Properties

Label 616.2.r.f.113.1
Level 616616
Weight 22
Character 616.113
Analytic conductor 4.9194.919
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [616,2,Mod(113,616)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(616, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("616.113"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 616=23711 616 = 2^{3} \cdot 7 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 616.r (of order 55, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.918784764514.91878476451
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x204x19+21x1858x17+225x16348x15+1296x14755x13++10000 x^{20} - 4 x^{19} + 21 x^{18} - 58 x^{17} + 225 x^{16} - 348 x^{15} + 1296 x^{14} - 755 x^{13} + \cdots + 10000 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 113.1
Root 2.750531.99838i2.75053 - 1.99838i of defining polynomial
Character χ\chi == 616.113
Dual form 616.2.r.f.169.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.050613.23344i)q3+(0.5561820.404090i)q5+(0.309017+0.951057i)q7+(6.92433+5.03082i)q9+(1.80996+2.77922i)q11+(3.70618+2.69270i)q13+(0.722272+2.22292i)q15+(3.813912.77097i)q17+(0.462816+1.42440i)q19+3.39984q212.19201q23+(1.399044.30579i)q25+(15.2900+11.1089i)q27+(2.42815+7.47307i)q29+(3.326752.41702i)q31+(7.084888.77227i)q33+(0.5561820.404090i)q35+(0.0655973+0.201888i)q37+(12.6004+9.15475i)q39+(0.1084640.333817i)q413.09382q43+5.88409q45+(2.506817.71517i)q47+(0.8090170.587785i)q49+(4.95284+15.2433i)q51+(10.3297+7.50494i)q53+(0.1163862.27714i)q55+(4.119482.99298i)q57+(2.372267.30106i)q59+(5.74134+4.17132i)q61+(2.644868.14003i)q63+3.14940q65+0.889399q67+(2.30295+7.08774i)q69+(3.95035+2.87010i)q71+(2.83347+8.72052i)q73+(12.4527+9.04740i)q75+(3.20250+0.862549i)q77+(12.6433+9.18587i)q79+(11.921436.6904i)q81+(9.798137.11876i)q83+(1.00151+3.08232i)q85+26.7148q8715.6209q89+(1.415634.35687i)q91+(11.31048.21750i)q93+(0.3181760.979246i)q95+(2.27459+1.65258i)q97+(26.514510.1386i)q99+O(q100)q+(-1.05061 - 3.23344i) q^{3} +(-0.556182 - 0.404090i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-6.92433 + 5.03082i) q^{9} +(1.80996 + 2.77922i) q^{11} +(-3.70618 + 2.69270i) q^{13} +(-0.722272 + 2.22292i) q^{15} +(-3.81391 - 2.77097i) q^{17} +(0.462816 + 1.42440i) q^{19} +3.39984 q^{21} -2.19201 q^{23} +(-1.39904 - 4.30579i) q^{25} +(15.2900 + 11.1089i) q^{27} +(-2.42815 + 7.47307i) q^{29} +(3.32675 - 2.41702i) q^{31} +(7.08488 - 8.77227i) q^{33} +(0.556182 - 0.404090i) q^{35} +(-0.0655973 + 0.201888i) q^{37} +(12.6004 + 9.15475i) q^{39} +(-0.108464 - 0.333817i) q^{41} -3.09382 q^{43} +5.88409 q^{45} +(-2.50681 - 7.71517i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-4.95284 + 15.2433i) q^{51} +(-10.3297 + 7.50494i) q^{53} +(0.116386 - 2.27714i) q^{55} +(4.11948 - 2.99298i) q^{57} +(2.37226 - 7.30106i) q^{59} +(5.74134 + 4.17132i) q^{61} +(-2.64486 - 8.14003i) q^{63} +3.14940 q^{65} +0.889399 q^{67} +(2.30295 + 7.08774i) q^{69} +(3.95035 + 2.87010i) q^{71} +(-2.83347 + 8.72052i) q^{73} +(-12.4527 + 9.04740i) q^{75} +(-3.20250 + 0.862549i) q^{77} +(-12.6433 + 9.18587i) q^{79} +(11.9214 - 36.6904i) q^{81} +(-9.79813 - 7.11876i) q^{83} +(1.00151 + 3.08232i) q^{85} +26.7148 q^{87} -15.6209 q^{89} +(-1.41563 - 4.35687i) q^{91} +(-11.3104 - 8.21750i) q^{93} +(0.318176 - 0.979246i) q^{95} +(-2.27459 + 1.65258i) q^{97} +(-26.5145 - 10.1386i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20qq3+5q76q93q11+2q13+8q15+21q19+6q216q237q25+32q27+6q2918q3116q33+5q37+12q3912q4142q43+57q99+O(q100) 20 q - q^{3} + 5 q^{7} - 6 q^{9} - 3 q^{11} + 2 q^{13} + 8 q^{15} + 21 q^{19} + 6 q^{21} - 6 q^{23} - 7 q^{25} + 32 q^{27} + 6 q^{29} - 18 q^{31} - 16 q^{33} + 5 q^{37} + 12 q^{39} - 12 q^{41} - 42 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/616Z)×\left(\mathbb{Z}/616\mathbb{Z}\right)^\times.

nn 5757 309309 353353 463463
χ(n)\chi(n) e(45)e\left(\frac{4}{5}\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 −1.05061 3.23344i −0.606570 1.86683i −0.485618 0.874171i 0.661405π-0.661405\pi
−0.120952 0.992658i 0.538595π-0.538595\pi
44 0 0
55 −0.556182 0.404090i −0.248732 0.180714i 0.456433 0.889758i 0.349127π-0.349127\pi
−0.705165 + 0.709044i 0.749127π0.749127\pi
66 0 0
77 −0.309017 + 0.951057i −0.116797 + 0.359466i
88 0 0
99 −6.92433 + 5.03082i −2.30811 + 1.67694i
1010 0 0
1111 1.80996 + 2.77922i 0.545723 + 0.837965i
1212 0 0
1313 −3.70618 + 2.69270i −1.02791 + 0.746820i −0.967889 0.251378i 0.919116π-0.919116\pi
−0.0600200 + 0.998197i 0.519116π0.519116\pi
1414 0 0
1515 −0.722272 + 2.22292i −0.186490 + 0.573956i
1616 0 0
1717 −3.81391 2.77097i −0.925009 0.672058i 0.0197568 0.999805i 0.493711π-0.493711\pi
−0.944766 + 0.327747i 0.893711π0.893711\pi
1818 0 0
1919 0.462816 + 1.42440i 0.106177 + 0.326780i 0.990005 0.141033i 0.0450422π-0.0450422\pi
−0.883828 + 0.467813i 0.845042π0.845042\pi
2020 0 0
2121 3.39984 0.741907
2222 0 0
2323 −2.19201 −0.457065 −0.228533 0.973536i 0.573393π-0.573393\pi
−0.228533 + 0.973536i 0.573393π0.573393\pi
2424 0 0
2525 −1.39904 4.30579i −0.279807 0.861158i
2626 0 0
2727 15.2900 + 11.1089i 2.94257 + 2.13790i
2828 0 0
2929 −2.42815 + 7.47307i −0.450895 + 1.38771i 0.424992 + 0.905197i 0.360277π0.360277\pi
−0.875887 + 0.482516i 0.839723π0.839723\pi
3030 0 0
3131 3.32675 2.41702i 0.597501 0.434110i −0.247490 0.968890i 0.579606π-0.579606\pi
0.844991 + 0.534780i 0.179606π0.179606\pi
3232 0 0
3333 7.08488 8.77227i 1.23332 1.52706i
3434 0 0
3535 0.556182 0.404090i 0.0940119 0.0683037i
3636 0 0
3737 −0.0655973 + 0.201888i −0.0107841 + 0.0331902i −0.956304 0.292375i 0.905555π-0.905555\pi
0.945520 + 0.325565i 0.105555π0.105555\pi
