Properties

Label 819.2.j.h.235.1
Level 819819
Weight 22
Character 819.235
Analytic conductor 6.5406.540
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [819,2,Mod(235,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.235"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 819=32713 819 = 3^{2} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 819.j (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [10,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.539747925546.53974792554
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x10x9+8x8+7x7+41x6+18x5+58x4+28x3+64x2+16x+4 x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 235.1
Root 1.50426+2.60546i1.50426 + 2.60546i of defining polynomial
Character χ\chi == 819.235
Dual form 819.2.j.h.352.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.004261.73943i)q2+(1.01709+1.76164i)q4+(0.452861+0.784378i)q5+(0.2377092.63505i)q7+0.0686323q8+(0.9095821.57544i)q10+(0.3581810.620387i)q11+1.00000q13+(4.82222+2.23280i)q14+(1.96525+3.40391i)q16+(1.176142.03713i)q17+(3.317965.74687i)q191.84239q201.43883q22+(1.87953+3.25544i)q23+(2.089833.61970i)q25+(1.004261.73943i)q26+(4.40025+3.09883i)q283.25799q29+(0.785250+1.36009i)q31+(4.015886.95570i)q324.72459q34+(2.174521.00686i)q35+(2.604414.51098i)q37+(6.66419+11.5427i)q38+(0.0310809+0.0538337i)q404.92168q419.43766q43+(0.728600+1.26197i)q44+(3.775086.53863i)q46+(4.159937.20521i)q47+(6.886991.25275i)q498.39497q50+(1.01709+1.76164i)q52+(7.0416312.1965i)q53+0.648824q55+(0.01631450.180850i)q56+(3.27188+5.66706i)q58+(0.3581810.620387i)q59+(5.82633+10.0915i)q61+3.15439q628.27099q64+(0.452861+0.784378i)q65+(4.69587+8.13349i)q67+(2.39246+4.14386i)q68+(3.935162.77129i)q7010.9914q71+(1.736503.00771i)q73+(5.23103+9.06041i)q74+13.4986q76+(1.549611.09130i)q77+(6.5040811.2654i)q79+(1.77997+3.08299i)q80+(4.94265+8.56093i)q823.54083q83+2.13050q85+(9.47789+16.4162i)q86+(0.02458280.0425786i)q88+(6.02503+10.4357i)q89+(0.2377092.63505i)q917.64656q92+(8.35532+14.4718i)q94+(3.005145.20506i)q95+7.43766q97+(4.73727+13.2375i)q98+O(q100)q+(-1.00426 - 1.73943i) q^{2} +(-1.01709 + 1.76164i) q^{4} +(0.452861 + 0.784378i) q^{5} +(0.237709 - 2.63505i) q^{7} +0.0686323 q^{8} +(0.909582 - 1.57544i) q^{10} +(0.358181 - 0.620387i) q^{11} +1.00000 q^{13} +(-4.82222 + 2.23280i) q^{14} +(1.96525 + 3.40391i) q^{16} +(1.17614 - 2.03713i) q^{17} +(-3.31796 - 5.74687i) q^{19} -1.84239 q^{20} -1.43883 q^{22} +(1.87953 + 3.25544i) q^{23} +(2.08983 - 3.61970i) q^{25} +(-1.00426 - 1.73943i) q^{26} +(4.40025 + 3.09883i) q^{28} -3.25799 q^{29} +(-0.785250 + 1.36009i) q^{31} +(4.01588 - 6.95570i) q^{32} -4.72459 q^{34} +(2.17452 - 1.00686i) q^{35} +(-2.60441 - 4.51098i) q^{37} +(-6.66419 + 11.5427i) q^{38} +(0.0310809 + 0.0538337i) q^{40} -4.92168 q^{41} -9.43766 q^{43} +(0.728600 + 1.26197i) q^{44} +(3.77508 - 6.53863i) q^{46} +(-4.15993 - 7.20521i) q^{47} +(-6.88699 - 1.25275i) q^{49} -8.39497 q^{50} +(-1.01709 + 1.76164i) q^{52} +(7.04163 - 12.1965i) q^{53} +0.648824 q^{55} +(0.0163145 - 0.180850i) q^{56} +(3.27188 + 5.66706i) q^{58} +(0.358181 - 0.620387i) q^{59} +(5.82633 + 10.0915i) q^{61} +3.15439 q^{62} -8.27099 q^{64} +(0.452861 + 0.784378i) q^{65} +(-4.69587 + 8.13349i) q^{67} +(2.39246 + 4.14386i) q^{68} +(-3.93516 - 2.77129i) q^{70} -10.9914 q^{71} +(1.73650 - 3.00771i) q^{73} +(-5.23103 + 9.06041i) q^{74} +13.4986 q^{76} +(-1.54961 - 1.09130i) q^{77} +(-6.50408 - 11.2654i) q^{79} +(-1.77997 + 3.08299i) q^{80} +(4.94265 + 8.56093i) q^{82} -3.54083 q^{83} +2.13050 q^{85} +(9.47789 + 16.4162i) q^{86} +(0.0245828 - 0.0425786i) q^{88} +(6.02503 + 10.4357i) q^{89} +(0.237709 - 2.63505i) q^{91} -7.64656 q^{92} +(-8.35532 + 14.4718i) q^{94} +(3.00514 - 5.20506i) q^{95} +7.43766 q^{97} +(4.73727 + 13.2375i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+4q28q4+2q5+q718q8+5q10+11q11+10q1310q1410q165q179q192q20+16q22+10q239q25+4q26+37q28++7q98+O(q100) 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28}+ \cdots + 7 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/819Z)×\left(\mathbb{Z}/819\mathbb{Z}\right)^\times.

nn 9292 379379 703703
χ(n)\chi(n) 11 11 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 −1.00426 1.73943i −0.710121 1.22997i −0.964812 0.262942i 0.915307π-0.915307\pi
0.254691 0.967023i 0.418026π-0.418026\pi
33 0 0
44 −1.01709 + 1.76164i −0.508543 + 0.880822i
55 0.452861 + 0.784378i 0.202526 + 0.350784i 0.949342 0.314246i 0.101752π-0.101752\pi
−0.746816 + 0.665031i 0.768418π0.768418\pi
66 0 0
77 0.237709 2.63505i 0.0898454 0.995956i
88 0.0686323 0.0242652
99 0 0
1010 0.909582 1.57544i 0.287635 0.498199i
1111 0.358181 0.620387i 0.107996 0.187054i −0.806963 0.590603i 0.798890π-0.798890\pi
0.914958 + 0.403549i 0.132223π0.132223\pi
1212 0 0
1313 1.00000 0.277350
1414 −4.82222 + 2.23280i −1.28879 + 0.596742i
1515 0 0
1616 1.96525 + 3.40391i 0.491311 + 0.850976i
1717 1.17614 2.03713i 0.285255 0.494076i −0.687416 0.726264i 0.741255π-0.741255\pi
0.972671 + 0.232188i 0.0745885π0.0745885\pi
1818 0 0
1919 −3.31796 5.74687i −0.761191 1.31842i −0.942237 0.334947i 0.891282π-0.891282\pi
0.181046 0.983475i 0.442052π-0.442052\pi
2020 −1.84239 −0.411971
2121 0 0
2222 −1.43883 −0.306759
2323 1.87953 + 3.25544i 0.391909 + 0.678806i 0.992701 0.120599i 0.0384816π-0.0384816\pi
−0.600793 + 0.799405i 0.705148π0.705148\pi
2424 0 0
2525 2.08983 3.61970i 0.417967 0.723940i
2626 −1.00426 1.73943i −0.196952 0.341131i
2727 0 0
2828 4.40025 + 3.09883i 0.831569 + 0.585624i
2929 −3.25799 −0.604994 −0.302497 0.953150i 0.597820π-0.597820\pi
−0.302497 + 0.953150i 0.597820π0.597820\pi
3030 0 0
3131 −0.785250 + 1.36009i −0.141035 + 0.244280i −0.927887 0.372862i 0.878376π-0.878376\pi
0.786852 + 0.617142i 0.211710π0.211710\pi
3232 4.01588 6.95570i 0.709913 1.22961i
3333 0 0
3434 −4.72459 −0.810261
3535 2.17452 1.00686i 0.367562 0.170190i
3636 0 0
3737 −2.60441 4.51098i −0.428163 0.741600i 0.568547 0.822651i 0.307506π-0.307506\pi
−0.996710 + 0.0810508i 0.974172π0.974172\pi
3838 −6.66419 + 11.5427i −1.08108 + 1.87248i
3939 0 0
4040 0.0310809 + 0.0538337i 0.00491432 + 0.00851185i
4141 −4.92168 −0.768637 −0.384318 0.923201i 0.625563π-0.625563\pi
−0.384318 + 0.923201i 0.625563π0.625563\pi
4242 0 0
