Properties

Label 400.2.y.d.369.7
Level 400400
Weight 22
Character 400.369
Analytic conductor 3.1943.194
Analytic rank 00
Dimension 3232
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] = [400,2,Mod(129,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 1])) 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("400.129"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 400.y (of order 1010, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.194016080853.19401608085
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: no (minimal twist has level 200)
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 369.7
Character χ\chi == 400.369
Dual form 400.2.y.d.129.7

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+(1.31712+1.81286i)q3+(2.19384+0.432536i)q5+1.85909iq7+(0.624612+1.92236i)q9+(0.681343+2.09696i)q11+(4.552051.47905i)q13+(2.10542+4.54683i)q15+(3.761585.17737i)q17+(3.010052.18693i)q19+(3.37028+2.44865i)q21+(0.9051700.294107i)q23+(4.62582+1.89783i)q25+(2.085780.677713i)q27+(4.71315+3.42430i)q29+(5.427893.94359i)q31+(2.90409+3.99713i)q33+(0.804125+4.07854i)q35+(9.69306+3.14947i)q37+(3.3142910.2003i)q39+(1.82997+5.63206i)q41+3.96247iq43+(2.20178+3.94717i)q45+(5.930388.16246i)q47+3.54377q49+14.3403q51+(2.467593.39634i)q53+(0.587744+4.89509i)q558.33725iq57+(1.86474+5.73908i)q59+(1.136503.49779i)q61+(3.573841.16121i)q63+(9.346705.21372i)q65+(8.4553711.6378i)q67+(1.72540+1.25357i)q69+(7.825275.68539i)q71+(3.436981.11674i)q73+(2.65228+10.8857i)q75+(3.89844+1.26668i)q77+(9.13049+6.63369i)q79+(8.88160+6.45286i)q81+(4.084935.62242i)q83+(10.49179.73128i)q85+(12.41564.03407i)q87+(3.237579.96423i)q89+(2.749698.46268i)q9115.0342iq93+(5.657626.09971i)q95+(0.275879+0.379715i)q974.45668q99+O(q100)q+(1.31712 + 1.81286i) q^{3} +(2.19384 + 0.432536i) q^{5} +1.85909i q^{7} +(-0.624612 + 1.92236i) q^{9} +(0.681343 + 2.09696i) q^{11} +(-4.55205 - 1.47905i) q^{13} +(2.10542 + 4.54683i) q^{15} +(3.76158 - 5.17737i) q^{17} +(-3.01005 - 2.18693i) q^{19} +(-3.37028 + 2.44865i) q^{21} +(0.905170 - 0.294107i) q^{23} +(4.62582 + 1.89783i) q^{25} +(2.08578 - 0.677713i) q^{27} +(-4.71315 + 3.42430i) q^{29} +(-5.42789 - 3.94359i) q^{31} +(-2.90409 + 3.99713i) q^{33} +(-0.804125 + 4.07854i) q^{35} +(9.69306 + 3.14947i) q^{37} +(-3.31429 - 10.2003i) q^{39} +(-1.82997 + 5.63206i) q^{41} +3.96247i q^{43} +(-2.20178 + 3.94717i) q^{45} +(-5.93038 - 8.16246i) q^{47} +3.54377 q^{49} +14.3403 q^{51} +(-2.46759 - 3.39634i) q^{53} +(0.587744 + 4.89509i) q^{55} -8.33725i q^{57} +(-1.86474 + 5.73908i) q^{59} +(-1.13650 - 3.49779i) q^{61} +(-3.57384 - 1.16121i) q^{63} +(-9.34670 - 5.21372i) q^{65} +(8.45537 - 11.6378i) q^{67} +(1.72540 + 1.25357i) q^{69} +(7.82527 - 5.68539i) q^{71} +(3.43698 - 1.11674i) q^{73} +(2.65228 + 10.8857i) q^{75} +(-3.89844 + 1.26668i) q^{77} +(-9.13049 + 6.63369i) q^{79} +(8.88160 + 6.45286i) q^{81} +(4.08493 - 5.62242i) q^{83} +(10.4917 - 9.73128i) q^{85} +(-12.4156 - 4.03407i) q^{87} +(-3.23757 - 9.96423i) q^{89} +(2.74969 - 8.46268i) q^{91} -15.0342i q^{93} +(-5.65762 - 6.09971i) q^{95} +(0.275879 + 0.379715i) q^{97} -4.45668 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+2q5+10q96q1112q15+6q194q21+30q23+6q252q296q318q3540q37+12q3912q45+20q4760q49+60q5130q53+92q99+O(q100) 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53}+ \cdots - 92 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
χ(n)\chi(n) 11 e(910)e\left(\frac{9}{10}\right) 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 1.31712 + 1.81286i 0.760441 + 1.04666i 0.997177 + 0.0750833i 0.0239223π0.0239223\pi
−0.236736 + 0.971574i 0.576078π0.576078\pi
44 0 0
55 2.19384 + 0.432536i 0.981113 + 0.193436i
66 0 0
77 1.85909i 0.702671i 0.936250 + 0.351336i 0.114272π0.114272\pi
−0.936250 + 0.351336i 0.885728π0.885728\pi
88 0 0
99 −0.624612 + 1.92236i −0.208204 + 0.640786i
1010 0 0
1111 0.681343 + 2.09696i 0.205433 + 0.632257i 0.999695 + 0.0246823i 0.00785741π0.00785741\pi
−0.794263 + 0.607575i 0.792143π0.792143\pi
1212 0 0
1313 −4.55205 1.47905i −1.26251 0.410215i −0.400122 0.916462i 0.631032π-0.631032\pi
−0.862388 + 0.506247i 0.831032π0.831032\pi
1414 0 0
1515 2.10542 + 4.54683i 0.543617 + 1.17399i
1616 0 0
1717 3.76158 5.17737i 0.912317 1.25570i −0.0540522 0.998538i 0.517214π-0.517214\pi
0.966369 0.257159i 0.0827863π-0.0827863\pi
1818 0 0
1919 −3.01005 2.18693i −0.690552 0.501715i 0.186289 0.982495i 0.440354π-0.440354\pi
−0.876842 + 0.480779i 0.840354π0.840354\pi
2020 0 0
2121 −3.37028 + 2.44865i −0.735456 + 0.534340i
2222 0 0
2323 0.905170 0.294107i 0.188741 0.0613256i −0.213121 0.977026i 0.568363π-0.568363\pi
0.401862 + 0.915700i 0.368363π0.368363\pi
2424 0 0
2525 4.62582 + 1.89783i 0.925165 + 0.379565i
2626 0 0
2727 2.08578 0.677713i 0.401409 0.130426i
2828 0 0
2929 −4.71315 + 3.42430i −0.875210 + 0.635877i −0.931980 0.362510i 0.881920π-0.881920\pi
0.0567701 + 0.998387i 0.481920π0.481920\pi
3030 0 0
3131 −5.42789 3.94359i −0.974878 0.708290i −0.0183199 0.999832i 0.505832π-0.505832\pi
−0.956558 + 0.291542i 0.905832π0.905832\pi
3232 0 0
3333 −2.90409 + 3.99713i −0.505537 + 0.695812i
3434 0 0
3535 −0.804125 + 4.07854i −0.135922 + 0.689400i
3636 0 0
3737 9.69306 + 3.14947i 1.59353 + 0.517769i 0.965496 0.260418i 0.0838602π-0.0838602\pi
0.628033 + 0.778187i 0.283860π0.283860\pi
3838 0 0
3939 −3.31429 10.2003i −0.530711 1.63336i
4040 0 0
4141 −1.82997 + 5.63206i −0.285793 + 0.879580i 0.700367 + 0.713783i 0.253020π0.253020\pi
−0.986160 + 0.165797i 0.946980π0.946980\pi
4242 0 0
4343 3.96247i 0.604272i 0.953265 + 0.302136i 0.0976996π0.0976996\pi
−0.953265 + 0.302136i 0.902300π0.902300\pi
4444 0 0
4545 −2.20178 + 3.94717i −0.328223 + 0.588409i
4646 0 0
