Properties

Label 504.2.t.d.457.8
Level 504504
Weight 22
Character 504.457
Analytic conductor 4.0244.024
Analytic rank 00
Dimension 2222
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(193,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 504=23327 504 = 2^{3} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 504.t (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: 4.024460261874.02446026187
Analytic rank: 00
Dimension: 2222
Relative dimension: 1111 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 457.8
Character χ\chi == 504.457
Dual form 504.2.t.d.193.8

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+(0.577666+1.63288i)q3+1.85591q5+(2.60465+0.464545i)q7+(2.33261+1.88652i)q92.57601q11+(2.82227+4.88832i)q13+(1.07210+3.03049i)q15+(3.57951+6.19989i)q17+(0.6365991.10262i)q19+(2.263163.98473i)q21+0.241277q231.55558q25+(4.427932.71909i)q27+(0.9235711.59967i)q29+(1.495522.59031i)q31+(1.488074.20632i)q33+(4.83401+0.862156i)q35+(0.3382600.585884i)q37+(6.35171+7.43225i)q39+(0.7339331.27121i)q41+(4.142697.17535i)q43+(4.32912+3.50122i)q45+(6.15723+10.6646i)q47+(6.568402.41995i)q49+(8.05593+9.42638i)q51+(3.35508+5.81117i)q534.78085q55+(2.16819+0.402544i)q57+(1.04139+1.80375i)q59+(6.4797311.2232i)q61+(5.199255.99732i)q63+(5.23789+9.07230i)q65+(2.415514.18379i)q67+(0.139378+0.393977i)q691.53621q71+(6.5595411.3615i)q73+(0.8986062.54008i)q75+(6.709601.19667i)q77+(1.86009+3.22177i)q79+(1.882098.80101i)q81+(3.00173+5.19915i)q83+(6.64326+11.5065i)q85+(3.14559+0.584007i)q87+(6.6034911.4376i)q89+(9.6218711.4213i)q91+(5.09357+0.945667i)q93+(1.181472.04637i)q95+(6.4086011.1000i)q97+(6.008814.85969i)q99+O(q100)q+(0.577666 + 1.63288i) q^{3} +1.85591 q^{5} +(-2.60465 + 0.464545i) q^{7} +(-2.33261 + 1.88652i) q^{9} -2.57601 q^{11} +(2.82227 + 4.88832i) q^{13} +(1.07210 + 3.03049i) q^{15} +(3.57951 + 6.19989i) q^{17} +(0.636599 - 1.10262i) q^{19} +(-2.26316 - 3.98473i) q^{21} +0.241277 q^{23} -1.55558 q^{25} +(-4.42793 - 2.71909i) q^{27} +(0.923571 - 1.59967i) q^{29} +(1.49552 - 2.59031i) q^{31} +(-1.48807 - 4.20632i) q^{33} +(-4.83401 + 0.862156i) q^{35} +(0.338260 - 0.585884i) q^{37} +(-6.35171 + 7.43225i) q^{39} +(-0.733933 - 1.27121i) q^{41} +(4.14269 - 7.17535i) q^{43} +(-4.32912 + 3.50122i) q^{45} +(6.15723 + 10.6646i) q^{47} +(6.56840 - 2.41995i) q^{49} +(-8.05593 + 9.42638i) q^{51} +(3.35508 + 5.81117i) q^{53} -4.78085 q^{55} +(2.16819 + 0.402544i) q^{57} +(-1.04139 + 1.80375i) q^{59} +(-6.47973 - 11.2232i) q^{61} +(5.19925 - 5.99732i) q^{63} +(5.23789 + 9.07230i) q^{65} +(2.41551 - 4.18379i) q^{67} +(0.139378 + 0.393977i) q^{69} -1.53621 q^{71} +(-6.55954 - 11.3615i) q^{73} +(-0.898606 - 2.54008i) q^{75} +(6.70960 - 1.19667i) q^{77} +(1.86009 + 3.22177i) q^{79} +(1.88209 - 8.80101i) q^{81} +(-3.00173 + 5.19915i) q^{83} +(6.64326 + 11.5065i) q^{85} +(3.14559 + 0.584007i) q^{87} +(6.60349 - 11.4376i) q^{89} +(-9.62187 - 11.4213i) q^{91} +(5.09357 + 0.945667i) q^{93} +(1.18147 - 2.04637i) q^{95} +(6.40860 - 11.1000i) q^{97} +(6.00881 - 4.85969i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q+2q36q5+7q78q9+6q113q13q15+7q17q1915q214q23+20q254q27+9q294q3131q33+14q35+2q37+8q39+56q99+O(q100) 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/504Z)×\left(\mathbb{Z}/504\mathbb{Z}\right)^\times.

nn 7373 127127 253253 281281
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.577666 + 1.63288i 0.333515 + 0.942745i
44 0 0
55 1.85591 0.829990 0.414995 0.909824i 0.363783π-0.363783\pi
0.414995 + 0.909824i 0.363783π0.363783\pi
66 0 0
77 −2.60465 + 0.464545i −0.984465 + 0.175582i
88 0 0
99 −2.33261 + 1.88652i −0.777535 + 0.628840i
1010 0 0
1111 −2.57601 −0.776696 −0.388348 0.921513i 0.626954π-0.626954\pi
−0.388348 + 0.921513i 0.626954π0.626954\pi
1212 0 0
1313 2.82227 + 4.88832i 0.782757 + 1.35578i 0.930330 + 0.366724i 0.119521π0.119521\pi
−0.147573 + 0.989051i 0.547146π0.547146\pi
1414 0 0
1515 1.07210 + 3.03049i 0.276814 + 0.782469i
1616 0 0
1717 3.57951 + 6.19989i 0.868158 + 1.50369i 0.863876 + 0.503704i 0.168030π0.168030\pi
0.00428199 + 0.999991i 0.498637π0.498637\pi
1818 0 0
1919 0.636599 1.10262i 0.146046 0.252959i −0.783717 0.621118i 0.786679π-0.786679\pi
0.929763 + 0.368160i 0.120012π0.120012\pi
2020 0 0
2121 −2.26316 3.98473i −0.493863 0.869540i
2222 0 0
2323 0.241277 0.0503098 0.0251549 0.999684i 0.491992π-0.491992\pi
0.0251549 + 0.999684i 0.491992π0.491992\pi
2424 0 0
2525 −1.55558 −0.311116
2626 0 0
2727 −4.42793 2.71909i −0.852155 0.523289i
2828 0 0
2929 0.923571 1.59967i 0.171503 0.297051i −0.767443 0.641118i 0.778471π-0.778471\pi
0.938945 + 0.344066i 0.111804π0.111804\pi
3030 0 0
3131 1.49552 2.59031i 0.268602 0.465233i −0.699899 0.714242i 0.746772π-0.746772\pi
0.968501 + 0.249009i 0.0801049π0.0801049\pi
3232 0 0
3333 −1.48807 4.20632i −0.259040 0.732226i
3434 0 0
3535 −4.83401 + 0.862156i −0.817096 + 0.145731i
3636 0 0
3737 0.338260 0.585884i 0.0556097 0.0963188i −0.836880 0.547386i 0.815623π-0.815623\pi
0.892490 + 0.451067i 0.148956π0.148956\pi
3838 0 0
3939 −6.35171 + 7.43225i −1.01709 + 1.19011i
4040 0 0
4141 −0.733933 1.27121i −0.114621 0.198529i 0.803007 0.595969i 0.203232π-0.203232\pi
−0.917628 + 0.397440i 0.869899π0.869899\pi
4242 0 0
4343 4.14269 7.17535i 0.631754 1.09423i −0.355439 0.934700i 0.615669π-0.615669\pi
0.987193 0.159531i 0.0509981π-0.0509981\pi
4444 0 0
4545 −4.32912 + 3.50122i −0.645346 + 0.521931i
4646 0 0
4747 6.15723 + 10.6646i 0.898124 + 1.55560i 0.829890 + 0.557928i 0.188403π0.188403\pi
0.0682346 + 0.997669i 0.478263π0.478263\pi
4848 0 0
4949 6.56840 2.41995i 0.938342 0.345708i
5050 0 0
5151 −8.05593 + 9.42638i −1.12806 + 1.31996i
5252 0 0