3838 0 0
3939 12.6004 + 9.15475i 2.01768 + 1.46593i
4040 0 0
4141 −0.108464 0.333817i −0.0169392 0.0521335i 0.942230 0.334968i 0.108725π-0.108725\pi
−0.959169 + 0.282834i 0.908725π0.908725\pi
4242 0 0
4343 −3.09382 −0.471803 −0.235901 0.971777i 0.575804π-0.575804\pi
−0.235901 + 0.971777i 0.575804π0.575804\pi
4444 0 0
4545 5.88409 0.877148
4646 0 0
4747 −2.50681 7.71517i −0.365656 1.12537i −0.949569 0.313557i 0.898479π-0.898479\pi
0.583913 0.811816i 0.301521π-0.301521\pi
4848 0 0
4949 −0.809017 0.587785i −0.115574 0.0839693i
5050 0 0
5151 −4.95284 + 15.2433i −0.693536 + 2.13448i
5252 0 0
5353 −10.3297 + 7.50494i −1.41889 + 1.03088i −0.426934 + 0.904283i 0.640406π0.640406\pi
−0.991954 + 0.126600i 0.959594π0.959594\pi
5454 0 0
5555 0.116386 2.27714i 0.0156935 0.307049i
5656 0 0
5757 4.11948 2.99298i 0.545639 0.396430i
5858 0 0
5959 2.37226 7.30106i 0.308842 0.950517i −0.669374 0.742926i 0.733438π-0.733438\pi
0.978216 0.207591i 0.0665624π-0.0665624\pi
6060 0 0
6161 5.74134 + 4.17132i 0.735103 + 0.534083i 0.891174 0.453662i 0.149883π-0.149883\pi
−0.156071 + 0.987746i 0.549883π0.549883\pi
6262 0 0
6363 −2.64486 8.14003i −0.333221 1.02555i
6464 0 0
6565 3.14940 0.390635
6666 0 0
6767 0.889399 0.108657 0.0543287 0.998523i 0.482698π-0.482698\pi
0.0543287 + 0.998523i 0.482698π0.482698\pi
6868 0 0
6969 2.30295 + 7.08774i 0.277242 + 0.853263i
7070 0 0
7171 3.95035 + 2.87010i 0.468821 + 0.340618i 0.796981 0.604004i 0.206429π-0.206429\pi
−0.328161 + 0.944622i 0.606429π0.606429\pi
7272 0 0
7373 −2.83347 + 8.72052i −0.331632 + 1.02066i 0.636725 + 0.771091i 0.280289π0.280289\pi
−0.968357 + 0.249568i 0.919711π0.919711\pi
7474 0 0
7575 −12.4527 + 9.04740i −1.43791 + 1.04470i
7676 0 0
7777 −3.20250 + 0.862549i −0.364959 + 0.0982966i
7878 0 0
7979 −12.6433 + 9.18587i −1.42248 + 1.03349i −0.431123 + 0.902293i 0.641882π0.641882\pi
−0.991356 + 0.131198i 0.958118π0.958118\pi
8080 0 0
8181 11.9214 36.6904i 1.32460 4.07671i
8282 0 0
8383 −9.79813 7.11876i −1.07548 0.781385i −0.0985942 0.995128i 0.531435π-0.531435\pi
−0.976890 + 0.213743i 0.931435π0.931435\pi
8484 0 0
8585 1.00151 + 3.08232i 0.108629 + 0.334325i
8686 0 0
8787 26.7148 2.86412
8888 0 0
8989 −15.6209 −1.65582 −0.827908 0.560864i 0.810469π-0.810469\pi
−0.827908 + 0.560864i 0.810469π0.810469\pi
9090 0 0
9191 −1.41563 4.35687i −0.148399 0.456725i
9292 0 0
9393 −11.3104 8.21750i −1.17284 0.852115i
9494 0 0
9595 0.318176 0.979246i 0.0326442 0.100468i
9696 0 0
9797 −2.27459 + 1.65258i −0.230949 + 0.167795i −0.697242 0.716836i 0.745590π-0.745590\pi
0.466292 + 0.884631i 0.345590π0.345590\pi
9898 0 0
9999 −26.5145 10.1386i −2.66481 1.01897i
100100 0 0
101101 7.77190 5.64662i 0.773333 0.561860i −0.129637 0.991561i 0.541381π-0.541381\pi
0.902971 + 0.429702i 0.141381π0.141381\pi
102102 0 0
103103 −2.06829 + 6.36555i −0.203795 + 0.627216i 0.795966 + 0.605341i 0.206963π0.206963\pi
−0.999761 + 0.0218745i 0.993037π0.993037\pi
104104 0 0
105105 −1.89093 1.37384i −0.184536 0.134073i
106106 0 0
107107 0.863587 + 2.65785i 0.0834861 + 0.256944i 0.984082 0.177713i 0.0568698π-0.0568698\pi
−0.900596 + 0.434657i 0.856870π0.856870\pi
108108 0 0
109109 9.96649 0.954616 0.477308 0.878736i 0.341613π-0.341613\pi
0.477308 + 0.878736i 0.341613π0.341613\pi
110110 0 0
111111 0.721710 0.0685017
112112 0 0
113113 −5.19640 15.9929i −0.488836 1.50448i −0.826347 0.563161i 0.809585π-0.809585\pi
0.337512 0.941321i 0.390415π-0.390415\pi
114114 0 0
115115 1.21916 + 0.885769i 0.113687 + 0.0825983i
116116 0 0
117117 12.1163 37.2902i 1.12015 3.44748i
118118 0 0
119119 3.81391 2.77097i 0.349620 0.254014i
120120 0 0
121121 −4.44809 + 10.0605i −0.404372 + 0.914595i
122122 0 0
123123 −0.965425 + 0.701423i −0.0870495 + 0.0632452i
124124 0 0
125125 −2.02402 + 6.22929i −0.181034 + 0.557165i
126126 0 0
127127 −4.56217 3.31461i −0.404827 0.294124i 0.366677 0.930348i 0.380495π-0.380495\pi
−0.771504 + 0.636224i 0.780495π0.780495\pi
128128 0 0
129129 3.25039 + 10.0037i 0.286181 + 0.880775i
130130 0 0
131131 −11.2444 −0.982430 −0.491215 0.871038i 0.663447π-0.663447\pi
−0.491215 + 0.871038i 0.663447π0.663447\pi
132132 0 0
133133 −1.49770 −0.129867
134134 0 0
135135 −4.01506 12.3571i −0.345562 1.06353i
136136 0 0
137137 −15.5886 11.3258i −1.33182 0.967625i −0.999703 0.0243882i 0.992236π-0.992236\pi
−0.332120 0.943237i 0.607764π-0.607764\pi
138138 0 0
139139 0.918385 2.82650i 0.0778964 0.239741i −0.904524 0.426423i 0.859774π-0.859774\pi
0.982420 + 0.186682i 0.0597735π0.0597735\pi
140140 0 0
141141 −22.3129 + 16.2113i −1.87908 + 1.36523i
142142 0 0
143143 −14.1916 5.42660i −1.18676 0.453795i
144144 0 0
145145 4.37028 3.17520i 0.362932 0.263686i
146146 0 0
147147 −1.05061 + 3.23344i −0.0866528 + 0.266690i
148148 0 0
149149 5.58991 + 4.06131i 0.457944 + 0.332715i 0.792724 0.609581i 0.208662π-0.208662\pi
−0.334780 + 0.942296i 0.608662π0.608662\pi
150150 0 0
151151 0.819507 + 2.52218i 0.0666906 + 0.205252i 0.978849 0.204586i 0.0655849π-0.0655849\pi
−0.912158 + 0.409839i 0.865585π0.865585\pi
152152 0 0
153153 40.3490 3.26202
154154 0 0
155155 −2.82697 −0.227068
156156 0 0
157157 3.53551 + 10.8812i 0.282164 + 0.868412i 0.987234 + 0.159275i 0.0509156π0.0509156\pi
−0.705070 + 0.709138i 0.749084π0.749084\pi
158158 0 0
159159 35.1192 + 25.5156i 2.78514 + 2.02352i
160160 0 0
161161 0.677368 2.08472i 0.0533841 0.164299i
162162 0 0
163163 6.66271 4.84075i 0.521864 0.379156i −0.295442 0.955361i 0.595467π-0.595467\pi
0.817306 + 0.576204i 0.195467π0.195467\pi
164164 0 0
165165 −7.48527 + 2.01605i −0.582727 + 0.156950i
166166 0 0
167167 11.4674 8.33155i 0.887373 0.644714i −0.0478185 0.998856i 0.515227π-0.515227\pi