4747 −5.93038 8.16246i −0.865034 1.19062i −0.980345 0.197288i 0.936786π-0.936786\pi
0.115311 0.993329i 0.463214π-0.463214\pi
4848 0 0
4949 3.54377 0.506253
5050 0 0
5151 14.3403 2.00805
5252 0 0
5353 −2.46759 3.39634i −0.338949 0.466523i 0.605185 0.796085i 0.293099π-0.293099\pi
−0.944134 + 0.329562i 0.893099π0.893099\pi
5454 0 0
5555 0.587744 + 4.89509i 0.0792513 + 0.660053i
5656 0 0
5757 8.33725i 1.10430i
5858 0 0
5959 −1.86474 + 5.73908i −0.242769 + 0.747165i 0.753227 + 0.657761i 0.228496π0.228496\pi
−0.995995 + 0.0894039i 0.971504π0.971504\pi
6060 0 0
6161 −1.13650 3.49779i −0.145514 0.447847i 0.851563 0.524253i 0.175655π-0.175655\pi
−0.997077 + 0.0764064i 0.975655π0.975655\pi
6262 0 0
6363 −3.57384 1.16121i −0.450262 0.146299i
6464 0 0
6565 −9.34670 5.21372i −1.15931 0.646682i
6666 0 0
6767 8.45537 11.6378i 1.03299 1.42179i 0.130307 0.991474i 0.458404π-0.458404\pi
0.902680 0.430312i 0.141596π-0.141596\pi
6868 0 0
6969 1.72540 + 1.25357i 0.207713 + 0.150913i
7070 0 0
7171 7.82527 5.68539i 0.928688 0.674732i −0.0169829 0.999856i 0.505406π-0.505406\pi
0.945671 + 0.325124i 0.105406π0.105406\pi
7272 0 0
7373 3.43698 1.11674i 0.402268 0.130705i −0.100894 0.994897i 0.532170π-0.532170\pi
0.503161 + 0.864193i 0.332170π0.332170\pi
7474 0 0
7575 2.65228 + 10.8857i 0.306258 + 1.25697i
7676 0 0
7777 −3.89844 + 1.26668i −0.444269 + 0.144352i
7878 0 0
7979 −9.13049 + 6.63369i −1.02726 + 0.746348i −0.967759 0.251880i 0.918951π-0.918951\pi
−0.0595020 + 0.998228i 0.518951π0.518951\pi
8080 0 0
8181 8.88160 + 6.45286i 0.986844 + 0.716984i
8282 0 0
8383 4.08493 5.62242i 0.448379 0.617141i −0.523669 0.851922i 0.675437π-0.675437\pi
0.972048 + 0.234781i 0.0754371π0.0754371\pi
8484 0 0
8585 10.4917 9.73128i 1.13798 1.05551i
8686 0 0
8787 −12.4156 4.03407i −1.33109 0.432498i
8888 0 0
8989 −3.23757 9.96423i −0.343182 1.05621i −0.962550 0.271105i 0.912611π-0.912611\pi
0.619368 0.785101i 0.287389π-0.287389\pi
9090 0 0
9191 2.74969 8.46268i 0.288246 0.887130i
9292 0 0
9393 15.0342i 1.55898i
9494 0 0
9595 −5.65762 6.09971i −0.580460 0.625817i
9696 0 0
9797 0.275879 + 0.379715i 0.0280113 + 0.0385542i 0.822793 0.568341i 0.192415π-0.192415\pi
−0.794782 + 0.606895i 0.792415π0.792415\pi
9898 0 0
9999 −4.45668 −0.447913
100100 0 0
101101 −1.01547 −0.101043 −0.0505214 0.998723i 0.516088π-0.516088\pi
−0.0505214 + 0.998723i 0.516088π0.516088\pi
102102 0 0
103103 −9.68658 13.3324i −0.954447 1.31368i −0.949524 0.313696i 0.898433π-0.898433\pi
−0.00492362 0.999988i 0.501567π-0.501567\pi
104104 0 0
105105 −8.45298 + 3.91417i −0.824926 + 0.381984i
106106 0 0
107107 14.9910i 1.44923i 0.689153 + 0.724616i 0.257983π0.257983\pi
−0.689153 + 0.724616i 0.742017π0.742017\pi
108108 0 0
109109 −3.03784 + 9.34952i −0.290972 + 0.895521i 0.693572 + 0.720387i 0.256036π0.256036\pi
−0.984545 + 0.175134i 0.943964π0.943964\pi
110110 0 0
111111 7.05739 + 21.7204i 0.669858 + 2.06161i
112112 0 0
113113 −15.9570 5.18475i −1.50111 0.487740i −0.560769 0.827973i 0.689494π-0.689494\pi
−0.940341 + 0.340232i 0.889494π0.889494\pi
114114 0 0
115115 2.11301 0.253704i 0.197039 0.0236581i
116116 0 0
117117 5.68652 7.82683i 0.525719 0.723591i
118118 0 0
119119 9.62521 + 6.99313i 0.882342 + 0.641059i
120120 0 0
121121 4.96618 3.60814i 0.451471 0.328013i
122122 0 0
123123 −12.6204 + 4.10063i −1.13795 + 0.369741i
124124 0 0
125125 9.32742 + 6.16436i 0.834270 + 0.551357i
126126 0 0
127127 3.78159 1.22871i 0.335562 0.109031i −0.136389 0.990655i 0.543550π-0.543550\pi
0.471951 + 0.881625i 0.343550π0.343550\pi
128128 0 0
129129 −7.18342 + 5.21906i −0.632465 + 0.459513i
130130 0 0
131131 −8.60768 6.25385i −0.752057 0.546401i 0.144407 0.989518i 0.453873π-0.453873\pi
−0.896464 + 0.443117i 0.853873π0.853873\pi
132132 0 0
133133 4.06570 5.59596i 0.352541 0.485231i
134134 0 0
135135 4.86900 0.584612i 0.419057 0.0503154i
136136 0 0
137137 −10.7203 3.48323i −0.915896 0.297593i −0.187114 0.982338i 0.559913π-0.559913\pi
−0.728782 + 0.684745i 0.759913π0.759913\pi
138138 0 0
139139 1.12959 + 3.47652i 0.0958105 + 0.294874i 0.987464 0.157844i 0.0504543π-0.0504543\pi
−0.891654 + 0.452718i 0.850454π0.850454\pi
140140 0 0
141141 6.98640 21.5019i 0.588361 1.81079i
142142 0 0
143143 10.5532i 0.882502i
144144 0 0
145145 −11.8210 + 5.47375i −0.981681 + 0.454570i
146146 0 0
147147 4.66758 + 6.42438i 0.384976 + 0.529874i
148148 0 0
149149 −8.64836 −0.708501 −0.354250 0.935151i 0.615264π-0.615264\pi
−0.354250 + 0.935151i 0.615264π0.615264\pi
150150 0 0
151151 −6.30755 −0.513301 −0.256650 0.966504i 0.582619π-0.582619\pi
−0.256650 + 0.966504i 0.582619π0.582619\pi
152152 0 0
153153 7.60323 + 10.4649i 0.614685 + 0.846041i
154154 0 0
155155 −10.2021 10.9994i −0.819456 0.883489i
156156 0 0
157157 11.9460i 0.953395i 0.879067 + 0.476698i 0.158166π0.158166\pi
−0.879067 + 0.476698i 0.841834π0.841834\pi
158158 0 0
159159 2.90699 8.94679i 0.230539 0.709527i
160160 0 0
161161 0.546773 + 1.68279i 0.0430918 + 0.132623i
162162 0 0
163163 16.4856 + 5.35650i 1.29125 + 0.419553i 0.872530 0.488561i 0.162478π-0.162478\pi
0.418723 + 0.908114i 0.362478π0.362478\pi
164164 0 0
165165 −8.10000 + 7.51293i −0.630584 + 0.584881i
166166 0 0
167167 4.09258 5.63295i 0.316693 0.435891i −0.620761 0.784000i 0.713176π-0.713176\pi
0.937454 + 0.348109i 0.113176π0.113176\pi
168168 0 0
169169 8.01632 + 5.82419i 0.616640 + 0.448015i
170170 0 0
171171 6.08417 4.42041i 0.465268 0.338037i
172172 0 0
173173 −1.36718 + 0.444224i −0.103945 + 0.0337737i −0.360528 0.932749i 0.617403π-0.617403\pi
0.256583 + 0.966522i 0.417403π0.417403\pi
174174 0 0
175175 −3.52824 + 8.59984i −0.266710 + 0.650087i
176176 0 0
177177 −12.8603 + 4.17855i −0.966636 + 0.314079i
178178 0 0
