Properties

Label 171.3.z.a.101.13
Level $171$
Weight $3$
Character 171.101
Analytic conductor $4.659$
Analytic rank $0$
Dimension $228$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [171,3,Mod(5,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([15, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.z (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: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(38\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.13
Character \(\chi\) \(=\) 171.101
Dual form 171.3.z.a.149.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65813 + 0.292373i) q^{2} +(-2.05416 - 2.18642i) q^{3} +(-1.09486 + 0.398496i) q^{4} +(-2.50704 - 2.98778i) q^{5} +(4.04531 + 3.02478i) q^{6} +(-4.44332 - 7.69605i) q^{7} +(7.53145 - 4.34828i) q^{8} +(-0.560853 + 8.98251i) q^{9} +O(q^{10})\) \(q+(-1.65813 + 0.292373i) q^{2} +(-2.05416 - 2.18642i) q^{3} +(-1.09486 + 0.398496i) q^{4} +(-2.50704 - 2.98778i) q^{5} +(4.04531 + 3.02478i) q^{6} +(-4.44332 - 7.69605i) q^{7} +(7.53145 - 4.34828i) q^{8} +(-0.560853 + 8.98251i) q^{9} +(5.03055 + 4.22113i) q^{10} +8.81040i q^{11} +(3.12030 + 1.57525i) q^{12} +(-8.50826 - 7.13928i) q^{13} +(9.61771 + 11.4619i) q^{14} +(-1.38267 + 11.6188i) q^{15} +(-7.64664 + 6.41629i) q^{16} +(7.52161 + 8.96390i) q^{17} +(-1.69628 - 15.0581i) q^{18} +(0.563651 + 18.9916i) q^{19} +(3.93548 + 2.27215i) q^{20} +(-7.69950 + 25.5239i) q^{21} +(-2.57592 - 14.6088i) q^{22} +(5.84619 + 16.0623i) q^{23} +(-24.9780 - 7.53483i) q^{24} +(1.69965 - 9.63920i) q^{25} +(16.1951 + 9.35026i) q^{26} +(20.7916 - 17.2252i) q^{27} +(7.93165 + 6.65545i) q^{28} +(11.6593 + 32.0336i) q^{29} +(-1.10439 - 19.6698i) q^{30} -21.0387 q^{31} +(-11.5570 + 13.7731i) q^{32} +(19.2632 - 18.0980i) q^{33} +(-15.0926 - 12.6642i) q^{34} +(-11.8545 + 32.5700i) q^{35} +(-2.96544 - 10.0581i) q^{36} +29.2078 q^{37} +(-6.48725 - 31.3258i) q^{38} +(1.86788 + 33.2678i) q^{39} +(-31.8734 - 11.6010i) q^{40} +(-11.1761 + 1.97065i) q^{41} +(5.30428 - 44.5730i) q^{42} +(-67.8830 - 24.7074i) q^{43} +(-3.51091 - 9.64615i) q^{44} +(28.2438 - 20.8438i) q^{45} +(-14.3899 - 24.9240i) q^{46} +(-6.02402 - 16.5509i) q^{47} +(29.7361 + 3.53866i) q^{48} +(-14.9861 + 25.9567i) q^{49} +16.4800i q^{50} +(4.14826 - 34.8587i) q^{51} +(12.1603 + 4.42600i) q^{52} +(51.8959 + 9.15064i) q^{53} +(-29.4390 + 34.6406i) q^{54} +(26.3235 - 22.0881i) q^{55} +(-66.9292 - 38.6416i) q^{56} +(40.3658 - 40.2442i) q^{57} +(-28.6984 - 49.7070i) q^{58} +(18.6114 - 51.1344i) q^{59} +(-3.11623 - 13.2720i) q^{60} +(58.9585 + 49.4721i) q^{61} +(34.8848 - 6.15113i) q^{62} +(71.6219 - 35.5958i) q^{63} +(35.1001 - 60.7951i) q^{64} +43.3193i q^{65} +(-26.6495 + 35.6408i) q^{66} +(-12.1216 + 68.7448i) q^{67} +(-11.8072 - 6.81688i) q^{68} +(23.1098 - 45.7767i) q^{69} +(10.1337 - 57.4712i) q^{70} +(-52.7164 + 9.29533i) q^{71} +(34.8345 + 70.0900i) q^{72} +(-94.3854 - 34.3535i) q^{73} +(-48.4303 + 8.53957i) q^{74} +(-24.5667 + 16.0843i) q^{75} +(-8.18522 - 20.5686i) q^{76} +(67.8052 - 39.1474i) q^{77} +(-12.8238 - 54.6163i) q^{78} +(-70.7527 + 59.3686i) q^{79} +(38.3409 + 6.76054i) q^{80} +(-80.3709 - 10.0757i) q^{81} +(17.9552 - 6.53517i) q^{82} +(-84.2519 + 48.6429i) q^{83} +(-1.74129 - 31.0133i) q^{84} +(7.92516 - 44.9458i) q^{85} +(119.783 + 21.1209i) q^{86} +(46.0889 - 91.2942i) q^{87} +(38.3101 + 66.3550i) q^{88} +(29.9699 + 82.3415i) q^{89} +(-40.7378 + 42.8195i) q^{90} +(-17.1393 + 97.2021i) q^{91} +(-12.8015 - 15.2562i) q^{92} +(43.2168 + 45.9993i) q^{93} +(14.8276 + 25.6822i) q^{94} +(55.3297 - 49.2969i) q^{95} +(53.8537 - 3.02371i) q^{96} +(20.8974 + 118.515i) q^{97} +(17.2599 - 47.4211i) q^{98} +(-79.1395 - 4.94134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21} + 81 q^{22} + 207 q^{23} - 222 q^{24} - 3 q^{25} - 216 q^{26} - 33 q^{27} - 36 q^{28} - 9 q^{29} + 171 q^{30} - 6 q^{31} - 9 q^{32} + 30 q^{33} + 33 q^{34} + 225 q^{35} - 246 q^{36} - 24 q^{37} - 9 q^{38} - 60 q^{39} - 177 q^{40} - 9 q^{41} - 15 q^{42} + 93 q^{43} + 441 q^{44} - 57 q^{45} - 6 q^{46} - 9 q^{47} - 774 q^{48} - 543 q^{49} - 81 q^{51} + 213 q^{52} + 393 q^{54} + 63 q^{55} - 459 q^{56} + 84 q^{57} - 6 q^{58} + 126 q^{59} - 333 q^{60} - 24 q^{61} - 36 q^{62} + 369 q^{63} + 372 q^{64} + 894 q^{66} + 39 q^{67} + 747 q^{68} + 231 q^{69} + 291 q^{70} + 204 q^{72} - 51 q^{73} + 333 q^{74} + 324 q^{75} - 3 q^{76} - 18 q^{77} - 1569 q^{78} - 105 q^{79} - 756 q^{80} + 1050 q^{81} + 132 q^{82} + 99 q^{83} - 69 q^{84} - 3 q^{85} - 495 q^{86} - 483 q^{87} + 387 q^{88} - 648 q^{89} - 339 q^{90} + 225 q^{91} + 27 q^{92} + 396 q^{93} - 6 q^{94} - 1305 q^{95} - 663 q^{96} - 543 q^{97} + 1125 q^{98} - 300 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65813 + 0.292373i −0.829065 + 0.146186i −0.572048 0.820220i \(-0.693851\pi\)
−0.257017 + 0.966407i \(0.582740\pi\)
\(3\) −2.05416 2.18642i −0.684720 0.728806i
\(4\) −1.09486 + 0.398496i −0.273715 + 0.0996241i
\(5\) −2.50704 2.98778i −0.501409 0.597556i 0.454672 0.890659i \(-0.349757\pi\)
−0.956081 + 0.293103i \(0.905312\pi\)
\(6\) 4.04531 + 3.02478i 0.674219 + 0.504131i
\(7\) −4.44332 7.69605i −0.634759 1.09944i −0.986566 0.163363i \(-0.947766\pi\)
0.351807 0.936073i \(-0.385567\pi\)
\(8\) 7.53145 4.34828i 0.941431 0.543535i
\(9\) −0.560853 + 8.98251i −0.0623170 + 0.998056i
\(10\) 5.03055 + 4.22113i 0.503055 + 0.422113i
\(11\) 8.81040i 0.800945i 0.916309 + 0.400473i \(0.131154\pi\)
−0.916309 + 0.400473i \(0.868846\pi\)
\(12\) 3.12030 + 1.57525i 0.260025 + 0.131271i
\(13\) −8.50826 7.13928i −0.654482 0.549175i 0.253945 0.967219i \(-0.418272\pi\)
−0.908427 + 0.418043i \(0.862716\pi\)
\(14\) 9.61771 + 11.4619i 0.686979 + 0.818710i
\(15\) −1.38267 + 11.6188i −0.0921777 + 0.774588i
\(16\) −7.64664 + 6.41629i −0.477915 + 0.401018i
\(17\) 7.52161 + 8.96390i 0.442448 + 0.527288i 0.940470 0.339875i \(-0.110385\pi\)
−0.498023 + 0.867164i \(0.665940\pi\)
\(18\) −1.69628 15.0581i −0.0942375 0.836563i
\(19\) 0.563651 + 18.9916i 0.0296658 + 0.999560i
\(20\) 3.93548 + 2.27215i 0.196774 + 0.113608i
\(21\) −7.69950 + 25.5239i −0.366643 + 1.21542i
\(22\) −2.57592 14.6088i −0.117087 0.664035i
\(23\) 5.84619 + 16.0623i 0.254182 + 0.698359i 0.999499 + 0.0316492i \(0.0100759\pi\)
−0.745317 + 0.666710i \(0.767702\pi\)
\(24\) −24.9780 7.53483i −1.04075 0.313951i
\(25\) 1.69965 9.63920i 0.0679861 0.385568i
\(26\) 16.1951 + 9.35026i 0.622890 + 0.359626i
\(27\) 20.7916 17.2252i 0.770059 0.637972i
\(28\) 7.93165 + 6.65545i 0.283273 + 0.237695i
\(29\) 11.6593 + 32.0336i 0.402044 + 1.10461i 0.961274 + 0.275595i \(0.0888747\pi\)
−0.559230 + 0.829013i \(0.688903\pi\)
\(30\) −1.10439 19.6698i −0.0368131 0.655659i
\(31\) −21.0387 −0.678666 −0.339333 0.940666i \(-0.610201\pi\)
−0.339333 + 0.940666i \(0.610201\pi\)
\(32\) −11.5570 + 13.7731i −0.361157 + 0.430410i
\(33\) 19.2632 18.0980i 0.583734 0.548423i
\(34\) −15.0926 12.6642i −0.443900 0.372476i
\(35\) −11.8545 + 32.5700i −0.338700 + 0.930571i
\(36\) −2.96544 10.0581i −0.0823734 0.279391i
\(37\) 29.2078 0.789400 0.394700 0.918810i \(-0.370849\pi\)
0.394700 + 0.918810i \(0.370849\pi\)
\(38\) −6.48725 31.3258i −0.170717 0.824363i
\(39\) 1.86788 + 33.2678i 0.0478943 + 0.853022i
\(40\) −31.8734 11.6010i −0.796835 0.290024i
\(41\) −11.1761 + 1.97065i −0.272587 + 0.0480645i −0.308271 0.951299i \(-0.599750\pi\)
0.0356834 + 0.999363i \(0.488639\pi\)
\(42\) 5.30428 44.5730i 0.126292 1.06126i
\(43\) −67.8830 24.7074i −1.57867 0.574591i −0.603759 0.797167i \(-0.706331\pi\)
−0.974915 + 0.222576i \(0.928553\pi\)
\(44\) −3.51091 9.64615i −0.0797934 0.219231i
\(45\) 28.2438 20.8438i 0.627641 0.463196i
\(46\) −14.3899 24.9240i −0.312824 0.541827i
\(47\) −6.02402 16.5509i −0.128171 0.352146i 0.858964 0.512036i \(-0.171108\pi\)
−0.987135 + 0.159890i \(0.948886\pi\)
\(48\) 29.7361 + 3.53866i 0.619503 + 0.0737222i
\(49\) −14.9861 + 25.9567i −0.305839 + 0.529729i
\(50\) 16.4800i 0.329600i
\(51\) 4.14826 34.8587i 0.0813384 0.683503i
