Properties

Label 990.2.bh.c.73.1
Level 990990
Weight 22
Character 990.73
Analytic conductor 7.9057.905
Analytic rank 00
Dimension 4848
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [990,2,Mod(73,990)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(990, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 15, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("990.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 990=232511 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 990.bh (of order 2020, degree 88, 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: 7.905189800117.90518980011
Analytic rank: 00
Dimension: 4848
Relative dimension: 66 over Q(ζ20)\Q(\zeta_{20})
Twist minimal: no (minimal twist has level 110)
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 73.1
Character χ\chi == 990.73
Dual form 990.2.bh.c.217.1

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+(0.1564340.987688i)q2+(0.951057+0.309017i)q4+(2.149090.617590i)q5+(0.00697389+0.0136870i)q7+(0.453990+0.891007i)q8+(0.273795+2.21924i)q10+(2.43343+2.25353i)q11+(2.31203+0.366190i)q13+(0.0146095+0.00474691i)q14+(0.8090170.587785i)q16+(3.88580+0.615451i)q17+(1.784565.49230i)q19+(2.234750.0767418i)q20+(2.60646+2.05094i)q22+(4.75841+4.75841i)q23+(4.23716+2.65451i)q25+(0.723362+2.22628i)q26+(0.002403040.0151722i)q28+(1.28099+3.94247i)q29+(4.70277+3.41676i)q31+(0.7071070.707107i)q323.93424iq34+(0.02344050.0251076i)q35+(1.005210.512178i)q37+(5.703850.903401i)q38+(0.4253892.19523i)q40+(4.46390+1.45041i)q41+(5.68946+5.68946i)q43+(1.617952.89521i)q44+(3.955445.44420i)q46+(0.703097+1.37991i)q47+(4.11436+5.66293i)q49+(1.958994.60026i)q50+(2.085711.06272i)q52+(2.1955913.8624i)q53+(6.621423.34018i)q550.0153613q56+(3.693541.88195i)q58+(1.86696+0.606613i)q59+(4.84534+6.66904i)q61+(2.639025.17937i)q62+(0.587785+0.809017i)q64+(5.19491+0.640913i)q65+(3.676403.67640i)q67+(3.88580+0.615451i)q68+(0.02846540.0192242i)q70+(5.200513.77839i)q71+(4.10721+2.09273i)q73+(0.348623+1.07295i)q74+5.77495iq76+(0.01387370.0490224i)q77+(3.84472+2.79336i)q79+(2.10166+0.763562i)q80+(0.7342444.63584i)q82+(2.08413+13.1587i)q83+(7.970843.72249i)q85+(6.50944+4.72938i)q86+(3.112671.14512i)q88+9.48232iq89+(0.01111180.0341986i)q91+(5.995943.05509i)q92+(1.252930.910306i)q94+(7.22716+10.7013i)q95+(4.396150.696283i)q97+(4.949584.94958i)q98+O(q100)q+(-0.156434 - 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(-2.14909 - 0.617590i) q^{5} +(-0.00697389 + 0.0136870i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.273795 + 2.21924i) q^{10} +(-2.43343 + 2.25353i) q^{11} +(-2.31203 + 0.366190i) q^{13} +(0.0146095 + 0.00474691i) q^{14} +(0.809017 - 0.587785i) q^{16} +(3.88580 + 0.615451i) q^{17} +(1.78456 - 5.49230i) q^{19} +(2.23475 - 0.0767418i) q^{20} +(2.60646 + 2.05094i) q^{22} +(4.75841 + 4.75841i) q^{23} +(4.23716 + 2.65451i) q^{25} +(0.723362 + 2.22628i) q^{26} +(0.00240304 - 0.0151722i) q^{28} +(1.28099 + 3.94247i) q^{29} +(4.70277 + 3.41676i) q^{31} +(-0.707107 - 0.707107i) q^{32} -3.93424i q^{34} +(0.0234405 - 0.0251076i) q^{35} +(-1.00521 - 0.512178i) q^{37} +(-5.70385 - 0.903401i) q^{38} +(-0.425389 - 2.19523i) q^{40} +(4.46390 + 1.45041i) q^{41} +(-5.68946 + 5.68946i) q^{43} +(1.61795 - 2.89521i) q^{44} +(3.95544 - 5.44420i) q^{46} +(0.703097 + 1.37991i) q^{47} +(4.11436 + 5.66293i) q^{49} +(1.95899 - 4.60026i) q^{50} +(2.08571 - 1.06272i) q^{52} +(-2.19559 - 13.8624i) q^{53} +(6.62142 - 3.34018i) q^{55} -0.0153613 q^{56} +(3.69354 - 1.88195i) q^{58} +(-1.86696 + 0.606613i) q^{59} +(4.84534 + 6.66904i) q^{61} +(2.63902 - 5.17937i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(5.19491 + 0.640913i) q^{65} +(3.67640 - 3.67640i) q^{67} +(-3.88580 + 0.615451i) q^{68} +(-0.0284654 - 0.0192242i) q^{70} +(5.20051 - 3.77839i) q^{71} +(4.10721 + 2.09273i) q^{73} +(-0.348623 + 1.07295i) q^{74} +5.77495i q^{76} +(-0.0138737 - 0.0490224i) q^{77} +(3.84472 + 2.79336i) q^{79} +(-2.10166 + 0.763562i) q^{80} +(0.734244 - 4.63584i) q^{82} +(-2.08413 + 13.1587i) q^{83} +(-7.97084 - 3.72249i) q^{85} +(6.50944 + 4.72938i) q^{86} +(-3.11267 - 1.14512i) q^{88} +9.48232i q^{89} +(0.0111118 - 0.0341986i) q^{91} +(-5.99594 - 3.05509i) q^{92} +(1.25293 - 0.910306i) q^{94} +(-7.22716 + 10.7013i) q^{95} +(4.39615 - 0.696283i) q^{97} +(4.94958 - 4.94958i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+8q520q712q11+12q16+20q17+4q204q22+8q2320q258q2620q28+16q31+20q37+36q38+20q41+40q4640q47++72q97+O(q100) 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/990Z)×\left(\mathbb{Z}/990\mathbb{Z}\right)^\times.

nn 397397 541541 551551
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(710)e\left(\frac{7}{10}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.156434 0.987688i −0.110616 0.698401i
33 0 0
44 −0.951057 + 0.309017i −0.475528 + 0.154508i
55 −2.14909 0.617590i −0.961102 0.276195i
66 0 0
77 −0.00697389 + 0.0136870i −0.00263588 + 0.00517321i −0.892321 0.451402i 0.850924π-0.850924\pi
0.889685 + 0.456575i 0.150924π0.150924\pi
88 0.453990 + 0.891007i 0.160510 + 0.315018i
99 0 0
1010 −0.273795 + 2.21924i −0.0865816 + 0.701786i
1111 −2.43343 + 2.25353i −0.733708 + 0.679465i
1212 0 0
1313 −2.31203 + 0.366190i −0.641242 + 0.101563i −0.468584 0.883419i 0.655236π-0.655236\pi
−0.172658 + 0.984982i 0.555236π0.555236\pi
1414 0.0146095 + 0.00474691i 0.00390455 + 0.00126866i
1515 0 0
1616 0.809017 0.587785i 0.202254 0.146946i
1717 3.88580 + 0.615451i 0.942446 + 0.149269i 0.608705 0.793396i 0.291689π-0.291689\pi
0.333740 + 0.942665i 0.391689π0.391689\pi
1818 0 0
1919 1.78456 5.49230i 0.409406 1.26002i −0.507755 0.861502i 0.669524π-0.669524\pi
0.917160 0.398519i 0.130476π-0.130476\pi
2020 2.23475 0.0767418i 0.499705 0.0171600i
2121 0 0
2222 2.60646 + 2.05094i 0.555699 + 0.437263i
2323 4.75841 + 4.75841i 0.992196 + 0.992196i 0.999970 0.00777340i 0.00247437π-0.00247437\pi
−0.00777340 + 0.999970i 0.502474π0.502474\pi
2424 0 0
2525 4.23716 + 2.65451i 0.847433 + 0.530902i
2626 0.723362 + 2.22628i 0.141863 + 0.436609i
2727 0 0
2828 0.00240304 0.0151722i 0.000454132 0.00286728i
2929 1.28099 + 3.94247i 0.237873 + 0.732099i 0.996727 + 0.0808379i 0.0257596π0.0257596\pi
−0.758854 + 0.651261i 0.774240π0.774240\pi
3030 0 0
3131 4.70277 + 3.41676i 0.844642 + 0.613668i 0.923663 0.383205i 0.125180π-0.125180\pi
−0.0790218 + 0.996873i 0.525180π0.525180\pi
3232 −0.707107 0.707107i −0.125000 0.125000i
3333 0 0
3434 3.93424i 0.674716i
3535 0.0234405 0.0251076i 0.00396217 0.00424397i
3636 0 0
3737 −1.00521 0.512178i −0.165255 0.0842015i 0.369407 0.929268i 0.379561π-0.379561\pi
−0.534662 + 0.845066i 0.679561π0.679561\pi
3838 −5.70385 0.903401i −0.925287 0.146551i
3939 0 0
4040 −0.425389 2.19523i −0.0672599 0.347097i
4141 4.46390 + 1.45041i 0.697144 + 0.226516i 0.636086 0.771618i 0.280552π-0.280552\pi
