Properties

Label 441.2.f.g.295.3
Level 441441
Weight 22
Character 441.295
Analytic conductor 3.5213.521
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(148,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 441=3272 441 = 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 441.f (of order 33, degree 22, 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: 3.521402729143.52140272914
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x127x10+37x878x6+123x436x2+9 x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 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 295.3
Root 1.295890.748185i-1.29589 - 0.748185i of defining polynomial
Character χ\chi == 441.295
Dual form 441.2.f.g.148.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.119562+0.207087i)q2+(1.124411.31746i)q3+(0.971410+1.68253i)q4+(1.29589+2.24456i)q5+(0.4072650.0753324i)q60.942820q8+(0.471410+2.96273i)q90.619757q10+(2.09097+3.62167i)q11+(1.124413.17165i)q12+(1.841553.18966i)q13+(1.500004.23109i)q15+(1.83009+3.16982i)q16+1.71107q17+(0.5571800.451852i)q187.15561q19+(2.51769+4.36077i)q20+(0.5000000.866025i)q22+(2.56238+4.43818i)q23+(1.06012+1.24213i)q24+(0.858685+1.48729i)q25+0.880716q26+(4.433342.71026i)q27+(1.062381.84010i)q29+(0.696860+0.816506i)q30+(3.26793+5.66021i)q31+(1.380442.39099i)q32+(7.122521.31746i)q33+(0.204579+0.354341i)q34+(5.44282+2.08486i)q36+1.66019q37+(0.8555361.48183i)q38+(2.13160+6.01266i)q39+(1.221802.11621i)q40+(5.10948+8.84988i)q41+(0.8300951.43777i)q438.12476q44+(7.26091+2.78128i)q451.22545q46+(4.66912+8.08715i)q47+(6.233891.15309i)q48+(0.2053320.355645i)q50+(1.923952.25427i)q51+(3.577806.19694i)q52+10.6465q53+(0.0312007+1.24213i)q5410.8387q55+(8.04583+9.42724i)q57+(0.254040+0.440011i)q58+(3.032155.25183i)q59+(8.576051.58632i)q60+(3.992986.91605i)q611.56287q626.66019q64+(4.772928.26693i)q65+(0.578751+1.63250i)q66+(4.131607.15614i)q67+(1.66215+2.87893i)q68+(2.965968.36616i)q69+6.23912q71+(0.4444552.79332i)q72+7.15561q73+(0.198495+0.343803i)q74+(2.924950.541033i)q75+(6.9510312.0395i)q76+(0.9902851.16031i)q78+(4.914238.51170i)q799.48644q80+(8.555552.79332i)q812.44359q82+(3.44733+5.97094i)q83+(2.21737+3.84060i)q85+(0.198495+0.343803i)q86+(3.61881+0.669376i)q87+(1.971413.41458i)q885.03538q89+(0.2921601.83617i)q90+(4.97825+8.62258i)q92+(3.7826310.6698i)q93+(1.116501.93383i)q94+(9.2729216.0612i)q95+(1.59786+4.50712i)q96+(1.53167+2.65294i)q97+(9.744337.90228i)q99+O(q100)q+(-0.119562 + 0.207087i) q^{2} +(-1.12441 - 1.31746i) q^{3} +(0.971410 + 1.68253i) q^{4} +(1.29589 + 2.24456i) q^{5} +(0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 + 2.96273i) q^{9} -0.619757 q^{10} +(-2.09097 + 3.62167i) q^{11} +(1.12441 - 3.17165i) q^{12} +(-1.84155 - 3.18966i) q^{13} +(1.50000 - 4.23109i) q^{15} +(-1.83009 + 3.16982i) q^{16} +1.71107 q^{17} +(-0.557180 - 0.451852i) q^{18} -7.15561 q^{19} +(-2.51769 + 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.56238 + 4.43818i) q^{23} +(1.06012 + 1.24213i) q^{24} +(-0.858685 + 1.48729i) q^{25} +0.880716 q^{26} +(4.43334 - 2.71026i) q^{27} +(1.06238 - 1.84010i) q^{29} +(0.696860 + 0.816506i) q^{30} +(3.26793 + 5.66021i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(7.12252 - 1.31746i) q^{33} +(-0.204579 + 0.354341i) q^{34} +(-5.44282 + 2.08486i) q^{36} +1.66019 q^{37} +(0.855536 - 1.48183i) q^{38} +(-2.13160 + 6.01266i) q^{39} +(-1.22180 - 2.11621i) q^{40} +(5.10948 + 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} -8.12476 q^{44} +(-7.26091 + 2.78128i) q^{45} -1.22545 q^{46} +(-4.66912 + 8.08715i) q^{47} +(6.23389 - 1.15309i) q^{48} +(-0.205332 - 0.355645i) q^{50} +(-1.92395 - 2.25427i) q^{51} +(3.57780 - 6.19694i) q^{52} +10.6465 q^{53} +(0.0312007 + 1.24213i) q^{54} -10.8387 q^{55} +(8.04583 + 9.42724i) q^{57} +(0.254040 + 0.440011i) q^{58} +(-3.03215 - 5.25183i) q^{59} +(8.57605 - 1.58632i) q^{60} +(3.99298 - 6.91605i) q^{61} -1.56287 q^{62} -6.66019 q^{64} +(4.77292 - 8.26693i) q^{65} +(-0.578751 + 1.63250i) q^{66} +(-4.13160 - 7.15614i) q^{67} +(1.66215 + 2.87893i) q^{68} +(2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(0.444455 - 2.79332i) q^{72} +7.15561 q^{73} +(-0.198495 + 0.343803i) q^{74} +(2.92495 - 0.541033i) q^{75} +(-6.95103 - 12.0395i) q^{76} +(-0.990285 - 1.16031i) q^{78} +(4.91423 - 8.51170i) q^{79} -9.48644 q^{80} +(-8.55555 - 2.79332i) q^{81} -2.44359 q^{82} +(-3.44733 + 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(0.198495 + 0.343803i) q^{86} +(-3.61881 + 0.669376i) q^{87} +(1.97141 - 3.41458i) q^{88} -5.03538 q^{89} +(0.292160 - 1.83617i) q^{90} +(-4.97825 + 8.62258i) q^{92} +(3.78263 - 10.6698i) q^{93} +(-1.11650 - 1.93383i) q^{94} +(-9.27292 - 16.0612i) q^{95} +(-1.59786 + 4.50712i) q^{96} +(-1.53167 + 2.65294i) q^{97} +(-9.74433 - 7.90228i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q2q26q4+24q8+12q98q11+18q156q1642q186q224q2312q2522q2948q3016q3230q3612q37+24q396q43+48q99+O(q100) 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/441Z)×\left(\mathbb{Z}/441\mathbb{Z}\right)^\times.

nn 199199 344344
χ(n)\chi(n) 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 −0.119562 + 0.207087i −0.0845428 + 0.146433i −0.905196 0.424994i 0.860276π-0.860276\pi
0.820653 + 0.571426i 0.193610π0.193610\pi
33 −1.12441 1.31746i −0.649178 0.760637i
44 0.971410 + 1.68253i 0.485705 + 0.841266i
55 1.29589 + 2.24456i 0.579542 + 1.00380i 0.995532 + 0.0944264i 0.0301017π0.0301017\pi
−0.415990 + 0.909369i 0.636565π0.636565\pi
66 0.407265 0.0753324i 0.166265 0.0307543i
77 0 0
88 −0.942820 −0.333337
99 −0.471410 + 2.96273i −0.157137 + 0.987577i
1010 −0.619757 −0.195984
1111 −2.09097 + 3.62167i −0.630452 + 1.09197i 0.357008 + 0.934101i 0.383797π0.383797\pi
−0.987459 + 0.157873i 0.949536π0.949536\pi
1212 1.12441 3.17165i 0.324589 0.915576i
1313 −1.84155 3.18966i −0.510755 0.884653i −0.999922 0.0124633i 0.996033π-0.996033\pi
0.489168 0.872190i 0.337301π-0.337301\pi
1414 0 0
1515 1.50000 4.23109i 0.387298 1.09246i
1616 −1.83009 + 3.16982i −0.457524 + 0.792454i
1717 1.71107 0.414996 0.207498 0.978235i 0.433468π-0.433468\pi
0.207498 + 0.978235i 0.433468π0.433468\pi
1818 −0.557180 0.451852i −0.131329 0.106502i
1919 −7.15561 −1.64161 −0.820805 0.571209i 0.806475π-0.806475\pi
−0.820805 + 0.571209i 0.806475π0.806475\pi
2020 −2.51769 + 4.36077i −0.562973 + 0.975097i
2121 0 0
2222 −0.500000 0.866025i −0.106600 0.184637i
2323 2.56238 + 4.43818i 0.534294 + 0.925424i 0.999197 + 0.0400622i 0.0127556π0.0127556\pi
−0.464904 + 0.885361i 0.653911π0.653911\pi
2424 1.06012 + 1.24213i 0.216395 + 0.253549i
2525 −0.858685 + 1.48729i −0.171737 + 0.297457i
2626 0.880716 0.172723
2727 4.43334 2.71026i 0.853197 0.521589i
2828 0 0
2929 1.06238 1.84010i 0.197279 0.341698i −0.750366 0.661023i 0.770123π-0.770123\pi
0.947645 + 0.319325i 0.103456π0.103456\pi
3030 0.696860 + 0.816506i 0.127229 + 0.149073i
3131 3.26793 + 5.66021i 0.586937 + 1.01660i 0.994631 + 0.103486i 0.0329997π0.0329997\pi
−0.407694 + 0.913119i 0.633667π0.633667\pi
3232 −1.38044 2.39099i −0.244029 0.422671i
3333 7.12252 1.31746i 1.23987 0.229341i
3434 −0.204579 + 0.354341i −0.0350850 + 0.0607689i
3535 0 0
3636 −5.44282 + 2.08486i −0.907137 + 0.347477i
3737 1.66019 0.272934 0.136467 0.990645i 0.456425π-0.456425\pi
0.136467 + 0.990645i 0.456425π0.456425\pi
3838 0.855536 1.48183i 0.138786 0.240385i