\(52\) 12.1603 + 4.42600i 0.233852 + 0.0851153i
\(53\) 51.8959 + 9.15064i 0.979168 + 0.172654i 0.640254 0.768164i \(-0.278829\pi\)
0.338914 + 0.940817i \(0.389940\pi\)
\(54\) −29.4390 + 34.6406i −0.545166 + 0.641492i
\(55\) 26.3235 22.0881i 0.478609 0.401601i
\(56\) −66.9292 38.6416i −1.19516 0.690028i
\(57\) 40.3658 40.2442i 0.708173 0.706039i
\(58\) −28.6984 49.7070i −0.494799 0.857017i
\(59\) 18.6114 51.1344i 0.315448 0.866686i −0.676084 0.736824i \(-0.736325\pi\)
0.991532 0.129861i \(-0.0414532\pi\)
\(60\) −3.11623 13.2720i −0.0519372 0.221200i
\(61\) 58.9585 + 49.4721i 0.966533 + 0.811017i 0.982003 0.188863i \(-0.0604802\pi\)
−0.0154705 + 0.999880i \(0.504925\pi\)
\(62\) 34.8848 6.15113i 0.562658 0.0992119i
\(63\) 71.6219 35.5958i 1.13685 0.565012i
\(64\) 35.1001 60.7951i 0.548439 0.949924i
\(65\) 43.3193i 0.666451i
\(66\) −26.6495 + 35.6408i −0.403781 + 0.540012i
\(67\) −12.1216 + 68.7448i −0.180919 + 1.02604i 0.750169 + 0.661246i \(0.229972\pi\)
−0.931088 + 0.364796i \(0.881139\pi\)
\(68\) −11.8072 6.81688i −0.173635 0.100248i
\(69\) 23.1098 45.7767i 0.334925 0.663430i
\(70\) 10.1337 57.4712i 0.144767 0.821017i
\(71\) −52.7164 + 9.29533i −0.742485 + 0.130920i −0.532080 0.846694i \(-0.678589\pi\)
−0.210405 + 0.977614i \(0.567478\pi\)
\(72\) 34.8345 + 70.0900i 0.483812 + 0.973473i
\(73\) −94.3854 34.3535i −1.29295 0.470596i −0.398256 0.917274i \(-0.630385\pi\)
−0.894695 + 0.446678i \(0.852607\pi\)
\(74\) −48.4303 + 8.53957i −0.654464 + 0.115400i
\(75\) −24.5667 + 16.0843i −0.327556 + 0.214458i
\(76\) −8.18522 20.5686i −0.107700 0.270639i
\(77\) 67.8052 39.1474i 0.880588 0.508407i
\(78\) −12.8238 54.6163i −0.164408 0.700209i
\(79\) −70.7527 + 59.3686i −0.895604 + 0.751501i −0.969326 0.245778i \(-0.920957\pi\)
0.0737220 + 0.997279i \(0.476512\pi\)
\(80\) 38.3409 + 6.76054i 0.479262 + 0.0845068i
\(81\) −80.3709 10.0757i −0.992233 0.124392i
\(82\) 17.9552 6.53517i 0.218966 0.0796972i
\(83\) −84.2519 + 48.6429i −1.01508 + 0.586059i −0.912676 0.408684i \(-0.865988\pi\)
−0.102407 + 0.994743i \(0.532655\pi\)
\(84\) −1.74129 31.0133i −0.0207297 0.369206i
\(85\) 7.92516 44.9458i 0.0932372 0.528774i
\(86\) 119.783 + 21.1209i 1.39282 + 0.245592i
\(87\) 46.0889 91.2942i 0.529757 1.04936i
\(88\) 38.3101 + 66.3550i 0.435342 + 0.754035i
\(89\) 29.9699 + 82.3415i 0.336740 + 0.925186i 0.986313 + 0.164886i \(0.0527257\pi\)
−0.649573 + 0.760300i \(0.725052\pi\)
\(90\) −40.7378 + 42.8195i −0.452642 + 0.475772i
\(91\) −17.1393 + 97.2021i −0.188344 + 1.06815i
\(92\) −12.8015 15.2562i −0.139147 0.165829i
\(93\) 43.2168 + 45.9993i 0.464697 + 0.494616i
\(94\) 14.8276 + 25.6822i 0.157741 + 0.273215i
\(95\) 55.3297 49.2969i 0.582418 0.518915i
\(96\) 53.8537 3.02371i 0.560976 0.0314969i
\(97\) 20.8974 + 118.515i 0.215437 + 1.22181i 0.880146 + 0.474703i \(0.157444\pi\)
−0.664709 + 0.747102i \(0.731444\pi\)
\(98\) 17.2599 47.4211i 0.176121 0.483889i
\(99\) −79.1395 4.94134i −0.799388 0.0499125i
\(100\) 1.98031 + 11.2309i 0.0198031 + 0.112309i
\(101\) −37.0485 6.53265i −0.366817 0.0646797i −0.0127983 0.999918i \(-0.504074\pi\)
−0.354019 + 0.935238i \(0.615185\pi\)
\(102\) 3.31338 + 59.0130i 0.0324842 + 0.578559i
\(103\) −30.4971 + 52.8226i −0.296089 + 0.512840i −0.975238 0.221160i \(-0.929016\pi\)
0.679149 + 0.734000i \(0.262349\pi\)
\(104\) −95.1231 16.7728i −0.914646 0.161277i
\(105\) 95.5627 40.9850i 0.910121 0.390334i
\(106\) −88.7255 −0.837033
\(107\) 65.3314 + 37.7191i 0.610573 + 0.352515i 0.773190 0.634175i \(-0.218660\pi\)
−0.162616 + 0.986689i \(0.551993\pi\)
\(108\) −15.8997 + 27.1446i −0.147219 + 0.251339i
\(109\) 12.0318 + 68.2356i 0.110383 + 0.626014i 0.988933 + 0.148363i \(0.0474005\pi\)
−0.878550 + 0.477651i \(0.841488\pi\)
\(110\) −37.1899 + 44.3211i −0.338090 + 0.402919i
\(111\) −59.9975 63.8605i −0.540518 0.575320i
\(112\) 83.3566 + 30.3393i 0.744255 + 0.270887i
\(113\) −190.703 + 110.102i −1.68764 + 0.974358i −0.731316 + 0.682039i \(0.761093\pi\)
−0.956321 + 0.292319i \(0.905573\pi\)
\(114\) −55.1655 + 78.5320i −0.483908 + 0.688877i
\(115\) 33.3339 57.7359i 0.289860 0.502052i
\(116\) −25.5306 30.4261i −0.220091 0.262294i
\(117\) 68.9005 72.4214i 0.588893 0.618987i
\(118\) −15.9098 + 90.2290i −0.134829 + 0.764653i
\(119\) 35.5658 97.7161i 0.298872 0.821144i
\(120\) 40.1085 + 93.5188i 0.334237 + 0.779323i
\(121\) 43.3769 0.358487
\(122\) −112.225 64.7932i −0.919878 0.531092i
\(123\) 27.2661 + 20.3876i 0.221676 + 0.165753i
\(124\) 23.0344 8.38383i 0.185761 0.0676115i
\(125\) −117.504 + 67.8411i −0.940034 + 0.542729i
\(126\) −108.351 + 79.9627i −0.859929 + 0.634624i
\(127\) 103.499 37.6707i 0.814956 0.296620i 0.0992867 0.995059i \(-0.468344\pi\)
0.715670 + 0.698439i \(0.246122\pi\)
\(128\) −15.8282 + 43.4877i −0.123658 + 0.339747i
\(129\) 85.4219 + 199.174i 0.662185 + 1.54398i
\(130\) −12.6654 71.8290i −0.0974261 0.552531i
\(131\) 72.1862 198.330i 0.551040 1.51397i −0.281254 0.959633i \(-0.590750\pi\)
0.832293 0.554335i \(-0.187027\pi\)
\(132\) −13.8785 + 27.4911i −0.105140 + 0.208266i
\(133\) 143.656 88.7237i 1.08012 0.667096i
\(134\) 117.532i 0.877103i
\(135\) −103.591 18.9363i −0.767339 0.140269i
\(136\) 95.6262 + 34.8051i 0.703134 + 0.255920i
\(137\) −160.308 + 191.047i −1.17013 + 1.39451i −0.267791 + 0.963477i \(0.586294\pi\)
−0.902338 + 0.431029i \(0.858151\pi\)
\(138\) −24.9352 + 82.6603i −0.180690 + 0.598988i
\(139\) −22.4269 18.8184i −0.161344 0.135384i 0.558541 0.829477i \(-0.311361\pi\)
−0.719886 + 0.694093i \(0.755806\pi\)
\(140\) 40.3835i 0.288454i
\(141\) −23.8128 + 47.1691i −0.168885 + 0.334533i
\(142\) 84.6930 30.8257i 0.596429 0.217082i
\(143\) 62.8999 74.9612i 0.439859 0.524204i
\(144\) −53.3458 72.2846i −0.370457 0.501977i
\(145\) 66.4790 115.145i 0.458476 0.794104i
\(146\) 166.547 + 29.3668i 1.14073 + 0.201142i
\(147\) 87.5361 20.5533i 0.595483 0.139818i
\(148\) −31.9784 + 11.6392i −0.216071 + 0.0786432i
\(149\) 38.9188 6.86244i 0.261200 0.0460566i −0.0415144 0.999138i \(-0.513218\pi\)
0.302714 + 0.953081i \(0.402107\pi\)
\(150\) 36.0321 33.8525i 0.240214 0.225683i
\(151\) −101.770 + 176.271i −0.673974 + 1.16736i 0.302794 + 0.953056i \(0.402081\pi\)
−0.976768 + 0.214301i \(0.931253\pi\)
\(152\) 86.8261 + 140.584i 0.571224 + 0.924892i
\(153\) −84.7368 + 62.5355i −0.553836 + 0.408729i
\(154\) −100.984 + 84.7358i −0.655742 + 0.550233i
\(155\) 52.7449 + 62.8589i 0.340289 + 0.405541i
\(156\) −15.3022 35.6793i −0.0980909 0.228713i
\(157\) 140.985 118.300i 0.897993 0.753506i −0.0718039 0.997419i \(-0.522876\pi\)
0.969797 + 0.243913i \(0.0784311\pi\)
\(158\) 99.9594 119.127i 0.632655 0.753968i
\(159\) −86.5953 132.263i −0.544625 0.831843i
\(160\) 70.1249 0.438281
\(161\) 97.6395 116.362i 0.606457 0.722747i
\(162\) 136.211 6.79141i 0.840810 0.0419223i
\(163\) −81.8983 141.852i −0.502444 0.870258i −0.999996 0.00282394i \(-0.999101\pi\)
0.497552 0.867434i \(-0.334232\pi\)
\(164\) 11.4510 6.61121i 0.0698229 0.0403123i
\(165\) −102.366 12.1818i −0.620403 0.0738293i
\(166\) 125.479 105.289i 0.755896 0.634272i
\(167\) 10.7711 + 29.5933i 0.0644974 + 0.177205i 0.967755 0.251894i \(-0.0810534\pi\)
−0.903257 + 0.429099i \(0.858831\pi\)
\(168\) 52.9966 + 225.711i 0.315456 + 1.34352i
\(169\) −7.92533 44.9468i −0.0468954 0.265957i
\(170\) 76.8431i 0.452018i
\(171\) −170.909 5.58852i −0.999466 0.0326814i
\(172\) 84.1682 0.489350
\(173\) 323.216 56.9917i 1.86830 0.329432i 0.879175 0.476499i \(-0.158095\pi\)
0.989126 + 0.147068i \(0.0469835\pi\)
\(174\) −49.7293 + 164.853i −0.285801 + 0.947430i
\(175\) −81.7359 + 29.7494i −0.467062 + 0.169997i
\(176\) −56.5301 67.3699i −0.321194 0.382784i
\(177\) −150.032 + 64.3460i −0.847639 + 0.363537i
\(178\) −73.7683 127.771i −0.414429 0.717812i
\(179\) −200.240 + 115.609i −1.11866 + 0.645859i −0.941059 0.338243i \(-0.890167\pi\)
−0.177602 + 0.984102i \(0.556834\pi\)
\(180\) −22.6168 + 34.0761i −0.125649 + 0.189312i
\(181\) −121.661 102.086i −0.672162 0.564011i 0.241542 0.970390i \(-0.422347\pi\)
