Properties

Label 287.2.e.c.247.2
Level $287$
Weight $2$
Character 287.247
Analytic conductor $2.292$
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] = [287,2,Mod(165,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, 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("287.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.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: \(2.29170653801\)
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: \( x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 247.2
Root \(-0.580000 + 1.00459i\) of defining polynomial
Character \(\chi\) \(=\) 287.247
Dual form 287.2.e.c.165.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.678233 + 1.17473i) q^{2} +(1.11395 + 1.92942i) q^{3} +(0.0800004 + 0.138565i) q^{4} +(-1.11395 + 1.92942i) q^{5} -3.02207 q^{6} +(2.60927 - 0.437865i) q^{7} -2.92997 q^{8} +(-0.981768 + 1.70047i) q^{9} +O(q^{10})\) \(q+(-0.678233 + 1.17473i) q^{2} +(1.11395 + 1.92942i) q^{3} +(0.0800004 + 0.138565i) q^{4} +(-1.11395 + 1.92942i) q^{5} -3.02207 q^{6} +(2.60927 - 0.437865i) q^{7} -2.92997 q^{8} +(-0.981768 + 1.70047i) q^{9} +(-1.51103 - 2.61719i) q^{10} +(0.564283 + 0.977367i) q^{11} +(-0.178233 + 0.308708i) q^{12} +2.22790 q^{13} +(-1.25532 + 3.36217i) q^{14} -4.96354 q^{15} +(1.82720 - 3.16480i) q^{16} +(-2.02675 - 3.51044i) q^{17} +(-1.33173 - 2.30663i) q^{18} +(1.80790 - 3.13137i) q^{19} -0.356466 q^{20} +(3.75142 + 4.54661i) q^{21} -1.53086 q^{22} +(1.34292 - 2.32600i) q^{23} +(-3.26384 - 5.65313i) q^{24} +(0.0182320 + 0.0315788i) q^{25} +(-1.51103 + 2.61719i) q^{26} +2.30914 q^{27} +(0.269415 + 0.326523i) q^{28} -3.72230 q^{29} +(3.36643 - 5.83083i) q^{30} +(-0.172630 - 0.299004i) q^{31} +(-0.451434 - 0.781907i) q^{32} +(-1.25717 + 2.17748i) q^{33} +5.49844 q^{34} +(-2.06177 + 5.52212i) q^{35} -0.314167 q^{36} +(-1.67465 + 2.90058i) q^{37} +(2.45235 + 4.24760i) q^{38} +(2.48177 + 4.29855i) q^{39} +(3.26384 - 5.65313i) q^{40} -1.00000 q^{41} +(-7.88539 + 1.32326i) q^{42} -12.6805 q^{43} +(-0.0902858 + 0.156380i) q^{44} +(-2.18728 - 3.78848i) q^{45} +(1.82162 + 3.15514i) q^{46} +(3.65642 - 6.33310i) q^{47} +8.14163 q^{48} +(6.61655 - 2.28501i) q^{49} -0.0494623 q^{50} +(4.51540 - 7.82090i) q^{51} +(0.178233 + 0.308708i) q^{52} +(4.17809 + 7.23666i) q^{53} +(-1.56613 + 2.71262i) q^{54} -2.51433 q^{55} +(-7.64507 + 1.28293i) q^{56} +8.05564 q^{57} +(2.52458 - 4.37271i) q^{58} +(2.61250 + 4.52499i) q^{59} +(-0.397085 - 0.687771i) q^{60} +(-2.80432 + 4.85722i) q^{61} +0.468334 q^{62} +(-1.81712 + 4.86687i) q^{63} +8.53351 q^{64} +(-2.48177 + 4.29855i) q^{65} +(-1.70530 - 2.95367i) q^{66} +(4.41625 + 7.64916i) q^{67} +(0.324282 - 0.561673i) q^{68} +5.98377 q^{69} +(-5.08867 - 6.16732i) q^{70} +9.92933 q^{71} +(2.87655 - 4.98233i) q^{72} +(-0.407898 - 0.706500i) q^{73} +(-2.27161 - 3.93454i) q^{74} +(-0.0406192 + 0.0703545i) q^{75} +0.578531 q^{76} +(1.90032 + 2.30313i) q^{77} -6.73287 q^{78} +(4.42092 - 7.65726i) q^{79} +(4.07082 + 7.05086i) q^{80} +(5.51757 + 9.55671i) q^{81} +(0.678233 - 1.17473i) q^{82} -7.48907 q^{83} +(-0.329885 + 0.883544i) q^{84} +9.03080 q^{85} +(8.60034 - 14.8962i) q^{86} +(-4.14645 - 7.18186i) q^{87} +(-1.65333 - 2.86365i) q^{88} +(7.88183 - 13.6517i) q^{89} +5.93394 q^{90} +(5.81318 - 0.975519i) q^{91} +0.429735 q^{92} +(0.384603 - 0.666151i) q^{93} +(4.95981 + 8.59064i) q^{94} +(4.02782 + 6.97639i) q^{95} +(1.00575 - 1.74201i) q^{96} -2.10829 q^{97} +(-1.80328 + 9.32245i) q^{98} -2.21598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.678233 + 1.17473i −0.479583 + 0.830662i −0.999726 0.0234171i \(-0.992545\pi\)
0.520143 + 0.854079i \(0.325879\pi\)
\(3\) 1.11395 + 1.92942i 0.643139 + 1.11395i 0.984728 + 0.174100i \(0.0557017\pi\)
−0.341589 + 0.939850i \(0.610965\pi\)
\(4\) 0.0800004 + 0.138565i 0.0400002 + 0.0692824i
\(5\) −1.11395 + 1.92942i −0.498173 + 0.862862i −0.999998 0.00210783i \(-0.999329\pi\)
0.501824 + 0.864970i \(0.332662\pi\)
\(6\) −3.02207 −1.23375
\(7\) 2.60927 0.437865i 0.986210 0.165497i
\(8\) −2.92997 −1.03590
\(9\) −0.981768 + 1.70047i −0.327256 + 0.566824i
\(10\) −1.51103 2.61719i −0.477831 0.827628i
\(11\) 0.564283 + 0.977367i 0.170138 + 0.294687i 0.938468 0.345367i \(-0.112245\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(12\) −0.178233 + 0.308708i −0.0514514 + 0.0891164i
\(13\) 2.22790 0.617908 0.308954 0.951077i \(-0.400021\pi\)
0.308954 + 0.951077i \(0.400021\pi\)
\(14\) −1.25532 + 3.36217i −0.335497 + 0.898577i
\(15\) −4.96354 −1.28158
\(16\) 1.82720 3.16480i 0.456800 0.791200i
\(17\) −2.02675 3.51044i −0.491560 0.851406i 0.508393 0.861125i \(-0.330240\pi\)
−0.999953 + 0.00971895i \(0.996906\pi\)
\(18\) −1.33173 2.30663i −0.313893 0.543678i
\(19\) 1.80790 3.13137i 0.414761 0.718387i −0.580643 0.814159i \(-0.697199\pi\)
0.995403 + 0.0957720i \(0.0305320\pi\)
\(20\) −0.356466 −0.0797082
\(21\) 3.75142 + 4.54661i 0.818626 + 0.992151i
\(22\) −1.53086 −0.326381
\(23\) 1.34292 2.32600i 0.280017 0.485004i −0.691371 0.722500i \(-0.742993\pi\)
0.971389 + 0.237495i \(0.0763264\pi\)
\(24\) −3.26384 5.65313i −0.666228 1.15394i
\(25\) 0.0182320 + 0.0315788i 0.00364641 + 0.00631577i
\(26\) −1.51103 + 2.61719i −0.296338 + 0.513273i
\(27\) 2.30914 0.444394
\(28\) 0.269415 + 0.326523i 0.0509147 + 0.0617071i
\(29\) −3.72230 −0.691213 −0.345607 0.938380i \(-0.612327\pi\)
−0.345607 + 0.938380i \(0.612327\pi\)
\(30\) 3.36643 5.83083i 0.614624 1.06456i
\(31\) −0.172630 0.299004i −0.0310053 0.0537027i 0.850106 0.526611i \(-0.176538\pi\)
−0.881112 + 0.472908i \(0.843204\pi\)
\(32\) −0.451434 0.781907i −0.0798030 0.138223i
\(33\) −1.25717 + 2.17748i −0.218845 + 0.379050i
\(34\) 5.49844 0.942974
\(35\) −2.06177 + 5.52212i −0.348502 + 0.933409i
\(36\) −0.314167 −0.0523612
\(37\) −1.67465 + 2.90058i −0.275311 + 0.476852i −0.970214 0.242251i \(-0.922114\pi\)
0.694903 + 0.719104i \(0.255447\pi\)
\(38\) 2.45235 + 4.24760i 0.397824 + 0.689052i
\(39\) 2.48177 + 4.29855i 0.397401 + 0.688319i
\(40\) 3.26384 5.65313i 0.516058 0.893838i
\(41\) −1.00000 −0.156174
\(42\) −7.88539 + 1.32326i −1.21674 + 0.204183i
\(43\) −12.6805 −1.93376 −0.966880 0.255232i \(-0.917848\pi\)
−0.966880 + 0.255232i \(0.917848\pi\)
\(44\) −0.0902858 + 0.156380i −0.0136111 + 0.0235751i
\(45\) −2.18728 3.78848i −0.326060 0.564753i
\(46\) 1.82162 + 3.15514i 0.268583 + 0.465200i
\(47\) 3.65642 6.33310i 0.533344 0.923778i −0.465898 0.884838i \(-0.654269\pi\)
0.999242 0.0389396i \(-0.0123980\pi\)
\(48\) 8.14163 1.17514
\(49\) 6.61655 2.28501i 0.945221 0.326430i
\(50\) −0.0494623 −0.00699502
\(51\) 4.51540 7.82090i 0.632282 1.09515i
\(52\) 0.178233 + 0.308708i 0.0247164 + 0.0428101i
\(53\) 4.17809 + 7.23666i 0.573904 + 0.994031i 0.996160 + 0.0875544i \(0.0279052\pi\)
−0.422256 + 0.906477i \(0.638762\pi\)
\(54\) −1.56613 + 2.71262i −0.213124 + 0.369141i
\(55\) −2.51433 −0.339032
\(56\) −7.64507 + 1.28293i −1.02161 + 0.171439i
\(57\) 8.05564 1.06700
\(58\) 2.52458 4.37271i 0.331494 0.574165i
\(59\) 2.61250 + 4.52499i 0.340119 + 0.589103i 0.984455 0.175640i \(-0.0561994\pi\)
−0.644336 + 0.764743i \(0.722866\pi\)
\(60\) −0.397085 0.687771i −0.0512634 0.0887909i
\(61\) −2.80432 + 4.85722i −0.359056 + 0.621903i −0.987803 0.155706i \(-0.950235\pi\)
0.628747 + 0.777610i \(0.283568\pi\)
\(62\) 0.468334 0.0594785
