Properties

Label 216.3.x.a.5.16
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 5.16
Character \(\chi\) \(=\) 216.5
Dual form 216.3.x.a.173.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.59804 - 1.20262i) q^{2} +(2.77706 + 1.13487i) q^{3} +(1.10743 + 3.84364i) q^{4} +(-6.71804 + 2.44517i) q^{5} +(-3.07303 - 5.15330i) q^{6} +(-0.389417 - 2.20849i) q^{7} +(2.85270 - 7.47409i) q^{8} +(6.42414 + 6.30321i) q^{9} +O(q^{10})\) \(q+(-1.59804 - 1.20262i) q^{2} +(2.77706 + 1.13487i) q^{3} +(1.10743 + 3.84364i) q^{4} +(-6.71804 + 2.44517i) q^{5} +(-3.07303 - 5.15330i) q^{6} +(-0.389417 - 2.20849i) q^{7} +(2.85270 - 7.47409i) q^{8} +(6.42414 + 6.30321i) q^{9} +(13.6763 + 4.17175i) q^{10} +(-8.35856 - 3.04227i) q^{11} +(-1.28663 + 11.9308i) q^{12} +(-10.1762 + 12.1275i) q^{13} +(-2.03367 + 3.99757i) q^{14} +(-21.4314 - 0.833733i) q^{15} +(-13.5472 + 8.51316i) q^{16} +(-3.82500 - 2.20837i) q^{17} +(-2.68566 - 17.7985i) q^{18} +(-2.69133 + 1.55384i) q^{19} +(-16.8381 - 23.1139i) q^{20} +(1.42492 - 6.57506i) q^{21} +(9.69860 + 14.9138i) q^{22} +(-39.4297 - 6.95252i) q^{23} +(16.4043 - 17.5186i) q^{24} +(20.0021 - 16.7838i) q^{25} +(30.8466 - 7.14213i) q^{26} +(10.6869 + 24.7950i) q^{27} +(8.05741 - 3.94254i) q^{28} +(-25.8356 + 21.6786i) q^{29} +(33.2454 + 27.1060i) q^{30} +(0.648484 - 3.67773i) q^{31} +(31.8869 + 2.68771i) q^{32} +(-19.7597 - 17.9345i) q^{33} +(3.45667 + 8.12905i) q^{34} +(8.01626 + 13.8846i) q^{35} +(-17.1130 + 31.6725i) q^{36} +(15.3411 + 8.85718i) q^{37} +(6.16951 + 0.753543i) q^{38} +(-42.0230 + 22.1301i) q^{39} +(-0.889177 + 57.1866i) q^{40} +(-23.0494 + 27.4692i) q^{41} +(-10.1843 + 8.79355i) q^{42} +(-13.2637 + 36.4418i) q^{43} +(2.43684 - 35.4964i) q^{44} +(-58.5700 - 26.6372i) q^{45} +(54.6488 + 58.5291i) q^{46} +(62.3405 - 10.9923i) q^{47} +(-47.2827 + 8.26726i) q^{48} +(41.3191 - 15.0389i) q^{49} +(-52.1485 + 2.76621i) q^{50} +(-8.11605 - 10.4736i) q^{51} +(-57.8831 - 25.6832i) q^{52} -38.6255 q^{53} +(12.7408 - 52.4754i) q^{54} +63.5920 q^{55} +(-17.6174 - 3.38964i) q^{56} +(-9.23740 + 1.26080i) q^{57} +(67.3572 - 3.57295i) q^{58} +(90.7704 - 33.0377i) q^{59} +(-20.5292 - 83.2978i) q^{60} +(9.90215 - 1.74602i) q^{61} +(-5.45920 + 5.09727i) q^{62} +(11.4189 - 16.6422i) q^{63} +(-47.7242 - 42.6428i) q^{64} +(38.7102 - 106.355i) q^{65} +(10.0084 + 52.4232i) q^{66} +(-38.7410 + 46.1697i) q^{67} +(4.25223 - 17.1476i) q^{68} +(-101.608 - 64.0552i) q^{69} +(3.88752 - 31.8285i) q^{70} +(102.151 + 58.9768i) q^{71} +(65.4370 - 30.0334i) q^{72} +(-64.0047 - 110.859i) q^{73} +(-13.8638 - 32.6035i) q^{74} +(74.5945 - 23.9097i) q^{75} +(-8.95288 - 8.62374i) q^{76} +(-3.46386 + 19.6446i) q^{77} +(93.7682 + 15.1727i) q^{78} +(41.9483 - 35.1988i) q^{79} +(70.1944 - 90.3169i) q^{80} +(1.53902 + 80.9854i) q^{81} +(69.8685 - 16.1772i) q^{82} +(19.4523 - 16.3225i) q^{83} +(26.8502 - 1.80456i) q^{84} +(31.0963 + 5.48312i) q^{85} +(65.0213 - 42.2841i) q^{86} +(-96.3494 + 30.8828i) q^{87} +(-46.5827 + 53.7940i) q^{88} +(-106.847 + 61.6879i) q^{89} +(61.5627 + 113.004i) q^{90} +(30.7462 + 17.7514i) q^{91} +(-16.9428 - 159.253i) q^{92} +(5.97463 - 9.47734i) q^{93} +(-112.842 - 57.4055i) q^{94} +(14.2811 - 17.0195i) q^{95} +(85.5017 + 43.6515i) q^{96} +(57.7071 + 21.0037i) q^{97} +(-84.1155 - 25.6583i) q^{98} +(-34.5205 - 72.2297i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59804 1.20262i −0.799018 0.601308i
\(3\) 2.77706 + 1.13487i 0.925687 + 0.378290i
\(4\) 1.10743 + 3.84364i 0.276858 + 0.960911i
\(5\) −6.71804 + 2.44517i −1.34361 + 0.489033i −0.910947 0.412523i \(-0.864647\pi\)
−0.432661 + 0.901557i \(0.642425\pi\)
\(6\) −3.07303 5.15330i −0.512171 0.858883i
\(7\) −0.389417 2.20849i −0.0556310 0.315499i 0.944276 0.329156i \(-0.106764\pi\)
−0.999907 + 0.0136563i \(0.995653\pi\)
\(8\) 2.85270 7.47409i 0.356588 0.934262i
\(9\) 6.42414 + 6.30321i 0.713793 + 0.700357i
\(10\) 13.6763 + 4.17175i 1.36763 + 0.417175i
\(11\) −8.35856 3.04227i −0.759869 0.276570i −0.0671168 0.997745i \(-0.521380\pi\)
−0.692753 + 0.721175i \(0.743602\pi\)
\(12\) −1.28663 + 11.9308i −0.107219 + 0.994235i
\(13\) −10.1762 + 12.1275i −0.782782 + 0.932883i −0.999056 0.0434497i \(-0.986165\pi\)
0.216274 + 0.976333i \(0.430610\pi\)
\(14\) −2.03367 + 3.99757i −0.145262 + 0.285541i
\(15\) −21.4314 0.833733i −1.42876 0.0555822i
\(16\) −13.5472 + 8.51316i −0.846699 + 0.532073i
\(17\) −3.82500 2.20837i −0.225000 0.129904i 0.383263 0.923639i \(-0.374800\pi\)
−0.608263 + 0.793735i \(0.708134\pi\)
\(18\) −2.68566 17.7985i −0.149203 0.988807i
\(19\) −2.69133 + 1.55384i −0.141649 + 0.0817811i −0.569150 0.822234i \(-0.692727\pi\)
0.427501 + 0.904015i \(0.359394\pi\)
\(20\) −16.8381 23.1139i −0.841907 1.15569i
\(21\) 1.42492 6.57506i 0.0678534 0.313098i
\(22\) 9.69860 + 14.9138i 0.440846 + 0.677899i
\(23\) −39.4297 6.95252i −1.71433 0.302283i −0.771669 0.636024i \(-0.780578\pi\)
−0.942665 + 0.333740i \(0.891689\pi\)
\(24\) 16.4043 17.5186i 0.683511 0.729940i
\(25\) 20.0021 16.7838i 0.800084 0.671350i
\(26\) 30.8466 7.14213i 1.18641 0.274697i
\(27\) 10.6869 + 24.7950i 0.395810 + 0.918332i
\(28\) 8.05741 3.94254i 0.287765 0.140805i
\(29\) −25.8356 + 21.6786i −0.890882 + 0.747539i −0.968387 0.249453i \(-0.919749\pi\)
0.0775049 + 0.996992i \(0.475305\pi\)
\(30\) 33.2454 + 27.1060i 1.10818 + 0.903533i
\(31\) 0.648484 3.67773i 0.0209188 0.118637i −0.972560 0.232651i \(-0.925260\pi\)
0.993479 + 0.114015i \(0.0363711\pi\)
\(32\) 31.8869 + 2.68771i 0.996467 + 0.0839910i
\(33\) −19.7597 17.9345i −0.598778 0.543468i
\(34\) 3.45667 + 8.12905i 0.101667 + 0.239090i
\(35\) 8.01626 + 13.8846i 0.229036 + 0.396702i
\(36\) −17.1130 + 31.6725i −0.475361 + 0.879791i
\(37\) 15.3411 + 8.85718i 0.414624 + 0.239383i 0.692775 0.721154i \(-0.256388\pi\)
−0.278151 + 0.960537i \(0.589721\pi\)
\(38\) 6.16951 + 0.753543i 0.162356 + 0.0198301i
\(39\) −42.0230 + 22.1301i −1.07751 + 0.567439i
\(40\) −0.889177 + 57.1866i −0.0222294 + 1.42966i
\(41\) −23.0494 + 27.4692i −0.562180 + 0.669980i −0.970006 0.243080i \(-0.921842\pi\)
0.407827 + 0.913059i \(0.366287\pi\)
\(42\) −10.1843 + 8.79355i −0.242484 + 0.209370i
\(43\) −13.2637 + 36.4418i −0.308459 + 0.847483i 0.684499 + 0.729014i \(0.260021\pi\)
−0.992958 + 0.118469i \(0.962201\pi\)
\(44\) 2.43684 35.4964i 0.0553826 0.806737i
\(45\) −58.5700 26.6372i −1.30156 0.591937i
\(46\) 54.6488 + 58.5291i 1.18802 + 1.27237i
\(47\) 62.3405 10.9923i 1.32639 0.233879i 0.534827 0.844962i \(-0.320377\pi\)
0.791567 + 0.611083i \(0.209266\pi\)
\(48\) −47.2827 + 8.26726i −0.985056 + 0.172235i
\(49\) 41.3191 15.0389i 0.843248 0.306917i
\(50\) −52.1485 + 2.76621i −1.04297 + 0.0553241i
\(51\) −8.11605 10.4736i −0.159138 0.205366i
\(52\) −57.8831 25.6832i −1.11314 0.493907i
\(53\) −38.6255 −0.728783 −0.364392 0.931246i \(-0.618723\pi\)
−0.364392 + 0.931246i \(0.618723\pi\)
\(54\) 12.7408 52.4754i 0.235941 0.971767i
\(55\) 63.5920 1.15622
\(56\) −17.6174 3.38964i −0.314596 0.0605293i
\(57\) −9.23740 + 1.26080i −0.162060 + 0.0221192i
\(58\) 67.3572 3.57295i 1.16133 0.0616026i
\(59\) 90.7704 33.0377i 1.53848 0.559962i 0.572801 0.819694i \(-0.305857\pi\)
0.965681 + 0.259733i \(0.0836344\pi\)
\(60\) −20.5292 83.2978i −0.342154 1.38830i
\(61\) 9.90215 1.74602i 0.162330 0.0286232i −0.0918922 0.995769i \(-0.529292\pi\)
0.254223 + 0.967146i \(0.418180\pi\)
\(62\) −5.45920 + 5.09727i −0.0880516 + 0.0822141i
\(63\) 11.4189 16.6422i 0.181253 0.264163i
\(64\) −47.7242 42.6428i −0.745690 0.666293i
\(65\) 38.7102 106.355i 0.595541 1.63624i
\(66\) 10.0084 + 52.4232i 0.151642 + 0.794290i
\(67\) −38.7410 + 46.1697i −0.578223 + 0.689100i −0.973297 0.229550i \(-0.926275\pi\)
0.395074 + 0.918649i \(0.370719\pi\)
\(68\) 4.25223 17.1476i 0.0625328 0.252170i
\(69\) −101.608 64.0552i −1.47259 0.928336i
\(70\) 3.88752 31.8285i 0.0555361 0.454693i
\(71\) 102.151 + 58.9768i 1.43874 + 0.830659i 0.997763 0.0668576i \(-0.0212973\pi\)
