Properties

Label 177.4.f.a.89.15
Level $177$
Weight $4$
Character 177.89
Analytic conductor $10.443$
Analytic rank $0$
Dimension $1624$
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] = [177,4,Mod(2,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([29, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\), degree \(28\), 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: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(1624\)
Relative dimension: \(58\) over \(\Q(\zeta_{58})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label 89.15
Character \(\chi\) \(=\) 177.89
Dual form 177.4.f.a.2.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.181075 - 3.33974i) q^{2} +(-4.07453 + 3.22462i) q^{3} +(-3.16798 + 0.344538i) q^{4} +(5.90079 + 17.5129i) q^{5} +(11.5072 + 13.0240i) q^{6} +(-10.9419 + 16.1380i) q^{7} +(-2.60452 - 15.8869i) q^{8} +(6.20361 - 26.2777i) q^{9} +O(q^{10})\) \(q+(-0.181075 - 3.33974i) q^{2} +(-4.07453 + 3.22462i) q^{3} +(-3.16798 + 0.344538i) q^{4} +(5.90079 + 17.5129i) q^{5} +(11.5072 + 13.0240i) q^{6} +(-10.9419 + 16.1380i) q^{7} +(-2.60452 - 15.8869i) q^{8} +(6.20361 - 26.2777i) q^{9} +(57.4202 - 22.8783i) q^{10} +(-44.9372 - 9.89142i) q^{11} +(11.7970 - 11.6194i) q^{12} +(-47.2303 - 40.1178i) q^{13} +(55.8781 + 33.6208i) q^{14} +(-80.5156 - 52.3291i) q^{15} +(-77.4836 + 17.0554i) q^{16} +(92.6168 - 62.7957i) q^{17} +(-88.8839 - 15.9602i) q^{18} +(-59.2307 - 111.721i) q^{19} +(-24.7274 - 53.4475i) q^{20} +(-7.45614 - 101.038i) q^{21} +(-24.8978 + 151.870i) q^{22} +(26.4430 + 25.0482i) q^{23} +(61.8413 + 56.3329i) q^{24} +(-172.372 + 131.034i) q^{25} +(-125.431 + 165.001i) q^{26} +(59.4588 + 127.073i) q^{27} +(29.1034 - 54.8948i) q^{28} +(47.2340 + 2.56095i) q^{29} +(-160.186 + 278.377i) q^{30} +(-86.0183 - 45.6040i) q^{31} +(36.5357 + 131.590i) q^{32} +(214.994 - 104.603i) q^{33} +(-226.492 - 297.945i) q^{34} +(-347.190 - 96.3968i) q^{35} +(-10.5992 + 85.3844i) q^{36} +(-8.67226 - 1.42174i) q^{37} +(-362.394 + 218.045i) q^{38} +(321.806 + 11.1612i) q^{39} +(262.857 - 139.358i) q^{40} +(159.215 + 168.082i) q^{41} +(-336.091 + 43.1971i) q^{42} +(1.92073 + 8.72597i) q^{43} +(145.768 + 15.8532i) q^{44} +(496.805 - 46.4157i) q^{45} +(78.8662 - 92.8485i) q^{46} +(-516.013 - 173.865i) q^{47} +(260.712 - 319.348i) q^{48} +(-13.7544 - 34.5210i) q^{49} +(468.830 + 551.950i) q^{50} +(-174.877 + 554.517i) q^{51} +(163.447 + 110.820i) q^{52} +(-349.864 - 139.399i) q^{53} +(413.626 - 221.587i) q^{54} +(-91.9372 - 845.349i) q^{55} +(284.881 + 131.800i) q^{56} +(601.595 + 264.214i) q^{57} -158.213i q^{58} +(-84.1067 + 445.315i) q^{59} +(273.101 + 138.037i) q^{60} +(-463.822 + 25.1477i) q^{61} +(-136.730 + 295.537i) q^{62} +(356.191 + 387.640i) q^{63} +(-168.623 + 56.8157i) q^{64} +(423.884 - 1063.87i) q^{65} +(-388.276 - 699.083i) q^{66} +(-171.940 + 28.1882i) q^{67} +(-271.772 + 230.845i) q^{68} +(-188.514 - 16.7907i) q^{69} +(-259.073 + 1176.98i) q^{70} +(-265.508 + 787.999i) q^{71} +(-433.627 - 30.1152i) q^{72} +(140.842 - 234.081i) q^{73} +(-3.17793 + 29.2205i) q^{74} +(279.800 - 1089.73i) q^{75} +(226.134 + 333.522i) q^{76} +(651.324 - 616.967i) q^{77} +(-20.9957 - 1076.77i) q^{78} +(188.717 - 87.3100i) q^{79} +(-755.905 - 1256.32i) q^{80} +(-652.031 - 326.033i) q^{81} +(532.519 - 562.174i) q^{82} +(196.501 - 707.734i) q^{83} +(58.4324 + 317.518i) q^{84} +(1646.25 + 1251.45i) q^{85} +(28.7947 - 7.99480i) q^{86} +(-200.715 + 141.877i) q^{87} +(-40.1039 + 739.673i) q^{88} +(-56.5030 + 1042.14i) q^{89} +(-244.976 - 1650.80i) q^{90} +(1164.21 - 323.241i) q^{91} +(-92.4009 - 70.2414i) q^{92} +(497.540 - 91.5617i) q^{93} +(-487.227 + 1754.83i) q^{94} +(1607.05 - 1696.55i) q^{95} +(-573.193 - 418.353i) q^{96} +(-780.352 - 1296.96i) q^{97} +(-112.800 + 52.1870i) q^{98} +(-538.696 + 1119.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9} - 58 q^{10} - 57 q^{12} - 58 q^{13} - 11 q^{15} - 926 q^{16} - 29 q^{18} + 126 q^{19} + 159 q^{21} + 2 q^{22} - 29 q^{24} + 656 q^{25} - 99 q^{27} - 54 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 859 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 1703 q^{45} + 602 q^{46} + 9507 q^{48} - 1192 q^{49} + 1511 q^{51} - 58 q^{52} - 7743 q^{54} - 58 q^{55} - 7441 q^{57} - 18722 q^{60} - 58 q^{61} - 3251 q^{63} - 4634 q^{64} - 1751 q^{66} - 58 q^{67} + 6003 q^{69} - 58 q^{70} + 21547 q^{72} - 58 q^{73} + 3869 q^{75} + 5622 q^{76} - 3253 q^{78} + 1446 q^{79} + 247 q^{81} - 58 q^{82} + 3303 q^{84} + 790 q^{85} - 2199 q^{87} - 5818 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 946 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{57}{58}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.181075 3.33974i −0.0640198 1.18078i −0.837311 0.546726i \(-0.815874\pi\)
0.773292 0.634050i \(-0.218609\pi\)
\(3\) −4.07453 + 3.22462i −0.784144 + 0.620579i
\(4\) −3.16798 + 0.344538i −0.395997 + 0.0430673i
\(5\) 5.90079 + 17.5129i 0.527783 + 1.56640i 0.797409 + 0.603439i \(0.206203\pi\)
−0.269626 + 0.962965i \(0.586900\pi\)
\(6\) 11.5072 + 13.0240i 0.782966 + 0.886169i
\(7\) −10.9419 + 16.1380i −0.590805 + 0.871372i −0.999140 0.0414602i \(-0.986799\pi\)
0.408335 + 0.912832i \(0.366109\pi\)
\(8\) −2.60452 15.8869i −0.115104 0.702106i
\(9\) 6.20361 26.2777i 0.229763 0.973247i
\(10\) 57.4202 22.8783i 1.81578 0.723475i
\(11\) −44.9372 9.89142i −1.23173 0.271125i −0.449028 0.893518i \(-0.648230\pi\)
−0.782705 + 0.622393i \(0.786161\pi\)
\(12\) 11.7970 11.6194i 0.283792 0.279518i
\(13\) −47.2303 40.1178i −1.00764 0.855899i −0.0180550 0.999837i \(-0.505747\pi\)
−0.989587 + 0.143938i \(0.954023\pi\)
\(14\) 55.8781 + 33.6208i 1.06672 + 0.641823i
\(15\) −80.5156 52.3291i −1.38594 0.900755i
\(16\) −77.4836 + 17.0554i −1.21068 + 0.266491i
\(17\) 92.6168 62.7957i 1.32134 0.895894i 0.322628 0.946526i \(-0.395434\pi\)
0.998717 + 0.0506319i \(0.0161235\pi\)
\(18\) −88.8839 15.9602i −1.16390 0.208992i
\(19\) −59.2307 111.721i −0.715182 1.34898i −0.928257 0.371940i \(-0.878693\pi\)
0.213075 0.977036i \(-0.431652\pi\)
\(20\) −24.7274 53.4475i −0.276461 0.597561i
\(21\) −7.45614 101.038i −0.0774792 1.04992i
\(22\) −24.8978 + 151.870i −0.241283 + 1.47176i
\(23\) 26.4430 + 25.0482i 0.239728 + 0.227083i 0.798126 0.602491i \(-0.205825\pi\)
−0.558397 + 0.829574i \(0.688584\pi\)
\(24\) 61.8413 + 56.3329i 0.525971 + 0.479121i
\(25\) −172.372 + 131.034i −1.37897 + 1.04827i
\(26\) −125.431 + 165.001i −0.946116 + 1.24459i
\(27\) 59.4588 + 127.073i 0.423809 + 0.905752i
\(28\) 29.1034 54.8948i 0.196429 0.370505i
\(29\) 47.2340 + 2.56095i 0.302453 + 0.0163985i 0.204741 0.978816i \(-0.434365\pi\)
0.0977121 + 0.995215i \(0.468848\pi\)
\(30\) −160.186 + 278.377i −0.974863 + 1.69415i
\(31\) −86.0183 45.6040i −0.498366 0.264217i 0.200210 0.979753i \(-0.435838\pi\)
−0.698576 + 0.715536i \(0.746182\pi\)
\(32\) 36.5357 + 131.590i 0.201833 + 0.726937i
\(33\) 214.994 104.603i 1.13411 0.551787i
\(34\) −226.492 297.945i −1.14244 1.50286i
\(35\) −347.190 96.3968i −1.67674 0.465544i
\(36\) −10.5992 + 85.3844i −0.0490705 + 0.395298i
\(37\) −8.67226 1.42174i −0.0385327 0.00631712i 0.142485 0.989797i \(-0.454491\pi\)
−0.181018 + 0.983480i \(0.557939\pi\)
\(38\) −362.394 + 218.045i −1.54705 + 0.930831i
\(39\) 321.806 + 11.1612i 1.32129 + 0.0458263i
\(40\) 262.857 139.358i 1.03903 0.550860i
\(41\) 159.215 + 168.082i 0.606470 + 0.640243i 0.954842 0.297114i \(-0.0960240\pi\)
−0.348372 + 0.937356i \(0.613265\pi\)
\(42\) −336.091 + 43.1971i −1.23476 + 0.158701i
\(43\) 1.92073 + 8.72597i 0.00681183 + 0.0309465i 0.979904 0.199470i \(-0.0639221\pi\)
−0.973092 + 0.230417i \(0.925991\pi\)
\(44\) 145.768 + 15.8532i 0.499439 + 0.0543173i
\(45\) 496.805 46.4157i 1.64576 0.153761i
\(46\) 78.8662 92.8485i 0.252787 0.297604i
\(47\) −516.013 173.865i −1.60145 0.539592i −0.629953 0.776633i \(-0.716926\pi\)
−0.971500 + 0.237041i \(0.923822\pi\)
\(48\) 260.712 319.348i 0.783969 0.960291i
\(49\) −13.7544 34.5210i −0.0401003 0.100644i
\(50\) 468.830 + 551.950i 1.32605 + 1.56115i
\(51\) −174.877 + 554.517i −0.480151 + 1.52251i
