Properties

Label 315.2.bl.j.146.8
Level $315$
Weight $2$
Character 315.146
Analytic conductor $2.515$
Analytic rank $0$
Dimension $24$
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(41,315)]
 
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([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bl (of order \(6\), 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: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 146.8
Character \(\chi\) \(=\) 315.146
Dual form 315.2.bl.j.41.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.02342 + 0.590871i) q^{2} +(-1.63294 + 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.01241 - 0.373820i) q^{6} +(2.45705 + 0.981280i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} +O(q^{10})\) \(q+(1.02342 + 0.590871i) q^{2} +(-1.63294 + 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.01241 - 0.373820i) q^{6} +(2.45705 + 0.981280i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} -1.18174i q^{10} +(5.38278 + 3.10775i) q^{11} +(0.794556 + 0.679171i) q^{12} +(0.534292 - 0.308474i) q^{13} +(1.93478 + 2.45606i) q^{14} +(1.31661 + 1.12541i) q^{15} +(1.21441 - 2.10343i) q^{16} +2.15945 q^{17} +(3.50202 - 0.551763i) q^{18} -4.75589i q^{19} +(-0.301744 + 0.522636i) q^{20} +(-4.57890 - 0.183398i) q^{21} +(3.67255 + 6.36105i) q^{22} +(-3.22334 + 1.86099i) q^{23} +(1.77680 + 5.02397i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.729072 q^{26} +(-2.72036 + 4.42715i) q^{27} +(-0.228548 - 1.58024i) q^{28} +(-4.09268 - 2.36291i) q^{29} +(0.682467 + 1.92971i) q^{30} +(7.25875 - 4.19084i) q^{31} +(-2.84321 + 1.64153i) q^{32} +(-10.5845 - 1.96615i) q^{33} +(2.21002 + 1.27596i) q^{34} +(-0.378711 - 2.61851i) q^{35} +(-1.68969 - 0.650179i) q^{36} -2.00832 q^{37} +(2.81012 - 4.86727i) q^{38} +(-0.694319 + 0.812277i) q^{39} +(-2.66446 + 1.53832i) q^{40} +(0.261960 + 0.453727i) q^{41} +(-4.57777 - 2.89323i) q^{42} +(2.75507 - 4.77192i) q^{43} -3.75098i q^{44} +(-2.79987 - 1.07737i) q^{45} -4.39843 q^{46} +(-3.25401 + 5.63611i) q^{47} +(-0.768310 + 4.13610i) q^{48} +(5.07418 + 4.82211i) q^{49} +(-1.02342 + 0.590871i) q^{50} +(-3.52625 + 1.24710i) q^{51} +(-0.322439 - 0.186160i) q^{52} +12.7283i q^{53} +(-5.39993 + 2.92345i) q^{54} -6.21549i q^{55} +(3.01905 - 7.55948i) q^{56} +(2.74658 + 7.76607i) q^{57} +(-2.79235 - 4.83649i) q^{58} +(2.72719 + 4.72363i) q^{59} +(0.190901 - 1.02769i) q^{60} +(-12.3587 - 7.13527i) q^{61} +9.90498 q^{62} +(7.58297 - 2.34489i) q^{63} -8.73737 q^{64} +(-0.534292 - 0.308474i) q^{65} +(-9.67061 - 8.26625i) q^{66} +(-0.146773 - 0.254218i) q^{67} +(-0.651601 - 1.12861i) q^{68} +(4.18876 - 4.90040i) q^{69} +(1.15962 - 2.90360i) q^{70} -5.45805i q^{71} +(-5.80279 - 7.17771i) q^{72} -0.406885i q^{73} +(-2.05535 - 1.18666i) q^{74} +(0.316330 - 1.70292i) q^{75} +(-2.48560 + 1.43506i) q^{76} +(10.1762 + 12.9179i) q^{77} +(-1.19053 + 0.421047i) q^{78} +(-2.85397 + 4.94322i) q^{79} -2.42883 q^{80} +(1.88544 - 8.80029i) q^{81} +0.619137i q^{82} +(-6.40891 + 11.1006i) q^{83} +(1.28581 + 2.44844i) q^{84} +(-1.07973 - 1.87014i) q^{85} +(5.63917 - 3.25578i) q^{86} +(8.04769 + 1.49492i) q^{87} +(9.56144 - 16.5609i) q^{88} +0.957722 q^{89} +(-2.22885 - 2.75696i) q^{90} +(1.61548 - 0.233645i) q^{91} +(1.94525 + 1.12309i) q^{92} +(-9.43283 + 11.0354i) q^{93} +(-6.66043 + 3.84540i) q^{94} +(-4.11872 + 2.37795i) q^{95} +(3.69478 - 4.32249i) q^{96} +(2.17426 + 1.25531i) q^{97} +(2.34376 + 7.93321i) q^{98} +(18.4193 - 2.90205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.02342 + 0.590871i 0.723666 + 0.417809i 0.816100 0.577910i \(-0.196132\pi\)
−0.0924347 + 0.995719i \(0.529465\pi\)
\(3\) −1.63294 + 0.577510i −0.942776 + 0.333426i
\(4\) −0.301744 0.522636i −0.150872 0.261318i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −2.01241 0.373820i −0.821563 0.152611i
\(7\) 2.45705 + 0.981280i 0.928677 + 0.370889i
\(8\) 3.07665i 1.08776i
\(9\) 2.33296 1.88607i 0.777655 0.628692i
\(10\) 1.18174i 0.373699i
\(11\) 5.38278 + 3.10775i 1.62297 + 0.937021i 0.986121 + 0.166031i \(0.0530951\pi\)
0.636847 + 0.770990i \(0.280238\pi\)
\(12\) 0.794556 + 0.679171i 0.229369 + 0.196060i
\(13\) 0.534292 0.308474i 0.148186 0.0855552i −0.424074 0.905628i \(-0.639400\pi\)
0.572260 + 0.820072i \(0.306067\pi\)
\(14\) 1.93478 + 2.45606i 0.517091 + 0.656409i
\(15\) 1.31661 + 1.12541i 0.339946 + 0.290580i
\(16\) 1.21441 2.10343i 0.303603 0.525856i
\(17\) 2.15945 0.523744 0.261872 0.965103i \(-0.415660\pi\)
0.261872 + 0.965103i \(0.415660\pi\)
\(18\) 3.50202 0.551763i 0.825435 0.130052i
\(19\) 4.75589i 1.09108i −0.838086 0.545538i \(-0.816325\pi\)
0.838086 0.545538i \(-0.183675\pi\)
\(20\) −0.301744 + 0.522636i −0.0674720 + 0.116865i
\(21\) −4.57890 0.183398i −0.999199 0.0400207i
\(22\) 3.67255 + 6.36105i 0.782991 + 1.35618i
\(23\) −3.22334 + 1.86099i −0.672112 + 0.388044i −0.796877 0.604142i \(-0.793516\pi\)
0.124764 + 0.992186i \(0.460183\pi\)
\(24\) 1.77680 + 5.02397i 0.362687 + 1.02551i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0.729072 0.142983
\(27\) −2.72036 + 4.42715i −0.523533 + 0.852006i
\(28\) −0.228548 1.58024i −0.0431914 0.298637i
\(29\) −4.09268 2.36291i −0.759992 0.438781i 0.0693012 0.997596i \(-0.477923\pi\)
−0.829293 + 0.558814i \(0.811256\pi\)
\(30\) 0.682467 + 1.92971i 0.124601 + 0.352315i
\(31\) 7.25875 4.19084i 1.30371 0.752698i 0.322672 0.946511i \(-0.395419\pi\)
0.981038 + 0.193813i \(0.0620856\pi\)
\(32\) −2.84321 + 1.64153i −0.502613 + 0.290184i
\(33\) −10.5845 1.96615i −1.84252 0.342262i
\(34\) 2.21002 + 1.27596i 0.379015 + 0.218825i
\(35\) −0.378711 2.61851i −0.0640138 0.442608i
\(36\) −1.68969 0.650179i −0.281615 0.108363i
\(37\) −2.00832 −0.330166 −0.165083 0.986280i \(-0.552789\pi\)
−0.165083 + 0.986280i \(0.552789\pi\)
\(38\) 2.81012 4.86727i 0.455861 0.789575i
\(39\) −0.694319 + 0.812277i −0.111180 + 0.130068i
\(40\) −2.66446 + 1.53832i −0.421287 + 0.243230i
\(41\) 0.261960 + 0.453727i 0.0409112 + 0.0708603i 0.885756 0.464151i \(-0.153641\pi\)
−0.844845 + 0.535012i \(0.820307\pi\)
\(42\) −4.57777 2.89323i −0.706365 0.446435i
\(43\) 2.75507 4.77192i 0.420144 0.727710i −0.575809 0.817584i \(-0.695313\pi\)
0.995953 + 0.0898736i \(0.0286463\pi\)
\(44\) 3.75098i 0.565481i
\(45\) −2.79987 1.07737i −0.417380 0.160605i
\(46\) −4.39843 −0.648513
\(47\) −3.25401 + 5.63611i −0.474646 + 0.822112i −0.999578 0.0290325i \(-0.990757\pi\)
0.524932 + 0.851144i \(0.324091\pi\)
\(48\) −0.768310 + 4.13610i −0.110896 + 0.596994i
\(49\) 5.07418 + 4.82211i 0.724883 + 0.688872i
\(50\) −1.02342 + 0.590871i −0.144733 + 0.0835617i
\(51\) −3.52625 + 1.24710i −0.493773 + 0.174630i
\(52\) −0.322439 0.186160i −0.0447142 0.0258158i
\(53\) 12.7283i 1.74837i 0.485596 + 0.874183i \(0.338603\pi\)
−0.485596 + 0.874183i \(0.661397\pi\)
\(54\) −5.39993 + 2.92345i −0.734838 + 0.397831i
\(55\) 6.21549i 0.838097i
\(56\) 3.01905 7.55948i 0.403438 1.01018i
\(57\) 2.74658 + 7.76607i 0.363793 + 1.02864i
\(58\) −2.79235 4.83649i −0.366653 0.635062i
\(59\) 2.72719 + 4.72363i 0.355050 + 0.614965i 0.987127 0.159941i \(-0.0511305\pi\)
−0.632076 + 0.774906i \(0.717797\pi\)
\(60\) 0.190901 1.02769i 0.0246453 0.132674i
\(61\) −12.3587 7.13527i −1.58236 0.913578i −0.994513 0.104608i \(-0.966641\pi\)
−0.587850 0.808970i \(-0.700026\pi\)
\(62\) 9.90498 1.25793
\(63\) 7.58297 2.34489i 0.955365 0.295428i
\(64\) −8.73737 −1.09217
\(65\) −0.534292 0.308474i −0.0662708 0.0382615i
\(66\) −9.67061 8.26625i −1.19037 1.01751i
\(67\) −0.146773 0.254218i −0.0179312 0.0310577i 0.856921 0.515448i \(-0.172375\pi\)