179179 −14.6030 + 10.6097i −1.09148 + 0.793006i −0.979648 0.200722i 0.935671π-0.935671\pi
−0.111830 + 0.993727i 0.535671π0.535671\pi
180180 0 0
181181 16.1239 + 11.7147i 1.19848 + 0.870745i 0.994134 0.108154i 0.0344941π-0.0344941\pi
0.204343 + 0.978899i 0.434494π0.434494\pi
182182 0 0
183183 4.84411 6.66735i 0.358087 0.492864i
184184 0 0
185185 19.9027 + 11.1020i 1.46328 + 0.816236i
186186 0 0
187187 13.4197 + 4.36031i 0.981343 + 0.318858i
188188 0 0
189189 1.25993 + 3.87767i 0.0916465 + 0.282059i
190190 0 0
191191 −5.97693 + 18.3951i −0.432476 + 1.33102i 0.463176 + 0.886266i 0.346710π0.346710\pi
−0.895652 + 0.444756i 0.853290π0.853290\pi
192192 0 0
193193 1.51392i 0.108974i −0.998514 0.0544872i 0.982648π-0.982648\pi
0.998514 0.0544872i 0.0173524π-0.0173524\pi
194194 0 0
195195 −2.85899 23.8114i −0.204736 1.70517i
196196 0 0
197197 4.41595 + 6.07803i 0.314623 + 0.433042i 0.936816 0.349822i 0.113758π-0.113758\pi
−0.622193 + 0.782864i 0.713758π0.713758\pi
198198 0 0
199199 21.1916 1.50223 0.751117 0.660169i 0.229515π-0.229515\pi
0.751117 + 0.660169i 0.229515π0.229515\pi
200200 0 0
201201 32.2345 2.27365
202202 0 0
203203 −6.36610 8.76218i −0.446812 0.614985i
204204 0 0
205205 −6.45072 + 11.5643i −0.450538 + 0.807684i
206206 0 0
207207 1.92376i 0.133711i
208208 0 0
209209 2.53502 7.80199i 0.175351 0.539675i
210210 0 0
211211 1.83425 + 5.64523i 0.126275 + 0.388634i 0.994131 0.108181i 0.0345027π-0.0345027\pi
−0.867856 + 0.496815i 0.834503π0.834503\pi
212212 0 0
213213 20.6137 + 6.69779i 1.41243 + 0.458925i
214214 0 0
215215 −1.71391 + 8.69301i −0.116888 + 0.592859i
216216 0 0
217217 7.33151 10.0910i 0.497695 0.685019i
218218 0 0
219219 6.55142 + 4.75988i 0.442704 + 0.321643i
220220 0 0
221221 −24.7805 + 18.0041i −1.66691 + 1.21108i
222222 0 0
223223 1.31652 0.427764i 0.0881609 0.0286452i −0.264604 0.964357i 0.585241π-0.585241\pi
0.352765 + 0.935712i 0.385241π0.385241\pi
224224 0 0
225225 −6.53765 + 7.70708i −0.435843 + 0.513806i
226226 0 0
227227 −9.45162 + 3.07102i −0.627326 + 0.203831i −0.605390 0.795929i 0.706983π-0.706983\pi
−0.0219357 + 0.999759i 0.506983π0.506983\pi
228228 0 0
229229 −11.6668 + 8.47640i −0.770962 + 0.560136i −0.902253 0.431207i 0.858088π-0.858088\pi
0.131291 + 0.991344i 0.458088π0.458088\pi
230230 0 0
231231 −7.43104 5.39897i −0.488927 0.355226i
232232 0 0
233233 −7.85246 + 10.8080i −0.514431 + 0.708054i −0.984659 0.174491i 0.944172π-0.944172\pi
0.470227 + 0.882545i 0.344172π0.344172\pi
234234 0 0
235235 −9.47971 20.4722i −0.618388 1.33546i
236236 0 0
237237 −24.0520 7.81495i −1.56234 0.507636i
238238 0 0
239239 4.26572 + 13.1285i 0.275926 + 0.849213i 0.988973 + 0.148097i 0.0473148π0.0473148\pi
−0.713047 + 0.701117i 0.752685π0.752685\pi
240240 0 0
241241 4.40966 13.5715i 0.284051 0.874219i −0.702631 0.711555i 0.747991π-0.747991\pi
0.986682 0.162664i 0.0520087π-0.0520087\pi
242242 0 0
243243 18.0210i 1.15605i
244244 0 0
245245 7.77445 + 1.53281i 0.496692 + 0.0979277i
246246 0 0
247247 10.4673 + 14.4070i 0.666018 + 0.916695i
248248 0 0
249249 15.5730 0.986902
250250 0 0
251251 −0.758323 −0.0478649 −0.0239325 0.999714i 0.507619π-0.507619\pi
−0.0239325 + 0.999714i 0.507619π0.507619\pi
252252 0 0
253253 1.23346 + 1.69772i 0.0775471 + 0.106734i
254254 0 0
255255 31.4603 + 6.20271i 1.97012 + 0.388429i
256256 0 0
257257 15.3091i 0.954957i 0.878643 + 0.477478i 0.158449π0.158449\pi
−0.878643 + 0.477478i 0.841551π0.841551\pi
258258 0 0
259259 −5.85515 + 18.0203i −0.363821 + 1.11973i
260260 0 0
261261 −3.63885 11.1992i −0.225239 0.693214i
262262 0 0
263263 −12.8524 4.17599i −0.792511 0.257502i −0.115338 0.993326i 0.536795π-0.536795\pi
−0.677173 + 0.735824i 0.736795π0.736795\pi
264264 0 0
265265 −3.94443 8.51833i −0.242305 0.523277i
266266 0 0
267267 13.7995 18.9934i 0.844516 1.16238i
268268 0 0
269269 −10.2780 7.46742i −0.626662 0.455296i 0.228580 0.973525i 0.426592π-0.426592\pi
−0.855242 + 0.518229i 0.826592π0.826592\pi
270270 0 0
271271 −7.85337 + 5.70581i −0.477058 + 0.346603i −0.800186 0.599752i 0.795266π-0.795266\pi
0.323127 + 0.946356i 0.395266π0.395266\pi
272272 0 0
273273 18.9634 6.16157i 1.14771 0.372915i
274274 0 0
275275 −0.827891 + 10.9932i −0.0499237 + 0.662917i
276276 0 0
277277 −4.87910 + 1.58532i −0.293157 + 0.0952524i −0.451903 0.892067i 0.649255π-0.649255\pi
0.158746 + 0.987319i 0.449255π0.449255\pi
278278 0 0
279279 10.9713 7.97113i 0.656836 0.477219i
280280 0 0
281281 −20.1560 14.6442i −1.20241 0.873599i −0.207887 0.978153i 0.566659π-0.566659\pi
−0.994519 + 0.104554i 0.966659π0.966659\pi
282282 0 0
283283 −8.99734 + 12.3838i −0.534836 + 0.736139i −0.987858 0.155361i 0.950346π-0.950346\pi
0.453021 + 0.891500i 0.350346π0.350346\pi
284284 0 0
285285 3.60617 18.2906i 0.213611 1.08344i
286286 0 0
287287 −10.4705 3.40208i −0.618055 0.200818i
288288 0 0
289289 −7.40239 22.7822i −0.435435 1.34013i
290290 0 0
291291 −0.325005 + 1.00026i −0.0190521 + 0.0586365i
292292 0 0
293293 14.5144i 0.847941i 0.905676 + 0.423971i 0.139364π0.139364\pi
−0.905676 + 0.423971i 0.860636π0.860636\pi
294294 0 0
295295 −6.57329 + 11.7840i −0.382712 + 0.686093i
296296 0 0
297297 2.84227 + 3.91205i 0.164925 + 0.227000i
298298 0 0
299299 −4.55537 −0.263444
300300 0 0
301301 −7.36661 −0.424604
302302 0 0
303303 −1.33750 1.84091i −0.0768371 0.105757i
304304 0 0
305305 −0.980375 8.16516i −0.0561361 0.467536i
306306 0 0
307307 24.0722i 1.37387i −0.726717 0.686937i 0.758955π-0.758955\pi
0.726717 0.686937i 0.241045π-0.241045\pi
308308 0 0
309309 11.4115 35.1209i 0.649176 1.99796i
310310 0 0
311311 2.30411 + 7.09133i 0.130654 + 0.402113i 0.994889 0.100977i 0.0321967π-0.0321967\pi
−0.864235 + 0.503089i 0.832197π0.832197\pi
312312 0 0
313313 −1.21839 0.395878i −0.0688672 0.0223763i 0.274381 0.961621i 0.411527π-0.411527\pi
