Properties

Label 325.2.c.g.51.4
Level 325325
Weight 22
Character 325.51
Analytic conductor 2.5952.595
Analytic rank 00
Dimension 66
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] = [325,2,Mod(51,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("325.51"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 325.c (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,4,-10,0,0,0,0,6,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.595138065692.59513806569
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.5089536.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+2x4+2x3+16x224x+18 x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 23 2\cdot 3
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 51.4
Root 1.33641+1.33641i-1.33641 + 1.33641i of defining polynomial
Character χ\chi == 325.51
Dual form 325.2.c.g.51.3

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+0.571993iq2+0.428007q3+1.67282q4+0.244817iq6+2.67282iq7+2.10083iq82.81681q9+5.10083iq11+0.715980q12+(1.571993.24482i)q131.52884q14+2.14399q16+5.34565q171.61120iq186.24482iq19+1.14399iq212.91764q222.42801q23+0.899170iq24+(1.85601+0.899170i)q262.48963q27+4.47116iq28+2.67282q29+0.244817iq31+5.42801iq32+2.18319iq33+3.05767iq344.71203q363.32718iq37+3.57199q38+(0.6728241.38880i)q396.48963iq410.654353q4210.9176q43+8.53279iq441.38880iq462.67282iq47+0.917641q480.143987q49+2.28797q51+(2.629675.42801i)q52+4.20166q531.42405iq545.61515q562.67282iq57+1.52884iq580.899170iq595.81681q610.140034q627.52884iq63+1.18319q641.24877q66+2.18319iq67+8.94233q681.03920q696.24482iq715.91764iq7210.9608iq73+1.90312q7410.4465iq7613.6336q77+(0.794386+0.384851i)q783.63362q79+7.38485q81+3.71203q82+9.81681iq83+1.91369iq846.24482iq86+1.14399q8710.7160q88+7.63362iq89+(8.67282+4.20166i)q914.06163q92+0.104783iq93+1.52884q94+2.32322iq9611.3456iq970.0823593iq9814.3681iq99+O(q100)q+0.571993i q^{2} +0.428007 q^{3} +1.67282 q^{4} +0.244817i q^{6} +2.67282i q^{7} +2.10083i q^{8} -2.81681 q^{9} +5.10083i q^{11} +0.715980 q^{12} +(1.57199 - 3.24482i) q^{13} -1.52884 q^{14} +2.14399 q^{16} +5.34565 q^{17} -1.61120i q^{18} -6.24482i q^{19} +1.14399i q^{21} -2.91764 q^{22} -2.42801 q^{23} +0.899170i q^{24} +(1.85601 + 0.899170i) q^{26} -2.48963 q^{27} +4.47116i q^{28} +2.67282 q^{29} +0.244817i q^{31} +5.42801i q^{32} +2.18319i q^{33} +3.05767i q^{34} -4.71203 q^{36} -3.32718i q^{37} +3.57199 q^{38} +(0.672824 - 1.38880i) q^{39} -6.48963i q^{41} -0.654353 q^{42} -10.9176 q^{43} +8.53279i q^{44} -1.38880i q^{46} -2.67282i q^{47} +0.917641 q^{48} -0.143987 q^{49} +2.28797 q^{51} +(2.62967 - 5.42801i) q^{52} +4.20166 q^{53} -1.42405i q^{54} -5.61515 q^{56} -2.67282i q^{57} +1.52884i q^{58} -0.899170i q^{59} -5.81681 q^{61} -0.140034 q^{62} -7.52884i q^{63} +1.18319 q^{64} -1.24877 q^{66} +2.18319i q^{67} +8.94233 q^{68} -1.03920 q^{69} -6.24482i q^{71} -5.91764i q^{72} -10.9608i q^{73} +1.90312 q^{74} -10.4465i q^{76} -13.6336 q^{77} +(0.794386 + 0.384851i) q^{78} -3.63362 q^{79} +7.38485 q^{81} +3.71203 q^{82} +9.81681i q^{83} +1.91369i q^{84} -6.24482i q^{86} +1.14399 q^{87} -10.7160 q^{88} +7.63362i q^{89} +(8.67282 + 4.20166i) q^{91} -4.06163 q^{92} +0.104783i q^{93} +1.52884 q^{94} +2.32322i q^{96} -11.3456i q^{97} -0.0823593i q^{98} -14.3681i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+4q310q4+6q9+8q13+8q14+10q168q17+24q2216q23+14q26+28q274q2934q36+20q3816q3944q4224q4336q48+8q94+O(q100) 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 8 q^{14} + 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} + 14 q^{26} + 28 q^{27} - 4 q^{29} - 34 q^{36} + 20 q^{38} - 16 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48}+ \cdots - 8 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/325Z)×\left(\mathbb{Z}/325\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) 11 1-1