−0.913705 + 0.406379i \(0.866791\pi\)
\(182\) 166.185i 0.913103i
\(183\) −12.9436 230.532i −0.0707299 1.25974i
\(184\) 113.874 + 95.5512i 0.618878 + 0.519300i
\(185\) −73.2253 87.2665i −0.395812 0.471711i
\(186\) −85.1080 63.6374i −0.457570 0.342137i
\(187\) −78.9755 + 66.2684i −0.422329 + 0.354376i
\(188\) 13.1909 + 15.7203i 0.0701644 + 0.0836187i
\(189\) −224.950 83.4760i −1.19021 0.441672i
\(190\) −77.3307 + 97.9176i −0.407004 + 0.515356i
\(191\) −15.2148 8.78425i −0.0796584 0.0459908i 0.459642 0.888104i \(-0.347978\pi\)
−0.539300 + 0.842114i \(0.681311\pi\)
\(192\) −205.025 + 48.1395i −1.06784 + 0.250726i
\(193\) −7.79637 44.2154i −0.0403957 0.229095i 0.957925 0.287017i \(-0.0926637\pi\)
−0.998321 + 0.0579218i \(0.981553\pi\)
\(194\) −69.3012 190.404i −0.357223 0.981461i
\(195\) 94.7141 88.9848i 0.485713 0.456332i
\(196\) 6.06403 34.3908i 0.0309390 0.175464i
\(197\) −17.8065 10.2806i −0.0903886 0.0521859i 0.454124 0.890938i \(-0.349952\pi\)
−0.544513 + 0.838752i \(0.683285\pi\)
\(198\) 132.668 14.9449i 0.670041 0.0754791i
\(199\) −280.463 235.336i −1.40936 1.18259i −0.956759 0.290882i \(-0.906051\pi\)
−0.452602 0.891713i \(-0.649504\pi\)
\(200\) −29.1131 79.9877i −0.145566 0.399939i
\(201\) 175.205 114.710i 0.871664 0.570697i
\(202\) 63.3412 0.313570
\(203\) 194.726 232.066i 0.959243 1.14318i
\(204\) 9.34929 + 39.8184i 0.0458299 + 0.195188i
\(205\) 33.9068 + 28.4512i 0.165399 + 0.138786i
\(206\) 35.1243 96.5032i 0.170506 0.468462i
\(207\) −147.558 + 43.5048i −0.712842 + 0.210168i
\(208\) 110.867 0.533016
\(209\) −167.324 + 4.96599i −0.800593 + 0.0237607i
\(210\) −146.472 + 95.8984i −0.697487 + 0.456659i
\(211\) −56.4992 20.5640i −0.267769 0.0974599i 0.204647 0.978836i \(-0.434396\pi\)
−0.472415 + 0.881376i \(0.656618\pi\)
\(212\) −60.4652 + 10.6616i −0.285213 + 0.0502908i
\(213\) 128.611 + 96.1661i 0.603810 + 0.451484i
\(214\) −119.356 43.4420i −0.557738 0.203000i
\(215\) 96.3655 + 264.762i 0.448212 + 1.23145i
\(216\) 81.6906 220.139i 0.378197 1.01916i
\(217\) 93.4814 + 161.915i 0.430790 + 0.746150i
\(218\) −39.9005 109.626i −0.183030 0.502870i
\(219\) 118.772 + 276.934i 0.542336 + 1.26454i
\(220\) −20.0186 + 34.6731i −0.0909934 + 0.157605i
\(221\) 129.966i 0.588082i
\(222\) 118.155 + 88.3473i 0.532228 + 0.397961i
\(223\) 141.135 + 51.3690i 0.632893 + 0.230354i 0.638490 0.769630i \(-0.279559\pi\)
−0.00559674 + 0.999984i \(0.501782\pi\)
\(224\) 157.350 + 27.7450i 0.702455 + 0.123862i
\(225\) 85.6310 + 20.6733i 0.380582 + 0.0918814i
\(226\) 284.019 238.320i 1.25672 1.05452i
\(227\) −196.196 113.274i −0.864300 0.499004i 0.00114966 0.999999i \(-0.499634\pi\)
−0.865450 + 0.500995i \(0.832967\pi\)
\(228\) −28.1577 + 60.1474i −0.123499 + 0.263805i
\(229\) 180.354 + 312.381i 0.787570 + 1.36411i 0.927452 + 0.373943i \(0.121994\pi\)
−0.139882 + 0.990168i \(0.544672\pi\)
\(230\) −38.3914 + 105.480i −0.166919 + 0.458607i
\(231\) −224.875 67.8357i −0.973486 0.293661i
\(232\) 227.102 + 190.562i 0.978890 + 0.821386i
\(233\) −120.547 + 21.2556i −0.517368 + 0.0912259i −0.426234 0.904613i \(-0.640160\pi\)
−0.0911335 + 0.995839i \(0.529049\pi\)
\(234\) −93.0719 + 140.229i −0.397743 + 0.599268i
\(235\) −34.3478 + 59.4922i −0.146161 + 0.253158i
\(236\) 63.4016i 0.268651i
\(237\) 275.142 + 32.7425i 1.16094 + 0.138154i
\(238\) −30.4031 + 172.424i −0.127744 + 0.724472i
\(239\) 89.0446 + 51.4099i 0.372572 + 0.215104i 0.674581 0.738201i \(-0.264324\pi\)
−0.302010 + 0.953305i \(0.597658\pi\)
\(240\) −63.9771 97.7166i −0.266571 0.407152i
\(241\) 34.1761 193.822i 0.141809 0.804241i −0.828064 0.560633i \(-0.810558\pi\)
0.969874 0.243608i \(-0.0783311\pi\)
\(242\) −71.9245 + 12.6822i −0.297209 + 0.0524059i
\(243\) 143.065 + 196.422i 0.588744 + 0.808319i
\(244\) −84.2657 30.6702i −0.345351 0.125698i
\(245\) 115.124 20.2994i 0.469893 0.0828548i
\(246\) −51.1715 25.8334i −0.208014 0.105014i
\(247\) 130.791 165.610i 0.529518 0.670485i
\(248\) −158.452 + 91.4820i −0.638918 + 0.368879i
\(249\) 279.421 + 84.2897i 1.12217 + 0.338513i
\(250\) 175.002 146.844i 0.700009 0.587377i
\(251\) −100.093 17.6492i −0.398779 0.0703154i −0.0293375 0.999570i \(-0.509340\pi\)
−0.369441 + 0.929254i \(0.620451\pi\)
\(252\) −64.2311 + 67.5134i −0.254885 + 0.267910i
\(253\) −141.515 + 51.5072i −0.559348 + 0.203586i
\(254\) −160.602 + 92.7234i −0.632290 + 0.365053i
\(255\) −114.550 + 74.9982i −0.449215 + 0.294110i
\(256\) −35.2299 + 199.799i −0.137617 + 0.780464i
\(257\) 333.259 + 58.7625i 1.29673 + 0.228648i 0.779068 0.626939i \(-0.215693\pi\)
0.517659 + 0.855587i \(0.326804\pi\)
\(258\) −199.873 305.281i −0.774703 1.18326i
\(259\) −129.779 224.785i −0.501079 0.867894i
\(260\) −17.2626 47.4286i −0.0663945 0.182418i
\(261\) −294.281 + 86.7634i −1.12751 + 0.332427i
\(262\) −61.7077 + 349.962i −0.235526 + 1.33573i
\(263\) −45.3299 54.0221i −0.172357 0.205407i 0.672950 0.739688i \(-0.265027\pi\)
−0.845307 + 0.534281i \(0.820583\pi\)
\(264\) 66.3848 220.066i 0.251458 0.833583i
\(265\) −102.765 177.995i −0.387793 0.671677i
\(266\) −212.260 + 189.117i −0.797970 + 0.710965i
\(267\) 118.470 234.669i 0.443708 0.878911i
\(268\) −14.1231 80.0963i −0.0526983 0.298867i
\(269\) −2.52172 + 6.92838i −0.00937443 + 0.0257560i −0.944292 0.329110i \(-0.893251\pi\)
0.934917 + 0.354866i \(0.115474\pi\)
\(270\) 177.303 + 1.11164i 0.656679 + 0.00411719i
\(271\) 21.0870 + 119.590i 0.0778119 + 0.441293i 0.998677 + 0.0514130i \(0.0163725\pi\)
−0.920866 + 0.389880i \(0.872516\pi\)
\(272\) −115.030 20.2829i −0.422905 0.0745695i
\(273\) 247.731 162.195i 0.907441 0.594120i
\(274\) 209.954 363.651i 0.766255 1.32719i
\(275\) 84.9252 + 14.9746i 0.308819 + 0.0544531i
\(276\) −7.06019 + 59.3282i −0.0255804 + 0.214957i
\(277\) 9.64082 0.0348044 0.0174022 0.999849i \(-0.494460\pi\)
0.0174022 + 0.999849i \(0.494460\pi\)
\(278\) 42.6887 + 24.6463i 0.153556 + 0.0886558i
\(279\) 11.7996 188.980i 0.0422925 0.677347i
\(280\) 52.3419 + 296.846i 0.186935 + 1.06016i
\(281\) −234.004 + 278.875i −0.832754 + 0.992437i 0.167225 + 0.985919i \(0.446519\pi\)
−0.999979 + 0.00651863i \(0.997925\pi\)
\(282\) 25.6937 85.1748i 0.0911125 0.302038i
\(283\) −292.793 106.568i −1.03460 0.376565i −0.231772 0.972770i \(-0.574452\pi\)
−0.802832 + 0.596205i \(0.796675\pi\)
\(284\) 54.0129 31.1844i 0.190186 0.109804i
\(285\) −221.440 19.7101i −0.776982 0.0691583i
\(286\) −82.3795 + 142.686i −0.288040 + 0.498900i
\(287\) 64.8251 + 77.2555i 0.225871 + 0.269183i
\(288\) −117.235 111.536i −0.407067 0.387276i
\(289\) 26.4073 149.764i 0.0913749 0.518213i
\(290\) −76.5655 + 210.362i −0.264019 + 0.725386i
\(291\) 216.197 289.139i 0.742945 0.993606i
\(292\) 117.029 0.400783
\(293\) 164.392 + 94.9120i 0.561066 + 0.323932i 0.753573 0.657364i \(-0.228328\pi\)
−0.192507 + 0.981296i \(0.561662\pi\)
\(294\) −139.137 + 59.6732i −0.473255 + 0.202970i
\(295\) −199.438 + 72.5895i −0.676061 + 0.246066i
\(296\) 219.977 127.004i 0.743166 0.429067i
\(297\) 151.761 + 183.182i 0.510981 + 0.616775i
\(298\) −62.5260 + 22.7576i −0.209819 + 0.0763678i
\(299\) 64.9321 178.400i 0.217164 0.596654i
\(300\) 20.4875 27.3998i 0.0682918 0.0913327i
\(301\) 111.476 + 632.214i 0.370353 + 2.10038i
\(302\) 117.211 322.035i 0.388116 1.06634i
\(303\) 61.8205 + 94.4227i 0.204028 + 0.311626i
\(304\) −126.166 141.606i −0.415020 0.465808i
\(305\) 300.184i 0.984209i
\(306\) 122.221 128.467i 0.399415 0.419826i
\(307\) −121.994 44.4021i −0.397374 0.144632i 0.135600 0.990764i \(-0.456704\pi\)
−0.532975 + 0.846131i \(0.678926\pi\)
\(308\) −58.6371 + 69.8810i −0.190380 + 0.226886i
\(309\) 178.138 41.8265i 0.576499 0.135361i
\(310\) −105.836 88.8070i −0.341407 0.286474i
\(311\) 548.443i 1.76348i 0.471733 + 0.881742i \(0.343629\pi\)
−0.471733 + 0.881742i \(0.656371\pi\)
\(312\) 158.726 + 242.433i 0.508737 + 0.777029i
\(313\) −378.572 + 137.789i −1.20950 + 0.440220i −0.866529 0.499127i \(-0.833654\pi\)
−0.342967 + 0.939348i \(0.611432\pi\)
\(314\) −199.183 + 237.378i −0.634342 + 0.755979i
\(315\) −285.911 124.750i −0.907655 0.396032i
