Properties

Label 216.3.x.a.5.9
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 5.9
Character \(\chi\) \(=\) 216.5
Dual form 216.3.x.a.173.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.86507 + 0.722171i) q^{2} +(-1.09942 - 2.79129i) q^{3} +(2.95694 - 2.69379i) q^{4} +(6.30966 - 2.29653i) q^{5} +(4.06627 + 4.41197i) q^{6} +(1.48683 + 8.43221i) q^{7} +(-3.56950 + 7.15952i) q^{8} +(-6.58256 + 6.13758i) q^{9} +O(q^{10})\) \(q+(-1.86507 + 0.722171i) q^{2} +(-1.09942 - 2.79129i) q^{3} +(2.95694 - 2.69379i) q^{4} +(6.30966 - 2.29653i) q^{5} +(4.06627 + 4.41197i) q^{6} +(1.48683 + 8.43221i) q^{7} +(-3.56950 + 7.15952i) q^{8} +(-6.58256 + 6.13758i) q^{9} +(-10.1094 + 8.83983i) q^{10} +(14.8232 + 5.39522i) q^{11} +(-10.7701 - 5.29206i) q^{12} +(5.15695 - 6.14581i) q^{13} +(-8.86253 - 14.6529i) q^{14} +(-13.3472 - 15.0872i) q^{15} +(1.48696 - 15.9308i) q^{16} +(6.43164 + 3.71331i) q^{17} +(7.84453 - 16.2007i) q^{18} +(-20.0523 + 11.5772i) q^{19} +(12.4709 - 23.7876i) q^{20} +(21.9021 - 13.4207i) q^{21} +(-31.5426 + 0.642483i) q^{22} +(22.7177 + 4.00574i) q^{23} +(23.9086 + 2.09221i) q^{24} +(15.3866 - 12.9109i) q^{25} +(-5.17972 + 15.1865i) q^{26} +(24.3687 + 11.6261i) q^{27} +(27.1111 + 20.9283i) q^{28} +(31.1660 - 26.1514i) q^{29} +(35.7890 + 18.4997i) q^{30} +(-2.50360 + 14.1986i) q^{31} +(8.73146 + 30.7857i) q^{32} +(-1.23732 - 47.3075i) q^{33} +(-14.6771 - 2.28082i) q^{34} +(28.7462 + 49.7898i) q^{35} +(-2.93087 + 35.8805i) q^{36} +(-28.7830 - 16.6179i) q^{37} +(29.0381 - 36.0734i) q^{38} +(-22.8244 - 7.63771i) q^{39} +(-6.08031 + 53.3715i) q^{40} +(45.7312 - 54.5003i) q^{41} +(-31.1568 + 40.8475i) q^{42} +(11.8398 - 32.5297i) q^{43} +(58.3650 - 23.9774i) q^{44} +(-27.4386 + 53.8430i) q^{45} +(-45.2628 + 8.93508i) q^{46} +(-70.6731 + 12.4616i) q^{47} +(-46.1021 + 13.3640i) q^{48} +(-22.8466 + 8.31547i) q^{49} +(-19.3732 + 35.1915i) q^{50} +(3.29386 - 22.0350i) q^{51} +(-1.30677 - 32.0645i) q^{52} -74.3739 q^{53} +(-53.8453 - 4.08499i) q^{54} +105.920 q^{55} +(-65.6778 - 19.4538i) q^{56} +(54.3612 + 43.2436i) q^{57} +(-39.2408 + 71.2812i) q^{58} +(91.3890 - 33.2629i) q^{59} +(-80.1087 - 8.65735i) q^{60} +(32.3319 - 5.70098i) q^{61} +(-5.58445 - 28.2893i) q^{62} +(-61.5405 - 46.3801i) q^{63} +(-38.5173 - 51.1118i) q^{64} +(18.4246 - 50.6211i) q^{65} +(36.4718 + 87.3380i) q^{66} +(-25.3389 + 30.1977i) q^{67} +(29.0209 - 6.34549i) q^{68} +(-13.7950 - 67.8155i) q^{69} +(-89.5702 - 72.1016i) q^{70} +(-18.2728 - 10.5498i) q^{71} +(-20.4456 - 69.0361i) q^{72} +(21.2203 + 36.7547i) q^{73} +(65.6830 + 10.2072i) q^{74} +(-52.9544 - 28.7540i) q^{75} +(-28.1068 + 88.2498i) q^{76} +(-23.4540 + 133.014i) q^{77} +(48.0847 - 2.23826i) q^{78} +(-35.0712 + 29.4282i) q^{79} +(-27.2032 - 103.932i) q^{80} +(5.66032 - 80.8020i) q^{81} +(-45.9331 + 134.672i) q^{82} +(-63.9688 + 53.6762i) q^{83} +(28.6105 - 98.6837i) q^{84} +(49.1092 + 8.65928i) q^{85} +(1.40993 + 69.2203i) q^{86} +(-107.260 - 58.2419i) q^{87} +(-91.5387 + 86.8690i) q^{88} +(-84.3952 + 48.7256i) q^{89} +(12.2909 - 120.236i) q^{90} +(59.4903 + 34.3467i) q^{91} +(77.9654 - 49.3520i) q^{92} +(42.3849 - 8.62193i) q^{93} +(122.811 - 74.2797i) q^{94} +(-99.9358 + 119.099i) q^{95} +(76.3323 - 58.2184i) q^{96} +(13.9771 + 5.08726i) q^{97} +(36.6051 - 32.0080i) q^{98} +(-130.688 + 55.4644i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86507 + 0.722171i −0.932533 + 0.361086i
\(3\) −1.09942 2.79129i −0.366472 0.930429i
\(4\) 2.95694 2.69379i 0.739234 0.673448i
\(5\) 6.30966 2.29653i 1.26193 0.459305i 0.377515 0.926004i \(-0.376779\pi\)
0.884417 + 0.466698i \(0.154557\pi\)
\(6\) 4.06627 + 4.41197i 0.677712 + 0.735328i
\(7\) 1.48683 + 8.43221i 0.212404 + 1.20460i 0.885355 + 0.464915i \(0.153915\pi\)
−0.672952 + 0.739686i \(0.734974\pi\)
\(8\) −3.56950 + 7.15952i −0.446188 + 0.894939i
\(9\) −6.58256 + 6.13758i −0.731396 + 0.681953i
\(10\) −10.1094 + 8.83983i −1.01094 + 0.883983i
\(11\) 14.8232 + 5.39522i 1.34757 + 0.490474i 0.912188 0.409773i \(-0.134392\pi\)
0.435379 + 0.900247i \(0.356614\pi\)
\(12\) −10.7701 5.29206i −0.897505 0.441005i
\(13\) 5.15695 6.14581i 0.396688 0.472755i −0.530319 0.847798i \(-0.677928\pi\)
0.927007 + 0.375043i \(0.122372\pi\)
\(14\) −8.86253 14.6529i −0.633038 1.04663i
\(15\) −13.3472 15.0872i −0.889814 1.00581i
\(16\) 1.48696 15.9308i 0.0929348 0.995672i
\(17\) 6.43164 + 3.71331i 0.378332 + 0.218430i 0.677092 0.735898i \(-0.263240\pi\)
−0.298760 + 0.954328i \(0.596573\pi\)
\(18\) 7.84453 16.2007i 0.435807 0.900040i
\(19\) −20.0523 + 11.5772i −1.05538 + 0.609327i −0.924152 0.382025i \(-0.875227\pi\)
−0.131233 + 0.991352i \(0.541894\pi\)
\(20\) 12.4709 23.7876i 0.623545 1.18938i
\(21\) 21.9021 13.4207i 1.04296 0.639080i
\(22\) −31.5426 + 0.642483i −1.43375 + 0.0292038i
\(23\) 22.7177 + 4.00574i 0.987725 + 0.174163i 0.644097 0.764944i \(-0.277233\pi\)
0.343627 + 0.939106i \(0.388344\pi\)
\(24\) 23.9086 + 2.09221i 0.996193 + 0.0871754i
\(25\) 15.3866 12.9109i 0.615465 0.516436i
\(26\) −5.17972 + 15.1865i −0.199220 + 0.584098i
\(27\) 24.3687 + 11.6261i 0.902545 + 0.430595i
\(28\) 27.1111 + 20.9283i 0.968253 + 0.747440i
\(29\) 31.1660 26.1514i 1.07469 0.901771i 0.0792199 0.996857i \(-0.474757\pi\)
0.995469 + 0.0950861i \(0.0303126\pi\)
\(30\) 35.7890 + 18.4997i 1.19297 + 0.616656i
\(31\) −2.50360 + 14.1986i −0.0807612 + 0.458019i 0.917430 + 0.397898i \(0.130260\pi\)
−0.998191 + 0.0601219i \(0.980851\pi\)
\(32\) 8.73146 + 30.7857i 0.272858 + 0.962054i
\(33\) −1.23732 47.3075i −0.0374945 1.43356i
\(34\) −14.6771 2.28082i −0.431679 0.0670830i
\(35\) 28.7462 + 49.7898i 0.821319 + 1.42257i
\(36\) −2.93087 + 35.8805i −0.0814131 + 0.996680i
\(37\) −28.7830 16.6179i −0.777918 0.449131i 0.0577739 0.998330i \(-0.481600\pi\)
−0.835692 + 0.549199i \(0.814933\pi\)
\(38\) 29.0381 36.0734i 0.764162 0.949301i
\(39\) −22.8244 7.63771i −0.585240 0.195839i
\(40\) −6.08031 + 53.3715i −0.152008 + 1.33429i
\(41\) 45.7312 54.5003i 1.11539 1.32928i 0.176803 0.984246i \(-0.443424\pi\)
0.938592 0.345029i \(-0.112131\pi\)
\(42\) −31.1568 + 40.8475i −0.741828 + 0.972559i
\(43\) 11.8398 32.5297i 0.275345 0.756504i −0.722530 0.691340i \(-0.757021\pi\)
0.997875 0.0651638i \(-0.0207570\pi\)
\(44\) 58.3650 23.9774i 1.32648 0.544941i
\(45\) −27.4386 + 53.8430i −0.609747 + 1.19651i
\(46\) −45.2628 + 8.93508i −0.983973 + 0.194241i
\(47\) −70.6731 + 12.4616i −1.50368 + 0.265140i −0.863997 0.503497i \(-0.832047\pi\)
−0.639686 + 0.768637i \(0.720936\pi\)
\(48\) −46.1021 + 13.3640i −0.960460 + 0.278417i
\(49\) −22.8466 + 8.31547i −0.466257 + 0.169703i
\(50\) −19.3732 + 35.1915i −0.387463 + 0.703829i
\(51\) 3.29386 22.0350i 0.0645855 0.432060i
\(52\) −1.30677 32.0645i −0.0251302 0.616626i
\(53\) −74.3739 −1.40328 −0.701641 0.712531i \(-0.747549\pi\)
−0.701641 + 0.712531i \(0.747549\pi\)
\(54\) −53.8453 4.08499i −0.997135 0.0756481i
\(55\) 105.920 1.92581
\(56\) −65.6778 19.4538i −1.17282 0.347390i
\(57\) 54.3612 + 43.2436i 0.953704 + 0.758659i
\(58\) −39.2408 + 71.2812i −0.676566 + 1.22899i
\(59\) 91.3890 33.2629i 1.54897 0.563778i 0.580792 0.814052i \(-0.302743\pi\)
0.968175 + 0.250275i \(0.0805209\pi\)
\(60\) −80.1087 8.65735i −1.33515 0.144289i
\(61\) 32.3319 5.70098i 0.530030 0.0934586i 0.0977726 0.995209i \(-0.468828\pi\)
0.432258 + 0.901750i \(0.357717\pi\)
\(62\) −5.58445 28.2893i −0.0900718 0.456280i
\(63\) −61.5405 46.3801i −0.976833 0.736191i
\(64\) −38.5173 51.1118i −0.601833 0.798622i
\(65\) 18.4246 50.6211i 0.283455 0.778785i
\(66\) 36.4718 + 87.3380i 0.552603 + 1.32330i
\(67\) −25.3389 + 30.1977i −0.378192 + 0.450712i −0.921243 0.388988i \(-0.872825\pi\)
0.543051 + 0.839700i \(0.317269\pi\)
\(68\) 29.0209 6.34549i 0.426777 0.0933160i
\(69\) −13.7950 67.8155i −0.199928 0.982834i
\(70\) −89.5702 72.1016i −1.27957 1.03002i
