Properties

Label 162.5.d.d.107.4
Level 162162
Weight 55
Character 162.107
Analytic conductor 16.74616.746
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,5,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 162=234 162 = 2 \cdot 3^{4}
Weight: k k == 5 5
Character orbit: [χ][\chi] == 162.d (of order 66, degree 22, not 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: 16.745934019616.7459340196
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ24)\Q(\zeta_{24})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x4+1 x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 36 3^{6}
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 107.4
Root 0.965926+0.258819i-0.965926 + 0.258819i of defining polynomial
Character χ\chi == 162.107
Dual form 162.5.d.d.53.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(2.44949+1.41421i)q2+(4.00000+6.92820i)q4+(7.97262+4.60300i)q5+(27.2750+47.2417i)q7+22.6274iq826.0385q10+(34.316419.8126i)q11+(107.873186.842i)q13+(133.620+77.1453i)q14+(32.0000+55.4256i)q1628.2272iq17254.435q19+(63.781036.8240i)q20+(56.038597.0615i)q22+(801.737+462.883i)q23+(270.125+467.870i)q25610.222iq26436.400q28+(1164.65+672.411i)q29+(588.2961018.96i)q31+(156.767+90.5097i)q32+(39.919369.1422i)q34502.187iq352344.80q37+(623.235359.825i)q38+(104.154180.400i)q40+(1257.92726.261i)q41+(837.359+1450.35i)q43317.001iq442618.46q46+(2878.47+1661.88i)q47+(287.350497.705i)q49+(1323.34+764.028i)q50+(862.9851494.73i)q521743.30iq53+364.789q55+(1068.96617.163i)q56+(1901.86+3294.13i)q58+(709.264409.494i)q59+(393.925+682.298i)q613327.91iq62512.000q64+(1720.06+993.079i)q65+(1428.922474.97i)q67+(195.564112.909i)q68+(710.1991230.10i)q70+7906.95iq71+7112.40q73+(5743.573316.05i)q74+(1017.741762.77i)q76+(1871.961080.78i)q77+(1737.803009.96i)q79589.183iq80+4108.35q82+(996.961+575.596i)q83+(129.930+225.045i)q85+(4102.21+2368.41i)q86+(448.308776.492i)q88+10793.5iq89+11768.9q91+(6413.893703.06i)q92+(4700.51+8141.53i)q94+(2028.511171.16i)q95+(4982.60+8630.11i)q971625.50iq98+O(q100)q+(2.44949 + 1.41421i) q^{2} +(4.00000 + 6.92820i) q^{4} +(-7.97262 + 4.60300i) q^{5} +(-27.2750 + 47.2417i) q^{7} +22.6274i q^{8} -26.0385 q^{10} +(-34.3164 - 19.8126i) q^{11} +(-107.873 - 186.842i) q^{13} +(-133.620 + 77.1453i) q^{14} +(-32.0000 + 55.4256i) q^{16} -28.2272i q^{17} -254.435 q^{19} +(-63.7810 - 36.8240i) q^{20} +(-56.0385 - 97.0615i) q^{22} +(-801.737 + 462.883i) q^{23} +(-270.125 + 467.870i) q^{25} -610.222i q^{26} -436.400 q^{28} +(1164.65 + 672.411i) q^{29} +(-588.296 - 1018.96i) q^{31} +(-156.767 + 90.5097i) q^{32} +(39.9193 - 69.1422i) q^{34} -502.187i q^{35} -2344.80 q^{37} +(-623.235 - 359.825i) q^{38} +(-104.154 - 180.400i) q^{40} +(1257.92 - 726.261i) q^{41} +(-837.359 + 1450.35i) q^{43} -317.001i q^{44} -2618.46 q^{46} +(2878.47 + 1661.88i) q^{47} +(-287.350 - 497.705i) q^{49} +(-1323.34 + 764.028i) q^{50} +(862.985 - 1494.73i) q^{52} -1743.30i q^{53} +364.789 q^{55} +(-1068.96 - 617.163i) q^{56} +(1901.86 + 3294.13i) q^{58} +(709.264 - 409.494i) q^{59} +(-393.925 + 682.298i) q^{61} -3327.91i q^{62} -512.000 q^{64} +(1720.06 + 993.079i) q^{65} +(-1428.92 - 2474.97i) q^{67} +(195.564 - 112.909i) q^{68} +(710.199 - 1230.10i) q^{70} +7906.95i q^{71} +7112.40 q^{73} +(-5743.57 - 3316.05i) q^{74} +(-1017.74 - 1762.77i) q^{76} +(1871.96 - 1080.78i) q^{77} +(1737.80 - 3009.96i) q^{79} -589.183i q^{80} +4108.35 q^{82} +(996.961 + 575.596i) q^{83} +(129.930 + 225.045i) q^{85} +(-4102.21 + 2368.41i) q^{86} +(448.308 - 776.492i) q^{88} +10793.5i q^{89} +11768.9 q^{91} +(-6413.89 - 3703.06i) q^{92} +(4700.51 + 8141.53i) q^{94} +(2028.51 - 1171.16i) q^{95} +(-4982.60 + 8630.11i) q^{97} -1625.50i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+32q4+52q7624q10572q13256q16248q19864q22+1892q25+832q283584q31+1608q3418800q372496q403020q434320q46+46304q97+O(q100) 8 q + 32 q^{4} + 52 q^{7} - 624 q^{10} - 572 q^{13} - 256 q^{16} - 248 q^{19} - 864 q^{22} + 1892 q^{25} + 832 q^{28} - 3584 q^{31} + 1608 q^{34} - 18800 q^{37} - 2496 q^{40} - 3020 q^{43} - 4320 q^{46}+ \cdots - 46304 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/162Z)×\left(\mathbb{Z}/162\mathbb{Z}\right)^\times.

nn 8383
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.44949 + 1.41421i 0.612372 + 0.353553i
33 0 0
44 4.00000 + 6.92820i 0.250000 + 0.433013i
55 −7.97262 + 4.60300i −0.318905 + 0.184120i −0.650904 0.759160i 0.725610π-0.725610\pi
0.331999 + 0.943280i 0.392277π0.392277\pi
66 0 0
77 −27.2750 + 47.2417i −0.556632 + 0.964116i 0.441142 + 0.897437i 0.354573π0.354573\pi
−0.997775 + 0.0666784i 0.978760π0.978760\pi
88 22.6274i 0.353553i
99 0 0
1010 −26.0385 −0.260385
1111 −34.3164 19.8126i −0.283607 0.163740i 0.351448 0.936207i 0.385689π-0.385689\pi
−0.635055 + 0.772467i 0.719023π0.719023\pi
1212 0 0
1313 −107.873 186.842i −0.638302 1.10557i −0.985805 0.167893i 0.946304π-0.946304\pi
0.347503 0.937679i 0.387030π-0.387030\pi
1414 −133.620 + 77.1453i −0.681733 + 0.393599i
1515 0 0
1616 −32.0000 + 55.4256i −0.125000 + 0.216506i
1717 28.2272i 0.0976719i −0.998807 0.0488360i 0.984449π-0.984449\pi
0.998807 0.0488360i 0.0155512π-0.0155512\pi
1818 0 0
1919 −254.435 −0.704805 −0.352402 0.935849i 0.614635π-0.614635\pi
−0.352402 + 0.935849i 0.614635π0.614635\pi
2020 −63.7810 36.8240i −0.159452 0.0920599i
2121 0 0
2222 −56.0385 97.0615i −0.115782 0.200540i
2323 −801.737 + 462.883i −1.51557 + 0.875015i −0.515737 + 0.856747i 0.672482π0.672482\pi
−0.999833 + 0.0182680i 0.994185π0.994185\pi
2424 0 0
2525 −270.125 + 467.870i −0.432200 + 0.748592i
2626 610.222i 0.902696i
2727 0 0
2828 −436.400 −0.556632
2929 1164.65 + 672.411i 1.38484 + 0.799537i 0.992728 0.120381i 0.0384115π-0.0384115\pi
0.392111 + 0.919918i 0.371745π0.371745\pi
3030 0 0
3131 −588.296 1018.96i −0.612171 1.06031i −0.990874 0.134793i 0.956963π-0.956963\pi
0.378703 0.925518i 0.376370π-0.376370\pi
3232 −156.767 + 90.5097i −0.153093 + 0.0883883i
3333 0 0
3434 39.9193 69.1422i 0.0345322 0.0598116i
3535 502.187i 0.409948i
3636 0 0
3737 −2344.80 −1.71279 −0.856393 0.516325i 0.827300π-0.827300\pi
−0.856393 + 0.516325i 0.827300π0.827300\pi
3838 −623.235 359.825i −0.431603 0.249186i
