Properties

Label 784.2.x.o.165.1
Level $784$
Weight $2$
Character 784.165
Analytic conductor $6.260$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), not 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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 165.1
Character \(\chi\) \(=\) 784.165
Dual form 784.2.x.o.765.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41419 + 0.00789795i) q^{2} +(-0.814813 - 3.04092i) q^{3} +(1.99988 - 0.0223384i) q^{4} +(-0.501787 + 1.87270i) q^{5} +(1.17632 + 4.29401i) q^{6} +(-2.82803 + 0.0473857i) q^{8} +(-5.98523 + 3.45557i) q^{9} +O(q^{10})\) \(q+(-1.41419 + 0.00789795i) q^{2} +(-0.814813 - 3.04092i) q^{3} +(1.99988 - 0.0223384i) q^{4} +(-0.501787 + 1.87270i) q^{5} +(1.17632 + 4.29401i) q^{6} +(-2.82803 + 0.0473857i) q^{8} +(-5.98523 + 3.45557i) q^{9} +(0.694833 - 2.65231i) q^{10} +(-1.11913 + 0.299871i) q^{11} +(-1.69745 - 6.06327i) q^{12} +(-0.00680742 + 0.00680742i) q^{13} +6.10359 q^{15} +(3.99900 - 0.0893481i) q^{16} +(-1.52290 + 2.63774i) q^{17} +(8.43697 - 4.93411i) q^{18} +(4.64620 + 1.24495i) q^{19} +(-0.961679 + 3.75637i) q^{20} +(1.58030 - 0.432914i) q^{22} +(4.27392 - 2.46755i) q^{23} +(2.44841 + 8.56122i) q^{24} +(1.07493 + 0.620609i) q^{25} +(0.00957323 - 0.00968076i) q^{26} +(8.70665 + 8.70665i) q^{27} +(-1.45434 + 1.45434i) q^{29} +(-8.63165 + 0.0482059i) q^{30} +(-2.60906 + 4.51902i) q^{31} +(-5.65465 + 0.157939i) q^{32} +(1.82377 + 3.15886i) q^{33} +(2.13284 - 3.74229i) q^{34} +(-11.8925 + 7.04442i) q^{36} +(2.28095 - 8.51263i) q^{37} +(-6.58045 - 1.72390i) q^{38} +(0.0262476 + 0.0151541i) q^{39} +(1.33033 - 5.31982i) q^{40} +6.02687i q^{41} +(7.17315 + 7.17315i) q^{43} +(-2.23143 + 0.624704i) q^{44} +(-3.46793 - 12.9425i) q^{45} +(-6.02466 + 3.52334i) q^{46} +(-0.796989 - 1.38043i) q^{47} +(-3.53014 - 12.0879i) q^{48} +(-1.52505 - 0.869170i) q^{50} +(9.26203 + 2.48175i) q^{51} +(-0.0134619 + 0.0137661i) q^{52} +(-0.787777 + 0.211084i) q^{53} +(-12.3816 - 12.2441i) q^{54} -2.24627i q^{55} -15.1431i q^{57} +(2.04523 - 2.06820i) q^{58} +(7.25156 - 1.94305i) q^{59} +(12.2064 - 0.136345i) q^{60} +(9.21796 + 2.46994i) q^{61} +(3.65401 - 6.41136i) q^{62} +(7.99551 - 0.268016i) q^{64} +(-0.00933235 - 0.0161641i) q^{65} +(-2.60411 - 4.45283i) q^{66} +(-1.70317 - 6.35630i) q^{67} +(-2.98668 + 5.30916i) q^{68} +(-10.9861 - 10.9861i) q^{69} +6.77044i q^{71} +(16.7627 - 10.0561i) q^{72} +(3.43645 + 1.98403i) q^{73} +(-3.15847 + 12.0565i) q^{74} +(1.01136 - 3.77445i) q^{75} +(9.31963 + 2.38595i) q^{76} +(-0.0372388 - 0.0212235i) q^{78} +(-2.81227 - 4.87099i) q^{79} +(-1.83933 + 7.53375i) q^{80} +(9.01525 - 15.6149i) q^{81} +(-0.0475999 - 8.52314i) q^{82} +(11.3733 - 11.3733i) q^{83} +(-4.17551 - 4.17551i) q^{85} +(-10.2009 - 10.0876i) q^{86} +(5.60755 + 3.23752i) q^{87} +(3.15073 - 0.901075i) q^{88} +(-3.59386 + 2.07492i) q^{89} +(5.00653 + 18.2758i) q^{90} +(8.49219 - 5.03026i) q^{92} +(15.8679 + 4.25179i) q^{93} +(1.13800 + 1.94589i) q^{94} +(-4.66281 + 8.07622i) q^{95} +(5.08777 + 17.0667i) q^{96} -0.390669 q^{97} +(5.66204 - 5.66204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41419 + 0.00789795i −0.999984 + 0.00558469i
\(3\) −0.814813 3.04092i −0.470433 1.75568i −0.638218 0.769855i \(-0.720328\pi\)
0.167786 0.985823i \(-0.446338\pi\)
\(4\) 1.99988 0.0223384i 0.999938 0.0111692i
\(5\) −0.501787 + 1.87270i −0.224406 + 0.837495i 0.758235 + 0.651981i \(0.226062\pi\)
−0.982642 + 0.185514i \(0.940605\pi\)
\(6\) 1.17632 + 4.29401i 0.480230 + 1.75302i
\(7\) 0 0
\(8\) −2.82803 + 0.0473857i −0.999860 + 0.0167534i
\(9\) −5.98523 + 3.45557i −1.99508 + 1.15186i
\(10\) 0.694833 2.65231i 0.219726 0.838735i
\(11\) −1.11913 + 0.299871i −0.337431 + 0.0904145i −0.423556 0.905870i \(-0.639218\pi\)
0.0861247 + 0.996284i \(0.472552\pi\)
\(12\) −1.69745 6.06327i −0.490013 1.75031i
\(13\) −0.00680742 + 0.00680742i −0.00188804 + 0.00188804i −0.708050 0.706162i \(-0.750425\pi\)
0.706162 + 0.708050i \(0.250425\pi\)
\(14\) 0 0
\(15\) 6.10359 1.57594
\(16\) 3.99900 0.0893481i 0.999750 0.0223370i
\(17\) −1.52290 + 2.63774i −0.369357 + 0.639745i −0.989465 0.144771i \(-0.953755\pi\)
0.620108 + 0.784516i \(0.287089\pi\)
\(18\) 8.43697 4.93411i 1.98861 1.16298i
\(19\) 4.64620 + 1.24495i 1.06591 + 0.285610i 0.748812 0.662782i \(-0.230625\pi\)
0.317099 + 0.948392i \(0.397291\pi\)
\(20\) −0.961679 + 3.75637i −0.215038 + 0.839949i
\(21\) 0 0
\(22\) 1.58030 0.432914i 0.336921 0.0922975i
\(23\) 4.27392 2.46755i 0.891174 0.514520i 0.0168479 0.999858i \(-0.494637\pi\)
0.874326 + 0.485338i \(0.161304\pi\)
\(24\) 2.44841 + 8.56122i 0.499780 + 1.74755i
\(25\) 1.07493 + 0.620609i 0.214985 + 0.124122i
\(26\) 0.00957323 0.00968076i 0.00187746 0.00189855i
\(27\) 8.70665 + 8.70665i 1.67559 + 1.67559i
\(28\) 0 0
\(29\) −1.45434 + 1.45434i −0.270064 + 0.270064i −0.829126 0.559062i \(-0.811161\pi\)
0.559062 + 0.829126i \(0.311161\pi\)
\(30\) −8.63165 + 0.0482059i −1.57592 + 0.00880114i
\(31\) −2.60906 + 4.51902i −0.468600 + 0.811639i −0.999356 0.0358855i \(-0.988575\pi\)
0.530756 + 0.847525i \(0.321908\pi\)
\(32\) −5.65465 + 0.157939i −0.999610 + 0.0279200i
\(33\) 1.82377 + 3.15886i 0.317478 + 0.549887i
\(34\) 2.13284 3.74229i 0.365778 0.641798i
\(35\) 0 0
\(36\) −11.8925 + 7.04442i −1.98209 + 1.17407i
\(37\) 2.28095 8.51263i 0.374986 1.39947i −0.478379 0.878154i \(-0.658775\pi\)
0.853365 0.521314i \(-0.174558\pi\)
\(38\) −6.58045 1.72390i −1.06749 0.279653i
\(39\) 0.0262476 + 0.0151541i 0.00420298 + 0.00242659i
\(40\) 1.33033 5.31982i 0.210344 0.841137i
\(41\) 6.02687i 0.941238i 0.882336 + 0.470619i \(0.155969\pi\)
−0.882336 + 0.470619i \(0.844031\pi\)
\(42\) 0 0
\(43\) 7.17315 + 7.17315i 1.09389 + 1.09389i 0.995109 + 0.0987862i \(0.0314960\pi\)
0.0987862 + 0.995109i \(0.468504\pi\)
\(44\) −2.23143 + 0.624704i −0.336400 + 0.0941777i
\(45\) −3.46793 12.9425i −0.516968 1.92935i
\(46\) −6.02466 + 3.52334i −0.888287 + 0.519489i
\(47\) −0.796989 1.38043i −0.116253 0.201356i 0.802027 0.597288i \(-0.203755\pi\)
−0.918280 + 0.395932i \(0.870422\pi\)
\(48\) −3.53014 12.0879i −0.509532 1.74473i
\(49\) 0 0
\(50\) −1.52505 0.869170i −0.215675 0.122919i
\(51\) 9.26203 + 2.48175i 1.29694 + 0.347515i
\(52\) −0.0134619 + 0.0137661i −0.00186683 + 0.00190901i
\(53\) −0.787777 + 0.211084i −0.108209 + 0.0289946i −0.312517 0.949912i \(-0.601172\pi\)
0.204308 + 0.978907i \(0.434506\pi\)
\(54\) −12.3816 12.2441i −1.68493 1.66621i
\(55\) 2.24627i 0.302887i
\(56\) 0 0
\(57\) 15.1431i 2.00576i
\(58\) 2.04523 2.06820i 0.268552 0.271568i
\(59\) 7.25156 1.94305i 0.944073 0.252964i 0.246228 0.969212i \(-0.420809\pi\)
0.697845 + 0.716248i \(0.254142\pi\)
\(60\) 12.2064 0.136345i 1.57584 0.0176020i
\(61\) 9.21796 + 2.46994i 1.18024 + 0.316244i 0.795021 0.606582i \(-0.207460\pi\)
0.385217 + 0.922826i \(0.374126\pi\)
\(62\) 3.65401 6.41136i 0.464060 0.814244i
\(63\) 0 0
\(64\) 7.99551 0.268016i 0.999439 0.0335021i
\(65\) −0.00933235 0.0161641i −0.00115754 0.00200491i
\(66\) −2.60411 4.45283i −0.320544 0.548106i
\(67\) −1.70317 6.35630i −0.208075 0.776546i −0.988490 0.151284i \(-0.951659\pi\)
0.780416 0.625261i \(-0.215008\pi\)
\(68\) −2.98668 + 5.30916i −0.362188 + 0.643830i
\(69\) −10.9861 10.9861i −1.32257 1.32257i
\(70\) 0 0
\(71\) 6.77044i 0.803504i 0.915749 + 0.401752i \(0.131599\pi\)
−0.915749 + 0.401752i \(0.868401\pi\)
\(72\) 16.7627 10.0561i 1.97550 1.18512i