−0.874852 + 0.484391i \(0.839041\pi\)
\(68\) −0.651601 1.12861i −0.0790183 0.136864i
\(69\) 4.18876 4.90040i 0.504268 0.589938i
\(70\) 1.15962 2.90360i 0.138601 0.347046i
\(71\) 5.45805i 0.647751i −0.946100 0.323876i \(-0.895014\pi\)
0.946100 0.323876i \(-0.104986\pi\)
\(72\) −5.80279 7.17771i −0.683865 0.845901i
\(73\) 0.406885i 0.0476223i −0.999716 0.0238111i \(-0.992420\pi\)
0.999716 0.0238111i \(-0.00758004\pi\)
\(74\) −2.05535 1.18666i −0.238929 0.137946i
\(75\) 0.316330 1.70292i 0.0365266 0.196636i
\(76\) −2.48560 + 1.43506i −0.285118 + 0.164613i
\(77\) 10.1762 + 12.9179i 1.15968 + 1.47213i
\(78\) −1.19053 + 0.421047i −0.134801 + 0.0476741i
\(79\) −2.85397 + 4.94322i −0.321097 + 0.556156i −0.980715 0.195445i \(-0.937385\pi\)
0.659618 + 0.751601i \(0.270718\pi\)
\(80\) −2.42883 −0.271551
\(81\) 1.88544 8.80029i 0.209494 0.977810i
\(82\) 0.619137i 0.0683722i
\(83\) −6.40891 + 11.1006i −0.703469 + 1.21844i 0.263772 + 0.964585i \(0.415033\pi\)
−0.967241 + 0.253859i \(0.918300\pi\)
\(84\) 1.28581 + 2.44844i 0.140293 + 0.267147i
\(85\) −1.07973 1.87014i −0.117113 0.202845i
\(86\) 5.63917 3.25578i 0.608087 0.351079i
\(87\) 8.04769 + 1.49492i 0.862803 + 0.160272i
\(88\) 9.56144 16.5609i 1.01925 1.76540i
\(89\) 0.957722 0.101518 0.0507592 0.998711i \(-0.483836\pi\)
0.0507592 + 0.998711i \(0.483836\pi\)
\(90\) −2.22885 2.75696i −0.234942 0.290609i
\(91\) 1.61548 0.233645i 0.169348 0.0244926i
\(92\) 1.94525 + 1.12309i 0.202806 + 0.117090i
\(93\) −9.43283 + 11.0354i −0.978139 + 1.14432i
\(94\) −6.66043 + 3.84540i −0.686971 + 0.396623i
\(95\) −4.11872 + 2.37795i −0.422572 + 0.243972i
\(96\) 3.69478 4.32249i 0.377097 0.441162i
\(97\) 2.17426 + 1.25531i 0.220762 + 0.127457i 0.606303 0.795234i \(-0.292652\pi\)
−0.385541 + 0.922691i \(0.625985\pi\)
\(98\) 2.34376 + 7.93321i 0.236756 + 0.801375i
\(99\) 18.4193 2.90205i 1.85121 0.291667i
\(100\) 0.603488 0.0603488
\(101\) −5.94095 + 10.2900i −0.591147 + 1.02390i 0.402932 + 0.915230i \(0.367991\pi\)
−0.994078 + 0.108666i \(0.965342\pi\)
\(102\) −4.34570 0.807246i −0.430289 0.0799293i
\(103\) 3.77246 2.17803i 0.371711 0.214608i −0.302494 0.953151i \(-0.597819\pi\)
0.674206 + 0.738543i \(0.264486\pi\)
\(104\) −0.949065 1.64383i −0.0930635 0.161191i
\(105\) 2.13063 + 4.05715i 0.207928 + 0.395937i
\(106\) −7.52078 + 13.0264i −0.730482 + 1.26523i
\(107\) 16.8978i 1.63357i −0.576943 0.816784i \(-0.695755\pi\)
0.576943 0.816784i \(-0.304245\pi\)
\(108\) 3.13464 + 0.0858893i 0.301631 + 0.00826470i
\(109\) −7.49502 −0.717892 −0.358946 0.933358i \(-0.616864\pi\)
−0.358946 + 0.933358i \(0.616864\pi\)
\(110\) 3.67255 6.36105i 0.350164 0.606502i
\(111\) 3.27946 1.15982i 0.311272 0.110086i
\(112\) 5.04792 3.97654i 0.476984 0.375748i
\(113\) −10.8082 + 6.24010i −1.01675 + 0.587020i −0.913160 0.407601i \(-0.866366\pi\)
−0.103588 + 0.994620i \(0.533032\pi\)
\(114\) −1.77785 + 9.57081i −0.166511 + 0.896388i
\(115\) 3.22334 + 1.86099i 0.300578 + 0.173539i
\(116\) 2.85198i 0.264799i
\(117\) 0.664680 1.72737i 0.0614497 0.159696i
\(118\) 6.44567i 0.593372i
\(119\) 5.30588 + 2.11903i 0.486389 + 0.194251i
\(120\) 3.46249 4.05074i 0.316081 0.369780i
\(121\) 13.8162 + 23.9303i 1.25602 + 2.17548i
\(122\) −8.43205 14.6047i −0.763402 1.32225i
\(123\) −0.689796 0.589624i −0.0621968 0.0531646i
\(124\) −4.38057 2.52912i −0.393387 0.227122i
\(125\) 1.00000 0.0894427
\(126\) 9.14608 + 2.08076i 0.814797 + 0.185369i
\(127\) −10.3479 −0.918228 −0.459114 0.888377i \(-0.651833\pi\)
−0.459114 + 0.888377i \(0.651833\pi\)
\(128\) −3.25557 1.87960i −0.287754 0.166135i
\(129\) −1.74302 + 9.38332i −0.153464 + 0.826155i
\(130\) −0.364536 0.631395i −0.0319719 0.0553770i
\(131\) −5.47102 9.47609i −0.478005 0.827929i 0.521677 0.853143i \(-0.325307\pi\)
−0.999682 + 0.0252138i \(0.991973\pi\)
\(132\) 2.16623 + 6.12511i 0.188546 + 0.533122i
\(133\) 4.66686 11.6855i 0.404668 1.01326i
\(134\) 0.346896i 0.0299672i
\(135\) 5.19420 + 0.142322i 0.447046 + 0.0122491i
\(136\) 6.64387i 0.569707i
\(137\) 12.7922 + 7.38559i 1.09291 + 0.630994i 0.934351 0.356355i \(-0.115981\pi\)
0.158563 + 0.987349i \(0.449314\pi\)
\(138\) 7.18235 2.54014i 0.611403 0.216231i
\(139\) 2.22917 1.28701i 0.189076 0.109163i −0.402474 0.915431i \(-0.631850\pi\)
0.591550 + 0.806268i \(0.298516\pi\)
\(140\) −1.25425 + 0.988047i −0.106004 + 0.0835052i
\(141\) 2.05868 11.0826i 0.173372 0.933327i
\(142\) 3.22500 5.58586i 0.270636 0.468755i
\(143\) 3.83463 0.320668
\(144\) −1.13403 7.19769i −0.0945029 0.599807i
\(145\) 4.72582i 0.392458i
\(146\) 0.240416 0.416413i 0.0198970 0.0344626i
\(147\) −11.0706 4.94381i −0.913090 0.407758i
\(148\) 0.605998 + 1.04962i 0.0498127 + 0.0862782i
\(149\) 2.37768 1.37275i 0.194787 0.112460i −0.399435 0.916762i \(-0.630794\pi\)
0.594222 + 0.804301i \(0.297460\pi\)
\(150\) 1.32994 1.55589i 0.108589 0.127038i
\(151\) 4.45760 7.72079i 0.362754 0.628309i −0.625659 0.780097i \(-0.715170\pi\)
0.988413 + 0.151788i \(0.0485031\pi\)
\(152\) −14.6322 −1.18683
\(153\) 5.03792 4.07289i 0.407292 0.329273i
\(154\) 2.78167 + 19.2332i 0.224153 + 1.54986i
\(155\) −7.25875 4.19084i −0.583037 0.336617i
\(156\) 0.634032 + 0.117776i 0.0507632 + 0.00942963i
\(157\) −15.1714 + 8.75923i −1.21081 + 0.699063i −0.962936 0.269729i \(-0.913066\pi\)
−0.247876 + 0.968792i \(0.579733\pi\)
\(158\) −5.84161 + 3.37265i −0.464733 + 0.268314i
\(159\) −7.35072 20.7845i −0.582950 1.64832i
\(160\) 2.84321 + 1.64153i 0.224775 + 0.129774i
\(161\) −9.74605 + 1.40956i −0.768097 + 0.111089i
\(162\) 7.12943 7.89232i 0.560141 0.620079i
\(163\) 11.8497 0.928143 0.464071 0.885798i \(-0.346388\pi\)
0.464071 + 0.885798i \(0.346388\pi\)
\(164\) 0.158090 0.273819i 0.0123447 0.0213817i
\(165\) 3.58951 + 10.1495i 0.279443 + 0.790138i
\(166\) −13.1180 + 7.57367i −1.01815 + 0.587831i
\(167\) 0.847165 + 1.46733i 0.0655556 + 0.113546i 0.896940 0.442152i \(-0.145785\pi\)
−0.831385 + 0.555697i \(0.812451\pi\)
\(168\) −0.564251 + 14.0877i −0.0435329 + 1.08689i
\(169\) −6.30969 + 10.9287i −0.485361 + 0.840669i
\(170\) 2.55191i 0.195723i
\(171\) −8.96997 11.0953i −0.685951 0.848481i
\(172\) −3.32530 −0.253552
\(173\) −4.39665 + 7.61522i −0.334271 + 0.578974i −0.983345 0.181751i \(-0.941823\pi\)
0.649074 + 0.760726i \(0.275157\pi\)
\(174\) 7.35285 + 6.28507i 0.557418 + 0.476470i
\(175\) −2.07834 + 1.63723i −0.157108 + 0.123763i
\(176\) 13.0738 7.54818i 0.985477 0.568965i
\(177\) −7.18128 6.13841i −0.539778 0.461392i
\(178\) 0.980150 + 0.565890i 0.0734653 + 0.0424152i
\(179\) 10.0909i 0.754226i −0.926167 0.377113i \(-0.876917\pi\)
0.926167 0.377113i \(-0.123083\pi\)
\(180\) 0.281773 + 1.78840i 0.0210021 + 0.133300i
\(181\) 0.795517i 0.0591303i −0.999563 0.0295652i \(-0.990588\pi\)
0.999563 0.0295652i \(-0.00941226\pi\)
\(182\) 1.79137 + 0.715424i 0.132785 + 0.0530308i
\(183\) 24.3016 + 4.51420i 1.79643 + 0.333699i
\(184\) 5.72563 + 9.91708i 0.422099 + 0.731097i
\(185\) 1.00416 + 1.73925i 0.0738273 + 0.127873i
\(186\) −16.1742 + 5.72023i −1.18595 + 0.419427i
\(187\) 11.6238 + 6.71103i 0.850019 + 0.490759i
\(188\) 3.92751 0.286443
\(189\) −11.0283 + 8.20830i −0.802192 + 0.597066i
\(190\) −5.62023 −0.407735
\(191\) 14.7531 + 8.51768i 1.06749 + 0.616318i 0.927496 0.373834i \(-0.121957\pi\)
0.139998 + 0.990152i \(0.455290\pi\)
\(192\) 14.2676 5.04592i 1.02967 0.364158i
\(193\) −9.88703 17.1248i −0.711684 1.23267i −0.964225 0.265086i \(-0.914600\pi\)
0.252541 0.967586i \(-0.418734\pi\)
\(194\) 1.48345 + 2.56941i 0.106505 + 0.184473i
\(195\) 1.05061 + 0.195159i 0.0752359 + 0.0139756i
\(196\) 0.989103 4.10699i 0.0706502 0.293356i
