Properties

Label 162.4.c.j.55.1
Level 162162
Weight 44
Character 162.55
Analytic conductor 9.5589.558
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,4,Mod(55,162)]
 
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([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 162=234 162 = 2 \cdot 3^{4}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 162.c (of order 33, 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: 9.558309420939.55830942093
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 33 3^{3}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 55.1
Root 0.8660250.500000i-0.866025 - 0.500000i of defining polynomial
Character χ\chi == 162.55
Dual form 162.4.c.j.109.1

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+(1.000001.73205i)q2+(2.000003.46410i)q4+(0.401924+0.696152i)q5+(1.196152.07180i)q78.00000q8+1.60770q10+(29.784651.5885i)q11+(38.873167.3301i)q13+(2.392304.14359i)q14+(8.00000+13.8564i)q162.84232q17118.315q19+(1.607702.78461i)q20+(59.5692103.177i)q22+(55.3923+95.9423i)q23+(62.1769107.694i)q25155.492q269.56922q28+(62.8135108.796i)q29+(31.530754.6128i)q31+(16.0000+27.7128i)q32+(2.84232+4.92305i)q34+1.92305q35227.392q37+(118.315+204.928i)q38+(3.215395.56922i)q40+(162.315+281.138i)q41+(136.412236.272i)q43238.277q44+221.569q46+(2.46926+4.27688i)q47+(168.638+292.090i)q49+(124.354215.387i)q50+(155.492+269.321i)q52+598.908q53+47.8846q55+(9.56922+16.5744i)q56+(125.627217.592i)q58+(335.138580.477i)q59+(232.265+402.295i)q61126.123q62+64.0000q64+(31.248054.1232i)q65+(384.535+666.033i)q67+(5.68465+9.84610i)q68+(1.923053.33082i)q70+611.569q71+923.831q73+(227.392+393.855i)q74+(236.631+409.856i)q76+(71.2539123.415i)q77+(19.9038+34.4744i)q7912.8616q80+649.261q82+(221.885384.315i)q83+(1.142401.97869i)q85+(272.823472.543i)q86+(238.277+412.708i)q88+78.4576q89185.992q91+(221.569383.769i)q92+(4.93851+8.55376i)q94+(47.553882.3655i)q95+(45.507778.8217i)q97+674.554q98+O(q100)q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(0.401924 + 0.696152i) q^{5} +(1.19615 - 2.07180i) q^{7} -8.00000 q^{8} +1.60770 q^{10} +(29.7846 - 51.5885i) q^{11} +(-38.8731 - 67.3301i) q^{13} +(-2.39230 - 4.14359i) q^{14} +(-8.00000 + 13.8564i) q^{16} -2.84232 q^{17} -118.315 q^{19} +(1.60770 - 2.78461i) q^{20} +(-59.5692 - 103.177i) q^{22} +(55.3923 + 95.9423i) q^{23} +(62.1769 - 107.694i) q^{25} -155.492 q^{26} -9.56922 q^{28} +(62.8135 - 108.796i) q^{29} +(-31.5307 - 54.6128i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-2.84232 + 4.92305i) q^{34} +1.92305 q^{35} -227.392 q^{37} +(-118.315 + 204.928i) q^{38} +(-3.21539 - 5.56922i) q^{40} +(162.315 + 281.138i) q^{41} +(136.412 - 236.272i) q^{43} -238.277 q^{44} +221.569 q^{46} +(-2.46926 + 4.27688i) q^{47} +(168.638 + 292.090i) q^{49} +(-124.354 - 215.387i) q^{50} +(-155.492 + 269.321i) q^{52} +598.908 q^{53} +47.8846 q^{55} +(-9.56922 + 16.5744i) q^{56} +(-125.627 - 217.592i) q^{58} +(-335.138 - 580.477i) q^{59} +(-232.265 + 402.295i) q^{61} -126.123 q^{62} +64.0000 q^{64} +(31.2480 - 54.1232i) q^{65} +(384.535 + 666.033i) q^{67} +(5.68465 + 9.84610i) q^{68} +(1.92305 - 3.33082i) q^{70} +611.569 q^{71} +923.831 q^{73} +(-227.392 + 393.855i) q^{74} +(236.631 + 409.856i) q^{76} +(-71.2539 - 123.415i) q^{77} +(-19.9038 + 34.4744i) q^{79} -12.8616 q^{80} +649.261 q^{82} +(221.885 - 384.315i) q^{83} +(-1.14240 - 1.97869i) q^{85} +(-272.823 - 472.543i) q^{86} +(-238.277 + 412.708i) q^{88} +78.4576 q^{89} -185.992 q^{91} +(221.569 - 383.769i) q^{92} +(4.93851 + 8.55376i) q^{94} +(-47.5538 - 82.3655i) q^{95} +(45.5077 - 78.8217i) q^{97} +674.554 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q28q4+12q516q732q8+48q10+36q1110q13+32q1432q16240q1716q19+48q2072q22+180q23+124q2540q26++1368q98+O(q100) 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 16 q^{7} - 32 q^{8} + 48 q^{10} + 36 q^{11} - 10 q^{13} + 32 q^{14} - 32 q^{16} - 240 q^{17} - 16 q^{19} + 48 q^{20} - 72 q^{22} + 180 q^{23} + 124 q^{25} - 40 q^{26}+ \cdots + 1368 q^{98}+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(23)e\left(\frac{2}{3}\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 1.00000 1.73205i 0.353553 0.612372i
33 0 0
44 −2.00000 3.46410i −0.250000 0.433013i
55 0.401924 + 0.696152i 0.0359492 + 0.0622658i 0.883440 0.468544i 0.155221π-0.155221\pi
−0.847491 + 0.530810i 0.821888π0.821888\pi
66 0 0
77 1.19615 2.07180i 0.0645862 0.111867i −0.831924 0.554889i 0.812761π-0.812761\pi
0.896510 + 0.443023i 0.146094π0.146094\pi
88 −8.00000 −0.353553
99 0 0
1010 1.60770 0.0508398
1111 29.7846 51.5885i 0.816400 1.41405i −0.0919186 0.995767i 0.529300π-0.529300\pi
0.908318 0.418279i 0.137367π-0.137367\pi
1212 0 0
1313 −38.8731 67.3301i −0.829342 1.43646i −0.898555 0.438861i 0.855382π-0.855382\pi
0.0692128 0.997602i 0.477951π-0.477951\pi
1414 −2.39230 4.14359i −0.0456693 0.0791016i
1515 0 0
1616 −8.00000 + 13.8564i −0.125000 + 0.216506i
1717 −2.84232 −0.0405509 −0.0202754 0.999794i 0.506454π-0.506454\pi
−0.0202754 + 0.999794i 0.506454π0.506454\pi
1818 0 0
1919 −118.315 −1.42860 −0.714300 0.699840i 0.753255π-0.753255\pi
−0.714300 + 0.699840i 0.753255π0.753255\pi
2020 1.60770 2.78461i 0.0179746 0.0311329i
2121 0 0
2222 −59.5692 103.177i −0.577282 0.999881i
2323 55.3923 + 95.9423i 0.502178 + 0.869798i 0.999997 + 0.00251677i 0.000801112π0.000801112\pi
−0.497819 + 0.867281i 0.665866π0.665866\pi
2424 0 0
2525 62.1769 107.694i 0.497415 0.861549i
2626 −155.492 −1.17287
2727 0 0
2828 −9.56922 −0.0645862
2929 62.8135 108.796i 0.402213 0.696653i −0.591780 0.806100i 0.701575π-0.701575\pi
0.993993 + 0.109447i 0.0349079π0.0349079\pi
3030 0 0
3131 −31.5307 54.6128i −0.182680 0.316412i 0.760112 0.649792i 0.225144π-0.225144\pi
−0.942792 + 0.333380i 0.891811π0.891811\pi
3232 16.0000 + 27.7128i 0.0883883 + 0.153093i
3333 0 0
3434 −2.84232 + 4.92305i −0.0143369 + 0.0248322i
3535 1.92305 0.00928727
3636 0 0
3737 −227.392 −1.01035 −0.505177 0.863016i 0.668573π-0.668573\pi
−0.505177 + 0.863016i 0.668573π0.668573\pi
3838 −118.315 + 204.928i −0.505086 + 0.874835i
3939 0 0
4040 −3.21539 5.56922i −0.0127099 0.0220143i