3939 −2.13160 + 6.01266i −0.341329 + 0.962796i
4040 −1.22180 2.11621i −0.193183 0.334602i
4141 5.10948 + 8.84988i 0.797967 + 1.38212i 0.920938 + 0.389708i 0.127424π0.127424\pi
−0.122972 + 0.992410i 0.539242π0.539242\pi
4242 0 0
4343 0.830095 1.43777i 0.126588 0.219257i −0.795764 0.605606i 0.792931π-0.792931\pi
0.922353 + 0.386349i 0.126264π0.126264\pi
4444 −8.12476 −1.22485
4545 −7.26091 + 2.78128i −1.08239 + 0.414609i
4646 −1.22545 −0.180683
4747 −4.66912 + 8.08715i −0.681061 + 1.17963i 0.293596 + 0.955930i 0.405148π0.405148\pi
−0.974657 + 0.223703i 0.928185π0.928185\pi
4848 6.23389 1.15309i 0.899784 0.166434i
4949 0 0
5050 −0.205332 0.355645i −0.0290383 0.0502958i
5151 −1.92395 2.25427i −0.269406 0.315661i
5252 3.57780 6.19694i 0.496152 0.859361i
5353 10.6465 1.46241 0.731206 0.682157i 0.238958π-0.238958\pi
0.731206 + 0.682157i 0.238958π0.238958\pi
5454 0.0312007 + 1.24213i 0.00424588 + 0.169032i
5555 −10.8387 −1.46149
5656 0 0
5757 8.04583 + 9.42724i 1.06570 + 1.24867i
5858 0.254040 + 0.440011i 0.0333571 + 0.0577762i
5959 −3.03215 5.25183i −0.394752 0.683730i 0.598318 0.801259i 0.295836π-0.295836\pi
−0.993069 + 0.117529i 0.962503π0.962503\pi
6060 8.57605 1.58632i 1.10716 0.204794i
6161 3.99298 6.91605i 0.511249 0.885509i −0.488666 0.872471i 0.662516π-0.662516\pi
0.999915 0.0130384i 0.00415038π-0.00415038\pi
6262 −1.56287 −0.198485
6363 0 0
6464 −6.66019 −0.832524
6565 4.77292 8.26693i 0.592007 1.02539i
6666 −0.578751 + 1.63250i −0.0712393 + 0.200947i
6767 −4.13160 7.15614i −0.504755 0.874262i −0.999985 0.00549964i 0.998249π-0.998249\pi
0.495230 0.868762i 0.335084π-0.335084\pi
6868 1.66215 + 2.87893i 0.201566 + 0.349122i
6969 2.96596 8.36616i 0.357060 1.00717i
7070 0 0
7171 6.23912 0.740448 0.370224 0.928943i 0.379281π-0.379281\pi
0.370224 + 0.928943i 0.379281π0.379281\pi
7272 0.444455 2.79332i 0.0523795 0.329196i
7373 7.15561 0.837501 0.418750 0.908101i 0.362468π-0.362468\pi
0.418750 + 0.908101i 0.362468π0.362468\pi
7474 −0.198495 + 0.343803i −0.0230746 + 0.0399663i
7575 2.92495 0.541033i 0.337745 0.0624731i
7676 −6.95103 12.0395i −0.797338 1.38103i
7777 0 0
7878 −0.990285 1.16031i −0.112128 0.131379i
7979 4.91423 8.51170i 0.552894 0.957641i −0.445170 0.895446i 0.646857π-0.646857\pi
0.998064 0.0621945i 0.0198099π-0.0198099\pi
8080 −9.48644 −1.06062
8181 −8.55555 2.79332i −0.950616 0.310369i
8282 −2.44359 −0.269849
8383 −3.44733 + 5.97094i −0.378393 + 0.655396i −0.990829 0.135124i 0.956857π-0.956857\pi
0.612436 + 0.790521i 0.290190π0.290190\pi
8484 0 0
8585 2.21737 + 3.84060i 0.240508 + 0.416571i
8686 0.198495 + 0.343803i 0.0214043 + 0.0370733i
8787 −3.61881 + 0.669376i −0.387977 + 0.0717647i
8888 1.97141 3.41458i 0.210153 0.363996i
8989 −5.03538 −0.533749 −0.266875 0.963731i 0.585991π-0.585991\pi
−0.266875 + 0.963731i 0.585991π0.585991\pi
9090 0.292160 1.83617i 0.0307963 0.193550i
9191 0 0
9292 −4.97825 + 8.62258i −0.519018 + 0.898966i
9393 3.78263 10.6698i 0.392240 1.10640i
9494 −1.11650 1.93383i −0.115158 0.199459i
9595 −9.27292 16.0612i −0.951381 1.64784i
9696 −1.59786 + 4.50712i −0.163081 + 0.460006i
9797 −1.53167 + 2.65294i −0.155518 + 0.269365i −0.933247 0.359234i 0.883038π-0.883038\pi
0.777730 + 0.628599i 0.216371π0.216371\pi
9898 0 0
9999 −9.74433 7.90228i −0.979342 0.794209i
100100 −3.33654 −0.333654
101101 5.54984 9.61260i 0.552229 0.956489i −0.445884 0.895091i 0.647111π-0.647111\pi
0.998113 0.0613986i 0.0195561π-0.0195561\pi
102102 0.696860 0.128899i 0.0689994 0.0127629i
103103 −3.99298 6.91605i −0.393440 0.681459i 0.599460 0.800404i 0.295382π-0.295382\pi
−0.992901 + 0.118946i 0.962049π0.962049\pi
104104 1.73625 + 3.00728i 0.170254 + 0.294888i
105105 0 0
106106 −1.27292 + 2.20475i −0.123636 + 0.214145i
107107 3.95649 0.382489 0.191244 0.981542i 0.438748π-0.438748\pi
0.191244 + 0.981542i 0.438748π0.438748\pi
108108 8.86668 + 4.82647i 0.853197 + 0.464427i
109109 7.26320 0.695688 0.347844 0.937552i 0.386914π-0.386914\pi
0.347844 + 0.937552i 0.386914π0.386914\pi
110110 1.29589 2.24456i 0.123559 0.214010i
111111 −1.86673 2.18724i −0.177182 0.207603i
112112 0 0
113113 −3.46457 6.00082i −0.325920 0.564509i 0.655778 0.754953i 0.272341π-0.272341\pi
−0.981698 + 0.190444i 0.939007π0.939007\pi
114114 −2.91423 + 0.539049i −0.272943 + 0.0504866i
115115 −6.64115 + 11.5028i −0.619291 + 1.07264i
116116 4.12803 0.383278
117117 10.3182 3.95238i 0.953921 0.365398i
118118 1.45011 0.133494
119119 0 0
120120 −1.41423 + 3.98916i −0.129101 + 0.364158i
121121 −3.24433 5.61934i −0.294939 0.510849i
122122 0.954815 + 1.65379i 0.0864449 + 0.149727i
123123 5.91423 16.6824i 0.533268 1.50420i
124124 −6.34899 + 10.9968i −0.570156 + 0.987540i
125125 8.50788 0.760968
126126 0 0
127127 9.11109 0.808479 0.404239 0.914653i 0.367536π-0.367536\pi
0.404239 + 0.914653i 0.367536π0.367536\pi
128128 3.55718 6.16122i 0.314413 0.544580i
129129 −2.82757 + 0.523019i −0.248954 + 0.0460493i
130130 1.14132 + 1.97682i 0.100100 + 0.173378i
131131 2.15143 + 3.72639i 0.187971 + 0.325576i 0.944574 0.328299i 0.106475π-0.106475\pi
−0.756602 + 0.653875i 0.773142π0.773142\pi
132132 9.13555 + 10.7041i 0.795148 + 0.931669i
133133 0 0
134134 1.97592 0.170694
135135 11.8285 + 6.43867i 1.01803 + 0.554153i
136136 −1.61323 −0.138334
137137 −10.2947 + 17.8309i −0.879533 + 1.52340i −0.0276785 + 0.999617i 0.508811π0.508811\pi
−0.851854 + 0.523779i 0.824522π0.824522\pi
138138 1.37791 + 1.61448i 0.117295 + 0.137434i
139139 7.88067 + 13.6497i 0.668429 + 1.15775i 0.978343 + 0.206989i 0.0663665π0.0663665\pi
−0.309914 + 0.950765i 0.600300π0.600300\pi
140140 0 0
141141 15.9045 2.94188i 1.33940 0.247751i
142142 −0.745960 + 1.29204i −0.0625996 + 0.108426i
143143 15.4025 1.28802
144144 −8.52859 6.91636i −0.710716 0.576364i
145145 5.50694 0.457326
146146 −0.855536 + 1.48183i −0.0708047 + 0.122637i
147147 0 0
148148 1.61273 + 2.79332i 0.132565 + 0.229610i
149149 −3.03379 5.25468i −0.248538 0.430480i 0.714582 0.699551i 0.246617π-0.246617\pi
−0.963120 + 0.269071i 0.913283π0.913283\pi
150150 −0.237672 + 0.670406i −0.0194058 + 0.0547385i
151151 −2.24433 + 3.88728i −0.182641 + 0.316343i −0.942779 0.333418i 0.891798π-0.891798\pi
0.760138 + 0.649761i 0.225131π0.225131\pi
152152 6.74645 0.547210
153153 −0.806617 + 5.06945i −0.0652111 + 0.409841i
154154 0 0
155155 −8.46978 + 14.6701i −0.680309 + 1.17833i
156156 −12.1871 + 2.25427i −0.975753 + 0.180486i
157157 −0.514457 0.891066i −0.0410582 0.0711148i 0.844766 0.535136i 0.179740π-0.179740\pi
−0.885824 + 0.464021i 0.846406π0.846406\pi
158158 1.17511 + 2.03534i 0.0934865 + 0.161923i
159159 −11.9710 14.0264i −0.949365 1.11236i
160160 3.57780 6.19694i 0.282850 0.489911i
161161 0 0
162162 1.60138 1.43777i 0.125816 0.112962i
163163 6.82846 0.534846 0.267423 0.963579i 0.413828π-0.413828\pi
0.267423 + 0.963579i 0.413828π0.413828\pi
164164 −9.92680 + 17.1937i −0.775153 + 1.34260i
165165 12.1871 + 14.2796i 0.948768 + 1.11166i
166166 −0.824336 1.42779i −0.0639809 0.110818i
167167 −8.99716 15.5835i −0.696221 1.20589i −0.969767 0.244032i 0.921530π-0.921530\pi
0.273546 0.961859i 0.411803π-0.411803\pi
168168 0 0
169169 −0.282630 + 0.489530i −0.0217408 + 0.0376561i
170170 −1.06045 −0.0813328
171171 3.37323 21.2001i 0.257957 1.62122i
172172 3.22545 0.245938
173173 0.415178 0.719110i 0.0315654 0.0546729i −0.849811 0.527087i 0.823284π-0.823284\pi
0.881377 + 0.472414i 0.156617π0.156617\pi
