Properties

Label 315.2.i.e.211.1
Level $315$
Weight $2$
Character 315.211
Analytic conductor $2.515$
Analytic rank $0$
Dimension $12$
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] = [315,2,Mod(106,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 2 x^{10} - x^{9} - 4 x^{8} + 20 x^{7} - 38 x^{6} + 60 x^{5} - 36 x^{4} - 27 x^{3} + 162 x^{2} - 243 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(1.24736 - 1.20170i\) of defining polynomial
Character \(\chi\) \(=\) 315.211
Dual form 315.2.i.e.106.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35359 - 2.34448i) q^{2} +(1.24736 + 1.20170i) q^{3} +(-2.66438 + 4.61485i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.12895 - 4.55102i) q^{6} +(-0.500000 - 0.866025i) q^{7} +9.01155 q^{8} +(0.111834 + 2.99791i) q^{9} +O(q^{10})\) \(q+(-1.35359 - 2.34448i) q^{2} +(1.24736 + 1.20170i) q^{3} +(-2.66438 + 4.61485i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.12895 - 4.55102i) q^{6} +(-0.500000 - 0.866025i) q^{7} +9.01155 q^{8} +(0.111834 + 2.99791i) q^{9} -2.70717 q^{10} +(2.08384 + 3.60931i) q^{11} +(-8.86912 + 2.55461i) q^{12} +(-1.08055 + 1.87156i) q^{13} +(-1.35359 + 2.34448i) q^{14} +(1.66438 - 0.479399i) q^{15} +(-6.86912 - 11.8977i) q^{16} +6.91475 q^{17} +(6.87717 - 4.32013i) q^{18} +2.44928 q^{19} +(2.66438 + 4.61485i) q^{20} +(0.417021 - 1.68110i) q^{21} +(5.64130 - 9.77102i) q^{22} +(3.23517 - 5.60347i) q^{23} +(11.2407 + 10.8292i) q^{24} +(-0.500000 - 0.866025i) q^{25} +5.85045 q^{26} +(-3.46310 + 3.87388i) q^{27} +5.32877 q^{28} +(-2.24736 - 3.89255i) q^{29} +(-3.37683 - 3.25321i) q^{30} +(-2.65462 + 4.59794i) q^{31} +(-9.58434 + 16.6006i) q^{32} +(-1.73801 + 7.00627i) q^{33} +(-9.35970 - 16.2115i) q^{34} -1.00000 q^{35} +(-14.1329 - 7.47150i) q^{36} +3.98774 q^{37} +(-3.31531 - 5.74228i) q^{38} +(-3.59689 + 1.03603i) q^{39} +(4.50577 - 7.80423i) q^{40} +(-1.13553 + 1.96680i) q^{41} +(-4.50577 + 1.29781i) q^{42} +(2.98010 + 5.16168i) q^{43} -22.2086 q^{44} +(2.65219 + 1.40211i) q^{45} -17.5163 q^{46} +(-1.41418 - 2.44943i) q^{47} +(5.72913 - 23.0954i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.35359 + 2.34448i) q^{50} +(8.62521 + 8.30945i) q^{51} +(-5.75799 - 9.97313i) q^{52} -1.20654 q^{53} +(13.7698 + 2.87552i) q^{54} +4.16767 q^{55} +(-4.50577 - 7.80423i) q^{56} +(3.05514 + 2.94330i) q^{57} +(-6.08400 + 10.5378i) q^{58} +(4.59534 - 7.95935i) q^{59} +(-2.22221 + 8.95819i) q^{60} +(-3.98623 - 6.90435i) q^{61} +14.3730 q^{62} +(2.54035 - 1.59581i) q^{63} +24.4164 q^{64} +(1.08055 + 1.87156i) q^{65} +(18.7786 - 5.40887i) q^{66} +(-2.89263 + 5.01018i) q^{67} +(-18.4235 + 31.9105i) q^{68} +(10.7691 - 3.10187i) q^{69} +(1.35359 + 2.34448i) q^{70} -15.4161 q^{71} +(1.00780 + 27.0158i) q^{72} -6.40221 q^{73} +(-5.39775 - 9.34917i) q^{74} +(0.417021 - 1.68110i) q^{75} +(-6.52582 + 11.3031i) q^{76} +(2.08384 - 3.60931i) q^{77} +(7.29764 + 7.03049i) q^{78} +(5.67491 + 9.82924i) q^{79} -13.7382 q^{80} +(-8.97499 + 0.670539i) q^{81} +6.14814 q^{82} +(5.11199 + 8.85423i) q^{83} +(6.64692 + 6.40358i) q^{84} +(3.45737 - 5.98835i) q^{85} +(8.06763 - 13.9736i) q^{86} +(1.87439 - 7.55608i) q^{87} +(18.7786 + 32.5255i) q^{88} -1.00740 q^{89} +(-0.302754 - 8.11587i) q^{90} +2.16109 q^{91} +(17.2395 + 29.8596i) q^{92} +(-8.83662 + 2.54524i) q^{93} +(-3.82843 + 6.63103i) q^{94} +(1.22464 - 2.12114i) q^{95} +(-31.9041 + 9.18944i) q^{96} +(-4.43975 - 7.68987i) q^{97} +2.70717 q^{98} +(-10.5874 + 6.65081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 7 q^{11} - 37 q^{12} - 10 q^{13} + 3 q^{14} - q^{15} - 13 q^{16} + 14 q^{17} + 24 q^{18} + 30 q^{19} + 11 q^{20} - 2 q^{21} + 7 q^{22} + 14 q^{23} + 6 q^{24} - 6 q^{25} - 26 q^{26} - 2 q^{27} + 22 q^{28} - 13 q^{29} - 9 q^{30} - 10 q^{31} - 18 q^{32} - 14 q^{33} - 15 q^{34} - 12 q^{35} - 4 q^{36} + 42 q^{37} - 4 q^{38} - 11 q^{39} + 3 q^{40} - 4 q^{41} - 3 q^{42} - 13 q^{43} - 78 q^{44} - 30 q^{46} + 8 q^{47} + 42 q^{48} - 6 q^{49} + 3 q^{50} - 19 q^{51} - 31 q^{52} + 20 q^{53} + 84 q^{54} + 14 q^{55} - 3 q^{56} - 22 q^{57} - 3 q^{58} + 21 q^{59} - 17 q^{60} - 2 q^{61} + 50 q^{62} + 3 q^{63} + 62 q^{64} + 10 q^{65} + 19 q^{66} - 6 q^{67} - 33 q^{68} - 19 q^{69} - 3 q^{70} - 58 q^{71} + 51 q^{72} + 16 q^{73} - 5 q^{74} - 2 q^{75} - 31 q^{76} + 7 q^{77} - 5 q^{78} + 22 q^{79} - 26 q^{80} + 21 q^{81} + 36 q^{82} + 5 q^{83} + 20 q^{84} + 7 q^{85} + 23 q^{86} - 19 q^{87} + 19 q^{88} + 2 q^{89} + 9 q^{90} + 20 q^{91} + 9 q^{92} + 31 q^{93} - 31 q^{94} + 15 q^{95} - 66 q^{96} - 32 q^{97} - 6 q^{98} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35359 2.34448i −0.957129 1.65780i −0.729419 0.684067i \(-0.760209\pi\)
−0.227710 0.973729i \(-0.573124\pi\)
\(3\) 1.24736 + 1.20170i 0.720166 + 0.693802i
\(4\) −2.66438 + 4.61485i −1.33219 + 2.30742i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.12895 4.55102i 0.460890 1.85795i
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 9.01155 3.18606
\(9\) 0.111834 + 2.99791i 0.0372781 + 0.999305i
\(10\) −2.70717 −0.856082
\(11\) 2.08384 + 3.60931i 0.628301 + 1.08825i 0.987893 + 0.155139i \(0.0495825\pi\)
−0.359592 + 0.933110i \(0.617084\pi\)
\(12\) −8.86912 + 2.55461i −2.56030 + 0.737451i
\(13\) −1.08055 + 1.87156i −0.299690 + 0.519078i −0.976065 0.217479i \(-0.930217\pi\)
0.676375 + 0.736557i \(0.263550\pi\)
\(14\) −1.35359 + 2.34448i −0.361761 + 0.626588i
\(15\) 1.66438 0.479399i 0.429742 0.123780i
\(16\) −6.86912 11.8977i −1.71728 2.97442i
\(17\) 6.91475 1.67707 0.838536 0.544846i \(-0.183412\pi\)
0.838536 + 0.544846i \(0.183412\pi\)
\(18\) 6.87717 4.32013i 1.62096 1.01826i
\(19\) 2.44928 0.561903 0.280951 0.959722i \(-0.409350\pi\)
0.280951 + 0.959722i \(0.409350\pi\)
\(20\) 2.66438 + 4.61485i 0.595775 + 1.03191i
\(21\) 0.417021 1.68110i 0.0910014 0.366846i
\(22\) 5.64130 9.77102i 1.20273 2.08319i
\(23\) 3.23517 5.60347i 0.674579 1.16840i −0.302013 0.953304i \(-0.597659\pi\)
0.976592 0.215101i \(-0.0690081\pi\)
\(24\) 11.2407 + 10.8292i 2.29449 + 2.21050i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 5.85045 1.14737
\(27\) −3.46310 + 3.87388i −0.666473 + 0.745529i
\(28\) 5.32877 1.00704
\(29\) −2.24736 3.89255i −0.417325 0.722828i 0.578344 0.815793i \(-0.303699\pi\)
−0.995669 + 0.0929646i \(0.970366\pi\)
\(30\) −3.37683 3.25321i −0.616521 0.593951i
\(31\) −2.65462 + 4.59794i −0.476784 + 0.825814i −0.999646 0.0266035i \(-0.991531\pi\)
0.522862 + 0.852417i \(0.324864\pi\)
\(32\) −9.58434 + 16.6006i −1.69429 + 2.93459i
\(33\) −1.73801 + 7.00627i −0.302548 + 1.21964i
\(34\) −9.35970 16.2115i −1.60518 2.78024i
\(35\) −1.00000 −0.169031
\(36\) −14.1329 7.47150i −2.35548 1.24525i
\(37\) 3.98774 0.655580 0.327790 0.944751i \(-0.393696\pi\)
0.327790 + 0.944751i \(0.393696\pi\)
\(38\) −3.31531 5.74228i −0.537814 0.931521i
\(39\) −3.59689 + 1.03603i −0.575964 + 0.165897i
\(40\) 4.50577 7.80423i 0.712425 1.23396i
\(41\) −1.13553 + 1.96680i −0.177340 + 0.307162i −0.940969 0.338494i \(-0.890083\pi\)
0.763629 + 0.645656i \(0.223416\pi\)
\(42\) −4.50577 + 1.29781i −0.695256 + 0.200257i
\(43\) 2.98010 + 5.16168i 0.454461 + 0.787149i 0.998657 0.0518088i \(-0.0164986\pi\)
−0.544196 + 0.838958i \(0.683165\pi\)
\(44\) −22.2086 −3.34807
\(45\) 2.65219 + 1.40211i 0.395365 + 0.209014i
\(46\) −17.5163 −2.58264
\(47\) −1.41418 2.44943i −0.206279 0.357287i 0.744260 0.667890i \(-0.232802\pi\)
−0.950540 + 0.310603i \(0.899469\pi\)
\(48\) 5.72913 23.0954i 0.826929 3.33353i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −1.35359 + 2.34448i −0.191426 + 0.331559i
