Properties

Label 27.3.f.a.2.4
Level 2727
Weight 33
Character 27.2
Analytic conductor 0.7360.736
Analytic rank 00
Dimension 3030
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,3,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 27=33 27 = 3^{3}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 27.f (of order 1818, degree 66, 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: 0.7356967137730.735696713773
Analytic rank: 00
Dimension: 3030
Relative dimension: 55 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 2.4
Character χ\chi == 27.2
Dual form 27.3.f.a.14.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.14332+0.201599i)q2+(1.10490+2.78912i)q3+(2.492220.907094i)q4+(3.460134.12362i)q5+(0.700975+3.41162i)q6+(9.899073.60297i)q7+(6.688243.86146i)q8+(6.55839+6.16340i)q9+(3.124735.41219i)q10+(7.54888+8.99640i)q11+(0.2236587.95335i)q12+(1.95057+11.0622i)q13+(12.04422.12372i)q14+(7.6781814.2069i)q15+(1.25834+1.05588i)q16+(2.736301.57980i)q17+(8.74091+5.72460i)q18+(2.260513.91532i)q19+(4.88289+13.4156i)q20+(20.9866+23.6288i)q21+(10.4445+8.76396i)q22+(6.8088018.7070i)q23+(3.3802422.9208i)q24+(0.690550+3.91630i)q25+13.0409iq26+(24.436811.4822i)q2727.9389q28+(24.9744+4.40366i)q29+(11.642814.6952i)q30+(20.78747.56598i)q31+(21.0826+25.1253i)q32+(33.432811.1146i)q33+(3.446961.25459i)q34+(49.109328.3533i)q35+(21.93589.41147i)q36+(8.8280715.2907i)q37+(3.373824.02076i)q38+(28.6987+17.6630i)q39+(7.21898+40.9409i)q40+(12.2557+2.16101i)q41+(19.2309+31.2462i)q42+(27.9211+23.4286i)q43+(26.974115.5735i)q44+(48.1084+5.71818i)q45+(11.556020.0156i)q46+(4.2409111.6518i)q47+(1.55462+4.67631i)q48+(47.474039.8354i)q49+(1.57905+4.33839i)q50+(7.42960+5.88634i)q51+(5.1732329.3388i)q52+84.6210iq53+(25.624418.0543i)q54+63.2178q55+(80.120014.1273i)q56+(13.4179+1.97880i)q57+(27.6661+10.0696i)q58+(43.885452.3006i)q59+(32.0227+28.4419i)q60+(73.3637+26.7022i)q61+(22.241412.8411i)q62+(42.7155+84.6415i)q63+(15.7537+27.2863i)q64+(38.867246.3201i)q65+(35.983919.4476i)q66+(16.865495.6483i)q67+(8.25249+1.45514i)q68+(59.69921.67882i)q69+(50.431942.3174i)q70+(105.36460.8322i)q71+(67.663815.8973i)q72+(45.5705+78.9304i)q73+(7.0107619.2619i)q74+(11.6860+2.40109i)q75+(9.18525+7.70734i)q76+(42.3131+116.254i)q77+(36.3728+14.4089i)q78+(3.54032+20.0781i)q798.84240iq80+(5.0250680.8440i)q8114.4479q82+(31.1219+5.48763i)q83+(30.869777.9250i)q84+(15.98245.81713i)q85+(27.1997+32.4154i)q86+(15.3119+74.5223i)q87+(85.227931.0204i)q88+(59.7756+34.5114i)q89+(53.8507+16.2363i)q90+(59.1656+102.478i)q91+(33.9381+40.4458i)q92+(1.8655166.3381i)q93+(2.4997414.1767i)q94+(23.9669+4.22602i)q95+(46.7833+86.5629i)q96+(61.133551.2971i)q97+(62.308935.9741i)q98+(5.93989105.529i)q99+O(q100)q+(1.14332 + 0.201599i) q^{2} +(1.10490 + 2.78912i) q^{3} +(-2.49222 - 0.907094i) q^{4} +(-3.46013 - 4.12362i) q^{5} +(0.700975 + 3.41162i) q^{6} +(9.89907 - 3.60297i) q^{7} +(-6.68824 - 3.86146i) q^{8} +(-6.55839 + 6.16340i) q^{9} +(-3.12473 - 5.41219i) q^{10} +(-7.54888 + 8.99640i) q^{11} +(-0.223658 - 7.95335i) q^{12} +(1.95057 + 11.0622i) q^{13} +(12.0442 - 2.12372i) q^{14} +(7.67818 - 14.2069i) q^{15} +(1.25834 + 1.05588i) q^{16} +(2.73630 - 1.57980i) q^{17} +(-8.74091 + 5.72460i) q^{18} +(2.26051 - 3.91532i) q^{19} +(4.88289 + 13.4156i) q^{20} +(20.9866 + 23.6288i) q^{21} +(-10.4445 + 8.76396i) q^{22} +(6.80880 - 18.7070i) q^{23} +(3.38024 - 22.9208i) q^{24} +(-0.690550 + 3.91630i) q^{25} +13.0409i q^{26} +(-24.4368 - 11.4822i) q^{27} -27.9389 q^{28} +(24.9744 + 4.40366i) q^{29} +(11.6428 - 14.6952i) q^{30} +(-20.7874 - 7.56598i) q^{31} +(21.0826 + 25.1253i) q^{32} +(-33.4328 - 11.1146i) q^{33} +(3.44696 - 1.25459i) q^{34} +(-49.1093 - 28.3533i) q^{35} +(21.9358 - 9.41147i) q^{36} +(-8.82807 - 15.2907i) q^{37} +(3.37382 - 4.02076i) q^{38} +(-28.6987 + 17.6630i) q^{39} +(7.21898 + 40.9409i) q^{40} +(-12.2557 + 2.16101i) q^{41} +(19.2309 + 31.2462i) q^{42} +(27.9211 + 23.4286i) q^{43} +(26.9741 - 15.5735i) q^{44} +(48.1084 + 5.71818i) q^{45} +(11.5560 - 20.0156i) q^{46} +(-4.24091 - 11.6518i) q^{47} +(-1.55462 + 4.67631i) q^{48} +(47.4740 - 39.8354i) q^{49} +(-1.57905 + 4.33839i) q^{50} +(7.42960 + 5.88634i) q^{51} +(5.17323 - 29.3388i) q^{52} +84.6210i q^{53} +(-25.6244 - 18.0543i) q^{54} +63.2178 q^{55} +(-80.1200 - 14.1273i) q^{56} +(13.4179 + 1.97880i) q^{57} +(27.6661 + 10.0696i) q^{58} +(-43.8854 - 52.3006i) q^{59} +(-32.0227 + 28.4419i) q^{60} +(-73.3637 + 26.7022i) q^{61} +(-22.2414 - 12.8411i) q^{62} +(-42.7155 + 84.6415i) q^{63} +(15.7537 + 27.2863i) q^{64} +(38.8672 - 46.3201i) q^{65} +(-35.9839 - 19.4476i) q^{66} +(-16.8654 - 95.6483i) q^{67} +(-8.25249 + 1.45514i) q^{68} +(59.6992 - 1.67882i) q^{69} +(-50.4319 - 42.3174i) q^{70} +(105.364 - 60.8322i) q^{71} +(67.6638 - 15.8973i) q^{72} +(-45.5705 + 78.9304i) q^{73} +(-7.01076 - 19.2619i) q^{74} +(-11.6860 + 2.40109i) q^{75} +(-9.18525 + 7.70734i) q^{76} +(-42.3131 + 116.254i) q^{77} +(-36.3728 + 14.4089i) q^{78} +(-3.54032 + 20.0781i) q^{79} -8.84240i q^{80} +(5.02506 - 80.8440i) q^{81} -14.4479 q^{82} +(31.1219 + 5.48763i) q^{83} +(-30.8697 - 77.9250i) q^{84} +(-15.9824 - 5.81713i) q^{85} +(27.1997 + 32.4154i) q^{86} +(15.3119 + 74.5223i) q^{87} +(85.2279 - 31.0204i) q^{88} +(59.7756 + 34.5114i) q^{89} +(53.8507 + 16.2363i) q^{90} +(59.1656 + 102.478i) q^{91} +(-33.9381 + 40.4458i) q^{92} +(-1.86551 - 66.3381i) q^{93} +(-2.49974 - 14.1767i) q^{94} +(-23.9669 + 4.22602i) q^{95} +(-46.7833 + 86.5629i) q^{96} +(-61.1335 - 51.2971i) q^{97} +(62.3089 - 35.9741i) q^{98} +(-5.93989 - 105.529i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 30q6q26q36q415q518q66q79q83q106q1115q126q1315q149q1518q169q17+63q183q19+213q20++513q99+O(q100) 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/27Z)×\left(\mathbb{Z}/27\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(118)e\left(\frac{1}{18}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.14332 + 0.201599i 0.571662 + 0.100799i 0.452004 0.892016i 0.350709π-0.350709\pi
0.119658 + 0.992815i 0.461820π0.461820\pi
33 1.10490 + 2.78912i 0.368300 + 0.929707i
44 −2.49222 0.907094i −0.623055 0.226774i
55 −3.46013 4.12362i −0.692026 0.824724i 0.299574 0.954073i 0.403156π-0.403156\pi
−0.991599 + 0.129349i 0.958711π0.958711\pi
66 0.700975 + 3.41162i 0.116829 + 0.568603i
77 9.89907 3.60297i 1.41415 0.514709i 0.481807 0.876278i 0.339981π-0.339981\pi
0.932346 + 0.361568i 0.117759π0.117759\pi
88 −6.68824 3.86146i −0.836030 0.482682i
99 −6.55839 + 6.16340i −0.728710 + 0.684822i
1010 −3.12473 5.41219i −0.312473 0.541219i
1111 −7.54888 + 8.99640i −0.686262 + 0.817855i −0.990898 0.134614i 0.957021π-0.957021\pi
0.304636 + 0.952469i 0.401465π0.401465\pi
1212 −0.223658 7.95335i −0.0186382 0.662780i
1313 1.95057 + 11.0622i 0.150044 + 0.850940i 0.963178 + 0.268864i 0.0866482π0.0866482\pi
−0.813134 + 0.582076i 0.802241π0.802241\pi
1414 12.0442 2.12372i 0.860300 0.151694i
1515 7.67818 14.2069i 0.511879 0.947127i
1616 1.25834 + 1.05588i 0.0786465 + 0.0659923i
1717 2.73630 1.57980i 0.160959 0.0929296i −0.417357 0.908743i 0.637044π-0.637044\pi
0.578316 + 0.815813i 0.303710π0.303710\pi
1818 −8.74091 + 5.72460i −0.485606 + 0.318033i
1919 2.26051 3.91532i 0.118974 0.206069i −0.800387 0.599483i 0.795373π-0.795373\pi
0.919361 + 0.393414i 0.128706π0.128706\pi
2020 4.88289 + 13.4156i 0.244145 + 0.670782i
2121 20.9866 + 23.6288i 0.999361 + 1.12518i
2222 −10.4445 + 8.76396i −0.474749 + 0.398362i
2323 6.80880 18.7070i 0.296035 0.813349i −0.699118 0.715007i 0.746424π-0.746424\pi
0.995153 0.0983427i 0.0313541π-0.0313541\pi
2424 3.38024 22.9208i 0.140843 0.955035i
2525 −0.690550 + 3.91630i −0.0276220 + 0.156652i
2626 13.0409i 0.501575i
2727 −24.4368 11.4822i −0.905068 0.425267i
2828 −27.9389 −0.997818
2929 24.9744 + 4.40366i 0.861187 + 0.151851i 0.586763 0.809758i 0.300402π-0.300402\pi
0.274424 + 0.961609i 0.411513π0.411513\pi
3030 11.6428 14.6952i 0.388092 0.489840i
3131 −20.7874 7.56598i −0.670560 0.244064i −0.0157712 0.999876i 0.505020π-0.505020\pi
−0.654789 + 0.755812i 0.727243π0.727243\pi
3232 21.0826 + 25.1253i 0.658832 + 0.785165i
3333 −33.4328 11.1146i −1.01312 0.336807i
3434 3.44696 1.25459i 0.101381 0.0368998i
3535 −49.1093 28.3533i −1.40312 0.810093i
3636 21.9358 9.41147i 0.609326 0.261430i
