Properties

Label 39.3.g.a.34.2
Level 3939
Weight 33
Character 39.34
Analytic conductor 1.0631.063
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,3,Mod(31,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 39=313 39 = 3 \cdot 13
Weight: k k == 3 3
Character orbit: [χ][\chi] == 39.g (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.062673031011.06267303101
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: 8.0.1579585536.10
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x74x6+28x538x4+8x3+200x2352x+484 x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 34.2
Root 1.11361+1.42401i1.11361 + 1.42401i of defining polynomial
Character χ\chi == 39.34
Dual form 39.3.g.a.31.2

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+(0.6764240.676424i)q2+1.73205q33.08490iq4+(1.58008+1.58008i)q5+(1.171601.17160i)q6+(3.964003.96400i)q7+(4.79240+4.79240i)q8+3.00000q92.13761iq10+(10.0345+10.0345i)q115.34320iq12+(5.41846+11.8170i)q135.36270q14+(2.73677+2.73677i)q155.85621q16+6.40175iq17+(2.029272.02927i)q18+(7.73551+7.73551i)q19+(4.874384.87438i)q20+(6.865856.86585i)q21+13.5752q2234.8297iq23+(8.30068+8.30068i)q2420.0067iq25+(11.65854.32810i)q26+5.19615q27+(12.228512.2285i)q28+8.25124q293.70244iq30+(13.8633+13.8633i)q31+(23.1309+23.1309i)q32+(17.3803+17.3803i)q33+(4.330304.33030i)q34+12.5269q359.25470iq36+(37.2522+37.2522i)q3710.4650iq38+(9.38504+20.4676i)q3915.1447q40+(28.702028.7020i)q419.28846q4242.7195iq43+(30.9555+30.9555i)q44+(4.74023+4.74023i)q45+(23.5597+23.5597i)q46+(37.596437.5964i)q4710.1432q48+17.5734iq49+(13.5330+13.5330i)q50+11.0882iq51+(36.4541+16.7154i)q5296.7934q53+(3.514803.51480i)q5431.7107q55+37.9942iq56+(13.3983+13.3983i)q57+(5.581345.58134i)q58+(37.893537.8935i)q59+(8.442678.44267i)q60+91.2864q6118.7549iq62+(11.892011.8920i)q637.86776iq64+(27.2333+10.1101i)q65+23.5129q66+(42.450042.4500i)q67+19.7488q6860.3268iq69+(8.473478.47347i)q70+(29.8579+29.8579i)q71+(14.3772+14.3772i)q72+(10.9949+10.9949i)q73+50.3966q7434.6526iq75+(23.863323.8633i)q76+79.5538iq77+(20.19307.49649i)q78+102.031q79+(9.253269.25326i)q80+9.00000q81+38.8295iq82+(85.275885.2758i)q83+(21.180521.1805i)q84+(10.1153+10.1153i)q85+(28.8965+28.8965i)q86+14.2916q8796.1790iq88+(63.8510+63.8510i)q896.41282iq90+(25.3636+68.3212i)q91107.446q92+(24.0119+24.0119i)q9350.8623q94+24.4454iq95+(40.0639+40.0639i)q96+(58.702358.7023i)q97+(11.887111.8871i)q98+(30.1036+30.1036i)q99+O(q100)q+(-0.676424 - 0.676424i) q^{2} +1.73205 q^{3} -3.08490i q^{4} +(1.58008 + 1.58008i) q^{5} +(-1.17160 - 1.17160i) q^{6} +(3.96400 - 3.96400i) q^{7} +(-4.79240 + 4.79240i) q^{8} +3.00000 q^{9} -2.13761i q^{10} +(-10.0345 + 10.0345i) q^{11} -5.34320i q^{12} +(-5.41846 + 11.8170i) q^{13} -5.36270 q^{14} +(2.73677 + 2.73677i) q^{15} -5.85621 q^{16} +6.40175i q^{17} +(-2.02927 - 2.02927i) q^{18} +(7.73551 + 7.73551i) q^{19} +(4.87438 - 4.87438i) q^{20} +(6.86585 - 6.86585i) q^{21} +13.5752 q^{22} -34.8297i q^{23} +(-8.30068 + 8.30068i) q^{24} -20.0067i q^{25} +(11.6585 - 4.32810i) q^{26} +5.19615 q^{27} +(-12.2285 - 12.2285i) q^{28} +8.25124 q^{29} -3.70244i q^{30} +(13.8633 + 13.8633i) q^{31} +(23.1309 + 23.1309i) q^{32} +(-17.3803 + 17.3803i) q^{33} +(4.33030 - 4.33030i) q^{34} +12.5269 q^{35} -9.25470i q^{36} +(-37.2522 + 37.2522i) q^{37} -10.4650i q^{38} +(-9.38504 + 20.4676i) q^{39} -15.1447 q^{40} +(-28.7020 - 28.7020i) q^{41} -9.28846 q^{42} -42.7195i q^{43} +(30.9555 + 30.9555i) q^{44} +(4.74023 + 4.74023i) q^{45} +(-23.5597 + 23.5597i) q^{46} +(37.5964 - 37.5964i) q^{47} -10.1432 q^{48} +17.5734i q^{49} +(-13.5330 + 13.5330i) q^{50} +11.0882i q^{51} +(36.4541 + 16.7154i) q^{52} -96.7934 q^{53} +(-3.51480 - 3.51480i) q^{54} -31.7107 q^{55} +37.9942i q^{56} +(13.3983 + 13.3983i) q^{57} +(-5.58134 - 5.58134i) q^{58} +(37.8935 - 37.8935i) q^{59} +(8.44267 - 8.44267i) q^{60} +91.2864 q^{61} -18.7549i q^{62} +(11.8920 - 11.8920i) q^{63} -7.86776i q^{64} +(-27.2333 + 10.1101i) q^{65} +23.5129 q^{66} +(-42.4500 - 42.4500i) q^{67} +19.7488 q^{68} -60.3268i q^{69} +(-8.47347 - 8.47347i) q^{70} +(29.8579 + 29.8579i) q^{71} +(-14.3772 + 14.3772i) q^{72} +(-10.9949 + 10.9949i) q^{73} +50.3966 q^{74} -34.6526i q^{75} +(23.8633 - 23.8633i) q^{76} +79.5538i q^{77} +(20.1930 - 7.49649i) q^{78} +102.031 q^{79} +(-9.25326 - 9.25326i) q^{80} +9.00000 q^{81} +38.8295i q^{82} +(-85.2758 - 85.2758i) q^{83} +(-21.1805 - 21.1805i) q^{84} +(-10.1153 + 10.1153i) q^{85} +(-28.8965 + 28.8965i) q^{86} +14.2916 q^{87} -96.1790i q^{88} +(-63.8510 + 63.8510i) q^{89} -6.41282i q^{90} +(25.3636 + 68.3212i) q^{91} -107.446 q^{92} +(24.0119 + 24.0119i) q^{93} -50.8623 q^{94} +24.4454i q^{95} +(40.0639 + 40.0639i) q^{96} +(-58.7023 - 58.7023i) q^{97} +(11.8871 - 11.8871i) q^{98} +(-30.1036 + 30.1036i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q220q5+8q724q8+24q920q11+8q1316q14+12q15+56q16+12q1840q19+44q2048q21128q22+36q2432q26+32q28+60q99+O(q100) 8 q + 4 q^{2} - 20 q^{5} + 8 q^{7} - 24 q^{8} + 24 q^{9} - 20 q^{11} + 8 q^{13} - 16 q^{14} + 12 q^{15} + 56 q^{16} + 12 q^{18} - 40 q^{19} + 44 q^{20} - 48 q^{21} - 128 q^{22} + 36 q^{24} - 32 q^{26} + 32 q^{28}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/39Z)×\left(\mathbb{Z}/39\mathbb{Z}\right)^\times.

