Properties

Label 144.3.w.a.29.13
Level $144$
Weight $3$
Character 144.29
Analytic conductor $3.924$
Analytic rank $0$
Dimension $184$
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] = [144,3,Mod(5,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 10]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.w (of order \(12\), degree \(4\), 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: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(46\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 29.13
Character \(\chi\) \(=\) 144.29
Dual form 144.3.w.a.5.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26432 - 1.54968i) q^{2} +(-2.98386 + 0.310733i) q^{3} +(-0.803013 + 3.91857i) q^{4} +(2.23236 - 8.33129i) q^{5} +(4.25408 + 4.23117i) q^{6} +(-3.69610 - 2.13394i) q^{7} +(7.08778 - 3.70989i) q^{8} +(8.80689 - 1.85437i) q^{9} +O(q^{10})\) \(q+(-1.26432 - 1.54968i) q^{2} +(-2.98386 + 0.310733i) q^{3} +(-0.803013 + 3.91857i) q^{4} +(2.23236 - 8.33129i) q^{5} +(4.25408 + 4.23117i) q^{6} +(-3.69610 - 2.13394i) q^{7} +(7.08778 - 3.70989i) q^{8} +(8.80689 - 1.85437i) q^{9} +(-15.7332 + 7.07393i) q^{10} +(-15.6229 + 4.18615i) q^{11} +(1.17845 - 11.9420i) q^{12} +(-5.18329 + 19.3443i) q^{13} +(1.36611 + 8.42575i) q^{14} +(-4.07226 + 25.5531i) q^{15} +(-14.7103 - 6.29332i) q^{16} +10.6727i q^{17} +(-14.0084 - 11.3033i) q^{18} +(-12.2363 - 12.2363i) q^{19} +(30.8541 + 15.4378i) q^{20} +(11.6917 + 5.21890i) q^{21} +(26.2395 + 18.9179i) q^{22} +(9.25997 + 16.0387i) q^{23} +(-19.9962 + 13.2722i) q^{24} +(-42.7763 - 24.6969i) q^{25} +(36.5308 - 16.4249i) q^{26} +(-25.7023 + 8.26978i) q^{27} +(11.3300 - 12.7698i) q^{28} +(-6.80700 - 25.4041i) q^{29} +(44.7477 - 25.9965i) q^{30} +(6.33170 + 10.9668i) q^{31} +(8.84588 + 30.7531i) q^{32} +(45.3159 - 17.3455i) q^{33} +(16.5392 - 13.4936i) q^{34} +(-26.0295 + 26.0295i) q^{35} +(0.194430 + 35.9995i) q^{36} +(-18.0450 + 18.0450i) q^{37} +(-3.49179 + 34.4328i) q^{38} +(9.45532 - 59.3314i) q^{39} +(-15.0857 - 67.3322i) q^{40} +(-7.43075 - 12.8704i) q^{41} +(-6.69444 - 24.7168i) q^{42} +(4.70515 + 17.5598i) q^{43} +(-3.85830 - 64.5810i) q^{44} +(4.21087 - 77.5124i) q^{45} +(13.1474 - 34.6280i) q^{46} +(-16.1577 - 9.32866i) q^{47} +(45.8492 + 14.2074i) q^{48} +(-15.3926 - 26.6607i) q^{49} +(15.8105 + 97.5143i) q^{50} +(-3.31635 - 31.8458i) q^{51} +(-71.6397 - 35.8448i) q^{52} +(-38.0269 - 38.0269i) q^{53} +(45.3114 + 29.3748i) q^{54} +139.504i q^{55} +(-34.1139 - 1.41280i) q^{56} +(40.3136 + 32.7091i) q^{57} +(-30.7620 + 42.6674i) q^{58} +(16.9990 - 63.4412i) q^{59} +(-96.8615 - 36.4769i) q^{60} +(-11.9218 + 3.19445i) q^{61} +(8.98980 - 23.6776i) q^{62} +(-36.5083 - 11.9395i) q^{63} +(36.4734 - 52.5898i) q^{64} +(149.592 + 86.3670i) q^{65} +(-84.1735 - 48.2950i) q^{66} +(8.10824 - 30.2604i) q^{67} +(-41.8216 - 8.57029i) q^{68} +(-32.6143 - 44.9801i) q^{69} +(73.2470 + 7.42790i) q^{70} +38.1082 q^{71} +(55.5418 - 45.8160i) q^{72} +127.821i q^{73} +(50.7786 + 5.14939i) q^{74} +(135.313 + 60.4002i) q^{75} +(57.7745 - 38.1227i) q^{76} +(66.6769 + 17.8660i) q^{77} +(-103.899 + 60.3609i) q^{78} +(7.54888 - 13.0750i) q^{79} +(-85.2703 + 108.507i) q^{80} +(74.1226 - 32.6625i) q^{81} +(-10.5502 + 27.7876i) q^{82} +(-29.3816 - 109.654i) q^{83} +(-29.8392 + 41.6241i) q^{84} +(88.9171 + 23.8253i) q^{85} +(21.2633 - 29.4927i) q^{86} +(28.2050 + 73.6871i) q^{87} +(-95.2018 + 87.6299i) q^{88} -102.393 q^{89} +(-125.443 + 91.4746i) q^{90} +(60.4377 - 60.4377i) q^{91} +(-70.2848 + 23.4065i) q^{92} +(-22.3007 - 30.7561i) q^{93} +(5.97202 + 36.8337i) q^{94} +(-129.260 + 74.6281i) q^{95} +(-35.9509 - 89.0142i) q^{96} +(40.9773 - 70.9747i) q^{97} +(-21.8545 + 57.5611i) q^{98} +(-129.827 + 65.8377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26432 1.54968i −0.632158 0.774840i
\(3\) −2.98386 + 0.310733i −0.994621 + 0.103578i
\(4\) −0.803013 + 3.91857i −0.200753 + 0.979642i
\(5\) 2.23236 8.33129i 0.446472 1.66626i −0.265547 0.964098i \(-0.585552\pi\)
0.712019 0.702160i \(-0.247781\pi\)
\(6\) 4.25408 + 4.23117i 0.709014 + 0.705195i
\(7\) −3.69610 2.13394i −0.528014 0.304849i 0.212193 0.977228i \(-0.431939\pi\)
−0.740208 + 0.672378i \(0.765273\pi\)
\(8\) 7.08778 3.70989i 0.885973 0.463737i
\(9\) 8.80689 1.85437i 0.978543 0.206041i
\(10\) −15.7332 + 7.07393i −1.57332 + 0.707393i
\(11\) −15.6229 + 4.18615i −1.42027 + 0.380559i −0.885578 0.464491i \(-0.846237\pi\)
−0.534688 + 0.845050i \(0.679571\pi\)
\(12\) 1.17845 11.9420i 0.0982044 0.995166i
\(13\) −5.18329 + 19.3443i −0.398715 + 1.48802i 0.416645 + 0.909069i \(0.363206\pi\)
−0.815360 + 0.578954i \(0.803461\pi\)
\(14\) 1.36611 + 8.42575i 0.0975791 + 0.601839i
\(15\) −4.07226 + 25.5531i −0.271484 + 1.70354i
\(16\) −14.7103 6.29332i −0.919396 0.393332i
\(17\) 10.6727i 0.627804i 0.949455 + 0.313902i \(0.101636\pi\)
−0.949455 + 0.313902i \(0.898364\pi\)
\(18\) −14.0084 11.3033i −0.778243 0.627964i
\(19\) −12.2363 12.2363i −0.644014 0.644014i 0.307526 0.951540i \(-0.400499\pi\)
−0.951540 + 0.307526i \(0.900499\pi\)
\(20\) 30.8541 + 15.4378i 1.54271 + 0.771890i
\(21\) 11.6917 + 5.21890i 0.556750 + 0.248519i
\(22\) 26.2395 + 18.9179i 1.19270 + 0.859905i
\(23\) 9.25997 + 16.0387i 0.402608 + 0.697337i 0.994040 0.109018i \(-0.0347706\pi\)
−0.591432 + 0.806355i \(0.701437\pi\)
\(24\) −19.9962 + 13.2722i −0.833175 + 0.553009i
\(25\) −42.7763 24.6969i −1.71105 0.987877i
\(26\) 36.5308 16.4249i 1.40503 0.631726i
\(27\) −25.7023 + 8.26978i −0.951939 + 0.306288i
\(28\) 11.3300 12.7698i 0.404644 0.456066i
\(29\) −6.80700 25.4041i −0.234724 0.876002i −0.978273 0.207321i \(-0.933526\pi\)
0.743549 0.668681i \(-0.233141\pi\)
\(30\) 44.7477 25.9965i 1.49159 0.866550i
\(31\) 6.33170 + 10.9668i 0.204248 + 0.353769i 0.949893 0.312575i \(-0.101192\pi\)
−0.745645 + 0.666344i \(0.767858\pi\)
\(32\) 8.84588 + 30.7531i 0.276434 + 0.961033i
\(33\) 45.3159 17.3455i 1.37321 0.525620i
\(34\) 16.5392 13.4936i 0.486447 0.396871i
\(35\) −26.0295 + 26.0295i −0.743701 + 0.743701i
\(36\) 0.194430 + 35.9995i 0.00540085 + 0.999985i
\(37\) −18.0450 + 18.0450i −0.487703 + 0.487703i −0.907581 0.419878i \(-0.862073\pi\)
0.419878 + 0.907581i \(0.362073\pi\)
\(38\) −3.49179 + 34.4328i −0.0918892 + 0.906126i
\(39\) 9.45532 59.3314i 0.242444 1.52132i
\(40\) −15.0857 67.3322i −0.377142 1.68331i
\(41\) −7.43075 12.8704i −0.181238 0.313913i 0.761065 0.648676i \(-0.224677\pi\)
−0.942302 + 0.334763i \(0.891344\pi\)
\(42\) −6.69444 24.7168i −0.159391 0.588495i
\(43\) 4.70515 + 17.5598i 0.109422 + 0.408369i 0.998809 0.0487861i \(-0.0155353\pi\)
−0.889387 + 0.457155i \(0.848869\pi\)
\(44\) −3.85830 64.5810i −0.0876887 1.46775i
\(45\) 4.21087 77.5124i 0.0935749 1.72250i
\(46\) 13.1474 34.6280i 0.285813 0.752783i
\(47\) −16.1577 9.32866i −0.343781 0.198482i 0.318162 0.948036i \(-0.396935\pi\)
−0.661943 + 0.749554i \(0.730268\pi\)
\(48\) 45.8492 + 14.2074i 0.955192 + 0.295988i
\(49\) −15.3926 26.6607i −0.314134 0.544096i
\(50\) 15.8105 + 97.5143i 0.316209 + 1.95029i
\(51\) −3.31635 31.8458i −0.0650265 0.624427i
\(52\) −71.6397 35.8448i −1.37769 0.689323i
\(53\) −38.0269 38.0269i −0.717489 0.717489i 0.250602 0.968090i \(-0.419372\pi\)
−0.968090 + 0.250602i \(0.919372\pi\)
\(54\) 45.3114 + 29.3748i 0.839100 + 0.543978i
\(55\) 139.504i 2.53644i
\(56\) −34.1139 1.41280i −0.609176 0.0252286i
\(57\) 40.3136 + 32.7091i 0.707255 + 0.573844i
\(58\) −30.7620 + 42.6674i −0.530378 + 0.735645i
\(59\) 16.9990 63.4412i 0.288119 1.07527i −0.658411 0.752658i \(-0.728771\pi\)
0.946530 0.322616i \(-0.104562\pi\)
\(60\) −96.8615 36.4769i −1.61436 0.607948i
\(61\) −11.9218 + 3.19445i −0.195440 + 0.0523680i −0.355211 0.934786i \(-0.615591\pi\)
0.159771 + 0.987154i \(0.448924\pi\)
\(62\) 8.98980 23.6776i 0.144997 0.381897i
\(63\) −36.5083 11.9395i −0.579496 0.189516i
\(64\) 36.4734 52.5898i 0.569897 0.821716i
\(65\) 149.592 + 86.3670i 2.30142 + 1.32872i