\(73\) 3.43645 + 1.98403i 0.402206 + 0.232214i 0.687435 0.726246i \(-0.258737\pi\)
−0.285230 + 0.958459i \(0.592070\pi\)
\(74\) −3.15847 + 12.0565i −0.367165 + 1.40154i
\(75\) 1.01136 3.77445i 0.116782 0.435836i
\(76\) 9.31963 + 2.38595i 1.06903 + 0.273687i
\(77\) 0 0
\(78\) −0.0372388 0.0212235i −0.00421647 0.00240308i
\(79\) −2.81227 4.87099i −0.316405 0.548029i 0.663330 0.748327i \(-0.269142\pi\)
−0.979735 + 0.200298i \(0.935809\pi\)
\(80\) −1.83933 + 7.53375i −0.205643 + 0.842299i
\(81\) 9.01525 15.6149i 1.00169 1.73499i
\(82\) −0.0475999 8.52314i −0.00525653 0.941224i
\(83\) 11.3733 11.3733i 1.24838 1.24838i 0.291940 0.956437i \(-0.405699\pi\)
0.956437 0.291940i \(-0.0943007\pi\)
\(84\) 0 0
\(85\) −4.17551 4.17551i −0.452897 0.452897i
\(86\) −10.2009 10.0876i −1.09999 1.08777i
\(87\) 5.60755 + 3.23752i 0.601193 + 0.347099i
\(88\) 3.15073 0.901075i 0.335869 0.0960549i
\(89\) −3.59386 + 2.07492i −0.380948 + 0.219941i −0.678231 0.734849i \(-0.737253\pi\)
0.297282 + 0.954790i \(0.403920\pi\)
\(90\) 5.00653 + 18.2758i 0.527735 + 1.92643i
\(91\) 0 0
\(92\) 8.49219 5.03026i 0.885372 0.524441i
\(93\) 15.8679 + 4.25179i 1.64542 + 0.440890i
\(94\) 1.13800 + 1.94589i 0.117376 + 0.200703i
\(95\) −4.66281 + 8.07622i −0.478394 + 0.828603i
\(96\) 5.08777 + 17.0667i 0.519268 + 1.74186i
\(97\) −0.390669 −0.0396664 −0.0198332 0.999803i \(-0.506314\pi\)
−0.0198332 + 0.999803i \(0.506314\pi\)
\(98\) 0 0
\(99\) 5.66204 5.66204i 0.569057 0.569057i
\(100\) 2.16358 + 1.21713i 0.216358 + 0.121713i
\(101\) −3.75110 + 1.00511i −0.373249 + 0.100012i −0.440567 0.897720i \(-0.645222\pi\)
0.0673179 + 0.997732i \(0.478556\pi\)
\(102\) −13.1179 3.43653i −1.29886 0.340267i
\(103\) 1.83121 1.05725i 0.180434 0.104174i −0.407062 0.913400i \(-0.633447\pi\)
0.587497 + 0.809227i \(0.300113\pi\)
\(104\) 0.0189290 0.0195742i 0.00185614 0.00191940i
\(105\) 0 0
\(106\) 1.11240 0.304735i 0.108046 0.0295985i
\(107\) −3.89744 + 14.5454i −0.376779 + 1.40616i 0.473948 + 0.880553i \(0.342828\pi\)
−0.850728 + 0.525607i \(0.823838\pi\)
\(108\) 17.6067 + 17.2177i 1.69421 + 1.65678i
\(109\) −0.887009 3.31036i −0.0849600 0.317075i 0.910347 0.413847i \(-0.135815\pi\)
−0.995307 + 0.0967715i \(0.969148\pi\)
\(110\) 0.0177409 + 3.17665i 0.00169153 + 0.302882i
\(111\) −27.7448 −2.63342
\(112\) 0 0
\(113\) −2.54270 −0.239197 −0.119599 0.992822i \(-0.538161\pi\)
−0.119599 + 0.992822i \(0.538161\pi\)
\(114\) 0.119600 + 21.4153i 0.0112015 + 2.00573i
\(115\) 2.47637 + 9.24194i 0.230923 + 0.861816i
\(116\) −2.87601 + 2.94098i −0.267031 + 0.273064i
\(117\) 0.0172204 0.0642675i 0.00159203 0.00594153i
\(118\) −10.2398 + 2.80512i −0.942646 + 0.258232i
\(119\) 0 0
\(120\) −17.2611 + 0.289223i −1.57572 + 0.0264023i
\(121\) −8.36374 + 4.82881i −0.760340 + 0.438983i
\(122\) −13.0555 3.42017i −1.18199 0.309648i
\(123\) 18.3272 4.91077i 1.65251 0.442789i
\(124\) −5.11684 + 9.09575i −0.459506 + 0.816823i
\(125\) −8.55614 + 8.55614i −0.765285 + 0.765285i
\(126\) 0 0
\(127\) −0.663876 −0.0589095 −0.0294547 0.999566i \(-0.509377\pi\)
−0.0294547 + 0.999566i \(0.509377\pi\)
\(128\) −11.3051 + 0.442175i −0.999236 + 0.0390831i
\(129\) 15.9682 27.6578i 1.40592 2.43513i
\(130\) 0.0133254 + 0.0227854i 0.00116871 + 0.00199841i
\(131\) 4.20367 + 1.12637i 0.367276 + 0.0984113i 0.437737 0.899103i \(-0.355780\pi\)
−0.0704606 + 0.997515i \(0.522447\pi\)
\(132\) 3.71788 + 6.27659i 0.323600 + 0.546307i
\(133\) 0 0
\(134\) 2.45880 + 8.97557i 0.212408 + 0.775372i
\(135\) −20.6738 + 11.9360i −1.77932 + 1.02729i
\(136\) 4.18181 7.53176i 0.358587 0.645843i
\(137\) 12.1604 + 7.02081i 1.03893 + 0.599828i 0.919531 0.393018i \(-0.128569\pi\)
0.119402 + 0.992846i \(0.461902\pi\)
\(138\) 15.6232 + 15.4497i 1.32993 + 1.31516i
\(139\) 9.59908 + 9.59908i 0.814183 + 0.814183i 0.985258 0.171075i \(-0.0547239\pi\)
−0.171075 + 0.985258i \(0.554724\pi\)
\(140\) 0 0
\(141\) −3.54837 + 3.54837i −0.298827 + 0.298827i
\(142\) −0.0534726 9.57471i −0.00448732 0.803491i
\(143\) 0.00557706 0.00965975i 0.000466377 0.000807789i
\(144\) −23.6262 + 14.3536i −1.96885 + 1.19613i
\(145\) −1.99377 3.45330i −0.165573 0.286781i
\(146\) −4.87546 2.77866i −0.403496 0.229964i
\(147\) 0 0
\(148\) 4.37146 17.0751i 0.359332 1.40357i
\(149\) 1.23001 4.59048i 0.100767 0.376067i −0.897064 0.441901i \(-0.854304\pi\)
0.997831 + 0.0658345i \(0.0209709\pi\)
\(150\) −1.40045 + 5.34578i −0.114346 + 0.436481i
\(151\) −9.37492 5.41261i −0.762920 0.440472i 0.0674232 0.997724i \(-0.478522\pi\)
−0.830343 + 0.557252i \(0.811856\pi\)
\(152\) −13.1986 3.30058i −1.07055 0.267712i
\(153\) 21.0499i 1.70179i
\(154\) 0 0
\(155\) −7.15355 7.15355i −0.574587 0.574587i
\(156\) 0.0528305 + 0.0297199i 0.00422982 + 0.00237950i
\(157\) −0.113562 0.423817i −0.00906320 0.0338243i 0.961246 0.275692i \(-0.0889068\pi\)
−0.970309 + 0.241867i \(0.922240\pi\)
\(158\) 4.01556 + 6.86630i 0.319460 + 0.546254i
\(159\) 1.28378 + 2.22358i 0.101811 + 0.176341i
\(160\) 2.54166 10.6687i 0.200936 0.843434i
\(161\) 0 0
\(162\) −12.6260 + 22.1536i −0.991989 + 1.74055i
\(163\) 13.0407 + 3.49423i 1.02142 + 0.273689i 0.730395 0.683025i \(-0.239336\pi\)
0.291028 + 0.956715i \(0.406003\pi\)
\(164\) 0.134631 + 12.0530i 0.0105129 + 0.941179i
\(165\) −6.83073 + 1.83029i −0.531772 + 0.142488i
\(166\) −15.9941 + 16.1738i −1.24139 + 1.25533i
\(167\) 3.70883i 0.286998i 0.989650 + 0.143499i \(0.0458353\pi\)
−0.989650 + 0.143499i \(0.954165\pi\)
\(168\) 0 0
\(169\) 12.9999i 0.999993i
\(170\) 5.93795 + 5.87199i 0.455420 + 0.450361i
\(171\) −32.1106 + 8.60400i −2.45556 + 0.657964i
\(172\) 14.5056 + 14.1852i 1.10604 + 1.08161i
\(173\) 5.15933 + 1.38244i 0.392257 + 0.105105i 0.449556 0.893252i \(-0.351582\pi\)
−0.0572992 + 0.998357i \(0.518249\pi\)
\(174\) −7.95572 4.53419i −0.603122 0.343736i
\(175\) 0 0
\(176\) −4.44862 + 1.29918i −0.335328 + 0.0979291i
\(177\) −11.8173 20.4682i −0.888246 1.53849i
\(178\) 5.06602 2.96271i 0.379714 0.222065i
\(179\) 0.926668 + 3.45837i 0.0692624 + 0.258491i 0.991871 0.127246i \(-0.0406139\pi\)
−0.922609 + 0.385737i \(0.873947\pi\)
\(180\) −7.22453 25.8059i −0.538485 1.92346i
\(181\) 10.2442 + 10.2442i 0.761447 + 0.761447i 0.976584 0.215137i \(-0.0690199\pi\)
−0.215137 + 0.976584i \(0.569020\pi\)
\(182\) 0 0
\(183\) 30.0437i 2.22089i
\(184\) −11.9699 + 7.18083i −0.882429 + 0.529378i
\(185\) 14.7970 + 8.54306i 1.08790 + 0.628098i
\(186\) −22.4738 5.88752i −1.64786 0.431694i
\(187\) 0.913345 3.40865i 0.0667904 0.249265i
\(188\) −1.62472 2.74288i −0.118495 0.200045i
\(189\) 0 0
\(190\) 6.53032 11.4581i 0.473759 0.831262i
\(191\) 8.01270 + 13.8784i 0.579779 + 1.00421i 0.995504 + 0.0947160i \(0.0301943\pi\)
−0.415726 + 0.909490i \(0.636472\pi\)
\(192\) −7.32987 24.0954i −0.528988 1.73893i
\(193\) −3.59186 + 6.22128i −0.258548 + 0.447818i −0.965853 0.259090i \(-0.916577\pi\)
0.707305 + 0.706908i \(0.249911\pi\)
\(194\) 0.552481 0.00308548i 0.0396658 0.000221525i
\(195\) −0.0415497 + 0.0415497i −0.00297544 + 0.00297544i
\(196\) 0 0
\(197\) 13.9009 + 13.9009i 0.990395 + 0.990395i 0.999954 0.00955923i \(-0.00304285\pi\)
−0.00955923 + 0.999954i \(0.503043\pi\)
\(198\) −7.96249 + 8.05193i −0.565870 + 0.572226i
\(199\) −23.8518 13.7709i −1.69081 0.976191i −0.953863 0.300242i \(-0.902933\pi\)
−0.736949 0.675949i \(-0.763734\pi\)
\(200\) −3.06933 1.70416i −0.217035 0.120503i