0.0610584 + 0.998134i 0.480552π0.480552\pi
4242 0 0
4343 −5.68946 + 5.68946i −0.867634 + 0.867634i −0.992210 0.124576i 0.960243π-0.960243\pi
0.124576 + 0.992210i 0.460243π0.460243\pi
4444 1.61795 2.89521i 0.243915 0.436469i
4545 0 0
4646 3.95544 5.44420i 0.583198 0.802704i
4747 0.703097 + 1.37991i 0.102557 + 0.201280i 0.936583 0.350445i 0.113970π-0.113970\pi
−0.834026 + 0.551725i 0.813970π0.813970\pi
4848 0 0
4949 4.11436 + 5.66293i 0.587765 + 0.808990i
5050 1.95899 4.60026i 0.277043 0.650574i
5151 0 0
5252 2.08571 1.06272i 0.289236 0.147373i
5353 −2.19559 13.8624i −0.301587 1.90415i −0.413635 0.910443i 0.635741π-0.635741\pi
0.112048 0.993703i 0.464259π-0.464259\pi
5454 0 0
5555 6.62142 3.34018i 0.892832 0.450389i
5656 −0.0153613 −0.00205274
5757 0 0
5858 3.69354 1.88195i 0.484986 0.247113i
5959 −1.86696 + 0.606613i −0.243058 + 0.0789743i −0.428013 0.903773i 0.640786π-0.640786\pi
0.184955 + 0.982747i 0.440786π0.440786\pi
6060 0 0
6161 4.84534 + 6.66904i 0.620382 + 0.853883i 0.997381 0.0723312i 0.0230439π-0.0230439\pi
−0.376999 + 0.926214i 0.623044π0.623044\pi
6262 2.63902 5.17937i 0.335156 0.657780i
6363 0 0
6464 −0.587785 + 0.809017i −0.0734732 + 0.101127i
6565 5.19491 + 0.640913i 0.644350 + 0.0794955i
6666 0 0
6767 3.67640 3.67640i 0.449143 0.449143i −0.445926 0.895070i 0.647126π-0.647126\pi
0.895070 + 0.445926i 0.147126π0.147126\pi
6868 −3.88580 + 0.615451i −0.471223 + 0.0746344i
6969 0 0
7070 −0.0284654 0.0192242i −0.00340227 0.00229773i
7171 5.20051 3.77839i 0.617187 0.448413i −0.234751 0.972056i 0.575427π-0.575427\pi
0.851938 + 0.523643i 0.175427π0.175427\pi
7272 0 0
7373 4.10721 + 2.09273i 0.480713 + 0.244935i 0.677517 0.735508i 0.263056π-0.263056\pi
−0.196804 + 0.980443i 0.563056π0.563056\pi
7474 −0.348623 + 1.07295i −0.0405266 + 0.124728i
7575 0 0
7676 5.77495i 0.662432i
7777 −0.0138737 0.0490224i −0.00158105 0.00558662i
7878 0 0
7979 3.84472 + 2.79336i 0.432565 + 0.314277i 0.782674 0.622432i 0.213855π-0.213855\pi
−0.350109 + 0.936709i 0.613855π0.613855\pi
8080 −2.10166 + 0.763562i −0.234973 + 0.0853688i
8181 0 0
8282 0.734244 4.63584i 0.0810837 0.511943i
8383 −2.08413 + 13.1587i −0.228763 + 1.44436i 0.559405 + 0.828895i 0.311030π0.311030\pi
−0.788168 + 0.615460i 0.788970π0.788970\pi
8484 0 0
8585 −7.97084 3.72249i −0.864559 0.403761i
8686 6.50944 + 4.72938i 0.701931 + 0.509983i
8787 0 0
8888 −3.11267 1.14512i −0.331811 0.122070i
8989 9.48232i 1.00512i 0.864541 + 0.502562i 0.167609π0.167609\pi
−0.864541 + 0.502562i 0.832391π0.832391\pi
9090 0 0
9191 0.0111118 0.0341986i 0.00116483 0.00358499i
9292 −5.99594 3.05509i −0.625120 0.318515i
9393 0 0
9494 1.25293 0.910306i 0.129230 0.0938909i
9595 −7.22716 + 10.7013i −0.741491 + 1.09793i
9696 0 0
9797 4.39615 0.696283i 0.446362 0.0706968i 0.0707925 0.997491i 0.477447π-0.477447\pi
0.375569 + 0.926794i 0.377447π0.377447\pi
9898 4.94958 4.94958i 0.499983 0.499983i
9999 0 0
100100 −4.85007 1.21523i −0.485007 0.121523i
101101 10.2067 14.0483i 1.01561 1.39786i 0.100365 0.994951i 0.467999π-0.467999\pi
0.915240 0.402910i 0.132001π-0.132001\pi
102102 0 0
103103 −0.155063 + 0.304328i −0.0152788 + 0.0299864i −0.898520 0.438933i 0.855357π-0.855357\pi
0.883241 + 0.468919i 0.155357π0.155357\pi
104104 −1.37592 1.89379i −0.134920 0.185701i
105105 0 0
106106 −13.3483 + 4.33711i −1.29650 + 0.421257i
107107 2.04336 1.04115i 0.197539 0.100651i −0.352423 0.935841i 0.614642π-0.614642\pi
0.549962 + 0.835190i 0.314642π0.314642\pi
108108 0 0
109109 −2.42843 −0.232602 −0.116301 0.993214i 0.537104π-0.537104\pi
−0.116301 + 0.993214i 0.537104π0.537104\pi
110110 −4.33487 6.01738i −0.413314 0.573735i
111111 0 0
112112 0.00240304 + 0.0151722i 0.000227066 + 0.00143364i
113113 −9.70357 + 4.94421i −0.912835 + 0.465113i −0.846321 0.532673i 0.821188π-0.821188\pi
−0.0665137 + 0.997786i 0.521188π0.521188\pi
114114 0 0
115115 −7.28749 13.1650i −0.679562 1.22764i
116116 −2.43658 3.35367i −0.226231 0.311380i
117117 0 0
118118 0.891202 + 1.74908i 0.0820418 + 0.161016i
119119 −0.0355229 + 0.0488930i −0.00325638 + 0.00448202i
120120 0 0
121121 0.843188 10.9676i 0.0766535 0.997058i
122122 5.82895 5.82895i 0.527728 0.527728i
123123 0 0
124124 −5.52843 1.79630i −0.496468 0.161312i
125125 −7.46664 8.32161i −0.667837 0.744308i
126126 0 0
127127 −17.3079 2.74131i −1.53583 0.243252i −0.669535 0.742781i 0.733506π-0.733506\pi
−0.866297 + 0.499529i 0.833506π0.833506\pi
128128 0.891007 + 0.453990i 0.0787546 + 0.0401275i
129129 0 0
130130 −0.179641 5.23122i −0.0157556 0.458808i
131131 3.65271i 0.319138i 0.987187 + 0.159569i 0.0510105π0.0510105\pi
−0.987187 + 0.159569i 0.948989π0.948989\pi
132132 0 0
133133 0.0627280 + 0.0627280i 0.00543921 + 0.00543921i
134134 −4.20625 3.05602i −0.363364 0.264000i
135135 0 0
136136 1.21575 + 3.74168i 0.104249 + 0.320847i
137137 −2.63360 + 16.6279i −0.225004 + 1.42062i 0.573784 + 0.819006i 0.305475π0.305475\pi
−0.798788 + 0.601612i 0.794525π0.794525\pi
138138 0 0
139139 6.84479 + 21.0661i 0.580567 + 1.78680i 0.616386 + 0.787444i 0.288596π0.288596\pi
−0.0358190 + 0.999358i 0.511404π0.511404\pi
140140 −0.0145345 + 0.0311223i −0.00122839 + 0.00263031i
141141 0 0
142142 −4.54541 4.54541i −0.381443 0.381443i
143143 4.80095 6.10133i 0.401476 0.510219i
144144 0 0
145145 −0.318123 9.26385i −0.0264186 0.769321i
146146 1.42445 4.38402i 0.117889 0.362824i
147147 0 0
148148 1.11428 + 0.176484i 0.0915932 + 0.0145069i
149149 −11.4310 + 8.30508i −0.936461 + 0.680379i −0.947566 0.319560i 0.896465π-0.896465\pi
0.0111054 + 0.999938i 0.496465π0.496465\pi
150150 0 0
151151 3.14883 + 1.02312i 0.256248 + 0.0832600i 0.434324 0.900757i 0.356987π-0.356987\pi
−0.178076 + 0.984017i 0.556987π0.556987\pi
152152 5.70385 0.903401i 0.462643 0.0732755i
153153 0 0
154154 −0.0462485 + 0.0213716i −0.00372681 + 0.00172218i
155155 −7.99650 10.2473i −0.642295 0.823083i
156156 0 0
157157 5.84266 + 11.4669i 0.466295 + 0.915155i 0.997683 + 0.0680269i 0.0216704π0.0216704\pi
−0.531389 + 0.847128i 0.678330π0.678330\pi
158158 2.15752 4.23437i 0.171643 0.336868i
159159 0 0
160160 1.08293 + 1.95634i 0.0856134 + 0.154662i
161161 −0.0983131 + 0.0319439i −0.00774816 + 0.00251753i
162162 0 0
163163 −0.263165 1.66156i −0.0206127 0.130143i 0.975236 0.221166i 0.0709864π-0.0709864\pi
−0.995849 + 0.0910229i 0.970986π0.970986\pi
164164 −4.69362 −0.366510
165165 0 0
166166 13.3227 1.03404
167167 −2.54594 16.0744i −0.197011 1.24388i −0.865787 0.500413i 0.833182π-0.833182\pi
0.668776 0.743464i 0.266818π-0.266818\pi
168168 0 0
169169 −7.15235 + 2.32394i −0.550181 + 0.178764i
170170 −2.42975 + 8.45503i −0.186353 + 0.648471i
171171 0 0
172172 3.65286 7.16914i 0.278528 0.546642i
173173 −6.86850 13.4802i −0.522202 1.02488i −0.990003 0.141046i 0.954954π-0.954954\pi
0.467801 0.883834i 0.345046π-0.345046\pi
