Properties

Label 1456.2.cc.f.673.7
Level 14561456
Weight 22
Character 1456.673
Analytic conductor 11.62611.626
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1456,2,Mod(225,1456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1456, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1456.225");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1456=24713 1456 = 2^{4} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1456.cc (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.626218534311.6262185343
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+38x14+587x12+4762x10+21849x8+56552x6+76456x4+42624x2+2704 x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 364)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 673.7
Root 1.77673i-1.77673i of defining polynomial
Character χ\chi == 1456.673
Dual form 1456.2.cc.f.225.7

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+(0.888364+1.53869i)q33.82804iq5+(0.866025+0.500000i)q7+(0.0783804+0.135759i)q9+(3.747352.16353i)q11+(0.930395+3.48344i)q13+(5.890183.40069i)q15+(1.457442.52436i)q17+(4.726862.72905i)q19+1.77673iq21+(0.307112+0.531934i)q239.65391q25+5.05166q27+(4.628728.01717i)q29+5.30753iq31+(6.65802+3.84401i)q33+(1.914023.31518i)q35+(0.974022+0.562352i)q37+(6.18647+1.66297i)q39+(10.41306.01195i)q41+(0.641552+1.11120i)q43+(0.519691+0.300044i)q455.68074iq47+(0.500000+0.866025i)q49+5.17895q513.96013q53+(8.2821014.3450i)q559.69757iq57+(6.68359+3.85877i)q59+(7.1730812.4241i)q61+(0.135759+0.0783804i)q63+(13.3348+3.56159i)q65+(0.468974+0.270762i)q67+(0.545654+0.945101i)q69+(7.969184.60101i)q71+7.36798iq73+(8.5761814.8544i)q75+4.32707q770.331686q79+(4.72285+8.18022i)q81+16.6777iq83+(9.663355.57914i)q85+(8.2239714.2443i)q87+(2.558361.47707i)q89+(2.54747+2.55155i)q91+(8.16665+4.71502i)q93+(10.4469+18.0946i)q95+(8.36220+4.82792i)q97+0.678314iq99+O(q100)q+(0.888364 + 1.53869i) q^{3} -3.82804i q^{5} +(0.866025 + 0.500000i) q^{7} +(-0.0783804 + 0.135759i) q^{9} +(3.74735 - 2.16353i) q^{11} +(-0.930395 + 3.48344i) q^{13} +(5.89018 - 3.40069i) q^{15} +(1.45744 - 2.52436i) q^{17} +(-4.72686 - 2.72905i) q^{19} +1.77673i q^{21} +(0.307112 + 0.531934i) q^{23} -9.65391 q^{25} +5.05166 q^{27} +(-4.62872 - 8.01717i) q^{29} +5.30753i q^{31} +(6.65802 + 3.84401i) q^{33} +(1.91402 - 3.31518i) q^{35} +(-0.974022 + 0.562352i) q^{37} +(-6.18647 + 1.66297i) q^{39} +(10.4130 - 6.01195i) q^{41} +(-0.641552 + 1.11120i) q^{43} +(0.519691 + 0.300044i) q^{45} -5.68074i q^{47} +(0.500000 + 0.866025i) q^{49} +5.17895 q^{51} -3.96013 q^{53} +(-8.28210 - 14.3450i) q^{55} -9.69757i q^{57} +(6.68359 + 3.85877i) q^{59} +(7.17308 - 12.4241i) q^{61} +(-0.135759 + 0.0783804i) q^{63} +(13.3348 + 3.56159i) q^{65} +(-0.468974 + 0.270762i) q^{67} +(-0.545654 + 0.945101i) q^{69} +(-7.96918 - 4.60101i) q^{71} +7.36798i q^{73} +(-8.57618 - 14.8544i) q^{75} +4.32707 q^{77} -0.331686 q^{79} +(4.72285 + 8.18022i) q^{81} +16.6777i q^{83} +(-9.66335 - 5.57914i) q^{85} +(8.22397 - 14.2443i) q^{87} +(2.55836 - 1.47707i) q^{89} +(-2.54747 + 2.55155i) q^{91} +(-8.16665 + 4.71502i) q^{93} +(-10.4469 + 18.0946i) q^{95} +(8.36220 + 4.82792i) q^{97} +0.678314i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q14q96q11+10q136q15+2q1744q25+12q2722q29+42q33+6q35+12q3724q39+36q416q4330q45+8q49+4q51+8q53+42q97+O(q100) 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1456Z)×\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times.

nn 561561 911911 10931093 12491249
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.888364 + 1.53869i 0.512897 + 0.888364i 0.999888 + 0.0149568i 0.00476108π0.00476108\pi
−0.486991 + 0.873407i 0.661906π0.661906\pi
44 0 0
55 3.82804i 1.71195i −0.517015 0.855976i 0.672957π-0.672957\pi
0.517015 0.855976i 0.327043π-0.327043\pi
66 0 0
77 0.866025 + 0.500000i 0.327327 + 0.188982i
88 0 0
99 −0.0783804 + 0.135759i −0.0261268 + 0.0452529i
1010 0 0
1111 3.74735 2.16353i 1.12987 0.652330i 0.185966 0.982556i 0.440458π-0.440458\pi
0.943902 + 0.330227i 0.107125π0.107125\pi
1212 0 0
1313 −0.930395 + 3.48344i −0.258045 + 0.966133i
1414 0 0
1515 5.89018 3.40069i 1.52084 0.878056i
1616 0 0
1717 1.45744 2.52436i 0.353481 0.612247i −0.633376 0.773844i 0.718331π-0.718331\pi
0.986857 + 0.161597i 0.0516646π0.0516646\pi
1818 0 0
1919 −4.72686 2.72905i −1.08442 0.626088i −0.152331 0.988329i 0.548678π-0.548678\pi
−0.932084 + 0.362242i 0.882011π0.882011\pi
2020 0 0
2121 1.77673i 0.387714i
2222 0 0
2323 0.307112 + 0.531934i 0.0640373 + 0.110916i 0.896267 0.443516i 0.146269π-0.146269\pi
−0.832229 + 0.554432i 0.812936π0.812936\pi
2424 0 0
2525 −9.65391 −1.93078
2626 0 0
2727 5.05166 0.972193
2828 0 0
2929 −4.62872 8.01717i −0.859531 1.48875i −0.872377 0.488834i 0.837422π-0.837422\pi
0.0128452 0.999917i 0.495911π-0.495911\pi
3030 0 0
3131 5.30753i 0.953261i 0.879104 + 0.476630i 0.158142π0.158142\pi
−0.879104 + 0.476630i 0.841858π0.841858\pi
3232 0 0
3333 6.65802 + 3.84401i 1.15901 + 0.669156i
3434 0 0
3535 1.91402 3.31518i 0.323529 0.560368i
3636 0 0
3737 −0.974022 + 0.562352i −0.160128 + 0.0924501i −0.577923 0.816091i 0.696137π-0.696137\pi
0.417795 + 0.908542i 0.362803π0.362803\pi
3838 0 0
3939 −6.18647 + 1.66297i −0.990628 + 0.266289i
4040 0 0
4141 10.4130 6.01195i 1.62624 0.938909i 0.641037 0.767510i 0.278505π-0.278505\pi
0.985202 0.171399i 0.0548287π-0.0548287\pi
4242 0 0
4343 −0.641552 + 1.11120i −0.0978358 + 0.169457i −0.910789 0.412873i 0.864525π-0.864525\pi
0.812953 + 0.582330i 0.197859π0.197859\pi
4444 0 0
4545 0.519691 + 0.300044i 0.0774709 + 0.0447278i
4646 0 0
