768i 0.282666 0.205369i
\(171\) 38.5039 + 27.9748i 2.94447 + 2.13928i
\(172\) 0.938592 + 2.88869i 0.0715670 + 0.220261i
\(173\) 18.0283 1.37067 0.685334 0.728229i \(-0.259656\pi\)
0.685334 + 0.728229i \(0.259656\pi\)
\(174\) 3.15222 + 9.70153i 0.238969 + 0.735471i
\(175\) 0.624924 + 1.92332i 0.0472398 + 0.145389i
\(176\) 3.09359 9.52110i 0.233188 0.717680i
\(177\) −1.40939 + 1.02398i −0.105936 + 0.0769672i
\(178\) −11.8082 −0.885059
\(179\) 1.96928 6.06083i 0.147191 0.453008i −0.850095 0.526629i \(-0.823456\pi\)
0.997286 + 0.0736214i \(0.0234556\pi\)
\(180\) 20.0978 + 14.6019i 1.49800 + 1.08836i
\(181\) −2.52645 7.77560i −0.187789 0.577956i 0.812196 0.583385i \(-0.198272\pi\)
−0.999985 + 0.00542871i \(0.998272\pi\)
\(182\) 0.982759 0.714016i 0.0728470 0.0529264i
\(183\) −5.29391 3.84625i −0.391337 0.284323i
\(184\) −3.37612 2.45290i −0.248891 0.180830i
\(185\) 4.00927 + 2.91290i 0.294767 + 0.214161i
\(186\) 6.39977 + 4.64970i 0.469254 + 0.340933i
\(187\) −13.6707 + 9.93233i −0.999699 + 0.726324i
\(188\) −4.32423 13.3086i −0.315377 0.970630i
\(189\) 7.36656 + 5.35212i 0.535838 + 0.389309i
\(190\) 4.31327 13.2749i 0.312917 0.963060i
\(191\) −7.84984 −0.567994 −0.283997 0.958825i \(-0.591661\pi\)
−0.283997 + 0.958825i \(0.591661\pi\)
\(192\) 1.92970 1.40201i 0.139264 0.101181i
\(193\) 1.86166 5.72961i 0.134005 0.412426i −0.861429 0.507879i \(-0.830430\pi\)
0.995434 + 0.0954525i \(0.0304298\pi\)
\(194\) 0.00623336 + 0.0191843i 0.000447529 + 0.00137735i
\(195\) −4.47915 13.7854i −0.320758 0.987193i
\(196\) −1.55463 −0.111045
\(197\) −0.665921 2.04949i −0.0474449 0.146020i 0.924528 0.381115i \(-0.124460\pi\)
−0.971972 + 0.235095i \(0.924460\pi\)
\(198\) 21.3571 + 15.5168i 1.51778 + 1.10273i
\(199\) −0.708312 + 0.514619i −0.0502109 + 0.0364803i −0.612608 0.790387i \(-0.709879\pi\)
0.562397 + 0.826868i \(0.309879\pi\)
\(200\) 1.48246 4.56255i 0.104826 0.322621i
\(201\) 6.49023 19.9749i 0.457786 1.40892i
\(202\) 5.10438 0.359143
\(203\) −4.11511 + 2.98981i −0.288824 + 0.209843i
\(204\) 12.0340 0.842549
\(205\) 16.0698 + 5.44746i 1.12237 + 0.380467i
\(206\) −6.78803 −0.472945
\(207\) −8.58199 + 6.23518i −0.596489 + 0.433375i
\(208\) 2.77787 0.192611
\(209\) −15.9992 + 49.2405i −1.10669 + 3.40604i
\(210\) 1.64222 5.05424i 0.113324 0.348775i
\(211\) 20.4740 14.8752i 1.40949 1.02405i 0.416093 0.909322i \(-0.363399\pi\)
0.993396 0.114732i \(-0.0366010\pi\)
\(212\) 7.56965 + 5.49967i 0.519886 + 0.377719i
\(213\) −7.41331 22.8158i −0.507952 1.56331i
\(214\) 8.40529 0.574574
\(215\) −1.59989 4.92396i −0.109112 0.335812i
\(216\) −6.67492 20.5433i −0.454171 1.39779i
\(217\) −1.21893 + 3.75148i −0.0827464 + 0.254667i
\(218\) 3.61446 2.62606i 0.244802 0.177859i
\(219\) −20.1692 −1.36291
\(220\) −8.35108 + 25.7020i −0.563030 + 1.73283i
\(221\) −3.79334 2.75602i −0.255168 0.185390i
\(222\) −1.15894 3.56684i −0.0777828 0.239391i
\(223\) 3.33687 2.42438i 0.223453 0.162348i −0.470426 0.882439i \(-0.655900\pi\)
0.693880 + 0.720091i \(0.255900\pi\)
\(224\) 4.66231 + 3.38736i 0.311514 + 0.226328i
\(225\) −9.86571 7.16786i −0.657714 0.477857i
\(226\) −1.52803 1.11018i −0.101643 0.0738480i
\(227\) −7.05295 5.12427i −0.468121 0.340110i 0.328588 0.944474i \(-0.393427\pi\)
−0.796709 + 0.604364i \(0.793427\pi\)
\(228\) 29.8299 21.6727i 1.97553 1.43531i
\(229\) 2.13274 + 6.56391i 0.140936 + 0.433755i 0.996466 0.0839974i \(-0.0267687\pi\)
−0.855530 + 0.517753i \(0.826769\pi\)
\(230\) 2.51689 + 1.82863i 0.165959 + 0.120576i
\(231\) −6.09150 + 18.7477i −0.400791 + 1.23351i
\(232\) 12.0665 0.792204
\(233\) −9.52984 + 6.92384i −0.624321 + 0.453596i −0.854428 0.519570i \(-0.826092\pi\)
0.230107 + 0.973165i \(0.426092\pi\)
\(234\) −2.26359 + 6.96662i −0.147976 + 0.455422i
\(235\) 7.37093 + 22.6854i 0.480827 + 1.47983i
\(236\) 0.278506 + 0.857153i 0.0181292 + 0.0557959i
\(237\) −26.4684 −1.71931
\(238\) −0.531230 1.63496i −0.0344345 0.105979i
\(239\) −20.1639 14.6500i −1.30430 0.947628i −0.304310 0.952573i \(-0.598426\pi\)
−0.999988 + 0.00494564i \(0.998426\pi\)
\(240\) 9.83173 7.14317i 0.634635 0.461089i
\(241\) 7.15550 22.0224i 0.460926 1.41858i −0.403109 0.915152i \(-0.632070\pi\)
0.864035 0.503432i \(-0.167930\pi\)
\(242\) −6.60583 + 20.3306i −0.424639 + 1.30690i
\(243\) −0.545852 −0.0350164
\(244\) −2.73877 + 1.98983i −0.175332 + 0.127386i
\(245\) 2.64996 0.169300
\(246\) −7.41556 10.4835i −0.472799 0.668401i
\(247\) −14.3664 −0.914112
\(248\) 7.57027 5.50012i 0.480712 0.349258i
\(249\) 21.4246 1.35773
\(250\) 1.62730 5.00830i 0.102919 0.316753i
\(251\) −6.09844 + 18.7691i −0.384930 + 1.18469i 0.551601 + 0.834108i \(0.314017\pi\)
−0.936531 + 0.350585i \(0.885983\pi\)
\(252\) 7.58420 5.51024i 0.477759 0.347113i
\(253\) −9.33591 6.78294i −0.586944 0.426440i
\(254\) −3.42082 10.5282i −0.214641 0.660598i
\(255\) −20.5128 −1.28456
\(256\) −2.75826 8.48907i −0.172392 0.530567i
\(257\) 4.35474 + 13.4025i 0.271641 + 0.836026i 0.990089 + 0.140445i \(0.0448532\pi\)
−0.718447 + 0.695582i \(0.755147\pi\)
\(258\) −1.21077 + 3.72636i −0.0753791 + 0.231993i
\(259\) 1.51295 1.09922i 0.0940103 0.0683025i
\(260\) −7.49880 −0.465056
\(261\) 9.47835 29.1714i 0.586695 1.80566i
\(262\) −10.8958 7.91623i −0.673142 0.489066i
\(263\) −6.27944 19.3261i −0.387207 1.19170i −0.934866 0.355000i \(-0.884481\pi\)
0.547659 0.836701i \(-0.315519\pi\)
\(264\) 37.8317 27.4864i 2.32838 1.69167i
\(265\) −12.9030 9.37456i −0.792623 0.575875i
\(266\) −4.26130 3.09601i −0.261277 0.189829i
\(267\) 43.0154 + 31.2525i 2.63250 + 1.91262i
\(268\) −8.79051 6.38668i −0.536966 0.390129i
\(269\) −2.37722 + 1.72715i −0.144942 + 0.105306i −0.657893 0.753111i \(-0.728552\pi\)
0.512951 + 0.858418i \(0.328552\pi\)
\(270\) 4.97613 + 15.3150i 0.302838 + 0.932039i
