Properties

Label 315.2.u.a.59.17
Level $315$
Weight $2$
Character 315.59
Analytic conductor $2.515$
Analytic rank $0$
Dimension $88$
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] = [315,2,Mod(59,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.u (of order \(6\), degree \(2\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.17
Character \(\chi\) \(=\) 315.59
Dual form 315.2.u.a.299.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.413705 + 0.716558i) q^{2} +(1.72082 + 0.196965i) q^{3} +(0.657696 + 1.13916i) q^{4} +(-2.23428 + 0.0894268i) q^{5} +(-0.853047 + 1.15158i) q^{6} +(-1.49622 + 2.18205i) q^{7} -2.74319 q^{8} +(2.92241 + 0.677881i) q^{9} +O(q^{10})\) \(q+(-0.413705 + 0.716558i) q^{2} +(1.72082 + 0.196965i) q^{3} +(0.657696 + 1.13916i) q^{4} +(-2.23428 + 0.0894268i) q^{5} +(-0.853047 + 1.15158i) q^{6} +(-1.49622 + 2.18205i) q^{7} -2.74319 q^{8} +(2.92241 + 0.677881i) q^{9} +(0.860253 - 1.63799i) q^{10} -0.680855i q^{11} +(0.907398 + 2.08983i) q^{12} +(-2.83242 + 4.90589i) q^{13} +(-0.944570 - 1.97485i) q^{14} +(-3.86240 - 0.286188i) q^{15} +(-0.180521 + 0.312672i) q^{16} +(-0.121625 - 0.0702202i) q^{17} +(-1.69476 + 1.81363i) q^{18} +(5.71783 - 3.30119i) q^{19} +(-1.57135 - 2.48639i) q^{20} +(-3.00450 + 3.46020i) q^{21} +(0.487872 + 0.281673i) q^{22} +3.85953 q^{23} +(-4.72052 - 0.540312i) q^{24} +(4.98401 - 0.399609i) q^{25} +(-2.34357 - 4.05919i) q^{26} +(4.89541 + 1.74212i) q^{27} +(-3.46977 - 0.269314i) q^{28} +(5.41301 - 3.12520i) q^{29} +(1.80296 - 2.64923i) q^{30} +(-3.62325 + 2.09188i) q^{31} +(-2.89255 - 5.01005i) q^{32} +(0.134105 - 1.17163i) q^{33} +(0.100634 - 0.0581009i) q^{34} +(3.14784 - 5.00910i) q^{35} +(1.14984 + 3.77494i) q^{36} +(3.51452 - 2.02911i) q^{37} +5.46287i q^{38} +(-5.84036 + 7.88425i) q^{39} +(6.12905 - 0.245315i) q^{40} +(-3.69597 + 6.40161i) q^{41} +(-1.23645 - 3.58440i) q^{42} +(-1.46959 + 0.848469i) q^{43} +(0.775605 - 0.447796i) q^{44} +(-6.59010 - 1.25323i) q^{45} +(-1.59671 + 2.76558i) q^{46} +(-0.604618 - 0.349076i) q^{47} +(-0.372229 + 0.502494i) q^{48} +(-2.52266 - 6.52964i) q^{49} +(-1.77557 + 3.73665i) q^{50} +(-0.195463 - 0.144792i) q^{51} -7.45148 q^{52} +(-2.01127 + 3.48363i) q^{53} +(-3.27359 + 2.78712i) q^{54} +(0.0608867 + 1.52122i) q^{55} +(4.10441 - 5.98577i) q^{56} +(10.4895 - 4.55452i) q^{57} +5.17165i q^{58} +(0.288174 + 0.499132i) q^{59} +(-2.21427 - 4.58812i) q^{60} +(7.48252 + 4.32004i) q^{61} -3.46169i q^{62} +(-5.85173 + 5.36258i) q^{63} +4.06457 q^{64} +(5.88969 - 11.2144i) q^{65} +(0.784058 + 0.580801i) q^{66} +(8.42002 - 4.86130i) q^{67} -0.184734i q^{68} +(6.64154 + 0.760193i) q^{69} +(2.28704 + 4.32790i) q^{70} -13.5808i q^{71} +(-8.01672 - 1.85956i) q^{72} +(5.74989 - 9.95910i) q^{73} +3.35781i q^{74} +(8.65526 + 0.294022i) q^{75} +(7.52118 + 4.34236i) q^{76} +(1.48566 + 1.01871i) q^{77} +(-3.23334 - 7.44671i) q^{78} +(-2.05544 + 3.56013i) q^{79} +(0.375374 - 0.714740i) q^{80} +(8.08095 + 3.96209i) q^{81} +(-3.05808 - 5.29676i) q^{82} +(-6.39254 + 3.69073i) q^{83} +(-5.91778 - 1.14686i) q^{84} +(0.278024 + 0.146015i) q^{85} -1.40406i q^{86} +(9.93034 - 4.31172i) q^{87} +1.86771i q^{88} +(4.72665 + 8.18679i) q^{89} +(3.62437 - 4.20372i) q^{90} +(-6.46697 - 13.5208i) q^{91} +(2.53840 + 4.39664i) q^{92} +(-6.64697 + 2.88609i) q^{93} +(0.500267 - 0.288829i) q^{94} +(-12.4800 + 7.88710i) q^{95} +(-3.99075 - 9.19110i) q^{96} +(-6.39767 - 11.0811i) q^{97} +(5.72250 + 0.893715i) q^{98} +(0.461539 - 1.98974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9} - 6 q^{10} - 12 q^{14} - 6 q^{15} - 26 q^{16} - 12 q^{19} + 6 q^{20} - 12 q^{21} - 42 q^{24} - 2 q^{25} + 12 q^{26} + 6 q^{29} - 18 q^{30} - 6 q^{31} + 12 q^{34} - 36 q^{36} - 6 q^{41} + 84 q^{44} - 12 q^{45} - 18 q^{46} + 10 q^{49} + 30 q^{50} - 6 q^{51} - 48 q^{54} - 90 q^{56} - 6 q^{59} + 54 q^{60} + 12 q^{61} - 8 q^{64} + 54 q^{65} + 78 q^{66} - 60 q^{69} - 30 q^{70} + 12 q^{75} + 48 q^{76} + 8 q^{79} + 69 q^{80} + 42 q^{81} + 120 q^{84} - 7 q^{85} - 72 q^{89} - 33 q^{90} + 20 q^{91} - 6 q^{94} - 93 q^{95} - 12 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.413705 + 0.716558i −0.292534 + 0.506683i −0.974408 0.224786i \(-0.927832\pi\)
0.681874 + 0.731469i \(0.261165\pi\)
\(3\) 1.72082 + 0.196965i 0.993513 + 0.113718i
\(4\) 0.657696 + 1.13916i 0.328848 + 0.569582i
\(5\) −2.23428 + 0.0894268i −0.999200 + 0.0399929i
\(6\) −0.853047 + 1.15158i −0.348255 + 0.470130i
\(7\) −1.49622 + 2.18205i −0.565518 + 0.824736i
\(8\) −2.74319 −0.969864
\(9\) 2.92241 + 0.677881i 0.974137 + 0.225960i
\(10\) 0.860253 1.63799i 0.272036 0.517977i
\(11\) 0.680855i 0.205286i −0.994718 0.102643i \(-0.967270\pi\)
0.994718 0.102643i \(-0.0327299\pi\)
\(12\) 0.907398 + 2.08983i 0.261943 + 0.603283i
\(13\) −2.83242 + 4.90589i −0.785571 + 1.36065i 0.143086 + 0.989710i \(0.454298\pi\)
−0.928657 + 0.370939i \(0.879036\pi\)
\(14\) −0.944570 1.97485i −0.252447 0.527801i
\(15\) −3.86240 0.286188i −0.997266 0.0738934i
\(16\) −0.180521 + 0.312672i −0.0451303 + 0.0781680i
\(17\) −0.121625 0.0702202i −0.0294984 0.0170309i 0.485178 0.874415i \(-0.338755\pi\)
−0.514677 + 0.857384i \(0.672088\pi\)
\(18\) −1.69476 + 1.81363i −0.399458 + 0.427478i
\(19\) 5.71783 3.30119i 1.31176 0.757344i 0.329372 0.944200i \(-0.393163\pi\)
0.982387 + 0.186856i \(0.0598297\pi\)
\(20\) −1.57135 2.48639i −0.351364 0.555974i
\(21\) −3.00450 + 3.46020i −0.655636 + 0.755077i
\(22\) 0.487872 + 0.281673i 0.104015 + 0.0600529i
\(23\) 3.85953 0.804768 0.402384 0.915471i \(-0.368182\pi\)
0.402384 + 0.915471i \(0.368182\pi\)
\(24\) −4.72052 0.540312i −0.963572 0.110291i
\(25\) 4.98401 0.399609i 0.996801 0.0799217i
\(26\) −2.34357 4.05919i −0.459612 0.796072i
\(27\) 4.89541 + 1.74212i 0.942122 + 0.335271i
\(28\) −3.46977 0.269314i −0.655724 0.0508956i
\(29\) 5.41301 3.12520i 1.00517 0.580335i 0.0953962 0.995439i \(-0.469588\pi\)
0.909774 + 0.415104i \(0.136255\pi\)
\(30\) 1.80296 2.64923i 0.329174 0.483682i
\(31\) −3.62325 + 2.09188i −0.650755 + 0.375713i −0.788745 0.614720i \(-0.789269\pi\)
0.137991 + 0.990434i \(0.455936\pi\)
\(32\) −2.89255 5.01005i −0.511336 0.885660i
\(33\) 0.134105 1.17163i 0.0233446 0.203954i
\(34\) 0.100634 0.0581009i 0.0172585 0.00996423i
\(35\) 3.14784 5.00910i 0.532082 0.846693i
\(36\) 1.14984 + 3.77494i 0.191640 + 0.629157i
\(37\) 3.51452 2.02911i 0.577783 0.333583i −0.182469 0.983212i \(-0.558409\pi\)
0.760252 + 0.649628i \(0.225076\pi\)
\(38\) 5.46287i 0.886195i
\(39\) −5.84036 + 7.88425i −0.935206 + 1.26249i
\(40\) 6.12905 0.245315i 0.969088 0.0387876i
\(41\) −3.69597 + 6.40161i −0.577214 + 0.999763i 0.418584 + 0.908178i \(0.362527\pi\)
−0.995797 + 0.0915850i \(0.970807\pi\)
\(42\) −1.23645 3.58440i −0.190789 0.553085i
\(43\) −1.46959 + 0.848469i −0.224111 + 0.129390i −0.607852 0.794050i \(-0.707969\pi\)
0.383742 + 0.923441i \(0.374635\pi\)
\(44\) 0.775605 0.447796i 0.116927 0.0675078i
\(45\) −6.59010 1.25323i −0.982394 0.186821i
\(46\) −1.59671 + 2.76558i −0.235422 + 0.407763i
\(47\) −0.604618 0.349076i −0.0881926 0.0509180i 0.455255 0.890361i \(-0.349548\pi\)
−0.543448 + 0.839443i \(0.682881\pi\)
\(48\) −0.372229 + 0.502494i −0.0537266 + 0.0725288i
\(49\) −2.52266 6.52964i −0.360380 0.932806i
\(50\) −1.77557 + 3.73665i −0.251103 + 0.528442i
\(51\) −0.195463 0.144792i −0.0273703 0.0202749i
\(52\) −7.45148 −1.03333
\(53\) −2.01127 + 3.48363i −0.276270 + 0.478513i −0.970455 0.241283i \(-0.922432\pi\)
0.694185 + 0.719797i \(0.255765\pi\)
\(54\) −3.27359 + 2.78712i −0.445479 + 0.379279i
\(55\) 0.0608867 + 1.52122i 0.00820996 + 0.205121i
\(56\) 4.10441 5.98577i 0.548475 0.799882i
\(57\) 10.4895 4.55452i 1.38937 0.603261i
\(58\) 5.17165i 0.679070i
\(59\) 0.288174 + 0.499132i 0.0375170 + 0.0649814i 0.884174 0.467157i \(-0.154722\pi\)
−0.846657 + 0.532139i \(0.821388\pi\)
\(60\) −2.21427 4.58812i −0.285861 0.592324i