4141 162.315 + 281.138i 0.618278 + 1.07089i 0.989800 + 0.142465i 0.0455028π0.0455028\pi
−0.371522 + 0.928424i 0.621164π0.621164\pi
4242 0 0
4343 136.412 236.272i 0.483781 0.837933i −0.516046 0.856561i 0.672597π-0.672597\pi
0.999826 + 0.0186284i 0.00592994π0.00592994\pi
4444 −238.277 −0.816400
4545 0 0
4646 221.569 0.710187
4747 −2.46926 + 4.27688i −0.00766336 + 0.0132733i −0.869832 0.493349i 0.835773π-0.835773\pi
0.862168 + 0.506622i 0.169106π0.169106\pi
4848 0 0
4949 168.638 + 292.090i 0.491657 + 0.851575i
5050 −124.354 215.387i −0.351726 0.609207i
5151 0 0
5252 −155.492 + 269.321i −0.414671 + 0.718231i
5353 598.908 1.55219 0.776097 0.630614i 0.217197π-0.217197\pi
0.776097 + 0.630614i 0.217197π0.217197\pi
5454 0 0
5555 47.8846 0.117396
5656 −9.56922 + 16.5744i −0.0228347 + 0.0395508i
5757 0 0
5858 −125.627 217.592i −0.284407 0.492608i
5959 −335.138 580.477i −0.739514 1.28088i −0.952714 0.303867i 0.901722π-0.901722\pi
0.213201 0.977008i 0.431611π-0.431611\pi
6060 0 0
6161 −232.265 + 402.295i −0.487517 + 0.844404i −0.999897 0.0143547i 0.995431π-0.995431\pi
0.512380 + 0.858759i 0.328764π0.328764\pi
6262 −126.123 −0.258349
6363 0 0
6464 64.0000 0.125000
6565 31.2480 54.1232i 0.0596283 0.103279i
6666 0 0
6767 384.535 + 666.033i 0.701170 + 1.21446i 0.968056 + 0.250734i 0.0806718π0.0806718\pi
−0.266886 + 0.963728i 0.585995π0.585995\pi
6868 5.68465 + 9.84610i 0.0101377 + 0.0175590i
6969 0 0
7070 1.92305 3.33082i 0.00328355 0.00568727i
7171 611.569 1.02225 0.511126 0.859506i 0.329228π-0.329228\pi
0.511126 + 0.859506i 0.329228π0.329228\pi
7272 0 0
7373 923.831 1.48118 0.740590 0.671957i 0.234546π-0.234546\pi
0.740590 + 0.671957i 0.234546π0.234546\pi
7474 −227.392 + 393.855i −0.357214 + 0.618712i
7575 0 0
7676 236.631 + 409.856i 0.357150 + 0.618602i
7777 −71.2539 123.415i −0.105456 0.182656i
7878 0 0
7979 −19.9038 + 34.4744i −0.0283462 + 0.0490971i −0.879851 0.475251i 0.842357π-0.842357\pi
0.851504 + 0.524348i 0.175691π0.175691\pi
8080 −12.8616 −0.0179746
8181 0 0
8282 649.261 0.874377
8383 221.885 384.315i 0.293434 0.508242i −0.681186 0.732111i 0.738535π-0.738535\pi
0.974619 + 0.223869i 0.0718687π0.0718687\pi
8484 0 0
8585 −1.14240 1.97869i −0.00145777 0.00252493i
8686 −272.823 472.543i −0.342085 0.592508i
8787 0 0
8888 −238.277 + 412.708i −0.288641 + 0.499941i
8989 78.4576 0.0934437 0.0467218 0.998908i 0.485123π-0.485123\pi
0.0467218 + 0.998908i 0.485123π0.485123\pi
9090 0 0
9191 −185.992 −0.214256
9292 221.569 383.769i 0.251089 0.434899i
9393 0 0
9494 4.93851 + 8.55376i 0.00541882 + 0.00938566i
9595 −47.5538 82.3655i −0.0513570 0.0889529i
9696 0 0
9797 45.5077 78.8217i 0.0476352 0.0825065i −0.841225 0.540686i 0.818165π-0.818165\pi
0.888860 + 0.458179i 0.151498π0.151498\pi
9898 674.554 0.695308
9999 0 0
100100 −497.415 −0.497415
101101 −811.261 + 1405.15i −0.799243 + 1.38433i 0.120867 + 0.992669i 0.461433π0.461433\pi
−0.920110 + 0.391661i 0.871901π0.871901\pi
102102 0 0
103103 374.115 + 647.987i 0.357890 + 0.619884i 0.987608 0.156940i 0.0501629π-0.0501629\pi
−0.629718 + 0.776824i 0.716830π0.716830\pi
104104 310.985 + 538.641i 0.293217 + 0.507866i
105105 0 0
106106 598.908 1037.34i 0.548783 0.950521i
107107 −1435.00 −1.29651 −0.648255 0.761423i 0.724501π-0.724501\pi
−0.648255 + 0.761423i 0.724501π0.724501\pi
108108 0 0
109109 −83.1305 −0.0730501 −0.0365250 0.999333i 0.511629π-0.511629\pi
−0.0365250 + 0.999333i 0.511629π0.511629\pi
110110 47.8846 82.9385i 0.0415056 0.0718898i
111111 0 0
112112 19.1384 + 33.1487i 0.0161465 + 0.0279666i
113113 486.098 + 841.946i 0.404675 + 0.700917i 0.994284 0.106772i 0.0340514π-0.0340514\pi
−0.589609 + 0.807689i 0.700718π0.700718\pi
114114 0 0
115115 −44.5270 + 77.1230i −0.0361058 + 0.0625370i
116116 −502.508 −0.402213
117117 0 0
118118 −1340.55 −1.04583
119119 −3.39985 + 5.88872i −0.00261902 + 0.00453628i
120120 0 0
121121 −1108.75 1920.40i −0.833017 1.44283i
122122 464.531 + 804.591i 0.344727 + 0.597084i
123123 0 0
124124 −126.123 + 218.451i −0.0913401 + 0.158206i
125125 200.442 0.143425
126126 0 0
127127 −1316.13 −0.919588 −0.459794 0.888026i 0.652077π-0.652077\pi
−0.459794 + 0.888026i 0.652077π0.652077\pi
128128 64.0000 110.851i 0.0441942 0.0765466i
129129 0 0
130130 −62.4960 108.246i −0.0421636 0.0730295i
131131 −557.638 965.858i −0.371917 0.644179i 0.617944 0.786222i 0.287966π-0.287966\pi
−0.989860 + 0.142044i 0.954633π0.954633\pi
132132 0 0
133133 −141.523 + 245.125i −0.0922678 + 0.159813i
134134 1538.14 0.991604
135135 0 0
136136 22.7386 0.0143369
137137 308.571 534.461i 0.192431 0.333300i −0.753624 0.657305i 0.771696π-0.771696\pi
0.946055 + 0.324005i 0.105030π0.105030\pi
138138 0 0
139139 −1078.28 1867.64i −0.657978 1.13965i −0.981138 0.193307i 0.938079π-0.938079\pi
0.323161 0.946344i 0.395255π-0.395255\pi
140140 −3.84610 6.66164i −0.00232182 0.00402151i
141141 0 0
142142 611.569 1059.27i 0.361421 0.625999i
143143 −4631.28 −2.70830
144144 0 0
145145 100.985 0.0578368
146146 923.831 1600.12i 0.523676 0.907034i
147147 0 0
148148 454.785 + 787.710i 0.252588 + 0.437496i
149149 1785.84 + 3093.17i 0.981893 + 1.70069i 0.655004 + 0.755626i 0.272667π0.272667\pi
0.326889 + 0.945063i 0.394000π0.394000\pi
150150 0 0
151151 1130.72 1958.46i 0.609379 1.05548i −0.381963 0.924177i 0.624752π-0.624752\pi
0.991343 0.131299i 0.0419147π-0.0419147\pi
152152 946.523 0.505086
153153 0 0
154154 −285.015 −0.149138
155155 25.3459 43.9004i 0.0131344 0.0227495i
156156 0 0
157157 −914.627 1584.18i −0.464937 0.805295i 0.534261 0.845319i 0.320590π-0.320590\pi
−0.999199 + 0.0400243i 0.987256π0.987256\pi
158158 39.8076 + 68.9488i 0.0200438 + 0.0347169i
159159 0 0
160160 −12.8616 + 22.2769i −0.00635497 + 0.0110071i
161161 265.031 0.129735
162162 0 0
163163 268.554 0.129048 0.0645238 0.997916i 0.479447π-0.479447\pi
0.0645238 + 0.997916i 0.479447π0.479447\pi
164164 649.261 1124.55i 0.309139 0.535444i
165165 0 0
166166 −443.769 768.631i −0.207489 0.359381i
167167 −2027.26 3511.32i −0.939366 1.62703i −0.766657 0.642057i 0.778081π-0.778081\pi
−0.172710 0.984973i 0.555252π-0.555252\pi
168168 0 0
169169 −1923.73 + 3332.00i −0.875617 + 1.51661i
170170 −4.56959 −0.00206160
171171 0 0