3939 0 0
4040 −104.154 180.400i −0.0650962 0.112750i
4141 1257.92 726.261i 0.748317 0.432041i −0.0767684 0.997049i 0.524460π-0.524460\pi
0.825086 + 0.565008i 0.191127π0.191127\pi
4242 0 0
4343 −837.359 + 1450.35i −0.452872 + 0.784397i −0.998563 0.0535896i 0.982934π-0.982934\pi
0.545691 + 0.837986i 0.316267π0.316267\pi
4444 317.001i 0.163740i
4545 0 0
4646 −2618.46 −1.23746
4747 2878.47 + 1661.88i 1.30306 + 0.752324i 0.980928 0.194370i 0.0622663π-0.0622663\pi
0.322134 + 0.946694i 0.395600π0.395600\pi
4848 0 0
4949 −287.350 497.705i −0.119679 0.207291i
5050 −1323.34 + 764.028i −0.529334 + 0.305611i
5151 0 0
5252 862.985 1494.73i 0.319151 0.552786i
5353 1743.30i 0.620611i −0.950637 0.310305i 0.899569π-0.899569\pi
0.950637 0.310305i 0.100431π-0.100431\pi
5454 0 0
5555 364.789 0.120591
5656 −1068.96 617.163i −0.340866 0.196799i
5757 0 0
5858 1901.86 + 3294.13i 0.565358 + 0.979229i
5959 709.264 409.494i 0.203753 0.117637i −0.394652 0.918831i 0.629135π-0.629135\pi
0.598405 + 0.801194i 0.295801π0.295801\pi
6060 0 0
6161 −393.925 + 682.298i −0.105865 + 0.183364i −0.914091 0.405508i 0.867095π-0.867095\pi
0.808226 + 0.588872i 0.200428π0.200428\pi
6262 3327.91i 0.865740i
6363 0 0
6464 −512.000 −0.125000
6565 1720.06 + 993.079i 0.407115 + 0.235048i
6666 0 0
6767 −1428.92 2474.97i −0.318317 0.551341i 0.661820 0.749663i 0.269784π-0.269784\pi
−0.980137 + 0.198322i 0.936451π0.936451\pi
6868 195.564 112.909i 0.0422932 0.0244180i
6969 0 0
7070 710.199 1230.10i 0.144939 0.251041i
7171 7906.95i 1.56853i 0.620427 + 0.784264i 0.286959π0.286959\pi
−0.620427 + 0.784264i 0.713041π0.713041\pi
7272 0 0
7373 7112.40 1.33466 0.667330 0.744762i 0.267437π-0.267437\pi
0.667330 + 0.744762i 0.267437π0.267437\pi
7474 −5743.57 3316.05i −1.04886 0.605561i
7575 0 0
7676 −1017.74 1762.77i −0.176201 0.305189i
7777 1871.96 1080.78i 0.315729 0.182286i
7878 0 0
7979 1737.80 3009.96i 0.278449 0.482288i −0.692550 0.721370i 0.743513π-0.743513\pi
0.971000 + 0.239081i 0.0768463π0.0768463\pi
8080 589.183i 0.0920599i
8181 0 0
8282 4108.35 0.610998
8383 996.961 + 575.596i 0.144718 + 0.0835529i 0.570611 0.821221i 0.306707π-0.306707\pi
−0.425893 + 0.904774i 0.640040π0.640040\pi
8484 0 0
8585 129.930 + 225.045i 0.0179833 + 0.0311481i
8686 −4102.21 + 2368.41i −0.554652 + 0.320229i
8787 0 0
8888 448.308 776.492i 0.0578910 0.100270i
8989 10793.5i 1.36265i 0.731983 + 0.681323i 0.238595π0.238595\pi
−0.731983 + 0.681323i 0.761405π0.761405\pi
9090 0 0
9191 11768.9 1.42120
9292 −6413.89 3703.06i −0.757785 0.437507i
9393 0 0
9494 4700.51 + 8141.53i 0.531973 + 0.921404i
9595 2028.51 1171.16i 0.224766 0.129769i
9696 0 0
9797 −4982.60 + 8630.11i −0.529556 + 0.917219i 0.469849 + 0.882747i 0.344308π0.344308\pi
−0.999406 + 0.0344720i 0.989025π0.989025\pi
9898 1625.50i 0.169252i
9999 0 0
100100 −4322.00 −0.432200
101101 −8556.31 4939.99i −0.838772 0.484265i 0.0180748 0.999837i 0.494246π-0.494246\pi
−0.856847 + 0.515572i 0.827580π0.827580\pi
102102 0 0
103103 6752.51 + 11695.7i 0.636489 + 1.10243i 0.986198 + 0.165572i 0.0529471π0.0529471\pi
−0.349709 + 0.936858i 0.613720π0.613720\pi
104104 4227.74 2440.89i 0.390879 0.225674i
105105 0 0
106106 2465.39 4270.18i 0.219419 0.380045i
107107 9.72286i 0.000849233i −1.00000 0.000424616i 0.999865π-0.999865\pi
1.00000 0.000424616i 0.000135160π-0.000135160\pi
108108 0 0
109109 18929.2 1.59324 0.796618 0.604484i 0.206620π-0.206620\pi
0.796618 + 0.604484i 0.206620π0.206620\pi
110110 893.547 + 515.890i 0.0738469 + 0.0426355i
111111 0 0
112112 −1745.60 3023.47i −0.139158 0.241029i
113113 5106.30 2948.13i 0.399898 0.230881i −0.286542 0.958068i 0.592506π-0.592506\pi
0.686440 + 0.727186i 0.259172π0.259172\pi
114114 0 0
115115 4261.30 7380.78i 0.322215 0.558093i
116116 10758.6i 0.799537i
117117 0 0
118118 2316.45 0.166363
119119 1333.50 + 769.896i 0.0941670 + 0.0543674i
120120 0 0
121121 −6535.42 11319.7i −0.446378 0.773150i
122122 −1929.83 + 1114.19i −0.129658 + 0.0748581i
123123 0 0
124124 4706.37 8151.67i 0.306085 0.530155i
125125 10727.3i 0.686546i
126126 0 0
127127 −20216.9 −1.25345 −0.626724 0.779241i 0.715605π-0.715605\pi
−0.626724 + 0.779241i 0.715605π0.715605\pi
128128 −1254.14 724.077i −0.0765466 0.0441942i
129129 0 0
130130 2808.85 + 4865.07i 0.166204 + 0.287874i
131131 12179.1 7031.58i 0.709694 0.409742i −0.101254 0.994861i 0.532285π-0.532285\pi
0.810948 + 0.585119i 0.198952π0.198952\pi
132132 0 0
133133 6939.70 12019.9i 0.392317 0.679513i
134134 8083.22i 0.450168i
135135 0 0
136136 638.708 0.0345322
137137 12773.7 + 7374.92i 0.680576 + 0.392931i 0.800072 0.599904i 0.204795π-0.204795\pi
−0.119496 + 0.992835i 0.538128π0.538128\pi
138138 0 0
139139 7069.12 + 12244.1i 0.365878 + 0.633719i 0.988917 0.148472i 0.0474355π-0.0474355\pi
−0.623039 + 0.782191i 0.714102π0.714102\pi
140140 3479.25 2008.75i 0.177513 0.102487i
141141 0 0
142142 −11182.1 + 19368.0i −0.554559 + 0.960524i
143143 8548.98i 0.418064i
144144 0 0
145145 −12380.4 −0.588843
146146 17421.8 + 10058.5i 0.817309 + 0.471873i
147147 0 0
148148 −9379.22 16245.3i −0.428196 0.741658i
149149 −9451.21 + 5456.66i −0.425711 + 0.245784i −0.697518 0.716567i 0.745712π-0.745712\pi
0.271807 + 0.962352i 0.412379π0.412379\pi
150150 0 0
151151 −1394.36 + 2415.10i −0.0611534 + 0.105921i −0.894981 0.446104i 0.852811π-0.852811\pi
0.833828 + 0.552025i 0.186145π0.186145\pi
152152 5757.20i 0.249186i
153153 0 0
154154 6113.80 0.257792
155155 9380.53 + 5415.85i 0.390449 + 0.225426i
156156 0 0
157157 1238.42 + 2145.01i 0.0502423 + 0.0870222i 0.890053 0.455857i 0.150667π-0.150667\pi
−0.839811 + 0.542880i 0.817334π0.817334\pi
158158 8513.46 4915.25i 0.341029 0.196893i
159159 0 0
160160 833.231 1443.20i 0.0325481 0.0563750i
161161 50500.5i 1.94825i
162162 0 0
163163 −35547.0 −1.33791 −0.668957 0.743301i 0.733259π-0.733259\pi
−0.668957 + 0.743301i 0.733259π0.733259\pi
164164 10063.4 + 5810.09i 0.374159 + 0.216021i
165165 0 0
166166 1628.03 + 2819.83i 0.0590808 + 0.102331i
167167 −45892.8 + 26496.2i −1.64555 + 0.950060i −0.666743 + 0.745287i 0.732312π0.732312\pi
−0.978810 + 0.204773i 0.934354π0.934354\pi
168168 0 0
169169 −8992.70 + 15575.8i −0.314859 + 0.545352i