4747 5.68074i 0.828620i −0.910136 0.414310i 0.864023π-0.864023\pi
0.910136 0.414310i 0.135977π-0.135977\pi
4848 0 0
4949 0.500000 + 0.866025i 0.0714286 + 0.123718i
5050 0 0
5151 5.17895 0.725197
5252 0 0
5353 −3.96013 −0.543966 −0.271983 0.962302i 0.587679π-0.587679\pi
−0.271983 + 0.962302i 0.587679π0.587679\pi
5454 0 0
5555 −8.28210 14.3450i −1.11676 1.93428i
5656 0 0
5757 9.69757i 1.28447i
5858 0 0
5959 6.68359 + 3.85877i 0.870129 + 0.502369i 0.867391 0.497627i 0.165795π-0.165795\pi
0.00273800 + 0.999996i 0.499128π0.499128\pi
6060 0 0
6161 7.17308 12.4241i 0.918419 1.59075i 0.116601 0.993179i 0.462800π-0.462800\pi
0.801817 0.597569i 0.203867π-0.203867\pi
6262 0 0
6363 −0.135759 + 0.0783804i −0.0171040 + 0.00987500i
6464 0 0
6565 13.3348 + 3.56159i 1.65397 + 0.441761i
6666 0 0
6767 −0.468974 + 0.270762i −0.0572943 + 0.0330789i −0.528374 0.849012i 0.677198π-0.677198\pi
0.471079 + 0.882091i 0.343865π0.343865\pi
6868 0 0
6969 −0.545654 + 0.945101i −0.0656891 + 0.113777i
7070 0 0
7171 −7.96918 4.60101i −0.945768 0.546040i −0.0540044 0.998541i 0.517199π-0.517199\pi
−0.891764 + 0.452501i 0.850532π0.850532\pi
7272 0 0
7373 7.36798i 0.862357i 0.902267 + 0.431179i 0.141902π0.141902\pi
−0.902267 + 0.431179i 0.858098π0.858098\pi
7474 0 0
7575 −8.57618 14.8544i −0.990293 1.71524i
7676 0 0
7777 4.32707 0.493115
7878 0 0
7979 −0.331686 −0.0373176 −0.0186588 0.999826i 0.505940π-0.505940\pi
−0.0186588 + 0.999826i 0.505940π0.505940\pi
8080 0 0
8181 4.72285 + 8.18022i 0.524762 + 0.908914i
8282 0 0
8383 16.6777i 1.83061i 0.402758 + 0.915306i 0.368052π0.368052\pi
−0.402758 + 0.915306i 0.631948π0.631948\pi
8484 0 0
8585 −9.66335 5.57914i −1.04814 0.605143i
8686 0 0
8787 8.22397 14.2443i 0.881702 1.52715i
8888 0 0
8989 2.55836 1.47707i 0.271185 0.156569i −0.358241 0.933629i 0.616623π-0.616623\pi
0.629426 + 0.777060i 0.283290π0.283290\pi
9090 0 0
9191 −2.54747 + 2.55155i −0.267047 + 0.267475i
9292 0 0
9393 −8.16665 + 4.71502i −0.846842 + 0.488925i
9494 0 0
9595 −10.4469 + 18.0946i −1.07183 + 1.85647i
9696 0 0
9797 8.36220 + 4.82792i 0.849052 + 0.490201i 0.860331 0.509736i 0.170257π-0.170257\pi
−0.0112787 + 0.999936i 0.503590π0.503590\pi
9898 0 0
9999 0.678314i 0.0681731i
100100 0 0
101101 −3.17528 5.49975i −0.315952 0.547246i 0.663687 0.748010i 0.268991π-0.268991\pi
−0.979639 + 0.200765i 0.935657π0.935657\pi
102102 0 0
103103 5.07117 0.499678 0.249839 0.968287i 0.419622π-0.419622\pi
0.249839 + 0.968287i 0.419622π0.419622\pi
104104 0 0
105105 6.80139 0.663748
106106 0 0
107107 −2.74289 4.75083i −0.265166 0.459280i 0.702441 0.711742i 0.252093π-0.252093\pi
−0.967607 + 0.252461i 0.918760π0.918760\pi
108108 0 0
109109 6.80685i 0.651978i 0.945374 + 0.325989i 0.105697π0.105697\pi
−0.945374 + 0.325989i 0.894303π0.894303\pi
110110 0 0
111111 −1.73057 0.999146i −0.164259 0.0948347i
112112 0 0
113113 3.28384 5.68778i 0.308918 0.535061i −0.669208 0.743075i 0.733367π-0.733367\pi
0.978126 + 0.208014i 0.0666999π0.0666999\pi
114114 0 0
115115 2.03626 1.17564i 0.189883 0.109629i
116116 0 0
117117 −0.399983 0.399343i −0.0369785 0.0369193i
118118 0 0
119119 2.52436 1.45744i 0.231408 0.133603i
120120 0 0
121121 3.86175 6.68874i 0.351068 0.608067i
122122 0 0
123123 18.5011 + 10.6816i 1.66819 + 0.963128i
124124 0 0
125125 17.8154i 1.59346i
126126 0 0
127127 10.1425 + 17.5674i 0.900003 + 1.55885i 0.827488 + 0.561483i 0.189769π0.189769\pi
0.0725145 + 0.997367i 0.476898π0.476898\pi
128128 0 0
129129 −2.27973 −0.200719
130130 0 0
131131 −4.92442 −0.430249 −0.215124 0.976587i 0.569016π-0.569016\pi
−0.215124 + 0.976587i 0.569016π0.569016\pi
132132 0 0
133133 −2.72905 4.72686i −0.236639 0.409871i
134134 0 0
135135 19.3380i 1.66435i
136136 0 0
137137 11.1993 + 6.46589i 0.956817 + 0.552419i 0.895192 0.445681i 0.147038π-0.147038\pi
0.0616251 + 0.998099i 0.480372π0.480372\pi
138138 0 0
139139 7.90466 13.6913i 0.670464 1.16128i −0.307308 0.951610i 0.599428π-0.599428\pi
0.977773 0.209668i 0.0672384π-0.0672384\pi
140140 0 0
141141 8.74090 5.04656i 0.736116 0.424997i
142142 0 0
143143 4.05003 + 15.0666i 0.338680 + 1.25993i
144144 0 0
145145 −30.6901 + 17.7189i −2.54867 + 1.47148i
146146 0 0
147147 −0.888364 + 1.53869i −0.0732710 + 0.126909i
148148 0 0
149149 13.7967 + 7.96552i 1.13027 + 0.652561i 0.944002 0.329939i 0.107028π-0.107028\pi
0.186266 + 0.982499i 0.440361π0.440361\pi
150150 0 0
151151 6.37358i 0.518675i 0.965787 + 0.259337i 0.0835041π0.0835041\pi
−0.965787 + 0.259337i 0.916496π0.916496\pi
152152 0 0
153153 0.228469 + 0.395721i 0.0184707 + 0.0319921i
154154 0 0
155155 20.3175 1.63194
156156 0 0
157157 −7.38800 −0.589627 −0.294813 0.955555i 0.595257π-0.595257\pi
−0.294813 + 0.955555i 0.595257π0.595257\pi
158158 0 0
159159 −3.51804 6.09342i −0.278999 0.483240i
160160 0 0
161161 0.614224i 0.0484076i
162162 0 0
163163 0.0758325 + 0.0437819i 0.00593966 + 0.00342926i 0.502967 0.864306i 0.332242π-0.332242\pi
−0.497027 + 0.867735i 0.665575π0.665575\pi
164164 0 0
165165 14.7150 25.4872i 1.14556 1.98417i
166166 0 0
167167 −16.0309 + 9.25542i −1.24050 + 0.716206i −0.969197 0.246287i 0.920789π-0.920789\pi
−0.271308 + 0.962493i 0.587456π0.587456\pi
168168 0 0
169169 −11.2687 6.48195i −0.866826 0.498612i
170170 0 0
171171 0.740986 0.427808i 0.0566646 0.0327153i
172172 0 0
173173 0.205452 0.355853i 0.0156202 0.0270550i −0.858110 0.513466i 0.828361π-0.828361\pi
0.873730 + 0.486412i 0.161694π0.161694\pi
174174 0 0
175175 −8.36053 4.82696i −0.631997 0.364884i
176176 0 0
177177 13.7120i 1.03065i
178178 0 0
179179 −1.07738 1.86607i −0.0805268 0.139477i 0.822950 0.568114i 0.192327π-0.192327\pi