0.440981 + 0.897516i \(0.354631\pi\)
\(72\) 65.4370 30.0334i 0.908847 0.417130i
\(73\) −64.0047 110.859i −0.876777 1.51862i −0.854858 0.518862i \(-0.826356\pi\)
−0.0219185 0.999760i \(-0.506977\pi\)
\(74\) −13.8638 32.6035i −0.187349 0.440588i
\(75\) 74.5945 23.9097i 0.994593 0.318796i
\(76\) −8.95288 8.62374i −0.117801 0.113470i
\(77\) −3.46386 + 19.6446i −0.0449853 + 0.255124i
\(78\) 93.7682 + 15.1727i 1.20216 + 0.194522i
\(79\) 41.9483 35.1988i 0.530991 0.445555i −0.337452 0.941343i \(-0.609565\pi\)
0.868444 + 0.495788i \(0.165121\pi\)
\(80\) 70.1944 90.3169i 0.877430 1.12896i
\(81\) 1.53902 + 80.9854i 0.0190003 + 0.999819i
\(82\) 69.8685 16.1772i 0.852055 0.197283i
\(83\) 19.4523 16.3225i 0.234366 0.196656i −0.518040 0.855357i \(-0.673338\pi\)
0.752405 + 0.658701i \(0.228894\pi\)
\(84\) 26.8502 1.80456i 0.319645 0.0214828i
\(85\) 31.0963 + 5.48312i 0.365839 + 0.0645073i
\(86\) 65.0213 42.2841i 0.756062 0.491675i
\(87\) −96.3494 + 30.8828i −1.10746 + 0.354975i
\(88\) −46.5827 + 53.7940i −0.529349 + 0.611295i
\(89\) −106.847 + 61.6879i −1.20052 + 0.693122i −0.960672 0.277687i \(-0.910432\pi\)
−0.239852 + 0.970810i \(0.577099\pi\)
\(90\) 61.5627 + 113.004i 0.684030 + 1.25560i
\(91\) 30.7462 + 17.7514i 0.337871 + 0.195070i
\(92\) −16.9428 159.253i −0.184161 1.73101i
\(93\) 5.97463 9.47734i 0.0642434 0.101907i
\(94\) −112.842 57.4055i −1.20045 0.610697i
\(95\) 14.2811 17.0195i 0.150327 0.179153i
\(96\) 85.5017 + 43.6515i 0.890643 + 0.454703i
\(97\) 57.7071 + 21.0037i 0.594918 + 0.216533i 0.621891 0.783104i \(-0.286365\pi\)
−0.0269730 + 0.999636i \(0.508587\pi\)
\(98\) −84.1155 25.6583i −0.858321 0.261819i
\(99\) −34.5205 72.2297i −0.348692 0.729593i
\(100\) 86.6618 + 58.2940i 0.866618 + 0.582940i
\(101\) −24.7773 140.519i −0.245320 1.39128i −0.819749 0.572722i \(-0.805887\pi\)
0.574430 0.818554i \(-0.305224\pi\)
\(102\) 0.373968 + 26.4977i 0.00366636 + 0.259782i
\(103\) −165.824 + 60.3549i −1.60994 + 0.585970i −0.981428 0.191831i \(-0.938557\pi\)
−0.628511 + 0.777801i \(0.716335\pi\)
\(104\) 61.6123 + 110.654i 0.592426 + 1.06398i
\(105\) 6.50444 + 47.6557i 0.0619471 + 0.453864i
\(106\) 61.7249 + 46.4516i 0.582311 + 0.438223i
\(107\) −1.10560 −0.0103327 −0.00516637 0.999987i \(-0.501645\pi\)
−0.00516637 + 0.999987i \(0.501645\pi\)
\(108\) −83.4680 + 68.5353i −0.772852 + 0.634587i
\(109\) 35.4306i 0.325051i −0.986704 0.162526i \(-0.948036\pi\)
0.986704 0.162526i \(-0.0519640\pi\)
\(110\) −101.622 76.4767i −0.923839 0.695243i
\(111\) 32.5514 + 42.0071i 0.293256 + 0.378442i
\(112\) 24.0768 + 26.6037i 0.214971 + 0.237533i
\(113\) 69.5250 + 191.018i 0.615265 + 1.69043i 0.718285 + 0.695749i \(0.244927\pi\)
−0.103020 + 0.994679i \(0.532851\pi\)
\(114\) 16.2779 + 9.09424i 0.142789 + 0.0797740i
\(115\) 281.890 49.7049i 2.45122 0.432216i
\(116\) −111.936 75.2951i −0.964966 0.649096i
\(117\) −141.815 + 13.7660i −1.21210 + 0.117658i
\(118\) −184.786 56.3664i −1.56598 0.477682i
\(119\) −3.38764 + 9.30747i −0.0284676 + 0.0782140i
\(120\) −67.3687 + 157.802i −0.561406 + 1.31501i
\(121\) −32.0812 26.9193i −0.265134 0.222474i
\(122\) −17.9238 9.11828i −0.146916 0.0747400i
\(123\) −95.1835 + 50.1255i −0.773849 + 0.407524i
\(124\) 14.8540 1.58031i 0.119791 0.0127444i
\(125\) −3.97099 + 6.87795i −0.0317679 + 0.0550236i
\(126\) −38.2621 + 12.8623i −0.303667 + 0.102082i
\(127\) 18.9663 + 32.8506i 0.149341 + 0.258666i 0.930984 0.365060i \(-0.118952\pi\)
−0.781643 + 0.623726i \(0.785618\pi\)
\(128\) 24.9821 + 125.538i 0.195172 + 0.980769i
\(129\) −78.1909 + 86.1484i −0.606131 + 0.667817i
\(130\) −189.765 + 123.406i −1.45973 + 0.949278i
\(131\) −29.4405 + 166.965i −0.224737 + 1.27454i 0.638452 + 0.769662i \(0.279575\pi\)
−0.863188 + 0.504882i \(0.831536\pi\)
\(132\) 47.0511 95.8103i 0.356448 0.725836i
\(133\) 4.47970 + 5.33870i 0.0336819 + 0.0401406i
\(134\) 117.434 27.1903i 0.876372 0.202913i
\(135\) −132.423 140.442i −0.980909 1.04031i
\(136\) −27.4171 + 22.2886i −0.201597 + 0.163887i
\(137\) −2.38325 2.84024i −0.0173959 0.0207317i 0.757276 0.653095i \(-0.226530\pi\)
−0.774672 + 0.632363i \(0.782085\pi\)
\(138\) 85.3402 + 224.558i 0.618407 + 1.62723i
\(139\) 2.47862 + 0.437048i 0.0178318 + 0.00314423i 0.182557 0.983195i \(-0.441563\pi\)
−0.164725 + 0.986340i \(0.552674\pi\)
\(140\) −44.4898 + 46.1879i −0.317784 + 0.329913i
\(141\) 185.598 + 40.2221i 1.31630 + 0.285263i
\(142\) −92.3142 217.095i −0.650100 1.52884i
\(143\) 121.953 70.4097i 0.852819 0.492375i
\(144\) −140.689 30.7011i −0.977008 0.213202i
\(145\) 120.557 208.810i 0.831425 1.44007i
\(146\) −31.0394 + 254.130i −0.212599 + 1.74062i
\(147\) 131.813 + 5.12785i 0.896687 + 0.0348834i
\(148\) −17.0546 + 68.7744i −0.115234 + 0.464692i
\(149\) 162.553 + 136.398i 1.09096 + 0.915424i 0.996784 0.0801318i \(-0.0255341\pi\)
0.0941753 + 0.995556i \(0.469979\pi\)
\(150\) −147.959 51.4999i −0.986392 0.343332i
\(151\) 124.098 + 45.1680i 0.821841 + 0.299126i 0.718506 0.695521i \(-0.244826\pi\)
0.103335 + 0.994647i \(0.467049\pi\)
\(152\) 3.93598 + 24.5479i 0.0258946 + 0.161499i
\(153\) −10.6525 38.2966i −0.0696244 0.250305i
\(154\) 29.1602 27.2270i 0.189352 0.176799i
\(155\) 4.63613 + 26.2928i 0.0299105 + 0.169631i
\(156\) −131.598 137.014i −0.843576 0.878292i
\(157\) −4.39315 12.0701i −0.0279819 0.0768795i 0.924915 0.380174i \(-0.124136\pi\)
−0.952897 + 0.303294i \(0.901914\pi\)
\(158\) −109.366 + 5.80127i −0.692187 + 0.0367169i
\(159\) −107.265 43.8350i −0.674625 0.275692i
\(160\) −220.790 + 59.9127i −1.37993 + 0.374454i
\(161\) 89.7877i 0.557687i
\(162\) 94.9348 131.268i 0.586017 0.810298i
\(163\) 196.169i 1.20349i −0.798688 0.601746i \(-0.794472\pi\)
0.798688 0.601746i \(-0.205528\pi\)
\(164\) −131.107 58.1732i −0.799435 0.354715i
\(165\) 176.599 + 72.1687i 1.07030 + 0.437386i
\(166\) −50.7152 + 2.69018i −0.305513 + 0.0162059i
\(167\) 45.3843 + 124.692i 0.271763 + 0.746662i 0.998231 + 0.0594613i \(0.0189383\pi\)
−0.726468 + 0.687200i \(0.758839\pi\)
\(168\) −45.0777 29.4067i −0.268320 0.175040i
\(169\) −14.1749 80.3900i −0.0838753 0.475680i
\(170\) −43.0989 46.1591i −0.253523 0.271524i
\(171\) −27.0837 6.98195i −0.158384 0.0408301i
\(172\) −154.758 10.6241i −0.899755 0.0617683i
\(173\) −44.0936 16.0487i −0.254876 0.0927673i 0.211422 0.977395i \(-0.432190\pi\)
−0.466298 + 0.884628i \(0.654413\pi\)
\(174\) 191.110 + 66.5194i 1.09833 + 0.382296i
\(175\) −44.8560 37.6386i −0.256320 0.215078i
\(176\) 139.134 29.9436i 0.790536 0.170134i
\(177\) 289.569 + 11.2649i 1.63598 + 0.0636437i
\(178\) 244.931 + 29.9159i 1.37602 + 0.168067i
\(179\) −142.015 + 245.977i −0.793379 + 1.37417i 0.130484 + 0.991450i \(0.458347\pi\)
−0.923863 + 0.382722i \(0.874987\pi\)
\(180\) 37.5213 254.621i 0.208452 1.41456i
\(181\) −222.513 + 128.468i −1.22935 + 0.709766i −0.966894 0.255177i \(-0.917866\pi\)
−0.262457 + 0.964944i \(0.584533\pi\)
\(182\) −27.7855 65.3432i −0.152668 0.359028i
\(183\) 29.4804 + 6.38887i 0.161095 + 0.0349119i
\(184\) −164.445 + 274.868i −0.893723 + 1.49385i
\(185\) −124.719 21.9914i −0.674158 0.118872i
\(186\) −20.9453 + 7.95995i −0.112609 + 0.0427954i
\(187\) 25.2531 + 30.0954i 0.135043 + 0.160938i
\(188\) 111.289 + 227.441i 0.591960 + 1.20979i
\(189\) 50.5979 33.2575i 0.267714 0.175966i
\(190\) −43.2896 + 10.0232i −0.227840 + 0.0527534i
\(191\) 175.078 + 208.650i 0.916639 + 1.09241i 0.995428 + 0.0955161i \(0.0304501\pi\)
−0.0787892 + 0.996891i \(0.525105\pi\)
\(192\) −84.1389 172.582i −0.438223 0.898866i
\(193\) 48.3018 273.933i 0.250268 1.41934i −0.557664 0.830067i \(-0.688302\pi\)
0.807932 0.589276i \(-0.200587\pi\)
\(194\) −66.9586 102.964i −0.345148 0.530742i
\(195\) 228.200 251.424i 1.17026 1.28935i
\(196\) 103.563 + 142.161i 0.528380 + 0.725313i
\(197\) −159.727 276.655i −0.810795 1.40434i −0.912308 0.409504i \(-0.865702\pi\)
0.101514 0.994834i \(-0.467631\pi\)