170170 734.993i 0.0254323i
171171 0 0
172172 −13397.8 −0.452872
173173 −46242.8 26698.3i −1.54508 0.892054i −0.998506 0.0546443i 0.982598π-0.982598\pi
−0.546576 0.837409i 0.684069π-0.684069\pi
174174 0 0
175175 −14735.3 25522.3i −0.481153 0.833381i
176176 2196.25 1268.01i 0.0709017 0.0409351i
177177 0 0
178178 −15264.3 + 26438.6i −0.481768 + 0.834447i
179179 32448.3i 1.01271i 0.862324 + 0.506356i 0.169008π0.169008\pi
−0.862324 + 0.506356i 0.830992π0.830992\pi
180180 0 0
181181 −50381.3 −1.53784 −0.768921 0.639344i 0.779206π-0.779206\pi
−0.768921 + 0.639344i 0.779206π0.779206\pi
182182 28827.9 + 16643.8i 0.870303 + 0.502470i
183183 0 0
184184 −10473.8 18141.2i −0.309364 0.535835i
185185 18694.2 10793.1i 0.546216 0.315358i
186186 0 0
187187 −559.254 + 968.656i −0.0159928 + 0.0277004i
188188 26590.1i 0.752324i
189189 0 0
190190 6625.09 0.183520
191191 1953.74 + 1127.99i 0.0535551 + 0.0309201i 0.526538 0.850151i 0.323490π-0.323490\pi
−0.472983 + 0.881071i 0.656823π0.656823\pi
192192 0 0
193193 −12016.0 20812.3i −0.322586 0.558736i 0.658435 0.752638i 0.271219π-0.271219\pi
−0.981021 + 0.193902i 0.937886π0.937886\pi
194194 −24409.6 + 14092.9i −0.648572 + 0.374453i
195195 0 0
196196 2298.80 3981.64i 0.0598397 0.103645i
197197 66824.6i 1.72189i −0.508702 0.860943i 0.669875π-0.669875\pi
0.508702 0.860943i 0.330125π-0.330125\pi
198198 0 0
199199 −8425.29 −0.212754 −0.106377 0.994326i 0.533925π-0.533925\pi
−0.106377 + 0.994326i 0.533925π0.533925\pi
200200 −10586.7 6112.23i −0.264667 0.152806i
201201 0 0
202202 −13972.4 24200.9i −0.342427 0.593101i
203203 −63531.6 + 36680.0i −1.54169 + 0.890097i
204204 0 0
205205 −6685.95 + 11580.4i −0.159095 + 0.275560i
206206 38197.9i 0.900131i
207207 0 0
208208 13807.8 0.319151
209209 8731.28 + 5041.01i 0.199887 + 0.115405i
210210 0 0
211211 16850.0 + 29185.0i 0.378473 + 0.655534i 0.990840 0.135039i 0.0431160π-0.0431160\pi
−0.612367 + 0.790573i 0.709783π0.709783\pi
212212 12077.9 6973.18i 0.268732 0.155153i
213213 0 0
214214 13.7502 23.8161i 0.000300249 0.000520047i
215215 15417.4i 0.333531i
216216 0 0
217217 64183.1 1.36302
218218 46367.0 + 26770.0i 0.975653 + 0.563294i
219219 0 0
220220 1459.16 + 2527.33i 0.0301479 + 0.0522176i
221221 −5274.01 + 3044.95i −0.107983 + 0.0623442i
222222 0 0
223223 10265.6 17780.6i 0.206432 0.357550i −0.744156 0.668006i 0.767148π-0.767148\pi
0.950588 + 0.310455i 0.100482π0.100482\pi
224224 9874.60i 0.196799i
225225 0 0
226226 16677.1 0.326516
227227 −50720.2 29283.3i −0.984305 0.568289i −0.0807378 0.996735i 0.525728π-0.525728\pi
−0.903567 + 0.428447i 0.859061π0.859061\pi
228228 0 0
229229 3644.28 + 6312.07i 0.0694929 + 0.120365i 0.898678 0.438609i 0.144529π-0.144529\pi
−0.829185 + 0.558974i 0.811195π0.811195\pi
230230 20876.0 12052.8i 0.394631 0.227841i
231231 0 0
232232 −15214.9 + 26353.0i −0.282679 + 0.489615i
233233 13584.9i 0.250232i 0.992142 + 0.125116i 0.0399304π0.0399304\pi
−0.992142 + 0.125116i 0.960070π0.960070\pi
234234 0 0
235235 −30598.6 −0.554071
236236 5674.11 + 3275.95i 0.101876 + 0.0588184i
237237 0 0
238238 2177.60 + 3771.71i 0.0384435 + 0.0665862i
239239 22418.8 12943.5i 0.392479 0.226598i −0.290755 0.956798i 0.593906π-0.593906\pi
0.683234 + 0.730200i 0.260573π0.260573\pi
240240 0 0
241241 4680.48 8106.84i 0.0805855 0.139578i −0.822916 0.568163i 0.807654π-0.807654\pi
0.903502 + 0.428585i 0.140988π0.140988\pi
242242 36969.9i 0.631274i
243243 0 0
244244 −6302.80 −0.105865
245245 4581.87 + 2645.34i 0.0763327 + 0.0440707i
246246 0 0
247247 27446.6 + 47539.0i 0.449878 + 0.779212i
248248 23056.4 13311.6i 0.374877 0.216435i
249249 0 0
250250 15170.7 26276.4i 0.242731 0.420422i
251251 109546.i 1.73879i 0.494117 + 0.869396i 0.335492π0.335492\pi
−0.494117 + 0.869396i 0.664508π0.664508\pi
252252 0 0
253253 36683.6 0.573101
254254 −49521.0 28591.0i −0.767577 0.443161i
255255 0 0
256256 −2048.00 3547.24i −0.0312500 0.0541266i
257257 83266.7 48074.1i 1.26068 0.727855i 0.287475 0.957788i 0.407184π-0.407184\pi
0.973206 + 0.229933i 0.0738508π0.0738508\pi
258258 0 0
259259 63954.5 110772.i 0.953392 1.65132i
260260 15889.3i 0.235048i
261261 0 0
262262 39776.6 0.579463
263263 11913.5 + 6878.28i 0.172238 + 0.0994417i 0.583641 0.812012i 0.301628π-0.301628\pi
−0.411403 + 0.911454i 0.634961π0.634961\pi
264264 0 0
265265 8024.38 + 13898.6i 0.114267 + 0.197916i
266266 33997.4 19628.4i 0.480489 0.277410i
267267 0 0
268268 11431.4 19799.8i 0.159158 0.275670i
269269 65136.7i 0.900163i −0.892988 0.450081i 0.851395π-0.851395\pi
0.892988 0.450081i 0.148605π-0.148605\pi
270270 0 0
271271 9569.63 0.130304 0.0651518 0.997875i 0.479247π-0.479247\pi
0.0651518 + 0.997875i 0.479247π0.479247\pi
272272 1564.51 + 903.270i 0.0211466 + 0.0122090i
273273 0 0
274274 20859.4 + 36129.6i 0.277844 + 0.481240i
275275 18539.4 10703.7i 0.245150 0.141537i
276276 0 0
277277 −22168.3 + 38396.6i −0.288916 + 0.500418i −0.973551 0.228468i 0.926628π-0.926628\pi
0.684635 + 0.728886i 0.259962π0.259962\pi
278278 39989.0i 0.517429i
279279 0 0
280280 11363.2 0.144939
281281 −105192. 60732.4i −1.33220 0.769145i −0.346561 0.938027i 0.612651π-0.612651\pi
−0.985636 + 0.168883i 0.945984π0.945984\pi
282282 0 0
283283 58191.1 + 100790.i 0.726581 + 1.25848i 0.958320 + 0.285697i 0.0922251π0.0922251\pi
−0.231739 + 0.972778i 0.574442π0.574442\pi
284284 −54781.0 + 31627.8i −0.679193 + 0.392132i
285285 0 0
286286 −12090.1 + 20940.6i −0.147808 + 0.256011i
287287 79235.1i 0.961952i
288288 0 0
289289 82724.2 0.990460
290290 −30325.7 17508.6i −0.360591 0.208187i
291291 0 0
292292 28449.6 + 49276.2i 0.333665 + 0.577925i
293293 137541. 79409.4i 1.60213 0.924990i 0.611068 0.791578i 0.290740π-0.290740\pi
0.991061 0.133412i 0.0425933π-0.0425933\pi
294294 0 0
295295 −3769.79 + 6529.47i −0.0433185 + 0.0750299i
296296 53056.9i 0.605561i
297297 0 0
298298 −30867.5 −0.347592
299299 172972. + 99865.2i 1.93478 + 1.11705i
300300 0 0
301301 −45677.9 79116.5i −0.504166 0.873241i
302302 −6830.94 + 3943.84i −0.0748973 + 0.0432420i
303303 0 0
304304 8141.91 14102.2i 0.0881006 0.152595i
305305 7252.94i 0.0779676i
306306 0 0
307307 100162. 1.06274 0.531370 0.847140i 0.321677π-0.321677\pi