\(66\) −84.1735 48.2950i −1.27536 0.731742i
\(67\) 8.10824 30.2604i 0.121019 0.451647i −0.878648 0.477470i \(-0.841554\pi\)
0.999667 + 0.0258228i \(0.00822056\pi\)
\(68\) −41.8216 8.57029i −0.615023 0.126034i
\(69\) −32.6143 44.9801i −0.472671 0.651885i
\(70\) 73.2470 + 7.42790i 1.04639 + 0.106113i
\(71\) 38.1082 0.536735 0.268367 0.963317i \(-0.413516\pi\)
0.268367 + 0.963317i \(0.413516\pi\)
\(72\) 55.5418 45.8160i 0.771414 0.636333i
\(73\) 127.821i 1.75098i 0.483240 + 0.875488i \(0.339460\pi\)
−0.483240 + 0.875488i \(0.660540\pi\)
\(74\) 50.7786 + 5.14939i 0.686197 + 0.0695864i
\(75\) 135.313 + 60.4002i 1.80417 + 0.805336i
\(76\) 57.7745 38.1227i 0.760191 0.501615i
\(77\) 66.6769 + 17.8660i 0.865934 + 0.232026i
\(78\) −103.899 + 60.3609i −1.33204 + 0.773858i
\(79\) 7.54888 13.0750i 0.0955554 0.165507i −0.814285 0.580465i \(-0.802871\pi\)
0.909840 + 0.414959i \(0.136204\pi\)
\(80\) −85.2703 + 108.507i −1.06588 + 1.35634i
\(81\) 74.1226 32.6625i 0.915094 0.403240i
\(82\) −10.5502 + 27.7876i −0.128661 + 0.338873i
\(83\) −29.3816 109.654i −0.353996 1.32113i −0.881744 0.471729i \(-0.843630\pi\)
0.527748 0.849401i \(-0.323037\pi\)
\(84\) −29.8392 + 41.6241i −0.355229 + 0.495525i
\(85\) 88.9171 + 23.8253i 1.04608 + 0.280297i
\(86\) 21.2633 29.4927i 0.247248 0.342938i
\(87\) 28.2050 + 73.6871i 0.324196 + 0.846978i
\(88\) −95.2018 + 87.6299i −1.08184 + 0.995794i
\(89\) −102.393 −1.15049 −0.575243 0.817983i \(-0.695092\pi\)
−0.575243 + 0.817983i \(0.695092\pi\)
\(90\) −125.443 + 91.4746i −1.39381 + 1.01638i
\(91\) 60.4377 60.4377i 0.664150 0.664150i
\(92\) −70.2848 + 23.4065i −0.763965 + 0.254419i
\(93\) −22.3007 30.7561i −0.239792 0.330710i
\(94\) 5.97202 + 36.8337i 0.0635321 + 0.391847i
\(95\) −129.260 + 74.6281i −1.36063 + 0.785559i
\(96\) −35.9509 89.0142i −0.374489 0.927232i
\(97\) 40.9773 70.9747i 0.422446 0.731698i −0.573732 0.819043i \(-0.694505\pi\)
0.996178 + 0.0873452i \(0.0278383\pi\)
\(98\) −21.8545 + 57.5611i −0.223005 + 0.587358i
\(99\) −129.827 + 65.8377i −1.31138 + 0.665027i
\(100\) 131.126 147.790i 1.31126 1.47790i
\(101\) −95.5779 + 25.6100i −0.946316 + 0.253565i −0.698798 0.715319i \(-0.746282\pi\)
−0.247518 + 0.968883i \(0.579615\pi\)
\(102\) −45.1579 + 45.4024i −0.442724 + 0.445122i
\(103\) −171.623 + 99.0866i −1.66624 + 0.962006i −0.696608 + 0.717452i \(0.745308\pi\)
−0.969636 + 0.244554i \(0.921359\pi\)
\(104\) 35.0273 + 156.338i 0.336801 + 1.50325i
\(105\) 69.5804 85.7569i 0.662670 0.816732i
\(106\) −10.8515 + 107.007i −0.102373 + 1.00950i
\(107\) −49.9526 49.9526i −0.466846 0.466846i 0.434045 0.900891i \(-0.357086\pi\)
−0.900891 + 0.434045i \(0.857086\pi\)
\(108\) −11.7664 107.357i −0.108948 0.994047i
\(109\) −85.4760 85.4760i −0.784184 0.784184i 0.196350 0.980534i \(-0.437091\pi\)
−0.980534 + 0.196350i \(0.937091\pi\)
\(110\) 216.187 176.377i 1.96533 1.60343i
\(111\) 48.2367 59.4510i 0.434565 0.535595i
\(112\) 40.9413 + 54.6518i 0.365547 + 0.487962i
\(113\) 17.2776 9.97525i 0.152899 0.0882765i −0.421598 0.906783i \(-0.638531\pi\)
0.574498 + 0.818506i \(0.305197\pi\)
\(114\) −0.280381 103.828i −0.00245948 0.910770i
\(115\) 154.295 41.3432i 1.34170 0.359506i
\(116\) 105.014 6.27389i 0.905290 0.0540853i
\(117\) −9.77716 + 179.975i −0.0835655 + 1.53825i
\(118\) −119.806 + 53.8666i −1.01530 + 0.456497i
\(119\) 22.7749 39.4473i 0.191386 0.331490i
\(120\) 65.9360 + 196.223i 0.549467 + 1.63519i
\(121\) 121.763 70.2998i 1.00630 0.580990i
\(122\) 20.0233 + 14.4362i 0.164126 + 0.118330i
\(123\) 26.1716 + 36.0946i 0.212777 + 0.293452i
\(124\) −48.0587 + 16.0047i −0.387570 + 0.129070i
\(125\) −148.776 + 148.776i −1.19021 + 1.19021i
\(126\) 27.6556 + 71.6714i 0.219489 + 0.568821i
\(127\) 76.3214 0.600956 0.300478 0.953789i \(-0.402854\pi\)
0.300478 + 0.953789i \(0.402854\pi\)
\(128\) −127.611 + 9.96809i −0.996963 + 0.0778757i
\(129\) −19.4959 50.9342i −0.151131 0.394838i
\(130\) −55.2904 341.015i −0.425310 2.62319i
\(131\) −26.4201 7.07925i −0.201680 0.0540401i 0.156565 0.987668i \(-0.449958\pi\)
−0.358245 + 0.933628i \(0.616625\pi\)
\(132\) 31.5801 + 191.502i 0.239243 + 1.45077i
\(133\) 19.1150 + 71.3380i 0.143721 + 0.536376i
\(134\) −57.1453 + 25.6935i −0.426457 + 0.191742i
\(135\) 11.5210 + 232.595i 0.0853407 + 1.72292i
\(136\) 39.5945 + 75.6456i 0.291136 + 0.556217i
\(137\) 103.573 179.394i 0.756009 1.30945i −0.188863 0.982003i \(-0.560480\pi\)
0.944871 0.327442i \(-0.106187\pi\)
\(138\) −28.4699 + 107.411i −0.206304 + 0.778338i
\(139\) 35.0078 + 9.38031i 0.251855 + 0.0674842i 0.382537 0.923940i \(-0.375050\pi\)
−0.130683 + 0.991424i \(0.541717\pi\)
\(140\) −81.0965 122.901i −0.579261 0.877861i
\(141\) 51.1112 + 22.8147i 0.362490 + 0.161807i
\(142\) −48.1807 59.0554i −0.339301 0.415883i
\(143\) 323.913i 2.26512i
\(144\) −141.222 28.1462i −0.980712 0.195459i
\(145\) −226.844 −1.56444
\(146\) 198.082 161.606i 1.35673 1.10689i
\(147\) 54.2137 + 74.7689i 0.368800 + 0.508632i
\(148\) −56.2202 85.2009i −0.379866 0.575682i
\(149\) −24.5447 + 91.6021i −0.164730 + 0.614779i 0.833345 + 0.552753i \(0.186423\pi\)
−0.998075 + 0.0620258i \(0.980244\pi\)
\(150\) −77.4772 286.057i −0.516514 1.90704i
\(151\) 85.7840 + 49.5274i 0.568106 + 0.327996i 0.756393 0.654118i \(-0.226960\pi\)
−0.188286 + 0.982114i \(0.560293\pi\)
\(152\) −132.123 41.3328i −0.869232 0.271926i
\(153\) 19.7911 + 93.9930i 0.129353 + 0.614333i
\(154\) −56.6140 125.916i −0.367624 0.817637i
\(155\) 105.502 28.2693i 0.680661 0.182383i
\(156\) 224.901 + 84.6952i 1.44168 + 0.542918i
\(157\) 9.17060 34.2252i 0.0584115 0.217995i −0.930551 0.366163i \(-0.880671\pi\)
0.988962 + 0.148169i \(0.0473378\pi\)
\(158\) −29.8063 + 4.83263i −0.188647 + 0.0305863i
\(159\) 125.283 + 101.651i 0.787945 + 0.639314i
\(160\) 275.960 5.04566i 1.72475 0.0315354i
\(161\) 79.0411i 0.490938i
\(162\) −144.331 73.5706i −0.890930 0.454140i
\(163\) 79.4058 + 79.4058i 0.487152 + 0.487152i 0.907406 0.420254i \(-0.138059\pi\)
−0.420254 + 0.907406i \(0.638059\pi\)
\(164\) 56.4007 18.7828i 0.343906 0.114529i
\(165\) −43.3485 416.261i −0.262718 2.52280i
\(166\) −132.781 + 184.169i −0.799883 + 1.10945i
\(167\) −148.694 257.546i −0.890384 1.54219i −0.839415 0.543491i \(-0.817102\pi\)
−0.0509694 0.998700i \(-0.516231\pi\)
\(168\) 102.230 6.38470i 0.608513 0.0380041i
\(169\) −200.977 116.034i −1.18922 0.686594i
\(170\) −75.4977 167.916i −0.444104 0.987739i
\(171\) −130.454 85.0729i −0.762889 0.497502i
\(172\) −72.5877 + 4.33665i −0.422022 + 0.0252131i
\(173\) 7.21216 + 26.9161i 0.0416888 + 0.155585i 0.983633 0.180186i \(-0.0576700\pi\)
−0.941944 + 0.335771i \(0.891003\pi\)
\(174\) 78.5313 136.872i 0.451329 0.786623i
\(175\) 105.404 + 182.565i 0.602307 + 1.04323i
\(176\) 256.163 + 36.7404i 1.45547 + 0.208752i
\(177\) −31.0095 + 194.582i −0.175195 + 1.09933i
\(178\) 129.457 + 158.677i 0.727288 + 0.891442i
\(179\) 38.8769 38.8769i 0.217190 0.217190i −0.590123 0.807313i \(-0.700921\pi\)
0.807313 + 0.590123i \(0.200921\pi\)
\(180\) 300.356 + 78.7440i 1.66865 + 0.437467i
\(181\) −174.343 + 174.343i −0.963219 + 0.963219i −0.999347 0.0361282i \(-0.988498\pi\)
0.0361282 + 0.999347i \(0.488498\pi\)
\(182\) −170.071 17.2467i −0.934457 0.0947622i
\(183\) 34.5805 13.2363i 0.188965 0.0723295i
\(184\) 125.135 + 79.3257i 0.680080 + 0.431118i
\(185\) 110.055 + 190.621i 0.594893 + 1.03038i
\(186\) −19.4669 + 73.4443i −0.104661 + 0.394862i
\(187\) −44.6774 166.738i −0.238917 0.891649i
\(188\) 49.5298 55.8241i 0.263457 0.296937i
\(189\) 112.646 + 24.2814i 0.596009 + 0.128473i
\(190\) 279.075 + 105.958i 1.46881 + 0.557671i
\(191\) −18.5440 10.7064i −0.0970889 0.0560543i 0.450669 0.892691i \(-0.351185\pi\)
−0.547758 + 0.836637i \(0.684519\pi\)
\(192\) −92.4902 + 168.254i −0.481720 + 0.876325i
\(193\) 62.0847 + 107.534i 0.321683 + 0.557171i 0.980835 0.194839i \(-0.0624183\pi\)
−0.659153 + 0.752009i \(0.729085\pi\)
