Properties

Label 32.3.h.a.11.5
Level $32$
Weight $3$
Character 32.11
Analytic conductor $0.872$
Analytic rank $0$
Dimension $28$
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] = [32,3,Mod(3,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.h (of order \(8\), 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: \(0.871936845953\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 11.5
Character \(\chi\) \(=\) 32.11
Dual form 32.3.h.a.3.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.682385 + 1.87999i) q^{2} +(0.299792 + 0.723762i) q^{3} +(-3.06870 + 2.56575i) q^{4} +(1.34740 - 3.25291i) q^{5} +(-1.15609 + 1.05749i) q^{6} +(0.583225 - 0.583225i) q^{7} +(-6.91761 - 4.01829i) q^{8} +(5.93000 - 5.93000i) q^{9} +O(q^{10})\) \(q+(0.682385 + 1.87999i) q^{2} +(0.299792 + 0.723762i) q^{3} +(-3.06870 + 2.56575i) q^{4} +(1.34740 - 3.25291i) q^{5} +(-1.15609 + 1.05749i) q^{6} +(0.583225 - 0.583225i) q^{7} +(-6.91761 - 4.01829i) q^{8} +(5.93000 - 5.93000i) q^{9} +(7.03487 + 0.313357i) q^{10} +(-3.03620 + 7.33003i) q^{11} +(-2.77696 - 1.45182i) q^{12} +(-6.38385 - 15.4120i) q^{13} +(1.49444 + 0.698471i) q^{14} +2.75827 q^{15} +(2.83386 - 15.7470i) q^{16} +19.0889i q^{17} +(15.1949 + 7.10179i) q^{18} +(-29.6679 + 12.2888i) q^{19} +(4.21138 + 13.4393i) q^{20} +(0.596962 + 0.247270i) q^{21} +(-15.8522 - 0.706111i) q^{22} +(15.2998 + 15.2998i) q^{23} +(0.834442 - 6.21136i) q^{24} +(8.91173 + 8.91173i) q^{25} +(24.6181 - 22.5185i) q^{26} +(12.5835 + 5.21227i) q^{27} +(-0.293334 + 3.28615i) q^{28} +(-20.5148 + 8.49749i) q^{29} +(1.88220 + 5.18552i) q^{30} -53.6582i q^{31} +(31.5380 - 5.41792i) q^{32} -6.21542 q^{33} +(-35.8868 + 13.0260i) q^{34} +(-1.11134 - 2.68301i) q^{35} +(-2.98251 + 33.4123i) q^{36} +(-3.80237 + 9.17973i) q^{37} +(-43.3477 - 47.3895i) q^{38} +(9.24078 - 9.24078i) q^{39} +(-22.3919 + 17.0881i) q^{40} +(14.5108 - 14.5108i) q^{41} +(-0.0575061 + 1.29101i) q^{42} +(20.3685 - 49.1739i) q^{43} +(-9.48983 - 30.2838i) q^{44} +(-11.2997 - 27.2799i) q^{45} +(-18.3230 + 39.2037i) q^{46} +4.73351 q^{47} +(12.2467 - 2.66980i) q^{48} +48.3197i q^{49} +(-10.6727 + 22.8352i) q^{50} +(-13.8158 + 5.72269i) q^{51} +(59.1334 + 30.9154i) q^{52} +(61.4006 + 25.4330i) q^{53} +(-1.21219 + 27.2137i) q^{54} +(19.7530 + 19.7530i) q^{55} +(-6.37809 + 1.69095i) q^{56} +(-17.7884 - 17.7884i) q^{57} +(-29.9741 - 32.7689i) q^{58} +(42.4656 + 17.5898i) q^{59} +(-8.46431 + 7.07703i) q^{60} +(-27.7452 + 11.4924i) q^{61} +(100.877 - 36.6155i) q^{62} -6.91705i q^{63} +(31.7067 + 55.5939i) q^{64} -58.7354 q^{65} +(-4.24131 - 11.6849i) q^{66} +(-9.42323 - 22.7497i) q^{67} +(-48.9772 - 58.5780i) q^{68} +(-6.48665 + 15.6602i) q^{69} +(4.28567 - 3.92015i) q^{70} +(-95.1299 + 95.1299i) q^{71} +(-64.8499 + 17.1930i) q^{72} +(37.1241 - 37.1241i) q^{73} +(-19.8524 - 0.884295i) q^{74} +(-3.77831 + 9.12164i) q^{75} +(59.5118 - 113.831i) q^{76} +(2.50427 + 6.04584i) q^{77} +(23.6783 + 11.0668i) q^{78} -70.3394 q^{79} +(-47.4053 - 30.4358i) q^{80} -64.8066i q^{81} +(37.1821 + 17.3782i) q^{82} +(14.5221 - 6.01526i) q^{83} +(-2.46633 + 0.772858i) q^{84} +(62.0944 + 25.7203i) q^{85} +(106.345 + 4.73698i) q^{86} +(-12.3003 - 12.3003i) q^{87} +(50.4574 - 38.5060i) q^{88} +(-60.8411 - 60.8411i) q^{89} +(43.5750 - 39.8586i) q^{90} +(-12.7119 - 5.26543i) q^{91} +(-86.2059 - 7.69507i) q^{92} +(38.8357 - 16.0863i) q^{93} +(3.23007 + 8.89893i) q^{94} +113.065i q^{95} +(13.3761 + 21.2018i) q^{96} +31.8287 q^{97} +(-90.8404 + 32.9726i) q^{98} +(25.4624 + 61.4718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.682385 + 1.87999i 0.341192 + 0.939993i
\(3\) 0.299792 + 0.723762i 0.0999307 + 0.241254i 0.965936 0.258781i \(-0.0833206\pi\)
−0.866005 + 0.500035i \(0.833321\pi\)
\(4\) −3.06870 + 2.56575i −0.767175 + 0.641437i
\(5\) 1.34740 3.25291i 0.269480 0.650582i −0.729979 0.683469i \(-0.760470\pi\)
0.999459 + 0.0328874i \(0.0104703\pi\)
\(6\) −1.15609 + 1.05749i −0.192682 + 0.176248i
\(7\) 0.583225 0.583225i 0.0833178 0.0833178i −0.664220 0.747537i \(-0.731236\pi\)
0.747537 + 0.664220i \(0.231236\pi\)
\(8\) −6.91761 4.01829i −0.864701 0.502286i
\(9\) 5.93000 5.93000i 0.658889 0.658889i
\(10\) 7.03487 + 0.313357i 0.703487 + 0.0313357i
\(11\) −3.03620 + 7.33003i −0.276018 + 0.666366i −0.999718 0.0237484i \(-0.992440\pi\)
0.723700 + 0.690115i \(0.242440\pi\)
\(12\) −2.77696 1.45182i −0.231414 0.120985i
\(13\) −6.38385 15.4120i −0.491065 1.18554i −0.954179 0.299238i \(-0.903268\pi\)
0.463113 0.886299i \(-0.346732\pi\)
\(14\) 1.49444 + 0.698471i 0.106746 + 0.0498908i
\(15\) 2.75827 0.183885
\(16\) 2.83386 15.7470i 0.177116 0.984190i
\(17\) 19.0889i 1.12287i 0.827519 + 0.561437i \(0.189751\pi\)
−0.827519 + 0.561437i \(0.810249\pi\)
\(18\) 15.1949 + 7.10179i 0.844160 + 0.394544i
\(19\) −29.6679 + 12.2888i −1.56147 + 0.646781i −0.985343 0.170582i \(-0.945435\pi\)
−0.576123 + 0.817363i \(0.695435\pi\)
\(20\) 4.21138 + 13.4393i 0.210569 + 0.671965i
\(21\) 0.596962 + 0.247270i 0.0284268 + 0.0117748i
\(22\) −15.8522 0.706111i −0.720555 0.0320959i
\(23\) 15.2998 + 15.2998i 0.665208 + 0.665208i 0.956603 0.291395i \(-0.0941194\pi\)
−0.291395 + 0.956603i \(0.594119\pi\)
\(24\) 0.834442 6.21136i 0.0347684 0.258806i
\(25\) 8.91173 + 8.91173i 0.356469 + 0.356469i
\(26\) 24.6181 22.5185i 0.946849 0.866094i
\(27\) 12.5835 + 5.21227i 0.466057 + 0.193047i
\(28\) −0.293334 + 3.28615i −0.0104762 + 0.117363i
\(29\) −20.5148 + 8.49749i −0.707405 + 0.293017i −0.707231 0.706983i \(-0.750056\pi\)
−0.000174983 1.00000i \(0.500056\pi\)
\(30\) 1.88220 + 5.18552i 0.0627401 + 0.172851i
\(31\) 53.6582i 1.73091i −0.500988 0.865454i \(-0.667030\pi\)
0.500988 0.865454i \(-0.332970\pi\)
\(32\) 31.5380 5.41792i 0.985563 0.169310i
\(33\) −6.21542 −0.188346
\(34\) −35.8868 + 13.0260i −1.05549 + 0.383116i
\(35\) −1.11134 2.68301i −0.0317526 0.0766575i
\(36\) −2.98251 + 33.4123i −0.0828476 + 0.928120i
\(37\) −3.80237 + 9.17973i −0.102767 + 0.248101i −0.966897 0.255168i \(-0.917869\pi\)
0.864130 + 0.503268i \(0.167869\pi\)
\(38\) −43.3477 47.3895i −1.14073 1.24709i
\(39\) 9.24078 9.24078i 0.236943 0.236943i
\(40\) −22.3919 + 17.0881i −0.559798 + 0.427203i
\(41\) 14.5108 14.5108i 0.353922 0.353922i −0.507644 0.861567i \(-0.669484\pi\)
0.861567 + 0.507644i \(0.169484\pi\)
\(42\) −0.0575061 + 1.29101i −0.00136919 + 0.0307384i
\(43\) 20.3685 49.1739i 0.473686 1.14358i −0.488837 0.872375i \(-0.662579\pi\)
0.962522 0.271203i \(-0.0874214\pi\)
\(44\) −9.48983 30.2838i −0.215678 0.688268i
\(45\) −11.2997 27.2799i −0.251104 0.606219i
\(46\) −18.3230 + 39.2037i −0.398327 + 0.852255i
\(47\) 4.73351 0.100713 0.0503565 0.998731i \(-0.483964\pi\)
0.0503565 + 0.998731i \(0.483964\pi\)
\(48\) 12.2467 2.66980i 0.255139 0.0556207i
\(49\) 48.3197i 0.986116i
\(50\) −10.6727 + 22.8352i −0.213454 + 0.456703i
\(51\) −13.8158 + 5.72269i −0.270898 + 0.112210i
\(52\) 59.1334 + 30.9154i 1.13718 + 0.594527i
\(53\) 61.4006 + 25.4330i 1.15850 + 0.479867i 0.877376 0.479803i \(-0.159292\pi\)
0.281126 + 0.959671i \(0.409292\pi\)
\(54\) −1.21219 + 27.2137i −0.0224479 + 0.503957i
\(55\) 19.7530 + 19.7530i 0.359145 + 0.359145i
\(56\) −6.37809 + 1.69095i −0.113894 + 0.0301956i
\(57\) −17.7884 17.7884i −0.312077 0.312077i
\(58\) −29.9741 32.7689i −0.516795 0.564981i
\(59\) 42.4656 + 17.5898i 0.719757 + 0.298133i 0.712335 0.701840i \(-0.247638\pi\)
0.00742152 + 0.999972i \(0.497638\pi\)
\(60\) −8.46431 + 7.07703i −0.141072 + 0.117951i
\(61\) −27.7452 + 11.4924i −0.454839 + 0.188400i −0.598328 0.801251i \(-0.704168\pi\)
0.143489 + 0.989652i \(0.454168\pi\)
\(62\) 100.877 36.6155i 1.62704 0.590573i
\(63\) 6.91705i 0.109794i
\(64\) 31.7067 + 55.5939i 0.495417 + 0.868655i
\(65\) −58.7354 −0.903621
\(66\) −4.24131 11.6849i −0.0642623 0.177044i
