Properties

Label 76.4.k.a.3.3
Level $76$
Weight $4$
Character 76.3
Analytic conductor $4.484$
Analytic rank $0$
Dimension $168$
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] = [76,4,Mod(3,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 76.k (of order \(18\), degree \(6\), 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: \(4.48414516044\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(28\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 76.3
Dual form 76.4.k.a.51.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.67496 + 0.919012i) q^{2} +(-7.61194 + 2.77052i) q^{3} +(6.31083 - 4.91664i) q^{4} +(2.53263 - 14.3633i) q^{5} +(17.8155 - 14.4065i) q^{6} +(-10.1706 + 5.87199i) q^{7} +(-12.3628 + 18.9516i) q^{8} +(29.5827 - 24.8228i) q^{9} +O(q^{10})\) \(q+(-2.67496 + 0.919012i) q^{2} +(-7.61194 + 2.77052i) q^{3} +(6.31083 - 4.91664i) q^{4} +(2.53263 - 14.3633i) q^{5} +(17.8155 - 14.4065i) q^{6} +(-10.1706 + 5.87199i) q^{7} +(-12.3628 + 18.9516i) q^{8} +(29.5827 - 24.8228i) q^{9} +(6.42533 + 40.7487i) q^{10} +(28.3521 + 16.3691i) q^{11} +(-34.4160 + 54.9095i) q^{12} +(-17.6504 + 48.4941i) q^{13} +(21.8095 - 25.0543i) q^{14} +(20.5155 + 116.349i) q^{15} +(15.6532 - 62.0562i) q^{16} +(81.6344 + 68.4994i) q^{17} +(-56.3201 + 93.5870i) q^{18} +(20.1743 - 80.3243i) q^{19} +(-54.6361 - 103.096i) q^{20} +(61.1495 - 72.8751i) q^{21} +(-90.8840 - 17.7307i) q^{22} +(37.0419 - 6.53149i) q^{23} +(41.5990 - 178.510i) q^{24} +(-82.4276 - 30.0012i) q^{25} +(2.64748 - 145.941i) q^{26} +(-47.0534 + 81.4990i) q^{27} +(-35.3144 + 87.0623i) q^{28} +(148.555 + 177.041i) q^{29} +(-161.804 - 292.375i) q^{30} +(84.4478 + 146.268i) q^{31} +(15.1587 + 180.384i) q^{32} +(-261.165 - 46.0504i) q^{33} +(-281.321 - 108.210i) q^{34} +(58.5826 + 160.954i) q^{35} +(64.6464 - 302.100i) q^{36} -380.764i q^{37} +(19.8537 + 233.405i) q^{38} -418.035i q^{39} +(240.896 + 225.567i) q^{40} +(12.5475 + 34.4739i) q^{41} +(-96.5994 + 251.135i) q^{42} +(28.2235 + 4.97657i) q^{43} +(259.406 - 36.0945i) q^{44} +(-281.615 - 487.771i) q^{45} +(-93.0832 + 51.5135i) q^{46} +(201.568 + 240.219i) q^{47} +(52.7767 + 515.736i) q^{48} +(-102.539 + 177.603i) q^{49} +(248.062 + 4.50005i) q^{50} +(-811.175 - 295.244i) q^{51} +(127.039 + 392.819i) q^{52} +(404.995 - 71.4115i) q^{53} +(50.9676 - 261.249i) q^{54} +(306.919 - 365.771i) q^{55} +(14.4533 - 265.343i) q^{56} +(68.9748 + 667.318i) q^{57} +(-560.083 - 337.054i) q^{58} +(-417.475 - 350.303i) q^{59} +(701.517 + 633.392i) q^{60} +(55.5403 + 314.985i) q^{61} +(-360.317 - 313.652i) q^{62} +(-155.114 + 426.172i) q^{63} +(-206.324 - 468.588i) q^{64} +(651.832 + 376.335i) q^{65} +(740.927 - 116.831i) q^{66} +(75.4476 - 63.3080i) q^{67} +(851.968 + 30.9209i) q^{68} +(-263.866 + 152.343i) q^{69} +(-304.625 - 376.709i) q^{70} +(-107.761 + 611.141i) q^{71} +(104.707 + 867.518i) q^{72} +(-961.042 + 349.791i) q^{73} +(349.927 + 1018.53i) q^{74} +710.553 q^{75} +(-267.610 - 606.103i) q^{76} -384.476 q^{77} +(384.180 + 1118.23i) q^{78} +(611.831 - 222.688i) q^{79} +(-851.686 - 381.997i) q^{80} +(-48.6844 + 276.103i) q^{81} +(-65.2460 - 80.6852i) q^{82} +(639.853 - 369.419i) q^{83} +(27.6032 - 760.553i) q^{84} +(1190.62 - 999.053i) q^{85} +(-80.0703 + 12.6256i) q^{86} +(-1621.29 - 936.053i) q^{87} +(-660.729 + 334.949i) q^{88} +(120.266 - 330.429i) q^{89} +(1201.58 + 1045.96i) q^{90} +(-105.242 - 596.857i) q^{91} +(201.652 - 223.341i) q^{92} +(-1048.05 - 879.419i) q^{93} +(-759.951 - 457.334i) q^{94} +(-1102.63 - 493.200i) q^{95} +(-615.143 - 1331.07i) q^{96} +(-460.544 + 548.855i) q^{97} +(111.069 - 569.317i) q^{98} +(1245.06 - 219.537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67496 + 0.919012i −0.945742 + 0.324920i
\(3\) −7.61194 + 2.77052i −1.46492 + 0.533187i −0.946716 0.322070i \(-0.895621\pi\)
−0.518204 + 0.855257i \(0.673399\pi\)
\(4\) 6.31083 4.91664i 0.788854 0.614581i
\(5\) 2.53263 14.3633i 0.226525 1.28469i −0.633222 0.773970i \(-0.718268\pi\)
0.859747 0.510719i \(-0.170621\pi\)
\(6\) 17.8155 14.4065i 1.21219 0.980239i
\(7\) −10.1706 + 5.87199i −0.549160 + 0.317058i −0.748783 0.662815i \(-0.769362\pi\)
0.199623 + 0.979873i \(0.436028\pi\)
\(8\) −12.3628 + 18.9516i −0.546363 + 0.837549i
\(9\) 29.5827 24.8228i 1.09566 0.919364i
\(10\) 6.42533 + 40.7487i 0.203187 + 1.28859i
\(11\) 28.3521 + 16.3691i 0.777133 + 0.448678i 0.835413 0.549622i \(-0.185228\pi\)
−0.0582801 + 0.998300i \(0.518562\pi\)
\(12\) −34.4160 + 54.9095i −0.827921 + 1.32092i
\(13\) −17.6504 + 48.4941i −0.376565 + 1.03460i 0.596205 + 0.802832i \(0.296674\pi\)
−0.972770 + 0.231772i \(0.925548\pi\)
\(14\) 21.8095 25.0543i 0.416345 0.478288i
\(15\) 20.5155 + 116.349i 0.353138 + 2.00275i
\(16\) 15.6532 62.0562i 0.244582 0.969629i
\(17\) 81.6344 + 68.4994i 1.16466 + 0.977267i 0.999959 0.00907602i \(-0.00288903\pi\)
0.164703 + 0.986343i \(0.447333\pi\)
\(18\) −56.3201 + 93.5870i −0.737487 + 1.22548i
\(19\) 20.1743 80.3243i 0.243594 0.969877i
\(20\) −54.6361 103.096i −0.610850 1.15265i
\(21\) 61.1495 72.8751i 0.635424 0.757269i
\(22\) −90.8840 17.7307i −0.880752 0.171827i
\(23\) 37.0419 6.53149i 0.335816 0.0592135i −0.00319739 0.999995i \(-0.501018\pi\)
0.339014 + 0.940781i \(0.389907\pi\)
\(24\) 41.5990 178.510i 0.353807 1.51825i
\(25\) −82.4276 30.0012i −0.659421 0.240010i
\(26\) 2.64748 145.941i 0.0199698 1.10082i
\(27\) −47.0534 + 81.4990i −0.335387 + 0.580907i
\(28\) −35.3144 + 87.0623i −0.238350 + 0.587616i
\(29\) 148.555 + 177.041i 0.951242 + 1.13365i 0.990923 + 0.134434i \(0.0429215\pi\)
−0.0396805 + 0.999212i \(0.512634\pi\)
\(30\) −161.804 292.375i −0.984710 1.77934i
\(31\) 84.4478 + 146.268i 0.489267 + 0.847435i 0.999924 0.0123495i \(-0.00393107\pi\)
−0.510657 + 0.859785i \(0.670598\pi\)
\(32\) 15.1587 + 180.384i 0.0837407 + 0.996488i
\(33\) −261.165 46.0504i −1.37767 0.242920i
\(34\) −281.321 108.210i −1.41900 0.545820i
\(35\) 58.5826 + 160.954i 0.282922 + 0.777322i
\(36\) 64.6464 302.100i 0.299289 1.39861i
\(37\) 380.764i 1.69182i −0.533329 0.845908i \(-0.679059\pi\)
0.533329 0.845908i \(-0.320941\pi\)
\(38\) 19.8537 + 233.405i 0.0847550 + 0.996402i
\(39\) 418.035i 1.71639i
\(40\) 240.896 + 225.567i 0.952225 + 0.891633i
\(41\) 12.5475 + 34.4739i 0.0477948 + 0.131315i 0.961293 0.275527i \(-0.0888522\pi\)
−0.913499 + 0.406842i \(0.866630\pi\)
\(42\) −96.5994 + 251.135i −0.354895 + 0.922643i
\(43\) 28.2235 + 4.97657i 0.100094 + 0.0176493i 0.223471 0.974711i \(-0.428261\pi\)
−0.123377 + 0.992360i \(0.539372\pi\)
\(44\) 259.406 36.0945i 0.888793 0.123669i
\(45\) −281.615 487.771i −0.932904 1.61584i
\(46\) −93.0832 + 51.5135i −0.298356 + 0.165114i
\(47\) 201.568 + 240.219i 0.625568 + 0.745523i 0.982017 0.188792i \(-0.0604570\pi\)
−0.356449 + 0.934315i \(0.616013\pi\)
\(48\) 52.7767 + 515.736i 0.158701 + 1.55084i
\(49\) −102.539 + 177.603i −0.298949 + 0.517794i
\(50\) 248.062 + 4.50005i 0.701626 + 0.0127281i
\(51\) −811.175 295.244i −2.22720 0.810635i
\(52\) 127.039 + 392.819i 0.338792 + 1.04758i
\(53\) 404.995 71.4115i 1.04963 0.185078i 0.377878 0.925855i \(-0.376654\pi\)
0.671750 + 0.740778i \(0.265543\pi\)
\(54\) 50.9676 261.249i 0.128441 0.658361i
\(55\) 306.919 365.771i 0.752452 0.896738i
\(56\) 14.4533 265.343i 0.0344893 0.633177i
\(57\) 68.9748 + 667.318i 0.160280 + 1.55067i
\(58\) −560.083 337.054i −1.26797 0.763059i
\(59\) −417.475 350.303i −0.921197 0.772976i 0.0530186 0.998594i \(-0.483116\pi\)
−0.974216 + 0.225617i \(0.927560\pi\)
\(60\) 701.517 + 633.392i 1.50942 + 1.36284i
\(61\) 55.5403 + 314.985i 0.116577 + 0.661142i 0.985957 + 0.166998i \(0.0534073\pi\)
−0.869380 + 0.494144i \(0.835482\pi\)
\(62\) −360.317 313.652i −0.738069 0.642482i
\(63\) −155.114 + 426.172i −0.310199 + 0.852264i
\(64\) −206.324 468.588i −0.402976 0.915211i
\(65\) 651.832 + 376.335i 1.24384 + 0.718133i
\(66\) 740.927 116.831i 1.38185 0.217892i