nn 1414 2828
χ(n)\chi(n) 11 e(14)e\left(\frac{1}{4}\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 −0.676424 0.676424i −0.338212 0.338212i 0.517482 0.855694i 0.326869π-0.326869\pi
−0.855694 + 0.517482i 0.826869π0.826869\pi
33 1.73205 0.577350
44 3.08490i 0.771225i
55 1.58008 + 1.58008i 0.316015 + 0.316015i 0.847234 0.531219i 0.178266π-0.178266\pi
−0.531219 + 0.847234i 0.678266π0.678266\pi
66 −1.17160 1.17160i −0.195267 0.195267i
77 3.96400 3.96400i 0.566286 0.566286i −0.364800 0.931086i 0.618863π-0.618863\pi
0.931086 + 0.364800i 0.118863π0.118863\pi
88 −4.79240 + 4.79240i −0.599050 + 0.599050i
99 3.00000 0.333333
1010 2.13761i 0.213761i
1111 −10.0345 + 10.0345i −0.912230 + 0.912230i −0.996447 0.0842172i 0.973161π-0.973161\pi
0.0842172 + 0.996447i 0.473161π0.473161\pi
1212 5.34320i 0.445267i
1313 −5.41846 + 11.8170i −0.416804 + 0.908996i
1414 −5.36270 −0.383050
1515 2.73677 + 2.73677i 0.182452 + 0.182452i
1616 −5.85621 −0.366013
1717 6.40175i 0.376574i 0.982114 + 0.188287i 0.0602934π0.0602934\pi
−0.982114 + 0.188287i 0.939707π0.939707\pi
1818 −2.02927 2.02927i −0.112737 0.112737i
1919 7.73551 + 7.73551i 0.407132 + 0.407132i 0.880737 0.473605i 0.157048π-0.157048\pi
−0.473605 + 0.880737i 0.657048π0.657048\pi
2020 4.87438 4.87438i 0.243719 0.243719i
2121 6.86585 6.86585i 0.326945 0.326945i
2222 13.5752 0.617055
2323 34.8297i 1.51434i −0.653221 0.757168i 0.726583π-0.726583\pi
0.653221 0.757168i 0.273417π-0.273417\pi
2424 −8.30068 + 8.30068i −0.345862 + 0.345862i
2525 20.0067i 0.800269i
2626 11.6585 4.32810i 0.448402 0.166465i
2727 5.19615 0.192450
2828 −12.2285 12.2285i −0.436734 0.436734i
2929 8.25124 0.284526 0.142263 0.989829i 0.454562π-0.454562\pi
0.142263 + 0.989829i 0.454562π0.454562\pi
3030 3.70244i 0.123415i
3131 13.8633 + 13.8633i 0.447202 + 0.447202i 0.894423 0.447221i 0.147586π-0.147586\pi
−0.447221 + 0.894423i 0.647586π0.647586\pi
3232 23.1309 + 23.1309i 0.722840 + 0.722840i
3333 −17.3803 + 17.3803i −0.526676 + 0.526676i
3434 4.33030 4.33030i 0.127362 0.127362i
3535 12.5269 0.357910
3636 9.25470i 0.257075i
3737 −37.2522 + 37.2522i −1.00682 + 1.00682i −0.00683875 + 0.999977i 0.502177π0.502177\pi
−0.999977 + 0.00683875i 0.997823π0.997823\pi
3838 10.4650i 0.275394i
3939 −9.38504 + 20.4676i −0.240642 + 0.524809i
4040 −15.1447 −0.378618
4141 −28.7020 28.7020i −0.700050 0.700050i 0.264371 0.964421i 0.414836π-0.414836\pi
−0.964421 + 0.264371i 0.914836π0.914836\pi
4242 −9.28846 −0.221154
4343 42.7195i 0.993477i −0.867900 0.496739i 0.834531π-0.834531\pi
0.867900 0.496739i 0.165469π-0.165469\pi
4444 30.9555 + 30.9555i 0.703535 + 0.703535i
4545 4.74023 + 4.74023i 0.105338 + 0.105338i
4646 −23.5597 + 23.5597i −0.512167 + 0.512167i
4747 37.5964 37.5964i 0.799924 0.799924i −0.183159 0.983083i 0.558632π-0.558632\pi
0.983083 + 0.183159i 0.0586323π0.0586323\pi
4848 −10.1432 −0.211318
4949 17.5734i 0.358641i
5050 −13.5330 + 13.5330i −0.270661 + 0.270661i
5151 11.0882i 0.217415i
5252 36.4541 + 16.7154i 0.701041 + 0.321450i
5353 −96.7934 −1.82629 −0.913145 0.407635i 0.866354π-0.866354\pi
−0.913145 + 0.407635i 0.866354π0.866354\pi
5454 −3.51480 3.51480i −0.0650890 0.0650890i
5555 −31.7107 −0.576558
5656 37.9942i 0.678467i
5757 13.3983 + 13.3983i 0.235058 + 0.235058i
5858 −5.58134 5.58134i −0.0962300 0.0962300i
5959 37.8935 37.8935i 0.642262 0.642262i −0.308849 0.951111i 0.599944π-0.599944\pi
0.951111 + 0.308849i 0.0999437π0.0999437\pi
6060 8.44267 8.44267i 0.140711 0.140711i
6161 91.2864 1.49650 0.748249 0.663418i 0.230895π-0.230895\pi
0.748249 + 0.663418i 0.230895π0.230895\pi
6262 18.7549i 0.302499i
6363 11.8920 11.8920i 0.188762 0.188762i
6464 7.86776i 0.122934i
6565 −27.2333 + 10.1101i −0.418973 + 0.155540i
6666 23.5129 0.356257
6767 −42.4500 42.4500i −0.633581 0.633581i 0.315383 0.948964i 0.397867π-0.397867\pi
−0.948964 + 0.315383i 0.897867π0.897867\pi
6868 19.7488 0.290423
6969 60.3268i 0.874302i
7070 −8.47347 8.47347i −0.121050 0.121050i
7171 29.8579 + 29.8579i 0.420534 + 0.420534i 0.885388 0.464853i 0.153893π-0.153893\pi
−0.464853 + 0.885388i 0.653893π0.653893\pi
7272 −14.3772 + 14.3772i −0.199683 + 0.199683i
7373 −10.9949 + 10.9949i −0.150615 + 0.150615i −0.778393 0.627777i 0.783965π-0.783965\pi
0.627777 + 0.778393i 0.283965π0.283965\pi
7474 50.3966 0.681035
7575 34.6526i 0.462035i
7676 23.8633 23.8633i 0.313990 0.313990i
7777 79.5538i 1.03317i
7878 20.1930 7.49649i 0.258885 0.0961088i
7979 102.031 1.29153 0.645764 0.763537i 0.276539π-0.276539\pi
0.645764 + 0.763537i 0.276539π0.276539\pi
8080 −9.25326 9.25326i −0.115666 0.115666i
8181 9.00000 0.111111
8282 38.8295i 0.473531i
8383 −85.2758 85.2758i −1.02742 1.02742i −0.999613 0.0278064i 0.991148π-0.991148\pi
−0.0278064 0.999613i 0.508852π-0.508852\pi
8484 −21.1805 21.1805i −0.252148 0.252148i
8585 −10.1153 + 10.1153i −0.119003 + 0.119003i
8686 −28.8965 + 28.8965i −0.336006 + 0.336006i
8787 14.2916 0.164271
8888 96.1790i 1.09294i
8989 −63.8510 + 63.8510i −0.717427 + 0.717427i −0.968078 0.250651i 0.919355π-0.919355\pi
0.250651 + 0.968078i 0.419355π0.419355\pi
9090 6.41282i 0.0712535i
9191 25.3636 + 68.3212i 0.278721 + 0.750782i
9292 −107.446 −1.16789
9393 24.0119 + 24.0119i 0.258192 + 0.258192i
9494 −50.8623 −0.541088
9595 24.4454i 0.257320i
9696 40.0639 + 40.0639i 0.417332 + 0.417332i
9797 −58.7023 58.7023i −0.605178 0.605178i 0.336504 0.941682i 0.390755π-0.390755\pi
−0.941682 + 0.336504i 0.890755π0.890755\pi
9898 11.8871 11.8871i 0.121297 0.121297i
9999 −30.1036 + 30.1036i −0.304077 + 0.304077i
100100 −61.7187 −0.617187
101101 130.126i 1.28837i 0.764869 + 0.644186i 0.222804π0.222804\pi
−0.764869 + 0.644186i 0.777196π0.777196\pi
102102 7.50030 7.50030i 0.0735324 0.0735324i
103103 27.9217i 0.271085i 0.990772 + 0.135542i 0.0432777π0.0432777\pi
−0.990772 + 0.135542i 0.956722π0.956722\pi
104104 −30.6641 82.5990i −0.294847 0.794221i
105105 21.6971 0.206640
106106 65.4734 + 65.4734i 0.617674 + 0.617674i
107107 166.168 1.55297 0.776486 0.630134i 0.217000π-0.217000\pi
0.776486 + 0.630134i 0.217000π0.217000\pi
108108 16.0296i 0.148422i
109109 −4.56393 4.56393i −0.0418709 0.0418709i 0.685861 0.727732i 0.259426π-0.259426\pi
−0.727732 + 0.685861i 0.759426π0.759426\pi
110110 21.4499 + 21.4499i 0.194999 + 0.194999i
111111 −64.5226 + 64.5226i −0.581285 + 0.581285i
112112 −23.2140 + 23.2140i −0.207268 + 0.207268i
113113 −60.7525 −0.537633 −0.268817 0.963191i 0.586633π-0.586633\pi
−0.268817 + 0.963191i 0.586633π0.586633\pi
114114 18.1259i 0.158999i
115115 55.0336 55.0336i 0.478553 0.478553i
116116 25.4543i 0.219433i
117117 −16.2554 + 35.4509i −0.138935 + 0.302999i
118118 −51.2641 −0.434442
119119 25.3765 + 25.3765i 0.213248 + 0.213248i
120120 −26.2314 −0.218595
121121 80.3837i 0.664328i
122122 −61.7484 61.7484i −0.506134 0.506134i
123123 −49.7134 49.7134i −0.404174 0.404174i
124124 42.7668 42.7668i 0.344893 0.344893i
125125 71.1141 71.1141i 0.568913 0.568913i
126126 −16.0881 −0.127683
127127 130.207i 1.02525i 0.858613 + 0.512624i 0.171327π0.171327\pi
−0.858613 + 0.512624i 0.828673π0.828673\pi
128128 87.2016 87.2016i 0.681262 0.681262i
129129 73.9924i 0.573584i
130130 25.2600 + 11.5825i 0.194308 + 0.0890963i
131131 135.531 1.03459 0.517293 0.855809i 0.326940π-0.326940\pi
0.517293 + 0.855809i 0.326940π0.326940\pi
132132 53.6165 + 53.6165i 0.406186 + 0.406186i
133133 61.3271 0.461106
134134 57.4284i 0.428570i