\(71\) −18.2728 10.5498i −0.257363 0.148589i 0.365768 0.930706i \(-0.380806\pi\)
−0.623131 + 0.782117i \(0.714140\pi\)
\(72\) −20.4456 69.0361i −0.283967 0.958834i
\(73\) 21.2203 + 36.7547i 0.290689 + 0.503489i 0.973973 0.226664i \(-0.0727821\pi\)
−0.683284 + 0.730153i \(0.739449\pi\)
\(74\) 65.6830 + 10.2072i 0.887609 + 0.137934i
\(75\) −52.9544 28.7540i −0.706058 0.383387i
\(76\) −28.1068 + 88.2498i −0.369827 + 1.16118i
\(77\) −23.4540 + 133.014i −0.304598 + 1.72746i
\(78\) 48.0847 2.23826i 0.616470 0.0286957i
\(79\) −35.0712 + 29.4282i −0.443939 + 0.372509i −0.837181 0.546926i \(-0.815798\pi\)
0.393242 + 0.919435i \(0.371354\pi\)
\(80\) −27.2032 103.932i −0.340040 1.29916i
\(81\) 5.66032 80.8020i 0.0698805 0.997555i
\(82\) −45.9331 + 134.672i −0.560160 + 1.64235i
\(83\) −63.9688 + 53.6762i −0.770708 + 0.646701i −0.940890 0.338712i \(-0.890009\pi\)
0.170182 + 0.985413i \(0.445564\pi\)
\(84\) 28.6105 98.6837i 0.340602 1.17481i
\(85\) 49.1092 + 8.65928i 0.577755 + 0.101874i
\(86\) 1.40993 + 69.2203i 0.0163946 + 0.804887i
\(87\) −107.260 58.2419i −1.23288 0.669448i
\(88\) −91.5387 + 86.8690i −1.04021 + 0.987147i
\(89\) −84.3952 + 48.7256i −0.948261 + 0.547479i −0.892540 0.450968i \(-0.851079\pi\)
−0.0557207 + 0.998446i \(0.517746\pi\)
\(90\) 12.2909 120.236i 0.136566 1.33596i
\(91\) 59.4903 + 34.3467i 0.653739 + 0.377437i
\(92\) 77.9654 49.3520i 0.847450 0.536435i
\(93\) 42.3849 8.62193i 0.455751 0.0927089i
\(94\) 122.811 74.2797i 1.30650 0.790210i
\(95\) −99.9358 + 119.099i −1.05196 + 1.25367i
\(96\) 76.3323 58.2184i 0.795128 0.606441i
\(97\) 13.9771 + 5.08726i 0.144094 + 0.0524460i 0.413061 0.910704i \(-0.364460\pi\)
−0.268966 + 0.963150i \(0.586682\pi\)
\(98\) 36.6051 32.0080i 0.373522 0.326613i
\(99\) −130.688 + 55.4644i −1.32009 + 0.560246i
\(100\) 10.7180 79.6251i 0.107180 0.796251i
\(101\) 8.05818 + 45.7002i 0.0797840 + 0.452477i 0.998361 + 0.0572348i \(0.0182284\pi\)
−0.918577 + 0.395243i \(0.870661\pi\)
\(102\) 9.76981 + 43.4755i 0.0957825 + 0.426231i
\(103\) −79.6455 + 28.9886i −0.773257 + 0.281442i −0.698358 0.715749i \(-0.746086\pi\)
−0.0748988 + 0.997191i \(0.523863\pi\)
\(104\) 25.5933 + 58.8588i 0.246089 + 0.565950i
\(105\) 107.374 134.979i 1.02261 1.28551i
\(106\) 138.712 53.7107i 1.30861 0.506705i
\(107\) 23.5892 0.220460 0.110230 0.993906i \(-0.464841\pi\)
0.110230 + 0.993906i \(0.464841\pi\)
\(108\) 103.375 31.2667i 0.957176 0.289507i
\(109\) 160.231i 1.47001i −0.678061 0.735005i \(-0.737180\pi\)
0.678061 0.735005i \(-0.262820\pi\)
\(110\) −197.547 + 76.4922i −1.79589 + 0.695384i
\(111\) −14.7407 + 98.6115i −0.132799 + 0.888392i
\(112\) 136.542 11.1479i 1.21913 0.0995351i
\(113\) 29.1996 + 80.2254i 0.258404 + 0.709959i 0.999266 + 0.0383020i \(0.0121949\pi\)
−0.740862 + 0.671657i \(0.765583\pi\)
\(114\) −132.616 41.3940i −1.16330 0.363105i
\(115\) 152.540 26.8969i 1.32643 0.233886i
\(116\) 21.7095 161.283i 0.187151 1.39037i
\(117\) 3.77444 + 72.1064i 0.0322602 + 0.616294i
\(118\) −146.425 + 128.036i −1.24089 + 1.08505i
\(119\) −21.7487 + 59.7540i −0.182762 + 0.502135i
\(120\) 155.660 41.7057i 1.29717 0.347547i
\(121\) 97.9286 + 82.1719i 0.809327 + 0.679106i
\(122\) −56.1839 + 33.9818i −0.460524 + 0.278540i
\(123\) −202.404 67.7303i −1.64556 0.550653i
\(124\) 30.8451 + 48.7285i 0.248751 + 0.392972i
\(125\) −16.4984 + 28.5761i −0.131987 + 0.228609i
\(126\) 148.271 + 42.0591i 1.17676 + 0.333802i
\(127\) 32.6341 + 56.5240i 0.256962 + 0.445071i 0.965427 0.260675i \(-0.0839452\pi\)
−0.708465 + 0.705746i \(0.750612\pi\)
\(128\) 108.749 + 67.5107i 0.849600 + 0.527428i
\(129\) −103.816 + 2.71530i −0.804779 + 0.0210489i
\(130\) 2.19407 + 107.717i 0.0168774 + 0.828594i
\(131\) 29.2007 165.606i 0.222906 1.26416i −0.643741 0.765243i \(-0.722619\pi\)
0.866647 0.498921i \(-0.166270\pi\)
\(132\) −131.095 136.552i −0.993146 1.03449i
\(133\) −127.436 151.872i −0.958163 1.14189i
\(134\) 25.4507 74.6196i 0.189931 0.556863i
\(135\) 180.458 + 17.3931i 1.33672 + 0.128838i
\(136\) −49.5433 + 32.7928i −0.364289 + 0.241123i
\(137\) 114.535 + 136.497i 0.836021 + 0.996331i 0.999951 + 0.00985941i \(0.00313840\pi\)
−0.163930 + 0.986472i \(0.552417\pi\)
\(138\) 74.7030 + 116.518i 0.541326 + 0.844333i
\(139\) −199.355 35.1517i −1.43421 0.252890i −0.598086 0.801432i \(-0.704072\pi\)
−0.836123 + 0.548542i \(0.815183\pi\)
\(140\) 219.124 + 69.7891i 1.56517 + 0.498494i
\(141\) 112.483 + 183.568i 0.797752 + 1.30190i
\(142\) 41.6987 + 6.47998i 0.293653 + 0.0456337i
\(143\) 109.601 63.2780i 0.766438 0.442503i
\(144\) 87.9882 + 113.992i 0.611029 + 0.791608i
\(145\) 136.589 236.580i 0.941995 1.63158i
\(146\) −66.1204 53.2252i −0.452880 0.364556i
\(147\) 48.3288 + 54.6292i 0.328767 + 0.371627i
\(148\) −129.874 + 28.3974i −0.877530 + 0.191874i
\(149\) 55.9340 + 46.9342i 0.375396 + 0.314995i 0.810892 0.585196i \(-0.198982\pi\)
−0.435496 + 0.900191i \(0.643427\pi\)
\(150\) 119.529 + 15.3860i 0.796858 + 0.102573i
\(151\) 8.25097 + 3.00311i 0.0546422 + 0.0198881i 0.369197 0.929351i \(-0.379633\pi\)
−0.314554 + 0.949239i \(0.601855\pi\)
\(152\) −11.3104 184.890i −0.0744108 1.21638i
\(153\) −65.1275 + 15.0316i −0.425670 + 0.0982457i
\(154\) −52.3159 265.018i −0.339713 1.72090i
\(155\) 16.8106 + 95.3379i 0.108456 + 0.615083i
\(156\) −88.0646 + 38.8999i −0.564517 + 0.249358i
\(157\) −24.0149 65.9804i −0.152961 0.420257i 0.839417 0.543488i \(-0.182897\pi\)
−0.992378 + 0.123231i \(0.960674\pi\)
\(158\) 44.1579 80.2130i 0.279480 0.507677i
\(159\) 81.7679 + 207.599i 0.514264 + 1.30565i
\(160\) 125.793 + 174.195i 0.786205 + 1.08872i
\(161\) 197.516i 1.22681i
\(162\) 47.7960 + 154.789i 0.295037 + 0.955486i
\(163\) 191.352i 1.17394i 0.809610 + 0.586968i \(0.199679\pi\)
−0.809610 + 0.586968i \(0.800321\pi\)
\(164\) −11.5883 284.344i −0.0706603 1.73381i
\(165\) −116.450 295.653i −0.705758 1.79183i
\(166\) 80.5426 146.306i 0.485196 0.881361i
\(167\) −7.69637 21.1456i −0.0460860 0.126620i 0.914514 0.404553i \(-0.132573\pi\)
−0.960601 + 0.277933i \(0.910351\pi\)
\(168\) 17.9060 + 204.713i 0.106583 + 1.21853i
\(169\) 18.1697 + 103.045i 0.107513 + 0.609735i
\(170\) −97.8453 + 19.3151i −0.575561 + 0.113618i
\(171\) 60.9396 199.280i 0.356372 1.16538i
\(172\) −52.6185 128.082i −0.305922 0.744664i
\(173\) −225.848 82.2020i −1.30548 0.475156i −0.406702 0.913561i \(-0.633321\pi\)
−0.898778 + 0.438405i \(0.855544\pi\)
\(174\) 242.108 + 31.1647i 1.39143 + 0.179107i
\(175\) 131.745 + 110.547i 0.752827 + 0.631697i
\(176\) 107.991 228.123i 0.613588 1.29615i
\(177\) −193.321 218.523i −1.09221 1.23459i
\(178\) 122.214 151.824i 0.686598 0.852945i
\(179\) 139.297 241.269i 0.778194 1.34787i −0.154788 0.987948i \(-0.549469\pi\)
0.932982 0.359924i \(-0.117197\pi\)
\(180\) 63.9077 + 233.124i 0.355043 + 1.29514i
\(181\) −25.6831 + 14.8282i −0.141896 + 0.0819236i −0.569267 0.822153i \(-0.692773\pi\)
0.427371 + 0.904076i \(0.359440\pi\)
\(182\) −135.757 21.0967i −0.745920 0.115916i
\(183\) −51.4592 83.9797i −0.281198 0.458906i
\(184\) −109.770 + 148.349i −0.596576 + 0.806245i
\(185\) −219.774 38.7521i −1.18797 0.209471i
\(186\) −72.8240 + 46.6896i −0.391527 + 0.251019i
\(187\) 75.3037 + 89.7434i 0.402693 + 0.479911i
\(188\) −175.407 + 227.227i −0.933016 + 1.20865i
\(189\) −61.8014 + 222.768i −0.326992 + 1.17867i
\(190\) 100.377 294.298i 0.528300 1.54894i
\(191\) −186.650 222.440i −0.977223 1.16461i −0.986352 0.164651i \(-0.947350\pi\)
0.00912903 0.999958i \(-0.497094\pi\)
\(192\) −100.321 + 163.706i −0.522506 + 0.852636i
\(193\) −9.94444 + 56.3977i −0.0515256 + 0.292216i −0.999672 0.0256184i \(-0.991845\pi\)
0.948146 + 0.317834i \(0.102956\pi\)
\(194\) −29.7422 + 0.605811i −0.153310 + 0.00312274i
\(195\) −161.554 + 4.22542i −0.828483 + 0.0216688i
\(196\) −45.1557 + 86.1323i −0.230386 + 0.439450i
\(197\) 10.0061 + 17.3311i 0.0507926 + 0.0879753i 0.890304 0.455367i \(-0.150492\pi\)
−0.839511 + 0.543342i \(0.817159\pi\)