\(67\) 75.4476 63.3080i 0.137573 0.115437i −0.571404 0.820669i \(-0.693601\pi\)
0.708977 + 0.705231i \(0.249157\pi\)
\(68\) 851.968 + 30.9209i 1.51936 + 0.0551429i
\(69\) −263.866 + 152.343i −0.460372 + 0.265796i
\(70\) −304.625 376.709i −0.520139 0.643219i
\(71\) −107.761 + 611.141i −0.180124 + 1.02154i 0.751937 + 0.659235i \(0.229120\pi\)
−0.932061 + 0.362301i \(0.881991\pi\)
\(72\) 104.707 + 867.518i 0.171387 + 1.41997i
\(73\) −961.042 + 349.791i −1.54084 + 0.560821i −0.966247 0.257617i \(-0.917063\pi\)
−0.574595 + 0.818438i \(0.694841\pi\)
\(74\) 349.927 + 1018.53i 0.549705 + 1.60002i
\(75\) 710.553 1.09397
\(76\) −267.610 606.103i −0.403907 0.914800i
\(77\) −384.476 −0.569028
\(78\) 384.180 + 1118.23i 0.557689 + 1.62326i
\(79\) 611.831 222.688i 0.871346 0.317144i 0.132634 0.991165i \(-0.457656\pi\)
0.738712 + 0.674021i \(0.235434\pi\)
\(80\) −851.686 381.997i −1.19027 0.533857i
\(81\) −48.6844 + 276.103i −0.0667825 + 0.378742i
\(82\) −65.2460 80.6852i −0.0878685 0.108661i
\(83\) 639.853 369.419i 0.846180 0.488542i −0.0131801 0.999913i \(-0.504195\pi\)
0.859360 + 0.511371i \(0.170862\pi\)
\(84\) 27.6032 760.553i 0.0358542 0.987894i
\(85\) 1190.62 999.053i 1.51931 1.27485i
\(86\) −80.0703 + 12.6256i −0.100398 + 0.0158309i
\(87\) −1621.29 936.053i −1.99794 1.15351i
\(88\) −660.729 + 334.949i −0.800386 + 0.405746i
\(89\) 120.266 330.429i 0.143238 0.393543i −0.847241 0.531209i \(-0.821738\pi\)
0.990479 + 0.137666i \(0.0439600\pi\)
\(90\) 1201.58 + 1045.96i 1.40730 + 1.22504i
\(91\) −105.242 596.857i −0.121235 0.687556i
\(92\) 201.652 223.341i 0.228519 0.253097i
\(93\) −1048.05 879.419i −1.16858 0.980553i
\(94\) −759.951 457.334i −0.833861 0.501813i
\(95\) −1102.63 493.200i −1.19081 0.532645i
\(96\) −615.143 1331.07i −0.653988 1.41512i
\(97\) −460.544 + 548.855i −0.482074 + 0.574513i −0.951183 0.308627i \(-0.900131\pi\)
0.469109 + 0.883140i \(0.344575\pi\)
\(98\) 111.069 569.317i 0.114487 0.586834i
\(99\) 1245.06 219.537i 1.26397 0.222872i
\(100\) −667.692 + 215.935i −0.667692 + 0.215935i
\(101\) 616.659 + 224.445i 0.607523 + 0.221120i 0.627419 0.778682i \(-0.284111\pi\)
−0.0198959 + 0.999802i \(0.506333\pi\)
\(102\) 2441.20 + 44.2852i 2.36975 + 0.0429891i
\(103\) −637.228 + 1103.71i −0.609592 + 1.05584i 0.381716 + 0.924280i \(0.375333\pi\)
−0.991308 + 0.131564i \(0.958000\pi\)
\(104\) −700.831 934.025i −0.660790 0.880660i
\(105\) −891.856 1062.87i −0.828916 0.987864i
\(106\) −1017.72 + 563.218i −0.932542 + 0.516081i
\(107\) 7.84900 + 13.5949i 0.00709151 + 0.0122828i 0.869549 0.493846i \(-0.164409\pi\)
−0.862458 + 0.506129i \(0.831076\pi\)
\(108\) 103.755 + 745.671i 0.0924428 + 0.664373i
\(109\) 364.022 + 64.1869i 0.319881 + 0.0564036i 0.331283 0.943531i \(-0.392518\pi\)
−0.0114025 + 0.999935i \(0.503630\pi\)
\(110\) −484.847 + 1260.49i −0.420258 + 1.09257i
\(111\) 1054.91 + 2898.35i 0.902054 + 2.47837i
\(112\) 205.191 + 723.064i 0.173114 + 0.610028i
\(113\) 1079.64i 0.898793i −0.893333 0.449396i \(-0.851639\pi\)
0.893333 0.449396i \(-0.148361\pi\)
\(114\) −797.778 1721.66i −0.655428 1.41446i
\(115\) 548.585i 0.444833i
\(116\) 1807.96 + 386.885i 1.44711 + 0.309667i
\(117\) 681.614 + 1872.72i 0.538592 + 1.47977i
\(118\) 1438.66 + 553.383i 1.12237 + 0.431721i
\(119\) −1232.50 217.323i −0.949436 0.167411i
\(120\) −2458.63 1049.60i −1.87034 0.798456i
\(121\) −129.607 224.487i −0.0973760 0.168660i
\(122\) −438.043 791.530i −0.325070 0.587391i
\(123\) −191.022 227.651i −0.140031 0.166883i
\(124\) 1252.08 + 507.872i 0.906777 + 0.367809i
\(125\) 271.879 470.908i 0.194541 0.336954i
\(126\) 23.2664 1282.55i 0.0164503 0.906812i
\(127\) 1230.15 + 447.738i 0.859513 + 0.312837i 0.733913 0.679244i \(-0.237692\pi\)
0.125600 + 0.992081i \(0.459914\pi\)
\(128\) 982.545 + 1063.84i 0.678481 + 0.734618i
\(129\) −228.623 + 40.3125i −0.156040 + 0.0275141i
\(130\) −2089.48 407.641i −1.40969 0.275019i
\(131\) 1341.25 1598.44i 0.894544 1.06608i −0.102905 0.994691i \(-0.532814\pi\)
0.997449 0.0713850i \(-0.0227419\pi\)
\(132\) −1874.58 + 993.439i −1.23607 + 0.655059i
\(133\) 266.480 + 935.409i 0.173735 + 0.609852i
\(134\) −143.638 + 238.684i −0.0926006 + 0.153874i
\(135\) 1051.42 + 882.248i 0.670311 + 0.562458i
\(136\) −2307.40 + 700.257i −1.45484 + 0.441519i
\(137\) 131.120 + 743.616i 0.0817686 + 0.463733i 0.998007 + 0.0630999i \(0.0200987\pi\)
−0.916239 + 0.400633i \(0.868790\pi\)
\(138\) 565.825 650.007i 0.349031 0.400958i
\(139\) −1050.78 + 2887.00i −0.641195 + 1.76167i 0.00674491 + 0.999977i \(0.497853\pi\)
−0.647940 + 0.761691i \(0.724369\pi\)
\(140\) 1161.06 + 727.727i 0.700911 + 0.439315i
\(141\) −2199.86 1270.09i −1.31391 0.758587i
\(142\) −273.391 1733.81i −0.161566 1.02464i
\(143\) −1294.23 + 1085.99i −0.756845 + 0.635068i
\(144\) −1077.35 2224.35i −0.623465 1.28724i
\(145\) 2919.13 1685.36i 1.67186 0.965251i
\(146\) 2249.29 1818.89i 1.27502 1.03104i
\(147\) 288.470 1635.99i 0.161854 0.917922i
\(148\) −1872.08 2402.94i −1.03976 1.33460i
\(149\) 101.722 37.0239i 0.0559290 0.0203565i −0.313904 0.949455i \(-0.601637\pi\)
0.369833 + 0.929098i \(0.379415\pi\)
\(150\) −1900.70 + 653.007i −1.03461 + 0.355452i
\(151\) 2935.07 1.58181 0.790903 0.611941i \(-0.209611\pi\)
0.790903 + 0.611941i \(0.209611\pi\)
\(152\) 1272.86 + 1375.37i 0.679228 + 0.733927i
\(153\) 4115.31 2.17453
\(154\) 1028.46 353.338i 0.538153 0.184888i
\(155\) 2314.76 842.504i 1.19952 0.436590i
\(156\) −2055.33 2638.15i −1.05486 1.35398i
\(157\) −92.0804 + 522.214i −0.0468077 + 0.265460i −0.999226 0.0393339i \(-0.987476\pi\)
0.952418 + 0.304794i \(0.0985875\pi\)
\(158\) −1431.97 + 1157.96i −0.721022 + 0.583054i
\(159\) −2884.95 + 1665.63i −1.43894 + 0.830772i
\(160\) 2629.29 + 239.117i 1.29915 + 0.118149i
\(161\) −338.386 + 283.939i −0.165643 + 0.138991i
\(162\) −123.513 783.307i −0.0599020 0.379891i
\(163\) −917.706 529.838i −0.440983 0.254602i 0.263031 0.964787i \(-0.415278\pi\)
−0.704015 + 0.710185i \(0.748611\pi\)
\(164\) 248.681 + 155.868i 0.118407 + 0.0742148i
\(165\) −1322.87 + 3634.55i −0.624153 + 1.71485i
\(166\) −1372.08 + 1576.21i −0.641530 + 0.736975i
\(167\) 481.871 + 2732.83i 0.223283 + 1.26630i 0.865940 + 0.500148i \(0.166721\pi\)
−0.642656 + 0.766155i \(0.722168\pi\)
\(168\) 625.120 + 2059.82i 0.287078 + 0.945942i
\(169\) −357.142 299.678i −0.162559 0.136403i
\(170\) −2266.73 + 3766.63i −1.02265 + 1.69934i
\(171\) −1397.07 2876.99i −0.624775 1.28660i
\(172\) 202.582 107.359i 0.0898065 0.0475932i
\(173\) −554.593 + 660.938i −0.243728 + 0.290464i −0.874015 0.485898i \(-0.838493\pi\)
0.630287 + 0.776362i \(0.282937\pi\)
\(174\) 5197.13 + 1013.92i 2.26433 + 0.441753i
\(175\) 1014.50 178.885i 0.438225 0.0772708i
\(176\) 1459.60 1503.19i 0.625124 0.643792i
\(177\) 4148.32 + 1509.87i 1.76162 + 0.641178i
\(178\) −18.0394 + 994.410i −0.00759612 + 0.418731i
\(179\) 108.039 187.128i 0.0451128 0.0781376i −0.842587 0.538560i \(-0.818969\pi\)
0.887700 + 0.460422i \(0.152302\pi\)
\(180\) −4175.42 1693.64i −1.72899 0.701315i
\(181\) −594.801 708.856i −0.244261 0.291099i 0.629960 0.776628i \(-0.283071\pi\)
−0.874220 + 0.485529i \(0.838627\pi\)
\(182\) 830.037 + 1499.85i 0.338057 + 0.610859i
\(183\) −1295.44 2243.77i −0.523288 0.906362i
\(184\) −334.159 + 782.750i −0.133883 + 0.313615i
\(185\) −5469.01 964.334i −2.17346 0.383239i
\(186\) 3611.69 + 1389.24i 1.42377 + 0.547656i
\(187\) 1193.23 + 3278.38i 0.466619 + 1.28202i
\(188\) 2453.13 + 524.946i 0.951666 + 0.203647i
\(189\) 1105.19i 0.425348i
\(190\) 3402.74 + 305.965i 1.29927 + 0.116827i
\(191\) 942.661i 0.357113i 0.983930 + 0.178556i \(0.0571427\pi\)
−0.983930 + 0.178556i \(0.942857\pi\)
\(192\) 2868.76 + 2995.24i 1.07831 + 1.12585i
\(193\) −1540.38 4232.16i −0.574503 1.57843i −0.797310 0.603570i \(-0.793744\pi\)
0.222807 0.974863i \(-0.428478\pi\)
\(194\) 727.533 1891.41i 0.269246 0.699976i