3737 −8.82807 15.2907i −0.238596 0.413261i 0.721715 0.692190i 0.243354π-0.243354\pi
−0.960312 + 0.278929i 0.910021π0.910021\pi
3838 3.37382 4.02076i 0.0887847 0.105810i
3939 −28.6987 + 17.6630i −0.735864 + 0.452898i
4040 7.21898 + 40.9409i 0.180475 + 1.02352i
4141 −12.2557 + 2.16101i −0.298920 + 0.0527076i −0.321096 0.947046i 0.604051π-0.604051\pi
0.0221770 + 0.999754i 0.492940π0.492940\pi
4242 19.2309 + 31.2462i 0.457880 + 0.743958i
4343 27.9211 + 23.4286i 0.649329 + 0.544851i 0.906867 0.421417i 0.138467π-0.138467\pi
−0.257539 + 0.966268i 0.582911π0.582911\pi
4444 26.9741 15.5735i 0.613047 0.353943i
4545 48.1084 + 5.71818i 1.06908 + 0.127071i
4646 11.5560 20.0156i 0.251217 0.435121i
4747 −4.24091 11.6518i −0.0902320 0.247910i 0.886365 0.462987i 0.153222π-0.153222\pi
−0.976597 + 0.215076i 0.931000π0.931000\pi
4848 −1.55462 + 4.67631i −0.0323880 + 0.0974232i
4949 47.4740 39.8354i 0.968857 0.812967i
5050 −1.57905 + 4.33839i −0.0315809 + 0.0867679i
5151 7.42960 + 5.88634i 0.145678 + 0.115419i
5252 5.17323 29.3388i 0.0994852 0.564209i
5353 84.6210i 1.59662i 0.602245 + 0.798311i 0.294273π0.294273\pi
−0.602245 + 0.798311i 0.705727π0.705727\pi
5454 −25.6244 18.0543i −0.474526 0.334340i
5555 63.2178 1.14942
5656 −80.1200 14.1273i −1.43071 0.252274i
5757 13.4179 + 1.97880i 0.235402 + 0.0347158i
5858 27.6661 + 10.0696i 0.477002 + 0.173614i
5959 −43.8854 52.3006i −0.743820 0.886451i 0.252890 0.967495i 0.418619π-0.418619\pi
−0.996711 + 0.0810443i 0.974174π0.974174\pi
6060 −32.0227 + 28.4419i −0.533712 + 0.474032i
6161 −73.3637 + 26.7022i −1.20268 + 0.437741i −0.864160 0.503217i 0.832150π-0.832150\pi
−0.338523 + 0.940958i 0.609927π0.609927\pi
6262 −22.2414 12.8411i −0.358733 0.207114i
6363 −42.7155 + 84.6415i −0.678023 + 1.34352i
6464 15.7537 + 27.2863i 0.246152 + 0.426348i
6565 38.8672 46.3201i 0.597956 0.712617i
6666 −35.9839 19.4476i −0.545210 0.294661i
6767 −16.8654 95.6483i −0.251722 1.42759i −0.804349 0.594157i 0.797486π-0.797486\pi
0.552627 0.833429i 0.313625π-0.313625\pi
6868 −8.25249 + 1.45514i −0.121360 + 0.0213991i
6969 59.6992 1.67882i 0.865206 0.0243307i
7070 −50.4319 42.3174i −0.720455 0.604534i
7171 105.364 60.8322i 1.48401 0.856791i 0.484171 0.874973i 0.339121π-0.339121\pi
0.999835 + 0.0181820i 0.00578784π0.00578784\pi
7272 67.6638 15.8973i 0.939775 0.220796i
7373 −45.5705 + 78.9304i −0.624254 + 1.08124i 0.364431 + 0.931230i 0.381263π0.381263\pi
−0.988685 + 0.150009i 0.952070π0.952070\pi
7474 −7.01076 19.2619i −0.0947401 0.260296i
7575 −11.6860 + 2.40109i −0.155814 + 0.0320146i
7676 −9.18525 + 7.70734i −0.120859 + 0.101412i
7777 −42.3131 + 116.254i −0.549521 + 1.50980i
7878 −36.3728 + 14.4089i −0.466317 + 0.184730i
7979 −3.54032 + 20.0781i −0.0448142 + 0.254154i −0.998982 0.0451196i 0.985633π-0.985633\pi
0.954167 + 0.299273i 0.0967442π0.0967442\pi
8080 8.84240i 0.110530i
8181 5.02506 80.8440i 0.0620378 0.998074i
8282 −14.4479 −0.176194
8383 31.1219 + 5.48763i 0.374963 + 0.0661161i 0.357954 0.933739i 0.383474π-0.383474\pi
0.0170090 + 0.999855i 0.494586π0.494586\pi
8484 −30.8697 77.9250i −0.367496 0.927678i
8585 −15.9824 5.81713i −0.188029 0.0684369i
8686 27.1997 + 32.4154i 0.316276 + 0.376923i
8787 15.3119 + 74.5223i 0.175999 + 0.856578i
8888 85.2279 31.0204i 0.968499 0.352505i
8989 59.7756 + 34.5114i 0.671636 + 0.387769i 0.796696 0.604380i 0.206579π-0.206579\pi
−0.125060 + 0.992149i 0.539912π0.539912\pi
9090 53.8507 + 16.2363i 0.598341 + 0.180404i
9191 59.1656 + 102.478i 0.650171 + 1.12613i
9292 −33.9381 + 40.4458i −0.368892 + 0.439629i
9393 −1.86551 66.3381i −0.0200592 0.713313i
9494 −2.49974 14.1767i −0.0265930 0.150816i
9595 −23.9669 + 4.22602i −0.252283 + 0.0444844i
9696 −46.7833 + 86.5629i −0.487326 + 0.901696i
9797 −61.1335 51.2971i −0.630243 0.528836i 0.270762 0.962646i 0.412724π-0.412724\pi
−0.901004 + 0.433810i 0.857169π0.857169\pi
9898 62.3089 35.9741i 0.635806 0.367083i
9999 −5.93989 105.529i −0.0599989 1.06595i
100100 5.27346 9.13390i 0.0527346 0.0913390i
101101 −1.63372 4.48862i −0.0161755 0.0444417i 0.931342 0.364145i 0.118639π-0.118639\pi
−0.947518 + 0.319704i 0.896417π0.896417\pi
102102 7.30776 + 8.22780i 0.0716447 + 0.0806647i
103103 −55.3795 + 46.4689i −0.537665 + 0.451154i −0.870738 0.491746i 0.836359π-0.836359\pi
0.333074 + 0.942901i 0.391914π0.391914\pi
104104 29.6704 81.5188i 0.285293 0.783835i
105105 24.8199 168.299i 0.236380 1.60285i
106106 −17.0595 + 96.7493i −0.160939 + 0.912729i
107107 158.133i 1.47788i 0.673773 + 0.738938i 0.264672π0.264672\pi
−0.673773 + 0.738938i 0.735328π0.735328\pi
108108 50.4865 + 50.7827i 0.467468 + 0.470211i
109109 −18.5788 −0.170448 −0.0852240 0.996362i 0.527161π-0.527161\pi
−0.0852240 + 0.996362i 0.527161π0.527161\pi
110110 72.2785 + 12.7447i 0.657077 + 0.115860i
111111 32.8934 41.5172i 0.296337 0.374029i
112112 16.2607 + 5.91842i 0.145185 + 0.0528430i
113113 −11.5806 13.8012i −0.102483 0.122134i 0.712365 0.701809i 0.247624π-0.247624\pi
−0.814848 + 0.579675i 0.803180π0.803180\pi
114114 14.9421 + 4.96746i 0.131071 + 0.0435742i
115115 −100.700 + 36.6518i −0.875652 + 0.318711i
116116 −58.2473 33.6291i −0.502131 0.289906i
117117 −80.9734 60.5283i −0.692081 0.517336i
118118 −39.6315 68.6438i −0.335860 0.581727i
119119 21.3948 25.4974i 0.179788 0.214264i
120120 −106.213 + 65.3702i −0.885107 + 0.544752i
121121 −2.93828 16.6638i −0.0242833 0.137717i
122122 −89.2617 + 15.7392i −0.731653 + 0.129010i
123123 −19.5686 31.7949i −0.159095 0.258495i
124124 44.9437 + 37.7122i 0.362449 + 0.304131i
125125 −98.0067 + 56.5842i −0.784054 + 0.452674i
126126 −65.9013 + 88.1614i −0.523026 + 0.699693i
127127 78.1067 135.285i 0.615013 1.06523i −0.375369 0.926876i 0.622484π-0.622484\pi
0.990382 0.138359i 0.0441827π-0.0441827\pi
128128 −32.3605 88.9098i −0.252817 0.694608i
129129 −34.4952 + 103.762i −0.267405 + 0.804354i
130130 53.7759 45.1233i 0.413661 0.347102i
131131 33.6955 92.5776i 0.257217 0.706699i −0.742119 0.670268i 0.766179π-0.766179\pi
0.999336 0.0364307i 0.0115988π-0.0115988\pi
132132 73.2400 + 58.0268i 0.554848 + 0.439597i
133133 8.27018 46.9025i 0.0621818 0.352651i
134134 112.757i 0.841471i
135135 37.2062 + 140.498i 0.275602 + 1.04073i
136136 −24.4014 −0.179422
137137 −64.6590 11.4011i −0.471963 0.0832199i −0.0673925 0.997727i 0.521468π-0.521468\pi
−0.404571 + 0.914507i 0.632579π0.632579\pi
138138 68.5941 + 10.1159i 0.497058 + 0.0733034i
139139 117.744 + 42.8553i 0.847080 + 0.308312i 0.728849 0.684674i 0.240056π-0.240056\pi
0.118231 + 0.992986i 0.462278π0.462278\pi
140140 96.6721 + 115.209i 0.690515 + 0.822924i
141141 27.8125 24.7025i 0.197252 0.175195i
142142 132.729 48.3096i 0.934714 0.340208i
143143 −114.245 65.9593i −0.798915 0.461254i
144144 −14.7605 + 0.830824i −0.102503 + 0.00576961i
145145 −68.2557 118.222i −0.470729 0.815326i
146146 −68.0142 + 81.0562i −0.465851 + 0.555179i
147147 163.560 + 88.3966i 1.11265 + 0.601337i
148148 8.13142 + 46.1156i 0.0549420 + 0.311592i
149149 198.691 35.0346i 1.33350 0.235132i 0.538953 0.842336i 0.318820π-0.318820\pi
0.794546 + 0.607204i 0.207709π0.207709\pi
150150 −13.8450 + 0.389338i −0.0922999 + 0.00259559i
151151 98.1613 + 82.3671i 0.650075 + 0.545478i 0.907094 0.420929i 0.138296π-0.138296\pi
−0.257019 + 0.966406i 0.582740π0.582740\pi
152152 −30.2377 + 17.4577i −0.198932 + 0.114853i
153153 −8.20877 + 27.2259i −0.0536521 + 0.177947i
154154 −71.8144 + 124.386i −0.466327 + 0.807703i
155155 40.7277 + 111.898i 0.262759 + 0.721926i
156156 87.5455 17.9877i 0.561189 0.115306i
157157 −106.439 + 89.3129i −0.677955 + 0.568872i −0.915408 0.402527i 0.868132π-0.868132\pi
0.237453 + 0.971399i 0.423687π0.423687\pi
158158 −8.09547 + 22.2421i −0.0512371 + 0.140773i
159159 −236.018 + 93.4977i −1.48439 + 0.588036i
160160 30.6586 173.873i 0.191616 1.08671i
161161 209.714i 1.30257i
162162 22.0433 91.4179i 0.136070 0.564308i
163163 39.8569 0.244521 0.122261 0.992498i 0.460986π-0.460986\pi
0.122261 + 0.992498i 0.460986π0.460986\pi
164164 32.5042 + 5.73136i 0.198196 + 0.0349473i
165165 69.8494 + 176.322i 0.423329 + 1.06862i
166166 34.4762 + 12.5483i 0.207688 + 0.0755921i
167167 −106.672 127.127i −0.638757 0.761241i 0.345416 0.938450i 0.387738π-0.387738\pi
−0.984173 + 0.177208i 0.943293π0.943293\pi
168168 −49.1218 239.074i −0.292391 1.42306i
169169 40.2401 14.6462i 0.238107 0.0866639i
