Properties

Label 128.4.k.a.5.12
Level $128$
Weight $4$
Character 128.5
Analytic conductor $7.552$
Analytic rank $0$
Dimension $752$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,4,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.k (of order \(32\), degree \(16\), 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: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(752\)
Relative dimension: \(47\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 5.12
Character \(\chi\) \(=\) 128.5
Dual form 128.4.k.a.77.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.14725 + 1.84101i) q^{2} +(3.92169 + 1.18963i) q^{3} +(1.22134 - 7.90622i) q^{4} +(-5.31043 - 0.523032i) q^{5} +(-10.6110 + 4.66546i) q^{6} +(-0.627511 - 0.939136i) q^{7} +(11.9329 + 19.2251i) q^{8} +(-8.48522 - 5.66964i) q^{9} +O(q^{10})\) \(q+(-2.14725 + 1.84101i) q^{2} +(3.92169 + 1.18963i) q^{3} +(1.22134 - 7.90622i) q^{4} +(-5.31043 - 0.523032i) q^{5} +(-10.6110 + 4.66546i) q^{6} +(-0.627511 - 0.939136i) q^{7} +(11.9329 + 19.2251i) q^{8} +(-8.48522 - 5.66964i) q^{9} +(12.3657 - 8.65350i) q^{10} +(-31.5877 + 59.0965i) q^{11} +(14.1952 - 29.5528i) q^{12} +(6.94021 + 70.4651i) q^{13} +(3.07638 + 0.861302i) q^{14} +(-20.2037 - 8.36864i) q^{15} +(-61.0167 - 19.3124i) q^{16} +(60.8570 - 25.2078i) q^{17} +(28.6577 - 3.44728i) q^{18} +(-20.3907 + 24.8461i) q^{19} +(-10.6210 + 41.3467i) q^{20} +(-1.34368 - 4.42951i) q^{21} +(-40.9707 - 185.048i) q^{22} +(34.8546 + 175.226i) q^{23} +(23.9265 + 89.5908i) q^{24} +(-94.6710 - 18.8312i) q^{25} +(-144.630 - 138.529i) q^{26} +(-96.7275 - 117.863i) q^{27} +(-8.19142 + 3.81423i) q^{28} +(-145.489 + 77.7653i) q^{29} +(58.7891 - 19.2257i) q^{30} +(-155.257 - 155.257i) q^{31} +(166.572 - 70.8641i) q^{32} +(-194.180 + 194.180i) q^{33} +(-84.2672 + 166.166i) q^{34} +(2.84116 + 5.31543i) q^{35} +(-55.1888 + 60.1614i) q^{36} +(-31.7806 + 26.0816i) q^{37} +(-1.95820 - 90.8903i) q^{38} +(-56.6103 + 284.599i) q^{39} +(-53.3137 - 108.335i) q^{40} +(144.356 - 28.7143i) q^{41} +(11.0400 + 7.03753i) q^{42} +(525.759 - 159.487i) q^{43} +(428.650 + 321.916i) q^{44} +(42.0948 + 34.5463i) q^{45} +(-397.435 - 312.086i) q^{46} +(167.389 + 404.114i) q^{47} +(-216.314 - 148.325i) q^{48} +(130.772 - 315.712i) q^{49} +(237.951 - 133.855i) q^{50} +(268.651 - 26.4598i) q^{51} +(565.589 + 31.1910i) q^{52} +(-266.715 - 142.562i) q^{53} +(424.685 + 75.0039i) q^{54} +(198.654 - 297.306i) q^{55} +(10.5670 - 23.2706i) q^{56} +(-109.524 + 73.1815i) q^{57} +(169.233 - 434.828i) q^{58} +(12.3285 - 125.173i) q^{59} +(-90.8399 + 149.514i) q^{60} +(-235.158 + 775.214i) q^{61} +(619.205 + 47.5449i) q^{62} +11.5265i q^{63} +(-227.210 + 458.824i) q^{64} -377.830i q^{65} +(59.4646 - 774.442i) q^{66} +(63.9047 - 210.665i) q^{67} +(-124.971 - 511.936i) q^{68} +(-71.7655 + 728.648i) q^{69} +(-15.8864 - 6.18293i) q^{70} +(657.579 - 439.380i) q^{71} +(7.74588 - 230.785i) q^{72} +(-232.535 + 348.014i) q^{73} +(20.2241 - 114.512i) q^{74} +(-348.869 - 186.474i) q^{75} +(171.535 + 191.559i) q^{76} +(75.3213 - 7.41850i) q^{77} +(-402.394 - 715.325i) q^{78} +(130.419 - 314.859i) q^{79} +(313.924 + 134.471i) q^{80} +(-133.679 - 322.729i) q^{81} +(-257.106 + 327.419i) q^{82} +(875.707 + 718.674i) q^{83} +(-36.6618 + 5.21348i) q^{84} +(-336.362 + 102.034i) q^{85} +(-835.316 + 1310.39i) q^{86} +(-663.074 + 131.894i) q^{87} +(-1513.07 + 97.9172i) q^{88} +(-170.685 + 858.094i) q^{89} +(-153.988 + 3.31763i) q^{90} +(61.8213 - 50.7354i) q^{91} +(1427.95 - 61.5579i) q^{92} +(-424.171 - 793.569i) q^{93} +(-1103.41 - 559.566i) q^{94} +(121.279 - 121.279i) q^{95} +(737.547 - 79.7475i) q^{96} +(-764.616 - 764.616i) q^{97} +(300.430 + 918.665i) q^{98} +(603.084 - 322.355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{32}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14725 + 1.84101i −0.759166 + 0.650897i
\(3\) 3.92169 + 1.18963i 0.754731 + 0.228945i 0.644126 0.764919i \(-0.277221\pi\)
0.110605 + 0.993864i \(0.464721\pi\)
\(4\) 1.22134 7.90622i 0.152667 0.988278i
\(5\) −5.31043 0.523032i −0.474980 0.0467814i −0.142305 0.989823i \(-0.545451\pi\)
−0.332675 + 0.943042i \(0.607951\pi\)
\(6\) −10.6110 + 4.66546i −0.721986 + 0.317444i
\(7\) −0.627511 0.939136i −0.0338824 0.0507086i 0.814142 0.580666i \(-0.197208\pi\)
−0.848024 + 0.529958i \(0.822208\pi\)
\(8\) 11.9329 + 19.2251i 0.527366 + 0.849638i
\(9\) −8.48522 5.66964i −0.314267 0.209987i
\(10\) 12.3657 8.65350i 0.391038 0.273648i
\(11\) −31.5877 + 59.0965i −0.865823 + 1.61984i −0.0838934 + 0.996475i \(0.526736\pi\)
−0.781930 + 0.623367i \(0.785764\pi\)
\(12\) 14.1952 29.5528i 0.341484 0.710931i
\(13\) 6.94021 + 70.4651i 0.148067 + 1.50335i 0.726245 + 0.687436i \(0.241264\pi\)
−0.578178 + 0.815911i \(0.696236\pi\)
\(14\) 3.07638 + 0.861302i 0.0587284 + 0.0164423i
\(15\) −20.2037 8.36864i −0.347771 0.144052i
\(16\) −61.0167 19.3124i −0.953385 0.301756i
\(17\) 60.8570 25.2078i 0.868235 0.359635i 0.0963124 0.995351i \(-0.469295\pi\)
0.771923 + 0.635716i \(0.219295\pi\)
\(18\) 28.6577 3.44728i 0.375261 0.0451406i
\(19\) −20.3907 + 24.8461i −0.246208 + 0.300005i −0.881421 0.472332i \(-0.843412\pi\)
0.635213 + 0.772337i \(0.280912\pi\)
\(20\) −10.6210 + 41.3467i −0.118747 + 0.462270i
\(21\) −1.34368 4.42951i −0.0139626 0.0460285i
\(22\) −40.9707 185.048i −0.397045 1.79329i
\(23\) 34.8546 + 175.226i 0.315987 + 1.58857i 0.733362 + 0.679838i \(0.237950\pi\)
−0.417375 + 0.908734i \(0.637050\pi\)
\(24\) 23.9265 + 89.5908i 0.203499 + 0.761986i
\(25\) −94.6710 18.8312i −0.757368 0.150650i
\(26\) −144.630 138.529i −1.09093 1.04491i
\(27\) −96.7275 117.863i −0.689452 0.840100i
\(28\) −8.19142 + 3.81423i −0.0552869 + 0.0257437i
\(29\) −145.489 + 77.7653i −0.931606 + 0.497954i −0.866085 0.499897i \(-0.833371\pi\)
−0.0655213 + 0.997851i \(0.520871\pi\)
\(30\) 58.7891 19.2257i 0.357779 0.117004i
\(31\) −155.257 155.257i −0.899515 0.899515i 0.0958784 0.995393i \(-0.469434\pi\)
−0.995393 + 0.0958784i \(0.969434\pi\)
\(32\) 166.572 70.8641i 0.920190 0.391472i
\(33\) −194.180 + 194.180i −1.02432 + 1.02432i
\(34\) −84.2672 + 166.166i −0.425050 + 0.838154i
\(35\) 2.84116 + 5.31543i 0.0137212 + 0.0256706i
\(36\) −55.1888 + 60.1614i −0.255504 + 0.278525i
\(37\) −31.7806 + 26.0816i −0.141208 + 0.115886i −0.702346 0.711836i \(-0.747864\pi\)
0.561138 + 0.827723i \(0.310364\pi\)
\(38\) −1.95820 90.8903i −0.00835954 0.388009i
\(39\) −56.6103 + 284.599i −0.232433 + 1.16852i
\(40\) −53.3137 108.335i −0.210741 0.428232i
\(41\) 144.356 28.7143i 0.549870 0.109376i 0.0876668 0.996150i \(-0.472059\pi\)
0.462204 + 0.886774i \(0.347059\pi\)
\(42\) 11.0400 + 7.03753i 0.0405597 + 0.0258551i
\(43\) 525.759 159.487i 1.86459 0.565618i 0.866843 0.498582i \(-0.166146\pi\)
0.997751 0.0670361i \(-0.0213543\pi\)
\(44\) 428.650 + 321.916i 1.46867 + 1.10297i
\(45\) 42.0948 + 34.5463i 0.139447 + 0.114441i
\(46\) −397.435 312.086i −1.27388 1.00032i
\(47\) 167.389 + 404.114i 0.519495 + 1.25417i 0.938214 + 0.346056i \(0.112479\pi\)
−0.418719 + 0.908116i \(0.637521\pi\)
\(48\) −216.314 148.325i −0.650464 0.446017i
\(49\) 130.772 315.712i 0.381260 0.920443i
\(50\) 237.951 133.855i 0.673026 0.378600i
\(51\) 268.651 26.4598i 0.737620 0.0726492i
\(52\) 565.589 + 31.1910i 1.50833 + 0.0831811i
\(53\) −266.715 142.562i −0.691247 0.369479i 0.0880655 0.996115i \(-0.471932\pi\)
−0.779313 + 0.626635i \(0.784432\pi\)
\(54\) 424.685 + 75.0039i 1.07023 + 0.189014i
\(55\) 198.654 297.306i 0.487027 0.728887i
\(56\) 10.5670 23.2706i 0.0252155 0.0555298i
\(57\) −109.524 + 73.1815i −0.254505 + 0.170055i
\(58\) 169.233 434.828i 0.383128 0.984409i
\(59\) 12.3285 125.173i 0.0272039 0.276206i −0.971954 0.235172i \(-0.924435\pi\)
0.999158 0.0410341i \(-0.0130652\pi\)
\(60\) −90.8399 + 149.514i −0.195456 + 0.321703i
\(61\) −235.158 + 775.214i −0.493590 + 1.62715i 0.257024 + 0.966405i \(0.417258\pi\)
−0.750613 + 0.660742i \(0.770242\pi\)
\(62\) 619.205 + 47.5449i 1.26837 + 0.0973904i
\(63\) 11.5265i 0.0230509i