\(195\) −6004.35 1058.73i −2.20503 0.388806i
\(196\) 226.104 + 1624.98i 0.0823994 + 0.592192i
\(197\) 2085.29 + 3611.83i 0.754167 + 1.30626i 0.945787 + 0.324787i \(0.105293\pi\)
−0.191620 + 0.981469i \(0.561374\pi\)
\(198\) −3128.72 + 1731.48i −1.12297 + 0.621468i
\(199\) 147.987 + 176.364i 0.0527161 + 0.0628245i 0.791758 0.610835i \(-0.209166\pi\)
−0.739042 + 0.673659i \(0.764722\pi\)
\(200\) 1587.60 1191.23i 0.561303 0.421165i
\(201\) −398.907 + 690.926i −0.139984 + 0.242459i
\(202\) −1855.81 33.6658i −0.646406 0.0117263i
\(203\) −2550.48 928.299i −0.881816 0.320955i
\(204\) −6570.80 + 2125.03i −2.25514 + 0.729322i
\(205\) 526.937 92.9131i 0.179526 0.0316553i
\(206\) 690.236 3538.01i 0.233452 1.19662i
\(207\) 933.670 1112.71i 0.313500 0.373615i
\(208\) 2733.08 + 1854.41i 0.911081 + 0.618173i
\(209\) 1886.82 1947.13i 0.624468 0.644428i
\(210\) 3362.47 + 2023.52i 1.10492 + 0.664932i
\(211\) −71.9895 60.4063i −0.0234880 0.0197087i 0.630968 0.775809i \(-0.282658\pi\)
−0.654456 + 0.756100i \(0.727102\pi\)
\(212\) 2204.75 2441.88i 0.714259 0.791081i
\(213\) −872.911 4950.52i −0.280802 1.59251i
\(214\) −33.4896 29.1524i −0.0106977 0.00931223i
\(215\) 142.960 392.778i 0.0453477 0.124592i
\(216\) −962.822 1899.29i −0.303295 0.598288i
\(217\) −1717.77 991.754i −0.537372 0.310252i
\(218\) −1032.73 + 162.843i −0.320851 + 0.0505924i
\(219\) 6346.30 5325.18i 1.95819 1.64311i
\(220\) 138.544 3817.33i 0.0424576 1.16984i
\(221\) −4762.70 + 2749.75i −1.44965 + 0.836959i
\(222\) −5485.48 6783.50i −1.65838 2.05081i
\(223\) 972.046 5512.75i 0.291897 1.65543i −0.387657 0.921804i \(-0.626715\pi\)
0.679554 0.733626i \(-0.262174\pi\)
\(224\) −1213.38 1745.60i −0.361931 0.520681i
\(225\) −3183.15 + 1158.57i −0.943155 + 0.343280i
\(226\) 992.198 + 2887.98i 0.292036 + 0.850025i
\(227\) −6536.88 −1.91131 −0.955656 0.294487i \(-0.904851\pi\)
−0.955656 + 0.294487i \(0.904851\pi\)
\(228\) 3716.25 + 3872.20i 1.07945 + 1.12475i
\(229\) −916.612 −0.264504 −0.132252 0.991216i \(-0.542221\pi\)
−0.132252 + 0.991216i \(0.542221\pi\)
\(230\) 504.156 + 1467.44i 0.144535 + 0.420697i
\(231\) 2926.61 1065.20i 0.833579 0.303398i
\(232\) −5191.76 + 626.633i −1.46921 + 0.177330i
\(233\) 856.300 4856.32i 0.240764 1.36544i −0.589363 0.807868i \(-0.700621\pi\)
0.830128 0.557574i \(-0.188268\pi\)
\(234\) −3544.34 4383.04i −0.990175 1.22448i
\(235\) 3960.83 2286.79i 1.09947 0.634781i
\(236\) −4356.93 158.129i −1.20175 0.0436156i
\(237\) −4040.26 + 3390.18i −1.10735 + 0.929181i
\(238\) 3496.61 551.351i 0.952316 0.150163i
\(239\) −456.109 263.335i −0.123444 0.0712707i 0.437006 0.899458i \(-0.356039\pi\)
−0.560451 + 0.828188i \(0.689372\pi\)
\(240\) 7541.32 + 548.124i 2.02829 + 0.147422i
\(241\) −488.559 + 1342.30i −0.130584 + 0.358778i −0.987703 0.156341i \(-0.950030\pi\)
0.857119 + 0.515119i \(0.172252\pi\)
\(242\) 553.001 + 481.382i 0.146894 + 0.127870i
\(243\) −835.587 4738.85i −0.220588 1.25102i
\(244\) 1899.17 + 1714.74i 0.498287 + 0.449898i
\(245\) 2291.27 + 1922.60i 0.597485 + 0.501350i
\(246\) 720.189 + 433.405i 0.186657 + 0.112329i
\(247\) 3539.17 + 2396.09i 0.911709 + 0.617245i
\(248\) −3816.01 207.859i −0.977085 0.0532220i
\(249\) −3847.04 + 4584.72i −0.979101 + 1.16685i
\(250\) −294.495 + 1509.52i −0.0745020 + 0.381882i
\(251\) −1994.04 + 351.602i −0.501444 + 0.0884181i −0.418648 0.908148i \(-0.637496\pi\)
−0.0827958 + 0.996567i \(0.526385\pi\)
\(252\) 1116.44 + 3452.14i 0.279083 + 0.862955i
\(253\) 1157.13 + 421.161i 0.287542 + 0.104657i
\(254\) −3702.08 67.1587i −0.914524 0.0165902i
\(255\) −6295.07 + 10903.4i −1.54593 + 2.67763i
\(256\) −3605.95 1942.76i −0.880360 0.474307i
\(257\) 3225.67 + 3844.21i 0.782926 + 0.933054i 0.999062 0.0433089i \(-0.0137900\pi\)
−0.216136 + 0.976363i \(0.569346\pi\)
\(258\) 574.511 317.942i 0.138634 0.0767217i
\(259\) 2235.84 + 3872.59i 0.536404 + 0.929078i
\(260\) 5963.91 829.836i 1.42256 0.197939i
\(261\) 8789.33 + 1549.80i 2.08447 + 0.367548i
\(262\) −2118.80 + 5508.38i −0.499618 + 1.29889i
\(263\) 61.7945 + 169.779i 0.0144883 + 0.0398062i 0.946726 0.322040i \(-0.104369\pi\)
−0.932238 + 0.361847i \(0.882146\pi\)
\(264\) 4101.45 4380.17i 0.956163 1.02114i
\(265\) 5997.91i 1.39037i
\(266\) −1572.48 2257.28i −0.362461 0.520312i
\(267\) 2848.40i 0.652882i
\(268\) 164.874 770.475i 0.0375794 0.175613i
\(269\) −1310.44 3600.40i −0.297021 0.816060i −0.994994 0.0999352i \(-0.968136\pi\)
0.697972 0.716125i \(-0.254086\pi\)
\(270\) −3623.31 1393.71i −0.816695 0.314142i
\(271\) −986.505 173.948i −0.221129 0.0389910i 0.0619859 0.998077i \(-0.480257\pi\)
−0.283115 + 0.959086i \(0.591368\pi\)
\(272\) 5528.66 3993.69i 1.23244 0.890268i
\(273\) 2454.70 + 4251.67i 0.544195 + 0.942573i
\(274\) −1034.13 1868.64i −0.228008 0.412003i
\(275\) −1845.90 2199.86i −0.404771 0.482387i
\(276\) −916.196 + 2258.74i −0.199813 + 0.492610i
\(277\) −616.578 + 1067.94i −0.133742 + 0.231648i −0.925116 0.379684i \(-0.876033\pi\)
0.791374 + 0.611332i \(0.209366\pi\)
\(278\) 157.612 8688.29i 0.0340035 1.87442i
\(279\) 6128.98 + 2230.77i 1.31517 + 0.478683i
\(280\) −3774.58 879.612i −0.805623 0.187739i
\(281\) −1779.56 + 313.785i −0.377793 + 0.0666151i −0.359320 0.933214i \(-0.616991\pi\)
−0.0184727 + 0.999829i \(0.505880\pi\)
\(282\) 7051.76 + 1375.74i 1.48910 + 0.290511i
\(283\) 1997.64 2380.69i 0.419601 0.500061i −0.514291 0.857616i \(-0.671945\pi\)
0.933892 + 0.357555i \(0.116389\pi\)
\(284\) 2324.70 + 4386.63i 0.485725 + 0.916544i
\(285\) 9759.55 + 699.365i 2.02844 + 0.145357i
\(286\) 2463.98 4094.38i 0.509433 0.846525i
\(287\) −330.046 276.942i −0.0678816 0.0569594i
\(288\) 4926.06 + 4959.95i 1.00789 + 1.01482i
\(289\) 1118.87 + 6345.45i 0.227738 + 1.29156i
\(290\) −6259.68 + 7190.98i −1.26752 + 1.45610i
\(291\) 1985.02 5453.80i 0.399876 1.09865i
\(292\) −4345.18 + 6932.58i −0.870830 + 1.38938i
\(293\) −7291.43 4209.71i −1.45382 0.839365i −0.455127 0.890426i \(-0.650406\pi\)
−0.998696 + 0.0510612i \(0.983740\pi\)
\(294\) 731.853 + 4641.33i 0.145179 + 0.920707i
\(295\) −6088.81 + 5109.12i −1.20171 + 1.00835i
\(296\) 7216.07 + 4707.30i 1.41698 + 0.924345i
\(297\) −2668.12 + 1540.44i −0.521280 + 0.300961i
\(298\) −238.078 + 192.522i −0.0462801 + 0.0374244i
\(299\) −337.067 + 1911.60i −0.0651942 + 0.369735i
\(300\) 4484.18 3493.54i 0.862982 0.672332i
\(301\) −316.272 + 115.114i −0.0605635 + 0.0220433i
\(302\) −7851.20 + 2697.37i −1.49598 + 0.513960i
\(303\) −5315.80 −1.00787
\(304\) −4668.83 2509.27i −0.880842 0.473410i
\(305\) 4664.87 0.875770
\(306\) −11008.3 + 3782.02i −2.05655 + 0.706549i
\(307\) −5840.57 + 2125.79i −1.08579 + 0.395197i −0.822061 0.569399i \(-0.807176\pi\)
−0.263733 + 0.964596i \(0.584954\pi\)
\(308\) −2426.36 + 1890.33i −0.448880 + 0.349713i
\(309\) 1792.69 10166.8i 0.330040 1.87175i
\(310\) −5417.62 + 4380.96i −0.992581 + 0.802650i
\(311\) 3157.81 1823.16i 0.575765 0.332418i −0.183684 0.982985i \(-0.558802\pi\)
0.759448 + 0.650568i \(0.225469\pi\)
\(312\) 7922.42 + 5168.08i 1.43756 + 0.937772i
\(313\) 6630.35 5563.52i 1.19735 1.00469i 0.197644 0.980274i \(-0.436671\pi\)
0.999702 0.0244189i \(-0.00777354\pi\)
\(314\) −233.609 1481.52i −0.0419852 0.266265i
\(315\) 5728.38 + 3307.28i 1.02463 + 0.591569i
\(316\) 2766.28 4413.50i 0.492455 0.785693i
\(317\) 290.670 798.611i 0.0515006 0.141497i −0.911275 0.411798i \(-0.864901\pi\)
0.962776 + 0.270301i \(0.0871232\pi\)
\(318\) 6186.40 7106.79i 1.09093 1.25324i
\(319\) 1313.85 + 7451.19i 0.230600 + 1.30780i
\(320\) −7252.99 + 1776.72i −1.26705 + 0.310380i
\(321\) −97.4110 81.7375i −0.0169375 0.0142123i
\(322\) 644.224 1070.51i 0.111494 0.185270i
\(323\) 7149.08 5175.30i 1.23153 0.891522i
\(324\) 1050.26 + 1981.81i 0.180086 + 0.339816i
\(325\) 2909.76 3467.72i 0.496630 0.591860i
\(326\) 2941.76 + 573.912i 0.499781 + 0.0975033i
\(327\) −2948.75 + 519.944i −0.498673 + 0.0879295i