174174 0.294052 0.829440i 0.0222920 0.0628797i
175175 0 0
176176 −7.65335 13.2560i −0.576893 0.999208i
177177 −3.50972 + 9.89994i −0.263806 + 0.744125i
178178 0.602038 1.04276i 0.0451247 0.0781582i
179179 7.57893 0.566476 0.283238 0.959050i 0.408591π-0.408591\pi
0.283238 + 0.959050i 0.408591π0.408591\pi
180180 −11.7329 9.51495i −0.874520 0.709202i
181181 0.409157 0.0304124 0.0152062 0.999884i 0.495160π-0.495160\pi
0.0152062 + 0.999884i 0.495160π0.495160\pi
182182 0 0
183183 −13.6014 + 2.51586i −1.00544 + 0.185978i
184184 −2.41586 4.18440i −0.178100 0.308478i
185185 2.15143 + 3.72639i 0.158176 + 0.273969i
186186 1.75731 + 2.05903i 0.128852 + 0.150975i
187187 −3.57780 + 6.19694i −0.261635 + 0.453165i
188188 −18.1425 −1.32318
189189 0 0
190190 4.43474 0.321730
191191 −8.01204 + 13.8773i −0.579731 + 1.00412i 0.415779 + 0.909466i 0.363509π0.363509\pi
−0.995510 + 0.0946575i 0.969824π0.969824\pi
192192 7.48878 + 8.77454i 0.540456 + 0.633248i
193193 6.18715 + 10.7164i 0.445360 + 0.771387i 0.998077 0.0619822i 0.0197422π-0.0197422\pi
−0.552717 + 0.833369i 0.686409π0.686409\pi
194194 −0.366259 0.634379i −0.0262959 0.0455458i
195195 −16.2581 + 3.00728i −1.16426 + 0.215356i
196196 0 0
197197 23.1021 1.64595 0.822977 0.568075i 0.192312π-0.192312\pi
0.822977 + 0.568075i 0.192312π0.192312\pi
198198 2.80150 1.07311i 0.199094 0.0762628i
199199 −6.74645 −0.478243 −0.239122 0.970990i 0.576859π-0.576859\pi
−0.239122 + 0.970990i 0.576859π0.576859\pi
200200 0.809585 1.40224i 0.0572463 0.0991536i
201201 −4.78233 + 13.4897i −0.337320 + 0.951487i
202202 1.32710 + 2.29860i 0.0933741 + 0.161729i
203203 0 0
204204 1.92395 5.42692i 0.134703 0.379961i
205205 −13.2427 + 22.9370i −0.924910 + 1.60199i
206206 1.90963 0.133050
207207 −14.3571 + 5.49945i −0.997884 + 0.382238i
208208 13.4809 0.934730
209209 14.9622 25.9153i 1.03496 1.79260i
210210 0 0
211211 −8.44282 14.6234i −0.581228 1.00672i −0.995334 0.0964875i 0.969239π-0.969239\pi
0.414106 0.910228i 0.364094π-0.364094\pi
212212 10.3421 + 17.9131i 0.710301 + 1.23028i
213213 −7.01532 8.21981i −0.480682 0.563212i
214214 −0.473045 + 0.819338i −0.0323367 + 0.0560088i
215215 4.30286 0.293453
216216 −4.17984 + 2.55528i −0.284402 + 0.173865i
217217 0 0
218218 −0.868400 + 1.50411i −0.0588155 + 0.101871i
219219 −8.04583 9.42724i −0.543687 0.637034i
220220 −10.5288 18.2365i −0.709854 1.22950i
221221 −3.15103 5.45774i −0.211961 0.367128i
222222 0.676137 0.125066i 0.0453794 0.00839388i
223223 2.25071 3.89834i 0.150719 0.261052i −0.780773 0.624815i 0.785175π-0.785175\pi
0.931492 + 0.363762i 0.118508π0.118508\pi
224224 0 0
225225 −4.00163 3.24517i −0.266776 0.216345i
226226 1.65692 0.110217
227227 3.03215 5.25183i 0.201251 0.348576i −0.747681 0.664058i 0.768833π-0.768833\pi
0.948932 + 0.315482i 0.102166π0.102166\pi
228228 −8.04583 + 22.6951i −0.532848 + 1.50302i
229229 5.52466 + 9.56899i 0.365080 + 0.632336i 0.988789 0.149320i 0.0477084π-0.0477084\pi
−0.623709 + 0.781656i 0.714375π0.714375\pi
230230 −1.58805 2.75059i −0.104713 0.181369i
231231 0 0
232232 −1.00163 + 1.73488i −0.0657605 + 0.113901i
233233 −8.13844 −0.533167 −0.266583 0.963812i 0.585895π-0.585895\pi
−0.266583 + 0.963812i 0.585895π0.585895\pi
234234 −0.415178 + 2.60932i −0.0271411 + 0.170577i
235235 −24.2028 −1.57881
236236 5.89092 10.2034i 0.383466 0.664183i
237237 −16.7394 + 3.09632i −1.08734 + 0.201127i
238238 0 0
239239 −10.5813 18.3273i −0.684445 1.18549i −0.973611 0.228214i 0.926711π-0.926711\pi
0.289166 0.957279i 0.406622π-0.406622\pi
240240 10.6666 + 12.4980i 0.688528 + 0.806744i
241241 −6.84573 + 11.8572i −0.440972 + 0.763786i −0.997762 0.0668671i 0.978700π-0.978700\pi
0.556790 + 0.830654i 0.312033π0.312033\pi
242242 1.55159 0.0997398
243243 5.93984 + 14.4124i 0.381041 + 0.924558i
244244 15.5153 0.993265
245245 0 0
246246 2.74759 + 3.21934i 0.175180 + 0.205257i
247247 13.1774 + 22.8240i 0.838460 + 1.45225i
248248 −3.08107 5.33656i −0.195648 0.338872i
249249 11.7427 2.17206i 0.744163 0.137649i
250250 −1.01722 + 1.76187i −0.0643344 + 0.111430i
251251 15.2040 0.959667 0.479833 0.877360i 0.340697π-0.340697\pi
0.479833 + 0.877360i 0.340697π0.340697\pi
252252 0 0
253253 −21.4315 −1.34738
254254 −1.08934 + 1.88679i −0.0683511 + 0.118388i
255255 2.56661 7.23970i 0.160727 0.453368i
256256 −5.80959 10.0625i −0.363099 0.628906i
257257 −12.8107 22.1889i −0.799112 1.38410i −0.920195 0.391461i 0.871970π-0.871970\pi
0.121082 0.992642i 0.461363π-0.461363\pi
258258 0.229758 0.648085i 0.0143041 0.0403480i
259259 0 0
260260 18.5458 1.15016
261261 4.95090 + 4.01499i 0.306453 + 0.248522i
262262 −1.02891 −0.0635665
263263 −3.55034 + 6.14938i −0.218924 + 0.379187i −0.954479 0.298278i 0.903588π-0.903588\pi
0.735556 + 0.677464i 0.236921π0.236921\pi
264264 −6.71525 + 1.24213i −0.413295 + 0.0764478i
265265 13.7968 + 23.8967i 0.847528 + 1.46796i
266266 0 0
267267 5.66182 + 6.63392i 0.346498 + 0.405989i
268268 8.02696 13.9031i 0.490324 0.849267i
269269 −16.4314 −1.00184 −0.500922 0.865493i 0.667006π-0.667006\pi
−0.500922 + 0.865493i 0.667006π0.667006\pi
270270 −2.74759 + 1.67970i −0.167213 + 0.102223i
271271 12.6980 0.771348 0.385674 0.922635i 0.373969π-0.373969\pi
0.385674 + 0.922635i 0.373969π0.373969\pi
272272 −3.13143 + 5.42379i −0.189871 + 0.328865i
273273 0 0
274274 −2.46169 4.26378i −0.148716 0.257584i
275275 −3.59097 6.21975i −0.216544 0.375065i
276276 16.9575 3.13665i 1.02072 0.188804i
277277 0.414230 0.717468i 0.0248887 0.0431084i −0.853313 0.521399i 0.825410π-0.825410\pi
0.878201 + 0.478291i 0.158744π0.158744\pi
278278 −3.76890 −0.226044
279279 −18.3102 + 7.01370i −1.09620 + 0.419899i
280280 0 0
281281 −2.60985 + 4.52039i −0.155690 + 0.269664i −0.933310 0.359071i 0.883094π-0.883094\pi
0.777620 + 0.628735i 0.216427π0.216427\pi
282282 −1.29235 + 3.64535i −0.0769580 + 0.217078i
283283 3.67708 + 6.36890i 0.218580 + 0.378592i 0.954374 0.298614i 0.0965242π-0.0965242\pi
−0.735794 + 0.677205i 0.763191π0.763191\pi
284284 6.06075 + 10.4975i 0.359639 + 0.622913i
285285 −10.7334 + 30.2760i −0.635793 + 1.79340i
286286 −1.84155 + 3.18966i −0.108893 + 0.188609i
287287 0 0
288288 7.73461 2.96273i 0.455766 0.174581i
289289 −14.0722 −0.827778
290290 −0.658419 + 1.14041i −0.0386637 + 0.0669674i
291291 5.21737 0.965064i 0.305848 0.0565731i
292292 6.95103 + 12.0395i 0.406778 + 0.704561i
293293 −3.91286 6.77728i −0.228592 0.395933i 0.728799 0.684728i 0.240079π-0.240079\pi
−0.957391 + 0.288795i 0.906745π0.906745\pi
294294 0 0
295295 7.85868 13.6116i 0.457550 0.792500i
296296 −1.56526 −0.0909789
297297 0.545658 + 21.7232i 0.0316623 + 1.26051i
298298 1.45090 0.0840484
299299 9.43752 16.3463i 0.545786 0.945329i
300300 3.75164 + 4.39576i 0.216601 + 0.253790i
301301 0 0
302302 −0.536670 0.929540i −0.0308819 0.0534890i
303303 −18.9045 + 3.49679i −1.08604 + 0.200886i
304304 13.0954 22.6820i 0.751075 1.30090i
305305 20.6979 1.18516
306306 −0.953375 0.773151i −0.0545008 0.0441981i
307307 22.6709 1.29390 0.646948 0.762534i 0.276045π-0.276045\pi
0.646948 + 0.762534i 0.276045π0.276045\pi
308308 0 0
309309 −4.62188 + 13.0371i −0.262930 + 0.741653i
310310 −2.02532 3.50796i −0.115030 0.199239i
311311 16.1588 + 27.9879i 0.916281 + 1.58705i 0.805015 + 0.593255i 0.202157π0.202157\pi
0.111266 + 0.993791i 0.464509π0.464509\pi
312312 2.00972 5.66886i 0.113778 0.320936i
