Properties

Label 143.4.q.a.3.18
Level $143$
Weight $4$
Character 143.3
Analytic conductor $8.437$
Analytic rank $0$
Dimension $320$
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] = [143,4,Mod(3,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([24, 10]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.q (of order \(15\), degree \(8\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(40\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 3.18
Character \(\chi\) \(=\) 143.3
Dual form 143.4.q.a.48.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.868356 - 0.386617i) q^{2} +(2.30554 - 2.56056i) q^{3} +(-4.74848 - 5.27372i) q^{4} +(13.8209 + 10.0415i) q^{5} +(-2.99199 + 1.33212i) q^{6} +(9.48972 + 10.5394i) q^{7} +(4.43431 + 13.6474i) q^{8} +(1.58131 + 15.0451i) q^{9} +O(q^{10})\) \(q+(-0.868356 - 0.386617i) q^{2} +(2.30554 - 2.56056i) q^{3} +(-4.74848 - 5.27372i) q^{4} +(13.8209 + 10.0415i) q^{5} +(-2.99199 + 1.33212i) q^{6} +(9.48972 + 10.5394i) q^{7} +(4.43431 + 13.6474i) q^{8} +(1.58131 + 15.0451i) q^{9} +(-8.11928 - 14.0630i) q^{10} +(-25.2403 + 26.3425i) q^{11} -24.4515 q^{12} +(29.5165 - 36.4112i) q^{13} +(-4.16575 - 12.8208i) q^{14} +(57.5766 - 12.2383i) q^{15} +(-4.50852 + 42.8957i) q^{16} +(51.8537 - 23.0867i) q^{17} +(4.44357 - 13.6759i) q^{18} +(88.6267 + 18.8382i) q^{19} +(-12.6724 - 120.569i) q^{20} +48.8657 q^{21} +(32.1020 - 13.1164i) q^{22} +(-39.3337 - 68.1280i) q^{23} +(45.1685 + 20.1103i) q^{24} +(51.5595 + 158.684i) q^{25} +(-39.7080 + 20.2063i) q^{26} +(117.433 + 85.3201i) q^{27} +(10.5201 - 100.092i) q^{28} +(-226.658 + 48.1776i) q^{29} +(-54.7285 - 11.6329i) q^{30} +(157.454 - 114.397i) q^{31} +(77.8981 - 134.923i) q^{32} +(9.25921 + 125.363i) q^{33} -53.9532 q^{34} +(25.3254 + 240.955i) q^{35} +(71.8350 - 79.7808i) q^{36} +(312.174 - 66.3546i) q^{37} +(-69.6763 - 50.6228i) q^{38} +(-25.1817 - 159.526i) q^{39} +(-75.7540 + 233.147i) q^{40} +(-222.722 + 247.358i) q^{41} +(-42.4329 - 18.8923i) q^{42} +(-109.166 + 189.080i) q^{43} +(258.776 + 8.02319i) q^{44} +(-129.221 + 223.817i) q^{45} +(7.81623 + 74.3664i) q^{46} +(-187.739 - 577.800i) q^{47} +(99.4425 + 110.442i) q^{48} +(14.8291 - 141.089i) q^{49} +(16.5779 - 157.728i) q^{50} +(60.4357 - 186.002i) q^{51} +(-332.181 + 17.2362i) q^{52} +(147.007 - 106.807i) q^{53} +(-68.9875 - 119.490i) q^{54} +(-613.363 + 110.628i) q^{55} +(-101.755 + 176.245i) q^{56} +(252.569 - 183.502i) q^{57} +(215.446 + 45.7945i) q^{58} +(365.073 + 405.454i) q^{59} +(-337.942 - 245.529i) q^{60} +(-421.985 + 187.880i) q^{61} +(-180.954 + 38.4630i) q^{62} +(-143.561 + 159.440i) q^{63} +(159.349 - 115.774i) q^{64} +(773.569 - 206.847i) q^{65} +(40.4272 - 112.440i) q^{66} +(-268.915 - 465.774i) q^{67} +(-367.979 - 163.835i) q^{68} +(-265.131 - 56.3554i) q^{69} +(71.1660 - 219.026i) q^{70} +(-648.639 + 288.793i) q^{71} +(-198.315 + 88.2955i) q^{72} +(-191.613 + 589.724i) q^{73} +(-296.732 - 63.0723i) q^{74} +(525.192 + 233.831i) q^{75} +(-321.494 - 556.844i) q^{76} +(-517.158 - 16.0342i) q^{77} +(-39.8089 + 148.261i) q^{78} +(-223.524 + 162.400i) q^{79} +(-493.049 + 547.586i) q^{80} +(89.6835 - 19.0628i) q^{81} +(289.035 - 128.687i) q^{82} +(-1108.99 - 805.728i) q^{83} +(-232.038 - 257.704i) q^{84} +(948.492 + 201.608i) q^{85} +(167.896 - 121.984i) q^{86} +(-399.207 + 691.447i) q^{87} +(-471.430 - 227.653i) q^{88} +(779.964 + 1350.94i) q^{89} +(198.741 - 144.394i) q^{90} +(663.856 - 34.4461i) q^{91} +(-172.512 + 530.939i) q^{92} +(70.0959 - 666.918i) q^{93} +(-60.3634 + 574.319i) q^{94} +(1035.74 + 1150.31i) q^{95} +(-165.883 - 510.534i) q^{96} +(-37.7502 - 359.169i) q^{97} +(-67.4243 + 116.782i) q^{98} +(-436.240 - 338.088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9} - 80 q^{10} + 30 q^{11} - 220 q^{12} - 114 q^{13} + 4 q^{14} - 33 q^{15} + 637 q^{16} + 143 q^{17} + 72 q^{18} + 17 q^{19} - 377 q^{20} - 524 q^{21} + 283 q^{22} + 196 q^{23} - 1137 q^{24} - 1324 q^{25} + 632 q^{26} + 192 q^{27} - 279 q^{28} + 943 q^{29} + 1617 q^{30} + 260 q^{31} - 52 q^{32} - 1244 q^{33} - 3508 q^{34} + 1253 q^{35} + 282 q^{36} + 333 q^{37} - 694 q^{38} - 1106 q^{39} - 296 q^{40} - 1751 q^{41} - 895 q^{42} - 2200 q^{43} - 252 q^{44} - 282 q^{45} + 485 q^{46} + 2116 q^{47} - 825 q^{48} + 1607 q^{49} + 348 q^{50} + 1768 q^{51} - 2431 q^{52} + 428 q^{53} + 8326 q^{54} - 1379 q^{55} + 7630 q^{56} - 888 q^{57} - 331 q^{58} - 1097 q^{59} - 1820 q^{60} + 885 q^{61} - 437 q^{62} + 540 q^{63} + 1148 q^{64} + 2324 q^{65} - 1686 q^{66} - 5184 q^{67} + 3834 q^{68} - 4905 q^{69} + 4078 q^{70} + 843 q^{71} + 1155 q^{72} - 972 q^{73} + 5631 q^{74} - 3431 q^{75} - 3090 q^{76} + 602 q^{77} + 1252 q^{78} + 1140 q^{79} + 8631 q^{80} - 3809 q^{81} + 4015 q^{82} - 5292 q^{83} - 5060 q^{84} + 391 q^{85} + 3388 q^{86} - 7600 q^{87} - 7229 q^{88} + 6276 q^{89} + 7374 q^{90} - 4602 q^{91} + 8158 q^{92} - 2599 q^{93} + 11081 q^{94} + 2305 q^{95} - 30114 q^{96} + 1377 q^{97} + 5102 q^{98} - 5812 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.868356 0.386617i −0.307010 0.136690i 0.247448 0.968901i \(-0.420408\pi\)
−0.554459 + 0.832211i \(0.687075\pi\)
\(3\) 2.30554 2.56056i 0.443701 0.492780i −0.479260 0.877673i \(-0.659095\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(4\) −4.74848 5.27372i −0.593559 0.659214i
\(5\) 13.8209 + 10.0415i 1.23618 + 0.898139i 0.997338 0.0729190i \(-0.0232314\pi\)
0.238844 + 0.971058i \(0.423231\pi\)
\(6\) −2.99199 + 1.33212i −0.203579 + 0.0906392i
\(7\) 9.48972 + 10.5394i 0.512397 + 0.569074i 0.942713 0.333604i \(-0.108265\pi\)
−0.430317 + 0.902678i \(0.641598\pi\)
\(8\) 4.43431 + 13.6474i 0.195971 + 0.603136i
\(9\) 1.58131 + 15.0451i 0.0585669 + 0.557227i
\(10\) −8.11928 14.0630i −0.256754 0.444711i
\(11\) −25.2403 + 26.3425i −0.691839 + 0.722052i
\(12\) −24.4515 −0.588211
\(13\) 29.5165 36.4112i 0.629723 0.776820i
\(14\) −4.16575 12.8208i −0.0795244 0.244751i
\(15\) 57.5766 12.2383i 0.991081 0.210661i
\(16\) −4.50852 + 42.8957i −0.0704456 + 0.670245i
\(17\) 51.8537 23.0867i 0.739786 0.329374i −0.00201149 0.999998i \(-0.500640\pi\)
0.741797 + 0.670624i \(0.233974\pi\)
\(18\) 4.44357 13.6759i 0.0581866 0.179080i
\(19\) 88.6267 + 18.8382i 1.07012 + 0.227462i 0.709109 0.705099i \(-0.249097\pi\)
0.361014 + 0.932560i \(0.382431\pi\)
\(20\) −12.6724 120.569i −0.141681 1.34801i
\(21\) 48.8657 0.507780
\(22\) 32.1020 13.1164i 0.311099 0.127110i
\(23\) −39.3337 68.1280i −0.356593 0.617638i 0.630796 0.775949i \(-0.282728\pi\)
−0.987389 + 0.158311i \(0.949395\pi\)
\(24\) 45.1685 + 20.1103i 0.384166 + 0.171042i
\(25\) 51.5595 + 158.684i 0.412476 + 1.26947i
\(26\) −39.7080 + 20.2063i −0.299515 + 0.152415i
\(27\) 117.433 + 85.3201i 0.837037 + 0.608143i
\(28\) 10.5201 100.092i 0.0710041 0.675559i
\(29\) −226.658 + 48.1776i −1.45136 + 0.308495i −0.865087 0.501622i \(-0.832737\pi\)
−0.586269 + 0.810117i \(0.699404\pi\)
\(30\) −54.7285 11.6329i −0.333067 0.0707956i
\(31\) 157.454 114.397i 0.912245 0.662785i −0.0293367 0.999570i \(-0.509339\pi\)
0.941582 + 0.336785i \(0.109339\pi\)
\(32\) 77.8981 134.923i 0.430330 0.745354i
\(33\) 9.25921 + 125.363i 0.0488431 + 0.661300i
\(34\) −53.9532 −0.272144
\(35\) 25.3254 + 240.955i 0.122308 + 1.16368i
\(36\) 71.8350 79.7808i 0.332569 0.369356i
\(37\) 312.174 66.3546i 1.38706 0.294828i 0.546912 0.837190i \(-0.315803\pi\)
0.840145 + 0.542362i \(0.182470\pi\)
\(38\) −69.6763 50.6228i −0.297447 0.216108i
\(39\) −25.1817 159.526i −0.103392 0.654991i
\(40\) −75.7540 + 233.147i −0.299444 + 0.921594i
\(41\) −222.722 + 247.358i −0.848375 + 0.942215i −0.998924 0.0463871i \(-0.985229\pi\)
0.150549 + 0.988603i \(0.451896\pi\)
\(42\) −42.4329 18.8923i −0.155894 0.0694083i
\(43\) −109.166 + 189.080i −0.387154 + 0.670570i −0.992065 0.125723i \(-0.959875\pi\)
0.604912 + 0.796292i \(0.293208\pi\)
\(44\) 258.776 + 8.02319i 0.886635 + 0.0274896i
\(45\) −129.221 + 223.817i −0.428068 + 0.741436i
\(46\) 7.81623 + 74.3664i 0.0250530 + 0.238364i
\(47\) −187.739 577.800i −0.582649 1.79321i −0.608513 0.793544i \(-0.708234\pi\)