\(67\) −9.42323 22.7497i −0.140645 0.339548i 0.837824 0.545940i \(-0.183828\pi\)
−0.978469 + 0.206393i \(0.933828\pi\)
\(68\) −48.9772 58.5780i −0.720254 0.861442i
\(69\) −6.48665 + 15.6602i −0.0940094 + 0.226959i
\(70\) 4.28567 3.92015i 0.0612238 0.0560022i
\(71\) −95.1299 + 95.1299i −1.33986 + 1.33986i −0.443664 + 0.896193i \(0.646322\pi\)
−0.896193 + 0.443664i \(0.853678\pi\)
\(72\) −64.8499 + 17.1930i −0.900694 + 0.238791i
\(73\) 37.1241 37.1241i 0.508550 0.508550i −0.405531 0.914081i \(-0.632913\pi\)
0.914081 + 0.405531i \(0.132913\pi\)
\(74\) −19.8524 0.884295i −0.268276 0.0119499i
\(75\) −3.77831 + 9.12164i −0.0503774 + 0.121622i
\(76\) 59.5118 113.831i 0.783050 1.49778i
\(77\) 2.50427 + 6.04584i 0.0325230 + 0.0785174i
\(78\) 23.6783 + 11.0668i 0.303568 + 0.141882i
\(79\) −70.3394 −0.890372 −0.445186 0.895438i \(-0.646862\pi\)
−0.445186 + 0.895438i \(0.646862\pi\)
\(80\) −47.4053 30.4358i −0.592567 0.380448i
\(81\) 64.8066i 0.800081i
\(82\) 37.1821 + 17.3782i 0.453440 + 0.211929i
\(83\) 14.5221 6.01526i 0.174965 0.0724730i −0.293481 0.955965i \(-0.594814\pi\)
0.468447 + 0.883492i \(0.344814\pi\)
\(84\) −2.46633 + 0.772858i −0.0293611 + 0.00920069i
\(85\) 62.0944 + 25.7203i 0.730522 + 0.302592i
\(86\) 106.345 + 4.73698i 1.23657 + 0.0550812i
\(87\) −12.3003 12.3003i −0.141383 0.141383i
\(88\) 50.4574 38.5060i 0.573380 0.437568i
\(89\) −60.8411 60.8411i −0.683608 0.683608i 0.277204 0.960811i \(-0.410592\pi\)
−0.960811 + 0.277204i \(0.910592\pi\)
\(90\) 43.5750 39.8586i 0.484167 0.442874i
\(91\) −12.7119 5.26543i −0.139691 0.0578618i
\(92\) −86.2059 7.69507i −0.937020 0.0836420i
\(93\) 38.8357 16.0863i 0.417589 0.172971i
\(94\) 3.23007 + 8.89893i 0.0343625 + 0.0946695i
\(95\) 113.065i 1.19016i
\(96\) 13.3761 + 21.2018i 0.139335 + 0.220852i
\(97\) 31.8287 0.328131 0.164066 0.986449i \(-0.447539\pi\)
0.164066 + 0.986449i \(0.447539\pi\)
\(98\) −90.8404 + 32.9726i −0.926943 + 0.336455i
\(99\) 25.4624 + 61.4718i 0.257196 + 0.620927i
\(100\) −50.2127 4.48218i −0.502127 0.0448218i
\(101\) 11.0397 26.6521i 0.109304 0.263883i −0.859758 0.510702i \(-0.829385\pi\)
0.969061 + 0.246820i \(0.0793855\pi\)
\(102\) −20.1863 22.0684i −0.197905 0.216357i
\(103\) 56.0862 56.0862i 0.544526 0.544526i −0.380326 0.924852i \(-0.624188\pi\)
0.924852 + 0.380326i \(0.124188\pi\)
\(104\) −17.7688 + 132.266i −0.170854 + 1.27179i
\(105\) 1.60869 1.60869i 0.0153209 0.0153209i
\(106\) −5.91480 + 132.787i −0.0558000 + 1.25271i
\(107\) 5.85623 14.1382i 0.0547311 0.132133i −0.894149 0.447770i \(-0.852218\pi\)
0.948880 + 0.315637i \(0.102218\pi\)
\(108\) −51.9885 + 16.2913i −0.481375 + 0.150845i
\(109\) 37.6258 + 90.8367i 0.345191 + 0.833364i 0.997174 + 0.0751304i \(0.0239373\pi\)
−0.651983 + 0.758233i \(0.726063\pi\)
\(110\) −23.6562 + 50.6144i −0.215056 + 0.460131i
\(111\) −7.78386 −0.0701248
\(112\) −7.53128 10.8368i −0.0672436 0.0967575i
\(113\) 82.4104i 0.729295i −0.931146 0.364648i \(-0.881189\pi\)
0.931146 0.364648i \(-0.118811\pi\)
\(114\) 21.3034 45.5804i 0.186872 0.399828i
\(115\) 70.3837 29.1539i 0.612032 0.253512i
\(116\) 41.1512 78.7120i 0.354752 0.678552i
\(117\) −129.249 53.5368i −1.10470 0.457580i
\(118\) −4.09077 + 91.8379i −0.0346675 + 0.778287i
\(119\) 11.1331 + 11.1331i 0.0935555 + 0.0935555i
\(120\) −19.0807 11.0835i −0.159005 0.0923628i
\(121\) 41.0491 + 41.0491i 0.339249 + 0.339249i
\(122\) −40.5385 44.3183i −0.332283 0.363265i
\(123\) 14.8526 + 6.15215i 0.120753 + 0.0500175i
\(124\) 137.673 + 164.661i 1.11027 + 1.32791i
\(125\) 122.319 50.6664i 0.978556 0.405331i
\(126\) 13.0040 4.72009i 0.103206 0.0374610i
\(127\) 60.4972i 0.476356i −0.971221 0.238178i \(-0.923450\pi\)
0.971221 0.238178i \(-0.0765502\pi\)
\(128\) −82.8797 + 97.5446i −0.647498 + 0.762067i
\(129\) 41.6965 0.323229
\(130\) −40.0801 110.422i −0.308309 0.849398i
\(131\) −56.4124 136.192i −0.430629 1.03963i −0.979085 0.203451i \(-0.934784\pi\)
0.548456 0.836179i \(-0.315216\pi\)
\(132\) 19.0733 15.9472i 0.144495 0.120812i
\(133\) −10.1359 + 24.4702i −0.0762096 + 0.183986i
\(134\) 36.3389 33.2396i 0.271185 0.248057i
\(135\) 33.9101 33.9101i 0.251186 0.251186i
\(136\) 76.7046 132.049i 0.564005 0.970951i
\(137\) −139.949 + 139.949i −1.02152 + 1.02152i −0.0217604 + 0.999763i \(0.506927\pi\)
−0.999763 + 0.0217604i \(0.993073\pi\)
\(138\) −33.8673 1.50856i −0.245415 0.0109316i
\(139\) −2.63118 + 6.35223i −0.0189293 + 0.0456995i −0.933062 0.359717i \(-0.882873\pi\)
0.914132 + 0.405416i \(0.132873\pi\)
\(140\) 10.2943 + 5.38195i 0.0735308 + 0.0384425i
\(141\) 1.41907 + 3.42593i 0.0100643 + 0.0242974i
\(142\) −243.758 113.928i −1.71661 0.802308i
\(143\) 132.353 0.925545
\(144\) −76.5752 110.185i −0.531772 0.765172i
\(145\) 78.1822i 0.539187i
\(146\) 95.1258 + 44.4599i 0.651547 + 0.304520i
\(147\) −34.9720 + 14.4859i −0.237905 + 0.0985433i
\(148\) −11.8845 37.9258i −0.0803010 0.256255i
\(149\) −134.849 55.8563i −0.905027 0.374874i −0.118876 0.992909i \(-0.537929\pi\)
−0.786151 + 0.618035i \(0.787929\pi\)
\(150\) −19.7268 0.878699i −0.131512 0.00585799i
\(151\) −131.423 131.423i −0.870353 0.870353i 0.122158 0.992511i \(-0.461019\pi\)
−0.992511 + 0.122158i \(0.961019\pi\)
\(152\) 254.611 + 34.2048i 1.67507 + 0.225031i
\(153\) 113.197 + 113.197i 0.739850 + 0.739850i
\(154\) −9.65723 + 8.83358i −0.0627093 + 0.0573609i
\(155\) −174.545 72.2990i −1.12610 0.466445i
\(156\) −4.64767 + 52.0667i −0.0297928 + 0.333761i
\(157\) −151.775 + 62.8673i −0.966720 + 0.400429i −0.809490 0.587133i \(-0.800256\pi\)
−0.157230 + 0.987562i \(0.550256\pi\)
\(158\) −47.9985 132.237i −0.303788 0.836944i
\(159\) 52.0640i 0.327447i
\(160\) 24.8703 109.890i 0.155439 0.686815i
\(161\) 17.8464 0.110847
\(162\) 121.835 44.2230i 0.752071 0.272982i
\(163\) 75.6492 + 182.633i 0.464106 + 1.12045i 0.966696 + 0.255926i \(0.0823802\pi\)
−0.502591 + 0.864524i \(0.667620\pi\)
\(164\) −7.29825 + 81.7605i −0.0445015 + 0.498540i
\(165\) −8.37466 + 20.2182i −0.0507555 + 0.122535i
\(166\) 21.2183 + 23.1967i 0.127821 + 0.139739i
\(167\) 148.515 148.515i 0.889310 0.889310i −0.105147 0.994457i \(-0.533531\pi\)
0.994457 + 0.105147i \(0.0335313\pi\)
\(168\) −3.13595 4.10928i −0.0186664 0.0244600i
\(169\) −77.2745 + 77.2745i −0.457246 + 0.457246i
\(170\) −5.98163 + 134.288i −0.0351860 + 0.789928i
\(171\) −103.058 + 248.803i −0.602677 + 1.45499i
\(172\) 63.6630 + 203.160i 0.370134 + 1.18116i
\(173\) 14.9093 + 35.9942i 0.0861808 + 0.208059i 0.961094 0.276220i \(-0.0890819\pi\)
−0.874914 + 0.484279i \(0.839082\pi\)
\(174\) 14.7309 31.5180i 0.0846603 0.181138i
\(175\) 10.3951 0.0594005
\(176\) 106.822 + 68.5834i 0.606944 + 0.389678i
\(177\) 36.0083i 0.203437i
\(178\) 72.8634 155.897i 0.409345 0.875829i
\(179\) 276.876 114.686i 1.54679 0.640703i 0.564062 0.825733i \(-0.309238\pi\)
0.982733 + 0.185029i \(0.0592379\pi\)
\(180\) 104.669 + 54.7216i 0.581492 + 0.304009i
\(181\) −82.1686 34.0354i −0.453970 0.188041i 0.143969 0.989582i \(-0.454014\pi\)
−0.597939 + 0.801542i \(0.704014\pi\)
\(182\) 1.22455 27.4912i 0.00672830 0.151051i
\(183\) −16.6356 16.6356i −0.0909047 0.0909047i
\(184\) −44.3590 167.317i −0.241081 0.909331i
\(185\) 24.7375 + 24.7375i 0.133716 + 0.133716i
\(186\) 56.7429 + 62.0336i 0.305070 + 0.333514i
\(187\) −139.922 57.9576i −0.748246 0.309933i
\(188\) −14.5257 + 12.1450i −0.0772645 + 0.0646010i
\(189\) 10.3790 4.29911i 0.0549151 0.0227466i
\(190\) −212.560 + 77.1537i −1.11874 + 0.406072i
\(191\) 178.857i 0.936426i 0.883616 + 0.468213i \(0.155102\pi\)
−0.883616 + 0.468213i \(0.844898\pi\)
\(192\) −30.7314 + 39.6147i −0.160059 + 0.206327i
\(193\) 197.034 1.02090 0.510450 0.859908i \(-0.329479\pi\)
0.510450 + 0.859908i \(0.329479\pi\)
\(194\) 21.7194 + 59.8376i 0.111956 + 0.308441i
\(195\) −17.6084 42.5104i −0.0902995 0.218002i