174174 0 0
175175 −0.0658819 + 0.0394819i −0.00498021 + 0.00298455i
176176 −0.644096 + 3.25348i −0.0485505 + 0.245240i
177177 0 0
178178 9.36557 1.48336i 0.701979 0.111183i
179179 22.4795 + 7.30404i 1.68020 + 0.545930i 0.984950 0.172839i 0.0552939π-0.0552939\pi
0.695249 + 0.718769i 0.255294π0.255294\pi
180180 0 0
181181 −15.4698 + 11.2395i −1.14986 + 0.835423i −0.988462 0.151466i 0.951601π-0.951601\pi
−0.161399 + 0.986889i 0.551601π0.551601\pi
182182 −0.0355158 0.00562515i −0.00263261 0.000416964i
183183 0 0
184184 −2.07950 + 6.40004i −0.153303 + 0.471817i
185185 1.84396 + 1.72152i 0.135571 + 0.126569i
186186 0 0
187187 −10.8428 + 7.25912i −0.792902 + 0.530840i
188188 −1.09510 1.09510i −0.0798683 0.0798683i
189189 0 0
190190 11.7001 + 5.46413i 0.848818 + 0.396410i
191191 3.70271 + 11.3958i 0.267919 + 0.824569i 0.991007 + 0.133813i 0.0427222π0.0427222\pi
−0.723088 + 0.690756i 0.757278π0.757278\pi
192192 0 0
193193 2.50920 15.8424i 0.180616 1.14036i −0.716179 0.697917i 0.754110π-0.754110\pi
0.896795 0.442447i 0.145890π-0.145890\pi
194194 −1.37542 4.23311i −0.0987494 0.303919i
195195 0 0
196196 −5.66293 4.11436i −0.404495 0.293883i
197197 −5.90309 5.90309i −0.420578 0.420578i 0.464825 0.885403i 0.346117π-0.346117\pi
−0.885403 + 0.464825i 0.846117π0.846117\pi
198198 0 0
199199 8.46646i 0.600171i 0.953912 + 0.300086i 0.0970153π0.0970153\pi
−0.953912 + 0.300086i 0.902985π0.902985\pi
200200 −0.441555 + 4.98046i −0.0312226 + 0.352172i
201201 0 0
202202 −15.4720 7.88340i −1.08861 0.554674i
203203 −0.0628942 0.00996146i −0.00441431 0.000699158i
204204 0 0
205205 −8.69756 5.87392i −0.607464 0.410252i
206206 0.324839 + 0.105546i 0.0226326 + 0.00735377i
207207 0 0
208208 −1.65523 + 1.65523i −0.114770 + 0.114770i
209209 8.03448 + 17.3867i 0.555757 + 1.20266i
210210 0 0
211211 4.11272 5.66067i 0.283131 0.389697i −0.643637 0.765331i 0.722575π-0.722575\pi
0.926768 + 0.375635i 0.122575π0.122575\pi
212212 6.37184 + 12.5054i 0.437620 + 0.858877i
213213 0 0
214214 −1.34798 1.85533i −0.0921460 0.126828i
215215 15.7409 8.71340i 1.07352 0.594249i
216216 0 0
217217 −0.0795619 + 0.0405388i −0.00540101 + 0.00275195i
218218 0.379891 + 2.39853i 0.0257294 + 0.162449i
219219 0 0
220220 −5.26518 + 5.22283i −0.354978 + 0.352123i
221221 −9.20946 −0.619496
222222 0 0
223223 −16.6612 + 8.48928i −1.11571 + 0.568484i −0.911854 0.410516i 0.865349π-0.865349\pi
−0.203860 + 0.979000i 0.565349π0.565349\pi
224224 0.0146095 0.00474691i 0.000976137 0.000317166i
225225 0 0
226226 6.40132 + 8.81066i 0.425809 + 0.586076i
227227 4.59950 9.02703i 0.305280 0.599145i −0.686496 0.727134i 0.740852π-0.740852\pi
0.991776 + 0.127989i 0.0408521π0.0408521\pi
228228 0 0
229229 6.38012 8.78149i 0.421610 0.580297i −0.544392 0.838831i 0.683239π-0.683239\pi
0.966002 + 0.258534i 0.0832395π0.0832395\pi
230230 −11.8629 + 9.25723i −0.782215 + 0.610404i
231231 0 0
232232 −2.93121 + 2.93121i −0.192444 + 0.192444i
233233 4.69333 0.743350i 0.307470 0.0486985i −0.000792791 1.00000i 0.500252π-0.500252\pi
0.308263 + 0.951301i 0.400252π0.400252\pi
234234 0 0
235235 −0.658802 3.39977i −0.0429755 0.221776i
236236 1.58813 1.15385i 0.103379 0.0751091i
237237 0 0
238238 0.0538481 + 0.0274370i 0.00349045 + 0.00177847i
239239 −4.17166 + 12.8391i −0.269842 + 0.830490i 0.720696 + 0.693252i 0.243823π0.243823\pi
−0.990538 + 0.137238i 0.956177π0.956177\pi
240240 0 0
241241 21.5441i 1.38778i −0.720081 0.693890i 0.755895π-0.755895\pi
0.720081 0.693890i 0.244105π-0.244105\pi
242242 −10.9645 + 0.882909i −0.704825 + 0.0567555i
243243 0 0
244244 −6.66904 4.84534i −0.426941 0.310191i
245245 −5.34475 14.7111i −0.341464 0.939859i
246246 0 0
247247 −2.11473 + 13.3519i −0.134557 + 0.849558i
248248 −0.909344 + 5.74137i −0.0577434 + 0.364577i
249249 0 0
250250 −7.05112 + 8.67650i −0.445952 + 0.548750i
251251 15.8467 + 11.5133i 1.00023 + 0.726713i 0.962138 0.272561i 0.0878707π-0.0878707\pi
0.0380961 + 0.999274i 0.487871π0.487871\pi
252252 0 0
253253 −22.3025 0.856041i −1.40215 0.0538188i
254254 17.5237i 1.09953i
255255 0 0
256256 0.309017 0.951057i 0.0193136 0.0594410i
257257 −17.5999 8.96760i −1.09785 0.559384i −0.191323 0.981527i 0.561278π-0.561278\pi
−0.906529 + 0.422143i 0.861278π0.861278\pi
258258 0 0
259259 0.0140204 0.0101864i 0.000871185 0.000632953i
260260 −5.13871 + 0.995772i −0.318689 + 0.0617551i
261261 0 0
262262 3.60774 0.571409i 0.222887 0.0353018i
263263 −20.0880 + 20.0880i −1.23868 + 1.23868i −0.278140 + 0.960541i 0.589718π0.589718\pi
−0.960541 + 0.278140i 0.910282π0.910282\pi
264264 0 0
265265 −3.84276 + 31.1475i −0.236059 + 1.91337i
266266 0.0521429 0.0717686i 0.00319709 0.00440041i
267267 0 0
268268 −2.36039 + 4.63253i −0.144184 + 0.282977i
269269 5.50591 + 7.57823i 0.335701 + 0.462053i 0.943180 0.332283i 0.107819π-0.107819\pi
−0.607479 + 0.794336i 0.707819π0.707819\pi
270270 0 0
271271 5.85356 1.90194i 0.355578 0.115534i −0.125780 0.992058i 0.540143π-0.540143\pi
0.481359 + 0.876524i 0.340143π0.340143\pi
272272 3.50543 1.78611i 0.212548 0.108299i
273273 0 0
274274 16.8352 1.01705
275275 −16.2929 + 3.08901i −0.982498 + 0.186274i
276276 0 0
277277 −4.66256 29.4382i −0.280146 1.76877i −0.579834 0.814734i 0.696883π-0.696883\pi
0.299688 0.954037i 0.403117π-0.403117\pi
278278 19.7360 10.0560i 1.18368 0.603117i
279279 0 0
280280 0.0330128 + 0.00948700i 0.00197289 + 0.000566957i
281281 −3.35941 4.62383i −0.200406 0.275835i 0.696972 0.717099i 0.254530π-0.254530\pi
−0.897377 + 0.441264i 0.854530π0.854530\pi
282282 0 0
283283 −1.97387 3.87395i −0.117335 0.230282i 0.824868 0.565325i 0.191249π-0.191249\pi
−0.942203 + 0.335043i 0.891249π0.891249\pi
284284 −3.77839 + 5.20051i −0.224206 + 0.308594i
285285 0 0
286286 −6.77725 3.78738i −0.400747 0.223953i
287287 −0.0509826 + 0.0509826i −0.00300941 + 0.00300941i
288288 0 0
289289 −1.44728 0.470250i −0.0851341 0.0276618i
290290 −9.10003 + 1.76339i −0.534372 + 0.103550i
291291 0 0
292292 −4.55288 0.721105i −0.266437 0.0421995i
293293 −12.1120 6.17139i −0.707593 0.360537i 0.0628696 0.998022i 0.479975π-0.479975\pi
−0.770463 + 0.637485i 0.779975π0.779975\pi
294294 0 0
295295 4.38691 0.150647i 0.255416 0.00877103i
296296 1.12817i 0.0655735i
297297 0 0
298298 9.99102 + 9.99102i 0.578765 + 0.578765i
299299 −12.7441 9.25910i −0.737008 0.535468i
300300 0 0
301301 −0.0381941 0.117549i −0.00220147 0.00677544i
302302 0.517934 3.27011i 0.0298038 0.188174i
303303 0 0
304304 −1.78456 5.49230i −0.102351 0.315005i
305305 −6.29433 17.3248i −0.360412 0.992014i
306306 0 0
307307 16.8816 + 16.8816i 0.963484 + 0.963484i 0.999356 0.0358726i 0.0114211π-0.0114211\pi
−0.0358726 + 0.999356i 0.511421π0.511421\pi
308308 0.0283434 + 0.0423358i 0.00161501 + 0.00241231i
309309 0 0
310310 −8.87021 + 9.50108i −0.503794 + 0.539625i
