Properties

Label 91.2.e.c.79.4
Level $91$
Weight $2$
Character 91.79
Analytic conductor $0.727$
Analytic rank $0$
Dimension $10$
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] = [91,2,Mod(53,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.e (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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.4
Root \(0.597828 - 1.03547i\) of defining polynomial
Character \(\chi\) \(=\) 91.79
Dual form 91.2.e.c.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0978281 - 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(-1.96625 + 3.40565i) q^{5} +0.0508292 q^{6} +(1.12324 - 2.39548i) q^{7} +0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +O(q^{10})\) \(q+(0.0978281 - 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(-1.96625 + 3.40565i) q^{5} +0.0508292 q^{6} +(1.12324 - 2.39548i) q^{7} +0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +(0.384710 + 0.666337i) q^{10} +(-2.25314 - 3.90255i) q^{11} +(-0.254816 + 0.441354i) q^{12} +1.00000 q^{13} +(-0.296013 - 0.424671i) q^{14} -1.02162 q^{15} +(-1.88589 + 3.26645i) q^{16} +(1.14070 + 1.97576i) q^{17} +(-0.286882 - 0.496894i) q^{18} +(0.893841 - 1.54818i) q^{19} -7.71448 q^{20} +(0.684846 - 0.0584481i) q^{21} -0.881681 q^{22} +(-0.870106 + 1.50707i) q^{23} +(0.100686 + 0.174393i) q^{24} +(-5.23232 - 9.06264i) q^{25} +(0.0978281 - 0.169443i) q^{26} +1.54120 q^{27} +(5.17142 - 0.441354i) q^{28} +1.65110 q^{29} +(-0.0999432 + 0.173107i) q^{30} +(-2.80262 - 4.85427i) q^{31} +(1.14412 + 1.98168i) q^{32} +(0.585339 - 1.01384i) q^{33} +0.446372 q^{34} +(5.94959 + 8.53550i) q^{35} +5.75276 q^{36} +(-3.57204 + 6.18695i) q^{37} +(-0.174886 - 0.302911i) q^{38} +(0.129894 + 0.224983i) q^{39} +(-1.52411 + 2.63984i) q^{40} -8.11574 q^{41} +(0.0570936 - 0.121760i) q^{42} +6.81353 q^{43} +(4.42002 - 7.65570i) q^{44} +(5.76606 + 9.98711i) q^{45} +(0.170242 + 0.294867i) q^{46} +(-1.77271 + 3.07043i) q^{47} -0.979864 q^{48} +(-4.47665 - 5.38141i) q^{49} -2.04747 q^{50} +(-0.296342 + 0.513279i) q^{51} +(0.980859 + 1.69890i) q^{52} +(-1.64483 - 2.84892i) q^{53} +(0.150772 - 0.261146i) q^{54} +17.7210 q^{55} +(0.870665 - 1.85682i) q^{56} +0.464419 q^{57} +(0.161524 - 0.279768i) q^{58} +(-2.25314 - 3.90255i) q^{59} +(-1.00207 - 1.73563i) q^{60} +(-3.77234 + 6.53388i) q^{61} -1.09670 q^{62} +(-4.43667 - 6.36500i) q^{63} -7.09585 q^{64} +(-1.96625 + 3.40565i) q^{65} +(-0.114525 - 0.198364i) q^{66} +(6.33263 + 10.9684i) q^{67} +(-2.23774 + 3.87588i) q^{68} -0.452087 q^{69} +(2.02832 - 0.173107i) q^{70} +9.54869 q^{71} +(1.13655 - 1.96855i) q^{72} +(-0.540019 - 0.935340i) q^{73} +(0.698891 + 1.21052i) q^{74} +(1.35930 - 2.35437i) q^{75} +3.50693 q^{76} +(-11.8793 + 1.01384i) q^{77} +0.0508292 q^{78} +(-0.395849 + 0.685630i) q^{79} +(-7.41628 - 12.8454i) q^{80} +(-4.19857 - 7.27214i) q^{81} +(-0.793947 + 1.37516i) q^{82} -7.14643 q^{83} +(0.771035 + 1.10615i) q^{84} -8.97166 q^{85} +(0.666555 - 1.15451i) q^{86} +(0.214468 + 0.371470i) q^{87} +(-1.74649 - 3.02500i) q^{88} +(5.63281 - 9.75631i) q^{89} +2.25633 q^{90} +(1.12324 - 2.39548i) q^{91} -3.41381 q^{92} +(0.728087 - 1.26108i) q^{93} +(0.346843 + 0.600749i) q^{94} +(3.51504 + 6.08823i) q^{95} +(-0.297229 + 0.514816i) q^{96} -8.81353 q^{97} +(-1.34979 + 0.232085i) q^{98} -13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0978281 0.169443i 0.0691749 0.119815i −0.829363 0.558710i \(-0.811297\pi\)
0.898538 + 0.438895i \(0.144630\pi\)
\(3\) 0.129894 + 0.224983i 0.0749945 + 0.129894i 0.901084 0.433645i \(-0.142773\pi\)
−0.826089 + 0.563539i \(0.809439\pi\)
\(4\) 0.980859 + 1.69890i 0.490430 + 0.849449i
\(5\) −1.96625 + 3.40565i −0.879336 + 1.52305i −0.0272650 + 0.999628i \(0.508680\pi\)
−0.852071 + 0.523426i \(0.824654\pi\)
\(6\) 0.0508292 0.0207509
\(7\) 1.12324 2.39548i 0.424546 0.905406i
\(8\) 0.775135 0.274052
\(9\) 1.46625 2.53963i 0.488752 0.846543i
\(10\) 0.384710 + 0.666337i 0.121656 + 0.210714i
\(11\) −2.25314 3.90255i −0.679346 1.17666i −0.975178 0.221422i \(-0.928930\pi\)
0.295832 0.955240i \(-0.404403\pi\)
\(12\) −0.254816 + 0.441354i −0.0735590 + 0.127408i
\(13\) 1.00000 0.277350
\(14\) −0.296013 0.424671i −0.0791129 0.113498i
\(15\) −1.02162 −0.263781
\(16\) −1.88589 + 3.26645i −0.471472 + 0.816614i
\(17\) 1.14070 + 1.97576i 0.276661 + 0.479192i 0.970553 0.240888i \(-0.0774386\pi\)
−0.693891 + 0.720080i \(0.744105\pi\)
\(18\) −0.286882 0.496894i −0.0676187 0.117119i
\(19\) 0.893841 1.54818i 0.205061 0.355177i −0.745091 0.666963i \(-0.767594\pi\)
0.950152 + 0.311786i \(0.100927\pi\)
\(20\) −7.71448 −1.72501
\(21\) 0.684846 0.0584481i 0.149446 0.0127544i
\(22\) −0.881681 −0.187975
\(23\) −0.870106 + 1.50707i −0.181430 + 0.314245i −0.942368 0.334579i \(-0.891406\pi\)
0.760938 + 0.648825i \(0.224739\pi\)
\(24\) 0.100686 + 0.174393i 0.0205524 + 0.0355977i
\(25\) −5.23232 9.06264i −1.04646 1.81253i
\(26\) 0.0978281 0.169443i 0.0191857 0.0332306i
\(27\) 1.54120 0.296604
\(28\) 5.17142 0.441354i 0.977307 0.0834081i
\(29\) 1.65110 0.306602 0.153301 0.988180i \(-0.451010\pi\)
0.153301 + 0.988180i \(0.451010\pi\)
\(30\) −0.0999432 + 0.173107i −0.0182471 + 0.0316048i
\(31\) −2.80262 4.85427i −0.503365 0.871853i −0.999992 0.00388953i \(-0.998762\pi\)
0.496628 0.867964i \(-0.334571\pi\)
\(32\) 1.14412 + 1.98168i 0.202254 + 0.350314i
\(33\) 0.585339 1.01384i 0.101894 0.176486i
\(34\) 0.446372 0.0765522
\(35\) 5.94959 + 8.53550i 1.00566 + 1.44276i
\(36\) 5.75276 0.958793
\(37\) −3.57204 + 6.18695i −0.587239 + 1.01713i 0.407353 + 0.913271i \(0.366452\pi\)
−0.994592 + 0.103857i \(0.966881\pi\)
\(38\) −0.174886 0.302911i −0.0283702 0.0491386i
\(39\) 0.129894 + 0.224983i 0.0207997 + 0.0360262i
\(40\) −1.52411 + 2.63984i −0.240983 + 0.417396i
\(41\) −8.11574 −1.26746 −0.633732 0.773552i \(-0.718478\pi\)
−0.633732 + 0.773552i \(0.718478\pi\)
\(42\) 0.0570936 0.121760i 0.00880973 0.0187880i
\(43\) 6.81353 1.03905 0.519527 0.854454i \(-0.326108\pi\)
0.519527 + 0.854454i \(0.326108\pi\)
\(44\) 4.42002 7.65570i 0.666343 1.15414i
\(45\) 5.76606 + 9.98711i 0.859554 + 1.48879i
\(46\) 0.170242 + 0.294867i 0.0251008 + 0.0434758i
\(47\) −1.77271 + 3.07043i −0.258577 + 0.447868i −0.965861 0.259061i \(-0.916587\pi\)
0.707284 + 0.706929i \(0.249920\pi\)
\(48\) −0.979864 −0.141431
\(49\) −4.47665 5.38141i −0.639522 0.768773i
\(50\) −2.04747 −0.289556
\(51\) −0.296342 + 0.513279i −0.0414962 + 0.0718735i
\(52\) 0.980859 + 1.69890i 0.136021 + 0.235595i
\(53\) −1.64483 2.84892i −0.225934 0.391330i 0.730665 0.682736i \(-0.239210\pi\)
−0.956599 + 0.291406i \(0.905877\pi\)
\(54\) 0.150772 0.261146i 0.0205175 0.0355374i
\(55\) 17.7210 2.38949
\(56\) 0.870665 1.85682i 0.116347 0.248128i
\(57\) 0.464419 0.0615138
\(58\) 0.161524 0.279768i 0.0212092 0.0367353i
\(59\) −2.25314 3.90255i −0.293333 0.508068i 0.681262 0.732039i \(-0.261431\pi\)
−0.974596 + 0.223971i \(0.928098\pi\)
\(60\) −1.00207 1.73563i −0.129366 0.224069i
\(61\) −3.77234 + 6.53388i −0.482998 + 0.836577i −0.999809 0.0195220i \(-0.993786\pi\)
0.516811 + 0.856099i \(0.327119\pi\)
\(62\) −1.09670 −0.139281
\(63\) −4.43667 6.36500i −0.558968 0.801915i
\(64\) −7.09585 −0.886981
\(65\) −1.96625 + 3.40565i −0.243884 + 0.422419i
\(66\) −0.114525 0.198364i −0.0140971 0.0244169i
\(67\) 6.33263 + 10.9684i 0.773653 + 1.34001i 0.935548 + 0.353199i \(0.114906\pi\)
−0.161895 + 0.986808i \(0.551761\pi\)