170170 −17.1004 9.87292i −0.100591 0.0580760i
171171 9.30634 + 39.6106i 0.0544231 + 0.231641i
172172 −48.3337 83.7164i −0.281010 0.486723i
173173 −7.00006 + 8.34234i −0.0404628 + 0.0482216i −0.785896 0.618358i 0.787798π-0.787798\pi
0.745434 + 0.666580i 0.232243π0.232243\pi
174174 2.48282 + 88.2901i 0.0142691 + 0.507414i
175175 7.27451 + 41.2558i 0.0415686 + 0.235747i
176176 −18.9982 + 3.34989i −0.107944 + 0.0190335i
177177 97.3837 180.189i 0.550191 1.01801i
178178 61.3854 + 51.5085i 0.344862 + 0.289374i
179179 −244.720 + 141.289i −1.36715 + 0.789326i −0.990564 0.137054i 0.956237π-0.956237\pi
−0.376590 + 0.926380i 0.622903π0.622903\pi
180180 −114.710 57.8898i −0.637277 0.321610i
181181 54.3996 94.2228i 0.300550 0.520568i −0.675711 0.737167i 0.736163π-0.736163\pi
0.976261 + 0.216599i 0.0694964π0.0694964\pi
182182 46.9861 + 129.093i 0.258165 + 0.709303i
183183 −155.535 175.117i −0.849919 0.956923i
184184 −117.775 + 98.8252i −0.640083 + 0.537094i
185185 −32.5066 + 89.3112i −0.175711 + 0.482763i
186186 11.2408 76.2221i 0.0604345 0.409796i
187187 −6.44344 + 36.5426i −0.0344569 + 0.195415i
188188 32.8857i 0.174924i
189189 −283.272 25.6182i −1.49879 0.135546i
190190 −28.2539 −0.148705
191191 106.979 + 18.8633i 0.560100 + 0.0987607i 0.446529 0.894769i 0.352660π-0.352660\pi
0.113571 + 0.993530i 0.463771π0.463771\pi
192192 −58.6984 + 74.0877i −0.305721 + 0.385873i
193193 −188.040 68.4410i −0.974301 0.354617i −0.194679 0.980867i 0.562367π-0.562367\pi
−0.779622 + 0.626250i 0.784589π0.784589\pi
194194 −59.5540 70.9737i −0.306980 0.365844i
195195 172.137 + 57.2262i 0.882752 + 0.293468i
196196 −154.450 + 56.2152i −0.788011 + 0.286812i
197197 253.494 + 146.355i 1.28677 + 0.742918i 0.978077 0.208243i 0.0667746π-0.0667746\pi
0.308694 + 0.951161i 0.400108π0.400108\pi
198198 14.4833 121.851i 0.0731478 0.615409i
199199 41.1548 + 71.2822i 0.206808 + 0.358202i 0.950707 0.310090i 0.100359π-0.100359\pi
−0.743899 + 0.668292i 0.767026π0.767026\pi
200200 19.7412 23.5267i 0.0987060 0.117633i
201201 248.140 152.721i 1.23453 0.759807i
202202 −0.962975 5.46130i −0.00476720 0.0270361i
203203 263.090 46.3898i 1.29601 0.228521i
204204 −13.1767 21.4094i −0.0645918 0.104948i
205205 51.3175 + 43.0605i 0.250329 + 0.210051i
206206 −72.6848 + 41.9646i −0.352839 + 0.203712i
207207 70.6441 + 164.653i 0.341276 + 0.795427i
208208 −9.22585 + 15.9796i −0.0443550 + 0.0768252i
209209 18.1595 + 49.8927i 0.0868874 + 0.238721i
210210 62.3061 187.417i 0.296696 0.892462i
211211 88.7425 74.4638i 0.420581 0.352909i −0.407803 0.913070i 0.633705π-0.633705\pi
0.828384 + 0.560161i 0.189261π0.189261\pi
212212 76.7592 210.894i 0.362072 0.994784i
213213 286.085 + 226.661i 1.34312 + 1.06413i
214214 −31.8794 + 180.797i −0.148969 + 0.844846i
215215 196.202i 0.912568i
216216 119.101 + 171.158i 0.551395 + 0.792396i
217217 −233.036 −1.07390
218218 −21.2416 3.74547i −0.0974387 0.0171811i
219219 −270.497 39.8915i −1.23515 0.182153i
220220 −157.553 57.3445i −0.716149 0.260657i
221221 22.8135 + 27.1880i 0.103228 + 0.123023i
222222 45.9776 40.8364i 0.207106 0.183948i
223223 186.281 67.8007i 0.835341 0.304039i 0.111292 0.993788i 0.464501π-0.464501\pi
0.724049 + 0.689749i 0.242279π0.242279\pi
224224 299.224 + 172.757i 1.33582 + 0.771236i
225225 −19.6088 29.9408i −0.0871504 0.133070i
226226 −10.4580 18.1138i −0.0462745 0.0801498i
227227 −3.31155 + 3.94655i −0.0145883 + 0.0173857i −0.773289 0.634053i 0.781390π-0.781390\pi
0.758701 + 0.651439i 0.225834π0.225834\pi
228228 −31.6455 17.1029i −0.138796 0.0750129i
229229 61.3581 + 347.979i 0.267939 + 1.51956i 0.760533 + 0.649299i 0.224938π0.224938\pi
−0.492594 + 0.870259i 0.663951π0.663951\pi
230230 −122.522 + 21.6039i −0.532703 + 0.0939300i
231231 −370.999 + 10.4330i −1.60606 + 0.0451643i
232232 −150.030 125.890i −0.646683 0.542631i
233233 121.729 70.2803i 0.522442 0.301632i −0.215491 0.976506i 0.569135π-0.569135\pi
0.737933 + 0.674874i 0.235802π0.235802\pi
234234 −80.3765 85.5276i −0.343489 0.365503i
235235 −33.3735 + 57.8046i −0.142015 + 0.245977i
236236 61.9306 + 170.153i 0.262418 + 0.720987i
237237 −59.9121 + 12.3100i −0.252794 + 0.0519407i
238238 29.6015 24.8386i 0.124376 0.104364i
239239 −50.5074 + 138.768i −0.211328 + 0.580619i −0.999388 0.0349794i 0.988863π-0.988863\pi
0.788060 + 0.615598i 0.211086π0.211086\pi
240240 24.6625 9.76996i 0.102761 0.0407082i
241241 52.8609 299.789i 0.219340 1.24394i −0.653875 0.756602i 0.726858π-0.726858\pi
0.873215 0.487335i 0.162031π-0.162031\pi
242242 19.6445i 0.0811755i
243243 231.036 75.3090i 0.950765 0.309913i
244244 207.060 0.848606
245245 −328.532 57.9291i −1.34095 0.236445i
246246 −15.9635 40.2970i −0.0648922 0.163809i
247247 47.7214 + 17.3692i 0.193204 + 0.0703205i
248248 109.815 + 130.873i 0.442803 + 0.527712i
249249 19.0809 + 92.8661i 0.0766302 + 0.372956i
250250 −123.461 + 44.9361i −0.493843 + 0.179744i
251251 −108.072 62.3955i −0.430567 0.248588i 0.269021 0.963134i 0.413300π-0.413300\pi
−0.699588 + 0.714546i 0.746633π0.746633\pi
252252 183.234 172.198i 0.727120 0.683327i
253253 116.897 + 202.472i 0.462044 + 0.800284i
254254 116.575 138.928i 0.458955 0.546961i
255255 −1.43430 51.0043i −0.00562472 0.200017i
256256 −40.9593 232.292i −0.159997 0.907390i
257257 −450.088 + 79.3627i −1.75132 + 0.308804i −0.955116 0.296231i 0.904270π-0.904270\pi
−0.796199 + 0.605035i 0.793159π0.793159\pi
258258 −60.3575 + 111.679i −0.233944 + 0.432865i
259259 −142.481 119.556i −0.550121 0.461606i
260260 −138.882 + 80.1837i −0.534163 + 0.308399i
261261 −190.934 + 125.046i −0.731547 + 0.479105i
262262 57.1884 99.0533i 0.218276 0.378066i
263263 −160.047 439.726i −0.608545 1.67196i −0.733408 0.679789i 0.762071π-0.762071\pi
0.124863 0.992174i 0.460151π-0.460151\pi
264264 180.688 + 203.437i 0.684425 + 0.770593i
265265 348.945 292.799i 1.31677 1.10490i
266266 18.9110 51.9576i 0.0710940 0.195329i
267267 −30.2106 + 204.853i −0.113148 + 0.767240i
268268 −44.7298 + 253.675i −0.166902 + 0.946549i
269269 317.049i 1.17862i −0.807907 0.589310i 0.799399π-0.799399\pi
0.807907 0.589310i 0.200601π-0.200601\pi
270270 14.2145 + 168.136i 0.0526464 + 0.622725i
271271 115.698 0.426931 0.213465 0.976951i 0.431525π-0.431525\pi
0.213465 + 0.976951i 0.431525π0.431525\pi
272272 5.11128 + 0.901257i 0.0187915 + 0.00331344i
273273 −220.451 + 278.248i −0.807513 + 1.01922i
274274 −71.6277 26.0704i −0.261415 0.0951473i
275275 −30.0198 35.7762i −0.109163 0.130095i
276276 −150.307 49.9689i −0.544589 0.181047i
277277 108.352 39.4370i 0.391163 0.142372i −0.138949 0.990300i 0.544372π-0.544372\pi
0.530112 + 0.847928i 0.322150π0.322150\pi
278278 125.980 + 72.7347i 0.453166 + 0.261635i
279279 182.964 78.5001i 0.655785 0.281362i
280280 218.970 + 379.267i 0.782035 + 1.35452i
281281 −52.4463 + 62.5031i −0.186642 + 0.222431i −0.851249 0.524762i 0.824154π-0.824154\pi
0.664607 + 0.747193i 0.268599π0.268599\pi
282282 36.7787 22.6360i 0.130421 0.0802694i
283283 −72.4355 410.802i −0.255956 1.45160i −0.793608 0.608430i 0.791800π-0.791800\pi
0.537652 0.843167i 0.319311π-0.319311\pi
284284 −317.772 + 56.0318i −1.11892 + 0.197295i
285285 −38.2679 62.1773i −0.134273 0.218166i
286286 −117.322 98.4445i −0.410215 0.344211i
287287 −113.534 + 65.5489i −0.395589 + 0.228393i
288288 −293.125 34.8410i −1.01780 0.120976i
289289 −139.508 + 241.636i −0.482728 + 0.836110i
290290 −54.2049 148.927i −0.186913 0.513540i
291291 75.5275 227.187i 0.259545 0.780712i
292292 185.169 155.375i 0.634141 0.532107i
293293 −118.282 + 324.977i −0.403693 + 1.10914i 0.556755 + 0.830676i 0.312046π0.312046\pi
−0.960448 + 0.278460i 0.910176π0.910176\pi
294294 169.181 + 134.039i 0.575446 + 0.455917i
295295 −63.8186 + 361.933i −0.216334 + 1.22689i
296296 136.357i 0.460665i
297297 287.769 133.166i 0.968920 0.448369i
298298 234.232 0.786012
299299 220.222 + 38.8311i 0.736529 + 0.129870i
300300 31.3022 + 4.61628i 0.104341 + 0.0153876i
301301 360.806 + 131.323i 1.19869 + 0.436287i
302302 95.6252 + 113.962i 0.316640 + 0.377356i
303303 10.7142 9.51612i 0.0353604 0.0314063i
304304 6.97859 2.54000i 0.0229559 0.00835526i
305305 363.957 + 210.131i 1.19330 + 0.688954i
306306 −14.8740 + 29.4731i −0.0486078 + 0.0963174i
307307 −288.668 499.988i −0.940286 1.62862i −0.764925 0.644120i 0.777224π-0.777224\pi
−0.175362 0.984504i 0.556110π-0.556110\pi