311311 −8.96103 + 27.5792i −0.508133 + 1.56387i 0.287305 + 0.957839i 0.407241π0.407241\pi
−0.795439 + 0.606034i 0.792759π0.792759\pi
312312 0 0
313313 17.0901 + 2.70681i 0.965990 + 0.152998i 0.619449 0.785037i 0.287356π-0.287356\pi
0.346541 + 0.938035i 0.387356π0.387356\pi
314314 10.4117 7.56454i 0.587566 0.426891i
315315 0 0
316316 −4.51974 1.46855i −0.254255 0.0826126i
317317 20.4927 3.24572i 1.15098 0.182298i 0.448355 0.893855i 0.352010π-0.352010\pi
0.702628 + 0.711558i 0.252010π0.252010\pi
318318 0 0
319319 −12.0017 6.70700i −0.671965 0.375520i
320320 1.76284 1.37564i 0.0985460 0.0769006i
321321 0 0
322322 0.0469301 + 0.0921056i 0.00261531 + 0.00513284i
323323 10.3147 20.2437i 0.573924 1.12639i
324324 0 0
325325 −10.7685 4.58571i −0.597329 0.254369i
326326 −1.59994 + 0.519851i −0.0886122 + 0.0287919i
327327 0 0
328328 0.734244 + 4.63584i 0.0405419 + 0.255971i
329329 −0.0237901 −0.00131159
330330 0 0
331331 27.7235 1.52382 0.761912 0.647681i 0.224261π-0.224261\pi
0.761912 + 0.647681i 0.224261π0.224261\pi
332332 −2.08413 13.1587i −0.114382 0.722178i
333333 0 0
334334 −15.4782 + 5.02919i −0.846932 + 0.275185i
335335 −10.1714 + 5.63039i −0.555723 + 0.307621i
336336 0 0
337337 3.19123 6.26314i 0.173837 0.341175i −0.787606 0.616180i 0.788680π-0.788680\pi
0.961443 + 0.275005i 0.0886795π0.0886795\pi
338338 3.41420 + 6.70075i 0.185708 + 0.364473i
339339 0 0
340340 8.73103 + 1.07718i 0.473507 + 0.0584180i
341341 −19.1436 + 2.28338i −1.03669 + 0.123652i
342342 0 0
343343 −0.212407 + 0.0336420i −0.0114689 + 0.00181650i
344344 −7.65230 2.48638i −0.412585 0.134057i
345345 0 0
346346 −12.2398 + 8.89270i −0.658013 + 0.478075i
347347 21.4415 + 3.39601i 1.15104 + 0.182307i 0.702654 0.711532i 0.251998π-0.251998\pi
0.448388 + 0.893839i 0.351998π0.351998\pi
348348 0 0
349349 −3.67193 + 11.3010i −0.196554 + 0.604930i 0.803401 + 0.595438i 0.203021π0.203021\pi
−0.999955 + 0.00949216i 0.996979π0.996979\pi
350350 0.0493021 + 0.0588945i 0.00263531 + 0.00314804i
351351 0 0
352352 3.31418 + 0.127209i 0.176647 + 0.00678026i
353353 −0.766521 0.766521i −0.0407978 0.0407978i 0.686414 0.727211i 0.259184π-0.259184\pi
−0.727211 + 0.686414i 0.759184π0.759184\pi
354354 0 0
355355 −13.5099 + 4.90832i −0.717029 + 0.260506i
356356 −2.93020 9.01822i −0.155300 0.477965i
357357 0 0
358358 3.69755 23.3454i 0.195421 1.23384i
359359 −2.56417 7.89171i −0.135332 0.416508i 0.860310 0.509772i 0.170270π-0.170270\pi
−0.995641 + 0.0932633i 0.970270π0.970270\pi
360360 0 0
361361 −11.6094 8.43474i −0.611022 0.443934i
362362 13.5211 + 13.5211i 0.710653 + 0.710653i
363363 0 0
364364 0.0359585i 0.00188474i
365365 −7.53431 7.03403i −0.394364 0.368178i
366366 0 0
367367 13.4231 + 6.83943i 0.700683 + 0.357016i 0.767765 0.640732i 0.221369π-0.221369\pi
−0.0670822 + 0.997747i 0.521369π0.521369\pi
368368 6.64655 + 1.05271i 0.346476 + 0.0548763i
369369 0 0
370370 1.41187 2.09056i 0.0733995 0.108683i
371371 0.205047 + 0.0666237i 0.0106455 + 0.00345893i
372372 0 0
373373 −5.33739 + 5.33739i −0.276360 + 0.276360i −0.831654 0.555294i 0.812606π-0.812606\pi
0.555294 + 0.831654i 0.312606π0.312606\pi
374374 8.86593 + 9.57371i 0.458447 + 0.495045i
375375 0 0
376376 −0.910306 + 1.25293i −0.0469454 + 0.0646149i
377377 −4.40537 8.64603i −0.226888 0.445293i
378378 0 0
379379 5.86042 + 8.06617i 0.301029 + 0.414331i 0.932557 0.361022i 0.117572π-0.117572\pi
−0.631528 + 0.775353i 0.717572π0.717572\pi
380380 3.56655 12.4109i 0.182960 0.636665i
381381 0 0
382382 10.6762 5.43982i 0.546244 0.278325i
383383 3.72711 + 23.5321i 0.190447 + 1.20243i 0.878848 + 0.477103i 0.158313π0.158313\pi
−0.688401 + 0.725330i 0.741687π0.741687\pi
384384 0 0
385385 −0.000459977 0.113922i −2.34426e−5 0.00580598i
386386 −16.0399 −0.816410
387387 0 0
388388 −3.96583 + 2.02069i −0.201334 + 0.102585i
389389 4.97947 1.61793i 0.252469 0.0820322i −0.180048 0.983658i 0.557625π-0.557625\pi
0.432517 + 0.901626i 0.357625π0.357625\pi
390390 0 0
391391 15.5617 + 21.4188i 0.786987 + 1.08319i
392392 −3.17783 + 6.23684i −0.160504 + 0.315008i
393393 0 0
394394 −4.90697 + 6.75386i −0.247209 + 0.340255i
395395 −6.53750 8.37763i −0.328938 0.421524i
396396 0 0
397397 1.68624 1.68624i 0.0846300 0.0846300i −0.663525 0.748155i 0.730940π-0.730940\pi
0.748155 + 0.663525i 0.230940π0.230940\pi
398398 8.36222 1.32445i 0.419160 0.0663885i
399399 0 0
400400 4.98822 0.342998i 0.249411 0.0171499i
401401 12.7078 9.23274i 0.634596 0.461061i −0.223393 0.974728i 0.571713π-0.571713\pi
0.857989 + 0.513667i 0.171713π0.171713\pi
402402 0 0
403403 −12.1241 6.17755i −0.603945 0.307725i
404404 −5.36598 + 16.5148i −0.266968 + 0.821642i
405405 0 0
406406 0.0636782i 0.00316030i
407407 3.60031 1.01891i 0.178461 0.0505056i
408408 0 0
409409 1.39836 + 1.01597i 0.0691444 + 0.0502363i 0.621820 0.783160i 0.286393π-0.286393\pi
−0.552676 + 0.833396i 0.686393π0.686393\pi
410410 −4.44100 + 9.50936i −0.219326 + 0.469634i
411411 0 0
412412 0.0534311 0.337350i 0.00263236 0.0166201i
413413 0.00471727 0.0297837i 0.000232122 0.00146556i
414414 0 0
415415 12.6057 26.9921i 0.618788 1.32499i
416416 1.89379 + 1.37592i 0.0928506 + 0.0674599i
417417 0 0
418418 15.9158 10.6554i 0.778466 0.521175i
419419 16.7994i 0.820703i 0.911927 + 0.410351i 0.134594π0.134594\pi
−0.911927 + 0.410351i 0.865406π0.865406\pi
420420 0 0
421421 3.47207 10.6859i 0.169219 0.520801i −0.830104 0.557609i 0.811719π-0.811719\pi
0.999322 + 0.0368077i 0.0117189π0.0117189\pi
422422 −6.23435 3.17656i −0.303483 0.154632i
423423 0 0
424424 11.3547 8.24968i 0.551433 0.400640i
425425 14.8311 + 12.9227i 0.719412 + 0.626842i
426426 0 0
427427 −0.125070 + 0.0198092i −0.00605257 + 0.000958633i
428428 −1.62162 + 1.62162i −0.0783840 + 0.0783840i
429429 0 0
430430 −11.0685 14.1840i −0.533772 0.684015i
431431 22.5280 31.0071i 1.08513 1.49356i 0.231392 0.972861i 0.425672π-0.425672\pi
0.853741 0.520697i 0.174328π-0.174328\pi
432432 0 0
433433 8.91179 17.4904i 0.428273 0.840533i −0.571528 0.820583i 0.693649π-0.693649\pi
0.999801 0.0199507i 0.00635091π-0.00635091\pi
434434 0.0524859 + 0.0722407i 0.00251940 + 0.00346766i
435435 0 0
436436 2.30958 0.750427i 0.110609 0.0359389i
437437 34.6263 17.6430i 1.65640 0.843977i
438438 0 0
439439 1.05214 0.0502158 0.0251079 0.999685i 0.492007π-0.492007\pi
0.0251079 + 0.999685i 0.492007π0.492007\pi
440440 5.98218 + 4.38332i 0.285189 + 0.208967i
441441 0 0
442442 1.44068 + 9.09608i 0.0685260 + 0.432656i
443443 0.280755 0.143052i 0.0133391 0.00679659i −0.447308 0.894380i 0.647617π-0.647617\pi
0.460647 + 0.887583i 0.347617π0.347617\pi
444444 0 0
445445 5.85619 20.3783i 0.277610 0.966026i
446446 10.9911 + 15.1280i 0.520446 + 0.716332i
447447 0 0
448448 −0.00697389 0.0136870i −0.000329485 0.000646652i
449449 19.7505 27.1842i 0.932084 1.28290i −0.0269576 0.999637i 0.508582π-0.508582\pi