\(51\) 8.62521 + 8.30945i 1.20777 + 1.16356i
\(52\) −5.75799 9.97313i −0.798489 1.38302i
\(53\) −1.20654 −0.165732 −0.0828658 0.996561i \(-0.526407\pi\)
−0.0828658 + 0.996561i \(0.526407\pi\)
\(54\) 13.7698 + 2.87552i 1.87384 + 0.391309i
\(55\) 4.16767 0.561969
\(56\) −4.50577 7.80423i −0.602109 1.04288i
\(57\) 3.05514 + 2.94330i 0.404663 + 0.389849i
\(58\) −6.08400 + 10.5378i −0.798868 + 1.38368i
\(59\) 4.59534 7.95935i 0.598262 1.03622i −0.394816 0.918760i \(-0.629192\pi\)
0.993078 0.117460i \(-0.0374750\pi\)
\(60\) −2.22221 + 8.95819i −0.286886 + 1.15650i
\(61\) −3.98623 6.90435i −0.510384 0.884012i −0.999928 0.0120326i \(-0.996170\pi\)
0.489543 0.871979i \(-0.337164\pi\)
\(62\) 14.3730 1.82537
\(63\) 2.54035 1.59581i 0.320054 0.201053i
\(64\) 24.4164 3.05205
\(65\) 1.08055 + 1.87156i 0.134025 + 0.232139i
\(66\) 18.7786 5.40887i 2.31149 0.665786i
\(67\) −2.89263 + 5.01018i −0.353391 + 0.612090i −0.986841 0.161693i \(-0.948305\pi\)
0.633451 + 0.773783i \(0.281638\pi\)
\(68\) −18.4235 + 31.9105i −2.23418 + 3.86972i
\(69\) 10.7691 3.10187i 1.29645 0.373421i
\(70\) 1.35359 + 2.34448i 0.161784 + 0.280219i
\(71\) −15.4161 −1.82955 −0.914775 0.403965i \(-0.867632\pi\)
−0.914775 + 0.403965i \(0.867632\pi\)
\(72\) 1.00780 + 27.0158i 0.118770 + 3.18385i
\(73\) −6.40221 −0.749321 −0.374661 0.927162i \(-0.622241\pi\)
−0.374661 + 0.927162i \(0.622241\pi\)
\(74\) −5.39775 9.34917i −0.627475 1.08682i
\(75\) 0.417021 1.68110i 0.0481534 0.194117i
\(76\) −6.52582 + 11.3031i −0.748563 + 1.29655i
\(77\) 2.08384 3.60931i 0.237475 0.411319i
\(78\) 7.29764 + 7.03049i 0.826295 + 0.796046i
\(79\) 5.67491 + 9.82924i 0.638478 + 1.10588i 0.985767 + 0.168118i \(0.0537688\pi\)
−0.347289 + 0.937758i \(0.612898\pi\)
\(80\) −13.7382 −1.53598
\(81\) −8.97499 + 0.670539i −0.997221 + 0.0745044i
\(82\) 6.14814 0.678949
\(83\) 5.11199 + 8.85423i 0.561114 + 0.971878i 0.997400 + 0.0720699i \(0.0229605\pi\)
−0.436285 + 0.899808i \(0.643706\pi\)
\(84\) 6.64692 + 6.40358i 0.725238 + 0.698688i
\(85\) 3.45737 5.98835i 0.375005 0.649527i
\(86\) 8.06763 13.9736i 0.869955 1.50681i
\(87\) 1.87439 7.55608i 0.200956 0.810097i
\(88\) 18.7786 + 32.5255i 2.00180 + 3.46723i
\(89\) −1.00740 −0.106784 −0.0533919 0.998574i \(-0.517003\pi\)
−0.0533919 + 0.998574i \(0.517003\pi\)
\(90\) −0.302754 8.11587i −0.0319131 0.855487i
\(91\) 2.16109 0.226544
\(92\) 17.2395 + 29.8596i 1.79734 + 3.11308i
\(93\) −8.83662 + 2.54524i −0.916314 + 0.263929i
\(94\) −3.82843 + 6.63103i −0.394872 + 0.683939i
\(95\) 1.22464 2.12114i 0.125645 0.217624i
\(96\) −31.9041 + 9.18944i −3.25619 + 0.937894i
\(97\) −4.43975 7.68987i −0.450788 0.780787i 0.547647 0.836709i \(-0.315524\pi\)
−0.998435 + 0.0559218i \(0.982190\pi\)
\(98\) 2.70717 0.273465
\(99\) −10.5874 + 6.65081i −1.06407 + 0.668432i
\(100\) 5.32877 0.532877
\(101\) 0.124032 + 0.214829i 0.0123416 + 0.0213763i 0.872130 0.489274i \(-0.162738\pi\)
−0.859789 + 0.510650i \(0.829405\pi\)
\(102\) 7.80638 31.4692i 0.772946 3.11591i
\(103\) 1.98623 3.44025i 0.195709 0.338978i −0.751424 0.659820i \(-0.770633\pi\)
0.947133 + 0.320842i \(0.103966\pi\)
\(104\) −9.73740 + 16.8657i −0.954831 + 1.65382i
\(105\) −1.24736 1.20170i −0.121730 0.117274i
\(106\) 1.63316 + 2.82872i 0.158627 + 0.274749i
\(107\) 4.46799 0.431937 0.215969 0.976400i \(-0.430709\pi\)
0.215969 + 0.976400i \(0.430709\pi\)
\(108\) −8.65037 26.3032i −0.832382 2.53102i
\(109\) −5.57683 −0.534164 −0.267082 0.963674i \(-0.586059\pi\)
−0.267082 + 0.963674i \(0.586059\pi\)
\(110\) −5.64130 9.77102i −0.537877 0.931630i
\(111\) 4.97416 + 4.79207i 0.472127 + 0.454843i
\(112\) −6.86912 + 11.8977i −0.649071 + 1.12422i
\(113\) 6.32523 10.9556i 0.595028 1.03062i −0.398515 0.917162i \(-0.630474\pi\)
0.993543 0.113456i \(-0.0361922\pi\)
\(114\) 2.76510 11.1467i 0.258976 1.04399i
\(115\) −3.23517 5.60347i −0.301681 0.522527i
\(116\) 23.9514 2.22383
\(117\) −5.73163 3.03008i −0.529889 0.280131i
\(118\) −24.8807 −2.29046
\(119\) −3.45737 5.98835i −0.316937 0.548951i
\(120\) 14.9987 4.32013i 1.36919 0.394372i
\(121\) −3.18476 + 5.51616i −0.289523 + 0.501469i
\(122\) −10.7914 + 18.6913i −0.977007 + 1.69223i
\(123\) −3.77992 + 1.08874i −0.340824 + 0.0981687i
\(124\) −14.1459 24.5013i −1.27034 2.20029i
\(125\) −1.00000 −0.0894427
\(126\) −7.17992 3.79574i −0.639638 0.338151i
\(127\) −9.68630 −0.859520 −0.429760 0.902943i \(-0.641402\pi\)
−0.429760 + 0.902943i \(0.641402\pi\)
\(128\) −13.8810 24.0425i −1.22692 2.12508i
\(129\) −2.48553 + 10.0197i −0.218838 + 0.882184i
\(130\) 2.92523 5.06664i 0.256559 0.444374i
\(131\) 3.31847 5.74777i 0.289936 0.502185i −0.683858 0.729615i \(-0.739699\pi\)
0.973794 + 0.227431i \(0.0730325\pi\)
\(132\) −27.7022 26.6880i −2.41117 2.32290i
\(133\) −1.22464 2.12114i −0.106190 0.183926i
\(134\) 15.6617 1.35296
\(135\) 1.62333 + 4.93607i 0.139714 + 0.424829i
\(136\) 62.3126 5.34326
\(137\) −10.2885 17.8201i −0.879003 1.52248i −0.852437 0.522830i \(-0.824876\pi\)
−0.0265659 0.999647i \(-0.508457\pi\)
\(138\) −21.8492 21.0493i −1.85993 1.79184i
\(139\) −4.57816 + 7.92960i −0.388314 + 0.672580i −0.992223 0.124473i \(-0.960276\pi\)
0.603909 + 0.797054i \(0.293609\pi\)
\(140\) 2.66438 4.61485i 0.225182 0.390026i
\(141\) 1.17949 4.75476i 0.0993306 0.400423i
\(142\) 20.8669 + 36.1426i 1.75111 + 3.03302i
\(143\) −9.00674 −0.753181
\(144\) 34.9000 21.9236i 2.90833 1.82697i
\(145\) −4.49473 −0.373267
\(146\) 8.66593 + 15.0098i 0.717197 + 1.24222i
\(147\) −1.66438 + 0.479399i −0.137276 + 0.0395402i
\(148\) −10.6249 + 18.4028i −0.873359 + 1.51270i
\(149\) −11.2617 + 19.5058i −0.922592 + 1.59798i −0.127203 + 0.991877i \(0.540600\pi\)
−0.795389 + 0.606099i \(0.792733\pi\)
\(150\) −4.50577 + 1.29781i −0.367895 + 0.105966i
\(151\) −0.275128 0.476536i −0.0223896 0.0387800i 0.854613 0.519265i \(-0.173794\pi\)
−0.877003 + 0.480485i \(0.840461\pi\)
\(152\) 22.0718 1.79026
\(153\) 0.773306 + 20.7298i 0.0625181 + 1.67591i
\(154\) −11.2826 −0.909178
\(155\) 2.65462 + 4.59794i 0.213224 + 0.369315i
\(156\) 4.80240 19.3595i 0.384500 1.55000i
\(157\) 8.65486 14.9907i 0.690733 1.19638i −0.280865 0.959747i \(-0.590621\pi\)
0.971598 0.236637i \(-0.0760453\pi\)
\(158\) 15.3630 26.6094i 1.22221 2.11693i
\(159\) −1.50500 1.44990i −0.119354 0.114985i
\(160\) 9.58434 + 16.6006i 0.757708 + 1.31239i
\(161\) −6.47033 −0.509934
\(162\) 13.7205 + 20.1340i 1.07798 + 1.58188i
\(163\) −9.60379 −0.752227 −0.376114 0.926574i \(-0.622740\pi\)
−0.376114 + 0.926574i \(0.622740\pi\)
\(164\) −6.05098 10.4806i −0.472502 0.818397i
\(165\) 5.19861 + 5.00829i 0.404711 + 0.389895i
\(166\) 13.8390 23.9699i 1.07412 1.86043i
\(167\) 11.7916 20.4236i 0.912458 1.58042i 0.101878 0.994797i \(-0.467515\pi\)
0.810581 0.585627i \(-0.199152\pi\)
\(168\) 3.75800 15.1493i 0.289936 1.16879i
\(169\) 4.16484 + 7.21371i 0.320372 + 0.554900i
\(170\) −18.7194 −1.43571
\(171\) 0.273913 + 7.34273i 0.0209467 + 0.561512i
\(172\) −31.7605 −2.42172
\(173\) −7.63921 13.2315i −0.580799 1.00597i −0.995385 0.0959626i \(-0.969407\pi\)
0.414586 0.910010i \(-0.363926\pi\)
\(174\) −20.2522 + 5.83332i −1.53532 + 0.442223i
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) 28.6283 49.5856i 2.15794 3.73766i
\(177\) 15.2968 4.40600i 1.14978 0.331175i
\(178\) 1.36360 + 2.36182i 0.102206 + 0.177026i
\(179\) 1.93428 0.144575 0.0722874 0.997384i \(-0.476970\pi\)
0.0722874 + 0.997384i \(0.476970\pi\)
\(180\) −13.5370 + 8.50370i −1.00899 + 0.633828i
