Properties

Label 216.3.x.a.5.2
Level $216$
Weight $3$
Character 216.5
Analytic conductor $5.886$
Analytic rank $0$
Dimension $420$
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] = [216,3,Mod(5,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.x (of order \(18\), degree \(6\), 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: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(420\)
Relative dimension: \(70\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 216.5
Dual form 216.3.x.a.173.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.98021 + 0.280686i) q^{2} +(-1.96788 + 2.26438i) q^{3} +(3.84243 - 1.11163i) q^{4} +(8.66971 - 3.15552i) q^{5} +(3.26123 - 5.03630i) q^{6} +(-0.680238 - 3.85782i) q^{7} +(-7.29678 + 3.27978i) q^{8} +(-1.25487 - 8.91209i) q^{9} +O(q^{10})\) \(q+(-1.98021 + 0.280686i) q^{2} +(-1.96788 + 2.26438i) q^{3} +(3.84243 - 1.11163i) q^{4} +(8.66971 - 3.15552i) q^{5} +(3.26123 - 5.03630i) q^{6} +(-0.680238 - 3.85782i) q^{7} +(-7.29678 + 3.27978i) q^{8} +(-1.25487 - 8.91209i) q^{9} +(-16.2821 + 8.68204i) q^{10} +(-9.73105 - 3.54181i) q^{11} +(-5.04429 + 10.8883i) q^{12} +(5.92748 - 7.06410i) q^{13} +(2.42985 + 7.44835i) q^{14} +(-9.91568 + 25.8412i) q^{15} +(13.5285 - 8.54275i) q^{16} +(-27.6417 - 15.9589i) q^{17} +(4.98640 + 17.2955i) q^{18} +(0.562002 - 0.324472i) q^{19} +(29.8050 - 21.7624i) q^{20} +(10.0742 + 6.05143i) q^{21} +(20.2636 + 4.28214i) q^{22} +(-2.10097 - 0.370458i) q^{23} +(6.93253 - 22.9769i) q^{24} +(46.0555 - 38.6452i) q^{25} +(-9.75484 + 15.6521i) q^{26} +(22.6498 + 14.6965i) q^{27} +(-6.90225 - 14.0672i) q^{28} +(8.17972 - 6.86360i) q^{29} +(12.3818 - 53.9542i) q^{30} +(9.84529 - 55.8354i) q^{31} +(-24.3915 + 20.7137i) q^{32} +(27.1696 - 15.0650i) q^{33} +(59.2157 + 23.8433i) q^{34} +(-18.0709 - 31.2997i) q^{35} +(-14.7287 - 32.8491i) q^{36} +(39.0031 + 22.5185i) q^{37} +(-1.02180 + 0.800267i) q^{38} +(4.33123 + 27.3234i) q^{39} +(-52.9116 + 51.4599i) q^{40} +(-15.1775 + 18.0879i) q^{41} +(-21.6476 - 9.15537i) q^{42} +(-17.1234 + 47.0461i) q^{43} +(-41.3281 - 2.79180i) q^{44} +(-39.0016 - 73.3055i) q^{45} +(4.26434 + 0.143869i) q^{46} +(-11.8961 + 2.09761i) q^{47} +(-7.27853 + 47.4449i) q^{48} +(31.6249 - 11.5105i) q^{49} +(-80.3522 + 89.4525i) q^{50} +(90.5328 - 31.1861i) q^{51} +(14.9233 - 33.7325i) q^{52} -12.7638 q^{53} +(-48.9764 - 22.7445i) q^{54} -95.5416 q^{55} +(17.6164 + 25.9187i) q^{56} +(-0.371225 + 1.91111i) q^{57} +(-14.2710 + 15.8873i) q^{58} +(58.3990 - 21.2555i) q^{59} +(-9.37432 + 110.316i) q^{60} +(-42.4438 + 7.48398i) q^{61} +(-3.82346 + 113.329i) q^{62} +(-33.5276 + 10.9034i) q^{63} +(42.4861 - 47.8637i) q^{64} +(29.0987 - 79.9480i) q^{65} +(-49.5729 + 37.4578i) q^{66} +(11.4303 - 13.6221i) q^{67} +(-123.952 - 30.5937i) q^{68} +(4.97333 - 4.02839i) q^{69} +(44.5695 + 56.9076i) q^{70} +(19.1726 + 11.0693i) q^{71} +(38.3862 + 60.9139i) q^{72} +(53.0930 + 91.9597i) q^{73} +(-83.5548 - 33.6435i) q^{74} +(-3.12442 + 180.337i) q^{75} +(1.79876 - 1.87150i) q^{76} +(-7.04425 + 39.9499i) q^{77} +(-16.2461 - 52.8903i) q^{78} +(73.2113 - 61.4316i) q^{79} +(90.3318 - 116.753i) q^{80} +(-77.8506 + 22.3670i) q^{81} +(24.9776 - 40.0779i) q^{82} +(17.4066 - 14.6058i) q^{83} +(45.4365 + 12.0533i) q^{84} +(-290.004 - 51.1356i) q^{85} +(20.7026 - 97.9673i) q^{86} +(-0.554914 + 32.0288i) q^{87} +(82.6217 - 6.07189i) q^{88} +(104.861 - 60.5417i) q^{89} +(97.8070 + 134.213i) q^{90} +(-31.2842 - 18.0619i) q^{91} +(-8.48466 + 0.912053i) q^{92} +(107.058 + 132.171i) q^{93} +(22.9680 - 7.49277i) q^{94} +(3.84852 - 4.58648i) q^{95} +(1.09583 - 95.9937i) q^{96} +(-113.618 - 41.3534i) q^{97} +(-59.3929 + 31.6698i) q^{98} +(-19.3538 + 91.1685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 51 q^{12} + 39 q^{14} - 12 q^{15} - 6 q^{16} - 18 q^{17} - 27 q^{18} + 57 q^{20} - 6 q^{22} - 12 q^{23} + 126 q^{24} - 12 q^{25} - 12 q^{28} + 87 q^{30} - 12 q^{31} + 84 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{36} - 108 q^{38} - 12 q^{39} + 69 q^{40} - 84 q^{41} + 114 q^{42} - 657 q^{44} - 3 q^{46} - 12 q^{47} - 453 q^{48} - 12 q^{49} + 153 q^{50} + 21 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 66 q^{57} + 129 q^{58} + 210 q^{60} - 900 q^{62} + 468 q^{63} - 3 q^{64} - 12 q^{65} - 855 q^{66} + 279 q^{68} + 153 q^{70} - 18 q^{71} - 156 q^{72} - 6 q^{73} + 423 q^{74} - 54 q^{76} + 642 q^{78} - 12 q^{79} - 12 q^{81} - 12 q^{82} + 192 q^{84} + 606 q^{86} - 588 q^{87} + 186 q^{88} - 18 q^{89} - 534 q^{90} - 735 q^{92} + 345 q^{94} - 162 q^{95} - 486 q^{96} - 12 q^{97} - 1548 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98021 + 0.280686i −0.990103 + 0.140343i
\(3\) −1.96788 + 2.26438i −0.655961 + 0.754795i
\(4\) 3.84243 1.11163i 0.960608 0.277908i
\(5\) 8.66971 3.15552i 1.73394 0.631103i 0.735044 0.678020i \(-0.237162\pi\)
0.998899 + 0.0469162i \(0.0149394\pi\)
\(6\) 3.26123 5.03630i 0.543539 0.839384i
\(7\) −0.680238 3.85782i −0.0971769 0.551118i −0.994059 0.108847i \(-0.965284\pi\)
0.896882 0.442271i \(-0.145827\pi\)
\(8\) −7.29678 + 3.27978i −0.912098 + 0.409973i
\(9\) −1.25487 8.91209i −0.139430 0.990232i
\(10\) −16.2821 + 8.68204i −1.62821 + 0.868204i
\(11\) −9.73105 3.54181i −0.884641 0.321983i −0.140560 0.990072i \(-0.544890\pi\)
−0.744081 + 0.668089i \(0.767112\pi\)
\(12\) −5.04429 + 10.8883i −0.420358 + 0.907359i
\(13\) 5.92748 7.06410i 0.455960 0.543392i −0.488264 0.872696i \(-0.662370\pi\)
0.944224 + 0.329304i \(0.106814\pi\)
\(14\) 2.42985 + 7.44835i 0.173561 + 0.532025i
\(15\) −9.91568 + 25.8412i −0.661046 + 1.72275i
\(16\) 13.5285 8.54275i 0.845534 0.533922i
\(17\) −27.6417 15.9589i −1.62598 0.938761i −0.985275 0.170975i \(-0.945308\pi\)
−0.640706 0.767786i \(-0.721358\pi\)
\(18\) 4.98640 + 17.2955i 0.277022 + 0.960864i
\(19\) 0.562002 0.324472i 0.0295790 0.0170775i −0.485138 0.874438i \(-0.661230\pi\)
0.514717 + 0.857360i \(0.327897\pi\)
\(20\) 29.8050 21.7624i 1.49025 1.08812i
\(21\) 10.0742 + 6.05143i 0.479725 + 0.288163i
\(22\) 20.2636 + 4.28214i 0.921073 + 0.194643i
\(23\) −2.10097 0.370458i −0.0913467 0.0161069i 0.127788 0.991802i \(-0.459212\pi\)
−0.219135 + 0.975695i \(0.570323\pi\)
\(24\) 6.93253 22.9769i 0.288856 0.957373i
\(25\) 46.0555 38.6452i 1.84222 1.54581i
\(26\) −9.75484 + 15.6521i −0.375186 + 0.602005i
\(27\) 22.6498 + 14.6965i 0.838882 + 0.544313i
\(28\) −6.90225 14.0672i −0.246509 0.502401i
\(29\) 8.17972 6.86360i 0.282059 0.236676i −0.490771 0.871289i \(-0.663285\pi\)
0.772830 + 0.634613i \(0.218840\pi\)
\(30\) 12.3818 53.9542i 0.412727 1.79847i
\(31\) 9.84529 55.8354i 0.317590 1.80114i −0.239725 0.970841i \(-0.577057\pi\)
0.557315 0.830301i \(-0.311832\pi\)
\(32\) −24.3915 + 20.7137i −0.762233 + 0.647303i
\(33\) 27.1696 15.0650i 0.823321 0.456514i
\(34\) 59.2157 + 23.8433i 1.74164 + 0.701274i
\(35\) −18.0709 31.2997i −0.516311 0.894277i
\(36\) −14.7287 32.8491i −0.409131 0.912476i
\(37\) 39.0031 + 22.5185i 1.05414 + 0.608607i 0.923805 0.382863i \(-0.125062\pi\)
0.130333 + 0.991470i \(0.458395\pi\)
\(38\) −1.02180 + 0.800267i −0.0268896 + 0.0210597i
\(39\) 4.33123 + 27.3234i 0.111057 + 0.700601i
\(40\) −52.9116 + 51.4599i −1.32279 + 1.28650i
\(41\) −15.1775 + 18.0879i −0.370184 + 0.441168i −0.918690 0.394978i \(-0.870752\pi\)
0.548507 + 0.836146i \(0.315197\pi\)
\(42\) −21.6476 9.15537i −0.515419 0.217985i
\(43\) −17.1234 + 47.0461i −0.398218 + 1.09410i 0.564933 + 0.825136i \(0.308902\pi\)
−0.963152 + 0.268959i \(0.913320\pi\)
\(44\) −41.3281 2.79180i −0.939274 0.0634500i
\(45\) −39.0016 73.3055i −0.866702 1.62901i
\(46\) 4.26434 + 0.143869i 0.0927031 + 0.00312759i
\(47\) −11.8961 + 2.09761i −0.253109 + 0.0446299i −0.298763 0.954327i \(-0.596574\pi\)
0.0456539 + 0.998957i \(0.485463\pi\)
\(48\) −7.27853 + 47.4449i −0.151636 + 0.988436i
\(49\) 31.6249 11.5105i 0.645405 0.234908i
\(50\) −80.3522 + 89.4525i −1.60704 + 1.78905i
\(51\) 90.5328 31.1861i 1.77515 0.611491i
\(52\) 14.9233 33.7325i 0.286986 0.648702i
\(53\) −12.7638 −0.240826 −0.120413 0.992724i \(-0.538422\pi\)