\(197\) 3.88854i 0.277047i −0.990359 0.138523i \(-0.955764\pi\)
0.990359 0.138523i \(-0.0442356\pi\)
\(198\) 20.5653 + 7.91339i 1.46152 + 0.562380i
\(199\) 1.72285i 0.122130i 0.998134 + 0.0610649i \(0.0194497\pi\)
−0.998134 + 0.0610649i \(0.980550\pi\)
\(200\) 2.66446 + 1.53832i 0.188405 + 0.108776i
\(201\) 0.386485 + 0.330360i 0.0272605 + 0.0233018i
\(202\) −12.1601 + 7.02066i −0.855585 + 0.493972i
\(203\) −7.73724 9.82185i −0.543048 0.689359i
\(204\) 1.71581 + 1.46664i 0.120130 + 0.102685i
\(205\) 0.261960 0.453727i 0.0182961 0.0316897i
\(206\) 5.14774 0.358660
\(207\) −4.00996 + 10.4211i −0.278711 + 0.724316i
\(208\) 1.49846i 0.103899i
\(209\) 14.7801 25.5999i 1.02236 1.77078i
\(210\) −0.216729 + 5.41108i −0.0149557 + 0.373400i
\(211\) −5.79495 10.0372i −0.398941 0.690986i 0.594655 0.803981i \(-0.297289\pi\)
−0.993596 + 0.112995i \(0.963955\pi\)
\(212\) 6.65227 3.84069i 0.456880 0.263780i
\(213\) 3.15208 + 8.91265i 0.215977 + 0.610684i
\(214\) 9.98439 17.2935i 0.682519 1.18216i
\(215\) −5.51013 −0.375788
\(216\) 13.6208 + 8.36958i 0.926777 + 0.569478i
\(217\) 21.9475 3.17424i 1.48989 0.215481i
\(218\) −7.67053 4.42858i −0.519514 0.299942i
\(219\) 0.234980 + 0.664417i 0.0158785 + 0.0448972i
\(220\) −3.24844 + 1.87549i −0.219010 + 0.126445i
\(221\) 1.15378 0.666134i 0.0776115 0.0448090i
\(222\) 4.04156 + 0.750750i 0.271252 + 0.0503870i
\(223\) 21.1708 + 12.2230i 1.41770 + 0.818511i 0.996097 0.0882674i \(-0.0281330\pi\)
0.421607 + 0.906779i \(0.361466\pi\)
\(224\) −8.59670 + 1.24333i −0.574391 + 0.0830734i
\(225\) 0.466907 + 2.96344i 0.0311271 + 0.197563i
\(226\) −14.7484 −0.981047
\(227\) −1.06827 + 1.85031i −0.0709039 + 0.122809i −0.899298 0.437337i \(-0.855922\pi\)
0.828394 + 0.560146i \(0.189255\pi\)
\(228\) 3.23007 3.77882i 0.213916 0.250259i
\(229\) 20.4349 11.7981i 1.35037 0.779639i 0.362072 0.932150i \(-0.382069\pi\)
0.988302 + 0.152511i \(0.0487360\pi\)
\(230\) 2.19921 + 3.80915i 0.145012 + 0.251168i
\(231\) −24.0773 15.2173i −1.58417 1.00122i
\(232\) −7.26984 + 12.5917i −0.477289 + 0.826688i
\(233\) 0.828258i 0.0542610i −0.999632 0.0271305i \(-0.991363\pi\)
0.999632 0.0271305i \(-0.00863697\pi\)
\(234\) 1.70090 1.37508i 0.111191 0.0898921i
\(235\) 6.50802 0.424537
\(236\) 1.64583 2.85066i 0.107134 0.185562i
\(237\) 1.80559 9.72017i 0.117286 0.631393i
\(238\) 4.17806 + 5.30374i 0.270823 + 0.343790i
\(239\) 16.2406 9.37651i 1.05052 0.606516i 0.127723 0.991810i \(-0.459233\pi\)
0.922794 + 0.385294i \(0.125900\pi\)
\(240\) 3.96612 1.40267i 0.256012 0.0905421i
\(241\) 15.8128 + 9.12955i 1.01859 + 0.588086i 0.913697 0.406397i \(-0.133215\pi\)
0.104898 + 0.994483i \(0.466548\pi\)
\(242\) 32.6543i 2.09910i
\(243\) 2.00345 + 15.4592i 0.128521 + 0.991707i
\(244\) 8.61210i 0.551333i
\(245\) 1.63898 6.80542i 0.104710 0.434782i
\(246\) −0.357558 1.01101i −0.0227971 0.0644597i
\(247\) −1.46707 2.54104i −0.0933473 0.161682i
\(248\) −12.8938 22.3326i −0.818754 1.41812i
\(249\) 4.05466 21.8277i 0.256953 1.38327i
\(250\) 1.02342 + 0.590871i 0.0647266 + 0.0373699i
\(251\) −15.0543 −0.950219 −0.475109 0.879927i \(-0.657592\pi\)
−0.475109 + 0.879927i \(0.657592\pi\)
\(252\) −3.51364 3.25558i −0.221338 0.205082i
\(253\) −23.1340 −1.45442
\(254\) −10.5902 6.11427i −0.664490 0.383643i
\(255\) 2.84315 + 2.43027i 0.178045 + 0.152189i
\(256\) 6.51617 + 11.2863i 0.407261 + 0.705396i
\(257\) −12.8086 22.1852i −0.798979 1.38387i −0.920282 0.391257i \(-0.872040\pi\)
0.121302 0.992616i \(-0.461293\pi\)
\(258\) −7.32816 + 8.57315i −0.456232 + 0.533741i
\(259\) −4.93454 1.97072i −0.306617 0.122455i
\(260\) 0.372320i 0.0230903i
\(261\) −14.0047 + 2.20652i −0.866869 + 0.136580i
\(262\) 12.9307i 0.798859i
\(263\) −15.7710 9.10540i −0.972483 0.561463i −0.0724906 0.997369i \(-0.523095\pi\)
−0.899992 + 0.435906i \(0.856428\pi\)
\(264\) −6.04914 + 32.5647i −0.372299 + 2.00422i
\(265\) 11.0230 6.36415i 0.677139 0.390947i
\(266\) 11.6807 9.20160i 0.716192 0.564186i
\(267\) −1.56390 + 0.553094i −0.0957091 + 0.0338488i
\(268\) −0.0885758 + 0.153418i −0.00541063 + 0.00937148i
\(269\) −22.2650 −1.35752 −0.678761 0.734359i \(-0.737483\pi\)
−0.678761 + 0.734359i \(0.737483\pi\)
\(270\) 5.23175 + 3.21476i 0.318394 + 0.195644i
\(271\) 27.3015i 1.65845i 0.558918 + 0.829223i \(0.311217\pi\)
−0.558918 + 0.829223i \(0.688783\pi\)
\(272\) 2.62247 4.54224i 0.159010 0.275414i
\(273\) −2.50305 + 1.31448i −0.151491 + 0.0795562i
\(274\) 8.72786 + 15.1171i 0.527269 + 0.913257i
\(275\) −5.38278 + 3.10775i −0.324594 + 0.187404i
\(276\) −3.82506 0.710533i −0.230241 0.0427690i
\(277\) −7.57578 + 13.1216i −0.455185 + 0.788403i −0.998699 0.0509971i \(-0.983760\pi\)
0.543514 + 0.839400i \(0.317093\pi\)
\(278\) 3.04183 0.182437
\(279\) 9.03017 23.4676i 0.540622 1.40497i
\(280\) −8.05623 + 1.16516i −0.481452 + 0.0696317i
\(281\) −13.4999 7.79419i −0.805338 0.464962i 0.0399960 0.999200i \(-0.487265\pi\)
−0.845334 + 0.534237i \(0.820599\pi\)
\(282\) 8.65530 10.1258i 0.515415 0.602980i
\(283\) −12.1672 + 7.02475i −0.723266 + 0.417578i −0.815954 0.578117i \(-0.803788\pi\)
0.0926875 + 0.995695i \(0.470454\pi\)
\(284\) −2.85257 + 1.64693i −0.169269 + 0.0977275i
\(285\) 5.35233 6.26164i 0.317044 0.370908i
\(286\) 3.92443 + 2.26577i 0.232056 + 0.133978i
\(287\) 0.198414 + 1.37189i 0.0117120 + 0.0809799i
\(288\) −3.53706 + 9.19213i −0.208423 + 0.541651i
\(289\) −12.3368 −0.725692
\(290\) −2.79235 + 4.83649i −0.163972 + 0.284008i
\(291\) −4.27538 0.794183i −0.250627 0.0465558i
\(292\) −0.212653 + 0.122775i −0.0124446 + 0.00718487i
\(293\) 3.34242 + 5.78924i 0.195266 + 0.338211i 0.946988 0.321270i \(-0.104110\pi\)
−0.751721 + 0.659481i \(0.770776\pi\)
\(294\) −8.40873 11.6009i −0.490407 0.676577i
\(295\) 2.72719 4.72363i 0.158783 0.275021i
\(296\) 6.17889i 0.359141i
\(297\) −28.4015 + 15.3762i −1.64802 + 0.892217i
\(298\) 3.24448 0.187948
\(299\) −1.14814 + 1.98863i −0.0663984 + 0.115005i
\(300\) −0.985458 + 0.348520i −0.0568954 + 0.0201218i
\(301\) 11.4519 9.02134i 0.660078 0.519981i
\(302\) 9.12397 5.26773i 0.525026 0.303124i
\(303\) 3.75860 20.2339i 0.215926 1.16241i
\(304\) −10.0037 5.77562i −0.573749 0.331254i
\(305\) 14.2705i 0.817129i
\(306\) 7.56245 1.19150i 0.432316 0.0681138i
\(307\) 14.6061i 0.833615i −0.908995 0.416808i \(-0.863149\pi\)
0.908995 0.416808i \(-0.136851\pi\)
\(308\) 3.68076 9.21633i 0.209731 0.525149i
\(309\) −4.90235 + 5.73522i −0.278885 + 0.326265i
\(310\) −4.95249 8.57797i −0.281283 0.487196i
\(311\) 9.43641 + 16.3443i 0.535090 + 0.926803i 0.999159 + 0.0410038i \(0.0130556\pi\)
−0.464069 + 0.885799i \(0.653611\pi\)
\(312\) 2.49909 + 2.13617i 0.141483 + 0.120937i
\(313\) −15.4266 8.90656i −0.871964 0.503429i −0.00396365 0.999992i \(-0.501262\pi\)
−0.868000 + 0.496563i \(0.834595\pi\)
\(314\) −20.7023 −1.16830
\(315\) −5.82222 5.39461i −0.328045 0.303952i
\(316\) 3.44467 0.193778
\(317\) −22.7317 13.1242i −1.27674 0.737127i −0.300494 0.953784i \(-0.597152\pi\)
−0.976248 + 0.216656i \(0.930485\pi\)
\(318\) 4.75809 25.6146i 0.266821 1.43639i
\(319\) −14.6866 25.4380i −0.822295 1.42426i
\(320\) 4.36869 + 7.56679i 0.244217 + 0.422996i
\(321\) 9.75863 + 27.5930i 0.544674 + 1.54009i
\(322\) −10.8072 4.31609i −0.602259 0.240526i
\(323\) 10.2701i 0.571445i
\(324\) −5.16827 + 1.67003i −0.287126 + 0.0927797i
\(325\) 0.616947i 0.0342221i
\(326\) 12.1272 + 7.00166i 0.671665 + 0.387786i
\(327\) 12.2389 4.32845i 0.676812 0.239364i
\(328\) 1.39596 0.805958i 0.0770790 0.0445016i
\(329\) −13.5259 + 10.6551i −0.745705 + 0.587435i
\(330\) −2.32348 + 12.5081i −0.127903 + 0.688549i