0.959041 0.283266i 0.0914181π-0.0914181\pi
450450 0 0
451451 −14.1311 + 6.53007i −0.665410 + 0.307489i
452452 7.70080 7.70080i 0.362215 0.362215i
453453 0 0
454454 −9.63541 3.13074i −0.452212 0.146933i
455455 −0.0450010 + 0.0666333i −0.00210968 + 0.00312382i
456456 0 0
457457 29.5629 + 4.68231i 1.38290 + 0.219029i 0.803154 0.595771i 0.203153π-0.203153\pi
0.579742 + 0.814800i 0.303153π0.303153\pi
458458 −9.67144 4.92785i −0.451917 0.230263i
459459 0 0
460460 10.9990 + 10.2687i 0.512832 + 0.478780i
461461 27.6150i 1.28616i −0.765800 0.643079i 0.777657π-0.777657\pi
0.765800 0.643079i 0.222343π-0.222343\pi
462462 0 0
463463 −26.6620 26.6620i −1.23909 1.23909i −0.960373 0.278717i 0.910091π-0.910091\pi
−0.278717 0.960373i 0.589909π-0.589909\pi
464464 3.35367 + 2.43658i 0.155690 + 0.113115i
465465 0 0
466466 −1.46840 4.51926i −0.0680221 0.209351i
467467 −4.66728 + 29.4680i −0.215976 + 1.36362i 0.606620 + 0.794992i 0.292525π0.292525\pi
−0.822596 + 0.568626i 0.807475π0.807475\pi
468468 0 0
469469 0.0246802 + 0.0759577i 0.00113962 + 0.00350740i
470470 −3.25485 + 1.18253i −0.150135 + 0.0545461i
471471 0 0
472472 −1.38808 1.38808i −0.0638916 0.0638916i
473473 1.02354 26.6663i 0.0470623 1.22612i
474474 0 0
475475 22.1408 18.5347i 1.01589 0.850429i
476476 0.0186755 0.0574772i 0.000855989 0.00263446i
477477 0 0
478478 13.3336 + 2.11183i 0.609864 + 0.0965929i
479479 5.27658 3.83366i 0.241093 0.175165i −0.460677 0.887568i 0.652393π-0.652393\pi
0.701770 + 0.712403i 0.252393π0.252393\pi
480480 0 0
481481 2.51162 + 0.816075i 0.114520 + 0.0372098i
482482 −21.2789 + 3.37025i −0.969227 + 0.153510i
483483 0 0
484484 2.58727 + 10.6914i 0.117603 + 0.485973i
485485 −9.87774 1.21865i −0.448525 0.0553360i
486486 0 0
487487 3.88945 + 7.63347i 0.176248 + 0.345906i 0.962183 0.272403i 0.0878183π-0.0878183\pi
−0.785936 + 0.618308i 0.787818π0.787818\pi
488488 −3.74242 + 7.34491i −0.169411 + 0.332488i
489489 0 0
490490 −13.6939 + 7.58028i −0.618627 + 0.342442i
491491 24.6223 8.00027i 1.11119 0.361047i 0.304790 0.952419i 0.401414π-0.401414\pi
0.806399 + 0.591372i 0.201414π0.201414\pi
492492 0 0
493493 2.55126 + 16.1081i 0.114903 + 0.725470i
494494 13.5183 0.608217
495495 0 0
496496 5.81294 0.261009
497497 0.0154472 + 0.0975297i 0.000692901 + 0.00437480i
498498 0 0
499499 15.9071 5.16853i 0.712099 0.231375i 0.0695049 0.997582i 0.477858π-0.477858\pi
0.642594 + 0.766207i 0.277858π0.277858\pi
500500 9.67272 + 5.60700i 0.432577 + 0.250753i
501501 0 0
502502 8.89258 17.4527i 0.396895 0.778951i
503503 −6.24553 12.2575i −0.278475 0.546537i 0.708829 0.705380i 0.249224π-0.249224\pi
−0.987304 + 0.158843i 0.949224π0.949224\pi
504504 0 0
505505 −30.6112 + 23.8875i −1.36218 + 1.06298i
506506 2.64338 + 22.1618i 0.117512 + 0.985213i
507507 0 0
508508 17.3079 2.74131i 0.767916 0.121626i
509509 −32.6519 10.6092i −1.44727 0.470246i −0.523113 0.852263i 0.675229π-0.675229\pi
−0.924155 + 0.382017i 0.875229π0.875229\pi
510510 0 0
511511 −0.0572865 + 0.0416211i −0.00253421 + 0.00184121i
512512 −0.987688 0.156434i −0.0436501 0.00691349i
513513 0 0
514514 −6.10397 + 18.7861i −0.269234 + 0.828618i
515515 0.521194 0.558263i 0.0229666 0.0246000i
516516 0 0
517517 −4.82060 1.77346i −0.212010 0.0779965i
518518 −0.0122543 0.0122543i −0.000538422 0.000538422i
519519 0 0
520520 1.78738 + 4.91967i 0.0783819 + 0.215742i
521521 −1.49330 4.59591i −0.0654227 0.201351i 0.913002 0.407956i 0.133758π-0.133758\pi
−0.978424 + 0.206606i 0.933758π0.933758\pi
522522 0 0
523523 −2.62342 + 16.5636i −0.114714 + 0.724276i 0.861547 + 0.507678i 0.169496π0.169496\pi
−0.976261 + 0.216598i 0.930504π0.930504\pi
524524 −1.12875 3.47393i −0.0493096 0.151759i
525525 0 0
526526 22.9832 + 16.6982i 1.00211 + 0.728078i
527527 16.1712 + 16.1712i 0.704427 + 0.704427i
528528 0 0
529529 22.2849i 0.968907i
530530 31.3651 1.07709i 1.36241 0.0467856i
531531 0 0
532532 −0.0790419 0.0402739i −0.00342690 0.00174609i
533533 −10.8518 1.71876i −0.470044 0.0744476i
534534 0 0
535535 −5.03437 + 0.975553i −0.217655 + 0.0421768i
536536 4.94474 + 1.60664i 0.213580 + 0.0693964i
537537 0 0
538538 6.62361 6.62361i 0.285564 0.285564i
539539 −22.7736 4.50852i −0.980928 0.194196i
540540 0 0
541541 6.42200 8.83913i 0.276103 0.380024i −0.648335 0.761355i 0.724534π-0.724534\pi
0.924438 + 0.381331i 0.124534π0.124534\pi
542542 −2.79422 5.48397i −0.120022 0.235556i
543543 0 0
544544 −2.31249 3.18287i −0.0991471 0.136464i
545545 5.21892 + 1.49978i 0.223554 + 0.0642433i
546546 0 0
547547 31.3306 15.9637i 1.33960 0.682559i 0.370407 0.928870i 0.379218π-0.379218\pi
0.969191 + 0.246310i 0.0792182π0.0792182\pi
548548 −2.63360 16.6279i −0.112502 0.710309i
549549 0 0
550550 5.59975 + 15.6091i 0.238774 + 0.665573i
551551 23.9392 1.01985
552552 0 0
553553 −0.0650454 + 0.0331423i −0.00276601 + 0.00140935i
554554 −28.3464 + 9.21031i −1.20432 + 0.391308i
555555 0 0
556556 −13.0196 17.9199i −0.552152 0.759972i
557557 1.38133 2.71100i 0.0585286 0.114869i −0.859889 0.510481i 0.829467π-0.829467\pi
0.918418 + 0.395612i 0.129467π0.129467\pi
558558 0 0
559559 11.0708 15.2376i 0.468244 0.644483i
560560 0.00420585 0.0340905i 0.000177730 0.00144059i
561561 0 0
562562 −4.04138 + 4.04138i −0.170475 + 0.170475i
563563 −36.3351 + 5.75492i −1.53134 + 0.242541i −0.864490 0.502649i 0.832359π-0.832359\pi
−0.666852 + 0.745190i 0.732359π0.732359\pi
564564 0 0
565565 23.9073 4.63273i 1.00579 0.194900i
566566 −3.51747 + 2.55559i −0.147850 + 0.107419i
567567 0 0
568568 5.72756 + 2.91834i 0.240323 + 0.122451i
569569 5.11991 15.7575i 0.214638 0.660587i −0.784541 0.620077i 0.787102π-0.787102\pi
0.999179 0.0405107i 0.0128985π-0.0128985\pi
570570 0 0
571571 10.4437i 0.437057i 0.975831 + 0.218529i 0.0701257π0.0701257\pi
−0.975831 + 0.218529i 0.929874π0.929874\pi
572572 −2.68056 + 7.28629i −0.112080 + 0.304655i
573573 0 0
574574 0.0583303 + 0.0423795i 0.00243466 + 0.00176888i
575575 7.53091 + 32.7934i 0.314061 + 1.36758i
576576 0 0
577577 −0.310767 + 1.96210i −0.0129374 + 0.0816834i −0.993312 0.115459i 0.963166π-0.963166\pi
0.980375 + 0.197142i 0.0631661π0.0631661\pi
578578 −0.238056 + 1.50302i −0.00990181 + 0.0625176i
579579 0 0
580580 3.16524 + 8.71214i 0.131429 + 0.361752i
581581 −0.165569 0.120293i −0.00686896 0.00499059i
582582 0 0
583583 36.5822 + 28.7854i 1.51508 + 1.19217i
584584 4.60963i 0.190748i
585585 0 0
586586 −4.20067 + 12.9283i −0.173528 + 0.534065i
587587 −12.4878 6.36284i −0.515426 0.262623i 0.176873 0.984234i 0.443402π-0.443402\pi
−0.692299 + 0.721611i 0.743402π0.743402\pi
588588 0 0
589589 27.1582 19.7316i 1.11904 0.813027i
590590 −0.835057 4.30933i −0.0343787 0.177412i
591591 0 0
592592 −1.11428 + 0.176484i −0.0457966 + 0.00725347i
593593 24.8101 24.8101i 1.01883 1.01883i 0.0190108 0.999819i 0.493948π-0.493948\pi
0.999819 0.0190108i 0.00605170π-0.00605170\pi
