Properties

Label 177.3.h.a.104.1
Level $177$
Weight $3$
Character 177.104
Analytic conductor $4.823$
Analytic rank $0$
Dimension $1064$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [177,3,Mod(5,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([29, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.h (of order \(58\), degree \(28\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(1064\)
Relative dimension: \(38\) over \(\Q(\zeta_{58})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label 104.1
Character \(\chi\) \(=\) 177.104
Dual form 177.3.h.a.80.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96521 - 3.26621i) q^{2} +(1.61314 - 2.52938i) q^{3} +(-4.93243 + 9.30356i) q^{4} +(0.764614 + 7.03051i) q^{5} +(-11.4317 - 0.298077i) q^{6} +(-7.86182 + 2.64896i) q^{7} +(24.8556 - 1.34763i) q^{8} +(-3.79556 - 8.16050i) q^{9} +O(q^{10})\) \(q+(-1.96521 - 3.26621i) q^{2} +(1.61314 - 2.52938i) q^{3} +(-4.93243 + 9.30356i) q^{4} +(0.764614 + 7.03051i) q^{5} +(-11.4317 - 0.298077i) q^{6} +(-7.86182 + 2.64896i) q^{7} +(24.8556 - 1.34763i) q^{8} +(-3.79556 - 8.16050i) q^{9} +(21.4605 - 16.3138i) q^{10} +(11.9787 + 8.12173i) q^{11} +(15.5756 + 27.4840i) q^{12} +(2.93899 + 2.78396i) q^{13} +(24.1022 + 20.4726i) q^{14} +(19.0163 + 9.40719i) q^{15} +(-29.6107 - 43.6724i) q^{16} +(1.83265 - 5.43910i) q^{17} +(-19.1948 + 28.4342i) q^{18} +(3.75933 + 22.9309i) q^{19} +(-69.1801 - 27.5639i) q^{20} +(-5.98200 + 24.1587i) q^{21} +(2.98666 - 55.0857i) q^{22} +(28.1430 - 7.81385i) q^{23} +(36.6869 - 65.0434i) q^{24} +(-24.4279 + 5.37698i) q^{25} +(3.31725 - 15.0704i) q^{26} +(-26.7638 - 3.56360i) q^{27} +(14.1332 - 86.2088i) q^{28} +(-18.9428 + 31.4832i) q^{29} +(-6.64518 - 80.5983i) q^{30} +(-6.27098 + 38.2513i) q^{31} +(-42.6444 + 92.1744i) q^{32} +(39.8662 - 17.1971i) q^{33} +(-21.3668 + 4.70318i) q^{34} +(-24.6348 - 53.2472i) q^{35} +(94.6430 + 4.93892i) q^{36} +(-1.73558 + 32.0109i) q^{37} +(67.5092 - 57.3429i) q^{38} +(11.7827 - 2.94291i) q^{39} +(28.4795 + 173.717i) q^{40} +(24.6707 + 6.84979i) q^{41} +(90.6633 - 27.9386i) q^{42} +(-22.2709 - 32.8472i) q^{43} +(-134.645 + 71.3842i) q^{44} +(54.4703 - 32.9243i) q^{45} +(-80.8286 - 76.5650i) q^{46} +(-4.55759 + 41.9063i) q^{47} +(-158.230 + 4.44692i) q^{48} +(15.7828 - 11.9977i) q^{49} +(65.5684 + 69.2197i) q^{50} +(-10.8012 - 13.4095i) q^{51} +(-40.3971 + 13.6114i) q^{52} +(45.2679 - 59.5489i) q^{53} +(40.9571 + 94.4194i) q^{54} +(-47.9408 + 90.4260i) q^{55} +(-191.841 + 76.4364i) q^{56} +(64.0653 + 27.4820i) q^{57} +140.057 q^{58} +(-54.5351 + 22.5150i) q^{59} +(-181.317 + 130.519i) q^{60} +(30.4446 - 18.3179i) q^{61} +(137.261 - 54.6896i) q^{62} +(51.4568 + 54.1021i) q^{63} +(175.046 - 19.0374i) q^{64} +(-17.3254 + 22.7912i) q^{65} +(-134.515 - 96.4154i) q^{66} +(0.462564 + 8.53149i) q^{67} +(41.5636 + 43.8781i) q^{68} +(25.6343 - 83.7892i) q^{69} +(-125.504 + 185.104i) q^{70} +(-1.53603 + 14.1236i) q^{71} +(-105.338 - 197.719i) q^{72} +(5.70265 - 6.71368i) q^{73} +(107.965 - 57.2394i) q^{74} +(-25.8051 + 70.4613i) q^{75} +(-231.882 - 78.1300i) q^{76} +(-115.688 - 32.1207i) q^{77} +(-32.7677 - 32.7013i) q^{78} +(11.3096 - 28.3849i) q^{79} +(284.399 - 241.570i) q^{80} +(-52.1875 + 61.9473i) q^{81} +(-26.1104 - 94.0410i) q^{82} +(-9.32514 - 20.1560i) q^{83} +(-195.256 - 174.815i) q^{84} +(39.6409 + 8.72562i) q^{85} +(-63.5187 + 137.293i) q^{86} +(49.0756 + 98.7003i) q^{87} +(308.682 + 185.728i) q^{88} +(38.2081 - 63.5024i) q^{89} +(-214.584 - 113.208i) q^{90} +(-30.4804 - 14.1017i) q^{91} +(-66.1167 + 300.371i) q^{92} +(86.6362 + 77.5664i) q^{93} +(145.832 - 67.4689i) q^{94} +(-158.341 + 43.9633i) q^{95} +(164.353 + 256.554i) q^{96} +(36.4907 + 42.9602i) q^{97} +(-70.2036 - 27.9717i) q^{98} +(20.8117 - 128.578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9} - 94 q^{10} - 29 q^{12} - 54 q^{13} - 12 q^{15} - 158 q^{16} - 27 q^{18} - 30 q^{19} - 18 q^{21} - 142 q^{22} - 23 q^{24} + 108 q^{25} - 32 q^{27} - 70 q^{28} - 131 q^{30} - 18 q^{31} + 17 q^{33} + 90 q^{34} + 67 q^{36} - 170 q^{37} - 91 q^{39} - 2 q^{40} - 43 q^{42} - 222 q^{43} - 461 q^{45} - 54 q^{46} - 1645 q^{48} - 300 q^{49} - 893 q^{51} - 66 q^{52} - 859 q^{54} + 170 q^{55} - 27 q^{57} - 36 q^{58} + 510 q^{60} - 70 q^{61} + 610 q^{63} - 106 q^{64} + 1619 q^{66} - 182 q^{67} + 1487 q^{69} - 206 q^{70} + 2241 q^{72} + 134 q^{73} + 542 q^{75} + 246 q^{76} - 273 q^{78} - 122 q^{79} + 127 q^{81} + 122 q^{82} - 329 q^{84} - 6 q^{85} + 54 q^{87} + 38 q^{88} + 347 q^{90} + 274 q^{91} - 483 q^{93} - 826 q^{94} + 693 q^{96} - 474 q^{97} - 523 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{24}{29}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96521 3.26621i −0.982607 1.63311i −0.751007 0.660294i \(-0.770431\pi\)
−0.231600 0.972811i \(-0.574396\pi\)
\(3\) 1.61314 2.52938i 0.537713 0.843128i
\(4\) −4.93243 + 9.30356i −1.23311 + 2.32589i
\(5\) 0.764614 + 7.03051i 0.152923 + 1.40610i 0.779334 + 0.626609i \(0.215558\pi\)
−0.626411 + 0.779493i \(0.715477\pi\)
\(6\) −11.4317 0.298077i −1.90528 0.0496794i
\(7\) −7.86182 + 2.64896i −1.12312 + 0.378422i −0.818760 0.574135i \(-0.805338\pi\)
−0.304357 + 0.952558i \(0.598442\pi\)
\(8\) 24.8556 1.34763i 3.10695 0.168454i
\(9\) −3.79556 8.16050i −0.421729 0.906722i
\(10\) 21.4605 16.3138i 2.14605 1.63138i
\(11\) 11.9787 + 8.12173i 1.08897 + 0.738339i 0.967148 0.254213i \(-0.0818165\pi\)
0.121820 + 0.992552i \(0.461127\pi\)
\(12\) 15.5756 + 27.4840i 1.29796 + 2.29033i
\(13\) 2.93899 + 2.78396i 0.226076 + 0.214151i 0.792350 0.610066i \(-0.208857\pi\)
−0.566274 + 0.824217i \(0.691616\pi\)
\(14\) 24.1022 + 20.4726i 1.72159 + 1.46233i
\(15\) 19.0163 + 9.40719i 1.26775 + 0.627146i
\(16\) −29.6107 43.6724i −1.85067 2.72953i
\(17\) 1.83265 5.43910i 0.107803 0.319947i −0.880152 0.474693i \(-0.842559\pi\)
0.987954 + 0.154746i \(0.0494558\pi\)
\(18\) −19.1948 + 28.4342i −1.06638 + 1.57968i
\(19\) 3.75933 + 22.9309i 0.197859 + 1.20689i 0.879751 + 0.475435i \(0.157709\pi\)
−0.681891 + 0.731454i \(0.738842\pi\)
\(20\) −69.1801 27.5639i −3.45901 1.37819i
\(21\) −5.98200 + 24.1587i −0.284857 + 1.15041i
\(22\) 2.98666 55.0857i 0.135757 2.50390i
\(23\) 28.1430 7.81385i 1.22361 0.339733i 0.405123 0.914262i \(-0.367229\pi\)
0.818484 + 0.574529i \(0.194815\pi\)
\(24\) 36.6869 65.0434i 1.52862 2.71014i
\(25\) −24.4279 + 5.37698i −0.977115 + 0.215079i
\(26\) 3.31725 15.0704i 0.127587 0.579632i
\(27\) −26.7638 3.56360i −0.991252 0.131985i
\(28\) 14.1332 86.2088i 0.504757 3.07888i
\(29\) −18.9428 + 31.4832i −0.653200 + 1.08563i 0.336392 + 0.941722i \(0.390793\pi\)
−0.989592 + 0.143904i \(0.954034\pi\)
\(30\) −6.64518 80.5983i −0.221506 2.68661i
\(31\) −6.27098 + 38.2513i −0.202290 + 1.23391i 0.669045 + 0.743222i \(0.266703\pi\)
−0.871334 + 0.490690i \(0.836745\pi\)
\(32\) −42.6444 + 92.1744i −1.33264 + 2.88045i
\(33\) 39.8662 17.1971i 1.20807 0.521125i
\(34\) −21.3668 + 4.70318i −0.628435 + 0.138329i
\(35\) −24.6348 53.2472i −0.703851 1.52135i
\(36\) 94.6430 + 4.93892i 2.62897 + 0.137192i
\(37\) −1.73558 + 32.0109i −0.0469075 + 0.865159i 0.876515 + 0.481374i \(0.159862\pi\)
−0.923423 + 0.383784i \(0.874621\pi\)
\(38\) 67.5092 57.3429i 1.77656 1.50902i
\(39\) 11.7827 2.94291i 0.302120 0.0754593i
\(40\) 28.4795 + 173.717i 0.711988 + 4.34293i
\(41\) 24.6707 + 6.84979i 0.601724 + 0.167068i 0.555015 0.831841i \(-0.312713\pi\)
0.0467097 + 0.998909i \(0.485126\pi\)
\(42\) 90.6633 27.9386i 2.15865 0.665204i
\(43\) −22.2709 32.8472i −0.517929 0.763888i 0.475330 0.879808i \(-0.342329\pi\)
−0.993259 + 0.115920i \(0.963018\pi\)
\(44\) −134.645 + 71.3842i −3.06011 + 1.62237i
\(45\) 54.4703 32.9243i 1.21045 0.731652i
\(46\) −80.8286 76.5650i −1.75714 1.66446i
\(47\) −4.55759 + 41.9063i −0.0969700 + 0.891624i 0.840088 + 0.542450i \(0.182503\pi\)
−0.937058 + 0.349174i \(0.886462\pi\)
\(48\) −158.230 + 4.44692i −3.29647 + 0.0926441i
\(49\) 15.7828 11.9977i 0.322097 0.244852i
\(50\) 65.5684 + 69.2197i 1.31137 + 1.38439i
\(51\) −10.8012 13.4095i −0.211789 0.262931i