\(194\) −161.796 + 26.2328i −0.834001 + 0.135221i
\(195\) −473.199 211.224i −2.42666 1.08320i
\(196\) 116.832 38.9079i 0.596082 0.198510i
\(197\) 234.620 + 234.620i 1.19096 + 1.19096i 0.976797 + 0.214168i \(0.0687040\pi\)
0.214168 + 0.976797i \(0.431296\pi\)
\(198\) 266.169 + 117.950i 1.34429 + 0.595708i
\(199\) 202.984i 1.02002i −0.860169 0.510010i \(-0.829642\pi\)
0.860169 0.510010i \(-0.170358\pi\)
\(200\) −394.812 16.3509i −1.97406 0.0817544i
\(201\) −14.7910 + 92.8123i −0.0735870 + 0.461753i
\(202\) 160.528 + 115.736i 0.794693 + 0.572951i
\(203\) −29.0515 + 108.422i −0.143111 + 0.534097i
\(204\) 127.453 + 12.5772i 0.624769 + 0.0616531i
\(205\) −123.815 + 33.1763i −0.603978 + 0.161835i
\(206\) 370.538 + 140.684i 1.79873 + 0.682932i
\(207\) 111.293 + 124.080i 0.537649 + 0.599420i
\(208\) 197.988 251.941i 0.951865 1.21126i
\(209\) 242.389 + 139.943i 1.15976 + 0.669586i
\(210\) −220.867 + 0.596439i −1.05175 + 0.00284019i
\(211\) 50.6135 188.892i 0.239875 0.895224i −0.736016 0.676964i \(-0.763295\pi\)
0.975891 0.218260i \(-0.0700381\pi\)
\(212\) 179.547 118.475i 0.846920 0.558844i
\(213\) −113.710 + 11.8415i −0.533848 + 0.0555937i
\(214\) −14.2547 + 140.566i −0.0666106 + 0.656852i
\(215\) 156.800 0.729301
\(216\) −151.493 + 153.967i −0.701355 + 0.712812i
\(217\) 54.0460i 0.249060i
\(218\) −24.3918 + 240.529i −0.111889 + 1.10334i
\(219\) −39.7183 381.401i −0.181362 1.74156i
\(220\) −546.656 112.024i −2.48480 0.509198i
\(221\) −206.455 55.3196i −0.934187 0.250315i
\(222\) −153.116 + 0.413482i −0.689713 + 0.00186253i
\(223\) 98.9068 171.312i 0.443528 0.768214i −0.554420 0.832237i \(-0.687060\pi\)
0.997948 + 0.0640232i \(0.0203932\pi\)
\(224\) 32.9300 132.543i 0.147009 0.591710i
\(225\) −422.524 138.180i −1.87788 0.614133i
\(226\) −37.3028 14.1629i −0.165057 0.0626679i
\(227\) 67.3687 + 251.423i 0.296778 + 1.10759i 0.939795 + 0.341740i \(0.111016\pi\)
−0.643016 + 0.765853i \(0.722317\pi\)
\(228\) −160.545 + 131.706i −0.704146 + 0.577656i
\(229\) 108.797 + 29.1520i 0.475095 + 0.127301i 0.488418 0.872610i \(-0.337574\pi\)
−0.0133229 + 0.999911i \(0.504241\pi\)
\(230\) −259.146 186.837i −1.12672 0.812335i
\(231\) −204.506 32.5911i −0.885309 0.141087i
\(232\) −142.493 154.805i −0.614193 0.667264i
\(233\) −281.212 −1.20692 −0.603460 0.797394i \(-0.706212\pi\)
−0.603460 + 0.797394i \(0.706212\pi\)
\(234\) 291.265 212.394i 1.24472 0.907665i
\(235\) −113.790 + 113.790i −0.484211 + 0.484211i
\(236\) 234.948 + 117.556i 0.995543 + 0.498118i
\(237\) −18.4620 + 41.3598i −0.0778986 + 0.174514i
\(238\) −89.9252 + 14.5800i −0.377837 + 0.0612605i
\(239\) −237.936 + 137.372i −0.995546 + 0.574779i −0.906927 0.421287i \(-0.861579\pi\)
−0.0886186 + 0.996066i \(0.528245\pi\)
\(240\) 220.718 350.267i 0.919659 1.45945i
\(241\) −58.8394 + 101.913i −0.244147 + 0.422875i −0.961891 0.273432i \(-0.911841\pi\)
0.717745 + 0.696306i \(0.245175\pi\)
\(242\) −262.889 99.8122i −1.08632 0.412447i
\(243\) −211.023 + 120.493i −0.868405 + 0.495855i
\(244\) −2.94427 49.2817i −0.0120667 0.201974i
\(245\) −256.480 + 68.7235i −1.04686 + 0.280504i
\(246\) 22.8460 86.1926i 0.0928698 0.350377i
\(247\) 300.126 173.278i 1.21509 0.701530i
\(248\) 85.5635 + 54.2406i 0.345014 + 0.218712i
\(249\) 121.744 + 318.062i 0.488931 + 1.27736i
\(250\) 418.656 + 42.4554i 1.67462 + 0.169822i
\(251\) 162.917 + 162.917i 0.649070 + 0.649070i 0.952768 0.303698i \(-0.0982215\pi\)
−0.303698 + 0.952768i \(0.598222\pi\)
\(252\) 76.1023 133.473i 0.301993 0.529653i
\(253\) −211.808 211.808i −0.837188 0.837188i
\(254\) −96.4944 118.274i −0.379899 0.465645i
\(255\) −272.720 43.4619i −1.06949 0.170439i
\(256\) 176.788 + 185.154i 0.690579 + 0.723257i
\(257\) 128.327 74.0896i 0.499327 0.288286i −0.229109 0.973401i \(-0.573581\pi\)
0.728435 + 0.685114i \(0.240248\pi\)
\(258\) −54.2826 + 94.6093i −0.210398 + 0.366703i
\(259\) 105.203 28.1891i 0.406190 0.108838i
\(260\) −458.559 + 516.833i −1.76369 + 1.98782i
\(261\) −107.057 211.108i −0.410180 0.808843i
\(262\) 22.4328 + 49.8931i 0.0856214 + 0.190432i
\(263\) −116.549 + 201.869i −0.443153 + 0.767563i −0.997921 0.0644415i \(-0.979473\pi\)
0.554769 + 0.832005i \(0.312807\pi\)
\(264\) 256.840 291.058i 0.972877 1.10249i
\(265\) −401.703 + 231.923i −1.51586 + 0.875182i
\(266\) 86.3837 119.816i 0.324751 0.450435i
\(267\) 305.527 31.8170i 1.14430 0.119165i
\(268\) 112.066 + 56.0722i 0.418158 + 0.209224i
\(269\) 105.443 105.443i 0.391983 0.391983i −0.483411 0.875394i \(-0.660602\pi\)
0.875394 + 0.483411i \(0.160602\pi\)
\(270\) 345.881 311.927i 1.28104 1.15529i
\(271\) 95.2203 0.351367 0.175683 0.984447i \(-0.443787\pi\)
0.175683 + 0.984447i \(0.443787\pi\)
\(272\) 67.1665 156.999i 0.246936 0.577201i
\(273\) −161.558 + 199.118i −0.591787 + 0.729369i
\(274\) −408.952 + 66.3054i −1.49253 + 0.241990i
\(275\) 771.676 + 206.770i 2.80610 + 0.751891i
\(276\) 202.447 91.6817i 0.733504 0.332180i
\(277\) 48.0221 + 179.221i 0.173365 + 0.647007i 0.996824 + 0.0796318i \(0.0253745\pi\)
−0.823459 + 0.567375i \(0.807959\pi\)
\(278\) −29.7244 66.1105i −0.106922 0.237808i
\(279\) 76.0991 + 84.8423i 0.272757 + 0.304094i
\(280\) −87.9250 + 281.059i −0.314018 + 1.00378i
\(281\) 121.707 210.803i 0.433123 0.750190i −0.564018 0.825763i \(-0.690745\pi\)
0.997140 + 0.0755723i \(0.0240784\pi\)
\(282\) −29.2651 108.051i −0.103777 0.383159i
\(283\) 103.140 + 27.6363i 0.364453 + 0.0976548i 0.436398 0.899754i \(-0.356254\pi\)
−0.0719452 + 0.997409i \(0.522921\pi\)
\(284\) −30.6013 + 149.329i −0.107751 + 0.525808i
\(285\) 362.504 262.845i 1.27194 0.922264i
\(286\) −501.961 + 409.528i −1.75511 + 1.43192i
\(287\) 63.4272i 0.221001i
\(288\) 134.932 + 254.435i 0.468515 + 0.883456i
\(289\) 175.094 0.605862
\(290\) 286.803 + 351.536i 0.988975 + 1.21219i
\(291\) −100.216 + 224.512i −0.344386 + 0.771518i
\(292\) −500.876 102.642i −1.71533 0.351514i
\(293\) −65.6590 + 245.043i −0.224092 + 0.836324i 0.758674 + 0.651471i \(0.225848\pi\)
−0.982766 + 0.184853i \(0.940819\pi\)
\(294\) 47.3247 178.545i 0.160968 0.607297i
\(295\) −490.599 283.247i −1.66305 0.960160i
\(296\) −60.9541 + 194.844i −0.205926 + 0.658257i
\(297\) 366.927 236.792i 1.23545 0.797280i
\(298\) 172.986 77.7775i 0.580490 0.260998i
\(299\) −358.256 + 95.9943i −1.19818 + 0.321051i
\(300\) −345.340 + 481.730i −1.15113 + 1.60577i
\(301\) 20.0810 74.9435i 0.0667144 0.248982i
\(302\) −31.7064 195.556i −0.104988 0.647537i
\(303\) 277.234 106.116i 0.914963 0.350218i
\(304\) 102.993 + 257.006i 0.338792 + 0.845415i
\(305\) 106.455i 0.349034i
\(306\) 120.637 149.507i 0.394238 0.488584i
\(307\) −62.8799 62.8799i −0.204821 0.204821i 0.597241 0.802062i \(-0.296264\pi\)
−0.802062 + 0.597241i \(0.796264\pi\)
\(308\) −123.552 + 246.931i −0.401142 + 0.801725i
\(309\) 481.310 348.990i 1.55764 1.12942i
\(310\) −177.197 127.754i −0.571602 0.412109i
\(311\) −146.124 253.095i −0.469853 0.813809i 0.529553 0.848277i \(-0.322360\pi\)
−0.999406 + 0.0344676i \(0.989026\pi\)
\(312\) −153.096 455.606i −0.490692 1.46028i
\(313\) −118.420 68.3697i −0.378338 0.218434i 0.298757 0.954329i \(-0.403428\pi\)
−0.677095 + 0.735896i \(0.736761\pi\)
\(314\) −64.6326 + 29.0599i −0.205836 + 0.0925474i
\(315\) −180.971 + 277.508i −0.574511 + 0.880977i
\(316\) 45.1736 + 40.0802i 0.142954 + 0.126836i
\(317\) 34.1866 + 127.586i 0.107844 + 0.402480i 0.998652 0.0518996i \(-0.0165276\pi\)
−0.890808 + 0.454380i \(0.849861\pi\)
\(318\) −0.871345 322.668i −0.00274008 1.01468i
\(319\) 212.690 + 368.391i 0.666741 + 1.15483i
\(320\) −356.719 421.270i −1.11475 1.31647i
\(321\) 164.574 + 133.530i 0.512690 + 0.415980i
\(322\) −122.488 + 99.9329i −0.380399 + 0.310351i
\(323\) 130.594 130.594i 0.404314 0.404314i
\(324\) 68.4687 + 316.683i 0.211323 + 0.977416i
\(325\) 699.467 699.467i 2.15221 2.15221i
\(326\) 22.6596 223.448i 0.0695078 0.685422i
\(327\) 281.609 + 228.489i 0.861190 + 0.698742i
\(328\) −100.415 63.6556i −0.306145 0.194072i