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 0.571993i 0.404460i 0.979338 + 0.202230i 0.0648189π0.0648189\pi
−0.979338 + 0.202230i 0.935181π0.935181\pi
33 0.428007 0.247110 0.123555 0.992338i 0.460570π-0.460570\pi
0.123555 + 0.992338i 0.460570π0.460570\pi
44 1.67282 0.836412
55 0 0
66 0.244817i 0.0999461i
77 2.67282i 1.01023i 0.863051 + 0.505116i 0.168550π0.168550\pi
−0.863051 + 0.505116i 0.831450π0.831450\pi
88 2.10083i 0.742756i
99 −2.81681 −0.938937
1010 0 0
1111 5.10083i 1.53796i 0.639274 + 0.768979i 0.279235π0.279235\pi
−0.639274 + 0.768979i 0.720765π0.720765\pi
1212 0.715980 0.206686
1313 1.57199 3.24482i 0.435992 0.899950i
1414 −1.52884 −0.408599
1515 0 0
1616 2.14399 0.535997
1717 5.34565 1.29651 0.648255 0.761423i 0.275499π-0.275499\pi
0.648255 + 0.761423i 0.275499π0.275499\pi
1818 1.61120i 0.379763i
1919 6.24482i 1.43266i −0.697762 0.716330i 0.745821π-0.745821\pi
0.697762 0.716330i 0.254179π-0.254179\pi
2020 0 0
2121 1.14399i 0.249638i
2222 −2.91764 −0.622043
2323 −2.42801 −0.506274 −0.253137 0.967430i 0.581462π-0.581462\pi
−0.253137 + 0.967430i 0.581462π0.581462\pi
2424 0.899170i 0.183542i
2525 0 0
2626 1.85601 + 0.899170i 0.363994 + 0.176342i
2727 −2.48963 −0.479130
2828 4.47116i 0.844970i
2929 2.67282 0.496331 0.248165 0.968718i 0.420172π-0.420172\pi
0.248165 + 0.968718i 0.420172π0.420172\pi
3030 0 0
3131 0.244817i 0.0439704i 0.999758 + 0.0219852i 0.00699867π0.00699867\pi
−0.999758 + 0.0219852i 0.993001π0.993001\pi
3232 5.42801i 0.959545i
3333 2.18319i 0.380045i
3434 3.05767i 0.524387i
3535 0 0
3636 −4.71203 −0.785338
3737 3.32718i 0.546984i −0.961874 0.273492i 0.911821π-0.911821\pi
0.961874 0.273492i 0.0881788π-0.0881788\pi
3838 3.57199 0.579454
3939 0.672824 1.38880i 0.107738 0.222387i
4040 0 0
4141 6.48963i 1.01351i −0.862090 0.506755i 0.830845π-0.830845\pi
0.862090 0.506755i 0.169155π-0.169155\pi
4242 −0.654353 −0.100969
4343 −10.9176 −1.66492 −0.832462 0.554082i 0.813070π-0.813070\pi
−0.832462 + 0.554082i 0.813070π0.813070\pi
4444 8.53279i 1.28637i
4545 0 0
4646 1.38880i 0.204768i
4747 2.67282i 0.389871i −0.980816 0.194936i 0.937550π-0.937550\pi
0.980816 0.194936i 0.0624498π-0.0624498\pi
4848 0.917641 0.132450
4949 −0.143987 −0.0205695
5050 0 0
5151 2.28797 0.320380
5252 2.62967 5.42801i 0.364669 0.752729i
5353 4.20166 0.577143 0.288571 0.957458i 0.406820π-0.406820\pi
0.288571 + 0.957458i 0.406820π0.406820\pi
5454 1.42405i 0.193789i
5555 0 0
5656 −5.61515 −0.750356
5757 2.67282i 0.354024i
5858 1.52884i 0.200746i
5959 0.899170i 0.117062i −0.998286 0.0585310i 0.981358π-0.981358\pi
0.998286 0.0585310i 0.0186416π-0.0186416\pi
6060 0 0
6161 −5.81681 −0.744766 −0.372383 0.928079i 0.621459π-0.621459\pi
−0.372383 + 0.928079i 0.621459π0.621459\pi
6262 −0.140034 −0.0177843
6363 7.52884i 0.948544i
6464 1.18319 0.147899
6565 0 0
6666 −1.24877 −0.153713
6767 2.18319i 0.266719i 0.991068 + 0.133360i 0.0425765π0.0425765\pi
−0.991068 + 0.133360i 0.957423π0.957423\pi
6868 8.94233 1.08442
6969 −1.03920 −0.125105
7070 0 0
7171 6.24482i 0.741123i −0.928808 0.370562i 0.879165π-0.879165\pi
0.928808 0.370562i 0.120835π-0.120835\pi
