Properties

Label 220.3.s.b.31.2
Level 220220
Weight 33
Character 220.31
Analytic conductor 5.9955.995
Analytic rank 00
Dimension 9696
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [220,3,Mod(31,220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(220, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("220.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 220=22511 220 = 2^{2} \cdot 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 220.s (of order 1010, degree 44, 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: 5.994565815935.99456581593
Analytic rank: 00
Dimension: 9696
Relative dimension: 2424 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 31.2
Character χ\chi == 220.31
Dual form 220.3.s.b.71.2

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+(1.965160.371672i)q2+(0.447988+0.616603i)q3+(3.72372+1.46079i)q4+(0.6909832.12663i)q5+(0.6511951.37823i)q6+(5.62557+7.74293i)q7+(6.774784.25469i)q8+(2.601658.00705i)q9+(0.567486+4.43598i)q10+(8.562956.90477i)q11+(0.767455+2.95047i)q12+(0.964498+2.96842i)q13+(13.933013.1252i)q14+(1.001731.37877i)q15+(11.7322+10.8791i)q16+(0.5055521.55593i)q17+(8.08865+14.7682i)q18+(8.8888812.2345i)q19+(0.5335278.92835i)q207.29450q21+(14.2613+16.7516i)q229.12329iq23+(0.4115686.08339i)q24+(4.04508+2.93893i)q25+(2.998675.47495i)q26+(12.62644.10257i)q27+(32.2588+20.6147i)q28+(40.161129.1787i)q29+(2.48101+2.33718i)q30+(33.648810.9332i)q31+(19.012225.7398i)q32+(0.4213978.37319i)q33+(0.415197+3.24555i)q34+(20.3535+6.61325i)q35+(21.384426.0155i)q36+(42.906131.1731i)q37+(12.9209+27.3465i)q38+(2.26242+0.735104i)q39+(4.36688+17.3473i)q40+(3.78700+2.75142i)q41+(14.3349+2.71116i)q42+24.1885iq43+(21.799638.2201i)q4418.8257q45+(3.39087+17.9287i)q46+(6.89694+9.49282i)q47+(1.45223+12.1078i)q48+(13.164140.5150i)q49+(9.041564.27202i)q50+(0.7329091.00876i)q51+(7.92776+9.64464i)q52+(11.5593+35.5760i)q53+(26.3377+3.36933i)q54+(8.76701+22.9813i)q55+(71.055728.5216i)q56+(3.5617110.9618i)q57+(68.0781+72.2677i)q58+(33.006345.4293i)q59+(5.744253.67082i)q60+(27.3220+84.0884i)q61+(62.0618+33.9917i)q62+(47.3623+65.1886i)q63+(27.7953+57.6491i)q64+6.97917q65+(3.94019+16.2981i)q6658.1153iq67+(0.3903516.53235i)q68+(5.625444.08712i)q69+(37.539920.5609i)q70+(95.027730.8764i)q71+(51.6931+43.1768i)q72+(29.724421.5961i)q73+(72.7312+77.2071i)q74+(3.624301.17761i)q75+(15.227758.5426i)q76+(101.63527.4591i)q77+(4.719240.603722i)q78+(70.8877+23.0328i)q79+(15.029132.4673i)q80+(53.114738.5901i)q81+(8.464693.99946i)q82+(38.8899+12.6361i)q83+(27.162710.6557i)q84+(2.95955+2.15024i)q85+(8.9901747.5343i)q8637.8351iq87+(28.6345+83.2110i)q88+116.343q89+(36.9955+6.99698i)q90+(17.558424.1671i)q91+(13.327233.9726i)q92+(8.3328525.6459i)q93+(10.025421.2183i)q94+(19.8761+27.3572i)q95+(7.3540023.2541i)q96+(13.766842.3699i)q97+(10.8113+84.5112i)q98+(77.5646+50.6002i)q99+O(q100)q+(-1.96516 - 0.371672i) q^{2} +(0.447988 + 0.616603i) q^{3} +(3.72372 + 1.46079i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-0.651195 - 1.37823i) q^{6} +(-5.62557 + 7.74293i) q^{7} +(-6.77478 - 4.25469i) q^{8} +(2.60165 - 8.00705i) q^{9} +(0.567486 + 4.43598i) q^{10} +(-8.56295 - 6.90477i) q^{11} +(0.767455 + 2.95047i) q^{12} +(-0.964498 + 2.96842i) q^{13} +(13.9330 - 13.1252i) q^{14} +(1.00173 - 1.37877i) q^{15} +(11.7322 + 10.8791i) q^{16} +(-0.505552 - 1.55593i) q^{17} +(-8.08865 + 14.7682i) q^{18} +(-8.88888 - 12.2345i) q^{19} +(0.533527 - 8.92835i) q^{20} -7.29450 q^{21} +(14.2613 + 16.7516i) q^{22} -9.12329i q^{23} +(-0.411568 - 6.08339i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(2.99867 - 5.47495i) q^{26} +(12.6264 - 4.10257i) q^{27} +(-32.2588 + 20.6147i) q^{28} +(-40.1611 - 29.1787i) q^{29} +(-2.48101 + 2.33718i) q^{30} +(-33.6488 - 10.9332i) q^{31} +(-19.0122 - 25.7398i) q^{32} +(0.421397 - 8.37319i) q^{33} +(0.415197 + 3.24555i) q^{34} +(20.3535 + 6.61325i) q^{35} +(21.3844 - 26.0155i) q^{36} +(-42.9061 - 31.1731i) q^{37} +(12.9209 + 27.3465i) q^{38} +(-2.26242 + 0.735104i) q^{39} +(-4.36688 + 17.3473i) q^{40} +(-3.78700 + 2.75142i) q^{41} +(14.3349 + 2.71116i) q^{42} +24.1885i q^{43} +(-21.7996 - 38.2201i) q^{44} -18.8257 q^{45} +(-3.39087 + 17.9287i) q^{46} +(6.89694 + 9.49282i) q^{47} +(-1.45223 + 12.1078i) q^{48} +(-13.1641 - 40.5150i) q^{49} +(9.04156 - 4.27202i) q^{50} +(0.732909 - 1.00876i) q^{51} +(-7.92776 + 9.64464i) q^{52} +(-11.5593 + 35.5760i) q^{53} +(-26.3377 + 3.36933i) q^{54} +(-8.76701 + 22.9813i) q^{55} +(71.0557 - 28.5216i) q^{56} +(3.56171 - 10.9618i) q^{57} +(68.0781 + 72.2677i) q^{58} +(33.0063 - 45.4293i) q^{59} +(5.74425 - 3.67082i) q^{60} +(27.3220 + 84.0884i) q^{61} +(62.0618 + 33.9917i) q^{62} +(47.3623 + 65.1886i) q^{63} +(27.7953 + 57.6491i) q^{64} +6.97917 q^{65} +(-3.94019 + 16.2981i) q^{66} -58.1153i q^{67} +(0.390351 - 6.53235i) q^{68} +(5.62544 - 4.08712i) q^{69} +(-37.5399 - 20.5609i) q^{70} +(95.0277 - 30.8764i) q^{71} +(-51.6931 + 43.1768i) q^{72} +(-29.7244 - 21.5961i) q^{73} +(72.7312 + 77.2071i) q^{74} +(-3.62430 - 1.17761i) q^{75} +(-15.2277 - 58.5426i) q^{76} +(101.635 - 27.4591i) q^{77} +(4.71924 - 0.603722i) q^{78} +(70.8877 + 23.0328i) q^{79} +(15.0291 - 32.4673i) q^{80} +(-53.1147 - 38.5901i) q^{81} +(8.46469 - 3.99946i) q^{82} +(-38.8899 + 12.6361i) q^{83} +(-27.1627 - 10.6557i) q^{84} +(-2.95955 + 2.15024i) q^{85} +(8.99017 - 47.5343i) q^{86} -37.8351i q^{87} +(28.6345 + 83.2110i) q^{88} +116.343 q^{89} +(36.9955 + 6.99698i) q^{90} +(-17.5584 - 24.1671i) q^{91} +(13.3272 - 33.9726i) q^{92} +(-8.33285 - 25.6459i) q^{93} +(-10.0254 - 21.2183i) q^{94} +(-19.8761 + 27.3572i) q^{95} +(7.35400 - 23.2541i) q^{96} +(13.7668 - 42.3699i) q^{97} +(10.8113 + 84.5112i) q^{98} +(-77.5646 + 50.6002i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q+2q2+16q4120q520q610q8+64q910q1070q12+20q13+83q144q16+24q17+45q1825q20+35q2262q24120q25+1042q98+O(q100) 96 q + 2 q^{2} + 16 q^{4} - 120 q^{5} - 20 q^{6} - 10 q^{8} + 64 q^{9} - 10 q^{10} - 70 q^{12} + 20 q^{13} + 83 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} - 25 q^{20} + 35 q^{22} - 62 q^{24} - 120 q^{25}+ \cdots - 1042 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/220Z)×\left(\mathbb{Z}/220\mathbb{Z}\right)^\times.