5353 3.35508 + 5.81117i 0.460856 + 0.798226i 0.999004 0.0446243i 0.0142091π-0.0142091\pi
−0.538148 + 0.842851i 0.680876π0.680876\pi
5454 0 0
5555 −4.78085 −0.644650
5656 0 0
5757 2.16819 + 0.402544i 0.287184 + 0.0533182i
5858 0 0
5959 −1.04139 + 1.80375i −0.135578 + 0.234828i −0.925818 0.377969i 0.876622π-0.876622\pi
0.790240 + 0.612797i 0.209956π0.209956\pi
6060 0 0
6161 −6.47973 11.2232i −0.829644 1.43699i −0.898317 0.439347i 0.855210π-0.855210\pi
0.0686730 0.997639i 0.478123π-0.478123\pi
6262 0 0
6363 5.19925 5.99732i 0.655043 0.755591i
6464 0 0
6565 5.23789 + 9.07230i 0.649681 + 1.12528i
6666 0 0
6767 2.41551 4.18379i 0.295102 0.511131i −0.679907 0.733298i 0.737980π-0.737980\pi
0.975009 + 0.222167i 0.0713132π0.0713132\pi
6868 0 0
6969 0.139378 + 0.393977i 0.0167791 + 0.0474293i
7070 0 0
7171 −1.53621 −0.182314 −0.0911572 0.995837i 0.529057π-0.529057\pi
−0.0911572 + 0.995837i 0.529057π0.529057\pi
7272 0 0
7373 −6.55954 11.3615i −0.767736 1.32976i −0.938788 0.344496i 0.888050π-0.888050\pi
0.171052 0.985262i 0.445283π-0.445283\pi
7474 0 0
7575 −0.898606 2.54008i −0.103762 0.293303i
7676 0 0
7777 6.70960 1.19667i 0.764630 0.136373i
7878 0 0
7979 1.86009 + 3.22177i 0.209277 + 0.362478i 0.951487 0.307689i 0.0995558π-0.0995558\pi
−0.742210 + 0.670167i 0.766222π0.766222\pi
8080 0 0
8181 1.88209 8.80101i 0.209121 0.977890i
8282 0 0
8383 −3.00173 + 5.19915i −0.329483 + 0.570681i −0.982409 0.186740i 0.940208π-0.940208\pi
0.652926 + 0.757421i 0.273541π0.273541\pi
8484 0 0
8585 6.64326 + 11.5065i 0.720563 + 1.24805i
8686 0 0
8787 3.14559 + 0.584007i 0.337242 + 0.0626121i
8888 0 0
8989 6.60349 11.4376i 0.699968 1.21238i −0.268509 0.963277i 0.586531π-0.586531\pi
0.968477 0.249103i 0.0801359π-0.0801359\pi
9090 0 0
9191 −9.62187 11.4213i −1.00865 1.19728i
9292 0 0
9393 5.09357 + 0.945667i 0.528179 + 0.0980611i
9494 0 0
9595 1.18147 2.04637i 0.121217 0.209953i
9696 0 0
9797 6.40860 11.1000i 0.650695 1.12704i −0.332260 0.943188i 0.607811π-0.607811\pi
0.982955 0.183848i 0.0588556π-0.0588556\pi
9898 0 0
9999 6.00881 4.85969i 0.603908 0.488417i
100100 0 0
101101 12.2013 1.21408 0.607039 0.794672i 0.292357π-0.292357\pi
0.607039 + 0.794672i 0.292357π0.292357\pi
102102 0 0
103103 13.6433 1.34431 0.672155 0.740411i 0.265369π-0.265369\pi
0.672155 + 0.740411i 0.265369π0.265369\pi
104104 0 0
105105 −4.20024 7.39532i −0.409901 0.721710i
106106 0 0
107107 −6.48002 + 11.2237i −0.626448 + 1.08504i 0.361811 + 0.932251i 0.382158π0.382158\pi
−0.988259 + 0.152788i 0.951175π0.951175\pi
108108 0 0
109109 7.70089 + 13.3383i 0.737612 + 1.27758i 0.953568 + 0.301178i 0.0973799π0.0973799\pi
−0.215956 + 0.976403i 0.569287π0.569287\pi
110110 0 0
111111 1.15208 + 0.213894i 0.109351 + 0.0203019i
112112 0 0
113113 −7.73446 13.3965i −0.727597 1.26023i −0.957896 0.287115i 0.907304π-0.907304\pi
0.230299 0.973120i 0.426029π-0.426029\pi
114114 0 0
115115 0.447790 0.0417566
116116 0 0
117117 −15.8051 6.07824i −1.46119 0.561934i
118118 0 0
119119 −12.2035 14.4857i −1.11869 1.32790i
120120 0 0
121121 −4.36418 −0.396744
122122 0 0
123123 1.65177 1.93276i 0.148935 0.174271i
124124 0 0
125125 −12.1666 −1.08821
126126 0 0
127127 −3.19404 −0.283425 −0.141713 0.989908i 0.545261π-0.545261\pi
−0.141713 + 0.989908i 0.545261π0.545261\pi
128128 0 0
129129 14.1096 + 2.61957i 1.24228 + 0.230640i
130130 0 0
131131 14.0868 1.23077 0.615383 0.788229i 0.289002π-0.289002\pi
0.615383 + 0.788229i 0.289002π0.289002\pi
132132 0 0
133133 −1.14590 + 3.16767i −0.0993620 + 0.274672i
134134 0 0
135135 −8.21785 5.04640i −0.707280 0.434325i
136136 0 0
137137 13.6964 1.17016 0.585079 0.810976i 0.301063π-0.301063\pi
0.585079 + 0.810976i 0.301063π0.301063\pi
138138 0 0
139139 −4.94131 8.55859i −0.419116 0.725931i 0.576735 0.816932i 0.304327π-0.304327\pi
−0.995851 + 0.0910010i 0.970993π0.970993\pi
140140 0 0
141141 −13.8573 + 16.2146i −1.16699 + 1.36552i
142142 0 0
143143 −7.27019 12.5923i −0.607964 1.05302i
144144 0 0
145145 1.71407 2.96885i 0.142346 0.246550i
146146 0 0
147147 7.74583 + 9.32749i 0.638866 + 0.769318i
148148 0 0
149149 −3.92029 −0.321163 −0.160581 0.987023i 0.551337π-0.551337\pi
−0.160581 + 0.987023i 0.551337π0.551337\pi
150150 0 0
151151 19.5784 1.59327 0.796634 0.604462i 0.206612π-0.206612\pi
0.796634 + 0.604462i 0.206612π0.206612\pi
152152 0 0
153153 −20.0458 7.70909i −1.62061 0.623243i
154154 0 0
155155 2.77555 4.80739i 0.222937 0.386139i
156156 0 0
157157 −7.39637 + 12.8109i −0.590295 + 1.02242i 0.403898 + 0.914804i 0.367655π0.367655\pi
−0.994193 + 0.107616i 0.965678π0.965678\pi
158158 0 0
159159 −7.55084 + 8.83537i −0.598821 + 0.700690i
160160 0 0
161161 −0.628443 + 0.112084i −0.0495282 + 0.00883347i
162162 0 0
163163 7.54686 13.0715i 0.591116 1.02384i −0.402967 0.915215i 0.632021π-0.632021\pi
0.994082 0.108628i 0.0346456π-0.0346456\pi
164164 0 0
165165 −2.76173 7.80656i −0.215001 0.607740i
166166 0 0
167167 1.92946 + 3.34192i 0.149306 + 0.258605i 0.930971 0.365093i 0.118963π-0.118963\pi
−0.781665 + 0.623698i 0.785629π0.785629\pi
168168 0 0
169169 −9.43043 + 16.3340i −0.725418 + 1.25646i
170170 0 0
171171 0.595183 + 3.77293i 0.0455147 + 0.288524i
172172 0 0
173173 −0.325786 0.564277i −0.0247690 0.0429012i 0.853375 0.521297i 0.174552π-0.174552\pi
−0.878144 + 0.478396i 0.841218π0.841218\pi
174174 0 0
175175 4.05174 0.722638i 0.306283 0.0546263i
176176 0 0
177177 −3.54688 0.658511i −0.266600 0.0494967i
178178 0 0
179179 10.9059 + 18.8896i 0.815145 + 1.41187i 0.909223 + 0.416308i 0.136676π0.136676\pi
−0.0940781 + 0.995565i 0.529990π0.529990\pi
180180 0 0
181181 −25.0338 −1.86075 −0.930374 0.366613i 0.880517π-0.880517\pi
−0.930374 + 0.366613i 0.880517π0.880517\pi