308308 210.907 251.350i 0.684764 0.816070i
309309 −190.796 103.117i −0.617463 0.333711i
310310 24.0064 + 136.147i 0.0774399 + 0.439184i
311311 442.280 77.9859i 1.42212 0.250759i 0.590921 0.806730i 0.298765π-0.298765\pi
0.831202 + 0.555971i 0.187653π0.187653\pi
312312 260.149 7.31570i 0.833810 0.0234478i
313313 8.30206 + 6.96625i 0.0265241 + 0.0222564i 0.655953 0.754801i 0.272267π-0.272267\pi
−0.629429 + 0.777058i 0.716711π0.716711\pi
314314 −139.700 + 80.6557i −0.444904 + 0.256865i
315315 496.830 116.728i 1.57724 0.370566i
316316 27.0360 46.8278i 0.0855570 0.148189i
317317 −74.6402 205.072i −0.235458 0.646916i −0.999997 0.00233841i 0.999256π-0.999256\pi
0.764539 0.644577i 0.222967π-0.222967\pi
318318 −288.694 + 59.3172i −0.907844 + 0.186532i
319319 −228.146 + 191.437i −0.715191 + 0.600117i
320320 58.0083 159.376i 0.181276 0.498051i
321321 −441.051 + 174.721i −1.37399 + 0.544302i
322322 42.2781 239.771i 0.131299 0.744631i
323323 14.2846i 0.0442249i
324324 −85.8567 + 196.923i −0.264990 + 0.607787i
325325 −44.6700 −0.137446
326326 45.5694 + 8.03512i 0.139784 + 0.0246476i
327327 −20.5277 51.8186i −0.0627760 0.158467i
328328 90.3137 + 32.8715i 0.275347 + 0.100218i
329329 −83.9620 100.062i −0.255204 0.304140i
330330 44.3141 + 215.675i 0.134285 + 0.653561i
331331 −564.453 + 205.444i −1.70530 + 0.620677i −0.996411 0.0846470i 0.973024π-0.973024\pi
−0.708885 + 0.705324i 0.750802π0.750802\pi
332332 −72.5849 41.9069i −0.218629 0.126226i
333333 152.140 + 45.8713i 0.456878 + 0.137752i
334334 −96.3325 166.853i −0.288421 0.499559i
335335 −336.061 + 400.502i −1.00317 + 1.19553i
336336 1.45928 + 51.8924i 0.00434309 + 0.154442i
337337 78.0147 + 442.443i 0.231498 + 1.31289i 0.849865 + 0.527000i 0.176683π0.176683\pi
−0.618368 + 0.785889i 0.712206π0.712206\pi
338338 48.9602 8.63300i 0.144853 0.0255414i
339339 25.6978 47.5485i 0.0758047 0.140261i
340340 34.5551 + 28.9952i 0.101633 + 0.0852799i
341341 224.988 129.897i 0.659789 0.380929i
342342 2.65471 + 47.1639i 0.00776232 + 0.137906i
343343 68.3305 118.352i 0.199214 0.345049i
344344 −96.2747 264.512i −0.279868 0.768932i
345345 −213.490 240.368i −0.618811 0.696719i
346346 −9.68515 + 8.12680i −0.0279918 + 0.0234879i
347347 −80.7717 + 221.918i −0.232771 + 0.639534i −0.999998 0.00184170i 0.999414π-0.999414\pi
0.767227 + 0.641376i 0.221636π0.221636\pi
348348 29.4382 199.615i 0.0845925 0.573607i
349349 41.6381 236.141i 0.119307 0.676622i −0.865221 0.501391i 0.832822π-0.832822\pi
0.984527 0.175231i 0.0560672π-0.0560672\pi
350350 48.6353i 0.138958i
351351 79.3531 292.722i 0.226077 0.833967i
352352 −385.187 −1.09428
353353 25.2020 + 4.44379i 0.0713937 + 0.0125886i 0.209231 0.977866i 0.432904π-0.432904\pi
−0.137837 + 0.990455i 0.544015π0.544015\pi
354354 147.667 186.382i 0.417139 0.526502i
355355 −615.423 223.996i −1.73359 0.630974i
356356 −117.669 140.232i −0.330530 0.393911i
357357 94.7544 + 31.5007i 0.265418 + 0.0882374i
358358 −308.279 + 112.204i −0.861114 + 0.313420i
359359 16.7796 + 9.68773i 0.0467399 + 0.0269853i 0.523188 0.852217i 0.324743π-0.324743\pi
−0.476448 + 0.879203i 0.658076π0.658076\pi
360360 −299.680 224.013i −0.832444 0.622258i
361361 170.280 + 294.934i 0.471690 + 0.816992i
362362 81.1916 96.7604i 0.224286 0.267294i
363363 43.2308 26.6070i 0.119093 0.0732976i
364364 −54.4967 309.066i −0.149716 0.849083i
365365 483.159 85.1939i 1.32372 0.233408i
366366 −142.524 231.571i −0.389409 0.632709i
367367 299.305 + 251.147i 0.815545 + 0.684324i 0.951924 0.306333i 0.0991021π-0.0991021\pi
−0.136379 + 0.990657i 0.543547π0.543547\pi
368368 28.3201 16.3506i 0.0769569 0.0444311i
369369 67.0585 89.7095i 0.181730 0.243115i
370370 −55.1707 + 95.5584i −0.149110 + 0.258266i
371371 304.886 + 837.669i 0.821796 + 2.25787i
372372 −55.5257 + 167.022i −0.149263 + 0.448983i
373373 −136.986 + 114.945i −0.367255 + 0.308164i −0.807675 0.589628i 0.799274π-0.799274\pi
0.440419 + 0.897792i 0.354830π0.354830\pi
374374 −14.7339 + 40.4810i −0.0393954 + 0.108238i
375375 −266.108 210.833i −0.709621 0.562221i
376376 −16.6287 + 94.3061i −0.0442253 + 0.250814i
377377 284.862i 0.755603i
378378 −318.707 86.3973i −0.843140 0.228564i
379379 3.48118 0.00918518 0.00459259 0.999989i 0.498538π-0.498538\pi
0.00459259 + 0.999989i 0.498538π0.498538\pi
380380 63.5643 + 11.2081i 0.167274 + 0.0294950i
381381 463.626 + 68.3730i 1.21687 + 0.179457i
382382 118.509 + 43.1337i 0.310233 + 0.112916i
383383 11.0730 + 13.1963i 0.0289112 + 0.0344550i 0.780306 0.625398i 0.215063π-0.215063\pi
−0.751395 + 0.659853i 0.770619π0.770619\pi
384384 212.225 188.494i 0.552670 0.490870i
385385 625.797 227.772i 1.62545 0.591615i
386386 −201.193 116.159i −0.521226 0.300930i
387387 −327.518 + 18.4350i −0.846299 + 0.0476356i
388388 105.827 + 183.298i 0.272750 + 0.472417i
389389 203.618 242.662i 0.523439 0.623810i −0.437952 0.898999i 0.644296π-0.644296\pi
0.961390 + 0.275189i 0.0887403π0.0887403\pi
390390 185.271 + 100.131i 0.475055 + 0.256745i
391391 −10.9225 61.9446i −0.0279348 0.158426i
392392 −471.340 + 83.1100i −1.20240 + 0.212015i
393393 295.440 8.30814i 0.751756 0.0211403i
394394 260.321 + 218.435i 0.660713 + 0.554404i
395395 95.0446 54.8740i 0.240619 0.138922i
396396 −80.9210 + 268.389i −0.204346 + 0.677750i
397397 −134.041 + 232.165i −0.337634 + 0.584800i −0.983987 0.178239i 0.942960π-0.942960\pi
0.646353 + 0.763039i 0.276293π0.276293\pi
398398 32.6829 + 89.7955i 0.0821178 + 0.225617i
399399 139.955 28.7560i 0.350763 0.0720703i
400400 −5.00408 + 4.19892i −0.0125102 + 0.0104973i
401401 33.3356 91.5887i 0.0831311 0.228401i −0.891162 0.453685i 0.850109π-0.850109\pi
0.974293 + 0.225285i 0.0723312π0.0723312\pi
402402 314.493 124.585i 0.782321 0.309914i
403403 43.1494 244.712i 0.107070 0.607227i
404404 12.6686i 0.0313578i
405405 −350.757 + 259.009i −0.866067 + 0.639528i
406406 310.149 0.763914
407407 204.203 + 36.0065i 0.501727 + 0.0884680i
408408 −26.9611 68.0584i −0.0660810 0.166810i
409409 380.898 + 138.636i 0.931292 + 0.338962i 0.762721 0.646727i 0.223863π-0.223863\pi
0.168570 + 0.985690i 0.446085π0.446085\pi
410410 49.9916 + 59.5777i 0.121931 + 0.145311i
411411 −39.6426 192.939i −0.0964539 0.469437i
412412 180.170 65.5764i 0.437305 0.159166i
413413 −622.862 359.609i −1.50814 0.870725i
414414 47.5751 + 202.494i 0.114916 + 0.489116i
415415 −85.0569 147.323i −0.204956 0.354995i
416416 −236.818 + 282.229i −0.569275 + 0.678435i
417417 10.5666 + 375.753i 0.0253397 + 0.901087i
418418 10.7038 + 60.7045i 0.0256073 + 0.145226i
419419 115.552 20.3750i 0.275781 0.0486277i −0.0340470 0.999420i 0.510840π-0.510840\pi
0.309828 + 0.950793i 0.399728π0.399728\pi
420420 −214.520 + 396.925i −0.510762 + 0.945060i
421421 −399.365 335.107i −0.948610 0.795979i 0.0304527 0.999536i 0.490305π-0.490305\pi
−0.979063 + 0.203558i 0.934750π0.934750\pi
422422 116.473 67.2459i 0.276003 0.159351i
423423 99.6282 + 50.2787i 0.235528 + 0.118862i
424424 326.760 565.966i 0.770661 1.33482i
425425 4.29744 + 11.8071i 0.0101116 + 0.0277814i
426426 281.394 + 316.821i 0.660549 + 0.743712i
427427 −630.025 + 528.654i −1.47547 + 1.23806i
428428 143.441 394.102i 0.335143 0.920799i
429429 57.7393 391.521i 0.134591 0.912636i
430430 39.5541 224.323i 0.0919864 0.521681i
431431 263.580i 0.611555i −0.952103 0.305777i 0.901084π-0.901084\pi
0.952103 0.305777i 0.0989163π-0.0989163\pi
432432 −18.6261 40.2509i −0.0431161 0.0931733i
433433 −702.013 −1.62128 −0.810639 0.585547i 0.800880π-0.800880\pi
−0.810639 + 0.585547i 0.800880π0.800880\pi
434434 −266.435 46.9797i −0.613906 0.108248i
435435 254.321 320.997i 0.584645 0.737924i
436436 46.3025 + 16.8527i 0.106198 + 0.0386531i
437437 −57.8526 68.9461i −0.132386 0.157771i
438438 −301.224 100.141i −0.687727 0.228632i
439439 416.204 151.486i 0.948073 0.345070i 0.178724 0.983899i 0.442803π-0.442803\pi
0.769349 + 0.638829i 0.220581π0.220581\pi
440440 −422.816 244.113i −0.960946 0.554802i
441441 −65.8317 + 553.857i −0.149278 + 1.25591i
442442 20.6021 + 35.6839i 0.0466111 + 0.0807328i
443443 −390.071 + 464.868i −0.880520 + 1.04936i 0.117891 + 0.993026i 0.462387π0.462387\pi
−0.998412 + 0.0563369i 0.982058π0.982058\pi
444444 −119.638 + 73.6326i −0.269454 + 0.165839i
445445 −64.5191 365.906i −0.144987 0.822260i
446446 226.648 39.9642i 0.508180 0.0896058i
447447 317.250 + 515.464i 0.709731 + 1.15316i