\(52\) −40.3971 + 13.6114i −0.776867 + 0.261757i
\(53\) 45.2679 59.5489i 0.854111 1.12356i −0.137005 0.990570i \(-0.543748\pi\)
0.991117 0.132994i \(-0.0424591\pi\)
\(54\) 40.9571 + 94.4194i 0.758465 + 1.74851i
\(55\) −47.9408 + 90.4260i −0.871651 + 1.64411i
\(56\) −191.841 + 76.4364i −3.42573 + 1.36494i
\(57\) 64.0653 + 27.4820i 1.12395 + 0.482140i
\(58\) 140.057 2.41478
\(59\) −54.5351 + 22.5150i −0.924324 + 0.381609i
\(60\) −181.317 + 130.519i −3.02195 + 2.17531i
\(61\) 30.4446 18.3179i 0.499091 0.300293i −0.243660 0.969861i \(-0.578348\pi\)
0.742751 + 0.669567i \(0.233520\pi\)
\(62\) 137.261 54.6896i 2.21388 0.882090i
\(63\) 51.4568 + 54.1021i 0.816775 + 0.858764i
\(64\) 175.046 19.0374i 2.73510 0.297460i
\(65\) −17.3254 + 22.7912i −0.266545 + 0.350634i
\(66\) −134.515 96.4154i −2.03811 1.46084i
\(67\) 0.462564 + 8.53149i 0.00690394 + 0.127336i 0.999954 + 0.00963909i \(0.00306827\pi\)
−0.993050 + 0.117697i \(0.962449\pi\)
\(68\) 41.5636 + 43.8781i 0.611229 + 0.645266i
\(69\) 25.6343 83.7892i 0.371512 1.21434i
\(70\) −125.504 + 185.104i −1.79291 + 2.64435i
\(71\) −1.53603 + 14.1236i −0.0216342 + 0.198923i −0.999967 0.00811480i \(-0.997417\pi\)
0.978333 + 0.207038i \(0.0663825\pi\)
\(72\) −105.338 197.719i −1.46303 2.74610i
\(73\) 5.70265 6.71368i 0.0781185 0.0919682i −0.721714 0.692191i \(-0.756646\pi\)
0.799833 + 0.600223i \(0.204921\pi\)
\(74\) 107.965 57.2394i 1.45899 0.773506i
\(75\) −25.8051 + 70.4613i −0.344069 + 0.939484i
\(76\) −231.882 78.1300i −3.05107 1.02803i
\(77\) −115.688 32.1207i −1.50244 0.417151i
\(78\) −32.7677 32.7013i −0.420099 0.419247i
\(79\) 11.3096 28.3849i 0.143159 0.359303i −0.839860 0.542802i \(-0.817363\pi\)
0.983020 + 0.183499i \(0.0587426\pi\)
\(80\) 284.399 241.570i 3.55498 3.01963i
\(81\) −52.1875 + 61.9473i −0.644290 + 0.764781i
\(82\) −26.1104 94.0410i −0.318419 1.14684i
\(83\) −9.32514 20.1560i −0.112351 0.242843i 0.843241 0.537536i \(-0.180645\pi\)
−0.955592 + 0.294693i \(0.904783\pi\)
\(84\) −195.256 174.815i −2.32448 2.08113i
\(85\) 39.6409 + 8.72562i 0.466363 + 0.102654i
\(86\) −63.5187 + 137.293i −0.738589 + 1.59643i
\(87\) 49.0756 + 98.7003i 0.564088 + 1.13449i
\(88\) 308.682 + 185.728i 3.50775 + 2.11054i
\(89\) 38.2081 63.5024i 0.429305 0.713510i −0.564405 0.825498i \(-0.690894\pi\)
0.993710 + 0.111988i \(0.0357219\pi\)
\(90\) −214.584 113.208i −2.38426 1.25787i
\(91\) −30.4804 14.1017i −0.334949 0.154964i
\(92\) −66.1167 + 300.371i −0.718659 + 3.26490i
\(93\) 86.6362 + 77.5664i 0.931572 + 0.834047i
\(94\) 145.832 67.4689i 1.55140 0.717754i
\(95\) −158.341 + 43.9633i −1.66675 + 0.462771i
\(96\) 164.353 + 256.554i 1.71201 + 2.67244i
\(97\) 36.4907 + 42.9602i 0.376193 + 0.442888i 0.917379 0.398014i \(-0.130301\pi\)
−0.541186 + 0.840903i \(0.682025\pi\)
\(98\) −70.2036 27.9717i −0.716364 0.285425i
\(99\) 20.8117 128.578i 0.210219 1.29877i
\(100\) 70.4639 253.788i 0.704639 2.53788i
\(101\) 33.6679 99.9227i 0.333345 0.989334i −0.641629 0.767015i \(-0.721741\pi\)
0.974974 0.222318i \(-0.0713624\pi\)
\(102\) −22.5715 + 61.6317i −0.221289 + 0.604232i
\(103\) −22.8317 43.0652i −0.221667 0.418109i 0.747589 0.664162i \(-0.231211\pi\)
−0.969257 + 0.246052i \(0.920866\pi\)
\(104\) 76.8022 + 65.2363i 0.738482 + 0.627273i
\(105\) −174.422 23.5844i −1.66116 0.224613i
\(106\) −283.460 30.8282i −2.67416 0.290832i
\(107\) −68.1767 46.2250i −0.637166 0.432009i 0.199368 0.979925i \(-0.436111\pi\)
−0.836534 + 0.547916i \(0.815421\pi\)
\(108\) 165.165 231.421i 1.52930 2.14279i
\(109\) 64.4864 61.0848i 0.591618 0.560411i −0.332216 0.943203i \(-0.607796\pi\)
0.923834 + 0.382793i \(0.125038\pi\)
\(110\) 389.564 21.1216i 3.54149 0.192014i
\(111\) 78.1680 + 56.0280i 0.704216 + 0.504756i
\(112\) 348.480 + 264.908i 3.11143 + 2.36525i
\(113\) 5.81155 + 53.4364i 0.0514297 + 0.472888i 0.991326 + 0.131428i \(0.0419561\pi\)
−0.939896 + 0.341461i \(0.889078\pi\)
\(114\) −36.1402 263.259i −0.317020 2.30929i
\(115\) 76.4539 + 191.885i 0.664816 + 1.66856i
\(116\) −199.471 331.524i −1.71958 2.85797i
\(117\) 11.5634 34.5503i 0.0988323 0.295301i
\(118\) 180.712 + 133.876i 1.53146 + 1.13455i
\(119\) 47.6158i 0.400133i
\(120\) 485.339 + 208.195i 4.04449 + 1.73496i
\(121\) 32.7389 + 82.1685i 0.270570 + 0.679079i
\(122\) −119.660 63.4398i −0.980821 0.519999i
\(123\) 57.1230 51.3520i 0.464415 0.417496i
\(124\) −324.942 247.014i −2.62050 1.99205i
\(125\) −0.0286064 0.0849008i −0.000228851 0.000679206i
\(126\) 75.5853 274.391i 0.599883 2.17771i
\(127\) −44.8089 + 42.4452i −0.352826 + 0.334214i −0.843500 0.537129i \(-0.819509\pi\)
0.490675 + 0.871343i \(0.336750\pi\)
\(128\) −160.335 210.917i −1.25262 1.64779i
\(129\) −119.009 + 3.34464i −0.922552 + 0.0259275i
\(130\) 108.489 + 11.7989i 0.834532 + 0.0907608i
\(131\) 49.0976 51.8317i 0.374791 0.395662i −0.511126 0.859506i \(-0.670772\pi\)
0.885917 + 0.463844i \(0.153530\pi\)
\(132\) −36.6431 + 455.721i −0.277599 + 3.45243i
\(133\) −90.2981 170.320i −0.678933 1.28060i
\(134\) 26.9566 18.2770i 0.201169 0.136396i
\(135\) 4.58998 190.888i 0.0339999 1.41398i
\(136\) 38.2217 137.662i 0.281042 1.01222i
\(137\) 85.3934 13.9995i 0.623310 0.102186i 0.158153 0.987415i \(-0.449446\pi\)
0.465157 + 0.885228i \(0.345998\pi\)
\(138\) −324.050 + 80.9366i −2.34819 + 0.586497i
\(139\) −54.9541 64.6970i −0.395353 0.465446i 0.528086 0.849191i \(-0.322910\pi\)
−0.923439 + 0.383745i \(0.874634\pi\)
\(140\) 616.898 + 33.4472i 4.40641 + 0.238909i
\(141\) 98.6452 + 79.1287i 0.699611 + 0.561196i
\(142\) 49.1492 22.7388i 0.346121 0.160133i
\(143\) 12.5946 + 57.2177i 0.0880739 + 0.400124i
\(144\) −244.000 + 407.399i −1.69444 + 2.82916i
\(145\) −235.827 109.105i −1.62639 0.752448i
\(146\) −33.1352 5.43224i −0.226954 0.0372071i
\(147\) −4.88709 59.2747i −0.0332455 0.403229i
\(148\) −289.254 174.039i −1.95442 1.17594i
\(149\) −137.904 22.6083i −0.925532 0.151733i −0.319876 0.947459i \(-0.603641\pi\)
−0.605657 + 0.795726i \(0.707089\pi\)
\(150\) 280.854 54.1865i 1.87236 0.361243i
\(151\) −217.221 47.8140i −1.43855 0.316649i −0.573859 0.818954i \(-0.694554\pi\)
−0.864690 + 0.502305i \(0.832485\pi\)
\(152\) 124.343 + 564.896i 0.818046 + 3.71642i
\(153\) −51.3417 + 5.68911i −0.335566 + 0.0371838i
\(154\) 122.439 + 440.986i 0.795059 + 2.86355i
\(155\) −273.721 14.8407i −1.76594 0.0957465i
\(156\) −30.7378 + 124.137i −0.197037 + 0.795748i
\(157\) 31.0033 77.8125i 0.197473 0.495621i −0.796578 0.604536i \(-0.793358\pi\)
0.994051 + 0.108915i \(0.0347378\pi\)
\(158\) −114.937 + 18.8430i −0.727449 + 0.119259i
\(159\) −77.5985 210.561i −0.488041 1.32428i
\(160\) −680.639 229.334i −4.25399 1.43334i
\(161\) −200.556 + 135.981i −1.24569 + 0.844600i
\(162\) 304.893 + 48.7156i 1.88205 + 0.300714i
\(163\) −143.373 + 168.792i −0.879589 + 1.03553i 0.119499 + 0.992834i \(0.461871\pi\)
−0.999088 + 0.0426980i \(0.986405\pi\)
\(164\) −185.414 + 195.739i −1.13057 + 1.19353i
\(165\) 151.387 + 267.130i 0.917495 + 1.61897i
\(166\) −47.5077 + 70.0687i −0.286191 + 0.422101i
\(167\) 23.0925 + 30.3776i 0.138278 + 0.181902i 0.860020 0.510261i \(-0.170451\pi\)
−0.721741 + 0.692163i \(0.756658\pi\)
\(168\) −116.129 + 608.542i −0.691246 + 3.62227i
\(169\) −8.26224 152.388i −0.0488890 0.901705i
\(170\) −49.4031 146.623i −0.290606 0.862489i
\(171\) 172.859 117.714i 1.01087 0.688383i
\(172\) 415.446 45.1824i 2.41538 0.262689i
\(173\) 238.381 + 126.382i 1.37793 + 0.730531i 0.982200 0.187837i \(-0.0601477\pi\)
0.395727 + 0.918368i \(0.370493\pi\)
\(174\) 225.932 354.259i 1.29846 2.03597i
\(175\) 177.804 106.981i 1.01602 0.611322i
\(176\) 763.627i 4.33879i
\(177\) −31.0238 + 174.260i −0.175276 + 0.984519i
\(178\) −282.499 −1.58707
\(179\) −78.7748 130.925i −0.440083 0.731424i 0.554852 0.831949i \(-0.312775\pi\)
−0.994934 + 0.100526i \(0.967947\pi\)
\(180\) 37.6422 + 669.165i 0.209123 + 3.71758i
\(181\) −15.0671 + 28.4196i −0.0832436 + 0.157014i −0.921639 0.388048i \(-0.873149\pi\)
0.838395 + 0.545063i \(0.183494\pi\)
\(182\) 13.8413 + 127.268i 0.0760509 + 0.699276i