\(52\) 163.447 + 110.820i 0.435884 + 0.295537i
\(53\) −349.864 139.399i −0.906746 0.361281i −0.130307 0.991474i \(-0.541596\pi\)
−0.776439 + 0.630193i \(0.782976\pi\)
\(54\) 413.626 221.587i 1.04236 0.558410i
\(55\) −91.9372 845.349i −0.225397 2.07249i
\(56\) 284.881 + 131.800i 0.679800 + 0.314509i
\(57\) 601.595 + 264.214i 1.39795 + 0.613964i
\(58\) 158.213i 0.358179i
\(59\) −84.1067 + 445.315i −0.185589 + 0.982627i
\(60\) 273.101 + 138.037i 0.587619 + 0.297008i
\(61\) −463.822 + 25.1477i −0.973546 + 0.0527841i −0.534043 0.845457i \(-0.679328\pi\)
−0.439503 + 0.898241i \(0.644845\pi\)
\(62\) −136.730 + 295.537i −0.280076 + 0.605374i
\(63\) 356.191 + 387.640i 0.712314 + 0.775208i
\(64\) −168.623 + 56.8157i −0.329342 + 0.110968i
\(65\) 423.884 1063.87i 0.808867 2.03010i
\(66\) −388.276 699.083i −0.724143 1.30381i
\(67\) −171.940 + 28.1882i −0.313520 + 0.0513991i −0.316488 0.948597i \(-0.602504\pi\)
0.00296748 + 0.999996i \(0.499055\pi\)
\(68\) −271.772 + 230.845i −0.484665 + 0.411678i
\(69\) −188.514 16.7907i −0.328904 0.0292952i
\(70\) −259.073 + 1176.98i −0.442359 + 2.00966i
\(71\) −265.508 + 787.999i −0.443803 + 1.31716i 0.459509 + 0.888173i \(0.348025\pi\)
−0.903311 + 0.428986i \(0.858871\pi\)
\(72\) −433.627 30.1152i −0.709769 0.0492932i
\(73\) 140.842 234.081i 0.225812 0.375303i −0.723151 0.690690i \(-0.757307\pi\)
0.948963 + 0.315387i \(0.102134\pi\)
\(74\) −3.17793 + 29.2205i −0.00499225 + 0.0459030i
\(75\) 279.800 1089.73i 0.430780 1.67776i
\(76\) 226.134 + 333.522i 0.341307 + 0.503390i
\(77\) 651.324 616.967i 0.963965 0.913116i
\(78\) −20.9957 1076.77i −0.0304781 1.56308i
\(79\) 188.717 87.3100i 0.268764 0.124344i −0.280879 0.959743i \(-0.590626\pi\)
0.549643 + 0.835400i \(0.314764\pi\)
\(80\) −755.905 1256.32i −1.05641 1.75577i
\(81\) −652.031 326.033i −0.894418 0.447233i
\(82\) 532.519 562.174i 0.717158 0.757094i
\(83\) 196.501 707.734i 0.259865 0.935950i −0.712343 0.701832i \(-0.752366\pi\)
0.972208 0.234118i \(-0.0752204\pi\)
\(84\) 58.4324 + 317.518i 0.0758988 + 0.412429i
\(85\) 1646.25 + 1251.45i 2.10072 + 1.59692i
\(86\) 28.7947 7.99480i 0.0361048 0.0100244i
\(87\) −200.715 + 141.877i −0.247343 + 0.174837i
\(88\) −40.1039 + 739.673i −0.0485806 + 0.896016i
\(89\) −56.5030 + 1042.14i −0.0672956 + 1.24119i 0.748611 + 0.663010i \(0.230721\pi\)
−0.815906 + 0.578184i \(0.803762\pi\)
\(90\) −244.976 1650.80i −0.286919 1.93343i
\(91\) 1164.21 323.241i 1.34113 0.372362i
\(92\) −92.4009 70.2414i −0.104712 0.0795997i
\(93\) 497.540 91.5617i 0.554758 0.102091i
\(94\) −487.227 + 1754.83i −0.534613 + 1.92550i
\(95\) 1607.05 1696.55i 1.73558 1.83223i
\(96\) −573.193 418.353i −0.609388 0.444770i
\(97\) −780.352 1296.96i −0.816833 1.35759i −0.931335 0.364164i \(-0.881355\pi\)
0.114502 0.993423i \(-0.463473\pi\)
\(98\) −112.800 + 52.1870i −0.116271 + 0.0537927i
\(99\) −538.696 + 1119.48i −0.546879 + 1.13649i
\(100\) 500.923 474.500i 0.500923 0.474500i
\(101\) −37.5219 55.3407i −0.0369661 0.0545209i 0.808757 0.588143i \(-0.200141\pi\)
−0.845723 + 0.533622i \(0.820830\pi\)
\(102\) 1883.61 + 483.635i 1.82848 + 0.469481i
\(103\) 5.71117 52.5133i 0.00546348 0.0502358i −0.991089 0.133202i \(-0.957474\pi\)
0.996552 + 0.0829666i \(0.0264395\pi\)
\(104\) −514.334 + 854.829i −0.484948 + 0.805989i
\(105\) 1725.48 726.785i 1.60371 0.675495i
\(106\) −402.203 + 1193.70i −0.368542 + 1.09379i
\(107\) −207.955 + 944.749i −0.187886 + 0.853574i 0.784488 + 0.620144i \(0.212926\pi\)
−0.972374 + 0.233430i \(0.925005\pi\)
\(108\) −232.146 382.080i −0.206835 0.340423i
\(109\) 45.2877 38.4677i 0.0397961 0.0338031i −0.627268 0.778804i \(-0.715827\pi\)
0.667064 + 0.745001i \(0.267551\pi\)
\(110\) −2806.60 + 460.118i −2.43272 + 0.398823i
\(111\) 39.9200 22.1718i 0.0341355 0.0189591i
\(112\) 572.573 1437.05i 0.483063 1.21240i
\(113\) −1365.56 + 460.111i −1.13682 + 0.383040i −0.823898 0.566738i \(-0.808205\pi\)
−0.312925 + 0.949778i \(0.601309\pi\)
\(114\) 773.471 2057.02i 0.635458 1.68997i
\(115\) −282.632 + 610.899i −0.229179 + 0.495362i
\(116\) −150.519 + 8.16088i −0.120477 + 0.00653206i
\(117\) −1347.20 + 992.228i −1.06452 + 0.784030i
\(118\) 1502.46 + 200.259i 1.17214 + 0.156232i
\(119\) 2181.75i 1.68068i
\(120\) −621.641 + 1415.43i −0.472898 + 1.07675i
\(121\) 713.527 + 330.113i 0.536083 + 0.248019i
\(122\) 167.973 + 1544.49i 0.124652 + 1.14616i
\(123\) −1190.73 171.444i −0.872881 0.125680i
\(124\) 288.216 + 114.836i 0.208731 + 0.0831658i
\(125\) −1399.92 949.168i −1.00170 0.679169i
\(126\) 1230.12 1259.78i 0.869745 0.890713i
\(127\) 699.397 + 823.394i 0.488673 + 0.575311i 0.950131 0.311852i \(-0.100949\pi\)
−0.461458 + 0.887162i \(0.652673\pi\)
\(128\) 624.674 + 1567.81i 0.431359 + 1.08263i
\(129\) −35.9640 29.3606i −0.0245462 0.0200392i
\(130\) −3629.80 1223.02i −2.44888 0.825124i
\(131\) 1030.03 1212.64i 0.686976 0.808771i −0.302549 0.953134i \(-0.597838\pi\)
0.989525 + 0.144363i \(0.0461134\pi\)
\(132\) −645.056 + 405.452i −0.425340 + 0.267349i
\(133\) 2451.05 + 266.568i 1.59799 + 0.173792i
\(134\) 125.276 + 569.132i 0.0807624 + 0.366907i
\(135\) −1874.57 + 1791.13i −1.19509 + 1.14190i
\(136\) −1238.85 1307.84i −0.781106 0.824603i
\(137\) 1744.40 924.823i 1.08784 0.576737i 0.174800 0.984604i \(-0.444072\pi\)
0.913041 + 0.407867i \(0.133727\pi\)
\(138\) −21.9414 + 632.628i −0.0135346 + 0.390238i
\(139\) −1608.95 + 968.074i −0.981795 + 0.590727i −0.913457 0.406936i \(-0.866597\pi\)
−0.0683384 + 0.997662i \(0.521770\pi\)
\(140\) 1133.10 + 185.763i 0.684032 + 0.112141i
\(141\) 2663.16 955.530i 1.59063 0.570710i
\(142\) 2679.79 + 744.040i 1.58368 + 0.439707i
\(143\) 1725.58 + 2269.96i 1.00909 + 1.32744i
\(144\) −32.5011 + 2141.89i −0.0188085 + 1.23952i
\(145\) 233.868 + 842.318i 0.133943 + 0.482419i
\(146\) −807.273 427.989i −0.457606 0.242607i
\(147\) 167.360 + 96.3039i 0.0939021 + 0.0540341i
\(148\) 27.9634 + 1.51613i 0.0155309 + 0.000842061i
\(149\) −184.771 + 348.515i −0.101591 + 0.191621i −0.929097 0.369836i \(-0.879414\pi\)
0.827506 + 0.561456i \(0.189759\pi\)
\(150\) −3690.10 737.135i −2.00863 0.401246i
\(151\) −358.632 + 471.772i −0.193278 + 0.254253i −0.882516 0.470282i \(-0.844152\pi\)
0.689238 + 0.724535i \(0.257945\pi\)
\(152\) −1620.63 + 1231.97i −0.864804 + 0.657407i
\(153\) −1075.57 2823.31i −0.568329 1.49184i
\(154\) −2178.45 2063.54i −1.13990 1.07977i
\(155\) 291.084 1775.53i 0.150841 0.920092i
\(156\) −1023.32 + 75.5161i −0.525200 + 0.0387572i
\(157\) −496.555 1073.29i −0.252417 0.545590i 0.739399 0.673268i \(-0.235110\pi\)
−0.991816 + 0.127678i \(0.959248\pi\)
\(158\) −325.765 614.457i −0.164028 0.309390i
\(159\) 1875.04 560.196i 0.935222 0.279412i
\(160\) −2088.93 + 1416.33i −1.03215 + 0.699818i
\(161\) −693.564 + 152.665i −0.339506 + 0.0747310i
\(162\) −970.797 + 2236.65i −0.470821 + 1.08474i
\(163\) −2934.78 1765.80i −1.41025 0.848516i −0.412205 0.911091i \(-0.635241\pi\)
−0.998040 + 0.0625749i \(0.980069\pi\)
\(164\) −562.301 477.623i −0.267734 0.227415i
\(165\) 3100.53 + 3147.94i 1.46289 + 1.48525i
\(166\) −2399.23 528.110i −1.12178 0.246923i
\(167\) −1620.97 + 645.852i −0.751103 + 0.299267i −0.714096 0.700048i \(-0.753162\pi\)
−0.0370073 + 0.999315i \(0.511782\pi\)
\(168\) −1585.76 + 381.610i −0.728239 + 0.175249i
\(169\) 265.831 + 1621.50i 0.120997 + 0.738051i
\(170\) 3881.41 5724.65i 1.75112 2.58271i
\(171\) −3303.21 + 863.371i −1.47721 + 0.386103i
\(172\) −9.09125 26.9819i −0.00403024 0.0119613i
\(173\) −176.948 + 19.2443i −0.0777637 + 0.00845731i −0.146918 0.989149i \(-0.546935\pi\)
0.0691545 + 0.997606i \(0.477970\pi\)
\(174\) 510.178 + 644.644i 0.222279 + 0.280864i
\(175\) −228.557 4215.49i −0.0987275 1.82092i
\(176\) 3650.60 1.56349
\(177\) −1093.28 2085.66i −0.464269 0.885694i
\(178\) 3490.70 1.46988
\(179\) −77.7757 1434.49i −0.0324761 0.598987i −0.968799 0.247847i \(-0.920277\pi\)
0.936323 0.351140i \(-0.114206\pi\)
\(180\) −1557.87 + 318.212i −0.645095 + 0.131767i
\(181\) 3485.50 379.071i 1.43135 0.155669i 0.640633 0.767847i \(-0.278672\pi\)
0.790720 + 0.612178i \(0.209706\pi\)
\(182\) −1290.35 3829.63i −0.525534 1.55973i