\(63\) −1.81712 + 4.86687i −0.228935 + 0.613168i
\(64\) 8.53351 1.06669
\(65\) −2.48177 + 4.29855i −0.307825 + 0.533169i
\(66\) −1.70530 2.95367i −0.209908 0.363572i
\(67\) 4.41625 + 7.64916i 0.539530 + 0.934494i 0.998929 + 0.0462640i \(0.0147315\pi\)
−0.459399 + 0.888230i \(0.651935\pi\)
\(68\) 0.324282 0.561673i 0.0393250 0.0681128i
\(69\) 5.98377 0.720361
\(70\) −5.08867 6.16732i −0.608212 0.737135i
\(71\) 9.92933 1.17839 0.589197 0.807989i \(-0.299444\pi\)
0.589197 + 0.807989i \(0.299444\pi\)
\(72\) 2.87655 4.98233i 0.339004 0.587173i
\(73\) −0.407898 0.706500i −0.0477408 0.0826895i 0.841168 0.540775i \(-0.181869\pi\)
−0.888908 + 0.458085i \(0.848535\pi\)
\(74\) −2.27161 3.93454i −0.264069 0.457381i
\(75\) −0.0406192 + 0.0703545i −0.00469030 + 0.00812383i
\(76\) 0.578531 0.0663620
\(77\) 1.90032 + 2.30313i 0.216562 + 0.262466i
\(78\) −6.73287 −0.762347
\(79\) 4.42092 7.65726i 0.497392 0.861509i −0.502603 0.864517i \(-0.667624\pi\)
0.999995 + 0.00300848i \(0.000957632\pi\)
\(80\) 4.07082 + 7.05086i 0.455131 + 0.788310i
\(81\) 5.51757 + 9.55671i 0.613063 + 1.06186i
\(82\) 0.678233 1.17473i 0.0748983 0.129728i
\(83\) −7.48907 −0.822033 −0.411016 0.911628i \(-0.634826\pi\)
−0.411016 + 0.911628i \(0.634826\pi\)
\(84\) −0.329885 + 0.883544i −0.0359934 + 0.0964026i
\(85\) 9.03080 0.979528
\(86\) 8.60034 14.8962i 0.927398 1.60630i
\(87\) −4.14645 7.18186i −0.444546 0.769977i
\(88\) −1.65333 2.86365i −0.176246 0.305266i
\(89\) 7.88183 13.6517i 0.835473 1.44708i −0.0581725 0.998307i \(-0.518527\pi\)
0.893645 0.448774i \(-0.148139\pi\)
\(90\) 5.93394 0.625492
\(91\) 5.81318 0.975519i 0.609387 0.102262i
\(92\) 0.429735 0.0448030
\(93\) 0.384603 0.666151i 0.0398814 0.0690767i
\(94\) 4.95981 + 8.59064i 0.511565 + 0.886057i
\(95\) 4.02782 + 6.97639i 0.413246 + 0.715762i
\(96\) 1.00575 1.74201i 0.102649 0.177793i
\(97\) −2.10829 −0.214064 −0.107032 0.994256i \(-0.534135\pi\)
−0.107032 + 0.994256i \(0.534135\pi\)
\(98\) −1.80328 + 9.32245i −0.182159 + 0.941710i
\(99\) −2.21598 −0.222714
\(100\) −0.00291714 + 0.00505264i −0.000291714 + 0.000505264i
\(101\) −3.92090 6.79119i −0.390144 0.675749i 0.602324 0.798251i \(-0.294241\pi\)
−0.992468 + 0.122503i \(0.960908\pi\)
\(102\) 6.12498 + 10.6088i 0.606464 + 1.05043i
\(103\) 3.45455 5.98346i 0.340387 0.589568i −0.644118 0.764927i \(-0.722775\pi\)
0.984505 + 0.175359i \(0.0561086\pi\)
\(104\) −6.52767 −0.640091
\(105\) −12.9512 + 2.17336i −1.26391 + 0.212098i
\(106\) −11.3349 −1.10094
\(107\) −9.78377 + 16.9460i −0.945833 + 1.63823i −0.191758 + 0.981442i \(0.561419\pi\)
−0.754075 + 0.656788i \(0.771915\pi\)
\(108\) 0.184732 + 0.319965i 0.0177758 + 0.0307887i
\(109\) −1.96105 3.39664i −0.187835 0.325339i 0.756693 0.653770i \(-0.226814\pi\)
−0.944528 + 0.328431i \(0.893480\pi\)
\(110\) 1.70530 2.95367i 0.162594 0.281621i
\(111\) −7.46191 −0.708253
\(112\) 3.38190 9.05788i 0.319559 0.855889i
\(113\) −5.10800 −0.480520 −0.240260 0.970709i \(-0.577233\pi\)
−0.240260 + 0.970709i \(0.577233\pi\)
\(114\) −5.46360 + 9.46323i −0.511713 + 0.886313i
\(115\) 2.99188 + 5.18209i 0.278994 + 0.483233i
\(116\) −0.297785 0.515779i −0.0276487 0.0478889i
\(117\) −2.18728 + 3.78848i −0.202214 + 0.350245i
\(118\) −7.08754 −0.652461
\(119\) −6.82543 8.27222i −0.625686 0.758314i
\(120\) 14.5430 1.32759
\(121\) 4.86317 8.42326i 0.442106 0.765751i
\(122\) −3.80396 6.58865i −0.344394 0.596509i
\(123\) −1.11395 1.92942i −0.100441 0.173970i
\(124\) 0.0276210 0.0478409i 0.00248044 0.00429624i
\(125\) −11.2207 −1.00361
\(126\) −4.48484 5.43550i −0.399542 0.484233i
\(127\) −19.3732 −1.71909 −0.859547 0.511056i \(-0.829254\pi\)
−0.859547 + 0.511056i \(0.829254\pi\)
\(128\) −4.88484 + 8.46078i −0.431763 + 0.747835i
\(129\) −14.1254 24.4660i −1.24368 2.15411i
\(130\) −3.36643 5.83083i −0.295256 0.511398i
\(131\) 0.154545 0.267680i 0.0135027 0.0233873i −0.859195 0.511648i \(-0.829035\pi\)
0.872698 + 0.488261i \(0.162368\pi\)
\(132\) −0.402295 −0.0350153
\(133\) 3.34617 8.96221i 0.290150 0.777122i
\(134\) −11.9810 −1.03500
\(135\) −2.57226 + 4.45529i −0.221385 + 0.383450i
\(136\) 5.93832 + 10.2855i 0.509206 + 0.881971i
\(137\) 8.68377 + 15.0407i 0.741905 + 1.28502i 0.951627 + 0.307256i \(0.0994107\pi\)
−0.209722 + 0.977761i \(0.567256\pi\)
\(138\) −4.05839 + 7.02933i −0.345473 + 0.598376i
\(139\) −15.1514 −1.28512 −0.642562 0.766233i \(-0.722129\pi\)
−0.642562 + 0.766233i \(0.722129\pi\)
\(140\) −0.930114 + 0.156084i −0.0786090 + 0.0131915i
\(141\) 16.2923 1.37206
\(142\) −6.73440 + 11.6643i −0.565138 + 0.978848i
\(143\) 1.25717 + 2.17748i 0.105130 + 0.182090i
\(144\) 3.58777 + 6.21420i 0.298981 + 0.517850i
\(145\) 4.14645 7.18186i 0.344344 0.596421i
\(146\) 1.10660 0.0915828
\(147\) 11.7792 + 10.2207i 0.971536 + 0.842989i
\(148\) −0.535891 −0.0440500
\(149\) 5.24670 9.08756i 0.429827 0.744482i −0.567031 0.823697i \(-0.691908\pi\)
0.996858 + 0.0792148i \(0.0252413\pi\)
\(150\) −0.0550985 0.0954334i −0.00449877 0.00779211i
\(151\) 2.55975 + 4.43361i 0.208309 + 0.360802i 0.951182 0.308630i \(-0.0998706\pi\)
−0.742873 + 0.669433i \(0.766537\pi\)
\(152\) −5.29709 + 9.17482i −0.429650 + 0.744176i
\(153\) 7.95920 0.643463
\(154\) −3.99443 + 0.670310i −0.321880 + 0.0540151i
\(155\) 0.769205 0.0617841
\(156\) −0.397085 + 0.687771i −0.0317922 + 0.0550658i
\(157\) −7.54790 13.0733i −0.602388 1.04337i −0.992458 0.122582i \(-0.960883\pi\)
0.390070 0.920785i \(-0.372451\pi\)
\(158\) 5.99683 + 10.3868i 0.477082 + 0.826330i
\(159\) −9.30835 + 16.1225i −0.738201 + 1.27860i
\(160\) 2.01150 0.159023
\(161\) 2.48555 6.65717i 0.195889 0.524658i
\(162\) −14.9688 −1.17606
\(163\) −3.80812 + 6.59586i −0.298275 + 0.516628i −0.975741 0.218926i \(-0.929745\pi\)
0.677466 + 0.735554i \(0.263078\pi\)
\(164\) −0.0800004 0.138565i −0.00624698 0.0108201i
\(165\) −2.80084 4.85120i −0.218045 0.377665i
\(166\) 5.07934 8.79767i 0.394233 0.682831i
\(167\) 8.24963 0.638375 0.319188 0.947692i \(-0.396590\pi\)
0.319188 + 0.947692i \(0.396590\pi\)
\(168\) −10.9915 13.3214i −0.848015 1.02777i
\(169\) −8.03646 −0.618190
\(170\) −6.12498 + 10.6088i −0.469765 + 0.813657i
\(171\) 3.54988 + 6.14857i 0.271466 + 0.470193i
\(172\) −1.01445 1.75707i −0.0773508 0.133975i
\(173\) 11.8690 20.5578i 0.902386 1.56298i 0.0779974 0.996954i \(-0.475147\pi\)
0.824388 0.566025i \(-0.191519\pi\)
\(174\) 11.2490 0.852787
\(175\) 0.0613995 + 0.0744144i 0.00464137 + 0.00562520i
\(176\) 4.12423 0.310876
\(177\) −5.82039 + 10.0812i −0.437487 + 0.757750i
\(178\) 10.6914 + 18.5181i 0.801357 + 1.38799i
\(179\) −5.72773 9.92072i −0.428111 0.741509i 0.568595 0.822618i \(-0.307487\pi\)
−0.996705 + 0.0811086i \(0.974154\pi\)
\(180\) 0.349967 0.606160i 0.0260850 0.0451805i
\(181\) 17.7517 1.31948 0.659738 0.751495i \(-0.270667\pi\)
0.659738 + 0.751495i \(0.270667\pi\)
\(182\) −2.79672 + 7.49057i −0.207307 + 0.555238i
\(183\) −12.4955 −0.923692
\(184\) −3.93470 + 6.81510i −0.290070 + 0.502416i
\(185\) −3.73095 6.46220i −0.274305 0.475111i
\(186\) 0.521700 + 0.903612i 0.0382529 + 0.0662560i
\(187\) 2.28732 3.96176i 0.167266 0.289713i
\(188\) 1.17006 0.0853354
\(189\) 6.02516 1.01109i 0.438266 0.0735460i
\(190\) −10.9272 −0.792742
\(191\) −8.22890 + 14.2529i −0.595423 + 1.03130i 0.398065 + 0.917357i \(0.369682\pi\)
−0.993487 + 0.113945i \(0.963651\pi\)