0.531370 + 0.847140i 0.321677π0.321677\pi
308308 14975.7 + 8646.21i 0.157865 + 0.0911432i
309309 0 0
310310 15318.3 + 26532.1i 0.159400 + 0.276089i
311311 −46738.2 + 26984.3i −0.483227 + 0.278991i −0.721760 0.692143i 0.756667π-0.756667\pi
0.238534 + 0.971134i 0.423333π0.423333\pi
312312 0 0
313313 −37756.9 + 65396.9i −0.385396 + 0.667526i −0.991824 0.127613i 0.959269π-0.959269\pi
0.606428 + 0.795139i 0.292602π0.292602\pi
314314 7005.58i 0.0710534i
315315 0 0
316316 27804.8 0.278449
317317 −57648.6 33283.4i −0.573680 0.331215i 0.184938 0.982750i 0.440792π-0.440792\pi
−0.758618 + 0.651536i 0.774125π0.774125\pi
318318 0 0
319319 −26644.4 46149.5i −0.261833 0.453508i
320320 4081.98 2356.73i 0.0398631 0.0230150i
321321 0 0
322322 71418.5 123700.i 0.688809 1.19305i
323323 7181.97i 0.0688397i
324324 0 0
325325 116557. 1.10350
326326 −87072.1 50271.1i −0.819302 0.473024i
327327 0 0
328328 16433.4 + 28463.5i 0.152750 + 0.264570i
329329 −157020. + 90655.7i −1.45065 + 0.837535i
330330 0 0
331331 34710.1 60119.7i 0.316811 0.548732i −0.663010 0.748611i 0.730721π-0.730721\pi
0.979821 + 0.199878i 0.0640546π0.0640546\pi
332332 9209.53i 0.0835529i
333333 0 0
334334 −149885. −1.34359
335335 22784.5 + 13154.7i 0.203026 + 0.117217i
336336 0 0
337337 −44393.0 76890.9i −0.390890 0.677041i 0.601677 0.798739i 0.294499π-0.294499\pi
−0.992567 + 0.121698i 0.961166π0.961166\pi
338338 −44055.0 + 25435.2i −0.385622 + 0.222639i
339339 0 0
340340 −1039.44 + 1800.36i −0.00899167 + 0.0155740i
341341 46622.7i 0.400948i
342342 0 0
343343 −99624.6 −0.846795
344344 −32817.7 18947.3i −0.277326 0.160114i
345345 0 0
346346 −75514.1 130794.i −0.630777 1.09254i
347347 95033.8 54867.8i 0.789259 0.455679i −0.0504428 0.998727i 0.516063π-0.516063\pi
0.839701 + 0.543048i 0.182730π0.182730\pi
348348 0 0
349349 −69389.6 + 120186.i −0.569696 + 0.986743i 0.426899 + 0.904299i 0.359606π0.359606\pi
−0.996596 + 0.0824438i 0.973728π0.973728\pi
350350 83355.5i 0.680453i
351351 0 0
352352 7172.92 0.0578910
353353 67397.6 + 38912.0i 0.540873 + 0.312273i 0.745433 0.666581i 0.232243π-0.232243\pi
−0.204560 + 0.978854i 0.565576π0.565576\pi
354354 0 0
355355 −36395.7 63039.2i −0.288797 0.500212i
356356 −74779.7 + 43174.1i −0.590043 + 0.340662i
357357 0 0
358358 −45888.9 + 79481.8i −0.358048 + 0.620157i
359359 195283.i 1.51522i 0.652708 + 0.757610i 0.273633π0.273633\pi
−0.652708 + 0.757610i 0.726367π0.726367\pi
360360 0 0
361361 −65584.1 −0.503250
362362 −123408. 71249.8i −0.941732 0.543709i
363363 0 0
364364 47075.8 + 81537.7i 0.355300 + 0.615397i
365365 −56704.5 + 32738.4i −0.425630 + 0.245737i
366366 0 0
367367 −42902.7 + 74309.6i −0.318531 + 0.551713i −0.980182 0.198100i 0.936523π-0.936523\pi
0.661650 + 0.749812i 0.269856π0.269856\pi
368368 59249.0i 0.437507i
369369 0 0
370370 61055.1 0.445983
371371 82356.2 + 47548.4i 0.598340 + 0.345452i
372372 0 0
373373 −6159.02 10667.7i −0.0442684 0.0766751i 0.843042 0.537847i 0.180762π-0.180762\pi
−0.887311 + 0.461172i 0.847429π0.847429\pi
374374 −2739.77 + 1581.81i −0.0195872 + 0.0113086i
375375 0 0
376376 −37604.1 + 65132.2i −0.265987 + 0.460702i
377377 290140.i 2.04139i
378378 0 0
379379 −216174. −1.50496 −0.752479 0.658617i 0.771142π-0.771142\pi
−0.752479 + 0.658617i 0.771142π0.771142\pi
380380 16228.1 + 9369.29i 0.112383 + 0.0648843i
381381 0 0
382382 3190.45 + 5526.02i 0.0218638 + 0.0378692i
383383 −205867. + 118857.i −1.40342 + 0.810266i −0.994742 0.102411i 0.967344π-0.967344\pi
−0.408680 + 0.912678i 0.634011π0.634011\pi
384384 0 0
385385 −9949.62 + 17233.2i −0.0671251 + 0.116264i
386386 67972.8i 0.456206i
387387 0 0
388388 −79721.5 −0.529556
389389 161345. + 93152.6i 1.06624 + 0.615596i 0.927153 0.374684i 0.122249π-0.122249\pi
0.139091 + 0.990280i 0.455582π0.455582\pi
390390 0 0
391391 13065.9 + 22630.8i 0.0854644 + 0.148029i
392392 11261.8 6501.99i 0.0732884 0.0423131i
393393 0 0
394394 94504.3 163686.i 0.608778 1.05444i
395395 31996.4i 0.205072i
396396 0 0
397397 5004.70 0.0317539 0.0158769 0.999874i 0.494946π-0.494946\pi
0.0158769 + 0.999874i 0.494946π0.494946\pi
398398 −20637.7 11915.2i −0.130285 0.0752200i
399399 0 0
400400 −17288.0 29943.7i −0.108050 0.187148i
401401 152835. 88239.4i 0.950461 0.548749i 0.0572371 0.998361i 0.481771π-0.481771\pi
0.893224 + 0.449612i 0.148438π0.148438\pi
402402 0 0
403403 −126923. + 219836.i −0.781500 + 1.35360i
404404 79039.8i 0.484265i
405405 0 0
406406 −207493. −1.25879
407407 80465.3 + 46456.6i 0.485758 + 0.280452i
408408 0 0
409409 −94356.8 163431.i −0.564062 0.976984i −0.997136 0.0756254i 0.975905π-0.975905\pi
0.433075 0.901358i 0.357429π-0.357429\pi
410410 −32754.3 + 18910.7i −0.194850 + 0.112497i
411411 0 0
412412 −54020.1 + 93565.5i −0.318244 + 0.551215i
413413 44675.7i 0.261922i
414414 0 0
415415 −10597.9 −0.0615349
416416 33821.9 + 19527.1i 0.195439 + 0.112837i
417417 0 0
418418 14258.1 + 24695.8i 0.0816037 + 0.141342i
419419 −10397.0 + 6002.70i −0.0592215 + 0.0341915i −0.529318 0.848423i 0.677552π-0.677552\pi
0.470097 + 0.882615i 0.344219π0.344219\pi
420420 0 0
421421 27797.6 48146.8i 0.156835 0.271646i −0.776891 0.629635i 0.783204π-0.783204\pi
0.933726 + 0.357989i 0.116538π0.116538\pi
422422 95317.9i 0.535241i
423423 0 0
424424 39446.3 0.219419
425425 13206.7 + 7624.87i 0.0731164 + 0.0422138i
426426 0 0
427427 −21488.6 37219.3i −0.117856 0.204133i
428428 67.3620 38.8915i 0.000367728 0.000212308i
429429 0 0
430430 21803.6 37764.9i 0.117921 0.204245i
431431 52071.6i 0.280315i −0.990129 0.140158i 0.955239π-0.955239\pi
0.990129 0.140158i 0.0447609π-0.0447609\pi
432432 0 0
433433 −205361. −1.09532 −0.547662 0.836700i 0.684482π-0.684482\pi
−0.547662 + 0.836700i 0.684482π0.684482\pi
434434 157216. + 90768.6i 0.834674 + 0.481899i
435435 0 0
436436 75716.9 + 131146.i 0.398309 + 0.689891i
437437 203990. 117773.i 1.06818 0.616715i
438438 0 0
439439 162282. 281081.i 0.842058 1.45849i −0.0460931 0.998937i 0.514677π-0.514677\pi
0.888152 0.459551i 0.151990π-0.151990\pi
440440 8254.24i 0.0426355i
441441 0 0
442442 −17224.9 −0.0881680
443443 −148975. 86010.6i −0.759111 0.438273i 0.0698657 0.997556i 0.477743π-0.477743\pi
