Properties

Label 32.4.g.a.5.2
Level $32$
Weight $4$
Character 32.5
Analytic conductor $1.888$
Analytic rank $0$
Dimension $44$
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] = [32,4,Mod(5,32)]
 
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([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.g (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: \(1.88806112018\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 32.5
Dual form 32.4.g.a.13.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.51802 + 1.28824i) q^{2} +(-0.998206 - 2.40988i) q^{3} +(4.68088 - 6.48763i) q^{4} +(17.4005 + 7.20752i) q^{5} +(5.61801 + 4.78221i) q^{6} +(4.37099 + 4.37099i) q^{7} +(-3.42892 + 22.3661i) q^{8} +(14.2808 - 14.2808i) q^{9} +O(q^{10})\) \(q+(-2.51802 + 1.28824i) q^{2} +(-0.998206 - 2.40988i) q^{3} +(4.68088 - 6.48763i) q^{4} +(17.4005 + 7.20752i) q^{5} +(5.61801 + 4.78221i) q^{6} +(4.37099 + 4.37099i) q^{7} +(-3.42892 + 22.3661i) q^{8} +(14.2808 - 14.2808i) q^{9} +(-53.0999 + 4.26731i) q^{10} +(11.7977 - 28.4821i) q^{11} +(-20.3069 - 4.80437i) q^{12} +(-12.9230 + 5.35288i) q^{13} +(-16.6372 - 5.37537i) q^{14} -49.1278i q^{15} +(-20.1788 - 60.7356i) q^{16} +72.9239i q^{17} +(-17.5622 + 54.3563i) q^{18} +(-143.136 + 59.2889i) q^{19} +(128.209 - 79.1506i) q^{20} +(6.17043 - 14.8967i) q^{21} +(6.98496 + 86.9167i) q^{22} +(83.6411 - 83.6411i) q^{23} +(57.3225 - 14.0627i) q^{24} +(162.441 + 162.441i) q^{25} +(25.6446 - 30.1266i) q^{26} +(-113.737 - 47.1114i) q^{27} +(48.8175 - 7.89733i) q^{28} +(-39.6554 - 95.7367i) q^{29} +(63.2883 + 123.705i) q^{30} -29.0324 q^{31} +(129.053 + 126.939i) q^{32} -80.4149 q^{33} +(-93.9435 - 183.624i) q^{34} +(44.5534 + 107.562i) q^{35} +(-25.8019 - 159.495i) q^{36} +(-267.681 - 110.877i) q^{37} +(284.041 - 333.684i) q^{38} +(25.7996 + 25.7996i) q^{39} +(-220.869 + 364.467i) q^{40} +(-124.918 + 124.918i) q^{41} +(3.65329 + 45.4593i) q^{42} +(-27.0156 + 65.2215i) q^{43} +(-129.558 - 209.860i) q^{44} +(351.421 - 145.564i) q^{45} +(-102.860 + 318.360i) q^{46} +282.627i q^{47} +(-126.223 + 109.255i) q^{48} -304.789i q^{49} +(-618.292 - 199.767i) q^{50} +(175.738 - 72.7931i) q^{51} +(-25.7634 + 108.896i) q^{52} +(-51.4343 + 124.173i) q^{53} +(347.083 - 27.8929i) q^{54} +(410.570 - 410.570i) q^{55} +(-112.750 + 82.7743i) q^{56} +(285.759 + 285.759i) q^{57} +(223.185 + 189.981i) q^{58} +(-222.476 - 92.1524i) q^{59} +(-318.723 - 229.961i) q^{60} +(-226.809 - 547.566i) q^{61} +(73.1043 - 37.4007i) q^{62} +124.842 q^{63} +(-488.485 - 153.383i) q^{64} -263.447 q^{65} +(202.487 - 103.594i) q^{66} +(356.015 + 859.496i) q^{67} +(473.104 + 341.348i) q^{68} +(-285.056 - 118.074i) q^{69} +(-250.752 - 213.447i) q^{70} +(690.837 + 690.837i) q^{71} +(270.437 + 368.373i) q^{72} +(223.345 - 223.345i) q^{73} +(816.862 - 65.6462i) q^{74} +(229.314 - 553.612i) q^{75} +(-285.357 + 1206.14i) q^{76} +(176.062 - 72.9275i) q^{77} +(-98.2001 - 31.7279i) q^{78} -698.000i q^{79} +(86.6322 - 1202.27i) q^{80} -224.174i q^{81} +(153.622 - 475.470i) q^{82} +(-915.116 + 379.053i) q^{83} +(-67.7616 - 109.761i) q^{84} +(-525.601 + 1268.91i) q^{85} +(-15.9950 - 199.032i) q^{86} +(-191.130 + 191.130i) q^{87} +(596.580 + 361.530i) q^{88} +(-163.738 - 163.738i) q^{89} +(-697.366 + 819.247i) q^{90} +(-79.8837 - 33.0889i) q^{91} +(-151.119 - 934.147i) q^{92} +(28.9803 + 69.9647i) q^{93} +(-364.091 - 711.661i) q^{94} -2917.97 q^{95} +(177.086 - 437.713i) q^{96} -839.460 q^{97} +(392.641 + 767.465i) q^{98} +(-238.266 - 575.225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51802 + 1.28824i −0.890255 + 0.455462i
\(3\) −0.998206 2.40988i −0.192105 0.463782i 0.798252 0.602324i \(-0.205758\pi\)
−0.990357 + 0.138542i \(0.955758\pi\)
\(4\) 4.68088 6.48763i 0.585110 0.810954i
\(5\) 17.4005 + 7.20752i 1.55635 + 0.644661i 0.984450 0.175664i \(-0.0562073\pi\)
0.571898 + 0.820325i \(0.306207\pi\)
\(6\) 5.61801 + 4.78221i 0.382257 + 0.325388i
\(7\) 4.37099 + 4.37099i 0.236012 + 0.236012i 0.815196 0.579185i \(-0.196629\pi\)
−0.579185 + 0.815196i \(0.696629\pi\)
\(8\) −3.42892 + 22.3661i −0.151538 + 0.988451i
\(9\) 14.2808 14.2808i 0.528917 0.528917i
\(10\) −53.0999 + 4.26731i −1.67917 + 0.134944i
\(11\) 11.7977 28.4821i 0.323375 0.780697i −0.675678 0.737197i \(-0.736149\pi\)
0.999053 0.0435002i \(-0.0138509\pi\)
\(12\) −20.3069 4.80437i −0.488508 0.115575i
\(13\) −12.9230 + 5.35288i −0.275707 + 0.114202i −0.516253 0.856436i \(-0.672674\pi\)
0.240546 + 0.970638i \(0.422674\pi\)
\(14\) −16.6372 5.37537i −0.317605 0.102616i
\(15\) 49.1278i 0.845649i
\(16\) −20.1788 60.7356i −0.315294 0.948994i
\(17\) 72.9239i 1.04039i 0.854047 + 0.520195i \(0.174141\pi\)
−0.854047 + 0.520195i \(0.825859\pi\)
\(18\) −17.5622 + 54.3563i −0.229970 + 0.711773i
\(19\) −143.136 + 59.2889i −1.72830 + 0.715884i −0.728783 + 0.684745i \(0.759914\pi\)
−0.999515 + 0.0311397i \(0.990086\pi\)
\(20\) 128.209 79.1506i 1.43342 0.884930i
\(21\) 6.17043 14.8967i 0.0641190 0.154797i
\(22\) 6.98496 + 86.9167i 0.0676909 + 0.842305i
\(23\) 83.6411 83.6411i 0.758278 0.758278i −0.217731 0.976009i \(-0.569866\pi\)
0.976009 + 0.217731i \(0.0698656\pi\)
\(24\) 57.3225 14.0627i 0.487537 0.119605i
\(25\) 162.441 + 162.441i 1.29953 + 1.29953i
\(26\) 25.6446 30.1266i 0.193435 0.227243i
\(27\) −113.737 47.1114i −0.810692 0.335800i
\(28\) 48.8175 7.89733i 0.329487 0.0533020i
\(29\) −39.6554 95.7367i −0.253925 0.613030i 0.744589 0.667523i \(-0.232646\pi\)
−0.998514 + 0.0544937i \(0.982646\pi\)
\(30\) 63.2883 + 123.705i 0.385161 + 0.752844i
\(31\) −29.0324 −0.168206 −0.0841029 0.996457i \(-0.526802\pi\)
−0.0841029 + 0.996457i \(0.526802\pi\)
\(32\) 129.053 + 126.939i 0.712922 + 0.701243i
\(33\) −80.4149 −0.424195
\(34\) −93.9435 183.624i −0.473858 0.926214i
\(35\) 44.5534 + 107.562i 0.215169 + 0.519463i
\(36\) −25.8019 159.495i −0.119453 0.738402i
\(37\) −267.681 110.877i −1.18936 0.492650i −0.301815 0.953366i \(-0.597593\pi\)
−0.887547 + 0.460716i \(0.847593\pi\)
\(38\) 284.041 333.684i 1.21257 1.42449i
\(39\) 25.7996 + 25.7996i 0.105929 + 0.105929i
\(40\) −220.869 + 364.467i −0.873062 + 1.44068i
\(41\) −124.918 + 124.918i −0.475827 + 0.475827i −0.903794 0.427968i \(-0.859230\pi\)
0.427968 + 0.903794i \(0.359230\pi\)
\(42\) 3.65329 + 45.4593i 0.0134218 + 0.167012i
\(43\) −27.0156 + 65.2215i −0.0958103 + 0.231306i −0.964517 0.264020i \(-0.914952\pi\)
0.868707 + 0.495326i \(0.164952\pi\)
\(44\) −129.558 209.860i −0.443900 0.719036i
\(45\) 351.421 145.564i 1.16415 0.482207i
\(46\) −102.860 + 318.360i −0.329694 + 1.02043i
\(47\) 282.627i 0.877136i 0.898698 + 0.438568i \(0.144514\pi\)
−0.898698 + 0.438568i \(0.855486\pi\)
\(48\) −126.223 + 109.255i −0.379557 + 0.328534i
\(49\) 304.789i 0.888597i
\(50\) −618.292 199.767i −1.74879 0.565026i
\(51\) 175.738 72.7931i 0.482515 0.199864i
\(52\) −25.7634 + 108.896i −0.0687065 + 0.290406i
\(53\) −51.4343 + 124.173i −0.133303 + 0.321821i −0.976410 0.215924i \(-0.930724\pi\)
0.843107 + 0.537745i \(0.180724\pi\)
\(54\) 347.083 27.8929i 0.874667 0.0702916i
\(55\) 410.570 410.570i 1.00657 1.00657i
\(56\) −112.750 + 82.7743i −0.269051 + 0.197521i
\(57\) 285.759 + 285.759i 0.664029 + 0.664029i
\(58\) 223.185 + 189.981i 0.505270 + 0.430100i
\(59\) −222.476 92.1524i −0.490913 0.203343i 0.123474 0.992348i \(-0.460596\pi\)
−0.614387 + 0.789005i \(0.710596\pi\)
\(60\) −318.723 229.961i −0.685783 0.494797i
\(61\) −226.809 547.566i −0.476065 1.14932i −0.961440 0.275016i \(-0.911317\pi\)
0.485374 0.874306i \(-0.338683\pi\)
\(62\) 73.1043 37.4007i 0.149746 0.0766112i
\(63\) 124.842 0.249661
\(64\) −488.485 153.383i −0.954072 0.299577i
\(65\) −263.447 −0.502717
\(66\) 202.487 103.594i 0.377642 0.193205i
