Properties

Label 287.3.o.a.139.7
Level $287$
Weight $3$
Character 287.139
Analytic conductor $7.820$
Analytic rank $0$
Dimension $216$
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] = [287,3,Mod(139,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.139");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.o (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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(54\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 139.7
Character \(\chi\) \(=\) 287.139
Dual form 287.3.o.a.223.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.961384 + 2.95883i) q^{2} -3.57784i q^{3} +(-4.59437 - 3.33801i) q^{4} +(5.23870 - 7.21045i) q^{5} +(10.5862 + 3.43967i) q^{6} +(-6.98907 + 0.391037i) q^{7} +(4.22583 - 3.07025i) q^{8} -3.80091 q^{9} +O(q^{10})\) \(q+(-0.961384 + 2.95883i) q^{2} -3.57784i q^{3} +(-4.59437 - 3.33801i) q^{4} +(5.23870 - 7.21045i) q^{5} +(10.5862 + 3.43967i) q^{6} +(-6.98907 + 0.391037i) q^{7} +(4.22583 - 3.07025i) q^{8} -3.80091 q^{9} +(16.2981 + 22.4324i) q^{10} +(-5.00282 + 3.63476i) q^{11} +(-11.9428 + 16.4379i) q^{12} +(14.7509 + 4.79284i) q^{13} +(5.56216 - 21.0554i) q^{14} +(-25.7978 - 18.7432i) q^{15} +(-1.99787 - 6.14883i) q^{16} +(-15.9587 - 21.9653i) q^{17} +(3.65413 - 11.2463i) q^{18} +(-16.1006 + 5.23139i) q^{19} +(-48.1371 + 15.6407i) q^{20} +(1.39907 + 25.0057i) q^{21} +(-5.94503 - 18.2969i) q^{22} +(-3.84353 + 11.8292i) q^{23} +(-10.9848 - 15.1193i) q^{24} +(-16.8212 - 51.7703i) q^{25} +(-28.3625 + 39.0376i) q^{26} -18.6015i q^{27} +(33.4157 + 21.5330i) q^{28} +(-26.6947 - 19.3948i) q^{29} +(80.2596 - 58.3120i) q^{30} +(-26.4073 - 36.3465i) q^{31} +41.0077 q^{32} +(13.0046 + 17.8993i) q^{33} +(80.3340 - 26.1021i) q^{34} +(-33.7941 + 52.4428i) q^{35} +(17.4628 + 12.6875i) q^{36} +(29.7323 + 21.6018i) q^{37} -52.6683i q^{38} +(17.1480 - 52.7761i) q^{39} -46.5542i q^{40} +(27.4094 + 30.4914i) q^{41} +(-75.3329 - 19.9005i) q^{42} +(-10.4487 + 32.1579i) q^{43} +35.1177 q^{44} +(-19.9118 + 27.4063i) q^{45} +(-31.3055 - 22.7447i) q^{46} +(-42.5869 - 13.8373i) q^{47} +(-21.9995 + 7.14807i) q^{48} +(48.6942 - 5.46598i) q^{49} +169.351 q^{50} +(-78.5881 + 57.0976i) q^{51} +(-51.7724 - 71.2586i) q^{52} +(-31.8297 - 23.1257i) q^{53} +(55.0387 + 17.8832i) q^{54} +55.1140i q^{55} +(-28.3340 + 23.1106i) q^{56} +(18.7171 + 57.6052i) q^{57} +(83.0499 - 60.3393i) q^{58} +(78.9556 + 25.6542i) q^{59} +(55.9598 + 172.227i) q^{60} +(-35.4894 + 11.5312i) q^{61} +(132.931 - 43.1918i) q^{62} +(26.5648 - 1.48630i) q^{63} +(-31.4327 + 96.7398i) q^{64} +(111.834 - 81.2520i) q^{65} +(-65.4634 + 21.2703i) q^{66} +(-70.7125 - 51.3756i) q^{67} +154.187i q^{68} +(42.3229 + 13.7515i) q^{69} +(-122.681 - 150.409i) q^{70} +(65.5822 - 47.6483i) q^{71} +(-16.0620 + 11.6697i) q^{72} -37.9168i q^{73} +(-92.5003 + 67.2054i) q^{74} +(-185.225 + 60.1834i) q^{75} +(91.4344 + 29.7089i) q^{76} +(33.5437 - 27.3599i) q^{77} +(139.670 + 101.476i) q^{78} +38.3425 q^{79} +(-54.8020 - 17.8063i) q^{80} -100.761 q^{81} +(-116.570 + 51.7858i) q^{82} -38.6566i q^{83} +(77.0415 - 119.556i) q^{84} -241.982 q^{85} +(-85.1046 - 61.8321i) q^{86} +(-69.3915 + 95.5092i) q^{87} +(-9.98146 + 30.7198i) q^{88} +(119.009 - 38.6683i) q^{89} +(-61.9477 - 85.2637i) q^{90} +(-104.969 - 27.7294i) q^{91} +(57.1445 - 41.5179i) q^{92} +(-130.042 + 94.4809i) q^{93} +(81.8848 - 112.705i) q^{94} +(-46.6253 + 143.498i) q^{95} -146.719i q^{96} +(-11.1028 + 15.2817i) q^{97} +(-30.6409 + 149.333i) q^{98} +(19.0153 - 13.8154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9} - 22 q^{11} + 82 q^{14} + 36 q^{15} - 182 q^{16} + 24 q^{18} + 131 q^{21} - 38 q^{22} - 66 q^{23} + 244 q^{25} + 56 q^{28} - 230 q^{29} - 184 q^{30} + 56 q^{32} - 120 q^{35} + 100 q^{37} + 148 q^{39} - 164 q^{42} - 44 q^{43} + 448 q^{44} - 260 q^{46} - 151 q^{49} - 116 q^{50} + 114 q^{51} + 388 q^{53} + 77 q^{56} + 180 q^{57} + 222 q^{58} - 382 q^{60} - 29 q^{63} - 82 q^{64} + 636 q^{65} + 426 q^{67} - 527 q^{70} + 360 q^{71} - 466 q^{72} - 236 q^{74} + 34 q^{77} - 150 q^{78} - 96 q^{79} + 1384 q^{81} + 858 q^{84} - 252 q^{85} - 420 q^{86} + 284 q^{88} + 878 q^{91} - 26 q^{92} - 120 q^{93} - 1406 q^{95} + 641 q^{98} - 398 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.961384 + 2.95883i −0.480692 + 1.47942i 0.357433 + 0.933939i \(0.383652\pi\)
−0.838125 + 0.545478i \(0.816348\pi\)
\(3\) 3.57784i 1.19261i −0.802757 0.596306i \(-0.796634\pi\)
0.802757 0.596306i \(-0.203366\pi\)
\(4\) −4.59437 3.33801i −1.14859 0.834502i
\(5\) 5.23870 7.21045i 1.04774 1.44209i 0.156987 0.987601i \(-0.449822\pi\)
0.890753 0.454488i \(-0.150178\pi\)
\(6\) 10.5862 + 3.43967i 1.76437 + 0.573279i
\(7\) −6.98907 + 0.391037i −0.998438 + 0.0558625i
\(8\) 4.22583 3.07025i 0.528229 0.383781i
\(9\) −3.80091 −0.422324
\(10\) 16.2981 + 22.4324i 1.62981 + 2.24324i
\(11\) −5.00282 + 3.63476i −0.454802 + 0.330433i −0.791489 0.611184i \(-0.790694\pi\)
0.336687 + 0.941617i \(0.390694\pi\)
\(12\) −11.9428 + 16.4379i −0.995237 + 1.36983i
\(13\) 14.7509 + 4.79284i 1.13468 + 0.368680i 0.815353 0.578964i \(-0.196543\pi\)
0.319328 + 0.947644i \(0.396543\pi\)
\(14\) 5.56216 21.0554i 0.397297 1.50396i
\(15\) −25.7978 18.7432i −1.71985 1.24955i
\(16\) −1.99787 6.14883i −0.124867 0.384302i
\(17\) −15.9587 21.9653i −0.938747 1.29207i −0.956348 0.292230i \(-0.905603\pi\)
0.0176009 0.999845i \(-0.494397\pi\)
\(18\) 3.65413 11.2463i 0.203007 0.624793i
\(19\) −16.1006 + 5.23139i −0.847398 + 0.275336i −0.700356 0.713794i \(-0.746975\pi\)
−0.147042 + 0.989130i \(0.546975\pi\)
\(20\) −48.1371 + 15.6407i −2.40685 + 0.782034i
\(21\) 1.39907 + 25.0057i 0.0666223 + 1.19075i
\(22\) −5.94503 18.2969i −0.270229 0.831678i
\(23\) −3.84353 + 11.8292i −0.167110 + 0.514312i −0.999186 0.0403504i \(-0.987153\pi\)
0.832076 + 0.554662i \(0.187153\pi\)
\(24\) −10.9848 15.1193i −0.457702 0.629972i
\(25\) −16.8212 51.7703i −0.672847 2.07081i
\(26\) −28.3625 + 39.0376i −1.09086 + 1.50145i
\(27\) 18.6015i 0.688944i
\(28\) 33.4157 + 21.5330i 1.19342 + 0.769036i
\(29\) −26.6947 19.3948i −0.920506 0.668787i 0.0231437 0.999732i \(-0.492632\pi\)
−0.943650 + 0.330945i \(0.892632\pi\)
\(30\) 80.2596 58.3120i 2.67532 1.94373i
\(31\) −26.4073 36.3465i −0.851847 1.17247i −0.983453 0.181165i \(-0.942013\pi\)
0.131605 0.991302i \(-0.457987\pi\)
\(32\) 41.0077 1.28149
\(33\) 13.0046 + 17.8993i 0.394078 + 0.542402i
\(34\) 80.3340 26.1021i 2.36277 0.767709i
\(35\) −33.7941 + 52.4428i −0.965544 + 1.49837i
\(36\) 17.4628 + 12.6875i 0.485078 + 0.352430i
\(37\) 29.7323 + 21.6018i 0.803576 + 0.583832i 0.911961 0.410277i \(-0.134568\pi\)
−0.108385 + 0.994109i \(0.534568\pi\)
\(38\) 52.6683i 1.38601i
\(39\) 17.1480 52.7761i 0.439692 1.35323i
\(40\) 46.5542i 1.16386i
\(41\) 27.4094 + 30.4914i 0.668521 + 0.743693i
\(42\) −75.3329 19.9005i −1.79364 0.473821i
\(43\) −10.4487 + 32.1579i −0.242994 + 0.747858i 0.752966 + 0.658059i \(0.228622\pi\)
−0.995960 + 0.0897988i \(0.971378\pi\)
\(44\) 35.1177 0.798129
\(45\) −19.9118 + 27.4063i −0.442485 + 0.609028i
\(46\) −31.3055 22.7447i −0.680553 0.494451i
\(47\) −42.5869 13.8373i −0.906105 0.294411i −0.181351 0.983419i \(-0.558047\pi\)
−0.724755 + 0.689007i \(0.758047\pi\)
\(48\) −21.9995 + 7.14807i −0.458323 + 0.148918i
\(49\) 48.6942 5.46598i 0.993759 0.111551i
\(50\) 169.351 3.38702
\(51\) −78.5881 + 57.0976i −1.54094 + 1.11956i
\(52\) −51.7724 71.2586i −0.995623 1.37036i
\(53\) −31.8297 23.1257i −0.600561 0.436333i 0.245517 0.969392i \(-0.421042\pi\)
−0.846078 + 0.533059i \(0.821042\pi\)
\(54\) 55.0387 + 17.8832i 1.01924 + 0.331170i