\(331\) −9.75588 + 16.8977i −0.536232 + 0.928781i 0.462871 + 0.886426i \(0.346819\pi\)
−0.999103 + 0.0423550i \(0.986514\pi\)
\(332\) 7.73540 0.424535
\(333\) −4.68534 + 3.78784i −0.256755 + 0.207572i
\(334\) 2.00226i 0.109559i
\(335\) −0.146773 + 0.254218i −0.00801907 + 0.0138894i
\(336\) −5.94644 + 9.40866i −0.324405 + 0.513285i
\(337\) 10.2676 + 17.7840i 0.559311 + 0.968755i 0.997554 + 0.0698988i \(0.0222677\pi\)
−0.438243 + 0.898857i \(0.644399\pi\)
\(338\) −12.9149 + 7.45642i −0.702478 + 0.405576i
\(339\) 14.0453 16.4315i 0.762838 0.892438i
\(340\) −0.651601 + 1.12861i −0.0353380 + 0.0612073i
\(341\) 52.0963 2.82117
\(342\) −2.62412 16.6552i −0.141896 0.900613i
\(343\) 7.73567 + 16.8273i 0.417687 + 0.908591i
\(344\) −14.6815 8.47637i −0.791574 0.457015i
\(345\) −6.33825 1.17738i −0.341240 0.0633878i
\(346\) −8.99921 + 5.19570i −0.483801 + 0.279322i
\(347\) −5.28238 + 3.04978i −0.283573 + 0.163721i −0.635040 0.772479i \(-0.719016\pi\)
0.351467 + 0.936200i \(0.385683\pi\)
\(348\) −1.64704 4.65709i −0.0882909 0.249646i
\(349\) −27.8341 16.0700i −1.48992 0.860207i −0.489989 0.871729i \(-0.662999\pi\)
−0.999934 + 0.0115214i \(0.996333\pi\)
\(350\) −3.09440 + 0.447538i −0.165402 + 0.0239219i
\(351\) −0.0878049 + 3.20455i −0.00468668 + 0.171046i
\(352\) −20.4058 −1.08763
\(353\) 0.948987 1.64369i 0.0505095 0.0874850i −0.839665 0.543104i \(-0.817249\pi\)
0.890175 + 0.455619i \(0.150582\pi\)
\(354\) −3.72244 10.5254i −0.197845 0.559417i
\(355\) −4.72681 + 2.72902i −0.250873 + 0.144842i
\(356\) −0.288987 0.500540i −0.0153163 0.0265286i
\(357\) −9.88792 0.396038i −0.523324 0.0209606i
\(358\) 5.96239 10.3272i 0.315122 0.545807i
\(359\) 11.5006i 0.606976i 0.952835 + 0.303488i \(0.0981513\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(360\) −3.31469 + 8.61422i −0.174699 + 0.454009i
\(361\) −3.61851 −0.190448
\(362\) 0.470048 0.814147i 0.0247052 0.0427906i
\(363\) −36.3809 31.0977i −1.90950 1.63221i
\(364\) −0.609573 0.773808i −0.0319503 0.0405585i
\(365\) −0.352373 + 0.203442i −0.0184440 + 0.0106487i
\(366\) 22.2034 + 18.9790i 1.16059 + 0.992049i
\(367\) 16.0654 + 9.27534i 0.838605 + 0.484169i 0.856790 0.515666i \(-0.172455\pi\)
−0.0181848 + 0.999835i \(0.505789\pi\)
\(368\) 9.04007i 0.471246i
\(369\) 1.46691 + 0.564454i 0.0763641 + 0.0293843i
\(370\) 2.37331i 0.123383i
\(371\) −12.4900 + 31.2741i −0.648450 + 1.62367i
\(372\) 8.61379 + 1.60007i 0.446604 + 0.0829600i
\(373\) −10.2802 17.8058i −0.532288 0.921950i −0.999289 0.0376935i \(-0.987999\pi\)
0.467001 0.884257i \(-0.345334\pi\)
\(374\) 7.93070 + 13.7364i 0.410087 + 0.710291i
\(375\) −1.63294 + 0.577510i −0.0843245 + 0.0298225i
\(376\) 17.3403 + 10.0115i 0.894260 + 0.516301i
\(377\) −2.91558 −0.150160
\(378\) −16.1366 + 1.88421i −0.829978 + 0.0969131i
\(379\) 9.97838 0.512555 0.256278 0.966603i \(-0.417504\pi\)
0.256278 + 0.966603i \(0.417504\pi\)
\(380\) 2.48560 + 1.43506i 0.127509 + 0.0736171i
\(381\) 16.8975 5.97602i 0.865684 0.306161i
\(382\) 10.0657 + 17.4343i 0.515006 + 0.892016i
\(383\) −1.97163 3.41496i −0.100746 0.174496i 0.811246 0.584704i \(-0.198789\pi\)
−0.911992 + 0.410208i \(0.865456\pi\)
\(384\) 6.40162 + 1.18915i 0.326681 + 0.0606835i
\(385\) 6.09914 15.2718i 0.310841 0.778322i
\(386\) 23.3678i 1.18939i
\(387\) −2.57272 16.3290i −0.130779 0.830048i
\(388\) 1.51513i 0.0769189i
\(389\) 28.2571 + 16.3142i 1.43269 + 0.827165i 0.997325 0.0730880i \(-0.0232854\pi\)
0.435367 + 0.900253i \(0.356619\pi\)
\(390\) 0.959901 + 0.820505i 0.0486065 + 0.0415479i
\(391\) −6.96064 + 4.01873i −0.352015 + 0.203236i
\(392\) 14.8359 15.6115i 0.749328 0.788498i
\(393\) 14.4064 + 12.3143i 0.726705 + 0.621173i
\(394\) 2.29762 3.97960i 0.115753 0.200489i
\(395\) 5.70794 0.287198
\(396\) −7.07462 8.75089i −0.355513 0.439749i
\(397\) 16.7556i 0.840940i −0.907306 0.420470i \(-0.861865\pi\)
0.907306 0.420470i \(-0.138135\pi\)
\(398\) −1.01798 + 1.76320i −0.0510269 + 0.0883812i
\(399\) −0.872220 + 21.7768i −0.0436656 + 1.09020i
\(400\) 1.21441 + 2.10343i 0.0607207 + 0.105171i
\(401\) 6.75815 3.90182i 0.337486 0.194848i −0.321674 0.946851i \(-0.604245\pi\)
0.659160 + 0.752003i \(0.270912\pi\)
\(402\) 0.200336 + 0.566458i 0.00999184 + 0.0282524i
\(403\) 2.58553 4.47827i 0.128794 0.223078i
\(404\) 7.17058 0.356750
\(405\) −8.56400 + 2.76730i −0.425548 + 0.137508i
\(406\) −2.11499 14.6236i −0.104965 0.725755i
\(407\) −10.8103 6.24135i −0.535848 0.309372i
\(408\) 3.83690 + 10.8490i 0.189955 + 0.537107i
\(409\) 16.2794 9.39890i 0.804963 0.464746i −0.0402405 0.999190i \(-0.512812\pi\)
0.845204 + 0.534444i \(0.179479\pi\)
\(410\) 0.536188 0.309568i 0.0264805 0.0152885i
\(411\) −25.1541 4.67257i −1.24076 0.230481i
\(412\) −2.27663 1.31442i −0.112162 0.0647566i
\(413\) 2.06563 + 14.2823i 0.101643 + 0.702788i
\(414\) −10.2614 + 8.29576i −0.504319 + 0.407715i
\(415\) 12.8178 0.629202
\(416\) −1.01274 + 1.75411i −0.0496535 + 0.0860023i
\(417\) −2.89683 + 3.38898i −0.141859 + 0.165959i
\(418\) 30.2525 17.4663i 1.47970 0.854303i
\(419\) 13.0224 + 22.5554i 0.636185 + 1.10190i 0.986263 + 0.165184i \(0.0528217\pi\)
−0.350078 + 0.936721i \(0.613845\pi\)
\(420\) 1.47751 2.33776i 0.0720950 0.114071i
\(421\) −19.4365 + 33.6651i −0.947279 + 1.64074i −0.196157 + 0.980572i \(0.562846\pi\)
−0.751122 + 0.660163i \(0.770487\pi\)
\(422\) 13.6963i 0.666724i
\(423\) 3.03864 + 19.2862i 0.147744 + 0.937725i
\(424\) 39.1605 1.90180
\(425\) −1.07973 + 1.87014i −0.0523744 + 0.0907151i
\(426\) −2.04033 + 10.9838i −0.0988542 + 0.532168i
\(427\) −23.3641 29.6590i −1.13067 1.43530i
\(428\) −8.83138 + 5.09880i −0.426881 + 0.246460i
\(429\) −6.26171 + 2.21454i −0.302318 + 0.106919i
\(430\) −5.63917 3.25578i −0.271945 0.157007i
\(431\) 3.12892i 0.150715i 0.997157 + 0.0753573i \(0.0240097\pi\)
−0.997157 + 0.0753573i \(0.975990\pi\)
\(432\) 6.00855 + 11.0985i 0.289086 + 0.533975i
\(433\) 18.1302i 0.871282i −0.900120 0.435641i \(-0.856522\pi\)
0.900120 0.435641i \(-0.143478\pi\)
\(434\) 24.3370 + 9.71956i 1.16821 + 0.466554i
\(435\) −2.72921 7.71696i −0.130856 0.370000i
\(436\) 2.26158 + 3.91716i 0.108310 + 0.187598i
\(437\) 8.85069 + 15.3298i 0.423386 + 0.733326i
\(438\) −0.152102 + 0.818819i −0.00726770 + 0.0391247i
\(439\) 1.68550 + 0.973121i 0.0804443 + 0.0464445i 0.539683 0.841869i \(-0.318544\pi\)
−0.459238 + 0.888313i \(0.651878\pi\)
\(440\) −19.1229 −0.911648
\(441\) 20.9327 + 1.67952i 0.996797 + 0.0799772i
\(442\) 1.57440 0.0748864
\(443\) 0.462264 + 0.266888i 0.0219628 + 0.0126802i 0.510941 0.859616i \(-0.329297\pi\)
−0.488978 + 0.872296i \(0.662630\pi\)
\(444\) −1.59572 1.36399i −0.0757296 0.0647322i
\(445\) −0.478861 0.829412i −0.0227002 0.0393179i
\(446\) 14.4444 + 25.0184i 0.683962 + 1.18466i
\(447\) −3.08982 + 3.61475i −0.146144 + 0.170972i
\(448\) −21.4682 8.57381i −1.01427 0.405074i
\(449\) 19.0944i 0.901120i −0.892746 0.450560i \(-0.851224\pi\)
0.892746 0.450560i \(-0.148776\pi\)
\(450\) −1.27317 + 3.30872i −0.0600179 + 0.155975i
\(451\) 3.25642i 0.153339i
\(452\) 6.52261 + 3.76583i 0.306798 + 0.177130i
\(453\) −2.82014 + 15.1819i −0.132502 + 0.713306i
\(454\) −2.18658 + 1.26242i −0.102621 + 0.0592485i
\(455\) −1.01008 1.28223i −0.0473534 0.0601116i
\(456\) 23.8935 8.45025i 1.11891 0.395719i
\(457\) 11.5372 19.9830i 0.539688 0.934767i −0.459233 0.888316i \(-0.651876\pi\)
0.998921 0.0464507i \(-0.0147910\pi\)
\(458\) 27.8845 1.30296
\(459\) −5.87447 + 9.56022i −0.274197 + 0.446233i
\(460\) 2.24618i 0.104728i
\(461\) 11.3755 19.7029i 0.529808 0.917655i −0.469587 0.882886i \(-0.655597\pi\)
0.999395 0.0347688i \(-0.0110695\pi\)