\(67\) 356.015 + 859.496i 0.649166 + 1.56723i 0.813975 + 0.580900i \(0.197299\pi\)
−0.164808 + 0.986326i \(0.552701\pi\)
\(68\) 473.104 + 341.348i 0.843709 + 0.608743i
\(69\) −285.056 118.074i −0.497344 0.206007i
\(70\) −250.752 213.447i −0.428151 0.364454i
\(71\) 690.837 + 690.837i 1.15475 + 1.15475i 0.985588 + 0.169163i \(0.0541063\pi\)
0.169163 + 0.985588i \(0.445894\pi\)
\(72\) 270.437 + 368.373i 0.442658 + 0.602960i
\(73\) 223.345 223.345i 0.358089 0.358089i −0.505019 0.863108i \(-0.668515\pi\)
0.863108 + 0.505019i \(0.168515\pi\)
\(74\) 816.862 65.6462i 1.28322 0.103125i
\(75\) 229.314 553.612i 0.353052 0.852342i
\(76\) −285.357 + 1206.14i −0.430694 + 1.82044i
\(77\) 176.062 72.9275i 0.260574 0.107933i
\(78\) −98.2001 31.7279i −0.142551 0.0460574i
\(79\) 698.000i 0.994065i −0.867732 0.497033i \(-0.834423\pi\)
0.867732 0.497033i \(-0.165577\pi\)
\(80\) 86.6322 1202.27i 0.121072 1.68022i
\(81\) 224.174i 0.307509i
\(82\) 153.622 475.470i 0.206886 0.640328i
\(83\) −915.116 + 379.053i −1.21020 + 0.501283i −0.894283 0.447502i \(-0.852314\pi\)
−0.315922 + 0.948785i \(0.602314\pi\)
\(84\) −67.7616 109.761i −0.0880166 0.142571i
\(85\) −525.601 + 1268.91i −0.670699 + 1.61921i
\(86\) −15.9950 199.032i −0.0200556 0.249560i
\(87\) −191.130 + 191.130i −0.235532 + 0.235532i
\(88\) 596.580 + 361.530i 0.722677 + 0.437946i
\(89\) −163.738 163.738i −0.195014 0.195014i 0.602845 0.797859i \(-0.294034\pi\)
−0.797859 + 0.602845i \(0.794034\pi\)
\(90\) −697.366 + 819.247i −0.816765 + 0.959514i
\(91\) −79.8837 33.0889i −0.0920229 0.0381171i
\(92\) −151.119 934.147i −0.171253 1.05860i
\(93\) 28.9803 + 69.9647i 0.0323131 + 0.0780108i
\(94\) −364.091 711.661i −0.399502 0.780875i
\(95\) −2917.97 −3.15134
\(96\) 177.086 437.713i 0.188268 0.465353i
\(97\) −839.460 −0.878704 −0.439352 0.898315i \(-0.644792\pi\)
−0.439352 + 0.898315i \(0.644792\pi\)
\(98\) 392.641 + 767.465i 0.404722 + 0.791078i
\(99\) −238.266 575.225i −0.241885 0.583963i
\(100\) 1814.22 293.491i 1.81422 0.293491i
\(101\) 1561.02 + 646.594i 1.53789 + 0.637015i 0.981076 0.193622i \(-0.0620235\pi\)
0.556814 + 0.830637i \(0.312024\pi\)
\(102\) −348.737 + 409.687i −0.338531 + 0.397697i
\(103\) −80.1481 80.1481i −0.0766721 0.0766721i 0.667731 0.744403i \(-0.267266\pi\)
−0.744403 + 0.667731i \(0.767266\pi\)
\(104\) −75.4110 307.391i −0.0711025 0.289829i
\(105\) 214.737 214.737i 0.199583 0.199583i
\(106\) −30.4524 378.931i −0.0279037 0.347218i
\(107\) 552.814 1334.61i 0.499463 1.20581i −0.450310 0.892872i \(-0.648687\pi\)
0.949773 0.312939i \(-0.101313\pi\)
\(108\) −838.030 + 517.361i −0.746662 + 0.460955i
\(109\) 490.666 203.241i 0.431168 0.178596i −0.156535 0.987672i \(-0.550032\pi\)
0.587703 + 0.809077i \(0.300032\pi\)
\(110\) −504.912 + 1562.74i −0.437650 + 1.35456i
\(111\) 755.757i 0.646246i
\(112\) 177.274 353.676i 0.149561 0.298386i
\(113\) 109.197i 0.0909060i −0.998966 0.0454530i \(-0.985527\pi\)
0.998966 0.0454530i \(-0.0144731\pi\)
\(114\) −1087.67 351.421i −0.893595 0.288716i
\(115\) 2058.24 852.552i 1.66898 0.691312i
\(116\) −806.727 190.862i −0.645713 0.152768i
\(117\) −108.107 + 260.993i −0.0854230 + 0.206229i
\(118\) 678.913 54.5601i 0.529653 0.0425649i
\(119\) −318.750 + 318.750i −0.245544 + 0.245544i
\(120\) 1098.80 + 168.455i 0.835883 + 0.128148i
\(121\) 269.116 + 269.116i 0.202191 + 0.202191i
\(122\) 1276.51 + 1086.60i 0.947292 + 0.806362i
\(123\) 425.731 + 176.344i 0.312088 + 0.129271i
\(124\) −135.897 + 188.352i −0.0984188 + 0.136407i
\(125\) 754.814 + 1822.28i 0.540101 + 1.30392i
\(126\) −314.356 + 160.827i −0.222262 + 0.113711i
\(127\) 1519.49 1.06167 0.530837 0.847474i \(-0.321878\pi\)
0.530837 + 0.847474i \(0.321878\pi\)
\(128\) 1427.61 243.063i 0.985814 0.167843i
\(129\) 184.143 0.125681
\(130\) 663.366 339.383i 0.447547 0.228968i
\(131\) 386.047 + 932.000i 0.257474 + 0.621597i 0.998770 0.0495811i \(-0.0157886\pi\)
−0.741296 + 0.671178i \(0.765789\pi\)
\(132\) −376.412 + 521.703i −0.248201 + 0.344003i
\(133\) −884.798 366.495i −0.576855 0.238941i
\(134\) −2003.69 1705.60i −1.29174 1.09956i
\(135\) −1639.52 1639.52i −1.04524 1.04524i
\(136\) −1631.02 250.050i −1.02838 0.157659i
\(137\) 121.798 121.798i 0.0759557 0.0759557i −0.668108 0.744064i \(-0.732896\pi\)
0.744064 + 0.668108i \(0.232896\pi\)
\(138\) 869.887 69.9075i 0.536592 0.0431226i
\(139\) −2.36667 + 5.71364i −0.00144416 + 0.00348651i −0.924600 0.380939i \(-0.875601\pi\)
0.923156 + 0.384426i \(0.125601\pi\)
\(140\) 906.369 + 214.436i 0.547158 + 0.129451i
\(141\) 681.098 282.120i 0.406800 0.168502i
\(142\) −2629.51 849.580i −1.55397 0.502079i
\(143\) 431.225i 0.252174i
\(144\) −1155.52 579.182i −0.668704 0.335175i
\(145\) 1951.68i 1.11778i
\(146\) −274.665 + 850.108i −0.155695 + 0.481886i
\(147\) −734.505 + 304.242i −0.412115 + 0.170704i
\(148\) −1972.31 + 1217.61i −1.09542 + 0.676265i
\(149\) 311.513 752.060i 0.171276 0.413497i −0.814811 0.579727i \(-0.803159\pi\)
0.986087 + 0.166229i \(0.0531592\pi\)
\(150\) 135.768 + 1689.42i 0.0739029 + 0.919604i
\(151\) 571.254 571.254i 0.307868 0.307868i −0.536214 0.844082i \(-0.680146\pi\)
0.844082 + 0.536214i \(0.180146\pi\)
\(152\) −835.259 3404.69i −0.445713 1.81682i
\(153\) 1041.41 + 1041.41i 0.550281 + 0.550281i
\(154\) −349.381 + 410.444i −0.182818 + 0.214769i
\(155\) −505.179 209.252i −0.261787 0.108436i
\(156\) 288.143 46.6136i 0.147884 0.0239236i
\(157\) −219.641 530.260i −0.111651 0.269550i 0.858171 0.513365i \(-0.171601\pi\)
−0.969822 + 0.243814i \(0.921601\pi\)
\(158\) 899.192 + 1757.58i 0.452758 + 0.884972i
\(159\) 350.585 0.174863
\(160\) 1330.67 + 3138.95i 0.657492 + 1.55097i
\(161\) 731.190 0.357924
\(162\) 288.790 + 564.475i 0.140058 + 0.273761i
\(163\) −570.638 1377.64i −0.274207 0.661995i 0.725447 0.688278i \(-0.241633\pi\)
−0.999655 + 0.0262826i \(0.991633\pi\)
\(164\) 225.696 + 1395.15i 0.107463 + 0.664284i
\(165\) −1399.26 579.593i −0.660196 0.273462i
\(166\) 1815.97 2133.35i 0.849076 0.997472i
\(167\) 642.374 + 642.374i 0.297655 + 0.297655i 0.840095 0.542440i \(-0.182499\pi\)
−0.542440 + 0.840095i \(0.682499\pi\)
\(168\) 312.024 + 189.088i 0.143293 + 0.0868361i
\(169\) −1415.16 + 1415.16i −0.644134 + 0.644134i
\(170\) −311.189 3872.25i −0.140395 1.74699i
\(171\) −1197.40 + 2890.78i −0.535483 + 1.29277i
\(172\) 296.676 + 480.561i 0.131519 + 0.213037i
\(173\) −1861.21 + 770.937i −0.817948 + 0.338805i −0.752120 0.659026i \(-0.770969\pi\)
−0.0658275 + 0.997831i \(0.520969\pi\)
\(174\) 235.048 727.491i 0.102408 0.316959i
\(175\) 1420.06i 0.613406i
\(176\) −1967.94 141.804i −0.842835 0.0607324i
\(177\) 628.127i 0.266740i
\(178\) 623.231 + 201.363i 0.262434 + 0.0847909i
\(179\) −317.221 + 131.397i −0.132459 + 0.0548664i −0.447928 0.894069i \(-0.647838\pi\)
0.315469 + 0.948936i \(0.397838\pi\)
\(180\) 700.597 2961.26i 0.290108 1.22622i
\(181\) 532.578 1285.76i 0.218708 0.528008i −0.776002 0.630731i \(-0.782755\pi\)
0.994710 + 0.102722i \(0.0327553\pi\)
\(182\) 243.775 19.5907i 0.0992848 0.00797891i
\(183\) −1093.17 + 1093.17i −0.441581 + 0.441581i
\(184\) 1583.93 + 2157.53i 0.634612 + 0.864429i
\(185\) −3858.63 3858.63i −1.53347 1.53347i
\(186\) −163.105 138.839i −0.0642979 0.0547322i
\(187\) 2077.02 + 860.331i 0.812230 + 0.336437i
\(188\) 1833.58 + 1322.94i 0.711317 + 0.513221i
\(189\) −291.220 703.067i −0.112080 0.270585i
\(190\) 7347.50 3759.04i 2.80549 1.43531i
\(191\) 3161.63 1.19773 0.598867 0.800848i \(-0.295618\pi\)
0.598867 + 0.800848i \(0.295618\pi\)
\(192\) 117.973 + 1330.30i 0.0443436 + 0.500032i
\(193\) −1428.55 −0.532796 −0.266398 0.963863i \(-0.585834\pi\)
−0.266398 + 0.963863i \(0.585834\pi\)
\(194\) 2113.78 1081.43i 0.782271 0.400216i
\(195\) 262.975 + 634.877i 0.0965744 + 0.233151i