7272 5.91764i 0.697401i
7373 10.9608i 1.28286i −0.767180 0.641432i 0.778341π-0.778341\pi
0.767180 0.641432i 0.221659π-0.221659\pi
7474 1.90312 0.221233
7575 0 0
7676 10.4465i 1.19829i
7777 −13.6336 −1.55370
7878 0.794386 + 0.384851i 0.0899465 + 0.0435758i
7979 −3.63362 −0.408814 −0.204407 0.978886i 0.565527π-0.565527\pi
−0.204407 + 0.978886i 0.565527π0.565527\pi
8080 0 0
8181 7.38485 0.820539
8282 3.71203 0.409925
8383 9.81681i 1.07753i 0.842455 + 0.538767i 0.181110π0.181110\pi
−0.842455 + 0.538767i 0.818890π0.818890\pi
8484 1.91369i 0.208800i
8585 0 0
8686 6.24482i 0.673396i
8787 1.14399 0.122648
8888 −10.7160 −1.14233
8989 7.63362i 0.809162i 0.914502 + 0.404581i 0.132583π0.132583\pi
−0.914502 + 0.404581i 0.867417π0.867417\pi
9090 0 0
9191 8.67282 + 4.20166i 0.909159 + 0.440454i
9292 −4.06163 −0.423454
9393 0.104783i 0.0108655i
9494 1.52884 0.157688
9595 0 0
9696 2.32322i 0.237113i
9797 11.3456i 1.15198i −0.817458 0.575988i 0.804617π-0.804617\pi
0.817458 0.575988i 0.195383π-0.195383\pi
9898 0.0823593i 0.00831955i
9999 14.3681i 1.44405i
100100 0 0
101101 −10.8560 −1.08021 −0.540107 0.841596i 0.681616π-0.681616\pi
−0.540107 + 0.841596i 0.681616π0.681616\pi
102102 1.30871i 0.129581i
103103 10.6297 1.04737 0.523686 0.851911i 0.324556π-0.324556\pi
0.523686 + 0.851911i 0.324556π0.324556\pi
104104 6.81681 + 3.30249i 0.668443 + 0.323836i
105105 0 0
106106 2.40332i 0.233431i
107107 −0.140034 −0.0135376 −0.00676878 0.999977i 0.502155π-0.502155\pi
−0.00676878 + 0.999977i 0.502155π0.502155\pi
108108 −4.16472 −0.400750
109109 9.05767i 0.867568i −0.901017 0.433784i 0.857178π-0.857178\pi
0.901017 0.433784i 0.142822π-0.142822\pi
110110 0 0
111111 1.42405i 0.135165i
112112 5.73050i 0.541481i
113113 −12.9793 −1.22099 −0.610493 0.792021i 0.709029π-0.709029\pi
−0.610493 + 0.792021i 0.709029π0.709029\pi
114114 1.52884 0.143189
115115 0 0
116116 4.47116 0.415137
117117 −4.42801 + 9.14003i −0.409369 + 0.844996i
118118 0.514319 0.0473469
119119 14.2880i 1.30978i
120120 0 0
121121 −15.0185 −1.36532
122122 3.32718i 0.301228i
123123 2.77761i 0.250448i
124124 0.409536i 0.0367774i
125125 0 0
126126 4.30644 0.383649
127127 12.0616 1.07030 0.535148 0.844758i 0.320256π-0.320256\pi
0.535148 + 0.844758i 0.320256π0.320256\pi
128128 11.5328i 1.01936i
129129 −4.67282 −0.411419
130130 0 0
131131 7.63362 0.666953 0.333476 0.942758i 0.391778π-0.391778\pi
0.333476 + 0.942758i 0.391778π0.391778\pi
132132 3.65209i 0.317874i
133133 16.6913 1.44732
134134 −1.24877 −0.107877
135135 0 0
136136 11.2303i 0.962990i
137137 3.43196i 0.293212i 0.989195 + 0.146606i 0.0468350π0.0468350\pi
−0.989195 + 0.146606i 0.953165π0.953165\pi
138138 0.594417i 0.0506002i
139139 −0.942326 −0.0799270 −0.0399635 0.999201i 0.512724π-0.512724\pi
−0.0399635 + 0.999201i 0.512724π0.512724\pi
140140 0 0
141141 1.14399i 0.0963410i
142142 3.57199 0.299755
143143 16.5513 + 8.01847i 1.38409 + 0.670538i
144144 −6.03920 −0.503267
145145 0 0
146146 6.26950 0.518868
147147 −0.0616272 −0.00508293
148148 5.56578i 0.457504i
149149 11.3456i 0.929472i 0.885449 + 0.464736i 0.153851π0.153851\pi
−0.885449 + 0.464736i 0.846149π0.846149\pi
150150 0 0
151151 21.0224i 1.71078i 0.517984 + 0.855390i 0.326683π0.326683\pi
−0.517984 + 0.855390i 0.673317π0.673317\pi
152152 13.1193 1.06412
153153 −15.0577 −1.21734
154154 7.79834i 0.628408i
155155 0 0
156156 1.12552 2.32322i 0.0901134 0.186007i
157157 9.83528 0.784941 0.392470 0.919765i 0.371621π-0.371621\pi
0.392470 + 0.919765i 0.371621π0.371621\pi
