Properties

Label 33.4.f.a.2.7
Level $33$
Weight $4$
Character 33.2
Analytic conductor $1.947$
Analytic rank $0$
Dimension $40$
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] = [33,4,Mod(2,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 33.f (of order \(10\), degree \(4\), 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: \(1.94706303019\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 33.2
Dual form 33.4.f.a.17.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.448331 - 1.37982i) q^{2} +(-2.40765 + 4.60470i) q^{3} +(4.76923 + 3.46505i) q^{4} +(14.6309 - 4.75385i) q^{5} +(5.27423 + 5.38655i) q^{6} +(-7.94038 + 10.9290i) q^{7} +(16.3093 - 11.8494i) q^{8} +(-15.4064 - 22.1730i) q^{9} +O(q^{10})\) \(q+(0.448331 - 1.37982i) q^{2} +(-2.40765 + 4.60470i) q^{3} +(4.76923 + 3.46505i) q^{4} +(14.6309 - 4.75385i) q^{5} +(5.27423 + 5.38655i) q^{6} +(-7.94038 + 10.9290i) q^{7} +(16.3093 - 11.8494i) q^{8} +(-15.4064 - 22.1730i) q^{9} -22.3193i q^{10} +(-36.2331 + 4.26212i) q^{11} +(-27.4381 + 13.6182i) q^{12} +(21.5263 + 6.99432i) q^{13} +(11.5201 + 15.8561i) q^{14} +(-13.3359 + 78.8163i) q^{15} +(5.53539 + 17.0362i) q^{16} +(-27.3125 - 84.0591i) q^{17} +(-37.5019 + 11.3173i) q^{18} +(-60.6101 - 83.4226i) q^{19} +(86.2503 + 28.0244i) q^{20} +(-31.2070 - 62.8762i) q^{21} +(-10.3634 + 51.9060i) q^{22} -42.7256i q^{23} +(15.2958 + 103.629i) q^{24} +(90.3358 - 65.6328i) q^{25} +(19.3018 - 26.5667i) q^{26} +(139.193 - 17.5571i) q^{27} +(-75.7390 + 24.6091i) q^{28} +(-6.11293 - 4.44131i) q^{29} +(102.773 + 53.7370i) q^{30} +(-67.5285 + 207.831i) q^{31} +187.264 q^{32} +(67.6108 - 177.104i) q^{33} -128.232 q^{34} +(-64.2197 + 197.648i) q^{35} +(3.35364 - 159.132i) q^{36} +(251.735 + 182.896i) q^{37} +(-142.282 + 46.2301i) q^{38} +(-84.0346 + 82.2822i) q^{39} +(182.289 - 250.899i) q^{40} +(-268.856 + 195.335i) q^{41} +(-100.749 + 14.8708i) q^{42} -419.586i q^{43} +(-187.572 - 105.222i) q^{44} +(-330.817 - 251.170i) q^{45} +(-58.9536 - 19.1552i) q^{46} +(100.176 + 137.880i) q^{47} +(-91.7736 - 15.5284i) q^{48} +(49.5995 + 152.652i) q^{49} +(-50.0612 - 154.072i) q^{50} +(452.826 + 76.6194i) q^{51} +(78.4283 + 107.947i) q^{52} +(-329.367 - 107.018i) q^{53} +(38.1789 - 199.933i) q^{54} +(-509.859 + 234.605i) q^{55} +272.333i q^{56} +(530.064 - 78.2385i) q^{57} +(-8.86882 + 6.44358i) q^{58} +(-30.0319 + 41.3354i) q^{59} +(-336.704 + 329.683i) q^{60} +(52.8443 - 17.1701i) q^{61} +(256.495 + 186.354i) q^{62} +(364.662 + 7.68508i) q^{63} +(39.6731 - 122.101i) q^{64} +348.198 q^{65} +(-214.060 - 172.692i) q^{66} -5.78593 q^{67} +(161.010 - 495.536i) q^{68} +(196.738 + 102.868i) q^{69} +(243.927 + 177.223i) q^{70} +(69.3325 - 22.5275i) q^{71} +(-514.005 - 179.069i) q^{72} +(-170.116 + 234.145i) q^{73} +(365.225 - 265.351i) q^{74} +(84.7220 + 573.990i) q^{75} -607.879i q^{76} +(241.124 - 429.834i) q^{77} +(75.8594 + 152.842i) q^{78} +(605.982 + 196.896i) q^{79} +(161.975 + 222.939i) q^{80} +(-254.283 + 683.214i) q^{81} +(148.991 + 458.548i) q^{82} +(360.606 + 1109.83i) q^{83} +(69.0357 - 408.005i) q^{84} +(-799.210 - 1100.02i) q^{85} +(-578.953 - 188.113i) q^{86} +(35.1687 - 17.4551i) q^{87} +(-540.432 + 498.852i) q^{88} -1316.37i q^{89} +(-494.885 + 343.860i) q^{90} +(-247.368 + 179.723i) q^{91} +(148.046 - 203.768i) q^{92} +(-794.415 - 811.333i) q^{93} +(235.162 - 76.4088i) q^{94} +(-1283.36 - 932.413i) q^{95} +(-450.866 + 862.293i) q^{96} +(189.307 - 582.626i) q^{97} +232.869 q^{98} +(652.726 + 737.731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9} - 90 q^{12} - 10 q^{13} + 33 q^{15} + 310 q^{16} + 225 q^{18} - 460 q^{19} - 340 q^{22} - 565 q^{24} - 604 q^{25} - 435 q^{27} + 1190 q^{28} + 910 q^{30} + 840 q^{31} + 1208 q^{33} - 188 q^{34} + 1991 q^{36} + 126 q^{37} - 1075 q^{39} - 90 q^{40} - 3340 q^{42} - 1662 q^{45} + 430 q^{46} - 346 q^{48} + 376 q^{49} - 210 q^{51} - 4270 q^{52} - 546 q^{55} + 1800 q^{57} - 4582 q^{58} + 674 q^{60} + 650 q^{61} + 3945 q^{63} + 7238 q^{64} + 3504 q^{66} + 4556 q^{67} + 3860 q^{69} + 2964 q^{70} - 1640 q^{72} + 3860 q^{73} - 6048 q^{75} - 7640 q^{78} - 3550 q^{79} - 2453 q^{81} - 5812 q^{82} - 7080 q^{84} - 8230 q^{85} - 9298 q^{88} + 9220 q^{90} - 6766 q^{91} + 5659 q^{93} + 3530 q^{94} + 14890 q^{96} + 8004 q^{97} + 955 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.448331 1.37982i 0.158509 0.487840i −0.839991 0.542601i \(-0.817440\pi\)
0.998500 + 0.0547607i \(0.0174396\pi\)
\(3\) −2.40765 + 4.60470i −0.463353 + 0.886174i
\(4\) 4.76923 + 3.46505i 0.596154 + 0.433131i
\(5\) 14.6309 4.75385i 1.30862 0.425198i 0.430050 0.902805i \(-0.358496\pi\)
0.878573 + 0.477607i \(0.158496\pi\)
\(6\) 5.27423 + 5.38655i 0.358866 + 0.366509i
\(7\) −7.94038 + 10.9290i −0.428740 + 0.590110i −0.967664 0.252245i \(-0.918831\pi\)
0.538923 + 0.842355i \(0.318831\pi\)
\(8\) 16.3093 11.8494i 0.720776 0.523675i
\(9\) −15.4064 22.1730i −0.570609 0.821222i
\(10\) 22.3193i 0.705797i
\(11\) −36.2331 + 4.26212i −0.993152 + 0.116825i
\(12\) −27.4381 + 13.6182i −0.660059 + 0.327604i
\(13\) 21.5263 + 6.99432i 0.459256 + 0.149221i 0.529502 0.848308i \(-0.322379\pi\)
−0.0702467 + 0.997530i \(0.522379\pi\)
\(14\) 11.5201 + 15.8561i 0.219920 + 0.302695i
\(15\) −13.3359 + 78.8163i −0.229555 + 1.35668i
\(16\) 5.53539 + 17.0362i 0.0864904 + 0.266190i
\(17\) −27.3125 84.0591i −0.389662 1.19925i −0.933042 0.359768i \(-0.882856\pi\)
0.543380 0.839487i \(-0.317144\pi\)
\(18\) −37.5019 + 11.3173i −0.491072 + 0.148195i
\(19\) −60.6101 83.4226i −0.731837 1.00729i −0.999047 0.0436489i \(-0.986102\pi\)
0.267210 0.963638i \(-0.413898\pi\)
\(20\) 86.2503 + 28.0244i 0.964308 + 0.313323i
\(21\) −31.2070 62.8762i −0.324283 0.653368i
\(22\) −10.3634 + 51.9060i −0.100431 + 0.503018i
\(23\) 42.7256i 0.387343i −0.981066 0.193672i \(-0.937960\pi\)
0.981066 0.193672i \(-0.0620397\pi\)
\(24\) 15.2958 + 103.629i 0.130093 + 0.881379i
\(25\) 90.3358 65.6328i 0.722686 0.525062i
\(26\) 19.3018 26.5667i 0.145592 0.200391i
\(27\) 139.193 17.5571i 0.992139 0.125144i
\(28\) −75.7390 + 24.6091i −0.511190 + 0.166096i
\(29\) −6.11293 4.44131i −0.0391429 0.0284390i 0.568042 0.823000i \(-0.307701\pi\)
−0.607185 + 0.794561i \(0.707701\pi\)
\(30\) 102.773 + 53.7370i 0.625459 + 0.327033i
\(31\) −67.5285 + 207.831i −0.391241 + 1.20412i 0.540609 + 0.841274i \(0.318194\pi\)
−0.931850 + 0.362843i \(0.881806\pi\)
\(32\) 187.264 1.03450
\(33\) 67.6108 177.104i 0.356652 0.934237i
\(34\) −128.232 −0.646810
\(35\) −64.2197 + 197.648i −0.310146 + 0.954532i
\(36\) 3.35364 159.132i 0.0155261 0.736723i
\(37\) 251.735 + 182.896i 1.11851 + 0.812648i 0.983983 0.178262i \(-0.0570474\pi\)
0.134530 + 0.990909i \(0.457047\pi\)
\(38\) −142.282 + 46.2301i −0.607398 + 0.197356i
\(39\) −84.0346 + 82.2822i −0.345033 + 0.337839i
\(40\) 182.289 250.899i 0.720560 0.991766i
\(41\) −268.856 + 195.335i −1.02410 + 0.744055i −0.967120 0.254320i \(-0.918148\pi\)
−0.0569834 + 0.998375i \(0.518148\pi\)
\(42\) −100.749 + 14.8708i −0.370141 + 0.0546335i
\(43\) 419.586i 1.48805i −0.668150 0.744026i \(-0.732914\pi\)
0.668150 0.744026i \(-0.267086\pi\)
\(44\) −187.572 105.222i −0.642672 0.360519i
\(45\) −330.817 251.170i −1.09589 0.832049i
\(46\) −58.9536 19.1552i −0.188962 0.0613974i
\(47\) 100.176 + 137.880i 0.310897 + 0.427913i 0.935661 0.352901i \(-0.114805\pi\)
−0.624764 + 0.780814i \(0.714805\pi\)
\(48\) −91.7736 15.5284i −0.275966 0.0466943i
\(49\) 49.5995 + 152.652i 0.144605 + 0.445048i
\(50\) −50.0612 154.072i −0.141594 0.435783i
\(51\) 452.826 + 76.6194i 1.24330 + 0.210370i
\(52\) 78.4283 + 107.947i 0.209155 + 0.287877i
\(53\) −329.367 107.018i −0.853623 0.277359i −0.150660 0.988586i \(-0.548140\pi\)
−0.702963 + 0.711227i \(0.748140\pi\)
\(54\) 38.1789 199.933i 0.0962128 0.503842i
\(55\) −509.859 + 234.605i −1.24999 + 0.575166i
\(56\) 272.333i 0.649858i