−0.120413 + 0.992724i \(0.538422\pi\)
\(54\) −48.9764 22.7445i −0.906970 0.421195i
\(55\) −95.5416 −1.73712
\(56\) 17.6164 + 25.9187i 0.314578 + 0.462833i
\(57\) −0.371225 + 1.91111i −0.00651272 + 0.0335283i
\(58\) −14.2710 + 15.8873i −0.246052 + 0.273918i
\(59\) 58.3990 21.2555i 0.989813 0.360263i 0.204165 0.978936i \(-0.434552\pi\)
0.785648 + 0.618674i \(0.212330\pi\)
\(60\) −9.37432 + 110.316i −0.156239 + 1.83860i
\(61\) −42.4438 + 7.48398i −0.695799 + 0.122688i −0.510352 0.859966i \(-0.670485\pi\)
−0.185448 + 0.982654i \(0.559374\pi\)
\(62\) −3.82346 + 113.329i −0.0616686 + 1.82789i
\(63\) −33.5276 + 10.9034i −0.532185 + 0.173070i
\(64\) 42.4861 47.8637i 0.663845 0.747870i
\(65\) 29.0987 79.9480i 0.447672 1.22997i
\(66\) −49.5729 + 37.4578i −0.751104 + 0.567543i
\(67\) 11.4303 13.6221i 0.170601 0.203315i −0.673969 0.738760i \(-0.735412\pi\)
0.844570 + 0.535445i \(0.179856\pi\)
\(68\) −123.952 30.5937i −1.82282 0.449907i
\(69\) 4.97333 4.02839i 0.0720773 0.0583825i
\(70\) 44.5695 + 56.9076i 0.636707 + 0.812966i
\(71\) 19.1726 + 11.0693i 0.270037 + 0.155906i 0.628904 0.777483i \(-0.283504\pi\)
−0.358867 + 0.933389i \(0.616837\pi\)
\(72\) 38.3862 + 60.9139i 0.533142 + 0.846026i
\(73\) 53.0930 + 91.9597i 0.727301 + 1.25972i 0.958020 + 0.286702i \(0.0925589\pi\)
−0.230719 + 0.973020i \(0.574108\pi\)
\(74\) −83.5548 33.6435i −1.12912 0.454642i
\(75\) −3.12442 + 180.337i −0.0416589 + 2.40449i
\(76\) 1.79876 1.87150i 0.0236679 0.0246250i
\(77\) −7.04425 + 39.9499i −0.0914838 + 0.518830i
\(78\) −16.2461 52.8903i −0.208283 0.678081i
\(79\) 73.2113 61.4316i 0.926726 0.777615i −0.0485010 0.998823i \(-0.515444\pi\)
0.975227 + 0.221208i \(0.0710000\pi\)
\(80\) 90.3318 116.753i 1.12915 1.45941i
\(81\) −77.8506 + 22.3670i −0.961119 + 0.276135i
\(82\) 24.9776 40.0779i 0.304605 0.488754i
\(83\) 17.4066 14.6058i 0.209718 0.175974i −0.531878 0.846821i \(-0.678514\pi\)
0.741596 + 0.670847i \(0.234069\pi\)
\(84\) 45.4365 + 12.0533i 0.540910 + 0.143492i
\(85\) −290.004 51.1356i −3.41181 0.601595i
\(86\) 20.7026 97.9673i 0.240728 1.13915i
\(87\) −0.554914 + 32.0288i −0.00637832 + 0.368147i
\(88\) 82.6217 6.07189i 0.938883 0.0689987i
\(89\) 104.861 60.5417i 1.17822 0.680244i 0.222616 0.974906i \(-0.428540\pi\)
0.955602 + 0.294662i \(0.0952070\pi\)
\(90\) 97.8070 + 134.213i 1.08674 + 1.49125i
\(91\) −31.2842 18.0619i −0.343782 0.198483i
\(92\) −8.48466 + 0.912053i −0.0922246 + 0.00991362i
\(93\) 107.058 + 132.171i 1.15117 + 1.42119i
\(94\) 22.9680 7.49277i 0.244340 0.0797104i
\(95\) 3.84852 4.58648i 0.0405107 0.0482788i
\(96\) 1.09583 95.9937i 0.0114149 0.999935i
\(97\) −113.618 41.3534i −1.17132 0.426324i −0.318189 0.948027i \(-0.603075\pi\)
−0.853127 + 0.521703i \(0.825297\pi\)
\(98\) −59.3929 + 31.6698i −0.606050 + 0.323162i
\(99\) −19.3538 + 91.1685i −0.195493 + 0.920893i
\(100\) 134.006 199.688i 1.34006 1.99688i
\(101\) 3.67262 + 20.8285i 0.0363626 + 0.206222i 0.997576 0.0695825i \(-0.0221667\pi\)
−0.961214 + 0.275805i \(0.911056\pi\)
\(102\) −170.520 + 87.1661i −1.67177 + 0.854570i
\(103\) −129.484 + 47.1282i −1.25712 + 0.457555i −0.882802 0.469745i \(-0.844346\pi\)
−0.374320 + 0.927300i \(0.622124\pi\)
\(104\) −20.0829 + 70.9861i −0.193104 + 0.682558i
\(105\) 106.436 + 20.6748i 1.01368 + 0.196902i
\(106\) 25.2749 3.58262i 0.238443 0.0337983i
\(107\) −57.5776 −0.538109 −0.269054 0.963125i \(-0.586711\pi\)
−0.269054 + 0.963125i \(0.586711\pi\)
\(108\) 103.367 + 31.2918i 0.957106 + 0.289739i
\(109\) 5.13351i 0.0470964i 0.999723 + 0.0235482i \(0.00749632\pi\)
−0.999723 + 0.0235482i \(0.992504\pi\)
\(110\) 189.192 26.8172i 1.71993 0.243793i
\(111\) −127.744 + 44.0043i −1.15085 + 0.396435i
\(112\) −42.1591 46.3796i −0.376420 0.414104i
\(113\) 8.16742 + 22.4398i 0.0722781 + 0.198582i 0.970571 0.240814i \(-0.0774145\pi\)
−0.898293 + 0.439397i \(0.855192\pi\)
\(114\) 0.198680 3.88859i 0.00174280 0.0341104i
\(115\) −19.3838 + 3.41789i −0.168555 + 0.0297208i
\(116\) 23.8002 35.4657i 0.205174 0.305739i
\(117\) −70.3941 43.9618i −0.601659 0.375742i
\(118\) −109.676 + 58.4821i −0.929457 + 0.495611i
\(119\) −42.7638 + 117.493i −0.359360 + 0.987333i
\(120\) −12.4011 221.079i −0.103342 1.84233i
\(121\) −10.5425 8.84622i −0.0871282 0.0731093i
\(122\) 81.9467 26.7332i 0.671695 0.219125i
\(123\) −11.0903 69.9626i −0.0901649 0.568802i
\(124\) −24.2387 225.488i −0.195473 1.81845i
\(125\) 162.016 280.620i 1.29613 2.24496i
\(126\) 63.3312 31.0017i 0.502629 0.246045i
\(127\) 51.5334 + 89.2585i 0.405775 + 0.702822i 0.994411 0.105575i \(-0.0336684\pi\)
−0.588637 + 0.808398i \(0.700335\pi\)
\(128\) −70.6964 + 106.705i −0.552316 + 0.833635i
\(129\) −72.8336 131.355i −0.564602 1.01826i
\(130\) −35.1811 + 166.481i −0.270624 + 1.28062i
\(131\) −28.6637 + 162.560i −0.218807 + 1.24092i 0.655370 + 0.755308i \(0.272513\pi\)
−0.874177 + 0.485608i \(0.838598\pi\)
\(132\) 87.6505 88.0887i 0.664019 0.667338i
\(133\) −1.63405 1.94738i −0.0122861 0.0146420i
\(134\) −18.8108 + 30.1828i −0.140379 + 0.225245i
\(135\) 242.742 + 55.9421i 1.79809 + 0.414386i
\(136\) 254.037 + 25.7902i 1.86792 + 0.189634i
\(137\) 47.0817 + 56.1098i 0.343662 + 0.409560i 0.909997 0.414615i \(-0.136084\pi\)
−0.566335 + 0.824175i \(0.691639\pi\)
\(138\) −8.71751 + 9.37299i −0.0631703 + 0.0679202i
\(139\) 104.420 + 18.4121i 0.751224 + 0.132461i 0.536134 0.844133i \(-0.319884\pi\)
0.215090 + 0.976594i \(0.430995\pi\)
\(140\) −104.230 100.179i −0.744500 0.715562i
\(141\) 18.6604 31.0652i 0.132343 0.220321i
\(142\) −41.0727 16.5380i −0.289245 0.116465i
\(143\) −82.7004 + 47.7471i −0.578324 + 0.333896i
\(144\) −93.1103 109.848i −0.646599 0.762830i
\(145\) 49.2576 85.3166i 0.339707 0.588391i
\(146\) −130.947 167.197i −0.896896 1.14518i
\(147\) −36.1698 + 94.2622i −0.246053 + 0.641239i
\(148\) 174.899 + 43.1684i 1.18175 + 0.291679i
\(149\) −46.4763 38.9982i −0.311921 0.261733i 0.473364 0.880867i \(-0.343039\pi\)
−0.785286 + 0.619134i \(0.787484\pi\)
\(150\) −44.4310 357.981i −0.296207 2.38654i
\(151\) 135.099 + 49.1720i 0.894696 + 0.325643i 0.748125 0.663558i \(-0.230954\pi\)
0.146571 + 0.989200i \(0.453176\pi\)
\(152\) −3.03661 + 4.21084i −0.0199777 + 0.0277029i
\(153\) −107.541 + 266.371i −0.702881 + 1.74099i
\(154\) 2.73566 81.0863i 0.0177640 0.526535i
\(155\) −90.8338 515.144i −0.586024 3.32351i
\(156\) 47.0161 + 100.174i 0.301385 + 0.642139i
\(157\) 23.9849 + 65.8979i 0.152770 + 0.419732i 0.992343 0.123515i \(-0.0394168\pi\)
−0.839573 + 0.543247i \(0.817195\pi\)
\(158\) −127.730 + 142.197i −0.808421 + 0.899979i
\(159\) 25.1177 28.9021i 0.157973 0.181774i
\(160\) −146.105 + 256.549i −0.913154 + 1.60343i
\(161\) 8.35719i 0.0519080i
\(162\) 147.882 66.1428i 0.912853 0.408289i
\(163\) 276.197i 1.69446i −0.531227 0.847229i \(-0.678269\pi\)
0.531227 0.847229i \(-0.321731\pi\)
\(164\) −38.2115 + 86.3733i −0.232997 + 0.526667i
\(165\) 188.015 216.343i 1.13948 1.31117i
\(166\) −30.3689 + 33.8084i −0.182945 + 0.203665i
\(167\) 38.7800 + 106.547i 0.232215 + 0.638007i 0.999996 0.00270572i \(-0.000861258\pi\)
−0.767781 + 0.640713i \(0.778639\pi\)
\(168\) −93.3568 11.1147i −0.555695 0.0661589i
\(169\) 14.5801 + 82.6878i 0.0862727 + 0.489277i
\(170\) 588.621 + 19.8587i 3.46248 + 0.116816i
\(171\) −3.59696 4.60144i −0.0210348 0.0269090i
\(172\) −13.4974 + 199.806i −0.0784730 + 1.16166i
\(173\) 116.502 + 42.4032i 0.673421 + 0.245105i 0.656020 0.754743i \(-0.272239\pi\)
0.0174009 + 0.999849i \(0.494461\pi\)
\(174\) −7.89120 63.5793i −0.0453517 0.365398i
\(175\) −180.415 151.386i −1.03094 0.865063i
\(176\) −161.904 + 35.2144i −0.919907 + 0.200082i
\(177\) −66.7918 + 174.066i −0.377355 + 0.983424i
\(178\) −190.654 + 149.318i −1.07109 + 0.838867i
\(179\) −32.4312 + 56.1725i −0.181180 + 0.313813i −0.942283 0.334818i \(-0.891325\pi\)
0.761103 + 0.648631i \(0.224658\pi\)
\(180\) −231.350 238.316i −1.28528 1.32398i
\(181\) −135.565 + 78.2687i −0.748980 + 0.432424i −0.825325 0.564657i \(-0.809008\pi\)
0.0763450 + 0.997081i \(0.475675\pi\)
\(182\) 67.0188 + 26.9853i 0.368235 + 0.148271i