\(201\) −17.9413 + 10.3584i −1.26548 + 0.730625i
\(202\) 5.29684 1.45104i 0.372684 0.102095i
\(203\) 0 0
\(204\) 18.5784 + 4.75630i 1.30074 + 0.333008i
\(205\) −11.2865 3.02421i −0.788283 0.211220i
\(206\) −2.58133 + 1.50962i −0.179850 + 0.105180i
\(207\) −17.0536 + 29.5377i −1.18531 + 2.05301i
\(208\) −0.0266146 + 0.0278311i −0.00184539 + 0.00192974i
\(209\) −5.57304 −0.385495
\(210\) 0 0
\(211\) −0.278791 + 0.278791i −0.0191928 + 0.0191928i −0.716638 0.697445i \(-0.754320\pi\)
0.697445 + 0.716638i \(0.254320\pi\)
\(212\) −1.57074 + 0.439740i −0.107879 + 0.0302014i
\(213\) 20.5884 5.51665i 1.41069 0.377995i
\(214\) 5.39684 20.6008i 0.368920 1.40824i
\(215\) −17.0325 + 9.83373i −1.16161 + 0.670655i
\(216\) −25.0352 24.2101i −1.70343 1.64729i
\(217\) 0 0
\(218\) 1.28055 + 4.67448i 0.0867295 + 0.316596i
\(219\) 3.23323 12.0666i 0.218482 0.815385i
\(220\) −0.0501781 4.49226i −0.00338301 0.302868i
\(221\) −0.00758917 0.0283232i −0.000510503 0.00190522i
\(222\) 39.2365 0.219127i 2.63338 0.0147068i
\(223\) 17.0225 1.13991 0.569956 0.821676i \(-0.306960\pi\)
0.569956 + 0.821676i \(0.306960\pi\)
\(224\) 0 0
\(225\) −8.57824 −0.571883
\(226\) 3.59587 0.0200821i 0.239193 0.00133584i
\(227\) −0.584192 2.18023i −0.0387742 0.144707i 0.943825 0.330445i \(-0.107199\pi\)
−0.982599 + 0.185738i \(0.940532\pi\)
\(228\) −0.338274 30.2844i −0.0224027 2.00563i
\(229\) 3.59412 13.4134i 0.237506 0.886384i −0.739497 0.673160i \(-0.764937\pi\)
0.977003 0.213225i \(-0.0683966\pi\)
\(230\) −3.57506 13.0503i −0.235732 0.860513i
\(231\) 0 0
\(232\) 4.04400 4.18183i 0.265502 0.274551i
\(233\) 1.84701 1.06637i 0.121002 0.0698605i −0.438277 0.898840i \(-0.644411\pi\)
0.559279 + 0.828979i \(0.311078\pi\)
\(234\) −0.0238454 + 0.0910225i −0.00155882 + 0.00595033i
\(235\) 2.98504 0.799838i 0.194722 0.0521757i
\(236\) 14.4588 4.04785i 0.941189 0.263492i
\(237\) −12.5208 + 12.5208i −0.813316 + 0.813316i
\(238\) 0 0
\(239\) −17.5943 −1.13808 −0.569041 0.822309i \(-0.692685\pi\)
−0.569041 + 0.822309i \(0.692685\pi\)
\(240\) 24.4083 0.545344i 1.57555 0.0352018i
\(241\) −4.20427 + 7.28200i −0.270821 + 0.469075i −0.969072 0.246777i \(-0.920628\pi\)
0.698252 + 0.715852i \(0.253962\pi\)
\(242\) 11.7898 6.89492i 0.757877 0.443222i
\(243\) −19.1489 5.13093i −1.22840 0.329149i
\(244\) 18.4899 + 4.73366i 1.18370 + 0.303042i
\(245\) 0 0
\(246\) −25.8794 + 7.08952i −1.65001 + 0.452011i
\(247\) −0.0401035 + 0.0231537i −0.00255172 + 0.00147324i
\(248\) 7.16435 12.9035i 0.454937 0.819376i
\(249\) −43.8523 25.3181i −2.77903 1.60447i
\(250\) 12.0324 12.1676i 0.760999 0.769546i
\(251\) −5.35828 5.35828i −0.338212 0.338212i 0.517482 0.855694i \(-0.326869\pi\)
−0.855694 + 0.517482i \(0.826869\pi\)
\(252\) 0 0
\(253\) −4.04314 + 4.04314i −0.254190 + 0.254190i
\(254\) 0.938848 0.00524326i 0.0589086 0.000328991i
\(255\) −9.29515 + 16.0997i −0.582085 + 1.00820i
\(256\) 15.9840 0.714607i 0.999002 0.0446629i
\(257\) −0.615501 1.06608i −0.0383939 0.0665002i 0.846190 0.532881i \(-0.178891\pi\)
−0.884584 + 0.466381i \(0.845557\pi\)
\(258\) −22.3637 + 39.2395i −1.39230 + 2.44295i
\(259\) 0 0
\(260\) −0.0190246 0.0321177i −0.00117986 0.00199186i
\(261\) 3.67898 13.7301i 0.227723 0.849873i
\(262\) −5.95368 1.55970i −0.367820 0.0963586i
\(263\) −17.4432 10.0709i −1.07560 0.620996i −0.145891 0.989301i \(-0.546605\pi\)
−0.929705 + 0.368305i \(0.879938\pi\)
\(264\) −5.30736 8.84693i −0.326645 0.544491i
\(265\) 1.58119i 0.0971315i
\(266\) 0 0
\(267\) 9.23799 + 9.23799i 0.565356 + 0.565356i
\(268\) −3.54811 12.6738i −0.216735 0.774173i
\(269\) 3.23015 + 12.0551i 0.196946 + 0.735011i 0.991755 + 0.128151i \(0.0409044\pi\)
−0.794809 + 0.606860i \(0.792429\pi\)
\(270\) 29.1424 17.0431i 1.77355 1.03721i
\(271\) 13.7567 + 23.8273i 0.835660 + 1.44741i 0.893492 + 0.449079i \(0.148248\pi\)
−0.0578325 + 0.998326i \(0.518419\pi\)
\(272\) −5.85439 + 10.6844i −0.354975 + 0.647836i
\(273\) 0 0
\(274\) −17.2526 9.83273i −1.04227 0.594017i
\(275\) −1.38909 0.372205i −0.0837652 0.0224448i
\(276\) −22.2162 21.7254i −1.33726 1.30771i
\(277\) 5.53100 1.48203i 0.332326 0.0890464i −0.0887978 0.996050i \(-0.528303\pi\)
0.421124 + 0.907003i \(0.361636\pi\)
\(278\) −13.6508 13.4991i −0.818718 0.809624i
\(279\) 36.0631i 2.15904i
\(280\) 0 0
\(281\) 15.6051i 0.930919i 0.885069 + 0.465460i \(0.154111\pi\)
−0.885069 + 0.465460i \(0.845889\pi\)
\(282\) 4.99005 5.04610i 0.297153 0.300491i
\(283\) −8.14066 + 2.18128i −0.483912 + 0.129664i −0.492524 0.870299i \(-0.663925\pi\)
0.00861163 + 0.999963i \(0.497259\pi\)
\(284\) 0.151241 + 13.5400i 0.00897450 + 0.803454i
\(285\) 28.3585 + 7.59864i 1.67981 + 0.450104i
\(286\) −0.00781074 + 0.0137048i −0.000461859 + 0.000810381i
\(287\) 0 0
\(288\) 33.2986 20.4854i 1.96214 1.20711i
\(289\) 3.86157 + 6.68843i 0.227151 + 0.393437i
\(290\) 2.84684 + 4.86789i 0.167172 + 0.285852i
\(291\) 0.318322 + 1.18800i 0.0186604 + 0.0696415i
\(292\) 6.91679 + 3.89106i 0.404774 + 0.227707i
\(293\) −10.7837 10.7837i −0.629991 0.629991i 0.318075 0.948066i \(-0.396964\pi\)
−0.948066 + 0.318075i \(0.896964\pi\)
\(294\) 0 0
\(295\) 14.5550i 0.847423i
\(296\) −6.04722 + 24.1821i −0.351488 + 1.40555i
\(297\) −12.3548 7.13303i −0.716896 0.413900i
\(298\) −1.70322 + 6.50153i −0.0986649 + 0.376623i
\(299\) −0.0122967 + 0.0458920i −0.000711138 + 0.00265400i
\(300\) 1.93828 7.57102i 0.111907 0.437113i
\(301\) 0 0
\(302\) 13.3007 + 7.58043i 0.765368 + 0.436205i
\(303\) 6.11290 + 10.5879i 0.351177 + 0.608256i
\(304\) 18.6914 + 4.56341i 1.07202 + 0.261729i
\(305\) −9.25091 + 16.0230i −0.529706 + 0.917477i
\(306\) 0.166251 + 29.7686i 0.00950395 + 1.70176i
\(307\) −12.4028 + 12.4028i −0.707863 + 0.707863i −0.966085 0.258223i \(-0.916863\pi\)
0.258223 + 0.966085i \(0.416863\pi\)
\(308\) 0 0
\(309\) −4.70711 4.70711i −0.267778 0.267778i
\(310\) 10.1730 + 10.0600i 0.577787 + 0.571369i
\(311\) 30.2727 + 17.4780i 1.71661 + 0.991084i 0.924922 + 0.380157i \(0.124130\pi\)
0.791687 + 0.610927i \(0.209203\pi\)
\(312\) −0.0749471 0.0416124i −0.00424305 0.00235584i
\(313\) 6.83406 3.94565i 0.386284 0.223021i −0.294265 0.955724i \(-0.595075\pi\)
0.680549 + 0.732703i \(0.261741\pi\)
\(314\) 0.163945 + 0.598462i 0.00925196 + 0.0337732i
\(315\) 0 0
\(316\) −5.73299 9.67855i −0.322506 0.544461i
\(317\) −6.72441 1.80180i −0.377681 0.101199i 0.0649843 0.997886i \(-0.479300\pi\)
−0.442665 + 0.896687i \(0.645967\pi\)
\(318\) −1.83308 3.13442i −0.102794 0.175770i
\(319\) 1.19149 2.06371i 0.0667104 0.115546i
\(320\) −3.51013 + 15.1076i −0.196222 + 0.844543i
\(321\) 47.4072 2.64601
\(322\) 0 0
\(323\) −10.3595 + 10.3595i −0.576419 + 0.576419i
\(324\) 17.6806 31.4292i 0.982253 1.74607i
\(325\) −0.0115422 + 0.00309273i −0.000640247 + 0.000171554i
\(326\) −18.4696 4.83852i −1.02294 0.267981i
\(327\) −9.34382 + 5.39465i −0.516714 + 0.298325i
\(328\) −0.285587 17.0442i −0.0157689 0.941106i
\(329\) 0 0
\(330\) 9.64551 2.64233i 0.530968 0.145455i
\(331\) −0.541330 + 2.02027i −0.0297542 + 0.111044i −0.979206 0.202869i \(-0.934973\pi\)
0.949452 + 0.313913i \(0.101640\pi\)
\(332\) 22.4910 22.9991i 1.23436 1.26224i
\(333\) 15.7640 + 58.8320i 0.863861 + 3.22397i
\(334\) −0.0292921 5.24499i −0.00160279 0.286993i
\(335\) 12.7580 0.697047
\(336\) 0 0
\(337\) 35.7263 1.94613 0.973066 0.230525i \(-0.0740442\pi\)
0.973066 + 0.230525i \(0.0740442\pi\)
\(338\) −0.102673 18.3844i −0.00558465 0.999977i