\(198\) −31.6996 + 156.941i −0.160099 + 0.792629i
\(199\) −113.536 + 196.651i −0.570535 + 0.988196i 0.425976 + 0.904734i \(0.359931\pi\)
−0.996511 + 0.0834612i \(0.973403\pi\)
\(200\) −68.3833 197.377i −0.341916 0.986883i
\(201\) −159.983 + 84.2500i −0.795934 + 0.419154i
\(202\) −129.395 + 254.352i −0.640570 + 1.25917i
\(203\) 57.9379 + 48.6157i 0.285409 + 0.239486i
\(204\) 31.2690 42.7941i 0.153279 0.209775i
\(205\) 87.6799 240.898i 0.427707 1.17511i
\(206\) 337.576 + 102.973i 1.63872 + 0.499868i
\(207\) −209.478 293.198i −1.01197 1.41641i
\(208\) 34.6151 250.924i 0.166419 1.20637i
\(209\) 27.2229 4.80012i 0.130253 0.0229671i
\(210\) 46.9171 83.9778i 0.223415 0.399894i
\(211\) −49.4811 135.948i −0.234508 0.644304i −1.00000 0.000859038i \(-0.999727\pi\)
0.765492 0.643445i \(-0.222496\pi\)
\(212\) −42.7752 148.463i −0.201770 0.700296i
\(213\) 216.748 + 279.710i 1.01760 + 1.31319i
\(214\) 1.76679 + 1.32961i 0.00825603 + 0.00621315i
\(215\) 277.249i 1.28953i
\(216\) 215.806 9.14203i 0.999104 0.0423242i
\(217\) −8.37478 −0.0385935
\(218\) −42.6094 + 56.6194i −0.195456 + 0.259722i
\(219\) −51.9338 380.500i −0.237141 1.73744i
\(220\) 70.4240 + 244.425i 0.320109 + 1.11102i
\(221\) 65.7057 23.9149i 0.297311 0.108212i
\(222\) −1.49989 106.276i −0.00675626 0.478719i
\(223\) 21.5786 + 122.378i 0.0967651 + 0.548782i 0.994192 + 0.107619i \(0.0343227\pi\)
−0.897427 + 0.441163i \(0.854566\pi\)
\(224\) −6.48152 71.4687i −0.0289354 0.319057i
\(225\) 234.288 + 18.2564i 1.04128 + 0.0811395i
\(226\) 118.618 388.866i 0.524859 1.72065i
\(227\) −368.916 134.274i −1.62518 0.591517i −0.640820 0.767691i \(-0.721406\pi\)
−0.984359 + 0.176174i \(0.943628\pi\)
\(228\) −15.0759 34.1090i −0.0661222 0.149601i
\(229\) 43.9453 52.3719i 0.191901 0.228698i −0.661511 0.749935i \(-0.730085\pi\)
0.853412 + 0.521237i \(0.174529\pi\)
\(230\) −510.246 259.575i −2.21846 1.12859i
\(231\) −31.9134 + 50.6231i −0.138153 + 0.219148i
\(232\) 88.3268 + 254.940i 0.380719 + 1.09888i
\(233\) −5.71645 3.30039i −0.0245341 0.0141648i 0.487683 0.873021i \(-0.337842\pi\)
−0.512217 + 0.858856i \(0.671176\pi\)
\(234\) 243.181 + 148.550i 1.03923 + 0.634831i
\(235\) −391.928 + 226.280i −1.66778 + 0.962892i
\(236\) 227.508 + 312.302i 0.964015 + 1.32331i
\(237\) 156.439 50.1433i 0.660081 0.211575i
\(238\) 16.6069 10.7996i 0.0697768 0.0453766i
\(239\) 31.4765 + 5.55016i 0.131701 + 0.0232224i 0.239110 0.970992i \(-0.423144\pi\)
−0.107409 + 0.994215i \(0.534255\pi\)
\(240\) 297.432 171.154i 1.23930 0.713141i
\(241\) −315.684 + 264.890i −1.30989 + 1.09913i −0.321547 + 0.946894i \(0.604203\pi\)
−0.988344 + 0.152235i \(0.951353\pi\)
\(242\) 18.8933 + 81.5993i 0.0780715 + 0.337187i
\(243\) −87.6340 + 226.648i −0.360634 + 0.932707i
\(244\) 17.6770 + 36.1267i 0.0724469 + 0.148060i
\(245\) −240.811 + 202.064i −0.982902 + 0.824752i
\(246\) 212.388 + 34.3668i 0.863367 + 0.139702i
\(247\) 8.54325 48.4512i 0.0345881 0.196159i
\(248\) −25.6378 15.3383i −0.103378 0.0618480i
\(249\) 72.5442 23.2526i 0.291342 0.0933837i
\(250\) 14.6173 6.21564i 0.0584692 0.0248626i
\(251\) −45.3509 78.5501i −0.180681 0.312949i 0.761432 0.648245i \(-0.224497\pi\)
−0.942113 + 0.335297i \(0.891163\pi\)
\(252\) 76.6126 + 25.4601i 0.304018 + 0.101032i
\(253\) 308.424 + 178.069i 1.21907 + 0.703829i
\(254\) 9.19779 75.3055i 0.0362118 0.296478i
\(255\) 80.1338 + 50.5173i 0.314250 + 0.198107i
\(256\) 111.052 230.659i 0.433798 0.901010i
\(257\) −176.182 + 209.965i −0.685531 + 0.816984i −0.990807 0.135279i \(-0.956807\pi\)
0.305276 + 0.952264i \(0.401251\pi\)
\(258\) 228.555 43.6347i 0.885873 0.169127i
\(259\) 13.5870 37.3298i 0.0524593 0.144131i
\(260\) 451.661 + 31.0066i 1.73716 + 0.119256i
\(261\) −302.616 23.5807i −1.15945 0.0903476i
\(262\) 247.842 231.411i 0.945961 0.883248i
\(263\) 3.12309 0.550685i 0.0118749 0.00209386i −0.167708 0.985837i \(-0.553636\pi\)
0.179582 + 0.983743i \(0.442525\pi\)
\(264\) −190.412 + 96.5238i −0.721259 + 0.365621i
\(265\) 259.488 94.4458i 0.979199 0.356399i
\(266\) −0.738319 13.9188i −0.00277564 0.0523262i
\(267\) −366.727 + 50.0540i −1.37351 + 0.187468i
\(268\) −220.363 97.7766i −0.822249 0.364838i
\(269\) 257.359 0.956727 0.478363 0.878162i \(-0.341230\pi\)
0.478363 + 0.878162i \(0.341230\pi\)
\(270\) 42.7180 + 383.685i 0.158215 + 1.42106i
\(271\) 53.3971 0.197037 0.0985186 0.995135i \(-0.468590\pi\)
0.0985186 + 0.995135i \(0.468590\pi\)
\(272\) 70.6181 2.64573i 0.259626 0.00972693i
\(273\) 65.2387 + 84.1896i 0.238970 + 0.308387i
\(274\) 0.392793 + 7.40493i 0.00143355 + 0.0270253i
\(275\) −218.250 + 79.4363i −0.793635 + 0.288859i
\(276\) 133.681 461.483i 0.484350 1.67204i
\(277\) 245.732 43.3293i 0.887121 0.156423i 0.288523 0.957473i \(-0.406836\pi\)
0.598598 + 0.801050i \(0.295725\pi\)
\(278\) −3.43533 3.67925i −0.0123573 0.0132347i
\(279\) 27.3475 19.5387i 0.0980196 0.0700313i
\(280\) 126.643 20.3057i 0.452295 0.0725203i
\(281\) −142.185 + 390.650i −0.505996 + 1.39021i 0.379339 + 0.925258i \(0.376152\pi\)
−0.885335 + 0.464954i \(0.846071\pi\)
\(282\) −248.221 287.480i −0.880216 1.01943i
\(283\) −178.121 + 212.276i −0.629401 + 0.750091i −0.982656 0.185436i \(-0.940630\pi\)
0.353255 + 0.935527i \(0.385075\pi\)
\(284\) −113.560 + 457.944i −0.399861 + 1.61248i
\(285\) 58.9743 31.0570i 0.206927 0.108972i
\(286\) −279.561 34.1455i −0.977487 0.119390i
\(287\) 69.6413 + 40.2074i 0.242653 + 0.140096i
\(288\) 187.905 + 218.256i 0.652447 + 0.757834i
\(289\) −134.746 233.387i −0.466250 0.807569i
\(290\) −443.772 + 188.703i −1.53025 + 0.650699i
\(291\) 136.420 + 123.819i 0.468796 + 0.425493i
\(292\) 355.223 368.781i 1.21652 1.26295i
\(293\) −38.4190 + 217.885i −0.131123 + 0.743634i 0.846359 + 0.532613i \(0.178790\pi\)
−0.977482 + 0.211021i \(0.932321\pi\)
\(294\) −204.475 166.715i −0.695493 0.567057i
\(295\) −529.017 + 443.898i −1.79328 + 1.50474i
\(296\) 109.963 89.3938i 0.371497 0.302006i
\(297\) −13.8940 239.763i −0.0467812 0.807282i
\(298\) −95.7309 413.458i −0.321245 1.38744i
\(299\) 485.560 407.433i 1.62395 1.36265i
\(300\) 174.509 + 260.236i 0.581696 + 0.867454i
\(301\) 85.6466 + 15.1018i 0.284540 + 0.0501721i
\(302\) −143.993 221.422i −0.476799 0.733186i
\(303\) 90.6628 418.348i 0.299217 1.38069i
\(304\) 23.2318 43.9619i 0.0764205 0.144611i
\(305\) −62.2538 + 35.9422i −0.204111 + 0.117843i
\(306\) −29.0330 + 74.0103i −0.0948791 + 0.241864i
\(307\) −246.292 142.197i −0.802256 0.463182i 0.0420037 0.999117i \(-0.486626\pi\)
−0.844259 + 0.535935i \(0.819959\pi\)
\(308\) −79.3426 + 8.44118i −0.257606 + 0.0274064i
\(309\) −528.997 20.5793i −1.71197 0.0665997i
\(310\) 24.2114 47.5923i 0.0781014 0.153524i
\(311\) 198.948 237.097i 0.639705 0.762370i −0.344619 0.938743i \(-0.611992\pi\)
0.984324 + 0.176372i \(0.0564363\pi\)
\(312\) 45.5235 + 377.214i 0.145909 + 1.20902i
\(313\) 40.3078 + 14.6709i 0.128779 + 0.0468717i 0.405606 0.914048i \(-0.367061\pi\)
−0.276827 + 0.960920i \(0.589283\pi\)
\(314\) −7.49525 + 24.5717i −0.0238702 + 0.0782538i
\(315\) −36.0198 + 139.724i −0.114349 + 0.443570i
\(316\) 181.747 + 122.254i 0.575148 + 0.386880i
\(317\) −70.4296 399.426i −0.222175 1.26002i −0.868012 0.496543i \(-0.834602\pi\)
0.645837 0.763475i \(-0.276509\pi\)
\(318\) 118.697 + 199.049i 0.373262 + 0.625940i
\(319\) 281.901 102.603i 0.883701 0.321641i
\(320\) 424.881 + 169.782i 1.32775 + 0.530569i
\(321\) −3.07032 1.25472i −0.00956487 0.00390877i
\(322\) 107.980 143.484i 0.335342 0.445602i
\(323\) 13.7258 0.0424947
\(324\) −309.575 + 95.6014i −0.955477 + 0.295066i
\(325\) 413.369i 1.27191i
\(326\) −235.916 + 313.485i −0.723669 + 0.961611i
\(327\) 40.2092 98.3930i 0.122964 0.300896i
\(328\) 139.554 + 250.635i 0.425470 + 0.764130i
\(329\) −48.5529 133.398i −0.147577 0.405465i
\(330\) −195.420 327.709i −0.592182 0.993057i
\(331\) 336.541 59.3413i 1.01674 0.179279i 0.359647 0.933088i \(-0.382897\pi\)
0.657093 + 0.753810i \(0.271786\pi\)