\(183\) 1808.76 1598.12i 0.730643 0.645552i
\(184\) 329.065 485.335i 0.131842 0.194453i
\(185\) −26.2743 160.266i −0.0104418 0.0636919i
\(186\) −395.885 1645.08i −0.156063 0.648510i
\(187\) −4783.07 + 1905.75i −1.87044 + 0.745253i
\(188\) 1694.62 + 373.014i 0.657409 + 0.144707i
\(189\) −2701.30 430.872i −1.03963 0.165827i
\(190\) −5957.02 5059.94i −2.27457 1.93203i
\(191\) 2338.21 + 1406.86i 0.885797 + 0.532966i 0.884240 0.467033i \(-0.154677\pi\)
0.00155662 + 0.999999i \(0.499505\pi\)
\(192\) 503.850 775.243i 0.189387 0.291398i
\(193\) 1409.93 310.350i 0.525851 0.115749i 0.0558921 0.998437i \(-0.482200\pi\)
0.469959 + 0.882688i \(0.344269\pi\)
\(194\) −4190.19 + 2841.02i −1.55071 + 1.05141i
\(195\) 1703.45 + 5701.63i 0.625571 + 2.09386i
\(196\) 55.4674 + 104.623i 0.0202141 + 0.0381278i
\(197\) −1817.79 3929.08i −0.657422 1.42099i −0.893412 0.449238i \(-0.851696\pi\)
0.235991 0.971755i \(-0.424167\pi\)
\(198\) 3836.32 + 1596.39i 1.37695 + 0.572984i
\(199\) −420.728 + 2566.33i −0.149872 + 0.914181i 0.799646 + 0.600471i \(0.205020\pi\)
−0.949519 + 0.313710i \(0.898428\pi\)
\(200\) 2530.66 + 2397.17i 0.894722 + 0.847526i
\(201\) 609.680 669.297i 0.213948 0.234869i
\(202\) −178.029 + 135.334i −0.0620104 + 0.0471391i
\(203\) −558.157 + 734.242i −0.192980 + 0.253861i
\(204\) 362.955 1816.95i 0.124568 0.623588i
\(205\) −2004.11 + 3780.14i −0.682794 + 1.28789i
\(206\) −176.415 9.56494i −0.0596671 0.00323505i
\(207\) 822.250 539.472i 0.276088 0.181140i
\(208\) 4343.80 + 2302.94i 1.44802 + 0.767693i
\(209\) 1556.58 + 5606.30i 0.515172 + 1.85548i
\(210\) −2739.71 5631.05i −0.900277 1.85038i
\(211\) −1682.82 2213.71i −0.549053 0.722267i 0.434943 0.900458i \(-0.356768\pi\)
−0.983996 + 0.178191i \(0.942975\pi\)
\(212\) 1156.39 + 321.070i 0.374628 + 0.104015i
\(213\) −1459.18 4066.89i −0.469396 1.30826i
\(214\) 3192.87 + 523.445i 1.01991 + 0.167205i
\(215\) −141.483 + 85.1277i −0.0448795 + 0.0270031i
\(216\) 1863.94 1275.58i 0.587152 0.401815i
\(217\) 1677.16 889.174i 0.524668 0.278161i
\(218\) −136.673 144.284i −0.0424617 0.0448262i
\(219\) 180.959 + 1407.93i 0.0558359 + 0.434426i
\(220\) 582.510 + 2646.37i 0.178513 + 0.810992i
\(221\) −6893.55 749.719i −2.09824 0.228197i
\(222\) −81.2767 129.308i −0.0245718 0.0390926i
\(223\) 1408.98 1658.78i 0.423105 0.498117i −0.508768 0.860904i \(-0.669899\pi\)
0.931872 + 0.362787i \(0.118175\pi\)
\(224\) −2523.37 850.222i −0.752677 0.253606i
\(225\) 2373.93 + 5342.41i 0.703386 + 1.58294i
\(226\) 1783.92 + 4477.30i 0.525064 + 1.31781i
\(227\) −3476.25 4092.55i −1.01642 1.19662i −0.980349 0.197269i \(-0.936793\pi\)
−0.0360672 0.999349i \(-0.511483\pi\)
\(228\) −1996.87 629.750i −0.580026 0.182922i
\(229\) 4236.60 + 2872.49i 1.22254 + 0.828905i 0.989637 0.143594i \(-0.0458660\pi\)
0.232907 + 0.972499i \(0.425176\pi\)
\(230\) 2091.42 + 833.299i 0.599584 + 0.238896i
\(231\) −664.354 + 4614.13i −0.189226 + 1.31423i
\(232\) −82.3363 757.070i −0.0233002 0.214242i
\(233\) 5634.72 + 2606.90i 1.58430 + 0.732977i 0.997074 0.0764441i \(-0.0243567\pi\)
0.587229 + 0.809421i \(0.300219\pi\)
\(234\) 3557.73 + 4319.63i 0.993914 + 1.20677i
\(235\) 10062.8i 2.79331i
\(236\) 113.020 1439.72i 0.0311737 0.397110i
\(237\) −487.393 + 964.290i −0.133585 + 0.264293i
\(238\) 7286.49 395.062i 1.98451 0.107597i
\(239\) 2333.91 5044.66i 0.631665 1.36532i −0.282221 0.959349i \(-0.591071\pi\)
0.913886 0.405971i \(-0.133067\pi\)
\(240\) 7131.13 + 2681.42i 1.91797 + 0.721188i
\(241\) −4366.19 + 1471.14i −1.16702 + 0.393214i −0.835102 0.550095i \(-0.814591\pi\)
−0.331915 + 0.943309i \(0.607695\pi\)
\(242\) 973.288 2442.77i 0.258535 0.648873i
\(243\) 3708.05 774.123i 0.978895 0.204362i
\(244\) 1460.71 239.472i 0.383248 0.0628303i
\(245\) 523.401 444.581i 0.136485 0.115932i
\(246\) −356.968 + 4007.77i −0.0925180 + 1.03872i
\(247\) −1684.51 + 7652.83i −0.433940 + 1.97141i
\(248\) −500.468 + 1485.34i −0.128144 + 0.380318i
\(249\) 1481.52 + 3517.33i 0.377059 + 0.895187i
\(250\) −2916.48 + 4847.23i −0.737818 + 1.22626i
\(251\) 215.895 1985.12i 0.0542914 0.499201i −0.935148 0.354256i \(-0.884734\pi\)
0.989440 0.144945i \(-0.0463005\pi\)
\(252\) −1261.96 1105.31i −0.315460 0.276302i
\(253\) −940.513 1387.15i −0.233714 0.344702i
\(254\) 2623.28 2484.90i 0.648028 0.613845i
\(255\) −10743.1 + 209.478i −2.63828 + 0.0514432i
\(256\) 3831.05 1772.43i 0.935314 0.432722i
\(257\) −748.698 1244.35i −0.181722 0.302024i 0.752584 0.658496i \(-0.228807\pi\)
−0.934306 + 0.356472i \(0.883980\pi\)
\(258\) −91.5445 + 125.427i −0.0220904 + 0.0302665i
\(259\) 117.835 124.397i 0.0282699 0.0298441i
\(260\) −976.311 + 3516.35i −0.232878 + 0.838750i
\(261\) 360.317 1225.31i 0.0854524 0.290594i
\(262\) −4236.42 3220.44i −0.998958 0.759388i
\(263\) 6969.42 1935.05i 1.63404 0.453689i 0.675201 0.737634i \(-0.264057\pi\)
0.958841 + 0.283945i \(0.0916432\pi\)
\(264\) −2221.76 3143.14i −0.517954 0.732753i
\(265\) 376.802 6949.71i 0.0873463 1.61101i
\(266\) 446.442 8234.14i 0.102906 1.89800i
\(267\) −3130.28 4428.42i −0.717490 1.01504i
\(268\) 534.991 148.540i 0.121940 0.0338563i
\(269\) 2730.95 + 2076.01i 0.618992 + 0.470546i 0.867064 0.498196i \(-0.166004\pi\)
−0.248072 + 0.968742i \(0.579797\pi\)
\(270\) 6321.35 + 5936.26i 1.42483 + 1.33803i
\(271\) −1386.77 + 4994.71i −0.310850 + 1.11958i 0.628834 + 0.777540i \(0.283533\pi\)
−0.939684 + 0.342043i \(0.888881\pi\)
\(272\) −6105.27 + 6445.26i −1.36098 + 1.43677i
\(273\) −3701.28 + 5071.20i −0.820555 + 1.12426i
\(274\) −3404.54 5658.38i −0.750641 1.24757i
\(275\) 9042.01 4183.28i 1.98274 0.917313i
\(276\) 602.992 11.7576i 0.131507 0.00256422i
\(277\) −2378.79 + 2253.31i −0.515984 + 0.488766i −0.900804 0.434226i \(-0.857022\pi\)
0.384820 + 0.922991i \(0.374263\pi\)
\(278\) 3524.46 + 5198.19i 0.760371 + 1.12146i
\(279\) −1731.99 + 1977.45i −0.371654 + 0.424326i
\(280\) −627.180 + 5766.82i −0.133861 + 1.23083i
\(281\) −456.952 + 759.460i −0.0970087 + 0.161230i −0.901561 0.432652i \(-0.857578\pi\)
0.804552 + 0.593882i \(0.202405\pi\)
\(282\) −3673.45 8721.25i −0.775713 1.84164i
\(283\) 1404.40 4168.12i 0.294994 0.875510i −0.692989 0.720948i \(-0.743707\pi\)
0.987983 0.154562i \(-0.0493967\pi\)
\(284\) 569.627 2587.84i 0.119018 0.540704i
\(285\) −1077.27 + 12094.8i −0.223901 + 2.51380i
\(286\) 7268.61 6174.01i 1.50280 1.27649i
\(287\) −4454.62 + 730.298i −0.916195 + 0.150203i
\(288\) 3684.52 143.742i 0.753863 0.0294100i
\(289\) 2816.07 7067.81i 0.573188 1.43859i
\(290\) 2770.78 933.583i 0.561053 0.189041i
\(291\) 7361.76 + 2768.14i 1.48300 + 0.557634i
\(292\) −365.534 + 790.089i −0.0732577 + 0.158344i
\(293\) −1743.87 + 94.5499i −0.347706 + 0.0188521i −0.227165 0.973856i \(-0.572946\pi\)
−0.120541 + 0.992708i \(0.538463\pi\)
\(294\) 291.325 576.377i 0.0577906 0.114337i
\(295\) −8295.06 + 1154.75i −1.63714 + 0.227906i
\(296\) 141.478i 0.0277812i
\(297\) −1414.97 6298.45i −0.276448 1.23055i
\(298\) 1197.41 + 553.980i 0.232765 + 0.107689i
\(299\) −244.036 2243.87i −0.0472005 0.434001i
\(300\) −510.945 + 3548.65i −0.0983313 + 0.682939i
\(301\) −161.836 64.4815i −0.0309903 0.0123477i
\(302\) 1640.54 + 1112.31i 0.312590 + 0.211941i
\(303\) 331.337 + 104.493i 0.0628212 + 0.0198118i
\(304\) 6494.86 + 7646.34i 1.22535 + 1.44259i
\(305\) −3177.33 7974.49i −0.596502 1.49711i
\(306\) −9234.37 + 4103.35i −1.72514 + 0.766577i
\(307\) −5713.45 1925.09i −1.06216 0.357884i −0.266633 0.963798i \(-0.585911\pi\)
−0.795530 + 0.605914i \(0.792808\pi\)
\(308\) −1850.81 + 2178.94i −0.342402 + 0.403106i
\(309\) 146.065 + 232.383i 0.0268912 + 0.0427826i
\(310\) −5982.53 650.639i −1.09608 0.119206i
\(311\) 1177.44 + 5349.16i 0.214683 + 0.975315i 0.953496 + 0.301405i \(0.0974556\pi\)
−0.738813 + 0.673910i \(0.764613\pi\)
\(312\) −660.834 5141.56i −0.119911 0.932960i
\(313\) 3786.20 + 3997.04i 0.683734 + 0.721809i 0.971801 0.235801i \(-0.0757714\pi\)
−0.288068 + 0.957610i \(0.593013\pi\)
\(314\) −3494.59 + 1852.71i −0.628060 + 0.332976i
\(315\) −4686.91 + 8525.33i −0.838341 + 1.52491i
\(316\) −567.771 + 341.616i −0.101075 + 0.0608146i