313313 12.1598 21.0614i 0.687312 1.19046i −0.285392 0.958411i 0.592124π-0.592124\pi
0.972704 0.232048i 0.0745428π-0.0745428\pi
314314 0.246037 0.0138847
315315 0 0
316316 19.0949 1.07417
317317 −2.56922 + 4.45002i −0.144302 + 0.249938i −0.929112 0.369798i 0.879427π-0.879427\pi
0.784811 + 0.619736i 0.212760π0.212760\pi
318318 4.33595 0.802027i 0.243148 0.0449755i
319319 4.44282 + 7.69519i 0.248750 + 0.430848i
320320 −8.63090 14.9492i −0.482482 0.835684i
321321 −4.44872 5.21253i −0.248303 0.290935i
322322 0 0
323323 −12.2438 −0.681262
324324 −3.61109 17.1084i −0.200616 0.950469i
325325 6.32525 0.350862
326326 −0.816422 + 1.41408i −0.0452174 + 0.0783189i
327327 −8.16681 9.56899i −0.451625 0.529166i
328328 −4.81732 8.34384i −0.265992 0.460712i
329329 0 0
330330 −4.41423 + 0.816506i −0.242995 + 0.0449472i
331331 5.84897 10.1307i 0.321488 0.556834i −0.659307 0.751874i 0.729150π-0.729150\pi
0.980795 + 0.195040i 0.0624835π0.0624835\pi
332332 −13.3951 −0.735150
333333 −0.782630 + 4.91870i −0.0428879 + 0.269543i
334334 4.30286 0.235442
335335 10.7082 18.5472i 0.585053 1.01334i
336336 0 0
337337 16.8473 + 29.1804i 0.917733 + 1.58956i 0.802850 + 0.596181i 0.203316π0.203316\pi
0.114883 + 0.993379i 0.463351π0.463351\pi
338338 −0.0675835 0.117058i −0.00367606 0.00636711i
339339 −4.01025 + 11.3118i −0.217807 + 0.614373i
340340 −4.30795 + 7.46159i −0.233631 + 0.404661i
341341 −27.3326 −1.48014
342342 3.98696 + 3.23327i 0.215590 + 0.174835i
343343 0 0
344344 −0.782630 + 1.35556i −0.0421966 + 0.0730866i
345345 22.6219 4.18440i 1.21792 0.225281i
346346 0.0992788 + 0.171956i 0.00533726 + 0.00924441i
347347 −13.6557 23.6523i −0.733075 1.26972i −0.955563 0.294788i 0.904751π-0.904751\pi
0.222488 0.974936i 0.428582π-0.428582\pi
348348 −4.64160 5.43852i −0.248816 0.291536i
349349 −11.4585 + 19.8467i −0.613358 + 1.06237i 0.377312 + 0.926086i 0.376848π0.376848\pi
−0.990670 + 0.136281i 0.956485π0.956485\pi
350350 0 0
351351 −16.8090 9.14978i −0.897200 0.488379i
352352 11.5458 0.615395
353353 −5.13466 + 8.89349i −0.273290 + 0.473353i −0.969702 0.244289i 0.921445π-0.921445\pi
0.696412 + 0.717642i 0.254779π0.254779\pi
354354 −1.63052 1.91047i −0.0866612 0.101540i
355355 8.08525 + 14.0041i 0.429120 + 0.743258i
356356 −4.89142 8.47218i −0.259245 0.449025i
357357 0 0
358358 −0.906150 + 1.56950i −0.0478915 + 0.0829505i
359359 10.1007 0.533094 0.266547 0.963822i 0.414117π-0.414117\pi
0.266547 + 0.963822i 0.414117π0.414117\pi
360360 6.84573 2.62225i 0.360802 0.138205i
361361 32.2028 1.69488
362362 −0.0489195 + 0.0847311i −0.00257115 + 0.00445337i
363363 −3.75531 + 10.5927i −0.197103 + 0.555973i
364364 0 0
365365 9.27292 + 16.0612i 0.485367 + 0.840680i
366366 1.10520 3.11747i 0.0577697 0.162953i
367367 3.88768 6.73367i 0.202935 0.351494i −0.746538 0.665343i 0.768285π-0.768285\pi
0.949473 + 0.313849i 0.101619π0.101619\pi
368368 −18.7576 −0.977808
369369 −28.6285 + 10.9661i −1.49034 + 0.570872i
370370 −1.02891 −0.0534907
371371 0 0
372372 21.6267 4.00032i 1.12129 0.207407i
373373 −12.0555 20.8808i −0.624212 1.08117i −0.988693 0.149957i 0.952087π-0.952087\pi
0.364480 0.931211i 0.381247π-0.381247\pi
374374 −0.855536 1.48183i −0.0442387 0.0766237i
375375 −9.56634 11.2088i −0.494004 0.578821i
376376 4.40214 7.62473i 0.227023 0.393215i
377377 −7.82573 −0.403045
378378 0 0
379379 −13.3581 −0.686161 −0.343081 0.939306i 0.611470π-0.611470\pi
−0.343081 + 0.939306i 0.611470π0.611470\pi
380380 18.0156 31.2039i 0.924181 1.60073i
381381 −10.2446 12.0035i −0.524846 0.614959i
382382 −1.91586 3.31838i −0.0980242 0.169783i
383383 4.62020 + 8.00242i 0.236081 + 0.408905i 0.959586 0.281414i 0.0908035π-0.0908035\pi
−0.723505 + 0.690319i 0.757470π0.757470\pi
384384 −12.1169 + 2.24128i −0.618337 + 0.114375i
385385 0 0
386386 −2.95898 −0.150608
387387 3.86840 + 3.13713i 0.196642 + 0.159469i
388388 −5.95153 −0.302143
389389 −5.22421 + 9.04859i −0.264878 + 0.458782i −0.967532 0.252750i 0.918665π-0.918665\pi
0.702654 + 0.711532i 0.251998π0.251998\pi
390390 1.32107 3.72639i 0.0668952 0.188693i
391391 4.38442 + 7.59404i 0.221730 + 0.384047i
392392 0 0
393393 2.49028 7.02441i 0.125618 0.354335i
394394 −2.76212 + 4.78413i −0.139154 + 0.241021i
395395 25.4733 1.28170
396396 3.83009 24.0715i 0.192470 1.20964i
397397 −0.409157 −0.0205350 −0.0102675 0.999947i 0.503268π-0.503268\pi
−0.0102675 + 0.999947i 0.503268π0.503268\pi
398398 0.806617 1.39710i 0.0404321 0.0700304i
399399 0 0
400400 −3.14295 5.44375i −0.157147 0.272187i
401401 −7.62640 13.2093i −0.380844 0.659641i 0.610339 0.792140i 0.291033π-0.291033\pi
−0.991183 + 0.132499i 0.957700π0.957700\pi
402402 −2.22175 2.60320i −0.110811 0.129836i
403403 12.0361 20.8472i 0.599562 1.03847i
404404 21.5647 1.07288
405405 −4.81732 22.8232i −0.239375 1.13410i
406406 0 0
407407 −3.47141 + 6.01266i −0.172071 + 0.298036i
408408 1.81393 + 2.12537i 0.0898031 + 0.105222i
409409 3.06335 + 5.30587i 0.151473 + 0.262359i 0.931769 0.363051i 0.118265π-0.118265\pi
−0.780296 + 0.625410i 0.784932π0.784932\pi
410410 −3.16664 5.48477i −0.156389 0.270874i
411411 35.0669 6.48638i 1.72972 0.319949i
412412 7.75765 13.4366i 0.382192 0.661976i
413413 0 0
414414 0.577690 3.63068i 0.0283919 0.178438i
415415 −17.8695 −0.877178
416416 −5.08430 + 8.80626i −0.249278 + 0.431763i
417417 9.12188 25.7303i 0.446701 1.26002i
418418 3.57780 + 6.19694i 0.174996 + 0.303102i
419419 −0.781437 1.35349i −0.0381757 0.0661223i 0.846306 0.532697i 0.178821π-0.178821\pi
−0.884482 + 0.466574i 0.845488π0.845488\pi
420420 0 0
421421 −11.6316 + 20.1465i −0.566889 + 0.981881i 0.429982 + 0.902838i 0.358520π0.358520\pi
−0.996871 + 0.0790438i 0.974813π0.974813\pi
422422 4.03775 0.196555
423423 −21.7590 17.6457i −1.05796 0.857964i
424424 −10.0377 −0.487476
425425 −1.46927 + 2.54485i −0.0712702 + 0.123444i
426426 2.54098 0.470008i 0.123111 0.0227720i
427427 0 0
428428 3.84338 + 6.65692i 0.185777 + 0.321775i
429429 −17.3187 20.2922i −0.836157 0.979719i
430430 −0.514457 + 0.891066i −0.0248093 + 0.0429710i
431431 1.00576 0.0484456 0.0242228 0.999707i 0.492289π-0.492289\pi
0.0242228 + 0.999707i 0.492289π0.492289\pi
432432 0.477580 + 19.0129i 0.0229776 + 0.914759i
433433 13.1071 0.629889 0.314945 0.949110i 0.398014π-0.398014\pi
0.314945 + 0.949110i 0.398014π0.398014\pi
434434 0 0
435435 −6.19205 7.25518i −0.296886 0.347859i
436436 7.05555 + 12.2206i 0.337899 + 0.585259i
437437 −18.3354 31.7579i −0.877101 1.51918i
438438 2.91423 0.539049i 0.139247 0.0257568i
439439 −9.30704 + 16.1203i −0.444201 + 0.769378i −0.997996 0.0632744i 0.979846π-0.979846\pi
0.553795 + 0.832653i 0.313179π0.313179\pi
440440 10.2190 0.487170
441441 0 0
442442 1.50697 0.0716792
443443 0.559503 0.969088i 0.0265828 0.0460427i −0.852428 0.522845i 0.824871π-0.824871\pi
0.879011 + 0.476802i 0.158204π0.158204\pi
444444 1.86673 5.26554i 0.0885912 0.249891i
445445 −6.52532 11.3022i −0.309330 0.535775i
446446 0.538197 + 0.932185i 0.0254844 + 0.0441402i
447447 −3.51162 + 9.90531i −0.166094 + 0.468505i
448448 0 0
449449 −39.4419 −1.86138 −0.930689 0.365813i 0.880791π-0.880791\pi
−0.930689 + 0.365813i 0.880791π0.880791\pi
450450 1.15047 0.440688i 0.0542339 0.0207742i
451451 −42.7351 −2.01232
452452 6.73104 11.6585i 0.316602 0.548370i
453453 7.64489 1.41409i 0.359188 0.0664395i
454454 0.725057 + 1.25584i 0.0340286 + 0.0589393i
455455 0 0
456456 −7.58577 8.88819i −0.355236 0.416228i