\(57\) 530.064 78.2385i 1.23173 0.181806i
\(58\) −8.86882 + 6.44358i −0.0200782 + 0.0145876i
\(59\) −30.0319 + 41.3354i −0.0662681 + 0.0912103i −0.840865 0.541245i \(-0.817953\pi\)
0.774596 + 0.632456i \(0.217953\pi\)
\(60\) −336.704 + 329.683i −0.724473 + 0.709366i
\(61\) 52.8443 17.1701i 0.110918 0.0360395i −0.253032 0.967458i \(-0.581428\pi\)
0.363950 + 0.931418i \(0.381428\pi\)
\(62\) 256.495 + 186.354i 0.525401 + 0.381726i
\(63\) 364.662 + 7.68508i 0.729255 + 0.0153687i
\(64\) 39.6731 122.101i 0.0774865 0.238479i
\(65\) 348.198 0.664442
\(66\) −214.060 172.692i −0.399226 0.322074i
\(67\) −5.78593 −0.0105502 −0.00527510 0.999986i \(-0.501679\pi\)
−0.00527510 + 0.999986i \(0.501679\pi\)
\(68\) 161.010 495.536i 0.287136 0.883715i
\(69\) 196.738 + 102.868i 0.343254 + 0.179477i
\(70\) 243.927 + 177.223i 0.416498 + 0.302604i
\(71\) 69.3325 22.5275i 0.115891 0.0376553i −0.250497 0.968117i \(-0.580594\pi\)
0.366388 + 0.930462i \(0.380594\pi\)
\(72\) −514.005 179.069i −0.841334 0.293104i
\(73\) −170.116 + 234.145i −0.272748 + 0.375406i −0.923315 0.384043i \(-0.874531\pi\)
0.650567 + 0.759449i \(0.274531\pi\)
\(74\) 365.225 265.351i 0.573737 0.416844i
\(75\) 84.7220 + 573.990i 0.130438 + 0.883715i
\(76\) 607.879i 0.917480i
\(77\) 241.124 429.834i 0.356865 0.636157i
\(78\) 75.8594 + 152.842i 0.110120 + 0.221872i
\(79\) 605.982 + 196.896i 0.863017 + 0.280411i 0.706888 0.707326i \(-0.250099\pi\)
0.156129 + 0.987737i \(0.450099\pi\)
\(80\) 161.975 + 222.939i 0.226367 + 0.311567i
\(81\) −254.283 + 683.214i −0.348811 + 0.937193i
\(82\) 148.991 + 458.548i 0.200650 + 0.617538i
\(83\) 360.606 + 1109.83i 0.476887 + 1.46771i 0.843396 + 0.537292i \(0.180553\pi\)
−0.366509 + 0.930414i \(0.619447\pi\)
\(84\) 69.0357 408.005i 0.0896715 0.529965i
\(85\) −799.210 1100.02i −1.01984 1.40369i
\(86\) −578.953 188.113i −0.725932 0.235870i
\(87\) 35.1687 17.4551i 0.0433388 0.0215101i
\(88\) −540.432 + 498.852i −0.654662 + 0.604294i
\(89\) 1316.37i 1.56780i −0.620885 0.783902i \(-0.713227\pi\)
0.620885 0.783902i \(-0.286773\pi\)
\(90\) −494.885 + 343.860i −0.579616 + 0.402734i
\(91\) −247.368 + 179.723i −0.284958 + 0.207034i
\(92\) 148.046 203.768i 0.167771 0.230916i
\(93\) −794.415 811.333i −0.885774 0.904638i
\(94\) 235.162 76.4088i 0.258033 0.0838400i
\(95\) −1283.36 932.413i −1.38600 1.00698i
\(96\) −450.866 + 862.293i −0.479336 + 0.916744i
\(97\) 189.307 582.626i 0.198157 0.609863i −0.801769 0.597635i \(-0.796107\pi\)
0.999925 0.0122287i \(-0.00389261\pi\)
\(98\) 232.869 0.240034
\(99\) 652.726 + 737.731i 0.662641 + 0.748937i
\(100\) 658.253 0.658253
\(101\) −403.105 + 1240.63i −0.397133 + 1.22225i 0.530155 + 0.847901i \(0.322134\pi\)
−0.927288 + 0.374349i \(0.877866\pi\)
\(102\) 308.737 590.467i 0.299701 0.573186i
\(103\) 490.092 + 356.073i 0.468837 + 0.340630i 0.796988 0.603995i \(-0.206425\pi\)
−0.328151 + 0.944625i \(0.606425\pi\)
\(104\) 433.958 141.001i 0.409164 0.132945i
\(105\) −755.490 771.580i −0.702174 0.717128i
\(106\) −295.331 + 406.488i −0.270614 + 0.372468i
\(107\) 412.951 300.026i 0.373098 0.271072i −0.385396 0.922751i \(-0.625935\pi\)
0.758494 + 0.651680i \(0.225935\pi\)
\(108\) 724.681 + 398.577i 0.645671 + 0.355121i
\(109\) 480.195i 0.421966i 0.977490 + 0.210983i \(0.0676665\pi\)
−0.977490 + 0.210983i \(0.932334\pi\)
\(110\) 95.1274 + 808.695i 0.0824549 + 0.700964i
\(111\) −1448.27 + 718.813i −1.23841 + 0.614655i
\(112\) −230.141 74.7774i −0.194163 0.0630875i
\(113\) −249.991 344.083i −0.208117 0.286448i 0.692180 0.721725i \(-0.256650\pi\)
−0.900297 + 0.435277i \(0.856650\pi\)
\(114\) 129.689 766.469i 0.106548 0.629706i
\(115\) −203.111 625.112i −0.164698 0.506887i
\(116\) −13.7647 42.3632i −0.0110174 0.0339080i
\(117\) −176.559 585.060i −0.139512 0.462298i
\(118\) 43.5712 + 59.9706i 0.0339920 + 0.0467859i
\(119\) 1135.55 + 368.964i 0.874756 + 0.284226i
\(120\) 716.426 + 1443.46i 0.545004 + 1.09808i
\(121\) 1294.67 308.859i 0.972704 0.232050i
\(122\) 80.6135i 0.0598230i
\(123\) −252.148 1708.30i −0.184841 1.25229i
\(124\) −1042.20 + 757.206i −0.754780 + 0.548380i
\(125\) −120.614 + 166.012i −0.0863047 + 0.118788i
\(126\) 174.093 499.722i 0.123091 0.353324i
\(127\) 450.079 146.240i 0.314473 0.102178i −0.147528 0.989058i \(-0.547132\pi\)
0.462001 + 0.886879i \(0.347132\pi\)
\(128\) 1061.31 + 771.084i 0.732868 + 0.532460i
\(129\) 1932.07 + 1010.22i 1.31867 + 0.689493i
\(130\) 156.108 480.451i 0.105320 0.324141i
\(131\) −1881.17 −1.25465 −0.627324 0.778759i \(-0.715850\pi\)
−0.627324 + 0.778759i \(0.715850\pi\)
\(132\) 936.125 610.375i 0.617267 0.402472i
\(133\) 1392.99 0.908179
\(134\) −2.59401 + 7.98354i −0.00167230 + 0.00514681i
\(135\) 1953.05 918.580i 1.24513 0.585621i
\(136\) −1441.50 1047.31i −0.908878 0.660339i
\(137\) 1034.24 336.045i 0.644971 0.209564i 0.0317758 0.999495i \(-0.489884\pi\)
0.613196 + 0.789931i \(0.289884\pi\)
\(138\) 230.144 225.345i 0.141965 0.139004i
\(139\) −1497.20 + 2060.72i −0.913606 + 1.25747i 0.0523145 + 0.998631i \(0.483340\pi\)
−0.965920 + 0.258840i \(0.916660\pi\)
\(140\) −991.139 + 720.105i −0.598332 + 0.434714i
\(141\) −876.085 + 129.312i −0.523260 + 0.0772342i
\(142\) 105.766i 0.0625050i
\(143\) −809.775 161.678i −0.473544 0.0945468i
\(144\) 292.462 385.203i 0.169249 0.222918i
\(145\) −110.551 35.9201i −0.0633155 0.0205724i
\(146\) 246.810 + 339.705i 0.139905 + 0.192563i
\(147\) −822.332 139.141i −0.461393 0.0780691i
\(148\) 566.838 + 1744.55i 0.314823 + 0.968926i
\(149\) −76.9381 236.791i −0.0423021 0.130193i 0.927675 0.373389i \(-0.121804\pi\)
−0.969977 + 0.243196i \(0.921804\pi\)
\(150\) 829.986 + 140.436i 0.451787 + 0.0764437i
\(151\) −1196.13 1646.33i −0.644633 0.887261i 0.354219 0.935162i \(-0.384747\pi\)
−0.998852 + 0.0479013i \(0.984747\pi\)
\(152\) −1977.02 642.372i −1.05498 0.342784i
\(153\) −1443.05 + 1900.65i −0.762510 + 1.00430i
\(154\) −484.990 525.415i −0.253777 0.274930i
\(155\) 3361.77i 1.74209i
\(156\) −685.892 + 101.239i −0.352021 + 0.0519591i
\(157\) −2128.45 + 1546.41i −1.08197 + 0.786094i −0.978025 0.208489i \(-0.933145\pi\)
−0.103941 + 0.994583i \(0.533145\pi\)
\(158\) 543.361 747.872i 0.273592 0.376567i
\(159\) 1285.78 1258.97i 0.641317 0.627944i
\(160\) 2739.83 890.225i 1.35377 0.439865i
\(161\) 466.948 + 339.257i 0.228575 + 0.166070i
\(162\) 828.709 + 657.171i 0.401911 + 0.318718i
\(163\) 656.968 2021.94i 0.315692 0.971599i −0.659777 0.751461i \(-0.729349\pi\)
0.975469 0.220138i \(-0.0706507\pi\)
\(164\) −1959.08 −0.932797
\(165\) 147.278 2912.59i 0.0694882 1.37421i
\(166\) 1693.04 0.791597
\(167\) 700.253 2155.16i 0.324474 0.998630i −0.647203 0.762318i \(-0.724061\pi\)
0.971677 0.236312i \(-0.0759387\pi\)
\(168\) −1254.01 655.683i −0.575887 0.301113i
\(169\) −1362.95 990.240i −0.620368 0.450724i
\(170\) −1876.14 + 609.594i −0.846431 + 0.275022i
\(171\) −915.943 + 2629.15i −0.409614 + 1.17577i
\(172\) 1453.89 2001.10i 0.644522 0.887108i
\(173\) −815.683 + 592.629i −0.358470 + 0.260443i −0.752414 0.658691i \(-0.771110\pi\)
0.393944 + 0.919135i \(0.371110\pi\)
\(174\) −8.31769 56.3521i −0.00362392 0.0245520i
\(175\) 1508.43i 0.651580i
\(176\) −273.174 593.680i −0.116996 0.254263i
\(177\) −118.030 237.809i −0.0501227 0.100988i
\(178\) −1816.35 590.167i −0.764838 0.248511i
\(179\) −743.933 1023.94i −0.310638 0.427556i 0.624942 0.780671i \(-0.285123\pi\)
−0.935580 + 0.353115i \(0.885123\pi\)
\(180\) −707.425 2344.18i −0.292935 0.970695i
\(181\) 145.915 + 449.081i 0.0599215 + 0.184420i 0.976537 0.215351i \(-0.0690897\pi\)
−0.916615 + 0.399771i \(0.869090\pi\)
\(182\) 137.083 + 421.899i 0.0558313 + 0.171831i
\(183\) −48.1672 + 284.671i −0.0194570 + 0.114992i
\(184\) −506.273 696.825i −0.202842 0.279188i
\(185\) 4552.56 + 1479.22i 1.80925 + 0.587861i
\(186\) −1475.66 + 732.404i −0.581722 + 0.288723i
\(187\) 1347.88 + 2929.31i 0.527097 + 1.14552i