\(462\) −15.6497 29.8002i −0.728088 1.38643i
\(463\) 6.06653 + 10.5075i 0.281935 + 0.488327i 0.971861 0.235553i \(-0.0756903\pi\)
−0.689926 + 0.723880i \(0.742357\pi\)
\(464\) −9.94041 + 5.73910i −0.461472 + 0.266431i
\(465\) 14.2733 + 2.65138i 0.661910 + 0.122955i
\(466\) 0.489393 0.847654i 0.0226707 0.0392668i
\(467\) 4.61293 0.213461 0.106731 0.994288i \(-0.465962\pi\)
0.106731 + 0.994288i \(0.465962\pi\)
\(468\) −1.10335 + 0.173839i −0.0510024 + 0.00803570i
\(469\) −0.111169 0.768653i −0.00513331 0.0354931i
\(470\) 6.66043 + 3.84540i 0.307223 + 0.177375i
\(471\) 19.7155 23.0649i 0.908440 1.06278i
\(472\) 14.5330 8.39061i 0.668934 0.386209i
\(473\) 29.6598 17.1241i 1.36376 0.787367i
\(474\) 7.59124 8.88092i 0.348677 0.407914i
\(475\) 4.11872 + 2.37795i 0.188980 + 0.109108i
\(476\) −0.493537 3.41245i −0.0226212 0.156409i
\(477\) 24.0065 + 29.6947i 1.09918 + 1.35963i
\(478\) 22.1612 1.01363
\(479\) 4.54166 7.86639i 0.207514 0.359424i −0.743417 0.668828i \(-0.766796\pi\)
0.950931 + 0.309404i \(0.100129\pi\)
\(480\) −5.59078 1.03853i −0.255183 0.0474021i
\(481\) −1.07303 + 0.619513i −0.0489259 + 0.0282474i
\(482\) 10.7888 + 18.6867i 0.491415 + 0.851155i
\(483\) 15.1007 7.93016i 0.687104 0.360835i
\(484\) 8.33790 14.4417i 0.378995 0.656439i
\(485\) 2.51062i 0.114001i
\(486\) −7.08401 + 17.0050i −0.321337 + 0.771361i
\(487\) 23.6659 1.07240 0.536201 0.844090i \(-0.319859\pi\)
0.536201 + 0.844090i \(0.319859\pi\)
\(488\) −21.9527 + 38.0232i −0.993753 + 1.72123i
\(489\) −19.3499 + 6.84334i −0.875031 + 0.309466i
\(490\) 5.69848 5.99637i 0.257431 0.270888i
\(491\) −9.25604 + 5.34398i −0.417719 + 0.241170i −0.694101 0.719878i \(-0.744198\pi\)
0.276382 + 0.961048i \(0.410865\pi\)
\(492\) −0.100017 + 0.538427i −0.00450911 + 0.0242742i
\(493\) −8.83794 5.10259i −0.398041 0.229809i
\(494\) 3.46739i 0.156005i
\(495\) −11.7229 14.5005i −0.526905 0.651750i
\(496\) 20.3577i 0.914086i
\(497\) 5.35587 13.4107i 0.240244 0.601552i
\(498\) 17.0470 19.9431i 0.763892 0.893671i
\(499\) 10.4045 + 18.0211i 0.465768 + 0.806734i 0.999236 0.0390866i \(-0.0124448\pi\)
−0.533468 + 0.845820i \(0.679111\pi\)
\(500\) −0.301744 0.522636i −0.0134944 0.0233730i
\(501\) −2.23077 1.90682i −0.0996633 0.0851903i
\(502\) −15.4068 8.89514i −0.687641 0.397010i
\(503\) −11.7879 −0.525595 −0.262797 0.964851i \(-0.584645\pi\)
−0.262797 + 0.964851i \(0.584645\pi\)
\(504\) −7.21439 23.3301i −0.321355 1.03921i
\(505\) 11.8819 0.528738
\(506\) −23.6757 13.6692i −1.05252 0.607670i
\(507\) 3.99189 21.4898i 0.177286 0.954395i
\(508\) 3.12242 + 5.40819i 0.138535 + 0.239949i
\(509\) −2.14843 3.72118i −0.0952273 0.164938i 0.814476 0.580197i \(-0.197024\pi\)
−0.909703 + 0.415259i \(0.863691\pi\)
\(510\) 1.47375 + 4.16711i 0.0652590 + 0.184523i
\(511\) 0.399268 0.999736i 0.0176626 0.0442257i
\(512\) 22.9193i 1.01290i
\(513\) 21.0551 + 12.9377i 0.929603 + 0.571214i
\(514\) 30.2729i 1.33528i
\(515\) −3.77246 2.17803i −0.166234 0.0959755i
\(516\) 5.43000 1.92039i 0.239043 0.0845406i
\(517\) −35.0312 + 20.2253i −1.54067 + 0.889507i
\(518\) −3.88565 4.93255i −0.170726 0.216724i
\(519\) 2.78158 14.9743i 0.122098 0.657298i
\(520\) −0.949065 + 1.64383i −0.0416193 + 0.0720867i
\(521\) 24.7319 1.08352 0.541761 0.840533i \(-0.317758\pi\)
0.541761 + 0.840533i \(0.317758\pi\)
\(522\) −15.6364 6.01678i −0.684388 0.263347i
\(523\) 11.1055i 0.485608i 0.970075 + 0.242804i \(0.0780671\pi\)
−0.970075 + 0.242804i \(0.921933\pi\)
\(524\) −3.30170 + 5.71870i −0.144235 + 0.249823i
\(525\) 2.44828 3.87375i 0.106852 0.169064i
\(526\) −10.7602 18.6373i −0.469168 0.812623i
\(527\) 15.6749 9.04992i 0.682810 0.394221i
\(528\) −16.9896 + 19.8760i −0.739377 + 0.864990i
\(529\) −4.57340 + 7.92136i −0.198843 + 0.344407i
\(530\) 15.0416 0.653363
\(531\) 15.2716 + 5.87638i 0.662730 + 0.255013i
\(532\) −7.51544 + 1.08695i −0.325836 + 0.0471251i
\(533\) 0.279926 + 0.161615i 0.0121249 + 0.00700034i
\(534\) −1.92733 0.358016i −0.0834037 0.0154929i
\(535\) −14.6339 + 8.44888i −0.632678 + 0.365277i
\(536\) −0.782141 + 0.451569i −0.0337833 + 0.0195048i
\(537\) 5.82757 + 16.4777i 0.251478 + 0.711066i
\(538\) −22.7864 13.1558i −0.982393 0.567185i
\(539\) 12.3273 + 41.7256i 0.530973 + 1.79725i
\(540\) −1.49294 2.75762i −0.0642458 0.118669i
\(541\) 26.6470 1.14564 0.572821 0.819680i \(-0.305849\pi\)
0.572821 + 0.819680i \(0.305849\pi\)
\(542\) −16.1316 + 27.9408i −0.692913 + 1.20016i
\(543\) 0.459419 + 1.29903i 0.0197156 + 0.0557467i
\(544\) −6.13977 + 3.54480i −0.263240 + 0.151982i
\(545\) 3.74751 + 6.49087i 0.160526 + 0.278039i
\(546\) −3.33835 0.133710i −0.142868 0.00572227i
\(547\) −5.24179 + 9.07905i −0.224123 + 0.388192i −0.956056 0.293184i \(-0.905285\pi\)
0.731933 + 0.681377i \(0.238618\pi\)
\(548\) 8.91424i 0.380797i
\(549\) −42.2900 + 6.66301i −1.80489 + 0.284370i
\(550\) −7.34510 −0.313196
\(551\) −11.2377 + 19.4643i −0.478744 + 0.829209i
\(552\) −15.0768 12.8874i −0.641711 0.548522i
\(553\) −11.8630 + 9.34519i −0.504467 + 0.397398i
\(554\) −15.5064 + 8.95261i −0.658803 + 0.380360i
\(555\) −2.64417 2.26018i −0.112239 0.0959393i
\(556\) −1.34528 0.776697i −0.0570525 0.0329393i
\(557\) 21.2672i 0.901121i −0.892746 0.450560i \(-0.851224\pi\)
0.892746 0.450560i \(-0.148776\pi\)
\(558\) 23.1080 18.6815i 0.978238 0.790853i
\(559\) 3.39946i 0.143782i
\(560\) −5.96774 2.38336i −0.252183 0.100715i
\(561\) −22.8567 4.24580i −0.965010 0.179258i
\(562\) −9.21071 15.9534i −0.388531 0.672955i
\(563\) −4.07042 7.05018i −0.171548 0.297130i 0.767413 0.641153i \(-0.221544\pi\)
−0.938961 + 0.344023i \(0.888210\pi\)
\(564\) −6.41338 + 2.26818i −0.270052 + 0.0955076i
\(565\) 10.8082 + 6.24010i 0.454703 + 0.262523i
\(566\) −16.6029 −0.697871
\(567\) 13.2682 19.7726i 0.557211 0.830371i
\(568\) −16.7925 −0.704597
\(569\) 30.1838 + 17.4266i 1.26537 + 0.730562i 0.974108 0.226081i \(-0.0725915\pi\)
0.291262 + 0.956643i \(0.405925\pi\)
\(570\) 9.17749 3.24574i 0.384403 0.135949i
\(571\) 5.67837 + 9.83523i 0.237633 + 0.411592i 0.960034 0.279882i \(-0.0902953\pi\)
−0.722402 + 0.691473i \(0.756962\pi\)
\(572\) −1.15708 2.00412i −0.0483798 0.0837963i
\(573\) −29.0099 5.38879i −1.21190 0.225120i
\(574\) −0.607547 + 1.52125i −0.0253585 + 0.0634957i
\(575\) 3.72199i 0.155218i
\(576\) −20.3840 + 16.4793i −0.849332 + 0.686639i
\(577\) 24.7185i 1.02905i −0.857477 0.514523i \(-0.827969\pi\)
0.857477 0.514523i \(-0.172031\pi\)
\(578\) −12.6257 7.28943i −0.525159 0.303201i
\(579\) 26.0347 + 22.2539i 1.08196 + 0.924841i
\(580\) 2.46988 1.42599i 0.102556 0.0592109i
\(581\) −26.6397 + 20.9857i −1.10520 + 0.870632i
\(582\) −3.90624 3.33898i −0.161919 0.138405i
\(583\) −39.5563 + 68.5136i −1.63826 + 2.83754i
\(584\) −1.25184 −0.0518016
\(585\) −1.82829 + 0.288057i −0.0755904 + 0.0119097i
\(586\) 7.89975i 0.326336i
\(587\) 13.1643 22.8013i 0.543351 0.941111i −0.455358 0.890308i \(-0.650489\pi\)
0.998709 0.0508027i \(-0.0161780\pi\)
\(588\) 0.756685 + 7.27767i 0.0312052 + 0.300126i
\(589\) −19.9312 34.5218i −0.821251 1.42245i
\(590\) 5.58211 3.22283i 0.229812 0.132682i
\(591\) 2.24567 + 6.34974i 0.0923745 + 0.261193i
\(592\) −2.43893 + 4.22435i −0.100239 + 0.173620i
\(593\) 40.8936 1.67930 0.839649 0.543129i \(-0.182761\pi\)
0.839649 + 0.543129i \(0.182761\pi\)
\(594\) −38.1520 1.04537i −1.56539 0.0428919i
\(595\) −0.817808 5.65454i −0.0335268 0.231813i
\(596\) −1.43490 0.828441i −0.0587758 0.0339342i
\(597\) −0.994965 2.81331i −0.0407212 0.115141i
\(598\) −2.35005 + 1.35680i −0.0961005 + 0.0554836i
\(599\) 1.97542 1.14051i 0.0807133 0.0465998i −0.459100 0.888385i \(-0.651828\pi\)