nn 101101 111111 177177
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\right) 1-1 11

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 −1.96516 0.371672i −0.982581 0.185836i
33 0.447988 + 0.616603i 0.149329 + 0.205534i 0.877128 0.480257i 0.159456π-0.159456\pi
−0.727799 + 0.685791i 0.759456π0.759456\pi
44 3.72372 + 1.46079i 0.930930 + 0.365197i
55 −0.690983 2.12663i −0.138197 0.425325i
66 −0.651195 1.37823i −0.108533 0.229705i
77 −5.62557 + 7.74293i −0.803652 + 1.10613i 0.188619 + 0.982050i 0.439599π0.439599\pi
−0.992272 + 0.124082i 0.960401π0.960401\pi
88 −6.77478 4.25469i −0.846847 0.531836i
99 2.60165 8.00705i 0.289072 0.889672i
1010 0.567486 + 4.43598i 0.0567486 + 0.443598i
1111 −8.56295 6.90477i −0.778450 0.627706i
1212 0.767455 + 2.95047i 0.0639546 + 0.245873i
1313 −0.964498 + 2.96842i −0.0741921 + 0.228340i −0.981275 0.192612i 0.938304π-0.938304\pi
0.907083 + 0.420952i 0.138304π0.138304\pi
1414 13.9330 13.1252i 0.995212 0.937517i
1515 1.00173 1.37877i 0.0667821 0.0919177i
1616 11.7322 + 10.8791i 0.733262 + 0.679946i
1717 −0.505552 1.55593i −0.0297384 0.0915253i 0.935086 0.354422i 0.115322π-0.115322\pi
−0.964824 + 0.262896i 0.915322π0.915322\pi
1818 −8.08865 + 14.7682i −0.449369 + 0.820455i
1919 −8.88888 12.2345i −0.467836 0.643921i 0.508275 0.861195i 0.330283π-0.330283\pi
−0.976111 + 0.217274i 0.930283π0.930283\pi
2020 0.533527 8.92835i 0.0266763 0.446417i
2121 −7.29450 −0.347357
2222 14.2613 + 16.7516i 0.648240 + 0.761436i
2323 9.12329i 0.396665i −0.980135 0.198332i 0.936447π-0.936447\pi
0.980135 0.198332i 0.0635525π-0.0635525\pi
2424 −0.411568 6.08339i −0.0171486 0.253475i
2525 −4.04508 + 2.93893i −0.161803 + 0.117557i
2626 2.99867 5.47495i 0.115334 0.210575i
2727 12.6264 4.10257i 0.467645 0.151947i
2828 −32.2588 + 20.6147i −1.15210 + 0.736240i
2929 −40.1611 29.1787i −1.38486 1.00616i −0.996407 0.0846969i 0.973008π-0.973008\pi
−0.388458 0.921466i 0.626992π-0.626992\pi
3030 −2.48101 + 2.33718i −0.0827004 + 0.0779060i
3131 −33.6488 10.9332i −1.08545 0.352683i −0.288961 0.957341i 0.593310π-0.593310\pi
−0.796485 + 0.604658i 0.793310π0.793310\pi
3232 −19.0122 25.7398i −0.594131 0.804369i
3333 0.421397 8.37319i 0.0127696 0.253733i
3434 0.415197 + 3.24555i 0.0122117 + 0.0954574i
3535 20.3535 + 6.61325i 0.581528 + 0.188950i
3636 21.3844 26.0155i 0.594012 0.722654i
3737 −42.9061 31.1731i −1.15962 0.842516i −0.169893 0.985462i 0.554342π-0.554342\pi
−0.989730 + 0.142946i 0.954342π0.954342\pi
3838 12.9209 + 27.3465i 0.340023 + 0.719645i
3939 −2.26242 + 0.735104i −0.0580107 + 0.0188488i
4040 −4.36688 + 17.3473i −0.109172 + 0.433684i
4141 −3.78700 + 2.75142i −0.0923659 + 0.0671077i −0.633010 0.774144i 0.718181π-0.718181\pi
0.540644 + 0.841252i 0.318181π0.318181\pi
4242 14.3349 + 2.71116i 0.341306 + 0.0645513i
4343 24.1885i 0.562523i 0.959631 + 0.281261i 0.0907528π0.0907528\pi
−0.959631 + 0.281261i 0.909247π0.909247\pi
4444 −21.7996 38.2201i −0.495446 0.868639i
4545 −18.8257 −0.418349
4646 −3.39087 + 17.9287i −0.0737145 + 0.389755i
4747 6.89694 + 9.49282i 0.146743 + 0.201975i 0.876061 0.482200i 0.160162π-0.160162\pi
−0.729318 + 0.684175i 0.760162π0.760162\pi
4848 −1.45223 + 12.1078i −0.0302548 + 0.252246i
4949 −13.1641 40.5150i −0.268655 0.826836i
5050 9.04156 4.27202i 0.180831 0.0854404i
5151 0.732909 1.00876i 0.0143708 0.0197797i
5252 −7.92776 + 9.64464i −0.152457 + 0.185474i
5353 −11.5593 + 35.5760i −0.218101 + 0.671244i 0.780818 + 0.624758i 0.214802π0.214802\pi
−0.998919 + 0.0464864i 0.985198π0.985198\pi
5454 −26.3377 + 3.36933i −0.487736 + 0.0623951i
5555 −8.76701 + 22.9813i −0.159400 + 0.417842i
5656 71.0557 28.5216i 1.26885 0.509314i
5757 3.56171 10.9618i 0.0624861 0.192313i
5858 68.0781 + 72.2677i 1.17376 + 1.24599i
5959 33.0063 45.4293i 0.559430 0.769989i −0.431824 0.901958i 0.642130π-0.642130\pi
0.991254 + 0.131969i 0.0421299π0.0421299\pi
6060 5.74425 3.67082i 0.0957376 0.0611803i
6161 27.3220 + 84.0884i 0.447902 + 1.37850i 0.879270 + 0.476323i 0.158031π0.158031\pi
−0.431369 + 0.902176i 0.641969π0.641969\pi
6262 62.0618 + 33.9917i 1.00100 + 0.548254i
6363 47.3623 + 65.1886i 0.751782 + 1.03474i
6464 27.7953 + 57.6491i 0.434301 + 0.900768i
6565 6.97917 0.107372
6666 −3.94019 + 16.2981i −0.0596999 + 0.246940i
6767 58.1153i 0.867392i −0.901059 0.433696i 0.857209π-0.857209\pi
0.901059 0.433696i 0.142791π-0.142791\pi
6868 0.390351 6.53235i 0.00574045 0.0960640i
6969 5.62544 4.08712i 0.0815281 0.0592337i
7070 −37.5399 20.5609i −0.536285 0.293727i
7171 95.0277 30.8764i 1.33842 0.434878i 0.449637 0.893211i 0.351553π-0.351553\pi
0.888781 + 0.458333i 0.151553π0.151553\pi
7272 −51.6931 + 43.1768i −0.717959 + 0.599677i
7373 −29.7244 21.5961i −0.407184 0.295836i 0.365277 0.930899i 0.380974π-0.380974\pi
−0.772461 + 0.635063i 0.780974π0.780974\pi
7474 72.7312 + 77.2071i 0.982855 + 1.04334i
7575 −3.62430 1.17761i −0.0483240 0.0157014i
7676 −15.2277 58.5426i −0.200364 0.770298i
7777 101.635 27.4591i 1.31993 0.356612i
7878 4.71924 0.603722i 0.0605030 0.00774003i
7979 70.8877 + 23.0328i 0.897313 + 0.291555i 0.721127 0.692802i 0.243624π-0.243624\pi
0.176185 + 0.984357i 0.443624π0.443624\pi
8080 15.0291 32.4673i 0.187864 0.405841i
8181 −53.1147 38.5901i −0.655737 0.476421i
8282 8.46469 3.99946i 0.103228 0.0487739i
8383 −38.8899 + 12.6361i −0.468553 + 0.152242i −0.533771 0.845629i 0.679226π-0.679226\pi
0.0652183 + 0.997871i 0.479226π0.479226\pi
8484 −27.1627 10.6557i −0.323365 0.126854i
8585 −2.95955 + 2.15024i −0.0348183 + 0.0252970i
8686 8.99017 47.5343i 0.104537 0.552724i
8787 37.8351i 0.434887i
8888 28.6345 + 83.2110i 0.325392 + 0.945579i
8989 116.343 1.30722 0.653612 0.756830i 0.273253π-0.273253\pi
0.653612 + 0.756830i 0.273253π0.273253\pi
9090 36.9955 + 6.99698i 0.411062 + 0.0777442i
9191 −17.5584 24.1671i −0.192950 0.265572i
9292 13.3272 33.9726i 0.144861 0.369267i
9393 −8.33285 25.6459i −0.0896005 0.275762i
9494 −10.0254 21.2183i −0.106653 0.225727i
9595 −19.8761 + 27.3572i −0.209223 + 0.287970i
9696 7.35400 23.2541i 0.0766041 0.242230i
9797 13.7668 42.3699i 0.141926 0.436803i −0.854677 0.519160i 0.826245π-0.826245\pi
0.996603 + 0.0823573i 0.0262449π0.0262449\pi
9898 10.8113 + 84.5112i 0.110320 + 0.862359i
9999 −77.5646 + 50.6002i −0.783481 + 0.511113i
100100 −19.3559 + 5.03472i −0.193559 + 0.0503472i
101101 −38.1746 + 117.489i −0.377967 + 1.16326i 0.563489 + 0.826124i 0.309459π0.309459\pi
−0.941455 + 0.337138i 0.890541π0.890541\pi
102102 −1.81521 + 1.70998i −0.0177962 + 0.0167645i
103103 −115.343 + 158.756i −1.11983 + 1.54132i −0.313761 + 0.949502i 0.601589π0.601589\pi
−0.806073 + 0.591816i 0.798411π0.798411\pi
104104 19.1640 16.0067i 0.184269 0.153911i
105105 5.04037 + 15.5127i 0.0480035 + 0.147740i
106106 35.9385 65.6162i 0.339043 0.619021i
107107 28.1635 + 38.7638i 0.263211 + 0.362278i 0.920083 0.391723i 0.128121π-0.128121\pi
−0.656872 + 0.754002i 0.728121π0.728121\pi
108108 53.0102 + 3.16771i 0.490835 + 0.0293306i
109109 11.5938 0.106365 0.0531824 0.998585i 0.483064π-0.483064\pi
0.0531824 + 0.998585i 0.483064π0.483064\pi
110110 25.7701 41.9035i 0.234273 0.380941i
111111 40.4212i 0.364155i
112112 −150.237 + 29.6401i −1.34140 + 0.264644i
113113 −108.027 + 78.4859i −0.955988 + 0.694566i −0.952215 0.305427i 0.901201π-0.901201\pi
−0.00377227 + 0.999993i 0.501201π0.501201\pi
114114 −11.0735 + 20.2179i −0.0971362 + 0.177350i
115115 −19.4018 + 6.30404i −0.168712 + 0.0548177i
116116 −106.925 167.320i −0.921764 1.44242i
117117 21.2590 + 15.4456i 0.181701 + 0.132013i
118118 −81.7476 + 77.0085i −0.692776 + 0.652614i
119119 14.8915 + 4.83853i 0.125138 + 0.0406599i
120120 −12.6527 + 5.07877i −0.105439 + 0.0423231i
121121 25.6484 + 118.250i 0.211970 + 0.977276i
122122 −22.4388 175.402i −0.183925 1.43772i
123123 −3.39306 1.10247i −0.0275859 0.00896319i
124124 −109.328 89.8659i −0.881675 0.724725i
125125 9.04508 + 6.57164i 0.0723607 + 0.0525731i
126126 −68.8458 145.709i −0.546395 1.15642i
127127 −4.42432 + 1.43755i −0.0348372 + 0.0113193i −0.326384 0.945237i 0.605830π-0.605830\pi
0.291547 + 0.956557i 0.405830π0.405830\pi
128128 −33.1956 123.621i −0.259341 0.965786i
129129 −14.9147 + 10.8361i −0.115618 + 0.0840012i
130130 −13.7152 2.59396i −0.105502 0.0199535i
131131 234.292i 1.78849i −0.447576 0.894246i 0.647712π-0.647712\pi
0.447576 0.894246i 0.352288π-0.352288\pi
132132 13.8006 30.5639i 0.104550 0.231544i
133133 144.736 1.08824
134134 −21.5998 + 114.206i −0.161193 + 0.852283i
135135 −17.4493 24.0169i −0.129254 0.177903i
136136 −3.19499 + 12.6920i −0.0234926 + 0.0933239i