0.0258646 0.999665i \(-0.491766\pi\)
\(48\) 99.4425 + 110.442i 0.299027 + 0.332103i
\(49\) 14.8291 141.089i 0.0432334 0.411338i
\(50\) 16.5779 157.728i 0.0468893 0.446122i
\(51\) 60.4357 186.002i 0.165935 0.510696i
\(52\) −332.181 + 17.2362i −0.885869 + 0.0459659i
\(53\) 147.007 106.807i 0.380999 0.276812i −0.380758 0.924675i \(-0.624337\pi\)
0.761757 + 0.647862i \(0.224337\pi\)
\(54\) −68.9875 119.490i −0.173852 0.301121i
\(55\) −613.363 + 110.628i −1.50374 + 0.271220i
\(56\) −101.755 + 176.245i −0.242814 + 0.420567i
\(57\) 252.569 183.502i 0.586904 0.426411i
\(58\) 215.446 + 45.7945i 0.487749 + 0.103674i
\(59\) 365.073 + 405.454i 0.805567 + 0.894672i 0.996209 0.0869871i \(-0.0277239\pi\)
−0.190643 + 0.981659i \(0.561057\pi\)
\(60\) −337.942 245.529i −0.727136 0.528295i
\(61\) −421.985 + 187.880i −0.885732 + 0.394353i −0.798613 0.601845i \(-0.794433\pi\)
−0.0871188 + 0.996198i \(0.527766\pi\)
\(62\) −180.954 + 38.4630i −0.370664 + 0.0787872i
\(63\) −143.561 + 159.440i −0.287094 + 0.318850i
\(64\) 159.349 115.774i 0.311228 0.226121i
\(65\) 773.569 206.847i 1.47614 0.394712i
\(66\) 40.4272 112.440i 0.0753976 0.209702i
\(67\) −268.915 465.774i −0.490346 0.849304i 0.509592 0.860416i \(-0.329796\pi\)
−0.999938 + 0.0111118i \(0.996463\pi\)
\(68\) −367.979 163.835i −0.656235 0.292175i
\(69\) −265.131 56.3554i −0.462581 0.0983245i
\(70\) 71.1660 219.026i 0.121514 0.373981i
\(71\) −648.639 + 288.793i −1.08421 + 0.482724i −0.869490 0.493951i \(-0.835552\pi\)
−0.214725 + 0.976675i \(0.568886\pi\)
\(72\) −198.315 + 88.2955i −0.324606 + 0.144524i
\(73\) −191.613 + 589.724i −0.307214 + 0.945506i 0.671628 + 0.740888i \(0.265595\pi\)
−0.978842 + 0.204618i \(0.934405\pi\)
\(74\) −296.732 63.0723i −0.466141 0.0990812i
\(75\) 525.192 + 233.831i 0.808586 + 0.360006i
\(76\) −321.494 556.844i −0.485236 0.840453i
\(77\) −517.158 16.0342i −0.765397 0.0237307i
\(78\) −39.8089 + 148.261i −0.0577881 + 0.215222i
\(79\) −223.524 + 162.400i −0.318334 + 0.231283i −0.735464 0.677563i \(-0.763036\pi\)
0.417130 + 0.908847i \(0.363036\pi\)
\(80\) −493.049 + 547.586i −0.689057 + 0.765275i
\(81\) 89.6835 19.0628i 0.123023 0.0261493i
\(82\) 289.035 128.687i 0.389251 0.173306i
\(83\) −1108.99 805.728i −1.46659 1.06554i −0.981583 0.191036i \(-0.938815\pi\)
−0.485012 0.874508i \(-0.661185\pi\)
\(84\) −232.038 257.704i −0.301397 0.334736i
\(85\) 948.492 + 201.608i 1.21033 + 0.257264i
\(86\) 167.896 121.984i 0.210520 0.152952i
\(87\) −399.207 + 691.447i −0.491948 + 0.852079i
\(88\) −471.430 227.653i −0.571075 0.275772i
\(89\) 779.964 + 1350.94i 0.928945 + 1.60898i 0.785091 + 0.619380i \(0.212616\pi\)
0.143853 + 0.989599i \(0.454051\pi\)
\(90\) 198.741 144.394i 0.232768 0.169116i
\(91\) 663.856 34.4461i 0.764736 0.0396806i
\(92\) −172.512 + 530.939i −0.195496 + 0.601676i
\(93\) 70.0959 666.918i 0.0781571 0.743615i
\(94\) −60.3634 + 574.319i −0.0662341 + 0.630176i
\(95\) 1035.74 + 1150.31i 1.11858 + 1.24230i
\(96\) −165.883 510.534i −0.176358 0.542773i
\(97\) −37.7502 359.169i −0.0395149 0.375959i −0.996352 0.0853354i \(-0.972804\pi\)
0.956837 0.290624i \(-0.0938629\pi\)
\(98\) −67.4243 + 116.782i −0.0694988 + 0.120375i
\(99\) −436.240 338.088i −0.442866 0.343223i
\(100\) 592.024 1025.42i 0.592024 1.02542i
\(101\) 471.999 + 210.148i 0.465007 + 0.207034i 0.625847 0.779946i \(-0.284754\pi\)
−0.160840 + 0.986981i \(0.551420\pi\)
\(102\) −124.391 + 138.150i −0.120751 + 0.134107i
\(103\) 358.994 1104.87i 0.343424 1.05695i −0.618997 0.785393i \(-0.712461\pi\)
0.962422 0.271559i \(-0.0875391\pi\)
\(104\) 627.804 + 241.365i 0.591935 + 0.227575i
\(105\) 675.370 + 490.685i 0.627708 + 0.456057i
\(106\) −168.948 + 35.9110i −0.154808 + 0.0329055i
\(107\) 323.979 359.815i 0.292712 0.325090i −0.578794 0.815473i \(-0.696477\pi\)
0.871507 + 0.490384i \(0.163143\pi\)
\(108\) −107.674 1024.45i −0.0959345 0.912756i
\(109\) 1485.52 1.30539 0.652694 0.757621i \(-0.273639\pi\)
0.652694 + 0.757621i \(0.273639\pi\)
\(110\) 575.388 + 141.072i 0.498737 + 0.122279i
\(111\) 549.824 952.324i 0.470153 0.814330i
\(112\) −494.880 + 359.551i −0.417515 + 0.303343i
\(113\) 88.5197 + 18.8155i 0.0736924 + 0.0156638i 0.244610 0.969621i \(-0.421340\pi\)
−0.170918 + 0.985285i \(0.554673\pi\)
\(114\) −290.264 + 61.6976i −0.238472 + 0.0506887i
\(115\) 140.478 1336.56i 0.113910 1.08378i
\(116\) 1330.35 + 966.559i 1.06483 + 0.773645i
\(117\) 594.486 + 386.502i 0.469746 + 0.305403i
\(118\) −160.258 493.222i −0.125025 0.384786i
\(119\) 735.397 + 327.420i 0.566502 + 0.252223i
\(120\) 422.333 + 731.503i 0.321280 + 0.556473i
\(121\) −56.8574 1329.79i −0.0427178 0.999087i
\(122\) 439.071 0.325833
\(123\) 119.881 + 1140.59i 0.0878802 + 0.836125i
\(124\) −1350.96 287.156i −0.978389 0.207963i
\(125\) −220.931 + 679.957i −0.158086 + 0.486538i
\(126\) 186.304 82.9479i 0.131724 0.0586475i
\(127\) 34.0235 323.712i 0.0237724 0.226179i −0.976185 0.216940i \(-0.930392\pi\)
0.999957 0.00923929i \(-0.00294100\pi\)
\(128\) −1402.27 + 298.061i −0.968312 + 0.205821i
\(129\) 232.466 + 715.458i 0.158663 + 0.488314i
\(130\) −751.704 119.458i −0.507145 0.0805934i
\(131\) −884.608 −0.589989 −0.294994 0.955499i \(-0.595318\pi\)
−0.294994 + 0.955499i \(0.595318\pi\)
\(132\) 617.162 644.114i 0.406947 0.424719i
\(133\) 642.499 + 1112.84i 0.418885 + 0.725531i
\(134\) 53.4376 + 508.425i 0.0344501 + 0.327770i
\(135\) 766.293 + 2358.41i 0.488533 + 1.50355i
\(136\) 545.009 + 605.294i 0.343633 + 0.381644i
\(137\) 385.074 171.446i 0.240139 0.106917i −0.283139 0.959079i \(-0.591376\pi\)
0.523278 + 0.852162i \(0.324709\pi\)
\(138\) 208.440 + 151.441i 0.128577 + 0.0934167i
\(139\) −494.258 548.929i −0.301600 0.334961i 0.573227 0.819397i \(-0.305691\pi\)
−0.874827 + 0.484436i \(0.839025\pi\)
\(140\) 1150.47 1277.73i 0.694520 0.771342i
\(141\) −1912.33 851.425i −1.14218 0.508531i
\(142\) 674.902 0.398848
\(143\) 214.159 + 1696.57i 0.125237 + 0.992127i
\(144\) −652.501 −0.377605
\(145\) −3616.40 1610.13i −2.07121 0.922163i
\(146\) 394.386 438.010i 0.223559 0.248287i
\(147\) −327.078 363.257i −0.183517 0.203816i
\(148\) −1832.29 1331.23i −1.01766 0.739370i
\(149\) −1956.56 + 871.119i −1.07576 + 0.478958i −0.866641 0.498932i \(-0.833726\pi\)
−0.209117 + 0.977891i \(0.567059\pi\)
\(150\) −365.651 406.096i −0.199035 0.221051i
\(151\) −513.209 1579.49i −0.276585 0.851241i −0.988796 0.149275i \(-0.952306\pi\)
0.712211 0.701966i \(-0.247694\pi\)
\(152\) 135.906 + 1293.06i 0.0725225 + 0.690005i
\(153\) 429.340 + 743.638i 0.226863 + 0.392938i
\(154\) 442.878 + 213.865i 0.231741 + 0.111908i
\(155\) 3324.88 1.72297
\(156\) −721.722 + 890.308i −0.370410 + 0.456934i
\(157\) 491.958 + 1514.09i 0.250080 + 0.769666i 0.994759 + 0.102244i \(0.0326023\pi\)
−0.744680 + 0.667422i \(0.767398\pi\)
\(158\) 256.885 54.6026i 0.129346 0.0274933i
\(159\) 65.4451 622.668i 0.0326423 0.310571i
\(160\) 2431.46 1082.56i 1.20140 0.534897i
\(161\) 344.762 1061.07i 0.168764 0.519404i
\(162\) −85.2473 18.1199i −0.0413436 0.00878785i
\(163\) −99.4256 945.971i −0.0477768 0.454565i −0.992091 0.125521i \(-0.959940\pi\)
0.944314 0.329045i \(-0.106727\pi\)
\(164\) 2362.09 1.12468
\(165\) −1130.86 + 1825.61i −0.533560 + 0.861355i
\(166\) 651.490 + 1128.41i 0.304611 + 0.527601i
\(167\) −2831.89 1260.84i −1.31220 0.584231i −0.373076 0.927801i \(-0.621697\pi\)
−0.939127 + 0.343570i \(0.888364\pi\)
\(168\) 216.686 + 666.890i 0.0995099 + 0.306260i
\(169\) −454.553 2149.46i −0.206897 0.978363i
\(170\) −745.683 541.771i −0.336419 0.244423i
\(171\) −143.277 + 1363.19i −0.0640740 + 0.609624i
\(172\) 1515.53 322.135i 0.671848 0.142806i
\(173\) 1926.81 + 409.556i 0.846777 + 0.179988i 0.610814 0.791774i \(-0.290842\pi\)
0.235963 + 0.971762i \(0.424176\pi\)
\(174\) 613.979 446.082i 0.267504 0.194353i
\(175\) −1183.15 + 2049.27i −0.511071 + 0.885202i
\(176\) −1016.18 1201.46i −0.435215 0.514567i
\(177\) 1879.88 0.798308
\(178\) −154.991 1474.64i −0.0652645 0.620950i
\(179\) 887.513 985.683i 0.370591 0.411583i −0.528787 0.848754i \(-0.677353\pi\)
0.899378 + 0.437171i \(0.144020\pi\)