\(183\) 2.77839 106.555i 0.0151825 0.582270i
\(184\) 688.981 232.145i 3.74446 1.26166i
\(185\) −226.380 + 12.2739i −1.22367 + 0.0663457i
\(186\) 83.0895 435.406i 0.446718 2.34089i
\(187\) 66.1275 50.2688i 0.353623 0.268817i
\(188\) −367.398 249.102i −1.95425 1.32501i
\(189\) 219.852 42.8797i 1.16324 0.226877i
\(190\) 454.768 + 430.779i 2.39352 + 2.26726i
\(191\) 247.931 + 210.594i 1.29807 + 1.10259i 0.988421 + 0.151735i \(0.0484861\pi\)
0.309645 + 0.950852i \(0.399790\pi\)
\(192\) 234.221 473.469i 1.21990 2.46598i
\(193\) −143.246 211.272i −0.742206 1.09467i −0.991983 0.126369i \(-0.959668\pi\)
0.249777 0.968303i \(-0.419643\pi\)
\(194\) 68.6050 203.612i 0.353634 1.04955i
\(195\) 29.6994 + 80.5881i 0.152305 + 0.413272i
\(196\) 33.7743 + 206.014i 0.172318 + 1.05109i
\(197\) 350.585 + 139.686i 1.77962 + 0.709066i 0.996153 + 0.0876351i \(0.0279310\pi\)
0.783469 + 0.621431i \(0.213448\pi\)
\(198\) −460.863 + 184.708i −2.32759 + 0.932871i
\(199\) −18.6456 + 343.899i −0.0936967 + 1.72813i 0.453608 + 0.891201i \(0.350137\pi\)
−0.547305 + 0.836933i \(0.684346\pi\)
\(200\) −599.925 + 166.568i −2.99962 + 0.832841i
\(201\) 22.3256 + 12.5925i 0.111073 + 0.0626492i
\(202\) −392.533 + 86.4031i −1.94323 + 0.427738i
\(203\) 65.5274 297.694i 0.322795 1.46647i
\(204\) 178.032 34.3486i 0.872708 0.168376i
\(205\) −29.2939 + 178.685i −0.142897 + 0.871634i
\(206\) −95.7909 + 159.206i −0.465004 + 0.772843i
\(207\) −170.583 200.003i −0.824073 0.966196i
\(208\) 34.5569 210.788i 0.166139 1.01340i
\(209\) −141.207 + 305.213i −0.675630 + 1.46035i
\(210\) 265.745 + 616.047i 1.26545 + 2.93356i
\(211\) 256.189 56.3915i 1.21417 0.267259i 0.438693 0.898637i \(-0.355442\pi\)
0.775475 + 0.631379i \(0.217511\pi\)
\(212\) 330.736 + 714.874i 1.56007 + 3.37205i
\(213\) 33.2461 + 26.6685i 0.156085 + 0.125204i
\(214\) −16.9986 + 313.522i −0.0794329 + 1.46505i
\(215\) 213.904 181.691i 0.994901 0.845076i
\(216\) −670.034 52.5079i −3.10201 0.243092i
\(217\) −52.0247 317.336i −0.239745 1.46238i
\(218\) −326.245 90.5816i −1.49654 0.415512i
\(219\) −7.78229 25.2543i −0.0355356 0.115316i
\(220\) −604.818 892.041i −2.74917 4.05473i
\(221\) 20.5283 10.8834i 0.0928884 0.0492463i
\(222\) 29.3822 365.420i 0.132352 1.64604i
\(223\) 225.711 + 213.805i 1.01216 + 0.958766i 0.999153 0.0411498i \(-0.0131021\pi\)
0.0130036 + 0.999915i \(0.495861\pi\)
\(224\) 91.0969 837.622i 0.406682 3.73938i
\(225\) 136.596 + 178.935i 0.607095 + 0.795267i
\(226\) 163.113 123.996i 0.721741 0.548653i
\(227\) −280.860 296.501i −1.23727 1.30617i −0.935730 0.352716i \(-0.885258\pi\)
−0.301539 0.953454i \(-0.597500\pi\)
\(228\) −571.678 + 460.483i −2.50736 + 2.01966i
\(229\) −158.753 + 53.4902i −0.693245 + 0.233581i −0.643798 0.765195i \(-0.722642\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(230\) 476.488 626.809i 2.07169 2.72526i
\(231\) −267.867 + 240.805i −1.15960 + 1.04244i
\(232\) −428.407 + 808.062i −1.84658 + 3.48303i
\(233\) 231.117 92.0854i 0.991918 0.395216i 0.182984 0.983116i \(-0.441424\pi\)
0.808934 + 0.587899i \(0.200045\pi\)
\(234\) −135.573 + 30.1303i −0.579372 + 0.128762i
\(235\) −298.108 −1.26854
\(236\) 59.5216 618.424i 0.252210 2.62044i
\(237\) −53.5524 74.3952i −0.225960 0.313904i
\(238\) 155.523 93.5753i 0.653459 0.393174i
\(239\) 324.567 129.320i 1.35802 0.541086i 0.426407 0.904531i \(-0.359779\pi\)
0.931616 + 0.363445i \(0.118400\pi\)
\(240\) −152.249 1109.04i −0.634372 4.62100i
\(241\) 147.021 15.9895i 0.610046 0.0663465i 0.202119 0.979361i \(-0.435217\pi\)
0.407927 + 0.913015i \(0.366252\pi\)
\(242\) 204.041 268.411i 0.843143 1.10914i
\(243\) 72.5028 + 231.932i 0.298365 + 0.954452i
\(244\) 20.2557 + 373.595i 0.0830152 + 1.53113i
\(245\) 96.4179 + 101.787i 0.393543 + 0.415458i
\(246\) −279.985 85.6582i −1.13815 0.348204i
\(247\) −52.7900 + 77.8594i −0.213725 + 0.315220i
\(248\) −104.320 + 959.211i −0.420647 + 3.86779i
\(249\) −66.0249 8.92754i −0.265160 0.0358536i
\(250\) −0.221086 + 0.260283i −0.000884345 + 0.00104113i
\(251\) −165.258 + 87.6142i −0.658398 + 0.349061i −0.763878 0.645361i \(-0.776707\pi\)
0.105480 + 0.994421i \(0.466362\pi\)
\(252\) −757.150 + 211.876i −3.00456 + 0.840779i
\(253\) 400.577 + 134.970i 1.58331 + 0.533478i
\(254\) 226.694 + 62.9413i 0.892496 + 0.247800i
\(255\) 86.0167 86.1913i 0.337320 0.338005i
\(256\) −113.114 + 283.893i −0.441850 + 1.10896i
\(257\) 225.788 191.786i 0.878552 0.746249i −0.0897675 0.995963i \(-0.528612\pi\)
0.968320 + 0.249714i \(0.0803365\pi\)
\(258\) 244.803 + 382.136i 0.948849 + 1.48115i
\(259\) −71.1506 256.261i −0.274713 0.989426i
\(260\) −126.583 273.604i −0.486857 1.05232i
\(261\) 328.817 + 35.0864i 1.25983 + 0.134431i
\(262\) −265.780 58.5027i −1.01443 0.223293i
\(263\) 202.298 437.261i 0.769195 1.66259i 0.0203946 0.999792i \(-0.493508\pi\)
0.748800 0.662796i \(-0.230630\pi\)
\(264\) 967.725 481.170i 3.66562 1.82261i
\(265\) 453.272 + 272.724i 1.71046 + 1.02915i
\(266\) −378.847 + 629.649i −1.42424 + 2.36710i
\(267\) −98.9868 199.081i −0.370737 0.745622i
\(268\) −81.6548 37.7775i −0.304682 0.140961i
\(269\) 6.59144 29.9452i 0.0245035 0.111321i −0.962781 0.270281i \(-0.912883\pi\)
0.987285 + 0.158961i \(0.0508143\pi\)
\(270\) −632.500 + 360.144i −2.34259 + 1.33387i
\(271\) 284.934 131.824i 1.05142 0.486436i 0.183433 0.983032i \(-0.441279\pi\)
0.867982 + 0.496596i \(0.165417\pi\)
\(272\) −291.805 + 81.0191i −1.07281 + 0.297864i
\(273\) −84.8378 + 54.3485i −0.310761 + 0.199079i
\(274\) −213.542 251.401i −0.779350 0.917521i
\(275\) −336.284 133.988i −1.22285 0.487228i
\(276\) 653.098 + 651.775i 2.36630 + 2.36150i
\(277\) 29.0757 104.721i 0.104966 0.378055i −0.892343 0.451357i \(-0.850940\pi\)
0.997310 + 0.0733023i \(0.0233538\pi\)
\(278\) −103.317 + 306.635i −0.371645 + 1.10300i
\(279\) 335.951 94.0106i 1.20413 0.336956i
\(280\) −684.071 1290.29i −2.44311 4.60819i
\(281\) −73.8138 62.6980i −0.262682 0.223124i 0.506360 0.862322i \(-0.330991\pi\)
−0.769042 + 0.639198i \(0.779267\pi\)
\(282\) 64.5921 477.701i 0.229050 1.69397i
\(283\) −232.132 25.2459i −0.820256 0.0892082i −0.311638 0.950201i \(-0.600878\pi\)
−0.508618 + 0.860993i \(0.669843\pi\)
\(284\) −123.823 83.9541i −0.435997 0.295613i
\(285\) −144.227 + 471.425i −0.506059 + 1.65412i
\(286\) 162.134 153.582i 0.566902 0.536998i
\(287\) −212.102 + 11.4998i −0.739030 + 0.0400690i
\(288\) 914.048 1.85363i 3.17378 0.00643621i
\(289\) 203.846 + 154.959i 0.705348 + 0.536192i
\(290\) 107.090 + 984.674i 0.369275 + 3.39543i
\(291\) 167.527 22.9982i 0.575695 0.0790316i
\(292\) 34.3331 + 86.1697i 0.117579 + 0.295102i
\(293\) −102.601 170.525i −0.350175 0.581996i 0.630843 0.775910i \(-0.282709\pi\)
−0.981018 + 0.193915i \(0.937882\pi\)
\(294\) −183.999 + 132.450i −0.625848 + 0.450509i
\(295\) −199.990 366.194i −0.677932 1.24134i
\(296\) 797.989i 2.69591i
\(297\) −291.652 260.055i −0.981992 0.875607i
\(298\) 197.168 + 494.855i 0.661638 + 1.66059i
\(299\) 104.465 + 55.3840i 0.349382 + 0.185231i
\(300\) −528.259 587.626i −1.76086 1.95875i
\(301\) 262.101 + 199.244i 0.870767 + 0.661940i
\(302\) 270.715 + 803.454i 0.896408 + 2.66044i
\(303\) −198.432 246.348i −0.654890 0.813031i
\(304\) 890.132 843.178i 2.92807 2.77361i
\(305\) 152.062 + 200.035i 0.498565 + 0.655851i
\(306\) 119.479 + 156.512i 0.390455 + 0.511478i
\(307\) −143.975 15.6582i −0.468974 0.0510040i −0.129419 0.991590i \(-0.541311\pi\)
−0.339555 + 0.940586i \(0.610277\pi\)
\(308\) 869.461 917.879i 2.82292 2.98013i
\(309\) −145.759 11.7200i −0.471713 0.0379289i
\(310\) 489.447 + 923.195i 1.57886 + 2.97805i
\(311\) −237.148 + 160.790i −0.762532 + 0.517010i −0.879369 0.476141i \(-0.842035\pi\)
0.116836 + 0.993151i \(0.462725\pi\)
\(312\) 288.900 89.0267i 0.925963 0.285342i
\(313\) −94.2240 + 339.364i −0.301035 + 1.08423i 0.646063 + 0.763284i \(0.276414\pi\)
−0.947098 + 0.320946i \(0.895999\pi\)
\(314\) −315.080 + 51.6548i −1.00344 + 0.164506i
\(315\) −341.021 + 403.135i −1.08261 + 1.27979i
\(316\) 208.297 + 245.226i 0.659168 + 0.776033i