\(192\) 9.50590 + 16.4647i 0.686029 + 1.18824i
\(193\) −9.85481 17.0690i −0.709365 1.22866i −0.965093 0.261907i \(-0.915649\pi\)
0.255729 0.966749i \(-0.417685\pi\)
\(194\) 1.42991 2.47668i 0.102662 0.177815i
\(195\) −11.0583 −0.791898
\(196\) 0.845949 + 0.734019i 0.0604249 + 0.0524299i
\(197\) 12.9492 0.922592 0.461296 0.887246i \(-0.347385\pi\)
0.461296 + 0.887246i \(0.347385\pi\)
\(198\) 1.50295 2.60319i 0.106810 0.185000i
\(199\) −12.8566 22.2682i −0.911378 1.57855i −0.812119 0.583492i \(-0.801686\pi\)
−0.0992595 0.995062i \(-0.531647\pi\)
\(200\) −0.0534193 0.0925249i −0.00377731 0.00654250i
\(201\) −9.83895 + 17.0416i −0.693986 + 1.20202i
\(202\) 10.6371 0.748425
\(203\) −9.71247 + 1.62986i −0.681681 + 0.114394i
\(204\) 1.44494 0.101166
\(205\) 1.11395 1.92942i 0.0778016 0.134756i
\(206\) 4.68598 + 8.11636i 0.326488 + 0.565493i
\(207\) 2.63686 + 4.56718i 0.183275 + 0.317441i
\(208\) 4.07082 7.05086i 0.282260 0.488889i
\(209\) 4.08067 0.282266
\(210\) 6.23081 16.6882i 0.429967 1.15160i
\(211\) 13.4799 0.927993 0.463996 0.885837i \(-0.346415\pi\)
0.463996 + 0.885837i \(0.346415\pi\)
\(212\) −0.668497 + 1.15787i −0.0459126 + 0.0795229i
\(213\) 11.0608 + 19.1578i 0.757872 + 1.31267i
\(214\) −13.2713 22.9867i −0.907211 1.57134i
\(215\) 14.1254 24.4660i 0.963348 1.66857i
\(216\) −6.76570 −0.460347
\(217\) −0.581362 0.704593i −0.0394654 0.0478309i
\(218\) 5.32019 0.360329
\(219\) 0.908755 1.57401i 0.0614080 0.106362i
\(220\) −0.201148 0.348398i −0.0135614 0.0234890i
\(221\) −4.51540 7.82090i −0.303739 0.526091i
\(222\) 5.06091 8.76575i 0.339666 0.588319i
\(223\) −2.59701 −0.173909 −0.0869544 0.996212i \(-0.527713\pi\)
−0.0869544 + 0.996212i \(0.527713\pi\)
\(224\) −1.52028 1.84254i −0.101578 0.123110i
\(225\) −0.0715986 −0.00477324
\(226\) 3.46441 6.00053i 0.230449 0.399150i
\(227\) 5.05559 + 8.75653i 0.335551 + 0.581192i 0.983591 0.180415i \(-0.0577441\pi\)
−0.648039 + 0.761607i \(0.724411\pi\)
\(228\) 0.644454 + 1.11623i 0.0426800 + 0.0739240i
\(229\) 6.79492 11.7691i 0.449021 0.777727i −0.549302 0.835624i \(-0.685106\pi\)
0.998323 + 0.0578971i \(0.0184395\pi\)
\(230\) −8.11677 −0.535204
\(231\) −2.32684 + 6.23208i −0.153095 + 0.410041i
\(232\) 10.9062 0.716028
\(233\) −4.63114 + 8.02136i −0.303396 + 0.525497i −0.976903 0.213684i \(-0.931454\pi\)
0.673507 + 0.739181i \(0.264787\pi\)
\(234\) −2.96697 5.13894i −0.193957 0.335943i
\(235\) 8.14613 + 14.1095i 0.531395 + 0.920403i
\(236\) −0.418002 + 0.724001i −0.0272096 + 0.0471285i
\(237\) 19.6987 1.27957
\(238\) 14.3469 2.40757i 0.929971 0.156060i
\(239\) −10.5580 −0.682942 −0.341471 0.939892i \(-0.610925\pi\)
−0.341471 + 0.939892i \(0.610925\pi\)
\(240\) −9.06937 + 15.7086i −0.585425 + 1.01399i
\(241\) −4.50762 7.80743i −0.290362 0.502921i 0.683534 0.729919i \(-0.260442\pi\)
−0.973895 + 0.226998i \(0.927109\pi\)
\(242\) 6.59672 + 11.4259i 0.424053 + 0.734482i
\(243\) −8.82888 + 15.2921i −0.566373 + 0.980986i
\(244\) −0.897386 −0.0574493
\(245\) −2.96176 + 15.3115i −0.189220 + 0.978214i
\(246\) 3.02207 0.192680
\(247\) 4.02782 6.97639i 0.256284 0.443897i
\(248\) 0.505801 + 0.876073i 0.0321184 + 0.0556307i
\(249\) −8.34245 14.4495i −0.528681 0.915703i
\(250\) 7.61027 13.1814i 0.481316 0.833663i
\(251\) 21.2912 1.34389 0.671945 0.740601i \(-0.265459\pi\)
0.671945 + 0.740601i \(0.265459\pi\)
\(252\) −0.819746 + 0.137563i −0.0516392 + 0.00866564i
\(253\) 3.03114 0.190566
\(254\) 13.1395 22.7584i 0.824449 1.42799i
\(255\) 10.0599 + 17.4242i 0.629973 + 1.09114i
\(256\) 1.90739 + 3.30370i 0.119212 + 0.206481i
\(257\) −4.22897 + 7.32479i −0.263796 + 0.456908i −0.967247 0.253836i \(-0.918308\pi\)
0.703452 + 0.710743i \(0.251641\pi\)
\(258\) 38.3214 2.38578
\(259\) −3.09955 + 8.30166i −0.192597 + 0.515840i
\(260\) −0.794170 −0.0492523
\(261\) 3.65443 6.32966i 0.226204 0.391796i
\(262\) 0.209635 + 0.363099i 0.0129513 + 0.0224323i
\(263\) 1.36129 + 2.35782i 0.0839405 + 0.145389i 0.904939 0.425541i \(-0.139916\pi\)
−0.820999 + 0.570930i \(0.806583\pi\)
\(264\) 3.68346 6.37993i 0.226701 0.392658i
\(265\) −18.6167 −1.14362
\(266\) 8.25872 + 10.0093i 0.506375 + 0.613711i
\(267\) 35.1199 2.14930
\(268\) −0.706603 + 1.22387i −0.0431627 + 0.0747599i
\(269\) −14.7894 25.6160i −0.901726 1.56183i −0.825253 0.564763i \(-0.808968\pi\)
−0.0764725 0.997072i \(-0.524366\pi\)
\(270\) −3.48919 6.04345i −0.212345 0.367793i
\(271\) −4.05801 + 7.02867i −0.246506 + 0.426961i −0.962554 0.271090i \(-0.912616\pi\)
0.716048 + 0.698051i \(0.245949\pi\)
\(272\) −14.8131 −0.898177
\(273\) 8.35778 + 10.1294i 0.505836 + 0.613058i
\(274\) −23.5585 −1.42322
\(275\) −0.0205761 + 0.0356388i −0.00124078 + 0.00214910i
\(276\) 0.478704 + 0.829139i 0.0288146 + 0.0499083i
\(277\) 0.546971 + 0.947382i 0.0328643 + 0.0569226i 0.881990 0.471269i \(-0.156204\pi\)
−0.849125 + 0.528191i \(0.822870\pi\)
\(278\) 10.2762 17.7989i 0.616324 1.06750i
\(279\) 0.677931 0.0405867
\(280\) 6.04091 16.1796i 0.361014 0.966919i
\(281\) 7.95015 0.474266 0.237133 0.971477i \(-0.423792\pi\)
0.237133 + 0.971477i \(0.423792\pi\)
\(282\) −11.0500 + 19.1391i −0.658015 + 1.13972i
\(283\) 13.8297 + 23.9537i 0.822089 + 1.42390i 0.904124 + 0.427271i \(0.140525\pi\)
−0.0820341 + 0.996630i \(0.526142\pi\)
\(284\) 0.794350 + 1.37586i 0.0471360 + 0.0816420i
\(285\) −8.97358 + 15.5427i −0.531549 + 0.920669i
\(286\) −3.41061 −0.201673
\(287\) −2.60927 + 0.437865i −0.154020 + 0.0258463i
\(288\) 1.77281 0.104464
\(289\) 0.284554 0.492862i 0.0167385 0.0289919i
\(290\) 5.62452 + 9.74195i 0.330283 + 0.572067i
\(291\) −2.34853 4.06777i −0.137673 0.238457i
\(292\) 0.0652640 0.113041i 0.00381929 0.00661520i
\(293\) −9.57574 −0.559421 −0.279710 0.960084i \(-0.590238\pi\)
−0.279710 + 0.960084i \(0.590238\pi\)
\(294\) −19.9957 + 6.90546i −1.16617 + 0.402735i
\(295\) −11.6408 −0.677753
\(296\) 4.90667 8.49860i 0.285195 0.493971i
\(297\) 1.30301 + 2.25688i 0.0756082 + 0.130957i
\(298\) 7.11697 + 12.3270i 0.412275 + 0.714082i
\(299\) 2.99188 5.18209i 0.173025 0.299688i
\(300\) −0.0129982 −0.000750451
\(301\) −33.0868 + 5.55235i −1.90709 + 0.320032i
\(302\) −6.94442 −0.399606
\(303\) 8.73536 15.1301i 0.501833 0.869201i
\(304\) −6.60679 11.4433i −0.378925 0.656318i
\(305\) −6.24774 10.8214i −0.357744 0.619632i
\(306\) −5.39819 + 9.34994i −0.308594 + 0.534501i
\(307\) 8.24141 0.470362 0.235181 0.971952i \(-0.424432\pi\)
0.235181 + 0.971952i \(0.424432\pi\)
\(308\) −0.167107 + 0.447569i −0.00952178 + 0.0255026i
\(309\) 15.3928 0.875665
\(310\) −0.521700 + 0.903612i −0.0296306 + 0.0513217i
\(311\) 5.83211 + 10.1015i 0.330709 + 0.572804i 0.982651 0.185464i \(-0.0593789\pi\)
−0.651942 + 0.758269i \(0.726046\pi\)
\(312\) −7.27150 12.5946i −0.411668 0.713029i
\(313\) −15.3091 + 26.5161i −0.865319 + 1.49878i 0.00141158 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498777i \(0.833783\pi\)
\(314\) 20.4769 1.15558
\(315\) −7.36604 8.92742i −0.415029 0.503003i
\(316\) 1.41470 0.0795832
\(317\) 10.4058 18.0234i 0.584450 1.01230i −0.410494 0.911863i \(-0.634644\pi\)
0.994944 0.100434i \(-0.0320231\pi\)
\(318\) −12.6265 21.8697i −0.708057 1.22639i
\(319\) −2.10043 3.63805i −0.117601 0.203692i
\(320\) −9.50590 + 16.4647i −0.531396 + 0.920404i
\(321\) −43.5945 −2.43321
\(322\) 6.13462 + 7.43498i 0.341869 + 0.414335i
\(323\) −14.6567 −0.815518