\(64\) −227.210 + 458.824i −0.443769 + 0.896141i
\(65\) 377.830i 0.720986i
\(66\) 59.4646 774.442i 0.110903 1.44435i
\(67\) 63.9047 210.665i 0.116525 0.384133i −0.879205 0.476444i \(-0.841926\pi\)
0.995730 + 0.0923113i \(0.0294255\pi\)
\(68\) −124.971 511.936i −0.222868 0.912962i
\(69\) −71.7655 + 728.648i −0.125211 + 1.27129i
\(70\) −15.8864 6.18293i −0.0271256 0.0105572i
\(71\) 657.579 439.380i 1.09916 0.734434i 0.132674 0.991160i \(-0.457644\pi\)
0.966484 + 0.256726i \(0.0826437\pi\)
\(72\) 7.74588 230.785i 0.0126786 0.377753i
\(73\) −232.535 + 348.014i −0.372824 + 0.557971i −0.969680 0.244377i \(-0.921416\pi\)
0.596856 + 0.802349i \(0.296416\pi\)
\(74\) 20.2241 114.512i 0.0317703 0.179889i
\(75\) −348.869 186.474i −0.537118 0.287096i
\(76\) 171.535 + 191.559i 0.258900 + 0.289122i
\(77\) 75.3213 7.41850i 0.111476 0.0109794i
\(78\) −402.394 715.325i −0.584131 1.03839i
\(79\) 130.419 314.859i 0.185738 0.448411i −0.803393 0.595449i \(-0.796974\pi\)
0.989131 + 0.147038i \(0.0469741\pi\)
\(80\) 313.924 + 134.471i 0.438722 + 0.187928i
\(81\) −133.679 322.729i −0.183373 0.442701i
\(82\) −257.106 + 327.419i −0.346251 + 0.440943i
\(83\) 875.707 + 718.674i 1.15809 + 0.950419i 0.999319 0.0368968i \(-0.0117473\pi\)
0.158770 + 0.987316i \(0.449247\pi\)
\(84\) −36.6618 + 5.21348i −0.0476206 + 0.00677187i
\(85\) −336.362 + 102.034i −0.429218 + 0.130202i
\(86\) −835.316 + 1310.39i −1.04738 + 1.64306i
\(87\) −663.074 + 131.894i −0.817115 + 0.162534i
\(88\) −1513.07 + 97.9172i −1.83288 + 0.118614i
\(89\) −170.685 + 858.094i −0.203288 + 1.02200i 0.735506 + 0.677518i \(0.236944\pi\)
−0.938794 + 0.344479i \(0.888056\pi\)
\(90\) −153.988 + 3.31763i −0.180353 + 0.00388565i
\(91\) 61.8213 50.7354i 0.0712157 0.0584453i
\(92\) 1427.95 61.5579i 1.61819 0.0697593i
\(93\) −424.171 793.569i −0.472952 0.884831i
\(94\) −1103.41 559.566i −1.21072 0.613988i
\(95\) 121.279 121.279i 0.130978 0.130978i
\(96\) 737.547 79.7475i 0.784121 0.0847833i
\(97\) −764.616 764.616i −0.800361 0.800361i 0.182791 0.983152i \(-0.441487\pi\)
−0.983152 + 0.182791i \(0.941487\pi\)
\(98\) 300.430 + 918.665i 0.309673 + 0.946931i
\(99\) 603.084 322.355i 0.612245 0.327252i
\(100\) −264.509 + 725.491i −0.264509 + 0.725491i
\(101\) 165.420 + 201.565i 0.162970 + 0.198579i 0.848092 0.529849i \(-0.177751\pi\)
−0.685122 + 0.728428i \(0.740251\pi\)
\(102\) −528.147 + 551.405i −0.512689 + 0.535267i
\(103\) 126.295 + 25.1216i 0.120817 + 0.0240321i 0.255129 0.966907i \(-0.417882\pi\)
−0.134311 + 0.990939i \(0.542882\pi\)
\(104\) −1271.88 + 974.282i −1.19922 + 0.918618i
\(105\) 4.81874 + 24.2254i 0.00447867 + 0.0225158i
\(106\) 835.161 184.910i 0.765264 0.169434i
\(107\) −174.275 574.507i −0.157456 0.519063i 0.842346 0.538936i \(-0.181174\pi\)
−0.999803 + 0.0198735i \(0.993674\pi\)
\(108\) −1049.99 + 620.798i −0.935509 + 0.553114i
\(109\) −132.561 + 161.526i −0.116486 + 0.141939i −0.827989 0.560745i \(-0.810515\pi\)
0.711503 + 0.702683i \(0.248015\pi\)
\(110\) 120.786 + 1004.11i 0.104696 + 0.870351i
\(111\) −155.661 + 64.4770i −0.133105 + 0.0551341i
\(112\) 20.1517 + 69.4217i 0.0170014 + 0.0585690i
\(113\) −1090.69 451.780i −0.907999 0.376106i −0.120709 0.992688i \(-0.538517\pi\)
−0.787290 + 0.616582i \(0.788517\pi\)
\(114\) 100.447 358.773i 0.0825236 0.294756i
\(115\) −93.4444 948.757i −0.0757716 0.769322i
\(116\) 437.139 + 1245.24i 0.349891 + 0.996707i
\(117\) 340.623 637.260i 0.269150 0.503545i
\(118\) 203.973 + 291.474i 0.159129 + 0.227393i
\(119\) −61.8620 41.3349i −0.0476545 0.0318417i
\(120\) −80.2013 488.281i −0.0610112 0.371448i
\(121\) −1755.14 2626.76i −1.31867 1.97352i
\(122\) −922.235 2097.51i −0.684387 1.55655i
\(123\) 600.281 + 59.1225i 0.440045 + 0.0433407i
\(124\) −1417.12 + 1037.87i −1.02630 + 0.751644i
\(125\) 1131.19 + 343.143i 0.809413 + 0.245533i
\(126\) −21.2205 24.7503i −0.0150038 0.0174995i
\(127\) −638.211 −0.445922 −0.222961 0.974827i \(-0.571572\pi\)
−0.222961 + 0.974827i \(0.571572\pi\)
\(128\) −356.826 1403.51i −0.246400 0.969168i
\(129\) 2251.60 1.53676
\(130\) 695.591 + 811.295i 0.469287 + 0.547348i
\(131\) 1356.99 + 411.638i 0.905044 + 0.274542i 0.708299 0.705913i \(-0.249463\pi\)
0.196745 + 0.980455i \(0.436963\pi\)
\(132\) 1298.07 + 1772.39i 0.855930 + 1.16869i
\(133\) 36.1293 + 3.55842i 0.0235549 + 0.00231996i
\(134\) 250.619 + 570.000i 0.161568 + 0.367467i
\(135\) 452.019 + 676.494i 0.288175 + 0.431284i
\(136\) 1210.83 + 869.180i 0.763437 + 0.548026i
\(137\) 1636.80 + 1093.67i 1.02074 + 0.682035i 0.948963 0.315386i \(-0.102134\pi\)
0.0717737 + 0.997421i \(0.477134\pi\)
\(138\) −1187.35 1696.71i −0.732421 1.04662i
\(139\) 495.858 927.686i 0.302577 0.566081i −0.683980 0.729501i \(-0.739752\pi\)
0.986557 + 0.163420i \(0.0522524\pi\)
\(140\) 45.4950 15.9709i 0.0274645 0.00964132i
\(141\) 175.703 + 1783.94i 0.104942 + 1.06550i
\(142\) −603.079 + 2154.07i −0.356404 + 1.27300i
\(143\) −4383.46 1815.69i −2.56338 1.06179i
\(144\) 408.245 + 509.812i 0.236253 + 0.295030i
\(145\) 813.282 336.872i 0.465789 0.192936i
\(146\) −141.387 1175.37i −0.0801457 0.666263i
\(147\) 888.430 1082.56i 0.498479 0.607399i
\(148\) 167.392 + 283.119i 0.0929700 + 0.157245i
\(149\) 53.3901 + 176.004i 0.0293550 + 0.0967703i 0.970394 0.241528i \(-0.0776486\pi\)
−0.941039 + 0.338299i \(0.890149\pi\)
\(150\) 1092.41 241.866i 0.594632 0.131655i
\(151\) 298.674 + 1501.54i 0.160965 + 0.809228i 0.973918 + 0.226898i \(0.0728585\pi\)
−0.812953 + 0.582329i \(0.802141\pi\)
\(152\) −720.990 95.5259i −0.384737 0.0509748i
\(153\) −659.304 131.144i −0.348376 0.0692964i
\(154\) −148.076 + 154.597i −0.0774824 + 0.0808946i
\(155\) 743.277 + 905.685i 0.385171 + 0.469332i
\(156\) 2180.96 + 795.165i 1.11934 + 0.408104i
\(157\) 4.44285 2.37475i 0.00225846 0.00120717i −0.470267 0.882524i \(-0.655842\pi\)
0.472526 + 0.881317i \(0.343342\pi\)
\(158\) 299.618 + 916.184i 0.150863 + 0.461314i
\(159\) −876.377 876.377i −0.437115 0.437115i
\(160\) −921.634 + 289.196i −0.455385 + 0.142894i
\(161\) 142.690 142.690i 0.0698479 0.0698479i
\(162\) 881.189 + 446.874i 0.427363 + 0.216727i
\(163\) 1050.51 + 1965.36i 0.504797 + 0.944409i 0.997253 + 0.0740718i \(0.0235994\pi\)
−0.492456 + 0.870338i \(0.663901\pi\)
\(164\) −50.7132 1176.38i −0.0241466 0.560123i
\(165\) 1132.75 929.620i 0.534449 0.438611i
\(166\) −3203.45 + 69.0174i −1.49781 + 0.0322698i
\(167\) 175.898 884.297i 0.0815052 0.409754i −0.918396 0.395664i \(-0.870515\pi\)
0.999901 0.0140907i \(-0.00448536\pi\)
\(168\) 69.1239 78.6895i 0.0317442 0.0361371i
\(169\) −2762.38 + 549.472i −1.25734 + 0.250101i
\(170\) 534.405 838.339i 0.241100 0.378222i
\(171\) 313.888 95.2169i 0.140372 0.0425814i
\(172\) −618.811 4351.56i −0.274325 1.92909i
\(173\) −633.874 520.207i −0.278570 0.228616i 0.484725 0.874667i \(-0.338920\pi\)
−0.763295 + 0.646050i \(0.776420\pi\)
\(174\) 1180.97 1503.94i 0.514534 0.655248i
\(175\) 41.7220 + 100.726i 0.0180222 + 0.0435095i
\(176\) 3068.67 2995.84i 1.31426 1.28307i
\(177\) 197.258 476.224i 0.0837675 0.202233i
\(178\) −1213.26 2156.77i −0.510885 0.908185i
\(179\) −1340.64 + 132.042i −0.559800 + 0.0551355i −0.373960 0.927445i \(-0.622000\pi\)
−0.185839 + 0.982580i \(0.559500\pi\)
\(180\) 324.543 290.618i 0.134389 0.120341i
\(181\) 3005.27 + 1606.35i 1.23415 + 0.659664i 0.953860 0.300252i \(-0.0970709\pi\)
0.280286 + 0.959917i \(0.409571\pi\)
\(182\) −39.3410 + 222.755i −0.0160228 + 0.0907238i
\(183\) −1844.44 + 2760.40i −0.745054 + 1.11505i
\(184\) −2952.82 + 2761.05i −1.18307 + 1.10623i
\(185\) 182.410 121.883i 0.0724922 0.0484377i
\(186\) 2371.77 + 923.083i 0.934982 + 0.363891i
\(187\) −432.642 + 4392.69i −0.169187 + 1.71778i
\(188\) 3399.45 829.858i 1.31878 0.321934i
\(189\) −49.9917 + 164.800i −0.0192400 + 0.0634257i
\(190\) −37.1396 + 483.691i −0.0141810 + 0.184688i
\(191\) 537.985i 0.203808i 0.994794 + 0.101904i \(0.0324934\pi\)
−0.994794 + 0.101904i \(0.967507\pi\)
\(192\) −1436.88 + 1529.07i −0.540093 + 0.574746i