0.935192 + 0.354142i 0.115227π0.115227\pi
168168 0 0
169169 2.46793 7.59550i 0.189840 0.584269i
170170 0 0
171171 −10.3706 7.53468i −0.793059 0.576191i
172172 0 0
173173 0.0867525 + 0.266997i 0.00659567 + 0.0202994i 0.954300 0.298850i 0.0966029π-0.0966029\pi
−0.947705 + 0.319149i 0.896603π0.896603\pi
174174 0 0
175175 4.52737 0.342237
176176 0 0
177177 −26.0999 −1.96179
178178 0 0
179179 5.90770 + 18.1820i 0.441562 + 1.35899i 0.886210 + 0.463283i 0.153329π0.153329\pi
−0.444648 + 0.895705i 0.646671π0.646671\pi
180180 0 0
181181 9.15549 + 6.65185i 0.680522 + 0.494428i 0.873531 0.486769i 0.161825π-0.161825\pi
−0.193009 + 0.981197i 0.561825π0.561825\pi
182182 0 0
183183 7.45584 22.9467i 0.551152 1.69627i
184184 0 0
185185 0.118065 0.0857792i 0.00868030 0.00630661i
186186 0 0
187187 0.798095 15.6150i 0.0583625 1.14188i
188188 0 0
189189 −15.2900 + 11.1089i −1.11219 + 0.808050i
190190 0 0
191191 4.26518 13.1269i 0.308618 0.949827i −0.669685 0.742645i 0.733571π-0.733571\pi
0.978302 0.207182i 0.0664292π-0.0664292\pi
192192 0 0
193193 17.0820 + 12.4108i 1.22959 + 0.893348i 0.996859 0.0791943i 0.0252348π-0.0252348\pi
0.232728 + 0.972542i 0.425235π0.425235\pi
194194 0 0
195195 −3.30879 10.1834i −0.236947 0.729249i
196196 0 0
197197 −11.2684 −0.802843 −0.401422 0.915893i 0.631484π-0.631484\pi
−0.401422 + 0.915893i 0.631484π0.631484\pi
198198 0 0
199199 −3.21305 −0.227767 −0.113883 0.993494i 0.536329π-0.536329\pi
−0.113883 + 0.993494i 0.536329π0.536329\pi
200200 0 0
201201 −0.934411 2.87582i −0.0659083 0.202845i
202202 0 0
203203 −6.35697 4.61861i −0.446172 0.324163i
204204 0 0
205205 −0.0745665 + 0.229492i −0.00520795 + 0.0160284i
206206 0 0
207207 15.1782 11.0276i 1.05496 0.766471i
208208 0 0
209209 −3.12104 + 3.86438i −0.215887 + 0.267304i
210210 0 0
211211 15.4008 11.1893i 1.06024 0.770306i 0.0861038 0.996286i 0.472558π-0.472558\pi
0.974132 + 0.225980i 0.0725583π0.0725583\pi
212212 0 0
213213 5.13003 15.7886i 0.351504 1.08182i
214214 0 0
215215 1.72072 + 1.25018i 0.117352 + 0.0852615i
216216 0 0
217217 1.27070 + 3.91082i 0.0862610 + 0.265484i
218218 0 0
219219 31.1742 2.10655
220220 0 0
221221 21.5964 1.45273
222222 0 0
223223 −5.32283 16.3820i −0.356443 1.09702i −0.955168 0.296065i 0.904326π-0.904326\pi
0.598724 0.800955i 0.295674π-0.295674\pi
224224 0 0
225225 31.3490 + 22.7764i 2.08993 + 1.51843i
226226 0 0
227227 −1.61210 + 4.96154i −0.106999 + 0.329309i −0.990194 0.139696i 0.955387π-0.955387\pi
0.883195 + 0.469005i 0.155387π0.155387\pi
228228 0 0
229229 −8.74272 + 6.35195i −0.577735 + 0.419749i −0.837907 0.545813i 0.816221π-0.816221\pi
0.260172 + 0.965562i 0.416221π0.416221\pi
230230 0 0
231231 6.15358 + 9.44890i 0.404876 + 0.621692i
232232 0 0
233233 −1.84254 + 1.33869i −0.120709 + 0.0877003i −0.646502 0.762912i 0.723769π-0.723769\pi
0.525793 + 0.850613i 0.323769π0.323769\pi
234234 0 0
235235 −1.72338 + 5.30401i −0.112421 + 0.345996i
236236 0 0
237237 42.9851 + 31.2305i 2.79218 + 2.02864i
238238 0 0
239239 0.0308175 + 0.0948465i 0.00199342 + 0.00613511i 0.952048 0.305948i 0.0989733π-0.0989733\pi
−0.950055 + 0.312083i 0.898973π0.898973\pi
240240 0 0
241241 −28.3692 −1.82742 −0.913711 0.406365i 0.866796π-0.866796\pi
−0.913711 + 0.406365i 0.866796π0.866796\pi
242242 0 0
243243 −74.4626 −4.77678
244244 0 0
245245 0.212443 + 0.653831i 0.0135725 + 0.0417717i
246246 0 0
247247 −5.55076 4.03286i −0.353186 0.256605i
248248 0 0
249249 −12.7241 + 39.1607i −0.806356 + 2.48171i
250250 0 0
251251 5.65500 4.10860i 0.356940 0.259332i −0.394834 0.918752i 0.629198π-0.629198\pi
0.751775 + 0.659420i 0.229198π0.229198\pi
252252 0 0
253253 −3.96745 6.09207i −0.249431 0.383005i
254254 0 0
255255 8.91433 6.47664i 0.558237 0.405583i
256256 0 0
257257 −6.78903 + 20.8945i −0.423488 + 1.30336i 0.480946 + 0.876750i 0.340293π0.340293\pi
−0.904434 + 0.426613i 0.859707π0.859707\pi
258258 0 0
259259 −0.171736 0.124774i −0.0106712 0.00775305i
260260 0 0
261261 −20.7824 63.9615i −1.28640 3.95912i
262262 0 0
263263 13.4087 0.826816 0.413408 0.910546i 0.364338π-0.364338\pi
0.413408 + 0.910546i 0.364338π0.364338\pi
264264 0 0
265265 8.77784 0.539218
266266 0 0
267267 16.4115 + 50.5094i 1.00437 + 3.09113i
268268 0 0
269269 −25.6050 18.6031i −1.56116 1.13425i −0.935049 0.354518i 0.884645π-0.884645\pi
−0.626113 0.779733i 0.715355π-0.715355\pi
270270 0 0
271271 −6.71934 + 20.6800i −0.408171 + 1.25622i 0.510047 + 0.860146i 0.329628π0.329628\pi
−0.918218 + 0.396075i 0.870372π0.870372\pi
272272 0 0
273273 −12.6004 + 9.15475i −0.762613 + 0.554071i
274274 0 0
275275 9.43452 11.6815i 0.568923 0.704422i
276276 0 0
277277 −15.6638 + 11.3804i −0.941147 + 0.683783i −0.948696 0.316189i 0.897597π-0.897597\pi
0.00754984 + 0.999971i 0.497597π0.497597\pi
278278 0 0
279279 −10.8759 + 33.4725i −0.651122 + 2.00395i
280280 0 0
281281 −17.1956 12.4933i −1.02580 0.745290i −0.0583390 0.998297i 0.518580π-0.518580\pi
−0.967464 + 0.253007i 0.918580π0.918580\pi
282282 0 0
283283 0.807861 + 2.48634i 0.0480224 + 0.147798i 0.972192 0.234184i 0.0752418π-0.0752418\pi
−0.924170 + 0.381982i 0.875242π0.875242\pi
284284 0 0
285285 −3.50061 −0.207358
286286 0 0
287287 0.350996 0.0207186
288288 0 0
289289 1.61436 + 4.96847i 0.0949621 + 0.292263i
290290 0 0
291291 7.73324 + 5.61853i 0.453331 + 0.329364i
292292 0 0
293293 5.75975 17.7267i 0.336488 1.03560i −0.629496 0.777004i 0.716739π-0.716739\pi
0.965984 0.258601i 0.0832614π-0.0832614\pi
294294 0 0
295295 −4.26969 + 3.10211i −0.248591 + 0.180612i
296296 0 0
297297 −3.19958 + 62.6009i −0.185658 + 3.63247i
298298 0 0
299299 8.12398 5.90241i 0.469822 0.341345i
300300 0 0
301301 0.956042 2.94239i 0.0551053 0.169597i