\(339\) 2.07183 + 7.73216i 0.112526 + 0.419953i
\(340\) −8.44377 8.25722i −0.457928 0.447811i
\(341\) 1.56476 5.83976i 0.0847365 0.316241i
\(342\) 45.3425 12.4213i 2.45184 0.671667i
\(343\) 0 0
\(344\) −20.6258 19.9460i −1.11207 1.07541i
\(345\) 26.0863 15.0609i 1.40444 0.810853i
\(346\) −7.30720 1.91428i −0.392838 0.102913i
\(347\) 20.1610 5.40213i 1.08230 0.290002i 0.326763 0.945106i \(-0.394042\pi\)
0.755538 + 0.655105i \(0.227375\pi\)
\(348\) 11.2867 + 6.34937i 0.605032 + 0.340362i
\(349\) −10.2714 + 10.2714i −0.549813 + 0.549813i −0.926387 0.376574i \(-0.877102\pi\)
0.376574 + 0.926387i \(0.377102\pi\)
\(350\) 0 0
\(351\) −0.118540 −0.00632717
\(352\) 6.28094 1.87242i 0.334775 0.0998003i
\(353\) −15.0632 + 26.0903i −0.801735 + 1.38865i 0.116739 + 0.993163i \(0.462756\pi\)
−0.918473 + 0.395483i \(0.870577\pi\)
\(354\) 16.8736 + 28.8527i 0.896824 + 1.53350i
\(355\) −12.6790 3.39732i −0.672931 0.180311i
\(356\) −7.14092 + 4.22986i −0.378468 + 0.224182i
\(357\) 0 0
\(358\) −1.33780 4.88348i −0.0707049 0.258100i
\(359\) 18.1770 10.4945i 0.959347 0.553879i 0.0633748 0.997990i \(-0.479814\pi\)
0.895972 + 0.444111i \(0.146480\pi\)
\(360\) 10.4207 + 36.4374i 0.549218 + 1.92042i
\(361\) 3.58279 + 2.06853i 0.188568 + 0.108870i
\(362\) −14.5682 14.4064i −0.765687 0.757182i
\(363\) 21.4989 + 21.4989i 1.12840 + 1.12840i
\(364\) 0 0
\(365\) −5.43986 + 5.43986i −0.284735 + 0.284735i
\(366\) 0.237283 + 42.4875i 0.0124030 + 2.22086i
\(367\) 3.31261 5.73760i 0.172917 0.299500i −0.766522 0.642218i \(-0.778014\pi\)
0.939438 + 0.342718i \(0.111348\pi\)
\(368\) 16.8710 10.2496i 0.879459 0.534298i
\(369\) −20.8263 36.0722i −1.08417 1.87784i
\(370\) −20.9933 11.9647i −1.09139 0.622013i
\(371\) 0 0
\(372\) 31.8288 + 8.14858i 1.65024 + 0.422484i
\(373\) −5.63908 + 21.0453i −0.291981 + 1.08969i 0.651605 + 0.758558i \(0.274096\pi\)
−0.943586 + 0.331128i \(0.892571\pi\)
\(374\) −1.26472 + 4.82770i −0.0653973 + 0.249634i
\(375\) 32.9902 + 19.0469i 1.70361 + 0.983579i
\(376\) 2.31932 + 3.86612i 0.119610 + 0.199380i
\(377\) 0.0198006i 0.00101978i
\(378\) 0 0
\(379\) −0.217504 0.217504i −0.0111724 0.0111724i 0.701499 0.712671i \(-0.252515\pi\)
−0.712671 + 0.701499i \(0.752515\pi\)
\(380\) −9.14462 + 16.2556i −0.469109 + 0.833894i
\(381\) 0.540935 + 2.01880i 0.0277129 + 0.103426i
\(382\) −11.4411 19.5634i −0.585378 1.00095i
\(383\) −11.0347 19.1127i −0.563848 0.976614i −0.997156 0.0753677i \(-0.975987\pi\)
0.433308 0.901246i \(-0.357346\pi\)
\(384\) 10.5561 + 34.0176i 0.538691 + 1.73595i
\(385\) 0 0
\(386\) 5.03044 8.82645i 0.256043 0.449255i
\(387\) −67.7203 18.1456i −3.44241 0.922392i
\(388\) −0.781289 + 0.00872693i −0.0396640 + 0.000443043i
\(389\) 32.8412 8.79977i 1.66511 0.446166i 0.701327 0.712840i \(-0.252591\pi\)
0.963787 + 0.266674i \(0.0859246\pi\)
\(390\) 0.0584311 0.0590874i 0.00295877 0.00299201i
\(391\) 15.0313i 0.760166i
\(392\) 0 0
\(393\) 13.7008i 0.691114i
\(394\) −19.7683 19.5487i −0.995911 0.984849i
\(395\) 10.5330 2.82232i 0.529975 0.142006i
\(396\) 11.1969 11.4499i 0.562665 0.575377i
\(397\) −36.3522 9.74055i −1.82447 0.488864i −0.827144 0.561991i \(-0.810036\pi\)
−0.997323 + 0.0731264i \(0.976702\pi\)
\(398\) 33.8398 + 19.2863i 1.69624 + 0.966733i
\(399\) 0 0
\(400\) 4.35408 + 2.38577i 0.217704 + 0.119289i
\(401\) −14.3983 24.9385i −0.719015 1.24537i −0.961390 0.275188i \(-0.911260\pi\)
0.242375 0.970183i \(-0.422073\pi\)
\(402\) 25.2906 14.7905i 1.26138 0.737681i
\(403\) −0.0130019 0.0485238i −0.000647671 0.00241714i
\(404\) −7.47929 + 2.09388i −0.372108 + 0.104174i
\(405\) 24.7182 + 24.7182i 1.22826 + 1.22826i
\(406\) 0 0
\(407\) 10.2108i 0.506128i
\(408\) −26.3109 6.57959i −1.30258 0.325738i
\(409\) −17.3533 10.0189i −0.858066 0.495405i 0.00529806 0.999986i \(-0.498314\pi\)
−0.863364 + 0.504581i \(0.831647\pi\)
\(410\) 15.9851 + 4.18767i 0.789450 + 0.206814i
\(411\) 11.4413 42.6995i 0.564358 2.10621i
\(412\) 3.63857 2.15527i 0.179260 0.106183i
\(413\) 0 0
\(414\) 23.8838 41.9066i 1.17382 2.05960i
\(415\) 15.5917 + 27.0056i 0.765366 + 1.32565i
\(416\) 0.0374184 0.0395687i 0.00183459 0.00194002i
\(417\) 21.3686 37.0115i 1.04643 1.81246i
\(418\) 7.88134 0.0440156i 0.385489 0.00215287i
\(419\) 11.3829 11.3829i 0.556093 0.556093i −0.372100 0.928193i \(-0.621362\pi\)
0.928193 + 0.372100i \(0.121362\pi\)
\(420\) 0 0
\(421\) −28.3916 28.3916i −1.38372 1.38372i −0.837905 0.545816i \(-0.816220\pi\)
−0.545816 0.837905i \(-0.683780\pi\)
\(422\) 0.392062 0.396466i 0.0190853 0.0192997i
\(423\) 9.54032 + 5.50811i 0.463866 + 0.267813i
\(424\) 2.21785 0.634282i 0.107708 0.0308034i
\(425\) −3.27401 + 1.89025i −0.158813 + 0.0916905i
\(426\) −29.0724 + 7.96420i −1.40856 + 0.385867i
\(427\) 0 0
\(428\) −7.46946 + 29.1761i −0.361050 + 1.41028i
\(429\) −0.0339188 0.00908853i −0.00163762 0.000438798i
\(430\) 24.0096 14.0413i 1.15785 0.677132i
\(431\) 11.6251 20.1352i 0.559961 0.969880i −0.437538 0.899200i \(-0.644150\pi\)
0.997499 0.0706806i \(-0.0225171\pi\)
\(432\) 35.5958 + 34.0400i 1.71260 + 1.63775i
\(433\) −19.0385 −0.914932 −0.457466 0.889227i \(-0.651243\pi\)
−0.457466 + 0.889227i \(0.651243\pi\)
\(434\) 0 0
\(435\) −8.87669 + 8.87669i −0.425605 + 0.425605i
\(436\) −1.84786 6.60050i −0.0884962 0.316106i
\(437\) 22.9295 6.14393i 1.09686 0.293904i
\(438\) −4.47711 + 17.0900i −0.213925 + 0.816592i
\(439\) 22.9131 13.2289i 1.09358 0.631380i 0.159055 0.987270i \(-0.449155\pi\)
0.934528 + 0.355889i \(0.115822\pi\)
\(440\) 0.106441 + 6.35251i 0.00507438 + 0.302844i
\(441\) 0 0
\(442\) 0.0109562 + 0.0399944i 0.000521135 + 0.00190234i
\(443\) 8.64233 32.2536i 0.410609 1.53241i −0.382861 0.923806i \(-0.625061\pi\)
0.793470 0.608609i \(-0.208272\pi\)
\(444\) −55.4862 + 0.619775i −2.63326 + 0.0294132i
\(445\) −2.08233 7.77138i −0.0987121 0.368399i
\(446\) −24.0731 + 0.134443i −1.13989 + 0.00636605i
\(447\) −14.9615 −0.707656
\(448\) 0 0
\(449\) −28.6036 −1.34989 −0.674945 0.737868i \(-0.735833\pi\)
−0.674945 + 0.737868i \(0.735833\pi\)
\(450\) 12.1313 0.0677505i 0.571874 0.00319379i
\(451\) −1.80728 6.74486i −0.0851015 0.317603i
\(452\) −5.08508 + 0.0567999i −0.239182 + 0.00267164i
\(453\) −8.82054 + 32.9187i −0.414425 + 1.54665i
\(454\) 0.843378 + 3.07865i 0.0395817 + 0.144488i
\(455\) 0 0
\(456\) 0.717569 + 42.8253i 0.0336032 + 2.00548i
\(457\) −28.3772 + 16.3836i −1.32743 + 0.766392i −0.984902 0.173115i \(-0.944617\pi\)
−0.342529 + 0.939507i \(0.611283\pi\)
\(458\) −4.97683 + 18.9975i −0.232552 + 0.887697i
\(459\) −36.2252 + 9.70650i −1.69085 + 0.453061i
\(460\) 5.15888 + 18.4274i 0.240534 + 0.859183i
\(461\) −17.2919 + 17.2919i −0.805362 + 0.805362i −0.983928 0.178566i \(-0.942854\pi\)
0.178566 + 0.983928i \(0.442854\pi\)
\(462\) 0 0
\(463\) 1.66786 0.0775121 0.0387560 0.999249i \(-0.487660\pi\)
0.0387560 + 0.999249i \(0.487660\pi\)
\(464\) −5.68596 + 5.94585i −0.263964 + 0.276029i
\(465\) −15.9246 + 27.5822i −0.738486 + 1.27910i
\(466\) −2.60361 + 1.52265i −0.120610 + 0.0705352i
\(467\) −2.87255 0.769699i −0.132926 0.0356174i 0.191743 0.981445i \(-0.438586\pi\)
−0.324669 + 0.945828i \(0.605253\pi\)
\(468\) 0.0330030 0.128912i 0.00152557 0.00595894i
\(469\) 0 0
\(470\) −4.21510 + 1.15470i −0.194428 + 0.0532623i
\(471\) −1.19627 + 0.690664i −0.0551210 + 0.0318241i
\(472\) −20.4156 + 5.83863i −0.939703 + 0.268745i
\(473\) −10.1787 5.87669i −0.468018 0.270211i