\(193\) 4907.18i 1.83019i −0.403240 0.915094i \(-0.632116\pi\)
0.403240 0.915094i \(-0.367884\pi\)
\(194\) 3049.49 + 234.151i 1.12856 + 0.0866550i
\(195\) 449.479 1481.74i 0.165066 0.544150i
\(196\) −2336.37 1419.51i −0.851447 0.517313i
\(197\) −143.298 + 1454.93i −0.0518253 + 0.526191i 0.933865 + 0.357625i \(0.116414\pi\)
−0.985690 + 0.168566i \(0.946086\pi\)
\(198\) −701.511 + 1802.46i −0.251789 + 0.646947i
\(199\) 658.964 440.306i 0.234737 0.156847i −0.432639 0.901567i \(-0.642417\pi\)
0.667376 + 0.744721i \(0.267417\pi\)
\(200\) −767.671 2044.77i −0.271413 0.722936i
\(201\) 501.229 750.143i 0.175890 0.263239i
\(202\) −726.283 128.269i −0.252976 0.0446783i
\(203\) 164.328 + 87.8351i 0.0568156 + 0.0303686i
\(204\) 118.917 2156.33i 0.0408130 0.740065i
\(205\) −781.614 + 76.9822i −0.266294 + 0.0262277i
\(206\) −317.435 + 178.568i −0.107363 + 0.0603953i
\(207\) 697.720 1684.44i 0.234275 0.565589i
\(208\) 937.379 4433.58i 0.312479 1.47795i
\(209\) −824.223 1989.85i −0.272788 0.658568i
\(210\) −54.9463 43.1466i −0.0180555 0.0141781i
\(211\) −1860.12 1526.56i −0.606899 0.498069i 0.280020 0.959994i \(-0.409659\pi\)
−0.886919 + 0.461925i \(0.847159\pi\)
\(212\) −1452.88 + 1934.59i −0.470679 + 0.626736i
\(213\) 3101.52 940.837i 0.997713 0.302653i
\(214\) 1431.89 + 912.767i 0.457392 + 0.291568i
\(215\) −2875.43 + 571.958i −0.912104 + 0.181429i
\(216\) 1111.68 3266.05i 0.350187 1.02883i
\(217\) −48.3820 + 243.233i −0.0151354 + 0.0760908i
\(218\) −12.7304 590.881i −0.00395509 0.183576i
\(219\) −1325.94 + 1088.17i −0.409127 + 0.335762i
\(220\) −2107.95 1933.71i −0.645990 0.592595i
\(221\) 2198.63 + 4113.35i 0.669212 + 1.25201i
\(222\) 215.540 425.022i 0.0651626 0.128494i
\(223\) −1735.84 + 1735.84i −0.521258 + 0.521258i −0.917951 0.396693i \(-0.870158\pi\)
0.396693 + 0.917951i \(0.370158\pi\)
\(224\) −171.077 111.966i −0.0510293 0.0333975i
\(225\) 696.538 + 696.538i 0.206382 + 0.206382i
\(226\) 3173.72 1037.90i 0.934128 0.305487i
\(227\) 2390.54 1277.77i 0.698967 0.373606i −0.0833207 0.996523i \(-0.526553\pi\)
0.782288 + 0.622917i \(0.214053\pi\)
\(228\) 444.823 + 955.299i 0.129207 + 0.277483i
\(229\) 3910.47 + 4764.93i 1.12843 + 1.37500i 0.917612 + 0.397476i \(0.130114\pi\)
0.210822 + 0.977525i \(0.432386\pi\)
\(230\) 1947.32 + 1865.18i 0.558272 + 0.534724i
\(231\) 304.212 + 60.5116i 0.0866481 + 0.0172354i
\(232\) −3231.16 1869.07i −0.914378 0.528924i
\(233\) 574.639 + 2888.91i 0.161570 + 0.812268i 0.973531 + 0.228556i \(0.0734004\pi\)
−0.811961 + 0.583712i \(0.801600\pi\)
\(234\) 441.804 + 1995.45i 0.123426 + 0.557463i
\(235\) −677.546 2233.57i −0.188078 0.620009i
\(236\) −974.588 250.350i −0.268815 0.0690526i
\(237\) 886.031 1079.63i 0.242843 0.295906i
\(238\) 208.931 25.1326i 0.0569033 0.00684498i
\(239\) −3801.13 + 1574.48i −1.02876 + 0.426128i −0.832266 0.554377i \(-0.812957\pi\)
−0.196497 + 0.980504i \(0.562957\pi\)
\(240\) 1071.14 + 900.807i 0.288092 + 0.242279i
\(241\) 1919.52 + 795.091i 0.513058 + 0.212516i 0.624165 0.781293i \(-0.285439\pi\)
−0.111106 + 0.993809i \(0.535439\pi\)
\(242\) 8604.63 + 2409.06i 2.28565 + 0.639917i
\(243\) 263.195 + 2672.26i 0.0694812 + 0.705455i
\(244\) 5841.80 + 2806.01i 1.53272 + 0.736216i
\(245\) −859.585 + 1608.17i −0.224150 + 0.419356i
\(246\) −1397.80 + 978.175i −0.362278 + 0.253521i
\(247\) −1892.30 1264.39i −0.487466 0.325715i
\(248\) 1132.16 4837.50i 0.289888 1.23864i
\(249\) 2579.30 + 3860.19i 0.656451 + 0.982449i
\(250\) −3060.67 + 1345.72i −0.774296 + 0.340444i
\(251\) −2365.72 233.003i −0.594911 0.0585936i −0.203919 0.978988i \(-0.565368\pi\)
−0.390992 + 0.920394i \(0.627868\pi\)
\(252\) 91.1313 + 14.0778i 0.0227807 + 0.00351912i
\(253\) −11456.2 3475.21i −2.84682 0.863575i
\(254\) 1370.40 1174.96i 0.338529 0.290249i
\(255\) −1440.49 −0.353753
\(256\) 3350.07 + 2356.75i 0.817887 + 0.575379i
\(257\) −2908.24 −0.705879 −0.352939 0.935646i \(-0.614818\pi\)
−0.352939 + 0.935646i \(0.614818\pi\)
\(258\) −4834.74 + 4145.22i −1.16666 + 1.00027i
\(259\) 44.4369 + 13.4798i 0.0106609 + 0.00323395i
\(260\) −2987.21 461.459i −0.712534 0.110071i
\(261\) 1675.40 + 165.013i 0.397337 + 0.0391343i
\(262\) −3671.62 + 1614.35i −0.865777 + 0.380667i
\(263\) 2922.02 + 4373.12i 0.685094 + 1.02532i 0.997164 + 0.0752564i \(0.0239775\pi\)
−0.312070 + 0.950059i \(0.601022\pi\)
\(264\) −6050.29 1416.00i −1.41049 0.330108i
\(265\) 1341.81 + 896.566i 0.311043 + 0.207833i
\(266\) −84.1296 + 58.8736i −0.0193922 + 0.0135706i
\(267\) −1690.19 + 3162.13i −0.387409 + 0.724791i
\(268\) −1587.52 762.539i −0.361840 0.173804i
\(269\) −801.802 8140.83i −0.181735 1.84519i −0.463982 0.885845i \(-0.653580\pi\)
0.282247 0.959342i \(-0.408920\pi\)
\(270\) −2216.03 620.427i −0.499494 0.139844i
\(271\) 4017.90 + 1664.27i 0.900627 + 0.373052i 0.784461 0.620178i \(-0.212940\pi\)
0.116166 + 0.993230i \(0.462940\pi\)
\(272\) −4200.11 + 362.803i −0.936284 + 0.0808757i
\(273\) 302.801 125.424i 0.0671294 0.0278059i
\(274\) −5528.07 + 664.979i −1.21884 + 0.146616i
\(275\) 4103.30 4999.89i 0.899776 1.09638i
\(276\) 5673.20 + 1457.32i 1.23727 + 0.317827i
\(277\) −393.153 1296.05i −0.0852789 0.281127i 0.903921 0.427699i \(-0.140676\pi\)
−0.989200 + 0.146573i \(0.953176\pi\)
\(278\) 643.152 + 2904.85i 0.138754 + 0.626696i
\(279\) 437.138 + 2197.64i 0.0938019 + 0.471574i
\(280\) −68.2864 + 118.050i −0.0145746 + 0.0251959i
\(281\) −3243.44 645.160i −0.688567 0.136965i −0.161608 0.986855i \(-0.551668\pi\)
−0.526959 + 0.849890i \(0.676668\pi\)
\(282\) −3661.54 3507.10i −0.773197 0.740583i
\(283\) −208.193 253.684i −0.0437307 0.0532860i 0.750686 0.660659i \(-0.229723\pi\)
−0.794417 + 0.607373i \(0.792223\pi\)
\(284\) −2670.71 5735.60i −0.558019 1.19840i
\(285\) 619.895 331.341i 0.128840 0.0688664i
\(286\) 12755.1 4171.28i 2.63715 0.862423i
\(287\) −117.552 117.552i −0.0241772 0.0241772i
\(288\) −1815.17 343.107i −0.371390 0.0702006i
\(289\) −405.872 + 405.872i −0.0826118 + 0.0826118i
\(290\) −1126.13 + 2220.61i −0.228030 + 0.449651i
\(291\) −2088.98 3908.20i −0.420818 0.787295i
\(292\) 2467.47 + 2263.52i 0.494512 + 0.453638i
\(293\) −7314.58 + 6002.92i −1.45844 + 1.19691i −0.518727 + 0.854940i \(0.673594\pi\)
−0.939711 + 0.341969i \(0.888906\pi\)
\(294\) 85.3197 + 3960.13i 0.0169250 + 0.785576i
\(295\) −130.939 + 658.275i −0.0258426 + 0.129919i
\(296\) −880.658 299.754i −0.172930 0.0588610i
\(297\) 10020.7 1993.24i 1.95777 0.389425i
\(298\) −438.667 279.631i −0.0852728 0.0543577i
\(299\) −12105.4 + 3672.14i −2.34139 + 0.710252i
\(300\) −1900.39 + 2530.48i −0.365731 + 0.486992i
\(301\) −479.700 393.679i −0.0918586 0.0753864i
\(302\) −3405.68 2674.31i −0.648923 0.509567i
\(303\) 408.940 + 987.268i 0.0775346 + 0.187185i
\(304\) 1724.01 1122.23i 0.325259 0.211726i
\(305\) 1654.26 3993.73i 0.310565 0.749771i
\(306\) 1657.13 932.190i 0.309580 0.174149i
\(307\) 7235.85 712.669i 1.34518 0.132489i 0.600349 0.799738i \(-0.295028\pi\)
0.744835 + 0.667249i \(0.232528\pi\)
\(308\) 33.3406 604.567i 0.00616803 0.111845i
\(309\) 465.404 + 248.764i 0.0856825 + 0.0457983i
\(310\) −3263.38 576.348i −0.597895 0.105595i
\(311\) −297.792 + 445.677i −0.0542965 + 0.0812605i −0.857625 0.514276i \(-0.828061\pi\)
0.803328 + 0.595537i \(0.203061\pi\)
\(312\) −6146.97 + 2307.76i −1.11540 + 0.418755i
\(313\) −4033.14 + 2694.86i −0.728327 + 0.486653i −0.863614 0.504154i \(-0.831805\pi\)
0.135287 + 0.990807i \(0.456805\pi\)
\(314\) −5.16795 + 13.2785i −0.000928803 + 0.00238647i
\(315\) 6.02875 61.2109i 0.00107835 0.0109487i
\(316\) −2330.06 1415.67i −0.414798 0.252018i
\(317\) −2073.48 + 6835.34i −0.367376 + 1.21107i 0.557298 + 0.830313i \(0.311838\pi\)
−0.924673 + 0.380762i \(0.875662\pi\)
\(318\) 3495.22 + 268.376i 0.616359 + 0.0473264i
\(319\) 11054.3i 1.94019i
\(320\) 1446.56 2317.72i 0.252704 0.404889i
\(321\) 2460.37i 0.427801i
\(322\) −43.6963 + 569.083i −0.00756243 + 0.0984899i
\(323\) −614.600 + 2026.07i −0.105874 + 0.349019i
\(324\) −2714.83 + 662.731i −0.465506 + 0.113637i
