Properties

Label 845.2.bg.a.621.8
Level $845$
Weight $2$
Character 845.621
Analytic conductor $6.747$
Analytic rank $0$
Dimension $1440$
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] = [845,2,Mod(36,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 47]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.bg (of order \(78\), degree \(24\), 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(1440\)
Relative dimension: \(60\) over \(\Q(\zeta_{78})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label 621.8
Character \(\chi\) \(=\) 845.621
Dual form 845.2.bg.a.381.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.81669 - 1.48328i) q^{2} +(2.31724 + 0.187067i) q^{3} +(0.700192 + 3.42977i) q^{4} +(0.992709 - 0.120537i) q^{5} +(-3.93224 - 3.77697i) q^{6} +(-1.01235 - 1.60091i) q^{7} +(1.63544 - 3.11607i) q^{8} +(2.37346 + 0.385725i) q^{9} +O(q^{10})\) \(q+(-1.81669 - 1.48328i) q^{2} +(2.31724 + 0.187067i) q^{3} +(0.700192 + 3.42977i) q^{4} +(0.992709 - 0.120537i) q^{5} +(-3.93224 - 3.77697i) q^{6} +(-1.01235 - 1.60091i) q^{7} +(1.63544 - 3.11607i) q^{8} +(2.37346 + 0.385725i) q^{9} +(-1.98224 - 1.25349i) q^{10} +(-0.802936 - 4.94067i) q^{11} +(0.980917 + 8.07858i) q^{12} +(1.52988 - 3.26488i) q^{13} +(-0.535468 + 4.40997i) q^{14} +(2.32289 - 0.0936094i) q^{15} +(-1.15232 + 0.490956i) q^{16} +(-0.255210 + 0.161385i) q^{17} +(-3.73971 - 4.22126i) q^{18} +(-2.60166 - 1.50207i) q^{19} +(1.10850 + 3.32036i) q^{20} +(-2.04639 - 3.89908i) q^{21} +(-5.86972 + 10.1667i) q^{22} +(3.17393 + 5.49741i) q^{23} +(4.37262 - 6.91475i) q^{24} +(0.970942 - 0.239316i) q^{25} +(-7.62208 + 3.66204i) q^{26} +(-1.34395 - 0.331254i) q^{27} +(4.78191 - 4.59308i) q^{28} +(4.15866 - 5.09343i) q^{29} +(-4.35884 - 3.27545i) q^{30} +(-1.77546 + 7.20334i) q^{31} +(-3.93882 - 1.14089i) q^{32} +(-0.936362 - 11.5989i) q^{33} +(0.703019 + 0.0853620i) q^{34} +(-1.19794 - 1.46721i) q^{35} +(0.338932 + 8.41050i) q^{36} +(-9.84499 + 2.85163i) q^{37} +(2.49842 + 6.58779i) q^{38} +(4.15586 - 7.27933i) q^{39} +(1.24791 - 3.29048i) q^{40} +(0.182813 - 2.26454i) q^{41} +(-2.06577 + 10.1188i) q^{42} +(-0.792581 + 2.73631i) q^{43} +(16.3831 - 6.21330i) q^{44} +(2.40265 + 0.0968235i) q^{45} +(2.38816 - 14.6950i) q^{46} +(6.85935 - 7.74261i) q^{47} +(-2.76203 + 0.922102i) q^{48} +(1.46279 - 3.08277i) q^{49} +(-2.11888 - 1.00542i) q^{50} +(-0.621574 + 0.326227i) q^{51} +(12.2690 + 2.96110i) q^{52} +(-2.05213 - 1.07704i) q^{53} +(1.95020 + 2.59525i) q^{54} +(-1.39261 - 4.80786i) q^{55} +(-6.64419 + 0.536375i) q^{56} +(-5.74768 - 3.96734i) q^{57} +(-15.1100 + 3.08473i) q^{58} +(2.32423 - 5.45517i) q^{59} +(1.94753 + 7.90144i) q^{60} +(0.380670 - 9.44624i) q^{61} +(13.9101 - 10.4527i) q^{62} +(-1.78527 - 4.19019i) q^{63} +(6.88641 + 9.97669i) q^{64} +(1.12519 - 3.42548i) q^{65} +(-15.5034 + 22.4606i) q^{66} +(6.08393 + 1.24204i) q^{67} +(-0.732210 - 0.762311i) q^{68} +(6.32638 + 13.3326i) q^{69} +4.44236i q^{70} +(11.7373 - 5.56942i) q^{71} +(5.08360 - 6.76504i) q^{72} +(-0.270775 - 0.102692i) q^{73} +(22.1151 + 9.42237i) q^{74} +(2.29467 - 0.372921i) q^{75} +(3.33008 - 9.97481i) q^{76} +(-7.09671 + 6.28714i) q^{77} +(-18.3472 + 7.05999i) q^{78} +(-7.14938 - 6.33380i) q^{79} +(-1.08474 + 0.626272i) q^{80} +(-9.89485 - 3.30338i) q^{81} +(-3.69108 + 3.84282i) q^{82} +(2.14560 - 1.48100i) q^{83} +(11.9400 - 9.74875i) q^{84} +(-0.233897 + 0.190971i) q^{85} +(5.49860 - 3.79541i) q^{86} +(10.5894 - 11.0248i) q^{87} +(-16.7086 - 5.57815i) q^{88} +(5.05753 - 2.91997i) q^{89} +(-4.22126 - 3.73971i) q^{90} +(-6.77557 + 0.856012i) q^{91} +(-16.6325 + 14.7351i) q^{92} +(-5.46169 + 16.3598i) q^{93} +(-23.9458 + 3.89158i) q^{94} +(-2.76374 - 1.17752i) q^{95} +(-8.91377 - 3.38055i) q^{96} +(-7.67223 + 10.2099i) q^{97} +(-7.23008 + 3.43072i) q^{98} -12.0362i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{17}{78}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81669 1.48328i −1.28460 1.04884i −0.995810 0.0914470i \(-0.970851\pi\)
−0.288786 0.957394i \(-0.593252\pi\)
\(3\) 2.31724 + 0.187067i 1.33786 + 0.108003i 0.728585 0.684956i \(-0.240178\pi\)
0.609275 + 0.792959i \(0.291461\pi\)
\(4\) 0.700192 + 3.42977i 0.350096 + 1.71488i
\(5\) 0.992709 0.120537i 0.443953 0.0539056i
\(6\) −3.93224 3.77697i −1.60533 1.54194i
\(7\) −1.01235 1.60091i −0.382634 0.605087i 0.597868 0.801594i \(-0.296015\pi\)
−0.980502 + 0.196507i \(0.937040\pi\)
\(8\) 1.63544 3.11607i 0.578215 1.10170i
\(9\) 2.37346 + 0.385725i 0.791154 + 0.128575i
\(10\) −1.98224 1.25349i −0.626839 0.396389i
\(11\) −0.802936 4.94067i −0.242094 1.48967i −0.768729 0.639575i \(-0.779110\pi\)
0.526634 0.850092i \(-0.323454\pi\)
\(12\) 0.980917 + 8.07858i 0.283166 + 2.33208i
\(13\) 1.52988 3.26488i 0.424313 0.905515i
\(14\) −0.535468 + 4.40997i −0.143110 + 1.17862i
\(15\) 2.32289 0.0936094i 0.599769 0.0241699i
\(16\) −1.15232 + 0.490956i −0.288079 + 0.122739i
\(17\) −0.255210 + 0.161385i −0.0618976 + 0.0391417i −0.565056 0.825052i \(-0.691146\pi\)
0.503159 + 0.864194i \(0.332171\pi\)
\(18\) −3.73971 4.22126i −0.881459 0.994961i
\(19\) −2.60166 1.50207i −0.596861 0.344598i 0.170945 0.985281i \(-0.445318\pi\)
−0.767806 + 0.640683i \(0.778651\pi\)
\(20\) 1.10850 + 3.32036i 0.247868 + 0.742455i
\(21\) −2.04639 3.89908i −0.446559 0.850848i
\(22\) −5.86972 + 10.1667i −1.25143 + 2.16754i
\(23\) 3.17393 + 5.49741i 0.661810 + 1.14629i 0.980140 + 0.198309i \(0.0635449\pi\)
−0.318329 + 0.947980i \(0.603122\pi\)
\(24\) 4.37262 6.91475i 0.892557 1.41147i
\(25\) 0.970942 0.239316i 0.194188 0.0478631i
\(26\) −7.62208 + 3.66204i −1.49481 + 0.718185i
\(27\) −1.34395 0.331254i −0.258643 0.0637499i
\(28\) 4.78191 4.59308i 0.903696 0.868011i
\(29\) 4.15866 5.09343i 0.772244 0.945827i −0.227365 0.973810i \(-0.573011\pi\)
0.999608 + 0.0279829i \(0.00890838\pi\)
\(30\) −4.35884 3.27545i −0.795811 0.598013i
\(31\) −1.77546 + 7.20334i −0.318883 + 1.29376i 0.564627 + 0.825346i \(0.309020\pi\)
−0.883510 + 0.468412i \(0.844826\pi\)
\(32\) −3.93882 1.14089i −0.696291 0.201683i
\(33\) −0.936362 11.5989i −0.163000 2.01911i
\(34\) 0.703019 + 0.0853620i 0.120567 + 0.0146395i
\(35\) −1.19794 1.46721i −0.202489 0.248004i
\(36\) 0.338932 + 8.41050i 0.0564886 + 1.40175i
\(37\) −9.84499 + 2.85163i −1.61851 + 0.468806i −0.959120 0.282999i \(-0.908671\pi\)
−0.659385 + 0.751805i \(0.729183\pi\)
\(38\) 2.49842 + 6.58779i 0.405297 + 1.06868i
\(39\) 4.15586 7.27933i 0.665470 1.16563i
\(40\) 1.24791 3.29048i 0.197313 0.520270i
\(41\) 0.182813 2.26454i 0.0285506 0.353662i −0.966671 0.256021i \(-0.917588\pi\)
0.995222 0.0976409i \(-0.0311296\pi\)
\(42\) −2.06577 + 10.1188i −0.318755 + 1.56137i
\(43\) −0.792581 + 2.73631i −0.120868 + 0.417283i −0.998018 0.0629330i \(-0.979955\pi\)
0.877150 + 0.480216i \(0.159442\pi\)
\(44\) 16.3831 6.21330i 2.46985 0.936690i
\(45\) 2.40265 + 0.0968235i 0.358166 + 0.0144336i
\(46\) 2.38816 14.6950i 0.352115 2.16665i
\(47\) 6.85935 7.74261i 1.00054 1.12938i 0.00894913 0.999960i \(-0.497151\pi\)
0.991590 0.129416i \(-0.0413102\pi\)
\(48\) −2.76203 + 0.922102i −0.398665 + 0.133094i
\(49\) 1.46279 3.08277i 0.208971 0.440396i
\(50\) −2.11888 1.00542i −0.299654 0.142188i
\(51\) −0.621574 + 0.326227i −0.0870378 + 0.0456809i
\(52\) 12.2690 + 2.96110i 1.70140 + 0.410630i
\(53\) −2.05213 1.07704i −0.281882 0.147943i 0.317857 0.948139i \(-0.397037\pi\)
−0.599739 + 0.800196i \(0.704729\pi\)
\(54\) 1.95020 + 2.59525i 0.265389 + 0.353169i
\(55\) −1.39261 4.80786i −0.187780 0.648292i
\(56\) −6.64419 + 0.536375i −0.887868 + 0.0716761i
\(57\) −5.74768 3.96734i −0.761298 0.525486i
\(58\) −15.1100 + 3.08473i −1.98404 + 0.405045i
\(59\) 2.32423 5.45517i 0.302589 0.710202i −0.697390 0.716692i \(-0.745655\pi\)
0.999979 + 0.00648941i \(0.00206566\pi\)
\(60\) 1.94753 + 7.90144i 0.251425 + 1.02007i
\(61\) 0.380670 9.44624i 0.0487398 1.20947i −0.771039 0.636787i \(-0.780263\pi\)
0.819779 0.572680i \(-0.194096\pi\)
\(62\) 13.9101 10.4527i 1.76658 1.32750i