\(183\) 66.5778 110.837i 0.363813 0.605664i
\(184\) 16.5454 4.18758i 0.0899205 0.0227586i
\(185\) 409.203 + 72.1536i 2.21191 + 0.390019i
\(186\) −249.096 231.676i −1.33923 1.24557i
\(187\) 212.459 + 253.199i 1.13614 + 1.35400i
\(188\) −43.3782 + 21.2840i −0.230735 + 0.113213i
\(189\) 41.2890 97.3761i 0.218461 0.515217i
\(190\) −6.33349 + 10.1624i −0.0333342 + 0.0534864i
\(191\) −229.963 274.060i −1.20400 1.43487i −0.870538 0.492102i \(-0.836229\pi\)
−0.333458 0.942765i \(-0.608216\pi\)
\(192\) 24.7742 + 190.395i 0.129032 + 0.991640i
\(193\) 1.66315 9.43220i 0.00861737 0.0488715i −0.980196 0.198030i \(-0.936546\pi\)
0.988813 + 0.149159i \(0.0476566\pi\)
\(194\) 236.594 + 49.9974i 1.21956 + 0.257719i
\(195\) 123.770 + 223.219i 0.634719 + 1.14471i
\(196\) 108.721 79.3836i 0.554698 0.405018i
\(197\) 149.551 + 259.030i 0.759143 + 1.31487i 0.943288 + 0.331976i \(0.107715\pi\)
−0.184145 + 0.982899i \(0.558951\pi\)
\(198\) 12.7347 185.965i 0.0643166 0.939215i
\(199\) 35.2631 61.0775i 0.177202 0.306922i −0.763719 0.645548i \(-0.776629\pi\)
0.940921 + 0.338626i \(0.109962\pi\)
\(200\) −209.309 + 433.037i −1.04655 + 2.16519i
\(201\) 8.35215 + 52.6892i 0.0415530 + 0.262135i
\(202\) −13.1188 40.2138i −0.0649446 0.199078i
\(203\) −32.0427 26.8870i −0.157846 0.132448i
\(204\) 313.198 220.470i 1.53529 1.08073i
\(205\) −74.5083 + 204.710i −0.363455 + 0.998584i
\(206\) 243.176 129.668i 1.18047 0.629455i
\(207\) −0.665115 + 19.1889i −0.00321311 + 0.0927002i
\(208\) 19.8434 146.204i 0.0954008 0.702904i
\(209\) −6.61808 + 1.16695i −0.0316655 + 0.00558348i
\(210\) −216.568 11.0651i −1.03128 0.0526911i
\(211\) −28.6804 78.7989i −0.135926 0.373454i 0.852990 0.521927i \(-0.174787\pi\)
−0.988917 + 0.148472i \(0.952564\pi\)
\(212\) −49.0440 + 14.1887i −0.231340 + 0.0669277i
\(213\) −62.7947 + 21.6310i −0.294811 + 0.101554i
\(214\) 114.016 16.1613i 0.532783 0.0755199i
\(215\) 461.909i 2.14842i
\(216\) −213.472 32.9503i −0.988296 0.152548i
\(217\) −222.100 −1.02350
\(218\) −1.44091 10.1654i −0.00660966 0.0466303i
\(219\) −312.713 60.7432i −1.42791 0.277366i
\(220\) −367.112 + 106.207i −1.66869 + 0.482761i
\(221\) −276.581 + 100.667i −1.25150 + 0.455508i
\(222\) 240.608 122.994i 1.08382 0.554025i
\(223\) 7.40825 + 42.0143i 0.0332209 + 0.188405i 0.996902 0.0786495i \(-0.0250608\pi\)
−0.963681 + 0.267054i \(0.913950\pi\)
\(224\) 96.5017 + 80.0077i 0.430811 + 0.357177i
\(225\) −402.203 361.956i −1.78757 1.60869i
\(226\) −22.4717 42.1430i −0.0994324 0.186473i
\(227\) −70.3185 25.5939i −0.309773 0.112748i 0.182455 0.983214i \(-0.441595\pi\)
−0.492229 + 0.870466i \(0.663818\pi\)
\(228\) 0.698048 + 7.75598i 0.00306161 + 0.0340174i
\(229\) −255.084 + 303.997i −1.11390 + 1.32750i −0.174510 + 0.984655i \(0.555834\pi\)
−0.939393 + 0.342842i \(0.888610\pi\)
\(230\) 37.4246 12.2089i 0.162716 0.0530822i
\(231\) −76.5997 94.5677i −0.331600 0.409384i
\(232\) −37.1745 + 76.9098i −0.160235 + 0.331508i
\(233\) −255.444 147.480i −1.09632 0.632963i −0.161071 0.986943i \(-0.551495\pi\)
−0.935253 + 0.353979i \(0.884828\pi\)
\(234\) 151.734 + 67.2947i 0.648437 + 0.287584i
\(235\) −96.5169 + 55.7241i −0.410710 + 0.237124i
\(236\) 200.766 146.591i 0.850702 0.621148i
\(237\) −4.96667 + 286.669i −0.0209564 + 1.20957i
\(238\) 51.7026 244.663i 0.217238 1.02799i
\(239\) 75.8631 + 13.3767i 0.317419 + 0.0559695i 0.330088 0.943950i \(-0.392922\pi\)
−0.0126689 + 0.999920i \(0.504033\pi\)
\(240\) 86.6106 + 434.302i 0.360878 + 1.80959i
\(241\) −11.3321 + 9.50875i −0.0470211 + 0.0394554i −0.665995 0.745956i \(-0.731993\pi\)
0.618974 + 0.785411i \(0.287549\pi\)
\(242\) 23.3594 + 14.5582i 0.0965263 + 0.0601578i
\(243\) 102.554 220.299i 0.422031 0.906581i
\(244\) −154.768 + 75.9386i −0.634294 + 0.311224i
\(245\) 237.857 199.586i 0.970844 0.814635i
\(246\) 41.5986 + 135.428i 0.169100 + 0.550518i
\(247\) 1.03915 5.89334i 0.00420710 0.0238597i
\(248\) 111.289 + 439.709i 0.448746 + 1.77302i
\(249\) −1.18087 + 68.1577i −0.00474243 + 0.273726i
\(250\) −242.059 + 601.162i −0.968236 + 2.40465i
\(251\) 28.6727 + 49.6626i 0.114234 + 0.197859i 0.917473 0.397797i \(-0.130225\pi\)
−0.803239 + 0.595656i \(0.796892\pi\)
\(252\) −116.707 + 79.1660i −0.463123 + 0.314151i
\(253\) 19.1326 + 11.0462i 0.0756229 + 0.0436609i
\(254\) −127.100 162.285i −0.500395 0.638919i
\(255\) 686.485 556.052i 2.69210 2.18060i
\(256\) 110.043 231.142i 0.429855 0.902898i
\(257\) 21.4521 25.5656i 0.0834713 0.0994772i −0.722692 0.691170i \(-0.757096\pi\)
0.806164 + 0.591693i \(0.201540\pi\)
\(258\) 181.095 + 239.667i 0.701919 + 0.928941i
\(259\) 60.3408 165.785i 0.232976 0.640097i
\(260\) 22.9368 339.542i 0.0882184 1.30593i
\(261\) −71.4334 64.2854i −0.273691 0.246304i
\(262\) 11.1317 329.948i 0.0424873 1.25934i
\(263\) 449.746 79.3023i 1.71006 0.301530i 0.768869 0.639406i \(-0.220820\pi\)
0.941190 + 0.337877i \(0.109709\pi\)
\(264\) −148.841 + 199.036i −0.563791 + 0.753924i
\(265\) −110.658 + 40.2764i −0.417579 + 0.151986i
\(266\) 3.78236 + 3.39757i 0.0142194 + 0.0127728i
\(267\) −69.2653 + 356.586i −0.259420 + 1.33553i
\(268\) 28.7773 65.0482i 0.107378 0.242717i
\(269\) 186.713 0.694101 0.347051 0.937846i \(-0.387183\pi\)
0.347051 + 0.937846i \(0.387183\pi\)
\(270\) −496.382 42.6424i −1.83845 0.157935i
\(271\) −261.998 −0.966781 −0.483391 0.875405i \(-0.660595\pi\)
−0.483391 + 0.875405i \(0.660595\pi\)
\(272\) −510.285 + 20.2350i −1.87605 + 0.0743932i
\(273\) 102.463 35.2956i 0.375321 0.129288i
\(274\) −108.981 97.8937i −0.397740 0.357276i
\(275\) −585.042 + 212.938i −2.12743 + 0.774320i
\(276\) 14.6316 21.0073i 0.0530130 0.0761136i
\(277\) 217.239 38.3051i 0.784256 0.138286i 0.232839 0.972515i \(-0.425198\pi\)
0.551417 + 0.834230i \(0.314087\pi\)
\(278\) −211.941 7.15040i −0.762379 0.0257209i
\(279\) −509.965 17.6761i −1.82783 0.0633551i
\(280\) 234.516 + 169.119i 0.837556 + 0.603995i
\(281\) 123.106 338.230i 0.438099 1.20367i −0.502628 0.864503i \(-0.667634\pi\)
0.940727 0.339164i \(-0.110144\pi\)
\(282\) −28.2318 + 66.7533i −0.100113 + 0.236714i
\(283\) 164.555 196.109i 0.581465 0.692964i −0.392476 0.919762i \(-0.628381\pi\)
0.973942 + 0.226799i \(0.0728259\pi\)
\(284\) 85.9745 + 21.2201i 0.302727 + 0.0747188i
\(285\) 2.81213 + 17.7402i 0.00986711 + 0.0622463i
\(286\) 150.362 117.762i 0.525740 0.411755i
\(287\) 80.1042 + 46.2482i 0.279109 + 0.161143i
\(288\) 215.210 + 191.386i 0.747258 + 0.664534i
\(289\) 364.875 + 631.983i 1.26254 + 2.18679i
\(290\) −73.5929 + 182.770i −0.253769 + 0.630243i
\(291\) 317.226 175.895i 1.09013 0.604451i
\(292\) 306.232 + 294.329i 1.04874 + 1.00798i
\(293\) 36.3263 206.016i 0.123980 0.703128i −0.857928 0.513770i \(-0.828248\pi\)
0.981908 0.189358i \(-0.0606405\pi\)
\(294\) 45.1656 196.811i 0.153625 0.669425i
\(295\) 439.230 368.558i 1.48892 1.24935i
\(296\) −358.453 36.3906i −1.21099 0.122941i
\(297\) −168.354 223.233i −0.566850 0.751627i
\(298\) 102.979 + 64.1793i 0.345567 + 0.215367i
\(299\) −15.0704 + 12.6456i −0.0504028 + 0.0422930i
\(300\) 188.463 + 696.404i 0.628210 + 2.32135i
\(301\) 193.144 + 34.0564i 0.641673 + 0.113144i
\(302\) −281.326 59.4503i −0.931543 0.196855i
\(303\) −54.3909 32.6718i −0.179508 0.107828i
\(304\) 4.83118 9.19067i 0.0158920 0.0302325i
\(305\) −344.359 + 198.816i −1.12905 + 0.651856i
\(306\) 138.186 557.656i 0.451588 1.82240i
\(307\) −254.721 147.063i −0.829712 0.479034i 0.0240423 0.999711i \(-0.492346\pi\)
−0.853754 + 0.520677i \(0.825680\pi\)
\(308\) 17.3427 + 161.335i 0.0563073 + 0.523816i
\(309\) 148.092 385.943i 0.479263 1.24901i
\(310\) 324.463 + 994.595i 1.04666 + 3.20837i
\(311\) 223.765 266.672i 0.719500 0.857467i −0.275082 0.961421i \(-0.588705\pi\)
0.994582 + 0.103954i \(0.0331495\pi\)
\(312\) −121.219 185.168i −0.388522 0.593486i
\(313\) 4.07031 + 1.48147i 0.0130042 + 0.00473313i 0.348514 0.937304i \(-0.386686\pi\)
−0.335510 + 0.942037i \(0.608909\pi\)
\(314\) −65.9917 123.759i −0.210165 0.394138i
\(315\) −256.269 + 200.326i −0.813553 + 0.635957i
\(316\) 213.020 317.431i 0.674114 1.00453i
