Properties

Label 980.2.g.a.391.20
Level 980980
Weight 22
Character 980.391
Analytic conductor 7.8257.825
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(391,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.391");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 980=22572 980 = 2^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 980.g (of order 22, degree 11, 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: 7.825339398097.82533939809
Analytic rank: 00
Dimension: 3232
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 391.20
Character χ\chi == 980.391
Dual form 980.2.g.a.391.18

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+(0.0982654+1.41080i)q2+0.662355q3+(1.98069+0.277265i)q4+1.00000iq5+(0.0650866+0.934447i)q6+(0.5857972.76710i)q82.56129q9+(1.41080+0.0982654i)q103.61296iq11+(1.31192+0.183648i)q125.83027iq13+0.662355iq15+(3.846251.09835i)q161.36813iq17+(0.2516863.61345i)q184.09577q19+(0.2772651.98069i)q20+(5.097150.355029i)q223.24519iq23+(0.3880051.83280i)q241.00000q25+(8.225320.572914i)q263.68354q27+5.19327q29+(0.934447+0.0650866i)q308.86809q31+(1.92750+5.31834i)q322.39306iq33+(1.930140.134439i)q34+(5.073110.710155i)q36+10.7958q37+(0.4024725.77829i)q383.86171iq39+(2.767100.585797i)q40+0.832730iq41+3.10642iq43+(1.00175+7.15615i)q442.56129iq45+(4.578300.318890i)q466.89601q47+(2.547580.727497i)q48+(0.09826541.41080i)q500.906184iq51+(1.61653+11.5479i)q527.41752q53+(0.3619655.19673i)q54+3.61296q552.71285q57+(0.510319+7.32664i)q58+7.47856q59+(0.1836481.31192i)q601.48554iq61+(0.87142712.5111i)q62+(7.31368+3.24192i)q64+5.83027q65+(3.376120.235155i)q662.53761iq67+(0.379333+2.70983i)q682.14947iq693.52502iq71+(1.50039+7.08734i)q725.16984iq73+(1.06085+15.2306i)q740.662355q75+(8.112441.13561i)q76+(5.448080.379472i)q7811.3401iq79+(1.09835+3.84625i)q80+5.24405q81+(1.17481+0.0818286i)q826.49145q83+1.36813q85+(4.38252+0.305254i)q86+3.43978q87+(9.99743+2.11646i)q889.39121iq89+(3.613450.251686i)q90+(0.899777+6.42771i)q925.87382q93+(0.6776409.72886i)q944.09577iq95+(1.27669+3.52263i)q96+0.343189iq97+9.25383iq99+O(q100)q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(-1.41080 + 0.0982654i) q^{10} -3.61296i q^{11} +(-1.31192 + 0.183648i) q^{12} -5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} -1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} -4.09577 q^{19} +(-0.277265 - 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(-0.388005 - 1.83280i) q^{24} -1.00000 q^{25} +(8.22532 - 0.572914i) q^{26} -3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} -8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} -2.39306i q^{33} +(1.93014 - 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(-0.402472 - 5.77829i) q^{38} -3.86171i q^{39} +(2.76710 - 0.585797i) q^{40} +0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} -2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} -6.89601 q^{47} +(2.54758 - 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(1.61653 + 11.5479i) q^{52} -7.41752 q^{53} +(-0.361965 - 5.19673i) q^{54} +3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} +7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} -1.48554i q^{61} +(-0.871427 - 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(3.37612 - 0.235155i) q^{66} -2.53761i q^{67} +(0.379333 + 2.70983i) q^{68} -2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} -5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} -0.662355 q^{75} +(8.11244 - 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(1.09835 + 3.84625i) q^{80} +5.24405 q^{81} +(-1.17481 + 0.0818286i) q^{82} -6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} +3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} -9.39121i q^{89} +(3.61345 - 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(-0.677640 - 9.72886i) q^{94} -4.09577i q^{95} +(1.27669 + 3.52263i) q^{96} +0.343189i q^{97} +9.25383i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q4q2+4q44q8+32q9+28q168q2232q2540q294q32+60q3616q37+36q444q46+4q50+16q53+48q574q5828q60++16q93+O(q100) 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60}+ \cdots + 16 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/980Z)×\left(\mathbb{Z}/980\mathbb{Z}\right)^\times.

nn 101101 197197 491491
χ(n)\chi(n) 1-1 11 1-1

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 0.0982654 + 1.41080i 0.0694842 + 0.997583i
33 0.662355 0.382411 0.191205 0.981550i 0.438760π-0.438760\pi
0.191205 + 0.981550i 0.438760π0.438760\pi
44 −1.98069 + 0.277265i −0.990344 + 0.138632i
55 1.00000i 0.447214i
66 0.0650866 + 0.934447i 0.0265715 + 0.381486i
77 0 0
88 −0.585797 2.76710i −0.207111 0.978318i
99 −2.56129 −0.853762
1010 −1.41080 + 0.0982654i −0.446133 + 0.0310743i
1111 3.61296i 1.08935i −0.838648 0.544674i 0.816653π-0.816653\pi
0.838648 0.544674i 0.183347π-0.183347\pi
1212 −1.31192 + 0.183648i −0.378718 + 0.0530145i
1313 5.83027i 1.61703i −0.588478 0.808513i 0.700273π-0.700273\pi
0.588478 0.808513i 0.299727π-0.299727\pi
1414 0 0
1515 0.662355i 0.171019i
1616 3.84625 1.09835i 0.961562 0.274588i
1717 1.36813i 0.331819i −0.986141 0.165910i 0.946944π-0.946944\pi
0.986141 0.165910i 0.0530560π-0.0530560\pi
1818 −0.251686 3.61345i −0.0593229 0.851699i
1919 −4.09577 −0.939634 −0.469817 0.882764i 0.655680π-0.655680\pi
−0.469817 + 0.882764i 0.655680π0.655680\pi
2020 −0.277265 1.98069i −0.0619983 0.442895i
2121 0 0
2222 5.09715 0.355029i 1.08672 0.0756925i
2323 3.24519i 0.676669i −0.941026 0.338334i 0.890136π-0.890136\pi
0.941026 0.338334i 0.109864π-0.109864\pi
2424 −0.388005 1.83280i −0.0792013 0.374119i
2525 −1.00000 −0.200000
2626 8.22532 0.572914i 1.61312 0.112358i
2727 −3.68354 −0.708898
2828 0 0
2929 5.19327 0.964365 0.482183 0.876071i 0.339844π-0.339844\pi
0.482183 + 0.876071i 0.339844π0.339844\pi
3030 −0.934447 + 0.0650866i −0.170606 + 0.0118831i
3131 −8.86809 −1.59276 −0.796378 0.604799i 0.793254π-0.793254\pi
−0.796378 + 0.604799i 0.793254π0.793254\pi
3232 1.92750 + 5.31834i 0.340737 + 0.940159i
3333 2.39306i 0.416579i
3434 1.93014 0.134439i 0.331017 0.0230562i
3535 0 0
3636 5.07311 0.710155i 0.845518 0.118359i
3737 10.7958 1.77482 0.887408 0.460985i 0.152504π-0.152504\pi
0.887408 + 0.460985i 0.152504π0.152504\pi
3838 −0.402472 5.77829i −0.0652897 0.937363i
3939 3.86171i 0.618368i
4040 2.76710 0.585797i 0.437517 0.0926227i
4141 0.832730i 0.130051i 0.997884 + 0.0650253i 0.0207128π0.0207128\pi
−0.997884 + 0.0650253i 0.979287π0.979287\pi
4242 0 0
4343 3.10642i 0.473725i 0.971543 + 0.236862i 0.0761190π0.0761190\pi
−0.971543 + 0.236862i 0.923881π0.923881\pi
4444 1.00175 + 7.15615i 0.151019 + 1.07883i