\(188\) 1004.70i 0.389761i
\(189\) −913.365 + 1660.65i −0.351521 + 0.639125i
\(190\) −1861.93 + 1352.77i −0.710940 + 0.516528i
\(191\) 1511.15 2079.92i 0.572477 0.787946i −0.420369 0.907353i \(-0.638099\pi\)
0.992845 + 0.119407i \(0.0380993\pi\)
\(192\) 466.720 + 476.659i 0.175430 + 0.179166i
\(193\) 2442.70 793.680i 0.911032 0.296012i 0.184249 0.982880i \(-0.441015\pi\)
0.726783 + 0.686867i \(0.241015\pi\)
\(194\) −719.048 522.419i −0.266106 0.193338i
\(195\) −838.340 + 1603.35i −0.307871 + 0.588811i
\(196\) −292.394 + 899.895i −0.106557 + 0.327950i
\(197\) 5180.24 1.87348 0.936742 0.350020i \(-0.113825\pi\)
0.936742 + 0.350020i \(0.113825\pi\)
\(198\) 1310.57 569.898i 0.470396 0.204550i
\(199\) 4242.24 1.51118 0.755590 0.655045i \(-0.227350\pi\)
0.755590 + 0.655045i \(0.227350\pi\)
\(200\) 695.605 2140.85i 0.245933 0.756905i
\(201\) 13.9305 26.6424i 0.00488846 0.00934931i
\(202\) 1531.12 + 1112.43i 0.533314 + 0.387475i
\(203\) 97.0781 31.5426i 0.0335643 0.0109057i
\(204\) 1894.14 + 1934.48i 0.650080 + 0.663924i
\(205\) −3005.00 + 4136.02i −1.02380 + 1.40913i
\(206\) 711.040 516.601i 0.240488 0.174725i
\(207\) −947.354 + 658.249i −0.318095 + 0.221022i
\(208\) 405.442i 0.135156i
\(209\) 2551.65 + 2764.33i 0.844502 + 0.914893i
\(210\) −1403.35 + 696.518i −0.461145 + 0.228878i
\(211\) −2779.83 903.222i −0.906974 0.294694i −0.181861 0.983324i \(-0.558212\pi\)
−0.725112 + 0.688631i \(0.758212\pi\)
\(212\) −1200.00 1651.67i −0.388758 0.535079i
\(213\) −63.1962 + 373.494i −0.0203293 + 0.120147i
\(214\) −228.844 704.309i −0.0731003 0.224979i
\(215\) −1994.65 6138.90i −0.632716 1.94730i
\(216\) 2062.10 1935.70i 0.649576 0.609758i
\(217\) −1735.19 2388.28i −0.542821 0.747129i
\(218\) 662.583 + 215.286i 0.205852 + 0.0668854i
\(219\) −668.586 1347.07i −0.206296 0.415647i
\(220\) −3244.56 647.801i −0.994308 0.198522i
\(221\) 2000.52i 0.608911i
\(222\) 342.528 + 2320.62i 0.103554 + 0.701576i
\(223\) 2533.88 1840.97i 0.760902 0.552828i −0.138285 0.990393i \(-0.544159\pi\)
0.899187 + 0.437565i \(0.144159\pi\)
\(224\) −1486.95 + 2046.61i −0.443530 + 0.610467i
\(225\) −2847.03 991.847i −0.843564 0.293881i
\(226\) −586.852 + 190.680i −0.172729 + 0.0561231i
\(227\) −1387.28 1007.92i −0.405627 0.294705i 0.366202 0.930535i \(-0.380658\pi\)
−0.771829 + 0.635830i \(0.780658\pi\)
\(228\) 2799.10 + 1463.56i 0.813047 + 0.425117i
\(229\) 1020.78 3141.64i 0.294564 0.906574i −0.688804 0.724948i \(-0.741864\pi\)
0.983368 0.181626i \(-0.0581362\pi\)
\(230\) −953.603 −0.273386
\(231\) 1398.71 + 2145.19i 0.398392 + 0.611009i
\(232\) −152.325 −0.0431060
\(233\) −1254.78 + 3861.83i −0.352805 + 1.08582i 0.604466 + 0.796631i \(0.293387\pi\)
−0.957271 + 0.289192i \(0.906613\pi\)
\(234\) −886.435 18.6812i −0.247641 0.00521893i
\(235\) 2121.12 + 1541.09i 0.588795 + 0.427784i
\(236\) −286.458 + 93.0759i −0.0790120 + 0.0256726i
\(237\) −2365.64 + 2316.31i −0.648374 + 0.634854i
\(238\) 1018.21 1401.44i 0.277313 0.381689i
\(239\) 1214.08 882.084i 0.328588 0.238733i −0.411243 0.911526i \(-0.634905\pi\)
0.739831 + 0.672792i \(0.234905\pi\)
\(240\) −1416.55 + 209.085i −0.380990 + 0.0562350i
\(241\) 386.818i 0.103391i 0.998663 + 0.0516953i \(0.0164625\pi\)
−0.998663 + 0.0516953i \(0.983538\pi\)
\(242\) 154.270 1924.88i 0.0409786 0.511306i
\(243\) −2533.77 2815.84i −0.668894 0.743358i
\(244\) 311.522 + 101.220i 0.0817342 + 0.0265570i
\(245\) 1451.37 + 1997.64i 0.378467 + 0.520915i
\(246\) −2470.19 417.964i −0.640218 0.108327i
\(247\) −721.227 2219.71i −0.185792 0.571808i
\(248\) 1361.33 + 4189.76i 0.348568 + 1.07278i
\(249\) −5978.64 1011.60i −1.52161 0.257461i
\(250\) 174.991 + 240.854i 0.0442696 + 0.0609319i
\(251\) −3507.99 1139.81i −0.882160 0.286631i −0.167306 0.985905i \(-0.553507\pi\)
−0.714854 + 0.699274i \(0.753507\pi\)
\(252\) 1712.53 + 1300.22i 0.428091 + 0.325025i
\(253\) 182.102 + 1548.08i 0.0452515 + 0.384691i
\(254\) 686.592i 0.169609i
\(255\) 6989.46 1031.66i 1.71646 0.253353i
\(256\) 2370.70 1722.41i 0.578784 0.420511i
\(257\) −2603.71 + 3583.70i −0.631966 + 0.869826i −0.998155 0.0607142i \(-0.980662\pi\)
0.366190 + 0.930540i \(0.380662\pi\)
\(258\) 2260.12 2212.99i 0.545384 0.534011i
\(259\) −3997.75 + 1298.95i −0.959103 + 0.311632i
\(260\) 1660.64 + 1206.52i 0.396109 + 0.287790i
\(261\) −4.29851 + 203.967i −0.00101943 + 0.0483725i
\(262\) −843.388 + 2595.68i −0.198873 + 0.612068i
\(263\) −6282.05 −1.47288 −0.736441 0.676502i \(-0.763495\pi\)
−0.736441 + 0.676502i \(0.763495\pi\)
\(264\) −995.891 3689.59i −0.232170 0.860146i
\(265\) −5327.67 −1.23500
\(266\) 624.522 1922.08i 0.143954 0.443046i
\(267\) 6061.46 + 3169.35i 1.38935 + 0.726446i
\(268\) −27.5944 20.0485i −0.00628954 0.00456962i
\(269\) 392.748 127.612i 0.0890196 0.0289242i −0.264169 0.964477i \(-0.585098\pi\)
0.353188 + 0.935552i \(0.385098\pi\)
\(270\) −391.863 3106.69i −0.0883259 0.700249i
\(271\) 1266.94 1743.79i 0.283989 0.390878i −0.643061 0.765815i \(-0.722336\pi\)
0.927050 + 0.374937i \(0.122336\pi\)
\(272\) 1280.86 930.599i 0.285528 0.207448i
\(273\) −231.996 1571.77i −0.0514323 0.348453i
\(274\) 1577.73i 0.347861i
\(275\) −2993.41 + 2763.10i −0.656397 + 0.605895i
\(276\) 581.847 + 1172.31i 0.126895 + 0.255670i
\(277\) 5557.55 + 1805.76i 1.20549 + 0.391688i 0.841778 0.539823i \(-0.181509\pi\)
0.363713 + 0.931511i \(0.381509\pi\)
\(278\) 2172.19 + 2989.76i 0.468630 + 0.645014i
\(279\) 5648.62 1704.63i 1.21209 0.365784i
\(280\) 1294.63 + 3984.47i 0.276318 + 0.850420i
\(281\) −60.6140 186.551i −0.0128681 0.0396038i 0.944416 0.328752i \(-0.106628\pi\)
−0.957284 + 0.289148i \(0.906628\pi\)
\(282\) −214.349 + 1266.81i −0.0452634 + 0.267510i
\(283\) −863.504 1188.51i −0.181378 0.249645i 0.708641 0.705570i \(-0.249309\pi\)
−0.890019 + 0.455924i \(0.849309\pi\)
\(284\) 408.722 + 132.802i 0.0853985 + 0.0277477i
\(285\) 7383.35 3664.54i 1.53457 0.761644i
\(286\) −586.134 + 1044.86i −0.121185 + 0.216027i
\(287\) 4489.36i 0.923340i
\(288\) −2885.07 4152.20i −0.590293 0.849551i
\(289\) −2345.27 + 1703.94i −0.477359 + 0.346822i
\(290\) −99.1267 + 136.436i −0.0200721 + 0.0276269i
\(291\) 2227.03 + 2274.46i 0.448629 + 0.458183i
\(292\) −1622.65 + 527.231i −0.325200 + 0.105664i
\(293\) 3161.32 + 2296.83i 0.630328 + 0.457960i 0.856514 0.516124i \(-0.172626\pi\)
−0.226186 + 0.974084i \(0.572626\pi\)
\(294\) −560.667 + 1072.29i −0.111220 + 0.212712i
\(295\) −242.890 + 747.539i −0.0479377 + 0.147537i
\(296\) 6272.84 1.23176
\(297\) −4968.56 + 1229.41i −0.970725 + 0.240193i
\(298\) −361.223 −0.0702184
\(299\) 298.837 919.724i 0.0577999 0.177890i
\(300\) −1584.84 + 3031.06i −0.305003 + 0.583327i
\(301\) 4585.65 + 3331.67i 0.878115 + 0.637988i
\(302\) −2807.90 + 912.343i −0.535022 + 0.173839i
\(303\) −4742.19 4843.18i −0.899114 0.918262i
\(304\) 1085.70 1494.34i 0.204833 0.281928i
\(305\) 691.533 502.428i 0.129826 0.0943244i
\(306\) 1975.59 + 2843.28i 0.369075 + 0.531174i
\(307\) 8159.29i 1.51686i −0.651756 0.758429i \(-0.725967\pi\)
0.651756 0.758429i \(-0.274033\pi\)
\(308\) 2639.37 1214.47i 0.488286 0.224678i
\(309\) −2819.58 + 1399.43i −0.519094 + 0.257639i
\(310\) 4638.64 + 1507.19i 0.849862 + 0.276137i
\(311\) −780.936 1074.87i −0.142388 0.195981i 0.731866 0.681448i \(-0.238649\pi\)
−0.874255 + 0.485467i \(0.838649\pi\)
\(312\) −395.550 + 2337.73i −0.0717744 + 0.424191i
\(313\) −771.697 2375.04i −0.139357 0.428898i 0.856885 0.515508i \(-0.172397\pi\)
−0.996242 + 0.0866096i \(0.972397\pi\)
\(314\) 1179.52 + 3630.18i 0.211987 + 0.652429i
\(315\) 5371.85 1621.11i 0.960855 0.289965i
\(316\) 2207.82 + 3038.80i 0.393036 + 0.540968i
\(317\) −4709.49 1530.21i −0.834421 0.271120i −0.139515 0.990220i \(-0.544554\pi\)
−0.694907 + 0.719100i \(0.744554\pi\)
\(318\) −1160.70 2338.59i −0.204682 0.412395i
\(319\) 240.420 + 134.868i 0.0421972 + 0.0236714i