\(196\) −123.976 148.279i −0.632532 0.756524i
\(197\) 62.3398 150.502i 0.316446 0.763968i −0.682992 0.730426i \(-0.739321\pi\)
0.999437 0.0335413i \(-0.0106785\pi\)
\(198\) −98.1909 + 89.8165i −0.495914 + 0.453618i
\(199\) 22.3835 22.3835i 0.112480 0.112480i −0.648627 0.761107i \(-0.724656\pi\)
0.761107 + 0.648627i \(0.224656\pi\)
\(200\) −25.8380 97.4578i −0.129190 0.487289i
\(201\) 13.6404 13.6404i 0.0678625 0.0678625i
\(202\) 57.6390 + 2.56744i 0.285342 + 0.0127101i
\(203\) −7.00877 + 16.9207i −0.0345260 + 0.0833530i
\(204\) 27.7136 53.0091i 0.135851 0.259849i
\(205\) −27.6505 66.7542i −0.134881 0.325630i
\(206\) 143.714 + 67.1690i 0.697640 + 0.326063i
\(207\) 181.456 0.876597
\(208\) −260.784 + 56.8513i −1.25377 + 0.273324i
\(209\) 254.778i 1.21903i
\(210\) 4.12207 + 1.92657i 0.0196289 + 0.00917416i
\(211\) −315.926 + 130.861i −1.49728 + 0.620194i −0.972887 0.231282i \(-0.925708\pi\)
−0.524394 + 0.851476i \(0.675708\pi\)
\(212\) −253.675 + 79.4924i −1.19658 + 0.374964i
\(213\) −97.3706 40.3322i −0.457139 0.189353i
\(214\) 30.5758 + 1.36195i 0.142878 + 0.00636425i
\(215\) −132.514 132.514i −0.616343 0.616343i
\(216\) −66.1036 86.6208i −0.306035 0.401022i
\(217\) −31.2948 31.2948i −0.144216 0.144216i
\(218\) −145.096 + 132.722i −0.665580 + 0.608814i
\(219\) 37.9986 + 15.7395i 0.173509 + 0.0718699i
\(220\) −111.297 9.93480i −0.505896 0.0451582i
\(221\) 294.197 121.860i 1.33121 0.551405i
\(222\) −5.31159 14.6336i −0.0239261 0.0659169i
\(223\) 103.995i 0.466346i −0.972435 0.233173i \(-0.925089\pi\)
0.972435 0.233173i \(-0.0749109\pi\)
\(224\) 15.2339 21.5536i 0.0680084 0.0962215i
\(225\) 105.693 0.469748
\(226\) 154.930 56.2356i 0.685533 0.248830i
\(227\) 19.9655 + 48.2010i 0.0879538 + 0.212339i 0.961736 0.273979i \(-0.0883397\pi\)
−0.873782 + 0.486318i \(0.838340\pi\)
\(228\) 100.228 + 8.94671i 0.439595 + 0.0392400i
\(229\) 52.0405 125.637i 0.227251 0.548633i −0.768590 0.639742i \(-0.779041\pi\)
0.995841 + 0.0911090i \(0.0290412\pi\)
\(230\) 102.838 + 112.426i 0.447120 + 0.488810i
\(231\) −3.62499 + 3.62499i −0.0156926 + 0.0156926i
\(232\) 176.059 + 23.6519i 0.758873 + 0.101948i
\(233\) −0.497550 + 0.497550i −0.00213541 + 0.00213541i −0.708174 0.706038i \(-0.750481\pi\)
0.706038 + 0.708174i \(0.250481\pi\)
\(234\) 12.4508 279.520i 0.0532084 1.19453i
\(235\) 6.37793 15.3977i 0.0271401 0.0655220i
\(236\) −175.446 + 54.9782i −0.743413 + 0.232958i
\(237\) −21.0872 50.9090i −0.0889755 0.214806i
\(238\) −13.3330 + 28.5271i −0.0560211 + 0.119862i
\(239\) −80.2602 −0.335817 −0.167908 0.985803i \(-0.553701\pi\)
−0.167908 + 0.985803i \(0.553701\pi\)
\(240\) 7.81656 43.4346i 0.0325690 0.180978i
\(241\) 9.94799i 0.0412780i 0.999787 + 0.0206390i \(0.00657006\pi\)
−0.999787 + 0.0206390i \(0.993430\pi\)
\(242\) −49.1605 + 105.183i −0.203142 + 0.434641i
\(243\) 160.156 66.3389i 0.659080 0.273000i
\(244\) 55.6550 106.454i 0.228094 0.436287i
\(245\) 157.180 + 65.1059i 0.641549 + 0.265738i
\(246\) −1.43077 + 32.1208i −0.00581614 + 0.130573i
\(247\) 378.790 + 378.790i 1.53356 + 1.53356i
\(248\) −215.614 + 371.186i −0.869412 + 1.49672i
\(249\) 8.70723 + 8.70723i 0.0349688 + 0.0349688i
\(250\) 178.721 + 195.385i 0.714884 + 0.781540i
\(251\) −37.4569 15.5152i −0.149231 0.0618134i 0.306818 0.951768i \(-0.400736\pi\)
−0.456049 + 0.889955i \(0.650736\pi\)
\(252\) 17.7474 + 21.2264i 0.0704263 + 0.0842316i
\(253\) −158.601 + 65.6947i −0.626881 + 0.259663i
\(254\) 113.734 41.2824i 0.447772 0.162529i
\(255\) 52.6523i 0.206480i
\(256\) −239.938 89.2499i −0.937260 0.348632i
\(257\) −351.412 −1.36736 −0.683680 0.729782i \(-0.739622\pi\)
−0.683680 + 0.729782i \(0.739622\pi\)
\(258\) 28.4530 + 78.3888i 0.110283 + 0.303833i
\(259\) 3.13621 + 7.57148i 0.0121089 + 0.0292335i
\(260\) 180.241 150.700i 0.693236 0.579616i
\(261\) −71.2625 + 172.043i −0.273036 + 0.659168i
\(262\) 217.543 198.990i 0.830318 0.759502i
\(263\) −347.609 + 347.609i −1.32171 + 1.32171i −0.409316 + 0.912393i \(0.634233\pi\)
−0.912393 + 0.409316i \(0.865767\pi\)
\(264\) 42.9959 + 24.9754i 0.162863 + 0.0946037i
\(265\) 165.462 165.462i 0.624386 0.624386i
\(266\) −52.9202 2.35724i −0.198948 0.00886182i
\(267\) 25.7948 62.2741i 0.0966097 0.233236i
\(268\) 87.2871 + 45.6344i 0.325698 + 0.170278i
\(269\) 77.8419 + 187.927i 0.289375 + 0.698613i 0.999988 0.00497024i \(-0.00158208\pi\)
−0.710613 + 0.703584i \(0.751582\pi\)
\(270\) 86.8903 + 40.6108i 0.321816 + 0.150410i
\(271\) −380.417 −1.40375 −0.701876 0.712299i \(-0.747654\pi\)
−0.701876 + 0.712299i \(0.747654\pi\)
\(272\) 300.593 + 54.0952i 1.10512 + 0.198879i
\(273\) 10.7789i 0.0394832i
\(274\) −358.601 167.603i −1.30876 0.611689i
\(275\) −92.3810 + 38.2655i −0.335931 + 0.139147i
\(276\) −20.2744 64.6995i −0.0734581 0.234418i
\(277\) 130.082 + 53.8819i 0.469612 + 0.194519i 0.604924 0.796284i \(-0.293204\pi\)
−0.135312 + 0.990803i \(0.543204\pi\)
\(278\) −13.7376 0.611918i −0.0494158 0.00220114i
\(279\) −318.193 318.193i −1.14048 1.14048i
\(280\) −3.09331 + 23.0257i −0.0110475 + 0.0822348i
\(281\) −40.5881 40.5881i −0.144442 0.144442i 0.631188 0.775630i \(-0.282568\pi\)
−0.775630 + 0.631188i \(0.782568\pi\)
\(282\) −5.47236 + 5.00563i −0.0194055 + 0.0177505i
\(283\) 442.450 + 183.269i 1.56343 + 0.647593i 0.985681 0.168622i \(-0.0539316\pi\)
0.577748 + 0.816215i \(0.303932\pi\)
\(284\) 47.8458 536.005i 0.168471 1.88734i
\(285\) −81.8320 + 33.8959i −0.287130 + 0.118933i
\(286\) 90.3156 + 248.822i 0.315789 + 0.870006i
\(287\) 16.9261i 0.0589761i
\(288\) 154.892 219.149i 0.537820 0.760933i
\(289\) −75.3848 −0.260847
\(290\) −146.981 + 53.3503i −0.506833 + 0.183967i
\(291\) 9.54200 + 23.0364i 0.0327904 + 0.0791629i
\(292\) −18.6717 + 209.174i −0.0639441 + 0.716350i
\(293\) −141.261 + 341.035i −0.482120 + 1.16394i 0.476479 + 0.879186i \(0.341913\pi\)
−0.958600 + 0.284756i \(0.908087\pi\)
\(294\) −51.0976 55.8619i −0.173801 0.190006i
\(295\) 114.436 114.436i 0.387920 0.387920i
\(296\) 63.1901 48.2228i 0.213480 0.162915i
\(297\) −76.4122 + 76.4122i −0.257280 + 0.257280i
\(298\) 12.9902 291.630i 0.0435912 0.978623i
\(299\) 138.128 333.471i 0.461968 1.11529i
\(300\) −11.8093 37.6858i −0.0393645 0.125619i
\(301\) −16.8000 40.5588i −0.0558140 0.134747i
\(302\) 157.393 336.755i 0.521168 1.11508i
\(303\) 22.5994 0.0745856
\(304\) 109.438 + 502.006i 0.359994 + 1.65134i
\(305\) 105.737i 0.346680i
\(306\) −135.565 + 290.053i −0.443023 + 0.947885i
\(307\) 27.5569 11.4145i 0.0897620 0.0371807i −0.337351 0.941379i \(-0.609531\pi\)
0.427113 + 0.904198i \(0.359531\pi\)
\(308\) −23.1970 12.1276i −0.0753148 0.0393752i
\(309\) 57.4073 + 23.7789i 0.185784 + 0.0769543i
\(310\) 16.8142 377.478i 0.0542392 1.21767i
\(311\) 262.516 + 262.516i 0.844102 + 0.844102i 0.989389 0.145288i \(-0.0464108\pi\)
−0.145288 + 0.989389i \(0.546411\pi\)
\(312\) −101.056 + 26.7920i −0.323898 + 0.0858717i
\(313\) −346.338 346.338i −1.10651 1.10651i −0.993606 0.112907i \(-0.963984\pi\)
−0.112907 0.993606i \(-0.536016\pi\)
\(314\) −221.759 242.435i −0.706238 0.772087i
\(315\) −22.5005 9.32003i −0.0714303 0.0295874i
\(316\) 215.851 180.473i 0.683071 0.571118i
\(317\) 37.8371 15.6726i 0.119360 0.0494405i −0.322204 0.946670i \(-0.604424\pi\)
0.441564 + 0.897230i \(0.354424\pi\)
\(318\) −97.8797 + 35.5277i −0.307798 + 0.111722i
\(319\) 176.174i 0.552269i
\(320\) 223.564 28.2317i 0.698636 0.0882241i
\(321\) 11.9883 0.0373469
\(322\) 12.1781 + 33.5510i 0.0378203 + 0.104196i
\(323\) −234.580 566.326i −0.726253 1.75333i
\(324\) 166.277 + 198.872i 0.513202 + 0.613802i
\(325\) 80.4563 194.239i 0.247558 0.597657i
\(326\) −291.726 + 266.846i −0.894866 + 0.818545i
\(327\) −54.4642 + 54.4642i −0.166557 + 0.166557i
\(328\) −158.689 + 42.0715i −0.483807 + 0.128267i
\(329\) 2.76070 2.76070i 0.00839118 0.00839118i