\(271\) 1.48800 + 1.08110i 0.0903896 + 0.0656719i 0.632062 0.774918i \(-0.282209\pi\)
−0.541673 + 0.840590i \(0.682209\pi\)
\(272\) 1.21480 3.73878i 0.0736582 0.226697i
\(273\) −5.46983 −0.331049
\(274\) 1.69300 1.23004i 0.102278 0.0743093i
\(275\) 4.09941 12.6167i 0.247204 0.760816i
\(276\) 2.53956 + 7.81597i 0.152864 + 0.470466i
\(277\) −1.06517e−6 0 3.27824e-6i −6.39996e−8 0 1.96971e-7i 0.951056 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(278\) −1.25494 −0.0752663
\(279\) −7.35031 22.6219i −0.440051 1.35434i
\(280\) −5.08574 3.69500i −0.303931 0.220819i
\(281\) −16.5538 + 12.0270i −0.987514 + 0.717471i −0.959375 0.282133i \(-0.908958\pi\)
−0.0281387 + 0.999604i \(0.508958\pi\)
\(282\) 5.57818 17.1679i 0.332176 1.02233i
\(283\) 1.42695 4.39169i 0.0848231 0.261059i −0.899645 0.436622i \(-0.856175\pi\)
0.984468 + 0.175563i \(0.0561747\pi\)
\(284\) −12.4111 −0.736460
\(285\) −50.8470 + 36.9425i −3.01192 + 2.18829i
\(286\) −7.96865 −0.471196
\(287\) 3.82900 5.13213i 0.226018 0.302940i
\(288\) −34.7512 −2.04773
\(289\) 8.38504 6.09209i 0.493237 0.358358i
\(290\) −8.99553 −0.528236
\(291\) 0.0280677 0.0863834i 0.00164536 0.00506389i
\(292\) −3.22440 + 9.92370i −0.188694 + 0.580740i
\(293\) −11.0368 + 8.01874i −0.644780 + 0.468460i −0.861489 0.507776i \(-0.830468\pi\)
0.216709 + 0.976236i \(0.430468\pi\)
\(294\) −1.62244 1.17877i −0.0946223 0.0687472i
\(295\) −0.474732 1.46107i −0.0276400 0.0850671i
\(296\) −4.43634 −0.257857
\(297\) −18.4580 56.8079i −1.07104 3.29633i
\(298\) −1.95079 6.00391i −0.113006 0.347797i
\(299\) 0.989494 3.04535i 0.0572239 0.176117i
\(300\) −7.64319 + 5.55310i −0.441280 + 0.320609i
\(301\) −1.95375 −0.112612
\(302\) −1.77816 + 5.47261i −0.102322 + 0.314914i
\(303\) −18.5945 13.5097i −1.06823 0.776112i
\(304\) −3.72211 11.4555i −0.213478 0.657017i
\(305\) 4.66841 3.39180i 0.267312 0.194214i
\(306\) 8.38657 + 6.09320i 0.479428 + 0.348325i
\(307\) 2.33220 + 1.69444i 0.133106 + 0.0967068i 0.652346 0.757921i \(-0.273785\pi\)
−0.519240 + 0.854628i \(0.673785\pi\)
\(308\) 8.25046 + 5.99431i 0.470114 + 0.341558i
\(309\) 24.7278 + 17.9658i 1.40672 + 1.02204i
\(310\) −5.64361 + 4.10032i −0.320535 + 0.232883i
\(311\) 4.29837 + 13.2290i 0.243738 + 0.750149i 0.995841 + 0.0911034i \(0.0290394\pi\)
−0.752103 + 0.659045i \(0.770961\pi\)
\(312\) 10.4975 + 7.62691i 0.594307 + 0.431789i
\(313\) 9.42260 28.9998i 0.532597 1.63916i −0.216189 0.976352i \(-0.569363\pi\)
0.748786 0.662812i \(-0.230637\pi\)
\(314\) 15.2958 0.863192
\(315\) −12.9278 + 9.39257i −0.728397 + 0.529211i
\(316\) −4.23145 + 13.0231i −0.238038 + 0.732604i
\(317\) −7.47659 23.0106i −0.419927 1.29240i −0.907769 0.419470i \(-0.862216\pi\)
0.487842 0.872932i \(-0.337784\pi\)
\(318\) 3.72979 + 11.4791i 0.209156 + 0.643717i
\(319\) 33.3672 1.86820
\(320\) 0.649991 + 2.00047i 0.0363356 + 0.111829i
\(321\) −30.6192 22.2462i −1.70900 1.24166i
\(322\) 0.949783 0.690058i 0.0529294 0.0384554i
\(323\) −6.28263 + 19.3359i −0.349575 + 1.07588i
\(324\) −4.45433 + 13.7090i −0.247463 + 0.761612i
\(325\) 3.68105 0.204188
\(326\) 8.63100 6.27079i 0.478027 0.347307i
\(327\) −20.1173 −1.11249
\(328\) −14.5046 + 4.51045i −0.800880 + 0.249048i
\(329\) 9.00121 0.496253
\(330\) −28.2034 + 20.4910i −1.55255 + 1.12799i
\(331\) 2.49496 0.137136 0.0685678 0.997646i \(-0.478157\pi\)
0.0685678 + 0.997646i \(0.478157\pi\)
\(332\) 3.42510 10.5414i 0.187977 0.578533i
\(333\) −3.48479 + 10.7251i −0.190965 + 0.587730i
\(334\) −6.14645 + 4.46565i −0.336319 + 0.244350i
\(335\) 14.9840 + 10.8865i 0.818664 + 0.594794i
\(336\) −1.41715 4.36153i −0.0773117 0.237941i
\(337\) 5.15517 0.280820 0.140410 0.990093i \(-0.455158\pi\)
0.140410 + 0.990093i \(0.455158\pi\)
\(338\) 1.99767 + 6.14819i 0.108659 + 0.334418i
\(339\) 2.62809 + 8.08843i 0.142738 + 0.439303i
\(340\) −3.27933 + 10.0927i −0.177847 + 0.547356i
\(341\) 20.9339 15.2093i 1.13363 0.823632i
\(342\) 31.7622 1.71750
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) 3.74959 + 2.72423i 0.202164 + 0.146881i
\(345\) −4.32885 13.3228i −0.233058 0.717278i
\(346\) 9.73366 7.07191i 0.523285 0.380189i
\(347\) −6.34348 4.60881i −0.340536 0.247414i 0.404352 0.914603i \(-0.367497\pi\)
−0.744888 + 0.667190i \(0.767497\pi\)
\(348\) −19.2245 13.9674i −1.03054 0.748731i
\(349\) 23.2871 + 16.9190i 1.24653 + 0.905655i 0.998015 0.0629733i \(-0.0200583\pi\)
0.248512 + 0.968629i \(0.420058\pi\)
\(350\) 1.09186 + 0.793279i 0.0583621 + 0.0424026i
\(351\) 13.4088 9.74210i 0.715711 0.519995i
\(352\) −11.6821 35.9538i −0.622658 1.91634i
\(353\) 17.3328 + 12.5930i 0.922534 + 0.670260i 0.944153 0.329506i \(-0.106882\pi\)
−0.0216196 + 0.999766i \(0.506882\pi\)
\(354\) −0.359268 + 1.10571i −0.0190949 + 0.0587680i
\(355\) 21.1555 1.12282
\(356\) 22.2537 16.1683i 1.17944 0.856917i
\(357\) −2.39203 + 7.36191i −0.126600 + 0.389634i
\(358\) −1.31423 4.04478i −0.0694592 0.213773i
\(359\) −4.59942 14.1555i −0.242748 0.747101i −0.995999 0.0893678i \(-0.971515\pi\)
0.753251 0.657733i \(-0.228485\pi\)
\(360\) 37.9073 1.99789
\(361\) 13.3784 + 41.1746i 0.704128 + 2.16708i
\(362\) −4.41416 3.20708i −0.232003 0.168560i
\(363\) 77.8729 56.5780i 4.08727 2.96957i
\(364\) −0.874449 + 2.69128i −0.0458336 + 0.141061i
\(365\) 5.49621 16.9156i 0.287685 0.885403i
\(366\) −4.36698 −0.228266
\(367\) 23.1852 16.8450i 1.21026 0.879304i 0.215004 0.976613i \(-0.431024\pi\)
0.995254 + 0.0973095i \(0.0310237\pi\)
\(368\) 2.68466 0.139948
\(369\) −0.489223 + 38.6085i −0.0254680 + 2.00988i
\(370\) 3.30727 0.171937
\(371\) −4.86912 + 3.53762i −0.252792 + 0.183664i
\(372\) −18.4276 −0.955428
\(373\) 8.80281 27.0923i 0.455792 1.40278i −0.414411 0.910090i \(-0.636012\pi\)
0.870203 0.492694i \(-0.163988\pi\)
\(374\) −3.48480 + 10.7251i −0.180195 + 0.554582i