\(61\) 7.48252 + 4.32004i 0.958039 + 0.553124i 0.895569 0.444923i \(-0.146769\pi\)
0.0624701 + 0.998047i \(0.480102\pi\)
\(62\) 3.46169i 0.439635i
\(63\) −5.85173 + 5.36258i −0.737249 + 0.675621i
\(64\) 4.06457 0.508072
\(65\) 5.88969 11.2144i 0.730527 1.39098i
\(66\) 0.784058 + 0.580801i 0.0965109 + 0.0714917i
\(67\) 8.42002 4.86130i 1.02867 0.593902i 0.112066 0.993701i \(-0.464253\pi\)
0.916603 + 0.399799i \(0.130920\pi\)
\(68\) 0.184734i 0.0224023i
\(69\) 6.64154 + 0.760193i 0.799548 + 0.0915165i
\(70\) 2.28704 + 4.32790i 0.273353 + 0.517283i
\(71\) 13.5808i 1.61175i −0.592087 0.805874i \(-0.701696\pi\)
0.592087 0.805874i \(-0.298304\pi\)
\(72\) −8.01672 1.85956i −0.944780 0.219151i
\(73\) 5.74989 9.95910i 0.672974 1.16562i −0.304083 0.952645i \(-0.598350\pi\)
0.977057 0.212979i \(-0.0683166\pi\)
\(74\) 3.35781i 0.390337i
\(75\) 8.65526 + 0.294022i 0.999424 + 0.0339508i
\(76\) 7.52118 + 4.34236i 0.862739 + 0.498103i
\(77\) 1.48566 + 1.01871i 0.169306 + 0.116093i
\(78\) −3.23334 7.44671i −0.366103 0.843174i
\(79\) −2.05544 + 3.56013i −0.231256 + 0.400546i −0.958178 0.286173i \(-0.907617\pi\)
0.726922 + 0.686720i \(0.240950\pi\)
\(80\) 0.375374 0.714740i 0.0419680 0.0799103i
\(81\) 8.08095 + 3.96209i 0.897884 + 0.440232i
\(82\) −3.05808 5.29676i −0.337709 0.584929i
\(83\) −6.39254 + 3.69073i −0.701672 + 0.405111i −0.807970 0.589224i \(-0.799434\pi\)
0.106298 + 0.994334i \(0.466100\pi\)
\(84\) −5.91778 1.14686i −0.645683 0.125133i
\(85\) 0.278024 + 0.146015i 0.0301559 + 0.0158376i
\(86\) 1.40406i 0.151404i
\(87\) 9.93034 4.31172i 1.06464 0.462265i
\(88\) 1.86771i 0.199099i
\(89\) 4.72665 + 8.18679i 0.501024 + 0.867798i 0.999999 + 0.00118245i \(0.000376385\pi\)
−0.498976 + 0.866616i \(0.666290\pi\)
\(90\) 3.62437 4.20372i 0.382042 0.443111i
\(91\) −6.46697 13.5208i −0.677922 1.41736i
\(92\) 2.53840 + 4.39664i 0.264647 + 0.458381i
\(93\) −6.64697 + 2.88609i −0.689259 + 0.299274i
\(94\) 0.500267 0.288829i 0.0515986 0.0297905i
\(95\) −12.4800 + 7.88710i −1.28042 + 0.809200i
\(96\) −3.99075 9.19110i −0.407304 0.938063i
\(97\) −6.39767 11.0811i −0.649584 1.12511i −0.983222 0.182412i \(-0.941610\pi\)
0.333638 0.942701i \(-0.391724\pi\)
\(98\) 5.72250 + 0.893715i 0.578060 + 0.0902789i
\(99\) 0.461539 1.98974i 0.0463864 0.199976i
\(100\) 3.73318 + 5.41478i 0.373318 + 0.541478i
\(101\) −15.6725 −1.55947 −0.779736 0.626109i \(-0.784647\pi\)
−0.779736 + 0.626109i \(0.784647\pi\)
\(102\) 0.184616 0.0801596i 0.0182797 0.00793698i
\(103\) 10.3306 1.01790 0.508951 0.860795i \(-0.330033\pi\)
0.508951 + 0.860795i \(0.330033\pi\)
\(104\) 7.76986 13.4578i 0.761897 1.31965i
\(105\) 6.40347 7.99973i 0.624914 0.780693i
\(106\) −1.66415 2.88239i −0.161636 0.279963i
\(107\) 4.89261 + 8.47425i 0.472987 + 0.819237i 0.999522 0.0309163i \(-0.00984253\pi\)
−0.526535 + 0.850153i \(0.676509\pi\)
\(108\) 1.23513 + 6.72245i 0.118851 + 0.646869i
\(109\) 2.89816 5.01976i 0.277593 0.480806i −0.693193 0.720752i \(-0.743797\pi\)
0.970786 + 0.239947i \(0.0771299\pi\)
\(110\) −1.11523 0.585708i −0.106333 0.0558450i
\(111\) 6.44750 2.79948i 0.611969 0.265715i
\(112\) −0.412165 0.861731i −0.0389460 0.0814260i
\(113\) 0.865706 1.49945i 0.0814388 0.141056i −0.822429 0.568867i \(-0.807382\pi\)
0.903868 + 0.427811i \(0.140715\pi\)
\(114\) −1.07600 + 9.40059i −0.100776 + 0.880446i
\(115\) −8.62327 + 0.345145i −0.804124 + 0.0321850i
\(116\) 7.12023 + 4.11087i 0.661097 + 0.381684i
\(117\) −11.6031 + 12.4170i −1.07271 + 1.14795i
\(118\) −0.476876 −0.0439000
\(119\) 0.335201 0.160327i 0.0307279 0.0146971i
\(120\) 10.5953 + 0.785068i 0.967212 + 0.0716666i
\(121\) 10.5364 0.957858
\(122\) −6.19112 + 3.57444i −0.560517 + 0.323615i
\(123\) −7.62097 + 10.2880i −0.687160 + 0.927638i
\(124\) −4.76599 2.75165i −0.427999 0.247105i
\(125\) −11.0999 + 1.33854i −0.992807 + 0.119723i
\(126\) −1.42171 6.41163i −0.126656 0.571194i
\(127\) 0.129214i 0.0114659i 0.999984 + 0.00573294i \(0.00182486\pi\)
−0.999984 + 0.00573294i \(0.998175\pi\)
\(128\) 4.10357 7.10760i 0.362708 0.628229i
\(129\) −2.69601 + 1.17060i −0.237371 + 0.103066i
\(130\) 5.59919 + 8.85977i 0.491082 + 0.777054i
\(131\) 4.64296 0.405657 0.202829 0.979214i \(-0.434987\pi\)
0.202829 + 0.979214i \(0.434987\pi\)
\(132\) 1.42287 0.617807i 0.123845 0.0537732i
\(133\) −1.35177 + 17.4159i −0.117214 + 1.51015i
\(134\) 8.04457i 0.694945i
\(135\) −11.0935 3.45460i −0.954776 0.297325i
\(136\) 0.333640 + 0.192627i 0.0286094 + 0.0165177i
\(137\) 2.23918 0.191306 0.0956529 0.995415i \(-0.469506\pi\)
0.0956529 + 0.995415i \(0.469506\pi\)
\(138\) −3.29236 + 4.44456i −0.280265 + 0.378346i
\(139\) −12.9285 7.46426i −1.09658 0.633110i −0.161259 0.986912i \(-0.551555\pi\)
−0.935320 + 0.353802i \(0.884889\pi\)
\(140\) 7.77651 + 0.291433i 0.657235 + 0.0246306i
\(141\) −0.971680 0.719784i −0.0818302 0.0606168i
\(142\) 9.73145 + 5.61846i 0.816645 + 0.471490i
\(143\) 3.34020 + 1.92847i 0.279322 + 0.161266i
\(144\) −0.739511 + 0.791383i −0.0616259 + 0.0659486i
\(145\) −11.8147 + 7.46664i −0.981157 + 0.620071i
\(146\) 4.75752 + 8.24026i 0.393735 + 0.681969i
\(147\) −3.05491 11.7332i −0.251965 0.967736i
\(148\) 4.62297 + 2.66907i 0.380006 + 0.219396i
\(149\) 6.18686i 0.506848i 0.967355 + 0.253424i \(0.0815567\pi\)
−0.967355 + 0.253424i \(0.918443\pi\)
\(150\) −3.79141 + 6.08036i −0.309567 + 0.496459i
\(151\) −17.4515 −1.42018 −0.710091 0.704110i \(-0.751346\pi\)
−0.710091 + 0.704110i \(0.751346\pi\)
\(152\) −15.6851 + 9.05578i −1.27223 + 0.734521i
\(153\) −0.307837 0.287659i −0.0248872 0.0232559i
\(154\) −1.34459 + 0.643115i −0.108350 + 0.0518237i
\(155\) 7.90828 4.99787i 0.635208 0.401438i
\(156\) −12.8226 1.46768i −1.02663 0.117509i
\(157\) −2.51702 4.35961i −0.200880 0.347935i 0.747932 0.663775i \(-0.231047\pi\)
−0.948812 + 0.315840i \(0.897714\pi\)
\(158\) −1.70070 2.94569i −0.135300 0.234347i
\(159\) −4.14719 + 5.59853i −0.328893 + 0.443993i
\(160\) 6.91081 + 10.9352i 0.546347 + 0.864502i
\(161\) −5.77471 + 8.42168i −0.455111 + 0.663721i
\(162\) −6.18220 + 4.15134i −0.485720 + 0.326160i
\(163\) −6.96029 + 4.01853i −0.545172 + 0.314755i −0.747172 0.664630i \(-0.768589\pi\)
0.202000 + 0.979385i \(0.435256\pi\)
\(164\) −9.72330 −0.759262
\(165\) −0.194853 + 2.62973i −0.0151693 + 0.204724i
\(166\) 6.10750i 0.474034i
\(167\) 3.08628 + 1.78186i 0.238823 + 0.137885i 0.614636 0.788811i \(-0.289303\pi\)
−0.375812 + 0.926696i \(0.622636\pi\)
\(168\) 8.24192 9.49197i 0.635878 0.732322i
\(169\) −9.54519 16.5327i −0.734245 1.27175i
\(170\) −0.219648 + 0.138813i −0.0168462 + 0.0106465i
\(171\) 18.9476 5.77142i 1.44896 0.441351i
\(172\) −1.93309 1.11607i −0.147397 0.0850995i
\(173\) −20.9958 12.1219i −1.59628 0.921614i −0.992195 0.124696i \(-0.960204\pi\)
−0.604087 0.796918i \(-0.706462\pi\)
\(174\) −1.01863 + 8.89945i −0.0772224 + 0.674665i
\(175\) −6.58520 + 11.4732i −0.497794 + 0.867295i
\(176\) 0.212884 + 0.122909i 0.0160468 + 0.00926460i
\(177\) 0.397582 + 0.915674i 0.0298841 + 0.0688262i
\(178\) −7.82175 −0.586265
\(179\) 17.9602 + 10.3693i 1.34241 + 0.775038i 0.987160 0.159735i \(-0.0510639\pi\)
0.355246 + 0.934773i \(0.384397\pi\)
\(180\) −2.90665 8.33145i −0.216649 0.620989i
\(181\) 19.1810i 1.42571i 0.701309 + 0.712857i \(0.252599\pi\)
−0.701309 + 0.712857i \(0.747401\pi\)
\(182\) 12.3638 + 0.959647i 0.916468 + 0.0711338i
\(183\) 12.0251 + 8.90778i 0.888924 + 0.658482i
\(184\) −10.5874 −0.780516
\(185\) −7.67096 + 4.84788i −0.563980 + 0.356424i
\(186\) 0.681832 5.95693i 0.0499944 0.436783i
\(187\) −0.0478098 + 0.0828090i −0.00349620 + 0.00605559i
\(188\) 0.918345i 0.0669772i
\(189\) −11.1260 + 8.07541i −0.809297 + 0.587400i
\(190\) −0.488527 12.2056i −0.0354415 0.885486i
\(191\) 11.9445 + 6.89617i 0.864274 + 0.498989i 0.865441 0.501010i \(-0.167038\pi\)
−0.00116695 + 0.999999i \(0.500371\pi\)