457457 17.1202 29.6531i 0.800852 1.38712i −0.118205 0.992989i 0.537714π-0.537714\pi
0.919056 0.394126i 0.128953π-0.128953\pi
458458 −2.64215 −0.123459
459459 7.58577 4.63744i 0.354073 0.216457i
460460 −25.8051 −1.20317
461461 −10.1938 + 17.6561i −0.474772 + 0.822328i −0.999583 0.0288903i 0.990803π-0.990803\pi
0.524811 + 0.851219i 0.324136π0.324136\pi
462462 0 0
463463 −3.40451 5.89679i −0.158221 0.274047i 0.776006 0.630725i 0.217243π-0.217243\pi
−0.934227 + 0.356678i 0.883909π0.883909\pi
464464 3.88852 + 6.73511i 0.180520 + 0.312670i
465465 28.8508 5.33656i 1.33792 0.247477i
466466 0.973045 1.68536i 0.0450754 0.0780729i
467467 24.7911 1.14720 0.573598 0.819137i 0.305547π-0.305547\pi
0.573598 + 0.819137i 0.305547π0.305547\pi
468468 16.6733 + 13.5214i 0.770721 + 0.625026i
469469 0 0
470470 2.89372 5.01207i 0.133477 0.231190i
471471 −0.595485 + 1.67970i −0.0274385 + 0.0773965i
472472 2.85877 + 4.95153i 0.131586 + 0.227913i
473473 3.47141 + 6.01266i 0.159616 + 0.276462i
474474 1.36019 3.83672i 0.0624755 0.176226i
475475 6.14441 10.6424i 0.281925 0.488309i
476476 0 0
477477 −5.01887 + 31.5428i −0.229798 + 1.44424i
478478 5.06045 0.231460
479479 5.54984 9.61260i 0.253579 0.439211i −0.710930 0.703263i 0.751726π-0.751726\pi
0.964508 + 0.264052i 0.0850590π0.0850590\pi
480480 −12.1871 + 2.25427i −0.556265 + 0.102893i
481481 −3.05733 5.29545i −0.139402 0.241452i
482482 −1.63697 2.83532i −0.0745621 0.129145i
483483 0 0
484484 6.30314 10.9174i 0.286506 0.496244i
485485 −7.93955 −0.360516
486486 −3.69480 0.493113i −0.167600 0.0223681i
487487 −10.0377 −0.454854 −0.227427 0.973795i 0.573031π-0.573031\pi
−0.227427 + 0.973795i 0.573031π0.573031\pi
488488 −3.76466 + 6.52059i −0.170418 + 0.295173i
489489 −7.67798 8.99623i −0.347210 0.406824i
490490 0 0
491491 6.19398 + 10.7283i 0.279530 + 0.484161i 0.971268 0.237988i 0.0764879π-0.0764879\pi
−0.691738 + 0.722149i 0.743155π0.743155\pi
492492 33.8138 6.25459i 1.52445 0.281979i
493493 1.81781 3.14854i 0.0818702 0.141803i
494494 −6.30206 −0.283543
495495 5.10948 32.1122i 0.229654 1.44334i
496496 −23.9225 −1.07415
497497 0 0
498498 −0.954170 + 2.69145i −0.0427574 + 0.120607i
499499 −5.11109 8.85267i −0.228804 0.396300i 0.728650 0.684886i 0.240148π-0.240148\pi
−0.957454 + 0.288586i 0.906815π0.906815\pi
500500 8.26464 + 14.3148i 0.369606 + 0.640177i
501501 −10.4142 + 29.3757i −0.465273 + 1.31241i
502502 −1.81781 + 3.14854i −0.0811329 + 0.140526i
503503 −8.45753 −0.377102 −0.188551 0.982063i 0.560379π-0.560379\pi
−0.188551 + 0.982063i 0.560379π0.560379\pi
504504 0 0
505505 28.7680 1.28016
506506 2.56238 4.43818i 0.113912 0.197301i
507507 0.962729 0.178077i 0.0427563 0.00790869i
508508 8.85060 + 15.3297i 0.392682 + 0.680145i
509509 5.28286 + 9.15018i 0.234159 + 0.405574i 0.959028 0.283312i 0.0914332π-0.0914332\pi
−0.724869 + 0.688886i 0.758100π0.758100\pi
510510 1.19238 + 1.39710i 0.0527994 + 0.0618647i
511511 0 0
512512 17.0071 0.751616
513513 −31.7233 + 19.3935i −1.40062 + 0.856245i
514514 6.12670 0.270237
515515 10.3490 17.9249i 0.456030 0.789867i
516516 −3.62672 4.24941i −0.159658 0.187070i
517517 −19.5260 33.8200i −0.858752 1.48740i
518518 0 0
519519 −1.41423 + 0.261592i −0.0620778 + 0.0114826i
520520 −4.50000 + 7.79423i −0.197338 + 0.341800i
521521 19.7558 0.865515 0.432758 0.901510i 0.357541π-0.357541\pi
0.432758 + 0.901510i 0.357541π0.357541\pi
522522 −1.42339 + 0.545227i −0.0623001 + 0.0238639i
523523 −32.5282 −1.42236 −0.711179 0.703011i 0.751839π-0.751839\pi
−0.711179 + 0.703011i 0.751839π0.751839\pi
524524 −4.17984 + 7.23970i −0.182597 + 0.316268i
525525 0 0
526526 −0.848970 1.47046i −0.0370168 0.0641150i
527527 5.59166 + 9.68504i 0.243577 + 0.421887i
528528 −8.85877 + 24.9882i −0.385528 + 1.08747i
529529 −1.63160 + 2.82601i −0.0709391 + 0.122870i
530530 −6.59825 −0.286610
531531 16.9891 6.50767i 0.737266 0.282409i
532532 0 0
533533 18.8187 32.5950i 0.815130 1.41185i
534534 −2.05073 + 0.379327i −0.0887440 + 0.0164151i
535535 5.12720 + 8.88057i 0.221668 + 0.383940i
536536 3.89536 + 6.74695i 0.168254 + 0.291424i
537537 −8.52182 9.98495i −0.367744 0.430883i
538538 1.96457 3.40274i 0.0846987 0.146702i
539539 0 0
540540 0.657014 + 26.1563i 0.0282734 + 1.12559i
541541 15.2222 0.654453 0.327226 0.944946i 0.393886π-0.393886\pi
0.327226 + 0.944946i 0.393886π0.393886\pi
542542 −1.51819 + 2.62959i −0.0652119 + 0.112950i
543543 −0.460060 0.539049i −0.0197431 0.0231328i
544544 −2.36203 4.09116i −0.101271 0.175407i
545545 9.41234 + 16.3027i 0.403180 + 0.698329i
546546 0 0
547547 −11.6871 + 20.2427i −0.499706 + 0.865517i −1.00000 0.000339172i 0.999892π-0.999892\pi
0.500294 + 0.865856i 0.333225π0.333225\pi
548548 −40.0014 −1.70877
549549 18.6081 + 15.0904i 0.794173 + 0.644044i
550550 1.71737 0.0732289
551551 −7.60199 + 13.1670i −0.323856 + 0.560934i
552552 −2.79637 + 7.88779i −0.119021 + 0.335726i
553553 0 0
554554 0.0990521 + 0.171563i 0.00420832 + 0.00728902i
555555 2.49028 7.02441i 0.105707 0.298170i
556556 −15.3107 + 26.5189i −0.649319 + 1.12465i
557557 27.6673 1.17230 0.586151 0.810202i 0.300643π-0.300643\pi
0.586151 + 0.810202i 0.300643π0.300643\pi
558558 0.736755 4.63038i 0.0311893 0.196019i
559559 −6.11465 −0.258622
560560 0 0
561561 12.1871 2.25427i 0.514542 0.0951755i
562562 −0.624075 1.08093i −0.0263250 0.0455963i
563563 4.27912 + 7.41166i 0.180343 + 0.312364i 0.941998 0.335620i 0.108946π-0.108946\pi
−0.761654 + 0.647984i 0.775612π0.775612\pi
564564 20.3996 + 23.9021i 0.858979 + 1.00646i
565565 8.97944 15.5529i 0.377768 0.654313i
566566 −1.75855 −0.0739175
567567 0 0
568568 −5.88237 −0.246819
569569 −6.86389 + 11.8886i −0.287749 + 0.498396i −0.973272 0.229655i 0.926240π-0.926240\pi
0.685523 + 0.728051i 0.259574π0.259574\pi
570570 −4.98646 5.84260i −0.208860 0.244720i
571571 −5.35868 9.28151i −0.224254 0.388419i 0.731841 0.681475i 0.238661π-0.238661\pi
−0.956095 + 0.293056i 0.905328π0.905328\pi
572572 14.9622 + 25.9153i 0.625600 + 1.08357i
573573 27.2916 5.04816i 1.14012 0.210890i
574574 0 0
575575 −8.80111 −0.367032
576576 3.13968 19.7323i 0.130820 0.822181i
577577 45.6353 1.89982 0.949912 0.312518i 0.101173π-0.101173\pi
0.949912 + 0.312518i 0.101173π0.101173\pi
578578 1.68250 2.91417i 0.0699827 0.121214i
579579 7.16163 20.2010i 0.297627 0.839525i
580580 5.34950 + 9.26560i 0.222126 + 0.384733i
581581 0 0
582582 −0.423945 + 1.19583i −0.0175731 + 0.0495689i
583583 −22.2616 + 38.5582i −0.921980 + 1.59692i
584584 −6.74645 −0.279170
585585 22.2427 + 18.0380i 0.919622 + 0.745779i
586586 1.87131 0.0773032
587587 −5.10948 + 8.84988i −0.210891 + 0.365274i −0.951994 0.306118i 0.900970π-0.900970\pi
0.741103 + 0.671392i 0.234303π0.234303\pi
588588 0 0
589589 −23.3840 40.5023i −0.963521 1.66887i
590590 1.87919 + 3.25486i 0.0773652 + 0.134000i
591591 −25.9762 30.4361i −1.06852 1.25197i
592592 −3.03831 + 5.26250i −0.124874 + 0.216287i
593593 −11.3961 −0.467981 −0.233990 0.972239i 0.575178π-0.575178\pi
−0.233990 + 0.972239i 0.575178π0.575178\pi
594594 −4.56382 2.48426i −0.187256 0.101930i
595595 0 0
596596 5.89411 10.2089i 0.241432 0.418173i
597597 7.58577 + 8.88819i 0.310465 + 0.363769i
598598 2.25673 + 3.90877i 0.0922846 + 0.159842i
599599 17.2873 + 29.9424i 0.706339 + 1.22341i 0.966206 + 0.257771i 0.0829879π0.0829879\pi
−0.259867 + 0.965644i 0.583679π0.583679\pi