\(55\) 55.1140i 1.00207i
\(56\) −28.3340 + 23.1106i −0.505965 + 0.412690i
\(57\) 18.7171 + 57.6052i 0.328369 + 1.01062i
\(58\) 83.0499 60.3393i 1.43189 1.04033i
\(59\) 78.9556 + 25.6542i 1.33823 + 0.434817i 0.888717 0.458457i \(-0.151598\pi\)
0.449513 + 0.893274i \(0.351598\pi\)
\(60\) 55.9598 + 172.227i 0.932663 + 2.87044i
\(61\) −35.4894 + 11.5312i −0.581793 + 0.189036i −0.585104 0.810958i \(-0.698946\pi\)
0.00331051 + 0.999995i \(0.498946\pi\)
\(62\) 132.931 43.1918i 2.14404 0.696642i
\(63\) 26.5648 1.48630i 0.421664 0.0235921i
\(64\) −31.4327 + 96.7398i −0.491135 + 1.51156i
\(65\) 111.834 81.2520i 1.72052 1.25003i
\(66\) −65.4634 + 21.2703i −0.991869 + 0.322278i
\(67\) −70.7125 51.3756i −1.05541 0.766800i −0.0821763 0.996618i \(-0.526187\pi\)
−0.973234 + 0.229817i \(0.926187\pi\)
\(68\) 154.187i 2.26746i
\(69\) 42.3229 + 13.7515i 0.613375 + 0.199298i
\(70\) −122.681 150.409i −1.75258 2.14870i
\(71\) 65.5822 47.6483i 0.923694 0.671103i −0.0207471 0.999785i \(-0.506604\pi\)
0.944441 + 0.328682i \(0.106604\pi\)
\(72\) −16.0620 + 11.6697i −0.223084 + 0.162080i
\(73\) 37.9168i 0.519409i −0.965688 0.259704i \(-0.916375\pi\)
0.965688 0.259704i \(-0.0836251\pi\)
\(74\) −92.5003 + 67.2054i −1.25000 + 0.908181i
\(75\) −185.225 + 60.1834i −2.46967 + 0.802445i
\(76\) 91.4344 + 29.7089i 1.20308 + 0.390906i
\(77\) 33.5437 27.3599i 0.435633 0.355323i
\(78\) 139.670 + 101.476i 1.79064 + 1.30098i
\(79\) 38.3425 0.485349 0.242674 0.970108i \(-0.421975\pi\)
0.242674 + 0.970108i \(0.421975\pi\)
\(80\) −54.8020 17.8063i −0.685025 0.222578i
\(81\) −100.761 −1.24397
\(82\) −116.570 + 51.7858i −1.42159 + 0.631534i
\(83\) 38.6566i 0.465742i −0.972508 0.232871i \(-0.925188\pi\)
0.972508 0.232871i \(-0.0748120\pi\)
\(84\) 77.0415 119.556i 0.917161 1.42328i
\(85\) −241.982 −2.84685
\(86\) −85.1046 61.8321i −0.989589 0.718978i
\(87\) −69.3915 + 95.5092i −0.797603 + 1.09781i
\(88\) −9.98146 + 30.7198i −0.113426 + 0.349088i
\(89\) 119.009 38.6683i 1.33718 0.434475i 0.448818 0.893623i \(-0.351845\pi\)
0.888360 + 0.459148i \(0.151845\pi\)
\(90\) −61.9477 85.2637i −0.688308 0.947375i
\(91\) −104.969 27.7294i −1.15350 0.304718i
\(92\) 57.1445 41.5179i 0.621136 0.451282i
\(93\) −130.042 + 94.4809i −1.39830 + 1.01592i
\(94\) 81.8848 112.705i 0.871115 1.19899i
\(95\) −46.6253 + 143.498i −0.490793 + 1.51050i
\(96\) 146.719i 1.52832i
\(97\) −11.1028 + 15.2817i −0.114462 + 0.157543i −0.862404 0.506221i \(-0.831042\pi\)
0.747942 + 0.663764i \(0.231042\pi\)
\(98\) −30.6409 + 149.333i −0.312662 + 1.52381i
\(99\) 19.0153 13.8154i 0.192074 0.139550i
\(100\) −95.5268 + 294.001i −0.955268 + 2.94001i
\(101\) 121.094 39.3458i 1.19895 0.389562i 0.359575 0.933116i \(-0.382922\pi\)
0.839374 + 0.543554i \(0.182922\pi\)
\(102\) −93.3891 287.422i −0.915579 2.81786i
\(103\) 76.2036 24.7601i 0.739841 0.240389i 0.0852368 0.996361i \(-0.472835\pi\)
0.654604 + 0.755972i \(0.272835\pi\)
\(104\) 77.0498 25.0350i 0.740864 0.240721i
\(105\) 187.632 + 120.910i 1.78697 + 1.15152i
\(106\) 99.0256 71.9463i 0.934204 0.678739i
\(107\) −31.3592 96.5136i −0.293076 0.901996i −0.983861 0.178935i \(-0.942735\pi\)
0.690784 0.723061i \(-0.257265\pi\)
\(108\) −62.0919 + 85.4622i −0.574925 + 0.791317i
\(109\) 61.4019 0.563320 0.281660 0.959514i \(-0.409115\pi\)
0.281660 + 0.959514i \(0.409115\pi\)
\(110\) −163.073 52.9857i −1.48248 0.481688i
\(111\) 77.2877 106.377i 0.696285 0.958355i
\(112\) 16.3677 + 42.1933i 0.146140 + 0.376726i
\(113\) 21.7215 15.7816i 0.192225 0.139660i −0.487510 0.873117i \(-0.662095\pi\)
0.679735 + 0.733458i \(0.262095\pi\)
\(114\) −188.438 −1.65297
\(115\) 65.1585 + 89.6830i 0.566596 + 0.779852i
\(116\) 57.9053 + 178.214i 0.499184 + 1.53633i
\(117\) −56.0667 18.2172i −0.479203 0.155702i
\(118\) −151.813 + 208.953i −1.28655 + 1.77079i
\(119\) 120.126 + 147.276i 1.00946 + 1.23762i
\(120\) −166.563 −1.38803
\(121\) −25.5743 + 78.7097i −0.211358 + 0.650494i
\(122\) 116.093i 0.951583i
\(123\) 109.093 98.0662i 0.886938 0.797286i
\(124\) 255.137i 2.05756i
\(125\) −249.498 81.0668i −1.99598 0.648534i
\(126\) −21.1413 + 80.0299i −0.167788 + 0.635158i
\(127\) 16.6392 + 12.0891i 0.131017 + 0.0951896i 0.651364 0.758766i \(-0.274197\pi\)
−0.520347 + 0.853955i \(0.674197\pi\)
\(128\) −123.314 89.5931i −0.963394 0.699946i
\(129\) 115.056 + 37.3839i 0.891905 + 0.289797i
\(130\) 132.896 + 409.012i 1.02228 + 3.14625i
\(131\) 95.5625 + 131.530i 0.729485 + 1.00405i 0.999155 + 0.0410967i \(0.0130852\pi\)
−0.269671 + 0.962953i \(0.586915\pi\)
\(132\) 125.645i 0.951859i
\(133\) 110.482 42.8585i 0.830694 0.322244i
\(134\) 219.994 159.835i 1.64174 1.19280i
\(135\) −134.125 97.4475i −0.993518 0.721833i
\(136\) −134.878 43.8244i −0.991747 0.322238i
\(137\) 101.589 0.741523 0.370762 0.928728i \(-0.379097\pi\)
0.370762 + 0.928728i \(0.379097\pi\)
\(138\) −81.3770 + 112.006i −0.589688 + 0.811636i
\(139\) 125.207 40.6821i 0.900766 0.292677i 0.178213 0.983992i \(-0.442968\pi\)
0.722553 + 0.691315i \(0.242968\pi\)
\(140\) 330.317 128.137i 2.35941 0.915266i
\(141\) −49.5077 + 152.369i −0.351119 + 1.08063i
\(142\) 77.9337 + 239.855i 0.548829 + 1.68912i
\(143\) −91.2167 + 29.6381i −0.637879 + 0.207259i
\(144\) 7.59375 + 23.3712i 0.0527344 + 0.162300i
\(145\) −279.691 + 90.8770i −1.92890 + 0.626738i
\(146\) 112.190 + 36.4526i 0.768422 + 0.249675i
\(147\) −19.5564 174.220i −0.133037 1.18517i
\(148\) −64.4944 198.493i −0.435773 1.34117i
\(149\) 100.390 + 72.9376i 0.673758 + 0.489514i 0.871281 0.490784i \(-0.163290\pi\)
−0.197523 + 0.980298i \(0.563290\pi\)
\(150\) 605.911i 4.03941i
\(151\) −28.3843 + 87.3578i −0.187975 + 0.578528i −0.999987 0.00511276i \(-0.998373\pi\)
0.812012 + 0.583641i \(0.198373\pi\)
\(152\) −51.9766 + 71.5397i −0.341951 + 0.470656i
\(153\) 60.6576 + 83.4881i 0.396455 + 0.545674i
\(154\) 48.7050 + 125.554i 0.316266 + 0.815284i
\(155\) −400.414 −2.58332
\(156\) −254.952 + 185.233i −1.63430 + 1.18739i
\(157\) −116.974 + 38.0071i −0.745057 + 0.242084i −0.656853 0.754019i \(-0.728113\pi\)
−0.0882042 + 0.996102i \(0.528113\pi\)
\(158\) −36.8619 + 113.449i −0.233303 + 0.718033i
\(159\) −82.7398 + 113.882i −0.520376 + 0.716236i
\(160\) 214.827 295.684i 1.34267 1.84803i
\(161\) 22.2371 84.1779i 0.138118 0.522844i
\(162\) 96.8702 298.136i 0.597964 1.84035i
\(163\) 96.1409 0.589822 0.294911 0.955525i \(-0.404710\pi\)
0.294911 + 0.955525i \(0.404710\pi\)
\(164\) −24.1483 231.582i −0.147245 1.41208i
\(165\) 197.189 1.19508
\(166\) 114.378 + 37.1638i 0.689027 + 0.223878i
\(167\) 60.8933i 0.364631i −0.983240 0.182315i \(-0.941641\pi\)
0.983240 0.182315i \(-0.0583592\pi\)
\(168\) 82.6860 + 101.375i 0.492179 + 0.603420i
\(169\) 57.8925 + 42.0613i 0.342559 + 0.248884i
\(170\) 232.638 715.985i 1.36846 4.21168i
\(171\) 61.1968 19.8841i 0.357876 0.116281i
\(172\) 155.349 112.867i 0.903190 0.656206i
\(173\) 196.733i 1.13718i −0.822620 0.568591i \(-0.807489\pi\)
0.822620 0.568591i \(-0.192511\pi\)
\(174\) −215.884 297.139i −1.24071 1.70769i
\(175\) 137.808 + 355.248i 0.787477 + 2.02999i
\(176\) 32.3445 + 23.4997i 0.183776 + 0.133521i
\(177\) 91.7866 282.490i 0.518568 1.59599i
\(178\) 389.302i 2.18709i
\(179\) 194.367 + 141.216i 1.08585 + 0.788915i 0.978693 0.205328i \(-0.0658260\pi\)
0.107155 + 0.994242i \(0.465826\pi\)
\(180\) 182.965 59.4489i 1.01647 0.330271i
\(181\) −111.005 152.786i −0.613289 0.844120i 0.383554 0.923519i \(-0.374700\pi\)
−0.996843 + 0.0793983i \(0.974700\pi\)
\(182\) 182.962 283.927i 1.00529 1.56004i
\(183\) 41.2568 + 126.975i 0.225447 + 0.693854i
\(184\) 20.0764 + 61.7887i 0.109111 + 0.335808i