\(320\) 1975.05i 0.345026i
\(321\) 387.289 + 2623.87i 0.0673407 + 0.456231i
\(322\) 677.461 492.205i 0.117247 0.0851847i
\(323\) −5357.02 + 7373.31i −0.922825 + 1.27016i
\(324\) −3580.10 + 2377.30i −0.613873 + 0.407630i
\(325\) 2403.65 780.994i 0.410248 0.133298i
\(326\) −2495.38 1813.00i −0.423945 0.308014i
\(327\) −2211.15 1156.14i −0.373935 0.195519i
\(328\) −2070.25 + 6371.57i −0.348507 + 1.07259i
\(329\) −2302.33 −0.385810
\(330\) −3952.83 1509.02i −0.659382 0.251724i
\(331\) −1393.22 −0.231354 −0.115677 0.993287i \(-0.536904\pi\)
−0.115677 + 0.993287i \(0.536904\pi\)
\(332\) −2125.80 + 6542.55i −0.351412 + 1.08153i
\(333\) 177.016 8399.50i 0.0291303 1.38225i
\(334\) −2659.79 1932.45i −0.435740 0.316583i
\(335\) −84.6531 + 27.5055i −0.0138062 + 0.00448592i
\(336\) 898.427 879.693i 0.145873 0.142831i
\(337\) 617.756 850.268i 0.0998556 0.137439i −0.756165 0.654381i \(-0.772929\pi\)
0.856021 + 0.516941i \(0.172929\pi\)
\(338\) −1977.41 + 1436.67i −0.318215 + 0.231197i
\(339\) 2186.29 322.701i 0.350274 0.0517012i
\(340\) 8015.54i 1.27854i
\(341\) 1560.96 7818.18i 0.247891 1.24158i
\(342\) 3217.11 + 2442.57i 0.508659 + 0.386196i
\(343\) −6468.97 2101.89i −1.01834 0.330879i
\(344\) −4971.84 6843.15i −0.779255 1.07255i
\(345\) 3367.47 + 569.786i 0.525503 + 0.0889166i
\(346\) 452.025 + 1391.19i 0.0702342 + 0.216159i
\(347\) 768.435 + 2365.00i 0.118881 + 0.365878i 0.992737 0.120307i \(-0.0383879\pi\)
−0.873856 + 0.486186i \(0.838388\pi\)
\(348\) 228.210 + 38.6138i 0.0351533 + 0.00594804i
\(349\) 459.813 + 632.878i 0.0705250 + 0.0970694i 0.842822 0.538192i \(-0.180892\pi\)
−0.772297 + 0.635261i \(0.780892\pi\)
\(350\) 2081.36 + 676.275i 0.317867 + 0.103281i
\(351\) 3119.12 + 595.622i 0.474320 + 0.0905753i
\(352\) −6785.14 + 798.141i −1.02741 + 0.120855i
\(353\) 3896.79i 0.587551i 0.955874 + 0.293775i \(0.0949118\pi\)
−0.955874 + 0.293775i \(0.905088\pi\)
\(354\) −381.050 + 56.2438i −0.0572107 + 0.00844442i
\(355\) 907.302 659.194i 0.135647 0.0985531i
\(356\) 4561.27 6278.05i 0.679064 0.934652i
\(357\) −4432.98 + 4340.54i −0.657194 + 0.643490i
\(358\) −1746.38 + 567.432i −0.257818 + 0.0837702i
\(359\) 4185.00 + 3040.58i 0.615253 + 0.447008i 0.851260 0.524744i \(-0.175839\pi\)
−0.236007 + 0.971751i \(0.575839\pi\)
\(360\) −8371.60 176.428i −1.22562 0.0258293i
\(361\) −1166.20 + 3589.20i −0.170025 + 0.523284i
\(362\) 685.070 0.0994654
\(363\) −1694.91 + 6705.18i −0.245068 + 0.969506i
\(364\) −1802.51 −0.259552
\(365\) −1375.86 + 4234.45i −0.197303 + 0.607237i
\(366\) 371.201 + 194.089i 0.0530136 + 0.0277191i
\(367\) 384.330 + 279.232i 0.0546645 + 0.0397161i 0.614782 0.788697i \(-0.289244\pi\)
−0.560117 + 0.828413i \(0.689244\pi\)
\(368\) 727.880 236.503i 0.103107 0.0335015i
\(369\) 8473.28 + 2951.92i 1.19540 + 0.416452i
\(370\) 4082.11 5618.54i 0.573564 0.789443i
\(371\) 3784.90 2749.89i 0.529655 0.384817i
\(372\) −977.439 6622.12i −0.136231 0.922960i
\(373\) 6086.24i 0.844862i 0.906395 + 0.422431i \(0.138823\pi\)
−0.906395 + 0.422431i \(0.861177\pi\)
\(374\) 4646.22 546.538i 0.642381 0.0755637i
\(375\) −474.035 955.091i −0.0652775 0.131522i
\(376\) 3267.60 + 1061.71i 0.448174 + 0.145621i
\(377\) −100.525 138.361i −0.0137329 0.0189017i
\(378\) 1881.91 + 2004.80i 0.256072 + 0.272793i
\(379\) 2172.00 + 6684.72i 0.294374 + 0.905991i 0.983431 + 0.181284i \(0.0580252\pi\)
−0.689056 + 0.724708i \(0.741975\pi\)
\(380\) −2889.77 8893.79i −0.390110 1.20064i
\(381\) −410.244 + 2424.57i −0.0551639 + 0.326022i
\(382\) −2192.42 3017.61i −0.293649 0.404174i
\(383\) −1109.08 360.362i −0.147967 0.0480774i 0.234097 0.972213i \(-0.424787\pi\)
−0.382064 + 0.924136i \(0.624787\pi\)
\(384\) −6105.86 + 3030.49i −0.811428 + 0.402732i
\(385\) 1484.48 7435.10i 0.196509 0.984229i
\(386\) 3726.31i 0.491358i
\(387\) −9303.48 + 6464.32i −1.22202 + 0.849096i
\(388\) 2921.68 2122.72i 0.382283 0.277745i
\(389\) 5959.68 8202.79i 0.776780 1.06915i −0.218849 0.975759i \(-0.570230\pi\)
0.995630 0.0933879i \(-0.0297697\pi\)
\(390\) 1836.48 + 1875.59i 0.238445 + 0.243524i
\(391\) −3591.47 + 1166.94i −0.464523 + 0.150933i
\(392\) 2617.76 + 1901.92i 0.337288 + 0.245054i
\(393\) 4529.21 8662.23i 0.581344 1.11184i
\(394\) 2322.46 7147.80i 0.296964 0.913961i
\(395\) 9802.05 1.24859
\(396\) 556.728 + 5780.14i 0.0706480 + 0.733492i
\(397\) −5816.72 −0.735348 −0.367674 0.929955i \(-0.619846\pi\)
−0.367674 + 0.929955i \(0.619846\pi\)
\(398\) 1901.93 5853.54i 0.239535 0.737214i
\(399\) −3353.84 + 6414.31i −0.420807 + 0.804804i
\(400\) 1618.17 + 1175.67i 0.202272 + 0.146959i
\(401\) 11162.4 3626.87i 1.39008 0.451664i 0.484109 0.875008i \(-0.339144\pi\)
0.905969 + 0.423344i \(0.139144\pi\)
\(402\) −30.5163 31.1662i −0.00378611 0.00386674i
\(403\) −2907.28 + 4001.53i −0.359360 + 0.494616i
\(404\) −6221.34 + 4520.07i −0.766147 + 0.556639i
\(405\) −472.483 + 11204.8i −0.0579701 + 1.37475i
\(406\) 148.092i 0.0181026i
\(407\) −9900.66 5553.97i −1.20579 0.676412i
\(408\) 8293.16 4116.10i 1.00631 0.499455i
\(409\) 8887.64 + 2887.77i 1.07449 + 0.349122i 0.792234 0.610218i \(-0.208918\pi\)
0.282254 + 0.959340i \(0.408918\pi\)
\(410\) 4359.74 + 6000.67i 0.525152 + 0.722809i
\(411\) −942.704 + 5571.44i −0.113139 + 0.668659i
\(412\) 1103.55 + 3396.38i 0.131961 + 0.406136i
\(413\) −213.289 656.437i −0.0254123 0.0782110i
\(414\) 483.538 + 1602.29i 0.0574024 + 0.190213i
\(415\) 10551.9 + 14523.5i 1.24813 + 1.71791i
\(416\) 4031.10 + 1309.78i 0.475098 + 0.154369i
\(417\) −5884.27 11855.7i −0.691016 1.39227i
\(418\) 4958.26 2281.48i 0.580183 0.266964i
\(419\) 14142.8i 1.64898i 0.565879 + 0.824488i \(0.308537\pi\)
−0.565879 + 0.824488i \(0.691463\pi\)
\(420\) −929.546 6297.65i −0.107993 0.731652i
\(421\) 4563.61 3315.66i 0.528306 0.383837i −0.291418 0.956596i \(-0.594127\pi\)
0.819724 + 0.572759i \(0.194127\pi\)
\(422\) −2492.57 + 3430.73i −0.287527 + 0.395747i
\(423\) 1513.86 4345.44i 0.174011 0.499486i
\(424\) −6639.84 + 2157.42i −0.760517 + 0.247107i
\(425\) −7984.33 5800.95i −0.911287 0.662089i
\(426\) 487.021 + 254.648i 0.0553903 + 0.0289618i
\(427\) −231.951 + 713.872i −0.0262878 + 0.0809056i
\(428\) 3009.07 0.339833
\(429\) 2694.13 3339.50i 0.303203 0.375834i
\(430\) −9364.85 −1.05026
\(431\) 1950.16 6001.98i 0.217949 0.670777i −0.780982 0.624553i \(-0.785281\pi\)
0.998931 0.0462242i \(-0.0147189\pi\)
\(432\) 1069.59 + 2274.13i 0.119122 + 0.253274i
\(433\) −10100.5 7338.42i −1.12101 0.814462i −0.136648 0.990620i \(-0.543633\pi\)
−0.984362 + 0.176158i \(0.943633\pi\)
\(434\) −4073.33 + 1323.51i −0.450521 + 0.146383i
\(435\) 431.569 422.570i 0.0475682 0.0465762i
\(436\) −1663.90 + 2290.16i −0.182767 + 0.251557i
\(437\) −3564.28 + 2589.60i −0.390166 + 0.283472i
\(438\) −2158.47 + 318.594i −0.235469 + 0.0347558i
\(439\) 12454.1i 1.35399i 0.735989 + 0.676994i \(0.236718\pi\)
−0.735989 + 0.676994i \(0.763282\pi\)
\(440\) −5535.52 + 9867.78i −0.599763 + 1.06915i
\(441\) 2620.59 3451.59i 0.282971 0.372701i
\(442\) −2760.35 896.893i −0.297051 0.0965178i
\(443\) 2857.23 + 3932.64i 0.306436 + 0.421773i 0.934266 0.356578i \(-0.116057\pi\)
−0.627830 + 0.778351i \(0.716057\pi\)
\(444\) −9397.87 1590.15i −1.00451 0.169966i
\(445\) −6257.81 19259.6i −0.666626 2.05166i
\(446\) −1404.19 4321.67i −0.149082 0.458827i
\(447\) 1275.59 + 215.834i 0.134974 + 0.0228380i
\(448\) 1019.42 + 1403.12i 0.107507 + 0.147971i
\(449\) −1733.11 563.123i −0.182162 0.0591880i 0.216516 0.976279i \(-0.430531\pi\)
−0.398678 + 0.917091i \(0.630531\pi\)
\(450\) −2644.98 + 3483.71i −0.277079 + 0.364942i
\(451\) 8908.93 8223.49i 0.930167 0.858601i
\(452\) 2507.24i 0.260909i
\(453\) 10460.7 1544.02i 1.08496 0.160142i
\(454\) −2012.71 + 1462.32i −0.208064 + 0.151168i
\(455\) −2764.83 + 3805.46i −0.284873 + 0.392094i
\(456\) 7717.89 7556.95i 0.792595 0.776067i
\(457\) 3465.51 1126.01i 0.354726 0.115258i −0.126233 0.992001i \(-0.540289\pi\)