\(181\) −6.95394 −0.516882 −0.258441 0.966027i \(-0.583209\pi\)
−0.258441 + 0.966027i \(0.583209\pi\)
\(182\) −2.92523 5.06664i −0.216832 0.375564i
\(183\) 3.32468 13.4025i 0.245767 0.990741i
\(184\) 29.1539 50.4960i 2.14925 3.72261i
\(185\) 1.99387 3.45348i 0.146592 0.253905i
\(186\) 17.9284 + 17.2720i 1.31457 + 1.26645i
\(187\) 14.4092 + 24.9575i 1.05371 + 1.82507i
\(188\) 15.0717 1.09922
\(189\) 5.08643 + 1.06219i 0.369983 + 0.0772628i
\(190\) −6.63061 −0.481035
\(191\) 0.318146 + 0.551045i 0.0230202 + 0.0398722i 0.877306 0.479931i \(-0.159338\pi\)
−0.854286 + 0.519804i \(0.826005\pi\)
\(192\) 30.4561 + 29.3412i 2.19798 + 2.11752i
\(193\) 3.59304 6.22333i 0.258633 0.447965i −0.707243 0.706970i \(-0.750061\pi\)
0.965876 + 0.259005i \(0.0833947\pi\)
\(194\) −12.0191 + 20.8178i −0.862924 + 1.49463i
\(195\) −0.901221 + 3.63301i −0.0645378 + 0.260166i
\(196\) −2.66438 4.61485i −0.190313 0.329632i
\(197\) −16.2961 −1.16105 −0.580524 0.814243i \(-0.697152\pi\)
−0.580524 + 0.814243i \(0.697152\pi\)
\(198\) 29.9236 + 15.8194i 2.12658 + 1.12424i
\(199\) 10.0816 0.714666 0.357333 0.933977i \(-0.383686\pi\)
0.357333 + 0.933977i \(0.383686\pi\)
\(200\) −4.50577 7.80423i −0.318606 0.551842i
\(201\) −9.62889 + 2.77344i −0.679169 + 0.195624i
\(202\) 0.335774 0.581578i 0.0236250 0.0409197i
\(203\) −2.24736 + 3.89255i −0.157734 + 0.273203i
\(204\) −61.3277 + 17.6645i −4.29380 + 1.23676i
\(205\) 1.13553 + 1.96680i 0.0793088 + 0.137367i
\(206\) −10.7541 −0.749275
\(207\) 17.1605 + 9.07209i 1.19274 + 0.630554i
\(208\) 29.6896 2.05861
\(209\) 5.10390 + 8.84021i 0.353044 + 0.611490i
\(210\) −1.12895 + 4.55102i −0.0779047 + 0.314050i
\(211\) 3.56402 6.17306i 0.245357 0.424971i −0.716875 0.697202i \(-0.754428\pi\)
0.962232 + 0.272231i \(0.0877615\pi\)
\(212\) 3.21470 5.56802i 0.220786 0.382413i
\(213\) −19.2294 18.5255i −1.31758 1.26934i
\(214\) −6.04781 10.4751i −0.413420 0.716064i
\(215\) 5.96020 0.406482
\(216\) −31.2078 + 34.9097i −2.12343 + 2.37530i
\(217\) 5.30924 0.360415
\(218\) 7.54872 + 13.0748i 0.511264 + 0.885535i
\(219\) −7.98588 7.69353i −0.539636 0.519881i
\(220\) −11.1043 + 19.2332i −0.748651 + 1.29670i
\(221\) −7.47171 + 12.9414i −0.502602 + 0.870532i
\(222\) 4.50194 18.1483i 0.302151 1.21803i
\(223\) −7.95304 13.7751i −0.532575 0.922447i −0.999277 0.0380320i \(-0.987891\pi\)
0.466702 0.884415i \(-0.345442\pi\)
\(224\) 19.1687 1.28076
\(225\) 2.54035 1.59581i 0.169357 0.106387i
\(226\) −34.2469 −2.27807
\(227\) −0.267906 0.464026i −0.0177815 0.0307985i 0.856998 0.515320i \(-0.172327\pi\)
−0.874779 + 0.484522i \(0.838994\pi\)
\(228\) −21.7229 + 6.25694i −1.43864 + 0.414376i
\(229\) 0.653745 1.13232i 0.0432007 0.0748257i −0.843617 0.536946i \(-0.819578\pi\)
0.886817 + 0.462120i \(0.152911\pi\)
\(230\) −8.75815 + 15.1696i −0.577495 + 1.00025i
\(231\) 6.93661 1.99798i 0.456396 0.131457i
\(232\) −20.2522 35.0779i −1.32962 2.30298i
\(233\) −23.6393 −1.54866 −0.774331 0.632781i \(-0.781913\pi\)
−0.774331 + 0.632781i \(0.781913\pi\)
\(234\) 0.654281 + 17.5392i 0.0427717 + 1.14657i
\(235\) −2.82836 −0.184502
\(236\) 24.4875 + 42.4136i 1.59400 + 2.76089i
\(237\) −4.73311 + 19.0802i −0.307449 + 1.23939i
\(238\) −9.35970 + 16.2115i −0.606699 + 1.05083i
\(239\) 0.230521 0.399273i 0.0149111 0.0258268i −0.858474 0.512858i \(-0.828587\pi\)
0.873385 + 0.487031i \(0.161920\pi\)
\(240\) −17.1366 16.5092i −1.10616 1.06567i
\(241\) −12.3586 21.4058i −0.796090 1.37887i −0.922145 0.386845i \(-0.873565\pi\)
0.126055 0.992023i \(-0.459769\pi\)
\(242\) 17.2434 1.10845
\(243\) −12.0009 9.94883i −0.769856 0.638218i
\(244\) 42.4834 2.71972
\(245\) 0.500000 + 0.866025i 0.0319438 + 0.0553283i
\(246\) 7.66897 + 7.38823i 0.488956 + 0.471056i
\(247\) −2.64656 + 4.58398i −0.168397 + 0.291672i
\(248\) −23.9222 + 41.4345i −1.51906 + 2.63109i
\(249\) −4.26361 + 17.1875i −0.270196 + 1.08922i
\(250\) 1.35359 + 2.34448i 0.0856082 + 0.148278i
\(251\) 9.94783 0.627901 0.313951 0.949439i \(-0.398347\pi\)
0.313951 + 0.949439i \(0.398347\pi\)
\(252\) 0.595939 + 15.9752i 0.0375406 + 1.00634i
\(253\) 26.9662 1.69535
\(254\) 13.1112 + 22.7093i 0.822672 + 1.42491i
\(255\) 11.5088 3.31492i 0.720709 0.207589i
\(256\) −13.1618 + 22.7968i −0.822609 + 1.42480i
\(257\) 11.2625 19.5073i 0.702538 1.21683i −0.265034 0.964239i \(-0.585383\pi\)
0.967573 0.252593i \(-0.0812833\pi\)
\(258\) 26.8553 7.73523i 1.67194 0.481574i
\(259\) −1.99387 3.45348i −0.123893 0.214589i
\(260\) −11.5160 −0.714190
\(261\) 11.4182 7.17273i 0.706769 0.443981i
\(262\) −17.9673 −1.11003
\(263\) 6.02991 + 10.4441i 0.371820 + 0.644011i 0.989846 0.142147i \(-0.0454006\pi\)
−0.618026 + 0.786158i \(0.712067\pi\)
\(264\) −15.6621 + 63.1374i −0.963937 + 3.88584i
\(265\) −0.603272 + 1.04490i −0.0370587 + 0.0641876i
\(266\) −3.31531 + 5.74228i −0.203274 + 0.352082i
\(267\) −1.25659 1.21059i −0.0769020 0.0740868i
\(268\) −15.4141 26.6981i −0.941568 1.63084i
\(269\) −4.28838 −0.261467 −0.130733 0.991418i \(-0.541733\pi\)
−0.130733 + 0.991418i \(0.541733\pi\)
\(270\) 9.37519 10.4873i 0.570556 0.638234i
\(271\) 4.49009 0.272753 0.136377 0.990657i \(-0.456454\pi\)
0.136377 + 0.990657i \(0.456454\pi\)
\(272\) −47.4983 82.2694i −2.88000 4.98831i
\(273\) 2.69567 + 2.59699i 0.163149 + 0.157177i
\(274\) −27.8526 + 48.2422i −1.68264 + 2.91441i
\(275\) 2.08384 3.60931i 0.125660 0.217650i
\(276\) −14.3784 + 57.9625i −0.865479 + 3.48893i
\(277\) 0.839410 + 1.45390i 0.0504352 + 0.0873564i 0.890141 0.455685i \(-0.150606\pi\)
−0.839706 + 0.543042i \(0.817272\pi\)
\(278\) 24.7877 1.48667
\(279\) −14.0811 7.44412i −0.843013 0.445668i
\(280\) −9.01155 −0.538543
\(281\) 8.87866 + 15.3783i 0.529656 + 0.917391i 0.999402 + 0.0345895i \(0.0110124\pi\)
−0.469745 + 0.882802i \(0.655654\pi\)
\(282\) −12.7440 + 3.67069i −0.758891 + 0.218586i
\(283\) −1.17892 + 2.04195i −0.0700794 + 0.121381i −0.898936 0.438080i \(-0.855659\pi\)
0.828856 + 0.559461i \(0.188992\pi\)
\(284\) 41.0743 71.1428i 2.43731 4.22155i
\(285\) 4.07654 1.17418i 0.241473 0.0695525i
\(286\) 12.1914 + 21.1161i 0.720892 + 1.24862i
\(287\) 2.27106 0.134056
\(288\) −50.8389 26.8765i −2.99571 1.58371i
\(289\) 30.8137 1.81257
\(290\) 6.08400 + 10.5378i 0.357265 + 0.618800i
\(291\) 3.70293 14.9273i 0.217070 0.875054i
\(292\) 17.0579 29.5452i 0.998240 1.72900i
\(293\) 5.54018 9.59587i 0.323661 0.560597i −0.657580 0.753385i \(-0.728420\pi\)
0.981240 + 0.192788i \(0.0617530\pi\)
\(294\) 3.37683 + 3.25321i 0.196941 + 0.189731i
\(295\) −4.59534 7.95935i −0.267551 0.463412i
\(296\) 35.9357 2.08872
\(297\) −21.1986 4.42685i −1.23007 0.256872i
\(298\) 60.9745 3.53216
\(299\) 6.99150 + 12.1096i 0.404329 + 0.700318i
\(300\) 6.64692 + 6.40358i 0.383760 + 0.369711i
\(301\) 2.98010 5.16168i 0.171770 0.297514i
\(302\) −0.744819 + 1.29006i −0.0428595 + 0.0742349i
\(303\) −0.103447 + 0.417019i −0.00594290 + 0.0239571i
\(304\) −16.8244 29.1407i −0.964945 1.67133i
\(305\) −7.97246 −0.456502
\(306\) 47.5539 29.8726i 2.71847 1.70770i
\(307\) 25.0379 1.42899 0.714494 0.699642i \(-0.246657\pi\)
0.714494 + 0.699642i \(0.246657\pi\)
\(308\) 11.1043 + 19.2332i 0.632726 + 1.09591i
\(309\) 6.61170 1.90439i 0.376126 0.108337i
\(310\) 7.18651 12.4474i 0.408166 0.706964i
\(311\) 3.94817 6.83843i 0.223880 0.387772i −0.732103 0.681194i \(-0.761461\pi\)
0.955983 + 0.293422i \(0.0947942\pi\)
\(312\) −32.4136 + 9.33620i −1.83506 + 0.528558i
\(313\) 0.416010 + 0.720550i 0.0235143 + 0.0407279i 0.877543 0.479498i \(-0.159181\pi\)
−0.854029 + 0.520226i \(0.825848\pi\)
\(314\) −46.8603 −2.64448