−0.828976 + 0.559284i 0.811076π0.811076\pi
444444 0 0
445445 −49682.5 86052.7i −0.250890 0.434555i
446446 50291.2 29035.6i 0.252826 0.145969i
447447 0 0
448448 13964.8 24187.7i 0.0695791 0.120514i
449449 121635.i 0.603345i −0.953412 0.301672i 0.902455π-0.902455\pi
0.953412 0.301672i 0.0975449π-0.0975449\pi
450450 0 0
451451 −57556.5 −0.282970
452452 40850.4 + 23585.0i 0.199949 + 0.115441i
453453 0 0
454454 −82825.8 143459.i −0.401841 0.696009i
455455 −93829.4 + 54172.4i −0.453227 + 0.261671i
456456 0 0
457457 −23274.4 + 40312.4i −0.111441 + 0.193022i −0.916352 0.400375i 0.868880π-0.868880\pi
0.804910 + 0.593396i 0.202213π0.202213\pi
458458 20615.1i 0.0982778i
459459 0 0
460460 68180.7 0.322215
461461 176904. + 102136.i 0.832409 + 0.480591i 0.854677 0.519161i 0.173755π-0.173755\pi
−0.0222679 + 0.999752i 0.507089π0.507089\pi
462462 0 0
463463 8635.53 + 14957.2i 0.0402835 + 0.0697731i 0.885464 0.464708i 0.153841π-0.153841\pi
−0.845181 + 0.534481i 0.820507π0.820507\pi
464464 −74537.6 + 43034.3i −0.346210 + 0.199884i
465465 0 0
466466 −19211.9 + 33276.0i −0.0884705 + 0.153235i
467467 219664.i 1.00722i −0.863930 0.503611i 0.832004π-0.832004\pi
0.863930 0.503611i 0.167996π-0.167996\pi
468468 0 0
469469 155896. 0.708742
470470 −74950.9 43272.9i −0.339298 0.195894i
471471 0 0
472472 9265.78 + 16048.8i 0.0415909 + 0.0720375i
473473 57470.4 33180.5i 0.256875 0.148307i
474474 0 0
475475 68729.1 119042.i 0.304617 0.527611i
476476 12318.3i 0.0543674i
477477 0 0
478478 73219.4 0.320457
479479 −78854.6 45526.7i −0.343682 0.198425i 0.318217 0.948018i 0.396916π-0.396916\pi
−0.661899 + 0.749593i 0.730249π0.730249\pi
480480 0 0
481481 252941. + 438107.i 1.09327 + 1.89361i
482482 22929.6 13238.4i 0.0986966 0.0569825i
483483 0 0
484484 52283.4 90557.5i 0.223189 0.386575i
485485 91739.5i 0.390007i
486486 0 0
487487 146600. 0.618126 0.309063 0.951042i 0.399985π-0.399985\pi
0.309063 + 0.951042i 0.399985π0.399985\pi
488488 −15438.6 8913.50i −0.0648290 0.0374290i
489489 0 0
490490 7482.16 + 12959.5i 0.0311627 + 0.0539754i
491491 41966.3 24229.2i 0.174075 0.100502i −0.410431 0.911892i 0.634622π-0.634622\pi
0.584506 + 0.811389i 0.301288π0.301288\pi
492492 0 0
493493 18980.3 32874.8i 0.0780924 0.135260i
494494 155262.i 0.636224i
495495 0 0
496496 75301.9 0.306085
497497 −373538. 215662.i −1.51224 0.873094i
498498 0 0
499499 124007. + 214786.i 0.498016 + 0.862590i 0.999997 0.00228889i 0.000728578π-0.000728578\pi
−0.501981 + 0.864879i 0.667395π0.667395\pi
500500 74320.8 42909.1i 0.297283 0.171636i
501501 0 0
502502 −154921. + 268331.i −0.614755 + 1.06479i
503503 486322.i 1.92215i 0.276286 + 0.961076i 0.410896π0.410896\pi
−0.276286 + 0.961076i 0.589104π0.589104\pi
504504 0 0
505505 90955.0 0.356651
506506 89856.2 + 51878.5i 0.350951 + 0.202622i
507507 0 0
508508 −80867.4 140066.i −0.313362 0.542759i
509509 −246292. + 142196.i −0.950635 + 0.548850i −0.893278 0.449504i 0.851601π-0.851601\pi
−0.0573571 + 0.998354i 0.518267π0.518267\pi
510510 0 0
511511 −193991. + 336002.i −0.742915 + 1.28677i
512512 11585.2i 0.0441942i
513513 0 0
514514 271948. 1.02934
515515 −107670. 62163.5i −0.405959 0.234380i
516516 0 0
517517 −65852.4 114060.i −0.246372 0.426728i
518518 313312. 180891.i 1.16766 0.674150i
519519 0 0
520520 −22470.8 + 38920.6i −0.0831021 + 0.143937i
521521 248390.i 0.915079i 0.889189 + 0.457539i 0.151269π0.151269\pi
−0.889189 + 0.457539i 0.848731π0.848731\pi
522522 0 0
523523 113565. 0.415186 0.207593 0.978215i 0.433437π-0.433437\pi
0.207593 + 0.978215i 0.433437π0.433437\pi
524524 97432.5 + 56252.7i 0.354847 + 0.204871i
525525 0 0
526526 19454.7 + 33696.6i 0.0703159 + 0.121791i
527527 −28762.3 + 16605.9i −0.103563 + 0.0597919i
528528 0 0
529529 288601. 499871.i 1.03130 1.78627i
530530 45392.8i 0.161598i
531531 0 0
532532 111035. 0.392317
533533 −271392. 156688.i −0.955305 0.551546i
534534 0 0
535535 44.7543 + 77.5167i 0.000156361 + 0.000270824i
536536 56002.2 32332.9i 0.194928 0.112542i
537537 0 0
538538 92117.2 159552.i 0.318256 0.551235i
539539 22772.6i 0.0783854i
540540 0 0
541541 68803.4 0.235080 0.117540 0.993068i 0.462499π-0.462499\pi
0.117540 + 0.993068i 0.462499π0.462499\pi
542542 23440.7 + 13533.5i 0.0797943 + 0.0460693i
543543 0 0
544544 2554.83 + 4425.10i 0.00863306 + 0.0149529i
545545 −150916. + 87131.2i −0.508091 + 0.293346i
546546 0 0
547547 70749.2 122541.i 0.236454 0.409551i −0.723240 0.690597i 0.757348π-0.757348\pi
0.959694 + 0.281046i 0.0906814π0.0906814\pi
548548 117999.i 0.392931i
549549 0 0
550550 60549.5 0.200164
551551 −296327. 171085.i −0.976041 0.563518i
552552 0 0
553553 94797.1 + 164193.i 0.309988 + 0.536915i
554554 −108602. + 62701.3i −0.353849 + 0.204295i
555555 0 0
556556 −56553.0 + 97952.7i −0.182939 + 0.316859i
557557 59163.4i 0.190697i 0.995444 + 0.0953483i 0.0303965π0.0303965\pi
−0.995444 + 0.0953483i 0.969604π0.969604\pi
558558 0 0
559559 361314. 1.15628
560560 27834.0 + 16070.0i 0.0887564 + 0.0512435i
561561 0 0
562562 −171777. 297527.i −0.543867 0.942006i
563563 359369. 207482.i 1.13377 0.654580i 0.188886 0.981999i 0.439512π-0.439512\pi
0.944879 + 0.327419i 0.106179π0.106179\pi
564564 0 0
565565 −27140.4 + 47008.6i −0.0850197 + 0.147258i
566566 329179.i 1.02754i
567567 0 0
568568 −178914. −0.554559
569569 −229601. 132560.i −0.709169 0.409439i 0.101584 0.994827i 0.467609π-0.467609\pi
−0.810753 + 0.585388i 0.800942π0.800942\pi
570570 0 0
571571 16370.1 + 28353.8i 0.0502086 + 0.0869639i 0.890037 0.455887i 0.150678π-0.150678\pi
−0.839829 + 0.542851i 0.817345π0.817345\pi
572572 −59229.1 + 34195.9i −0.181027 + 0.104516i
573573 0 0
574574 −112055. + 194085.i −0.340102 + 0.589073i
575575 500145.i 1.51272i
576576 0 0
577577 136483. 0.409946 0.204973 0.978768i 0.434289π-0.434289\pi
0.204973 + 0.978768i 0.434289π0.434289\pi
578578 202632. + 116990.i 0.606531 + 0.350181i
579579 0 0
580580 −49521.7 85774.0i −0.147211 0.254976i
581581 −54384.2 + 31398.7i −0.161109 + 0.0930165i
582582 0 0
583583 −34539.2 + 59823.7i −0.101619 + 0.176009i
584584 160935.i 0.471873i
585585 0 0
586586 449208. 1.30813
587587 249463. + 144027.i 0.723984 + 0.417992i 0.816217 0.577745i 0.196067π-0.196067\pi