\(185\) 311.517 101.218i 1.68388 0.547125i
\(186\) −154.533 475.604i −0.830824 2.55701i
\(187\) 159.677 + 51.8822i 0.853888 + 0.277445i
\(188\) 149.471 + 205.730i 0.795060 + 1.09431i
\(189\) 7.27388 + 130.007i 0.0384861 + 0.687868i
\(190\) −379.762 275.913i −1.99875 1.45217i
\(191\) 120.561 0.631207 0.315603 0.948891i \(-0.397793\pi\)
0.315603 + 0.948891i \(0.397793\pi\)
\(192\) 346.119 + 112.461i 1.80270 + 0.585734i
\(193\) −87.4026 63.5017i −0.452863 0.329025i 0.337862 0.941196i \(-0.390296\pi\)
−0.790725 + 0.612171i \(0.790296\pi\)
\(194\) −34.5420 47.5430i −0.178051 0.245067i
\(195\) −290.706 400.123i −1.49080 2.05191i
\(196\) −241.965 137.429i −1.23451 0.701168i
\(197\) −27.7155 + 20.1365i −0.140688 + 0.102216i −0.655903 0.754845i \(-0.727712\pi\)
0.515215 + 0.857061i \(0.327712\pi\)
\(198\) 22.5965 + 69.5450i 0.114124 + 0.351237i
\(199\) −314.162 102.077i −1.57870 0.512951i −0.616980 0.786979i \(-0.711644\pi\)
−0.961722 + 0.274028i \(0.911644\pi\)
\(200\) −230.031 167.127i −1.15015 0.835636i
\(201\) −183.814 + 252.998i −0.914495 + 1.25869i
\(202\) 396.123i 1.96100i
\(203\) 194.155 + 125.113i 0.956429 + 0.616321i
\(204\) 551.656 2.70419
\(205\) 363.446 37.8985i 1.77291 0.184870i
\(206\) 249.278i 1.21009i
\(207\) 14.6089 44.9617i 0.0705745 0.217206i
\(208\) 100.276i 0.482096i
\(209\) 61.5334 84.6934i 0.294418 0.405232i
\(210\) −538.138 + 438.931i −2.56256 + 2.09015i
\(211\) −91.7490 + 282.374i −0.434830 + 1.33827i 0.458432 + 0.888730i \(0.348411\pi\)
−0.893261 + 0.449538i \(0.851589\pi\)
\(212\) 69.0441 + 212.496i 0.325680 + 1.00234i
\(213\) −170.478 234.643i −0.800365 1.10161i
\(214\) 315.716 1.47531
\(215\) 177.135 + 243.805i 0.823884 + 1.13398i
\(216\) −57.1111 78.6067i −0.264403 0.363920i
\(217\) 198.775 + 243.702i 0.916014 + 1.12305i
\(218\) −59.0308 + 181.678i −0.270783 + 0.833385i
\(219\) −135.660 −0.619453
\(220\) 183.971 253.214i 0.836231 1.15097i
\(221\) −130.128 400.494i −0.588816 1.81219i
\(222\) 240.450 + 330.951i 1.08311 + 1.49077i
\(223\) −66.0083 21.4474i −0.296001 0.0961767i 0.157252 0.987559i \(-0.449737\pi\)
−0.453253 + 0.891382i \(0.649737\pi\)
\(224\) −286.606 + 16.0356i −1.27949 + 0.0715873i
\(225\) 63.9358 + 196.774i 0.284159 + 0.874552i
\(226\) 25.8124 + 79.4424i 0.114214 + 0.351515i
\(227\) 82.1462 26.6909i 0.361877 0.117581i −0.122434 0.992477i \(-0.539070\pi\)
0.484312 + 0.874896i \(0.339070\pi\)
\(228\) 106.293 327.137i 0.466199 1.43481i
\(229\) −169.057 232.687i −0.738241 1.01610i −0.998718 0.0506214i \(-0.983880\pi\)
0.260477 0.965480i \(-0.416120\pi\)
\(230\) −328.000 + 106.574i −1.42609 + 0.463363i
\(231\) −97.8892 120.014i −0.423763 0.519541i
\(232\) −172.354 −0.742906
\(233\) 25.9988 80.0160i 0.111583 0.343416i −0.879636 0.475647i \(-0.842214\pi\)
0.991219 + 0.132231i \(0.0422140\pi\)
\(234\) 107.803 148.378i 0.460698 0.634096i
\(235\) −322.873 + 234.581i −1.37393 + 0.998218i
\(236\) −277.117 381.419i −1.17423 1.61618i
\(237\) 137.183i 0.578833i
\(238\) −551.253 + 213.843i −2.31619 + 0.898500i
\(239\) −26.8814 82.7325i −0.112475 0.346161i 0.878937 0.476937i \(-0.158253\pi\)
−0.991412 + 0.130776i \(0.958253\pi\)
\(240\) −63.7079 + 196.073i −0.265450 + 0.816970i
\(241\) 114.119 157.071i 0.473523 0.651748i −0.503721 0.863866i \(-0.668036\pi\)
0.977244 + 0.212118i \(0.0680362\pi\)
\(242\) −208.302 151.340i −0.860753 0.625374i
\(243\) 193.094i 0.794626i
\(244\) 201.543 + 65.4852i 0.825995 + 0.268382i
\(245\) 215.682 379.741i 0.880334 1.54996i
\(246\) 185.281 + 417.068i 0.753175 + 1.69540i
\(247\) −262.570 −1.06304
\(248\) −223.185 72.5173i −0.899941 0.292408i
\(249\) −138.307 −0.555450
\(250\) 479.726 660.287i 1.91891 2.64115i
\(251\) −130.380 + 179.452i −0.519441 + 0.714949i −0.985476 0.169818i \(-0.945682\pi\)
0.466035 + 0.884766i \(0.345682\pi\)
\(252\) −127.010 81.8451i −0.504008 0.324782i
\(253\) −23.7677 73.1496i −0.0939436 0.289129i
\(254\) −51.7662 + 37.6103i −0.203804 + 0.148072i
\(255\) 865.773i 3.39519i
\(256\) 54.4765 39.5795i 0.212799 0.154607i
\(257\) −238.542 328.325i −0.928181 1.27753i −0.960565 0.278056i \(-0.910310\pi\)
0.0323844 0.999475i \(-0.489690\pi\)
\(258\) −221.225 + 304.491i −0.857462 + 1.18020i
\(259\) −216.248 139.350i −0.834936 0.538031i
\(260\) −785.026 −3.01933
\(261\) 101.464 + 73.7180i 0.388752 + 0.282445i
\(262\) −481.049 + 156.302i −1.83607 + 0.596574i
\(263\) 180.930 131.453i 0.687946 0.499822i −0.188038 0.982162i \(-0.560213\pi\)
0.875984 + 0.482340i \(0.160213\pi\)
\(264\) 109.910 + 35.7120i 0.416327 + 0.135273i
\(265\) −333.493 + 108.358i −1.25846 + 0.408899i
\(266\) 20.5953 + 368.102i 0.0774258 + 1.38384i
\(267\) −138.349 425.794i −0.518161 1.59473i
\(268\) 153.387 + 472.078i 0.572341 + 1.76148i
\(269\) 109.068 + 35.4383i 0.405457 + 0.131741i 0.504643 0.863328i \(-0.331624\pi\)
−0.0991863 + 0.995069i \(0.531624\pi\)
\(270\) 417.277 303.169i 1.54547 1.12285i
\(271\) 437.394 142.118i 1.61400 0.524420i 0.643484 0.765460i \(-0.277488\pi\)
0.970515 + 0.241040i \(0.0774884\pi\)
\(272\) −103.177 + 142.011i −0.379328 + 0.522100i
\(273\) −99.2112 + 375.562i −0.363411 + 1.37568i
\(274\) −97.6657 + 300.584i −0.356444 + 1.09702i
\(275\) 272.326 + 197.856i 0.990276 + 0.719477i
\(276\) −148.544 204.454i −0.538204 0.740774i
\(277\) 84.6547 61.5053i 0.305613 0.222041i −0.424399 0.905475i \(-0.639515\pi\)
0.730012 + 0.683435i \(0.239515\pi\)
\(278\) 409.576i 1.47330i
\(279\) 100.372 + 138.150i 0.359755 + 0.495161i
\(280\) 18.2044 + 325.371i 0.0650159 + 1.16204i
\(281\) −40.8802 + 125.816i −0.145481 + 0.447745i −0.997073 0.0764612i \(-0.975638\pi\)
0.851591 + 0.524206i \(0.175638\pi\)
\(282\) −403.239 292.970i −1.42993 1.03890i
\(283\) 211.952 291.727i 0.748947 1.03084i −0.249107 0.968476i \(-0.580137\pi\)
0.998054 0.0623605i \(-0.0198629\pi\)
\(284\) −460.360 −1.62099
\(285\) 513.412 + 166.818i 1.80145 + 0.585325i
\(286\) 298.389i 1.04332i
\(287\) −203.489 202.389i −0.709022 0.705187i
\(288\) −155.867 −0.541204
\(289\) −138.487 + 426.219i −0.479194 + 1.47481i
\(290\) 914.926i 3.15492i
\(291\) 54.6755 + 39.7240i 0.187888 + 0.136509i
\(292\) −126.567 + 174.204i −0.433448 + 0.596589i
\(293\) 332.810 + 108.136i 1.13587 + 0.369066i 0.815804 0.578329i \(-0.196295\pi\)
0.320066 + 0.947395i \(0.396295\pi\)
\(294\) 534.289 + 109.628i 1.81731 + 0.372884i
\(295\) 598.603 434.910i 2.02916 1.47427i
\(296\) 191.967 0.648536
\(297\) 67.6120 + 93.0599i 0.227650 + 0.313333i
\(298\) −312.324 + 226.916i −1.04807 + 0.761464i
\(299\) −113.391 + 156.069i −0.379233 + 0.521970i
\(300\) 1051.89 + 341.779i 3.50629 + 1.13926i
\(301\) 60.4520 228.840i 0.200837 0.760264i
\(302\) −231.189 167.969i −0.765527 0.556188i
\(303\) −140.773 433.254i −0.464596 1.42988i
\(304\) 64.3338 + 88.5479i 0.211624 + 0.291276i
\(305\) −102.773 + 316.303i −0.336961 + 1.03706i
\(306\) −305.343 + 99.2118i −0.997852 + 0.324222i
\(307\) 8.36682 2.71854i 0.0272535 0.00885519i −0.295359 0.955386i \(-0.595439\pi\)
0.322612 + 0.946531i \(0.395439\pi\)
\(308\) −245.440 + 13.7323i −0.796883 + 0.0445855i
\(309\) −88.5874 272.644i −0.286691 0.882343i
\(310\) 384.951 1184.76i 1.24178 3.82180i
\(311\) 293.462 + 403.916i 0.943607 + 1.29876i 0.954309 + 0.298821i \(0.0965935\pi\)
−0.0107016 + 0.999943i \(0.503406\pi\)
\(312\) −89.5711 275.672i −0.287087 0.883563i
\(313\) −99.8701 + 137.459i −0.319074 + 0.439167i −0.938184 0.346137i \(-0.887493\pi\)
0.619110 + 0.785304i \(0.287493\pi\)
\(314\) 382.646i 1.21862i
\(315\) 128.448 199.331i 0.407772 0.632796i
\(316\) −176.160 127.988i −0.557468 0.405025i
\(317\) −120.829 + 87.7876i −0.381165 + 0.276932i −0.761825 0.647782i \(-0.775697\pi\)