\(330\) −43.7247 1.94765i −0.132499 0.00590196i
\(331\) 123.850 298.999i 0.374168 0.903321i −0.618867 0.785496i \(-0.712408\pi\)
0.993034 0.117825i \(-0.0375921\pi\)
\(332\) −29.1304 + 55.7192i −0.0877422 + 0.167829i
\(333\) 31.8878 + 76.9839i 0.0957591 + 0.231183i
\(334\) 380.550 + 177.862i 1.13937 + 0.532520i
\(335\) −86.6995 −0.258805
\(336\) 5.58548 8.69966i 0.0166234 0.0258918i
\(337\) 553.901i 1.64362i 0.569759 + 0.821812i \(0.307037\pi\)
−0.569759 + 0.821812i \(0.692963\pi\)
\(338\) −198.006 92.5441i −0.585817 0.273799i
\(339\) 59.6455 24.7060i 0.175945 0.0728790i
\(340\) −256.541 + 80.3905i −0.754532 + 0.236443i
\(341\) 393.316 + 162.917i 1.15342 + 0.477762i
\(342\) −538.072 23.9675i −1.57331 0.0700805i
\(343\) 56.7593 + 56.7593i 0.165479 + 0.165479i
\(344\) −338.496 + 258.319i −0.984000 + 0.750928i
\(345\) 42.2010 + 42.2010i 0.122322 + 0.122322i
\(346\) −57.4947 + 52.5912i −0.166170 + 0.151998i
\(347\) 149.596 + 61.9645i 0.431111 + 0.178572i 0.587677 0.809095i \(-0.300042\pi\)
−0.156566 + 0.987667i \(0.550042\pi\)
\(348\) 69.3056 + 6.18648i 0.199154 + 0.0177772i
\(349\) −354.488 + 146.834i −1.01572 + 0.420727i −0.827540 0.561407i \(-0.810260\pi\)
−0.188184 + 0.982134i \(0.560260\pi\)
\(350\) 7.09345 + 19.5426i 0.0202670 + 0.0558361i
\(351\) 227.212i 0.647327i
\(352\) −56.0421 + 247.624i −0.159211 + 0.703478i
\(353\) −360.254 −1.02055 −0.510275 0.860011i \(-0.670456\pi\)
−0.510275 + 0.860011i \(0.670456\pi\)
\(354\) −67.6952 + 24.5715i −0.191229 + 0.0694111i
\(355\) 181.271 + 437.627i 0.510622 + 1.23275i
\(356\) 342.806 + 30.6002i 0.962939 + 0.0859556i
\(357\) −4.72010 + 11.3953i −0.0132216 + 0.0319197i
\(358\) 404.544 + 442.264i 1.13001 + 1.23537i
\(359\) 92.0047 92.0047i 0.256280 0.256280i −0.567259 0.823539i \(-0.691996\pi\)
0.823539 + 0.567259i \(0.191996\pi\)
\(360\) −31.4516 + 234.117i −0.0873655 + 0.650325i
\(361\) 473.901 473.901i 1.31275 1.31275i
\(362\) 7.91541 177.701i 0.0218658 0.490887i
\(363\) −17.4036 + 42.0160i −0.0479438 + 0.115746i
\(364\) 52.5187 16.4574i 0.144282 0.0452127i
\(365\) −70.7404 170.782i −0.193809 0.467897i
\(366\) 19.9228 42.6265i 0.0544339 0.116466i
\(367\) 254.513 0.693496 0.346748 0.937958i \(-0.387286\pi\)
0.346748 + 0.937958i \(0.387286\pi\)
\(368\) 284.284 197.569i 0.772510 0.536872i
\(369\) 172.098i 0.466391i
\(370\) −29.6257 + 63.3867i −0.0800695 + 0.171315i
\(371\) 50.6435 20.9772i 0.136505 0.0565424i
\(372\) −77.9019 + 149.007i −0.209414 + 0.400556i
\(373\) 440.477 + 182.452i 1.18090 + 0.489147i 0.884783 0.466004i \(-0.154307\pi\)
0.296122 + 0.955150i \(0.404307\pi\)
\(374\) 13.4789 302.601i 0.0360397 0.809093i
\(375\) 73.3408 + 73.3408i 0.195575 + 0.195575i
\(376\) −32.7446 19.0206i −0.0870866 0.0505867i
\(377\) 261.926 + 261.926i 0.694765 + 0.694765i
\(378\) 15.1647 + 16.5787i 0.0401183 + 0.0438589i
\(379\) 124.964 + 51.7618i 0.329720 + 0.136575i 0.541402 0.840764i \(-0.317894\pi\)
−0.211681 + 0.977339i \(0.567894\pi\)
\(380\) −290.096 346.962i −0.763411 0.913059i
\(381\) 43.7856 18.1366i 0.114923 0.0476026i
\(382\) −336.250 + 122.050i −0.880235 + 0.319502i
\(383\) 182.483i 0.476458i −0.971209 0.238229i \(-0.923433\pi\)
0.971209 0.238229i \(-0.0765669\pi\)
\(384\) −95.4458 30.7421i −0.248557 0.0800576i
\(385\) 23.0408 0.0598463
\(386\) 134.453 + 370.421i 0.348323 + 0.959639i
\(387\) −170.816 412.386i −0.441385 1.06560i
\(388\) −97.6728 + 81.6645i −0.251734 + 0.210476i
\(389\) −134.979 + 325.868i −0.346990 + 0.837708i 0.649982 + 0.759949i \(0.274776\pi\)
−0.996972 + 0.0777583i \(0.975224\pi\)
\(390\) 67.9034 62.1120i 0.174111 0.159262i
\(391\) −292.055 + 292.055i −0.746945 + 0.746945i
\(392\) 194.163 334.257i 0.495313 0.852696i
\(393\) 81.6583 81.6583i 0.207782 0.207782i
\(394\) 325.481 + 14.4980i 0.826093 + 0.0367970i
\(395\) −94.7752 + 228.808i −0.239937 + 0.579260i
\(396\) −235.858 123.308i −0.595600 0.311385i
\(397\) −272.283 657.350i −0.685852 1.65579i −0.752976 0.658048i \(-0.771382\pi\)
0.0671236 0.997745i \(-0.478618\pi\)
\(398\) 57.3549 + 26.8066i 0.144108 + 0.0673532i
\(399\) −20.7492 −0.0520031
\(400\) 165.588 115.079i 0.413970 0.287697i
\(401\) 74.4996i 0.185785i 0.995676 + 0.0928923i \(0.0296112\pi\)
−0.995676 + 0.0928923i \(0.970389\pi\)
\(402\) 34.9517 + 16.3357i 0.0869444 + 0.0406361i
\(403\) −826.978 + 342.546i −2.05206 + 0.849989i
\(404\) 34.5052 + 110.113i 0.0854090 + 0.272556i
\(405\) −210.810 87.3203i −0.520518 0.215606i
\(406\) −36.5933 1.62999i −0.0901313 0.00401475i
\(407\) −55.7429 55.7429i −0.136961 0.136961i
\(408\) 118.568 + 15.9285i 0.290607 + 0.0390406i
\(409\) −289.633 289.633i −0.708149 0.708149i 0.257997 0.966146i \(-0.416938\pi\)
−0.966146 + 0.257997i \(0.916938\pi\)
\(410\) 106.629 97.5347i 0.260070 0.237889i
\(411\) −143.245 59.3341i −0.348528 0.144365i
\(412\) −28.2087 + 316.015i −0.0684678 + 0.767027i
\(413\) 35.0258 14.5082i 0.0848083 0.0351288i
\(414\) 123.823 + 341.134i 0.299088 + 0.823995i
\(415\) 55.3441i 0.133359i
\(416\) −284.835 451.476i −0.684699 1.08528i
\(417\) −5.38631 −0.0129168
\(418\) 478.979 173.856i 1.14588 0.415924i
\(419\) 234.290 + 565.626i 0.559165 + 1.34994i 0.910428 + 0.413667i \(0.135752\pi\)
−0.351264 + 0.936277i \(0.614248\pi\)
\(420\) −0.809096 + 9.06410i −0.00192642 + 0.0215812i
\(421\) 205.463 496.031i 0.488035 1.17822i −0.467672 0.883902i \(-0.654907\pi\)
0.955707 0.294319i \(-0.0950929\pi\)
\(422\) −461.600 504.640i −1.09384 1.19583i
\(423\) 28.0697 28.0697i 0.0663587 0.0663587i
\(424\) −322.549 422.661i −0.760728 0.996842i
\(425\) −170.115 + 170.115i −0.400270 + 0.400270i
\(426\) 9.37983 210.577i 0.0220184 0.494313i
\(427\) −9.47901 + 22.8843i −0.0221991 + 0.0535933i
\(428\) 18.3040 + 58.4115i 0.0427664 + 0.136476i
\(429\) 39.6783 + 95.7920i 0.0924903 + 0.223291i
\(430\) 158.699 339.549i 0.369067 0.789649i
\(431\) −94.1706 −0.218493 −0.109247 0.994015i \(-0.534844\pi\)
−0.109247 + 0.994015i \(0.534844\pi\)
\(432\) 117.738 183.383i 0.272541 0.424497i
\(433\) 66.2703i 0.153049i 0.997068 + 0.0765246i \(0.0243824\pi\)
−0.997068 + 0.0765246i \(0.975618\pi\)
\(434\) 37.4787 80.1888i 0.0863564 0.184767i
\(435\) −56.5853 + 23.4384i −0.130081 + 0.0538814i
\(436\) −348.526 182.212i −0.799372 0.417918i
\(437\) −641.928 265.895i −1.46894 0.608456i
\(438\) −3.66045 + 82.1772i −0.00835719 + 0.187619i
\(439\) 393.404 + 393.404i 0.896137 + 0.896137i 0.995092 0.0989551i \(-0.0315500\pi\)
−0.0989551 + 0.995092i \(0.531550\pi\)
\(440\) −57.2701 216.016i −0.130159 0.490946i
\(441\) 286.536 + 286.536i 0.649742 + 0.649742i
\(442\) 429.852 + 469.931i 0.972515 + 1.06319i
\(443\) 124.298 + 51.4859i 0.280583 + 0.116221i 0.518537 0.855055i \(-0.326477\pi\)
−0.237954 + 0.971276i \(0.576477\pi\)
\(444\) 23.8863 19.9714i 0.0537981 0.0449807i
\(445\) −279.888 + 115.933i −0.628961 + 0.260524i
\(446\) 195.510 70.9647i 0.438362 0.159114i
\(447\) 114.344i 0.255803i
\(448\) 50.9159 + 13.9317i 0.113652 + 0.0310974i
\(449\) 621.505 1.38420 0.692099 0.721802i \(-0.256686\pi\)
0.692099 + 0.721802i \(0.256686\pi\)
\(450\) 72.1235 + 198.702i 0.160274 + 0.441560i
\(451\) 62.3070 + 150.422i 0.138153 + 0.333531i
\(452\) 211.444 + 252.893i 0.467797 + 0.559498i
\(453\) 55.7195 134.519i 0.123001 0.296951i
\(454\) −76.9931 + 70.4265i −0.169588 + 0.155124i
\(455\) −34.2559 + 34.2559i −0.0752877 + 0.0752877i
\(456\) 51.5742 + 194.532i 0.113101 + 0.426605i
\(457\) −121.890 + 121.890i −0.266718 + 0.266718i −0.827776 0.561058i \(-0.810394\pi\)
0.561058 + 0.827776i \(0.310394\pi\)
\(458\) 271.708 + 12.1028i 0.593248 + 0.0264253i
\(459\) −99.4964 + 240.205i −0.216768 + 0.523323i
\(460\) −141.185 + 270.052i −0.306924 + 0.587069i
\(461\) 92.0148 + 222.143i 0.199598 + 0.481873i 0.991709 0.128505i \(-0.0410177\pi\)
−0.792111 + 0.610378i \(0.791018\pi\)
\(462\) −9.28857 4.34130i −0.0201051 0.00939674i