\(329\) 39.8137 + 68.9594i 0.121014 + 0.209603i
\(330\) −590.265 + 593.462i −1.78868 + 1.79837i
\(331\) −54.4461 203.196i −0.164490 0.613884i −0.998105 0.0615381i \(-0.980399\pi\)
0.833615 0.552346i \(-0.186267\pi\)
\(332\) 453.280 27.0806i 1.36530 0.0815679i
\(333\) −125.458 + 192.383i −0.376752 + 0.577725i
\(334\) −211.117 + 556.048i −0.632088 + 1.66481i
\(335\) −234.007 135.104i −0.698530 0.403296i
\(336\) −139.145 150.352i −0.414123 0.447475i
\(337\) −214.471 371.475i −0.636414 1.10230i −0.986214 0.165476i \(-0.947084\pi\)
0.349800 0.936824i \(-0.386249\pi\)
\(338\) 74.2828 + 458.155i 0.219772 + 1.35549i
\(339\) −48.4545 + 35.1335i −0.142934 + 0.103639i
\(340\) −164.762 + 329.296i −0.484595 + 0.968517i
\(341\) −144.828 144.828i −0.424717 0.424717i
\(342\) 33.0993 + 309.721i 0.0967817 + 0.905616i
\(343\) 340.514i 0.992752i
\(344\) 98.4942 + 107.005i 0.286320 + 0.311061i
\(345\) −447.549 + 171.307i −1.29724 + 0.496543i
\(346\) 32.5929 45.2070i 0.0941993 0.130656i
\(347\) −75.0550 + 280.109i −0.216297 + 0.807231i 0.769409 + 0.638756i \(0.220551\pi\)
−0.985706 + 0.168475i \(0.946116\pi\)
\(348\) −311.397 + 51.3516i −0.894818 + 0.147562i
\(349\) 359.896 96.4340i 1.03122 0.276315i 0.296751 0.954955i \(-0.404097\pi\)
0.734471 + 0.678640i \(0.237430\pi\)
\(350\) 149.653 394.161i 0.427580 1.12617i
\(351\) −26.7504 540.059i −0.0762121 1.53863i
\(352\) −266.935 443.422i −0.758339 1.25972i
\(353\) −364.255 210.302i −1.03188 0.595758i −0.114359 0.993439i \(-0.536481\pi\)
−0.917523 + 0.397682i \(0.869815\pi\)
\(354\) 340.745 197.958i 0.962558 0.559204i
\(355\) 85.0712 317.490i 0.239637 0.894339i
\(356\) 82.2231 401.235i 0.230964 1.12706i
\(357\) −55.6996 + 124.782i −0.156021 + 0.349530i
\(358\) −109.399 11.0941i −0.305585 0.0309890i
\(359\) 626.317 1.74462 0.872308 0.488956i \(-0.162622\pi\)
0.872308 + 0.488956i \(0.162622\pi\)
\(360\) −257.717 565.013i −0.715880 1.56948i
\(361\) 61.5478i 0.170492i
\(362\) 490.599 + 49.7511i 1.35525 + 0.137434i
\(363\) −341.479 + 247.601i −0.940714 + 0.682096i
\(364\) 188.297 + 285.361i 0.517299 + 0.783959i
\(365\) 1064.92 + 285.343i 2.91758 + 0.781762i
\(366\) −64.2327 36.8539i −0.175499 0.100694i
\(367\) −112.057 + 194.088i −0.305331 + 0.528849i −0.977335 0.211699i \(-0.932101\pi\)
0.672004 + 0.740548i \(0.265434\pi\)
\(368\) −35.2804 294.211i −0.0958707 0.799487i
\(369\) −89.3083 99.5691i −0.242028 0.269835i
\(370\) 156.257 411.556i 0.422317 1.11231i
\(371\) 59.4039 + 221.699i 0.160118 + 0.597570i
\(372\) 138.427 62.6892i 0.372117 0.168519i
\(373\) 306.789 + 82.2039i 0.822491 + 0.220386i 0.645435 0.763815i \(-0.276676\pi\)
0.177056 + 0.984201i \(0.443343\pi\)
\(374\) −201.905 + 280.045i −0.539852 + 0.748785i
\(375\) 397.698 490.158i 1.06053 1.30709i
\(376\) −149.131 6.17615i −0.396624 0.0164259i
\(377\) 526.706 1.39710
\(378\) −104.791 205.264i −0.277226 0.543027i
\(379\) −275.758 + 275.758i −0.727594 + 0.727594i −0.970140 0.242546i \(-0.922017\pi\)
0.242546 + 0.970140i \(0.422017\pi\)
\(380\) −188.638 566.440i −0.496416 1.49063i
\(381\) −227.733 + 23.7156i −0.597724 + 0.0622456i
\(382\) 6.85400 + 42.2735i 0.0179424 + 0.110664i
\(383\) 153.374 88.5508i 0.400456 0.231203i −0.286225 0.958162i \(-0.592400\pi\)
0.686681 + 0.726959i \(0.259067\pi\)
\(384\) 377.677 69.3965i 0.983535 0.180720i
\(385\) 297.694 515.621i 0.773231 1.33928i
\(386\) 88.1484 232.168i 0.228364 0.601472i
\(387\) 74.0002 + 145.923i 0.191215 + 0.377061i
\(388\) 245.214 + 217.566i 0.631994 + 0.560736i
\(389\) −239.507 + 64.1757i −0.615699 + 0.164976i −0.553172 0.833067i \(-0.686583\pi\)
−0.0625273 + 0.998043i \(0.519916\pi\)
\(390\) 270.944 + 1000.36i 0.694727 + 2.56503i
\(391\) −171.176 + 98.8286i −0.437791 + 0.252759i
\(392\) −208.007 131.861i −0.530631 0.336379i
\(393\) 81.0338 + 12.9139i 0.206193 + 0.0328598i
\(394\) 66.9521 660.220i 0.169929 1.67568i
\(395\) −92.0801 92.0801i −0.233114 0.233114i
\(396\) −153.737 561.603i −0.388224 1.41819i
\(397\) 264.780 + 264.780i 0.666953 + 0.666953i 0.957009 0.290057i \(-0.0936742\pi\)
−0.290057 + 0.957009i \(0.593674\pi\)
\(398\) −314.560 + 256.636i −0.790352 + 0.644813i
\(399\) −79.2035 206.923i −0.198505 0.518604i
\(400\) 473.829 + 632.505i 1.18457 + 1.58126i
\(401\) 424.888 245.309i 1.05957 0.611744i 0.134258 0.990946i \(-0.457135\pi\)
0.925314 + 0.379202i \(0.123802\pi\)
\(402\) 162.530 94.4228i 0.404303 0.234883i
\(403\) −244.965 + 65.6381i −0.607853 + 0.162874i
\(404\) −23.6043 395.094i −0.0584266 0.977955i
\(405\) −106.652 690.452i −0.263338 1.70482i
\(406\) 204.749 92.0587i 0.504308 0.226746i
\(407\) 206.377 357.455i 0.507068 0.878267i
\(408\) −141.650 213.413i −0.347182 0.523071i
\(409\) 472.092 272.563i 1.15426 0.666412i 0.204338 0.978900i \(-0.434496\pi\)
0.949922 + 0.312488i \(0.101162\pi\)
\(410\) 207.954 + 149.929i 0.507206 + 0.365681i
\(411\) −253.305 + 567.471i −0.616313 + 1.38071i
\(412\) −250.462 752.084i −0.607918 1.82545i
\(413\) −198.210 + 198.210i −0.479927 + 0.479927i
\(414\) 51.5744 329.345i 0.124576 0.795520i
\(415\) −979.148 −2.35939
\(416\) −640.747 + 11.7154i −1.54026 + 0.0281621i
\(417\) −107.373 17.1115i −0.257490 0.0410348i
\(418\) −89.5888 552.558i −0.214327 1.32191i
\(419\) −746.051 199.904i −1.78055 0.477097i −0.789867 0.613278i \(-0.789850\pi\)
−0.990684 + 0.136181i \(0.956517\pi\)
\(420\) 280.170 + 341.519i 0.667072 + 0.813141i
\(421\) 76.7375 + 286.388i 0.182274 + 0.680257i 0.995198 + 0.0978865i \(0.0312082\pi\)
−0.812923 + 0.582371i \(0.802125\pi\)
\(422\) −356.714 + 160.385i −0.845294 + 0.380059i
\(423\) −159.598 52.1941i −0.377300 0.123390i
\(424\) −410.602 128.451i −0.968401 0.302950i
\(425\) 263.582 456.537i 0.620193 1.07421i
\(426\) 162.115 + 161.242i 0.380552 + 0.378503i
\(427\) 50.8811 + 13.6335i 0.119159 + 0.0319287i
\(428\) 235.855 155.630i 0.551063 0.363621i
\(429\) 100.650 + 966.511i 0.234616 + 2.25294i
\(430\) −198.244 242.989i −0.461033 0.565092i
\(431\) 629.535i 1.46064i 0.683107 + 0.730318i \(0.260628\pi\)
−0.683107 + 0.730318i \(0.739372\pi\)
\(432\) 430.135 + 40.1018i 0.995682 + 0.0928282i
\(433\) −848.660 −1.95995 −0.979977 0.199112i \(-0.936194\pi\)
−0.979977 + 0.199112i \(0.936194\pi\)
\(434\) −83.7540 + 68.3312i −0.192981 + 0.157445i
\(435\) 676.872 70.4880i 1.55603 0.162041i
\(436\) 403.582 266.305i 0.925647 0.610792i
\(437\) 82.9468 309.562i 0.189810 0.708379i
\(438\) −540.833 + 543.762i −1.23478 + 1.24147i
\(439\) −395.202 228.170i −0.900233 0.519750i −0.0229572 0.999736i \(-0.507308\pi\)
−0.877276 + 0.479987i \(0.840641\pi\)
\(440\) 517.545 + 988.775i 1.17624 + 2.24722i
\(441\) −184.999 206.254i −0.419500 0.467697i
\(442\) 175.297 + 389.881i 0.396600 + 0.882084i
\(443\) −64.7626 + 17.3531i −0.146191 + 0.0391718i −0.331172 0.943570i \(-0.607444\pi\)
0.184981 + 0.982742i \(0.440778\pi\)
\(444\) 194.228 + 236.759i 0.437451 + 0.533240i
\(445\) −228.579 + 853.068i −0.513660 + 1.91701i
\(446\) −390.528 + 63.3181i −0.875623 + 0.141969i
\(447\) 44.7743 280.955i 0.100166 0.628535i
\(448\) −247.033 + 116.545i −0.551413 + 0.260145i
\(449\) 692.689i 1.54274i 0.636388 + 0.771369i \(0.280428\pi\)
−0.636388 + 0.771369i \(0.719572\pi\)
\(450\) 320.069 + 829.479i 0.711263 + 1.84329i
\(451\) 169.968 + 169.968i 0.376868 + 0.376868i
\(452\) 25.2145 + 75.7138i 0.0557843 + 0.167508i
\(453\) −271.358 121.127i −0.599024 0.267389i
\(454\) 304.450 422.278i 0.670596 0.930129i
\(455\) −368.605 638.442i −0.810121 1.40317i
\(456\) 407.081 + 82.2763i 0.892722 + 0.180431i
\(457\) −17.1245 9.88683i −0.0374715 0.0216342i 0.481147 0.876640i \(-0.340220\pi\)
−0.518619 + 0.855006i \(0.673554\pi\)
\(458\) −92.3771 205.457i −0.201697 0.448597i
\(459\) −88.2606 274.313i −0.192289 0.597631i
\(460\) 38.1053 + 637.815i 0.0828377 + 1.38655i
\(461\) −117.395 438.124i −0.254653 0.950376i −0.968283 0.249854i \(-0.919617\pi\)
0.713631 0.700522i \(-0.247049\pi\)