448448 254.259 + 213.348i 0.567542 + 0.476224i
449449 347.745 200.771i 0.774488 0.447151i −0.0599853 0.998199i 0.519105π-0.519105\pi
0.834473 + 0.551048i 0.185772π0.185772\pi
450450 −16.3832 38.1852i −0.0364072 0.0848560i
451451 73.0755 126.570i 0.162030 0.280644i
452452 16.3423 + 44.9002i 0.0361556 + 0.0993368i
453453 −121.274 + 364.791i −0.267712 + 0.805279i
454454 −4.58180 + 3.84458i −0.0100921 + 0.00846825i
455455 217.859 598.563i 0.478811 1.31552i
456456 −82.1013 65.0475i −0.180047 0.142648i
457457 −25.5458 + 144.878i −0.0558990 + 0.317019i −0.999917 0.0128747i 0.995902π-0.995902\pi
0.944018 + 0.329894i 0.107013π0.107013\pi
458458 410.223i 0.895683i
459459 −85.0061 + 7.18658i −0.185198 + 0.0156570i
460460 284.213 0.617855
461461 −773.480 136.385i −1.67783 0.295847i −0.747963 0.663740i 0.768968π-0.768968\pi
−0.929868 + 0.367893i 0.880079π0.880079\pi
462462 −426.276 62.8648i −0.922675 0.136071i
463463 336.835 + 122.598i 0.727506 + 0.264791i 0.679109 0.734037i 0.262366π-0.262366\pi
0.0483975 + 0.998828i 0.484589π0.484589\pi
464464 26.7767 + 31.9112i 0.0577084 + 0.0687742i
465465 −267.098 + 237.231i −0.574405 + 0.510174i
466466 153.344 55.8128i 0.329065 0.119770i
467467 −88.2727 50.9643i −0.189021 0.109131i 0.402503 0.915419i 0.368140π-0.368140\pi
−0.591524 + 0.806287i 0.701474π0.701474\pi
468468 146.899 + 224.300i 0.313886 + 0.479274i
469469 −511.569 886.063i −1.09077 1.88926i
470470 −49.8101 + 59.3613i −0.105979 + 0.126301i
471471 −366.709 198.189i −0.778575 0.420784i
472472 91.5597 + 519.261i 0.193982 + 1.10013i
473473 −421.547 + 74.3300i −0.891219 + 0.157146i
474474 −70.9806 + 1.99606i −0.149748 + 0.00421110i
475475 13.7726 + 11.5566i 0.0289949 + 0.0243296i
476476 −76.4491 + 44.1379i −0.160607 + 0.0927267i
477477 −521.553 554.978i −1.09340 1.16348i
478478 −85.7219 + 148.475i −0.179334 + 0.310616i
479479 43.2210 + 118.749i 0.0902318 + 0.247910i 0.976597 0.215077i 0.0690001π-0.0690001\pi
−0.886365 + 0.462986i 0.846778π0.846778\pi
480480 518.828 106.602i 1.08089 0.222088i
481481 151.929 127.483i 0.315860 0.265038i
482482 120.874 332.099i 0.250776 0.689003i
483483 584.918 231.713i 1.21101 0.479737i
484484 −7.79280 + 44.1952i −0.0161008 + 0.0913123i
485485 429.586i 0.885745i
486486 279.331 39.5260i 0.574756 0.0813292i
487487 454.010 0.932258 0.466129 0.884717i 0.345648π-0.345648\pi
0.466129 + 0.884717i 0.345648π0.345648\pi
488488 593.783 + 104.700i 1.21677 + 0.214549i
489489 44.0379 + 111.166i 0.0900571 + 0.227333i
490490 −363.940 132.463i −0.742735 0.270334i
491491 203.177 + 242.137i 0.413803 + 0.493151i 0.932177 0.362003i 0.117907π-0.117907\pi
−0.518374 + 0.855154i 0.673463π0.673463\pi
492492 19.9284 + 96.9906i 0.0405048 + 0.197135i
493493 75.2944 27.4049i 0.152727 0.0555881i
494494 51.0594 + 29.4792i 0.103359 + 0.0596744i
495495 −414.607 + 389.637i −0.837591 + 0.787145i
496496 −18.1689 31.4695i −0.0366309 0.0634466i
497497 823.833 981.806i 1.65761 1.97547i
498498 3.09398 + 110.023i 0.00621280 + 0.220929i
499499 21.2323 + 120.414i 0.0425497 + 0.241312i 0.998663 0.0516842i 0.0164589π-0.0164589\pi
−0.956114 + 0.292996i 0.905348π0.905348\pi
500500 295.582 52.1190i 0.591163 0.104238i
501501 236.711 437.985i 0.472477 0.874222i
502502 −110.983 93.1256i −0.221081 0.185509i
503503 −391.041 + 225.768i −0.777418 + 0.448843i −0.835515 0.549468i 0.814830π-0.814830\pi
0.0580963 + 0.998311i 0.481497π0.481497\pi
504504 612.531 401.159i 1.21534 0.795951i
505505 −12.8565 + 22.2680i −0.0254583 + 0.0440951i
506506 92.8333 + 255.057i 0.183465 + 0.504066i
507507 85.3113 + 96.0519i 0.168267 + 0.189452i
508508 −317.375 + 266.309i −0.624754 + 0.524231i
509509 −170.911 + 469.573i −0.335778 + 0.922541i 0.650800 + 0.759249i 0.274434π0.274434\pi
−0.986578 + 0.163292i 0.947789π0.947789\pi
510510 8.64255 58.6037i 0.0169462 0.114909i
511511 −166.722 + 945.527i −0.326266 + 1.85035i
512512 104.621i 0.204338i
513513 −100.196 + 69.7223i −0.195314 + 0.135911i
514514 −530.596 −1.03229
515515 383.240 + 67.5756i 0.744156 + 0.131215i
516516 180.091 227.307i 0.349014 0.440517i
517517 136.838 + 49.8051i 0.264678 + 0.0963348i
518518 −138.800 165.415i −0.267954 0.319335i
519519 −31.0022 10.3066i −0.0597344 0.0198585i
520520 −438.816 + 159.716i −0.843877 + 0.307146i
521521 −595.632 343.888i −1.14325 0.660054i −0.196015 0.980601i 0.562800π-0.562800\pi
−0.947233 + 0.320546i 0.896133π0.896133\pi
522522 −243.508 + 104.477i −0.466491 + 0.200147i
523523 260.218 + 450.711i 0.497549 + 0.861780i 0.999996 0.00282784i 0.000900130π-0.000900130\pi
−0.502447 + 0.864608i 0.667567π0.667567\pi
524524 −167.953 + 200.159i −0.320521 + 0.381983i
525525 −107.030 + 65.8730i −0.203866 + 0.125472i
526526 −94.3376 535.015i −0.179349 1.01714i
527527 −68.8332 + 12.1372i −0.130613 + 0.0230306i
528528 −30.3343 49.2869i −0.0574514 0.0933465i
529529 101.644 + 85.2896i 0.192144 + 0.161228i
530530 457.985 264.418i 0.864123 0.498902i
531531 610.167 + 72.5247i 1.14909 + 0.136581i
532532 −63.1561 + 109.390i −0.118715 + 0.205620i
533533 −47.8111 131.360i −0.0897020 0.246454i
534534 −75.8387 + 228.123i −0.142020 + 0.427197i
535535 652.079 547.160i 1.21884 1.02273i
536536 −256.542 + 704.844i −0.478623 + 1.31501i
537537 −664.465 526.444i −1.23736 0.980343i
538538 63.9168 362.490i 0.118804 0.673773i
539539 727.808i 1.35029i
540540 34.7189 383.902i 0.0642942 0.710930i
541541 803.120 1.48451 0.742255 0.670117i 0.233756π-0.233756\pi
0.742255 + 0.670117i 0.233756π0.233756\pi
542542 132.281 + 23.3247i 0.244060 + 0.0430344i
543543 322.905 + 47.6203i 0.594668 + 0.0876984i
544544 97.3813 + 35.4439i 0.179010 + 0.0651542i
545545 64.2851 + 76.6120i 0.117954 + 0.140572i
546546 −308.142 + 273.685i −0.564362 + 0.501254i
547547 64.5461 23.4929i 0.118000 0.0429486i −0.282345 0.959313i 0.591112π-0.591112\pi
0.400345 + 0.916364i 0.368890π0.368890\pi
548548 150.803 + 87.0659i 0.275187 + 0.158879i
549549 316.572 627.293i 0.576633 1.14261i
550550 −27.1099 46.9557i −0.0492907 0.0853741i
551551 73.6967 87.8283i 0.133751 0.159398i
552552 −405.765 219.298i −0.735082 0.397278i
553553 37.2950 + 211.511i 0.0674412 + 0.382478i
554554 131.832 23.2456i 0.237964 0.0419595i
555555 −285.016 + 8.01501i −0.513543 + 0.0144415i
556556 −254.570 213.610i −0.457861 0.384191i
557557 575.120 332.045i 1.03253 0.596132i 0.114822 0.993386i 0.463370π-0.463370\pi
0.917709 + 0.397254i 0.130037π0.130037\pi
558558 225.013 52.8658i 0.403249 0.0947415i
559559 −204.710 + 354.569i −0.366208 + 0.634291i
560560 −31.8589 87.5315i −0.0568908 0.156306i
561561 −109.041 + 22.4043i −0.194369 + 0.0399364i
562562 −72.5637 + 60.8882i −0.129117 + 0.108342i
563563 −118.905 + 326.689i −0.211199 + 0.580264i −0.999381 0.0351778i 0.988800π-0.988800\pi
0.788182 + 0.615442i 0.211022π0.211022\pi
564564 −91.7223 + 36.3354i −0.162628 + 0.0644246i
565565 −16.8406 + 95.5076i −0.0298063 + 0.169040i
566566 484.283i 0.855623i
567567 −241.535 818.385i −0.425987 1.44336i
568568 −939.603 −1.65423
569569 −385.078 67.8997i −0.676763 0.119332i −0.175306 0.984514i 0.556091π-0.556091\pi
−0.501457 + 0.865182i 0.667203π0.667203\pi
570570 −31.2178 78.8037i −0.0547680 0.138252i
571571 −804.118 292.675i −1.40826 0.512566i −0.477644 0.878554i 0.658509π-0.658509\pi
−0.930620 + 0.365988i 0.880731π0.880731\pi
572572 224.892 + 268.016i 0.393168 + 0.468559i
573573 65.5891 + 319.219i 0.114466 + 0.557102i
574574 −143.021 + 52.0553i −0.249165 + 0.0906887i
575575 68.5606 + 39.5835i 0.119236 + 0.0688408i
576576 −271.495 81.8576i −0.471346 0.142114i
577577 313.746 + 543.423i 0.543753 + 0.941808i 0.998684 + 0.0512815i 0.0163306π0.0163306\pi
−0.454931 + 0.890527i 0.650336π0.650336\pi
578578 −208.217 + 248.143i −0.360237 + 0.429314i
579579 −16.8752 600.087i −0.0291454 1.03642i
580580 62.8694 + 356.550i 0.108396 + 0.614742i
581581 327.850 57.8088i 0.564285 0.0994987i
582582 132.153 244.522i 0.227067 0.420141i
583583 −761.285 638.794i −1.30581 1.09570i
584584 609.573 351.937i 1.04379 0.602632i
585585 30.5829 + 543.339i 0.0522785 + 0.928785i
586586 −200.750 + 347.709i −0.342576 + 0.593359i
587587 −254.654 699.655i −0.433822 1.19192i −0.943448 0.331520i 0.892439π-0.892439\pi
0.509626 0.860396i 0.329784π-0.329784\pi
588588 −327.443 368.668i −0.556876 0.626986i
589589 −76.6133 + 64.2862i −0.130073 + 0.109145i