\(198\) 203.688 197.824i 1.02873 0.999112i
\(199\) 99.5221 172.377i 0.500111 0.866218i −0.499889 0.866090i \(-0.666626\pi\)
1.00000 0.000128296i \(-4.08378e-5\pi\)
\(200\) 37.5133 + 156.246i 0.187566 + 0.781231i
\(201\) 112.148 + 37.5282i 0.557952 + 0.186707i
\(202\) −48.0324 79.4145i −0.237784 0.393141i
\(203\) 266.852 + 223.916i 1.31454 + 1.10303i
\(204\) −49.6181 74.0292i −0.243226 0.362888i
\(205\) 163.387 448.901i 0.797008 2.18976i
\(206\) 127.609 111.583i 0.619462 0.541666i
\(207\) −174.126 + 113.063i −0.841189 + 0.546200i
\(208\) −90.2393 91.2927i −0.433843 0.438907i
\(209\) −359.702 + 63.4251i −1.72106 + 0.303469i
\(210\) −102.781 + 329.286i −0.489434 + 1.56803i
\(211\) 70.3176 + 193.196i 0.333259 + 0.915620i 0.987258 + 0.159126i \(0.0508675\pi\)
−0.654000 + 0.756495i \(0.726910\pi\)
\(212\) −219.919 + 200.348i −1.03735 + 0.945037i
\(213\) −9.35810 + 62.6032i −0.0439348 + 0.293912i
\(214\) −43.9954 + 17.0354i −0.205586 + 0.0796048i
\(215\) 232.441i 1.08112i
\(216\) −170.221 + 132.969i −0.788061 + 0.615597i
\(217\) −123.448 −0.568885
\(218\) 115.714 + 298.842i 0.530800 + 1.37083i
\(219\) 79.2629 99.6407i 0.361931 0.454980i
\(220\) 313.198 285.326i 1.42363 1.29694i
\(221\) 55.9890 20.3783i 0.253344 0.0922096i
\(222\) −43.7220 194.562i −0.196946 0.876406i
\(223\) −43.0564 244.185i −0.193078 1.09500i −0.915129 0.403160i \(-0.867912\pi\)
0.722052 0.691839i \(-0.243199\pi\)
\(224\) −246.610 + 119.399i −1.10094 + 0.533029i
\(225\) −22.0418 + 179.423i −0.0979633 + 0.797438i
\(226\) −112.396 128.538i −0.497326 0.568754i
\(227\) −227.693 82.8736i −1.00305 0.365082i −0.212293 0.977206i \(-0.568093\pi\)
−0.790762 + 0.612124i \(0.790315\pi\)
\(228\) 277.232 18.5692i 1.21593 0.0814437i
\(229\) −132.146 + 157.486i −0.577058 + 0.687711i −0.973064 0.230537i \(-0.925952\pi\)
0.396005 + 0.918248i \(0.370396\pi\)
\(230\) −265.073 + 160.325i −1.15249 + 0.697063i
\(231\) 397.067 80.7714i 1.71891 0.349660i
\(232\) 75.9841 + 316.481i 0.327518 + 1.36414i
\(233\) 155.653 + 89.8665i 0.668040 + 0.385693i 0.795334 0.606172i \(-0.207296\pi\)
−0.127294 + 0.991865i \(0.540629\pi\)
\(234\) −59.1127 131.757i −0.252619 0.563066i
\(235\) −417.305 + 240.931i −1.77576 + 1.02524i
\(236\) 180.628 344.539i 0.765374 1.45991i
\(237\) 120.700 + 65.5399i 0.509285 + 0.276540i
\(238\) −2.58992 127.151i −0.0108820 0.534250i
\(239\) 47.2222 + 8.32655i 0.197583 + 0.0348391i 0.271564 0.962421i \(-0.412459\pi\)
−0.0739810 + 0.997260i \(0.523570\pi\)
\(240\) −260.198 + 190.197i −1.08416 + 0.792488i
\(241\) 102.971 86.4032i 0.427267 0.358519i −0.403653 0.914912i \(-0.632260\pi\)
0.830919 + 0.556393i \(0.187815\pi\)
\(242\) −241.985 82.5347i −0.999940 0.341052i
\(243\) −231.765 + 73.0355i −0.953764 + 0.300558i
\(244\) 80.2460 103.953i 0.328877 0.426036i
\(245\) −125.057 + 104.936i −0.510438 + 0.428308i
\(246\) 426.409 19.8486i 1.73337 0.0806855i
\(247\) −32.2574 + 182.941i −0.130597 + 0.740651i
\(248\) −92.7185 68.6065i −0.373865 0.276639i
\(249\) 220.154 + 119.543i 0.884153 + 0.480091i
\(250\) 10.1338 65.2109i 0.0405351 0.260844i
\(251\) 46.8237 + 81.1011i 0.186549 + 0.323112i 0.944097 0.329667i \(-0.106936\pi\)
−0.757549 + 0.652779i \(0.773603\pi\)
\(252\) −306.910 + 28.6343i −1.21790 + 0.113628i
\(253\) 315.138 + 181.945i 1.24560 + 0.719149i
\(254\) −101.685 81.8535i −0.400334 0.322258i
\(255\) −29.8210 146.598i −0.116945 0.574894i
\(256\) −251.578 47.3767i −0.982726 0.185065i
\(257\) −72.2432 + 86.0961i −0.281102 + 0.335004i −0.888058 0.459731i \(-0.847946\pi\)
0.606956 + 0.794735i \(0.292390\pi\)
\(258\) 191.664 80.0375i 0.742882 0.310223i
\(259\) 97.3300 267.412i 0.375791 1.03248i
\(260\) −81.8824 199.315i −0.314932 0.766597i
\(261\) −44.6461 + 363.427i −0.171058 + 1.39244i
\(262\) 65.1343 + 329.953i 0.248604 + 1.25936i
\(263\) −39.8459 + 7.02591i −0.151505 + 0.0267145i −0.248886 0.968533i \(-0.580065\pi\)
0.0973810 + 0.995247i \(0.468953\pi\)
\(264\) 343.115 + 160.006i 1.29968 + 0.606082i
\(265\) −469.274 + 170.802i −1.77084 + 0.644535i
\(266\) 347.354 + 191.221i 1.30584 + 0.718875i
\(267\) 228.793 + 182.002i 0.856901 + 0.681654i
\(268\) 6.42087 + 157.550i 0.0239585 + 0.587874i
\(269\) −333.401 −1.23941 −0.619705 0.784835i \(-0.712748\pi\)
−0.619705 + 0.784835i \(0.712748\pi\)
\(270\) −349.126 + 97.8822i −1.29306 + 0.362527i
\(271\) −311.416 −1.14914 −0.574568 0.818457i \(-0.694830\pi\)
−0.574568 + 0.818457i \(0.694830\pi\)
\(272\) 68.7194 96.9394i 0.252645 0.356395i
\(273\) 30.4670 203.816i 0.111601 0.746578i
\(274\) −312.190 171.863i −1.13938 0.627236i
\(275\) 297.737 108.367i 1.08268 0.394063i
\(276\) −223.472 163.365i −0.809681 0.591903i
\(277\) 25.0100 4.40993i 0.0902887 0.0159203i −0.128321 0.991733i \(-0.540959\pi\)
0.218610 + 0.975812i \(0.429848\pi\)
\(278\) 397.196 78.4083i 1.42876 0.282044i
\(279\) −70.6649 108.829i −0.253279 0.390069i
\(280\) −459.080 + 28.0838i −1.63957 + 0.100299i
\(281\) 10.0227 27.5371i 0.0356679 0.0979969i −0.920580 0.390553i \(-0.872284\pi\)
0.956248 + 0.292556i \(0.0945059\pi\)
\(282\) −342.356 261.135i −1.21403 0.926011i
\(283\) 197.105 234.900i 0.696482 0.830035i −0.295641 0.955299i \(-0.595533\pi\)
0.992123 + 0.125264i \(0.0399777\pi\)
\(284\) −82.4505 + 18.0280i −0.290319 + 0.0634789i
\(285\) 442.310 + 148.010i 1.55197 + 0.519334i
\(286\) −158.715 + 197.168i −0.554947 + 0.689399i
\(287\) 527.552 + 304.582i 1.83816 + 1.06126i
\(288\) −246.425 149.059i −0.855643 0.517566i
\(289\) −116.923 202.516i −0.404577 0.700747i
\(290\) −83.8970 + 539.877i −0.289300 + 1.86165i
\(291\) −1.16669 44.6072i −0.00400926 0.153289i
\(292\) 161.757 + 51.5181i 0.553961 + 0.176432i
\(293\) 48.6000 275.624i 0.165870 0.940697i −0.782292 0.622912i \(-0.785950\pi\)
0.948163 0.317786i \(-0.102939\pi\)
\(294\) −129.588 66.9853i −0.440775 0.227841i
\(295\) 500.244 419.755i 1.69574 1.42290i
\(296\) 221.717 146.755i 0.749043 0.495793i
\(297\) 298.498 + 303.811i 1.00504 + 1.02293i
\(298\) −138.215 47.1415i −0.463809 0.158193i
\(299\) 141.772 118.961i 0.474155 0.397863i
\(300\) −234.040 + 57.6243i −0.780134 + 0.192081i
\(301\) 291.901 + 51.4700i 0.969769 + 0.170997i
\(302\) −17.5574 + 0.357622i −0.0581369 + 0.00118418i
\(303\) 118.703 72.7363i 0.391760 0.240054i
\(304\) 154.617 + 336.663i 0.508608 + 1.10744i
\(305\) 190.910 110.222i 0.625936 0.361384i
\(306\) 110.612 75.0681i 0.361476 0.245321i
\(307\) 299.330 + 172.818i 0.975016 + 0.562926i 0.900762 0.434313i \(-0.143009\pi\)
0.0742544 + 0.997239i \(0.476342\pi\)
\(308\) 288.961 + 456.496i 0.938186 + 1.48213i
\(309\) 168.479 + 190.443i 0.545239 + 0.616320i
\(310\) −100.203 165.671i −0.323236 0.534423i
\(311\) −106.997 + 127.514i −0.344043 + 0.410014i −0.910125 0.414335i \(-0.864014\pi\)
0.566082 + 0.824349i \(0.308459\pi\)
\(312\) 136.154 136.149i 0.436391 0.436374i
\(313\) −384.385 139.905i −1.22807 0.446980i −0.355132 0.934816i \(-0.615564\pi\)
−0.872935 + 0.487836i \(0.837786\pi\)
\(314\) 92.4385 + 105.715i 0.294390 + 0.336672i
\(315\) −494.812 151.313i −1.57083 0.480358i
\(316\) −24.4298 + 181.492i −0.0773094 + 0.574342i
\(317\) −15.3024 86.7842i −0.0482726 0.273767i 0.951112 0.308846i \(-0.0999429\pi\)
−0.999385 + 0.0350789i \(0.988832\pi\)
\(318\) −302.424 328.135i −0.951020 1.03187i
\(319\) 603.073 219.501i 1.89051 0.688090i
\(320\) −360.411 234.042i −1.12628 0.731381i
\(321\) −25.9344 65.8442i −0.0807924 0.205122i
\(322\) −142.640 368.380i −0.442983 1.14404i
\(323\) −171.959 −0.532381
\(324\) −200.927 254.174i −0.620144 0.784488i
\(325\) 161.144i 0.495828i
\(326\) −138.189 356.883i −0.423891 1.09473i
\(327\) −447.251 + 176.161i −1.36774 + 0.538718i
\(328\) 226.958 + 521.952i 0.691946 + 1.59132i
\(329\) −210.157 577.402i −0.638776 1.75502i
\(330\) 430.699 + 467.314i 1.30515 + 1.41610i
\(331\) −485.193 + 85.5526i −1.46584 + 0.258467i −0.848904 0.528547i \(-0.822737\pi\)