137137 −18.7864 57.8185i −0.137127 0.422033i 0.858788 0.512331i 0.171218π-0.171218\pi
−0.995915 + 0.0902985i 0.971218π0.971218\pi
138138 −12.5740 + 5.94104i −0.0911157 + 0.0430510i
139139 4.30579 5.92642i 0.0309769 0.0426361i −0.793248 0.608899i 0.791611π-0.791611\pi
0.824225 + 0.566263i 0.191611π0.191611\pi
140140 66.1301 + 54.3581i 0.472358 + 0.388272i
141141 −2.76355 + 8.50534i −0.0195997 + 0.0603215i
142142 −198.221 + 25.3580i −1.39592 + 0.178577i
143143 28.7552 18.7588i 0.201085 0.131180i
144144 117.633 65.6365i 0.816895 0.455809i
145145 −34.3017 + 105.570i −0.236563 + 0.728067i
146146 50.3867 + 53.4875i 0.345114 + 0.366353i
147147 19.0843 26.2672i 0.129825 0.178689i
148148 −114.233 178.757i −0.771844 1.20782i
149149 −22.0579 67.8872i −0.148039 0.455619i 0.849350 0.527830i 0.176994π-0.176994\pi
−0.997389 + 0.0722117i 0.976994π0.976994\pi
150150 6.68465 + 3.66123i 0.0445643 + 0.0244082i
151151 −26.4721 36.4357i −0.175312 0.241296i 0.712315 0.701860i 0.247647π-0.247647\pi
−0.887626 + 0.460565i 0.847647π0.847647\pi
152152 8.16624 + 120.705i 0.0537252 + 0.794115i
153153 −13.7737 −0.0900240
154154 −209.934 + 16.1869i −1.36321 + 0.105110i
155155 79.1131i 0.510407i
156156 −9.49845 0.567594i −0.0608875 0.00363842i
157157 215.708 156.721i 1.37393 0.998222i 0.376517 0.926410i 0.377122π-0.377122\pi
0.997418 0.0718124i 0.0228783π-0.0228783\pi
158158 −130.745 71.6101i −0.827501 0.453229i
159159 −27.1147 + 8.81009i −0.170532 + 0.0554094i
160160 −41.6019 + 58.2176i −0.260012 + 0.363860i
161161 70.6410 + 51.3237i 0.438764 + 0.318781i
162162 90.0361 + 95.5769i 0.555778 + 0.589981i
163163 −73.9072 24.0139i −0.453418 0.147324i 0.0733999 0.997303i 0.476615π-0.476615\pi
−0.526818 + 0.849978i 0.676615π0.676615\pi
164164 −18.1210 + 4.71350i −0.110494 + 0.0287408i
165165 −18.0978 + 4.88958i −0.109684 + 0.0296338i
166166 81.1214 10.3777i 0.488683 0.0625162i
167167 35.7406 + 11.6128i 0.214016 + 0.0695379i 0.414063 0.910248i 0.364109π-0.364109\pi
−0.200047 + 0.979786i 0.564109π0.564109\pi
168168 49.4186 + 31.0358i 0.294158 + 0.184737i
169169 128.843 + 93.6096i 0.762382 + 0.553903i
170170 6.61519 3.12559i 0.0389129 0.0183858i
171171 −121.088 + 39.3439i −0.708117 + 0.230081i
172172 −35.3343 + 90.0712i −0.205432 + 0.523670i
173173 243.517 176.926i 1.40761 1.02269i 0.413949 0.910300i 0.364149π-0.364149\pi
0.993664 0.112391i 0.0358509π-0.0358509\pi
174174 −14.0622 + 74.3522i −0.0808175 + 0.427311i
175175 47.8539i 0.273451i
176176 −25.3442 174.166i −0.144001 0.989577i
177177 42.7983 0.241798
178178 −228.633 43.2413i −1.28445 0.242929i
179179 −183.916 253.139i −1.02746 1.41418i −0.906835 0.421486i 0.861509π-0.861509\pi
−0.120629 0.992698i 0.538491π-0.538491\pi
180180 −70.1016 27.5004i −0.389454 0.152780i
181181 73.7817 + 227.077i 0.407634 + 1.25457i 0.918676 + 0.395012i 0.129260π0.129260\pi
−0.511042 + 0.859556i 0.670740π0.670740\pi
182182 25.5229 + 54.0182i 0.140236 + 0.296803i
183183 −39.6092 + 54.5174i −0.216444 + 0.297909i
184184 −38.8167 + 61.8083i −0.210961 + 0.335914i
185185 −36.6462 + 112.785i −0.198087 + 0.609650i
186186 6.84355 + 53.4953i 0.0367933 + 0.287609i
187187 −6.41431 + 16.8141i −0.0343011 + 0.0899149i
188188 11.8153 + 45.4236i 0.0628471 + 0.241615i
189189 −39.2648 + 120.845i −0.207750 + 0.639390i
190190 49.2277 46.3739i 0.259093 0.244073i
191191 −181.210 + 249.414i −0.948742 + 1.30583i 0.00334140 + 0.999994i 0.498936π0.498936\pi
−0.952084 + 0.305837i 0.901064π0.901064\pi
192192 −23.0947 + 42.9647i −0.120285 + 0.223775i
193193 −105.817 325.671i −0.548274 1.68741i −0.713075 0.701088i 0.752698π-0.752698\pi
0.164801 0.986327i 0.447302π-0.447302\pi
194194 −42.8017 + 78.1469i −0.220627 + 0.402819i
195195 3.12659 + 4.30338i 0.0160338 + 0.0220686i
196196 10.1644 170.096i 0.0518590 0.867839i
197197 −310.061 −1.57391 −0.786956 0.617009i 0.788344π-0.788344\pi
−0.786956 + 0.617009i 0.788344π0.788344\pi
198198 171.234 70.6090i 0.864816 0.356611i
199199 275.222i 1.38302i 0.722365 + 0.691512i 0.243055π0.243055\pi
−0.722365 + 0.691512i 0.756945π0.756945\pi
200200 39.9088 2.70000i 0.199544 0.0135000i
201201 35.8340 26.0349i 0.178279 0.129527i
202202 118.687 216.697i 0.587559 1.07276i
203203 451.858 146.817i 2.22590 0.723239i
204204 4.20274 2.68572i 0.0206017 0.0131653i
205205 8.46799 + 6.15236i 0.0413073 + 0.0300115i
206206 285.672 269.111i 1.38676 1.30636i
207207 −73.0506 23.7356i −0.352901 0.114665i
208208 −43.6095 + 24.3331i −0.209661 + 0.116986i
209209 −8.36127 + 166.139i −0.0400061 + 0.794924i
210210 −4.13953 32.3583i −0.0197120 0.154087i
211211 158.344 + 51.4490i 0.750445 + 0.243834i 0.659173 0.751992i 0.270907π-0.270907\pi
0.0912723 + 0.995826i 0.470907π0.470907\pi
212212 −95.0127 + 115.589i −0.448173 + 0.545232i
213213 61.6097 + 44.7621i 0.289247 + 0.210151i
214214 −40.9385 86.6447i −0.191301 0.404882i
215215 51.4399 16.7138i 0.239255 0.0777388i
216216 −102.996 25.9274i −0.476835 0.120034i
217217 273.948 199.035i 1.26243 0.917212i
218218 −22.7836 4.30907i −0.104512 0.0197664i
219219 28.0029i 0.127867i
220220 −66.2167 + 72.7691i −0.300985 + 0.330769i
221221 5.10626 0.0231052
222222 −15.0234 + 79.4341i −0.0676730 + 0.357811i
223223 157.104 + 216.236i 0.704504 + 0.969666i 0.999898 + 0.0142908i 0.00454904π0.00454904\pi
−0.295394 + 0.955375i 0.595451π0.595451\pi
224224 306.256 2.40899i 1.36721 0.0107544i
225225 13.0082 + 40.0352i 0.0578144 + 0.177934i
226226 241.461 114.087i 1.06841 0.504810i
227227 −76.5696 + 105.389i −0.337311 + 0.464269i −0.943654 0.330935i 0.892636π-0.892636\pi
0.606342 + 0.795204i 0.292636π0.292636\pi
228228 29.2757 35.6158i 0.128402 0.156210i
229229 85.0594 261.786i 0.371438 1.14317i −0.574412 0.818566i 0.694769π-0.694769\pi
0.945850 0.324603i 0.105231π-0.105231\pi
230230 40.4708 5.17734i 0.175960 0.0225102i
231231 62.4624 + 50.3668i 0.270400 + 0.218038i
232232 147.936 + 368.552i 0.637655 + 1.58859i
233233 −117.614 + 361.980i −0.504783 + 1.55356i 0.296353 + 0.955079i 0.404230π0.404230\pi
−0.801136 + 0.598483i 0.795770π0.795770\pi
234234 −36.0367 38.2544i −0.154003 0.163480i
235235 15.4220 21.2266i 0.0656256 0.0903259i
236236 189.269 120.951i 0.801988 0.512504i
237237 17.5547 + 54.0280i 0.0740707 + 0.227966i
238238 −27.4658 15.0432i −0.115403 0.0632069i
239239 −34.6444 47.6840i −0.144956 0.199514i 0.730365 0.683057i 0.239350π-0.239350\pi
−0.875321 + 0.483542i 0.839350π0.839350\pi
240240 26.7523 5.27795i 0.111468 0.0219915i
241241 −370.100 −1.53568 −0.767842 0.640639i 0.778670π-0.778670\pi
−0.767842 + 0.640639i 0.778670π0.778670\pi
242242 −6.45285 241.914i −0.0266647 0.999644i
243243 169.524i 0.697631i
244244 −21.0961 + 353.034i −0.0864592 + 1.44686i
245245 −77.0640 + 55.9903i −0.314547 + 0.228532i
246246 6.25816 + 3.42764i 0.0254397 + 0.0139335i
247247 44.8904 14.5858i 0.181743 0.0590518i
248248 181.446 + 217.235i 0.731637 + 0.875947i
249249 −25.2136 18.3188i −0.101260 0.0735694i
250250 −15.3326 16.2761i −0.0613302 0.0651045i
251251 −125.908 40.9099i −0.501624 0.162988i 0.0472655 0.998882i 0.484949π-0.484949\pi
−0.548890 + 0.835895i 0.684949π0.684949\pi
252252 81.1371 + 311.930i 0.321972 + 1.23782i
253253 −62.9942 + 78.1223i −0.248989 + 0.308784i
254254 9.22880 1.18062i 0.0363339 0.00464812i
255255 −2.65169 0.861586i −0.0103988 0.00337877i
256256 19.2885 + 255.272i 0.0753456 + 0.997157i
257257 −250.554 182.038i −0.974917 0.708319i −0.0183500 0.999832i 0.505841π-0.505841\pi
−0.956567 + 0.291513i 0.905841π0.905841\pi
258258 33.3372 15.7514i 0.129214 0.0610520i
259259 482.742 156.852i 1.86387 0.605608i
260260 25.9885 + 10.1951i 0.0999557 + 0.0392119i
261261 −338.120 + 245.659i −1.29548 + 0.941222i
262262 −87.0799 + 460.423i −0.332366 + 1.75734i
263263 189.659i 0.721138i −0.932733 0.360569i 0.882583π-0.882583\pi
0.932733 0.360569i 0.117417π-0.117417\pi
264264 −38.4802 + 54.9336i −0.145758 + 0.208082i
265265 83.6441 0.315638
266266 −284.429 53.7942i −1.06928 0.202234i
267267 52.1202 + 71.7373i 0.195207 + 0.268679i
268268 84.8942 216.405i 0.316769 0.807482i
269269 −102.424 315.227i −0.380757 1.17185i −0.939512 0.342516i 0.888721π-0.888721\pi
0.558755 0.829333i 0.311279π-0.311279\pi
270270 25.3643 + 53.6824i 0.0939417 + 0.198824i
271271 15.6229 21.5031i 0.0576491 0.0793471i −0.779219 0.626752i 0.784384π-0.784384\pi
0.836868 + 0.547405i 0.184384π0.184384\pi
272272 10.9960 23.7544i 0.0404263 0.0873325i
273273 7.03553 21.6531i 0.0257712 0.0793155i
274274 15.4287 + 120.605i 0.0563093 + 0.440164i
275275 54.9305 + 2.76448i 0.199747 + 0.0100527i