600600 −2.75771 + 0.510097i −0.112583 + 0.0208246i
601601 −19.4207 + 33.6376i −0.792187 + 1.37211i 0.132423 + 0.991193i 0.457724π0.457724\pi
−0.924610 + 0.380915i 0.875609π0.875609\pi
602602 0 0
603603 23.1494 8.86734i 0.942716 0.361106i
604604 −8.72064 −0.354838
605605 8.40861 14.5641i 0.341858 0.592116i
606606 1.53611 4.33296i 0.0624004 0.176014i
607607 −20.6662 35.7950i −0.838817 1.45287i −0.890885 0.454229i 0.849915π-0.849915\pi
0.0520683 0.998644i 0.483419π-0.483419\pi
608608 9.87788 + 17.1090i 0.400601 + 0.693861i
609609 0 0
610610 −2.47468 + 4.28627i −0.100197 + 0.173546i
611611 34.3937 1.39142
612612 −9.31306 + 3.56735i −0.376458 + 0.144202i
613613 −28.6569 −1.15744 −0.578721 0.815526i 0.696448π-0.696448\pi
−0.578721 + 0.815526i 0.696448π0.696448\pi
614614 −2.71057 + 4.69485i −0.109390 + 0.189469i
615615 45.1088 8.34384i 1.81896 0.336456i
616616 0 0
617617 16.8518 + 29.1883i 0.678430 + 1.17508i 0.975454 + 0.220205i 0.0706726π0.0706726\pi
−0.297024 + 0.954870i 0.595994π0.595994\pi
618618 −2.14721 2.51586i −0.0863733 0.101203i
619619 0.719036 1.24541i 0.0289005 0.0500571i −0.851213 0.524820i 0.824133π-0.824133\pi
0.880114 + 0.474763i 0.157466π0.157466\pi
620620 −32.9105 −1.32172
621621 23.3885 + 12.7312i 0.938548 + 0.510887i
622622 −7.72789 −0.309860
623623 0 0
624624 −15.1580 17.7605i −0.606806 0.710990i
625625 15.3187 + 26.5328i 0.612750 + 1.06131i
626626 2.90769 + 5.03626i 0.116215 + 0.201290i
627627 −50.9660 + 9.42724i −2.03538 + 0.376488i
628628 0.999498 1.73118i 0.0398843 0.0690816i
629629 2.84071 0.113266
630630 0 0
631631 −30.7680 −1.22486 −0.612428 0.790527i 0.709807π-0.709807\pi
−0.612428 + 0.790527i 0.709807π0.709807\pi
632632 −4.63323 + 8.02500i −0.184300 + 0.319217i
633633 −9.77258 + 27.5658i −0.388425 + 1.09564i
634634 −0.614360 1.06410i −0.0243993 0.0422609i
635635 11.8070 + 20.4503i 0.468547 + 0.811547i
636636 11.9710 33.7670i 0.474682 1.33895i
637637 0 0
638638 −2.12476 −0.0841202
639639 −2.94119 + 18.4848i −0.116351 + 0.731249i
640640 18.4389 0.728862
641641 −4.61956 + 8.00132i −0.182462 + 0.316033i −0.942718 0.333590i 0.891740π-0.891740\pi
0.760257 + 0.649623i 0.225073π0.225073\pi
642642 1.61134 0.298052i 0.0635946 0.0117632i
643643 −12.7795 22.1348i −0.503976 0.872912i −0.999989 0.00459728i 0.998537π-0.998537\pi
0.496013 0.868315i 0.334797π-0.334797\pi
644644 0 0
645645 −4.83818 5.66886i −0.190503 0.223211i
646646 1.46389 2.53552i 0.0575958 0.0997588i
647647 −28.3111 −1.11302 −0.556512 0.830839i 0.687861π-0.687861\pi
−0.556512 + 0.830839i 0.687861π0.687861\pi
648648 8.06634 + 2.63360i 0.316876 + 0.103458i
649649 25.3605 0.995488
650650 −0.756258 + 1.30988i −0.0296629 + 0.0513776i
651651 0 0
652652 6.63323 + 11.4891i 0.259778 + 0.449948i
653653 4.17511 + 7.23150i 0.163385 + 0.282990i 0.936080 0.351786i 0.114426π-0.114426\pi
−0.772696 + 0.634776i 0.781092π0.781092\pi
654654 2.95805 0.547154i 0.115669 0.0213954i
655655 −5.57605 + 9.65801i −0.217874 + 0.377370i
656656 −37.4033 −1.46035
657657 −3.37323 + 21.2001i −0.131602 + 0.827096i
658658 0 0
659659 16.7862 29.0745i 0.653897 1.13258i −0.328272 0.944583i 0.606466π-0.606466\pi
0.982169 0.188000i 0.0602005π-0.0602005\pi
660660 −12.1871 + 34.3766i −0.474384 + 1.33811i
661661 −8.47668 14.6820i −0.329705 0.571065i 0.652748 0.757575i 0.273616π-0.273616\pi
−0.982453 + 0.186509i 0.940283π0.940283\pi
662662 1.39862 + 2.42249i 0.0543591 + 0.0941527i
663663 −3.64732 + 10.2881i −0.141650 + 0.399557i
664664 3.25021 5.62952i 0.126133 0.218468i
665665 0 0
666666 −0.925025 0.750160i −0.0358440 0.0290681i
667667 10.8889 0.421620
668668 17.4799 30.2760i 0.676316 1.17141i
669669 −7.66664 + 1.41811i −0.296409 + 0.0548272i
670670 2.56059 + 4.43507i 0.0989242 + 0.171342i
671671 16.6984 + 28.9225i 0.644636 + 1.11654i
672672 0 0
673673 22.2157 38.4788i 0.856354 1.48325i −0.0190299 0.999819i 0.506058π-0.506058\pi
0.875384 0.483429i 0.160609π-0.160609\pi
674674 −8.05718 −0.310351
675675 0.224082 + 8.92090i 0.00862490 + 0.343366i
676676 −1.09820 −0.0422384
677677 −7.18681 + 12.4479i −0.276212 + 0.478412i −0.970440 0.241342i 0.922412π-0.922412\pi
0.694229 + 0.719755i 0.255746π0.255746\pi
678678 −1.86306 2.18293i −0.0715502 0.0838349i
679679 0 0
680680 −2.09058 3.62099i −0.0801701 0.138859i
681681 −10.3285 + 1.91047i −0.395787 + 0.0732093i
682682 3.26793 5.66021i 0.125135 0.216741i
683683 −32.3092 −1.23628 −0.618138 0.786069i 0.712113π-0.712113\pi
−0.618138 + 0.786069i 0.712113π0.712113\pi
684684 38.9467 14.9185i 1.48916 0.570422i
685685 −53.3632 −2.03890
686686 0 0
687687 6.39480 18.0380i 0.243977 0.688192i
688688 3.03831 + 5.26250i 0.115834 + 0.200631i
689689 −19.6061 33.9588i −0.746934 1.29373i
690690 −1.83818 + 5.18499i −0.0699781 + 0.197389i
691691 −14.4981 + 25.1114i −0.551533 + 0.955283i 0.446631 + 0.894718i 0.352624π0.352624\pi
−0.998164 + 0.0605650i 0.980710π0.980710\pi
692692 1.61323 0.0613259
693693 0 0
694694 6.53078 0.247905
695695 −20.4250 + 35.3772i −0.774765 + 1.34193i
696696 3.41189 0.631101i 0.129327 0.0239218i
697697 8.74269 + 15.1428i 0.331153 + 0.573574i
698698 −2.73999 4.74580i −0.103710 0.179631i
699699 9.15093 + 10.7221i 0.346120 + 0.405546i
700700 0 0
701701 −26.3912 −0.996783 −0.498392 0.866952i 0.666076π-0.666076\pi
−0.498392 + 0.866952i 0.666076π0.666076\pi
702702 3.90451 2.38697i 0.147366 0.0900902i
703703 −11.8797 −0.448050
704704 13.9263 24.1210i 0.524866 0.909095i
705705 27.2138 + 31.8862i 1.02493 + 1.20090i
706706 −1.22782 2.12664i −0.0462095 0.0800372i
707707 0 0
708708 −20.0663 + 3.71170i −0.754139 + 0.139494i
709709 3.94282 6.82916i 0.148076 0.256475i −0.782441 0.622725i 0.786025π-0.786025\pi
0.930516 + 0.366251i 0.119359π0.119359\pi
710710 −3.86674 −0.145116
711711 22.9012 + 18.5720i 0.858864 + 0.696506i
712712 4.74746 0.177918
713713 −16.7473 + 29.0073i −0.627193 + 1.08633i
714714 0 0
715715 19.9601 + 34.5718i 0.746464 + 1.29291i
716716 7.36225 + 12.7518i 0.275140 + 0.476557i
717717 −12.2478 + 34.5477i −0.457403 + 1.29021i
718718 −1.20765 + 2.09172i −0.0450693 + 0.0780623i
719719 33.1508 1.23632 0.618159 0.786053i 0.287879π-0.287879\pi
0.618159 + 0.786053i 0.287879π0.287879\pi
720720 4.47200 28.1058i 0.166662 1.04744i
721721 0 0
722722 −3.85021 + 6.66877i −0.143290 + 0.248186i
723723 23.3187 4.31330i 0.867233 0.160413i
724724 0.397460 + 0.688420i 0.0147715 + 0.0255849i
725725 1.82450 + 3.16013i 0.0677603 + 0.117364i
726726 −1.74462 2.04416i −0.0647489 0.0758658i
727727 16.5502 28.6658i 0.613814 1.06316i −0.376777 0.926304i 0.622968π-0.622968\pi
0.990591 0.136853i 0.0436989π-0.0436989\pi
728728 0 0
729729 12.3090 24.0310i 0.455890 0.890036i
730730 −4.43474 −0.164137
731731 1.42035 2.46012i 0.0525337 0.0909910i
732732 −17.4455 20.4408i −0.644805 0.755514i
733733 −22.2795 38.5892i −0.822911 1.42532i −0.903505 0.428577i 0.859015π-0.859015\pi
0.0805946 0.996747i 0.474318π-0.474318\pi
734734 0.929636 + 1.61018i 0.0343135 + 0.0594327i
735735 0 0
736736 7.07442 12.2533i 0.260767 0.451661i
737737 34.5562 1.27290
738738 1.15193 7.23970i 0.0424032 0.266497i
739739 39.8090 1.46440 0.732199 0.681090i 0.238494π-0.238494\pi
0.732199 + 0.681090i 0.238494π0.238494\pi
740740 −4.17984 + 7.23970i −0.153654 + 0.266137i
741741 15.2529 43.0242i 0.560329 1.58053i
742742 0 0
743743 −5.37072 9.30237i −0.197033 0.341271i 0.750532 0.660834i 0.229797π-0.229797\pi