0.380661 + 0.924715i \(0.375697\pi\)
\(318\) −257.412 354.297i −0.809472 1.11414i
\(319\) 204.044 0.639637
\(320\) 532.871 + 733.434i 1.66522 + 2.29198i
\(321\) −345.310 + 112.198i −1.07573 + 0.349526i
\(322\) 227.690 + 146.723i 0.707112 + 0.455662i
\(323\) 371.853 + 270.167i 1.15125 + 0.836431i
\(324\) 462.935 + 336.342i 1.42881 + 1.03809i
\(325\) 844.277i 2.59777i
\(326\) −92.4283 + 284.465i −0.283522 + 0.872592i
\(327\) 219.686i 0.671822i
\(328\) 209.444 + 44.6981i 0.638547 + 0.136275i
\(329\) 303.054 + 80.0570i 0.921137 + 0.243334i
\(330\) −189.574 + 583.449i −0.574467 + 1.76803i
\(331\) −516.152 −1.55937 −0.779686 0.626170i \(-0.784622\pi\)
−0.779686 + 0.626170i \(0.784622\pi\)
\(332\) −129.036 + 177.603i −0.388663 + 0.534948i
\(333\) −113.010 82.1065i −0.339369 0.246566i
\(334\) 180.173 + 58.5419i 0.539441 + 0.175275i
\(335\) −740.882 + 240.727i −2.21159 + 0.718589i
\(336\) 150.961 58.5610i 0.449288 0.174289i
\(337\) −327.486 −0.971768 −0.485884 0.874023i \(-0.661502\pi\)
−0.485884 + 0.874023i \(0.661502\pi\)
\(338\) −180.109 + 130.857i −0.532868 + 0.387151i
\(339\) −56.4639 77.7159i −0.166560 0.229250i
\(340\) 1111.76 + 807.739i 3.26987 + 2.37570i
\(341\) 264.222 + 85.8508i 0.774843 + 0.251762i
\(342\) 200.188i 0.585344i
\(343\) −338.190 + 57.2433i −0.985975 + 0.166890i
\(344\) 54.5781 + 167.974i 0.158657 + 0.488297i
\(345\) 320.871 233.127i 0.930061 0.675729i
\(346\) 582.099 + 189.135i 1.68237 + 0.546634i
\(347\) −45.0442 138.632i −0.129810 0.399516i 0.864936 0.501882i \(-0.167359\pi\)
−0.994747 + 0.102366i \(0.967359\pi\)
\(348\) 637.621 207.176i 1.83224 0.595332i
\(349\) −171.820 + 55.8277i −0.492321 + 0.159965i −0.544647 0.838665i \(-0.683336\pi\)
0.0523264 + 0.998630i \(0.483336\pi\)
\(350\) −1183.61 + 66.2227i −3.38174 + 0.189208i
\(351\) 89.1540 274.388i 0.254000 0.781732i
\(352\) −205.154 + 149.053i −0.582825 + 0.423447i
\(353\) 15.8582 5.15263i 0.0449240 0.0145967i −0.286469 0.958090i \(-0.592481\pi\)
0.331393 + 0.943493i \(0.392481\pi\)
\(354\) 747.599 + 543.163i 2.11186 + 1.53436i
\(355\) 722.492i 2.03519i
\(356\) −675.846 219.596i −1.89844 0.616842i
\(357\) 526.931 429.790i 1.47600 1.20389i
\(358\) −604.695 + 439.337i −1.68909 + 1.22720i
\(359\) −166.539 + 120.998i −0.463898 + 0.337041i −0.795058 0.606533i \(-0.792560\pi\)
0.331161 + 0.943574i \(0.392560\pi\)
\(360\) 176.948i 0.491524i
\(361\) −60.1944 + 43.7338i −0.166744 + 0.121146i
\(362\) 558.787 181.561i 1.54361 0.501549i
\(363\) 281.611 + 91.5008i 0.775787 + 0.252068i
\(364\) 389.706 + 477.786i 1.07062 + 1.31260i
\(365\) −273.397 198.635i −0.749034 0.544205i
\(366\) −415.362 −1.13487
\(367\) −174.347 56.6489i −0.475061 0.154357i 0.0616937 0.998095i \(-0.480350\pi\)
−0.536754 + 0.843739i \(0.680350\pi\)
\(368\) 80.4144 0.218517
\(369\) −104.181 115.895i −0.282332 0.314079i
\(370\) 1019.04i 2.75415i
\(371\) 231.503 + 149.180i 0.623998 + 0.402103i
\(372\) 912.839 2.45387
\(373\) 328.791 + 238.881i 0.881477 + 0.640431i 0.933642 0.358208i \(-0.116612\pi\)
−0.0521648 + 0.998638i \(0.516612\pi\)
\(374\) −307.022 + 422.579i −0.820914 + 1.12989i
\(375\) −290.044 + 892.663i −0.773450 + 2.38043i
\(376\) −222.449 + 72.2782i −0.591620 + 0.192229i
\(377\) −300.813 414.034i −0.797912 1.09823i
\(378\) −391.662 103.464i −1.03614 0.273715i
\(379\) −18.8733 + 13.7122i −0.0497976 + 0.0361801i −0.612406 0.790544i \(-0.709798\pi\)
0.562608 + 0.826724i \(0.309798\pi\)
\(380\) 693.211 503.648i 1.82424 1.32539i
\(381\) 43.2527 59.5323i 0.113524 0.156253i
\(382\) −115.905 + 356.719i −0.303416 + 0.933818i
\(383\) 114.604i 0.299227i −0.988745 0.149614i \(-0.952197\pi\)
0.988745 0.149614i \(-0.0478030\pi\)
\(384\) −320.550 + 441.199i −0.834765 + 1.14895i
\(385\) −21.5516 385.195i −0.0559783 1.00051i
\(386\) 271.919 197.560i 0.704452 0.511815i
\(387\) 39.7147 122.229i 0.102622 0.315838i
\(388\) 102.021 33.1486i 0.262941 0.0854346i
\(389\) 181.774 + 559.442i 0.467285 + 1.43816i 0.856086 + 0.516834i \(0.172889\pi\)
−0.388801 + 0.921322i \(0.627111\pi\)
\(390\) 1463.38 475.480i 3.75225 1.21918i
\(391\) 321.169 104.354i 0.821404 0.266890i
\(392\) 188.991 172.601i 0.482121 0.440310i
\(393\) 470.594 341.907i 1.19744 0.869992i
\(394\) −32.9353 101.365i −0.0835922 0.257270i
\(395\) 200.865 276.467i 0.508519 0.699916i
\(396\) −133.479 −0.337069
\(397\) −397.439 129.136i −1.00111 0.325279i −0.237799 0.971314i \(-0.576426\pi\)
−0.763308 + 0.646035i \(0.776426\pi\)
\(398\) 604.060 831.417i 1.51774 2.08899i
\(399\) −153.341 395.288i −0.384312 0.990696i
\(400\) −284.720 + 206.861i −0.711799 + 0.517152i
\(401\) 679.711 1.69504 0.847520 0.530763i \(-0.178095\pi\)
0.847520 + 0.530763i \(0.178095\pi\)
\(402\) −571.863 787.102i −1.42254 1.95796i
\(403\) −215.327 662.707i −0.534309 1.64444i
\(404\) −687.687 223.443i −1.70220 0.553077i
\(405\) −527.858 + 726.534i −1.30335 + 1.79391i
\(406\) −556.847 + 454.191i −1.37154 + 1.11870i
\(407\) −227.263 −0.558385
\(408\) −156.796 + 482.570i −0.384305 + 1.18277i
\(409\) 167.551i 0.409660i 0.978798 + 0.204830i \(0.0656641\pi\)
−0.978798 + 0.204830i \(0.934336\pi\)
\(410\) −237.276 + 1111.81i −0.578722 + 2.71174i
\(411\) 363.468i 0.884350i
\(412\) −432.757 140.611i −1.05038 0.341290i
\(413\) −561.858 148.425i −1.36043 0.359381i
\(414\) 118.989 + 86.4508i 0.287414 + 0.208818i
\(415\) −278.731 202.510i −0.671642 0.487976i
\(416\) 604.899 + 196.544i 1.45408 + 0.472461i
\(417\) −145.554 447.968i −0.349050 1.07426i
\(418\) 191.437 + 263.490i 0.457982 + 0.630359i
\(419\) 568.612i 1.35707i −0.734568 0.678535i \(-0.762615\pi\)
0.734568 0.678535i \(-0.237385\pi\)
\(420\) −458.454 1181.82i −1.09156 2.81386i
\(421\) 457.391 332.314i 1.08644 0.789345i 0.107646 0.994189i \(-0.465669\pi\)
0.978795 + 0.204844i \(0.0656688\pi\)
\(422\) −747.293 542.940i −1.77084 1.28659i
\(423\) 161.869 + 52.5945i 0.382670 + 0.124337i
\(424\) −205.509 −0.484690
\(425\) −868.704 + 1195.67i −2.04401 + 2.81334i
\(426\) 858.163 278.834i 2.01447 0.654540i
\(427\) 243.529 94.4700i 0.570325 0.221241i
\(428\) −178.087 + 548.097i −0.416092 + 1.28060i
\(429\) 106.040 + 326.358i 0.247180 + 0.760742i
\(430\) −891.675 + 289.723i −2.07366 + 0.673774i
\(431\) 12.5725 + 38.6942i 0.0291706 + 0.0897778i 0.964582 0.263784i \(-0.0849705\pi\)
−0.935411 + 0.353561i \(0.884971\pi\)
\(432\) −114.377 + 37.1634i −0.264762 + 0.0860265i
\(433\) 116.612 + 37.8895i 0.269312 + 0.0875047i 0.440560 0.897723i \(-0.354780\pi\)
−0.171248 + 0.985228i \(0.554780\pi\)
\(434\) −912.172 + 353.851i −2.10178 + 0.815326i
\(435\) 325.143 + 1000.69i 0.747455 + 2.30043i
\(436\) −282.103 204.960i −0.647026 0.470092i
\(437\) 210.563i 0.481838i
\(438\) 130.421 401.396i 0.297766 0.916429i
\(439\) −305.941 + 421.092i −0.696905 + 0.959207i 0.303076 + 0.952967i \(0.401987\pi\)
−0.999981 + 0.00624092i \(0.998013\pi\)
\(440\) 169.213 + 232.902i 0.384576 + 0.529324i
\(441\) −185.082 + 20.7757i −0.419688 + 0.0471104i
\(442\) 1310.10 2.96402
\(443\) 94.7567 68.8448i 0.213898 0.155406i −0.475678 0.879620i \(-0.657797\pi\)
0.689576 + 0.724214i \(0.257797\pi\)
\(444\) −710.177 + 230.751i −1.59950 + 0.519708i
\(445\) 344.635 1060.68i 0.774461 2.38355i
\(446\) 126.919 174.688i 0.284571 0.391678i
\(447\) 260.959 359.179i 0.583800 0.803532i
\(448\) 181.856 688.413i 0.405929 1.53664i
\(449\) 103.440 318.354i 0.230378 0.709030i −0.767323 0.641260i \(-0.778412\pi\)
0.997701 0.0677692i \(-0.0215882\pi\)
\(450\) −643.689 −1.43042
\(451\) −247.953 52.9166i −0.549785 0.117332i
\(452\) −152.476 −0.337335
\(453\) 312.552 + 101.554i 0.689960 + 0.224182i