−0.343248 + 0.939245i 0.611527π0.611527\pi
314314 0 0
315315 −7.33815 4.09332i −0.413458 0.230633i
316316 0 0
317317 9.21939 12.6894i 0.517813 0.712708i −0.467400 0.884046i 0.654809π-0.654809\pi
0.985212 + 0.171338i 0.0548091π0.0548091\pi
318318 0 0
319319 −10.3919 7.55015i −0.581834 0.422727i
320320 0 0
321321 −27.1766 + 19.7449i −1.51685 + 1.10206i
322322 0 0
323323 −22.6451 + 7.35783i −1.26000 + 0.409400i
324324 0 0
325325 −18.2500 15.4808i −1.01233 0.858721i
326326 0 0
327327 −20.9506 + 6.80726i −1.15857 + 0.376443i
328328 0 0
329329 15.1748 11.0251i 0.836613 0.607835i
330330 0 0
331331 −17.9852 13.0670i −0.988557 0.718228i −0.0289521 0.999581i 0.509217π-0.509217\pi
−0.959605 + 0.281352i 0.909217π0.909217\pi
332332 0 0
333333 −12.1088 + 16.6663i −0.663558 + 0.913309i
334334 0 0
335335 23.5835 21.8742i 1.28850 1.19511i
336336 0 0
337337 −1.72123 0.559261i −0.0937613 0.0304649i 0.261761 0.965133i 0.415697π-0.415697\pi
−0.355522 + 0.934668i 0.615697π0.615697\pi
338338 0 0
339339 −11.6181 35.7568i −0.631009 1.94205i
340340 0 0
341341 4.57130 14.0690i 0.247550 0.761879i
342342 0 0
343343 19.6019i 1.05840i
344344 0 0
345345 3.24302 + 3.49643i 0.174598 + 0.188241i
346346 0 0
347347 12.8352 + 17.6661i 0.689030 + 0.948368i 0.999998 0.00205222i 0.000653241π-0.000653241\pi
−0.310968 + 0.950420i 0.600653π0.600653\pi
348348 0 0
349349 10.7589 0.575909 0.287955 0.957644i 0.407025π-0.407025\pi
0.287955 + 0.957644i 0.407025π0.407025\pi
350350 0 0
351351 −10.4970 −0.560286
352352 0 0
353353 15.1356 + 20.8324i 0.805586 + 1.10879i 0.991989 + 0.126321i 0.0403170π0.0403170\pi
−0.186403 + 0.982473i 0.559683π0.559683\pi
354354 0 0
355355 19.6265 9.08809i 1.04167 0.482346i
356356 0 0
357357 26.6600i 1.41100i
358358 0 0
359359 3.91090 12.0365i 0.206409 0.635263i −0.793243 0.608905i 0.791609π-0.791609\pi
0.999653 0.0263579i 0.00839095π-0.00839095\pi
360360 0 0
361361 −1.59359 4.90457i −0.0838732 0.258135i
362362 0 0
363363 13.0821 + 4.25064i 0.686634 + 0.223101i
364364 0 0
365365 8.02319 0.963329i 0.419953 0.0504229i
366366 0 0
367367 6.61059 9.09869i 0.345070 0.474948i −0.600844 0.799366i 0.705169π-0.705169\pi
0.945914 + 0.324419i 0.105169π0.105169\pi
368368 0 0
369369 −9.68381 7.03570i −0.504119 0.366264i
370370 0 0
371371 6.31411 4.58747i 0.327812 0.238170i
372372 0 0
373373 7.66947 2.49196i 0.397110 0.129029i −0.103652 0.994614i 0.533053π-0.533053\pi
0.500763 + 0.865585i 0.333053π0.333053\pi
374374 0 0
375375 1.11021 + 25.0285i 0.0573311 + 1.29247i
376376 0 0
377377 26.5192 8.61660i 1.36581 0.443778i
378378 0 0
379379 6.51391 4.73263i 0.334597 0.243099i −0.407782 0.913079i 0.633698π-0.633698\pi
0.742379 + 0.669980i 0.233698π0.233698\pi
380380 0 0
381381 7.20831 + 5.23714i 0.369293 + 0.268307i
382382 0 0
383383 14.4091 19.8324i 0.736270 1.01339i −0.262555 0.964917i 0.584565π-0.584565\pi
0.998825 0.0484712i 0.0154349π-0.0154349\pi
384384 0 0
385385 −9.10042 + 1.09267i −0.463801 + 0.0556876i
386386 0 0
387387 −7.61729 2.47501i −0.387209 0.125812i
388388 0 0
389389 −0.720320 2.21692i −0.0365217 0.112402i 0.931134 0.364678i 0.118821π-0.118821\pi
−0.967655 + 0.252276i 0.918821π0.918821\pi
390390 0 0
391391 1.88216 5.79271i 0.0951852 0.292950i
392392 0 0
393393 23.8416i 1.20265i
394394 0 0
395395 −22.9001 + 10.6040i −1.15223 + 0.533543i
396396 0 0
397397 −9.42301 12.9697i −0.472927 0.650929i 0.504199 0.863587i 0.331788π-0.331788\pi
−0.977127 + 0.212659i 0.931788π0.931788\pi
398398 0 0
399399 15.4997 0.775957
400400 0 0
401401 −19.3238 −0.964984 −0.482492 0.875900i 0.660268π-0.660268\pi
−0.482492 + 0.875900i 0.660268π0.660268\pi
402402 0 0
403403 18.8752 + 25.9795i 0.940243 + 1.29413i
404404 0 0
405405 16.6937 + 17.9981i 0.829515 + 0.894334i
406406 0 0
407407 22.4718i 1.11389i
408408 0 0
409409 −11.9419 + 36.7534i −0.590490 + 1.81734i −0.0144830 + 0.999895i 0.504610π0.504610\pi
−0.576007 + 0.817445i 0.695390π0.695390\pi
410410 0 0
411411 −7.80531 24.0223i −0.385008 1.18493i
412412 0 0
413413 −10.6695 3.46673i −0.525011 0.170586i
414414 0 0
415415 11.3936 10.5678i 0.559288 0.518752i
416416 0 0
417417 −4.81465 + 6.62679i −0.235774 + 0.324515i
418418 0 0
419419 −3.88236 2.82070i −0.189666 0.137800i 0.488900 0.872340i 0.337398π-0.337398\pi
−0.678566 + 0.734540i 0.737398π0.737398\pi
420420 0 0
421421 −26.0151 + 18.9011i −1.26790 + 0.921182i −0.999117 0.0420195i 0.986621π-0.986621\pi
−0.268781 + 0.963201i 0.586621π0.586621\pi
422422 0 0
423423 19.3954 6.30193i 0.943035 0.306411i
424424 0 0
425425 27.2262 16.8108i 1.32066 0.815443i
426426 0 0
427427 6.50272 2.11286i 0.314689 0.102249i
428428 0 0
429429 19.1315 13.8998i 0.923678 0.671091i
430430 0 0
431431 −1.16017 0.842909i −0.0558832 0.0406015i 0.559493 0.828835i 0.310996π-0.310996\pi
−0.615376 + 0.788234i 0.710996π0.710996\pi
432432 0 0
433433 0.854327 1.17588i 0.0410563 0.0565092i −0.787995 0.615681i 0.788881π-0.788881\pi
0.829052 + 0.559172i 0.188881π0.188881\pi
434434 0 0
435435 −25.4929 14.2203i −1.22229 0.681810i
436436 0 0
437437 −3.36779 1.09426i −0.161103 0.0523457i
438438 0 0
439439 2.54098 + 7.82032i 0.121274 + 0.373244i 0.993204 0.116387i 0.0371314π-0.0371314\pi
−0.871930 + 0.489631i 0.837131π0.837131\pi
440440 0 0
441441 −2.21348 + 6.81240i −0.105404 + 0.324400i
442442 0 0
443443 22.7301i 1.07994i −0.841684 0.539971i 0.818435π-0.818435\pi
0.841684 0.539971i 0.181565π-0.181565\pi
444444 0 0
445445 −2.79281 23.2602i −0.132392 1.10264i
446446 0 0
447447 −11.3909 15.6783i −0.538773 0.741558i
448448 0 0
449449 −5.30862 −0.250529 −0.125265 0.992123i 0.539978π-0.539978\pi
−0.125265 + 0.992123i 0.539978π0.539978\pi
450450 0 0
451451 −13.0570 −0.614832
452452 0 0