\(317\) 94.9943 + 538.739i 0.299666 + 1.69949i 0.647606 + 0.761976i \(0.275770\pi\)
−0.347939 + 0.937517i \(0.613118\pi\)
\(318\) −41.6257 + 64.2824i −0.130898 + 0.202146i
\(319\) −103.907 + 37.8190i −0.325727 + 0.118555i
\(320\) 217.307 549.030i 0.679085 1.71572i
\(321\) 113.306 130.378i 0.352978 0.406161i
\(322\) −2.34575 16.5489i −0.00728493 0.0513942i
\(323\) −20.7129 −0.0641266
\(324\) −274.272 + 172.485i −0.846518 + 0.532361i
\(325\) 554.410i 1.70588i
\(326\) 77.5247 + 546.926i 0.237806 + 1.67769i
\(327\) −11.6242 10.1021i −0.0355481 0.0308934i
\(328\) 51.4229 181.762i 0.156777 0.554154i
\(329\) 16.1844 + 44.4662i 0.0491927 + 0.135156i
\(330\) −311.584 + 481.177i −0.944193 + 1.45811i
\(331\) 565.418 99.6984i 1.70821 0.301204i 0.767660 0.640857i \(-0.221421\pi\)
0.940551 + 0.339654i \(0.110310\pi\)
\(332\) 50.6472 75.4717i 0.152552 0.227324i
\(333\) 151.743 375.857i 0.455684 1.12870i
\(334\) −106.699 200.100i −0.319457 0.599103i
\(335\) 56.1126 154.168i 0.167500 0.460203i
\(336\) 187.985 4.19460i 0.559480 0.0124839i
\(337\) −156.900 131.654i −0.465577 0.390666i 0.379601 0.925150i \(-0.376061\pi\)
−0.845178 + 0.534485i \(0.820506\pi\)
\(338\) −52.0809 159.646i −0.154086 0.472327i
\(339\) −66.8849 25.6648i −0.197301 0.0757073i
\(340\) −1171.16 + 125.894i −3.44460 + 0.370275i
\(341\) −293.563 + 508.467i −0.860890 + 1.49111i
\(342\) 8.41428 + 8.10218i 0.0246032 + 0.0236906i
\(343\) −161.893 280.406i −0.471990 0.817511i
\(344\) −29.3554 399.446i −0.0853354 1.16118i
\(345\) 30.4057 50.6184i 0.0881325 0.146720i
\(346\) −242.600 51.2666i −0.701155 0.148169i
\(347\) 28.6119 162.266i 0.0824550 0.467625i −0.915422 0.402496i \(-0.868143\pi\)
0.997877 0.0651296i \(-0.0207461\pi\)
\(348\) 33.4721 + 123.685i 0.0961841 + 0.355417i
\(349\) 245.683 + 292.793i 0.703961 + 0.838949i 0.992969 0.118378i \(-0.0377696\pi\)
−0.289007 + 0.957327i \(0.593325\pi\)
\(350\) 399.751 + 249.136i 1.14214 + 0.711816i
\(351\) 238.074 72.8876i 0.678273 0.207657i
\(352\) 310.718 115.176i 0.882723 0.327204i
\(353\) −22.5100 26.8264i −0.0637677 0.0759954i 0.733218 0.679994i \(-0.238018\pi\)
−0.796985 + 0.603999i \(0.793573\pi\)
\(354\) 83.4036 363.434i 0.235603 1.02665i
\(355\) 201.151 + 35.4683i 0.566621 + 0.0999106i
\(356\) 335.622 349.195i 0.942759 0.980885i
\(357\) −181.894 328.045i −0.509507 0.918895i
\(358\) 48.4536 120.336i 0.135345 0.336135i
\(359\) −256.950 + 148.350i −0.715738 + 0.413231i −0.813182 0.582010i \(-0.802267\pi\)
0.0974440 + 0.995241i \(0.468933\pi\)
\(360\) 525.012 + 406.977i 1.45837 + 1.13049i
\(361\) −180.289 + 312.270i −0.499417 + 0.865015i
\(362\) 246.479 193.040i 0.680880 0.533259i
\(363\) 40.7777 6.46397i 0.112335 0.0178071i
\(364\) −140.285 34.6251i −0.385399 0.0951240i
\(365\) 750.481 + 629.729i 2.05611 + 1.72528i
\(366\) −100.727 + 238.167i −0.275212 + 0.650729i
\(367\) −191.410 69.6676i −0.521553 0.189830i 0.0678096 0.997698i \(-0.478399\pi\)
−0.589363 + 0.807868i \(0.700621\pi\)
\(368\) −31.5878 + 12.9363i −0.0858365 + 0.0351531i
\(369\) 180.247 + 112.566i 0.488473 + 0.305056i
\(370\) −830.559 28.0211i −2.24475 0.0757328i
\(371\) 8.68242 + 49.2405i 0.0234028 + 0.132724i
\(372\) 558.290 + 388.848i 1.50078 + 1.04529i
\(373\) −141.543 388.885i −0.379471 1.04259i −0.971576 0.236727i \(-0.923925\pi\)
0.592105 0.805861i \(-0.298297\pi\)
\(374\) −491.782 441.751i −1.31493 1.18115i
\(375\) 316.603 + 919.095i 0.844274 + 2.45092i
\(376\) 79.9237 54.3225i 0.212563 0.144475i
\(377\) 98.4662i 0.261184i
\(378\) −54.4286 + 204.414i −0.143991 + 0.540778i
\(379\) 357.515i 0.943311i 0.881783 + 0.471655i \(0.156343\pi\)
−0.881783 + 0.471655i \(0.843657\pi\)
\(380\) 9.68917 21.9014i 0.0254978 0.0576352i
\(381\) −303.527 58.9589i −0.796659 0.154748i
\(382\) 532.299 + 478.147i 1.39345 + 1.25169i
\(383\) −148.667 408.460i −0.388166 1.06648i −0.967826 0.251619i \(-0.919037\pi\)
0.579661 0.814858i \(-0.303185\pi\)
\(384\) −102.499 370.067i −0.266925 0.963717i
\(385\) 64.9911 + 368.583i 0.168808 + 0.957358i
\(386\) −0.645891 + 19.1445i −0.00167329 + 0.0495972i
\(387\) 440.767 + 93.5685i 1.13893 + 0.241779i
\(388\) −482.538 32.5965i −1.24365 0.0840116i
\(389\) −76.9360 28.0024i −0.197779 0.0719857i 0.241231 0.970468i \(-0.422449\pi\)
−0.439011 + 0.898482i \(0.644671\pi\)
\(390\) −307.745 407.279i −0.789089 1.04431i
\(391\) 52.1623 + 43.7694i 0.133408 + 0.111942i
\(392\) −193.008 + 187.712i −0.492367 + 0.478858i
\(393\) −311.691 384.805i −0.793107 0.979147i
\(394\) −368.849 470.956i −0.936164 1.19532i
\(395\) 440.873 763.614i 1.11613 1.93320i
\(396\) 26.9804 + 371.823i 0.0681324 + 0.938946i
\(397\) −97.6947 + 56.4040i −0.246082 + 0.142076i −0.617969 0.786202i \(-0.712044\pi\)
0.371887 + 0.928278i \(0.378711\pi\)
\(398\) −52.6846 + 130.844i −0.132373 + 0.328754i
\(399\) 7.62525 + 0.132111i 0.0191109 + 0.000331105i
\(400\) 292.928 916.254i 0.732320 2.29063i
\(401\) 285.239 + 50.2954i 0.711320 + 0.125425i 0.517588 0.855630i \(-0.326830\pi\)
0.193731 + 0.981055i \(0.437941\pi\)
\(402\) −31.3281 101.991i −0.0779307 0.253709i
\(403\) −336.069 400.512i −0.833919 0.993825i
\(404\) 37.2654 + 75.9493i 0.0922412 + 0.187993i
\(405\) −604.363 + 439.574i −1.49225 + 1.08537i
\(406\) 70.9979 + 44.2479i 0.174872 + 0.108985i
\(407\) −299.785 357.270i −0.736573 0.877813i
\(408\) −558.315 + 524.486i −1.36842 + 1.28550i
\(409\) 21.9368 124.410i 0.0536353 0.304181i −0.946175 0.323655i \(-0.895088\pi\)
0.999810 + 0.0194744i \(0.00619928\pi\)
\(410\) 90.0824 426.281i 0.219713 1.03971i
\(411\) −219.705 3.80650i −0.534563 0.00926156i
\(412\) −445.142 + 325.025i −1.08044 + 0.788896i
\(413\) −121.725 210.834i −0.294734 0.510494i
\(414\) −4.06901 38.1847i −0.00982853 0.0922337i
\(415\) 104.821 181.555i 0.252581 0.437482i
\(416\) 1.74355 + 295.084i 0.00419124 + 0.709336i
\(417\) −247.179 + 200.214i −0.592755 + 0.480130i
\(418\) 12.7776 4.16840i 0.0305685 0.00997225i
\(419\) 292.681 + 245.589i 0.698524 + 0.586131i 0.921353 0.388726i \(-0.127085\pi\)
−0.222829 + 0.974857i \(0.571529\pi\)
\(420\) 431.956 38.8766i 1.02847 0.0925632i
\(421\) −180.517 + 495.967i −0.428782 + 1.17807i 0.517771 + 0.855519i \(0.326762\pi\)
−0.946553 + 0.322549i \(0.895460\pi\)
\(422\) 78.9109 + 147.988i 0.186993 + 0.350682i
\(423\) 33.6221 + 103.387i 0.0794849 + 0.244414i
\(424\) 93.1346 41.8625i 0.219657 0.0987322i
\(425\) −1889.79 + 333.221i −4.44656 + 0.784049i
\(426\) 118.275 60.4595i 0.277640 0.141924i
\(427\) 57.7437 + 158.650i 0.135231 + 0.371545i
\(428\) −221.238 + 64.0052i −0.516911 + 0.149545i
\(429\) 54.6270 281.226i 0.127336 0.655539i
\(430\) −129.652 914.676i −0.301516 2.12715i
\(431\) 448.708i 1.04109i 0.853835 + 0.520543i \(0.174271\pi\)
−0.853835 + 0.520543i \(0.825729\pi\)
\(432\) 431.967 + 5.32978i 0.999924 + 0.0123374i
\(433\) 505.648 1.16778 0.583889 0.811834i \(-0.301530\pi\)
0.583889 + 0.811834i \(0.301530\pi\)
\(434\) 439.804 62.3405i 1.01337 0.143642i
\(435\) 96.2564 + 279.431i 0.221279 + 0.642371i
\(436\) 5.70658 + 19.7251i 0.0130885 + 0.0452412i
\(437\) −1.30095 + 0.473509i −0.00297701 + 0.00108354i
\(438\) 636.286 + 32.5097i 1.45271 + 0.0742232i
\(439\) 0.332361 + 1.88491i 0.000757087 + 0.00429365i 0.985184 0.171501i \(-0.0548617\pi\)
−0.984427 + 0.175795i \(0.943751\pi\)
\(440\) 697.147 313.356i 1.58442 0.712172i
\(441\) −142.268 267.399i −0.322602 0.606348i
\(442\) 519.432 276.975i 1.17519 0.626639i
\(443\) 192.570 + 70.0897i 0.434695 + 0.158216i 0.550093 0.835103i \(-0.314592\pi\)
−0.115398 + 0.993319i \(0.536814\pi\)
\(444\) −441.931 + 311.088i −0.995340 + 0.700649i
\(445\) 718.078 855.772i 1.61366 1.92308i
\(446\) −26.4627 81.1175i −0.0593334 0.181878i
\(447\) 179.767 28.4961i 0.402163 0.0637498i
\(448\) −213.550 131.345i −0.476675 0.293181i
\(449\) 80.4509 + 46.4484i 0.179178 + 0.103448i 0.586906 0.809655i \(-0.300346\pi\)
−0.407728 + 0.913103i \(0.633679\pi\)
\(450\) 898.040 + 603.855i 1.99565 + 1.34190i
\(451\) 211.757 122.258i 0.469528 0.271082i
\(452\) 56.3276 + 77.1442i 0.124619 + 0.170673i
\(453\) −377.204 + 209.151i −0.832679 + 0.461703i
\(454\) 146.429 + 30.9436i 0.322531 + 0.0681578i