\(454\) 268.717i 0.591888i
\(455\) −749.841 + 611.607i −1.64800 + 1.34419i
\(456\) 255.957 + 185.964i 0.561310 + 0.407815i
\(457\) −96.6613 + 297.493i −0.211513 + 0.650969i 0.787870 + 0.615841i \(0.211184\pi\)
−0.999383 + 0.0351276i \(0.988816\pi\)
\(458\) 851.012 276.510i 1.85810 0.603735i
\(459\) −408.587 + 296.856i −0.890167 + 0.646744i
\(460\) 629.537i 1.36856i
\(461\) −48.7184 67.0551i −0.105680 0.145456i 0.752901 0.658133i \(-0.228654\pi\)
−0.858581 + 0.512678i \(0.828654\pi\)
\(462\) 449.211 174.258i 0.972317 0.377183i
\(463\) 36.8838 + 26.7977i 0.0796627 + 0.0578784i 0.626904 0.779097i \(-0.284322\pi\)
−0.547241 + 0.836975i \(0.684322\pi\)
\(464\) −65.9228 + 202.889i −0.142075 + 0.437262i
\(465\) 1432.62i 3.08089i
\(466\) 211.759 + 153.852i 0.454419 + 0.330155i
\(467\) −655.988 + 213.143i −1.40469 + 0.456410i −0.910703 0.413062i \(-0.864459\pi\)
−0.493982 + 0.869472i \(0.664459\pi\)
\(468\) 196.782 + 270.848i 0.420475 + 0.578734i
\(469\) 514.304 + 331.417i 1.09660 + 0.706645i
\(470\) −383.682 1180.85i −0.816345 2.51245i
\(471\) 135.983 + 418.514i 0.288712 + 0.888564i
\(472\) 412.418 134.003i 0.873766 0.283904i
\(473\) −64.6131 198.859i −0.136603 0.420420i
\(474\) 405.903 + 131.886i 0.856335 + 0.278240i
\(475\) 541.661 + 745.532i 1.14034 + 1.56954i
\(476\) −60.2929 1077.62i −0.126666 2.26391i
\(477\) 120.982 + 87.8986i 0.253631 + 0.184274i
\(478\) 270.635 0.566182
\(479\) 362.873 + 117.905i 0.757563 + 0.246147i 0.662232 0.749298i \(-0.269609\pi\)
0.0953308 + 0.995446i \(0.469609\pi\)
\(480\) −1057.91 768.616i −2.20398 1.60128i
\(481\) 335.043 + 461.147i 0.696555 + 0.958726i
\(482\) 355.036 + 488.665i 0.736589 + 1.01383i
\(483\) −301.175 79.5606i −0.623550 0.164722i
\(484\) 380.232 276.255i 0.785603 0.570774i
\(485\) 52.0237 + 160.112i 0.107265 + 0.330129i
\(486\) −571.333 185.637i −1.17558 0.381970i
\(487\) −660.322 479.752i −1.35590 0.985118i −0.998694 0.0510915i \(-0.983730\pi\)
−0.357204 0.934026i \(-0.616270\pi\)
\(488\) −114.569 + 157.690i −0.234772 + 0.323135i
\(489\) 343.977i 0.703428i
\(490\) 916.239 + 1003.24i 1.86987 + 2.04744i
\(491\) −393.114 −0.800640 −0.400320 0.916376i \(-0.631101\pi\)
−0.400320 + 0.916376i \(0.631101\pi\)
\(492\) −828.561 + 86.3985i −1.68407 + 0.175607i
\(493\) 895.872i 1.81718i
\(494\) 252.431 776.902i 0.510993 1.57268i
\(495\) 209.483i 0.423199i
\(496\) −170.730 + 234.989i −0.344213 + 0.473769i
\(497\) −439.727 + 358.662i −0.884762 + 0.721655i
\(498\) 132.966 409.227i 0.267000 0.821742i
\(499\) −257.976 793.967i −0.516985 1.59112i −0.779641 0.626227i \(-0.784598\pi\)
0.262656 0.964890i \(-0.415402\pi\)
\(500\) 875.685 + 1205.28i 1.75137 + 2.41056i
\(501\) −217.866 −0.434863
\(502\) −405.624 558.294i −0.808017 1.11214i
\(503\) −239.447 329.571i −0.476039 0.655211i 0.501699 0.865042i \(-0.332709\pi\)
−0.977738 + 0.209831i \(0.932709\pi\)
\(504\) 107.695 87.8414i 0.213681 0.174289i
\(505\) 350.673 1079.26i 0.694402 2.13715i
\(506\) 239.287 0.472900
\(507\) 150.489 207.130i 0.296822 0.408540i
\(508\) −36.0932 111.083i −0.0710496 0.218668i
\(509\) 113.768 + 156.588i 0.223512 + 0.307638i 0.906016 0.423244i \(-0.139109\pi\)
−0.682504 + 0.730882i \(0.739109\pi\)
\(510\) −2561.68 832.340i −5.02290 1.63204i
\(511\) 14.8269 + 265.003i 0.0290155 + 0.518598i
\(512\) −123.671 380.621i −0.241545 0.743400i
\(513\) 97.3116 + 299.494i 0.189691 + 0.583810i
\(514\) 1200.79 390.161i 2.33617 0.759068i
\(515\) 220.677 679.172i 0.428498 1.31878i
\(516\) −403.821 555.812i −0.782599 1.07716i
\(517\) 263.350 85.5677i 0.509382 0.165508i
\(518\) 620.211 505.874i 1.19732 0.976591i
\(519\) −703.877 −1.35622
\(520\) 223.127 686.714i 0.429090 1.32060i
\(521\) 395.315 544.104i 0.758761 1.04435i −0.238555 0.971129i \(-0.576674\pi\)
0.997316 0.0732163i \(-0.0233263\pi\)
\(522\) −315.665 + 229.344i −0.604723 + 0.439357i
\(523\) −227.226 312.750i −0.434467 0.597992i 0.534505 0.845166i \(-0.320498\pi\)
−0.968971 + 0.247174i \(0.920498\pi\)
\(524\) 923.289i 1.76200i
\(525\) 1271.02 493.056i 2.42099 0.939155i
\(526\) 215.005 + 661.718i 0.408755 + 1.25802i
\(527\) −376.935 + 1160.09i −0.715246 + 2.20130i
\(528\) 84.0780 115.723i 0.159239 0.219173i
\(529\) 302.813 + 220.007i 0.572426 + 0.415892i
\(530\) 1090.92i 2.05835i
\(531\) −300.103 97.5094i −0.565166 0.183634i
\(532\) −650.659 171.883i −1.22304 0.323088i
\(533\) 258.171 + 581.143i 0.484373 + 1.09033i
\(534\) 1392.86 2.60835
\(535\) −860.187 279.492i −1.60783 0.522415i
\(536\) −456.555 −0.851781
\(537\) 505.247 695.413i 0.940869 1.29500i
\(538\) −209.712 + 288.644i −0.389800 + 0.536514i
\(539\) −223.741 + 204.337i −0.415103 + 0.379104i
\(540\) 290.940 + 895.421i 0.538777 + 1.65819i
\(541\) −339.775 + 246.861i −0.628050 + 0.456305i −0.855724 0.517432i \(-0.826888\pi\)
0.227674 + 0.973737i \(0.426888\pi\)
\(542\) 1430.81i 2.63986i
\(543\) −546.642 + 397.159i −1.00671 + 0.731416i
\(544\) −654.430 900.746i −1.20300 1.65578i
\(545\) 321.666 442.735i 0.590213 0.812358i
\(546\) −1015.84 654.608i −1.86052 1.19892i
\(547\) 591.461 1.08128 0.540641 0.841253i \(-0.318182\pi\)
0.540641 + 0.841253i \(0.318182\pi\)
\(548\) −466.736 339.104i −0.851709 0.618803i
\(549\) 134.892 43.8291i 0.245705 0.0798344i
\(550\) −847.234 + 615.551i −1.54042 + 1.11918i
\(551\) 531.261 + 172.617i 0.964177 + 0.313280i
\(552\) 221.070 71.8299i 0.400489 0.130127i
\(553\) −267.979 + 14.9934i −0.484591 + 0.0271128i
\(554\) 100.598 + 309.610i 0.181585 + 0.558862i
\(555\) −362.142 1114.56i −0.652507 2.00821i
\(556\) −711.043 231.032i −1.27885 0.415525i
\(557\) −383.887 + 278.910i −0.689204 + 0.500736i −0.876398 0.481587i \(-0.840061\pi\)
0.187194 + 0.982323i \(0.440061\pi\)
\(558\) −505.258 + 164.168i −0.905480 + 0.294208i
\(559\) −308.255 + 424.277i −0.551441 + 0.758993i
\(560\) 389.978 + 103.020i 0.696390 + 0.183963i
\(561\) 185.626 571.298i 0.330884 1.01836i
\(562\) −332.968 241.916i −0.592470 0.430455i
\(563\) −405.419 558.011i −0.720104 0.991138i −0.999520 0.0309680i \(-0.990141\pi\)
0.279416 0.960170i \(-0.409859\pi\)
\(564\) 736.066 534.784i 1.30508 0.948198i
\(565\) 239.296i 0.423533i
\(566\) 659.404 + 907.592i 1.16502 + 1.60352i
\(567\) 704.228 39.4014i 1.24202 0.0694911i
\(568\) 130.848 402.707i 0.230365 0.708992i
\(569\) 837.919 + 608.783i 1.47262 + 1.06992i 0.979845 + 0.199759i \(0.0640160\pi\)
0.492771 + 0.870159i \(0.335984\pi\)
\(570\) −987.172 + 1358.73i −1.73188 + 2.38373i
\(571\) 615.173 1.07736 0.538680 0.842510i \(-0.318923\pi\)
0.538680 + 0.842510i \(0.318923\pi\)
\(572\) 518.016 + 168.314i 0.905622 + 0.294255i
\(573\) 431.346i 0.752785i
\(574\) 794.465 407.518i 1.38409 0.709961i
\(575\) 677.052 1.17748
\(576\) 119.473 367.700i 0.207418 0.638367i
\(577\) 675.899i 1.17140i 0.810527 + 0.585701i \(0.199181\pi\)
−0.810527 + 0.585701i \(0.800819\pi\)
\(578\) −1127.97 819.520i −1.95151 1.41786i
\(579\) −227.199 + 312.712i −0.392399 + 0.540090i
\(580\) 1588.35 + 516.087i 2.73854 + 0.889805i
\(581\) 15.1162 + 270.174i 0.0260175 + 0.465015i
\(582\) −170.101 + 123.586i −0.292270 + 0.212346i
\(583\) 243.295 0.417315
\(584\) −116.414 160.230i −0.199339 0.274367i
\(585\) −425.070 + 308.832i −0.726616 + 0.527917i
\(586\) −639.916 + 880.768i −1.09201 + 1.50302i
\(587\) 381.166 + 123.848i 0.649345 + 0.210985i 0.615125 0.788429i \(-0.289105\pi\)
0.0342198 + 0.999414i \(0.489105\pi\)
\(588\) −491.698 + 865.710i −0.836221 + 1.47230i
\(589\) 615.315 + 447.052i 1.04468 + 0.759002i
\(590\) 711.341 + 2189.28i 1.20566 + 3.71065i
\(591\) 72.0451 + 99.1616i 0.121904 + 0.167786i
\(592\) 73.4242 225.977i 0.124027 0.381717i