\(375\) −19.1834 + 13.9376i −0.990627 + 0.719732i
\(376\) −17.2749 12.5509i −0.890884 0.647265i
\(377\) 2.86110 + 8.80556i 0.147354 + 0.453510i
\(378\) 6.07673 0.312553
\(379\) −4.49995 13.8494i −0.231147 0.711397i −0.997609 0.0691077i \(-0.977985\pi\)
0.766462 0.642289i \(-0.222015\pi\)
\(380\) 10.0478 + 30.9238i 0.515439 + 1.58636i
\(381\) −15.4033 + 47.4066i −0.789136 + 2.42871i
\(382\) −4.23820 + 3.07923i −0.216845 + 0.157547i
\(383\) −8.19279 −0.418632 −0.209316 0.977848i \(-0.567124\pi\)
−0.209316 + 0.977848i \(0.567124\pi\)
\(384\) −10.2110 + 31.4263i −0.521079 + 1.60372i
\(385\) −14.0635 10.2177i −0.716740 0.520742i
\(386\) −1.24241 3.82374i −0.0632369 0.194623i
\(387\) 9.53131 6.92491i 0.484504 0.352013i
\(388\) −0.0380155 0.0276199i −0.00192994 0.00140219i
\(389\) 8.76902 + 6.37106i 0.444607 + 0.323026i 0.787463 0.616362i \(-0.211394\pi\)
−0.342856 + 0.939388i \(0.611394\pi\)
\(390\) −7.82589 5.68584i −0.396279 0.287914i
\(391\) −3.66606 2.66355i −0.185401 0.134701i
\(392\) −1.91917 + 1.39436i −0.0969329 + 0.0704259i
\(393\) 18.7399 + 57.6753i 0.945301 + 2.90934i
\(394\) −1.16349 0.845321i −0.0586155 0.0425867i
\(395\) 7.21279 22.1987i 0.362915 1.11694i
\(396\) −61.4960 −3.09029
\(397\) −25.4638 + 18.5006i −1.27799 + 0.928517i −0.999490 0.0319189i \(-0.989838\pi\)
−0.278503 + 0.960435i \(0.589838\pi\)
\(398\) −0.180556 + 0.555694i −0.00905046 + 0.0278544i
\(399\) 7.32910 + 22.5567i 0.366914 + 1.12924i
\(400\) 0.953702 + 2.93519i 0.0476851 + 0.146760i
\(401\) 17.5634 0.877072 0.438536 0.898714i \(-0.355497\pi\)
0.438536 + 0.898714i \(0.355497\pi\)
\(402\) −4.33135 13.3305i −0.216028 0.664866i
\(403\) 5.80873 + 4.22029i 0.289353 + 0.210228i
\(404\) −9.61975 + 6.98916i −0.478600 + 0.347724i
\(405\) 7.59270 23.3679i 0.377284 1.16116i
\(406\) −1.04899 + 3.22845i −0.0520603 + 0.160225i
\(407\) −12.2677 −0.608087
\(408\) 14.8559 10.7934i 0.735476 0.534355i
\(409\) −8.20219 −0.405572 −0.202786 0.979223i \(-0.565000\pi\)
−0.202786 + 0.979223i \(0.565000\pi\)
\(410\) 10.8131 3.36253i 0.534021 0.166063i
\(411\) −9.42288 −0.464796
\(412\) 12.7928 9.29449i 0.630254 0.457907i
\(413\) −0.579731 −0.0285267
\(414\) −2.18764 + 6.73286i −0.107517 + 0.330902i
\(415\) −5.83831 + 17.9685i −0.286591 + 0.882038i
\(416\) 8.48648 6.16579i 0.416084 0.302303i
\(417\) 4.57156 + 3.32144i 0.223870 + 0.162651i
\(418\) 10.6773 + 32.8614i 0.522244 + 1.60730i
\(419\) 0.798443 0.0390065 0.0195032 0.999810i \(-0.493792\pi\)
0.0195032 + 0.999810i \(0.493792\pi\)
\(420\) 3.82555 + 11.7738i 0.186668 + 0.574505i
\(421\) 3.42160 + 10.5306i 0.166759 + 0.513230i 0.999162 0.0409406i \(-0.0130354\pi\)
−0.832403 + 0.554171i \(0.813035\pi\)
\(422\) 5.21904 16.0626i 0.254059 0.781913i
\(423\) −43.9121 + 31.9040i −2.13508 + 1.55123i
\(424\) 14.2774 0.693372
\(425\) 1.60977 4.95437i 0.0780854 0.240322i
\(426\) −12.9524 9.41047i −0.627546 0.455939i
\(427\) −0.672906 2.07099i −0.0325642 0.100222i
\(428\) −15.8407 + 11.5089i −0.765687 + 0.556304i
\(429\) 29.0286 + 21.0905i 1.40151 + 1.01826i
\(430\) −2.79530 2.03091i −0.134802 0.0979390i
\(431\) −18.7327 13.6101i −0.902322 0.655576i 0.0367391 0.999325i \(-0.488303\pi\)
−0.939061 + 0.343749i \(0.888303\pi\)
\(432\) 11.2422 + 8.16792i 0.540890 + 0.392979i
\(433\) 10.5956 7.69814i 0.509191 0.369949i −0.303325 0.952887i \(-0.598097\pi\)
0.812517 + 0.582938i \(0.198097\pi\)
\(434\) 0.813471 + 2.50361i 0.0390479 + 0.120177i
\(435\) 32.7694 + 23.8083i 1.57117 + 1.14152i
\(436\) −3.21611 + 9.89818i −0.154024 + 0.474037i
\(437\) −13.8843 −0.664179
\(438\) −10.8895 + 7.91170i −0.520321 + 0.378036i
\(439\) −1.71225 + 5.26976i −0.0817211 + 0.251512i −0.983566 0.180548i \(-0.942213\pi\)
0.901845 + 0.432060i \(0.142213\pi\)
\(440\) 12.7431 + 39.2191i 0.607501 + 1.86970i
\(441\) 1.86341 + 5.73499i 0.0887338 + 0.273095i
\(442\) −3.12916 −0.148839
\(443\) 7.47436 + 23.0037i 0.355118 + 1.09294i 0.955941 + 0.293558i \(0.0948395\pi\)
−0.600823 + 0.799382i \(0.705161\pi\)
\(444\) 7.06802 + 5.13522i 0.335434 + 0.243707i
\(445\) −37.9329 + 27.5599i −1.79819 + 1.30646i
\(446\) 0.850603 2.61789i 0.0402772 0.123961i
\(447\) −8.78403 + 27.0345i −0.415470 + 1.27869i
\(448\) 0.793753 0.0375013
\(449\) 13.1114 9.52597i 0.618764 0.449558i −0.233726 0.972303i \(-0.575092\pi\)
0.852490 + 0.522744i \(0.175092\pi\)
\(450\) −8.13830 −0.383643
\(451\) −40.1091 + 12.4726i −1.88866 + 0.587314i
\(452\) 4.39984 0.206951
\(453\) 20.9619 15.2297i 0.984875 0.715553i
\(454\) −5.81803 −0.273054
\(455\) 1.49056 4.58746i 0.0698784 0.215064i
\(456\) 17.3863 53.5095i 0.814188 2.50581i
\(457\) 24.0377 17.4644i 1.12443 0.816949i 0.139559 0.990214i \(-0.455432\pi\)
0.984875 + 0.173264i \(0.0554315\pi\)
\(458\) 3.72629 + 2.70731i 0.174118 + 0.126504i
\(459\) −7.24815 22.3075i −0.338315 1.04123i
\(460\) −7.24718 −0.337902
\(461\) 0.780257 + 2.40138i 0.0363402 + 0.111844i 0.967581 0.252561i \(-0.0812727\pi\)
−0.931241 + 0.364404i \(0.881273\pi\)
\(462\) 4.06525 + 12.5115i 0.189132 + 0.582090i
\(463\) −4.64527 + 14.2967i −0.215884 + 0.664423i 0.783206 + 0.621763i \(0.213583\pi\)
−0.999090 + 0.0426600i \(0.986417\pi\)
\(464\) −6.28012 + 4.56277i −0.291547 + 0.211821i
\(465\) 31.4111 1.45666
\(466\) −2.42926 + 7.47648i −0.112533 + 0.346341i
\(467\) 4.33532 + 3.14979i 0.200615 + 0.145755i 0.683557 0.729897i \(-0.260432\pi\)
−0.482942 + 0.875652i \(0.660432\pi\)
\(468\) −5.27304 16.2287i −0.243746 0.750174i
\(469\) 5.65443 4.10818i 0.261097 0.189698i
\(470\) 12.8784 + 9.35668i 0.594035 + 0.431591i
\(471\) −55.7204 40.4832i −2.56746 1.86537i
\(472\) 1.11260 + 0.808355i 0.0512118 + 0.0372075i
\(473\) 10.3686 + 7.53326i 0.476750 + 0.346379i
\(474\) −14.2905 + 10.3827i −0.656386 + 0.476892i
\(475\) −4.93229 15.1800i −0.226309 0.696507i
\(476\) 3.23982 + 2.35387i 0.148497 + 0.107889i