453453 −8.30781 11.4347i −0.390335 0.537250i
454454 0 0
455455 9.69278 17.3764i 0.454405 0.814617i
456456 0 0
457457 25.3646i 1.18651i 0.805016 + 0.593253i 0.202156π0.202156\pi
−0.805016 + 0.593253i 0.797844π0.797844\pi
458458 0 0
459459 4.33708 13.3481i 0.202437 0.623038i
460460 0 0
461461 7.82214 + 24.0741i 0.364314 + 1.12124i 0.950410 + 0.311000i 0.100664π0.100664\pi
−0.586096 + 0.810241i 0.699336π0.699336\pi
462462 0 0
463463 30.8240 + 10.0153i 1.43251 + 0.465452i 0.919555 0.392962i 0.128550π-0.128550\pi
0.512958 + 0.858414i 0.328550π0.328550\pi
464464 0 0
465465 6.50285 32.9826i 0.301562 1.52953i
466466 0 0
467467 −13.9120 + 19.1483i −0.643773 + 0.886077i −0.998810 0.0487749i 0.984468π-0.984468\pi
0.355037 + 0.934852i 0.384468π0.384468\pi
468468 0 0
469469 21.6358 + 15.7193i 0.999048 + 0.725851i
470470 0 0
471471 −21.6565 + 15.7344i −0.997878 + 0.725001i
472472 0 0
473473 −8.30914 + 2.69980i −0.382055 + 0.124137i
474474 0 0
475475 −9.77354 15.8289i −0.448441 0.726279i
476476 0 0
477477 8.07026 2.62219i 0.369512 0.120062i
478478 0 0
479479 25.7721 18.7245i 1.17756 0.855546i 0.185664 0.982613i 0.440556π-0.440556\pi
0.991894 + 0.127067i 0.0405565π0.0405565\pi
480480 0 0
481481 −39.4650 28.6730i −1.79945 1.30738i
482482 0 0
483483 −2.33051 + 3.20767i −0.106042 + 0.145954i
484484 0 0
485485 0.440993 + 0.952360i 0.0200245 + 0.0432445i
486486 0 0
487487 −10.7893 3.50567i −0.488912 0.158857i 0.0541786 0.998531i 0.482746π-0.482746\pi
−0.543091 + 0.839674i 0.682746π0.682746\pi
488488 0 0
489489 12.0030 + 36.9413i 0.542793 + 1.67054i
490490 0 0
491491 8.29887 25.5413i 0.374523 1.15266i −0.569277 0.822146i 0.692777π-0.692777\pi
0.943800 0.330517i 0.107223π-0.107223\pi
492492 0 0
493493 37.2825i 1.67912i
494494 0 0
495495 −9.77722 1.92768i −0.439453 0.0866426i
496496 0 0
497497 10.5697 + 14.5479i 0.474114 + 0.652563i
498498 0 0
499499 −36.3336 −1.62651 −0.813257 0.581904i 0.802308π-0.802308\pi
−0.813257 + 0.581904i 0.802308π0.802308\pi
500500 0 0
501501 15.6022 0.697055
502502 0 0
503503 −2.99740 4.12557i −0.133648 0.183950i 0.736948 0.675949i 0.236266π-0.236266\pi
−0.870596 + 0.491999i 0.836266π0.836266\pi
504504 0 0
505505 −2.22777 0.439227i −0.0991344 0.0195453i
506506 0 0
507507 22.2037i 0.986099i
508508 0 0
509509 −4.80173 + 14.7782i −0.212833 + 0.655032i 0.786468 + 0.617631i 0.211908π0.211908\pi
−0.999300 + 0.0374003i 0.988092π0.988092\pi
510510 0 0
511511 2.07613 + 6.38966i 0.0918424 + 0.282662i
512512 0 0
513513 −7.76042 2.52151i −0.342631 0.111327i
514514 0 0
515515 −15.4840 33.4390i −0.682306 1.47350i
516516 0 0
517517 13.0757 17.9972i 0.575070 0.791516i
518518 0 0
519519 −2.60606 1.89341i −0.114393 0.0831116i
520520 0 0
521521 7.86009 5.71069i 0.344357 0.250190i −0.402141 0.915578i 0.631734π-0.631734\pi
0.746498 + 0.665388i 0.231734π0.231734\pi
522522 0 0
523523 −2.08311 + 0.676843i −0.0910880 + 0.0295963i −0.354206 0.935167i 0.615249π-0.615249\pi
0.263118 + 0.964764i 0.415249π0.415249\pi
524524 0 0
525525 −20.2375 + 4.93083i −0.883235 + 0.215199i
526526 0 0
527527 −40.8349 + 13.2681i −1.77880 + 0.577966i
528528 0 0
529529 −17.8746 + 12.9866i −0.777155 + 0.564636i
530530 0 0
531531 −9.86783 7.16940i −0.428227 0.311125i
532532 0 0
533533 16.6602 22.9308i 0.721633 0.993242i
534534 0 0
535535 −6.48414 + 32.8877i −0.280334 + 1.42186i
536536 0 0
537537 −38.4679 12.4990i −1.66001 0.539370i
538538 0 0
539539 2.41453 + 7.43115i 0.104001 + 0.320082i
540540 0 0
541541 13.5299 41.6406i 0.581694 1.79027i −0.0304661 0.999536i 0.509699π-0.509699\pi
0.612160 0.790734i 0.290301π-0.290301\pi
542542 0 0
543543 44.6600i 1.91655i
544544 0 0
545545 −10.7085 + 19.1973i −0.458703 + 0.822323i
546546 0 0
547547 16.5184 + 22.7356i 0.706275 + 0.972104i 0.999869 + 0.0161740i 0.00514857π0.00514857\pi
−0.293594 + 0.955930i 0.594851π0.594851\pi
548548 0 0
549549 7.43388 0.317270
550550 0 0
551551 21.6755 0.923407
552552 0 0
553553 −12.3326 16.9744i −0.524438 0.721826i
554554 0 0
555555 6.08788 + 50.7036i 0.258416 + 2.15225i
556556 0 0
557557 24.1061i 1.02141i −0.859757 0.510703i 0.829385π-0.829385\pi
0.859757 0.510703i 0.170615π-0.170615\pi
558558 0 0
559559 5.86069 18.0374i 0.247881 0.762899i
560560 0 0
561561 9.77068 + 30.0711i 0.412519 + 1.26960i
562562 0 0
563563 27.4814 + 8.92924i 1.15820 + 0.376323i 0.824227 0.566259i 0.191610π-0.191610\pi
0.333975 + 0.942582i 0.391610π0.391610\pi
564564 0 0
565565 −32.7645 18.2765i −1.37841 0.768897i
566566 0 0
567567 −11.9965 + 16.5117i −0.503804 + 0.693427i
568568 0 0
569569 0.0640223 + 0.0465149i 0.00268395 + 0.00195001i 0.589126 0.808041i 0.299472π-0.299472\pi
−0.586442 + 0.809991i 0.699472π0.699472\pi
570570 0 0
571571 22.3019 16.2033i 0.933307 0.678088i −0.0134930 0.999909i 0.504295π-0.504295\pi
0.946800 + 0.321821i 0.104295π0.104295\pi
572572 0 0
573573 −41.2202 + 13.3932i −1.72200 + 0.559511i
574574 0 0
575575 4.74532 + 0.357366i 0.197894 + 0.0149032i
576576 0 0
577577 13.8267 4.49258i 0.575615 0.187029i −0.00672030 0.999977i 0.502139π-0.502139\pi
0.582335 + 0.812949i 0.302139π0.302139\pi
578578 0 0
579579 2.74453 1.99402i 0.114059 0.0828686i
580580 0 0
581581 10.4526 + 7.59427i 0.433647 + 0.315063i
582582 0 0
583583 5.44071 7.48850i 0.225331 0.310142i
584584 0 0
585585 15.8607 14.7111i 0.655759 0.608231i
586586 0 0
587587 −20.0294 6.50795i −0.826702 0.268612i −0.135046 0.990839i 0.543118π-0.543118\pi
−0.691656 + 0.722227i 0.743118π0.743118\pi
588588 0 0
589589 7.71385 + 23.7408i 0.317844 + 0.978223i
590590 0 0
591591 −5.20230 + 16.0110i −0.213994 + 0.658605i
592592 0 0
593593 19.9763i 0.820328i −0.912012 0.410164i 0.865471π-0.865471\pi
0.912012 0.410164i 0.134529π-0.134529\pi
594594 0 0
595595 18.0913 + 19.5050i 0.741673 + 0.799628i