\(63\) −1.78527 4.19019i −0.224923 0.527915i
\(64\) 6.88641 + 9.97669i 0.860801 + 1.24709i
\(65\) 1.12519 3.42548i 0.139563 0.424879i
\(66\) −15.5034 + 22.4606i −1.90834 + 2.76471i
\(67\) 6.08393 + 1.24204i 0.743270 + 0.151740i 0.556714 0.830705i \(-0.312062\pi\)
0.186557 + 0.982444i \(0.440267\pi\)
\(68\) −0.732210 0.762311i −0.0887935 0.0924438i
\(69\) 6.32638 + 13.3326i 0.761607 + 1.60505i
\(70\) 4.44236i 0.530964i
\(71\) 11.7373 5.56942i 1.39296 0.660969i 0.423429 0.905929i \(-0.360826\pi\)
0.969533 + 0.244961i \(0.0787751\pi\)
\(72\) 5.08360 6.76504i 0.599108 0.797268i
\(73\) −0.270775 0.102692i −0.0316919 0.0120191i 0.338708 0.940892i \(-0.390010\pi\)
−0.370400 + 0.928872i \(0.620779\pi\)
\(74\) 22.1151 + 9.42237i 2.57083 + 1.09533i
\(75\) 2.29467 0.372921i 0.264966 0.0430612i
\(76\) 3.33008 9.97481i 0.381986 1.14419i
\(77\) −7.09671 + 6.28714i −0.808745 + 0.716486i
\(78\) −18.3472 + 7.05999i −2.07742 + 0.799386i
\(79\) −7.14938 6.33380i −0.804368 0.712608i 0.157082 0.987586i \(-0.449791\pi\)
−0.961451 + 0.274977i \(0.911330\pi\)
\(80\) −1.08474 + 0.626272i −0.121277 + 0.0700194i
\(81\) −9.89485 3.30338i −1.09943 0.367043i
\(82\) −3.69108 + 3.84282i −0.407611 + 0.424368i
\(83\) 2.14560 1.48100i 0.235510 0.162561i −0.444465 0.895796i \(-0.646606\pi\)
0.679975 + 0.733236i \(0.261991\pi\)
\(84\) 11.9400 9.74875i 1.30277 1.06368i
\(85\) −0.233897 + 0.190971i −0.0253697 + 0.0207137i
\(86\) 5.49860 3.79541i 0.592929 0.409270i
\(87\) 10.5894 11.0248i 1.13531 1.18198i
\(88\) −16.7086 5.57815i −1.78114 0.594633i
\(89\) 5.05753 2.91997i 0.536097 0.309516i −0.207399 0.978257i \(-0.566500\pi\)
0.743496 + 0.668741i \(0.233166\pi\)
\(90\) −4.22126 3.73971i −0.444960 0.394200i
\(91\) −6.77557 + 0.856012i −0.710273 + 0.0897344i
\(92\) −16.6325 + 14.7351i −1.73405 + 1.53624i
\(93\) −5.46169 + 16.3598i −0.566351 + 1.69643i
\(94\) −23.9458 + 3.89158i −2.46982 + 0.401386i
\(95\) −2.76374 1.17752i −0.283554 0.120811i
\(96\) −8.91377 3.38055i −0.909758 0.345026i
\(97\) −7.67223 + 10.2099i −0.778997 + 1.03666i 0.219143 + 0.975693i \(0.429674\pi\)
−0.998140 + 0.0609640i \(0.980583\pi\)
\(98\) −7.23008 + 3.43072i −0.730348 + 0.346555i
\(99\) 12.0362i 1.20968i
\(100\) 1.50064 + 3.16254i 0.150064 + 0.316254i
\(101\) 9.92969 + 10.3379i 0.988041 + 1.02866i 0.999587 + 0.0287263i \(0.00914513\pi\)
−0.0115463 + 0.999933i \(0.503675\pi\)
\(102\) 1.61310 + 0.329316i 0.159720 + 0.0326072i
\(103\) −4.40021 + 6.37480i −0.433565 + 0.628128i −0.977484 0.211010i \(-0.932325\pi\)
0.543919 + 0.839138i \(0.316940\pi\)
\(104\) −7.67157 10.1067i −0.752259 0.991047i
\(105\) −2.50145 3.62398i −0.244117 0.353664i
\(106\) 2.13053 + 5.00055i 0.206936 + 0.485696i
\(107\) 1.42136 1.06808i 0.137408 0.103256i −0.529816 0.848113i \(-0.677739\pi\)
0.667224 + 0.744857i \(0.267482\pi\)
\(108\) 0.195101 4.84138i 0.0187736 0.465862i
\(109\) −0.294253 1.19383i −0.0281843 0.114348i 0.955165 0.296074i \(-0.0956777\pi\)
−0.983349 + 0.181726i \(0.941832\pi\)
\(110\) −4.60147 + 10.8001i −0.438733 + 1.02974i
\(111\) −23.3467 + 4.76625i −2.21597 + 0.452393i
\(112\) 1.95253 + 1.34773i 0.184497 + 0.127349i
\(113\) −14.6291 + 1.18098i −1.37619 + 0.111098i −0.746312 0.665596i \(-0.768177\pi\)
−0.629878 + 0.776694i \(0.716895\pi\)
\(114\) 4.55708 + 15.7329i 0.426810 + 1.47352i
\(115\) 3.81343 + 5.07475i 0.355604 + 0.473223i
\(116\) 20.3811 + 10.6968i 1.89234 + 0.993177i
\(117\) 4.89047 7.15896i 0.452124 0.661846i
\(118\) −12.3140 + 6.46288i −1.13359 + 0.594956i
\(119\) 0.516727 + 0.245190i 0.0473683 + 0.0224765i
\(120\) 3.50726 7.39139i 0.320167 0.674739i
\(121\) −13.3316 + 4.45074i −1.21196 + 0.404612i
\(122\) −14.7030 + 16.5963i −1.33115 + 1.50256i
\(123\) 0.847242 5.21329i 0.0763933 0.470067i
\(124\) −25.9489 1.04571i −2.33028 0.0939072i
\(125\) 0.935016 0.354605i 0.0836304 0.0317168i
\(126\) −2.97195 + 10.2604i −0.264762 + 0.914066i
\(127\) 2.67549 13.1054i 0.237411 1.16292i −0.669898 0.742453i \(-0.733662\pi\)
0.907310 0.420463i \(-0.138132\pi\)
\(128\) 1.62783 20.1642i 0.143881 1.78228i
\(129\) −2.34848 + 6.19242i −0.206772 + 0.545212i
\(130\) −7.12510 + 4.55408i −0.624912 + 0.399419i
\(131\) 4.53871 + 11.9676i 0.396549 + 1.04561i 0.973470 + 0.228814i \(0.0734849\pi\)
−0.576921 + 0.816800i \(0.695746\pi\)
\(132\) 39.1259 11.3330i 3.40548 0.986408i
\(133\) 0.229124 + 5.68564i 0.0198675 + 0.493008i
\(134\) −9.21033 11.2806i −0.795651 0.974496i
\(135\) −1.37408 0.166844i −0.118262 0.0143596i
\(136\) 0.0855066 + 1.05919i 0.00733213 + 0.0908247i
\(137\) 15.1368 + 4.38442i 1.29322 + 0.374586i 0.852344 0.522981i \(-0.175180\pi\)
0.440877 + 0.897567i \(0.354667\pi\)
\(138\) 8.28289 33.6050i 0.705086 2.86065i
\(139\) 13.1644 + 9.89239i 1.11659 + 0.839061i 0.988277 0.152673i \(-0.0487880\pi\)
0.128311 + 0.991734i \(0.459044\pi\)
\(140\) 4.19341 5.13599i 0.354408 0.434070i
\(141\) 17.3432 16.6583i 1.46056 1.40288i
\(142\) −29.5841 7.29183i −2.48264 0.611917i
\(143\) −17.3591 4.93715i −1.45164 0.412865i
\(144\) −2.92435 + 0.720788i −0.243696 + 0.0600656i
\(145\) 3.51439 5.55757i 0.291854 0.461531i
\(146\) 0.339595 + 0.588196i 0.0281051 + 0.0486794i
\(147\) 3.96633 6.86989i 0.327138 0.566619i
\(148\) −16.6738 31.7693i −1.37058 2.61142i
\(149\) 5.21793 + 15.6296i 0.427469 + 1.28043i 0.913626 + 0.406555i \(0.133270\pi\)
−0.486157 + 0.873871i \(0.661602\pi\)
\(150\) −4.72187 2.72617i −0.385539 0.222591i
\(151\) 9.91431 + 11.1909i 0.806815 + 0.910706i 0.997480 0.0709494i \(-0.0226029\pi\)
−0.190665 + 0.981655i \(0.561064\pi\)
\(152\) −8.93539 + 5.65040i −0.724756 + 0.458308i
\(153\) −0.667983 + 0.284601i −0.0540032 + 0.0230086i
\(154\) 22.2182 0.895361i 1.79039 0.0721503i
\(155\) −0.894252 + 7.36483i −0.0718281 + 0.591558i
\(156\) 27.8763 + 9.15670i 2.23189 + 0.733123i
\(157\) 0.332677 + 2.73984i 0.0265505 + 0.218663i 0.999945 0.0104720i \(-0.00333340\pi\)
−0.973395 + 0.229135i \(0.926410\pi\)
\(158\) 3.59341 + 22.1111i 0.285876 + 1.75907i
\(159\) −4.55380 2.87965i −0.361140 0.228371i
\(160\) −4.04762 0.657802i −0.319992 0.0520038i
\(161\) 5.58772 10.6465i 0.440374 0.839063i
\(162\) 13.0760 + 20.6781i 1.02735 + 1.62463i
\(163\) 11.1790 + 10.7376i 0.875606 + 0.841031i 0.988288 0.152600i \(-0.0487646\pi\)
−0.112682 + 0.993631i \(0.535944\pi\)
\(164\) 7.89485 0.958609i 0.616484 0.0748548i
\(165\) −2.32763 11.4015i −0.181206 0.887604i
\(166\) −6.09463 0.492010i −0.473035 0.0381874i
\(167\) −1.41570 1.15588i −0.109550 0.0894451i 0.576087 0.817388i \(-0.304579\pi\)
−0.685637 + 0.727943i \(0.740476\pi\)
\(168\) −15.4965 −1.19558
\(169\) −8.31891 9.98978i −0.639916 0.768445i
\(170\) 0.708183 0.0543152
\(171\) −5.59555 4.56862i −0.427902 0.349371i
\(172\) −9.93985 0.802428i −0.757907 0.0611846i
\(173\) −1.81309 8.88111i −0.137847 0.675218i −0.988711 0.149833i \(-0.952126\pi\)
0.850865 0.525385i \(-0.176079\pi\)
\(174\) −35.5906 + 4.32148i −2.69812 + 0.327611i
\(175\) −1.36606 1.31212i −0.103264 0.0991869i
\(176\) 3.35088 + 5.29900i 0.252582 + 0.399427i
\(177\) 6.40628 12.2062i 0.481526 0.917471i
\(178\) −13.5191 2.19707i −1.01330 0.164677i
\(179\) 21.8948 + 13.8454i 1.63649 + 1.03486i 0.952120 + 0.305725i \(0.0988988\pi\)
0.684374 + 0.729131i \(0.260076\pi\)
\(180\) 1.35023 + 8.30832i 0.100641 + 0.619266i
\(181\) 0.0530603 + 0.436991i 0.00394394 + 0.0324813i 0.994548 0.104280i \(-0.0332538\pi\)
−0.990604 + 0.136761i \(0.956331\pi\)
\(182\) 13.5788 + 8.49499i 1.00653 + 0.629690i
\(183\) 2.64918 21.8180i 0.195833 1.61283i
\(184\) 22.3211 0.899509i 1.64553 0.0663127i
\(185\) −9.42948 + 4.01753i −0.693269 + 0.295374i
\(186\) 34.1884 21.6194i 2.50681 1.58521i
\(187\) 1.00227 + 1.13133i 0.0732931 + 0.0827309i
\(188\) 31.3582 + 18.1047i 2.28703 + 1.32042i
\(189\) 0.830246 + 2.48689i 0.0603915 + 0.180895i
\(190\) 3.27427 + 6.23861i 0.237541 + 0.452596i
\(191\) 5.90420 10.2264i 0.427213 0.739954i −0.569412 0.822053i \(-0.692829\pi\)
0.996624 + 0.0820987i \(0.0261623\pi\)
\(192\) 14.0912 + 24.4066i 1.01694 + 1.76140i