\(455\) −328.219 57.8739i −0.721361 0.127195i
\(456\) −3.55928 15.1625i −0.00780543 0.0332511i
\(457\) 591.485 496.315i 1.29428 1.08603i 0.303173 0.952935i \(-0.401954\pi\)
0.991104 0.133092i \(-0.0424906\pi\)
\(458\) 419.791 673.575i 0.916573 1.47069i
\(459\) −391.539 767.702i −0.853027 1.67255i
\(460\) −70.6816 + 34.6807i −0.153656 + 0.0753929i
\(461\) 226.108 189.727i 0.490474 0.411556i −0.363722 0.931507i \(-0.618494\pi\)
0.854196 + 0.519951i \(0.174050\pi\)
\(462\) 178.227 + 165.763i 0.385773 + 0.358794i
\(463\) −74.4212 + 422.063i −0.160737 + 0.911584i 0.792615 + 0.609722i \(0.208719\pi\)
−0.953352 + 0.301861i \(0.902392\pi\)
\(464\) 52.0256 162.732i 0.112124 0.350715i
\(465\) 1345.23 + 808.061i 2.89298 + 1.73777i
\(466\) 547.227 + 220.342i 1.17431 + 0.472837i
\(467\) 116.967 + 202.592i 0.250464 + 0.433817i 0.963654 0.267155i \(-0.0860834\pi\)
−0.713189 + 0.700971i \(0.752750\pi\)
\(468\) −319.354 90.6675i −0.682380 0.193734i
\(469\) −60.3269 34.8297i −0.128629 0.0742639i
\(470\) 175.482 137.436i 0.373367 0.292417i
\(471\) −196.418 75.3685i −0.417023 0.160018i
\(472\) −356.411 + 346.633i −0.755109 + 0.734391i
\(473\) 333.257 397.160i 0.704560 0.839662i
\(474\) −70.6290 569.057i −0.149006 1.20054i
\(475\) 13.3440 36.6624i 0.0280927 0.0771839i
\(476\) −33.7082 + 498.995i −0.0708155 + 1.04831i
\(477\) 16.0169 + 113.752i 0.0335783 + 0.238474i
\(478\) −153.979 5.19490i −0.322132 0.0108680i
\(479\) 502.569 88.6164i 1.04920 0.185003i 0.377642 0.925952i \(-0.376735\pi\)
0.671562 + 0.740949i \(0.265624\pi\)
\(480\) −293.409 835.696i −0.611270 1.74103i
\(481\) 390.263 142.044i 0.811358 0.295310i
\(482\) 19.7709 22.0100i 0.0410184 0.0456640i
\(483\) −18.9239 16.4460i −0.0391799 0.0340496i
\(484\) −50.3426 22.2716i −0.104014 0.0460156i
\(485\) −1115.52 −2.30005
\(486\) −141.242 + 465.023i −0.290622 + 0.956838i
\(487\) 453.337 0.930877 0.465438 0.885080i \(-0.345897\pi\)
0.465438 + 0.885080i \(0.345897\pi\)
\(488\) 285.157 193.815i 0.584338 0.397162i
\(489\) 625.416 + 543.523i 1.27897 + 1.11150i
\(490\) −414.985 + 461.984i −0.846907 + 0.942824i
\(491\) −526.380 + 191.587i −1.07206 + 0.390197i −0.816946 0.576714i \(-0.804335\pi\)
−0.255112 + 0.966912i \(0.582112\pi\)
\(492\) −120.386 256.498i −0.244688 0.521338i
\(493\) −335.637 + 59.1818i −0.680805 + 0.120044i
\(494\) −0.403560 + 11.9617i −0.000816923 + 0.0242140i
\(495\) 119.892 + 851.475i 0.242206 + 1.72015i
\(496\) −343.796 839.477i −0.693136 1.69249i
\(497\) 29.6615 81.4944i 0.0596811 0.163973i
\(498\) −16.7926 135.298i −0.0337201 0.271682i
\(499\) −51.4796 + 61.3511i −0.103166 + 0.122948i −0.815157 0.579241i \(-0.803349\pi\)
0.711991 + 0.702189i \(0.247794\pi\)
\(500\) 310.589 1258.37i 0.621178 2.51673i
\(501\) −317.578 121.860i −0.633888 0.243233i
\(502\) −70.7175 90.2942i −0.140872 0.179869i
\(503\) −428.849 247.596i −0.852583 0.492239i 0.00893873 0.999960i \(-0.497155\pi\)
−0.861521 + 0.507721i \(0.830488\pi\)
\(504\) 208.883 189.523i 0.414451 0.376038i
\(505\) 97.5652 + 168.988i 0.193198 + 0.334629i
\(506\) −40.9870 16.5035i −0.0810019 0.0326156i
\(507\) −215.929 129.705i −0.425895 0.255829i
\(508\) 297.236 + 285.683i 0.585111 + 0.562368i
\(509\) 83.0060 470.750i 0.163077 0.924854i −0.787949 0.615741i \(-0.788857\pi\)
0.951025 0.309113i \(-0.100032\pi\)
\(510\) −1203.31 + 1293.78i −2.35942 + 2.53683i
\(511\) 318.648 267.378i 0.623578 0.523244i
\(512\) −153.029 + 488.596i −0.298885 + 0.954289i
\(513\) 17.4978 + 0.910203i 0.0341088 + 0.00177427i
\(514\) −35.3037 + 56.6465i −0.0686842 + 0.110207i
\(515\) −973.872 + 817.175i −1.89101 + 1.58675i
\(516\) −425.877 423.759i −0.825343 0.821238i
\(517\) 123.191 + 21.7219i 0.238281 + 0.0420153i
\(518\) −72.9536 + 345.225i −0.140837 + 0.666458i
\(519\) −325.279 + 180.360i −0.626742 + 0.347515i
\(520\) 49.8852 + 678.801i 0.0959331 + 1.30539i
\(521\) 440.723 254.451i 0.845917 0.488390i −0.0133541 0.999911i \(-0.504251\pi\)
0.859271 + 0.511520i \(0.170918\pi\)
\(522\) 159.497 + 107.248i 0.305550 + 0.205456i
\(523\) 536.132 + 309.536i 1.02511 + 0.591847i 0.915580 0.402136i \(-0.131732\pi\)
0.109530 + 0.993984i \(0.465065\pi\)
\(524\) 70.5689 + 656.489i 0.134673 + 1.25284i
\(525\) 697.832 110.618i 1.32920 0.210702i
\(526\) −868.330 + 283.272i −1.65082 + 0.538541i
\(527\) −1163.21 + 1386.26i −2.20724 + 2.63048i
\(528\) 238.869 435.910i 0.452403 0.825587i
\(529\) −492.821 179.372i −0.931608 0.339078i
\(530\) 207.821 110.816i 0.392116 0.209087i
\(531\) −262.714 493.784i −0.494753 0.929914i
\(532\) −8.44350 5.66623i −0.0158712 0.0106508i
\(533\) 37.8100 + 214.431i 0.0709381 + 0.402310i
\(534\) 37.0708 725.555i 0.0694209 1.35872i
\(535\) −499.181 + 181.687i −0.933049 + 0.339602i
\(536\) −38.7268 + 136.886i −0.0722515 + 0.255385i
\(537\) −63.3753 183.978i −0.118017 0.342603i
\(538\) −369.731 + 52.4079i −0.687232 + 0.0974124i
\(539\) −348.511 −0.646588
\(540\) 994.908 54.8869i 1.84242 0.101642i
\(541\) 455.741i 0.842404i 0.906967 + 0.421202i \(0.138392\pi\)
−0.906967 + 0.421202i \(0.861608\pi\)
\(542\) 518.809 73.5392i 0.957213 0.135681i
\(543\) 89.5466 460.996i 0.164911 0.848980i
\(544\) 1004.79 183.299i 1.84704 0.336948i
\(545\) 16.1989 + 44.5060i 0.0297227 + 0.0816625i
\(546\) −192.990 + 98.6524i −0.353462 + 0.180682i
\(547\) −393.878 + 69.4513i −0.720070 + 0.126968i −0.521662 0.853152i \(-0.674688\pi\)
−0.198407 + 0.980120i \(0.563577\pi\)
\(548\) 243.282 + 163.260i 0.443945 + 0.297920i
\(549\) 119.959 + 368.871i 0.218505 + 0.671897i
\(550\) 1098.74 585.875i 1.99770 1.06523i
\(551\) 2.36997 6.51144i 0.00430122 0.0118175i
\(552\) −23.0771 + 45.7057i −0.0418063 + 0.0828003i
\(553\) −286.793 240.648i −0.518614 0.435169i
\(554\) −419.426 + 136.828i −0.757087 + 0.246982i
\(555\) −968.648 + 784.603i −1.74531 + 1.41370i
\(556\) 421.694 45.3298i 0.758443 0.0815284i
\(557\) −318.973 + 552.477i −0.572662 + 0.991879i 0.423630 + 0.905836i \(0.360756\pi\)
−0.996291 + 0.0860438i \(0.972578\pi\)
\(558\) 1014.80 108.138i 1.81863 0.193796i
\(559\) 230.840 + 399.826i 0.412951 + 0.715253i
\(560\) −511.859 269.064i −0.914033 0.480472i
\(561\) −991.434 17.1771i −1.76726 0.0306187i
\(562\) −148.838 + 704.320i −0.264837 + 1.25324i
\(563\) 52.4639 297.538i 0.0931863 0.528486i −0.902102 0.431523i \(-0.857976\pi\)
0.995288 0.0969625i \(-0.0309127\pi\)
\(564\) 37.1681 140.109i 0.0659009 0.248421i
\(565\) 141.618 + 168.774i 0.250652 + 0.298716i
\(566\) −270.807 + 434.524i −0.478458 + 0.767710i
\(567\) 139.245 + 285.119i 0.245582 + 0.502855i
\(568\) −176.203 17.8884i −0.310217 0.0314936i
\(569\) 149.205 + 177.816i 0.262224 + 0.312506i 0.881051 0.473021i \(-0.156836\pi\)
−0.618827 + 0.785527i \(0.712392\pi\)
\(570\) −10.5480 34.3399i −0.0185053 0.0602454i
\(571\) 579.188 + 102.127i 1.01434 + 0.178856i 0.656020 0.754743i \(-0.272239\pi\)
0.358320 + 0.933599i \(0.383350\pi\)
\(572\) −264.693 + 275.397i −0.462750 + 0.481464i
\(573\) 1073.12 + 18.5923i 1.87280 + 0.0324472i
\(574\) −171.604 69.0968i −0.298962 0.120378i
\(575\) −111.078 + 64.1308i −0.193179 + 0.111532i
\(576\) −479.880 318.577i −0.833125 0.553085i
\(577\) −273.569 + 473.835i −0.474122 + 0.821204i −0.999561 0.0296273i \(-0.990568\pi\)
0.525439 + 0.850832i \(0.323901\pi\)
\(578\) −899.917 1149.04i −1.55695 1.98796i
\(579\) 18.0852 + 22.3275i 0.0312353 + 0.0385622i
\(580\) 94.4280 382.580i 0.162807 0.659620i
\(581\) −68.1874 57.2160i −0.117362 0.0984785i
\(582\) −578.802 + 437.350i −0.994506 + 0.751460i
\(583\) 124.205 + 45.2070i 0.213045 + 0.0775420i
\(584\) −689.016 496.877i −1.17982 0.850816i
\(585\) −749.019 159.006i −1.28037 0.271805i
\(586\) −14.1074 + 418.151i −0.0240741 + 0.713569i
\(587\) 140.356 + 796.000i 0.239108 + 1.35605i 0.833788 + 0.552085i \(0.186168\pi\)
−0.594680 + 0.803962i \(0.702721\pi\)
\(588\) −34.1951 + 402.403i −0.0581549 + 0.684360i
\(589\) −12.5839 34.5741i −0.0213649 0.0586997i
\(590\) −766.317 + 853.107i −1.29884 + 1.44594i
\(591\) −880.844 171.100i −1.49043 0.289510i
\(592\) 720.025 28.5520i 1.21626 0.0482298i