\(315\) −0.111834 2.99791i −0.00630115 0.168913i
\(316\) −60.4806 −3.40230
\(317\) −9.22282 15.9744i −0.518005 0.897211i −0.999781 0.0209167i \(-0.993342\pi\)
0.481776 0.876294i \(-0.339992\pi\)
\(318\) −1.36212 + 5.49101i −0.0763841 + 0.307920i
\(319\) 9.36628 16.2229i 0.524411 0.908307i
\(320\) 12.2082 21.1452i 0.682458 1.18205i
\(321\) 5.57321 + 5.36919i 0.311066 + 0.299679i
\(322\) 8.75815 + 15.1696i 0.488072 + 0.845366i
\(323\) 16.9361 0.942352
\(324\) 20.8184 43.2048i 1.15658 2.40027i
\(325\) 2.16109 0.119876
\(326\) 12.9995 + 22.5159i 0.719978 + 1.24704i
\(327\) −6.95634 6.70168i −0.384687 0.370604i
\(328\) −10.2329 + 17.7239i −0.565016 + 0.978637i
\(329\) −1.41418 + 2.44943i −0.0779663 + 0.135042i
\(330\) 4.70508 18.9672i 0.259006 1.04411i
\(331\) −4.70826 8.15495i −0.258789 0.448236i 0.707128 0.707085i \(-0.249990\pi\)
−0.965918 + 0.258849i \(0.916657\pi\)
\(332\) −54.4813 −2.99005
\(333\) 0.445966 + 11.9549i 0.0244388 + 0.655125i
\(334\) −63.8435 −3.49336
\(335\) 2.89263 + 5.01018i 0.158041 + 0.273735i
\(336\) −22.8657 + 6.58610i −1.24743 + 0.359301i
\(337\) −4.51261 + 7.81606i −0.245817 + 0.425768i −0.962361 0.271774i \(-0.912390\pi\)
0.716544 + 0.697542i \(0.245723\pi\)
\(338\) 11.2749 19.5287i 0.613275 1.06222i
\(339\) 21.0552 6.06462i 1.14356 0.329385i
\(340\) 18.4235 + 31.9105i 0.999157 + 1.73059i
\(341\) −22.1272 −1.19825
\(342\) 16.8441 10.5812i 0.910825 0.572165i
\(343\) 1.00000 0.0539949
\(344\) 26.8553 + 46.5147i 1.44794 + 2.50791i
\(345\) 2.69826 10.8773i 0.145270 0.585613i
\(346\) −20.6806 + 35.8199i −1.11180 + 1.92569i
\(347\) 3.76937 6.52875i 0.202351 0.350481i −0.746935 0.664897i \(-0.768475\pi\)
0.949285 + 0.314416i \(0.101809\pi\)
\(348\) 29.8761 + 28.7824i 1.60153 + 1.54290i
\(349\) −2.51662 4.35891i −0.134711 0.233327i 0.790776 0.612106i \(-0.209677\pi\)
−0.925487 + 0.378779i \(0.876344\pi\)
\(350\) 2.70717 0.144704
\(351\) −3.50818 10.6673i −0.187253 0.569379i
\(352\) −79.8888 −4.25809
\(353\) 1.26788 + 2.19603i 0.0674824 + 0.116883i 0.897792 0.440419i \(-0.145170\pi\)
−0.830310 + 0.557302i \(0.811837\pi\)
\(354\) −31.0353 29.8991i −1.64951 1.58912i
\(355\) −7.70803 + 13.3507i −0.409100 + 0.708581i
\(356\) 2.68409 4.64898i 0.142257 0.246395i
\(357\) 2.88359 11.6244i 0.152616 0.615227i
\(358\) −2.61821 4.53487i −0.138377 0.239675i
\(359\) 24.3845 1.28696 0.643481 0.765462i \(-0.277489\pi\)
0.643481 + 0.765462i \(0.277489\pi\)
\(360\) 23.9003 + 12.6351i 1.25966 + 0.665930i
\(361\) −13.0010 −0.684265
\(362\) 9.41274 + 16.3033i 0.494723 + 0.856885i
\(363\) −10.6013 + 3.05354i −0.556425 + 0.160269i
\(364\) −5.75799 + 9.97313i −0.301801 + 0.522734i
\(365\) −3.20110 + 5.54447i −0.167553 + 0.290211i
\(366\) −35.9221 + 10.3468i −1.87768 + 0.540834i
\(367\) 13.7397 + 23.7978i 0.717204 + 1.24223i 0.962103 + 0.272685i \(0.0879117\pi\)
−0.244899 + 0.969548i \(0.578755\pi\)
\(368\) −88.8910 −4.63377
\(369\) −6.02328 3.18427i −0.313559 0.165766i
\(370\) −10.7955 −0.561231
\(371\) 0.603272 + 1.04490i 0.0313203 + 0.0542484i
\(372\) 11.7982 47.5612i 0.611710 2.46593i
\(373\) −18.5770 + 32.1763i −0.961880 + 1.66603i −0.244108 + 0.969748i \(0.578495\pi\)
−0.717772 + 0.696278i \(0.754838\pi\)
\(374\) 39.0082 67.5642i 2.01707 3.49366i
\(375\) −1.24736 1.20170i −0.0644136 0.0620555i
\(376\) −12.7440 22.0732i −0.657219 1.13834i
\(377\) 9.71353 0.500272
\(378\) −4.39464 13.3628i −0.226036 0.687307i
\(379\) 34.3188 1.76284 0.881420 0.472333i \(-0.156588\pi\)
0.881420 + 0.472333i \(0.156588\pi\)
\(380\) 6.52582 + 11.3031i 0.334767 + 0.579834i
\(381\) −12.0823 11.6400i −0.618997 0.596337i
\(382\) 0.861276 1.49177i 0.0440667 0.0763258i
\(383\) −15.7901 + 27.3492i −0.806835 + 1.39748i 0.108210 + 0.994128i \(0.465488\pi\)
−0.915045 + 0.403351i \(0.867845\pi\)
\(384\) 11.5773 46.6705i 0.590801 2.38165i
\(385\) −2.08384 3.60931i −0.106202 0.183948i
\(386\) −19.4539 −0.990179
\(387\) −15.1410 + 9.51134i −0.769661 + 0.483488i
\(388\) 47.3168 2.40214
\(389\) 2.12369 + 3.67833i 0.107675 + 0.186499i 0.914828 0.403844i \(-0.132326\pi\)
−0.807153 + 0.590343i \(0.798993\pi\)
\(390\) 9.73740 2.80470i 0.493072 0.142022i
\(391\) 22.3704 38.7466i 1.13132 1.95950i
\(392\) −4.50577 + 7.80423i −0.227576 + 0.394173i
\(393\) 11.0464 3.18175i 0.557219 0.160498i
\(394\) 22.0581 + 38.2058i 1.11127 + 1.92478i
\(395\) 11.3498 0.571072
\(396\) −2.48368 66.5794i −0.124810 3.34574i
\(397\) −12.5714 −0.630940 −0.315470 0.948936i \(-0.602162\pi\)
−0.315470 + 0.948936i \(0.602162\pi\)
\(398\) −13.6463 23.6361i −0.684028 1.18477i
\(399\) 1.02140 4.11748i 0.0511339 0.206132i
\(400\) −6.86912 + 11.8977i −0.343456 + 0.594883i
\(401\) −18.6480 + 32.2992i −0.931236 + 1.61295i −0.150023 + 0.988683i \(0.547935\pi\)
−0.781213 + 0.624265i \(0.785399\pi\)
\(402\) 19.5358 + 18.8206i 0.974357 + 0.938687i
\(403\) −5.73688 9.93657i −0.285775 0.494976i
\(404\) −1.32187 −0.0657655
\(405\) −3.90679 + 8.10784i −0.194130 + 0.402882i
\(406\) 12.1680 0.603887
\(407\) 8.30980 + 14.3930i 0.411902 + 0.713434i
\(408\) 77.7265 + 74.8810i 3.84803 + 3.70716i
\(409\) 2.27904 3.94742i 0.112691 0.195187i −0.804163 0.594409i \(-0.797386\pi\)
0.916855 + 0.399221i \(0.130720\pi\)
\(410\) 3.07407 5.32445i 0.151818 0.262956i
\(411\) 8.58100 34.5918i 0.423270 1.70629i
\(412\) 10.5842 + 18.3323i 0.521444 + 0.903167i
\(413\) −9.19067 −0.452243
\(414\) −1.95892 52.5124i −0.0962758 2.58084i
\(415\) 10.2240 0.501876
\(416\) −20.7127 35.8754i −1.01552 1.75894i
\(417\) −15.2396 + 4.38953i −0.746288 + 0.214956i
\(418\) 13.8171 23.9320i 0.675817 1.17055i
\(419\) 8.36903 14.4956i 0.408854 0.708155i −0.585908 0.810378i \(-0.699262\pi\)
0.994762 + 0.102222i \(0.0325953\pi\)
\(420\) 8.86912 2.55461i 0.432769 0.124652i
\(421\) 12.0704 + 20.9065i 0.588275 + 1.01892i 0.994458 + 0.105130i \(0.0335259\pi\)
−0.406184 + 0.913791i \(0.633141\pi\)
\(422\) −19.2968 −0.939353
\(423\) 7.18504 4.51352i 0.349348 0.219455i
\(424\) −10.8728 −0.528031
\(425\) −3.45737 5.98835i −0.167707 0.290478i
\(426\) −17.4039 + 70.1588i −0.843221 + 3.39920i
\(427\) −3.98623 + 6.90435i −0.192907 + 0.334125i
\(428\) −11.9045 + 20.6191i −0.575423 + 0.996663i
\(429\) −11.2347 10.8234i −0.542416 0.522559i
\(430\) −8.06763 13.9736i −0.389056 0.673865i
\(431\) −19.9625 −0.961562 −0.480781 0.876841i \(-0.659647\pi\)
−0.480781 + 0.876841i \(0.659647\pi\)
\(432\) 69.8786 + 14.5926i 3.36204 + 0.702087i
\(433\) 7.61796 0.366096 0.183048 0.983104i \(-0.441404\pi\)
0.183048 + 0.983104i \(0.441404\pi\)
\(434\) −7.18651 12.4474i −0.344963 0.597494i
\(435\) −5.60656 5.40131i −0.268814 0.258973i
\(436\) 14.8588 25.7362i 0.711609 1.23254i
\(437\) 7.92382 13.7245i 0.379048 0.656530i
\(438\) −7.22774 + 29.1366i −0.345355 + 1.39220i
\(439\) 4.91263 + 8.50892i 0.234467 + 0.406109i 0.959118 0.283008i \(-0.0913322\pi\)
−0.724651 + 0.689116i \(0.757999\pi\)
\(440\) 37.5572 1.79047
\(441\) −2.65219 1.40211i −0.126295 0.0667670i
\(442\) 40.4544 1.92422
\(443\) −0.208919 0.361858i −0.00992605 0.0171924i 0.861020 0.508572i \(-0.169826\pi\)
−0.870946 + 0.491379i \(0.836493\pi\)
\(444\) −35.3678 + 10.1871i −1.67848 + 0.483459i
\(445\) −0.503698 + 0.872430i −0.0238776 + 0.0413572i
\(446\) −21.5302 + 37.2915i −1.01949 + 1.76580i
\(447\) −37.4875 + 10.7977i −1.77310 + 0.510712i
\(448\) −12.2082 21.1452i −0.576783 0.999017i
\(449\) −30.5529 −1.44188 −0.720941 0.692996i \(-0.756290\pi\)
−0.720941 + 0.692996i \(0.756290\pi\)
\(450\) −7.17992 3.79574i −0.338465 0.178933i
\(451\) −9.46504 −0.445691