0.480959 + 0.876743i \(0.340289\pi\)
\(458\) −3877.25 2816.99i −0.395572 0.287400i
\(459\) −5277.55 11220.9i −0.536677 1.14106i
\(460\) 1197.36 3685.09i 0.121363 0.373518i
\(461\) −18754.5 −1.89476 −0.947380 0.320110i \(-0.896280\pi\)
−0.947380 + 0.320110i \(0.896280\pi\)
\(462\) 3587.06 968.217i 0.361224 0.0975012i
\(463\) 5661.62 0.568289 0.284144 0.958782i \(-0.408291\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(464\) 41.8254 128.725i 0.00418469 0.0128791i
\(465\) −15479.9 8093.97i −1.54380 0.807202i
\(466\) 4766.07 + 3462.75i 0.473785 + 0.344225i
\(467\) −4207.51 + 1367.10i −0.416917 + 0.135465i −0.509961 0.860197i \(-0.670340\pi\)
0.0930439 + 0.995662i \(0.470340\pi\)
\(468\) 1185.21 3402.07i 0.117065 0.336028i
\(469\) 45.9425 63.2344i 0.00452330 0.00622578i
\(470\) 3077.39 2235.85i 0.302020 0.219430i
\(471\) −1996.18 13524.1i −0.195285 1.32305i
\(472\) 1030.01i 0.100445i
\(473\) 1788.33 + 15202.9i 0.173842 + 1.47786i
\(474\) 2135.50 + 4302.63i 0.206934 + 0.416933i
\(475\) −10950.5 3558.04i −1.05778 0.343693i
\(476\) 4137.24 + 5694.42i 0.398382 + 0.548326i
\(477\) 2701.47 + 8951.81i 0.259312 + 0.859277i
\(478\) −672.806 2070.68i −0.0643795 0.198140i
\(479\) 1801.66 + 5544.95i 0.171858 + 0.528925i 0.999476 0.0323669i \(-0.0103045\pi\)
−0.827618 + 0.561292i \(0.810305\pi\)
\(480\) −2497.34 + 14759.4i −0.237474 + 1.40349i
\(481\) 4139.69 + 5697.80i 0.392419 + 0.540119i
\(482\) 533.739 + 173.422i 0.0504381 + 0.0163883i
\(483\) −2686.42 + 1333.34i −0.253078 + 0.125609i
\(484\) 7244.79 + 3013.07i 0.680389 + 0.282971i
\(485\) 9424.26i 0.882337i
\(486\) −5021.32 + 2233.72i −0.468666 + 0.208484i
\(487\) 1799.47 1307.39i 0.167437 0.121650i −0.500911 0.865499i \(-0.667002\pi\)
0.668348 + 0.743849i \(0.267002\pi\)
\(488\) 658.397 906.206i 0.0610743 0.0840615i
\(489\) 7728.67 + 7893.27i 0.714729 + 0.729951i
\(490\) 3407.07 1107.02i 0.314114 0.102062i
\(491\) −2341.85 1701.45i −0.215247 0.156386i 0.474938 0.880019i \(-0.342471\pi\)
−0.690184 + 0.723634i \(0.742471\pi\)
\(492\) 4716.79 9020.98i 0.432214 0.826620i
\(493\) −206.373 + 635.151i −0.0188531 + 0.0580239i
\(494\) −3386.15 −0.308401
\(495\) 13057.0 + 7690.68i 1.18559 + 0.698324i
\(496\) −3914.45 −0.354362
\(497\) −304.324 + 936.612i −0.0274664 + 0.0845328i
\(498\) −4076.24 + 7795.92i −0.366789 + 0.701493i
\(499\) −14922.3 10841.7i −1.33870 0.972623i −0.999491 0.0319126i \(-0.989840\pi\)
−0.339210 0.940711i \(-0.610160\pi\)
\(500\) −1150.48 + 373.813i −0.102902 + 0.0334348i
\(501\) 8237.88 + 8413.32i 0.734614 + 0.750258i
\(502\) −3145.48 + 4329.38i −0.279660 + 0.384920i
\(503\) −85.9348 + 62.4353i −0.00761758 + 0.00553450i −0.591588 0.806241i \(-0.701499\pi\)
0.583970 + 0.811775i \(0.301499\pi\)
\(504\) 6038.44 4195.68i 0.533678 0.370815i
\(505\) 20067.8i 1.76833i
\(506\) 2217.71 + 442.784i 0.194841 + 0.0389015i
\(507\) 7841.26 3891.81i 0.686869 0.340910i
\(508\) 2653.26 + 862.096i 0.231731 + 0.0752939i
\(509\) −3878.88 5338.82i −0.337777 0.464910i 0.606014 0.795454i \(-0.292768\pi\)
−0.943790 + 0.330544i \(0.892768\pi\)
\(510\) 1710.09 10106.7i 0.148478 0.877517i
\(511\) −1208.18 3718.40i −0.104593 0.321903i
\(512\) 1929.30 + 5937.77i 0.166531 + 0.512529i
\(513\) −9901.17 10547.7i −0.852139 0.907784i
\(514\) 3777.54 + 5199.34i 0.324164 + 0.446173i
\(515\) 8863.18 + 2879.82i 0.758366 + 0.246408i
\(516\) 5714.02 + 11512.7i 0.487491 + 0.982202i
\(517\) −4217.34 4568.86i −0.358759 0.388662i
\(518\) 6098.53i 0.517286i
\(519\) −764.994 5182.82i −0.0647004 0.438344i
\(520\) 5678.88 4125.94i 0.478914 0.347951i
\(521\) 10898.5 15000.5i 0.916450 1.26139i −0.0484651 0.998825i \(-0.515433\pi\)
0.964915 0.262561i \(-0.0845670\pi\)
\(522\) 279.510 + 97.3758i 0.0234365 + 0.00816479i
\(523\) −729.790 + 237.123i −0.0610162 + 0.0198254i −0.339366 0.940654i \(-0.610213\pi\)
0.278350 + 0.960480i \(0.410213\pi\)
\(524\) −8971.75 6518.36i −0.747963 0.543427i
\(525\) −6945.86 3631.77i −0.577413 0.301911i
\(526\) −2816.44 + 8668.11i −0.233465 + 0.718531i
\(527\) 19314.5 1.59649
\(528\) 3391.42 + 171.490i 0.279532 + 0.0141347i
\(529\) 10341.5 0.849965
\(530\) −2388.56 + 7351.23i −0.195759 + 0.602485i
\(531\) 1379.21 + 29.0663i 0.112717 + 0.00237546i
\(532\) 6643.50 + 4826.79i 0.541414 + 0.393360i
\(533\) −7153.72 + 2324.38i −0.581354 + 0.188893i
\(534\) 7090.67 6942.82i 0.574613 0.562631i
\(535\) 4615.55 6352.75i 0.372986 0.513371i
\(536\) −94.3645 + 68.5598i −0.00760434 + 0.00552487i
\(537\) 6506.04 960.305i 0.522824 0.0771699i
\(538\) 599.134i 0.0480121i
\(539\) −2447.76 5319.63i −0.195608 0.425107i
\(540\) 12497.5 + 2386.50i 0.995937 + 0.190183i
\(541\) −14327.7 4655.35i −1.13862 0.369961i −0.321776 0.946816i \(-0.604280\pi\)
−0.816847 + 0.576855i \(0.804280\pi\)
\(542\) −1838.11 2529.95i −0.145671 0.200499i
\(543\) −2419.19 409.335i −0.191193 0.0323503i
\(544\) −5114.64 15741.2i −0.403103 1.24062i
\(545\) 2282.78 + 7025.66i 0.179419 + 0.552195i
\(546\) −2272.77 384.559i −0.178142 0.0301421i
\(547\) −857.235 1179.88i −0.0670068 0.0922270i 0.774198 0.632943i \(-0.218153\pi\)
−0.841205 + 0.540716i \(0.818153\pi\)
\(548\) 6096.94 + 1981.02i 0.475271 + 0.154425i
\(549\) −1194.86 907.185i −0.0928874 0.0705240i
\(550\) 2470.54 + 5369.15i 0.191535 + 0.416257i
\(551\) 779.145i 0.0602408i
\(552\) 4427.59 653.522i 0.341396 0.0503908i
\(553\) −6963.60 + 5059.35i −0.535484 + 0.389052i
\(554\) 4983.25 6858.85i 0.382162 0.526001i
\(555\) −17772.3 + 17401.7i −1.35927 + 1.33092i
\(556\) −14281.0 + 4640.19i −1.08930 + 0.353935i
\(557\) 9092.63 + 6606.18i 0.691682 + 0.502537i 0.877213 0.480102i \(-0.159400\pi\)
−0.185530 + 0.982639i \(0.559400\pi\)
\(558\) 180.363 8558.32i 0.0136834 0.649288i
\(559\) 2934.72 9032.14i 0.222049 0.683397i
\(560\) −3722.65 −0.280912
\(561\) −16733.8 846.159i −1.25936 0.0636806i
\(562\) −284.582 −0.0213600
\(563\) 1166.11 3588.91i 0.0872922 0.268658i −0.897876 0.440248i \(-0.854891\pi\)
0.985168 + 0.171590i \(0.0548905\pi\)
\(564\) −4626.32 2418.96i −0.345396 0.180597i
\(565\) −5293.31 3845.81i −0.394143 0.286362i
\(566\) −2027.07 + 658.634i −0.150537 + 0.0489125i
\(567\) −5447.74 8204.04i −0.403498 0.607649i
\(568\) 863.828 1188.96i 0.0638124 0.0878302i
\(569\) −5393.37 + 3918.51i −0.397367 + 0.288704i −0.768468 0.639889i \(-0.778980\pi\)
0.371101 + 0.928593i \(0.378980\pi\)
\(570\) −1746.22 11830.6i −0.128318 0.869352i
\(571\) 18746.8i 1.37396i 0.726676 + 0.686980i \(0.241064\pi\)
−0.726676 + 0.686980i \(0.758936\pi\)
\(572\) −3301.78 3576.99i −0.241354 0.261471i
\(573\) 5939.08 + 11966.1i 0.432999 + 0.872411i
\(574\) −6194.51 2012.72i −0.450443 0.146358i
\(575\) −2804.20 3859.65i −0.203379 0.279928i
\(576\) −3318.57 + 1001.47i −0.240059 + 0.0724446i
\(577\) 3449.07 + 10615.1i 0.248850 + 0.765882i 0.994979 + 0.100081i \(0.0319102\pi\)
−0.746129 + 0.665801i \(0.768090\pi\)
\(578\) 1299.67 + 3999.97i 0.0935279 + 0.287849i
\(579\) −2226.50 + 13158.8i −0.159811 + 0.944491i
\(580\) −402.777 554.375i −0.0288352 0.0396883i
\(581\) −14992.7 4871.42i −1.07057 0.347849i
\(582\) 4136.79 2053.19i 0.294632 0.146233i
\(583\) 12390.1 + 2473.78i 0.880180 + 0.175735i
\(584\) 5834.52i 0.413415i
\(585\) −5364.50 7720.60i −0.379136 0.545654i
\(586\) 4586.53 3332.31i 0.323324 0.234909i
\(587\) 4926.21 6780.35i 0.346382 0.476754i −0.599910 0.800068i \(-0.704797\pi\)
0.946292 + 0.323313i \(0.104797\pi\)
\(588\) −3439.76 3513.02i −0.241247 0.246385i
\(589\) 21430.7 6963.27i 1.49922 0.487125i
\(590\) 922.575 + 670.290i 0.0643759 + 0.0467719i
\(591\) −12472.2 + 23853.4i −0.868084 + 1.66023i
\(592\) −1722.40 + 5301.00i −0.119578 + 0.368023i
\(593\) −18293.3 −1.26681 −0.633404 0.773821i \(-0.718343\pi\)
−0.633404 + 0.773821i \(0.718343\pi\)
\(594\) −531.200 + 7406.91i −0.0366926 + 0.511632i
\(595\) 18368.1 1.26558