−0.947565 + 0.319563i 0.896464π0.896464\pi
744744 −3.56634 + 10.0597i −0.130748 + 0.368805i
745745 7.86295 13.6190i 0.288076 0.498962i
746746 5.76552 0.211091
747747 −16.0652 13.0283i −0.587795 0.476679i
748748 −13.9021 −0.508310
749749 0 0
750750 3.46496 0.640919i 0.126523 0.0234031i
751751 −9.85705 17.0729i −0.359689 0.622999i 0.628220 0.778036i 0.283784π-0.283784\pi
−0.987909 + 0.155036i 0.950450π0.950450\pi
752752 −17.0899 29.6005i −0.623203 1.07942i
753753 −17.0955 20.0307i −0.622994 0.729958i
754754 0.935657 1.62060i 0.0340746 0.0590189i
755755 −11.6336 −0.423391
756756 0 0
757757 35.3549 1.28499 0.642497 0.766288i 0.277898π-0.277898\pi
0.642497 + 0.766288i 0.277898π0.277898\pi
758758 1.59712 2.76629i 0.0580100 0.100476i
759759 24.0977 + 28.2351i 0.874692 + 1.02487i
760760 8.74269 + 15.1428i 0.317131 + 0.549286i
761761 −19.5572 33.8741i −0.708948 1.22793i −0.965248 0.261336i 0.915837π-0.915837\pi
0.256300 0.966597i 0.417497π-0.417497\pi
762762 3.71063 0.686360i 0.134422 0.0248642i
763763 0 0
764764 −31.1319 −1.12631
765765 −12.4239 + 4.75897i −0.449189 + 0.172061i
766766 −2.20960 −0.0798359
767767 −11.1677 + 19.3430i −0.403243 + 0.698437i
768768 −6.72460 + 18.9683i −0.242653 + 0.684458i
769769 −18.9240 32.7773i −0.682415 1.18198i −0.974242 0.225507i 0.927596π-0.927596\pi
0.291826 0.956471i 0.405737π-0.405737\pi
770770 0 0
771771 −14.8285 + 41.8270i −0.534034 + 1.50636i
772772 −12.0205 + 20.8201i −0.432628 + 0.749333i
773773 −29.8265 −1.07279 −0.536393 0.843969i 0.680213π-0.680213\pi
−0.536393 + 0.843969i 0.680213π0.680213\pi
774774 −1.11217 + 0.426015i −0.0399761 + 0.0153128i
775775 −11.2245 −0.403195
776776 1.44409 2.50124i 0.0518399 0.0897894i
777777 0 0
778778 −1.24923 2.16373i −0.0447870 0.0775734i
779779 −36.5614 63.3263i −1.30995 2.26890i
780780 −20.8531 24.4334i −0.746661 0.874857i
781781 −13.0458 + 22.5960i −0.466817 + 0.808550i
782782 −2.09683 −0.0749827
783783 −0.277238 11.0371i −0.00990768 0.394434i
784784 0 0
785785 1.33336 2.30946i 0.0475898 0.0824280i
786786 1.15692 + 1.35556i 0.0412660 + 0.0483511i
787787 8.81030 + 15.2599i 0.314053 + 0.543956i 0.979236 0.202724i 0.0649796π-0.0649796\pi
−0.665182 + 0.746681i 0.731646π0.731646\pi
788788 22.4416 + 38.8700i 0.799448 + 1.38468i
789789 12.0936 2.23697i 0.430544 0.0796382i
790790 −3.04563 + 5.27518i −0.108359 + 0.187683i
791791 0 0
792792 9.18715 + 7.45043i 0.326451 + 0.264739i
793793 −29.4132 −1.04449
794794 0.0489195 0.0847311i 0.00173609 0.00300699i
795795 15.9698 45.0464i 0.566390 1.59763i
796796 −6.55357 11.3511i −0.232285 0.402330i
797797 5.06056 + 8.76515i 0.179254 + 0.310477i 0.941625 0.336663i 0.109298π-0.109298\pi
−0.762371 + 0.647140i 0.775965π0.775965\pi
798798 0 0
799799 −7.98921 + 13.8377i −0.282638 + 0.489543i
800800 4.74145 0.167635
801801 2.37373 14.9185i 0.0838716 0.527118i
802802 3.64730 0.128791
803803 −14.9622 + 25.9153i −0.528004 + 0.914529i
804804 −27.3424 + 5.05756i −0.964291 + 0.178366i
805805 0 0
806806 2.87812 + 4.98504i 0.101377 + 0.175591i
807807 18.4757 + 21.6478i 0.650374 + 0.762039i
808808 −5.23250 + 9.06295i −0.184079 + 0.318834i
809809 −47.1469 −1.65760 −0.828799 0.559546i 0.810975π-0.810975\pi
−0.828799 + 0.559546i 0.810975π0.810975\pi
810810 5.30236 + 1.73118i 0.186306 + 0.0608275i
811811 −21.0577 −0.739435 −0.369717 0.929144i 0.620546π-0.620546\pi
−0.369717 + 0.929144i 0.620546π0.620546\pi
812812 0 0
813813 −14.2777 16.7291i −0.500742 0.586715i
814814 −0.830095 1.43777i −0.0290948 0.0503937i
815815 8.84896 + 15.3269i 0.309966 + 0.536876i
816816 10.6666 1.97302i 0.373407 0.0690696i
817817 −5.93984 + 10.2881i −0.207809 + 0.359935i
818818 −1.46504 −0.0512238
819819 0 0
820820 −51.4563 −1.79693
821821 −5.58018 + 9.66515i −0.194750 + 0.337316i −0.946818 0.321768i 0.895723π-0.895723\pi
0.752069 + 0.659085i 0.229056π0.229056\pi
822822 −2.84942 + 8.03742i −0.0993848 + 0.280337i
823823 −4.71737 8.17072i −0.164437 0.284814i 0.772018 0.635601i 0.219247π-0.219247\pi
−0.936455 + 0.350787i 0.885914π0.885914\pi
824824 3.76466 + 6.52059i 0.131148 + 0.227156i
825825 −4.15656 + 11.7245i −0.144713 + 0.408195i
826826 0 0
827827 17.2646 0.600348 0.300174 0.953884i 0.402955π-0.402955\pi
0.300174 + 0.953884i 0.402955π0.402955\pi
828828 −23.1996 18.8140i −0.806241 0.653831i
829829 48.4526 1.68283 0.841415 0.540390i 0.181723π-0.181723\pi
0.841415 + 0.540390i 0.181723π0.181723\pi
830830 2.13650 3.70053i 0.0741591 0.128447i
831831 −1.41100 + 0.260995i −0.0489470 + 0.00905380i
832832 12.2651 + 21.2438i 0.425215 + 0.736495i
833833 0 0
834834 4.23779 + 4.96538i 0.146743 + 0.171937i
835835 23.3187 40.3893i 0.806978 1.39773i
836836 58.1376 2.01073
837837 29.8285 + 16.2367i 1.03102 + 0.561224i
838838 0.373720 0.0129099
839839 −7.43429 + 12.8766i −0.256660 + 0.444548i −0.965345 0.260977i 0.915955π-0.915955\pi
0.708685 + 0.705525i 0.249289π0.249289\pi
840840 0 0
841841 12.2427 + 21.2050i 0.422162 + 0.731206i
842842 −2.78139 4.81750i −0.0958529 0.166022i
843843 8.88997 1.64439i 0.306187 0.0566358i
844844 16.4029 28.4106i 0.564610 0.977934i
845845 −1.46504 −0.0503988
846846 6.25574 2.39625i 0.215077 0.0823848i
847847 0 0
848848 −19.4841 + 33.7475i −0.669088 + 1.15889i
849849 4.25623 12.0057i 0.146073 0.412033i
850850 −0.351337 0.608534i −0.0120508 0.0208725i
851851 4.25404 + 7.36821i 0.145827 + 0.252579i
852852 7.01532 19.7883i 0.240341 0.677936i
853853 3.99900 6.92648i 0.136923 0.237158i −0.789407 0.613870i 0.789612π-0.789612\pi
0.926331 + 0.376712i 0.122945π0.122945\pi
854854 0 0
855855 51.9562 19.9018i 1.77687 0.680626i
856856 −3.73026 −0.127498
857857 −21.5661 + 37.3536i −0.736684 + 1.27597i 0.217296 + 0.976106i 0.430276π0.430276\pi
−0.953980 + 0.299869i 0.903057π0.903057\pi
858858 6.27292 1.16031i 0.214154 0.0396123i
859859 −1.22180 2.11621i −0.0416871 0.0722042i 0.844429 0.535667i 0.179940π-0.179940\pi
−0.886116 + 0.463463i 0.846607π0.846607\pi
860860 4.17984 + 7.23970i 0.142531 + 0.246872i
861861 0 0
862862 −0.120250 + 0.208279i −0.00409573 + 0.00709401i
863863 25.7187 0.875476 0.437738 0.899103i 0.355780π-0.355780\pi
0.437738 + 0.899103i 0.355780π0.355780\pi
864864 −12.6001 6.85873i −0.428666 0.233339i
865865 2.15211 0.0731739
866866 −1.56711 + 2.71432i −0.0532526 + 0.0922362i
867867 15.8229 + 18.5396i 0.537375 + 0.629639i
868868 0 0
869869 20.5510 + 35.5954i 0.697146 + 1.20749i
870870 2.24278 0.414851i 0.0760375 0.0140648i
871871 −15.2171 + 26.3568i −0.515612 + 0.893067i
872872 −6.84789 −0.231899
873873 −7.13789 5.78856i −0.241581 0.195913i
874874 8.76884 0.296611
875875 0 0
876876 8.04583 22.6951i 0.271843 0.766796i
877877 10.9795 + 19.0170i 0.370751 + 0.642160i 0.989681 0.143286i 0.0457670π-0.0457670\pi
−0.618930 + 0.785446i 0.712434π0.712434\pi
878878 −2.22553 3.85473i −0.0751080 0.130091i
879879 −4.52915 + 12.7755i −0.152764 + 0.430906i
880880 19.8359 34.3567i 0.668667 1.15817i
881881 35.0576 1.18112 0.590560 0.806994i 0.298907π-0.298907\pi
0.590560 + 0.806994i 0.298907π0.298907\pi
882882 0 0
883883 26.3009 0.885097 0.442549 0.896744i 0.354074π-0.354074\pi
0.442549 + 0.896744i 0.354074π0.354074\pi
884884 6.12188 10.6034i 0.205901 0.356631i
885885 −26.7692 + 4.95153i −0.899836 + 0.166444i
886886 0.133790 + 0.231731i 0.00449477 + 0.00778517i
887887 23.9090 + 41.4116i 0.802785 + 1.39046i 0.917776 + 0.397098i 0.129983π0.129983\pi
−0.114991 + 0.993366i 0.536684π0.536684\pi