\(68\) −2.23774 + 3.87588i −0.271366 + 0.470020i
\(69\) −0.452087 −0.0544249
\(70\) 2.02832 0.173107i 0.242431 0.0206902i
\(71\) 9.54869 1.13322 0.566610 0.823986i \(-0.308254\pi\)
0.566610 + 0.823986i \(0.308254\pi\)
\(72\) 1.13655 1.96855i 0.133943 0.231996i
\(73\) −0.540019 0.935340i −0.0632044 0.109473i 0.832692 0.553737i \(-0.186799\pi\)
−0.895896 + 0.444264i \(0.853465\pi\)
\(74\) 0.698891 + 1.21052i 0.0812445 + 0.140720i
\(75\) 1.35930 2.35437i 0.156958 0.271859i
\(76\) 3.50693 0.402273
\(77\) −11.8793 + 1.01384i −1.35377 + 0.115537i
\(78\) 0.0508292 0.00575528
\(79\) −0.395849 + 0.685630i −0.0445365 + 0.0771394i −0.887434 0.460934i \(-0.847514\pi\)
0.842898 + 0.538074i \(0.180848\pi\)
\(80\) −7.41628 12.8454i −0.829165 1.43616i
\(81\) −4.19857 7.27214i −0.466508 0.808016i
\(82\) −0.793947 + 1.37516i −0.0876768 + 0.151861i
\(83\) −7.14643 −0.784422 −0.392211 0.919875i \(-0.628290\pi\)
−0.392211 + 0.919875i \(0.628290\pi\)
\(84\) 0.771035 + 1.10615i 0.0841268 + 0.120691i
\(85\) −8.97166 −0.973114
\(86\) 0.666555 1.15451i 0.0718765 0.124494i
\(87\) 0.214468 + 0.371470i 0.0229934 + 0.0398258i
\(88\) −1.74649 3.02500i −0.186176 0.322466i
\(89\) 5.63281 9.75631i 0.597077 1.03417i −0.396174 0.918176i \(-0.629662\pi\)
0.993250 0.115992i \(-0.0370045\pi\)
\(90\) 2.25633 0.237838
\(91\) 1.12324 2.39548i 0.117748 0.251115i
\(92\) −3.41381 −0.355914
\(93\) 0.728087 1.26108i 0.0754991 0.130768i
\(94\) 0.346843 + 0.600749i 0.0357741 + 0.0619625i
\(95\) 3.51504 + 6.08823i 0.360636 + 0.624639i
\(96\) −0.297229 + 0.514816i −0.0303358 + 0.0525432i
\(97\) −8.81353 −0.894879 −0.447439 0.894314i \(-0.647664\pi\)
−0.447439 + 0.894314i \(0.647664\pi\)
\(98\) −1.34979 + 0.232085i −0.136349 + 0.0234441i
\(99\) −13.2147 −1.32813
\(100\) 10.2643 17.7783i 1.02643 1.77783i
\(101\) 7.15855 + 12.3990i 0.712303 + 1.23374i 0.963991 + 0.265936i \(0.0856810\pi\)
−0.251688 + 0.967808i \(0.580986\pi\)
\(102\) 0.0579811 + 0.100426i 0.00574099 + 0.00994368i
\(103\) 3.74607 6.48839i 0.369111 0.639320i −0.620315 0.784352i \(-0.712995\pi\)
0.989427 + 0.145033i \(0.0463287\pi\)
\(104\) 0.775135 0.0760082
\(105\) −1.14753 + 2.44727i −0.111987 + 0.238829i
\(106\) −0.643641 −0.0625160
\(107\) −5.48919 + 9.50756i −0.530660 + 0.919130i 0.468700 + 0.883357i \(0.344723\pi\)
−0.999360 + 0.0357726i \(0.988611\pi\)
\(108\) 1.51170 + 2.61834i 0.145463 + 0.251950i
\(109\) 6.22314 + 10.7788i 0.596068 + 1.03242i 0.993395 + 0.114744i \(0.0366046\pi\)
−0.397327 + 0.917677i \(0.630062\pi\)
\(110\) 1.73361 3.00270i 0.165293 0.286296i
\(111\) −1.85595 −0.176159
\(112\) 5.70642 + 8.18663i 0.539206 + 0.773564i
\(113\) −1.65110 −0.155323 −0.0776613 0.996980i \(-0.524745\pi\)
−0.0776613 + 0.996980i \(0.524745\pi\)
\(114\) 0.0454333 0.0786927i 0.00425522 0.00737025i
\(115\) −3.42170 5.92656i −0.319075 0.552654i
\(116\) 1.61950 + 2.80505i 0.150367 + 0.260443i
\(117\) 1.46625 2.53963i 0.135555 0.234789i
\(118\) −0.881681 −0.0811653
\(119\) 6.01418 0.513279i 0.551319 0.0470522i
\(120\) −0.791894 −0.0722897
\(121\) −4.65325 + 8.05967i −0.423023 + 0.732697i
\(122\) 0.738081 + 1.27839i 0.0668227 + 0.115740i
\(123\) −1.05419 1.82591i −0.0950528 0.164636i
\(124\) 5.49794 9.52272i 0.493730 0.855165i
\(125\) 21.4897 1.92210
\(126\) −1.51254 + 0.129087i −0.134748 + 0.0115000i
\(127\) −4.49297 −0.398687 −0.199343 0.979930i \(-0.563881\pi\)
−0.199343 + 0.979930i \(0.563881\pi\)
\(128\) −2.98242 + 5.16569i −0.263611 + 0.456587i
\(129\) 0.885039 + 1.53293i 0.0779233 + 0.134967i
\(130\) 0.384710 + 0.666337i 0.0337413 + 0.0584417i
\(131\) 6.32836 10.9610i 0.552911 0.957670i −0.445151 0.895455i \(-0.646850\pi\)
0.998063 0.0622152i \(-0.0198165\pi\)
\(132\) 2.29654 0.199888
\(133\) −2.70463 3.88016i −0.234521 0.336453i
\(134\) 2.47804 0.214070
\(135\) −3.03039 + 5.24878i −0.260814 + 0.451743i
\(136\) 0.884200 + 1.53148i 0.0758195 + 0.131323i
\(137\) 4.64321 + 8.04227i 0.396696 + 0.687097i 0.993316 0.115426i \(-0.0368234\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(138\) −0.0442268 + 0.0766031i −0.00376484 + 0.00652089i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −8.66523 + 18.4799i −0.732346 + 1.56183i
\(141\) −0.921061 −0.0775673
\(142\) 0.934130 1.61796i 0.0783905 0.135776i
\(143\) −2.25314 3.90255i −0.188417 0.326347i
\(144\) 5.53039 + 9.57891i 0.460866 + 0.798243i
\(145\) −3.24649 + 5.62308i −0.269606 + 0.466971i
\(146\) −0.211316 −0.0174887
\(147\) 0.629237 1.70619i 0.0518986 0.140724i
\(148\) −14.0147 −1.15200
\(149\) 7.58243 13.1332i 0.621177 1.07591i −0.368090 0.929790i \(-0.619988\pi\)
0.989267 0.146120i \(-0.0466786\pi\)
\(150\) −0.265955 0.460647i −0.0217151 0.0376117i
\(151\) −2.57079 4.45274i −0.209208 0.362359i 0.742257 0.670115i \(-0.233755\pi\)
−0.951465 + 0.307756i \(0.900422\pi\)
\(152\) 0.692848 1.20005i 0.0561974 0.0973367i
\(153\) 6.69025 0.540875
\(154\) −0.990341 + 2.11205i −0.0798040 + 0.170194i
\(155\) 22.0426 1.77051
\(156\) −0.254816 + 0.441354i −0.0204016 + 0.0353366i
\(157\) 5.36557 + 9.29344i 0.428219 + 0.741697i 0.996715 0.0809889i \(-0.0258078\pi\)
−0.568496 + 0.822686i \(0.692474\pi\)
\(158\) 0.0774503 + 0.134148i 0.00616162 + 0.0106722i
\(159\) 0.427307 0.740117i 0.0338877 0.0586951i
\(160\) −8.99853 −0.711397
\(161\) 2.63281 + 3.77712i 0.207495 + 0.297679i
\(162\) −1.64295 −0.129083
\(163\) −1.18620 + 2.05455i −0.0929101 + 0.160925i −0.908734 0.417375i \(-0.862950\pi\)
0.815824 + 0.578300i \(0.196284\pi\)
\(164\) −7.96039 13.7878i −0.621602 1.07665i
\(165\) 2.30185 + 3.98692i 0.179199 + 0.310382i
\(166\) −0.699122 + 1.21091i −0.0542624 + 0.0939852i
\(167\) 12.0784 0.934653 0.467327 0.884085i \(-0.345217\pi\)
0.467327 + 0.884085i \(0.345217\pi\)
\(168\) 0.530848 0.0453052i 0.0409558 0.00349537i
\(169\) 1.00000 0.0769231
\(170\) −0.877681 + 1.52019i −0.0673151 + 0.116593i
\(171\) −2.62120 4.54005i −0.200448 0.347186i
\(172\) 6.68312 + 11.5755i 0.509583 + 0.882624i
\(173\) 9.70485 16.8093i 0.737846 1.27799i −0.215618 0.976478i \(-0.569176\pi\)
0.953463 0.301509i \(-0.0974902\pi\)
\(174\) 0.0839242 0.00636228
\(175\) −27.5865 + 2.35437i −2.08535 + 0.177974i
\(176\) 16.9967 1.28117
\(177\) 0.585339 1.01384i 0.0439968 0.0762046i
\(178\) −1.10209 1.90888i −0.0826055 0.143077i
\(179\) −7.32219 12.6824i −0.547286 0.947928i −0.998459 0.0554912i \(-0.982328\pi\)
0.451173 0.892437i \(-0.351006\pi\)
\(180\) −11.3114 + 19.5919i −0.843101 + 1.46029i
\(181\) −9.44627 −0.702136 −0.351068 0.936350i \(-0.614181\pi\)
−0.351068 + 0.936350i \(0.614181\pi\)
\(182\) −0.296013 0.424671i −0.0219420 0.0314787i
\(183\) −1.96002 −0.144889
\(184\) −0.674450 + 1.16818i −0.0497211 + 0.0861194i
\(185\) −14.0471 24.3302i −1.03276 1.78879i
\(186\) −0.142455 0.246739i −0.0104453 0.0180918i
\(187\) 5.14033 8.90331i 0.375898 0.651074i
\(188\) −6.95513 −0.507255
\(189\) 1.73114 3.69191i 0.125922 0.268547i
\(190\) 1.37548 0.0997878
\(191\) −6.27687 + 10.8719i −0.454179 + 0.786660i −0.998641 0.0521252i \(-0.983401\pi\)
0.544462 + 0.838786i \(0.316734\pi\)
\(192\) −0.921709 1.59645i −0.0665186 0.115214i
\(193\) 4.68430 + 8.11344i 0.337183 + 0.584018i 0.983902 0.178710i \(-0.0571925\pi\)
−0.646719 + 0.762729i \(0.723859\pi\)
\(194\) −0.862212 + 1.49339i −0.0619032 + 0.107219i
\(195\) −1.02162 −0.0731598
\(196\) 4.75151 12.8838i 0.339393 0.920270i
\(197\) −7.62276 −0.543099 −0.271550 0.962424i \(-0.587536\pi\)
−0.271550 + 0.962424i \(0.587536\pi\)