−0.903476 + 0.428638i 0.858994π0.858994\pi
180180 0 0
181181 6.50124 0.483233 0.241617 0.970372i 0.422322π-0.422322\pi
0.241617 + 0.970372i 0.422322π0.422322\pi
182182 0 0
183183 25.4892 1.88422
184184 0 0
185185 2.15271 + 3.72860i 0.158270 + 0.274132i
186186 0 0
187187 12.6129i 0.922344i
188188 0 0
189189 4.37487 + 2.52583i 0.318225 + 0.183727i
190190 0 0
191191 −9.38751 + 16.2596i −0.679256 + 1.17651i 0.295949 + 0.955204i 0.404364π0.404364\pi
−0.975205 + 0.221303i 0.928969π0.928969\pi
192192 0 0
193193 −22.1852 + 12.8086i −1.59693 + 0.921986i −0.604851 + 0.796339i 0.706767π0.706767\pi
−0.992075 + 0.125647i 0.959899π0.959899\pi
194194 0 0
195195 6.36593 + 23.6821i 0.455874 + 1.69591i
196196 0 0
197197 −0.510570 + 0.294778i −0.0363766 + 0.0210021i −0.518078 0.855333i 0.673352π-0.673352\pi
0.481701 + 0.876335i 0.340019π0.340019\pi
198198 0 0
199199 −8.04513 + 13.9346i −0.570304 + 0.987796i 0.426230 + 0.904615i 0.359841π0.359841\pi
−0.996534 + 0.0831814i 0.973492π0.973492\pi
200200 0 0
201201 −0.833240 0.481071i −0.0587722 0.0339321i
202202 0 0
203203 9.25744i 0.649745i
204204 0 0
205205 −23.0140 39.8614i −1.60737 2.78404i
206206 0 0
207207 −0.0962862 −0.00669236
208208 0 0
209209 −23.6176 −1.63366
210210 0 0
211211 −5.69247 9.85965i −0.391886 0.678766i 0.600812 0.799390i 0.294844π-0.294844\pi
−0.992698 + 0.120624i 0.961510π0.961510\pi
212212 0 0
213213 16.3495i 1.12025i
214214 0 0
215215 4.25373 + 2.45589i 0.290102 + 0.167490i
216216 0 0
217217 −2.65377 + 4.59646i −0.180149 + 0.312028i
218218 0 0
219219 −11.3370 + 6.54545i −0.766087 + 0.442300i
220220 0 0
221221 7.43746 + 7.42556i 0.500298 + 0.499497i
222222 0 0
223223 2.03182 1.17307i 0.136060 0.0785545i −0.430425 0.902626i 0.641636π-0.641636\pi
0.566485 + 0.824072i 0.308303π0.308303\pi
224224 0 0
225225 0.756677 1.31060i 0.0504452 0.0873736i
226226 0 0
227227 7.14587 + 4.12567i 0.474288 + 0.273830i 0.718033 0.696009i 0.245043π-0.245043\pi
−0.243745 + 0.969839i 0.578376π0.578376\pi
228228 0 0
229229 17.2750i 1.14156i −0.821103 0.570780i 0.806641π-0.806641\pi
0.821103 0.570780i 0.193359π-0.193359\pi
230230 0 0
231231 3.84401 + 6.65802i 0.252917 + 0.438065i
232232 0 0
233233 −4.13778 −0.271075 −0.135537 0.990772i 0.543276π-0.543276\pi
−0.135537 + 0.990772i 0.543276π0.543276\pi
234234 0 0
235235 −21.7461 −1.41856
236236 0 0
237237 −0.294658 0.510363i −0.0191401 0.0331516i
238238 0 0
239239 5.83879i 0.377680i −0.982008 0.188840i 0.939527π-0.939527\pi
0.982008 0.188840i 0.0604727π-0.0604727\pi
240240 0 0
241241 24.6356 + 14.2234i 1.58692 + 0.916207i 0.993811 + 0.111084i 0.0354322π0.0354322\pi
0.593107 + 0.805124i 0.297901π0.297901\pi
242242 0 0
243243 −0.813733 + 1.40943i −0.0522010 + 0.0904148i
244244 0 0
245245 3.31518 1.91402i 0.211799 0.122282i
246246 0 0
247247 13.9043 13.9266i 0.884712 0.886131i
248248 0 0
249249 −25.6618 + 14.8158i −1.62625 + 0.938916i
250250 0 0
251251 6.39001 11.0678i 0.403334 0.698595i −0.590792 0.806824i 0.701185π-0.701185\pi
0.994126 + 0.108229i 0.0345180π0.0345180\pi
252252 0 0
253253 2.30171 + 1.32889i 0.144707 + 0.0835468i
254254 0 0
255255 19.8252i 1.24150i
256256 0 0
257257 0.335695 + 0.581441i 0.0209401 + 0.0362693i 0.876306 0.481756i 0.160001π-0.160001\pi
−0.855365 + 0.518025i 0.826667π0.826667\pi
258258 0 0
259259 −1.12470 −0.0698857
260260 0 0
261261 1.45120 0.0898272
262262 0 0
263263 −9.48512 16.4287i −0.584878 1.01304i −0.994891 0.100958i 0.967809π-0.967809\pi
0.410013 0.912080i 0.365524π-0.365524\pi
264264 0 0
265265 15.1596i 0.931244i
266266 0 0
267267 4.54550 + 2.62435i 0.278180 + 0.160607i
268268 0 0
269269 4.79241 8.30070i 0.292198 0.506102i −0.682131 0.731230i 0.738947π-0.738947\pi
0.974329 + 0.225128i 0.0722799π0.0722799\pi
270270 0 0
271271 −9.06856 + 5.23574i −0.550876 + 0.318048i −0.749475 0.662032i 0.769694π-0.769694\pi
0.198599 + 0.980081i 0.436361π0.436361\pi
272272 0 0
273273 −6.18913 1.65306i −0.374583 0.100048i
274274 0 0
275275 −36.1766 + 20.8866i −2.18153 + 1.25951i
276276 0 0
277277 −9.66856 + 16.7464i −0.580927 + 1.00620i 0.414443 + 0.910075i 0.363977π0.363977\pi
−0.995370 + 0.0961199i 0.969357π0.969357\pi
278278 0 0
279279 −0.720544 0.416006i −0.0431379 0.0249057i
280280 0 0
281281 18.7039i 1.11578i 0.829915 + 0.557890i 0.188389π0.188389\pi
−0.829915 + 0.557890i 0.811611π0.811611\pi
282282 0 0
283283 −0.587956 1.01837i −0.0349504 0.0605358i 0.848021 0.529962i 0.177794π-0.177794\pi
−0.882971 + 0.469427i 0.844461π0.844461\pi
284284 0 0
285285 −37.1227 −2.19896
286286 0 0
287287 12.0239 0.709749
288288 0 0
289289 4.25174 + 7.36423i 0.250102 + 0.433190i
290290 0 0
291291 17.1558i 1.00569i
292292 0 0
293293 −5.63521 3.25349i −0.329213 0.190071i 0.326279 0.945274i 0.394205π-0.394205\pi
−0.655491 + 0.755203i 0.727538π0.727538\pi
294294 0 0
295295 14.7715 25.5851i 0.860033 1.48962i
296296 0 0
297297 18.9303 10.9294i 1.09845 0.634190i
298298 0 0
299299 −2.13869 + 0.574899i −0.123684 + 0.0332472i
300300 0 0
301301 −1.11120 + 0.641552i −0.0640486 + 0.0369785i
302302 0 0
303303 5.64161 9.77156i 0.324102 0.561361i
304304 0 0
305305 −47.5601 27.4589i −2.72329 1.57229i
306306 0 0
307307 27.0573i 1.54424i −0.635475 0.772121i 0.719196π-0.719196\pi
0.635475 0.772121i 0.280804π-0.280804\pi
308308 0 0
309309 4.50505 + 7.80297i 0.256283 + 0.443895i
310310 0 0
311311 −30.9061 −1.75253 −0.876263 0.481834i 0.839971π-0.839971\pi
−0.876263 + 0.481834i 0.839971π0.839971\pi
312312 0 0
313313 30.0816 1.70031 0.850157 0.526530i 0.176507π-0.176507\pi
0.850157 + 0.526530i 0.176507π0.176507\pi
314314 0 0
315315 0.300044 + 0.519691i 0.0169055 + 0.0292812i