\(593\) 80.7272i 0.136133i −0.997681 0.0680667i \(-0.978317\pi\)
0.997681 0.0680667i \(-0.0216831\pi\)
\(594\) 396.035 + 394.793i 0.666725 + 0.664635i
\(595\) 1153.57i 1.93877i
\(596\) −221.934 98.1834i −0.372372 0.164737i
\(597\) 68.9092 + 200.043i 0.115426 + 0.335080i
\(598\) 26.2931 29.2710i 0.0439685 0.0489481i
\(599\) 156.491 + 429.954i 0.261253 + 0.717787i 0.999084 + 0.0428007i \(0.0136281\pi\)
−0.737831 + 0.674986i \(0.764150\pi\)
\(600\) −568.666 1326.12i −0.947777 2.21021i
\(601\) −51.1357 290.005i −0.0850843 0.482537i −0.997338 0.0729122i \(-0.976771\pi\)
0.912254 0.409625i \(-0.134340\pi\)
\(602\) −392.023 13.2259i −0.651201 0.0219700i
\(603\) −135.745 84.7738i −0.225116 0.140587i
\(604\) 573.770 + 38.7594i 0.949950 + 0.0641712i
\(605\) −119.315 43.4271i −0.197215 0.0717803i
\(606\) 116.876 + 49.4301i 0.192864 + 0.0815678i
\(607\) 360.380 + 302.394i 0.593706 + 0.498179i 0.889416 0.457099i \(-0.151112\pi\)
−0.295710 + 0.955278i \(0.595556\pi\)
\(608\) −6.98704 + 19.5555i −0.0114918 + 0.0321636i
\(609\) 123.939 19.6464i 0.203512 0.0322602i
\(610\) 626.098 490.354i 1.02639 0.803858i
\(611\) −55.6964 + 96.4689i −0.0911561 + 0.157887i
\(612\) −117.110 + 1143.06i −0.191357 + 1.86774i
\(613\) −9.61147 + 5.54919i −0.0156794 + 0.00905251i −0.507819 0.861464i \(-0.669548\pi\)
0.492140 + 0.870516i \(0.336215\pi\)
\(614\) 545.680 + 219.719i 0.888729 + 0.357849i
\(615\) −316.918 571.560i −0.515314 0.929366i
\(616\) −79.6267 314.610i −0.129264 0.510730i
\(617\) 1086.86 + 191.642i 1.76152 + 0.310603i 0.958444 0.285279i \(-0.0920864\pi\)
0.803072 + 0.595882i \(0.203197\pi\)
\(618\) −184.924 + 805.815i −0.299230 + 1.30391i
\(619\) −683.364 814.401i −1.10398 1.31567i −0.944515 0.328469i \(-0.893467\pi\)
−0.159466 0.987203i \(-0.550977\pi\)
\(620\) −921.674 1878.43i −1.48657 3.02973i
\(621\) −42.1423 39.2677i −0.0678619 0.0632330i
\(622\) −368.249 + 590.873i −0.592039 + 0.949957i
\(623\) −304.890 363.354i −0.489390 0.583232i
\(624\) 292.013 + 332.645i 0.467969 + 0.533086i
\(625\) 258.133 1463.95i 0.413013 2.34231i
\(626\) −8.47588 1.79114i −0.0135397 0.00286124i
\(627\) 10.3812 17.2823i 0.0165569 0.0275635i
\(628\) 165.415 + 226.546i 0.263399 + 0.360742i
\(629\) −718.741 1244.90i −1.14267 1.97917i
\(630\) 451.237 468.619i 0.716249 0.743839i
\(631\) −561.043 + 971.756i −0.889134 + 1.54002i −0.0482324 + 0.998836i \(0.515359\pi\)
−0.840901 + 0.541189i \(0.817975\pi\)
\(632\) −332.725 + 688.370i −0.526463 + 1.08919i
\(633\) 234.871 + 90.1235i 0.371044 + 0.142375i
\(634\) −339.325 1040.15i −0.535213 1.64062i
\(635\) 728.436 + 611.231i 1.14714 + 0.962568i
\(636\) 64.3843 138.976i 0.101233 0.218516i
\(637\) 106.145 291.630i 0.166632 0.457817i
\(638\) 195.142 104.055i 0.305864 0.163095i
\(639\) 74.5917 184.759i 0.116732 0.289137i
\(640\) −276.208 + 1148.19i −0.431574 + 1.79404i
\(641\) 828.308 146.053i 1.29221 0.227852i 0.515054 0.857157i \(-0.327772\pi\)
0.777158 + 0.629306i \(0.216661\pi\)
\(642\) −187.774 + 289.978i −0.292483 + 0.451680i
\(643\) −161.612 444.026i −0.251341 0.690554i −0.999631 0.0271817i \(-0.991347\pi\)
0.748289 0.663373i \(-0.230876\pi\)
\(644\) 9.29013 + 32.1119i 0.0144257 + 0.0498632i
\(645\) −1045.94 908.984i −1.62161 1.40928i
\(646\) 41.0158 5.81383i 0.0634920 0.00899974i
\(647\) 49.9792i 0.0772477i −0.999254 0.0386238i \(-0.987703\pi\)
0.999254 0.0386238i \(-0.0122974\pi\)
\(648\) 494.700 418.540i 0.763426 0.645895i
\(649\) −643.566 −0.991628
\(650\) 155.615 + 1097.84i 0.239408 + 1.68899i
\(651\) 437.067 502.920i 0.671379 0.772535i
\(652\) −307.030 1061.27i −0.470904 1.62771i
\(653\) 863.281 314.209i 1.32202 0.481177i 0.417917 0.908485i \(-0.362760\pi\)
0.904106 + 0.427308i \(0.140538\pi\)
\(654\) 25.8539 + 16.7416i 0.0395320 + 0.0255987i
\(655\) 264.455 + 1499.80i 0.403748 + 2.28977i
\(656\) −50.8096 + 374.361i −0.0774537 + 0.570672i
\(657\) 752.929 588.566i 1.14601 0.895839i
\(658\) −44.5295 83.5096i −0.0676740 0.126914i
\(659\) 1016.60 + 370.011i 1.54264 + 0.561474i 0.966676 0.256003i \(-0.0824056\pi\)
0.575962 + 0.817477i \(0.304628\pi\)
\(660\) 481.940 1040.29i 0.730212 1.57619i
\(661\) 253.636 302.272i 0.383716 0.457295i −0.539268 0.842134i \(-0.681299\pi\)
0.922983 + 0.384840i \(0.125743\pi\)
\(662\) −1091.66 + 356.128i −1.64903 + 0.537958i
\(663\) 316.330 824.388i 0.477120 1.24342i
\(664\) −79.1079 + 163.665i −0.119138 + 0.246484i
\(665\) −20.3118 11.7270i −0.0305440 0.0176346i
\(666\) −194.984 + 786.866i −0.292769 + 1.18148i
\(667\) −19.7280 + 11.3900i −0.0295773 + 0.0170765i
\(668\) 267.451 + 366.291i 0.400375 + 0.548340i
\(669\) −109.715 65.9041i −0.163999 0.0985113i
\(670\) −67.8416 + 321.034i −0.101256 + 0.479156i
\(671\) 439.529 + 77.5009i 0.655036 + 0.115501i
\(672\) −371.072 + 61.0711i −0.552191 + 0.0908796i
\(673\) −496.280 + 416.429i −0.737415 + 0.618765i −0.932142 0.362093i \(-0.882062\pi\)
0.194727 + 0.980858i \(0.437618\pi\)
\(674\) 347.647 + 216.663i 0.515797 + 0.321459i
\(675\) 1611.10 198.453i 2.38681 0.294005i
\(676\) 147.942 + 301.514i 0.218848 + 0.446027i
\(677\) 86.1473 72.2862i 0.127249 0.106774i −0.576942 0.816785i \(-0.695754\pi\)
0.704191 + 0.710011i \(0.251310\pi\)
\(678\) 139.650 + 32.0478i 0.205973 + 0.0472682i
\(679\) −82.2472 + 466.447i −0.121130 + 0.686962i
\(680\) 2283.81 578.025i 3.35855 0.850037i
\(681\) 196.333 108.862i 0.288301 0.159857i
\(682\) 438.596 1089.27i 0.643103 1.59717i
\(683\) −100.528 174.119i −0.147185 0.254933i 0.783001 0.622021i \(-0.213688\pi\)
−0.930186 + 0.367088i \(0.880355\pi\)
\(684\) −18.9362 13.6822i −0.0276845 0.0200032i
\(685\) 585.240 + 337.889i 0.854365 + 0.493268i
\(686\) 399.287 + 509.821i 0.582051 + 0.743180i
\(687\) −186.391 1175.84i −0.271311 1.71156i
\(688\) 170.249 + 782.746i 0.247455 + 1.13771i
\(689\) −75.6572 + 90.1648i −0.109807 + 0.130863i
\(690\) −46.0016 + 108.769i −0.0666690 + 0.157637i
\(691\) 287.328 789.426i 0.415814 1.14244i −0.538236 0.842794i \(-0.680909\pi\)
0.954050 0.299646i \(-0.0968686\pi\)
\(692\) 494.787 + 33.4240i 0.715010 + 0.0483005i
\(693\) 364.877 + 12.6471i 0.526518 + 0.0182498i
\(694\) −11.1115 + 329.351i −0.0160109 + 0.474569i
\(695\) 963.392 169.872i 1.38618 0.244420i
\(696\) −100.998 235.527i −0.145113 0.338401i
\(697\) 708.196 257.762i 1.01606 0.369817i
\(698\) −568.685 510.831i −0.814735 0.731849i
\(699\) 836.636 288.198i 1.19690 0.412300i
\(700\) −861.518 381.135i −1.23074 0.544479i
\(701\) −660.538 −0.942279 −0.471140 0.882059i \(-0.656157\pi\)
−0.471140 + 0.882059i \(0.656157\pi\)
\(702\) −450.976 + 211.157i −0.642416 + 0.300793i
\(703\) 29.2264 0.0415739
\(704\) −582.958 + 315.286i −0.828066 + 0.447850i
\(705\) 63.7534 328.210i 0.0904303 0.465546i
\(706\) 52.1043 + 46.8035i 0.0738021 + 0.0662939i
\(707\) 77.8543 28.3366i 0.110119 0.0400801i
\(708\) −63.1452 + 743.085i −0.0891882 + 1.04955i
\(709\) −1004.43 + 177.109i −1.41669 + 0.249800i −0.828983 0.559274i \(-0.811080\pi\)
−0.587706 + 0.809075i \(0.699969\pi\)
\(710\) −408.275 13.7742i −0.575035 0.0194003i
\(711\) −639.354 575.377i −0.899232 0.809251i
\(712\) −566.587 + 785.682i −0.795768 + 1.10349i
\(713\) −41.3694 + 113.661i −0.0580216 + 0.159413i
\(714\) 452.266 + 598.542i 0.633425 + 0.838295i
\(715\) −566.322 + 674.916i −0.792058 + 0.943938i
\(716\) −62.1714 + 251.891i −0.0868316 + 0.351803i
\(717\) −179.580 + 145.459i −0.250460 + 0.202872i
\(718\) 467.174 365.886i 0.650660 0.509591i
\(719\) 139.179 + 80.3549i 0.193573 + 0.111759i 0.593654 0.804720i \(-0.297685\pi\)
−0.400081 + 0.916480i \(0.631018\pi\)
\(720\) −1153.87 658.535i −1.60259 0.914632i
\(721\) 269.892 + 467.466i 0.374330 + 0.648358i
\(722\) 269.360 668.965i 0.373075 0.926544i
\(723\) 0.768771 44.3723i 0.00106331 0.0613725i
\(724\) −433.895 + 451.441i −0.599302 + 0.623538i
\(725\) 111.476 632.213i 0.153760 0.872018i
\(726\) −78.9339 + 24.2457i −0.108724 + 0.0333963i
\(727\) 708.427 594.441i 0.974453 0.817663i −0.00879055 0.999961i \(-0.502798\pi\)
0.983243 + 0.182298i \(0.0583537\pi\)
\(728\) 287.513 + 29.1887i 0.394935 + 0.0400943i