\(198\) −1.29277 + 2.23914i −0.0918731 + 0.159129i
\(199\) −6.76443 11.7163i −0.479518 0.830549i 0.520206 0.854041i \(-0.325855\pi\)
−0.999724 + 0.0234914i \(0.992522\pi\)
\(200\) −4.05575 7.02477i −0.286785 0.496726i
\(201\) −1.64514 + 2.84947i −0.116039 + 0.200986i
\(202\) 2.80123 0.197094
\(203\) 1.85459 3.95518i 0.130167 0.277599i
\(204\) −1.16268 −0.0814038
\(205\) 15.9576 27.6394i 1.11453 1.93042i
\(206\) −0.732942 1.26949i −0.0510665 0.0884498i
\(207\) 2.55159 + 4.41949i 0.177348 + 0.307176i
\(208\) −1.88589 + 3.26645i −0.130763 + 0.226488i
\(209\) −8.05579 −0.557231
\(210\) 0.302413 + 0.433853i 0.0208685 + 0.0299387i
\(211\) −15.7995 −1.08768 −0.543840 0.839189i \(-0.683030\pi\)
−0.543840 + 0.839189i \(0.683030\pi\)
\(212\) 3.22669 5.58879i 0.221610 0.383839i
\(213\) 1.24032 + 2.14830i 0.0849853 + 0.147199i
\(214\) 1.07399 + 1.86021i 0.0734167 + 0.127162i
\(215\) −13.3971 + 23.2045i −0.913678 + 1.58254i
\(216\) 1.19464 0.0812847
\(217\) −14.7763 + 1.26108i −1.00308 + 0.0856080i
\(218\) 2.43519 0.164932
\(219\) 0.140291 0.242991i 0.00947997 0.0164198i
\(220\) 17.3818 + 30.1061i 1.17188 + 2.02975i
\(221\) 1.14070 + 1.97576i 0.0767321 + 0.132904i
\(222\) −0.181564 + 0.314478i −0.0121858 + 0.0211064i
\(223\) 22.4737 1.50495 0.752474 0.658622i \(-0.228861\pi\)
0.752474 + 0.658622i \(0.228861\pi\)
\(224\) 6.03219 0.514816i 0.403043 0.0343976i
\(225\) −30.6876 −2.04584
\(226\) −0.161524 + 0.279768i −0.0107444 + 0.0186099i
\(227\) 4.60124 + 7.96959i 0.305395 + 0.528960i 0.977349 0.211633i \(-0.0678781\pi\)
−0.671954 + 0.740593i \(0.734545\pi\)
\(228\) 0.455530 + 0.789001i 0.0301682 + 0.0522529i
\(229\) −7.64611 + 13.2435i −0.505269 + 0.875152i 0.494712 + 0.869057i \(0.335274\pi\)
−0.999981 + 0.00609528i \(0.998060\pi\)
\(230\) −1.33895 −0.0882880
\(231\) −1.77115 2.54095i −0.116533 0.167182i
\(232\) 1.27983 0.0840247
\(233\) 4.02789 6.97652i 0.263876 0.457047i −0.703392 0.710802i \(-0.748332\pi\)
0.967269 + 0.253755i \(0.0816656\pi\)
\(234\) −0.286882 0.496894i −0.0187541 0.0324830i
\(235\) −6.97121 12.0745i −0.454752 0.787653i
\(236\) 4.42002 7.65570i 0.287719 0.498344i
\(237\) −0.205674 −0.0133600
\(238\) 0.501384 1.06928i 0.0324999 0.0693108i
\(239\) 21.7258 1.40533 0.702663 0.711523i \(-0.251994\pi\)
0.702663 + 0.711523i \(0.251994\pi\)
\(240\) 1.92666 3.33708i 0.124366 0.215407i
\(241\) 10.2490 + 17.7518i 0.660195 + 1.14349i 0.980564 + 0.196199i \(0.0628598\pi\)
−0.320369 + 0.947293i \(0.603807\pi\)
\(242\) 0.910438 + 1.57692i 0.0585252 + 0.101369i
\(243\) 3.40254 5.89337i 0.218273 0.378060i
\(244\) −14.8005 −0.947507
\(245\) 27.1295 4.66470i 1.73324 0.298017i
\(246\) −0.412517 −0.0263011
\(247\) 0.893841 1.54818i 0.0568738 0.0985083i
\(248\) −2.17241 3.76272i −0.137948 0.238933i
\(249\) −0.928280 1.60783i −0.0588273 0.101892i
\(250\) 2.10230 3.64129i 0.132961 0.230295i
\(251\) 2.60871 0.164660 0.0823301 0.996605i \(-0.473764\pi\)
0.0823301 + 0.996605i \(0.473764\pi\)
\(252\) 6.46175 13.7806i 0.407052 0.868098i
\(253\) 7.84187 0.493014
\(254\) −0.439539 + 0.761304i −0.0275791 + 0.0477685i
\(255\) −1.16537 2.01848i −0.0729781 0.126402i
\(256\) −6.51232 11.2797i −0.407020 0.704979i
\(257\) 4.49838 7.79142i 0.280601 0.486016i −0.690932 0.722920i \(-0.742799\pi\)
0.971533 + 0.236904i \(0.0761328\pi\)
\(258\) 0.346327 0.0215614
\(259\) 10.8084 + 15.5062i 0.671604 + 0.963508i
\(260\) −7.71448 −0.478432
\(261\) 2.42094 4.19318i 0.149852 0.259551i
\(262\) −1.23818 2.14460i −0.0764952 0.132494i
\(263\) −0.716961 1.24181i −0.0442097 0.0765735i 0.843074 0.537798i \(-0.180744\pi\)
−0.887284 + 0.461224i \(0.847410\pi\)
\(264\) 0.453717 0.785860i 0.0279243 0.0483664i
\(265\) 12.9366 0.794689
\(266\) −0.922056 + 0.0786927i −0.0565349 + 0.00482496i
\(267\) 2.92668 0.179110
\(268\) −12.4228 + 21.5170i −0.758845 + 1.31436i
\(269\) 4.08416 + 7.07397i 0.249016 + 0.431308i 0.963253 0.268596i \(-0.0865596\pi\)
−0.714237 + 0.699904i \(0.753226\pi\)
\(270\) 0.592914 + 1.02696i 0.0360836 + 0.0624986i
\(271\) 0.106159 0.183872i 0.00644867 0.0111694i −0.862783 0.505574i \(-0.831281\pi\)
0.869232 + 0.494405i \(0.164614\pi\)
\(272\) −8.60497 −0.521753
\(273\) 0.684846 0.0584481i 0.0414488 0.00353744i
\(274\) 1.81695 0.109766
\(275\) −23.5783 + 40.8387i −1.42182 + 2.46267i
\(276\) −0.443434 0.768049i −0.0266916 0.0462311i
\(277\) −11.4875 19.8969i −0.690215 1.19549i −0.971767 0.235942i \(-0.924182\pi\)
0.281552 0.959546i \(-0.409151\pi\)
\(278\) −0.391313 + 0.677773i −0.0234694 + 0.0406501i
\(279\) −16.4374 −0.984081
\(280\) 4.61174 + 6.61617i 0.275604 + 0.395392i
\(281\) −0.345228 −0.0205946 −0.0102973 0.999947i \(-0.503278\pi\)
−0.0102973 + 0.999947i \(0.503278\pi\)
\(282\) −0.0901057 + 0.156068i −0.00536572 + 0.00929369i
\(283\) 14.4857 + 25.0900i 0.861087 + 1.49145i 0.870880 + 0.491495i \(0.163549\pi\)
−0.00979277 + 0.999952i \(0.503117\pi\)
\(284\) 9.36592 + 16.2222i 0.555765 + 0.962613i
\(285\) −0.913167 + 1.58165i −0.0540913 + 0.0936889i
\(286\) −0.881681 −0.0521349
\(287\) −9.11594 + 19.4411i −0.538097 + 1.14757i
\(288\) 6.71029 0.395408
\(289\) 5.89759 10.2149i 0.346917 0.600878i
\(290\) 0.635195 + 1.10019i 0.0372999 + 0.0646054i
\(291\) −1.14483 1.98290i −0.0671109 0.116240i
\(292\) 1.05937 1.83487i 0.0619947 0.107378i
\(293\) 31.5427 1.84274 0.921372 0.388682i \(-0.127070\pi\)
0.921372 + 0.388682i \(0.127070\pi\)
\(294\) −0.227545 0.273533i −0.0132707 0.0159528i
\(295\) 17.7210 1.03175
\(296\) −2.76881 + 4.79572i −0.160934 + 0.278746i
\(297\) −3.47253 6.01460i −0.201497 0.349002i
\(298\) −1.48355 2.56958i −0.0859398 0.148852i
\(299\) −0.870106 + 1.50707i −0.0503195 + 0.0871560i
\(300\) 5.33311 0.307907
\(301\) 7.65325 16.3217i 0.441126 0.940766i
\(302\) −1.00598 −0.0578879
\(303\) −1.85971 + 3.22111i −0.106838 + 0.185048i
\(304\) 3.37137 + 5.83939i 0.193361 + 0.334912i
\(305\) −14.8348 25.6945i −0.849435 1.47127i
\(306\) 0.654495 1.13362i 0.0374150 0.0648047i
\(307\) −18.1941 −1.03839 −0.519197 0.854655i \(-0.673769\pi\)
−0.519197 + 0.854655i \(0.673769\pi\)
\(308\) −13.3743 19.1873i −0.762073 1.09330i
\(309\) 1.94637 0.110725
\(310\) 2.15639 3.73498i 0.122475 0.212132i
\(311\) 0.188312 + 0.326165i 0.0106782 + 0.0184951i 0.871315 0.490724i \(-0.163268\pi\)
−0.860637 + 0.509219i \(0.829934\pi\)
\(312\) 0.100686 + 0.174393i 0.00570020 + 0.00987303i
\(313\) −5.49415 + 9.51615i −0.310548 + 0.537884i −0.978481 0.206337i \(-0.933846\pi\)
0.667933 + 0.744221i \(0.267179\pi\)
\(314\) 2.09961 0.118488
\(315\) 30.4006 2.59454i 1.71288 0.146186i
\(316\) −1.55309 −0.0873680
\(317\) −13.0903 + 22.6731i −0.735225 + 1.27345i 0.219400 + 0.975635i \(0.429590\pi\)
−0.954625 + 0.297812i \(0.903743\pi\)
\(318\) −0.0836053 0.144809i −0.00468835 0.00812046i
\(319\) −3.72016 6.44350i −0.208289 0.360767i
\(320\) 13.9522 24.1660i 0.779954 1.35092i
\(321\) −2.85206 −0.159186
\(322\) 0.897571 0.0766031i 0.0500197 0.00426892i
\(323\) 4.07844 0.226930
\(324\) 8.23642 14.2659i 0.457579 0.792550i
\(325\) −5.23232 9.06264i −0.290237 0.502705i
\(326\) 0.232087 + 0.401986i 0.0128541 + 0.0222639i
\(327\) −1.61670 + 2.80020i −0.0894037 + 0.154852i
\(328\) −6.29079 −0.347351
\(329\) 5.36397 + 7.69534i 0.295725 + 0.424258i
\(330\) 0.900743 0.0495843
\(331\) 17.0466 29.5256i 0.936967 1.62287i 0.165878 0.986146i \(-0.446954\pi\)
0.771089 0.636728i \(-0.219712\pi\)
\(332\) −7.00964 12.1411i −0.384704 0.666327i