276276 26.9180 7.00172i 0.0975290 0.0253685i
277277 94.9161 292.122i 0.342657 1.05459i −0.620169 0.784469i 0.712936π-0.712936\pi
0.962826 0.270123i 0.0870642π-0.0870642\pi
278278 −10.6643 + 10.0460i −0.0383607 + 0.0361368i
279279 −175.085 + 240.983i −0.627544 + 0.863740i
280280 −109.753 131.401i −0.391975 0.469290i
281281 52.6783 + 162.127i 0.187467 + 0.576965i 0.999982 0.00597528i 0.00190200π-0.00190200\pi
−0.812515 + 0.582941i 0.801902π0.801902\pi
282282 8.59202 15.6872i 0.0304681 0.0556285i
283283 −219.344 301.901i −0.775066 1.06679i −0.995809 0.0914550i 0.970848π-0.970848\pi
0.220743 0.975332i 0.429152π-0.429152\pi
284284 398.960 + 23.8405i 1.40479 + 0.0839454i
285285 −25.7728 −0.0904308
286286 −63.4807 + 26.1766i −0.221961 + 0.0915265i
287287 44.8008i 0.156100i
288288 −255.563 + 85.2655i −0.887371 + 0.296061i
289289 231.641 168.297i 0.801524 0.582342i
290290 106.646 194.712i 0.367743 0.671422i
291291 32.2927 10.4925i 0.110972 0.0360568i
292292 −79.1381 123.839i −0.271021 0.424105i
293293 −253.670 184.302i −0.865769 0.629018i 0.0636796 0.997970i 0.479716π-0.479716\pi
−0.929448 + 0.368953i 0.879716π0.879716\pi
294294 −47.2664 + 44.5263i −0.160770 + 0.151450i
295295 −119.418 38.8013i −0.404807 0.131530i
296296 158.047 + 393.743i 0.533944 + 1.33021i
297297 −136.447 52.0523i −0.459416 0.175260i
298298 18.1156 + 141.608i 0.0607905 + 0.475193i
299299 27.0817 + 8.79939i 0.0905744 + 0.0294294i
300300 −11.7756 9.67941i −0.0392521 0.0322647i
301301 −187.290 136.074i −0.622225 0.452073i
302302 38.4798 + 81.4409i 0.127417 + 0.269672i
303303 −89.5461 + 29.0953i −0.295532 + 0.0960240i
304304 28.8148 240.241i 0.0947855 0.790266i
305305 159.946 116.207i 0.524412 0.381008i
306306 27.0675 + 5.11928i 0.0884559 + 0.0167297i
307307 265.822i 0.865871i −0.901425 0.432935i 0.857478π-0.857478\pi
0.901425 0.432935i 0.142522π-0.142522\pi
308308 418.571 + 46.2167i 1.35900 + 0.150054i
309309 −149.561 −0.484018
310310 29.4041 155.470i 0.0948519 0.501516i
311311 197.511 + 271.850i 0.635082 + 0.874116i 0.998341 0.0575722i 0.0183359π-0.0183359\pi
−0.363259 + 0.931688i 0.618336π0.618336\pi
312312 18.4550 + 4.64572i 0.0591507 + 0.0148901i
313313 −104.875 322.772i −0.335064 1.03122i −0.966690 0.255949i 0.917612π-0.917612\pi
0.631626 0.775273i 0.282388π-0.282388\pi
314314 −482.149 + 227.809i −1.53551 + 0.725508i
315315 105.905 145.766i 0.336207 0.462749i
316316 230.320 + 189.320i 0.728860 + 0.599113i
317317 −11.9209 + 36.6887i −0.0376053 + 0.115737i −0.968097 0.250576i 0.919380π-0.919380\pi
0.930492 + 0.366313i 0.119380π0.119380\pi
318318 56.5592 7.23550i 0.177859 0.0227531i
319319 142.425 + 527.159i 0.446474 + 1.65254i
320320 103.392 98.9447i 0.323101 0.309202i
321321 −11.2849 + 34.7314i −0.0351555 + 0.108198i
322322 −119.745 127.115i −0.371880 0.394766i
323323 −14.5422 + 20.0157i −0.0450224 + 0.0619680i
324324 −141.412 221.288i −0.436458 0.682988i
325325 −4.82249 14.8421i −0.0148384 0.0456680i
326326 136.314 + 74.6604i 0.418142 + 0.229020i
327327 5.19386 + 7.14874i 0.0158834 + 0.0218616i
328328 37.3625 2.52773i 0.113910 0.00770650i
329329 −112.301 −0.341342
330330 37.3825 2.88236i 0.113280 0.00873443i
331331 276.676i 0.835878i 0.908475 + 0.417939i 0.137247π0.137247\pi
−0.908475 + 0.417939i 0.862753π0.862753\pi
332332 −163.274 9.75667i −0.491788 0.0293876i
333333 −361.231 + 262.450i −1.08478 + 0.788137i
334334 −65.9199 36.1049i −0.197365 0.108098i
335335 −123.590 + 40.1567i −0.368924 + 0.119871i
336336 −85.5804 79.3579i −0.254704 0.236184i
337337 28.3271 + 20.5808i 0.0840567 + 0.0610707i 0.629020 0.777389i 0.283456π-0.283456\pi
−0.544963 + 0.838460i 0.683456π0.683456\pi
338338 −218.405 231.845i −0.646167 0.685933i
339339 −96.7892 31.4487i −0.285514 0.0927691i
340340 −14.1616 + 3.68361i −0.0416518 + 0.0108342i
341341 212.642 + 325.957i 0.623584 + 0.955887i
342342 252.580 32.3121i 0.738539 0.0944798i
343343 −58.2556 18.9284i −0.169841 0.0551848i
344344 102.914 163.872i 0.299170 0.476371i
345345 −12.5789 9.13909i −0.0364605 0.0264901i
346346 −544.309 + 257.179i −1.57315 + 0.743292i
347347 254.573 82.7158i 0.733640 0.238374i 0.0817130 0.996656i 0.473961π-0.473961\pi
0.651927 + 0.758282i 0.273961π0.273961\pi
348348 55.2692 140.888i 0.158819 0.404849i
349349 −81.7493 + 59.3944i −0.234239 + 0.170184i −0.698713 0.715402i 0.746243π-0.746243\pi
0.464474 + 0.885587i 0.346243π0.346243\pi
350350 −17.7859 + 94.0407i −0.0508170 + 0.268688i
351351 41.4374i 0.118055i
352352 −14.9269 + 351.683i −0.0424060 + 0.999100i
353353 265.736 0.752792 0.376396 0.926459i 0.377163π-0.377163\pi
0.376396 + 0.926459i 0.377163π0.377163\pi
354354 −84.1056 15.9069i −0.237586 0.0449348i
355355 −131.325 180.753i −0.369930 0.509165i
356356 433.228 + 169.952i 1.21693 + 0.477394i
357357 3.68775 + 11.3497i 0.0103298 + 0.0317919i
358358 267.340 + 565.815i 0.746761 + 1.58049i
359359 338.315 465.651i 0.942383 1.29708i −0.0124461 0.999923i 0.503962π-0.503962\pi
0.954829 0.297156i 0.0960382π-0.0960382\pi
360360 127.540 + 80.0975i 0.354278 + 0.222493i
361361 40.8845 125.829i 0.113253 0.348558i
362362 −60.5950 473.665i −0.167389 1.30847i
363363 −61.4233 + 68.7896i −0.169210 + 0.189503i
364364 −30.0796 115.641i −0.0826363 0.317694i
365365 −25.3877 + 78.1353i −0.0695553 + 0.214069i
366366 98.1011 92.4139i 0.268036 0.252497i
367367 −220.806 + 303.914i −0.601652 + 0.828103i −0.995858 0.0909189i 0.971020π-0.971020\pi
0.394206 + 0.919022i 0.371020π0.371020\pi
368368 99.2536 107.036i 0.269711 0.290859i
369369 12.1783 + 37.4809i 0.0330035 + 0.101574i
370370 113.935 208.021i 0.307932 0.562219i
371371 −210.434 289.638i −0.567208 0.780695i
372372 6.43402 107.671i 0.0172957 0.289437i
373373 569.644 1.52719 0.763597 0.645693i 0.223431π-0.223431\pi
0.763597 + 0.645693i 0.223431π0.223431\pi
374374 18.8545 30.6584i 0.0504130 0.0819742i
375375 8.52124i 0.0227233i
376376 −6.33623 93.6561i −0.0168517 0.249085i
377377 125.350 91.0721i 0.332493 0.241571i
378378 122.076 222.886i 0.322953 0.589645i
379379 −338.309 + 109.923i −0.892635 + 0.290035i −0.719194 0.694810i 0.755489π-0.755489\pi
−0.173441 + 0.984844i 0.555489π0.555489\pi
380380 −113.976 + 72.8356i −0.299938 + 0.191673i
381381 −2.86844 2.08404i −0.00752871 0.00546993i
382382 448.807 422.788i 1.17489 1.10678i
383383 −476.382 154.786i −1.24382 0.404140i −0.388115 0.921611i 0.626874π-0.626874\pi
−0.855701 + 0.517471i 0.826874π0.826874\pi
384384 61.3535 75.8490i 0.159775 0.197524i
385385 −128.623 197.165i −0.334086 0.512117i
386386 86.9047 + 679.325i 0.225142 + 1.75991i
387387 193.678 + 62.9299i 0.500461 + 0.162610i
388388 113.157 137.663i 0.291642 0.354802i
389389 −546.381 396.969i −1.40458 1.02049i −0.994083 0.108623i 0.965356π-0.965356\pi
−0.410495 0.911863i 0.634644π-0.634644\pi
390390 −4.54480 9.61889i −0.0116533 0.0246638i
391391 −14.1952 + 4.61230i −0.0363049 + 0.0117962i
392392 −83.1946 + 330.489i −0.212231 + 0.843084i
393393 144.465 104.960i 0.367596 0.267074i
394394 609.319 + 115.241i 1.54650 + 0.292489i
395395 166.667i 0.421942i
396396 −362.745 + 75.1155i −0.916023 + 0.189686i
397397 −25.3917 −0.0639590 −0.0319795 0.999489i 0.510181π-0.510181\pi
−0.0319795 + 0.999489i 0.510181π0.510181\pi
398398 102.292 540.856i 0.257015 1.35893i
399399 64.8399 + 89.2445i 0.162506 + 0.223670i
400400 −79.4307 9.52702i −0.198577 0.0238176i
401401 −3.42431 10.5389i −0.00853942 0.0262816i 0.946696 0.322128i 0.104398π-0.104398\pi
−0.955235 + 0.295847i 0.904398π0.904398\pi
402402 −80.0961 + 37.8444i −0.199244 + 0.0941403i
403403 64.9084 89.3388i 0.161063 0.221684i
404404 −313.779 + 381.733i −0.776681 + 0.944883i
405405 −45.3654 + 139.620i −0.112013 + 0.344741i
406406 −942.541 + 120.577i −2.32153 + 0.296989i
407407 152.160 + 563.190i 0.373857 + 1.38376i
408408 −9.25727 + 3.71584i −0.0226894 + 0.00910746i
409409 81.7829 251.702i 0.199958 0.615408i −0.799925 0.600101i 0.795127π-0.795127\pi
0.999883 0.0153078i 0.00487281π-0.00487281\pi
410410 −14.3543 15.2377i −0.0350105 0.0371651i
411411 27.2349 37.4857i 0.0662651 0.0912060i
412412 −661.413 + 422.671i −1.60537 + 1.02590i
413413 166.077 + 511.132i 0.402123 + 1.23761i
414414 134.734 + 73.7951i 0.325445 + 0.178249i
415415 53.7445 + 73.9729i 0.129505 + 0.178248i
416416 94.7437 31.6101i 0.227749 0.0759859i
417417 5.58319 0.0133889
418418 78.1804 323.383i 0.187035 0.773642i
419419 179.325i 0.427983i −0.976836 0.213992i 0.931353π-0.931353\pi
0.976836 0.213992i 0.0686465π-0.0686465\pi
420420 −3.89181 + 65.1278i −0.00926621 + 0.155066i