\(193\) −11.0885 + 17.5351i −0.798167 + 1.26220i 0.163107 + 0.986608i \(0.447848\pi\)
−0.961275 + 0.275593i \(0.911126\pi\)
\(194\) 29.0823 7.16813i 2.08798 0.514642i
\(195\) 3.24813 7.72719i 0.232604 0.553355i
\(196\) 11.5974 + 2.85851i 0.828388 + 0.204179i
\(197\) −0.0384103 + 0.0368936i −0.00273662 + 0.00262856i −0.694091 0.719887i \(-0.744194\pi\)
0.691355 + 0.722515i \(0.257014\pi\)
\(198\) −17.8531 + 21.8661i −1.26876 + 1.55395i
\(199\) 2.56298 + 1.92595i 0.181685 + 0.136527i 0.687693 0.726001i \(-0.258623\pi\)
−0.506009 + 0.862528i \(0.668880\pi\)
\(200\) 0.842192 3.41691i 0.0595520 0.241612i
\(201\) 13.8656 + 4.01622i 0.978003 + 0.283282i
\(202\) −2.70515 33.5094i −0.190334 2.35771i
\(203\) −12.3642 1.50128i −0.867795 0.105369i
\(204\) −1.55410 1.90343i −0.108809 0.133267i
\(205\) −0.0914806 2.27007i −0.00638928 0.158548i
\(206\) 17.4495 5.05430i 1.21576 0.352150i
\(207\) 5.41271 + 14.2722i 0.376210 + 0.991983i
\(208\) −0.159996 + 4.51328i −0.0110937 + 0.312940i
\(209\) −5.33225 + 14.0600i −0.368839 + 0.972549i
\(210\) −0.831020 + 10.2940i −0.0573458 + 0.710356i
\(211\) 2.10369 10.3045i 0.144824 0.709394i −0.840923 0.541155i \(-0.817987\pi\)
0.985746 0.168238i \(-0.0538078\pi\)
\(212\) 2.25711 7.79246i 0.155019 0.535189i
\(213\) 28.2400 10.7100i 1.93497 0.733839i
\(214\) −4.16645 0.167902i −0.284813 0.0114776i
\(215\) −0.456977 + 2.81189i −0.0311656 + 0.191769i
\(216\) −3.23016 + 3.64610i −0.219785 + 0.248085i
\(217\) 13.3293 4.44998i 0.904853 0.302084i
\(218\) −1.23622 + 2.60528i −0.0837275 + 0.176452i
\(219\) −0.608242 0.288614i −0.0411012 0.0195027i
\(220\) 15.5147 8.14276i 1.04600 0.548985i
\(221\) 0.136462 + 1.08013i 0.00917941 + 0.0726576i
\(222\) 49.4834 + 25.9709i 3.32111 + 1.74305i
\(223\) 8.55080 + 11.3790i 0.572604 + 0.761997i 0.989117 0.147133i \(-0.0470044\pi\)
−0.416513 + 0.909130i \(0.636748\pi\)
\(224\) 2.16101 + 7.46069i 0.144389 + 0.498488i
\(225\) 2.39680 0.193490i 0.159787 0.0128993i
\(226\) 28.3283 + 19.5536i 1.88437 + 1.30069i
\(227\) −11.1015 + 2.26638i −0.736829 + 0.150425i −0.553761 0.832676i \(-0.686808\pi\)
−0.183068 + 0.983100i \(0.558603\pi\)
\(228\) 9.58255 22.4911i 0.634620 1.48951i
\(229\) 0.321604 + 1.30480i 0.0212522 + 0.0862235i 0.980610 0.195968i \(-0.0627848\pi\)
−0.959358 + 0.282191i \(0.908939\pi\)
\(230\) 0.599469 14.8757i 0.0395278 0.980873i
\(231\) −17.6209 + 13.2413i −1.15937 + 0.871210i
\(232\) −9.07025 21.2887i −0.595491 1.39767i
\(233\) 15.9051 + 23.0425i 1.04198 + 1.50956i 0.849023 + 0.528356i \(0.177191\pi\)
0.192954 + 0.981208i \(0.438193\pi\)
\(234\) −19.5033 + 5.75168i −1.27497 + 0.375999i
\(235\) 5.87607 8.51296i 0.383313 0.555324i
\(236\) 20.3374 + 4.15190i 1.32385 + 0.270266i
\(237\) −15.3820 16.0144i −0.999168 1.04024i
\(238\) −0.575048 1.21189i −0.0372748 0.0785550i
\(239\) 14.2985i 0.924890i 0.886648 + 0.462445i \(0.153028\pi\)
−0.886648 + 0.462445i \(0.846972\pi\)
\(240\) −2.63075 + 1.24831i −0.169814 + 0.0805778i
\(241\) 3.71099 4.93843i 0.239046 0.318112i −0.663937 0.747788i \(-0.731116\pi\)
0.902983 + 0.429676i \(0.141372\pi\)
\(242\) 30.8211 + 11.6889i 1.98126 + 0.751391i
\(243\) −18.4906 7.87809i −1.18617 0.505380i
\(244\) 32.6649 5.30857i 2.09116 0.339846i
\(245\) 1.08054 3.23662i 0.0690333 0.206780i
\(246\) −9.27198 + 8.21425i −0.591160 + 0.523722i
\(247\) −8.88430 + 6.19611i −0.565295 + 0.394249i
\(248\) 19.5424 + 17.3131i 1.24095 + 1.09938i
\(249\) 5.24891 3.03046i 0.332636 0.192048i
\(250\) −2.22462 0.742687i −0.140697 0.0469716i
\(251\) −2.05027 + 2.13456i −0.129412 + 0.134732i −0.782755 0.622330i \(-0.786186\pi\)
0.653343 + 0.757062i \(0.273366\pi\)
\(252\) 13.1213 9.05701i 0.826567 0.570538i
\(253\) 24.6124 20.0954i 1.54737 1.26339i
\(254\) −24.2996 + 19.8400i −1.52469 + 1.24487i
\(255\) −0.577720 + 0.398771i −0.0361782 + 0.0249720i
\(256\) −16.0714 + 16.7321i −1.00446 + 1.04575i
\(257\) −12.5195 4.17962i −0.780944 0.260718i −0.101880 0.994797i \(-0.532486\pi\)
−0.679064 + 0.734079i \(0.737614\pi\)
\(258\) 13.4516 7.76627i 0.837459 0.483507i
\(259\) 14.5318 + 12.8741i 0.902964 + 0.799956i
\(260\) 12.5365 + 1.46065i 0.777478 + 0.0905854i
\(261\) 11.8351 10.4850i 0.732573 0.649003i
\(262\) 9.50591 28.4737i 0.587277 1.75911i
\(263\) −0.255054 + 0.0414502i −0.0157273 + 0.00255593i −0.168270 0.985741i \(-0.553818\pi\)
0.152543 + 0.988297i \(0.451254\pi\)
\(264\) −37.6744 16.0516i −2.31870 0.987905i
\(265\) −2.16699 0.821832i −0.133117 0.0504847i
\(266\) 8.01718 10.6689i 0.491565 0.654154i
\(267\) 12.2657 5.82017i 0.750652 0.356189i
\(268\) 21.7361i 1.32774i
\(269\) 4.11034 + 8.66235i 0.250612 + 0.528153i 0.989300 0.145894i \(-0.0466058\pi\)
−0.738689 + 0.674047i \(0.764555\pi\)
\(270\) 2.24881 + 2.34125i 0.136858 + 0.142484i
\(271\) −7.03854 1.43693i −0.427561 0.0872871i −0.0185739 0.999827i \(-0.505913\pi\)
−0.408987 + 0.912540i \(0.634118\pi\)
\(272\) 0.214850 0.311264i 0.0130272 0.0188731i
\(273\) −15.8608 + 0.716100i −0.959937 + 0.0433403i
\(274\) −20.9955 30.4173i −1.26839 1.83758i
\(275\) −1.96198 4.60494i −0.118312 0.277689i
\(276\) −41.2979 + 31.0333i −2.48584 + 1.86799i
\(277\) 0.480365 11.9201i 0.0288624 0.716212i −0.918381 0.395697i \(-0.870503\pi\)
0.947243 0.320515i \(-0.103856\pi\)
\(278\) −9.24241 37.4979i −0.554323 2.24898i
\(279\) −6.99251 + 16.4120i −0.418630 + 0.982562i
\(280\) −6.53110 + 1.33333i −0.390308 + 0.0796819i
\(281\) −7.06684 4.87789i −0.421572 0.290990i 0.338330 0.941027i \(-0.390138\pi\)
−0.759902 + 0.650037i \(0.774753\pi\)
\(282\) −56.2163 + 4.53825i −3.34763 + 0.270249i
\(283\) 4.84208 + 16.7168i 0.287832 + 0.993711i 0.965944 + 0.258752i \(0.0833114\pi\)
−0.678112 + 0.734959i \(0.737201\pi\)
\(284\) 27.3202 + 36.3565i 1.62115 + 2.15736i
\(285\) −6.18398 3.24560i −0.366307 0.192253i
\(286\) 24.2130 + 34.7178i 1.43174 + 2.05290i
\(287\) −3.81040 + 1.99985i −0.224921 + 0.118048i
\(288\) −8.90856 4.22717i −0.524942 0.249088i
\(289\) −7.24869 + 15.2763i −0.426393 + 0.898605i
\(290\) −14.6280 + 4.88355i −0.858987 + 0.286772i
\(291\) −19.6883 + 22.2235i −1.15415 + 1.30277i
\(292\) 0.162613 1.00060i 0.00951622 0.0585557i
\(293\) −22.7768 0.917874i −1.33064 0.0536228i −0.635276 0.772285i \(-0.719114\pi\)
−0.695359 + 0.718662i \(0.744755\pi\)
\(294\) −17.3956 + 6.59728i −1.01453 + 0.384761i
\(295\) 1.64974 5.69555i 0.0960513 0.331608i
\(296\) −7.21498 + 35.3413i −0.419362 + 2.05417i
\(297\) −0.557509 + 6.90599i −0.0323500 + 0.400726i
\(298\) 13.7038 36.1339i 0.793838 2.09318i
\(299\) 22.8041 1.95211i 1.31880 0.112894i
\(300\) 2.88574 + 7.60908i 0.166608 + 0.439310i
\(301\) 5.18296 1.50126i 0.298741 0.0865313i
\(302\) −1.41191 35.0362i −0.0812464 2.01611i
\(303\) 21.0756 + 25.8129i 1.21076 + 1.48291i
\(304\) 3.73538 + 0.453557i 0.214239 + 0.0260133i
\(305\) −0.760723 9.42325i −0.0435589 0.539574i
\(306\) 1.63566 + 0.473776i 0.0935047 + 0.0270840i
\(307\) −5.38047 + 21.8294i −0.307080 + 1.24587i 0.591228 + 0.806504i \(0.298643\pi\)
−0.898308 + 0.439366i \(0.855203\pi\)
\(308\) −26.5325 19.9379i −1.51183 1.13606i
\(309\) −11.3889 + 13.9488i −0.647889 + 0.793520i
\(310\) 12.5487 12.0532i 0.712720 0.684576i
\(311\) −29.6877 7.31737i −1.68344 0.414930i −0.722428 0.691446i \(-0.756974\pi\)
−0.961009 + 0.276516i \(0.910820\pi\)
\(312\) −15.8862 24.8548i −0.899381 1.40713i
\(313\) −13.3124 + 3.28122i −0.752463 + 0.185465i −0.596850 0.802353i \(-0.703581\pi\)
−0.155613 + 0.987818i \(0.549735\pi\)
\(314\) 3.45959 5.47090i 0.195236 0.308741i
\(315\) −2.27733 3.94445i −0.128313 0.222245i
\(316\) 16.7175 28.9556i 0.940434 1.62888i
\(317\) 1.28025 + 2.43931i 0.0719059 + 0.137005i 0.918755 0.394828i \(-0.129196\pi\)
−0.846849 + 0.531833i \(0.821503\pi\)
\(318\) 4.00152 + 11.9860i 0.224394 + 0.672143i
\(319\) −28.5041 16.4568i −1.59592 0.921407i
\(320\) 8.03876 + 9.07388i 0.449380 + 0.507245i
\(321\) 3.49344 2.20912i 0.194985 0.123301i
\(322\) −25.9430 + 11.0533i −1.44575 + 0.615975i
\(323\) 0.906381 0.0365259i 0.0504324 0.00203236i
\(324\) 4.40155 36.2500i 0.244530 2.01389i