135135 8.21032 + 8.21032i 0.0608172 + 0.0608172i
136136 −30.6797 30.6797i −0.225586 0.225586i
137137 135.519 135.519i 0.989190 0.989190i −0.0107526 0.999942i 0.503423π-0.503423\pi
0.999942 + 0.0107526i 0.00342272π0.00342272\pi
138138 −40.8065 + 40.8065i −0.295700 + 0.295700i
139139 −244.006 −1.75544 −0.877720 0.479174i 0.840936π-0.840936\pi
−0.877720 + 0.479174i 0.840936π0.840936\pi
140140 38.6441i 0.276029i
141141 65.1189 65.1189i 0.461836 0.461836i
142142 40.3933i 0.284460i
143143 −64.2059 172.949i −0.448992 1.20944i
144144 −17.5686 −0.122004
145145 13.0376 + 13.0376i 0.0899145 + 0.0899145i
146146 14.8745 0.101880
147147 30.4380i 0.207061i
148148 114.919 + 114.919i 0.776481 + 0.776481i
149149 174.887 + 174.887i 1.17374 + 1.17374i 0.981312 + 0.192425i 0.0616351π0.0616351\pi
0.192425 + 0.981312i 0.438365π0.438365\pi
150150 −23.4399 + 23.4399i −0.156266 + 0.156266i
151151 −38.1095 + 38.1095i −0.252381 + 0.252381i −0.821946 0.569565i 0.807112π-0.807112\pi
0.569565 + 0.821946i 0.307112π0.307112\pi
152152 −74.1433 −0.487785
153153 19.2053i 0.125525i
154154 53.8121 53.8121i 0.349429 0.349429i
155155 43.8101i 0.282646i
156156 63.1404 + 28.9519i 0.404746 + 0.185589i
157157 150.359 0.957699 0.478849 0.877897i 0.341054π-0.341054\pi
0.478849 + 0.877897i 0.341054π0.341054\pi
158158 −69.0161 69.0161i −0.436810 0.436810i
159159 −167.651 −1.05441
160160 73.0971i 0.456857i
161161 −138.065 138.065i −0.857547 0.857547i
162162 −6.08782 6.08782i −0.0375791 0.0375791i
163163 −167.544 + 167.544i −1.02788 + 1.02788i −0.0282759 + 0.999600i 0.509002π0.509002\pi
−0.999600 + 0.0282759i 0.990998π0.990998\pi
164164 −88.5429 + 88.5429i −0.539896 + 0.539896i
165165 −54.9245 −0.332876
166166 115.365i 0.694972i
167167 −33.7608 + 33.7608i −0.202160 + 0.202160i −0.800925 0.598765i 0.795658π-0.795658\pi
0.598765 + 0.800925i 0.295658π0.295658\pi
168168 65.8078i 0.391713i
169169 −110.281 128.059i −0.652548 0.757747i
170170 13.6844 0.0804966
171171 23.2065 + 23.2065i 0.135711 + 0.135711i
172172 −131.785 −0.766195
173173 150.230i 0.868383i 0.900821 + 0.434191i 0.142966π0.142966\pi
−0.900821 + 0.434191i 0.857034π0.857034\pi
174174 −9.66717 9.66717i −0.0555584 0.0555584i
175175 −79.3066 79.3066i −0.453181 0.453181i
176176 58.7643 58.7643i 0.333888 0.333888i
177177 65.6334 65.6334i 0.370810 0.370810i
178178 86.3808 0.485285
179179 247.106i 1.38048i 0.723582 + 0.690239i 0.242495π0.242495\pi
−0.723582 + 0.690239i 0.757505π0.757505\pi
180180 14.6231 14.6231i 0.0812396 0.0812396i
181181 111.674i 0.616986i −0.951227 0.308493i 0.900175π-0.900175\pi
0.951227 0.308493i 0.0998247π-0.0998247\pi
182182 29.0575 63.3707i 0.159657 0.348191i
183183 158.113 0.864004
184184 166.918 + 166.918i 0.907162 + 0.907162i
185185 −117.723 −0.636338
186186 32.4845i 0.174648i
187187 −64.2386 64.2386i −0.343522 0.343522i
188188 −115.981 115.981i −0.616921 0.616921i
189189 20.5976 20.5976i 0.108982 0.108982i
190190 16.5355 16.5355i 0.0870288 0.0870288i
191191 −64.6991 −0.338739 −0.169369 0.985553i 0.554173π-0.554173\pi
−0.169369 + 0.985553i 0.554173π0.554173\pi
192192 13.6274i 0.0709759i
193193 97.0986 97.0986i 0.503102 0.503102i −0.409299 0.912400i 0.634227π-0.634227\pi
0.912400 + 0.409299i 0.134227π0.134227\pi
194194 79.4153i 0.409357i
195195 −47.1694 + 17.5112i −0.241894 + 0.0898012i
196196 54.2121 0.276593
197197 48.8725 + 48.8725i 0.248084 + 0.248084i 0.820184 0.572100i 0.193871π-0.193871\pi
−0.572100 + 0.820184i 0.693871π0.693871\pi
198198 40.7256 0.205685
199199 139.570i 0.701358i −0.936496 0.350679i 0.885951π-0.885951\pi
0.936496 0.350679i 0.114049π-0.114049\pi
200200 95.8802 + 95.8802i 0.479401 + 0.479401i
201201 −73.5255 73.5255i −0.365798 0.365798i
202202 88.0201 88.0201i 0.435743 0.435743i
203203 32.7079 32.7079i 0.161123 0.161123i
204204 34.2059 0.167676
205205 90.7029i 0.442453i
206206 18.8869 18.8869i 0.0916842 0.0916842i
207207 104.489i 0.504778i
208208 31.7316 69.2025i 0.152556 0.332704i
209209 −155.244 −0.742796
210210 −14.6765 14.6765i −0.0698880 0.0698880i
211211 52.9556 0.250975 0.125487 0.992095i 0.459951π-0.459951\pi
0.125487 + 0.992095i 0.459951π0.459951\pi
212212 298.598i 1.40848i
213213 51.7154 + 51.7154i 0.242796 + 0.242796i
214214 −112.400 112.400i −0.525234 0.525234i
215215 67.5001 67.5001i 0.313954 0.313954i
216216 −24.9020 + 24.9020i −0.115287 + 0.115287i
217217 109.908 0.506489
218218 6.17430i 0.0283225i
219219 −19.0438 + 19.0438i −0.0869578 + 0.0869578i
220220 97.8242i 0.444656i
221221 −75.6492 34.6876i −0.342304 0.156958i
222222 87.2894 0.393195
223223 70.4483 + 70.4483i 0.315912 + 0.315912i 0.847195 0.531283i 0.178290π-0.178290\pi
−0.531283 + 0.847195i 0.678290π0.678290\pi
224224 183.382 0.818668
225225 60.0201i 0.266756i
226226 41.0945 + 41.0945i 0.181834 + 0.181834i
227227 −95.0195 95.0195i −0.418588 0.418588i 0.466129 0.884717i 0.345648π-0.345648\pi
−0.884717 + 0.466129i 0.845648π0.845648\pi
228228 41.3324 41.3324i 0.181282 0.181282i
229229 66.9011 66.9011i 0.292144 0.292144i −0.545782 0.837927i 0.683767π-0.683767\pi
0.837927 + 0.545782i 0.183767π0.183767\pi
230230 −74.4522 −0.323705
231231 137.791i 0.596499i
232232 −39.5433 + 39.5433i −0.170445 + 0.170445i
233233 81.9200i 0.351588i 0.984427 + 0.175794i 0.0562493π0.0562493\pi
−0.984427 + 0.175794i 0.943751π0.943751\pi
234234 34.9754 12.9843i 0.149467 0.0554884i
235235 118.811 0.505577
236236 −116.898 116.898i −0.495329 0.495329i
237237 176.722 0.745664
238238 34.3306i 0.144246i
239239 5.12005 + 5.12005i 0.0214228 + 0.0214228i 0.717737 0.696314i 0.245178π-0.245178\pi
−0.696314 + 0.717737i 0.745178π0.745178\pi
240240 −16.0271 16.0271i −0.0667796 0.0667796i
241241 −152.203 + 152.203i −0.631546 + 0.631546i −0.948456 0.316910i 0.897355π-0.897355\pi
0.316910 + 0.948456i 0.397355π0.397355\pi
242242 −54.3735 + 54.3735i −0.224684 + 0.224684i
243243 15.5885 0.0641500
244244 281.609i 1.15414i
245245 −27.7673 + 27.7673i −0.113336 + 0.113336i
246246 67.2547i 0.273393i
247247 −133.325 + 49.4956i −0.539776 + 0.200387i
248248 −132.877 −0.535793
249249 −147.702 147.702i −0.593181 0.593181i
250250 −96.2066 −0.384826
251251 221.877i 0.883974i −0.897022 0.441987i 0.854274π-0.854274\pi
0.897022 0.441987i 0.145726π-0.145726\pi
252252 −36.6856 36.6856i −0.145578 0.145578i
253253 349.500 + 349.500i 1.38142 + 1.38142i
254254 88.0749 88.0749i 0.346751 0.346751i
255255 −17.5201 + 17.5201i −0.0687064 + 0.0687064i
256256 −149.442 −0.583756
257257 15.0363i 0.0585068i −0.999572 0.0292534i 0.990687π-0.990687\pi
0.999572 0.0292534i 0.00931298π-0.00931298\pi
258258 −50.0503 + 50.0503i −0.193993 + 0.193993i
259259 295.335i 1.14029i
260260 31.1887 + 84.0119i 0.119956 + 0.323123i
261261 24.7537 0.0948419
262262 −91.6763 91.6763i −0.349909 0.349909i
263263 −105.723 −0.401990 −0.200995 0.979592i 0.564418π-0.564418\pi
−0.200995 + 0.979592i 0.564418π0.564418\pi
264264 166.587i 0.631011i
265265 −152.941 152.941i −0.577136 0.577136i
266266 −41.4832 41.4832i −0.155952 0.155952i
267267 −110.593 + 110.593i −0.414207 + 0.414207i
268268 −130.954 + 130.954i −0.488634 + 0.488634i
269269 168.740 0.627286 0.313643 0.949541i 0.398451π-0.398451\pi
0.313643 + 0.949541i 0.398451π0.398451\pi
270270 11.1073i 0.0411382i
271271 −52.4787 + 52.4787i −0.193648 + 0.193648i −0.797271 0.603622i 0.793724π-0.793724\pi
0.603622 + 0.797271i 0.293724π0.293724\pi
272272 37.4900i 0.137831i
273273 43.9311 + 118.336i 0.160920 + 0.433464i