\(593\) −589.395 + 191.506i −0.993921 + 0.322945i −0.760434 0.649415i \(-0.775014\pi\)
−0.233487 + 0.972360i \(0.575014\pi\)
\(594\) −340.350 + 110.586i −0.572979 + 0.186172i
\(595\) 1691.23 94.6241i 2.84240 0.159032i
\(596\) −217.763 670.205i −0.365374 1.12451i
\(597\) −365.216 + 1124.02i −0.611752 + 1.88278i
\(598\) −352.770 485.547i −0.589917 0.811951i
\(599\) 169.599 + 521.972i 0.283137 + 0.871406i 0.986951 + 0.161022i \(0.0514789\pi\)
−0.703814 + 0.710384i \(0.748521\pi\)
\(600\) −597.954 + 823.013i −0.996590 + 1.37169i
\(601\) 454.153i 0.755663i −0.925874 0.377831i \(-0.876670\pi\)
0.925874 0.377831i \(-0.123330\pi\)
\(602\) 618.981 + 398.870i 1.02821 + 0.662575i
\(603\) 268.772 + 195.274i 0.445725 + 0.323838i
\(604\) 422.009 306.608i 0.698690 0.507628i
\(605\) 433.556 + 596.739i 0.716622 + 0.986345i
\(606\) 1417.26 2.33872
\(607\) 219.809 + 302.542i 0.362124 + 0.498421i 0.950739 0.309992i \(-0.100327\pi\)
−0.588615 + 0.808414i \(0.700327\pi\)
\(608\) −660.248 + 214.528i −1.08593 + 0.352841i
\(609\) 447.634 694.655i 0.735032 1.14065i
\(610\) −837.083 608.177i −1.37227 0.997011i
\(611\) −561.874 408.225i −0.919597 0.668126i
\(612\) 586.051i 0.957600i
\(613\) 185.826 571.913i 0.303142 0.932974i −0.677222 0.735778i \(-0.736817\pi\)
0.980364 0.197196i \(-0.0631835\pi\)
\(614\) 27.3696i 0.0445759i
\(615\) −135.594 1300.35i −0.220479 2.11439i
\(616\) 57.7485 218.606i 0.0937476 0.354879i
\(617\) 204.585 629.648i 0.331580 1.02050i −0.636801 0.771028i \(-0.719743\pi\)
0.968382 0.249472i \(-0.0802571\pi\)
\(618\) 891.875 1.44316
\(619\) 532.229 732.550i 0.859820 1.18344i −0.121792 0.992556i \(-0.538864\pi\)
0.981612 0.190885i \(-0.0611359\pi\)
\(620\) 1839.65 + 1336.59i 2.96718 + 2.15578i
\(621\) 220.040 + 71.4954i 0.354332 + 0.115129i
\(622\) −1477.25 + 479.987i −2.37500 + 0.771684i
\(623\) −816.640 + 316.792i −1.31082 + 0.508495i
\(624\) −358.771 −0.574953
\(625\) −790.611 + 574.413i −1.26498 + 0.919061i
\(626\) −310.706 427.650i −0.496336 0.683147i
\(627\) −303.019 220.156i −0.483284 0.351127i
\(628\) 664.290 + 215.841i 1.05779 + 0.343696i
\(629\) 997.815i 1.58635i
\(630\) 466.298 + 571.690i 0.740156 + 0.907445i
\(631\) −85.8696 264.279i −0.136085 0.418826i 0.859672 0.510846i \(-0.170668\pi\)
−0.995757 + 0.0920196i \(0.970668\pi\)
\(632\) 162.029 117.721i 0.256375 0.186267i
\(633\) 1010.29 + 328.263i 1.59603 + 0.518583i
\(634\) −143.586 441.911i −0.226476 0.697021i
\(635\) 174.335 56.6449i 0.274544 0.0892046i
\(636\) 760.276 247.028i 1.19540 0.388410i
\(637\) 744.478 + 152.756i 1.16873 + 0.239805i
\(638\) −196.165 + 603.733i −0.307468 + 0.946290i
\(639\) −249.272 + 181.107i −0.390098 + 0.283422i
\(640\) −1292.01 + 419.800i −2.01877 + 0.655938i
\(641\) −316.615 230.034i −0.493940 0.358868i 0.312758 0.949833i \(-0.398747\pi\)
−0.806697 + 0.590965i \(0.798747\pi\)
\(642\) 1129.58i 1.75947i
\(643\) −780.471 253.590i −1.21380 0.394386i −0.368977 0.929438i \(-0.620292\pi\)
−0.844819 + 0.535052i \(0.820292\pi\)
\(644\) −383.152 + 312.517i −0.594956 + 0.485275i
\(645\) 872.296 633.760i 1.35240 0.982574i
\(646\) −1156.87 + 840.517i −1.79083 + 1.30111i
\(647\) 598.818i 0.925530i 0.886481 + 0.462765i \(0.153143\pi\)
−0.886481 + 0.462765i \(0.846857\pi\)
\(648\) −425.800 + 309.362i −0.657099 + 0.477410i
\(649\) −488.247 + 158.641i −0.752307 + 0.244439i
\(650\) 2498.07 + 811.674i 3.84319 + 1.24873i
\(651\) 871.925 711.185i 1.33936 1.09245i
\(652\) −441.707 320.919i −0.677465 0.492207i
\(653\) 1153.82 1.76695 0.883476 0.468477i \(-0.155197\pi\)
0.883476 + 0.468477i \(0.155197\pi\)
\(654\) 650.014 + 211.202i 0.993906 + 0.322940i
\(655\) 1449.02 2.21224
\(656\) 132.726 229.453i 0.202326 0.349777i
\(657\) 144.119i 0.219359i
\(658\) −528.227 + 819.721i −0.802776 + 1.24578i
\(659\) −992.690 −1.50636 −0.753179 0.657816i \(-0.771481\pi\)
−0.753179 + 0.657816i \(0.771481\pi\)
\(660\) −905.959 658.218i −1.37267 0.997300i
\(661\) −518.404 + 713.522i −0.784272 + 1.07946i 0.210526 + 0.977588i \(0.432482\pi\)
−0.994798 + 0.101869i \(0.967518\pi\)
\(662\) 496.220 1527.21i 0.749578 2.30696i
\(663\) −1432.90 + 465.578i −2.16124 + 0.702229i
\(664\) −118.685 163.356i −0.178743 0.246018i
\(665\) 269.754 1021.15i 0.405646 1.53556i
\(666\) 351.586 255.442i 0.527906 0.383546i
\(667\) 332.027 241.231i 0.497791 0.361666i
\(668\) −203.262 + 279.767i −0.304285 + 0.418813i
\(669\) −76.7353 + 236.167i −0.114701 + 0.353015i
\(670\) 2423.58i 3.61728i
\(671\) 135.634 186.684i 0.202137 0.278218i
\(672\) 57.3726 + 1025.43i 0.0853759 + 1.52594i
\(673\) −811.620 + 589.676i −1.20597 + 0.876191i −0.994859 0.101271i \(-0.967709\pi\)
−0.211114 + 0.977461i \(0.567709\pi\)
\(674\) 314.839 968.976i 0.467121 1.43765i
\(675\) −963.004 + 312.899i −1.42667 + 0.463554i
\(676\) −125.579 386.491i −0.185767 0.571732i
\(677\) −1242.21 + 403.620i −1.83488 + 0.596189i −0.836007 + 0.548718i \(0.815116\pi\)
−0.998873 + 0.0474702i \(0.984884\pi\)
\(678\) 284.232 92.3525i 0.419221 0.136213i
\(679\) 71.6226 111.147i 0.105482 0.163692i
\(680\) −1022.58 + 742.945i −1.50379 + 1.09257i
\(681\) −95.4957 293.906i −0.140229 0.431579i
\(682\) −508.037 + 699.252i −0.744922 + 1.02530i
\(683\) 206.661 0.302579 0.151289 0.988490i \(-0.451657\pi\)
0.151289 + 0.988490i \(0.451657\pi\)
\(684\) −347.534 112.921i −0.508091 0.165089i
\(685\) 532.192 732.500i 0.776923 1.06934i
\(686\) 155.756 1055.68i 0.227050 1.53889i
\(687\) −832.517 + 604.859i −1.21181 + 0.880435i
\(688\) 218.609 0.317745
\(689\) −358.678 493.678i −0.520578 0.716514i
\(690\) 381.303 + 1173.53i 0.552612 + 1.70077i
\(691\) −244.983 79.5998i −0.354534 0.115195i 0.126335 0.991988i \(-0.459679\pi\)
−0.480869 + 0.876793i \(0.659679\pi\)
\(692\) −656.695 + 903.863i −0.948981 + 1.30616i
\(693\) −127.497 + 103.993i −0.183978 + 0.150061i
\(694\) 453.494 0.653449
\(695\) 362.583 1115.92i 0.521702 1.60563i
\(696\) 616.655i 0.885998i
\(697\) 232.334 1088.66i 0.333335 1.56192i
\(698\) 562.058i 0.805241i
\(699\) −286.284 93.0193i −0.409562 0.133075i
\(700\) 552.678 2092.15i 0.789540 2.98878i
\(701\) −533.129 387.341i −0.760526 0.552555i 0.138545 0.990356i \(-0.455757\pi\)
−0.899072 + 0.437801i \(0.855757\pi\)
\(702\) 726.157 + 527.584i 1.03441 + 0.751544i
\(703\) −591.715 192.260i −0.841699 0.273485i
\(704\) −194.374 598.222i −0.276100 0.849747i
\(705\) 839.293 + 1155.19i 1.19049 + 1.63856i
\(706\) 51.8753i 0.0734778i
\(707\) −830.947 + 322.342i −1.17531 + 0.455930i
\(708\) −1364.66 + 991.481i −1.92748 + 1.40040i
\(709\) 582.270 + 423.044i 0.821256 + 0.596677i 0.917072 0.398722i \(-0.130546\pi\)
−0.0958162 + 0.995399i \(0.530546\pi\)
\(710\) 2137.73 + 694.592i 3.01089 + 0.978299i
\(711\) −145.737 −0.204974
\(712\) 384.190 528.792i 0.539593 0.742686i
\(713\) 531.446 172.677i 0.745366 0.242184i
\(714\) 765.096 + 1972.29i 1.07156 + 2.76232i
\(715\) −264.153 + 812.978i −0.369444 + 1.13703i
\(716\) −421.615 1297.60i −0.588847 1.81229i
\(717\) −296.003 + 96.1773i −0.412836 + 0.134139i
\(718\) −197.905 609.088i −0.275633 0.848311i
\(719\) 315.147 102.397i 0.438313 0.142416i −0.0815443 0.996670i \(-0.525985\pi\)
0.519857 + 0.854253i \(0.325985\pi\)
\(720\) 208.298 + 67.6800i 0.289302 + 0.0940001i
\(721\) −522.910 + 202.848i −0.725257 + 0.281343i
\(722\) −71.5312 220.150i −0.0990736 0.304917i
\(723\) −561.975 408.299i −0.777283 0.564729i
\(724\) 1072.49i 1.48134i
\(725\) −555.039 + 1708.23i −0.765571 + 2.35619i
\(726\) −541.471 + 745.271i −0.745828 + 1.02654i
\(727\) −234.150 322.279i −0.322077 0.443300i 0.617023 0.786945i \(-0.288338\pi\)
−0.939100 + 0.343645i \(0.888338\pi\)
\(728\) −528.717 + 205.101i −0.726260 + 0.281732i