\(317\) 8126.80 + 1332.32i 1.43989 + 0.236059i 0.830593 0.556880i \(-0.188002\pi\)
0.609302 + 0.792939i \(0.291450\pi\)
\(318\) −2210.43 6160.71i −0.389795 1.08640i
\(319\) −2097.23 582.294i −0.368095 0.102201i
\(320\) −1990.02 2617.82i −0.347642 0.457315i
\(321\) −2199.14 4519.99i −0.382380 0.785922i
\(322\) 635.449 + 2288.68i 0.109976 + 0.396097i
\(323\) −12501.4 6627.80i −2.15354 1.14174i
\(324\) 2177.95 + 808.214i 0.373448 + 0.138583i
\(325\) 13398.0 + 726.416i 2.28672 + 0.123983i
\(326\) −5365.90 + 10121.2i −0.911625 + 1.71951i
\(327\) −60.4823 + 302.774i −0.0102284 + 0.0512031i
\(328\) 2255.61 2967.20i 0.379711 0.499501i
\(329\) 8451.98 6425.03i 1.41633 1.07667i
\(330\) 9951.86 10925.0i 1.66010 1.82243i
\(331\) −1052.49 996.969i −0.174773 0.165554i 0.595313 0.803494i \(-0.297028\pi\)
−0.770086 + 0.637940i \(0.779787\pi\)
\(332\) −378.670 + 2309.79i −0.0625970 + 0.381825i
\(333\) −91.1594 + 219.067i −0.0150015 + 0.0360504i
\(334\) 2450.50 + 5296.66i 0.401453 + 0.867726i
\(335\) −1508.24 2844.85i −0.245983 0.463972i
\(336\) 2300.98 + 7701.64i 0.373597 + 1.25047i
\(337\) 2176.01 1475.37i 0.351735 0.238482i −0.372505 0.928030i \(-0.621501\pi\)
0.724240 + 0.689548i \(0.242191\pi\)
\(338\) 5367.25 1181.42i 0.863728 0.190121i
\(339\) 4080.33 6278.15i 0.653726 1.00585i
\(340\) −5646.45 3397.36i −0.900652 0.541904i
\(341\) 3414.33 + 2900.16i 0.542218 + 0.460564i
\(342\) 3481.57 + 10875.5i 0.550472 + 1.71954i
\(343\) −5823.76 1281.91i −0.916773 0.201797i
\(344\) 133.626 53.2413i 0.0209436 0.00834470i
\(345\) −818.327 3400.51i −0.127702 0.530659i
\(346\) 96.3118 + 587.476i 0.0149646 + 0.0912801i
\(347\) 85.6592 126.338i 0.0132520 0.0195452i −0.821005 0.570921i \(-0.806586\pi\)
0.834257 + 0.551375i \(0.185897\pi\)
\(348\) 586.977 518.617i 0.0904174 0.0798874i
\(349\) −2014.30 5978.22i −0.308948 0.916925i −0.983846 0.179014i \(-0.942709\pi\)
0.674899 0.737911i \(-0.264187\pi\)
\(350\) −14037.3 + 1526.64i −2.14378 + 0.233150i
\(351\) 2289.65 8387.08i 0.348184 1.27541i
\(352\) −340.202 6274.66i −0.0515138 0.950115i
\(353\) −1429.73 −0.215572 −0.107786 0.994174i \(-0.534376\pi\)
−0.107786 + 0.994174i \(0.534376\pi\)
\(354\) −6767.60 + 4028.92i −1.01608 + 0.604900i
\(355\) −15366.9 −2.29743
\(356\) −180.056 3320.93i −0.0268060 0.494407i
\(357\) −7035.33 8889.62i −1.04300 1.31790i
\(358\) −4776.73 + 519.501i −0.705191 + 0.0766941i
\(359\) 4253.38 + 12623.6i 0.625306 + 1.85584i 0.505033 + 0.863100i \(0.331480\pi\)
0.120272 + 0.992741i \(0.461623\pi\)
\(360\) −2031.34 7771.78i −0.297391 1.13780i
\(361\) −5124.12 + 7557.51i −0.747065 + 1.10184i
\(362\) −1897.14 11572.0i −0.275445 1.68014i
\(363\) −3971.78 + 955.801i −0.574282 + 0.138200i
\(364\) −3576.82 + 1425.14i −0.515045 + 0.205213i
\(365\) 4930.53 + 1085.29i 0.707056 + 0.155635i
\(366\) −5664.81 5751.42i −0.809029 0.821398i
\(367\) −293.709 249.479i −0.0417752 0.0354841i 0.626256 0.779618i \(-0.284587\pi\)
−0.668031 + 0.744134i \(0.732863\pi\)
\(368\) −2476.11 1489.82i −0.350750 0.211039i
\(369\) 5404.50 3141.10i 0.762459 0.443141i
\(370\) −530.490 + 116.770i −0.0745374 + 0.0164069i
\(371\) 6077.78 4120.84i 0.850519 0.576666i
\(372\) −1544.65 + 461.487i −0.215286 + 0.0643198i
\(373\) 1683.69 + 3175.78i 0.233722 + 0.440847i 0.972435 0.233173i \(-0.0749109\pi\)
−0.738713 + 0.674020i \(0.764566\pi\)
\(374\) 7230.81 + 15629.1i 0.999723 + 2.16087i
\(375\) 8764.72 646.794i 1.20695 0.0890675i
\(376\) −1418.20 + 8650.66i −0.194517 + 1.18650i
\(377\) −2128.14 2015.88i −0.290729 0.275393i
\(378\) −949.860 + 9099.67i −0.129247 + 1.23819i
\(379\) −479.103 + 364.205i −0.0649338 + 0.0493614i −0.637138 0.770750i \(-0.719882\pi\)
0.572204 + 0.820111i \(0.306089\pi\)
\(380\) −4506.58 + 5928.31i −0.608376 + 0.800304i
\(381\) −5504.85 1099.65i −0.740216 0.147866i
\(382\) 4275.14 8063.77i 0.572605 1.08005i
\(383\) −5955.91 322.920i −0.794603 0.0430821i −0.347633 0.937631i \(-0.613014\pi\)
−0.446971 + 0.894549i \(0.647497\pi\)
\(384\) −7600.87 4373.77i −1.01010 0.581245i
\(385\) 14648.2 + 7766.00i 1.93907 + 1.02803i
\(386\) −1291.79 4652.62i −0.170338 0.613502i
\(387\) 241.213 + 3.66017i 0.0316836 + 0.000480767i
\(388\) 2918.99 + 3839.86i 0.381931 + 0.502421i
\(389\) −11872.9 3296.49i −1.54750 0.429662i −0.614318 0.789059i \(-0.710569\pi\)
−0.933185 + 0.359396i \(0.882983\pi\)
\(390\) 18733.5 6721.50i 2.43233 0.872708i
\(391\) 4021.99 + 659.371i 0.520206 + 0.0852835i
\(392\) −512.606 + 308.425i −0.0660472 + 0.0397393i
\(393\) −286.565 + 8262.39i −0.0367819 + 1.06052i
\(394\) −12793.0 + 6782.40i −1.63579 + 0.867240i
\(395\) 2642.64 + 2789.80i 0.336621 + 0.355367i
\(396\) 1320.87 3732.09i 0.167617 0.473597i
\(397\) 2138.52 + 9715.42i 0.270351 + 1.22822i 0.894555 + 0.446957i \(0.147492\pi\)
−0.624204 + 0.781261i \(0.714577\pi\)
\(398\) 8647.05 + 940.423i 1.08904 + 0.118440i
\(399\) −10846.5 + 6817.58i −1.36091 + 0.855403i
\(400\) 11121.1 13092.8i 1.39014 1.63660i
\(401\) 3521.85 + 1186.65i 0.438586 + 0.147777i 0.529928 0.848043i \(-0.322219\pi\)
−0.0913420 + 0.995820i \(0.529116\pi\)
\(402\) −2345.68 1914.98i −0.291024 0.237589i
\(403\) 2233.14 + 5604.76i 0.276031 + 0.692787i
\(404\) 137.936 + 162.390i 0.0169865 + 0.0199981i
\(405\) 1862.29 13342.8i 0.228488 1.63706i
\(406\) 2553.25 + 1731.14i 0.312107 + 0.211614i
\(407\) 375.644 + 149.670i 0.0457493 + 0.0182282i
\(408\) 9265.01 + 1334.00i 1.12423 + 0.161870i
\(409\) −1414.37 13004.9i −0.170993 1.57226i −0.694030 0.719946i \(-0.744166\pi\)
0.523037 0.852310i \(-0.324799\pi\)
\(410\) 12987.6 + 6008.70i 1.56442 + 0.723777i
\(411\) −4125.41 + 9393.26i −0.495113 + 1.12734i
\(412\) 168.329i 0.0201285i
\(413\) −6266.22 6229.88i −0.746587 0.742258i
\(414\) −1950.59 2648.41i −0.231561 0.314402i
\(415\) 13554.0 734.877i 1.60323 0.0869245i
\(416\) 3553.50 7680.76i 0.418809 0.905241i
\(417\) 3434.05 9132.71i 0.403276 1.07250i
\(418\) 18441.7 6213.74i 2.15793 0.727091i
\(419\) −2169.84 + 5445.88i −0.252991 + 0.634961i −0.999539 0.0303718i \(-0.990331\pi\)
0.746547 + 0.665332i \(0.231710\pi\)
\(420\) −5215.87 + 2896.93i −0.605972 + 0.336561i
\(421\) −4287.29 + 702.866i −0.496318 + 0.0813672i −0.404742 0.914431i \(-0.632639\pi\)
−0.0915759 + 0.995798i \(0.529190\pi\)
\(422\) −7088.51 + 6021.03i −0.817685 + 0.694548i
\(423\) −7769.91 + 12481.0i −0.893111 + 1.43463i
\(424\) −1303.38 + 5921.31i −0.149287 + 0.678217i
\(425\) −7736.16 + 22960.1i −0.882962 + 2.62054i
\(426\) −13318.1 + 5609.70i −1.51471 + 0.638007i
\(427\) 4669.24 7760.33i 0.529181 0.879505i
\(428\) 333.294 3064.59i 0.0376411 0.346104i
\(429\) −14350.7 3684.68i −1.61505 0.414680i
\(430\) 309.924 + 457.103i 0.0347578 + 0.0512639i
\(431\) −9804.52 + 9287.34i −1.09575 + 1.03795i −0.0966569 + 0.995318i \(0.530815\pi\)
−0.999091 + 0.0426297i \(0.986426\pi\)
\(432\) −6774.37 8832.01i −0.754472 0.983635i
\(433\) −13324.1 + 6164.39i −1.47879 + 0.684161i −0.982886 0.184217i \(-0.941025\pi\)
−0.495903 + 0.868378i \(0.665163\pi\)
\(434\) −3273.30 5440.27i −0.362036 0.601708i
\(435\) −3669.06 2677.91i −0.404409 0.295163i
\(436\) −130.217 + 137.468i −0.0143033 + 0.0150998i
\(437\) 1232.17 4437.86i 0.134880 0.485793i
\(438\) 4669.36 859.297i 0.509386 0.0937416i
\(439\) −6148.70 4674.12i −0.668477 0.508163i 0.215014 0.976611i \(-0.431020\pi\)
−0.883491 + 0.468448i \(0.844813\pi\)
\(440\) −13190.5 + 3662.32i −1.42916 + 0.396805i
\(441\) −992.457 + 147.279i −0.107165 + 0.0159032i
\(442\) −1255.61 + 23158.4i −0.135121 + 2.49216i
\(443\) −583.782 + 10767.2i −0.0626102 + 1.15478i 0.783368 + 0.621558i \(0.213500\pi\)
−0.845978 + 0.533218i \(0.820983\pi\)
\(444\) −118.826 + 83.9938i −0.0127010 + 0.00897786i
\(445\) −18584.3 + 5159.90i −1.97973 + 0.549669i
\(446\) −5795.03 4405.27i −0.615252 0.467703i
\(447\) −370.975 2015.85i −0.0392539 0.213303i
\(448\) 928.155 3342.91i 0.0978821 0.352540i
\(449\) −8894.77 + 9390.10i −0.934901 + 0.986962i −0.999940 0.0109202i \(-0.996524\pi\)
0.0650399 + 0.997883i \(0.479283\pi\)
\(450\) 17412.4 8895.69i 1.82406 0.931882i
\(451\) −5492.13 9127.98i −0.573424 0.953038i
\(452\) 4167.53 1928.11i 0.433682 0.200643i