274274 −183.337 −0.669112
275275 200.758 + 200.758i 0.730029 + 0.730029i
276276 −186.102 −0.674283
277277 153.018i 0.552412i 0.961098 + 0.276206i 0.0890772π0.0890772\pi
−0.961098 + 0.276206i 0.910923π0.910923\pi
278278 165.052 + 165.052i 0.593711 + 0.593711i
279279 41.5898 + 41.5898i 0.149067 + 0.149067i
280280 −60.0337 + 60.0337i −0.214406 + 0.214406i
281281 37.8887 37.8887i 0.134835 0.134835i −0.636468 0.771303i 0.719605π-0.719605\pi
0.771303 + 0.636468i 0.219605π0.219605\pi
282282 −88.0961 −0.312397
283283 34.7222i 0.122693i −0.998117 0.0613467i 0.980460π-0.980460\pi
0.998117 0.0613467i 0.0195395π-0.0195395\pi
284284 92.1087 92.1087i 0.324326 0.324326i
285285 42.3407i 0.148564i
286286 −73.5567 + 160.418i −0.257191 + 0.560901i
287287 −227.550 −0.792857
288288 69.3926 + 69.3926i 0.240947 + 0.240947i
289289 248.018 0.858192
290290 17.6379i 0.0608203i
291291 −101.675 101.675i −0.349400 0.349400i
292292 33.9182 + 33.9182i 0.116158 + 0.116158i
293293 54.4668 54.4668i 0.185894 0.185894i −0.608025 0.793918i 0.708038π-0.708038\pi
0.793918 + 0.608025i 0.208038π0.208038\pi
294294 20.5890 20.5890i 0.0700306 0.0700306i
295295 119.749 0.405929
296296 357.055i 1.20627i
297297 −52.1410 + 52.1410i −0.175559 + 0.175559i
298298 236.595i 0.793944i
299299 411.581 + 188.723i 1.37652 + 0.631182i
300300 −106.900 −0.356333
301301 −169.340 169.340i −0.562592 0.562592i
302302 51.5565 0.170717
303303 225.384i 0.743842i
304304 −45.3007 45.3007i −0.149016 0.149016i
305305 144.240 + 144.240i 0.472916 + 0.472916i
306306 12.9909 12.9909i 0.0424539 0.0424539i
307307 223.385 223.385i 0.727639 0.727639i −0.242510 0.970149i 0.577971π-0.577971\pi
0.970149 + 0.242510i 0.0779707π0.0779707\pi
308308 245.416 0.796804
309309 48.3619i 0.156511i
310310 29.6342 29.6342i 0.0955942 0.0955942i
311311 516.479i 1.66070i −0.557240 0.830352i 0.688140π-0.688140\pi
0.557240 0.830352i 0.311860π-0.311860\pi
312312 −53.1118 143.066i −0.170230 0.458544i
313313 −149.235 −0.476788 −0.238394 0.971169i 0.576621π-0.576621\pi
−0.238394 + 0.971169i 0.576621π0.576621\pi
314314 −101.706 101.706i −0.323905 0.323905i
315315 37.5806 0.119303
316316 314.754i 0.996058i
317317 −188.163 188.163i −0.593574 0.593574i 0.345021 0.938595i 0.387872π-0.387872\pi
−0.938595 + 0.345021i 0.887872π0.887872\pi
318318 113.403 + 113.403i 0.356614 + 0.356614i
319319 −82.7974 + 82.7974i −0.259553 + 0.259553i
320320 12.4317 12.4317i 0.0388490 0.0388490i
321321 287.811 0.896609
322322 186.781i 0.580066i
323323 −49.5208 + 49.5208i −0.153315 + 0.153315i
324324 27.7641i 0.0856917i
325325 236.418 + 108.406i 0.727441 + 0.333555i
326326 226.661 0.695281
327327 −7.90495 7.90495i −0.0241742 0.0241742i
328328 275.103 0.838730
329329 298.065i 0.905972i
330330 37.1523 + 37.1523i 0.112583 + 0.112583i
331331 −133.749 133.749i −0.404074 0.404074i 0.475592 0.879666i 0.342234π-0.342234\pi
−0.879666 + 0.475592i 0.842234π0.842234\pi
332332 −263.067 + 263.067i −0.792372 + 0.792372i
333333 −111.757 + 111.757i −0.335605 + 0.335605i
334334 45.6732 0.136746
335335 134.148i 0.400443i
336336 −40.2078 + 40.2078i −0.119666 + 0.119666i
337337 202.419i 0.600651i −0.953837 0.300325i 0.902905π-0.902905\pi
0.953837 0.300325i 0.0970952π-0.0970952\pi
338338 −12.0259 + 161.219i −0.0355796 + 0.476979i
339339 −105.226 −0.310403
340340 31.2046 + 31.2046i 0.0917781 + 0.0917781i
341341 −278.223 −0.815903
342342 31.3949i 0.0917980i
343343 263.897 + 263.897i 0.769379 + 0.769379i
344344 204.729 + 204.729i 0.595143 + 0.595143i
345345 95.3210 95.3210i 0.276293 0.276293i
346346 101.619 101.619i 0.293698 0.293698i
347347 190.870 0.550059 0.275029 0.961436i 0.411312π-0.411312\pi
0.275029 + 0.961436i 0.411312π0.411312\pi
348348 44.0881i 0.126690i
349349 −472.034 + 472.034i −1.35253 + 1.35253i −0.469713 + 0.882819i 0.655643π0.655643\pi
−0.882819 + 0.469713i 0.844357π0.844357\pi
350350 107.290i 0.306543i
351351 −28.1551 + 61.4027i −0.0802140 + 0.174936i
352352 −464.215 −1.31879
353353 −298.499 298.499i −0.845606 0.845606i 0.143975 0.989581i 0.454012π-0.454012\pi
−0.989581 + 0.143975i 0.954012π0.954012\pi
354354 −88.7921 −0.250825
355355 94.3556i 0.265791i
356356 196.974 + 196.974i 0.553298 + 0.553298i
357357 43.9535 + 43.9535i 0.123119 + 0.123119i
358358 167.148 167.148i 0.466894 0.466894i
359359 −86.3614 + 86.3614i −0.240561 + 0.240561i −0.817082 0.576521i 0.804410π-0.804410\pi
0.576521 + 0.817082i 0.304410π0.304410\pi
360360 −45.4342 −0.126206
361361 241.324i 0.668487i
362362 −75.5394 + 75.5394i −0.208672 + 0.208672i
363363 139.229i 0.383550i
364364 210.764 78.2443i 0.579022 0.214957i
365365 −34.7456 −0.0951935
366366 −106.951 106.951i −0.292217 0.292217i
367367 −54.1950 −0.147670 −0.0738352 0.997270i 0.523524π-0.523524\pi
−0.0738352 + 0.997270i 0.523524π0.523524\pi
368368 203.970i 0.554266i
369369 −86.1061 86.1061i −0.233350 0.233350i
370370 79.6304 + 79.6304i 0.215217 + 0.215217i
371371 −383.689 + 383.689i −1.03420 + 1.03420i
372372 74.0743 74.0743i 0.199124 0.199124i
373373 −17.9362 −0.0480862 −0.0240431 0.999711i 0.507654π-0.507654\pi
−0.0240431 + 0.999711i 0.507654π0.507654\pi
374374 86.9051i 0.232367i
375375 123.173 123.173i 0.328462 0.328462i
376376 360.354i 0.958389i
377377 −44.7090 + 97.5045i −0.118592 + 0.258633i
378378 −27.8654 −0.0737179
379379 −281.565 281.565i −0.742916 0.742916i 0.230222 0.973138i 0.426055π-0.426055\pi
−0.973138 + 0.230222i 0.926055π0.926055\pi
380380 75.4116 0.198452
381381 225.524i 0.591927i
382382 43.7641 + 43.7641i 0.114566 + 0.114566i
383383 −244.827 244.827i −0.639236 0.639236i 0.311131 0.950367i 0.399292π-0.399292\pi
−0.950367 + 0.311131i 0.899292π0.899292\pi
384384 151.038 151.038i 0.393327 0.393327i
385385 −125.701 + 125.701i −0.326496 + 0.326496i
386386 −131.360 −0.340310
387387 128.159i 0.331159i
388388 −181.091 + 181.091i −0.466728 + 0.466728i
389389 582.261i 1.49681i 0.663240 + 0.748407i 0.269181π0.269181\pi
−0.663240 + 0.748407i 0.730819π0.730819\pi
390390 43.7516 + 20.0615i 0.112184 + 0.0514398i
391391 222.971 0.570259
392392 −84.2187 84.2187i −0.214844 0.214844i
393393 234.746 0.597318
394394 66.1171i 0.167810i
395395 161.216 + 161.216i 0.408143 + 0.408143i
396396 92.8666 + 92.8666i 0.234512 + 0.234512i
397397 372.060 372.060i 0.937179 0.937179i −0.0609613 0.998140i 0.519417π-0.519417\pi
0.998140 + 0.0609613i 0.0194166π0.0194166\pi
398398 −94.4087 + 94.4087i −0.237208 + 0.237208i
399399 106.222 0.266220
400400 117.163i 0.292909i
401401 −380.251 + 380.251i −0.948258 + 0.948258i −0.998726 0.0504677i 0.983929π-0.983929\pi
0.0504677 + 0.998726i 0.483929π0.483929\pi
402402 99.4689i 0.247435i
403403 −238.939 + 88.7040i −0.592901 + 0.220109i
404404 401.424 0.993625
405405 14.2207 + 14.2207i 0.0351128 + 0.0351128i
406406 −44.2489 −0.108987
407407 747.616i 1.83689i
408408 −53.1389 53.1389i −0.130242 0.130242i
409409 58.5825 + 58.5825i 0.143233 + 0.143233i 0.775087 0.631854i 0.217706π-0.217706\pi
−0.631854 + 0.775087i 0.717706π0.717706\pi
410410 −61.3537 + 61.3537i −0.149643 + 0.149643i
411411 234.726 234.726i 0.571109 0.571109i
412412 86.1358 0.209067
413413 300.420i 0.727408i
414414 −70.6790 + 70.6790i −0.170722 + 0.170722i
415415 269.485i 0.649361i
416416 −398.670 + 148.003i −0.958342 + 0.355776i
417417 −422.631 −1.01350
418418 105.011 + 105.011i 0.251223 + 0.251223i
419419 −451.990 −1.07874 −0.539368 0.842070i 0.681337π-0.681337\pi