\(180\) 1793.95 381.315i 0.742849 0.157897i
\(181\) −2415.83 1755.20i −0.992083 0.720791i −0.0317069 0.999497i \(-0.510094\pi\)
−0.960376 + 0.278707i \(0.910094\pi\)
\(182\) −589.781 226.747i −0.240206 0.0923493i
\(183\) −491.826 + 1513.68i −0.198671 + 0.611446i
\(184\) 755.352 838.903i 0.302637 0.336113i
\(185\) 4980.84 + 2217.61i 1.97945 + 0.881308i
\(186\) −318.710 + 552.022i −0.125640 + 0.217614i
\(187\) −700.637 + 1948.67i −0.273988 + 0.762037i
\(188\) −2155.68 + 3733.75i −0.836273 + 1.44847i
\(189\) 215.184 + 2047.34i 0.0828166 + 0.787947i
\(190\) −454.663 1399.31i −0.173604 0.534298i
\(191\) −1927.78 2141.01i −0.730309 0.811091i 0.257579 0.966257i \(-0.417075\pi\)
−0.987888 + 0.155166i \(0.950409\pi\)
\(192\) 70.9395 674.944i 0.0266647 0.253697i
\(193\) 328.678 3127.16i 0.122584 1.16631i −0.744315 0.667828i \(-0.767224\pi\)
0.866899 0.498483i \(-0.166109\pi\)
\(194\) −106.080 + 326.481i −0.0392583 + 0.120825i
\(195\) 1253.85 2457.67i 0.460461 0.902549i
\(196\) −814.479 + 591.753i −0.296822 + 0.215654i
\(197\) −621.911 1077.18i −0.224921 0.389574i 0.731375 0.681975i \(-0.238879\pi\)
−0.956296 + 0.292402i \(0.905546\pi\)
\(198\) 248.101 + 462.238i 0.0890493 + 0.165908i
\(199\) 665.330 1152.39i 0.237005 0.410505i −0.722849 0.691007i \(-0.757168\pi\)
0.959853 + 0.280502i \(0.0905009\pi\)
\(200\) −1936.99 + 1407.31i −0.684829 + 0.497558i
\(201\) −1812.64 385.288i −0.636088 0.135205i
\(202\) −328.617 364.966i −0.114462 0.127123i
\(203\) −2658.68 1931.65i −0.919227 0.667857i
\(204\) −1267.90 + 564.505i −0.435150 + 0.193741i
\(205\) −5562.07 + 1182.26i −1.89499 + 0.402792i
\(206\) −738.896 + 820.627i −0.249909 + 0.277552i
\(207\) 962.796 699.512i 0.323280 0.234877i
\(208\) 1428.81 + 1430.29i 0.476298 + 0.476792i
\(209\) −2733.21 + 1859.17i −0.904592 + 0.615318i
\(210\) −396.755 687.199i −0.130375 0.225815i
\(211\) −629.525 280.283i −0.205395 0.0914477i 0.301461 0.953479i \(-0.402526\pi\)
−0.506856 + 0.862031i \(0.669192\pi\)
\(212\) −1261.33 268.104i −0.408624 0.0868558i
\(213\) −755.991 + 2326.70i −0.243191 + 0.748465i
\(214\) −420.440 + 187.192i −0.134302 + 0.0597952i
\(215\) −3407.42 + 1517.08i −1.08086 + 0.481229i
\(216\) −643.663 + 1980.99i −0.202758 + 0.624025i
\(217\) 2699.87 + 573.876i 0.844605 + 0.179526i
\(218\) −1289.96 574.329i −0.400768 0.178433i
\(219\) 1068.25 + 1850.27i 0.329616 + 0.570911i
\(220\) 3495.96 + 2709.38i 1.07135 + 0.830303i
\(221\) 689.922 2569.49i 0.209996 0.782095i
\(222\) −845.628 + 614.385i −0.255652 + 0.185742i
\(223\) 1599.75 1776.71i 0.480392 0.533529i −0.453418 0.891298i \(-0.649796\pi\)
0.933810 + 0.357769i \(0.116462\pi\)
\(224\) 2161.24 459.387i 0.644662 0.137027i
\(225\) −2305.89 + 1026.65i −0.683226 + 0.304192i
\(226\) −69.5923 50.5618i −0.0204832 0.0148819i
\(227\) −673.002 747.444i −0.196778 0.218544i 0.636678 0.771130i \(-0.280308\pi\)
−0.833456 + 0.552585i \(0.813641\pi\)
\(228\) −2167.05 460.621i −0.629459 0.133796i
\(229\) −4442.16 + 3227.42i −1.28186 + 0.931327i −0.999608 0.0280128i \(-0.991082\pi\)
−0.282254 + 0.959340i \(0.591082\pi\)
\(230\) −638.723 + 1106.30i −0.183114 + 0.317162i
\(231\) −1233.38 + 1287.25i −0.351302 + 0.366643i
\(232\) −1662.57 2879.66i −0.470488 0.814908i
\(233\) 2986.49 2169.81i 0.839705 0.610082i −0.0825831 0.996584i \(-0.526317\pi\)
0.922288 + 0.386503i \(0.126317\pi\)
\(234\) −366.798 565.460i −0.102471 0.157971i
\(235\) 3207.26 9870.92i 0.890291 2.74003i
\(236\) 404.712 3850.58i 0.111629 1.06208i
\(237\) −99.5091 + 946.766i −0.0272735 + 0.259490i
\(238\) −512.001 568.634i −0.139446 0.154870i
\(239\) 973.415 + 2995.86i 0.263452 + 0.810821i 0.992046 + 0.125876i \(0.0401740\pi\)
−0.728594 + 0.684945i \(0.759826\pi\)
\(240\) 265.384 + 2524.96i 0.0713771 + 0.679107i
\(241\) 252.905 438.045i 0.0675978 0.117083i −0.830246 0.557398i \(-0.811800\pi\)
0.897843 + 0.440315i \(0.145133\pi\)
\(242\) −464.745 + 1176.71i −0.123450 + 0.312569i
\(243\) −1801.64 + 3120.53i −0.475618 + 0.823794i
\(244\) 2994.61 + 1333.29i 0.785698 + 0.349815i
\(245\) 1621.70 1801.08i 0.422883 0.469659i
\(246\) 336.872 1036.78i 0.0873096 0.268711i
\(247\) 3301.87 2670.97i 0.850578 0.688055i
\(248\) 2259.42 + 1641.57i 0.578522 + 0.420321i
\(249\) −4619.93 + 981.997i −1.17581 + 0.249926i
\(250\) 454.730 505.029i 0.115039 0.127763i
\(251\) −478.286 4550.59i −0.120275 1.14434i −0.873583 0.486676i \(-0.838209\pi\)
0.753307 0.657669i \(-0.228457\pi\)
\(252\) 1522.54 0.380598
\(253\) 2787.46 + 683.419i 0.692671 + 0.169827i
\(254\) −154.697 + 267.943i −0.0382148 + 0.0661900i
\(255\) 2703.02 1963.86i 0.663802 0.482280i
\(256\) −208.394 44.2956i −0.0508776 0.0108144i
\(257\) 417.136 88.6649i 0.101246 0.0215205i −0.157010 0.987597i \(-0.550186\pi\)
0.258256 + 0.966077i \(0.416852\pi\)
\(258\) 74.7446 711.148i 0.0180364 0.171605i
\(259\) 3661.78 + 2660.44i 0.878502 + 0.638269i
\(260\) −4764.13 3097.37i −1.13638 0.738811i
\(261\) −1083.25 3333.92i −0.256903 0.790667i
\(262\) 768.155 + 342.005i 0.181133 + 0.0806455i
\(263\) 316.581 + 548.334i 0.0742252 + 0.128562i 0.900749 0.434340i \(-0.143018\pi\)
−0.826524 + 0.562902i \(0.809685\pi\)
\(264\) −1669.82 + 682.262i −0.389282 + 0.159054i
\(265\) 3104.28 0.719601
\(266\) −127.675 1214.74i −0.0294295 0.280003i
\(267\) 5257.40 + 1117.49i 1.20505 + 0.256141i
\(268\) −1179.43 + 3629.90i −0.268824 + 0.827356i
\(269\) −934.228 + 415.945i −0.211751 + 0.0942774i −0.509871 0.860251i \(-0.670307\pi\)
0.298121 + 0.954528i \(0.403640\pi\)
\(270\) 246.385 2344.20i 0.0555353 0.528383i
\(271\) 4031.34 856.888i 0.903640 0.192075i 0.267418 0.963581i \(-0.413830\pi\)
0.636222 + 0.771506i \(0.280496\pi\)
\(272\) 756.538 + 2328.39i 0.168647 + 0.519041i
\(273\) 1442.34 1779.26i 0.319761 0.394453i
\(274\) −400.665 −0.0883397
\(275\) −5481.51 2647.01i −1.20199 0.580440i
\(276\) 961.767 + 1665.83i 0.209752 + 0.363301i
\(277\) −202.387 1925.58i −0.0438998 0.417679i −0.994298 0.106642i \(-0.965990\pi\)
0.950398 0.311037i \(-0.100676\pi\)
\(278\) 216.966 + 667.754i 0.0468086 + 0.144062i
\(279\) 1970.10 + 2188.02i 0.422749 + 0.469510i
\(280\) −3176.11 + 1414.10i −0.677890 + 0.301816i
\(281\) −1867.15 1356.56i −0.396386 0.287992i 0.371681 0.928360i \(-0.378781\pi\)
−0.768068 + 0.640369i \(0.778781\pi\)
\(282\) 1331.41 + 1478.68i 0.281150 + 0.312249i
\(283\) −3946.30 + 4382.81i −0.828915 + 0.920603i −0.997884 0.0650180i \(-0.979290\pi\)
0.168969 + 0.985621i \(0.445956\pi\)
\(284\) 4603.05 + 2049.41i 0.961764 + 0.428205i
\(285\) 5333.37 1.10850
\(286\) 469.956 1556.02i 0.0971646 0.321712i
\(287\) −4720.58 −0.970895
\(288\) 2153.12 + 958.632i 0.440535 + 0.196139i
\(289\) −1131.63 + 1256.81i −0.230335 + 0.255813i
\(290\) 2517.82 + 2796.32i 0.509833 + 0.566227i
\(291\) −1006.71 731.416i −0.202798 0.147342i
\(292\) 4019.91 1789.78i 0.805641 0.358694i
\(293\) 3928.79 + 4363.36i 0.783353 + 0.870002i 0.994203 0.107517i \(-0.0342899\pi\)
−0.210850 + 0.977518i \(0.567623\pi\)
\(294\) 143.579 + 441.891i 0.0284820 + 0.0876584i
\(295\) 974.278 + 9269.64i 0.192287 + 1.82949i
\(296\) 2289.84 + 3966.13i 0.449643 + 0.778805i
\(297\) −5211.59 + 939.981i −1.01821 + 0.183647i
\(298\) 2035.78 0.395738
\(299\) −3641.62 578.711i −0.704348 0.111932i
\(300\) −1260.71 3880.05i −0.242623 0.746716i
\(301\) −3028.75 + 643.780i −0.579980 + 0.123279i
\(302\) −165.011 + 1569.98i −0.0314415 + 0.299146i
\(303\) 1626.31 724.079i 0.308347 0.137285i
\(304\) −1207.65 + 3716.77i −0.227841 + 0.701221i
\(305\) −7718.82 1640.69i −1.44911 0.308018i
\(306\) −85.3166 811.733i −0.0159386 0.151646i
\(307\) −1602.07 −0.297835 −0.148917 0.988850i \(-0.547579\pi\)
−0.148917 + 0.988850i \(0.547579\pi\)
\(308\) 2371.15 + 2803.48i 0.438665 + 0.518646i
\(309\) −2001.41 3466.55i −0.368467 0.638204i
\(310\) −2887.18 1285.46i −0.528971 0.235513i
\(311\) −821.635 2528.73i −0.149809 0.461065i 0.847789 0.530334i \(-0.177933\pi\)
−0.997598 + 0.0692687i \(0.977933\pi\)
\(312\) 2065.46 1051.05i 0.374787 0.190719i
\(313\) 2000.38 + 1453.36i 0.361241 + 0.262457i 0.753569 0.657368i \(-0.228330\pi\)