421421 360.024 261.573i 0.855163 0.621312i −0.0714016 0.997448i 0.522747π-0.522747\pi
0.926565 + 0.376135i 0.122747π0.122747\pi
422422 −292.049 159.958i −0.692060 0.379046i
423423 93.9528 30.5271i 0.222111 0.0721682i
424424 229.677 191.838i 0.541690 0.452448i
425425 6.61777 + 4.80809i 0.0155712 + 0.0113131i
426426 −104.436 110.863i −0.245155 0.260242i
427427 −804.793 261.493i −1.88476 0.612396i
428428 48.2474 + 185.486i 0.112728 + 0.433380i
429429 24.4487 + 9.32681i 0.0569900 + 0.0217408i
430430 −107.300 + 13.7266i −0.249534 + 0.0319224i
431431 200.900 + 65.2764i 0.466125 + 0.151453i 0.532657 0.846331i 0.321193π-0.321193\pi
−0.0665320 + 0.997784i 0.521193π0.521193\pi
432432 192.768 + 89.2324i 0.446222 + 0.206557i
433433 292.628 + 212.607i 0.675816 + 0.491009i 0.871967 0.489565i 0.162844π-0.162844\pi
−0.196151 + 0.980574i 0.562844π0.562844\pi
434434 −612.328 + 289.317i −1.41089 + 0.666630i
435435 −80.4612 + 26.1434i −0.184968 + 0.0600999i
436436 43.1719 + 16.9360i 0.0990181 + 0.0388441i
437437 −111.619 + 81.0958i −0.255421 + 0.185574i
438438 −10.4079 + 55.0303i −0.0237623 + 0.125640i
439439 568.506i 1.29500i −0.762064 0.647502i 0.775814π-0.775814\pi
0.762064 0.647502i 0.224186π-0.224186\pi
440440 157.173 118.392i 0.357211 0.269073i
441441 −358.654 −0.813273
442442 −10.0346 1.89785i −0.0227028 0.00429378i
443443 −320.253 440.790i −0.722919 0.995012i −0.999422 0.0339992i 0.989176π-0.989176\pi
0.276503 0.961013i 0.410824π-0.410824\pi
444444 59.0468 150.517i 0.132988 0.339003i
445445 −80.3909 247.418i −0.180654 0.555995i
446446 −228.367 483.329i −0.512033 1.08370i
447447 31.9777 44.0136i 0.0715386 0.0984644i
448448 −602.737 109.092i −1.34540 0.243510i
449449 −114.167 + 351.370i −0.254270 + 0.782561i 0.739703 + 0.672933i 0.234966π0.234966\pi
−0.993973 + 0.109628i 0.965034π0.965034\pi
450450 −10.6833 83.5105i −0.0237407 0.185579i
451451 51.4258 + 2.58810i 0.114026 + 0.00573859i
452452 −516.912 + 134.456i −1.14361 + 0.297468i
453453 10.6072 32.6455i 0.0234154 0.0720651i
454454 189.642 178.648i 0.417713 0.393497i
455455 −39.2618 + 54.0392i −0.0862897 + 0.118768i
456456 −70.7689 + 59.1099i −0.155195 + 0.129627i
457457 74.5127 + 229.327i 0.163048 + 0.501809i 0.998887 0.0471650i 0.0150187π-0.0150187\pi
−0.835840 + 0.548974i 0.815019π0.815019\pi
458458 −264.454 + 482.837i −0.577410 + 1.05423i
459459 −12.7666 17.5717i −0.0278140 0.0382827i
460460 −81.4559 4.86752i −0.177078 0.0105816i
461461 −81.6794 −0.177179 −0.0885894 0.996068i 0.528236π-0.528236\pi
−0.0885894 + 0.996068i 0.528236π0.528236\pi
462462 −104.029 122.194i −0.225171 0.264490i
463463 196.860i 0.425183i 0.977141 + 0.212592i 0.0681904π0.0681904\pi
−0.977141 + 0.212592i 0.931810π0.931810\pi
464464 −153.738 779.249i −0.331331 1.67942i
465465 −48.7813 + 35.4417i −0.104906 + 0.0762187i
466466 365.669 667.635i 0.784697 1.43269i
467467 276.586 89.8681i 0.592261 0.192437i 0.00247492 0.999997i 0.499212π-0.499212\pi
0.589786 + 0.807560i 0.299212π0.299212\pi
468468 56.5998 + 88.5699i 0.120940 + 0.189252i
469469 449.983 + 326.931i 0.959451 + 0.697082i
470470 −38.1961 + 35.9817i −0.0812682 + 0.0765569i
471471 193.269 + 62.7969i 0.410338 + 0.133327i
472472 −416.898 + 167.342i −0.883259 + 0.354538i
473473 167.016 207.125i 0.353099 0.437896i
474474 −14.4173 112.698i −0.0304162 0.237760i
475475 71.9126 + 23.3658i 0.151395 + 0.0491912i
476476 48.3836 + 39.7706i 0.101646 + 0.0835518i
477477 254.785 + 185.112i 0.534141 + 0.388076i
478478 50.3591 + 106.583i 0.105354 + 0.222977i
479479 −372.369 + 120.990i −0.777388 + 0.252589i −0.670725 0.741706i 0.734017π-0.734017\pi
−0.106663 + 0.994295i 0.534017π0.534017\pi
480480 −54.5342 + 0.428963i −0.113613 + 0.000893673i
481481 133.918 97.2969i 0.278415 0.202280i
482482 727.306 + 137.556i 1.50893 + 0.285385i
483483 66.5498i 0.137784i
484484 −77.2316 + 477.798i −0.159570 + 0.987187i
485485 −99.6175 −0.205397
486486 −63.0074 + 333.143i −0.129645 + 0.685479i
487487 256.315 + 352.787i 0.526314 + 0.724409i 0.986563 0.163381i 0.0522400π-0.0522400\pi
−0.460249 + 0.887790i 0.652240π0.652240\pi
488488 172.670 685.927i 0.353831 1.40559i
489489 −18.3025 56.3293i −0.0374284 0.115193i
490490 172.253 81.3875i 0.351537 0.166097i
491491 −561.929 + 773.429i −1.14446 + 1.57521i −0.387337 + 0.921938i 0.626605π0.626605\pi
−0.757122 + 0.653274i 0.773395π0.773395\pi
492492 −11.0243 9.06185i −0.0224072 0.0184184i
493493 −25.0965 + 77.2392i −0.0509058 + 0.156672i
494494 −93.6381 + 11.9789i −0.189551 + 0.0242488i
495495 161.204 + 129.987i 0.325664 + 0.262600i
496496 −275.831 494.340i −0.556110 0.996653i
497497 −295.511 + 909.490i −0.594590 + 1.82996i
498498 42.7403 + 45.3706i 0.0858239 + 0.0911055i
499499 −87.5613 + 120.518i −0.175474 + 0.241519i −0.887690 0.460441i 0.847691π-0.847691\pi
0.712217 + 0.701960i 0.247691π0.247691\pi
500500 24.0816 + 37.6839i 0.0481632 + 0.0753678i
501501 8.85087 + 27.2402i 0.0176664 + 0.0543716i
502502 232.224 + 127.191i 0.462597 + 0.253368i
503503 −168.942 232.529i −0.335870 0.462285i 0.607360 0.794427i 0.292229π-0.292229\pi
−0.943229 + 0.332142i 0.892229π0.892229\pi
504504 −43.5118 643.150i −0.0863330 1.27609i
505505 276.234 0.546999
506506 152.830 130.110i 0.302035 0.257134i
507507 121.381i 0.239410i
508508 −18.5749 1.10997i −0.0365647 0.00218498i
509509 −79.7845 + 57.9668i −0.156747 + 0.113884i −0.663394 0.748270i 0.730885π-0.730885\pi
0.506647 + 0.862154i 0.330885π0.330885\pi
510510 4.89077 + 2.67871i 0.00958975 + 0.00525238i
511511 334.433 108.664i 0.654469 0.212650i
512512 56.9725 508.820i 0.111274 0.993790i
513513 −162.428 118.011i −0.316623 0.230040i
514514 424.720 + 450.857i 0.826304 + 0.877155i
515515 417.314 + 135.594i 0.810319 + 0.263289i
516516 −71.3674 + 18.5636i −0.138309 + 0.0359759i
517517 6.48756 128.908i 0.0125485 0.249339i
518518 −1006.96 + 128.819i −1.94395 + 0.248685i
519519 218.185 + 70.8928i 0.420396 + 0.136595i
520520 −47.2823 29.6942i −0.0909276 0.0571042i
521521 267.153 + 194.098i 0.512770 + 0.372549i 0.813874 0.581042i 0.197355π-0.197355\pi
−0.301103 + 0.953592i 0.597355π0.597355\pi
522522 755.766 357.090i 1.44783 0.684080i
523523 836.001 271.633i 1.59847 0.519375i 0.631744 0.775177i 0.282339π-0.282339\pi
0.966729 + 0.255802i 0.0823395π0.0823395\pi
524524 342.252 872.440i 0.653153 1.66496i
525525 29.5069 21.4380i 0.0562035 0.0408343i
526526 −70.4910 + 372.711i −0.134013 + 0.708576i
527527 57.8825i 0.109834i
528528 96.0371 93.6514i 0.181888 0.177370i
529529 445.766 0.842657
530530 −164.374 31.0881i −0.310140 0.0586569i
531531 −277.884 382.475i −0.523322 0.720291i
532532 538.956 + 211.429i 1.01307 + 0.397422i
533533 −4.51481 13.8951i −0.00847055 0.0260697i
534534 −75.7619 160.347i −0.141876 0.300275i
535535 62.9756 86.6784i 0.117711 0.162016i
536536 −247.262 + 393.718i −0.461311 + 0.734549i
537537 73.6938 226.806i 0.137232 0.422358i
538538 84.1178 + 657.541i 0.156353 + 1.22219i
539539 −167.023 + 437.823i −0.309875 + 0.812287i
540540 −29.8926 114.922i −0.0553567 0.212818i
541541 236.223 727.020i 0.436641 1.34384i −0.454754 0.890617i 0.650273π-0.650273\pi
0.891395 0.453227i 0.149727π-0.149727\pi
542542 −38.6936 + 36.4504i −0.0713904 + 0.0672517i
543543 −106.963 + 147.222i −0.196985 + 0.271126i
544544 −30.4377 + 42.5944i −0.0559516 + 0.0782986i
545545 −8.01109 24.6556i −0.0146992 0.0452396i
546546 −21.8738 + 39.9370i −0.0400619 + 0.0731447i
547547 −219.118 301.590i −0.400581 0.551353i 0.560308 0.828284i 0.310683π-0.310683\pi
−0.960890 + 0.276931i 0.910683π0.910683\pi
548548 14.5055 242.743i 0.0264698 0.442961i
549549 744.382 1.35589
550550 −106.920 25.8488i −0.194400 0.0469977i
551551 750.717i 1.36246i
552552 −55.5006 + 3.75485i −0.100544 + 0.00680226i
553553 −577.125 + 419.306i −1.04363 + 0.758238i
554554 −295.099 + 538.789i −0.532669 + 0.972543i
555555 −85.9608 + 27.9303i −0.154884 + 0.0503249i
556556 24.6908 15.7785i 0.0444080 0.0283785i
557557 90.6342 + 65.8496i 0.162719 + 0.118222i 0.666165 0.745805i 0.267935π-0.267935\pi
−0.503446 + 0.864027i 0.667935π0.667935\pi
558558 433.636 408.497i 0.777126 0.732074i
559559 −71.8016 23.3297i −0.128446 0.0417348i
560560 166.845 + 299.016i 0.297937 + 0.533958i
561561 −13.2411 + 3.57742i −0.0236027 + 0.00637687i
562562 −43.2634 338.185i −0.0769811 0.601753i
563563 846.470 + 275.035i 1.50350 + 0.488517i 0.941036 0.338306i 0.109854π-0.109854\pi
0.562463 + 0.826822i 0.309854π0.309854\pi
564564 −22.7152 + 27.6345i −0.0402752 + 0.0489974i
565565 241.555 + 175.500i 0.427531 + 0.310619i
566566 318.838 + 674.808i 0.563318 + 1.19224i