\(462\) 208.055 + 358.125i 0.450335 + 0.775162i
\(463\) 250.824 + 434.441i 0.541737 + 0.938316i 0.998804 + 0.0488843i \(0.0155666\pi\)
−0.457067 + 0.889432i \(0.651100\pi\)
\(464\) −59.7426 + 416.541i −0.128756 + 0.897717i
\(465\) −306.021 + 117.135i −0.658109 + 0.251903i
\(466\) 355.541 + 435.789i 0.762963 + 0.935169i
\(467\) −233.073 + 233.073i −0.499086 + 0.499086i −0.911153 0.412067i \(-0.864807\pi\)
0.412067 + 0.911153i \(0.364807\pi\)
\(468\) −697.393 182.835i −1.49016 0.390672i
\(469\) −94.5428 + 94.5428i −0.201584 + 0.201584i
\(470\) 320.204 + 32.4715i 0.681284 + 0.0690882i
\(471\) −16.7289 + 104.973i −0.0355179 + 0.222872i
\(472\) −114.875 512.722i −0.243378 1.08628i
\(473\) −147.016 254.640i −0.310817 0.538350i
\(474\) 87.4362 23.6817i 0.184465 0.0499614i
\(475\) 221.224 + 825.620i 0.465735 + 1.73815i
\(476\) 136.288 + 120.922i 0.286320 + 0.254037i
\(477\) −405.415 264.383i −0.849926 0.554261i
\(478\) 513.708 + 195.042i 1.07470 + 0.408038i
\(479\) −90.3640 52.1717i −0.188651 0.108918i 0.402700 0.915332i \(-0.368072\pi\)
−0.591351 + 0.806414i \(0.701405\pi\)
\(480\) −821.859 + 100.805i −1.71221 + 0.210011i
\(481\) −255.536 442.601i −0.531259 0.920168i
\(482\) 232.324 37.6677i 0.481999 0.0781488i
\(483\) 24.5607 + 235.848i 0.0508503 + 0.488298i
\(484\) 177.697 + 533.588i 0.367143 + 1.10245i
\(485\) −499.835 499.835i −1.03059 1.03059i
\(486\) 453.524 + 174.676i 0.933177 + 0.359417i
\(487\) 29.0400i 0.0596304i 0.999555 + 0.0298152i \(0.00949188\pi\)
−0.999555 + 0.0298152i \(0.990508\pi\)
\(488\) −72.6484 + 66.8703i −0.148870 + 0.137029i
\(489\) −261.610 212.262i −0.534990 0.434074i
\(490\) 430.771 + 310.573i 0.879124 + 0.633823i
\(491\) 205.184 765.757i 0.417890 1.55959i −0.361086 0.932533i \(-0.617594\pi\)
0.778976 0.627054i \(-0.215739\pi\)
\(492\) −162.455 + 73.5708i −0.330194 + 0.149534i
\(493\) 271.129 72.6488i 0.549957 0.147361i
\(494\) −647.979 246.021i −1.31170 0.498019i
\(495\) 258.692 + 1228.60i 0.522611 + 2.48202i
\(496\) −24.1237 201.173i −0.0486365 0.405591i
\(497\) −140.852 81.3207i −0.283404 0.163623i
\(498\) 338.972 590.795i 0.680666 1.18634i
\(499\) 192.975 720.192i 0.386723 1.44327i −0.448709 0.893678i \(-0.648116\pi\)
0.835432 0.549593i \(-0.185217\pi\)
\(500\) −463.521 702.459i −0.927041 1.40492i
\(501\) 523.711 + 722.278i 1.04533 + 1.44167i
\(502\) 46.4905 458.446i 0.0926106 0.913239i
\(503\) 22.4731 0.0446781 0.0223390 0.999750i \(-0.492889\pi\)
0.0223390 + 0.999750i \(0.492889\pi\)
\(504\) −303.057 + 50.8174i −0.601304 + 0.100828i
\(505\) 853.458i 1.69002i
\(506\) −60.4425 + 596.028i −0.119452 + 1.17792i
\(507\) 635.745 + 283.780i 1.25393 + 0.559725i
\(508\) −61.2871 + 299.071i −0.120644 + 0.588722i
\(509\) −810.744 217.238i −1.59282 0.426794i −0.649954 0.759974i \(-0.725212\pi\)
−0.942863 + 0.333180i \(0.891878\pi\)
\(510\) 277.452 + 477.578i 0.544023 + 0.936427i
\(511\) 272.763 472.440i 0.533784 0.924540i
\(512\) 63.4128 508.058i 0.123853 0.992301i
\(513\) 415.692 + 213.309i 0.810316 + 0.415808i
\(514\) −277.061 105.193i −0.539029 0.204656i
\(515\) 442.394 + 1651.04i 0.859018 + 3.20590i
\(516\) 215.244 35.4954i 0.417140 0.0687895i
\(517\) 291.482 + 78.1024i 0.563795 + 0.151068i
\(518\) −176.694 127.391i −0.341108 0.245929i
\(519\) −29.8838 78.0731i −0.0575796 0.150430i
\(520\) 1380.69 + 57.1803i 2.65517 + 0.109962i
\(521\) −860.751 −1.65211 −0.826057 0.563587i \(-0.809421\pi\)
−0.826057 + 0.563587i \(0.809421\pi\)
\(522\) −191.796 + 432.811i −0.367425 + 0.829140i
\(523\) 590.670 590.670i 1.12939 1.12939i 0.139112 0.990277i \(-0.455575\pi\)
0.990277 0.139112i \(-0.0444248\pi\)
\(524\) 48.9562 97.8443i 0.0934279 0.186726i
\(525\) −371.239 511.996i −0.707122 0.975230i
\(526\) 460.187 74.6124i 0.874881 0.141849i
\(527\) −117.045 + 67.5761i −0.222097 + 0.128228i
\(528\) −775.773 30.0298i −1.46927 0.0568747i
\(529\) 93.0058 161.091i 0.175814 0.304519i
\(530\) 867.286 + 329.287i 1.63639 + 0.621295i
\(531\) 32.0650 590.242i 0.0603860 1.11157i
\(532\) −294.892 + 17.6179i −0.554309 + 0.0331164i
\(533\) 287.485 77.0315i 0.539372 0.144524i
\(534\) −435.589 433.243i −0.815710 0.811316i
\(535\) −527.681 + 304.657i −0.986320 + 0.569452i
\(536\) −54.7933 244.560i −0.102226 0.456268i
\(537\) −103.923 + 128.084i −0.193525 + 0.238517i
\(538\) −296.717 30.0897i −0.551519 0.0559289i
\(539\) 352.082 + 352.082i 0.653214 + 0.653214i
\(540\) −920.690 141.631i −1.70498 0.262279i
\(541\) 709.094 + 709.094i 1.31071 + 1.31071i 0.920892 + 0.389817i \(0.127462\pi\)
0.389817 + 0.920892i \(0.372538\pi\)
\(542\) −120.389 147.561i −0.222119 0.272253i
\(543\) 466.041 574.389i 0.858270 1.05781i
\(544\) −328.217 + 94.4092i −0.603340 + 0.173546i
\(545\) −902.939 + 521.312i −1.65677 + 0.956536i
\(546\) 512.829 1.38486i 0.939247 0.00253638i
\(547\) −376.806 + 100.965i −0.688860 + 0.184579i −0.586235 0.810141i \(-0.699391\pi\)
−0.102624 + 0.994720i \(0.532724\pi\)
\(548\) 619.797 + 549.914i 1.13102 + 1.00349i
\(549\) −99.0706 + 50.2406i −0.180456 + 0.0915130i
\(550\) −655.215 1457.27i −1.19130 2.64959i
\(551\) −227.558 + 394.143i −0.412992 + 0.715323i
\(552\) −398.034 197.813i −0.721076 0.358358i
\(553\) −55.8028 + 32.2178i −0.100909 + 0.0582600i
\(554\) 217.020 301.011i 0.391733 0.543341i
\(555\) −387.622 534.590i −0.698418 0.963225i
\(556\) −64.8691 + 129.648i −0.116671 + 0.233180i
\(557\) 121.809 121.809i 0.218688 0.218688i −0.589257 0.807946i \(-0.700580\pi\)
0.807946 + 0.589257i \(0.200580\pi\)
\(558\) 35.2651 225.197i 0.0631990 0.403578i
\(559\) −364.071 −0.651290
\(560\) 546.716 219.091i 0.976278 0.391234i
\(561\) 185.122 + 483.642i 0.329986 + 0.862106i
\(562\) −480.554 + 77.9146i −0.855079 + 0.138638i
\(563\) −701.738 188.030i −1.24643 0.333979i −0.425472 0.904972i \(-0.639892\pi\)
−0.820955 + 0.570993i \(0.806558\pi\)
\(564\) −130.444 + 181.962i −0.231284 + 0.322628i
\(565\) −44.5367 166.213i −0.0788261 0.294183i
\(566\) −87.5742 194.775i −0.154725 0.344126i
\(567\) −343.665 37.4498i −0.606110 0.0660490i
\(568\) 270.102 141.377i 0.475533 0.248904i
\(569\) −114.358 + 198.073i −0.200980 + 0.348108i −0.948845 0.315744i \(-0.897746\pi\)
0.747864 + 0.663852i \(0.231079\pi\)
\(570\) −865.645 229.445i −1.51868 0.402536i
\(571\) −277.397 74.3283i −0.485809 0.130172i 0.00759710 0.999971i \(-0.497582\pi\)
−0.493406 + 0.869799i \(0.664248\pi\)
\(572\) 1269.27 + 260.106i 2.21901 + 0.454731i
\(573\) 58.6596 + 26.1841i 0.102373 + 0.0456966i
\(574\) 98.2919 80.1920i 0.171240 0.139707i
\(575\) 914.771i 1.59091i
\(576\) 223.696 530.788i 0.388361 0.921507i
\(577\) 1015.70 1.76031 0.880156 0.474685i \(-0.157438\pi\)
0.880156 + 0.474685i \(0.157438\pi\)
\(578\) −221.374 271.340i −0.383000 0.469446i
\(579\) −218.667 301.575i −0.377663 0.520855i
\(580\) 182.159 888.904i 0.314067 1.53259i
\(581\) −125.398 + 467.990i −0.215831 + 0.805491i
\(582\) 474.626 128.550i 0.815509 0.220877i
\(583\) 753.278 + 434.905i 1.29207 + 0.745978i
\(584\) 474.203 + 905.969i 0.811991 + 1.55132i
\(585\) 1477.60 + 483.226i 2.52581 + 0.826027i
\(586\) 462.752 208.061i 0.789678 0.355053i
\(587\) 19.9763 5.35264i 0.0340312 0.00911864i −0.241763 0.970335i \(-0.577726\pi\)
0.275794 + 0.961217i \(0.411059\pi\)
\(588\) −336.521 + 152.400i −0.572315 + 0.259183i
\(589\) 56.7166 211.669i 0.0962931 0.359371i
\(590\) 181.329 + 1118.38i 0.307337 + 1.89557i
\(591\) −772.979 627.170i −1.30792 1.06120i
\(592\) 379.011 151.885i 0.640222 0.256563i
\(593\) 938.907i 1.58332i −0.610964 0.791659i \(-0.709218\pi\)
0.610964 0.791659i \(-0.290782\pi\)
\(594\) −830.864 269.240i −1.39876 0.453266i
\(595\) −277.805 277.805i −0.466899 0.466899i
\(596\) −339.239 169.738i −0.569193 0.284795i
\(597\) 63.0738 + 605.676i 0.105651 + 1.01453i
\(598\) 601.708 + 433.814i 1.00620 + 0.725442i
\(599\) 337.675 + 584.869i 0.563730 + 0.976410i 0.997167 + 0.0752255i \(0.0239677\pi\)
−0.433436 + 0.901184i \(0.642699\pi\)