158158 2.07841i 0.165349i
159159 1.79834 0.142618
160160 0 0
161161 6.48963i 0.511455i
162162 4.22408i 0.331875i
163163 12.3849i 0.970056i −0.874499 0.485028i 0.838809π-0.838809\pi
0.874499 0.485028i 0.161191π-0.161191\pi
164164 10.8560i 0.847712i
165165 0 0
166166 −5.61515 −0.435820
167167 8.50811i 0.658377i 0.944264 + 0.329188i 0.106775π0.106775\pi
−0.944264 + 0.329188i 0.893225π0.893225\pi
168168 −2.40332 −0.185420
169169 −8.05767 10.2017i −0.619821 0.784743i
170170 0 0
171171 17.5905i 1.34518i
172172 −18.2633 −1.39256
173173 −21.5473 −1.63821 −0.819106 0.573643i 0.805530π-0.805530\pi
−0.819106 + 0.573643i 0.805530π0.805530\pi
174174 0.654353i 0.0496063i
175175 0 0
176176 10.9361i 0.824340i
177177 0.384851i 0.0289271i
178178 −4.36638 −0.327274
179179 −2.56804 −0.191944 −0.0959722 0.995384i 0.530596π-0.530596\pi
−0.0959722 + 0.995384i 0.530596π0.530596\pi
180180 0 0
181181 13.7305 1.02058 0.510290 0.860002i 0.329538π-0.329538\pi
0.510290 + 0.860002i 0.329538π0.329538\pi
182182 −2.40332 + 4.96080i −0.178146 + 0.367719i
183183 −2.48963 −0.184039
184184 5.10083i 0.376038i
185185 0 0
186186 −0.0599353 −0.00439467
187187 27.2672i 1.99398i
188188 4.47116i 0.326093i
189189 6.65435i 0.484033i
190190 0 0
191191 −10.6913 −0.773595 −0.386797 0.922165i 0.626419π-0.626419\pi
−0.386797 + 0.922165i 0.626419π0.626419\pi
192192 0.506413 0.0365472
193193 19.2593i 1.38632i 0.720785 + 0.693159i 0.243781π0.243781\pi
−0.720785 + 0.693159i 0.756219π0.756219\pi
194194 6.48963 0.465929
195195 0 0
196196 −0.240864 −0.0172046
197197 17.1809i 1.22409i −0.790823 0.612045i 0.790347π-0.790347\pi
0.790823 0.612045i 0.209653π-0.209653\pi
198198 8.21844 0.584059
199199 −11.5473 −0.818567 −0.409283 0.912407i 0.634221π-0.634221\pi
−0.409283 + 0.912407i 0.634221π0.634221\pi
200200 0 0
201201 0.934420i 0.0659089i
202202 6.20957i 0.436904i
203203 7.14399i 0.501410i
204204 3.82738 0.267970
205205 0 0
206206 6.08010i 0.423621i
207207 6.83923 0.475360
208208 3.37033 6.95684i 0.233691 0.482370i
209209 31.8538 2.20337
210210 0 0
211211 24.1233 1.66071 0.830357 0.557232i 0.188137π-0.188137\pi
0.830357 + 0.557232i 0.188137π0.188137\pi
212212 7.02864 0.482729
213213 2.67282i 0.183139i
214214 0.0800983i 0.00547541i
215215 0 0
216216 5.23030i 0.355877i
217217 −0.654353 −0.0444203
218218 5.18093 0.350897
219219 4.69129i 0.317008i
220220 0 0
221221 8.40332 17.3456i 0.565269 1.16679i
222222 0.814549 0.0546690
223223 5.73050i 0.383743i 0.981420 + 0.191871i 0.0614556π0.0614556\pi
−0.981420 + 0.191871i 0.938544π0.938544\pi
224224 −14.5081 −0.969364
225225 0 0
226226 7.42405i 0.493841i
227227 2.95289i 0.195990i 0.995187 + 0.0979951i 0.0312430π0.0312430\pi
−0.995187 + 0.0979951i 0.968757π0.968757\pi
228228 4.47116i 0.296110i
229229 25.2593i 1.66918i 0.550869 + 0.834592i 0.314297π0.314297\pi
−0.550869 + 0.834592i 0.685703π0.685703\pi
230230 0 0
231231 −5.83528 −0.383933
232232 5.61515i 0.368653i
233233 23.3456 1.52942 0.764712 0.644372i 0.222881π-0.222881\pi
0.764712 + 0.644372i 0.222881π0.222881\pi
234234 −5.22804 2.53279i −0.341768 0.165574i
235235 0 0
236236 1.50415i 0.0979120i
237237 −1.55521 −0.101022
238238 −8.17262 −0.529753
239239 3.79213i 0.245292i 0.992450 + 0.122646i 0.0391380π0.0391380\pi
−0.992450 + 0.122646i 0.960862π0.960862\pi
240240 0 0
241241 3.43196i 0.221072i −0.993872 0.110536i 0.964743π-0.964743\pi
0.993872 0.110536i 0.0352567π-0.0352567\pi
242242 8.59046i 0.552216i
243243 10.6297 0.681893
244244 −9.73050 −0.622931