\(196\) −1977.36 1426.68i −0.720612 0.519927i
\(197\) 1377.48 + 570.573i 0.498181 + 0.206353i 0.617603 0.786490i \(-0.288104\pi\)
−0.119421 + 0.992844i \(0.538104\pi\)
\(198\) 1340.99 + 1141.49i 0.481312 + 0.409707i
\(199\) 1207.72 + 1207.72i 0.430217 + 0.430217i 0.888702 0.458485i \(-0.151608\pi\)
−0.458485 + 0.888702i \(0.651608\pi\)
\(200\) −4190.16 + 3076.17i −1.48145 + 1.08759i
\(201\) 1715.91 1715.91i 0.602143 0.602143i
\(202\) −4763.64 + 382.825i −1.65925 + 0.133344i
\(203\) 245.131 591.798i 0.0847528 0.204611i
\(204\) 350.353 1480.86i 0.120243 0.508240i
\(205\) −3073.98 + 1273.28i −1.04730 + 0.433805i
\(206\) 305.065 + 98.5648i 0.103179 + 0.0333366i
\(207\) 2388.92i 0.802132i
\(208\) 585.880 + 676.871i 0.195305 + 0.225637i
\(209\) 4776.28i 1.58078i
\(210\) −264.080 + 817.346i −0.0867774 + 0.268582i
\(211\) −627.654 + 259.983i −0.204784 + 0.0848245i −0.482718 0.875776i \(-0.660350\pi\)
0.277934 + 0.960600i \(0.410350\pi\)
\(212\) 564.834 + 914.928i 0.182986 + 0.296403i
\(213\) 975.239 2354.43i 0.313720 0.757386i
\(214\) 327.301 + 4072.74i 0.104551 + 1.30097i
\(215\) −940.170 + 940.170i −0.298228 + 0.298228i
\(216\) 1443.69 2382.31i 0.454773 0.750443i
\(217\) −126.901 126.901i −0.0396985 0.0396985i
\(218\) −973.686 + 1143.86i −0.302506 + 0.355376i
\(219\) −761.178 315.290i −0.234866 0.0972846i
\(220\) −741.801 4585.46i −0.227328 1.40523i
\(221\) −390.353 942.394i −0.118814 0.286843i
\(222\) −973.596 1903.01i −0.294340 0.575324i
\(223\) 1684.85 0.505946 0.252973 0.967473i \(-0.418592\pi\)
0.252973 + 0.967473i \(0.418592\pi\)
\(224\) 9.24107 + 1118.94i 0.00275645 + 0.333759i
\(225\) 4639.56 1.37468
\(226\) 140.672 + 274.960i 0.0414042 + 0.0809295i
\(227\) −1751.96 4229.60i −0.512254 1.23669i −0.942569 0.334011i \(-0.891598\pi\)
0.430315 0.902679i \(-0.358402\pi\)
\(228\) 3191.50 516.297i 0.927027 0.149967i
\(229\) 1072.62 + 444.292i 0.309521 + 0.128208i 0.532037 0.846721i \(-0.321427\pi\)
−0.222515 + 0.974929i \(0.571427\pi\)
\(230\) −4084.41 + 4798.26i −1.17095 + 1.37560i
\(231\) −351.493 351.493i −0.100115 0.100115i
\(232\) 2277.23 558.664i 0.644429 0.158095i
\(233\) −224.008 + 224.008i −0.0629840 + 0.0629840i −0.737897 0.674913i \(-0.764181\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(234\) −64.0062 796.455i −0.0178813 0.222504i
\(235\) −2037.04 + 4917.85i −0.565455 + 1.36513i
\(236\) −1639.23 + 1011.99i −0.452139 + 0.279130i
\(237\) −1682.10 + 696.748i −0.461030 + 0.190965i
\(238\) 391.993 1213.25i 0.106761 0.330433i
\(239\) 5695.35i 1.54143i −0.637181 0.770714i \(-0.719899\pi\)
0.637181 0.770714i \(-0.280101\pi\)
\(240\) −2983.81 + 991.339i −0.802516 + 0.266628i
\(241\) 5864.62i 1.56752i 0.621061 + 0.783762i \(0.286702\pi\)
−0.621061 + 0.783762i \(0.713298\pi\)
\(242\) −1024.32 330.954i −0.272091 0.0879112i
\(243\) −3611.13 + 1495.78i −0.953309 + 0.394874i
\(244\) −4614.08 1091.63i −1.21060 0.286413i
\(245\) 2196.77 5303.48i 0.572844 1.38297i
\(246\) −1299.17 + 104.407i −0.336717 + 0.0270598i
\(247\) 1532.38 1532.38i 0.394749 0.394749i
\(248\) 99.5499 649.342i 0.0254896 0.166263i
\(249\) 1826.95 + 1826.95i 0.464972 + 0.464972i
\(250\) −4248.18 3616.17i −1.07471 0.914826i
\(251\) 1284.55 + 532.079i 0.323029 + 0.133803i 0.538305 0.842750i \(-0.319065\pi\)
−0.215276 + 0.976553i \(0.569065\pi\)
\(252\) 584.371 809.931i 0.146079 0.202464i
\(253\) −1395.50 3369.04i −0.346777 0.837193i
\(254\) −3826.10 + 1957.46i −0.945161 + 0.483552i
\(255\) 3582.59 0.879805
\(256\) −3281.63 + 2451.14i −0.801180 + 0.598424i
\(257\) 6068.35 1.47289 0.736446 0.676497i \(-0.236503\pi\)
0.736446 + 0.676497i \(0.236503\pi\)
\(258\) −463.677 + 237.221i −0.111889 + 0.0572431i
\(259\) −685.388 1654.67i −0.164432 0.396974i
\(260\) −1233.16 + 1709.15i −0.294145 + 0.407681i
\(261\) −1933.50 800.883i −0.458547 0.189937i
\(262\) −2172.71 1849.48i −0.512331 0.436111i
\(263\) −1919.51 1919.51i −0.450046 0.450046i 0.445324 0.895370i \(-0.353089\pi\)
−0.895370 + 0.445324i \(0.853089\pi\)
\(264\) 275.737 1798.57i 0.0642819 0.419296i
\(265\) −1789.97 + 1789.97i −0.414931 + 0.414931i
\(266\) 2700.08 216.989i 0.622377 0.0500166i
\(267\) −231.146 + 558.035i −0.0529808 + 0.127907i
\(268\) 7242.56 + 1713.50i 1.65078 + 0.390555i
\(269\) 3969.40 1644.18i 0.899697 0.372667i 0.115593 0.993297i \(-0.463123\pi\)
0.784103 + 0.620630i \(0.213123\pi\)
\(270\) 6240.46 + 2016.26i 1.40660 + 0.454465i
\(271\) 4538.69i 1.01736i 0.860954 + 0.508682i \(0.169867\pi\)
−0.860954 + 0.508682i \(0.830133\pi\)
\(272\) 4429.08 1471.52i 0.987325 0.328029i
\(273\) 225.540i 0.0500011i
\(274\) −149.786 + 463.597i −0.0330251 + 0.102215i
\(275\) 6543.07 2710.23i 1.43477 0.594301i
\(276\) −2100.34 + 1296.65i −0.458063 + 0.282787i
\(277\) −1889.91 + 4562.63i −0.409940 + 0.989683i 0.575213 + 0.818004i \(0.304919\pi\)
−0.985153 + 0.171679i \(0.945081\pi\)
\(278\) −1.40122 17.4359i −0.000302300 0.00376164i
\(279\) −414.605 + 414.605i −0.0889669 + 0.0889669i
\(280\) −2558.50 + 627.667i −0.546071 + 0.133965i
\(281\) −30.7223 30.7223i −0.00652220 0.00652220i 0.703838 0.710360i \(-0.251468\pi\)
−0.710360 + 0.703838i \(0.751468\pi\)
\(282\) −1351.58 + 1587.80i −0.285410 + 0.335292i
\(283\) −5549.45 2298.66i −1.16565 0.482830i −0.285901 0.958259i \(-0.592293\pi\)
−0.879754 + 0.475429i \(0.842293\pi\)
\(284\) 7715.62 1248.18i 1.61211 0.260794i
\(285\) 2912.73 + 7031.95i 0.605387 + 1.46153i
\(286\) −555.521 1085.83i −0.114855 0.224499i
\(287\) −1092.03 −0.224601
\(288\) 3655.75 30.1921i 0.747976 0.00617738i
\(289\) −404.895 −0.0824130
\(290\) 2514.24 + 4914.38i 0.509107 + 0.995112i
\(291\) 837.954 + 2023.00i 0.168803 + 0.407527i
\(292\) −403.530 2494.43i −0.0808725 0.499915i
\(293\) 2663.79 + 1103.38i 0.531128 + 0.220000i 0.632097 0.774889i \(-0.282194\pi\)
−0.100969 + 0.994890i \(0.532194\pi\)
\(294\) 1457.56 1712.31i 0.289139 0.339673i
\(295\) −3207.00 3207.00i −0.632944 0.632944i
\(296\) 3397.74 5606.78i 0.667195 1.10097i
\(297\) −2683.66 + 2683.66i −0.524316 + 0.524316i
\(298\) 184.436 + 2295.01i 0.0358526 + 0.446128i
\(299\) −633.173 + 1528.61i −0.122466 + 0.295659i
\(300\) −2518.25 4079.09i −0.484637 0.785022i
\(301\) −403.168 + 166.998i −0.0772033 + 0.0319787i
\(302\) −702.518 + 2174.34i −0.133859 + 0.414303i
\(303\) 4407.30i 0.835620i
\(304\) 6489.26 + 7497.08i 1.22429 + 1.41443i
\(305\) 11162.7i 2.09565i
\(306\) −3963.88 1280.71i −0.740522 0.239259i
\(307\) 401.539 166.323i 0.0746484 0.0309204i −0.345047 0.938585i \(-0.612137\pi\)
0.419695 + 0.907665i \(0.362137\pi\)
\(308\) 351.000 1483.59i 0.0649353 0.274466i
\(309\) −113.143 + 273.152i −0.0208301 + 0.0502883i
\(310\) 1541.62 123.890i 0.282445 0.0226984i
\(311\) −5345.11 + 5345.11i −0.974577 + 0.974577i −0.999685 0.0251081i \(-0.992007\pi\)
0.0251081 + 0.999685i \(0.492007\pi\)
\(312\) −665.501 + 488.572i −0.120758 + 0.0886536i
\(313\) −1787.53 1787.53i −0.322803 0.322803i 0.527039 0.849841i \(-0.323302\pi\)
−0.849841 + 0.527039i \(0.823302\pi\)
\(314\) 1236.16 + 1052.26i 0.222168 + 0.189116i
\(315\) 2172.32 + 899.804i 0.388560 + 0.160947i
\(316\) −4528.37 3267.25i −0.806141 0.581637i
\(317\) 2370.77 + 5723.55i 0.420050 + 1.01409i 0.982332 + 0.187145i \(0.0599234\pi\)
−0.562282 + 0.826945i \(0.690077\pi\)
\(318\) −882.782 + 451.638i −0.155673 + 0.0796434i
\(319\) −3194.62 −0.560703
\(320\) −7394.37 6189.71i −1.29174 1.08130i
\(321\) −3768.08 −0.655183
\(322\) −1841.15 + 941.948i −0.318644 + 0.163021i
\(323\) −4323.58 10438.0i −0.744800 1.79811i
\(324\) −1454.36 1049.33i −0.249375 0.179926i
\(325\) −2968.74 1229.69i −0.506696 0.209880i
\(326\) 3211.61 + 2733.81i 0.545628 + 0.464454i
\(327\) −979.572 979.572i −0.165659 0.165659i
\(328\) −2365.59 3222.26i −0.398225 0.542437i