\(729\) −215.993 −0.296286
\(730\) 850.567 617.973i 1.16516 0.846538i
\(731\) 873.105 283.689i 1.19440 0.388084i
\(732\) 234.295 721.087i 0.320076 0.985092i
\(733\) 314.598 433.007i 0.429193 0.590733i −0.538575 0.842578i \(-0.681037\pi\)
0.967768 + 0.251844i \(0.0810371\pi\)
\(734\) 335.229 461.403i 0.456716 0.628615i
\(735\) −1358.65 771.674i −1.84851 1.04990i
\(736\) −157.615 + 485.088i −0.214150 + 0.659087i
\(737\) 540.500 0.733378
\(738\) 443.072 196.833i 0.600369 0.266712i
\(739\) 161.618 0.218698 0.109349 0.994003i \(-0.465123\pi\)
0.109349 + 0.994003i \(0.465123\pi\)
\(740\) −1769.09 574.813i −2.39067 0.776775i
\(741\) 939.434i 1.26779i
\(742\) −663.963 + 541.560i −0.894829 + 0.729866i
\(743\) 1076.04 + 781.786i 1.44823 + 1.05220i 0.986240 + 0.165318i \(0.0528650\pi\)
0.461992 + 0.886884i \(0.347135\pi\)
\(744\) −259.455 + 798.520i −0.348730 + 1.07328i
\(745\) 1051.83 341.759i 1.41185 0.458737i
\(746\) −1022.90 + 743.182i −1.37118 + 0.996223i
\(747\) 146.930i 0.196694i
\(748\) −560.433 771.370i −0.749242 1.03124i
\(749\) 256.912 + 662.278i 0.343006 + 0.884216i
\(750\) −2362.40 1716.38i −3.14986 2.28851i
\(751\) 313.058 963.494i 0.416855 1.28295i −0.493726 0.869617i \(-0.664365\pi\)
0.910581 0.413330i \(-0.135635\pi\)
\(752\) 289.505i 0.384980i
\(753\) 642.050 + 466.477i 0.852656 + 0.619491i
\(754\) 1514.25 492.011i 2.00829 0.652534i
\(755\) 481.192 + 662.304i 0.637341 + 0.877224i
\(756\) 400.546 621.581i 0.529822 0.822198i
\(757\) 391.505 + 1204.93i 0.517180 + 1.59172i 0.779280 + 0.626676i \(0.215585\pi\)
−0.262100 + 0.965041i \(0.584415\pi\)
\(758\) −22.4278 69.0257i −0.0295881 0.0910629i
\(759\) −261.717 + 85.0370i −0.344818 + 0.112038i
\(760\) 243.543 + 749.549i 0.320452 + 0.986249i
\(761\) −685.202 222.636i −0.900397 0.292557i −0.177996 0.984031i \(-0.556961\pi\)
−0.722401 + 0.691475i \(0.756961\pi\)
\(762\) 134.564 + 185.211i 0.176593 + 0.243059i
\(763\) −429.142 + 24.0104i −0.562440 + 0.0314685i
\(764\) −553.900 402.432i −0.725000 0.526744i
\(765\) 919.753 1.20229
\(766\) 339.095 + 110.178i 0.442682 + 0.143836i
\(767\) 1041.71 + 756.843i 1.35816 + 0.986758i
\(768\) −141.609 194.908i −0.184387 0.253786i
\(769\) 160.957 + 221.538i 0.209307 + 0.288086i 0.900744 0.434350i \(-0.143022\pi\)
−0.691437 + 0.722437i \(0.743022\pi\)
\(770\) 1160.45 + 306.553i 1.50708 + 0.398121i
\(771\) −1174.69 + 853.466i −1.52360 + 1.10696i
\(772\) 189.591 + 583.502i 0.245584 + 0.755831i
\(773\) −1260.35 409.514i −1.63047 0.529772i −0.656090 0.754682i \(-0.727791\pi\)
−0.974379 + 0.224911i \(0.927791\pi\)
\(774\) 323.475 + 235.019i 0.417927 + 0.303642i
\(775\) −1437.47 + 1978.50i −1.85479 + 2.55291i
\(776\) 98.6663i 0.127147i
\(777\) −498.571 + 773.701i −0.641662 + 0.995754i
\(778\) −1830.05 −2.35225
\(779\) −600.819 347.540i −0.771269 0.446136i
\(780\) 2808.69i 3.60089i
\(781\) −154.906 + 476.752i −0.198343 + 0.610437i
\(782\) 1050.61i 1.34349i
\(783\) −360.772 + 496.561i −0.460757 + 0.634177i
\(784\) −130.894 288.492i −0.166957 0.367974i
\(785\) −338.743 + 1042.54i −0.431519 + 1.32808i
\(786\) 559.224 + 1721.11i 0.711481 + 2.18971i
\(787\) 694.822 + 956.340i 0.882874 + 1.21517i 0.975617 + 0.219482i \(0.0704367\pi\)
−0.0927425 + 0.995690i \(0.529563\pi\)
\(788\) 194.551 0.246892
\(789\) −470.318 647.337i −0.596094 0.820452i
\(790\) 624.911 + 860.117i 0.791027 + 1.08876i
\(791\) −145.642 + 118.792i −0.184123 + 0.150180i
\(792\) 37.9387 116.763i 0.0479023 0.147428i
\(793\) −578.766 −0.729844
\(794\) 764.184 1051.81i 0.962448 1.32470i
\(795\) 387.688 + 1193.18i 0.487658 + 1.50086i
\(796\) 1102.64 + 1517.66i 1.38523 + 1.90660i
\(797\) −267.531 86.9262i −0.335673 0.109067i 0.136331 0.990663i \(-0.456469\pi\)
−0.472004 + 0.881597i \(0.656469\pi\)
\(798\) 1317.01 73.6865i 1.65039 0.0923390i
\(799\) 375.692 + 1156.26i 0.470202 + 1.44713i
\(800\) −689.798 2122.98i −0.862248 2.65373i
\(801\) −452.342 + 146.975i −0.564722 + 0.183489i
\(802\) −653.463 + 2011.15i −0.814792 + 2.50767i
\(803\) 137.819 + 189.691i 0.171630 + 0.236228i
\(804\) 1689.02 548.795i 2.10077 0.682581i
\(805\) −490.467 601.321i −0.609276 0.746983i
\(806\) 2167.85 2.68964
\(807\) 126.793 390.227i 0.157116 0.483553i
\(808\) 390.921 538.056i 0.483813 0.665911i
\(809\) −227.576 + 165.343i −0.281305 + 0.204380i −0.719486 0.694507i \(-0.755623\pi\)
0.438182 + 0.898886i \(0.355623\pi\)
\(810\) −1642.22 2260.32i −2.02743 2.79052i
\(811\) 957.603i 1.18077i 0.807122 + 0.590384i \(0.201024\pi\)
−0.807122 + 0.590384i \(0.798976\pi\)
\(812\) −474.392 1222.91i −0.584227 1.50604i
\(813\) −508.474 1564.92i −0.625430 1.92487i
\(814\) 218.487 672.433i 0.268411 0.826085i
\(815\) 503.653 693.219i 0.617979 0.850576i
\(816\) 508.093 + 369.151i 0.622663 + 0.452391i
\(817\) 572.422i 0.700639i
\(818\) −495.755 161.081i −0.606058 0.196920i
\(819\) 398.978 + 105.397i 0.487152 + 0.128690i
\(820\) −1796.31 1039.07i −2.19063 1.26715i
\(821\) −330.038 −0.401995 −0.200998 0.979592i \(-0.564418\pi\)
−0.200998 + 0.979592i \(0.564418\pi\)
\(822\) 1075.44 + 349.432i 1.30832 + 0.425100i
\(823\) −345.738 −0.420094 −0.210047 0.977691i \(-0.567362\pi\)
−0.210047 + 0.977691i \(0.567362\pi\)
\(824\) 246.004 338.596i 0.298549 0.410917i
\(825\) 707.897 974.337i 0.858058 1.18101i
\(826\) 979.324 1519.75i 1.18562 1.83989i
\(827\) −361.373 1112.19i −0.436969 1.34485i −0.891056 0.453894i \(-0.850035\pi\)
0.454087 0.890957i \(-0.349965\pi\)
\(828\) −217.201 + 157.806i −0.262320 + 0.190587i
\(829\) 1270.59i 1.53267i 0.642439 + 0.766337i \(0.277922\pi\)
−0.642439 + 0.766337i \(0.722078\pi\)
\(830\) 867.162 630.030i 1.04477 0.759072i
\(831\) −220.056 302.881i −0.264808 0.364477i
\(832\) −927.317 + 1276.34i −1.11456 + 1.53407i
\(833\) −897.158 982.351i −1.07702 1.17929i
\(834\) 1465.40 1.75707
\(835\) −439.068 319.002i −0.525830 0.382038i
\(836\) −565.415 + 183.714i −0.676333 + 0.219754i
\(837\) −676.098 + 491.214i −0.807764 + 0.586875i
\(838\) 1682.43 + 546.655i 2.00767 + 0.652332i
\(839\) −26.5580 + 8.62920i −0.0316543 + 0.0102851i −0.324801 0.945782i \(-0.605297\pi\)
0.293147 + 0.956067i \(0.405297\pi\)
\(840\) 1164.12 65.1325i 1.38586 0.0775387i
\(841\) 76.5636 + 235.639i 0.0910388 + 0.280189i
\(842\) 543.534 + 1672.83i 0.645528 + 1.98673i
\(843\) 450.150 + 146.263i 0.533986 + 0.173503i
\(844\) 1364.10 991.075i 1.61623 1.17426i
\(845\) 606.562 197.084i 0.717825 0.233235i
\(846\) −311.237 + 428.381i −0.367892 + 0.506360i
\(847\) 147.962 560.108i 0.174690 0.661285i
\(848\) −78.6038 + 241.918i −0.0926932 + 0.285280i
\(849\) −1043.75 758.329i −1.22939 0.893203i
\(850\) −2702.63 3719.85i −3.17956 4.37629i
\(851\) −369.809 + 268.682i −0.434558 + 0.315725i
\(852\) 1647.09i 1.93321i
\(853\) 831.608 + 1144.61i 0.974921 + 1.34186i 0.939521 + 0.342491i \(0.111271\pi\)
0.0354000 + 0.999373i \(0.488729\pi\)
\(854\) 45.3968 + 811.383i 0.0531578 + 0.950097i
\(855\) 177.219 545.423i 0.207273 0.637922i
\(856\) −428.839 311.570i −0.500980 0.363983i
\(857\) −621.381 + 855.257i −0.725065 + 0.997967i 0.274275 + 0.961651i \(0.411562\pi\)
−0.999340 + 0.0363154i \(0.988438\pi\)
\(858\) −1067.59 −1.24427
\(859\) −698.374 226.916i −0.813009 0.264163i −0.127137 0.991885i \(-0.540579\pi\)
−0.685872 + 0.727723i \(0.740579\pi\)
\(860\) 1711.41i 1.99001i
\(861\) −724.113 + 728.051i −0.841014 + 0.845588i
\(862\) −126.577 −0.146841
\(863\) 229.768 707.152i 0.266243 0.819412i −0.725161 0.688579i \(-0.758235\pi\)
0.991404 0.130833i \(-0.0417651\pi\)
\(864\) 762.805i 0.882876i
\(865\) −1418.53 1030.62i −1.63992 1.19147i
\(866\) −224.218 + 308.609i −0.258912 + 0.356361i