\(324\) −0.882815 + 1.52908i −0.0490453 + 0.0849489i
\(325\) 0.0406192 + 0.0703545i 0.00225315 + 0.00390256i
\(326\) −5.16559 8.94706i −0.286095 0.495532i
\(327\) 4.36902 7.56737i 0.241607 0.418476i
\(328\) 2.92997 0.161780
\(329\) 6.76753 18.1258i 0.373106 0.999306i
\(330\) 7.59849 0.418283
\(331\) 0.333500 0.577639i 0.0183308 0.0317499i −0.856714 0.515791i \(-0.827498\pi\)
0.875045 + 0.484041i \(0.160831\pi\)
\(332\) −0.599129 1.03772i −0.0328815 0.0569524i
\(333\) −3.28824 5.69539i −0.180194 0.312106i
\(334\) −5.59517 + 9.69112i −0.306154 + 0.530274i
\(335\) −19.6779 −1.07512
\(336\) 21.2437 3.56493i 1.15894 0.194483i
\(337\) 0.0671610 0.00365849 0.00182925 0.999998i \(-0.499418\pi\)
0.00182925 + 0.999998i \(0.499418\pi\)
\(338\) 5.45059 9.44071i 0.296473 0.513507i
\(339\) −5.69005 9.85546i −0.309041 0.535275i
\(340\) 0.722468 + 1.25135i 0.0391813 + 0.0678640i
\(341\) 0.194825 0.337446i 0.0105503 0.0182737i
\(342\) −9.63057 −0.520762
\(343\) 16.2638 8.85936i 0.878164 0.478360i
\(344\) 37.1535 2.00318
\(345\) −6.66561 + 11.5452i −0.358865 + 0.621572i
\(346\) 16.0999 + 27.8859i 0.865538 + 1.49916i
\(347\) −14.2567 24.6933i −0.765338 1.32560i −0.940068 0.340988i \(-0.889238\pi\)
0.174729 0.984617i \(-0.444095\pi\)
\(348\) 0.663436 1.14910i 0.0355639 0.0615984i
\(349\) 30.8596 1.65188 0.825938 0.563761i \(-0.190646\pi\)
0.825938 + 0.563761i \(0.190646\pi\)
\(350\) −0.129060 + 0.0216578i −0.00689856 + 0.00115766i
\(351\) 5.14453 0.274595
\(352\) 0.509473 0.882434i 0.0271550 0.0470339i
\(353\) −9.43292 16.3383i −0.502064 0.869600i −0.999997 0.00238442i \(-0.999241\pi\)
0.497934 0.867215i \(-0.334092\pi\)
\(354\) −7.89516 13.6748i −0.419623 0.726809i
\(355\) −11.0608 + 19.1578i −0.587045 + 1.01679i
\(356\) 2.52220 0.133676
\(357\) 8.35739 22.3840i 0.442320 1.18468i
\(358\) 15.5389 0.821258
\(359\) 0.323788 0.560817i 0.0170889 0.0295988i −0.857355 0.514726i \(-0.827894\pi\)
0.874443 + 0.485128i \(0.161227\pi\)
\(360\) 6.40866 + 11.1001i 0.337766 + 0.585028i
\(361\) 2.96300 + 5.13206i 0.155947 + 0.270108i
\(362\) −12.0398 + 20.8536i −0.632799 + 1.09604i
\(363\) 21.6693 1.13734
\(364\) 0.600230 + 0.727461i 0.0314606 + 0.0381293i
\(365\) 1.81751 0.0951329
\(366\) 8.47484 14.6789i 0.442987 0.767276i
\(367\) 5.08183 + 8.80199i 0.265269 + 0.459460i 0.967634 0.252357i \(-0.0812058\pi\)
−0.702365 + 0.711817i \(0.747872\pi\)
\(368\) −4.90755 8.50013i −0.255824 0.443100i
\(369\) 0.981768 1.70047i 0.0511088 0.0885230i
\(370\) 10.1218 0.526208
\(371\) 14.0704 + 17.0529i 0.730500 + 0.885344i
\(372\) 0.123073 0.00638106
\(373\) −3.48449 + 6.03531i −0.180420 + 0.312496i −0.942024 0.335547i \(-0.891079\pi\)
0.761604 + 0.648043i \(0.224412\pi\)
\(374\) 3.10268 + 5.37399i 0.160436 + 0.277883i
\(375\) −12.4993 21.6495i −0.645463 1.11797i
\(376\) −10.7132 + 18.5558i −0.552490 + 0.956941i
\(377\) −8.29290 −0.427106
\(378\) −2.89870 + 7.76371i −0.149093 + 0.399322i
\(379\) −36.4593 −1.87279 −0.936394 0.350950i \(-0.885859\pi\)
−0.936394 + 0.350950i \(0.885859\pi\)
\(380\) −0.644454 + 1.11623i −0.0330598 + 0.0572613i
\(381\) −21.5808 37.3790i −1.10562 1.91498i
\(382\) −11.1622 19.3335i −0.571109 0.989190i
\(383\) 10.0892 17.4750i 0.515534 0.892932i −0.484303 0.874900i \(-0.660927\pi\)
0.999837 0.0180314i \(-0.00573989\pi\)
\(384\) −21.7658 −1.11073
\(385\) −6.56056 + 1.10094i −0.334357 + 0.0561090i
\(386\) 26.7354 1.36080
\(387\) 12.4493 21.5628i 0.632834 1.09610i
\(388\) −0.168664 0.292135i −0.00856262 0.0148309i
\(389\) 9.11942 + 15.7953i 0.462373 + 0.800853i 0.999079 0.0429163i \(-0.0136649\pi\)
−0.536706 + 0.843769i \(0.680332\pi\)
\(390\) 7.50007 12.9905i 0.379781 0.657800i
\(391\) −10.8870 −0.550581
\(392\) −19.3863 + 6.69501i −0.979154 + 0.338149i
\(393\) 0.688623 0.0347364
\(394\) −8.78257 + 15.2119i −0.442460 + 0.766362i
\(395\) 9.84936 + 17.0596i 0.495575 + 0.858362i
\(396\) −0.177279 0.307057i −0.00890862 0.0154302i
\(397\) −18.8370 + 32.6266i −0.945400 + 1.63748i −0.190452 + 0.981697i \(0.560995\pi\)
−0.754948 + 0.655784i \(0.772338\pi\)
\(398\) 34.8790 1.74833
\(399\) 21.0193 3.52728i 1.05228 0.176585i
\(400\) 0.133254 0.00666272
\(401\) 12.8116 22.1903i 0.639780 1.10813i −0.345701 0.938345i \(-0.612359\pi\)
0.985481 0.169787i \(-0.0543080\pi\)
\(402\) −13.3462 23.1163i −0.665648 1.15294i
\(403\) −0.384603 0.666151i −0.0191584 0.0331834i
\(404\) 0.627347 1.08660i 0.0312117 0.0540602i
\(405\) −24.5852 −1.22165
\(406\) 4.67266 12.5150i 0.231900 0.621108i
\(407\) −3.77991 −0.187363
\(408\) −13.2300 + 22.9150i −0.654981 + 1.13446i
\(409\) 2.04568 + 3.54322i 0.101152 + 0.175201i 0.912160 0.409835i \(-0.134414\pi\)
−0.811007 + 0.585036i \(0.801080\pi\)
\(410\) 1.51103 + 2.61719i 0.0746247 + 0.129254i
\(411\) −19.3466 + 33.5092i −0.954296 + 1.65289i
\(412\) 1.10546 0.0544622
\(413\) 8.79805 + 10.6630i 0.432924 + 0.524691i
\(414\) −7.15363 −0.351582
\(415\) 8.34245 14.4495i 0.409515 0.709300i
\(416\) −1.00575 1.74201i −0.0493109 0.0854091i
\(417\) −16.8779 29.2334i −0.826514 1.43156i
\(418\) −2.76764 + 4.79370i −0.135370 + 0.234468i
\(419\) −33.7334 −1.64798 −0.823992 0.566602i \(-0.808258\pi\)
−0.823992 + 0.566602i \(0.808258\pi\)
\(420\) −1.33725 1.62071i −0.0652512 0.0790825i
\(421\) 0.804296 0.0391990 0.0195995 0.999808i \(-0.493761\pi\)
0.0195995 + 0.999808i \(0.493761\pi\)
\(422\) −9.14250 + 15.8353i −0.445050 + 0.770849i
\(423\) 7.17951 + 12.4353i 0.349080 + 0.604624i
\(424\) −12.2417 21.2032i −0.594507 1.02972i
\(425\) 0.0739037 0.128005i 0.00358485 0.00620915i
\(426\) −30.0071 −1.45385
\(427\) −5.19041 + 13.9017i −0.251181 + 0.672750i
\(428\) −3.13082 −0.151334
\(429\) −2.80084 + 4.85120i −0.135226 + 0.234218i
\(430\) 19.1607 + 33.1873i 0.924010 + 1.60043i
\(431\) 19.9140 + 34.4920i 0.959221 + 1.66142i 0.724398 + 0.689382i \(0.242118\pi\)
0.234824 + 0.972038i \(0.424549\pi\)
\(432\) 4.21925 7.30796i 0.202999 0.351605i
\(433\) −6.07965 −0.292169 −0.146085 0.989272i \(-0.546667\pi\)
−0.146085 + 0.989272i \(0.546667\pi\)
\(434\) 1.22201 0.205067i 0.0586583 0.00984353i
\(435\) 18.4758 0.885845
\(436\) 0.313770 0.543465i 0.0150268 0.0260272i
\(437\) −4.85572 8.41035i −0.232280 0.402321i
\(438\) 1.23270 + 2.13509i 0.0589005 + 0.102019i
\(439\) −20.0450 + 34.7189i −0.956694 + 1.65704i −0.226252 + 0.974069i \(0.572647\pi\)
−0.730442 + 0.682974i \(0.760686\pi\)
\(440\) 7.36691 0.351204
\(441\) −2.61032 + 13.4946i −0.124301 + 0.642600i
\(442\) 12.2500 0.582672
\(443\) −9.04105 + 15.6595i −0.429553 + 0.744008i −0.996834 0.0795170i \(-0.974662\pi\)
0.567280 + 0.823525i \(0.307996\pi\)
\(444\) −0.596956 1.03396i −0.0283303 0.0490694i
\(445\) 17.5599 + 30.4147i 0.832421 + 1.44179i
\(446\) 1.76138 3.05080i 0.0834037 0.144459i
\(447\) 23.3783 1.10575
\(448\) 22.2662 3.73652i 1.05198 0.176534i
\(449\) −11.4042 −0.538200 −0.269100 0.963112i \(-0.586726\pi\)
−0.269100 + 0.963112i \(0.586726\pi\)
\(450\) 0.0485605 0.0841092i 0.00228916 0.00396495i
\(451\) −0.564283 0.977367i −0.0265711 0.0460224i
\(452\) −0.408642 0.707788i −0.0192209 0.0332916i
\(453\) −5.70286 + 9.87764i −0.267944 + 0.464092i
\(454\) −13.7155 −0.643698
\(455\) −4.59341 + 12.3027i −0.215343 + 0.576761i
\(456\) −23.6028 −1.10530
\(457\) −14.0878 + 24.4008i −0.658999 + 1.14142i 0.321876 + 0.946782i \(0.395687\pi\)
−0.980875 + 0.194638i \(0.937647\pi\)