172172 −1091.29 −0.483781
173173 873.675 1513.25i 0.383955 0.665030i −0.607668 0.794191i 0.707895π-0.707895\pi
0.991624 + 0.129161i 0.0412283π0.0412283\pi
174174 0 0
175175 −148.746 257.636i −0.0642523 0.111288i
176176 476.554 + 825.415i 0.204100 + 0.353511i
177177 0 0
178178 78.4576 135.892i 0.0330373 0.0572223i
179179 2037.71 0.850868 0.425434 0.904989i 0.360121π-0.360121\pi
0.425434 + 0.904989i 0.360121π0.360121\pi
180180 0 0
181181 2820.68 1.15834 0.579169 0.815207i 0.303377π-0.303377\pi
0.579169 + 0.815207i 0.303377π0.303377\pi
182182 −185.992 + 322.148i −0.0757510 + 0.131205i
183183 0 0
184184 −443.138 767.538i −0.177547 0.307520i
185185 −91.3944 158.300i −0.0363213 0.0629104i
186186 0 0
187187 −84.6575 + 146.631i −0.0331057 + 0.0573408i
188188 19.7541 0.00766336
189189 0 0
190190 −190.215 −0.0726297
191191 219.862 380.811i 0.0832912 0.144265i −0.821371 0.570395i 0.806790π-0.806790\pi
0.904662 + 0.426130i 0.140123π0.140123\pi
192192 0 0
193193 231.338 + 400.689i 0.0862802 + 0.149442i 0.905936 0.423415i 0.139169π-0.139169\pi
−0.819656 + 0.572856i 0.805835π0.805835\pi
194194 −91.0155 157.643i −0.0336831 0.0583409i
195195 0 0
196196 674.554 1168.36i 0.245829 0.425788i
197197 −1036.60 −0.374896 −0.187448 0.982275i 0.560022π-0.560022\pi
−0.187448 + 0.982275i 0.560022π0.560022\pi
198198 0 0
199199 −1190.22 −0.423980 −0.211990 0.977272i 0.567994π-0.567994\pi
−0.211990 + 0.977272i 0.567994π0.567994\pi
200200 −497.415 + 861.549i −0.175863 + 0.304603i
201201 0 0
202202 1622.52 + 2810.29i 0.565150 + 0.978869i
203203 −150.269 260.273i −0.0519547 0.0899883i
204204 0 0
205205 −130.477 + 225.992i −0.0444531 + 0.0769951i
206206 1496.46 0.506133
207207 0 0
208208 1243.94 0.414671
209209 −3523.98 + 6103.71i −1.16631 + 2.02011i
210210 0 0
211211 2464.00 + 4267.78i 0.803929 + 1.39245i 0.917012 + 0.398860i 0.130594π0.130594\pi
−0.113083 + 0.993586i 0.536073π0.536073\pi
212212 −1197.82 2074.68i −0.388049 0.672120i
213213 0 0
214214 −1435.00 + 2485.49i −0.458386 + 0.793947i
215215 219.308 0.0695660
216216 0 0
217217 −150.862 −0.0471945
218218 −83.1305 + 143.986i −0.0258271 + 0.0447339i
219219 0 0
220220 −95.7691 165.877i −0.0293489 0.0508338i
221221 110.490 + 191.374i 0.0336305 + 0.0582498i
222222 0 0
223223 735.235 1273.46i 0.220785 0.382410i −0.734262 0.678866i 0.762472π-0.762472\pi
0.955046 + 0.296456i 0.0958049π0.0958049\pi
224224 76.5538 0.0228347
225225 0 0
226226 1944.39 0.572296
227227 1051.13 1820.61i 0.307339 0.532327i −0.670440 0.741964i 0.733895π-0.733895\pi
0.977779 + 0.209637i 0.0672281π0.0672281\pi
228228 0 0
229229 500.519 + 866.924i 0.144433 + 0.250166i 0.929161 0.369674i 0.120531π-0.120531\pi
−0.784728 + 0.619840i 0.787197π0.787197\pi
230230 89.0539 + 154.246i 0.0255306 + 0.0442203i
231231 0 0
232232 −502.508 + 870.369i −0.142204 + 0.246304i
233233 6280.78 1.76596 0.882978 0.469415i 0.155535π-0.155535\pi
0.882978 + 0.469415i 0.155535π0.155535\pi
234234 0 0
235235 −3.96981 −0.00110197
236236 −1340.55 + 2321.91i −0.369757 + 0.640438i
237237 0 0
238238 6.79970 + 11.7774i 0.00185193 + 0.00320764i
239239 −508.685 881.068i −0.137674 0.238458i 0.788942 0.614468i 0.210629π-0.210629\pi
−0.926616 + 0.376010i 0.877296π0.877296\pi
240240 0 0
241241 460.646 797.862i 0.123124 0.213257i −0.797874 0.602824i 0.794042π-0.794042\pi
0.920998 + 0.389567i 0.127375π0.127375\pi
242242 −4434.98 −1.17806
243243 0 0
244244 1858.12 0.487517
245245 −135.560 + 234.796i −0.0353493 + 0.0612268i
246246 0 0
247247 4599.28 + 7966.19i 1.18480 + 2.05213i
248248 252.246 + 436.903i 0.0645872 + 0.111868i
249249 0 0
250250 200.442 347.177i 0.0507084 0.0878295i
251251 −2262.40 −0.568930 −0.284465 0.958686i 0.591816π-0.591816\pi
−0.284465 + 0.958686i 0.591816π0.591816\pi
252252 0 0
253253 6599.35 1.63991
254254 −1316.13 + 2279.60i −0.325124 + 0.563130i
255255 0 0
256256 −128.000 221.703i −0.0312500 0.0541266i
257257 2393.32 + 4145.36i 0.580901 + 1.00615i 0.995373 + 0.0960877i 0.0306329π0.0306329\pi
−0.414472 + 0.910062i 0.636034π0.636034\pi
258258 0 0
259259 −271.996 + 471.111i −0.0652548 + 0.113025i
260260 −249.984 −0.0596283
261261 0 0
262262 −2230.55 −0.525970
263263 −1503.96 + 2604.94i −0.352617 + 0.610750i −0.986707 0.162509i 0.948041π-0.948041\pi
0.634090 + 0.773259i 0.281375π0.281375\pi
264264 0 0
265265 240.715 + 416.931i 0.0558001 + 0.0966485i
266266 283.046 + 490.251i 0.0652432 + 0.113005i
267267 0 0
268268 1538.14 2664.13i 0.350585 0.607231i
269269 6559.73 1.48682 0.743409 0.668837i 0.233208π-0.233208\pi
0.743409 + 0.668837i 0.233208π0.233208\pi
270270 0 0
271271 −5147.64 −1.15386 −0.576931 0.816793i 0.695750π-0.695750\pi
−0.576931 + 0.816793i 0.695750π0.695750\pi
272272 22.7386 39.3844i 0.00506886 0.00877952i
273273 0 0
274274 −617.143 1068.92i −0.136069 0.235679i
275275 −3703.83 6415.22i −0.812180 1.40674i
276276 0 0
277277 533.831 924.622i 0.115793 0.200560i −0.802303 0.596917i 0.796392π-0.796392\pi
0.918097 + 0.396357i 0.129726π0.129726\pi
278278 −4313.14 −0.930521
279279 0 0
280280 −15.3844 −0.00328355
281281 2093.24 3625.59i 0.444384 0.769696i −0.553625 0.832766i 0.686756π-0.686756\pi
0.998009 + 0.0630699i 0.0200891π0.0200891\pi
282282 0 0
283283 −2678.48 4639.26i −0.562611 0.974471i −0.997268 0.0738746i 0.976464π-0.976464\pi
0.434657 0.900596i 0.356870π-0.356870\pi
284284 −1223.14 2118.54i −0.255563 0.442648i
285285 0 0
286286 −4631.28 + 8021.61i −0.957528 + 1.65849i
287287 776.616 0.159729
288288 0 0
289289 −4904.92 −0.998356
290290 100.985 174.911i 0.0204484 0.0354177i
291291 0 0
292292 −1847.66 3200.24i −0.370295 0.641370i
293293 1447.89 + 2507.83i 0.288692 + 0.500030i 0.973498 0.228696i 0.0734462π-0.0734462\pi
−0.684805 + 0.728726i 0.740113π0.740113\pi
294294 0 0
295295 269.400 466.615i 0.0531698 0.0920928i
296296 1819.14 0.357214
297297 0 0
298298 7143.38 1.38861
299299 4306.54 7459.14i 0.832955 1.44272i
300300 0 0
301301 −326.338 565.234i −0.0624911 0.108238i
302302 −2261.43 3916.91i −0.430896 0.746334i
303303 0 0
304304 946.523 1639.43i 0.178575 0.309301i
305305 −373.412 −0.0701033
306306 0 0
307307 1855.49 0.344947 0.172473 0.985014i 0.444824π-0.444824\pi