\(867\) 1524.94 + 495.484i 1.75887 + 0.571492i
\(868\) −99.7681 1783.17i −0.114940 2.05434i
\(869\) −191.821 + 139.366i −0.220737 + 0.160375i
\(870\) −3273.46 −3.76259
\(871\) −796.834 1096.75i −0.914850 1.25918i
\(872\) 259.474 188.519i 0.297562 0.216191i
\(873\) 42.2008 58.0844i 0.0483400 0.0665343i
\(874\) 623.022 + 202.432i 0.712840 + 0.231616i
\(875\) 1775.46 + 469.018i 2.02910 + 0.536021i
\(876\) 623.274 + 452.835i 0.711500 + 0.516935i
\(877\) 369.333 + 1136.69i 0.421132 + 1.29611i 0.906650 + 0.421884i \(0.138631\pi\)
−0.485518 + 0.874227i \(0.661369\pi\)
\(878\) −951.815 1310.06i −1.08407 1.49210i
\(879\) 386.895 1190.74i 0.440153 1.35465i
\(880\) 338.886 110.111i 0.385098 0.125126i
\(881\) −36.6720 + 11.9155i −0.0416254 + 0.0135249i −0.329756 0.944066i \(-0.606966\pi\)
0.288130 + 0.957591i \(0.406966\pi\)
\(882\) 116.463 567.601i 0.132045 0.643539i
\(883\) 295.868 + 910.588i 0.335071 + 1.03124i 0.966687 + 0.255962i \(0.0823921\pi\)
−0.631616 + 0.775282i \(0.717608\pi\)
\(884\) −738.994 + 2274.39i −0.835966 + 2.57284i
\(885\) −1556.04 2141.70i −1.75823 2.42000i
\(886\) 112.603 + 346.556i 0.127091 + 0.391146i
\(887\) 839.652 1155.68i 0.946620 1.30291i −0.00639274 0.999980i \(-0.502035\pi\)
0.953013 0.302931i \(-0.0979651\pi\)
\(888\) 686.825i 0.773452i
\(889\) −121.020 77.9848i −0.136130 0.0877220i
\(890\) 2807.04 + 2039.44i 3.15398 + 2.29150i
\(891\) 504.091 366.243i 0.565758 0.411047i
\(892\) 231.675 + 318.874i 0.259726 + 0.357482i
\(893\) 758.062 0.848894
\(894\) 811.869 + 1117.44i 0.908131 + 1.24994i
\(895\) 2036.46 661.685i 2.27537 0.739313i
\(896\) 896.887 + 577.952i 1.00099 + 0.645036i
\(897\) 558.389 + 405.694i 0.622508 + 0.452278i
\(898\) 842.513 + 612.121i 0.938210 + 0.681649i
\(899\) 1482.42i 1.64897i
\(900\) 363.089 1117.47i 0.403432 1.24164i
\(901\) 1068.20i 1.18558i
\(902\) 394.950 682.779i 0.437860 0.756961i
\(903\) −818.751 216.287i −0.906701 0.239521i
\(904\) 43.3380 133.381i 0.0479402 0.147545i
\(905\) −1683.18 −1.85986
\(906\) −600.965 + 827.157i −0.663316 + 0.912977i
\(907\) −433.317 314.823i −0.477748 0.347104i 0.322705 0.946500i \(-0.395408\pi\)
−0.800453 + 0.599395i \(0.795408\pi\)
\(908\) −466.505 151.577i −0.513772 0.166935i
\(909\) −460.267 + 149.550i −0.506344 + 0.164521i
\(910\) −1088.76 2806.65i −1.19644 3.08423i
\(911\) 1113.09 1.22184 0.610918 0.791694i \(-0.290800\pi\)
0.610918 + 0.791694i \(0.290800\pi\)
\(912\) 316.810 230.176i 0.347379 0.252386i
\(913\) 140.507 + 193.392i 0.153896 + 0.211820i
\(914\) −787.303 572.009i −0.861382 0.625831i
\(915\) 1131.68 + 367.705i 1.23681 + 0.401863i
\(916\) 1633.37i 1.78315i
\(917\) −719.326 881.907i −0.784434 0.961731i
\(918\) −485.538 1494.33i −0.528908 1.62781i
\(919\) 30.9897 22.5153i 0.0337211 0.0244998i −0.570797 0.821091i \(-0.693366\pi\)
0.604518 + 0.796591i \(0.293366\pi\)
\(920\) 550.698 + 178.933i 0.598585 + 0.194492i
\(921\) −9.72651 29.9351i −0.0105608 0.0325028i
\(922\) 245.242 79.6839i 0.265989 0.0864251i
\(923\) 1195.76 388.528i 1.29552 0.420940i
\(924\) 49.1320 + 878.144i 0.0531732 + 0.950372i
\(925\) 618.198 1902.62i 0.668322 2.05688i
\(926\) −114.749 + 83.3703i −0.123919 + 0.0900328i
\(927\) −289.643 + 94.1108i −0.312452 + 0.101522i
\(928\) −1094.69 795.338i −1.17962 0.857045i
\(929\) 92.8975i 0.0999973i −0.998749 0.0499987i \(-0.984078\pi\)
0.998749 0.0499987i \(-0.0159217\pi\)
\(930\) −4238.87 1377.29i −4.55793 1.48096i
\(931\) −755.409 + 342.744i −0.811395 + 0.368146i
\(932\) −386.542 + 280.839i −0.414745 + 0.301330i
\(933\) 1445.14 1049.96i 1.54892 1.12536i
\(934\) 2145.87i 2.29751i
\(935\) 1210.59 879.548i 1.29475 0.940693i
\(936\) −292.860 + 95.1559i −0.312884 + 0.101662i
\(937\) 93.3892 + 30.3440i 0.0996683 + 0.0323842i 0.358427 0.933558i \(-0.383313\pi\)
−0.258758 + 0.965942i \(0.583313\pi\)
\(938\) −1475.05 + 1203.12i −1.57255 + 1.28265i
\(939\) 491.807 + 357.319i 0.523756 + 0.380531i
\(940\) 2266.44 2.41110
\(941\) −308.142 100.121i −0.327462 0.106399i 0.140672 0.990056i \(-0.455074\pi\)
−0.468134 + 0.883657i \(0.655074\pi\)
\(942\) −1369.05 −1.45334
\(943\) −466.037 + 207.035i −0.494207 + 0.219550i
\(944\) 536.738i 0.568578i
\(945\) 975.515 + 628.620i 1.03229 + 0.665206i
\(946\) 650.508 0.687641
\(947\) 684.348 + 497.208i 0.722648 + 0.525035i 0.887229 0.461329i \(-0.152627\pi\)
−0.164581 + 0.986364i \(0.552627\pi\)
\(948\) −457.919 + 630.272i −0.483037 + 0.664844i
\(949\) 181.729 559.306i 0.191496 0.589363i
\(950\) −2726.65 + 885.942i −2.87016 + 0.932571i
\(951\) 314.090 + 432.307i 0.330273 + 0.454582i
\(952\) 959.806 + 253.549i 1.00820 + 0.266333i
\(953\) −524.896 + 381.359i −0.550783 + 0.400167i −0.828074 0.560619i \(-0.810563\pi\)
0.277291 + 0.960786i \(0.410563\pi\)
\(954\) −376.388 + 273.462i −0.394536 + 0.286647i
\(955\) 631.580 869.295i 0.661340 0.910257i
\(956\) −152.658 + 469.834i −0.159685 + 0.491459i
\(957\) 730.037i 0.762839i
\(958\) −697.720 + 960.329i −0.728309 + 1.00243i
\(959\) −710.010 + 39.7250i −0.740365 + 0.0414233i
\(960\) 2624.11 1906.53i 2.73344 1.98596i
\(961\) −326.758 + 1005.66i −0.340019 + 1.04647i
\(962\) −1686.56 + 547.998i −1.75318 + 0.569644i
\(963\) 119.193 + 366.840i 0.123773 + 0.380934i
\(964\) −1048.61 + 340.714i −1.08777 + 0.353438i
\(965\) −915.752 + 297.546i −0.948966 + 0.308338i
\(966\) 524.951 814.638i 0.543427 0.843310i
\(967\) −273.290 + 198.557i −0.282616 + 0.205333i −0.720058 0.693914i \(-0.755885\pi\)
0.437441 + 0.899247i \(0.355885\pi\)
\(968\) 133.585 + 411.134i 0.138001 + 0.424725i
\(969\) 966.613 1330.43i 0.997537 1.37299i
\(970\) −523.761 −0.539960
\(971\) −330.824 107.491i −0.340704 0.110702i 0.133667 0.991026i \(-0.457325\pi\)
−0.474372 + 0.880325i \(0.657325\pi\)
\(972\) 644.549 887.146i 0.663117 0.912702i
\(973\) −859.169 + 333.290i −0.883010 + 0.342539i
\(974\) 2054.33 1492.56i 2.10917 1.53240i
\(975\) −3020.68 −3.09814
\(976\) 141.807 + 195.180i 0.145294 + 0.199980i
\(977\) −185.462 570.795i −0.189828 0.584232i 0.810170 0.586196i \(-0.199375\pi\)
−0.999998 + 0.00196359i \(0.999375\pi\)
\(978\) 1017.77 + 330.693i 1.04066 + 0.338132i
\(979\) −454.830 + 626.019i −0.464586 + 0.639448i
\(980\) −2258.50 + 1024.73i −2.30460 + 1.04564i
\(981\) −233.383 −0.237903
\(982\) 377.933 1163.16i 0.384861 1.18448i
\(983\) 1118.21i 1.13755i 0.822492 + 0.568776i \(0.192583\pi\)
−0.822492 + 0.568776i \(0.807417\pi\)
\(984\) 159.923 749.355i 0.162523 0.761539i
\(985\) 305.330i 0.309980i
\(986\) −2650.74 861.277i −2.68837 0.873506i
\(987\) 286.431 1084.28i 0.290204 1.09856i
\(988\) 1206.35 + 876.462i 1.22100 + 0.887107i
\(989\) −340.241 247.200i −0.344026 0.249949i
\(990\) 619.827 + 201.394i 0.626088 + 0.203428i
\(991\) 449.760 + 1384.22i 0.453844 + 1.39679i 0.872487 + 0.488638i \(0.162506\pi\)
−0.418642 + 0.908151i \(0.637494\pi\)
\(992\) −1082.90 1490.49i −1.09164 1.50251i
\(993\) 1846.71i 1.85973i
\(994\) −638.476 1645.89i −0.642330 1.65583i
\(995\) −2381.82 + 1730.49i −2.39379 + 1.73919i
\(996\) 635.434 + 461.670i 0.637986 + 0.463524i
\(997\) −403.809 131.206i −0.405024 0.131600i 0.0994180 0.995046i \(-0.468302\pi\)
−0.504442 + 0.863445i \(0.668302\pi\)
\(998\) 2597.23 2.60244
\(999\) 401.825 553.065i 0.402228 0.553619i
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 287.3.o.a.139.7 216
7.6 odd 2 inner 287.3.o.a.139.8 yes 216
41.18 even 5 inner 287.3.o.a.223.7 yes 216
287.223 odd 10 inner 287.3.o.a.223.8 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.o.a.139.7 216 1.1 even 1 trivial
287.3.o.a.139.8 yes 216 7.6 odd 2 inner
287.3.o.a.223.7 yes 216 41.18 even 5 inner
287.3.o.a.223.8 yes 216 287.223 odd 10 inner