\(452\) 33.7057 + 58.3800i 1.58538 + 2.74596i
\(453\) 0.229468 0.925036i 0.0107814 0.0434620i
\(454\) −0.725266 + 1.25620i −0.0340384 + 0.0589563i
\(455\) 1.08055 1.87156i 0.0506568 0.0877402i
\(456\) 27.5315 + 26.5237i 1.28928 + 1.24208i
\(457\) −2.53414 4.38927i −0.118542 0.205321i 0.800648 0.599135i \(-0.204489\pi\)
−0.919190 + 0.393814i \(0.871155\pi\)
\(458\) −3.53960 −0.165394
\(459\) −23.9464 + 26.7869i −1.11772 + 1.25031i
\(460\) 34.4789 1.60759
\(461\) 2.69575 + 4.66918i 0.125554 + 0.217465i 0.921949 0.387311i \(-0.126596\pi\)
−0.796396 + 0.604776i \(0.793263\pi\)
\(462\) −14.0735 13.5583i −0.654759 0.630789i
\(463\) −3.15089 + 5.45749i −0.146434 + 0.253631i −0.929907 0.367795i \(-0.880113\pi\)
0.783473 + 0.621426i \(0.213446\pi\)
\(464\) −30.8748 + 53.4768i −1.43333 + 2.48260i
\(465\) −2.21406 + 8.92536i −0.102675 + 0.413903i
\(466\) 31.9978 + 55.4218i 1.48227 + 2.56737i
\(467\) −3.84708 −0.178022 −0.0890109 0.996031i \(-0.528371\pi\)
−0.0890109 + 0.996031i \(0.528371\pi\)
\(468\) 29.2546 18.3773i 1.35230 0.849491i
\(469\) 5.78525 0.267138
\(470\) 3.82843 + 6.63103i 0.176592 + 0.305867i
\(471\) 28.8100 8.29826i 1.32750 0.382364i
\(472\) 41.4111 71.7261i 1.90610 3.30146i
\(473\) −12.4201 + 21.5122i −0.571076 + 0.989133i
\(474\) 51.1397 14.7300i 2.34893 0.676570i
\(475\) −1.22464 2.12114i −0.0561903 0.0973244i
\(476\) 36.8471 1.68888
\(477\) −0.134933 3.61712i −0.00617816 0.165616i
\(478\) −1.24812 −0.0570875
\(479\) 10.0389 + 17.3879i 0.458690 + 0.794474i 0.998892 0.0470609i \(-0.0149855\pi\)
−0.540202 + 0.841535i \(0.681652\pi\)
\(480\) −7.99373 + 32.2244i −0.364862 + 1.47084i
\(481\) −4.30894 + 7.46331i −0.196471 + 0.340297i
\(482\) −33.4569 + 57.9491i −1.52392 + 2.63951i
\(483\) −8.07086 7.77540i −0.367237 0.353793i
\(484\) −16.9708 29.3944i −0.771402 1.33611i
\(485\) −8.87949 −0.403197
\(486\) −7.08064 + 41.6024i −0.321184 + 1.88712i
\(487\) −22.0173 −0.997699 −0.498849 0.866689i \(-0.666244\pi\)
−0.498849 + 0.866689i \(0.666244\pi\)
\(488\) −35.9221 62.2189i −1.62612 2.81652i
\(489\) −11.9794 11.5409i −0.541728 0.521897i
\(490\) 1.35359 2.34448i 0.0611487 0.105913i
\(491\) −4.89080 + 8.47111i −0.220719 + 0.382296i −0.955026 0.296521i \(-0.904174\pi\)
0.734308 + 0.678817i \(0.237507\pi\)
\(492\) 5.04676 20.3446i 0.227526 0.917205i
\(493\) −15.5400 26.9160i −0.699884 1.21224i
\(494\) 14.3294 0.644709
\(495\) 0.466089 + 12.4943i 0.0209491 + 0.561579i
\(496\) 72.9396 3.27509
\(497\) 7.70803 + 13.3507i 0.345752 + 0.598861i
\(498\) 46.0670 13.2688i 2.06431 0.594591i
\(499\) −7.01594 + 12.1520i −0.314077 + 0.543997i −0.979241 0.202700i \(-0.935028\pi\)
0.665164 + 0.746697i \(0.268362\pi\)
\(500\) 2.66438 4.61485i 0.119155 0.206382i
\(501\) 39.2514 11.3057i 1.75362 0.505102i
\(502\) −13.4652 23.3225i −0.600983 1.04093i
\(503\) 17.7596 0.791862 0.395931 0.918280i \(-0.370422\pi\)
0.395931 + 0.918280i \(0.370422\pi\)
\(504\) 22.8925 14.3807i 1.01971 0.640567i
\(505\) 0.248063 0.0110387
\(506\) −36.5011 63.2218i −1.62267 2.81055i
\(507\) −3.47364 + 14.0030i −0.154270 + 0.621895i
\(508\) 25.8080 44.7008i 1.14505 1.98328i
\(509\) 16.5982 28.7489i 0.735700 1.27427i −0.218715 0.975789i \(-0.570186\pi\)
0.954415 0.298482i \(-0.0964802\pi\)
\(510\) −23.3499 22.4951i −1.03395 0.996100i
\(511\) 3.20110 + 5.54447i 0.141608 + 0.245273i
\(512\) 15.7383 0.695543
\(513\) −8.48209 + 9.48822i −0.374493 + 0.418915i
\(514\) −60.9792 −2.68968
\(515\) −1.98623 3.44025i −0.0875237 0.151595i
\(516\) −39.6169 38.1666i −1.74404 1.68019i
\(517\) 5.89385 10.2084i 0.259211 0.448967i
\(518\) −5.39775 + 9.34917i −0.237163 + 0.410779i
\(519\) 6.37142 25.6845i 0.279674 1.12743i
\(520\) 9.73740 + 16.8657i 0.427013 + 0.739609i
\(521\) −42.7520 −1.87300 −0.936500 0.350668i \(-0.885955\pi\)
−0.936500 + 0.350668i \(0.885955\pi\)
\(522\) −32.2718 17.0608i −1.41250 0.746732i
\(523\) 24.9327 1.09023 0.545114 0.838362i \(-0.316486\pi\)
0.545114 + 0.838362i \(0.316486\pi\)
\(524\) 17.6834 + 30.6285i 0.772502 + 1.33801i
\(525\) −1.66438 + 0.479399i −0.0726397 + 0.0209227i
\(526\) 16.3240 28.2740i 0.711759 1.23280i
\(527\) −18.3560 + 31.7936i −0.799601 + 1.38495i
\(528\) 95.2969 27.4487i 4.14727 1.19455i
\(529\) −9.43261 16.3378i −0.410113 0.710337i
\(530\) 3.26632 0.141880
\(531\) 24.3754 + 12.8863i 1.05780 + 0.559218i
\(532\) 13.0516 0.565860
\(533\) −2.45399 4.25043i −0.106294 0.184107i
\(534\) −1.13730 + 4.58468i −0.0492156 + 0.198398i
\(535\) 2.23400 3.86940i 0.0965841 0.167289i
\(536\) −26.0670 + 45.1494i −1.12592 + 1.95016i
\(537\) 2.41275 + 2.32442i 0.104118 + 0.100306i
\(538\) 5.80468 + 10.0540i 0.250258 + 0.433459i
\(539\) −4.16767 −0.179514
\(540\) −27.1044 5.66015i −1.16639 0.243574i
\(541\) 17.2838 0.743090 0.371545 0.928415i \(-0.378828\pi\)
0.371545 + 0.928415i \(0.378828\pi\)
\(542\) −6.07772 10.5269i −0.261060 0.452170i
\(543\) −8.67409 8.35654i −0.372241 0.358614i
\(544\) −66.2733 + 114.789i −2.84144 + 4.92152i
\(545\) −2.78842 + 4.82968i −0.119443 + 0.206881i
\(546\) 2.43976 9.83519i 0.104412 0.420907i
\(547\) 12.5504 + 21.7379i 0.536616 + 0.929446i 0.999083 + 0.0428094i \(0.0136308\pi\)
−0.462468 + 0.886636i \(0.653036\pi\)
\(548\) 109.650 4.68400
\(549\) 20.2529 12.7225i 0.864371 0.542984i
\(550\) −11.2826 −0.481092
\(551\) −5.50442 9.53394i −0.234496 0.406159i
\(552\) 97.0465 27.9527i 4.13057 1.18974i
\(553\) 5.67491 9.82924i 0.241322 0.417982i
\(554\) 2.27242 3.93595i 0.0965461 0.167223i
\(555\) 6.63713 1.91172i 0.281731 0.0811479i
\(556\) −24.3959 42.2550i −1.03462 1.79201i
\(557\) 33.9496 1.43849 0.719245 0.694756i \(-0.244488\pi\)
0.719245 + 0.694756i \(0.244488\pi\)
\(558\) 1.60740 + 43.0891i 0.0680465 + 1.82411i
\(559\) −12.8806 −0.544789
\(560\) 6.86912 + 11.8977i 0.290273 + 0.502768i
\(561\) −12.0179 + 48.4466i −0.507395 + 2.04542i
\(562\) 24.0360 41.6316i 1.01390 1.75612i
\(563\) −0.0831908 + 0.144091i −0.00350608 + 0.00607270i −0.867773 0.496961i \(-0.834449\pi\)
0.864267 + 0.503033i \(0.167783\pi\)
\(564\) 18.7999 + 18.1116i 0.791618 + 0.762638i
\(565\) −6.32523 10.9556i −0.266104 0.460906i
\(566\) 6.38306 0.268300
\(567\) 5.06820 + 7.43730i 0.212844 + 0.312337i
\(568\) −138.922 −5.82906
\(569\) 0.808497 + 1.40036i 0.0338939 + 0.0587060i 0.882475 0.470360i \(-0.155876\pi\)
−0.848581 + 0.529066i \(0.822542\pi\)
\(570\) −8.27079 7.96801i −0.346425 0.333743i
\(571\) 0.582809 1.00946i 0.0243898 0.0422444i −0.853573 0.520973i \(-0.825569\pi\)
0.877963 + 0.478729i \(0.158902\pi\)
\(572\) 23.9974 41.5648i 1.00338 1.73791i
\(573\) −0.265347 + 1.06967i −0.0110850 + 0.0446861i
\(574\) −3.07407 5.32445i −0.128309 0.222238i
\(575\) −6.47033 −0.269832
\(576\) 2.73059 + 73.1982i 0.113774 + 3.04993i
\(577\) −21.5482 −0.897062 −0.448531 0.893767i \(-0.648053\pi\)
−0.448531 + 0.893767i \(0.648053\pi\)
\(578\) −41.7090 72.2421i −1.73487 3.00488i
\(579\) 11.9604 3.44500i 0.497057 0.143169i
\(580\) 11.9757 20.7425i 0.497263 0.861285i
\(581\) 5.11199 8.85423i 0.212081 0.367335i
\(582\) −40.0090 + 11.5239i −1.65843 + 0.477682i
\(583\) −2.51424 4.35480i −0.104129 0.180357i
\(584\) −57.6938 −2.38738
\(585\) −5.48994 + 3.44869i −0.226981 + 0.142586i
\(586\) −29.9964 −1.23914
\(587\) −17.5719 30.4354i −0.725268 1.25620i −0.958863 0.283868i \(-0.908382\pi\)
0.233595 0.972334i \(-0.424951\pi\)
\(588\) 2.22221 8.95819i 0.0916423 0.369429i
\(589\) −6.50190 + 11.2616i −0.267906 + 0.464027i
\(590\) −12.4404 + 21.5473i −0.512161 + 0.887089i
\(591\) −20.3272 19.5830i −0.836148 0.805537i
\(592\) −27.3923 47.4448i −1.12582 1.94997i