\(463\) −133.158 −0.287598 −0.143799 0.989607i \(-0.545932\pi\)
−0.143799 + 0.989607i \(0.545932\pi\)
\(464\) 75.6743 + 347.127i 0.163091 + 0.748119i
\(465\) 148.004i 0.318288i
\(466\) −1.27491 0.595867i −0.00273586 0.00127869i
\(467\) −414.267 + 171.595i −0.887082 + 0.367441i −0.779239 0.626727i \(-0.784394\pi\)
−0.107843 + 0.994168i \(0.534394\pi\)
\(468\) 533.990 167.333i 1.14100 0.357549i
\(469\) −18.7640 7.77232i −0.0400086 0.0165721i
\(470\) 33.2996 + 1.48328i 0.0708503 + 0.00315591i
\(471\) −91.0019 91.0019i −0.193210 0.193210i
\(472\) −223.080 292.319i −0.472626 0.619320i
\(473\) 298.603 + 298.603i 0.631296 + 0.631296i
\(474\) 81.3186 74.3831i 0.171558 0.156926i
\(475\) −373.907 154.877i −0.787172 0.326058i
\(476\) −62.7289 5.59942i −0.131783 0.0117635i
\(477\) 514.924 213.288i 1.07950 0.447145i
\(478\) −54.7683 150.888i −0.114578 0.315665i
\(479\) 293.655i 0.613059i 0.951861 + 0.306530i \(0.0991679\pi\)
−0.951861 + 0.306530i \(0.900832\pi\)
\(480\) 86.9904 14.9441i 0.181230 0.0311335i
\(481\) 165.752 0.344598
\(482\) −18.7021 + 6.78836i −0.0388010 + 0.0140837i
\(483\) 5.35022 + 12.9166i 0.0110771 + 0.0267424i
\(484\) −231.289 20.6458i −0.477870 0.0426565i
\(485\) 42.8860 103.536i 0.0884247 0.213476i
\(486\) 234.005 + 255.823i 0.481491 + 0.526385i
\(487\) 468.368 468.368i 0.961741 0.961741i −0.0375532 0.999295i \(-0.511956\pi\)
0.999295 + 0.0375532i \(0.0119564\pi\)
\(488\) 238.110 + 31.9881i 0.487931 + 0.0655493i
\(489\) −109.504 + 109.504i −0.223935 + 0.223935i
\(490\) −15.1413 + 339.923i −0.0309006 + 0.693720i
\(491\) −120.443 + 290.775i −0.245301 + 0.592210i −0.997794 0.0663911i \(-0.978851\pi\)
0.752492 + 0.658601i \(0.228851\pi\)
\(492\) −61.3631 + 19.2289i −0.124722 + 0.0390832i
\(493\) −162.207 391.603i −0.329021 0.794328i
\(494\) −453.640 + 970.602i −0.918300 + 1.96478i
\(495\) 234.270 0.473273
\(496\) −844.957 152.060i −1.70354 0.306572i
\(497\) 110.964i 0.223268i
\(498\) −10.4278 + 22.3112i −0.0209394 + 0.0448015i
\(499\) 572.626 237.190i 1.14755 0.475330i 0.273837 0.961776i \(-0.411707\pi\)
0.873711 + 0.486446i \(0.161707\pi\)
\(500\) −245.365 + 469.321i −0.490729 + 0.938642i
\(501\) 152.013 + 62.9658i 0.303419 + 0.125680i
\(502\) 3.60827 81.0058i 0.00718779 0.161366i
\(503\) −397.129 397.129i −0.789520 0.789520i 0.191895 0.981415i \(-0.438537\pi\)
−0.981415 + 0.191895i \(0.938537\pi\)
\(504\) −27.7947 + 47.8495i −0.0551483 + 0.0949394i
\(505\) −71.8222 71.8222i −0.142222 0.142222i
\(506\) −231.732 253.339i −0.457968 0.500669i
\(507\) −79.0946 32.7621i −0.156005 0.0646195i
\(508\) 155.221 + 185.648i 0.305553 + 0.365449i
\(509\) −16.5014 + 6.83509i −0.0324192 + 0.0134285i −0.398834 0.917023i \(-0.630585\pi\)
0.366415 + 0.930452i \(0.380585\pi\)
\(510\) −98.9856 + 35.9291i −0.194089 + 0.0704493i
\(511\) 43.3034i 0.0847425i
\(512\) 4.05825 511.984i 0.00792626 0.999969i
\(513\) −437.380 −0.852592
\(514\) −239.798 660.649i −0.466533 1.28531i
\(515\) −106.873 258.014i −0.207520 0.500998i
\(516\) −127.954 + 106.983i −0.247973 + 0.207331i
\(517\) −14.3719 + 34.6968i −0.0277986 + 0.0671117i
\(518\) −12.0942 + 11.0627i −0.0233478 + 0.0213566i
\(519\) −21.5815 + 21.5815i −0.0415829 + 0.0415829i
\(520\) 406.308 + 236.016i 0.781362 + 0.453877i
\(521\) −11.8175 + 11.8175i −0.0226824 + 0.0226824i −0.718357 0.695675i \(-0.755106\pi\)
0.695675 + 0.718357i \(0.255106\pi\)
\(522\) −372.067 16.5731i −0.712771 0.0317492i
\(523\) 141.420 341.417i 0.270401 0.652806i −0.729100 0.684408i \(-0.760061\pi\)
0.999501 + 0.0316019i \(0.0100609\pi\)
\(524\) 522.546 + 273.191i 0.997225 + 0.521357i
\(525\) 3.11636 + 7.52357i 0.00593593 + 0.0143306i
\(526\) −890.705 416.298i −1.69335 0.791441i
\(527\) 1024.27 1.94359
\(528\) −17.6137 + 97.8745i −0.0333592 + 0.185368i
\(529\) 60.8334i 0.114997i
\(530\) 423.976 + 198.158i 0.799955 + 0.373883i
\(531\) 356.129 147.514i 0.670677 0.277803i
\(532\) −31.6804 101.098i −0.0595495 0.190034i
\(533\) −316.275 131.006i −0.593387 0.245789i
\(534\) 134.677 + 5.99895i 0.252203 + 0.0112340i
\(535\) −38.0996 38.0996i −0.0712142 0.0712142i
\(536\) −26.2286 + 195.239i −0.0489340 + 0.364251i
\(537\) 166.011 + 166.011i 0.309145 + 0.309145i
\(538\) −300.182 + 274.580i −0.557959 + 0.510372i
\(539\) −354.185 146.708i −0.657115 0.272186i
\(540\) −17.0552 + 191.065i −0.0315837 + 0.353824i
\(541\) −117.048 + 48.4829i −0.216355 + 0.0896172i −0.488229 0.872716i \(-0.662357\pi\)
0.271874 + 0.962333i \(0.412357\pi\)
\(542\) −259.591 715.178i −0.478949 1.31952i
\(543\) 69.6741i 0.128313i
\(544\) 103.422 + 602.025i 0.190114 + 1.10666i
\(545\) 346.180 0.635193
\(546\) 20.2642 7.35536i 0.0371139 0.0134714i
\(547\) −113.911 275.005i −0.208247 0.502752i 0.784901 0.619622i \(-0.212714\pi\)
−0.993147 + 0.116870i \(0.962714\pi\)
\(548\) 70.3876 788.534i 0.128445 1.43893i
\(549\) −96.3789 + 232.679i −0.175553 + 0.423824i
\(550\) −134.978 147.563i −0.245415 0.268297i
\(551\) 504.205 504.205i 0.915072 0.915072i
\(552\) 107.799 82.2656i 0.195288 0.149032i
\(553\) −41.0237 + 41.0237i −0.0741838 + 0.0741838i
\(554\) −12.5310 + 281.321i −0.0226191 + 0.507800i
\(555\) −10.4880 + 25.3202i −0.0188972 + 0.0456220i
\(556\) −8.22392 26.2440i −0.0147912 0.0472015i
\(557\) 87.2197 + 210.567i 0.156588 + 0.378037i 0.982631 0.185570i \(-0.0594131\pi\)
−0.826043 + 0.563607i \(0.809413\pi\)
\(558\) 381.069 815.329i 0.682919 1.46116i
\(559\) −887.896 −1.58836
\(560\) −45.3989 + 9.89703i −0.0810695 + 0.0176733i
\(561\) 118.645i 0.211489i
\(562\) 48.6084 104.002i 0.0864918 0.185057i
\(563\) 697.221 288.798i 1.23840 0.512963i 0.335188 0.942151i \(-0.391200\pi\)
0.903215 + 0.429188i \(0.141200\pi\)
\(564\) −13.1448 6.87220i −0.0233064 0.0121847i
\(565\) −268.074 111.040i −0.474466 0.196530i
\(566\) −42.6218 + 956.861i −0.0753035 + 1.69057i
\(567\) −37.7968 37.7968i −0.0666610 0.0666610i
\(568\) 1040.33 275.812i 1.83157 0.485584i
\(569\) −252.850 252.850i −0.444376 0.444376i 0.449104 0.893480i \(-0.351743\pi\)
−0.893480 + 0.449104i \(0.851743\pi\)
\(570\) −119.565 130.713i −0.209763 0.229321i
\(571\) 352.993 + 146.215i 0.618202 + 0.256068i 0.669731 0.742604i \(-0.266409\pi\)
−0.0515290 + 0.998672i \(0.516409\pi\)
\(572\) −406.152 + 339.584i −0.710055 + 0.593679i
\(573\) −129.450 + 53.6200i −0.225917 + 0.0935777i
\(574\) 31.8209 11.5501i 0.0554371 0.0201222i
\(575\) 272.695i 0.474252i
\(576\) 517.693 + 141.652i 0.898773 + 0.245923i
\(577\) −197.099 −0.341593 −0.170797 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(578\) −51.4414 141.722i −0.0889990 0.245194i
\(579\) 59.0691 + 142.605i 0.102019 + 0.246296i
\(580\) −200.596 239.918i −0.345855 0.413651i
\(581\) 4.96141 11.9779i 0.00853944 0.0206160i
\(582\) −36.7968 + 33.6585i −0.0632248 + 0.0578325i
\(583\) −372.849 + 372.849i −0.639535 + 0.639535i
\(584\) −405.986 + 107.635i −0.695181 + 0.184306i
\(585\) −348.301 + 348.301i −0.595386 + 0.595386i
\(586\) −737.536 32.8523i −1.25859 0.0560620i
\(587\) −238.745 + 576.382i −0.406721 + 0.981912i 0.579273 + 0.815134i \(0.303336\pi\)
−0.985994 + 0.166778i \(0.946664\pi\)
\(588\) 70.1514 134.182i 0.119305 0.228201i
\(589\) 659.396 + 1591.92i 1.11952 + 2.70276i
\(590\) 293.228 + 137.049i 0.496997 + 0.232287i
\(591\) 127.616 0.215933
\(592\) 133.778 + 85.8901i 0.225977 + 0.145085i
\(593\) 276.598i 0.466438i −0.972424 0.233219i \(-0.925074\pi\)
0.972424 0.233219i \(-0.0749260\pi\)
\(594\) −195.797 91.5114i −0.329624 0.154060i
\(595\) 51.2157 21.2142i 0.0860768 0.0356542i
\(596\) 557.124 174.582i 0.934772 0.292923i
\(597\) 22.9108 + 9.48995i 0.0383765 + 0.0158961i
\(598\) 721.179 + 32.1237i 1.20598 + 0.0537186i
\(599\) −710.727 710.727i −1.18652 1.18652i −0.978022 0.208501i \(-0.933141\pi\)
−0.208501 0.978022i \(-0.566859\pi\)
\(600\) 62.7903 47.9176i 0.104650 0.0798627i