\(600\) 1183.15 73.8924i 1.97191 0.123154i
\(601\) −744.438 429.801i −1.23866 0.715144i −0.269844 0.962904i \(-0.586972\pi\)
−0.968821 + 0.247761i \(0.920305\pi\)
\(602\) −141.527 + 63.6330i −0.235095 + 0.105703i
\(603\) 15.2945 281.535i 0.0253639 0.466891i
\(604\) −262.962 + 296.379i −0.435368 + 0.490694i
\(605\) −313.869 1171.38i −0.518792 1.93616i
\(606\) −514.957 295.459i −0.849764 0.487556i
\(607\) −46.7213 80.9237i −0.0769708 0.133317i 0.824971 0.565175i \(-0.191192\pi\)
−0.901942 + 0.431858i \(0.857858\pi\)
\(608\) 268.062 484.543i 0.440891 0.796946i
\(609\) 52.9955 332.543i 0.0870206 0.546047i
\(610\) 164.972 134.593i 0.270446 0.220645i
\(611\) 264.207 264.207i 0.432417 0.432417i
\(612\) −384.210 + 2.07509i −0.627795 + 0.00339067i
\(613\) 74.1488 74.1488i 0.120960 0.120960i −0.644035 0.764996i \(-0.722741\pi\)
0.764996 + 0.644035i \(0.222741\pi\)
\(614\) −17.9437 + 176.944i −0.0292242 + 0.288182i
\(615\) 359.140 137.467i 0.583967 0.223524i
\(616\) 538.873 120.734i 0.874793 0.195996i
\(617\) −386.923 670.170i −0.627103 1.08617i −0.988130 0.153619i \(-0.950907\pi\)
0.361027 0.932555i \(-0.382426\pi\)
\(618\) −1149.35 304.643i −1.85979 0.492951i
\(619\) 187.068 + 698.147i 0.302210 + 1.12786i 0.935321 + 0.353802i \(0.115111\pi\)
−0.633111 + 0.774061i \(0.718222\pi\)
\(620\) 26.0553 + 436.119i 0.0420247 + 0.703418i
\(621\) −370.640 335.655i −0.596844 0.540508i
\(622\) −207.468 + 546.437i −0.333551 + 0.878517i
\(623\) 378.456 + 218.501i 0.607473 + 0.350725i
\(624\) −512.482 + 813.280i −0.821286 + 1.30333i
\(625\) 289.953 + 502.213i 0.463924 + 0.803540i
\(626\) 43.7689 + 269.954i 0.0699183 + 0.431236i
\(627\) −766.741 342.254i −1.22287 0.545859i
\(628\) 126.749 + 63.4189i 0.201830 + 0.100985i
\(629\) −192.588 192.588i −0.306182 0.306182i
\(630\) 658.853 70.4105i 1.04580 0.111763i
\(631\) 232.499i 0.368461i −0.982883 0.184231i \(-0.941021\pi\)
0.982883 0.184231i \(-0.0589793\pi\)
\(632\) 4.99782 120.679i 0.00790795 0.190947i
\(633\) −92.3288 + 579.356i −0.145859 + 0.915255i
\(634\) 154.495 214.288i 0.243683 0.337993i
\(635\) 170.377 635.856i 0.268310 1.00135i
\(636\) −498.930 + 409.304i −0.784481 + 0.643560i
\(637\) 595.517 159.568i 0.934877 0.250500i
\(638\) 301.979 795.364i 0.473322 1.24665i
\(639\) 335.614 70.6667i 0.525218 0.110589i
\(640\) −201.828 + 1085.42i −0.315356 + 1.69597i
\(641\) −154.261 89.0624i −0.240656 0.138943i 0.374822 0.927097i \(-0.377704\pi\)
−0.615478 + 0.788154i \(0.711037\pi\)
\(642\) −1.14461 423.860i −0.00178288 0.660218i
\(643\) 119.295 445.215i 0.185529 0.692402i −0.808988 0.587825i \(-0.799984\pi\)
0.994517 0.104577i \(-0.0333489\pi\)
\(644\) 309.728 + 63.4710i 0.480944 + 0.0985575i
\(645\) −467.869 + 48.7229i −0.725379 + 0.0755393i
\(646\) −367.490 37.2667i −0.568869 0.0576884i
\(647\) −978.908 −1.51300 −0.756498 0.653996i \(-0.773091\pi\)
−0.756498 + 0.653996i \(0.773091\pi\)
\(648\) 404.191 506.492i 0.623751 0.781623i
\(649\) 1062.30i 1.63682i
\(650\) −1968.30 199.603i −3.02815 0.307081i
\(651\) 16.7939 + 161.266i 0.0257970 + 0.247720i
\(652\) −374.921 + 247.393i −0.575032 + 0.379437i
\(653\) −123.593 33.1167i −0.189270 0.0507148i 0.162939 0.986636i \(-0.447903\pi\)
−0.352209 + 0.935921i \(0.614569\pi\)
\(654\) −1.95859 725.286i −0.00299479 1.10900i
\(655\) −117.959 + 204.310i −0.180089 + 0.311924i
\(656\) 28.3111 + 236.093i 0.0431572 + 0.359897i
\(657\) 237.028 + 1125.71i 0.360773 + 1.71341i
\(658\) 56.5278 148.885i 0.0859085 0.226269i
\(659\) 119.886 + 447.422i 0.181922 + 0.678941i 0.995269 + 0.0971622i \(0.0309766\pi\)
−0.813347 + 0.581779i \(0.802357\pi\)
\(660\) 1665.96 + 164.399i 2.52418 + 0.249089i
\(661\) −1025.09 274.672i −1.55082 0.415541i −0.621076 0.783750i \(-0.713304\pi\)
−0.929743 + 0.368210i \(0.879971\pi\)
\(662\) −246.051 + 341.277i −0.371678 + 0.515525i
\(663\) 633.224 + 100.914i 0.955090 + 0.152207i
\(664\) −615.055 668.200i −0.926287 1.00632i
\(665\) 637.009 0.957908
\(666\) 456.750 48.8121i 0.685811 0.0732914i
\(667\) 344.417 344.417i 0.516367 0.516367i
\(668\) 1128.61 375.856i 1.68954 0.562658i
\(669\) −241.892 + 541.904i −0.361573 + 0.810022i
\(670\) 86.4909 + 533.451i 0.129091 + 0.796195i
\(671\) 172.882 99.8132i 0.257648 0.148753i
\(672\) −57.0733 + 405.723i −0.0849305 + 0.603754i
\(673\) −477.904 + 827.754i −0.710110 + 1.22995i 0.254705 + 0.967019i \(0.418021\pi\)
−0.964815 + 0.262928i \(0.915312\pi\)
\(674\) −304.508 + 802.024i −0.451793 + 1.18995i
\(675\) 1303.69 + 281.018i 1.93139 + 0.416323i
\(676\) 616.076 694.366i 0.911355 1.02717i
\(677\) 903.751 242.159i 1.33493 0.357695i 0.480382 0.877060i \(-0.340498\pi\)
0.854553 + 0.519365i \(0.173831\pi\)
\(678\) 115.707 + 30.6691i 0.170660 + 0.0452346i
\(679\) −302.912 + 174.886i −0.446115 + 0.257565i
\(680\) 718.614 161.005i 1.05679 0.236771i
\(681\) −279.145 729.280i −0.409904 1.07090i
\(682\) −41.3288 + 407.547i −0.0605995 + 0.597576i
\(683\) −393.319 393.319i −0.575870 0.575870i 0.357893 0.933763i \(-0.383495\pi\)
−0.933763 + 0.357893i \(0.883495\pi\)
\(684\) 438.120 442.878i 0.640526 0.647483i
\(685\) −1263.37 1263.37i −1.84434 1.84434i
\(686\) 527.688 430.517i 0.769224 0.627576i
\(687\) −333.693 53.1788i −0.485725 0.0774073i
\(688\) 41.2954 287.922i 0.0600224 0.418492i
\(689\) 932.708 538.499i 1.35371 0.781567i
\(690\) 831.314 + 476.971i 1.20480 + 0.691262i
\(691\) 358.967 96.1850i 0.519489 0.139197i 0.0104590 0.999945i \(-0.496671\pi\)
0.509030 + 0.860749i \(0.330004\pi\)
\(692\) −111.264 + 6.64732i −0.160786 + 0.00960596i
\(693\) 620.346 + 33.7004i 0.895161 + 0.0486297i
\(694\) 528.972 237.835i 0.762208 0.342702i
\(695\) 156.300 270.720i 0.224892 0.389525i
\(696\) 473.282 + 417.641i 0.680003 + 0.600058i
\(697\) 137.362 79.3059i 0.197076 0.113782i
\(698\) −604.464 435.801i −0.865995 0.624357i
\(699\) 839.099 87.3819i 1.20043 0.125010i
\(700\) −800.032 + 266.430i −1.14290 + 0.380614i
\(701\) 314.121 314.121i 0.448105 0.448105i −0.446619 0.894724i \(-0.647372\pi\)
0.894724 + 0.446619i \(0.147372\pi\)
\(702\) −803.097 + 724.259i −1.14401 + 1.03171i
\(703\) 441.607 0.628175
\(704\) −349.672 + 974.290i −0.496693 + 1.38394i
\(705\) 304.175 374.891i 0.431453 0.531760i
\(706\) 134.631 + 830.366i 0.190696 + 1.17616i
\(707\) 407.916 + 109.301i 0.576968 + 0.154598i
\(708\) −737.582 277.764i −1.04178 0.392323i
\(709\) 158.573 + 591.802i 0.223657 + 0.834699i 0.982938 + 0.183936i \(0.0588840\pi\)
−0.759281 + 0.650763i \(0.774449\pi\)
\(710\) −599.565 + 269.575i −0.844458 + 0.379683i
\(711\) 42.2362 129.149i 0.0594039 0.181644i
\(712\) −725.741 + 379.868i −1.01930 + 0.533522i
\(713\) −117.263 + 203.105i −0.164464 + 0.284860i
\(714\) 263.794 71.4475i 0.369460 0.100067i
\(715\) −2698.61 723.091i −3.77428 1.01132i
\(716\) 121.123 + 183.561i 0.169166 + 0.256369i
\(717\) 667.281 483.834i 0.930657 0.674804i
\(718\) −791.863 970.591i −1.10287 1.35180i
\(719\) 1339.60i 1.86314i 0.363563 + 0.931570i \(0.381560\pi\)
−0.363563 + 0.931570i \(0.618440\pi\)
\(720\) −549.754 + 1113.73i −0.763547 + 1.54685i
\(721\) 845.782 1.17307
\(722\) −95.3793 + 77.8158i −0.132104 + 0.107778i
\(723\) 143.901 322.377i 0.199033 0.445888i
\(724\) −543.174 823.173i −0.750240 1.13698i
\(725\) −336.224 + 1254.80i −0.463757 + 1.73076i
\(726\) 815.439 + 216.138i 1.12319 + 0.297711i
\(727\) 89.3724 + 51.5992i 0.122933 + 0.0709755i 0.560206 0.828354i \(-0.310722\pi\)
−0.437272 + 0.899329i \(0.644055\pi\)
\(728\) 204.152 652.586i 0.280428 0.896410i
\(729\) 592.221 425.106i 0.812375 0.583135i
\(730\) −904.199 2011.04i −1.23863 2.75485i
\(731\) −187.410 + 50.2165i −0.256375 + 0.0686956i
\(732\) 24.0987 + 146.135i 0.0329218 + 0.199638i
\(733\) −95.9769 + 358.191i −0.130937 + 0.488664i −0.999982 0.00607015i \(-0.998068\pi\)
0.869045 + 0.494734i \(0.164734\pi\)
\(734\) 442.448 71.7363i 0.602791 0.0977333i
\(735\) 743.946 284.758i 1.01217 0.387426i
\(736\) −411.328 + 426.649i −0.558869 + 0.579687i