\(317\) 164.821 + 8.93634i 0.519940 + 0.0281904i 0.312242 0.950003i \(-0.398920\pi\)
0.207698 + 0.978193i \(0.433403\pi\)
\(318\) −535.238 + 667.250i −1.68314 + 2.09827i
\(319\) −482.607 + 223.278i −1.51287 + 0.699930i
\(320\) 267.685 + 1216.11i 0.836517 + 3.80034i
\(321\) −226.899 + 97.8777i −0.706851 + 0.304915i
\(322\) 838.278 + 387.829i 2.60335 + 1.20444i
\(323\) 131.613 + 21.5768i 0.407470 + 0.0668013i
\(324\) −318.919 791.080i −0.984318 2.44161i
\(325\) −86.7625 52.2033i −0.266962 0.160626i
\(326\) 833.068 + 136.575i 2.55542 + 0.418940i
\(327\) −50.4812 261.649i −0.154377 0.800150i
\(328\) 622.437 + 137.009i 1.89767 + 0.417710i
\(329\) −75.1771 341.533i −0.228502 1.03809i
\(330\) 574.997 1019.43i 1.74242 3.08918i
\(331\) −135.973 489.732i −0.410796 1.47955i −0.822779 0.568362i \(-0.807577\pi\)
0.411983 0.911192i \(-0.364836\pi\)
\(332\) 233.518 + 12.6610i 0.703367 + 0.0381355i
\(333\) 267.812 107.336i 0.804241 0.322330i
\(334\) 53.8381 135.123i 0.161192 0.404561i
\(335\) −59.6270 + 9.77535i −0.177991 + 0.0291802i
\(336\) 1232.20 454.107i 3.66726 1.35151i
\(337\) 542.038 + 182.634i 1.60842 + 0.541940i 0.973115 0.230320i \(-0.0739772\pi\)
0.635307 + 0.772260i \(0.280874\pi\)
\(338\) −481.495 + 326.461i −1.42454 + 0.965862i
\(339\) 144.536 + 71.5007i 0.426359 + 0.210916i
\(340\) −276.705 + 325.763i −0.813839 + 0.958126i
\(341\) −385.784 + 407.267i −1.13133 + 1.19433i
\(342\) −724.182 333.261i −2.11749 0.974447i
\(343\) 135.828 200.331i 0.395999 0.584055i
\(344\) −597.824 786.425i −1.73786 2.28612i
\(345\) 608.681 + 116.156i 1.76429 + 0.336683i
\(346\) −55.6808 1026.97i −0.160927 2.96813i
\(347\) −88.1158 261.518i −0.253936 0.753655i −0.996478 0.0838557i \(-0.973277\pi\)
0.742542 0.669800i \(-0.233620\pi\)
\(348\) −1160.33 30.2551i −3.33427 0.0869399i
\(349\) −157.230 + 17.0998i −0.450517 + 0.0489967i −0.330565 0.943783i \(-0.607239\pi\)
−0.119952 + 0.992780i \(0.538274\pi\)
\(350\) −698.847 370.505i −1.99671 1.05859i
\(351\) −68.7375 84.9826i −0.195833 0.242116i
\(352\) −1259.44 + 757.778i −3.57795 + 2.15278i
\(353\) 328.101i 0.929464i −0.885451 0.464732i \(-0.846151\pi\)
0.885451 0.464732i \(-0.153849\pi\)
\(354\) 630.138 241.128i 1.78005 0.681152i
\(355\) −100.470 −0.283015
\(356\) 402.339 + 668.693i 1.13017 + 1.87835i
\(357\) 120.439 + 76.8110i 0.337363 + 0.215157i
\(358\) −272.819 + 514.591i −0.762063 + 1.43740i
\(359\) 33.1956 + 305.228i 0.0924668 + 0.850218i 0.944895 + 0.327374i \(0.106164\pi\)
−0.852428 + 0.522844i \(0.824871\pi\)
\(360\) 1309.52 891.761i 3.63757 2.47711i
\(361\) −169.590 + 57.1416i −0.469779 + 0.158287i
\(362\) 122.434 6.63820i 0.338216 0.0183376i
\(363\) 260.648 + 49.7400i 0.718039 + 0.137025i
\(364\) 281.539 214.020i 0.773458 0.587968i
\(365\) 51.5609 + 34.9591i 0.141263 + 0.0957785i
\(366\) −353.492 + 200.329i −0.965826 + 0.547348i
\(367\) 85.3082 + 80.8082i 0.232447 + 0.220186i 0.795054 0.606539i \(-0.207443\pi\)
−0.562606 + 0.826725i \(0.690201\pi\)
\(368\) −1174.58 997.699i −3.19180 2.71114i
\(369\) −37.7414 227.324i −0.102280 0.616054i
\(370\) 484.974 + 715.283i 1.31074 + 1.93320i
\(371\) −198.146 + 588.076i −0.534086 + 1.58511i
\(372\) −1148.97 + 423.434i −3.08863 + 1.13826i
\(373\) −32.1647 196.196i −0.0862324 0.525994i −0.994252 0.107066i \(-0.965854\pi\)
0.908020 0.418928i \(-0.137594\pi\)
\(374\) −294.143 117.197i −0.786479 0.313362i
\(375\) −0.260893 0.0646003i −0.000695714 0.000172267i
\(376\) −56.8074 + 1047.75i −0.151084 + 2.78657i
\(377\) −143.320 + 39.7927i −0.380160 + 0.105551i
\(378\) −572.111 633.816i −1.51352 1.67676i
\(379\) −42.5385 + 9.36343i −0.112239 + 0.0247056i −0.270735 0.962654i \(-0.587267\pi\)
0.158496 + 0.987360i \(0.449336\pi\)
\(380\) 371.994 1689.98i 0.978931 4.44733i
\(381\) 35.0772 + 181.809i 0.0920663 + 0.477189i
\(382\) 200.608 1223.66i 0.525153 3.20329i
\(383\) −234.618 + 389.939i −0.612581 + 1.01812i 0.382958 + 0.923766i \(0.374905\pi\)
−0.995539 + 0.0943512i \(0.969922\pi\)
\(384\) −792.132 + 65.3098i −2.06284 + 0.170078i
\(385\) 137.368 837.906i 0.356799 2.17638i
\(386\) −408.549 + 883.065i −1.05842 + 2.28773i
\(387\) −183.519 + 306.415i −0.474209 + 0.791771i
\(388\) −579.671 + 127.595i −1.49400 + 0.328853i
\(389\) −272.470 588.934i −0.700437 1.51397i −0.850886 0.525351i \(-0.823934\pi\)
0.150449 0.988618i \(-0.451928\pi\)
\(390\) 204.852 255.377i 0.525262 0.654814i
\(391\) 9.07575 167.392i 0.0232116 0.428113i
\(392\) 376.122 319.481i 0.959495 0.815002i
\(393\) −51.9009 207.798i −0.132063 0.528749i
\(394\) −232.731 1419.60i −0.590689 3.60304i
\(395\) 208.208 + 57.8087i 0.527109 + 0.146351i
\(396\) 1093.58 + 827.826i 2.76157 + 2.09047i
\(397\) 89.7013 + 132.299i 0.225948 + 0.333248i 0.923718 0.383074i \(-0.125135\pi\)
−0.697770 + 0.716322i \(0.745824\pi\)
\(398\) 1159.89 614.934i 2.91429 1.54506i
\(399\) −576.469 46.3520i −1.44478 0.116170i
\(400\) 958.152 + 907.610i 2.39538 + 2.26902i
\(401\) −27.8575 + 256.146i −0.0694702 + 0.638768i 0.906702 + 0.421771i \(0.138592\pi\)
−0.976172 + 0.216996i \(0.930374\pi\)
\(402\) −2.74484 97.6670i −0.00682796 0.242953i
\(403\) −124.920 + 94.9619i −0.309976 + 0.235637i
\(404\) 763.572 + 806.093i 1.89003 + 1.99528i
\(405\) −475.424 319.539i −1.17389 0.788984i
\(406\) −1101.11 + 371.006i −2.71208 + 0.913807i
\(407\) −280.773 + 369.351i −0.689861 + 0.907497i
\(408\) −286.543 318.745i −0.702311 0.781238i
\(409\) −136.979 + 258.371i −0.334913 + 0.631713i −0.992580 0.121596i \(-0.961199\pi\)
0.657667 + 0.753309i \(0.271544\pi\)
\(410\) 641.192 255.474i 1.56388 0.623108i
\(411\) 102.341 238.576i 0.249006 0.580477i
\(412\) 513.276 1.24582
\(413\) 369.104 321.470i 0.893715 0.778377i
\(414\) −318.018 + 950.209i −0.768160 + 2.29519i
\(415\) 134.577 80.9720i 0.324281 0.195113i
\(416\) −381.941 + 152.179i −0.918127 + 0.365815i
\(417\) −252.292 + 34.6347i −0.605017 + 0.0830569i
\(418\) 1274.39 138.599i 3.04879 0.331576i
\(419\) −134.681 + 177.170i −0.321435 + 0.422840i −0.928224 0.372023i \(-0.878664\pi\)
0.606789 + 0.794863i \(0.292457\pi\)
\(420\) 1079.74 1506.42i 2.57082 3.58670i
\(421\) −7.87864 145.313i −0.0187141 0.345161i −0.992863 0.119257i \(-0.961949\pi\)
0.974149 0.225905i \(-0.0725338\pi\)
\(422\) −687.654 725.947i −1.62951 1.72025i
\(423\) 359.275 121.866i 0.849350 0.288099i
\(424\) 1044.91 1541.13i 2.46442 3.63474i
\(425\) −15.5217 + 142.720i −0.0365217 + 0.335811i
\(426\) 21.7693 160.998i 0.0511016 0.377930i
\(427\) −190.827 + 224.658i −0.446901 + 0.526132i
\(428\) 766.334 406.285i 1.79050 0.949263i
\(429\) 165.042 + 60.4437i 0.384714 + 0.140894i
\(430\) −1013.81 341.592i −2.35770 0.794400i
\(431\) −263.121 73.0552i −0.610490 0.169502i −0.0514954 0.998673i \(-0.516399\pi\)
−0.558994 + 0.829172i \(0.688813\pi\)
\(432\) 636.862 + 1274.36i 1.47422 + 2.94991i
\(433\) 167.008 419.159i 0.385701 0.968036i −0.600071 0.799947i \(-0.704861\pi\)
0.985772 0.168089i \(-0.0537596\pi\)
\(434\) −934.248 + 793.557i −2.15264 + 1.82847i
\(435\) −656.390 + 420.494i −1.50894 + 0.966653i
\(436\) 250.231 + 901.250i 0.573924 + 2.06709i
\(437\) 284.977 + 615.968i 0.652122 + 1.40954i
\(438\) −67.1920 + 75.0487i −0.153406 + 0.171344i
\(439\) 811.467 + 178.617i 1.84844 + 0.406873i 0.993690 0.112159i \(-0.0357766\pi\)
0.854755 + 0.519032i \(0.173708\pi\)
\(440\) −1069.74 + 2312.20i −2.43122 + 5.25501i
\(441\) −157.812 83.2570i −0.357850 0.188791i
\(442\) −75.8902 45.6616i −0.171697 0.103307i
\(443\) 29.1589 48.4624i 0.0658214 0.109396i −0.822199 0.569200i \(-0.807253\pi\)
0.888020 + 0.459804i \(0.152080\pi\)
\(444\) −906.818 + 450.887i −2.04238 + 1.01551i
\(445\) 475.668 + 220.068i 1.06892 + 0.494534i
\(446\) 254.761 1157.39i 0.571213 2.59505i
\(447\) −279.644 + 312.343i −0.625602 + 0.698753i
\(448\) −1325.75 + 613.359i −2.95927 + 1.36910i
\(449\) 135.466 37.6119i 0.301706 0.0837681i −0.113377 0.993552i \(-0.536167\pi\)
0.415082 + 0.909784i \(0.363753\pi\)
\(450\) 315.999 797.798i 0.702219 1.77288i
\(451\) 239.890 + 282.420i 0.531906 + 0.626208i
\(452\) −525.813 209.503i −1.16330 0.463503i
\(453\) −471.348 + 472.305i −1.04050 + 1.04261i