\(329\) −1235.36 + 1235.36i −0.207014 + 0.207014i
\(330\) 4270.02 343.156i 0.712294 0.0572427i
\(331\) 1696.86 4096.57i 0.281775 0.680265i −0.718102 0.695938i \(-0.754989\pi\)
0.999877 + 0.0156724i \(0.00498888\pi\)
\(332\) −1824.38 + 7711.24i −0.301584 + 1.27473i
\(333\) −5406.09 + 2239.28i −0.889646 + 0.368503i
\(334\) −2445.04 789.980i −0.400559 0.129419i
\(335\) 17521.6i 2.85764i
\(336\) −1029.27 74.1667i −0.167118 0.0120420i
\(337\) 927.470i 0.149918i 0.997187 + 0.0749592i \(0.0238826\pi\)
−0.997187 + 0.0749592i \(0.976117\pi\)
\(338\) 1740.34 5386.48i 0.280066 0.866823i
\(339\) −263.152 + 109.001i −0.0421606 + 0.0174635i
\(340\) 5771.97 + 9349.53i 0.920673 + 1.49132i
\(341\) −342.515 + 826.904i −0.0543936 + 0.131318i
\(342\) −708.938 8821.60i −0.112091 1.39479i
\(343\) 2831.48 2831.48i 0.445731 0.445731i
\(344\) −1366.12 827.873i −0.214116 0.129756i
\(345\) −4109.10 4109.10i −0.641237 0.641237i
\(346\) 3693.41 4338.92i 0.573870 0.674167i
\(347\) 3765.13 + 1559.57i 0.582487 + 0.241274i 0.654415 0.756136i \(-0.272915\pi\)
−0.0719277 + 0.997410i \(0.522915\pi\)
\(348\) 345.326 + 2134.64i 0.0531937 + 0.328818i
\(349\) −1631.14 3937.93i −0.250181 0.603990i 0.748037 0.663657i \(-0.230996\pi\)
−0.998218 + 0.0596662i \(0.980996\pi\)
\(350\) −1829.37 3575.73i −0.279383 0.546088i
\(351\) 1722.00 0.261862
\(352\) 5137.99 2178.11i 0.778000 0.329812i
\(353\) −11289.2 −1.70216 −0.851080 0.525037i \(-0.824052\pi\)
−0.851080 + 0.525037i \(0.824052\pi\)
\(354\) −809.178 1581.64i −0.121490 0.237466i
\(355\) 7041.69 + 17000.1i 1.05277 + 2.54162i
\(356\) −1828.71 + 295.836i −0.272252 + 0.0440429i
\(357\) 1086.33 + 449.972i 0.161049 + 0.0667088i
\(358\) 629.498 739.518i 0.0929330 0.109175i
\(359\) 2970.97 + 2970.97i 0.436774 + 0.436774i 0.890925 0.454151i \(-0.150057\pi\)
−0.454151 + 0.890925i \(0.650057\pi\)
\(360\) 2050.69 + 8359.05i 0.300225 + 1.22378i
\(361\) 12122.7 12122.7i 1.76742 1.76742i
\(362\) 315.320 + 3923.65i 0.0457813 + 0.569676i
\(363\) 379.904 917.170i 0.0549306 0.132614i
\(364\) −588.594 + 363.371i −0.0847547 + 0.0523237i
\(365\) 5496.07 2276.55i 0.788157 0.326465i
\(366\) 1344.36 4160.89i 0.191997 0.594243i
\(367\) 12266.5i 1.74470i −0.488882 0.872350i \(-0.662595\pi\)
0.488882 0.872350i \(-0.337405\pi\)
\(368\) −6767.78 3392.22i −0.958681 0.480521i
\(369\) 3567.84i 0.503346i
\(370\) 14687.0 + 4745.28i 2.06362 + 0.666744i
\(371\) −767.581 + 317.942i −0.107415 + 0.0444926i
\(372\) 589.559 + 139.482i 0.0821699 + 0.0194404i
\(373\) −905.804 + 2186.80i −0.125739 + 0.303561i −0.974196 0.225703i \(-0.927532\pi\)
0.848457 + 0.529265i \(0.177532\pi\)
\(374\) −6338.31 + 509.371i −0.876326 + 0.0704250i
\(375\) 3638.03 3638.03i 0.500979 0.500979i
\(376\) −6321.26 969.106i −0.867006 0.132920i
\(377\) 1024.93 + 1024.93i 0.140018 + 0.140018i
\(378\) 1639.02 + 1395.18i 0.223021 + 0.189842i
\(379\) 6881.62 + 2850.46i 0.932679 + 0.386328i 0.796694 0.604383i \(-0.206580\pi\)
0.135985 + 0.990711i \(0.456580\pi\)
\(380\) −13658.6 + 18930.7i −1.84388 + 2.55559i
\(381\) −1516.76 3661.78i −0.203953 0.492385i
\(382\) −7961.05 + 4072.93i −1.06629 + 0.545522i
\(383\) −2433.37 −0.324645 −0.162323 0.986738i \(-0.551899\pi\)
−0.162323 + 0.986738i \(0.551899\pi\)
\(384\) −2010.80 3197.75i −0.267222 0.424959i
\(385\) 3589.20 0.475124
\(386\) 3597.13 1840.32i 0.474325 0.242668i
\(387\) 545.609 + 1317.22i 0.0716663 + 0.173018i
\(388\) −3929.41 + 5446.11i −0.514138 + 0.712589i
\(389\) 4253.32 + 1761.78i 0.554375 + 0.229630i 0.642241 0.766503i \(-0.278005\pi\)
−0.0878663 + 0.996132i \(0.528005\pi\)
\(390\) −1480.05 1259.86i −0.192167 0.163578i
\(391\) 6099.44 + 6099.44i 0.788905 + 0.788905i
\(392\) 6816.94 + 1045.10i 0.878335 + 0.134657i
\(393\) 1860.66 1860.66i 0.238824 0.238824i
\(394\) −4203.57 + 337.815i −0.537495 + 0.0431952i
\(395\) 5030.85 12145.6i 0.640835 1.54711i
\(396\) −4847.15 1146.77i −0.615097 0.145524i
\(397\) −306.541 + 126.974i −0.0387528 + 0.0160519i −0.401976 0.915650i \(-0.631676\pi\)
0.363223 + 0.931702i \(0.381676\pi\)
\(398\) −4596.91 1485.24i −0.578950 0.187056i
\(399\) 2498.10i 0.313437i
\(400\) 6588.08 13143.8i 0.823510 1.64297i
\(401\) 10975.6i 1.36682i −0.730036 0.683409i \(-0.760497\pi\)
0.730036 0.683409i \(-0.239503\pi\)
\(402\) −2110.19 + 6531.20i −0.261808 + 0.810315i
\(403\) 375.186 155.407i 0.0463755 0.0192094i
\(404\) 11501.8 7100.68i 1.41642 0.874435i
\(405\) 1615.74 3900.74i 0.198239 0.478591i
\(406\) 145.133 + 1805.95i 0.0177410 + 0.220758i
\(407\) −6316.01 + 6316.01i −0.769221 + 0.769221i
\(408\) 1025.51 + 4180.18i 0.124436 + 0.507229i
\(409\) 8384.88 + 8384.88i 1.01371 + 1.01371i 0.999905 + 0.0138007i \(0.00439304\pi\)
0.0138007 + 0.999905i \(0.495607\pi\)
\(410\) 6100.06 7166.19i 0.734782 0.863202i
\(411\) −415.100 171.940i −0.0498184 0.0206355i
\(412\) −895.135 + 144.808i −0.107039 + 0.0173160i
\(413\) −569.642 1375.24i −0.0678698 0.163852i
\(414\) 3077.50 + 6015.35i 0.365340 + 0.714102i
\(415\) −18655.5 −2.20666
\(416\) −2347.23 949.622i −0.276641 0.111921i
\(417\) 16.1316 0.00189441
\(418\) −6153.00 12026.8i −0.719983 1.40729i
\(419\) 533.639 + 1288.32i 0.0622195 + 0.150211i 0.951931 0.306311i \(-0.0990948\pi\)
−0.889712 + 0.456522i \(0.849095\pi\)
\(420\) −387.978 2398.29i −0.0450748 0.278630i
\(421\) 1963.49 + 813.303i 0.227303 + 0.0941520i 0.493428 0.869786i \(-0.335744\pi\)
−0.266125 + 0.963938i \(0.585744\pi\)
\(422\) 1245.53 1463.21i 0.143676 0.168787i
\(423\) 4036.13 + 4036.13i 0.463932 + 0.463932i
\(424\) −2600.91 1576.17i −0.297904 0.180532i
\(425\) −11845.8 + 11845.8i −1.35201 + 1.35201i
\(426\) 577.403 + 7184.86i 0.0656697 + 0.817154i
\(427\) 1402.03 3384.79i 0.158897 0.383610i
\(428\) −6070.82 9833.61i −0.685617 1.11057i
\(429\) 1039.20 430.451i 0.116954 0.0484438i
\(430\) 1156.21 3578.54i 0.129668 0.401331i
\(431\) 4521.29i 0.505297i −0.967558 0.252649i \(-0.918698\pi\)
0.967558 0.252649i \(-0.0813016\pi\)
\(432\) −566.264 + 7858.54i −0.0630658 + 0.875217i
\(433\) 2122.80i 0.235601i −0.993037 0.117801i \(-0.962416\pi\)
0.993037 0.117801i \(-0.0375844\pi\)
\(434\) 483.017 + 156.060i 0.0534229 + 0.0172607i
\(435\) −4703.33 + 1948.18i −0.518408 + 0.214732i
\(436\) 978.197 4134.61i 0.107448 0.454155i
\(437\) −7013.07 + 16931.1i −0.767691 + 1.85337i
\(438\) 2322.83 186.672i 0.253400 0.0203642i
\(439\) 8028.12 8028.12i 0.872805 0.872805i −0.119972 0.992777i \(-0.538281\pi\)
0.992777 + 0.119972i \(0.0382806\pi\)
\(440\) 7775.04 + 10590.7i 0.842411 + 1.14748i
\(441\) −4352.62 4352.62i −0.469994 0.469994i
\(442\) 2196.95 + 1870.10i 0.236421 + 0.201248i
\(443\) 3136.09 + 1299.01i 0.336343 + 0.139318i 0.544462 0.838786i \(-0.316734\pi\)
−0.208119 + 0.978104i \(0.566734\pi\)
\(444\) 4903.07 + 3537.60i 0.524076 + 0.378124i
\(445\) −1668.98 4029.28i −0.177792 0.429227i
\(446\) −4242.50 + 2170.49i −0.450422 + 0.230439i
\(447\) −2123.33 −0.224676
\(448\) −1464.73 2805.60i −0.154468 0.295876i
\(449\) −16955.9 −1.78218 −0.891088 0.453832i \(-0.850057\pi\)
−0.891088 + 0.453832i \(0.850057\pi\)
\(450\) −11682.5 + 5976.86i −1.22382 + 0.626115i
\(451\) 2084.18 + 5031.66i 0.217606 + 0.525347i
\(452\) −708.429 511.137i −0.0737206 0.0531900i
\(453\) −1946.88 806.426i −0.201926 0.0836406i
\(454\) 9860.21 + 8393.29i 1.01930 + 0.867658i
\(455\) −1151.53 1151.53i −0.118647 0.118647i
\(456\) −7371.15 + 5411.46i −0.756986 + 0.555734i
\(457\) 6223.46 6223.46i 0.637027 0.637027i −0.312794 0.949821i \(-0.601265\pi\)
0.949821 + 0.312794i \(0.101265\pi\)
\(458\) −3273.22 + 263.049i −0.333947 + 0.0268373i
\(459\) 3435.55 8294.14i 0.349363 0.843437i
\(460\) 4103.33 17343.8i 0.415911 1.75796i
\(461\) 10872.5 4503.54i 1.09844 0.454991i 0.241501 0.970401i \(-0.422360\pi\)
0.856944 + 0.515410i \(0.172360\pi\)