\(325\) 669.909 6801.70i 0.114338 1.16089i
\(326\) −5873.95 2286.11i −0.997938 0.388393i
\(327\) −712.019 + 475.756i −0.120412 + 0.0804567i
\(328\) 2274.63 + 2432.62i 0.382913 + 0.409509i
\(329\) 274.479 410.787i 0.0459956 0.0688372i
\(330\) −720.841 + 4081.52i −0.120245 + 0.680850i
\(331\) 5537.22 + 2959.71i 0.919497 + 0.491481i 0.862025 0.506866i \(-0.169196\pi\)
0.0574717 + 0.998347i \(0.481696\pi\)
\(332\) 6751.53 6045.79i 1.11608 0.999415i
\(333\) 417.538 41.1239i 0.0687116 0.00676750i
\(334\) 1250.31 + 2222.63i 0.204832 + 0.364123i
\(335\) −449.546 + 1085.30i −0.0733174 + 0.177004i
\(336\) −3.55760 + 296.224i −0.000577628 + 0.0480962i
\(337\) 760.523 + 1836.06i 0.122933 + 0.296786i 0.973351 0.229322i \(-0.0736509\pi\)
−0.850418 + 0.526108i \(0.823651\pi\)
\(338\) 4919.93 6265.43i 0.791743 1.00827i
\(339\) −3739.92 3069.27i −0.599187 0.491740i
\(340\) 395.893 + 2783.97i 0.0631480 + 0.444064i
\(341\) 14079.3 4270.92i 2.23589 0.678250i
\(342\) −498.699 + 782.326i −0.0788496 + 0.123694i
\(343\) −758.528 + 150.881i −0.119407 + 0.0237516i
\(344\) 9340.01 + 8204.62i 1.46389 + 1.28594i
\(345\) 762.212 3831.90i 0.118945 0.597978i
\(346\) 2318.79 49.9577i 0.360286 0.00776226i
\(347\) −5814.99 + 4772.24i −0.899612 + 0.738292i −0.965738 0.259519i \(-0.916436\pi\)
0.0661263 + 0.997811i \(0.478936\pi\)
\(348\) 232.942 + 5403.50i 0.0358822 + 0.832351i
\(349\) 945.156 + 1768.26i 0.144966 + 0.271212i 0.943916 0.330185i \(-0.107111\pi\)
−0.798951 + 0.601397i \(0.794611\pi\)
\(350\) −275.025 139.472i −0.0420020 0.0213003i
\(351\) 7633.90 7633.90i 1.16088 1.16088i
\(352\) −1073.82 + 12082.3i −0.162599 + 1.82951i
\(353\) 2877.29 + 2877.29i 0.433833 + 0.433833i 0.889930 0.456097i \(-0.150753\pi\)
−0.456097 + 0.889930i \(0.650753\pi\)
\(354\) 453.172 + 1385.73i 0.0680390 + 0.208052i
\(355\) −3721.84 + 1989.36i −0.556436 + 0.297421i
\(356\) 6575.81 + 2397.50i 0.978982 + 0.356931i
\(357\) −193.431 235.696i −0.0286763 0.0349421i
\(358\) 2635.60 2751.66i 0.389094 0.406229i
\(359\) 3150.92 + 626.757i 0.463229 + 0.0921419i 0.421187 0.906974i \(-0.361614\pi\)
0.0420419 + 0.999116i \(0.486614\pi\)
\(360\) −161.842 + 1221.52i −0.0236939 + 0.178832i
\(361\) 1136.57 + 5713.95i 0.165706 + 0.833058i
\(362\) −9410.38 + 2083.51i −1.36630 + 0.302506i
\(363\) −3758.26 12389.3i −0.543409 1.79138i
\(364\) −325.621 550.738i −0.0468878 0.0793036i
\(365\) 1416.88 1726.48i 0.203187 0.247584i
\(366\) −1121.46 9322.90i −0.160164 1.33146i
\(367\) 1272.55 527.106i 0.180998 0.0749720i −0.290344 0.956922i \(-0.593770\pi\)
0.471342 + 0.881950i \(0.343770\pi\)
\(368\) 1257.32 11364.8i 0.178104 1.60987i
\(369\) −1387.70 574.802i −0.195774 0.0810922i
\(370\) −167.292 + 597.531i −0.0235057 + 0.0839572i
\(371\) 33.4812 + 339.941i 0.00468533 + 0.0475710i
\(372\) −6792.19 + 2384.38i −0.946663 + 0.332323i
\(373\) 2360.99 4417.09i 0.327741 0.613159i −0.663048 0.748577i \(-0.730738\pi\)
0.990789 + 0.135417i \(0.0432375\pi\)
\(374\) −7158.01 10228.7i −0.989658 1.41421i
\(375\) 4027.97 + 2691.40i 0.554675 + 0.370622i
\(376\) −5771.69 + 8040.35i −0.791628 + 1.10279i
\(377\) −6489.47 9712.17i −0.886537 1.32680i
\(378\) −196.055 445.903i −0.0266772 0.0606739i
\(379\) 7517.82 + 740.440i 1.01890 + 0.100353i 0.593652 0.804722i \(-0.297686\pi\)
0.425251 + 0.905075i \(0.360186\pi\)
\(380\) −810.734 1106.98i −0.109447 0.149439i
\(381\) −2502.87 759.237i −0.336551 0.102092i
\(382\) −990.438 1155.19i −0.132658 0.154724i
\(383\) 5257.69 0.701451 0.350725 0.936478i \(-0.385935\pi\)
0.350725 + 0.936478i \(0.385935\pi\)
\(384\) 270.294 5928.61i 0.0359203 0.787873i
\(385\) −403.869 −0.0534625
\(386\) 9034.18 + 10536.9i 1.19126 + 1.38942i
\(387\) −5365.41 1627.58i −0.704753 0.213784i
\(388\) −6979.08 + 5111.37i −0.913168 + 0.668790i
\(389\) −3820.85 376.321i −0.498008 0.0490495i −0.154104 0.988055i \(-0.549249\pi\)
−0.343903 + 0.939005i \(0.611749\pi\)
\(390\) 1762.75 + 4009.15i 0.228873 + 0.520541i
\(391\) 6538.22 + 9785.13i 0.845657 + 1.26561i
\(392\) 7630.10 1253.26i 0.983107 0.161478i
\(393\) 4832.00 + 3228.64i 0.620209 + 0.414410i
\(394\) −2370.85 3387.91i −0.303152 0.433200i
\(395\) −857.263 + 1603.83i −0.109199 + 0.204297i
\(396\) −1812.04 5161.82i −0.229946 0.655029i
\(397\) −305.601 3102.82i −0.0386340 0.392257i −0.994984 0.100034i \(-0.968105\pi\)
0.956350 0.292223i \(-0.0943951\pi\)
\(398\) −604.350 + 2158.61i −0.0761139 + 0.271862i
\(399\) 137.455 + 56.9356i 0.0172465 + 0.00714372i
\(400\) 5412.83 + 2977.34i 0.676604 + 0.372167i
\(401\) −2783.55 + 1152.99i −0.346643 + 0.143584i −0.549211 0.835684i \(-0.685072\pi\)
0.202567 + 0.979268i \(0.435072\pi\)
\(402\) 304.760 + 2533.51i 0.0378110 + 0.314329i
\(403\) 9862.68 12017.7i 1.21909 1.48547i
\(404\) 1795.66 1061.67i 0.221132 0.130743i
\(405\) 541.094 + 1783.75i 0.0663881 + 0.218852i
\(406\) −514.558 + 113.926i −0.0628993 + 0.0139263i
\(407\) −537.457 2701.98i −0.0654564 0.329071i
\(408\) 3714.49 + 4849.10i 0.450722 + 0.588397i
\(409\) 4562.93 + 907.623i 0.551644 + 0.109729i 0.463039 0.886338i \(-0.346759\pi\)
0.0886050 + 0.996067i \(0.471759\pi\)
\(410\) 1536.59 1604.26i 0.185090 0.193241i
\(411\) 5117.95 + 6236.24i 0.614233 + 0.748445i
\(412\) 352.866 967.832i 0.0421952 0.115732i
\(413\) −125.291 + 66.9693i −0.0149277 + 0.00797904i
\(414\) 1602.91 + 4901.43i 0.190287 + 0.581865i
\(415\) −4274.50 4274.50i −0.505607 0.505607i
\(416\) 6149.49 + 11245.7i 0.724768 + 1.32540i
\(417\) 3048.21 3048.21i 0.357965 0.357965i
\(418\) 5433.15 + 2755.29i 0.635751 + 0.322406i
\(419\) 2368.58 + 4431.29i 0.276164 + 0.516666i 0.981319 0.192387i \(-0.0616229\pi\)
−0.705156 + 0.709053i \(0.749123\pi\)
\(420\) 197.417 8.51053i 0.0229356 0.000988741i
\(421\) 7811.15 6410.45i 0.904257 0.742105i −0.0624343 0.998049i \(-0.519886\pi\)
0.966692 + 0.255944i \(0.0823864\pi\)
\(422\) 6804.55 146.602i 0.784929 0.0169111i
\(423\) 870.845 4378.03i 0.100099 0.503232i
\(424\) −441.921 6828.81i −0.0506169 0.782161i
\(425\) −6236.09 + 1240.44i −0.711753 + 0.141576i
\(426\) −4927.64 + 7730.16i −0.560435 + 0.879172i
\(427\) 875.596 265.609i 0.0992343 0.0301024i
\(428\) −4755.03 + 676.187i −0.537017 + 0.0763662i
\(429\) −15030.6 12335.3i −1.69157 1.38824i
\(430\) 5121.27 6521.83i 0.574347 0.731420i
\(431\) −291.399 703.499i −0.0325666 0.0786227i 0.906760 0.421648i \(-0.138548\pi\)
−0.939326 + 0.343026i \(0.888548\pi\)
\(432\) 3625.78 + 9059.63i 0.403809 + 1.00898i
\(433\) −2639.34 + 6371.92i −0.292929 + 0.707194i 0.707071 + 0.707143i \(0.250016\pi\)
−1.00000 5.10969e-5i \(0.999984\pi\)
\(434\) −343.907 611.353i −0.0380370 0.0676172i
\(435\) 3590.20 353.604i 0.395717 0.0389747i
\(436\) 1115.16 + 1245.33i 0.122491 + 0.136790i
\(437\) −5064.40 2706.98i −0.554378 0.296321i
\(438\) 843.784 4777.65i 0.0920492 0.521198i
\(439\) 4504.54 6741.52i 0.489726 0.732927i −0.501492 0.865162i \(-0.667215\pi\)
0.991218 + 0.132235i \(0.0422153\pi\)
\(440\) 8086.27 + 271.402i 0.876132 + 0.0294058i
\(441\) −2899.60 + 1937.45i −0.313098 + 0.209206i
\(442\) −12293.7 4784.67i −1.32297 0.514895i
\(443\) 89.6936 910.674i 0.00961957 0.0976692i −0.989176 0.146734i \(-0.953124\pi\)
0.998796 + 0.0490645i \(0.0156240\pi\)
\(444\) 319.654 + 1309.44i 0.0341669 + 0.139962i
\(445\) 1355.22 4467.58i 0.144368 0.475918i
\(446\) 531.573 6922.99i 0.0564366 0.735007i
\(447\) 753.747i 0.0797562i
\(448\) 573.475 74.5362i 0.0604780 0.00786050i
\(449\) 7697.08i 0.809015i −0.914535 0.404507i \(-0.867443\pi\)
0.914535 0.404507i \(-0.132557\pi\)
\(450\) −2777.97 213.303i −0.291011 0.0223449i
\(451\) −2862.98 + 9437.97i −0.298919 + 0.985403i
\(452\) −4903.98 + 8071.49i −0.510319 + 0.839936i
\(453\) −614.969 + 6243.88i −0.0637831 + 0.647601i
\(454\) −2780.69 + 7144.70i −0.287454 + 0.738584i
\(455\) −354.834 + 237.093i −0.0365602 + 0.0244287i
\(456\) −2713.86 1232.34i −0.278702 0.126556i
\(457\) −4446.00 + 6653.91i −0.455088 + 0.681087i −0.986077 0.166292i \(-0.946821\pi\)
0.530989 + 0.847379i \(0.321821\pi\)