\(328\) −808.457 188.399i −0.136096 0.0317152i
\(329\) −3460.63 1259.57i −0.579911 0.211070i
\(330\) 198.425 10938.0i 0.0330997 1.82460i
\(331\) −2637.94 + 4569.05i −0.438049 + 0.758723i −0.997539 0.0701138i \(-0.977664\pi\)
0.559490 + 0.828837i \(0.310997\pi\)
\(332\) 2221.70 5477.27i 0.367264 0.905434i
\(333\) −9451.64 11264.0i −1.55540 1.85365i
\(334\) −3800.49 6867.36i −0.622615 1.12505i
\(335\) −718.229 1244.01i −0.117137 0.202888i
\(336\) −3565.17 4935.44i −0.578857 0.801340i
\(337\) 4815.66 + 849.130i 0.778414 + 0.137255i 0.548719 0.836007i \(-0.315116\pi\)
0.229695 + 0.973263i \(0.426227\pi\)
\(338\) 1230.75 + 473.409i 0.198059 + 0.0761835i
\(339\) 2991.15 + 8218.12i 0.479224 + 1.31666i
\(340\) 2601.85 12158.7i 0.415015 1.93941i
\(341\) 5529.33i 0.878093i
\(342\) 6381.10 + 6411.92i 1.00892 + 1.01379i
\(343\) 6436.63i 1.01325i
\(344\) −443.235 + 473.356i −0.0694698 + 0.0741908i
\(345\) 1519.87 + 4175.80i 0.237179 + 0.651645i
\(346\) 876.104 2277.66i 0.136126 0.353896i
\(347\) 2366.12 + 417.211i 0.366052 + 0.0645448i 0.353649 0.935378i \(-0.384941\pi\)
0.0124029 + 0.999923i \(0.496052\pi\)
\(348\) −14833.9 + 2064.04i −2.28501 + 0.317943i
\(349\) −2079.57 3601.93i −0.318960 0.552455i 0.661311 0.750111i \(-0.270000\pi\)
−0.980271 + 0.197657i \(0.936667\pi\)
\(350\) −2549.36 + 1410.85i −0.389340 + 0.215466i
\(351\) −3121.71 3720.31i −0.474713 0.565741i
\(352\) −2522.93 + 5362.38i −0.382024 + 0.811976i
\(353\) −3397.45 + 5884.56i −0.512261 + 0.887262i 0.487638 + 0.873046i \(0.337859\pi\)
−0.999899 + 0.0142160i \(0.995475\pi\)
\(354\) −12484.2 226.473i −1.87437 0.0340026i
\(355\) 8505.06 + 3095.59i 1.27155 + 0.462808i
\(356\) −865.620 2676.59i −0.128870 0.398480i
\(357\) 9983.80 1760.41i 1.48011 0.260983i
\(358\) −117.026 + 599.850i −0.0172766 + 0.0885560i
\(359\) −3239.06 + 3860.16i −0.476187 + 0.567497i −0.949649 0.313317i \(-0.898560\pi\)
0.473462 + 0.880814i \(0.343004\pi\)
\(360\) 12725.6 + 693.164i 1.86305 + 0.101480i
\(361\) −6045.00 3240.97i −0.881323 0.472513i
\(362\) 2242.52 + 1349.53i 0.325591 + 0.195939i
\(363\) 1608.51 + 1349.70i 0.232575 + 0.195154i
\(364\) −3598.70 3249.23i −0.518195 0.467873i
\(365\) 2590.17 + 14689.6i 0.371441 + 2.10654i
\(366\) 5527.31 + 4811.47i 0.789391 + 0.687157i
\(367\) 3673.23 10092.1i 0.522456 1.43544i −0.345323 0.938484i \(-0.612231\pi\)
0.867778 0.496951i \(-0.165547\pi\)
\(368\) 174.506 2400.92i 0.0247194 0.340100i
\(369\) 1226.93 + 708.368i 0.173093 + 0.0999354i
\(370\) 15515.6 2446.53i 2.18005 0.343755i
\(371\) −3699.71 + 3104.42i −0.517734 + 0.434430i
\(372\) −10937.9 396.974i −1.52447 0.0553283i
\(373\) 2502.23 1444.66i 0.347347 0.200541i −0.316169 0.948703i \(-0.602397\pi\)
0.663516 + 0.748162i \(0.269063\pi\)
\(374\) −6204.72 7672.94i −0.857856 1.06085i
\(375\) −764.866 + 4337.77i −0.105327 + 0.597337i
\(376\) −7044.47 + 850.250i −0.966199 + 0.116618i
\(377\) −11207.5 + 4079.20i −1.53108 + 0.557267i
\(378\) 1015.68 + 2956.34i 0.138204 + 0.402269i
\(379\) 4731.78 0.641306 0.320653 0.947197i \(-0.396098\pi\)
0.320653 + 0.947197i \(0.396098\pi\)
\(380\) −9383.38 + 2308.71i −1.26673 + 0.311670i
\(381\) −10604.3 −1.42592
\(382\) −866.317 2521.58i −0.116033 0.337737i
\(383\) −1772.93 + 645.295i −0.236535 + 0.0860915i −0.457568 0.889175i \(-0.651279\pi\)
0.221033 + 0.975266i \(0.429057\pi\)
\(384\) −10426.5 5375.73i −1.38561 0.714399i
\(385\) −973.736 + 5522.33i −0.128899 + 0.731024i
\(386\) 8009.86 + 9905.23i 1.05620 + 1.30612i
\(387\) 958.460 553.367i 0.125895 0.0726854i
\(388\) −207.892 + 5728.06i −0.0272013 + 0.749480i
\(389\) 505.496 424.161i 0.0658860 0.0552849i −0.609250 0.792978i \(-0.708529\pi\)
0.675136 + 0.737693i \(0.264085\pi\)
\(390\) 17034.4 2686.01i 2.21172 0.348748i
\(391\) 3471.30 + 2004.16i 0.448980 + 0.259219i
\(392\) −2098.19 4138.95i −0.270344 0.533288i
\(393\) −5781.00 + 15883.2i −0.742017 + 2.03867i
\(394\) −8897.40 7745.10i −1.13768 0.990337i
\(395\) −1648.99 9351.88i −0.210050 1.19125i
\(396\) 6777.96 7506.96i 0.860114 0.952624i
\(397\) 34.3737 + 28.8430i 0.00434551 + 0.00364632i 0.644958 0.764218i \(-0.276875\pi\)
−0.640612 + 0.767865i \(0.721319\pi\)
\(398\) −557.939 335.764i −0.0702687 0.0422873i
\(399\) −4620.00 6381.99i −0.579672 0.800750i
\(400\) −3152.02 + 4645.53i −0.394002 + 0.580692i
\(401\) 6334.05 7548.63i 0.788796 0.940051i −0.210499 0.977594i \(-0.567509\pi\)
0.999295 + 0.0375433i \(0.0119532\pi\)
\(402\) 432.090 2214.80i 0.0536086 0.274787i
\(403\) −8583.67 + 1513.53i −1.06100 + 0.187083i
\(404\) 4995.15 1615.45i 0.615144 0.198940i
\(405\) 3842.44 + 1398.54i 0.471438 + 0.171590i
\(406\) 7675.55 + 139.241i 0.938254 + 0.0170207i
\(407\) 6232.75 10795.4i 0.759081 1.31477i
\(408\) 15623.7 11723.0i 1.89581 1.42249i
\(409\) 951.582 + 1134.05i 0.115043 + 0.137103i 0.820493 0.571657i \(-0.193699\pi\)
−0.705449 + 0.708760i \(0.749255\pi\)
\(410\) −1324.15 + 732.800i −0.159500 + 0.0882693i
\(411\) −3058.28 5297.09i −0.367041 0.635733i
\(412\) 1405.12 + 10098.4i 0.168022 + 1.20755i
\(413\) 6302.95 + 1111.38i 0.750963 + 0.132415i
\(414\) −1474.94 + 3834.50i −0.175095 + 0.455206i
\(415\) −3685.55 10126.0i −0.435944 1.19775i
\(416\) −9015.10 2448.74i −1.06250 0.288604i
\(417\) 24886.9i 2.92258i
\(418\) −3257.73 + 6942.49i −0.381198 + 0.812365i
\(419\) 939.736i 0.109568i 0.998498 + 0.0547841i \(0.0174471\pi\)
−0.998498 + 0.0547841i \(0.982553\pi\)
\(420\) −10854.1 2322.67i −1.26102 0.269845i
\(421\) 2622.69 + 7205.77i 0.303615 + 0.834175i 0.993865 + 0.110604i \(0.0352785\pi\)
−0.690250 + 0.723571i \(0.742499\pi\)
\(422\) 248.083 + 95.4254i 0.0286173 + 0.0110077i
\(423\) 11925.9 + 2102.85i 1.37081 + 0.241712i
\(424\) −3653.50 + 8558.13i −0.418466 + 0.980235i
\(425\) −4673.86 8095.37i −0.533449 0.923960i
\(426\) 6884.60 + 12440.2i 0.783004 + 1.41486i
\(427\) −2414.47 2877.45i −0.273640 0.326111i
\(428\) 116.375 + 47.2042i 0.0131430 + 0.00533107i
\(429\) 6842.85 11852.2i 0.770107 1.33386i
\(430\) −21.4433 + 1182.05i −0.00240485 + 0.132566i
\(431\) 1447.02 + 526.674i 0.161719 + 0.0588607i 0.421611 0.906777i \(-0.361465\pi\)
−0.259892 + 0.965638i \(0.583687\pi\)
\(432\) 4320.98 + 4195.68i 0.481234 + 0.467280i
\(433\) −7907.30 + 1394.27i −0.877600 + 0.154744i −0.594258 0.804275i \(-0.702554\pi\)
−0.283342 + 0.959019i \(0.591443\pi\)
\(434\) 5506.40 + 1074.25i 0.609022 + 0.118815i
\(435\) −17550.9 + 20916.4i −1.93449 + 2.30543i
\(436\) 2612.87 1384.69i 0.287004 0.152098i
\(437\) 222.656 3107.14i 0.0243732 0.340125i
\(438\) −12082.2 + 20077.0i −1.31806 + 2.19022i
\(439\) 2098.68 + 1761.00i 0.228165 + 0.191453i 0.749702 0.661776i \(-0.230197\pi\)
−0.521537 + 0.853228i \(0.674641\pi\)
\(440\) 3137.57 + 10338.5i 0.339950 + 1.12016i
\(441\) 1375.23 + 7799.31i 0.148497 + 0.842167i
\(442\) 10213.0 11732.4i 1.09905 1.26257i
\(443\) 4691.95 12891.0i 0.503208 1.38255i −0.384917 0.922951i \(-0.625770\pi\)
0.888125 0.459602i \(-0.152008\pi\)
\(444\) 20907.6 + 13104.4i 2.23475 + 1.40069i
\(445\) −4441.44 2564.27i −0.473134 0.273164i
\(446\) 2466.10 + 15639.7i 0.261823 + 1.66045i
\(447\) −671.729 + 563.648i −0.0710776 + 0.0596412i
\(448\) 4849.98 + 3554.28i 0.511473 + 0.374831i
\(449\) 2731.78 1577.19i 0.287128 0.165774i −0.349518 0.936930i \(-0.613655\pi\)
0.636646 + 0.771156i \(0.280321\pi\)
\(450\) 7450.05 6024.48i 0.780442 0.631104i
\(451\) −208.559 + 1182.80i −0.0217753 + 0.123494i
\(452\) −5308.18 6813.40i −0.552380 0.709016i
\(453\) −22341.6 + 8131.68i −2.31722 + 0.843399i
\(454\) 17485.9 6007.47i 1.80761 0.621023i
\(455\) −8839.35 −0.910759
\(456\) −13499.4 6942.72i −1.38634 0.712988i
\(457\) 6731.40 0.689019 0.344510 0.938783i \(-0.388045\pi\)
0.344510 + 0.938783i \(0.388045\pi\)
\(458\) 2451.90 842.378i 0.250152 0.0859426i
\(459\) −9423.81 + 3429.99i −0.958313 + 0.348797i
\(460\) −2697.20 3462.03i −0.273386 0.350909i
\(461\) 1197.37 6790.65i 0.120970 0.686057i −0.862650 0.505802i \(-0.831197\pi\)