182182 0 0
183183 14.5831 17.0639i 1.07801 1.26140i
184184 0 0
185185 0.627782 1.08735i 0.0461555 0.0799436i
186186 0 0
187187 −9.22085 15.9710i −0.674295 1.16791i
188188 0 0
189189 12.7963 + 5.02531i 0.930797 + 0.365537i
190190 0 0
191191 −4.33036 7.50041i −0.313334 0.542711i 0.665748 0.746177i 0.268113π-0.268113\pi
−0.979082 + 0.203466i 0.934779π0.934779\pi
192192 0 0
193193 −0.808322 + 1.40006i −0.0581843 + 0.100778i −0.893650 0.448764i 0.851864π-0.851864\pi
0.835466 + 0.549542i 0.185198π0.185198\pi
194194 0 0
195195 −11.7882 + 13.7936i −0.844173 + 0.987781i
196196 0 0
197197 10.7746 0.767659 0.383829 0.923404i 0.374605π-0.374605\pi
0.383829 + 0.923404i 0.374605π0.374605\pi
198198 0 0
199199 2.38768 + 4.13558i 0.169258 + 0.293163i 0.938159 0.346204i 0.112530π-0.112530\pi
−0.768901 + 0.639368i 0.779196π0.779196\pi
200200 0 0
201201 8.22699 + 1.52741i 0.580287 + 0.107735i
202202 0 0
203203 −1.66246 + 4.59562i −0.116682 + 0.322549i
204204 0 0
205205 −1.36212 2.35925i −0.0951343 0.164777i
206206 0 0
207207 −0.562805 + 0.455174i −0.0391176 + 0.0316368i
208208 0 0
209209 −1.63988 + 2.84036i −0.113433 + 0.196472i
210210 0 0
211211 2.42787 + 4.20520i 0.167142 + 0.289498i 0.937414 0.348218i 0.113213π-0.113213\pi
−0.770272 + 0.637715i 0.779880π0.779880\pi
212212 0 0
213213 −0.887415 2.50845i −0.0608046 0.171876i
214214 0 0
215215 7.68848 13.3168i 0.524350 0.908200i
216216 0 0
217217 −2.69198 + 7.44158i −0.182743 + 0.505167i
218218 0 0
219219 14.7627 17.2741i 0.997570 1.16727i
220220 0 0
221221 −20.2047 + 34.9955i −1.35911 + 2.35406i
222222 0 0
223223 3.86187 6.68896i 0.258610 0.447926i −0.707260 0.706954i 0.750069π-0.750069\pi
0.965870 + 0.259028i 0.0834021π0.0834021\pi
224224 0 0
225225 3.62856 2.93463i 0.241904 0.195642i
226226 0 0
227227 −13.9491 −0.925837 −0.462919 0.886401i 0.653198π-0.653198\pi
−0.462919 + 0.886401i 0.653198π0.653198\pi
228228 0 0
229229 1.60027 0.105749 0.0528745 0.998601i 0.483162π-0.483162\pi
0.0528745 + 0.998601i 0.483162π0.483162\pi
230230 0 0
231231 5.82993 + 10.2647i 0.383581 + 0.675368i
232232 0 0
233233 3.69939 6.40753i 0.242355 0.419771i −0.719030 0.694979i 0.755413π-0.755413\pi
0.961385 + 0.275208i 0.0887468π0.0887468\pi
234234 0 0
235235 11.4273 + 19.7926i 0.745434 + 1.29113i
236236 0 0
237237 −4.18626 + 4.89841i −0.271927 + 0.318186i
238238 0 0
239239 −1.25117 2.16709i −0.0809316 0.140178i 0.822719 0.568449i 0.192456π-0.192456\pi
−0.903650 + 0.428271i 0.859123π0.859123\pi
240240 0 0
241241 4.24297 0.273314 0.136657 0.990618i 0.456364π-0.456364\pi
0.136657 + 0.990618i 0.456364π0.456364\pi
242242 0 0
243243 15.4582 2.01080i 0.991645 0.128993i
244244 0 0
245245 12.1904 4.49123i 0.778815 0.286934i
246246 0 0
247247 7.18661 0.457273
248248 0 0
249249 −10.2236 1.89810i −0.647894 0.120287i
250250 0 0
251251 −13.5381 −0.854516 −0.427258 0.904130i 0.640520π-0.640520\pi
−0.427258 + 0.904130i 0.640520π0.640520\pi
252252 0 0
253253 −0.621532 −0.0390754
254254 0 0
255255 −14.9511 + 17.4946i −0.936275 + 1.09555i
256256 0 0
257257 −6.15495 −0.383935 −0.191968 0.981401i 0.561487π-0.561487\pi
−0.191968 + 0.981401i 0.561487π0.561487\pi
258258 0 0
259259 −0.608880 + 1.68316i −0.0378340 + 0.104586i
260260 0 0
261261 0.863485 + 5.47373i 0.0534484 + 0.338816i
262262 0 0
263263 −25.3411 −1.56260 −0.781300 0.624156i 0.785443π-0.785443\pi
−0.781300 + 0.624156i 0.785443π0.785443\pi
264264 0 0
265265 6.22675 + 10.7850i 0.382506 + 0.662520i
266266 0 0
267267 22.4908 + 4.17562i 1.37642 + 0.255544i
268268 0 0
269269 −5.42092 9.38931i −0.330519 0.572476i 0.652095 0.758138i 0.273891π-0.273891\pi
−0.982614 + 0.185662i 0.940557π0.940557\pi
270270 0 0
271271 −15.0184 + 26.0127i −0.912306 + 1.58016i −0.101507 + 0.994835i 0.532366π0.532366\pi
−0.810799 + 0.585325i 0.800967π0.800967\pi
272272 0 0
273273 13.0914 22.3091i 0.792326 1.35021i
274274 0 0
275275 4.00719 0.241643
276276 0 0
277277 19.7629 1.18744 0.593720 0.804672i 0.297659π-0.297659\pi
0.593720 + 0.804672i 0.297659π0.297659\pi
278278 0 0
279279 1.39822 + 8.86348i 0.0837092 + 0.530643i
280280 0 0
281281 −3.98596 + 6.90388i −0.237782 + 0.411851i −0.960078 0.279734i 0.909754π-0.909754\pi
0.722295 + 0.691585i 0.243087π0.243087\pi
282282 0 0
283283 −11.6063 + 20.1028i −0.689926 + 1.19499i 0.281936 + 0.959433i 0.409023π0.409023\pi
−0.971861 + 0.235553i 0.924310π0.924310\pi
284284 0 0
285285 4.02398 + 0.747087i 0.238360 + 0.0442536i
286286 0 0
287287 2.50217 + 2.97011i 0.147698 + 0.175320i
288288 0 0
289289 −17.1258 + 29.6627i −1.00740 + 1.74486i
290290 0 0
291291 21.8270 + 4.05239i 1.27952 + 0.237555i
292292 0 0
293293 11.8556 + 20.5345i 0.692612 + 1.19964i 0.970979 + 0.239164i 0.0768735π0.0768735\pi
−0.278367 + 0.960475i 0.589793π0.589793\pi
294294 0 0
295295 −1.93274 + 3.34760i −0.112528 + 0.194905i
296296 0 0
297297 11.4064 + 7.00440i 0.661865 + 0.406437i
298298 0 0
299299 0.680950 + 1.17944i 0.0393803 + 0.0682088i
300300 0 0
301301 −7.45698 + 20.6137i −0.429813 + 1.18816i
302302 0 0
303303 7.04829 + 19.9233i 0.404913 + 1.14456i
304304 0 0
305305 −12.0258 20.8293i −0.688597 1.19268i
306306 0 0
307307 3.87810 0.221335 0.110668 0.993857i 0.464701π-0.464701\pi
0.110668 + 0.993857i 0.464701π0.464701\pi
308308 0 0
309309 7.88124 + 22.2778i 0.448348 + 1.26734i
310310 0 0
311311 3.46220 5.99670i 0.196323 0.340042i −0.751010 0.660290i 0.770433π-0.770433\pi
0.947333 + 0.320249i 0.103767π0.103767\pi
312312 0 0
313313 −15.1157 26.1811i −0.854388 1.47984i −0.877212 0.480104i 0.840599π-0.840599\pi
0.0228236 0.999740i 0.492734π-0.492734\pi
314314 0 0
315315 9.64935 11.1305i 0.543679 0.627133i
316316 0 0
317317 −4.68699 8.11811i −0.263248 0.455959i 0.703855 0.710343i 0.251460π-0.251460\pi