\(729\) 297.029 + 665.744i 0.407447 + 0.913229i
\(730\) −1662.86 1036.34i −2.27790 1.41965i
\(731\) 1224.12 1027.16i 1.67459 1.40515i
\(732\) 132.611 499.892i 0.181162 0.682913i
\(733\) −387.908 68.3987i −0.529206 0.0933133i −0.0973403 0.995251i \(-0.531034\pi\)
−0.431866 + 0.901938i \(0.642145\pi\)
\(734\) 398.586 + 84.2299i 0.543033 + 0.114755i
\(735\) −16.1363 + 931.361i −0.0219541 + 1.26716i
\(736\) 58.9194 34.4829i 0.0800535 0.0468518i
\(737\) −159.475 + 92.0732i −0.216385 + 0.124930i
\(738\) −388.521 172.310i −0.526451 0.233483i
\(739\) −1106.45 638.807i −1.49722 0.864421i −0.497227 0.867621i \(-0.665648\pi\)
−0.999995 + 0.00319951i \(0.998982\pi\)
\(740\) 1652.54 177.639i 2.23317 0.240053i
\(741\) 11.2998 + 13.9505i 0.0152495 + 0.0188265i
\(742\) −31.0141 95.0692i −0.0417980 0.128126i
\(743\) 578.271 689.156i 0.778292 0.927532i −0.220563 0.975373i \(-0.570790\pi\)
0.998855 + 0.0478408i \(0.0152340\pi\)
\(744\) −1214.67 613.296i −1.63263 0.824322i
\(745\) −525.996 191.447i −0.706034 0.256975i
\(746\) 389.439 + 730.344i 0.522036 + 0.979013i
\(747\) −152.011 136.800i −0.203496 0.183133i
\(748\) 1097.82 + 736.722i 1.46768 + 0.984923i
\(749\) 39.1665 + 222.124i 0.0522917 + 0.296561i
\(750\) −884.916 1731.13i −1.17989 2.30817i
\(751\) −710.580 + 258.630i −0.946178 + 0.344381i −0.768603 0.639727i \(-0.779048\pi\)
−0.177575 + 0.984107i \(0.556825\pi\)
\(752\) −143.018 + 130.003i −0.190183 + 0.172877i
\(753\) −168.880 32.8042i −0.224276 0.0435647i
\(754\) 27.6381 + 194.983i 0.0366553 + 0.258599i
\(755\) 1326.43 1.75687
\(756\) 50.4037 420.059i 0.0666716 0.555634i
\(757\) 873.422i 1.15379i −0.816817 0.576897i \(-0.804263\pi\)
0.816817 0.576897i \(-0.195737\pi\)
\(758\) −100.350 707.953i −0.132387 0.933975i
\(759\) −62.6635 + 21.5859i −0.0825607 + 0.0284399i
\(760\) −13.0391 + 46.0889i −0.0171567 + 0.0606433i
\(761\) 403.599 + 1108.88i 0.530353 + 1.45713i 0.858651 + 0.512560i \(0.171303\pi\)
−0.328298 + 0.944574i \(0.606475\pi\)
\(762\) 617.595 + 31.5548i 0.810492 + 0.0414105i
\(763\) 19.8042 3.49201i 0.0259557 0.00457668i
\(764\) −1188.27 797.420i −1.55533 1.04374i
\(765\) −91.8079 + 2648.71i −0.120010 + 3.46237i
\(766\) 409.041 + 767.107i 0.533997 + 1.00145i
\(767\) 196.008 538.528i 0.255552 0.702123i
\(768\) 306.843 + 704.040i 0.399535 + 0.916718i
\(769\) −933.341 783.166i −1.21371 1.01842i −0.999130 0.0417150i \(-0.986718\pi\)
−0.214578 0.976707i \(-0.568838\pi\)
\(770\) −232.152 711.628i −0.301496 0.924192i
\(771\) 15.6751 + 98.8860i 0.0203309 + 0.128257i
\(772\) −4.09461 38.0914i −0.00530390 0.0493412i
\(773\) 343.120 594.302i 0.443881 0.768825i −0.554092 0.832455i \(-0.686934\pi\)
0.997974 + 0.0636301i \(0.0202678\pi\)
\(774\) −899.072 61.5676i −1.16159 0.0795447i
\(775\) −1704.34 2952.00i −2.19915 3.80903i
\(776\) 964.674 70.8941i 1.24314 0.0913583i
\(777\) 256.657 + 462.880i 0.330318 + 0.595728i
\(778\) 160.209 + 33.8557i 0.205924 + 0.0435163i
\(779\) −2.66079 + 15.0901i −0.00341565 + 0.0193711i
\(780\) 723.716 + 720.116i 0.927841 + 0.923226i
\(781\) −147.364 175.622i −0.188687 0.224868i
\(782\) −115.578 72.0312i −0.147798 0.0921115i
\(783\) 286.140 35.2464i 0.365440 0.0450146i
\(784\) 329.507 425.884i 0.420289 0.543219i
\(785\) 415.884 + 495.631i 0.529789 + 0.631378i
\(786\) 725.222 + 674.505i 0.922675 + 0.858149i
\(787\) 278.322 + 49.0758i 0.353650 + 0.0623580i 0.347651 0.937624i \(-0.386979\pi\)
0.00599885 + 0.999982i \(0.498090\pi\)
\(788\) 862.587 + 829.060i 1.09465 + 1.05211i
\(789\) −705.476 + 1174.45i −0.894140 + 1.48854i
\(790\) −658.683 + 1635.86i −0.833775 + 2.07071i
\(791\) 81.0130 46.7729i 0.102418 0.0591313i
\(792\) −157.792 728.712i −0.199233 0.920092i
\(793\) −198.717 + 344.188i −0.250589 + 0.434033i
\(794\) 177.624 139.113i 0.223707 0.175205i
\(795\) 126.562 329.832i 0.159197 0.414884i
\(796\) 67.6003 273.886i 0.0849250 0.344078i
\(797\) −394.132 330.716i −0.494519 0.414951i 0.361124 0.932518i \(-0.382393\pi\)
−0.855642 + 0.517567i \(0.826838\pi\)
\(798\) −15.1366 + 1.87870i −0.0189682 + 0.00235426i
\(799\) 362.304 + 131.868i 0.453447 + 0.165041i
\(800\) −322.878 + 1896.59i −0.403597 + 2.37074i
\(801\) −671.140 858.562i −0.837878 1.07186i
\(802\) −578.950 19.5324i −0.721882 0.0243546i
\(803\) −190.946 1082.91i −0.237791 1.34858i
\(804\) 90.6637 + 193.170i 0.112766 + 0.240261i
\(805\) 26.3712 + 72.4544i 0.0327593 + 0.0900055i
\(806\) 777.904 + 698.765i 0.965142 + 0.866955i
\(807\) −367.430 + 422.790i −0.455303 + 0.523904i
\(808\) −95.1112 139.935i −0.117712 0.173187i
\(809\) 1348.61i 1.66701i −0.552509 0.833507i \(-0.686330\pi\)
0.552509 0.833507i \(-0.313670\pi\)
\(810\) 1073.38 1040.08i 1.32516 1.28405i
\(811\) 1368.20i 1.68706i 0.537085 + 0.843528i \(0.319525\pi\)
−0.537085 + 0.843528i \(0.680475\pi\)
\(812\) −153.010 67.6917i −0.188436 0.0833642i
\(813\) 515.581 593.263i 0.634171 0.729721i
\(814\) 693.917 + 623.322i 0.852478 + 0.765752i
\(815\) −871.544 2394.55i −1.06938 2.93809i
\(816\) 958.362 1195.30i 1.17446 1.46483i
\(817\) 5.64177 + 31.9960i 0.00690547 + 0.0391629i
\(818\) −8.51926 + 252.515i −0.0104147 + 0.308698i
\(819\) −121.712 + 301.472i −0.148610 + 0.368098i
\(820\) −58.7305 + 869.409i −0.0716225 + 1.06025i
\(821\) −444.400 161.748i −0.541291 0.197014i 0.0568818 0.998381i \(-0.481884\pi\)
−0.598173 + 0.801367i \(0.704106\pi\)
\(822\) 436.130 54.1307i 0.530572 0.0658524i
\(823\) −623.738 523.378i −0.757883 0.635939i 0.179692 0.983723i \(-0.442490\pi\)
−0.937575 + 0.347784i \(0.886934\pi\)
\(824\) 790.243 768.562i 0.959033 0.932721i
\(825\) 669.122 1743.80i 0.811057 2.11369i
\(826\) 300.219 + 383.328i 0.363461 + 0.464078i
\(827\) −490.273 + 849.177i −0.592833 + 1.02682i 0.401016 + 0.916071i \(0.368657\pi\)
−0.993849 + 0.110745i \(0.964676\pi\)
\(828\) 18.7754 + 74.4715i 0.0226756 + 0.0899415i
\(829\) 611.531 353.067i 0.737673 0.425895i −0.0835499 0.996504i \(-0.526626\pi\)
0.821222 + 0.570608i \(0.193292\pi\)
\(830\) −156.607 + 388.938i −0.188683 + 0.468601i
\(831\) −340.764 + 567.292i −0.410065 + 0.682662i
\(832\) −86.2786 583.837i −0.103700 0.701727i
\(833\) −1057.86 186.529i −1.26994 0.223925i
\(834\) 433.267 465.845i 0.519505 0.558568i
\(835\) 672.423 + 801.362i 0.805297 + 0.959715i
\(836\) −24.1323 + 11.8408i −0.0288664 + 0.0141636i
\(837\) 1043.58 1119.97i 1.24681 1.33808i
\(838\) −648.503 404.165i −0.773870 0.482297i
\(839\) 894.241 + 1065.72i 1.06584 + 1.27022i 0.961242 + 0.275706i \(0.0889117\pi\)
0.104600 + 0.994514i \(0.466644\pi\)
\(840\) −844.449 + 198.228i −1.00530 + 0.235985i
\(841\) −126.239 + 715.939i −0.150106 + 0.851295i
\(842\) 218.250 1032.79i 0.259204 1.22659i
\(843\) 523.625 + 944.357i 0.621145 + 1.12023i
\(844\) −197.798 270.897i −0.234358 0.320968i
\(845\) 387.328 + 670.872i 0.458376 + 0.793931i
\(846\) −95.5980 195.290i −0.113000 0.230840i
\(847\) −26.9557 + 46.6887i −0.0318249 + 0.0551224i
\(848\) −172.676 + 109.038i −0.203627 + 0.128582i
\(849\) 120.241 + 758.534i 0.141626 + 0.893444i
\(850\) 3648.64 1190.28i 4.29252 1.40033i
\(851\) −73.6024 61.7597i −0.0864893 0.0725731i
\(852\) −217.238 + 152.920i −0.254975 + 0.179484i
\(853\) 124.495 342.047i 0.145949 0.400992i −0.845080 0.534641i \(-0.820447\pi\)
0.991029 + 0.133648i \(0.0426692\pi\)
\(854\) −158.875 297.951i −0.186037 0.348889i
\(855\) −45.7045 28.5429i −0.0534556 0.0333835i
\(856\) 420.131 188.842i 0.490808 0.220610i
\(857\) −646.569 + 114.008i −0.754456 + 0.133031i −0.537632 0.843180i \(-0.680681\pi\)
−0.216824 + 0.976211i \(0.569570\pi\)
\(858\) −29.2364 + 572.218i −0.0340750 + 0.666921i
\(859\) 281.344 + 772.987i 0.327525 + 0.899868i 0.988736 + 0.149668i \(0.0478205\pi\)
−0.661211 + 0.750200i \(0.729957\pi\)
\(860\) 513.474 + 1774.85i 0.597063 + 2.06378i
\(861\) −262.359 + 90.3756i −0.304715 + 0.104966i
\(862\) −125.946 888.535i −0.146109 1.03078i
\(863\) 40.1634i 0.0465393i −0.999729 0.0232696i \(-0.992592\pi\)
0.999729 0.0232696i \(-0.00740762\pi\)
\(864\) −856.880 + 110.693i −0.991759 + 0.128117i
\(865\) 1143.84 1.32236
\(866\) −1001.29 + 141.928i −1.15622 + 0.163890i