\(596\) 453.557 1395.91i 0.0311719 0.0959371i
\(597\) −10213.8 + 19534.2i −0.700209 + 1.33917i
\(598\) −1135.08 824.682i −0.0776200 0.0563942i
\(599\) 5914.61 1921.77i 0.403446 0.131088i −0.100263 0.994961i \(-0.531968\pi\)
0.503709 + 0.863873i \(0.331968\pi\)
\(600\) 8183.19 + 8357.47i 0.556796 + 0.568654i
\(601\) 14070.3 19366.2i 0.954977 1.31441i 0.00569594 0.999984i \(-0.498187\pi\)
0.949281 0.314429i \(-0.101813\pi\)
\(602\) 6653.00 4833.69i 0.450425 0.327253i
\(603\) 89.1405 + 128.291i 0.00602004 + 0.00866406i
\(604\) 11996.4i 0.808155i
\(605\) 17473.8 10673.5i 1.17424 0.717258i
\(606\) −8808.79 + 4372.02i −0.590483 + 0.293071i
\(607\) −1685.10 547.521i −0.112679 0.0366115i 0.252135 0.967692i \(-0.418867\pi\)
−0.364814 + 0.931081i \(0.618867\pi\)
\(608\) −11350.1 15622.0i −0.757083 1.04203i
\(609\) −88.4861 + 522.958i −0.00588774 + 0.0347969i
\(610\) −383.225 1179.44i −0.0254366 0.0782858i
\(611\) 1192.04 + 3668.72i 0.0789275 + 0.242914i
\(612\) −13468.1 + 4064.39i −0.889569 + 0.268453i
\(613\) −385.212 530.199i −0.0253810 0.0349340i 0.796138 0.605115i \(-0.206873\pi\)
−0.821519 + 0.570181i \(0.806873\pi\)
\(614\) −11258.4 3658.06i −0.739984 0.240435i
\(615\) −11810.2 23795.2i −0.774360 1.56019i
\(616\) −1160.72 9867.46i −0.0759198 0.645408i
\(617\) 11423.5i 0.745371i −0.927958 0.372685i \(-0.878437\pi\)
0.927958 0.372685i \(-0.121563\pi\)
\(618\) 666.853 + 4517.91i 0.0434058 + 0.294073i
\(619\) −9294.19 + 6752.62i −0.603497 + 0.438467i −0.847119 0.531404i \(-0.821665\pi\)
0.243621 + 0.969870i \(0.421665\pi\)
\(620\) −11648.7 + 16033.1i −0.754554 + 1.03855i
\(621\) −750.139 5947.11i −0.0484735 0.384298i
\(622\) −1833.24 + 595.656i −0.118177 + 0.0383981i
\(623\) 14386.6 + 10452.4i 0.925177 + 0.672180i
\(624\) −1866.94 976.163i −0.119771 0.0626247i
\(625\) −5288.65 + 16276.8i −0.338474 + 1.04171i
\(626\) −3623.10 −0.231323
\(627\) −18872.4 + 5094.01i −1.20206 + 0.324458i
\(628\) −15509.4 −0.985500
\(629\) 8498.59 26156.0i 0.538730 1.65804i
\(630\) 171.525 8138.98i 0.0108472 0.514706i
\(631\) −24595.4 17869.6i −1.55171 1.12738i −0.942421 0.334428i \(-0.891457\pi\)
−0.609284 0.792952i \(-0.708543\pi\)
\(632\) 12216.2 3969.30i 0.768886 0.249826i
\(633\) 10851.9 10625.6i 0.681398 0.667190i
\(634\) −4222.82 + 5812.22i −0.264526 + 0.364089i
\(635\) 5889.84 4279.22i 0.368081 0.267426i
\(636\) 10494.6 1549.03i 0.654305 0.0965768i
\(637\) 3632.94i 0.225969i
\(638\) 293.881 271.271i 0.0182365 0.0168334i
\(639\) −1567.67 1190.24i −0.0970517 0.0736858i
\(640\) 19193.4 + 6236.33i 1.18545 + 0.385176i
\(641\) 17113.1 + 23554.2i 1.05449 + 1.45138i 0.884852 + 0.465872i \(0.154259\pi\)
0.169636 + 0.985507i \(0.445741\pi\)
\(642\) 3794.11 + 641.974i 0.233242 + 0.0394652i
\(643\) 4258.42 + 13106.1i 0.261175 + 0.803815i 0.992550 + 0.121839i \(0.0388791\pi\)
−0.731375 + 0.681976i \(0.761121\pi\)
\(644\) 1051.44 + 3235.99i 0.0643361 + 0.198006i
\(645\) 33070.2 + 5595.57i 2.01882 + 0.341590i
\(646\) 7772.12 + 10697.4i 0.473359 + 0.651523i
\(647\) 12296.9 + 3995.51i 0.747204 + 0.242781i 0.657778 0.753212i \(-0.271497\pi\)
0.0894265 + 0.995993i \(0.471497\pi\)
\(648\) 3948.49 + 14155.8i 0.239370 + 0.858170i
\(649\) 911.971 1625.71i 0.0551587 0.0983275i
\(650\) 3666.76i 0.221265i
\(651\) 15175.0 2239.86i 0.913603 0.134850i
\(652\) 10139.4 7366.68i 0.609031 0.442487i
\(653\) −8745.07 + 12036.6i −0.524075 + 0.721327i −0.986213 0.165481i \(-0.947082\pi\)
0.462138 + 0.886808i \(0.347082\pi\)
\(654\) −2586.59 + 2532.66i −0.154654 + 0.151429i
\(655\) −27523.2 + 8942.82i −1.64186 + 0.533473i
\(656\) −4815.99 3499.02i −0.286635 0.208253i
\(657\) 7812.59 + 164.647i 0.463924 + 0.00977699i
\(658\) −1032.20 + 3176.80i −0.0611543 + 0.188214i
\(659\) 12908.1 0.763018 0.381509 0.924365i \(-0.375405\pi\)
0.381509 + 0.924365i \(0.375405\pi\)
\(660\) 10794.7 13380.5i 0.636640 0.789145i
\(661\) −26821.7 −1.57828 −0.789139 0.614214i \(-0.789473\pi\)
−0.789139 + 0.614214i \(0.789473\pi\)
\(662\) −624.622 + 1922.39i −0.0366716 + 0.112864i
\(663\) 9211.76 + 4816.54i 0.539601 + 0.282140i
\(664\) 19032.1 + 13827.6i 1.11233 + 0.808155i
\(665\) 20380.7 6622.08i 1.18846 0.386155i
\(666\) −11510.4 4010.01i −0.669701 0.233310i
\(667\) −189.757 + 261.179i −0.0110156 + 0.0151617i
\(668\) 10807.4 7852.04i 0.625974 0.454797i
\(669\) 2376.42 + 16100.2i 0.137336 + 0.930446i
\(670\) 129.138i 0.00744630i
\(671\) −1841.53 + 847.355i −0.105948 + 0.0487508i
\(672\) −5843.95 11774.4i −0.335469 0.675906i
\(673\) −508.935 165.363i −0.0291501 0.00947143i 0.294406 0.955681i \(-0.404878\pi\)
−0.323556 + 0.946209i \(0.604878\pi\)
\(674\) −896.259 1233.59i −0.0512205 0.0704989i
\(675\) 11421.8 10721.7i 0.651297 0.611374i
\(676\) −3068.99 9445.37i −0.174612 0.537402i
\(677\) −2521.66 7760.86i −0.143154 0.440582i 0.853615 0.520904i \(-0.174405\pi\)
−0.996769 + 0.0803221i \(0.974405\pi\)
\(678\) 534.912 3161.36i 0.0302997 0.179073i
\(679\) 4864.35 + 6695.21i 0.274929 + 0.378407i
\(680\) −26069.1 8470.37i −1.47015 0.477682i
\(681\) 7981.26 3961.30i 0.449108 0.222904i
\(682\) −10087.9 5658.98i −0.566399 0.317732i
\(683\) 12367.2i 0.692851i 0.938078 + 0.346425i \(0.112605\pi\)
−0.938078 + 0.346425i \(0.887395\pi\)
\(684\) −13478.5 + 9365.25i −0.753454 + 0.523522i
\(685\) 13534.3 9833.25i 0.754919 0.548481i
\(686\) −5800.47 + 7983.67i −0.322833 + 0.444341i
\(687\) 12008.6 + 12264.4i 0.666896 + 0.681098i
\(688\) 7148.14 2322.57i 0.396105 0.128702i
\(689\) −6341.54 4607.40i −0.350643 0.254757i
\(690\) 2295.94 4391.05i 0.126674 0.242267i
\(691\) 3138.02 9657.84i 0.172758 0.531696i −0.826766 0.562546i \(-0.809822\pi\)
0.999524 + 0.0308510i \(0.00982173\pi\)
\(692\) −5943.67 −0.326509
\(693\) −13245.6 + 1275.78i −0.726056 + 0.0699318i
\(694\) 3607.79 0.197334
\(695\) −12109.0 + 37267.7i −0.660893 + 2.03402i
\(696\) 366.744 701.408i 0.0199733 0.0381994i
\(697\) 23762.8 + 17264.7i 1.29136 + 0.938232i
\(698\) 1079.41 350.721i 0.0585332 0.0190186i
\(699\) −14761.5 15075.8i −0.798755 0.815766i
\(700\) −5226.78 + 7194.05i −0.282220 + 0.388442i
\(701\) −23035.4 + 16736.2i −1.24113 + 0.901735i −0.997673 0.0681761i \(-0.978282\pi\)
−0.243459 + 0.969911i \(0.578282\pi\)
\(702\) 2220.25 4036.79i 0.119370 0.217035i
\(703\) 32085.8i 1.72139i
\(704\) −917.067 + 4593.19i −0.0490955 + 0.245898i
\(705\) −12203.1 + 6056.72i −0.651911 + 0.323560i
\(706\) 5376.88 + 1747.05i 0.286631 + 0.0931320i
\(707\) −10358.0 14256.6i −0.550996 0.758380i
\(708\) 261.105 1543.15i 0.0138601 0.0819138i
\(709\) 1091.67 + 3359.81i 0.0578257 + 0.177969i 0.975797 0.218677i \(-0.0701740\pi\)
−0.917972 + 0.396646i \(0.870174\pi\)
\(710\) −502.797 1547.45i −0.0265770 0.0817955i
\(711\) −4970.26 16469.9i −0.262165 0.868733i
\(712\) −15598.1 21469.0i −0.821019 1.13004i
\(713\) 8879.71 + 2885.19i 0.466407 + 0.151545i
\(714\) 4001.73 + 8062.72i 0.209749 + 0.422605i
\(715\) −12616.3 + 1484.06i −0.659892 + 0.0776235i
\(716\) 7461.15i 0.389436i
\(717\) 1138.64 + 7714.24i 0.0593071 + 0.401804i
\(718\) 6071.72 4411.37i 0.315592 0.229291i
\(719\) 3259.56 4486.40i 0.169070 0.232705i −0.716072 0.698027i \(-0.754062\pi\)
0.885141 + 0.465322i \(0.154062\pi\)
\(720\) 2447.78 7026.17i 0.126699 0.363680i
\(721\) −7783.03 + 2528.86i −0.402018 + 0.130624i
\(722\) 4429.61 + 3218.30i 0.228328 + 0.165890i
\(723\) −1781.18 931.322i −0.0916220 0.0479063i
\(724\) −860.184 + 2647.37i −0.0441554 + 0.135896i
\(725\) −843.712 −0.0432203
\(726\) 8492.07 + 5344.81i 0.434119 + 0.273229i
\(727\) 13898.0 0.709010 0.354505 0.935054i \(-0.384649\pi\)
0.354505 + 0.935054i \(0.384649\pi\)
\(728\) −1904.79 + 5862.33i −0.0969726 + 0.298451i
\(729\) 19066.5 4887.67i 0.968678 0.248319i
\(730\) 5225.95 + 3796.87i 0.264960 + 0.192505i
\(731\) −35270.0 + 11459.9i −1.78455 + 0.579837i
\(732\) −1216.12 + 1190.76i −0.0614059 + 0.0601254i