−0.616935 + 0.787014i \(0.711626\pi\)
\(332\) −44.5592 + 331.036i −0.134214 + 0.997096i
\(333\) 291.459 67.2695i 0.875252 0.202011i
\(334\) 29.6250 + 33.8798i 0.0886975 + 0.101437i
\(335\) −90.5297 + 248.728i −0.270238 + 0.742473i
\(336\) −181.234 368.873i −0.539387 1.09783i
\(337\) −374.666 314.382i −1.11177 0.932885i −0.113610 0.993525i \(-0.536241\pi\)
−0.998160 + 0.0606403i \(0.980686\pi\)
\(338\) −108.304 179.064i −0.320426 0.529776i
\(339\) 191.829 169.706i 0.565869 0.500607i
\(340\) 168.539 106.685i 0.495703 0.313780i
\(341\) −113.716 + 196.962i −0.333478 + 0.577601i
\(342\) 30.2581 + 415.680i 0.0884739 + 1.21544i
\(343\) 105.689 + 183.059i 0.308132 + 0.533701i
\(344\) 190.634 + 200.882i 0.554169 + 0.583959i
\(345\) −242.782 396.212i −0.703716 1.14844i
\(346\) 480.585 9.78893i 1.38897 0.0282917i
\(347\) 35.8254 203.176i 0.103243 0.585521i −0.888664 0.458558i \(-0.848366\pi\)
0.991907 0.126963i \(-0.0405229\pi\)
\(348\) −474.054 + 116.719i −1.36222 + 0.335401i
\(349\) 256.116 + 305.227i 0.733858 + 0.874577i 0.995898 0.0904794i \(-0.0288399\pi\)
−0.262041 + 0.965057i \(0.584395\pi\)
\(350\) −325.546 111.035i −0.930132 0.317243i
\(351\) 197.120 89.8105i 0.561595 0.255870i
\(352\) −36.6672 + 503.452i −0.104168 + 1.43026i
\(353\) 295.022 + 351.593i 0.835755 + 0.996014i 0.999954 + 0.00958707i \(0.00305170\pi\)
−0.164199 + 0.986427i \(0.552504\pi\)
\(354\) 518.367 + 267.949i 1.46431 + 0.756919i
\(355\) −139.523 24.6017i −0.393022 0.0693005i
\(356\) −118.295 + 371.422i −0.332288 + 1.04332i
\(357\) 190.702 4.98776i 0.534178 0.0139713i
\(358\) −85.5600 + 550.579i −0.238994 + 1.53793i
\(359\) 330.481 190.803i 0.920560 0.531485i 0.0367462 0.999325i \(-0.488301\pi\)
0.883814 + 0.467839i \(0.154967\pi\)
\(360\) −287.548 388.640i −0.798744 1.07956i
\(361\) 87.5634 151.664i 0.242558 0.420123i
\(362\) 37.1923 46.2031i 0.102741 0.127633i
\(363\) 121.701 363.688i 0.335264 1.00190i
\(364\) 268.432 58.6934i 0.737451 0.161246i
\(365\) 218.301 + 183.176i 0.598085 + 0.501853i
\(366\) 156.623 + 119.465i 0.427931 + 0.326408i
\(367\) −676.872 246.361i −1.84434 0.671284i −0.987913 0.155012i \(-0.950458\pi\)
−0.856425 0.516272i \(-0.827320\pi\)
\(368\) 97.5946 355.953i 0.265203 0.967264i
\(369\) 33.4713 + 639.430i 0.0907081 + 1.73287i
\(370\) 437.878 86.4393i 1.18346 0.233620i
\(371\) −110.581 627.136i −0.298062 1.69039i
\(372\) 102.104 139.671i 0.274472 0.375458i
\(373\) −134.688 370.053i −0.361094 0.992099i −0.978643 0.205566i \(-0.934096\pi\)
0.617549 0.786533i \(-0.288126\pi\)
\(374\) −205.256 112.995i −0.548814 0.302126i
\(375\) 97.9027 + 14.6348i 0.261074 + 0.0390260i
\(376\) 163.049 550.467i 0.433641 1.46401i
\(377\) 326.402i 0.865787i
\(378\) −45.6130 460.108i −0.120669 1.21722i
\(379\) 351.090i 0.926359i 0.886265 + 0.463179i \(0.153291\pi\)
−0.886265 + 0.463179i \(0.846709\pi\)
\(380\) 25.3238 + 621.374i 0.0666415 + 1.63520i
\(381\) 121.896 153.235i 0.319937 0.402191i
\(382\) 508.754 + 280.073i 1.33182 + 0.733175i
\(383\) −259.254 712.294i −0.676903 1.85978i −0.473841 0.880611i \(-0.657133\pi\)
−0.203063 0.979166i \(-0.565089\pi\)
\(384\) 68.8816 377.772i 0.179379 0.983780i
\(385\) 157.484 + 893.138i 0.409050 + 2.31984i
\(386\) −22.1818 112.367i −0.0574657 0.291106i
\(387\) 121.717 + 286.796i 0.314514 + 0.741076i
\(388\) 55.0336 22.6088i 0.141839 0.0582701i
\(389\) −483.578 176.008i −1.24313 0.452463i −0.365057 0.930985i \(-0.618950\pi\)
−0.878075 + 0.478522i \(0.841173\pi\)
\(390\) 298.258 124.550i 0.764763 0.319360i
\(391\) 131.237 + 110.121i 0.335646 + 0.281640i
\(392\) 22.0161 193.252i 0.0561636 0.492991i
\(393\) −494.356 + 100.562i −1.25790 + 0.255883i
\(394\) −31.1781 25.0976i −0.0791323 0.0636994i
\(395\) −153.704 + 266.224i −0.389125 + 0.673985i
\(396\) −237.028 + 516.052i −0.598556 + 1.30316i
\(397\) −563.555 + 325.369i −1.41953 + 0.819568i −0.996258 0.0864327i \(-0.972453\pi\)
−0.423276 + 0.906001i \(0.639120\pi\)
\(398\) −61.1293 + 393.367i −0.153591 + 0.988359i
\(399\) −283.813 + 522.680i −0.711311 + 1.30998i
\(400\) −182.801 264.318i −0.457003 0.660796i
\(401\) 482.881 + 85.1449i 1.20419 + 0.212331i 0.739510 0.673146i \(-0.235057\pi\)
0.464682 + 0.885478i \(0.346169\pi\)
\(402\) −236.266 + 10.9978i −0.587726 + 0.0273577i
\(403\) 74.3510 + 88.6081i 0.184494 + 0.219871i
\(404\) 146.934 + 113.426i 0.363699 + 0.280757i
\(405\) −149.849 522.832i −0.369998 1.29094i
\(406\) −659.402 224.904i −1.62414 0.553951i
\(407\) −337.000 401.621i −0.828009 0.986783i
\(408\) 146.003 + 102.237i 0.357850 + 0.250580i
\(409\) 2.05082 11.6308i 0.00501423 0.0284371i −0.982198 0.187849i \(-0.939849\pi\)
0.987212 + 0.159412i \(0.0509597\pi\)
\(410\) 19.4567 + 955.223i 0.0474554 + 2.32981i
\(411\) 255.082 469.767i 0.620637 1.14299i
\(412\) −157.417 + 300.266i −0.382081 + 0.728800i
\(413\) 416.359 + 721.155i 1.00813 + 1.74614i
\(414\) 243.105 336.619i 0.587211 0.813090i
\(415\) −280.352 + 485.584i −0.675548 + 1.17008i
\(416\) 234.231 + 105.099i 0.563056 + 0.252641i
\(417\) 121.056 + 595.103i 0.290302 + 1.42711i
\(418\) 625.063 378.058i 1.49537 0.904445i
\(419\) 145.685 + 122.244i 0.347697 + 0.291753i 0.799865 0.600180i \(-0.204905\pi\)
−0.452167 + 0.891933i \(0.649349\pi\)
\(420\) −46.1072 688.365i −0.109779 1.63897i
\(421\) 110.926 304.767i 0.263482 0.723912i −0.735444 0.677585i \(-0.763026\pi\)
0.998926 0.0463262i \(-0.0147514\pi\)
\(422\) −270.667 309.542i −0.641392 0.733511i
\(423\) 388.726 515.791i 0.918975 1.21936i
\(424\) 265.478 532.481i 0.626127 1.25585i
\(425\) 146.904 25.9031i 0.345655 0.0609484i
\(426\) −27.7568 123.517i −0.0651568 0.289947i
\(427\) 96.1437 + 264.153i 0.225161 + 0.618624i
\(428\) 69.7518 63.5444i 0.162971 0.148468i
\(429\) −297.124 236.358i −0.692596 0.550951i
\(430\) 167.863 + 433.518i 0.390378 + 1.00818i
\(431\) 111.208i 0.258024i 0.991643 + 0.129012i \(0.0411806\pi\)
−0.991643 + 0.129012i \(0.958819\pi\)
\(432\) 221.447 370.925i 0.512610 0.858622i
\(433\) 428.029 0.988519 0.494260 0.869314i \(-0.335439\pi\)
0.494260 + 0.869314i \(0.335439\pi\)
\(434\) 230.239 89.1506i 0.530504 0.205416i
\(435\) −810.530 121.160i −1.86329 0.278529i
\(436\) −431.630 473.794i −0.989976 1.08668i
\(437\) −501.917 + 182.683i −1.14855 + 0.418039i
\(438\) −75.8727 + 243.078i −0.173225 + 0.554972i
\(439\) 77.3604 + 438.733i 0.176220 + 0.999391i 0.936727 + 0.350062i \(0.113839\pi\)
−0.760507 + 0.649330i \(0.775050\pi\)
\(440\) −378.081 + 758.334i −0.859275 + 1.72349i
\(441\) 99.3522 194.960i 0.225288 0.442085i
\(442\) −89.7065 + 78.4406i −0.202956 + 0.177467i
\(443\) 443.091 + 161.272i 1.00021 + 0.364045i 0.789664 0.613540i \(-0.210255\pi\)
0.210542 + 0.977585i \(0.432477\pi\)
\(444\) 222.052 + 331.296i 0.500116 + 0.746163i
\(445\) −420.605 + 501.258i −0.945180 + 1.12642i
\(446\) 256.646 + 424.327i 0.575440 + 0.951405i
\(447\) 69.5121 207.728i 0.155508 0.464716i
\(448\) 373.717 400.780i 0.834189 0.894599i
\(449\) 173.821 + 100.355i 0.387128 + 0.223509i 0.680915 0.732362i \(-0.261582\pi\)
−0.293787 + 0.955871i \(0.594916\pi\)
\(450\) −88.4652 350.554i −0.196589 0.779010i
\(451\) 971.925 561.141i 2.15504 1.24422i
\(452\) 302.452 + 158.564i 0.669142 + 0.350804i
\(453\) −0.688722 26.3325i −0.00152036 0.0581291i
\(454\) 484.512 9.86891i 1.06721 0.0217377i
\(455\) 454.241 + 80.0950i 0.998333 + 0.176033i
\(456\) −503.645 + 234.842i −1.10449 + 0.515003i
\(457\) −315.393 + 264.646i −0.690137 + 0.579094i −0.918949 0.394377i \(-0.870960\pi\)
0.228812 + 0.973471i \(0.426516\pi\)
\(458\) 132.730 389.154i 0.289803 0.849681i
\(459\) 113.560 + 165.263i 0.247407 + 0.360051i
\(460\) 378.596 490.444i 0.823036 1.06618i
\(461\) 70.0397 58.7703i 0.151930 0.127484i −0.563654 0.826011i \(-0.690605\pi\)
0.715584 + 0.698526i \(0.246161\pi\)
\(462\) −682.225 + 437.394i −1.47668 + 0.946741i
\(463\) −31.3677 + 177.895i −0.0677487 + 0.384222i 0.932014 + 0.362423i \(0.118050\pi\)