316316 0 0
317317 3.78351i 0.212503i 0.994339 + 0.106251i 0.0338848π0.0338848\pi
−0.994339 + 0.106251i 0.966115π0.966115\pi
318318 0 0
319319 −34.6908 20.0288i −1.94231 1.12140i
320320 0 0
321321 4.87338 8.44093i 0.272005 0.471127i
322322 0 0
323323 −13.7782 + 7.95486i −0.766641 + 0.442620i
324324 0 0
325325 8.98195 33.6288i 0.498229 1.86539i
326326 0 0
327327 −10.4736 + 6.04696i −0.579194 + 0.334398i
328328 0 0
329329 2.84037 4.91966i 0.156595 0.271230i
330330 0 0
331331 −20.1396 11.6276i −1.10697 0.639110i −0.168928 0.985628i 0.554031π-0.554031\pi
−0.938043 + 0.346518i 0.887364π0.887364\pi
332332 0 0
333333 0.176309i 0.00966170i
334334 0 0
335335 1.03649 + 1.79525i 0.0566295 + 0.0980852i
336336 0 0
337337 6.51910 0.355118 0.177559 0.984110i 0.443180π-0.443180\pi
0.177559 + 0.984110i 0.443180π0.443180\pi
338338 0 0
339339 11.6690 0.633772
340340 0 0
341341 11.4830 + 19.8892i 0.621840 + 1.07706i
342342 0 0
343343 1.00000i 0.0539949i
344344 0 0
345345 3.61789 + 2.08879i 0.194780 + 0.112457i
346346 0 0
347347 −6.55696 + 11.3570i −0.351996 + 0.609675i −0.986599 0.163163i 0.947830π-0.947830\pi
0.634603 + 0.772838i 0.281164π0.281164\pi
348348 0 0
349349 8.41298 4.85724i 0.450336 0.260002i −0.257636 0.966242i 0.582943π-0.582943\pi
0.707972 + 0.706240i 0.249610π0.249610\pi
350350 0 0
351351 −4.70004 + 17.5972i −0.250869 + 0.939267i
352352 0 0
353353 −26.2632 + 15.1631i −1.39785 + 0.807049i −0.994167 0.107850i 0.965603π-0.965603\pi
−0.403683 + 0.914899i 0.632270π0.632270\pi
354354 0 0
355355 −17.6129 + 30.5064i −0.934794 + 1.61911i
356356 0 0
357357 4.48510 + 2.58947i 0.237377 + 0.137049i
358358 0 0
359359 10.5854i 0.558677i 0.960193 + 0.279339i 0.0901152π0.0901152\pi
−0.960193 + 0.279339i 0.909885π0.909885\pi
360360 0 0
361361 5.39545 + 9.34520i 0.283971 + 0.491853i
362362 0 0
363363 13.7225 0.720247
364364 0 0
365365 28.2050 1.47631
366366 0 0
367367 13.3188 + 23.0688i 0.695234 + 1.20418i 0.970102 + 0.242699i 0.0780328π0.0780328\pi
−0.274867 + 0.961482i 0.588634π0.588634\pi
368368 0 0
369369 1.88488i 0.0981228i
370370 0 0
371371 −3.42958 1.98007i −0.178055 0.102800i
372372 0 0
373373 3.07064 5.31851i 0.158992 0.275382i −0.775514 0.631331i 0.782509π-0.782509\pi
0.934505 + 0.355949i 0.115842π0.115842\pi
374374 0 0
375375 −27.4124 + 15.8265i −1.41557 + 0.817278i
376376 0 0
377377 32.2339 8.66473i 1.66013 0.446256i
378378 0 0
379379 −20.4175 + 11.7880i −1.04877 + 0.605510i −0.922306 0.386460i 0.873698π-0.873698\pi
−0.126469 + 0.991971i 0.540364π0.540364\pi
380380 0 0
381381 −18.0205 + 31.2124i −0.923217 + 1.59906i
382382 0 0
383383 17.4736 + 10.0884i 0.892860 + 0.515493i 0.874877 0.484346i 0.160942π-0.160942\pi
0.0179828 + 0.999838i 0.494276π0.494276\pi
384384 0 0
385385 16.5642i 0.844189i
386386 0 0
387387 −0.100570 0.174193i −0.00511227 0.00885472i
388388 0 0
389389 −32.8506 −1.66559 −0.832795 0.553581i 0.813261π-0.813261\pi
−0.832795 + 0.553581i 0.813261π0.813261\pi
390390 0 0
391391 1.79039 0.0905438
392392 0 0
393393 −4.37468 7.57716i −0.220673 0.382217i
394394 0 0
395395 1.26971i 0.0638860i
396396 0 0
397397 21.8789 + 12.6318i 1.09807 + 0.633970i 0.935713 0.352762i 0.114758π-0.114758\pi
0.162355 + 0.986732i 0.448091π0.448091\pi
398398 0 0
399399 4.84878 8.39834i 0.242743 0.420443i
400400 0 0
401401 −25.3059 + 14.6104i −1.26372 + 0.729608i −0.973792 0.227441i 0.926964π-0.926964\pi
−0.289926 + 0.957049i 0.593631π0.593631\pi
402402 0 0
403403 −18.4885 4.93810i −0.920977 0.245984i
404404 0 0
405405 31.3142 18.0793i 1.55602 0.898367i
406406 0 0
407407 −2.43333 + 4.21466i −0.120616 + 0.208913i
408408 0 0
409409 23.6697 + 13.6657i 1.17039 + 0.675727i 0.953773 0.300529i 0.0971633π-0.0971633\pi
0.216620 + 0.976256i 0.430497π0.430497\pi
410410 0 0
411411 22.9763i 1.13334i
412412 0 0
413413 3.85877 + 6.68359i 0.189878 + 0.328878i
414414 0 0
415415 63.8429 3.13392
416416 0 0
417417 28.0889 1.37552
418418 0 0
419419 10.1693 + 17.6137i 0.496802 + 0.860486i 0.999993 0.00368888i 0.00117421π-0.00117421\pi
−0.503191 + 0.864175i 0.667841π0.667841\pi
420420 0 0
421421 21.0712i 1.02695i 0.858106 + 0.513473i 0.171641π0.171641\pi
−0.858106 + 0.513473i 0.828359π0.828359\pi
422422 0 0
423423 0.771210 + 0.445258i 0.0374975 + 0.0216492i
424424 0 0
425425 −14.0700 + 24.3699i −0.682495 + 1.18212i
426426 0 0
427427 12.4241 7.17308i 0.601246 0.347130i
428428 0 0
429429 −19.5850 + 19.6164i −0.945571 + 0.947087i
430430 0 0
431431 25.6632 14.8167i 1.23615 0.713694i 0.267848 0.963461i 0.413687π-0.413687\pi
0.968306 + 0.249767i 0.0803541π0.0803541\pi
432432 0 0
433433 −14.2983 + 24.7653i −0.687130 + 1.19014i 0.285632 + 0.958339i 0.407796π0.407796\pi
−0.972762 + 0.231805i 0.925537π0.925537\pi
434434 0 0
435435 −54.5279 31.4817i −2.61441 1.50943i
436436 0 0
437437 3.35250i 0.160372i
438438 0 0
439439 10.9124 + 18.9009i 0.520821 + 0.902088i 0.999707 + 0.0242113i 0.00770744π0.00770744\pi
−0.478886 + 0.877877i 0.658959π0.658959\pi
440440 0 0
441441 −0.156761 −0.00746480
442442 0 0
443443 6.32956 0.300726 0.150363 0.988631i 0.451956π-0.451956\pi
0.150363 + 0.988631i 0.451956π0.451956\pi
444444 0 0
445445 −5.65428 9.79350i −0.268039 0.464256i
446446 0 0
447447 28.3051i 1.33879i
448448 0 0
449449 21.2777 + 12.2847i 1.00415 + 0.579749i 0.909475 0.415759i 0.136484π-0.136484\pi
0.0946799 + 0.995508i 0.469817π0.469817\pi
450450 0 0
451451 26.0141 45.0578i 1.22496 2.12169i
452452 0 0
453453 −9.80697 + 5.66206i −0.460772 + 0.266027i
454454 0 0
455455 9.76745 + 9.75181i 0.457905 + 0.457172i
456456 0 0
457457 −3.90240 + 2.25305i −0.182547 + 0.105393i −0.588489 0.808505i 0.700277π-0.700277\pi