\(601\) −215.219 215.219i −0.358102 0.358102i 0.505011 0.863113i \(-0.331488\pi\)
−0.863113 + 0.505011i \(0.831488\pi\)
\(602\) 64.7860 59.2605i 0.107618 0.0984394i
\(603\) −190.786 79.0260i −0.316394 0.131055i
\(604\) 740.498 + 66.0997i 1.22599 + 0.109437i
\(605\) 188.839 78.2195i 0.312130 0.129288i
\(606\) 15.4215 + 42.4866i 0.0254480 + 0.0701099i
\(607\) 683.779i 1.12649i 0.826290 + 0.563245i \(0.190447\pi\)
−0.826290 + 0.563245i \(0.809553\pi\)
\(608\) −869.086 + 548.303i −1.42942 + 0.901815i
\(609\) −14.3477 −0.0235595
\(610\) −198.785 + 72.1536i −0.325877 + 0.118285i
\(611\) −30.2180 72.9527i −0.0494566 0.119399i
\(612\) −637.803 56.9328i −1.04216 0.0930274i
\(613\) −296.111 + 714.875i −0.483052 + 1.16619i 0.475100 + 0.879932i \(0.342412\pi\)
−0.958152 + 0.286259i \(0.907588\pi\)
\(614\) 40.2635 + 44.0176i 0.0655757 + 0.0716900i
\(615\) 40.0248 40.0248i 0.0650809 0.0650809i
\(616\) 6.97039 51.8856i 0.0113156 0.0842299i
\(617\) −275.822 + 275.822i −0.447037 + 0.447037i −0.894368 0.447331i \(-0.852374\pi\)
0.447331 + 0.894368i \(0.352374\pi\)
\(618\) −5.53012 + 124.151i −0.00894841 + 0.200892i
\(619\) 201.130 485.570i 0.324927 0.784443i −0.674027 0.738707i \(-0.735437\pi\)
0.998954 0.0457357i \(-0.0145632\pi\)
\(620\) 721.128 225.975i 1.16311 0.364476i
\(621\) 112.779 + 272.272i 0.181608 + 0.438441i
\(622\) −314.389 + 672.663i −0.505449 + 1.08145i
\(623\) −70.9681 −0.113913
\(624\) −119.328 171.702i −0.191230 0.275163i
\(625\) 151.085i 0.241735i
\(626\) 414.775 887.448i 0.662581 1.41765i
\(627\) 184.398 76.3803i 0.294096 0.121819i
\(628\) 304.451 582.338i 0.484794 0.927289i
\(629\) −175.231 72.5829i −0.278586 0.115394i
\(630\) 2.16751 48.6606i 0.00344048 0.0772390i
\(631\) 48.9545 + 48.9545i 0.0775823 + 0.0775823i 0.744833 0.667251i \(-0.232529\pi\)
−0.667251 + 0.744833i \(0.732529\pi\)
\(632\) 486.580 + 282.644i 0.769906 + 0.447222i
\(633\) −189.424 189.424i −0.299249 0.299249i
\(634\) 55.2838 + 60.4385i 0.0871984 + 0.0953288i
\(635\) −196.792 81.5139i −0.309909 0.128368i
\(636\) −133.583 159.769i −0.210037 0.251209i
\(637\) 744.702 308.466i 1.16908 0.484248i
\(638\) 331.205 120.218i 0.519129 0.188430i
\(639\) 1128.24i 1.76564i
\(640\) 205.632 + 401.032i 0.321299 + 0.626612i
\(641\) 320.295 0.499680 0.249840 0.968287i \(-0.419622\pi\)
0.249840 + 0.968287i \(0.419622\pi\)
\(642\) 8.18066 + 22.5379i 0.0127425 + 0.0351058i
\(643\) 39.8184 + 96.1302i 0.0619260 + 0.149503i 0.951813 0.306677i \(-0.0992173\pi\)
−0.889887 + 0.456180i \(0.849217\pi\)
\(644\) −54.7653 + 45.7894i −0.0850394 + 0.0711016i
\(645\) 56.1818 135.635i 0.0871036 0.210287i
\(646\) 904.612 827.459i 1.40033 1.28090i
\(647\) −134.372 + 134.372i −0.207684 + 0.207684i −0.803282 0.595598i \(-0.796915\pi\)
0.595598 + 0.803282i \(0.296915\pi\)
\(648\) −260.412 + 448.306i −0.401870 + 0.691831i
\(649\) −257.868 + 257.868i −0.397331 + 0.397331i
\(650\) 420.068 + 18.7113i 0.646259 + 0.0287865i
\(651\) 13.2680 32.0319i 0.0203810 0.0492041i
\(652\) −700.736 366.350i −1.07475 0.561887i
\(653\) −358.760 866.123i −0.549403 1.32638i −0.917924 0.396756i \(-0.870136\pi\)
0.368521 0.929619i \(-0.379864\pi\)
\(654\) −139.558 65.2265i −0.213391 0.0997347i
\(655\) −519.029 −0.792410
\(656\) −187.381 269.624i −0.285641 0.411012i
\(657\) 440.293i 0.670156i
\(658\) 7.07394 + 3.30622i 0.0107507 + 0.00502465i
\(659\) 596.224 246.964i 0.904741 0.374756i 0.118700 0.992930i \(-0.462127\pi\)
0.786041 + 0.618174i \(0.212127\pi\)
\(660\) −26.1755 83.5309i −0.0396599 0.126562i
\(661\) 16.3196 + 6.75978i 0.0246892 + 0.0102266i 0.394994 0.918684i \(-0.370747\pi\)
−0.370305 + 0.928910i \(0.620747\pi\)
\(662\) 646.628 + 28.8030i 0.976779 + 0.0435090i
\(663\) 176.396 + 176.396i 0.266057 + 0.266057i
\(664\) −124.629 16.7429i −0.187695 0.0252152i
\(665\) 65.9422 + 65.9422i 0.0991612 + 0.0991612i
\(666\) −122.969 + 112.481i −0.184638 + 0.168891i
\(667\) −443.881 183.862i −0.665489 0.275655i
\(668\) −74.6959 + 836.799i −0.111820 + 1.25269i
\(669\) 75.2678 31.1769i 0.112508 0.0466023i
\(670\) −59.1625 162.994i −0.0883022 0.243275i
\(671\) 238.266i 0.355091i
\(672\) 20.1667 + 4.56411i 0.0300099 + 0.00679183i
\(673\) −334.752 −0.497403 −0.248701 0.968580i \(-0.580004\pi\)
−0.248701 + 0.968580i \(0.580004\pi\)
\(674\) −1041.33 + 377.974i −1.54500 + 0.560792i
\(675\) 65.6908 + 158.592i 0.0973197 + 0.234950i
\(676\) 38.8654 435.399i 0.0574932 0.644082i
\(677\) 294.364 710.658i 0.434807 1.04972i −0.542911 0.839790i \(-0.682678\pi\)
0.977717 0.209926i \(-0.0673222\pi\)
\(678\) 87.1481 + 95.2738i 0.128537 + 0.140522i
\(679\) 18.5633 18.5633i 0.0273392 0.0273392i
\(680\) −326.193 427.436i −0.479695 0.628583i
\(681\) −28.9006 + 28.9006i −0.0424384 + 0.0424384i
\(682\) −37.8886 + 850.601i −0.0555551 + 1.24721i
\(683\) −118.311 + 285.628i −0.173223 + 0.418196i −0.986518 0.163655i \(-0.947672\pi\)
0.813295 + 0.581851i \(0.197672\pi\)
\(684\) −322.114 1027.92i −0.470926 1.50281i
\(685\) 266.674 + 643.807i 0.389305 + 0.939865i
\(686\) −67.9750 + 145.438i −0.0990889 + 0.212009i
\(687\) 106.533 0.155069
\(688\) −716.621 460.095i −1.04160 0.668743i
\(689\) 1108.67i 1.60909i
\(690\) −50.5400 + 108.135i −0.0732463 + 0.156717i
\(691\) −13.1275 + 5.43758i −0.0189978 + 0.00786914i −0.392162 0.919896i \(-0.628273\pi\)
0.373164 + 0.927765i \(0.378273\pi\)
\(692\) −138.104 72.2020i −0.199573 0.104338i
\(693\) 50.7022 + 21.0015i 0.0731633 + 0.0303052i
\(694\) −14.4107 + 323.522i −0.0207647 + 0.466169i
\(695\) 17.1180 + 17.1180i 0.0246302 + 0.0246302i
\(696\) 35.6626 + 134.515i 0.0512393 + 0.193269i
\(697\) 276.995 + 276.995i 0.397410 + 0.397410i
\(698\) −517.942 566.235i −0.742038 0.811225i
\(699\) −0.509270 0.210946i −0.000728569 0.000301783i
\(700\) −31.8994 + 26.6712i −0.0455706 + 0.0381017i
\(701\) −100.100 + 41.4627i −0.142796 + 0.0591480i −0.452937 0.891543i \(-0.649624\pi\)
0.310141 + 0.950691i \(0.399624\pi\)
\(702\) 427.155 155.046i 0.608483 0.220863i
\(703\) 319.070i 0.453869i
\(704\) −503.773 + 63.6166i −0.715587 + 0.0903645i
\(705\) 13.0563 0.0185196
\(706\) −245.832 677.273i −0.348204 0.959310i
\(707\) −9.10558 21.9828i −0.0128792 0.0310931i
\(708\) −92.3883 110.499i −0.130492 0.156072i
\(709\) 273.663 660.681i 0.385985 0.931849i −0.604797 0.796380i \(-0.706746\pi\)
0.990781 0.135470i \(-0.0432543\pi\)
\(710\) −699.036 + 639.417i −0.984558 + 0.900587i
\(711\) −417.113 + 417.113i −0.586657 + 0.586657i
\(712\) 176.398 + 665.352i 0.247750 + 0.934483i
\(713\) 820.958 820.958i 1.15141 1.15141i
\(714\) −24.6440 1.09773i −0.0345154 0.00153743i
\(715\) 178.332 430.532i 0.249416 0.602143i
\(716\) −555.395 + 1062.33i −0.775692 + 1.48370i
\(717\) −24.0614 58.0893i −0.0335584 0.0810171i
\(718\) 235.750 + 110.185i 0.328343 + 0.153461i
\(719\) −532.079 −0.740026 −0.370013 0.929026i \(-0.620647\pi\)
−0.370013 + 0.929026i \(0.620647\pi\)
\(720\) −461.599 + 100.629i −0.641109 + 0.139763i
\(721\) 65.4218i 0.0907375i
\(722\) 1214.31 + 567.545i 1.68187 + 0.786074i
\(723\) −7.19998 + 2.98233i −0.00995848 + 0.00412494i
\(724\) 339.477 106.380i 0.468891 0.146933i
\(725\) −258.549 107.095i −0.356620 0.147717i
\(726\) −90.8654 4.04745i −0.125159 0.00557500i
\(727\) 305.054 + 305.054i 0.419606 + 0.419606i 0.885068 0.465462i \(-0.154112\pi\)
−0.465462 + 0.885068i \(0.654112\pi\)
\(728\) 66.7777 + 87.5042i 0.0917276 + 0.120198i
\(729\) −316.399 316.399i −0.434018 0.434018i
\(730\) 272.797 249.530i 0.373694 0.341823i
\(731\) 938.673 + 388.811i 1.28409 + 0.531889i
\(732\) 93.7323 + 8.36690i 0.128050 + 0.0114302i
\(733\) 344.710 142.783i 0.470272 0.194793i −0.134946 0.990853i \(-0.543086\pi\)
0.605218 + 0.796060i \(0.293086\pi\)
\(734\) 173.676 + 478.481i 0.236616 + 0.651882i
\(735\) 133.279i 0.181332i
\(736\) 565.418 + 399.632i 0.768230 + 0.542978i