\(333\) 10.4750 + 18.1433i 0.574028 + 0.994246i
\(334\) 1.18161 2.04660i 0.0646546 0.111985i
\(335\) −49.8062 −2.72120
\(336\) −1.10063 + 2.34725i −0.0600440 + 0.128053i
\(337\) 14.7532 0.803657 0.401829 0.915715i \(-0.368375\pi\)
0.401829 + 0.915715i \(0.368375\pi\)
\(338\) 0.0978281 0.169443i 0.00532115 0.00921650i
\(339\) −0.214468 0.371470i −0.0116483 0.0201755i
\(340\) −8.79994 15.2419i −0.477244 0.826610i
\(341\) −12.6294 + 21.8747i −0.683918 + 1.18458i
\(342\) −1.02571 −0.0554639
\(343\) −17.9194 + 4.67910i −0.967558 + 0.252648i
\(344\) 5.28141 0.284754
\(345\) 0.888918 1.53965i 0.0478577 0.0828920i
\(346\) −1.89881 3.28884i −0.102081 0.176809i
\(347\) −14.9733 25.9345i −0.803809 1.39224i −0.917092 0.398675i \(-0.869470\pi\)
0.113284 0.993563i \(-0.463863\pi\)
\(348\) −0.420727 + 0.728720i −0.0225533 + 0.0390635i
\(349\) −13.4793 −0.721532 −0.360766 0.932656i \(-0.617485\pi\)
−0.360766 + 0.932656i \(0.617485\pi\)
\(350\) −2.29981 + 4.90468i −0.122930 + 0.262166i
\(351\) 1.54120 0.0822630
\(352\) 5.15572 8.92997i 0.274801 0.475969i
\(353\) −0.0817659 0.141623i −0.00435196 0.00753781i 0.863841 0.503764i \(-0.168052\pi\)
−0.868193 + 0.496226i \(0.834719\pi\)
\(354\) −0.114525 0.198364i −0.00608695 0.0105429i
\(355\) −18.7752 + 32.5195i −0.996482 + 1.72596i
\(356\) 22.1000 1.17130
\(357\) 0.896686 + 1.28642i 0.0474577 + 0.0680845i
\(358\) −2.86527 −0.151434
\(359\) −4.46065 + 7.72607i −0.235424 + 0.407766i −0.959396 0.282063i \(-0.908981\pi\)
0.723972 + 0.689830i \(0.242315\pi\)
\(360\) 4.46948 + 7.74136i 0.235562 + 0.408006i
\(361\) 7.90209 + 13.6868i 0.415900 + 0.720359i
\(362\) −0.924111 + 1.60061i −0.0485702 + 0.0841261i
\(363\) −2.41772 −0.126898
\(364\) 5.17142 0.441354i 0.271056 0.0231332i
\(365\) 4.24726 0.222312
\(366\) −0.191745 + 0.332112i −0.0100227 + 0.0173598i
\(367\) −18.3276 31.7443i −0.956693 1.65704i −0.730445 0.682971i \(-0.760687\pi\)
−0.226248 0.974070i \(-0.572646\pi\)
\(368\) −3.28185 5.68432i −0.171078 0.296316i
\(369\) −11.8997 + 20.6110i −0.619476 + 1.07296i
\(370\) −5.49679 −0.285765
\(371\) −8.67208 + 0.740117i −0.450232 + 0.0384250i
\(372\) 2.85660 0.148108
\(373\) −13.5637 + 23.4930i −0.702302 + 1.21642i 0.265355 + 0.964151i \(0.414511\pi\)
−0.967656 + 0.252271i \(0.918822\pi\)
\(374\) −1.00574 1.74199i −0.0520054 0.0900761i
\(375\) 2.79139 + 4.83483i 0.144147 + 0.249670i
\(376\) −1.37409 + 2.38000i −0.0708634 + 0.122739i
\(377\) 1.65110 0.0850360
\(378\) −0.456215 0.654502i −0.0234652 0.0336640i
\(379\) −15.8943 −0.816434 −0.408217 0.912885i \(-0.633849\pi\)
−0.408217 + 0.912885i \(0.633849\pi\)
\(380\) −6.89552 + 11.9434i −0.353733 + 0.612683i
\(381\) −0.583611 1.01084i −0.0298993 0.0517871i
\(382\) 1.22811 + 2.12715i 0.0628355 + 0.108834i
\(383\) −0.575394 + 0.996611i −0.0294013 + 0.0509245i −0.880352 0.474322i \(-0.842693\pi\)
0.850950 + 0.525246i \(0.176027\pi\)
\(384\) −1.54959 −0.0790774
\(385\) 19.9049 42.4502i 1.01445 2.16346i
\(386\) 1.83302 0.0932985
\(387\) 9.99038 17.3038i 0.507839 0.879604i
\(388\) −8.64484 14.9733i −0.438875 0.760154i
\(389\) 7.15651 + 12.3954i 0.362850 + 0.628474i 0.988429 0.151687i \(-0.0484705\pi\)
−0.625579 + 0.780161i \(0.715137\pi\)
\(390\) −0.0999432 + 0.173107i −0.00506082 + 0.00876560i
\(391\) −3.97013 −0.200778
\(392\) −3.47001 4.17132i −0.175262 0.210684i
\(393\) 3.28807 0.165861
\(394\) −0.745721 + 1.29163i −0.0375689 + 0.0650712i
\(395\) −1.55668 2.69625i −0.0783251 0.135663i
\(396\) −12.9618 22.4504i −0.651353 1.12818i
\(397\) 12.9588 22.4453i 0.650383 1.12650i −0.332647 0.943051i \(-0.607942\pi\)
0.983030 0.183445i \(-0.0587248\pi\)
\(398\) −2.64701 −0.132682
\(399\) 0.521656 1.11251i 0.0261154 0.0556950i
\(400\) 39.4703 1.97351
\(401\) 2.14816 3.72072i 0.107274 0.185804i −0.807391 0.590017i \(-0.799121\pi\)
0.914665 + 0.404213i \(0.132455\pi\)
\(402\) 0.321882 + 0.557517i 0.0160540 + 0.0278064i
\(403\) −2.80262 4.85427i −0.139608 0.241809i
\(404\) −14.0431 + 24.3233i −0.698669 + 1.21013i
\(405\) 33.0219 1.64087
\(406\) −0.488748 0.701175i −0.0242562 0.0347987i
\(407\) 32.1931 1.59575
\(408\) −0.229705 + 0.397861i −0.0113721 + 0.0196970i
\(409\) 12.3536 + 21.3970i 0.610844 + 1.05801i 0.991098 + 0.133131i \(0.0425030\pi\)
−0.380255 + 0.924882i \(0.624164\pi\)
\(410\) −3.12221 5.40782i −0.154195 0.267073i
\(411\) −1.20625 + 2.08929i −0.0595000 + 0.103057i
\(412\) 14.6975 0.724093
\(413\) −11.8793 + 1.01384i −0.584542 + 0.0498876i
\(414\) 0.998471 0.0490722
\(415\) 14.0517 24.3383i 0.689771 1.19472i
\(416\) 1.14412 + 1.98168i 0.0560951 + 0.0971596i
\(417\) −0.519577 0.899934i −0.0254438 0.0440699i
\(418\) −0.788083 + 1.36500i −0.0385464 + 0.0667643i
\(419\) −24.9293 −1.21787 −0.608937 0.793218i \(-0.708404\pi\)
−0.608937 + 0.793218i \(0.708404\pi\)
\(420\) −5.28323 + 0.450896i −0.257795 + 0.0220015i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −1.54563 + 2.67712i −0.0752402 + 0.130320i
\(423\) 5.19850 + 9.00407i 0.252760 + 0.437793i
\(424\) −1.27496 2.20830i −0.0619177 0.107245i
\(425\) 11.9371 20.6756i 0.579032 1.00291i
\(426\) 0.485352 0.0235154
\(427\) 11.4145 + 16.3757i 0.552388 + 0.792475i
\(428\) −21.5365 −1.04101
\(429\) 0.585339 1.01384i 0.0282604 0.0489485i
\(430\) 2.62124 + 4.54011i 0.126407 + 0.218944i
\(431\) 2.84426 + 4.92639i 0.137003 + 0.237296i 0.926361 0.376637i \(-0.122920\pi\)
−0.789358 + 0.613933i \(0.789586\pi\)
\(432\) −2.90653 + 5.03425i −0.139840 + 0.242211i
\(433\) 12.2598 0.589169 0.294584 0.955625i \(-0.404819\pi\)
0.294584 + 0.955625i \(0.404819\pi\)
\(434\) −1.23186 + 2.62712i −0.0591311 + 0.126106i
\(435\) −1.68680 −0.0808758
\(436\) −12.2080 + 21.1450i −0.584659 + 1.01266i
\(437\) 1.55547 + 2.69416i 0.0744084 + 0.128879i
\(438\) −0.0274487 0.0475426i −0.00131155 0.00227167i
\(439\) −2.51158 + 4.35019i −0.119871 + 0.207623i −0.919717 0.392583i \(-0.871582\pi\)
0.799845 + 0.600206i \(0.204915\pi\)
\(440\) 13.7361 0.654845
\(441\) −20.2307 + 3.47851i −0.963367 + 0.165643i
\(442\) 0.446372 0.0212317
\(443\) −0.289401 + 0.501258i −0.0137499 + 0.0238155i −0.872818 0.488045i \(-0.837710\pi\)
0.859069 + 0.511860i \(0.171044\pi\)
\(444\) −1.82042 3.15307i −0.0863935 0.149638i
\(445\) 22.1511 + 38.3668i 1.05006 + 1.81876i
\(446\) 2.19856 3.80801i 0.104105 0.180315i
\(447\) 3.93966 0.186339
\(448\) −7.97036 + 16.9980i −0.376564 + 0.803078i
\(449\) −7.36359 −0.347509 −0.173755 0.984789i \(-0.555590\pi\)
−0.173755 + 0.984789i \(0.555590\pi\)
\(450\) −3.00212 + 5.19982i −0.141521 + 0.245122i
\(451\) 18.2859 + 31.6720i 0.861048 + 1.49138i
\(452\) −1.61950 2.80505i −0.0761748 0.131939i
\(453\) 0.667862 1.15677i 0.0313789 0.0543499i
\(454\) 1.80052 0.0845028
\(455\) 5.94959 + 8.53550i 0.278921 + 0.400150i
\(456\) 0.359988 0.0168580
\(457\) −3.95912 + 6.85739i −0.185200 + 0.320775i −0.943644 0.330963i \(-0.892627\pi\)
0.758444 + 0.651738i \(0.225960\pi\)
\(458\) 1.49601 + 2.59117i 0.0699040 + 0.121077i
\(459\) 1.75805 + 3.04503i 0.0820588 + 0.142130i
\(460\) 6.71241 11.6262i 0.312968 0.542076i
\(461\) −9.53600 −0.444136 −0.222068 0.975031i \(-0.571281\pi\)
−0.222068 + 0.975031i \(0.571281\pi\)
\(462\) −0.603816 + 0.0515325i −0.0280920 + 0.00239751i
\(463\) 2.16049 0.100406 0.0502032 0.998739i \(-0.484013\pi\)
0.0502032 + 0.998739i \(0.484013\pi\)
\(464\) −3.11379 + 5.39325i −0.144554 + 0.250375i
\(465\) 2.86321 + 4.95923i 0.132778 + 0.229979i