4545 2.56129i 0.381814i
4646 4.57830 0.318890i 0.675033 0.0470178i
4747 −6.89601 −1.00589 −0.502943 0.864319i 0.667750π-0.667750\pi
−0.502943 + 0.864319i 0.667750π0.667750\pi
4848 2.54758 0.727497i 0.367712 0.105005i
4949 0 0
5050 −0.0982654 1.41080i −0.0138968 0.199517i
5151 0.906184i 0.126891i
5252 1.61653 + 11.5479i 0.224172 + 1.60141i
5353 −7.41752 −1.01887 −0.509437 0.860508i 0.670146π-0.670146\pi
−0.509437 + 0.860508i 0.670146π0.670146\pi
5454 −0.361965 5.19673i −0.0492572 0.707185i
5555 3.61296 0.487172
5656 0 0
5757 −2.71285 −0.359326
5858 0.510319 + 7.32664i 0.0670081 + 0.962034i
5959 7.47856 0.973626 0.486813 0.873506i 0.338159π-0.338159\pi
0.486813 + 0.873506i 0.338159π0.338159\pi
6060 −0.183648 1.31192i −0.0237088 0.169368i
6161 1.48554i 0.190204i −0.995468 0.0951022i 0.969682π-0.969682\pi
0.995468 0.0951022i 0.0303178π-0.0303178\pi
6262 −0.871427 12.5111i −0.110671 1.58891i
6363 0 0
6464 −7.31368 + 3.24192i −0.914210 + 0.405240i
6565 5.83027 0.723156
6666 3.37612 0.235155i 0.415572 0.0289456i
6767 2.53761i 0.310018i −0.987913 0.155009i 0.950459π-0.950459\pi
0.987913 0.155009i 0.0495407π-0.0495407\pi
6868 0.379333 + 2.70983i 0.0460009 + 0.328615i
6969 2.14947i 0.258765i
7070 0 0
7171 3.52502i 0.418342i −0.977879 0.209171i 0.932923π-0.932923\pi
0.977879 0.209171i 0.0670766π-0.0670766\pi
7272 1.50039 + 7.08734i 0.176823 + 0.835250i
7373 5.16984i 0.605084i −0.953136 0.302542i 0.902165π-0.902165\pi
0.953136 0.302542i 0.0978353π-0.0978353\pi
7474 1.06085 + 15.2306i 0.123322 + 1.77053i
7575 −0.662355 −0.0764821
7676 8.11244 1.13561i 0.930561 0.130264i
7777 0 0
7878 5.44808 0.379472i 0.616873 0.0429668i
7979 11.3401i 1.27586i −0.770094 0.637931i 0.779791π-0.779791\pi
0.770094 0.637931i 0.220209π-0.220209\pi
8080 1.09835 + 3.84625i 0.122799 + 0.430024i
8181 5.24405 0.582672
8282 −1.17481 + 0.0818286i −0.129736 + 0.00903646i
8383 −6.49145 −0.712529 −0.356264 0.934385i 0.615950π-0.615950\pi
−0.356264 + 0.934385i 0.615950π0.615950\pi
8484 0 0
8585 1.36813 0.148394
8686 −4.38252 + 0.305254i −0.472580 + 0.0329164i
8787 3.43978 0.368783
8888 −9.99743 + 2.11646i −1.06573 + 0.225616i
8989 9.39121i 0.995466i −0.867330 0.497733i 0.834166π-0.834166\pi
0.867330 0.497733i 0.165834π-0.165834\pi
9090 3.61345 0.251686i 0.380891 0.0265300i
9191 0 0
9292 0.899777 + 6.42771i 0.0938083 + 0.670135i
9393 −5.87382 −0.609087
9494 −0.677640 9.72886i −0.0698932 1.00346i
9595 4.09577i 0.420217i
9696 1.27669 + 3.52263i 0.130302 + 0.359527i
9797 0.343189i 0.0348455i 0.999848 + 0.0174228i 0.00554612π0.00554612\pi
−0.999848 + 0.0174228i 0.994454π0.994454\pi
9898 0 0
9999 9.25383i 0.930045i
100100 1.98069 0.277265i 0.198069 0.0277265i
101101 4.53635i 0.451384i 0.974199 + 0.225692i 0.0724642π0.0724642\pi
−0.974199 + 0.225692i 0.927536π0.927536\pi
102102 1.27844 0.0890466i 0.126584 0.00881693i
103103 −6.13812 −0.604807 −0.302404 0.953180i 0.597789π-0.597789\pi
−0.302404 + 0.953180i 0.597789π0.597789\pi
104104 −16.1329 + 3.41536i −1.58196 + 0.334903i
105105 0 0
106106 −0.728886 10.4646i −0.0707957 1.01641i
107107 7.66797i 0.741291i −0.928775 0.370645i 0.879137π-0.879137\pi
0.928775 0.370645i 0.120863π-0.120863\pi
108108 7.29595 1.02132i 0.702053 0.0982763i
109109 1.29523 0.124061 0.0620304 0.998074i 0.480242π-0.480242\pi
0.0620304 + 0.998074i 0.480242π0.480242\pi
110110 0.355029 + 5.09715i 0.0338507 + 0.485994i
111111 7.15064 0.678709
112112 0 0
113113 7.10591 0.668468 0.334234 0.942490i 0.391522π-0.391522\pi
0.334234 + 0.942490i 0.391522π0.391522\pi
114114 −0.266580 3.82728i −0.0249675 0.358457i
115115 3.24519 0.302616
116116 −10.2862 + 1.43991i −0.955053 + 0.133692i
117117 14.9330i 1.38056i
118118 0.734884 + 10.5507i 0.0676516 + 0.971273i
119119 0 0
120120 1.83280 0.388005i 0.167311 0.0354199i
121121 −2.05349 −0.186681
122122 2.09580 0.145978i 0.189745 0.0132162i
123123 0.551563i 0.0497327i
124124 17.5649 2.45881i 1.57738 0.220808i
125125 1.00000i 0.0894427i
126126 0 0
127127 17.0178i 1.51008i 0.655677 + 0.755041i 0.272383π0.272383\pi
−0.655677 + 0.755041i 0.727617π0.727617\pi
128128 −5.29237 9.99954i −0.467784 0.883843i
129129 2.05755i 0.181157i
130130 0.572914 + 8.22532i 0.0502479 + 0.721408i
131131 −1.20613 −0.105380 −0.0526901 0.998611i 0.516780π-0.516780\pi
−0.0526901 + 0.998611i 0.516780π0.516780\pi
132132 0.663512 + 4.73991i 0.0577513 + 0.412556i
133133 0 0
134134 3.58005 0.249359i 0.309269 0.0215414i
135135 3.68354i 0.317029i
136136 −3.78574 + 0.801444i −0.324624 + 0.0687233i
137137 2.14490 0.183252 0.0916258 0.995794i 0.470794π-0.470794\pi
0.0916258 + 0.995794i 0.470794π0.470794\pi
138138 3.03246 0.211218i 0.258140 0.0179801i
139139 3.39555 0.288007 0.144004 0.989577i 0.454002π-0.454002\pi
0.144004 + 0.989577i 0.454002π0.454002\pi
140140 0 0
141141 −4.56761 −0.384662
142142 4.97308 0.346387i 0.417331 0.0290682i
143143 −21.0645 −1.76151
144144 −9.85134 + 2.81319i −0.820945 + 0.234432i
145145 5.19327i 0.431277i
146146 7.29359 0.508017i 0.603622 0.0420438i
147147 0 0
148148 −21.3831 + 2.99329i −1.75768 + 0.246047i
149149 −19.0864 −1.56362 −0.781808 0.623519i 0.785703π-0.785703\pi
−0.781808 + 0.623519i 0.785703π0.785703\pi
150150 −0.0650866 0.934447i −0.00531430 0.0762973i
151151 9.60595i 0.781721i 0.920450 + 0.390861i 0.127823π0.127823\pi
−0.920450 + 0.390861i 0.872177π0.872177\pi
152152 2.39929 + 11.3334i 0.194608 + 0.919260i
153153 3.50416i 0.283295i
154154 0 0
155155 8.86809i 0.712302i
156156 1.07072 + 7.64883i 0.0857258 + 0.612397i
157157 16.4624i 1.31384i 0.753961 + 0.656919i 0.228141π0.228141\pi
−0.753961 + 0.656919i 0.771859π0.771859\pi
158158 15.9986 1.11434i 1.27278 0.0886522i
159159 −4.91303 −0.389629
160160 −5.31834 + 1.92750i −0.420452 + 0.152382i
161161 0 0
162162 0.515309 + 7.39828i 0.0404865 + 0.581264i
163163 7.15612i 0.560510i 0.959926 + 0.280255i 0.0904191π0.0904191\pi
−0.959926 + 0.280255i 0.909581π0.909581\pi
164164 −0.230887 1.64938i −0.0180292 0.128795i
165165 2.39306 0.186300
166166 −0.637885 9.15810i −0.0495095 0.710807i
167167 −13.7127 −1.06112 −0.530562 0.847646i 0.678019π-0.678019\pi
−0.530562 + 0.847646i 0.678019π0.678019\pi
168168 0 0
169169 −20.9920 −1.61477
170170 0.134439 + 1.93014i 0.0103110 + 0.148035i
171171 10.4904 0.802224
172172 −0.861301 6.15285i −0.0656736 0.469150i
173173 3.92439i 0.298366i −0.988810 0.149183i 0.952336π-0.952336\pi
0.988810 0.149183i 0.0476643π-0.0476643\pi
174174 0.338012 + 4.85283i 0.0256246 + 0.367892i
175175 0 0
176176 −3.96830 13.8963i −0.299122 1.04748i
177177 4.95346 0.372325
178178 13.2491 0.922831i 0.993060 0.0691691i
179179 20.5539i 1.53627i −0.640289 0.768134i 0.721185π-0.721185\pi