\(477\) 11.2150 34.5164i 0.513502 1.58040i
\(478\) −16.6334 −0.760794
\(479\) 18.4156 13.3797i 0.841429 0.611334i −0.0813408 0.996686i \(-0.525920\pi\)
0.922769 + 0.385353i \(0.125920\pi\)
\(480\) 14.1812 43.6452i 0.647279 1.99212i
\(481\) −1.05191 3.23743i −0.0479628 0.147614i
\(482\) −4.77532 14.6969i −0.217510 0.669427i
\(483\) −5.28629 −0.240534
\(484\) −15.3883 47.3603i −0.699467 2.15274i
\(485\) 0.0647999 + 0.0470799i 0.00294241 + 0.00213779i
\(486\) −0.294710 + 0.214120i −0.0133683 + 0.00971266i
\(487\) 1.27379 3.92032i 0.0577210 0.177647i −0.918039 0.396490i \(-0.870228\pi\)
0.975760 + 0.218843i \(0.0702282\pi\)
\(488\) −1.59629 + 4.91287i −0.0722605 + 0.222395i
\(489\) −48.0383 −2.17237
\(490\) 1.43074 1.03949i 0.0646341 0.0469595i
\(491\) −14.6553 −0.661385 −0.330692 0.943739i \(-0.607282\pi\)
−0.330692 + 0.943739i \(0.607282\pi\)
\(492\) 28.3298 + 9.60344i 1.27721 + 0.432957i
\(493\) 13.1027 0.590117
\(494\) −7.75655 + 5.63546i −0.348984 + 0.253551i
\(495\) 104.824 4.71149
\(496\) −1.86022 + 5.72518i −0.0835265 + 0.257068i
\(497\) 2.46698 7.59258i 0.110659 0.340574i
\(498\) 11.5673 8.40415i 0.518344 0.376599i
\(499\) −28.0791 20.4006i −1.25699 0.913258i −0.258385 0.966042i \(-0.583190\pi\)
−0.998606 + 0.0527844i \(0.983190\pi\)
\(500\) 3.79079 + 11.6668i 0.169529 + 0.521757i
\(501\) 34.2098 1.52838
\(502\) 4.06988 + 12.5258i 0.181648 + 0.559054i
\(503\) 6.39411 + 19.6790i 0.285099 + 0.877445i 0.986369 + 0.164549i \(0.0526169\pi\)
−0.701270 + 0.712896i \(0.747383\pi\)
\(504\) 4.42044 13.6047i 0.196902 0.606002i
\(505\) 16.3975 11.9135i 0.729679 0.530143i
\(506\) −7.70126 −0.342363
\(507\) 8.99513 27.6842i 0.399488 1.22950i
\(508\) 20.8626 + 15.1576i 0.925629 + 0.672508i
\(509\) −7.21483 22.2050i −0.319792 0.984217i −0.973737 0.227676i \(-0.926887\pi\)
0.653945 0.756542i \(-0.273113\pi\)
\(510\) −11.0750 + 8.04647i −0.490410 + 0.356304i
\(511\) −5.42999 3.94512i −0.240209 0.174522i
\(512\) 12.9729 + 9.42539i 0.573328 + 0.416547i
\(513\) −58.1415 42.2423i −2.56701 1.86504i
\(514\) 7.60853 + 5.52792i 0.335598 + 0.243826i
\(515\) −21.8061 + 15.8431i −0.960892 + 0.698129i
\(516\) −2.82049 8.68056i −0.124165 0.382140i
\(517\) −47.7698 34.7068i −2.10091 1.52640i
\(518\) 0.385667 1.18696i 0.0169453 0.0521521i
\(519\) −54.1754 −2.37804
\(520\) −9.25722 + 6.72576i −0.405956 + 0.294944i
\(521\) −8.12350 + 25.0016i −0.355897 + 1.09534i 0.599591 + 0.800307i \(0.295330\pi\)
−0.955488 + 0.295031i \(0.904670\pi\)
\(522\) −6.32551 19.4679i −0.276860 0.852088i
\(523\) 3.08516 + 9.49515i 0.134905 + 0.415194i 0.995575 0.0939684i \(-0.0299553\pi\)
−0.860670 + 0.509162i \(0.829955\pi\)
\(524\) 31.3735 1.37056
\(525\) −1.87791 5.77960i −0.0819585 0.252242i
\(526\) −10.9713 7.97114i −0.478373 0.347558i
\(527\) 8.22038 5.97246i 0.358086 0.260164i
\(528\) −9.29630 + 28.6111i −0.404569 + 1.24514i
\(529\) −6.15110 + 18.9311i −0.267439 + 0.823093i
\(530\) −10.6438 −0.462335
\(531\) 2.82820 2.05481i 0.122734 0.0891711i
\(532\) 12.2701 0.531975
\(533\) −6.73071 9.51527i −0.291540 0.412152i
\(534\) 35.4837 1.53553
\(535\) 27.0014 19.6177i 1.16737 0.848147i
\(536\) −16.5801 −0.716152
\(537\) −5.91773 + 18.2129i −0.255369 + 0.785945i
\(538\) −0.605978 + 1.86501i −0.0261256 + 0.0804062i
\(539\) −5.30704 + 3.85579i −0.228591 + 0.166081i
\(540\) −30.3480 22.0491i −1.30597 0.948843i
\(541\) 11.8241 + 36.3909i 0.508358 + 1.56457i 0.795051 + 0.606543i \(0.207444\pi\)
−0.286693 + 0.958023i \(0.592556\pi\)
\(542\) 1.22746 0.0527241
\(543\) 7.59201 + 23.3658i 0.325804 + 1.00272i
\(544\) −4.58736 14.1185i −0.196682 0.605324i
\(545\) 5.48208 16.8721i 0.234826 0.722722i
\(546\) −2.95321 + 2.14563i −0.126386 + 0.0918245i
\(547\) −14.4287 −0.616927 −0.308463 0.951236i \(-0.599815\pi\)
−0.308463 + 0.951236i \(0.599815\pi\)
\(548\) −1.50642 + 4.63627i −0.0643509 + 0.198052i
\(549\) 10.6232 + 7.71822i 0.453388 + 0.329405i
\(550\) −2.73580 8.41993i −0.116655 0.359027i
\(551\) 32.4791 23.5974i 1.38365 1.00528i
\(552\) 10.1453 + 7.37100i 0.431813 + 0.313730i
\(553\) −7.12588 5.17726i −0.303023 0.220159i
\(554\) −1.86104e−6 0 1.35212e-6i −7.90680e−8 0 5.74463e-8i
\(555\) −12.0479 8.75332i −0.511405 0.371558i
\(556\) 2.36507 1.71832i 0.100301 0.0728731i
\(557\) 6.87824 + 21.1691i 0.291441 + 0.896962i 0.984394 + 0.175979i \(0.0563092\pi\)
−0.692953 + 0.720982i \(0.743691\pi\)
\(558\) −12.8423 9.33049i −0.543659 0.394991i
\(559\) −1.09895 + 3.38222i −0.0464806 + 0.143053i
\(560\) 4.04413 0.170896
\(561\) 41.0806 29.8468i 1.73443 1.26013i
\(562\) −4.21972 + 12.9870i −0.177998 + 0.547822i
\(563\) 1.66033 + 5.10998i 0.0699747 + 0.215360i 0.979928 0.199350i \(-0.0638831\pi\)
−0.909954 + 0.414710i \(0.863883\pi\)
\(564\) 12.9944 + 39.9926i 0.547162 + 1.68399i
\(565\) −7.49982 −0.315520
\(566\) −0.952292 2.93085i −0.0400278 0.123193i
\(567\) −7.50122 5.44995i −0.315022 0.228877i
\(568\) −15.3214 + 11.1316i −0.642870 + 0.467072i
\(569\) −1.31538 + 4.04833i −0.0551437 + 0.169715i −0.974835 0.222927i \(-0.928439\pi\)
0.919691 + 0.392642i \(0.128439\pi\)
\(570\) −12.9614 + 39.8912i −0.542895 + 1.67086i
\(571\) 18.1641 0.760146 0.380073 0.924957i \(-0.375899\pi\)
0.380073 + 0.924957i \(0.375899\pi\)
\(572\) 15.0178 10.9110i 0.627924 0.456213i
\(573\) 23.5889 0.985440
\(574\) 0.0541432 4.27287i 0.00225989 0.178346i
\(575\) 3.55753 0.148359
\(576\) −3.87230 + 2.81339i −0.161346 + 0.117225i
\(577\) −33.6722 −1.40179 −0.700896 0.713264i \(-0.747216\pi\)
−0.700896 + 0.713264i \(0.747216\pi\)
\(578\) 2.13743 6.57834i 0.0889055 0.273623i
\(579\) −5.59433 + 17.2176i −0.232492 + 0.715538i
\(580\) 16.9530 12.3171i 0.703936 0.511439i
\(581\) 5.76797 + 4.19068i 0.239296 + 0.173858i
\(582\) −0.0187314 0.0576492i −0.000776440 0.00238964i