\(466\) −0.788083 1.36500i −0.0365072 0.0632324i
\(467\) 4.05950 7.03126i 0.187851 0.325368i −0.756682 0.653783i \(-0.773181\pi\)
0.944534 + 0.328415i \(0.106514\pi\)
\(468\) 5.75276 0.265921
\(469\) 33.3877 2.84947i 1.54170 0.131576i
\(470\) −2.72792 −0.125830
\(471\) −1.39391 + 2.41433i −0.0642281 + 0.111246i
\(472\) −1.74649 3.02500i −0.0803885 0.139237i
\(473\) −15.3518 26.5901i −0.705878 1.22262i
\(474\) −0.0201207 + 0.0348501i −0.000924174 + 0.00160072i
\(475\) −18.7074 −0.858357
\(476\) 6.77107 + 9.71402i 0.310352 + 0.445241i
\(477\) −9.64694 −0.441703
\(478\) 2.12540 3.68129i 0.0972133 0.168378i
\(479\) −7.27663 12.6035i −0.332478 0.575868i 0.650519 0.759490i \(-0.274551\pi\)
−0.982997 + 0.183621i \(0.941218\pi\)
\(480\) −1.16886 2.02452i −0.0533508 0.0924063i
\(481\) −3.57204 + 6.18695i −0.162871 + 0.282101i
\(482\) 4.01056 0.182676
\(483\) −0.507803 + 1.08297i −0.0231058 + 0.0492766i
\(484\) −18.2567 −0.829852
\(485\) 17.3297 30.0158i 0.786899 1.36295i
\(486\) −0.665728 1.15307i −0.0301980 0.0523045i
\(487\) 16.6295 + 28.8031i 0.753554 + 1.30519i 0.946090 + 0.323904i \(0.104995\pi\)
−0.192536 + 0.981290i \(0.561671\pi\)
\(488\) −2.92407 + 5.06464i −0.132366 + 0.229265i
\(489\) −0.616320 −0.0278710
\(490\) 1.86362 5.05324i 0.0841899 0.228282i
\(491\) −22.5563 −1.01795 −0.508977 0.860780i \(-0.669976\pi\)
−0.508977 + 0.860780i \(0.669976\pi\)
\(492\) 2.06802 3.58191i 0.0932335 0.161485i
\(493\) 1.88342 + 3.26218i 0.0848249 + 0.146921i
\(494\) −0.174886 0.302911i −0.00786848 0.0136286i
\(495\) 25.9835 45.0047i 1.16787 2.02281i
\(496\) 21.1417 0.949290
\(497\) 10.7255 22.8737i 0.481104 1.02603i
\(498\) −0.363248 −0.0162775
\(499\) 5.69271 9.86007i 0.254841 0.441397i −0.710011 0.704190i \(-0.751310\pi\)
0.964852 + 0.262793i \(0.0846436\pi\)
\(500\) 21.0784 + 36.5089i 0.942655 + 1.63273i
\(501\) 1.56891 + 2.71743i 0.0700938 + 0.121406i
\(502\) 0.255205 0.442028i 0.0113904 0.0197287i
\(503\) −8.81825 −0.393186 −0.196593 0.980485i \(-0.562988\pi\)
−0.196593 + 0.980485i \(0.562988\pi\)
\(504\) −3.43902 4.93374i −0.153186 0.219766i
\(505\) −56.3022 −2.50541
\(506\) 0.767156 1.32875i 0.0341042 0.0590702i
\(507\) 0.129894 + 0.224983i 0.00576880 + 0.00999186i
\(508\) −4.40697 7.63310i −0.195528 0.338664i
\(509\) −9.64188 + 16.7002i −0.427369 + 0.740225i −0.996638 0.0819263i \(-0.973893\pi\)
0.569269 + 0.822151i \(0.307226\pi\)
\(510\) −0.456023 −0.0201930
\(511\) −2.84716 + 0.242991i −0.125951 + 0.0107493i
\(512\) −14.4780 −0.639844
\(513\) 1.37759 2.38605i 0.0608219 0.105347i
\(514\) −0.880136 1.52444i −0.0388211 0.0672402i
\(515\) 14.7315 + 25.5156i 0.649146 + 1.12435i
\(516\) −1.73620 + 3.00718i −0.0764318 + 0.132384i
\(517\) 15.9767 0.702653
\(518\) 3.68479 0.314478i 0.161900 0.0138174i
\(519\) 5.04241 0.221337
\(520\) −1.52411 + 2.63984i −0.0668368 + 0.115765i
\(521\) −12.5584 21.7518i −0.550193 0.952963i −0.998260 0.0589629i \(-0.981221\pi\)
0.448067 0.894000i \(-0.352113\pi\)
\(522\) −0.473671 0.820422i −0.0207320 0.0359089i
\(523\) 14.9824 25.9503i 0.655134 1.13473i −0.326726 0.945119i \(-0.605946\pi\)
0.981860 0.189606i \(-0.0607212\pi\)
\(524\) 24.8289 1.08466
\(525\) −4.11303 5.90069i −0.179507 0.257527i
\(526\) −0.280556 −0.0122328
\(527\) 6.39391 11.0746i 0.278523 0.482416i
\(528\) 2.20777 + 3.82397i 0.0960808 + 0.166417i
\(529\) 9.98583 + 17.2960i 0.434167 + 0.751999i
\(530\) 1.26556 2.19202i 0.0549726 0.0952153i
\(531\) −13.2147 −0.573469
\(532\) 3.93913 8.40078i 0.170783 0.364220i
\(533\) −8.11574 −0.351532
\(534\) 0.286311 0.495906i 0.0123899 0.0214599i
\(535\) −21.5863 37.3886i −0.933257 1.61645i
\(536\) 4.90864 + 8.50201i 0.212021 + 0.367231i
\(537\) 1.90222 3.29474i 0.0820869 0.142179i
\(538\) 1.59818 0.0689026
\(539\) −10.9147 + 29.5954i −0.470130 + 1.27476i
\(540\) −11.8895 −0.511644
\(541\) −2.54987 + 4.41650i −0.109627 + 0.189880i −0.915619 0.402046i \(-0.868299\pi\)
0.805992 + 0.591926i \(0.201632\pi\)
\(542\) −0.0207706 0.0359757i −0.000892173 0.00154529i
\(543\) −1.22702 2.12525i −0.0526563 0.0912034i
\(544\) −2.61021 + 4.52101i −0.111912 + 0.193837i
\(545\) −48.9451 −2.09658
\(546\) 0.0570936 0.121760i 0.00244338 0.00521087i
\(547\) 2.92025 0.124861 0.0624305 0.998049i \(-0.480115\pi\)
0.0624305 + 0.998049i \(0.480115\pi\)
\(548\) −9.10867 + 15.7767i −0.389103 + 0.673946i
\(549\) 11.0624 + 19.1607i 0.472132 + 0.817757i
\(550\) 4.61323 + 7.99035i 0.196709 + 0.340710i
\(551\) 1.47582 2.55620i 0.0628722 0.108898i
\(552\) −0.350428 −0.0149152
\(553\) 1.19778 + 1.71838i 0.0509348 + 0.0730728i
\(554\) −4.49519 −0.190982
\(555\) 3.64927 6.32071i 0.154903 0.268299i
\(556\) −3.92344 6.79559i −0.166391 0.288197i
\(557\) −12.9937 22.5058i −0.550561 0.953600i −0.998234 0.0594024i \(-0.981080\pi\)
0.447673 0.894197i \(-0.352253\pi\)
\(558\) −1.60804 + 2.78521i −0.0680738 + 0.117907i
\(559\) 6.81353 0.288182
\(560\) −39.1011 + 3.33708i −1.65232 + 0.141017i
\(561\) 2.67079 0.112761
\(562\) −0.0337730 + 0.0584965i −0.00142463 + 0.00246753i
\(563\) −1.82534 3.16159i −0.0769291 0.133245i 0.824994 0.565141i \(-0.191178\pi\)
−0.901924 + 0.431896i \(0.857845\pi\)
\(564\) −0.903431 1.56479i −0.0380413 0.0658895i
\(565\) 3.24649 5.62308i 0.136581 0.236565i
\(566\) 5.66845 0.238263
\(567\) −22.1363 + 1.88922i −0.929637 + 0.0793397i
\(568\) 7.40152 0.310561
\(569\) 12.6766 21.9566i 0.531432 0.920468i −0.467895 0.883784i \(-0.654987\pi\)
0.999327 0.0366835i \(-0.0116793\pi\)
\(570\) 0.178667 + 0.309460i 0.00748353 + 0.0129619i
\(571\) −13.8626 24.0108i −0.580133 1.00482i −0.995463 0.0951493i \(-0.969667\pi\)
0.415330 0.909671i \(-0.363666\pi\)
\(572\) 4.42002 7.65570i 0.184810 0.320101i
\(573\) −3.26132 −0.136244
\(574\) 2.40237 + 3.44652i 0.100273 + 0.143855i
\(575\) 18.2107 0.759438
\(576\) −10.4043 + 18.0208i −0.433513 + 0.750867i
\(577\) −19.7877 34.2733i −0.823773 1.42682i −0.902854 0.429948i \(-0.858532\pi\)
0.0790809 0.996868i \(-0.474801\pi\)
\(578\) −1.15390 1.99861i −0.0479959 0.0831313i
\(579\) −1.21693 + 2.10778i −0.0505737 + 0.0875963i
\(580\) −12.7374 −0.528891
\(581\) −8.02717 + 17.1191i −0.333023 + 0.710221i
\(582\) −0.447985 −0.0185696
\(583\) −7.41204 + 12.8380i −0.306975 + 0.531697i
\(584\) −0.418588 0.725015i −0.0173213 0.0300013i
\(585\) 5.76606 + 9.98711i 0.238397 + 0.412916i
\(586\) 3.08576 5.34470i 0.127472 0.220787i
\(587\) −8.24177 −0.340174 −0.170087 0.985429i \(-0.554405\pi\)
−0.170087 + 0.985429i \(0.554405\pi\)
\(588\) 3.51583 0.604519i 0.144990 0.0249299i
\(589\) −10.0204 −0.412882
\(590\) 1.73361 3.00270i 0.0713716 0.123619i
\(591\) −0.990153 1.71500i −0.0407295 0.0705455i
\(592\) −13.4729 23.3358i −0.553734 0.959095i
\(593\) 5.96149 10.3256i 0.244809 0.424021i −0.717269 0.696796i \(-0.754608\pi\)
0.962078 + 0.272775i \(0.0879415\pi\)
\(594\) −1.35884 −0.0557540
\(595\) −10.0774 + 21.4914i −0.413131 + 0.881063i
\(596\) 29.7492 1.21857
\(597\) 1.75732 3.04377i 0.0719224 0.124573i
\(598\) 0.170242 + 0.294867i 0.00696170 + 0.0120580i
\(599\) 17.8079 + 30.8442i 0.727611 + 1.26026i 0.957890 + 0.287135i \(0.0927027\pi\)
−0.230279 + 0.973125i \(0.573964\pi\)
\(600\) 1.05364 1.82495i 0.0430146 0.0745034i
\(601\) 38.9252 1.58779 0.793896 0.608054i \(-0.208050\pi\)
0.793896 + 0.608054i \(0.208050\pi\)
\(602\) −2.01690 2.89351i −0.0822026 0.117931i
\(603\) 37.1410 1.51250
\(604\) 5.04317 8.73503i 0.205204 0.355423i
\(605\) −18.2990 31.6947i −0.743959 1.28857i