\(453\) −60.0308 3078.70i −0.00622626 0.319316i
\(454\) −13038.6 + 12350.8i −1.34787 + 1.27677i
\(455\) 12530.7 + 18481.4i 1.29109 + 1.90422i
\(456\) 2630.66 10245.6i 0.270158 1.05218i
\(457\) −956.511 + 8794.98i −0.0979075 + 0.900244i 0.837444 + 0.546524i \(0.184049\pi\)
−0.935351 + 0.353721i \(0.884916\pi\)
\(458\) 8826.22 14669.3i 0.900485 1.49662i
\(459\) 13486.5 + 8035.37i 1.37146 + 0.817122i
\(460\) 684.893 2032.69i 0.0694203 0.206032i
\(461\) 549.427 2496.07i 0.0555084 0.252177i −0.940693 0.339260i \(-0.889823\pi\)
0.996201 + 0.0870827i \(0.0277544\pi\)
\(462\) 15530.3 + 1383.27i 1.56393 + 0.139297i
\(463\) 9468.14 8042.31i 0.950371 0.807252i −0.0309717 0.999520i \(-0.509860\pi\)
0.981342 + 0.192268i \(0.0615843\pi\)
\(464\) −3703.54 + 607.164i −0.370544 + 0.0607476i
\(465\) 4539.39 + 8173.10i 0.452708 + 0.815093i
\(466\) 7686.05 19290.5i 0.764055 1.91763i
\(467\) −2129.70 + 717.578i −0.211029 + 0.0711040i −0.422831 0.906209i \(-0.638963\pi\)
0.211802 + 0.977313i \(0.432067\pi\)
\(468\) 3926.04 3607.51i 0.387780 0.356319i
\(469\) 1426.45 3083.21i 0.140442 0.303560i
\(470\) −33607.3 + 1822.13i −3.29827 + 0.178827i
\(471\) 5484.18 + 2771.94i 0.536513 + 0.271176i
\(472\) 7293.70 + 176.362i 0.711271 + 0.0171985i
\(473\) 411.119i 0.0399646i
\(474\) 3308.73 + 1453.16i 0.320623 + 0.140814i
\(475\) 24848.9 + 11496.3i 2.40031 + 1.11050i
\(476\) −751.697 6911.74i −0.0723823 0.665545i
\(477\) −5833.49 + 8328.84i −0.559952 + 0.799478i
\(478\) −17270.5 6881.18i −1.65258 0.658447i
\(479\) 2398.92 + 1626.51i 0.228830 + 0.155151i 0.670214 0.742168i \(-0.266202\pi\)
−0.441384 + 0.897318i \(0.645512\pi\)
\(480\) 3944.28 12506.9i 0.375065 1.18929i
\(481\) 352.557 + 415.062i 0.0334204 + 0.0393455i
\(482\) 5703.84 + 14315.6i 0.539010 + 1.35281i
\(483\) 2333.66 2858.52i 0.219845 0.269290i
\(484\) −2374.17 799.952i −0.222969 0.0751269i
\(485\) 18108.8 21319.3i 1.69542 1.99600i
\(486\) −3256.81 12243.8i −0.303975 1.14277i
\(487\) 4352.09 + 473.318i 0.404952 + 0.0440412i 0.308329 0.951280i \(-0.400230\pi\)
0.0966234 + 0.995321i \(0.469196\pi\)
\(488\) 1607.55 + 7303.17i 0.149120 + 0.677457i
\(489\) 17651.9 2268.76i 1.63241 0.209810i
\(490\) −1579.56 1667.52i −0.145627 0.153737i
\(491\) 5353.47 2838.23i 0.492054 0.260871i −0.203854 0.979001i \(-0.565347\pi\)
0.695908 + 0.718131i \(0.255002\pi\)
\(492\) 3831.27 + 132.880i 0.351071 + 0.0121762i
\(493\) 4535.48 2728.91i 0.414336 0.249298i
\(494\) 25863.5 + 4240.10i 2.35557 + 0.386177i
\(495\) −22784.1 2828.32i −2.06883 0.256815i
\(496\) 7442.80 + 2066.48i 0.673774 + 0.187072i
\(497\) −9811.60 12906.9i −0.885534 1.16490i
\(498\) 11478.7 5584.81i 1.03288 0.502533i
\(499\) 3450.84 + 12428.8i 0.309581 + 1.11501i 0.940677 + 0.339304i \(0.110192\pi\)
−0.631096 + 0.775705i \(0.717395\pi\)
\(500\) 4761.93 + 2524.62i 0.425920 + 0.225808i
\(501\) 4522.05 7858.55i 0.403254 0.700787i
\(502\) −6668.87 361.576i −0.592921 0.0321472i
\(503\) 7132.32 13453.0i 0.632235 1.19252i −0.335854 0.941914i \(-0.609025\pi\)
0.968089 0.250608i \(-0.0806304\pi\)
\(504\) 5230.68 6668.36i 0.462288 0.589350i
\(505\) 747.769 983.674i 0.0658917 0.0866790i
\(506\) −4462.43 + 3392.25i −0.392054 + 0.298031i
\(507\) −6311.86 5749.64i −0.552899 0.503650i
\(508\) −2499.36 2367.52i −0.218290 0.206775i
\(509\) 2355.70 14369.1i 0.205136 1.25128i −0.660585 0.750751i \(-0.729692\pi\)
0.865722 0.500526i \(-0.166860\pi\)
\(510\) 2644.92 + 35841.4i 0.229645 + 3.11193i
\(511\) 2236.54 + 4834.19i 0.193617 + 0.418497i
\(512\) −288.985 545.083i −0.0249442 0.0470498i
\(513\) 10675.0 14169.4i 0.918737 1.21949i
\(514\) −4020.22 + 2725.78i −0.344989 + 0.233908i
\(515\) 953.362 209.851i 0.0815731 0.0179556i
\(516\) 124.049 + 80.6226i 0.0105832 + 0.00687832i
\(517\) 21468.4 + 12917.1i 1.82627 + 1.09883i
\(518\) −436.790 371.012i −0.0370491 0.0314698i
\(519\) 658.925 649.002i 0.0557295 0.0548902i
\(520\) −18005.5 3963.32i −1.51845 0.334237i
\(521\) 7732.81 3081.03i 0.650251 0.259084i −0.0216039 0.999767i \(-0.506877\pi\)
0.671855 + 0.740683i \(0.265498\pi\)
\(522\) −4157.47 981.492i −0.348597 0.0822964i
\(523\) −1048.81 6397.48i −0.0876891 0.534880i −0.993741 0.111712i \(-0.964366\pi\)
0.906051 0.423168i \(-0.139082\pi\)
\(524\) −2845.30 + 4196.50i −0.237209 + 0.349857i
\(525\) 14524.6 + 16439.1i 1.20744 + 1.36660i
\(526\) −7724.56 22925.7i −0.640317 1.90039i
\(527\) −10830.5 + 1177.89i −0.895224 + 0.0973615i
\(528\) −14874.5 + 11771.8i −1.22600 + 0.970268i
\(529\) −586.885 10824.5i −0.0482358 0.889657i
\(530\) −23278.5 −1.90783
\(531\) 11180.1 + 4972.68i 0.913697 + 0.406396i
\(532\) −7856.71 −0.640285
\(533\) −776.730 14325.9i −0.0631217 1.16421i
\(534\) −14223.0 + 11256.2i −1.15260 + 0.912177i
\(535\) −17772.4 + 1932.87i −1.43620 + 0.156197i
\(536\) 895.644 + 2658.18i 0.0721752 + 0.214208i
\(537\) 4942.58 + 5594.07i 0.397185 + 0.449538i
\(538\) 6438.84 9496.58i 0.515981 0.761016i
\(539\) 276.623 + 1687.32i 0.0221057 + 0.134839i
\(540\) 5321.49 6320.12i 0.424075 0.503657i
\(541\) 13719.7 5466.42i 1.09031 0.434417i 0.245448 0.969410i \(-0.421065\pi\)
0.844857 + 0.534992i \(0.179686\pi\)
\(542\) 16932.1 + 3727.04i 1.34188 + 0.295369i
\(543\) −12979.4 + 12783.9i −1.02578 + 1.01033i
\(544\) 11647.1 + 9893.13i 0.917950 + 0.779714i
\(545\) 940.916 + 566.130i 0.0739531 + 0.0444961i
\(546\) 17606.7 + 11443.0i 1.38003 + 0.896918i
\(547\) 17417.6 3833.91i 1.36147 0.299682i 0.526592 0.850118i \(-0.323470\pi\)
0.834877 + 0.550436i \(0.185539\pi\)
\(548\) −5207.58 + 3530.83i −0.405943 + 0.275236i
\(549\) −2216.55 + 12344.2i −0.172313 + 0.959628i
\(550\) −15608.3 29440.5i −1.21008 2.28245i
\(551\) −2511.59 5428.72i −0.194188 0.419730i
\(552\) 224.236 + 3038.62i 0.0172901 + 0.234298i
\(553\) −655.908 + 4000.86i −0.0504377 + 0.307656i
\(554\) 7956.20 + 7536.51i 0.610156 + 0.577971i
\(555\) 623.853 + 568.285i 0.0477137 + 0.0434637i
\(556\) 4763.58 3621.18i 0.363347 0.276209i
\(557\) 1104.13 1452.45i 0.0839916 0.110489i −0.752178 0.658960i \(-0.770997\pi\)
0.836170 + 0.548471i \(0.184790\pi\)
\(558\) 6917.79 + 5426.33i 0.524827 + 0.411676i
\(559\) 259.350 489.186i 0.0196231 0.0370132i
\(560\) 28545.6 + 1547.70i 2.15406 + 0.116790i
\(561\) 13343.5 23188.7i 1.00421 1.74514i
\(562\) 2619.14 + 1388.58i 0.196587 + 0.104224i
\(563\) −3752.34 13514.7i −0.280892 1.01168i −0.960539 0.278144i \(-0.910281\pi\)
0.679647 0.733539i \(-0.262133\pi\)
\(564\) −8107.61 + 3944.66i −0.605305 + 0.294503i
\(565\) −16115.8 21199.9i −1.19999 1.57856i
\(566\) −14174.8 3935.60i −1.05267 0.292272i
\(567\) 12395.9 6955.09i 0.918132 0.515143i
\(568\) 13210.3 + 2165.73i 0.975869 + 0.159986i
\(569\) −5856.90 + 3523.98i −0.431518 + 0.259636i −0.714701 0.699430i \(-0.753437\pi\)
0.283183 + 0.959066i \(0.408610\pi\)
\(570\) 40588.5 + 1407.73i 2.98257 + 0.103444i
\(571\) −14358.8 + 7612.54i −1.05236 + 0.557924i −0.902458 0.430777i \(-0.858239\pi\)
−0.149898 + 0.988701i \(0.547895\pi\)
\(572\) −6248.67 6596.64i −0.456766 0.482202i
\(573\) −14063.7 + 1807.58i −1.02534 + 0.131785i
\(574\) 3245.63 + 14745.0i 0.236010 + 1.07221i
\(575\) −7840.18 852.671i −0.568623 0.0618415i
\(576\) 446.913 + 4783.48i 0.0323287 + 0.346027i
\(577\) 7677.35 9038.47i 0.553921 0.652126i −0.411933 0.911214i \(-0.635146\pi\)
0.965854 + 0.259088i \(0.0834221\pi\)
\(578\) −24114.6 8125.15i −1.73535 0.584709i
\(579\) −4744.06 + 5811.04i −0.340512 + 0.417096i
\(580\) −1031.10 2587.87i −0.0738174 0.185268i
\(581\) 9271.34 + 10915.1i 0.662031 + 0.779403i
\(582\) 7911.85 25087.6i 0.563499 1.78680i
\(583\) 14343.1 + 9724.83i 1.01892 + 0.690843i
\(584\) −4085.64 1627.87i −0.289495 0.115345i
\(585\) −25326.4 17738.5i −1.78994 1.25367i
\(586\) 631.544 + 5806.95i 0.0445202 + 0.409357i
\(587\) −14105.6 6525.93i −0.991822 0.458866i −0.144247 0.989542i \(-0.546076\pi\)
−0.847575 + 0.530676i \(0.821938\pi\)
\(588\) −563.372 247.427i −0.0395120 0.0173532i
\(589\) 12311.2i 0.861247i
\(590\) 5358.61 + 27494.2i 0.373916 + 1.91851i
\(591\) 20076.5 + 10147.5i 1.39735 + 0.706281i
\(592\) 696.206 37.7472i 0.0483343 0.00262061i