\(737\) 506.698i 0.687514i
\(738\) −41.3863 + 264.286i −0.0560790 + 0.358111i
\(739\) 499.501 + 499.501i 0.675915 + 0.675915i 0.959073 0.283158i \(-0.0913821\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(740\) −835.338 + 278.187i −1.12883 + 0.375929i
\(741\) −841.692 + 610.297i −1.13589 + 0.823612i
\(742\) 268.456 372.354i 0.361801 0.501825i
\(743\) 347.803 + 602.412i 0.468106 + 0.810784i 0.999336 0.0364442i \(-0.0116031\pi\)
−0.531229 + 0.847228i \(0.678270\pi\)
\(744\) −272.164 135.259i −0.365812 0.181800i
\(745\) 708.371 + 408.978i 0.950833 + 0.548964i
\(746\) −260.489 579.356i −0.349180 0.776617i
\(747\) −462.100 911.224i −0.618607 1.21985i
\(748\) 689.252 41.1784i 0.921460 0.0550513i
\(749\) 78.0337 + 291.226i 0.104184 + 0.388819i
\(750\) −1262.40 + 3.40905i −1.68320 + 0.00454540i
\(751\) 68.1628 + 118.062i 0.0907628 + 0.157206i 0.907832 0.419333i \(-0.137736\pi\)
−0.817070 + 0.576539i \(0.804403\pi\)
\(752\) 178.977 + 238.913i 0.238002 + 0.317704i
\(753\) −536.744 435.497i −0.712808 0.578349i
\(754\) −665.923 816.226i −0.883187 1.08253i
\(755\) 604.128 604.128i 0.800170 0.800170i
\(756\) −185.604 + 421.912i −0.245509 + 0.558084i
\(757\) −490.578 + 490.578i −0.648056 + 0.648056i −0.952523 0.304467i \(-0.901522\pi\)
0.304467 + 0.952523i \(0.401522\pi\)
\(758\) 775.981 + 78.6914i 1.02372 + 0.103814i
\(759\) 697.824 + 566.192i 0.919399 + 0.745971i
\(760\) −639.302 + 1008.49i −0.841187 + 1.32696i
\(761\) 219.368 + 379.956i 0.288263 + 0.499286i 0.973395 0.229133i \(-0.0735890\pi\)
−0.685132 + 0.728418i \(0.740256\pi\)
\(762\) 324.678 + 322.929i 0.426086 + 0.423791i
\(763\) 133.527 + 498.329i 0.175003 + 0.653118i
\(764\) 56.8447 64.0685i 0.0744041 0.0838593i
\(765\) 827.264 + 44.9412i 1.08139 + 0.0587467i
\(766\) −331.139 125.725i −0.432296 0.164132i
\(767\) 1139.11 + 657.668i 1.48516 + 0.857455i
\(768\) −585.046 497.540i −0.761778 0.647838i
\(769\) −4.71464 8.16600i −0.00613087 0.0106190i 0.862944 0.505300i \(-0.168618\pi\)
−0.869075 + 0.494681i \(0.835285\pi\)
\(770\) −1175.43 + 190.578i −1.52653 + 0.247503i
\(771\) −359.888 + 260.949i −0.466781 + 0.338455i
\(772\) −471.234 + 156.932i −0.610406 + 0.203280i
\(773\) −99.7597 99.7597i −0.129055 0.129055i 0.639629 0.768684i \(-0.279088\pi\)
−0.768684 + 0.639629i \(0.779088\pi\)
\(774\) 132.574 299.169i 0.171284 0.386523i
\(775\) 625.494i 0.807089i
\(776\) 27.1295 655.075i 0.0349607 0.844168i
\(777\) −305.153 + 116.803i −0.392732 + 0.150325i
\(778\) 402.264 + 290.021i 0.517049 + 0.372777i
\(779\) −66.5614 + 248.411i −0.0854447 + 0.318884i
\(780\) 1207.68 1684.65i 1.54831 2.15981i
\(781\) −595.361 + 159.527i −0.762306 + 0.204259i
\(782\) 369.573 + 140.318i 0.472600 + 0.179434i
\(783\) 385.042 + 596.651i 0.491752 + 0.762007i
\(784\) 58.6455 + 489.058i 0.0748030 + 0.623799i
\(785\) −264.668 152.806i −0.337156 0.194657i
\(786\) −82.4399 141.904i −0.104885 0.180539i
\(787\) −381.041 + 1422.06i −0.484169 + 1.80694i 0.0996051 + 0.995027i \(0.468242\pi\)
−0.583774 + 0.811916i \(0.698425\pi\)
\(788\) −1107.78 + 730.972i −1.40581 + 0.927629i
\(789\) 285.040 638.566i 0.361267 0.809335i
\(790\) −26.2763 + 259.113i −0.0332612 + 0.327991i
\(791\) −85.1465 −0.107644
\(792\) −675.933 + 948.286i −0.853451 + 1.19733i
\(793\) 247.177i 0.311699i
\(794\) 75.5587 745.090i 0.0951621 0.938401i
\(795\) 1126.56 816.850i 1.41706 1.02748i
\(796\) 795.406 + 162.999i 0.999254 + 0.204772i
\(797\) 405.134 + 108.555i 0.508324 + 0.136205i 0.503861 0.863785i \(-0.331913\pi\)
0.00446366 + 0.999990i \(0.498579\pi\)
\(798\) −220.526 + 384.356i −0.276349 + 0.481649i
\(799\) 99.5617 172.446i 0.124608 0.215827i
\(800\) 381.111 1533.97i 0.476389 1.91746i
\(801\) −901.766 + 189.875i −1.12580 + 0.237047i
\(802\) −917.344 348.292i −1.14382 0.434280i
\(803\) −535.079 1996.94i −0.666350 2.48685i
\(804\) −351.814 132.489i −0.437580 0.164787i
\(805\) −658.514 176.448i −0.818030 0.219191i
\(806\) 411.431 + 296.630i 0.510460 + 0.368027i
\(807\) −281.864 + 347.393i −0.349274 + 0.430475i
\(808\) −582.425 + 536.102i −0.720824 + 0.663493i
\(809\) 550.664 0.680673 0.340336 0.940304i \(-0.389459\pi\)
0.340336 + 0.940304i \(0.389459\pi\)
\(810\) −935.137 + 1038.22i −1.15449 + 1.28176i
\(811\) 722.538 722.538i 0.890923 0.890923i −0.103687 0.994610i \(-0.533064\pi\)
0.994610 + 0.103687i \(0.0330640\pi\)
\(812\) −401.529 200.904i −0.494494 0.247419i
\(813\) −284.125 + 29.5881i −0.349477 + 0.0363937i
\(814\) −814.866 + 132.118i −1.00106 + 0.162307i
\(815\) 838.815 484.290i 1.02922 0.594221i
\(816\) −151.631 + 489.333i −0.185822 + 0.599673i
\(817\) 157.293 272.440i 0.192526 0.333464i
\(818\) −1019.26 386.987i −1.24604 0.473089i
\(819\) 420.194 644.342i 0.513057 0.786742i
\(820\) −30.5780 511.820i −0.0372902 0.624171i
\(821\) −562.850 + 150.815i −0.685566 + 0.183697i −0.584757 0.811209i \(-0.698810\pi\)
−0.100810 + 0.994906i \(0.532143\pi\)
\(822\) 1199.65 324.921i 1.45943 0.395281i
\(823\) 1297.92 749.355i 1.57706 0.910516i 0.581793 0.813337i \(-0.302351\pi\)
0.995267 0.0971789i \(-0.0309819\pi\)
\(824\) −848.827 + 1339.01i −1.03013 + 1.62501i
\(825\) −2366.83 377.188i −2.86888 0.457198i
\(826\) 557.762 + 56.5620i 0.675257 + 0.0684770i
\(827\) 724.214 + 724.214i 0.875712 + 0.875712i 0.993088 0.117375i \(-0.0374481\pi\)
−0.117375 + 0.993088i \(0.537448\pi\)
\(828\) −575.586 + 336.473i −0.695152 + 0.406368i
\(829\) −191.121 191.121i −0.230544 0.230544i 0.582375 0.812920i \(-0.302123\pi\)
−0.812920 + 0.582375i \(0.802123\pi\)
\(830\) 1237.95 + 1517.37i 1.49151 + 1.82815i
\(831\) −198.981 519.849i −0.239448 0.625570i
\(832\) 828.262 + 978.141i 0.995507 + 1.17565i
\(833\) 284.541 164.280i 0.341586 0.197214i
\(834\) 109.236 + 188.028i 0.130979 + 0.225454i
\(835\) −2477.63 + 663.879i −2.96722 + 0.795064i
\(836\) −743.019 + 837.441i −0.888779 + 1.00172i
\(837\) −253.433 229.511i −0.302787 0.274207i
\(838\) 633.457 + 1408.88i 0.755915 + 1.68124i
\(839\) −316.759 + 548.642i −0.377543 + 0.653924i −0.990704 0.136034i \(-0.956564\pi\)
0.613161 + 0.789958i \(0.289898\pi\)
\(840\) 175.022 865.962i 0.208360 1.03091i
\(841\) 129.297 74.6494i 0.153741 0.0887627i
\(842\) 346.790 481.004i 0.411864 0.571264i
\(843\) −297.655 + 666.827i −0.353090 + 0.791017i
\(844\) 699.544 + 350.016i 0.828844 + 0.414710i
\(845\) −1415.37 + 1415.37i −1.67499 + 1.67499i
\(846\) 120.898 + 313.316i 0.142906 + 0.370349i
\(847\) −600.064 −0.708458
\(848\) 320.073 + 798.704i 0.377445 + 0.941868i
\(849\) −316.344 50.4140i −0.372607 0.0593804i
\(850\) −1040.74 + 168.740i −1.22440 + 0.198517i
\(851\) −456.516 122.323i −0.536446 0.143740i
\(852\) 44.9087 455.088i 0.0527097 0.534140i
\(853\) −77.8998 290.726i −0.0913245 0.340828i 0.905112 0.425173i \(-0.139787\pi\)
−0.996437 + 0.0843454i \(0.973120\pi\)
\(854\) −43.2021 96.0865i −0.0505880 0.112513i
\(855\) −999.987 + 896.937i −1.16958 + 1.04905i
\(856\) −539.372 168.734i −0.630107 0.197120i
\(857\) 26.3700 45.6742i 0.0307701 0.0532955i −0.850230 0.526411i \(-0.823537\pi\)
0.881000 + 0.473116i \(0.156871\pi\)
\(858\) 1370.53 1377.95i 1.59735 1.60600i
\(859\) 1519.02 + 407.020i 1.76836 + 0.473830i 0.988383 0.151981i \(-0.0485652\pi\)
0.779975 + 0.625811i \(0.215232\pi\)
\(860\) −125.912 + 614.431i −0.146410 + 0.714454i
\(861\) −19.7089 189.258i −0.0228908 0.219812i
\(862\) 975.577 795.930i 1.13176 0.923353i
\(863\) 1189.26i 1.37805i −0.724738 0.689025i \(-0.758039\pi\)
0.724738 0.689025i \(-0.241961\pi\)
\(864\) −481.681 717.272i −0.557501 0.830176i
\(865\) 240.346 0.277857
\(866\) 1072.97 + 1315.15i 1.23900 + 1.51865i
\(867\) −522.457 + 54.4075i −0.602603 + 0.0627538i
\(868\) 211.783 + 43.3996i 0.243989 + 0.0499996i
\(869\) −63.2015 + 235.871i −0.0727289 + 0.271428i
\(870\) −965.014 959.816i −1.10921 1.10324i
\(871\) 543.339 + 313.697i 0.623810 + 0.360157i
\(872\) −922.943 288.729i −1.05842 0.331111i
\(873\) 229.269 701.053i 0.262622 0.803039i