\(583\) 39.4810 1.63513
\(584\) 4.92017 + 15.1427i 0.203598 + 0.626611i
\(585\) 8.98824 + 27.6630i 0.371618 + 1.14372i
\(586\) −2.81341 + 8.65878i −0.116221 + 0.357691i
\(587\) −1.71846 + 1.24854i −0.0709286 + 0.0515326i −0.622685 0.782473i \(-0.713958\pi\)
0.551756 + 0.834006i \(0.313958\pi\)
\(588\) 4.67167 0.192657
\(589\) 9.62057 29.6091i 0.396409 1.22002i
\(590\) −0.829443 0.602626i −0.0341476 0.0248097i
\(591\) 2.00110 + 6.15876i 0.0823144 + 0.253338i
\(592\) 2.30893 1.67754i 0.0948965 0.0689464i
\(593\) 8.48921 + 6.16777i 0.348610 + 0.253280i 0.748286 0.663377i \(-0.230877\pi\)
−0.399676 + 0.916657i \(0.630877\pi\)
\(594\) −32.2495 23.4306i −1.32321 0.961370i
\(595\) −5.52249 4.01232i −0.226400 0.164489i
\(596\) 11.8973 + 8.64389i 0.487332 + 0.354067i
\(597\) 2.12849 1.54644i 0.0871132 0.0632915i
\(598\) −0.660353 2.03236i −0.0270038 0.0831092i
\(599\) −34.7157 25.2224i −1.41845 1.03056i −0.992026 0.126036i \(-0.959775\pi\)
−0.426420 0.904525i \(-0.640225\pi\)
\(600\) −4.45482 + 13.7105i −0.181867 + 0.559730i
\(601\) 16.0677 0.655414 0.327707 0.944779i \(-0.393724\pi\)
0.327707 + 0.944779i \(0.393724\pi\)
\(602\) −1.05485 + 0.766391i −0.0429924 + 0.0312358i
\(603\) −13.0239 + 40.0833i −0.530372 + 1.63232i
\(604\) −4.14223 12.7485i −0.168545 0.518727i
\(605\) 26.2303 + 80.7287i 1.06641 + 3.28209i
\(606\) −15.3388 −0.623094
\(607\) 6.38944 + 19.6647i 0.259339 + 0.798164i 0.992944 + 0.118587i \(0.0378365\pi\)
−0.733604 + 0.679577i \(0.762163\pi\)
\(608\) −36.7978 26.7352i −1.49235 1.08426i
\(609\) 12.3660 8.98441i 0.501095 0.364067i
\(610\) 1.19003 3.66253i 0.0481828 0.148291i
\(611\) 5.06302 15.5824i 0.204828 0.630395i
\(612\) −24.1485 −0.976144
\(613\) −2.22041 + 1.61322i −0.0896816 + 0.0651575i −0.631722 0.775195i \(-0.717652\pi\)
0.542041 + 0.840352i \(0.317652\pi\)
\(614\) 1.92385 0.0776401
\(615\) −48.2901 16.3697i −1.94724 0.660090i
\(616\) 15.5615 0.626991
\(617\) −8.60637 + 6.25289i −0.346479 + 0.251732i −0.747391 0.664385i \(-0.768694\pi\)
0.400911 + 0.916117i \(0.368694\pi\)
\(618\) 20.3981 0.820534
\(619\) 1.19571 3.68003i 0.0480598 0.147913i −0.924147 0.382038i \(-0.875222\pi\)
0.972207 + 0.234125i \(0.0752225\pi\)
\(620\) 5.02163 15.4550i 0.201673 0.620687i
\(621\) 12.9589 9.41521i 0.520024 0.377819i
\(622\) 7.51003 + 5.45636i 0.301125 + 0.218780i
\(623\) 5.46766 + 16.8277i 0.219057 + 0.674189i
\(624\) −8.34755 −0.334170
\(625\) −9.58626 29.5035i −0.383451 1.18014i
\(626\) −6.28830 19.3534i −0.251331 0.773518i
\(627\) 48.0779 147.969i 1.92005 5.90930i
\(628\) −28.8266 + 20.9437i −1.15030 + 0.835745i
\(629\) −4.81732 −0.192079
\(630\) −3.29542 + 10.1423i −0.131293 + 0.404077i
\(631\) 23.3722 + 16.9809i 0.930433 + 0.675999i 0.946099 0.323878i \(-0.104987\pi\)
−0.0156659 + 0.999877i \(0.504987\pi\)
\(632\) 6.45684 + 19.8721i 0.256839 + 0.790470i
\(633\) −61.5248 + 44.7004i −2.44539 + 1.77668i
\(634\) −13.0630 9.49079i −0.518796 0.376928i
\(635\) −35.5617 25.8371i −1.41122 1.02531i
\(636\) −22.7469 16.5266i −0.901974 0.655323i
\(637\) −1.47260 1.06991i −0.0583465 0.0423912i
\(638\) 18.0152 13.0888i 0.713230 0.518192i
\(639\) 14.8762 + 45.7842i 0.588493 + 1.81119i
\(640\) −23.5742 17.1277i −0.931853 0.677031i
\(641\) −0.999445 + 3.07597i −0.0394757 + 0.121494i −0.968852 0.247639i \(-0.920345\pi\)
0.929377 + 0.369133i \(0.120345\pi\)
\(642\) −25.2580 −0.996855
\(643\) −3.57921 + 2.60045i −0.141150 + 0.102552i −0.656120 0.754657i \(-0.727803\pi\)
0.514969 + 0.857209i \(0.327803\pi\)
\(644\) −0.845108 + 2.60097i −0.0333019 + 0.102493i
\(645\) 4.80770 + 14.7966i 0.189303 + 0.582615i
\(646\) 4.19280 + 12.9041i 0.164964 + 0.507706i
\(647\) −13.4900 −0.530348 −0.265174 0.964201i \(-0.585429\pi\)
−0.265174 + 0.964201i \(0.585429\pi\)
\(648\) 6.79694 + 20.9188i 0.267009 + 0.821769i
\(649\) 3.07666 + 2.23532i 0.120769 + 0.0877441i
\(650\) 1.98743 1.44395i 0.0779534 0.0566364i
\(651\) 3.66291 11.2733i 0.143561 0.441834i
\(652\) −7.67978 + 23.6359i −0.300763 + 0.925654i
\(653\) −26.5091 −1.03738 −0.518690 0.854962i \(-0.673580\pi\)
−0.518690 + 0.854962i \(0.673580\pi\)
\(654\) −10.8615 + 7.89136i −0.424719 + 0.308577i
\(655\) −53.4782 −2.08956
\(656\) 5.84347 7.83220i 0.228149 0.305796i
\(657\) 40.4732 1.57901
\(658\) 4.85983 3.53087i 0.189456 0.137648i
\(659\) 10.2076 0.397632 0.198816 0.980037i \(-0.436290\pi\)
0.198816 + 0.980037i \(0.436290\pi\)
\(660\) 25.0951 77.2349i 0.976827 3.00636i
\(661\) 13.7875 42.4335i 0.536271 1.65047i −0.204614 0.978843i \(-0.565594\pi\)
0.740886 0.671631i \(-0.234406\pi\)
\(662\) 1.34705 0.978691i 0.0523547 0.0380379i
\(663\) 11.3991 + 8.28190i 0.442702 + 0.321642i
\(664\) −5.22642 16.0853i −0.202824 0.624229i
\(665\) −20.9151 −0.811055
\(666\) 2.32562 + 7.15753i 0.0901160 + 0.277349i
\(667\) 2.76510 + 8.51010i 0.107065 + 0.329512i
\(668\) 5.46905 16.8320i 0.211604 0.651249i
\(669\) −10.0273 + 7.28529i −0.387680 + 0.281666i
\(670\) 12.3604 0.477525
\(671\) −4.41417 + 13.5854i −0.170407 + 0.524460i
\(672\) −14.0103 10.1791i −0.540459 0.392667i
\(673\) 0.131620 + 0.405084i 0.00507357 + 0.0156148i 0.953561 0.301199i \(-0.0973869\pi\)
−0.948488 + 0.316814i \(0.897387\pi\)
\(674\) 2.78332 2.02220i 0.107210 0.0778923i
\(675\) 14.8974 + 10.8236i 0.573400 + 0.416599i
\(676\) −12.1832 8.85162i −0.468585 0.340447i
\(677\) 14.6506 + 10.6443i 0.563067 + 0.409092i 0.832580 0.553905i \(-0.186863\pi\)
−0.269513 + 0.962997i \(0.586863\pi\)
\(678\) 4.59175 + 3.33610i 0.176345 + 0.128122i
\(679\) 0.0244532 0.0177663i 0.000938426 0.000681806i
\(680\) 5.00399 + 15.4007i 0.191894 + 0.590589i
\(681\) 21.1942 + 15.3985i 0.812165 + 0.590072i
\(682\) 5.33626 16.4233i 0.204336 0.628882i
\(683\) 15.9308 0.609576 0.304788 0.952420i \(-0.401414\pi\)
0.304788 + 0.952420i \(0.401414\pi\)