−0.539368 + 0.842070i 0.681337π0.681337\pi
420420 66.9335i 0.159366i
421421 54.5548 + 54.5548i 0.129584 + 0.129584i 0.768924 0.639340i 0.220792π-0.220792\pi
−0.639340 + 0.768924i 0.720792π0.720792\pi
422422 −35.8205 35.8205i −0.0848827 0.0848827i
423423 112.789 112.789i 0.266641 0.266641i
424424 463.872 463.872i 1.09404 1.09404i
425425 128.078 0.301360
426426 69.9632i 0.164233i
427427 361.859 361.859i 0.847446 0.847446i
428428 512.612i 1.19769i
429429 −111.208 299.557i −0.259226 0.698268i
430430 −91.3175 −0.212366
431431 422.858 + 422.858i 0.981110 + 0.981110i 0.999825 0.0187153i 0.00595760π-0.00595760\pi
−0.0187153 + 0.999825i 0.505958π0.505958\pi
432432 −30.4297 −0.0704392
433433 621.635i 1.43565i 0.696225 + 0.717824i 0.254862π0.254862\pi
−0.696225 + 0.717824i 0.745138π0.745138\pi
434434 −74.3445 74.3445i −0.171301 0.171301i
435435 22.5818 + 22.5818i 0.0519121 + 0.0519121i
436436 −14.0793 + 14.0793i −0.0322919 + 0.0322919i
437437 269.425 269.425i 0.616534 0.616534i
438438 25.7633 0.0588204
439439 416.992i 0.949868i −0.880021 0.474934i 0.842472π-0.842472\pi
0.880021 0.474934i 0.157528π-0.157528\pi
440440 151.970 151.970i 0.345387 0.345387i
441441 52.7202i 0.119547i
442442 27.7074 + 74.6345i 0.0626864 + 0.168856i
443443 581.904 1.31355 0.656776 0.754086i 0.271920π-0.271920\pi
0.656776 + 0.754086i 0.271920π0.271920\pi
444444 199.046 + 199.046i 0.448302 + 0.448302i
445445 −201.779 −0.453436
446446 95.3060i 0.213690i
447447 302.913 + 302.913i 0.677657 + 0.677657i
448448 −31.1878 31.1878i −0.0696157 0.0696157i
449449 −66.7587 + 66.7587i −0.148683 + 0.148683i −0.777530 0.628846i 0.783527π-0.783527\pi
0.628846 + 0.777530i 0.283527π0.283527\pi
450450 −40.5991 + 40.5991i −0.0902202 + 0.0902202i
451451 576.023 1.27721
452452 187.415i 0.414636i
453453 −66.0077 + 66.0077i −0.145712 + 0.145712i
454454 128.547i 0.283143i
455455 −67.8762 + 148.029i −0.149179 + 0.325339i
456456 −128.420 −0.281623
457457 −103.815 103.815i −0.227167 0.227167i 0.584341 0.811508i 0.301353π-0.301353\pi
−0.811508 + 0.584341i 0.801353π0.801353\pi
458458 −90.5071 −0.197614
459459 33.2645i 0.0724716i
460460 −169.773 169.773i −0.369072 0.369072i
461461 −203.938 203.938i −0.442381 0.442381i 0.450430 0.892812i 0.351271π-0.351271\pi
−0.892812 + 0.450430i 0.851271π0.851271\pi
462462 93.2054 93.2054i 0.201743 0.201743i
463463 −481.370 + 481.370i −1.03968 + 1.03968i −0.0404953 + 0.999180i 0.512894π0.512894\pi
−0.999180 + 0.0404953i 0.987106π0.987106\pi
464464 −48.3210 −0.104140
465465 75.8812i 0.163185i
466466 55.4127 55.4127i 0.118911 0.118911i
467467 7.71730i 0.0165253i 0.999966 + 0.00826263i 0.00263011π0.00263011\pi
−0.999966 + 0.00826263i 0.997370π0.997370\pi
468468 109.362 + 50.1462i 0.233680 + 0.107150i
469469 −336.543 −0.717576
470470 −80.3663 80.3663i −0.170992 0.170992i
471471 260.429 0.552928
472472 363.201i 0.769494i
473473 428.670 + 428.670i 0.906280 + 0.906280i
474474 −119.539 119.539i −0.252193 0.252193i
475475 154.762 154.762i 0.325815 0.325815i
476476 78.2841 78.2841i 0.164462 0.164462i
477477 −290.380 −0.608763
478478 6.92665i 0.0144909i
479479 24.7867 24.7867i 0.0517467 0.0517467i −0.680760 0.732507i 0.738350π-0.738350\pi
0.732507 + 0.680760i 0.238350π0.238350\pi
480480 126.608i 0.263767i
481481 −238.358 642.056i −0.495546 1.33484i
482482 205.907 0.427193
483483 −239.136 239.136i −0.495105 0.495105i
484484 −247.976 −0.512346
485485 185.508i 0.382491i
486486 −10.5444 10.5444i −0.0216963 0.0216963i
487487 245.469 + 245.469i 0.504044 + 0.504044i 0.912692 0.408648i 0.134000π-0.134000\pi
−0.408648 + 0.912692i 0.634000π0.634000\pi
488488 −437.481 + 437.481i −0.896477 + 0.896477i
489489 −290.194 + 290.194i −0.593444 + 0.593444i
490490 37.5650 0.0766632
491491 25.3996i 0.0517304i −0.999665 0.0258652i 0.991766π-0.991766\pi
0.999665 0.0258652i 0.00823406π-0.00823406\pi
492492 −153.361 + 153.361i −0.311709 + 0.311709i
493493 52.8224i 0.107145i
494494 123.664 + 56.7040i 0.250332 + 0.114785i
495495 −95.1320 −0.192186
496496 −81.1861 81.1861i −0.163682 0.163682i
497497 236.714 0.476285
498498 199.819i 0.401242i
499499 −328.094 328.094i −0.657502 0.657502i 0.297286 0.954788i 0.403918π-0.403918\pi
−0.954788 + 0.297286i 0.903918π0.903918\pi
500500 −219.380 219.380i −0.438760 0.438760i
501501 −58.4753 + 58.4753i −0.116717 + 0.116717i
502502 −150.083 + 150.083i −0.298971 + 0.298971i
503503 −399.152 −0.793543 −0.396771 0.917918i 0.629869π-0.629869\pi
−0.396771 + 0.917918i 0.629869π0.629869\pi
504504 113.982i 0.226156i
505505 −205.608 + 205.608i −0.407145 + 0.407145i
506506 472.820i 0.934428i
507507 −191.012 221.805i −0.376749 0.437486i
508508 401.674 0.790697
509509 655.020 + 655.020i 1.28688 + 1.28688i 0.936674 + 0.350203i 0.113887π0.113887\pi
0.350203 + 0.936674i 0.386113π0.386113\pi
510510 23.7021 0.0464747
511511 87.1678i 0.170583i
512512 −247.720 247.720i −0.483829 0.483829i
513513 40.1949 + 40.1949i 0.0783526 + 0.0783526i
514514 −10.1709 + 10.1709i −0.0197877 + 0.0197877i
515515 −44.1185 + 44.1185i −0.0856670 + 0.0856670i
516516 −228.259 −0.442363
517517 754.525i 1.45943i
518518 199.772 199.772i 0.385660 0.385660i
519519 260.206i 0.501361i
520520 82.0610 178.964i 0.157810 0.344162i
521521 287.758 0.552318 0.276159 0.961112i 0.410938π-0.410938\pi
0.276159 + 0.961112i 0.410938π0.410938\pi
522522 −16.7440 16.7440i −0.0320767 0.0320767i
523523 −148.325 −0.283604 −0.141802 0.989895i 0.545290π-0.545290\pi
−0.141802 + 0.989895i 0.545290π0.545290\pi
524524 418.099i 0.797898i
525525 −137.363 137.363i −0.261644 0.261644i
526526 71.5139 + 71.5139i 0.135958 + 0.135958i
527527 −88.7492 + 88.7492i −0.168405 + 0.168405i
528528 101.783 101.783i 0.192770 0.192770i
529529 −684.108 −1.29321
530530 206.906i 0.390389i
531531 113.680 113.680i 0.214087 0.214087i
532532 189.188i 0.355617i
533533 494.692 183.650i 0.928127 0.344559i
534534 149.616 0.280180
535535 262.558 + 262.558i 0.490763 + 0.490763i
536536 406.874 0.759094
537537 427.999i 0.797019i
538538 −114.140 114.140i −0.212156 0.212156i
539539 −176.341 176.341i −0.327163 0.327163i
540540 25.3280 25.3280i 0.0469037 0.0469037i
541541 −378.819 + 378.819i −0.700221 + 0.700221i −0.964458 0.264237i 0.914880π-0.914880\pi
0.264237 + 0.964458i 0.414880π0.414880\pi
542542 70.9958 0.130989
543543 193.426i 0.356217i
544544 −148.078 + 148.078i −0.272202 + 0.272202i
545545 14.4227i 0.0264637i
546546 50.3291 109.761i 0.0921779 0.201028i
547547 63.2197 0.115575 0.0577876 0.998329i 0.481595π-0.481595\pi
0.0577876 + 0.998329i 0.481595π0.481595\pi
548548 −418.062 418.062i −0.762888 0.762888i
549549 273.859 0.498833
550550 271.595i 0.493810i
551551 63.8276 + 63.8276i 0.115839 + 0.115839i
552552 289.110 + 289.110i 0.523750 + 0.523750i
553553 404.450 404.450i 0.731374 0.731374i
554554 103.505 103.505i 0.186832 0.186832i
555555 −203.901 −0.367390
556556 752.735i 1.35384i
557557 599.495 599.495i 1.07629 1.07629i 0.0794543 0.996839i 0.474682π-0.474682\pi
0.996839 0.0794543i 0.0253178π-0.0253178\pi
558558 56.2647i 0.100833i
559559 504.815 + 231.474i 0.903067 + 0.414086i
560560 −73.3598 −0.131000
561561 −111.264 111.264i −0.198332 0.198332i
562562 −51.2578 −0.0912060
563563 79.3967i 0.141024i 0.997511 + 0.0705122i 0.0224634π0.0224634\pi
−0.997511 + 0.0705122i 0.977537π0.977537\pi
564564 −200.885 200.885i −0.356180 0.356180i
565565 −95.9937 95.9937i −0.169900 0.169900i
566566 −23.4870 + 23.4870i −0.0414964 + 0.0414964i