\(593\) −37.2623 −1.53018 −0.765090 0.643923i \(-0.777306\pi\)
−0.765090 + 0.643923i \(0.777306\pi\)
\(594\) 18.3154 + 55.6917i 0.751491 + 2.28506i
\(595\) −6.91475 −0.283477
\(596\) −60.0108 103.942i −2.45814 4.25762i
\(597\) 12.5754 + 12.1151i 0.514678 + 0.495837i
\(598\) 18.9272 32.7828i 0.773990 1.34059i
\(599\) −17.4631 + 30.2470i −0.713522 + 1.23586i 0.250004 + 0.968245i \(0.419568\pi\)
−0.963527 + 0.267612i \(0.913765\pi\)
\(600\) 3.75800 15.1493i 0.153420 0.618468i
\(601\) −4.96606 8.60146i −0.202570 0.350861i 0.746786 0.665064i \(-0.231596\pi\)
−0.949356 + 0.314203i \(0.898263\pi\)
\(602\) −16.1353 −0.657624
\(603\) −15.3436 8.11154i −0.624839 0.330327i
\(604\) 2.93219 0.119309
\(605\) 3.18476 + 5.51616i 0.129479 + 0.224264i
\(606\) 1.11772 0.321940i 0.0454041 0.0130779i
\(607\) −14.4965 + 25.1087i −0.588394 + 1.01913i 0.406048 + 0.913852i \(0.366906\pi\)
−0.994443 + 0.105277i \(0.966427\pi\)
\(608\) −23.4747 + 40.6594i −0.952025 + 1.64896i
\(609\) −7.48096 + 2.15477i −0.303144 + 0.0873156i
\(610\) 10.7914 + 18.6913i 0.436931 + 0.756787i
\(611\) 6.11236 0.247280
\(612\) −97.7254 51.6635i −3.95032 2.08837i
\(613\) 37.4502 1.51260 0.756299 0.654226i \(-0.227006\pi\)
0.756299 + 0.654226i \(0.227006\pi\)
\(614\) −33.8909 58.7008i −1.36773 2.36897i
\(615\) −0.947079 + 3.81788i −0.0381899 + 0.153952i
\(616\) 18.7786 32.5255i 0.756611 1.31049i
\(617\) 18.4575 31.9694i 0.743072 1.28704i −0.208018 0.978125i \(-0.566701\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(618\) −13.4143 12.9232i −0.539602 0.519848i
\(619\) 15.0361 + 26.0434i 0.604353 + 1.04677i 0.992153 + 0.125027i \(0.0399018\pi\)
−0.387800 + 0.921744i \(0.626765\pi\)
\(620\) −28.2917 −1.13622
\(621\) 10.5035 + 31.9380i 0.421491 + 1.28163i
\(622\) −21.3767 −0.857129
\(623\) 0.503698 + 0.872430i 0.0201802 + 0.0349532i
\(624\) 37.0338 + 35.6780i 1.48254 + 1.42827i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 1.12621 1.95065i 0.0450124 0.0779637i
\(627\) −4.25686 + 17.1603i −0.170003 + 0.685317i
\(628\) 46.1197 + 79.8817i 1.84038 + 3.18763i
\(629\) 27.5742 1.09946
\(630\) −6.87717 + 4.32013i −0.273993 + 0.172118i
\(631\) −23.0115 −0.916074 −0.458037 0.888933i \(-0.651447\pi\)
−0.458037 + 0.888933i \(0.651447\pi\)
\(632\) 51.1397 + 88.5766i 2.03423 + 3.52339i
\(633\) 11.8638 3.41717i 0.471543 0.135820i
\(634\) −24.9677 + 43.2454i −0.991595 + 1.71749i
\(635\) −4.84315 + 8.38858i −0.192195 + 0.332891i
\(636\) 10.7010 3.08225i 0.424322 0.122219i
\(637\) −1.08055 1.87156i −0.0428128 0.0741540i
\(638\) −50.7122 −2.00772
\(639\) −1.72404 46.2160i −0.0682021 1.82828i
\(640\) −27.7619 −1.09739
\(641\) 14.8746 + 25.7635i 0.587510 + 1.01760i 0.994557 + 0.104190i \(0.0332249\pi\)
−0.407048 + 0.913407i \(0.633442\pi\)
\(642\) 5.04412 20.3339i 0.199076 0.802516i
\(643\) −16.7292 + 28.9758i −0.659735 + 1.14269i 0.320950 + 0.947096i \(0.395998\pi\)
−0.980684 + 0.195598i \(0.937335\pi\)
\(644\) 17.2395 29.8596i 0.679330 1.17663i
\(645\) 7.43454 + 7.16237i 0.292735 + 0.282018i
\(646\) −22.9245 39.7064i −0.901953 1.56223i
\(647\) 32.8534 1.29160 0.645799 0.763507i \(-0.276524\pi\)
0.645799 + 0.763507i \(0.276524\pi\)
\(648\) −80.8785 + 6.04259i −3.17721 + 0.237376i
\(649\) 38.3037 1.50355
\(650\) −2.92523 5.06664i −0.114737 0.198730i
\(651\) 6.62255 + 6.38011i 0.259558 + 0.250056i
\(652\) 25.5882 44.3201i 1.00211 1.73571i
\(653\) 6.20437 10.7463i 0.242796 0.420534i −0.718714 0.695306i \(-0.755269\pi\)
0.961510 + 0.274772i \(0.0886022\pi\)
\(654\) −6.29594 + 25.3803i −0.246191 + 0.992448i
\(655\) −3.31847 5.74777i −0.129664 0.224584i
\(656\) 31.2004 1.21817
\(657\) −0.715986 19.1933i −0.0279333 0.748801i
\(658\) 7.65686 0.298495
\(659\) −21.7394 37.6537i −0.846847 1.46678i −0.884008 0.467472i \(-0.845165\pi\)
0.0371610 0.999309i \(-0.488169\pi\)
\(660\) −36.9636 + 10.6468i −1.43881 + 0.414425i
\(661\) 14.6646 25.3998i 0.570386 0.987938i −0.426140 0.904657i \(-0.640127\pi\)
0.996526 0.0832809i \(-0.0265399\pi\)
\(662\) −12.7461 + 22.0768i −0.495390 + 0.858040i
\(663\) −24.8716 + 7.16386i −0.965933 + 0.278221i
\(664\) 46.0670 + 79.7903i 1.78774 + 3.09646i
\(665\) −2.44928 −0.0949789
\(666\) 27.4244 17.2275i 1.06267 0.667554i
\(667\) −29.0824 −1.12607
\(668\) 62.8345 + 108.833i 2.43114 + 4.21086i
\(669\) 6.63316 26.7397i 0.256453 1.03382i
\(670\) 7.83083 13.5634i 0.302531 0.524000i
\(671\) 16.6133 28.7751i 0.641350 1.11085i
\(672\) 23.9103 + 23.0350i 0.922361 + 0.888594i
\(673\) −3.89576 6.74766i −0.150171 0.260103i 0.781119 0.624382i \(-0.214649\pi\)
−0.931290 + 0.364278i \(0.881316\pi\)
\(674\) 24.4328 0.941115
\(675\) 5.08643 + 1.06219i 0.195777 + 0.0408836i
\(676\) −44.3869 −1.70719
\(677\) 11.3246 + 19.6148i 0.435240 + 0.753858i 0.997315 0.0732280i \(-0.0233301\pi\)
−0.562075 + 0.827086i \(0.689997\pi\)
\(678\) −42.7184 41.1546i −1.64059 1.58053i
\(679\) −4.43975 + 7.68987i −0.170382 + 0.295110i
\(680\) 31.1563 53.9643i 1.19479 2.06943i
\(681\) 0.223444 0.900752i 0.00856241 0.0345169i
\(682\) 29.9510 + 51.8767i 1.14688 + 1.98646i
\(683\) 22.0281 0.842880 0.421440 0.906856i \(-0.361525\pi\)
0.421440 + 0.906856i \(0.361525\pi\)
\(684\) −34.6154 18.2998i −1.32355 0.699710i
\(685\) −20.5769 −0.786204
\(686\) −1.35359 2.34448i −0.0516801 0.0895126i
\(687\) 2.17617 0.626809i 0.0830259 0.0239143i
\(688\) 40.9413 70.9125i 1.56087 2.70351i
\(689\) 1.30373 2.25812i 0.0496681 0.0860277i
\(690\) −29.1539 + 8.39729i −1.10987 + 0.319679i
\(691\) 14.8236 + 25.6752i 0.563915 + 0.976729i 0.997150 + 0.0754481i \(0.0240387\pi\)
−0.433235 + 0.901281i \(0.642628\pi\)
\(692\) 81.4152 3.09494
\(693\) 11.0535 + 5.84352i 0.419886 + 0.221977i
\(694\) −20.4087 −0.774702
\(695\) 4.57816 + 7.92960i 0.173659 + 0.300787i
\(696\) 16.8912 68.0920i 0.640259 2.58102i
\(697\) −7.85190 + 13.5999i −0.297412 + 0.515133i
\(698\) −6.81291 + 11.8003i −0.257872 + 0.446648i
\(699\) −29.4868 28.4073i −1.11529 1.07446i
\(700\) −2.66438 4.61485i −0.100704 0.174425i
\(701\) 32.4868 1.22701 0.613505 0.789691i \(-0.289759\pi\)
0.613505 + 0.789691i \(0.289759\pi\)
\(702\) −20.2607 + 22.6640i −0.764690 + 0.855396i
\(703\) 9.76708 0.368373
\(704\) 50.8798 + 88.1263i 1.91760 + 3.32139i
\(705\) −3.52800 3.39884i −0.132872 0.128008i
\(706\) 3.43236 5.94503i 0.129179 0.223744i
\(707\) 0.124032 0.214829i 0.00466469 0.00807947i
\(708\) −20.4236 + 82.3318i −0.767565 + 3.09422i
\(709\) 4.59556 + 7.95974i 0.172590 + 0.298934i 0.939325 0.343030i \(-0.111453\pi\)
−0.766735 + 0.641964i \(0.778120\pi\)
\(710\) 41.7339 1.56624
\(711\) −28.8326 + 18.1121i −1.08131 + 0.679259i
\(712\) −9.07819 −0.340220
\(713\) 17.1763 + 29.7502i 0.643257 + 1.11415i
\(714\) −31.1563 + 8.97406i −1.16599 + 0.335846i
\(715\) −4.50337 + 7.80007i −0.168416 + 0.291706i
\(716\) −5.15366 + 8.92640i −0.192601 + 0.333595i
\(717\) 0.767350 0.221023i 0.0286572 0.00825424i
\(718\) −33.0064 57.1688i −1.23179 2.13352i
\(719\) 32.0782 1.19632 0.598158 0.801378i \(-0.295900\pi\)
0.598158 + 0.801378i \(0.295900\pi\)
\(720\) −1.53641 41.1861i −0.0572585 1.53491i
\(721\) −3.97246 −0.147942
\(722\) 17.5980 + 30.4806i 0.654930 + 1.13437i
\(723\) 10.3076 41.5522i 0.383344 1.54534i
\(724\) 18.5280 32.0914i 0.688586 1.19267i
\(725\) −2.24736 + 3.89255i −0.0834650 + 0.144566i
\(726\) 21.5087 + 20.7213i 0.798264 + 0.769041i
\(727\) −26.5430 45.9738i −0.984425 1.70507i −0.644463 0.764636i \(-0.722919\pi\)
−0.339963 0.940439i \(-0.610414\pi\)
\(728\) 19.4748 0.721784
\(729\) −3.01393 26.8313i −0.111627 0.993750i