\(474\) 17.6080 17.8058i 0.808761 0.817845i
\(475\) 4.22170 + 4.22170i 0.193705 + 0.193705i
\(476\) 0 0
\(477\) 3.98561 3.98561i 0.182488 0.182488i
\(478\) 24.8817 0.138959i 1.13806 0.00635584i
\(479\) 3.91759 6.78546i 0.178999 0.310035i −0.762539 0.646942i \(-0.776047\pi\)
0.941538 + 0.336907i \(0.109381\pi\)
\(480\) −34.5137 + 0.963997i −1.57533 + 0.0440002i
\(481\) 0.0424216 + 0.0734764i 0.00193426 + 0.00335023i
\(482\) 5.88813 10.3314i 0.268197 0.470580i
\(483\) 0 0
\(484\) −16.6186 + 9.84385i −0.755390 + 0.447448i
\(485\) 0.196033 0.731604i 0.00890139 0.0332204i
\(486\) 27.1207 + 7.10488i 1.23022 + 0.322284i
\(487\) −14.2879 8.24910i −0.647445 0.373802i 0.140032 0.990147i \(-0.455279\pi\)
−0.787477 + 0.616345i \(0.788613\pi\)
\(488\) −26.1857 6.54828i −1.18537 0.296427i
\(489\) 42.5028i 1.92204i
\(490\) 0 0
\(491\) −13.4608 13.4608i −0.607477 0.607477i 0.334809 0.942286i \(-0.391328\pi\)
−0.942286 + 0.334809i \(0.891328\pi\)
\(492\) 36.5425 10.2303i 1.64746 0.461219i
\(493\) −1.62135 6.05097i −0.0730221 0.272522i
\(494\) 0.0565311 0.0330606i 0.00254346 0.00148747i
\(495\) 7.76214 + 13.4444i 0.348882 + 0.604282i
\(496\) −10.0299 + 18.3047i −0.450354 + 0.821904i
\(497\) 0 0
\(498\) 62.2155 + 35.4583i 2.78794 + 1.58893i
\(499\) 13.4940 + 3.61570i 0.604074 + 0.161861i 0.547877 0.836559i \(-0.315436\pi\)
0.0561963 + 0.998420i \(0.482103\pi\)
\(500\) −16.9201 + 17.3023i −0.756689 + 0.773784i
\(501\) 11.2783 3.02200i 0.503876 0.135013i
\(502\) 7.61995 + 7.53531i 0.340095 + 0.336318i
\(503\) 31.1020i 1.38677i −0.720568 0.693384i \(-0.756119\pi\)
0.720568 0.693384i \(-0.243881\pi\)
\(504\) 0 0
\(505\) 7.52903i 0.335037i
\(506\) 5.68584 5.74971i 0.252767 0.255606i
\(507\) 39.5317 10.5925i 1.75567 0.470429i
\(508\) −1.32767 + 0.0148299i −0.0589058 + 0.000657972i
\(509\) −39.7462 10.6500i −1.76172 0.472051i −0.774655 0.632383i \(-0.782077\pi\)
−0.987063 + 0.160332i \(0.948743\pi\)
\(510\) 13.0180 22.8414i 0.576445 1.01144i
\(511\) 0 0
\(512\) −22.5988 + 1.13683i −0.998737 + 0.0502413i
\(513\) 29.6135 + 51.2921i 1.30747 + 2.26460i
\(514\) 0.878856 + 1.50278i 0.0387647 + 0.0662847i
\(515\) 1.06103 + 3.95981i 0.0467545 + 0.174490i
\(516\) 31.3166 55.6688i 1.37864 2.45068i
\(517\) 1.30589 + 1.30589i 0.0574328 + 0.0574328i
\(518\) 0 0
\(519\) 16.8156i 0.738122i
\(520\) 0.0271581 + 0.0452703i 0.00119096 + 0.00198524i
\(521\) 6.59720 + 3.80889i 0.289028 + 0.166871i 0.637504 0.770447i \(-0.279967\pi\)
−0.348475 + 0.937318i \(0.613300\pi\)
\(522\) −5.09434 + 19.4461i −0.222973 + 0.851132i
\(523\) 5.14314 19.1945i 0.224894 0.839315i −0.757553 0.652773i \(-0.773605\pi\)
0.982447 0.186542i \(-0.0597280\pi\)
\(524\) 8.43197 + 2.15869i 0.368352 + 0.0943030i
\(525\) 0 0
\(526\) 24.7476 + 14.1044i 1.07905 + 0.614979i
\(527\) −7.94665 13.7640i −0.346161 0.599569i
\(528\) 7.57550 + 12.4693i 0.329681 + 0.542658i
\(529\) 0.677604 1.17365i 0.0294611 0.0510281i
\(530\) 0.0124881 + 2.23610i 0.000542449 + 0.0971299i
\(531\) −36.6879 + 36.6879i −1.59212 + 1.59212i
\(532\) 0 0
\(533\) −0.0410274 0.0410274i −0.00177709 0.00177709i
\(534\) −13.1373 12.9913i −0.568504 0.562190i
\(535\) −25.2835 14.5974i −1.09310 0.631102i
\(536\) 5.11780 + 17.8951i 0.221055 + 0.772951i
\(537\) 9.76158 5.63585i 0.421243 0.243205i
\(538\) −4.66326 17.0227i −0.201047 0.733900i
\(539\) 0 0
\(540\) −41.0784 + 24.3324i −1.76773 + 1.04710i
\(541\) 15.2423 + 4.08415i 0.655316 + 0.175591i 0.571131 0.820859i \(-0.306505\pi\)
0.0841847 + 0.996450i \(0.473171\pi\)
\(542\) −19.6428 33.5877i −0.843730 1.44272i
\(543\) 22.8048 39.4990i 0.978646 1.69507i
\(544\) 8.19485 15.1560i 0.351351 0.649808i
\(545\) 6.64439 0.284615
\(546\) 0 0
\(547\) 8.04855 8.04855i 0.344131 0.344131i −0.513787 0.857918i \(-0.671758\pi\)
0.857918 + 0.513787i \(0.171758\pi\)
\(548\) 24.4761 + 13.7691i 1.04557 + 0.588187i
\(549\) −63.7066 + 17.0701i −2.71893 + 0.728536i
\(550\) 1.96738 + 0.515398i 0.0838892 + 0.0219767i
\(551\) −8.56772 + 4.94658i −0.364997 + 0.210731i
\(552\) 31.5896 + 30.5484i 1.34454 + 1.30023i
\(553\) 0 0
\(554\) −7.81019 + 2.13956i −0.331823 + 0.0909010i
\(555\) 13.9220 51.9576i 0.590956 2.20548i
\(556\) 19.4114 + 18.9825i 0.823226 + 0.805039i
\(557\) 7.81587 + 29.1692i 0.331169 + 1.23594i 0.907963 + 0.419050i \(0.137637\pi\)
−0.576794 + 0.816890i \(0.695696\pi\)
\(558\) 0.284825 + 51.0002i 0.0120576 + 2.15901i
\(559\) −0.0976612 −0.00413063
\(560\) 0 0
\(561\) −11.1097 −0.469050
\(562\) −0.123248 22.0685i −0.00519890 0.930905i
\(563\) 0.151794 + 0.566504i 0.00639736 + 0.0238753i 0.969051 0.246862i \(-0.0793993\pi\)
−0.962653 + 0.270737i \(0.912733\pi\)
\(564\) −7.01704 + 7.17557i −0.295471 + 0.302146i
\(565\) 1.27590 4.76171i 0.0536773 0.200326i
\(566\) 11.4952 3.14905i 0.483180 0.132364i
\(567\) 0 0
\(568\) −0.320822 19.1470i −0.0134614 0.803391i
\(569\) 30.9006 17.8405i 1.29542 0.747912i 0.315812 0.948822i \(-0.397723\pi\)
0.979610 + 0.200910i \(0.0643898\pi\)
\(570\) −40.1644 10.5220i −1.68230 0.440716i
\(571\) 12.8771 3.45040i 0.538888 0.144395i 0.0208985 0.999782i \(-0.493347\pi\)
0.517989 + 0.855387i \(0.326681\pi\)
\(572\) 0.0109376 0.0194429i 0.000457326 0.000812948i
\(573\) 35.6743 35.6743i 1.49032 1.49032i
\(574\) 0 0
\(575\) 6.12553 0.255452
\(576\) −46.9288 + 29.2332i −1.95537 + 1.21805i
\(577\) 6.90735 11.9639i 0.287557 0.498063i −0.685669 0.727913i \(-0.740490\pi\)
0.973226 + 0.229850i \(0.0738237\pi\)
\(578\) −5.51382 9.42822i −0.229345 0.392162i
\(579\) 21.8451 + 5.85339i 0.907853 + 0.243259i
\(580\) −4.06443 6.86164i −0.168766 0.284914i
\(581\) 0 0
\(582\) −0.459551 1.67754i −0.0190490 0.0695362i
\(583\) 0.818329 0.472462i 0.0338917 0.0195674i
\(584\) −9.81239 5.44807i −0.406040 0.225443i
\(585\) 0.111712 + 0.0644972i 0.00461874 + 0.00266663i
\(586\) 15.3354 + 15.1651i 0.633499 + 0.626462i
\(587\) −26.0019 26.0019i −1.07321 1.07321i −0.997099 0.0761137i \(-0.975749\pi\)
−0.0761137 0.997099i \(-0.524251\pi\)
\(588\) 0 0
\(589\) −17.7481 + 17.7481i −0.731298 + 0.731298i
\(590\) −0.114954 20.5835i −0.00473260 0.847410i
\(591\) 30.9449 53.5981i 1.27290 2.20473i
\(592\) 8.36094 34.2458i 0.343633 1.40749i
\(593\) 19.0574 + 33.0084i 0.782593 + 1.35549i 0.930426 + 0.366479i \(0.119437\pi\)
−0.147833 + 0.989012i \(0.547230\pi\)
\(594\) 17.5283 + 9.98989i 0.719197 + 0.409890i
\(595\) 0 0
\(596\) 2.35733 9.20786i 0.0965601 0.377169i
\(597\) −22.4414 + 83.7523i −0.918464 + 3.42775i
\(598\) 0.0170275 0.0649972i 0.000696305 0.00265793i
\(599\) −29.1573 16.8340i −1.19133 0.687817i −0.232725 0.972543i \(-0.574764\pi\)
−0.958609 + 0.284726i \(0.908098\pi\)
\(600\) −2.68130 + 10.7222i −0.109464 + 0.437731i
\(601\) 27.9742i 1.14109i −0.821265 0.570546i \(-0.806731\pi\)
0.821265 0.570546i \(-0.193269\pi\)
\(602\) 0 0
\(603\) 32.1585 + 32.1585i 1.30959 + 1.30959i
\(604\) −18.8696 10.6151i −0.767792 0.431923i
\(605\) −4.84607 18.0858i −0.197021 0.735292i
\(606\) −8.72843 14.9250i −0.354568 0.606286i
\(607\) −2.51294 4.35254i −0.101997 0.176664i 0.810510 0.585724i \(-0.199190\pi\)
−0.912507 + 0.409060i \(0.865857\pi\)
\(608\) −26.4692 6.30591i −1.07347 0.255738i
\(609\) 0 0
\(610\) 12.9560 22.7327i 0.524573 0.920421i
\(611\) 0.0148226 + 0.00397170i 0.000599657 + 0.000160678i
\(612\) −0.470222 42.0972i −0.0190076 1.70168i
\(613\) −32.2373 + 8.63795i −1.30205 + 0.348883i −0.842225 0.539126i \(-0.818755\pi\)