\(454\) −416.483 + 1500.04i −0.917363 + 3.30404i
\(455\) 75.8366 225.075i 0.166674 0.494670i
\(456\) 1629.42 + 596.745i 3.57329 + 1.30865i
\(457\) −57.6721 108.781i −0.126197 0.238033i 0.812361 0.583155i \(-0.198182\pi\)
−0.938558 + 0.345123i \(0.887837\pi\)
\(458\) 486.694 + 413.402i 1.06265 + 0.902624i
\(459\) −68.4313 + 139.040i −0.149088 + 0.302920i
\(460\) −2162.31 235.166i −4.70068 0.511230i
\(461\) −506.580 343.470i −1.09887 0.745053i −0.129728 0.991550i \(-0.541410\pi\)
−0.969144 + 0.246496i \(0.920721\pi\)
\(462\) 1312.93 + 401.677i 2.84185 + 0.869430i
\(463\) −275.654 + 261.113i −0.595364 + 0.563959i −0.924913 0.380180i \(-0.875862\pi\)
0.329548 + 0.944139i \(0.393103\pi\)
\(464\) 1935.86 104.959i 4.17210 0.226205i
\(465\) −479.088 + 668.404i −1.03030 + 1.43743i
\(466\) −754.965 573.909i −1.62010 1.23157i
\(467\) −6.29970 57.9248i −0.0134897 0.124036i 0.985457 0.169926i \(-0.0543530\pi\)
−0.998946 + 0.0458904i \(0.985387\pi\)
\(468\) 264.405 + 277.998i 0.564968 + 0.594012i
\(469\) −26.2362 65.8478i −0.0559406 0.140400i
\(470\) 585.845 + 973.682i 1.24648 + 2.07166i
\(471\) −146.805 203.942i −0.311688 0.432997i
\(472\) −1325.16 + 633.117i −2.80755 + 1.34135i
\(473\) 574.343i 1.21426i
\(474\) −137.748 + 321.116i −0.290608 + 0.677460i
\(475\) −215.131 539.939i −0.452908 1.13671i
\(476\) −442.997 234.862i −0.930665 0.493408i
\(477\) −657.766 143.387i −1.37896 0.300602i
\(478\) −1060.23 805.965i −2.21805 1.68612i
\(479\) −29.7920 88.4195i −0.0621962 0.184592i 0.912050 0.410079i \(-0.134499\pi\)
−0.974246 + 0.225488i \(0.927602\pi\)
\(480\) −1678.04 + 1351.65i −3.49592 + 2.81594i
\(481\) −94.2177 + 89.2478i −0.195879 + 0.185546i
\(482\) −341.153 448.779i −0.707786 0.931076i
\(483\) 20.4215 + 726.640i 0.0422806 + 1.50443i
\(484\) −925.942 100.702i −1.91310 0.208063i
\(485\) −274.131 + 289.396i −0.565218 + 0.596693i
\(486\) 615.055 692.605i 1.26554 1.42511i
\(487\) −342.417 645.867i −0.703115 1.32622i −0.935408 0.353570i \(-0.884968\pi\)
0.232293 0.972646i \(-0.425377\pi\)
\(488\) 732.034 496.331i 1.50007 1.01707i
\(489\) 195.658 + 634.930i 0.400119 + 1.29843i
\(490\) 142.976 514.955i 0.291789 1.05093i
\(491\) 41.3865 6.78498i 0.0842903 0.0138187i −0.119489 0.992835i \(-0.538126\pi\)
0.203780 + 0.979017i \(0.434677\pi\)
\(492\) 196.001 + 784.738i 0.398375 + 1.59500i
\(493\) 136.525 + 160.729i 0.276926 + 0.326023i
\(494\) 358.049 + 19.4128i 0.724795 + 0.0392973i
\(495\) 919.883 + 48.0039i 1.85835 + 0.0969775i
\(496\) 1856.21 858.776i 3.74237 1.73140i
\(497\) −25.3367 115.106i −0.0509793 0.231601i
\(498\) 100.594 + 233.196i 0.201996 + 0.468265i
\(499\) 415.654 + 192.302i 0.832975 + 0.385375i 0.789553 0.613682i \(-0.210312\pi\)
0.0434211 + 0.999057i \(0.486174\pi\)
\(500\) 0.930979 + 0.152626i 0.00186196 + 0.000305252i
\(501\) 114.088 9.40634i 0.227721 0.0187751i
\(502\) 610.934 + 367.587i 1.21700 + 0.732244i
\(503\) 381.680 + 62.5732i 0.758807 + 0.124400i 0.528750 0.848777i \(-0.322661\pi\)
0.230056 + 0.973177i \(0.426109\pi\)
\(504\) 1351.90 + 1275.40i 2.68235 + 2.53055i
\(505\) 728.250 + 160.300i 1.44208 + 0.317426i
\(506\) −346.378 1573.61i −0.684542 3.10991i
\(507\) −398.776 224.925i −0.786541 0.443639i
\(508\) −173.875 626.240i −0.342273 1.23276i
\(509\) 598.316 + 32.4397i 1.17547 + 0.0637323i 0.631504 0.775373i \(-0.282438\pi\)
0.543969 + 0.839105i \(0.316921\pi\)
\(510\) −450.560 111.564i −0.883452 0.218754i
\(511\) −27.0490 + 67.8878i −0.0529334 + 0.132853i
\(512\) 103.749 17.0088i 0.202635 0.0332203i
\(513\) −18.8973 627.114i −0.0368368 1.22245i
\(514\) −1070.14 360.570i −2.08197 0.701499i
\(515\) 285.313 193.447i 0.554006 0.375625i
\(516\) 555.888 1123.71i 1.07730 2.17773i
\(517\) −394.946 + 464.966i −0.763918 + 0.899354i
\(518\) −697.177 + 736.001i −1.34590 + 1.42085i
\(519\) 704.211 399.086i 1.35686 0.768953i
\(520\) −399.921 + 589.839i −0.769078 + 1.13431i
\(521\) 115.593 + 152.060i 0.221867 + 0.291861i 0.893537 0.448989i \(-0.148216\pi\)
−0.671670 + 0.740850i \(0.734423\pi\)
\(522\) −531.596 1142.94i −1.01838 2.18954i
\(523\) 30.8441 + 568.886i 0.0589753 + 1.08774i 0.866910 + 0.498464i \(0.166102\pi\)
−0.807935 + 0.589271i \(0.799415\pi\)
\(524\) 240.049 + 712.439i 0.458108 + 1.35962i
\(525\) 16.2265 622.311i 0.0309077 1.18535i
\(526\) −1825.74 + 198.562i −3.47100 + 0.377494i
\(527\) 196.560 + 104.209i 0.372979 + 0.197741i
\(528\) −1931.50 1231.84i −3.65815 2.33302i
\(529\) 277.692 167.082i 0.524939 0.315845i
\(530\) 2016.44i 3.80461i
\(531\) 390.724 + 359.577i 0.735827 + 0.677169i
\(532\) 2029.97 3.81574
\(533\) 53.4374 + 88.8136i 0.100258 + 0.166630i
\(534\) −455.711 + 714.549i −0.853391 + 1.33811i
\(535\) 272.856 514.661i 0.510012 0.961984i
\(536\) 22.9946 + 211.432i 0.0429005 + 0.394463i
\(537\) −458.234 11.9483i −0.853322 0.0222501i
\(538\) −110.761 + 37.3197i −0.205875 + 0.0693675i
\(539\) 286.499 15.5335i 0.531537 0.0288191i
\(540\) 1753.30 + 984.245i 3.24685 + 1.82268i
\(541\) −205.385 + 156.130i −0.379640 + 0.288595i −0.777540 0.628834i \(-0.783532\pi\)
0.397899 + 0.917429i \(0.369739\pi\)
\(542\) −990.521 671.590i −1.82753 1.23910i
\(543\) 47.5786 + 83.9552i 0.0876218 + 0.154614i
\(544\) 423.193 + 400.870i 0.777929 + 0.736893i
\(545\) 478.764 + 406.666i 0.878466 + 0.746176i
\(546\) 344.238 + 170.292i 0.630473 + 0.311890i
\(547\) 272.540 + 401.966i 0.498245 + 0.734856i 0.990787 0.135433i \(-0.0432425\pi\)
−0.492542 + 0.870289i \(0.663932\pi\)
\(548\) −290.952 + 863.514i −0.530934 + 1.57576i
\(549\) −265.037 178.916i −0.482764 0.325895i
\(550\) 223.237 + 1361.69i 0.405886 + 2.47580i
\(551\) −793.149 316.020i −1.43947 0.573538i
\(552\) 524.240 2117.18i 0.949710 3.83547i
\(553\) −13.7236 + 253.116i −0.0248165 + 0.457714i
\(554\) −399.182 + 110.832i −0.720544 + 0.200058i
\(555\) −334.137 + 592.401i −0.602048 + 1.06739i
\(556\) 872.970 192.155i 1.57009 0.345603i
\(557\) 56.9539 258.744i 0.102251 0.464531i −0.897474 0.441068i \(-0.854600\pi\)
0.999725 0.0234633i \(-0.00746928\pi\)
\(558\) −967.275 912.537i −1.73347 1.63537i
\(559\) 25.9911 158.539i 0.0464957 0.283611i
\(560\) −1595.98 + 2652.54i −2.84997 + 4.73669i
\(561\) −20.4762 248.352i −0.0364994 0.442696i
\(562\) −59.7250 + 364.306i −0.106272 + 0.648232i
\(563\) −3.60470 + 7.79144i −0.00640267 + 0.0138391i −0.910750 0.412957i \(-0.864496\pi\)
0.904348 + 0.426796i \(0.140358\pi\)
\(564\) −1222.74 + 527.454i −2.16798 + 0.935202i
\(565\) −371.241 + 81.7163i −0.657064 + 0.144631i
\(566\) 373.731 + 807.807i 0.660303 + 1.42722i
\(567\) 246.193 625.261i 0.434203 1.10275i
\(568\) −19.1456 + 353.120i −0.0337071 + 0.621691i
\(569\) −125.612 + 106.696i −0.220760 + 0.187515i −0.750941 0.660369i \(-0.770400\pi\)
0.530181 + 0.847884i \(0.322124\pi\)
\(570\) 1823.21 455.375i 3.19861 0.798904i
\(571\) −149.850 914.043i −0.262434 1.60078i −0.708456 0.705755i \(-0.750608\pi\)
0.446022 0.895022i \(-0.352840\pi\)
\(572\) −594.450 165.048i −1.03925 0.288546i
\(573\) 932.620 287.394i 1.62761 0.501560i
\(574\) 454.386 + 670.169i 0.791613 + 1.16754i
\(575\) −645.458 + 342.200i −1.12254 + 0.595131i
\(576\) −819.753 1356.21i −1.42318 2.35453i
\(577\) −58.8043 55.7024i −0.101914 0.0965380i 0.635046 0.772474i \(-0.280981\pi\)
−0.736960 + 0.675936i \(0.763740\pi\)
\(578\) 105.530 970.332i 0.182578 1.67877i
\(579\) −765.463 + 21.5126i −1.32204 + 0.0371548i
\(580\) 2178.26 1655.87i 3.75563 2.85495i
\(581\) 126.705 + 133.761i 0.218081 + 0.230225i
\(582\) −404.344 501.983i −0.694749 0.862514i
\(583\) 1025.89 345.662i 1.75967 0.592902i
\(584\) 132.695 174.558i 0.227218 0.298900i
\(585\) 251.747 + 54.8788i 0.430338 + 0.0938099i
\(586\) −355.336 + 670.235i −0.606376 + 1.14375i
\(587\) 373.465 148.802i 0.636227 0.253496i −0.0296466 0.999560i \(-0.509438\pi\)
0.665874 + 0.746064i \(0.268059\pi\)
\(588\) 575.571 + 246.901i 0.978862 + 0.419900i
\(589\) −900.710 −1.52922
\(590\) −803.045 + 1372.86i −1.36109 + 2.32688i
\(591\) 918.863 661.432i 1.55476 1.11917i
\(592\) 1449.38 872.066i 2.44828 1.47308i