\(593\) 2201.09 4757.59i 0.152425 0.329462i −0.816288 0.577645i \(-0.803972\pi\)
0.968713 + 0.248184i \(0.0798337\pi\)
\(594\) −20779.0 + 5866.14i −1.43531 + 0.405203i
\(595\) −38208.9 + 12874.1i −2.63263 + 0.887035i
\(596\) 465.274 1167.75i 0.0319771 0.0802565i
\(597\) −6561.17 11813.3i −0.449800 0.809857i
\(598\) −7449.76 + 1221.33i −0.509437 + 0.0835179i
\(599\) 4821.30 4095.25i 0.328870 0.279345i −0.467705 0.883885i \(-0.654919\pi\)
0.796575 + 0.604540i \(0.206643\pi\)
\(600\) −18041.2 1606.91i −1.22755 0.109336i
\(601\) 2233.48 10146.8i 0.151590 0.688680i −0.838108 0.545505i \(-0.816338\pi\)
0.989697 0.143175i \(-0.0457311\pi\)
\(602\) −186.047 + 552.167i −0.0125958 + 0.0373831i
\(603\) −325.931 + 4693.06i −0.0220115 + 0.316942i
\(604\) 973.593 1618.12i 0.0655876 0.109008i
\(605\) −1570.87 + 14443.9i −0.105562 + 0.970623i
\(606\) 288.984 1125.50i 0.0193716 0.0754462i
\(607\) 2837.21 + 4184.58i 0.189718 + 0.279813i 0.910638 0.413205i \(-0.135591\pi\)
−0.720920 + 0.693018i \(0.756280\pi\)
\(608\) 12537.3 11876.0i 0.836274 0.792161i
\(609\) −93.4290 4791.54i −0.00621664 0.318823i
\(610\) −26057.4 + 12055.4i −1.72956 + 0.800180i
\(611\) 17396.4 + 28913.0i 1.15185 + 1.91440i
\(612\) 4380.11 + 8573.61i 0.289306 + 0.566287i
\(613\) −5576.80 + 5887.36i −0.367447 + 0.387909i −0.883331 0.468749i \(-0.844705\pi\)
0.515884 + 0.856658i \(0.327463\pi\)
\(614\) −5394.72 + 19430.0i −0.354582 + 1.27709i
\(615\) −4023.75 21864.8i −0.263827 1.43362i
\(616\) −11498.0 8740.59i −0.752061 0.571702i
\(617\) −2489.18 + 691.117i −0.162416 + 0.0450945i −0.347784 0.937575i \(-0.613066\pi\)
0.185369 + 0.982669i \(0.440652\pi\)
\(618\) 749.652 529.899i 0.0487952 0.0344914i
\(619\) 327.193 6034.72i 0.0212455 0.391851i −0.968500 0.249012i \(-0.919894\pi\)
0.989746 0.142839i \(-0.0456231\pi\)
\(620\) −310.408 + 5725.13i −0.0201069 + 0.370850i
\(621\) −1610.69 + 4849.54i −0.104082 + 0.313374i
\(622\) 17651.6 4900.94i 1.13789 0.315932i
\(623\) −16199.8 12314.8i −1.04178 0.791943i
\(624\) −25125.1 + 4623.73i −1.61187 + 0.296631i
\(625\) 1121.36 4038.77i 0.0717670 0.258481i
\(626\) 12663.5 13368.7i 0.808523 0.853547i
\(627\) −24420.6 17823.7i −1.55544 1.13526i
\(628\) 1942.86 + 3229.06i 0.123453 + 0.205181i
\(629\) −892.476 + 412.903i −0.0565745 + 0.0261741i
\(630\) 29321.1 + 14109.3i 1.85425 + 0.892269i
\(631\) −3124.29 + 2959.48i −0.197109 + 0.186712i −0.779888 0.625919i \(-0.784724\pi\)
0.582779 + 0.812631i \(0.301965\pi\)
\(632\) −1878.60 2770.73i −0.118238 0.174389i
\(633\) 13995.1 + 3593.38i 0.878760 + 0.225630i
\(634\) 2978.04 27382.7i 0.186551 1.71531i
\(635\) −10293.0 + 17107.2i −0.643255 + 1.06910i
\(636\) −5747.07 + 2420.71i −0.358312 + 0.150924i
\(637\) −735.280 + 2182.23i −0.0457345 + 0.135735i
\(638\) −1564.95 + 7109.65i −0.0971114 + 0.441181i
\(639\) 19059.7 + 11865.4i 1.17995 + 0.734564i
\(640\) −23770.9 + 20191.2i −1.46817 + 1.24708i
\(641\) 505.069 82.8019i 0.0311217 0.00510215i −0.146201 0.989255i \(-0.546705\pi\)
0.177323 + 0.984153i \(0.443256\pi\)
\(642\) −14697.4 + 8163.02i −0.903519 + 0.501821i
\(643\) 2401.87 6028.23i 0.147310 0.369720i −0.836743 0.547596i \(-0.815543\pi\)
0.984053 + 0.177876i \(0.0569225\pi\)
\(644\) 2144.59 722.598i 0.131225 0.0442148i
\(645\) 301.974 803.086i 0.0184344 0.0490256i
\(646\) −19871.4 + 42951.4i −1.21027 + 2.61595i
\(647\) 15370.3 833.353i 0.933954 0.0506375i 0.419123 0.907929i \(-0.362337\pi\)
0.514831 + 0.857292i \(0.327855\pi\)
\(648\) −3481.41 + 11207.9i −0.211053 + 0.679455i
\(649\) 8184.31 19179.2i 0.495011 1.16002i
\(650\) 44877.2i 2.70805i
\(651\) −3966.39 + 9031.17i −0.238794 + 0.543717i
\(652\) 9905.71 + 4582.87i 0.594996 + 0.275274i
\(653\) −2195.71 20189.2i −0.131584 1.20990i −0.854681 0.519153i \(-0.826248\pi\)
0.723097 0.690746i \(-0.242718\pi\)
\(654\) 1022.14 + 147.170i 0.0611143 + 0.00879940i
\(655\) 27314.9 + 10883.2i 1.62944 + 0.649227i
\(656\) −15203.3 10308.1i −0.904861 0.613511i
\(657\) −5277.38 5153.14i −0.313379 0.306002i
\(658\) −22988.4 27064.0i −1.36198 1.60344i
\(659\) 1886.54 + 4734.87i 0.111516 + 0.279885i 0.974134 0.225972i \(-0.0725557\pi\)
−0.862617 + 0.505857i \(0.831176\pi\)
\(660\) −10907.0 8904.34i −0.643264 0.525153i
\(661\) −2243.75 756.006i −0.132030 0.0444860i 0.252511 0.967594i \(-0.418744\pi\)
−0.384541 + 0.923108i \(0.625640\pi\)
\(662\) −3139.04 + 3695.56i −0.184293 + 0.216967i
\(663\) 30505.5 19174.3i 1.78693 1.12318i
\(664\) −11755.5 1278.48i −0.687048 0.0747210i
\(665\) 9794.76 + 44498.0i 0.571165 + 2.59483i
\(666\) 748.133 + 264.781i 0.0435279 + 0.0154055i
\(667\) 1184.86 + 1250.85i 0.0687828 + 0.0726131i
\(668\) 4912.66 2604.53i 0.284546 0.150857i
\(669\) −391.994 + 11302.2i −0.0226537 + 0.653166i
\(670\) −9227.95 + 5552.27i −0.532100 + 0.320154i
\(671\) 21091.6 + 3457.79i 1.21346 + 0.198937i
\(672\) 13023.2 4672.66i 0.747590 0.268232i
\(673\) 8954.71 + 2486.26i 0.512896 + 0.142405i 0.514327 0.857594i \(-0.328042\pi\)
−0.00143129 + 0.999999i \(0.500456\pi\)
\(674\) −5321.37 7000.15i −0.304112 0.400053i
\(675\) −26899.9 14112.8i −1.53389 0.804742i
\(676\) −1400.82 5045.28i −0.0797004 0.287055i
\(677\) −9335.63 4949.44i −0.529981 0.280978i 0.181853 0.983326i \(-0.441791\pi\)
−0.711834 + 0.702347i \(0.752135\pi\)
\(678\) −21706.2 12490.4i −1.22953 0.707510i
\(679\) 29468.8 + 1597.75i 1.66555 + 0.0903036i
\(680\) 15593.9 29413.1i 0.879408 1.65874i
\(681\) 27361.0 + 5465.65i 1.53961 + 0.307554i
\(682\) 9067.53 11928.1i 0.509111 0.669724i
\(683\) −4127.34 + 3137.53i −0.231228 + 0.175775i −0.714372 0.699766i \(-0.753288\pi\)
0.483145 + 0.875541i \(0.339495\pi\)
\(684\) 10167.0 3873.22i 0.568342 0.216515i
\(685\) 26489.7 + 25092.4i 1.47755 + 1.39961i
\(686\) −3226.69 + 19682.0i −0.179586 + 1.09542i
\(687\) −26524.8 + 1957.41i −1.47305 + 0.108704i
\(688\) −297.650 643.360i −0.0164939 0.0356510i
\(689\) 10931.8 + 20619.6i 0.604455 + 1.14012i
\(690\) −11208.6 + 3348.75i −0.618414 + 0.184760i
\(691\) 7618.11 5165.20i 0.419401 0.284361i −0.333176 0.942865i \(-0.608120\pi\)
0.752578 + 0.658503i \(0.228810\pi\)
\(692\) 553.937 121.931i 0.0304299 0.00669814i
\(693\) −12171.9 20942.7i −0.667203 1.14798i
\(694\) −437.447 263.203i −0.0239269 0.0143963i
\(695\) −26447.9 22465.1i −1.44349 1.22611i
\(696\) 2776.75 + 2819.20i 0.151225 + 0.153537i
\(697\) 25300.8 + 5569.13i 1.37495 + 0.302648i
\(698\) −19601.0 + 7809.74i −1.06290 + 0.423500i
\(699\) −31365.1 + 7547.96i −1.69719 + 0.408426i
\(700\) 2176.46 + 13275.8i 0.117518 + 0.716827i
\(701\) −5074.93 + 7484.96i −0.273434 + 0.403285i −0.939468 0.342636i \(-0.888680\pi\)
0.666034 + 0.745921i \(0.267991\pi\)
\(702\) −28425.3 6128.15i −1.52827 0.329476i
\(703\) 354.825 + 1053.08i 0.0190363 + 0.0564976i
\(704\) 8139.43 885.216i 0.435747 0.0473904i
\(705\) 32448.9 + 41001.4i 1.73347 + 2.19036i
\(706\) 258.890 + 4774.94i 0.0138009 + 0.254543i
\(707\) 1303.65 0.0693477
\(708\) 4182.06 + 6230.65i 0.221994 + 0.330737i
\(709\) −28269.4 −1.49743 −0.748715 0.662892i \(-0.769329\pi\)
−0.748715 + 0.662892i \(0.769329\pi\)
\(710\) 2782.57 + 51321.4i 0.147081 + 2.71276i
\(711\) −1123.57 5500.69i −0.0592648 0.290143i
\(712\) 16703.4 1816.61i 0.879196 0.0956184i
\(713\) −1132.29 3360.51i −0.0594734 0.176511i
\(714\) −28415.1 + 25105.9i −1.48937 + 1.31592i
\(715\) −29571.3 + 43614.4i −1.54672 + 2.28124i
\(716\) 740.627 + 4517.63i 0.0386572 + 0.235798i
\(717\) 6757.54 + 28080.6i 0.351974 + 1.46261i
\(718\) 41389.3 16491.0i 2.15130 0.857157i
\(719\) 17710.5 + 3898.38i 0.918624 + 0.202204i 0.649024 0.760768i \(-0.275177\pi\)
0.269600 + 0.962972i \(0.413108\pi\)
\(720\) −37702.6 + 12069.7i −1.95152 + 0.624736i
\(721\) 784.971 + 666.760i 0.0405462 + 0.0344403i
\(722\) 26168.0 + 15744.7i 1.34885 + 0.811577i
\(723\) 13046.3 20073.5i 0.671089 1.03256i
\(724\) −10911.4 + 2401.77i −0.560107 + 0.123289i
\(725\) −8477.38 + 5747.81i −0.434265 + 0.294439i
\(726\) 3911.32 + 13091.6i 0.199949 + 0.669251i
\(727\) −13803.0 26035.2i −0.704160 1.32819i −0.934809 0.355150i \(-0.884430\pi\)
0.230649 0.973037i \(-0.425915\pi\)
\(728\) −8167.49 17653.7i −0.415807 0.898752i