−0.999762 + 0.0217989i \(0.993061\pi\)
\(464\) −370.268 535.384i −0.797992 1.15384i
\(465\) 247.633 151.739i 0.532545 0.326321i
\(466\) −355.203 55.1985i −0.762237 0.118452i
\(467\) 61.6193 + 106.728i 0.131947 + 0.228539i 0.924427 0.381359i \(-0.124544\pi\)
−0.792480 + 0.609898i \(0.791210\pi\)
\(468\) 205.400 + 203.047i 0.438890 + 0.433860i
\(469\) −292.308 168.764i −0.623257 0.359838i
\(470\) 604.307 750.717i 1.28576 1.59727i
\(471\) −157.768 + 139.572i −0.334964 + 0.296332i
\(472\) −88.0671 + 773.033i −0.186583 + 1.63778i
\(473\) 351.009 418.316i 0.742091 0.884390i
\(474\) −272.445 35.0697i −0.574779 0.0739868i
\(475\) −159.065 + 437.028i −0.334874 + 0.920058i
\(476\) 96.6555 + 235.275i 0.203058 + 0.494276i
\(477\) 489.571 456.475i 1.02635 0.956972i
\(478\) −94.0857 + 18.5730i −0.196832 + 0.0388556i
\(479\) 674.144 118.870i 1.40740 0.248162i 0.582218 0.813033i \(-0.302185\pi\)
0.825180 + 0.564870i \(0.191074\pi\)
\(480\) 347.931 542.637i 0.724855 1.13049i
\(481\) −250.563 + 91.1973i −0.520920 + 0.189599i
\(482\) −129.650 + 235.510i −0.268984 + 0.488611i
\(483\) 551.324 217.152i 1.14146 0.449591i
\(484\) 510.923 20.8224i 1.05563 0.0430214i
\(485\) 99.8740 0.205926
\(486\) 379.512 303.590i 0.780889 0.624670i
\(487\) −172.305 −0.353808 −0.176904 0.984228i \(-0.556608\pi\)
−0.176904 + 0.984228i \(0.556608\pi\)
\(488\) −74.5924 + 251.830i −0.152853 + 0.516045i
\(489\) 534.117 210.375i 1.09226 0.430215i
\(490\) 157.459 286.024i 0.321344 0.583723i
\(491\) −395.827 + 144.069i −0.806166 + 0.293420i −0.712039 0.702140i \(-0.752228\pi\)
−0.0941269 + 0.995560i \(0.530006\pi\)
\(492\) −780.946 + 344.959i −1.58729 + 0.701137i
\(493\) 297.557 52.4673i 0.603563 0.106424i
\(494\) −71.9524 364.492i −0.145653 0.737838i
\(495\) −697.224 + 650.091i −1.40853 + 1.31331i
\(496\) 222.472 + 60.9969i 0.448532 + 0.122978i
\(497\) 61.7897 169.766i 0.124325 0.341581i
\(498\) −496.932 63.9661i −0.997855 0.128446i
\(499\) −385.364 + 459.259i −0.772273 + 0.920359i −0.998557 0.0537020i \(-0.982898\pi\)
0.226284 + 0.974061i \(0.427342\pi\)
\(500\) 28.1933 + 128.941i 0.0563866 + 0.257882i
\(501\) −50.5619 + 44.7306i −0.100922 + 0.0892826i
\(502\) −145.898 117.444i −0.290634 0.233952i
\(503\) −418.709 241.742i −0.832423 0.480600i 0.0222583 0.999752i \(-0.492914\pi\)
−0.854682 + 0.519152i \(0.826248\pi\)
\(504\) 551.727 275.046i 1.09470 0.545727i
\(505\) 155.796 + 269.847i 0.308507 + 0.534350i
\(506\) −719.147 111.756i −1.42124 0.220861i
\(507\) 267.653 164.006i 0.527915 0.323484i
\(508\) 248.761 + 79.2283i 0.489687 + 0.155961i
\(509\) 76.0045 431.043i 0.149321 0.846843i −0.814474 0.580200i \(-0.802974\pi\)
0.963795 0.266643i \(-0.0859145\pi\)
\(510\) 161.487 + 251.879i 0.316641 + 0.493880i
\(511\) −278.372 + 233.582i −0.544760 + 0.457108i
\(512\) 503.423 93.3217i 0.983249 0.182269i
\(513\) −623.247 + 48.9921i −1.21491 + 0.0955012i
\(514\) 72.5622 212.747i 0.141172 0.413904i
\(515\) −435.962 + 365.816i −0.846529 + 0.710322i
\(516\) −299.664 + 287.689i −0.580745 + 0.557537i
\(517\) −1114.84 196.576i −2.15636 0.380224i
\(518\) 11.5904 + 569.029i 0.0223753 + 1.09851i
\(519\) 18.8519 + 720.781i 0.0363235 + 1.38879i
\(520\) 296.656 + 312.603i 0.570492 + 0.601159i
\(521\) −564.224 + 325.755i −1.08296 + 0.625249i −0.931694 0.363244i \(-0.881669\pi\)
−0.151269 + 0.988493i \(0.548336\pi\)
\(522\) −179.188 710.057i −0.343273 1.36026i
\(523\) −313.666 181.095i −0.599743 0.346262i 0.169198 0.985582i \(-0.445882\pi\)
−0.768940 + 0.639320i \(0.779216\pi\)
\(524\) −359.762 568.346i −0.686569 1.08463i
\(525\) 163.726 489.274i 0.311859 0.931951i
\(526\) 69.2413 41.8793i 0.131637 0.0796185i
\(527\) −68.8261 + 82.0237i −0.130600 + 0.155643i
\(528\) −755.484 50.6328i −1.43084 0.0958955i
\(529\) 2.94922 + 1.07343i 0.00557508 + 0.00202916i
\(530\) 751.878 657.452i 1.41864 1.24048i
\(531\) −397.421 + 779.862i −0.748438 + 1.46867i
\(532\) −785.931 105.790i −1.47731 0.198854i
\(533\) −99.1153 562.111i −0.185957 1.05462i
\(534\) −558.150 174.217i −1.04522 0.326250i
\(535\) 148.840 54.1732i 0.278205 0.101258i
\(536\) −125.754 289.205i −0.234615 0.539561i
\(537\) −826.596 123.562i −1.53929 0.230097i
\(538\) 621.815 240.773i 1.15579 0.447533i
\(539\) −383.524 −0.711547
\(540\) 580.456 434.686i 1.07492 0.804974i
\(541\) 328.371i 0.606971i 0.952836 + 0.303485i \(0.0981503\pi\)
−0.952836 + 0.303485i \(0.901850\pi\)
\(542\) 580.811 224.896i 1.07161 0.414936i
\(543\) 69.6262 + 55.3867i 0.128225 + 0.102001i
\(544\) −58.1594 + 230.426i −0.106911 + 0.423576i
\(545\) −367.975 1011.00i −0.675184 1.85505i
\(546\) 90.3671 + 402.132i 0.165507 + 0.736506i
\(547\) −653.614 + 115.250i −1.19491 + 0.210694i −0.735496 0.677530i \(-0.763051\pi\)
−0.459411 + 0.888224i \(0.651939\pi\)
\(548\) 706.368 + 95.0809i 1.28899 + 0.173505i
\(549\) −177.836 + 235.966i −0.323928 + 0.429811i
\(550\) −477.039 + 417.129i −0.867343 + 0.758416i
\(551\) −322.190 + 885.210i −0.584737 + 1.60655i
\(552\) 534.768 + 143.302i 0.968782 + 0.259605i
\(553\) −300.290 251.973i −0.543019 0.455647i
\(554\) −43.4605 + 26.2863i −0.0784486 + 0.0474482i
\(555\) 133.455 + 656.057i 0.240460 + 1.18208i
\(556\) −684.172 + 433.080i −1.23052 + 0.778921i
\(557\) 114.717 198.696i 0.205955 0.356725i −0.744481 0.667643i \(-0.767303\pi\)
0.950437 + 0.310918i \(0.100636\pi\)
\(558\) 210.388 + 151.941i 0.377039 + 0.272297i
\(559\) −138.864 240.519i −0.248415 0.430267i
\(560\) 835.934 383.913i 1.49274 0.685558i
\(561\) 167.710 308.860i 0.298947 0.550552i
\(562\) 1.19354 + 58.5966i 0.00212374 + 0.104264i
\(563\) 100.148 567.968i 0.177883 1.00882i −0.756880 0.653554i \(-0.773277\pi\)
0.934763 0.355271i \(-0.115611\pi\)
\(564\) 827.101 + 239.794i 1.46649 + 0.425167i
\(565\) 368.480 + 439.137i 0.652176 + 0.777233i
\(566\) −197.975 + 580.447i −0.349779 + 1.02553i
\(567\) 689.755 72.4095i 1.21650 0.127706i
\(568\) 140.756 93.1668i 0.247810 0.164026i
\(569\) 679.955 + 810.339i 1.19500 + 1.42415i 0.879947 + 0.475073i \(0.157578\pi\)
0.315054 + 0.949074i \(0.397977\pi\)
\(570\) −931.826 + 43.3750i −1.63478 + 0.0760965i
\(571\) −642.796 113.342i −1.12574 0.198498i −0.420379 0.907348i \(-0.638103\pi\)
−0.705359 + 0.708851i \(0.749214\pi\)
\(572\) 153.625 482.351i 0.268574 0.843270i
\(573\) −415.689 + 765.547i −0.725461 + 1.33603i
\(574\) −1203.88 187.083i −2.09735 0.325929i
\(575\) 401.266 231.671i 0.697854 0.402906i
\(576\) 567.245 + 100.044i 0.984801 + 0.173687i
\(577\) 328.460 568.909i 0.569254 0.985977i −0.427386 0.904069i \(-0.640565\pi\)
0.996640 0.0819080i \(-0.0261014\pi\)
\(578\) 364.320 + 293.267i 0.630311 + 0.507383i
\(579\) 168.355 34.2468i 0.290769 0.0591482i
\(580\) −233.411 1067.49i −0.402432 1.84051i
\(581\) −547.719 459.591i −0.942718 0.791034i
\(582\) 34.3900 + 82.3529i 0.0590894 + 0.141500i
\(583\) −1102.46 401.263i −1.89102 0.688273i
\(584\) −338.892 + 20.7313i −0.580294 + 0.0354989i
\(585\) 189.410 + 446.298i 0.323777 + 0.762903i
\(586\) 108.406 + 549.155i 0.184993 + 0.937125i
\(587\) −35.1290 199.227i −0.0598450 0.339398i 0.940154 0.340750i \(-0.110681\pi\)
−0.999999 + 0.00135167i \(0.999570\pi\)
\(588\) 290.065 + 31.3473i 0.493307 + 0.0533117i
\(589\) −114.177 313.699i −0.193849 0.532597i
\(590\) −629.853 + 1144.13i −1.06755 + 1.93921i
\(591\) 37.3752 46.9841i 0.0632407 0.0794994i
\(592\) −307.534 + 433.824i −0.519483 + 0.732811i
\(593\) 484.111i 0.816376i 0.912898 + 0.408188i \(0.133839\pi\)
−0.912898 + 0.408188i \(0.866161\pi\)
\(594\) −776.122 351.060i −1.30660 0.591010i
\(595\) 426.974i 0.717603i
\(596\) 291.825 11.8931i 0.489639 0.0199549i
\(597\) −590.571 88.2802i −0.989231 0.147873i
\(598\) −178.504 + 324.254i −0.298502 + 0.542231i
\(599\) 363.928 + 999.885i 0.607560 + 1.66926i 0.735540 + 0.677481i \(0.236928\pi\)
−0.127980 + 0.991777i \(0.540849\pi\)
\(600\) 394.885 276.490i 0.658142 0.460817i