0.983620 0.180255i \(-0.0576922\pi\)
\(462\) −6849.64 + 5538.96i −0.689771 + 0.557783i
\(463\) −4185.19 + 2416.32i −0.420091 + 0.242540i −0.695116 0.718897i \(-0.744647\pi\)
0.275025 + 0.961437i \(0.411314\pi\)
\(464\) 13311.9 6447.51i 1.33187 0.645083i
\(465\) −15285.6 + 12826.2i −1.52442 + 1.27914i
\(466\) 2172.45 + 13777.4i 0.215958 + 1.36958i
\(467\) 2409.77 + 1391.28i 0.238781 + 0.137860i 0.614617 0.788826i \(-0.289311\pi\)
−0.375835 + 0.926687i \(0.622644\pi\)
\(468\) 13509.1 + 8467.17i 1.33431 + 0.836314i
\(469\) −395.602 + 1086.91i −0.0389493 + 0.107012i
\(470\) −8493.49 + 9757.12i −0.833564 + 0.957580i
\(471\) −745.894 4230.17i −0.0729702 0.413835i
\(472\) 11799.9 3581.09i 1.15071 0.349222i
\(473\) 718.733 + 603.088i 0.0698676 + 0.0586259i
\(474\) 7691.92 12781.7i 0.745362 1.23857i
\(475\) −4072.74 + 6015.69i −0.393411 + 0.581092i
\(476\) −8846.59 + 4688.27i −0.851854 + 0.451442i
\(477\) 10208.2 12165.7i 0.979877 1.16777i
\(478\) 1462.08 + 285.240i 0.139904 + 0.0272941i
\(479\) 5632.43 993.149i 0.537270 0.0947351i 0.101572 0.994828i \(-0.467613\pi\)
0.435698 + 0.900093i \(0.356502\pi\)
\(480\) −20676.5 + 5464.35i −1.96614 + 0.519609i
\(481\) 18464.8 + 6720.64i 1.75036 + 0.637079i
\(482\) 73.2816 4039.60i 0.00692507 0.381740i
\(483\) 1789.11 3098.83i 0.168545 0.291929i
\(484\) −1921.65 779.464i −0.180471 0.0732029i
\(485\) 6716.96 + 8004.96i 0.628869 + 0.749457i
\(486\) 6590.22 + 11908.3i 0.615100 + 1.11147i
\(487\) −2854.16 4943.55i −0.265573 0.459987i 0.702140 0.712039i \(-0.252228\pi\)
−0.967714 + 0.252052i \(0.918895\pi\)
\(488\) −6656.09 2841.51i −0.617432 0.263584i
\(489\) 8453.45 + 1490.57i 0.781755 + 0.137845i
\(490\) −7895.96 3037.19i −0.727965 0.280012i
\(491\) 2260.87 + 6211.70i 0.207804 + 0.570937i 0.999184 0.0403876i \(-0.0128593\pi\)
−0.791380 + 0.611324i \(0.790637\pi\)
\(492\) −2324.78 497.480i −0.213027 0.0455856i
\(493\) 24628.6i 2.24993i
\(494\) −11669.2 3156.91i −1.06280 0.287522i
\(495\) 18439.1i 1.67429i
\(496\) 10398.7 2950.95i 0.941363 0.267140i
\(497\) −2492.63 6848.43i −0.224969 0.618097i
\(498\) 6077.26 15799.4i 0.546845 1.42167i
\(499\) −5819.06 1026.06i −0.522038 0.0920494i −0.0935812 0.995612i \(-0.529831\pi\)
−0.428457 + 0.903562i \(0.640943\pi\)
\(500\) −599.505 4308.55i −0.0536213 0.385368i
\(501\) −11239.3 19467.1i −1.00227 1.73598i
\(502\) 5010.84 2773.07i 0.445508 0.246550i
\(503\) 4720.62 + 5625.82i 0.418453 + 0.498693i 0.933554 0.358436i \(-0.116690\pi\)
−0.515101 + 0.857130i \(0.672246\pi\)
\(504\) −6158.99 8208.33i −0.544332 0.725452i
\(505\) 4785.54 8288.80i 0.421691 0.730389i
\(506\) −3482.33 63.1722i −0.305945 0.00555009i
\(507\) 3548.81 + 1291.66i 0.310864 + 0.113145i
\(508\) 9964.64 3222.61i 0.870294 0.281457i
\(509\) −633.425 + 111.690i −0.0551592 + 0.00972606i −0.201160 0.979558i \(-0.564471\pi\)
0.146000 + 0.989285i \(0.453360\pi\)
\(510\) 6818.73 34951.4i 0.592036 3.03465i
\(511\) 7720.40 9200.81i 0.668357 0.796517i
\(512\) 11431.2 + 1882.89i 0.986704 + 0.162525i
\(513\) 5597.08 + 5423.72i 0.481710 + 0.466790i
\(514\) −12161.4 7318.67i −1.04361 0.628040i
\(515\) 14239.0 + 11948.0i 1.21834 + 1.02231i
\(516\) −1244.60 + 1378.47i −0.106183 + 0.117604i
\(517\) 1782.70 + 10110.2i 0.151650 + 0.860050i
\(518\) −9539.75 8304.27i −0.809175 0.704380i
\(519\) 2390.39 6567.54i 0.202170 0.555458i
\(520\) −15190.6 + 7700.68i −1.28106 + 0.649418i
\(521\) 7161.13 + 4134.48i 0.602178 + 0.347668i 0.769898 0.638167i \(-0.220307\pi\)
−0.167720 + 0.985835i \(0.553640\pi\)
\(522\) −24935.4 + 3931.86i −2.09079 + 0.329680i
\(523\) −5195.71 + 4359.72i −0.434402 + 0.364507i −0.833610 0.552354i \(-0.813730\pi\)
0.399207 + 0.916861i \(0.369285\pi\)
\(524\) 605.445 16681.9i 0.0504752 1.39075i
\(525\) −7226.75 + 4172.36i −0.600764 + 0.346851i
\(526\) −321.327 397.362i −0.0266360 0.0329388i
\(527\) −3125.42 + 17725.1i −0.258340 + 1.46512i
\(528\) −6945.79 + 15486.1i −0.572494 + 1.27641i
\(529\) −10103.8 + 3677.48i −0.830426 + 0.302250i
\(530\) 5512.15 + 16044.2i 0.451759 + 1.31493i
\(531\) −21045.6 −1.71996
\(532\) 6280.78 + 4593.02i 0.511854 + 0.374310i
\(533\) −1893.25 −0.153857
\(534\) −2617.72 7619.37i −0.212134 0.617458i
\(535\) 215.145 78.3065i 0.0173861 0.00632801i
\(536\) 267.045 + 2212.51i 0.0215197 + 0.178295i
\(537\) −303.941 + 1723.73i −0.0244246 + 0.138519i
\(538\) 6814.18 + 8426.61i 0.546060 + 0.675273i
\(539\) −5814.40 + 3356.95i −0.464646 + 0.268263i
\(540\) 10973.0 + 398.251i 0.874453 + 0.0317370i
\(541\) −3993.09 + 3350.60i −0.317332 + 0.266273i −0.787514 0.616296i \(-0.788632\pi\)
0.470183 + 0.882569i \(0.344188\pi\)
\(542\) 2798.72 441.308i 0.221800 0.0349738i
\(543\) 6491.49 + 3747.87i 0.513033 + 0.296199i
\(544\) −11118.7 + 15763.9i −0.876305 + 1.24241i
\(545\) 1843.87 5065.98i 0.144922 0.398170i
\(546\) −10473.6 9117.14i −0.820929 0.714611i
\(547\) −3169.60 17975.7i −0.247756 1.40509i −0.814004 0.580859i \(-0.802717\pi\)
0.566249 0.824235i \(-0.308394\pi\)
\(548\) 4483.57 + 4048.17i 0.349505 + 0.315564i
\(549\) 9461.84 + 7939.43i 0.735559 + 0.617207i
\(550\) 6959.41 + 4188.13i 0.539546 + 0.324695i
\(551\) 17217.7 8360.92i 1.33121 0.646438i
\(552\) 374.975 6884.04i 0.0289131 0.530805i
\(553\) −4915.06 + 5857.54i −0.377956 + 0.450430i
\(554\) 667.868 3423.35i 0.0512184 0.262535i
\(555\) 44301.5 7811.55i 3.38828 0.597445i
\(556\) 7563.04 + 23385.7i 0.576878 + 1.78377i
\(557\) 3188.14 + 1160.39i 0.242524 + 0.0882714i 0.460422 0.887700i \(-0.347698\pi\)
−0.217899 + 0.975971i \(0.569920\pi\)
\(558\) −18444.9 334.605i −1.39934 0.0253852i
\(559\) −739.491 + 1280.84i −0.0559519 + 0.0969116i
\(560\) 10905.2 1115.96i 0.822911 0.0842107i
\(561\) −18165.6 21648.9i −1.36712 1.62927i
\(562\) 4471.89 2474.80i 0.335650 0.185753i
\(563\) 6233.36 + 10796.5i 0.466616 + 0.808203i 0.999273 0.0381284i \(-0.0121396\pi\)
−0.532657 + 0.846331i \(0.678806\pi\)
\(564\) −20127.5 + 2800.60i −1.50270 + 0.209090i
\(565\) −15507.1 2734.32i −1.15467 0.203599i
\(566\) −3155.71 + 8204.10i −0.234354 + 0.609265i
\(567\) −1126.13 3094.01i −0.0834089 0.229164i
\(568\) −10249.9 9597.63i −0.757173 0.708992i
\(569\) 8757.76i 0.645245i −0.946528 0.322623i \(-0.895436\pi\)
0.946528 0.322623i \(-0.104564\pi\)
\(570\) −26749.1 + 7098.37i −1.96561 + 0.521610i
\(571\) 301.034i 0.0220629i −0.999939 0.0110314i \(-0.996489\pi\)
0.999939 0.0110314i \(-0.00351149\pi\)
\(572\) −2828.25 + 13216.7i −0.206740 + 0.966119i
\(573\) −2611.66 7175.48i −0.190408 0.523142i
\(574\) 1137.37 + 437.492i 0.0827057 + 0.0318128i
\(575\) −3249.23 572.927i −0.235656 0.0415525i
\(576\) −17735.3 8740.56i −1.28293 0.632274i
\(577\) −2301.70 3986.67i −0.166068 0.287638i 0.770966 0.636876i \(-0.219774\pi\)
−0.937034 + 0.349238i \(0.886440\pi\)
\(578\) −8824.49 15945.6i −0.635036 1.14749i
\(579\) 23450.6 + 27947.3i 1.68320 + 2.00596i
\(580\) 10135.8 24988.3i 0.725632 1.78894i
\(581\) −4338.45 + 7514.42i −0.309792 + 0.536576i
\(582\) −297.744 + 16413.0i −0.0212060 + 1.16897i
\(583\) 12651.4 + 4604.72i 0.898741 + 0.327115i
\(584\) 5252.07 22537.6i 0.372144 1.59694i
\(585\) 28624.7 5047.30i 2.02305 0.356718i
\(586\) 23373.1 + 4559.90i 1.64767 + 0.321446i
\(587\) −14796.6 + 17633.9i −1.04041 + 1.23991i −0.0702318 + 0.997531i \(0.522374\pi\)
−0.970180 + 0.242384i \(0.922071\pi\)
\(588\) −6223.12 11742.8i −0.436458 0.823579i
\(589\) 13452.5 3832.37i 0.941091 0.268098i
\(590\) 11592.0 19262.4i 0.808872 1.34410i
\(591\) −25879.8 21715.7i −1.80127 1.51145i
\(592\) −23628.8 5960.18i −1.64043 0.413787i
\(593\) −3804.28 21575.2i −0.263446 1.49407i −0.773425 0.633888i \(-0.781458\pi\)
0.509980 0.860187i \(-0.329653\pi\)
\(594\) 5721.44 6572.66i 0.395208 0.454006i
\(595\) −6242.93 + 17152.3i −0.430143 + 1.18181i
\(596\) 459.919 733.784i 0.0316091 0.0504312i
\(597\) −1615.09 932.470i −0.110722 0.0639254i