−0.459825 + 0.888009i \(0.652088\pi\)
\(614\) 17.4419 17.6378i 0.703898 0.711805i
\(615\) 36.7855i 1.48334i
\(616\) 0 0
\(617\) 37.6332i 1.51506i −0.652803 0.757528i \(-0.726407\pi\)
0.652803 0.757528i \(-0.273593\pi\)
\(618\) 6.69393 + 6.61958i 0.269269 + 0.266278i
\(619\) 5.08719 1.36311i 0.204471 0.0547879i −0.155130 0.987894i \(-0.549580\pi\)
0.359601 + 0.933106i \(0.382913\pi\)
\(620\) −14.4660 14.1464i −0.580969 0.568134i
\(621\) 58.6956 + 15.7274i 2.35537 + 0.631120i
\(622\) −42.9495 24.4781i −1.72212 0.981482i
\(623\) 0 0
\(624\) 0.106318 + 0.0582560i 0.00425614 + 0.00233211i
\(625\) −8.62664 14.9418i −0.345066 0.597671i
\(626\) −9.63351 + 5.63388i −0.385033 + 0.225175i
\(627\) 4.54099 + 16.9472i 0.181350 + 0.676806i
\(628\) −0.236576 0.845045i −0.00944042 0.0337210i
\(629\) 18.9804 + 18.9804i 0.756798 + 0.756798i
\(630\) 0 0
\(631\) 40.9681i 1.63091i 0.578818 + 0.815457i \(0.303514\pi\)
−0.578818 + 0.815457i \(0.696486\pi\)
\(632\) 8.18399 + 13.6420i 0.325542 + 0.542651i
\(633\) 1.07495 + 0.620620i 0.0427253 + 0.0246674i
\(634\) 9.52384 + 2.49498i 0.378240 + 0.0990884i
\(635\) 0.333125 1.24324i 0.0132197 0.0493364i
\(636\) 2.61707 + 4.41820i 0.103774 + 0.175193i
\(637\) 0 0
\(638\) −1.66869 + 2.92790i −0.0660640 + 0.115916i
\(639\) −23.3958 40.5227i −0.925522 1.60305i
\(640\) 4.84468 21.3928i 0.191503 0.845626i
\(641\) −7.08895 + 12.2784i −0.279997 + 0.484968i −0.971384 0.237516i \(-0.923667\pi\)
0.691387 + 0.722485i \(0.257000\pi\)
\(642\) −67.0429 + 0.374420i −2.64597 + 0.0147772i
\(643\) 0.705913 0.705913i 0.0278385 0.0278385i −0.693051 0.720889i \(-0.743734\pi\)
0.720889 + 0.693051i \(0.243734\pi\)
\(644\) 0 0
\(645\) 43.7820 + 43.7820i 1.72391 + 1.72391i
\(646\) 14.5685 14.7322i 0.573191 0.579629i
\(647\) 0.498838 + 0.288004i 0.0196113 + 0.0113226i 0.509774 0.860309i \(-0.329729\pi\)
−0.490162 + 0.871631i \(0.663062\pi\)
\(648\) −24.7555 + 44.5865i −0.972487 + 1.75152i
\(649\) −7.53280 + 4.34906i −0.295688 + 0.170716i
\(650\) 0.0162985 0.00446487i 0.000639279 0.000175127i
\(651\) 0 0
\(652\) 26.1577 + 6.69672i 1.02442 + 0.262264i
\(653\) −18.1467 4.86239i −0.710135 0.190280i −0.114369 0.993438i \(-0.536485\pi\)
−0.595766 + 0.803158i \(0.703151\pi\)
\(654\) 13.1713 7.70287i 0.515040 0.301206i
\(655\) −4.21869 + 7.30699i −0.164838 + 0.285508i
\(656\) 0.538489 + 24.1014i 0.0210245 + 0.941003i
\(657\) −27.4239 −1.06991
\(658\) 0 0
\(659\) 26.5183 26.5183i 1.03301 1.03301i 0.0335689 0.999436i \(-0.489313\pi\)
0.999436 0.0335689i \(-0.0106873\pi\)
\(660\) −13.6197 + 3.81294i −0.530147 + 0.148418i
\(661\) −41.9426 + 11.2385i −1.63138 + 0.437127i −0.954316 0.298798i \(-0.903414\pi\)
−0.677063 + 0.735925i \(0.736748\pi\)
\(662\) 0.749588 2.86133i 0.0291336 0.111209i
\(663\) −0.0799449 + 0.0461562i −0.00310480 + 0.00179256i
\(664\) −31.6250 + 32.7028i −1.22729 + 1.26912i
\(665\) 0 0
\(666\) −22.7580 83.0752i −0.881853 3.21910i
\(667\) −2.62708 + 9.80439i −0.101721 + 0.379627i
\(668\) 0.0828493 + 7.41719i 0.00320554 + 0.286980i
\(669\) −13.8702 51.7642i −0.536251 2.00132i
\(670\) −18.0423 + 0.100762i −0.697036 + 0.00389279i
\(671\) −11.0568 −0.426842
\(672\) 0 0
\(673\) 30.5484 1.17756 0.588778 0.808295i \(-0.299609\pi\)
0.588778 + 0.808295i \(0.299609\pi\)
\(674\) −50.5238 + 0.282164i −1.94610 + 0.0108686i
\(675\) 3.95558 + 14.7624i 0.152250 + 0.568206i
\(676\) 0.290397 + 25.9982i 0.0111691 + 0.999930i
\(677\) 9.54210 35.6116i 0.366733 1.36867i −0.498324 0.866991i \(-0.666051\pi\)
0.865056 0.501675i \(-0.167283\pi\)
\(678\) −2.99103 10.9184i −0.114870 0.419318i
\(679\) 0 0
\(680\) 12.0063 + 11.6106i 0.460421 + 0.445246i
\(681\) −6.15392 + 3.55297i −0.235819 + 0.136150i
\(682\) −2.16675 + 8.27090i −0.0829690 + 0.316709i
\(683\) −5.87766 + 1.57491i −0.224902 + 0.0602624i −0.369510 0.929227i \(-0.620475\pi\)
0.144608 + 0.989489i \(0.453808\pi\)
\(684\) −64.0249 + 17.9242i −2.44805 + 0.685350i
\(685\) −19.2498 + 19.2498i −0.735496 + 0.735496i
\(686\) 0 0
\(687\) −43.7178 −1.66794
\(688\) 29.3263 + 28.0445i 1.11806 + 1.06919i
\(689\) 0.00392579 0.00679966i 0.000149561 0.000259046i
\(690\) −36.7720 + 21.5050i −1.39989 + 0.818683i
\(691\) 0.492824 + 0.132052i 0.0187479 + 0.00502349i 0.268181 0.963369i \(-0.413578\pi\)
−0.249433 + 0.968392i \(0.580244\pi\)
\(692\) 10.3489 + 2.64945i 0.393406 + 0.100717i
\(693\) 0 0
\(694\) −28.4689 + 7.79888i −1.08066 + 0.296042i
\(695\) −22.7929 + 13.1595i −0.864583 + 0.499167i
\(696\) −16.0117 8.89009i −0.606923 0.336978i
\(697\) −15.8973 9.17830i −0.602152 0.347653i
\(698\) 14.4445 14.6068i 0.546734 0.552875i
\(699\) −4.74774 4.74774i −0.179576 0.179576i
\(700\) 0 0
\(701\) 6.72808 6.72808i 0.254116 0.254116i −0.568540 0.822656i \(-0.692491\pi\)
0.822656 + 0.568540i \(0.192491\pi\)
\(702\) 0.167638 0.000936219i 0.00632707 3.53353e-5i
\(703\) 21.1955 36.7117i 0.799404 1.38461i
\(704\) −8.86767 + 2.69757i −0.334213 + 0.101668i
\(705\) −4.86450 8.42556i −0.183208 0.317325i
\(706\) 21.0962 37.0156i 0.793967 1.39310i
\(707\) 0 0
\(708\) −24.0904 40.6699i −0.905374 1.52847i
\(709\) −0.751876 + 2.80604i −0.0282373 + 0.105383i −0.978606 0.205742i \(-0.934039\pi\)
0.950369 + 0.311125i \(0.100706\pi\)
\(710\) 17.9573 + 4.70433i 0.673927 + 0.176550i
\(711\) 33.6641 + 19.4360i 1.26250 + 0.728907i
\(712\) 10.0652 6.03822i 0.377210 0.226292i
\(713\) 25.7519i 0.964416i
\(714\) 0 0
\(715\) 0.0152913 + 0.0152913i 0.000571862 + 0.000571862i
\(716\) 1.93047 + 6.89561i 0.0721452 + 0.257701i
\(717\) 14.3361 + 53.5030i 0.535391 + 1.99811i
\(718\) −25.6229 + 14.9848i −0.956239 + 0.559228i
\(719\) 11.0995 + 19.2250i 0.413943 + 0.716970i 0.995317 0.0966665i \(-0.0308180\pi\)
−0.581374 + 0.813636i \(0.697485\pi\)
\(720\) −15.0246 51.4471i −0.559935 1.91732i
\(721\) 0 0
\(722\) −5.08309 2.89699i −0.189173 0.107815i
\(723\) 25.5697 + 6.85139i 0.950948 + 0.254806i
\(724\) 20.7160 + 20.2583i 0.769904 + 0.752894i
\(725\) −2.46588 + 0.660731i −0.0915806 + 0.0245390i
\(726\) −30.5734 30.2338i −1.13469 1.12208i
\(727\) 11.9796i 0.444300i 0.975013 + 0.222150i \(0.0713074\pi\)
−0.975013 + 0.222150i \(0.928693\pi\)
\(728\) 0 0
\(729\) 8.31959i 0.308133i
\(730\) 7.65004 7.73597i 0.283141 0.286321i
\(731\) −29.8448 + 7.99690i −1.10385 + 0.295776i
\(732\) −0.671128 60.0836i −0.0248056 2.22075i
\(733\) 20.0603 + 5.37515i 0.740945 + 0.198536i 0.609498 0.792787i \(-0.291371\pi\)
0.131447 + 0.991323i \(0.458038\pi\)
\(734\) −4.63935 + 8.14023i −0.171241 + 0.300461i
\(735\) 0 0
\(736\) −23.7778 + 14.6281i −0.876461 + 0.539201i
\(737\) 3.81214 + 6.60282i 0.140422 + 0.243218i
\(738\) 29.7372 + 50.8485i 1.09464 + 1.87176i
\(739\) 11.5688 + 43.1754i 0.425565 + 1.58823i 0.762686 + 0.646769i \(0.223880\pi\)
−0.337120 + 0.941462i \(0.609453\pi\)
\(740\) 29.7830 + 16.7545i 1.09485 + 0.615908i
\(741\) 0.103086 + 0.103086i 0.00378695 + 0.00378695i
\(742\) 0 0
\(743\) 14.9156i 0.547200i 0.961844 + 0.273600i \(0.0882144\pi\)
−0.961844 + 0.273600i \(0.911786\pi\)
\(744\) −45.0763 11.2723i −1.65258 0.413261i
\(745\) 7.97936 + 4.60689i 0.292341 + 0.168783i
\(746\) 7.80853 29.8067i 0.285890 1.09130i
\(747\) −28.7704 + 107.373i −1.05265 + 3.92856i
\(748\) 1.75043 6.83728i 0.0640022 0.249996i
\(749\) 0 0
\(750\) −46.8049 26.6754i −1.70908 0.974049i
\(751\) 10.0879 + 17.4727i 0.368111 + 0.637587i 0.989270 0.146097i \(-0.0466712\pi\)
−0.621159 + 0.783685i \(0.713338\pi\)