\(601\) −136.847 776.098i −0.227699 1.29134i −0.857458 0.514554i \(-0.827957\pi\)
0.629759 0.776791i \(-0.283154\pi\)
\(602\) −581.584 + 114.807i −0.966086 + 0.190710i
\(603\) −18.5459 354.297i −0.0307560 0.587558i
\(604\) 32.4874 13.3464i 0.0537870 0.0220967i
\(605\) 806.606 + 293.581i 1.33323 + 0.485257i
\(606\) −168.861 + 221.382i −0.278649 + 0.365317i
\(607\) −9.70394 8.14258i −0.0159867 0.0134145i 0.634759 0.772710i \(-0.281099\pi\)
−0.650746 + 0.759296i \(0.725544\pi\)
\(608\) −531.499 516.239i −0.874176 0.849078i
\(609\) 331.631 991.037i 0.544550 1.62732i
\(610\) −276.461 + 343.442i −0.453215 + 0.563019i
\(611\) −287.871 + 498.607i −0.471147 + 0.816051i
\(612\) −152.086 + 219.887i −0.248506 + 0.359293i
\(613\) 223.124 128.821i 0.363987 0.210148i −0.306841 0.951761i \(-0.599272\pi\)
0.670828 + 0.741613i \(0.265939\pi\)
\(614\) −683.074 106.150i −1.11250 0.172882i
\(615\) −1432.64 + 37.4705i −2.32950 + 0.0609276i
\(616\) −868.599 642.715i −1.41006 1.04337i
\(617\) 382.646 + 67.4708i 0.620172 + 0.109353i 0.474902 0.880039i \(-0.342484\pi\)
0.145270 + 0.989392i \(0.453595\pi\)
\(618\) −451.757 233.518i −0.730998 0.377860i
\(619\) −70.8929 84.4869i −0.114528 0.136489i 0.705734 0.708476i \(-0.250617\pi\)
−0.820263 + 0.571987i \(0.806173\pi\)
\(620\) 306.529 + 236.624i 0.494401 + 0.381651i
\(621\) 507.030 + 361.732i 0.816473 + 0.582499i
\(622\) 107.470 315.093i 0.172781 0.506581i
\(623\) −536.346 639.192i −0.860908 1.02599i
\(624\) −155.613 + 352.252i −0.249380 + 0.564507i
\(625\) −125.670 + 712.711i −0.201072 + 1.14034i
\(626\) 817.938 16.6604i 1.30661 0.0266140i
\(627\) 572.500 + 934.300i 0.913078 + 1.49011i
\(628\) −248.748 130.409i −0.396096 0.207657i
\(629\) −123.415 213.760i −0.196208 0.339841i
\(630\) 1032.13 75.1307i 1.63830 0.119255i
\(631\) −368.499 + 638.259i −0.583992 + 1.01150i 0.411008 + 0.911632i \(0.365177\pi\)
−0.995000 + 0.0998727i \(0.968156\pi\)
\(632\) −85.5052 356.137i −0.135293 0.563508i
\(633\) 461.957 408.679i 0.729790 0.645623i
\(634\) 91.2131 + 150.807i 0.143869 + 0.237866i
\(635\) 335.719 + 281.702i 0.528692 + 0.443625i
\(636\) 801.011 + 393.591i 1.25945 + 0.618854i
\(637\) −66.7133 + 183.293i −0.104730 + 0.287744i
\(638\) −966.253 + 844.905i −1.51450 + 1.32430i
\(639\) 185.032 42.7059i 0.289565 0.0668324i
\(640\) 841.208 + 176.225i 1.31439 + 0.275352i
\(641\) 591.672 104.328i 0.923046 0.162758i 0.308124 0.951346i \(-0.400299\pi\)
0.614922 + 0.788588i \(0.289188\pi\)
\(642\) 95.9201 + 104.075i 0.149408 + 0.162110i
\(643\) −292.697 804.178i −0.455205 1.25067i −0.929016 0.370040i \(-0.879344\pi\)
0.473811 0.880627i \(-0.342878\pi\)
\(644\) 532.067 + 584.042i 0.826191 + 0.906898i
\(645\) −648.811 + 255.550i −1.00591 + 0.396202i
\(646\) 320.715 124.184i 0.496463 0.192235i
\(647\) 329.693i 0.509572i −0.966997 0.254786i \(-0.917995\pi\)
0.966997 0.254786i \(-0.0820050\pi\)
\(648\) 558.299 + 328.948i 0.861572 + 0.507636i
\(649\) 1534.14 2.36385
\(650\) 116.374 + 300.544i 0.179036 + 0.462376i
\(651\) 135.721 + 344.579i 0.208481 + 0.529307i
\(652\) 515.461 + 565.815i 0.790585 + 0.867814i
\(653\) 53.4323 19.4478i 0.0818258 0.0297822i −0.300783 0.953693i \(-0.597248\pi\)
0.382609 + 0.923910i \(0.375026\pi\)
\(654\) 706.934 651.544i 1.08094 0.996244i
\(655\) −196.071 1111.97i −0.299345 1.69767i
\(656\) −800.231 809.572i −1.21986 1.23410i
\(657\) −365.269 111.699i −0.555965 0.170013i
\(658\) 808.940 + 925.123i 1.22939 + 1.40596i
\(659\) 58.5498 + 21.3104i 0.0888465 + 0.0323375i 0.386061 0.922473i \(-0.373835\pi\)
−0.297215 + 0.954811i \(0.596058\pi\)
\(660\) −1140.76 560.534i −1.72843 0.849294i
\(661\) 453.255 540.168i 0.685711 0.817199i −0.305119 0.952314i \(-0.598696\pi\)
0.990830 + 0.135116i \(0.0431406\pi\)
\(662\) 843.133 509.953i 1.27361 0.770322i
\(663\) −118.437 133.877i −0.178638 0.201926i
\(664\) −155.959 649.583i −0.234878 0.978287i
\(665\) −1152.85 665.601i −1.73361 1.00090i
\(666\) −495.010 + 335.945i −0.743258 + 0.504423i
\(667\) 812.774 469.255i 1.21855 0.703531i
\(668\) −79.7195 41.7938i −0.119341 0.0625655i
\(669\) −634.253 + 388.644i −0.948061 + 0.580932i
\(670\) −10.7806 529.273i −0.0160905 0.789959i
\(671\) 510.021 + 89.9304i 0.760090 + 0.134024i
\(672\) 604.402 + 557.089i 0.899408 + 0.829002i
\(673\) 707.566 593.718i 1.05136 0.882197i 0.0581251 0.998309i \(-0.481488\pi\)
0.993236 + 0.116113i \(0.0370433\pi\)
\(674\) 925.815 + 315.770i 1.37361 + 0.468502i
\(675\) 525.055 135.736i 0.777860 0.201091i
\(676\) 331.309 + 255.753i 0.490102 + 0.378333i
\(677\) 376.061 315.553i 0.555481 0.466104i −0.321311 0.946974i \(-0.604123\pi\)
0.876792 + 0.480870i \(0.159679\pi\)
\(678\) −235.218 + 455.046i −0.346929 + 0.671159i
\(679\) −22.1153 + 125.422i −0.0325704 + 0.184716i
\(680\) −237.292 + 320.689i −0.348958 + 0.471601i
\(681\) 19.0059 + 726.670i 0.0279089 + 1.06706i
\(682\) 69.8475 449.469i 0.102416 0.659045i
\(683\) −424.228 734.784i −0.621124 1.07582i −0.989277 0.146053i \(-0.953343\pi\)
0.368153 0.929765i \(-0.379990\pi\)
\(684\) −356.625 753.418i −0.521382 1.10149i
\(685\) 1036.15 + 598.219i 1.51262 + 0.873313i
\(686\) −329.318 265.092i −0.480055 0.386432i
\(687\) 584.872 + 195.716i 0.851342 + 0.284885i
\(688\) −500.617 236.988i −0.727640 0.344459i
\(689\) −383.542 + 457.088i −0.556665 + 0.663408i
\(690\) 738.937 + 563.631i 1.07092 + 0.816856i
\(691\) 213.637 586.964i 0.309171 0.849442i −0.683647 0.729813i \(-0.739607\pi\)
0.992819 0.119629i \(-0.0381705\pi\)
\(692\) −889.254 + 365.322i −1.28505 + 0.527922i
\(693\) −661.998 1019.53i −0.955264 1.47118i
\(694\) 79.9111 + 404.808i 0.115146 + 0.583297i
\(695\) −1338.59 + 236.029i −1.92603 + 0.339610i
\(696\) 799.850 560.037i 1.14921 0.804652i
\(697\) 496.503 180.712i 0.712343 0.259272i
\(698\) −698.100 384.309i −1.00014 0.550587i
\(699\) 79.7153 533.274i 0.114042 0.762910i
\(700\) 687.351 28.0126i 0.981931 0.0400180i
\(701\) 998.783 1.42480 0.712399 0.701775i \(-0.247609\pi\)
0.712399 + 0.701775i \(0.247609\pi\)
\(702\) −302.783 + 309.857i −0.431315 + 0.441392i
\(703\) 769.553 1.09467
\(704\) −295.192 965.452i −0.419307 1.37138i
\(705\) 1131.30 + 899.933i 1.60468 + 1.27650i
\(706\) −804.145 442.688i −1.13902 0.627037i
\(707\) −373.373 + 135.897i −0.528109 + 0.192216i
\(708\) −1160.29 125.393i −1.63883 0.177109i
\(709\) −51.0048 + 8.99352i −0.0719391 + 0.0126848i −0.209502 0.977808i \(-0.567184\pi\)
0.137563 + 0.990493i \(0.456073\pi\)
\(710\) 277.986 54.8758i 0.391530 0.0772898i
\(711\) 50.2404 408.965i 0.0706617 0.575197i
\(712\) −47.6028 778.155i −0.0668579 1.09291i
\(713\) −113.752 + 312.530i −0.159540 + 0.438332i
\(714\) −352.069 + 147.022i −0.493093 + 0.205913i
\(715\) 546.223 650.963i 0.763948 0.910438i
\(716\) −238.037 1088.65i −0.332454 1.52047i
\(717\) −28.6751 140.965i −0.0399932 0.196604i
\(718\) −478.576 + 594.524i −0.666540 + 0.828028i
\(719\) 233.060 + 134.557i 0.324144 + 0.187145i 0.653238 0.757152i \(-0.273410\pi\)
−0.329094 + 0.944297i \(0.606743\pi\)
\(720\) 816.960 + 517.180i 1.13467 + 0.718306i
\(721\) −362.857 628.486i −0.503269 0.871687i
\(722\) −53.7839 + 346.100i −0.0744929 + 0.479362i
\(723\) −354.384 192.429i −0.490158 0.266154i
\(724\) −35.9994 + 113.031i −0.0497230 + 0.156120i
\(725\) 141.901 804.762i 0.195726 1.11002i
\(726\) 35.6649 + 766.191i 0.0491253 + 1.05536i
\(727\) 11.7221 9.83600i 0.0161239 0.0135296i −0.634690 0.772767i \(-0.718872\pi\)
0.650814 + 0.759237i \(0.274428\pi\)
\(728\) −458.257 + 303.321i −0.629473 + 0.416650i
\(729\) 458.669 + 566.625i 0.629175 + 0.777263i
\(730\) −539.430 183.985i −0.738946 0.252034i
\(731\) 196.942 165.254i 0.269415 0.226066i
\(732\) −378.386 109.702i −0.516920 0.149866i
\(733\) 340.424 + 60.0259i 0.464426 + 0.0818908i 0.400965 0.916094i \(-0.368675\pi\)
0.0634611 + 0.997984i \(0.479786\pi\)
\(734\) 1440.33 29.3376i 1.96230 0.0399695i