245245 0 0
246246 1.58877 0.101296
247247 −20.2633 9.81681i −1.28932 0.624629i
248248 −0.514319 −0.0326593
249249 4.20166i 0.266269i
250250 0 0
251251 −25.4689 −1.60758 −0.803791 0.594911i 0.797187π-0.797187\pi
−0.803791 + 0.594911i 0.797187π0.797187\pi
252252 12.5944i 0.793374i
253253 12.3849i 0.778629i
254254 6.89917i 0.432892i
255255 0 0
256256 −4.23030 −0.264394
257257 −9.26724 −0.578075 −0.289037 0.957318i 0.593335π-0.593335\pi
−0.289037 + 0.957318i 0.593335π0.593335\pi
258258 2.67282i 0.166403i
259259 8.89296 0.552581
260260 0 0
261261 −7.52884 −0.466023
262262 4.36638i 0.269756i
263263 8.14794 0.502423 0.251212 0.967932i 0.419171π-0.419171\pi
0.251212 + 0.967932i 0.419171π0.419171\pi
264264 −4.58651 −0.282280
265265 0 0
266266 9.54731i 0.585383i
267267 3.26724i 0.199952i
268268 3.65209i 0.223087i
269269 1.14399 0.0697501 0.0348750 0.999392i 0.488897π-0.488897\pi
0.0348750 + 0.999392i 0.488897π0.488897\pi
270270 0 0
271271 3.18714i 0.193605i −0.995304 0.0968026i 0.969138π-0.969138\pi
0.995304 0.0968026i 0.0308615π-0.0308615\pi
272272 11.4610 0.694925
273273 3.71203 + 1.79834i 0.224662 + 0.108840i
274274 −1.96306 −0.118593
275275 0 0
276276 −1.73840 −0.104640
277277 −7.62571 −0.458185 −0.229092 0.973405i 0.573576π-0.573576\pi
−0.229092 + 0.973405i 0.573576π0.573576\pi
278278 0.539004i 0.0323273i
279279 0.689603i 0.0412854i
280280 0 0
281281 20.2386i 1.20733i −0.797237 0.603667i 0.793706π-0.793706\pi
0.797237 0.603667i 0.206294π-0.206294\pi
282282 0.654353 0.0389661
283283 −19.8969 −1.18275 −0.591374 0.806397i 0.701414π-0.701414\pi
−0.591374 + 0.806397i 0.701414π0.701414\pi
284284 10.4465i 0.619884i
285285 0 0
286286 −4.58651 + 9.46721i −0.271206 + 0.559808i
287287 17.3456 1.02388
288288 15.2897i 0.900952i
289289 11.5759 0.680938
290290 0 0
291291 4.85601i 0.284665i
292292 18.3355i 1.07300i
293293 26.0185i 1.52002i 0.649914 + 0.760008i 0.274805π0.274805\pi
−0.649914 + 0.760008i 0.725195π0.725195\pi
294294 0.0352503i 0.00205584i
295295 0 0
296296 6.98983 0.406276
297297 12.6992i 0.736882i
298298 −6.48963 −0.375934
299299 −3.81681 + 7.87844i −0.220732 + 0.455622i
300300 0 0
301301 29.1809i 1.68196i
302302 −12.0247 −0.691943
303303 −4.64645 −0.266931
304304 13.3888i 0.767901i
305305 0 0
306306 8.61289i 0.492366i
307307 2.39276i 0.136562i 0.997666 + 0.0682809i 0.0217514π0.0217514\pi
−0.997666 + 0.0682809i 0.978249π0.978249\pi
308308 −22.8066 −1.29953
309309 4.54957 0.258816
310310 0 0
311311 3.54731 0.201149 0.100575 0.994930i 0.467932π-0.467932\pi
0.100575 + 0.994930i 0.467932π0.467932\pi
312312 2.91764 + 1.41349i 0.165179 + 0.0800230i
313313 −4.97927 −0.281445 −0.140722 0.990049i 0.544943π-0.544943\pi
−0.140722 + 0.990049i 0.544943π0.544943\pi
314314 5.62571i 0.317477i
315315 0 0
316316 −6.07841 −0.341937
317317 18.5944i 1.04437i −0.852833 0.522183i 0.825118π-0.825118\pi
0.852833 0.522183i 0.174882π-0.174882\pi
318318 1.02864i 0.0576831i
319319 13.6336i 0.763336i
320320 0 0
321321 −0.0599353 −0.00334526
322322 3.71203 0.206863
323323 33.3826i 1.85746i
324324 12.3536 0.686309
325325 0 0
326326 7.08405 0.392349
327327 3.87675i 0.214385i
328328 13.6336 0.752791
329329 7.14399 0.393861
330330 0 0
331331 5.91990i 0.325387i −0.986677 0.162694i 0.947982π-0.947982\pi
0.986677 0.162694i 0.0520182π-0.0520182\pi
332332 16.4218i 0.901263i
333333 9.37202i 0.513584i
334334 −4.86658 −0.266287
335335 0 0
336336 2.45269i 0.133805i
337337 −13.9216 −0.758358 −0.379179 0.925323i 0.623793π-0.623793\pi