\(462\) 1337.88 + 432.260i 0.134726 + 0.0435294i
\(463\) 13182.5i 1.32320i 0.749858 + 0.661599i \(0.230122\pi\)
−0.749858 + 0.661599i \(0.769878\pi\)
\(464\) −5014.43 + 4340.35i −0.501700 + 0.434258i
\(465\) 1426.30i 0.142243i
\(466\) 275.482 852.634i 0.0273851 0.0847586i
\(467\) 7043.25 2917.41i 0.697907 0.289083i −0.00538305 0.999986i \(-0.501713\pi\)
0.703290 + 0.710903i \(0.251713\pi\)
\(468\) 1187.19 + 1923.04i 0.117261 + 0.189941i
\(469\) −2200.71 + 5312.99i −0.216673 + 0.523094i
\(470\) −1206.06 15007.5i −0.118364 1.47286i
\(471\) −1058.62 + 1058.62i −0.103564 + 0.103564i
\(472\) 2823.94 4659.93i 0.275387 0.454429i
\(473\) 1538.92 + 1538.92i 0.149598 + 0.149598i
\(474\) 3337.98 3921.37i 0.323457 0.379989i
\(475\) −32882.1 13620.2i −3.17628 1.31566i
\(476\) 575.904 + 3559.96i 0.0554549 + 0.342795i
\(477\) 1038.77 + 2507.81i 0.0997107 + 0.240723i
\(478\) 7336.98 + 14341.0i 0.702062 + 1.37227i
\(479\) 4612.37 0.439968 0.219984 0.975503i \(-0.429399\pi\)
0.219984 + 0.975503i \(0.429399\pi\)
\(480\) 6236.21 6340.07i 0.593005 0.602882i
\(481\) 4052.74 0.384177
\(482\) −7555.04 14767.3i −0.713947 1.39550i
\(483\) −729.878 1762.08i −0.0687590 0.165999i
\(484\) 3005.62 486.227i 0.282271 0.0456637i
\(485\) −14607.0 6050.43i −1.36757 0.566466i
\(486\) 7165.98 8418.41i 0.668839 0.785734i
\(487\) −10988.9 10988.9i −1.02249 1.02249i −0.999741 0.0227515i \(-0.992757\pi\)
−0.0227515 0.999741i \(-0.507243\pi\)
\(488\) 13024.6 3195.28i 1.20819 0.296401i
\(489\) −2750.34 + 2750.34i −0.254345 + 0.254345i
\(490\) 1300.63 + 16184.2i 0.119911 + 1.49210i
\(491\) −7836.91 + 18920.0i −0.720316 + 1.73900i −0.0478645 + 0.998854i \(0.515242\pi\)
−0.672451 + 0.740142i \(0.734758\pi\)
\(492\) 3136.85 1936.55i 0.287439 0.177452i
\(493\) 6981.49 2891.83i 0.637790 0.264181i
\(494\) −1884.49 + 5832.64i −0.171634 + 0.531220i
\(495\) 11726.5i 1.06478i
\(496\) 585.839 + 1763.30i 0.0530342 + 0.159626i
\(497\) 6039.29i 0.545069i
\(498\) −6953.84 2246.75i −0.625721 0.202167i
\(499\) −6404.45 + 2652.81i −0.574554 + 0.237988i −0.650990 0.759086i \(-0.725646\pi\)
0.0764356 + 0.997075i \(0.475646\pi\)
\(500\) 15355.5 + 3632.92i 1.37344 + 0.324938i
\(501\) 906.824 2189.27i 0.0808661 0.195228i
\(502\) −3919.98 + 315.025i −0.348520 + 0.0280085i
\(503\) 2553.60 2553.60i 0.226361 0.226361i −0.584810 0.811171i \(-0.698831\pi\)
0.811171 + 0.584810i \(0.198831\pi\)
\(504\) −428.075 + 2792.24i −0.0378332 + 0.246778i
\(505\) 22502.1 + 22502.1i 1.98283 + 1.98283i
\(506\) 7854.04 + 6685.58i 0.690029 + 0.587372i
\(507\) 4823.00 + 1997.75i 0.422479 + 0.174997i
\(508\) 7112.52 9857.87i 0.621195 0.860969i
\(509\) 3141.82 + 7585.02i 0.273593 + 0.660511i 0.999632 0.0271425i \(-0.00864080\pi\)
−0.726039 + 0.687654i \(0.758641\pi\)
\(510\) −9021.04 + 4615.23i −0.783251 + 0.400718i
\(511\) 1952.48 0.169026
\(512\) 5105.56 10399.6i 0.440696 0.897657i
\(513\) 19073.0 1.64151
\(514\) −15280.2 + 7817.48i −1.31125 + 0.670845i
\(515\) −816.948 1972.29i −0.0699010 0.168756i
\(516\) 861.951 1194.65i 0.0735374 0.101922i
\(517\) 8049.80 + 3334.34i 0.684777 + 0.283644i
\(518\) 3857.44 + 3283.56i 0.327193 + 0.278516i
\(519\) 3715.74 + 3715.74i 0.314263 + 0.314263i
\(520\) 903.341 5892.29i 0.0761810 0.496912i
\(521\) −7065.05 + 7065.05i −0.594099 + 0.594099i −0.938736 0.344637i \(-0.888002\pi\)
0.344637 + 0.938736i \(0.388002\pi\)
\(522\) 5900.33 474.174i 0.494733 0.0397587i
\(523\) −111.041 + 268.077i −0.00928391 + 0.0224134i −0.928454 0.371449i \(-0.878861\pi\)
0.919170 + 0.393862i \(0.128861\pi\)
\(524\) 7853.51 + 1858.04i 0.654737 + 0.154903i
\(525\) 3422.17 1417.51i 0.284487 0.117838i
\(526\) 7306.16 + 2360.58i 0.605634 + 0.195677i
\(527\) 2117.16i 0.175000i
\(528\) 1622.68 + 4884.05i 0.133746 + 0.402559i
\(529\) 1824.68i 0.149970i
\(530\) 2201.27 6813.08i 0.180410 0.558380i
\(531\) −4493.13 + 1861.11i −0.367204 + 0.152101i
\(532\) −6519.32 + 4024.73i −0.531294 + 0.327996i
\(533\) 945.642 2282.98i 0.0768486 0.185529i
\(534\) −136.853 1702.92i −0.0110903 0.138001i
\(535\) 19238.5 19238.5i 1.55468 1.55468i
\(536\) −20444.3 + 5015.52i −1.64750 + 0.404174i
\(537\) 633.304 + 633.304i 0.0508921 + 0.0508921i
\(538\) −7876.94 + 9253.61i −0.631225 + 0.741546i
\(539\) −8681.02 3595.79i −0.693725 0.287350i
\(540\) −18311.0 + 2962.22i −1.45922 + 0.236063i
\(541\) −8420.37 20328.6i −0.669168 1.61552i −0.783005 0.622016i \(-0.786314\pi\)
0.113837 0.993499i \(-0.463686\pi\)
\(542\) −5846.92 11428.5i −0.463370 0.905714i
\(543\) −3630.14 −0.286896
\(544\) −9256.85 + 9411.03i −0.729567 + 0.741718i
\(545\) 10002.7 0.786181
\(546\) −290.549 567.914i −0.0227736 0.0445137i
\(547\) 646.357 + 1560.44i 0.0505233 + 0.121974i 0.947126 0.320862i \(-0.103972\pi\)
−0.896603 + 0.442836i \(0.853972\pi\)
\(548\) −220.060 1360.31i −0.0171542 0.106039i
\(549\) −11058.7 4580.65i −0.859696 0.356098i
\(550\) −12984.2 + 15253.5i −1.00663 + 1.18256i
\(551\) 11352.2 + 11352.2i 0.877717 + 0.877717i
\(552\) 3618.30 5970.73i 0.278994 0.460383i
\(553\) 3050.95 3050.95i 0.234611 0.234611i
\(554\) −1118.94 13923.5i −0.0858111 1.06778i
\(555\) −5447.14 + 13150.5i −0.416609 + 1.00578i
\(556\) 25.9899 + 42.0989i 0.00198241 + 0.00321114i
\(557\) −6482.01 + 2684.93i −0.493091 + 0.204245i −0.615351 0.788253i \(-0.710986\pi\)
0.122260 + 0.992498i \(0.460986\pi\)
\(558\) 509.874 1578.10i 0.0386823 0.119724i
\(559\) 987.467i 0.0747145i
\(560\) 5633.78 4876.44i 0.425126 0.367977i
\(561\) 5864.17i 0.441329i
\(562\) 116.937 + 37.7818i 0.00877704 + 0.00283581i
\(563\) −945.289 + 391.551i −0.0707623 + 0.0293107i −0.417784 0.908546i \(-0.637193\pi\)
0.347022 + 0.937857i \(0.387193\pi\)
\(564\) 1357.84 5739.28i 0.101375 0.428488i
\(565\) 787.039 1900.08i 0.0586035 0.141481i
\(566\) 16934.9 1360.95i 1.25764 0.101069i
\(567\) 979.862 979.862i 0.0725756 0.0725756i
\(568\) −17820.2 + 13082.5i −1.31640 + 0.966426i
\(569\) −3760.45 3760.45i −0.277058 0.277058i 0.554875 0.831934i \(-0.312766\pi\)
−0.831934 + 0.554875i \(0.812766\pi\)
\(570\) −16393.2 13954.3i −1.20462 1.02541i
\(571\) 2056.20 + 851.705i 0.150699 + 0.0624216i 0.456758 0.889591i \(-0.349010\pi\)
−0.306059 + 0.952013i \(0.599010\pi\)
\(572\) 2797.63 + 2018.51i 0.204501 + 0.147549i
\(573\) −3155.95 7619.15i −0.230091 0.555488i
\(574\) 2749.76 1406.80i 0.199952 0.102297i
\(575\) 27173.5 1.97080
\(576\) −9166.37 + 4785.51i −0.663076 + 0.346174i
\(577\) −23621.3 −1.70427 −0.852137 0.523318i \(-0.824694\pi\)
−0.852137 + 0.523318i \(0.824694\pi\)
\(578\) 1019.53 521.602i 0.0733686 0.0375359i
\(579\) 1425.99 + 3442.65i 0.102353 + 0.247101i
\(580\) −12661.8 9135.59i −0.906471 0.654026i
\(581\) −5656.80 2343.13i −0.403931 0.167314i
\(582\) −4716.10 4014.48i −0.335891 0.285920i
\(583\) 2929.91 + 2929.91i 0.208138 + 0.208138i
\(584\) 4229.51 + 5761.18i 0.299689 + 0.408218i
\(585\) −3762.23 + 3762.23i −0.265896 + 0.265896i
\(586\) −8128.91 + 653.271i −0.573041 + 0.0460518i
\(587\) 7316.12 17662.7i 0.514427 1.24194i −0.426857 0.904319i \(-0.640379\pi\)
0.941283 0.337617i \(-0.109621\pi\)
\(588\) −1464.32 + 6189.32i −0.102700 + 0.434087i
\(589\) 4155.59 1721.30i 0.290710 0.120416i
\(590\) 12206.7 + 3943.91i 0.851764 + 0.275200i
\(591\) 3889.13i 0.270689i
\(592\) −1332.71 + 18495.1i −0.0925235 + 1.28403i
\(593\) 16542.0i 1.14553i 0.819720 + 0.572764i \(0.194129\pi\)
−0.819720 + 0.572764i \(0.805871\pi\)
\(594\) 3300.32 10214.7i 0.227969 0.705580i
\(595\) −7843.81 + 3249.01i −0.540445 + 0.223860i
\(596\) −3420.93 5541.28i −0.235112 0.380839i
\(597\) 1704.91 4116.02i 0.116880 0.282174i
\(598\) −374.878 4664.76i −0.0256353 0.318990i
\(599\) −8579.81 + 8579.81i −0.585244 + 0.585244i −0.936340 0.351095i \(-0.885809\pi\)
0.351095 + 0.936340i \(0.385809\pi\)