596596 0 0
597597 27.9120 + 38.4175i 1.14236 + 1.57232i
598598 0 0
599599 33.0408 1.35001 0.675005 0.737813i 0.264141π-0.264141\pi
0.675005 + 0.737813i 0.264141π0.264141\pi
600600 0 0
601601 6.72970 0.274510 0.137255 0.990536i 0.456172π-0.456172\pi
0.137255 + 0.990536i 0.456172π0.456172\pi
602602 0 0
603603 17.0907 + 23.5234i 0.695988 + 0.957945i
604604 0 0
605605 12.4556 5.76761i 0.506393 0.234487i
606606 0 0
607607 4.56961i 0.185475i −0.995691 0.0927374i 0.970438π-0.970438\pi
0.995691 0.0927374i 0.0295617π-0.0295617\pi
608608 0 0
609609 7.49971 23.0817i 0.303904 0.935319i
610610 0 0
611611 14.9227 + 45.9272i 0.603706 + 1.85802i
612612 0 0
613613 21.3226 + 6.92814i 0.861213 + 0.279825i 0.706135 0.708077i 0.250437π-0.250437\pi
0.155078 + 0.987902i 0.450437π0.450437\pi
614614 0 0
615615 −29.4608 + 3.53731i −1.18798 + 0.142638i
616616 0 0
617617 −5.49011 + 7.55649i −0.221023 + 0.304213i −0.905101 0.425197i 0.860205π-0.860205\pi
0.684078 + 0.729409i 0.260205π0.260205\pi
618618 0 0
619619 12.9673 + 9.42126i 0.521198 + 0.378673i 0.817055 0.576560i 0.195605π-0.195605\pi
−0.295857 + 0.955232i 0.595605π0.595605\pi
620620 0 0
621621 1.68867 1.22689i 0.0677639 0.0492334i
622622 0 0
623623 18.5244 6.01895i 0.742166 0.241144i
624624 0 0
625625 17.7965 + 17.5580i 0.711860 + 0.702321i
626626 0 0
627627 17.4829 5.68053i 0.698199 0.226859i
628628 0 0
629629 52.7672 38.3376i 2.10396 1.52862i
630630 0 0
631631 0.205708 + 0.149456i 0.00818912 + 0.00594975i 0.591872 0.806032i 0.298389π-0.298389\pi
−0.583683 + 0.811982i 0.698389π0.698389\pi
632632 0 0
633633 −7.81811 + 10.7607i −0.310742 + 0.427699i
634634 0 0
635635 8.82765 1.05992i 0.350314 0.0420616i
636636 0 0
637637 −16.1314 5.24141i −0.639150 0.207672i
638638 0 0
639639 6.04160 + 18.5941i 0.239002 + 0.735572i
640640 0 0
641641 −14.0339 + 43.1918i −0.554305 + 1.70598i 0.143467 + 0.989655i 0.454175π0.454175\pi
−0.697772 + 0.716320i 0.745825π0.745825\pi
642642 0 0
643643 7.01215i 0.276532i −0.990395 0.138266i 0.955847π-0.955847\pi
0.990395 0.138266i 0.0441529π-0.0441529\pi
644644 0 0
645645 −18.0167 + 8.34267i −0.709406 + 0.328492i
646646 0 0
647647 7.34966 + 10.1159i 0.288945 + 0.397698i 0.928671 0.370904i 0.120952π-0.120952\pi
−0.639726 + 0.768603i 0.720952π0.720952\pi
648648 0 0
649649 −13.3051 −0.522273
650650 0 0
651651 27.9500 1.09545
652652 0 0
653653 11.0961 + 15.2725i 0.434224 + 0.597658i 0.968916 0.247389i 0.0795725π-0.0795725\pi
−0.534692 + 0.845047i 0.679572π0.679572\pi
654654 0 0
655655 −16.1788 17.4430i −0.632159 0.681556i
656656 0 0
657657 7.30463i 0.284981i
658658 0 0
659659 −7.82961 + 24.0971i −0.304998 + 0.938689i 0.674679 + 0.738111i 0.264282π0.264282\pi
−0.979678 + 0.200578i 0.935718π0.935718\pi
660660 0 0
661661 2.51468 + 7.73937i 0.0978095 + 0.301027i 0.987976 0.154609i 0.0494119π-0.0494119\pi
−0.890166 + 0.455636i 0.849412π0.849412\pi
662662 0 0
663663 −65.2778 21.2101i −2.53518 0.823730i
664664 0 0
665665 11.3399 10.5180i 0.439744 0.407872i
666666 0 0
667667 −3.25909 + 4.48575i −0.126192 + 0.173689i
668668 0 0
669669 2.50950 + 1.82326i 0.0970229 + 0.0704912i
670670 0 0
671671 6.56038 4.76640i 0.253261 0.184005i
672672 0 0
673673 41.5233 13.4917i 1.60061 0.520069i 0.633349 0.773866i 0.281680π-0.281680\pi
0.967257 + 0.253798i 0.0816797π0.0816797\pi
674674 0 0
675675 10.9347 + 0.823479i 0.420875 + 0.0316957i
676676 0 0
677677 −23.5415 + 7.64908i −0.904772 + 0.293978i −0.724205 0.689585i 0.757793π-0.757793\pi
−0.180567 + 0.983563i 0.557793π0.557793\pi
678678 0 0
679679 −0.705926 + 0.512885i −0.0270910 + 0.0196827i
680680 0 0
681681 −18.0163 13.0896i −0.690385 0.501594i
682682 0 0
683683 −11.0504 + 15.2095i −0.422830 + 0.581976i −0.966289 0.257460i 0.917114π-0.917114\pi
0.543459 + 0.839436i 0.317114π0.317114\pi
684684 0 0
685685 −22.0119 12.2786i −0.841032 0.469140i
686686 0 0
687687 −30.7331 9.98580i −1.17254 0.380982i
688688 0 0
689689 6.20921 + 19.1100i 0.236552 + 0.728032i
690690 0 0
691691 9.31610 28.6720i 0.354401 1.09073i −0.601955 0.798530i 0.705611π-0.705611\pi
0.956356 0.292204i 0.0943887π-0.0943887\pi
692692 0 0
693693 8.28538i 0.314736i
694694 0 0
695695 0.974412 + 8.11549i 0.0369615 + 0.307838i
696696 0 0
697697 22.2757 + 30.6599i 0.843752 + 1.16132i
698698 0 0
699699 −29.9360 −1.13228
700700 0 0
701701 −5.93443 −0.224140 −0.112070 0.993700i 0.535748π-0.535748\pi
−0.112070 + 0.993700i 0.535748π0.535748\pi
702702 0 0
703703 −22.2889 30.6781i −0.840642 1.15704i
704704 0 0
705705 24.6274 44.1498i 0.927521 1.66278i
706706 0 0
707707 1.88785i 0.0709999i
708708 0 0
709709 −2.05638 + 6.32887i −0.0772288 + 0.237686i −0.982216 0.187752i 0.939880π-0.939880\pi
0.904988 + 0.425438i 0.139880π0.139880\pi
710710 0 0
711711 −7.04931 21.6956i −0.264370 0.813647i
712712 0 0
713713 −6.07300 1.97324i −0.227436 0.0738983i
714714 0 0
715715 4.56464 23.1520i 0.170708 0.865834i
716716 0 0
717717 −18.1818 + 25.0250i −0.679010 + 0.934577i
718718 0 0
719719 −15.0272 10.9179i −0.560420 0.407169i 0.271192 0.962525i 0.412582π-0.412582\pi
−0.831613 + 0.555356i 0.812582π0.812582\pi
720720 0 0
721721 24.7862 18.0083i 0.923088 0.670662i
722722 0 0
723723 30.4114 9.88126i 1.13101 0.367488i
724724 0 0
725725 −28.3009 + 6.89548i −1.05107 + 0.256092i
726726 0 0
727727 35.3130 11.4739i 1.30969 0.425543i 0.430746 0.902473i 0.358250π-0.358250\pi
0.878942 + 0.476930i 0.158250π0.158250\pi
728728 0 0
729729 −6.02475 + 4.37724i −0.223139 + 0.162120i
730730 0 0
731731 20.5152 + 14.9052i 0.758782 + 0.551287i
732732 0 0
733733 14.6472 20.1602i 0.541008 0.744634i −0.447750 0.894159i 0.647774π-0.647774\pi
0.988758 + 0.149525i 0.0477744π0.0477744\pi
734734 0 0
735735 7.46113 + 16.1129i 0.275208 + 0.594334i
736736 0 0