−0.392329 + 0.919825i \(0.628330\pi\)
\(314\) 158.179 1504.97i 0.0284285 0.270479i
\(315\) −3585.16 + 762.049i −0.641273 + 0.136307i
\(316\) 1917.85 + 407.651i 0.341416 + 0.0725701i
\(317\) 6487.91 4713.74i 1.14952 0.835174i 0.161102 0.986938i \(-0.448495\pi\)
0.988417 + 0.151764i \(0.0484952\pi\)
\(318\) −297.564 + 515.396i −0.0524734 + 0.0908866i
\(319\) 4451.79 7186.76i 0.781355 1.26138i
\(320\) 3364.89 0.587823
\(321\) −174.382 1659.14i −0.0303211 0.288486i
\(322\) −709.604 + 788.095i −0.122810 + 0.136394i
\(323\) 5030.53 1069.27i 0.866582 0.184198i
\(324\) −526.392 382.446i −0.0902592 0.0655772i
\(325\) 7299.72 + 2806.44i 1.24589 + 0.478995i
\(326\) −279.392 + 859.879i −0.0474665 + 0.146087i
\(327\) 3424.94 3803.78i 0.579203 0.643270i
\(328\) −4363.41 1942.72i −0.734540 0.327038i
\(329\) 4308.08 7461.82i 0.721922 1.25041i
\(330\) 1687.80 1148.07i 0.281547 0.191513i
\(331\) −530.659 + 919.128i −0.0881197 + 0.152628i −0.906716 0.421741i \(-0.861419\pi\)
0.818597 + 0.574369i \(0.194752\pi\)
\(332\) 1016.83 + 9674.47i 0.168089 + 1.59926i
\(333\) 1491.96 + 4591.77i 0.245522 + 0.755638i
\(334\) 1971.63 + 2189.71i 0.323002 + 0.358730i
\(335\) 960.416 9137.75i 0.156636 1.49029i
\(336\) −220.312 + 2096.13i −0.0357709 + 0.340337i
\(337\) −2439.28 + 7507.32i −0.394290 + 1.21350i 0.535223 + 0.844711i \(0.320228\pi\)
−0.929513 + 0.368790i \(0.879772\pi\)
\(338\) −436.305 + 2042.24i −0.0702126 + 0.328648i
\(339\) 252.264 183.280i 0.0404162 0.0293641i
\(340\) −3440.66 5959.41i −0.548813 0.950571i
\(341\) −960.676 + 7035.15i −0.152562 + 1.11723i
\(342\) 651.448 1128.34i 0.103001 0.178403i
\(343\) 5563.17 4041.88i 0.875752 0.636271i
\(344\) −3064.53 651.386i −0.480315 0.102094i
\(345\) −3098.47 3441.20i −0.483525 0.537009i
\(346\) −1514.81 1100.58i −0.235367 0.171004i
\(347\) −467.647 + 208.210i −0.0723476 + 0.0322112i −0.442591 0.896723i \(-0.645941\pi\)
0.370244 + 0.928935i \(0.379274\pi\)
\(348\) 5542.12 1178.01i 0.853704 0.181460i
\(349\) −1832.41 + 2035.10i −0.281050 + 0.312138i −0.867097 0.498139i \(-0.834017\pi\)
0.586047 + 0.810277i \(0.300683\pi\)
\(350\) 1819.68 1322.07i 0.277902 0.201908i
\(351\) 6572.82 1757.53i 0.999519 0.267265i
\(352\) 1588.06 + 5457.54i 0.240465 + 0.826386i
\(353\) 2441.51 + 4228.82i 0.368126 + 0.637613i 0.989273 0.146081i \(-0.0466661\pi\)
−0.621146 + 0.783695i \(0.713333\pi\)
\(354\) −1632.41 726.794i −0.245089 0.109121i
\(355\) −11864.7 2521.92i −1.77384 0.377041i
\(356\) 3420.82 10528.2i 0.509279 1.56740i
\(357\) 2533.87 1128.15i 0.375648 0.167249i
\(358\) −1151.76 + 512.796i −0.170034 + 0.0757042i
\(359\) −849.909 + 2615.75i −0.124948 + 0.384552i −0.993892 0.110360i \(-0.964800\pi\)
0.868943 + 0.494912i \(0.164800\pi\)
\(360\) −3627.52 771.053i −0.531075 0.112883i
\(361\) 1233.80 + 549.322i 0.179880 + 0.0800878i
\(362\) 1419.21 + 2458.14i 0.206055 + 0.356898i
\(363\) −3536.08 2920.29i −0.511284 0.422246i
\(364\) −3333.96 3337.42i −0.480074 0.480572i
\(365\) −8569.98 + 6226.46i −1.22897 + 0.892898i
\(366\) 1012.30 1124.27i 0.144573 0.160564i
\(367\) 8571.80 1821.99i 1.21919 0.259148i 0.447000 0.894534i \(-0.352493\pi\)
0.772194 + 0.635386i \(0.219159\pi\)
\(368\) 3099.73 1380.09i 0.439089 0.195495i
\(369\) −4073.73 2959.74i −0.574715 0.417555i
\(370\) −3467.77 3851.35i −0.487246 0.541141i
\(371\) 2520.74 + 535.799i 0.352750 + 0.0749793i
\(372\) −3849.99 + 2797.18i −0.536593 + 0.389857i
\(373\) −1398.16 + 2421.69i −0.194086 + 0.336167i −0.946601 0.322409i \(-0.895507\pi\)
0.752514 + 0.658576i \(0.228841\pi\)
\(374\) 1361.79 1421.26i 0.188280 0.196502i
\(375\) 1231.71 + 2133.38i 0.169613 + 0.293779i
\(376\) 7052.98 5124.29i 0.967366 0.702833i
\(377\) −4935.94 + 9674.93i −0.674307 + 1.32171i
\(378\) 604.680 1861.01i 0.0822788 0.253228i
\(379\) 1463.49 13924.2i 0.198349 1.88717i −0.215027 0.976608i \(-0.568984\pi\)
0.413376 0.910560i \(-0.364350\pi\)
\(380\) 1148.20 10924.4i 0.155004 1.47476i
\(381\) −750.442 833.450i −0.100909 0.112071i
\(382\) 846.245 + 2604.47i 0.113345 + 0.348839i
\(383\) 93.9148 + 893.540i 0.0125296 + 0.119211i 0.998999 0.0447351i \(-0.0142444\pi\)
−0.986469 + 0.163946i \(0.947578\pi\)
\(384\) −2469.78 + 4277.78i −0.328217 + 0.568488i
\(385\) −6986.60 5414.64i −0.924857 0.716768i
\(386\) −1494.42 + 2588.42i −0.197057 + 0.341314i
\(387\) −3017.37 1343.42i −0.396334 0.176459i
\(388\) −1714.90 + 1904.59i −0.224383 + 0.249203i
\(389\) −2541.14 + 7820.81i −0.331210 + 1.01936i 0.637349 + 0.770575i \(0.280031\pi\)
−0.968559 + 0.248784i \(0.919969\pi\)
\(390\) −2038.96 + 1649.37i −0.264736 + 0.214151i
\(391\) −3612.45 2624.60i −0.467236 0.339467i
\(392\) 1991.25 423.254i 0.256565 0.0545346i
\(393\) −2039.50 + 2265.09i −0.261779 + 0.290735i
\(394\) 123.584 + 1175.82i 0.0158022 + 0.150348i
\(395\) −4720.05 −0.601244
\(396\) 288.494 + 3906.00i 0.0366095 + 0.495667i
\(397\) −5422.99 + 9392.90i −0.685572 + 1.18745i 0.287685 + 0.957725i \(0.407115\pi\)
−0.973257 + 0.229720i \(0.926219\pi\)
\(398\) −1023.28 + 743.453i −0.128875 + 0.0936330i
\(399\) 4330.81 + 920.541i 0.543387 + 0.115501i
\(400\) −7039.31 + 1496.25i −0.879913 + 0.187031i
\(401\) −454.475 + 4324.04i −0.0565970 + 0.538485i 0.929085 + 0.369867i \(0.120597\pi\)
−0.985682 + 0.168617i \(0.946070\pi\)
\(402\) 1425.06 + 1035.36i 0.176804 + 0.128456i
\(403\) 482.155 9109.70i 0.0595976 1.12602i
\(404\) −1133.02 3487.07i −0.139529 0.429426i
\(405\) 1430.93 + 637.091i 0.175564 + 0.0781662i
\(406\) 1561.88 + 2705.25i 0.190923 + 0.330688i
\(407\) −6131.41 + 9898.26i −0.746738 + 1.20550i
\(408\) 2806.43 0.340537
\(409\) 1387.81 + 13204.1i 0.167781 + 1.59633i 0.677190 + 0.735809i \(0.263198\pi\)
−0.509408 + 0.860525i \(0.670136\pi\)
\(410\) 5286.94 + 1123.77i 0.636838 + 0.135364i
\(411\) 448.805 1381.28i 0.0538636 0.165775i
\(412\) −7531.44 + 3353.21i −0.900601 + 0.400973i
\(413\) −808.808 + 7695.30i −0.0963653 + 0.916854i
\(414\) −1106.49 + 235.192i −0.131355 + 0.0279205i
\(415\) −7236.55 22271.8i −0.855972 2.63441i
\(416\) −2613.45 6818.83i −0.308017 0.803656i
\(417\) −2545.10 −0.298882
\(418\) 3092.18 557.717i 0.361827 0.0652604i
\(419\) 4495.85 + 7787.04i 0.524193 + 0.907928i 0.999603 + 0.0281643i \(0.00896615\pi\)
−0.475411 + 0.879764i \(0.657701\pi\)
\(420\) −619.244 5891.72i −0.0719429 0.684491i
\(421\) 874.962 + 2692.86i 0.101290 + 0.311738i 0.988842 0.148970i \(-0.0475956\pi\)
−0.887552 + 0.460708i \(0.847596\pi\)
\(422\) 438.290 + 486.770i 0.0505584 + 0.0561508i
\(423\) 8396.21 3738.23i 0.965101 0.429691i
\(424\) 2109.51 + 1532.65i 0.241620 + 0.175547i
\(425\) 6337.04 + 7037.99i 0.723274 + 0.803277i
\(426\) 1556.01 1728.13i 0.176970 0.196545i
\(427\) −5984.66 2664.54i −0.678263 0.301982i
\(428\) −3435.97 −0.388046
\(429\) 4837.92 + 3363.14i 0.544468 + 0.378494i
\(430\) 3545.39 0.397613
\(431\) −8036.98 3578.30i −0.898208 0.399908i −0.0949106 0.995486i \(-0.530257\pi\)
−0.803298 + 0.595578i \(0.796923\pi\)
\(432\) −4189.31 + 4652.70i −0.466571 + 0.518179i
\(433\) 1107.87 + 1230.41i 0.122958 + 0.136559i 0.801480 0.598021i \(-0.204046\pi\)
−0.678522 + 0.734580i \(0.737379\pi\)
\(434\) −2122.58 1542.15i −0.234763 0.170565i
\(435\) −12460.6 + 5547.81i −1.37342 + 0.611487i
\(436\) −7053.97 7834.23i −0.774826 0.860531i
\(437\) −2202.61 6778.93i −0.241110 0.742060i
\(438\) −212.279 2019.70i −0.0231577 0.220331i
\(439\) −93.3050 161.609i −0.0101440 0.0175699i 0.860909 0.508759i \(-0.169896\pi\)
−0.871053 + 0.491189i \(0.836562\pi\)
\(440\) −4229.63 7880.25i −0.458272 0.853809i
\(441\) 2146.15 0.231741
\(442\) −1592.51 + 1964.50i −0.171375 + 0.211407i
\(443\) 233.556 + 718.812i 0.0250488 + 0.0770921i 0.962799 0.270217i \(-0.0870955\pi\)
−0.937751 + 0.347309i \(0.887095\pi\)
\(444\) −7633.11 + 1622.47i −0.815882 + 0.173421i
\(445\) −2785.60 + 26503.2i −0.296742 + 2.82331i
\(446\) −2076.06 + 924.322i −0.220413 + 0.0981343i
\(447\) −2280.38 + 7018.30i −0.241294 + 0.742627i
\(448\) 2732.36 + 580.782i 0.288152 + 0.0612486i
\(449\) −469.160 4463.76i −0.0493118 0.469171i −0.991115 0.133006i \(-0.957537\pi\)
0.941803 0.336164i \(-0.109130\pi\)