−0.967103 + 0.254385i 0.918127π0.918127\pi
318318 0 0
319319 −2.37913 + 4.12077i −0.133205 + 0.230719i
320320 0 0
321321 −22.0703 4.09755i −1.23184 0.228703i
322322 0 0
323323 9.11484 0.507163
324324 0 0
325325 −4.39027 7.60418i −0.243529 0.421804i
326326 0 0
327327 −17.3314 + 20.2797i −0.958428 + 1.12147i
328328 0 0
329329 −20.9916 24.9173i −1.15731 1.37374i
330330 0 0
331331 −13.7720 23.8539i −0.756979 1.31113i −0.944384 0.328844i 0.893341π-0.893341\pi
0.187405 0.982283i 0.439992π-0.439992\pi
332332 0 0
333333 0.316254 + 2.00477i 0.0173306 + 0.109861i
334334 0 0
335335 4.48298 7.76475i 0.244931 0.424234i
336336 0 0
337337 −3.41673 5.91796i −0.186121 0.322372i 0.757832 0.652449i 0.226258π-0.226258\pi
−0.943954 + 0.330078i 0.892925π0.892925\pi
338338 0 0
339339 17.4069 20.3681i 0.945415 1.10625i
340340 0 0
341341 −3.85246 + 6.67266i −0.208622 + 0.361345i
342342 0 0
343343 −15.9842 + 9.35445i −0.863065 + 0.505093i
344344 0 0
345345 0.258673 + 0.731188i 0.0139265 + 0.0393658i
346346 0 0
347347 −10.0959 + 17.4867i −0.541979 + 0.938735i 0.456812 + 0.889564i 0.348991π0.348991\pi
−0.998790 + 0.0491714i 0.984342π0.984342\pi
348348 0 0
349349 −4.25154 + 7.36388i −0.227580 + 0.394180i −0.957090 0.289790i 0.906415π-0.906415\pi
0.729511 + 0.683970i 0.239748π0.239748\pi
350350 0 0
351351 0.794966 29.3191i 0.0424321 1.56494i
352352 0 0
353353 4.70904 0.250637 0.125318 0.992117i 0.460005π-0.460005\pi
0.125318 + 0.992117i 0.460005π0.460005\pi
354354 0 0
355355 −2.85107 −0.151319
356356 0 0
357357 16.6039 28.2948i 0.878771 1.49752i
358358 0 0
359359 6.03357 10.4504i 0.318440 0.551554i −0.661723 0.749748i 0.730175π-0.730175\pi
0.980163 + 0.198195i 0.0635079π0.0635079\pi
360360 0 0
361361 8.68948 + 15.0506i 0.457341 + 0.792138i
362362 0 0
363363 −2.52104 7.12619i −0.132320 0.374028i
364364 0 0
365365 −12.1739 21.0859i −0.637213 1.10369i
366366 0 0
367367 0.960711 0.0501487 0.0250744 0.999686i 0.492018π-0.492018\pi
0.0250744 + 0.999686i 0.492018π0.492018\pi
368368 0 0
369369 4.11013 + 1.58065i 0.213965 + 0.0822854i
370370 0 0
371371 −11.4384 13.5775i −0.593850 0.704908i
372372 0 0
373373 −7.04998 −0.365034 −0.182517 0.983203i 0.558425π-0.558425\pi
−0.182517 + 0.983203i 0.558425π0.558425\pi
374374 0 0
375375 −7.02822 19.8666i −0.362936 1.02591i
376376 0 0
377377 10.4263 0.536980
378378 0 0
379379 −37.1330 −1.90739 −0.953697 0.300769i 0.902757π-0.902757\pi
−0.953697 + 0.300769i 0.902757π0.902757\pi
380380 0 0
381381 −1.84509 5.21549i −0.0945267 0.267198i
382382 0 0
383383 32.1975 1.64522 0.822608 0.568609i 0.192518π-0.192518\pi
0.822608 + 0.568609i 0.192518π0.192518\pi
384384 0 0
385385 12.4524 2.22092i 0.634635 0.113189i
386386 0 0
387387 3.87317 + 24.5525i 0.196884 + 1.24807i
388388 0 0
389389 −25.7426 −1.30520 −0.652600 0.757702i 0.726322π-0.726322\pi
−0.652600 + 0.757702i 0.726322π0.726322\pi
390390 0 0
391391 0.863654 + 1.49589i 0.0436769 + 0.0756506i
392392 0 0
393393 8.13743 + 23.0020i 0.410479 + 1.16030i
394394 0 0
395395 3.45217 + 5.97933i 0.173697 + 0.300853i
396396 0 0
397397 9.44903 16.3662i 0.474233 0.821396i −0.525332 0.850898i 0.676059π-0.676059\pi
0.999565 + 0.0295016i 0.00939202π0.00939202\pi
398398 0 0
399399 −5.83438 0.0412635i −0.292084 0.00206576i
400400 0 0
401401 15.2039 0.759245 0.379622 0.925142i 0.376054π-0.376054\pi
0.379622 + 0.925142i 0.376054π0.376054\pi
402402 0 0
403403 16.8830 0.841002
404404 0 0
405405 3.49300 16.3339i 0.173569 0.811639i
406406 0 0
407407 −0.871362 + 1.50924i −0.0431918 + 0.0748104i
408408 0 0
409409 14.9729 25.9339i 0.740363 1.28235i −0.211967 0.977277i 0.567987π-0.567987\pi
0.952330 0.305070i 0.0986798π-0.0986798\pi
410410 0 0
411411 7.91191 + 22.3645i 0.390266 + 1.10316i
412412 0 0
413413 1.87454 5.18191i 0.0922403 0.254985i
414414 0 0
415415 −5.57096 + 9.64918i −0.273468 + 0.473660i
416416 0 0
417417 11.1207 13.0126i 0.544585 0.637229i
418418 0 0
419419 −12.2660 21.2453i −0.599231 1.03790i −0.992935 0.118661i 0.962140π-0.962140\pi
0.393704 0.919237i 0.371194π-0.371194\pi
420420 0 0
421421 −2.37791 + 4.11866i −0.115892 + 0.200731i −0.918136 0.396265i 0.870306π-0.870306\pi
0.802244 + 0.596996i 0.203639π0.203639\pi
422422 0 0
423423 −34.4814 13.2606i −1.67654 0.644755i
424424 0 0
425425 −5.56822 9.64444i −0.270098 0.467824i
426426 0 0
427427 22.0911 + 26.2224i 1.06906 + 1.26899i
428428 0 0
429429 16.3621 19.1455i 0.789968 0.924355i
430430 0 0
431431 1.36446 + 2.36331i 0.0657237 + 0.113837i 0.897015 0.442000i 0.145731π-0.145731\pi
−0.831291 + 0.555837i 0.812398π0.812398\pi
432432 0 0
433433 14.5592 0.699672 0.349836 0.936811i 0.386237π-0.386237\pi
0.349836 + 0.936811i 0.386237π0.386237\pi
434434 0 0
435435 5.83794 + 1.08387i 0.279908 + 0.0519674i
436436 0 0
437437 0.153597 0.266037i 0.00734753 0.0127263i
438438 0 0
439439 1.44066 + 2.49529i 0.0687587 + 0.119094i 0.898355 0.439270i 0.144763π-0.144763\pi
−0.829596 + 0.558363i 0.811429π0.811429\pi
440440 0 0
441441 −10.7562 + 18.0362i −0.512199 + 0.858867i
442442 0 0
443443 −12.4865 21.6273i −0.593254 1.02755i −0.993791 0.111265i 0.964510π-0.964510\pi
0.400537 0.916281i 0.368824π-0.368824\pi
444444 0 0
445445 12.2555 21.2272i 0.580967 1.00626i
446446 0 0
447447 −2.26462 6.40138i −0.107113 0.302775i
448448 0 0
449449 −2.99154 −0.141180 −0.0705898 0.997505i 0.522488π-0.522488\pi
−0.0705898 + 0.997505i 0.522488π0.522488\pi
450450 0 0
451451 1.89062 + 3.27464i 0.0890257 + 0.154197i
452452 0 0
453453 11.3098 + 31.9692i 0.531379 + 1.50205i
454454 0 0
455455 −17.8574 21.1969i −0.837166 0.993727i
456456 0 0
457457 12.8085 + 22.1850i 0.599158 + 1.03777i 0.992946 + 0.118571i 0.0378312π0.0378312\pi