0.172473 + 0.985014i 0.444824π0.444824\pi
308308 −285.015 + 493.661i −0.0527281 + 0.0913278i
309309 0 0
310310 −50.6918 87.8008i −0.00928743 0.0160863i
311311 3585.85 + 6210.87i 0.653809 + 1.13243i 0.982191 + 0.187886i 0.0601635π0.0601635\pi
−0.328382 + 0.944545i 0.606503π0.606503\pi
312312 0 0
313313 655.415 1135.21i 0.118359 0.205003i −0.800759 0.598987i 0.795570π-0.795570\pi
0.919117 + 0.393984i 0.128903π0.128903\pi
314314 −3658.51 −0.657521
315315 0 0
316316 159.230 0.0283462
317317 1844.63 3195.00i 0.326829 0.566085i −0.655052 0.755584i 0.727353π-0.727353\pi
0.981881 + 0.189499i 0.0606865π0.0606865\pi
318318 0 0
319319 −3741.75 6480.90i −0.656733 1.13749i
320320 25.7231 + 44.5538i 0.00449364 + 0.00778322i
321321 0 0
322322 265.031 459.046i 0.0458682 0.0794461i
323323 336.290 0.0579310
324324 0 0
325325 −9668.03 −1.65011
326326 268.554 465.149i 0.0456252 0.0790252i
327327 0 0
328328 −1298.52 2249.11i −0.218594 0.378616i
329329 5.90721 + 10.2316i 0.000989894 + 0.00171455i
330330 0 0
331331 1622.48 2810.22i 0.269425 0.466657i −0.699289 0.714839i 0.746500π-0.746500\pi
0.968713 + 0.248182i 0.0798331π0.0798331\pi
332332 −1775.08 −0.293434
333333 0 0
334334 −8109.04 −1.32846
335335 −309.107 + 535.389i −0.0504129 + 0.0873177i
336336 0 0
337337 −2150.83 3725.35i −0.347665 0.602174i 0.638169 0.769896i 0.279692π-0.279692\pi
−0.985834 + 0.167722i 0.946359π0.946359\pi
338338 3847.46 + 6664.00i 0.619155 + 1.07241i
339339 0 0
340340 −4.56959 + 7.91476i −0.000728885 + 0.00126247i
341341 −3756.52 −0.596561
342342 0 0
343343 1627.43 0.256189
344344 −1091.29 + 1890.17i −0.171042 + 0.296254i
345345 0 0
346346 −1747.35 3026.50i −0.271497 0.470247i
347347 −1652.10 2861.52i −0.255589 0.442693i 0.709466 0.704739i 0.248936π-0.248936\pi
−0.965055 + 0.262046i 0.915603π0.915603\pi
348348 0 0
349349 −2254.35 + 3904.65i −0.345767 + 0.598886i −0.985493 0.169717i 0.945715π-0.945715\pi
0.639726 + 0.768603i 0.279048π0.279048\pi
350350 −594.985 −0.0908665
351351 0 0
352352 1906.22 0.288641
353353 3443.37 5964.09i 0.519184 0.899254i −0.480567 0.876958i 0.659569π-0.659569\pi
0.999751 0.0222956i 0.00709751π-0.00709751\pi
354354 0 0
355355 245.804 + 425.745i 0.0367491 + 0.0636513i
356356 −156.915 271.785i −0.0233609 0.0404623i
357357 0 0
358358 2037.71 3529.41i 0.300827 0.521048i
359359 1529.31 0.224829 0.112415 0.993661i 0.464141π-0.464141\pi
0.112415 + 0.993661i 0.464141π0.464141\pi
360360 0 0
361361 7139.52 1.04090
362362 2820.68 4885.56i 0.409534 0.709335i
363363 0 0
364364 371.985 + 644.297i 0.0535640 + 0.0927756i
365365 371.310 + 643.127i 0.0532472 + 0.0922269i
366366 0 0
367367 5115.68 8860.62i 0.727620 1.26027i −0.230267 0.973128i 0.573960π-0.573960\pi
0.957886 0.287147i 0.0927069π-0.0927069\pi
368368 −1772.55 −0.251089
369369 0 0
370370 −365.578 −0.0513661
371371 716.385 1240.81i 0.100250 0.173639i
372372 0 0
373373 −473.215 819.632i −0.0656894 0.113777i 0.831310 0.555809i 0.187591π-0.187591\pi
−0.897000 + 0.442031i 0.854258π0.854258\pi
374374 169.315 + 293.262i 0.0234093 + 0.0405461i
375375 0 0
376376 19.7541 34.2150i 0.00270941 0.00469283i
377377 −9767.01 −1.33429
378378 0 0
379379 −8717.46 −1.18149 −0.590746 0.806857i 0.701167π-0.701167\pi
−0.590746 + 0.806857i 0.701167π0.701167\pi
380380 −190.215 + 329.462i −0.0256785 + 0.0444764i
381381 0 0
382382 −439.723 761.623i −0.0588958 0.102011i
383383 6130.77 + 10618.8i 0.817931 + 1.41670i 0.907204 + 0.420691i 0.138212π0.138212\pi
−0.0892728 + 0.996007i 0.528454π0.528454\pi
384384 0 0
385385 57.2772 99.2071i 0.00758213 0.0131326i
386386 925.353 0.122019
387387 0 0
388388 −364.062 −0.0476352
389389 −6605.53 + 11441.1i −0.860961 + 1.49123i 0.0100423 + 0.999950i 0.496803π0.496803\pi
−0.871003 + 0.491278i 0.836530π0.836530\pi
390390 0 0
391391 −157.443 272.699i −0.0203638 0.0352711i
392392 −1349.11 2336.72i −0.173827 0.301077i
393393 0 0
394394 −1036.60 + 1795.44i −0.132546 + 0.229576i
395395 −31.9993 −0.00407609
396396 0 0
397397 −5211.93 −0.658890 −0.329445 0.944175i 0.606862π-0.606862\pi
−0.329445 + 0.944175i 0.606862π0.606862\pi
398398 −1190.22 + 2061.51i −0.149900 + 0.259634i
399399 0 0
400400 994.831 + 1723.10i 0.124354 + 0.215387i
401401 492.817 + 853.584i 0.0613719 + 0.106299i 0.895079 0.445908i 0.147119π-0.147119\pi
−0.833707 + 0.552207i 0.813786π0.813786\pi
402402 0 0
403403 −2451.39 + 4245.94i −0.303009 + 0.524827i
404404 6490.09 0.799243
405405 0 0
406406 −601.076 −0.0734751
407407 −6772.79 + 11730.8i −0.824852 + 1.42869i
408408 0 0
409409 337.323 + 584.261i 0.0407813 + 0.0706354i 0.885696 0.464266i 0.153682π-0.153682\pi
−0.844914 + 0.534902i 0.820349π0.820349\pi
410410 260.954 + 451.985i 0.0314331 + 0.0544438i
411411 0 0
412412 1496.46 2591.95i 0.178945 0.309942i
413413 −1603.51 −0.191049
414414 0 0
415415 356.723 0.0421948
416416 1243.94 2154.56i 0.146608 0.253933i
417417 0 0
418418 7047.95 + 12207.4i 0.824705 + 1.42843i
419419 −3752.82 6500.07i −0.437559 0.757874i 0.559942 0.828532i 0.310823π-0.310823\pi
−0.997501 + 0.0706581i 0.977490π0.977490\pi
420420 0 0
421421 676.312 1171.41i 0.0782932 0.135608i −0.824220 0.566269i 0.808386π-0.808386\pi
0.902514 + 0.430661i 0.141720π0.141720\pi
422422 9856.01 1.13693
423423 0 0
424424 −4791.26 −0.548783
425425 −176.727 + 306.100i −0.0201706 + 0.0349365i
426426 0 0
427427 555.650 + 962.413i 0.0629737 + 0.109074i
428428 2870.00 + 4970.98i 0.324128 + 0.561406i
429429 0 0
430430 219.308 379.853i 0.0245953 0.0426003i
431431 −4003.21 −0.447397 −0.223698 0.974658i 0.571813π-0.571813\pi
−0.223698 + 0.974658i 0.571813π0.571813\pi
432432 0 0
433433 9975.38 1.10713 0.553564 0.832807i 0.313267π-0.313267\pi
0.553564 + 0.832807i 0.313267π0.313267\pi
434434 −150.862 + 261.301i −0.0166858 + 0.0289006i
435435 0 0
436436 166.261 + 287.973i 0.0182625 + 0.0316316i
437437 −6553.76 11351.4i −0.717412 1.24259i
438438 0 0
439439 −8680.46 + 15035.0i −0.943726 + 1.63458i −0.185444 + 0.982655i 0.559372π0.559372\pi
−0.758282 + 0.651927i 0.773961π0.773961\pi
440440 −383.077 −0.0415056
441441 0 0
442442 441.959 0.0475608
443443 4287.71 7426.54i 0.459854 0.796491i −0.539099 0.842243i 0.681235π-0.681235\pi