−0.0922331 + 0.995737i 0.529401π0.529401\pi
588588 0 0
589589 149683. + 259258.i 0.431461 + 0.747312i
590590 −18468.1 + 10662.6i −0.0530541 + 0.0306308i
591591 0 0
592592 75033.7 129962.i 0.214098 0.370829i
593593 272778.i 0.775711i 0.921720 + 0.387856i 0.126784π0.126784\pi
−0.921720 + 0.387856i 0.873216π0.873216\pi
594594 0 0
595595 −14175.3 −0.0400404
596596 −75609.7 43653.3i −0.212856 0.122892i
597597 0 0
598598 282461. + 489238.i 0.789872 + 1.36810i
599599 −68974.2 + 39822.3i −0.192235 + 0.110987i −0.593029 0.805181i 0.702068π-0.702068\pi
0.400793 + 0.916169i 0.368735π0.368735\pi
600600 0 0
601601 −59878.8 + 103713.i −0.165777 + 0.287134i −0.936931 0.349515i 0.886347π-0.886347\pi
0.771154 + 0.636649i 0.219680π0.219680\pi
602602 258393.i 0.712998i
603603 0 0
604604 −22309.7 −0.0611534
605605 104209. + 60165.0i 0.284704 + 0.164374i
606606 0 0
607607 −57220.1 99108.1i −0.155300 0.268987i 0.777868 0.628427i 0.216301π-0.216301\pi
−0.933168 + 0.359440i 0.882968π0.882968\pi
608608 39887.0 23028.8i 0.107901 0.0622965i
609609 0 0
610610 10257.2 17766.0i 0.0275657 0.0477452i
611611 717090.i 1.92084i
612612 0 0
613613 −598912. −1.59383 −0.796915 0.604091i 0.793536π-0.793536\pi
−0.796915 + 0.604091i 0.793536π0.793536\pi
614614 245346. + 141651.i 0.650793 + 0.375735i
615615 0 0
616616 24455.2 + 42357.6i 0.0644480 + 0.111627i
617617 −150704. + 87008.9i −0.395871 + 0.228556i −0.684701 0.728824i 0.740067π-0.740067\pi
0.288830 + 0.957381i 0.406734π0.406734\pi
618618 0 0
619619 368424. 638130.i 0.961540 1.66544i 0.242902 0.970051i 0.421901π-0.421901\pi
0.718638 0.695384i 0.244766π-0.244766\pi
620620 86653.6i 0.225426i
621621 0 0
622622 −152646. −0.394553
623623 −509904. 294393.i −1.31375 0.758493i
624624 0 0
625625 −119450. 206894.i −0.305793 0.529649i
626626 −184970. + 106793.i −0.472012 + 0.272516i
627627 0 0
628628 −9907.38 + 17160.1i −0.0251212 + 0.0435111i
629629 66187.2i 0.167291i
630630 0 0
631631 −26188.6 −0.0657739 −0.0328869 0.999459i 0.510470π-0.510470\pi
−0.0328869 + 0.999459i 0.510470π0.510470\pi
632632 68107.6 + 39322.0i 0.170515 + 0.0984467i
633633 0 0
634634 −94139.7 163055.i −0.234204 0.405653i
635635 161181. 93058.1i 0.399731 0.230785i
636636 0 0
637637 −61994.7 + 107378.i −0.152783 + 0.264628i
638638 150724.i 0.370288i
639639 0 0
640640 13331.7 0.0325481
641641 343687. + 198428.i 0.836462 + 0.482932i 0.856060 0.516876i 0.172905π-0.172905\pi
−0.0195978 + 0.999808i 0.506239π0.506239\pi
642642 0 0
643643 32175.0 + 55728.7i 0.0778209 + 0.134790i 0.902309 0.431089i 0.141870π-0.141870\pi
−0.824489 + 0.565879i 0.808537π0.808537\pi
644644 349878. 202002.i 0.843616 0.487062i
645645 0 0
646646 −10156.8 + 17592.2i −0.0243385 + 0.0421555i
647647 16209.2i 0.0387215i 0.999813 + 0.0193607i 0.00616310π0.00616310\pi
−0.999813 + 0.0193607i 0.993837π0.993837\pi
648648 0 0
649649 −32452.5 −0.0770476
650650 285505. + 164836.i 0.675751 + 0.390145i
651651 0 0
652652 −142188. 246277.i −0.334478 0.579334i
653653 96132.7 55502.2i 0.225447 0.130162i −0.383023 0.923739i 0.625117π-0.625117\pi
0.608470 + 0.793577i 0.291784π0.291784\pi
654654 0 0
655655 −64732.7 + 112120.i −0.150883 + 0.261337i
656656 92961.4i 0.216021i
657657 0 0
658658 −512826. −1.18445
659659 625726. + 361263.i 1.44083 + 0.831865i 0.997905 0.0646920i 0.0206065π-0.0206065\pi
0.442928 + 0.896557i 0.353940π0.353940\pi
660660 0 0
661661 −1621.86 2809.15i −0.00371203 0.00642942i 0.864163 0.503211i 0.167848π-0.167848\pi
−0.867875 + 0.496782i 0.834515π0.834515\pi
662662 170044. 98175.0i 0.388012 0.224019i
663663 0 0
664664 −13024.2 + 22558.6i −0.0295404 + 0.0511655i
665665 127774.i 0.288934i
666666 0 0
667667 −1.24499e6 −2.79843
668668 −367143. 211970.i −0.822776 0.475030i
669669 0 0
670670 37207.0 + 64444.4i 0.0828848 + 0.143561i
671671 27036.2 15609.3i 0.0600482 0.0346689i
672672 0 0
673673 −340188. + 589223.i −0.751085 + 1.30092i 0.196212 + 0.980561i 0.437136π0.437136\pi
−0.947297 + 0.320356i 0.896198π0.896198\pi
674674 251125.i 0.552802i
675675 0 0
676676 −143883. −0.314859
677677 71954.5 + 41542.9i 0.156993 + 0.0906400i 0.576438 0.817141i 0.304442π-0.304442\pi
−0.419445 + 0.907781i 0.637775π0.637775\pi
678678 0 0
679679 −271801. 470772.i −0.589537 1.02111i
680680 −5092.18 + 2939.97i −0.0110125 + 0.00635807i
681681 0 0
682682 −65934.4 + 114202.i −0.141757 + 0.245530i
683683 6386.51i 0.0136906i −0.999977 0.00684529i 0.997821π-0.997821\pi
0.999977 0.00684529i 0.00217894π-0.00217894\pi
684684 0 0
685685 −135787. −0.289385
686686 −244029. 140890.i −0.518554 0.299387i
687687 0 0
688688 −53591.0 92822.3i −0.113218 0.196099i
689689 −325720. + 188055.i −0.686130 + 0.396137i
690690 0 0
691691 −224531. + 388900.i −0.470242 + 0.814483i −0.999421 0.0340275i 0.989167π-0.989167\pi
0.529179 + 0.848510i 0.322500π0.322500\pi
692692 427172.i 0.892054i
693693 0 0
694694 310379. 0.644427
695695 −112719. 65078.3i −0.233360 0.134731i
696696 0 0
697697 −20500.3 35507.6i −0.0421983 0.0730896i
698698 −339938. + 196263.i −0.697733 + 0.402836i
699699 0 0
700700 117882. 204178.i 0.240576 0.416691i
701701 408122.i 0.830527i 0.909701 + 0.415264i 0.136311π0.136311\pi
−0.909701 + 0.415264i 0.863689π0.863689\pi
702702 0 0
703703 596599. 1.20718
704704 17570.0 + 10144.0i 0.0354508 + 0.0204676i
705705 0 0
706706 110060. + 190629.i 0.220810 + 0.382455i
707707 466747. 269476.i 0.933775 0.539115i
708708 0 0
709709 425844. 737584.i 0.847146 1.46730i −0.0365985 0.999330i 0.511652π-0.511652\pi
0.883744 0.467970i 0.155014π-0.155014\pi
710710 205885.i 0.408421i
711711 0 0
712712 −244230. −0.481768
713713 943317. + 544624.i 1.85558 + 1.07132i
714714 0 0
715715 −39350.9 68157.8i −0.0769738 0.133323i
716716 −224809. + 129793.i −0.438517 + 0.253178i
717717 0 0
718718 −276172. + 478344.i −0.535711 + 0.927879i
719719 951431.i 1.84043i −0.391412 0.920215i 0.628013π-0.628013\pi
0.391412 0.920215i 0.371987π-0.371987\pi
720720 0 0
721721 −736698. −1.41716
722722 −160647. 92749.9i −0.308176 0.177926i
723723 0 0
724724 −201525. 349052.i −0.384461 0.665905i
725725 −629202. + 363270.i −1.19705 + 0.691120i
726726 0 0