−0.393788 + 0.919201i 0.628835π0.628835\pi
458458 0 0
459459 1.00826 37.1857i 0.0470616 1.73568i
460460 0 0
461461 −6.45759 + 11.1849i −0.300760 + 0.520931i −0.976308 0.216384i 0.930574π-0.930574\pi
0.675548 + 0.737316i 0.263907π0.263907\pi
462462 0 0
463463 −12.2457 21.2102i −0.569108 0.985724i −0.996654 0.0817305i 0.973955π-0.973955\pi
0.427547 0.903993i 0.359378π-0.359378\pi
464464 0 0
465465 9.45324 + 1.75508i 0.438383 + 0.0813898i
466466 0 0
467467 −10.4087 + 18.0283i −0.481655 + 0.834251i −0.999778 0.0210550i 0.993297π-0.993297\pi
0.518123 + 0.855306i 0.326631π0.326631\pi
468468 0 0
469469 −4.34800 + 12.0194i −0.200772 + 0.555005i
470470 0 0
471471 −25.1913 4.67699i −1.16075 0.215504i
472472 0 0
473473 −10.6716 + 18.4838i −0.490681 + 0.849884i
474474 0 0
475475 −0.990281 + 1.71522i −0.0454372 + 0.0786996i
476476 0 0
477477 −18.7890 7.22575i −0.860288 0.330844i
478478 0 0
479479 27.4873 1.25592 0.627962 0.778244i 0.283889π-0.283889\pi
0.627962 + 0.778244i 0.283889π0.283889\pi
480480 0 0
481481 3.81865 0.174115
482482 0 0
483483 −0.546050 0.961425i −0.0248461 0.0437464i
484484 0 0
485485 11.8938 20.6007i 0.540070 0.935429i
486486 0 0
487487 −6.32927 10.9626i −0.286807 0.496763i 0.686239 0.727376i 0.259260π-0.259260\pi
−0.973046 + 0.230613i 0.925927π0.925927\pi
488488 0 0
489489 25.7038 + 4.77215i 1.16237 + 0.215804i
490490 0 0
491491 −1.40618 2.43557i −0.0634598 0.109916i 0.832550 0.553950i 0.186880π-0.186880\pi
−0.896010 + 0.444034i 0.853547π0.853547\pi
492492 0 0
493493 13.2237 0.595566
494494 0 0
495495 11.1518 9.01917i 0.501238 0.405381i
496496 0 0
497497 4.00128 0.713638i 0.179482 0.0320110i
498498 0 0
499499 −4.24205 −0.189900 −0.0949502 0.995482i 0.530269π-0.530269\pi
−0.0949502 + 0.995482i 0.530269π0.530269\pi
500500 0 0
501501 −4.34237 + 5.08108i −0.194003 + 0.227006i
502502 0 0
503503 22.2162 0.990570 0.495285 0.868730i 0.335064π-0.335064\pi
0.495285 + 0.868730i 0.335064π0.335064\pi
504504 0 0
505505 22.6446 1.00767
506506 0 0
507507 −32.1191 5.96319i −1.42646 0.264835i
508508 0 0
509509 −4.85469 −0.215180 −0.107590 0.994195i 0.534313π-0.534313\pi
−0.107590 + 0.994195i 0.534313π0.534313\pi
510510 0 0
511511 22.3632 + 26.5454i 0.989290 + 1.17430i
512512 0 0
513513 −5.81694 + 3.15136i −0.256824 + 0.139136i
514514 0 0
515515 25.3207 1.11576
516516 0 0
517517 −15.8611 27.4722i −0.697569 1.20823i
518518 0 0
519519 0.733203 0.857933i 0.0321840 0.0376591i
520520 0 0
521521 7.92316 + 13.7233i 0.347120 + 0.601229i 0.985737 0.168296i 0.0538263π-0.0538263\pi
−0.638617 + 0.769525i 0.720493π0.720493\pi
522522 0 0
523523 10.7605 18.6377i 0.470524 0.814972i −0.528908 0.848679i 0.677398π-0.677398\pi
0.999432 + 0.0337078i 0.0107316π0.0107316\pi
524524 0 0
525525 3.52054 + 6.19858i 0.153649 + 0.270528i
526526 0 0
527527 21.4128 0.932758
528528 0 0
529529 −22.9418 −0.997469
530530 0 0
531531 −0.973643 6.17204i −0.0422525 0.267844i
532532 0 0
533533 4.14271 7.17539i 0.179441 0.310801i
534534 0 0
535535 −12.0264 + 20.8303i −0.519945 + 0.900572i
536536 0 0
537537 −24.5445 + 28.7199i −1.05917 + 1.23936i
538538 0 0
539539 −16.9202 + 6.23382i −0.728806 + 0.268510i
540540 0 0
541541 7.55977 13.0939i 0.325020 0.562951i −0.656497 0.754329i 0.727962π-0.727962\pi
0.981516 + 0.191378i 0.0612957π0.0612957\pi
542542 0 0
543543 −14.4612 40.8772i −0.620588 1.75421i
544544 0 0
545545 14.2922 + 24.7548i 0.612211 + 1.06038i
546546 0 0
547547 −19.4532 + 33.6939i −0.831757 + 1.44065i 0.0648863 + 0.997893i 0.479332π0.479332\pi
−0.896644 + 0.442753i 0.854002π0.854002\pi
548548 0 0
549549 36.2875 + 13.9552i 1.54871 + 0.595594i
550550 0 0
551551 −1.17589 2.03670i −0.0500945 0.0867662i
552552 0 0
553553 −6.34154 7.52749i −0.269670 0.320101i
554554 0 0
555555 2.13816 + 0.396969i 0.0907600 + 0.0168504i
556556 0 0
557557 −5.37036 9.30173i −0.227549 0.394127i 0.729532 0.683947i 0.239738π-0.239738\pi
−0.957081 + 0.289820i 0.906405π0.906405\pi
558558 0 0
559559 46.7672 1.97804
560560 0 0
561561 20.7521 24.2824i 0.876156 1.02520i
562562 0 0
563563 11.7380 20.3308i 0.494697 0.856840i −0.505285 0.862953i 0.668612π-0.668612\pi
0.999981 + 0.00611281i 0.00194578π0.00194578\pi
564564 0 0
565565 −14.3545 24.8627i −0.603898 1.04598i
566566 0 0
567567 −0.813726 + 23.7979i −0.0341733 + 0.999416i
568568 0 0
569569 18.9681 + 32.8537i 0.795183 + 1.37730i 0.922723 + 0.385463i 0.125958π0.125958\pi
−0.127540 + 0.991833i 0.540708π0.540708\pi
570570 0 0
571571 2.15815 3.73803i 0.0903158 0.156432i −0.817328 0.576172i 0.804546π-0.804546\pi
0.907644 + 0.419741i 0.137879π0.137879\pi
572572 0 0
573573 9.74578 11.4037i 0.407136 0.476396i
574574 0 0
575575 −0.375326 −0.0156522
576576 0 0
577577 −5.05923 8.76284i −0.210618 0.364802i 0.741290 0.671185i 0.234214π-0.234214\pi
−0.951908 + 0.306383i 0.900881π0.900881\pi
578578 0 0
579579 −2.75306 0.511131i −0.114413 0.0212419i
580580 0 0
581581 5.40322 14.9364i 0.224163 0.619667i
582582 0 0
583583 −8.64272 14.9696i −0.357945 0.619979i
584584 0 0
585585 −29.3330 11.2807i −1.21277 0.466400i
586586 0 0
587587 −4.10992 + 7.11859i −0.169635 + 0.293816i −0.938291 0.345846i 0.887592π-0.887592\pi
0.768657 + 0.639661i 0.220925π0.220925\pi
588588 0 0
589589 −1.90409 3.29797i −0.0784565 0.135891i
590590 0 0
591591 6.22412 + 17.5937i 0.256026 + 0.723706i
592592 0 0
593593 21.8434 37.8339i 0.897002 1.55365i 0.0656957 0.997840i 0.479073π-0.479073\pi
0.831307 0.555814i 0.187593π-0.187593\pi
594594 0 0
595595 −22.6486 26.8842i −0.928504 1.10215i
596596 0 0
597597 −5.37363 + 6.28778i −0.219928 + 0.257342i
598598 0 0
599599 7.63946 13.2319i 0.312140 0.540642i −0.666686 0.745339i 0.732288π-0.732288\pi