0.998953 + 0.0457517i 0.0145683π0.0145683\pi
444444 0 0
445445 31.5340 + 54.6184i 0.00335922 + 0.00581834i
446446 −1470.47 2546.93i −0.156118 0.270405i
447447 0 0
448448 76.5538 132.595i 0.00807327 0.0139833i
449449 4703.77 0.494398 0.247199 0.968965i 0.420490π-0.420490\pi
0.247199 + 0.968965i 0.420490π0.420490\pi
450450 0 0
451451 19338.0 2.01905
452452 1944.39 3367.78i 0.202337 0.350459i
453453 0 0
454454 −2102.26 3641.22i −0.217322 0.376412i
455455 −74.7548 129.479i −0.00770233 0.0133408i
456456 0 0
457457 3523.40 6102.71i 0.360651 0.624667i −0.627417 0.778684i 0.715888π-0.715888\pi
0.988068 + 0.154017i 0.0492211π0.0492211\pi
458458 2002.08 0.204259
459459 0 0
460460 356.216 0.0361058
461461 −2885.13 + 4997.19i −0.291484 + 0.504864i −0.974161 0.225856i 0.927482π-0.927482\pi
0.682677 + 0.730720i 0.260816π0.260816\pi
462462 0 0
463463 6799.57 + 11777.2i 0.682511 + 1.18214i 0.974212 + 0.225634i 0.0724455π0.0724455\pi
−0.291701 + 0.956510i 0.594221π0.594221\pi
464464 1005.02 + 1740.74i 0.100553 + 0.174163i
465465 0 0
466466 6280.78 10878.6i 0.624359 1.08142i
467467 5730.52 0.567831 0.283915 0.958849i 0.408367π-0.408367\pi
0.283915 + 0.958849i 0.408367π0.408367\pi
468468 0 0
469469 1839.85 0.181143
470470 −3.96981 + 6.87592i −0.000389604 + 0.000674813i
471471 0 0
472472 2681.11 + 4643.81i 0.261458 + 0.452858i
473473 −8125.93 14074.5i −0.789917 1.36818i
474474 0 0
475475 −7356.48 + 12741.8i −0.710608 + 1.23081i
476476 27.1988 0.00261902
477477 0 0
478478 −2034.74 −0.194701
479479 −7284.14 + 12616.5i −0.694824 + 1.20347i 0.275416 + 0.961325i 0.411184π0.411184\pi
−0.970240 + 0.242145i 0.922149π0.922149\pi
480480 0 0
481481 8839.44 + 15310.4i 0.837928 + 1.45133i
482482 −921.292 1595.72i −0.0870616 0.150795i
483483 0 0
484484 −4434.98 + 7681.62i −0.416509 + 0.721414i
485485 73.1626 0.00684977
486486 0 0
487487 7164.51 0.666642 0.333321 0.942813i 0.391831π-0.391831\pi
0.333321 + 0.942813i 0.391831π0.391831\pi
488488 1858.12 3218.36i 0.172363 0.298542i
489489 0 0
490490 271.119 + 469.592i 0.0249957 + 0.0432939i
491491 4755.03 + 8235.96i 0.437050 + 0.756993i 0.997460 0.0712222i 0.0226899π-0.0226899\pi
−0.560410 + 0.828215i 0.689357π0.689357\pi
492492 0 0
493493 −178.536 + 309.234i −0.0163101 + 0.0282499i
494494 18397.1 1.67556
495495 0 0
496496 1008.98 0.0913401
497497 731.530 1267.05i 0.0660234 0.114356i
498498 0 0
499499 −10742.8 18607.1i −0.963756 1.66927i −0.712921 0.701245i 0.752628π-0.752628\pi
−0.250835 0.968030i 0.580705π-0.580705\pi
500500 −400.885 694.353i −0.0358562 0.0621048i
501501 0 0
502502 −2262.40 + 3918.59i −0.201147 + 0.348397i
503503 −11603.2 −1.02855 −0.514274 0.857626i 0.671939π-0.671939\pi
−0.514274 + 0.857626i 0.671939π0.671939\pi
504504 0 0
505505 −1304.26 −0.114928
506506 6599.35 11430.4i 0.579796 1.00424i
507507 0 0
508508 2632.26 + 4559.21i 0.229897 + 0.398193i
509509 −4469.87 7742.04i −0.389241 0.674184i 0.603107 0.797660i 0.293929π-0.293929\pi
−0.992348 + 0.123476i 0.960596π0.960596\pi
510510 0 0
511511 1105.04 1913.99i 0.0956638 0.165695i
512512 −512.000 −0.0441942
513513 0 0
514514 9573.30 0.821518
515515 −300.732 + 520.883i −0.0257317 + 0.0445686i
516516 0 0
517517 147.092 + 254.770i 0.0125127 + 0.0216727i
518518 543.992 + 942.221i 0.0461421 + 0.0799205i
519519 0 0
520520 −249.984 + 432.985i −0.0210818 + 0.0365147i
521521 −7410.10 −0.623114 −0.311557 0.950227i 0.600851π-0.600851\pi
−0.311557 + 0.950227i 0.600851π0.600851\pi
522522 0 0
523523 18970.8 1.58611 0.793054 0.609151i 0.208490π-0.208490\pi
0.793054 + 0.609151i 0.208490π0.208490\pi
524524 −2230.55 + 3863.43i −0.185958 + 0.322089i
525525 0 0
526526 3007.92 + 5209.88i 0.249338 + 0.431866i
527527 89.6206 + 155.227i 0.00740784 + 0.0128308i
528528 0 0
529529 −53.1149 + 91.9977i −0.00436549 + 0.00756124i
530530 962.861 0.0789132
531531 0 0
532532 1132.19 0.0922678
533533 12619.4 21857.4i 1.02553 1.77627i
534534 0 0
535535 −576.760 998.978i −0.0466085 0.0807282i
536536 −3076.28 5328.27i −0.247901 0.429377i
537537 0 0
538538 6559.73 11361.8i 0.525669 0.910486i
539539 20091.3 1.60556
540540 0 0
541541 −11440.4 −0.909169 −0.454584 0.890704i 0.650212π-0.650212\pi
−0.454584 + 0.890704i 0.650212π0.650212\pi
542542 −5147.64 + 8915.97i −0.407952 + 0.706594i
543543 0 0
544544 −45.4772 78.7688i −0.00358422 0.00620806i
545545 −33.4121 57.8715i −0.00262609 0.00454852i
546546 0 0
547547 −5126.48 + 8879.32i −0.400717 + 0.694063i −0.993813 0.111070i 0.964572π-0.964572\pi
0.593095 + 0.805132i 0.297906π0.297906\pi
548548 −2468.57 −0.192431
549549 0 0
550550 −14815.3 −1.14860
551551 −7431.80 + 12872.3i −0.574601 + 0.995238i
552552 0 0
553553 47.6160 + 82.4733i 0.00366155 + 0.00634199i
554554 −1067.66 1849.24i −0.0818783 0.141817i
555555 0 0
556556 −4313.14 + 7470.57i −0.328989 + 0.569825i
557557 −15336.5 −1.16666 −0.583328 0.812236i 0.698250π-0.698250\pi
−0.583328 + 0.812236i 0.698250π0.698250\pi
558558 0 0
559559 −21210.9 −1.60488
560560 −15.3844 + 26.6465i −0.00116091 + 0.00201075i
561561 0 0
562562 −4186.47 7251.18i −0.314227 0.544257i
563563 3850.69 + 6669.58i 0.288254 + 0.499271i 0.973393 0.229142i 0.0735919π-0.0735919\pi
−0.685139 + 0.728412i 0.740259π0.740259\pi
564564 0 0
565565 −390.749 + 676.796i −0.0290954 + 0.0503948i
566566 −10713.9 −0.795652
567567 0 0
568568 −4892.55 −0.361421
569569 −8869.63 + 15362.6i −0.653487 + 1.13187i 0.328784 + 0.944405i 0.393361π0.393361\pi
−0.982271 + 0.187467i 0.939972π0.939972\pi
570570 0 0
571571 −6911.55 11971.2i −0.506549 0.877369i −0.999971 0.00757865i 0.997588π-0.997588\pi
0.493422 0.869790i 0.335746π-0.335746\pi
572572 9262.55 + 16043.2i 0.677075 + 1.17273i
573573 0 0
574574 776.616 1345.14i 0.0564727 0.0978135i
575575 13776.5 0.999164
576576 0 0
577577 −15339.1 −1.10672 −0.553359 0.832943i 0.686654π-0.686654\pi
−0.553359 + 0.832943i 0.686654π0.686654\pi
578578 −4904.92 + 8495.57i −0.352972 + 0.611365i
579579 0 0
580580 −201.970 349.822i −0.0144592 0.0250441i
581581 −530.816 919.399i −0.0379035 0.0656508i
582582 0 0
583583 17838.2 30896.7i 1.26721 2.19487i
584584 −7390.65 −0.523676
585585 0 0
586586 5791.58 0.408273