\(729\) −12612.3 + 15111.3i −0.640772 + 0.767731i
\(730\) 2731.79 16663.2i 0.138504 0.844839i
\(731\) 725.845 + 687.557i 0.0367255 + 0.0347883i
\(732\) −5179.51 + 5685.98i −0.261530 + 0.287104i
\(733\) −12020.4 + 9137.70i −0.605710 + 0.460449i −0.862527 0.506012i \(-0.831119\pi\)
0.256817 + 0.966460i \(0.417326\pi\)
\(734\) −780.010 + 1026.09i −0.0392244 + 0.0515988i
\(735\) −699.008 + 3499.23i −0.0350793 + 0.175607i
\(736\) −2329.97 + 4394.79i −0.116690 + 0.220100i
\(737\) 8005.34 + 434.037i 0.400109 + 0.0216933i
\(738\) −11469.1 17480.9i −0.572063 0.871923i
\(739\) 1998.67 + 1059.63i 0.0994890 + 0.0527457i 0.517410 0.855738i \(-0.326896\pi\)
−0.417921 + 0.908483i \(0.637241\pi\)
\(740\) 138.454 + 498.667i 0.00687794 + 0.0247721i
\(741\) −17813.9 36613.6i −0.883143 1.81516i
\(742\) −14863.1 19552.0i −0.735364 0.967355i
\(743\) −5469.99 1518.74i −0.270087 0.0749892i 0.129844 0.991534i \(-0.458552\pi\)
−0.399931 + 0.916545i \(0.630966\pi\)
\(744\) −2750.48 7665.87i −0.135534 0.377748i
\(745\) −7193.82 1179.37i −0.353773 0.0579982i
\(746\) 10301.4 6198.16i 0.505579 0.304197i
\(747\) −17378.6 9554.09i −0.851203 0.467960i
\(748\) 14496.1 7685.32i 0.708594 0.375673i
\(749\) −12971.0 13693.3i −0.632776 0.668014i
\(750\) −3747.20 29154.8i −0.182438 1.41944i
\(751\) −3079.11 13988.5i −0.149612 0.679692i −0.990389 0.138311i \(-0.955833\pi\)
0.840777 0.541381i \(-0.182098\pi\)
\(752\) 42947.9 + 4670.87i 2.08264 + 0.226501i
\(753\) 5521.59 + 8784.60i 0.267222 + 0.425138i
\(754\) −6347.16 + 7472.46i −0.306565 + 0.360916i
\(755\) −10378.3 3496.86i −0.500273 0.168561i
\(756\) 8706.12 + 434.289i 0.418834 + 0.0208928i
\(757\) 1130.34 + 2836.95i 0.0542709 + 0.136210i 0.953612 0.301037i \(-0.0973329\pi\)
−0.899341 + 0.437247i \(0.855954\pi\)
\(758\) 1303.10 + 1534.13i 0.0624418 + 0.0735121i
\(759\) 8305.20 + 2619.20i 0.397180 + 0.125258i
\(760\) −31138.4 21112.3i −1.48619 1.00766i
\(761\) −5572.12 2220.14i −0.265426 0.105755i 0.233629 0.972326i \(-0.424940\pi\)
−0.499055 + 0.866570i \(0.666319\pi\)
\(762\) −2675.76 + 18583.9i −0.127208 + 0.883496i
\(763\) 125.262 + 1151.76i 0.00594336 + 0.0546482i
\(764\) −7892.12 3651.28i −0.373726 0.172904i
\(765\) 43097.8 35496.1i 2.03687 1.67760i
\(766\) 19949.7i 0.941007i
\(767\) 21837.4 17658.2i 1.02804 0.831291i
\(768\) −9894.30 + 19575.5i −0.464882 + 0.919753i
\(769\) −1030.21 + 55.8565i −0.0483100 + 0.00261929i −0.0782781 0.996932i \(-0.524942\pi\)
0.0299681 + 0.999551i \(0.490459\pi\)
\(770\) 23284.0 50327.5i 1.08974 2.35543i
\(771\) 7063.14 + 2655.86i 0.329926 + 0.124058i
\(772\) −4359.71 + 1468.96i −0.203250 + 0.0684830i
\(773\) 11453.9 28747.2i 0.532948 1.33760i −0.378278 0.925692i \(-0.623484\pi\)
0.911226 0.411907i \(-0.135137\pi\)
\(774\) −31.4538 806.253i −0.00146070 0.0374421i
\(775\) 20802.8 3410.44i 0.964204 0.158073i
\(776\) −18572.1 + 15775.3i −0.859149 + 0.729768i
\(777\) −78.9891 + 886.831i −0.00364700 + 0.0409458i
\(778\) −8859.53 + 40249.2i −0.408264 + 1.85476i
\(779\) 9347.81 27743.3i 0.429936 1.27600i
\(780\) −7360.91 17475.7i −0.337901 0.802220i
\(781\) 19725.6 32784.2i 0.903761 1.50206i
\(782\) 1473.85 13551.8i 0.0673972 0.619707i
\(783\) 2483.05 + 6154.46i 0.113329 + 0.280897i
\(784\) 1654.51 + 2440.22i 0.0753694 + 0.111162i
\(785\) 15866.3 15029.4i 0.721393 0.683340i
\(786\) 27646.1 539.065i 1.25459 0.0244629i
\(787\) −15590.6 + 7212.98i −0.706156 + 0.326703i −0.739890 0.672728i \(-0.765122\pi\)
0.0337336 + 0.999431i \(0.489260\pi\)
\(788\) 7112.43 + 11820.9i 0.321535 + 0.534396i
\(789\) −22157.3 + 30358.2i −0.999774 + 1.36981i
\(790\) 8838.68 9330.88i 0.398058 0.420225i
\(791\) 7516.48 27071.9i 0.337870 1.21690i
\(792\) 19188.1 + 5642.47i 0.860882 + 0.253152i
\(793\) 22915.3 + 17419.8i 1.02616 + 0.780069i
\(794\) 32059.7 8901.34i 1.43294 0.397855i
\(795\) 20874.9 + 29531.9i 0.931266 + 1.31747i
\(796\) 448.658 8275.01i 0.0199777 0.368467i
\(797\) −1146.23 + 21141.0i −0.0509432 + 0.939591i 0.855642 + 0.517568i \(0.173163\pi\)
−0.906585 + 0.422023i \(0.861320\pi\)
\(798\) 24733.0 + 34989.9i 1.09716 + 1.55217i
\(799\) −58709.5 + 16300.6i −2.59949 + 0.721745i
\(800\) −23540.4 17894.9i −1.04035 0.790852i
\(801\) 27034.4 + 7949.77i 1.19253 + 0.350676i
\(802\) 3325.38 11976.9i 0.146413 0.527332i
\(803\) −8644.43 + 9125.82i −0.379895 + 0.401050i
\(804\) −1700.85 + 2330.37i −0.0746076 + 0.102221i
\(805\) −6766.19 11245.5i −0.296245 0.492362i
\(806\) 18314.1 8473.00i 0.800355 0.370284i
\(807\) −17821.7 + 347.501i −0.777390 + 0.0151581i
\(808\) −781.464 + 740.242i −0.0340245 + 0.0322297i
\(809\) −15456.8 22797.0i −0.671732 0.990730i −0.998951 0.0457818i \(-0.985422\pi\)
0.327220 0.944948i \(-0.393888\pi\)
\(810\) −44898.8 3803.50i −1.94763 0.164989i
\(811\) 3976.04 36559.1i 0.172155 1.58294i −0.515494 0.856893i \(-0.672391\pi\)
0.687648 0.726044i \(-0.258643\pi\)
\(812\) 1515.25 2518.37i 0.0654863 0.108839i
\(813\) −10455.6 24822.9i −0.451038 1.07082i
\(814\) 431.840 1281.65i 0.0185946 0.0551867i
\(815\) 13606.8 61816.3i 0.584816 2.65685i
\(816\) 4092.59 45948.6i 0.175575 1.97123i
\(817\) 861.107 731.431i 0.0368743 0.0313213i
\(818\) −43177.0 + 7078.51i −1.84554 + 0.302560i
\(819\) −1271.72 32598.0i −0.0542584 1.39080i
\(820\) 5046.55 12665.9i 0.214919 0.539405i
\(821\) −31119.9 + 10485.5i −1.32289 + 0.445733i −0.890101 0.455764i \(-0.849366\pi\)
−0.432787 + 0.901496i \(0.642470\pi\)
\(822\) 32118.0 + 12076.9i 1.36283 + 0.512446i
\(823\) 2193.28 4740.69i 0.0928953 0.200790i −0.855558 0.517707i \(-0.826786\pi\)
0.948453 + 0.316917i \(0.102648\pi\)
\(824\) −849.146 + 46.0394i −0.0358998 + 0.00194643i
\(825\) −23352.4 + 46202.0i −0.985488 + 1.94975i
\(826\) −19671.5 + 22055.6i −0.828645 + 0.929071i
\(827\) 37054.5i 1.55805i 0.626990 + 0.779027i \(0.284287\pi\)
−0.626990 + 0.779027i \(0.715713\pi\)
\(828\) −2419.00 + 1992.33i −0.101529 + 0.0836211i
\(829\) 25387.7 + 11745.6i 1.06363 + 0.492089i 0.872065 0.489390i \(-0.162781\pi\)
0.191568 + 0.981479i \(0.438643\pi\)
\(830\) −4908.60 45133.8i −0.205277 1.88749i
\(831\) 2426.38 16851.9i 0.101288 0.703471i
\(832\) 10243.4 + 4081.36i 0.426836 + 0.170067i
\(833\) −3441.66 2333.50i −0.143153 0.0970601i
\(834\) −31122.7 9815.13i −1.29220 0.407518i
\(835\) −20875.8 24576.8i −0.865192 1.01858i
\(836\) −6862.80 17224.3i −0.283917 0.712579i
\(837\) 680.517 13642.2i 0.0281029 0.563373i
\(838\) 18580.7 + 6260.57i 0.765943 + 0.258076i
\(839\) −5170.43 + 6087.10i −0.212757 + 0.250477i −0.858180 0.513348i \(-0.828405\pi\)
0.645424 + 0.763825i \(0.276681\pi\)
\(840\) −16040.4 25519.5i −0.658863 1.04822i
\(841\) −22021.5 2394.99i −0.902929 0.0981995i
\(842\) 3123.71 + 14191.2i 0.127851 + 0.580832i
\(843\) −587.107 4567.94i −0.0239870 0.186629i
\(844\) 6093.84 + 6433.19i 0.248529 + 0.262369i
\(845\) −26828.6 + 14223.6i −1.09223 + 0.579062i
\(846\) 43090.3 + 23689.5i 1.75115 + 0.962720i
\(847\) −13134.7 + 7902.87i −0.532837 + 0.320597i
\(848\) 29486.2 + 4834.02i 1.19406 + 0.195756i
\(849\) 7718.34 + 21511.8i 0.312006 + 0.869593i
\(850\) 78081.7 + 21679.3i 3.15080 + 0.874815i
\(851\) −193.709 254.820i −0.00780288 0.0102645i
\(852\) 6023.85 + 12381.1i 0.242223 + 0.497850i
\(853\) −187.224 674.320i −0.00751515 0.0270671i 0.959697 0.281036i \(-0.0906779\pi\)
−0.967213 + 0.253968i \(0.918264\pi\)
\(854\) −26763.0 14188.8i −1.07238 0.568538i
\(855\) −34611.7 52754.3i −1.38444 2.11013i
\(856\) 15550.7 + 843.135i 0.620926 + 0.0336656i
\(857\) −5556.37 + 10480.4i −0.221473 + 0.417742i −0.969204 0.246260i \(-0.920798\pi\)
0.747731 + 0.664001i \(0.231143\pi\)
\(858\) −9707.31 + 48594.7i −0.386249 + 1.93356i
\(859\) 7807.52 10270.6i 0.310115 0.407950i −0.614461 0.788947i \(-0.710626\pi\)
0.924576 + 0.380998i \(0.124419\pi\)
\(860\) 418.886 318.429i 0.0166092 0.0126260i
\(861\) 15795.6 17340.1i 0.625216 0.686352i
\(862\) 32792.7 + 31062.9i 1.29573 + 1.22738i
\(863\) 6147.45 37497.8i 0.242482 1.47907i −0.532145 0.846654i \(-0.678614\pi\)
0.774626 0.632419i \(-0.217938\pi\)
\(864\) −14549.2 + 12466.9i −0.572886 + 0.490893i
\(865\) −1381.16 2985.32i −0.0542899 0.117346i