\(593\) −19.3592 + 7.71340i −0.0326462 + 0.0130074i −0.386404 0.922330i \(-0.626283\pi\)
0.353758 + 0.935337i \(0.384904\pi\)
\(594\) −276.238 + 1463.66i −0.465047 + 2.46407i
\(595\) −334.763 + 36.4077i −0.562628 + 0.0611894i
\(596\) 890.542 1171.49i 1.49420 1.96558i
\(597\) 839.774 + 601.919i 1.40666 + 1.00824i
\(598\) −24.4008 450.047i −0.0408041 0.752587i
\(599\) 410.926 + 433.809i 0.686020 + 0.724223i 0.972252 0.233938i \(-0.0751612\pi\)
−0.286231 + 0.958161i \(0.592403\pi\)
\(600\) −546.447 + 1786.14i −0.910746 + 2.97689i
\(601\) −126.261 + 186.221i −0.210085 + 0.309852i −0.918103 0.396342i \(-0.870279\pi\)
0.708018 + 0.706195i \(0.249590\pi\)
\(602\) 135.688 1247.63i 0.225396 2.07248i
\(603\) 67.8655 36.1565i 0.112546 0.0599611i
\(604\) 1516.27 1785.09i 2.51038 2.95545i
\(605\) −552.654 + 292.998i −0.913477 + 0.484295i
\(606\) −414.664 + 1132.25i −0.684265 + 1.86839i
\(607\) −605.657 204.069i −0.997787 0.336194i −0.227422 0.973796i \(-0.573030\pi\)
−0.770365 + 0.637603i \(0.779926\pi\)
\(608\) −2273.95 631.360i −3.74006 1.03842i
\(609\) −647.277 645.966i −1.06285 1.06070i
\(610\) 354.520 889.779i 0.581181 1.45865i
\(611\) −130.060 + 110.474i −0.212864 + 0.180809i
\(612\) 200.310 505.721i 0.327305 0.826342i
\(613\) 110.312 + 397.308i 0.179954 + 0.648137i 0.997396 + 0.0721250i \(0.0229781\pi\)
−0.817441 + 0.576012i \(0.804608\pi\)
\(614\) 231.799 + 501.025i 0.377522 + 0.816001i
\(615\) 404.708 + 362.339i 0.658061 + 0.589170i
\(616\) −2918.79 642.474i −4.73830 1.04298i
\(617\) 188.286 406.974i 0.305164 0.659601i −0.692950 0.720985i \(-0.743690\pi\)
0.998114 + 0.0613845i \(0.0195516\pi\)
\(618\) 248.168 + 499.113i 0.401566 + 0.807626i
\(619\) 767.369 + 461.710i 1.23969 + 0.745897i 0.975802 0.218656i \(-0.0701673\pi\)
0.263889 + 0.964553i \(0.414995\pi\)
\(620\) 1488.18 2473.38i 2.40029 3.98932i
\(621\) −781.058 + 108.838i −1.25774 + 0.175263i
\(622\) 991.220 + 458.587i 1.59360 + 0.737278i
\(623\) −132.170 + 600.456i −0.212151 + 0.963814i
\(624\) −477.417 427.437i −0.765092 0.684996i
\(625\) −566.947 + 262.298i −0.907115 + 0.419676i
\(626\) 1293.60 359.168i 2.06646 0.573750i
\(627\) 544.215 + 849.518i 0.867967 + 1.35489i
\(628\) 571.011 + 672.246i 0.909253 + 1.07046i
\(629\) 170.930 + 68.1045i 0.271748 + 0.108274i
\(630\) 1986.90 + 321.600i 3.15381 + 0.510476i
\(631\) −53.2387 + 191.748i −0.0843719 + 0.303880i −0.993681 0.112241i \(-0.964197\pi\)
0.909309 + 0.416121i \(0.136611\pi\)
\(632\) 242.855 720.767i 0.384264 1.14045i
\(633\) 270.634 738.969i 0.427541 1.16741i
\(634\) −294.721 555.902i −0.464859 0.876818i
\(635\) −332.673 282.575i −0.523894 0.445000i
\(636\) 2341.71 + 316.634i 3.68194 + 0.497852i
\(637\) 79.7865 + 8.67731i 0.125254 + 0.0136221i
\(638\) 1677.70 + 1137.51i 2.62962 + 1.78293i
\(639\) 121.085 41.0721i 0.189492 0.0642755i
\(640\) 1360.26 1288.51i 2.12540 2.01329i
\(641\) −259.349 + 14.0615i −0.404600 + 0.0219368i −0.255316 0.966858i \(-0.582180\pi\)
−0.149284 + 0.988794i \(0.547697\pi\)
\(642\) 765.595 + 548.750i 1.19252 + 0.854751i
\(643\) 567.093 + 431.093i 0.881949 + 0.670440i 0.944823 0.327582i \(-0.106234\pi\)
−0.0628744 + 0.998021i \(0.520027\pi\)
\(644\) −275.872 2536.60i −0.428373 3.93883i
\(645\) −114.511 834.138i −0.177536 1.29324i
\(646\) −188.173 472.278i −0.291289 0.731081i
\(647\) −72.8889 121.142i −0.112657 0.187237i 0.795399 0.606086i \(-0.207261\pi\)
−0.908056 + 0.418849i \(0.862434\pi\)
\(648\) −1213.67 + 1610.07i −1.87295 + 2.48467i
\(649\) −836.117 173.220i −1.28832 0.266904i
\(650\) 385.975i 0.593808i
\(651\) −886.588 380.318i −1.36189 0.584205i
\(652\) −863.186 2166.43i −1.32391 3.32275i
\(653\) 293.699 + 155.709i 0.449769 + 0.238452i 0.677865 0.735186i \(-0.262905\pi\)
−0.228096 + 0.973639i \(0.573250\pi\)
\(654\) −755.395 + 679.079i −1.15504 + 1.03835i
\(655\) 401.944 + 305.550i 0.613654 + 0.466488i
\(656\) −431.369 1280.26i −0.657574 1.95161i
\(657\) −76.4317 21.0543i −0.116334 0.0320461i
\(658\) −967.780 + 916.730i −1.47079 + 1.39321i
\(659\) 200.834 + 264.193i 0.304756 + 0.400900i 0.922822 0.385227i \(-0.125877\pi\)
−0.618066 + 0.786126i \(0.712084\pi\)
\(660\) −3231.97 + 90.8314i −4.89692 + 0.137623i
\(661\) 1131.72 + 123.082i 1.71213 + 0.186206i 0.911036 0.412327i \(-0.135284\pi\)
0.801098 + 0.598533i \(0.204249\pi\)
\(662\) −1332.35 + 1406.55i −2.01262 + 2.12469i
\(663\) 5.58670 69.4805i 0.00842640 0.104797i
\(664\) −258.945 488.423i −0.389978 0.735576i
\(665\) 1128.40 765.071i 1.69683 1.15048i
\(666\) −876.890 663.793i −1.31665 0.996686i
\(667\) −287.101 + 1034.05i −0.430437 + 1.55029i
\(668\) −396.522 + 65.0065i −0.593596 + 0.0973151i
\(669\) 904.897 226.012i 1.35261 0.337836i
\(670\) 149.108 + 175.544i 0.222550 + 0.262006i
\(671\) 513.458 + 27.8389i 0.765213 + 0.0414886i
\(672\) −1971.71 1581.62i −2.93410 2.35360i
\(673\) −773.318 + 357.775i −1.14906 + 0.531613i −0.899575 0.436766i \(-0.856124\pi\)
−0.249486 + 0.968378i \(0.580262\pi\)
\(674\) −468.700 2129.33i −0.695401 3.15924i
\(675\) 672.944 56.8572i 0.996955 0.0842329i
\(676\) 1458.50 + 674.776i 2.15755 + 0.998190i
\(677\) −961.261 157.591i −1.41988 0.232778i −0.597572 0.801815i \(-0.703868\pi\)
−0.822312 + 0.569037i \(0.807316\pi\)
\(678\) −50.5076 612.599i −0.0744950 0.903538i
\(679\) −400.683 241.083i −0.590108 0.355056i
\(680\) 997.058 + 163.459i 1.46626 + 0.240381i
\(681\) −1203.03 + 232.106i −1.76656 + 0.340831i
\(682\) 2088.37 + 459.685i 3.06213 + 0.674025i
\(683\) 111.185 + 505.119i 0.162789 + 0.739559i 0.985303 + 0.170814i \(0.0546398\pi\)
−0.822514 + 0.568745i \(0.807429\pi\)
\(684\) 242.540 + 2188.82i 0.354591 + 3.20002i
\(685\) 163.717 + 589.655i 0.239003 + 0.860810i
\(686\) −921.254 49.9489i −1.34294 0.0728118i
\(687\) −120.794 + 487.835i −0.175828 + 0.710094i
\(688\) −775.060 + 1945.25i −1.12654 + 2.82740i
\(689\) 298.823 48.9896i 0.433706 0.0711025i
\(690\) −816.799 2216.35i −1.18377 3.21210i
\(691\) −828.120 279.026i −1.19844 0.403800i −0.351853 0.936055i \(-0.614448\pi\)
−0.846584 + 0.532255i \(0.821345\pi\)
\(692\) −2351.60 + 1594.43i −3.39827 + 2.30408i
\(693\) 176.981 + 1065.99i 0.255383 + 1.53822i
\(694\) −681.008 + 801.745i −0.981279 + 1.15525i
\(695\) 412.834 435.824i 0.594006 0.627084i
\(696\) 1352.82 + 2387.12i 1.94370 + 3.42978i
\(697\) 82.4693 121.633i 0.118320 0.174509i
\(698\) 364.843 + 479.943i 0.522698 + 0.687597i
\(699\) 139.905 733.130i 0.200150 1.04883i
\(700\) 118.299 + 2181.89i 0.168998 + 3.11699i
\(701\) 265.566 + 788.173i 0.378839 + 1.12436i 0.952311 + 0.305130i \(0.0986998\pi\)
−0.573471 + 0.819226i \(0.694404\pi\)
\(702\) −142.487 + 391.520i −0.202973 + 0.557721i
\(703\) −740.562 + 80.5410i −1.05343 + 0.114568i
\(704\) 2251.43 + 1193.63i 3.19806 + 1.69550i
\(705\) −480.889 + 754.028i −0.682113 + 1.06954i
\(706\) −1071.65 + 644.788i −1.51791 + 0.913298i
\(707\) 874.759i 1.23728i
\(708\) −1468.21 1148.16i −2.07375 1.62169i
\(709\) −751.430 −1.05985 −0.529923 0.848046i \(-0.677779\pi\)
−0.529923 + 0.848046i \(0.677779\pi\)
\(710\) 197.446 + 328.157i 0.278092 + 0.462193i
\(711\) −274.561 + 15.4448i −0.386162 + 0.0217226i
\(712\) 864.109 1629.88i 1.21364 2.28916i
\(713\) 122.406 + 1125.50i 0.171677 + 1.57855i
\(714\) 14.1932 544.328i 0.0198784 0.762364i
\(715\) −392.640 + 132.296i −0.549146 + 0.185029i
\(716\) 1606.62 87.1083i 2.24388 0.121660i
\(717\) 196.474 1029.57i 0.274023 1.43594i
\(718\) 931.704 708.263i 1.29764 0.986438i
\(719\) 828.719 + 561.885i 1.15260 + 0.781481i 0.979105 0.203354i \(-0.0651841\pi\)
0.173494 + 0.984835i \(0.444494\pi\)
\(720\) −3050.79 1403.94i −4.23721 1.94992i
\(721\) 293.577 + 278.091i 0.407180 + 0.385702i
\(722\) 519.918 + 441.622i 0.720108 + 0.611665i
\(723\) 196.722 397.666i 0.272091 0.550022i
\(724\) −190.086 280.355i −0.262549 0.387231i
\(725\) 293.448 870.922i 0.404756 1.20127i
\(726\) −349.768 949.081i −0.481774 1.30727i
\(727\) −81.9732 500.015i −0.112755 0.687778i −0.981346 0.192248i \(-0.938422\pi\)
0.868591 0.495530i \(-0.165026\pi\)
\(728\) −776.613 309.431i −1.06678 0.425043i