587587 7383.26 12788.2i 0.519148 0.899191i −0.480604 0.876937i 0.659583π-0.659583\pi
0.999752 0.0222531i 0.00708396π-0.00708396\pi
588588 0 0
589589 3730.57 + 6461.54i 0.260977 + 0.452026i
590590 −538.800 933.230i −0.0375967 0.0651194i
591591 0 0
592592 1819.14 3150.84i 0.126294 0.218748i
593593 −17603.6 −1.21904 −0.609522 0.792769i 0.708639π-0.708639\pi
−0.609522 + 0.792769i 0.708639π0.708639\pi
594594 0 0
595595 −5.46593 −0.000376607
596596 7143.38 12372.7i 0.490946 0.850344i
597597 0 0
598598 −8613.08 14918.3i −0.588988 1.02016i
599599 11400.6 + 19746.3i 0.777653 + 1.34693i 0.933291 + 0.359120i 0.116923π0.116923\pi
−0.155638 + 0.987814i 0.549743π0.549743\pi
600600 0 0
601601 −952.624 + 1649.99i −0.0646562 + 0.111988i −0.896541 0.442960i 0.853928π-0.853928\pi
0.831885 + 0.554948i 0.187262π0.187262\pi
602602 −1305.35 −0.0883757
603603 0 0
604604 −9045.72 −0.609379
605605 891.263 1543.71i 0.0598925 0.103737i
606606 0 0
607607 1294.61 + 2242.33i 0.0865678 + 0.149940i 0.906058 0.423153i 0.139077π-0.139077\pi
−0.819490 + 0.573093i 0.805743π0.805743\pi
608608 −1893.05 3278.85i −0.126272 0.218709i
609609 0 0
610610 −373.412 + 646.768i −0.0247853 + 0.0429293i
611611 383.950 0.0254222
612612 0 0
613613 16930.4 1.11552 0.557759 0.830003i 0.311661π-0.311661\pi
0.557759 + 0.830003i 0.311661π0.311661\pi
614614 1855.49 3213.81i 0.121957 0.211236i
615615 0 0
616616 570.031 + 987.323i 0.0372844 + 0.0645785i
617617 6406.72 + 11096.8i 0.418030 + 0.724050i 0.995741 0.0921917i 0.0293872π-0.0293872\pi
−0.577711 + 0.816241i 0.696054π0.696054\pi
618618 0 0
619619 −5133.79 + 8891.99i −0.333351 + 0.577382i −0.983167 0.182711i 0.941513π-0.941513\pi
0.649815 + 0.760092i 0.274846π0.274846\pi
620620 −202.767 −0.0131344
621621 0 0
622622 14343.4 0.924626
623623 93.8472 162.548i 0.00603517 0.0104532i
624624 0 0
625625 −7691.55 13322.2i −0.492259 0.852618i
626626 −1310.83 2270.42i −0.0836922 0.144959i
627627 0 0
628628 −3658.51 + 6336.72i −0.232469 + 0.402648i
629629 646.322 0.0409707
630630 0 0
631631 −21887.5 −1.38087 −0.690433 0.723397i 0.742580π-0.742580\pi
−0.690433 + 0.723397i 0.742580π0.742580\pi
632632 159.230 275.795i 0.0100219 0.0173585i
633633 0 0
634634 −3689.26 6389.99i −0.231103 0.400282i
635635 −528.984 916.227i −0.0330584 0.0572589i
636636 0 0
637637 13111.0 22708.9i 0.815504 1.41249i
638638 −14967.0 −0.928760
639639 0 0
640640 102.892 0.00635497
641641 8601.84 14898.8i 0.530035 0.918047i −0.469351 0.883012i 0.655512π-0.655512\pi
0.999386 0.0350356i 0.0111545π-0.0111545\pi
642642 0 0
643643 −6282.79 10882.1i −0.385333 0.667416i 0.606482 0.795097i 0.292580π-0.292580\pi
−0.991815 + 0.127681i 0.959247π0.959247\pi
644644 −530.061 918.093i −0.0324337 0.0561769i
645645 0 0
646646 336.290 582.472i 0.0204817 0.0354753i
647647 −3552.55 −0.215866 −0.107933 0.994158i 0.534423π-0.534423\pi
−0.107933 + 0.994158i 0.534423π0.534423\pi
648648 0 0
649649 −39927.9 −2.41496
650650 −9668.03 + 16745.5i −0.583402 + 1.01048i
651651 0 0
652652 −537.108 930.297i −0.0322619 0.0558792i
653653 2885.50 + 4997.83i 0.172922 + 0.299511i 0.939440 0.342712i 0.111346π-0.111346\pi
−0.766518 + 0.642223i 0.778012π0.778012\pi
654654 0 0
655655 448.256 776.402i 0.0267402 0.0463153i
656656 −5194.09 −0.309139
657657 0 0
658658 23.6289 0.00139992
659659 8239.20 14270.7i 0.487032 0.843564i −0.512857 0.858474i 0.671413π-0.671413\pi
0.999889 + 0.0149104i 0.00474631π0.00474631\pi
660660 0 0
661661 2281.62 + 3951.88i 0.134258 + 0.232542i 0.925314 0.379202i 0.123801π-0.123801\pi
−0.791056 + 0.611744i 0.790468π0.790468\pi
662662 −3244.96 5620.44i −0.190512 0.329977i
663663 0 0
664664 −1775.08 + 3074.52i −0.103744 + 0.179691i
665665 −227.526 −0.0132678
666666 0 0
667667 13917.5 0.807929
668668 −8109.04 + 14045.3i −0.469683 + 0.813515i
669669 0 0
670670 618.214 + 1070.78i 0.0356473 + 0.0617430i
671671 13835.9 + 23964.4i 0.796017 + 1.37874i
672672 0 0
673673 6576.14 11390.2i 0.376659 0.652393i −0.613915 0.789372i 0.710406π-0.710406\pi
0.990574 + 0.136980i 0.0437395π0.0437395\pi
674674 −8603.32 −0.491673
675675 0 0
676676 15389.8 0.875617
677677 7438.07 12883.1i 0.422257 0.731371i −0.573903 0.818924i 0.694571π-0.694571\pi
0.996160 + 0.0875524i 0.0279045π0.0279045\pi
678678 0 0
679679 −108.868 188.566i −0.00615314 0.0106576i
680680 9.13918 + 15.8295i 0.000515399 + 0.000892698i
681681 0 0
682682 −3756.52 + 6506.49i −0.210916 + 0.365317i
683683 24082.4 1.34918 0.674588 0.738195i 0.264321π-0.264321\pi
0.674588 + 0.738195i 0.264321π0.264321\pi
684684 0 0
685685 496.089 0.0276709
686686 1627.43 2818.79i 0.0905766 0.156883i
687687 0 0
688688 2182.58 + 3780.35i 0.120945 + 0.209483i
689689 −23281.4 40324.5i −1.28730 2.22967i
690690 0 0
691691 −6445.10 + 11163.2i −0.354824 + 0.614573i −0.987088 0.160180i 0.948792π-0.948792\pi
0.632264 + 0.774753i 0.282126π0.282126\pi
692692 −6989.40 −0.383955
693693 0 0
694694 −6608.40 −0.361457
695695 866.776 1501.30i 0.0473075 0.0819390i
696696 0 0
697697 −461.353 799.086i −0.0250717 0.0434255i
698698 4508.71 + 7809.31i 0.244494 + 0.423477i
699699 0 0
700700 −594.985 + 1030.54i −0.0321261 + 0.0556441i
701701 11887.0 0.640467 0.320233 0.947339i 0.396239π-0.396239\pi
0.320233 + 0.947339i 0.396239π0.396239\pi
702702 0 0
703703 26904.0 1.44339
704704 1906.22 3301.66i 0.102050 0.176756i
705705 0 0
706706 −6886.74 11928.2i −0.367119 0.635868i
707707 1940.78 + 3361.54i 0.103240 + 0.178817i
708708 0 0
709709 −2907.22 + 5035.45i −0.153996 + 0.266728i −0.932693 0.360672i 0.882547π-0.882547\pi
0.778697 + 0.627400i 0.215881π0.215881\pi
710710 983.217 0.0519711
711711 0 0
712712 −627.661 −0.0330373
713713 3493.12 6050.26i 0.183476 0.317790i
714714 0 0
715715 −1861.42 3224.07i −0.0973611 0.168634i
716716 −4075.42 7058.83i −0.212717 0.368437i
717717 0 0
718718 1529.31 2648.84i 0.0794892 0.137679i
719719 −4488.23 −0.232800 −0.116400 0.993202i 0.537135π-0.537135\pi
−0.116400 + 0.993202i 0.537135π0.537135\pi
720720 0 0
721721 1790.00 0.0924590
722722 7139.52 12366.0i 0.368013 0.637418i
723723 0 0
724724 −5641.35 9771.11i −0.289585 0.501575i
725725 −7811.10 13529.2i −0.400134 0.693052i
726726 0 0