727727 −410863. + 711636.i −0.777371 + 1.34645i 0.156081 + 0.987744i 0.450114π0.450114\pi
−0.933452 + 0.358702i 0.883219π0.883219\pi
728728 266301.i 0.502470i
729729 0 0
730730 −185196. −0.347525
731731 40939.3 + 23636.3i 0.0766135 + 0.0442328i
732732 0 0
733733 224965. + 389651.i 0.418704 + 0.725217i 0.995809 0.0914530i 0.0291511π-0.0291511\pi
−0.577105 + 0.816670i 0.695818π0.695818\pi
734734 −210179. + 121347.i −0.390120 + 0.225236i
735735 0 0
736736 83790.8 145130.i 0.154682 0.267917i
737737 113243.i 0.208485i
738738 0 0
739739 533367. 0.976647 0.488323 0.872663i 0.337609π-0.337609\pi
0.488323 + 0.872663i 0.337609π0.337609\pi
740740 149554. + 86345.0i 0.273108 + 0.157679i
741741 0 0
742742 134487. + 232938.i 0.244271 + 0.423091i
743743 −505677. + 291952.i −0.915999 + 0.528852i −0.882357 0.470581i 0.844044π-0.844044\pi
−0.0336428 + 0.999434i 0.510711π0.510711\pi
744744 0 0
745745 50234.0 87007.8i 0.0905076 0.156764i
746746 34840.7i 0.0626050i
747747 0 0
748748 −8948.06 −0.0159928
749749 459.324 + 265.191i 0.000818758 + 0.000472710i
750750 0 0
751751 −296313. 513229.i −0.525377 0.909979i −0.999563 0.0295548i 0.990591π-0.990591\pi
0.474186 0.880424i 0.342742π-0.342742\pi
752752 −184222. + 106361.i −0.325766 + 0.188081i
753753 0 0
754754 410320. 710695.i 0.721739 1.25009i
755755 25672.9i 0.0450382i
756756 0 0
757757 −30185.2 −0.0526747 −0.0263373 0.999653i 0.508384π-0.508384\pi
−0.0263373 + 0.999653i 0.508384π0.508384\pi
758758 −529515. 305716.i −0.921594 0.532083i
759759 0 0
760760 26500.4 + 45900.0i 0.0458801 + 0.0794667i
761761 265213. 153121.i 0.457957 0.264402i −0.253228 0.967407i 0.581492π-0.581492\pi
0.711185 + 0.703005i 0.248159π0.248159\pi
762762 0 0
763763 −516295. + 894248.i −0.886846 + 1.53606i
764764 18047.9i 0.0309201i
765765 0 0
766766 −672358. −1.14589
767767 −153021. 88346.6i −0.260112 0.150176i
768768 0 0
769769 −444182. 769346.i −0.751118 1.30097i −0.947281 0.320403i 0.896182π-0.896182\pi
0.196163 0.980571i 0.437152π-0.437152\pi
770770 −48743.0 + 28141.8i −0.0822111 + 0.0474646i
771771 0 0
772772 96128.1 166499.i 0.161293 0.279368i
773773 456476.i 0.763939i 0.924175 + 0.381970i 0.124754π0.124754\pi
−0.924175 + 0.381970i 0.875246π0.875246\pi
774774 0 0
775775 635654. 1.05832
776776 −195277. 112743.i −0.324286 0.187226i
777777 0 0
778778 263475. + 456353.i 0.435292 + 0.753948i
779779 −320059. + 184786.i −0.527418 + 0.304505i
780780 0 0
781781 156657. 271338.i 0.256832 0.444845i
782782 73911.8i 0.120865i
783783 0 0
784784 36780.8 0.0598397
785785 −19747.0 11400.9i −0.0320450 0.0185012i
786786 0 0
787787 −269736. 467196.i −0.435501 0.754310i 0.561835 0.827249i 0.310095π-0.310095\pi
−0.997336 + 0.0729393i 0.976762π0.976762\pi
788788 462975. 267299.i 0.745598 0.430471i
789789 0 0
790790 −45249.7 + 78374.8i −0.0725039 + 0.125581i
791791 321640.i 0.514064i
792792 0 0
793793 169975. 0.270296
794794 12258.9 + 7077.71i 0.0194452 + 0.0112267i
795795 0 0
796796 −33701.1 58372.1i −0.0531886 0.0921254i
797797 435416. 251387.i 0.685468 0.395755i −0.116444 0.993197i 0.537150π-0.537150\pi
0.801912 + 0.597442i 0.203816π0.203816\pi
798798 0 0
799799 46910.3 81251.0i 0.0734809 0.127273i
800800 97795.6i 0.152806i
801801 0 0
802802 499157. 0.776048
803803 −244072. 140915.i −0.378519 0.218538i
804804 0 0
805805 232454. + 402621.i 0.358711 + 0.621305i
806806 −621791. + 358991.i −0.957138 + 0.552604i
807807 0 0
808808 111779. 193607.i 0.171214 0.296551i
809809 699315.i 1.06850i 0.845326 + 0.534251i 0.179406π0.179406\pi
−0.845326 + 0.534251i 0.820594π0.820594\pi
810810 0 0
811811 741168. 1.12687 0.563437 0.826159i 0.309479π-0.309479\pi
0.563437 + 0.826159i 0.309479π0.309479\pi
812812 −508253. 293440.i −0.770846 0.445048i
813813 0 0
814814 131399. + 227590.i 0.198310 + 0.343483i
815815 283403. 163623.i 0.426667 0.246336i
816816 0 0
817817 213053. 369019.i 0.319186 0.552846i
818818 533763.i 0.797704i
819819 0 0
820820 −106975. −0.159095
821821 58936.9 + 34027.3i 0.0874382 + 0.0504825i 0.543082 0.839680i 0.317257π-0.317257\pi
−0.455643 + 0.890162i 0.650591π0.650591\pi
822822 0 0
823823 −325915. 564502.i −0.481177 0.833423i 0.518590 0.855023i 0.326457π-0.326457\pi
−0.999767 + 0.0216000i 0.993124π0.993124\pi
824824 −264643. + 152792.i −0.389768 + 0.225033i
825825 0 0
826826 −63181.0 + 109433.i −0.0926033 + 0.160394i
827827 36453.4i 0.0532999i −0.999645 0.0266500i 0.991516π-0.991516\pi
0.999645 0.0266500i 0.00848395π-0.00848395\pi
828828 0 0
829829 78480.8 0.114197 0.0570984 0.998369i 0.481815π-0.481815\pi
0.0570984 + 0.998369i 0.481815π0.481815\pi
830830 −25959.3 14987.6i −0.0376823 0.0217559i
831831 0 0
832832 55231.0 + 95662.9i 0.0797878 + 0.138196i
833833 −14048.8 + 8111.09i −0.0202465 + 0.0116893i
834834 0 0
835835 243924. 422489.i 0.349850 0.605958i
836836 80656.1i 0.115405i
837837 0 0
838838 −33956.4 −0.0483541
839839 59633.8 + 34429.6i 0.0847166 + 0.0489111i 0.541760 0.840533i 0.317758π-0.317758\pi
−0.457043 + 0.889444i 0.651092π0.651092\pi
840840 0 0
841841 550632. + 953723.i 0.778520 + 1.34844i
842842 136180. 78623.4i 0.192083 0.110899i
843843 0 0
844844 −134800. + 233480.i −0.189236 + 0.327767i
845845 165573.i 0.231887i
846846 0 0
847847 713014. 0.993874
848848 96623.2 + 55785.5i 0.134366 + 0.0775763i
849849 0 0
850850 21566.4 + 37354.1i 0.0298497 + 0.0517011i
851851 1.87992e6 1.08537e6i 2.59585 1.49871i
852852 0 0
853853 −412386. + 714273.i −0.566768 + 0.981671i 0.430115 + 0.902774i 0.358473π0.358473\pi
−0.996883 + 0.0788970i 0.974860π0.974860\pi
854854 121558.i 0.166674i
855855 0 0
856856 220.003 0.000300249
857857 561077. + 323938.i 0.763942 + 0.441062i 0.830709 0.556706i 0.187935π-0.187935\pi
−0.0667670 + 0.997769i 0.521268π0.521268\pi
858858 0 0
859859 657566. + 1.13894e6i 0.891154 + 1.54352i 0.838493 + 0.544912i 0.183437π0.183437\pi
0.0526607 + 0.998612i 0.483230π0.483230\pi
860860 106815. 61669.8i 0.144423 0.0833826i
861861 0 0
862862 73640.4 127549.i 0.0991063 0.171657i
863863 1.27319e6i 1.70951i 0.519028 + 0.854757i 0.326294π0.326294\pi
−0.519028 + 0.854757i 0.673706π0.673706\pi
864864 0 0
865865 491568. 0.656979
866866 −503030. 290424.i −0.670746 0.387255i
867867 0 0