\(458\) 9.21707 + 15.9644i 0.430686 + 0.745969i
\(459\) −4.68005 8.10608i −0.218446 0.378360i
\(460\) −0.478704 + 0.829139i −0.0223197 + 0.0386588i
\(461\) 29.6306 1.38003 0.690017 0.723793i \(-0.257603\pi\)
0.690017 + 0.723793i \(0.257603\pi\)
\(462\) −5.74290 6.96022i −0.267184 0.323819i
\(463\) 29.1404 1.35427 0.677135 0.735859i \(-0.263221\pi\)
0.677135 + 0.735859i \(0.263221\pi\)
\(464\) −6.80138 + 11.7803i −0.315746 + 0.546888i
\(465\) 0.856856 + 1.48412i 0.0397358 + 0.0688243i
\(466\) −6.28198 10.8807i −0.291007 0.504039i
\(467\) −7.92955 + 13.7344i −0.366936 + 0.635551i −0.989085 0.147348i \(-0.952926\pi\)
0.622149 + 0.782899i \(0.286260\pi\)
\(468\) −0.699933 −0.0323544
\(469\) 14.8725 + 18.0250i 0.686747 + 0.832317i
\(470\) −22.0999 −1.01939
\(471\) 16.8160 29.1261i 0.774839 1.34206i
\(472\) −7.65455 13.2581i −0.352329 0.610252i
\(473\) −7.15540 12.3935i −0.329006 0.569854i
\(474\) −13.3603 + 23.1408i −0.613660 + 1.06289i
\(475\) 0.131847 0.00604955
\(476\) 0.600201 1.60755i 0.0275102 0.0736817i
\(477\) −16.4076 −0.751254
\(478\) 7.16080 12.4029i 0.327527 0.567294i
\(479\) −1.83916 3.18552i −0.0840333 0.145550i 0.820946 0.571006i \(-0.193447\pi\)
−0.904979 + 0.425456i \(0.860114\pi\)
\(480\) 2.24071 + 3.88102i 0.102274 + 0.177144i
\(481\) −3.73095 + 6.46220i −0.170117 + 0.294651i
\(482\) 12.2289 0.557010
\(483\) 15.6132 2.62008i 0.710427 0.119218i
\(484\) 1.55622 0.0707374
\(485\) 2.34853 4.06777i 0.106641 0.184708i
\(486\) −11.9761 20.7432i −0.543246 0.940929i
\(487\) −14.4907 25.0987i −0.656638 1.13733i −0.981480 0.191563i \(-0.938644\pi\)
0.324842 0.945768i \(-0.394689\pi\)
\(488\) 8.21656 14.2315i 0.371946 0.644230i
\(489\) −16.9682 −0.767330
\(490\) −15.9781 13.8640i −0.721819 0.626313i
\(491\) −39.5204 −1.78353 −0.891766 0.452496i \(-0.850534\pi\)
−0.891766 + 0.452496i \(0.850534\pi\)
\(492\) 0.178233 0.308708i 0.00803536 0.0139176i
\(493\) 7.54417 + 13.0669i 0.339772 + 0.588503i
\(494\) 5.46360 + 9.46323i 0.245819 + 0.425771i
\(495\) 2.46849 4.27555i 0.110950 0.192172i
\(496\) −1.26172 −0.0566528
\(497\) 25.9083 4.34770i 1.16215 0.195021i
\(498\) 22.6325 1.01419
\(499\) −2.69095 + 4.66086i −0.120463 + 0.208649i −0.919950 0.392035i \(-0.871771\pi\)
0.799487 + 0.600683i \(0.205105\pi\)
\(500\) −0.897663 1.55480i −0.0401447 0.0695327i
\(501\) 9.18967 + 15.9170i 0.410564 + 0.711118i
\(502\) −14.4404 + 25.0115i −0.644507 + 1.11632i
\(503\) 3.46954 0.154699 0.0773495 0.997004i \(-0.475354\pi\)
0.0773495 + 0.997004i \(0.475354\pi\)
\(504\) 5.32410 14.2598i 0.237154 0.635180i
\(505\) 17.4707 0.777437
\(506\) −2.05582 + 3.56078i −0.0913923 + 0.158296i
\(507\) −8.95222 15.5057i −0.397582 0.688632i
\(508\) −1.54986 2.68444i −0.0687641 0.119103i
\(509\) 16.8620 29.2059i 0.747397 1.29453i −0.201670 0.979453i \(-0.564637\pi\)
0.949067 0.315075i \(-0.102030\pi\)
\(510\) −27.2917 −1.20850
\(511\) −1.37367 1.66484i −0.0607674 0.0736483i
\(512\) −24.7140 −1.09221
\(513\) 4.17469 7.23077i 0.184317 0.319247i
\(514\) −5.73645 9.93582i −0.253024 0.438250i
\(515\) 7.69639 + 13.3305i 0.339144 + 0.587414i
\(516\) 2.26008 3.91458i 0.0994946 0.172330i
\(517\) 8.25302 0.362967
\(518\) −7.65002 9.27160i −0.336123 0.407371i
\(519\) 52.8860 2.32144
\(520\) 7.27150 12.5946i 0.318876 0.552310i
\(521\) −4.17464 7.23069i −0.182894 0.316782i 0.759971 0.649957i \(-0.225213\pi\)
−0.942865 + 0.333175i \(0.891880\pi\)
\(522\) 4.95711 + 8.58597i 0.216967 + 0.375798i
\(523\) 6.49731 11.2537i 0.284107 0.492089i −0.688285 0.725441i \(-0.741636\pi\)
0.972392 + 0.233352i \(0.0749694\pi\)
\(524\) 0.0494548 0.00216044
\(525\) −0.0751805 + 0.201359i −0.00328115 + 0.00878804i
\(526\) −3.69307 −0.161026
\(527\) −0.699757 + 1.21201i −0.0304819 + 0.0527962i
\(528\) 4.59419 + 7.95736i 0.199936 + 0.346300i
\(529\) 7.89315 + 13.6713i 0.343180 + 0.594406i
\(530\) 12.6265 21.8697i 0.548459 0.949958i
\(531\) −10.2595 −0.445224
\(532\) 1.50954 0.253318i 0.0654469 0.0109827i
\(533\) −2.22790 −0.0965010
\(534\) −23.8194 + 41.2565i −1.03077 + 1.78534i
\(535\) −21.7973 37.7540i −0.942378 1.63225i
\(536\) −12.9395 22.4118i −0.558899 0.968042i
\(537\) 12.7608 22.1024i 0.550669 0.953787i
\(538\) 40.1226 1.72981
\(539\) 5.96690 + 5.17740i 0.257013 + 0.223007i
\(540\) −0.823128 −0.0354218
\(541\) 17.9257 31.0483i 0.770687 1.33487i −0.166500 0.986042i \(-0.553246\pi\)
0.937187 0.348828i \(-0.113420\pi\)
\(542\) −5.50455 9.53415i −0.236440 0.409527i
\(543\) 19.7746 + 34.2505i 0.848607 + 1.46983i
\(544\) −1.82989 + 3.16946i −0.0784559 + 0.135890i
\(545\) 8.73804 0.374297
\(546\) −17.5678 + 2.94808i −0.751834 + 0.126166i
\(547\) −37.4317 −1.60046 −0.800232 0.599691i \(-0.795290\pi\)
−0.800232 + 0.599691i \(0.795290\pi\)
\(548\) −1.38941 + 2.40653i −0.0593527 + 0.102802i
\(549\) −5.50638 9.53733i −0.235007 0.407043i
\(550\) −0.0279107 0.0483428i −0.00119012 0.00206134i
\(551\) −6.72954 + 11.6559i −0.286688 + 0.496558i
\(552\) −17.5322 −0.746221
\(553\) 8.18252 21.9156i 0.347956 0.931946i
\(554\) −1.48389 −0.0630447
\(555\) 8.31219 14.3971i 0.352833 0.611124i
\(556\) −1.21212 2.09945i −0.0514052 0.0890365i
\(557\) 7.22341 + 12.5113i 0.306066 + 0.530121i 0.977498 0.210945i \(-0.0676539\pi\)
−0.671432 + 0.741066i \(0.734321\pi\)
\(558\) −0.459795 + 0.796389i −0.0194647 + 0.0337138i
\(559\) −28.2509 −1.19489
\(560\) 13.7092 + 16.6151i 0.579318 + 0.702117i
\(561\) 10.1919 0.430300
\(562\) −5.39205 + 9.33931i −0.227450 + 0.393955i
\(563\) 2.86790 + 4.96736i 0.120868 + 0.209349i 0.920110 0.391660i \(-0.128099\pi\)
−0.799242 + 0.601009i \(0.794766\pi\)
\(564\) 1.30339 + 2.25753i 0.0548825 + 0.0950593i
\(565\) 5.69005 9.85546i 0.239382 0.414622i
\(566\) −37.5190 −1.57704
\(567\) 18.5814 + 22.5201i 0.780343 + 0.945753i
\(568\) −29.0926 −1.22070
\(569\) −5.86822 + 10.1641i −0.246009 + 0.426099i −0.962415 0.271584i \(-0.912452\pi\)
0.716406 + 0.697684i \(0.245786\pi\)
\(570\) −12.1723 21.0831i −0.509844 0.883075i
\(571\) −3.58127 6.20294i −0.149872 0.259585i 0.781308 0.624145i \(-0.214553\pi\)
−0.931180 + 0.364560i \(0.881219\pi\)
\(572\) −0.201148 + 0.348398i −0.00841040 + 0.0145672i
\(573\) −36.6663 −1.53176
\(574\) 1.25532 3.36217i 0.0523959 0.140334i
\(575\) 0.0979365 0.00408423
\(576\) −8.37792 + 14.5110i −0.349080 + 0.604625i
\(577\) 14.5204 + 25.1500i 0.604491 + 1.04701i 0.992132 + 0.125198i \(0.0399566\pi\)
−0.387641 + 0.921810i \(0.626710\pi\)
\(578\) 0.385988 + 0.668550i 0.0160550 + 0.0278080i
\(579\) 21.9555 38.0281i 0.912440 1.58039i
\(580\) 1.32687 0.0550953
\(581\) −19.5410 + 3.27920i −0.810697 + 0.136044i
\(582\) 6.37140 0.264103
\(583\) −4.71525 + 8.16705i −0.195286 + 0.338245i
\(584\) 1.19513 + 2.07002i 0.0494547 + 0.0856581i
\(585\) −4.87304 8.44035i −0.201475 0.348966i
\(586\) 6.49458 11.2489i 0.268289 0.464690i
\(587\) 8.38291 0.346000 0.173000 0.984922i \(-0.444654\pi\)
0.173000 + 0.984922i \(0.444654\pi\)
\(588\) −0.473884 + 2.44985i −0.0195426 + 0.101030i
\(589\) −1.24839 −0.0514391
\(590\) 7.89516 13.6748i 0.325039 0.562984i
\(591\) 14.4248 + 24.9844i 0.593355 + 1.02772i
\(592\) 6.11984 + 10.5999i 0.251524 + 0.435652i
\(593\) −1.14553 + 1.98411i −0.0470412 + 0.0814778i −0.888587 0.458708i \(-0.848313\pi\)
0.841546 + 0.540185i \(0.181646\pi\)
\(594\) −3.53497 −0.145042
\(595\) 23.5638 3.95427i 0.966020 0.162109i
\(596\) 1.67895 0.0687726