\(598\) −855.144 5423.22i −0.0584773 0.370856i
\(599\) −11734.4 + 9846.31i −0.800423 + 0.671635i −0.948301 0.317371i \(-0.897200\pi\)
0.147879 + 0.989006i \(0.452756\pi\)
\(600\) −8784.41 + 13466.1i −0.597704 + 0.916252i
\(601\) −6822.14 + 3938.76i −0.463030 + 0.267330i −0.713317 0.700841i \(-0.752808\pi\)
0.250288 + 0.968172i \(0.419475\pi\)
\(602\) 740.225 598.582i 0.0501151 0.0405256i
\(603\) 660.458 3745.65i 0.0446036 0.252959i
\(604\) 18522.7 14430.7i 1.24781 0.972147i
\(605\) −3552.61 + 1293.04i −0.238734 + 0.0868921i
\(606\) 14219.6 4885.29i 0.953186 0.327477i
\(607\) −11698.8 −0.782270 −0.391135 0.920333i \(-0.627917\pi\)
−0.391135 + 0.920333i \(0.627917\pi\)
\(608\) 14795.0 + 2421.49i 0.986869 + 0.161521i
\(609\) 21986.0 1.46292
\(610\) −12478.4 + 4287.07i −0.828252 + 0.284555i
\(611\) −15207.0 + 5534.89i −1.00689 + 0.366477i
\(612\) 25971.1 20233.5i 1.71539 1.33643i
\(613\) −2078.30 + 11786.6i −0.136936 + 0.776603i 0.836556 + 0.547881i \(0.184566\pi\)
−0.973492 + 0.228721i \(0.926546\pi\)
\(614\) 13669.7 11054.0i 0.898474 0.726550i
\(615\) −3753.59 + 2167.14i −0.246113 + 0.142093i
\(616\) 4753.19 7286.42i 0.310895 0.476588i
\(617\) 10818.6 9077.86i 0.705898 0.592319i −0.217547 0.976050i \(-0.569805\pi\)
0.923445 + 0.383731i \(0.125361\pi\)
\(618\) 4548.08 + 28843.4i 0.296037 + 1.87743i
\(619\) −25062.6 14469.9i −1.62738 0.939571i −0.984869 0.173298i \(-0.944558\pi\)
−0.642515 0.766273i \(-0.722109\pi\)
\(620\) 10465.8 16697.7i 0.677928 1.08161i
\(621\) −1210.64 + 3326.21i −0.0782308 + 0.214937i
\(622\) −6771.50 + 7778.95i −0.436515 + 0.501459i
\(623\) 717.097 + 4066.86i 0.0461154 + 0.261533i
\(624\) −25941.7 6543.60i −1.66426 0.419797i
\(625\) −14474.7 12145.7i −0.926378 0.777323i
\(626\) −12623.0 + 20975.6i −0.805935 + 1.33922i
\(627\) −8967.79 + 20048.9i −0.571194 + 1.27699i
\(628\) 1986.44 + 3748.33i 0.126222 + 0.238176i
\(629\) 26082.1 31083.4i 1.65336 1.97039i
\(630\) −18362.6 3582.40i −1.16125 0.226549i
\(631\) 19107.6 3369.18i 1.20548 0.212559i 0.465417 0.885092i \(-0.345904\pi\)
0.740068 + 0.672532i \(0.234793\pi\)
\(632\) −3343.64 + 14348.2i −0.210447 + 0.903071i
\(633\) 715.337 + 260.361i 0.0449164 + 0.0163482i
\(634\) −43.5993 + 2403.38i −0.00273115 + 0.150553i
\(635\) 9546.49 16535.0i 0.596600 1.03334i
\(636\) −10017.1 + 24695.8i −0.624537 + 1.53970i
\(637\) −6802.86 8107.33i −0.423138 0.504277i
\(638\) −10362.2 18724.2i −0.643016 1.16191i
\(639\) 11982.4 + 20754.1i 0.741810 + 1.28485i
\(640\) 17768.6 11418.2i 1.09745 0.705228i
\(641\) 4887.71 + 861.835i 0.301175 + 0.0531052i 0.322193 0.946674i \(-0.395580\pi\)
−0.0210188 + 0.999779i \(0.506691\pi\)
\(642\) 335.688 + 129.123i 0.0206364 + 0.00793780i
\(643\) −4374.14 12017.9i −0.268273 0.737073i −0.998545 0.0539172i \(-0.982829\pi\)
0.730273 0.683156i \(-0.239393\pi\)
\(644\) −739.467 + 3455.61i −0.0452470 + 0.211444i
\(645\) 3385.88i 0.206696i
\(646\) −14367.3 + 20413.8i −0.875040 + 1.24330i
\(647\) 10768.5i 0.654334i 0.944967 + 0.327167i \(0.106094\pi\)
−0.944967 + 0.327167i \(0.893906\pi\)
\(648\) −4630.71 4336.05i −0.280728 0.262864i
\(649\) −6102.14 16765.5i −0.369076 1.01403i
\(650\) −4596.63 + 11950.1i −0.277376 + 0.721112i
\(651\) 15823.2 + 2790.06i 0.952629 + 0.167974i
\(652\) −8396.51 + 1168.32i −0.504345 + 0.0701760i
\(653\) 14850.6 + 25722.0i 0.889968 + 1.54147i 0.839912 + 0.542723i \(0.182607\pi\)
0.0500561 + 0.998746i \(0.484060\pi\)
\(654\) 7409.95 4100.76i 0.443046 0.245187i
\(655\) −19561.9 23312.9i −1.16694 1.39070i
\(656\) 2335.73 239.022i 0.139017 0.0142260i
\(657\) −19747.4 + 34203.6i −1.17263 + 2.03106i
\(658\) 10414.6 + 188.929i 0.617027 + 0.0111934i
\(659\) −20476.3 7452.75i −1.21038 0.440543i −0.343546 0.939136i \(-0.611628\pi\)
−0.866837 + 0.498592i \(0.833850\pi\)
\(660\) 9521.40 + 29441.1i 0.561546 + 1.73636i
\(661\) −8246.94 + 1454.16i −0.485278 + 0.0855676i −0.410934 0.911665i \(-0.634797\pi\)
−0.0743438 + 0.997233i \(0.523686\pi\)
\(662\) 2857.38 14646.3i 0.167757 0.859887i
\(663\) 28635.2 34126.1i 1.67737 1.99901i
\(664\) −909.285 + 16693.3i −0.0531432 + 0.975638i
\(665\) 14110.4 1458.47i 0.822825 0.0850483i
\(666\) 35634.5 + 21444.7i 2.07329 + 1.24769i
\(667\) 6659.12 + 5587.66i 0.386570 + 0.324371i
\(668\) 16477.4 + 14877.2i 0.954383 + 0.861703i
\(669\) 7874.02 + 44655.8i 0.455048 + 2.58071i
\(670\) 3064.50 + 2667.62i 0.176704 + 0.153819i
\(671\) −3581.32 + 9839.61i −0.206044 + 0.566101i
\(672\) 14072.4 + 9925.67i 0.807820 + 0.569778i
\(673\) −20558.5 11869.5i −1.17752 0.679844i −0.222083 0.975028i \(-0.571286\pi\)
−0.955440 + 0.295184i \(0.904619\pi\)
\(674\) −13662.1 + 2154.26i −0.780775 + 0.123114i
\(675\) 6323.57 5306.11i 0.360584 0.302566i
\(676\) −3727.28 135.276i −0.212066 0.00769663i
\(677\) −19671.6 + 11357.4i −1.11675 + 0.644756i −0.940569 0.339601i \(-0.889708\pi\)
−0.176181 + 0.984358i \(0.556375\pi\)
\(678\) −15553.8 19234.3i −0.881031 1.08951i
\(679\) 1461.13 8286.49i 0.0825818 0.468345i
\(680\) 4214.19 + 34915.3i 0.237657 + 1.96903i
\(681\) 49758.3 18110.5i 2.79992 1.01909i
\(682\) −5081.52 14790.7i −0.285310 0.830449i
\(683\) 25910.8 1.45161 0.725803 0.687902i \(-0.241468\pi\)
0.725803 + 0.687902i \(0.241468\pi\)
\(684\) −22961.8 11287.3i −1.28358 0.630968i
\(685\) 11012.8 0.614276
\(686\) 5915.34 + 17217.7i 0.329226 + 0.958274i
\(687\) 6977.20 2539.49i 0.387477 0.141030i
\(688\) 750.616 1673.55i 0.0415944 0.0927374i
\(689\) −3685.29 + 20900.3i −0.203771 + 1.15564i
\(690\) −7903.19 9773.32i −0.436043 0.539223i
\(691\) −19994.6 + 11543.9i −1.10077 + 0.635529i −0.936423 0.350874i \(-0.885884\pi\)
−0.164345 + 0.986403i \(0.552551\pi\)
\(692\) −250.346 + 6897.81i −0.0137525 + 0.378924i
\(693\) −11373.8 + 9543.79i −0.623458 + 0.523144i
\(694\) −6712.70 + 1058.47i −0.367162 + 0.0578948i
\(695\) 38805.5 + 22404.4i 2.11795 + 1.22280i
\(696\) 37783.3 19153.8i 2.05772 1.04314i
\(697\) −1337.14 + 3673.76i −0.0726653 + 0.199646i
\(698\) 8872.99 + 7723.86i 0.481157 + 0.418843i
\(699\) 6936.42 + 39338.4i 0.375336 + 2.12863i
\(700\) 5522.86 6116.87i 0.298206 0.330280i
\(701\) 1067.29 + 895.561i 0.0575049 + 0.0482523i 0.671087 0.741379i \(-0.265828\pi\)
−0.613582 + 0.789631i \(0.710272\pi\)
\(702\) 11769.5 + 7082.79i 0.632777 + 0.380801i
\(703\) −30584.6 7681.63i −1.64085 0.412117i
\(704\) 1820.65 16662.8i 0.0974692 0.892047i
\(705\) −23814.0 + 28380.5i −1.27218 + 1.51613i
\(706\) 3680.07 18863.3i 0.196177 1.00556i
\(707\) −7589.73 + 1338.27i −0.403736 + 0.0711895i
\(708\) 33602.8 10867.3i 1.78372 0.576862i
\(709\) −7642.38 2781.60i −0.404818 0.147342i 0.131583 0.991305i \(-0.457994\pi\)
−0.536400 + 0.843964i \(0.680216\pi\)
\(710\) −25595.6 464.325i −1.35294 0.0245434i
\(711\) 12571.9 21775.1i 0.663125 1.14857i
\(712\) 4775.32 + 6364.25i 0.251352 + 0.334986i
\(713\) 4083.46 + 4866.48i 0.214483 + 0.255611i
\(714\) −25088.4 + 13884.3i −1.31500 + 0.727739i
\(715\) 12320.5 + 21339.8i 0.644421 + 1.11617i
\(716\) −238.230 1712.12i −0.0124345 0.0893646i
\(717\) 4201.45 + 740.829i 0.218837 + 0.0385868i
\(718\) 5116.82 13302.5i 0.265958 0.691428i
\(719\) −3928.03 10792.2i −0.203743 0.559778i 0.795171 0.606386i \(-0.207381\pi\)
−0.998913 + 0.0466075i \(0.985159\pi\)
\(720\) −34677.4 + 9840.77i −1.79493 + 0.509366i
\(721\) 14967.2i 0.773103i
\(722\) 19148.6 + 3114.04i 0.987033 + 0.160516i
\(723\) 11571.1i 0.595206i
\(724\) −7238.88 1549.05i −0.371590 0.0795165i
\(725\) −6933.61 19049.9i −0.355183 0.975857i
\(726\) −5543.09 2132.15i −0.283366 0.108997i
\(727\) −26113.4 4604.49i −1.33218 0.234899i −0.538184 0.842827i \(-0.680890\pi\)
−0.793992 + 0.607929i \(0.792001\pi\)
\(728\) 12612.5 + 5384.31i 0.642100 + 0.274115i
\(729\) 15704.6 + 27201.2i 0.797877 + 1.38196i
\(730\) −20428.5 36913.7i −1.03575 1.87156i
\(731\) 1963.12 + 2339.55i 0.0993277 + 0.118374i
\(732\) −19207.1 7790.83i −0.969831 0.393385i