\(730\) 17.3319 0.641481
\(731\) 20.6066 + 35.6917i 0.762164 + 1.32011i
\(732\) 52.9923 + 51.0523i 1.95865 + 1.88695i
\(733\) −6.72493 + 11.6479i −0.248391 + 0.430226i −0.963080 0.269217i \(-0.913235\pi\)
0.714689 + 0.699443i \(0.246568\pi\)
\(734\) 37.1956 64.4246i 1.37291 2.37796i
\(735\) −0.417021 + 1.68110i −0.0153820 + 0.0620083i
\(736\) 62.0139 + 107.411i 2.28586 + 3.95923i
\(737\) −24.1111 −0.888142
\(738\) 0.687573 + 18.4316i 0.0253099 + 0.678477i
\(739\) −44.5198 −1.63769 −0.818844 0.574016i \(-0.805385\pi\)
−0.818844 + 0.574016i \(0.805385\pi\)
\(740\) 10.6249 + 18.4028i 0.390578 + 0.676501i
\(741\) −8.80979 + 2.53752i −0.323636 + 0.0932180i
\(742\) 1.63316 2.82872i 0.0599552 0.103845i
\(743\) 9.34029 16.1779i 0.342662 0.593508i −0.642264 0.766483i \(-0.722005\pi\)
0.984926 + 0.172975i \(0.0553381\pi\)
\(744\) −79.6316 + 22.9366i −2.91943 + 0.840896i
\(745\) 11.2617 + 19.5058i 0.412596 + 0.714637i
\(746\) 100.582 3.68258
\(747\) −25.9725 + 16.3155i −0.950285 + 0.596954i
\(748\) −153.567 −5.61496
\(749\) −2.23400 3.86940i −0.0816285 0.141385i
\(750\) −1.12895 + 4.55102i −0.0412233 + 0.166180i
\(751\) −14.6884 + 25.4410i −0.535986 + 0.928355i 0.463129 + 0.886291i \(0.346727\pi\)
−0.999115 + 0.0420642i \(0.986607\pi\)
\(752\) −19.4284 + 33.6509i −0.708480 + 1.22712i
\(753\) 12.4086 + 11.9543i 0.452193 + 0.435639i
\(754\) −13.1481 22.7732i −0.478825 0.829350i
\(755\) −0.550257 −0.0200259
\(756\) −18.4540 + 20.6430i −0.671167 + 0.750780i
\(757\) 22.3860 0.813631 0.406816 0.913510i \(-0.366639\pi\)
0.406816 + 0.913510i \(0.366639\pi\)
\(758\) −46.4535 80.4597i −1.68727 2.92243i
\(759\) 33.6367 + 32.4053i 1.22094 + 1.17624i
\(760\) 11.0359 19.1147i 0.400314 0.693364i
\(761\) −22.1153 + 38.3049i −0.801680 + 1.38855i 0.116830 + 0.993152i \(0.462727\pi\)
−0.918510 + 0.395399i \(0.870606\pi\)
\(762\) −10.9353 + 44.0826i −0.396144 + 1.59694i
\(763\) 2.78842 + 4.82968i 0.100947 + 0.174846i
\(764\) −3.39065 −0.122670
\(765\) 18.3392 + 9.69521i 0.663055 + 0.350531i
\(766\) 85.4928 3.08898
\(767\) 9.93096 + 17.2009i 0.358586 + 0.621089i
\(768\) −43.8124 + 12.6195i −1.58095 + 0.455366i
\(769\) 10.2249 17.7101i 0.368719 0.638641i −0.620646 0.784091i \(-0.713130\pi\)
0.989366 + 0.145450i \(0.0464630\pi\)
\(770\) −5.64130 + 9.77102i −0.203298 + 0.352123i
\(771\) 37.4904 10.7985i 1.35018 0.388899i
\(772\) 19.1465 + 33.1627i 0.689097 + 1.19355i
\(773\) 4.80680 0.172889 0.0864444 0.996257i \(-0.472450\pi\)
0.0864444 + 0.996257i \(0.472450\pi\)
\(774\) 42.7938 + 22.6234i 1.53819 + 0.813180i
\(775\) 5.30924 0.190713
\(776\) −40.0090 69.2976i −1.43624 2.48764i
\(777\) 1.66297 6.70379i 0.0596587 0.240497i
\(778\) 5.74918 9.95787i 0.206118 0.357007i
\(779\) −2.78123 + 4.81723i −0.0996479 + 0.172595i
\(780\) −14.3646 13.8387i −0.514336 0.495507i
\(781\) −32.1246 55.6414i −1.14951 1.99100i
\(782\) −121.121 −4.33127
\(783\) 22.8621 + 4.77425i 0.817025 + 0.170618i
\(784\) 13.7382 0.490652
\(785\) −8.65486 14.9907i −0.308905 0.535039i
\(786\) −22.4118 21.5914i −0.799403 0.770138i
\(787\) −19.4794 + 33.7394i −0.694367 + 1.20268i 0.276026 + 0.961150i \(0.410982\pi\)
−0.970394 + 0.241529i \(0.922351\pi\)
\(788\) 43.4191 75.2040i 1.54674 2.67903i
\(789\) −5.02919 + 20.2737i −0.179044 + 0.721764i
\(790\) −15.3630 26.6094i −0.546589 0.946720i
\(791\) −12.6505 −0.449799
\(792\) −95.4085 + 59.9341i −3.39019 + 2.12967i
\(793\) 17.2292 0.611828
\(794\) 17.0164 + 29.4733i 0.603891 + 1.04597i
\(795\) −2.00815 + 0.578416i −0.0712219 + 0.0205143i
\(796\) −26.8613 + 46.5251i −0.952073 + 1.64904i
\(797\) −9.44776 + 16.3640i −0.334657 + 0.579643i −0.983419 0.181349i \(-0.941954\pi\)
0.648762 + 0.760991i \(0.275287\pi\)
\(798\) −11.0359 + 3.17871i −0.390666 + 0.112525i
\(799\) −9.77870 16.9372i −0.345946 0.599195i
\(800\) 19.1687 0.677715
\(801\) −0.112661 3.02009i −0.00398069 0.106710i
\(802\) 100.967 3.56525
\(803\) −13.3412 23.1076i −0.470799 0.815448i
\(804\) 12.8560 51.8254i 0.453397 1.82774i
\(805\) −3.23517 + 5.60347i −0.114025 + 0.197496i
\(806\) −15.5307 + 26.9000i −0.547046 + 0.947512i
\(807\) −5.34917 5.15334i −0.188300 0.181406i
\(808\) 1.11772 + 1.93594i 0.0393211 + 0.0681061i
\(809\) 1.94753 0.0684716 0.0342358 0.999414i \(-0.489100\pi\)
0.0342358 + 0.999414i \(0.489100\pi\)
\(810\) 24.2968 1.81526i 0.853703 0.0637819i
\(811\) −51.0182 −1.79149 −0.895746 0.444565i \(-0.853358\pi\)
−0.895746 + 0.444565i \(0.853358\pi\)
\(812\) −11.9757 20.7425i −0.420264 0.727919i
\(813\) 5.60078 + 5.39574i 0.196428 + 0.189237i
\(814\) 22.4960 38.9643i 0.788486 1.36570i
\(815\) −4.80190 + 8.31713i −0.168203 + 0.291336i
\(816\) 39.6155 159.699i 1.38682 5.59057i
\(817\) 7.29909 + 12.6424i 0.255363 + 0.442301i
\(818\) −12.3395 −0.431441
\(819\) 0.241684 + 6.47878i 0.00844514 + 0.226387i
\(820\) −12.1020 −0.422619
\(821\) 8.23988 + 14.2719i 0.287574 + 0.498093i 0.973230 0.229833i \(-0.0738180\pi\)
−0.685656 + 0.727926i \(0.740485\pi\)
\(822\) −92.7149 + 26.7050i −3.23381 + 0.931445i
\(823\) −11.7457 + 20.3442i −0.409429 + 0.709153i −0.994826 0.101595i \(-0.967606\pi\)
0.585396 + 0.810747i \(0.300939\pi\)
\(824\) 17.8990 31.0020i 0.623541 1.08000i
\(825\) 6.93661 1.99798i 0.241502 0.0695607i
\(826\) 12.4404 + 21.5473i 0.432855 + 0.749727i
\(827\) −18.7714 −0.652744 −0.326372 0.945241i \(-0.605826\pi\)
−0.326372 + 0.945241i \(0.605826\pi\)
\(828\) −87.5886 + 55.0218i −3.04392 + 1.91214i
\(829\) 40.9504 1.42227 0.711134 0.703057i \(-0.248182\pi\)
0.711134 + 0.703057i \(0.248182\pi\)
\(830\) −13.8390 23.9699i −0.480360 0.832008i
\(831\) −0.700102 + 2.82226i −0.0242863 + 0.0979032i
\(832\) −26.3830 + 45.6968i −0.914668 + 1.58425i
\(833\) −3.45737 + 5.98835i −0.119791 + 0.207484i
\(834\) 30.9193 + 29.7874i 1.07065 + 1.03145i
\(835\) −11.7916 20.4236i −0.408064 0.706787i
\(836\) −54.3950 −1.88129
\(837\) −8.61866 26.2068i −0.297904 0.905839i
\(838\) −45.3128 −1.56530
\(839\) 4.06342 + 7.03805i 0.140285 + 0.242981i 0.927604 0.373565i \(-0.121865\pi\)
−0.787319 + 0.616546i \(0.788531\pi\)
\(840\) −11.2407 10.8292i −0.387840 0.373642i
\(841\) 4.39871 7.61879i 0.151680 0.262717i
\(842\) 32.6766 56.5975i 1.12611 1.95048i
\(843\) −7.40517 + 29.8518i −0.255047 + 1.02815i
\(844\) 18.9918 + 32.8948i 0.653725 + 1.13229i
\(845\) 8.32967 0.286549
\(846\) −20.3074 10.7357i −0.698183 0.369102i
\(847\) 6.36951 0.218859
\(848\) 8.28790 + 14.3551i 0.284608 + 0.492955i
\(849\) −3.92435 + 1.13034i −0.134683 + 0.0387933i
\(850\) −9.35970 + 16.2115i −0.321035 + 0.556049i
\(851\) 12.9010 22.3452i 0.442241 0.765983i
\(852\) 136.727 39.3820i 4.68419 1.34920i
\(853\) −12.1844 21.1039i −0.417185 0.722585i 0.578470 0.815703i \(-0.303650\pi\)
−0.995655 + 0.0931183i \(0.970317\pi\)
\(854\) 21.5828 0.738548
\(855\) 6.49595 + 3.43415i 0.222157 + 0.117445i
\(856\) 40.2635 1.37618
\(857\) −6.52746 11.3059i −0.222974 0.386202i 0.732736 0.680513i \(-0.238243\pi\)
−0.955710 + 0.294311i \(0.904910\pi\)
\(858\) −10.1681 + 40.9899i −0.347134 + 1.39937i
\(859\) −4.02025 + 6.96328i −0.137169 + 0.237584i −0.926424 0.376482i \(-0.877134\pi\)
0.789255 + 0.614066i \(0.210467\pi\)
\(860\) −15.8803 + 27.5054i −0.541512 + 0.937927i
\(861\) 2.83284 + 2.72913i 0.0965429 + 0.0930086i
\(862\) 27.0210 + 46.8017i 0.920339 + 1.59407i
\(863\) −34.8130 −1.18505 −0.592523 0.805553i \(-0.701868\pi\)
−0.592523 + 0.805553i \(0.701868\pi\)
\(864\) −31.1171 94.6179i −1.05863 3.21897i
\(865\) −15.2784 −0.519482
\(866\) −10.3116 17.8601i −0.350401 0.606912i