\(737\) 195.367 0.265084
\(738\) 323.543 117.437i 0.438405 0.159129i
\(739\) 107.676 + 259.954i 0.145706 + 0.351765i 0.979836 0.199803i \(-0.0640301\pi\)
−0.834131 + 0.551567i \(0.814030\pi\)
\(740\) −139.382 12.4418i −0.188354 0.0168132i
\(741\) −160.596 + 387.713i −0.216728 + 0.523229i
\(742\) 73.9953 + 80.8946i 0.0997241 + 0.109022i
\(743\) −470.112 + 470.112i −0.632721 + 0.632721i −0.948750 0.316029i \(-0.897650\pi\)
0.316029 + 0.948750i \(0.397650\pi\)
\(744\) −333.290 44.7746i −0.447970 0.0601809i
\(745\) −363.391 + 363.391i −0.487773 + 0.487773i
\(746\) −42.4317 + 952.594i −0.0568790 + 1.27694i
\(747\) 50.4457 121.787i 0.0675311 0.163034i
\(748\) 578.083 181.150i 0.772839 0.242179i
\(749\) −4.83025 11.6612i −0.00644893 0.0155691i
\(750\) −87.8331 + 187.926i −0.117111 + 0.250569i
\(751\) 844.801 1.12490 0.562451 0.826831i \(-0.309859\pi\)
0.562451 + 0.826831i \(0.309859\pi\)
\(752\) 13.4141 74.5387i 0.0178379 0.0991207i
\(753\) 31.7612i 0.0421796i
\(754\) −313.684 + 671.153i −0.416026 + 0.890123i
\(755\) −604.588 + 250.428i −0.800778 + 0.331693i
\(756\) −20.8195 + 39.8225i −0.0275390 + 0.0526752i
\(757\) 1050.78 + 435.247i 1.38808 + 0.574962i 0.946630 0.322322i \(-0.104464\pi\)
0.441452 + 0.897285i \(0.354464\pi\)
\(758\) −12.0379 + 270.252i −0.0158812 + 0.356533i
\(759\) −95.0946 95.0946i −0.125289 0.125289i
\(760\) 454.327 782.139i 0.597799 1.02913i
\(761\) −44.1359 44.1359i −0.0579972 0.0579972i 0.677513 0.735511i \(-0.263058\pi\)
−0.735511 + 0.677513i \(0.763058\pi\)
\(762\) 63.9752 + 69.9402i 0.0839569 + 0.0917851i
\(763\) 74.9225 + 31.0339i 0.0981946 + 0.0406735i
\(764\) −458.903 548.860i −0.600659 0.718403i
\(765\) 520.741 215.698i 0.680708 0.281958i
\(766\) 343.066 124.524i 0.447867 0.162564i
\(767\) 766.771i 0.999701i
\(768\) −7.33597 200.415i −0.00955204 0.260957i
\(769\) 794.025 1.03254 0.516271 0.856425i \(-0.327320\pi\)
0.516271 + 0.856425i \(0.327320\pi\)
\(770\) 15.7227 + 43.3164i 0.0204191 + 0.0562551i
\(771\) −105.350 254.338i −0.136641 0.329881i
\(772\) −604.637 + 505.539i −0.783209 + 0.654843i
\(773\) −395.664 + 955.218i −0.511856 + 1.23573i 0.430947 + 0.902377i \(0.358180\pi\)
−0.942803 + 0.333351i \(0.891820\pi\)
\(774\) 658.719 602.538i 0.851058 0.778473i
\(775\) 478.187 478.187i 0.617016 0.617016i
\(776\) −220.179 127.897i −0.283735 0.164816i
\(777\) −4.53974 + 4.53974i −0.00584265 + 0.00584265i
\(778\) −704.736 31.3913i −0.905830 0.0403487i
\(779\) −252.184 + 608.826i −0.323728 + 0.781548i
\(780\) 163.106 + 85.2731i 0.209110 + 0.109324i
\(781\) −408.472 986.138i −0.523011 1.26266i
\(782\) −748.355 349.766i −0.956975 0.447271i
\(783\) −302.440 −0.386257
\(784\) 760.892 + 136.931i 0.970526 + 0.174657i
\(785\) 578.418i 0.736838i
\(786\) 209.239 + 97.7941i 0.266207 + 0.124420i
\(787\) −445.085 + 184.360i −0.565547 + 0.234257i −0.647091 0.762413i \(-0.724015\pi\)
0.0815444 + 0.996670i \(0.474015\pi\)
\(788\) 194.847 + 621.793i 0.247268 + 0.789077i
\(789\) −355.797 147.376i −0.450947 0.186788i
\(790\) −494.828 22.0413i −0.626365 0.0279004i
\(791\) −48.0638 48.0638i −0.0607633 0.0607633i
\(792\) 70.8722 527.553i 0.0894851 0.666103i
\(793\) 354.242 + 354.242i 0.446711 + 0.446711i
\(794\) 1050.01 960.455i 1.32243 1.20964i
\(795\) 169.360 + 70.1511i 0.213031 + 0.0882403i
\(796\) −11.2579 + 126.119i −0.0141430 + 0.158441i
\(797\) −1384.22 + 573.363i −1.73679 + 0.719402i −0.737773 + 0.675049i \(0.764123\pi\)
−0.999016 + 0.0443527i \(0.985877\pi\)
\(798\) −14.1590 39.0083i −0.0177431 0.0488826i
\(799\) 90.3573i 0.113088i
\(800\) 329.341 + 232.775i 0.411677 + 0.290969i
\(801\) −721.576 −0.900844
\(802\) −140.058 + 50.8374i −0.174636 + 0.0633883i
\(803\) 159.405 + 384.837i 0.198512 + 0.479249i
\(804\) −6.86045 + 76.8559i −0.00853290 + 0.0955919i
\(805\) 24.0463 58.0528i 0.0298711 0.0721153i
\(806\) −1208.30 1320.96i −1.49913 1.63891i
\(807\) −112.678 + 112.678i −0.139626 + 0.139626i
\(808\) −183.464 + 140.009i −0.227060 + 0.173278i
\(809\) 462.148 462.148i 0.571258 0.571258i −0.361222 0.932480i \(-0.617640\pi\)
0.932480 + 0.361222i \(0.117640\pi\)
\(810\) 20.3076 455.906i 0.0250711 0.562847i
\(811\) 32.9003 79.4282i 0.0405675 0.0979386i −0.902297 0.431115i \(-0.858120\pi\)
0.942865 + 0.333176i \(0.108120\pi\)
\(812\) −21.9064 69.9072i −0.0269783 0.0860926i
\(813\) −114.046 275.331i −0.140278 0.338661i
\(814\) 66.7578 142.834i 0.0820121 0.175472i
\(815\) 696.019 0.854012
\(816\) 50.9634 + 233.775i 0.0624551 + 0.286489i
\(817\) 1709.19i 2.09203i
\(818\) 346.865 742.147i 0.424040 0.907270i
\(819\) −106.605 + 44.1574i −0.130165 + 0.0539163i
\(820\) 256.126 + 133.905i 0.312349 + 0.163298i
\(821\) −724.768 300.209i −0.882787 0.365662i −0.105210 0.994450i \(-0.533551\pi\)
−0.777577 + 0.628788i \(0.783551\pi\)
\(822\) 13.7990 309.788i 0.0167871 0.376871i
\(823\) −378.179 378.179i −0.459513 0.459513i 0.438982 0.898496i \(-0.355339\pi\)
−0.898496 + 0.438982i \(0.855339\pi\)
\(824\) −613.353 + 162.612i −0.744361 + 0.197345i
\(825\) −55.3902 55.3902i −0.0671396 0.0671396i
\(826\) 51.1763 + 55.9480i 0.0619568 + 0.0677336i
\(827\) −1071.43 443.801i −1.29556 0.536639i −0.374924 0.927056i \(-0.622331\pi\)
−0.920638 + 0.390416i \(0.872331\pi\)
\(828\) −556.833 + 465.569i −0.672504 + 0.562282i
\(829\) −1023.61 + 423.991i −1.23475 + 0.511449i −0.902069 0.431592i \(-0.857952\pi\)
−0.332678 + 0.943041i \(0.607952\pi\)
\(830\) 104.046 37.7660i 0.125357 0.0455012i
\(831\) 110.302i 0.132734i
\(832\) 654.402 843.566i 0.786541 1.01390i
\(833\) −922.368 −1.10728
\(834\) −3.67553 10.1262i −0.00440712 0.0121417i
\(835\) −282.996 683.214i −0.338918 0.818220i
\(836\) 653.696 + 781.837i 0.781932 + 0.935211i
\(837\) 279.681 675.210i 0.334147 0.806702i
\(838\) −903.494 + 826.437i −1.07815 + 0.986202i
\(839\) 1157.38 1157.38i 1.37947 1.37947i 0.533966 0.845506i \(-0.320701\pi\)
0.845506 0.533966i \(-0.179299\pi\)
\(840\) −17.5925 + 4.66411i −0.0209435 + 0.00555252i
\(841\) −246.029 + 246.029i −0.292543 + 0.292543i
\(842\) 1072.74 + 47.7833i 1.27403 + 0.0567498i
\(843\) 17.2081 41.5441i 0.0204130 0.0492813i
\(844\) 633.727 1212.16i 0.750862 1.43621i
\(845\) 147.247 + 355.487i 0.174257 + 0.420694i
\(846\) 71.9251 + 33.6164i 0.0850178 + 0.0397357i
\(847\) 47.8817 0.0565309
\(848\) 574.495 894.805i 0.677470 1.05519i
\(849\) 375.171i 0.441898i
\(850\) −435.898 203.730i −0.512821 0.239682i
\(851\) −198.623 + 82.2724i −0.233400 + 0.0966773i
\(852\) 402.284 126.061i 0.472164 0.147959i
\(853\) 1189.88 + 492.862i 1.39493 + 0.577799i 0.948431 0.316985i \(-0.102671\pi\)
0.446499 + 0.894784i \(0.352671\pi\)
\(854\) −49.4906 2.20448i −0.0579515 0.00258136i
\(855\) 670.475 + 670.475i 0.784181 + 0.784181i
\(856\) −97.3225 + 74.2705i −0.113695 + 0.0867646i
\(857\) 240.773 + 240.773i 0.280948 + 0.280948i 0.833487 0.552539i \(-0.186341\pi\)
−0.552539 + 0.833487i \(0.686341\pi\)
\(858\) −153.012 + 139.962i −0.178335 + 0.163126i
\(859\) −577.833 239.346i −0.672682 0.278634i 0.0200823 0.999798i \(-0.493607\pi\)
−0.692764 + 0.721164i \(0.743607\pi\)
\(860\) 746.642 + 66.6481i 0.868188 + 0.0774978i
\(861\) 12.2505 5.07432i 0.0142282 0.00589352i
\(862\) −64.2606 177.040i −0.0745483 0.205382i
\(863\) 1084.57i 1.25675i −0.777912 0.628373i \(-0.783721\pi\)
0.777912 0.628373i \(-0.216279\pi\)
\(864\) 425.099 + 96.2082i 0.492013 + 0.111352i
\(865\) 137.175 0.158583
\(866\) −124.587 + 45.2218i −0.143865 + 0.0522192i
\(867\) −22.5998 54.5606i −0.0260666 0.0629304i
\(868\) 176.329 + 15.7398i 0.203144 + 0.0181334i
\(869\) 213.564 515.590i 0.245759 0.593314i
\(870\) −82.6768 90.3856i −0.0950308 0.103891i
\(871\) −290.461 + 290.461i −0.333480 + 0.333480i
\(872\) 104.728 779.564i 0.120101 0.893995i
\(873\) 188.744 188.744i 0.216202 0.216202i
\(874\) 61.8378 1388.26i 0.0707526 1.58840i