0.539813 + 0.841785i \(0.318495\pi\)
\(600\) −5.23929 0.973236i −0.213893 0.0397322i
\(601\) −20.8183 12.0194i −0.849195 0.490283i 0.0111841 0.999937i \(-0.496440\pi\)
−0.860379 + 0.509654i \(0.829773\pi\)
\(602\) 17.0505 2.46600i 0.694928 0.100506i
\(603\) −0.821891 0.316257i −0.0334700 0.0128790i
\(604\) −5.38022 −0.218918
\(605\) 13.8162 23.9303i 0.561708 0.972906i
\(606\) 15.8022 18.4869i 0.641922 0.750979i
\(607\) 34.2781 19.7905i 1.39131 0.803271i 0.397846 0.917452i \(-0.369758\pi\)
0.993460 + 0.114181i \(0.0364244\pi\)
\(608\) 7.80693 + 13.5220i 0.316613 + 0.548389i
\(609\) 18.3066 + 11.5701i 0.741822 + 0.468845i
\(610\) −8.43205 + 14.6047i −0.341404 + 0.591328i
\(611\) 4.01511i 0.162434i
\(612\) −3.64880 1.40403i −0.147494 0.0567546i
\(613\) −2.41792 −0.0976588 −0.0488294 0.998807i \(-0.515549\pi\)
−0.0488294 + 0.998807i \(0.515549\pi\)
\(614\) 8.63033 14.9482i 0.348292 0.603259i
\(615\) −0.165731 + 0.892192i −0.00668293 + 0.0359767i
\(616\) 39.7438 31.3085i 1.60132 1.26146i
\(617\) 2.49126 1.43833i 0.100294 0.0579050i −0.449014 0.893525i \(-0.648225\pi\)
0.549308 + 0.835620i \(0.314891\pi\)
\(618\) −8.40593 + 2.97287i −0.338136 + 0.119586i
\(619\) 31.1520 + 17.9856i 1.25211 + 0.722903i 0.971527 0.236928i \(-0.0761405\pi\)
0.280578 + 0.959831i \(0.409474\pi\)
\(620\) 5.05825i 0.203144i
\(621\) 0.529719 19.3328i 0.0212569 0.775797i
\(622\) 22.3028i 0.894260i
\(623\) 2.35317 + 0.939794i 0.0942778 + 0.0376520i
\(624\) 0.865375 + 2.44689i 0.0346427 + 0.0979539i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −10.5253 18.2303i −0.420674 0.728628i
\(627\) −9.35078 + 50.3387i −0.373434 + 2.01033i
\(628\) 9.15578 + 5.28609i 0.365355 + 0.210938i
\(629\) −4.33687 −0.172922
\(630\) −2.77105 8.96111i −0.110401 0.357019i
\(631\) 12.1096 0.482075 0.241038 0.970516i \(-0.422512\pi\)
0.241038 + 0.970516i \(0.422512\pi\)
\(632\) 15.2086 + 8.78067i 0.604964 + 0.349276i
\(633\) 15.2593 + 13.0434i 0.606504 + 0.518428i
\(634\) −15.5094 26.8630i −0.615956 1.06687i
\(635\) 5.17395 + 8.96155i 0.205322 + 0.355628i
\(636\) −8.64469 + 10.1134i −0.342784 + 0.401020i
\(637\) 4.19859 + 1.01116i 0.166354 + 0.0400637i
\(638\) 34.7116i 1.37425i
\(639\) −10.2943 12.7334i −0.407236 0.503727i
\(640\) 3.75920i 0.148596i
\(641\) −7.60755 4.39222i −0.300480 0.173482i 0.342178 0.939635i \(-0.388835\pi\)
−0.642659 + 0.766153i \(0.722169\pi\)
\(642\) −6.31672 + 34.0052i −0.249301 + 1.34208i
\(643\) 38.1679 22.0362i 1.50520 0.869025i 0.505213 0.862994i \(-0.331414\pi\)
0.999982 0.00603040i \(-0.00191955\pi\)
\(644\) 3.67750 + 4.66831i 0.144914 + 0.183957i
\(645\) 8.99770 3.18216i 0.354284 0.125297i
\(646\) 6.06831 10.5106i 0.238754 0.413535i
\(647\) −25.7941 −1.01407 −0.507036 0.861925i \(-0.669259\pi\)
−0.507036 + 0.861925i \(0.669259\pi\)
\(648\) −27.0754 5.80085i −1.06362 0.227879i
\(649\) 33.9017i 1.33076i
\(650\) −0.364536 + 0.631395i −0.0142983 + 0.0247653i
\(651\) −34.0057 + 17.8582i −1.33279 + 0.699919i
\(652\) −3.57559 6.19310i −0.140031 0.242540i
\(653\) −11.9806 + 6.91698i −0.468836 + 0.270682i −0.715752 0.698354i \(-0.753916\pi\)
0.246916 + 0.969037i \(0.420583\pi\)
\(654\) 15.0830 + 2.80179i 0.589794 + 0.109559i
\(655\) −5.47102 + 9.47609i −0.213770 + 0.370261i
\(656\) 1.27251 0.0496831
\(657\) −0.767415 0.949248i −0.0299397 0.0370337i
\(658\) −20.1384 + 2.91259i −0.785077 + 0.113545i
\(659\) 23.6785 + 13.6708i 0.922385 + 0.532539i 0.884395 0.466739i \(-0.154571\pi\)
0.0379897 + 0.999278i \(0.487905\pi\)
\(660\) 4.22138 4.93856i 0.164317 0.192233i
\(661\) −22.8640 + 13.2006i −0.889308 + 0.513442i −0.873716 0.486436i \(-0.838297\pi\)
−0.0155920 + 0.999878i \(0.504963\pi\)
\(662\) −19.9687 + 11.5289i −0.776105 + 0.448084i
\(663\) −1.49935 + 1.75407i −0.0582298 + 0.0681225i
\(664\) 34.1525 + 19.7180i 1.32537 + 0.765205i
\(665\) −12.4533 + 1.80111i −0.482920 + 0.0698440i
\(666\) −7.03318 + 1.10812i −0.272530 + 0.0429386i
\(667\) 17.5894 0.681066
\(668\) 0.511254 0.885518i 0.0197810 0.0342617i
\(669\) −41.6295 7.73299i −1.60949 0.298975i
\(670\) −0.300420 + 0.173448i −0.0116063 + 0.00670087i
\(671\) −44.3492 76.8151i −1.71208 2.96542i
\(672\) 13.3198 6.99496i 0.513824 0.269836i
\(673\) −5.09999 + 8.83344i −0.196590 + 0.340504i −0.947421 0.319991i \(-0.896320\pi\)
0.750831 + 0.660495i \(0.229653\pi\)
\(674\) 24.2673i 0.934740i
\(675\) −2.47385 4.56947i −0.0952184 0.175879i
\(676\) 7.61564 0.292909
\(677\) −2.80831 + 4.86413i −0.107932 + 0.186944i −0.914932 0.403607i \(-0.867756\pi\)
0.807000 + 0.590551i \(0.201090\pi\)
\(678\) 24.0832 8.51734i 0.924908 0.327106i
\(679\) 4.11045 + 5.21791i 0.157744 + 0.200245i
\(680\) −5.75376 + 3.32194i −0.220647 + 0.127390i
\(681\) 0.675854 3.63837i 0.0258988 0.139423i
\(682\) 53.3163 + 30.7822i 2.04159 + 1.17871i
\(683\) 41.9272i 1.60430i −0.597124 0.802149i \(-0.703690\pi\)
0.597124 0.802149i \(-0.296310\pi\)
\(684\) −3.09218 + 8.03598i −0.118233 + 0.307263i
\(685\) 14.7712i 0.564378i
\(686\) −2.02596 + 21.7922i −0.0773515 + 0.832029i
\(687\) −26.5553 + 31.0669i −1.01315 + 1.18527i
\(688\) −6.69158 11.5902i −0.255114 0.441871i
\(689\) 3.92635 + 6.80063i 0.149582 + 0.259083i
\(690\) −5.79100 4.95003i −0.220460 0.188445i
\(691\) −36.2770 20.9446i −1.38004 0.796769i −0.387880 0.921710i \(-0.626792\pi\)
−0.992164 + 0.124941i \(0.960126\pi\)
\(692\) 5.30665 0.201728
\(693\) 48.1048 + 10.9440i 1.82735 + 0.415727i
\(694\) −7.20811 −0.273616
\(695\) −2.22917 1.28701i −0.0845573 0.0488192i
\(696\) 4.59934 24.7599i 0.174337 0.938522i
\(697\) 0.565689 + 0.979802i 0.0214270 + 0.0371127i
\(698\) −18.9906 32.8926i −0.718804 1.24500i
\(699\) 0.478327 + 1.35249i 0.0180920 + 0.0511560i
\(700\) 1.48280 + 0.592191i 0.0560446 + 0.0223827i
\(701\) 26.4201i 0.997874i 0.866638 + 0.498937i \(0.166276\pi\)
−0.866638 + 0.498937i \(0.833724\pi\)
\(702\) −1.98334 + 3.22771i −0.0748562 + 0.121822i
\(703\) 9.55135i 0.360236i
\(704\) −47.0313 27.1535i −1.77256 1.02339i
\(705\) −10.6272 + 3.75845i −0.400243 + 0.141551i
\(706\) 1.94242 1.12146i 0.0731040 0.0422066i
\(707\) −24.6946 + 19.4534i −0.928736 + 0.731619i
\(708\) −1.04125 + 5.60542i −0.0391325 + 0.210665i
\(709\) 6.36004 11.0159i 0.238856 0.413711i −0.721530 0.692383i \(-0.756561\pi\)
0.960386 + 0.278672i \(0.0898942\pi\)
\(710\) −6.45000 −0.242064
\(711\) 2.66508 + 16.9152i 0.0999481 + 0.634368i
\(712\) 2.94657i 0.110428i
\(713\) −15.5983 + 27.0170i −0.584160 + 1.01179i
\(714\) −9.88547 6.24779i −0.369954 0.233818i
\(715\) −1.91732 3.32089i −0.0717036 0.124194i
\(716\) −5.27384 + 3.04486i −0.197093 + 0.113792i
\(717\) −21.1048 + 24.6904i −0.788174 + 0.922078i
\(718\) −6.79534 + 11.7699i −0.253600 + 0.439248i
\(719\) −45.3176 −1.69006 −0.845030 0.534718i \(-0.820418\pi\)
−0.845030 + 0.534718i \(0.820418\pi\)
\(720\) −5.66636 + 4.58095i −0.211173 + 0.170722i
\(721\) 11.4064 1.64969i 0.424796 0.0614376i
\(722\) −3.70325 2.13807i −0.137821 0.0795708i
\(723\) −31.0938 5.77590i −1.15639 0.214808i
\(724\) −0.415766 + 0.240043i −0.0154518 + 0.00892111i
\(725\) 4.09268 2.36291i 0.151998 0.0877563i
\(726\) −18.8582 53.3224i −0.699893 1.97898i
\(727\) −8.49387 4.90394i −0.315020 0.181877i 0.334150 0.942520i \(-0.391551\pi\)
−0.649171 + 0.760643i \(0.724884\pi\)
\(728\) −0.718843 4.97027i −0.0266421 0.184210i
\(729\) −12.1993 24.0868i −0.451827 0.892106i
\(730\) −0.480833 −0.0177964
\(731\) 5.94943 10.3047i 0.220048 0.381134i
\(732\) −4.97358 14.0630i −0.183829 0.519784i
\(733\) 0.977788 0.564526i 0.0361154 0.0208512i −0.481834 0.876263i \(-0.660029\pi\)
0.517949 + 0.855411i \(0.326696\pi\)