0.978825 + 0.204697i 0.0656209π0.0656209\pi
600600 0 0
601601 7.65696 13.2622i 0.312334 0.540978i −0.666533 0.745475i 0.732223π-0.732223\pi
0.978867 + 0.204497i 0.0655559π0.0655559\pi
602602 0 0
603603 2.25836 + 14.3160i 0.0919676 + 0.582994i
604604 0 0
605605 −8.09955 −0.329293
606606 0 0
607607 −2.66981 −0.108364 −0.0541821 0.998531i 0.517255π-0.517255\pi
−0.0541821 + 0.998531i 0.517255π0.517255\pi
608608 0 0
609609 −8.46445 0.0598647i −0.342997 0.00242584i
610610 0 0
611611 −34.7547 + 60.1970i −1.40603 + 2.43531i
612612 0 0
613613 −13.5875 23.5343i −0.548796 0.950542i −0.998357 0.0572929i 0.981753π-0.981753\pi
0.449562 0.893249i 0.351580π-0.351580\pi
614614 0 0
615615 3.06554 3.58703i 0.123614 0.144643i
616616 0 0
617617 −17.6058 30.4942i −0.708785 1.22765i −0.965308 0.261113i 0.915910π-0.915910\pi
0.256524 0.966538i 0.417423π-0.417423\pi
618618 0 0
619619 −31.2681 −1.25677 −0.628385 0.777902i 0.716284π-0.716284\pi
−0.628385 + 0.777902i 0.716284π0.716284\pi
620620 0 0
621621 −1.06836 0.656055i −0.0428717 0.0263266i
622622 0 0
623623 −11.8865 + 32.8585i −0.476223 + 1.31645i
624624 0 0
625625 −14.8023 −0.592090
626626 0 0
627627 −5.58528 1.03696i −0.223055 0.0414121i
628628 0 0
629629 4.84322 0.193112
630630 0 0
631631 15.5090 0.617403 0.308702 0.951159i 0.400106π-0.400106\pi
0.308702 + 0.951159i 0.400106π0.400106\pi
632632 0 0
633633 −5.46409 + 6.39363i −0.217178 + 0.254124i
634634 0 0
635635 −5.92787 −0.235240
636636 0 0
637637 30.3673 + 25.2786i 1.20320 + 1.00158i
638638 0 0
639639 3.58337 2.89809i 0.141756 0.114647i
640640 0 0
641641 −33.5310 −1.32440 −0.662198 0.749329i 0.730376π-0.730376\pi
−0.662198 + 0.749329i 0.730376π0.730376\pi
642642 0 0
643643 −10.2721 17.7918i −0.405093 0.701641i 0.589239 0.807958i 0.299427π-0.299427\pi
−0.994332 + 0.106317i 0.966094π0.966094\pi
644644 0 0
645645 26.1862 + 4.86170i 1.03108 + 0.191429i
646646 0 0
647647 −16.8855 29.2465i −0.663836 1.14980i −0.979599 0.200960i 0.935594π-0.935594\pi
0.315763 0.948838i 0.397739π-0.397739\pi
648648 0 0
649649 2.68264 4.64647i 0.105303 0.182390i
650650 0 0
651651 −13.7063 0.0969374i −0.537191 0.00379928i
652652 0 0
653653 18.0115 0.704845 0.352423 0.935841i 0.385358π-0.385358\pi
0.352423 + 0.935841i 0.385358π0.385358\pi
654654 0 0
655655 26.1438 1.02152
656656 0 0
657657 36.7344 + 14.1271i 1.43315 + 0.551150i
658658 0 0
659659 1.42710 2.47180i 0.0555918 0.0962878i −0.836890 0.547371i 0.815629π-0.815629\pi
0.892482 + 0.451083i 0.148962π0.148962\pi
660660 0 0
661661 −7.02746 + 12.1719i −0.273337 + 0.473433i −0.969714 0.244243i 0.921461π-0.921461\pi
0.696378 + 0.717676i 0.254794π0.254794\pi
662662 0 0
663663 −68.8151 12.7761i −2.67256 0.496184i
664664 0 0
665665 −2.12669 + 5.87892i −0.0824695 + 0.227975i
666666 0 0
667667 0.222837 0.385964i 0.00862827 0.0149446i
668668 0 0
669669 13.1532 + 2.44200i 0.508530 + 0.0944132i
670670 0 0
671671 16.6918 + 28.9111i 0.644381 + 1.11610i
672672 0 0
673673 −7.54157 + 13.0624i −0.290706 + 0.503518i −0.973977 0.226647i 0.927223π-0.927223\pi
0.683271 + 0.730165i 0.260557π0.260557\pi
674674 0 0
675675 6.88800 + 4.22977i 0.265119 + 0.162804i
676676 0 0
677677 18.1093 + 31.3663i 0.695998 + 1.20550i 0.969843 + 0.243731i 0.0783713π0.0783713\pi
−0.273845 + 0.961774i 0.588295π0.588295\pi
678678 0 0
679679 −11.5357 + 31.8887i −0.442699 + 1.22378i
680680 0 0
681681 −8.05794 22.7773i −0.308781 0.872828i
682682 0 0
683683 8.84350 + 15.3174i 0.338387 + 0.586104i 0.984130 0.177452i 0.0567853π-0.0567853\pi
−0.645742 + 0.763555i 0.723452π0.723452\pi
684684 0 0
685685 25.4193 0.971220
686686 0 0
687687 0.924422 + 2.61305i 0.0352689 + 0.0996942i
688688 0 0
689689 −18.9379 + 32.8014i −0.721477 + 1.24963i
690690 0 0
691691 −11.2049 19.4074i −0.426253 0.738292i 0.570283 0.821448i 0.306833π-0.306833\pi
−0.996537 + 0.0831559i 0.973500π0.973500\pi
692692 0 0
693693 −13.3933 + 15.4491i −0.508769 + 0.586865i
694694 0 0
695695 −9.17064 15.8840i −0.347862 0.602515i
696696 0 0
697697 5.25424 9.10061i 0.199018 0.344710i
698698 0 0
699699 12.5997 + 2.33925i 0.476566 + 0.0884787i
700700 0 0
701701 −31.1776 −1.17756 −0.588781 0.808293i 0.700392π-0.700392\pi
−0.588781 + 0.808293i 0.700392π0.700392\pi
702702 0 0
703703 −0.430672 0.745946i −0.0162431 0.0281339i
704704 0 0
705705 −25.7179 + 30.0929i −0.968592 + 1.13337i
706706 0 0
707707 −31.7802 + 5.66806i −1.19522 + 0.213170i
708708 0 0
709709 4.02492 + 6.97137i 0.151159 + 0.261815i 0.931654 0.363347i 0.118366π-0.118366\pi
−0.780495 + 0.625162i 0.785033π0.785033\pi
710710 0 0
711711 −10.4168 4.00602i −0.390660 0.150238i
712712 0 0
713713 0.360834 0.624982i 0.0135133 0.0234058i
714714 0 0
715715 −13.4929 23.3703i −0.504604 0.874000i
716716 0 0
717717 2.81585 3.29487i 0.105160 0.123049i
718718 0 0
719719 −20.9980 + 36.3696i −0.783093 + 1.35636i 0.147039 + 0.989131i 0.453026π0.453026\pi
−0.930132 + 0.367226i 0.880308π0.880308\pi
720720 0 0
721721 −35.5359 + 6.33791i −1.32343 + 0.236036i
722722 0 0
723723 2.45102 + 6.92827i 0.0911543 + 0.257665i
724724 0 0
725725 −1.43669 + 2.48842i −0.0533573 + 0.0924176i
726726 0 0
727727 0.668774 1.15835i 0.0248035 0.0429609i −0.853357 0.521327i 0.825437π-0.825437\pi
0.878161 + 0.478366i 0.158771π0.158771\pi
728728 0 0
729729 12.2131 + 24.0799i 0.452337 + 0.891847i
730730 0 0
731731 59.3152 2.19385
732732 0 0
733733 29.4749 1.08868 0.544340 0.838865i 0.316780π-0.316780\pi
0.544340 + 0.838865i 0.316780π0.316780\pi
734734 0 0
735735 14.3756 + 17.3110i 0.530252 + 0.638527i
736736 0 0
737737 −6.22238 + 10.7775i −0.229204 + 0.396993i
738738 0 0
739739 9.52146 + 16.4916i 0.350252 + 0.606655i 0.986294 0.165000i 0.0527625π-0.0527625\pi
−0.636041 + 0.771655i 0.719429π0.719429\pi