737737 30.1650 + 9.80121i 1.11114 + 0.361032i
738738 0 0
739739 12.3983 + 38.1581i 0.456080 + 1.40367i 0.869862 + 0.493294i 0.164207π0.164207\pi
−0.413782 + 0.910376i 0.635793π0.635793\pi
740740 0 0
741741 −12.3312 + 37.9516i −0.452998 + 1.39419i
742742 0 0
743743 31.3057i 1.14850i −0.818681 0.574248i 0.805295π-0.805295\pi
0.818681 0.574248i 0.194705π-0.194705\pi
744744 0 0
745745 −18.9731 3.74073i −0.695119 0.137050i
746746 0 0
747747 8.25681 + 11.3645i 0.302101 + 0.415806i
748748 0 0
749749 −27.8696 −1.01833
750750 0 0
751751 8.67841 0.316680 0.158340 0.987385i 0.449386π-0.449386\pi
0.158340 + 0.987385i 0.449386π0.449386\pi
752752 0 0
753753 −0.998805 1.37474i −0.0363985 0.0500982i
754754 0 0
755755 −13.8377 2.72824i −0.503606 0.0992909i
756756 0 0
757757 27.9929i 1.01742i −0.860938 0.508709i 0.830123π-0.830123\pi
0.860938 0.508709i 0.169877π-0.169877\pi
758758 0 0
759759 −1.45311 + 4.47220i −0.0527444 + 0.162331i
760760 0 0
761761 −7.51220 23.1202i −0.272317 0.838106i −0.989917 0.141650i 0.954759π-0.954759\pi
0.717600 0.696456i 0.245241π-0.245241\pi
762762 0 0
763763 −17.3816 5.64763i −0.629257 0.204458i
764764 0 0
765765 12.1538 + 26.2470i 0.439420 + 0.948964i
766766 0 0
767767 16.9768 23.3665i 0.612996 0.843716i
768768 0 0
769769 4.52205 + 3.28546i 0.163069 + 0.118477i 0.666327 0.745660i 0.267865π-0.267865\pi
−0.503258 + 0.864136i 0.667865π0.667865\pi
770770 0 0
771771 −27.7534 + 20.1640i −0.999513 + 0.726188i
772772 0 0
773773 −3.24785 + 1.05529i −0.116817 + 0.0379562i −0.366842 0.930283i 0.619561π-0.619561\pi
0.250025 + 0.968239i 0.419561π0.419561\pi
774774 0 0
775775 −17.6242 28.5436i −0.633080 1.02532i
776776 0 0
777777 −40.3803 + 13.1204i −1.44864 + 0.470690i
778778 0 0
779779 17.8252 12.9508i 0.638654 0.464009i
780780 0 0
781781 17.2537 + 12.5356i 0.617387 + 0.448558i
782782 0 0
783783 −7.50992 + 10.3365i −0.268383 + 0.369397i
784784 0 0
785785 −5.16708 + 26.2076i −0.184421 + 0.935388i
786786 0 0
787787 −45.8378 14.8936i −1.63394 0.530899i −0.658768 0.752346i 0.728922π-0.728922\pi
−0.975172 + 0.221447i 0.928922π0.928922\pi
788788 0 0
789789 −9.35764 28.7999i −0.333141 1.02530i
790790 0 0
791791 9.63893 29.6656i 0.342721 1.05479i
792792 0 0
793793 17.6031i 0.625103i
794794 0 0
795795 10.2473 18.3704i 0.363433 0.651531i
796796 0 0
797797 −6.10087 8.39713i −0.216104 0.297442i 0.687178 0.726489i 0.258849π-0.258849\pi
−0.903282 + 0.429048i 0.858849π0.858849\pi
798798 0 0
799799 −64.5677 −2.28424
800800 0 0
801801 21.1770 0.748254
802802 0 0
803803 4.68352 + 6.44631i 0.165278 + 0.227485i
804804 0 0
805805 0.471660 + 3.92827i 0.0166238 + 0.138453i
806806 0 0
807807 28.4681i 1.00213i
808808 0 0
809809 4.30668 13.2546i 0.151415 0.466007i −0.846365 0.532603i 0.821214π-0.821214\pi
0.997780 + 0.0665959i 0.0212138π0.0212138\pi
810810 0 0
811811 −3.49190 10.7470i −0.122617 0.377377i 0.870842 0.491563i 0.163574π-0.163574\pi
−0.993459 + 0.114186i 0.963574π0.963574\pi
812812 0 0
813813 −20.6877 6.72184i −0.725550 0.235745i
814814 0 0
815815 33.8498 + 18.8819i 1.18571 + 0.661404i
816816 0 0
817817 8.66564 11.9272i 0.303172 0.417281i
818818 0 0
819819 14.5508 + 10.5718i 0.508446 + 0.369408i
820820 0 0
821821 19.6322 14.2636i 0.685169 0.497805i −0.189899 0.981804i 0.560816π-0.560816\pi
0.875069 + 0.483999i 0.160816π0.160816\pi
822822 0 0
823823 1.00113 0.325286i 0.0348971 0.0113387i −0.291516 0.956566i 0.594160π-0.594160\pi
0.326414 + 0.945227i 0.394160π0.394160\pi
824824 0 0
825825 −21.0197 + 12.9786i −0.731811 + 0.451856i
826826 0 0
827827 30.3729 9.86874i 1.05617 0.343170i 0.271082 0.962556i 0.412619π-0.412619\pi
0.785086 + 0.619387i 0.212619π0.212619\pi
828828 0 0
829829 −23.5676 + 17.1229i −0.818536 + 0.594701i −0.916293 0.400509i 0.868833π-0.868833\pi
0.0977566 + 0.995210i 0.468833π0.468833\pi
830830 0 0
831831 −9.30034 6.75709i −0.322625 0.234401i
832832 0 0
833833 13.3302 18.3474i 0.461863 0.635700i
834834 0 0
835835 11.4149 10.5876i 0.395029 0.366398i
836836 0 0
837837 −13.9940 4.54694i −0.483705 0.157165i
838838 0 0
839839 3.70912 + 11.4155i 0.128053 + 0.394107i 0.994445 0.105258i 0.0335667π-0.0335667\pi
−0.866392 + 0.499365i 0.833567π0.833567\pi
840840 0 0
841841 1.52643 4.69786i 0.0526354 0.161995i
842842 0 0
843843 55.8283i 1.92283i
844844 0 0
845845 15.0673 + 16.2447i 0.518331 + 0.558834i
846846 0 0
847847 6.70787 + 9.23259i 0.230485 + 0.317236i
848848 0 0
849849 −34.3007 −1.17720
850850 0 0
851851 9.70015 0.332517
852852 0 0
853853 −4.02243 5.53640i −0.137725 0.189563i 0.734583 0.678519i 0.237378π-0.237378\pi
−0.872308 + 0.488956i 0.837378π0.837378\pi
854854 0 0
855855 15.2596 7.06602i 0.521869 0.241653i
856856 0 0
857857 51.2474i 1.75058i −0.483601 0.875289i 0.660671π-0.660671\pi
0.483601 0.875289i 0.339329π-0.339329\pi
858858 0 0
859859 4.14366 12.7529i 0.141380 0.435123i −0.855148 0.518384i 0.826534π-0.826534\pi
0.996528 + 0.0832616i 0.0265337π0.0265337\pi
860860 0 0
861861 −7.62346 23.4626i −0.259807 0.799603i
862862 0 0
863863 −12.3753 4.02097i −0.421260 0.136876i 0.0907135 0.995877i 0.471085π-0.471085\pi
−0.511973 + 0.859001i 0.671085π0.671085\pi
864864 0 0
865865 −3.19151 + 0.383198i −0.108515 + 0.0130291i
866866 0 0
867867 31.5512 43.4265i 1.07153 1.47484i
868868 0 0
869869 −20.1316 14.6264i −0.682917 0.496168i
870870 0 0
871871 −55.7021 + 40.4700i −1.88739 + 1.37127i
872872 0 0
873873 −0.902266 + 0.293164i −0.0305371 + 0.00992210i
874874 0 0
875875 −11.4601 + 17.3405i −0.387423 + 0.586217i
876876 0 0
877877 19.0208 6.18024i 0.642288 0.208692i 0.0302772 0.999542i 0.490361π-0.490361\pi
0.612011 + 0.790850i 0.290361π0.290361\pi
878878 0 0
879879 −26.3127 + 19.1173i −0.887504 + 0.644809i
880880 0 0