\(450\) 2399.25 0.251337
\(451\) −894.467 12110.4i −0.0933899 1.26443i
\(452\) −321.106 556.173i −0.0334150 0.0578765i
\(453\) −5227.62 2327.48i −0.542196 0.241401i
\(454\) 295.430 + 909.242i 0.0305402 + 0.0939930i
\(455\) 9521.00 + 6190.03i 0.980992 + 0.637787i
\(456\) 3624.29 + 2633.20i 0.372199 + 0.270419i
\(457\) −1.26927 + 12.0763i −0.000129921 + 0.00123612i −0.994587 0.103910i \(-0.966864\pi\)
0.994457 + 0.105147i \(0.0335312\pi\)
\(458\) 5105.15 1085.13i 0.520848 0.110710i
\(459\) 8059.10 + 1713.01i 0.819535 + 0.174197i
\(460\) −7715.70 + 5605.79i −0.782058 + 0.568198i
\(461\) 8590.00 14878.3i 0.867844 1.50315i 0.00364929 0.999993i \(-0.498838\pi\)
0.864195 0.503157i \(-0.167828\pi\)
\(462\) 1568.69 640.941i 0.157970 0.0645439i
\(463\) 6049.07 0.607179 0.303590 0.952803i \(-0.401815\pi\)
0.303590 + 0.952803i \(0.401815\pi\)
\(464\) −1044.72 9939.86i −0.104526 0.994496i
\(465\) 7665.65 8513.56i 0.764486 0.849048i
\(466\) −3432.22 + 729.541i −0.341190 + 0.0725222i
\(467\) 7621.39 + 5537.27i 0.755195 + 0.548681i 0.897433 0.441151i \(-0.145430\pi\)
−0.142238 + 0.989833i \(0.545430\pi\)
\(468\) −784.600 4970.45i −0.0774961 0.490938i
\(469\) 2357.06 7254.27i 0.232065 0.714224i
\(470\) −6601.31 + 7331.49i −0.647863 + 0.719525i
\(471\) 5011.15 + 2231.11i 0.490237 + 0.218268i
\(472\) −3914.55 + 6780.20i −0.381741 + 0.661195i
\(473\) −2225.49 7648.14i −0.216338 0.743471i
\(474\) 452.445 783.658i 0.0438428 0.0759380i
\(475\) 1580.23 + 15034.9i 0.152644 + 1.45231i
\(476\) −1765.30 5433.02i −0.169984 0.523156i
\(477\) 1839.39 + 2042.85i 0.176561 + 0.196091i
\(478\) 312.981 2977.81i 0.0299486 0.284942i
\(479\) −60.2129 + 572.887i −0.00574363 + 0.0546470i −0.997018 0.0771655i \(-0.975413\pi\)
0.991275 + 0.131812i \(0.0420797\pi\)
\(480\) 2833.88 8721.77i 0.269475 0.829360i
\(481\) 6798.23 13325.2i 0.644433 1.26315i
\(482\) −388.968 + 282.602i −0.0367572 + 0.0267057i
\(483\) −1922.07 3329.12i −0.181071 0.313624i
\(484\) −6742.92 + 6614.30i −0.633257 + 0.621178i
\(485\) 3084.85 5343.12i 0.288816 0.500244i
\(486\) 2770.91 2013.19i 0.258624 0.187901i
\(487\) 6416.91 + 1363.96i 0.597080 + 0.126913i 0.496531 0.868019i \(-0.334607\pi\)
0.100549 + 0.994932i \(0.467940\pi\)
\(488\) −4435.28 4925.88i −0.411426 0.456935i
\(489\) −2651.45 1926.39i −0.245200 0.178148i
\(490\) −2104.54 + 937.000i −0.194027 + 0.0863864i
\(491\) −4471.74 + 950.497i −0.411011 + 0.0873632i −0.408777 0.912634i \(-0.634045\pi\)
−0.00223446 + 0.999998i \(0.500711\pi\)
\(492\) 5445.89 6048.27i 0.499023 0.554222i
\(493\) −10640.8 + 7730.98i −0.972082 + 0.706259i
\(494\) −3899.84 + 1042.79i −0.355186 + 0.0949746i
\(495\) −2634.33 9053.19i −0.239201 0.822041i
\(496\) 4197.26 + 7269.86i 0.379965 + 0.658118i
\(497\) −9199.10 4095.70i −0.830254 0.369653i
\(498\) 4391.41 + 933.422i 0.395148 + 0.0839913i
\(499\) −1549.19 + 4767.93i −0.138981 + 0.427739i −0.996188 0.0872327i \(-0.972198\pi\)
0.857207 + 0.514972i \(0.172198\pi\)
\(500\) 4634.99 2063.63i 0.414566 0.184577i
\(501\) −9757.48 + 4344.31i −0.870124 + 0.387404i
\(502\) −1344.01 + 4136.44i −0.119494 + 0.367766i
\(503\) −8134.89 1729.12i −0.721107 0.153276i −0.167282 0.985909i \(-0.553499\pi\)
−0.553825 + 0.832633i \(0.686832\pi\)
\(504\) −2812.54 1252.22i −0.248572 0.110671i
\(505\) 4413.27 + 7644.02i 0.388887 + 0.673573i
\(506\) −2156.28 1671.13i −0.189444 0.146820i
\(507\) −6551.82 3791.76i −0.573919 0.332146i
\(508\) −1868.72 + 1357.71i −0.163211 + 0.118580i
\(509\) 6451.07 7164.63i 0.561765 0.623903i −0.393617 0.919274i \(-0.628777\pi\)
0.955383 + 0.295371i \(0.0954432\pi\)
\(510\) −3106.44 + 660.294i −0.269717 + 0.0573300i
\(511\) −8033.69 + 3576.83i −0.695479 + 0.309647i
\(512\) 9442.24 + 6860.19i 0.815024 + 0.592149i
\(513\) 8800.42 + 9773.86i 0.757404 + 0.841182i
\(514\) −396.502 84.2791i −0.0340252 0.00723228i
\(515\) 16056.2 11665.5i 1.37382 0.998142i
\(516\) 2669.26 4623.30i 0.227728 0.394437i
\(517\) 19959.3 + 9638.32i 1.69789 + 0.819909i
\(518\) −2151.16 3725.92i −0.182464 0.316037i
\(519\) 5491.02 3989.46i 0.464411 0.337414i
\(520\) 6253.17 + 9639.98i 0.527346 + 0.812963i
\(521\) −6156.55 + 18947.9i −0.517703 + 1.59333i 0.260606 + 0.965445i \(0.416078\pi\)
−0.778309 + 0.627881i \(0.783922\pi\)
\(522\) −348.298 + 3313.83i −0.0292042 + 0.277859i
\(523\) 1316.30 12523.7i 0.110053 1.04708i −0.790538 0.612413i \(-0.790199\pi\)
0.900591 0.434669i \(-0.143134\pi\)
\(524\) 4200.54 + 4665.17i 0.350193 + 0.388929i
\(525\) 2519.49 + 7754.20i 0.209447 + 0.644611i
\(526\) −62.9096 598.545i −0.00521481 0.0496156i
\(527\) 5523.52 9567.01i 0.456562 0.790788i
\(528\) −5419.28 168.021i −0.446674 0.0138489i
\(529\) 2989.22 5177.48i 0.245683 0.425535i
\(530\) −2695.62 1200.17i −0.220925 0.0983621i
\(531\) −5522.82 + 6133.72i −0.451356 + 0.501282i
\(532\) 2817.92 8672.66i 0.229647 0.706781i
\(533\) 2432.63 + 15410.7i 0.197690 + 1.25237i
\(534\) −4133.25 3002.98i −0.334950 0.243355i
\(535\) 8090.77 1719.75i 0.653822 0.138974i
\(536\) 5164.16 5735.38i 0.416152 0.462184i
\(537\) −477.705 4545.06i −0.0383883 0.365240i
\(538\) 972.055 0.0778964
\(539\) 3342.35 + 3951.76i 0.267097 + 0.315797i
\(540\) 8798.85 15240.1i 0.701189 1.21450i
\(541\) 17601.0 12787.8i 1.39875 1.01625i 0.403911 0.914798i \(-0.367650\pi\)
0.994840 0.101454i \(-0.0323496\pi\)
\(542\) −3831.93 814.501i −0.303681 0.0645495i
\(543\) −10064.1 + 2139.19i −0.795380 + 0.169063i
\(544\) 924.359 8794.69i 0.0728522 0.693142i
\(545\) 20531.3 + 14916.9i 1.61370 + 1.17242i
\(546\) −1940.36 + 987.397i −0.152088 + 0.0773932i
\(547\) 7053.13 + 21707.3i 0.551316 + 1.69678i 0.705479 + 0.708731i \(0.250732\pi\)
−0.154163 + 0.988045i \(0.549268\pi\)
\(548\) −2732.67 1216.66i −0.213018 0.0948417i
\(549\) −3493.97 6051.73i −0.271619 0.470458i
\(550\) 3736.52 + 4417.80i 0.289683 + 0.342501i
\(551\) −20995.5 −1.62330
\(552\) −406.569 3868.25i −0.0313492 0.298268i
\(553\) −3832.78 814.682i −0.294731 0.0626470i
\(554\) −568.719 + 1750.34i −0.0436147 + 0.134232i
\(555\) 17161.8 7640.95i 1.31258 0.584397i
\(556\) −547.924 + 5213.15i −0.0417934 + 0.397638i
\(557\) 6442.00 1369.29i 0.490047 0.104163i 0.0437406 0.999043i \(-0.486072\pi\)
0.446306 + 0.894880i \(0.352739\pi\)
\(558\) −864.825 2661.66i −0.0656110 0.201930i
\(559\) 3662.46 + 9555.85i 0.277112 + 0.723022i
\(560\) −10450.1 −0.788569
\(561\) 3374.35 + 6286.77i 0.253948 + 0.473133i
\(562\) 1096.88 + 1899.85i 0.0823292 + 0.142598i
\(563\) −691.188 6576.22i −0.0517409 0.492282i −0.989452 0.144864i \(-0.953725\pi\)
0.937711 0.347417i \(-0.112941\pi\)
\(564\) 4590.49 + 14128.1i 0.342721 + 1.05479i
\(565\) 1034.49 + 1148.92i 0.0770289 + 0.0855493i
\(566\) 5121.26 2280.13i 0.380323 0.169330i
\(567\) 1051.98 + 764.310i 0.0779173 + 0.0566102i
\(568\) −6817.53 7571.64i −0.503622 0.559329i
\(569\) −5417.37 + 6016.60i −0.399136 + 0.443285i −0.908891 0.417035i \(-0.863069\pi\)
0.509755 + 0.860320i \(0.329736\pi\)
\(570\) −4631.26 2061.97i −0.340320 0.151520i
\(571\) 5098.10 0.373641 0.186820 0.982394i \(-0.440182\pi\)
0.186820 + 0.982394i \(0.440182\pi\)
\(572\) 7930.29 9185.53i 0.579689 0.671444i
\(573\) −9926.77 −0.723729
\(574\) 4099.14 + 1825.06i 0.298075 + 0.132711i
\(575\) 8782.78 9754.26i 0.636986 0.707445i
\(576\) 1993.81 + 2214.35i 0.144228 + 0.160182i
\(577\) −15939.6 11580.8i −1.15004 0.835553i −0.161554 0.986864i \(-0.551651\pi\)
−0.988486 + 0.151310i \(0.951651\pi\)
\(578\) 1468.56 653.847i 0.105682 0.0470527i
\(579\) −7249.51 8051.40i −0.520345 0.577901i
\(580\) 8681.04 + 26717.5i 0.621484 + 1.91273i
\(581\) −2032.11 19334.2i −0.145105 1.38058i
\(582\) 591.403 + 1024.34i 0.0421211 + 0.0729558i
\(583\) −896.935 + 6568.37i −0.0637174 + 0.466611i
\(584\) −8897.87 −0.630473
\(585\) 4335.30 + 11311.4i 0.306397 + 0.799431i
\(586\) −1724.64 5307.89i −0.121577 0.374176i
\(587\) −13001.0 + 2763.45i −0.914155 + 0.194310i −0.640893 0.767630i \(-0.721436\pi\)
−0.273262 + 0.961940i \(0.588103\pi\)
\(588\) −362.592 + 3449.83i −0.0254304 + 0.241954i
\(589\) 16109.7 7172.48i 1.12697 0.501761i