567567 35.6760 35.6760i 0.0629207 0.0629207i
568568 −286.182 −0.503842
569569 27.2834i 0.0479497i −0.999713 0.0239748i 0.992368π-0.992368\pi
0.999713 0.0239748i 0.00763216π-0.00763216\pi
570570 28.6403 28.6403i 0.0502461 0.0502461i
571571 73.0650i 0.127960i 0.997951 + 0.0639799i 0.0203793π0.0203793\pi
−0.997951 + 0.0639799i 0.979621π0.979621\pi
572572 −533.531 + 198.069i −0.932747 + 0.346274i
573573 −112.062 −0.195571
574574 153.920 + 153.920i 0.268154 + 0.268154i
575575 −696.828 −1.21187
576576 23.6033i 0.0409779i
577577 172.432 + 172.432i 0.298841 + 0.298841i 0.840560 0.541719i 0.182226π-0.182226\pi
−0.541719 + 0.840560i 0.682226π0.682226\pi
578578 −167.765 167.765i −0.290251 0.290251i
579579 168.180 168.180i 0.290466 0.290466i
580580 40.2197 40.2197i 0.0693443 0.0693443i
581581 −676.067 −1.16363
582582 137.551i 0.236343i
583583 971.276 971.276i 1.66600 1.66600i
584584 105.384i 0.180452i
585585 −81.6998 + 30.3303i −0.139658 + 0.0518467i
586586 −73.6854 −0.125743
587587 766.322 + 766.322i 1.30549 + 1.30549i 0.924635 + 0.380854i 0.124370π0.124370\pi
0.380854 + 0.924635i 0.375630π0.375630\pi
588588 93.8982 0.159691
589589 214.479i 0.364141i
590590 −81.0013 81.0013i −0.137290 0.137290i
591591 84.6496 + 84.6496i 0.143231 + 0.143231i
592592 218.156 218.156i 0.368507 0.368507i
593593 120.360 120.360i 0.202969 0.202969i −0.598302 0.801271i 0.704158π-0.704158\pi
0.801271 + 0.598302i 0.204158π0.204158\pi
594594 70.5388 0.118752
595595 80.1938i 0.134779i
596596 539.508 539.508i 0.905215 0.905215i
597597 241.743i 0.404929i
598598 −150.746 406.060i −0.252084 0.679031i
599599 323.635 0.540292 0.270146 0.962819i 0.412928π-0.412928\pi
0.270146 + 0.962819i 0.412928π0.412928\pi
600600 166.069 + 166.069i 0.276782 + 0.276782i
601601 1108.97 1.84521 0.922607 0.385742i 0.126054π-0.126054\pi
0.922607 + 0.385742i 0.126054π0.126054\pi
602602 229.092i 0.380551i
603603 −127.350 127.350i −0.211194 0.211194i
604604 117.564 + 117.564i 0.194643 + 0.194643i
605605 127.012 127.012i 0.209938 0.209938i
606606 152.455 152.455i 0.251576 0.251576i
607607 −196.769 −0.324167 −0.162084 0.986777i 0.551821π-0.551821\pi
−0.162084 + 0.986777i 0.551821π0.551821\pi
608608 357.858i 0.588583i
609609 56.6518 56.6518i 0.0930243 0.0930243i
610610 195.134i 0.319892i
611611 240.561 + 647.990i 0.393716 + 1.06054i
612612 59.2463 0.0968076
613613 −702.697 702.697i −1.14633 1.14633i −0.987270 0.159055i 0.949155π-0.949155\pi
−0.159055 0.987270i 0.550845π-0.550845\pi
614614 −302.206 −0.492193
615615 157.102i 0.255450i
616616 −381.254 381.254i −0.618918 0.618918i
617617 −305.273 305.273i −0.494771 0.494771i 0.415035 0.909805i 0.363769π-0.363769\pi
−0.909805 + 0.415035i 0.863769π0.863769\pi
618618 32.7132 32.7132i 0.0529339 0.0529339i
619619 97.1707 97.1707i 0.156980 0.156980i −0.624247 0.781227i 0.714594π-0.714594\pi
0.781227 + 0.624247i 0.214594π0.214594\pi
620620 135.150 0.217983
621621 180.980i 0.291434i
622622 −349.359 + 349.359i −0.561670 + 0.561670i
623623 506.211i 0.812538i
624624 54.9607 119.862i 0.0880781 0.192087i
625625 −275.436 −0.440698
626626 100.946 + 100.946i 0.161255 + 0.161255i
627627 −268.891 −0.428854
628628 463.842i 0.738601i
629629 −238.479 238.479i −0.379140 0.379140i
630630 −25.4204 25.4204i −0.0403499 0.0403499i
631631 −368.719 + 368.719i −0.584341 + 0.584341i −0.936093 0.351752i 0.885586π-0.885586\pi
0.351752 + 0.936093i 0.385586π0.385586\pi
632632 −488.972 + 488.972i −0.773690 + 0.773690i
633633 91.7219 0.144900
634634 254.556i 0.401508i
635635 −205.736 + 205.736i −0.323994 + 0.323994i
636636 517.187i 0.813186i
637637 −207.664 95.2206i −0.326003 0.149483i
638638 112.012 0.175568
639639 89.5738 + 89.5738i 0.140178 + 0.140178i
640640 275.570 0.430579
641641 779.737i 1.21644i 0.793769 + 0.608219i 0.208116π0.208116\pi
−0.793769 + 0.608219i 0.791884π0.791884\pi
642642 −194.683 194.683i −0.303244 0.303244i
643643 −719.483 719.483i −1.11895 1.11895i −0.991896 0.127051i 0.959449π-0.959449\pi
−0.127051 0.991896i 0.540551π-0.540551\pi
644644 −425.917 + 425.917i −0.661361 + 0.661361i
645645 116.914 116.914i 0.181262 0.181262i
646646 66.9942 0.103706
647647 313.980i 0.485286i −0.970116 0.242643i 0.921986π-0.921986\pi
0.970116 0.242643i 0.0780144π-0.0780144\pi
648648 −43.1316 + 43.1316i −0.0665611 + 0.0665611i
649649 760.487i 1.17178i
650650 −86.5910 233.247i −0.133217 0.358842i
651651 190.366 0.292421
652652 516.856 + 516.856i 0.792724 + 0.792724i
653653 −280.037 −0.428847 −0.214424 0.976741i 0.568787π-0.568787\pi
−0.214424 + 0.976741i 0.568787π0.568787\pi
654654 10.6942i 0.0163520i
655655 214.149 + 214.149i 0.326945 + 0.326945i
656656 168.085 + 168.085i 0.256227 + 0.256227i
657657 −32.9848 + 32.9848i −0.0502051 + 0.0502051i
658658 −201.618 + 201.618i −0.306411 + 0.306411i
659659 −1021.28 −1.54974 −0.774871 0.632119i 0.782185π-0.782185\pi
−0.774871 + 0.632119i 0.782185π0.782185\pi
660660 169.437i 0.256722i
661661 638.747 638.747i 0.966334 0.966334i −0.0331178 0.999451i 0.510544π-0.510544\pi
0.999451 + 0.0331178i 0.0105436π0.0105436\pi
662662 180.942i 0.273326i
663663 −131.028 60.0807i −0.197629 0.0906195i
664664 817.352 1.23095
665665 96.9016 + 96.9016i 0.145717 + 0.145717i
666666 151.190 0.227012
667667 287.388i 0.430867i
668668 104.149 + 104.149i 0.155911 + 0.155911i
669669 122.020 + 122.020i 0.182392 + 0.182392i
670670 −90.7413 + 90.7413i −0.135435 + 0.135435i
671671 −916.016 + 916.016i −1.36515 + 1.36515i
672672 317.626 0.472658
673673 236.547i 0.351482i 0.984436 + 0.175741i 0.0562320π0.0562320\pi
−0.984436 + 0.175741i 0.943768π0.943768\pi
674674 −136.921 + 136.921i −0.203147 + 0.203147i
675675 103.958i 0.154012i
676676 −395.050 + 340.205i −0.584394 + 0.503261i
677677 −788.423 −1.16458 −0.582292 0.812980i 0.697844π-0.697844\pi
−0.582292 + 0.812980i 0.697844π0.697844\pi
678678 71.1778 + 71.1778i 0.104982 + 0.104982i
679679 −465.392 −0.685408
680680 96.9527i 0.142578i
681681 −164.579 164.579i −0.241672 0.241672i
682682 188.197 + 188.197i 0.275948 + 0.275948i
683683 −278.551 + 278.551i −0.407834 + 0.407834i −0.880983 0.473149i 0.843117π-0.843117\pi
0.473149 + 0.880983i 0.343117π0.343117\pi
684684 71.5898 71.5898i 0.104663 0.104663i
685685 428.261 0.625198
686686 357.013i 0.520427i
687687 115.876 115.876i 0.168670 0.168670i
688688 250.174i 0.363626i
689689 524.471 1143.80i 0.761206 1.66009i
690690 −128.955 −0.186891
691691 −64.4993 64.4993i −0.0933420 0.0933420i 0.658894 0.752236i 0.271025π-0.271025\pi
−0.752236 + 0.658894i 0.771025π0.771025\pi
692692 463.445 0.669718
693693 238.661i 0.344389i
694694 −129.109 129.109i −0.186037 0.186037i
695695 −385.549 385.549i −0.554746 0.554746i
696696 −68.4909 + 68.4909i −0.0984065 + 0.0984065i
697697 183.743 183.743i 0.263620 0.263620i
698698 638.590 0.914886
699699 141.890i 0.202989i
700700 −244.653 + 244.653i −0.349504 + 0.349504i
701701 136.339i 0.194493i 0.995260 + 0.0972463i 0.0310035π0.0310035\pi
−0.995260 + 0.0972463i 0.968997π0.968997\pi
702702 60.5791 22.4895i 0.0862950 0.0320363i
703703 −576.329 −0.819814
704704 78.9493 + 78.9493i 0.112144 + 0.112144i
705705 205.786 0.291895
706706 403.824i 0.571989i
707707 515.818 + 515.818i 0.729587 + 0.729587i
708708 −202.473 202.473i −0.285978 0.285978i
709709 789.276 789.276i 1.11322 1.11322i 0.120513 0.992712i 0.461546π-0.461546\pi
0.992712 0.120513i 0.0384540π-0.0384540\pi
710710 63.8245 63.8245i 0.0898936 0.0898936i