\(458\) −17169.0 3032.24i −1.75165 0.309361i
\(459\) −8857.61 4734.49i −0.900736 0.481453i
\(460\) −7615.21 419.962i −0.771871 0.0425670i
\(461\) −12065.9 + 1188.38i −1.21901 + 0.120062i −0.686988 0.726669i \(-0.741067\pi\)
−0.532021 + 0.846731i \(0.678567\pi\)
\(462\) −764.622 + 430.126i −0.0769987 + 0.0433144i
\(463\) 4868.85 11754.4i 0.488714 1.17986i −0.466653 0.884440i \(-0.654540\pi\)
0.955367 0.295420i \(-0.0954597\pi\)
\(464\) 10379.1 1935.25i 1.03844 0.193624i
\(465\) 1837.47 + 4436.05i 0.183249 + 0.442402i
\(466\) −6552.41 5145.28i −0.651361 0.511481i
\(467\) −1841.00 1510.87i −0.182423 0.149710i 0.538750 0.842466i \(-0.318897\pi\)
−0.721173 + 0.692755i \(0.756397\pi\)
\(468\) −4622.31 3471.35i −0.456552 0.342870i
\(469\) −237.944 + 72.1797i −0.0234270 + 0.00710650i
\(470\) 5566.89 + 3548.66i 0.546344 + 0.348271i
\(471\) 20.2486 4.02770i 0.00198090 0.000394026i
\(472\) 2553.58 1256.67i 0.249021 0.122548i
\(473\) −7182.40 + 36108.3i −0.698196 + 3.51007i
\(474\) 85.0893 + 3949.43i 0.00824532 + 0.382707i
\(475\) 2398.29 1968.23i 0.231665 0.190123i
\(476\) −402.357 + 438.611i −0.0387437 + 0.0422346i
\(477\) 1454.86 + 2721.85i 0.139651 + 0.261268i
\(478\) 5263.32 10378.7i 0.503637 0.993120i
\(479\) −680.258 + 680.258i −0.0648889 + 0.0648889i −0.738806 0.673918i \(-0.764610\pi\)
0.673918 + 0.738806i \(0.264610\pi\)
\(480\) −3958.41 + 37.7331i −0.376408 + 0.00358807i
\(481\) −2058.41 2058.41i −0.195126 0.195126i
\(482\) −5585.45 + 1826.60i −0.527822 + 0.172613i
\(483\) 729.333 389.837i 0.0687077 0.0367250i
\(484\) −22911.4 + 10668.4i −2.15171 + 1.00192i
\(485\) 3660.52 + 4460.36i 0.342713 + 0.417597i
\(486\) −5484.81 5253.46i −0.511926 0.490333i
\(487\) 15232.0 + 3029.83i 1.41730 + 0.281919i 0.843525 0.537090i \(-0.180477\pi\)
0.573780 + 0.819010i \(0.305477\pi\)
\(488\) −17709.7 + 4729.63i −1.64279 + 0.438730i
\(489\) 1781.71 + 8957.25i 0.164768 + 0.828345i
\(490\) −1114.92 5035.64i −0.102790 0.464260i
\(491\) −111.960 369.082i −0.0102906 0.0339235i 0.951645 0.307201i \(-0.0993923\pi\)
−0.961935 + 0.273277i \(0.911892\pi\)
\(492\) 1200.58 4673.75i 0.110013 0.428270i
\(493\) −6893.72 + 8400.02i −0.629771 + 0.767379i
\(494\) 6391.00 768.783i 0.582075 0.0700186i
\(495\) −3371.24 + 1396.41i −0.306113 + 0.126796i
\(496\) 6474.88 + 12471.6i 0.586150 + 1.12902i
\(497\) −825.276 341.840i −0.0744842 0.0308524i
\(498\) −12645.1 3540.26i −1.13783 0.318560i
\(499\) 720.594 + 7316.31i 0.0646457 + 0.656359i 0.971839 + 0.235645i \(0.0757203\pi\)
−0.907193 + 0.420714i \(0.861780\pi\)
\(500\) 4094.53 8524.34i 0.366226 0.762440i
\(501\) 1741.81 3258.69i 0.155326 0.290594i
\(502\) 5508.74 3855.00i 0.489775 0.342743i
\(503\) −4591.57 3067.99i −0.407014 0.271958i 0.335165 0.942159i \(-0.391208\pi\)
−0.742179 + 0.670201i \(0.766208\pi\)
\(504\) −221.599 + 137.545i −0.0195849 + 0.0121563i
\(505\) −773.029 1156.92i −0.0681175 0.101945i
\(506\) 30997.2 13628.9i 2.72331 1.19739i
\(507\) −11486.9 1131.36i −1.00621 0.0991035i
\(508\) −779.472 + 5045.84i −0.0680778 + 0.440695i
\(509\) −3242.98 983.749i −0.282402 0.0856658i 0.145906 0.989298i \(-0.453390\pi\)
−0.428308 + 0.903633i \(0.640890\pi\)
\(510\) 3093.09 2651.96i 0.268557 0.230257i
\(511\) 472.750 0.0409261
\(512\) −11532.2 + 1106.99i −0.995424 + 0.0955516i
\(513\) 4900.77 0.421782
\(514\) 6244.70 5354.10i 0.535880 0.459454i
\(515\) −657.540 199.463i −0.0562615 0.0170667i
\(516\) 2749.97 17801.6i 0.234613 1.51875i
\(517\) −29169.2 2872.91i −2.48135 0.244392i
\(518\) −120.233 + 52.8644i −0.0101984 + 0.00448403i
\(519\) −1867.01 2794.17i −0.157905 0.236321i
\(520\) 7263.83 4508.63i 0.612577 0.380224i
\(521\) −6739.43 4503.14i −0.566718 0.378669i 0.238954 0.971031i \(-0.423195\pi\)
−0.805672 + 0.592362i \(0.798195\pi\)
\(522\) −3901.30 + 2730.12i −0.327117 + 0.228916i
\(523\) −7281.10 + 13622.0i −0.608758 + 1.13891i 0.369051 + 0.929409i \(0.379683\pi\)
−0.977809 + 0.209497i \(0.932817\pi\)
\(524\) 4911.85 10225.9i 0.409494 0.852521i
\(525\) 43.7942 + 444.650i 0.00364064 + 0.0369640i
\(526\) −14325.3 4010.68i −1.18747 0.332460i
\(527\) −13362.2 5534.79i −1.10449 0.457493i
\(528\) 15598.3 8098.16i 1.28566 0.667476i
\(529\) −18248.5 + 7558.78i −1.49984 + 0.621252i
\(530\) −4531.78 + 545.134i −0.371411 + 0.0446776i
\(531\) −814.295 + 992.222i −0.0665488 + 0.0810900i
\(532\) 72.2598 281.300i 0.00588883 0.0229246i
\(533\) 3025.22 + 9972.81i 0.245848 + 0.810451i
\(534\) −2192.26 9901.54i −0.177656 0.802400i
\(535\) 624.990 + 3142.03i 0.0505059 + 0.253910i
\(536\) 4812.64 1285.28i 0.387825 0.103574i
\(537\) −5414.66 1077.04i −0.435121 0.0865509i
\(538\) 16709.0 + 16004.2i 1.33899 + 1.28251i
\(539\) 14526.7 + 17700.8i 1.16087 + 1.41452i
\(540\) 5900.58 2747.53i 0.470223 0.218954i
\(541\) 14490.9 7745.56i 1.15160 0.615541i 0.218738 0.975784i \(-0.429806\pi\)
0.932859 + 0.360243i \(0.117306\pi\)
\(542\) −11691.4 + 3823.41i −0.926544 + 0.303006i
\(543\) 9874.80 + 9874.80i 0.780420 + 0.780420i
\(544\) 8350.76 8511.50i 0.658154 0.670822i
\(545\) 788.437 788.437i 0.0619687 0.0619687i
\(546\) −419.280 + 826.777i −0.0328636 + 0.0648036i
\(547\) 5598.89 + 10474.8i 0.437644 + 0.818774i 0.999967 0.00814360i \(-0.00259222\pi\)
−0.562323 + 0.826918i \(0.690092\pi\)
\(548\) 10645.9 11605.1i 0.829873 0.904647i
\(549\) 6390.55 5244.59i 0.496798 0.407712i
\(550\) 394.058 + 18290.2i 0.0305503 + 1.41800i
\(551\) 1034.45 5200.52i 0.0799799 0.402086i
\(552\) −14864.7 + 7315.21i −1.14617 + 0.564051i
\(553\) −377.535 + 75.0964i −0.0290315 + 0.00577473i
\(554\) 3230.24 + 2059.14i 0.247725 + 0.157914i
\(555\) 860.352 260.985i 0.0658016 0.0199607i
\(556\) −6728.88 5053.39i −0.513252 0.385452i
\(557\) 5793.91 + 4754.94i 0.440747 + 0.361711i 0.828441 0.560077i \(-0.189228\pi\)
−0.387694 + 0.921788i \(0.626728\pi\)
\(558\) −4984.52 3914.10i −0.378157 0.296948i
\(559\) 14887.2 + 35940.8i 1.12640 + 2.71938i
\(560\) −70.7044 379.199i −0.00533537 0.0286144i
\(561\) −6922.38 + 16712.1i −0.520968 + 1.25773i
\(562\) 8152.22 4585.90i 0.611887 0.344207i
\(563\) 5638.05 555.299i 0.422052 0.0415685i 0.115238 0.993338i \(-0.463237\pi\)
0.306814 + 0.951769i \(0.400737\pi\)
\(564\) 14318.8 + 789.653i 1.06903 + 0.0589546i
\(565\) 5555.77 + 2969.62i 0.413686 + 0.221120i
\(566\) 914.077 + 161.436i 0.0678825 + 0.0119888i
\(567\) −219.201 + 328.058i −0.0162356 + 0.0242983i
\(568\) 16294.0 + 7398.93i 1.20366 + 0.546571i
\(569\) 10712.9 7158.12i 0.789292 0.527388i −0.0943566 0.995538i \(-0.530079\pi\)
0.883649 + 0.468150i \(0.155079\pi\)
\(570\) −721.065 + 1852.71i −0.0529861 + 0.136143i
\(571\) −1.22805 + 12.4686i −9.00042e−5 + 0.000913828i −0.995230 0.0975602i \(-0.968896\pi\)
0.995140 + 0.0984740i \(0.0313961\pi\)
\(572\) −19709.0 + 32439.1i −1.44069 + 2.37123i
\(573\) −640.005 + 2109.81i −0.0466607 + 0.153820i
\(574\) 468.827 + 35.9983i 0.0340914 + 0.00261767i
\(575\) 17245.2i 1.25074i
\(576\) 4529.29 2605.03i 0.327640 0.188442i
\(577\) 23168.5i 1.67161i −0.549030 0.835803i \(-0.685003\pi\)
0.549030 0.835803i \(-0.314997\pi\)
\(578\) 124.292 1618.72i 0.00894437 0.116488i
\(579\) 5837.74 19244.5i 0.419012 1.38130i
\(580\) −1670.09 6841.42i −0.119564 0.489784i
\(581\) 125.417 1273.38i 0.00895558 0.0909275i
\(582\) 11680.6 + 4546.04i 0.831919 + 0.323779i
\(583\) 16849.8 11258.7i 1.19700 0.799807i
\(584\) −9465.43 317.690i −0.670689 0.0225105i
\(585\) −2142.16 + 3205.97i −0.151397 + 0.226582i
\(586\) 4654.75 26356.0i 0.328133 1.85795i
\(587\) −15794.2 8442.20i −1.11056 0.593606i −0.189052 0.981967i \(-0.560541\pi\)
−0.921507 + 0.388361i \(0.873041\pi\)
\(588\) −7473.85 8346.29i −0.524177 0.585366i
\(589\) 7023.32 691.737i 0.491326 0.0483914i
\(590\) −930.734 1654.54i −0.0649453 0.115451i
\(591\) −2292.81 + 5535.33i −0.159583 + 0.385267i
\(592\) 2442.84 977.656i 0.169595 0.0678740i
\(593\) 7955.63 + 19206.6i 0.550925 + 1.33005i 0.916785 + 0.399381i \(0.130775\pi\)
−0.365860 + 0.930670i \(0.619225\pi\)
\(594\) −17847.3 + 22728.2i −1.23280 + 1.56995i