594594 0 0
595595 0.106538 0.0831369i 0.00436762 0.00340828i
596596 8.30508 11.4310i 0.340189 0.468230i
597597 0 0
598598 −7.15150 + 14.0356i −0.292446 + 0.573958i
599599 −6.95362 9.57083i −0.284117 0.391054i 0.642975 0.765887i 0.277700π-0.277700\pi
−0.927092 + 0.374833i 0.877700π0.877700\pi
600600 0 0
601601 −18.9484 + 6.15671i −0.772922 + 0.251138i −0.668815 0.743429i 0.733198π-0.733198\pi
−0.104107 + 0.994566i 0.533198π0.533198\pi
602602 −0.110127 + 0.0561127i −0.00448846 + 0.00228698i
603603 0 0
604604 −3.31087 −0.134717
605605 −8.58559 + 23.0497i −0.349054 + 0.937103i
606606 0 0
607607 −3.67280 23.1891i −0.149074 0.941218i −0.942901 0.333074i 0.891914π-0.891914\pi
0.793827 0.608144i 0.208086π-0.208086\pi
608608 −5.14552 + 2.62177i −0.208678 + 0.106327i
609609 0 0
610610 −16.1268 + 8.92703i −0.652957 + 0.361445i
611611 −2.13089 2.93292i −0.0862065 0.118653i
612612 0 0
613613 −11.3849 22.3442i −0.459833 0.902473i −0.998212 0.0597703i 0.980963π-0.980963\pi
0.538379 0.842703i 0.319037π-0.319037\pi
614614 14.0329 19.3146i 0.566322 0.779475i
615615 0 0
616616 0.0373807 0.0346172i 0.00150611 0.00139477i
617617 −25.6695 + 25.6695i −1.03341 + 1.03341i −0.0339923 + 0.999422i 0.510822π0.510822\pi
−0.999422 + 0.0339923i 0.989178π0.989178\pi
618618 0 0
619619 −15.3896 5.00040i −0.618562 0.200983i −0.0170601 0.999854i 0.505431π-0.505431\pi
−0.601502 + 0.798872i 0.705431π0.705431\pi
620620 10.7717 + 7.27471i 0.432603 + 0.292159i
621621 0 0
622622 28.6415 + 4.53636i 1.14842 + 0.181892i
623623 −0.129785 0.0661287i −0.00519972 0.00264939i
624624 0 0
625625 10.9071 + 22.4952i 0.436285 + 0.899808i
626626 17.3031i 0.691573i
627627 0 0
628628 −9.10015 9.10015i −0.363136 0.363136i
629629 −3.59081 2.60888i −0.143175 0.104023i
630630 0 0
631631 −4.71355 14.5068i −0.187644 0.577508i 0.812340 0.583184i 0.198193π-0.198193\pi
−0.999984 + 0.00567610i 0.998193π0.998193\pi
632632 −0.743430 + 4.69383i −0.0295720 + 0.186711i
633633 0 0
634634 −6.41152 19.7326i −0.254634 0.783683i
635635 35.5033 + 16.5805i 1.40891 + 0.657978i
636636 0 0
637637 −11.5862 11.5862i −0.459063 0.459063i
638638 −4.74694 + 12.9031i −0.187933 + 0.510840i
639639 0 0
640640 −1.63447 1.52594i −0.0646082 0.0603182i
641641 −3.02959 + 9.32412i −0.119662 + 0.368280i −0.992891 0.119029i 0.962022π-0.962022\pi
0.873229 + 0.487310i 0.162022π0.162022\pi
642642 0 0
643643 4.86380 + 0.770351i 0.191810 + 0.0303797i 0.251600 0.967831i 0.419043π-0.419043\pi
−0.0597904 + 0.998211i 0.519043π0.519043\pi
644644 0.0836301 0.0607608i 0.00329549 0.00239431i
645645 0 0
646646 −21.6080 7.02088i −0.850157 0.276233i
647647 8.21829 1.30165i 0.323094 0.0511731i 0.00721944 0.999974i 0.497702π-0.497702\pi
0.315875 + 0.948801i 0.397702π0.397702\pi
648648 0 0
649649 3.17611 5.68342i 0.124673 0.223094i
650650 −2.84468 + 11.3533i −0.111578 + 0.445313i
651651 0 0
652652 0.763736 + 1.49892i 0.0299102 + 0.0587021i
653653 −10.2557 + 20.1279i −0.401335 + 0.787665i −0.999910 0.0134022i 0.995734π-0.995734\pi
0.598575 + 0.801067i 0.295734π0.295734\pi
654654 0 0
655655 2.25588 7.84999i 0.0881444 0.306725i
656656 4.46390 1.45041i 0.174286 0.0566290i
657657 0 0
658658 0.00372160 + 0.0234972i 0.000145083 + 0.000916018i
659659 25.7362 1.00254 0.501270 0.865291i 0.332866π-0.332866\pi
0.501270 + 0.865291i 0.332866π0.332866\pi
660660 0 0
661661 −14.3297 −0.557360 −0.278680 0.960384i 0.589897π-0.589897\pi
−0.278680 + 0.960384i 0.589897π0.589897\pi
662662 −4.33692 27.3822i −0.168559 1.06424i
663663 0 0
664664 −12.6707 + 4.11695i −0.491717 + 0.159769i
665665 −0.0960679 0.173548i −0.00372535 0.00672991i
666666 0 0
667667 −12.6644 + 24.8553i −0.490369 + 0.962403i
668668 7.38860 + 14.5009i 0.285874 + 0.561058i
669669 0 0
670670 7.15223 + 9.16539i 0.276315 + 0.354090i
671671 −26.8197 5.30953i −1.03536 0.204972i
672672 0 0
673673 −36.8427 + 5.83531i −1.42018 + 0.224935i −0.818824 0.574045i 0.805373π-0.805373\pi
−0.601358 + 0.798980i 0.705373π0.705373\pi
674674 −6.68524 2.17217i −0.257506 0.0836688i
675675 0 0
676676 6.08415 4.42039i 0.234006 0.170015i
677677 10.9011 + 1.72656i 0.418963 + 0.0663572i 0.362357 0.932039i 0.381972π-0.381972\pi
0.0566060 + 0.998397i 0.481972π0.481972\pi
678678 0 0
679679 −0.0211283 + 0.0650261i −0.000810828 + 0.00249547i
680680 −0.301921 8.79204i −0.0115781 0.337160i
681681 0 0
682682 5.24999 + 18.5507i 0.201033 + 0.710345i
683683 4.64732 + 4.64732i 0.177825 + 0.177825i 0.790407 0.612582i 0.209869π-0.209869\pi
−0.612582 + 0.790407i 0.709869π0.709869\pi
684684 0 0
685685 15.9291 34.1084i 0.608619 1.30321i
686686 0.0664556 + 0.204529i 0.00253729 + 0.00780896i
687687 0 0
688688 −1.25869 + 7.94705i −0.0479871 + 0.302978i
689689 10.1525 + 31.2463i 0.386780 + 1.19039i
690690 0 0
691691 −1.72951 1.25656i −0.0657935 0.0478018i 0.554402 0.832249i 0.312947π-0.312947\pi
−0.620196 + 0.784447i 0.712947π0.712947\pi
692692 10.6979 + 10.6979i 0.406674 + 0.406674i
693693 0 0
694694 21.7088i 0.824055i
695695 −1.69985 49.5002i −0.0644789 1.87765i
696696 0 0
697697 16.4532 + 8.38331i 0.623209 + 0.317541i
698698 11.7363 + 1.85885i 0.444226 + 0.0703585i
699699 0 0
700700 0.0504568 0.0579082i 0.00190709 0.00218872i
701701 −16.0121 5.20265i −0.604769 0.196501i −0.00940286 0.999956i 0.502993π-0.502993\pi
−0.595366 + 0.803454i 0.702993π0.702993\pi
702702 0 0
703703 −4.60688 + 4.60688i −0.173752 + 0.173752i
704704 −0.392810 3.29328i −0.0148046 0.124120i
705705 0 0
706706 −0.637174 + 0.876995i −0.0239804 + 0.0330061i
707707 0.121099 + 0.237671i 0.00455441 + 0.00893854i
708708 0 0
709709 10.9910 + 15.1277i 0.412774 + 0.568134i 0.963892 0.266293i 0.0857988π-0.0857988\pi
−0.551118 + 0.834427i 0.685799π0.685799\pi
710710 6.96130 + 12.5757i 0.261253 + 0.471958i
711711 0 0
712712 −8.44881 + 4.30488i −0.316632 + 0.161332i
713713 6.11934 + 38.6360i 0.229171 + 1.44693i
714714 0 0
715715 −14.0858 + 10.1473i −0.526779 + 0.379487i
716716 −23.6364 −0.883333
717717 0 0
718718 −7.39342 + 3.76714i −0.275920 + 0.140588i
719719 −16.7305 + 5.43605i −0.623941 + 0.202731i −0.603889 0.797068i 0.706383π-0.706383\pi
−0.0200516 + 0.999799i 0.506383π0.506383\pi
720720 0 0
721721 −0.00308396 0.00424470i −0.000114853 0.000158081i
722722 −6.51478 + 12.7860i −0.242455 + 0.475845i
723723 0 0
724724 11.2395 15.4698i 0.417712 0.574931i
725725 −5.03759 + 20.1053i −0.187091 + 0.746692i
726726 0 0
727727 −3.51865 + 3.51865i −0.130500 + 0.130500i −0.769340 0.638840i 0.779415π-0.779415\pi
0.638840 + 0.769340i 0.279415π0.279415\pi
728728 0.0355158 0.00562515i 0.00131630 0.000208482i
729729 0 0
730730 −5.76881 + 8.54192i −0.213513 + 0.316151i
731731 −25.6097 + 18.6065i −0.947209 + 0.688187i
732732 0 0
733733 −8.32881 4.24374i −0.307631 0.156746i 0.293359 0.956002i 0.405227π-0.405227\pi
−0.600990 + 0.799256i 0.705227π0.705227\pi