\(600\) 11595.9 + 7027.15i 0.788998 + 0.478137i
\(601\) −13633.8 13633.8i −0.925346 0.925346i 0.0720542 0.997401i \(-0.477045\pi\)
−0.997401 + 0.0720542i \(0.977045\pi\)
\(602\) 800.052 939.880i 0.0541656 0.0636323i
\(603\) 17358.4 + 7190.09i 1.17229 + 0.485578i
\(604\) −1032.12 6380.06i −0.0695303 0.429803i
\(605\) 2743.09 + 6622.41i 0.184335 + 0.445023i
\(606\) 5677.66 + 11097.7i 0.380593 + 0.743915i
\(607\) −23984.1 −1.60376 −0.801881 0.597484i \(-0.796167\pi\)
−0.801881 + 0.597484i \(0.796167\pi\)
\(608\) −25998.1 10518.1i −1.73415 0.701587i
\(609\) −1670.86 −0.111176
\(610\) 14380.2 + 28107.8i 0.954487 + 1.86566i
\(611\) −1512.87 3652.38i −0.100170 0.241833i
\(612\) 11631.0 1881.57i 0.768227 0.124278i
\(613\) 18072.9 + 7486.04i 1.19080 + 0.493244i 0.888014 0.459816i \(-0.152085\pi\)
0.302782 + 0.953060i \(0.402085\pi\)
\(614\) −796.821 + 936.084i −0.0523731 + 0.0615265i
\(615\) 6136.93 + 6136.93i 0.402382 + 0.402382i
\(616\) 1027.40 + 4187.89i 0.0671998 + 0.273921i
\(617\) 18674.2 18674.2i 1.21847 1.21847i 0.250301 0.968168i \(-0.419470\pi\)
0.968168 0.250301i \(-0.0805297\pi\)
\(618\) −66.9880 833.558i −0.00436028 0.0542567i
\(619\) 3214.09 7759.51i 0.208700 0.503846i −0.784519 0.620105i \(-0.787090\pi\)
0.993219 + 0.116258i \(0.0370901\pi\)
\(620\) −3722.23 + 2297.93i −0.241110 + 0.148850i
\(621\) −13453.5 + 5572.64i −0.869359 + 0.360100i
\(622\) 6573.32 20344.9i 0.423740 1.31150i
\(623\) 1431.40i 0.0920511i
\(624\) 1046.35 2087.56i 0.0671274 0.133925i
\(625\) 8433.25i 0.539728i
\(626\) 6803.82 + 2198.28i 0.434401 + 0.140353i
\(627\) 11510.3 4767.71i 0.733136 0.303675i
\(628\) −4468.25 1057.13i −0.283921 0.0671723i
\(629\) 8085.58 19520.3i 0.512549 1.23740i
\(630\) −6629.11 + 532.741i −0.419222 + 0.0336903i
\(631\) −20023.0 + 20023.0i −1.26324 + 1.26324i −0.313722 + 0.949515i \(0.601576\pi\)
−0.949515 + 0.313722i \(0.898424\pi\)
\(632\) 15611.5 + 2393.39i 0.982585 + 0.150639i
\(633\) 1253.06 + 1253.06i 0.0786801 + 0.0786801i
\(634\) −13343.0 11357.9i −0.835831 0.711483i
\(635\) 26439.8 + 10951.7i 1.65233 + 0.684419i
\(636\) 1641.05 2274.47i 0.102314 0.141806i
\(637\) 1631.50 + 3938.78i 0.101479 + 0.244992i
\(638\) 8044.13 4115.44i 0.499169 0.255379i
\(639\) 19731.4 1.22154
\(640\) 26593.0 + 6060.11i 1.64247 + 0.374292i
\(641\) 8637.88 0.532255 0.266128 0.963938i \(-0.414256\pi\)
0.266128 + 0.963938i \(0.414256\pi\)
\(642\) 9488.11 4854.19i 0.583280 0.298411i
\(643\) 5274.73 + 12734.3i 0.323507 + 0.781015i 0.999045 + 0.0436901i \(0.0139114\pi\)
−0.675538 + 0.737325i \(0.736089\pi\)
\(644\) 3422.61 4743.69i 0.209425 0.290260i
\(645\) 3204.18 + 1327.22i 0.195604 + 0.0810219i
\(646\) 24333.6 + 20713.4i 1.48203 + 1.26155i
\(647\) −14785.3 14785.3i −0.898406 0.898406i 0.0968891 0.995295i \(-0.469111\pi\)
−0.995295 + 0.0968891i \(0.969111\pi\)
\(648\) 5013.89 + 768.675i 0.303957 + 0.0465994i
\(649\) −5249.38 + 5249.38i −0.317498 + 0.317498i
\(650\) 9059.51 728.057i 0.546682 0.0439335i
\(651\) −179.143 + 432.488i −0.0107852 + 0.0260377i
\(652\) −11608.7 2746.48i −0.697289 0.164970i
\(653\) −25046.7 + 10374.7i −1.50100 + 0.621733i −0.973677 0.227933i \(-0.926803\pi\)
−0.527321 + 0.849666i \(0.676803\pi\)
\(654\) 3728.51 + 1204.66i 0.222930 + 0.0720275i
\(655\) 18999.7i 1.13340i
\(656\) 10107.7 + 5066.27i 0.601582 + 0.301531i
\(657\) 6379.06i 0.378799i
\(658\) 1519.23 4702.11i 0.0900085 0.278583i
\(659\) −23962.3 + 9925.50i −1.41645 + 0.586711i −0.953965 0.299918i \(-0.903041\pi\)
−0.462481 + 0.886629i \(0.653041\pi\)
\(660\) −10309.9 + 6364.89i −0.608052 + 0.375383i
\(661\) −398.063 + 961.010i −0.0234234 + 0.0565491i −0.935158 0.354230i \(-0.884743\pi\)
0.911735 + 0.410779i \(0.134743\pi\)
\(662\) 1004.65 + 12501.2i 0.0589829 + 0.733948i
\(663\) −1881.41 + 1881.41i −0.110208 + 0.110208i
\(664\) −5340.08 21767.3i −0.312102 1.27219i
\(665\) −12754.4 12754.4i −0.743752 0.743752i
\(666\) 10727.9 12602.9i 0.624173 0.733261i
\(667\) −11324.4 4690.70i −0.657392 0.272301i
\(668\) 7174.36 1160.61i 0.415545 0.0672238i
\(669\) −1681.83 4060.30i −0.0971948 0.234649i
\(670\) −22572.1 44119.9i −1.30155 2.54403i
\(671\) −18271.6 −1.05122
\(672\) 2687.28 1139.20i 0.154262 0.0653952i
\(673\) −15307.7 −0.876775 −0.438387 0.898786i \(-0.644450\pi\)
−0.438387 + 0.898786i \(0.644450\pi\)
\(674\) −1194.80 2335.39i −0.0682821 0.133466i
\(675\) −10822.7 26128.3i −0.617135 1.48990i
\(676\) 2556.86 + 15805.3i 0.145474 + 0.899253i
\(677\) −1043.10 432.068i −0.0592168 0.0245284i 0.352878 0.935669i \(-0.385203\pi\)
−0.412095 + 0.911141i \(0.635203\pi\)
\(678\) 522.202 613.469i 0.0295797 0.0347495i
\(679\) −3669.28 3669.28i −0.207384 0.207384i
\(680\) −26578.4 16106.6i −1.49887 0.908326i
\(681\) −8444.03 + 8444.03i −0.475148 + 0.475148i
\(682\) −202.790 2523.40i −0.0113860 0.141680i
\(683\) −8946.40 + 21598.5i −0.501207 + 1.21002i 0.447619 + 0.894224i \(0.352272\pi\)
−0.948827 + 0.315797i \(0.897728\pi\)
\(684\) 13149.5 + 21299.7i 0.735061 + 1.19066i
\(685\) 2997.22 1241.49i 0.167179 0.0692479i
\(686\) −3482.11 + 10777.4i −0.193801 + 0.599827i
\(687\) 3028.37i 0.168180i
\(688\) 4506.41 + 324.719i 0.249717 + 0.0179939i
\(689\) 1880.01i 0.103952i
\(690\) 15640.3 + 5053.30i 0.862923 + 0.278806i
\(691\) 19676.4 8150.22i 1.08325 0.448696i 0.231600 0.972811i \(-0.425604\pi\)
0.851647 + 0.524115i \(0.175604\pi\)
\(692\) −3710.52 + 15683.5i −0.203834 + 0.861556i
\(693\) 1472.85 3555.77i 0.0807342 0.194910i
\(694\) −11489.8 + 923.364i −0.628453 + 0.0505049i
\(695\) −82.3624 + 82.3624i −0.00449523 + 0.00449523i
\(696\) −3619.46 4930.20i −0.197120 0.268504i
\(697\) −9109.50 9109.50i −0.495046 0.495046i
\(698\) 9180.26 + 7814.49i 0.497819 + 0.423758i
\(699\) 763.440 + 316.227i 0.0413104 + 0.0171113i
\(700\) 9212.80 + 6647.10i 0.497444 + 0.358910i
\(701\) 2739.27 + 6613.19i 0.147591 + 0.356315i 0.980334 0.197343i \(-0.0632313\pi\)
−0.832744 + 0.553658i \(0.813231\pi\)
\(702\) −4336.04 + 2218.35i −0.233124 + 0.119268i
\(703\) 44888.5 2.40825
\(704\) −10131.7 + 12103.5i −0.542402 + 0.647966i
\(705\) 13884.8 0.741749
\(706\) 28426.4 14543.2i 1.51536 0.775268i
\(707\) 3996.93 + 9649.45i 0.212617 + 0.513303i
\(708\) 4075.06 + 2940.19i 0.216314 + 0.156072i
\(709\) −2388.26 989.248i −0.126506 0.0524005i 0.318532 0.947912i \(-0.396810\pi\)
−0.445039 + 0.895511i \(0.646810\pi\)
\(710\) −39631.4 33735.4i −2.09484 1.78319i
\(711\) −9967.97 9967.97i −0.525778 0.525778i
\(712\) 4223.64 3100.74i 0.222314 0.163210i
\(713\) −2428.31 + 2428.31i −0.127547 + 0.127547i
\(714\) −3315.07 + 266.412i −0.173758 + 0.0139639i
\(715\) −3108.06 + 7503.53i −0.162566 + 0.392470i
\(716\) −632.415 + 2673.07i −0.0330090 + 0.139521i
\(717\) −13725.1 + 5685.13i −0.714887 + 0.296116i
\(718\) −11308.3 3653.65i −0.587774 0.189907i
\(719\) 11843.1i 0.614288i −0.951663 0.307144i \(-0.900627\pi\)
0.951663 0.307144i \(-0.0993734\pi\)
\(720\) −15932.2 18406.5i −0.824662 0.952736i
\(721\) 700.654i 0.0361910i
\(722\) −14908.3 + 46142.2i −0.768462 + 2.37844i
\(723\) 14133.0 5854.10i 0.726990 0.301129i
\(724\) −5848.59 9473.64i −0.300222 0.486305i
\(725\) 9109.88 21993.2i 0.466665 1.12663i
\(726\) 224.927 + 2798.86i 0.0114984 + 0.143079i
\(727\) −4691.36 + 4691.36i −0.239330 + 0.239330i −0.816573 0.577243i \(-0.804129\pi\)
0.577243 + 0.816573i \(0.304129\pi\)
\(728\) 1013.98 1673.23i 0.0516219 0.0851840i
\(729\) 2929.40 + 2929.40i 0.148829 + 0.148829i
\(730\) −10906.5 + 12812.6i −0.552969 + 0.649613i
\(731\) −4756.20 1970.08i −0.240649 0.0996801i
\(732\) 1975.09 + 12209.1i 0.0997288 + 0.616475i
\(733\) 13224.6 + 31927.0i 0.666386 + 1.60880i 0.787610 + 0.616174i \(0.211318\pi\)
−0.121224 + 0.992625i \(0.538682\pi\)
\(734\) 15802.2 + 30887.3i 0.794644 + 1.55323i