\(332\) 84.2799 + 56.6918i 0.253855 + 0.170759i
\(333\) 42.7245 + 153.598i 0.128302 + 0.461255i
\(334\) 77.4313 253.843i 0.231830 0.760009i
\(335\) 147.371 404.898i 0.439913 1.20865i
\(336\) 36.6709 + 101.204i 0.109140 + 0.301203i
\(337\) 29.1113 + 24.4273i 0.0863836 + 0.0724845i 0.684957 0.728584i \(-0.259821\pi\)
−0.598573 + 0.801068i \(0.704265\pi\)
\(338\) −74.0262 + 145.513i −0.219012 + 0.430512i
\(339\) −23.7061 + 609.372i −0.0699294 + 1.79756i
\(340\) 13.3620 + 125.595i 0.0392999 + 0.369398i
\(341\) −16.6090 + 28.7677i −0.0487069 + 0.0843628i
\(342\) 34.8840 + 43.7286i 0.102000 + 0.127861i
\(343\) −104.247 180.560i −0.303926 0.526415i
\(344\) 234.532 + 203.092i 0.681778 + 0.590383i
\(345\) 839.235 + 181.876i 2.43257 + 0.527176i
\(346\) 51.1626 + 78.6740i 0.147869 + 0.227382i
\(347\) 67.5303 382.983i 0.194612 1.10370i −0.718359 0.695673i \(-0.755106\pi\)
0.912971 0.408025i \(-0.133782\pi\)
\(348\) −225.403 336.132i −0.647710 0.965897i
\(349\) 16.9756 + 20.2308i 0.0486408 + 0.0579679i 0.789816 0.613343i \(-0.210176\pi\)
−0.741176 + 0.671311i \(0.765731\pi\)
\(350\) 26.4167 + 114.092i 0.0754762 + 0.325978i
\(351\) −409.452 122.713i −1.16653 0.349609i
\(352\) −258.352 119.474i −0.733955 0.339415i
\(353\) −353.831 421.680i −1.00235 1.19456i −0.980845 0.194791i \(-0.937597\pi\)
−0.0215099 0.999769i \(-0.506847\pi\)
\(354\) −449.194 366.241i −1.26891 1.03458i
\(355\) −830.461 146.433i −2.33933 0.412486i
\(356\) −355.432 342.365i −0.998404 0.961699i
\(357\) −19.9705 + 22.0029i −0.0559397 + 0.0616327i
\(358\) 522.760 222.291i 1.46022 0.620923i
\(359\) −40.5034 + 23.3847i −0.112823 + 0.0651383i −0.555350 0.831617i \(-0.687416\pi\)
0.442527 + 0.896755i \(0.354082\pi\)
\(360\) −366.171 + 361.770i −1.01714 + 1.00492i
\(361\) −175.671 + 304.271i −0.486624 + 0.842857i
\(362\) 510.080 + 62.3011i 1.40906 + 0.172102i
\(363\) −58.5415 111.165i −0.161271 0.306239i
\(364\) −34.1804 + 137.836i −0.0939023 + 0.378670i
\(365\) 701.056 + 588.256i 1.92070 + 1.61166i
\(366\) −39.4273 45.6632i −0.107725 0.124763i
\(367\) 200.395 + 72.9380i 0.546037 + 0.198741i 0.600285 0.799786i \(-0.295054\pi\)
−0.0542481 + 0.998527i \(0.517276\pi\)
\(368\) 593.349 241.484i 1.61236 0.656207i
\(369\) −321.216 + 31.1806i −0.870505 + 0.0845002i
\(370\) 172.859 + 185.132i 0.467186 + 0.500358i
\(371\) 15.0414 + 85.3042i 0.0405429 + 0.229930i
\(372\) 43.0440 + 12.4688i 0.115710 + 0.0335183i
\(373\) −166.241 456.744i −0.445686 1.22451i −0.935699 0.352798i \(-0.885230\pi\)
0.490013 0.871715i \(-0.336992\pi\)
\(374\) −4.16207 78.4633i −0.0111285 0.209795i
\(375\) −18.8333 + 14.5939i −0.0502220 + 0.0389172i
\(376\) 95.6814 497.297i 0.254472 1.32260i
\(377\) 533.926i 1.41625i
\(378\) −120.853 7.70313i −0.319717 0.0203787i
\(379\) 151.362i 0.399372i 0.979860 + 0.199686i \(0.0639923\pi\)
−0.979860 + 0.199686i \(0.936008\pi\)
\(380\) 81.2323 + 36.0433i 0.213769 + 0.0948509i
\(381\) 15.3894 + 112.752i 0.0403920 + 0.295938i
\(382\) −28.8554 543.981i −0.0755377 1.42403i
\(383\) −42.2909 116.193i −0.110420 0.303377i 0.872159 0.489223i \(-0.162720\pi\)
−0.982579 + 0.185846i \(0.940497\pi\)
\(384\) −73.0932 + 376.979i −0.190347 + 0.981717i
\(385\) −24.7638 140.443i −0.0643216 0.364786i
\(386\) −406.624 + 379.666i −1.05343 + 0.983592i
\(387\) −314.908 + 150.503i −0.813716 + 0.388896i
\(388\) −16.8238 + 245.065i −0.0433603 + 0.631612i
\(389\) 71.0914 + 25.8752i 0.182754 + 0.0665171i 0.431776 0.901981i \(-0.357887\pi\)
−0.249022 + 0.968498i \(0.580109\pi\)
\(390\) −667.038 + 127.348i −1.71035 + 0.326533i
\(391\) 135.465 + 113.669i 0.346458 + 0.290712i
\(392\) 5.46886 351.725i 0.0139512 0.897257i
\(393\) −271.242 + 430.262i −0.690183 + 1.09481i
\(394\) −77.4602 + 634.193i −0.196600 + 1.60963i
\(395\) −195.743 + 339.038i −0.495553 + 0.858323i
\(396\) 239.396 212.674i 0.604536 0.537056i
\(397\) −305.610 + 176.444i −0.769798 + 0.444443i −0.832802 0.553570i \(-0.813265\pi\)
0.0630047 + 0.998013i \(0.479932\pi\)
\(398\) 417.931 177.714i 1.05008 0.446519i
\(399\) 6.38166 + 19.9098i 0.0159941 + 0.0498992i
\(400\) −128.089 + 397.654i −0.320223 + 0.994134i
\(401\) −553.188 97.5420i −1.37952 0.243247i −0.565820 0.824529i \(-0.691440\pi\)
−0.813702 + 0.581282i \(0.802551\pi\)
\(402\) 356.978 + 57.7630i 0.888006 + 0.143689i
\(403\) 38.0026 + 45.2897i 0.0942992 + 0.112381i
\(404\) 512.665 250.850i 1.26897 0.620917i
\(405\) −208.362 540.300i −0.514474 1.33407i
\(406\) −34.1209 147.367i −0.0840416 0.362972i
\(407\) −101.284 120.705i −0.248854 0.296573i
\(408\) −101.434 + 30.7819i −0.248612 + 0.0754458i
\(409\) −54.8866 + 311.277i −0.134197 + 0.761069i 0.841219 + 0.540695i \(0.181839\pi\)
−0.975416 + 0.220374i \(0.929272\pi\)
\(410\) −429.824 + 279.519i −1.04835 + 0.681754i
\(411\) −3.39511 10.5922i −0.00826061 0.0257718i
\(412\) −415.621 570.528i −1.00879 1.38478i
\(413\) −108.311 187.601i −0.262255 0.454239i
\(414\) −17.8499 + 720.462i −0.0431158 + 1.74025i
\(415\) −90.7705 + 157.219i −0.218724 + 0.378841i
\(416\) −357.082 + 359.358i −0.858370 + 0.863840i
\(417\) 6.38730 + 4.02663i 0.0153173 + 0.00965618i
\(418\) −49.2758 25.0678i −0.117885 0.0599709i
\(419\) 17.9096 + 15.0279i 0.0427437 + 0.0358662i 0.663909 0.747813i \(-0.268896\pi\)
−0.621166 + 0.783679i \(0.713341\pi\)
\(420\) −175.968 + 77.7763i −0.418972 + 0.185182i
\(421\) −172.450 + 473.802i −0.409620 + 1.12542i 0.547771 + 0.836628i \(0.315476\pi\)
−0.957391 + 0.288794i \(0.906746\pi\)
\(422\) −84.4208 + 276.757i −0.200049 + 0.655822i
\(423\) 469.771 + 322.329i 1.11057 + 0.762008i
\(424\) −110.187 + 288.691i −0.259875 + 0.680874i
\(425\) −113.573 + 20.0259i −0.267230 + 0.0471199i
\(426\) −9.98723 707.651i −0.0234442 1.66115i
\(427\) −7.71214 21.1889i −0.0180612 0.0496228i
\(428\) −1.22438 4.24954i −0.00286070 0.00992883i
\(429\) 418.577 57.1309i 0.975705 0.133172i
\(430\) −333.424 + 443.054i −0.775405 + 1.03036i
\(431\) 114.847i 0.266465i 0.991085 + 0.133233i \(0.0425358\pi\)
−0.991085 + 0.133233i \(0.957464\pi\)
\(432\) −355.861 244.923i −0.823752 0.566951i
\(433\) −459.280 −1.06069 −0.530346 0.847781i \(-0.677938\pi\)
−0.530346 + 0.847781i \(0.677938\pi\)
\(434\) 13.3832 + 10.0716i 0.0308369 + 0.0232065i
\(435\) 571.766 443.062i 1.31440 1.01853i
\(436\) 136.183 39.2371i 0.312345 0.0899932i
\(437\) 116.921 42.5559i 0.267555 0.0973820i
\(438\) −374.603 + 670.509i −0.855259 + 1.53084i
\(439\) 73.5571 + 417.163i 0.167556 + 0.950258i 0.946390 + 0.323027i \(0.104701\pi\)
−0.778834 + 0.627231i \(0.784188\pi\)
\(440\) 181.409 475.293i 0.412294 1.08021i
\(441\) 360.233 + 163.831i 0.816856 + 0.371499i
\(442\) −133.761 40.8018i −0.302626 0.0923118i
\(443\) 580.544 + 211.301i 1.31048 + 0.476977i 0.900397 0.435070i \(-0.143276\pi\)
0.410086 + 0.912047i \(0.365499\pi\)
\(444\) −125.412 + 171.636i −0.282459 + 0.386567i
\(445\) 566.962 675.679i 1.27407 1.51838i
\(446\) 112.691 221.516i 0.252670 0.496672i
\(447\) 296.625 + 563.263i 0.663591 + 1.26010i
\(448\) −75.5917 + 122.004i −0.168731 + 0.272331i
\(449\) 23.4958 + 13.5653i 0.0523292 + 0.0302123i 0.525936 0.850524i \(-0.323715\pi\)
−0.473607 + 0.880736i \(0.657048\pi\)
\(450\) −352.445 310.932i −0.783211 0.690961i
\(451\) 276.228 159.480i 0.612479 0.353615i
\(452\) −657.212 + 478.769i −1.45401 + 1.05922i
\(453\) 293.368 + 266.270i 0.647611 + 0.587791i
\(454\) 428.060 + 658.239i 0.942863 + 1.44986i
\(455\) −249.959 44.0746i −0.549361 0.0968673i
\(456\) −16.9283 + 72.6378i −0.0371234 + 0.159294i
\(457\) 590.982 495.893i 1.29318 1.08510i 0.301895 0.953341i \(-0.402381\pi\)
0.991281 0.131763i \(-0.0420637\pi\)
\(458\) −133.209 + 30.8429i −0.290850 + 0.0673427i
\(459\) 13.8790 118.441i 0.0302375 0.258042i
\(460\) 503.223 + 1028.44i 1.09396 + 2.23574i
\(461\) −251.687 + 211.191i −0.545960 + 0.458115i −0.873570 0.486698i \(-0.838201\pi\)
0.327610 + 0.944813i \(0.393757\pi\)
\(462\) 111.879 42.5179i 0.242162 0.0920302i