734734 4.65539 14.3278i 0.171833 0.528849i
735735 0 0
736736 6.72940i 0.248049i
737737 −0.661386 + 17.2311i −0.0243625 + 0.634717i
738738 0 0
739739 −22.0128 15.9932i −0.809754 0.588321i 0.104005 0.994577i 0.466834π-0.466834\pi
−0.913759 + 0.406256i 0.866834π0.866834\pi
740740 −2.28569 1.06745i −0.0840236 0.0392402i
741741 0 0
742742 0.0337271 0.212945i 0.00123816 0.00781744i
743743 3.73190 23.5623i 0.136910 0.864417i −0.819646 0.572870i 0.805830π-0.805830\pi
0.956557 0.291547i 0.0941700π-0.0941700\pi
744744 0 0
745745 29.6953 10.7887i 1.08795 0.395267i
746746 6.10663 + 4.43673i 0.223580 + 0.162440i
747747 0 0
748748 8.06890 10.2544i 0.295028 0.374939i
749749 0.0352284i 0.00128722i
750750 0 0
751751 5.95219 18.3190i 0.217199 0.668469i −0.781792 0.623540i 0.785694π-0.785694\pi
0.998990 0.0449289i 0.0143061π-0.0143061\pi
752752 1.37991 + 0.703097i 0.0503200 + 0.0256393i
753753 0 0
754754 −7.85043 + 5.70367i −0.285896 + 0.207715i
755755 −6.13524 4.14345i −0.223284 0.150796i
756756 0 0
757757 −10.6845 + 1.69226i −0.388336 + 0.0615063i −0.347550 0.937662i 0.612986π-0.612986\pi
−0.0407860 + 0.999168i 0.512986π0.512986\pi
758758 7.05009 7.05009i 0.256071 0.256071i
759759 0 0
760760 −12.8160 1.58115i −0.464886 0.0573544i
761761 −13.9786 + 19.2399i −0.506723 + 0.697444i −0.983362 0.181655i 0.941855π-0.941855\pi
0.476640 + 0.879099i 0.341855π0.341855\pi
762762 0 0
763763 0.0169356 0.0332380i 0.000613111 0.00120330i
764764 −7.04298 9.69383i −0.254806 0.350710i
765765 0 0
766766 22.6593 7.36246i 0.818714 0.266016i
767767 4.09434 2.08617i 0.147838 0.0753273i
768768 0 0
769769 5.84739 0.210862 0.105431 0.994427i 0.466378π-0.466378\pi
0.105431 + 0.994427i 0.466378π0.466378\pi
770770 0.112591 0.0173670i 0.00405750 0.000625862i
771771 0 0
772772 2.50920 + 15.8424i 0.0903080 + 0.570182i
773773 8.04258 4.09790i 0.289272 0.147391i −0.303333 0.952885i 0.598100π-0.598100\pi
0.592605 + 0.805493i 0.298100π0.298100\pi
774774 0 0
775775 10.8566 + 26.9609i 0.389979 + 0.968465i
776776 2.61620 + 3.60090i 0.0939163 + 0.129265i
777777 0 0
778778 −2.37697 4.66507i −0.0852185 0.167251i
779779 15.9322 21.9288i 0.570829 0.785679i
780780 0 0
781781 −4.14037 + 20.9140i −0.148154 + 0.748361i
782782 18.7207 18.7207i 0.669451 0.669451i
783783 0 0
784784 6.65717 + 2.16305i 0.237756 + 0.0772516i
785785 −5.47457 28.2517i −0.195396 1.00835i
786786 0 0
787787 −46.5577 7.37402i −1.65960 0.262855i −0.744957 0.667112i 0.767530π-0.767530\pi
−0.914646 + 0.404257i 0.867530π0.867530\pi
788788 7.43833 + 3.79002i 0.264979 + 0.135014i
789789 0 0
790790 −7.25180 + 7.76757i −0.258007 + 0.276358i
791791 0.167293i 0.00594827i
792792 0 0
793793 −13.6447 13.6447i −0.484537 0.484537i
794794 −1.92927 1.40169i −0.0684671 0.0497443i
795795 0 0
796796 −2.61628 8.05208i −0.0927316 0.285398i
797797 −0.195418 + 1.23382i −0.00692208 + 0.0437043i −0.990908 0.134544i 0.957043π-0.957043\pi
0.983986 + 0.178248i 0.0570430π0.0570430\pi
798798 0 0
799799 1.88283 + 5.79476i 0.0666098 + 0.205004i
800800 −1.11910 4.87315i −0.0395663 0.172292i
801801 0 0
802802 −11.1070 11.1070i −0.392202 0.392202i
803803 −14.7107 + 4.16322i −0.519128 + 0.146917i
804804 0 0
805805 0.231012 0.00793300i 0.00814209 0.000279601i
806806 −4.20486 + 12.9412i −0.148110 + 0.455835i
807807 0 0
808808 17.1509 + 2.71643i 0.603366 + 0.0955638i
809809 16.9646 12.3255i 0.596442 0.433341i −0.248172 0.968716i 0.579830π-0.579830\pi
0.844614 + 0.535375i 0.179830π0.179830\pi
810810 0 0
811811 2.18611 + 0.710312i 0.0767649 + 0.0249424i 0.347148 0.937810i 0.387150π-0.387150\pi
−0.270383 + 0.962753i 0.587150π0.587150\pi
812812 0.0628942 0.00996146i 0.00220715 0.000349579i
813813 0 0
814814 −1.56958 3.39659i −0.0550138 0.119050i
815815 −0.460598 + 3.73337i −0.0161340 + 0.130774i
816816 0 0
817817 21.0951 + 41.4014i 0.738023 + 1.44845i
818818 0.784707 1.54007i 0.0274366 0.0538474i
819819 0 0
820820 10.0870 + 2.89874i 0.352254 + 0.101228i
821821 −28.7277 + 9.33418i −1.00260 + 0.325765i −0.763905 0.645329i 0.776720π-0.776720\pi
−0.238697 + 0.971094i 0.576720π0.576720\pi
822822 0 0
823823 0.511401 + 3.22886i 0.0178263 + 0.112551i 0.994997 0.0999048i 0.0318538π-0.0318538\pi
−0.977171 + 0.212456i 0.931854π0.931854\pi
824824 −0.341556 −0.0118987
825825 0 0
826826 −0.0301549 −0.00104922
827827 1.84276 + 11.6347i 0.0640791 + 0.404579i 0.998790 + 0.0491714i 0.0156580π0.0156580\pi
−0.934711 + 0.355408i 0.884342π0.884342\pi
828828 0 0
829829 −19.4970 + 6.33497i −0.677160 + 0.220023i −0.627351 0.778736i 0.715861π-0.715861\pi
−0.0498083 + 0.998759i 0.515861π0.515861\pi
830830 −28.6317 8.22798i −0.993821 0.285597i
831831 0 0
832832 1.06272 2.08571i 0.0368433 0.0723091i
833833 12.5023 + 24.5372i 0.433180 + 0.850164i
834834 0 0
835835 −4.45596 + 36.1177i −0.154205 + 1.24990i
836836 −13.0140 14.0529i −0.450100 0.486031i
837837 0 0
838838 16.5925 2.62800i 0.573180 0.0907828i
839839 15.2019 + 4.93940i 0.524828 + 0.170527i 0.559435 0.828874i 0.311018π-0.311018\pi
−0.0346074 + 0.999401i 0.511018π0.511018\pi
840840 0 0
841841 9.55933 6.94526i 0.329632 0.239492i
842842 −11.0975 1.75768i −0.382446 0.0605736i
843843 0 0
844844 −2.16218 + 6.65452i −0.0744254 + 0.229058i
845845 16.8063 0.577131i 0.578153 0.0198539i
846846 0 0
847847 0.144234 + 0.0880279i 0.00495594 + 0.00302467i
848848 −9.92438 9.92438i −0.340804 0.340804i
849849 0 0
850850 10.4435 16.6700i 0.358209 0.571777i
851851 −2.34603 7.22033i −0.0804208 0.247510i
852852 0 0
853853 −6.04382 + 38.1592i −0.206936 + 1.30655i 0.637317 + 0.770601i 0.280044π0.280044\pi
−0.844254 + 0.535944i 0.819956π0.819956\pi
854854 0.0391306 + 0.120432i 0.00133902 + 0.00412108i
855855 0 0
856856 1.85533 + 1.34798i 0.0634140 + 0.0460730i
857857 −26.7350 26.7350i −0.913251 0.913251i 0.0832758 0.996527i 0.473462π-0.473462\pi
−0.996527 + 0.0832758i 0.973462π0.973462\pi
858858 0 0
859859 35.7867i 1.22103i 0.792005 + 0.610514i 0.209037π0.209037\pi
−0.792005 + 0.610514i 0.790963π0.790963\pi
860860 −12.2779 + 13.1511i −0.418673 + 0.448450i
861861 0 0
862862 −34.1495 17.4000i −1.16314 0.592647i
863863 38.2576 + 6.05941i 1.30230 + 0.206265i 0.768776 0.639518i 0.220866π-0.220866\pi
0.533528 + 0.845782i 0.320866π0.320866\pi
864864 0 0
865865 6.43578 + 33.2120i 0.218823 + 1.12924i
866866 −18.6691 6.06597i −0.634403 0.206130i
867867 0 0
868868 0.0631407 0.0631407i 0.00214313 0.00214313i
869869 −15.6508 + 1.86677i −0.530917 + 0.0633257i
870870 0 0
871871 −7.15368 + 9.84619i −0.242393 + 0.333626i
872872 −1.10249 2.16375i −0.0373349 0.0732738i
873873 0 0
874874 −22.8425 31.4400i −0.772659 1.06347i
875875 0.165970 0.0441622i 0.00561080 0.00149295i
876876 0 0
877877 −9.96725 + 5.07857i −0.336570 + 0.171491i −0.614105 0.789225i 0.710483π-0.710483\pi
0.277534 + 0.960716i 0.410483π0.410483\pi
878878 −0.164590 1.03918i −0.00555466 0.0350707i