567567 597.600 194.172i 1.05397 0.342455i
568568 −775.161 195.133i −1.36472 0.343543i
569569 −443.404 + 322.152i −0.779268 + 0.566172i −0.904759 0.425923i 0.859949π-0.859949\pi
0.125491 + 0.992095i 0.459949π0.459949\pi
570570 50.6477 + 9.57901i 0.0888555 + 0.0168053i
571571 546.540i 0.957163i −0.878043 0.478581i 0.841151π-0.841151\pi
0.878043 0.478581i 0.158849π-0.158849\pi
572572 134.479 27.8473i 0.235103 0.0486840i
573573 −234.969 −0.410068
574574 −16.6512 + 88.0407i −0.0290090 + 0.153381i
575575 26.8127 + 36.9045i 0.0466307 + 0.0641817i
576576 533.913 72.5751i 0.926932 0.125999i
577577 262.876 + 809.048i 0.455590 + 1.40216i 0.870441 + 0.492273i 0.163834π0.163834\pi
−0.414850 + 0.909890i 0.636166π0.636166\pi
578578 −517.762 + 244.636i −0.895783 + 0.423246i
579579 153.405 211.144i 0.264948 0.364670i
580580 −281.945 + 343.004i −0.486112 + 0.591387i
581581 120.937 372.207i 0.208154 0.640631i
582582 −67.3602 + 8.61725i −0.115739 + 0.0148063i
583583 344.626 224.821i 0.591125 0.385627i
584584 109.492 + 272.777i 0.187486 + 0.467083i
585585 18.1573 55.8826i 0.0310382 0.0955258i
586586 430.003 + 456.466i 0.733794 + 0.778952i
587587 −141.943 + 195.368i −0.241811 + 0.332825i −0.912622 0.408804i 0.865946π-0.865946\pi
0.670811 + 0.741628i 0.265946π0.265946\pi
588588 109.435 69.9337i 0.186115 0.118935i
589589 165.339 + 508.860i 0.280711 + 0.863938i
590590 220.255 + 120.635i 0.373313 + 0.204466i
591591 −138.903 191.184i −0.235031 0.323493i
592592 −164.246 832.510i −0.277442 1.40627i
593593 542.114 0.914189 0.457094 0.889418i 0.348890π-0.348890\pi
0.457094 + 0.889418i 0.348890π0.348890\pi
594594 248.793 + 153.005i 0.418844 + 0.257583i
595595 35.0120i 0.0588436i
596596 17.0315 285.015i 0.0285763 0.478213i
597597 −169.703 + 123.296i −0.284259 + 0.206526i
598598 −49.9495 27.3577i −0.0835276 0.0457487i
599599 −224.218 + 72.8527i −0.374320 + 0.121624i −0.490134 0.871647i 0.663052π-0.663052\pi
0.115814 + 0.993271i 0.463052π0.463052\pi
600600 19.5435 + 23.3983i 0.0325725 + 0.0389971i
601601 123.566 + 89.7761i 0.205601 + 0.149378i 0.685821 0.727770i 0.259443π-0.259443\pi
−0.480220 + 0.877148i 0.659443π0.659443\pi
602602 317.480 + 337.018i 0.527375 + 0.559830i
603603 −465.332 151.195i −0.771695 0.250739i
604604 −45.3497 174.346i −0.0750823 0.288653i
605605 233.752 136.254i 0.386367 0.225212i
606606 186.786 23.8952i 0.308228 0.0394310i
607607 2.97708 + 0.967311i 0.00490457 + 0.00159359i 0.311468 0.950257i 0.399179π-0.399179\pi
−0.306564 + 0.951850i 0.599179π0.599179\pi
608608 −145.916 + 461.402i −0.239994 + 0.758886i
609609 292.955 + 212.844i 0.481042 + 0.349498i
610610 −357.510 + 168.919i −0.586082 + 0.276916i
611611 −34.8307 + 11.3172i −0.0570061 + 0.0185224i
612612 −51.2893 20.1204i −0.0838061 0.0328765i
613613 −162.834 + 118.306i −0.265635 + 0.192995i −0.712627 0.701543i 0.752495π-0.752495\pi
0.446993 + 0.894538i 0.352495π0.352495\pi
614614 −98.7986 + 522.384i −0.160910 + 0.850788i
615615 7.97757i 0.0129717i
616616 −805.382 246.394i −1.30744 0.399991i
617617 −463.153 −0.750654 −0.375327 0.926893i 0.622470π-0.622470\pi
−0.375327 + 0.926893i 0.622470π0.622470\pi
618618 293.912 + 55.5877i 0.475586 + 0.0899478i
619619 169.667 + 233.527i 0.274099 + 0.377265i 0.923768 0.382952i 0.125093π-0.125093\pi
−0.649669 + 0.760217i 0.725093π0.725093\pi
620620 −115.568 + 294.595i −0.186399 + 0.475153i
621621 −37.4289 115.194i −0.0602720 0.185498i
622622 −287.101 607.638i −0.461578 0.976911i
623623 −654.495 + 900.835i −1.05055 + 1.44596i
624624 −34.5404 15.9888i −0.0553532 0.0256231i
625625 7.72542 23.7764i 0.0123607 0.0380423i
626626 86.1312 + 673.279i 0.137590 + 1.07553i
627627 −106.188 + 69.2727i −0.169358 + 0.110483i
628628 1032.17 268.481i 1.64359 0.427518i
629629 −26.8119 + 82.5185i −0.0426262 + 0.131190i
630630 −262.298 + 247.092i −0.416346 + 0.392209i
631631 −31.4364 + 43.2685i −0.0498199 + 0.0685713i −0.833200 0.552972i 0.813494π-0.813494\pi
0.783380 + 0.621543i 0.213494π0.213494\pi
632632 −382.251 457.647i −0.604828 0.724125i
633633 39.2125 + 120.684i 0.0619471 + 0.190654i
634634 37.0626 67.6686i 0.0584584 0.106733i
635635 6.11426 + 8.41556i 0.00962875 + 0.0132528i
636636 −113.837 6.80251i −0.178989 0.0106958i
637637 132.962 0.208732
638638 −83.9583 1088.89i −0.131596 1.70672i
639639 841.221i 1.31646i
640640 −239.957 + 156.014i −0.374933 + 0.243773i
641641 708.110 514.472i 1.10470 0.802609i 0.122876 0.992422i 0.460788π-0.460788\pi
0.981820 + 0.189813i 0.0607883π0.0607883\pi
642642 35.0854 64.0585i 0.0546501 0.0997797i
643643 1023.68 332.614i 1.59204 0.517284i 0.626916 0.779087i 0.284317π-0.284317\pi
0.965121 + 0.261803i 0.0843169π0.0843169\pi
644644 188.074 + 294.307i 0.292041 + 0.456998i
645645 33.3502 + 24.2304i 0.0517058 + 0.0375665i
646646 36.0171 33.9291i 0.0557540 0.0525218i
647647 −215.802 70.1183i −0.333542 0.108374i 0.137458 0.990508i 0.456107π-0.456107\pi
−0.471000 + 0.882133i 0.656107π0.656107\pi
648648 195.651 + 487.426i 0.301931 + 0.752200i
649649 −596.311 + 161.108i −0.918815 + 0.248241i
650650 3.96059 + 30.9595i 0.00609321 + 0.0476300i
651651 245.451 + 79.7519i 0.377037 + 0.122507i
652652 −240.130 197.384i −0.368298 0.302736i
653653 −495.163 359.757i −0.758289 0.550929i 0.140096 0.990138i 0.455259π-0.455259\pi
−0.898385 + 0.439208i 0.855259π0.855259\pi
654654 −7.54980 15.9788i −0.0115440 0.0244325i
655655 −498.253 + 161.892i −0.760691 + 0.247164i
656656 −74.3629 8.91918i −0.113358 0.0135963i
657657 −250.253 + 181.820i −0.380903 + 0.276742i
658658 220.690 + 41.7392i 0.335396 + 0.0634335i
659659 312.111i 0.473613i −0.971557 0.236807i 0.923899π-0.923899\pi
0.971557 0.236807i 0.0761008π-0.0761008\pi
660660 −74.5339 8.22970i −0.112930 0.0124692i
661661 −101.013 −0.152819 −0.0764095 0.997077i 0.524346π-0.524346\pi
−0.0764095 + 0.997077i 0.524346π0.524346\pi
662662 102.832 543.712i 0.155336 0.821318i
663663 2.28754 + 3.14853i 0.00345029 + 0.00474892i
664664 317.233 + 79.8576i 0.477760 + 0.120268i
665665 −100.010 307.799i −0.150391 0.462856i
666666 807.422 381.497i 1.21235 0.572818i
667667 −266.206 + 366.401i −0.399109 + 0.549327i
668668 116.124 + 95.4525i 0.173839 + 0.142893i
669669 −62.9505 + 193.742i −0.0940965 + 0.289599i
670670 257.799 32.9796i 0.384774 0.0492233i
671671 346.654 908.698i 0.516623 1.35424i
672672 138.684 + 187.759i 0.206375 + 0.279403i
673673 125.465 386.143i 0.186427 0.573763i −0.813543 0.581505i 0.802464π-0.802464\pi
0.999970 + 0.00774135i 0.00246417π0.00246417\pi
674674 −48.0180 50.9731i −0.0712433 0.0756277i
675675 −39.0178 + 53.7033i −0.0578041 + 0.0795605i
676676 343.030 + 536.788i 0.507441 + 0.794065i
677677 −169.613 522.014i −0.250536 0.771070i −0.994676 0.103047i 0.967141π-0.967141\pi
0.744141 0.668023i 0.232859π-0.232859\pi
678678 178.518 + 97.7756i 0.263301 + 0.144212i
679679 250.621 + 344.950i 0.369103 + 0.508026i
680680 29.1989 1.97543i 0.0429396 0.00290505i
681681 −99.2854 −0.145794
682682 −296.727 719.592i −0.435084 1.05512i
683683 914.777i 1.33935i 0.742654 + 0.669675i 0.233567π0.233567\pi
−0.742654 + 0.669675i 0.766433π0.766433\pi
684684 −508.371 30.3785i −0.743232 0.0444130i
685685 −109.977 + 79.9031i −0.160551 + 0.116647i
686686 107.446 + 58.8493i 0.156628 + 0.0857861i
687687 199.523 64.8291i 0.290427 0.0943655i
688688 −263.150 + 283.784i −0.382485 + 0.412477i
689689 −94.4554 68.6259i −0.137091 0.0996021i
690690 21.3228 + 22.6350i 0.0309026 + 0.0328043i
691691 −117.626 38.2189i −0.170225 0.0553095i 0.222665 0.974895i 0.428525π-0.428525\pi
−0.392890 + 0.919586i 0.628525π0.628525\pi
692692 1165.24 303.094i 1.68387 0.437997i
693693 44.5510 885.232i 0.0642872 1.27739i
694694 −531.020 + 67.9323i −0.765159 + 0.0978852i
695695 −15.5785 5.06177i −0.0224151 0.00728312i
696696 −160.977 + 256.325i −0.231288 + 0.368283i
697697 6.19554 + 4.50132i 0.00888887 + 0.00645814i
698698 182.726 86.3356i 0.261785 0.123690i
699699 −275.887 + 89.6413i −0.394689 + 0.128242i
700700 69.9045 178.195i 0.0998636 0.254564i
701701 431.259 313.328i 0.615205 0.446972i −0.236038 0.971744i 0.575849π-0.575849\pi
0.851243 + 0.524771i 0.175849π0.175849\pi
702702 15.4011 81.4312i 0.0219389 0.115999i
703703 802.028i 1.14087i
704704 160.045 685.567i 0.227336 0.973816i
705705 19.9972 0.0283649
706706 −522.213 98.7663i −0.739679 0.139896i
707707 −694.958 956.528i −0.982968 1.35294i
708708 159.369 + 62.5193i 0.225097 + 0.0883041i
709709 340.137 + 1046.83i 0.479742 + 1.47649i 0.839454 + 0.543431i 0.182875π0.182875\pi
−0.359712 + 0.933063i 0.617125π0.617125\pi