\(590\) 2737.78 8426.02i 0.191038 0.587956i
\(591\) −4192.03 891.044i −0.291772 0.0620180i
\(592\) 1438.89 + 13690.1i 0.0998950 + 0.950437i
\(593\) −11459.8 −0.793588 −0.396794 0.917908i \(-0.629877\pi\)
−0.396794 + 0.917908i \(0.629877\pi\)
\(594\) 4888.93 + 1198.65i 0.337702 + 0.0827967i
\(595\) 6876.09 + 11909.7i 0.473769 + 0.820591i
\(596\) 13884.7 + 6181.88i 0.954263 + 0.424865i
\(597\) −1416.81 4360.49i −0.0971292 0.298933i
\(598\) 2938.48 + 1910.44i 0.200942 + 0.130641i
\(599\) 18732.4 + 13609.9i 1.27777 + 0.928357i 0.999483 0.0321393i \(-0.0102320\pi\)
0.278291 + 0.960497i \(0.410232\pi\)
\(600\) −862.315 + 8204.38i −0.0586731 + 0.558237i
\(601\) 18033.2 3833.07i 1.22394 0.260156i 0.449776 0.893141i \(-0.351504\pi\)
0.774164 + 0.632985i \(0.218171\pi\)
\(602\) 2878.93 + 611.935i 0.194911 + 0.0414296i
\(603\) 6582.40 4782.39i 0.444537 0.322975i
\(604\) −5892.85 + 10206.7i −0.396981 + 0.687591i
\(605\) 12567.2 18949.8i 0.844512 1.27342i
\(606\) −1692.16 −0.113431
\(607\) 2314.92 + 22025.0i 0.154793 + 1.47276i 0.745840 + 0.666125i \(0.232048\pi\)
−0.591047 + 0.806637i \(0.701285\pi\)
\(608\) 9445.56 10490.4i 0.630046 0.699737i
\(609\) −11075.8 + 2354.23i −0.736969 + 0.156648i
\(610\) 6068.37 + 4408.93i 0.402789 + 0.292643i
\(611\) −26579.8 10218.8i −1.75991 0.676612i
\(612\) 1883.03 5795.36i 0.124374 0.382784i
\(613\) −6805.46 + 7558.22i −0.448401 + 0.498000i −0.924389 0.381452i \(-0.875424\pi\)
0.475988 + 0.879452i \(0.342091\pi\)
\(614\) 1391.17 + 619.389i 0.0914383 + 0.0407109i
\(615\) −9796.35 + 16967.8i −0.642320 + 1.11253i
\(616\) −2074.41 7128.96i −0.135683 0.466289i
\(617\) 1917.37 3320.99i 0.125106 0.216690i −0.796668 0.604417i \(-0.793406\pi\)
0.921774 + 0.387727i \(0.126740\pi\)
\(618\) 397.712 + 3783.98i 0.0258873 + 0.246301i
\(619\) −3398.10 10458.3i −0.220648 0.679085i −0.998704 0.0508900i \(-0.983794\pi\)
0.778056 0.628195i \(-0.216206\pi\)
\(620\) −15788.1 17534.5i −1.02269 1.13581i
\(621\) 1193.61 11356.4i 0.0771302 0.733845i
\(622\) −264.179 + 2513.50i −0.0170299 + 0.162029i
\(623\) −6836.44 + 21040.4i −0.439640 + 1.35307i
\(624\) 6956.52 360.960i 0.446288 0.0231570i
\(625\) 6991.79 5079.84i 0.447475 0.325109i
\(626\) −1175.15 2035.42i −0.0750294 0.129955i
\(627\) −1541.00 + 11284.9i −0.0981524 + 0.718783i
\(628\) 5648.83 9784.07i 0.358938 0.621699i
\(629\) 14655.5 10647.8i 0.929016 0.674970i
\(630\) 3407.82 + 724.354i 0.215509 + 0.0458079i
\(631\) −10761.1 11951.5i −0.678913 0.754010i 0.300959 0.953637i \(-0.402693\pi\)
−0.979872 + 0.199628i \(0.936027\pi\)
\(632\) −3207.51 2330.39i −0.201879 0.146674i
\(633\) −2169.08 + 965.735i −0.136198 + 0.0606391i
\(634\) −7456.23 + 1584.87i −0.467074 + 0.0992796i
\(635\) 3720.79 4132.36i 0.232528 0.258248i
\(636\) −3594.54 + 2611.59i −0.224108 + 0.162824i
\(637\) −4699.52 4704.40i −0.292311 0.292614i
\(638\) −6644.26 + 4519.53i −0.412302 + 0.280454i
\(639\) −5370.62 9302.19i −0.332486 0.575882i
\(640\) −22373.6 9961.37i −1.38187 0.615246i
\(641\) −18972.7 4032.78i −1.16908 0.248495i −0.417835 0.908523i \(-0.637211\pi\)
−0.751241 + 0.660028i \(0.770544\pi\)
\(642\) −490.024 + 1508.14i −0.0301242 + 0.0927127i
\(643\) 4752.30 2115.86i 0.291465 0.129769i −0.255795 0.966731i \(-0.582337\pi\)
0.547261 + 0.836962i \(0.315671\pi\)
\(644\) −7232.87 + 3220.28i −0.442570 + 0.197045i
\(645\) −3971.37 + 12222.6i −0.242438 + 0.746147i
\(646\) −4781.69 1016.38i −0.291228 0.0619023i
\(647\) 6201.32 + 2761.01i 0.376815 + 0.167769i 0.586400 0.810022i \(-0.300545\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(648\) 657.842 + 1139.42i 0.0398804 + 0.0690749i
\(649\) −19895.2 616.840i −1.20332 0.0373083i
\(650\) −5253.74 5259.19i −0.317029 0.317358i
\(651\) 7694.11 5590.10i 0.463220 0.336549i
\(652\) −4516.66 + 5016.26i −0.271298 + 0.301307i
\(653\) 18968.5 4031.88i 1.13675 0.241623i 0.399163 0.916880i \(-0.369301\pi\)
0.737582 + 0.675257i \(0.235967\pi\)
\(654\) −4444.67 + 1978.89i −0.265750 + 0.118319i
\(655\) −12226.1 8882.79i −0.729334 0.529892i
\(656\) −9606.45 10669.0i −0.571751 0.634994i
\(657\) −9175.48 1950.31i −0.544854 0.115812i
\(658\) −6625.82 + 4813.94i −0.392555 + 0.285208i
\(659\) −12868.0 + 22288.1i −0.760648 + 1.31748i 0.181869 + 0.983323i \(0.441785\pi\)
−0.942517 + 0.334159i \(0.891548\pi\)
\(660\) 14997.6 2705.02i 0.884518 0.159535i
\(661\) −11629.1 20142.3i −0.684299 1.18524i −0.973657 0.228019i \(-0.926775\pi\)
0.289358 0.957221i \(-0.406558\pi\)
\(662\) 816.151 592.968i 0.0479163 0.0348133i
\(663\) −4988.71 7690.66i −0.292225 0.450498i
\(664\) 6078.49 18707.7i 0.355258 1.09337i
\(665\) −2294.65 + 21832.2i −0.133809 + 1.27311i
\(666\) 479.707 4564.11i 0.0279103 0.265549i
\(667\) 12197.5 + 13546.7i 0.708082 + 0.786405i
\(668\) 6797.85 + 20921.6i 0.393737 + 1.21180i
\(669\) −861.070 8192.53i −0.0497622 0.473455i
\(670\) −4366.79 + 7563.51i −0.251797 + 0.436125i
\(671\) 5701.79 15858.3i 0.328040 0.912373i
\(672\) 3806.55 6593.13i 0.218513 0.378476i
\(673\) 10135.7 + 4512.68i 0.580536 + 0.258471i 0.675927 0.736969i \(-0.263743\pi\)
−0.0953910 + 0.995440i \(0.530410\pi\)
\(674\) 5020.62 5575.96i 0.286924 0.318662i
\(675\) −7484.13 + 23033.8i −0.426762 + 1.31344i
\(676\) −9177.22 + 12603.9i −0.522145 + 0.717106i
\(677\) −13526.0 9827.25i −0.767870 0.557891i 0.133444 0.991056i \(-0.457396\pi\)
−0.901314 + 0.433166i \(0.857396\pi\)
\(678\) −289.914 + 61.6232i −0.0164220 + 0.00349060i
\(679\) 3427.19 3806.28i 0.193702 0.215127i
\(680\) 1454.48 + 13838.4i 0.0820246 + 0.780412i
\(681\) −3465.51 −0.195005
\(682\) 3554.12 5737.61i 0.199552 0.322147i
\(683\) −4134.44 + 7161.06i −0.231625 + 0.401186i −0.958286 0.285809i \(-0.907738\pi\)
0.726661 + 0.686996i \(0.241071\pi\)
\(684\) 7869.42 5717.47i 0.439905 0.319609i
\(685\) 7043.65 + 1497.17i 0.392882 + 0.0835097i
\(686\) −6393.47 + 1358.97i −0.355836 + 0.0756354i
\(687\) −1977.58 + 18815.4i −0.109824 + 1.04491i
\(688\) −7618.56 5535.21i −0.422173 0.306727i
\(689\) 450.164 8505.27i 0.0248910 0.470283i
\(690\) 1360.15 + 4186.11i 0.0750435 + 0.230960i
\(691\) 17600.7 + 7836.34i 0.968977 + 0.431416i 0.829314 0.558783i \(-0.188731\pi\)
0.139663 + 0.990199i \(0.455398\pi\)
\(692\) −6989.52 12106.2i −0.383962 0.665041i
\(693\) −576.549 7806.06i −0.0316036 0.427890i
\(694\) 486.582 0.0266144
\(695\) −1319.04 12549.8i −0.0719912 0.684951i
\(696\) −11206.7 2382.05i −0.610327 0.129729i
\(697\) −5838.27 + 17968.3i −0.317274 + 0.976470i
\(698\) 2377.99 1058.75i 0.128951 0.0574129i
\(699\) 1329.53 12649.7i 0.0719422 0.684484i
\(700\) 16425.4 3491.33i 0.886889 0.188514i
\(701\) 4863.54 + 14968.4i 0.262045 + 0.806491i 0.992360 + 0.123380i \(0.0393734\pi\)
−0.730315 + 0.683111i \(0.760627\pi\)
\(702\) −6387.04 1015.00i −0.343395 0.0545709i
\(703\) 28916.9 1.55138
\(704\) −972.237 + 7119.82i −0.0520491 + 0.381162i
\(705\) −17880.6 30970.2i −0.955211 1.65447i
\(706\) −485.167 4616.06i −0.0258633 0.246073i
\(707\) 2264.31 + 6968.83i 0.120450 + 0.370707i
\(708\) −8926.57 9913.96i −0.473843 0.526256i
\(709\) −14986.7 + 6672.49i −0.793845 + 0.353443i −0.763262 0.646090i \(-0.776403\pi\)
−0.0305835 + 0.999532i \(0.509737\pi\)
\(710\) 9327.77 + 6777.02i 0.493049 + 0.358221i
\(711\) −2796.79 3106.14i −0.147521 0.163839i
\(712\) −14978.2 + 16635.0i −0.788387 + 0.875592i
\(713\) −13986.9 6227.37i −0.734661 0.327092i
\(714\) −2636.46 −0.138189
\(715\) −14076.2 + 25598.6i −0.736252 + 1.33893i
\(716\) −9412.54 −0.491289
\(717\) 9915.34 + 4414.59i 0.516451 + 0.229939i
\(718\) 1749.32 1942.81i 0.0909247 0.100982i
\(719\) 16211.5 + 18004.7i 0.840874 + 0.933885i 0.998562 0.0536036i \(-0.0170707\pi\)
−0.157688 + 0.987489i \(0.550404\pi\)
\(720\) −9018.17 6552.09i −0.466788 0.339141i
\(721\) 15051.4 6701.32i 0.777454 0.346145i
\(722\) −858.999 954.015i −0.0442779 0.0491756i
\(723\) −538.558 1657.51i −0.0277029 0.0852607i
\(724\) 2215.06 + 21074.9i 0.113705 + 1.08183i
\(725\) −19331.4 33482.9i −0.990275 1.71521i
\(726\) 1941.55 + 3902.96i 0.0992529 + 0.199521i
\(727\) −32044.3 −1.63474 −0.817371 0.576111i \(-0.804570\pi\)
−0.817371 + 0.576111i \(0.804570\pi\)