\(325\) 0.704090 3.53614i 0.0390559 0.196150i
\(326\) −4.38194 36.0885i −0.242693 1.99876i
\(327\) −0.458528 2.82144i −0.0253567 0.156026i
\(328\) −6.75749 4.27318i −0.373120 0.235947i
\(329\) −19.3393 3.14295i −1.06621 0.173276i
\(330\) −12.6831 + 24.1655i −0.698179 + 1.33027i
\(331\) −10.2349 16.1852i −0.562561 0.889619i 0.437393 0.899271i \(-0.355902\pi\)
−0.999953 + 0.00965195i \(0.996928\pi\)
\(332\) 6.58181 + 6.32191i 0.361224 + 0.346960i
\(333\) −24.4666 + 2.97079i −1.34076 + 0.162798i
\(334\) 0.857391 + 4.19978i 0.0469143 + 0.229802i
\(335\) 6.18928 + 0.499650i 0.338157 + 0.0272988i
\(336\) 4.27236 + 3.48828i 0.233076 + 0.190301i
\(337\) 9.61965 0.524016 0.262008 0.965066i \(-0.415615\pi\)
0.262008 + 0.965066i \(0.415615\pi\)
\(338\) 0.295232 + 30.4877i 0.0160585 + 1.65831i
\(339\) −34.1201 −1.85315
\(340\) −0.818758 0.668495i −0.0444034 0.0362542i
\(341\) 37.0149 + 2.98815i 2.00447 + 0.161818i
\(342\) 3.38883 + 16.5996i 0.183247 + 0.897602i
\(343\) −19.5784 + 2.37725i −1.05714 + 0.128360i
\(344\) 7.23030 + 6.94480i 0.389832 + 0.374439i
\(345\) 7.88732 + 12.4728i 0.424639 + 0.671513i
\(346\) −9.87938 + 18.8236i −0.531119 + 1.01196i
\(347\) 22.1051 + 3.59243i 1.18667 + 0.192852i 0.721527 0.692386i \(-0.243440\pi\)
0.465139 + 0.885238i \(0.346005\pi\)
\(348\) 45.2270 + 28.5998i 2.42442 + 1.53311i
\(349\) −4.89645 30.1291i −0.262101 1.61277i −0.700269 0.713879i \(-0.746936\pi\)
0.438167 0.898893i \(-0.355628\pi\)
\(350\) 0.535468 + 4.40997i 0.0286220 + 0.235723i
\(351\) −3.13759 + 3.88106i −0.167472 + 0.207156i
\(352\) −2.47415 + 20.3765i −0.131873 + 1.08607i
\(353\) 10.8435 0.436978i 0.577141 0.0232580i 0.250021 0.968241i \(-0.419563\pi\)
0.327121 + 0.944983i \(0.393922\pi\)
\(354\) −29.7435 + 12.6725i −1.58085 + 0.673536i
\(355\) 10.9804 6.94359i 0.582779 0.368527i
\(356\) 13.5560 + 15.3016i 0.718469 + 0.810984i
\(357\) 1.15151 + 0.664827i 0.0609446 + 0.0351864i
\(358\) −19.2394 57.6291i −1.01684 3.04579i
\(359\) −1.72777 3.29199i −0.0911883 0.173745i 0.835590 0.549354i \(-0.185126\pi\)
−0.926778 + 0.375609i \(0.877434\pi\)
\(360\) 4.23110 7.32847i 0.222998 0.386245i
\(361\) −4.98759 8.63876i −0.262505 0.454672i
\(362\) 0.551787 0.872582i 0.0290013 0.0458619i
\(363\) −31.7251 + 7.81953i −1.66513 + 0.410419i
\(364\) −7.68012 22.6392i −0.402548 1.18662i
\(365\) −0.281179 0.0693044i −0.0147176 0.00362756i
\(366\) −37.1751 + 35.7071i −1.94317 + 1.86644i
\(367\) 22.2058 27.1972i 1.15914 1.41968i 0.269506 0.962999i \(-0.413139\pi\)
0.889629 0.456684i \(-0.150963\pi\)
\(368\) −6.35635 4.77649i −0.331348 0.248992i
\(369\) 1.30739 5.30429i 0.0680600 0.276130i
\(370\) 23.0896 + 6.68799i 1.20037 + 0.347692i
\(371\) 0.353237 + 4.37563i 0.0183392 + 0.227171i
\(372\) −59.9344 7.27735i −3.10745 0.377313i
\(373\) 19.6154 + 24.0245i 1.01564 + 1.24394i 0.969522 + 0.245003i \(0.0787891\pi\)
0.0461226 + 0.998936i \(0.485314\pi\)
\(374\) −0.142735 3.54193i −0.00738064 0.183149i
\(375\) 2.23299 0.646794i 0.115311 0.0334003i
\(376\) −12.9084 34.0368i −0.665702 1.75531i
\(377\) −10.2672 21.3699i −0.528787 1.10061i
\(378\) 2.18046 5.74941i 0.112151 0.295718i
\(379\) 0.286715 3.55160i 0.0147275 0.182433i −0.985211 0.171346i \(-0.945189\pi\)
0.999939 0.0110877i \(-0.00352941\pi\)
\(380\) 2.10347 10.3035i 0.107906 0.528557i
\(381\) 8.65134 29.8679i 0.443221 1.53018i
\(382\) −25.8947 + 9.82057i −1.32489 + 0.502464i
\(383\) 11.9812 + 0.482827i 0.612212 + 0.0246713i 0.344436 0.938810i \(-0.388070\pi\)
0.267776 + 0.963481i \(0.413711\pi\)
\(384\) 7.54413 46.4209i 0.384985 2.36891i
\(385\) −6.28714 + 7.09671i −0.320422 + 0.361682i
\(386\) 46.1539 15.4084i 2.34917 0.784268i
\(387\) −2.93662 + 6.18880i −0.149277 + 0.314595i
\(388\) −40.3895 19.1651i −2.05047 0.972959i
\(389\) 16.3950 8.60478i 0.831262 0.436280i 0.00528642 0.999986i \(-0.498317\pi\)
0.825975 + 0.563706i \(0.190625\pi\)
\(390\) −17.3625 + 9.22003i −0.879183 + 0.466874i
\(391\) −1.69722 0.890770i −0.0858322 0.0450482i
\(392\) −7.21382 9.59985i −0.364353 0.484866i
\(393\) 8.27855 + 28.5809i 0.417598 + 1.44171i
\(394\) 0.124503 0.0100510i 0.00627239 0.000506360i
\(395\) −7.86071 5.42586i −0.395515 0.273005i
\(396\) 41.2813 8.42765i 2.07447 0.423505i
\(397\) −14.4037 + 33.8068i −0.722902 + 1.69671i −0.00556861 + 0.999984i \(0.501773\pi\)
−0.717334 + 0.696730i \(0.754638\pi\)
\(398\) −1.79941 7.30049i −0.0901962 0.365940i
\(399\) −0.532662 + 13.2179i −0.0266665 + 0.661721i
\(400\) −1.00134 + 0.752456i −0.0500669 + 0.0376228i
\(401\) 3.20522 + 7.52293i 0.160061 + 0.375677i 0.980630 0.195871i \(-0.0627533\pi\)
−0.820569 + 0.571548i \(0.806343\pi\)
\(402\) −19.2323 27.8628i −0.959221 1.38967i
\(403\) 20.8018 + 16.8170i 1.03621 + 0.837712i
\(404\) −28.5039 + 41.2950i −1.41812 + 2.05450i
\(405\) −10.2209 2.08661i −0.507880 0.103684i
\(406\) 20.2351 + 21.0670i 1.00425 + 1.04554i
\(407\) 21.9939 + 46.3511i 1.09020 + 2.29754i
\(408\) 2.47039i 0.122303i
\(409\) 20.0976 9.53644i 0.993764 0.471547i 0.138848 0.990314i \(-0.455660\pi\)
0.854916 + 0.518767i \(0.173609\pi\)
\(410\) −3.20096 + 4.25971i −0.158084 + 0.210372i
\(411\) 34.2554 + 12.9913i 1.68969 + 0.640816i
\(412\) −24.9451 10.6281i −1.22895 0.523609i
\(413\) −11.0862 + 1.80168i −0.545516 + 0.0886549i
\(414\) 11.3364 33.9567i 0.557155 1.66888i
\(415\) 1.95144 1.72882i 0.0957923 0.0848646i
\(416\) −9.75081 + 11.1143i −0.478073 + 0.544926i
\(417\) 28.6545 + 25.3857i 1.40322 + 1.24314i
\(418\) 30.5420 17.6334i 1.49386 0.862480i
\(419\) −2.58047 0.861487i −0.126064 0.0420864i 0.252936 0.967483i \(-0.418604\pi\)
−0.379000 + 0.925397i \(0.623732\pi\)
\(420\) 10.6779 11.1169i 0.521029 0.542448i
\(421\) −22.8731 + 15.7881i −1.11476 + 0.769467i −0.975327 0.220764i \(-0.929145\pi\)
−0.139438 + 0.990231i \(0.544529\pi\)
\(422\) −19.1063 + 15.5998i −0.930081 + 0.759387i
\(423\) 19.2669 15.7310i 0.936790 0.764866i
\(424\) −6.71227 + 4.63315i −0.325977 + 0.225005i
\(425\) −0.209172 + 0.217772i −0.0101464 + 0.0105635i
\(426\) −67.1895 22.4311i −3.25534 1.08679i
\(427\) −15.5080 + 8.95352i −0.750483 + 0.433291i
\(428\) 4.65850 + 4.12707i 0.225177 + 0.199490i
\(429\) −39.3016 14.6879i −1.89750 0.709138i
\(430\) 5.00102 4.43052i 0.241171 0.213659i
\(431\) 12.2869 36.8038i 0.591840 1.77278i −0.0417723 0.999127i \(-0.513300\pi\)
0.633612 0.773651i \(-0.281571\pi\)
\(432\) 1.71129 0.278111i 0.0823343 0.0133806i
\(433\) 2.39967 + 1.02241i 0.115321 + 0.0491337i 0.448856 0.893604i \(-0.351831\pi\)
−0.333536 + 0.942738i \(0.608242\pi\)
\(434\) −30.8159 11.6869i −1.47921 0.560990i
\(435\) 9.18333 12.2208i 0.440307 0.585942i
\(436\) 3.88852 1.84513i 0.186226 0.0883655i
\(437\) 19.0698i 0.912233i
\(438\) 0.676892 + 1.42652i 0.0323431 + 0.0681617i
\(439\) −8.90466 9.27074i −0.424996 0.442468i 0.473934 0.880561i \(-0.342834\pi\)
−0.898930 + 0.438093i \(0.855654\pi\)
\(440\) −17.2592 3.52348i −0.822798 0.167975i
\(441\) 4.66099 6.75261i 0.221952 0.321553i
\(442\) 1.35423 2.16468i 0.0644144 0.102963i
\(443\) −0.351673 0.509486i −0.0167085 0.0242064i 0.814541 0.580107i \(-0.196989\pi\)
−0.831249 + 0.555900i \(0.812374\pi\)
\(444\) −32.6943 76.7363i −1.55160 3.64174i
\(445\) 4.66869 3.50829i 0.221317 0.166309i
\(446\) 1.34418 33.3555i 0.0636488 1.57943i
\(447\) 9.16741 + 37.1936i 0.433604 + 1.75920i
\(448\) 9.00030 21.1245i 0.425224 0.998038i
\(449\) 1.60580 0.327826i 0.0757822 0.0154710i −0.161985 0.986793i \(-0.551790\pi\)
0.237767 + 0.971322i \(0.423584\pi\)
\(450\) −4.64126 3.20363i −0.218791 0.151021i
\(451\) −11.3351 + 0.915067i −0.533751 + 0.0430888i
\(452\) −14.2937 49.3475i −0.672318 2.32111i
\(453\) 20.8804 + 27.7867i 0.981046 + 1.30554i
\(454\) 23.5296 + 12.3493i 1.10430 + 0.579581i
\(455\) −6.62299 + 1.66648i −0.310490 + 0.0781256i
\(456\) −21.7625 + 11.4218i −1.01912 + 0.534876i
\(457\) 3.47987 + 1.65122i 0.162781 + 0.0772407i 0.508340 0.861156i \(-0.330259\pi\)
−0.345559 + 0.938397i \(0.612311\pi\)
\(458\) 1.35113 2.84745i 0.0631343 0.133053i