\(752\) −3.31050 5.44912i −0.120721 0.198709i
\(753\) −11.9281 + 20.6601i −0.434685 + 0.752897i
\(754\) 0.000156384 0.0280018i 5.69517e−6 0.00101977i
\(755\) 14.8404 14.8404i 0.540097 0.540097i
\(756\) 0 0
\(757\) −15.2417 15.2417i −0.553968 0.553968i 0.373615 0.927584i \(-0.378118\pi\)
−0.927584 + 0.373615i \(0.878118\pi\)
\(758\) 0.309310 + 0.305874i 0.0112346 + 0.0111098i
\(759\) 15.5893 + 9.00048i 0.565856 + 0.326697i
\(760\) 12.8039 23.0607i 0.464445 0.836501i
\(761\) 27.5359 15.8978i 0.998174 0.576296i 0.0904666 0.995899i \(-0.471164\pi\)
0.907708 + 0.419603i \(0.137831\pi\)
\(762\) −0.780930 2.85069i −0.0282901 0.103270i
\(763\) 0 0
\(764\) 16.3344 + 27.5761i 0.590959 + 0.997668i
\(765\) 39.4201 + 10.5626i 1.42524 + 0.381891i
\(766\) 15.7562 + 26.9419i 0.569294 + 0.973450i
\(767\) −0.0361373 + 0.0625916i −0.00130484 + 0.00226005i
\(768\) −15.1971 48.0240i −0.548377 1.73292i
\(769\) 28.1015 1.01336 0.506682 0.862133i \(-0.330872\pi\)
0.506682 + 0.862133i \(0.330872\pi\)
\(770\) 0 0
\(771\) −2.74035 + 2.74035i −0.0986912 + 0.0986912i
\(772\) −7.04429 + 12.5220i −0.253530 + 0.450677i
\(773\) 21.6810 5.80940i 0.779811 0.208950i 0.153109 0.988209i \(-0.451071\pi\)
0.626701 + 0.779260i \(0.284405\pi\)
\(774\) 95.9127 + 25.1265i 3.44751 + 0.903153i
\(775\) −5.60908 + 3.23841i −0.201484 + 0.116327i
\(776\) 1.10482 0.0185121i 0.0396609 0.000664547i
\(777\) 0 0
\(778\) −46.3742 + 12.7039i −1.66260 + 0.455458i
\(779\) −7.50312 + 28.0020i −0.268827 + 1.00328i
\(780\) −0.0821660 + 0.0840224i −0.00294202 + 0.00300848i
\(781\) −2.03026 7.57703i −0.0726484 0.271127i
\(782\) −0.118716 21.2571i −0.00424529 0.760154i
\(783\) −25.3248 −0.905036
\(784\) 0 0
\(785\) 0.850665 0.0303615
\(786\) 0.108208 + 19.3756i 0.00385966 + 0.691104i
\(787\) −1.24497 4.64629i −0.0443784 0.165622i 0.940180 0.340677i \(-0.110656\pi\)
−0.984559 + 0.175055i \(0.943990\pi\)
\(788\) 28.1105 + 27.4895i 1.00140 + 0.979271i
\(789\) −16.4117 + 61.2495i −0.584274 + 2.18054i
\(790\) −14.8735 + 4.07449i −0.529174 + 0.144964i
\(791\) 0 0
\(792\) −15.7441 + 16.2807i −0.559443 + 0.578510i
\(793\) −0.0795644 + 0.0459365i −0.00282541 + 0.00163125i
\(794\) 51.4859 + 13.4879i 1.82717 + 0.478668i
\(795\) −4.80827 + 1.28837i −0.170532 + 0.0456938i
\(796\) −48.0083 27.0072i −1.70161 0.957245i
\(797\) 0.757921 0.757921i 0.0268469 0.0268469i −0.693556 0.720403i \(-0.743957\pi\)
0.720403 + 0.693556i \(0.243957\pi\)
\(798\) 0 0
\(799\) 4.85493 0.171755
\(800\) −6.17635 3.33955i −0.218367 0.118071i
\(801\) 14.3401 24.8377i 0.506681 0.877597i
\(802\) 20.5589 + 35.1541i 0.725959 + 1.24134i
\(803\) −4.44080 1.18991i −0.156712 0.0419909i
\(804\) −35.6489 + 21.1163i −1.25724 + 0.744714i
\(805\) 0 0
\(806\) 0.0187704 + 0.0685192i 0.000661160 + 0.00241349i
\(807\) 34.0266 19.6453i 1.19779 0.691547i
\(808\) 10.5606 3.02022i 0.371521 0.106251i
\(809\) 28.2323 + 16.2999i 0.992593 + 0.573074i 0.906048 0.423174i \(-0.139084\pi\)
0.0865449 + 0.996248i \(0.472417\pi\)
\(810\) −35.1514 34.7610i −1.23510 1.22138i
\(811\) −10.5979 10.5979i −0.372144 0.372144i 0.496113 0.868258i \(-0.334760\pi\)
−0.868258 + 0.496113i \(0.834760\pi\)
\(812\) 0 0
\(813\) 61.2479 61.2479i 2.14806 2.14806i
\(814\) −0.0806440 14.4400i −0.00282657 0.506120i
\(815\) −13.0873 + 22.6678i −0.458427 + 0.794019i
\(816\) 37.2606 + 9.09700i 1.30438 + 0.318459i
\(817\) 24.3977 + 42.2581i 0.853567 + 1.47842i
\(818\) 24.6200 + 14.0316i 0.860819 + 0.490605i
\(819\) 0 0
\(820\) −22.6391 5.79591i −0.790592 0.202402i
\(821\) 2.77480 10.3557i 0.0968411 0.361416i −0.900451 0.434957i \(-0.856763\pi\)
0.997292 + 0.0735415i \(0.0234301\pi\)
\(822\) −15.8430 + 60.4757i −0.552586 + 2.10933i
\(823\) −35.5874 20.5464i −1.24050 0.716202i −0.271303 0.962494i \(-0.587455\pi\)
−0.969196 + 0.246291i \(0.920788\pi\)
\(824\) −5.12862 + 3.07671i −0.178664 + 0.107182i
\(825\) 4.52739i 0.157624i
\(826\) 0 0
\(827\) −10.5960 10.5960i −0.368458 0.368458i 0.498457 0.866915i \(-0.333900\pi\)
−0.866915 + 0.498457i \(0.833900\pi\)
\(828\) −33.4452 + 59.4527i −1.16230 + 2.06612i
\(829\) 2.76435 + 10.3167i 0.0960097 + 0.358313i 0.997171 0.0751716i \(-0.0239504\pi\)
−0.901161 + 0.433485i \(0.857284\pi\)
\(830\) −22.2629 38.0679i −0.772757 1.32136i
\(831\) −9.01347 15.6118i −0.312674 0.541567i
\(832\) −0.0526043 + 0.0562533i −0.00182372 + 0.00195023i
\(833\) 0 0
\(834\) −29.9270 + 52.5102i −1.03629 + 1.81828i
\(835\) −6.94550 1.86104i −0.240359 0.0644040i
\(836\) −11.1454 + 0.124493i −0.385471 + 0.00430568i
\(837\) −62.0616 + 16.6294i −2.14516 + 0.574795i
\(838\) −16.0078 + 16.1876i −0.552979 + 0.559190i
\(839\) 23.6761i 0.817391i −0.912671 0.408696i \(-0.865984\pi\)
0.912671 0.408696i \(-0.134016\pi\)
\(840\) 0 0
\(841\) 24.7698i 0.854131i
\(842\) 40.3754 + 39.9269i 1.39143 + 1.37597i
\(843\) 47.4538 12.7152i 1.63440 0.437935i
\(844\) −0.551320 + 0.563775i −0.0189772 + 0.0194059i
\(845\) −24.3449 6.52319i −0.837489 0.224405i
\(846\) −13.5353 7.71417i −0.465355 0.265219i
\(847\) 0 0
\(848\) −3.13146 + 0.914512i −0.107535 + 0.0314045i
\(849\) 13.2662 + 22.9778i 0.455296 + 0.788596i
\(850\) 4.61514 2.69903i 0.158298 0.0925760i
\(851\) −11.2567 42.0107i −0.385876 1.44011i
\(852\) 41.0510 11.4925i 1.40638 0.393727i
\(853\) −10.1928 10.1928i −0.348995 0.348995i 0.510740 0.859735i \(-0.329372\pi\)
−0.859735 + 0.510740i \(0.829372\pi\)
\(854\) 0 0
\(855\) 64.4507i 2.20417i
\(856\) 10.3328 41.3196i 0.353168 1.41227i
\(857\) −37.5171 21.6605i −1.28156 0.739909i −0.304426 0.952536i \(-0.598465\pi\)
−0.977133 + 0.212627i \(0.931798\pi\)
\(858\) 0.0480395 + 0.0125850i 0.00164004 + 0.000429646i
\(859\) −2.92018 + 10.8983i −0.0996352 + 0.371844i −0.997681 0.0680575i \(-0.978320\pi\)
0.898046 + 0.439901i \(0.144987\pi\)
\(860\) −33.8433 + 20.0467i −1.15405 + 0.683587i
\(861\) 0 0
\(862\) −16.2811 + 28.5669i −0.554536 + 0.972993i
\(863\) −7.41990 12.8516i −0.252576 0.437475i 0.711658 0.702526i \(-0.247945\pi\)
−0.964234 + 0.265051i \(0.914611\pi\)
\(864\) −50.6082 47.8579i −1.72172 1.62816i
\(865\) −5.17778 + 8.96817i −0.176050 + 0.304927i
\(866\) 26.9241 0.150365i 0.914918 0.00510962i
\(867\) 17.1926 17.1926i 0.583890 0.583890i
\(868\) 0 0
\(869\) 4.60797 + 4.60797i 0.156315 + 0.156315i
\(870\) 12.4832 12.6235i 0.423221 0.427975i
\(871\) 0.0548641 + 0.0316758i 0.00185900 + 0.00107329i
\(872\) 2.66535 + 9.31977i 0.0902602 + 0.315607i
\(873\) 2.33824 1.34999i 0.0791375 0.0456901i
\(874\) −32.3781 + 8.86979i −1.09521 + 0.300025i
\(875\) 0 0
\(876\) 6.19652 24.2039i 0.209361 0.817774i
\(877\) −26.1904 7.01770i −0.884387 0.236971i −0.212088 0.977251i \(-0.568026\pi\)
−0.672299 + 0.740280i \(0.734693\pi\)
\(878\) −32.2990 + 18.8891i −1.09004 + 0.637478i
\(879\) −24.0057 + 41.5791i −0.809693 + 1.40243i
\(880\) −0.200700 8.98283i −0.00676559 0.302811i
\(881\) 5.53387 0.186441 0.0932204 0.995645i \(-0.470284\pi\)
0.0932204 + 0.995645i \(0.470284\pi\)
\(882\) 0 0
\(883\) −27.6942 + 27.6942i −0.931985 + 0.931985i −0.997830 0.0658444i \(-0.979026\pi\)
0.0658444 + 0.997830i \(0.479026\pi\)
\(884\) −0.0158101 0.0564733i −0.000531751 0.00189940i
\(885\) 44.2606 11.8596i 1.48780 0.398656i
\(886\) −11.9672 + 45.6810i −0.402045 + 1.53468i
\(887\) −29.1956 + 16.8561i −0.980291 + 0.565971i −0.902358 0.430987i \(-0.858165\pi\)
−0.0779332 + 0.996959i \(0.524832\pi\)
\(888\) 78.4632 1.31471i 2.63305 0.0441187i
\(889\) 0 0