0.640289 0.768134i 0.278815π-0.278815\pi
180180 0.710155 + 5.07311i 0.0529318 + 0.378127i
181181 13.0603i 0.970762i 0.874303 + 0.485381i 0.161319π0.161319\pi
−0.874303 + 0.485381i 0.838681π0.838681\pi
182182 0 0
183183 0.983957i 0.0727362i
184184 −8.97976 + 1.90102i −0.661997 + 0.140145i
185185 10.7958i 0.793722i
186186 −0.577194 8.28676i −0.0423219 0.607615i
187187 −4.94298 −0.361467
188188 13.6588 1.91202i 0.996174 0.139449i
189189 0 0
190190 5.77829 0.402472i 0.419201 0.0291984i
191191 12.4751i 0.902667i −0.892355 0.451334i 0.850948π-0.850948\pi
0.892355 0.451334i 0.149052π-0.149052\pi
192192 −4.84425 + 2.14730i −0.349604 + 0.154968i
193193 19.0645 1.37229 0.686147 0.727463i 0.259301π-0.259301\pi
0.686147 + 0.727463i 0.259301π0.259301\pi
194194 −0.484169 + 0.0337236i −0.0347613 + 0.00242121i
195195 3.86171 0.276543
196196 0 0
197197 1.93188 0.137641 0.0688203 0.997629i 0.478076π-0.478076\pi
0.0688203 + 0.997629i 0.478076π0.478076\pi
198198 −13.0553 + 0.909332i −0.927797 + 0.0646234i
199199 20.5646 1.45778 0.728892 0.684629i 0.240036π-0.240036\pi
0.728892 + 0.684629i 0.240036π0.240036\pi
200200 0.585797 + 2.76710i 0.0414221 + 0.195664i
201201 1.68080i 0.118554i
202202 −6.39986 + 0.445766i −0.450293 + 0.0313640i
203203 0 0
204204 0.251253 + 1.79487i 0.0175912 + 0.125666i
205205 −0.832730 −0.0581604
206206 −0.603165 8.65963i −0.0420245 0.603345i
207207 8.31186i 0.577714i
208208 −6.40368 22.4247i −0.444015 1.55487i
209209 14.7979i 1.02359i
210210 0 0
211211 9.98398i 0.687326i −0.939093 0.343663i 0.888332π-0.888332\pi
0.939093 0.343663i 0.111668π-0.111668\pi
212212 14.6918 2.05662i 1.00904 0.141249i
213213 2.33481i 0.159979i
214214 10.8179 0.753496i 0.739499 0.0515079i
215215 −3.10642 −0.211856
216216 2.15781 + 10.1927i 0.146820 + 0.693528i
217217 0 0
218218 0.127277 + 1.82731i 0.00862026 + 0.123761i
219219 3.42427i 0.231391i
220220 −7.15615 + 1.00175i −0.482467 + 0.0675378i
221221 −7.97654 −0.536560
222222 0.702661 + 10.0881i 0.0471595 + 0.677068i
223223 −16.8179 −1.12621 −0.563106 0.826384i 0.690394π-0.690394\pi
−0.563106 + 0.826384i 0.690394π0.690394\pi
224224 0 0
225225 2.56129 0.170752
226226 0.698266 + 10.0250i 0.0464479 + 0.666852i
227227 −19.8338 −1.31642 −0.658209 0.752835i 0.728686π-0.728686\pi
−0.658209 + 0.752835i 0.728686π0.728686\pi
228228 5.37331 0.752178i 0.355856 0.0498142i
229229 13.9331i 0.920725i −0.887731 0.460363i 0.847719π-0.847719\pi
0.887731 0.460363i 0.152281π-0.152281\pi
230230 0.318890 + 4.57830i 0.0210270 + 0.301884i
231231 0 0
232232 −3.04220 14.3703i −0.199730 0.943455i
233233 10.2257 0.669905 0.334953 0.942235i 0.391280π-0.391280\pi
0.334953 + 0.942235i 0.391280π0.391280\pi
234234 −21.0674 + 1.46740i −1.37722 + 0.0959267i
235235 6.89601i 0.449846i
236236 −14.8127 + 2.07354i −0.964225 + 0.134976i
237237 7.51117i 0.487903i
238238 0 0
239239 17.0835i 1.10504i −0.833501 0.552518i 0.813667π-0.813667\pi
0.833501 0.552518i 0.186333π-0.186333\pi
240240 0.727497 + 2.54758i 0.0469598 + 0.164446i
241241 18.4837i 1.19064i −0.803489 0.595320i 0.797025π-0.797025\pi
0.803489 0.595320i 0.202975π-0.202975\pi
242242 −0.201787 2.89705i −0.0129714 0.186230i
243243 14.5241 0.931718
244244 0.411889 + 2.94240i 0.0263685 + 0.188368i
245245 0 0
246246 −0.778142 + 0.0541995i −0.0496125 + 0.00345564i
247247 23.8794i 1.51941i
248248 5.19490 + 24.5389i 0.329877 + 1.55822i
249249 −4.29964 −0.272479
250250 1.41080 0.0982654i 0.0892265 0.00621485i
251251 −16.5313 −1.04344 −0.521722 0.853116i 0.674710π-0.674710\pi
−0.521722 + 0.853116i 0.674710π0.674710\pi
252252 0 0
253253 −11.7247 −0.737128
254254 −24.0086 + 1.67226i −1.50643 + 0.104927i
255255 0.906184 0.0567475
256256 13.5873 8.44906i 0.849203 0.528066i
257257 6.19499i 0.386433i 0.981156 + 0.193216i 0.0618919π0.0618919\pi
−0.981156 + 0.193216i 0.938108π0.938108\pi
258258 −2.90279 + 0.202186i −0.180720 + 0.0125876i
259259 0 0
260260 −11.5479 + 1.61653i −0.716173 + 0.100253i
261261 −13.3014 −0.823338
262262 −0.118521 1.70161i −0.00732226 0.105126i
263263 21.1536i 1.30439i 0.758053 + 0.652194i 0.226151π0.226151\pi
−0.758053 + 0.652194i 0.773849π0.773849\pi
264264 −6.62184 + 1.40185i −0.407546 + 0.0862778i
265265 7.41752i 0.455655i
266266 0 0
267267 6.22031i 0.380677i
268268 0.703590 + 5.02621i 0.0429786 + 0.307025i
269269 30.9866i 1.88928i −0.328102 0.944642i 0.606409π-0.606409\pi
0.328102 0.944642i 0.393591π-0.393591\pi
270270 5.19673 0.361965i 0.316263 0.0220285i
271271 23.0381 1.39946 0.699732 0.714405i 0.253303π-0.253303\pi
0.699732 + 0.714405i 0.253303π0.253303\pi
272272 −1.50268 5.26215i −0.0911134 0.319065i
273273 0 0
274274 0.210770 + 3.02602i 0.0127331 + 0.182809i
275275 3.61296i 0.217870i
276276 0.595972 + 4.25742i 0.0358733 + 0.256267i
277277 6.94562 0.417322 0.208661 0.977988i 0.433089π-0.433089\pi
0.208661 + 0.977988i 0.433089π0.433089\pi
278278 0.333665 + 4.79043i 0.0200119 + 0.287311i
279279 22.7137 1.35984
280280 0 0
281281 −4.24391 −0.253170 −0.126585 0.991956i 0.540402π-0.540402\pi
−0.126585 + 0.991956i 0.540402π0.540402\pi
282282 −0.448838 6.44396i −0.0267279 0.383732i
283283 −8.53198 −0.507174 −0.253587 0.967313i 0.581610π-0.581610\pi
−0.253587 + 0.967313i 0.581610π0.581610\pi
284284 0.977363 + 6.98195i 0.0579958 + 0.414303i
285285 2.71285i 0.160695i
286286 −2.06992 29.7178i −0.122397 1.75725i
287287 0 0
288288 −4.93688 13.6218i −0.290909 0.802672i
289289 15.1282 0.889896
290290 −7.32664 + 0.510319i −0.430235 + 0.0299669i
291291 0.227313i 0.0133253i
292292 1.43342 + 10.2398i 0.0838843 + 0.599241i
293293 25.2319i 1.47406i 0.675857 + 0.737032i 0.263773π0.263773\pi
−0.675857 + 0.737032i 0.736227π0.736227\pi
294294 0 0
295295 7.47856i 0.435419i
296296 −6.32414 29.8730i −0.367583 1.73633i
297297 13.3085i 0.772238i
298298 −1.87553 26.9270i −0.108647 1.55984i
299299 −18.9203 −1.09419
300300 1.31192 0.183648i 0.0757436 0.0106029i
301301 0 0
302302 −13.5520 + 0.943933i −0.779832 + 0.0543172i
303303 3.00467i 0.172614i
304304 −15.7533 + 4.49859i −0.903516 + 0.258012i
305305 1.48554 0.0850620
306306 −4.94365 + 0.344338i −0.282610 + 0.0196845i
307307 29.2635 1.67016 0.835078 0.550132i 0.185423π-0.185423\pi
0.835078 + 0.550132i 0.185423π0.185423\pi
308308 0 0
309309 −4.06561 −0.231285
310310 12.5111 0.871427i 0.710581 0.0494937i
311311 −22.7461 −1.28981 −0.644906 0.764262i 0.723104π-0.723104\pi
−0.644906 + 0.764262i 0.723104π0.723104\pi
312312 −10.6857 + 2.26218i −0.604960 + 0.128071i
313313 6.58481i 0.372195i −0.982531 0.186098i 0.940416π-0.940416\pi
0.982531 0.186098i 0.0595841π-0.0595841\pi
314314 −23.2250 + 1.61768i −1.31066 + 0.0912910i
315315 0 0
316316 3.14421 + 22.4612i 0.176876 + 1.26354i