\(729\) 703.601 + 190.751i 0.965160 + 0.261661i
\(730\) 12.8558 237.111i 0.0176107 0.324809i
\(731\) −219.474 + 60.9366i −0.300238 + 0.0833606i
\(732\) 977.639 + 551.426i 1.33557 + 0.753314i
\(733\) 417.605 91.9219i 0.569721 0.125405i 0.0792378 0.996856i \(-0.474751\pi\)
0.490483 + 0.871451i \(0.336820\pi\)
\(734\) 96.2878 437.440i 0.131182 0.595967i
\(735\) 412.994 79.6809i 0.561897 0.108409i
\(736\) −479.903 + 2927.28i −0.652042 + 3.97728i
\(737\) −63.7495 + 105.953i −0.0864987 + 0.143762i
\(738\) −668.318 + 570.012i −0.905580 + 0.772374i
\(739\) −190.474 + 1161.84i −0.257745 + 1.57218i 0.467693 + 0.883891i \(0.345085\pi\)
−0.725439 + 0.688287i \(0.758363\pi\)
\(740\) 1002.41 2166.68i 1.35461 2.92794i
\(741\) 111.779 + 259.124i 0.150848 + 0.349695i
\(742\) 2310.18 508.509i 3.11345 0.685322i
\(743\) 200.802 + 434.026i 0.270258 + 0.584154i 0.994422 0.105474i \(-0.0336360\pi\)
−0.724164 + 0.689628i \(0.757774\pi\)
\(744\) 2257.93 + 1811.21i 3.03485 + 2.43442i
\(745\) 53.5040 986.824i 0.0718175 1.32460i
\(746\) −577.606 + 490.623i −0.774271 + 0.657672i
\(747\) −129.089 + 152.601i −0.172809 + 0.204285i
\(748\) 141.509 + 863.169i 0.189184 + 1.15397i
\(749\) 658.442 + 182.815i 0.879094 + 0.244079i
\(750\) 0.301712 + 0.979084i 0.000402283 + 0.00130545i
\(751\) −525.049 774.389i −0.699133 1.03114i −0.997065 0.0765568i \(-0.975607\pi\)
0.297932 0.954587i \(-0.403703\pi\)
\(752\) 1965.11 1041.83i 2.61317 1.38542i
\(753\) −44.9743 + 559.335i −0.0597268 + 0.742808i
\(754\) 411.627 + 389.913i 0.545924 + 0.517127i
\(755\) 170.066 1563.73i 0.225253 2.07117i
\(756\) −685.472 + 2256.91i −0.906709 + 2.98533i
\(757\) −1025.24 + 779.370i −1.35435 + 1.02955i −0.358991 + 0.933341i \(0.616879\pi\)
−0.995361 + 0.0962103i \(0.969328\pi\)
\(758\) 114.180 + 120.539i 0.150633 + 0.159022i
\(759\) 987.577 795.486i 1.30116 1.04807i
\(760\) −3876.43 + 1306.12i −5.10056 + 1.71858i
\(761\) 690.785 908.712i 0.907733 1.19410i −0.0727206 0.997352i \(-0.523168\pi\)
0.980454 0.196750i \(-0.0630388\pi\)
\(762\) 524.892 471.863i 0.688835 0.619243i
\(763\) −345.170 + 651.060i −0.452385 + 0.853289i
\(764\) −3182.18 + 1267.90i −4.16515 + 1.65955i
\(765\) −79.2539 356.608i −0.103600 0.466154i
\(766\) 1734.70 2.26462
\(767\) −222.959 85.6522i −0.290689 0.111672i
\(768\) 535.607 + 744.067i 0.697406 + 0.968838i
\(769\) 891.634 536.478i 1.15947 0.697631i 0.200100 0.979775i \(-0.435873\pi\)
0.959372 + 0.282144i \(0.0910457\pi\)
\(770\) −3006.74 + 1197.99i −3.90485 + 1.55584i
\(771\) −120.873 880.482i −0.156774 1.14200i
\(772\) 2672.13 290.612i 3.46131 0.376440i
\(773\) 493.522 649.217i 0.638451 0.839867i −0.357103 0.934065i \(-0.616235\pi\)
0.995554 + 0.0941977i \(0.0300286\pi\)
\(774\) 1361.47 2.76097i 1.75901 0.00356715i
\(775\) −52.4898 968.117i −0.0677287 1.24918i
\(776\) 964.894 + 1018.63i 1.24342 + 1.31266i
\(777\) −762.959 233.418i −0.981929 0.300410i
\(778\) −1388.12 + 2047.33i −1.78422 + 2.63152i
\(779\) −64.3264 + 591.472i −0.0825756 + 0.759270i
\(780\) −896.247 121.186i −1.14903 0.155366i
\(781\) −133.107 + 156.706i −0.170432 + 0.200648i
\(782\) −564.574 + 299.318i −0.721962 + 0.382760i
\(783\) 619.175 775.104i 0.790772 0.989916i
\(784\) −991.308 334.011i −1.26442 0.426034i
\(785\) 570.767 + 158.473i 0.727091 + 0.201876i
\(786\) −576.717 + 577.888i −0.733736 + 0.735226i
\(787\) 189.136 474.696i 0.240325 0.603171i −0.758498 0.651676i \(-0.774066\pi\)
0.998823 + 0.0485048i \(0.0154456\pi\)
\(788\) −3028.82 + 2572.70i −3.84368 + 3.26485i
\(789\) −779.664 1217.05i −0.988167 1.54253i
\(790\) −220.358 793.658i −0.278934 1.00463i
\(791\) −187.240 404.713i −0.236713 0.511647i
\(792\) 344.011 3223.94i 0.434357 4.07063i
\(793\) 140.472 + 30.9203i 0.177141 + 0.0389916i
\(794\) 255.836 552.980i 0.322211 0.696449i
\(795\) 1421.02 706.555i 1.78744 0.888748i
\(796\) −3107.51 1869.73i −3.90391 2.34891i
\(797\) −59.0416 + 98.1279i −0.0740798 + 0.123122i −0.891683 0.452661i \(-0.850475\pi\)
0.817603 + 0.575782i \(0.195302\pi\)
\(798\) 981.489 + 1973.96i 1.22994 + 2.47364i
\(799\) 219.580 + 101.589i 0.274819 + 0.127145i
\(800\) 546.092 2480.92i 0.682616 3.10115i
\(801\) −663.232 70.7702i −0.828005 0.0883523i
\(802\) 891.373 412.393i 1.11144 0.514206i
\(803\) 122.837 34.1054i 0.152972 0.0424725i
\(804\) −227.274 + 145.596i −0.282680 + 0.181089i
\(805\) −1109.36 1306.04i −1.37809 1.62241i
\(806\) 555.660 + 221.395i 0.689405 + 0.274684i
\(807\) −65.1100 64.9781i −0.0806816 0.0805181i
\(808\) 702.177 2529.01i 0.869031 3.12997i
\(809\) −64.1971 + 190.530i −0.0793537 + 0.235513i −0.979985 0.199070i \(-0.936208\pi\)
0.900632 + 0.434583i \(0.143104\pi\)
\(810\) −109.370 + 2180.80i −0.135025 + 2.69234i
\(811\) 587.696 + 1108.51i 0.724656 + 1.36685i 0.922262 + 0.386565i \(0.126339\pi\)
−0.197606 + 0.980282i \(0.563317\pi\)
\(812\) 2446.40 + 2077.99i 3.01281 + 2.55910i
\(813\) 126.204 933.357i 0.155232 1.14804i
\(814\) 1758.16 + 191.211i 2.15990 + 0.234903i
\(815\) −1296.32 878.925i −1.59057 1.07844i
\(816\) −265.793 + 868.781i −0.325727 + 1.06468i
\(817\) 669.491 634.176i 0.819451 0.776225i
\(818\) 1113.09 60.3498i 1.36074 0.0737773i
\(819\) 0.612961 + 302.259i 0.000748426 + 0.369059i
\(820\) −1517.92 1153.89i −1.85112 1.40718i
\(821\) −85.0369 781.901i −0.103577 0.952377i −0.924460 0.381280i \(-0.875483\pi\)
0.820882 0.571097i \(-0.193482\pi\)
\(822\) −980.362 + 134.584i −1.19265 + 0.163728i
\(823\) 316.614 + 794.642i 0.384707 + 0.965543i 0.986035 + 0.166540i \(0.0532595\pi\)
−0.601327 + 0.799003i \(0.705361\pi\)
\(824\) −625.534 1039.65i −0.759143 1.26171i
\(825\) −881.378 + 634.449i −1.06834 + 0.769029i
\(826\) −1775.36 573.815i −2.14934 0.694692i
\(827\) 385.594i 0.466256i −0.972446 0.233128i \(-0.925104\pi\)
0.972446 0.233128i \(-0.0748962\pi\)
\(828\) 2702.13 600.531i 3.26344 0.725279i
\(829\) −124.944 313.585i −0.150716 0.378269i 0.834161 0.551520i \(-0.185952\pi\)
−0.984878 + 0.173251i \(0.944573\pi\)
\(830\) −528.943 280.428i −0.637281 0.337865i
\(831\) −217.977 242.474i −0.262307 0.291785i
\(832\) 567.458 + 431.370i 0.682041 + 0.518474i
\(833\) −36.3327 107.832i −0.0436167 0.129450i
\(834\) 608.932 + 755.975i 0.730135 + 0.906445i
\(835\) −195.913 + 185.579i −0.234627 + 0.222250i
\(836\) −2143.08 2819.17i −2.56349 3.37221i
\(837\) 304.148 1001.40i 0.363378 1.19642i
\(838\) 843.352 + 91.7201i 1.00639 + 0.109451i
\(839\) −854.776 + 902.376i −1.01880 + 1.07554i −0.0216782 + 0.999765i \(0.506901\pi\)
−0.997125 + 0.0757726i \(0.975858\pi\)
\(840\) −4367.15 351.148i −5.19899 0.418034i
\(841\) −238.429 449.725i −0.283506 0.534750i
\(842\) −459.140 + 311.304i −0.545296 + 0.369720i
\(843\) −277.659 + 85.5627i −0.329370 + 0.101498i
\(844\) −738.995 + 2661.62i −0.875587 + 3.15358i
\(845\) 1065.05 174.606i 1.26041 0.206634i
\(846\) −1104.09 933.976i −1.30507 1.10399i
\(847\) −475.049 559.270i −0.560860 0.660296i
\(848\) −3941.06 213.678i −4.64748 0.251979i
\(849\) −438.319 + 546.427i −0.516277 + 0.643612i
\(850\) 496.656 229.778i 0.584302 0.270327i
\(851\) 201.284 + 914.442i 0.236526 + 1.07455i
\(852\) −412.096 + 177.766i −0.483681 + 0.208646i
\(853\) −1202.68 556.420i −1.40994 0.652310i −0.440530 0.897738i \(-0.645209\pi\)
−0.969415 + 0.245428i \(0.921071\pi\)
\(854\) 1108.80 + 181.778i 1.29836 + 0.212855i
\(855\) 959.756 + 1125.28i 1.12252 + 1.31612i
\(856\) −1756.87 1057.07i −2.05242 1.23490i
\(857\) 517.640 + 84.8628i 0.604014 + 0.0990231i 0.456027 0.889966i \(-0.349272\pi\)
0.147988 + 0.988989i \(0.452720\pi\)
\(858\) −126.922 657.848i −0.147927 0.766722i
\(859\) −824.481 181.482i −0.959815 0.211271i −0.292682 0.956210i \(-0.594548\pi\)
−0.667133 + 0.744939i \(0.732479\pi\)
\(860\) 635.311 + 2886.25i 0.738734 + 3.35610i
\(861\) −313.062 + 555.037i −0.363603 + 0.644642i
\(862\) 278.475 + 1002.98i 0.323057 + 1.16355i
\(863\) −1698.30 92.0790i −1.96790 0.106696i −0.974731 0.223383i \(-0.928290\pi\)
−0.993169 + 0.116687i \(0.962773\pi\)
\(864\) 1469.80 2314.97i 1.70116 2.67936i
\(865\) −706.259 + 1772.58i −0.816484 + 2.04922i
\(866\) −1697.27 + 278.253i −1.95990 + 0.321309i