\(463\) −23.3329 + 132.327i −0.0503949 + 0.285804i −0.999582 0.0289084i \(-0.990797\pi\)
0.949187 + 0.314712i \(0.101908\pi\)
\(464\) 165.446 513.627i 0.356564 1.10695i
\(465\) −16.9641 + 78.2781i −0.0364820 + 0.168340i
\(466\) 5.16598 + 12.1488i 0.0110858 + 0.0260704i
\(467\) 130.635 + 226.266i 0.279732 + 0.484510i 0.971318 0.237784i \(-0.0764210\pi\)
−0.691586 + 0.722294i \(0.743088\pi\)
\(468\) −209.963 529.842i −0.448638 1.13214i
\(469\) 117.052 + 67.5799i 0.249578 + 0.144094i
\(470\) 898.442 + 109.735i 1.91158 + 0.233480i
\(471\) 1.49794 38.5050i 0.00318034 0.0817516i
\(472\) 12.0141 772.674i 0.0254535 1.63702i
\(473\) 221.731 264.249i 0.468776 0.558666i
\(474\) −310.298 108.005i −0.654638 0.227859i
\(475\) −27.7530 + 76.2507i −0.0584273 + 0.160528i
\(476\) −39.5262 2.71348i −0.0830382 0.00570058i
\(477\) −248.135 243.465i −0.520200 0.510408i
\(478\) −43.6259 46.7235i −0.0912676 0.0977479i
\(479\) 138.271 24.3809i 0.288666 0.0508996i −0.0274400 0.999623i \(-0.508736\pi\)
0.316106 + 0.948724i \(0.397624\pi\)
\(480\) −681.139 84.1865i −1.41904 0.175388i
\(481\) −263.529 + 95.9166i −0.547877 + 0.199411i
\(482\) 823.035 43.6577i 1.70754 0.0905762i
\(483\) −101.897 + 249.346i −0.210968 + 0.516244i
\(484\) 67.9404 153.120i 0.140373 0.316364i
\(485\) −439.036 −0.905228
\(486\) 412.612 256.801i 0.848997 0.528398i
\(487\) 31.9539 0.0656138 0.0328069 0.999462i \(-0.489555\pi\)
0.0328069 + 0.999462i \(0.489555\pi\)
\(488\) 15.1980 78.9905i 0.0311435 0.161866i
\(489\) 222.627 544.774i 0.455269 1.11406i
\(490\) 627.830 33.3031i 1.28129 0.0679656i
\(491\) −84.4368 + 30.7325i −0.171969 + 0.0625916i −0.426570 0.904455i \(-0.640278\pi\)
0.254601 + 0.967046i \(0.418056\pi\)
\(492\) −298.074 310.341i −0.605841 0.630774i
\(493\) 146.695 25.8664i 0.297557 0.0524673i
\(494\) −71.9205 + 67.1525i −0.145588 + 0.135936i
\(495\) 408.524 + 400.834i 0.825300 + 0.809766i
\(496\) 22.5240 + 55.3436i 0.0454113 + 0.111580i
\(497\) 90.4706 248.566i 0.182033 0.500133i
\(498\) −143.892 50.0844i −0.288940 0.100571i
\(499\) 126.068 150.242i 0.252642 0.301087i −0.624785 0.780796i \(-0.714814\pi\)
0.877427 + 0.479710i \(0.159258\pi\)
\(500\) −30.8340 7.64618i −0.0616680 0.0152924i
\(501\) −15.4748 + 397.784i −0.0308878 + 0.793980i
\(502\) −21.9932 + 180.066i −0.0438111 + 0.358696i
\(503\) −718.653 414.914i −1.42873 0.824880i −0.431712 0.902011i \(-0.642090\pi\)
−0.997021 + 0.0771317i \(0.975424\pi\)
\(504\) −91.8108 132.822i −0.182164 0.263535i
\(505\) 510.047 + 883.427i 1.00999 + 1.74936i
\(506\) −278.725 655.476i −0.550839 1.29541i
\(507\) 51.8676 239.335i 0.102303 0.472060i
\(508\) −105.262 + 109.279i −0.207209 + 0.215117i
\(509\) 126.609 718.035i 0.248741 1.41068i −0.562902 0.826524i \(-0.690315\pi\)
0.811643 0.584154i \(-0.198574\pi\)
\(510\) −67.3037 177.098i −0.131968 0.347252i
\(511\) −219.908 + 184.525i −0.430348 + 0.361105i
\(512\) −454.859 + 235.048i −0.888396 + 0.459077i
\(513\) −67.2893 50.1257i −0.131168 0.0977110i
\(514\) 534.051 123.653i 1.03901 0.240570i
\(515\) 966.432 810.933i 1.87657 1.57463i
\(516\) −417.715 205.134i −0.809525 0.397547i
\(517\) −554.519 97.7766i −1.07257 0.189123i
\(518\) −66.6059 + 43.3145i −0.128583 + 0.0836188i
\(519\) −104.237 94.6088i −0.200842 0.182291i
\(520\) −684.481 592.724i −1.31631 1.13985i
\(521\) 207.706 119.919i 0.398667 0.230171i −0.287241 0.957858i \(-0.592738\pi\)
0.685909 + 0.727687i \(0.259405\pi\)
\(522\) 455.233 + 401.614i 0.872094 + 0.769375i
\(523\) −15.8600 9.15677i −0.0303250 0.0175082i 0.484761 0.874647i \(-0.338907\pi\)
−0.515086 + 0.857139i \(0.672240\pi\)
\(524\) −674.358 + 71.7443i −1.28694 + 0.136917i
\(525\) −81.8528 155.431i −0.155910 0.296058i
\(526\) −5.65307 2.87586i −0.0107473 0.00546742i
\(527\) −10.6022 + 12.6352i −0.0201181 + 0.0239758i
\(528\) 420.367 + 74.7442i 0.796149 + 0.141561i
\(529\) 1009.27 + 367.343i 1.90787 + 0.694410i
\(530\) −528.252 161.136i −0.996703 0.304030i
\(531\) 791.365 + 359.906i 1.49033 + 0.677790i
\(532\) −15.5591 + 23.1306i −0.0292464 + 0.0434786i
\(533\) −98.5776 559.062i −0.184949 1.04890i
\(534\) 646.239 + 361.044i 1.21019 + 0.676112i
\(535\) 7.42748 2.70338i 0.0138831 0.00505305i
\(536\) 234.560 + 421.262i 0.437612 + 0.785937i
\(537\) −673.536 + 521.924i −1.25426 + 0.971926i
\(538\) −411.270 309.504i −0.764442 0.575287i
\(539\) −391.121 −0.725642
\(540\) 393.161 664.516i 0.728076 1.23059i
\(541\) 544.965i 1.00733i 0.863900 + 0.503664i \(0.168015\pi\)
−0.863900 + 0.503664i \(0.831985\pi\)
\(542\) −85.3304 64.2161i −0.157436 0.118480i
\(543\) −763.725 + 104.240i −1.40649 + 0.191970i
\(544\) −116.032 80.6985i −0.213294 0.148343i
\(545\) 86.6337 + 238.024i 0.158961 + 0.436742i
\(546\) −3.00604 212.995i −0.00550558 0.390101i
\(547\) 486.590 85.7989i 0.889561 0.156854i 0.289852 0.957072i \(-0.406394\pi\)
0.599709 + 0.800218i \(0.295283\pi\)
\(548\) 8.27759 12.3057i 0.0151051 0.0224557i
\(549\) 74.6183 + 51.1987i 0.135917 + 0.0932582i
\(550\) 444.302 + 135.528i 0.807822 + 0.246415i
\(551\) 35.8470 98.4887i 0.0650580 0.178745i
\(552\) −768.613 + 576.701i −1.39242 + 1.04475i
\(553\) −94.0718 78.9356i −0.170112 0.142741i
\(554\) −444.798 226.280i −0.802884 0.408447i
\(555\) −321.396 202.612i −0.579091 0.365066i
\(556\) 1.06505 + 10.0109i 0.00191557 + 0.0180053i
\(557\) 220.384 381.717i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(558\) −67.1998 1.66492i −0.120430 0.00298373i
\(559\) −306.973 531.693i −0.549147 0.951150i
\(560\) −226.799 119.853i −0.404999 0.214023i
\(561\) 35.9749 + 112.236i 0.0641263 + 0.200064i
\(562\) 697.018 453.278i 1.24024 0.806545i
\(563\) 107.125 607.536i 0.190275 1.07910i −0.728713 0.684819i \(-0.759881\pi\)
0.918988 0.394285i \(-0.129008\pi\)
\(564\) 50.9383 + 757.917i 0.0903162 + 1.34382i
\(565\) −934.143 1113.27i −1.65335 1.97039i
\(566\) 539.929 125.014i 0.953939 0.220872i
\(567\) 178.256 34.9360i 0.314385 0.0616155i
\(568\) 732.204 595.241i 1.28909 1.04796i
\(569\) 517.420 + 616.637i 0.909349 + 1.08372i 0.996165 + 0.0874958i \(0.0278864\pi\)
−0.0868157 + 0.996224i \(0.527669\pi\)
\(570\) −131.593 21.2932i −0.230864 0.0373564i
\(571\) 212.718 + 37.5079i 0.372535 + 0.0656880i 0.356782 0.934188i \(-0.383874\pi\)
0.0157539 + 0.999876i \(0.494985\pi\)
\(572\) 405.685 + 390.770i 0.709239 + 0.683165i
\(573\) 249.412 + 778.124i 0.435273 + 1.35798i
\(574\) −62.9352 148.005i −0.109643 0.257848i
\(575\) −905.366 + 522.713i −1.57455 + 0.909067i
\(576\) −37.8000 574.758i −0.0656251 0.997844i
\(577\) 177.731 307.839i 0.308026 0.533517i −0.669904 0.742447i \(-0.733665\pi\)
0.977931 + 0.208930i \(0.0669982\pi\)
\(578\) −65.3459 + 535.009i −0.113055 + 0.925621i
\(579\) 445.016 705.913i 0.768594 1.21919i
\(580\) 936.100 + 232.133i 1.61397 + 0.400229i
\(581\) −43.6231 36.6042i −0.0750828 0.0630020i
\(582\) −69.0973 361.927i −0.118724 0.621867i
\(583\) 322.854 + 117.509i 0.553780 + 0.201559i
\(584\) −1011.16 + 162.128i −1.73144 + 0.277617i
\(585\) 919.059 439.242i 1.57104 0.750842i
\(586\) 323.426 301.984i 0.551922 0.515332i
\(587\) −8.19482 46.4751i −0.0139605 0.0791740i 0.977032 0.213095i \(-0.0683543\pi\)
−0.990992 + 0.133921i \(0.957243\pi\)
\(588\) 126.265 + 512.321i 0.214736 + 0.871294i
\(589\) 3.96933 + 10.9056i 0.00673909 + 0.0185155i
\(590\) 1379.23 73.1608i 2.33767 0.124001i
\(591\) −129.603 949.556i −0.219295 1.60669i
\(592\) −283.231 + 10.6113i −0.478431 + 0.0179245i
\(593\) 100.618i 0.169676i 0.996395 + 0.0848380i \(0.0270373\pi\)
−0.996395 + 0.0848380i \(0.972963\pi\)
\(594\) −266.139 + 399.858i −0.448046 + 0.673162i
\(595\) 70.8113i 0.119011i
\(596\) −344.249 + 775.848i −0.577599 + 1.30176i
\(597\) −538.471 + 417.262i −0.901962 + 0.698932i
\(598\) −1265.93 + 67.1508i −2.11693 + 0.112292i
\(599\) 261.832 + 719.379i 0.437116 + 1.20097i 0.941360 + 0.337405i \(0.109549\pi\)
−0.504244 + 0.863561i \(0.668229\pi\)