590590 −145.931 + 400.942i −0.247340 + 0.679562i
591591 −128.116 + 868.733i −0.216778 + 1.46994i
592592 5.03630 28.5623i 0.00850726 0.0482471i
593593 625.722i 1.05518i 0.849499 + 0.527591i 0.176904π0.176904\pi
−0.849499 + 0.527591i 0.823096π0.823096\pi
594594 355.860 94.2376i 0.599091 0.158649i
595595 −179.170 −0.301126
596596 −526.963 92.9177i −0.884165 0.155902i
597597 −153.343 + 193.546i −0.256856 + 0.324197i
598598 243.957 + 88.7932i 0.407955 + 0.148484i
599599 −368.344 438.975i −0.614932 0.732847i 0.365258 0.930906i 0.380981π-0.380981\pi
−0.980190 + 0.198059i 0.936536π0.936536\pi
600600 87.4307 + 29.0660i 0.145718 + 0.0484434i
601601 −1063.24 + 386.989i −1.76912 + 0.643908i −0.769134 + 0.639088i 0.779312π0.779312\pi
−0.999988 + 0.00482034i 0.998466π0.998466\pi
602602 386.043 + 222.882i 0.641268 + 0.370236i
603603 700.128 + 523.351i 1.16107 + 0.867912i
604604 −169.925 294.319i −0.281333 0.487283i
605605 −58.5483 + 69.7752i −0.0967741 + 0.115331i
606606 14.1682 8.72004i 0.0233799 0.0143895i
607607 −40.3687 228.942i −0.0665052 0.377170i −0.999835 0.0181503i 0.994222π-0.994222\pi
0.933330 0.359019i 0.116889π-0.116889\pi
608608 146.031 25.7492i 0.240182 0.0423506i
609609 420.075 + 682.533i 0.689778 + 1.12074i
610610 373.759 + 313.621i 0.612720 + 0.514133i
611611 120.623 69.6414i 0.197418 0.113979i
612612 45.1545 60.4067i 0.0737819 0.0987038i
613613 533.889 924.724i 0.870945 1.50852i 0.00992514 0.999951i 0.496841π-0.496841\pi
0.861020 0.508571i 0.169826π-0.169826\pi
614614 −229.244 629.843i −0.373362 1.02580i
615615 −63.4002 + 190.708i −0.103090 + 0.310095i
616616 731.912 614.147i 1.18817 0.996991i
617617 144.247 396.317i 0.233788 0.642328i −0.766212 0.642588i 0.777861π-0.777861\pi
1.00000 0.000260046i 8.27751e5π8.27751e-5\pi
618618 −197.354 156.360i −0.319343 0.253010i
619619 104.335 591.711i 0.168554 0.955915i −0.776771 0.629783i 0.783144π-0.783144\pi
0.945324 0.326131i 0.105745π-0.105745\pi
620620 315.820i 0.509386i
621621 −381.184 + 378.960i −0.613823 + 0.610242i
622622 521.392 0.838250
623623 716.066 + 126.262i 1.14938 + 0.202667i
624624 −54.7628 8.07611i −0.0877609 0.0129425i
625625 665.870 + 242.357i 1.06539 + 0.387771i
626626 8.08756 + 9.63837i 0.0129194 + 0.0153968i
627627 −119.092 + 105.775i −0.189940 + 0.168701i
628628 346.285 126.037i 0.551409 0.200696i
629629 −48.3124 27.8932i −0.0768083 0.0443453i
630630 591.571 33.2977i 0.939001 0.0528535i
631631 554.621 + 960.632i 0.878956 + 1.52240i 0.852488 + 0.522747i 0.175093π0.175093\pi
0.0264679 + 0.999650i 0.491574π0.491574\pi
632632 101.209 120.617i 0.160141 0.190849i
633633 305.740 + 165.239i 0.483002 + 0.261040i
634634 −43.9956 249.512i −0.0693937 0.393551i
635635 −828.122 + 146.020i −1.30413 + 0.229953i
636636 673.021 18.9262i 1.05821 0.0297581i
637637 533.269 + 447.466i 0.837157 + 0.702458i
638638 −299.439 + 172.881i −0.469340 + 0.270973i
639639 −316.089 + 1048.36i −0.494661 + 1.64063i
640640 −254.659 + 441.082i −0.397904 + 0.689191i
641641 −56.5257 155.303i −0.0881837 0.242283i 0.887760 0.460308i 0.152261π-0.152261\pi
−0.975943 + 0.218025i 0.930039π0.930039\pi
642642 −539.489 + 110.847i −0.840325 + 0.172659i
643643 608.717 510.774i 0.946683 0.794361i −0.0320527 0.999486i 0.510204π-0.510204\pi
0.978736 + 0.205125i 0.0657600π0.0657600\pi
644644 −190.230 + 522.654i −0.295389 + 0.811574i
645645 547.231 216.784i 0.848421 0.336099i
646646 2.87977 16.3320i 0.00445785 0.0252817i
647647 222.504i 0.343900i 0.985106 + 0.171950i 0.0550068π0.0550068\pi
−0.985106 + 0.171950i 0.944993π0.944993\pi
648648 −345.784 + 521.300i −0.533618 + 0.804475i
649649 801.803 1.23544
650650 −51.0723 9.00542i −0.0785728 0.0138545i
651651 −257.481 649.964i −0.395516 0.998409i
652652 −99.3323 36.1540i −0.152350 0.0554509i
653653 −299.851 357.348i −0.459190 0.547241i 0.485916 0.874006i 0.338486π-0.338486\pi
−0.945106 + 0.326764i 0.894042π0.894042\pi
654654 −13.0233 63.3839i −0.0199133 0.0969172i
655655 −498.345 + 181.383i −0.760833 + 0.276920i
656656 −17.7037 10.2212i −0.0269873 0.0155811i
657657 −187.610 798.526i −0.285556 1.21541i
658658 −75.8234 131.330i −0.115233 0.199590i
659659 −133.876 + 159.547i −0.203150 + 0.242104i −0.857994 0.513659i 0.828290π-0.828290\pi
0.654845 + 0.755764i 0.272734π0.272734\pi
660660 −14.1392 502.794i −0.0214230 0.761809i
661661 −110.055 624.153i −0.166498 0.944256i −0.947507 0.319736i 0.896406π-0.896406\pi
0.781009 0.624520i 0.214705π-0.214705\pi
662662 −686.770 + 121.096i −1.03742 + 0.182925i
663663 −50.6241 + 93.6695i −0.0763561 + 0.141281i
664664 −186.961 156.879i −0.281567 0.236263i
665665 −222.024 + 128.186i −0.333871 + 0.192760i
666666 164.698 + 83.1171i 0.247295 + 0.124800i
667667 252.425 437.214i 0.378449 0.655493i
668668 150.535 + 413.591i 0.225352 + 0.619149i
669669 394.926 + 444.647i 0.590323 + 0.664645i
670670 −464.967 + 390.154i −0.693981 + 0.582319i
671671 313.590 861.581i 0.467347 1.28403i
672672 −151.228 + 1025.45i −0.225041 + 1.52597i
673673 19.1049 108.349i 0.0283877 0.160994i −0.967319 0.253564i 0.918397π-0.918397\pi
0.995706 + 0.0925699i 0.0295082π0.0295082\pi
674674 521.584i 0.773864i
675675 61.8427 87.7730i 0.0916188 0.130034i
676676 −113.573 −0.168007
677677 −140.866 24.8384i −0.208073 0.0366890i 0.0686398 0.997642i 0.478134π-0.478134\pi
−0.276713 + 0.960953i 0.589245π0.589245\pi
678678 38.9666 49.1827i 0.0574729 0.0725409i
679679 −789.987 287.532i −1.16346 0.423463i
680680 84.4318 + 100.622i 0.124164 + 0.147973i
681681 −14.6663 4.87577i −0.0215365 0.00715972i
682682 283.421 103.157i 0.415574 0.151257i
683683 784.050 + 452.671i 1.14795 + 0.662769i 0.948387 0.317116i 0.102714π-0.102714\pi
0.199563 + 0.979885i 0.436048π0.436048\pi
684684 12.7371 107.160i 0.0186215 0.156667i
685685 176.714 + 306.078i 0.257977 + 0.446830i
686686 101.984 121.539i 0.148664 0.177171i
687687 −902.761 + 555.617i −1.31406 + 0.808758i
688688 10.3967 + 58.9625i 0.0151115 + 0.0857013i
689689 −936.096 + 165.059i −1.35863 + 0.239563i
690690 −195.630 317.858i −0.283522 0.460664i
691691 407.543 + 341.969i 0.589788 + 0.494891i 0.888145 0.459564i 0.151994π-0.151994\pi
−0.298357 + 0.954454i 0.596439π0.596439\pi
692692 25.0130 14.4413i 0.0361459 0.0208689i
693693 −439.016 1023.23i −0.633500 1.47653i
694694 −137.087 + 237.441i −0.197531 + 0.342134i
695695 −230.690 633.817i −0.331929 0.911967i
696696 185.355 557.549i 0.266315 0.801077i
697697 −30.1213 + 25.2748i −0.0432156 + 0.0362622i
698698 95.2117 261.592i 0.136406 0.374773i
699699 330.519 + 261.864i 0.472845 + 0.374627i
700700 19.2932 109.417i 0.0275617 0.156310i
701701 905.026i 1.29105i −0.763739 0.645525i 0.776639π-0.776639\pi
0.763739 0.645525i 0.223361π-0.223361\pi
702702 149.739 318.679i 0.213303 0.453959i
703703 −79.8237 −0.113547
704704 −364.401 64.2538i −0.517616 0.0912696i
705705 −198.098 29.2144i −0.280991 0.0414389i
706706 27.9182 + 10.1614i 0.0395442 + 0.0143929i
707707 −32.3447 38.5469i −0.0457492 0.0545217i
708708 −406.150 + 360.734i −0.573658 + 0.509511i
709709 341.922 124.450i 0.482260 0.175528i −0.0894380 0.995992i 0.528507π-0.528507\pi
0.571698 + 0.820464i 0.306285π0.306285\pi
710710 −658.471 380.168i −0.927424 0.535449i
711711 −100.531 153.501i −0.141393 0.215894i
712712 −266.529 461.642i −0.374338 0.648373i
713713 −283.074 + 337.355i −0.397019 + 0.473148i
714714 101.984 + 55.1180i 0.142835 + 0.0771960i
715715 123.311 + 699.329i 0.172462 + 0.978083i
716716 738.060 130.140i 1.03081 0.181760i
717717 −442.846 + 12.4534i −0.617638 + 0.0173687i
718718 17.2315 + 14.4590i 0.0239994 + 0.0201379i
719719 −389.328 + 224.778i −0.541485 + 0.312626i −0.745680 0.666304i 0.767875π-0.767875\pi
0.204196 + 0.978930i 0.434542π0.434542\pi
720720 54.4992 + 57.9919i 0.0756934 + 0.0805444i
721721 −380.779 + 659.529i −0.528127 + 0.914742i
722722 135.227 + 371.534i 0.187295 + 0.514589i
723723 894.553 183.801i 1.23728 0.254220i
724724 −221.045 + 185.479i −0.305310 + 0.256186i
725725 −34.4922 + 94.7665i −0.0475754 + 0.130712i
726726 54.7908 21.7052i 0.0754695 0.0298969i
727727 100.606 570.564i 0.138385 0.784820i −0.834058 0.551677i 0.813988π-0.813988\pi
0.972443 0.233142i 0.0749009π-0.0749009\pi
728728 913.862i 1.25530i
729729 465.317 + 561.178i 0.638295 + 0.769792i
730730 569.582 0.780250
731731 113.413 + 19.9978i 0.155148 + 0.0273568i