\(192\) 6.99438 + 0.800579i 0.504776 + 0.0577768i
\(193\) −3.65940 + 2.11276i −0.263410 + 0.152080i −0.625889 0.779912i \(-0.715264\pi\)
0.362479 + 0.931992i \(0.381930\pi\)
\(194\) 10.5870 0.760101
\(195\) 12.3439 18.1379i 0.883967 1.29888i
\(196\) 5.77919 7.16824i 0.412799 0.512017i
\(197\) 4.24294 0.302297 0.151148 0.988511i \(-0.451703\pi\)
0.151148 + 0.988511i \(0.451703\pi\)
\(198\) 1.23482 + 1.15388i 0.0877550 + 0.0820030i
\(199\) −9.03350 5.21549i −0.640368 0.369716i 0.144388 0.989521i \(-0.453879\pi\)
−0.784756 + 0.619805i \(0.787212\pi\)
\(200\) −13.6721 + 1.09620i −0.966761 + 0.0775132i
\(201\) 15.4468 6.70695i 1.08953 0.473072i
\(202\) 6.48379 11.2303i 0.456198 0.790158i
\(203\) −1.27971 + 16.4874i −0.0898180 + 1.15719i
\(204\) 0.0363862 0.317894i 0.00254754 0.0222570i
\(205\) 7.68535 14.6335i 0.536768 1.02205i
\(206\) −4.27381 + 7.40246i −0.297771 + 0.515754i
\(207\) 11.2791 + 2.61630i 0.783954 + 0.181846i
\(208\) −1.02262 1.77124i −0.0709062 0.122813i
\(209\) −2.24763 3.89301i −0.155472 0.269285i
\(210\) 3.08312 + 7.89798i 0.212756 + 0.545013i
\(211\) −9.41906 + 16.3143i −0.648435 + 1.12312i 0.335062 + 0.942196i \(0.391243\pi\)
−0.983497 + 0.180926i \(0.942090\pi\)
\(212\) −5.29123 −0.363403
\(213\) 2.67495 23.3701i 0.183284 1.60129i
\(214\) −8.09639 −0.553458
\(215\) 3.20760 2.02714i 0.218757 0.138250i
\(216\) −13.4290 4.77897i −0.913730 0.325167i
\(217\) 0.856586 11.0360i 0.0581489 0.749174i
\(218\) 2.39797 + 4.15340i 0.162411 + 0.281304i
\(219\) 11.8561 16.0052i 0.801160 1.08153i
\(220\) −1.69287 + 1.06986i −0.114134 + 0.0721300i
\(221\) 0.688986 0.397786i 0.0463462 0.0267580i
\(222\) −0.661371 + 5.77817i −0.0443883 + 0.387805i
\(223\) −7.12080 12.3336i −0.476844 0.825918i 0.522804 0.852453i \(-0.324886\pi\)
−0.999648 + 0.0265350i \(0.991553\pi\)
\(224\) 15.2601 + 1.18445i 1.01961 + 0.0791391i
\(225\) 14.8362 + 2.21074i 0.989080 + 0.147383i
\(226\) 0.716294 + 1.24066i 0.0476472 + 0.0825273i
\(227\) 24.0451i 1.59593i 0.602706 + 0.797963i \(0.294089\pi\)
−0.602706 + 0.797963i \(0.705911\pi\)
\(228\) 12.0873 + 8.95381i 0.800499 + 0.592980i
\(229\) 21.9495i 1.45046i −0.688504 0.725232i \(-0.741732\pi\)
0.688504 0.725232i \(-0.258268\pi\)
\(230\) 3.32018 6.32187i 0.218926 0.416851i
\(231\) 2.35589 + 2.04563i 0.155006 + 0.134593i
\(232\) −14.8489 + 8.57302i −0.974878 + 0.562846i
\(233\) −14.8663 25.7491i −0.973922 1.68688i −0.683447 0.730000i \(-0.739520\pi\)
−0.290476 0.956882i \(-0.593813\pi\)
\(234\) −4.09723 13.4513i −0.267844 0.879337i
\(235\) 1.38210 + 0.725865i 0.0901584 + 0.0473502i
\(236\) −0.379062 + 0.656554i −0.0246748 + 0.0427380i
\(237\) −4.23826 + 5.72148i −0.275305 + 0.371650i
\(238\) −0.0237912 + 0.306519i −0.00154215 + 0.0198687i
\(239\) 10.9885 + 6.34422i 0.710788 + 0.410373i 0.811353 0.584557i \(-0.198732\pi\)
−0.100565 + 0.994930i \(0.532065\pi\)
\(240\) 0.786727 1.15600i 0.0507830 0.0746194i
\(241\) 5.73629i 0.369507i 0.982785 + 0.184753i \(0.0591486\pi\)
−0.982785 + 0.184753i \(0.940851\pi\)
\(242\) −4.35898 + 7.54997i −0.280206 + 0.485330i
\(243\) 13.1254 + 8.40969i 0.841997 + 0.539482i
\(244\) 11.3651i 0.727575i
\(245\) 6.22024 + 14.3634i 0.397397 + 0.917647i
\(246\) −4.21912 9.71707i −0.269001 0.619538i
\(247\) 37.4014i 2.37979i
\(248\) 9.93926 5.73843i 0.631144 0.364391i
\(249\) −11.7273 + 5.09196i −0.743189 + 0.322690i
\(250\) 3.63295 8.50750i 0.229768 0.538062i
\(251\) −7.11362 −0.449008 −0.224504 0.974473i \(-0.572076\pi\)
−0.224504 + 0.974473i \(0.572076\pi\)
\(252\) −9.95751 3.13913i −0.627264 0.197747i
\(253\) 2.62778i 0.165207i
\(254\) −0.0925892 0.0534564i −0.00580956 0.00335415i
\(255\) 0.449668 + 0.306026i 0.0281593 + 0.0191641i
\(256\) 7.45991 + 12.9209i 0.466244 + 0.807559i
\(257\) 28.6312i 1.78597i −0.450090 0.892983i \(-0.648608\pi\)
0.450090 0.892983i \(-0.351392\pi\)
\(258\) 0.276551 2.41613i 0.0172173 0.150422i
\(259\) −0.830880 + 10.7048i −0.0516284 + 0.665166i
\(260\) 16.6487 0.666362i 1.03251 0.0413260i
\(261\) 17.9375 5.46374i 1.11031 0.338197i
\(262\) −1.92082 + 3.32695i −0.118668 + 0.205540i
\(263\) 26.9796 1.66363 0.831815 0.555052i \(-0.187302\pi\)
0.831815 + 0.555052i \(0.187302\pi\)
\(264\) −0.367875 + 3.21399i −0.0226411 + 0.197808i
\(265\) 4.18222 7.96326i 0.256912 0.489179i
\(266\) −11.9202 8.17365i −0.730877 0.501159i
\(267\) 6.52117 + 15.0189i 0.399089 + 0.919144i
\(268\) 11.0756 + 6.39452i 0.676551 + 0.390607i
\(269\) 4.40270 7.62569i 0.268437 0.464947i −0.700021 0.714122i \(-0.746826\pi\)
0.968458 + 0.249175i \(0.0801595\pi\)
\(270\) 7.06486 6.51995i 0.429954 0.396792i
\(271\) 9.56861 5.52444i 0.581252 0.335586i −0.180379 0.983597i \(-0.557732\pi\)
0.761631 + 0.648011i \(0.224399\pi\)
\(272\) 0.0439118 0.0253525i 0.00266254 0.00153722i
\(273\) −8.46534 24.5405i −0.512346 1.48526i
\(274\) −0.926358 + 1.60450i −0.0559634 + 0.0969314i
\(275\) −0.272076 3.39339i −0.0164068 0.204629i
\(276\) 3.50213 + 8.06578i 0.210804 + 0.485503i
\(277\) 3.70887i 0.222845i 0.993773 + 0.111422i \(0.0355406\pi\)
−0.993773 + 0.111422i \(0.964459\pi\)
\(278\) 10.6972 6.17600i 0.641573 0.370412i
\(279\) −12.0067 + 3.65721i −0.718820 + 0.218951i
\(280\) −8.63511 + 13.7409i −0.516047 + 0.821177i
\(281\) −21.0669 + 12.1630i −1.25675 + 0.725583i −0.972441 0.233150i \(-0.925097\pi\)
−0.284306 + 0.958733i \(0.591763\pi\)
\(282\) 0.917756 0.398487i 0.0546516 0.0237295i
\(283\) −4.66170 8.07431i −0.277110 0.479968i 0.693556 0.720403i \(-0.256043\pi\)
−0.970665 + 0.240435i \(0.922710\pi\)
\(284\) 15.4708 8.93206i 0.918022 0.530020i
\(285\) −23.0293 + 11.1141i −1.36414 + 0.658344i
\(286\) −2.76372 + 1.59563i −0.163422 + 0.0943518i
\(287\) −8.43863 17.6430i −0.498116 1.04143i
\(288\) −5.05701 16.6022i −0.297987 0.978296i
\(289\) −8.49014 14.7054i −0.499420 0.865021i
\(290\) −0.462483 11.5549i −0.0271580 0.678527i
\(291\) −8.82661 20.3286i −0.517425 1.19168i
\(292\) 15.1267 0.885224
\(293\) −7.80154 4.50422i −0.455771 0.263139i 0.254494 0.967074i \(-0.418091\pi\)
−0.710264 + 0.703935i \(0.751425\pi\)
\(294\) 9.67134 + 2.66505i 0.564044 + 0.155429i
\(295\) −0.688496 1.08943i −0.0400858 0.0634290i
\(296\) −9.64099 + 5.56623i −0.560371 + 0.323530i
\(297\) 1.18613 3.33306i 0.0688263 0.193404i
\(298\) −4.43325 2.55954i −0.256811 0.148270i
\(299\) −10.9318 + 18.9345i −0.632203 + 1.09501i
\(300\) 5.35759 + 10.0531i 0.309321 + 0.580418i
\(301\) 0.347432 4.47621i 0.0200256 0.258005i
\(302\) 7.21977 12.5050i 0.415451 0.719582i
\(303\) −26.9695 3.08693i −1.54936 0.177340i
\(304\) 2.38374i 0.136717i
\(305\) −17.1044 8.98303i −0.979394 0.514367i
\(306\) 0.333479 0.101577i 0.0190637 0.00580677i
\(307\) 5.84917 0.333830 0.166915 0.985971i \(-0.446619\pi\)
0.166915 + 0.985971i \(0.446619\pi\)
\(308\) −0.183364 + 2.36241i −0.0104481 + 0.134611i
\(309\) 17.7770 + 2.03476i 1.01130 + 0.115754i
\(310\) 0.309568 + 7.73439i 0.0175823 + 0.439284i
\(311\) 8.10248 + 14.0339i 0.459449 + 0.795790i 0.998932 0.0462072i \(-0.0147135\pi\)
−0.539483 + 0.841997i \(0.681380\pi\)
\(312\) 16.0212 21.6280i 0.907022 1.22444i
\(313\) 13.8932 24.0637i 0.785290 1.36016i −0.143536 0.989645i \(-0.545847\pi\)
0.928826 0.370517i \(-0.120819\pi\)
\(314\) 4.16522 0.235057
\(315\) 12.5948 12.5048i 0.709639 0.704565i
\(316\) −5.40743 −0.304192
\(317\) 8.97622 15.5473i 0.504155 0.873222i −0.495834 0.868418i \(-0.665137\pi\)
0.999988 0.00480434i \(-0.00152927\pi\)
\(318\) −2.29596 5.28784i −0.128751 0.296527i
\(319\) −2.12781 3.68547i −0.119134 0.206347i
\(320\) −9.08139 + 0.363482i −0.507665 + 0.0203192i
\(321\) 6.75015 + 15.5463i 0.376757 + 0.867710i
\(322\) −3.64560 7.62201i −0.203161 0.424758i
\(323\) −0.927241 −0.0515930
\(324\) 0.801344 + 11.8114i 0.0445191 + 0.656188i
\(325\) −12.1564 + 25.5829i −0.674313 + 1.41908i
\(326\) 6.64994i 0.368306i
\(327\) 5.97591 8.06724i 0.330469 0.446119i
\(328\) 10.1387 17.5608i 0.559819 0.969634i