\(728\) 3413.84 + 8907.16i 0.173799 + 0.453463i
\(729\) 4601.55 + 14162.1i 0.233783 + 0.719509i
\(730\) 9849.05 2093.48i 0.499356 0.106141i
\(731\) −1295.39 + 12324.8i −0.0655426 + 0.623596i
\(732\) 10318.2 4593.94i 0.520997 0.231963i
\(733\) 11171.7 34383.0i 0.562942 1.73256i −0.111046 0.993815i \(-0.535420\pi\)
0.673988 0.738742i \(-0.264580\pi\)
\(734\) −8147.79 1731.87i −0.409728 0.0870904i
\(735\) −872.881 8304.91i −0.0438050 0.416777i
\(736\) −12256.1 −0.613812
\(737\) 19057.2 + 4672.37i 0.952482 + 0.233526i
\(738\) 2393.16 + 4145.08i 0.119368 + 0.206751i
\(739\) 16602.4 + 7391.89i 0.826429 + 0.367950i 0.775965 0.630776i \(-0.217263\pi\)
0.0504639 + 0.998726i \(0.483930\pi\)
\(740\) −11956.3 36797.8i −0.593950 1.82799i
\(741\) 773.414 14612.7i 0.0383429 0.724439i
\(742\) −1981.75 1439.82i −0.0980489 0.0712367i
\(743\) −2023.69 + 19254.1i −0.0999220 + 0.950694i 0.823606 + 0.567163i \(0.191959\pi\)
−0.923528 + 0.383531i \(0.874708\pi\)
\(744\) 9412.52 2000.69i 0.463817 0.0985874i
\(745\) −35788.9 7607.16i −1.76000 0.374101i
\(746\) 2150.37 1562.33i 0.105537 0.0766771i
\(747\) 10368.6 17959.0i 0.507856 0.879632i
\(748\) 13603.7 5558.26i 0.664974 0.271698i
\(749\) 6866.70 0.334985
\(750\) −244.759 2328.73i −0.0119165 0.113378i
\(751\) −12018.8 + 13348.2i −0.583983 + 0.648579i −0.960647 0.277771i \(-0.910404\pi\)
0.376664 + 0.926350i \(0.377071\pi\)
\(752\) 25631.6 5448.16i 1.24293 0.264194i
\(753\) −12754.8 9266.88i −0.617277 0.448478i
\(754\) 8026.65 6492.96i 0.387683 0.313607i
\(755\) 8767.46 26983.5i 0.422623 1.30070i
\(756\) 9775.29 10856.6i 0.470269 0.522287i
\(757\) −16478.7 7336.79i −0.791187 0.352259i −0.0289698 0.999580i \(-0.509223\pi\)
−0.762218 + 0.647321i \(0.775889\pi\)
\(758\) −6654.16 + 11525.3i −0.318852 + 0.552268i
\(759\) 8176.53 5561.80i 0.391027 0.265982i
\(760\) −11105.9 + 19236.0i −0.530070 + 0.918108i
\(761\) 4228.29 + 40229.5i 0.201413 + 1.91632i 0.367172 + 0.930153i \(0.380326\pi\)
−0.165759 + 0.986166i \(0.553007\pi\)
\(762\) 329.425 + 1013.87i 0.0156612 + 0.0482001i
\(763\) 14097.2 + 15656.5i 0.668877 + 0.742863i
\(764\) −2137.10 + 20333.1i −0.101201 + 0.962861i
\(765\) −1533.36 + 14589.0i −0.0724692 + 0.689498i
\(766\) 263.906 812.220i 0.0124482 0.0383116i
\(767\) 25538.8 1325.15i 1.20228 0.0623840i
\(768\) −593.883 + 431.482i −0.0279035 + 0.0202731i
\(769\) −1701.72 2947.46i −0.0797990 0.138216i 0.823364 0.567513i \(-0.192095\pi\)
−0.903163 + 0.429298i \(0.858761\pi\)
\(770\) 3973.46 + 7402.98i 0.185966 + 0.346474i
\(771\) 734.691 1272.52i 0.0343181 0.0594407i
\(772\) −18052.5 + 13115.9i −0.841610 + 0.611466i
\(773\) −6546.39 1391.48i −0.304602 0.0647452i 0.0530750 0.998591i \(-0.483098\pi\)
−0.357677 + 0.933845i \(0.616431\pi\)
\(774\) 2100.76 + 2333.13i 0.0975585 + 0.108350i
\(775\) 26271.2 + 19087.2i 1.21766 + 0.884685i
\(776\) 4734.32 2107.86i 0.219011 0.0975099i
\(777\) 15254.6 3242.47i 0.704319 0.149708i
\(778\) 5230.27 5808.80i 0.241021 0.267681i
\(779\) −24398.9 + 17726.8i −1.12218 + 0.815314i
\(780\) −18914.9 + 5057.72i −0.868285 + 0.232174i
\(781\) 8764.29 24376.0i 0.401551 1.11683i
\(782\) 2122.18 + 3675.72i 0.0970447 + 0.168086i
\(783\) −30727.7 13680.8i −1.40245 0.624410i
\(784\) 5985.25 + 1272.20i 0.272652 + 0.0579539i
\(785\) −8404.42 + 25866.1i −0.382123 + 1.17605i
\(786\) 2646.74 1178.40i 0.120109 0.0534761i
\(787\) −8491.22 + 3780.53i −0.384599 + 0.171234i −0.589923 0.807460i \(-0.700842\pi\)
0.205324 + 0.978694i \(0.434175\pi\)
\(788\) −2727.62 + 8394.76i −0.123309 + 0.379506i
\(789\) 2133.93 + 453.582i 0.0962865 + 0.0204663i
\(790\) 4098.68 + 1824.85i 0.184588 + 0.0821839i
\(791\) 641.724 + 1111.50i 0.0288459 + 0.0499625i
\(792\) 2679.60 7452.72i 0.120221 0.334370i
\(793\) −5614.58 + 20910.5i −0.251425 + 0.936387i
\(794\) 8340.54 6059.76i 0.372789 0.270847i
\(795\) 7157.03 7948.69i 0.319288 0.354605i
\(796\) −9236.65 + 1963.31i −0.411287 + 0.0874218i
\(797\) −1039.28 + 462.719i −0.0461899 + 0.0205651i −0.429702 0.902971i \(-0.641381\pi\)
0.383512 + 0.923536i \(0.374715\pi\)
\(798\) −3404.79 2473.72i −0.151038 0.109735i
\(799\) −23074.5 25626.8i −1.02167 1.13468i
\(800\) 25426.6 + 5404.58i 1.12371 + 0.238851i
\(801\) −19091.7 + 13870.9i −0.842162 + 0.611866i
\(802\) 2066.39 3579.10i 0.0909812 0.157584i
\(803\) −10698.5 19932.4i −0.470162 0.875962i
\(804\) 6575.37 + 11388.9i 0.288427 + 0.499570i
\(805\) 15419.7 11203.0i 0.675120 0.490503i
\(806\) −3940.65 + 7724.05i −0.172213 + 0.337554i
\(807\) −1088.85 + 3351.13i −0.0474960 + 0.146178i
\(808\) −774.978 + 7373.42i −0.0337421 + 0.321035i
\(809\) 3034.56 28872.0i 0.131878 1.25474i −0.705735 0.708476i \(-0.749383\pi\)
0.837614 0.546263i \(-0.183950\pi\)
\(810\) −996.246 1106.44i −0.0432155 0.0479956i
\(811\) 1361.59 + 4190.53i 0.0589541 + 0.181442i 0.976197 0.216887i \(-0.0695903\pi\)
−0.917243 + 0.398329i \(0.869590\pi\)
\(812\) 2437.74 + 23193.5i 0.105354 + 1.00238i
\(813\) 7100.30 12298.1i 0.306296 0.530520i
\(814\) 9151.08 6224.71i 0.394036 0.268029i
\(815\) 8124.81 14072.6i 0.349202 0.604836i
\(816\) 7706.20 + 3431.02i 0.330602 + 0.147193i
\(817\) −13236.9 + 14701.1i −0.566831 + 0.629530i
\(818\) 3899.82 12002.4i 0.166692 0.513025i
\(819\) 1568.01 + 9933.33i 0.0668994 + 0.423808i
\(820\) 32646.2 + 23718.9i 1.39031 + 1.01012i
\(821\) 12223.6 2598.21i 0.519619 0.110449i 0.0593663 0.998236i \(-0.481092\pi\)
0.460253 + 0.887788i \(0.347759\pi\)
\(822\) −923.750 + 1025.93i −0.0391964 + 0.0435320i
\(823\) −3440.36 32732.8i −0.145715 1.38639i −0.785990 0.618239i \(-0.787846\pi\)
0.640275 0.768146i \(-0.278820\pi\)
\(824\) 16670.5 0.704786
\(825\) −19415.7 + 7932.94i −0.819354 + 0.334775i
\(826\) 3677.47 6369.56i 0.154910 0.268312i
\(827\) 13943.9 10130.9i 0.586310 0.425979i −0.254684 0.967024i \(-0.581971\pi\)
0.840993 + 0.541046i \(0.181971\pi\)
\(828\) −8260.84 1755.90i −0.346720 0.0736976i
\(829\) −34845.5 + 7406.64i −1.45987 + 0.310306i −0.868338 0.495973i \(-0.834811\pi\)
−0.591536 + 0.806279i \(0.701478\pi\)
\(830\) −2326.76 + 22137.7i −0.0973049 + 0.925794i
\(831\) −5397.18 3921.28i −0.225302 0.163692i
\(832\) 487.957 9219.33i 0.0203328 0.384162i
\(833\) −2488.34 7658.34i −0.103501 0.318542i
\(834\) 2210.05 + 983.978i 0.0917599 + 0.0408542i
\(835\) −26478.6 45862.3i −1.09740 1.90076i
\(836\) 22783.3 + 5585.93i 0.942556 + 0.231093i
\(837\) 28250.7 1.16665
\(838\) −893.397 8500.10i −0.0368280 0.350395i
\(839\) 8598.16 + 1827.59i 0.353804 + 0.0752033i 0.381385 0.924416i \(-0.375447\pi\)
−0.0275814 + 0.999620i \(0.508781\pi\)
\(840\) −3701.78 + 11392.9i −0.152052 + 0.467967i
\(841\) 26772.3 11919.8i 1.09772 0.488736i
\(842\) 281.326 2676.63i 0.0115144 0.109552i
\(843\) −7778.34 + 1653.34i −0.317794 + 0.0675492i
\(844\) 1511.15 + 4650.85i 0.0616304 + 0.189679i
\(845\) 15301.5 34272.0i 0.622943 1.39526i
\(846\) −8736.17 −0.355030
\(847\) 13475.6 13218.5i 0.546666 0.536239i
\(848\) 3918.77 + 6787.51i 0.158692 + 0.274863i
\(849\) 2124.10 + 20209.5i 0.0858645 + 0.816946i
\(850\) −2781.80 8561.49i −0.112253 0.345479i
\(851\) −16799.6 18657.8i −0.676712 0.751564i
\(852\) 15860.2 7061.40i 0.637747 0.283943i
\(853\) −8020.61 5827.31i −0.321947 0.233908i 0.415059 0.909794i \(-0.363761\pi\)
−0.737006 + 0.675887i \(0.763761\pi\)
\(854\) 4166.66 + 4627.55i 0.166956 + 0.185423i
\(855\) −15668.7 + 17401.8i −0.626734 + 0.696059i
\(856\) 6347.16 + 2825.94i 0.253436 + 0.112837i
\(857\) −12603.2 −0.502353 −0.251176 0.967941i \(-0.580817\pi\)
−0.251176 + 0.967941i \(0.580817\pi\)
\(858\) −2900.79 4790.82i −0.115421 0.190625i
\(859\) 18001.8 0.715035 0.357517 0.933906i \(-0.383623\pi\)
0.357517 + 0.933906i \(0.383623\pi\)
\(860\) 24180.7 + 10766.0i 0.958786 + 0.426879i
\(861\) −10883.5 + 12087.3i −0.430787 + 0.478438i
\(862\) 5595.53 + 6214.47i 0.221096 + 0.245552i
\(863\) −3848.25 2795.91i −0.151791 0.110283i 0.509297 0.860591i \(-0.329905\pi\)
−0.661089 + 0.750308i \(0.729905\pi\)
\(864\) 20659.5 9198.20i 0.813484 0.362187i
\(865\) 22517.7 + 25008.5i 0.885117 + 0.983022i
\(866\) −486.326 1496.76i −0.0190832 0.0587320i