\(606\) 0.363864 + 0.630231i 0.0147810 + 0.0256014i
\(607\) 6.84828 11.8616i 0.277963 0.481446i −0.692915 0.721019i \(-0.743674\pi\)
0.970878 + 0.239573i \(0.0770074\pi\)
\(608\) 4.09065 0.165898
\(609\) 1.13075 0.0965037i 0.0458203 0.00391053i
\(610\) −5.80502 −0.235039
\(611\) −1.77271 + 3.07043i −0.0717163 + 0.124216i
\(612\) 6.56220 + 11.3661i 0.265261 + 0.459446i
\(613\) −1.58056 2.73761i −0.0638382 0.110571i 0.832340 0.554266i \(-0.187001\pi\)
−0.896178 + 0.443695i \(0.853667\pi\)
\(614\) −1.77990 + 3.08287i −0.0718308 + 0.124415i
\(615\) 8.29120 0.334334
\(616\) −9.20806 + 0.785860i −0.371003 + 0.0316632i
\(617\) 20.9297 0.842597 0.421299 0.906922i \(-0.361574\pi\)
0.421299 + 0.906922i \(0.361574\pi\)
\(618\) 0.190410 0.329800i 0.00765941 0.0132665i
\(619\) −15.4772 26.8073i −0.622082 1.07748i −0.989097 0.147262i \(-0.952954\pi\)
0.367016 0.930215i \(-0.380379\pi\)
\(620\) 21.6207 + 37.4482i 0.868309 + 1.50396i
\(621\) −1.34100 + 2.32269i −0.0538127 + 0.0932063i
\(622\) 0.0736887 0.00295465
\(623\) −17.0440 24.4520i −0.682855 0.979648i
\(624\) −0.979864 −0.0392260
\(625\) −16.0927 + 27.8734i −0.643708 + 1.11494i
\(626\) 1.07496 + 1.86189i 0.0429642 + 0.0744162i
\(627\) −1.04640 1.81242i −0.0417892 0.0723810i
\(628\) −10.5257 + 18.2311i −0.420023 + 0.727501i
\(629\) −16.2986 −0.649866
\(630\) 2.53441 5.40500i 0.100973 0.215340i
\(631\) −15.1218 −0.601988 −0.300994 0.953626i \(-0.597318\pi\)
−0.300994 + 0.953626i \(0.597318\pi\)
\(632\) −0.306836 + 0.531456i −0.0122053 + 0.0211402i
\(633\) −2.05226 3.55462i −0.0815700 0.141283i
\(634\) 2.56120 + 4.43613i 0.101718 + 0.176181i
\(635\) 8.83433 15.3015i 0.350580 0.607222i
\(636\) 1.67651 0.0664780
\(637\) −4.47665 5.38141i −0.177371 0.213219i
\(638\) −1.45574 −0.0576335
\(639\) 14.0008 24.2501i 0.553864 0.959320i
\(640\) −11.7284 20.3141i −0.463605 0.802987i
\(641\) 23.6207 + 40.9123i 0.932962 + 1.61594i 0.778229 + 0.627981i \(0.216118\pi\)
0.154733 + 0.987956i \(0.450548\pi\)
\(642\) −0.279011 + 0.483262i −0.0110117 + 0.0190728i
\(643\) 39.9249 1.57448 0.787241 0.616645i \(-0.211509\pi\)
0.787241 + 0.616645i \(0.211509\pi\)
\(644\) −3.83453 + 8.17770i −0.151102 + 0.322247i
\(645\) −6.96085 −0.274083
\(646\) 0.398986 0.691064i 0.0156979 0.0271895i
\(647\) 14.9139 + 25.8317i 0.586327 + 1.01555i 0.994709 + 0.102736i \(0.0327598\pi\)
−0.408382 + 0.912811i \(0.633907\pi\)
\(648\) −3.25446 5.63689i −0.127847 0.221438i
\(649\) −10.1533 + 17.5859i −0.398550 + 0.690309i
\(650\) −2.04747 −0.0803084
\(651\) −2.20308 3.16062i −0.0863456 0.123875i
\(652\) −4.65397 −0.182263
\(653\) −12.5774 + 21.7848i −0.492194 + 0.852504i −0.999960 0.00899079i \(-0.997138\pi\)
0.507766 + 0.861495i \(0.330471\pi\)
\(654\) 0.316317 + 0.547878i 0.0123690 + 0.0214237i
\(655\) 24.8863 + 43.1044i 0.972390 + 1.68423i
\(656\) 15.3054 26.5097i 0.597574 1.03503i
\(657\) −3.16722 −0.123565
\(658\) 1.82867 0.156068i 0.0712890 0.00608415i
\(659\) 17.3155 0.674517 0.337258 0.941412i \(-0.390500\pi\)
0.337258 + 0.941412i \(0.390500\pi\)
\(660\) −4.51558 + 7.82122i −0.175769 + 0.304441i
\(661\) 4.60037 + 7.96808i 0.178934 + 0.309922i 0.941516 0.336969i \(-0.109402\pi\)
−0.762582 + 0.646892i \(0.776069\pi\)
\(662\) −3.33528 5.77687i −0.129629 0.224524i
\(663\) −0.296342 + 0.513279i −0.0115090 + 0.0199341i
\(664\) −5.53945 −0.214972
\(665\) 18.5325 1.58165i 0.718659 0.0613338i
\(666\) 4.09901 0.158833
\(667\) −1.43663 + 2.48832i −0.0556266 + 0.0963482i
\(668\) 11.8472 + 20.5199i 0.458382 + 0.793940i
\(669\) 2.91920 + 5.05620i 0.112863 + 0.195484i
\(670\) −4.87245 + 8.43933i −0.188239 + 0.326040i
\(671\) 33.9984 1.31249
\(672\) 0.899372 + 1.29027i 0.0346940 + 0.0497733i
\(673\) 17.3609 0.669212 0.334606 0.942358i \(-0.391397\pi\)
0.334606 + 0.942358i \(0.391397\pi\)
\(674\) 1.44328 2.49983i 0.0555930 0.0962898i
\(675\) −8.06403 13.9673i −0.310385 0.537602i
\(676\) 0.980859 + 1.69890i 0.0377254 + 0.0653422i
\(677\) −24.9913 + 43.2861i −0.960492 + 1.66362i −0.239225 + 0.970964i \(0.576893\pi\)
−0.721267 + 0.692657i \(0.756440\pi\)
\(678\) −0.0839242 −0.00322309
\(679\) −9.89974 + 21.1126i −0.379917 + 0.810229i
\(680\) −6.95425 −0.266683
\(681\) −1.19535 + 2.07041i −0.0458059 + 0.0793382i
\(682\) 2.47101 + 4.27992i 0.0946200 + 0.163887i
\(683\) −16.8077 29.1117i −0.643128 1.11393i −0.984731 0.174086i \(-0.944303\pi\)
0.341603 0.939844i \(-0.389030\pi\)
\(684\) 5.14205 8.90630i 0.196611 0.340541i
\(685\) −36.5189 −1.39532
\(686\) −0.960183 + 3.49408i −0.0366599 + 0.133404i
\(687\) −3.97274 −0.151570
\(688\) −12.8496 + 22.2561i −0.489885 + 0.848506i
\(689\) −1.64483 2.84892i −0.0626629 0.108535i
\(690\) −0.173922 0.301242i −0.00662111 0.0114681i
\(691\) 7.56545 13.1038i 0.287803 0.498490i −0.685482 0.728090i \(-0.740408\pi\)
0.973285 + 0.229600i \(0.0737417\pi\)
\(692\) 38.0764 1.44745
\(693\) −14.8433 + 31.6555i −0.563851 + 1.20249i
\(694\) −5.85924 −0.222414
\(695\) 7.86502 13.6226i 0.298337 0.516735i
\(696\) 0.166242 + 0.287940i 0.00630139 + 0.0109143i
\(697\) −9.25766 16.0347i −0.350659 0.607359i
\(698\) −1.31866 + 2.28398i −0.0499119 + 0.0864500i
\(699\) 2.09280 0.0791570
\(700\) −31.0583 44.5574i −1.17390 1.68411i
\(701\) 2.02467 0.0764705 0.0382353 0.999269i \(-0.487826\pi\)
0.0382353 + 0.999269i \(0.487826\pi\)
\(702\) 0.150772 0.261146i 0.00569054 0.00985630i
\(703\) 6.38567 + 11.0603i 0.240840 + 0.417147i
\(704\) 15.9879 + 27.6919i 0.602567 + 1.04368i
\(705\) 1.81104 3.13681i 0.0682077 0.118139i
\(706\) −0.0319960 −0.00120419
\(707\) 37.7423 3.22111i 1.41945 0.121142i
\(708\) 2.29654 0.0863093
\(709\) 15.2276 26.3751i 0.571886 0.990536i −0.424486 0.905434i \(-0.639545\pi\)
0.996372 0.0851015i \(-0.0271215\pi\)
\(710\) 3.67348 + 6.36265i 0.137863 + 0.238786i
\(711\) 1.16083 + 2.01062i 0.0435346 + 0.0754041i
\(712\) 4.36619 7.56246i 0.163630 0.283415i
\(713\) 9.75429 0.365301
\(714\) 0.305696 0.0260896i 0.0114404 0.000976378i
\(715\) 17.7210 0.662727
\(716\) 14.3641 24.8793i 0.536811 0.929784i
\(717\) 2.82206 + 4.88795i 0.105392 + 0.182544i
\(718\) 0.872754 + 1.51165i 0.0325709 + 0.0564144i
\(719\) 12.2123 21.1523i 0.455442 0.788848i −0.543272 0.839557i \(-0.682815\pi\)
0.998713 + 0.0507089i \(0.0161481\pi\)
\(720\) −43.4966 −1.62102
\(721\) −11.3351 16.2617i −0.422139 0.605616i
\(722\) 3.09219 0.115079
\(723\) −2.66257 + 4.61170i −0.0990220 + 0.171511i
\(724\) −9.26547 16.0483i −0.344348 0.596429i
\(725\) −8.63908 14.9633i −0.320848 0.555724i
\(726\) −0.236521 + 0.409667i −0.00877813 + 0.0152042i
\(727\) −3.09307 −0.114716 −0.0573578 0.998354i \(-0.518268\pi\)
−0.0573578 + 0.998354i \(0.518268\pi\)
\(728\) 0.870665 1.85682i 0.0322690 0.0688184i
\(729\) −23.4236 −0.867539
\(730\) 0.415501 0.719670i 0.0153784 0.0266362i
\(731\) 7.77223 + 13.4619i 0.287466 + 0.497906i
\(732\) −1.92250 3.32987i −0.0710577 0.123076i
\(733\) 4.20713 7.28697i 0.155394 0.269150i −0.777808 0.628501i \(-0.783669\pi\)
0.933202 + 0.359351i \(0.117002\pi\)
\(734\) −7.17182 −0.264717
\(735\) 4.57344 + 5.49776i 0.168694 + 0.202788i
\(736\) −3.98203 −0.146779
\(737\) 28.5365 49.4267i 1.05116 1.82066i
\(738\) 2.32826 + 4.03266i 0.0857044 + 0.148444i
\(739\) 3.61379 + 6.25927i 0.132936 + 0.230251i 0.924807 0.380437i \(-0.124226\pi\)
−0.791871 + 0.610688i \(0.790893\pi\)
\(740\) 27.5564 47.7291i 1.01299 1.75456i
\(741\) 0.464419 0.0170609
\(742\) −0.722966 + 1.54183i −0.0265409 + 0.0566024i