−0.379179 + 0.925323i 0.623793π0.623793\pi
338338 5.83528 4.60894i 0.317397 0.250693i
339339 −5.55521 −0.301718
340340 0 0
341341 −1.24877 −0.0676247
342342 −10.0616 −0.544070
343343 18.3249i 0.989452i
344344 22.9361i 1.23663i
345345 0 0
346346 12.3249i 0.662592i
347347 −7.65831 −0.411119 −0.205560 0.978645i 0.565901π-0.565901\pi
−0.205560 + 0.978645i 0.565901π0.565901\pi
348348 1.91369 0.102584
349349 11.1809i 0.598501i 0.954175 + 0.299251i 0.0967367π0.0967367\pi
−0.954175 + 0.299251i 0.903263π0.903263\pi
350350 0 0
351351 −3.91369 + 8.07841i −0.208897 + 0.431193i
352352 −27.6873 −1.47574
353353 9.65209i 0.513729i −0.966447 0.256864i 0.917311π-0.917311\pi
0.966447 0.256864i 0.0826894π-0.0826894\pi
354354 0.220132 0.0116999
355355 0 0
356356 12.7697i 0.676793i
357357 6.11535i 0.323659i
358358 1.46890i 0.0776339i
359359 9.51206i 0.502027i 0.967984 + 0.251014i 0.0807639π0.0807639\pi
−0.967984 + 0.251014i 0.919236π0.919236\pi
360360 0 0
361361 −19.9977 −1.05251
362362 7.85375i 0.412784i
363363 −6.42801 −0.337383
364364 14.5081 + 7.02864i 0.760431 + 0.368401i
365365 0 0
366366 1.42405i 0.0744365i
367367 17.0040 0.887599 0.443800 0.896126i 0.353630π-0.353630\pi
0.443800 + 0.896126i 0.353630π0.353630\pi
368368 −5.20561 −0.271361
369369 18.2801i 0.951622i
370370 0 0
371371 11.2303i 0.583048i
372372 0.175284i 0.00908805i
373373 1.83528 0.0950273 0.0475136 0.998871i 0.484870π-0.484870\pi
0.0475136 + 0.998871i 0.484870π0.484870\pi
374374 −15.5967 −0.806485
375375 0 0
376376 5.61515 0.289579
377377 4.20166 8.67282i 0.216397 0.446673i
378378 3.80624 0.195772
379379 32.3681i 1.66264i −0.555797 0.831318i 0.687587π-0.687587\pi
0.555797 0.831318i 0.312413π-0.312413\pi
380380 0 0
381381 5.16246 0.264481
382382 6.11535i 0.312888i
383383 28.1417i 1.43798i 0.695023 + 0.718988i 0.255394π0.255394\pi
−0.695023 + 0.718988i 0.744606π0.744606\pi
384384 4.93611i 0.251895i
385385 0 0
386386 −11.0162 −0.560710
387387 30.7529 1.56326
388388 18.9793i 0.963526i
389389 −31.9585 −1.62036 −0.810181 0.586180i 0.800631π-0.800631\pi
−0.810181 + 0.586180i 0.800631π0.800631\pi
390390 0 0
391391 −12.9793 −0.656390
392392 0.302491i 0.0152781i
393393 3.26724 0.164811
394394 9.82738 0.495096
395395 0 0
396396 24.0353i 1.20782i
397397 12.7098i 0.637885i −0.947774 0.318942i 0.896672π-0.896672\pi
0.947774 0.318942i 0.103328π-0.103328\pi
398398 6.60498i 0.331078i
399399 7.14399 0.357647
400400 0 0
401401 0.979268i 0.0489023i −0.999701 0.0244512i 0.992216π-0.992216\pi
0.999701 0.0244512i 0.00778382π-0.00778382\pi
402402 −0.534482 −0.0266575
403403 0.794386 + 0.384851i 0.0395712 + 0.0191708i
404404 −18.1602 −0.903504
405405 0 0
406406 −4.08631 −0.202800
407407 16.9714 0.841239
408408 4.80664i 0.237964i
409409 7.79834i 0.385603i 0.981238 + 0.192802i 0.0617574π0.0617574\pi
−0.981238 + 0.192802i 0.938243π0.938243\pi
410410 0 0
411411 1.46890i 0.0724556i
412412 17.7816 0.876035
413413 2.40332 0.118260
414414 3.91200i 0.192264i
415415 0 0
416416 17.6129 + 8.53279i 0.863543 + 0.418354i
417417 −0.403322 −0.0197508
418418 18.2201i 0.891176i
419419 10.2017 0.498384 0.249192 0.968454i 0.419835π-0.419835\pi
0.249192 + 0.968454i 0.419835π0.419835\pi
420420 0 0
421421 31.1888i 1.52005i 0.649893 + 0.760025i 0.274814π0.274814\pi
−0.649893 + 0.760025i 0.725186π0.725186\pi
422422 13.7983i 0.671693i
423423 7.52884i 0.366065i
424424 8.82698i 0.428676i
425425 0 0
426426 1.52884 0.0740724
427427 15.5473i 0.752387i
428428 −0.234252 −0.0113230