740740 0 0
741741 4.15146 + 11.7349i 0.152508 + 0.431092i
742742 0 0
743743 21.6613 + 37.5185i 0.794676 + 1.37642i 0.923045 + 0.384693i 0.125693π0.125693\pi
−0.128369 + 0.991726i 0.540974π0.540974\pi
744744 0 0
745745 −7.27573 −0.266562
746746 0 0
747747 −2.80645 17.7904i −0.102682 0.650917i
748748 0 0
749749 11.6643 32.2441i 0.426203 1.17818i
750750 0 0
751751 34.8763 1.27265 0.636327 0.771420i 0.280453π-0.280453\pi
0.636327 + 0.771420i 0.280453π0.280453\pi
752752 0 0
753753 −7.82049 22.1061i −0.284994 0.805591i
754754 0 0
755755 36.3358 1.32240
756756 0 0
757757 8.67255 0.315209 0.157605 0.987502i 0.449623π-0.449623\pi
0.157605 + 0.987502i 0.449623π0.449623\pi
758758 0 0
759759 −0.359038 1.01489i −0.0130322 0.0368381i
760760 0 0
761761 −5.48977 −0.199004 −0.0995021 0.995037i 0.531725π-0.531725\pi
−0.0995021 + 0.995037i 0.531725π0.531725\pi
762762 0 0
763763 −26.2544 31.1643i −0.950473 1.12822i
764764 0 0
765765 −37.2033 14.3074i −1.34509 0.517285i
766766 0 0
767767 −11.7564 −0.424499
768768 0 0
769769 1.81365 + 3.14134i 0.0654021 + 0.113280i 0.896872 0.442290i 0.145834π-0.145834\pi
−0.831470 + 0.555569i 0.812500π0.812500\pi
770770 0 0
771771 −3.55550 10.0503i −0.128048 0.361953i
772772 0 0
773773 −6.96717 12.0675i −0.250592 0.434037i 0.713097 0.701065i 0.247292π-0.247292\pi
−0.963689 + 0.267028i 0.913958π0.913958\pi
774774 0 0
775775 −2.32640 + 4.02944i −0.0835666 + 0.144742i
776776 0 0
777777 −3.10013 0.0219256i −0.111217 0.000786577i
778778 0 0
779779 −1.86888 −0.0669597
780780 0 0
781781 3.95729 0.141603
782782 0 0
783783 −8.43916 + 4.57196i −0.301591 + 0.163388i
784784 0 0
785785 −13.7270 + 23.7759i −0.489939 + 0.848599i
786786 0 0
787787 −8.78923 + 15.2234i −0.313302 + 0.542655i −0.979075 0.203499i 0.934769π-0.934769\pi
0.665773 + 0.746154i 0.268102π0.268102\pi
788788 0 0
789789 −14.6387 41.3790i −0.521151 1.47313i
790790 0 0
791791 26.3688 + 31.3001i 0.937567 + 1.11290i
792792 0 0
793793 36.5751 63.3499i 1.29882 2.24962i
794794 0 0
795795 −14.0137 + 16.3977i −0.497015 + 0.581566i
796796 0 0
797797 5.57971 + 9.66434i 0.197644 + 0.342329i 0.947764 0.318973i 0.103338π-0.103338\pi
−0.750120 + 0.661301i 0.770004π0.770004\pi
798798 0 0
799799 −44.0797 + 76.3483i −1.55943 + 2.70101i
800800 0 0
801801 6.17388 + 39.1370i 0.218143 + 1.38284i
802802 0 0
803803 16.8974 + 29.2672i 0.596297 + 1.03282i
804804 0 0
805805 −1.16634 + 0.208019i −0.0411079 + 0.00733169i
806806 0 0
807807 12.2001 14.2756i 0.429466 0.502525i
808808 0 0
809809 14.3481 + 24.8517i 0.504453 + 0.873738i 0.999987 + 0.00514935i 0.00163910π0.00163910\pi
−0.495534 + 0.868589i 0.665028π0.665028\pi
810810 0 0
811811 47.1695 1.65635 0.828173 0.560473i 0.189380π-0.189380\pi
0.828173 + 0.560473i 0.189380π0.189380\pi
812812 0 0
813813 −51.1513 9.49670i −1.79396 0.333064i
814814 0 0
815815 14.0063 24.2597i 0.490620 0.849779i
816816 0 0
817817 −5.27446 9.13563i −0.184530 0.319615i
818818 0 0
819819 43.9905 + 8.48949i 1.53715 + 0.296647i
820820 0 0
821821 19.3854 + 33.5765i 0.676554 + 1.17183i 0.976012 + 0.217717i 0.0698609π0.0698609\pi
−0.299458 + 0.954110i 0.596806π0.596806\pi
822822 0 0
823823 11.3920 19.7316i 0.397101 0.687799i −0.596266 0.802787i 0.703350π-0.703350\pi
0.993367 + 0.114988i 0.0366830π0.0366830\pi
824824 0 0
825825 2.31482 + 6.54327i 0.0805916 + 0.227807i
826826 0 0
827827 −1.55152 −0.0539515 −0.0269758 0.999636i 0.508588π-0.508588\pi
−0.0269758 + 0.999636i 0.508588π0.508588\pi
828828 0 0
829829 −23.8972 41.3911i −0.829983 1.43757i −0.898051 0.439892i 0.855017π-0.855017\pi
0.0680673 0.997681i 0.478317π-0.478317\pi
830830 0 0
831831 11.4164 + 32.2706i 0.396030 + 1.11945i
832832 0 0
833833 38.5151 + 32.0611i 1.33447 + 1.11085i
834834 0 0
835835 3.58090 + 6.20231i 0.123922 + 0.214640i
836836 0 0
837837 −13.6653 + 7.40326i −0.472342 + 0.255894i
838838 0 0
839839 19.5804 33.9142i 0.675990 1.17085i −0.300188 0.953880i 0.597049π-0.597049\pi
0.976178 0.216970i 0.0696173π-0.0696173\pi
840840 0 0
841841 12.7940 + 22.1599i 0.441174 + 0.764135i
842842 0 0
843843 −13.5758 2.52046i −0.467574 0.0868093i
844844 0 0
845845 −17.5021 + 30.3145i −0.602089 + 1.04285i
846846 0 0
847847 11.3672 2.02736i 0.390580 0.0696609i
848848 0 0
849849 −39.5301 7.33911i −1.35667 0.251877i
850850 0 0
851851 0.0816145 0.141361i 0.00279771 0.00484578i
852852 0 0
853853 14.5234 25.1552i 0.497270 0.861298i −0.502725 0.864447i 0.667669π-0.667669\pi
0.999995 + 0.00314895i 0.00100234π0.00100234\pi
854854 0 0
855855 1.10461 + 7.00224i 0.0377768 + 0.239472i
856856 0 0
857857 −48.2584 −1.64848 −0.824239 0.566243i 0.808397π-0.808397\pi
−0.824239 + 0.566243i 0.808397π0.808397\pi
858858 0 0
859859 −10.1506 −0.346332 −0.173166 0.984893i 0.555400π-0.555400\pi
−0.173166 + 0.984893i 0.555400π0.555400\pi
860860 0 0
861861 −3.40442 + 5.80148i −0.116022 + 0.197714i
862862 0 0
863863 25.7981 44.6837i 0.878179 1.52105i 0.0248411 0.999691i 0.492092π-0.492092\pi
0.853338 0.521359i 0.174575π-0.174575\pi
864864 0 0
865865 −0.604630 1.04725i −0.0205580 0.0356076i
866866 0 0
867867 −58.3287 10.8292i −1.98094 0.367780i
868868 0 0
869869 −4.79161 8.29931i −0.162544 0.281535i
870870 0 0
871871 27.2689 0.923972
872872 0 0
873873 5.99167 + 37.9819i 0.202787 + 1.28549i
874874 0 0
875875 31.6897 5.65193i 1.07131 0.191070i
876876 0 0
877877 −10.3978 −0.351109 −0.175555 0.984470i 0.556172π-0.556172\pi
−0.175555 + 0.984470i 0.556172π0.556172\pi
878878 0 0
879879 −26.6819 + 31.2209i −0.899957 + 1.05305i
880880 0 0
881881 23.6562 0.796996 0.398498 0.917169i 0.369532π-0.369532\pi
0.398498 + 0.917169i 0.369532π0.369532\pi
882882 0 0
883883 41.8601 1.40871 0.704353 0.709850i 0.251237π-0.251237\pi