727727 −11592.0 + 20077.9i −0.591366 + 1.02428i 0.402682 + 0.915340i 0.368078π0.368078\pi
−0.994049 + 0.108937i 0.965255π0.965255\pi
728728 1487.94 0.0757510
729729 0 0
730730 1485.24 0.0753029
731731 −387.726 + 671.561i −0.0196177 + 0.0339789i
732732 0 0
733733 10338.7 + 17907.2i 0.520967 + 0.902341i 0.999703 + 0.0243822i 0.00776185π0.00776185\pi
−0.478736 + 0.877959i 0.658905π0.658905\pi
734734 −10231.4 17721.2i −0.514505 0.891149i
735735 0 0
736736 −1772.55 + 3070.15i −0.0887734 + 0.153760i
737737 45812.8 2.28974
738738 0 0
739739 −13001.7 −0.647191 −0.323595 0.946196i 0.604892π-0.604892\pi
−0.323595 + 0.946196i 0.604892π0.604892\pi
740740 −365.578 + 633.199i −0.0181607 + 0.0314552i
741741 0 0
742742 −1432.77 2481.63i −0.0708876 0.122781i
743743 4633.55 + 8025.54i 0.228786 + 0.396270i 0.957449 0.288603i 0.0931909π-0.0931909\pi
−0.728662 + 0.684873i 0.759858π0.759858\pi
744744 0 0
745745 −1435.55 + 2486.44i −0.0705964 + 0.122277i
746746 −1892.86 −0.0928988
747747 0 0
748748 677.260 0.0331057
749749 −1716.48 + 2973.03i −0.0837367 + 0.145036i
750750 0 0
751751 15361.1 + 26606.3i 0.746385 + 1.29278i 0.949545 + 0.313632i 0.101546π0.101546\pi
−0.203159 + 0.979146i 0.565121π0.565121\pi
752752 −39.5081 68.4300i −0.00191584 0.00331833i
753753 0 0
754754 −9767.01 + 16917.0i −0.471742 + 0.817081i
755755 1817.85 0.0876267
756756 0 0
757757 5356.86 0.257197 0.128599 0.991697i 0.458952π-0.458952\pi
0.128599 + 0.991697i 0.458952π0.458952\pi
758758 −8717.46 + 15099.1i −0.417721 + 0.723514i
759759 0 0
760760 380.430 + 658.924i 0.0181574 + 0.0314496i
761761 5009.51 + 8676.72i 0.238626 + 0.413313i 0.960320 0.278899i 0.0899696π-0.0899696\pi
−0.721694 + 0.692212i 0.756636π0.756636\pi
762762 0 0
763763 −99.4368 + 172.230i −0.00471802 + 0.00817186i
764764 −1758.89 −0.0832912
765765 0 0
766766 24523.1 1.15673
767767 −26055.7 + 45129.8i −1.22662 + 2.12457i
768768 0 0
769769 8775.55 + 15199.7i 0.411514 + 0.712764i 0.995056 0.0993198i 0.0316667π-0.0316667\pi
−0.583541 + 0.812084i 0.698333π0.698333\pi
770770 −114.554 198.414i −0.00536137 0.00928617i
771771 0 0
772772 925.353 1602.76i 0.0431401 0.0747209i
773773 −17144.5 −0.797731 −0.398866 0.917009i 0.630596π-0.630596\pi
−0.398866 + 0.917009i 0.630596π0.630596\pi
774774 0 0
775775 −7841.94 −0.363472
776776 −364.062 + 630.574i −0.0168416 + 0.0291705i
777777 0 0
778778 13211.1 + 22882.2i 0.608791 + 1.05446i
779779 −19204.4 33263.0i −0.883272 1.52987i
780780 0 0
781781 18215.4 31549.9i 0.834567 1.44551i
782782 −629.771 −0.0287987
783783 0 0
784784 −5396.43 −0.245829
785785 735.220 1273.44i 0.0334282 0.0578994i
786786 0 0
787787 4297.73 + 7443.89i 0.194660 + 0.337161i 0.946789 0.321855i 0.104306π-0.104306\pi
−0.752129 + 0.659016i 0.770973π0.770973\pi
788788 2073.19 + 3590.88i 0.0937239 + 0.162335i
789789 0 0
790790 −31.9993 + 55.4243i −0.00144112 + 0.00249609i
791791 2325.79 0.104546
792792 0 0
793793 36115.5 1.61727
794794 −5211.93 + 9027.33i −0.232953 + 0.403486i
795795 0 0
796796 2380.43 + 4123.03i 0.105995 + 0.183589i
797797 10418.9 + 18046.1i 0.463057 + 0.802039i 0.999112 0.0421447i 0.0134190π-0.0134190\pi
−0.536054 + 0.844184i 0.680086π0.680086\pi
798798 0 0
799799 7.01843 12.1563i 0.000310756 0.000538245i
800800 3979.32 0.175863
801801 0 0
802802 1971.27 0.0867929
803803 27515.9 47659.0i 1.20924 2.09446i
804804 0 0
805805 106.522 + 184.502i 0.00466386 + 0.00807805i
806806 4902.79 + 8491.88i 0.214260 + 0.371109i
807807 0 0
808808 6490.09 11241.2i 0.282575 0.489434i
809809 −6529.43 −0.283761 −0.141880 0.989884i 0.545315π-0.545315\pi
−0.141880 + 0.989884i 0.545315π0.545315\pi
810810 0 0
811811 29764.0 1.28873 0.644363 0.764720i 0.277123π-0.277123\pi
0.644363 + 0.764720i 0.277123π0.277123\pi
812812 −601.076 + 1041.09i −0.0259774 + 0.0449941i
813813 0 0
814814 13545.6 + 23461.6i 0.583258 + 1.01023i
815815 107.938 + 186.954i 0.00463915 + 0.00803525i
816816 0 0
817817 −16139.6 + 27954.6i −0.691129 + 1.19707i
818818 1349.29 0.0576735
819819 0 0
820820 1043.81 0.0444531
821821 −14785.6 + 25609.4i −0.628527 + 1.08864i 0.359321 + 0.933214i 0.383008π0.383008\pi
−0.987847 + 0.155426i 0.950325π0.950325\pi
822822 0 0
823823 −3056.22 5293.52i −0.129445 0.224205i 0.794017 0.607896i 0.207986π-0.207986\pi
−0.923462 + 0.383691i 0.874653π0.874653\pi
824824 −2992.92 5183.90i −0.126533 0.219162i
825825 0 0
826826 −1603.51 + 2777.35i −0.0675462 + 0.116993i
827827 3265.87 0.137322 0.0686612 0.997640i 0.478127π-0.478127\pi
0.0686612 + 0.997640i 0.478127π0.478127\pi
828828 0 0
829829 −19327.8 −0.809747 −0.404874 0.914373i 0.632685π-0.632685\pi
−0.404874 + 0.914373i 0.632685π0.632685\pi
830830 356.723 617.862i 0.0149181 0.0258389i
831831 0 0
832832 −2487.88 4309.13i −0.103668 0.179558i
833833 −479.325 830.215i −0.0199371 0.0345321i
834834 0 0
835835 1629.61 2822.57i 0.0675389 0.116981i
836836 28191.8 1.16631
837837 0 0
838838 −15011.3 −0.618801
839839 −18819.1 + 32595.6i −0.774382 + 1.34127i 0.160760 + 0.986994i 0.448606π0.448606\pi
−0.935141 + 0.354275i 0.884728π0.884728\pi
840840 0 0
841841 4303.44 + 7453.77i 0.176450 + 0.305620i
842842 −1352.62 2342.81i −0.0553617 0.0958892i
843843 0 0
844844 9856.01 17071.1i 0.401964 0.696223i
845845 −3092.77 −0.125911
846846 0 0
847847 −5304.92 −0.215206
848848 −4791.26 + 8298.71i −0.194024 + 0.336060i
849849 0 0
850850 353.454 + 612.200i 0.0142628 + 0.0247039i
851851 −12595.8 21816.5i −0.507377 0.878803i
852852 0 0
853853 −20934.8 + 36260.2i −0.840322 + 1.45548i 0.0493012 + 0.998784i 0.484301π0.484301\pi
−0.889623 + 0.456696i 0.849033π0.849033\pi
854854 2222.60 0.0890583
855855 0 0
856856 11480.0 0.458386
857857 −16536.5 + 28642.0i −0.659131 + 1.14165i 0.321711 + 0.946838i 0.395742π0.395742\pi
−0.980841 + 0.194810i 0.937591π0.937591\pi
858858 0 0
859859 7304.84 + 12652.4i 0.290149 + 0.502553i 0.973845 0.227214i 0.0729618π-0.0729618\pi
−0.683696 + 0.729767i 0.739628π0.739628\pi
860860 −438.616 759.706i −0.0173915 0.0301230i
861861 0 0
862862 −4003.21 + 6933.77i −0.158179 + 0.273973i
863863 118.786 0.00468543 0.00234271 0.999997i 0.499254π-0.499254\pi
0.00234271 + 0.999997i 0.499254π0.499254\pi
864864 0 0
865865 1404.60 0.0552115