\(867\) 609.104 + 5795.24i 0.0238596 + 0.227009i
\(868\) −9793.82 16963.4i −0.382977 0.663336i
\(869\) 1363.79 9987.20i 0.0532374 0.389865i
\(870\) 12965.1 0.505239
\(871\) −24896.8 3956.50i −0.968539 0.153916i
\(872\) 6587.27 + 20273.5i 0.255818 + 0.787326i
\(873\) 5344.05 1135.91i 0.207181 0.0440376i
\(874\) −708.202 + 6738.09i −0.0274088 + 0.260777i
\(875\) −9262.92 + 4124.12i −0.357879 + 0.159338i
\(876\) 4685.22 14419.6i 0.180706 0.556157i
\(877\) 11029.2 + 2344.34i 0.424665 + 0.0902653i 0.415286 0.909691i \(-0.363681\pi\)
0.00937849 + 0.999956i \(0.497015\pi\)
\(878\) 18.5412 + 176.408i 0.000712682 + 0.00678071i
\(879\) 20230.6 0.776295
\(880\) −1980.12 26809.4i −0.0758520 1.02698i
\(881\) 8321.38 + 14413.1i 0.318223 + 0.551178i 0.980117 0.198419i \(-0.0635806\pi\)
−0.661894 + 0.749597i \(0.730247\pi\)
\(882\) −1863.62 829.739i −0.0711468 0.0316766i
\(883\) 10430.1 + 32100.7i 0.397511 + 1.22341i 0.926989 + 0.375089i \(0.122388\pi\)
−0.529478 + 0.848324i \(0.677612\pi\)
\(884\) −16826.9 + 8562.73i −0.640213 + 0.325787i
\(885\) 25981.7 + 18876.8i 0.986854 + 0.716991i
\(886\) 75.0951 714.482i 0.00284748 0.0270920i
\(887\) −45220.3 + 9611.88i −1.71178 + 0.363850i −0.956541 0.291598i \(-0.905813\pi\)
−0.755240 + 0.655448i \(0.772480\pi\)
\(888\) 15434.8 + 3280.78i 0.583287 + 0.123982i
\(889\) 3734.61 2713.35i 0.140894 0.102365i
\(890\) 12665.5 21937.3i 0.477021 0.826224i
\(891\) −1761.47 + 2843.64i −0.0662307 + 0.106920i
\(892\) −16966.2 −0.636851
\(893\) −5753.95 54745.2i −0.215620 2.05149i
\(894\) 4693.58 5212.75i 0.175589 0.195012i
\(895\) 22164.0 4711.10i 0.827777 0.175949i
\(896\) −16448.5 11950.5i −0.613287 0.445579i
\(897\) −9877.71 + 7990.34i −0.367678 + 0.297424i
\(898\) −1318.37 + 4057.52i −0.0489916 + 0.150781i
\(899\) −30176.8 + 33514.8i −1.11953 + 1.24336i
\(900\) 16363.7 + 7285.59i 0.606063 + 0.269837i
\(901\) 5157.03 8932.24i 0.190683 0.330273i
\(902\) −3905.39 + 10862.0i −0.144163 + 0.400959i
\(903\) −5334.46 + 9239.55i −0.196589 + 0.340502i
\(904\) 135.742 + 1291.50i 0.00499415 + 0.0475161i
\(905\) −15764.1 48517.1i −0.579025 1.78206i
\(906\) 3639.59 + 4042.17i 0.133463 + 0.148225i
\(907\) 1465.94 13947.5i 0.0536668 0.510606i −0.934361 0.356328i \(-0.884028\pi\)
0.988028 0.154277i \(-0.0493049\pi\)
\(908\) −746.076 + 7098.44i −0.0272681 + 0.259438i
\(909\) −2415.32 + 7433.60i −0.0881312 + 0.271240i
\(910\) −5874.45 9056.13i −0.213996 0.329899i
\(911\) −21897.6 + 15909.5i −0.796377 + 0.578602i −0.909849 0.414939i \(-0.863803\pi\)
0.113472 + 0.993541i \(0.463803\pi\)
\(912\) 6732.73 + 11661.4i 0.244455 + 0.423408i
\(913\) 49216.1 8876.79i 1.78403 0.321773i
\(914\) 5.77108 9.99581i 0.000208852 0.000361742i
\(915\) −21997.1 + 15981.9i −0.794757 + 0.577425i
\(916\) 38114.0 + 8101.38i 1.37481 + 0.292224i
\(917\) −8394.68 9323.24i −0.302308 0.335748i
\(918\) −6335.89 4603.29i −0.227795 0.165502i
\(919\) 5526.45 2460.53i 0.198369 0.0883194i −0.305148 0.952305i \(-0.598706\pi\)
0.503517 + 0.863986i \(0.332039\pi\)
\(920\) 18863.5 4009.56i 0.675991 0.143686i
\(921\) −3693.65 + 4102.21i −0.132150 + 0.146767i
\(922\) −13211.4 + 9598.64i −0.471902 + 0.342857i
\(923\) −8630.25 + 32141.9i −0.307766 + 1.14622i
\(924\) 12645.3 + 392.059i 0.450215 + 0.0139586i
\(925\) 26624.9 + 46115.7i 0.946402 + 1.63922i
\(926\) −5252.75 2338.67i −0.186410 0.0829952i
\(927\) 17190.6 + 3653.97i 0.609076 + 0.129463i
\(928\) −11155.9 + 34334.4i −0.394624 + 1.21453i
\(929\) 19907.2 8863.25i 0.703050 0.313018i −0.0238942 0.999714i \(-0.507606\pi\)
0.726944 + 0.686696i \(0.240940\pi\)
\(930\) −9948.00 + 4429.14i −0.350761 + 0.156169i
\(931\) 3972.11 12224.9i 0.139829 0.430349i
\(932\) −25624.2 5446.60i −0.900590 0.191426i
\(933\) −8369.29 3726.25i −0.293674 0.130752i
\(934\) −4477.28 7754.88i −0.156854 0.271678i
\(935\) −29251.1 + 19897.0i −1.02311 + 0.695938i
\(936\) −2638.62 + 9827.06i −0.0921430 + 0.343171i
\(937\) −19077.1 + 13860.3i −0.665124 + 0.483241i −0.868389 0.495883i \(-0.834845\pi\)
0.203266 + 0.979124i \(0.434845\pi\)
\(938\) −4851.39 + 5388.01i −0.168874 + 0.187553i
\(939\) 8333.39 1771.32i 0.289616 0.0615599i
\(940\) −67286.0 + 29957.7i −2.33471 + 1.03948i
\(941\) 8989.51 + 6531.26i 0.311424 + 0.226263i 0.732507 0.680759i \(-0.238350\pi\)
−0.421083 + 0.907022i \(0.638350\pi\)
\(942\) −3488.88 3874.79i −0.120673 0.134021i
\(943\) 25612.5 + 5444.10i 0.884472 + 0.188000i
\(944\) −19038.2 + 13832.1i −0.656398 + 0.476901i
\(945\) −17584.3 + 30456.9i −0.605309 + 1.04843i
\(946\) −1024.39 + 7501.72i −0.0352069 + 0.257825i
\(947\) −2527.74 4378.18i −0.0867377 0.150234i 0.819393 0.573233i \(-0.194311\pi\)
−0.906130 + 0.422999i \(0.860978\pi\)
\(948\) 5465.49 3970.91i 0.187248 0.136043i
\(949\) 15816.8 + 24383.4i 0.541028 + 0.834057i
\(950\) 4440.54 13666.6i 0.151653 0.466740i
\(951\) 2888.31 27480.4i 0.0984856 0.937028i
\(952\) −1207.45 + 11488.1i −0.0411069 + 0.391106i
\(953\) 671.545 + 745.826i 0.0228263 + 0.0253512i 0.754450 0.656358i \(-0.227904\pi\)
−0.731624 + 0.681709i \(0.761237\pi\)
\(954\) −807.444 2485.06i −0.0274025 0.0843362i
\(955\) −5144.70 48948.6i −0.174323 1.65858i
\(956\) 11177.1 19359.3i 0.378131 0.654942i
\(957\) −8138.37 27968.4i −0.274897 0.944714i
\(958\) 273.774 474.191i 0.00923303 0.0159921i
\(959\) 5461.18 + 2431.47i 0.183890 + 0.0818732i
\(960\) 7757.90 8616.02i 0.260818 0.289668i
\(961\) 2499.17 7691.67i 0.0838902 0.258188i
\(962\) −11055.0 + 8942.70i −0.370508 + 0.299713i
\(963\) 5925.77 + 4305.33i 0.198292 + 0.144068i
\(964\) −3511.04 + 746.294i −0.117306 + 0.0249342i
\(965\) 35944.0 39919.9i 1.19905 1.33168i
\(966\) 381.946 + 3633.97i 0.0127214 + 0.121036i
\(967\) −1922.76 −0.0639417 −0.0319709 0.999489i \(-0.510178\pi\)
−0.0319709 + 0.999489i \(0.510178\pi\)
\(968\) 17896.0 6672.63i 0.594214 0.221556i
\(969\) 8860.15 15346.2i 0.293735 0.508764i
\(970\) −4744.49 + 3447.07i −0.157048 + 0.114102i
\(971\) 14520.6 + 3086.46i 0.479907 + 0.102007i 0.441512 0.897255i \(-0.354442\pi\)
0.0383946 + 0.999263i \(0.487776\pi\)
\(972\) 25011.8 5316.43i 0.825365 0.175437i
\(973\) 1095.01 10418.4i 0.0360787 0.343266i
\(974\) −5044.83 3665.28i −0.165962 0.120578i
\(975\) 24015.9 12221.0i 0.788845 0.401422i
\(976\) −6156.71 18948.4i −0.201917 0.621438i
\(977\) 35321.2 + 15726.0i 1.15663 + 0.514964i 0.893176 0.449708i \(-0.148472\pi\)
0.263453 + 0.964672i \(0.415139\pi\)
\(978\) 1557.63 + 2697.89i 0.0509278 + 0.0882095i
\(979\) −55273.6 13551.8i −1.80445 0.442408i
\(980\) −17198.9 −0.560613
\(981\) 2349.07 + 22349.9i 0.0764526 + 0.727398i
\(982\) 4250.54 + 903.480i 0.138126 + 0.0293597i
\(983\) −1485.22 + 4571.04i −0.0481904 + 0.148315i −0.972256 0.233919i \(-0.924845\pi\)
0.924066 + 0.382234i \(0.124845\pi\)
\(984\) −15034.5 + 6693.78i −0.487075 + 0.216860i
\(985\) 2221.12 21132.6i 0.0718486 0.683594i
\(986\) 12228.9 2599.34i 0.394978 0.0839551i
\(987\) −9173.99 28234.6i −0.295857 0.910555i
\(988\) −29764.8 4730.10i −0.958445 0.152312i
\(989\) 17175.6 0.552225
\(990\) −1212.58 + 8879.87i −0.0389275 + 0.285071i
\(991\) −283.864 491.666i −0.00909912 0.0157601i 0.861440 0.507859i \(-0.169563\pi\)
−0.870539 + 0.492099i \(0.836230\pi\)
\(992\) −3169.48 30155.6i −0.101443 0.965162i
\(993\) 1130.03 + 3477.87i 0.0361132 + 0.111145i
\(994\) 6404.63 + 7113.06i 0.204369 + 0.226974i
\(995\) 20767.2 9246.13i 0.661671 0.294595i
\(996\) 27116.4 + 19701.2i 0.862667 + 0.626765i
\(997\) 23170.3 + 25733.3i 0.736020 + 0.817433i 0.988667 0.150125i \(-0.0479677\pi\)
−0.252647 + 0.967559i \(0.581301\pi\)
\(998\) 3188.62 3541.32i 0.101136 0.112323i
\(999\) 42320.9 + 18842.5i 1.34032 + 0.596747i
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 143.4.q.a.3.18 320
11.4 even 5 inner 143.4.q.a.81.23 yes 320
13.9 even 3 inner 143.4.q.a.113.23 yes 320
143.48 even 15 inner 143.4.q.a.48.18 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.q.a.3.18 320 1.1 even 1 trivial
143.4.q.a.48.18 yes 320 143.48 even 15 inner
143.4.q.a.81.23 yes 320 11.4 even 5 inner
143.4.q.a.113.23 yes 320 13.9 even 3 inner