\(316\) 53.8061 93.1950i 0.170273 0.294921i
\(317\) 244.528 + 43.1169i 0.771381 + 0.136015i 0.545468 0.838132i \(-0.316352\pi\)
0.225914 + 0.974147i \(0.427463\pi\)
\(318\) 182.256 + 193.991i 0.573133 + 0.610035i
\(319\) −282.229 + 102.723i −0.884730 + 0.322015i
\(320\) −269.640 + 47.5448i −0.842625 + 0.148578i
\(321\) −51.7314 220.323i −0.161157 0.686364i
\(322\) −127.878 + 221.491i −0.397136 + 0.687860i
\(323\) −166.000 + 147.900i −0.513931 + 0.457895i
\(324\) 92.0100 20.9960i 0.283981 0.0648024i
\(325\) −83.2780 + 69.8786i −0.256240 + 0.215011i
\(326\) 177.272 + 211.264i 0.543778 + 0.648050i
\(327\) 124.476 166.473i 0.380662 0.509093i
\(328\) −75.6032 + 63.4386i −0.230497 + 0.193410i
\(329\) −100.610 + 119.902i −0.305804 + 0.364443i
\(330\) 173.298 9.73013i 0.525147 0.0294852i
\(331\) 288.177 0.870625 0.435312 0.900280i \(-0.356638\pi\)
0.435312 + 0.900280i \(0.356638\pi\)
\(332\) 72.8600 86.8312i 0.219458 0.261540i
\(333\) −16.3813 + 262.359i −0.0491930 + 0.787866i
\(334\) −26.5121 45.9203i −0.0793775 0.137486i
\(335\) 235.784 136.130i 0.703832 0.406357i
\(336\) −104.893 244.574i −0.312182 0.727899i
\(337\) 282.055 236.672i 0.836958 0.702291i −0.119919 0.992784i \(-0.538264\pi\)
0.956877 + 0.290492i \(0.0938191\pi\)
\(338\) 26.2824 + 72.2104i 0.0777587 + 0.213640i
\(339\) 632.464 + 190.789i 1.86568 + 0.562798i
\(340\) 9.23380 + 52.3675i 0.0271582 + 0.154022i
\(341\) 185.359i 0.543575i
\(342\) 285.023 40.7026i 0.833399 0.119013i
\(343\) −169.093 −0.492982
\(344\) −618.692 + 109.092i −1.79852 + 0.317128i
\(345\) −194.708 + 45.7171i −0.564371 + 0.132513i
\(346\) −519.271 + 188.999i −1.50078 + 0.546241i
\(347\) 335.079 + 399.332i 0.965647 + 1.15081i 0.988522 + 0.151075i \(0.0482734\pi\)
−0.0228756 + 0.999738i \(0.507282\pi\)
\(348\) −14.0804 + 118.321i −0.0404610 + 0.340002i
\(349\) 208.572 + 361.257i 0.597628 + 1.03512i 0.993170 + 0.116674i \(0.0372232\pi\)
−0.395543 + 0.918448i \(0.629443\pi\)
\(350\) 126.831 73.2257i 0.362373 0.209216i
\(351\) −299.876 1.88014i −0.854348 0.00535652i
\(352\) −121.347 101.822i −0.344734 0.289267i
\(353\) 339.929i 0.962972i −0.876454 0.481486i \(-0.840097\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(354\) 229.960 150.559i 0.649604 0.425309i
\(355\) 159.935 + 134.201i 0.450521 + 0.378032i
\(356\) −65.6256 78.2095i −0.184342 0.219690i
\(357\) −286.706 + 122.963i −0.803098 + 0.344434i
\(358\) 298.223 250.239i 0.833026 0.698992i
\(359\) 62.8804 + 74.9380i 0.175154 + 0.208741i 0.846478 0.532423i \(-0.178718\pi\)
−0.671324 + 0.741164i \(0.734274\pi\)
\(360\) 122.082 279.796i 0.339117 0.777212i
\(361\) −360.365 + 21.4093i −0.998240 + 0.0593056i
\(362\) 231.577 + 133.701i 0.639717 + 0.369341i
\(363\) −89.1031 94.8401i −0.245463 0.261267i
\(364\) −19.9695 113.253i −0.0548612 0.311133i
\(365\) 133.988 + 368.129i 0.367090 + 1.00857i
\(366\) 88.8633 + 378.467i 0.242796 + 1.03406i
\(367\) 99.5311 564.469i 0.271202 1.53806i −0.479571 0.877503i \(-0.659208\pi\)
0.750773 0.660560i \(-0.229681\pi\)
\(368\) −147.764 85.3115i −0.401532 0.231825i
\(369\) −11.4332 101.495i −0.0309843 0.275053i
\(370\) 146.931 + 123.290i 0.397112 + 0.333216i
\(371\) −160.166 440.052i −0.431714 1.18613i
\(372\) −65.6469 33.1411i −0.176470 0.0890889i
\(373\) −584.045 −1.56580 −0.782902 0.622145i \(-0.786261\pi\)
−0.782902 + 0.622145i \(0.786261\pi\)
\(374\) 111.577 132.972i 0.298333 0.355540i
\(375\) 389.701 + 117.557i 1.03920 + 0.313485i
\(376\) −117.337 98.4578i −0.312068 0.261856i
\(377\) 129.497 355.789i 0.343493 0.943738i
\(378\) 397.402 + 72.6447i 1.05133 + 0.192182i
\(379\) −181.268 −0.478278 −0.239139 0.970985i \(-0.576865\pi\)
−0.239139 + 0.970985i \(0.576865\pi\)
\(380\) −40.9336 + 76.0219i −0.107720 + 0.200058i
\(381\) −294.968 148.911i −0.774195 0.390844i
\(382\) 27.7963 + 10.1170i 0.0727652 + 0.0264844i
\(383\) −557.469 + 98.2968i −1.45553 + 0.256650i −0.844755 0.535153i \(-0.820254\pi\)
−0.610777 + 0.791803i \(0.709143\pi\)
\(384\) 127.596 54.7235i 0.332281 0.142509i
\(385\) −286.954 104.443i −0.745336 0.271280i
\(386\) 25.8548 + 71.0354i 0.0669813 + 0.184030i
\(387\) 260.007 595.902i 0.671852 1.53980i
\(388\) −70.1076 121.430i −0.180690 0.312964i
\(389\) 38.7263 + 106.400i 0.0995534 + 0.273521i 0.979464 0.201618i \(-0.0646200\pi\)
−0.879911 + 0.475139i \(0.842398\pi\)
\(390\) −131.032 + 175.240i −0.335978 + 0.449334i
\(391\) −100.008 + 173.219i −0.255775 + 0.443015i
\(392\) 260.655i 0.664937i
\(393\) −581.914 + 249.572i −1.48070 + 0.635044i
\(394\) 32.5313 + 11.8404i 0.0825668 + 0.0300519i
\(395\) 354.761 + 62.5539i 0.898128 + 0.158364i
\(396\) 88.6157 26.1267i 0.223777 0.0659765i
\(397\) 408.027 342.375i 1.02778 0.862406i 0.0371905 0.999308i \(-0.488159\pi\)
0.990585 + 0.136903i \(0.0437147\pi\)
\(398\) 533.850 + 308.218i 1.34133 + 0.774418i
\(399\) −489.080 131.840i −1.22576 0.330425i
\(400\) 48.8513 + 84.6130i 0.122128 + 0.211532i
\(401\) −218.167 + 599.408i −0.544057 + 1.49478i 0.297557 + 0.954704i \(0.403828\pi\)
−0.841614 + 0.540080i \(0.818394\pi\)
\(402\) −256.974 + 241.429i −0.639238 + 0.600570i
\(403\) 179.002 + 150.201i 0.444175 + 0.372707i
\(404\) 43.1662 7.61136i 0.106847 0.0188400i
\(405\) 171.389 + 265.391i 0.423184 + 0.655286i
\(406\) −255.032 + 441.728i −0.628157 + 1.08800i
\(407\) 257.332i 0.632266i
\(408\) −120.333 280.574i −0.294934 0.687682i
\(409\) −84.1442 + 477.206i −0.205732 + 1.16676i 0.690553 + 0.723282i \(0.257367\pi\)
−0.896284 + 0.443480i \(0.853744\pi\)
\(410\) −64.5402 37.2623i −0.157415 0.0908837i
\(411\) 747.007 41.9419i 1.81754 0.102049i
\(412\) 12.3405 69.9863i 0.0299526 0.169870i
\(413\) −476.230 + 83.9721i −1.15310 + 0.203322i
\(414\) 231.951 115.279i 0.560268 0.278451i
\(415\) 356.557 + 129.776i 0.859175 + 0.312714i
\(416\) 196.660 34.6765i 0.472741 0.0833569i
\(417\) 4.92353 + 87.6905i 0.0118070 + 0.210289i
\(418\) 275.993 57.1552i 0.660270 0.136735i
\(419\) 358.693 207.091i 0.856069 0.494252i −0.00662482 0.999978i \(-0.502109\pi\)
0.862694 + 0.505726i \(0.168775\pi\)
\(420\) −88.2953 + 82.9542i −0.210227 + 0.197510i
\(421\) 245.382 205.900i 0.582856 0.489074i −0.303028 0.952982i \(-0.597998\pi\)
0.885884 + 0.463908i \(0.153553\pi\)
\(422\) 99.6954 + 17.5790i 0.236245 + 0.0416564i
\(423\) 152.047 44.8282i 0.359449 0.105977i
\(424\) 430.641 156.740i 1.01566 0.369671i
\(425\) 99.1890 57.2668i 0.233386 0.134745i
\(426\) −241.371 121.853i −0.566598 0.286041i
\(427\) 118.768 673.568i 0.278146 1.57744i
\(428\) −86.5596 15.2628i −0.202242 0.0356607i
\(429\) −293.103 + 16.4567i −0.683224 + 0.0383607i
\(430\) −237.196 410.835i −0.551618 0.955430i
\(431\) 107.637 + 295.730i 0.249738 + 0.686150i 0.999696 + 0.0246639i \(0.00785154\pi\)
−0.749958 + 0.661486i \(0.769926\pi\)
\(432\) −48.4637 + 265.120i −0.112184 + 0.613705i
\(433\) 134.690 763.863i 0.311062 1.76412i −0.282439 0.959285i \(-0.591143\pi\)
0.593501 0.804833i \(-0.297745\pi\)
\(434\) −202.344 241.144i −0.466230 0.555631i
\(435\) −388.314 + 91.1754i −0.892675 + 0.209599i
\(436\) −40.3647 69.9138i −0.0925797 0.160353i
\(437\) −301.754 + 120.082i −0.690512 + 0.274788i
\(438\) −277.907 424.466i −0.634490 0.969101i
\(439\) −116.154 658.742i −0.264588 1.50055i −0.770207 0.637795i \(-0.779847\pi\)
0.505619 0.862757i \(-0.331264\pi\)
\(440\) 102.209 280.817i 0.232293 0.638221i
\(441\) −224.751 149.171i −0.509640 0.338256i
\(442\) 37.9986 + 215.501i 0.0859696 + 0.487558i
\(443\) 437.039 + 77.0618i 0.986545 + 0.173954i 0.643568 0.765389i \(-0.277454\pi\)
0.342977 + 0.939344i \(0.388565\pi\)
\(444\) 91.1370 + 46.0095i 0.205264 + 0.103625i
\(445\) 170.883 295.977i 0.384006 0.665117i
\(446\) −249.039 43.9124i −0.558384 0.0984582i
\(447\) −94.9496 70.9963i −0.212415 0.158828i
\(448\) −623.843 −1.39251
\(449\) −183.951 106.204i −0.409691 0.236535i 0.280966 0.959718i \(-0.409345\pi\)
−0.690657 + 0.723183i \(0.742678\pi\)
\(450\) −148.032 9.24284i −0.328959 0.0205397i
\(451\) −17.3622 98.4658i −0.0384970 0.218328i