711711 306.092 0.430509
712712 611.999i 0.859549i
713713 482.854 482.854i 0.677214 0.677214i
714714 59.4624i 0.0832807i
715715 171.823 374.723i 0.240312 0.524089i
716716 762.296 1.06466
717717 8.86818 + 8.86818i 0.0123685 + 0.0123685i
718718 116.834 0.162721
719719 949.863i 1.32109i −0.750787 0.660544i 0.770326π-0.770326\pi
0.750787 0.660544i 0.229674π-0.229674\pi
720720 −27.7598 27.7598i −0.0385552 0.0385552i
721721 110.682 + 110.682i 0.153512 + 0.153512i
722722 −163.237 + 163.237i −0.226091 + 0.226091i
723723 −263.623 + 263.623i −0.364623 + 0.364623i
724724 −344.505 −0.475835
725725 165.080i 0.227697i
726726 −94.1777 + 94.1777i −0.129721 + 0.129721i
727727 195.690i 0.269175i −0.990902 0.134588i 0.957029π-0.957029\pi
0.990902 0.134588i 0.0429710π-0.0429710\pi
728728 −448.975 205.870i −0.616724 0.282788i
729729 27.0000 0.0370370
730730 23.5028 + 23.5028i 0.0321956 + 0.0321956i
731731 273.480 0.374117
732732 487.762i 0.666341i
733733 −373.535 373.535i −0.509597 0.509597i 0.404806 0.914403i 0.367339π-0.367339\pi
−0.914403 + 0.404806i 0.867339π0.867339\pi
734734 36.6588 + 36.6588i 0.0499439 + 0.0499439i
735735 −48.0944 + 48.0944i −0.0654345 + 0.0654345i
736736 805.642 805.642i 1.09462 1.09462i
737737 851.931 1.15594
738738 116.489i 0.157844i
739739 −868.098 + 868.098i −1.17469 + 1.17469i −0.193615 + 0.981078i 0.562021π0.562021\pi
−0.981078 + 0.193615i 0.937979π0.937979\pi
740740 363.162i 0.490760i
741741 −230.925 + 85.7289i −0.311640 + 0.115694i
742742 519.073 0.699560
743743 −744.696 744.696i −1.00228 1.00228i −0.999997 0.00228459i 0.999273π-0.999273\pi
−0.00228459 0.999997i 0.500727π-0.500727\pi
744744 −230.149 −0.309340
745745 552.669i 0.741837i
746746 12.1325 + 12.1325i 0.0162633 + 0.0162633i
747747 −255.828 255.828i −0.342473 0.342473i
748748 −198.170 + 198.170i −0.264933 + 0.264933i
749749 658.690 658.690i 0.879426 0.879426i
750750 −166.635 −0.222180
751751 267.175i 0.355760i 0.984052 + 0.177880i 0.0569238π0.0569238\pi
−0.984052 + 0.177880i 0.943076π0.943076\pi
752752 −220.172 + 220.172i −0.292783 + 0.292783i
753753 384.303i 0.510362i
754754 96.1967 35.7122i 0.127582 0.0473636i
755755 −120.432 −0.159513
756756 −63.5414 63.5414i −0.0840495 0.0840495i
757757 −421.716 −0.557088 −0.278544 0.960423i 0.589852π-0.589852\pi
−0.278544 + 0.960423i 0.589852π0.589852\pi
758758 380.915i 0.502527i
759759 605.351 + 605.351i 0.797565 + 0.797565i
760760 −117.152 117.152i −0.154148 0.154148i
761761 937.965 937.965i 1.23254 1.23254i 0.269558 0.962984i 0.413122π-0.413122\pi
0.962984 0.269558i 0.0868776π-0.0868776\pi
762762 152.550 152.550i 0.200197 0.200197i
763763 −36.1828 −0.0474218
764764 199.590i 0.261244i
765765 −30.3458 + 30.3458i −0.0396677 + 0.0396677i
766766 331.214i 0.432395i
767767 242.461 + 653.109i 0.316116 + 0.851512i
768768 −258.840 −0.337032
769769 749.082 + 749.082i 0.974098 + 0.974098i 0.999673 0.0255747i 0.00814156π-0.00814156\pi
−0.0255747 + 0.999673i 0.508142π0.508142\pi
770770 170.055 0.220850
771771 26.0436i 0.0337789i
772772 −299.539 299.539i −0.388004 0.388004i
773773 292.773 + 292.773i 0.378749 + 0.378749i 0.870651 0.491902i 0.163698π-0.163698\pi
−0.491902 + 0.870651i 0.663698π0.663698\pi
774774 −86.6896 + 86.6896i −0.112002 + 0.112002i
775775 277.358 277.358i 0.357882 0.357882i
776776 562.650 0.725064
777777 511.536i 0.658347i
778778 393.855 393.855i 0.506241 0.506241i
779779 444.050i 0.570025i
780780 54.0204 + 145.513i 0.0692569 + 0.186555i
781781 −599.221 −0.767248
782782 −150.823 150.823i −0.192868 0.192868i
783783 42.8747 0.0547570
784784 102.913i 0.131267i
785785 237.578 + 237.578i 0.302648 + 0.302648i
786786 −158.788 158.788i −0.202020 0.202020i
787787 −992.205 + 992.205i −1.26074 + 1.26074i −0.310010 + 0.950733i 0.600332π0.600332\pi
−0.950733 + 0.310010i 0.899668π0.899668\pi
788788 150.767 150.767i 0.191328 0.191328i
789789 −183.118 −0.232089
790790 218.101i 0.276078i
791791 −240.823 + 240.823i −0.304454 + 0.304454i
792792 288.537i 0.364314i
793793 −494.631 + 1078.73i −0.623747 + 1.36031i
794794 −503.341 −0.633931
795795 −264.902 264.902i −0.333209 0.333209i
796796 −430.560 −0.540905
797797 96.6901i 0.121318i −0.998159 0.0606588i 0.980680π-0.980680\pi
0.998159 0.0606588i 0.0193202π-0.0193202\pi
798798 −71.8510 71.8510i −0.0900388 0.0900388i
799799 240.683 + 240.683i 0.301230 + 0.301230i
800800 462.773 462.773i 0.578466 0.578466i
801801 −191.553 + 191.553i −0.239142 + 0.239142i
802802 514.423 0.641425
803803 220.658i 0.274792i
804804 −226.819 + 226.819i −0.282113 + 0.282113i
805805 436.307i 0.541996i
806806 221.626 + 101.623i 0.274970 + 0.126083i
807807 292.266 0.362163
808808 −623.614 623.614i −0.771799 0.771799i
809809 −800.289 −0.989233 −0.494616 0.869111i 0.664691π-0.664691\pi
−0.494616 + 0.869111i 0.664691π0.664691\pi
810810 19.2384i 0.0237512i
811811 1015.91 + 1015.91i 1.25267 + 1.25267i 0.954520 + 0.298147i 0.0963686π0.0963686\pi
0.298147 + 0.954520i 0.403631π0.403631\pi
812812 −100.901 100.901i −0.124262 0.124262i
813813 −90.8958 + 90.8958i −0.111803 + 0.111803i
814814 −505.706 + 505.706i −0.621260 + 0.621260i
815815 −529.464 −0.649649
816816 64.9345i 0.0795766i
817817 330.457 330.457i 0.404476 0.404476i
818818 79.2532i 0.0968866i
819819 76.0909 + 204.964i 0.0929071 + 0.250261i
820820 −279.809 −0.341231
821821 −515.901 515.901i −0.628381 0.628381i 0.319280 0.947661i 0.396559π-0.396559\pi
−0.947661 + 0.319280i 0.896559π0.896559\pi
822822 −317.548 −0.386312
823823 563.080i 0.684179i 0.939667 + 0.342090i 0.111135π0.111135\pi
−0.939667 + 0.342090i 0.888865π0.888865\pi
824824 −133.812 133.812i −0.162393 0.162393i
825825 347.723 + 347.723i 0.421483 + 0.421483i
826826 −203.211 + 203.211i −0.246018 + 0.246018i
827827 −129.875 + 129.875i −0.157044 + 0.157044i −0.781255 0.624212i 0.785420π-0.785420\pi
0.624212 + 0.781255i 0.285420π0.285420\pi
828828 −322.338 −0.389298
829829 1140.27i 1.37548i −0.725957 0.687740i 0.758603π-0.758603\pi
0.725957 0.687740i 0.241397π-0.241397\pi
830830 −182.286 + 182.286i −0.219622 + 0.219622i
831831 265.035i 0.318935i
832832 92.9730 + 42.6311i 0.111746 + 0.0512394i
833833 −112.500 −0.135055
834834 285.878 + 285.878i 0.342779 + 0.342779i
835835 −106.689 −0.127771
836836 478.913i 0.572863i
837837 72.0356 + 72.0356i 0.0860641 + 0.0860641i
838838 305.737 + 305.737i 0.364841 + 0.364841i
839839 373.307 373.307i 0.444942 0.444942i −0.448727 0.893669i 0.648122π-0.648122\pi
0.893669 + 0.448727i 0.148122π0.148122\pi
840840 −103.981 + 103.981i −0.123787 + 0.123787i
841841 −772.917 −0.919045
842842 73.8044i 0.0876537i
843843 65.6252 65.6252i 0.0778473 0.0778473i
844844 163.363i 0.193558i
845845 28.0916 376.595i 0.0332445 0.445675i
846846 −152.587 −0.180363
847847 −318.641 318.641i −0.376200 0.376200i
848848 566.842 0.668446
849849 60.1406i 0.0708370i
850850 −86.6351 86.6351i −0.101924 0.101924i
851851 1297.48 + 1297.48i 1.52466 + 1.52466i
852852 159.537 159.537i 0.187250 0.187250i
853853 −65.1164 + 65.1164i −0.0763381 + 0.0763381i −0.744245 0.667907i 0.767190π-0.767190\pi
0.667907 + 0.744245i 0.267190π0.267190\pi
854854 −489.541 −0.573233
855855 73.3362i 0.0857733i
856856 −796.344 + 796.344i −0.930308 + 0.930308i
857857 98.7570i 0.115236i −0.998339 0.0576178i 0.981650π-0.981650\pi
0.998339 0.0576178i 0.0183505π-0.0183505\pi
858858 −127.404 + 277.851i −0.148489 + 0.323836i
859859 959.271 1.11673 0.558365 0.829595i 0.311429π-0.311429\pi