\(329\) 1.66634 0.797010i 0.0918684 0.0439406i
\(330\) −1.80374 1.22756i −0.0992929 0.0675748i
\(331\) −10.7927 + 18.6936i −0.593223 + 1.02749i 0.400572 + 0.916265i \(0.368811\pi\)
−0.993795 + 0.111227i \(0.964522\pi\)
\(332\) −8.40870 4.85476i −0.461487 0.266440i
\(333\) 11.6464 3.54746i 0.638216 0.194400i
\(334\) −2.55362 + 1.47433i −0.139728 + 0.0806718i
\(335\) −18.3779 + 11.6145i −1.00409 + 0.634566i
\(336\) −0.539530 1.56406i −0.0294337 0.0853266i
\(337\) −16.6595 9.61838i −0.907502 0.523946i −0.0278751 0.999611i \(-0.508874\pi\)
−0.879626 + 0.475665i \(0.842207\pi\)
\(338\) 15.7956 0.859166
\(339\) 1.78506 2.40976i 0.0969511 0.130880i
\(340\) 0.0165202 + 0.412748i 0.000895933 + 0.0223844i
\(341\) 1.42427 + 2.46691i 0.0771285 + 0.133591i
\(342\) −3.70318 + 15.9648i −0.200245 + 0.863275i
\(343\) 18.0224 + 4.26522i 0.973120 + 0.230300i
\(344\) 4.03137 2.32751i 0.217357 0.125491i
\(345\) −14.9070 1.10455i −0.802568 0.0594671i
\(346\) 17.3722 10.0298i 0.933933 0.539206i
\(347\) −8.39107 14.5338i −0.450456 0.780213i 0.547958 0.836506i \(-0.315405\pi\)
−0.998414 + 0.0562929i \(0.982072\pi\)
\(348\) 11.4429 + 8.47648i 0.613404 + 0.454387i
\(349\) 14.1376 8.16236i 0.756769 0.436921i −0.0713653 0.997450i \(-0.522736\pi\)
0.828135 + 0.560529i \(0.189402\pi\)
\(350\) −5.49691 9.46521i −0.293822 0.505937i
\(351\) −22.4125 + 19.0819i −1.19629 + 1.01852i
\(352\) −3.41112 + 1.96941i −0.181813 + 0.104970i
\(353\) 29.9814i 1.59575i 0.602822 + 0.797875i \(0.294043\pi\)
−0.602822 + 0.797875i \(0.705957\pi\)
\(354\) −0.820615 0.0939279i −0.0436152 0.00499221i
\(355\) 1.21449 + 30.3434i 0.0644584 + 1.61046i
\(356\) −6.21740 + 10.7688i −0.329521 + 0.570748i
\(357\) 0.608398 0.209869i 0.0321999 0.0111075i
\(358\) −14.8604 + 8.57967i −0.785398 + 0.453450i
\(359\) 0.535110 0.308946i 0.0282420 0.0163055i −0.485813 0.874063i \(-0.661476\pi\)
0.514055 + 0.857757i \(0.328143\pi\)
\(360\) 18.0779 + 3.43786i 0.952788 + 0.181191i
\(361\) 12.2957 21.2968i 0.647141 1.12088i
\(362\) −13.7443 7.93529i −0.722385 0.417069i
\(363\) 18.1313 + 2.07531i 0.951644 + 0.108926i
\(364\) 11.1491 16.2595i 0.584369 0.852229i
\(365\) −11.9562 + 22.7656i −0.625819 + 1.19161i
\(366\) −11.3578 + 4.93152i −0.593682 + 0.257775i
\(367\) 5.22261 0.272618 0.136309 0.990666i \(-0.456476\pi\)
0.136309 + 0.990666i \(0.456476\pi\)
\(368\) −0.696728 + 1.20677i −0.0363194 + 0.0629071i
\(369\) −15.1407 + 16.2027i −0.788192 + 0.843478i
\(370\) −0.300278 7.50228i −0.0156107 0.390025i
\(371\) −4.59214 9.60097i −0.238412 0.498458i
\(372\) −7.65942 5.67381i −0.397122 0.294173i
\(373\) 4.17547i 0.216197i −0.994140 0.108099i \(-0.965524\pi\)
0.994140 0.108099i \(-0.0344763\pi\)
\(374\) −0.0395583 0.0685170i −0.00204551 0.00354293i
\(375\) −19.3646 + 0.117084i −0.999982 + 0.00604618i
\(376\) 1.65858 + 0.957582i 0.0855348 + 0.0493835i
\(377\) 35.4075i 1.82358i
\(378\) −1.18363 11.3133i −0.0608791 0.581891i
\(379\) 13.3904 0.687821 0.343910 0.939002i \(-0.388248\pi\)
0.343910 + 0.939002i \(0.388248\pi\)
\(380\) −17.1927 9.02944i −0.881969 0.463201i
\(381\) −0.0254506 + 0.222353i −0.00130387 + 0.0113915i
\(382\) −9.88301 + 5.70596i −0.505659 + 0.291942i
\(383\) 9.43018i 0.481860i 0.970543 + 0.240930i \(0.0774524\pi\)
−0.970543 + 0.240930i \(0.922548\pi\)
\(384\) 8.46144 11.4226i 0.431796 0.582907i
\(385\) −3.41047 2.14322i −0.173814 0.109229i
\(386\) 3.49623i 0.177954i
\(387\) −4.86991 + 1.48337i −0.247551 + 0.0754037i
\(388\) 8.41544 14.5760i 0.427229 0.739983i
\(389\) 12.5755i 0.637604i −0.947821 0.318802i \(-0.896720\pi\)
0.947821 0.318802i \(-0.103280\pi\)
\(390\) 7.89011 + 16.3489i 0.399531 + 0.827858i
\(391\) −0.469416 0.271017i −0.0237394 0.0137059i
\(392\) 6.92012 + 17.9120i 0.349519 + 0.904695i
\(393\) 7.98967 + 0.914501i 0.403026 + 0.0461305i
\(394\) −1.75532 + 3.04031i −0.0884319 + 0.153169i
\(395\) 4.27407 8.13815i 0.215052 0.409475i
\(396\) 2.57019 0.782875i 0.129157 0.0393409i
\(397\) 5.95907 + 10.3214i 0.299077 + 0.518017i 0.975925 0.218106i \(-0.0699879\pi\)
−0.676848 + 0.736123i \(0.736655\pi\)
\(398\) 7.47441 4.31535i 0.374658 0.216309i
\(399\) −5.75647 + 29.7032i −0.288184 + 1.48702i
\(400\) −0.774772 + 1.63050i −0.0387386 + 0.0815248i
\(401\) 22.6413i 1.13065i −0.824868 0.565325i \(-0.808751\pi\)
0.824868 0.565325i \(-0.191249\pi\)
\(402\) −1.58450 + 13.8432i −0.0790277 + 0.690437i
\(403\) 23.7004i 1.18060i
\(404\) −10.3077 17.8535i −0.512829 0.888246i
\(405\) −18.4094 8.12976i −0.914772 0.403971i
\(406\) −11.2848 7.73791i −0.560054 0.384026i
\(407\) −1.38153 2.39288i −0.0684798 0.118611i
\(408\) 0.536193 + 0.397192i 0.0265455 + 0.0196639i
\(409\) 8.44454 4.87546i 0.417556 0.241076i −0.276475 0.961021i \(-0.589166\pi\)
0.694031 + 0.719945i \(0.255833\pi\)
\(410\) 7.30628 + 11.5610i 0.360832 + 0.570955i
\(411\) 3.85321 + 0.441039i 0.190065 + 0.0217549i
\(412\) 6.79438 + 11.7682i 0.334735 + 0.579778i
\(413\) −1.52030 0.118002i −0.0748091 0.00580648i
\(414\) −6.54097 + 6.99978i −0.321471 + 0.344020i
\(415\) 13.9527 8.81779i 0.684909 0.432849i
\(416\) 32.7717 1.60676
\(417\) −20.7773 15.3911i −1.01747 0.753704i
\(418\) 3.71943 0.181923
\(419\) 2.51167 4.35034i 0.122703 0.212528i −0.798130 0.602486i \(-0.794177\pi\)
0.920833 + 0.389958i \(0.127510\pi\)
\(420\) 13.3245 + 2.03320i 0.650171 + 0.0992101i
\(421\) −9.59165 16.6132i −0.467468 0.809679i 0.531841 0.846844i \(-0.321500\pi\)
−0.999309 + 0.0371654i \(0.988167\pi\)
\(422\) −7.79343 13.4986i −0.379378 0.657102i
\(423\) −1.53031 1.43000i −0.0744062 0.0695291i
\(424\) 5.51731 9.55626i 0.267944 0.464093i
\(425\) −0.634240 0.301376i −0.0307652 0.0146189i
\(426\) 15.6394 + 11.5851i 0.757731 + 0.561299i
\(427\) −20.6220 + 9.86349i −0.997969 + 0.477328i
\(428\) −6.43571 + 11.1470i −0.311082 + 0.538809i
\(429\) 5.36803 + 3.97644i 0.259171 + 0.191984i
\(430\) 0.125561 + 3.13707i 0.00605508 + 0.151283i
\(431\) −8.93656 5.15953i −0.430459 0.248526i 0.269083 0.963117i \(-0.413279\pi\)
−0.699542 + 0.714591i \(0.746613\pi\)
\(432\) −1.42844 + 1.21617i −0.0687257 + 0.0585128i
\(433\) −2.48188 −0.119272 −0.0596359 0.998220i \(-0.518994\pi\)
−0.0596359 + 0.998220i \(0.518994\pi\)
\(434\) 7.55357 + 5.17945i 0.362583 + 0.248622i
\(435\) −21.8016 + 10.5216i −1.04531 + 0.504473i
\(436\) 7.62443 0.365144
\(437\) 22.0681 12.7410i 1.05566 0.609487i
\(438\) 6.56376 + 15.1170i 0.313629 + 0.722320i
\(439\) 15.3078 + 8.83797i 0.730602 + 0.421813i 0.818642 0.574303i \(-0.194727\pi\)
−0.0880401 + 0.996117i \(0.528060\pi\)
\(440\) −0.167024 4.17300i −0.00796254 0.198940i
\(441\) −2.94592 20.7923i −0.140282 0.990112i
\(442\) 0.658264i 0.0313104i
\(443\) 6.19292 10.7265i 0.294235 0.509629i −0.680572 0.732681i \(-0.738269\pi\)
0.974807 + 0.223052i \(0.0716019\pi\)
\(444\) 7.42956 + 5.50354i 0.352591 + 0.261187i
\(445\) −11.2928 17.8689i −0.535329 0.847067i
\(446\) 11.7836 0.557972
\(447\) −1.21860 + 10.6464i −0.0576376 + 0.503560i
\(448\) −6.08149 + 8.86909i −0.287323 + 0.419025i
\(449\) 3.62937i 0.171281i 0.996326 + 0.0856404i \(0.0272936\pi\)
−0.996326 + 0.0856404i \(0.972706\pi\)
\(450\) −7.72193 + 9.71640i −0.364015 + 0.458035i
\(451\) 4.35857 + 2.51642i 0.205237 + 0.118494i
\(452\) 2.27749 0.107124
\(453\) −30.0308 3.43733i −1.41097 0.161500i
\(454\) −17.2297 9.94756i −0.808629 0.466862i
\(455\) 15.6581 + 29.6308i 0.734064 + 1.38911i
\(456\) −28.7748 + 12.4939i −1.34750 + 0.585081i
\(457\) 14.1867 + 8.19072i 0.663628 + 0.383146i 0.793658 0.608364i \(-0.208174\pi\)
−0.130030 + 0.991510i \(0.541507\pi\)
\(458\) 15.7281 + 9.08062i 0.734926 + 0.424310i
\(459\) −0.473072 0.555642i −0.0220811 0.0259351i
\(460\) −6.06467 9.59632i −0.282767 0.447431i
\(461\) −2.09653 3.63129i −0.0976449 0.169126i 0.813064 0.582174i \(-0.197798\pi\)
−0.910709 + 0.413048i \(0.864464\pi\)
\(462\) −2.44046 + 0.841846i −0.113540 + 0.0391662i