\(597\) 28.6432 49.6114i 1.17229 2.03046i
\(598\) 4.05839 + 7.02933i 0.165960 + 0.287451i
\(599\) −3.38508 5.86313i −0.138311 0.239561i 0.788547 0.614975i \(-0.210834\pi\)
−0.926857 + 0.375414i \(0.877501\pi\)
\(600\) 0.119013 0.206136i 0.00485868 0.00841548i
\(601\) −41.3732 −1.68765 −0.843824 0.536619i \(-0.819701\pi\)
−0.843824 + 0.536619i \(0.819701\pi\)
\(602\) 15.9180 42.6340i 0.648771 1.73763i
\(603\) −17.3429 −0.706258
\(604\) −0.409562 + 0.709382i −0.0166648 + 0.0288643i
\(605\) 10.8347 + 18.7662i 0.440491 + 0.762953i
\(606\) 11.8492 + 20.5234i 0.481342 + 0.833708i
\(607\) 8.78391 15.2142i 0.356528 0.617525i −0.630850 0.775905i \(-0.717294\pi\)
0.987378 + 0.158380i \(0.0506271\pi\)
\(608\) −3.26459 −0.132397
\(609\) −13.9639 16.9238i −0.565845 0.685788i
\(610\) 16.9497 0.686273
\(611\) 8.14613 14.1095i 0.329557 0.570810i
\(612\) 0.636739 + 1.10286i 0.0257387 + 0.0445807i
\(613\) 7.79078 + 13.4940i 0.314666 + 0.545018i 0.979367 0.202092i \(-0.0647740\pi\)
−0.664700 + 0.747110i \(0.731441\pi\)
\(614\) −5.58959 + 9.68146i −0.225578 + 0.390712i
\(615\) 4.96354 0.200149
\(616\) −5.56787 6.74810i −0.224336 0.271889i
\(617\) 3.07666 0.123862 0.0619309 0.998080i \(-0.480274\pi\)
0.0619309 + 0.998080i \(0.480274\pi\)
\(618\) −10.4399 + 18.0824i −0.419954 + 0.727382i
\(619\) 23.4870 + 40.6806i 0.944021 + 1.63509i 0.757699 + 0.652604i \(0.226324\pi\)
0.186322 + 0.982489i \(0.440343\pi\)
\(620\) 0.0615367 + 0.106585i 0.00247137 + 0.00428055i
\(621\) 3.10098 5.37105i 0.124438 0.215533i
\(622\) −15.8221 −0.634409
\(623\) 14.5882 39.0722i 0.584464 1.56539i
\(624\) 18.1387 0.726131
\(625\) 12.4082 21.4916i 0.496327 0.859664i
\(626\) −20.7662 35.9681i −0.829984 1.43758i
\(627\) 4.54566 + 7.87332i 0.181536 + 0.314430i
\(628\) 1.20767 2.09175i 0.0481913 0.0834698i
\(629\) 13.5764 0.541327
\(630\) 15.4832 2.59826i 0.616867 0.103517i
\(631\) 4.85357 0.193218 0.0966089 0.995322i \(-0.469200\pi\)
0.0966089 + 0.995322i \(0.469200\pi\)
\(632\) −12.9531 + 22.4355i −0.515249 + 0.892437i
\(633\) 15.0159 + 26.0083i 0.596829 + 1.03374i
\(634\) 14.1152 + 24.4482i 0.560585 + 0.970961i
\(635\) 21.5808 37.3790i 0.856407 1.48334i
\(636\) −2.97869 −0.118113
\(637\) 14.7410 5.09078i 0.584060 0.201704i
\(638\) 5.69832 0.225599
\(639\) −9.74830 + 16.8845i −0.385637 + 0.667942i
\(640\) −10.8829 18.8498i −0.430185 0.745103i
\(641\) 4.78914 + 8.29503i 0.189160 + 0.327634i 0.944970 0.327156i \(-0.106090\pi\)
−0.755811 + 0.654790i \(0.772757\pi\)
\(642\) 29.5672 51.2119i 1.16693 2.02117i
\(643\) 8.31243 0.327810 0.163905 0.986476i \(-0.447591\pi\)
0.163905 + 0.986476i \(0.447591\pi\)
\(644\) 1.12129 0.188166i 0.0441852 0.00741478i
\(645\) 62.9402 2.47827
\(646\) 9.94063 17.2177i 0.391109 0.677420i
\(647\) −10.1951 17.6584i −0.400810 0.694223i 0.593014 0.805192i \(-0.297938\pi\)
−0.993824 + 0.110969i \(0.964605\pi\)
\(648\) −16.1663 28.0008i −0.635072 1.09998i
\(649\) −2.94838 + 5.10675i −0.115734 + 0.200457i
\(650\) −0.110197 −0.00432228
\(651\) 0.711847 1.90657i 0.0278995 0.0747244i
\(652\) −1.21860 −0.0477243
\(653\) −7.81289 + 13.5323i −0.305742 + 0.529561i −0.977426 0.211277i \(-0.932238\pi\)
0.671684 + 0.740838i \(0.265571\pi\)
\(654\) 5.92643 + 10.2649i 0.231742 + 0.401388i
\(655\) 0.344311 + 0.596365i 0.0134534 + 0.0233019i
\(656\) −1.82720 + 3.16480i −0.0713401 + 0.123565i
\(657\) 1.60184 0.0624939
\(658\) 16.7030 + 20.2435i 0.651151 + 0.789175i
\(659\) 19.6929 0.767127 0.383564 0.923514i \(-0.374697\pi\)
0.383564 + 0.923514i \(0.374697\pi\)
\(660\) 0.448137 0.776195i 0.0174437 0.0302134i
\(661\) 16.4263 + 28.4512i 0.638910 + 1.10662i 0.985672 + 0.168672i \(0.0539478\pi\)
−0.346762 + 0.937953i \(0.612719\pi\)
\(662\) 0.452381 + 0.783548i 0.0175823 + 0.0304534i
\(663\) 10.0599 17.4242i 0.390692 0.676699i
\(664\) 21.9427 0.851543
\(665\) 13.5644 + 16.4396i 0.526004 + 0.637501i
\(666\) 8.92076 0.345673
\(667\) −4.99873 + 8.65806i −0.193552 + 0.335241i
\(668\) 0.659973 + 1.14311i 0.0255351 + 0.0442282i
\(669\) −2.89294 5.01072i −0.111848 0.193726i
\(670\) 13.3462 23.1163i 0.515609 0.893061i
\(671\) −6.32972 −0.244356
\(672\) 1.86151 4.98575i 0.0718091 0.192330i
\(673\) −2.56402 −0.0988358 −0.0494179 0.998778i \(-0.515737\pi\)
−0.0494179 + 0.998778i \(0.515737\pi\)
\(674\) −0.0455508 + 0.0788963i −0.00175455 + 0.00303897i
\(675\) 0.0421003 + 0.0729199i 0.00162044 + 0.00280669i
\(676\) −0.642920 1.11357i −0.0247277 0.0428296i
\(677\) −11.3542 + 19.6660i −0.436377 + 0.755826i −0.997407 0.0719689i \(-0.977072\pi\)
0.561030 + 0.827795i \(0.310405\pi\)
\(678\) 15.4367 0.592844
\(679\) −5.50109 + 0.923146i −0.211113 + 0.0354271i
\(680\) −26.4599 −1.01469
\(681\) −11.2633 + 19.5087i −0.431612 + 0.747574i
\(682\) 0.264273 + 0.457734i 0.0101195 + 0.0175275i
\(683\) −19.7307 34.1745i −0.754972 1.30765i −0.945388 0.325947i \(-0.894317\pi\)
0.190416 0.981704i \(-0.439016\pi\)
\(684\) −0.567983 + 0.983776i −0.0217174 + 0.0376156i
\(685\) −38.6931 −1.47839
\(686\) −0.623265 + 25.1144i −0.0237964 + 0.958871i
\(687\) 30.2768 1.15513
\(688\) −23.1698 + 40.1313i −0.883341 + 1.52999i
\(689\) 9.30835 + 16.1225i 0.354620 + 0.614220i
\(690\) −9.04168 15.6606i −0.344211 0.596190i
\(691\) −12.7937 + 22.1593i −0.486694 + 0.842978i −0.999883 0.0152972i \(-0.995131\pi\)
0.513189 + 0.858275i \(0.328464\pi\)
\(692\) 3.79811 0.144382
\(693\) −5.78208 + 0.970300i −0.219643 + 0.0368586i
\(694\) 38.6774 1.46817
\(695\) 16.8779 29.2334i 0.640215 1.10888i
\(696\) 12.1490 + 21.0426i 0.460505 + 0.797619i
\(697\) 2.02675 + 3.51044i 0.0767687 + 0.132967i
\(698\) −20.9300 + 36.2518i −0.792212 + 1.37215i
\(699\) −20.6354 −0.780503
\(700\) −0.00539923 + 0.0144610i −0.000204072 + 0.000546574i
\(701\) −28.4667 −1.07517 −0.537586 0.843209i \(-0.680664\pi\)
−0.537586 + 0.843209i \(0.680664\pi\)
\(702\) −3.48919 + 6.04345i −0.131691 + 0.228095i
\(703\) 6.05520 + 10.4879i 0.228376 + 0.395559i
\(704\) 4.81531 + 8.34037i 0.181484 + 0.314339i
\(705\) −18.1488 + 31.4346i −0.683522 + 1.18389i
\(706\) 25.5909 0.963125
\(707\) −13.2043 16.0032i −0.496598 0.601863i
\(708\) −1.86253 −0.0699983
\(709\) 9.29445 16.0985i 0.349061 0.604591i −0.637022 0.770845i \(-0.719834\pi\)
0.986083 + 0.166255i \(0.0531674\pi\)
\(710\) −15.0036 25.9869i −0.563074 0.975272i
\(711\) 8.68063 + 15.0353i 0.325549 + 0.563868i
\(712\) −23.0935 + 39.9991i −0.865466 + 1.49903i
\(713\) −0.927312 −0.0347281
\(714\) 20.6269 + 24.9992i 0.771944 + 0.935573i
\(715\) −5.60168 −0.209491
\(716\) 0.916441 1.58732i 0.0342490 0.0593210i
\(717\) −11.7611 20.3708i −0.439227 0.760763i
\(718\) 0.439207 + 0.760729i 0.0163911 + 0.0283902i
\(719\) −8.31292 + 14.3984i −0.310020 + 0.536970i −0.978366 0.206880i \(-0.933669\pi\)
0.668347 + 0.743850i \(0.267002\pi\)
\(720\) −15.9864 −0.595777
\(721\) 6.39390 17.1251i 0.238121 0.637771i
\(722\) −8.03841 −0.299158
\(723\) 10.0425 17.3942i 0.373486 0.646896i
\(724\) 1.42015 + 2.45977i 0.0527793 + 0.0914165i
\(725\) −0.0678651 0.117546i −0.00252045 0.00436554i
\(726\) −14.6968 + 25.4557i −0.545451 + 0.944748i
\(727\) −13.5357 −0.502010 −0.251005 0.967986i \(-0.580761\pi\)
−0.251005 + 0.967986i \(0.580761\pi\)
\(728\) −17.0324 + 2.85824i −0.631264 + 0.105933i
\(729\) −6.23430 −0.230900
\(730\) −1.23270 + 2.13509i −0.0456241 + 0.0790233i