317317 −14.1217 −0.793154 −0.396577 0.918001i 0.629802π-0.629802\pi
−0.396577 + 0.918001i 0.629802π0.629802\pi
318318 −0.482781 6.93128i −0.0270730 0.388687i
319319 18.7631i 1.05053i
320320 −3.24192 7.31368i −0.181229 0.408847i
321321 5.07891i 0.283477i
322322 0 0
323323 5.60352i 0.311788i
324324 −10.3868 + 1.45399i −0.577046 + 0.0807772i
325325 5.83027i 0.323405i
326326 −10.0958 + 0.703199i −0.559155 + 0.0389466i
327327 0.857903 0.0474422
328328 2.30425 0.487811i 0.127231 0.0269349i
329329 0 0
330330 0.235155 + 3.37612i 0.0129449 + 0.185849i
331331 20.3224i 1.11702i 0.829498 + 0.558510i 0.188627π0.188627\pi
−0.829498 + 0.558510i 0.811373π0.811373\pi
332332 12.8575 1.79985i 0.705649 0.0987796i
333333 −27.6511 −1.51527
334334 −1.34749 19.3459i −0.0737313 1.05856i
335335 2.53761 0.138644
336336 0 0
337337 15.7704 0.859067 0.429533 0.903051i 0.358678π-0.358678\pi
0.429533 + 0.903051i 0.358678π0.358678\pi
338338 −2.06279 29.6155i −0.112201 1.61087i
339339 4.70663 0.255629
340340 −2.70983 + 0.379333i −0.146961 + 0.0205722i
341341 32.0401i 1.73507i
342342 1.03085 + 14.7999i 0.0557418 + 0.800285i
343343 0 0
344344 8.59578 1.81973i 0.463453 0.0981134i
345345 2.14947 0.115723
346346 5.53651 0.385632i 0.297644 0.0207317i
347347 3.04784i 0.163616i 0.996648 + 0.0818082i 0.0260695π0.0260695\pi
−0.996648 + 0.0818082i 0.973930π0.973930\pi
348348 −6.81314 + 0.953731i −0.365222 + 0.0511254i
349349 8.40462i 0.449889i 0.974372 + 0.224944i 0.0722201π0.0722201\pi
−0.974372 + 0.224944i 0.927780π0.927780\pi
350350 0 0
351351 21.4761i 1.14631i
352352 19.2150 6.96399i 1.02416 0.371182i
353353 0.432821i 0.0230367i 0.999934 + 0.0115184i 0.00366649π0.00366649\pi
−0.999934 + 0.0115184i 0.996334π0.996334\pi
354354 0.486754 + 6.98832i 0.0258707 + 0.371425i
355355 3.52502 0.187088
356356 2.60385 + 18.6011i 0.138004 + 0.985854i
357357 0 0
358358 28.9973 2.01973i 1.53255 0.106746i
359359 26.9810i 1.42400i 0.702178 + 0.712002i 0.252211π0.252211\pi
−0.702178 + 0.712002i 0.747789π0.747789\pi
360360 −7.08734 + 1.50039i −0.373535 + 0.0790777i
361361 −2.22468 −0.117088
362362 −18.4254 + 1.28337i −0.968415 + 0.0674526i
363363 −1.36014 −0.0713888
364364 0 0
365365 5.16984 0.270602
366366 1.38816 0.0966889i 0.0725604 0.00505401i
367367 20.8212 1.08686 0.543430 0.839455i 0.317125π-0.317125\pi
0.543430 + 0.839455i 0.317125π0.317125\pi
368368 −3.56436 12.4818i −0.185805 0.650659i
369369 2.13286i 0.111032i
370370 −15.2306 + 1.06085i −0.791804 + 0.0551511i
371371 0 0
372372 11.6342 1.62860i 0.603206 0.0844392i
373373 −17.6614 −0.914475 −0.457237 0.889345i 0.651161π-0.651161\pi
−0.457237 + 0.889345i 0.651161π0.651161\pi
374374 −0.485724 6.97354i −0.0251162 0.360593i
375375 0.662355i 0.0342038i
376376 4.03966 + 19.0820i 0.208330 + 0.984077i
377377 30.2781i 1.55940i
378378 0 0
379379 15.0551i 0.773331i −0.922220 0.386665i 0.873627π-0.873627\pi
0.922220 0.386665i 0.126373π-0.126373\pi
380380 1.13561 + 8.11244i 0.0582557 + 0.416159i
381381 11.2718i 0.577472i
382382 17.5998 1.22587i 0.900486 0.0627211i
383383 30.3505 1.55084 0.775420 0.631446i 0.217538π-0.217538\pi
0.775420 + 0.631446i 0.217538π0.217538\pi
384384 −3.50542 6.62324i −0.178885 0.337991i
385385 0 0
386386 1.87338 + 26.8961i 0.0953527 + 1.36898i
387387 7.95643i 0.404448i
388388 −0.0951542 0.679750i −0.00483072 0.0345091i
389389 −6.27818 −0.318316 −0.159158 0.987253i 0.550878π-0.550878\pi
−0.159158 + 0.987253i 0.550878π0.550878\pi
390390 0.379472 + 5.44808i 0.0192153 + 0.275874i
391391 −4.43983 −0.224532
392392 0 0
393393 −0.798887 −0.0402985
394394 0.189837 + 2.72549i 0.00956384 + 0.137308i
395395 11.3401 0.570583
396396 −2.56576 18.3289i −0.128934 0.921064i
397397 9.72207i 0.487937i 0.969783 + 0.243968i 0.0784493π0.0784493\pi
−0.969783 + 0.243968i 0.921551π0.921551\pi
398398 2.02079 + 29.0124i 0.101293 + 1.45426i
399399 0 0
400400 −3.84625 + 1.09835i −0.192312 + 0.0549175i
401401 6.98744 0.348936 0.174468 0.984663i 0.444179π-0.444179\pi
0.174468 + 0.984663i 0.444179π0.444179\pi
402402 2.37126 0.165164i 0.118268 0.00823764i
403403 51.7034i 2.57553i
404404 −1.25777 8.98509i −0.0625764 0.447025i
405405 5.24405i 0.260579i
406406 0 0
407407 39.0048i 1.93339i
408408 −2.50750 + 0.530840i −0.124140 + 0.0262805i
409409 2.24559i 0.111037i 0.998458 + 0.0555186i 0.0176812π0.0176812\pi
−0.998458 + 0.0555186i 0.982319π0.982319\pi
410410 −0.0818286 1.17481i −0.00404123 0.0580198i
411411 1.42069 0.0700773
412412 12.1577 1.70189i 0.598967 0.0838459i
413413 0 0
414414 −11.7263 + 0.816769i −0.576318 + 0.0401420i
415415 6.49145i 0.318653i
416416 31.0074 11.2379i 1.52026 0.550981i
417417 2.24906 0.110137
418418 −20.8767 + 1.45412i −1.02111 + 0.0711232i
419419 18.3565 0.896775 0.448388 0.893839i 0.351998π-0.351998\pi
0.448388 + 0.893839i 0.351998π0.351998\pi
420420 0 0
421421 2.27310 0.110784 0.0553921 0.998465i 0.482359π-0.482359\pi
0.0553921 + 0.998465i 0.482359π0.482359\pi
422422 14.0854 0.981080i 0.685664 0.0477582i
423423 17.6627 0.858788
424424 4.34516 + 20.5250i 0.211020 + 0.996783i
425425 1.36813i 0.0663638i
426426 3.29394 0.229431i 0.159592 0.0111160i
427427 0 0
428428 2.12606 + 15.1879i 0.102767 + 0.734133i
429429 −13.9522 −0.673618
430430 −0.305254 4.38252i −0.0147206 0.211344i
431431 12.8610i 0.619490i 0.950820 + 0.309745i 0.100244π0.100244\pi
−0.950820 + 0.309745i 0.899756π0.899756\pi
432432 −14.1678 + 4.04582i −0.681650 + 0.194655i
433433 33.6307i 1.61619i −0.589054 0.808094i 0.700499π-0.700499\pi
0.589054 0.808094i 0.299501π-0.299501\pi
434434 0 0
435435 3.43978i 0.164925i
436436 −2.56545 + 0.359122i −0.122863 + 0.0171988i
437437 13.2915i 0.635821i
438438 4.83094 0.336487i 0.230831 0.0160780i
439439 24.8870 1.18779 0.593896 0.804542i 0.297589π-0.297589\pi
0.593896 + 0.804542i 0.297589π0.297589\pi
440440 −2.11646 9.99743i −0.100898 0.476609i
441441 0 0
442442 −0.783818 11.2533i −0.0372824 0.535263i
443443 7.94772i 0.377608i 0.982015 + 0.188804i 0.0604610π0.0604610\pi
−0.982015 + 0.188804i 0.939539π0.939539\pi
444444 −14.1632 + 1.98262i −0.672155 + 0.0940910i
445445 9.39121 0.445186
446446 −1.65262 23.7267i −0.0782540 1.12349i
447447 −12.6420 −0.597944
448448 0 0
449449 14.3027 0.674988 0.337494 0.941328i 0.390421π-0.390421\pi
0.337494 + 0.941328i 0.390421π0.390421\pi
450450 0.251686 + 3.61345i 0.0118646 + 0.170340i
451451 3.00862 0.141670
452452 −14.0746 + 1.97022i −0.662013 + 0.0926714i
453453 6.36255i 0.298939i
454454 −1.94898 27.9815i −0.0914702 1.31324i
455455 0 0
456456 1.58918 + 7.50673i 0.0744202 + 0.351535i
457457 22.1786 1.03747 0.518737 0.854934i 0.326403π-0.326403\pi
0.518737 + 0.854934i 0.326403π0.326403\pi