\(734\) 10.9611 + 18.9851i 0.404580 + 0.700753i
\(735\) 1.25385 + 12.0593i 0.0462491 + 0.444816i
\(736\) 6.10975 10.5824i 0.225208 0.390072i
\(737\) 1.82453i 0.0672076i
\(738\) 1.16774 + 1.44442i 0.0429851 + 0.0531700i
\(739\) 9.04830 0.332847 0.166423 0.986054i \(-0.446778\pi\)
0.166423 + 0.986054i \(0.446778\pi\)
\(740\) 0.605998 1.04962i 0.0222769 0.0385848i
\(741\) 3.86310 + 3.30210i 0.141915 + 0.121306i
\(742\) −31.2614 + 24.6264i −1.14764 + 0.904065i
\(743\) 28.5598 16.4890i 1.04776 0.604924i 0.125738 0.992064i \(-0.459870\pi\)
0.922021 + 0.387140i \(0.126537\pi\)
\(744\) 33.9520 + 29.0215i 1.24474 + 1.06398i
\(745\) −2.37768 1.37275i −0.0871114 0.0502938i
\(746\) 24.2971i 0.889578i
\(747\) 5.98472 + 37.9849i 0.218969 + 1.38979i
\(748\) 8.10005i 0.296167i
\(749\) 16.5814 41.5186i 0.605873 1.51706i
\(750\) −2.01241 0.373820i −0.0734828 0.0136500i
\(751\) −24.9073 43.1407i −0.908880 1.57423i −0.815623 0.578584i \(-0.803605\pi\)
−0.0932571 0.995642i \(-0.529728\pi\)
\(752\) 7.90343 + 13.6891i 0.288208 + 0.499192i
\(753\) 24.5827 8.69401i 0.895844 0.316827i
\(754\) −2.98386 1.72273i −0.108666 0.0627382i
\(755\) −8.91520 −0.324457
\(756\) 7.61768 + 3.28699i 0.277052 + 0.119547i
\(757\) 0.640276 0.0232712 0.0116356 0.999932i \(-0.496296\pi\)
0.0116356 + 0.999932i \(0.496296\pi\)
\(758\) 10.2121 + 5.89593i 0.370918 + 0.214150i
\(759\) 37.7764 13.3601i 1.37119 0.484942i
\(760\) 7.31611 + 12.6719i 0.265383 + 0.459657i
\(761\) −0.714506 1.23756i −0.0259008 0.0448615i 0.852784 0.522263i \(-0.174912\pi\)
−0.878685 + 0.477401i \(0.841579\pi\)
\(762\) 20.8242 + 3.86825i 0.754382 + 0.140132i
\(763\) −18.4156 7.35471i −0.666690 0.266258i
\(764\) 10.2806i 0.371940i
\(765\) −6.04618 2.32653i −0.218600 0.0841157i
\(766\) 4.65991i 0.168369i
\(767\) 2.91423 + 1.68253i 0.105227 + 0.0607528i
\(768\) −17.1585 14.6667i −0.619153 0.529240i
\(769\) −36.2876 + 20.9506i −1.30856 + 0.755500i −0.981856 0.189626i \(-0.939273\pi\)
−0.326707 + 0.945126i \(0.605939\pi\)
\(770\) 15.2656 12.0256i 0.550134 0.433373i
\(771\) 33.7278 + 28.8299i 1.21468 + 1.03828i
\(772\) −5.96670 + 10.3346i −0.214746 + 0.371952i
\(773\) −8.72402 −0.313781 −0.156891 0.987616i \(-0.550147\pi\)
−0.156891 + 0.987616i \(0.550147\pi\)
\(774\) 7.01534 18.2315i 0.252161 0.655318i
\(775\) 8.38169i 0.301079i
\(776\) 3.86214 6.68942i 0.138643 0.240136i
\(777\) 9.19590 + 0.368321i 0.329901 + 0.0132134i
\(778\) 19.2792 + 33.3926i 0.691193 + 1.19718i
\(779\) 2.15788 1.24585i 0.0773140 0.0446373i
\(780\) −0.215019 0.607976i −0.00769891 0.0217690i
\(781\) 16.9622 29.3794i 0.606956 1.05128i
\(782\) −9.49819 −0.339655
\(783\) 21.5945 11.6910i 0.771725 0.417801i
\(784\) 16.3051 4.81713i 0.582325 0.172040i
\(785\) 15.1714 + 8.75923i 0.541492 + 0.312630i
\(786\) 7.46759 + 21.1149i 0.266360 + 0.753145i
\(787\) 23.6087 13.6305i 0.841558 0.485874i −0.0162352 0.999868i \(-0.505168\pi\)
0.857794 + 0.513994i \(0.171835\pi\)
\(788\) −2.03229 + 1.17334i −0.0723973 + 0.0417986i
\(789\) 31.0115 + 5.76062i 1.10404 + 0.205084i
\(790\) 5.84161 + 3.37265i 0.207835 + 0.119994i
\(791\) −32.6795 + 4.72639i −1.16195 + 0.168051i
\(792\) −8.92860 56.6696i −0.317264 2.01367i
\(793\) −8.80418 −0.312646
\(794\) 9.90040 17.1480i 0.351352 0.608560i
\(795\) −14.3245 + 16.7582i −0.508039 + 0.594351i
\(796\) 0.900425 0.519861i 0.0319147 0.0184260i
\(797\) −13.0160 22.5444i −0.461051 0.798564i 0.537962 0.842969i \(-0.319194\pi\)
−0.999014 + 0.0444045i \(0.985861\pi\)
\(798\) −13.7599 + 21.7714i −0.487095 + 0.770698i
\(799\) −7.02688 + 12.1709i −0.248593 + 0.430576i
\(800\) 3.28305i 0.116073i
\(801\) 2.23433 1.80634i 0.0789462 0.0638237i
\(802\) 9.22189 0.325636
\(803\) 1.26450 2.19017i 0.0446231 0.0772894i
\(804\) 0.0560383 0.301675i 0.00197632 0.0106393i
\(805\) 6.09374 + 7.73555i 0.214776 + 0.272642i
\(806\) 5.29215 3.05543i 0.186408 0.107623i
\(807\) 36.3574 12.8583i 1.27984 0.452633i
\(808\) 31.6588 + 18.2782i 1.11375 + 0.643025i
\(809\) 31.6665i 1.11334i −0.830735 0.556668i \(-0.812080\pi\)
0.830735 0.556668i \(-0.187920\pi\)
\(810\) −10.3997 2.22811i −0.365407 0.0782877i
\(811\) 4.49997i 0.158015i 0.996874 + 0.0790076i \(0.0251751\pi\)
−0.996874 + 0.0790076i \(0.974825\pi\)
\(812\) −2.79859 + 7.00744i −0.0982111 + 0.245913i
\(813\) −15.7669 44.5816i −0.552968 1.56354i
\(814\) −7.37565 12.7750i −0.258517 0.447764i
\(815\) −5.92487 10.2622i −0.207539 0.359468i
\(816\) −1.65913 + 8.93170i −0.0580811 + 0.312672i
\(817\) −22.6947 13.1028i −0.793988 0.458409i
\(818\) 22.2141 0.776699
\(819\) 3.32819 3.59200i 0.116296 0.125515i
\(820\) −0.316179 −0.0110414
\(821\) 1.92522 + 1.11153i 0.0671907 + 0.0387926i 0.533219 0.845977i \(-0.320982\pi\)
−0.466028 + 0.884770i \(0.654316\pi\)
\(822\) −22.9823 19.6448i −0.801600 0.685192i
\(823\) 7.46182 + 12.9243i 0.260103 + 0.450511i 0.966269 0.257535i \(-0.0829102\pi\)
−0.706166 + 0.708046i \(0.749577\pi\)
\(824\) −6.70103 11.6065i −0.233442 0.404333i
\(825\) 6.99498 8.18336i 0.243534 0.284908i
\(826\) −6.32501 + 15.8373i −0.220075 + 0.551051i
\(827\) 11.9293i 0.414824i −0.978254 0.207412i \(-0.933496\pi\)
0.978254 0.207412i \(-0.0665040\pi\)
\(828\) 6.65642 1.04875i 0.231326 0.0364467i
\(829\) 7.29726i 0.253444i −0.991938 0.126722i \(-0.959554\pi\)
0.991938 0.126722i \(-0.0404457\pi\)
\(830\) 13.1180 + 7.57367i 0.455332 + 0.262886i
\(831\) 4.79289 25.8019i 0.166264 0.895058i
\(832\) −4.66831 + 2.69525i −0.161845 + 0.0934410i
\(833\) 10.9574 + 10.4131i 0.379653 + 0.360793i
\(834\) −4.96712 + 1.75669i −0.171997 + 0.0608292i
\(835\) 0.847165 1.46733i 0.0293174 0.0507792i
\(836\) −17.8392 −0.616983
\(837\) −1.19289 + 43.5362i −0.0412325 + 1.50483i
\(838\) 30.7782i 1.06321i
\(839\) −4.89427 + 8.47713i −0.168969 + 0.292663i −0.938058 0.346479i \(-0.887377\pi\)
0.769089 + 0.639142i \(0.220710\pi\)
\(840\) 12.4824 6.55518i 0.430684 0.226175i
\(841\) −3.33332 5.77347i −0.114942 0.199085i
\(842\) −39.7834 + 22.9690i −1.37103 + 0.791563i
\(843\) 26.5458 + 4.93107i 0.914284 + 0.169835i
\(844\) −3.49718 + 6.05730i −0.120378 + 0.208501i
\(845\) 12.6194 0.434120
\(846\) −8.28583 + 21.5332i −0.284873 + 0.740328i
\(847\) 10.4647 + 72.3555i 0.359571 + 2.48617i
\(848\) 26.7730 + 15.4574i 0.919389 + 0.530810i
\(849\) 15.8114 18.4977i 0.542647 0.634838i
\(850\) −2.21002 + 1.27596i −0.0758031 + 0.0437649i
\(851\) 6.47349 3.73747i 0.221908 0.128119i
\(852\) 3.70695 4.33673i 0.126998 0.148574i
\(853\) 37.9865 + 21.9315i 1.30063 + 0.750921i 0.980513 0.196456i \(-0.0629433\pi\)
0.320120 + 0.947377i \(0.396277\pi\)
\(854\) −6.38662 44.1587i −0.218545 1.51108i
\(855\) −5.12385 + 13.3159i −0.175232 + 0.455394i
\(856\) −51.9885 −1.77693
\(857\) 1.88477 3.26452i 0.0643825 0.111514i −0.832037 0.554720i \(-0.812826\pi\)
0.896420 + 0.443206i \(0.146159\pi\)
\(858\) −7.71685 1.43346i −0.263449 0.0489376i
\(859\) 6.80837 3.93081i 0.232299 0.134118i −0.379333 0.925260i \(-0.623847\pi\)
0.611632 + 0.791142i \(0.290513\pi\)
\(860\) 1.66265 + 2.87979i 0.0566959 + 0.0982002i
\(861\) −1.11628 2.12562i −0.0380426 0.0724408i
\(862\) −1.84879 + 3.20219i −0.0629699 + 0.109067i
\(863\) 50.5884i 1.72205i 0.508565 + 0.861024i \(0.330176\pi\)
−0.508565 + 0.861024i \(0.669824\pi\)
\(864\) 0.467249 17.0528i 0.0158961 0.580150i
\(865\) 8.79329 0.298981
\(866\) 10.7126 18.5548i 0.364029 0.630517i
\(867\) 20.1452 7.12461i 0.684166 0.241964i
\(868\) −8.28150 10.5127i −0.281092 0.356826i
\(869\) −30.7246 + 17.7388i −1.04226 + 0.601749i
\(870\) 1.76661 9.51029i 0.0598936 0.322429i
\(871\) −0.156839 0.0905513i −0.00531430 0.00306821i
\(872\) 23.0595i 0.780894i