\(463\) −3.62504 2.09292i −0.168470 0.0972662i 0.413394 0.910552i \(-0.364343\pi\)
−0.581864 + 0.813286i \(0.697676\pi\)
\(464\) 2.25666i 0.104763i
\(465\) 14.5931 7.04275i 0.676738 0.326600i
\(466\) 24.6010 1.13962
\(467\) −9.17709 + 5.29840i −0.424665 + 0.245181i −0.697071 0.717002i \(-0.745514\pi\)
0.272406 + 0.962182i \(0.412181\pi\)
\(468\) −21.7763 5.05122i −1.00661 0.233493i
\(469\) −1.99061 + 25.6464i −0.0919177 + 1.18424i
\(470\) −1.09191 + 0.690062i −0.0503659 + 0.0318302i
\(471\) −3.47264 7.99785i −0.160011 0.368522i
\(472\) −0.790515 1.36921i −0.0363864 0.0630231i
\(473\) 0.577684 + 1.00058i 0.0265620 + 0.0460067i
\(474\) −2.34638 5.40397i −0.107773 0.248212i
\(475\) 27.1785 18.7380i 1.24703 0.859760i
\(476\) 0.403099 + 0.276403i 0.0184760 + 0.0126689i
\(477\) −8.23926 + 8.81719i −0.377250 + 0.403711i
\(478\) −9.09201 + 5.24927i −0.415859 + 0.240096i
\(479\) 31.1455 1.42307 0.711537 0.702649i \(-0.247999\pi\)
0.711537 + 0.702649i \(0.247999\pi\)
\(480\) 9.73837 + 20.1786i 0.444494 + 0.921023i
\(481\) 22.9891i 1.04821i
\(482\) −4.11038 2.37313i −0.187223 0.108093i
\(483\) −11.5960 + 13.3547i −0.527635 + 0.607662i
\(484\) 6.92977 + 12.0027i 0.314990 + 0.545578i
\(485\) 15.2851 + 24.1861i 0.694061 + 1.09823i
\(486\) −11.4561 + 5.92601i −0.519659 + 0.268809i
\(487\) 12.4304 + 7.17670i 0.563275 + 0.325207i 0.754459 0.656347i \(-0.227899\pi\)
−0.191184 + 0.981554i \(0.561233\pi\)
\(488\) −20.5260 11.8507i −0.929167 0.536455i
\(489\) −12.7689 + 5.54421i −0.577429 + 0.250718i
\(490\) −12.8656 1.48506i −0.581208 0.0670884i
\(491\) −31.6186 18.2550i −1.42693 0.823836i −0.430049 0.902805i \(-0.641504\pi\)
−0.996877 + 0.0789693i \(0.974837\pi\)
\(492\) −16.7320 1.91515i −0.754337 0.0863417i
\(493\) −0.877809 −0.0395345
\(494\) −26.8003 15.4731i −1.20580 0.696170i
\(495\) −0.853271 + 4.48690i −0.0383517 + 0.201671i
\(496\) 1.51052i 0.0678242i
\(497\) 29.6340 + 20.3199i 1.32927 + 0.911472i
\(498\) 1.20296 10.5099i 0.0539061 0.470959i
\(499\) −0.318127 −0.0142413 −0.00712067 0.999975i \(-0.502267\pi\)
−0.00712067 + 0.999975i \(0.502267\pi\)
\(500\) −8.82519 11.7643i −0.394675 0.526114i
\(501\) 4.95995 + 3.67415i 0.221594 + 0.164149i
\(502\) 2.94294 5.09732i 0.131350 0.227505i
\(503\) 1.98119i 0.0883367i −0.999024 0.0441684i \(-0.985936\pi\)
0.999024 0.0441684i \(-0.0140638\pi\)
\(504\) 16.0524 14.7106i 0.715031 0.655260i
\(505\) 35.0167 1.40154i 1.55822 0.0623677i
\(506\) 1.88296 + 1.08713i 0.0837078 + 0.0483287i
\(507\) −13.1691 30.3299i −0.584862 1.34700i
\(508\) −0.147196 + 0.0849834i −0.00653075 + 0.00377053i
\(509\) −25.3654 −1.12430 −0.562150 0.827035i \(-0.690026\pi\)
−0.562150 + 0.827035i \(0.690026\pi\)
\(510\) −0.405315 + 0.195609i −0.0179477 + 0.00866169i
\(511\) 13.1281 + 27.4475i 0.580754 + 1.21421i
\(512\) 4.06948 0.179848
\(513\) 33.7422 6.19952i 1.48975 0.273716i
\(514\) 20.5159 + 11.8449i 0.904919 + 0.522455i
\(515\) −23.0814 + 0.923830i −1.01709 + 0.0407088i
\(516\) −3.10666 2.30130i −0.136763 0.101309i
\(517\) −0.237670 + 0.411657i −0.0104527 + 0.0181047i
\(518\) −7.32689 5.02402i −0.321925 0.220743i
\(519\) −33.7423 24.9951i −1.48112 1.09716i
\(520\) −16.1565 + 30.7633i −0.708511 + 1.34906i
\(521\) 17.1966 29.7854i 0.753397 1.30492i −0.192771 0.981244i \(-0.561747\pi\)
0.946167 0.323678i \(-0.104919\pi\)
\(522\) −3.50576 + 15.1137i −0.153443 + 0.661507i
\(523\) 19.8731 + 34.4213i 0.868991 + 1.50514i 0.863029 + 0.505154i \(0.168564\pi\)
0.00596176 + 0.999982i \(0.498102\pi\)
\(524\) 3.05366 + 5.28909i 0.133400 + 0.231055i
\(525\) −13.5917 + 18.4463i −0.593192 + 0.805061i
\(526\) −11.1616 + 19.3324i −0.486668 + 0.842934i
\(527\) 0.587570 0.0255950
\(528\) 0.342126 + 0.253434i 0.0148891 + 0.0110293i
\(529\) −8.10401 −0.352348
\(530\) 3.97594 + 6.29125i 0.172704 + 0.273274i
\(531\) 0.503810 + 1.65401i 0.0218635 + 0.0717781i
\(532\) −20.7286 + 9.91446i −0.898697 + 0.429846i
\(533\) −20.9371 36.2641i −0.906885 1.57077i
\(534\) −13.4598 1.54061i −0.582462 0.0666688i
\(535\) −11.6893 18.4963i −0.505372 0.799665i
\(536\) −23.0977 + 13.3355i −0.997669 + 0.576004i
\(537\) 28.8637 + 21.3812i 1.24556 + 0.922666i
\(538\) 3.64283 + 6.30957i 0.157054 + 0.272025i
\(539\) −4.44574 + 1.71756i −0.191492 + 0.0739807i
\(540\) −3.36080 14.9094i −0.144626 0.641598i
\(541\) −2.28062 3.95016i −0.0980517 0.169830i 0.812826 0.582506i \(-0.197928\pi\)
−0.910878 + 0.412675i \(0.864594\pi\)
\(542\) 9.14195i 0.392680i
\(543\) −3.77799 + 33.0070i −0.162129 + 1.41647i
\(544\) 0.812463i 0.0348341i
\(545\) −6.02639 + 11.4747i −0.258142 + 0.491523i
\(546\) 21.0868 + 4.08662i 0.902434 + 0.174891i
\(547\) 28.3756 16.3827i 1.21325 0.700472i 0.249786 0.968301i \(-0.419640\pi\)
0.963466 + 0.267829i \(0.0863063\pi\)
\(548\) 1.47270 + 2.55079i 0.0629105 + 0.108964i
\(549\) 18.9385 + 17.6972i 0.808277 + 0.755297i
\(550\) 2.54412 + 1.20890i 0.108482 + 0.0515478i
\(551\) 20.6338 35.7387i 0.879027 1.52252i
\(552\) −18.2190 2.08535i −0.775453 0.0887585i
\(553\) −4.69298 9.81182i −0.199566 0.417241i
\(554\) −2.65762 1.53438i −0.112912 0.0651895i
\(555\) −14.1552 + 6.83140i −0.600853 + 0.289977i
\(556\) 19.6369i 0.832788i
\(557\) −15.9777 + 27.6741i −0.676995 + 1.17259i 0.298886 + 0.954289i \(0.403385\pi\)
−0.975881 + 0.218301i \(0.929948\pi\)
\(558\) 2.34662 10.1165i 0.0993401 0.428265i
\(559\) 9.61287i 0.406581i
\(560\) 0.997954 + 1.88849i 0.0421713 + 0.0798033i
\(561\) −0.0985823 + 0.133082i −0.00416215 + 0.00561873i
\(562\) 20.1276i 0.849030i
\(563\) −12.3669 + 7.14002i −0.521201 + 0.300916i −0.737426 0.675428i \(-0.763959\pi\)
0.216225 + 0.976344i \(0.430626\pi\)
\(564\) 0.180882 1.58030i 0.00761650 0.0665427i
\(565\) −1.80014 + 3.42760i −0.0757324 + 0.144200i
\(566\) 7.71428 0.324255
\(567\) −20.7363 + 11.7049i −0.870845 + 0.491558i
\(568\) 37.2548i 1.56318i
\(569\) −12.2889 7.09501i −0.515178 0.297438i 0.219782 0.975549i \(-0.429466\pi\)
−0.734960 + 0.678111i \(0.762799\pi\)
\(570\) 1.56341 21.0998i 0.0654840 0.883772i
\(571\) −7.28331 12.6151i −0.304797 0.527924i 0.672419 0.740171i \(-0.265255\pi\)
−0.977216 + 0.212247i \(0.931922\pi\)
\(572\) 5.07338i 0.212129i
\(573\) 19.1960 + 14.2197i 0.801924 + 0.594036i
\(574\) 16.1333 + 1.25223i 0.673392 + 0.0522669i
\(575\) 19.2359 1.54230i 0.802194 0.0643185i
\(576\) 11.8783 + 2.75530i 0.494931 + 0.114804i
\(577\) −11.1217 + 19.2633i −0.463002 + 0.801943i −0.999109 0.0422073i \(-0.986561\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(578\) 14.0497 0.584389
\(579\) −6.71330 + 2.91489i −0.278995 + 0.121139i
\(580\) −16.2762 8.54808i −0.675832 0.354940i
\(581\) 1.51128 19.4710i 0.0626987 0.807792i
\(582\) 18.2182 + 2.08527i 0.755171 + 0.0864371i
\(583\) 2.37185 + 1.36939i 0.0982319 + 0.0567142i
\(584\) −15.7730 + 27.3197i −0.652693 + 1.13050i
\(585\) 24.8141 28.7806i 1.02594 1.18993i
\(586\) 6.45507 3.72684i 0.266657 0.153954i
\(587\) 28.6833 16.5603i 1.18389 0.683517i 0.226975 0.973901i \(-0.427116\pi\)
0.956910 + 0.290384i \(0.0937830\pi\)
\(588\) 11.3568 11.1969i 0.468347 0.461753i
\(589\) −13.8114 + 23.9221i −0.569089 + 0.985691i
\(590\) 1.06547 0.0426455i 0.0438649 0.00175569i
\(591\) 7.30131 + 0.835710i 0.300336 + 0.0343765i
\(592\) 1.46519i 0.0602188i
\(593\) 3.72499 2.15062i 0.152967 0.0883154i −0.421563 0.906799i \(-0.638518\pi\)
0.574530 + 0.818484i \(0.305185\pi\)
\(594\) 1.89763 + 2.22884i 0.0778605 + 0.0914503i
\(595\) −0.734596 + 0.388190i −0.0301155 + 0.0159143i
\(596\) −7.04785 + 4.06908i −0.288691 + 0.166676i
\(597\) −14.5177 10.7542i −0.594170 0.440139i
\(598\) −9.04509 15.6666i −0.369881 0.640653i
\(599\) 9.81077 5.66425i 0.400857 0.231435i −0.285997 0.958231i \(-0.592325\pi\)
0.686854 + 0.726796i \(0.258991\pi\)
\(600\) −23.7430 0.806559i −0.969305 0.0329276i
\(601\) −7.87784 + 4.54827i −0.321344 + 0.185528i −0.651991 0.758226i \(-0.726066\pi\)
0.330648 + 0.943754i \(0.392733\pi\)