302302 0 0
303303 −26.4233 19.1976i −1.51798 1.10287i
304304 0 0
305305 −1.50764 4.64003i −0.0863271 0.265687i
306306 0 0
307307 −5.45702 −0.311448 −0.155724 0.987801i 0.549771π-0.549771\pi
−0.155724 + 0.987801i 0.549771π0.549771\pi
308308 0 0
309309 22.7556 1.29452
310310 0 0
311311 −1.81887 5.59792i −0.103139 0.317429i 0.886150 0.463398i 0.153370π-0.153370\pi
−0.989289 + 0.145969i 0.953370π0.953370\pi
312312 0 0
313313 17.2655 + 12.5441i 0.975902 + 0.709034i 0.956789 0.290783i 0.0939158π-0.0939158\pi
0.0191128 + 0.999817i 0.493916π0.493916\pi
314314 0 0
315315 −1.81828 + 5.59610i −0.102449 + 0.315304i
316316 0 0
317317 5.87387 4.26762i 0.329910 0.239693i −0.410483 0.911868i 0.634640π-0.634640\pi
0.740392 + 0.672175i 0.234640π0.234640\pi
318318 0 0
319319 −25.1641 + 6.77761i −1.40892 + 0.379473i
320320 0 0
321321 7.68671 5.58472i 0.429030 0.311709i
322322 0 0
323323 2.18183 6.71499i 0.121400 0.373632i
324324 0 0
325325 16.7793 + 12.1908i 0.930746 + 0.676226i
326326 0 0
327327 −10.4709 32.2261i −0.579041 1.78211i
328328 0 0
329329 8.11221 0.447241
330330 0 0
331331 11.8008 0.648629 0.324315 0.945949i 0.394866π-0.394866\pi
0.324315 + 0.945949i 0.394866π0.394866\pi
332332 0 0
333333 −0.561443 1.72795i −0.0307669 0.0946908i
334334 0 0
335335 −0.494668 0.359397i −0.0270266 0.0196360i
336336 0 0
337337 5.38106 16.5612i 0.293125 0.902146i −0.690720 0.723123i 0.742706π-0.742706\pi
0.983845 0.179024i 0.0572938π-0.0572938\pi
338338 0 0
339339 −46.2526 + 33.6045i −2.51210 + 1.82515i
340340 0 0
341341 12.7387 + 4.87103i 0.689840 + 0.263781i
342342 0 0
343343 0.809017 0.587785i 0.0436828 0.0317374i
344344 0 0
345345 1.58323 4.87267i 0.0852380 0.262336i
346346 0 0
347347 −8.48193 6.16248i −0.455334 0.330819i 0.336364 0.941732i 0.390803π-0.390803\pi
−0.791698 + 0.610913i 0.790803π0.790803\pi
348348 0 0
349349 −4.83339 14.8757i −0.258726 0.796276i −0.993073 0.117501i 0.962512π-0.962512\pi
0.734347 0.678774i 0.237488π-0.237488\pi
350350 0 0
351351 −86.5804 −4.62132
352352 0 0
353353 12.3757 0.658692 0.329346 0.944209i 0.393172π-0.393172\pi
0.329346 + 0.944209i 0.393172π0.393172\pi
354354 0 0
355355 −1.03734 3.19259i −0.0550561 0.169445i
356356 0 0
357357 −12.9667 9.42086i −0.686270 0.498605i
358358 0 0
359359 −1.70334 + 5.24233i −0.0898987 + 0.276680i −0.985891 0.167390i 0.946466π-0.946466\pi
0.895992 + 0.444070i 0.146466π0.146466\pi
360360 0 0
361361 13.5566 9.84945i 0.713505 0.518392i
362362 0 0
363363 37.2034 + 3.81294i 1.95267 + 0.200128i
364364 0 0
365365 5.09980 3.70522i 0.266936 0.193940i
366366 0 0
367367 7.68865 23.6632i 0.401344 1.23521i −0.522565 0.852600i 0.675025π-0.675025\pi
0.923909 0.382612i 0.124975π-0.124975\pi
368368 0 0
369369 2.43041 + 1.76580i 0.126522 + 0.0919237i
370370 0 0
371371 −3.94558 12.1432i −0.204844 0.630446i
372372 0 0
373373 11.2320 0.581573 0.290786 0.956788i 0.406083π-0.406083\pi
0.290786 + 0.956788i 0.406083π0.406083\pi
374374 0 0
375375 22.2685 1.14994
376376 0 0
377377 −11.1236 34.2348i −0.572892 1.76318i
378378 0 0
379379 −3.25121 2.36214i −0.167003 0.121335i 0.501144 0.865364i 0.332913π-0.332913\pi
−0.668148 + 0.744029i 0.732913π0.732913\pi
380380 0 0
381381 −5.92455 + 18.2339i −0.303524 + 0.934150i
382382 0 0
383383 −11.0907 + 8.05786i −0.566708 + 0.411737i −0.833908 0.551904i 0.813902π-0.813902\pi
0.267200 + 0.963641i 0.413902π0.413902\pi
384384 0 0
385385 2.12972 + 0.814364i 0.108541 + 0.0415038i
386386 0 0
387387 21.4226 15.5644i 1.08897 0.791184i
388388 0 0
389389 −9.92146 + 30.5351i −0.503038 + 1.54819i 0.301007 + 0.953622i 0.402677π0.402677\pi
−0.804045 + 0.594569i 0.797323π0.797323\pi
390390 0 0
391391 8.36012 + 6.07398i 0.422790 + 0.307175i
392392 0 0
393393 11.8135 + 36.3582i 0.595912 + 1.83403i
394394 0 0
395395 10.7439 0.540583
396396 0 0
397397 23.1477 1.16175 0.580875 0.813993i 0.302711π-0.302711\pi
0.580875 + 0.813993i 0.302711π0.302711\pi
398398 0 0
399399 1.57350 + 4.84274i 0.0787736 + 0.242440i
400400 0 0
401401 4.51921 + 3.28340i 0.225678 + 0.163965i 0.694879 0.719127i 0.255458π-0.255458\pi
−0.469201 + 0.883092i 0.655458π0.655458\pi
402402 0 0
403403 −5.82121 + 17.9158i −0.289975 + 0.892451i
404404 0 0
405405 −21.4567 + 15.5892i −1.06619 + 0.774634i
406406 0 0
407407 −0.679819 + 0.183100i −0.0336974 + 0.00907592i
408408 0 0
409409 25.9473 18.8518i 1.28301 0.932164i 0.283374 0.959010i 0.408546π-0.408546\pi
0.999640 + 0.0268460i 0.00854639π0.00854639\pi
410410 0 0
411411 −20.2437 + 62.3037i −0.998549 + 3.07322i
412412 0 0
413413 6.21065 + 4.51230i 0.305606 + 0.222036i
414414 0 0
415415 2.57292 + 7.91865i 0.126300 + 0.388711i
416416 0 0
417417 −10.1042 −0.494804
418418 0 0
419419 −3.02921 −0.147987 −0.0739934 0.997259i 0.523574π-0.523574\pi
−0.0739934 + 0.997259i 0.523574π0.523574\pi
420420 0 0
421421 −0.960654 2.95659i −0.0468194 0.144095i 0.924914 0.380177i 0.124137π-0.124137\pi
−0.971733 + 0.236081i 0.924137π0.924137\pi
422422 0 0
423423 56.1716 + 40.8110i 2.73116 + 1.98430i
424424 0 0
425425 −6.59540 + 20.2986i −0.319924 + 0.984625i
426426 0 0
427427 −5.74134 + 4.17132i −0.277843 + 0.201865i
428428 0 0
429429 −2.63675 + 51.5890i −0.127304 + 2.49074i
430430 0 0
431431 17.9314 13.0280i 0.863727 0.627534i −0.0651693 0.997874i 0.520759π-0.520759\pi
0.928896 + 0.370340i 0.120759π0.120759\pi
432432 0 0
433433 0.684143 2.10558i 0.0328778 0.101188i −0.933271 0.359173i 0.883059π-0.883059\pi
0.966149 + 0.257986i 0.0830587π0.0830587\pi
434434 0 0
435435 −14.8583 10.7952i −0.712400 0.517589i
436436 0 0
437437 −1.01450 3.12230i −0.0485300 0.149360i
438438 0 0
439439 −9.12789 −0.435651 −0.217825 0.975988i 0.569896π-0.569896\pi