\(600\) 34.0925 625.733i 0.0568209 1.04289i
\(601\) −116.660 661.614i −0.194111 1.10086i −0.913680 0.406435i \(-0.866772\pi\)
0.719569 0.694421i \(-0.244339\pi\)
\(602\) −118.705 127.133i −0.197184 0.211184i
\(603\) −539.895 + 52.4077i −0.895347 + 0.0869117i
\(604\) −36.1792 + 527.009i −0.0598994 + 0.872532i
\(605\) 281.345 + 102.401i 0.465033 + 0.169258i
\(606\) −647.995 + 559.503i −1.06930 + 0.923273i
\(607\) 472.640 + 396.592i 0.778648 + 0.653364i 0.942908 0.333054i \(-0.108079\pi\)
−0.164259 + 0.986417i \(0.552523\pi\)
\(608\) −89.9945 + 42.3137i −0.148017 + 0.0695949i
\(609\) 105.725 + 200.761i 0.173604 + 0.329657i
\(610\) 142.708 + 17.4304i 0.233948 + 0.0285744i
\(611\) −501.078 + 867.893i −0.820095 + 1.42045i
\(612\) 135.402 83.3555i 0.221244 0.136202i
\(613\) −148.147 + 85.5326i −0.241675 + 0.139531i −0.615946 0.787788i \(-0.711226\pi\)
0.374271 + 0.927319i \(0.377893\pi\)
\(614\) 222.576 + 523.431i 0.362501 + 0.852493i
\(615\) 516.881 569.484i 0.840457 0.925991i
\(616\) 136.944 + 81.9293i 0.222311 + 0.133002i
\(617\) −379.315 66.8835i −0.614773 0.108401i −0.142414 0.989807i \(-0.545486\pi\)
−0.472359 + 0.881406i \(0.656598\pi\)
\(618\) 820.608 + 669.067i 1.32784 + 1.08263i
\(619\) 732.593 + 873.071i 1.18351 + 1.41045i 0.890886 + 0.454226i \(0.150084\pi\)
0.292625 + 0.956227i \(0.405471\pi\)
\(620\) −95.9259 + 46.9372i −0.154719 + 0.0757051i
\(621\) −248.993 1051.96i −0.400955 1.69398i
\(622\) −603.063 + 139.632i −0.969554 + 0.224488i
\(623\) 177.845 + 211.948i 0.285466 + 0.340205i
\(624\) 380.895 657.549i 0.610409 1.05376i
\(625\) −103.493 + 586.939i −0.165589 + 0.939103i
\(626\) −46.7700 71.9194i −0.0747124 0.114887i
\(627\) 81.0470 + 17.5642i 0.129262 + 0.0280131i
\(628\) 41.5280 30.2525i 0.0661273 0.0481728i
\(629\) −39.1198 67.7575i −0.0621936 0.107723i
\(630\) 225.596 179.967i 0.358088 0.285661i
\(631\) 112.803 195.380i 0.178768 0.309635i −0.762691 0.646763i \(-0.776122\pi\)
0.941459 + 0.337128i \(0.109456\pi\)
\(632\) −143.413 413.937i −0.226919 0.654964i
\(633\) 16.8717 433.691i 0.0266535 0.685136i
\(634\) −367.807 + 722.996i −0.580137 + 1.14037i
\(635\) −207.741 174.316i −0.327152 0.274513i
\(636\) 49.6967 460.834i 0.0781394 0.724582i
\(637\) −238.086 + 654.136i −0.373761 + 1.02690i
\(638\) −573.879 175.054i −0.899497 0.274379i
\(639\) 284.487 + 1022.75i 0.445207 + 1.60055i
\(640\) −474.793 782.287i −0.741864 1.22232i
\(641\) 740.201 130.517i 1.15476 0.203615i 0.436707 0.899604i \(-0.356145\pi\)
0.718053 + 0.695988i \(0.245034\pi\)
\(642\) 3.39755 + 5.69750i 0.00529213 + 0.00887461i
\(643\) 136.139 + 374.040i 0.211725 + 0.581711i 0.999409 0.0343689i \(-0.0109421\pi\)
−0.787684 + 0.616080i \(0.788720\pi\)
\(644\) −345.112 + 99.4339i −0.535888 + 0.154401i
\(645\) 314.642 769.938i 0.487817 1.19370i
\(646\) −21.9343 16.5068i −0.0339540 0.0255524i
\(647\) 290.596i 0.449144i −0.974457 0.224572i \(-0.927902\pi\)
0.974457 0.224572i \(-0.0720984\pi\)
\(648\) 609.683 + 219.525i 0.940868 + 0.338772i
\(649\) −859.220 −1.32391
\(650\) 497.124 660.579i 0.764807 1.01628i
\(651\) −23.2573 9.50430i −0.0357255 0.0145995i
\(652\) 754.004 217.244i 1.15645 0.333197i
\(653\) 515.718 187.706i 0.789767 0.287452i 0.0845277 0.996421i \(-0.473062\pi\)
0.705239 + 0.708970i \(0.250840\pi\)
\(654\) −182.585 + 108.879i −0.279181 + 0.166482i
\(655\) −210.476 1193.67i −0.321337 1.82239i
\(656\) 78.4045 568.353i 0.119519 0.866391i
\(657\) 287.595 1115.61i 0.437740 1.69804i
\(658\) −82.8372 + 271.565i −0.125892 + 0.412713i
\(659\) −198.634 72.2969i −0.301417 0.109707i 0.186884 0.982382i \(-0.440161\pi\)
−0.488302 + 0.872675i \(0.662383\pi\)
\(660\) −81.8193 + 758.705i −0.123969 + 1.14955i
\(661\) 57.8327 68.9223i 0.0874927 0.104270i −0.720522 0.693432i \(-0.756098\pi\)
0.808015 + 0.589162i \(0.200542\pi\)
\(662\) −609.169 309.900i −0.920195 0.468127i
\(663\) 209.609 + 8.15432i 0.316153 + 0.0122991i
\(664\) −66.5038 191.952i −0.100156 0.289084i
\(665\) −43.1488 24.9120i −0.0648854 0.0374616i
\(666\) 116.444 296.836i 0.174841 0.445700i
\(667\) 1169.41 675.159i 1.75324 1.01223i
\(668\) −429.013 + 312.530i −0.642235 + 0.467859i
\(669\) −78.9586 + 364.341i −0.118025 + 0.544606i
\(670\) −722.440 + 469.811i −1.07827 + 0.701210i
\(671\) −88.0796 15.5308i −0.131266 0.0231458i
\(672\) 63.1082 205.829i 0.0939111 0.306293i
\(673\) −718.250 + 602.683i −1.06724 + 0.895518i −0.994799 0.101855i \(-0.967522\pi\)
−0.0724372 + 0.997373i \(0.523078\pi\)
\(674\) −17.1443 74.0453i −0.0254366 0.109859i
\(675\) 629.913 + 316.586i 0.933204 + 0.469016i
\(676\) 293.292 143.510i 0.433865 0.212293i
\(677\) −694.220 + 582.520i −1.02544 + 0.860443i −0.990301 0.138940i \(-0.955631\pi\)
−0.0351349 + 0.999383i \(0.511186\pi\)
\(678\) 770.723 945.288i 1.13676 1.39423i
\(679\) 23.9143 135.625i 0.0352199 0.199742i
\(680\) 129.690 216.775i 0.190721 0.318787i
\(681\) −872.117 791.560i −1.28064 1.16235i
\(682\) 61.1383 25.9975i 0.0896456 0.0381195i
\(683\) 578.591 + 1002.15i 0.847132 + 1.46728i 0.883757 + 0.467947i \(0.155006\pi\)
−0.0366244 + 0.999329i \(0.511661\pi\)
\(684\) −3.15725 111.832i −0.00461586 0.163497i
\(685\) 22.9556 + 13.2534i 0.0335118 + 0.0193481i
\(686\) −50.5549 + 413.910i −0.0736952 + 0.603368i
\(687\) 181.474 95.5678i 0.264154 0.139109i
\(688\) −130.549 606.599i −0.189751 0.881685i
\(689\) 393.060 468.430i 0.570478 0.679870i
\(690\) −1122.40 1299.92i −1.62667 1.88394i
\(691\) −23.0137 + 63.2296i −0.0333049 + 0.0915045i −0.955231 0.295862i \(-0.904393\pi\)
0.921926 + 0.387367i \(0.126615\pi\)
\(692\) 12.8549 187.253i 0.0185765 0.270597i
\(693\) −146.076 + 104.366i −0.210788 + 0.150600i
\(694\) −568.497 + 530.808i −0.819160 + 0.764853i
\(695\) −17.7201 + 3.12454i −0.0254966 + 0.00449574i
\(696\) −44.0354 + 808.224i −0.0632692 + 1.16124i
\(697\) 148.826 54.1682i 0.213523 0.0777162i
\(698\) −2.79783 52.7447i −0.00400836 0.0755654i
\(699\) −12.1294 15.6528i −0.0173525 0.0223932i
\(700\) 94.9945 214.093i 0.135706 0.305847i
\(701\) −374.830 −0.534708 −0.267354 0.963598i \(-0.586149\pi\)
−0.267354 + 0.963598i \(0.586149\pi\)
\(702\) 506.743 + 688.512i 0.721855 + 0.980787i
\(703\) −55.0506 −0.0783081
\(704\) 269.175 + 501.622i 0.382350 + 0.712531i
\(705\) −1345.21 + 183.605i −1.90809 + 0.260432i
\(706\) 58.3165 + 1099.38i 0.0826013 + 1.55720i
\(707\) −300.686 + 109.441i −0.425299 + 0.154796i
\(708\) 277.380 + 1125.47i 0.391779 + 1.58965i
\(709\) −1173.80 + 206.972i −1.65557 + 0.291922i −0.921855 0.387536i \(-0.873326\pi\)
−0.733715 + 0.679457i \(0.762215\pi\)
\(710\) 1151.00 + 1232.73i 1.62113 + 1.73624i
\(711\) 491.347 + 38.2872i 0.691065 + 0.0538498i
\(712\) 156.259 + 974.559i 0.219466 + 1.36876i
\(713\) −51.1390 + 140.503i −0.0717237 + 0.197059i
\(714\) 58.3745 11.1446i 0.0817570 0.0156087i
\(715\) −647.123 + 771.211i −0.905067 + 1.07862i
\(716\) −1102.72 273.451i −1.54011 0.381915i
\(717\) 81.1135 + 51.1349i 0.113129 + 0.0713179i
\(718\) 92.8486 + 11.3405i 0.129316 + 0.0157946i
\(719\) −245.529 141.756i −0.341487 0.197158i 0.319442 0.947606i \(-0.396504\pi\)
−0.660929 + 0.750448i \(0.729838\pi\)
\(720\) 1020.22 137.757i 1.41698 0.191330i
\(721\) 197.868 + 342.717i 0.274435 + 0.475336i
\(722\) 646.650 274.972i 0.895637 0.380847i
\(723\) −1177.29 + 377.356i −1.62834 + 0.521930i
\(724\) −740.202 712.989i −1.02238 0.984792i
\(725\) −152.917 + 867.236i −0.210920 + 1.19619i
\(726\) −40.1369 + 248.048i −0.0552850 + 0.341664i
\(727\) −87.0046 + 73.0055i −0.119676 + 0.100420i −0.700662 0.713494i \(-0.747112\pi\)
0.580986 + 0.813914i \(0.302667\pi\)
\(728\) 220.385 179.161i 0.302727 0.246100i
\(729\) −500.581 + 529.962i −0.686668 + 0.726971i
\(730\) −412.867 1783.15i −0.565571 2.44268i
\(731\) 131.210 110.099i 0.179494 0.150614i
\(732\) 8.09103 + 120.387i 0.0110533 + 0.164464i
\(733\) 698.083 + 123.091i 0.952364 + 0.167927i 0.628181 0.778067i \(-0.283800\pi\)
0.324183 + 0.945994i \(0.394911\pi\)