\(867\) 720.784 265.633i 0.831354 0.306381i
\(868\) 3208.97 + 1081.23i 3.69696 + 1.24565i
\(869\) 366.008 248.160i 0.421183 0.285569i
\(870\) 2663.37 + 1317.55i 3.06134 + 1.51442i
\(871\) −22.3918 + 26.3617i −0.0257082 + 0.0302660i
\(872\) 1520.53 1605.21i 1.74373 1.84083i
\(873\) 212.074 460.840i 0.242925 0.527881i
\(874\) 1451.84 2141.31i 1.66115 2.45001i
\(875\) 0.449797 + 0.591698i 0.000514054 + 0.000676226i
\(876\) 273.340 + 52.1621i 0.312032 + 0.0595458i
\(877\) 24.1143 + 444.761i 0.0274963 + 0.507140i 0.979549 + 0.201206i \(0.0644859\pi\)
−0.952053 + 0.305934i \(0.901031\pi\)
\(878\) −1011.30 3001.44i −1.15183 3.41850i
\(879\) −596.833 15.5622i −0.678991 0.0177044i
\(880\) 5368.68 583.879i 6.10078 0.663499i
\(881\) −235.571 124.892i −0.267391 0.141762i 0.329319 0.944219i \(-0.393181\pi\)
−0.596710 + 0.802457i \(0.703526\pi\)
\(882\) 38.1991 + 679.065i 0.0433097 + 0.769915i
\(883\) 1197.65 720.600i 1.35634 0.816082i 0.363053 0.931768i \(-0.381734\pi\)
0.993286 + 0.115686i \(0.0369067\pi\)
\(884\) 244.668i 0.276774i
\(885\) −1248.86 84.8715i −1.41114 0.0959001i
\(886\) −215.592 −0.243332
\(887\) 311.616 + 517.911i 0.351315 + 0.583890i 0.981246 0.192761i \(-0.0617443\pi\)
−0.629931 + 0.776651i \(0.716917\pi\)
\(888\) 2018.42 + 1287.27i 2.27300 + 1.44963i
\(889\) 239.844 452.394i 0.269791 0.508879i
\(890\) −216.003 1986.11i −0.242700 2.23159i
\(891\) −1128.25 + 318.193i −1.26628 + 0.357119i
\(892\) −3102.45 + 1045.34i −3.47808 + 1.17190i
\(893\) −978.083 + 53.0301i −1.09528 + 0.0593842i
\(894\) 1569.74 + 299.556i 1.75586 + 0.335074i
\(895\) 860.235 653.934i 0.961157 0.730653i
\(896\) 1819.23 + 1233.47i 2.03040 + 1.37664i
\(897\) 308.604 174.891i 0.344041 0.194973i
\(898\) −389.068 368.544i −0.433260 0.410406i
\(899\) −1085.48 922.016i −1.20743 1.02560i
\(900\) −2338.49 + 388.247i −2.59832 + 0.431385i
\(901\) −240.932 355.349i −0.267405 0.394394i
\(902\) 451.009 1338.55i 0.500009 1.48398i
\(903\) 926.770 341.545i 1.02632 0.378234i
\(904\) 216.462 + 1320.36i 0.239450 + 1.46058i
\(905\) −211.324 84.1994i −0.233508 0.0930380i
\(906\) 2468.95 + 611.342i 2.72511 + 0.674770i
\(907\) 44.6532 823.580i 0.0492318 0.908027i −0.864733 0.502233i \(-0.832512\pi\)
0.913964 0.405794i \(-0.133005\pi\)
\(908\) 4143.83 1150.53i 4.56369 1.26710i
\(909\) −943.207 + 104.516i −1.03763 + 0.114979i
\(910\) −884.177 + 194.622i −0.971624 + 0.213871i
\(911\) 27.6340 125.543i 0.0303337 0.137808i −0.959020 0.283339i \(-0.908558\pi\)
0.989354 + 0.145531i \(0.0464890\pi\)
\(912\) −696.812 3611.65i −0.764048 3.96014i
\(913\) 51.9986 317.178i 0.0569536 0.347402i
\(914\) −241.964 + 402.147i −0.264731 + 0.439986i
\(915\) 751.262 61.9402i 0.821052 0.0676942i
\(916\) 285.391 1740.81i 0.311562 1.90044i
\(917\) −248.697 + 537.549i −0.271207 + 0.586204i
\(918\) 588.616 49.7323i 0.641194 0.0541746i
\(919\) −331.626 + 72.9964i −0.360855 + 0.0794302i −0.391698 0.920094i \(-0.628112\pi\)
0.0308424 + 0.999524i \(0.490181\pi\)
\(920\) 2158.90 + 4666.39i 2.34663 + 5.07216i
\(921\) −271.858 + 338.909i −0.295177 + 0.367980i
\(922\) −126.307 + 2329.59i −0.136992 + 2.52667i
\(923\) −43.8338 + 37.2327i −0.0474905 + 0.0403388i
\(924\) −919.105 3679.87i −0.994702 3.98254i
\(925\) −129.725 791.290i −0.140244 0.855449i
\(926\) 1394.57 + 387.200i 1.50601 + 0.418143i
\(927\) −264.775 + 349.775i −0.285625 + 0.377319i
\(928\) −2094.14 3088.62i −2.25661 3.32825i
\(929\) −1016.84 + 539.093i −1.09455 + 0.580294i −0.914999 0.403455i \(-0.867809\pi\)
−0.179550 + 0.983749i \(0.557464\pi\)
\(930\) 3124.66 + 251.244i 3.35985 + 0.270154i
\(931\) 334.451 + 316.809i 0.359239 + 0.340289i
\(932\) −283.247 + 2604.42i −0.303913 + 2.79444i
\(933\) 24.1474 + 859.214i 0.0258815 + 0.920915i
\(934\) −176.814 + 134.411i −0.189309 + 0.143909i
\(935\) 403.977 + 426.474i 0.432061 + 0.456121i
\(936\) 240.854 874.352i 0.257323 0.934137i
\(937\) 682.769 230.052i 0.728676 0.245519i 0.0695778 0.997577i \(-0.477835\pi\)
0.659098 + 0.752057i \(0.270938\pi\)
\(938\) −163.513 + 215.098i −0.174321 + 0.229315i
\(939\) 706.385 + 785.770i 0.752274 + 0.836816i
\(940\) 1470.40 2773.46i 1.56425 2.95049i
\(941\) 221.912 88.4178i 0.235826 0.0939615i −0.249232 0.968444i \(-0.580178\pi\)
0.485057 + 0.874482i \(0.338799\pi\)
\(942\) −377.614 + 880.285i −0.400864 + 0.934485i
\(943\) 747.830 0.793033
\(944\) 2598.10 + 1715.00i 2.75223 + 1.81674i
\(945\) 469.568 + 1512.89i 0.496897 + 1.60094i
\(946\) −1875.93 + 1128.71i −1.98301 + 1.19314i
\(947\) −932.669 + 371.609i −0.984867 + 0.392407i −0.806291 0.591519i \(-0.798528\pi\)
−0.178576 + 0.983926i \(0.557149\pi\)
\(948\) 956.284 131.279i 1.00874 0.138480i
\(949\) 35.4506 3.85549i 0.0373557 0.00406268i
\(950\) −1340.78 + 1763.76i −1.41134 + 1.85659i
\(951\) 288.483 402.480i 0.303347 0.423218i
\(952\) 64.1687 + 1183.52i 0.0674041 + 1.24320i
\(953\) −414.464 437.545i −0.434905 0.459124i 0.471293 0.881977i \(-0.343787\pi\)
−0.906198 + 0.422853i \(0.861029\pi\)
\(954\) 824.317 + 2430.19i 0.864064 + 2.54737i
\(955\) −1291.01 + 1904.10i −1.35185 + 1.99382i
\(956\) −397.776 + 3657.49i −0.416084 + 3.82583i
\(957\) −213.758 + 1580.88i −0.223362 + 1.65191i
\(958\) −230.249 + 271.070i −0.240343 + 0.282954i
\(959\) −634.264 + 336.265i −0.661380 + 0.350642i
\(960\) 3507.82 + 1284.67i 3.65397 + 1.33820i
\(961\) −513.140 172.897i −0.533964 0.179914i
\(962\) 476.660 + 132.344i 0.495489 + 0.137572i
\(963\) −118.450 + 731.806i −0.123001 + 0.759923i
\(964\) −576.412 + 1446.69i −0.597938 + 1.50071i
\(965\) 1375.82 1168.63i 1.42572 1.21102i
\(966\) 2333.23 1494.70i 2.41535 1.54731i
\(967\) −399.428 1438.61i −0.413059 1.48770i −0.818994 0.573803i \(-0.805468\pi\)
0.405934 0.913902i \(-0.366946\pi\)
\(968\) 924.480 + 1998.23i 0.955041 + 2.06429i
\(969\) 266.886 298.093i 0.275424 0.307629i
\(970\) 1483.95 + 326.643i 1.52985 + 0.336745i
\(971\) −272.694 + 589.419i −0.280839 + 0.607023i −0.995740 0.0922022i \(-0.970609\pi\)
0.714902 + 0.699225i \(0.246471\pi\)
\(972\) −2515.41 469.455i −2.58787 0.482978i
\(973\) 603.419 + 363.065i 0.620164 + 0.373140i
\(974\) −1436.62 + 2387.67i −1.47496 + 2.45141i
\(975\) −272.002 + 135.245i −0.278977 + 0.138712i
\(976\) −1701.47 787.184i −1.74331 0.806541i
\(977\) 258.474 1174.26i 0.264559 1.20190i −0.637556 0.770404i \(-0.720054\pi\)
0.902114 0.431497i \(-0.142015\pi\)
\(978\) 1689.31 1886.83i 1.72731 1.92928i
\(979\) 973.430 450.357i 0.994311 0.460017i
\(980\) −1422.56 + 394.971i −1.45159 + 0.403032i
\(981\) −743.244 294.390i −0.757639 0.300092i
\(982\) −103.495 121.843i −0.105392 0.124077i
\(983\) 220.595 + 87.8930i 0.224410 + 0.0894130i 0.479633 0.877469i \(-0.340770\pi\)
−0.255223 + 0.966882i \(0.582149\pi\)
\(984\) 1350.63 1353.37i 1.37259 1.37537i
\(985\) −714.001 + 2571.60i −0.724874 + 2.61076i
\(986\) 256.675 761.785i 0.260320 0.772602i
\(987\) −985.139 360.789i −0.998115 0.365541i
\(988\) −463.986 875.171i −0.469622 0.885801i
\(989\) −883.433 750.395i −0.893259 0.758741i
\(990\) −1650.98 3098.87i −1.66765 3.13017i
\(991\) −182.062 19.8004i −0.183715 0.0199802i 0.0157989 0.999875i \(-0.494971\pi\)
−0.199514 + 0.979895i \(0.563936\pi\)
\(992\) −3258.36 2209.23i −3.28464 2.22704i
\(993\) −1458.06 446.078i −1.46834 0.449222i
\(994\) −326.168 + 308.963i −0.328137 + 0.310828i
\(995\) −2432.04 + 131.861i −2.44426 + 0.132524i
\(996\) 408.722 570.232i 0.410363 0.572522i
\(997\) −1127.46 857.074i −1.13085 0.859653i −0.139417 0.990234i \(-0.544523\pi\)
−0.991438 + 0.130581i \(0.958316\pi\)
\(998\) −188.750 1735.53i −0.189128 1.73901i
\(999\) 160.525 850.547i 0.160685 0.851399i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.3.h.a.104.1 yes 1064
3.2 odd 2 inner 177.3.h.a.104.38 yes 1064
59.21 even 29 inner 177.3.h.a.80.38 yes 1064
177.80 odd 58 inner 177.3.h.a.80.1 1064
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.3.h.a.80.1 1064 177.80 odd 58 inner
177.3.h.a.80.38 yes 1064 59.21 even 29 inner
177.3.h.a.104.1 yes 1064 1.1 even 1 trivial
177.3.h.a.104.38 yes 1064 3.2 odd 2 inner