\(866\) 23000.1 + 43382.8i 0.902513 + 1.70232i
\(867\) 11316.8 + 37878.8i 0.443299 + 1.48377i
\(868\) −5006.84 + 3394.73i −0.195787 + 0.132747i
\(869\) −9344.05 + 2056.78i −0.364758 + 0.0802894i
\(870\) −8279.16 + 12738.6i −0.322632 + 0.496413i
\(871\) 9251.66 + 5566.54i 0.359909 + 0.216550i
\(872\) −729.084 619.289i −0.0283141 0.0240502i
\(873\) −38922.0 + 12460.0i −1.50894 + 0.483056i
\(874\) −15044.4 3311.53i −0.582249 0.128163i
\(875\) 30635.4 12206.3i 1.18362 0.471596i
\(876\) −1058.36 4397.95i −0.0408204 0.169627i
\(877\) −2222.57 13557.1i −0.0855769 0.521996i −0.994475 0.104977i \(-0.966523\pi\)
0.908898 0.417019i \(-0.136925\pi\)
\(878\) −14497.0 + 21381.4i −0.557231 + 0.821855i
\(879\) 6800.56 6008.57i 0.260953 0.230562i
\(880\) 21541.4 + 63932.6i 0.825183 + 2.44906i
\(881\) 20315.2 2209.41i 0.776886 0.0844914i 0.288919 0.957354i \(-0.406704\pi\)
0.487967 + 0.872862i \(0.337739\pi\)
\(882\) 671.584 + 3287.88i 0.0256388 + 0.125520i
\(883\) −1655.82 30539.9i −0.0631064 1.16393i −0.842963 0.537971i \(-0.819191\pi\)
0.779857 0.625958i \(-0.215292\pi\)
\(884\) 22096.9 0.840723
\(885\) 30074.8 31453.5i 1.14232 1.19469i
\(886\) 36065.4 1.36754
\(887\) 862.257 + 15903.4i 0.0326401 + 0.602011i 0.968404 + 0.249385i \(0.0802284\pi\)
−0.935764 + 0.352626i \(0.885289\pi\)
\(888\) −456.213 576.456i −0.0172404 0.0217845i
\(889\) −20940.7 + 2277.43i −0.790020 + 0.0859198i
\(890\) 20597.9 + 61132.3i 0.775778 + 2.30243i
\(891\) 26075.5 + 21100.5i 0.980428 + 0.793370i
\(892\) −3892.10 + 5740.42i −0.146096 + 0.215475i
\(893\) 11139.5 + 67947.7i 0.417433 + 2.54623i
\(894\) −6665.25 + 1603.98i −0.249351 + 0.0600058i
\(895\) 24663.1 9826.70i 0.921115 0.367006i
\(896\) −32136.5 7073.78i −1.19822 0.263748i
\(897\) 8229.97 + 8355.80i 0.306344 + 0.311028i
\(898\) 32971.1 + 28005.9i 1.22523 + 1.04072i
\(899\) −3946.20 2374.35i −0.146400 0.0880857i
\(900\) −9361.21 16106.7i −0.346712 0.596545i
\(901\) −41156.9 + 9059.32i −1.52179 + 0.334972i
\(902\) −29490.6 + 19995.1i −1.08861 + 0.738099i
\(903\) 867.335 259.129i 0.0319636 0.00954959i
\(904\) 10866.3 + 20496.1i 0.399789 + 0.754081i
\(905\) 27205.8 + 58804.4i 0.999284 + 2.15992i
\(906\) −10271.2 + 757.965i −0.376642 + 0.0277944i
\(907\) −1466.27 + 8943.85i −0.0536788 + 0.327426i 0.946312 + 0.323253i \(0.104777\pi\)
−0.999991 + 0.00417305i \(0.998672\pi\)
\(908\) 12422.7 + 11767.4i 0.454033 + 0.430083i
\(909\) −1687.00 + 642.677i −0.0615557 + 0.0234502i
\(910\) 59453.9 45195.7i 2.16580 1.64640i
\(911\) 2198.33 2891.86i 0.0799495 0.105172i −0.754380 0.656438i \(-0.772062\pi\)
0.834329 + 0.551267i \(0.185855\pi\)
\(912\) −51120.0 10211.8i −1.85609 0.370773i
\(913\) −15830.7 + 29859.9i −0.573844 + 1.08239i
\(914\) 29546.1 + 1601.95i 1.06926 + 0.0579733i
\(915\) 38660.8 + 22246.6i 1.39682 + 0.803771i
\(916\) −14411.1 7640.30i −0.519822 0.275592i
\(917\) 8299.24 + 29891.1i 0.298871 + 1.07644i
\(918\) 24394.0 46496.6i 0.877038 1.67169i
\(919\) 22788.7 + 29978.1i 0.817988 + 1.07604i 0.995761 + 0.0919732i \(0.0293174\pi\)
−0.177774 + 0.984071i \(0.556889\pi\)
\(920\) 10441.4 + 2899.04i 0.374176 + 0.103890i
\(921\) 29487.3 10579.9i 1.05498 0.378523i
\(922\) −8435.72 1382.97i −0.301319 0.0493987i
\(923\) 44152.8 26565.9i 1.57455 0.947374i
\(924\) 514.916 14846.3i 0.0183328 0.528581i
\(925\) 1681.15 891.289i 0.0597577 0.0316815i
\(926\) −28573.7 30164.9i −1.01403 1.07050i
\(927\) −1344.50 475.848i −0.0476365 0.0168597i
\(928\) 1388.73 + 6309.08i 0.0491244 + 0.223174i
\(929\) −8192.81 891.022i −0.289341 0.0314677i −0.0377022 0.999289i \(-0.512004\pi\)
−0.251638 + 0.967821i \(0.580969\pi\)
\(930\) 26474.1 16640.3i 0.933461 0.586730i
\(931\) −3042.03 + 3581.36i −0.107088 + 0.126073i
\(932\) −18748.8 6317.21i −0.658946 0.222025i
\(933\) −22046.5 17998.5i −0.773603 0.631560i
\(934\) 2782.16 + 6982.70i 0.0974680 + 0.244626i
\(935\) −61599.2 72520.2i −2.15456 2.53654i
\(936\) 19272.2 + 18818.5i 0.673003 + 0.657160i
\(937\) −32996.7 22372.3i −1.15043 0.780013i −0.171700 0.985149i \(-0.554926\pi\)
−0.978733 + 0.205136i \(0.934236\pi\)
\(938\) −10555.4 4205.66i −0.367427 0.146396i
\(939\) −28315.9 4077.01i −0.984085 0.141691i
\(940\) 3467.03 + 31878.9i 0.120300 + 1.10614i
\(941\) 12626.7 + 5841.74i 0.437427 + 0.202375i 0.626228 0.779640i \(-0.284598\pi\)
−0.188801 + 0.982015i \(0.560460\pi\)
\(942\) 8264.50 18817.7i 0.285851 0.650862i
\(943\) 8432.65i 0.291203i
\(944\) −1078.14 35939.0i −0.0371721 1.23911i
\(945\) −8394.01 49850.2i −0.288949 1.71601i
\(946\) −1373.03 + 74.4436i −0.0471893 + 0.00255853i
\(947\) −6210.50 + 13423.8i −0.213109 + 0.460627i −0.984420 0.175830i \(-0.943739\pi\)
0.771312 + 0.636458i \(0.219601\pi\)
\(948\) 1211.82 3222.77i 0.0415168 0.110412i
\(949\) −16042.8 + 5405.46i −0.548759 + 0.184899i
\(950\) 33895.2 85070.6i 1.15759 2.90532i
\(951\) −37409.1 + 20777.3i −1.27558 + 0.708464i
\(952\) 34661.2 5682.42i 1.18002 0.193454i
\(953\) −18847.9 + 16009.6i −0.640654 + 0.544177i −0.907760 0.419491i \(-0.862209\pi\)
0.267105 + 0.963667i \(0.413933\pi\)
\(954\) 28872.5 + 17974.2i 0.979853 + 0.609996i
\(955\) −10840.9 + 49250.5i −0.367332 + 1.66881i
\(956\) −5655.68 + 16785.5i −0.191337 + 0.567867i
\(957\) 10422.9 4390.21i 0.352064 0.148292i
\(958\) 4997.73 8306.30i 0.168549 0.280130i
\(959\) −4162.16 + 38270.5i −0.140149 + 1.28865i
\(960\) 16549.9 + 4249.35i 0.556401 + 0.142862i
\(961\) −11398.9 16812.1i −0.382629 0.564336i
\(962\) 1322.36 1252.60i 0.0443187 0.0419809i
\(963\) 23535.7 + 11325.4i 0.787568 + 0.378979i
\(964\) 13325.1 6164.86i 0.445201 0.205972i
\(965\) 13754.9 + 22860.8i 0.458844 + 0.762605i
\(966\) −9969.29 7276.21i −0.332046 0.242348i
\(967\) −10537.0 + 11123.7i −0.350410 + 0.369923i −0.877244 0.480045i \(-0.840620\pi\)
0.526834 + 0.849968i \(0.323379\pi\)
\(968\) 3386.06 12195.5i 0.112430 0.404935i
\(969\) 72309.3 13307.0i 2.39722 0.441158i
\(970\) −74480.1 56618.3i −2.46537 1.87413i
\(971\) −47717.0 + 13248.6i −1.57705 + 0.437865i −0.942277 0.334836i \(-0.891319\pi\)
−0.634771 + 0.772701i \(0.718905\pi\)
\(972\) −11480.3 + 3729.97i −0.378838 + 0.123085i
\(973\) 1982.11 36557.8i 0.0653068 1.20451i
\(974\) 792.703 14620.5i 0.0260779 0.480978i
\(975\) −56932.8 + 40243.6i −1.87006 + 1.32187i
\(976\) 35509.7 9859.21i 1.16459 0.323346i
\(977\) 27217.3 + 20690.1i 0.891258 + 0.677517i 0.947105 0.320923i \(-0.103993\pi\)
−0.0558476 + 0.998439i \(0.517786\pi\)
\(978\) −10773.4 58542.0i −0.352245 1.91408i
\(979\) 12847.3 46271.8i 0.419409 1.51057i
\(980\) −1504.95 + 1588.75i −0.0490549 + 0.0517866i
\(981\) −729.895 1428.69i −0.0237551 0.0464981i
\(982\) −10448.3 17365.3i −0.339531 0.564305i
\(983\) 48194.8 22297.3i 1.56376 0.723472i 0.568681 0.822558i \(-0.307454\pi\)
0.995079 + 0.0990863i \(0.0315920\pi\)
\(984\) 377.563 + 19363.5i 0.0122320 + 0.627322i
\(985\) 58083.4 55019.5i 1.87887 1.77976i
\(986\) −9935.11 14653.2i −0.320891 0.473278i
\(987\) −13719.6 + 53433.5i −0.442450 + 1.72321i
\(988\) 2699.81 24824.3i 0.0869356 0.799360i
\(989\) −167.780 + 278.852i −0.00539442 + 0.00896559i
\(990\) −5320.20 + 76605.2i −0.170795 + 2.45927i
\(991\) −1635.37 + 4853.62i −0.0524212 + 0.155581i −0.970666 0.240434i \(-0.922710\pi\)
0.918244 + 0.396014i \(0.129607\pi\)
\(992\) 2858.28 12985.3i 0.0914824 0.415609i
\(993\) 7503.24 + 668.305i 0.239787 + 0.0213575i
\(994\) −41329.2 + 35105.3i −1.31880 + 1.12020i
\(995\) −47426.5 + 7775.18i −1.51108 + 0.247729i
\(996\) −5905.28 10632.4i −0.187868 0.338252i
\(997\) 17767.3 44592.5i 0.564389 1.41651i −0.318948 0.947772i \(-0.603330\pi\)
0.883337 0.468738i \(-0.155291\pi\)
\(998\) 40884.1 13775.5i 1.29676 0.436928i
\(999\) −334.976 1186.55i −0.0106088 0.0375783i
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 177.4.f.a.89.15 yes 1624
3.2 odd 2 inner 177.4.f.a.89.44 yes 1624
59.2 odd 58 inner 177.4.f.a.2.44 yes 1624
177.2 even 58 inner 177.4.f.a.2.15 1624
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.f.a.2.15 1624 177.2 even 58 inner
177.4.f.a.2.44 yes 1624 59.2 odd 58 inner
177.4.f.a.89.15 yes 1624 1.1 even 1 trivial
177.4.f.a.89.44 yes 1624 3.2 odd 2 inner