\(874\) −584.592 + 262.843i −0.668870 + 0.300735i
\(875\) 867.372 232.412i 0.991283 0.265613i
\(876\) 1526.44 + 150.631i 1.74251 + 0.171953i
\(877\) 103.814 387.439i 0.118374 0.441778i −0.881143 0.472850i \(-0.843225\pi\)
0.999517 + 0.0310718i \(0.00989206\pi\)
\(878\) 146.070 + 900.916i 0.166366 + 1.02610i
\(879\) 119.775 751.577i 0.136262 0.855036i
\(880\) 877.944 2052.15i 0.997664 2.33199i
\(881\) 557.459i 0.632757i −0.948633 0.316379i \(-0.897533\pi\)
0.948633 0.316379i \(-0.102467\pi\)
\(882\) −85.7305 + 547.460i −0.0972001 + 0.620703i
\(883\) −6.13732 6.13732i −0.00695053 0.00695053i 0.703623 0.710574i \(-0.251564\pi\)
−0.710574 + 0.703623i \(0.751564\pi\)
\(884\) 382.560 764.587i 0.432760 0.864917i
\(885\) 1551.89 + 692.726i 1.75355 + 0.782742i
\(886\) 108.772 + 78.4215i 0.122768 + 0.0885118i
\(887\) 51.9793 + 90.0309i 0.0586013 + 0.101500i 0.893838 0.448391i \(-0.148003\pi\)
−0.835236 + 0.549891i \(0.814669\pi\)
\(888\) 121.334 600.329i 0.136638 0.676046i
\(889\) −282.092 162.866i −0.317313 0.183201i
\(890\) 1610.98 724.323i 1.81009 0.813846i
\(891\) −1021.28 + 820.572i −1.14622 + 0.920956i
\(892\) 591.873 + 525.139i 0.663535 + 0.588720i
\(893\) 83.5621 + 311.858i 0.0935746 + 0.349225i
\(894\) −491.999 + 285.830i −0.550334 + 0.319720i
\(895\) −237.108 410.682i −0.264925 0.458863i
\(896\) 492.935 + 235.472i 0.550151 + 0.262804i
\(897\) 1039.16 397.756i 1.15848 0.443429i
\(898\) 1073.45 875.778i 1.19537 0.975254i
\(899\) 235.502 235.502i 0.261960 0.261960i
\(900\) 880.759 1544.73i 0.978621 1.71636i
\(901\) 405.848 405.848i 0.450442 0.450442i
\(902\) 48.5026 478.288i 0.0537723 0.530253i
\(903\) −36.6317 + 229.861i −0.0405667 + 0.254553i
\(904\) 85.4531 134.801i 0.0945277 0.149116i
\(905\) 1063.30 + 1841.70i 1.17492 + 2.03502i
\(906\) 155.373 + 573.660i 0.171494 + 0.633179i
\(907\) −333.971 1246.40i −0.368215 1.37420i −0.863010 0.505187i \(-0.831424\pi\)
0.494795 0.869010i \(-0.335243\pi\)
\(908\) −1039.32 + 62.0926i −1.14462 + 0.0683839i
\(909\) −794.254 + 402.782i −0.873767 + 0.443104i
\(910\) −523.348 + 1378.41i −0.575108 + 1.51474i
\(911\) −852.908 492.427i −0.936233 0.540535i −0.0474557 0.998873i \(-0.515111\pi\)
−0.888778 + 0.458339i \(0.848445\pi\)
\(912\) −387.177 734.869i −0.424536 0.805777i
\(913\) 918.054 + 1590.12i 1.00554 + 1.74164i
\(914\) 6.32934 + 39.0375i 0.00692488 + 0.0427106i
\(915\) −33.0792 317.649i −0.0361522 0.347157i
\(916\) −201.599 + 402.918i −0.220086 + 0.439867i
\(917\) 82.5447 + 82.5447i 0.0900161 + 0.0900161i
\(918\) −313.507 + 483.593i −0.341511 + 0.526790i
\(919\) 273.336i 0.297428i −0.988880 0.148714i \(-0.952487\pi\)
0.988880 0.148714i \(-0.0475133\pi\)
\(920\) 940.231 865.450i 1.02199 0.940707i
\(921\) 207.164 + 168.086i 0.224934 + 0.182504i
\(922\) −530.527 + 735.851i −0.575409 + 0.798103i
\(923\) −197.526 + 737.176i −0.214004 + 0.798674i
\(924\) 291.932 775.201i 0.315943 0.838962i
\(925\) 1217.55 326.243i 1.31628 0.352695i
\(926\) 356.122 937.967i 0.384581 1.01292i
\(927\) −1327.72 + 1190.90i −1.43228 + 1.28468i
\(928\) 721.038 434.057i 0.776981 0.467734i
\(929\) −392.453 226.583i −0.422447 0.243900i 0.273677 0.961822i \(-0.411760\pi\)
−0.696124 + 0.717922i \(0.745093\pi\)
\(930\) 568.428 + 326.139i 0.611213 + 0.350687i
\(931\) −137.880 + 514.575i −0.148099 + 0.552712i
\(932\) 225.817 1101.95i 0.242293 1.18235i
\(933\) 514.660 + 709.795i 0.551618 + 0.760766i
\(934\) 655.867 + 66.5107i 0.702213 + 0.0712106i
\(935\) −1488.88 −1.59239
\(936\) 598.389 + 1311.90i 0.639305 + 1.40160i
\(937\) 1234.45i 1.31744i −0.752386 0.658722i \(-0.771097\pi\)
0.752386 0.658722i \(-0.228903\pi\)
\(938\) 266.043 + 26.9791i 0.283628 + 0.0287624i
\(939\) 374.593 + 167.209i 0.398928 + 0.178071i
\(940\) −354.518 537.267i −0.377147 0.571561i
\(941\) 496.355 + 132.998i 0.527476 + 0.141337i 0.512722 0.858554i \(-0.328637\pi\)
0.0147534 + 0.999891i \(0.495304\pi\)
\(942\) 183.825 106.794i 0.195143 0.113370i
\(943\) 137.617 238.360i 0.145935 0.252768i
\(944\) −649.317 + 826.261i −0.687836 + 0.875276i
\(945\) 453.762 884.279i 0.480171 0.935745i
\(946\) −208.735 + 549.773i −0.220650 + 0.581156i
\(947\) −192.442 718.202i −0.203212 0.758397i −0.989987 0.141158i \(-0.954918\pi\)
0.786775 0.617240i \(-0.211749\pi\)
\(948\) −147.246 105.557i −0.155323 0.111347i
\(949\) −2472.61 662.535i −2.60549 0.698140i
\(950\) 999.749 1386.67i 1.05237 1.45965i
\(951\) −141.654 370.077i −0.148952 0.389145i
\(952\) 15.0784 364.086i 0.0158386 0.382443i
\(953\) −1054.90 −1.10693 −0.553463 0.832874i \(-0.686694\pi\)
−0.553463 + 0.832874i \(0.686694\pi\)
\(954\) 102.864 + 962.526i 0.107823 + 1.00894i
\(955\) −130.595 + 130.595i −0.136749 + 0.136749i
\(956\) −347.237 1042.68i −0.363218 1.09067i
\(957\) −749.110 1033.14i −0.782769 1.07956i
\(958\) 33.3992 + 205.997i 0.0348635 + 0.215028i
\(959\) −765.634 + 442.039i −0.798367 + 0.460937i
\(960\) 1195.30 + 1146.17i 1.24511 + 1.19392i
\(961\) 400.319 693.373i 0.416565 0.721512i
\(962\) −362.812 + 955.585i −0.377143 + 0.993332i
\(963\) −532.557 347.296i −0.553019 0.360640i
\(964\) −352.103 312.403i −0.365252 0.324070i
\(965\) 1034.49 277.191i 1.07201 0.287245i
\(966\) 334.436 336.247i 0.346207 0.348082i
\(967\) −1491.54 + 861.139i −1.54244 + 0.890527i −0.543753 + 0.839245i \(0.682997\pi\)
−0.998684 + 0.0512814i \(0.983669\pi\)
\(968\) 602.224 949.997i 0.622132 0.981402i
\(969\) −349.094 + 430.253i −0.360262 + 0.444018i
\(970\) −142.635 + 1406.53i −0.147046 + 1.45003i
\(971\) 43.2692 + 43.2692i 0.0445615 + 0.0445615i 0.729036 0.684475i \(-0.239968\pi\)
−0.684475 + 0.729036i \(0.739968\pi\)
\(972\) −302.705 923.663i −0.311425 0.950271i
\(973\) −109.375 109.375i −0.112410 0.112410i
\(974\) 45.0027 36.7157i 0.0462040 0.0376958i
\(975\) −1869.77 + 2304.46i −1.91771 + 2.36355i
\(976\) 195.478 + 28.0365i 0.200285 + 0.0287260i
\(977\) 505.899 292.081i 0.517809 0.298957i −0.218229 0.975898i \(-0.570028\pi\)
0.736038 + 0.676941i \(0.236695\pi\)
\(978\) 1.81950 + 673.778i 0.00186043 + 0.688935i
\(979\) 1599.68 428.633i 1.63400 0.437828i
\(980\) −63.3413 1060.22i −0.0646340 1.08186i
\(981\) −911.282 594.274i −0.928932 0.605784i
\(982\) −1446.10 + 650.189i −1.47260 + 0.662107i
\(983\) −501.229 + 868.153i −0.509897 + 0.883167i 0.490037 + 0.871701i \(0.336983\pi\)
−0.999934 + 0.0114659i \(0.996350\pi\)
\(984\) 319.406 + 158.737i 0.324600 + 0.161318i
\(985\) 2478.45 1430.93i 2.51619 1.45272i
\(986\) −455.375 328.312i −0.461841 0.332974i
\(987\) −140.227 193.394i −0.142074 0.195941i
\(988\) 437.996 + 1315.21i 0.443316 + 1.33118i
\(989\) −238.068 + 238.068i −0.240716 + 0.240716i
\(990\) 1576.86 1954.22i 1.59279 1.97396i
\(991\) −560.194 −0.565281 −0.282641 0.959226i \(-0.591210\pi\)
−0.282641 + 0.959226i \(0.591210\pi\)
\(992\) −281.254 + 291.730i −0.283522 + 0.294083i
\(993\) 225.599 + 589.390i 0.227190 + 0.593545i
\(994\) 52.0598 + 321.090i 0.0523741 + 0.323028i
\(995\) −1691.12 453.134i −1.69962 0.455411i
\(996\) −1344.11 + 221.654i −1.34951 + 0.222544i
\(997\) 440.930 + 1645.57i 0.442257 + 1.65053i 0.723078 + 0.690766i \(0.242727\pi\)
−0.280821 + 0.959760i \(0.590607\pi\)
\(998\) −1360.05 + 611.501i −1.36277 + 0.612726i
\(999\) 314.571 613.027i 0.314886 0.613641i
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 144.3.w.a.29.13 yes 184
3.2 odd 2 432.3.x.a.413.34 184
9.4 even 3 432.3.x.a.125.44 184
9.5 odd 6 inner 144.3.w.a.77.3 yes 184
16.5 even 4 inner 144.3.w.a.101.3 yes 184
48.5 odd 4 432.3.x.a.197.44 184
144.5 odd 12 inner 144.3.w.a.5.13 184
144.85 even 12 432.3.x.a.341.34 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.3.w.a.5.13 184 144.5 odd 12 inner
144.3.w.a.29.13 yes 184 1.1 even 1 trivial
144.3.w.a.77.3 yes 184 9.5 odd 6 inner
144.3.w.a.101.3 yes 184 16.5 even 4 inner
432.3.x.a.125.44 184 9.4 even 3
432.3.x.a.197.44 184 48.5 odd 4
432.3.x.a.341.34 184 144.85 even 12
432.3.x.a.413.34 184 3.2 odd 2