\(735\) −14973.6 −0.751441
\(736\) 21411.4 176.832i 1.07233 0.00885615i
\(737\) 28680.4 1.43345
\(738\) −4596.24 8983.91i −0.229255 0.448106i
\(739\) −13199.0 31865.1i −0.657012 1.58617i −0.802396 0.596793i \(-0.796442\pi\)
0.145383 0.989375i \(-0.453558\pi\)
\(740\) −43095.1 + 6971.61i −2.14082 + 0.346326i
\(741\) −5222.48 2163.22i −0.258911 0.107244i
\(742\) 1523.20 1789.41i 0.0753617 0.0885329i
\(743\) −14307.6 14307.6i −0.706452 0.706452i 0.259335 0.965787i \(-0.416497\pi\)
−0.965787 + 0.259335i \(0.916497\pi\)
\(744\) −1664.21 + 408.274i −0.0820066 + 0.0201183i
\(745\) 10841.0 10841.0i 0.533131 0.533131i
\(746\) −536.293 6673.31i −0.0263205 0.327517i
\(747\) −7655.38 + 18481.7i −0.374961 + 0.905235i
\(748\) 15303.8 9447.86i 0.748078 0.461829i
\(749\) 8249.93 3417.23i 0.402464 0.166706i
\(750\) −4473.98 + 13847.3i −0.217822 + 0.674175i
\(751\) 15781.7i 0.766820i 0.923578 + 0.383410i \(0.125250\pi\)
−0.923578 + 0.383410i \(0.874750\pi\)
\(752\) 17165.5 5703.07i 0.832397 0.276555i
\(753\) 3626.75i 0.175519i
\(754\) −3901.16 1260.45i −0.188424 0.0608789i
\(755\) 14057.4 5822.78i 0.677619 0.280679i
\(756\) −5924.41 1401.64i −0.285011 0.0674302i
\(757\) −15069.9 + 36382.0i −0.723548 + 1.74680i −0.0605650 + 0.998164i \(0.519290\pi\)
−0.662983 + 0.748635i \(0.730710\pi\)
\(758\) −21000.2 + 1687.65i −1.00628 + 0.0808686i
\(759\) −6726.00 + 6726.00i −0.321658 + 0.321658i
\(760\) 10005.5 65263.5i 0.477548 3.11494i
\(761\) −12120.7 12120.7i −0.577363 0.577363i 0.356813 0.934176i \(-0.383863\pi\)
−0.934176 + 0.356813i \(0.883863\pi\)
\(762\) 8536.49 + 7266.50i 0.405833 + 0.345456i
\(763\) 3033.06 + 1256.34i 0.143911 + 0.0596100i
\(764\) 14799.2 20511.5i 0.700806 0.971308i
\(765\) 10615.1 + 25627.0i 0.501684 + 1.21117i
\(766\) 6127.27 3134.76i 0.289017 0.147864i
\(767\) 3368.33 0.158570
\(768\) 9182.71 + 5461.60i 0.431449 + 0.256613i
\(769\) 5213.88 0.244496 0.122248 0.992500i \(-0.460990\pi\)
0.122248 + 0.992500i \(0.460990\pi\)
\(770\) −9037.69 + 4623.75i −0.422982 + 0.216401i
\(771\) −6057.46 14624.0i −0.282950 0.683101i
\(772\) −6686.89 + 9267.94i −0.311744 + 0.432073i
\(773\) 25960.5 + 10753.2i 1.20793 + 0.500343i 0.893555 0.448954i \(-0.148203\pi\)
0.314380 + 0.949297i \(0.398203\pi\)
\(774\) −3070.74 2613.90i −0.142604 0.121389i
\(775\) −4716.05 4716.05i −0.218588 0.218588i
\(776\) 2878.44 18775.5i 0.133157 0.868556i
\(777\) −3303.41 + 3303.41i −0.152521 + 0.152521i
\(778\) −12979.5 + 1043.09i −0.598123 + 0.0480675i
\(779\) 10474.0 25286.5i 0.481733 1.16301i
\(780\) 5349.80 + 1265.70i 0.245582 + 0.0581016i
\(781\) 27826.7 11526.2i 1.27493 0.528093i
\(782\) −23216.1 7500.98i −1.06164 0.343011i
\(783\) 12757.0i 0.582246i
\(784\) −18511.5 + 6150.27i −0.843273 + 0.280169i
\(785\) 10809.9i 0.491491i
\(786\) −2288.20 + 7082.14i −0.103839 + 0.321389i
\(787\) 31369.3 12993.6i 1.42083 0.588528i 0.465762 0.884910i \(-0.345780\pi\)
0.955069 + 0.296382i \(0.0957801\pi\)
\(788\) 10149.5 6265.84i 0.458834 0.283263i
\(789\) −2709.73 + 6541.86i −0.122267 + 0.295179i
\(790\) 2978.58 + 37063.7i 0.134143 + 1.66920i
\(791\) 477.299 477.299i 0.0214549 0.0214549i
\(792\) 13682.5 3356.68i 0.613874 0.150599i
\(793\) 5862.11 + 5862.11i 0.262509 + 0.262509i
\(794\) 608.306 714.621i 0.0271889 0.0319408i
\(795\) 6100.36 + 2526.85i 0.272148 + 0.112727i
\(796\) 13488.5 2182.06i 0.600610 0.0971622i
\(797\) 8986.32 + 21694.9i 0.399387 + 0.964207i 0.987812 + 0.155654i \(0.0497485\pi\)
−0.588424 + 0.808552i \(0.700251\pi\)
\(798\) −3218.15 6290.27i −0.142758 0.279039i
\(799\) −20610.3 −0.912564
\(800\) 343.429 + 41583.4i 0.0151776 + 1.83774i
\(801\) −4676.62 −0.206292
\(802\) 14139.2 + 27636.7i 0.622533 + 1.21682i
\(803\) −3726.37 8996.26i −0.163762 0.395356i
\(804\) −3100.23 19164.1i −0.135991 0.840631i
\(805\) 12723.1 + 5270.07i 0.557055 + 0.230740i
\(806\) −744.524 + 874.647i −0.0325369 + 0.0382235i
\(807\) −7924.55 7924.55i −0.345672 0.345672i
\(808\) −19814.4 + 32696.7i −0.862708 + 1.42360i
\(809\) −13193.6 + 13193.6i −0.573376 + 0.573376i −0.933070 0.359694i \(-0.882881\pi\)
0.359694 + 0.933070i \(0.382881\pi\)
\(810\) 956.620 + 11903.6i 0.0414965 + 0.516358i
\(811\) 140.367 338.877i 0.00607764 0.0146727i −0.920812 0.390008i \(-0.872472\pi\)
0.926889 + 0.375335i \(0.122472\pi\)
\(812\) −2691.94 4360.45i −0.116341 0.188451i
\(813\) 10937.7 4530.55i 0.471835 0.195441i
\(814\) 7767.32 24040.4i 0.334453 1.03515i
\(815\) 28084.5i 1.20707i
\(816\) −7967.32 9204.68i −0.341804 0.394888i
\(817\) 10937.3i 0.468356i
\(818\) −31915.0 10311.6i −1.36416 0.440753i
\(819\) −1613.33 + 668.265i −0.0688333 + 0.0285117i
\(820\) −6128.32 + 25903.0i −0.260988 + 1.10313i
\(821\) 6304.96 15221.5i 0.268020 0.647058i −0.731370 0.681981i \(-0.761119\pi\)
0.999390 + 0.0349231i \(0.0111186\pi\)
\(822\) 1266.73 101.799i 0.0537497 0.00431954i
\(823\) −769.291 + 769.291i −0.0325830 + 0.0325830i −0.723211 0.690628i \(-0.757334\pi\)
0.690628 + 0.723211i \(0.257334\pi\)
\(824\) 2067.42 1517.78i 0.0874055 0.0641679i
\(825\) −13062.7 13062.7i −0.551253 0.551253i
\(826\) 3206.01 + 2729.04i 0.135050 + 0.114958i
\(827\) 22898.4 + 9484.82i 0.962823 + 0.398815i 0.808036 0.589133i \(-0.200531\pi\)
0.154788 + 0.987948i \(0.450531\pi\)
\(828\) −15498.4 11182.2i −0.650492 0.469335i
\(829\) −10844.8 26181.7i −0.454350 1.09690i −0.970651 0.240492i \(-0.922691\pi\)
0.516301 0.856407i \(-0.327309\pi\)
\(830\) 46975.0 24032.8i 1.96449 1.00505i
\(831\) 12881.9 0.537749
\(832\) 7133.72 632.630i 0.297257 0.0263612i
\(833\) 22226.4 0.924488
\(834\) −40.6198 + 20.7814i −0.00168651 + 0.000862831i
\(835\) 6547.70 + 15807.5i 0.271368 + 0.655141i
\(836\) 30986.8 + 22357.2i 1.28194 + 0.924927i
\(837\) 3302.06 + 1367.76i 0.136363 + 0.0564834i
\(838\) −3003.38 2556.56i −0.123807 0.105388i
\(839\) 23945.5 + 23945.5i 0.985327 + 0.985327i 0.999894 0.0145666i \(-0.00463684\pi\)
−0.0145666 + 0.999894i \(0.504637\pi\)
\(840\) 4066.52 + 5539.15i 0.167033 + 0.227522i
\(841\) 9652.67 9652.67i 0.395779 0.395779i
\(842\) −5991.84 + 481.527i −0.245240 + 0.0197085i
\(843\) −43.3699 + 104.704i −0.00177193 + 0.00427783i
\(844\) −1251.30 + 5288.94i −0.0510325 + 0.215702i
\(845\) −34824.4 + 14424.7i −1.41775 + 0.587249i
\(846\) −15362.6 4963.56i −0.624322 0.201715i
\(847\) 2352.61i 0.0954386i
\(848\) 8579.63 + 618.225i 0.347436 + 0.0250353i
\(849\) 15668.0i 0.633364i
\(850\) 14567.8 45088.3i 0.587848 1.81943i
\(851\) −31663.0 + 13115.2i −1.27543 + 0.528302i
\(852\) −10709.7 17347.8i −0.430645 0.697566i
\(853\) 8663.21 20914.8i 0.347740 0.839520i −0.649146 0.760664i \(-0.724873\pi\)
0.996886 0.0788554i \(-0.0251266\pi\)
\(854\) 830.089 + 10329.1i 0.0332612 + 0.413882i
\(855\) −41670.8 + 41670.8i −1.66680 + 1.66680i
\(856\) 27954.5 + 16940.6i 1.11620 + 0.676422i
\(857\) −9119.55 9119.55i −0.363498 0.363498i 0.501601 0.865099i \(-0.332745\pi\)
−0.865099 + 0.501601i \(0.832745\pi\)
\(858\) −2062.21 + 2422.63i −0.0820543 + 0.0963952i
\(859\) −30582.3 12667.6i −1.21473 0.503159i −0.319002 0.947754i \(-0.603348\pi\)
−0.895732 + 0.444595i \(0.853348\pi\)
\(860\) 1698.66 + 10500.3i 0.0673533 + 0.416346i
\(861\) 1090.07 + 2631.66i 0.0431470 + 0.104166i
\(862\) 5824.51 + 11384.7i 0.230143 + 0.449844i
\(863\) 1210.85 0.0477612 0.0238806 0.999715i \(-0.492398\pi\)
0.0238806 + 0.999715i \(0.492398\pi\)
\(864\) −8697.81 20517.5i −0.342483 0.807891i
\(865\) −37942.5 −1.49143
\(866\) 2734.68 + 5345.26i 0.107307 + 0.209745i
\(867\) 404.169 + 975.749i 0.0158319 + 0.0382217i
\(868\) −1417.29 + 229.279i −0.0554216 + 0.00896570i
\(869\) −19880.5 8234.77i −0.776064 0.321456i
\(870\) 9333.36 10964.6i 0.363713 0.427281i
\(871\) −9201.55 9201.55i −0.357959 0.357959i
\(872\) 2863.24 + 11671.2i 0.111195 + 0.453253i