868868 256732. + 444673.i 0.340754 + 0.590203i
869869 −119270. + 68860.7i −0.157940 + 0.0911868i
870870 0 0
871871 −308285. + 533965.i −0.406365 + 0.703844i
872872 428320.i 0.563294i
873873 0 0
874874 666227. 0.872166
875875 506775. + 292586.i 0.661910 + 0.382154i
876876 0 0
877877 352514. + 610572.i 0.458329 + 0.793848i 0.998873 0.0474673i 0.0151150π-0.0151150\pi
−0.540544 + 0.841316i 0.681782π0.681782\pi
878878 795018. 459004.i 1.03131 0.595425i
879879 0 0
880880 −11673.3 + 20218.7i −0.0150739 + 0.0261088i
881881 750647.i 0.967128i 0.875309 + 0.483564i 0.160658π0.160658\pi
−0.875309 + 0.483564i 0.839342π0.839342\pi
882882 0 0
883883 −638249. −0.818594 −0.409297 0.912401i 0.634226π-0.634226\pi
−0.409297 + 0.912401i 0.634226π0.634226\pi
884884 −42192.1 24359.6i −0.0539917 0.0311721i
885885 0 0
886886 −243275. 421364.i −0.309906 0.536772i
887887 −985132. + 568766.i −1.25212 + 0.722914i −0.971531 0.236914i 0.923864π-0.923864\pi
−0.280592 + 0.959827i 0.590531π0.590531\pi
888888 0 0
889889 551415. 955078.i 0.697710 1.20847i
890890 281047.i 0.354812i
891891 0 0
892892 164250. 0.206432
893893 −732381. 422840.i −0.918405 0.530241i
894894 0 0
895895 −149359. 258698.i −0.186460 0.322959i
896896 68413.2 39498.4i 0.0852166 0.0491998i
897897 0 0
898898 172018. 297944.i 0.213315 0.369472i
899899 1.58231e6i 1.95781i
900900 0 0
901901 −49208.3 −0.0606162
902902 −140984. 81397.1i −0.173283 0.100045i
903903 0 0
904904 66708.5 + 115542.i 0.0816289 + 0.141385i
905905 401671. 231905.i 0.490425 0.283147i
906906 0 0
907907 652106. 1.12948e6i 0.792690 1.37298i −0.131606 0.991302i 0.542013π-0.542013\pi
0.924296 0.381677i 0.124653π-0.124653\pi
908908 468534.i 0.568289i
909909 0 0
910910 −306445. −0.370059
911911 −936156. 540490.i −1.12801 0.651254i −0.184573 0.982819i 0.559090π-0.559090\pi
−0.943433 + 0.331564i 0.892424π0.892424\pi
912912 0 0
913913 −22808.1 39504.8i −0.0273620 0.0473923i
914914 −114021. + 65829.8i −0.136487 + 0.0788008i
915915 0 0
916916 −29154.2 + 50496.6i −0.0347465 + 0.0601826i
917917 767145.i 0.912303i
918918 0 0
919919 558574. 0.661378 0.330689 0.943740i 0.392719π-0.392719\pi
0.330689 + 0.943740i 0.392719π0.392719\pi
920920 167008. + 96422.1i 0.197316 + 0.113920i
921921 0 0
922922 288884. + 500361.i 0.339829 + 0.588602i
923923 1.47735e6 852947.i 1.73412 1.00120i
924924 0 0
925925 633390. 1.09706e6i 0.740266 1.28218i
926926 48849.9i 0.0569695i
927927 0 0
928928 −243439. −0.282679
929929 764452. + 441357.i 0.885765 + 0.511397i 0.872555 0.488516i 0.162462π-0.162462\pi
0.0132104 + 0.999913i 0.495795π0.495795\pi
930930 0 0
931931 73111.8 + 126633.i 0.0843506 + 0.146100i
932932 −94118.7 + 54339.5i −0.108354 + 0.0625581i
933933 0 0
934934 310652. 538065.i 0.356107 0.616795i
935935 10297.0i 0.0117784i
936936 0 0
937937 893683. 1.01790 0.508949 0.860797i 0.330034π-0.330034\pi
0.508949 + 0.860797i 0.330034π0.330034\pi
938938 381865. + 220470.i 0.434014 + 0.250578i
939939 0 0
940940 −122394. 211993.i −0.138518 0.239920i
941941 −408726. + 235978.i −0.461587 + 0.266497i −0.712711 0.701458i 0.752533π-0.752533\pi
0.251125 + 0.967955i 0.419200π0.419200\pi
942942 0 0
943943 −672348. + 1.16454e6i −0.756085 + 1.30958i
944944 52415.2i 0.0588184i
945945 0 0
946946 187697. 0.209737
947947 −629058. 363187.i −0.701441 0.404977i 0.106443 0.994319i 0.466054π-0.466054\pi
−0.807884 + 0.589342i 0.799387π0.799387\pi
948948 0 0
949949 −767237. 1.32889e6i −0.851916 1.47556i
950950 336702. 194395.i 0.373078 0.215396i
951951 0 0
952952 −17420.8 + 30173.7i −0.0192218 + 0.0332931i
953953 41574.8i 0.0457767i 0.999738 + 0.0228884i 0.00728623π0.00728623\pi
−0.999738 + 0.0228884i 0.992714π0.992714\pi
954954 0 0
955955 −20768.6 −0.0227720
956956 179350. + 103548.i 0.196239 + 0.113299i
957957 0 0
958958 −128769. 223035.i −0.140307 0.243020i
959959 −696807. + 402302.i −0.757662 + 0.437436i
960960 0 0
961961 −230424. + 399106.i −0.249506 + 0.432157i
962962 1.43085e6i 1.54612i
963963 0 0
964964 74887.7 0.0805855
965965 191598. + 110619.i 0.205749 + 0.118789i
966966 0 0
967967 600282. + 1.03972e6i 0.641952 + 1.11189i 0.984996 + 0.172575i 0.0552086π0.0552086\pi
−0.343044 + 0.939319i 0.611458π0.611458\pi
968968 256135. 147880.i 0.273350 0.157819i
969969 0 0
970970 129739. 224715.i 0.137888 0.238830i
971971 1.38244e6i 1.46625i −0.680092 0.733127i 0.738060π-0.738060\pi
0.680092 0.733127i 0.261940π-0.261940\pi
972972 0 0
973973 −771241. −0.814638
974974 359096. + 207324.i 0.378523 + 0.218541i
975975 0 0
976976 −25211.2 43667.1i −0.0264663 0.0458410i
977977 −124404. + 71824.7i −0.130330 + 0.0752463i −0.563748 0.825947i 0.690641π-0.690641\pi
0.433417 + 0.901193i 0.357308π0.357308\pi
978978 0 0
979979 213848. 370395.i 0.223120 0.386456i
980980 42325.5i 0.0440707i
981981 0 0
982982 137061. 0.142132
983983 −492098. 284113.i −0.509266 0.294025i 0.223266 0.974758i 0.428328π-0.428328\pi
−0.732532 + 0.680733i 0.761661π0.761661\pi
984984 0 0
985985 307594. + 532768.i 0.317033 + 0.549118i
986986 92983.9 53684.3i 0.0956432 0.0552196i
987987 0 0
988988 −219573. + 380312.i −0.224939 + 0.389606i
989989 1.55040e6i 1.58508i
990990 0 0
991991 −920749. −0.937549 −0.468774 0.883318i 0.655304π-0.655304\pi
−0.468774 + 0.883318i 0.655304π0.655304\pi
992992 184451. + 106493.i 0.187438 + 0.108218i
993993 0 0
994994 −609985. 1.05652e6i −0.617371 1.06932i
995995 67171.6 38781.6i 0.0678484 0.0391723i
996996 0 0
997997 −500709. + 867254.i −0.503727 + 0.872481i 0.496264 + 0.868172i 0.334705π0.334705\pi
−0.999991 + 0.00430895i 0.998628π0.998628\pi
998998 701487.i 0.704302i
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 162.5.d.d.107.4 8
3.2 odd 2 inner 162.5.d.d.107.1 8
9.2 odd 6 162.5.b.a.161.3 yes 4
9.4 even 3 inner 162.5.d.d.53.1 8
9.5 odd 6 inner 162.5.d.d.53.4 8
9.7 even 3 162.5.b.a.161.2 4
36.7 odd 6 1296.5.e.b.161.2 4
36.11 even 6 1296.5.e.b.161.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.5.b.a.161.2 4 9.7 even 3
162.5.b.a.161.3 yes 4 9.2 odd 6
162.5.d.d.53.1 8 9.4 even 3 inner
162.5.d.d.53.4 8 9.5 odd 6 inner
162.5.d.d.107.1 8 3.2 odd 2 inner
162.5.d.d.107.4 8 1.1 even 1 trivial
1296.5.e.b.161.2 4 36.7 odd 6
1296.5.e.b.161.3 4 36.11 even 6