710710 190.894 + 404.019i 0.268865 + 0.569041i
711711 368.850 507.678i 0.518776 0.714034i
712712 −788.197 495.003i −1.10702 0.695228i
713713 −99.7464 + 306.988i −0.139897 + 0.430558i
714714 −3.02865 23.6747i −0.00424181 0.0331578i
715715 −59.7623 48.1896i −0.0835837 0.0673980i
716716 −315.070 1211.28i −0.440041 1.69173i
717717 13.8818 42.7237i 0.0193609 0.0595867i
718718 −837.914 + 789.338i −1.16701 + 1.09936i
719719 −595.573 + 819.736i −0.828335 + 1.14011i 0.159896 + 0.987134i 0.448884π0.448884\pi
−0.988231 + 0.152971i 0.951116π0.951116\pi
720720 −220.867 204.807i −0.306759 0.284455i
721721 −580.366 1786.18i −0.804946 2.47737i
722722 −127.112 + 232.080i −0.176055 + 0.321440i
723723 −165.800 228.205i −0.229323 0.315636i
724724 −56.9689 + 953.350i −0.0786863 + 1.31678i
725725 248.209 0.342357
726726 146.274 112.353i 0.201479 0.154757i
727727 1172.43i 1.61270i −0.591438 0.806350i 0.701440π-0.701440\pi
0.591438 0.806350i 0.298560π-0.298560\pi
728728 16.1310 + 238.432i 0.0221579 + 0.327517i
729729 −373.503 + 271.366i −0.512350 + 0.372244i
730730 78.9316 144.113i 0.108125 0.197414i
731731 37.6356 12.2285i 0.0514851 0.0167285i
732732 −227.132 + 145.147i −0.310290 + 0.198288i
733733 −618.263 449.195i −0.843470 0.612817i 0.0798680 0.996805i 0.474550π-0.474550\pi
−0.923338 + 0.383989i 0.874550π0.874550\pi
734734 546.876 515.172i 0.745063 0.701870i
735735 −69.0475 22.4349i −0.0939422 0.0305237i
736736 −234.832 + 173.454i −0.319065 + 0.235671i
737737 −401.273 + 497.639i −0.544468 + 0.675222i
738738 −10.0017 78.1824i −0.0135525 0.105938i
739739 598.384 + 194.427i 0.809721 + 0.263094i 0.684480 0.729032i 0.260029π-0.260029\pi
0.125242 + 0.992126i 0.460029π0.460029\pi
740740 −301.216 + 366.449i −0.407048 + 0.495201i
741741 29.1040 + 21.1453i 0.0392767 + 0.0285362i
742742 305.887 + 647.398i 0.412247 + 0.872504i
743743 −780.309 + 253.538i −1.05021 + 0.341235i −0.782752 0.622333i 0.786185π-0.786185\pi
−0.267462 + 0.963568i 0.586185π0.586185\pi
744744 −52.6620 + 209.199i −0.0707822 + 0.281181i
745745 −129.129 + 93.8178i −0.173328 + 0.125930i
746746 −1119.44 211.720i −1.50059 0.283807i
747747 344.268i 0.460867i
748748 −48.4469 + 53.2410i −0.0647686 + 0.0711778i
749749 −458.581 −0.612258
750750 3.16710 16.7456i 0.00422280 0.0223275i
751751 −118.603 163.244i −0.157927 0.217368i 0.722720 0.691141i 0.242892π-0.242892\pi
−0.880647 + 0.473773i 0.842892π0.842892\pi
752752 −22.3576 + 186.404i −0.0297308 + 0.247878i
753753 −31.1800 95.9621i −0.0414077 0.127440i
754754 −280.182 + 132.382i −0.371594 + 0.175573i
755755 −59.1933 + 81.4726i −0.0784018 + 0.107911i
756756 −322.740 + 392.634i −0.426905 + 0.519357i
757757 −66.7243 + 205.356i −0.0881431 + 0.271277i −0.985406 0.170220i 0.945552π-0.945552\pi
0.897263 + 0.441496i 0.145552π0.145552\pi
758758 705.686 90.2770i 0.930985 0.119099i
759759 −76.3910 3.84453i −0.100647 0.00506525i
760760 251.053 100.772i 0.330332 0.132595i
761761 161.955 498.446i 0.212818 0.654988i −0.786483 0.617612i 0.788100π-0.788100\pi
0.999301 0.0373757i 0.0118998π-0.0118998\pi
762762 4.86236 + 5.16160i 0.00638106 + 0.00677375i
763763 −65.2215 + 89.7696i −0.0854803 + 0.117654i
764764 −1039.12 + 664.038i −1.36010 + 0.869160i
765765 9.51737 + 29.2915i 0.0124410 + 0.0382895i
766766 878.637 + 481.236i 1.14705 + 0.628246i
767767 103.019 + 141.793i 0.134314 + 0.184867i
768768 −148.761 + 126.252i −0.193699 + 0.164391i
769769 −714.080 −0.928583 −0.464291 0.885683i 0.653691π-0.653691\pi
−0.464291 + 0.885683i 0.653691π0.653691\pi
770770 179.484 + 435.267i 0.233097 + 0.565282i
771771 236.043i 0.306151i
772772 81.7041 1367.28i 0.105834 1.77109i
773773 −346.430 + 251.696i −0.448163 + 0.325609i −0.788870 0.614560i 0.789334π-0.789334\pi
0.340707 + 0.940169i 0.389334π0.389334\pi
774774 −357.220 195.652i −0.461525 0.252781i
775775 168.244 54.6658i 0.217089 0.0705365i
776776 −273.538 + 228.473i −0.352497 + 0.294424i
777777 312.978 + 227.392i 0.402803 + 0.292654i
778778 926.185 + 983.183i 1.19047 + 1.26373i
779779 67.3244 + 21.8750i 0.0864241 + 0.0280809i
780780 5.35620 + 20.5918i 0.00686693 + 0.0263998i
781781 −1026.91 391.751i −1.31487 0.501602i
782782 29.6101 3.78796i 0.0378646 0.00484394i
783783 −626.798 203.659i −0.800508 0.260101i
784784 286.324 618.543i 0.365209 0.788958i
785785 −482.337 350.439i −0.614442 0.446419i
786786 −322.908 + 152.570i −0.410825 + 0.194110i
787787 −5.56864 + 1.80936i −0.00707578 + 0.00229906i −0.312553 0.949900i 0.601184π-0.601184\pi
0.305477 + 0.952199i 0.401184π0.401184\pi
788788 −1154.58 452.933i −1.46520 0.574788i
789789 116.944 84.9651i 0.148218 0.107687i
790790 −61.9454 + 327.528i −0.0784119 + 0.414592i
791791 1277.97i 1.61564i
792792 740.771 12.7920i 0.935317 0.0161515i
793793 −275.962 −0.347997
794794 49.8989 + 9.43739i 0.0628449 + 0.0118859i
795795 37.4715 + 51.5752i 0.0471340 + 0.0648744i
796796 −402.041 + 1024.85i −0.505077 + 1.28750i
797797 88.5703 + 272.591i 0.111130 + 0.342022i 0.991120 0.132969i 0.0424512π-0.0424512\pi
−0.879991 + 0.474991i 0.842451π0.842451\pi
798798 −94.2513 199.479i −0.118109 0.249974i
799799 11.2834 15.5303i 0.0141219 0.0194371i
800800 152.553 + 48.2443i 0.190692 + 0.0603053i
801801 302.683 931.563i 0.377882 1.16300i
802802 2.81230 + 21.9834i 0.00350660 + 0.0274108i
803803 105.413 + 390.166i 0.131274 + 0.485886i
804804 171.467 44.6009i 0.213268 0.0554737i
805805 60.3346 185.691i 0.0749498 0.230672i
806806 −160.760 + 151.440i −0.199454 + 0.187891i
807807 148.485 204.373i 0.183997 0.253250i
808808 758.506 633.544i 0.938745 0.784089i
809809 −395.973 1218.68i −0.489459 1.50640i −0.825417 0.564524i 0.809060π-0.809060\pi
0.335958 0.941877i 0.390940π-0.390940\pi
810810 141.043 257.515i 0.174127 0.317920i
811811 −24.4211 33.6128i −0.0301124 0.0414461i 0.793695 0.608315i 0.208154π-0.208154\pi
−0.823808 + 0.566869i 0.808154π0.808154\pi
812812 1897.06 + 113.362i 2.33628 + 0.139608i
813813 20.2577 0.0249172
814814 −89.6968 1163.31i −0.110193 1.42913i
815815 173.766i 0.213210i
816816 19.5731 3.86157i 0.0239866 0.00473232i
817817 295.934 215.009i 0.362220 0.263168i
818818 −254.267 + 464.239i −0.310840 + 0.567529i
819819 −239.188 + 77.7168i −0.292049 + 0.0948923i
820820 22.5451 + 35.2796i 0.0274941 + 0.0430239i
821821 360.162 + 261.673i 0.438688 + 0.318725i 0.785113 0.619352i 0.212605π-0.212605\pi
−0.346426 + 0.938077i 0.612605π0.612605\pi
822822 −67.4534 + 63.5430i −0.0820601 + 0.0773029i
823823 −471.551 153.216i −0.572966 0.186168i 0.00818108 0.999967i 0.497396π-0.497396\pi
−0.581147 + 0.813799i 0.697396π0.697396\pi
824824 1456.88 584.788i 1.76806 0.709694i
825825 22.9036 + 35.1087i 0.0277619 + 0.0425560i
826826 −136.395 1066.18i −0.165127 1.29078i
827827 323.516 + 105.117i 0.391192 + 0.127106i 0.498007 0.867173i 0.334065π-0.334065\pi
−0.106815 + 0.994279i 0.534065π0.534065\pi
828828 −237.347 195.096i −0.286651 0.235623i
829829 157.617 + 114.515i 0.190128 + 0.138136i 0.678777 0.734344i 0.262510π-0.262510\pi
−0.488649 + 0.872480i 0.662510π0.662510\pi
830830 −78.1230 165.344i −0.0941241 0.199210i
831831 222.644 72.3415i 0.267923 0.0870536i
832832 −197.935 + 26.9055i −0.237903 + 0.0323383i
833833 −56.3833 + 40.9649i −0.0676870 + 0.0491775i
834834 −10.9719 2.07511i −0.0131557 0.00248814i
835835 84.0313i 0.100636i
836836 −273.829 + 606.441i −0.327547 + 0.725408i
837837 −469.718 −0.561192
838838 −66.6500 + 352.402i −0.0795346 + 0.420528i
839839 −705.545 971.100i −0.840936 1.15745i −0.985788 0.167996i 0.946271π-0.946271\pi
0.144852 0.989453i 0.453729π-0.453729\pi
840840 31.8542 126.540i 0.0379216 0.150643i
841841 501.631 + 1543.86i 0.596469 + 1.83574i
842842 −804.724 + 380.222i −0.955729 + 0.451570i
843843 −76.3688 + 105.113i −0.0905917 + 0.124689i
844844 514.472 + 422.889i 0.609564 + 0.501053i
845845 110.045 338.683i 0.130230 0.400808i
846846 −195.979 + 25.0711i −0.231653 + 0.0296349i
847847 −1059.89 466.632i −1.25135 0.550924i
848848 −522.652 + 291.628i −0.616335 + 0.343901i
849849 87.8894 270.496i 0.103521 0.318605i
850850 −11.2179 11.9083i −0.0131976 0.0140098i
851851 −284.401 + 391.445i −0.334196 + 0.459982i
852852 164.029 + 256.680i 0.192523 + 0.301268i
853853 321.857 + 990.574i 0.377323 + 1.16128i 0.941898 + 0.335900i 0.109040π0.109040\pi
−0.564574 + 0.825382i 0.690960π0.690960\pi
854854 1484.36 + 812.994i 1.73812 + 0.951984i
855855 167.339 + 230.323i 0.195719 + 0.269384i
856856 −25.8739 382.443i −0.0302265 0.446779i
857857 −681.252 −0.794926 −0.397463 0.917618i 0.630109π-0.630109\pi
−0.397463 + 0.917618i 0.630109π0.630109\pi