4343 −9.43766 −1.43923 −0.719615 0.694373i 0.755682π-0.755682\pi
−0.719615 + 0.694373i 0.755682π0.755682\pi
4444 0.728600 + 1.26197i 0.109841 + 0.190250i
4545 0 0
4646 3.77508 6.53863i 0.556605 0.964068i
4747 −4.15993 7.20521i −0.606788 1.05099i −0.991766 0.128062i 0.959124π-0.959124\pi
0.384978 0.922926i 0.374209π-0.374209\pi
4848 0 0
4949 −6.88699 1.25275i −0.983856 0.178964i
5050 −8.39497 −1.18723
5151 0 0
5252 −1.01709 + 1.76164i −0.141044 + 0.244296i
5353 7.04163 12.1965i 0.967243 1.67531i 0.263777 0.964584i 0.415032π-0.415032\pi
0.703465 0.710729i 0.251635π-0.251635\pi
5454 0 0
5555 0.648824 0.0874874
5656 0.0163145 0.180850i 0.00218012 0.0241671i
5757 0 0
5858 3.27188 + 5.66706i 0.429619 + 0.744122i
5959 0.358181 0.620387i 0.0466311 0.0807675i −0.841768 0.539840i 0.818485π-0.818485\pi
0.888399 + 0.459072i 0.151818π0.151818\pi
6060 0 0
6161 5.82633 + 10.0915i 0.745986 + 1.29208i 0.949733 + 0.313061i 0.101355π0.101355\pi
−0.203747 + 0.979024i 0.565312π0.565312\pi
6262 3.15439 0.400607
6363 0 0
6464 −8.27099 −1.03387
6565 0.452861 + 0.784378i 0.0561705 + 0.0972901i
6666 0 0
6767 −4.69587 + 8.13349i −0.573692 + 0.993664i 0.422490 + 0.906367i 0.361156π0.361156\pi
−0.996182 + 0.0872964i 0.972177π0.972177\pi
6868 2.39246 + 4.14386i 0.290128 + 0.502517i
6969 0 0
7070 −3.93516 2.77129i −0.470341 0.331233i
7171 −10.9914 −1.30444 −0.652220 0.758030i 0.726162π-0.726162\pi
−0.652220 + 0.758030i 0.726162π0.726162\pi
7272 0 0
7373 1.73650 3.00771i 0.203242 0.352025i −0.746329 0.665577i 0.768186π-0.768186\pi
0.949571 + 0.313552i 0.101519π0.101519\pi
7474 −5.23103 + 9.06041i −0.608095 + 1.05325i
7575 0 0
7676 13.4986 1.54839
7777 −1.54961 1.09130i −0.176594 0.124365i
7878 0 0
7979 −6.50408 11.2654i −0.731766 1.26746i −0.956128 0.292950i 0.905363π-0.905363\pi
0.224361 0.974506i 0.427970π-0.427970\pi
8080 −1.77997 + 3.08299i −0.199006 + 0.344689i
8181 0 0
8282 4.94265 + 8.56093i 0.545825 + 0.945396i
8383 −3.54083 −0.388656 −0.194328 0.980937i 0.562253π-0.562253\pi
−0.194328 + 0.980937i 0.562253π0.562253\pi
8484 0 0
8585 2.13050 0.231085
8686 9.47789 + 16.4162i 1.02203 + 1.77020i
8787 0 0
8888 0.0245828 0.0425786i 0.00262053 0.00453889i
8989 6.02503 + 10.4357i 0.638651 + 1.10618i 0.985729 + 0.168340i 0.0538408π0.0538408\pi
−0.347077 + 0.937836i 0.612826π0.612826\pi
9090 0 0
9191 0.237709 2.63505i 0.0249186 0.276228i
9292 −7.64656 −0.797209
9393 0 0
9494 −8.35532 + 14.4718i −0.861786 + 1.49266i
9595 3.00514 5.20506i 0.308321 0.534028i
9696 0 0
9797 7.43766 0.755180 0.377590 0.925973i 0.376753π-0.376753\pi
0.377590 + 0.925973i 0.376753π0.376753\pi
9898 4.73727 + 13.2375i 0.478537 + 1.33719i
9999 0 0
100100 4.25108 + 7.36309i 0.425108 + 0.736309i
101101 −0.599526 + 1.03841i −0.0596551 + 0.103326i −0.894311 0.447447i 0.852333π-0.852333\pi
0.834656 + 0.550772i 0.185667π0.185667\pi
102102 0 0
103103 7.20615 + 12.4814i 0.710043 + 1.22983i 0.964840 + 0.262837i 0.0846580π0.0846580\pi
−0.254797 + 0.966995i 0.582009π0.582009\pi
104104 0.0686323 0.00672995
105105 0 0
106106 −28.2866 −2.74744
107107 6.79661 + 11.7721i 0.657053 + 1.13805i 0.981375 + 0.192102i 0.0615305π0.0615305\pi
−0.324322 + 0.945947i 0.605136π0.605136\pi
108108 0 0
109109 6.86241 11.8860i 0.657299 1.13848i −0.324013 0.946053i 0.605032π-0.605032\pi
0.981312 0.192423i 0.0616346π-0.0616346\pi
110110 −0.651589 1.12859i −0.0621266 0.107606i
111111 0 0
112112 9.43662 4.36939i 0.891677 0.412868i
113113 3.25799 0.306486 0.153243 0.988189i 0.451028π-0.451028\pi
0.153243 + 0.988189i 0.451028π0.451028\pi
114114 0 0
115115 −1.70233 + 2.94852i −0.158743 + 0.274951i
116116 3.31366 5.73942i 0.307665 0.532892i
117117 0 0
118118 −1.43883 −0.132455
119119 −5.08836 3.58342i −0.466449 0.328492i
120120 0 0
121121 5.24341 + 9.08186i 0.476674 + 0.825623i
122122 11.7023 20.2690i 1.05948 1.83507i
123123 0 0
124124 −1.59733 2.76666i −0.143445 0.248453i
125125 8.31422 0.743647
126126 0 0
127127 −0.950834 −0.0843729 −0.0421865 0.999110i 0.513432π-0.513432\pi
−0.0421865 + 0.999110i 0.513432π0.513432\pi
128128 0.274489 + 0.475429i 0.0242617 + 0.0420224i
129129 0 0
130130 0.909582 1.57544i 0.0797756 0.138175i
131131 −9.40980 16.2983i −0.822138 1.42399i −0.904087 0.427349i 0.859448π-0.859448\pi
0.0819487 0.996637i 0.473886π-0.473886\pi
132132 0 0
133133 −15.9320 + 7.37690i −1.38148 + 0.639658i
134134 18.8635 1.62956
135135 0 0
136136 0.0807209 0.139813i 0.00692176 0.0119888i
137137 3.09090 5.35359i 0.264073 0.457388i −0.703247 0.710945i 0.748267π-0.748267\pi
0.967320 + 0.253557i 0.0816006π0.0816006\pi
138138 0 0
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 −0.437952 + 4.85480i −0.0370137 + 0.410305i
141141 0 0
142142 11.0383 + 19.1188i 0.926309 + 1.60441i
143143 0.358181 0.620387i 0.0299526 0.0518794i
144144 0 0
145145 −1.47542 2.55550i −0.122527 0.212223i
146146 −6.97560 −0.577305
147147 0 0
148148 10.5956 0.870956
149149 −10.5385 18.2533i −0.863351 1.49537i −0.868675 0.495382i 0.835028π-0.835028\pi
0.00532425 0.999986i 0.498305π-0.498305\pi
150150 0 0
151151 7.86171 13.6169i 0.639777 1.10813i −0.345704 0.938344i 0.612360π-0.612360\pi
0.985481 0.169783i 0.0543067π-0.0543067\pi
152152 −0.227719 0.394421i −0.0184705 0.0319918i
153153 0 0
154154 −0.342022 + 3.79139i −0.0275609 + 0.305519i
155155 −1.42244 −0.114253
156156 0 0
157157 3.89250 6.74200i 0.310655 0.538070i −0.667849 0.744297i 0.732785π-0.732785\pi
0.978504 + 0.206226i 0.0661183π0.0661183\pi
158158 −13.0636 + 22.6268i −1.03928 + 1.80009i
159159 0 0
160160 7.27453 0.575102
161161 9.02503 4.17881i 0.711272 0.329336i
162162 0 0
163163 −0.844956 1.46351i −0.0661820 0.114631i 0.831036 0.556219i 0.187748π-0.187748\pi
−0.897218 + 0.441588i 0.854415π0.854415\pi
164164 5.00576 8.67024i 0.390884 0.677032i
165165 0 0
166166 3.55592 + 6.15903i 0.275993 + 0.478034i
167167 21.8667 1.69210 0.846049 0.533105i 0.178975π-0.178975\pi
0.846049 + 0.533105i 0.178975π0.178975\pi
168168 0 0
169169 1.00000 0.0769231
170170 −2.13958 3.70587i −0.164099 0.284227i
171171 0 0
172172 9.59891 16.6258i 0.731910 1.26770i
173173 2.92061 + 5.05865i 0.222050 + 0.384602i 0.955430 0.295217i 0.0953918π-0.0953918\pi
−0.733380 + 0.679819i 0.762058π0.762058\pi
174174 0 0
175175 −9.04132 6.36725i −0.683460 0.481319i
176176 2.81565 0.212238