−0.217825 + 0.975988i 0.569896π0.569896\pi
440440 0 0
441441 8.55894 0.407568
442442 0 0
443443 −3.03131 9.32940i −0.144022 0.443253i 0.852862 0.522136i 0.174865π-0.174865\pi
−0.996884 + 0.0788829i 0.974865π0.974865\pi
444444 0 0
445445 8.68808 + 6.31226i 0.411855 + 0.299230i
446446 0 0
447447 7.25920 22.3415i 0.343348 1.05672i
448448 0 0
449449 0.832689 0.604984i 0.0392970 0.0285510i −0.567963 0.823054i 0.692268π-0.692268\pi
0.607260 + 0.794503i 0.292268π0.292268\pi
450450 0 0
451451 0.731435 0.905640i 0.0344419 0.0426449i
452452 0 0
453453 7.29436 5.29966i 0.342719 0.249000i
454454 0 0
455455 −0.973219 + 2.99526i −0.0456252 + 0.140420i
456456 0 0
457457 25.4777 + 18.5106i 1.19179 + 0.865889i 0.993453 0.114244i 0.0364445π-0.0364445\pi
0.198342 + 0.980133i 0.436444π0.436444\pi
458458 0 0
459459 −27.5325 84.7363i −1.28511 3.95515i
460460 0 0
461461 −14.9537 −0.696461 −0.348231 0.937409i 0.613217π-0.613217\pi
−0.348231 + 0.937409i 0.613217π0.613217\pi
462462 0 0
463463 41.6713 1.93663 0.968315 0.249731i 0.0803423π-0.0803423\pi
0.968315 + 0.249731i 0.0803423π0.0803423\pi
464464 0 0
465465 2.97004 + 9.14085i 0.137732 + 0.423897i
466466 0 0
467467 −14.4022 10.4638i −0.666455 0.484208i 0.202382 0.979307i 0.435132π-0.435132\pi
−0.868837 + 0.495099i 0.835132π0.835132\pi
468468 0 0
469469 −0.274839 + 0.845869i −0.0126909 + 0.0390586i
470470 0 0
471471 31.4692 22.8637i 1.45003 1.05351i
472472 0 0
473473 −5.59968 8.59838i −0.257474 0.395354i
474474 0 0
475475 5.48567 3.98558i 0.251700 0.182871i
476476 0 0
477477 33.7700 103.933i 1.54622 4.75878i
478478 0 0
479479 22.9900 + 16.7032i 1.05044 + 0.763190i 0.972296 0.233752i 0.0751002π-0.0751002\pi
0.0781452 + 0.996942i 0.475100π0.475100\pi
480480 0 0
481481 −0.300507 0.924866i −0.0137019 0.0421703i
482482 0 0
483483 −7.45249 −0.339100
484484 0 0
485485 1.93288 0.0877674
486486 0 0
487487 13.4010 + 41.2439i 0.607256 + 1.86894i 0.480470 + 0.877011i 0.340466π0.340466\pi
0.126786 + 0.991930i 0.459534π0.459534\pi
488488 0 0
489489 −22.6522 16.4578i −1.02437 0.744246i
490490 0 0
491491 −1.35385 + 4.16673i −0.0610986 + 0.188042i −0.976947 0.213482i 0.931519π-0.931519\pi
0.915848 + 0.401524i 0.131519π0.131519\pi
492492 0 0
493493 29.9684 21.7733i 1.34971 0.980619i
494494 0 0
495495 10.6500 + 16.3532i 0.478680 + 0.735020i
496496 0 0
497497 −3.95035 + 2.87010i −0.177198 + 0.128742i
498498 0 0
499499 −2.63267 + 8.10251i −0.117854 + 0.362718i −0.992532 0.121987i 0.961073π-0.961073\pi
0.874677 + 0.484706i 0.161073π0.161073\pi
500500 0 0
501501 −38.9873 28.3260i −1.74183 1.26551i
502502 0 0
503503 −4.88999 15.0499i −0.218034 0.671040i −0.998924 0.0463716i 0.985234π-0.985234\pi
0.780890 0.624668i 0.214766π-0.214766\pi
504504 0 0
505505 −6.60433 −0.293889
506506 0 0
507507 −27.1524 −1.20588
508508 0 0
509509 −0.0789642 0.243027i −0.00350002 0.0107720i 0.949291 0.314398i 0.101803π-0.101803\pi
−0.952791 + 0.303626i 0.901803π0.901803\pi
510510 0 0
511511 −7.41811 5.38958i −0.328158 0.238421i
512512 0 0
513513 −8.74700 + 26.9205i −0.386189 + 1.18857i
514514 0 0
515515 3.72260 2.70463i 0.164037 0.119180i
516516 0 0
517517 16.9049 20.9311i 0.743477 0.920549i
518518 0 0
519519 0.772175 0.561018i 0.0338947 0.0246260i
520520 0 0
521521 2.26388 6.96751i 0.0991824 0.305252i −0.889139 0.457638i 0.848696π-0.848696\pi
0.988321 + 0.152386i 0.0486956π0.0486956\pi
522522 0 0
523523 8.72460 + 6.33879i 0.381500 + 0.277176i 0.761964 0.647620i 0.224235π-0.224235\pi
−0.380463 + 0.924796i 0.624235π0.624235\pi
524524 0 0
525525 −4.75650 14.6390i −0.207591 0.638899i
526526 0 0
527527 −19.3854 −0.844441
528528 0 0
529529 −18.1951 −0.791091
530530 0 0
531531 20.3040 + 62.4893i 0.881119 + 2.71180i
532532 0 0
533533 1.30085 + 0.945126i 0.0563462 + 0.0409379i
534534 0 0
535535 0.593698 1.82721i 0.0256678 0.0789973i
536536 0 0
537537 52.5839 38.2044i 2.26916 1.64864i
538538 0 0
539539 0.169294 3.31230i 0.00729201 0.142671i
540540 0 0
541541 6.70061 4.86828i 0.288082 0.209304i −0.434353 0.900743i 0.643023π-0.643023\pi
0.722435 + 0.691439i 0.243023π0.243023\pi
542542 0 0
543543 11.8895 36.5923i 0.510229 1.57032i
544544 0 0
545545 −5.54318 4.02736i −0.237444 0.172513i
546546 0 0
547547 0.398348 + 1.22599i 0.0170321 + 0.0524195i 0.959211 0.282690i 0.0912267π-0.0912267\pi
−0.942179 + 0.335109i 0.891227π0.891227\pi
548548 0 0
549549 −60.7401 −2.59232
550550 0 0
551551 −11.7684 −0.501352
552552 0 0
553553 −4.82930 14.8631i −0.205363 0.632041i
554554 0 0
555555 −0.401402 0.291636i −0.0170386 0.0123792i
556556 0 0
557557 4.07289 12.5351i 0.172574 0.531127i −0.826941 0.562289i 0.809921π-0.809921\pi
0.999514 + 0.0311618i 0.00992073π0.00992073\pi
558558 0 0
559559 11.4662 8.33071i 0.484970 0.352351i
560560 0 0
561561 −51.3288 + 13.8247i −2.16710 + 0.583679i
562562 0 0
563563 9.32128 6.77231i 0.392845 0.285419i −0.373775 0.927519i 0.621937π-0.621937\pi
0.766620 + 0.642101i 0.221937π0.221937\pi
564564 0 0
565565 −3.57241 + 10.9948i −0.150293 + 0.462553i
566566 0 0
567567 31.2107 + 22.6759i 1.31073 + 0.952299i
568568 0 0
569569 −13.3186 40.9905i −0.558346 1.71841i −0.686939 0.726715i 0.741046π-0.741046\pi
0.128593 0.991697i 0.458954π-0.458954\pi
570570 0 0
571571 −33.9904 −1.42245 −0.711227 0.702962i 0.751860π-0.751860\pi
−0.711227 + 0.702962i 0.751860π0.751860\pi
572572 0 0
573573 −46.9260 −1.96036
574574 0 0
575575 3.06670 + 9.43832i 0.127890 + 0.393605i
576576 0 0
577577 −32.1619 23.3670i −1.33892 0.972781i −0.999483 0.0321518i 0.989764π-0.989764\pi
−0.339435 0.940629i 0.610236π-0.610236\pi
578578 0 0
579579 22.1831 68.2725i 0.921897 2.83731i
580580 0 0
581581 9.79813 7.11876i 0.406495 0.295336i
582582 0 0