\(459\) 0.396450 0.132354i 0.0185047 0.00617777i
\(460\) −14.7351 + 16.6325i −0.687027 + 0.775493i
\(461\) −1.66129 + 10.2223i −0.0773741 + 0.476102i 0.919227 + 0.393727i \(0.128815\pi\)
−0.996601 + 0.0823747i \(0.973750\pi\)
\(462\) 51.6523 + 2.08152i 2.40308 + 0.0968410i
\(463\) 13.5021 5.12068i 0.627497 0.237978i −0.0202969 0.999794i \(-0.506461\pi\)
0.647794 + 0.761816i \(0.275692\pi\)
\(464\) −2.29144 + 7.91096i −0.106377 + 0.367257i
\(465\) −3.44992 + 16.8988i −0.159986 + 0.783663i
\(466\) 5.28391 65.4529i 0.244772 3.03205i
\(467\) −4.89011 + 12.8942i −0.226287 + 0.596670i −0.999288 0.0377350i \(-0.987986\pi\)
0.773001 + 0.634405i \(0.218755\pi\)
\(468\) 27.9778 + 11.7605i 1.29328 + 0.543630i
\(469\) −4.17069 10.9972i −0.192585 0.507804i
\(470\) −23.3022 + 6.74956i −1.07485 + 0.311334i
\(471\) 0.258358 + 6.41110i 0.0119045 + 0.295408i
\(472\) −13.1975 16.1641i −0.607466 0.744011i
\(473\) 14.1556 + 1.71880i 0.650874 + 0.0790304i
\(474\) 4.19053 + 51.9091i 0.192478 + 2.38426i
\(475\) −2.88552 0.835802i −0.132397 0.0383492i
\(476\) −0.479136 + 1.94393i −0.0219612 + 0.0891000i
\(477\) −4.45521 3.34788i −0.203990 0.153289i
\(478\) 21.2087 25.9759i 0.970063 1.18811i
\(479\) 11.1869 10.7452i 0.511142 0.490959i −0.392199 0.919880i \(-0.628286\pi\)
0.903342 + 0.428921i \(0.141106\pi\)
\(480\) −9.25626 2.28146i −0.422488 0.104134i
\(481\) −5.75143 + 36.5054i −0.262243 + 1.66450i
\(482\) −14.0668 + 3.46716i −0.640726 + 0.157925i
\(483\) 14.9397 23.6253i 0.679780 1.07499i
\(484\) −24.5996 42.6078i −1.11817 1.93672i
\(485\) −6.38563 + 11.0602i −0.289956 + 0.502219i
\(486\) 21.9062 + 41.7388i 0.993687 + 1.89331i
\(487\) −8.30020 24.8621i −0.376118 1.12661i −0.951216 0.308526i \(-0.900164\pi\)
0.575098 0.818085i \(-0.304964\pi\)
\(488\) −28.8126 16.6349i −1.30428 0.753028i
\(489\) 23.8958 + 26.9727i 1.08060 + 1.21975i
\(490\) −6.76384 + 4.27719i −0.305559 + 0.193224i
\(491\) 4.21799 1.79712i 0.190355 0.0811027i −0.294686 0.955594i \(-0.595215\pi\)
0.485041 + 0.874491i \(0.338805\pi\)
\(492\) 18.4736 0.744461i 0.832854 0.0335629i
\(493\) −0.239328 + 1.97104i −0.0107788 + 0.0887713i
\(494\) 25.3307 + 1.92151i 1.13968 + 0.0864527i
\(495\) −1.45080 11.9484i −0.0652088 0.537042i
\(496\) −1.49063 9.17220i −0.0669311 0.411844i
\(497\) −20.7985 13.1522i −0.932939 0.589955i
\(498\) −14.0307 2.28021i −0.628731 0.102179i
\(499\) −16.0742 + 30.6268i −0.719580 + 1.37105i 0.200648 + 0.979663i \(0.435695\pi\)
−0.920228 + 0.391382i \(0.871997\pi\)
\(500\) 1.87090 + 2.95860i 0.0836693 + 0.132312i
\(501\) −3.06430 2.94330i −0.136903 0.131497i
\(502\) 6.89088 0.836705i 0.307555 0.0373440i
\(503\) −2.77125 13.5745i −0.123564 0.605256i −0.993665 0.112383i \(-0.964152\pi\)
0.870101 0.492873i \(-0.164053\pi\)
\(504\) −15.9766 1.28977i −0.711656 0.0574508i
\(505\) 11.1034 + 9.06563i 0.494094 + 0.403415i
\(506\) −74.5204 −3.31284
\(507\) −17.4082 24.7049i −0.773124 1.09718i
\(508\) 46.8218 2.07738
\(509\) −9.40359 7.67779i −0.416807 0.340312i 0.400722 0.916200i \(-0.368759\pi\)
−0.817529 + 0.575887i \(0.804657\pi\)
\(510\) 1.64103 + 0.132478i 0.0726661 + 0.00586621i
\(511\) 0.109721 + 0.537447i 0.00485376 + 0.0237753i
\(512\) 13.8504 1.68175i 0.612109 0.0743235i
\(513\) 2.99893 + 2.88051i 0.132406 + 0.127178i
\(514\) 16.5445 + 26.1631i 0.729747 + 1.15400i
\(515\) −3.59973 + 6.85871i −0.158623 + 0.302231i
\(516\) −22.8829 3.71884i −1.00736 0.163713i
\(517\) −43.7613 27.6730i −1.92462 1.21706i
\(518\) −7.30396 44.9431i −0.320918 1.97469i
\(519\) −2.54001 20.9188i −0.111494 0.918235i
\(520\) −8.83386 9.10834i −0.387391 0.399427i
\(521\) 3.80064 31.3011i 0.166509 1.37133i −0.634615 0.772828i \(-0.718841\pi\)
0.801124 0.598498i \(-0.204235\pi\)
\(522\) −37.0529 + 1.49318i −1.62176 + 0.0653548i
\(523\) 27.2355 11.6040i 1.19093 0.507406i 0.296677 0.954978i \(-0.404121\pi\)
0.894248 + 0.447572i \(0.147711\pi\)
\(524\) −37.8681 + 23.9463i −1.65428 + 1.04610i
\(525\) −2.92004 3.29604i −0.127441 0.143851i
\(526\) 0.524837 + 0.303015i 0.0228840 + 0.0132121i
\(527\) −0.709397 2.12490i −0.0309018 0.0925622i
\(528\) 6.77354 + 12.9059i 0.294780 + 0.561657i
\(529\) −8.64767 + 14.9782i −0.375986 + 0.651227i
\(530\) 2.71775 + 4.70728i 0.118052 + 0.204471i
\(531\) 7.62067 12.0511i 0.330709 0.522974i
\(532\) −19.3400 + 4.76688i −0.838495 + 0.206671i
\(533\) −7.11378 4.06135i −0.308132 0.175917i
\(534\) −30.9161 7.62013i −1.33787 0.329755i
\(535\) 1.28225 1.23162i 0.0554367 0.0532477i
\(536\) 13.8202 16.9267i 0.596941 0.731120i
\(537\) 48.1455 + 36.1790i 2.07763 + 1.56124i
\(538\) 5.38151 21.8336i 0.232013 0.941315i
\(539\) −16.4055 4.75191i −0.706634 0.204679i
\(540\) −0.389885 4.82959i −0.0167780 0.207833i
\(541\) −18.6295 2.26203i −0.800943 0.0972521i −0.290178 0.956973i \(-0.593715\pi\)
−0.510765 + 0.859721i \(0.670638\pi\)
\(542\) 10.6555 + 13.0506i 0.457693 + 0.560572i
\(543\) 0.0412069 + 1.02254i 0.00176836 + 0.0438813i
\(544\) 1.18935 0.344500i 0.0509930 0.0147703i
\(545\) −0.436007 1.14966i −0.0186765 0.0492459i
\(546\) 29.8763 + 22.2251i 1.27859 + 0.951146i
\(547\) −3.85088 + 10.1539i −0.164652 + 0.434151i −0.991795 0.127840i \(-0.959196\pi\)
0.827143 + 0.561992i \(0.189965\pi\)
\(548\) −4.43889 + 54.9855i −0.189620 + 2.34886i
\(549\) 4.54716 22.2735i 0.194068 0.950608i
\(550\) −3.26612 + 11.2760i −0.139268 + 0.480808i
\(551\) −18.4701 + 7.00478i −0.786852 + 0.298414i
\(552\) 51.8916 + 2.09116i 2.20865 + 0.0890056i
\(553\) −2.90214 + 17.8576i −0.123412 + 0.759382i
\(554\) −18.5536 + 20.9427i −0.788269 + 0.889772i
\(555\) −22.6019 + 7.54563i −0.959398 + 0.320294i
\(556\) −24.7110 + 52.0773i −1.04798 + 2.20857i
\(557\) −23.5725 11.1853i −0.998801 0.473937i −0.142156 0.989844i \(-0.545404\pi\)
−0.856644 + 0.515907i \(0.827455\pi\)
\(558\) 37.0469 19.4437i 1.56832 0.823119i
\(559\) 7.72117 + 6.77392i 0.326571 + 0.286506i
\(560\) 2.10074 + 1.10256i 0.0887726 + 0.0465915i
\(561\) 2.11086 + 2.80905i 0.0891208 + 0.118598i
\(562\) 5.60299 + 19.3438i 0.236348 + 0.815967i
\(563\) −15.4388 + 1.24635i −0.650670 + 0.0525275i −0.401395 0.915905i \(-0.631474\pi\)
−0.249275 + 0.968433i \(0.580192\pi\)
\(564\) 69.2777 + 47.8190i 2.91712 + 2.01354i
\(565\) −14.3801 + 2.93572i −0.604975 + 0.123507i
\(566\) 15.9992 37.5515i 0.672497 1.57841i
\(567\) 4.72867 + 19.1850i 0.198585 + 0.805693i
\(568\) 1.84095 45.6827i 0.0772445 1.91680i
\(569\) −16.4137 + 12.3341i −0.688097 + 0.517072i −0.886313 0.463087i \(-0.846742\pi\)
0.198216 + 0.980158i \(0.436485\pi\)
\(570\) 6.42024 + 15.0689i 0.268914 + 0.631165i
\(571\) 5.43649 + 7.87611i 0.227510 + 0.329605i 0.920069 0.391756i \(-0.128132\pi\)
−0.692559 + 0.721361i \(0.743517\pi\)
\(572\) 4.77858 62.9946i 0.199802 2.63394i
\(573\) 15.5945 22.5925i 0.651468 0.943814i
\(574\) 9.88868 + 2.01879i 0.412746 + 0.0842626i
\(575\) 4.39732 + 4.57809i 0.183381 + 0.190920i
\(576\) 12.4964 + 26.3356i 0.520682 + 1.09731i
\(577\) 31.8999i 1.32801i 0.747728 + 0.664005i \(0.231145\pi\)
−0.747728 + 0.664005i \(0.768855\pi\)
\(578\) 35.8277 17.0005i 1.49024 0.707126i
\(579\) −28.9750 + 38.5587i −1.20416 + 1.60244i
\(580\) 21.5219 + 8.16218i 0.893648 + 0.338916i
\(581\) −4.54305 1.93561i −0.188478 0.0803028i
\(582\) 68.7315 11.1700i 2.84901 0.463010i
\(583\) −3.67357 + 11.0037i −0.152144 + 0.455726i
\(584\) −0.762830 + 0.675809i −0.0315661 + 0.0279652i
\(585\) 3.99189 7.69624i 0.165044 0.318200i
\(586\) 40.0170 + 35.4520i 1.65309 + 1.46451i
\(587\) 30.8320 17.8008i 1.27257 0.734720i 0.297100 0.954846i \(-0.403980\pi\)
0.975471 + 0.220127i \(0.0706471\pi\)
\(588\) 26.3393 + 8.79335i 1.08621 + 0.362632i
\(589\) 15.4391 16.0738i 0.636155 0.662308i
\(590\) −11.4452 + 7.90004i −0.471191 + 0.325240i
\(591\) −0.0959075 + 0.0783061i −0.00394511 + 0.00322108i
\(592\) 9.94450 8.11943i 0.408716 0.333707i
\(593\) −17.8859 + 12.3457i −0.734486 + 0.506979i −0.875614 0.483012i \(-0.839543\pi\)
0.141128 + 0.989991i \(0.454927\pi\)
\(594\) 11.2564 11.7191i 0.461854 0.480841i
\(595\) 0.542514 + 0.181118i 0.0222409 + 0.00742510i