0.405942 + 0.913899i 0.366944π0.366944\pi
458458 0 0
459459 7.36249 12.7522i 0.343652 0.595222i
460460 0 0
461461 0.260026 + 0.150126i 0.0121106 + 0.00699206i 0.506043 0.862508i 0.331108π-0.331108\pi
−0.493932 + 0.869500i 0.664441π0.664441\pi
462462 0 0
463463 19.2907i 0.896514i 0.893905 + 0.448257i 0.147955π0.147955\pi
−0.893905 + 0.448257i 0.852045π0.852045\pi
464464 0 0
465465 18.0493 + 31.2623i 0.837016 + 1.44975i
466466 0 0
467467 −13.9509 −0.645570 −0.322785 0.946472i 0.604619π-0.604619\pi
−0.322785 + 0.946472i 0.604619π0.604619\pi
468468 0 0
469469 −0.541525 −0.0250053
470470 0 0
471471 −6.56323 11.3679i −0.302418 0.523803i
472472 0 0
473473 5.55208i 0.255285i
474474 0 0
475475 45.6327 + 26.3460i 2.09377 + 1.20884i
476476 0 0
477477 0.310397 0.537623i 0.0142121 0.0246161i
478478 0 0
479479 23.7743 13.7261i 1.08627 0.627160i 0.153692 0.988119i 0.450884π-0.450884\pi
0.932582 + 0.360959i 0.117550π0.117550\pi
480480 0 0
481481 −1.05270 3.91616i −0.0479988 0.178561i
482482 0 0
483483 −0.945101 + 0.545654i −0.0430036 + 0.0248281i
484484 0 0
485485 18.4815 32.0108i 0.839200 1.45354i
486486 0 0
487487 −12.1206 6.99785i −0.549238 0.317103i 0.199577 0.979882i 0.436043π-0.436043\pi
−0.748815 + 0.662780i 0.769377π0.769377\pi
488488 0 0
489489 0.155577i 0.00703543i
490490 0 0
491491 3.76330 + 6.51823i 0.169836 + 0.294164i 0.938362 0.345654i 0.112343π-0.112343\pi
−0.768526 + 0.639818i 0.779010π0.779010\pi
492492 0 0
493493 −26.9843 −1.21531
494494 0 0
495495 2.59662 0.116709
496496 0 0
497497 −4.60101 7.96918i −0.206384 0.357467i
498498 0 0
499499 1.16848i 0.0523083i −0.999658 0.0261541i 0.991674π-0.991674\pi
0.999658 0.0261541i 0.00832607π-0.00832607\pi
500500 0 0
501501 −28.4825 16.4444i −1.27250 0.734680i
502502 0 0
503503 −5.30877 + 9.19505i −0.236706 + 0.409987i −0.959767 0.280797i 0.909401π-0.909401\pi
0.723061 + 0.690784i 0.242735π0.242735\pi
504504 0 0
505505 −21.0533 + 12.1551i −0.936859 + 0.540896i
506506 0 0
507507 −0.0370126 23.0974i −0.00164379 1.02579i
508508 0 0
509509 −21.0450 + 12.1503i −0.932803 + 0.538554i −0.887697 0.460428i 0.847696π-0.847696\pi
−0.0451058 + 0.998982i 0.514363π0.514363\pi
510510 0 0
511511 −3.68399 + 6.38086i −0.162970 + 0.282273i
512512 0 0
513513 −23.8785 13.7862i −1.05426 0.608678i
514514 0 0
515515 19.4127i 0.855424i
516516 0 0
517517 −12.2905 21.2877i −0.540534 0.936232i
518518 0 0
519519 0.730063 0.0320462
520520 0 0
521521 11.3280 0.496289 0.248144 0.968723i 0.420179π-0.420179\pi
0.248144 + 0.968723i 0.420179π0.420179\pi
522522 0 0
523523 15.1328 + 26.2108i 0.661711 + 1.14612i 0.980166 + 0.198180i 0.0635029π0.0635029\pi
−0.318454 + 0.947938i 0.603164π0.603164\pi
524524 0 0
525525 17.1524i 0.748591i
526526 0 0
527527 13.3981 + 7.73541i 0.583631 + 0.336960i
528528 0 0
529529 11.3114 19.5919i 0.491798 0.851820i
530530 0 0
531531 −1.04772 + 0.604904i −0.0454674 + 0.0262506i
532532 0 0
533533 11.2541 + 41.8666i 0.487468 + 1.81344i
534534 0 0
535535 −18.1864 + 10.4999i −0.786266 + 0.453951i
536536 0 0
537537 1.91420 3.31550i 0.0826039 0.143074i
538538 0 0
539539 3.74735 + 2.16353i 0.161410 + 0.0931899i
540540 0 0
541541 11.1529i 0.479500i −0.970835 0.239750i 0.922935π-0.922935\pi
0.970835 0.239750i 0.0770654π-0.0770654\pi
542542 0 0
543543 5.77546 + 10.0034i 0.247849 + 0.429287i
544544 0 0
545545 26.0569 1.11616
546546 0 0
547547 −4.87804 −0.208570 −0.104285 0.994547i 0.533255π-0.533255\pi
−0.104285 + 0.994547i 0.533255π0.533255\pi
548548 0 0
549549 1.12446 + 1.94762i 0.0479907 + 0.0831223i
550550 0 0
551551 50.5281i 2.15257i
552552 0 0
553553 −0.287249 0.165843i −0.0122151 0.00705237i
554554 0 0
555555 −3.82477 + 6.62470i −0.162353 + 0.281203i
556556 0 0
557557 2.62046 1.51293i 0.111033 0.0641047i −0.443455 0.896297i 0.646248π-0.646248\pi
0.554488 + 0.832192i 0.312914π0.312914\pi
558558 0 0
559559 −3.27391 3.26867i −0.138472 0.138250i
560560 0 0
561561 19.4073 11.2048i 0.819377 0.473068i
562562 0 0
563563 13.6591 23.6583i 0.575664 0.997079i −0.420305 0.907383i 0.638077π-0.638077\pi
0.995969 0.0896963i 0.0285896π-0.0285896\pi
564564 0 0
565565 −21.7730 12.5707i −0.915999 0.528852i
566566 0 0
567567 9.44571i 0.396682i
568568 0 0
569569 −6.46871 11.2041i −0.271183 0.469702i 0.697982 0.716115i 0.254081π-0.254081\pi
−0.969165 + 0.246413i 0.920748π0.920748\pi
570570 0 0
571571 −10.6779 −0.446855 −0.223427 0.974721i 0.571725π-0.571725\pi
−0.223427 + 0.974721i 0.571725π0.571725\pi
572572 0 0
573573 −33.3581 −1.39355
574574 0 0
575575 −2.96483 5.13524i −0.123642 0.214154i
576576 0 0
577577 4.76467i 0.198356i −0.995070 0.0991778i 0.968379π-0.968379\pi
0.995070 0.0991778i 0.0316213π-0.0316213\pi
578578 0 0
579579 −39.4171 22.7575i −1.63812 0.945767i
580580 0 0
581581 −8.33884 + 14.4433i −0.345953 + 0.599209i
582582 0 0
583583 −14.8400 + 8.56788i −0.614610 + 0.354845i
584584 0 0
585585 −1.52870 + 1.53115i −0.0632040 + 0.0633054i
586586 0 0
587587 −27.6495 + 15.9634i −1.14122 + 0.658881i −0.946731 0.322024i 0.895637π-0.895637\pi
−0.194485 + 0.980906i 0.562303π0.562303\pi
588588 0 0
589589 14.4845 25.0879i 0.596825 1.03373i
590590 0 0
591591 −0.907144 0.523740i −0.0373149 0.0215438i
592592 0 0
593593 1.27362i 0.0523015i −0.999658 0.0261508i 0.991675π-0.991675\pi
0.999658 0.0261508i 0.00832499π-0.00832499\pi
594594 0 0
595595 −5.57914 9.66335i −0.228722 0.396159i
596596 0 0
597597 −28.5880 −1.17003
598598 0 0
599599 15.1462 0.618857 0.309428 0.950923i 0.399862π-0.399862\pi
0.309428 + 0.950923i 0.399862π0.399862\pi
600600 0 0
601601 −17.1425 29.6917i −0.699258 1.21115i −0.968724 0.248141i 0.920180π-0.920180\pi