\(684\) −59.8592 + 43.4903i −2.28877 + 1.66289i
\(685\) 2.56778 7.90283i 0.0981100 0.301952i
\(686\) −0.206227 0.634701i −0.00787378 0.0242330i
\(687\) −6.40893 19.7247i −0.244516 0.752543i
\(688\) −2.98164 −0.113674
\(689\) 3.38533 + 10.4190i 0.128971 + 0.396932i
\(690\) −7.56329 5.49505i −0.287930 0.209193i
\(691\) −3.44631 + 2.50389i −0.131104 + 0.0952526i −0.651405 0.758731i \(-0.725820\pi\)
0.520301 + 0.853983i \(0.325820\pi\)
\(692\) −8.66091 + 26.6555i −0.329238 + 1.01329i
\(693\) 12.2237 37.6208i 0.464341 1.42909i
\(694\) −5.23278 −0.198634
\(695\) −4.03141 + 2.92899i −0.152920 + 0.111103i
\(696\) −36.2600 −1.37443
\(697\) −15.7502 + 4.89780i −0.596580 + 0.185517i
\(698\) 19.2097 0.727097
\(699\) 28.6373 20.8062i 1.08316 0.786964i
\(700\) −3.14391 −0.118829
\(701\) 4.85512 14.9425i 0.183375 0.564372i −0.816541 0.577287i \(-0.804111\pi\)
0.999917 + 0.0129157i \(0.00411130\pi\)
\(702\) 3.41805 10.5197i 0.129006 0.397040i
\(703\) −11.9412 + 8.67577i −0.450370 + 0.327213i
\(704\) −4.21248 3.06055i −0.158764 0.115349i
\(705\) −22.1498 68.1700i −0.834209 2.56743i
\(706\) 14.2980 0.538112
\(707\) −2.36354 7.27423i −0.0888900 0.273575i
\(708\) −0.836915 2.57576i −0.0314532 0.0968030i
\(709\) 11.6090 35.7287i 0.435984 1.34182i −0.456091 0.889933i \(-0.650751\pi\)
0.892075 0.451888i \(-0.149249\pi\)
\(710\) 11.4220 8.29858i 0.428661 0.311440i
\(711\) 53.1138 1.99192
\(712\) 12.9705 39.9192i 0.486092 1.49604i
\(713\) 5.61382 + 4.07868i 0.210239 + 0.152748i
\(714\) 1.59636 + 4.91308i 0.0597421 + 0.183867i
\(715\) −25.5988 + 18.5986i −0.957339 + 0.695548i
\(716\) 8.01510 + 5.82331i 0.299539 + 0.217627i
\(717\) 60.5930 + 44.0234i 2.26289 + 1.64408i
\(718\) −8.03602 5.83851i −0.299901 0.217891i
\(719\) 5.27464 + 3.83225i 0.196711 + 0.142919i 0.681781 0.731557i \(-0.261206\pi\)
−0.485070 + 0.874475i \(0.661206\pi\)
\(720\) −19.7292 + 14.3341i −0.735263 + 0.534200i
\(721\) 3.14314 + 9.67358i 0.117057 + 0.360263i
\(722\) 23.3746 + 16.9826i 0.869911 + 0.632027i
\(723\) −21.5024 + 66.1775i −0.799682 + 2.46117i
\(724\) 12.7102 0.472372
\(725\) −8.32197 + 6.04627i −0.309070 + 0.224553i
\(726\) 19.8506 61.0939i 0.736726 2.26741i
\(727\) 1.19280 + 3.67105i 0.0442383 + 0.136152i 0.970736 0.240149i \(-0.0771962\pi\)
−0.926498 + 0.376300i \(0.877196\pi\)
\(728\) 1.33434 + 4.10667i 0.0494538 + 0.152203i
\(729\) −26.1758 −0.969472
\(730\) −3.66797 11.2889i −0.135758 0.417820i
\(731\) 4.07159 + 2.95818i 0.150593 + 0.109412i
\(732\) 8.23004 5.97948i 0.304191 0.221008i
\(733\) 0.893122 2.74875i 0.0329882 0.101527i −0.933207 0.359340i \(-0.883002\pi\)
0.966195 + 0.257813i \(0.0830018\pi\)
\(734\) 5.91015 18.1896i 0.218148 0.671389i
\(735\) −7.96318 −0.293726
\(736\) 8.20172 5.95890i 0.302319 0.219648i
\(737\) −45.8486 −1.68885
\(738\) 14.8807 + 21.0370i 0.547766 + 0.774382i
\(739\) −48.1123 −1.76984 −0.884920 0.465743i \(-0.845787\pi\)
−0.884920 + 0.465743i \(0.845787\pi\)
\(740\) −6.23291 + 4.52847i −0.229126 + 0.166470i
\(741\) 43.1713 1.58594
\(742\) −1.24119 + 3.81999i −0.0455655 + 0.140236i
\(743\) 2.94176 9.05380i 0.107923 0.332152i −0.882483 0.470345i \(-0.844130\pi\)
0.990405 + 0.138193i \(0.0441295\pi\)
\(744\) −22.7488 + 16.5280i −0.834010 + 0.605944i
\(745\) −20.2797 14.7341i −0.742991 0.539815i
\(746\) −5.87468 18.0804i −0.215087 0.661970i
\(747\) −42.9924 −1.57301
\(748\) −8.11784 24.9842i −0.296818 0.913511i
\(749\) −3.89199 11.9783i −0.142210 0.437678i
\(750\) −4.89005 + 15.0500i −0.178559 + 0.549549i
\(751\) 24.3637 17.7013i 0.889045 0.645929i −0.0465841 0.998914i \(-0.514834\pi\)
0.935629 + 0.352986i \(0.114834\pi\)
\(752\) 13.7368 0.500931
\(753\) 18.3259 56.4014i 0.667833 2.05538i
\(754\) 4.99886 + 3.63189i 0.182048 + 0.132266i
\(755\) 7.06070 + 21.7306i 0.256965 + 0.790857i
\(756\) −11.4522 + 8.32054i −0.416514 + 0.302615i
\(757\) −15.2035 11.0460i −0.552582 0.401474i 0.276155 0.961113i \(-0.410940\pi\)
−0.828736 + 0.559639i \(0.810940\pi\)
\(758\) −7.86223 5.71225i −0.285569 0.207478i
\(759\) 28.0546 + 20.3828i 1.01832 + 0.739850i
\(760\) 40.1398 + 29.1633i 1.45602 + 1.05786i
\(761\) −24.6714 + 17.9248i −0.894337 + 0.649774i −0.937005 0.349315i \(-0.886414\pi\)
0.0426683 + 0.999089i \(0.486414\pi\)
\(762\) 10.2796 + 31.6374i 0.372392 + 1.14610i
\(763\) −5.41603 3.93498i −0.196073 0.142456i
\(764\) 3.77111 11.6063i 0.136434 0.419900i
\(765\) 41.1626 1.48824
\(766\) −4.42336 + 3.21376i −0.159822 + 0.116118i
\(767\) −0.326089 + 1.00360i −0.0117744 + 0.0362378i
\(768\) 8.28863 + 25.5098i 0.299090 + 0.920505i
\(769\) −6.74515 20.7594i −0.243236 0.748605i −0.995921 0.0902241i \(-0.971242\pi\)
0.752685 0.658381i \(-0.228758\pi\)
\(770\) −11.6011 −0.418073
\(771\) −13.0861 40.2748i −0.471283 1.45046i
\(772\) 7.57708 + 5.50507i 0.272705 + 0.198132i
\(773\) 5.48813 3.98736i 0.197394 0.143415i −0.484698 0.874682i \(-0.661070\pi\)
0.682092 + 0.731266i \(0.261070\pi\)
\(774\) 2.42963 7.47764i 0.0873313 0.268778i
\(775\) −2.46504 + 7.58661i −0.0885468 + 0.272519i
\(776\) −0.0717024 −0.00257397
\(777\) −4.54645 + 3.30319i −0.163103 + 0.118501i
\(778\) 7.23363 0.259338
\(779\) −30.2208 + 40.5060i −1.08277 + 1.45128i
\(780\) 22.5340 0.806847
\(781\) −42.3678 + 30.7820i −1.51604 + 1.10147i
\(782\) −3.02416 −0.108144
\(783\) −14.3124 + 44.0492i −0.511485 + 1.57419i
\(784\) 0.471594 1.45142i 0.0168426 0.0518363i
\(785\) 49.1368 35.7000i 1.75377 1.27419i
\(786\) 32.7419 + 23.7884i 1.16787 + 0.848504i
\(787\) 5.13585 + 15.8065i 0.183073 + 0.563442i 0.999910 0.0134276i \(-0.00427425\pi\)
−0.816837 + 0.576869i \(0.804274\pi\)
\(788\) 3.35016 0.119345
\(789\) 18.8698 + 58.0754i 0.671784 + 2.06754i
\(790\) −4.81355 14.8146i −0.171259 0.527080i
\(791\) −0.874568 + 2.69164i −0.0310961 + 0.0957038i
\(792\) −75.9164 + 55.1565i −2.69757 + 1.95990i