177177 0 0
178178 12.1014 20.9603i 0.907039 1.57104i
179179 1.26714 2.19475i 0.0947103 0.164043i −0.814777 0.579774i 0.803141π-0.803141\pi
0.909488 + 0.415731i 0.136474π0.136474\pi
180180 0 0
181181 −10.7248 −0.797169 −0.398585 0.917132i 0.630498π-0.630498\pi
−0.398585 + 0.917132i 0.630498π0.630498\pi
182182 −4.82222 + 2.23280i −0.357447 + 0.165506i
183183 0 0
184184 0.128996 + 0.223428i 0.00950974 + 0.0164714i
185185 2.35887 4.08569i 0.173428 0.300386i
186186 0 0
187187 −0.842538 1.45932i −0.0616125 0.106716i
188188 16.9240 1.23431
189189 0 0
190190 −12.0718 −0.875781
191191 −0.839303 1.45371i −0.0607298 0.105187i 0.834062 0.551671i 0.186009π-0.186009\pi
−0.894792 + 0.446484i 0.852676π0.852676\pi
192192 0 0
193193 3.22408 5.58427i 0.232074 0.401964i −0.726344 0.687331i 0.758782π-0.758782\pi
0.958418 + 0.285367i 0.0921154π0.0921154\pi
194194 −7.46936 12.9373i −0.536269 0.928845i
195195 0 0
196196 9.21155 10.8583i 0.657968 0.775590i
197197 −1.87251 −0.133411 −0.0667054 0.997773i 0.521249π-0.521249\pi
−0.0667054 + 0.997773i 0.521249π0.521249\pi
198198 0 0
199199 5.69833 9.86979i 0.403944 0.699651i −0.590254 0.807217i 0.700972π-0.700972\pi
0.994198 + 0.107566i 0.0343058π0.0343058\pi
200200 0.143430 0.248428i 0.0101420 0.0175665i
201201 0 0
202202 2.40833 0.169449
203203 −0.774453 + 8.58498i −0.0543559 + 0.602547i
204204 0 0
205205 −2.22883 3.86045i −0.155669 0.269626i
206206 14.4737 25.0692i 1.00843 1.74666i
207207 0 0
208208 1.96525 + 3.40391i 0.136265 + 0.236018i
209209 −4.75371 −0.328821
210210 0 0
211211 7.53599 0.518799 0.259400 0.965770i 0.416475π-0.416475\pi
0.259400 + 0.965770i 0.416475π0.416475\pi
212212 14.3239 + 24.8097i 0.983768 + 1.70394i
213213 0 0
214214 13.6512 23.6445i 0.933174 1.61630i
215215 −4.27395 7.40269i −0.291481 0.504859i
216216 0 0
217217 3.39725 + 2.39248i 0.230621 + 0.162412i
218218 −27.5666 −1.86705
219219 0 0
220220 −0.659909 + 1.14300i −0.0444911 + 0.0770608i
221221 1.17614 2.03713i 0.0791154 0.137032i
222222 0 0
223223 17.6349 1.18092 0.590459 0.807067i 0.298947π-0.298947\pi
0.590459 + 0.807067i 0.298947π0.298947\pi
224224 −17.3740 12.2355i −1.16085 0.817517i
225225 0 0
226226 −3.27188 5.66706i −0.217642 0.376967i
227227 −2.66452 + 4.61509i −0.176851 + 0.306314i −0.940800 0.338962i 0.889924π-0.889924\pi
0.763950 + 0.645276i 0.223258π0.223258\pi
228228 0 0
229229 4.25950 + 7.37767i 0.281476 + 0.487530i 0.971748 0.236019i 0.0758428π-0.0758428\pi
−0.690273 + 0.723549i 0.742509π0.742509\pi
230230 6.83834 0.450907
231231 0 0
232232 −0.223604 −0.0146803
233233 2.37685 + 4.11683i 0.155713 + 0.269703i 0.933318 0.359050i 0.116899π-0.116899\pi
−0.777605 + 0.628752i 0.783566π0.783566\pi
234234 0 0
235235 3.76774 6.52592i 0.245780 0.425704i
236236 0.728600 + 1.26197i 0.0474278 + 0.0821474i
237237 0 0
238238 −1.12308 + 12.4495i −0.0727983 + 0.806984i
239239 −14.8314 −0.959365 −0.479682 0.877442i 0.659248π-0.659248\pi
−0.479682 + 0.877442i 0.659248π0.659248\pi
240240 0 0
241241 3.06066 5.30121i 0.197154 0.341481i −0.750450 0.660927i 0.770163π-0.770163\pi
0.947605 + 0.319446i 0.103497π0.103497\pi
242242 10.5315 18.2411i 0.676992 1.17258i
243243 0 0
244244 −23.7035 −1.51746
245245 −2.13622 5.96932i −0.136478 0.381366i
246246 0 0
247247 −3.31796 5.74687i −0.211116 0.365664i
248248 −0.0538935 + 0.0933463i −0.00342224 + 0.00592750i
249249 0 0
250250 −8.34966 14.4620i −0.528079 0.914660i
251251 13.9708 0.881832 0.440916 0.897548i 0.354654π-0.354654\pi
0.440916 + 0.897548i 0.354654π0.354654\pi
252252 0 0
253253 2.69284 0.169298
254254 0.954887 + 1.65391i 0.0599149 + 0.103776i
255255 0 0
256256 −7.71967 + 13.3709i −0.482479 + 0.835679i
257257 8.63253 + 14.9520i 0.538482 + 0.932679i 0.998986 + 0.0450210i 0.0143355π0.0143355\pi
−0.460504 + 0.887658i 0.652331π0.652331\pi
258258 0 0
259259 −12.5057 + 5.79047i −0.777069 + 0.359802i
260260 −1.84239 −0.114260
261261 0 0
262262 −18.8998 + 32.7354i −1.16763 + 2.02240i
263263 −1.30336 + 2.25749i −0.0803687 + 0.139203i −0.903408 0.428781i 0.858943π-0.858943\pi
0.823040 + 0.567984i 0.192276π0.192276\pi
264264 0 0
265265 12.7555 0.783565
266266 28.8315 + 20.3043i 1.76777 + 1.24494i
267267 0 0
268268 −9.55221 16.5449i −0.583494 1.01064i
269269 −7.24477 + 12.5483i −0.441721 + 0.765084i −0.997817 0.0660343i 0.978965π-0.978965\pi
0.556096 + 0.831118i 0.312299π0.312299\pi
270270 0 0
271271 4.31796 + 7.47892i 0.262297 + 0.454312i 0.966852 0.255338i 0.0821866π-0.0821866\pi
−0.704555 + 0.709650i 0.748853π0.748853\pi
272272 9.24558 0.560596
273273 0 0
274274 −12.4163 −0.750095
275275 −1.49708 2.59301i −0.0902771 0.156364i
276276 0 0
277277 −6.11349 + 10.5889i −0.367324 + 0.636223i −0.989146 0.146935i 0.953059π-0.953059\pi
0.621822 + 0.783158i 0.286393π0.286393\pi
278278 4.01705 + 6.95773i 0.240927 + 0.417297i
279279 0 0
280280 0.149243 0.0691030i 0.00891896 0.00412970i
281281 24.1822 1.44259 0.721293 0.692630i 0.243548π-0.243548\pi
0.721293 + 0.692630i 0.243548π0.243548\pi
282282 0 0
283283 15.3842 26.6461i 0.914493 1.58395i 0.106851 0.994275i 0.465923π-0.465923\pi
0.807642 0.589674i 0.200744π-0.200744\pi
284284 11.1792 19.3629i 0.663363 1.14898i
285285 0 0
286286 −1.43883 −0.0850797
287287 −1.16992 + 12.9689i −0.0690585 + 0.765528i
288288 0 0
289289 5.73341 + 9.93056i 0.337259 + 0.584150i
290290 −2.96341 + 5.13278i −0.174018 + 0.301407i
291291 0 0
292292 3.53234 + 6.11819i 0.206714 + 0.358040i
293293 31.8295 1.85950 0.929749 0.368193i 0.120024π-0.120024\pi
0.929749 + 0.368193i 0.120024π0.120024\pi
294294 0 0
295295 0.648824 0.0377760
296296 −0.178747 0.309599i −0.0103895 0.0179951i
297297 0 0
298298 −21.1669 + 36.6622i −1.22617 + 2.12378i
299299 1.87953 + 3.25544i 0.108696 + 0.188267i
300300 0 0
301301 −2.24341 + 24.8687i −0.129308 + 1.43341i
302302 −31.5809 −1.81728
303303 0 0
304304 13.0412 22.5880i 0.747964 1.29551i
305305 −5.27704 + 9.14010i −0.302162 + 0.523360i
306306 0 0
307307 28.7884 1.64304 0.821520 0.570179i 0.193126π-0.193126\pi
0.821520 + 0.570179i 0.193126π0.193126\pi
308308 3.49856 1.61992i 0.199349 0.0923034i
309309 0 0
310310 1.42850 + 2.47423i 0.0811332 + 0.140527i
311311 2.75931 4.77927i 0.156466 0.271007i −0.777126 0.629345i 0.783323π-0.783323\pi
0.933592 + 0.358338i 0.116656π0.116656\pi
312312 0 0