881881 −15.3624 11.1614i −0.517572 0.376038i 0.298116 0.954530i 0.403642π-0.403642\pi
−0.815689 + 0.578491i 0.803642π0.803642\pi
882882 0 0
883883 −16.1290 + 22.1997i −0.542784 + 0.747078i −0.989011 0.147842i 0.952767π-0.952767\pi
0.446227 + 0.894920i 0.352767π0.352767\pi
884884 0 0
885885 −30.0207 + 3.60452i −1.00913 + 0.121165i
886886 0 0
887887 0.524691 + 0.170483i 0.0176174 + 0.00572424i 0.317812 0.948154i 0.397052π-0.397052\pi
−0.300195 + 0.953878i 0.597052π0.597052\pi
888888 0 0
889889 2.28429 + 7.03033i 0.0766127 + 0.235790i
890890 0 0
891891 −7.47996 + 23.0210i −0.250588 + 0.771231i
892892 0 0
893893 37.5387i 1.25618i
894894 0 0
895895 −36.6256 + 16.9596i −1.22426 + 0.566897i
896896 0 0
897897 −5.99999 8.25827i −0.200334 0.275736i
898898 0 0
899899 39.0865 1.30361
900900 0 0
901901 −26.8661 −0.895040
902902 0 0
903903 −9.70272 13.3547i −0.322886 0.444415i
904904 0 0
905905 30.3061 + 32.6742i 1.00741 + 1.08613i
906906 0 0
907907 25.7362i 0.854556i 0.904120 + 0.427278i 0.140527π0.140527\pi
−0.904120 + 0.427278i 0.859473π0.859473\pi
908908 0 0
909909 0.634273 1.95209i 0.0210375 0.0647468i
910910 0 0
911911 −2.28613 7.03599i −0.0757429 0.233113i 0.906016 0.423244i 0.139109π-0.139109\pi
−0.981759 + 0.190131i 0.939109π0.939109\pi
912912 0 0
913913 14.5732 + 4.73513i 0.482304 + 0.156710i
914914 0 0
915915 13.5110 12.5318i 0.446661 0.414289i
916916 0 0
917917 11.6265 16.0025i 0.383940 0.528449i
918918 0 0
919919 −44.0259 31.9867i −1.45228 1.05514i −0.985292 0.170880i 0.945339π-0.945339\pi
−0.466989 0.884263i 0.654661π-0.654661\pi
920920 0 0
921921 43.6397 31.7061i 1.43798 1.04475i
922922 0 0
923923 −44.0300 + 14.3062i −1.44926 + 0.470894i
924924 0 0
925925 38.8613 + 32.9646i 1.27775 + 1.08387i
926926 0 0
927927 31.6801 10.2935i 1.04051 0.338082i
928928 0 0
929929 26.2460 19.0689i 0.861105 0.625629i −0.0670805 0.997748i 0.521368π-0.521368\pi
0.928185 + 0.372118i 0.121368π0.121368\pi
930930 0 0
931931 −10.6669 7.74997i −0.349594 0.253995i
932932 0 0
933933 −9.82082 + 13.5172i −0.321519 + 0.442533i
934934 0 0
935935 27.5545 + 15.3703i 0.901129 + 0.502662i
936936 0 0
937937 0.0671382 + 0.0218145i 0.00219331 + 0.000712649i 0.310113 0.950700i 0.399633π-0.399633\pi
−0.307920 + 0.951412i 0.599633π0.599633\pi
938938 0 0
939939 −0.887091 2.73019i −0.0289491 0.0890963i
940940 0 0
941941 12.1981 37.5418i 0.397646 1.22383i −0.529235 0.848475i 0.677521π-0.677521\pi
0.926881 0.375354i 0.122479π-0.122479\pi
942942 0 0
943943 5.63618i 0.183539i
944944 0 0
945945 1.08685 + 9.05193i 0.0353552 + 0.294459i
946946 0 0
947947 −12.9232 17.7872i −0.419946 0.578007i 0.545663 0.838005i 0.316278π-0.316278\pi
−0.965609 + 0.259998i 0.916278π0.916278\pi
948948 0 0
949949 −17.2970 −0.561484
950950 0 0
951951 35.1472 1.13973
952952 0 0
953953 −6.81994 9.38684i −0.220920 0.304070i 0.684143 0.729348i 0.260176π-0.260176\pi
−0.905063 + 0.425278i 0.860176π0.860176\pi
954954 0 0
955955 −21.0690 + 37.7706i −0.681775 + 1.22223i
956956 0 0
957957 28.7836i 0.930440i
958958 0 0
959959 6.47566 19.9300i 0.209110 0.643574i
960960 0 0
961961 4.33054 + 13.3280i 0.139695 + 0.429937i
962962 0 0
963963 −28.8180 9.36354i −0.928647 0.301736i
964964 0 0
965965 0.654826 3.32129i 0.0210796 0.106916i
966966 0 0
967967 2.31918 3.19207i 0.0745797 0.102650i −0.770097 0.637926i 0.779792π-0.779792\pi
0.844677 + 0.535276i 0.179792π0.179792\pi
968968 0 0
969969 −43.1651 31.3612i −1.38666 1.00747i
970970 0 0
971971 −38.8777 + 28.2463i −1.24765 + 0.906467i −0.998083 0.0618915i 0.980287π-0.980287\pi
−0.249562 + 0.968359i 0.580287π0.580287\pi
972972 0 0
973973 −6.46317 + 2.10001i −0.207200 + 0.0673233i
974974 0 0
975975 4.02715 53.4749i 0.128972 1.71257i
976976 0 0
977977 0.652788 0.212104i 0.0208845 0.00678580i −0.298556 0.954392i 0.596505π-0.596505\pi
0.319441 + 0.947606i 0.396505π0.396505\pi
978978 0 0
979979 18.6887 13.5781i 0.597293 0.433959i
980980 0 0
981981 −16.0756 11.6796i −0.513256 0.372902i
982982 0 0
983983 −7.37476 + 10.1505i −0.235218 + 0.323750i −0.910266 0.414024i 0.864123π-0.864123\pi
0.675048 + 0.737774i 0.264123π0.264123\pi
984984 0 0
985985 7.05889 + 15.2443i 0.224915 + 0.485722i
986986 0 0
987987 39.9741 + 12.9884i 1.27239 + 0.413424i
988988 0 0
989989 1.16539 + 3.58671i 0.0370573 + 0.114051i
990990 0 0
991991 0.697131 2.14555i 0.0221451 0.0681556i −0.939373 0.342896i 0.888592π-0.888592\pi
0.961518 + 0.274741i 0.0885920π0.0885920\pi
992992 0 0
993993 49.8156i 1.58085i
994994 0 0
995995 46.4909 + 9.16615i 1.47386 + 0.290586i
996996 0 0
997997 −8.75386 12.0487i −0.277238 0.381585i 0.647579 0.761998i 0.275782π-0.275782\pi
−0.924816 + 0.380414i 0.875782π0.875782\pi
998998 0 0
999999 22.3521 0.707188
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 400.2.y.d.369.7 32
4.3 odd 2 200.2.q.a.169.2 yes 32
20.3 even 4 1000.2.m.d.401.7 32
20.7 even 4 1000.2.m.e.401.2 32
20.19 odd 2 1000.2.q.c.849.7 32
25.2 odd 20 10000.2.a.br.1.3 16
25.4 even 10 inner 400.2.y.d.129.7 32
25.23 odd 20 10000.2.a.bq.1.14 16
100.3 even 20 1000.2.m.d.601.7 32
100.23 even 20 5000.2.a.r.1.3 16
100.27 even 20 5000.2.a.q.1.14 16
100.47 even 20 1000.2.m.e.601.2 32
100.71 odd 10 1000.2.q.c.649.7 32
100.79 odd 10 200.2.q.a.129.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.q.a.129.2 32 100.79 odd 10
200.2.q.a.169.2 yes 32 4.3 odd 2
400.2.y.d.129.7 32 25.4 even 10 inner
400.2.y.d.369.7 32 1.1 even 1 trivial
1000.2.m.d.401.7 32 20.3 even 4
1000.2.m.d.601.7 32 100.3 even 20
1000.2.m.e.401.2 32 20.7 even 4
1000.2.m.e.601.2 32 100.47 even 20
1000.2.q.c.649.7 32 100.71 odd 10
1000.2.q.c.849.7 32 20.19 odd 2
5000.2.a.q.1.14 16 100.27 even 20
5000.2.a.r.1.3 16 100.23 even 20
10000.2.a.bq.1.14 16 25.23 odd 20
10000.2.a.br.1.3 16 25.2 odd 20