\(793\) −3.96368 −0.140754
\(794\) −6.49100 + 19.9772i −0.230357 + 0.708966i
\(795\) 38.7736 + 28.1707i 1.37516 + 0.999112i
\(796\) −0.420605 1.29449i −0.0149080 0.0458820i
\(797\) −21.8756 + 15.8935i −0.774873 + 0.562978i −0.903436 0.428723i \(-0.858964\pi\)
0.128563 + 0.991701i \(0.458964\pi\)
\(798\) 12.8053 + 9.30357i 0.453302 + 0.329343i
\(799\) −18.7584 13.6288i −0.663625 0.482152i
\(800\) 9.42856 + 6.85025i 0.333350 + 0.242193i
\(801\) −86.3183 62.7139i −3.04991 2.21589i
\(802\) 9.48261 6.88952i 0.334843 0.243277i
\(803\) 13.6056 + 41.8738i 0.480132 + 1.47770i
\(804\) 26.4156 + 19.1921i 0.931608 + 0.676853i
\(805\) 1.44054 4.43353i 0.0507724 0.156262i
\(806\) 4.79166 0.168779
\(807\) 7.14358 5.19012i 0.251466 0.182701i
\(808\) −5.60686 + 17.2561i −0.197249 + 0.607069i
\(809\) −10.9990 33.8513i −0.386703 1.19015i −0.935237 0.354021i \(-0.884814\pi\)
0.548535 0.836128i \(-0.315186\pi\)
\(810\) −5.06709 15.5949i −0.178040 0.547949i
\(811\) 4.01117 0.140851 0.0704256 0.997517i \(-0.477564\pi\)
0.0704256 + 0.997517i \(0.477564\pi\)
\(812\) −2.44361 7.52067i −0.0857540 0.263924i
\(813\) −4.47147 3.24871i −0.156821 0.113937i
\(814\) −6.62343 + 4.81221i −0.232151 + 0.168668i
\(815\) 13.0907 40.2890i 0.458547 1.41126i
\(816\) −3.65050 + 11.2351i −0.127793 + 0.393307i
\(817\) 15.4202 0.539485
\(818\) −4.42844 + 3.21745i −0.154837 + 0.112495i
\(819\) 10.9762 0.383540
\(820\) −15.7743 + 21.1428i −0.550862 + 0.738340i
\(821\) −45.2684 −1.57988 −0.789939 0.613185i \(-0.789888\pi\)
−0.789939 + 0.613185i \(0.789888\pi\)
\(822\) −5.08750 + 3.69628i −0.177447 + 0.128923i
\(823\) 28.2477 0.984653 0.492327 0.870411i \(-0.336147\pi\)
0.492327 + 0.870411i \(0.336147\pi\)
\(824\) 7.45624 22.9480i 0.259751 0.799430i
\(825\) −12.3188 + 37.9134i −0.428886 + 1.31998i
\(826\) −0.313002 + 0.227409i −0.0108907 + 0.00791258i
\(827\) 41.5559 + 30.1921i 1.44504 + 1.04988i 0.986959 + 0.160972i \(0.0514630\pi\)
0.458081 + 0.888911i \(0.348537\pi\)
\(828\) −5.09610 15.6842i −0.177102 0.545064i
\(829\) 48.1386 1.67192 0.835961 0.548789i \(-0.184911\pi\)
0.835961 + 0.548789i \(0.184911\pi\)
\(830\) 3.89628 + 11.9915i 0.135242 + 0.416232i
\(831\) 3.20084e−6 0 9.85118e-6i 1.11036e−7 0 3.41734e-7i
\(832\) 0.446472 1.37410i 0.0154786 0.0476383i
\(833\) −2.08399 + 1.51411i −0.0722059 + 0.0524607i
\(834\) 3.77112 0.130583
\(835\) −9.32235 + 28.6913i −0.322613 + 0.992902i
\(836\) −65.1178 47.3109i −2.25215 1.63628i
\(837\) 11.0991 + 34.1594i 0.383640 + 1.18072i
\(838\) 0.431086 0.313202i 0.0148916 0.0108194i
\(839\) −6.85951 4.98372i −0.236817 0.172057i 0.463047 0.886334i \(-0.346756\pi\)
−0.699864 + 0.714276i \(0.746756\pi\)
\(840\) 15.2827 + 11.1035i 0.527304 + 0.383109i
\(841\) 2.52971 + 1.83795i 0.0872315 + 0.0633774i
\(842\) 5.97816 + 4.34339i 0.206021 + 0.149683i
\(843\) 49.7443 36.1413i 1.71328 1.24477i
\(844\) 12.1578 + 37.4177i 0.418487 + 1.28797i
\(845\) 20.7671 + 15.0882i 0.714410 + 0.519049i
\(846\) −11.1937 + 34.4505i −0.384846 + 1.18443i
\(847\) 32.0319 1.10063
\(848\) −7.43081 + 5.39880i −0.255175 + 0.185395i
\(849\) −4.28800 + 13.1971i −0.147164 + 0.452923i
\(850\) −1.07430 3.30637i −0.0368483 0.113408i
\(851\) −1.01661 3.12880i −0.0348489 0.107254i
\(852\) 37.2954 1.27772
\(853\) 1.14322 + 3.51846i 0.0391430 + 0.120470i 0.968719 0.248162i \(-0.0798264\pi\)
−0.929576 + 0.368632i \(0.879826\pi\)
\(854\) −1.17569 0.854188i −0.0402313 0.0292297i
\(855\) 102.034 74.1320i 3.48949 2.53526i
\(856\) −9.23270 + 28.4153i −0.315567 + 0.971216i
\(857\) 8.98814 27.6627i 0.307029 0.944938i −0.671883 0.740657i \(-0.734514\pi\)
0.978912 0.204281i \(-0.0654857\pi\)
\(858\) 23.9459 0.817500
\(859\) 28.9757 21.0521i 0.988638 0.718288i 0.0290158 0.999579i \(-0.490763\pi\)
0.959622 + 0.281291i \(0.0907627\pi\)
\(860\) 8.04886 0.274464
\(861\) −11.5062 + 15.4221i −0.392130 + 0.525585i
\(862\) −15.4527 −0.526323
\(863\) 8.87280 6.44647i 0.302034 0.219440i −0.426437 0.904517i \(-0.640231\pi\)
0.728471 + 0.685077i \(0.240231\pi\)
\(864\) 52.4748 1.78523
\(865\) 14.7631 45.4361i 0.501960 1.54487i
\(866\) 2.70092 8.31259i 0.0917812 0.282473i
\(867\) −25.1972 + 18.3068i −0.855741 + 0.621732i
\(868\) −4.96112 3.60447i −0.168392 0.122344i
\(869\) 17.8549 + 54.9519i 0.605687 + 1.86411i
\(870\) 27.0317 0.916461
\(871\) −3.93133 12.0994i −0.133208 0.409973i
\(872\) 4.90752 + 15.1038i 0.166190 + 0.511479i
\(873\) −0.0563230 + 0.173344i −0.00190624 + 0.00586682i
\(874\) −7.49628 + 5.44637i −0.253566 + 0.184226i
\(875\) −7.89080 −0.266758
\(876\) 9.68939 29.8209i 0.327374 1.00755i
\(877\) 25.2127 + 18.3181i 0.851373 + 0.618559i 0.925524 0.378688i \(-0.123625\pi\)
−0.0741512 + 0.997247i \(0.523625\pi\)
\(878\) 1.14269 + 3.51685i 0.0385640 + 0.118688i
\(879\) 33.1659 24.0964i 1.11866 0.812753i
\(880\) −21.4624 15.5933i −0.723497 0.525651i
\(881\) 2.35074 + 1.70792i 0.0791986 + 0.0575412i 0.626680 0.779277i \(-0.284413\pi\)
−0.547481 + 0.836818i \(0.684413\pi\)
\(882\) 3.25572 + 2.36542i 0.109626 + 0.0796477i
\(883\) −38.1236 27.6984i −1.28296 0.932125i −0.283322 0.959025i \(-0.591437\pi\)
−0.999638 + 0.0268993i \(0.991437\pi\)
\(884\) 5.89722 4.28458i 0.198345 0.144106i
\(885\) 1.42658 + 4.39055i 0.0479539 + 0.147587i
\(886\) 13.0591 + 9.48797i 0.438728 + 0.318755i
\(887\) −1.96435 + 6.04565i −0.0659565 + 0.202993i −0.978603 0.205756i \(-0.934035\pi\)
0.912647 + 0.408749i \(0.134035\pi\)
\(888\) 13.3313 0.447368
\(889\) −13.4197 + 9.74998i −0.450082 + 0.327004i
\(890\) −9.66950 + 29.7597i −0.324122 + 0.997546i
\(891\) 18.7954 + 57.8463i 0.629670 + 1.93792i
\(892\) 1.98148 + 6.09837i 0.0663448 + 0.204188i
\(893\) −71.0431 −2.37737
\(894\) 5.86215 + 18.0418i 0.196060 + 0.603409i
\(895\) −13.6623 9.92622i −0.456680 0.331797i