313313 2.42399 + 4.19848i 0.137012 + 0.237312i 0.926364 0.376629i 0.122917π-0.122917\pi
−0.789352 + 0.613941i 0.789583π0.789583\pi
314314 −15.6363 −0.882410
315315 0 0
316316 26.4608 1.48854
317317 −3.82756 6.62952i −0.214977 0.372351i 0.738288 0.674485i 0.235634π-0.235634\pi
−0.953265 + 0.302134i 0.902301π0.902301\pi
318318 0 0
319319 −1.16695 + 2.02122i −0.0653366 + 0.113166i
320320 −3.74561 6.48758i −0.209386 0.362667i
321321 0 0
322322 −16.3322 11.5018i −0.910161 0.640971i
323323 −15.6095 −0.868534
324324 0 0
325325 2.08983 3.61970i 0.115923 0.200785i
326326 −1.69711 + 2.93949i −0.0939945 + 0.162803i
327327 0 0
328328 −0.337786 −0.0186511
329329 −19.9750 + 9.24889i −1.10125 + 0.509908i
330330 0 0
331331 −5.67159 9.82348i −0.311739 0.539947i 0.667000 0.745058i 0.267578π-0.267578\pi
−0.978739 + 0.205110i 0.934245π0.934245\pi
332332 3.60132 6.23768i 0.197648 0.342337i
333333 0 0
334334 −21.9599 38.0357i −1.20159 2.08122i
335335 −8.50631 −0.464749
336336 0 0
337337 1.74149 0.0948649 0.0474324 0.998874i 0.484896π-0.484896\pi
0.0474324 + 0.998874i 0.484896π0.484896\pi
338338 −1.00426 1.73943i −0.0546247 0.0946127i
339339 0 0
340340 −2.16690 + 3.75319i −0.117517 + 0.203545i
341341 0.562522 + 0.974317i 0.0304623 + 0.0527622i
342342 0 0
343343 −4.93815 + 17.8498i −0.266635 + 0.963798i
344344 −0.647729 −0.0349232
345345 0 0
346346 5.86612 10.1604i 0.315365 0.546228i
347347 10.5251 18.2301i 0.565019 0.978641i −0.432029 0.901860i 0.642202π-0.642202\pi
0.997048 0.0767814i 0.0244643π-0.0244643\pi
348348 0 0
349349 −8.35601 −0.447287 −0.223643 0.974671i 0.571795π-0.571795\pi
−0.223643 + 0.974671i 0.571795π0.571795\pi
350350 −1.99556 + 22.1212i −0.106667 + 1.18243i
351351 0 0
352352 −2.87682 4.98279i −0.153335 0.265584i
353353 −4.26677 + 7.39027i −0.227097 + 0.393344i −0.956947 0.290264i 0.906257π-0.906257\pi
0.729849 + 0.683608i 0.239590π0.239590\pi
354354 0 0
355355 −4.97758 8.62141i −0.264182 0.457577i
356356 −24.5119 −1.29913
357357 0 0
358358 −5.09015 −0.269023
359359 −8.08565 14.0047i −0.426744 0.739142i 0.569837 0.821757i 0.307006π-0.307006\pi
−0.996582 + 0.0826150i 0.973673π0.973673\pi
360360 0 0
361361 −12.5177 + 21.6812i −0.658824 + 1.14112i
362362 10.7705 + 18.6551i 0.566086 + 0.980490i
363363 0 0
364364 4.40025 + 3.09883i 0.230636 + 0.162423i
365365 3.14557 0.164647
366366 0 0
367367 −14.0770 + 24.3821i −0.734813 + 1.27273i 0.219992 + 0.975502i 0.429397π0.429397\pi
−0.954805 + 0.297232i 0.903936π0.903936\pi
368368 −7.38747 + 12.7955i −0.385098 + 0.667010i
369369 0 0
370370 −9.47571 −0.492619
371371 −30.4644 21.4543i −1.58164 1.11385i
372372 0 0
373373 14.2518 + 24.6849i 0.737932 + 1.27814i 0.953425 + 0.301630i 0.0975308π0.0975308\pi
−0.215493 + 0.976505i 0.569136π0.569136\pi
374374 −1.69226 + 2.93108i −0.0875046 + 0.151562i
375375 0 0
376376 −0.285506 0.494511i −0.0147238 0.0255024i
377377 −3.25799 −0.167795
378378 0 0
379379 −7.26263 −0.373056 −0.186528 0.982450i 0.559724π-0.559724\pi
−0.186528 + 0.982450i 0.559724π0.559724\pi
380380 6.11297 + 10.5880i 0.313589 + 0.543152i
381381 0 0
382382 −1.68576 + 2.91982i −0.0862510 + 0.149391i
383383 6.46627 + 11.1999i 0.330411 + 0.572289i 0.982592 0.185774i 0.0594793π-0.0594793\pi
−0.652181 + 0.758063i 0.726146π0.726146\pi
384384 0 0
385385 0.154231 1.70968i 0.00786034 0.0871336i
386386 −12.9513 −0.659203
387387 0 0
388388 −7.56474 + 13.1025i −0.384041 + 0.665179i
389389 −10.5679 + 18.3041i −0.535811 + 0.928053i 0.463312 + 0.886195i 0.346661π0.346661\pi
−0.999124 + 0.0418574i 0.986672π0.986672\pi
390390 0 0
391391 8.84232 0.447175
392392 −0.472670 0.0859791i −0.0238734 0.00434260i
393393 0 0
394394 1.88049 + 3.25711i 0.0947378 + 0.164091i
395395 5.89089 10.2033i 0.296403 0.513384i
396396 0 0
397397 −9.60366 16.6340i −0.481994 0.834838i 0.517792 0.855506i 0.326754π-0.326754\pi
−0.999786 + 0.0206683i 0.993421π0.993421\pi
398398 −22.8905 −1.14740
399399 0 0
400400 16.4282 0.821408
401401 8.33460 + 14.4360i 0.416210 + 0.720897i 0.995555 0.0941856i 0.0300247π-0.0300247\pi
−0.579344 + 0.815083i 0.696691π0.696691\pi
402402 0 0
403403 −0.785250 + 1.36009i −0.0391161 + 0.0677510i
404404 −1.21954 2.11230i −0.0606743 0.105091i
405405 0 0
406406 15.7107 7.27446i 0.779711 0.361025i
407407 −3.73140 −0.184959
408408 0 0
409409 −6.17416 + 10.6940i −0.305293 + 0.528782i −0.977326 0.211738i 0.932088π-0.932088\pi
0.672034 + 0.740520i 0.265421π0.265421\pi
410410 −4.47667 + 7.75382i −0.221087 + 0.382934i
411411 0 0
412412 −29.3171 −1.44435
413413 −1.54961 1.09130i −0.0762513 0.0536991i
414414 0 0
415415 −1.60350 2.77735i −0.0787128 0.136335i
416416 4.01588 6.95570i 0.196895 0.341031i
417417 0 0
418418 4.77397 + 8.26876i 0.233502 + 0.404438i
419419 −4.35934 −0.212968 −0.106484 0.994314i 0.533959π-0.533959\pi
−0.106484 + 0.994314i 0.533959π0.533959\pi
420420 0 0
421421 −10.0000 −0.487370 −0.243685 0.969854i 0.578356π-0.578356\pi
−0.243685 + 0.969854i 0.578356π0.578356\pi
422422 −7.56811 13.1084i −0.368410 0.638105i
423423 0 0
424424 0.483284 0.837072i 0.0234703 0.0406518i
425425 −4.91586 8.51451i −0.238454 0.413015i
426426 0 0
427427 27.9766 12.9538i 1.35388 0.626881i
428428 −27.6509 −1.33656
429429 0 0
430430 −8.58433 + 14.8685i −0.413973 + 0.717022i
431431 −11.6813 + 20.2326i −0.562667 + 0.974569i 0.434595 + 0.900626i 0.356891π0.356891\pi
−0.997262 + 0.0739426i 0.976442π0.976442\pi
432432 0 0
433433 −2.71285 −0.130371 −0.0651856 0.997873i 0.520764π-0.520764\pi
−0.0651856 + 0.997873i 0.520764π0.520764\pi
434434 0.749825 8.31197i 0.0359927 0.398987i
435435 0 0
436436 13.9593 + 24.1782i 0.668529 + 1.15793i
437437 12.4724 21.6028i 0.596635 1.03340i
438438 0 0
439439 4.41760 + 7.65150i 0.210840 + 0.365186i 0.951978 0.306167i 0.0990467π-0.0990467\pi
−0.741137 + 0.671353i 0.765713π0.765713\pi
440440 0.0445303 0.00212290
441441 0 0
442442 −4.72459 −0.224726
443443 −1.45279 2.51630i −0.0690240 0.119553i 0.829448 0.558584i 0.188655π-0.188655\pi
−0.898472 + 0.439031i 0.855322π0.855322\pi
444444 0 0
445445 −5.45700 + 9.45179i −0.258686 + 0.448058i
446446 −17.7100 30.6747i −0.838595 1.45249i
447447 0 0
448448 −1.96609 + 21.7945i −0.0928888 + 1.02969i
449449 15.2777 0.720998 0.360499 0.932760i 0.382606π-0.382606\pi
0.360499 + 0.932760i 0.382606π0.382606\pi
450450 0 0