\(733\) 386.704 669.791i 0.0194860 0.0337507i −0.856118 0.516780i \(-0.827130\pi\)
0.875604 + 0.483030i \(0.160464\pi\)
\(734\) −550.969 + 30371.8i −0.0277066 + 1.52731i
\(735\) −22767.6 8286.74i −1.14258 0.415866i
\(736\) 1739.68 + 6582.75i 0.0871270 + 0.329678i
\(737\) 3175.39 559.906i 0.158707 0.0279843i
\(738\) −3932.99 767.294i −0.196172 0.0382716i
\(739\) 6042.15 7200.75i 0.300763 0.358435i −0.594404 0.804167i \(-0.702612\pi\)
0.895167 + 0.445731i \(0.147056\pi\)
\(740\) −39255.3 + 20803.4i −1.95007 + 1.03345i
\(741\) −33578.4 8433.56i −1.66469 0.418103i
\(742\) 7043.57 11704.3i 0.348487 0.579081i
\(743\) −28337.9 23778.3i −1.39921 1.17408i −0.961446 0.274993i \(-0.911324\pi\)
−0.437769 0.899088i \(-0.644231\pi\)
\(744\) 29623.2 8990.14i 1.45973 0.443003i
\(745\) −274.159 1554.83i −0.0134824 0.0764626i
\(746\) −5365.71 + 6164.00i −0.263341 + 0.302520i
\(747\) 9758.54 26811.4i 0.477974 1.31322i
\(748\) 23648.9 + 14822.6i 1.15600 + 0.724556i
\(749\) −159.658 92.1785i −0.00778875 0.00449683i
\(750\) −1940.48 12306.3i −0.0944749 0.599149i
\(751\) −18765.1 + 15745.7i −0.911780 + 0.765074i −0.972457 0.233083i \(-0.925118\pi\)
0.0606771 + 0.998157i \(0.480674\pi\)
\(752\) 18062.3 8748.34i 0.875883 0.424228i
\(753\) 14204.4 8200.90i 0.687432 0.396889i
\(754\) 26230.8 21211.6i 1.26694 1.02451i
\(755\) 7433.45 42157.2i 0.358319 2.03213i
\(756\) −5433.83 6974.67i −0.261411 0.335537i
\(757\) 2571.67 936.012i 0.123473 0.0449405i −0.279545 0.960133i \(-0.590184\pi\)
0.403018 + 0.915192i \(0.367961\pi\)
\(758\) −12657.3 + 4348.56i −0.606510 + 0.208373i
\(759\) −9974.84 −0.477027
\(760\) 22978.4 14799.2i 1.09673 0.706345i
\(761\) −24446.6 −1.16450 −0.582252 0.813008i \(-0.697828\pi\)
−0.582252 + 0.813008i \(0.697828\pi\)
\(762\) 28366.1 9745.48i 1.34855 0.463309i
\(763\) −4079.22 + 1484.72i −0.193549 + 0.0704461i
\(764\) 4634.73 + 5948.98i 0.219475 + 0.281710i
\(765\) 10422.6 59109.4i 0.492587 2.79360i
\(766\) 4149.50 3355.49i 0.195728 0.158275i
\(767\) 24356.3 14062.1i 1.14661 0.661998i
\(768\) 32830.8 + 4797.81i 1.54255 + 0.225425i
\(769\) −10141.9 + 8510.06i −0.475587 + 0.399065i −0.848828 0.528670i \(-0.822691\pi\)
0.373241 + 0.927734i \(0.378246\pi\)
\(770\) −2470.39 15666.9i −0.115619 0.733241i
\(771\) −35204.1 20325.1i −1.64442 0.949403i
\(772\) −30529.1 19135.0i −1.42327 0.892075i
\(773\) 1853.69 5092.97i 0.0862518 0.236975i −0.889067 0.457778i \(-0.848646\pi\)
0.975318 + 0.220803i \(0.0708678\pi\)
\(774\) −2055.29 + 2361.07i −0.0954470 + 0.109647i
\(775\) −2572.62 14590.0i −0.119240 0.676245i
\(776\) −4708.06 15513.4i −0.217796 0.717653i
\(777\) −27748.2 23283.5i −1.28116 1.07502i
\(778\) −962.372 + 1599.17i −0.0443480 + 0.0736929i
\(779\) 3022.23 312.382i 0.139002 0.0143675i
\(780\) −43097.9 + 22839.8i −1.97840 + 1.04846i
\(781\) −13059.0 + 15563.2i −0.598322 + 0.713052i
\(782\) −11127.4 2170.87i −0.508844 0.0992714i
\(783\) −21418.7 + 3776.70i −0.977577 + 0.172373i
\(784\) 9416.33 + 9143.28i 0.428951 + 0.416512i
\(785\) 7267.49 + 2645.15i 0.330430 + 0.120267i
\(786\) 867.124 47799.6i 0.0393502 2.16916i
\(787\) 11938.2 20677.6i 0.540726 0.936564i −0.458137 0.888882i \(-0.651483\pi\)
0.998863 0.0476828i \(-0.0151837\pi\)
\(788\) 30918.0 + 12541.0i 1.39773 + 0.566949i
\(789\) −940.753 1121.15i −0.0424483 0.0505879i
\(790\) 13005.5 + 23500.5i 0.585714 + 1.05837i
\(791\) 6339.61 + 10980.5i 0.284969 + 0.493581i
\(792\) −11231.8 + 26309.9i −0.503919 + 1.18040i
\(793\) −16255.2 2866.23i −0.727919 0.128352i
\(794\) −118.455 45.5640i −0.00529449 0.00203653i
\(795\) 16617.3 + 45655.7i 0.741328 + 2.03678i
\(796\) 1801.04 + 385.404i 0.0801960 + 0.0171611i
\(797\) 21112.3i 0.938315i −0.883114 0.469158i \(-0.844558\pi\)
0.883114 0.469158i \(-0.155442\pi\)
\(798\) 18223.4 + 12825.7i 0.808400 + 0.568956i
\(799\) 33417.4i 1.47963i
\(800\) 4162.23 15323.4i 0.183946 0.677203i
\(801\) −4644.38 12760.3i −0.204870 0.562876i
\(802\) −10006.1 + 26013.3i −0.440556 + 1.14534i
\(803\) −32973.3 5814.08i −1.44907 0.255510i
\(804\) 879.607 + 6321.60i 0.0385837 + 0.277296i
\(805\) 3221.29 + 5579.43i 0.141038 + 0.244285i
\(806\) 21570.0 11937.1i 0.942645 0.521672i
\(807\) 19950.0 + 23775.4i 0.870225 + 1.03709i
\(808\) −11877.2 + 8911.88i −0.517127 + 0.388018i
\(809\) −9894.21 + 17137.3i −0.429990 + 0.744764i −0.996872 0.0790347i \(-0.974816\pi\)
0.566882 + 0.823799i \(0.308150\pi\)
\(810\) −11563.7 209.774i −0.501612 0.00909964i
\(811\) 28751.6 + 10464.7i 1.24489 + 0.453103i 0.878672 0.477426i \(-0.158430\pi\)
0.366218 + 0.930529i \(0.380652\pi\)
\(812\) −20659.8 + 6681.46i −0.892876 + 0.288760i
\(813\) 7991.15 1409.06i 0.344726 0.0607844i
\(814\) −6751.22 + 34605.3i −0.290700 + 1.49007i
\(815\) −9934.41 + 11839.4i −0.426978 + 0.508853i
\(816\) −31019.2 + 45717.0i −1.33075 + 1.96129i
\(817\) 969.128 2166.64i 0.0415000 0.0927797i
\(818\) −3587.65 2159.03i −0.153349 0.0922844i
\(819\) −17929.0 15044.2i −0.764946 0.641866i
\(820\) 2868.59 3177.12i 0.122165 0.135305i
\(821\) −6658.47 37762.1i −0.283048 1.60524i −0.712176 0.702001i \(-0.752290\pi\)
0.429128 0.903244i \(-0.358821\pi\)
\(822\) 13048.9 + 11358.9i 0.553688 + 0.481981i
\(823\) −1487.58 + 4087.11i −0.0630060 + 0.173108i −0.967201 0.254012i \(-0.918250\pi\)
0.904195 + 0.427120i \(0.140472\pi\)
\(824\) −13039.2 25721.4i −0.551263 1.08744i
\(825\) 20145.6 + 11631.1i 0.850159 + 0.490840i
\(826\) −17881.5 + 2819.59i −0.753241 + 0.118772i
\(827\) 26225.8 22006.1i 1.10274 0.925305i 0.105129 0.994459i \(-0.466474\pi\)
0.997606 + 0.0691538i \(0.0220299\pi\)
\(828\) 421.463 11612.6i 0.0176894 0.487399i
\(829\) 27764.5 16029.8i 1.16321 0.671578i 0.211137 0.977456i \(-0.432283\pi\)
0.952071 + 0.305878i \(0.0989500\pi\)
\(830\) 19164.6 + 23699.5i 0.801462 + 0.991111i
\(831\) 1734.59 9837.38i 0.0724097 0.410656i
\(832\) 26365.4 1734.71i 1.09863 0.0722839i
\(833\) −20536.5 + 7474.66i −0.854197 + 0.310902i
\(834\) 22871.3 + 66571.4i 0.949604 + 2.76400i
\(835\) 40472.7 1.67739
\(836\) 2334.06 21564.8i 0.0965611 0.892146i
\(837\) −15894.2 −0.656374
\(838\) −863.629 2513.76i −0.0356009 0.103623i
\(839\) 19349.4 7042.61i 0.796204 0.289795i 0.0882917 0.996095i \(-0.471859\pi\)
0.707913 + 0.706300i \(0.249637\pi\)
\(840\) 31168.9 3762.01i 1.28027 0.154526i
\(841\) −5039.84 + 28582.3i −0.206644 + 1.17194i
\(842\) −13637.8 16864.9i −0.558181 0.690264i
\(843\) 12676.6 7318.83i 0.517918 0.299020i
\(844\) −751.310 27.2677i −0.0306412 0.00111208i
\(845\) −5208.86 + 4370.76i −0.212060 + 0.177939i
\(846\) −33833.7 + 5334.96i −1.37497 + 0.216808i
\(847\) 2636.37 + 1522.11i 0.106950 + 0.0617476i
\(848\) 1907.94 26250.3i 0.0772630 1.06302i
\(849\) −8610.14 + 23656.2i −0.348056 + 0.956275i
\(850\) 19942.2 + 17359.5i 0.804718 + 0.700500i
\(851\) −2486.96 14104.2i −0.100178 0.568140i
\(852\) −29848.8 26950.1i −1.20024 1.08368i
\(853\) 25473.2 + 21374.5i 1.02249 + 0.857973i 0.989939 0.141497i \(-0.0451917\pi\)
0.0325533 + 0.999470i \(0.489636\pi\)
\(854\) 9103.01 + 5478.14i 0.364753 + 0.219506i
\(855\) −44861.3 + 12780.1i −1.79441 + 0.511193i
\(856\) −354.679 19.3195i −0.0141620 0.000771408i
\(857\) −10542.9 + 12564.6i −0.420233 + 0.500814i −0.934078 0.357069i \(-0.883776\pi\)
0.513845 + 0.857883i \(0.328221\pi\)
\(858\) −7412.07 + 37992.7i −0.294923 + 1.51171i
\(859\) −12491.3 + 2202.56i −0.496156 + 0.0874857i −0.416126 0.909307i \(-0.636613\pi\)
−0.0800297 + 0.996792i \(0.525502\pi\)
\(860\) −1028.96 3181.64i −0.0407990 0.126155i
\(861\) 3279.57 + 1193.66i 0.129811 + 0.0472473i
\(862\) −4354.75 78.9987i −0.172069 0.00312147i
\(863\) −19935.0 + 34528.4i −0.786321 + 1.36195i 0.141886 + 0.989883i \(0.454683\pi\)
−0.928207 + 0.372064i \(0.878650\pi\)
\(864\) −15414.3 7252.25i −0.606952 0.285563i
\(865\) 8088.65 + 9639.68i 0.317945 + 0.378912i
\(866\) 19870.4 10996.5i 0.779703 0.431498i
\(867\) −26097.0 45201.4i −1.02226 1.77061i