\(452\) 164.918 196.541i 0.364862 0.434825i
\(453\) 594.454 139.577i 1.31226 0.308116i
\(454\) 358.437 + 130.460i 0.789508 + 0.287358i
\(455\) 333.387 192.481i 0.732720 0.423036i
\(456\) 129.020 478.619i 0.282938 1.04960i
\(457\) −410.811 + 711.546i −0.898930 + 1.55699i −0.0700663 + 0.997542i \(0.522321\pi\)
−0.828864 + 0.559450i \(0.811012\pi\)
\(458\) −390.381 465.238i −0.852361 1.01580i
\(459\) 310.792 + 56.8124i 0.677106 + 0.123774i
\(460\) −13.4883 + 76.4962i −0.0293225 + 0.166296i
\(461\) 155.222 426.469i 0.336707 0.925096i −0.649614 0.760264i \(-0.725070\pi\)
0.986322 0.164832i \(-0.0527081\pi\)
\(462\) 392.706 + 46.7328i 0.850012 + 0.101153i
\(463\) −656.278 −1.41745 −0.708723 0.705486i \(-0.750729\pi\)
−0.708723 + 0.705486i \(0.750729\pi\)
\(464\) −294.691 170.140i −0.635111 0.366681i
\(465\) 29.0894 244.445i 0.0625579 0.525687i
\(466\) 193.667 70.4892i 0.415595 0.151264i
\(467\) −192.950 + 111.400i −0.413170 + 0.238544i −0.692151 0.721753i \(-0.743337\pi\)
0.278981 + 0.960297i \(0.410003\pi\)
\(468\) −46.5767 + 106.748i −0.0995229 + 0.228094i
\(469\) 582.923 212.167i 1.24291 0.452381i
\(470\) 39.5592 108.688i 0.0841686 0.231251i
\(471\) −548.260 65.2441i −1.16403 0.138523i
\(472\) −82.1761 466.044i −0.174102 0.987381i
\(473\) 217.682 598.076i 0.460216 1.26443i
\(474\) −465.794 + 26.1528i −0.982688 + 0.0551746i
\(475\) 184.022 + 26.8460i 0.387415 + 0.0565179i
\(476\) 121.158i 0.254534i
\(477\) −111.302 + 461.023i −0.233337 + 0.966505i
\(478\) −162.678 59.2101i −0.340331 0.123870i
\(479\) 106.133 126.484i 0.221571 0.264058i −0.643795 0.765198i \(-0.722641\pi\)
0.865367 + 0.501139i \(0.167086\pi\)
\(480\) −144.048 153.322i −0.300100 0.319422i
\(481\) −248.508 208.523i −0.516648 0.433519i
\(482\) 331.374i 0.687499i
\(483\) −454.984 + 25.5458i −0.941996 + 0.0528899i
\(484\) −47.4916 + 17.2855i −0.0981232 + 0.0357139i
\(485\) 301.706 359.559i 0.622075 0.741360i
\(486\) −294.648 283.864i −0.606273 0.584082i
\(487\) 100.794 174.580i 0.206969 0.358481i −0.743789 0.668414i \(-0.766973\pi\)
0.950758 + 0.309933i \(0.100307\pi\)
\(488\) 659.161 + 116.228i 1.35074 + 0.238172i
\(489\) −141.916 + 470.451i −0.290216 + 0.962067i
\(490\) −184.955 + 67.3181i −0.377459 + 0.137384i
\(491\) −553.118 + 97.5296i −1.12651 + 0.198635i −0.705699 0.708512i \(-0.749367\pi\)
−0.420815 + 0.907147i \(0.638256\pi\)
\(492\) −37.9770 11.4561i −0.0771889 0.0232847i
\(493\) −199.450 + 345.457i −0.404563 + 0.700724i
\(494\) −168.448 + 312.842i −0.340989 + 0.633284i
\(495\) 183.643 + 248.839i 0.370995 + 0.502706i
\(496\) 160.875 134.990i 0.324345 0.272158i
\(497\) 305.773 + 364.406i 0.615237 + 0.733211i
\(498\) −487.960 58.0682i −0.979838 0.116603i
\(499\) 13.8640 11.6332i 0.0277835 0.0233131i −0.628790 0.777575i \(-0.716450\pi\)
0.656574 + 0.754262i \(0.272005\pi\)
\(500\) 101.616 121.101i 0.203232 0.242203i
\(501\) 42.5778 84.3394i 0.0849856 0.168342i
\(502\) 171.128 0.340892
\(503\) −328.648 + 391.667i −0.653375 + 0.778662i −0.986419 0.164250i \(-0.947480\pi\)
0.333044 + 0.942911i \(0.391924\pi\)
\(504\) 384.636 579.520i 0.763166 1.14984i
\(505\) 73.3641 + 127.070i 0.145276 + 0.251625i
\(506\) 219.591 126.781i 0.433974 0.250555i
\(507\) −81.9926 + 109.656i −0.161721 + 0.216284i
\(508\) −98.3057 + 82.4883i −0.193515 + 0.162379i
\(509\) −100.940 277.330i −0.198310 0.544854i 0.800181 0.599758i \(-0.204737\pi\)
−0.998492 + 0.0549049i \(0.982514\pi\)
\(510\) 168.011 157.848i 0.329434 0.309506i
\(511\) 154.998 + 879.038i 0.303323 + 1.72023i
\(512\) 526.707i 1.02872i
\(513\) 338.855 + 385.158i 0.660536 + 0.750794i
\(514\) −569.767 −1.10850
\(515\) 234.280 41.3098i 0.454912 0.0802133i
\(516\) −172.895 184.027i −0.335068 0.356641i
\(517\) 145.820 53.0740i 0.282050 0.102658i
\(518\) 280.912 + 334.778i 0.542301 + 0.646290i
\(519\) −788.545 589.616i −1.51936 1.13606i
\(520\) 188.365 + 326.257i 0.362240 + 0.627417i
\(521\) −288.325 + 166.465i −0.553408 + 0.319510i −0.750495 0.660876i \(-0.770185\pi\)
0.197088 + 0.980386i \(0.436852\pi\)
\(522\) 462.589 229.905i 0.886186 0.440431i
\(523\) 636.254 + 533.881i 1.21655 + 1.02080i 0.998998 + 0.0447552i \(0.0142508\pi\)
0.217549 + 0.976049i \(0.430194\pi\)
\(524\) 245.909i 0.469293i
\(525\) 232.943 + 117.599i 0.443701 + 0.223998i
\(526\) 90.9575 + 76.3224i 0.172923 + 0.145100i
\(527\) −158.245 188.589i −0.300274 0.357853i
\(528\) −31.1770 + 261.987i −0.0590474 + 0.496188i
\(529\) 181.419 152.229i 0.342947 0.287767i
\(530\) 222.439 + 265.092i 0.419696 + 0.500174i
\(531\) 448.877 + 195.856i 0.845343 + 0.368844i
\(532\) −121.927 + 154.386i −0.229186 + 0.290200i
\(533\) 109.158 + 63.0224i 0.204799 + 0.118241i
\(534\) −127.828 + 423.750i −0.239378 + 0.793539i
\(535\) −51.0923 289.759i −0.0954997 0.541606i
\(536\) 207.629 + 570.456i 0.387367 + 1.06428i
\(537\) 664.095 + 200.330i 1.23668 + 0.373054i
\(538\) 2.15567 12.2254i 0.00400683 0.0227238i
\(539\) −228.689 132.034i −0.424284 0.244960i
\(540\) 120.963 20.5480i 0.224006 0.0380518i
\(541\) 0.444884 + 0.373302i 0.000822337 + 0.000690023i 0.643199 0.765699i \(-0.277607\pi\)
−0.642376 + 0.766389i \(0.722051\pi\)
\(542\) −69.9300 192.131i −0.129022 0.354486i
\(543\) 26.7092 + 475.704i 0.0491882 + 0.876066i
\(544\) −210.388 −0.386743
\(545\) 173.709 207.018i 0.318731 0.379849i
\(546\) −363.349 + 341.370i −0.665475 + 0.625220i
\(547\) −271.047 227.435i −0.495515 0.415786i 0.360483 0.932766i \(-0.382612\pi\)
−0.855998 + 0.516979i \(0.827056\pi\)
\(548\) 99.3828 273.052i 0.181355 0.498270i
\(549\) −477.450 + 501.849i −0.869673 + 0.914114i
\(550\) −145.195 −0.263991
\(551\) −601.799 + 239.485i −1.09219 + 0.434636i
\(552\) −24.9995 445.253i −0.0452889 0.806617i
\(553\) 771.280 + 280.723i 1.39472 + 0.507637i
\(554\) −15.9857 + 2.81872i −0.0288551 + 0.00508793i
\(555\) −40.3846 + 339.360i −0.0727651 + 0.611460i
\(556\) 32.0533 + 11.6665i 0.0576499 + 0.0209828i
\(557\) 86.3619 + 237.277i 0.155048 + 0.425992i 0.992759 0.120122i \(-0.0383287\pi\)
−0.837711 + 0.546114i \(0.816107\pi\)
\(558\) 35.6874 + 316.803i 0.0639558 + 0.567747i
\(559\) 401.173 + 694.853i 0.717663 + 1.24303i
\(560\) −118.331 325.113i −0.211306 0.580559i
\(561\) 307.119 + 36.5478i 0.547449 + 0.0651476i
\(562\) 306.473 530.827i 0.545326 0.944532i
\(563\) 131.686i 0.233900i 0.993138 + 0.116950i \(0.0373117\pi\)
−0.993138 + 0.116950i \(0.962688\pi\)
\(564\) 7.27495 61.1329i 0.0128988 0.108392i
\(565\) 807.062 + 293.747i 1.42843 + 0.519906i
\(566\) 516.646 + 91.0987i 0.912803 + 0.160952i
\(567\) 279.570 + 663.308i 0.493069 + 1.16986i
\(568\) −356.612 + 299.233i −0.627839 + 0.526819i
\(569\) −792.594 457.604i −1.39296 0.804226i −0.399318 0.916813i \(-0.630753\pi\)
−0.993642 + 0.112587i \(0.964086\pi\)
\(570\) 372.939 32.0611i 0.654278 0.0562475i
\(571\) 154.941 + 268.367i 0.271351 + 0.469994i 0.969208 0.246243i \(-0.0791962\pi\)
−0.697857 + 0.716237i \(0.745863\pi\)
\(572\) −38.9948 + 107.137i −0.0681727 + 0.187303i
\(573\) 12.0475 + 51.3101i 0.0210253 + 0.0895464i
\(574\) −130.076 109.147i −0.226613 0.190151i
\(575\) 164.764 29.0523i 0.286546 0.0505258i
\(576\) 526.407 + 349.384i 0.913901 + 0.606569i
\(577\) 281.744 487.996i 0.488292 0.845746i −0.511617 0.859213i \(-0.670953\pi\)
0.999909 + 0.0134669i \(0.00428679\pi\)
\(578\) 256.048i 0.442990i
\(579\) −80.6584 + 107.872i −0.139306 + 0.186307i
\(580\) −26.9003 + 152.559i −0.0463799 + 0.263033i
\(581\) 748.716 + 432.271i 1.28867 + 0.744012i
\(582\) −273.946 + 542.641i −0.470698 + 0.932372i
\(583\) −80.6208 + 457.223i −0.138286 + 0.784260i
\(584\) −860.238 + 151.683i −1.47301 + 0.259731i
\(585\) −389.116 24.2958i −0.665155 0.0415312i
\(586\) −300.334 109.313i −0.512515 0.186540i
\(587\) −517.323 + 91.2180i −0.881300 + 0.155397i −0.595945 0.803025i \(-0.703223\pi\)
−0.285355 + 0.958422i \(0.592111\pi\)
\(588\) −87.6493 + 57.3858i −0.149063 + 0.0975949i
\(589\) −11.8585 399.559i −0.0201332 0.678368i
\(590\) 309.471 178.673i 0.524527 0.302836i
\(591\) 14.0998 + 60.0506i 0.0238575 + 0.101608i