\(733\) −8770.52 + 12071.6i −0.441946 + 0.608286i −0.970643 0.240524i \(-0.922681\pi\)
0.528697 + 0.848811i \(0.322681\pi\)
\(734\) 557.597 405.118i 0.0280399 0.0203722i
\(735\) −12692.9 + 1873.50i −0.636985 + 0.0940203i
\(736\) 8000.96i 0.400705i
\(737\) 209.642 24.6603i 0.0104780 0.00123253i
\(738\) 7871.95 10368.2i 0.392643 0.517151i
\(739\) −4896.28 1590.90i −0.243725 0.0791910i 0.184607 0.982812i \(-0.440899\pi\)
−0.428332 + 0.903621i \(0.640899\pi\)
\(740\) 16586.7 + 22829.6i 0.823970 + 1.13410i
\(741\) 11957.5 + 2023.25i 0.592809 + 0.100305i
\(742\) −2097.47 6455.34i −0.103774 0.319384i
\(743\) −8364.07 25742.0i −0.412985 1.27104i −0.914041 0.405623i \(-0.867055\pi\)
0.501055 0.865415i \(-0.332945\pi\)
\(744\) −22570.2 3818.94i −1.11218 0.188184i
\(745\) −2251.34 3098.71i −0.110715 0.152386i
\(746\) 8397.92 + 2728.65i 0.412158 + 0.133918i
\(747\) 19052.6 25094.2i 0.933197 1.22912i
\(748\) −3721.83 + 18641.0i −0.181930 + 0.911209i
\(749\) 6895.46i 0.336388i
\(750\) −1530.38 + 225.887i −0.0745087 + 0.0109976i
\(751\) 1855.06 1347.78i 0.0901357 0.0654874i −0.541805 0.840504i \(-0.682259\pi\)
0.631940 + 0.775017i \(0.282259\pi\)
\(752\) −1794.44 + 2469.83i −0.0870166 + 0.119768i
\(753\) 13694.5 13408.9i 0.662756 0.648936i
\(754\) −235.982 + 76.6751i −0.0113978 + 0.00370337i
\(755\) −25326.8 18401.0i −1.22084 0.886995i
\(756\) −10110.3 + 4755.18i −0.486386 + 0.228762i
\(757\) 231.753 713.263i 0.0111271 0.0342457i −0.945339 0.326090i \(-0.894269\pi\)
0.956466 + 0.291844i \(0.0942688\pi\)
\(758\) 10197.5 0.488640
\(759\) −7566.87 2888.71i −0.361871 0.138147i
\(760\) −31979.2 −1.52633
\(761\) −6376.24 + 19624.0i −0.303730 + 0.934784i 0.676418 + 0.736518i \(0.263531\pi\)
−0.980148 + 0.198267i \(0.936469\pi\)
\(762\) 3161.55 + 1653.07i 0.150303 + 0.0785886i
\(763\) −5248.05 3812.93i −0.249007 0.180914i
\(764\) 14414.1 4683.41i 0.682568 0.221780i
\(765\) −12077.7 + 34668.2i −0.570811 + 1.63847i
\(766\) −994.471 + 1368.77i −0.0469082 + 0.0645636i
\(767\) −935.589 + 679.745i −0.0440445 + 0.0320002i
\(768\) 2223.37 + 15063.3i 0.104465 + 0.707748i
\(769\) 3616.44i 0.169587i −0.996399 0.0847933i \(-0.972977\pi\)
0.996399 0.0847933i \(-0.0270230\pi\)
\(770\) −9593.57 5381.70i −0.448998 0.251874i
\(771\) −10233.0 20617.6i −0.477994 0.963068i
\(772\) 14399.9 + 4678.82i 0.671327 + 0.218127i
\(773\) −24429.3 33624.0i −1.13669 1.56452i −0.774695 0.632335i \(-0.782097\pi\)
−0.361993 0.932181i \(-0.617903\pi\)
\(774\) 4748.57 + 15735.3i 0.220522 + 0.730740i
\(775\) 7540.31 + 23206.7i 0.349492 + 1.07562i
\(776\) −3816.31 11745.4i −0.176543 0.543345i
\(777\) 3643.92 21535.8i 0.168243 0.994328i
\(778\) −8646.47 11900.9i −0.398446 0.548414i
\(779\) 32590.8 + 10589.4i 1.49895 + 0.487040i
\(780\) −9553.92 + 4741.85i −0.438571 + 0.217674i
\(781\) −2416.11 + 1111.74i −0.110698 + 0.0509364i
\(782\) 5478.77i 0.250537i
\(783\) −928.856 510.874i −0.0423941 0.0233169i
\(784\) −2326.05 + 1689.97i −0.105961 + 0.0769848i
\(785\) −23789.6 + 32743.6i −1.08164 + 1.48875i
\(786\) −9921.74 10133.0i −0.450250 0.459839i
\(787\) 40048.8 13012.6i 1.81396 0.589390i 0.813994 0.580874i \(-0.197289\pi\)
0.999964 0.00851680i \(-0.00271102\pi\)
\(788\) 24705.7 + 17949.8i 1.11689 + 0.811465i
\(789\) 15125.0 28926.9i 0.682464 1.30523i
\(790\) 4394.56 13525.1i 0.197913 0.609115i
\(791\) 5745.51 0.258264
\(792\) 19387.2 + 4297.47i 0.869815 + 0.192808i
\(793\) 1257.64 0.0563177
\(794\) −2607.82 + 8026.04i −0.116559 + 0.358732i
\(795\) 12827.2 24532.3i 0.572242 1.09443i
\(796\) 20232.2 + 14699.6i 0.900895 + 0.654539i
\(797\) −27082.3 + 8799.58i −1.20365 + 0.391088i −0.841101 0.540878i \(-0.818092\pi\)
−0.362545 + 0.931966i \(0.618092\pi\)
\(798\) 7346.96 + 7503.43i 0.325914 + 0.332855i
\(799\) 8854.04 12186.5i 0.392032 0.539586i
\(800\) 16916.6 12290.6i 0.747616 0.543175i
\(801\) −29187.8 + 20280.5i −1.28751 + 0.894602i
\(802\) 17028.1i 0.749729i
\(803\) 5165.88 9208.85i 0.227024 0.404699i
\(804\) 158.755 78.7941i 0.00696376 0.00345629i
\(805\) 8444.63 + 2743.83i 0.369732 + 0.120133i
\(806\) 4217.97 + 5805.53i 0.184332 + 0.253711i
\(807\) −357.987 + 2115.73i −0.0156156 + 0.0922890i
\(808\) 8126.36 + 25010.4i 0.353817 + 1.08894i
\(809\) 1714.60 + 5276.99i 0.0745143 + 0.229331i 0.981376 0.192097i \(-0.0615289\pi\)
−0.906862 + 0.421428i \(0.861529\pi\)
\(810\) 15248.8 + 5675.41i 0.661468 + 0.246190i
\(811\) 16923.3 + 23292.9i 0.732747 + 1.00854i 0.999003 + 0.0446375i \(0.0142133\pi\)
−0.266256 + 0.963902i \(0.585787\pi\)
\(812\) 572.284 + 185.946i 0.0247331 + 0.00803626i
\(813\) 4979.29 + 10032.3i 0.214799 + 0.432778i
\(814\) −12102.2 + 11171.1i −0.521110 + 0.481017i
\(815\) 32705.9i 1.40569i
\(816\) 1201.26 + 8138.53i 0.0515351 + 0.349149i
\(817\) −35003.0 + 25431.1i −1.49890 + 1.08901i
\(818\) 7969.21 10968.7i 0.340632 0.468839i
\(819\) 7796.07 + 2715.99i 0.332621 + 0.115878i
\(820\) −28663.1 + 9313.19i −1.22068 + 0.396623i
\(821\) 25740.8 + 18701.8i 1.09422 + 0.795001i 0.980108 0.198466i \(-0.0635960\pi\)
0.114117 + 0.993467i \(0.463596\pi\)
\(822\) 7264.94 + 3798.61i 0.308265 + 0.161182i
\(823\) 1216.06 3742.65i 0.0515058 0.158518i −0.921995 0.387201i \(-0.873442\pi\)
0.973501 + 0.228683i \(0.0734419\pi\)
\(824\) 12212.3 0.516306
\(825\) −5516.15 20436.3i −0.232785 0.862425i
\(826\) −1001.39 −0.0421826
\(827\) 11826.7 36398.7i 0.497283 1.53048i −0.316086 0.948731i \(-0.602369\pi\)
0.813368 0.581749i \(-0.197631\pi\)
\(828\) −6799.02 143.286i −0.285365 0.00601394i
\(829\) 11491.2 + 8348.86i 0.481431 + 0.349780i 0.801879 0.597486i \(-0.203834\pi\)
−0.320448 + 0.947266i \(0.603834\pi\)
\(830\) 24770.6 8048.45i 1.03590 0.336585i
\(831\) −21695.6 + 21243.2i −0.905671 + 0.886785i
\(832\) 1708.03 2350.90i 0.0711722 0.0979602i
\(833\) 11477.1 8338.58i 0.477379 0.346836i
\(834\) −18996.8 + 2803.97i −0.788736 + 0.116419i
\(835\) 34860.7i 1.44480i
\(836\) 2590.85 + 22025.3i 0.107185 + 0.911197i
\(837\) −5750.58 + 30114.3i −0.237478 + 1.24361i
\(838\) 19514.5 + 6340.66i 0.804437 + 0.261378i
\(839\) 13827.2 + 19031.5i 0.568971 + 0.783121i 0.992432 0.122793i \(-0.0391851\pi\)
−0.423461 + 0.905914i \(0.639185\pi\)
\(840\) −21464.3 3631.82i −0.881653 0.149178i
\(841\) −7518.97 23141.0i −0.308294 0.948830i
\(842\) −2529.01 7783.48i −0.103510 0.318571i
\(843\) 1004.95 + 170.040i 0.0410583 + 0.00694719i
\(844\) −10127.9 13939.9i −0.413055 0.568521i
\(845\) −24648.6 8008.81i −1.00348 0.326049i
\(846\) −5317.22 4037.06i −0.216087 0.164063i
\(847\) −6904.64 + 16601.9i −0.280102 + 0.673492i
\(848\) 6203.53i 0.251215i
\(849\) 7551.75 1114.65i 0.305271 0.0450587i
\(850\) −11583.9 + 8416.20i −0.467441 + 0.339615i
\(851\) 7814.35 10755.5i 0.314774 0.433249i
\(852\) −1595.57 + 1562.30i −0.0641589 + 0.0628210i
\(853\) 15023.8 4881.52i 0.603052 0.195944i 0.00845111 0.999964i \(-0.497310\pi\)
0.594601 + 0.804021i \(0.297310\pi\)
\(854\) 881.025 + 640.102i 0.0353022 + 0.0256485i
\(855\) −902.434 + 42821.0i −0.0360966 + 1.71280i
\(856\) 3179.81 9786.45i 0.126967 0.390764i
\(857\) 25125.8 1.00149 0.500747 0.865594i \(-0.333059\pi\)
0.500747 + 0.865594i \(0.333059\pi\)
\(858\) −3400.05 5214.62i −0.135287 0.207487i
\(859\) 21073.5 0.837042 0.418521 0.908207i \(-0.362549\pi\)
0.418521 + 0.908207i \(0.362549\pi\)
\(860\) 11758.7 36189.4i 0.466240 1.43494i
\(861\) 20672.1 + 10808.8i 0.818240 + 0.427832i
\(862\) −7407.33 5381.74i −0.292685 0.212648i
\(863\) −35289.1 + 11466.1i −1.39195 + 0.452272i −0.906579 0.422035i \(-0.861316\pi\)
−0.485372 + 0.874308i \(0.661316\pi\)
\(864\) 26065.9 3287.82i 1.02636 0.129460i
\(865\) −9116.88 + 12548.3i −0.358362 + 0.493243i
\(866\) −14654.1 + 10646.8i −0.575017 + 0.417775i
\(867\) −2199.52 14901.7i −0.0861588 0.583724i
\(868\) 17402.8i 0.680516i
\(869\) −22795.8 4551.36i −0.889866 0.177669i
\(870\) −389.585 784.939i −0.0151818 0.0305884i
\(871\) −124.550 40.4686i −0.00484524 0.00157431i