\(731\) 25.7002 + 44.5141i 0.950558 + 1.64641i
\(732\) −0.999643 1.73143i −0.0369479 0.0639956i
\(733\) −1.84531 + 3.19616i −0.0681579 + 0.118053i −0.898090 0.439811i \(-0.855046\pi\)
0.829933 + 0.557864i \(0.188379\pi\)
\(734\) −13.7867 −0.508875
\(735\) −32.8415 + 11.3417i −1.21138 + 0.418346i
\(736\) −2.42495 −0.0893850
\(737\) −4.98403 + 8.63259i −0.183589 + 0.317985i
\(738\) 1.33173 + 2.30663i 0.0490218 + 0.0849083i
\(739\) −15.1284 26.2031i −0.556505 0.963896i −0.997785 0.0665258i \(-0.978809\pi\)
0.441279 0.897370i \(-0.354525\pi\)
\(740\) 0.596956 1.03396i 0.0219445 0.0380090i
\(741\) 17.9472 0.659305
\(742\) −29.5757 + 4.96314i −1.08576 + 0.182202i
\(743\) −42.1181 −1.54516 −0.772581 0.634917i \(-0.781034\pi\)
−0.772581 + 0.634917i \(0.781034\pi\)
\(744\) −1.12687 + 1.95180i −0.0413132 + 0.0715565i
\(745\) 11.6891 + 20.2462i 0.428257 + 0.741762i
\(746\) −4.72659 8.18669i −0.173053 0.299736i
\(747\) 7.35253 12.7350i 0.269015 0.465948i
\(748\) 0.731947 0.0267626
\(749\) −18.1084 + 48.5006i −0.661667 + 1.77217i
\(750\) 33.9098 1.23821
\(751\) 9.61308 16.6503i 0.350786 0.607580i −0.635601 0.772018i \(-0.719248\pi\)
0.986387 + 0.164438i \(0.0525810\pi\)
\(752\) −13.3620 23.1437i −0.487262 0.843963i
\(753\) 23.7173 + 41.0796i 0.864308 + 1.49703i
\(754\) 5.62452 9.74195i 0.204833 0.354781i
\(755\) −11.4057 −0.415097
\(756\) 0.622116 + 0.753987i 0.0226262 + 0.0274222i
\(757\) 6.23128 0.226480 0.113240 0.993568i \(-0.463877\pi\)
0.113240 + 0.993568i \(0.463877\pi\)
\(758\) 24.7279 42.8300i 0.898157 1.55565i
\(759\) 3.37654 + 5.84833i 0.122561 + 0.212281i
\(760\) −11.8014 20.4406i −0.428081 0.741458i
\(761\) 14.2602 24.6995i 0.516933 0.895355i −0.482873 0.875690i \(-0.660407\pi\)
0.999807 0.0196647i \(-0.00625987\pi\)
\(762\) 58.5472 2.12094
\(763\) −6.60417 8.00406i −0.239087 0.289766i
\(764\) −2.63326 −0.0952681
\(765\) −8.86615 + 15.3566i −0.320556 + 0.555220i
\(766\) 13.6857 + 23.7043i 0.494483 + 0.856470i
\(767\) 5.82039 + 10.0812i 0.210162 + 0.364012i
\(768\) −4.24948 + 7.36032i −0.153340 + 0.265593i
\(769\) 13.9303 0.502340 0.251170 0.967943i \(-0.419185\pi\)
0.251170 + 0.967943i \(0.419185\pi\)
\(770\) 3.15628 8.45361i 0.113744 0.304647i
\(771\) −18.8434 −0.678629
\(772\) 1.57678 2.73106i 0.0567495 0.0982929i
\(773\) −19.8972 34.4630i −0.715654 1.23955i −0.962707 0.270547i \(-0.912795\pi\)
0.247053 0.969002i \(-0.420538\pi\)
\(774\) 16.8871 + 29.2493i 0.606993 + 1.05134i
\(775\) 0.00629480 0.0109029i 0.000226116 0.000391644i
\(776\) 6.17722 0.221749
\(777\) −19.4701 + 3.26731i −0.698486 + 0.117214i
\(778\) −24.7403 −0.886984
\(779\) −1.80790 + 3.13137i −0.0647747 + 0.112193i
\(780\) −0.884665 1.53228i −0.0316761 0.0548646i
\(781\) 5.60295 + 9.70460i 0.200489 + 0.347258i
\(782\) 7.38394 12.7894i 0.264049 0.457347i
\(783\) −8.59530 −0.307171
\(784\) 4.85814 25.1152i 0.173505 0.896973i
\(785\) 33.6319 1.20038
\(786\) −0.467047 + 0.808949i −0.0166590 + 0.0288542i
\(787\) 11.0350 + 19.1131i 0.393354 + 0.681309i 0.992890 0.119039i \(-0.0379814\pi\)
−0.599536 + 0.800348i \(0.704648\pi\)
\(788\) 1.03594 + 1.79430i 0.0369039 + 0.0639194i
\(789\) −3.03281 + 5.25298i −0.107971 + 0.187011i
\(790\) −26.7206 −0.950678
\(791\) −13.3281 + 2.23661i −0.473894 + 0.0795247i
\(792\) 6.49275 0.230710
\(793\) −6.24774 + 10.8214i −0.221864 + 0.384279i
\(794\) −25.5517 44.2568i −0.906796 1.57062i
\(795\) −20.7381 35.9194i −0.735504 1.27393i
\(796\) 2.05706 3.56294i 0.0729106 0.126285i
\(797\) 13.9948 0.495720 0.247860 0.968796i \(-0.420273\pi\)
0.247860 + 0.968796i \(0.420273\pi\)
\(798\) −10.1124 + 27.0844i −0.357974 + 0.958778i
\(799\) −29.6426 −1.04868
\(800\) 0.0164611 0.0285115i 0.000581989 0.00100803i
\(801\) 15.4763 + 26.8057i 0.546827 + 0.947132i
\(802\) 17.3785 + 30.1004i 0.613656 + 1.06288i
\(803\) 0.460340 0.797332i 0.0162450 0.0281372i
\(804\) −3.14848 −0.111038
\(805\) 10.0757 + 12.2114i 0.355121 + 0.430396i
\(806\) 1.04340 0.0367522
\(807\) 32.9493 57.0699i 1.15987 2.00895i
\(808\) 11.4881 + 19.8980i 0.404150 + 0.700008i
\(809\) 2.64582 + 4.58269i 0.0930219 + 0.161119i 0.908781 0.417273i \(-0.137014\pi\)
−0.815759 + 0.578391i \(0.803681\pi\)
\(810\) 16.6745 28.8810i 0.585881 1.01478i
\(811\) −19.4147 −0.681744 −0.340872 0.940110i \(-0.610722\pi\)
−0.340872 + 0.940110i \(0.610722\pi\)
\(812\) −1.00284 1.21542i −0.0351929 0.0426527i
\(813\) −18.0817 −0.634151
\(814\) 2.56366 4.44039i 0.0898562 0.155635i
\(815\) −8.48411 14.6949i −0.297185 0.514740i
\(816\) −16.5011 28.5807i −0.577653 1.00052i
\(817\) −22.9251 + 39.7074i −0.802047 + 1.38919i
\(818\) −5.54979 −0.194044
\(819\) −4.04836 + 10.8429i −0.141461 + 0.378881i
\(820\) 0.356466 0.0124483
\(821\) 1.72340 2.98501i 0.0601470 0.104178i −0.834384 0.551184i \(-0.814176\pi\)
0.894531 + 0.447006i \(0.147510\pi\)
\(822\) −26.2430 45.4541i −0.915328 1.58540i
\(823\) −19.8568 34.3931i −0.692166 1.19887i −0.971127 0.238564i \(-0.923323\pi\)
0.278961 0.960303i \(-0.410010\pi\)
\(824\) −10.1217 + 17.5313i −0.352607 + 0.610733i
\(825\) −0.0916828 −0.00319199
\(826\) −18.4933 + 3.10338i −0.643464 + 0.107981i
\(827\) 3.66589 0.127475 0.0637377 0.997967i \(-0.479698\pi\)
0.0637377 + 0.997967i \(0.479698\pi\)
\(828\) −0.421900 + 0.730753i −0.0146621 + 0.0253954i
\(829\) −2.88177 4.99138i −0.100088 0.173358i 0.811633 0.584168i \(-0.198579\pi\)
−0.911721 + 0.410810i \(0.865246\pi\)
\(830\) 11.3162 + 19.6003i 0.392793 + 0.680337i
\(831\) −1.21860 + 2.11067i −0.0422726 + 0.0732184i
\(832\) 19.0118 0.659115
\(833\) −21.4315 18.5958i −0.742557 0.644307i
\(834\) 45.7886 1.58553
\(835\) −9.18967 + 15.9170i −0.318022 + 0.550830i
\(836\) 0.326455 + 0.565437i 0.0112907 + 0.0195560i
\(837\) −0.398627 0.690442i −0.0137786 0.0238652i
\(838\) 22.8791 39.6277i 0.790345 1.36892i
\(839\) 2.49460 0.0861232 0.0430616 0.999072i \(-0.486289\pi\)
0.0430616 + 0.999072i \(0.486289\pi\)
\(840\) 37.9466 6.36787i 1.30928 0.219712i
\(841\) −15.1445 −0.522224
\(842\) −0.545500 + 0.944834i −0.0187992 + 0.0325611i
\(843\) 8.85607 + 15.3392i 0.305019 + 0.528309i
\(844\) 1.07840 + 1.86784i 0.0371199 + 0.0642936i
\(845\) 8.95222 15.5057i 0.307966 0.533412i
\(846\) −19.4775 −0.669651
\(847\) 9.00106 24.1079i 0.309280 0.828358i
\(848\) 30.5368 1.04864
\(849\) −30.8111 + 53.3665i −1.05744 + 1.83153i
\(850\) 0.100248 + 0.173634i 0.00343847 + 0.00595561i
\(851\) 4.49783 + 7.79047i 0.154184 + 0.267054i
\(852\) −1.76973 + 3.06527i −0.0606301 + 0.105014i
\(853\) 34.6227 1.18546 0.592729 0.805402i \(-0.298051\pi\)
0.592729 + 0.805402i \(0.298051\pi\)
\(854\) −12.8105 15.5259i −0.438366 0.531287i
\(855\) −15.8175 −0.540948
\(856\) 28.6661 49.6512i 0.979788 1.69704i
\(857\) −1.21181 2.09891i −0.0413946 0.0716975i 0.844586 0.535420i \(-0.179847\pi\)
−0.885980 + 0.463723i \(0.846513\pi\)
\(858\) −3.79924 6.58048i −0.129704 0.224654i
\(859\) 21.0938 36.5355i 0.719711 1.24658i −0.241403 0.970425i \(-0.577608\pi\)
0.961114 0.276151i \(-0.0890591\pi\)
\(860\) 4.52017 0.154136
\(861\) −3.75142 4.54661i −0.127848 0.154948i
\(862\) −54.0252 −1.84011
\(863\) −25.1325 + 43.5307i −0.855519 + 1.48180i 0.0206436 + 0.999787i \(0.493428\pi\)
−0.876163 + 0.482016i \(0.839905\pi\)
\(864\) −1.04242 1.80553i −0.0354640 0.0614254i
\(865\) 26.4430 + 45.8006i 0.899089 + 1.55727i
\(866\) 4.12342 7.14197i 0.140119 0.242694i
\(867\) 1.26791 0.0430606