\(743\) −53.9092 −1.97774 −0.988869 0.148791i \(-0.952462\pi\)
−0.988869 + 0.148791i \(0.952462\pi\)
\(744\) 0.564366 0.977510i 0.0206907 0.0358373i
\(745\) 29.8180 + 51.6463i 1.09245 + 1.89217i
\(746\) 2.65382 + 4.59656i 0.0971634 + 0.168292i
\(747\) −10.4785 + 18.1493i −0.383388 + 0.664047i
\(748\) 20.1678 0.737406
\(749\) 16.6095 + 23.8285i 0.606897 + 0.870676i
\(750\) 1.09231 0.0398854
\(751\) −14.6221 + 25.3262i −0.533568 + 0.924168i 0.465663 + 0.884962i \(0.345816\pi\)
−0.999231 + 0.0392053i \(0.987517\pi\)
\(752\) −6.68628 11.5810i −0.243824 0.422315i
\(753\) 0.338856 + 0.586916i 0.0123486 + 0.0213884i
\(754\) 0.161524 0.279768i 0.00588236 0.0101885i
\(755\) 20.2193 0.735857
\(756\) 7.97018 0.680214i 0.289873 0.0247391i
\(757\) −22.0597 −0.801773 −0.400887 0.916128i \(-0.631298\pi\)
−0.400887 + 0.916128i \(0.631298\pi\)
\(758\) −1.55491 + 2.69318i −0.0564768 + 0.0978206i
\(759\) 1.01861 + 1.76429i 0.0369733 + 0.0640397i
\(760\) 2.72463 + 4.71920i 0.0988328 + 0.171183i
\(761\) −8.90805 + 15.4292i −0.322917 + 0.559308i −0.981089 0.193560i \(-0.937997\pi\)
0.658172 + 0.752868i \(0.271330\pi\)
\(762\) −0.228374 −0.00827313
\(763\) 32.8105 2.80020i 1.18782 0.101374i
\(764\) −24.6269 −0.890971
\(765\) −13.1547 + 22.7847i −0.475611 + 0.823782i
\(766\) 0.112579 + 0.194993i 0.00406766 + 0.00704539i
\(767\) −2.25314 3.90255i −0.0813561 0.140913i
\(768\) 1.69182 2.93033i 0.0610485 0.105739i
\(769\) −11.3069 −0.407738 −0.203869 0.978998i \(-0.565352\pi\)
−0.203869 + 0.978998i \(0.565352\pi\)
\(770\) −5.24564 7.52559i −0.189040 0.271203i
\(771\) 2.33725 0.0841741
\(772\) −9.18927 + 15.9163i −0.330729 + 0.572840i
\(773\) 0.964104 + 1.66988i 0.0346764 + 0.0600613i 0.882843 0.469669i \(-0.155627\pi\)
−0.848166 + 0.529730i \(0.822293\pi\)
\(774\) −1.95468 3.38561i −0.0702595 0.121693i
\(775\) −29.3284 + 50.7982i −1.05351 + 1.82472i
\(776\) −6.83168 −0.245243
\(777\) −2.08468 + 4.44588i −0.0747875 + 0.159495i
\(778\) 2.80043 0.100400
\(779\) −7.25418 + 12.5646i −0.259908 + 0.450174i
\(780\) −1.00207 1.73563i −0.0358797 0.0621455i
\(781\) −21.5145 37.2642i −0.769849 1.33342i
\(782\) −0.388391 + 0.672713i −0.0138888 + 0.0240562i
\(783\) 2.54467 0.0909392
\(784\) 26.0206 4.47404i 0.929307 0.159787i
\(785\) −42.2003 −1.50619
\(786\) 0.321666 0.557141i 0.0114734 0.0198726i
\(787\) −2.76577 4.79046i −0.0985892 0.170761i 0.812512 0.582945i \(-0.198100\pi\)
−0.911101 + 0.412183i \(0.864766\pi\)
\(788\) −7.47686 12.9503i −0.266352 0.461335i
\(789\) 0.186258 0.322609i 0.00663097 0.0114852i
\(790\) −0.609148 −0.0216725
\(791\) −1.85459 + 3.95518i −0.0659415 + 0.140630i
\(792\) −10.2432 −0.363975
\(793\) −3.77234 + 6.53388i −0.133960 + 0.232025i
\(794\) −2.53547 4.39156i −0.0899804 0.155851i
\(795\) 1.68039 + 2.91052i 0.0595973 + 0.103225i
\(796\) 13.2699 22.9842i 0.470340 0.814652i
\(797\) −13.8038 −0.488955 −0.244477 0.969655i \(-0.578616\pi\)
−0.244477 + 0.969655i \(0.578616\pi\)
\(798\) −0.137474 0.197226i −0.00486654 0.00698171i
\(799\) −8.08857 −0.286153
\(800\) 11.9728 20.7375i 0.423303 0.733182i
\(801\) −16.5183 28.6105i −0.583644 1.01090i
\(802\) −0.420300 0.727982i −0.0148413 0.0257059i
\(803\) −2.43347 + 4.21490i −0.0858754 + 0.148741i
\(804\) −6.45461 −0.227637
\(805\) −18.0404 + 1.53965i −0.635839 + 0.0542656i
\(806\) −1.09670 −0.0386296
\(807\) −1.06102 + 1.83774i −0.0373496 + 0.0646914i
\(808\) 5.54885 + 9.61088i 0.195208 + 0.338110i
\(809\) −14.1498 24.5082i −0.497480 0.861661i 0.502515 0.864568i \(-0.332408\pi\)
−0.999996 + 0.00290700i \(0.999075\pi\)
\(810\) 3.23047 5.59533i 0.113507 0.196600i
\(811\) −12.2124 −0.428837 −0.214418 0.976742i \(-0.568786\pi\)
−0.214418 + 0.976742i \(0.568786\pi\)
\(812\) 8.53854 0.728720i 0.299644 0.0255731i
\(813\) 0.0551575 0.00193446
\(814\) 3.14940 5.45491i 0.110386 0.191195i
\(815\) −4.66473 8.07955i −0.163398 0.283014i
\(816\) −1.11774 1.93597i −0.0391286 0.0677727i
\(817\) 6.09022 10.5486i 0.213070 0.369048i
\(818\) 4.83410 0.169020
\(819\) −4.43667 6.36500i −0.155030 0.222411i
\(820\) 62.6087 2.18639
\(821\) 20.7005 35.8544i 0.722453 1.25133i −0.237560 0.971373i \(-0.576348\pi\)
0.960014 0.279953i \(-0.0903189\pi\)
\(822\) 0.236011 + 0.408782i 0.00823182 + 0.0142579i
\(823\) −23.5876 40.8550i −0.822213 1.42411i −0.904031 0.427467i \(-0.859406\pi\)
0.0818184 0.996647i \(-0.473927\pi\)
\(824\) 2.90371 5.02938i 0.101156 0.175207i
\(825\) −12.2507 −0.426515
\(826\) −0.990341 + 2.11205i −0.0344584 + 0.0734876i
\(827\) 21.1124 0.734150 0.367075 0.930191i \(-0.380359\pi\)
0.367075 + 0.930191i \(0.380359\pi\)
\(828\) −5.00551 + 8.66980i −0.173953 + 0.301296i
\(829\) 0.318376 + 0.551444i 0.0110577 + 0.0191524i 0.871501 0.490393i \(-0.163147\pi\)
−0.860444 + 0.509546i \(0.829813\pi\)
\(830\) −2.74930 4.76193i −0.0954297 0.165289i
\(831\) 2.98431 5.16898i 0.103525 0.179310i
\(832\) −7.09585 −0.246004
\(833\) 5.52583 14.9834i 0.191459 0.519143i
\(834\) −0.203317 −0.00704029
\(835\) −23.7492 + 41.1348i −0.821874 + 1.42353i
\(836\) −7.90160 13.6860i −0.273282 0.473339i
\(837\) −4.31938 7.48139i −0.149300 0.258595i
\(838\) −2.43878 + 4.22410i −0.0842464 + 0.145919i
\(839\) −26.9432 −0.930183 −0.465092 0.885263i \(-0.653979\pi\)
−0.465092 + 0.885263i \(0.653979\pi\)
\(840\) −0.889489 + 1.89697i −0.0306903 + 0.0654516i
\(841\) −26.2739 −0.905995
\(842\) −0.978281 + 1.69443i −0.0337138 + 0.0583940i
\(843\) −0.0448431 0.0776705i −0.00154448 0.00267511i
\(844\) −15.4971 26.8417i −0.533431 0.923929i
\(845\) −1.96625 + 3.40565i −0.0676412 + 0.117158i
\(846\) 2.03424 0.0699386
\(847\) 14.0800 + 20.1997i 0.483796 + 0.694071i
\(848\) 12.4078 0.426087
\(849\) −3.76323 + 6.51810i −0.129154 + 0.223701i
\(850\) −2.33556 4.04531i −0.0801090 0.138753i
\(851\) −6.21610 10.7666i −0.213085 0.369074i
\(852\) −2.43316 + 4.21435i −0.0833586 + 0.144381i
\(853\) 6.74784 0.231042 0.115521 0.993305i \(-0.463146\pi\)
0.115521 + 0.993305i \(0.463146\pi\)
\(854\) 3.89141 0.332112i 0.133161 0.0113646i
\(855\) 20.6158 0.705045
\(856\) −4.25486 + 7.36964i −0.145428 + 0.251889i
\(857\) 22.5134 + 38.9943i 0.769043 + 1.33202i 0.938082 + 0.346412i \(0.112600\pi\)
−0.169040 + 0.985609i \(0.554067\pi\)
\(858\) −0.114525 0.198364i −0.00390983 0.00677202i
\(859\) 18.3635 31.8065i 0.626554 1.08522i −0.361684 0.932301i \(-0.617798\pi\)
0.988238 0.152923i \(-0.0488687\pi\)
\(860\) −52.5629 −1.79238
\(861\) −5.55803 + 0.474349i −0.189417 + 0.0161658i
\(862\) 1.11299 0.0379087
\(863\) 21.7137 37.6093i 0.739144 1.28024i −0.213737 0.976891i \(-0.568563\pi\)
0.952881 0.303344i \(-0.0981032\pi\)
\(864\) 1.76332 + 3.05415i 0.0599892 + 0.103904i
\(865\) 38.1644 + 66.1027i 1.29763 + 2.24756i
\(866\) 1.19935 2.07734i 0.0407557 0.0705910i
\(867\) 3.06425 0.104067
\(868\) −16.6360 23.8665i −0.564661 0.810083i
\(869\) 3.56761 0.121023
\(870\) −0.165016 + 0.285817i −0.00559458 + 0.00969010i
\(871\) 6.33263 + 10.9684i 0.214573 + 0.371651i
\(872\) 4.82377 + 8.35502i 0.163354 + 0.282937i
\(873\) −12.9229 + 22.3831i −0.437373 + 0.757553i
\(874\) 0.608676 0.0205888
\(875\) 24.1382 51.4782i 0.816020 1.74028i
\(876\) 0.550422 0.0185970
\(877\) −20.0040 + 34.6480i −0.675488 + 1.16998i 0.300838 + 0.953675i \(0.402734\pi\)
−0.976326 + 0.216304i \(0.930600\pi\)
\(878\) 0.491407 + 0.851142i 0.0165842 + 0.0287247i
\(879\) 4.09721 + 7.09658i 0.138196 + 0.239362i
\(880\) −33.4198 + 57.8847i −1.12658 + 1.95129i