429429 7.08405 + 3.43196i 0.342021 + 0.165697i
430430 0 0
431431 22.9361i 1.10479i 0.833581 + 0.552397i 0.186287π0.186287\pi
−0.833581 + 0.552397i 0.813713π0.813713\pi
432432 −5.33774 −0.256812
433433 16.2880 0.782750 0.391375 0.920231i 0.372000π-0.372000\pi
0.391375 + 0.920231i 0.372000π0.372000\pi
434434 0.374285i 0.0179663i
435435 0 0
436436 15.1519i 0.725644i
437437 15.1625i 0.725319i
438438 2.68339 0.128217
439439 23.7569 1.13385 0.566927 0.823768i 0.308132π-0.308132\pi
0.566927 + 0.823768i 0.308132π0.308132\pi
440440 0 0
441441 0.405583 0.0193135
442442 9.92159 + 4.80664i 0.471922 + 0.228629i
443443 2.75292 0.130795 0.0653976 0.997859i 0.479168π-0.479168\pi
0.0653976 + 0.997859i 0.479168π0.479168\pi
444444 2.38219i 0.113054i
445445 0 0
446446 −3.27781 −0.155209
447447 4.85601i 0.229682i
448448 3.16246i 0.149412i
449449 27.1025i 1.27905i −0.768772 0.639524i 0.779132π-0.779132\pi
0.768772 0.639524i 0.220868π-0.220868\pi
450450 0 0
451451 33.1025 1.55874
452452 −21.7120 −1.02125
453453 8.99774i 0.422751i
454454 −1.68903 −0.0792703
455455 0 0
456456 5.61515 0.262953
457457 40.1523i 1.87824i 0.343583 + 0.939122i 0.388359π0.388359\pi
−0.343583 + 0.939122i 0.611641π0.611641\pi
458458 −14.4482 −0.675119
459459 −13.3087 −0.621197
460460 0 0
461461 2.00791i 0.0935175i −0.998906 0.0467587i 0.985111π-0.985111\pi
0.998906 0.0467587i 0.0148892π-0.0148892\pi
462462 3.33774i 0.155286i
463463 2.67282i 0.124217i −0.998069 0.0621083i 0.980218π-0.980218\pi
0.998069 0.0621083i 0.0197824π-0.0197824\pi
464464 5.73050 0.266032
465465 0 0
466466 13.3536i 0.618591i
467467 −31.8890 −1.47565 −0.737824 0.674994i 0.764146π-0.764146\pi
−0.737824 + 0.674994i 0.764146π0.764146\pi
468468 −7.40727 + 15.2897i −0.342401 + 0.706765i
469469 −5.83528 −0.269448
470470 0 0
471471 4.20957 0.193967
472472 1.88900 0.0869484
473473 55.6890i 2.56058i
474474 0.889572i 0.0408594i
475475 0 0
476476 23.9013i 1.09551i
477477 −11.8353 −0.541900
478478 −2.16907 −0.0992110
479479 6.73445i 0.307705i −0.988094 0.153852i 0.950832π-0.950832\pi
0.988094 0.153852i 0.0491680π-0.0491680\pi
480480 0 0
481481 −10.7961 5.23030i −0.492259 0.238481i
482482 1.96306 0.0894148
483483 2.77761i 0.126385i
484484 −25.1233 −1.14197
485485 0 0
486486 6.08010i 0.275799i
487487 39.6521i 1.79681i 0.439170 + 0.898404i 0.355273π0.355273\pi
−0.439170 + 0.898404i 0.644727π0.644727\pi
488488 12.2201i 0.553179i
489489 5.30080i 0.239710i
490490 0 0
491491 31.0946 1.40328 0.701640 0.712531i 0.252451π-0.252451\pi
0.701640 + 0.712531i 0.252451π0.252451\pi
492492 4.64645i 0.209478i
493493 14.2880 0.643498
494494 5.61515 11.5905i 0.252638 0.521480i
495495 0 0
496496 0.524884i 0.0235680i
497497 16.6913 0.748707
498498 −2.40332 −0.107695
499499 13.1087i 0.586828i −0.955986 0.293414i 0.905209π-0.905209\pi
0.955986 0.293414i 0.0947914π-0.0947914\pi
500500 0 0
501501 3.64153i 0.162691i
502502 14.5680i 0.650203i
503503 8.59273 0.383131 0.191565 0.981480i 0.438644π-0.438644\pi
0.191565 + 0.981480i 0.438644π0.438644\pi
504504 15.8168 0.704537
505505 0 0
506506 7.08405 0.314924
507507 −3.44874 4.36638i −0.153164 0.193918i
508508 20.1770 0.895209
509509 29.8353i 1.32243i −0.750198 0.661213i 0.770042π-0.770042\pi
0.750198 0.661213i 0.229958π-0.229958\pi
510510 0 0
511511 29.2963 1.29599
512512 20.6459i 0.912428i
513513 15.5473i 0.686430i
514514 5.30080i 0.233808i
515515 0 0
516516 −7.81681 −0.344116
517517 13.6336 0.599606
518518 5.08671i 0.223497i
519519 −9.22239 −0.404818
520520 0 0