0.269466 0.963010i 0.413153π-0.413153\pi
602602 0 0
603603 0.0848899i 0.00345698i
604604 0 0
605605 −25.6048 14.7829i −1.04098 0.601012i
606606 0 0
607607 4.73737 8.20537i 0.192284 0.333046i −0.753723 0.657192i 0.771744π-0.771744\pi
0.946007 + 0.324147i 0.105077π0.105077\pi
608608 0 0
609609 14.2443 8.22397i 0.577210 0.333252i
610610 0 0
611611 19.7885 + 5.28533i 0.800557 + 0.213821i
612612 0 0
613613 10.0837 5.82183i 0.407277 0.235141i −0.282342 0.959314i 0.591111π-0.591111\pi
0.689619 + 0.724172i 0.257778π0.257778\pi
614614 0 0
615615 40.8896 70.8229i 1.64883 2.85586i
616616 0 0
617617 −5.54295 3.20023i −0.223151 0.128836i 0.384257 0.923226i 0.374457π-0.374457\pi
−0.607408 + 0.794390i 0.707791π0.707791\pi
618618 0 0
619619 11.2065i 0.450425i 0.974310 + 0.225213i 0.0723077π0.0723077\pi
−0.974310 + 0.225213i 0.927692π0.927692\pi
620620 0 0
621621 1.55143 + 2.68715i 0.0622566 + 0.107832i
622622 0 0
623623 2.95414 0.118355
624624 0 0
625625 19.9284 0.797138
626626 0 0
627627 −20.9810 36.3402i −0.837900 1.45129i
628628 0 0
629629 3.27837i 0.130717i
630630 0 0
631631 −39.1148 22.5830i −1.55714 0.899013i −0.997529 0.0702554i 0.977619π-0.977619\pi
−0.559608 0.828758i 0.689048π-0.689048\pi
632632 0 0
633633 10.1140 17.5179i 0.401994 0.696274i
634634 0 0
635635 67.2486 38.8260i 2.66868 1.54076i
636636 0 0
637637 −3.48195 + 0.935975i −0.137960 + 0.0370847i
638638 0 0
639639 1.24926 0.721258i 0.0494198 0.0285325i
640640 0 0
641641 −3.57997 + 6.20069i −0.141400 + 0.244912i −0.928024 0.372520i 0.878494π-0.878494\pi
0.786624 + 0.617432i 0.211827π0.211827\pi
642642 0 0
643643 35.9015 + 20.7278i 1.41582 + 0.817423i 0.995928 0.0901516i 0.0287352π-0.0287352\pi
0.419890 + 0.907575i 0.362068π0.362068\pi
644644 0 0
645645 8.72690i 0.343621i
646646 0 0
647647 −7.79258 13.4971i −0.306358 0.530627i 0.671205 0.741272i 0.265777π-0.265777\pi
−0.977563 + 0.210645i 0.932444π0.932444\pi
648648 0 0
649649 33.3943 1.31084
650650 0 0
651651 −9.43004 −0.369592
652652 0 0
653653 11.9121 + 20.6323i 0.466156 + 0.807406i 0.999253 0.0386482i 0.0123052π-0.0123052\pi
−0.533097 + 0.846054i 0.678972π0.678972\pi
654654 0 0
655655 18.8509i 0.736565i
656656 0 0
657657 −1.00027 0.577505i −0.0390242 0.0225306i
658658 0 0
659659 2.01861 3.49634i 0.0786340 0.136198i −0.824027 0.566551i 0.808277π-0.808277\pi
0.902661 + 0.430353i 0.141611π0.141611\pi
660660 0 0
661661 32.2144 18.5990i 1.25299 0.723416i 0.281290 0.959623i 0.409238π-0.409238\pi
0.971703 + 0.236207i 0.0759043π0.0759043\pi
662662 0 0
663663 −4.81846 + 18.0406i −0.187134 + 0.700637i
664664 0 0
665665 −18.0946 + 10.4469i −0.701679 + 0.405115i
666666 0 0
667667 2.84307 4.92434i 0.110084 0.190671i
668668 0 0
669669 3.60998 + 2.08422i 0.139570 + 0.0805808i
670670 0 0
671671 62.0768i 2.39645i
672672 0 0
673673 −5.02863 8.70984i −0.193839 0.335740i 0.752680 0.658387i 0.228761π-0.228761\pi
−0.946519 + 0.322647i 0.895427π0.895427\pi
674674 0 0
675675 −48.7683 −1.87709
676676 0 0
677677 −19.8807 −0.764076 −0.382038 0.924147i 0.624778π-0.624778\pi
−0.382038 + 0.924147i 0.624778π0.624778\pi
678678 0 0
679679 4.82792 + 8.36220i 0.185278 + 0.320912i
680680 0 0
681681 14.6604i 0.561787i
682682 0 0
683683 17.2194 + 9.94161i 0.658881 + 0.380405i 0.791850 0.610715i 0.209118π-0.209118\pi
−0.132970 + 0.991120i 0.542451π0.542451\pi
684684 0 0
685685 24.7517 42.8712i 0.945715 1.63803i
686686 0 0
687687 26.5808 15.3464i 1.01412 0.585503i
688688 0 0
689689 3.68449 13.7949i 0.140368 0.525544i
690690 0 0
691691 16.5968 9.58219i 0.631373 0.364524i −0.149910 0.988700i 0.547899π-0.547899\pi
0.781284 + 0.624176i 0.214565π0.214565\pi
692692 0 0
693693 −0.339157 + 0.587437i −0.0128835 + 0.0223149i
694694 0 0
695695 −52.4108 30.2594i −1.98805 1.14780i
696696 0 0
697697 35.0482i 1.32755i
698698 0 0
699699 −3.67585 6.36676i −0.139033 0.240813i
700700 0 0
701701 18.5012 0.698780 0.349390 0.936977i 0.386389π-0.386389\pi
0.349390 + 0.936977i 0.386389π0.386389\pi
702702 0 0
703703 6.13875 0.231527
704704 0 0
705705 −19.3184 33.4605i −0.727575 1.26020i
706706 0 0
707707 6.35056i 0.238838i
708708 0 0
709709 −20.8032 12.0107i −0.781279 0.451072i 0.0556043 0.998453i 0.482291π-0.482291\pi
−0.836883 + 0.547381i 0.815625π0.815625\pi
710710 0 0
711711 0.0259977 0.0450294i 0.000974990 0.00168873i
712712 0 0
713713 −2.82325 + 1.63001i −0.105732 + 0.0610442i
714714 0 0
715715 57.6756 15.5037i 2.15695 0.579805i
716716 0 0
717717 8.98409 5.18697i 0.335517 0.193711i
718718 0 0
719719 −12.2149 + 21.1568i −0.455538 + 0.789015i −0.998719 0.0506008i 0.983886π-0.983886\pi
0.543181 + 0.839616i 0.317220π0.317220\pi
720720 0 0
721721 4.39176 + 2.53559i 0.163558 + 0.0944302i
722722 0 0
723723 50.5421i 1.87968i
724724 0 0
725725 44.6852 + 77.3971i 1.65957 + 2.87446i
726726 0 0
727727 −20.9000 −0.775138 −0.387569 0.921841i 0.626685π-0.626685\pi
−0.387569 + 0.921841i 0.626685π0.626685\pi
728728 0 0
729729 25.4456 0.942428
730730 0 0
731731 1.87005 + 3.23902i 0.0691662 + 0.119799i
732732 0 0
733733 7.08118i 0.261549i 0.991412 + 0.130775i 0.0417465π0.0417465\pi
−0.991412 + 0.130775i 0.958254π0.958254\pi
734734 0 0
735735 5.89018 + 3.40069i 0.217262 + 0.125437i
736736 0 0
737737 −1.17161 + 2.02928i −0.0431567 + 0.0747496i
738738 0 0
739739 20.5378 11.8575i 0.755496 0.436186i −0.0721806 0.997392i 0.522996π-0.522996\pi
0.827676 + 0.561206i 0.189662π0.189662\pi
740740 0 0
741741 33.7809 + 9.02256i 1.24097 + 0.331452i
742742 0 0
743743 36.5813 21.1202i 1.34204 0.774825i 0.354931 0.934893i 0.384504π-0.384504\pi