458458 19.6568 1.36914i 0.918500 0.0639758i
459459 5.03955i 0.235226i
460460 −6.42771 + 0.899777i −0.299693 + 0.0419523i
461461 32.8587i 1.53038i −0.643803 0.765192i 0.722644π-0.722644\pi
0.643803 0.765192i 0.277356π-0.277356\pi
462462 0 0
463463 3.31392i 0.154011i 0.997031 + 0.0770055i 0.0245359π0.0245359\pi
−0.997031 + 0.0770055i 0.975464π0.975464\pi
464464 19.9746 5.70402i 0.927297 0.264803i
465465 5.87382i 0.272392i
466466 1.00483 + 14.4263i 0.0465478 + 0.668286i
467467 35.1334 1.62578 0.812890 0.582417i 0.197893π-0.197893\pi
0.812890 + 0.582417i 0.197893π0.197893\pi
468468 −4.14039 29.5776i −0.191390 1.36722i
469469 0 0
470470 9.72886 0.677640i 0.448759 0.0312572i
471471 10.9039i 0.502426i
472472 −4.38092 20.6939i −0.201648 0.952516i
473473 11.2234 0.516051
474474 10.5967 0.738088i 0.486724 0.0339015i
475475 4.09577 0.187927
476476 0 0
477477 18.9984 0.869877
478478 24.1013 1.67871i 1.10237 0.0767825i
479479 22.3266 1.02013 0.510065 0.860136i 0.329621π-0.329621\pi
0.510065 + 0.860136i 0.329621π0.329621\pi
480480 −3.52263 + 1.27669i −0.160785 + 0.0582726i
481481 62.9423i 2.86992i
482482 26.0767 1.81631i 1.18776 0.0827306i
483483 0 0
484484 4.06732 0.569361i 0.184878 0.0258800i
485485 −0.343189 −0.0155834
486486 1.42721 + 20.4905i 0.0647397 + 0.929466i
487487 7.18519i 0.325592i 0.986660 + 0.162796i 0.0520512π0.0520512\pi
−0.986660 + 0.162796i 0.947949π0.947949\pi
488488 −4.11065 + 0.870227i −0.186080 + 0.0393933i
489489 4.73989i 0.214345i
490490 0 0
491491 5.80059i 0.261777i 0.991397 + 0.130889i 0.0417830π0.0417830\pi
−0.991397 + 0.130889i 0.958217π0.958217\pi
492492 −0.152929 1.09247i −0.00689457 0.0492525i
493493 7.10504i 0.319995i
494494 −33.6890 + 2.34652i −1.51574 + 0.105575i
495495 −9.25383 −0.415929
496496 −34.1089 + 9.74027i −1.53153 + 0.437351i
497497 0 0
498498 −0.422506 6.06591i −0.0189329 0.271820i
499499 39.6601i 1.77543i −0.460394 0.887715i 0.652292π-0.652292\pi
0.460394 0.887715i 0.347708π-0.347708\pi
500500 0.277265 + 1.98069i 0.0123997 + 0.0885791i
501501 −9.08270 −0.405785
502502 −1.62445 23.3222i −0.0725028 1.04092i
503503 −8.22384 −0.366683 −0.183341 0.983049i 0.558691π-0.558691\pi
−0.183341 + 0.983049i 0.558691π0.558691\pi
504504 0 0
505505 −4.53635 −0.201865
506506 −1.15214 16.5412i −0.0512187 0.735347i
507507 −13.9042 −0.617506
508508 −4.71843 33.7069i −0.209346 1.49550i
509509 32.5719i 1.44373i 0.692036 + 0.721863i 0.256714π0.256714\pi
−0.692036 + 0.721863i 0.743286π0.743286\pi
510510 0.0890466 + 1.27844i 0.00394305 + 0.0566103i
511511 0 0
512512 13.2550 + 18.3386i 0.585796 + 0.810459i
513513 15.0869 0.666105
514514 −8.73986 + 0.608753i −0.385499 + 0.0268509i
515515 6.13812i 0.270478i
516516 −0.570487 4.07537i −0.0251143 0.179408i
517517 24.9150i 1.09576i
518518 0 0
519519 2.59934i 0.114098i
520520 −3.41536 16.1329i −0.149773 0.707476i
521521 5.64398i 0.247267i −0.992328 0.123634i 0.960545π-0.960545\pi
0.992328 0.123634i 0.0394547π-0.0394547\pi
522522 −1.30707 18.7656i −0.0572090 0.821348i
523523 2.73410 0.119554 0.0597770 0.998212i 0.480961π-0.480961\pi
0.0597770 + 0.998212i 0.480961π0.480961\pi
524524 2.38897 0.334418i 0.104363 0.0146091i
525525 0 0
526526 −29.8434 + 2.07867i −1.30123 + 0.0906342i
527527 12.1327i 0.528507i
528528 −2.62842 9.20431i −0.114387 0.400566i
529529 12.4687 0.542119
530530 10.4646 0.728886i 0.454553 0.0316608i
531531 −19.1547 −0.831245
532532 0 0
533533 4.85504 0.210295
534534 8.77559 0.611242i 0.379757 0.0264510i
535535 7.66797 0.331515
536536 −7.02182 + 1.48652i −0.303296 + 0.0642081i
537537 13.6139i 0.587485i
538538 43.7157 3.04491i 1.88472 0.131275i
539539 0 0
540540 1.02132 + 7.29595i 0.0439505 + 0.313968i
541541 28.2999 1.21671 0.608355 0.793665i 0.291830π-0.291830\pi
0.608355 + 0.793665i 0.291830π0.291830\pi
542542 2.26385 + 32.5020i 0.0972406 + 1.39608i
543543 8.65052i 0.371230i
544544 7.27616 2.63706i 0.311963 0.113063i
545545 1.29523i 0.0554817i
546546 0 0
547547 20.7596i 0.887616i 0.896122 + 0.443808i 0.146373π0.146373\pi
−0.896122 + 0.443808i 0.853627π0.853627\pi
548548 −4.24839 + 0.594707i −0.181482 + 0.0254046i
549549 3.80490i 0.162389i
550550 −5.09715 + 0.355029i −0.217343 + 0.0151385i
551551 −21.2704 −0.906150
552552 −5.94779 + 1.25915i −0.253155 + 0.0535930i
553553 0 0
554554 0.682514 + 9.79885i 0.0289973 + 0.416313i
555555 7.15064i 0.303528i
556556 −6.72553 + 0.941468i −0.285226 + 0.0399271i
557557 −18.7575 −0.794781 −0.397391 0.917650i 0.630084π-0.630084\pi
−0.397391 + 0.917650i 0.630084π0.630084\pi
558558 2.23197 + 32.0444i 0.0944870 + 1.35655i
559559 18.1113 0.766025
560560 0 0
561561 −3.27401 −0.138229
562562 −0.417029 5.98728i −0.0175913 0.252558i
563563 −33.3740 −1.40655 −0.703274 0.710919i 0.748279π-0.748279\pi
−0.703274 + 0.710919i 0.748279π0.748279\pi
564564 9.04700 1.26644i 0.380947 0.0533266i
565565 7.10591i 0.298948i
566566 −0.838399 12.0369i −0.0352405 0.505948i
567567 0 0
568568 −9.75407 + 2.06494i −0.409272 + 0.0866431i
569569 13.0300 0.546247 0.273124 0.961979i 0.411943π-0.411943\pi
0.273124 + 0.961979i 0.411943π0.411943\pi
570570 3.82728 0.266580i 0.160307 0.0111658i
571571 32.9558i 1.37916i 0.724211 + 0.689579i 0.242204π0.242204\pi
−0.724211 + 0.689579i 0.757796π0.757796\pi
572572 41.7223 5.84046i 1.74450 0.244202i
573573 8.26295i 0.345190i
574574 0 0
575575 3.24519i 0.135334i
576576 18.7324 8.30348i 0.780518 0.345978i
577577 36.3874i 1.51483i −0.652935 0.757414i 0.726462π-0.726462\pi
0.652935 0.757414i 0.273538π-0.273538\pi
578578 1.48658 + 21.3428i 0.0618337 + 0.887745i
579579 12.6275 0.524780
580580 −1.43991 10.2862i −0.0597890 0.427113i
581581 0 0
582582 −0.320692 + 0.0223370i −0.0132931 + 0.000925898i
583583 26.7992i 1.10991i
584584 −14.3055 + 3.02848i −0.591964 + 0.125319i
585585 −14.9330 −0.617403
586586 −35.5971 + 2.47943i −1.47050 + 0.102424i
587587 28.4245 1.17321 0.586603 0.809875i 0.300465π-0.300465\pi
0.586603 + 0.809875i 0.300465π0.300465\pi
588588 0 0
589589 36.3217 1.49661
590590 −10.5507 + 0.734884i −0.434366 + 0.0302547i
591591 1.27959 0.0526352
592592 41.5233 11.8576i 1.70660 0.487342i
593593 7.57149i 0.310924i −0.987842 0.155462i 0.950313π-0.950313\pi
0.987842 0.155462i 0.0496866π-0.0496866\pi
594594 −18.7756 + 1.30777i −0.770371 + 0.0536583i
595595 0 0
596596 37.8042 5.29198i 1.54852 0.216768i
597597 13.6210 0.557472
598598 −1.85921 26.6927i −0.0760289 1.09155i
599599 47.4510i 1.93879i −0.245499 0.969397i 0.578952π-0.578952\pi
0.245499 0.969397i 0.421048π-0.421048\pi
600600 0.388005 + 1.83280i 0.0158403 + 0.0748238i
601601 13.3242i 0.543506i 0.962367 + 0.271753i 0.0876034π0.0876034\pi
−0.962367 + 0.271753i 0.912397π0.912397\pi