583583 −39.5541 15.1247i −1.63816 0.626402i
584584 0 0
585585 −21.8075 + 15.8441i −0.901628 + 0.655071i
586586 0 0
587587 −11.7049 + 36.0241i −0.483114 + 1.48687i 0.351580 + 0.936158i 0.385645π0.385645\pi
−0.834694 + 0.550714i 0.814355π0.814355\pi
588588 0 0
589589 4.98248 + 3.61998i 0.205300 + 0.149159i
590590 0 0
591591 11.8387 + 36.4359i 0.486980 + 1.49877i
592592 0 0
593593 −2.34186 −0.0961686 −0.0480843 0.998843i 0.515312π-0.515312\pi
−0.0480843 + 0.998843i 0.515312π0.515312\pi
594594 0 0
595595 −3.24095 −0.132866
596596 0 0
597597 3.37566 + 10.3892i 0.138156 + 0.425202i
598598 0 0
599599 14.0649 + 10.2188i 0.574677 + 0.417527i 0.836801 0.547507i 0.184423π-0.184423\pi
−0.262124 + 0.965034i 0.584423π0.584423\pi
600600 0 0
601601 −4.42219 + 13.6101i −0.180385 + 0.555168i −0.999838 0.0179781i 0.994277π-0.994277\pi
0.819453 + 0.573146i 0.194277π0.194277\pi
602602 0 0
603603 −6.15849 + 4.47440i −0.250793 + 0.182212i
604604 0 0
605605 6.53931 3.79806i 0.265861 0.154413i
606606 0 0
607607 19.8396 14.4143i 0.805263 0.585058i −0.107190 0.994239i 0.534185π-0.534185\pi
0.912453 + 0.409181i 0.134185π0.134185\pi
608608 0 0
609609 −8.25532 + 25.4073i −0.334522 + 1.02955i
610610 0 0
611611 30.0653 + 21.8437i 1.21631 + 0.883702i
612612 0 0
613613 11.8827 + 36.5713i 0.479939 + 1.47710i 0.839180 + 0.543854i 0.183036π0.183036\pi
−0.359241 + 0.933245i 0.616964π0.616964\pi
614614 0 0
615615 0.820390 0.0330813
616616 0 0
617617 −4.44911 −0.179114 −0.0895572 0.995982i 0.528545π-0.528545\pi
−0.0895572 + 0.995982i 0.528545π0.528545\pi
618618 0 0
619619 −7.92092 24.3781i −0.318369 0.979838i −0.974346 0.225057i 0.927743π-0.927743\pi
0.655977 0.754781i 0.272257π-0.272257\pi
620620 0 0
621621 −33.5159 24.3507i −1.34495 0.977160i
622622 0 0
623623 4.82713 14.8564i 0.193395 0.595209i
624624 0 0
625625 −14.6707 + 10.6589i −0.586828 + 0.426355i
626626 0 0
627627 15.7742 + 6.03176i 0.629962 + 0.240885i
628628 0 0
629629 0.809607 0.588214i 0.0322811 0.0234536i
630630 0 0
631631 −4.63016 + 14.2502i −0.184324 + 0.567291i −0.999936 0.0113084i 0.996400π-0.996400\pi
0.815612 + 0.578599i 0.196400π0.196400\pi
632632 0 0
633633 −52.3604 38.0420i −2.08114 1.51203i
634634 0 0
635635 1.19800 + 3.68705i 0.0475410 + 0.146316i
636636 0 0
637637 4.58109 0.181509
638638 0 0
639639 −41.7925 −1.65328
640640 0 0
641641 8.35393 + 25.7108i 0.329960 + 1.01551i 0.969151 + 0.246466i 0.0792693π0.0792693\pi
−0.639191 + 0.769048i 0.720731π0.720731\pi
642642 0 0
643643 −20.4006 14.8219i −0.804522 0.584519i 0.107716 0.994182i 0.465646π-0.465646\pi
−0.912237 + 0.409663i 0.865646π0.865646\pi
644644 0 0
645645 2.23458 6.87732i 0.0879863 0.270794i
646646 0 0
647647 5.54113 4.02587i 0.217844 0.158273i −0.473511 0.880788i 0.657014π-0.657014\pi
0.691356 + 0.722514i 0.257014π0.257014\pi
648648 0 0
649649 24.5849 6.62161i 0.965042 0.259921i
650650 0 0
651651 11.3104 8.21750i 0.443290 0.322069i
652652 0 0
653653 −11.1896 + 34.4382i −0.437885 + 1.34767i 0.452217 + 0.891908i 0.350633π0.350633\pi
−0.890102 + 0.455762i 0.849367π0.849367\pi
654654 0 0
655655 6.25394 + 4.54376i 0.244362 + 0.177539i
656656 0 0
657657 −24.2515 74.6384i −0.946140 2.91192i
658658 0 0
659659 −26.9081 −1.04819 −0.524096 0.851659i 0.675597π-0.675597\pi
−0.524096 + 0.851659i 0.675597π0.675597\pi
660660 0 0
661661 −37.9406 −1.47572 −0.737858 0.674956i 0.764163π-0.764163\pi
−0.737858 + 0.674956i 0.764163π0.764163\pi
662662 0 0
663663 −22.6894 69.8308i −0.881183 2.71200i
664664 0 0
665665 0.832996 + 0.605207i 0.0323022 + 0.0234689i
666666 0 0
667667 5.32252 16.3810i 0.206089 0.634276i
668668 0 0
669669 −47.3781 + 34.4222i −1.83174 + 1.33084i
670670 0 0
671671 −1.20143 + 23.5063i −0.0463805 + 0.907452i
672672 0 0
673673 22.3883 16.2660i 0.863005 0.627010i −0.0656956 0.997840i 0.520927π-0.520927\pi
0.928701 + 0.370830i 0.120927π0.120927\pi
674674 0 0
675675 26.4411 81.3773i 1.01772 3.13221i
676676 0 0
677677 4.98739 + 3.62355i 0.191681 + 0.139264i 0.679487 0.733688i 0.262203π-0.262203\pi
−0.487806 + 0.872952i 0.662203π0.662203\pi
678678 0 0
679679 −0.868815 2.67394i −0.0333421 0.102616i
680680 0 0
681681 17.7366 0.679667
682682 0 0
683683 7.80638 0.298703 0.149351 0.988784i 0.452281π-0.452281\pi
0.149351 + 0.988784i 0.452281π0.452281\pi
684684 0 0
685685 4.09346 + 12.5984i 0.156403 + 0.481359i
686686 0 0
687687 29.7239 + 21.5957i 1.13404 + 0.823926i
688688 0 0
689689 18.0750 55.6293i 0.688605 2.11931i
690690 0 0
691691 −13.2484 + 9.62555i −0.503994 + 0.366173i −0.810540 0.585683i 0.800826π-0.800826\pi
0.306547 + 0.951856i 0.400826π0.400826\pi
692692 0 0
693693 17.8358 22.0838i 0.677527 0.838893i
694694 0 0
695695 −1.65295 + 1.20094i −0.0626999 + 0.0455542i
696696 0 0
697697 −0.511325 + 1.57370i −0.0193678 + 0.0596080i
698698 0 0
699699 6.26436 + 4.55132i 0.236940 + 0.172147i
700700 0 0
701701 −0.353613 1.08831i −0.0133558 0.0411048i 0.944157 0.329497i 0.106879π-0.106879\pi
−0.957512 + 0.288392i 0.906879π0.906879\pi
702702 0 0
703703 −0.317929 −0.0119909
704704 0 0
705705 18.9608 0.714106
706706 0 0
707707 2.96860 + 9.13642i 0.111646 + 0.343610i
708708 0 0
709709 −7.89654 5.73718i −0.296561 0.215464i 0.429548 0.903044i 0.358673π-0.358673\pi
−0.726109 + 0.687580i 0.758673π0.758673\pi
710710 0 0
711711 41.3337 127.212i 1.55013 4.77082i
712712 0 0
713713 −7.29226 + 5.29813i −0.273097 + 0.198417i
714714 0 0
715715 5.70029 + 8.75287i 0.213179 + 0.327339i
716716 0 0
717717 0.274304 0.199293i 0.0102441 0.00744274i
718718 0 0
719719 −0.397370 + 1.22298i −0.0148194 + 0.0456094i −0.958193 0.286123i 0.907633π-0.907633\pi
0.943373 + 0.331733i 0.107633π0.107633\pi
720720 0 0
721721 −5.41486 3.93412i −0.201660 0.146514i