732732 228.780 + 577.515i 0.312542 + 0.788955i
733733 −879.854 320.241i −1.20035 0.436891i −0.337002 0.941504i 0.609413π-0.609413\pi
−0.863345 + 0.504613i 0.831635π0.831635\pi
734734 291.572 + 347.482i 0.397237 + 0.473409i
735735 −201.424 980.321i −0.274046 1.33377i
736736 613.567 223.320i 0.833650 0.303424i
737737 987.805 + 570.310i 1.34031 + 0.773826i
738738 94.7550 89.0482i 0.128394 0.120661i
739739 −263.918 457.119i −0.357128 0.618564i 0.630352 0.776310i 0.282911π-0.282911\pi
−0.987480 + 0.157746i 0.949577π0.949577\pi
740740 162.027 193.097i 0.218956 0.260942i
741741 4.28263 + 152.292i 0.00577953 + 0.205522i
742742 179.711 + 1019.19i 0.242198 + 1.37357i
743743 −36.2725 + 6.39582i −0.0488190 + 0.00860811i −0.198004 0.980201i 0.563446π-0.563446\pi
0.149185 + 0.988809i 0.452335π0.452335\pi
744744 −243.685 + 450.889i −0.327534 + 0.606034i
745745 −831.967 698.103i −1.11673 0.937051i
746746 −179.793 + 103.803i −0.241009 + 0.139146i
747747 −237.932 + 155.827i −0.318517 + 0.208603i
748748 49.2061 85.2274i 0.0657835 0.113940i
749749 569.747 + 1565.37i 0.760677 + 2.08994i
750750 −261.744 294.697i −0.348992 0.392930i
751751 75.4565 63.3155i 0.100475 0.0843082i −0.591167 0.806550i 0.701332π-0.701332\pi
0.691641 + 0.722241i 0.256888π0.256888\pi
752752 6.96633 19.1398i 0.00926374 0.0254519i
753753 54.6197 370.367i 0.0725362 0.491856i
754754 −57.4279 + 325.690i −0.0761644 + 0.431950i
755755 689.781i 0.913617i
756756 682.738 + 320.801i 0.903093 + 0.424339i
757757 −1385.09 −1.82971 −0.914857 0.403779i 0.867697π-0.867697\pi
−0.914857 + 0.403779i 0.867697π0.867697\pi
758758 3.98012 + 0.701803i 0.00525082 + 0.000925861i
759759 −435.559 + 549.752i −0.573859 + 0.724310i
760760 176.615 + 64.2827i 0.232388 + 0.0845825i
761761 935.204 + 1114.53i 1.22891 + 1.46456i 0.839374 + 0.543555i 0.182922π0.182922\pi
0.389541 + 0.921009i 0.372634π0.372634\pi
762762 516.291 + 171.639i 0.677547 + 0.225248i
763763 −183.913 + 66.9389i −0.241039 + 0.0877312i
764764 −249.505 144.052i −0.326577 0.188549i
765765 140.672 60.3551i 0.183886 0.0788956i
766766 9.99966 + 17.3199i 0.0130544 + 0.0226109i
767767 492.959 587.486i 0.642711 0.765953i
768768 602.634 370.900i 0.784680 0.482942i
769769 −17.3763 98.5458i −0.0225959 0.128148i 0.971423 0.237354i 0.0762802π-0.0762802\pi
−0.994019 + 0.109206i 0.965169π0.965169\pi
770770 761.408 134.257i 0.988842 0.174360i
771771 −718.654 1167.66i −0.932106 1.51448i
772772 406.555 + 341.140i 0.526626 + 0.441891i
773773 −547.928 + 316.347i −0.708834 + 0.409245i −0.810629 0.585560i 0.800875π-0.800875\pi
0.101795 + 0.994805i 0.467541π0.467541\pi
774774 −378.175 44.9501i −0.488599 0.0580750i
775775 43.9854 76.1850i 0.0567554 0.0983032i
776776 210.794 + 579.152i 0.271642 + 0.746330i
777777 176.029 529.495i 0.226549 0.681461i
778778 281.722 236.392i 0.362110 0.303846i
779779 −19.2431 + 52.8699i −0.0247023 + 0.0678690i
780780 −377.093 298.765i −0.483453 0.383031i
781781 −248.112 + 1407.12i −0.317686 + 1.80168i
782782 73.0247i 0.0933820i
783783 −559.732 394.373i −0.714856 0.503670i
784784 101.800 0.129847
785785 736.585 + 129.880i 0.938325 + 0.165452i
786786 339.459 + 50.0616i 0.431882 + 0.0636915i
787787 766.476 + 278.974i 0.973921 + 0.354478i 0.779474 0.626435i 0.215487π-0.215487\pi
0.194447 + 0.980913i 0.437709π0.437709\pi
788788 −499.005 594.691i −0.633256 0.754685i
789789 1049.61 932.244i 1.33031 1.18155i
790790 119.729 43.5779i 0.151556 0.0551619i
791791 −164.362 94.8944i −0.207790 0.119968i
792792 −367.767 + 728.738i −0.464353 + 0.920124i
793793 −438.486 759.481i −0.552946 0.957731i
794794 −200.056 + 238.418i −0.251960 + 0.300275i
795795 1202.20 + 649.735i 1.51220 + 0.817277i
796796 −37.9072 214.982i −0.0476221 0.270078i
797797 1233.67 217.529i 1.54789 0.272934i 0.666564 0.745448i 0.267764π-0.267764\pi
0.881323 + 0.472514i 0.156653π0.156653\pi
798798 165.811 4.66280i 0.207783 0.00584311i
799799 −30.0119 25.1830i −0.0375618 0.0315181i
800800 −112.957 + 65.2156i −0.141196 + 0.0815196i
801801 −604.740 + 142.081i −0.754981 + 0.177380i
802802 56.5776 97.9952i 0.0705456 0.122189i
803803 −366.084 1005.81i −0.455895 1.25256i
804804 −756.953 + 155.529i −0.941483 + 0.193444i
805805 −864.781 + 725.637i −1.07426 + 0.901413i
806806 98.6675 271.087i 0.122416 0.336336i
807807 884.288 350.307i 1.09577 0.434086i
808808 −6.40587 + 36.3295i −0.00792806 + 0.0449622i
809809 1021.88i 1.26313i 0.775321 + 0.631567i 0.217588π0.217588\pi
−0.775321 + 0.631567i 0.782412π0.782412\pi
810810 −453.245 + 225.419i −0.559562 + 0.278295i
811811 −365.788 −0.451034 −0.225517 0.974239i 0.572407π-0.572407\pi
−0.225517 + 0.974239i 0.572407π0.572407\pi
812812 −697.758 123.034i −0.859308 0.151519i
813813 127.835 + 322.696i 0.157239 + 0.396921i
814814 226.211 + 82.3342i 0.277901 + 0.101148i
815815 −137.910 164.355i −0.169215 0.201662i
816816 3.13374 + 15.2518i 0.00384037 + 0.0186909i
817817 154.846 56.3595i 0.189531 0.0689835i
818818 407.542 + 235.294i 0.498217 + 0.287646i
819819 −1019.64 307.429i −1.24498 0.375371i
820820 −88.8346 153.866i −0.108335 0.187641i
821821 −6.23245 + 7.42755i −0.00759129 + 0.00904695i −0.769827 0.638253i 0.779657π-0.779657\pi
0.762235 + 0.647300i 0.224102π0.224102\pi
822822 −6.42805 228.584i −0.00782001 0.278082i
823823 0.155222 + 0.880308i 0.000188605 + 0.00106963i 0.984902 0.173113i 0.0553827π-0.0553827\pi
−0.984713 + 0.174183i 0.944272π0.944272\pi
824824 549.829 96.9497i 0.667268 0.117657i
825825 66.6153 123.258i 0.0807458 0.149403i
826826 −639.636 536.719i −0.774378 0.649780i
827827 −583.611 + 336.948i −0.705696 + 0.407434i −0.809465 0.587168i 0.800243π-0.800243\pi
0.103769 + 0.994601i 0.466910π0.466910\pi
828828 −26.7044 474.434i −0.0322517 0.572988i
829829 −14.4804 + 25.0808i −0.0174673 + 0.0302542i −0.874627 0.484797i 0.838894π-0.838894\pi
0.857160 + 0.515051i 0.172227π0.172227\pi
830830 −67.5475 185.585i −0.0813825 0.223597i
831831 229.713 + 258.633i 0.276429 + 0.311231i
832832 −271.118 + 227.495i −0.325863 + 0.273431i
833833 66.9709 184.001i 0.0803972 0.220890i
834834 −63.6704 + 431.738i −0.0763434 + 0.517672i
835835 −155.124 + 879.753i −0.185778 + 1.05360i
836836 140.816i 0.168440i
837837 421.103 + 423.574i 0.503110 + 0.506062i
838838 136.221 0.162555
839839 629.012 + 110.912i 0.749716 + 0.132195i 0.535434 0.844577i 0.320148π-0.320148\pi
0.214282 + 0.976772i 0.431259π0.431259\pi
840840 −815.882 + 1029.79i −0.971288 + 1.22593i
841841 −185.952 67.6809i −0.221108 0.0804767i
842842 −389.047 463.648i −0.462051 0.550650i
843843 −232.277 77.2195i −0.275536 0.0916008i
844844 −288.712 + 105.082i −0.342075 + 0.124505i
845845 −199.631 115.257i −0.236250 0.136399i
846846 103.771 + 77.5698i 0.122661 + 0.0916900i
847847 −89.1253 154.370i −0.105225 0.182254i
848848 −89.3493 + 106.482i −0.105365 + 0.125569i
849849 1065.74 655.926i 1.25529 0.772587i
850850 2.53306 + 14.3657i 0.00298008 + 0.0169008i
851851 −346.151 + 61.0358i −0.406758 + 0.0717225i
852852 −507.386 824.395i −0.595523 0.967600i
853853 595.279 + 499.498i 0.697865 + 0.585578i 0.921165 0.389171i 0.127239π-0.127239\pi
−0.223300 + 0.974750i 0.571683π0.571683\pi
854854 −826.899 + 477.410i −0.968266 + 0.559029i
855855 131.138 175.434i 0.153378 0.205185i
856856 610.623 1057.63i 0.713345 1.23555i
857857 368.296 + 1011.88i 0.429750 + 1.18073i 0.945965 + 0.324269i 0.105118π0.105118\pi
−0.516215 + 0.856459i 0.672659π0.672659\pi
858858 144.945 435.995i 0.168934 0.508153i
859859 −62.0374 + 52.0556i −0.0722205 + 0.0606002i −0.678183 0.734893i 0.737232π-0.737232\pi
0.605963 + 0.795493i 0.292788π0.292788\pi
860860 −177.974 + 488.979i −0.206946 + 0.568580i
861861 −308.267 244.235i −0.358034 0.283664i
862862 53.1375 301.358i 0.0616444 0.349603i
863863 1599.17i 1.85304i −0.376244 0.926520i 0.622785π-0.622785\pi
0.376244 0.926520i 0.377215π-0.377215\pi
864864 −226.698 856.057i −0.262382 0.990807i
865865 58.6217 0.0677708
866866 −802.629 141.525i −0.926823 0.163424i
867867 −828.094 122.123i −0.955126 0.140857i
868868 580.776 + 211.385i 0.669097 + 0.243531i
869869 −153.906 183.418i −0.177107 0.211067i
870870 355.484 315.733i 0.408602 0.362912i
871871 1025.19 373.137i 1.17702 0.428400i
872872 124.260 + 71.7413i 0.142500 + 0.0822722i
873873 717.103 40.3635i 0.821423 0.0462354i
874874 −52.2449 90.4908i −0.0597767 0.103536i
875875 −766.304 + 913.245i −0.875776 + 1.04371i