\(596\) −49.9523 + 28.8400i −2.04613 + 1.18133i
\(597\) 5.57875 + 4.94234i 0.228323 + 0.202277i
\(598\) −44.3237 30.2786i −1.81253 1.23819i
\(599\) 21.1084 18.7004i 0.862467 0.764080i −0.110779 0.993845i \(-0.535334\pi\)
0.973246 + 0.229766i \(0.0737960\pi\)
\(600\) 2.59075 7.76025i 0.105767 0.316811i
\(601\) 45.7548 7.43588i 1.86638 0.303316i 0.880924 0.473258i \(-0.156922\pi\)
0.985454 + 0.169942i \(0.0543581\pi\)
\(602\) −11.6426 4.96047i −0.474519 0.202174i
\(603\) 13.9609 + 5.29467i 0.568531 + 0.215615i
\(604\) −31.4404 + 41.8396i −1.27929 + 1.70243i
\(605\) −12.6979 + 6.02523i −0.516243 + 0.244960i
\(606\) 78.1553i 3.17484i
\(607\) 11.8429 + 24.9583i 0.480687 + 1.01303i 0.988453 + 0.151531i \(0.0484202\pi\)
−0.507766 + 0.861495i \(0.669529\pi\)
\(608\) 8.53375 + 8.88458i 0.346089 + 0.360317i
\(609\) −28.3699 5.79176i −1.14961 0.234694i
\(610\) −12.5954 + 18.2475i −0.509971 + 0.738821i
\(611\) −14.7847 34.2403i −0.598125 1.38521i
\(612\) −1.44383 2.09175i −0.0583634 0.0845539i
\(613\) −17.4536 40.9651i −0.704944 1.65456i −0.754923 0.655813i \(-0.772326\pi\)
0.0499798 0.998750i \(-0.484084\pi\)
\(614\) 42.1539 31.6766i 1.70119 1.27836i
\(615\) 0.212672 5.27741i 0.00857577 0.212806i
\(616\) 7.98491 + 32.3961i 0.321721 + 1.30527i
\(617\) −3.48099 + 8.17018i −0.140139 + 0.328919i −0.975230 0.221193i \(-0.929005\pi\)
0.835091 + 0.550112i \(0.185415\pi\)
\(618\) 41.3801 8.44781i 1.66455 0.339821i
\(619\) 6.57746 + 4.54009i 0.264370 + 0.182482i 0.692875 0.721058i \(-0.256344\pi\)
−0.428504 + 0.903540i \(0.640959\pi\)
\(620\) −25.8858 + 2.08972i −1.03960 + 0.0839251i
\(621\) −2.44457 8.43962i −0.0980971 0.338670i
\(622\) 43.0798 + 57.3288i 1.72734 + 2.29867i
\(623\) −9.79462 5.14061i −0.392413 0.205954i
\(624\) −1.21503 + 10.4284i −0.0486403 + 0.417471i
\(625\) 0.885456 0.464723i 0.0354182 0.0185889i
\(626\) 29.0516 + 13.7851i 1.16113 + 0.550965i
\(627\) −14.9863 + 31.5829i −0.598494 + 1.26130i
\(628\) −9.16406 + 3.05941i −0.365686 + 0.122084i
\(629\) 2.05233 2.31660i 0.0818318 0.0923690i
\(630\) −1.71353 + 10.5438i −0.0682687 + 0.420074i
\(631\) 33.6424 + 1.35574i 1.33928 + 0.0539713i 0.699527 0.714606i \(-0.253394\pi\)
0.639757 + 0.768577i \(0.279035\pi\)
\(632\) −31.4289 + 11.9194i −1.25018 + 0.474129i
\(633\) 6.80239 23.4846i 0.270371 0.933428i
\(634\) 1.29237 6.33045i 0.0513266 0.251414i
\(635\) 1.07630 13.3323i 0.0427116 0.529078i
\(636\) 6.68799 17.6348i 0.265196 0.699265i
\(637\) −7.82699 9.49213i −0.310117 0.376092i
\(638\) 27.3730 + 72.1767i 1.08371 + 2.85750i
\(639\) 30.0063 8.69143i 1.18703 0.343828i
\(640\) −0.814574 20.2134i −0.0321989 0.799006i
\(641\) −6.03392 7.39021i −0.238325 0.291896i 0.641569 0.767066i \(-0.278284\pi\)
−0.879894 + 0.475170i \(0.842387\pi\)
\(642\) −9.62326 1.16848i −0.379800 0.0461160i
\(643\) 3.64802 + 45.1889i 0.143864 + 1.78208i 0.518672 + 0.854973i \(0.326427\pi\)
−0.374808 + 0.927103i \(0.622291\pi\)
\(644\) 40.4275 + 11.7100i 1.59307 + 0.461438i
\(645\) −1.58494 + 6.43035i −0.0624069 + 0.253195i
\(646\) −1.70080 1.27806i −0.0669169 0.0502848i
\(647\) −17.9707 + 22.0101i −0.706500 + 0.865305i −0.995764 0.0919443i \(-0.970692\pi\)
0.289265 + 0.957249i \(0.406589\pi\)
\(648\) −26.4760 + 25.4305i −1.04008 + 0.999006i
\(649\) −28.8184 7.10309i −1.13122 0.278821i
\(650\) −6.52421 + 5.37971i −0.255901 + 0.211010i
\(651\) 31.7197 7.81820i 1.24319 0.306419i
\(652\) −28.9999 + 45.8597i −1.13572 + 1.79600i
\(653\) −19.4982 33.7719i −0.763025 1.32160i −0.941284 0.337615i \(-0.890380\pi\)
0.178259 0.983984i \(-0.442953\pi\)
\(654\) −3.35199 + 5.80581i −0.131073 + 0.227025i
\(655\) 5.94816 + 11.3333i 0.232414 + 0.442827i
\(656\) 0.901132 + 2.69922i 0.0351833 + 0.105387i
\(657\) −0.603064 0.348179i −0.0235278 0.0135838i
\(658\) 30.4718 + 34.3955i 1.18791 + 1.34088i
\(659\) 21.0815 13.3312i 0.821221 0.519308i −0.0565443 0.998400i \(-0.518008\pi\)
0.877765 + 0.479092i \(0.159034\pi\)
\(660\) 37.4746 15.9664i 1.45870 0.621493i
\(661\) 22.1386 0.892154i 0.861091 0.0347008i 0.394209 0.919021i \(-0.371019\pi\)
0.466881 + 0.884320i \(0.345377\pi\)
\(662\) −5.41358 + 44.5848i −0.210405 + 1.73284i
\(663\) 0.114158 + 2.52846i 0.00443351 + 0.0981971i
\(664\) −1.10590 9.10791i −0.0429173 0.353455i
\(665\) 0.912782 + 5.61657i 0.0353962 + 0.217801i
\(666\) 48.8549 + 30.8940i 1.89309 + 1.19712i
\(667\) 41.2000 + 6.69565i 1.59527 + 0.259257i
\(668\) 2.97315 5.66487i 0.115035 0.219180i
\(669\) 17.6856 + 27.9676i 0.683765 + 1.08129i
\(670\) −10.5029 10.0882i −0.405763 0.389740i
\(671\) −46.9764 + 5.70396i −1.81350 + 0.220199i
\(672\) 3.61194 + 17.6925i 0.139334 + 0.682502i
\(673\) −33.0145 2.66521i −1.27262 0.102736i −0.574371 0.818595i \(-0.694753\pi\)
−0.698245 + 0.715859i \(0.746036\pi\)
\(674\) −17.4760 14.2687i −0.673148 0.549609i
\(675\) −1.38417 −0.0532768
\(676\) 28.4378 35.5267i 1.09376 1.36641i
\(677\) −6.66085 −0.255997 −0.127999 0.991774i \(-0.540855\pi\)
−0.127999 + 0.991774i \(0.540855\pi\)
\(678\) 61.9857 + 50.6098i 2.38055 + 1.94366i
\(679\) 24.1121 + 1.94653i 0.925339 + 0.0747011i
\(680\) 0.212554 + 1.04116i 0.00815108 + 0.0399266i
\(681\) −26.1487 + 3.17503i −1.00202 + 0.121667i
\(682\) −62.8125 60.3322i −2.40521 2.31024i
\(683\) 8.48742 + 13.4218i 0.324762 + 0.513570i 0.967619 0.252416i \(-0.0812252\pi\)
−0.642857 + 0.765987i \(0.722251\pi\)
\(684\) 11.7513 22.3903i 0.449324 0.856116i
\(685\) 15.5549 + 2.52792i 0.594322 + 0.0965867i
\(686\) 39.0942 + 24.7217i 1.49262 + 0.943877i
\(687\) 0.501149 + 3.08370i 0.0191200 + 0.117650i
\(688\) −0.430102 3.54221i −0.0163975 0.135046i
\(689\) −6.65594 + 5.05222i −0.253571 + 0.192474i
\(690\) 4.17186 34.3584i 0.158820 1.30800i
\(691\) −4.87147 + 0.196314i −0.185320 + 0.00746812i −0.132752 0.991149i \(-0.542381\pi\)
−0.0525674 + 0.998617i \(0.516740\pi\)
\(692\) 29.1906 12.4370i 1.10966 0.472782i
\(693\) −19.2689 + 12.1849i −0.731964 + 0.462866i
\(694\) −34.8297 39.3146i −1.32212 1.49236i
\(695\) 14.2608 + 8.23347i 0.540943 + 0.312313i
\(696\) −17.0356 51.0277i −0.645731 1.93420i
\(697\) 0.318808 + 0.607438i 0.0120757 + 0.0230084i
\(698\) −35.7946 + 61.9981i −1.35485 + 2.34666i
\(699\) 32.5454 + 56.3703i 1.23098 + 2.13212i
\(700\) 3.54376 5.60400i 0.133941 0.211811i
\(701\) −2.37447 + 0.585255i −0.0896826 + 0.0221048i −0.283902 0.958853i \(-0.591629\pi\)
0.194219 + 0.980958i \(0.437783\pi\)
\(702\) 11.4568 2.39675i 0.432408 0.0904597i
\(703\) 29.8966 + 7.36885i 1.12757 + 0.277922i
\(704\) 43.7621 42.0341i 1.64935 1.58422i
\(705\) 15.2088 18.6274i 0.572795 0.701547i
\(706\) −20.3475 15.2901i −0.765788 0.575452i
\(707\) 6.49769 26.3622i 0.244371 0.991452i
\(708\) 46.3499 + 13.4254i 1.74194 + 0.504558i
\(709\) −1.17258 14.5250i −0.0440371 0.545498i −0.980733 0.195354i \(-0.937415\pi\)
0.936696 0.350144i \(-0.113867\pi\)
\(710\) −30.2474 3.67269i −1.13516 0.137834i
\(711\) −14.5257 17.7907i −0.544756 0.667205i
\(712\) −0.827534 20.5350i −0.0310131 0.769583i
\(713\) −45.2349 + 13.1025i −1.69406 + 0.490691i
\(714\) −1.10582 2.91581i −0.0413843 0.109121i
\(715\) −17.8276 2.80875i −0.666716 0.105041i
\(716\) −32.1560 + 84.7885i −1.20173 + 3.16869i
\(717\) −2.67477 + 33.1330i −0.0998911 + 1.23737i
\(718\) −1.74413 + 8.54332i −0.0650904 + 0.318834i
\(719\) −1.11309 + 3.84283i −0.0415112 + 0.143313i −0.978597 0.205786i \(-0.934025\pi\)
0.937086 + 0.349099i \(0.113512\pi\)
\(720\) −2.81615 + 1.06802i −0.104952 + 0.0398029i
\(721\) 14.6601 + 0.590780i 0.545969 + 0.0220018i
\(722\) −3.75281 + 23.0920i −0.139665 + 0.859395i
\(723\) 9.52307 10.7493i 0.354167 0.399772i
\(724\) −1.46162 + 0.487962i −0.0543208 + 0.0181350i
\(725\) 2.81888 5.94066i 0.104691 0.220631i
\(726\) 69.2333 + 32.8516i 2.56949 + 1.21924i
\(727\) 44.7206 23.4712i 1.65859 0.870497i 0.666428 0.745569i \(-0.267822\pi\)
0.992166 0.124928i \(-0.0398699\pi\)
\(728\) −8.41364 + 22.5131i −0.311830 + 0.834391i
\(729\) −13.6629 7.17086i −0.506034 0.265587i
\(730\) 0.408018 + 0.542974i 0.0151014 + 0.0200964i