\(734\) −232.523 357.556i −0.316788 0.487134i
\(735\) −898.063 + 287.856i −1.22186 + 0.391640i
\(736\) −1238.61 327.670i −1.68289 0.445204i
\(737\) 464.279 268.052i 0.629958 0.363707i
\(738\) 550.813 + 336.472i 0.746359 + 0.455924i
\(739\) −153.019 88.3457i −0.207063 0.119548i 0.392883 0.919588i \(-0.371478\pi\)
−0.599945 + 0.800041i \(0.704811\pi\)
\(740\) −53.5914 503.731i −0.0724208 0.680717i
\(741\) 78.7110 124.856i 0.106223 0.168497i
\(742\) 78.5514 154.408i 0.105864 0.208097i
\(743\) 614.505 732.338i 0.827059 0.985650i −0.172941 0.984932i \(-0.555327\pi\)
1.00000 0.000718050i \(-0.000228562\pi\)
\(744\) −53.7907 71.6910i −0.0722993 0.0963589i
\(745\) −1425.55 518.859i −1.91349 0.696455i
\(746\) −283.628 + 929.816i −0.380198 + 1.24640i
\(747\) 227.848 + 17.7546i 0.305018 + 0.0237679i
\(748\) −87.7100 + 130.393i −0.117259 + 0.174322i
\(749\) 0.430540 + 2.44172i 0.000574820 + 0.00325997i
\(750\) 47.6471 0.672454i 0.0635295 0.000896605i
\(751\) 224.531 81.7225i 0.298976 0.108818i −0.188177 0.982135i \(-0.560258\pi\)
0.487152 + 0.873317i \(0.338036\pi\)
\(752\) −750.959 + 679.630i −0.998615 + 0.903763i
\(753\) −36.7980 269.606i −0.0488686 0.358042i
\(754\) −642.107 + 853.232i −0.851601 + 1.13161i
\(755\) −944.139 −1.25051
\(756\) 183.864 + 157.650i 0.243206 + 0.208531i
\(757\) 1152.06i 1.52187i 0.648828 + 0.760935i \(0.275259\pi\)
−0.648828 + 0.760935i \(0.724741\pi\)
\(758\) 182.030 241.882i 0.240146 0.319106i
\(759\) 654.428 + 844.530i 0.862223 + 1.11269i
\(760\) −86.4658 155.290i −0.113771 0.204328i
\(761\) 317.885 + 873.382i 0.417720 + 1.14768i 0.952992 + 0.302996i \(0.0979870\pi\)
−0.535272 + 0.844680i \(0.679791\pi\)
\(762\) 111.005 198.690i 0.145676 0.260748i
\(763\) −78.2483 + 13.7973i −0.102553 + 0.0180829i
\(764\) −608.088 + 904.003i −0.795927 + 1.18325i
\(765\) 165.206 + 231.231i 0.215955 + 0.302263i
\(766\) −72.1535 + 236.541i −0.0941952 + 0.308800i
\(767\) −523.030 + 1437.01i −0.681917 + 1.87355i
\(768\) 570.167 514.523i 0.742404 0.669952i
\(769\) −3.68137 3.08904i −0.00478722 0.00401695i 0.640391 0.768049i \(-0.278772\pi\)
−0.645178 + 0.764032i \(0.723217\pi\)
\(770\) −129.325 + 254.214i −0.167954 + 0.330147i
\(771\) −727.550 + 383.142i −0.943645 + 0.496942i
\(772\) 1106.39 117.708i 1.43315 0.152471i
\(773\) −153.427 + 265.743i −0.198482 + 0.343782i −0.948037 0.318161i \(-0.896935\pi\)
0.749554 + 0.661943i \(0.230268\pi\)
\(774\) 684.231 + 138.204i 0.884020 + 0.178559i
\(775\) −48.7551 84.4464i −0.0629099 0.108963i
\(776\) 321.604 371.391i 0.414439 0.478596i
\(777\) 80.0964 88.2478i 0.103084 0.113575i
\(778\) −82.4887 126.845i −0.106027 0.163040i
\(779\) 19.3508 109.744i 0.0248405 0.140878i
\(780\) 1219.10 + 598.684i 1.56295 + 0.767543i
\(781\) −674.411 803.731i −0.863522 1.02911i
\(782\) −79.7782 344.559i −0.102018 0.440612i
\(783\) −813.623 408.916i −1.03911 0.522242i
\(784\) −431.729 + 555.492i −0.550675 + 0.708535i
\(785\) 59.0267 + 70.3453i 0.0751933 + 0.0896119i
\(786\) 950.894 361.373i 1.20979 0.459763i
\(787\) −80.5429 14.2019i −0.102342 0.0180456i 0.122243 0.992500i \(-0.460991\pi\)
−0.224584 + 0.974455i \(0.572102\pi\)
\(788\) 886.475 920.309i 1.12497 1.16790i
\(789\) 9.29797 + 2.01502i 0.0117845 + 0.00255389i
\(790\) 720.537 306.390i 0.912072 0.387836i
\(791\) 394.789 227.931i 0.499101 0.288156i
\(792\) −638.329 + 51.9592i −0.805970 + 0.0656050i
\(793\) −79.5911 + 137.856i −0.100367 + 0.173841i
\(794\) 700.569 + 85.5673i 0.882329 + 0.107767i
\(795\) 827.797 + 32.2034i 1.04125 + 0.0405074i
\(796\) −881.590 218.616i −1.10753 0.274643i
\(797\) 62.7889 + 52.6862i 0.0787816 + 0.0661056i 0.681328 0.731978i \(-0.261403\pi\)
−0.602546 + 0.798084i \(0.705847\pi\)
\(798\) 13.7457 39.4912i 0.0172251 0.0494877i
\(799\) −262.728 95.6250i −0.328820 0.119681i
\(800\) 682.916 481.423i 0.853644 0.601778i
\(801\) −1075.23 277.185i −1.34236 0.346049i
\(802\) 766.709 + 821.148i 0.955996 + 1.02388i
\(803\) 197.723 + 1121.34i 0.246231 + 1.39644i
\(804\) −500.997 521.615i −0.623131 0.648775i
\(805\) −219.546 603.197i −0.272728 0.749313i
\(806\) −6.26337 118.077i −0.00777093 0.146497i
\(807\) 714.703 + 292.070i 0.885629 + 0.361920i
\(808\) −1120.93 215.671i −1.38729 0.266920i
\(809\) 187.114i 0.231291i 0.993291 + 0.115646i \(0.0368937\pi\)
−0.993291 + 0.115646i \(0.963106\pi\)
\(810\) −316.803 + 1114.00i −0.391115 + 1.37531i
\(811\) 684.038i 0.843450i −0.906724 0.421725i \(-0.861425\pi\)
0.906724 0.421725i \(-0.138575\pi\)
\(812\) −122.699 + 276.531i −0.151107 + 0.340556i
\(813\) 148.287 + 60.5988i 0.182395 + 0.0745372i
\(814\) 16.6930 + 314.696i 0.0205074 + 0.386604i
\(815\) 479.666 + 1317.87i 0.588547 + 1.61702i
\(816\) 199.113 + 72.7952i 0.244012 + 0.0892098i
\(817\) −20.9276 118.687i −0.0256152 0.145271i
\(818\) 462.057 431.425i 0.564862 0.527414i
\(819\) 85.6275 + 307.837i 0.104551 + 0.375870i
\(820\) 1023.03 + 70.2310i 1.24759 + 0.0856475i
\(821\) −992.842 361.365i −1.20931 0.440152i −0.342844 0.939392i \(-0.611390\pi\)
−0.866464 + 0.499240i \(0.833612\pi\)
\(822\) −7.31283 + 21.0097i −0.00889639 + 0.0255593i
\(823\) −1109.39 930.891i −1.34799 1.13109i −0.979496 0.201462i \(-0.935431\pi\)
−0.368489 0.929632i \(-0.620125\pi\)
\(824\) −21.9479 + 1411.56i −0.0266358 + 1.71305i
\(825\) −696.242 27.0856i −0.843930 0.0328310i
\(826\) −52.5261 + 430.049i −0.0635909 + 0.520640i
\(827\) 318.240 551.209i 0.384813 0.666516i −0.606930 0.794755i \(-0.707599\pi\)
0.991743 + 0.128239i \(0.0409326\pi\)
\(828\) 894.964 1129.86i 1.08087 1.36456i
\(829\) 848.900 490.113i 1.02401 0.591210i 0.108744 0.994070i \(-0.465317\pi\)
0.915262 + 0.402860i \(0.131984\pi\)
\(830\) 334.129 142.080i 0.402565 0.171180i
\(831\) 731.587 + 158.547i 0.880370 + 0.190790i
\(832\) 1002.80 144.834i 1.20529 0.174079i
\(833\) −191.257 33.7238i −0.229600 0.0404848i
\(834\) −5.36464 14.1162i −0.00643242 0.0169258i
\(835\) −609.788 726.717i −0.730285 0.870319i
\(836\) 48.5975 + 99.3191i 0.0581309 + 0.118803i
\(837\) 98.1196 23.2244i 0.117228 0.0277471i
\(838\) −10.5474 45.5535i −0.0125863 0.0543598i
\(839\) −251.366 299.566i −0.299602 0.357052i 0.595151 0.803614i \(-0.297092\pi\)
−0.894752 + 0.446563i \(0.852648\pi\)
\(840\) 374.738 + 87.3328i 0.446117 + 0.103968i
\(841\) 51.4762 291.936i 0.0612084 0.347130i
\(842\) 845.383 549.762i 1.00402 0.652924i
\(843\) −838.193 + 923.496i −0.994298 + 1.09549i
\(844\) 467.739 340.741i 0.554194 0.403722i
\(845\) 291.794 + 505.403i 0.345319 + 0.598110i
\(846\) −363.072 1080.05i −0.429163 1.27665i
\(847\) −46.9582 + 81.3340i −0.0554406 + 0.0960259i
\(848\) 523.267 328.825i 0.617060 0.387766i
\(849\) −735.558 + 387.359i −0.866381 + 0.456253i
\(850\) 205.577 + 104.582i 0.241855 + 0.123038i
\(851\) −543.315 455.895i −0.638443 0.535717i
\(852\) −835.072 + 1142.86i −0.980131 + 1.34139i
\(853\) 161.452 443.586i 0.189275 0.520030i −0.808365 0.588681i \(-0.799647\pi\)
0.997641 + 0.0686512i \(0.0218696\pi\)
\(854\) −13.1578 + 43.1354i −0.0154073 + 0.0505098i
\(855\) 199.021 19.3190i 0.232773 0.0225954i
\(856\) −3.15396 + 8.26337i −0.00368453 + 0.00965348i
\(857\) −149.108 + 26.2917i −0.173988 + 0.0306788i −0.259963 0.965618i \(-0.583711\pi\)
0.0859753 + 0.996297i \(0.472599\pi\)
\(858\) −737.608 412.090i −0.859683 0.480292i
\(859\) −160.044 439.716i −0.186314 0.511893i 0.811008 0.585035i \(-0.198919\pi\)
−0.997322 + 0.0731425i \(0.976697\pi\)
\(860\) 1065.65 307.035i 1.23912 0.357018i
\(861\) 147.768 + 190.692i 0.171624 + 0.221478i
\(862\) 138.116 183.529i 0.160228 0.212910i
\(863\) 817.763i 0.947582i 0.880637 + 0.473791i \(0.157115\pi\)
−0.880637 + 0.473791i \(0.842885\pi\)
\(864\) 274.130 + 819.359i 0.317280 + 0.948332i
\(865\) 335.464 0.387820
\(866\) 733.945 + 552.337i 0.847512 + 0.637802i
\(867\) −109.334 801.050i −0.126106 0.923934i
\(868\) −9.27452 32.1897i −0.0106849 0.0370849i
\(869\) −457.712 + 166.594i −0.526711 + 0.191707i