\(896\) −8.89606 + 6.46337i −0.297197 + 0.215926i
\(897\) −2.97345 + 9.15132i −0.0992804 + 0.305554i
\(898\) 3.34223 10.2863i 0.111532 0.343259i
\(899\) −20.0642 −0.669177
\(900\) 15.3375 11.1433i 0.511249 0.371444i
\(901\) 15.5035 0.516497
\(902\) −16.7627 + 22.4676i −0.558135 + 0.748088i
\(903\) 5.87105 0.195376
\(904\) 5.43157 3.94627i 0.180651 0.131251i
\(905\) −21.6654 −0.720183
\(906\) 5.34340 16.4453i 0.177523 0.546358i
\(907\) 9.73880 29.9729i 0.323371 0.995235i −0.648799 0.760960i \(-0.724728\pi\)
0.972170 0.234275i \(-0.0752716\pi\)
\(908\) 10.9647 7.96632i 0.363876 0.264372i
\(909\) 37.3134 + 27.1097i 1.23761 + 0.899173i
\(910\) −0.994744 3.06151i −0.0329754 0.101488i
\(911\) −27.9612 −0.926396 −0.463198 0.886255i \(-0.653298\pi\)
−0.463198 + 0.886255i \(0.653298\pi\)
\(912\) 11.1850 + 34.4239i 0.370373 + 1.13989i
\(913\) −14.4525 44.4802i −0.478308 1.47208i
\(914\) 6.12745 18.8584i 0.202678 0.623779i
\(915\) −14.0287 + 10.1924i −0.463773 + 0.336951i
\(916\) −10.7296 −0.354515
\(917\) −6.23619 + 19.1930i −0.205937 + 0.633809i
\(918\) −12.6638 9.20081i −0.417969 0.303672i
\(919\) 5.85693 + 18.0258i 0.193202 + 0.594616i 0.999993 + 0.00377826i \(0.00120266\pi\)
−0.806790 + 0.590838i \(0.798797\pi\)
\(920\) −8.94660 + 6.50008i −0.294961 + 0.214301i
\(921\) −7.00829 5.09182i −0.230931 0.167781i
\(922\) 1.36325 + 0.990460i 0.0448963 + 0.0326191i
\(923\) −11.7562 8.54138i −0.386960 0.281143i
\(924\) −24.7928 18.0130i −0.815622 0.592584i
\(925\) 3.05964 2.22296i 0.100600 0.0730904i
\(926\) 3.10009 + 9.54109i 0.101875 + 0.313540i
\(927\) −49.6209 36.0517i −1.62977 1.18409i
\(928\) −9.05837 + 27.8788i −0.297355 + 0.915166i
\(929\) −13.3132 −0.436791 −0.218395 0.975860i \(-0.570082\pi\)
−0.218395 + 0.975860i \(0.570082\pi\)
\(930\) 16.9591 12.3215i 0.556112 0.404039i
\(931\) −2.43896 + 7.50633i −0.0799335 + 0.246010i
\(932\) −5.65895 17.4165i −0.185365 0.570495i
\(933\) −12.9167 39.7534i −0.422873 1.30147i
\(934\) 3.57624 0.117018
\(935\) 13.8374 + 42.5871i 0.452531 + 1.39275i
\(936\) −21.0653 15.3048i −0.688540 0.500254i
\(937\) −10.0655 + 7.31300i −0.328825 + 0.238905i −0.739932 0.672682i \(-0.765142\pi\)
0.411107 + 0.911587i \(0.365142\pi\)
\(938\) 1.44137 4.43609i 0.0470625 0.144843i
\(939\) −28.3151 + 87.1448i −0.924027 + 2.84386i
\(940\) −37.0822 −1.20949
\(941\) 0.695430 0.505259i 0.0226704 0.0164710i −0.576392 0.817173i \(-0.695540\pi\)
0.599063 + 0.800702i \(0.295540\pi\)
\(942\) −45.9641 −1.49759
\(943\) −6.50487 9.19600i −0.211828 0.299463i
\(944\) −0.884733 −0.0287956
\(945\) 19.5211 14.1829i 0.635021 0.461370i
\(946\) 8.55316 0.278087
\(947\) −9.54256 + 29.3690i −0.310092 + 0.954364i 0.667636 + 0.744487i \(0.267306\pi\)
−0.977728 + 0.209876i \(0.932694\pi\)
\(948\) 12.7156 39.1345i 0.412983 1.27103i
\(949\) −9.88384 + 7.18103i −0.320843 + 0.233106i
\(950\) −8.61760 6.26105i −0.279592 0.203135i
\(951\) 22.4673 + 69.1471i 0.728551 + 2.24225i
\(952\) 6.11075 0.198050
\(953\) −0.289321 0.890440i −0.00937204 0.0288442i 0.946261 0.323404i \(-0.104827\pi\)
−0.955633 + 0.294559i \(0.904827\pi\)
\(954\) −7.48452 23.0350i −0.242320 0.745785i
\(955\) −6.42810 + 19.7837i −0.208008 + 0.640184i
\(956\) 31.3474 22.7752i 1.01385 0.736603i
\(957\) −100.269 −3.24123
\(958\) 4.69432 14.4476i 0.151667 0.466782i
\(959\) −2.53685 1.84313i −0.0819191 0.0595177i
\(960\) −1.95323 6.01143i −0.0630403 0.194018i
\(961\) 12.4917 9.07574i 0.402958 0.292766i
\(962\) −1.83787 1.33529i −0.0592553 0.0430515i
\(963\) 61.4432 + 44.6411i 1.97998 + 1.43854i
\(964\) 29.1233 + 21.1593i 0.937999 + 0.681496i
\(965\) −12.9156 9.38376i −0.415769 0.302074i
\(966\) −2.85411 + 2.07364i −0.0918296 + 0.0667181i
\(967\) −11.4384 35.2037i −0.367833 1.13207i −0.948188 0.317710i \(-0.897086\pi\)
0.580355 0.814364i \(-0.302914\pi\)
\(968\) −61.4747 44.6640i −1.97587 1.43555i
\(969\) 18.8794 58.1048i 0.606494 1.86660i
\(970\) 0.0534539 0.00171630
\(971\) 38.7863 28.1799i 1.24471 0.904337i 0.246810 0.969064i \(-0.420618\pi\)
0.997903 + 0.0647274i \(0.0206178\pi\)
\(972\) 0.262230 0.807062i 0.00841104 0.0258865i
\(973\) 0.581089 + 1.78841i 0.0186289 + 0.0573337i
\(974\) −0.850082 2.61628i −0.0272384 0.0838311i
\(975\) −11.0616 −0.354255
\(976\) −1.02693 3.16056i −0.0328712 0.101167i
\(977\) 19.3583 + 14.0646i 0.619326 + 0.449967i 0.852686 0.522424i \(-0.174972\pi\)
−0.233360 + 0.972390i \(0.574972\pi\)
\(978\) −25.9363 + 18.8438i −0.829351 + 0.602559i
\(979\) 35.8671 110.388i 1.14632 3.52800i
\(980\) −1.27306 + 3.91806i −0.0406663 + 0.125158i
\(981\) 40.3691 1.28889
\(982\) −7.91253 + 5.74879i −0.252499 + 0.183451i
\(983\) −6.52661 −0.208166 −0.104083 0.994569i \(-0.533191\pi\)
−0.104083 + 0.994569i \(0.533191\pi\)
\(984\) 43.5864 13.5540i 1.38948 0.432085i
\(985\) −5.71058 −0.181954
\(986\) 7.07428 5.13977i 0.225291 0.163684i
\(987\) −27.0488 −0.860972
\(988\) 6.90170 21.2413i 0.219572 0.675774i
\(989\) −1.06208 + 3.26873i −0.0337720 + 0.103940i
\(990\) 56.5954 41.1190i 1.79872 1.30685i
\(991\) 7.56301 + 5.49485i 0.240247 + 0.174550i 0.701393 0.712774i \(-0.252562\pi\)
−0.461146 + 0.887324i \(0.652562\pi\)
\(992\) 7.02461 + 21.6195i 0.223032 + 0.686421i
\(993\) −7.49740 −0.237923
\(994\) −1.64637 5.06701i −0.0522198 0.160716i
\(995\) 0.716950 + 2.20654i 0.0227288 + 0.0699522i
\(996\) −10.2925 + 31.6770i −0.326130 + 1.00372i
\(997\) −8.24459 + 5.99005i −0.261109 + 0.189707i −0.710636 0.703560i \(-0.751593\pi\)
0.449527 + 0.893267i \(0.351593\pi\)
\(998\) −23.1626 −0.733200
\(999\) 5.26208 16.1950i 0.166485 0.512387i
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 287.2.h.c.78.6 40
41.10 even 5 inner 287.2.h.c.92.6 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.h.c.78.6 40 1.1 even 1 trivial
287.2.h.c.92.6 yes 40 41.10 even 5 inner