\(731\) −0.239325 0.826245i −0.00885175 0.0305598i
\(732\) 76.6856 6.19070i 2.83438 0.228815i
\(733\) 3.75846 + 2.59428i 0.138822 + 0.0958218i 0.635452 0.772141i \(-0.280814\pi\)
−0.496630 + 0.867962i \(0.665429\pi\)
\(734\) −80.6824 + 16.4714i −2.97804 + 0.607972i
\(735\) 3.10934 7.29789i 0.114690 0.269187i
\(736\) −6.22958 25.2744i −0.229625 0.931627i
\(737\) 1.25151 31.0559i 0.0461000 1.14396i
\(738\) −10.2429 + 7.69704i −0.377046 + 0.283332i
\(739\) 0.212642 + 0.499088i 0.00782215 + 0.0183593i 0.923845 0.382767i \(-0.125029\pi\)
−0.916023 + 0.401127i \(0.868619\pi\)
\(740\) −20.3816 29.5279i −0.749243 1.08547i
\(741\) −21.7462 + 12.6959i −0.798865 + 0.466397i
\(742\) 5.84858 8.47313i 0.214708 0.311058i
\(743\) −12.5703 2.56624i −0.461159 0.0941463i −0.0361718 0.999346i \(-0.511516\pi\)
−0.424987 + 0.905199i \(0.639721\pi\)
\(744\) 42.0459 + 43.7744i 1.54148 + 1.60485i
\(745\) 7.06382 + 14.8867i 0.258798 + 0.545406i
\(746\) 72.7402i 2.66321i
\(747\) 5.66375 2.68748i 0.207226 0.0983299i
\(748\) −3.17841 + 4.22969i −0.116214 + 0.154653i
\(749\) −3.14883 1.19419i −0.115056 0.0436349i
\(750\) −5.01604 2.13714i −0.183160 0.0780372i
\(751\) −34.7793 + 5.65219i −1.26911 + 0.206251i −0.757427 0.652920i \(-0.773544\pi\)
−0.511688 + 0.859171i \(0.670980\pi\)
\(752\) −4.10286 + 12.2896i −0.149616 + 0.448154i
\(753\) −5.15029 + 4.56276i −0.187687 + 0.166276i
\(754\) −13.0453 + 54.0517i −0.475081 + 1.96845i
\(755\) 11.1909 + 9.91431i 0.407280 + 0.360819i
\(756\) −7.94812 + 4.58885i −0.289071 + 0.166895i
\(757\) −6.49681 2.16895i −0.236131 0.0788320i 0.196140 0.980576i \(-0.437159\pi\)
−0.432271 + 0.901744i \(0.642287\pi\)
\(758\) −5.78890 + 6.02688i −0.210262 + 0.218906i
\(759\) 60.7921 41.9617i 2.20661 1.52311i
\(760\) −8.18916 + 6.68624i −0.297052 + 0.242536i
\(761\) −25.5876 + 20.8916i −0.927549 + 0.757320i −0.970335 0.241764i \(-0.922274\pi\)
0.0427865 + 0.999084i \(0.486376\pi\)
\(762\) −60.0194 + 41.4284i −2.17427 + 1.50079i
\(763\) −1.61333 + 1.67965i −0.0584064 + 0.0608075i
\(764\) 39.2081 + 13.0896i 1.41850 + 0.473565i
\(765\) −0.628807 + 0.363042i −0.0227346 + 0.0131258i
\(766\) −21.0500 18.6487i −0.760569 0.673805i
\(767\) −14.2547 15.9341i −0.514707 0.575347i
\(768\) −40.3712 + 35.7658i −1.45677 + 1.29059i
\(769\) −0.753329 + 2.25650i −0.0271657 + 0.0813713i −0.961246 0.275691i \(-0.911093\pi\)
0.934081 + 0.357062i \(0.116222\pi\)
\(770\) 21.9482 3.56694i 0.790960 0.128543i
\(771\) −28.2288 12.0272i −1.01664 0.433148i
\(772\) −67.9052 25.7530i −2.44396 0.926873i
\(773\) 15.5125 20.6434i 0.557945 0.742490i −0.429043 0.903284i \(-0.641149\pi\)
0.986988 + 0.160794i \(0.0514054\pi\)
\(774\) 14.5147 6.88731i 0.521720 0.247559i
\(775\) 7.41892i 0.266496i
\(776\) 19.2672 + 40.6048i 0.691653 + 1.45763i
\(777\) 31.2654 + 32.5508i 1.12164 + 1.16775i
\(778\) −42.5481 8.68626i −1.52542 0.311418i
\(779\) −3.87711 + 5.61696i −0.138912 + 0.201249i
\(780\) 28.7768 + 5.72983i 1.03037 + 0.205161i
\(781\) −36.9410 53.5182i −1.32185 1.91503i
\(782\) 1.76207 + 4.13572i 0.0630113 + 0.147893i
\(783\) −7.27625 + 5.46775i −0.260032 + 0.195401i
\(784\) −0.172095 + 4.27049i −0.00614625 + 0.152518i
\(785\) 0.660502 + 2.67976i 0.0235743 + 0.0956448i
\(786\) 27.3540 64.2021i 0.975684 2.29001i
\(787\) 37.9774 7.75315i 1.35375 0.276370i 0.532254 0.846585i \(-0.321345\pi\)
0.821495 + 0.570215i \(0.193140\pi\)
\(788\) −0.153431 0.105906i −0.00546575 0.00377274i
\(789\) −0.598775 + 0.0483381i −0.0213169 + 0.00172088i
\(790\) 6.23242 + 21.5168i 0.221739 + 0.765533i
\(791\) 16.7005 + 22.2243i 0.593801 + 0.790206i
\(792\) −37.5056 19.6845i −1.33270 0.699457i
\(793\) −30.2585 15.6945i −1.07451 0.557328i
\(794\) 76.3122 40.0518i 2.70822 1.42138i
\(795\) −4.86770 2.30975i −0.172640 0.0819186i
\(796\) −4.81099 + 10.1389i −0.170521 + 0.359365i
\(797\) 36.8054 12.2875i 1.30372 0.435244i 0.421816 0.906681i \(-0.361393\pi\)
0.881900 + 0.471437i \(0.156265\pi\)
\(798\) 20.5735 23.2227i 0.728296 0.822076i
\(799\) −0.501035 + 3.08299i −0.0177254 + 0.109068i
\(800\) −4.09740 0.165119i −0.144865 0.00583785i
\(801\) 13.1302 4.97961i 0.463931 0.175946i
\(802\) 5.33574 18.4211i 0.188412 0.650472i
\(803\) −0.289949 + 1.42027i −0.0102321 + 0.0501201i
\(804\) −4.06611 + 50.3678i −0.143401 + 1.77634i
\(805\) 4.26368 11.2424i 0.150275 0.396243i
\(806\) −12.8462 61.4063i −0.452488 2.16294i
\(807\) 7.90420 + 20.8417i 0.278241 + 0.733662i
\(808\) 48.4530 14.0346i 1.70457 0.493735i
\(809\) −1.05459 26.1693i −0.0370774 0.920065i −0.905527 0.424288i \(-0.860524\pi\)
0.868450 0.495777i \(-0.165117\pi\)
\(810\) 15.4732 + 18.9512i 0.543672 + 0.665877i
\(811\) 4.57530 + 0.555542i 0.160660 + 0.0195077i 0.200472 0.979700i \(-0.435753\pi\)
−0.0398112 + 0.999207i \(0.512676\pi\)
\(812\) −3.50824 43.4574i −0.123115 1.52506i
\(813\) −16.0412 4.64639i −0.562589 0.162956i
\(814\) 28.7957 116.829i 1.00929 4.09485i
\(815\) 12.3918 + 9.31180i 0.434064 + 0.326178i
\(816\) 0.556086 0.681082i 0.0194669 0.0238426i
\(817\) 6.17214 5.92842i 0.215936 0.207409i
\(818\) −50.6565 12.4857i −1.77116 0.436552i
\(819\) −16.4117 0.581796i −0.573473 0.0203296i
\(820\) 7.72174 1.90324i 0.269655 0.0664640i
\(821\) −13.6653 + 21.6100i −0.476923 + 0.754194i −0.994864 0.101223i \(-0.967725\pi\)
0.517940 + 0.855417i \(0.326699\pi\)
\(822\) −42.9616 74.4117i −1.49846 2.59541i
\(823\) 9.45833 16.3823i 0.329697 0.571051i −0.652755 0.757569i \(-0.726387\pi\)
0.982452 + 0.186518i \(0.0597202\pi\)
\(824\) 12.6680 + 24.1369i 0.441312 + 0.840850i
\(825\) −3.68496 11.0378i −0.128294 0.384287i
\(826\) 22.8126 + 13.1709i 0.793752 + 0.458273i
\(827\) −19.1278 21.5908i −0.665137 0.750785i 0.315003 0.949091i \(-0.397995\pi\)
−0.980140 + 0.198306i \(0.936456\pi\)
\(828\) −45.1602 + 28.5576i −1.56943 + 0.992445i
\(829\) −11.2533 + 4.79458i −0.390843 + 0.166523i −0.578443 0.815723i \(-0.696339\pi\)
0.187600 + 0.982246i \(0.439929\pi\)
\(830\) −6.10950 + 0.246205i −0.212064 + 0.00854588i
\(831\) 3.34299 27.5320i 0.115967 0.955074i
\(832\) 43.1081 7.22015i 1.49451 0.250314i
\(833\) 0.124194 + 1.02283i 0.00430307 + 0.0354389i
\(834\) −14.4023 88.6207i −0.498710 3.06869i
\(835\) −1.54471 0.976813i −0.0534568 0.0338040i
\(836\) −51.9560 8.44368i −1.79694 0.292031i
\(837\) 4.77227 9.09281i 0.164954 0.314293i
\(838\) 3.41009 + 5.39262i 0.117800 + 0.186285i
\(839\) −2.35411 2.26116i −0.0812731 0.0780638i 0.650987 0.759089i \(-0.274355\pi\)
−0.732260 + 0.681025i \(0.761535\pi\)
\(840\) −15.3835 + 1.86790i −0.530783 + 0.0644487i
\(841\) −2.84787 13.9498i −0.0982024 0.481027i
\(842\) 64.9716 + 5.24505i 2.23907 + 0.180756i
\(843\) −15.4631 12.6252i −0.532577 0.434835i
\(844\) 36.8151 1.26723
\(845\) −9.46239 8.91421i −0.325516 0.306658i
\(846\) −58.3356 −2.00562
\(847\) 20.6215 + 16.8369i 0.708564 + 0.578524i
\(848\) 2.89348 + 0.233586i 0.0993626 + 0.00802138i
\(849\) 8.09311 + 39.6427i 0.277755 + 1.36053i
\(850\) 0.703019 0.0853620i 0.0241134 0.00292789i
\(851\) −46.9239 45.0710i −1.60853 1.54501i
\(852\) 56.5063 + 89.3576i 1.93587 + 3.06134i
\(853\) 19.6550 37.4495i 0.672975 1.28225i −0.274244 0.961660i \(-0.588428\pi\)
0.947219 0.320586i \(-0.103880\pi\)
\(854\) 41.4538 + 6.73690i 1.41852 + 0.230532i
\(855\) −6.10544 3.86084i −0.208801 0.132038i
\(856\) −1.00367 6.17584i −0.0343048 0.211086i
\(857\) −5.40530 44.5166i −0.184641 1.52066i −0.730576 0.682831i \(-0.760748\pi\)
0.545935 0.837828i \(-0.316175\pi\)
\(858\) 49.6127 + 84.9789i 1.69375 + 2.90113i
\(859\) −0.104073 + 0.857122i −0.00355094 + 0.0292446i −0.994377 0.105901i \(-0.966227\pi\)
0.990826 + 0.135146i \(0.0431503\pi\)
\(860\) −9.96410 + 0.401540i −0.339773 + 0.0136924i
\(861\) −9.20373 + 3.92134i −0.313662 + 0.133639i
\(862\) −76.9121 + 48.6363i −2.61964 + 1.65656i
\(863\) 36.7415 + 41.4726i 1.25070 + 1.41174i 0.874372 + 0.485256i \(0.161273\pi\)
0.376324 + 0.926488i \(0.377188\pi\)
\(864\) 4.91565 + 2.83805i 0.167234 + 0.0965525i
\(865\) −2.87037 8.59781i −0.0975955 0.292334i