876876 637.954 + 344.785i 0.728258 + 0.393590i
877877 −65.7402 372.831i −0.0749603 0.425121i −0.999075 0.0430055i 0.986307π-0.986307\pi
0.924115 0.382116i 0.124804π-0.124804\pi
878878 506.396 89.2913i 0.576761 0.101698i
879879 −1037.09 + 29.1642i −1.17985 + 0.0331789i
880880 79.5498 + 66.7502i 0.0903975 + 0.0758525i
881881 −1046.81 + 604.374i −1.18820 + 0.686009i −0.957898 0.287109i 0.907306π-0.907306\pi
−0.230305 + 0.973119i 0.573972π0.573972\pi
882882 −186.924 + 619.967i −0.211932 + 0.702910i
883883 298.144 516.401i 0.337649 0.584826i −0.646341 0.763049i 0.723702π-0.723702\pi
0.983990 + 0.178223i 0.0570349π0.0570349\pi
884884 −32.1941 88.4525i −0.0364186 0.100059i
885885 −1079.99 + 221.902i −1.22033 + 0.250737i
886886 −539.694 + 452.857i −0.609136 + 0.511126i
887887 34.7360 95.4364i 0.0391612 0.107595i −0.918571 0.395256i 0.870656π-0.870656\pi
0.957732 + 0.287662i 0.0928779π0.0928779\pi
888888 −380.316 + 150.661i −0.428283 + 0.169663i
889889 285.757 1620.61i 0.321436 1.82296i
890890 431.356i 0.484670i
891891 689.371 + 655.489i 0.773705 + 0.735678i
892892 −525.755 −0.589412
893893 −55.2071 9.73450i −0.0618220 0.0109009i
894894 258.802 + 653.301i 0.289488 + 0.730761i
895895 1429.39 + 520.255i 1.59708 + 0.581290i
896896 −640.678 763.531i −0.715043 0.852155i
897897 135.019 + 657.131i 0.150523 + 0.732588i
898898 438.061 159.441i 0.487818 0.177551i
899899 −485.835 280.497i −0.540417 0.312010i
900900 21.7104 + 92.4062i 0.0241227 + 0.102674i
901901 133.684 + 231.548i 0.148373 + 0.256990i
902902 109.065 129.979i 0.120915 0.144101i
903903 32.3796 + 1151.43i 0.0358578 + 1.27511i
904904 24.1609 + 137.023i 0.0267267 + 0.151575i
905905 −576.769 + 101.700i −0.637313 + 0.112376i
906906 −212.197 + 392.626i −0.234213 + 0.433362i
907907 1321.91 + 1109.21i 1.45745 + 1.22295i 0.926906 + 0.375293i 0.122458π0.122458\pi
0.530547 + 0.847656i 0.321987π0.321987\pi
908908 11.8330 6.83179i 0.0130319 0.00752400i
909909 38.3797 + 19.3688i 0.0422219 + 0.0213078i
910910 369.753 640.431i 0.406322 0.703771i
911911 106.953 + 293.850i 0.117401 + 0.322558i 0.984450 0.175666i 0.0562080π-0.0562080\pi
−0.867048 + 0.498224i 0.833986π0.833986\pi
912912 14.7950 + 16.6577i 0.0162226 + 0.0182650i
913913 −284.305 + 238.560i −0.311396 + 0.261292i
914914 −58.4144 + 160.492i −0.0639107 + 0.175593i
915915 −183.944 + 1247.30i −0.201032 + 1.36316i
916916 162.732 922.898i 0.177655 1.00753i
917917 1037.84i 1.13177i
918918 −98.6384 8.92054i −0.107449 0.00971737i
919919 198.504 0.216000 0.108000 0.994151i 0.465555π-0.465555\pi
0.108000 + 0.994151i 0.465555π0.465555\pi
920920 815.035 + 143.713i 0.885908 + 0.156209i
921921 1075.58 1357.57i 1.16784 1.47401i
922922 −856.844 311.866i −0.929332 0.338249i
923923 878.459 + 1046.91i 0.951743 + 1.13424i
924924 934.076 + 310.530i 1.01090 + 0.336072i
925925 65.9791 24.0144i 0.0713287 0.0259615i
926926 360.397 + 208.075i 0.389197 + 0.224703i
927927 76.7941 646.087i 0.0828416 0.696966i
928928 415.883 + 720.330i 0.448149 + 0.776218i
929929 854.746 1018.65i 0.920071 1.09650i −0.0749849 0.997185i 0.523891π-0.523891\pi
0.995056 0.0993136i 0.0316647π-0.0316647\pi
930930 −353.206 + 217.385i −0.379791 + 0.233748i
931931 −48.6528 275.924i −0.0522587 0.296374i
932932 −367.127 + 64.7343i −0.393913 + 0.0694574i
933933 706.187 + 1147.41i 0.756899 + 1.22980i
934934 −90.6501 76.0644i −0.0970557 0.0814394i
935935 172.983 99.8717i 0.185008 0.106815i
936936 307.843 + 717.503i 0.328892 + 0.766563i
937937 −675.671 + 1170.30i −0.721100 + 1.24898i 0.239459 + 0.970906i 0.423030π0.423030\pi
−0.960559 + 0.278076i 0.910303π0.910303\pi
938938 −406.260 1116.19i −0.433113 1.18997i
939939 −10.2568 + 30.8524i −0.0109231 + 0.0328567i
940940 135.608 113.789i 0.144264 0.121052i
941941 265.840 730.391i 0.282508 0.776186i −0.714553 0.699581i 0.753370π-0.753370\pi
0.997062 0.0766044i 0.0244078π-0.0244078\pi
942942 −379.313 300.523i −0.402667 0.319027i
943943 −43.0206 + 243.982i −0.0456210 + 0.258729i
944944 112.150i 0.118803i
945945 874.517 + 1256.75i 0.925415 + 1.32989i
946946 −496.949 −0.525316
947947 −270.124 47.6301i −0.285242 0.0502958i 0.0291967 0.999574i 0.490705π-0.490705\pi
−0.314438 + 0.949278i 0.601816π0.601816\pi
948948 160.480 + 23.6668i 0.169283 + 0.0249649i
949949 −962.034 350.152i −1.01373 0.368969i
950950 13.4167 + 15.9894i 0.0141229 + 0.0168310i
951951 489.501 434.765i 0.514723 0.457166i
952952 −241.551 + 87.9173i −0.253730 + 0.0923501i
953953 858.313 + 495.548i 0.900644 + 0.519987i 0.877409 0.479743i 0.159270π-0.159270\pi
0.0232347 + 0.999730i 0.492603π0.492603\pi
954954 −484.421 739.664i −0.507779 0.775329i
955955 −292.376 506.410i −0.306153 0.530272i
956956 251.751 300.025i 0.263338 0.313834i
957957 −786.020 424.808i −0.821338 0.443896i
958958 25.4760 + 144.482i 0.0265929 + 0.150816i
959959 −681.141 + 120.104i −0.710262 + 0.125238i
960960 508.613 14.3028i 0.529806 0.0148988i
961961 −361.298 303.165i −0.375961 0.315468i
962962 199.405 115.126i 0.207281 0.119674i
963963 −974.635 1037.10i −1.01208 1.07694i
964964 −403.678 + 699.190i −0.418753 + 0.725301i
965965 368.418 + 1012.22i 0.381780 + 1.04893i
966966 715.464 147.004i 0.740646 0.152178i
967967 239.352 200.840i 0.247520 0.207694i −0.510583 0.859828i 0.670571π-0.670571\pi
0.758104 + 0.652134i 0.226126π0.226126\pi
968968 −44.6946 + 122.797i −0.0461721 + 0.126857i
969969 39.8416 15.7831i 0.0411162 0.0162880i
970970 −86.6041 + 491.156i −0.0892826 + 0.506347i
971971 487.838i 0.502407i 0.967934 + 0.251204i 0.0808264π0.0808264\pi
−0.967934 + 0.251204i 0.919174π0.919174\pi
972972 −644.105 21.8847i −0.662659 0.0225151i
973973 1319.96 1.35659
974974 519.080 + 91.5279i 0.532937 + 0.0939711i
975975 −49.3558 124.590i −0.0506214 0.127785i
976976 −120.511 43.8624i −0.123474 0.0449410i
977977 −413.839 493.194i −0.423582 0.504805i 0.511478 0.859297i 0.329098π-0.329098\pi
−0.935059 + 0.354492i 0.884654π0.884654\pi
978978 27.9387 + 135.977i 0.0285672 + 0.139035i
979979 −761.718 + 277.243i −0.778057 + 0.283190i
980980 766.227 + 442.382i 0.781865 + 0.451410i
981981 121.847 114.509i 0.124207 0.116726i
982982 183.483 + 317.802i 0.186846 + 0.323627i
983983 −989.779 + 1179.57i −1.00690 + 1.19997i −0.0271699 + 0.999631i 0.508650π0.508650\pi
−0.979726 + 0.200341i 0.935795π0.935795\pi
984984 8.10498 + 288.216i 0.00823676 + 0.292902i
985985 −273.610 1551.72i −0.277777 1.57535i
986986 91.6108 16.1534i 0.0929115 0.0163828i
987987 186.316 344.739i 0.188770 0.349279i
988988 −103.177 86.5756i −0.104430 0.0876271i
989989 628.389 362.801i 0.635378 0.366836i
990990 −552.581 + 361.897i −0.558163 + 0.365552i
991991 −155.571 + 269.456i −0.156984 + 0.271903i −0.933780 0.357849i 0.883510π-0.883510\pi
0.776796 + 0.629752i 0.216844π0.216844\pi
992992 −248.155 681.799i −0.250156 0.687297i
993993 −1196.67 1347.33i −1.20511 1.35683i
994994 1139.84 956.439i 1.14672 0.962213i
995995 151.540 416.352i 0.152301 0.418445i
996996 36.6844 248.751i 0.0368318 0.249750i
997997 −8.37502 + 47.4971i −0.00840022 + 0.0476400i −0.988720 0.149777i 0.952144π-0.952144\pi
0.980320 + 0.197417i 0.0632554π0.0632554\pi
998998 141.953i 0.142238i
999999 40.1592 + 475.021i 0.0401994 + 0.475496i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 27.3.f.a.2.4 30
3.2 odd 2 81.3.f.a.8.2 30
4.3 odd 2 432.3.bc.a.353.3 30
9.2 odd 6 243.3.f.b.188.4 30
9.4 even 3 243.3.f.d.107.2 30
9.5 odd 6 243.3.f.a.107.4 30
9.7 even 3 243.3.f.c.188.2 30
27.4 even 9 243.3.f.a.134.4 30
27.5 odd 18 243.3.f.c.53.2 30
27.11 odd 18 729.3.b.a.728.12 30
27.13 even 9 81.3.f.a.71.2 30
27.14 odd 18 inner 27.3.f.a.14.4 yes 30
27.16 even 9 729.3.b.a.728.19 30
27.22 even 9 243.3.f.b.53.4 30
27.23 odd 18 243.3.f.d.134.2 30
108.95 even 18 432.3.bc.a.257.3 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.3.f.a.2.4 30 1.1 even 1 trivial
27.3.f.a.14.4 yes 30 27.14 odd 18 inner
81.3.f.a.8.2 30 3.2 odd 2
81.3.f.a.71.2 30 27.13 even 9
243.3.f.a.107.4 30 9.5 odd 6
243.3.f.a.134.4 30 27.4 even 9
243.3.f.b.53.4 30 27.22 even 9
243.3.f.b.188.4 30 9.2 odd 6
243.3.f.c.53.2 30 27.5 odd 18
243.3.f.c.188.2 30 9.7 even 3
243.3.f.d.107.2 30 9.4 even 3
243.3.f.d.134.2 30 27.23 odd 18
432.3.bc.a.257.3 30 108.95 even 18
432.3.bc.a.353.3 30 4.3 odd 2
729.3.b.a.728.12 30 27.11 odd 18
729.3.b.a.728.19 30 27.16 even 9