451451 −1.76285 + 3.05334i −0.0830093 + 0.143776i
452452 −3.31366 + 5.73942i −0.155861 + 0.269960i
453453 0 0
454454 10.7035 0.502341
455455 2.17452 1.00686i 0.101943 0.0472022i
456456 0 0
457457 −11.8300 20.4902i −0.553384 0.958489i −0.998027 0.0627815i 0.980003π-0.980003\pi
0.444643 0.895708i 0.353330π-0.353330\pi
458458 8.55531 14.8182i 0.399763 0.692410i
459459 0 0
460460 −3.46283 5.99779i −0.161455 0.279649i
461461 26.6170 1.23968 0.619839 0.784729i 0.287198π-0.287198\pi
0.619839 + 0.784729i 0.287198π0.287198\pi
462462 0 0
463463 −1.44250 −0.0670385 −0.0335193 0.999438i 0.510672π-0.510672\pi
−0.0335193 + 0.999438i 0.510672π0.510672\pi
464464 −6.40276 11.0899i −0.297240 0.514836i
465465 0 0
466466 4.77397 8.26876i 0.221150 0.383043i
467467 −4.19480 7.26560i −0.194112 0.336212i 0.752497 0.658596i 0.228849π-0.228849\pi
−0.946609 + 0.322384i 0.895516π0.895516\pi
468468 0 0
469469 20.3159 + 14.3073i 0.938102 + 0.660648i
470470 −15.1352 −0.698135
471471 0 0
472472 0.0245828 0.0425786i 0.00113151 0.00195984i
473473 −3.38039 + 5.85500i −0.155430 + 0.269213i
474474 0 0
475475 −27.7359 −1.27261
476476 11.4880 5.31922i 0.526552 0.243806i
477477 0 0
478478 14.8946 + 25.7983i 0.681265 + 1.17999i
479479 6.30608 10.9225i 0.288132 0.499060i −0.685232 0.728325i 0.740299π-0.740299\pi
0.973364 + 0.229265i 0.0736324π0.0736324\pi
480480 0 0
481481 −2.60441 4.51098i −0.118751 0.205683i
482482 −12.2948 −0.560013
483483 0 0
484484 −21.3320 −0.969636
485485 3.36823 + 5.83394i 0.152943 + 0.264905i
486486 0 0
487487 −10.7840 + 18.6785i −0.488671 + 0.846403i −0.999915 0.0130329i 0.995851π-0.995851\pi
0.511244 + 0.859435i 0.329185π0.329185\pi
488488 0.399875 + 0.692604i 0.0181015 + 0.0313527i
489489 0 0
490490 −8.23791 + 9.71058i −0.372151 + 0.438679i
491491 −39.2347 −1.77064 −0.885318 0.464987i 0.846059π-0.846059\pi
−0.885318 + 0.464987i 0.846059π0.846059\pi
492492 0 0
493493 −3.83184 + 6.63694i −0.172577 + 0.298913i
494494 −6.66419 + 11.5427i −0.299836 + 0.519332i
495495 0 0
496496 −6.17283 −0.277168
497497 −2.61275 + 28.9629i −0.117198 + 1.29916i
498498 0 0
499499 −4.58407 7.93984i −0.205211 0.355436i 0.744989 0.667077i 0.232455π-0.232455\pi
−0.950200 + 0.311641i 0.899121π0.899121\pi
500500 −8.45627 + 14.6467i −0.378176 + 0.655020i
501501 0 0
502502 −14.0304 24.3013i −0.626207 1.08462i
503503 −24.9370 −1.11188 −0.555942 0.831221i 0.687642π-0.687642\pi
−0.555942 + 0.831221i 0.687642π0.687642\pi
504504 0 0
505505 −1.08601 −0.0483267
506506 −2.70432 4.68402i −0.120222 0.208230i
507507 0 0
508508 0.967080 1.67503i 0.0429072 0.0743175i
509509 2.94904 + 5.10788i 0.130714 + 0.226403i 0.923952 0.382509i 0.124940π-0.124940\pi
−0.793238 + 0.608912i 0.791606π0.791606\pi
510510 0 0
511511 −7.51268 5.29072i −0.332341 0.234048i
512512 32.1083 1.41900
513513 0 0
514514 17.3386 30.0314i 0.764775 1.32463i
515515 −6.52677 + 11.3047i −0.287604 + 0.498144i
516516 0 0
517517 −5.96003 −0.262122
518518 22.6312 + 15.9378i 0.994357 + 0.700265i
519519 0 0
520520 0.0310809 + 0.0538337i 0.00136299 + 0.00236076i
521521 −18.5948 + 32.2071i −0.814652 + 1.41102i 0.0949259 + 0.995484i 0.469739π0.469739\pi
−0.909578 + 0.415534i 0.863595π0.863595\pi
522522 0 0
523523 2.54540 + 4.40876i 0.111303 + 0.192782i 0.916296 0.400502i 0.131164π-0.131164\pi
−0.804993 + 0.593284i 0.797831π0.797831\pi
524524 38.2823 1.67237
525525 0 0
526526 5.23567 0.228286
527527 1.84712 + 3.19931i 0.0804618 + 0.139364i
528528 0 0
529529 4.43475 7.68121i 0.192815 0.333966i
530530 −12.8099 22.1874i −0.556426 0.963758i
531531 0 0
532532 3.20873 35.5694i 0.139116 1.54213i
533533 −4.92168 −0.213181
534534 0 0
535535 −6.15583 + 10.6622i −0.266140 + 0.460968i
536536 −0.322289 + 0.558220i −0.0139208 + 0.0241114i
537537 0 0
538538 29.1026 1.25470
539539 −3.24397 + 3.82389i −0.139728 + 0.164707i
540540 0 0
541541 0.383425 + 0.664111i 0.0164847 + 0.0285524i 0.874150 0.485656i 0.161419π-0.161419\pi
−0.857665 + 0.514208i 0.828086π0.828086\pi
542542 8.67272 15.0216i 0.372525 0.645232i
543543 0 0
544544 −9.44643 16.3617i −0.405012 0.701502i
545545 12.4309 0.532480
546546 0 0
547547 14.1428 0.604702 0.302351 0.953197i 0.402229π-0.402229\pi
0.302351 + 0.953197i 0.402229π0.402229\pi
548548 6.28741 + 10.8901i 0.268585 + 0.465203i
549549 0 0
550550 −3.00691 + 5.20813i −0.128215 + 0.222075i
551551 10.8099 + 18.7233i 0.460516 + 0.797637i
552552 0 0
553553 −31.2310 + 14.4607i −1.32808 + 0.614932i
554554 24.5582 1.04338
555555 0 0
556556 4.06834 7.04657i 0.172536 0.298841i
557557 −12.4314 + 21.5317i −0.526733 + 0.912329i 0.472782 + 0.881180i 0.343250π0.343250\pi
−0.999515 + 0.0311490i 0.990083π0.990083\pi
558558 0 0
559559 −9.43766 −0.399171
560560 7.70072 + 5.42315i 0.325415 + 0.229170i
561561 0 0
562562 −24.2852 42.0633i −1.02441 1.77433i
563563 22.0047 38.1133i 0.927388 1.60628i 0.139713 0.990192i 0.455382π-0.455382\pi
0.787675 0.616091i 0.211285π-0.211285\pi
564564 0 0
565565 1.47542 + 2.55550i 0.0620713 + 0.107511i
566566 −61.7989 −2.59760
567567 0 0
568568 −0.754366 −0.0316525
569569 −16.6308 28.8054i −0.697199 1.20758i −0.969434 0.245353i 0.921096π-0.921096\pi
0.272235 0.962231i 0.412237π-0.412237\pi
570570 0 0
571571 6.17699 10.6989i 0.258499 0.447734i −0.707341 0.706873i 0.750105π-0.750105\pi
0.965840 + 0.259139i 0.0834387π0.0834387\pi
572572 0.728600 + 1.26197i 0.0304643 + 0.0527657i
573573 0 0
574574 23.7334 10.9891i 0.990613 0.458678i
575575 15.7116 0.655219
576576 0 0
577577 12.9829 22.4871i 0.540486 0.936150i −0.458390 0.888751i 0.651574π-0.651574\pi
0.998876 0.0473984i 0.0150930π-0.0150930\pi
578578 11.5157 19.9458i 0.478990 0.829635i
579579 0 0
580580 6.00250 0.249240
581581 −0.841685 + 9.33026i −0.0349190 + 0.387085i
582582 0 0
583583 −5.04435 8.73707i −0.208916 0.361853i
584584 0.119180 0.206426i 0.00493171 0.00854196i
585585 0 0
586586 −31.9652 55.3653i −1.32047 2.28712i
587587 23.9747 0.989543 0.494771 0.869023i 0.335252π-0.335252\pi
0.494771 + 0.869023i 0.335252π0.335252\pi
588588 0 0
589589 10.4217 0.429418
590590 −0.651589 1.12859i −0.0268255 0.0464631i
591591 0 0
592592 10.2366 17.7304i 0.420723 0.728713i
593593 23.5240 + 40.7448i 0.966015 + 1.67319i 0.706862 + 0.707352i 0.250110π0.250110\pi
0.259154 + 0.965836i 0.416556π0.416556\pi