879879 0 0
880880 3.39354 6.59423i 0.114396 0.222292i
881881 2.54074 0.0855998 0.0427999 0.999084i 0.486372π-0.486372\pi
0.0427999 + 0.999084i 0.486372π0.486372\pi
882882 0 0
883883 13.9170 7.09109i 0.468346 0.238634i −0.203858 0.979001i 0.565348π-0.565348\pi
0.672203 + 0.740366i 0.265348π0.265348\pi
884884 8.75872 2.84588i 0.294588 0.0957173i
885885 0 0
886886 −0.185210 0.254920i −0.00622226 0.00856421i
887887 1.38930 2.72665i 0.0466480 0.0915519i −0.866506 0.499167i 0.833639π-0.833639\pi
0.913154 + 0.407615i 0.133639π0.133639\pi
888888 0 0
889889 0.158224 0.217777i 0.00530667 0.00730400i
890890 −21.0436 2.59621i −0.705382 0.0870252i
891891 0 0
892892 13.2224 13.2224i 0.442718 0.442718i
893893 8.83358 1.39910i 0.295604 0.0468191i
894894 0 0
895895 −43.7996 29.5802i −1.46406 0.988756i
896896 −0.0124276 + 0.00902916i −0.000415176 + 0.000301643i
897897 0 0
898898 −29.9392 15.2548i −0.999084 0.509059i
899899 −7.44630 + 22.9173i −0.248348 + 0.764336i
900900 0 0
901901 55.2178i 1.83957i
902902 8.66027 + 12.9356i 0.288356 + 0.430710i
903903 0 0
904904 −8.81066 6.40132i −0.293038 0.212905i
905905 40.1874 14.6006i 1.33587 0.485341i
906906 0 0
907907 −8.26589 + 52.1888i −0.274464 + 1.73290i 0.336892 + 0.941543i 0.390624π0.390624\pi
−0.611356 + 0.791356i 0.709376π0.709376\pi
908908 −1.58488 + 10.0065i −0.0525961 + 0.332079i
909909 0 0
910910 0.0728526 + 0.0340232i 0.00241504 + 0.00112786i
911911 −9.97151 7.24473i −0.330371 0.240029i 0.410217 0.911988i 0.365453π-0.365453\pi
−0.740588 + 0.671959i 0.765453π0.765453\pi
912912 0 0
913913 −24.5820 36.7175i −0.813544 1.21517i
914914 29.9314i 0.990044i
915915 0 0
916916 −3.35423 + 10.3233i −0.110827 + 0.341090i
917917 −0.0499947 0.0254736i −0.00165097 0.000841212i
918918 0 0
919919 0.0894366 0.0649795i 0.00295024 0.00214348i −0.586309 0.810087i 0.699420π-0.699420\pi
0.589259 + 0.807944i 0.299420π0.299420\pi
920920 8.42163 12.4700i 0.277653 0.411123i
921921 0 0
922922 −27.2750 + 4.31993i −0.898254 + 0.142269i
923923 −10.6401 + 10.6401i −0.350224 + 0.350224i
924924 0 0
925925 −2.89964 4.83851i −0.0953396 0.159089i
926926 −22.1629 + 30.5047i −0.728319 + 1.00245i
927927 0 0
928928 1.88195 3.69354i 0.0617782 0.121247i
929929 6.25774 + 8.61305i 0.205310 + 0.282585i 0.899238 0.437459i 0.144122π-0.144122\pi
−0.693928 + 0.720044i 0.744122π0.744122\pi
930930 0 0
931931 38.4448 12.4915i 1.25998 0.409392i
932932 −4.23391 + 2.15729i −0.138686 + 0.0706643i
933933 0 0
934934 29.8354 0.976243
935935 27.7852 8.90411i 0.908675 0.291195i
936936 0 0
937937 4.09535 + 25.8570i 0.133789 + 0.844712i 0.959724 + 0.280946i 0.0906482π0.0906482\pi
−0.825934 + 0.563766i 0.809352π0.809352\pi
938938 0.0711617 0.0362587i 0.00232351 0.00118389i
939939 0 0
940940 1.67714 + 3.02979i 0.0547024 + 0.0988208i
941941 19.4803 + 26.8123i 0.635038 + 0.874055i 0.998339 0.0576167i 0.0183501π-0.0183501\pi
−0.363300 + 0.931672i 0.618350π0.618350\pi
942942 0 0
943943 14.3394 + 28.1427i 0.466956 + 0.916452i
944944 −1.15385 + 1.58813i −0.0375545 + 0.0516894i
945945 0 0
946946 −26.4981 + 3.16059i −0.861528 + 0.102760i
947947 −31.2894 + 31.2894i −1.01677 + 1.01677i −0.0169134 + 0.999857i 0.505384π0.505384\pi
−0.999857 + 0.0169134i 0.994616π0.994616\pi
948948 0 0
949949 −10.2623 3.33443i −0.333129 0.108240i
950950 −21.7701 18.9688i −0.706314 0.615429i
951951 0 0
952952 −0.0596910 0.00945413i −0.00193460 0.000306410i
953953 17.3932 + 8.86229i 0.563421 + 0.287078i 0.712412 0.701761i 0.247603π-0.247603\pi
−0.148991 + 0.988839i 0.547603π0.547603\pi
954954 0 0
955955 −0.919538 26.7773i −0.0297556 0.866493i
956956 13.4998i 0.436614i
957957 0 0
958958 −4.61190 4.61190i −0.149004 0.149004i
959959 −0.209220 0.152007i −0.00675608 0.00490858i
960960 0 0
961961 0.862234 + 2.65368i 0.0278140 + 0.0856027i
962962 0.413124 2.60836i 0.0133196 0.0840969i
963963 0 0
964964 6.65750 + 20.4897i 0.214424 + 0.659929i
965965 −15.1766 + 32.4972i −0.488553 + 1.04612i
966966 0 0
967967 −25.7251 25.7251i −0.827262 0.827262i 0.159875 0.987137i 0.448891π-0.448891\pi
−0.987137 + 0.159875i 0.948891π0.948891\pi
968968 10.1550 4.22792i 0.326395 0.135890i
969969 0 0
970970 0.341574 + 9.94677i 0.0109673 + 0.319372i
971971 12.5009 38.4738i 0.401173 1.23468i −0.522876 0.852409i 0.675141π-0.675141\pi
0.924049 0.382274i 0.124859π-0.124859\pi
972972 0 0
973973 −0.336067 0.0532278i −0.0107738 0.00170640i
974974 6.93105 5.03570i 0.222085 0.161354i
975975 0 0
976976 7.83992 + 2.54735i 0.250950 + 0.0815385i
977977 −37.1310 + 5.88097i −1.18792 + 0.188149i −0.718949 0.695063i 0.755377π-0.755377\pi
−0.468975 + 0.883211i 0.655377π0.655377\pi
978978 0 0
979979 −21.3687 23.0746i −0.682947 0.737467i
980980 9.62915 + 12.3395i 0.307592 + 0.394171i
981981 0 0
982982 −11.7536 23.0676i −0.375071 0.736118i
983983 −6.95538 + 13.6507i −0.221842 + 0.435390i −0.974924 0.222537i 0.928566π-0.928566\pi
0.753082 + 0.657927i 0.228566π0.228566\pi
984984 0 0
985985 9.04058 + 16.3320i 0.288057 + 0.520379i
986986 15.5106 5.03971i 0.493959 0.160497i
987987 0 0
988988 −2.11473 13.3519i −0.0672784 0.424779i
989989 −54.1455 −1.72173
990990 0 0
991991 −42.6744 −1.35560 −0.677798 0.735248i 0.737066π-0.737066\pi
−0.677798 + 0.735248i 0.737066π0.737066\pi
992992 −0.909344 5.74137i −0.0288717 0.182289i
993993 0 0
994994 0.0939125 0.0305140i 0.00297872 0.000967846i
995995 5.22880 18.1952i 0.165764 0.576826i
996996 0 0
997997 7.94283 15.5887i 0.251552 0.493698i −0.730354 0.683069i 0.760645π-0.760645\pi
0.981906 + 0.189371i 0.0606448π0.0606448\pi
998998 −7.59331 14.9027i −0.240362 0.471737i
999999 0 0
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 990.2.bh.c.73.1 48
3.2 odd 2 110.2.k.a.73.5 yes 48
5.2 odd 4 inner 990.2.bh.c.667.5 48
11.8 odd 10 inner 990.2.bh.c.613.5 48
12.11 even 2 880.2.cm.c.513.4 48
15.2 even 4 110.2.k.a.7.2 48
15.8 even 4 550.2.bh.b.7.5 48
15.14 odd 2 550.2.bh.b.293.2 48
33.8 even 10 110.2.k.a.63.2 yes 48
55.52 even 20 inner 990.2.bh.c.217.1 48
60.47 odd 4 880.2.cm.c.337.3 48
132.107 odd 10 880.2.cm.c.833.3 48
165.8 odd 20 550.2.bh.b.107.2 48
165.74 even 10 550.2.bh.b.393.5 48
165.107 odd 20 110.2.k.a.107.5 yes 48
660.107 even 20 880.2.cm.c.657.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
110.2.k.a.7.2 48 15.2 even 4
110.2.k.a.63.2 yes 48 33.8 even 10
110.2.k.a.73.5 yes 48 3.2 odd 2
110.2.k.a.107.5 yes 48 165.107 odd 20
550.2.bh.b.7.5 48 15.8 even 4
550.2.bh.b.107.2 48 165.8 odd 20
550.2.bh.b.293.2 48 15.14 odd 2
550.2.bh.b.393.5 48 165.74 even 10
880.2.cm.c.337.3 48 60.47 odd 4
880.2.cm.c.513.4 48 12.11 even 2
880.2.cm.c.657.4 48 660.107 even 20
880.2.cm.c.833.3 48 132.107 odd 10
990.2.bh.c.73.1 48 1.1 even 1 trivial
990.2.bh.c.217.1 48 55.52 even 20 inner
990.2.bh.c.613.5 48 11.8 odd 10 inner
990.2.bh.c.667.5 48 5.2 odd 4 inner