0.558365 + 0.829595i 0.311429π0.311429\pi
860860 −208.231 208.231i −0.242129 0.242129i
861861 −394.128 −0.457756
862862 572.063i 0.663647i
863863 −30.4807 30.4807i −0.0353194 0.0353194i 0.689227 0.724546i 0.257950π-0.257950\pi
−0.724546 + 0.689227i 0.757950π0.757950\pi
864864 120.192 + 120.192i 0.139111 + 0.139111i
865865 −237.375 + 237.375i −0.274422 + 0.274422i
866866 420.489 420.489i 0.485554 0.485554i
867867 429.579 0.495478
868868 339.055i 0.390617i
869869 −1023.83 + 1023.83i −1.17817 + 1.17817i
870870 30.5497i 0.0351146i
871871 731.642 271.616i 0.840003 0.311844i
872872 43.7443 0.0501655
873873 −176.107 176.107i −0.201726 0.201726i
874874 −364.492 −0.417039
875875 563.793i 0.644334i
876876 58.7481 + 58.7481i 0.0670640 + 0.0670640i
877877 66.1101 + 66.1101i 0.0753821 + 0.0753821i 0.743793 0.668410i 0.233025π-0.233025\pi
−0.668410 + 0.743793i 0.733025π0.733025\pi
878878 −282.064 + 282.064i −0.321257 + 0.321257i
879879 94.3393 94.3393i 0.107326 0.107326i
880880 185.704 0.211027
881881 825.315i 0.936794i 0.883518 + 0.468397i 0.155168π0.155168\pi
−0.883518 + 0.468397i 0.844832π0.844832\pi
882882 35.6612 35.6612i 0.0404322 0.0404322i
883883 1501.16i 1.70007i −0.526724 0.850037i 0.676580π-0.676580\pi
0.526724 0.850037i 0.323420π-0.323420\pi
884884 −107.008 + 233.370i −0.121050 + 0.263993i
885885 207.412 0.234363
886886 −393.614 393.614i −0.444260 0.444260i
887887 −122.414 −0.138009 −0.0690045 0.997616i 0.521982π-0.521982\pi
−0.0690045 + 0.997616i 0.521982π0.521982\pi
888888 618.437i 0.696438i
889889 516.139 + 516.139i 0.580584 + 0.580584i
890890 136.488 + 136.488i 0.153358 + 0.153358i
891891 −90.3108 + 90.3108i −0.101359 + 0.101359i
892892 217.326 217.326i 0.243639 0.243639i
893893 581.655 0.651349
894894 409.795i 0.458384i
895895 −390.446 + 390.446i −0.436252 + 0.436252i
896896 691.334i 0.771578i
897897 712.879 + 326.878i 0.794737 + 0.364413i
898898 90.3144 0.100573
899899 114.389 + 114.389i 0.127240 + 0.127240i
900900 −185.156 −0.205729
901901 619.647i 0.687732i
902902 −389.636 389.636i −0.431969 0.431969i
903903 −293.306 293.306i −0.324813 0.324813i
904904 291.150 291.150i 0.322069 0.322069i
905905 176.454 176.454i 0.194977 0.194977i
906906 89.2984 0.0985633
907907 976.517i 1.07665i −0.842739 0.538323i 0.819058π-0.819058\pi
0.842739 0.538323i 0.180942π-0.180942\pi
908908 −293.126 + 293.126i −0.322825 + 0.322825i
909909 390.377i 0.429457i
910910 146.044 54.2174i 0.160488 0.0595796i
911911 −1291.48 −1.41765 −0.708825 0.705384i 0.750775π-0.750775\pi
−0.708825 + 0.705384i 0.750775π0.750775\pi
912912 −78.4632 78.4632i −0.0860342 0.0860342i
913913 1711.41 1.87449
914914 140.446i 0.153661i
915915 249.830 + 249.830i 0.273038 + 0.273038i
916916 −206.383 206.383i −0.225309 0.225309i
917917 537.244 537.244i 0.585871 0.585871i
918918 22.5009 22.5009i 0.0245108 0.0245108i
919919 1651.58 1.79715 0.898575 0.438819i 0.144603π-0.144603\pi
0.898575 + 0.438819i 0.144603π0.144603\pi
920920 527.486i 0.573355i
921921 386.914 386.914i 0.420103 0.420103i
922922 275.897i 0.299238i
923923 −514.614 + 191.046i −0.557544 + 0.206983i
924924 425.072 0.460035
925925 745.293 + 745.293i 0.805723 + 0.805723i
926926 651.220 0.703262
927927 83.7652i 0.0903616i
928928 190.858 + 190.858i 0.205666 + 0.205666i
929929 644.310 + 644.310i 0.693552 + 0.693552i 0.963012 0.269460i 0.0868451π-0.0868451\pi
−0.269460 + 0.963012i 0.586845π0.586845\pi
930930 51.3279 51.3279i 0.0551913 0.0551913i
931931 −135.939 + 135.939i −0.146014 + 0.146014i
932932 252.715 0.271153
933933 894.567i 0.958807i
934934 5.22017 5.22017i 0.00558905 0.00558905i
935935 203.004i 0.217116i
936936 −91.9924 247.797i −0.0982825 0.264740i
937937 −939.846 −1.00304 −0.501519 0.865147i 0.667225π-0.667225\pi
−0.501519 + 0.865147i 0.667225π0.667225\pi
938938 227.646 + 227.646i 0.242693 + 0.242693i
939939 −258.482 −0.275273
940940 366.519i 0.389913i
941941 −767.549 767.549i −0.815674 0.815674i 0.169804 0.985478i 0.445687π-0.445687\pi
−0.985478 + 0.169804i 0.945687π0.945687\pi
942942 −176.160 176.160i −0.187007 0.187007i
943943 −999.684 + 999.684i −1.06011 + 1.06011i
944944 −221.912 + 221.912i −0.235076 + 0.235076i
945945 65.0914 0.0688798
946946 579.926i 0.613030i
947947 −518.599 + 518.599i −0.547623 + 0.547623i −0.925753 0.378130i 0.876567π-0.876567\pi
0.378130 + 0.925753i 0.376567π0.376567\pi
948948 545.171i 0.575075i
949949 −70.3509 189.502i −0.0741316 0.199686i
950950 −209.370 −0.220389
951951 −325.908 325.908i −0.342700 0.342700i
952952 −243.229 −0.255493
953953 1429.04i 1.49952i 0.661709 + 0.749761i 0.269831π0.269831\pi
−0.661709 + 0.749761i 0.730169π0.730169\pi
954954 196.420 + 196.420i 0.205891 + 0.205891i
955955 −102.230 102.230i −0.107047 0.107047i
956956 15.7948 15.7948i 0.0165218 0.0165218i
957957 −143.409 + 143.409i −0.149853 + 0.149853i
958958 −33.5326 −0.0350027
959959 1074.39i 1.12033i
960960 21.5323 21.5323i 0.0224295 0.0224295i
961961 576.620i 0.600020i
962962 −273.072 + 595.534i −0.283858 + 0.619058i
963963 498.504 0.517657
964964 469.530 + 469.530i 0.487064 + 0.487064i
965965 306.847 0.317976
966966 323.514i 0.334901i
967967 507.433 + 507.433i 0.524749 + 0.524749i 0.919002 0.394253i 0.128997π-0.128997\pi
−0.394253 + 0.919002i 0.628997π0.628997\pi
968968 385.231 + 385.231i 0.397966 + 0.397966i
969969 −85.7725 + 85.7725i −0.0885165 + 0.0885165i
970970 −125.482 + 125.482i −0.129363 + 0.129363i
971971 832.781 0.857652 0.428826 0.903387i 0.358927π-0.358927\pi
0.428826 + 0.903387i 0.358927π0.358927\pi
972972 48.0888i 0.0494741i
973973 −967.241 + 967.241i −0.994081 + 0.994081i
974974 332.083i 0.340947i
975975 409.489 + 187.764i 0.419988 + 0.192578i
976976 −534.592 −0.547738
977977 −562.185 562.185i −0.575419 0.575419i 0.358219 0.933638i 0.383384π-0.383384\pi
−0.933638 + 0.358219i 0.883384π0.883384\pi
978978 392.589 0.401420
979979 1281.43i 1.30892i
980980 85.6593 + 85.6593i 0.0874075 + 0.0874075i
981981 −13.6918 13.6918i −0.0139570 0.0139570i
982982 −17.1809 + 17.1809i −0.0174958 + 0.0174958i
983983 351.787 351.787i 0.357870 0.357870i −0.505157 0.863027i 0.668565π-0.668565\pi
0.863027 + 0.505157i 0.168565π0.168565\pi
984984 476.493 0.484241
985985 154.445i 0.156797i
986986 35.7304 35.7304i 0.0362377 0.0362377i
987987 516.263i 0.523063i
988988 152.689 + 411.293i 0.154543 + 0.416289i
989989 −1487.91 −1.50446
990990 64.3496 + 64.3496i 0.0649996 + 0.0649996i
991991 96.6030 0.0974803 0.0487401 0.998811i 0.484479π-0.484479\pi
0.0487401 + 0.998811i 0.484479π0.484479\pi
992992 641.339i 0.646511i
993993 −231.659 231.659i −0.233292 0.233292i
994994 −160.119 160.119i −0.161085 0.161085i
995995 220.532 220.532i 0.221640 0.221640i
996996 −455.646 + 455.646i −0.457476 + 0.457476i
997997 −1290.54 −1.29443 −0.647213 0.762309i 0.724065π-0.724065\pi
−0.647213 + 0.762309i 0.724065π0.724065\pi
998998 443.861i 0.444751i
999999 −193.568 + 193.568i −0.193762 + 0.193762i
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 39.3.g.a.34.2 yes 8
3.2 odd 2 117.3.j.b.73.3 8
4.3 odd 2 624.3.ba.b.385.2 8
13.5 odd 4 inner 39.3.g.a.31.2 8
39.5 even 4 117.3.j.b.109.3 8
52.31 even 4 624.3.ba.b.577.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.3.g.a.31.2 8 13.5 odd 4 inner
39.3.g.a.34.2 yes 8 1.1 even 1 trivial
117.3.j.b.73.3 8 3.2 odd 2
117.3.j.b.109.3 8 39.5 even 4
624.3.ba.b.385.2 8 4.3 odd 2
624.3.ba.b.577.2 8 52.31 even 4