\(602\) 3.06373 + 2.10079i 0.124868 + 0.0856217i
\(603\) 27.9021 8.49894i 1.13626 0.346103i
\(604\) −11.4778 19.8801i −0.467024 0.808910i
\(605\) −23.5413 + 0.942239i −0.957092 + 0.0383075i
\(606\) 13.3694 18.0481i 0.543094 0.733154i
\(607\) 11.3620 0.461170 0.230585 0.973052i \(-0.425936\pi\)
0.230585 + 0.973052i \(0.425936\pi\)
\(608\) −33.0782 19.0977i −1.34150 0.774515i
\(609\) −5.44959 + 28.1197i −0.220828 + 1.13947i
\(610\) 13.5130 8.53995i 0.547127 0.345773i
\(611\) 3.42506 1.97746i 0.138563 0.0799995i
\(612\) 0.125228 0.539869i 0.00506204 0.0218229i
\(613\) −21.0518 12.1542i −0.850273 0.490905i 0.0104700 0.999945i \(-0.496667\pi\)
−0.860743 + 0.509040i \(0.830001\pi\)
\(614\) −2.41983 + 4.19127i −0.0976565 + 0.169146i
\(615\) 16.1074 23.6678i 0.649511 0.954378i
\(616\) −4.07544 2.79451i −0.164204 0.112594i
\(617\) −3.63503 + 6.29606i −0.146341 + 0.253470i −0.929872 0.367882i \(-0.880083\pi\)
0.783532 + 0.621352i \(0.213416\pi\)
\(618\) −8.81247 + 11.8965i −0.354489 + 0.478546i
\(619\) 13.1691i 0.529310i 0.964343 + 0.264655i \(0.0852582\pi\)
−0.964343 + 0.264655i \(0.914742\pi\)
\(620\) 10.8946 + 5.72174i 0.437539 + 0.229791i
\(621\) 18.8940 + 6.72377i 0.758190 + 0.269816i
\(622\) −13.4081 −0.537618
\(623\) −24.9361 1.93547i −0.999043 0.0775430i
\(624\) −1.41087 3.24939i −0.0564802 0.130080i
\(625\) 24.6806 3.98330i 0.987225 0.159332i
\(626\) 11.4954 + 19.9106i 0.459447 + 0.795786i
\(627\) −3.10097 7.14186i −0.123841 0.285218i
\(628\) 3.31087 5.73460i 0.132118 0.228835i
\(629\) −0.569937 −0.0227249
\(630\) 3.74986 + 14.1982i 0.149398 + 0.565671i
\(631\) −4.37610 −0.174210 −0.0871050 0.996199i \(-0.527762\pi\)
−0.0871050 + 0.996199i \(0.527762\pi\)
\(632\) 5.63847 9.76612i 0.224286 0.388476i
\(633\) −19.4218 + 26.2187i −0.771948 + 1.04210i
\(634\) 7.42702 + 12.8640i 0.294965 + 0.510894i
\(635\) −0.0115552 0.288700i −0.000458553 0.0114567i
\(636\) −9.10523 1.04219i −0.361046 0.0413254i
\(637\) 39.1789 + 6.11879i 1.55233 + 0.242435i
\(638\) 3.52114 0.139403
\(639\) 9.20618 39.6887i 0.364191 1.57006i
\(640\) −8.53292 + 16.2473i −0.337293 + 0.642232i
\(641\) 15.2910i 0.603958i −0.953315 0.301979i \(-0.902353\pi\)
0.953315 0.301979i \(-0.0976473\pi\)
\(642\) −13.9324 1.59471i −0.549868 0.0629381i
\(643\) −11.7908 + 20.4223i −0.464984 + 0.805376i −0.999201 0.0399718i \(-0.987273\pi\)
0.534217 + 0.845347i \(0.320607\pi\)
\(644\) −13.3917 1.03943i −0.527706 0.0409591i
\(645\) 5.91896 2.85654i 0.233059 0.112476i
\(646\) 0.383604 0.664422i 0.0150927 0.0261413i
\(647\) −24.6808 14.2495i −0.970302 0.560204i −0.0709734 0.997478i \(-0.522611\pi\)
−0.899328 + 0.437274i \(0.855944\pi\)
\(648\) −22.1676 10.8688i −0.870825 0.426965i
\(649\) 0.339836 0.196205i 0.0133397 0.00770171i
\(650\) −13.3025 19.2945i −0.521765 0.756792i
\(651\) 3.64774 18.8222i 0.142966 0.737701i
\(652\) −9.15551 5.28594i −0.358558 0.207013i
\(653\) 14.7812 0.578434 0.289217 0.957264i \(-0.406605\pi\)
0.289217 + 0.957264i \(0.406605\pi\)
\(654\) 3.30838 + 7.61955i 0.129368 + 0.297948i
\(655\) −10.3737 + 0.415205i −0.405333 + 0.0162234i
\(656\) −1.33440 2.31125i −0.0520996 0.0902392i
\(657\) 23.5546 25.2068i 0.918953 0.983412i
\(658\) −0.118270 + 1.52376i −0.00461065 + 0.0594023i
\(659\) 2.63390 1.52068i 0.102602 0.0592373i −0.447821 0.894123i \(-0.647800\pi\)
0.550423 + 0.834886i \(0.314466\pi\)
\(660\) −3.12385 + 1.50760i −0.121596 + 0.0586831i
\(661\) 16.3090 9.41603i 0.634348 0.366241i −0.148086 0.988975i \(-0.547311\pi\)
0.782434 + 0.622733i \(0.213978\pi\)
\(662\) −8.93003 15.4673i −0.347075 0.601152i
\(663\) 1.26397 0.548810i 0.0490884 0.0213140i
\(664\) 17.5359 10.1244i 0.680527 0.392902i
\(665\) 1.46279 39.0328i 0.0567247 1.51363i
\(666\) −2.27619 + 9.81289i −0.0882007 + 0.380242i
\(667\) 20.8917 12.0618i 0.808929 0.467035i
\(668\) 4.68770i 0.181373i
\(669\) −9.82429 22.6264i −0.379829 0.874786i
\(670\) −0.719400 17.9738i −0.0277929 0.694389i
\(671\) 2.94132 5.09452i 0.113548 0.196672i
\(672\) 26.0265 + 5.04391i 1.00399 + 0.194573i
\(673\) 22.4784 12.9779i 0.866480 0.500263i 0.000303202 1.00000i \(-0.499903\pi\)
0.866177 + 0.499737i \(0.166570\pi\)
\(674\) 13.7843 7.95834i 0.530950 0.306544i
\(675\) 25.0949 + 6.72649i 0.965903 + 0.258903i
\(676\) 12.5557 21.7471i 0.482910 0.836425i
\(677\) 42.9391 + 24.7909i 1.65028 + 0.952791i 0.976955 + 0.213446i \(0.0684688\pi\)
0.673327 + 0.739345i \(0.264865\pi\)
\(678\) 0.988244 + 2.27603i 0.0379533 + 0.0874103i
\(679\) 33.7517 + 2.61972i 1.29527 + 0.100536i
\(680\) −0.762672 0.400547i −0.0292471 0.0153603i
\(681\) −4.73604 + 41.3771i −0.181485 + 1.58557i
\(682\) −2.35691 −0.0902508
\(683\) 19.6199 33.9826i 0.750733 1.30031i −0.196735 0.980457i \(-0.563034\pi\)
0.947468 0.319851i \(-0.103633\pi\)
\(684\) 19.0364 + 17.7886i 0.727874 + 0.680165i
\(685\) −5.00294 + 0.200242i −0.191153 + 0.00765086i
\(686\) −10.5122 + 11.1496i −0.401359 + 0.425693i
\(687\) 4.32329 37.7710i 0.164944 1.44106i
\(688\) 0.612666i 0.0233577i
\(689\) −11.3935 19.7342i −0.434059 0.751813i
\(690\) 6.95859 10.2248i 0.264909 0.389252i
\(691\) −27.1988 15.7033i −1.03469 0.597380i −0.116367 0.993206i \(-0.537125\pi\)
−0.918325 + 0.395826i \(0.870458\pi\)
\(692\) 31.8902i 1.21228i
\(693\) 3.65114 + 3.98418i 0.138695 + 0.151347i
\(694\) 13.8857 0.527094
\(695\) 29.5533 + 15.5211i 1.12102 + 0.588748i
\(696\) −27.2408 + 11.8279i −1.03256 + 0.448334i
\(697\) 0.899045 0.519064i 0.0340537 0.0196609i
\(698\) 13.5072i 0.511256i
\(699\) −20.5104 47.2377i −0.775776 1.78669i
\(700\) −17.4010 + 0.0442859i −0.657694 + 0.00167385i
\(701\) 38.6747i 1.46072i 0.683060 + 0.730362i \(0.260649\pi\)
−0.683060 + 0.730362i \(0.739351\pi\)
\(702\) −4.40115 23.9541i −0.166111 0.904091i
\(703\) 13.3969 23.2042i 0.505275 0.875162i
\(704\) 2.76739i 0.104300i
\(705\) 2.23537 + 1.52130i 0.0841890 + 0.0572957i
\(706\) −21.4834 12.4035i −0.808540 0.466811i
\(707\) 23.4495 34.1981i 0.881909 1.28615i
\(708\) −0.781613 + 1.05515i −0.0293748 + 0.0396548i
\(709\) 8.90332 15.4210i 0.334371 0.579148i −0.648993 0.760795i \(-0.724809\pi\)
0.983364 + 0.181647i \(0.0581427\pi\)
\(710\) −22.2452 11.6829i −0.834848 0.438453i
\(711\) −8.42020 + 9.01082i −0.315782 + 0.337932i
\(712\) −12.9661 22.4579i −0.485925 0.841646i
\(713\) −13.9840 + 8.07369i −0.523707 + 0.302362i
\(714\) −0.101314 + 0.522777i −0.00379158 + 0.0195644i
\(715\) −7.63540 4.01003i −0.285548 0.149967i
\(716\) 27.2794i 1.01948i
\(717\) 17.6596 + 13.0816i 0.659510 + 0.488541i
\(718\) 0.511250i 0.0190797i
\(719\) −13.6537 23.6488i −0.509196 0.881953i −0.999943 0.0106510i \(-0.996610\pi\)
0.490748 0.871302i \(-0.336724\pi\)
\(720\) 1.58150 1.83430i 0.0589392 0.0683605i
\(721\) −15.4568 + 22.5418i −0.575642 + 0.839501i
\(722\) 10.1736 + 17.6211i 0.378621 + 0.655791i
\(723\) −1.12985 + 9.87109i −0.0420195 + 0.367110i
\(724\) −21.8503 + 12.6153i −0.812061 + 0.468843i
\(725\) 25.7296 17.7391i 0.955573 0.658814i
\(726\) −8.98807 + 12.1335i −0.333579 + 0.450318i
\(727\) −21.0203 36.4082i −0.779598 1.35030i −0.932174 0.362012i \(-0.882090\pi\)
0.152575 0.988292i \(-0.451243\pi\)
\(728\) 17.7401 + 37.0900i 0.657493 + 1.37465i
\(729\) 20.9300 + 17.0568i 0.775186 + 0.631733i
\(730\) −11.3665 17.9856i −0.420694 0.665677i
\(731\) 0.238319 0.00881453
\(732\) −2.23853 + 19.5572i −0.0827383 + 0.722856i
\(733\) −38.9106 −1.43720 −0.718598 0.695426i \(-0.755216\pi\)
−0.718598 + 0.695426i \(0.755216\pi\)
\(734\) −2.16062 + 3.74231i −0.0797500 + 0.138131i
\(735\) 7.87479 + 25.9420i 0.290466 + 0.956885i
\(736\) −11.1639 19.3365i −0.411507 0.712751i
\(737\) −3.30984 5.73281i −0.121920 0.211171i
\(738\) −5.34640 17.5523i −0.196804 0.646109i
\(739\) −24.3794 + 42.2264i −0.896811 + 1.55332i −0.0652649 + 0.997868i \(0.520789\pi\)
−0.831547 + 0.555455i \(0.812544\pi\)
\(740\) −10.5677 5.55004i −0.388476 0.204023i