\(870\) −1446.53 + 20.4153i −1.66268 + 0.0234658i
\(871\) −165.688 939.661i −0.190227 1.07883i
\(872\) −264.812 101.073i −0.303683 0.115909i
\(873\) 238.327 + 498.670i 0.272998 + 0.571214i
\(874\) −238.023 72.6056i −0.272337 0.0830728i
\(875\) 16.7363 + 6.09151i 0.0191272 + 0.00696173i
\(876\) 1404.99 620.994i 1.60387 0.708897i
\(877\) 761.184 907.144i 0.867941 1.03437i −0.131134 0.991365i \(-0.541862\pi\)
0.999075 0.0430069i \(-0.0136937\pi\)
\(878\) 384.140 755.102i 0.437517 0.860025i
\(879\) −353.963 + 561.479i −0.402688 + 0.638770i
\(880\) −861.492 + 541.369i −0.978969 + 0.615192i
\(881\) 891.916 + 514.948i 1.01239 + 0.584504i 0.911891 0.410433i \(-0.134622\pi\)
0.100500 + 0.994937i \(0.467956\pi\)
\(882\) −378.640 695.030i −0.429297 0.788016i
\(883\) 181.566 104.827i 0.205624 0.118717i −0.393652 0.919259i \(-0.628789\pi\)
0.599276 + 0.800543i \(0.295455\pi\)
\(884\) 164.685 + 226.065i 0.186296 + 0.255730i
\(885\) −1972.88 + 632.365i −2.22924 + 0.714537i
\(886\) −673.616 1035.84i −0.760289 1.16912i
\(887\) −961.150 169.477i −1.08360 0.191067i −0.396792 0.917909i \(-0.629876\pi\)
−0.686805 + 0.726841i \(0.740988\pi\)
\(888\) 406.824 123.458i 0.458136 0.139030i
\(889\) 65.1645 54.6795i 0.0733009 0.0615067i
\(890\) −1718.61 + 397.922i −1.93102 + 0.447103i
\(891\) 233.515 681.604i 0.262082 0.764987i
\(892\) −446.482 + 218.466i −0.500540 + 0.244918i
\(893\) −150.699 + 126.451i −0.168755 + 0.141603i
\(894\) 203.371 1256.84i 0.227484 1.40586i
\(895\) 352.607 1999.73i 0.393974 2.23434i
\(896\) 267.522 104.060i 0.298574 0.116138i
\(897\) 1810.81 580.418i 2.01874 0.647066i
\(898\) −21.2333 49.9343i −0.0236451 0.0556061i
\(899\) 62.9742 + 109.075i 0.0700492 + 0.121329i
\(900\) 189.287 + 920.736i 0.210319 + 1.02304i
\(901\) 147.743 + 85.2992i 0.163976 + 0.0946717i
\(902\) −633.216 77.3408i −0.702013 0.0857437i
\(903\) 220.707 + 139.136i 0.244415 + 0.154082i
\(904\) 1626.02 + 25.2825i 1.79870 + 0.0279674i
\(905\) 1180.72 1407.13i 1.30467 1.55484i
\(906\) −148.593 778.317i −0.164009 0.859069i
\(907\) −156.109 + 428.906i −0.172116 + 0.472884i −0.995518 0.0945744i \(-0.969851\pi\)
0.823402 + 0.567458i \(0.192073\pi\)
\(908\) 107.553 1566.68i 0.118450 1.72542i
\(909\) 726.548 1058.89i 0.799283 1.16489i
\(910\) 346.439 + 371.038i 0.380703 + 0.407734i
\(911\) −236.891 + 41.7702i −0.260034 + 0.0458510i −0.302145 0.953262i \(-0.597703\pi\)
0.0421113 + 0.999113i \(0.486592\pi\)
\(912\) 114.407 95.7197i 0.125447 0.104956i
\(913\) −212.251 + 77.2530i −0.232476 + 0.0846145i
\(914\) −1540.78 + 81.7303i −1.68575 + 0.0894204i
\(915\) −213.672 + 29.1637i −0.233522 + 0.0318730i
\(916\) 249.965 + 110.911i 0.272888 + 0.121082i
\(917\) 380.206 0.414620
\(918\) −164.619 + 172.582i −0.179323 + 0.187998i
\(919\) 1365.29 1.48563 0.742813 0.669499i \(-0.233491\pi\)
0.742813 + 0.669499i \(0.233491\pi\)
\(920\) 432.651 2248.67i 0.470273 2.44420i
\(921\) −522.594 674.400i −0.567420 0.732247i
\(922\) 656.187 34.8073i 0.711699 0.0377520i
\(923\) −1754.74 + 638.674i −1.90113 + 0.691955i
\(924\) −229.919 66.6020i −0.248830 0.0720801i
\(925\) 455.511 80.3188i 0.492444 0.0868312i
\(926\) 196.425 183.403i 0.212122 0.198059i
\(927\) −1445.70 657.494i −1.55955 0.709271i
\(928\) −882.083 + 621.826i −0.950521 + 0.670071i
\(929\) 308.282 846.997i 0.331843 0.911730i −0.655790 0.754943i \(-0.727664\pi\)
0.987633 0.156787i \(-0.0501135\pi\)
\(930\) 121.248 104.690i 0.130374 0.112570i
\(931\) −87.8353 + 104.678i −0.0943452 + 0.112436i
\(932\) 6.35494 25.6269i 0.00681861 0.0274967i
\(933\) 821.566 432.653i 0.880564 0.463722i
\(934\) 63.3521 518.685i 0.0678288 0.555337i
\(935\) −243.240 140.434i −0.260149 0.150197i
\(936\) −301.668 + 1099.21i −0.322295 + 1.17437i
\(937\) 522.917 + 905.720i 0.558076 + 0.966616i 0.997657 + 0.0684134i \(0.0217937\pi\)
−0.439581 + 0.898203i \(0.644873\pi\)
\(938\) −105.780 248.763i −0.112772 0.265206i
\(939\) 95.2878 + 86.4861i 0.101478 + 0.0921044i
\(940\) −1303.77 1255.84i −1.38699 1.33600i
\(941\) −245.195 + 1390.57i −0.260569 + 1.47776i 0.520794 + 0.853682i \(0.325636\pi\)
−0.781363 + 0.624077i \(0.785475\pi\)
\(942\) −48.7005 + 59.7309i −0.0516990 + 0.0634086i
\(943\) 1099.81 922.850i 1.16629 0.978632i
\(944\) −948.428 + 1220.31i −1.00469 + 1.29270i
\(945\) −258.599 + 347.145i −0.273649 + 0.367350i
\(946\) −672.124 + 155.622i −0.710491 + 0.164505i
\(947\) 134.198 112.605i 0.141708 0.118907i −0.569178 0.822214i \(-0.692738\pi\)
0.710886 + 0.703307i \(0.248294\pi\)
\(948\) 365.979 + 545.766i 0.386054 + 0.575702i
\(949\) 1995.77 + 351.908i 2.10302 + 0.370819i
\(950\) 136.051 88.4752i 0.143211 0.0931318i
\(951\) 257.710 1189.16i 0.270988 1.25043i
\(952\) 59.9010 + 51.8710i 0.0629212 + 0.0544863i
\(953\) 470.776 271.803i 0.493994 0.285208i −0.232236 0.972660i \(-0.574604\pi\)
0.726230 + 0.687452i \(0.241271\pi\)
\(954\) 103.735 + 687.477i 0.108737 + 0.720626i
\(955\) −1686.36 973.623i −1.76583 1.01950i
\(956\) 13.5253 + 127.131i 0.0141478 + 0.132982i
\(957\) 899.297 + 34.9849i 0.939704 + 0.0365568i
\(958\) −250.283 127.325i −0.261256 0.132907i
\(959\) −5.34458 + 6.36942i −0.00557308 + 0.00664173i
\(960\) 987.241 + 953.681i 1.02838 + 0.993418i
\(961\) 889.939 + 323.911i 0.926056 + 0.337057i
\(962\) 536.479 + 163.645i 0.557670 + 0.170110i
\(963\) −7.10254 6.96885i −0.00737543 0.00723660i
\(964\) −1367.74 920.027i −1.41882 0.954385i
\(965\) 345.319 + 1958.40i 0.357843 + 2.02943i
\(966\) 462.703 275.920i 0.478988 0.285632i
\(967\) 20.2168 7.35832i 0.0209067 0.00760943i −0.331546 0.943439i \(-0.607570\pi\)
0.352452 + 0.935830i \(0.385348\pi\)
\(968\) −292.716 + 162.985i −0.302392 + 0.168373i
\(969\) 38.1173 + 15.5770i 0.0393368 + 0.0160753i
\(970\) 701.595 + 527.991i 0.723293 + 0.544321i
\(971\) 863.059 0.888835 0.444417 0.895820i \(-0.353411\pi\)
0.444417 + 0.895820i \(0.353411\pi\)
\(972\) −968.203 85.8362i −0.996093 0.0883089i
\(973\) 5.64422i 0.00580084i
\(974\) −51.0635 38.4283i −0.0524266 0.0394541i
\(975\) −469.121 + 1147.95i −0.481150 + 1.17739i
\(976\) −119.282 + 107.952i −0.122215 + 0.110607i
\(977\) 612.181 + 1681.95i 0.626593 + 1.72155i 0.690243 + 0.723577i \(0.257503\pi\)
−0.0636507 + 0.997972i \(0.520274\pi\)
\(978\) −1010.92 + 602.833i −1.03366 + 0.616394i
\(979\) 1080.76 190.566i 1.10394 0.194654i
\(980\) −1043.35 701.818i −1.06464 0.716141i
\(981\) 223.327 227.611i 0.227652 0.232019i
\(982\) 171.892 + 52.4334i 0.175043 + 0.0533945i
\(983\) −62.0026 + 170.351i −0.0630749 + 0.173297i −0.967227 0.253915i \(-0.918282\pi\)
0.904152 + 0.427211i \(0.140504\pi\)
\(984\) 103.112 + 854.403i 0.104789 + 0.868296i
\(985\) 1749.52 + 1468.02i 1.77616 + 1.49037i
\(986\) −265.532 135.083i −0.269302 0.137001i
\(987\) 16.5552 425.556i 0.0167732 0.431161i
\(988\) 195.690 20.8193i 0.198067 0.0210721i
\(989\) 776.346 1344.67i 0.784981 1.35963i
\(990\) −170.786 1131.84i −0.172511 1.14328i
\(991\) −116.979 202.614i −0.118042 0.204454i 0.800950 0.598731i \(-0.204328\pi\)
−0.918992 + 0.394277i \(0.870995\pi\)
\(992\) 30.5628 115.529i 0.0308093 0.116460i
\(993\) 1001.94 + 217.136i 1.00900 + 0.218667i
\(994\) −443.504 + 288.416i −0.446182 + 0.290157i
\(995\) 281.898 1598.72i 0.283315 1.60676i
\(996\) 169.712 + 253.084i 0.170394 + 0.254100i
\(997\) 516.809 + 615.909i 0.518364 + 0.617762i 0.960193 0.279337i \(-0.0901147\pi\)
−0.441829 + 0.897099i \(0.645670\pi\)
\(998\) −382.145 + 88.4809i −0.382911 + 0.0886582i
\(999\) −55.6652 + 475.037i −0.0557209 + 0.475513i
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.5.16 420
8.5 even 2 inner 216.3.x.a.5.25 yes 420
27.11 odd 18 inner 216.3.x.a.173.25 yes 420
216.173 odd 18 inner 216.3.x.a.173.16 yes 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.3.x.a.5.16 420 1.1 even 1 trivial
216.3.x.a.5.25 yes 420 8.5 even 2 inner
216.3.x.a.173.16 yes 420 216.173 odd 18 inner
216.3.x.a.173.25 yes 420 27.11 odd 18 inner