\(890\) 3.00620 + 10.9738i 0.100768 + 0.367842i
\(891\) −5.40682 + 20.1785i −0.181135 + 0.676006i
\(892\) 34.0429 0.380256i 1.13984 0.0127319i
\(893\) −1.98442 7.40594i −0.0664059 0.247830i
\(894\) 21.1585 0.118165i 0.707645 0.00395204i
\(895\) −6.94147 −0.232028
\(896\) 0 0
\(897\) 0.149574 0.00499412
\(898\) 40.4510 0.225910i 1.34987 0.00753872i
\(899\) −2.77773 10.3666i −0.0926425 0.345747i
\(900\) −17.1554 + 0.191624i −0.571847 + 0.00638748i
\(901\) 0.642919 2.39941i 0.0214187 0.0799358i
\(902\) 2.60911 + 9.52426i 0.0868739 + 0.317123i
\(903\) 0 0
\(904\) 7.19083 0.120488i 0.239164 0.00400736i
\(905\) −24.3247 + 14.0439i −0.808581 + 0.466835i
\(906\) 12.2139 46.6230i 0.405781 1.54895i
\(907\) 14.8478 3.97846i 0.493013 0.132102i −0.00374236 0.999993i \(-0.501191\pi\)
0.496756 + 0.867891i \(0.334525\pi\)
\(908\) −1.21701 4.34714i −0.0403880 0.144265i
\(909\) 18.9780 18.9780i 0.629460 0.629460i
\(910\) 0 0
\(911\) 54.1727 1.79482 0.897411 0.441196i \(-0.145446\pi\)
0.897411 + 0.441196i \(0.145446\pi\)
\(912\) −1.35301 60.5574i −0.0448027 2.00526i
\(913\) −9.31768 + 16.1387i −0.308370 + 0.534113i
\(914\) 40.0014 23.3937i 1.32313 0.773793i
\(915\) 56.2626 + 15.0755i 1.85999 + 0.498382i
\(916\) 6.88815 26.9055i 0.227591 0.888982i
\(917\) 0 0
\(918\) 51.1527 14.0130i 1.68829 0.462497i
\(919\) −24.5003 + 14.1453i −0.808191 + 0.466609i −0.846327 0.532663i \(-0.821191\pi\)
0.0381361 + 0.999273i \(0.487858\pi\)
\(920\) −7.44119 26.0191i −0.245329 0.857826i
\(921\) 47.8218 + 27.6099i 1.57578 + 0.909778i
\(922\) 24.3174 24.5906i 0.800852 0.809847i
\(923\) −0.0460892 0.0460892i −0.00151705 0.00151705i
\(924\) 0 0
\(925\) 7.73487 7.73487i 0.254321 0.254321i
\(926\) −2.35867 + 0.0131727i −0.0775109 + 0.000432881i
\(927\) −7.30680 + 12.6558i −0.239987 + 0.415669i
\(928\) 7.99408 8.45347i 0.262419 0.277499i
\(929\) −8.48566 14.6976i −0.278406 0.482212i 0.692583 0.721338i \(-0.256473\pi\)
−0.970989 + 0.239126i \(0.923139\pi\)
\(930\) 22.3026 39.1323i 0.731331 1.28320i
\(931\) 0 0
\(932\) 3.66998 2.17387i 0.120214 0.0712076i
\(933\) 28.4826 106.298i 0.932477 3.48005i
\(934\) 4.06842 + 1.06581i 0.133123 + 0.0348745i
\(935\) 5.92506 + 3.42084i 0.193770 + 0.111873i
\(936\) −0.0456545 + 0.182566i −0.00149226 + 0.00596737i
\(937\) 47.8526i 1.56328i 0.623732 + 0.781639i \(0.285616\pi\)
−0.623732 + 0.781639i \(0.714384\pi\)
\(938\) 0 0
\(939\) −17.5669 17.5669i −0.573274 0.573274i
\(940\) 5.95183 1.66626i 0.194127 0.0543473i
\(941\) −8.56722 31.9733i −0.279283 1.04230i −0.952916 0.303234i \(-0.901934\pi\)
0.673633 0.739066i \(-0.264733\pi\)
\(942\) 1.68629 0.986180i 0.0549424 0.0321315i
\(943\) 14.8716 + 25.7583i 0.484286 + 0.838807i
\(944\) 28.8254 8.41818i 0.938187 0.273988i
\(945\) 0 0
\(946\) 14.4411 + 8.23037i 0.469520 + 0.267593i
\(947\) −25.7374 6.89633i −0.836355 0.224101i −0.184871 0.982763i \(-0.559187\pi\)
−0.651484 + 0.758662i \(0.725853\pi\)
\(948\) −24.7604 + 25.3198i −0.804181 + 0.822349i
\(949\) −0.0368995 + 0.00988718i −0.00119781 + 0.000320952i
\(950\) −6.00363 5.93695i −0.194784 0.192620i
\(951\) 21.9166i 0.710693i
\(952\) 0 0
\(953\) 27.1790i 0.880415i 0.897896 + 0.440207i \(0.145095\pi\)
−0.897896 + 0.440207i \(0.854905\pi\)
\(954\) −5.60493 + 5.66789i −0.181466 + 0.183505i
\(955\) −30.0107 + 8.04134i −0.971124 + 0.260212i
\(956\) −35.1865 + 0.393029i −1.13801 + 0.0127115i
\(957\) −7.24643 1.94168i −0.234244 0.0627655i
\(958\) −5.48663 + 9.62688i −0.177265 + 0.311030i
\(959\) 0 0
\(960\) 48.8013 1.63586i 1.57506 0.0527973i
\(961\) 1.88566 + 3.26606i 0.0608278 + 0.105357i
\(962\) −0.0605726 0.103575i −0.00195294 0.00333938i
\(963\) −26.9357 100.526i −0.867992 3.23939i
\(964\) −8.24534 + 14.6570i −0.265565 + 0.472071i
\(965\) −9.84822 9.84822i −0.317025 0.317025i
\(966\) 0 0
\(967\) 53.5349i 1.72157i −0.508971 0.860784i \(-0.669974\pi\)
0.508971 0.860784i \(-0.330026\pi\)
\(968\) 23.4241 14.0523i 0.752879 0.451659i
\(969\) 39.9436 + 23.0615i 1.28317 + 0.740841i
\(970\) −0.271450 + 1.03618i −0.00871573 + 0.0332696i
\(971\) 3.64148 13.5902i 0.116861 0.436129i −0.882559 0.470202i \(-0.844181\pi\)
0.999419 + 0.0340726i \(0.0108477\pi\)
\(972\) −38.4100 9.83346i −1.23200 0.315408i
\(973\) 0 0
\(974\) 20.2709 + 11.5530i 0.649522 + 0.370181i
\(975\) 0.0188095 + 0.0325790i 0.000602386 + 0.00104336i
\(976\) 37.0833 + 9.05370i 1.18701 + 0.289802i
\(977\) −21.9868 + 38.0823i −0.703421 + 1.21836i 0.263837 + 0.964567i \(0.415012\pi\)
−0.967258 + 0.253794i \(0.918322\pi\)
\(978\) 0.335685 + 60.1071i 0.0107340 + 1.92201i
\(979\) 3.39980 3.39980i 0.108658 0.108658i
\(980\) 0 0
\(981\) 16.7481 + 16.7481i 0.534727 + 0.534727i
\(982\) 19.1424 + 18.9298i 0.610860 + 0.604075i
\(983\) −25.0685 14.4733i −0.799561 0.461627i 0.0437566 0.999042i \(-0.486067\pi\)
−0.843318 + 0.537415i \(0.819401\pi\)
\(984\) −51.5973 + 14.7563i −1.64486 + 0.470412i
\(985\) −33.0074 + 19.0568i −1.05170 + 0.607200i
\(986\) 2.34069 + 8.54443i 0.0745429 + 0.272110i
\(987\) 0 0
\(988\) −0.0796847 + 0.0472005i −0.00253511 + 0.00150165i
\(989\) 48.3576 + 12.9574i 1.53768 + 0.412021i
\(990\) −11.0833 18.9517i −0.352252 0.602324i
\(991\) 10.8966 18.8735i 0.346143 0.599537i −0.639418 0.768860i \(-0.720825\pi\)
0.985561 + 0.169322i \(0.0541579\pi\)
\(992\) 14.0396 25.9655i 0.445757 0.824406i
\(993\) 6.58458 0.208955
\(994\) 0 0
\(995\) 37.7572 37.7572i 1.19698 1.19698i
\(996\) −88.2647 49.6535i −2.79677 1.57333i
\(997\) −6.84507 + 1.83413i −0.216785 + 0.0580875i −0.365577 0.930781i \(-0.619128\pi\)
0.148792 + 0.988869i \(0.452462\pi\)
\(998\) −19.1116 5.00672i −0.604968 0.158485i
\(999\) 93.9759 54.2570i 2.97327 1.71662i
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 784.2.x.o.165.1 48
7.2 even 3 inner 784.2.x.o.373.9 48
7.3 odd 6 784.2.m.j.197.7 24
7.4 even 3 784.2.m.k.197.7 24
7.5 odd 6 112.2.w.c.37.9 48
7.6 odd 2 112.2.w.c.53.1 yes 48
16.13 even 4 inner 784.2.x.o.557.9 48
28.19 even 6 448.2.ba.c.177.12 48
28.27 even 2 448.2.ba.c.305.1 48
56.5 odd 6 896.2.ba.f.737.12 48
56.13 odd 2 896.2.ba.f.865.1 48
56.19 even 6 896.2.ba.e.737.1 48
56.27 even 2 896.2.ba.e.865.12 48
112.5 odd 12 896.2.ba.f.289.1 48
112.13 odd 4 112.2.w.c.109.9 yes 48
112.19 even 12 448.2.ba.c.401.1 48
112.27 even 4 896.2.ba.e.417.1 48
112.45 odd 12 784.2.m.j.589.7 24
112.61 odd 12 112.2.w.c.93.1 yes 48
112.69 odd 4 896.2.ba.f.417.12 48
112.75 even 12 896.2.ba.e.289.12 48
112.83 even 4 448.2.ba.c.81.12 48
112.93 even 12 inner 784.2.x.o.765.1 48
112.109 even 12 784.2.m.k.589.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.9 48 7.5 odd 6
112.2.w.c.53.1 yes 48 7.6 odd 2
112.2.w.c.93.1 yes 48 112.61 odd 12
112.2.w.c.109.9 yes 48 112.13 odd 4
448.2.ba.c.81.12 48 112.83 even 4
448.2.ba.c.177.12 48 28.19 even 6
448.2.ba.c.305.1 48 28.27 even 2
448.2.ba.c.401.1 48 112.19 even 12
784.2.m.j.197.7 24 7.3 odd 6
784.2.m.j.589.7 24 112.45 odd 12
784.2.m.k.197.7 24 7.4 even 3
784.2.m.k.589.7 24 112.109 even 12
784.2.x.o.165.1 48 1.1 even 1 trivial
784.2.x.o.373.9 48 7.2 even 3 inner
784.2.x.o.557.9 48 16.13 even 4 inner
784.2.x.o.765.1 48 112.93 even 12 inner
896.2.ba.e.289.12 48 112.75 even 12
896.2.ba.e.417.1 48 112.27 even 4
896.2.ba.e.737.1 48 56.19 even 6
896.2.ba.e.865.12 48 56.27 even 2
896.2.ba.f.289.1 48 112.5 odd 12
896.2.ba.f.417.12 48 112.69 odd 4
896.2.ba.f.737.12 48 56.5 odd 6
896.2.ba.f.865.1 48 56.13 odd 2