\(741\) −7.36677 + 64.3609i −0.270625 + 2.36436i
\(742\) 8.77944 + 0.681437i 0.322304 + 0.0250163i
\(743\) −11.7042 + 20.2722i −0.429384 + 0.743715i −0.996819 0.0797035i \(-0.974603\pi\)
0.567435 + 0.823418i \(0.307936\pi\)
\(744\) 18.2339 7.91710i 0.668487 0.290255i
\(745\) −0.553271 13.8232i −0.0202703 0.506442i
\(746\) 2.99196 + 1.72741i 0.109544 + 0.0632450i
\(747\) −21.1835 + 6.45246i −0.775064 + 0.236083i
\(748\) −0.125777 −0.00459887
\(749\) −25.8116 2.00343i −0.943137 0.0732038i
\(750\) 7.92732 13.9243i 0.289465 0.508443i
\(751\) 9.33718 0.340718 0.170359 0.985382i \(-0.445507\pi\)
0.170359 + 0.985382i \(0.445507\pi\)
\(752\) 0.218293 0.126031i 0.00796032 0.00459589i
\(753\) −12.2412 1.40113i −0.446095 0.0510602i
\(754\) −25.3715 14.6483i −0.923977 0.533458i
\(755\) 38.9915 1.56063i 1.41905 0.0567972i
\(756\) −16.5167 7.36315i −0.600708 0.267795i
\(757\) 26.1856i 0.951731i 0.879518 + 0.475865i \(0.157865\pi\)
−0.879518 + 0.475865i \(0.842135\pi\)
\(758\) −5.53969 + 9.59503i −0.201211 + 0.348507i
\(759\) 0.517581 4.52193i 0.0187870 0.164136i
\(760\) 34.2350 21.6358i 1.24183 0.784813i
\(761\) 25.1347 0.911130 0.455565 0.890202i \(-0.349437\pi\)
0.455565 + 0.890202i \(0.349437\pi\)
\(762\) −0.148800 0.110225i −0.00539045 0.00399305i
\(763\) 6.61707 + 13.8346i 0.239554 + 0.500845i
\(764\) 18.1423i 0.656366i
\(765\) 0.713518 + 0.615183i 0.0257973 + 0.0222420i
\(766\) −6.75727 3.90131i −0.244150 0.140960i
\(767\) −3.26492 −0.117889
\(768\) 10.2922 + 23.7039i 0.371386 + 0.855341i
\(769\) 13.1364 + 7.58433i 0.473712 + 0.273498i 0.717793 0.696257i \(-0.245153\pi\)
−0.244080 + 0.969755i \(0.578486\pi\)
\(770\) 2.94667 1.55714i 0.106191 0.0561155i
\(771\) 5.63935 49.2690i 0.203096 1.77438i
\(772\) −4.81355 2.77911i −0.173244 0.100022i
\(773\) 26.5947 + 15.3545i 0.956545 + 0.552261i 0.895108 0.445850i \(-0.147098\pi\)
0.0614368 + 0.998111i \(0.480432\pi\)
\(774\) 0.951788 4.10325i 0.0342113 0.147488i
\(775\) −17.2224 + 11.8738i −0.618645 + 0.426521i
\(776\) 17.5500 + 30.3975i 0.630009 + 1.09121i
\(777\) −3.53827 + 18.2574i −0.126935 + 0.654980i
\(778\) 9.01108 + 5.20255i 0.323063 + 0.186521i
\(779\) 48.8044i 1.74860i
\(780\) 28.7806 + 2.13253i 1.03051 + 0.0763567i
\(781\) −9.24658 −0.330869
\(782\) 0.388399 0.224242i 0.0138891 0.00801889i
\(783\) 31.9433 5.86902i 1.14156 0.209742i
\(784\) 2.49703 + 0.389975i 0.0891796 + 0.0139277i
\(785\) 6.01360 + 9.51550i 0.214635 + 0.339623i
\(786\) −3.96066 + 5.34673i −0.141272 + 0.190712i
\(787\) 0.445102 + 0.770939i 0.0158662 + 0.0274810i 0.873849 0.486197i \(-0.161616\pi\)
−0.857983 + 0.513678i \(0.828283\pi\)
\(788\) 2.79056 + 4.83340i 0.0994097 + 0.172183i
\(789\) 46.4268 + 5.31403i 1.65284 + 0.189184i
\(790\) 4.06325 + 6.42941i 0.144564 + 0.228748i
\(791\) 1.97658 + 4.13251i 0.0702790 + 0.146935i
\(792\) −1.26609 + 5.45823i −0.0449885 + 0.193950i
\(793\) −42.3873 + 24.4723i −1.50522 + 0.869037i
\(794\) −9.86119 −0.349961
\(795\) 8.76531 12.8796i 0.310874 0.456791i
\(796\) 13.7208i 0.486322i
\(797\) −21.7294 12.5455i −0.769695 0.444384i 0.0630709 0.998009i \(-0.479911\pi\)
−0.832766 + 0.553626i \(0.813244\pi\)
\(798\) −18.9026 16.4132i −0.669145 0.581022i
\(799\) 0.0490244 + 0.0849128i 0.00173436 + 0.00300400i
\(800\) −16.4186 23.8142i −0.580484 0.841960i
\(801\) 8.26353 + 27.1293i 0.291977 + 0.958566i
\(802\) 16.2238 + 9.36681i 0.572882 + 0.330753i
\(803\) −6.78071 3.91484i −0.239286 0.138152i
\(804\) 17.7996 + 13.1853i 0.627744 + 0.465009i
\(805\) 12.1492 19.3328i 0.428202 0.681392i
\(806\) 16.9827 + 9.80496i 0.598190 + 0.345365i
\(807\) 9.07822 12.2552i 0.319568 0.431404i
\(808\) 42.9926 1.51248
\(809\) 14.5627 + 8.40775i 0.511996 + 0.295601i 0.733654 0.679524i \(-0.237813\pi\)
−0.221658 + 0.975124i \(0.571147\pi\)
\(810\) 13.4415 9.82810i 0.472287 0.345324i
\(811\) 47.8923i 1.68173i 0.541248 + 0.840863i \(0.317952\pi\)
−0.541248 + 0.840863i \(0.682048\pi\)
\(812\) −19.6235 + 9.38592i −0.688651 + 0.329381i
\(813\) 17.5539 7.62186i 0.615643 0.267310i
\(814\) 2.28618 0.0801306
\(815\) 15.1919 9.60094i 0.532148 0.336306i
\(816\) 0.0805576 0.0349778i 0.00282008 0.00122447i
\(817\) −5.60191 + 9.70279i −0.195986 + 0.339458i
\(818\) 8.06800i 0.282091i
\(819\) −9.73366 43.8970i −0.340122 1.53389i
\(820\) 21.7246 0.869523i 0.758655 0.0303651i
\(821\) −18.3699 10.6059i −0.641114 0.370147i 0.143930 0.989588i \(-0.454026\pi\)
−0.785043 + 0.619441i \(0.787359\pi\)
\(822\) −1.91012 + 2.57859i −0.0666232 + 0.0899386i
\(823\) −25.4281 + 14.6809i −0.886369 + 0.511746i −0.872753 0.488162i \(-0.837668\pi\)
−0.0136162 + 0.999907i \(0.504334\pi\)
\(824\) −28.3387 −0.987226
\(825\) 0.200187 5.89298i 0.00696961 0.205167i
\(826\) 0.713511 1.04057i 0.0248262 0.0362059i
\(827\) −34.6613 −1.20529 −0.602646 0.798009i \(-0.705887\pi\)
−0.602646 + 0.798009i \(0.705887\pi\)
\(828\) 4.43785 + 14.5695i 0.154226 + 0.506325i
\(829\) −44.0905 25.4557i −1.53133 0.884112i −0.999301 0.0373844i \(-0.988097\pi\)
−0.532026 0.846728i \(-0.678569\pi\)
\(830\) 0.546174 + 13.6459i 0.0189580 + 0.473655i
\(831\) −0.730519 + 6.38229i −0.0253414 + 0.221399i
\(832\) −11.5126 + 19.9404i −0.399127 + 0.691307i
\(833\) −0.151695 + 0.971309i −0.00525591 + 0.0336539i
\(834\) 19.6243 8.52080i 0.679533 0.295051i
\(835\) −7.05495 3.70518i −0.244147 0.128223i
\(836\) 2.95652 5.12084i 0.102253 0.177108i
\(837\) −21.3816 + 3.92849i −0.739056 + 0.135788i
\(838\) 2.07818 + 3.59952i 0.0717896 + 0.124343i
\(839\) −5.68336 9.84386i −0.196211 0.339848i 0.751086 0.660205i \(-0.229531\pi\)
−0.947297 + 0.320357i \(0.896197\pi\)
\(840\) −17.5659 + 21.9448i −0.606082 + 0.757166i
\(841\) 5.03376 8.71873i 0.173578 0.300646i
\(842\) 15.8725 0.547001
\(843\) −38.6480 + 16.7808i −1.33111 + 0.577962i
\(844\) −24.7795 −0.852947
\(845\) 22.8051 + 36.0852i 0.784519 + 1.24137i
\(846\) 1.65778 0.504956i 0.0569955 0.0173607i
\(847\) −15.7648 + 22.9910i −0.541686 + 0.789980i
\(848\) −0.726156 1.25774i −0.0249363 0.0431909i
\(849\) −6.43157 14.8126i −0.220731 0.508367i
\(850\) 0.478342 0.329789i 0.0164070 0.0113117i
\(851\) 13.5644 7.83141i 0.464981 0.268457i
\(852\) 28.3817 12.3232i 0.972339 0.422186i
\(853\) 3.76286 + 6.51747i 0.128838 + 0.223154i 0.923227 0.384256i \(-0.125542\pi\)
−0.794389 + 0.607410i \(0.792209\pi\)
\(854\) 1.46367 18.8575i 0.0500856 0.645289i
\(855\) −41.8182 + 14.5894i −1.43015 + 0.498946i
\(856\) −13.4214 23.2465i −0.458733 0.794548i
\(857\) 35.9371i 1.22759i −0.789466 0.613795i \(-0.789642\pi\)
0.789466 0.613795i \(-0.210358\pi\)
\(858\) −5.07013 + 2.20143i −0.173091 + 0.0751557i
\(859\) 25.9184i 0.884324i 0.896935 + 0.442162i \(0.145788\pi\)
−0.896935 + 0.442162i \(0.854212\pi\)
\(860\) 4.41887 + 2.32074i 0.150682 + 0.0791366i
\(861\) −11.0463 32.0224i −0.376456 1.09132i
\(862\) 7.39420 4.26905i 0.251848 0.145404i
\(863\) 14.3542 + 24.8622i 0.488622 + 0.846319i 0.999914 0.0130885i \(-0.00416631\pi\)
−0.511292 + 0.859407i \(0.670833\pi\)
\(864\) −5.43212 29.5654i −0.184804 1.00584i
\(865\) 47.9945 + 25.2062i 1.63186 + 0.857037i
\(866\) 1.02677 1.77841i 0.0348910 0.0604330i
\(867\) −11.7135 26.9775i −0.397812 0.916202i
\(868\) 13.1352 6.28256i 0.445838 0.213244i
\(869\) 2.42394 + 1.39946i 0.0822264 + 0.0474734i
\(870\) 1.48006 19.9749i 0.0501788 0.677214i
\(871\) 55.0769i 1.86621i
\(872\) −7.95020 + 13.7701i −0.269228 + 0.466316i
\(873\) −11.1849 36.7203i −0.378553 1.24279i
\(874\) 21.0841i 0.713182i
\(875\) 13.6872 26.2233i 0.462710 0.886509i
\(876\) 26.0303 + 2.97944i 0.879482 + 0.100666i
\(877\) 24.4719i 0.826357i −0.910650 0.413178i \(-0.864419\pi\)
0.910650 0.413178i \(-0.135581\pi\)
\(878\) −12.6658 + 7.31263i −0.427452 + 0.246789i
\(879\) −12.5378 9.28756i −0.422891 0.313262i
\(880\) −0.486634 0.255575i −0.0164044 0.00861543i
\(881\) 13.1998 0.444713 0.222357 0.974965i \(-0.428625\pi\)
0.222357 + 0.974965i \(0.428625\pi\)