\(873\) 7.44007 1.17222i 0.251808 0.0396737i
\(874\) 20.9184i 0.707577i
\(875\) 2.45705 + 0.981280i 0.0830634 + 0.0331733i
\(876\) 0.276345 0.323293i 0.00933682 0.0109231i
\(877\) −1.56847 2.71668i −0.0529636 0.0917357i 0.838328 0.545166i \(-0.183533\pi\)
−0.891292 + 0.453430i \(0.850200\pi\)
\(878\) 1.14998 + 1.99182i 0.0388099 + 0.0672206i
\(879\) −8.80131 7.52319i −0.296861 0.253751i
\(880\) −13.0738 7.54818i −0.440719 0.254449i
\(881\) 14.8044 0.498774 0.249387 0.968404i \(-0.419771\pi\)
0.249387 + 0.968404i \(0.419771\pi\)
\(882\) 20.4305 + 14.0874i 0.687932 + 0.474347i
\(883\) 30.1484 1.01458 0.507288 0.861777i \(-0.330648\pi\)
0.507288 + 0.861777i \(0.330648\pi\)
\(884\) −0.696291 0.402004i −0.0234188 0.0135209i
\(885\) −1.72538 + 9.28838i −0.0579982 + 0.312225i
\(886\) 0.315393 + 0.546276i 0.0105958 + 0.0183525i
\(887\) −5.04001 8.72956i −0.169227 0.293110i 0.768921 0.639343i \(-0.220794\pi\)
−0.938148 + 0.346234i \(0.887460\pi\)
\(888\) −3.56837 10.0897i −0.119747 0.338589i
\(889\) −25.4253 10.1542i −0.852737 0.340561i
\(890\) 1.13178i 0.0379373i
\(891\) 37.4980 41.5105i 1.25623 1.39065i
\(892\) 14.7528i 0.493962i
\(893\) 26.8047 + 15.4757i 0.896987 + 0.517876i
\(894\) −5.29803 + 1.87372i −0.177193 + 0.0626666i
\(895\) −8.73894 + 5.04543i −0.292110 + 0.168650i
\(896\) −6.15467 7.81290i −0.205613 0.261011i
\(897\) 0.726379 3.91037i 0.0242531 0.130563i
\(898\) 11.2823 19.5415i 0.376496 0.652109i
\(899\) −39.6103 −1.32108
\(900\) 1.40792 1.13822i 0.0469305 0.0379408i
\(901\) 27.4861i 0.915696i
\(902\) −1.92412 + 3.33268i −0.0640662 + 0.110966i
\(903\) −13.4903 + 21.3449i −0.448931 + 0.710313i
\(904\) 19.1986 + 33.2530i 0.638536 + 1.10598i
\(905\) −0.688938 + 0.397759i −0.0229011 + 0.0132219i
\(906\) −11.8567 + 13.8711i −0.393913 + 0.460835i
\(907\) −17.3071 + 29.9767i −0.574672 + 0.995361i 0.421405 + 0.906873i \(0.361537\pi\)
−0.996077 + 0.0884889i \(0.971796\pi\)
\(908\) 1.28938 0.0427896
\(909\) 5.54774 + 35.2113i 0.184007 + 1.16789i
\(910\) −0.276108 1.90908i −0.00915288 0.0632854i
\(911\) −22.0123 12.7088i −0.729301 0.421062i 0.0888654 0.996044i \(-0.471676\pi\)
−0.818166 + 0.574981i \(0.805009\pi\)
\(912\) 19.6708 + 3.65400i 0.651366 + 0.120996i
\(913\) −68.9954 + 39.8345i −2.28341 + 1.31833i
\(914\) 23.6148 13.6340i 0.781107 0.450972i
\(915\) −8.24138 23.3029i −0.272452 0.770370i
\(916\) −12.3322 7.12000i −0.407467 0.235251i
\(917\) −4.14387 28.6518i −0.136843 0.946166i
\(918\) −11.6609 + 6.31304i −0.384867 + 0.208361i
\(919\) −15.4066 −0.508217 −0.254108 0.967176i \(-0.581782\pi\)
−0.254108 + 0.967176i \(0.581782\pi\)
\(920\) 5.72563 9.91708i 0.188768 0.326956i
\(921\) 8.43518 + 23.8509i 0.277949 + 0.785913i
\(922\) 23.2837 13.4429i 0.766808 0.442717i
\(923\) −1.68366 2.91619i −0.0554185 0.0959876i
\(924\) −0.687921 + 17.1754i −0.0226309 + 0.565028i
\(925\) 1.00416 1.73925i 0.0330166 0.0571863i
\(926\) 14.3381i 0.471180i
\(927\) 4.69308 12.1964i 0.154141 0.400583i
\(928\) 15.5151 0.509309
\(929\) 0.674311 1.16794i 0.0221234 0.0383189i −0.854752 0.519037i \(-0.826291\pi\)
0.876875 + 0.480718i \(0.159624\pi\)
\(930\) 13.0410 + 11.1472i 0.427630 + 0.365530i
\(931\) 22.9334 24.1322i 0.751612 0.790902i
\(932\) −0.432878 + 0.249922i −0.0141794 + 0.00818647i
\(933\) −24.8481 21.2397i −0.813490 0.695355i
\(934\) 4.72096 + 2.72565i 0.154475 + 0.0891859i
\(935\) 13.4221i 0.438948i
\(936\) −5.31452 2.04499i −0.173711 0.0668425i
\(937\) 50.1179i 1.63728i 0.574307 + 0.818640i \(0.305272\pi\)
−0.574307 + 0.818640i \(0.694728\pi\)
\(938\) 0.340402 0.852339i 0.0111145 0.0278299i
\(939\) 30.3343 + 5.63482i 0.989923 + 0.183886i
\(940\) −1.96376 3.40133i −0.0640507 0.110939i
\(941\) −11.4575 19.8449i −0.373503 0.646926i 0.616599 0.787278i \(-0.288510\pi\)
−0.990102 + 0.140351i \(0.955177\pi\)
\(942\) 33.8055 11.9558i 1.10144 0.389540i
\(943\) −1.68877 0.975011i −0.0549939 0.0317507i
\(944\) 13.2477 0.431177
\(945\) 12.6228 + 5.44666i 0.410618 + 0.177180i
\(946\) 40.4725 1.31587
\(947\) −1.16082 0.670199i −0.0377216 0.0217786i 0.481021 0.876709i \(-0.340266\pi\)
−0.518742 + 0.854931i \(0.673600\pi\)
\(948\) −5.62493 + 1.98933i −0.182689 + 0.0646106i
\(949\) −0.125513 0.217395i −0.00407433 0.00705695i
\(950\) 2.81012 + 4.86727i 0.0911722 + 0.157915i
\(951\) 44.6989 + 8.30314i 1.44946 + 0.269248i
\(952\) 6.51950 16.3243i 0.211298 0.529074i
\(953\) 13.3889i 0.433710i 0.976204 + 0.216855i \(0.0695800\pi\)
−0.976204 + 0.216855i \(0.930420\pi\)
\(954\) 7.02300 + 44.5748i 0.227378 + 1.44316i
\(955\) 17.0354i 0.551251i
\(956\) −9.80100 5.65861i −0.316987 0.183013i
\(957\) 38.6731 + 33.0570i 1.25012 + 1.06858i
\(958\) 9.29603 5.36707i 0.300341 0.173402i
\(959\) 24.1838 + 30.6995i 0.780935 + 0.991339i
\(960\) −11.5037 9.83312i −0.371280 0.317363i
\(961\) 19.6263 33.9938i 0.633107 1.09657i
\(962\) −1.46421 −0.0472080
\(963\) −31.8705 39.4219i −1.02701 1.27035i
\(964\) 11.0191i 0.354903i
\(965\) −9.88703 + 17.1248i −0.318275 + 0.551268i
\(966\) 20.1400 + 0.806662i 0.647993 + 0.0259539i
\(967\) −13.2117 22.8834i −0.424860 0.735879i 0.571547 0.820569i \(-0.306343\pi\)
−0.996407 + 0.0846898i \(0.973010\pi\)
\(968\) 73.6252 42.5075i 2.36640 1.36624i
\(969\) 5.93110 + 16.7704i 0.190534 + 0.538744i
\(970\) 1.48345 2.56941i 0.0476307 0.0824987i
\(971\) 18.2164 0.584593 0.292296 0.956328i \(-0.405581\pi\)
0.292296 + 0.956328i \(0.405581\pi\)
\(972\) 7.47499 5.71179i 0.239761 0.183206i
\(973\) 6.74011 0.974812i 0.216078 0.0312510i
\(974\) 24.2201 + 13.9835i 0.776061 + 0.448059i
\(975\) −0.356293 1.00744i −0.0114105 0.0322638i
\(976\) −30.0170 + 17.3303i −0.960822 + 0.554731i
\(977\) 7.55063 4.35936i 0.241566 0.139468i −0.374330 0.927295i \(-0.622127\pi\)
0.615896 + 0.787827i \(0.288794\pi\)
\(978\) −23.8465 4.42967i −0.762528 0.141645i
\(979\) 5.15520 + 2.97636i 0.164761 + 0.0951248i
\(980\) −4.05131 + 1.19691i −0.129414 + 0.0382338i
\(981\) −17.4856 + 14.1362i −0.558272 + 0.451333i
\(982\) −12.6304 −0.403052
\(983\) 1.76302 3.05363i 0.0562315 0.0973957i −0.836539 0.547907i \(-0.815425\pi\)
0.892771 + 0.450511i \(0.148758\pi\)
\(984\) −1.81407 + 2.12226i −0.0578303 + 0.0676551i
\(985\) −3.36757 + 1.94427i −0.107300 + 0.0619496i
\(986\) −6.02994 10.4442i −0.192032 0.332610i
\(987\) 15.9335 25.2104i 0.507168 0.802457i
\(988\) −0.885358 + 1.53348i −0.0281670 + 0.0487866i
\(989\) 20.5087i 0.652137i
\(990\) −3.42948 21.7668i −0.108996 0.691794i
\(991\) −42.4009 −1.34691 −0.673454 0.739229i \(-0.735190\pi\)
−0.673454 + 0.739229i \(0.735190\pi\)
\(992\) −13.7588 + 23.8309i −0.436841 + 0.756631i
\(993\) 6.17215 33.2270i 0.195867 1.05443i
\(994\) 13.4053 10.5601i 0.425190 0.334946i
\(995\) 1.49203 0.861427i 0.0473007 0.0273091i
\(996\) −12.6314 + 4.46727i −0.400242 + 0.141551i
\(997\) −46.4513 26.8186i −1.47113 0.849355i −0.471652 0.881785i \(-0.656342\pi\)
−0.999474 + 0.0324296i \(0.989676\pi\)
\(998\) 24.5908i 0.778407i
\(999\) 5.46334 8.89113i 0.172852 0.281303i
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.bl.j.146.8 yes 24
3.2 odd 2 945.2.bl.j.251.5 24
7.6 odd 2 315.2.bl.i.146.8 yes 24
9.4 even 3 945.2.bl.i.881.5 24
9.5 odd 6 315.2.bl.i.41.8 24
21.20 even 2 945.2.bl.i.251.5 24
63.13 odd 6 945.2.bl.j.881.5 24
63.41 even 6 inner 315.2.bl.j.41.8 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bl.i.41.8 24 9.5 odd 6
315.2.bl.i.146.8 yes 24 7.6 odd 2
315.2.bl.j.41.8 yes 24 63.41 even 6 inner
315.2.bl.j.146.8 yes 24 1.1 even 1 trivial
945.2.bl.i.251.5 24 21.20 even 2
945.2.bl.i.881.5 24 9.4 even 3
945.2.bl.j.251.5 24 3.2 odd 2
945.2.bl.j.881.5 24 63.13 odd 6