866866 9975.38 17277.9i 0.391429 0.677974i
867867 0 0
868868 301.725 + 522.602i 0.0117986 + 0.0204358i
869869 1185.65 + 2053.61i 0.0462837 + 0.0801658i
870870 0 0
871871 29896.1 51781.5i 1.16302 2.01441i
872872 665.044 0.0258271
873873 0 0
874874 −26215.0 −1.01457
875875 239.760 415.276i 0.00926327 0.0160444i
876876 0 0
877877 3180.09 + 5508.08i 0.122445 + 0.212080i 0.920731 0.390197i 0.127593π-0.127593\pi
−0.798287 + 0.602278i 0.794260π0.794260\pi
878878 17360.9 + 30070.0i 0.667315 + 1.15582i
879879 0 0
880880 −383.077 + 663.508i −0.0146744 + 0.0254169i
881881 −32601.5 −1.24673 −0.623367 0.781930i 0.714236π-0.714236\pi
−0.623367 + 0.781930i 0.714236π0.714236\pi
882882 0 0
883883 1478.26 0.0563392 0.0281696 0.999603i 0.491032π-0.491032\pi
0.0281696 + 0.999603i 0.491032π0.491032\pi
884884 441.959 765.496i 0.0168153 0.0291249i
885885 0 0
886886 −8575.43 14853.1i −0.325166 0.563204i
887887 22633.6 + 39202.5i 0.856776 + 1.48398i 0.874987 + 0.484146i 0.160870π0.160870\pi
−0.0182111 + 0.999834i 0.505797π0.505797\pi
888888 0 0
889889 −1574.29 + 2726.75i −0.0593927 + 0.102871i
890890 126.136 0.00475066
891891 0 0
892892 −5881.88 −0.220785
893893 292.151 506.020i 0.0109479 0.0189623i
894894 0 0
895895 819.003 + 1418.56i 0.0305880 + 0.0529800i
896896 −153.108 265.190i −0.00570866 0.00988770i
897897 0 0
898898 4703.77 8147.17i 0.174796 0.302756i
899899 −7922.22 −0.293905
900900 0 0
901901 −1702.29 −0.0629428
902902 19338.0 33494.4i 0.713841 1.23641i
903903 0 0
904904 −3888.78 6735.57i −0.143074 0.247812i
905905 1133.70 + 1963.62i 0.0416413 + 0.0721248i
906906 0 0
907907 −3630.76 + 6288.66i −0.132919 + 0.230222i −0.924801 0.380452i 0.875768π-0.875768\pi
0.791882 + 0.610675i 0.209102π0.209102\pi
908908 −8409.04 −0.307339
909909 0 0
910910 −299.019 −0.0108927
911911 −9717.20 + 16830.7i −0.353398 + 0.612103i −0.986842 0.161685i 0.948307π-0.948307\pi
0.633445 + 0.773788i 0.281640π0.281640\pi
912912 0 0
913913 −13217.5 22893.4i −0.479118 0.829857i
914914 −7046.80 12205.4i −0.255019 0.441706i
915915 0 0
916916 2002.08 3467.70i 0.0722166 0.125083i
917917 −2668.08 −0.0960827
918918 0 0
919919 −24010.2 −0.861830 −0.430915 0.902392i 0.641809π-0.641809\pi
−0.430915 + 0.902392i 0.641809π0.641809\pi
920920 356.216 616.984i 0.0127653 0.0221102i
921921 0 0
922922 5770.26 + 9994.38i 0.206110 + 0.356993i
923923 −23773.6 41177.0i −0.847797 1.46843i
924924 0 0
925925 −14138.6 + 24488.7i −0.502565 + 0.870468i
926926 27198.3 0.965217
927927 0 0
928928 4020.06 0.142204
929929 20777.3 35987.4i 0.733780 1.27094i −0.221477 0.975166i 0.571088π-0.571088\pi
0.955257 0.295778i 0.0955790π-0.0955790\pi
930930 0 0
931931 −19952.5 34558.8i −0.702382 1.21656i
932932 −12561.6 21757.3i −0.441489 0.764681i
933933 0 0
934934 5730.52 9925.55i 0.200758 0.347724i
935935 −136.103 −0.00476049
936936 0 0
937937 16811.0 0.586116 0.293058 0.956095i 0.405327π-0.405327\pi
0.293058 + 0.956095i 0.405327π0.405327\pi
938938 1839.85 3186.71i 0.0640439 0.110927i
939939 0 0
940940 7.93962 + 13.7518i 0.000275491 + 0.000477165i
941941 −5366.43 9294.93i −0.185909 0.322004i 0.757973 0.652286i 0.226190π-0.226190\pi
−0.943883 + 0.330281i 0.892856π0.892856\pi
942942 0 0
943943 −17982.0 + 31145.8i −0.620971 + 1.07555i
944944 10724.4 0.369757
945945 0 0
946946 −32503.7 −1.11711
947947 15774.7 27322.5i 0.541297 0.937553i −0.457533 0.889192i 0.651267π-0.651267\pi
0.998830 0.0483606i 0.0153997π-0.0153997\pi
948948 0 0
949949 −35912.1 62201.6i −1.22841 2.12766i
950950 14713.0 + 25483.6i 0.502475 + 0.870313i
951951 0 0
952952 27.1988 47.1097i 0.000925965 0.00160382i
953953 −31955.2 −1.08618 −0.543090 0.839675i 0.682746π-0.682746\pi
−0.543090 + 0.839675i 0.682746π0.682746\pi
954954 0 0
955955 353.470 0.0119770
956956 −2034.74 + 3524.27i −0.0688370 + 0.119229i
957957 0 0
958958 14568.3 + 25233.0i 0.491315 + 0.850982i
959959 −738.197 1278.59i −0.0248567 0.0430531i
960960 0 0
961961 12907.1 22355.8i 0.433256 0.750421i
962962 35357.7 1.18501
963963 0 0
964964 −3685.17 −0.123124
965965 −185.961 + 322.093i −0.00620340 + 0.0107446i
966966 0 0
967967 −19186.1 33231.3i −0.638038 1.10511i −0.985863 0.167555i 0.946413π-0.946413\pi
0.347825 0.937560i 0.386920π-0.386920\pi
968968 8869.97 + 15363.2i 0.294516 + 0.510117i
969969 0 0
970970 73.1626 126.721i 0.00242176 0.00419461i
971971 −46445.9 −1.53503 −0.767517 0.641028i 0.778508π-0.778508\pi
−0.767517 + 0.641028i 0.778508π0.778508\pi
972972 0 0
973973 −5159.17 −0.169985
974974 7164.51 12409.3i 0.235694 0.408233i
975975 0 0
976976 −3716.25 6436.73i −0.121879 0.211101i
977977 23954.1 + 41489.8i 0.784402 + 1.35862i 0.929356 + 0.369185i 0.120363π0.120363\pi
−0.144954 + 0.989438i 0.546303π0.546303\pi
978978 0 0
979979 2336.83 4047.50i 0.0762874 0.132134i
980980 1084.48 0.0353493
981981 0 0
982982 19020.1 0.618082
983983 20273.8 35115.3i 0.657818 1.13937i −0.323361 0.946276i 0.604813π-0.604813\pi
0.981179 0.193099i 0.0618538π-0.0618538\pi
984984 0 0
985985 −416.633 721.629i −0.0134772 0.0233432i
986986 357.072 + 618.467i 0.0115330 + 0.0199757i
987987 0 0
988988 18397.1 31864.8i 0.592399 1.02607i
989989 30224.6 0.971776
990990 0 0
991991 −10651.5 −0.341428 −0.170714 0.985321i 0.554607π-0.554607\pi
−0.170714 + 0.985321i 0.554607π0.554607\pi
992992 1008.98 1747.61i 0.0322936 0.0559342i
993993 0 0
994994 −1463.06 2534.09i −0.0466856 0.0808618i
995995 −478.376 828.571i −0.0152417 0.0263995i
996996 0 0
997997 9379.18 16245.2i 0.297935 0.516039i −0.677728 0.735313i 0.737035π-0.737035\pi
0.975663 + 0.219273i 0.0703687π0.0703687\pi
998998 −42971.2 −1.36296
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 162.4.c.j.55.1 4
3.2 odd 2 162.4.c.i.55.2 4
9.2 odd 6 162.4.a.h.1.1 yes 2
9.4 even 3 inner 162.4.c.j.109.1 4
9.5 odd 6 162.4.c.i.109.2 4
9.7 even 3 162.4.a.e.1.2 2
36.7 odd 6 1296.4.a.j.1.2 2
36.11 even 6 1296.4.a.s.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.4.a.e.1.2 2 9.7 even 3
162.4.a.h.1.1 yes 2 9.2 odd 6
162.4.c.i.55.2 4 3.2 odd 2
162.4.c.i.109.2 4 9.5 odd 6
162.4.c.j.55.1 4 1.1 even 1 trivial
162.4.c.j.109.1 4 9.4 even 3 inner
1296.4.a.j.1.2 2 36.7 odd 6
1296.4.a.s.1.1 2 36.11 even 6