722722 0 0
723723 29.8050 + 91.7302i 1.10846 + 3.41148i
724724 0 0
725725 35.5745 1.32120
726726 0 0
727727 −46.5455 −1.72628 −0.863138 0.504968i 0.831504π-0.831504\pi
−0.863138 + 0.504968i 0.831504π0.831504\pi
728728 0 0
729729 42.4668 + 130.699i 1.57285 + 4.84072i
730730 0 0
731731 11.7995 + 8.57286i 0.436421 + 0.317079i
732732 0 0
733733 −8.75507 + 26.9453i −0.323376 + 0.995249i 0.648792 + 0.760966i 0.275274π0.275274\pi
−0.972168 + 0.234284i 0.924726π0.924726\pi
734734 0 0
735735 1.89093 1.37384i 0.0697481 0.0506749i
736736 0 0
737737 1.60978 + 2.47183i 0.0592969 + 0.0910511i
738738 0 0
739739 33.5180 24.3523i 1.23298 0.895812i 0.235870 0.971785i 0.424206π-0.424206\pi
0.997110 + 0.0759722i 0.0242060π0.0242060\pi
740740 0 0
741741 −7.20835 + 22.1850i −0.264805 + 0.814987i
742742 0 0
743743 4.91182 + 3.56865i 0.180197 + 0.130921i 0.674227 0.738524i 0.264477π-0.264477\pi
−0.494030 + 0.869445i 0.664477π0.664477\pi
744744 0 0
745745 −1.46788 4.51765i −0.0537788 0.165514i
746746 0 0
747747 103.659 3.79267
748748 0 0
749749 −2.79463 −0.102113
750750 0 0
751751 −6.71573 20.6689i −0.245060 0.754218i −0.995627 0.0934229i 0.970219π-0.970219\pi
0.750566 0.660795i 0.229781π-0.229781\pi
752752 0 0
753753 −19.2261 13.9686i −0.700639 0.509044i
754754 0 0
755755 0.563394 1.73395i 0.0205040 0.0631048i
756756 0 0
757757 12.7860 9.28954i 0.464713 0.337634i −0.330664 0.943749i 0.607273π-0.607273\pi
0.795377 + 0.606115i 0.207273π0.207273\pi
758758 0 0
759759 −15.5301 + 19.2289i −0.563708 + 0.697965i
760760 0 0
761761 −14.9993 + 10.8977i −0.543726 + 0.395040i −0.825467 0.564451i 0.809088π-0.809088\pi
0.281741 + 0.959490i 0.409088π0.409088\pi
762762 0 0
763763 −3.07981 + 9.47869i −0.111497 + 0.343152i
764764 0 0
765765 −22.4414 16.3046i −0.811370 0.589495i
766766 0 0
767767 10.8675 + 33.4468i 0.392404 + 1.20769i
768768 0 0
769769 35.3343 1.27419 0.637093 0.770787i 0.280137π-0.280137\pi
0.637093 + 0.770787i 0.280137π0.280137\pi
770770 0 0
771771 74.6938 2.69003
772772 0 0
773773 6.57884 + 20.2476i 0.236625 + 0.728256i 0.996902 + 0.0786567i 0.0250631π0.0250631\pi
−0.760277 + 0.649599i 0.774937π0.774937\pi
774774 0 0
775775 −15.0614 10.9428i −0.541022 0.393076i
776776 0 0
777777 −0.223021 + 0.686387i −0.00800082 + 0.0246240i
778778 0 0
779779 0.425291 0.308992i 0.0152376 0.0110708i
780780 0 0
781781 −0.826647 + 16.1736i −0.0295797 + 0.578739i
782782 0 0
783783 −120.144 + 87.2895i −4.29358 + 3.11947i
784784 0 0
785785 2.43059 7.48058i 0.0867514 0.266993i
786786 0 0
787787 −21.4875 15.6116i −0.765945 0.556492i 0.134783 0.990875i 0.456966π-0.456966\pi
−0.900728 + 0.434383i 0.856966π0.856966\pi
788788 0 0
789789 −14.0873 43.3563i −0.501521 1.54352i
790790 0 0
791791 16.8159 0.597904
792792 0 0
793793 −32.5105 −1.15448
794794 0 0
795795 −9.22208 28.3827i −0.327074 1.00663i
796796 0 0
797797 11.8866 + 8.63608i 0.421043 + 0.305906i 0.778057 0.628193i 0.216205π-0.216205\pi
−0.357014 + 0.934099i 0.616205π0.616205\pi
798798 0 0
799799 −11.8177 + 36.3712i −0.418081 + 1.28672i
800800 0 0
801801 108.164 78.5861i 3.82180 2.77670i
802802 0 0
803803 −29.3647 + 7.90897i −1.03626 + 0.279101i
804804 0 0
805805 −1.21916 + 0.885769i −0.0429696 + 0.0312192i
806806 0 0
807807 −33.2512 + 102.337i −1.17050 + 3.60243i
808808 0 0
809809 12.5236 + 9.09895i 0.440307 + 0.319902i 0.785757 0.618535i 0.212274π-0.212274\pi
−0.345450 + 0.938437i 0.612274π0.612274\pi
810810 0 0
811811 5.18583 + 15.9604i 0.182099 + 0.560444i 0.999886 0.0150770i 0.00479933π-0.00479933\pi
−0.817787 + 0.575521i 0.804799π0.804799\pi
812812 0 0
813813 73.9270 2.59273
814814 0 0
815815 −5.66178 −0.198323
816816 0 0
817817 −1.43187 4.40684i −0.0500947 0.154176i
818818 0 0
819819 31.7210 + 23.0466i 1.10842 + 0.805314i
820820 0 0
821821 −4.23855 + 13.0449i −0.147926 + 0.455270i −0.997376 0.0723998i 0.976934π-0.976934\pi
0.849449 + 0.527670i 0.176934π0.176934\pi
822822 0 0
823823 −37.2133 + 27.0370i −1.29717 + 0.942451i −0.999924 0.0123492i 0.996069π-0.996069\pi
−0.297249 + 0.954800i 0.596069π0.596069\pi
824824 0 0
825825 −47.6835 18.2333i −1.66013 0.634801i
826826 0 0
827827 1.26848 0.921606i 0.0441094 0.0320474i −0.565512 0.824740i 0.691321π-0.691321\pi
0.609622 + 0.792693i 0.291321π0.291321\pi
828828 0 0
829829 −3.45203 + 10.6243i −0.119894 + 0.368996i −0.992936 0.118649i 0.962144π-0.962144\pi
0.873042 + 0.487644i 0.162144π0.162144\pi
830830 0 0
831831 53.2545 + 38.6916i 1.84738 + 1.34220i
832832 0 0
833833 1.45678 + 4.48352i 0.0504746 + 0.155345i
834834 0 0
835835 −9.74465 −0.337228
836836 0 0
837837 77.7164 2.68627
838838 0 0
839839 −14.0113 43.1224i −0.483724 1.48875i −0.833821 0.552036i 0.813851π-0.813851\pi
0.350097 0.936714i 0.386149π-0.386149\pi
840840 0 0
841841 −26.4893 19.2456i −0.913425 0.663642i
842842 0 0
843843 −22.3306 + 68.7266i −0.769108 + 2.36707i
844844 0 0
845845 −4.44188 + 3.22721i −0.152805 + 0.111020i
846846 0 0
847847 −8.19361 7.33926i −0.281536 0.252180i
848848 0 0
849849 7.19070 5.22435i 0.246784 0.179299i
850850 0 0
851851 0.143790 0.442540i 0.00492906 0.0151701i
852852 0 0
853853 14.8508 + 10.7897i 0.508482 + 0.369434i 0.812247 0.583313i 0.198244π-0.198244\pi
−0.303766 + 0.952747i 0.598244π0.598244\pi
854854 0 0
855855 2.72325 + 8.38130i 0.0931332 + 0.286634i
856856 0 0
857857 6.55371 0.223870 0.111935 0.993716i 0.464295π-0.464295\pi
0.111935 + 0.993716i 0.464295π0.464295\pi
858858 0 0
859859 −30.9945 −1.05752 −0.528759 0.848772i 0.677343π-0.677343\pi
−0.528759 + 0.848772i 0.677343π0.677343\pi
860860 0 0
861861 −0.368760 1.13493i −0.0125673 0.0386782i
862862 0 0
863863 −20.1805 14.6620i −0.686952 0.499100i 0.188705 0.982034i 0.439571π-0.439571\pi