\(867\) −2149.08 417.450i −2.47876 0.481488i
\(868\) −853.405 + 246.894i −0.983185 + 0.284440i
\(869\) −930.002 + 338.493i −1.07020 + 0.389520i
\(870\) −269.040 526.314i −0.309241 0.604958i
\(871\) −28.4749 161.489i −0.0326922 0.185407i
\(872\) −16.8368 37.4581i −0.0193082 0.0429565i
\(873\) −225.970 + 1064.46i −0.258844 + 1.21932i
\(874\) 2.44325 1.30280i 0.00279548 0.00149062i
\(875\) −1192.79 434.141i −1.36319 0.496161i
\(876\) −1269.10 + 114.221i −1.44875 + 0.130389i
\(877\) −966.128 + 1151.39i −1.10163 + 1.31287i −0.155951 + 0.987765i \(0.549844\pi\)
−0.945678 + 0.325105i \(0.894600\pi\)
\(878\) −1.18721 3.63923i −0.00135218 0.00414491i
\(879\) 395.015 + 487.673i 0.449391 + 0.554804i
\(880\) −1292.54 + 816.188i −1.46879 + 0.927487i
\(881\) −508.506 293.586i −0.577192 0.333242i 0.182825 0.983146i \(-0.441476\pi\)
−0.760017 + 0.649903i \(0.774809\pi\)
\(882\) 356.775 + 489.573i 0.404506 + 0.555072i
\(883\) −948.952 + 547.878i −1.07469 + 0.620473i −0.929459 0.368925i \(-0.879726\pi\)
−0.145231 + 0.989398i \(0.546393\pi\)
\(884\) −950.839 + 694.264i −1.07561 + 0.785367i
\(885\) −29.7975 + 1719.87i −0.0336695 + 1.94335i
\(886\) −401.001 84.7403i −0.452597 0.0956437i
\(887\) −65.5152 11.5521i −0.0738616 0.0130238i 0.136595 0.990627i \(-0.456384\pi\)
−0.210457 + 0.977603i \(0.567495\pi\)
\(888\) 787.796 740.063i 0.887158 0.833404i
\(889\) 309.288 259.524i 0.347906 0.291928i
\(890\) −1181.74 + 1896.16i −1.32780 + 2.13052i
\(891\) 836.788 + 58.0782i 0.939156 + 0.0651831i
\(892\) 75.1702 + 153.202i 0.0842715 + 0.171751i
\(893\) −6.00503 + 5.03881i −0.00672455 + 0.00564257i
\(894\) −347.977 + 106.886i −0.389236 + 0.119560i
\(895\) −103.916 + 589.337i −0.116107 + 0.658477i
\(896\) 459.740 + 200.149i 0.513103 + 0.223381i
\(897\) 1.02238 59.0104i 0.00113978 0.0657864i
\(898\) −172.347 69.3958i −0.191923 0.0772782i
\(899\) −302.700 524.292i −0.336707 0.583194i
\(900\) −1947.80 943.690i −2.16422 1.04854i
\(901\) 352.813 + 203.697i 0.391579 + 0.226078i
\(902\) −385.007 + 301.534i −0.426837 + 0.334294i
\(903\) −457.201 + 370.332i −0.506313 + 0.410113i
\(904\) −133.194 136.951i −0.147338 0.151495i
\(905\) −928.335 + 1106.35i −1.02578 + 1.22248i
\(906\) 688.235 520.038i 0.759641 0.573994i
\(907\) −167.009 + 458.852i −0.184133 + 0.505901i −0.997074 0.0764451i \(-0.975643\pi\)
0.812941 + 0.582346i \(0.197865\pi\)
\(908\) −298.645 20.1741i −0.328904 0.0222182i
\(909\) 181.017 58.8677i 0.199138 0.0647609i
\(910\) 666.186 + 22.4756i 0.732073 + 0.0246984i
\(911\) 188.809 33.2920i 0.207254 0.0365445i −0.0690571 0.997613i \(-0.521999\pi\)
0.276311 + 0.961068i \(0.410888\pi\)
\(912\) 11.3040 + 29.0258i 0.0123947 + 0.0318266i
\(913\) −221.115 + 80.4794i −0.242185 + 0.0881483i
\(914\) −1031.95 + 1148.83i −1.12905 + 1.25692i
\(915\) 227.464 1171.01i 0.248594 1.27979i
\(916\) −642.208 + 1451.65i −0.701101 + 1.58477i
\(917\) 646.626 0.705153
\(918\) 990.812 + 1410.31i 1.07932 + 1.53628i
\(919\) 1458.70 1.58727 0.793637 0.608392i \(-0.208185\pi\)
0.793637 + 0.608392i \(0.208185\pi\)
\(920\) 130.230 88.5143i 0.141554 0.0962112i
\(921\) 834.270 287.383i 0.905831 0.312034i
\(922\) −394.487 + 439.165i −0.427860 + 0.476318i
\(923\) 191.840 69.8241i 0.207844 0.0756491i
\(924\) −399.454 278.219i −0.432309 0.301103i
\(925\) 2666.54 470.183i 2.88274 0.508306i
\(926\) 28.9017 856.661i 0.0312114 0.925120i
\(927\) 582.495 + 1094.83i 0.628366 + 1.18105i
\(928\) −57.3448 + 336.845i −0.0617940 + 0.362980i
\(929\) −268.264 + 737.050i −0.288767 + 0.793380i 0.707473 + 0.706740i \(0.249835\pi\)
−0.996240 + 0.0866397i \(0.972387\pi\)
\(930\) −2890.65 1222.54i −3.10823 1.31456i
\(931\) 14.0384 16.7303i 0.0150788 0.0179703i
\(932\) −1145.47 282.724i −1.22904 0.303351i
\(933\) 163.506 + 1031.47i 0.175247 + 1.10554i
\(934\) −288.483 368.344i −0.308869 0.394372i
\(935\) 2640.93 + 1524.74i 2.82453 + 1.63074i
\(936\) 657.835 + 89.9021i 0.702816 + 0.0960492i
\(937\) −498.746 863.853i −0.532279 0.921935i −0.999290 0.0376831i \(-0.988002\pi\)
0.467010 0.884252i \(-0.345331\pi\)
\(938\) 129.236 + 52.0371i 0.137778 + 0.0554767i
\(939\) −11.3645 + 6.30138i −0.0121028 + 0.00671073i
\(940\) −308.915 + 321.407i −0.328633 + 0.341923i
\(941\) 188.816 1070.83i 0.200655 1.13797i −0.703477 0.710718i \(-0.748370\pi\)
0.904132 0.427253i \(-0.140518\pi\)
\(942\) 410.102 + 94.1133i 0.435353 + 0.0999080i
\(943\) 38.5884 32.3795i 0.0409209 0.0343367i
\(944\) 608.473 786.444i 0.644569 0.833097i
\(945\) 50.6922 974.511i 0.0536425 1.03123i
\(946\) −548.440 + 879.999i −0.579746 + 0.930232i
\(947\) 295.194 247.697i 0.311715 0.261560i −0.473485 0.880802i \(-0.657004\pi\)
0.785200 + 0.619242i \(0.212560\pi\)
\(948\) 299.587 + 1107.03i 0.316020 + 1.16775i
\(949\) 964.321 + 170.036i 1.01614 + 0.179174i
\(950\) −16.1333 + 76.3445i −0.0169824 + 0.0803627i
\(951\) −1406.85 845.073i −1.47934 0.888615i
\(952\) −73.3119 997.574i −0.0770083 1.04787i
\(953\) −262.318 + 151.450i −0.275255 + 0.158919i −0.631274 0.775560i \(-0.717467\pi\)
0.356018 + 0.934479i \(0.384134\pi\)
\(954\) −63.6454 220.757i −0.0667142 0.231401i
\(955\) −2858.51 1650.36i −2.99321 1.72813i
\(956\) 306.369 32.9329i 0.320469 0.0344487i
\(957\) 118.840 309.708i 0.124179 0.323624i
\(958\) −970.316 + 316.543i −1.01286 + 0.330421i
\(959\) 184.435 219.801i 0.192320 0.229198i
\(960\) 815.580 + 1572.49i 0.849562 + 1.63801i
\(961\) −2117.62 770.750i −2.20356 0.802029i
\(962\) −732.931 + 390.818i −0.761883 + 0.406256i
\(963\) 72.2523 + 513.137i 0.0750283 + 0.532852i
\(964\) −32.9725 + 49.1338i −0.0342038 + 0.0509687i
\(965\) −15.3444 87.0226i −0.0159010 0.0901788i
\(966\) 42.0893 + 27.2547i 0.0435707 + 0.0282140i
\(967\) 804.337 292.755i 0.831786 0.302745i 0.109194 0.994020i \(-0.465173\pi\)
0.722592 + 0.691275i \(0.242951\pi\)
\(968\) 105.940 + 29.9718i 0.109442 + 0.0309626i
\(969\) 40.7606 46.9020i 0.0420646 0.0484024i
\(970\) 2208.97 313.112i 2.27729 0.322796i
\(971\) 1093.20 1.12585 0.562925 0.826508i \(-0.309676\pi\)
0.562925 + 0.826508i \(0.309676\pi\)
\(972\) 149.163 960.487i 0.153460 0.988155i
\(973\) 415.359i 0.426885i
\(974\) −897.700 + 127.246i −0.921664 + 0.130642i
\(975\) 1255.40 + 1091.01i 1.28759 + 1.11899i
\(976\) −510.268 + 463.834i −0.522816 + 0.475240i
\(977\) −562.511 1545.49i −0.575753 1.58187i −0.795267 0.606259i \(-0.792669\pi\)
0.219514 0.975609i \(-0.429553\pi\)
\(978\) −1391.01 900.742i −1.42230 0.921004i
\(979\) −1234.84 + 217.735i −1.26133 + 0.222406i
\(980\) 692.082 1031.30i 0.706206 1.05235i
\(981\) 45.7503 6.44187i 0.0466364 0.00656664i
\(982\) 988.566 527.129i 1.00669 0.536791i
\(983\) 5.27861 14.5029i 0.00536990 0.0147537i −0.936979 0.349386i \(-0.886390\pi\)
0.942349 + 0.334633i \(0.108612\pi\)
\(984\) 310.386 + 474.128i 0.315432 + 0.481838i
\(985\) 2113.94 + 1773.81i 2.14613 + 1.80082i
\(986\) 648.018 211.401i 0.657220 0.214403i
\(987\) −132.538 50.8567i −0.134283 0.0515266i
\(988\) −2.55836 23.7999i −0.00258943 0.0240890i
\(989\) 53.4044 92.4991i 0.0539984 0.0935280i
\(990\) −476.409 1652.44i −0.481221 1.66914i
\(991\) 409.122 + 708.620i 0.412837 + 0.715055i 0.995199 0.0978748i \(-0.0312045\pi\)
−0.582361 + 0.812930i \(0.697871\pi\)
\(992\) 916.416 + 1565.84i 0.923806 + 1.57847i
\(993\) −886.921 + 1476.52i −0.893173 + 1.48693i
\(994\) −35.8616 + 169.701i −0.0360780 + 0.170726i
\(995\) 112.990 640.798i 0.113558 0.644018i
\(996\) 71.2291 + 263.204i 0.0715151 + 0.264261i
\(997\) −693.213 826.139i −0.695299 0.828625i 0.296687 0.954975i \(-0.404118\pi\)
−0.991986 + 0.126350i \(0.959674\pi\)
\(998\) 84.7199 135.937i 0.0848897 0.136210i
\(999\) 552.472 + 1083.25i 0.553025 + 1.08433i
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 216.3.x.a.5.2 420
8.5 even 2 inner 216.3.x.a.5.42 yes 420
27.11 odd 18 inner 216.3.x.a.173.42 yes 420
216.173 odd 18 inner 216.3.x.a.173.2 yes 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.3.x.a.5.2 420 1.1 even 1 trivial
216.3.x.a.5.42 yes 420 8.5 even 2 inner
216.3.x.a.173.2 yes 420 216.173 odd 18 inner
216.3.x.a.173.42 yes 420 27.11 odd 18 inner