\(595\) 306.895 + 251.862i 0.0211453 + 0.0173535i
\(596\) 1456.73 207.154i 0.100117 0.0142372i
\(597\) 3108.06 942.820i 0.213073 0.0646349i
\(598\) 19232.9 30171.3i 1.31520 2.06320i
\(599\) 4366.07 868.465i 0.297818 0.0592396i −0.0439198 0.999035i \(-0.513985\pi\)
0.341738 + 0.939795i \(0.388985\pi\)
\(600\) −578.042 8932.22i −0.0393308 0.607761i
\(601\) 3137.12 15771.4i 0.212921 1.07043i −0.715419 0.698696i \(-0.753764\pi\)
0.928340 0.371732i \(-0.121236\pi\)
\(602\) 1754.80 37.8067i 0.118805 0.00255961i
\(603\) −1736.64 + 1425.23i −0.117283 + 0.0962515i
\(604\) 12236.3 527.498i 0.824316 0.0355358i
\(605\) 7946.70 + 14867.2i 0.534015 + 0.999072i
\(606\) −2695.67 1367.04i −0.180700 0.0916376i
\(607\) 4140.00 4140.00i 0.276833 0.276833i −0.555010 0.831843i \(-0.687286\pi\)
0.831843 + 0.555010i \(0.187286\pi\)
\(608\) −1635.82 + 5583.64i −0.109114 + 0.372445i
\(609\) 539.953 + 539.953i 0.0359277 + 0.0359277i
\(610\) 3800.41 + 11621.0i 0.252252 + 0.771346i
\(611\) −27314.2 + 14599.8i −1.80854 + 0.966682i
\(612\) −1842.09 + 5052.43i −0.121670 + 0.333713i
\(613\) −16019.3 19519.6i −1.05549 1.28611i −0.956722 0.291002i \(-0.906011\pi\)
−0.0987635 0.995111i \(-0.531489\pi\)
\(614\) −14225.1 + 14851.6i −0.934982 + 0.976157i
\(615\) −3156.83 627.933i −0.206985 0.0411719i
\(616\) 1041.43 + 1359.54i 0.0681173 + 0.0889241i
\(617\) 1254.40 + 6306.28i 0.0818478 + 0.411477i 0.999888 + 0.0149886i \(0.00477119\pi\)
−0.918040 + 0.396488i \(0.870229\pi\)
\(618\) −1457.31 + 322.658i −0.0948572 + 0.0210020i
\(619\) −5098.85 16808.7i −0.331083 1.09143i −0.951625 0.307261i \(-0.900588\pi\)
0.620543 0.784173i \(-0.286912\pi\)
\(620\) 8068.34 4770.36i 0.522633 0.309004i
\(621\) 17281.2 21057.2i 1.11670 1.36071i
\(622\) −181.065 1505.22i −0.0116721 0.0970316i
\(623\) 912.974 378.166i 0.0587119 0.0243193i
\(624\) 8950.45 16272.0i 0.574206 1.04391i
\(625\) 5319.64 + 2203.47i 0.340457 + 0.141022i
\(626\) 3698.88 13211.6i 0.236161 0.843516i
\(627\) −865.159 8784.10i −0.0551054 0.559495i
\(628\) −13.3491 38.0265i −0.000848228 0.00241628i
\(629\) −1276.61 + 2388.37i −0.0809249 + 0.151400i
\(630\) 99.7449 + 142.534i 0.00630783 + 0.00901379i
\(631\) −10740.3 7176.41i −0.677596 0.452755i 0.168559 0.985692i \(-0.446089\pi\)
−0.846155 + 0.532936i \(0.821089\pi\)
\(632\) 7609.49 1249.88i 0.478939 0.0786669i
\(633\) −5478.77 8199.55i −0.344015 0.514855i
\(634\) −8131.68 18494.5i −0.509385 1.15853i
\(635\) 3389.18 + 333.805i 0.211804 + 0.0208609i
\(636\) −7999.19 + 5858.48i −0.498724 + 0.365258i
\(637\) 23154.3 + 7023.77i 1.44020 + 0.436879i
\(638\) 20351.1 + 23736.3i 1.26287 + 1.47293i
\(639\) −8070.83 −0.499651
\(640\) 1160.82 + 7639.85i 0.0716961 + 0.471862i
\(641\) 31893.7 1.96525 0.982624 0.185608i \(-0.0594254\pi\)
0.982624 + 0.185608i \(0.0594254\pi\)
\(642\) 4529.57 + 5283.01i 0.278454 + 0.324772i
\(643\) −17373.9 5270.33i −1.06557 0.323237i −0.291653 0.956524i \(-0.594205\pi\)
−0.773917 + 0.633287i \(0.781705\pi\)
\(644\) −953.863 1302.41i −0.0583656 0.0796926i
\(645\) −11957.0 1177.66i −0.729930 0.0718918i
\(646\) −2410.31 5481.95i −0.146800 0.333877i
\(647\) 7348.97 + 10998.5i 0.446550 + 0.668309i 0.984644 0.174576i \(-0.0558554\pi\)
−0.538094 + 0.842885i \(0.680855\pi\)
\(648\) 4609.32 6421.09i 0.279431 0.389266i
\(649\) 7007.85 + 4682.50i 0.423856 + 0.283211i
\(650\) 11083.6 + 15838.2i 0.668820 + 0.955733i
\(651\) −479.097 + 896.328i −0.0288438 + 0.0539629i
\(652\) 16821.6 5905.16i 1.01040 0.354699i
\(653\) −2599.74 26395.6i −0.155798 1.58184i −0.681917 0.731429i \(-0.738854\pi\)
0.526120 0.850410i \(-0.323646\pi\)
\(654\) 653.007 2332.40i 0.0390437 0.139456i
\(655\) −6990.90 2895.73i −0.417034 0.172741i
\(656\) −9362.69 1035.81i −0.557243 0.0616490i
\(657\) 3946.22 1634.58i 0.234333 0.0970639i
\(658\) 166.890 + 1387.38i 0.00988762 + 0.0821973i
\(659\) −15238.1 + 18567.6i −0.900745 + 1.09756i 0.0940399 + 0.995568i \(0.470022\pi\)
−0.994785 + 0.101993i \(0.967478\pi\)
\(660\) −5966.31 10091.1i −0.351876 0.595146i
\(661\) 294.025 + 969.270i 0.0173014 + 0.0570352i 0.965166 0.261638i \(-0.0842627\pi\)
−0.947865 + 0.318673i \(0.896763\pi\)
\(662\) −17338.6 + 3838.88i −1.01795 + 0.225381i
\(663\) 3728.98 + 18746.9i 0.218434 + 1.09814i
\(664\) −3366.83 + 25411.5i −0.196775 + 1.48518i
\(665\) −190.001 37.7935i −0.0110796 0.00220386i
\(666\) −820.848 + 856.997i −0.0477586 + 0.0498618i
\(667\) −18697.5 22782.9i −1.08541 1.32258i
\(668\) −6776.62 2470.71i −0.392508 0.143106i
\(669\) −8872.45 + 4742.43i −0.512749 + 0.274070i
\(670\) −1032.77 3158.03i −0.0595511 0.182098i
\(671\) −38384.3 38384.3i −2.20836 2.20836i
\(672\) −537.713 642.615i −0.0308671 0.0368890i
\(673\) −2455.27 + 2455.27i −0.140630 + 0.140630i −0.773917 0.633287i \(-0.781705\pi\)
0.633287 + 0.773917i \(0.281705\pi\)
\(674\) −5013.25 2542.35i −0.286503 0.145293i
\(675\) 6937.79 + 12979.7i 0.395608 + 0.740131i
\(676\) 970.440 + 22511.1i 0.0552139 + 1.28079i
\(677\) −1887.55 + 1549.07i −0.107155 + 0.0879402i −0.686445 0.727181i \(-0.740830\pi\)
0.579290 + 0.815122i \(0.303330\pi\)
\(678\) 13681.1 294.755i 0.774955 0.0166962i
\(679\) −238.274 + 1197.88i −0.0134670 + 0.0677033i
\(680\) −5975.40 5249.02i −0.336980 0.296016i
\(681\) 10895.0 2167.16i 0.613067 0.121947i
\(682\) −22369.0 + 35091.0i −1.25594 + 1.97024i
\(683\) 25983.0 7881.85i 1.45565 0.441567i 0.539360 0.842076i \(-0.318666\pi\)
0.916293 + 0.400508i \(0.131166\pi\)
\(684\) −369.442 2597.96i −0.0206520 0.145227i
\(685\) −8120.07 6663.97i −0.452923 0.371704i
\(686\) 1350.97 1720.44i 0.0751902 0.0957532i
\(687\) 9667.17 + 23338.6i 0.536864 + 1.29610i
\(688\) −35160.1 422.268i −1.94835 0.0233994i
\(689\) 8194.59 19783.5i 0.453105 1.09389i
\(690\) 5417.92 + 9631.28i 0.298923 + 0.531386i
\(691\) 16965.6 1670.96i 0.934010 0.0919919i 0.380450 0.924801i \(-0.375769\pi\)
0.553560 + 0.832809i \(0.313269\pi\)
\(692\) −4887.05 + 4376.20i −0.268465 + 0.240402i
\(693\) −681.177 364.097i −0.0373388 0.0199580i
\(694\) 3700.47 20952.7i 0.202403 1.14604i
\(695\) −3118.43 + 4667.06i −0.170200 + 0.254722i
\(696\) −10448.1 11173.8i −0.569015 0.608537i
\(697\) 8061.28 5386.37i 0.438081 0.292717i
\(698\) −5284.88 2056.85i −0.286584 0.111537i
\(699\) −1183.18 + 12013.0i −0.0640228 + 0.650034i
\(700\) 847.317 206.843i 0.0457508 0.0111685i
\(701\) −4905.01 + 16169.7i −0.264279 + 0.871212i 0.719906 + 0.694071i \(0.244185\pi\)
−0.984186 + 0.177141i \(0.943315\pi\)
\(702\) −2337.76 + 30446.0i −0.125688 + 1.63691i
\(703\) 1321.45i 0.0708951i
\(704\) −19937.8 27920.5i −1.06738 1.49474i
\(705\) 9565.41i 0.510999i
\(706\) −11475.4 881.124i −0.611731 0.0469710i
\(707\) 85.4943 281.837i 0.00454787 0.0149923i
\(708\) −3524.21 2141.20i −0.187073 0.113660i
\(709\) −989.650 + 10048.1i −0.0524219 + 0.532248i 0.932732 + 0.360572i \(0.117418\pi\)
−0.985153 + 0.171676i \(0.945082\pi\)
\(710\) 4329.26 11123.6i 0.228837 0.587974i
\(711\) −2891.77 + 1932.22i −0.152532 + 0.101918i
\(712\) −18533.7 + 6958.14i −0.975535 + 0.366246i
\(713\) 21793.6 32616.5i 1.14471 1.71318i
\(714\) 849.262 + 149.989i 0.0445138 + 0.00786162i
\(715\) 22328.4 + 11934.8i 1.16788 + 0.624246i
\(716\) −593.427 + 10760.7i −0.0309740 + 0.561655i
\(717\) −16779.9 + 1652.68i −0.873999 + 0.0860813i
\(718\) −7919.67 + 4455.08i −0.411643 + 0.231563i
\(719\) −12043.8 + 29076.3i −0.624699 + 1.50816i 0.221430 + 0.975176i \(0.428928\pi\)
−0.846128 + 0.532979i \(0.821072\pi\)
\(720\) −1901.31 2920.85i −0.0984135 0.151186i
\(721\) −55.6587 134.372i −0.00287495 0.00694074i
\(722\) −12960.0 10176.8i −0.668033 0.524573i
\(723\) 6581.90 + 5401.63i 0.338566 + 0.277854i
\(724\) 16370.6 21798.5i 0.840345 1.11897i
\(725\) 15238.0 4622.39i 0.780585 0.236788i
\(726\) 30878.8 + 19683.9i 1.57854 + 1.00625i
\(727\) −3611.34 + 718.340i −0.184233 + 0.0366461i −0.286344 0.958127i \(-0.592440\pi\)
0.102112 + 0.994773i \(0.467440\pi\)
\(728\) 1713.10 + 583.098i 0.0872141 + 0.0296855i
\(729\) −3986.86 + 20043.3i −0.202553 + 1.01830i