\(592\) −223.342 + 187.406i −0.377266 + 0.316564i
\(593\) −788.249 138.990i −1.32926 0.234384i −0.536488 0.843908i \(-0.680249\pi\)
−0.792768 + 0.609524i \(0.791361\pi\)
\(594\) −305.197 259.369i −0.513800 0.436648i
\(595\) −381.119 + 138.716i −0.640536 + 0.233136i
\(596\) −39.8760 + 23.0224i −0.0669060 + 0.0386282i
\(597\) 61.5720 + 1096.63i 0.103136 + 1.83690i
\(598\) −55.5067 + 314.794i −0.0928205 + 0.526411i
\(599\) 185.502 + 32.7091i 0.309687 + 0.0546061i 0.326332 0.945255i \(-0.394187\pi\)
−0.0166450 + 0.999861i \(0.505298\pi\)
\(600\) −115.084 + 227.961i −0.191806 + 0.379935i
\(601\) 89.3510 + 154.760i 0.148671 + 0.257505i 0.930736 0.365691i \(-0.119167\pi\)
−0.782066 + 0.623196i \(0.785834\pi\)
\(602\) −369.684 1015.70i −0.614094 1.68721i
\(603\) −610.702 147.438i −1.01277 0.244507i
\(604\) 41.1806 233.547i 0.0681798 0.386667i
\(605\) −108.748 129.601i −0.179748 0.214216i
\(606\) −130.113 138.490i −0.214708 0.228532i
\(607\) 132.775 + 229.973i 0.218739 + 0.378867i 0.954423 0.298458i \(-0.0964723\pi\)
−0.735684 + 0.677325i \(0.763139\pi\)
\(608\) −268.088 211.723i −0.440934 0.348229i
\(609\) −907.392 + 50.9470i −1.48997 + 0.0836569i
\(610\) 87.7656 + 497.743i 0.143878 + 0.815973i
\(611\) −66.9073 + 183.826i −0.109505 + 0.300861i
\(612\) 67.8548 102.235i 0.110874 0.167050i
\(613\) 45.3010 + 256.915i 0.0739006 + 0.419111i 0.999204 + 0.0398841i \(0.0126989\pi\)
−0.925304 + 0.379227i \(0.876190\pi\)
\(614\) 215.264 + 37.9568i 0.350592 + 0.0618189i
\(615\) −7.44380 132.578i −0.0121037 0.215574i
\(616\) 340.448 589.673i 0.552675 0.957261i
\(617\) −345.175 60.8637i −0.559441 0.0986446i −0.113224 0.993569i \(-0.536118\pi\)
−0.446217 + 0.894925i \(0.647229\pi\)
\(618\) −283.147 + 121.437i −0.458167 + 0.196499i
\(619\) 336.076 0.542934 0.271467 0.962448i \(-0.412491\pi\)
0.271467 + 0.962448i \(0.412491\pi\)
\(620\) −82.7972 47.8030i −0.133544 0.0771016i
\(621\) 398.228 + 233.258i 0.641269 + 0.375617i
\(622\) −160.350 909.390i −0.257797 1.46204i
\(623\) 500.539 596.519i 0.803433 0.957494i
\(624\) −227.739 242.402i −0.364967 0.388465i
\(625\) 267.342 + 97.3045i 0.427747 + 0.155687i
\(626\) 587.436 339.156i 0.938396 0.541783i
\(627\) 354.568 + 355.639i 0.565499 + 0.567207i
\(628\) −107.216 + 185.704i −0.170727 + 0.295707i
\(629\) 219.690 + 261.816i 0.349268 + 0.416241i
\(630\) 510.552 + 123.259i 0.810400 + 0.195649i
\(631\) −81.7227 + 463.472i −0.129513 + 0.734504i 0.849012 + 0.528374i \(0.177198\pi\)
−0.978525 + 0.206130i \(0.933913\pi\)
\(632\) −274.719 + 754.784i −0.434682 + 1.19428i
\(633\) 71.0968 + 165.773i 0.112317 + 0.261884i
\(634\) −418.065 −0.659409
\(635\) −372.029 214.791i −0.585873 0.338254i
\(636\) 147.516 + 110.302i 0.231943 + 0.173430i
\(637\) 312.818 113.856i 0.491080 0.178738i
\(638\) 437.938 252.844i 0.686424 0.396307i
\(639\) −53.9292 478.739i −0.0843962 0.749200i
\(640\) 169.614 61.7343i 0.265021 0.0964598i
\(641\) 281.160 772.481i 0.438627 1.20512i −0.501758 0.865008i \(-0.667313\pi\)
0.940386 0.340110i \(-0.110464\pi\)
\(642\) 150.194 + 350.199i 0.233947 + 0.545481i
\(643\) −24.8454 140.905i −0.0386398 0.219137i 0.959374 0.282139i \(-0.0910439\pi\)
−0.998013 + 0.0630014i \(0.979933\pi\)
\(644\) −60.5316 + 166.309i −0.0939932 + 0.258244i
\(645\) 380.930 754.559i 0.590590 1.16986i
\(646\) 232.007 293.771i 0.359144 0.454755i
\(647\) 459.167i 0.709686i −0.934926 0.354843i \(-0.884534\pi\)
0.934926 0.354843i \(-0.115466\pi\)
\(648\) −649.121 + 273.591i −1.00173 + 0.422208i
\(649\) 450.515 + 163.974i 0.694168 + 0.252656i
\(650\) 117.655 140.216i 0.181008 0.215717i
\(651\) 161.987 536.988i 0.248828 0.824866i
\(652\) 146.195 + 122.672i 0.224225 + 0.188147i
\(653\) 269.552i 0.412789i −0.978469 0.206395i \(-0.933827\pi\)
0.978469 0.206395i \(-0.0661731\pi\)
\(654\) −157.726 + 312.428i −0.241171 + 0.477718i
\(655\) −773.540 + 281.546i −1.18098 + 0.429840i
\(656\) 72.8153 86.7779i 0.110999 0.132283i
\(657\) 361.517 828.551i 0.550254 1.26111i
\(658\) 131.768 228.228i 0.200255 0.346851i
\(659\) 762.737 + 134.491i 1.15742 + 0.204084i 0.719211 0.694791i \(-0.244503\pi\)
0.438205 + 0.898875i \(0.355614\pi\)
\(660\) 116.931 27.4553i 0.177169 0.0415989i
\(661\) 324.931 118.265i 0.491575 0.178919i −0.0843258 0.996438i \(-0.526874\pi\)
0.575901 + 0.817520i \(0.304651\pi\)
\(662\) −477.834 + 84.2551i −0.721804 + 0.127274i
\(663\) −284.160 + 266.971i −0.428598 + 0.402671i
\(664\) −423.026 + 732.702i −0.637087 + 1.10347i
\(665\) −625.239 206.778i −0.940209 0.310945i
\(666\) −49.5445 439.815i −0.0743911 0.660383i
\(667\) −446.370 + 374.549i −0.669220 + 0.561543i
\(668\) −23.5856 28.1082i −0.0353078 0.0420782i
\(669\) −177.600 414.101i −0.265471 0.618985i
\(670\) −351.159 + 294.657i −0.524118 + 0.439787i
\(671\) −435.869 + 519.448i −0.649581 + 0.774140i
\(672\) −262.560 401.026i −0.390714 0.596764i
\(673\) 529.553 0.786854 0.393427 0.919356i \(-0.371289\pi\)
0.393427 + 0.919356i \(0.371289\pi\)
\(674\) −398.487 + 474.898i −0.591227 + 0.704597i
\(675\) −130.699 229.691i −0.193628 0.340284i
\(676\) 26.5882 + 46.0522i 0.0393317 + 0.0681246i
\(677\) −750.705 + 433.420i −1.10887 + 0.640206i −0.938536 0.345180i \(-0.887818\pi\)
−0.170333 + 0.985386i \(0.554484\pi\)
\(678\) −1104.49 131.437i −1.62904 0.193859i
\(679\) 819.244 687.427i 1.20655 1.01241i
\(680\) −135.749 372.968i −0.199631 0.548482i
\(681\) 155.354 + 661.650i 0.228127 + 0.971586i
\(682\) 54.1939 + 307.349i 0.0794633 + 0.450658i
\(683\) 346.858i 0.507844i −0.967225 0.253922i \(-0.918279\pi\)
0.967225 0.253922i \(-0.0817207\pi\)
\(684\) 189.348 61.9878i 0.276825 0.0906255i
\(685\) 972.706 1.42001
\(686\) 280.378 49.4382i 0.408714 0.0720673i
\(687\) 312.522 1036.01i 0.454908 1.50802i
\(688\) 677.607 246.629i 0.984894 0.358472i
\(689\) −376.215 448.355i −0.546030 0.650733i
\(690\) 309.485 132.732i 0.448528 0.192365i
\(691\) 134.024 + 232.137i 0.193957 + 0.335943i 0.946558 0.322533i \(-0.104534\pi\)
−0.752601 + 0.658477i \(0.771201\pi\)
\(692\) −331.165 + 191.198i −0.478563 + 0.276298i
\(693\) 313.613 + 631.017i 0.452544 + 0.910558i
\(694\) −672.359 564.176i −0.968817 0.812934i
\(695\) 114.185i 0.164295i
\(696\) −49.8574 887.985i −0.0716342 1.27584i
\(697\) −101.727 85.3589i −0.145950 0.122466i
\(698\) −451.461 538.031i −0.646793 0.770817i
\(699\) 294.096 + 219.903i 0.420738 + 0.314597i
\(700\) 77.6343 65.1429i 0.110906 0.0930613i
\(701\) −490.594 584.668i −0.699849 0.834048i 0.292660 0.956217i \(-0.405460\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(702\) 497.783 84.5582i 0.709093 0.120453i
\(703\) 16.4630 + 554.704i 0.0234182 + 0.789053i
\(704\) 535.629 + 309.246i 0.760837 + 0.439270i
\(705\) 200.631 47.1077i 0.284583 0.0668195i
\(706\) 99.3861 + 563.647i 0.140774 + 0.798366i
\(707\) 114.343 + 314.154i 0.161729 + 0.444348i
\(708\) 138.622 130.237i 0.195794 0.183951i
\(709\) 163.271 925.956i 0.230284 1.30600i −0.622039 0.782987i \(-0.713695\pi\)
0.852322 0.523017i \(-0.175194\pi\)
\(710\) −304.429 175.762i −0.428774 0.247553i
\(711\) −493.597 668.834i −0.694229 0.940695i
\(712\) 583.761 + 489.833i 0.819889 + 0.687968i
\(713\) −122.996 337.929i −0.172505 0.473953i
\(714\) 439.445 287.713i 0.615469 0.402960i
\(715\) −381.660 −0.533791
\(716\) 173.165 206.370i 0.241851 0.288227i
\(717\) −70.5082 300.293i −0.0983379 0.418819i
\(718\) −126.174 105.872i −0.175729 0.147454i
\(719\) −231.075 + 634.874i −0.321384 + 0.882996i 0.668827 + 0.743418i \(0.266797\pi\)
−0.990211 + 0.139578i \(0.955426\pi\)
\(720\) −82.2303 + 340.606i −0.114209 + 0.473064i
\(721\) 542.033 0.751780
\(722\) 591.272 140.860i 0.818936 0.195097i
\(723\) −493.979 + 323.418i −0.683236 + 0.447328i
\(724\) 173.883 + 63.2882i 0.240170 + 0.0874147i
\(725\) 328.595 57.9402i 0.453235 0.0799175i
\(726\) 175.473 + 131.206i 0.241699 + 0.180724i
\(727\) −443.517 161.427i −0.610064 0.222045i 0.0184671 0.999829i \(-0.494121\pi\)
−0.628531 + 0.777784i \(0.716344\pi\)
\(728\) 293.578 + 806.599i 0.403267 + 1.10797i