888888 1.75999 + 2.06217i 0.0590615 + 0.0692019i
889889 0 0
890890 3.12071 0.104607
891891 28.0059 25.1446i 0.938233 0.842376i
892892 8.74545 0.292819
893893 33.4104 57.8685i 1.11804 1.93650i
894894 −1.63141 1.91151i −0.0545623 0.0639303i
895895 9.82150 + 17.0113i 0.328296 + 0.568626i
896896 0 0
897897 −32.1472 + 5.94631i −1.07336 + 0.198542i
898898 4.71574 8.16789i 0.157366 0.272566i
899899 13.8871 0.463162
900900 1.57288 9.88527i 0.0524293 0.329509i
901901 18.2170 0.606895
902902 5.10948 8.84988i 0.170127 0.294669i
903903 0 0
904904 3.26647 + 5.65769i 0.108641 + 0.188172i
905905 0.530225 + 0.918376i 0.0176253 + 0.0305279i
906906 −0.621197 + 1.75223i −0.0206379 + 0.0582138i
907907 9.55718 16.5535i 0.317341 0.549651i −0.662591 0.748981i 0.730543π-0.730543\pi
0.979932 + 0.199330i 0.0638767π0.0638767\pi
908908 11.7818 0.390994
909909 25.8633 + 20.9741i 0.857831 + 0.695669i
910910 0 0
911911 9.02928 15.6392i 0.299153 0.518149i −0.676789 0.736177i 0.736629π-0.736629\pi
0.975942 + 0.218028i 0.0699625π0.0699625\pi
912912 −44.6073 + 8.25107i −1.47709 + 0.273220i
913913 −14.4165 24.9701i −0.477117 0.826391i
914914 4.09385 + 7.09076i 0.135413 + 0.234541i
915915 −23.2729 27.2687i −0.769380 0.901477i
916916 −10.7334 + 18.5908i −0.354642 + 0.614258i
917917 0 0
918918 0.0533866 + 2.12537i 0.00176202 + 0.0701478i
919919 16.2093 0.534695 0.267348 0.963600i 0.413853π-0.413853\pi
0.267348 + 0.963600i 0.413853π0.413853\pi
920920 6.26141 10.8451i 0.206433 0.357552i
921921 −25.4914 29.8680i −0.839969 0.984186i
922922 −2.43757 4.22199i −0.0802771 0.139044i
923923 −11.4897 19.9007i −0.378187 0.655039i
924924 0 0
925925 −1.42558 + 2.46918i −0.0468728 + 0.0811860i
926926 1.62820 0.0535059
927927 22.3727 8.56984i 0.734817 0.281470i
928928 −5.86621 −0.192568
929929 11.3415 19.6440i 0.372102 0.644499i −0.617787 0.786345i 0.711971π-0.711971\pi
0.989889 + 0.141846i 0.0453039π0.0453039\pi
930930 −2.34431 + 6.61266i −0.0768730 + 0.216838i
931931 0 0
932932 −7.90576 13.6932i −0.258962 0.448535i
933933 18.7038 52.7584i 0.612336 1.72723i
934934 −2.96407 + 5.13392i −0.0969873 + 0.167987i
935935 −18.5458 −0.606513
936936 −9.72824 + 3.72639i −0.317977 + 0.121801i
937937 51.2933 1.67568 0.837840 0.545915i 0.183818π-0.183818\pi
0.837840 + 0.545915i 0.183818π0.183818\pi
938938 0 0
939939 −41.4201 + 7.66154i −1.35169 + 0.250025i
940940 −23.5108 40.7219i −0.766838 1.32820i
941941 15.9659 + 27.6538i 0.520474 + 0.901487i 0.999717 + 0.0238048i 0.00757801π0.00757801\pi
−0.479243 + 0.877682i 0.659089π0.659089\pi
942942 −0.276647 0.324145i −0.00901363 0.0105612i
943943 −26.1849 + 45.3535i −0.852697 + 1.47691i
944944 22.1965 0.722433
945945 0 0
946946 −1.66019 −0.0539774
947947 2.24665 3.89131i 0.0730063 0.126451i −0.827211 0.561891i 0.810074π-0.810074\pi
0.900218 + 0.435440i 0.143407π0.143407\pi
948948 −21.4705 25.1568i −0.697330 0.817056i
949949 −13.1774 22.8240i −0.427757 0.740898i
950950 1.46927 + 2.54485i 0.0476695 + 0.0825660i
951951 8.75158 1.61879i 0.283789 0.0524929i
952952 0 0
953953 1.14635 0.0371340 0.0185670 0.999828i 0.494090π-0.494090\pi
0.0185670 + 0.999828i 0.494090π0.494090\pi
954954 −5.93203 4.81065i −0.192056 0.155750i
955955 −41.5310 −1.34391
956956 20.5575 35.6066i 0.664876 1.15160i
957957 5.14257 14.5058i 0.166236 0.468905i
958958 1.32710 + 2.29860i 0.0428765 + 0.0742643i
959959 0 0
960960 −9.99028 + 28.1799i −0.322435 + 0.909501i
961961 −5.85868 + 10.1475i −0.188990 + 0.327340i
962962 1.46216 0.0471418
963963 −1.86513 + 11.7220i −0.0601030 + 0.377737i
964964 −26.6000 −0.856730
965965 −16.0358 + 27.7748i −0.516210 + 0.894102i
966966 0 0
967967 −24.8080 42.9686i −0.797770 1.38178i −0.921065 0.389408i 0.872680π-0.872680\pi
0.123295 0.992370i 0.460654π-0.460654\pi
968968 3.05881 + 5.29802i 0.0983140 + 0.170285i
969969 13.7670 + 16.1307i 0.442260 + 0.518193i
970970 0.949266 1.64418i 0.0304791 0.0527913i
971971 −5.13322 −0.164733 −0.0823664 0.996602i 0.526248π-0.526248\pi
−0.0823664 + 0.996602i 0.526248π0.526248\pi
972972 −18.4794 + 23.9943i −0.592726 + 0.769619i
973973 0 0
974974 1.20013 2.07869i 0.0384546 0.0666054i
975975 −7.11217 8.33328i −0.227772 0.266878i
976976 14.6151 + 25.3141i 0.467817 + 0.810283i
977977 −15.5974 27.0155i −0.499006 0.864303i 0.500994 0.865451i 0.332968π-0.332968\pi
−0.999999 + 0.00114787i 0.999635π0.999635\pi
978978 2.78099 0.514404i 0.0889264 0.0164488i
979979 10.5288 18.2365i 0.336503 0.582840i
980980 0 0
981981 −3.42395 + 21.5189i −0.109318 + 0.687046i
982982 −2.96225 −0.0945292
983983 −10.1700 + 17.6150i −0.324374 + 0.561832i −0.981385 0.192049i 0.938487π-0.938487\pi
0.657012 + 0.753880i 0.271820π0.271820\pi
984984 −5.57605 + 15.7285i −0.177758 + 0.501407i
985985 29.9378 + 51.8539i 0.953899 + 1.65220i
986986 0.434681 + 0.752890i 0.0138431 + 0.0239769i
987987 0 0
988988 −25.6014 + 44.3429i −0.814488 + 1.41074i
989989 8.50808 0.270541
990990 6.03911 + 4.89749i 0.191936 + 0.155653i
991991 −12.9655 −0.411863 −0.205932 0.978566i 0.566022π-0.566022\pi
−0.205932 + 0.978566i 0.566022π0.566022\pi
992992 9.02234 15.6272i 0.286460 0.496163i
993993 −19.9235 + 3.68527i −0.632252 + 0.116948i
994994 0 0
995995 −8.74269 15.1428i −0.277162 0.480059i
996996 15.0615 + 17.6475i 0.477243 + 0.559182i
997997 24.7408 42.8523i 0.783548 1.35715i −0.146314 0.989238i 0.546741π-0.546741\pi
0.929863 0.367907i 0.119926π-0.119926\pi
998998 2.44436 0.0773749
999999 7.36019 4.49954i 0.232866 0.142359i
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 441.2.f.g.295.3 yes 12
3.2 odd 2 1323.2.f.g.883.3 12
7.2 even 3 441.2.h.g.214.4 12
7.3 odd 6 441.2.g.g.79.4 12
7.4 even 3 441.2.g.g.79.3 12
7.5 odd 6 441.2.h.g.214.3 12
7.6 odd 2 inner 441.2.f.g.295.4 yes 12
9.2 odd 6 3969.2.a.bd.1.4 6
9.4 even 3 inner 441.2.f.g.148.3 12
9.5 odd 6 1323.2.f.g.442.3 12
9.7 even 3 3969.2.a.be.1.3 6
21.2 odd 6 1323.2.h.g.802.3 12
21.5 even 6 1323.2.h.g.802.4 12
21.11 odd 6 1323.2.g.g.667.4 12
21.17 even 6 1323.2.g.g.667.3 12
21.20 even 2 1323.2.f.g.883.4 12
63.4 even 3 441.2.h.g.373.4 12
63.5 even 6 1323.2.g.g.361.3 12
63.13 odd 6 inner 441.2.f.g.148.4 yes 12
63.20 even 6 3969.2.a.bd.1.3 6
63.23 odd 6 1323.2.g.g.361.4 12
63.31 odd 6 441.2.h.g.373.3 12
63.32 odd 6 1323.2.h.g.226.3 12
63.34 odd 6 3969.2.a.be.1.4 6
63.40 odd 6 441.2.g.g.67.4 12
63.41 even 6 1323.2.f.g.442.4 12
63.58 even 3 441.2.g.g.67.3 12
63.59 even 6 1323.2.h.g.226.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.g.148.3 12 9.4 even 3 inner
441.2.f.g.148.4 yes 12 63.13 odd 6 inner
441.2.f.g.295.3 yes 12 1.1 even 1 trivial
441.2.f.g.295.4 yes 12 7.6 odd 2 inner
441.2.g.g.67.3 12 63.58 even 3
441.2.g.g.67.4 12 63.40 odd 6
441.2.g.g.79.3 12 7.4 even 3
441.2.g.g.79.4 12 7.3 odd 6
441.2.h.g.214.3 12 7.5 odd 6
441.2.h.g.214.4 12 7.2 even 3
441.2.h.g.373.3 12 63.31 odd 6
441.2.h.g.373.4 12 63.4 even 3
1323.2.f.g.442.3 12 9.5 odd 6
1323.2.f.g.442.4 12 63.41 even 6
1323.2.f.g.883.3 12 3.2 odd 2
1323.2.f.g.883.4 12 21.20 even 2
1323.2.g.g.361.3 12 63.5 even 6
1323.2.g.g.361.4 12 63.23 odd 6
1323.2.g.g.667.3 12 21.17 even 6
1323.2.g.g.667.4 12 21.11 odd 6
1323.2.h.g.226.3 12 63.32 odd 6
1323.2.h.g.226.4 12 63.59 even 6
1323.2.h.g.802.3 12 21.2 odd 6
1323.2.h.g.802.4 12 21.5 even 6
3969.2.a.bd.1.3 6 63.20 even 6
3969.2.a.bd.1.4 6 9.2 odd 6
3969.2.a.be.1.3 6 9.7 even 3
3969.2.a.be.1.4 6 63.34 odd 6