0.704353 + 0.709850i 0.251237π0.251237\pi
884884 0 0
885885 −6.58271 1.22214i −0.221276 0.0410818i
886886 0 0
887887 42.2505 1.41863 0.709316 0.704891i 0.249004π-0.249004\pi
0.709316 + 0.704891i 0.249004π0.249004\pi
888888 0 0
889889 8.31936 1.48378i 0.279022 0.0497643i
890890 0 0
891891 −4.84829 + 22.6715i −0.162424 + 0.759523i
892892 0 0
893893 15.6787 0.524669
894894 0 0
895895 20.2404 + 35.0574i 0.676563 + 1.17184i
896896 0 0
897897 −1.53252 + 1.79323i −0.0511695 + 0.0598743i
898898 0 0
899899 −2.76243 4.78467i −0.0921321 0.159578i
900900 0 0
901901 −24.0191 + 41.6023i −0.800192 + 1.38597i
902902 0 0
903903 −37.9674 0.268524i −1.26348 0.00893592i
904904 0 0
905905 −46.4606 −1.54440
906906 0 0
907907 −40.8807 −1.35742 −0.678711 0.734405i 0.737461π-0.737461\pi
−0.678711 + 0.734405i 0.737461π0.737461\pi
908908 0 0
909909 −28.4609 + 23.0180i −0.943988 + 0.763460i
910910 0 0
911911 14.4235 24.9823i 0.477873 0.827701i −0.521805 0.853065i 0.674741π-0.674741\pi
0.999678 + 0.0253641i 0.00807452π0.00807452\pi
912912 0 0
913913 7.73249 13.3931i 0.255908 0.443246i
914914 0 0
915915 27.0649 31.6691i 0.894739 1.04695i
916916 0 0
917917 −36.6910 + 6.54393i −1.21165 + 0.216100i
918918 0 0
919919 21.8195 37.7925i 0.719760 1.24666i −0.241335 0.970442i 0.577585π-0.577585\pi
0.961095 0.276219i 0.0890815π-0.0890815\pi
920920 0 0
921921 2.24025 + 6.33248i 0.0738186 + 0.208662i
922922 0 0
923923 −4.33560 7.50947i −0.142708 0.247177i
924924 0 0
925925 −0.526192 + 0.911391i −0.0173011 + 0.0299663i
926926 0 0
927927 −31.8243 + 25.7383i −1.04525 + 0.845355i
928928 0 0
929929 13.7377 + 23.7944i 0.450719 + 0.780668i 0.998431 0.0559990i 0.0178344π-0.0178344\pi
−0.547712 + 0.836667i 0.684501π0.684501\pi
930930 0 0
931931 1.51314 8.78299i 0.0495911 0.287851i
932932 0 0
933933 11.7919 + 2.18927i 0.386049 + 0.0716735i
934934 0 0
935935 −17.1131 29.6408i −0.559658 0.969356i
936936 0 0
937937 −3.11920 −0.101900 −0.0509500 0.998701i 0.516225π-0.516225\pi
−0.0509500 + 0.998701i 0.516225π0.516225\pi
938938 0 0
939939 34.0188 39.8060i 1.11016 1.29902i
940940 0 0
941941 13.0608 22.6219i 0.425769 0.737454i −0.570723 0.821143i 0.693337π-0.693337\pi
0.996492 + 0.0836892i 0.0266703π0.0266703\pi
942942 0 0
943943 −0.177081 0.306714i −0.00576656 0.00998797i
944944 0 0
945945 23.7489 + 9.32654i 0.772552 + 0.303392i
946946 0 0
947947 3.59015 + 6.21833i 0.116664 + 0.202068i 0.918444 0.395551i 0.129447π-0.129447\pi
−0.801780 + 0.597620i 0.796113π0.796113\pi
948948 0 0
949949 37.0256 64.1302i 1.20190 2.08176i
950950 0 0
951951 10.5484 12.3429i 0.342055 0.400245i
952952 0 0
953953 −32.1187 −1.04043 −0.520214 0.854036i 0.674148π-0.674148\pi
−0.520214 + 0.854036i 0.674148π0.674148\pi
954954 0 0
955955 −8.03678 13.9201i −0.260064 0.450444i
956956 0 0
957957 −8.10306 1.50441i −0.261935 0.0486305i
958958 0 0
959959 −35.6742 + 6.36257i −1.15198 + 0.205458i
960960 0 0
961961 11.0269 + 19.0991i 0.355705 + 0.616100i
962962 0 0
963963 −6.05844 38.4052i −0.195231 1.23759i
964964 0 0
965965 −1.50018 + 2.59838i −0.0482924 + 0.0836449i
966966 0 0
967967 −27.4860 47.6071i −0.883890 1.53094i −0.846981 0.531623i 0.821582π-0.821582\pi
−0.0369085 0.999319i 0.511751π-0.511751\pi
968968 0 0
969969 5.26533 + 14.8835i 0.169147 + 0.478126i
970970 0 0
971971 20.8518 36.1163i 0.669165 1.15903i −0.308973 0.951071i 0.599985π-0.599985\pi
0.978138 0.207957i 0.0666813π-0.0666813\pi
972972 0 0
973973 16.8462 + 19.9967i 0.540065 + 0.641064i
974974 0 0
975975 9.88061 11.5615i 0.316433 0.370263i
976976 0 0
977977 −2.61437 + 4.52823i −0.0836412 + 0.144871i −0.904811 0.425813i 0.859988π-0.859988\pi
0.821170 + 0.570683i 0.193322π0.193322\pi
978978 0 0
979979 −17.0106 + 29.4633i −0.543662 + 0.941651i
980980 0 0
981981 −43.1262 16.5852i −1.37691 0.529525i
982982 0 0
983983 6.90697 0.220298 0.110149 0.993915i 0.464867π-0.464867\pi
0.110149 + 0.993915i 0.464867π0.464867\pi
984984 0 0
985985 19.9967 0.637149
986986 0 0
987987 28.5609 48.6707i 0.909103 1.54921i
988988 0 0
989989 0.999537 1.73125i 0.0317834 0.0550505i
990990 0 0
991991 2.19861 + 3.80811i 0.0698412 + 0.120968i 0.898831 0.438295i 0.144417π-0.144417\pi
−0.828990 + 0.559263i 0.811084π0.811084\pi
992992 0 0
993993 30.9949 36.2676i 0.983593 1.15092i
994994 0 0
995995 4.43133 + 7.67528i 0.140482 + 0.243323i
996996 0 0
997997 −28.0359 −0.887907 −0.443954 0.896050i 0.646425π-0.646425\pi
−0.443954 + 0.896050i 0.646425π0.646425\pi
998998 0 0
999999 −3.09086 + 1.67449i −0.0977906 + 0.0529786i
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 504.2.t.d.457.8 yes 22
3.2 odd 2 1512.2.t.d.289.3 22
4.3 odd 2 1008.2.t.k.961.4 22
7.4 even 3 504.2.q.d.25.7 22
9.4 even 3 504.2.q.d.121.7 yes 22
9.5 odd 6 1512.2.q.c.793.9 22
12.11 even 2 3024.2.t.l.289.3 22
21.11 odd 6 1512.2.q.c.1369.9 22
28.11 odd 6 1008.2.q.k.529.5 22
36.23 even 6 3024.2.q.k.2305.9 22
36.31 odd 6 1008.2.q.k.625.5 22
63.4 even 3 inner 504.2.t.d.193.8 yes 22
63.32 odd 6 1512.2.t.d.361.3 22
84.11 even 6 3024.2.q.k.2881.9 22
252.67 odd 6 1008.2.t.k.193.4 22
252.95 even 6 3024.2.t.l.1873.3 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.7 22 7.4 even 3
504.2.q.d.121.7 yes 22 9.4 even 3
504.2.t.d.193.8 yes 22 63.4 even 3 inner
504.2.t.d.457.8 yes 22 1.1 even 1 trivial
1008.2.q.k.529.5 22 28.11 odd 6
1008.2.q.k.625.5 22 36.31 odd 6
1008.2.t.k.193.4 22 252.67 odd 6
1008.2.t.k.961.4 22 4.3 odd 2
1512.2.q.c.793.9 22 9.5 odd 6
1512.2.q.c.1369.9 22 21.11 odd 6
1512.2.t.d.289.3 22 3.2 odd 2
1512.2.t.d.361.3 22 63.32 odd 6
3024.2.q.k.2305.9 22 36.23 even 6
3024.2.q.k.2881.9 22 84.11 even 6
3024.2.t.l.289.3 22 12.11 even 2
3024.2.t.l.1873.3 22 252.95 even 6