0.987106 + 0.160067i 0.0511710π0.0511710\pi
744744 0 0
745745 30.4923 52.8143i 1.11715 1.93497i
746746 0 0
747747 −2.26414 1.30720i −0.0828406 0.0478281i
748748 0 0
749749 5.48579i 0.200446i
750750 0 0
751751 −12.0710 20.9076i −0.440478 0.762930i 0.557247 0.830347i 0.311858π-0.311858\pi
−0.997725 + 0.0674164i 0.978524π0.978524\pi
752752 0 0
753753 22.7066 0.827475
754754 0 0
755755 24.3983 0.887947
756756 0 0
757757 15.9716 + 27.6636i 0.580497 + 1.00545i 0.995420 + 0.0955942i 0.0304751π0.0304751\pi
−0.414923 + 0.909856i 0.636192π0.636192\pi
758758 0 0
759759 4.72216i 0.171404i
760760 0 0
761761 −36.6083 21.1358i −1.32705 0.766172i −0.342207 0.939625i 0.611174π-0.611174\pi
−0.984842 + 0.173452i 0.944508π0.944508\pi
762762 0 0
763763 −3.40342 + 5.89490i −0.123212 + 0.213410i
764764 0 0
765765 1.51484 0.874590i 0.0547690 0.0316209i
766766 0 0
767767 −19.6602 + 19.6917i −0.709888 + 0.711026i
768768 0 0
769769 −2.36768 + 1.36698i −0.0853808 + 0.0492946i −0.542083 0.840325i 0.682364π-0.682364\pi
0.456702 + 0.889620i 0.349031π0.349031\pi
770770 0 0
771771 −0.596439 + 1.03306i −0.0214802 + 0.0372048i
772772 0 0
773773 −16.9343 9.77703i −0.609085 0.351655i 0.163523 0.986540i 0.447714π-0.447714\pi
−0.772607 + 0.634884i 0.781048π0.781048\pi
774774 0 0
775775 51.2384i 1.84054i
776776 0 0
777777 −0.999146 1.73057i −0.0358442 0.0620839i
778778 0 0
779779 −65.6277 −2.35136
780780 0 0
781781 −39.8177 −1.42479
782782 0 0
783783 −23.3827 40.5001i −0.835630 1.44735i
784784 0 0
785785 28.2816i 1.00941i
786786 0 0
787787 −28.0930 16.2195i −1.00141 0.578163i −0.0927426 0.995690i 0.529563π-0.529563\pi
−0.908664 + 0.417528i 0.862897π0.862897\pi
788788 0 0
789789 16.8525 29.1893i 0.599964 1.03917i
790790 0 0
791791 5.68778 3.28384i 0.202234 0.116760i
792792 0 0
793793 36.6050 + 36.5464i 1.29988 + 1.29780i
794794 0 0
795795 −23.3259 + 13.4672i −0.827284 + 0.477632i
796796 0 0
797797 12.9397 22.4123i 0.458349 0.793883i −0.540525 0.841328i 0.681774π-0.681774\pi
0.998874 + 0.0474447i 0.0151078π0.0151078\pi
798798 0 0
799799 −14.3402 8.27933i −0.507320 0.292902i
800800 0 0
801801 0.463093i 0.0163626i
802802 0 0
803803 15.9409 + 27.6104i 0.562541 + 0.974350i
804804 0 0
805805 2.35128 0.0828716
806806 0 0
807807 17.0296 0.599471
808808 0 0
809809 −11.2066 19.4105i −0.394004 0.682435i 0.598969 0.800772i 0.295577π-0.295577\pi
−0.992974 + 0.118337i 0.962244π0.962244\pi
810810 0 0
811811 5.44486i 0.191195i −0.995420 0.0955974i 0.969524π-0.969524\pi
0.995420 0.0955974i 0.0304761π-0.0304761\pi
812812 0 0
813813 −16.1124 9.30247i −0.565085 0.326252i
814814 0 0
815815 0.167599 0.290290i 0.00587074 0.0101684i
816816 0 0
817817 6.06505 3.50166i 0.212189 0.122508i
818818 0 0
819819 −0.146724 0.545833i −0.00512696 0.0190729i
820820 0 0
821821 26.6843 15.4062i 0.931288 0.537679i 0.0440690 0.999028i 0.485968π-0.485968\pi
0.887219 + 0.461349i 0.152635π0.152635\pi
822822 0 0
823823 −0.102850 + 0.178141i −0.00358513 + 0.00620962i −0.867812 0.496892i 0.834475π-0.834475\pi
0.864227 + 0.503102i 0.167808π0.167808\pi
824824 0 0
825825 −64.2759 37.1097i −2.23780 1.29199i
826826 0 0
827827 9.66411i 0.336054i 0.985782 + 0.168027i 0.0537396π0.0537396\pi
−0.985782 + 0.168027i 0.946260π0.946260\pi
828828 0 0
829829 15.2667 + 26.4427i 0.530234 + 0.918393i 0.999378 + 0.0352709i 0.0112294π0.0112294\pi
−0.469143 + 0.883122i 0.655437π0.655437\pi
830830 0 0
831831 −34.3568 −1.19182
832832 0 0
833833 2.91488 0.100995
834834 0 0
835835 35.4301 + 61.3668i 1.22611 + 2.12369i
836836 0 0
837837 26.8119i 0.926753i
838838 0 0
839839 33.0722 + 19.0942i 1.14178 + 0.659206i 0.946871 0.321615i 0.104226π-0.104226\pi
0.194909 + 0.980821i 0.437559π0.437559\pi
840840 0 0
841841 −28.3501 + 49.1037i −0.977588 + 1.69323i
842842 0 0
843843 −28.7795 + 16.6158i −0.991218 + 0.572280i
844844 0 0
845845 −24.8132 + 43.1372i −0.853599 + 1.48396i
846846 0 0
847847 6.68874 3.86175i 0.229828 0.132691i
848848 0 0
849849 1.04464 1.80937i 0.0358519 0.0620973i
850850 0 0
851851 −0.598268 0.345410i −0.0205084 0.0118405i
852852 0 0
853853 28.3480i 0.970618i −0.874343 0.485309i 0.838707π-0.838707\pi
0.874343 0.485309i 0.161293π-0.161293\pi
854854 0 0
855855 −1.63767 2.83653i −0.0560071 0.0970071i
856856 0 0
857857 25.8488 0.882978 0.441489 0.897267i 0.354450π-0.354450\pi
0.441489 + 0.897267i 0.354450π0.354450\pi
858858 0 0
859859 −19.6084 −0.669029 −0.334514 0.942391i 0.608572π-0.608572\pi
−0.334514 + 0.942391i 0.608572π0.608572\pi
860860 0 0
861861 10.6816 + 18.5011i 0.364028 + 0.630515i
862862 0 0
863863 13.4368i 0.457395i −0.973498 0.228697i 0.926553π-0.926553\pi
0.973498 0.228697i 0.0734466π-0.0734466\pi
864864 0 0
865865 −1.36222 0.786477i −0.0463168 0.0267410i
866866 0 0
867867 −7.55418 + 13.0842i −0.256554 + 0.444364i
868868 0 0
869869 −1.24294 + 0.717614i −0.0421640 + 0.0243434i
870870 0 0
871871 −0.506854 1.88556i −0.0171741 0.0638898i
872872 0 0
873873 −1.31086 + 0.756828i −0.0443660 + 0.0256147i
874874 0 0
875875 −8.90769 + 15.4286i −0.301135 + 0.521581i
876876 0 0
877877 26.1038 + 15.0711i 0.881464 + 0.508914i 0.871141 0.491033i 0.163381π-0.163381\pi
0.0103233 + 0.999947i 0.496714π0.496714\pi
878878 0 0
879879 11.5611i 0.389947i
880880 0 0
881881 4.52477 + 7.83714i 0.152443 + 0.264040i 0.932125 0.362136i 0.117952π-0.117952\pi
−0.779682 + 0.626176i 0.784619π0.784619\pi
882882 0 0
883883 −47.3475 −1.59337 −0.796685 0.604395i 0.793415π-0.793415\pi
−0.796685 + 0.604395i 0.793415π0.793415\pi
884884 0 0
885885 52.4900 1.76443
886886 0 0
887887 18.9895 + 32.8908i 0.637605 + 1.10436i 0.985957 + 0.167001i 0.0534082π0.0534082\pi