602602 0 0
603603 6.49954i 0.264682i
604604 −2.66339 19.0264i −0.108372 0.774173i
605605 2.05349i 0.0834862i
606606 −4.23898 + 0.295255i −0.172197 + 0.0119939i
607607 15.0816 0.612143 0.306072 0.952008i 0.400985π-0.400985\pi
0.306072 + 0.952008i 0.400985π0.400985\pi
608608 −7.89460 21.7827i −0.320168 0.883405i
609609 0 0
610610 0.145978 + 2.09580i 0.00591046 + 0.0848564i
611611 40.2056i 1.62654i
612612 −0.971581 6.94065i −0.0392738 0.280559i
613613 −5.20469 −0.210215 −0.105108 0.994461i 0.533519π-0.533519\pi
−0.105108 + 0.994461i 0.533519π0.533519\pi
614614 2.87559 + 41.2848i 0.116049 + 1.66612i
615615 −0.551563 −0.0222412
616616 0 0
617617 −35.7404 −1.43885 −0.719426 0.694569i 0.755595π-0.755595\pi
−0.719426 + 0.694569i 0.755595π0.755595\pi
618618 −0.399509 5.73575i −0.0160706 0.230726i
619619 38.2437 1.53715 0.768573 0.639762i 0.220967π-0.220967\pi
0.768573 + 0.639762i 0.220967π0.220967\pi
620620 2.45881 + 17.5649i 0.0987482 + 0.705424i
621621 11.9538i 0.479689i
622622 −2.23515 32.0901i −0.0896215 1.28670i
623623 0 0
624624 −4.24151 14.8531i −0.169796 0.594599i
625625 1.00000 0.0400000
626626 9.28981 0.647059i 0.371296 0.0258617i
627627 9.80143i 0.391431i
628628 −4.56443 32.6068i −0.182141 1.30115i
629629 14.7700i 0.588918i
630630 0 0
631631 12.0334i 0.479042i 0.970891 + 0.239521i 0.0769904π0.0769904\pi
−0.970891 + 0.239521i 0.923010π0.923010\pi
632632 −31.3792 + 6.64300i −1.24820 + 0.264244i
633633 6.61294i 0.262841i
634634 −1.38768 19.9229i −0.0551117 0.791237i
635635 −17.0178 −0.675329
636636 9.73118 1.36221i 0.385866 0.0540152i
637637 0 0
638638 26.4709 1.84376i 1.04799 0.0729952i
639639 9.02857i 0.357165i
640640 9.99954 5.29237i 0.395267 0.209199i
641641 22.9352 0.905888 0.452944 0.891539i 0.350374π-0.350374\pi
0.452944 + 0.891539i 0.350374π0.350374\pi
642642 7.16531 0.499082i 0.282792 0.0196972i
643643 1.23955 0.0488833 0.0244416 0.999701i 0.492219π-0.492219\pi
0.0244416 + 0.999701i 0.492219π0.492219\pi
644644 0 0
645645 −2.05755 −0.0810160
646646 −7.90543 + 0.550633i −0.311035 + 0.0216644i
647647 −14.1415 −0.555962 −0.277981 0.960587i 0.589665π-0.589665\pi
−0.277981 + 0.960587i 0.589665π0.589665\pi
648648 −3.07195 14.5108i −0.120678 0.570038i
649649 27.0198i 1.06062i
650650 −8.22532 + 0.572914i −0.322624 + 0.0224715i
651651 0 0
652652 −1.98414 14.1740i −0.0777049 0.555098i
653653 −17.0916 −0.668845 −0.334423 0.942423i 0.608541π-0.608541\pi
−0.334423 + 0.942423i 0.608541π0.608541\pi
654654 0.0843022 + 1.21033i 0.00329648 + 0.0473275i
655655 1.20613i 0.0471275i
656656 0.914629 + 3.20289i 0.0357103 + 0.125052i
657657 13.2414i 0.516598i
658658 0 0
659659 3.45765i 0.134691i −0.997730 0.0673455i 0.978547π-0.978547\pi
0.997730 0.0673455i 0.0214530π-0.0214530\pi
660660 −4.73991 + 0.663512i −0.184501 + 0.0258272i
661661 15.1632i 0.589780i 0.955531 + 0.294890i 0.0952830π0.0952830\pi
−0.955531 + 0.294890i 0.904717π0.904717\pi
662662 −28.6707 + 1.99699i −1.11432 + 0.0776152i
663663 −5.28330 −0.205186
664664 3.80267 + 17.9625i 0.147572 + 0.697079i
665665 0 0
666666 −2.71715 39.0100i −0.105287 1.51161i
667667 16.8531i 0.652556i
668668 27.1607 3.80206i 1.05088 0.147106i
669669 −11.1394 −0.430676
670670 0.249359 + 3.58005i 0.00963359 + 0.138309i
671671 −5.36721 −0.207199
672672 0 0
673673 −11.2116 −0.432175 −0.216087 0.976374i 0.569330π-0.569330\pi
−0.216087 + 0.976374i 0.569330π0.569330\pi
674674 1.54968 + 22.2488i 0.0596915 + 0.856991i
675675 3.68354 0.141780
676676 41.5787 5.82036i 1.59918 0.223860i
677677 3.67637i 0.141294i −0.997501 0.0706471i 0.977494π-0.977494\pi
0.997501 0.0706471i 0.0225064π-0.0225064\pi
678678 0.462500 + 6.64010i 0.0177622 + 0.255011i
679679 0 0
680680 −0.801444 3.78574i −0.0307340 0.145176i
681681 −13.1370 −0.503412
682682 −45.2020 + 3.14843i −1.73087 + 0.120560i
683683 42.1877i 1.61427i −0.590369 0.807133i 0.701018π-0.701018\pi
0.590369 0.807133i 0.298982π-0.298982\pi
684684 −20.7783 + 2.90863i −0.794477 + 0.111214i
685685 2.14490i 0.0819526i
686686 0 0
687687 9.22865i 0.352095i
688688 3.41194 + 11.9481i 0.130079 + 0.455516i
689689 43.2461i 1.64755i
690690 0.211218 + 3.03246i 0.00804094 + 0.115444i
691691 −23.1230 −0.879640 −0.439820 0.898086i 0.644958π-0.644958\pi
−0.439820 + 0.898086i 0.644958π0.644958\pi
692692 1.08809 + 7.77298i 0.0413631 + 0.295485i
693693 0 0
694694 −4.29987 + 0.299497i −0.163221 + 0.0113688i
695695 3.39555i 0.128801i
696696 −2.01502 9.51822i −0.0763790 0.360787i
697697 1.13928 0.0431533
698698 −11.8572 + 0.825884i −0.448802 + 0.0312602i
699699 6.77301 0.256179
700700 0 0
701701 29.3192 1.10737 0.553686 0.832725i 0.313221π-0.313221\pi
0.553686 + 0.832725i 0.313221π0.313221\pi
702702 −30.2983 + 2.11035i −1.14354 + 0.0796502i
703703 −44.2170 −1.66768
704704 11.7129 + 26.4241i 0.441448 + 0.995894i
705705 4.56761i 0.172026i
706706 −0.610622 + 0.0425314i −0.0229811 + 0.00160069i
707707 0 0
708708 −9.81126 + 1.37342i −0.368730 + 0.0516163i
709709 3.35439 0.125977 0.0629884 0.998014i 0.479937π-0.479937\pi
0.0629884 + 0.998014i 0.479937π0.479937\pi
710710 0.346387 + 4.97308i 0.0129997 + 0.186636i
711711 29.0453i 1.08928i
712712 −25.9864 + 5.50134i −0.973882 + 0.206172i
713713 28.7786i 1.07777i
714714 0 0
715715 21.0645i 0.787769i
716716 5.69886 + 40.7108i 0.212977 + 1.52143i
717717 11.3153i 0.422578i
718718 −38.0647 + 2.65130i −1.42056 + 0.0989457i
719719 −31.0284 −1.15717 −0.578583 0.815624i 0.696394π-0.696394\pi
−0.578583 + 0.815624i 0.696394π0.696394\pi
720720 −2.81319 9.85134i −0.104841 0.367138i
721721 0 0
722722 −0.218609 3.13857i −0.00813579 0.116805i
723723 12.2428i 0.455313i
724724 −3.62115 25.8683i −0.134579 0.961388i
725725 −5.19327 −0.192873
726726 −0.133655 1.91888i −0.00496039 0.0712162i
727727 −37.9906 −1.40899 −0.704497 0.709707i 0.748827π-0.748827\pi
−0.704497 + 0.709707i 0.748827π0.748827\pi
728728 0 0
729729 −6.11207 −0.226373
730730 0.508017 + 7.29359i 0.0188025 + 0.269948i
731731 4.24997 0.157191
732732 0.272817 + 1.94891i 0.0100836 + 0.0720338i
733733 30.9751i 1.14409i 0.820222 + 0.572046i 0.193850π0.193850\pi
−0.820222 + 0.572046i 0.806150π0.806150\pi
734734 2.04601 + 29.3745i 0.0755195 + 1.08423i
735735 0 0
736736 17.2590 6.25511i 0.636176 0.230566i
737737 −9.16828 −0.337718
738738 3.00903 0.209586i 0.110764 0.00771498i
739739 2.92228i 0.107498i −0.998554 0.0537488i 0.982883π-0.982883\pi
0.998554 0.0537488i 0.0171170π-0.0171170\pi
740740 −2.99329 21.3831i −0.110036 0.786058i
741741 15.8167i 0.581039i
742742 0 0
743743 36.6505i 1.34457i −0.740290 0.672287i 0.765312π-0.765312\pi
0.740290 0.672287i 0.234688π-0.234688\pi
744744 3.44087 + 16.2535i 0.126148 + 0.595881i