\(867\) 38.4359 + 37.0289i 1.30535 + 1.25757i
\(868\) −14.1459 + 24.5013i −0.480142 + 0.831630i
\(869\) −23.6512 + 40.9651i −0.802312 + 1.38964i
\(870\) −5.07430 + 20.4556i −0.172035 + 0.693510i
\(871\) −6.25124 10.8275i −0.211815 0.366875i
\(872\) −50.2559 −1.70188
\(873\) 22.5570 14.1700i 0.763440 0.479581i
\(874\) −42.9023 −1.45119
\(875\) 0.500000 + 0.866025i 0.0169031 + 0.0292770i
\(876\) 56.7819 16.3551i 1.91848 0.552588i
\(877\) 20.1118 34.8347i 0.679127 1.17628i −0.296117 0.955152i \(-0.595692\pi\)
0.975244 0.221131i \(-0.0709750\pi\)
\(878\) 13.2993 23.0351i 0.448830 0.777397i
\(879\) 18.4420 5.31191i 0.622032 0.179166i
\(880\) −28.6283 49.5856i −0.965059 1.67153i
\(881\) 25.8229 0.869995 0.434998 0.900432i \(-0.356749\pi\)
0.434998 + 0.900432i \(0.356749\pi\)
\(882\) 0.302754 + 8.11587i 0.0101943 + 0.273275i
\(883\) −25.4291 −0.855756 −0.427878 0.903836i \(-0.640739\pi\)
−0.427878 + 0.903836i \(0.640739\pi\)
\(884\) −39.8150 68.9617i −1.33912 2.31943i
\(885\) 3.83270 15.4504i 0.128835 0.519360i
\(886\) −0.565579 + 0.979612i −0.0190010 + 0.0329107i
\(887\) −6.63820 + 11.4977i −0.222889 + 0.386055i −0.955684 0.294394i \(-0.904882\pi\)
0.732795 + 0.680449i \(0.238215\pi\)
\(888\) 44.8249 + 43.1839i 1.50423 + 1.44916i
\(889\) 4.84315 + 8.38858i 0.162434 + 0.281344i
\(890\) 2.72719 0.0914157
\(891\) −21.1226 30.9962i −0.707634 1.03841i
\(892\) 84.7598 2.83797
\(893\) −3.46372 5.99934i −0.115909 0.200760i
\(894\) 76.0574 + 73.2731i 2.54374 + 2.45062i
\(895\) 0.967139 1.67513i 0.0323279 0.0559936i
\(896\) −13.8810 + 24.0425i −0.463730 + 0.803205i
\(897\) −5.83120 + 23.5068i −0.194698 + 0.784870i
\(898\) 41.3560 + 71.6307i 1.38007 + 2.39035i
\(899\) 23.8636 0.795895
\(900\) 0.595939 + 15.9752i 0.0198646 + 0.532507i
\(901\) −8.34295 −0.277944
\(902\) 12.8117 + 22.1906i 0.426584 + 0.738865i
\(903\) 9.92006 2.85731i 0.330119 0.0950854i
\(904\) 57.0001 98.7271i 1.89580 3.28361i
\(905\) −3.47697 + 6.02228i −0.115578 + 0.200188i
\(906\) −2.47933 + 0.714131i −0.0823702 + 0.0237254i
\(907\) −3.02387 5.23750i −0.100406 0.173908i 0.811446 0.584428i \(-0.198681\pi\)
−0.911852 + 0.410519i \(0.865348\pi\)
\(908\) 2.85521 0.0947536
\(909\) −0.630168 + 0.395861i −0.0209013 + 0.0131299i
\(910\) −5.85045 −0.193941
\(911\) 1.75861 + 3.04600i 0.0582652 + 0.100918i 0.893687 0.448691i \(-0.148110\pi\)
−0.835422 + 0.549610i \(0.814776\pi\)
\(912\) 14.0322 56.5669i 0.464654 1.87312i
\(913\) −21.3051 + 36.9016i −0.705097 + 1.22126i
\(914\) −6.86036 + 11.8825i −0.226920 + 0.393038i
\(915\) −9.94456 9.58050i −0.328757 0.316722i
\(916\) 3.48365 + 6.03387i 0.115103 + 0.199365i
\(917\) −6.63695 −0.219171
\(918\) 95.2149 + 19.8835i 3.14256 + 0.656254i
\(919\) −21.2381 −0.700581 −0.350290 0.936641i \(-0.613917\pi\)
−0.350290 + 0.936641i \(0.613917\pi\)
\(920\) −29.1539 50.4960i −0.961174 1.66480i
\(921\) 31.2314 + 30.0880i 1.02911 + 0.991434i
\(922\) 7.29786 12.6403i 0.240342 0.416285i
\(923\) 16.6578 28.8521i 0.548297 0.949679i
\(924\) −9.26144 + 37.3348i −0.304679 + 1.22823i
\(925\) −1.99387 3.45348i −0.0655580 0.113550i
\(926\) 17.0600 0.560625
\(927\) 10.5357 + 5.56981i 0.346038 + 0.182936i
\(928\) 86.1580 2.82827
\(929\) −16.7596 29.0285i −0.549866 0.952395i −0.998283 0.0585710i \(-0.981346\pi\)
0.448418 0.893824i \(-0.351988\pi\)
\(930\) 23.9222 6.89041i 0.784441 0.225945i
\(931\) −1.22464 + 2.12114i −0.0401359 + 0.0695175i
\(932\) 62.9842 109.092i 2.06312 3.57342i
\(933\) 13.1426 3.78550i 0.430268 0.123932i
\(934\) 5.20736 + 9.01941i 0.170390 + 0.295124i
\(935\) 28.8184 0.942463
\(936\) −51.6508 27.3057i −1.68826 0.892516i
\(937\) −20.2231 −0.660661 −0.330330 0.943865i \(-0.607160\pi\)
−0.330330 + 0.943865i \(0.607160\pi\)
\(938\) −7.83083 13.5634i −0.255686 0.442861i
\(939\) −0.346969 + 1.39871i −0.0113229 + 0.0456451i
\(940\) 7.53584 13.0525i 0.245792 0.425724i
\(941\) −12.4190 + 21.5104i −0.404848 + 0.701218i −0.994304 0.106583i \(-0.966009\pi\)
0.589456 + 0.807801i \(0.299342\pi\)
\(942\) −58.4519 56.3121i −1.90447 1.83475i
\(943\) 7.34726 + 12.7258i 0.239260 + 0.414410i
\(944\) −126.264 −4.10953
\(945\) 3.46310 3.87388i 0.112655 0.126017i
\(946\) 67.2466 2.18637
\(947\) −21.9742 38.0605i −0.714067 1.23680i −0.963318 0.268361i \(-0.913518\pi\)
0.249251 0.968439i \(-0.419815\pi\)
\(948\) −75.4413 72.6795i −2.45022 2.36052i
\(949\) 6.91789 11.9821i 0.224564 0.388956i
\(950\) −3.31531 + 5.74228i −0.107563 + 0.186304i
\(951\) 7.69221 31.0089i 0.249437 1.00553i
\(952\) −31.1563 53.9643i −1.00978 1.74899i
\(953\) 14.6532 0.474665 0.237332 0.971428i \(-0.423727\pi\)
0.237332 + 0.971428i \(0.423727\pi\)
\(954\) −8.29761 + 5.21242i −0.268645 + 0.168758i
\(955\) 0.636292 0.0205899
\(956\) 1.22839 + 2.12764i 0.0397290 + 0.0688126i
\(957\) 31.1782 8.98037i 1.00785 0.290294i
\(958\) 27.1771 47.0721i 0.878051 1.52083i
\(959\) −10.2885 + 17.8201i −0.332232 + 0.575442i
\(960\) 40.6382 11.7052i 1.31159 0.377783i
\(961\) 1.40599 + 2.43525i 0.0453545 + 0.0785563i
\(962\) 23.3301 0.752192
\(963\) 0.499675 + 13.3947i 0.0161018 + 0.431637i
\(964\) 131.713 4.24218
\(965\) −3.59304 6.22333i −0.115664 0.200336i
\(966\) −7.30466 + 29.4466i −0.235023 + 0.947430i
\(967\) −20.1998 + 34.9871i −0.649583 + 1.12511i 0.333640 + 0.942701i \(0.391723\pi\)
−0.983223 + 0.182410i \(0.941610\pi\)
\(968\) −28.6996 + 49.7091i −0.922440 + 1.59771i
\(969\) 21.1255 + 20.3522i 0.678650 + 0.653806i
\(970\) 12.0191 + 20.8178i 0.385912 + 0.668418i
\(971\) 55.6840 1.78699 0.893493 0.449077i \(-0.148247\pi\)
0.893493 + 0.449077i \(0.148247\pi\)
\(972\) 77.8873 28.8747i 2.49824 0.926155i
\(973\) 9.15632 0.293538
\(974\) 29.8023 + 51.6191i 0.954927 + 1.65398i
\(975\) 2.69567 + 2.59699i 0.0863306 + 0.0831702i
\(976\) −54.7638 + 94.8537i −1.75295 + 3.03619i
\(977\) −14.7158 + 25.4886i −0.470801 + 0.815452i −0.999442 0.0333938i \(-0.989368\pi\)
0.528641 + 0.848845i \(0.322702\pi\)
\(978\) −10.8422 + 43.7071i −0.346694 + 1.39760i
\(979\) −2.09925 3.63601i −0.0670923 0.116207i
\(980\) −5.32877 −0.170221
\(981\) −0.623681 16.7189i −0.0199126 0.533792i
\(982\) 26.4804 0.845025
\(983\) 4.62544 + 8.01149i 0.147529 + 0.255527i 0.930313 0.366765i \(-0.119535\pi\)
−0.782785 + 0.622292i \(0.786202\pi\)
\(984\) −34.0629 + 9.81126i −1.08589 + 0.312772i
\(985\) −8.14805 + 14.1128i −0.259618 + 0.449672i
\(986\) −42.0693 + 72.8662i −1.33976 + 2.32053i
\(987\) −4.70748 + 1.35591i −0.149841 + 0.0431592i
\(988\) −14.1029 24.4270i −0.448673 0.777125i
\(989\) 38.5645 1.22628
\(990\) 28.6618 18.0049i 0.910932 0.572233i
\(991\) −12.0283 −0.382091 −0.191046 0.981581i \(-0.561188\pi\)
−0.191046 + 0.981581i \(0.561188\pi\)
\(992\) −50.8855 88.1363i −1.61562 2.79833i
\(993\) 3.92688 15.8301i 0.124616 0.502353i
\(994\) 20.8669 36.1426i 0.661859 1.14637i
\(995\) 5.04080 8.73093i 0.159804 0.276789i
\(996\) −67.9580 65.4701i −2.15333 2.07450i
\(997\) −9.58480 16.6014i −0.303554 0.525770i 0.673385 0.739292i \(-0.264840\pi\)
−0.976938 + 0.213522i \(0.931506\pi\)
\(998\) 37.9867 1.20245
\(999\) −13.8099 + 15.4480i −0.436927 + 0.488754i
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 315.2.i.e.211.1 yes 12
3.2 odd 2 945.2.i.e.631.6 12
9.2 odd 6 945.2.i.e.316.6 12
9.4 even 3 2835.2.a.u.1.6 6
9.5 odd 6 2835.2.a.v.1.1 6
9.7 even 3 inner 315.2.i.e.106.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.i.e.106.1 12 9.7 even 3 inner
315.2.i.e.211.1 yes 12 1.1 even 1 trivial
945.2.i.e.316.6 12 9.2 odd 6
945.2.i.e.631.6 12 3.2 odd 2
2835.2.a.u.1.6 6 9.4 even 3
2835.2.a.v.1.1 6 9.5 odd 6