\(730\) 136.070 + 6315.68i 0.00689885 + 0.320211i
\(731\) 27975.8 22959.2i 1.41549 1.16166i
\(732\) 19571.6 + 17953.9i 0.988236 + 0.906552i
\(733\) 2375.80 + 4444.81i 0.119717 + 0.223974i 0.934641 0.355594i \(-0.115721\pi\)
−0.814924 + 0.579568i \(0.803221\pi\)
\(734\) −1762.06 + 3474.60i −0.0886089 + 0.174727i
\(735\) −5284.16 + 5284.16i −0.265183 + 0.265183i
\(736\) 18223.0 + 26717.8i 0.912650 + 1.33809i
\(737\) 10431.0 + 10431.0i 0.521344 + 0.521344i
\(738\) 4037.94 1320.52i 0.201407 0.0658660i
\(739\) −29439.5 + 15735.7i −1.46542 + 0.783286i −0.995068 0.0991907i \(-0.968375\pi\)
−0.470356 + 0.882477i \(0.655875\pi\)
\(740\) −740.845 1591.03i −0.0368027 0.0790373i
\(741\) −5916.86 7209.71i −0.293335 0.357430i
\(742\) −697.728 668.297i −0.0345207 0.0330646i
\(743\) −22152.1 4406.33i −1.09379 0.217568i −0.384948 0.922938i \(-0.625780\pi\)
−0.708838 + 0.705371i \(0.750780\pi\)
\(744\) 10194.8 17624.3i 0.502367 0.868468i
\(745\) −191.469 962.580i −0.00941595 0.0473372i
\(746\) 3062.31 + 13831.2i 0.150294 + 0.678815i
\(747\) −3355.94 11063.1i −0.164374 0.541869i
\(748\) 34201.2 + 8785.53i 1.67182 + 0.429453i
\(749\) −430.181 + 524.178i −0.0209860 + 0.0255715i
\(750\) −13603.9 + 1636.44i −0.662328 + 0.0796723i
\(751\) 14376.6 5954.99i 0.698548 0.289348i −0.00500814 0.999987i \(-0.501594\pi\)
0.703557 + 0.710639i \(0.251594\pi\)
\(752\) −2409.15 27890.4i −0.116825 1.35247i
\(753\) −9000.43 3728.10i −0.435583 0.180424i
\(754\) 31814.7 + 8907.24i 1.53664 + 0.430216i
\(755\) −800.738 8130.03i −0.0385985 0.391897i
\(756\) 1241.89 + 596.522i 0.0597449 + 0.0286975i
\(757\) 14032.9 26253.7i 0.673759 1.26051i −0.280017 0.959995i \(-0.590340\pi\)
0.953776 0.300519i \(-0.0971598\pi\)
\(758\) −17505.8 + 12250.5i −0.838837 + 0.587016i
\(759\) −40793.6 27257.4i −1.95087 1.30353i
\(760\) 3778.81 + 884.385i 0.180358 + 0.0422105i
\(761\) −13045.5 19524.0i −0.621418 0.930018i −0.999990 0.00444602i \(-0.998585\pi\)
0.378572 0.925572i \(-0.376415\pi\)
\(762\) 6772.04 2977.55i 0.321949 0.141555i
\(763\) 234.878 + 23.1334i 0.0111444 + 0.00109762i
\(764\) 4253.43 + 657.062i 0.201418 + 0.0311148i
\(765\) 3432.60 + 1041.27i 0.162230 + 0.0492119i
\(766\) −11289.6 + 9679.48i −0.532518 + 0.456572i
\(767\) 8905.89 0.419261
\(768\) 10334.3 + 13227.8i 0.485554 + 0.621507i
\(769\) −3153.43 −0.147875 −0.0739373 0.997263i \(-0.523556\pi\)
−0.0739373 + 0.997263i \(0.523556\pi\)
\(770\) 867.206 743.528i 0.0405869 0.0347985i
\(771\) −11405.2 3459.74i −0.532748 0.161607i
\(772\) −38797.2 5993.33i −1.80873 0.279410i
\(773\) 8858.43 + 872.479i 0.412181 + 0.0405962i 0.301983 0.953313i \(-0.402352\pi\)
0.110198 + 0.993910i \(0.464852\pi\)
\(774\) 14517.3 6382.98i 0.674176 0.296423i
\(775\) 11774.6 + 17622.0i 0.545752 + 0.816776i
\(776\) 5575.71 23823.9i 0.257933 1.10210i
\(777\) 158.232 + 105.727i 0.00730571 + 0.00488152i
\(778\) 8897.13 6226.19i 0.409997 0.286915i
\(779\) −2230.09 + 4172.20i −0.102569 + 0.191893i
\(780\) −11166.0 5363.39i −0.512571 0.246205i
\(781\) 5194.40 + 52739.6i 0.237990 + 2.41635i
\(782\) −32053.7 8974.15i −1.46578 0.410377i
\(783\) 23238.4 + 9625.66i 1.06063 + 0.439327i
\(784\) −14076.4 + 16738.2i −0.641237 + 0.762490i
\(785\) −24.8355 + 10.2872i −0.00112920 + 0.000467728i
\(786\) −16319.5 + 1963.09i −0.740580 + 0.0890854i
\(787\) 16645.9 20283.1i 0.753957 0.918699i −0.244748 0.969587i \(-0.578705\pi\)
0.998704 + 0.0508878i \(0.0162051\pi\)
\(788\) 11328.0 + 2909.92i 0.512111 + 0.131550i
\(789\) 6256.88 + 20626.2i 0.282320 + 0.930686i
\(790\) −1111.91 5022.04i −0.0500759 0.226173i
\(791\) 260.139 + 1307.81i 0.0116934 + 0.0587867i
\(792\) 13393.9 + 7747.72i 0.600923 + 0.347605i
\(793\) −56257.6 11190.3i −2.51925 0.501110i
\(794\) 6368.54 + 6099.91i 0.284648 + 0.272642i
\(795\) 4195.57 + 5112.32i 0.187172 + 0.228069i
\(796\) −2676.34 5747.68i −0.119171 0.255931i
\(797\) 23247.2 12425.9i 1.03320 0.552255i 0.134541 0.990908i \(-0.457044\pi\)
0.898657 + 0.438653i \(0.144544\pi\)
\(798\) −399.968 + 130.801i −0.0177428 + 0.00580239i
\(799\) 20373.7 + 20373.7i 0.902088 + 0.902088i
\(800\) −17104.0 + 3572.02i −0.755898 + 0.157862i
\(801\) 6313.39 6313.39i 0.278493 0.278493i
\(802\) 3854.32 7600.30i 0.169701 0.334634i
\(803\) −13221.1 24735.0i −0.581025 1.08702i
\(804\) −5318.62 4879.01i −0.233300 0.214017i
\(805\) −832.374 + 683.112i −0.0364439 + 0.0299087i
\(806\) 947.155 + 43962.3i 0.0413922 + 1.92122i
\(807\) 6540.18 32879.7i 0.285285 1.43423i
\(808\) −1901.17 + 5585.50i −0.0827757 + 0.243189i
\(809\) 10276.4 2044.11i 0.446600 0.0888343i 0.0333333 0.999444i \(-0.489388\pi\)
0.413267 + 0.910610i \(0.364388\pi\)
\(810\) −4445.76 2833.99i −0.192850 0.122933i
\(811\) −13951.7 + 4232.20i −0.604082 + 0.183246i −0.577487 0.816400i \(-0.695967\pi\)
−0.0265953 + 0.999646i \(0.508467\pi\)
\(812\) 895.144 1191.94i 0.0386865 0.0515133i
\(813\) 13777.1 + 11306.6i 0.594322 + 0.487748i
\(814\) 6128.43 + 4812.35i 0.263884 + 0.207215i
\(815\) −4550.70 10986.4i −0.195588 0.472190i
\(816\) −16903.2 3573.79i −0.725158 0.153318i
\(817\) −6757.95 + 16315.1i −0.289389 + 0.698646i
\(818\) −11468.7 + 6451.52i −0.490211 + 0.275761i
\(819\) −812.219 + 79.9966i −0.0346535 + 0.00341307i
\(820\) −345.977 + 6273.63i −0.0147342 + 0.267176i
\(821\) −19984.1 10681.7i −0.849513 0.454074i −0.0116351 0.999932i \(-0.503704\pi\)
−0.837877 + 0.545858i \(0.816204\pi\)
\(822\) −22470.5 3968.53i −0.953465 0.168392i
\(823\) 5913.14 8849.63i 0.250448 0.374822i −0.684849 0.728685i \(-0.740132\pi\)
0.935297 + 0.353862i \(0.115132\pi\)
\(824\) 1024.10 + 2727.80i 0.0432965 + 0.115325i
\(825\) 22039.9 14726.6i 0.930099 0.621472i
\(826\) 145.739 374.462i 0.00613911 0.0157738i
\(827\) 1164.68 11825.2i 0.0489719 0.497220i −0.939146 0.343520i \(-0.888381\pi\)
0.988117 0.153701i \(-0.0491192\pi\)
\(828\) −12465.4 7573.61i −0.523193 0.317876i
\(829\) −7056.95 + 23263.6i −0.295655 + 0.974643i 0.675733 + 0.737146i \(0.263827\pi\)
−0.971388 + 0.237497i \(0.923673\pi\)
\(830\) 17047.8 + 1308.99i 0.712937 + 0.0547420i
\(831\) 5550.42i 0.231699i
\(832\) −33908.0 12826.0i −1.41292 0.534450i
\(833\) 22509.8i 0.936276i
\(834\) −933.465 + 12157.1i −0.0387569 + 0.504754i
\(835\) −1396.61 + 4604.00i −0.0578822 + 0.190812i
\(836\) −16738.8 + 4086.20i −0.692494 + 0.169048i
\(837\) −3281.40 + 33316.6i −0.135510 + 1.37585i
\(838\) −13244.0 5154.50i −0.545950 0.212481i
\(839\) −36912.5 + 24664.1i −1.51890 + 1.01490i −0.533281 + 0.845938i \(0.679041\pi\)
−0.985623 + 0.168961i \(0.945959\pi\)
\(840\) −408.235 + 381.721i −0.0167684 + 0.0156793i
\(841\) 1569.71 2349.24i 0.0643615 0.0963238i
\(842\) −4970.76 + 28145.3i −0.203448 + 1.15196i
\(843\) −11952.3 6388.63i −0.488325 0.261015i
\(844\) −14341.1 + 12842.1i −0.584885 + 0.523746i
\(845\) 14956.8 1473.12i 0.608912 0.0599726i
\(846\) 6190.10 + 11004.0i 0.251560 + 0.447191i
\(847\) −1365.51 + 3296.64i −0.0553950 + 0.133735i
\(848\) 13520.8 + 13849.5i 0.547532 + 0.560844i
\(849\) −514.678 1242.54i −0.0208053 0.0502285i
\(850\) 11106.8 14144.2i 0.448187 0.570757i
\(851\) −5677.88 4659.72i −0.228714 0.187700i
\(852\) −3650.45 25670.4i −0.146787 1.03222i
\(853\) −10944.8 + 3320.06i −0.439322 + 0.133267i −0.502195 0.864755i \(-0.667474\pi\)
0.0628725 + 0.998022i \(0.479974\pi\)
\(854\) −1391.13 + 2182.31i −0.0557418 + 0.0874440i
\(855\) −1716.68 + 341.469i −0.0686658 + 0.0136585i
\(856\) 8965.36 10206.0i 0.357979 0.407517i
\(857\) 7929.50 39864.3i 0.316064 1.58896i −0.417069 0.908875i \(-0.636943\pi\)
0.733133 0.680085i \(-0.238057\pi\)
\(858\) 54983.9 1184.61i 2.18778 0.0471352i
\(859\) 11577.8 9501.62i 0.459870 0.377405i −0.375743 0.926724i \(-0.622613\pi\)
0.835613 + 0.549318i \(0.185113\pi\)
\(860\) 1010.15 + 23432.3i 0.0400534 + 0.929110i
\(861\) −321.159 600.846i −0.0127120 0.0237826i
\(862\) 1920.86 + 974.118i 0.0758987 + 0.0384902i
\(863\) −12484.5 + 12484.5i −0.492441 + 0.492441i −0.909074 0.416634i \(-0.863210\pi\)
0.416634 + 0.909074i \(0.363210\pi\)
\(864\) −24464.3 12778.1i −0.963303 0.503150i