\(729\) 135.582 716.281i 0.185983 0.982553i
\(730\) −329.800 571.230i −0.451781 0.782507i
\(731\) −289.115 794.336i −0.395506 1.08664i
\(732\) 106.037 + 247.242i 0.144860 + 0.337762i
\(733\) −541.175 + 937.343i −0.738302 + 1.27878i 0.214958 + 0.976623i \(0.431039\pi\)
−0.953259 + 0.302153i \(0.902295\pi\)
\(734\) 965.063i 1.31480i
\(735\) −280.866 210.010i −0.382130 0.285728i
\(736\) −288.792 105.112i −0.392380 0.142815i
\(737\) −605.669 106.796i −0.821803 0.144906i
\(738\) 48.6320 + 164.948i 0.0658970 + 0.223507i
\(739\) −632.310 + 530.571i −0.855629 + 0.717958i −0.961022 0.276472i \(-0.910835\pi\)
0.105392 + 0.994431i \(0.466390\pi\)
\(740\) 114.947 + 66.3645i 0.155333 + 0.0896818i
\(741\) −630.758 + 54.2255i −0.851225 + 0.0731788i
\(742\) 394.235 + 682.836i 0.531314 + 0.920264i
\(743\) 422.258 1160.14i 0.568314 1.56143i −0.238821 0.971064i \(-0.576761\pi\)
0.807135 0.590367i \(-0.201017\pi\)
\(744\) 525.503 + 158.523i 0.706321 + 0.213068i
\(745\) −118.075 99.0764i −0.158489 0.132988i
\(746\) 968.422 170.759i 1.29815 0.228899i
\(747\) −389.682 784.075i −0.521663 1.04963i
\(748\) 60.0594 104.026i 0.0802934 0.139072i
\(749\) 670.391i 0.895048i
\(750\) −680.546 80.9864i −0.907395 0.107982i
\(751\) −109.928 + 623.432i −0.146375 + 0.830136i 0.819877 + 0.572540i \(0.194042\pi\)
−0.966253 + 0.257597i \(0.917069\pi\)
\(752\) 152.259 + 87.9066i 0.202472 + 0.116897i
\(753\) 167.019 + 255.100i 0.221805 + 0.338779i
\(754\) −110.699 + 627.806i −0.146816 + 0.832634i
\(755\) 781.800 137.852i 1.03550 0.182586i
\(756\) 279.554 + 1.75272i 0.369780 + 0.00231841i
\(757\) −879.887 320.253i −1.16233 0.423055i −0.312403 0.949950i \(-0.601134\pi\)
−0.849931 + 0.526895i \(0.823356\pi\)
\(758\) 300.565 52.9977i 0.396524 0.0699178i
\(759\) 403.311 + 203.607i 0.531371 + 0.268257i
\(760\) 202.356 611.867i 0.266258 0.805088i
\(761\) −466.242 + 269.185i −0.612671 + 0.353726i −0.774010 0.633173i \(-0.781752\pi\)
0.161339 + 0.986899i \(0.448419\pi\)
\(762\) 532.633 + 160.674i 0.698994 + 0.210858i
\(763\) 471.683 395.789i 0.618196 0.518728i
\(764\) 20.1585 + 3.55449i 0.0263855 + 0.00465247i
\(765\) 399.281 + 96.3958i 0.521936 + 0.126008i
\(766\) 895.616 325.978i 1.16921 0.425558i
\(767\) −523.414 + 302.193i −0.682417 + 0.393994i
\(768\) 509.212 333.391i 0.663036 0.434103i
\(769\) 106.996 606.804i 0.139136 0.789082i −0.832753 0.553644i \(-0.813237\pi\)
0.971890 0.235437i \(-0.0756522\pi\)
\(770\) 506.344 + 89.2821i 0.657589 + 0.115951i
\(771\) −556.087 849.351i −0.721255 1.10162i
\(772\) 26.1556 + 45.3028i 0.0338803 + 0.0586824i
\(773\) −323.783 889.587i −0.418865 1.15082i −0.952348 0.305013i \(-0.901339\pi\)
0.533483 0.845811i \(-0.320883\pi\)
\(774\) −256.899 + 1064.10i −0.331911 + 1.37481i
\(775\) −35.7584 + 202.796i −0.0461399 + 0.261672i
\(776\) 672.725 + 801.722i 0.866913 + 1.03315i
\(777\) −224.886 + 745.496i −0.289428 + 0.959454i
\(778\) −95.3215 165.102i −0.122521 0.212213i
\(779\) −43.7252 211.141i −0.0561299 0.271042i
\(780\) −68.2386 + 135.169i −0.0874853 + 0.173294i
\(781\) −81.8955 464.453i −0.104860 0.594690i
\(782\) 115.182 316.459i 0.147291 0.404679i
\(783\) 794.202 + 465.196i 1.01431 + 0.594120i
\(784\) −51.9524 294.637i −0.0662659 0.375812i
\(785\) −706.911 124.647i −0.900524 0.158787i
\(786\) 891.921 583.959i 1.13476 0.742950i
\(787\) −121.449 + 210.355i −0.154319 + 0.267288i −0.932811 0.360367i \(-0.882652\pi\)
0.778492 + 0.627654i \(0.215985\pi\)
\(788\) 23.5925 + 4.15999i 0.0299397 + 0.00527917i
\(789\) −25.0000 + 210.080i −0.0316857 + 0.266262i
\(790\) −606.528 −0.767757
\(791\) 1694.71 + 978.439i 2.14249 + 1.23697i
\(792\) −617.521 + 306.905i −0.779698 + 0.387507i
\(793\) −148.440 841.843i −0.187187 1.06159i
\(794\) −576.460 + 686.998i −0.726020 + 0.865237i
\(795\) −178.074 + 590.317i −0.223993 + 0.742537i
\(796\) 400.848 + 145.897i 0.503578 + 0.183287i
\(797\) 252.148 145.578i 0.316372 0.182657i −0.333403 0.942785i \(-0.608197\pi\)
0.649774 + 0.760127i \(0.274863\pi\)
\(798\) 849.504 + 75.6134i 1.06454 + 0.0947537i
\(799\) 103.050 178.488i 0.128974 0.223389i
\(800\) 113.119 + 134.810i 0.141399 + 0.168512i
\(801\) −756.442 + 223.023i −0.944372 + 0.278431i
\(802\) 186.498 1057.68i 0.232541 1.31881i
\(803\) 302.668 831.573i 0.376921 1.03558i
\(804\) −146.113 + 195.410i −0.181732 + 0.243047i
\(805\) −592.451 −0.735964
\(806\) −340.724 196.717i −0.422734 0.244066i
\(807\) 20.3284 8.71845i 0.0251900 0.0108035i
\(808\) −307.435 + 111.897i −0.380489 + 0.138487i
\(809\) 533.645 308.100i 0.659635 0.380841i −0.132503 0.991183i \(-0.542301\pi\)
0.792138 + 0.610342i \(0.208968\pi\)
\(810\) −361.779 389.943i −0.446640 0.481411i
\(811\) −1294.74 + 471.245i −1.59647 + 0.581067i −0.978700 0.205294i \(-0.934185\pi\)
−0.617768 + 0.786361i \(0.711963\pi\)
\(812\) −120.721 + 331.677i −0.148671 + 0.408470i
\(813\) 218.159 291.763i 0.268338 0.358872i
\(814\) −75.2370 426.690i −0.0924287 0.524189i
\(815\) −218.500 + 600.323i −0.268098 + 0.736593i
\(816\) 191.943 + 293.168i 0.235225 + 0.359275i
\(817\) 430.972 1303.14i 0.527505 1.59503i
\(818\) 815.870i 0.997396i
\(819\) −863.506 208.470i −1.05434 0.254543i
\(820\) −48.4609 17.6383i −0.0590986 0.0215101i
\(821\) −95.9485 + 114.347i −0.116868 + 0.139278i −0.821306 0.570487i \(-0.806754\pi\)
0.704439 + 0.709765i \(0.251199\pi\)
\(822\) −1226.37 + 287.950i −1.49194 + 0.350304i
\(823\) −954.678 801.070i −1.16000 0.973354i −0.160092 0.987102i \(-0.551179\pi\)
−0.999905 + 0.0137483i \(0.995624\pi\)
\(824\) 530.440i 0.643738i
\(825\) −141.709 216.442i −0.171769 0.262354i
\(826\) 765.099 278.473i 0.926270 0.337135i
\(827\) −543.091 + 647.230i −0.656700 + 0.782624i −0.986908 0.161284i \(-0.948437\pi\)
0.330208 + 0.943908i \(0.392881\pi\)
\(828\) 144.219 106.433i 0.174178 0.128542i
\(829\) −374.108 + 647.975i −0.451277 + 0.781634i −0.998466 0.0553750i \(-0.982365\pi\)
0.547189 + 0.837009i \(0.315698\pi\)
\(830\) −629.161 110.938i −0.758026 0.133660i
\(831\) −19.8038 21.0789i −0.0238313 0.0253657i
\(832\) −732.674 + 266.672i −0.880618 + 0.320519i
\(833\) −345.393 + 60.9021i −0.414637 + 0.0731118i
\(834\) −33.8022 143.963i −0.0405302 0.172617i
\(835\) 61.4146 106.373i 0.0735504 0.127393i
\(836\) 181.217 72.1150i 0.216767 0.0862620i
\(837\) −437.427 + 362.396i −0.522613 + 0.432970i
\(838\) −534.211 + 448.257i −0.637484 + 0.534912i
\(839\) 54.4192 + 64.8542i 0.0648619 + 0.0772994i 0.797500 0.603319i \(-0.206156\pi\)
−0.732638 + 0.680619i \(0.761711\pi\)
\(840\) 541.511 724.210i 0.644655 0.862155i
\(841\) −245.970 + 206.393i −0.292473 + 0.245414i
\(842\) −346.676 + 413.152i −0.411729 + 0.490680i
\(843\) 1090.42 61.2234i 1.29350 0.0726256i
\(844\) 70.0534 0.0830016
\(845\) −114.422 + 136.363i −0.135411 + 0.161376i
\(846\) −239.007 + 118.785i −0.282514 + 0.140408i
\(847\) −192.737 333.831i −0.227553 0.394133i
\(848\) −455.542 + 263.008i −0.537196 + 0.310150i
\(849\) 368.442 + 859.076i 0.433971 + 1.01187i
\(850\) −147.725 + 123.956i −0.173794 + 0.145830i
\(851\) 170.754 + 469.143i 0.200651 + 0.551285i
\(852\) −179.133 54.0372i −0.210250 0.0634239i
\(853\) −103.346 586.102i −0.121156 0.687107i −0.983517 0.180814i \(-0.942127\pi\)
0.862362 0.506293i \(-0.168984\pi\)
\(854\) 1151.59i 1.34846i
\(855\) 411.778 + 524.648i 0.481612 + 0.613623i
\(856\) 656.053 0.766417
\(857\) 184.897 32.6023i 0.215749 0.0380424i −0.0647287 0.997903i \(-0.520618\pi\)
0.280478 + 0.959861i \(0.409507\pi\)
\(858\) 481.191 112.983i 0.560829 0.131682i
\(859\) 678.693 247.024i 0.790096 0.287571i 0.0847201 0.996405i \(-0.473000\pi\)
0.705376 + 0.708833i \(0.250778\pi\)
\(860\) −211.013 251.476i −0.245364 0.292414i
\(861\) 35.7518 300.430i 0.0415236 0.348931i
\(862\) −264.940 458.889i −0.307355 0.532354i
\(863\) 325.785 188.092i 0.377503 0.217952i −0.299228 0.954182i \(-0.596729\pi\)
0.676731 + 0.736230i \(0.263396\pi\)
\(864\) −3.04355 + 485.437i −0.00352263 + 0.561849i
\(865\) −980.596 822.818i −1.13364 0.951234i
\(866\) 1305.96i 1.50804i