\(866\) −2.84295 5.41679i −0.0966075 0.184070i
\(867\) −19.6546 + 34.0428i −0.667507 + 1.15616i
\(868\) 24.5955 + 42.6006i 0.834824 + 1.44596i
\(869\) −25.5527 + 40.4084i −0.866816 + 1.37076i
\(870\) −34.8102 + 8.57995i −1.18018 + 0.290888i
\(871\) 13.3628 17.9631i 0.452782 0.608657i
\(872\) −4.20129 1.03552i −0.142274 0.0350673i
\(873\) −22.1480 + 21.2734i −0.749595 + 0.719995i
\(874\) −28.2860 + 34.6440i −0.956787 + 1.17185i
\(875\) −1.51426 1.13789i −0.0511913 0.0384678i
\(876\) 0.563993 2.28821i 0.0190556 0.0773115i
\(877\) 1.17671 + 0.340839i 0.0397348 + 0.0115093i 0.298025 0.954558i \(-0.403672\pi\)
−0.258291 + 0.966067i \(0.583159\pi\)
\(878\) 2.42591 + 30.0502i 0.0818704 + 1.01415i
\(879\) −52.6076 6.38772i −1.77441 0.215453i
\(880\) 3.96518 + 4.85646i 0.133666 + 0.163711i
\(881\) −0.543521 13.4873i −0.0183117 0.454399i −0.982171 0.187989i \(-0.939803\pi\)
0.963860 0.266411i \(-0.0858378\pi\)
\(882\) −18.4836 + 5.35385i −0.622376 + 0.180273i
\(883\) 8.46200 + 22.3124i 0.284769 + 0.750874i 0.998715 + 0.0506734i \(0.0161368\pi\)
−0.713946 + 0.700200i \(0.753094\pi\)
\(884\) −3.60905 + 1.22433i −0.121386 + 0.0411787i
\(885\) 4.88829 12.8894i 0.164318 0.433271i
\(886\) −0.116831 + 1.44721i −0.00392501 + 0.0486200i
\(887\) 9.99448 48.9562i 0.335582 1.64379i −0.365575 0.930782i \(-0.619128\pi\)
0.701157 0.713007i \(-0.252667\pi\)
\(888\) −23.3301 + 80.5447i −0.782905 + 2.70290i
\(889\) −23.6891 + 8.98410i −0.794508 + 0.301317i
\(890\) −13.6854 0.551502i −0.458735 0.0184864i
\(891\) −8.37599 + 51.5395i −0.280606 + 1.72664i
\(892\) −33.0403 + 37.2947i −1.10627 + 1.24872i
\(893\) −29.4756 + 9.84040i −0.986363 + 0.329296i
\(894\) 38.5144 81.1673i 1.28811 2.71464i
\(895\) 23.4040 + 11.1054i 0.782311 + 0.371211i
\(896\) −33.9291 + 17.8074i −1.13349 + 0.594902i
\(897\) 53.2079 0.257618i 1.77656 0.00860160i
\(898\) −3.40350 1.78629i −0.113576 0.0596094i
\(899\) 29.3062 + 38.9995i 0.977416 + 1.30070i
\(900\) 2.34185 + 8.08499i 0.0780616 + 0.269500i
\(901\) 0.697544 0.0563116i 0.0232386 0.00187601i
\(902\) 21.9498 + 15.1508i 0.730848 + 0.504468i
\(903\) 12.2910 2.50923i 0.409019 0.0835018i
\(904\) −20.2450 + 47.5167i −0.673338 + 1.58038i
\(905\) 0.105347 + 0.427409i 0.00350185 + 0.0142076i
\(906\) 3.28239 81.4516i 0.109050 2.70605i
\(907\) 14.4426 10.8529i 0.479558 0.360364i −0.333306 0.942819i \(-0.608164\pi\)
0.812863 + 0.582455i \(0.197908\pi\)
\(908\) −15.5463 36.4885i −0.515922 1.21091i
\(909\) 19.5802 + 28.3667i 0.649433 + 0.940866i
\(910\) 14.5038 + 6.79630i 0.480796 + 0.225295i
\(911\) 14.3212 20.7478i 0.474483 0.687407i −0.510536 0.859857i \(-0.670553\pi\)
0.985018 + 0.172450i \(0.0551682\pi\)
\(912\) 8.57092 + 1.74977i 0.283812 + 0.0579406i
\(913\) −9.03990 9.41153i −0.299177 0.311476i
\(914\) −3.87263 8.16139i −0.128095 0.269955i
\(915\) 21.9782i 0.726578i
\(916\) −4.24997 + 2.01664i −0.140423 + 0.0666315i
\(917\) 14.5643 19.3815i 0.480955 0.640035i
\(918\) −0.916547 0.347600i −0.0302506 0.0114725i
\(919\) 27.1669 + 11.5747i 0.896153 + 0.381815i 0.790410 0.612578i \(-0.209868\pi\)
0.105743 + 0.994393i \(0.466278\pi\)
\(920\) 22.0499 3.58346i 0.726964 0.118143i
\(921\) −16.5514 + 49.5775i −0.545387 + 1.63363i
\(922\) 18.1807 16.1067i 0.598749 0.530446i
\(923\) −0.226793 46.8415i −0.00746499 1.54181i
\(924\) −57.7524 51.1642i −1.89991 1.68318i
\(925\) −8.87647 + 5.12483i −0.291856 + 0.168503i
\(926\) −32.1246 10.7248i −1.05568 0.352438i
\(927\) −12.9026 + 13.4331i −0.423778 + 0.441200i
\(928\) −22.1913 + 15.3175i −0.728464 + 0.502822i
\(929\) −21.9846 + 17.9499i −0.721293 + 0.588917i −0.920362 0.391068i \(-0.872106\pi\)
0.199069 + 0.979985i \(0.436208\pi\)
\(930\) 31.3332 25.5827i 1.02746 0.838891i
\(931\) −8.43622 + 5.82310i −0.276486 + 0.190844i
\(932\) −67.8938 + 70.6849i −2.22393 + 2.31536i
\(933\) −67.4248 22.5097i −2.20739 0.736935i
\(934\) 28.0095 16.1713i 0.916500 0.529141i
\(935\) 1.13133 + 1.00227i 0.0369984 + 0.0327777i
\(936\) −14.3097 26.9471i −0.467729 0.880793i
\(937\) −35.4371 + 31.3945i −1.15768 + 1.02561i −0.158411 + 0.987373i \(0.550637\pi\)
−0.999269 + 0.0382416i \(0.987824\pi\)
\(938\) −8.73513 + 26.1649i −0.285212 + 0.854314i
\(939\) −31.4619 + 5.11306i −1.02672 + 0.166858i
\(940\) 33.3118 + 14.1928i 1.08651 + 0.462920i
\(941\) 23.2813 + 8.82943i 0.758949 + 0.287831i 0.703562 0.710634i \(-0.251592\pi\)
0.0553865 + 0.998465i \(0.482361\pi\)
\(942\) 9.04012 12.0302i 0.294543 0.391966i
\(943\) 13.0294 6.18250i 0.424294 0.201330i
\(944\) 7.42717i 0.241734i
\(945\) 1.12395 + 2.36868i 0.0365623 + 0.0770533i
\(946\) −23.1669 24.1193i −0.753220 0.784185i
\(947\) −5.67520 1.15860i −0.184419 0.0376495i 0.106928 0.994267i \(-0.465898\pi\)
−0.291348 + 0.956617i \(0.594104\pi\)
\(948\) 44.1552 63.9698i 1.43409 2.07764i
\(949\) −0.749530 + 0.726943i −0.0243308 + 0.0235976i
\(950\) 4.00238 + 5.79845i 0.129854 + 0.188127i
\(951\) 2.51033 + 5.89196i 0.0814030 + 0.191060i
\(952\) 1.60910 1.20916i 0.0521514 0.0391892i
\(953\) 0.232781 5.77640i 0.00754051 0.187116i −0.991029 0.133647i \(-0.957331\pi\)
0.998570 0.0534689i \(-0.0170278\pi\)
\(954\) 3.12791 + 12.6904i 0.101270 + 0.410867i
\(955\) 4.62849 10.8635i 0.149775 0.351534i
\(956\) −49.0404 + 10.0117i −1.58608 + 0.323800i
\(957\) −62.9723 43.4667i −2.03561 1.40508i
\(958\) −36.2613 + 2.92731i −1.17155 + 0.0945773i
\(959\) −8.30472 28.6712i −0.268173 0.925842i
\(960\) 16.9303 + 22.5302i 0.546424 + 0.727158i
\(961\) −21.2867 11.1721i −0.686669 0.360392i
\(962\) 64.5965 57.7881i 2.08267 1.86316i
\(963\) 3.78553 1.98680i 0.121987 0.0640238i
\(964\) 19.5361 + 9.26998i 0.629214 + 0.298566i
\(965\) −8.89403 + 18.7438i −0.286309 + 0.603383i
\(966\) −62.1838 + 20.7600i −2.00073 + 0.667943i
\(967\) 1.77514 2.00372i 0.0570847 0.0644353i −0.719275 0.694726i \(-0.755526\pi\)
0.776359 + 0.630290i \(0.217064\pi\)
\(968\) −7.93419 + 48.8210i −0.255014 + 1.56917i
\(969\) 2.10714 + 0.0849147i 0.0676910 + 0.00272785i
\(970\) 28.0062 10.6213i 0.899225 0.341031i
\(971\) −13.8027 + 47.6524i −0.442949 + 1.52924i 0.359862 + 0.933005i \(0.382824\pi\)
−0.802811 + 0.596233i \(0.796663\pi\)
\(972\) 14.0731 68.9345i 0.451394 2.21107i
\(973\) 2.50981 31.0896i 0.0804609 0.996687i
\(974\) −21.7987 + 57.4785i −0.698475 + 1.84173i
\(975\) 2.29304 8.06237i 0.0734361 0.258202i
\(976\) 4.19903 + 11.0719i 0.134408 + 0.354404i
\(977\) −33.2061 + 9.61826i −1.06236 + 0.307715i −0.762982 0.646420i \(-0.776265\pi\)
−0.299375 + 0.954136i \(0.596778\pi\)
\(978\) −3.40304 84.4454i −0.108817 2.70027i
\(979\) −18.4875 22.6430i −0.590862 0.723674i
\(980\) 11.8574 + 1.43975i 0.378772 + 0.0459912i
\(981\) −0.237907 2.94701i −0.00759579 0.0940908i
\(982\) −10.3284 2.99166i −0.329593 0.0954678i
\(983\) 8.32612 33.7804i 0.265562 1.07743i −0.675003 0.737815i \(-0.735858\pi\)
0.940565 0.339613i \(-0.110296\pi\)
\(984\) −14.8594 11.1661i −0.473699 0.355962i
\(985\) −0.0336832 + 0.0412545i −0.00107324 + 0.00131448i
\(986\) 3.35840 3.22579i 0.106953 0.102730i
\(987\) −44.2259 10.9007i −1.40773 0.346974i
\(988\) −27.4719 26.1326i −0.873999 0.831389i
\(989\) −17.5582 + 4.32771i −0.558318 + 0.137613i
\(990\) −15.0873 + 23.8586i −0.479505 + 0.758276i
\(991\) −18.9120 32.7565i −0.600759 1.04055i −0.992706 0.120558i \(-0.961532\pi\)
0.391947 0.919988i \(-0.371802\pi\)
\(992\) 15.2115 26.3470i 0.482965 0.836520i
\(993\) −20.6890 39.4196i −0.656546 1.25094i
\(994\) 18.2761 + 54.7435i 0.579681 + 1.73636i
\(995\) 2.77644 + 1.60298i 0.0880189 + 0.0508178i
\(996\) 14.0690 + 15.8806i 0.445794 + 0.503197i
\(997\) −39.5416 + 25.0046i −1.25230 + 0.791904i −0.985141 0.171749i \(-0.945058\pi\)
−0.267156 + 0.963653i \(0.586084\pi\)
\(998\) 74.6302 31.7970i 2.36238 1.00652i
\(999\) 14.1758 0.571265i 0.448502 0.0180740i
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 845.2.bg.a.621.8 yes 1440
169.43 even 78 inner 845.2.bg.a.381.8 1440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.bg.a.381.8 1440 169.43 even 78 inner
845.2.bg.a.621.8 yes 1440 1.1 even 1 trivial