\(872\) 5690.02 + 7831.64i 0.220973 + 0.304143i
\(873\) −15835.1 + 4778.70i −0.613903 + 0.185263i
\(874\) 1975.21 + 6079.06i 0.0764444 + 0.235272i
\(875\) −856.615 2636.39i −0.0330959 0.101859i
\(876\) 1479.03 8741.19i 0.0570456 0.337143i
\(877\) −28631.0 39407.3i −1.10240 1.51732i −0.832169 0.554522i \(-0.812901\pi\)
−0.270228 0.962796i \(-0.587099\pi\)
\(878\) 17184.4 + 5583.55i 0.660530 + 0.214619i
\(879\) −18187.6 + 9026.93i −0.697896 + 0.346383i
\(880\) −6819.04 7387.42i −0.261216 0.282988i
\(881\) 9114.38i 0.348549i 0.984697 + 0.174274i \(0.0557579\pi\)
−0.984697 + 0.174274i \(0.944242\pi\)
\(882\) −3587.68 5163.40i −0.136965 0.197121i
\(883\) −10282.3 + 7470.51i −0.391875 + 0.284714i −0.766224 0.642574i \(-0.777867\pi\)
0.374348 + 0.927288i \(0.377867\pi\)
\(884\) 6931.88 9540.92i 0.263738 0.363004i
\(885\) −2857.40 2918.25i −0.108531 0.110843i
\(886\) 6707.32 2179.34i 0.254331 0.0826370i
\(887\) −5155.82 3745.92i −0.195170 0.141799i 0.485909 0.874010i \(-0.338489\pi\)
−0.681078 + 0.732211i \(0.738489\pi\)
\(888\) −15102.8 + 28884.5i −0.570739 + 1.09155i
\(889\) −1975.55 + 6080.11i −0.0745306 + 0.229382i
\(890\) −29380.3 −1.10655
\(891\) 6301.52 25838.7i 0.236935 0.971526i
\(892\) 18463.7 0.693062
\(893\) 5430.66 16713.9i 0.203505 0.626325i
\(894\) 869.699 1663.32i 0.0325359 0.0622257i
\(895\) −15752.0 11444.5i −0.588304 0.427428i
\(896\) −16854.3 + 5476.31i −0.628420 + 0.204186i
\(897\) 3515.56 + 3590.43i 0.130860 + 0.133646i
\(898\) −1554.02 + 2138.92i −0.0577486 + 0.0794841i
\(899\) 1335.84 970.545i 0.0495581 0.0360061i
\(900\) −10141.3 14595.4i −0.375605 0.540572i
\(901\) 30609.2i 1.13179i
\(902\) −7352.79 15979.6i −0.271420 0.589869i
\(903\) −26382.0 + 13094.0i −0.972245 + 0.482549i
\(904\) −8154.36 2649.51i −0.300011 0.0974795i
\(905\) 4269.73 + 5876.78i 0.156829 + 0.215857i
\(906\) 2559.39 15126.1i 0.0938520 0.554671i
\(907\) 6037.04 + 18580.1i 0.221010 + 0.680200i 0.998672 + 0.0515172i \(0.0164057\pi\)
−0.777662 + 0.628683i \(0.783594\pi\)
\(908\) −3123.78 9614.01i −0.114170 0.351379i
\(909\) 33718.9 10175.6i 1.23035 0.371292i
\(910\) 4011.29 + 5521.07i 0.146124 + 0.201123i
\(911\) −12284.5 3991.49i −0.446767 0.145163i 0.0769884 0.997032i \(-0.475470\pi\)
−0.523756 + 0.851868i \(0.675470\pi\)
\(912\) 4266.99 + 8597.17i 0.154928 + 0.312150i
\(913\) −17796.1 38675.6i −0.645087 1.40194i
\(914\) 5286.61i 0.191319i
\(915\) 648.558 + 4393.97i 0.0234324 + 0.158754i
\(916\) 15754.3 11446.2i 0.568271 0.412873i
\(917\) 14937.2 20559.3i 0.537918 0.740380i
\(918\) −17849.0 + 2251.38i −0.641725 + 0.0809440i
\(919\) −42147.2 + 13694.4i −1.51285 + 0.491554i −0.943734 0.330705i \(-0.892713\pi\)
−0.569113 + 0.822259i \(0.692713\pi\)
\(920\) −10719.8 7788.40i −0.384154 0.279104i
\(921\) 37571.0 + 19644.7i 1.34420 + 0.702840i
\(922\) −8408.23 + 25877.9i −0.300336 + 0.924341i
\(923\) 1650.04 0.0588426
\(924\) −762.406 + 15077.5i −0.0271443 + 0.536812i
\(925\) 34744.7 1.23502
\(926\) 2538.28 7812.02i 0.0900788 0.277234i
\(927\) 344.624 16352.6i 0.0122103 0.579385i
\(928\) −1144.73 831.696i −0.0404932 0.0294200i
\(929\) −13934.5 + 4527.60i −0.492118 + 0.159899i −0.544554 0.838726i \(-0.683301\pi\)
0.0524368 + 0.998624i \(0.483301\pi\)
\(930\) −18108.4 + 17730.8i −0.638491 + 0.625177i
\(931\) 9728.36 13389.9i 0.342464 0.471362i
\(932\) −19365.8 + 14070.1i −0.680630 + 0.494507i
\(933\) 6829.65 1008.07i 0.239649 0.0353727i
\(934\) 6418.53i 0.224861i
\(935\) 33646.2 + 36450.7i 1.17684 + 1.27494i
\(936\) −9812.17 7449.81i −0.342650 0.260155i
\(937\) −16510.0 5364.42i −0.575621 0.187031i 0.00671665 0.999977i \(-0.497862\pi\)
−0.582338 + 0.812947i \(0.697862\pi\)
\(938\) −66.6547 91.7423i −0.00232021 0.00319349i
\(939\) 12794.3 + 2164.83i 0.444650 + 0.0752361i
\(940\) 4776.18 + 14699.6i 0.165725 + 0.510051i
\(941\) 8359.43 + 25727.7i 0.289596 + 0.891284i 0.984983 + 0.172649i \(0.0552327\pi\)
−0.695388 + 0.718635i \(0.744767\pi\)
\(942\) −19555.7 3308.89i −0.676391 0.114447i
\(943\) 8345.81 + 11487.0i 0.288205 + 0.396680i
\(944\) −870.434 282.821i −0.0300108 0.00975111i
\(945\) −5468.81 + 28638.8i −0.188255 + 0.985841i
\(946\) 21779.0 + 4348.35i 0.748517 + 0.149447i
\(947\) 38557.0i 1.32306i 0.749920 + 0.661529i \(0.230092\pi\)
−0.749920 + 0.661529i \(0.769908\pi\)
\(948\) −19308.4 + 2849.96i −0.661506 + 0.0976396i
\(949\) −5299.67 + 3850.43i −0.181280 + 0.131707i
\(950\) −9818.91 + 13514.6i −0.335334 + 0.461548i
\(951\) 18385.0 18001.6i 0.626891 0.613818i
\(952\) 22892.1 7438.09i 0.779345 0.253225i
\(953\) 6467.09 + 4698.62i 0.219821 + 0.159710i 0.692246 0.721661i \(-0.256621\pi\)
−0.472425 + 0.881371i \(0.656621\pi\)
\(954\) 13563.0 + 285.835i 0.460293 + 0.00970048i
\(955\) 12221.8 37614.8i 0.414124 1.27454i
\(956\) 8846.71 0.299292
\(957\) −1199.87 + 782.344i −0.0405291 + 0.0264259i
\(958\) 8458.77 0.285272
\(959\) −4539.63 + 13971.5i −0.152859 + 0.470453i
\(960\) 9094.48 + 4755.22i 0.305753 + 0.159869i
\(961\) −14532.3 10558.4i −0.487810 0.354414i
\(962\) 9717.89 3157.54i 0.325694 0.105824i
\(963\) −13014.6 4534.02i −0.435503 0.151720i
\(964\) −1340.34 + 1844.82i −0.0447817 + 0.0616367i
\(965\) 31965.7 23224.4i 1.06633 0.774737i
\(966\) 635.362 + 4304.56i 0.0211619 + 0.143372i
\(967\) 40870.3i 1.35915i 0.733605 + 0.679576i \(0.237836\pi\)
−0.733605 + 0.679576i \(0.762164\pi\)
\(968\) 17455.4 20378.3i 0.579583 0.676637i
\(969\) −21054.0 42419.8i −0.697990 1.40632i
\(970\) −13003.8 4225.19i −0.430440 0.139858i
\(971\) −16820.1 23150.9i −0.555904 0.765136i 0.434895 0.900481i \(-0.356786\pi\)
−0.990798 + 0.135346i \(0.956786\pi\)
\(972\) −2327.10 22209.0i −0.0767921 0.732875i
\(973\) −10633.3 32725.9i −0.350347 1.07826i
\(974\) −997.207 3069.09i −0.0328055 0.100965i
\(975\) −2190.92 + 12948.5i −0.0719646 + 0.425315i
\(976\) 585.027 + 805.220i 0.0191867 + 0.0264083i
\(977\) −23686.2 7696.11i −0.775628 0.252017i −0.105656 0.994403i \(-0.533694\pi\)
−0.669972 + 0.742386i \(0.733694\pi\)
\(978\) 14356.3 7125.39i 0.469390 0.232970i
\(979\) 5610.51 + 47696.0i 0.183159 + 1.55707i
\(980\) 14556.2i 0.474472i
\(981\) 10647.4 7398.09i 0.346528 0.240778i
\(982\) −3397.62 + 2468.52i −0.110410 + 0.0802174i
\(983\) 8089.74 11134.6i 0.262485 0.361280i −0.657350 0.753586i \(-0.728323\pi\)
0.919835 + 0.392306i \(0.128323\pi\)
\(984\) −24354.7 24873.4i −0.789023 0.805827i
\(985\) 75791.3 24626.1i 2.45169 0.796601i
\(986\) 783.871 + 569.516i 0.0253180 + 0.0183946i
\(987\) 5543.20 10601.5i 0.178766 0.341895i
\(988\) 4251.70 13085.4i 0.136907 0.421358i
\(989\) −17927.1 −0.576387
\(990\) 16465.6 14568.4i 0.528598 0.467690i
\(991\) −8059.62 −0.258347 −0.129174 0.991622i \(-0.541232\pi\)
−0.129174 + 0.991622i \(0.541232\pi\)
\(992\) −12645.6 + 38919.3i −0.404737 + 1.24565i
\(993\) 3354.38 6415.34i 0.107198 0.205020i
\(994\) 1155.92 + 839.824i 0.0368848 + 0.0267984i
\(995\) 62067.7 20167.0i 1.97757 0.642550i
\(996\) −25008.3 25540.9i −0.795600 0.812543i
\(997\) −20503.3 + 28220.4i −0.651300 + 0.896437i −0.999155 0.0411112i \(-0.986910\pi\)
0.347855 + 0.937548i \(0.386910\pi\)
\(998\) −21649.6 + 15729.4i −0.686681 + 0.498903i
\(999\) 38250.9 + 21038.2i 1.21142 + 0.666284i
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 33.4.f.a.2.7 yes 40
3.2 odd 2 inner 33.4.f.a.2.4 40
11.4 even 5 363.4.d.d.362.25 40
11.6 odd 10 inner 33.4.f.a.17.4 yes 40
11.7 odd 10 363.4.d.d.362.15 40
33.17 even 10 inner 33.4.f.a.17.7 yes 40
33.26 odd 10 363.4.d.d.362.16 40
33.29 even 10 363.4.d.d.362.26 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.f.a.2.4 40 3.2 odd 2 inner
33.4.f.a.2.7 yes 40 1.1 even 1 trivial
33.4.f.a.17.4 yes 40 11.6 odd 10 inner
33.4.f.a.17.7 yes 40 33.17 even 10 inner
363.4.d.d.362.15 40 11.7 odd 10
363.4.d.d.362.16 40 33.26 odd 10
363.4.d.d.362.25 40 11.4 even 5
363.4.d.d.362.26 40 33.29 even 10