\(867\) −381.691 + 249.901i −0.440243 + 0.288236i
\(868\) −166.871 140.022i −0.192248 0.161315i
\(869\) −523.061 623.360i −0.601911 0.717330i
\(870\) 617.217 264.713i 0.709445 0.304268i
\(871\) 593.922 498.360i 0.681885 0.572169i
\(872\) 387.324 + 461.595i 0.444179 + 0.529352i
\(873\) −1076.28 + 121.242i −1.23286 + 0.138879i
\(874\) 465.238 287.336i 0.532308 0.328760i
\(875\) 1044.22 + 602.879i 1.19339 + 0.689004i
\(876\) −240.395 255.873i −0.274424 0.292093i
\(877\) 159.456 + 904.317i 0.181819 + 1.03115i 0.929974 + 0.367624i \(0.119829\pi\)
−0.748155 + 0.663524i \(0.769060\pi\)
\(878\) 385.197 + 1058.32i 0.438721 + 1.20538i
\(879\) −130.171 554.395i −0.148090 0.630711i
\(880\) −59.5631 + 337.799i −0.0676853 + 0.383862i
\(881\) 1390.01 + 802.521i 1.57776 + 0.910921i 0.995171 + 0.0981544i \(0.0312939\pi\)
0.582590 + 0.812766i \(0.302039\pi\)
\(882\) 416.280 + 181.633i 0.471973 + 0.205933i
\(883\) 604.305 + 507.072i 0.684377 + 0.574261i 0.917282 0.398239i \(-0.130379\pi\)
−0.232904 + 0.972500i \(0.574823\pi\)
\(884\) 51.7910 + 142.295i 0.0585871 + 0.160967i
\(885\) 568.389 + 286.945i 0.642247 + 0.324231i
\(886\) −747.199 −0.843339
\(887\) 166.026 197.862i 0.187177 0.223069i −0.664293 0.747473i \(-0.731267\pi\)
0.851470 + 0.524403i \(0.175712\pi\)
\(888\) −729.551 220.076i −0.821567 0.247833i
\(889\) −749.796 629.154i −0.843415 0.707710i
\(890\) −196.810 + 540.730i −0.221134 + 0.607562i
\(891\) 88.7712 708.099i 0.0996310 0.794724i
\(892\) −174.994 −0.196181
\(893\) 310.932 123.735i 0.348189 0.138561i
\(894\) 178.196 + 89.9603i 0.199325 + 0.100627i
\(895\) 847.425 + 308.437i 0.946844 + 0.344623i
\(896\) 405.013 71.4147i 0.452023 0.0797039i
\(897\) −523.437 + 224.492i −0.583542 + 0.250270i
\(898\) 336.066 + 122.318i 0.374238 + 0.136212i
\(899\) −245.296 673.944i −0.272854 0.749660i
\(900\) −101.992 + 11.4893i −0.113325 + 0.0127658i
\(901\) 308.315 + 534.017i 0.342192 + 0.592694i
\(902\) 57.5774 + 158.193i 0.0638331 + 0.175380i
\(903\) 1153.29 1542.40i 1.27718 1.70809i
\(904\) −957.513 + 1658.46i −1.05920 + 1.83458i
\(905\) 619.431i 0.684455i
\(906\) −944.873 + 405.238i −1.04291 + 0.447283i
\(907\) 1486.62 + 541.084i 1.63905 + 0.596564i 0.986872 0.161505i \(-0.0516347\pi\)
0.652175 + 0.758069i \(0.273857\pi\)
\(908\) 259.947 + 45.8356i 0.286285 + 0.0504797i
\(909\) 79.4584 329.125i 0.0874129 0.362073i
\(910\) −496.523 + 416.632i −0.545630 + 0.457838i
\(911\) −550.059 317.577i −0.603797 0.348603i 0.166737 0.986001i \(-0.446677\pi\)
−0.770534 + 0.637399i \(0.780010\pi\)
\(912\) −50.4442 + 566.732i −0.0553117 + 0.621417i
\(913\) −428.563 742.293i −0.469401 0.813026i
\(914\) 473.141 1299.94i 0.517660 1.42226i
\(915\) −656.327 + 616.625i −0.717298 + 0.673907i
\(916\) −321.945 270.144i −0.351468 0.294917i
\(917\) −1847.10 + 325.694i −2.01429 + 0.355173i
\(918\) −531.943 3.33513i −0.579459 0.00363304i
\(919\) 362.301 627.525i 0.394234 0.682834i −0.598769 0.800922i \(-0.704343\pi\)
0.993003 + 0.118088i \(0.0376764\pi\)
\(920\) 579.780i 0.630196i
\(921\) 153.513 + 357.939i 0.166681 + 0.388641i
\(922\) −132.690 + 752.524i −0.143916 + 0.816186i
\(923\) 514.887 + 297.270i 0.557841 + 0.322070i
\(924\) 273.239 15.3415i 0.295713 0.0166033i
\(925\) 49.6431 281.540i 0.0536682 0.304367i
\(926\) 1088.19 191.878i 1.17516 0.207212i
\(927\) −457.375 303.566i −0.493392 0.327472i
\(928\) −575.949 209.628i −0.620634 0.225892i
\(929\) −333.732 + 58.8459i −0.359237 + 0.0633433i −0.350354 0.936617i \(-0.613939\pi\)
−0.00888327 + 0.999961i \(0.502828\pi\)
\(930\) 23.2349 + 413.826i 0.0249838 + 0.444974i
\(931\) −501.407 269.980i −0.538568 0.289989i
\(932\) 123.511 71.3094i 0.132523 0.0765122i
\(933\) 1199.13 1126.59i 1.28524 1.20749i
\(934\) 287.366 241.129i 0.307673 0.258168i
\(935\) 395.990 + 69.8238i 0.423519 + 0.0746779i
\(936\) 204.012 845.037i 0.217961 0.902818i
\(937\) −285.912 + 104.064i −0.305136 + 0.111060i −0.490050 0.871694i \(-0.663022\pi\)
0.184914 + 0.982755i \(0.440799\pi\)
\(938\) −904.530 + 522.231i −0.964318 + 0.556749i
\(939\) 1078.91 + 544.677i 1.14900 + 0.580060i
\(940\) 13.8986 78.8231i 0.0147858 0.0838543i
\(941\) 531.012 + 93.6318i 0.564306 + 0.0995024i 0.448522 0.893772i \(-0.351951\pi\)
0.115785 + 0.993274i \(0.463062\pi\)
\(942\) 928.161 52.1131i 0.985309 0.0553218i
\(943\) −96.9905 167.993i −0.102853 0.178147i
\(944\) 185.779 + 510.423i 0.196800 + 0.540702i
\(945\) 314.552 + 881.379i 0.332859 + 0.932676i
\(946\) −186.084 + 1055.33i −0.196706 + 1.11557i
\(947\) −399.906 476.589i −0.422287 0.503262i 0.512394 0.858751i \(-0.328759\pi\)
−0.934681 + 0.355489i \(0.884314\pi\)
\(948\) −314.290 + 73.7946i −0.331529 + 0.0778425i
\(949\) 557.797 + 966.132i 0.587773 + 1.01805i
\(950\) −312.982 + 9.28896i −0.329454 + 0.00977785i
\(951\) −408.028 623.209i −0.429052 0.655320i
\(952\) −157.036 890.594i −0.164953 0.935498i
\(953\) −203.055 + 557.889i −0.213069 + 0.585403i −0.999478 0.0323034i \(-0.989716\pi\)
0.786409 + 0.617706i \(0.211938\pi\)
\(954\) 49.7619 796.977i 0.0521614 0.835406i
\(955\) 11.8987 + 67.4808i 0.0124594 + 0.0706606i
\(956\) −117.978 20.8027i −0.123408 0.0217601i
\(957\) 804.338 + 406.061i 0.840479 + 0.424306i
\(958\) −139.001 + 240.757i −0.145095 + 0.251312i
\(959\) 2182.61 + 384.853i 2.27592 + 0.401306i
\(960\) 657.837 + 491.881i 0.685246 + 0.512376i
\(961\) −518.375 −0.539412
\(962\) 473.024 + 273.101i 0.491709 + 0.283888i
\(963\) −375.453 + 565.685i −0.389879 + 0.587419i
\(964\) 39.8194 + 225.827i 0.0413064 + 0.234260i
\(965\) −112.560 + 134.144i −0.116643 + 0.139009i
\(966\) 746.953 175.383i 0.773243 0.181556i
\(967\) −917.489 333.939i −0.948799 0.345335i −0.179165 0.983819i \(-0.557339\pi\)
−0.769635 + 0.638484i \(0.779562\pi\)
\(968\) 326.691 188.615i 0.337491 0.194850i
\(969\) 664.362 + 59.1341i 0.685616 + 0.0610259i
\(970\) −395.142 + 684.407i −0.407363 + 0.705574i
\(971\) 1141.78 + 1360.72i 1.17588 + 1.40135i 0.897575 + 0.440861i \(0.145327\pi\)
0.278301 + 0.960494i \(0.410229\pi\)
\(972\) −234.909 158.043i −0.241676 0.162596i
\(973\) −45.1775 + 256.214i −0.0464312 + 0.263324i
\(974\) −116.087 + 318.946i −0.119186 + 0.327460i
\(975\) 323.850 + 38.5389i 0.332154 + 0.0395271i
\(976\) −768.262 −0.787154
\(977\) −911.292 526.135i −0.932745 0.538521i −0.0450665 0.998984i \(-0.514350\pi\)
−0.887679 + 0.460463i \(0.847683\pi\)
\(978\) 97.7675 821.561i 0.0999668 0.840041i
\(979\) −725.462 + 264.046i −0.741023 + 0.269710i
\(980\) −117.955 + 68.1014i −0.120362 + 0.0694912i
\(981\) −619.675 + 69.8054i −0.631677 + 0.0711574i
\(982\) 888.626 323.434i 0.904915 0.329362i
\(983\) −102.862 + 282.612i −0.104641 + 0.287500i −0.980953 0.194245i \(-0.937774\pi\)
0.876312 + 0.481744i \(0.159997\pi\)
\(984\) 294.004 + 34.9872i 0.298785 + 0.0355561i
\(985\) 13.9256 + 78.9760i 0.0141377 + 0.0801787i
\(986\) 229.711 631.126i 0.232973 0.640087i
\(987\) 468.824 26.3229i 0.474999 0.0266696i
\(988\) −77.2028 + 233.439i −0.0781405 + 0.236275i
\(989\) 1234.80i 1.24853i
\(990\) −377.257 358.916i −0.381068 0.362541i
\(991\) −325.800 118.581i −0.328759 0.119658i 0.172367 0.985033i \(-0.444858\pi\)
−0.501126 + 0.865374i \(0.667081\pi\)
\(992\) 243.144 289.768i 0.245105 0.292105i
\(993\) −591.961 630.075i −0.596134 0.634517i
\(994\) −613.554 514.833i −0.617257 0.517940i
\(995\) 1427.96i 1.43514i
\(996\) −339.515 + 19.0627i −0.340879 + 0.0191392i
\(997\) 37.0147 13.4723i 0.0371261 0.0135128i −0.323390 0.946266i \(-0.604823\pi\)
0.360516 + 0.932753i \(0.382600\pi\)
\(998\) −19.5870 + 23.3429i −0.0196262 + 0.0233896i
\(999\) 607.277 503.112i 0.607885 0.503615i
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 171.3.z.a.101.13 228
9.5 odd 6 171.3.bf.a.158.13 yes 228
19.16 even 9 171.3.bf.a.92.13 yes 228
171.149 odd 18 inner 171.3.z.a.149.13 yes 228
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.3.z.a.101.13 228 1.1 even 1 trivial
171.3.z.a.149.13 yes 228 171.149 odd 18 inner
171.3.bf.a.92.13 yes 228 19.16 even 9
171.3.bf.a.158.13 yes 228 9.5 odd 6