\(873\) −11988.1 + 11988.1i −0.464762 + 0.464762i
\(874\) −4152.18 51667.3i −0.160698 1.99963i
\(875\) −4665.90 + 11264.5i −0.180270 + 0.435210i
\(876\) −5608.47 + 3462.41i −0.216316 + 0.133543i
\(877\) −36421.4 + 15086.2i −1.40235 + 0.580873i −0.950361 0.311150i \(-0.899286\pi\)
−0.451990 + 0.892023i \(0.649286\pi\)
\(878\) −9872.85 + 30557.1i −0.379490 + 1.17455i
\(879\) 7520.83i 0.288591i
\(880\) −33221.1 16651.4i −1.27259 0.637863i
\(881\) 39286.1i 1.50236i 0.660095 + 0.751182i \(0.270516\pi\)
−0.660095 + 0.751182i \(0.729484\pi\)
\(882\) 16567.2 + 5352.77i 0.632479 + 0.204351i
\(883\) −234.092 + 96.9642i −0.00892167 + 0.00369548i −0.387140 0.922021i \(-0.626537\pi\)
0.378218 + 0.925717i \(0.376537\pi\)
\(884\) −7941.10 1878.77i −0.302136 0.0714816i
\(885\) −4527.24 + 10929.7i −0.171957 + 0.415140i
\(886\) −9570.17 + 769.096i −0.362885 + 0.0291629i
\(887\) 13552.8 13552.8i 0.513032 0.513032i −0.402422 0.915454i \(-0.631832\pi\)
0.915454 + 0.402422i \(0.131832\pi\)
\(888\) −16903.3 2591.43i −0.638782 0.0979310i
\(889\) 6641.66 + 6641.66i 0.250567 + 0.250567i
\(890\) 9393.21 + 7995.77i 0.353777 + 0.301145i
\(891\) −6384.93 2644.73i −0.240071 0.0994407i
\(892\) 7886.59 10930.7i 0.296034 0.410299i
\(893\) −16756.6 40454.1i −0.627928 1.51595i
\(894\) 5346.59 2735.36i 0.200019 0.102331i
\(895\) −6466.85 −0.241523
\(896\) 7302.51 + 5177.65i 0.272276 + 0.193050i
\(897\) 4315.82 0.160648
\(898\) 42695.2 21843.2i 1.58659 0.811712i
\(899\) 1151.29 + 2779.47i 0.0427117 + 0.103115i
\(900\) 21717.2 30099.7i 0.804340 1.11481i
\(901\) −9055.21 3750.79i −0.334820 0.138687i
\(902\) −11730.0 9984.90i −0.433000 0.368582i
\(903\) 804.889 + 804.889i 0.0296623 + 0.0296623i
\(904\) 2442.31 + 374.428i 0.0898561 + 0.0137757i
\(905\) 18534.2 18534.2i 0.680772 0.680772i
\(906\) 5941.17 477.455i 0.217861 0.0175082i
\(907\) −2600.00 + 6276.95i −0.0951835 + 0.229793i −0.964299 0.264816i \(-0.914689\pi\)
0.869115 + 0.494609i \(0.164689\pi\)
\(908\) −35640.8 8432.18i −1.30262 0.308185i
\(909\) 31526.4 13058.6i 1.15034 0.476488i
\(910\) 4383.01 + 1416.13i 0.159665 + 0.0515870i
\(911\) 22984.1i 0.835891i −0.908472 0.417946i \(-0.862750\pi\)
0.908472 0.417946i \(-0.137250\pi\)
\(912\) 11589.5 23122.0i 0.420795 0.839524i
\(913\) 30536.3i 1.10691i
\(914\) −7653.51 + 23688.1i −0.276975 + 0.857258i
\(915\) −26900.7 + 11142.6i −0.971924 + 0.402584i
\(916\) 7903.18 4879.06i 0.285075 0.175992i
\(917\) −2386.36 + 5761.17i −0.0859372 + 0.207471i
\(918\) 2034.06 + 25310.6i 0.0731307 + 0.909995i
\(919\) 38048.0 38048.0i 1.36571 1.36571i 0.499258 0.866453i \(-0.333606\pi\)
0.866453 0.499258i \(-0.166394\pi\)
\(920\) 12010.7 + 48958.2i 0.430415 + 1.75446i
\(921\) −801.638 801.638i −0.0286806 0.0286806i
\(922\) −21575.6 + 25346.4i −0.770666 + 0.905358i
\(923\) −12625.6 5229.71i −0.450247 0.186499i
\(924\) −3925.66 + 635.063i −0.139767 + 0.0226104i
\(925\) −25471.3 61493.2i −0.905396 2.18582i
\(926\) −16982.2 33193.7i −0.602666 1.17798i
\(927\) −2289.15 −0.0811064
\(928\) 7035.03 17388.9i 0.248854 0.615106i
\(929\) 28435.1 1.00423 0.502113 0.864802i \(-0.332556\pi\)
0.502113 + 0.864802i \(0.332556\pi\)
\(930\) −1837.41 3591.45i −0.0647862 0.126633i
\(931\) 18070.6 + 43626.3i 0.636133 + 1.53576i
\(932\) 404.729 + 2501.84i 0.0142246 + 0.0879297i
\(933\) 18216.6 + 7545.57i 0.639212 + 0.264770i
\(934\) −13976.7 + 16419.5i −0.489650 + 0.575227i
\(935\) 29940.4 + 29940.4i 1.04723 + 1.04723i
\(936\) −5466.71 3312.86i −0.190903 0.115688i
\(937\) 10599.3 10599.3i 0.369546 0.369546i −0.497766 0.867311i \(-0.665846\pi\)
0.867311 + 0.497766i \(0.165846\pi\)
\(938\) −1302.96 16213.3i −0.0453552 0.564373i
\(939\) −2523.42 + 6092.07i −0.0876982 + 0.211722i
\(940\) 22370.1 + 36235.4i 0.776204 + 1.25731i
\(941\) −17446.0 + 7226.38i −0.604383 + 0.250344i −0.663825 0.747888i \(-0.731068\pi\)
0.0594418 + 0.998232i \(0.481068\pi\)
\(942\) 1301.87 4029.38i 0.0450289 0.139368i
\(943\) 20896.5i 0.721617i
\(944\) −1107.64 + 15371.7i −0.0381893 + 0.529986i
\(945\) 14332.7i 0.493378i
\(946\) −5857.54 1892.54i −0.201316 0.0650441i
\(947\) −8125.64 + 3365.75i −0.278826 + 0.115493i −0.517714 0.855554i \(-0.673217\pi\)
0.238889 + 0.971047i \(0.423217\pi\)
\(948\) −3353.45 + 14174.2i −0.114889 + 0.485609i
\(949\) −1690.74 + 4081.81i −0.0578333 + 0.139622i
\(950\) 100344. 8064.02i 3.42693 0.275401i
\(951\) 11426.6 11426.6i 0.389623 0.389623i
\(952\) −6036.22 8222.16i −0.205499 0.279918i
\(953\) 20053.9 + 20053.9i 0.681648 + 0.681648i 0.960371 0.278723i \(-0.0899113\pi\)
−0.278723 + 0.960371i \(0.589911\pi\)
\(954\) −5846.31 4976.55i −0.198408 0.168891i
\(955\) 55013.9 + 22787.5i 1.86409 + 0.772132i
\(956\) −36949.3 26659.2i −1.25003 0.901905i
\(957\) 3188.89 + 7698.66i 0.107714 + 0.260044i
\(958\) −11614.1 + 5941.84i −0.391684 + 0.200389i
\(959\) 1064.76 0.0358529
\(960\) −7535.38 + 23998.2i −0.253337 + 0.806810i
\(961\) −28948.1 −0.971707
\(962\) −10204.9 + 5220.90i −0.342016 + 0.174978i
\(963\) −11164.7 26953.9i −0.373599 0.901949i
\(964\) 38047.5 + 27451.6i 1.27119 + 0.917174i
\(965\) −24857.6 10296.3i −0.829216 0.343473i
\(966\) 4107.83 + 3496.70i 0.136819 + 0.116464i
\(967\) 17483.6 + 17483.6i 0.581421 + 0.581421i 0.935294 0.353872i \(-0.115135\pi\)
−0.353872 + 0.935294i \(0.615135\pi\)
\(968\) −6941.84 + 5096.29i −0.230495 + 0.169216i
\(969\) −20838.6 + 20838.6i −0.690849 + 0.690849i
\(970\) 44575.2 3582.24i 1.47549 0.118576i
\(971\) 2567.45 6198.36i 0.0848540 0.204856i −0.875757 0.482752i \(-0.839637\pi\)
0.960611 + 0.277896i \(0.0896372\pi\)
\(972\) −7199.18 + 30429.2i −0.237566 + 1.00413i
\(973\) −35.3190 + 14.6296i −0.00116369 + 0.000482018i
\(974\) 41826.6 + 13513.9i 1.37599 + 0.444574i
\(975\) 8381.81i 0.275316i
\(976\) −28680.0 + 24824.6i −0.940600 + 0.814157i
\(977\) 31111.6i 1.01878i −0.860536 0.509390i \(-0.829871\pi\)
0.860536 0.509390i \(-0.170129\pi\)
\(978\) 3382.32 10468.5i 0.110588 0.342276i
\(979\) −6595.34 + 2731.88i −0.215309 + 0.0891841i
\(980\) −24124.2 39076.8i −0.786347 1.27374i
\(981\) 4104.66 9909.52i 0.133590 0.322514i
\(982\) −4639.95 57736.8i −0.150781 1.87623i
\(983\) 17048.2 17048.2i 0.553156 0.553156i −0.374194 0.927350i \(-0.622081\pi\)
0.927350 + 0.374194i \(0.122081\pi\)
\(984\) −5403.92 + 8917.28i −0.175072 + 0.288895i
\(985\) 19856.5 + 19856.5i 0.642316 + 0.642316i
\(986\) −13854.2 + 16275.5i −0.447472 + 0.525678i
\(987\) 4210.22 + 1743.93i 0.135778 + 0.0562410i
\(988\) −2768.64 17114.4i −0.0891519 0.551094i
\(989\) 3195.58 + 7714.81i 0.102744 + 0.248045i
\(990\) 15106.6 + 29527.6i 0.484968 + 0.947929i
\(991\) 32857.3 1.05323 0.526613 0.850105i \(-0.323462\pi\)
0.526613 + 0.850105i \(0.323462\pi\)
\(992\) −3746.71 3685.33i −0.119918 0.117953i
\(993\) −11566.1 −0.369625
\(994\) −7780.06 15207.1i −0.248258 0.485251i
\(995\) 12310.3 + 29719.7i 0.392223 + 0.946911i
\(996\) 20404.3 3300.85i 0.649131 0.105012i
\(997\) −30160.2 12492.8i −0.958057 0.396840i −0.151804 0.988411i \(-0.548508\pi\)
−0.806253 + 0.591570i \(0.798508\pi\)
\(998\) 12709.1 14930.3i 0.403106 0.473558i
\(999\) 25221.6 + 25221.6i 0.798775 + 0.798775i
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 32.4.g.a.5.2 44
4.3 odd 2 128.4.g.a.113.7 44
8.3 odd 2 256.4.g.a.225.5 44
8.5 even 2 256.4.g.b.225.7 44
32.3 odd 8 256.4.g.a.33.5 44
32.13 even 8 inner 32.4.g.a.13.2 yes 44
32.19 odd 8 128.4.g.a.17.7 44
32.29 even 8 256.4.g.b.33.7 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.5.2 44 1.1 even 1 trivial
32.4.g.a.13.2 yes 44 32.13 even 8 inner
128.4.g.a.17.7 44 32.19 odd 8
128.4.g.a.113.7 44 4.3 odd 2
256.4.g.a.33.5 44 32.3 odd 8
256.4.g.a.225.5 44 8.3 odd 2
256.4.g.b.33.7 44 32.29 even 8
256.4.g.b.225.7 44 8.5 even 2