\(882\) 16.1177 + 6.49098i 0.542710 + 0.218563i
\(883\) 0.983617i 0.0331014i −0.999863 0.0165507i \(-0.994732\pi\)
0.999863 0.0165507i \(-0.00526849\pi\)
\(884\) 0.906287 + 0.523245i 0.0304817 + 0.0175986i
\(885\) −0.970196 2.01032i −0.0326128 0.0675760i
\(886\) 5.12409 + 8.87518i 0.172147 + 0.298168i
\(887\) 17.1729i 0.576609i −0.957539 0.288305i \(-0.906908\pi\)
0.957539 0.288305i \(-0.0930916\pi\)
\(888\) −17.6867 + 7.67951i −0.593527 + 0.257707i
\(889\) −0.281951 0.193332i −0.00945632 0.00648415i
\(890\) 17.4760 0.699474i 0.585796 0.0234464i
\(891\) 2.69761 5.50196i 0.0903734 0.184323i
\(892\) 9.36665 16.2235i 0.313618 0.543203i
\(893\) −4.60947 −0.154250
\(894\) −7.12466 5.27768i −0.238284 0.176512i
\(895\) −41.0553 21.5618i −1.37233 0.720732i
\(896\) 9.36927 + 19.5887i 0.313005 + 0.654413i
\(897\) −22.5411 + 30.4295i −0.752624 + 1.01601i
\(898\) −2.60066 1.50149i −0.0867851 0.0501054i
\(899\) −13.0751 + 22.6468i −0.436079 + 0.755312i
\(900\) 7.23931 + 18.3548i 0.241310 + 0.611828i
\(901\) 0.489243 0.282464i 0.0162990 0.00941025i
\(902\) −3.60632 + 2.08211i −0.120077 + 0.0693267i
\(903\) 1.47952 7.63430i 0.0492354 0.254054i
\(904\) −2.37480 + 4.11327i −0.0789846 + 0.136805i
\(905\) −1.71530 42.8558i −0.0570184 1.42457i
\(906\) 14.8869 20.0968i 0.494585 0.667670i
\(907\) 22.9622i 0.762449i 0.924483 + 0.381224i \(0.124497\pi\)
−0.924483 + 0.381224i \(0.875503\pi\)
\(908\) −27.3912 + 15.8143i −0.909010 + 0.524817i
\(909\) −45.8015 10.6241i −1.51914 0.352379i
\(910\) −27.7101 1.03846i −0.918580 0.0344247i
\(911\) −15.2679 + 8.81490i −0.505847 + 0.292051i −0.731125 0.682244i \(-0.761004\pi\)
0.225278 + 0.974295i \(0.427671\pi\)
\(912\) −0.469513 + 4.10197i −0.0155471 + 0.135830i
\(913\) 2.51286 + 4.35239i 0.0831634 + 0.144043i
\(914\) −11.7383 + 6.77709i −0.388267 + 0.224166i
\(915\) −27.6641 18.8271i −0.914548 0.622405i
\(916\) 25.0041 14.4361i 0.826158 0.476982i
\(917\) −6.94688 + 10.1312i −0.229406 + 0.334560i
\(918\) 0.593862 0.109112i 0.0196004 0.00360122i
\(919\) −1.25518 2.17404i −0.0414046 0.0717148i 0.844580 0.535429i \(-0.179850\pi\)
−0.885985 + 0.463714i \(0.846517\pi\)
\(920\) 23.6553 0.946799i 0.779891 0.0312151i
\(921\) 10.0653 + 1.15208i 0.331664 + 0.0379624i
\(922\) 3.46937 0.114258
\(923\) 66.6261 + 38.4666i 2.19302 + 1.26614i
\(924\) −0.780847 + 4.02915i −0.0256880 + 0.132549i
\(925\) 16.7055 11.5175i 0.549274 0.378694i
\(926\) 2.99940 1.73170i 0.0985662 0.0569072i
\(927\) 30.1902 + 7.00290i 0.991576 + 0.230005i
\(928\) −31.3148 18.0796i −1.02796 0.593493i
\(929\) 2.76218 4.78423i 0.0906241 0.156965i −0.817150 0.576425i \(-0.804447\pi\)
0.907774 + 0.419460i \(0.137780\pi\)
\(930\) −0.990695 + 13.3704i −0.0324862 + 0.438433i
\(931\) −35.9797 29.0076i −1.17919 0.950685i
\(932\) 19.5550 33.8702i 0.640545 1.10946i
\(933\) 11.1787 + 25.7457i 0.365973 + 0.842875i
\(934\) 8.76789i 0.286894i
\(935\) 0.0994151 0.189294i 0.00325122 0.00619057i
\(936\) 31.8295 34.0621i 1.04038 1.11336i
\(937\) 10.6252 0.347109 0.173555 0.984824i \(-0.444475\pi\)
0.173555 + 0.984824i \(0.444475\pi\)
\(938\) −17.5536 12.0364i −0.573147 0.393004i
\(939\) 28.6473 38.6727i 0.934870 1.26204i
\(940\) 0.0821246 + 2.05184i 0.00267861 + 0.0669236i
\(941\) −13.5119 23.4033i −0.440476 0.762927i 0.557249 0.830346i \(-0.311857\pi\)
−0.997725 + 0.0674189i \(0.978524\pi\)
\(942\) 7.16757 + 0.820403i 0.233532 + 0.0267302i
\(943\) −14.2647 + 24.7072i −0.464523 + 0.804578i
\(944\) −0.208086 −0.00677262
\(945\) 24.1364 19.0377i 0.785157 0.619296i
\(946\) −0.955964 −0.0310811
\(947\) −28.7829 + 49.8534i −0.935318 + 1.62002i −0.161253 + 0.986913i \(0.551553\pi\)
−0.774066 + 0.633105i \(0.781780\pi\)
\(948\) −9.30519 1.06508i −0.302219 0.0345920i
\(949\) 32.5722 + 56.4167i 1.05734 + 1.83136i
\(950\) 2.18301 + 27.2270i 0.0708262 + 0.883360i
\(951\) 18.5087 24.9860i 0.600185 0.810226i
\(952\) −0.919521 + 0.439806i −0.0298018 + 0.0142542i
\(953\) −38.1754 −1.23662 −0.618311 0.785934i \(-0.712183\pi\)
−0.618311 + 0.785934i \(0.712183\pi\)
\(954\) −2.90941 9.55162i −0.0941955 0.309245i
\(955\) −27.3041 14.3398i −0.883539 0.464025i
\(956\) 16.6903i 0.539802i
\(957\) −2.93566 6.76112i −0.0948963 0.218556i
\(958\) −12.8850 + 22.3176i −0.416297 + 0.721048i
\(959\) −3.35030 + 4.88599i −0.108187 + 0.157777i
\(960\) −15.6990 1.16323i −0.506683 0.0375432i
\(961\) −6.74804 + 11.6880i −0.217679 + 0.377031i
\(962\) −16.4730 9.51072i −0.531112 0.306638i
\(963\) 8.55368 + 28.0818i 0.275639 + 0.904925i
\(964\) −6.53457 + 3.77273i −0.210464 + 0.121512i
\(965\) 7.98719 5.04774i 0.257117 0.162492i
\(966\) −4.77213 13.8341i −0.153541 0.445105i
\(967\) −26.1648 15.1062i −0.841402 0.485784i 0.0163387 0.999867i \(-0.494799\pi\)
−0.857740 + 0.514083i \(0.828132\pi\)
\(968\) −28.9034 −0.928992
\(969\) −1.59561 0.182634i −0.0512584 0.00586705i
\(970\) −23.6543 + 0.946760i −0.759493 + 0.0303986i
\(971\) 19.7231 + 34.1613i 0.632943 + 1.09629i 0.986947 + 0.161045i \(0.0514866\pi\)
−0.354004 + 0.935244i \(0.615180\pi\)
\(972\) −0.947464 + 20.4830i −0.0303899 + 0.656994i
\(973\) 35.6312 17.0424i 1.14228 0.546353i
\(974\) −10.2850 + 5.93807i −0.329554 + 0.190268i
\(975\) −25.9578 + 41.6290i −0.831314 + 1.33319i
\(976\) −2.70151 + 1.55972i −0.0864732 + 0.0499253i
\(977\) 5.01299 + 8.68275i 0.160380 + 0.277786i 0.935005 0.354635i \(-0.115395\pi\)
−0.774625 + 0.632421i \(0.782061\pi\)
\(978\) 1.30981 11.4433i 0.0418830 0.365917i
\(979\) 5.57402 3.21816i 0.178147 0.102853i
\(980\) −12.2713 + 16.5327i −0.391992 + 0.528116i
\(981\) 11.8724 12.7052i 0.379057 0.405645i
\(982\) 26.1615 15.1044i 0.834848 0.482000i
\(983\) 36.8586i 1.17561i 0.809004 + 0.587803i \(0.200007\pi\)
−0.809004 + 0.587803i \(0.799993\pi\)
\(984\) 20.9058 28.2220i 0.666452 0.899683i
\(985\) −9.47990 + 0.379432i −0.302055 + 0.0120897i
\(986\) 0.363154 0.629001i 0.0115652 0.0200315i
\(987\) 3.02445 1.04330i 0.0962693 0.0332085i
\(988\) −42.6063 + 24.5987i −1.35549 + 0.782590i
\(989\) −5.67194 + 3.27469i −0.180357 + 0.104129i
\(990\) −2.86212 2.46767i −0.0909643 0.0784278i
\(991\) −2.19100 + 3.79492i −0.0695994 + 0.120550i −0.898725 0.438513i \(-0.855505\pi\)
0.829126 + 0.559062i \(0.188839\pi\)
\(992\) 20.9609 + 12.1018i 0.665509 + 0.384232i
\(993\) −22.2543 + 30.0424i −0.706219 + 0.953367i
\(994\) −26.8201 + 12.8280i −0.850683 + 0.406881i
\(995\) 20.6498 + 10.8450i 0.654641 + 0.343811i
\(996\) −13.5136 10.0104i −0.428195 0.317191i
\(997\) −42.0185 −1.33074 −0.665370 0.746514i \(-0.731726\pi\)
−0.665370 + 0.746514i \(0.731726\pi\)
\(998\) 0.131611 0.227957i 0.00416607 0.00721584i
\(999\) 20.7399 3.81060i 0.656183 0.120562i
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 315.2.u.a.59.17 88
3.2 odd 2 945.2.u.a.584.28 88
5.4 even 2 inner 315.2.u.a.59.28 yes 88
7.5 odd 6 315.2.bq.a.194.28 yes 88
9.2 odd 6 315.2.bq.a.164.17 yes 88
9.7 even 3 945.2.bq.a.899.28 88
15.14 odd 2 945.2.u.a.584.17 88
21.5 even 6 945.2.bq.a.719.17 88
35.19 odd 6 315.2.bq.a.194.17 yes 88
45.29 odd 6 315.2.bq.a.164.28 yes 88
45.34 even 6 945.2.bq.a.899.17 88
63.47 even 6 inner 315.2.u.a.299.28 yes 88
63.61 odd 6 945.2.u.a.89.17 88
105.89 even 6 945.2.bq.a.719.28 88
315.124 odd 6 945.2.u.a.89.28 88
315.299 even 6 inner 315.2.u.a.299.17 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.u.a.59.17 88 1.1 even 1 trivial
315.2.u.a.59.28 yes 88 5.4 even 2 inner
315.2.u.a.299.17 yes 88 315.299 even 6 inner
315.2.u.a.299.28 yes 88 63.47 even 6 inner
315.2.bq.a.164.17 yes 88 9.2 odd 6
315.2.bq.a.164.28 yes 88 45.29 odd 6
315.2.bq.a.194.17 yes 88 35.19 odd 6
315.2.bq.a.194.28 yes 88 7.5 odd 6
945.2.u.a.89.17 88 63.61 odd 6
945.2.u.a.89.28 88 315.124 odd 6
945.2.u.a.584.17 88 15.14 odd 2
945.2.u.a.584.28 88 3.2 odd 2
945.2.bq.a.719.17 88 21.5 even 6
945.2.bq.a.719.28 88 105.89 even 6
945.2.bq.a.899.17 88 45.34 even 6
945.2.bq.a.899.28 88 9.7 even 3