−0.875657 + 0.482934i 0.839571π0.839571\pi
864864 0 0
865865 0.0596405 0.183554i 0.00202784 0.00624104i
866866 0 0
867867 14.3692 10.4399i 0.488004 0.354556i
868868 0 0
869869 −48.4133 18.5123i −1.64231 0.627987i
870870 0 0
871871 −3.29627 + 2.39488i −0.111690 + 0.0811475i
872872 0 0
873873 7.43613 22.8861i 0.251675 0.774576i
874874 0 0
875875 −5.29895 3.84991i −0.179137 0.130151i
876876 0 0
877877 9.86414 + 30.3587i 0.333088 + 1.02514i 0.967656 + 0.252273i 0.0811782π0.0811782\pi
−0.634568 + 0.772867i 0.718822π0.718822\pi
878878 0 0
879879 −63.3695 −2.13740
880880 0 0
881881 30.7462 1.03587 0.517933 0.855421i 0.326702π-0.326702\pi
0.517933 + 0.855421i 0.326702π0.326702\pi
882882 0 0
883883 14.1731 + 43.6202i 0.476961 + 1.46794i 0.843294 + 0.537452i 0.180613π0.180613\pi
−0.366333 + 0.930484i 0.619387π0.619387\pi
884884 0 0
885885 14.5163 + 10.5467i 0.487959 + 0.354523i
886886 0 0
887887 −13.5824 + 41.8022i −0.456051 + 1.40358i 0.413846 + 0.910347i 0.364185π0.364185\pi
−0.869897 + 0.493234i 0.835815π0.835815\pi
888888 0 0
889889 4.56217 3.31461i 0.153010 0.111168i
890890 0 0
891891 123.548 33.2759i 4.13901 1.11479i
892892 0 0
893893 9.82930 7.14141i 0.328925 0.238978i
894894 0 0
895895 4.06142 12.4998i 0.135758 0.417821i
896896 0 0
897897 −27.6203 20.0673i −0.922213 0.670027i
898898 0 0
899899 9.98474 + 30.7299i 0.333010 + 1.02490i
900900 0 0
901901 60.1923 2.00530
902902 0 0
903903 −10.5185 −0.350033
904904 0 0
905905 −2.40417 7.39928i −0.0799174 0.245961i
906906 0 0
907907 −10.3097 7.49045i −0.342329 0.248716i 0.403315 0.915061i 0.367858π-0.367858\pi
−0.745644 + 0.666345i 0.767858π0.767858\pi
908908 0 0
909909 −25.4081 + 78.1981i −0.842733 + 2.59367i
910910 0 0
911911 −10.1547 + 7.37785i −0.336441 + 0.244439i −0.743159 0.669115i 0.766673π-0.766673\pi
0.406718 + 0.913554i 0.366673π0.366673\pi
912912 0 0
913913 2.05035 40.1158i 0.0678566 1.32764i
914914 0 0
915915 −13.4193 + 9.74972i −0.443630 + 0.322316i
916916 0 0
917917 3.47472 10.6941i 0.114745 0.353150i
918918 0 0
919919 28.3212 + 20.5766i 0.934230 + 0.678758i 0.947025 0.321160i 0.104073π-0.104073\pi
−0.0127946 + 0.999918i 0.504073π0.504073\pi
920920 0 0
921921 5.73319 + 17.6450i 0.188915 + 0.581421i
922922 0 0
923923 −22.3690 −0.736285
924924 0 0
925925 0.961059 0.0315994
926926 0 0
927927 −17.7024 54.4823i −0.581422 1.78943i
928928 0 0
929929 −24.3329 17.6789i −0.798336 0.580025i 0.112089 0.993698i 0.464246π-0.464246\pi
−0.910426 + 0.413673i 0.864246π0.864246\pi
930930 0 0
931931 0.462816 1.42440i 0.0151682 0.0466829i
932932 0 0
933933 −16.1896 + 11.7625i −0.530025 + 0.385086i
934934 0 0
935935 −6.75376 + 8.36229i −0.220871 + 0.273476i
936936 0 0
937937 2.16391 1.57217i 0.0706917 0.0513605i −0.551878 0.833925i 0.686089π-0.686089\pi
0.622570 + 0.782564i 0.286089π0.286089\pi
938938 0 0
939939 22.4214 69.0058i 0.731693 2.25192i
940940 0 0
941941 −14.4251 10.4805i −0.470246 0.341654i 0.327291 0.944924i 0.393864π-0.393864\pi
−0.797537 + 0.603270i 0.793864π0.793864\pi
942942 0 0
943943 0.237753 + 0.731730i 0.00774232 + 0.0238284i
944944 0 0
945945 12.9930 0.422663
946946 0 0
947947 27.4082 0.890647 0.445323 0.895370i 0.353089π-0.353089\pi
0.445323 + 0.895370i 0.353089π0.353089\pi
948948 0 0
949949 −12.9804 39.9495i −0.421361 1.29681i
950950 0 0
951951 −19.9703 14.5092i −0.647580 0.470494i
952952 0 0
953953 −12.5821 + 38.7239i −0.407576 + 1.25439i 0.511150 + 0.859492i 0.329220π0.329220\pi
−0.918725 + 0.394897i 0.870780π0.870780\pi
954954 0 0
955955 −7.67665 + 5.57742i −0.248411 + 0.180481i
956956 0 0
957957 48.3527 + 74.2461i 1.56302 + 2.40004i
958958 0 0
959959 15.5886 11.3258i 0.503381 0.365728i
960960 0 0
961961 −4.35429 + 13.4011i −0.140461 + 0.432294i
962962 0 0
963963 −19.3509 14.0593i −0.623574 0.453053i
964964 0 0
965965 −4.48562 13.8053i −0.144397 0.444408i
966966 0 0
967967 −59.5033 −1.91350 −0.956749 0.290915i 0.906040π-0.906040\pi
−0.956749 + 0.290915i 0.906040π0.906040\pi
968968 0 0
969969 −24.0048 −0.771145
970970 0 0
971971 12.9013 + 39.7061i 0.414022 + 1.27423i 0.913122 + 0.407685i 0.133664π0.133664\pi
−0.499100 + 0.866544i 0.666336π0.666336\pi
972972 0 0
973973 2.40436 + 1.74687i 0.0770804 + 0.0560022i
974974 0 0
975975 21.7900 67.0626i 0.697837 2.14772i
976976 0 0
977977 −7.56447 + 5.49591i −0.242009 + 0.175830i −0.702178 0.712002i 0.747789π-0.747789\pi
0.460169 + 0.887831i 0.347789π0.347789\pi
978978 0 0
979979 −28.2733 43.4140i −0.903618 1.38752i
980980 0 0
981981 −69.0112 + 50.1396i −2.20336 + 1.60083i
982982 0 0
983983 −2.16872 + 6.67464i −0.0691715 + 0.212888i −0.979667 0.200631i 0.935701π-0.935701\pi
0.910495 + 0.413519i 0.135701π0.135701\pi
984984 0 0
985985 6.26730 + 4.55346i 0.199693 + 0.145085i
986986 0 0
987987 −8.52276 26.2304i −0.271283 0.834922i
988988 0 0
989989 6.78167 0.215645
990990 0 0
991991 −17.8273 −0.566303 −0.283152 0.959075i 0.591380π-0.591380\pi
−0.283152 + 0.959075i 0.591380π0.591380\pi
992992 0 0
993993 −12.3980 38.1571i −0.393439 1.21088i
994994 0 0
995995 1.78704 + 1.29836i 0.0566529 + 0.0411607i
996996 0 0
997997 −16.0391 + 49.3632i −0.507963 + 1.56335i 0.287768 + 0.957700i 0.407087π0.407087\pi
−0.795731 + 0.605650i 0.792913π0.792913\pi
998998 0 0
999999 −3.24573 + 2.35816i −0.102690 + 0.0746089i
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 616.2.r.f.113.1 20
11.2 odd 10 6776.2.a.bn.1.1 10
11.4 even 5 inner 616.2.r.f.169.1 yes 20
11.9 even 5 6776.2.a.bm.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
616.2.r.f.113.1 20 1.1 even 1 trivial
616.2.r.f.169.1 yes 20 11.4 even 5 inner
6776.2.a.bm.1.1 10 11.9 even 5
6776.2.a.bn.1.1 10 11.2 odd 10