745745 19.0864i 0.699271i
746746 −1.73551 24.9167i −0.0635415 0.912265i
747747 16.6265 0.608330
748748 9.79051 1.37052i 0.357976 0.0501110i
749749 0 0
750750 0.934447 0.0650866i 0.0341212 0.00237663i
751751 36.1831i 1.32034i −0.751116 0.660170i 0.770484π-0.770484\pi
0.751116 0.660170i 0.229516π-0.229516\pi
752752 −26.5238 + 7.57424i −0.967223 + 0.276204i
753753 −10.9496 −0.399024
754754 42.7163 2.97529i 1.55563 0.108354i
755755 −9.60595 −0.349596
756756 0 0
757757 −1.44394 −0.0524807 −0.0262404 0.999656i 0.508354π-0.508354\pi
−0.0262404 + 0.999656i 0.508354π0.508354\pi
758758 21.2397 1.47940i 0.771462 0.0537342i
759759 −7.76594 −0.281886
760760 −11.3334 + 2.39929i −0.411106 + 0.0870314i
761761 28.2334i 1.02346i 0.859146 + 0.511730i 0.170995π0.170995\pi
−0.859146 + 0.511730i 0.829005π0.829005\pi
762762 −15.9022 + 1.10763i −0.576076 + 0.0401251i
763763 0 0
764764 3.45891 + 24.7093i 0.125139 + 0.893951i
765765 −3.50416 −0.126693
766766 2.98241 + 42.8184i 0.107759 + 1.54709i
767767 43.6020i 1.57438i
768768 8.99958 5.59627i 0.324744 0.201938i
769769 38.3866i 1.38426i −0.721774 0.692129i 0.756673π-0.756673\pi
0.721774 0.692129i 0.243327π-0.243327\pi
770770 0 0
771771 4.10328i 0.147776i
772772 −37.7608 + 5.28592i −1.35904 + 0.190244i
773773 19.0817i 0.686322i 0.939277 + 0.343161i 0.111498π0.111498\pi
−0.939277 + 0.343161i 0.888502π0.888502\pi
774774 11.2249 0.781842i 0.403471 0.0281027i
775775 8.86809 0.318551
776776 0.949638 0.201039i 0.0340900 0.00721688i
777777 0 0
778778 −0.616928 8.85722i −0.0221179 0.317547i
779779 3.41067i 0.122200i
780780 −7.64883 + 1.07072i −0.273872 + 0.0383378i
781781 −12.7357 −0.455721
782782 −0.436281 6.26369i −0.0156014 0.223989i
783783 −19.1296 −0.683637
784784 0 0
785785 −16.4624 −0.587567
786786 −0.0785030 1.12707i −0.00280011 0.0402011i
787787 5.10214 0.181872 0.0909358 0.995857i 0.471014π-0.471014\pi
0.0909358 + 0.995857i 0.471014π0.471014\pi
788788 −3.82645 + 0.535642i −0.136312 + 0.0190815i
789789 14.0112i 0.498811i
790790 1.11434 + 15.9986i 0.0396464 + 0.569203i
791791 0 0
792792 25.6063 5.42087i 0.909879 0.192622i
793793 −8.66112 −0.307565
794794 −13.7159 + 0.955344i −0.486758 + 0.0339039i
795795 4.91303i 0.174247i
796796 −40.7320 + 5.70183i −1.44371 + 0.202096i
797797 25.6101i 0.907155i 0.891217 + 0.453578i 0.149852π0.149852\pi
−0.891217 + 0.453578i 0.850148π0.850148\pi
798798 0 0
799799 9.43461i 0.333772i
800800 −1.92750 5.31834i −0.0681475 0.188032i
801801 24.0536i 0.849891i
802802 0.686624 + 9.85785i 0.0242455 + 0.348093i
803803 −18.6784 −0.659148
804804 0.466026 + 3.32913i 0.0164355 + 0.117409i
805805 0 0
806806 −72.9429 + 5.08065i −2.56930 + 0.178958i
807807 20.5241i 0.722483i
808808 12.5525 2.65738i 0.441597 0.0934863i
809809 50.4761 1.77465 0.887323 0.461148i 0.152562π-0.152562\pi
0.887323 + 0.461148i 0.152562π0.152562\pi
810810 −7.39828 + 0.515309i −0.259949 + 0.0181061i
811811 3.15050 0.110629 0.0553145 0.998469i 0.482384π-0.482384\pi
0.0553145 + 0.998469i 0.482384π0.482384\pi
812812 0 0
813813 15.2594 0.535170
814814 55.0277 3.83282i 1.92872 0.134340i
815815 −7.15612 −0.250668
816816 −0.995308 3.48541i −0.0348427 0.122014i
817817 12.7232i 0.445128i
818818 −3.16807 + 0.220664i −0.110769 + 0.00771533i
819819 0 0
820820 1.64938 0.230887i 0.0575988 0.00806292i
821821 −35.4832 −1.23837 −0.619187 0.785244i 0.712538π-0.712538\pi
−0.619187 + 0.785244i 0.712538π0.712538\pi
822822 0.139604 + 2.00430i 0.00486927 + 0.0699080i
823823 8.41130i 0.293199i −0.989196 0.146600i 0.953167π-0.953167\pi
0.989196 0.146600i 0.0468329π-0.0468329\pi
824824 3.59569 + 16.9848i 0.125262 + 0.591693i
825825 2.39306i 0.0833157i
826826 0 0
827827 4.33435i 0.150720i 0.997156 + 0.0753601i 0.0240106π0.0240106\pi
−0.997156 + 0.0753601i 0.975989π0.975989\pi
828828 −2.30459 16.4632i −0.0800899 0.572136i
829829 24.1798i 0.839801i 0.907570 + 0.419900i 0.137935π0.137935\pi
−0.907570 + 0.419900i 0.862065π0.862065\pi
830830 9.15810 0.637885i 0.317882 0.0221413i
831831 4.60046 0.159588
832832 18.9013 + 42.6407i 0.655283 + 1.47830i
833833 0 0
834834 0.221005 + 3.17296i 0.00765277 + 0.109871i
835835 13.7127i 0.474549i
836836 −4.10293 29.3099i −0.141903 1.01371i
837837 32.6660 1.12910
838838 1.80381 + 25.8973i 0.0623117 + 0.894608i
839839 18.3056 0.631979 0.315989 0.948763i 0.397664π-0.397664\pi
0.315989 + 0.948763i 0.397664π0.397664\pi
840840 0 0
841841 −2.02999 −0.0699998
842842 0.223367 + 3.20688i 0.00769774 + 0.110516i
843843 −2.81097 −0.0968150
844844 2.76821 + 19.7752i 0.0952856 + 0.680689i
845845 20.9920i 0.722148i
846846 1.73563 + 24.9184i 0.0596722 + 0.856712i
847847 0 0
848848 −28.5296 + 8.14704i −0.979711 + 0.279770i
849849 −5.65120 −0.193949
850850 −1.93014 + 0.134439i −0.0662034 + 0.00461123i
851851 35.0344i 1.20096i
852852 0.647361 + 4.62453i 0.0221782 + 0.158434i
853853 16.9533i 0.580469i −0.956956 0.290234i 0.906267π-0.906267\pi
0.956956 0.290234i 0.0937332π-0.0937332\pi
854854 0 0
855855 10.4904i 0.358765i
856856 −21.2180 + 4.49187i −0.725218 + 0.153529i
857857 50.5745i 1.72759i −0.503843 0.863795i 0.668081π-0.668081\pi
0.503843 0.863795i 0.331919π-0.331919\pi
858858 −1.37102 19.6837i −0.0468058 0.671990i
859859 −5.03849 −0.171911 −0.0859555 0.996299i 0.527394π-0.527394\pi
−0.0859555 + 0.996299i 0.527394π0.527394\pi
860860 6.15285 0.861301i 0.209810 0.0293701i
861861 0 0
862862 −18.1442 + 1.26379i −0.617993 + 0.0430448i
863863 11.7417i 0.399691i −0.979827 0.199846i 0.935956π-0.935956\pi
0.979827 0.199846i 0.0640441π-0.0640441\pi
864864 −7.10003 19.5903i −0.241548 0.666477i
865865 3.92439 0.133433
866866 47.4460 3.30473i 1.61228 0.112299i
867867 10.0203 0.340306
868868 0 0
869869 −40.9714 −1.38986
870870 −4.85283 + 0.338012i −0.164526 + 0.0114597i
871871 −14.7949 −0.501307
872872 −0.758743 3.58404i −0.0256943 0.121371i
873873 0.879005i 0.0297498i
874874 −18.7517 + 1.30610i −0.634284 + 0.0441795i
875875 0 0
876876 0.949429 + 6.78241i 0.0320782 + 0.229156i
877877 −24.1824 −0.816581 −0.408290 0.912852i 0.633875π-0.633875\pi
−0.408290 + 0.912852i 0.633875π0.633875\pi
878878 2.44553 + 35.1105i 0.0825327 + 1.18492i
879879 16.7125i 0.563698i
880880 13.8963 3.96830i 0.468446 0.133771i
881881 19.6285i 0.661301i −0.943753 0.330651i 0.892732π-0.892732\pi
0.943753 0.330651i 0.107268π-0.107268\pi
882882 0 0
883883 11.2418i 0.378315i 0.981947 + 0.189158i 0.0605757π0.0605757\pi
−0.981947 + 0.189158i 0.939424π0.939424\pi
884884 15.7990 2.21161i 0.531379 0.0743846i
885885 4.95346i 0.166509i
886886 −11.2126 + 0.780987i −0.376695 + 0.0262378i
887887 −41.8099 −1.40384 −0.701920 0.712256i 0.747674π-0.747674\pi