\(868\) 0.0511226 0.136924i 0.00173522 0.00464750i
\(869\) 9.97860 0.338501
\(870\) −12.5309 + 21.7041i −0.424836 + 0.735838i
\(871\) 9.83895 + 17.0416i 0.333380 + 0.577432i
\(872\) 5.74581 + 9.95204i 0.194578 + 0.337019i
\(873\) 2.06985 3.58509i 0.0700539 0.121337i
\(874\) 13.1732 0.445591
\(875\) −29.2779 + 4.91316i −0.989774 + 0.166095i
\(876\) 0.290803 0.00982533
\(877\) −5.30500 + 9.18854i −0.179137 + 0.310275i −0.941585 0.336775i \(-0.890664\pi\)
0.762448 + 0.647049i \(0.223997\pi\)
\(878\) −27.1903 47.0950i −0.917629 1.58938i
\(879\) −10.6669 18.4756i −0.359785 0.623166i
\(880\) −4.59419 + 7.95736i −0.154870 + 0.268243i
\(881\) 2.45538 0.0827238 0.0413619 0.999144i \(-0.486830\pi\)
0.0413619 + 0.999144i \(0.486830\pi\)
\(882\) −14.0822 12.2189i −0.474171 0.411432i
\(883\) −47.5296 −1.59950 −0.799750 0.600333i \(-0.795035\pi\)
−0.799750 + 0.600333i \(0.795035\pi\)
\(884\) 0.722468 1.25135i 0.0242992 0.0420875i
\(885\) −12.9672 22.4599i −0.435889 0.754982i
\(886\) −12.2639 21.2416i −0.412013 0.713627i
\(887\) 2.17409 3.76563i 0.0729988 0.126438i −0.827215 0.561885i \(-0.810076\pi\)
0.900214 + 0.435447i \(0.143410\pi\)
\(888\) 21.8631 0.733679
\(889\) −50.5499 + 8.48285i −1.69539 + 0.284506i
\(890\) −47.6389 −1.59686
\(891\) −6.22694 + 10.7854i −0.208610 + 0.361324i
\(892\) −0.207762 0.359854i −0.00695638 0.0120488i
\(893\) −13.2209 22.8992i −0.442420 0.766294i
\(894\) −15.8559 + 27.4632i −0.530301 + 0.918508i
\(895\) 25.5216 0.853093
\(896\) −9.04116 + 24.2153i −0.302044 + 0.808978i
\(897\) 13.3312 0.445117
\(898\) 7.73473 13.3970i 0.258111 0.447062i
\(899\) 0.642581 + 1.11298i 0.0214313 + 0.0371200i
\(900\) −0.00572791 0.00992104i −0.000190930 0.000330701i
\(901\) 16.9359 29.3338i 0.564216 0.977251i
\(902\) 1.53086 0.0509721
\(903\) −47.5699 57.6533i −1.58303 1.91858i
\(904\) 14.9663 0.497770
\(905\) −19.7746 + 34.2505i −0.657328 + 1.13853i
\(906\) −7.73573 13.3987i −0.257003 0.445141i
\(907\) −6.49434 11.2485i −0.215641 0.373501i 0.737830 0.674987i \(-0.235851\pi\)
−0.953471 + 0.301486i \(0.902517\pi\)
\(908\) −0.808898 + 1.40105i −0.0268442 + 0.0464956i
\(909\) 15.3976 0.510707
\(910\) −11.3370 13.7402i −0.375819 0.455482i
\(911\) −15.4395 −0.511535 −0.255767 0.966738i \(-0.582328\pi\)
−0.255767 + 0.966738i \(0.582328\pi\)
\(912\) 14.7193 25.4945i 0.487403 0.844207i
\(913\) −4.22596 7.31957i −0.139859 0.242243i
\(914\) −19.1096 33.0988i −0.632090 1.09481i
\(915\) 13.9193 24.1090i 0.460159 0.797019i
\(916\) 2.17438 0.0718437
\(917\) 0.286042 0.766120i 0.00944595 0.0252995i
\(918\) 12.6967 0.419052
\(919\) −20.1114 + 34.8340i −0.663415 + 1.14907i 0.316298 + 0.948660i \(0.397560\pi\)
−0.979712 + 0.200408i \(0.935773\pi\)
\(920\) −8.76612 15.1834i −0.289010 0.500581i
\(921\) 9.18051 + 15.9011i 0.302508 + 0.523960i
\(922\) −20.0964 + 34.8081i −0.661841 + 1.14634i
\(923\) 22.1216 0.728140
\(924\) −1.04970 + 0.176151i −0.0345324 + 0.00579494i
\(925\) −0.122129 −0.00401559
\(926\) −19.7640 + 34.2322i −0.649485 + 1.12494i
\(927\) 6.78313 + 11.7487i 0.222787 + 0.385879i
\(928\) 1.68037 + 2.91049i 0.0551609 + 0.0955415i
\(929\) −6.75514 + 11.7003i −0.221629 + 0.383873i −0.955303 0.295629i \(-0.904471\pi\)
0.733674 + 0.679502i \(0.237804\pi\)
\(930\) −2.32459 −0.0762264
\(931\) 4.80683 24.8500i 0.157537 0.814425i
\(932\) −1.48197 −0.0485436
\(933\) −12.9934 + 22.5052i −0.425384 + 0.736786i
\(934\) −10.7562 18.6302i −0.351952 0.609599i
\(935\) 5.09593 + 8.82641i 0.166655 + 0.288654i
\(936\) 6.40866 11.1001i 0.209474 0.362819i
\(937\) −35.6590 −1.16493 −0.582465 0.812856i \(-0.697912\pi\)
−0.582465 + 0.812856i \(0.697912\pi\)
\(938\) −31.2616 + 5.24605i −1.02073 + 0.171289i
\(939\) −68.2141 −2.22608
\(940\) −1.30339 + 2.25753i −0.0425118 + 0.0736326i
\(941\) 6.90672 + 11.9628i 0.225153 + 0.389976i 0.956365 0.292174i \(-0.0943786\pi\)
−0.731213 + 0.682150i \(0.761045\pi\)
\(942\) 22.8103 + 39.5086i 0.743199 + 1.28726i
\(943\) −1.34292 + 2.32600i −0.0437314 + 0.0757450i
\(944\) 19.0942 0.621465
\(945\) −4.76091 + 12.7513i −0.154872 + 0.414801i
\(946\) 19.4121 0.631142
\(947\) −26.7218 + 46.2836i −0.868343 + 1.50401i −0.00465353 + 0.999989i \(0.501481\pi\)
−0.863689 + 0.504025i \(0.831852\pi\)
\(948\) 1.57591 + 2.72955i 0.0511831 + 0.0886516i
\(949\) −0.908755 1.57401i −0.0294994 0.0510945i
\(950\) −0.0894229 + 0.154885i −0.00290126 + 0.00502513i
\(951\) 46.3663 1.50353
\(952\) 19.9983 + 24.2373i 0.648148 + 0.785537i
\(953\) 43.4781 1.40840 0.704198 0.710004i \(-0.251307\pi\)
0.704198 + 0.710004i \(0.251307\pi\)
\(954\) 11.1282 19.2746i 0.360289 0.624039i
\(955\) −18.3332 31.7540i −0.593247 1.02753i
\(956\) −0.844646 1.46297i −0.0273178 0.0473158i
\(957\) 4.67955 8.10521i 0.151268 0.262004i
\(958\) 4.98951 0.161204
\(959\) 29.2441 + 35.4430i 0.944341 + 1.14451i
\(960\) −42.3564 −1.36705
\(961\) 15.4404 26.7436i 0.498077 0.862695i
\(962\) −5.06091 8.76575i −0.163170 0.282619i
\(963\) −19.2108 33.2741i −0.619059 1.07224i
\(964\) 0.721223 1.24920i 0.0232290 0.0402339i
\(965\) 43.9110 1.41355
\(966\) −7.51152 + 20.1184i −0.241679 + 0.647300i
\(967\) −60.5248 −1.94635 −0.973173 0.230075i \(-0.926103\pi\)
−0.973173 + 0.230075i \(0.926103\pi\)
\(968\) −14.2489 + 24.6799i −0.457978 + 0.793241i
\(969\) −16.3268 28.2788i −0.524492 0.908446i
\(970\) 3.18570 + 5.51779i 0.102287 + 0.177166i
\(971\) −8.15874 + 14.1314i −0.261826 + 0.453497i −0.966727 0.255809i \(-0.917658\pi\)
0.704901 + 0.709306i \(0.250991\pi\)
\(972\) −2.82526 −0.0906201
\(973\) −39.5340 + 6.63426i −1.26740 + 0.212685i
\(974\) 39.3124 1.25965
\(975\) −0.0904954 + 0.156743i −0.00289817 + 0.00501978i
\(976\) 10.2481 + 17.7502i 0.328033 + 0.568171i
\(977\) 7.07755 + 12.2587i 0.226431 + 0.392190i 0.956748 0.290919i \(-0.0939609\pi\)
−0.730317 + 0.683109i \(0.760628\pi\)
\(978\) 11.5084 19.9331i 0.367998 0.637392i
\(979\) 17.7903 0.568582
\(980\) −2.35857 + 0.814528i −0.0753418 + 0.0260192i
\(981\) 7.70118 0.245880
\(982\) 26.8041 46.4260i 0.855352 1.48151i
\(983\) −12.6583 21.9249i −0.403738 0.699295i 0.590436 0.807085i \(-0.298956\pi\)
−0.994174 + 0.107790i \(0.965623\pi\)
\(984\) 3.26384 + 5.65313i 0.104047 + 0.180215i
\(985\) −14.4248 + 24.9844i −0.459611 + 0.796070i
\(986\) −20.4668 −0.651796
\(987\) 42.5109 7.13381i 1.35314 0.227072i
\(988\) 1.28891 0.0410056
\(989\) −17.0289 + 29.4949i −0.541486 + 0.937882i
\(990\) 3.34842 + 5.79964i 0.106420 + 0.184325i
\(991\) 17.9260 + 31.0487i 0.569437 + 0.986294i 0.996622 + 0.0821299i \(0.0261722\pi\)
−0.427184 + 0.904165i \(0.640494\pi\)
\(992\) −0.155862 + 0.269961i −0.00494863 + 0.00857128i
\(993\) 1.48601 0.0471571
\(994\) −12.4644 + 33.3841i −0.395348 + 1.05888i
\(995\) 57.2863 1.81610
\(996\) 1.33480 2.31194i 0.0422947 0.0732566i
\(997\) −11.7124 20.2865i −0.370937 0.642481i 0.618773 0.785570i \(-0.287630\pi\)
−0.989710 + 0.143089i \(0.954297\pi\)
\(998\) −3.65018 6.32229i −0.115544 0.200129i
\(999\) −3.86700 + 6.69784i −0.122346 + 0.211910i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 287.2.e.c.247.2 yes 10
7.2 even 3 2009.2.a.l.1.4 5
7.4 even 3 inner 287.2.e.c.165.2 10
7.5 odd 6 2009.2.a.m.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.e.c.165.2 10 7.4 even 3 inner
287.2.e.c.247.2 yes 10 1.1 even 1 trivial
2009.2.a.l.1.4 5 7.2 even 3
2009.2.a.m.1.4 5 7.5 odd 6