\(875\) 41.7899 100.890i 0.0477598 0.115302i
\(876\) −156.990 + 49.1949i −0.179212 + 0.0561585i
\(877\) −331.246 799.700i −0.377704 0.911858i −0.992395 0.123090i \(-0.960719\pi\)
0.614691 0.788768i \(-0.289281\pi\)
\(878\) −471.142 + 1008.05i −0.536608 + 1.14812i
\(879\) −289.177 −0.328984
\(880\) 367.028 255.073i 0.417077 0.289856i
\(881\) 995.281i 1.12972i 0.825188 + 0.564859i \(0.191069\pi\)
−0.825188 + 0.564859i \(0.808931\pi\)
\(882\) −343.156 + 734.212i −0.389066 + 0.832440i
\(883\) −587.282 + 243.260i −0.665098 + 0.275493i −0.689582 0.724207i \(-0.742206\pi\)
0.0244838 + 0.999700i \(0.492206\pi\)
\(884\) −590.140 + 1128.79i −0.667579 + 1.27691i
\(885\) 117.132 + 48.5176i 0.132352 + 0.0548221i
\(886\) −11.9738 + 268.812i −0.0135144 + 0.303400i
\(887\) 679.194 + 679.194i 0.765720 + 0.765720i 0.977350 0.211630i \(-0.0678772\pi\)
−0.211630 + 0.977350i \(0.567877\pi\)
\(888\) 53.8457 + 31.2778i 0.0606370 + 0.0352228i
\(889\) −35.2835 35.2835i −0.0396890 0.0396890i
\(890\) −408.944 447.074i −0.459488 0.502331i
\(891\) 475.034 + 196.765i 0.533147 + 0.220837i
\(892\) 266.826 + 319.130i 0.299132 + 0.357769i
\(893\) −140.433 + 58.1693i −0.157260 + 0.0651392i
\(894\) 214.965 78.0265i 0.240453 0.0872779i
\(895\) 1055.18i 1.17897i
\(896\) 8.55291 + 105.228i 0.00954566 + 0.117442i
\(897\) 282.764 0.315233
\(898\) 424.106 + 1168.42i 0.472278 + 1.30114i
\(899\) 455.960 + 1100.78i 0.507185 + 1.22445i
\(900\) −324.341 + 271.182i −0.360379 + 0.301314i
\(901\) −485.487 + 1172.07i −0.538831 + 1.30085i
\(902\) −240.275 + 219.782i −0.266380 + 0.243661i
\(903\) 24.3184 24.3184i 0.0269307 0.0269307i
\(904\) −331.149 + 570.083i −0.366315 + 0.630623i
\(905\) −221.428 + 221.428i −0.244672 + 0.244672i
\(906\) 290.916 + 12.9584i 0.321099 + 0.0143028i
\(907\) 77.7483 187.701i 0.0857203 0.206947i −0.875207 0.483749i \(-0.839275\pi\)
0.960927 + 0.276802i \(0.0892746\pi\)
\(908\) −184.940 96.6880i −0.203678 0.106485i
\(909\) −92.5820 223.513i −0.101850 0.245889i
\(910\) −87.7764 41.0250i −0.0964576 0.0450824i
\(911\) 300.365 0.329710 0.164855 0.986318i \(-0.447284\pi\)
0.164855 + 0.986318i \(0.447284\pi\)
\(912\) −330.524 + 229.705i −0.362417 + 0.251869i
\(913\) 124.711i 0.136595i
\(914\) −312.328 145.976i −0.341716 0.159711i
\(915\) −76.5287 + 31.6992i −0.0836380 + 0.0346440i
\(916\) 162.656 + 519.065i 0.177572 + 0.566665i
\(917\) −112.331 46.5292i −0.122499 0.0507407i
\(918\) −519.478 23.1393i −0.565880 0.0252062i
\(919\) −149.768 149.768i −0.162968 0.162968i 0.620912 0.783880i \(-0.286762\pi\)
−0.783880 + 0.620912i \(0.786762\pi\)
\(920\) −604.036 81.1470i −0.656561 0.0882033i
\(921\) 16.5227 + 16.5227i 0.0179400 + 0.0179400i
\(922\) −354.837 + 324.574i −0.384856 + 0.352032i
\(923\) 2073.43 + 858.845i 2.24641 + 0.930493i
\(924\) 1.82320 20.4248i 0.00197316 0.0221048i
\(925\) −115.693 + 47.9216i −0.125073 + 0.0518071i
\(926\) −90.8649 250.335i −0.0981262 0.270340i
\(927\) 665.183i 0.717565i
\(928\) −600.956 + 379.141i −0.647582 + 0.408557i
\(929\) 1235.73 1.33017 0.665086 0.746767i \(-0.268395\pi\)
0.665086 + 0.746767i \(0.268395\pi\)
\(930\) 278.245 100.996i 0.299188 0.108597i
\(931\) −593.793 1433.54i −0.637801 1.53979i
\(932\) 0.250244 2.80342i 0.000268502 0.00300796i
\(933\) −111.299 + 268.699i −0.119291 + 0.287995i
\(934\) −605.286 661.723i −0.648058 0.708483i
\(935\) −377.061 + 377.061i −0.403274 + 0.403274i
\(936\) 678.970 + 889.709i 0.725396 + 0.950543i
\(937\) 955.999 955.999i 1.02028 1.02028i 0.0204864 0.999790i \(-0.493479\pi\)
0.999790 0.0204864i \(-0.00652149\pi\)
\(938\) 1.80756 40.5799i 0.00192704 0.0432621i
\(939\) 146.837 354.496i 0.156376 0.377525i
\(940\) 19.9346 + 63.6150i 0.0212070 + 0.0676756i
\(941\) −337.224 814.132i −0.358368 0.865177i −0.995530 0.0944471i \(-0.969892\pi\)
0.637162 0.770730i \(-0.280108\pi\)
\(942\) 108.984 233.181i 0.115694 0.247538i
\(943\) 444.025 0.470864
\(944\) 397.330 618.861i 0.420900 0.655573i
\(945\) 39.5544i 0.0418565i
\(946\) −357.608 + 765.132i −0.378021 + 0.808808i
\(947\) −1611.78 + 667.619i −1.70198 + 0.704983i −0.999974 0.00718706i \(-0.997712\pi\)
−0.702007 + 0.712171i \(0.747712\pi\)
\(948\) 195.330 + 102.120i 0.206044 + 0.107722i
\(949\) −809.151 335.161i −0.852636 0.353173i
\(950\) 36.0189 808.626i 0.0379147 0.851185i
\(951\) 22.6865 + 22.6865i 0.0238554 + 0.0238554i
\(952\) −32.2784 121.750i −0.0339059 0.127889i
\(953\) 661.490 + 661.490i 0.694114 + 0.694114i 0.963134 0.269021i \(-0.0867000\pi\)
−0.269021 + 0.963134i \(0.586700\pi\)
\(954\) 752.355 + 822.505i 0.788633 + 0.862165i
\(955\) 581.807 + 240.992i 0.609222 + 0.252348i
\(956\) 246.295 205.927i 0.257630 0.215405i
\(957\) 127.508 52.8155i 0.133237 0.0551886i
\(958\) −552.068 + 200.386i −0.576272 + 0.209171i
\(959\) 163.243i 0.170222i
\(960\) 87.4556 + 153.343i 0.0910996 + 0.159733i
\(961\) −1918.20 −1.99604
\(962\) 113.106 + 311.611i 0.117574 + 0.323920i
\(963\) −49.1121 118.567i −0.0509990 0.123123i
\(964\) −25.5241 30.5274i −0.0264772 0.0316674i
\(965\) 265.483 640.932i 0.275112 0.664179i
\(966\) −20.6321 + 18.8724i −0.0213582 + 0.0195366i
\(967\) 38.7070 38.7070i 0.0400279 0.0400279i −0.686810 0.726837i \(-0.740989\pi\)
0.726837 + 0.686810i \(0.240989\pi\)
\(968\) −119.014 448.909i −0.122949 0.463749i
\(969\) 339.560 339.560i 0.350423 0.350423i
\(970\) 223.911 + 9.97375i 0.230836 + 0.0102822i
\(971\) 253.057 610.934i 0.260615 0.629180i −0.738362 0.674405i \(-0.764400\pi\)
0.998977 + 0.0452246i \(0.0144003\pi\)
\(972\) −321.263 + 614.496i −0.330518 + 0.632197i
\(973\) 2.17021 + 5.23934i 0.00223043 + 0.00538473i
\(974\) 1200.13 + 560.919i 1.23217 + 0.575892i
\(975\) 164.703 0.168926
\(976\) 102.346 + 469.472i 0.104862 + 0.481017i
\(977\) 122.372i 0.125253i −0.998037 0.0626263i \(-0.980052\pi\)
0.998037 0.0626263i \(-0.0199476\pi\)
\(978\) −280.590 131.142i −0.286902 0.134092i
\(979\) 630.692 261.241i 0.644221 0.266845i
\(980\) −649.383 + 203.493i −0.662636 + 0.207646i
\(981\) 761.783 + 315.541i 0.776537 + 0.321652i
\(982\) −628.842 28.0107i −0.640368 0.0285242i
\(983\) 696.783 + 696.783i 0.708833 + 0.708833i 0.966290 0.257457i \(-0.0828845\pi\)
−0.257457 + 0.966290i \(0.582884\pi\)
\(984\) −78.0234 102.240i −0.0792921 0.103903i
\(985\) −405.572 405.572i −0.411748 0.411748i
\(986\) 625.521 572.172i 0.634403 0.580296i
\(987\) 2.82573 + 1.17045i 0.00286294 + 0.00118587i
\(988\) −2134.28 190.514i −2.16020 0.192828i
\(989\) 1063.98 440.716i 1.07582 0.445618i
\(990\) 159.862 + 440.425i 0.161477 + 0.444874i
\(991\) 536.777i 0.541652i −0.962628 0.270826i \(-0.912703\pi\)
0.962628 0.270826i \(-0.0872968\pi\)
\(992\) −290.715 1692.27i −0.293060 1.70592i
\(993\) 253.533 0.255321
\(994\) −208.611 + 75.7203i −0.209870 + 0.0761773i
\(995\) −42.6521 102.971i −0.0428664 0.103489i
\(996\) −49.0605 4.37933i −0.0492575 0.00439691i
\(997\) 250.176 603.979i 0.250929 0.605796i −0.747351 0.664430i \(-0.768674\pi\)
0.998280 + 0.0586337i \(0.0186744\pi\)
\(998\) 836.665 + 914.676i 0.838342 + 0.916509i
\(999\) −95.6945 + 95.6945i −0.0957903 + 0.0957903i
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 32.3.h.a.11.5 yes 28
3.2 odd 2 288.3.u.a.235.3 28
4.3 odd 2 128.3.h.a.79.4 28
8.3 odd 2 256.3.h.a.159.4 28
8.5 even 2 256.3.h.b.159.4 28
32.3 odd 8 inner 32.3.h.a.3.5 28
32.13 even 8 256.3.h.a.95.4 28
32.19 odd 8 256.3.h.b.95.4 28
32.29 even 8 128.3.h.a.47.4 28
96.35 even 8 288.3.u.a.163.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.3.5 28 32.3 odd 8 inner
32.3.h.a.11.5 yes 28 1.1 even 1 trivial
128.3.h.a.47.4 28 32.29 even 8
128.3.h.a.79.4 28 4.3 odd 2
256.3.h.a.95.4 28 32.13 even 8
256.3.h.a.159.4 28 8.3 odd 2
256.3.h.b.95.4 28 32.19 odd 8
256.3.h.b.159.4 28 8.5 even 2
288.3.u.a.163.3 28 96.35 even 8
288.3.u.a.235.3 28 3.2 odd 2