\(735\) 430.395 + 233.703i 0.585572 + 0.317963i
\(736\) 75.0388 + 734.356i 0.101955 + 0.997767i
\(737\) −538.527 + 310.919i −0.730701 + 0.421871i
\(738\) −524.204 1168.41i −0.710304 1.58321i
\(739\) −147.912 85.3969i −0.200151 0.115557i 0.396575 0.918002i \(-0.370199\pi\)
−0.596726 + 0.802445i \(0.703532\pi\)
\(740\) −754.248 + 477.438i −1.01925 + 0.645187i
\(741\) 546.105 111.089i 0.736983 0.149917i
\(742\) 659.141 + 1089.79i 0.888330 + 1.46872i
\(743\) −274.368 + 326.979i −0.369270 + 0.440079i −0.918397 0.395660i \(-0.870516\pi\)
0.549127 + 0.835739i \(0.314960\pi\)
\(744\) −89.5640 + 334.231i −0.120382 + 0.449235i
\(745\) 460.710 + 167.685i 0.618403 + 0.225080i
\(746\) 518.444 + 592.905i 0.694965 + 0.794779i
\(747\) 91.6370 745.940i 0.122673 0.998581i
\(748\) 464.418 + 62.5132i 0.620880 + 0.0835738i
\(749\) 35.0730 + 198.909i 0.0468265 + 0.265566i
\(750\) −193.164 + 43.4077i −0.257552 + 0.0578769i
\(751\) −117.359 + 42.7151i −0.156270 + 0.0568777i −0.418971 0.908000i \(-0.637609\pi\)
0.262701 + 0.964877i \(0.415387\pi\)
\(752\) 93.4344 + 1144.41i 0.124248 + 1.52182i
\(753\) 174.898 219.862i 0.232268 0.291982i
\(754\) 235.718 + 608.760i 0.312623 + 0.807374i
\(755\) 58.9575 0.0780894
\(756\) 417.348 + 825.192i 0.552048 + 1.09152i
\(757\) 580.749i 0.767171i 0.923505 + 0.383586i \(0.125311\pi\)
−0.923505 + 0.383586i \(0.874689\pi\)
\(758\) −253.547 654.806i −0.334495 0.863860i
\(759\) 161.392 1079.67i 0.212638 1.42249i
\(760\) −495.969 1140.62i −0.652591 1.50081i
\(761\) −384.425 1056.20i −0.505158 1.38791i −0.886179 0.463343i \(-0.846650\pi\)
0.381021 0.924566i \(-0.375572\pi\)
\(762\) −116.683 + 373.823i −0.153127 + 0.490581i
\(763\) 1351.10 238.236i 1.77078 0.312236i
\(764\) −1151.12 154.947i −1.50670 0.202810i
\(765\) −376.411 + 244.411i −0.492041 + 0.319492i
\(766\) 997.924 + 1141.25i 1.30277 + 1.48988i
\(767\) 266.861 733.195i 0.347928 0.955926i
\(768\) 144.347 + 754.313i 0.187952 + 0.982178i
\(769\) 357.797 + 300.227i 0.465275 + 0.390412i 0.845068 0.534660i \(-0.179560\pi\)
−0.379792 + 0.925072i \(0.624005\pi\)
\(770\) −938.717 1552.03i −1.21911 2.01562i
\(771\) 319.744 + 106.996i 0.414714 + 0.138776i
\(772\) 122.519 + 193.553i 0.158703 + 0.250716i
\(773\) −496.649 + 860.222i −0.642496 + 1.11284i 0.342378 + 0.939562i \(0.388768\pi\)
−0.984874 + 0.173273i \(0.944566\pi\)
\(774\) −434.126 446.994i −0.560886 0.577511i
\(775\) 144.795 + 250.792i 0.186832 + 0.323603i
\(776\) −86.3138 + 81.9106i −0.111229 + 0.105555i
\(777\) −853.429 + 22.3213i −1.09836 + 0.0287275i
\(778\) 1029.01 20.9597i 1.32264 0.0269405i
\(779\) −286.055 + 1622.30i −0.367207 + 2.08254i
\(780\) −466.323 + 447.688i −0.597850 + 0.573959i
\(781\) −213.943 254.968i −0.273935 0.326463i
\(782\) −324.293 110.607i −0.414697 0.141442i
\(783\) 1063.51 274.937i 1.35825 0.351133i
\(784\) 98.4999 + 376.328i 0.125638 + 0.480010i
\(785\) −303.052 361.163i −0.386053 0.460080i
\(786\) 849.384 544.564i 1.08064 0.692830i
\(787\) 1174.22 + 207.046i 1.49201 + 0.263082i 0.859368 0.511358i \(-0.170857\pi\)
0.632647 + 0.774441i \(0.281969\pi\)
\(788\) 76.2740 + 24.2926i 0.0967944 + 0.0308282i
\(789\) 63.4186 + 103.497i 0.0803784 + 0.131175i
\(790\) 94.4096 607.526i 0.119506 0.769020i
\(791\) −633.062 + 365.499i −0.800332 + 0.462072i
\(792\) 69.3946 1133.65i 0.0876195 1.43137i
\(793\) 131.697 228.105i 0.166074 0.287648i
\(794\) 816.095 1013.82i 1.02783 1.27685i
\(795\) 992.684 + 1122.10i 1.24866 + 1.41144i
\(796\) −170.068 777.801i −0.213654 0.977137i
\(797\) 570.978 + 479.108i 0.716409 + 0.601139i 0.926389 0.376567i \(-0.122895\pi\)
−0.209980 + 0.977706i \(0.567340\pi\)
\(798\) 151.866 1179.79i 0.190308 1.47844i
\(799\) −500.818 182.283i −0.626806 0.228139i
\(800\) 531.820 + 360.957i 0.664774 + 0.451197i
\(801\) 256.480 838.722i 0.320200 1.04709i
\(802\) −962.094 + 189.922i −1.19962 + 0.236810i
\(803\) 116.254 + 659.311i 0.144775 + 0.821060i
\(804\) 432.709 191.136i 0.538195 0.237731i
\(805\) 453.601 + 1246.26i 0.563479 + 1.54815i
\(806\) −202.660 111.566i −0.251439 0.138419i
\(807\) 366.547 + 930.618i 0.454209 + 1.15318i
\(808\) −355.955 105.434i −0.440539 0.130488i
\(809\) 1534.63i 1.89695i 0.316850 + 0.948476i \(0.397375\pi\)
−0.316850 + 0.948476i \(0.602625\pi\)
\(810\) 657.053 + 866.899i 0.811176 + 1.07025i
\(811\) 29.9304i 0.0369055i −0.999830 0.0184528i \(-0.994126\pi\)
0.999830 0.0184528i \(-0.00587403\pi\)
\(812\) 1392.25 56.7403i 1.71459 0.0698772i
\(813\) 342.376 + 869.251i 0.421126 + 1.06919i
\(814\) 918.566 + 505.677i 1.12846 + 0.621225i
\(815\) 439.444 + 1207.36i 0.539195 + 1.48143i
\(816\) −346.137 85.2388i −0.424188 0.104459i
\(817\) 139.187 + 789.367i 0.170363 + 0.966177i
\(818\) 4.57450 + 23.1732i 0.00559230 + 0.0283291i
\(819\) −602.404 + 139.037i −0.735536 + 0.169764i
\(820\) −726.123 1767.50i −0.885515 2.15549i
\(821\) −318.883 116.064i −0.388408 0.141369i 0.140432 0.990090i \(-0.455151\pi\)
−0.528840 + 0.848721i \(0.677373\pi\)
\(822\) −136.492 + 1060.36i −0.166048 + 1.28998i
\(823\) 690.346 + 579.269i 0.838816 + 0.703850i 0.957297 0.289106i \(-0.0933580\pi\)
−0.118481 + 0.992956i \(0.537802\pi\)
\(824\) 76.7504 673.698i 0.0931437 0.817594i
\(825\) −629.821 711.928i −0.763419 0.862943i
\(826\) −1297.33 1044.32i −1.57062 1.26431i
\(827\) 226.647 392.564i 0.274059 0.474684i −0.695838 0.718198i \(-0.744967\pi\)
0.969897 + 0.243515i \(0.0783003\pi\)
\(828\) −210.310 + 803.381i −0.253998 + 0.970267i
\(829\) 393.501 227.188i 0.474670 0.274051i −0.243523 0.969895i \(-0.578303\pi\)
0.718193 + 0.695844i \(0.244970\pi\)
\(830\) 172.200 1108.11i 0.207470 1.33507i
\(831\) −39.8058 64.9616i −0.0479010 0.0781729i
\(832\) −512.755 26.8607i −0.616293 0.0322845i
\(833\) −177.819 31.3543i −0.213468 0.0376402i
\(834\) −655.544 1022.48i −0.786024 1.22600i
\(835\) −97.1229 115.747i −0.116315 0.138619i
\(836\) −892.761 + 1156.51i −1.06790 + 1.38338i
\(837\) −226.083 + 316.895i −0.270112 + 0.378608i
\(838\) −359.994 122.784i −0.429587 0.146520i
\(839\) −347.757 414.440i −0.414490 0.493969i 0.517892 0.855446i \(-0.326717\pi\)
−0.932381 + 0.361477i \(0.882273\pi\)
\(840\) 583.111 + 1250.55i 0.694179 + 1.48875i
\(841\) 141.386 801.842i 0.168117 0.953439i
\(842\) 13.2095 + 648.518i 0.0156882 + 0.770211i
\(843\) −87.8831 + 2.29857i −0.104250 + 0.00272665i
\(844\) 728.354 + 381.847i 0.862979 + 0.452426i
\(845\) 351.290 + 608.453i 0.415728 + 0.720062i
\(846\) −352.511 + 1242.71i −0.416680 + 1.46892i
\(847\) −547.288 + 947.930i −0.646148 + 1.11916i
\(848\) −110.591 + 1184.83i −0.130414 + 1.39721i
\(849\) −872.373 291.922i −1.02753 0.343842i
\(850\) −255.278 + 154.400i −0.300327 + 0.181648i
\(851\) −587.315 492.816i −0.690147 0.579102i
\(852\) 140.969 + 210.323i 0.165456 + 0.246858i
\(853\) −67.8779 + 186.493i −0.0795755 + 0.218632i −0.973100 0.230382i \(-0.926002\pi\)
0.893525 + 0.449014i \(0.148225\pi\)
\(854\) −370.078 423.230i −0.433346 0.495585i
\(855\) −73.1444 1397.34i −0.0855490 1.63432i
\(856\) −84.2017 + 168.887i −0.0983664 + 0.197298i
\(857\) 919.735 162.174i 1.07320 0.189235i 0.390995 0.920393i \(-0.372131\pi\)
0.682208 + 0.731158i \(0.261020\pi\)
\(858\) 724.846 + 226.249i 0.844809 + 0.263693i
\(859\) −450.052 1236.51i −0.523925 1.43947i −0.866116 0.499843i \(-0.833391\pi\)
0.342191 0.939630i \(-0.388831\pi\)
\(860\) −626.149 687.315i −0.728080 0.799203i
\(861\) 270.177 1807.41i 0.313795 2.09920i
\(862\) −80.3115 207.411i −0.0931688 0.240616i
\(863\) 224.521i 0.260163i −0.991503 0.130082i \(-0.958476\pi\)
0.991503 0.130082i \(-0.0415239\pi\)
\(864\) −145.143 + 851.722i −0.167989 + 0.985789i
\(865\) −1613.80 −1.86567
\(866\) −798.302 + 309.110i −0.921826 + 0.356940i
\(867\) −436.733 + 549.014i −0.503729 + 0.633234i
\(868\) −365.028 + 332.543i −0.420539 + 0.383114i
\(869\) −678.640 + 247.005i −0.780944 + 0.284240i
\(870\) 1599.19 359.370i 1.83815 0.413069i