594594 0 0
595595 0.506439 5.61398i 0.0207620 0.230151i
596596 42.8744 1.75620
597597 0 0
598598 3.77508 6.53863i 0.154374 0.267384i
599599 10.0868 17.4708i 0.412135 0.713840i −0.582988 0.812481i 0.698116π-0.698116\pi
0.995123 + 0.0986415i 0.0314497π0.0314497\pi
600600 0 0
601601 29.5773 1.20648 0.603242 0.797558i 0.293875π-0.293875\pi
0.603242 + 0.797558i 0.293875π0.293875\pi
602602 45.5105 21.0724i 1.85487 0.858849i
603603 0 0
604604 15.9921 + 27.6991i 0.650708 + 1.12706i
605605 −4.74907 + 8.22564i −0.193077 + 0.334420i
606606 0 0
607607 7.72099 + 13.3732i 0.313385 + 0.542799i 0.979093 0.203413i 0.0652035π-0.0652035\pi
−0.665708 + 0.746213i 0.731870π0.731870\pi
608608 −53.2980 −2.16152
609609 0 0
610610 21.1981 0.858287
611611 −4.15993 7.20521i −0.168293 0.291492i
612612 0 0
613613 −0.997423 + 1.72759i −0.0402855 + 0.0697766i −0.885465 0.464706i 0.846160π-0.846160\pi
0.845180 + 0.534482i 0.179493π0.179493\pi
614614 −28.9111 50.0755i −1.16676 2.02088i
615615 0 0
616616 −0.106353 0.0748982i −0.00428510 0.00301773i
617617 2.85584 0.114972 0.0574858 0.998346i 0.481692π-0.481692\pi
0.0574858 + 0.998346i 0.481692π0.481692\pi
618618 0 0
619619 −15.9911 + 27.6975i −0.642738 + 1.11326i 0.342080 + 0.939671i 0.388868π0.388868\pi
−0.984819 + 0.173585i 0.944465π0.944465\pi
620620 1.44674 2.50582i 0.0581024 0.100636i
621621 0 0
622622 −11.0843 −0.444440
623623 28.9307 13.3956i 1.15908 0.536684i
624624 0 0
625625 −6.68398 11.5770i −0.267359 0.463080i
626626 4.86865 8.43275i 0.194590 0.337040i
627627 0 0
628628 7.91800 + 13.7144i 0.315963 + 0.547263i
629629 −12.2526 −0.488542
630630 0 0
631631 32.1115 1.27834 0.639169 0.769066i 0.279278π-0.279278\pi
0.639169 + 0.769066i 0.279278π0.279278\pi
632632 −0.446390 0.773171i −0.0177565 0.0307551i
633633 0 0
634634 −7.68774 + 13.3156i −0.305319 + 0.528828i
635635 −0.430596 0.745814i −0.0170877 0.0295967i
636636 0 0
637637 −6.88699 1.25275i −0.272872 0.0496357i
638638 4.68769 0.185588
639639 0 0
640640 −0.248611 + 0.430607i −0.00982721 + 0.0170212i
641641 16.5124 28.6003i 0.652200 1.12964i −0.330387 0.943845i 0.607179π-0.607179\pi
0.982588 0.185799i 0.0594873π-0.0594873\pi
642642 0 0
643643 15.7942 0.622863 0.311432 0.950269i 0.399192π-0.399192\pi
0.311432 + 0.950269i 0.399192π0.399192\pi
644644 −1.81765 + 20.1491i −0.0716256 + 0.793985i
645645 0 0
646646 15.6760 + 27.1516i 0.616764 + 1.06827i
647647 −2.32036 + 4.01898i −0.0912227 + 0.158002i −0.908026 0.418914i 0.862411π-0.862411\pi
0.816803 + 0.576916i 0.195744π0.195744\pi
648648 0 0
649649 −0.256587 0.444421i −0.0100719 0.0174451i
650650 −8.39497 −0.329278
651651 0 0
652652 3.43757 0.134626
653653 13.4143 + 23.2342i 0.524941 + 0.909225i 0.999578 + 0.0290430i 0.00924599π0.00924599\pi
−0.474637 + 0.880182i 0.657421π0.657421\pi
654654 0 0
655655 8.52266 14.7617i 0.333008 0.576787i
656656 −9.67230 16.7529i −0.377640 0.654092i
657657 0 0
658658 36.1479 + 25.4568i 1.40919 + 0.992409i
659659 42.9889 1.67461 0.837306 0.546735i 0.184129π-0.184129\pi
0.837306 + 0.546735i 0.184129π0.184129\pi
660660 0 0
661661 14.7349 25.5216i 0.573122 0.992676i −0.423121 0.906073i 0.639066π-0.639066\pi
0.996243 0.0866030i 0.0276012π-0.0276012\pi
662662 −11.3915 + 19.7307i −0.442744 + 0.766855i
663663 0 0
664664 −0.243015 −0.00943082
665665 −13.0013 9.15599i −0.504167 0.355054i
666666 0 0
667667 −6.12349 10.6062i −0.237102 0.410673i
668668 −22.2403 + 38.5214i −0.860504 + 1.49044i
669669 0 0
670670 8.54256 + 14.7962i 0.330028 + 0.571625i
671671 8.34752 0.322252
672672 0 0
673673 −20.1702 −0.777504 −0.388752 0.921342i 0.627094π-0.627094\pi
−0.388752 + 0.921342i 0.627094π0.627094\pi
674674 −1.74891 3.02920i −0.0673655 0.116680i
675675 0 0
676676 −1.01709 + 1.76164i −0.0391187 + 0.0677555i
677677 −3.10241 5.37353i −0.119235 0.206521i 0.800230 0.599694i 0.204711π-0.204711\pi
−0.919465 + 0.393172i 0.871378π0.871378\pi
678678 0 0
679679 1.76800 19.5986i 0.0678495 0.752126i
680680 0.146221 0.00560733
681681 0 0
682682 1.12984 1.95694i 0.0432638 0.0749351i
683683 −0.884758 + 1.53245i −0.0338543 + 0.0586374i −0.882456 0.470395i 0.844112π-0.844112\pi
0.848602 + 0.529032i 0.177445π0.177445\pi
684684 0 0
685685 5.59899 0.213926
686686 36.0077 9.33627i 1.37478 0.356460i
687687 0 0
688688 −18.5473 32.1249i −0.707110 1.22475i
689689 7.04163 12.1965i 0.268265 0.464648i
690690 0 0
691691 −22.4658 38.9120i −0.854641 1.48028i −0.876977 0.480531i 0.840444π-0.840444\pi
0.0223363 0.999751i 0.492890π-0.492890\pi
692692 −11.8820 −0.451688
693693 0 0
694694 −42.2800 −1.60493
695695 −1.81144 3.13751i −0.0687120 0.119013i
696696 0 0
697697 −5.78856 + 10.0261i −0.219257 + 0.379765i
698698 8.39162 + 14.5347i 0.317628 + 0.550147i
699699 0 0
700700 20.4126 9.45154i 0.771525 0.357235i
701701 −38.5707 −1.45679 −0.728397 0.685156i 0.759734π-0.759734\pi
−0.728397 + 0.685156i 0.759734π0.759734\pi
702702 0 0
703703 −17.2827 + 29.9344i −0.651828 + 1.12900i
704704 −2.96251 + 5.13121i −0.111654 + 0.193390i
705705 0 0
706706 17.1398 0.645066
707707 2.59375 + 1.82662i 0.0975480 + 0.0686972i
708708 0 0
709709 −4.38866 7.60137i −0.164819 0.285476i 0.771772 0.635900i 0.219371π-0.219371\pi
−0.936591 + 0.350424i 0.886037π0.886037\pi
710710 −9.99758 + 17.3163i −0.375203 + 0.649870i
711711 0 0
712712 0.413512 + 0.716223i 0.0154970 + 0.0268416i
713713 −5.90360 −0.221091
714714 0 0
715715 0.648824 0.0242646
716716 2.57757 + 4.46449i 0.0963284 + 0.166846i
717717 0 0
718718 −16.2402 + 28.1289i −0.606080 + 1.04976i
719719 2.10218 + 3.64109i 0.0783982 + 0.135790i 0.902559 0.430566i 0.141686π-0.141686\pi
−0.824161 + 0.566356i 0.808353π0.808353\pi
720720 0 0
721721 34.6022 16.0216i 1.28865 0.596677i
722722 50.2840 1.87138
723723 0 0
724724 10.9080 18.8933i 0.405394 0.702164i
725725 −6.80866 + 11.7930i −0.252867 + 0.437979i
726726 0 0
727727 −28.9856 −1.07502 −0.537509 0.843258i 0.680634π-0.680634\pi
−0.537509 + 0.843258i 0.680634π0.680634\pi
728728 0.0163145 0.180850i 0.000604656 0.00670274i
729729 0 0
730730 −3.15898 5.47151i −0.116919 0.202510i
731731 −11.1000 + 19.2257i −0.410547 + 0.711089i
732732 0 0
733733 12.0172 + 20.8145i 0.443867 + 0.768800i 0.997972 0.0636467i 0.0202731π-0.0202731\pi
−0.554106 + 0.832446i 0.686940π0.686940\pi
734734 56.5480 2.08722
735735 0 0