\(868\) −15716.6 + 2186.86i −0.614583 + 0.0855149i
\(869\) 20991.9 + 3701.43i 0.819448 + 0.144491i
\(870\) 27725.6 72079.9i 1.08044 2.80890i
\(871\) 1738.39 + 4776.18i 0.0676268 + 0.185803i
\(872\) −5716.77 + 6105.26i −0.222012 + 0.237099i
\(873\) 27668.6i 1.07267i
\(874\) 2259.90 + 8516.09i 0.0874626 + 0.329589i
\(875\) 6385.88i 0.246722i
\(876\) 13868.4 64808.8i 0.534898 2.49964i
\(877\) 3973.52 + 10917.2i 0.152995 + 0.420349i 0.992384 0.123181i \(-0.0393095\pi\)
−0.839390 + 0.543530i \(0.817087\pi\)
\(878\) −7232.25 2781.89i −0.277992 0.106930i
\(879\) 67165.1 + 11843.0i 2.57727 + 0.454443i
\(880\) −17894.1 24771.7i −0.685467 0.948925i
\(881\) 317.217 + 549.435i 0.0121309 + 0.0210113i 0.872027 0.489458i \(-0.162805\pi\)
−0.859896 + 0.510469i \(0.829472\pi\)
\(882\) −10846.3 19599.0i −0.414076 0.748223i
\(883\) 15074.9 + 17965.6i 0.574531 + 0.684699i 0.972554 0.232676i \(-0.0747482\pi\)
−0.398023 + 0.917375i \(0.630304\pi\)
\(884\) −16537.1 + 40769.7i −0.629188 + 1.55117i
\(885\) 32192.8 55759.5i 1.22277 2.11789i
\(886\) −703.772 + 38795.0i −0.0266859 + 1.47104i
\(887\) 15340.1 + 5583.35i 0.580689 + 0.211354i 0.615629 0.788036i \(-0.288902\pi\)
−0.0349402 + 0.999389i \(0.511124\pi\)
\(888\) −67970.0 15839.4i −2.56861 0.598576i
\(889\) −15140.5 + 2669.67i −0.571198 + 0.100718i
\(890\) 14237.3 + 2777.58i 0.536219 + 0.104612i
\(891\) −5899.85 + 7031.17i −0.221832 + 0.264369i
\(892\) −20969.8 39569.2i −0.787131 1.48529i
\(893\) 23361.9 11344.6i 0.875451 0.425119i
\(894\) 1278.85 2125.06i 0.0478424 0.0794997i
\(895\) −2414.15 2025.71i −0.0901634 0.0756561i
\(896\) −16239.9 5050.38i −0.605511 0.188305i
\(897\) −2730.39 15484.8i −0.101633 0.576392i
\(898\) −5857.94 + 6729.47i −0.217686 + 0.250073i
\(899\) −13350.3 + 36679.6i −0.495280 + 1.36077i
\(900\) −14392.0 + 22961.9i −0.533038 + 0.850442i
\(901\) 37953.1 + 21912.3i 1.40333 + 0.810214i
\(902\) −529.118 3355.61i −0.0195318 0.123869i
\(903\) 2088.52 1752.48i 0.0769675 0.0645834i
\(904\) 20460.8 + 13347.3i 0.752783 + 0.491067i
\(905\) −11687.9 + 6748.01i −0.429303 + 0.247858i
\(906\) 52289.8 42284.1i 1.91745 1.55055i
\(907\) 1433.16 8127.87i 0.0524668 0.297554i −0.947271 0.320432i \(-0.896172\pi\)
0.999738 + 0.0228782i \(0.00728298\pi\)
\(908\) −41253.1 + 32139.5i −1.50775 + 1.17465i
\(909\) 23813.8 8667.52i 0.868926 0.316263i
\(910\) 23644.9 8123.47i 0.861342 0.295924i
\(911\) 12279.1 0.446568 0.223284 0.974753i \(-0.428322\pi\)
0.223284 + 0.974753i \(0.428322\pi\)
\(912\) 42490.9 + 6165.35i 1.54278 + 0.223854i
\(913\) 24188.2 0.876793
\(914\) −18006.2 + 6186.24i −0.651634 + 0.223876i
\(915\) −35508.7 + 12924.1i −1.28293 + 0.466949i
\(916\) −5784.58 + 4506.65i −0.208655 + 0.162559i
\(917\) −4255.27 + 24132.8i −0.153240 + 0.869069i
\(918\) 22056.1 17835.7i 0.792985 0.641247i
\(919\) −11737.6 + 6776.68i −0.421312 + 0.243245i −0.695639 0.718392i \(-0.744879\pi\)
0.274326 + 0.961637i \(0.411545\pi\)
\(920\) 10396.5 + 6782.03i 0.372570 + 0.243040i
\(921\) 38568.5 32362.8i 1.37989 1.15786i
\(922\) 3037.76 + 19265.1i 0.108507 + 0.688138i
\(923\) −27734.7 16012.6i −0.989057 0.571032i
\(924\) 13232.1 21111.4i 0.471110 0.751639i
\(925\) −11423.4 + 31385.5i −0.406052 + 1.11562i
\(926\) 8974.59 10309.8i 0.318492 0.365876i
\(927\) 8546.32 + 48468.6i 0.302802 + 1.71728i
\(928\) −29683.4 + 29480.6i −1.05001 + 1.04283i
\(929\) −21933.4 18404.3i −0.774607 0.649973i 0.167277 0.985910i \(-0.446503\pi\)
−0.941884 + 0.335937i \(0.890947\pi\)
\(930\) 29101.1 48357.2i 1.02609 1.70505i
\(931\) 12197.2 + 11819.4i 0.429375 + 0.416075i
\(932\) −18472.8 34857.5i −0.649246 1.22510i
\(933\) −18985.9 + 22626.6i −0.666208 + 0.793955i
\(934\) −7724.65 1507.02i −0.270619 0.0527956i
\(935\) 50110.2 8835.78i 1.75271 0.309049i
\(936\) −43917.6 10234.4i −1.53365 0.357394i
\(937\) 44273.3 + 16114.2i 1.54359 + 0.561821i 0.966903 0.255143i \(-0.0821226\pi\)
0.576688 + 0.816965i \(0.304345\pi\)
\(938\) 59.3385 3271.00i 0.00206554 0.113861i
\(939\) −35056.0 + 60718.7i −1.21833 + 2.11020i
\(940\) 13752.8 33905.5i 0.477200 1.17646i
\(941\) 24775.4 + 29526.2i 0.858296 + 1.02288i 0.999459 + 0.0328905i \(0.0104713\pi\)
−0.141163 + 0.989986i \(0.545084\pi\)
\(942\) 5882.82 + 10630.1i 0.203474 + 0.367671i
\(943\) 689.950 + 1195.03i 0.0238259 + 0.0412677i
\(944\) −28273.3 + 20423.6i −0.974808 + 0.704164i
\(945\) −15874.1 2799.04i −0.546440 0.0963521i
\(946\) −2476.83 952.714i −0.0851254 0.0327435i
\(947\) −8128.27 22332.2i −0.278916 0.766315i −0.997486 0.0708607i \(-0.977425\pi\)
0.718570 0.695454i \(-0.244797\pi\)
\(948\) −8829.09 + 41259.4i −0.302485 + 1.41355i
\(949\) 52778.9i 1.80535i
\(950\) 5365.94 19834.6i 0.183257 0.677390i
\(951\) 6884.29i 0.234741i
\(952\) 19355.7 20671.1i 0.658951 0.703732i
\(953\) 4736.46 + 13013.3i 0.160996 + 0.442332i 0.993793 0.111246i \(-0.0354842\pi\)
−0.832797 + 0.553578i \(0.813262\pi\)
\(954\) −16126.2 + 41924.1i −0.547278 + 1.42279i
\(955\) 13539.7 + 2387.41i 0.458779 + 0.0808952i
\(956\) −4173.15 + 580.664i −0.141181 + 0.0196444i
\(957\) −30644.6 53078.0i −1.03511 1.79286i
\(958\) −14153.8 + 7832.90i −0.477337 + 0.264165i
\(959\) −5700.07 6793.08i −0.191934 0.228738i
\(960\) 50286.9 33618.9i 1.69063 1.13025i
\(961\) 632.637 1095.76i 0.0212359 0.0367816i
\(962\) −55569.0 1008.07i −1.86239 0.0337852i
\(963\) 569.657 + 207.338i 0.0190623 + 0.00693809i
\(964\) 3516.42 + 10873.1i 0.117486 + 0.363278i
\(965\) −64688.9 + 11406.4i −2.15794 + 0.380502i
\(966\) −1937.94 + 9933.47i −0.0645468 + 0.330853i
\(967\) 31295.4 37296.4i 1.04074 1.24030i 0.0706605 0.997500i \(-0.477489\pi\)
0.970076 0.242801i \(-0.0780662\pi\)
\(968\) 5856.68 + 319.015i 0.194464 + 0.0105925i
\(969\) −40080.1 + 59200.8i −1.32875 + 1.96265i
\(970\) −25324.3 15240.0i −0.838261 0.504460i
\(971\) −3082.67 2586.67i −0.101882 0.0854893i 0.590424 0.807093i \(-0.298961\pi\)
−0.692306 + 0.721604i \(0.743405\pi\)
\(972\) −28572.5 25797.8i −0.942863 0.851301i
\(973\) −6265.37 35532.7i −0.206432 1.17073i
\(974\) 12177.9 + 10600.8i 0.400623 + 0.348738i
\(975\) −12541.6 + 34457.7i −0.411950 + 1.13182i
\(976\) 20416.2 + 1483.90i 0.669575 + 0.0486666i
\(977\) 22632.7 + 13067.0i 0.741131 + 0.427892i 0.822480 0.568793i \(-0.192590\pi\)
−0.0813493 + 0.996686i \(0.525923\pi\)
\(978\) −23982.5 + 3781.61i −0.784127 + 0.123643i
\(979\) 8818.60 7399.68i 0.287889 0.241568i
\(980\) 23912.6 + 867.873i 0.779449 + 0.0282890i
\(981\) 12362.1 7137.24i 0.402334 0.232288i
\(982\) −11756.4 14538.3i −0.382038 0.472439i
\(983\) −2201.24 + 12483.8i −0.0714228 + 0.405059i 0.928046 + 0.372466i \(0.121488\pi\)
−0.999469 + 0.0325929i \(0.989624\pi\)
\(984\) 6675.89 805.764i 0.216280 0.0261045i
\(985\) 57159.0 20804.2i 1.84897 0.672971i
\(986\) −22634.0 65880.5i −0.731048 2.12785i
\(987\) 29831.8 0.962063
\(988\) 34115.9 2279.52i 1.09855 0.0734021i
\(989\) 1077.96 0.0346583
\(990\) 16945.7 + 49323.8i 0.544011 + 1.58345i
\(991\) 28290.6 10296.9i 0.906841 0.330063i 0.153850 0.988094i \(-0.450833\pi\)
0.752991 + 0.658031i \(0.228611\pi\)
\(992\) −25104.2 + 17450.2i −0.803487 + 0.558513i
\(993\) 7421.21 42087.8i 0.237165 1.34503i
\(994\) 12961.5 + 16028.5i 0.413595 + 0.511463i
\(995\) 2907.95 1678.91i 0.0926516 0.0534924i
\(996\) −1736.57 + 47847.9i −0.0552463 + 1.52221i
\(997\) −27086.9 + 22728.6i −0.860431 + 0.721987i −0.962061 0.272835i \(-0.912039\pi\)
0.101630 + 0.994822i \(0.467594\pi\)
\(998\) 16508.7 2603.13i 0.523622 0.0825656i
\(999\) 31031.9 + 17916.3i 0.982787 + 0.567413i
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 76.4.k.a.3.3 168
4.3 odd 2 inner 76.4.k.a.3.13 yes 168
19.13 odd 18 inner 76.4.k.a.51.13 yes 168
76.51 even 18 inner 76.4.k.a.51.3 yes 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.4.k.a.3.3 168 1.1 even 1 trivial
76.4.k.a.3.13 yes 168 4.3 odd 2 inner
76.4.k.a.51.3 yes 168 76.51 even 18 inner
76.4.k.a.51.13 yes 168 19.13 odd 18 inner