−0.348352 + 0.937364i 0.613258π0.613258\pi
888888 0 0
889889 20.2850i 0.680338i
890890 0 0
891891 35.3964 + 20.4361i 1.18582 + 0.684635i
892892 0 0
893893 −15.5030 + 26.8520i −0.518789 + 0.898569i
894894 0 0
895895 −7.14339 + 4.12424i −0.238777 + 0.137858i
896896 0 0
897897 −2.78453 2.78007i −0.0929728 0.0928239i
898898 0 0
899899 42.5514 24.5671i 1.41917 0.819358i
900900 0 0
901901 −5.77165 + 9.99680i −0.192282 + 0.333042i
902902 0 0
903903 −1.97430 1.13986i −0.0657007 0.0379323i
904904 0 0
905905 24.8870i 0.827272i
906906 0 0
907907 −13.9433 24.1506i −0.462981 0.801906i 0.536127 0.844137i 0.319887π-0.319887\pi
−0.999108 + 0.0422309i 0.986553π0.986553\pi
908908 0 0
909909 0.995519 0.0330193
910910 0 0
911911 26.1435 0.866172 0.433086 0.901353i 0.357425π-0.357425\pi
0.433086 + 0.901353i 0.357425π0.357425\pi
912912 0 0
913913 36.0827 + 62.4971i 1.19416 + 2.06835i
914914 0 0
915915 97.5738i 3.22569i
916916 0 0
917917 −4.26467 2.46221i −0.140832 0.0813094i
918918 0 0
919919 −1.54406 + 2.67439i −0.0509338 + 0.0882199i −0.890368 0.455241i 0.849553π-0.849553\pi
0.839434 + 0.543461i 0.182886π0.182886\pi
920920 0 0
921921 41.6329 24.0367i 1.37185 0.792038i
922922 0 0
923923 23.4418 23.4794i 0.771598 0.772835i
924924 0 0
925925 9.40312 5.42889i 0.309173 0.178501i
926926 0 0
927927 −0.397481 + 0.688457i −0.0130550 + 0.0226119i
928928 0 0
929929 33.4087 + 19.2885i 1.09610 + 0.632836i 0.935195 0.354133i 0.115224π-0.115224\pi
0.160910 + 0.986969i 0.448557π0.448557\pi
930930 0 0
931931 5.45810i 0.178882i
932932 0 0
933933 −27.4559 47.5550i −0.898865 1.55688i
934934 0 0
935935 −48.2826 −1.57901
936936 0 0
937937 8.28836 0.270769 0.135384 0.990793i 0.456773π-0.456773\pi
0.135384 + 0.990793i 0.456773π0.456773\pi
938938 0 0
939939 26.7234 + 46.2863i 0.872086 + 1.51050i
940940 0 0
941941 7.72406i 0.251797i −0.992043 0.125899i 0.959819π-0.959819\pi
0.992043 0.125899i 0.0401814π-0.0401814\pi
942942 0 0
943943 6.39592 + 3.69269i 0.208280 + 0.120250i
944944 0 0
945945 9.66899 16.7472i 0.314532 0.544786i
946946 0 0
947947 −44.8430 + 25.8901i −1.45720 + 0.841316i −0.998873 0.0474661i 0.984885π-0.984885\pi
−0.458330 + 0.888782i 0.651552π0.651552\pi
948948 0 0
949949 −25.6659 6.85513i −0.833152 0.222527i
950950 0 0
951951 −5.82165 + 3.36113i −0.188780 + 0.108992i
952952 0 0
953953 24.3912 42.2468i 0.790109 1.36851i −0.135791 0.990738i 0.543357π-0.543357\pi
0.925899 0.377771i 0.123309π-0.123309\pi
954954 0 0
955955 62.2426 + 35.9358i 2.01412 + 1.16285i
956956 0 0
957957 71.1713i 2.30064i
958958 0 0
959959 6.46589 + 11.1993i 0.208795 + 0.361643i
960960 0 0
961961 2.83011 0.0912938
962962 0 0
963963 0.859956 0.0277117
964964 0 0
965965 49.0320 + 84.9259i 1.57840 + 2.73386i
966966 0 0
967967 3.09186i 0.0994274i −0.998764 0.0497137i 0.984169π-0.984169\pi
0.998764 0.0497137i 0.0158309π-0.0158309\pi
968968 0 0
969969 −24.4801 14.1336i −0.786415 0.454037i
970970 0 0
971971 27.2381 47.1777i 0.874111 1.51400i 0.0164037 0.999865i 0.494778π-0.494778\pi
0.857707 0.514139i 0.171888π-0.171888\pi
972972 0 0
973973 13.6913 7.90466i 0.438922 0.253412i
974974 0 0
975975 59.7236 16.0542i 1.91269 0.514146i
976976 0 0
977977 16.7476 9.66925i 0.535804 0.309347i −0.207573 0.978220i 0.566556π-0.566556\pi
0.743377 + 0.668873i 0.233223π0.233223\pi
978978 0 0
979979 6.39137 11.0702i 0.204269 0.353804i
980980 0 0
981981 −0.924090 0.533524i −0.0295039 0.0170341i
982982 0 0
983983 4.93770i 0.157488i 0.996895 + 0.0787440i 0.0250910π0.0250910\pi
−0.996895 + 0.0787440i 0.974909π0.974909\pi
984984 0 0
985985 1.12842 + 1.95449i 0.0359545 + 0.0622751i
986986 0 0
987987 10.0931 0.321268
988988 0 0
989989 −0.788114 −0.0250606
990990 0 0
991991 24.1717 + 41.8666i 0.767839 + 1.32994i 0.938733 + 0.344646i 0.112001π0.112001\pi
−0.170894 + 0.985289i 0.554666π0.554666\pi
992992 0 0
993993 41.3181i 1.31119i
994994 0 0
995995 53.3422 + 30.7971i 1.69106 + 0.976334i
996996 0 0
997997 21.6634 37.5222i 0.686088 1.18834i −0.287005 0.957929i 0.592660π-0.592660\pi
0.973094 0.230411i 0.0740069π-0.0740069\pi
998998 0 0
999999 −4.92043 + 2.84081i −0.155675 + 0.0898793i
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 1456.2.cc.f.673.7 16
4.3 odd 2 364.2.u.a.309.2 yes 16
12.11 even 2 3276.2.cf.c.1765.7 16
13.4 even 6 inner 1456.2.cc.f.225.7 16
28.3 even 6 2548.2.bb.c.569.7 16
28.11 odd 6 2548.2.bb.d.569.2 16
28.19 even 6 2548.2.bq.c.361.2 16
28.23 odd 6 2548.2.bq.e.361.7 16
28.27 even 2 2548.2.u.c.1765.7 16
52.3 odd 6 4732.2.g.k.337.13 16
52.11 even 12 4732.2.a.t.1.7 8
52.15 even 12 4732.2.a.s.1.7 8
52.23 odd 6 4732.2.g.k.337.14 16
52.43 odd 6 364.2.u.a.225.2 16
156.95 even 6 3276.2.cf.c.2773.2 16
364.95 odd 6 2548.2.bq.e.1941.7 16
364.199 even 6 2548.2.bq.c.1941.2 16
364.251 even 6 2548.2.u.c.589.7 16
364.303 odd 6 2548.2.bb.d.1733.2 16
364.355 even 6 2548.2.bb.c.1733.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
364.2.u.a.225.2 16 52.43 odd 6
364.2.u.a.309.2 yes 16 4.3 odd 2
1456.2.cc.f.225.7 16 13.4 even 6 inner
1456.2.cc.f.673.7 16 1.1 even 1 trivial
2548.2.u.c.589.7 16 364.251 even 6
2548.2.u.c.1765.7 16 28.27 even 2
2548.2.bb.c.569.7 16 28.3 even 6
2548.2.bb.c.1733.7 16 364.355 even 6
2548.2.bb.d.569.2 16 28.11 odd 6
2548.2.bb.d.1733.2 16 364.303 odd 6
2548.2.bq.c.361.2 16 28.19 even 6
2548.2.bq.c.1941.2 16 364.199 even 6
2548.2.bq.e.361.7 16 28.23 odd 6
2548.2.bq.e.1941.7 16 364.95 odd 6
3276.2.cf.c.1765.7 16 12.11 even 2
3276.2.cf.c.2773.2 16 156.95 even 6
4732.2.a.s.1.7 8 52.15 even 12
4732.2.a.t.1.7 8 52.11 even 12
4732.2.g.k.337.13 16 52.3 odd 6
4732.2.g.k.337.14 16 52.23 odd 6