858858 −44.5792 27.4156i −0.0519571 0.0319529i
859859 856.203i 0.996744i −0.866963 0.498372i 0.833931π-0.833931\pi
0.866963 0.498372i 0.166069π-0.166069\pi
860860 215.963 + 12.9052i 0.251120 + 0.0150061i
861861 27.6243 20.0702i 0.0320839 0.0233103i
862862 −370.540 202.947i −0.429860 0.235438i
863863 −630.616 + 204.900i −0.730725 + 0.237427i −0.650667 0.759363i 0.725511π-0.725511\pi
−0.0800582 + 0.996790i 0.525511π0.525511\pi
864864 −345.655 247.002i −0.400063 0.285882i
865865 −544.521 395.618i −0.629504 0.457361i
866866 −496.042 526.568i −0.572797 0.608047i
867867 207.544 + 67.4353i 0.239382 + 0.0777800i
868868 1310.86 340.970i 1.51020 0.392823i
869869 −447.972 686.692i −0.515503 0.790209i
870870 167.836 21.4709i 0.192915 0.0246792i
871871 172.511 + 56.0521i 0.198060 + 0.0643537i
872872 −78.5451 49.3278i −0.0900747 0.0565686i
873873 −303.441 220.463i −0.347584 0.252535i
874874 249.490 117.881i 0.285458 0.134875i
875875 −101.767 + 33.0663i −0.116306 + 0.0377900i
876876 40.9064 104.275i 0.0466968 0.119035i
877877 −1166.19 + 847.283i −1.32974 + 0.966116i −0.329989 + 0.943985i 0.607045π0.607045\pi
−0.999755 + 0.0221308i 0.992955π0.992955\pi
878878 −211.298 + 1117.21i −0.240658 + 1.27245i
879879 238.979i 0.271876i
880880 −352.873 + 174.243i −0.400992 + 0.198004i
881881 338.683 0.384431 0.192215 0.981353i 0.438433π-0.438433\pi
0.192215 + 0.981353i 0.438433π0.438433\pi
882882 704.812 + 133.301i 0.799107 + 0.151135i
883883 783.323 + 1078.15i 0.887116 + 1.22101i 0.974399 + 0.224827i 0.0721816π0.0721816\pi
−0.0872829 + 0.996184i 0.527818π0.527818\pi
884884 19.0143 + 7.45917i 0.0215094 + 0.00843797i
885885 −29.5729 91.0160i −0.0334157 0.102843i
886886 465.520 + 985.253i 0.525417 + 1.11202i
887887 952.972 1311.65i 1.07438 1.47875i 0.208811 0.977956i 0.433041π-0.433041\pi
0.865565 0.500796i 0.166959π-0.166959\pi
888888 −171.979 + 273.844i −0.193671 + 0.308383i
889889 13.7585 42.3442i 0.0154763 0.0476313i
890890 66.0230 + 516.095i 0.0741831 + 0.579882i
891891 188.363 + 697.190i 0.211406 + 0.782480i
892892 269.138 + 1034.70i 0.301724 + 1.15997i
893893 54.8338 168.761i 0.0614040 0.188982i
894894 −79.2000 + 74.6086i −0.0885906 + 0.0834548i
895895 −411.249 + 566.036i −0.459496 + 0.632442i
896896 1143.93 + 438.405i 1.27671 + 0.489291i
897897 6.70657 + 20.6407i 0.00747666 + 0.0230108i
898898 354.951 648.066i 0.395268 0.721677i
899899 1032.36 + 1420.92i 1.14834 + 1.58055i
900900 −10.0440 + 168.082i −0.0111600 + 0.186758i
901901 61.1975 0.0679218
902902 −100.098 24.1996i −0.110974 0.0268288i
903903 176.443i 0.195396i
904904 1065.79 72.1052i 1.17897 0.0797624i
905905 431.926 313.812i 0.477266 0.346754i
906906 −32.9782 + 60.2113i −0.0363998 + 0.0664584i
907907 −702.346 + 228.206i −0.774362 + 0.251605i −0.669431 0.742874i 0.733462π-0.733462\pi
−0.104931 + 0.994480i 0.533462π0.533462\pi
908908 −439.075 + 280.587i −0.483563 + 0.309017i
909909 841.427 + 611.332i 0.925662 + 0.672533i
910910 97.2406 91.6033i 0.106858 0.100663i
911911 1556.35 + 505.690i 1.70840 + 0.555093i 0.990066 0.140603i 0.0449042π-0.0449042\pi
0.718336 + 0.695697i 0.244904π0.244904\pi
912912 161.042 89.8577i 0.176581 0.0985282i
913913 420.262 + 160.323i 0.460308 + 0.175601i
914914 −61.1954 478.358i −0.0669534 0.523368i
915915 143.308 + 46.5634i 0.156620 + 0.0508890i
916916 699.151 850.563i 0.763266 0.928563i
917917 1814.11 + 1318.03i 1.97831 + 1.43733i
918918 18.5576 + 39.2763i 0.0202152 + 0.0427847i
919919 855.560 277.988i 0.930968 0.302490i 0.196010 0.980602i 0.437202π-0.437202\pi
0.734959 + 0.678112i 0.237202π0.237202\pi
920920 158.265 + 39.8403i 0.172027 + 0.0433047i
921921 163.907 119.085i 0.177966 0.129300i
922922 160.513 + 30.3579i 0.174092 + 0.0329262i
923923 311.862i 0.337879i
924924 159.017 + 278.796i 0.172097 + 0.301728i
925925 265.174 0.286675
926926 73.1672 386.861i 0.0790142 0.417777i
927927 971.084 + 1336.58i 1.04756 + 1.44184i
928928 12.4950 + 1588.49i 0.0134644 + 1.71173i
929929 −140.272 431.712i −0.150992 0.464707i 0.846741 0.532006i 0.178562π-0.178562\pi
−0.997733 + 0.0672996i 0.978562π0.978562\pi
930930 109.036 51.5181i 0.117243 0.0553958i
931931 −378.666 + 521.189i −0.406730 + 0.559816i
932932 −966.739 + 1176.10i −1.03727 + 1.26191i
933933 −79.1411 + 243.571i −0.0848243 + 0.261062i
934934 −576.937 + 73.8064i −0.617706 + 0.0790218i
935935 40.1895 + 2.02261i 0.0429834 + 0.00216322i
936936 −78.3089 195.091i −0.0836634 0.208430i
937937 336.677 1036.19i 0.359314 1.10585i −0.594152 0.804353i 0.702512π-0.702512\pi
0.953466 0.301501i 0.0974877π-0.0974877\pi
938938 −762.777 809.719i −0.813195 0.863240i
939939 152.039 209.264i 0.161916 0.222859i
940940 88.4349 56.5136i 0.0940796 0.0601208i
941941 −524.773 1615.08i −0.557676 1.71635i −0.688771 0.724979i 0.741849π-0.741849\pi
0.131095 0.991370i 0.458151π-0.458151\pi
942942 −356.465 195.239i −0.378413 0.207260i
943943 25.1020 + 34.5499i 0.0266193 + 0.0366383i
944944 881.469 173.905i 0.933760 0.184221i
945945 284.123 0.300659
946946 −405.196 + 344.959i −0.428325 + 0.364650i
947947 343.409i 0.362628i −0.983425 0.181314i 0.941965π-0.941965\pi
0.983425 0.181314i 0.0580350π-0.0580350\pi
948948 −13.5545 + 226.829i −0.0142980 + 0.239271i
949949 92.7753 67.4052i 0.0977611 0.0710276i
950950 −132.635 72.6454i −0.139616 0.0764689i
951951 −27.9628 + 9.08566i −0.0294035 + 0.00955379i
952952 −80.3000 96.1386i −0.0843487 0.100986i
953953 793.582 + 576.571i 0.832720 + 0.605006i 0.920327 0.391149i 0.127922π-0.127922\pi
−0.0876078 + 0.996155i 0.527922π0.527922\pi
954954 −431.893 458.472i −0.452718 0.480578i
955955 655.623 + 213.025i 0.686516 + 0.223063i
956956 −59.3499 228.170i −0.0620815 0.238672i
957957 −261.243 + 323.981i −0.272981 + 0.338538i
958958 776.734 99.3660i 0.810787 0.103722i
959959 553.368 + 179.800i 0.577026 + 0.187487i
960960 107.328 + 19.4258i 0.111800 + 0.0202353i
961961 235.243 + 170.914i 0.244790 + 0.177850i
962962 −299.332 + 141.431i −0.311156 + 0.147017i
963963 383.655 124.657i 0.398396 0.129447i
964964 −1378.15 540.638i −1.42962 0.560828i
965965 −619.463 + 450.066i −0.641931 + 0.466390i
966966 24.7347 130.781i 0.0256052 0.135384i
967967 1153.83i 1.19321i 0.802536 + 0.596604i 0.203484π0.203484\pi
−0.802536 + 0.596604i 0.796516π0.796516\pi
968968 329.357 910.246i 0.340245 0.940337i
969969 −18.8564 −0.0194597
970970 195.765 + 37.0250i 0.201819 + 0.0381701i
971971 −92.5275 127.353i −0.0952910 0.131157i 0.758709 0.651429i 0.225830π-0.225830\pi
−0.854000 + 0.520273i 0.825830π0.825830\pi
972972 247.639 631.261i 0.254773 0.649445i
973973 21.6653 + 66.6789i 0.0222665 + 0.0685292i
974974 −372.579 788.548i −0.382525 0.809598i
975975 6.99126 9.62264i 0.00717052 0.00986937i
976976 −594.264 + 1283.78i −0.608877 + 1.31535i
977977 95.6163 294.277i 0.0978672 0.301204i −0.890123 0.455720i 0.849382π-0.849382\pi
0.987990 + 0.154516i 0.0493818π0.0493818\pi
978978 15.0314 + 117.499i 0.0153695 + 0.120142i
979979 −996.239 803.321i −1.01761 0.820552i
980980 −368.755 + 95.9179i −0.376281 + 0.0978754i
981981 30.1629 92.8318i 0.0307471 0.0946297i
982982 1391.74 1311.06i 1.41725 1.33509i
983983 719.649 990.512i 0.732094 1.00764i −0.266940 0.963713i 0.586013π-0.586013\pi
0.999035 0.0439284i 0.0139873π-0.0139873\pi
984984 18.2966 + 21.9054i 0.0185941 + 0.0222616i
985985 214.247 + 659.383i 0.217509 + 0.669425i
986986 78.0264 142.460i 0.0791343 0.144483i
987987 −50.3097 69.2453i −0.0509723 0.0701574i
988988 188.466 + 11.2621i 0.190755 + 0.0113989i
989989 220.679 0.223133
990990 −268.479 315.360i −0.271191 0.318546i
991991 2.98244i 0.00300952i 0.999999 + 0.00150476i 0.000478980π0.000478980\pi
−0.999999 + 0.00150476i 0.999521π0.999521\pi
992992 358.320 + 1073.98i 0.361209 + 1.08264i
993993 −170.599 + 123.947i −0.171802 + 0.124821i
994994 918.759 1677.46i 0.924304 1.68759i
995995 585.294 190.174i 0.588236 0.191129i
996996 −67.1287 105.046i −0.0673983 0.105468i
997997 −1322.62 960.939i −1.32660 0.963830i −0.999825 0.0187281i 0.994038π-0.994038\pi
−0.326774 0.945102i 0.605962π-0.605962\pi
998998 216.865 204.293i 0.217300 0.204702i
999999 −669.640 217.579i −0.670310 0.217797i
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 220.3.s.b.31.2 96
4.3 odd 2 inner 220.3.s.b.31.21 yes 96
11.5 even 5 inner 220.3.s.b.71.21 yes 96
44.27 odd 10 inner 220.3.s.b.71.2 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
220.3.s.b.31.2 96 1.1 even 1 trivial
220.3.s.b.31.21 yes 96 4.3 odd 2 inner
220.3.s.b.71.2 yes 96 44.27 odd 10 inner
220.3.s.b.71.21 yes 96 11.5 even 5 inner