\(881\) 35.4308 1.19370 0.596848 0.802355i \(-0.296420\pi\)
0.596848 + 0.802355i \(0.296420\pi\)
\(882\) −1.38972 + 3.76825i −0.0467944 + 0.126884i
\(883\) 22.6654 0.762751 0.381375 0.924420i \(-0.375451\pi\)
0.381375 + 0.924420i \(0.375451\pi\)
\(884\) −2.23774 + 3.87588i −0.0752634 + 0.130360i
\(885\) 2.30185 + 3.98692i 0.0773759 + 0.134019i
\(886\) 0.0566232 + 0.0980742i 0.00190229 + 0.00329487i
\(887\) −22.3440 + 38.7010i −0.750240 + 1.29945i 0.197467 + 0.980310i \(0.436729\pi\)
−0.947706 + 0.319144i \(0.896605\pi\)
\(888\) −1.43861 −0.0482766
\(889\) −5.04670 + 10.7628i −0.169261 + 0.360974i
\(890\) 8.66800 0.290552
\(891\) −18.9199 + 32.7703i −0.633841 + 1.09784i
\(892\) 22.0435 + 38.1804i 0.738071 + 1.27838i
\(893\) 3.16905 + 5.48896i 0.106048 + 0.183681i
\(894\) 0.385409 0.667548i 0.0128900 0.0223262i
\(895\) 57.5892 1.92499
\(896\) 9.02434 + 12.9466i 0.301482 + 0.432517i
\(897\) −0.452087 −0.0150947
\(898\) −0.720366 + 1.24771i −0.0240389 + 0.0416366i
\(899\) −4.62740 8.01489i −0.154332 0.267312i
\(900\) −30.1003 52.1352i −1.00334 1.73784i
\(901\) 3.75252 6.49956i 0.125015 0.216532i
\(902\) 7.15549 0.238252
\(903\) 4.66622 0.398238i 0.155282 0.0132525i
\(904\) −1.27983 −0.0425664
\(905\) 18.5738 32.1707i 0.617413 1.06939i
\(906\) −0.130671 0.226330i −0.00434127 0.00751930i
\(907\) −27.2374 47.1766i −0.904403 1.56647i −0.821717 0.569896i \(-0.806983\pi\)
−0.0826860 0.996576i \(-0.526350\pi\)
\(908\) −9.02635 + 15.6341i −0.299550 + 0.518836i
\(909\) 41.9851 1.39256
\(910\) 2.02832 0.173107i 0.0672382 0.00573843i
\(911\) −27.4793 −0.910431 −0.455215 0.890381i \(-0.650438\pi\)
−0.455215 + 0.890381i \(0.650438\pi\)
\(912\) −0.875843 + 1.51700i −0.0290021 + 0.0502330i
\(913\) 16.1019 + 27.8893i 0.532895 + 0.923000i
\(914\) 0.774626 + 1.34169i 0.0256224 + 0.0443792i
\(915\) 3.85390 6.67514i 0.127406 0.220673i
\(916\) −29.9990 −0.991196
\(917\) −19.1487 27.4714i −0.632345 0.907184i
\(918\) 0.687947 0.0227056
\(919\) 24.1440 41.8186i 0.796437 1.37947i −0.125486 0.992095i \(-0.540049\pi\)
0.921923 0.387374i \(-0.126618\pi\)
\(920\) −2.65228 4.59388i −0.0874431 0.151456i
\(921\) −2.36331 4.09337i −0.0778737 0.134881i
\(922\) −0.932889 + 1.61581i −0.0307231 + 0.0532139i
\(923\) 9.54869 0.314299
\(924\) 2.57957 5.50132i 0.0848617 0.180980i
\(925\) 74.7601 2.45810
\(926\) 0.211356 0.366080i 0.00694560 0.0120301i
\(927\) −10.9854 19.0273i −0.360808 0.624937i
\(928\) 1.88906 + 3.27195i 0.0620114 + 0.107407i
\(929\) −21.6577 + 37.5122i −0.710566 + 1.23074i 0.254079 + 0.967183i \(0.418228\pi\)
−0.964645 + 0.263553i \(0.915106\pi\)
\(930\) 1.12041 0.0367397
\(931\) −12.3328 + 2.12053i −0.404191 + 0.0694975i
\(932\) 15.8032 0.517651
\(933\) −0.0489212 + 0.0847339i −0.00160161 + 0.00277406i
\(934\) −0.794266 1.37571i −0.0259892 0.0450146i
\(935\) 20.2144 + 35.0123i 0.661081 + 1.14503i
\(936\) 1.13655 1.96855i 0.0371492 0.0643442i
\(937\) −37.2211 −1.21596 −0.607980 0.793952i \(-0.708020\pi\)
−0.607980 + 0.793952i \(0.708020\pi\)
\(938\) 2.78344 5.93609i 0.0908824 0.193820i
\(939\) −2.85463 −0.0931574
\(940\) 13.6756 23.6868i 0.446048 0.772577i
\(941\) −7.98754 13.8348i −0.260386 0.451002i 0.705958 0.708253i \(-0.250517\pi\)
−0.966345 + 0.257251i \(0.917183\pi\)
\(942\) 0.272728 + 0.472378i 0.00888595 + 0.0153909i
\(943\) 7.06155 12.2310i 0.229956 0.398295i
\(944\) 16.9967 0.553194
\(945\) 9.16950 + 13.1549i 0.298284 + 0.427929i
\(946\) −6.00736 −0.195316
\(947\) −13.8786 + 24.0384i −0.450994 + 0.781144i −0.998448 0.0556912i \(-0.982264\pi\)
0.547454 + 0.836836i \(0.315597\pi\)
\(948\) −0.201737 0.349419i −0.00655212 0.0113486i
\(949\) −0.540019 0.935340i −0.0175298 0.0303624i
\(950\) −1.83011 + 3.16985i −0.0593768 + 0.102844i
\(951\) −6.80142 −0.220551
\(952\) 4.66180 0.397861i 0.151090 0.0128947i
\(953\) 12.0303 0.389700 0.194850 0.980833i \(-0.437578\pi\)
0.194850 + 0.980833i \(0.437578\pi\)
\(954\) −0.943742 + 1.63461i −0.0305548 + 0.0529224i
\(955\) −24.6839 42.7537i −0.798751 1.38348i
\(956\) 21.3100 + 36.9099i 0.689213 + 1.19375i
\(957\) 0.966454 1.67395i 0.0312410 0.0541110i
\(958\) −2.84744 −0.0919965
\(959\) 24.4805 2.08929i 0.790518 0.0674666i
\(960\) 7.24926 0.233969
\(961\) −0.209310 + 0.362536i −0.00675194 + 0.0116947i
\(962\) 0.698891 + 1.21052i 0.0225332 + 0.0390286i
\(963\) 16.0971 + 27.8810i 0.518722 + 0.898453i
\(964\) −20.1056 + 34.8240i −0.647559 + 1.12160i
\(965\) −36.8421 −1.18599
\(966\) 0.133824 + 0.191988i 0.00430571 + 0.00617712i
\(967\) 5.40788 0.173906 0.0869528 0.996212i \(-0.472287\pi\)
0.0869528 + 0.996212i \(0.472287\pi\)
\(968\) −3.60690 + 6.24733i −0.115930 + 0.200797i
\(969\) 0.529765 + 0.917580i 0.0170185 + 0.0294769i
\(970\) −3.39066 5.87279i −0.108867 0.188564i
\(971\) −21.1376 + 36.6114i −0.678338 + 1.17492i 0.297143 + 0.954833i \(0.403966\pi\)
−0.975481 + 0.220083i \(0.929367\pi\)
\(972\) 13.3496 0.428190
\(973\) −4.49297 + 9.58192i −0.144038 + 0.307182i
\(974\) 6.50733 0.208508
\(975\) 1.35930 2.35437i 0.0435323 0.0754001i
\(976\) −14.2284 24.6443i −0.455440 0.788846i
\(977\) 5.41508 + 9.37920i 0.173244 + 0.300067i 0.939552 0.342406i \(-0.111242\pi\)
−0.766308 + 0.642473i \(0.777908\pi\)
\(978\) −0.0602935 + 0.104431i −0.00192797 + 0.00333935i
\(979\) −50.7660 −1.62249
\(980\) 34.5350 + 41.5148i 1.10318 + 1.32614i
\(981\) 36.4988 1.16532
\(982\) −2.20664 + 3.82202i −0.0704169 + 0.121966i
\(983\) −10.7805 18.6723i −0.343844 0.595555i 0.641299 0.767291i \(-0.278396\pi\)
−0.985143 + 0.171736i \(0.945062\pi\)
\(984\) −0.817137 1.41532i −0.0260494 0.0451189i
\(985\) 14.9883 25.9605i 0.477567 0.827170i
\(986\) 0.737005 0.0234710
\(987\) −1.03458 + 2.20638i −0.0329309 + 0.0702300i
\(988\) 3.50693 0.111570
\(989\) −5.92850 + 10.2685i −0.188515 + 0.326518i
\(990\) −5.08383 8.80545i −0.161575 0.279855i
\(991\) −4.31312 7.47054i −0.137011 0.237310i 0.789353 0.613940i \(-0.210416\pi\)
−0.926364 + 0.376630i \(0.877083\pi\)
\(992\) 6.41306 11.1078i 0.203615 0.352671i
\(993\) 8.85703 0.281069
\(994\) −2.82654 4.05505i −0.0896524 0.128618i
\(995\) 53.2024 1.68663
\(996\) 1.82102 3.15411i 0.0577013 0.0999417i
\(997\) −10.8484 18.7899i −0.343571 0.595082i 0.641522 0.767105i \(-0.278303\pi\)
−0.985093 + 0.172022i \(0.944970\pi\)
\(998\) −1.11381 1.92918i −0.0352572 0.0610672i
\(999\) −5.50521 + 9.53531i −0.174177 + 0.301684i
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 91.2.e.c.79.4 yes 10
3.2 odd 2 819.2.j.h.352.2 10
4.3 odd 2 1456.2.r.p.625.3 10
7.2 even 3 637.2.a.l.1.2 5
7.3 odd 6 637.2.e.m.508.4 10
7.4 even 3 inner 91.2.e.c.53.4 10
7.5 odd 6 637.2.a.k.1.2 5
7.6 odd 2 637.2.e.m.79.4 10
13.12 even 2 1183.2.e.f.170.2 10
21.2 odd 6 5733.2.a.bl.1.4 5
21.5 even 6 5733.2.a.bm.1.4 5
21.11 odd 6 819.2.j.h.235.2 10
28.11 odd 6 1456.2.r.p.417.3 10
91.12 odd 6 8281.2.a.bx.1.4 5
91.25 even 6 1183.2.e.f.508.2 10
91.51 even 6 8281.2.a.bw.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.4 10 7.4 even 3 inner
91.2.e.c.79.4 yes 10 1.1 even 1 trivial
637.2.a.k.1.2 5 7.5 odd 6
637.2.a.l.1.2 5 7.2 even 3
637.2.e.m.79.4 10 7.6 odd 2
637.2.e.m.508.4 10 7.3 odd 6
819.2.j.h.235.2 10 21.11 odd 6
819.2.j.h.352.2 10 3.2 odd 2
1183.2.e.f.170.2 10 13.12 even 2
1183.2.e.f.508.2 10 91.25 even 6
1456.2.r.p.417.3 10 28.11 odd 6
1456.2.r.p.625.3 10 4.3 odd 2
5733.2.a.bl.1.4 5 21.2 odd 6
5733.2.a.bm.1.4 5 21.5 even 6
8281.2.a.bw.1.4 5 91.51 even 6
8281.2.a.bx.1.4 5 91.12 odd 6