−0.701920 + 0.712256i 0.747674π0.747674\pi
888888 −4.18882 19.7865i −0.140568 0.663993i
889889 0 0
890890 0.922831 + 13.2491i 0.0309334 + 0.444110i
891891 18.9465i 0.634733i
892892 33.3111 4.66303i 1.11534 0.156130i
893893 28.2445 0.945165
894894 −1.24227 17.8352i −0.0415476 0.596499i
895895 20.5539 0.687040
896896 0 0
897897 −12.5320 −0.418430
898898 1.40546 + 20.1782i 0.0469009 + 0.673356i
899899 −46.0544 −1.53600
900900 −5.07311 + 0.710155i −0.169104 + 0.0236718i
901901 10.1481i 0.338082i
902902 0.295644 + 4.24455i 0.00984385 + 0.141328i
903903 0 0
904904 −4.16262 19.6628i −0.138447 0.653974i
905905 −13.0603 −0.434138
906906 −8.97625 + 0.625218i −0.298216 + 0.0207715i
907907 21.8089i 0.724151i 0.932149 + 0.362076i 0.117932π0.117932\pi
−0.932149 + 0.362076i 0.882068π0.882068\pi
908908 39.2846 5.49923i 1.30371 0.182498i
909909 11.6189i 0.385374i
910910 0 0
911911 2.40991i 0.0798440i −0.999203 0.0399220i 0.987289π-0.987289\pi
0.999203 0.0399220i 0.0127109π-0.0127109\pi
912912 −10.4343 + 2.97966i −0.345514 + 0.0986664i
913913 23.4533i 0.776192i
914914 2.17939 + 31.2895i 0.0720879 + 1.03497i
915915 0.983957 0.0325286
916916 3.86316 + 27.5971i 0.127642 + 0.911835i
917917 0 0
918918 −7.10977 + 0.495214i −0.234657 + 0.0163445i
919919 15.2029i 0.501498i −0.968052 0.250749i 0.919323π-0.919323\pi
0.968052 0.250749i 0.0806768π-0.0806768\pi
920920 −1.90102 8.97976i −0.0626749 0.296054i
921921 19.3828 0.638685
922922 46.3569 3.22888i 1.52668 0.106337i
923923 −20.5518 −0.676470
924924 0 0
925925 −10.7958 −0.354963
926926 −4.67526 + 0.325644i −0.153639 + 0.0107013i
927927 15.7215 0.516361
928928 10.0100 + 27.6196i 0.328595 + 0.906656i
929929 20.8695i 0.684704i −0.939572 0.342352i 0.888776π-0.888776\pi
0.939572 0.342352i 0.111224π-0.111224\pi
930930 8.28676 0.577194i 0.271734 0.0189269i
931931 0 0
932932 −20.2538 + 2.83522i −0.663437 + 0.0928706i
933933 −15.0660 −0.493238
934934 3.45240 + 49.5661i 0.112966 + 1.62185i
935935 4.94298i 0.161653i
936936 41.3211 8.74770i 1.35062 0.285928i
937937 10.9083i 0.356358i 0.983998 + 0.178179i 0.0570206π0.0570206\pi
−0.983998 + 0.178179i 0.942979π0.942979\pi
938938 0 0
939939 4.36148i 0.142331i
940940 1.91202 + 13.6588i 0.0623633 + 0.445502i
941941 49.3714i 1.60946i −0.593641 0.804730i 0.702310π-0.702310\pi
0.593641 0.804730i 0.297690π-0.297690\pi
942942 −15.3832 + 1.07148i −0.501212 + 0.0349106i
943943 2.70237 0.0880012
944944 28.7644 8.21408i 0.936202 0.267346i
945945 0 0
946946 1.10287 + 15.8339i 0.0358574 + 0.514804i
947947 14.5586i 0.473091i 0.971620 + 0.236545i 0.0760152π0.0760152\pi
−0.971620 + 0.236545i 0.923985π0.923985\pi
948948 2.08258 + 14.8773i 0.0676392 + 0.483192i
949949 −30.1416 −0.978437
950950 0.402472 + 5.77829i 0.0130579 + 0.187473i
951951 −9.35358 −0.303311
952952 0 0
953953 −9.87954 −0.320030 −0.160015 0.987115i 0.551154π-0.551154\pi
−0.160015 + 0.987115i 0.551154π0.551154\pi
954954 1.86689 + 26.8028i 0.0604426 + 0.867774i
955955 12.4751 0.403685
956956 4.73664 + 33.8370i 0.153194 + 1.09437i
957957 12.4278i 0.401734i
958958 2.19394 + 31.4983i 0.0708829 + 1.01766i
959959 0 0
960960 −2.14730 4.84425i −0.0693038 0.156348i
961961 47.6431 1.53687
962962 88.7988 6.18506i 2.86299 0.199414i
963963 19.6399i 0.632886i
964964 5.12488 + 36.6104i 0.165061 + 1.17914i
965965 19.0645i 0.613708i
966966 0 0
967967 15.5047i 0.498597i 0.968427 + 0.249298i 0.0802000π0.0802000\pi
−0.968427 + 0.249298i 0.919800π0.919800\pi
968968 1.20293 + 5.68221i 0.0386636 + 0.182633i
969969 3.71152i 0.119231i
970970 −0.0337236 0.484169i −0.00108280 0.0155457i
971971 33.0347 1.06013 0.530067 0.847956i 0.322167π-0.322167\pi
0.530067 + 0.847956i 0.322167π0.322167\pi
972972 −28.7676 + 4.02701i −0.922721 + 0.129166i
973973 0 0
974974 −10.1368 + 0.706056i −0.324805 + 0.0226235i
975975 3.86171i 0.123674i
976976 −1.63165 5.71377i −0.0522278 0.182893i
977977 −50.9720 −1.63074 −0.815369 0.578941i 0.803466π-0.803466\pi
−0.815369 + 0.578941i 0.803466π0.803466\pi
978978 −6.68701 + 0.465767i −0.213827 + 0.0148936i
979979 −33.9301 −1.08441
980980 0 0
981981 −3.31746 −0.105918
982982 −8.18345 + 0.569998i −0.261144 + 0.0181894i
983983 24.5284 0.782336 0.391168 0.920319i 0.372071π-0.372071\pi
0.391168 + 0.920319i 0.372071π0.372071\pi
984984 1.52623 0.323104i 0.0486544 0.0103002i
985985 1.93188i 0.0615548i
986986 10.0238 0.698180i 0.319221 0.0222346i
987987 0 0
988988 −6.62093 47.2977i −0.210640 1.50474i
989989 10.0809 0.320555
990990 −0.909332 13.0553i −0.0289005 0.414923i
991991 52.9169i 1.68096i −0.541841 0.840481i 0.682273π-0.682273\pi
0.541841 0.840481i 0.317727π-0.317727\pi
992992 −17.0933 47.1635i −0.542712 1.49744i
993993 13.4606i 0.427160i
994994 0 0
995995 20.5646i 0.651941i
996996 8.51624 1.19214i 0.269847 0.0377744i
997997 17.0230i 0.539123i 0.962983 + 0.269561i 0.0868787π0.0868787\pi
−0.962983 + 0.269561i 0.913121π0.913121\pi
998998 55.9523 3.89722i 1.77114 0.123364i
999999 −39.7667 −1.25816
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 980.2.g.a.391.20 32
4.3 odd 2 inner 980.2.g.a.391.17 32
7.2 even 3 980.2.o.f.31.14 32
7.3 odd 6 980.2.o.f.411.2 32
7.4 even 3 140.2.o.a.131.2 yes 32
7.5 odd 6 140.2.o.a.31.14 yes 32
7.6 odd 2 inner 980.2.g.a.391.19 32
28.3 even 6 980.2.o.f.411.14 32
28.11 odd 6 140.2.o.a.131.14 yes 32
28.19 even 6 140.2.o.a.31.2 32
28.23 odd 6 980.2.o.f.31.2 32
28.27 even 2 inner 980.2.g.a.391.18 32
35.4 even 6 700.2.p.c.551.15 32
35.12 even 12 700.2.t.c.199.12 32
35.18 odd 12 700.2.t.c.299.7 32
35.19 odd 6 700.2.p.c.451.3 32
35.32 odd 12 700.2.t.d.299.10 32
35.33 even 12 700.2.t.d.199.5 32
140.19 even 6 700.2.p.c.451.15 32
140.39 odd 6 700.2.p.c.551.3 32
140.47 odd 12 700.2.t.c.199.7 32
140.67 even 12 700.2.t.d.299.5 32
140.103 odd 12 700.2.t.d.199.10 32
140.123 even 12 700.2.t.c.299.12 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.2 32 28.19 even 6
140.2.o.a.31.14 yes 32 7.5 odd 6
140.2.o.a.131.2 yes 32 7.4 even 3
140.2.o.a.131.14 yes 32 28.11 odd 6
700.2.p.c.451.3 32 35.19 odd 6
700.2.p.c.451.15 32 140.19 even 6
700.2.p.c.551.3 32 140.39 odd 6
700.2.p.c.551.15 32 35.4 even 6
700.2.t.c.199.7 32 140.47 odd 12
700.2.t.c.199.12 32 35.12 even 12
700.2.t.c.299.7 32 35.18 odd 12
700.2.t.c.299.12 32 140.123 even 12
700.2.t.d.199.5 32 35.33 even 12
700.2.t.d.199.10 32 140.103 odd 12
700.2.t.d.299.5 32 140.67 even 12
700.2.t.d.299.10 32 35.32 odd 12
980.2.g.a.391.17 32 4.3 odd 2 inner
980.2.g.a.391.18 32 28.27 even 2 inner
980.2.g.a.391.19 32 7.6 odd 2 inner
980.2.g.a.391.20 32 1.1 even 1 trivial
980.2.o.f.31.2 32 28.23 odd 6
980.2.o.f.31.14 32 7.2 even 3
980.2.o.f.411.2 32 7.3 odd 6
980.2.o.f.411.14 32 28.3 even 6