\(871\) 54.9181 + 311.456i 0.0630517 + 0.357584i
\(872\) 1147.18 + 571.945i 1.31557 + 0.655901i
\(873\) −123.229 + 52.2985i −0.141156 + 0.0599067i
\(874\) 804.180 703.186i 0.920114 0.804560i
\(875\) −265.490 96.6304i −0.303417 0.110435i
\(876\) −34.0362 508.149i −0.0388541 0.580079i
\(877\) −482.550 + 575.081i −0.550228 + 0.655737i −0.967448 0.253069i \(-0.918560\pi\)
0.417220 + 0.908806i \(0.363004\pi\)
\(878\) −461.122 762.398i −0.525196 0.868335i
\(879\) −822.778 + 167.370i −0.936039 + 0.190409i
\(880\) 157.498 1687.38i 0.178975 1.91748i
\(881\) −120.900 69.8014i −0.137230 0.0792297i 0.429813 0.902918i \(-0.358579\pi\)
−0.567043 + 0.823688i \(0.691913\pi\)
\(882\) −44.5040 + 435.362i −0.0504581 + 0.493608i
\(883\) 378.614 218.593i 0.428782 0.247557i −0.270046 0.962847i \(-0.587039\pi\)
0.698827 + 0.715290i \(0.253706\pi\)
\(884\) 110.661 211.080i 0.125182 0.238779i
\(885\) −1721.63 934.840i −1.94535 1.05632i
\(886\) −942.860 + 19.2049i −1.06418 + 0.0216760i
\(887\) −830.031 146.357i −0.935773 0.165002i −0.315089 0.949062i \(-0.602034\pi\)
−0.620685 + 0.784060i \(0.713145\pi\)
\(888\) −653.393 457.530i −0.735803 0.515237i
\(889\) −428.101 + 359.219i −0.481553 + 0.404071i
\(890\) 422.462 1238.63i 0.474677 1.39172i
\(891\) 519.848 1167.21i 0.583444 1.31000i
\(892\) −785.098 606.054i −0.880155 0.679433i
\(893\) 1272.89 1068.08i 1.42541 1.19606i
\(894\) 20.3708 + 437.626i 0.0227861 + 0.489515i
\(895\) 324.834 1842.22i 0.362943 2.05835i
\(896\) −407.574 + 1017.37i −0.454882 + 1.13546i
\(897\) −487.922 264.940i −0.543948 0.295362i
\(898\) −396.660 61.6411i −0.441715 0.0686426i
\(899\) 293.286 + 507.986i 0.326236 + 0.565056i
\(900\) 418.154 + 589.920i 0.464615 + 0.655466i
\(901\) −478.347 276.173i −0.530906 0.306519i
\(902\) −1407.46 + 1748.46i −1.56038 + 1.93843i
\(903\) −177.253 871.365i −0.196294 0.964967i
\(904\) −678.603 77.3093i −0.750667 0.0855191i
\(905\) −127.999 + 152.543i −0.141435 + 0.168555i
\(906\) 20.3011 + 48.6144i 0.0224074 + 0.0536583i
\(907\) −210.425 + 578.137i −0.232001 + 0.637416i −0.999995 0.00303969i \(-0.999032\pi\)
0.767995 + 0.640456i \(0.221255\pi\)
\(908\) −896.519 + 368.307i −0.987356 + 0.405624i
\(909\) −333.532 251.367i −0.366922 0.276531i
\(910\) −905.032 + 178.658i −0.994541 + 0.196327i
\(911\) 63.3790 11.1754i 0.0695708 0.0122672i −0.138754 0.990327i \(-0.544310\pi\)
0.208325 + 0.978060i \(0.433199\pi\)
\(912\) 769.735 801.713i 0.844008 0.879071i
\(913\) −1237.82 + 450.529i −1.35577 + 0.493460i
\(914\) 397.108 721.349i 0.434473 0.789222i
\(915\) −517.552 411.706i −0.565631 0.449952i
\(916\) 33.4859 + 821.651i 0.0365567 + 0.896999i
\(917\) 1439.84 1.57016
\(918\) −331.145 226.218i −0.360724 0.246424i
\(919\) 471.159 0.512687 0.256344 0.966586i \(-0.417482\pi\)
0.256344 + 0.966586i \(0.417482\pi\)
\(920\) −351.923 + 1188.12i −0.382525 + 1.29144i
\(921\) 153.297 1025.52i 0.166446 1.11348i
\(922\) −88.1864 + 160.191i −0.0956468 + 0.173743i
\(923\) −159.069 + 57.8964i −0.172339 + 0.0627263i
\(924\) 956.521 1308.45i 1.03520 1.41607i
\(925\) −657.424 + 115.922i −0.710729 + 0.125321i
\(926\) −69.9678 354.438i −0.0755592 0.382763i
\(927\) 346.352 679.649i 0.373626 0.733171i
\(928\) 1077.21 + 731.128i 1.16079 + 0.787854i
\(929\) 394.793 1084.68i 0.424965 1.16758i −0.523866 0.851801i \(-0.675511\pi\)
0.948832 0.315782i \(-0.102267\pi\)
\(930\) −352.271 + 461.838i −0.378786 + 0.496600i
\(931\) 361.857 431.244i 0.388675 0.463205i
\(932\) 702.339 153.568i 0.753582 0.164773i
\(933\) 473.564 + 158.469i 0.507571 + 0.169849i
\(934\) −192.000 154.554i −0.205567 0.165476i
\(935\) 681.239 + 393.313i 0.728597 + 0.420656i
\(936\) −529.720 230.361i −0.565940 0.246112i
\(937\) 417.800 + 723.650i 0.445891 + 0.772306i 0.998114 0.0613908i \(-0.0195536\pi\)
−0.552223 + 0.833697i \(0.686220\pi\)
\(938\) 667.049 + 103.659i 0.711140 + 0.110511i
\(939\) 32.0852 + 1226.74i 0.0341696 + 1.30643i
\(940\) −584.926 + 1836.55i −0.622261 + 1.95378i
\(941\) −101.798 + 577.324i −0.108181 + 0.613522i 0.881722 + 0.471770i \(0.156385\pi\)
−0.989902 + 0.141752i \(0.954726\pi\)
\(942\) 193.452 374.247i 0.205363 0.397290i
\(943\) 1257.22 1054.93i 1.33321 1.11870i
\(944\) −394.011 1505.36i −0.417385 1.59466i
\(945\) 121.647 + 1547.52i 0.128727 + 1.63759i
\(946\) −352.559 + 1033.68i −0.372684 + 1.09268i
\(947\) −743.785 + 624.110i −0.785412 + 0.659039i −0.944605 0.328208i \(-0.893555\pi\)
0.159193 + 0.987247i \(0.449111\pi\)
\(948\) 533.455 131.345i 0.562716 0.138549i
\(949\) 335.319 + 59.1259i 0.353340 + 0.0623033i
\(950\) −18.9421 929.957i −0.0199390 0.978902i
\(951\) −225.416 + 138.125i −0.237030 + 0.145242i
\(952\) −350.178 369.002i −0.367834 0.387607i
\(953\) −902.774 + 521.217i −0.947297 + 0.546922i −0.892240 0.451561i \(-0.850867\pi\)
−0.0550568 + 0.998483i \(0.517534\pi\)
\(954\) −583.428 + 1204.91i −0.611560 + 1.26301i
\(955\) −1688.54 974.876i −1.76810 1.02081i
\(956\) 162.063 102.586i 0.169522 0.107307i
\(957\) −1275.72 1442.03i −1.33304 1.50682i
\(958\) −1171.48 + 708.547i −1.22284 + 0.739610i
\(959\) −980.681 + 1168.73i −1.02261 + 1.21870i
\(960\) −257.036 + 1263.32i −0.267746 + 1.31596i
\(961\) 707.712 + 257.586i 0.736433 + 0.268040i
\(962\) 401.455 351.038i 0.417313 0.364904i
\(963\) −155.277 + 144.780i −0.161243 + 0.150343i
\(964\) 71.7274 532.872i 0.0744060 0.552772i
\(965\) 66.7729 + 378.688i 0.0691947 + 0.392423i
\(966\) −871.434 + 803.154i −0.902105 + 0.831422i
\(967\) 1126.08 409.861i 1.16451 0.423848i 0.313805 0.949488i \(-0.398396\pi\)
0.850707 + 0.525640i \(0.176174\pi\)
\(968\) −937.867 + 407.809i −0.968871 + 0.421290i
\(969\) 189.055 + 479.987i 0.195103 + 0.495343i
\(970\) −186.272 + 72.1261i −0.192033 + 0.0743569i
\(971\) −16.5428 −0.0170368 −0.00851841 0.999964i \(-0.502712\pi\)
−0.00851841 + 0.999964i \(0.502712\pi\)
\(972\) −488.571 + 840.287i −0.502645 + 0.864493i
\(973\) 1733.27i 1.78136i
\(974\) 321.360 124.434i 0.329938 0.127755i
\(975\) −449.800 + 177.165i −0.461333 + 0.181707i
\(976\) −42.7448 523.548i −0.0437959 0.536422i
\(977\) −470.579 1292.91i −0.481657 1.32334i −0.908072 0.418815i \(-0.862446\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(978\) −844.236 + 778.087i −0.863227 + 0.795590i
\(979\) −1513.90 + 266.941i −1.54637 + 0.272667i
\(980\) −87.1120 + 647.166i −0.0888898 + 0.660374i
\(981\) 983.431 + 1054.73i 1.00248 + 1.07516i
\(982\) 634.201 554.554i 0.645826 0.564719i
\(983\) −222.764 + 612.038i −0.226616 + 0.622623i −0.999935 0.0113944i \(-0.996373\pi\)
0.773319 + 0.634017i \(0.218595\pi\)
\(984\) 1207.40 1207.35i 1.22703 1.22698i
\(985\) 102.937 + 86.3741i 0.104504 + 0.0876895i
\(986\) −517.072 + 312.742i −0.524414 + 0.317182i
\(987\) −1380.64 + 1221.41i −1.39883 + 1.23750i
\(988\) 397.422 + 627.839i 0.402249 + 0.635465i
\(989\) 399.279 691.571i 0.403719 0.699263i
\(990\) 830.891 1715.98i 0.839284 1.73331i
\(991\) −345.174 597.859i −0.348309 0.603289i 0.637640 0.770334i \(-0.279911\pi\)
−0.985949 + 0.167045i \(0.946577\pi\)
\(992\) −458.974 + 46.8995i −0.462676 + 0.0472777i
\(993\) 772.231 + 1260.25i 0.777675 + 1.26914i
\(994\) 7.35815 + 361.247i 0.00740257 + 0.363427i
\(995\) 232.081 1316.20i 0.233247 1.32281i
\(996\) 973.005 239.569i 0.976913 0.240531i
\(997\) −105.594 125.842i −0.105912 0.126221i 0.710484 0.703713i \(-0.248476\pi\)
−0.816396 + 0.577492i \(0.804031\pi\)
\(998\) 387.066 1134.85i 0.387842 1.13712i
\(999\) −508.204 739.589i −0.508712 0.740329i
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.5.9 420
8.5 even 2 inner 216.3.x.a.5.48 yes 420
27.11 odd 18 inner 216.3.x.a.173.48 yes 420
216.173 odd 18 inner 216.3.x.a.173.9 yes 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.3.x.a.5.9 420 1.1 even 1 trivial
216.3.x.a.5.48 yes 420 8.5 even 2 inner
216.3.x.a.173.9 yes 420 216.173 odd 18 inner
216.3.x.a.173.48 yes 420 27.11 odd 18 inner