736736 30.1918 1.11288
737737 3.36394 + 5.82652i 0.123912 + 0.214622i
738738 0 0
739739 −5.90276 + 10.2239i −0.217136 + 0.376091i −0.953931 0.300025i 0.903005π-0.903005\pi
0.736795 + 0.676116i 0.236338π0.236338\pi
740740 4.79835 + 8.31099i 0.176391 + 0.305518i
741741 0 0
742742 −6.72396 + 74.5366i −0.246844 + 2.73632i
743743 −47.2786 −1.73448 −0.867241 0.497888i 0.834109π-0.834109\pi
−0.867241 + 0.497888i 0.834109π0.834109\pi
744744 0 0
745745 9.54499 16.5324i 0.349701 0.605700i
746746 28.6252 49.5802i 1.04804 1.81526i
747747 0 0
748748 3.42773 0.125330
749749 32.6356 15.1111i 1.19248 0.552147i
750750 0 0
751751 −2.73850 4.74322i −0.0999294 0.173083i 0.811726 0.584039i 0.198528π-0.198528\pi
−0.911655 + 0.410956i 0.865195π0.865195\pi
752752 16.3506 28.3200i 0.596244 1.03273i
753753 0 0
754754 3.27188 + 5.66706i 0.119155 + 0.206382i
755755 14.2410 0.518285
756756 0 0
757757 10.7453 0.390546 0.195273 0.980749i 0.437441π-0.437441\pi
0.195273 + 0.980749i 0.437441π0.437441\pi
758758 7.29358 + 12.6329i 0.264915 + 0.458846i
759759 0 0
760760 0.206250 0.357236i 0.00748148 0.0129583i
761761 −16.5200 28.6134i −0.598848 1.03724i −0.992991 0.118186i 0.962292π-0.962292\pi
0.394143 0.919049i 0.371041π-0.371041\pi
762762 0 0
763763 −29.6891 20.9082i −1.07482 0.756928i
764764 3.41457 0.123535
765765 0 0
766766 12.9877 22.4953i 0.469263 0.812788i
767767 0.358181 0.620387i 0.0129332 0.0224009i
768768 0 0
769769 2.98332 0.107581 0.0537907 0.998552i 0.482870π-0.482870\pi
0.0537907 + 0.998552i 0.482870π0.482870\pi
770770 −3.12877 + 1.44870i −0.112753 + 0.0522074i
771771 0 0
772772 6.55833 + 11.3594i 0.236039 + 0.408832i
773773 −10.9543 + 18.9733i −0.393998 + 0.682424i −0.992973 0.118344i 0.962242π-0.962242\pi
0.598975 + 0.800768i 0.295575π0.295575\pi
774774 0 0
775775 3.28208 + 5.68473i 0.117896 + 0.204202i
776776 0.510464 0.0183246
777777 0 0
778778 42.4516 1.52196
779779 16.3299 + 28.2842i 0.585079 + 1.01339i
780780 0 0
781781 −3.93691 + 6.81892i −0.140874 + 0.244000i
782782 −8.88001 15.3806i −0.317548 0.550010i
783783 0 0
784784 −9.27039 25.9046i −0.331085 0.925165i
785785 7.05104 0.251662
786786 0 0
787787 6.68161 11.5729i 0.238174 0.412529i −0.722017 0.691876i 0.756785π-0.756785\pi
0.960190 + 0.279347i 0.0901179π0.0901179\pi
788788 1.90450 3.29869i 0.0678451 0.117511i
789789 0 0
790790 −23.6640 −0.841927
791791 0.774453 8.58498i 0.0275364 0.305247i
792792 0 0
793793 5.82633 + 10.0915i 0.206899 + 0.358360i
794794 −19.2892 + 33.4099i −0.684548 + 1.18567i
795795 0 0
796796 11.5914 + 20.0768i 0.410845 + 0.711605i
797797 −32.5388 −1.15258 −0.576292 0.817244i 0.695501π-0.695501\pi
−0.576292 + 0.817244i 0.695501π0.695501\pi
798798 0 0
799799 −19.5706 −0.692357
800800 −16.7850 29.0725i −0.593440 1.02787i
801801 0 0
802802 16.7403 28.9950i 0.591119 1.02385i
803803 −1.24396 2.15460i −0.0438984 0.0760343i
804804 0 0
805805 7.36484 + 5.18661i 0.259577 + 0.182804i
806806 3.15439 0.111109
807807 0 0
808808 −0.0411469 + 0.0712685i −0.00144754 + 0.00250722i
809809 3.84413 6.65824i 0.135153 0.234091i −0.790503 0.612458i 0.790181π-0.790181\pi
0.925656 + 0.378367i 0.123514π0.123514\pi
810810 0 0
811811 −48.3178 −1.69667 −0.848334 0.529461i 0.822394π-0.822394\pi
−0.848334 + 0.529461i 0.822394π0.822394\pi
812812 −14.3360 10.0960i −0.503094 0.354299i
813813 0 0
814814 3.74731 + 6.49052i 0.131343 + 0.227493i
815815 0.765295 1.32553i 0.0268071 0.0464313i
816816 0 0
817817 31.3137 + 54.2370i 1.09553 + 1.89751i
818818 24.8019 0.867178
819819 0 0
820820 9.06766 0.316656
821821 −1.86721 3.23410i −0.0651661 0.112871i 0.831602 0.555373i 0.187424π-0.187424\pi
−0.896768 + 0.442502i 0.854091π0.854091\pi
822822 0 0
823823 −7.11590 + 12.3251i −0.248045 + 0.429626i −0.962983 0.269561i 0.913121π-0.913121\pi
0.714939 + 0.699187i 0.246455π0.246455\pi
824824 0.494575 + 0.856629i 0.0172293 + 0.0298421i
825825 0 0
826826 −0.342022 + 3.79139i −0.0119005 + 0.131919i
827827 −48.3016 −1.67961 −0.839805 0.542888i 0.817331π-0.817331\pi
−0.839805 + 0.542888i 0.817331π0.817331\pi
828828 0 0
829829 −5.75506 + 9.96806i −0.199882 + 0.346205i −0.948490 0.316808i 0.897389π-0.897389\pi
0.748608 + 0.663013i 0.230722π0.230722\pi
830830 −3.22067 + 5.57837i −0.111791 + 0.193628i
831831 0 0
832832 −8.27099 −0.286745
833833 −10.6520 + 12.5563i −0.369071 + 0.435049i
834834 0 0
835835 9.90258 + 17.1518i 0.342693 + 0.593562i
836836 4.83493 8.37434i 0.167219 0.289633i
837837 0 0
838838 4.37792 + 7.58278i 0.151233 + 0.261943i
839839 −13.1103 −0.452616 −0.226308 0.974056i 0.572666π-0.572666\pi
−0.226308 + 0.974056i 0.572666π0.572666\pi
840840 0 0
841841 −18.3855 −0.633982
842842 10.0426 + 17.3943i 0.346092 + 0.599448i
843843 0 0
844844 −7.66475 + 13.2757i −0.263831 + 0.456969i
845845 0.452861 + 0.784378i 0.0155789 + 0.0269834i
846846 0 0
847847 25.1776 11.6578i 0.865111 0.400568i
848848 55.3541 1.90087
849849 0 0
850850 −9.87362 + 17.1016i −0.338662 + 0.586580i
851851 9.79014 16.9570i 0.335602 0.581279i
852852 0 0
853853 8.80346 0.301425 0.150712 0.988578i 0.451843π-0.451843\pi
0.150712 + 0.988578i 0.451843π0.451843\pi
854854 −50.6282 35.6544i −1.73246 1.22007i
855855 0 0
856856 0.466467 + 0.807945i 0.0159435 + 0.0276150i
857857 8.48254 14.6922i 0.289758 0.501876i −0.683994 0.729488i 0.739758π-0.739758\pi
0.973752 + 0.227612i 0.0730918π0.0730918\pi
858858 0 0
859859 −7.27049 12.5929i −0.248066 0.429663i 0.714923 0.699203i 0.246462π-0.246462\pi
−0.962989 + 0.269540i 0.913128π0.913128\pi
860860 17.3879 0.592922
861861 0 0
862862 46.9243 1.59825
863863 19.5222 + 33.8135i 0.664544 + 1.15102i 0.979409 + 0.201887i 0.0647074π0.0647074\pi
−0.314865 + 0.949136i 0.601959π0.601959\pi
864864 0 0
865865 −2.64526 + 4.58173i −0.0899416 + 0.155783i
866866 2.72441 + 4.71882i 0.0925793 + 0.160352i
867867 0 0
868868 −7.66999 + 3.55139i −0.260336 + 0.120542i
869869 −9.31854 −0.316110
870870 0 0
871871 −4.69587 + 8.13349i −0.159114 + 0.275593i
872872 0.470983 0.815767i 0.0159495 0.0276253i
873873 0 0
874874 −50.1022 −1.69473
875875 1.97636 21.9084i 0.0668133 0.740639i
876876 0 0
877877 −16.2971 28.2273i −0.550312 0.953169i −0.998252 0.0591051i 0.981175π-0.981175\pi
0.447939 0.894064i 0.352158π-0.352158\pi
878878 8.87285 15.3682i 0.299444 0.518652i
879879 0 0