\(865\) 3094.06 + 3094.06i 0.121620 + 0.121620i
\(866\) −6063.49 18541.1i −0.237928 0.727545i
\(867\) −2074.54 + 1108.87i −0.0812632 + 0.0434361i
\(868\) 1863.96 + 679.588i 0.0728882 + 0.0265746i
\(869\) 14487.4 + 17653.0i 0.565538 + 0.689110i
\(870\) −7058.05 + 7368.88i −0.275046 + 0.287159i
\(871\) 15288.1 + 3040.99i 0.594738 + 0.118301i
\(872\) −4687.19 621.018i −0.182028 0.0241173i
\(873\) 2152.83 + 10823.0i 0.0834621 + 0.419592i
\(874\) 15858.1 3511.08i 0.613739 0.135885i
\(875\) −387.576 1277.67i −0.0149742 0.0493634i
\(876\) 6983.90 + 11812.2i 0.269365 + 0.455591i
\(877\) 26480.5 32266.6i 1.01959 1.24238i 0.0497199 0.998763i \(-0.484167\pi\)
0.969872 0.243614i \(-0.0783329\pi\)
\(878\) 2738.87 + 22768.6i 0.105276 + 0.875175i
\(879\) −35826.8 + 14840.0i −1.37475 + 0.569442i
\(880\) −17862.9 + 14304.2i −0.684270 + 0.547947i
\(881\) 5294.92 + 2193.23i 0.202486 + 0.0838725i 0.481622 0.876379i \(-0.340048\pi\)
−0.279136 + 0.960252i \(0.590048\pi\)
\(882\) 2659.29 9498.40i 0.101523 0.362617i
\(883\) 4366.17 + 44330.5i 0.166403 + 1.68951i 0.609299 + 0.792940i \(0.291451\pi\)
−0.442897 + 0.896573i \(0.646049\pi\)
\(884\) 35206.3 12359.1i 1.33950 0.470227i
\(885\) −1296.61 + 2425.78i −0.0492486 + 0.0921376i
\(886\) 1483.97 + 2120.57i 0.0562697 + 0.0804085i
\(887\) −33198.4 22182.5i −1.25670 0.839701i −0.264505 0.964384i \(-0.585209\pi\)
−0.992197 + 0.124683i \(0.960209\pi\)
\(888\) −3097.07 2223.20i −0.117039 0.0840156i
\(889\) 400.484 + 599.367i 0.0151089 + 0.0226121i
\(890\) 5314.87 + 12088.0i 0.200174 + 0.455269i
\(891\) 23294.7 + 2294.33i 0.875873 + 0.0862659i
\(892\) 11603.9 + 15844.0i 0.435568 + 0.594727i
\(893\) −13453.9 4081.18i −0.504161 0.152936i
\(894\) −1387.66 1618.48i −0.0519130 0.0605482i
\(895\) 7188.44 0.268473
\(896\) −1094.17 + 1215.82i −0.0407965 + 0.0453324i
\(897\) −51842.3 −1.92973
\(898\) 14170.4 + 16527.5i 0.526585 + 0.614177i
\(899\) 34661.7 + 10514.5i 1.28591 + 0.390077i
\(900\) 6357.69 4656.27i 0.235470 0.172455i
\(901\) −19825.1 1952.61i −0.733042 0.0721984i
\(902\) −11227.9 25536.4i −0.414466 0.942650i
\(903\) −1412.90 2114.56i −0.0520691 0.0779270i
\(904\) −4329.66 26359.8i −0.159295 0.969816i
\(905\) −15119.1 10102.3i −0.555334 0.371062i
\(906\) −10174.6 14539.3i −0.373099 0.533153i
\(907\) 12936.6 24202.6i 0.473597 0.886037i −0.525776 0.850623i \(-0.676225\pi\)
0.999373 0.0354141i \(-0.0112750\pi\)
\(908\) −7182.67 20460.7i −0.262517 0.747811i
\(909\) −260.825 2648.20i −0.00951707 0.0966285i
\(910\) 325.426 1162.35i 0.0118547 0.0423424i
\(911\) 6683.85 + 2768.54i 0.243080 + 0.100687i 0.500897 0.865507i \(-0.333003\pi\)
−0.257818 + 0.966194i \(0.583003\pi\)
\(912\) 8096.08 2350.13i 0.293956 0.0853294i
\(913\) −70132.7 + 29049.9i −2.54223 + 1.05303i
\(914\) −2703.28 22472.7i −0.0978298 0.813274i
\(915\) 11238.6 13694.2i 0.406049 0.494772i
\(916\) 42448.6 25097.5i 1.53116 0.905288i
\(917\) −464.941 1532.71i −0.0167434 0.0551956i
\(918\) 27735.7 6140.85i 0.997185 0.220783i
\(919\) −5587.55 28090.5i −0.200562 1.00829i −0.941575 0.336802i \(-0.890655\pi\)
0.741014 0.671490i \(-0.234345\pi\)
\(920\) 17124.9 13117.9i 0.613686 0.470093i
\(921\) 29224.6 + 5813.13i 1.04558 + 0.207980i
\(922\) 23720.6 24765.2i 0.847283 0.884596i
\(923\) 35524.7 + 43287.0i 1.26686 + 1.54367i
\(924\) 849.964 2331.26i 0.0302617 0.0830011i
\(925\) 3499.85 1870.71i 0.124405 0.0664957i
\(926\) 11185.5 + 34203.3i 0.396952 + 1.21381i
\(927\) −929.208 929.208i −0.0329225 0.0329225i
\(928\) −18723.6 + 23263.5i −0.662319 + 0.822910i
\(929\) −5227.93 + 5227.93i −0.184632 + 0.184632i −0.793371 0.608739i \(-0.791676\pi\)
0.608739 + 0.793371i \(0.291676\pi\)
\(930\) −12112.3 6142.48i −0.427074 0.216581i
\(931\) 5177.68 + 9686.77i 0.182268 + 0.341000i
\(932\) 23542.2 1014.89i 0.827413 0.0356693i
\(933\) −1698.04 + 1393.55i −0.0595834 + 0.0488988i
\(934\) 6734.62 145.095i 0.235935 0.00508316i
\(935\) 4595.04 23100.8i 0.160721 0.807997i
\(936\) 16316.0 1055.88i 0.569772 0.0368723i
\(937\) 49947.9 9935.26i 1.74144 0.346393i 0.780924 0.624626i \(-0.214749\pi\)
0.960514 + 0.278233i \(0.0897486\pi\)
\(938\) 378.042 593.047i 0.0131594 0.0206436i
\(939\) −19022.6 + 5770.45i −0.661108 + 0.200545i
\(940\) −18486.6 + 2628.88i −0.641454 + 0.0912177i
\(941\) −10307.7 8459.30i −0.357089 0.293056i 0.438695 0.898636i \(-0.355441\pi\)
−0.795784 + 0.605581i \(0.792941\pi\)
\(942\) −36.0637 + 45.9264i −0.00124737 + 0.00158850i
\(943\) 10063.0 + 24294.2i 0.347503 + 0.838948i
\(944\) −3169.63 + 7399.55i −0.109282 + 0.255121i
\(945\) 351.673 849.014i 0.0121057 0.0292259i
\(946\) −51053.6 90756.4i −1.75465 3.11918i
\(947\) 50916.8 5014.86i 1.74717 0.172081i 0.826636 0.562738i \(-0.190252\pi\)
0.920537 + 0.390656i \(0.127752\pi\)
\(948\) −7453.66 8323.75i −0.255363 0.285172i
\(949\) −26136.7 13970.3i −0.894027 0.477868i
\(950\) −1526.19 + 8641.55i −0.0521223 + 0.295125i
\(951\) −16263.1 + 24339.4i −0.554539 + 0.829926i
\(952\) 56.4718 1682.55i 0.00192255 0.0572813i
\(953\) 31871.0 21295.5i 1.08332 0.723850i 0.120152 0.992756i \(-0.461662\pi\)
0.963167 + 0.268905i \(0.0866619\pi\)
\(954\) −8134.89 3166.07i −0.276076 0.107448i
\(955\) 281.383 2856.93i 0.00953440 0.0968044i
\(956\) 7805.70 + 31975.5i 0.264074 + 1.08176i
\(957\) 13150.6 43351.6i 0.444198 1.46432i
\(958\) 208.318 2713.04i 0.00702551 0.0914974i
\(959\) 2223.47i 0.0748691i
\(960\) 8430.21 7368.50i 0.283421 0.247726i
\(961\) 18418.4i 0.618253i
\(962\) 8209.47 + 630.354i 0.275139 + 0.0211262i
\(963\) −1778.49 + 5862.90i −0.0595130 + 0.196188i
\(964\) 8630.55 14205.1i 0.288352 0.474600i
\(965\) −2566.61 + 26059.2i −0.0856188 + 0.869302i
\(966\) −848.364 + 2179.79i −0.0282564 + 0.0726020i
\(967\) −39052.1 + 26093.8i −1.29869 + 0.867756i −0.996343 0.0854423i \(-0.972770\pi\)
−0.302346 + 0.953198i \(0.597770\pi\)
\(968\) 29555.7 65087.8i 0.981360 2.16116i
\(969\) −4820.55 + 7214.46i −0.159813 + 0.239176i
\(970\) −16071.6 2838.42i −0.531989 0.0939550i
\(971\) 24600.6 + 13149.3i 0.813049 + 0.434584i 0.824853 0.565347i \(-0.191258\pi\)
−0.0118045 + 0.999930i \(0.503758\pi\)
\(972\) 21448.9 + 1182.86i 0.707793 + 0.0390332i
\(973\) −1182.38 + 116.454i −0.0389572 + 0.00383695i
\(974\) −38284.8 + 21536.5i −1.25947 + 0.708495i
\(975\) 10718.7 25877.2i 0.352075 0.849984i
\(976\) 29319.8 42759.5i 0.961582 1.40235i
\(977\) 2591.95 + 6257.53i 0.0848761 + 0.204909i 0.960619 0.277869i \(-0.0896280\pi\)
−0.875743 + 0.482778i \(0.839628\pi\)
\(978\) −20316.2 15953.3i −0.664254 0.521605i
\(979\) −45318.7 37192.1i −1.47946 1.21416i
\(980\) 11664.7 + 8760.19i 0.380220 + 0.285545i
\(981\) 2040.60 619.009i 0.0664131 0.0201462i
\(982\) 919.890 + 586.391i 0.0298930 + 0.0190555i
\(983\) 30661.6 6098.97i 0.994866 0.197891i 0.329296 0.944227i \(-0.393189\pi\)
0.665570 + 0.746336i \(0.268189\pi\)
\(984\) 6026.48 + 12246.0i 0.195241 + 0.396735i
\(985\) 1521.95 7651.37i 0.0492319 0.247506i
\(986\) −662.033 30728.3i −0.0213828 0.992484i
\(987\) 1565.11 1284.45i 0.0504742 0.0414231i
\(988\) −12307.7 + 13416.7i −0.396317 + 0.432026i
\(989\) 46271.5 + 86567.8i 1.48771 + 2.78331i
\(990\) 4668.07 9204.95i 0.149860 0.295507i
\(991\) −17338.5 + 17338.5i −0.555778 + 0.555778i −0.928103 0.372324i \(-0.878561\pi\)
0.372324 + 0.928103i \(0.378561\pi\)
\(992\) −36863.6 14859.3i −1.17986 0.475589i
\(993\) 18194.3 + 18194.3i 0.581450 + 0.581450i
\(994\) 2401.40 785.328i 0.0766276 0.0250594i
\(995\) −3729.68 + 1993.56i −0.118833 + 0.0635176i
\(996\) 33669.7 15677.9i 1.07115 0.498768i
\(997\) −10548.1 12852.9i −0.335066 0.408279i 0.578036 0.816012i \(-0.303819\pi\)
−0.913101 + 0.407733i \(0.866319\pi\)
\(998\) −15016.7 14383.3i −0.476299 0.456208i
\(999\) 6148.11 + 1222.93i 0.194712 + 0.0387307i
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 128.4.k.a.5.12 752
128.77 even 32 inner 128.4.k.a.77.12 yes 752
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.k.a.5.12 752 1.1 even 1 trivial
128.4.k.a.77.12 yes 752 128.77 even 32 inner