880880 1.27510 + 2.20853i 0.0429835 + 0.0744497i
881881 43.4141 1.46266 0.731330 0.682024i 0.238900π-0.238900\pi
0.731330 + 0.682024i 0.238900π0.238900\pi
882882 0 0
883883 28.2902 0.952040 0.476020 0.879434i 0.342079π-0.342079\pi
0.476020 + 0.879434i 0.342079π0.342079\pi
884884 2.39246 + 4.14386i 0.0804672 + 0.139373i
885885 0 0
886886 −2.91796 + 5.05406i −0.0980308 + 0.169794i
887887 −25.1325 43.5307i −0.843866 1.46162i −0.886602 0.462532i 0.846941π-0.846941\pi
0.0427364 0.999086i 0.486392π-0.486392\pi
888888 0 0
889889 −0.226022 + 2.50550i −0.00758052 + 0.0840317i
890890 21.9210 0.734794
891891 0 0
892892 −17.9362 + 31.0664i −0.600548 + 1.04018i
893893 −27.6049 + 47.8131i −0.923764 + 1.60001i
894894 0 0
895895 2.29535 0.0767250
896896 1.31803 0.610280i 0.0440323 0.0203880i
897897 0 0
898898 −15.3428 26.5745i −0.511996 0.886803i
899899 2.55834 4.43117i 0.0853253 0.147788i
900900 0 0
901901 −16.5638 28.6894i −0.551821 0.955782i
902902 7.08145 0.235786
903903 0 0
904904 0.223604 0.00743695
905905 −4.85685 8.41231i −0.161447 0.279635i
906906 0 0
907907 −13.4138 + 23.2334i −0.445399 + 0.771453i −0.998080 0.0619394i 0.980271π-0.980271\pi
0.552681 + 0.833393i 0.313605π0.313605\pi
908908 −5.42009 9.38787i −0.179872 0.311548i
909909 0 0
910910 −3.93516 2.77129i −0.130449 0.0918674i
911911 22.3560 0.740687 0.370344 0.928895i 0.379240π-0.379240\pi
0.370344 + 0.928895i 0.379240π0.379240\pi
912912 0 0
913913 −1.26826 + 2.19668i −0.0419731 + 0.0726996i
914914 −23.7608 + 41.1550i −0.785939 + 1.36129i
915915 0 0
916916 −17.3291 −0.572569
917917 −45.1835 + 20.9211i −1.49209 + 0.690875i
918918 0 0
919919 4.31122 + 7.46725i 0.142214 + 0.246322i 0.928330 0.371757i 0.121245π-0.121245\pi
−0.786116 + 0.618079i 0.787911π0.787911\pi
920920 −0.116835 + 0.202364i −0.00385193 + 0.00667174i
921921 0 0
922922 −26.7305 46.2985i −0.880321 1.52476i
923923 −10.9914 −0.361786
924924 0 0
925925 −21.7712 −0.715832
926926 1.44865 + 2.50913i 0.0476054 + 0.0824550i
927927 0 0
928928 −13.0837 + 22.6616i −0.429493 + 0.743904i
929929 20.6930 + 35.8414i 0.678916 + 1.17592i 0.975308 + 0.220851i 0.0708834π0.0708834\pi
−0.296391 + 0.955067i 0.595783π0.595783\pi
930930 0 0
931931 15.6513 + 43.7352i 0.512952 + 1.43336i
932932 −9.66985 −0.316747
933933 0 0
934934 −8.42535 + 14.5931i −0.275686 + 0.477502i
935935 0.763105 1.32174i 0.0249562 0.0432254i
936936 0 0
937937 21.3818 0.698514 0.349257 0.937027i 0.386434π-0.386434\pi
0.349257 + 0.937027i 0.386434π0.386434\pi
938938 4.48403 49.7064i 0.146409 1.62297i
939939 0 0
940940 7.66423 + 13.2748i 0.249979 + 0.432977i
941941 −26.5740 + 46.0275i −0.866288 + 1.50046i −0.000525658 1.00000i 0.500167π0.500167\pi
−0.865762 + 0.500455i 0.833166π0.833166\pi
942942 0 0
943943 −9.25043 16.0222i −0.301235 0.521755i
944944 2.81565 0.0916416
945945 0 0
946946 13.5792 0.441497
947947 −4.43468 7.68109i −0.144108 0.249602i 0.784932 0.619582i 0.212698π-0.212698\pi
−0.929040 + 0.369980i 0.879365π0.879365\pi
948948 0 0
949949 1.73650 3.00771i 0.0563692 0.0976343i
950950 27.8541 + 48.2448i 0.903707 + 1.56527i
951951 0 0
952952 −0.349226 0.245939i −0.0113185 0.00797091i
953953 39.8167 1.28979 0.644894 0.764272i 0.276901π-0.276901\pi
0.644894 + 0.764272i 0.276901π0.276901\pi
954954 0 0
955955 0.760174 1.31666i 0.0245987 0.0426061i
956956 15.0848 26.1277i 0.487878 0.845029i
957957 0 0
958958 −25.3319 −0.818435
959959 −13.3723 9.41727i −0.431813 0.304099i
960960 0 0
961961 14.2668 + 24.7108i 0.460218 + 0.797121i
962962 −5.23103 + 9.06041i −0.168655 + 0.292119i
963963 0 0
964964 6.22589 + 10.7836i 0.200523 + 0.347315i
965965 5.84024 0.188004
966966 0 0
967967 −22.1611 −0.712652 −0.356326 0.934362i 0.615971π-0.615971\pi
−0.356326 + 0.934362i 0.615971π0.615971\pi
968968 0.359868 + 0.623309i 0.0115666 + 0.0200339i
969969 0 0
970970 6.76516 11.7176i 0.217216 0.376230i
971971 18.0212 + 31.2136i 0.578327 + 1.00169i 0.995671 + 0.0929428i 0.0296274π0.0296274\pi
−0.417345 + 0.908748i 0.637039π0.637039\pi
972972 0 0
973973 −0.950834 + 10.5402i −0.0304824 + 0.337903i
974974 43.3199 1.38806
975975 0 0
976976 −22.9004 + 39.6646i −0.733022 + 1.26963i
977977 16.4708 28.5283i 0.526947 0.912700i −0.472559 0.881299i 0.656670π-0.656670\pi
0.999507 0.0314009i 0.00999687π-0.00999687\pi
978978 0 0
979979 8.63219 0.275886
980980 12.6885 + 2.30805i 0.405320 + 0.0737281i
981981 0 0
982982 39.4019 + 68.2461i 1.25736 + 2.17782i
983983 −2.09973 + 3.63683i −0.0669709 + 0.115997i −0.897567 0.440879i 0.854667π-0.854667\pi
0.830596 + 0.556876i 0.188000π0.188000\pi
984984 0 0
985985 −0.847986 1.46876i −0.0270191 0.0467984i
986986 15.3927 0.490203
987987 0 0
988988 13.4986 0.429447
989989 −17.7383 30.7237i −0.564047 0.976958i
990990 0 0
991991 6.70693 11.6167i 0.213053 0.369018i −0.739616 0.673029i 0.764993π-0.764993\pi
0.952668 + 0.304011i 0.0983261π0.0983261\pi
992992 6.30693 + 10.9239i 0.200245 + 0.346835i
993993 0 0
994994 53.0029 24.5416i 1.68115 0.778414i
995995 10.3222 0.327236
996996 0 0
997997 23.9434 41.4712i 0.758295 1.31341i −0.185424 0.982659i 0.559366π-0.559366\pi
0.943719 0.330747i 0.107301π-0.107301\pi
998998 −9.20722 + 15.9474i −0.291449 + 0.504805i
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 819.2.j.h.235.1 10
3.2 odd 2 91.2.e.c.53.5 10
7.2 even 3 inner 819.2.j.h.352.1 10
7.3 odd 6 5733.2.a.bm.1.5 5
7.4 even 3 5733.2.a.bl.1.5 5
12.11 even 2 1456.2.r.p.417.4 10
21.2 odd 6 91.2.e.c.79.5 yes 10
21.5 even 6 637.2.e.m.79.5 10
21.11 odd 6 637.2.a.l.1.1 5
21.17 even 6 637.2.a.k.1.1 5
21.20 even 2 637.2.e.m.508.5 10
39.38 odd 2 1183.2.e.f.508.1 10
84.23 even 6 1456.2.r.p.625.4 10
273.38 even 6 8281.2.a.bx.1.5 5
273.116 odd 6 8281.2.a.bw.1.5 5
273.233 odd 6 1183.2.e.f.170.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.5 10 3.2 odd 2
91.2.e.c.79.5 yes 10 21.2 odd 6
637.2.a.k.1.1 5 21.17 even 6
637.2.a.l.1.1 5 21.11 odd 6
637.2.e.m.79.5 10 21.5 even 6
637.2.e.m.508.5 10 21.20 even 2
819.2.j.h.235.1 10 1.1 even 1 trivial
819.2.j.h.352.1 10 7.2 even 3 inner
1183.2.e.f.170.1 10 273.233 odd 6
1183.2.e.f.508.1 10 39.38 odd 2
1456.2.r.p.417.4 10 12.11 even 2
1456.2.r.p.625.4 10 84.23 even 6
5733.2.a.bl.1.5 5 7.4 even 3
5733.2.a.bm.1.5 5 7.3 odd 6
8281.2.a.bw.1.5 5 273.116 odd 6
8281.2.a.bx.1.5 5 273.38 even 6