521521 10.0969 0.442352 0.221176 0.975234i 0.429010π-0.429010\pi
0.221176 + 0.975234i 0.429010π0.429010\pi
522522 4.30644i 0.188488i
523523 −16.1479 −0.706100 −0.353050 0.935604i 0.614855π-0.614855\pi
−0.353050 + 0.935604i 0.614855π0.614855\pi
524524 12.7697 0.557847
525525 0 0
526526 4.66057i 0.203210i
527527 1.30871i 0.0570081i
528528 4.68073i 0.203703i
529529 −17.1048 −0.743686
530530 0 0
531531 2.53279i 0.109914i
532532 27.9216 1.21055
533533 −21.0577 10.2017i −0.912109 0.441883i
534534 −1.86884 −0.0808726
535535 0 0
536536 −4.58651 −0.198107
537537 −1.09914 −0.0474313
538538 0.654353i 0.0282111i
539539 0.734451i 0.0316350i
540540 0 0
541541 26.7776i 1.15126i 0.817711 + 0.575630i 0.195243π0.195243\pi
−0.817711 + 0.575630i 0.804757π0.804757\pi
542542 1.82302 0.0783056
543543 5.87675 0.252195
544544 29.0162i 1.24406i
545545 0 0
546546 −1.02864 + 2.12325i −0.0440216 + 0.0908669i
547547 −12.3865 −0.529610 −0.264805 0.964302i 0.585308π-0.585308\pi
−0.264805 + 0.964302i 0.585308π0.585308\pi
548548 5.74106i 0.245246i
549549 16.3849 0.699288
550550 0 0
551551 16.6913i 0.711073i
552552 2.18319i 0.0929227i
553553 9.71203i 0.412997i
554554 4.36186i 0.185318i
555555 0 0
556556 −1.57634 −0.0668519
557557 10.4218i 0.441586i −0.975321 0.220793i 0.929136π-0.929136\pi
0.975321 0.220793i 0.0708644π-0.0708644\pi
558558 0.394448 0.0166983
559559 −17.1625 + 35.4257i −0.725895 + 1.49835i
560560 0 0
561561 11.6706i 0.492732i
562562 11.5763 0.488319
563563 −9.78156 −0.412244 −0.206122 0.978526i 0.566084π-0.566084\pi
−0.206122 + 0.978526i 0.566084π0.566084\pi
564564 1.91369i 0.0805808i
565565 0 0
566566 11.3809i 0.478375i
567567 19.7384i 0.828935i
568568 13.1193 0.550474
569569 −30.2201 −1.26689 −0.633447 0.773786i 0.718361π-0.718361\pi
−0.633447 + 0.773786i 0.718361π0.718361\pi
570570 0 0
571571 −39.8643 −1.66827 −0.834135 0.551561i 0.814033π-0.814033\pi
−0.834135 + 0.551561i 0.814033π0.814033\pi
572572 27.6873 + 13.4135i 1.15767 + 0.560846i
573573 −4.57595 −0.191163
574574 9.92159i 0.414119i
575575 0 0
576576 −3.33282 −0.138868
577577 8.46326i 0.352330i −0.984361 0.176165i 0.943631π-0.943631\pi
0.984361 0.176165i 0.0563692π-0.0563692\pi
578578 6.62136i 0.275412i
579579 8.24313i 0.342573i
580580 0 0
581581 −26.2386 −1.08856
582582 2.77761 0.115136
583583 21.4320i 0.887621i
584584 23.0268 0.952855
585585 0 0
586586 −14.8824 −0.614786
587587 9.32718i 0.384974i −0.981300 0.192487i 0.938345π-0.938345\pi
0.981300 0.192487i 0.0616553π-0.0616553\pi
588588 −0.103091 −0.00425142
589589 1.52884 0.0629946
590590 0 0
591591 7.35355i 0.302485i
592592 7.13342i 0.293182i
593593 8.07841i 0.331740i 0.986148 + 0.165870i 0.0530433π0.0530433\pi
−0.986148 + 0.165870i 0.946957π0.946957\pi
594594 7.26386 0.298040
595595 0 0
596596 18.9793i 0.777421i
597597 −4.94233 −0.202276
598598 −4.50641 2.18319i −0.184281 0.0892773i
599599 19.1440 0.782202 0.391101 0.920348i 0.372094π-0.372094\pi
0.391101 + 0.920348i 0.372094π0.372094\pi
600600 0 0
601601 −4.28797 −0.174910 −0.0874550 0.996168i 0.527873π-0.527873\pi
−0.0874550 + 0.996168i 0.527873π0.527873\pi
602602 16.6913 0.680286
603603 6.14963i 0.250432i
604604 35.1668i 1.43092i
605605 0 0
606606 2.65774i 0.107963i
607607 −29.2426 −1.18692 −0.593459 0.804864i 0.702238π-0.702238\pi
−0.593459 + 0.804864i 0.702238π0.702238\pi
608608 33.8969 1.37470
609609 3.05767i 0.123903i
610610 0 0
611611 −8.67282 4.20166i −0.350865 0.169981i
612612 −25.1888 −1.01820
613613 1.42405i 0.0575170i 0.999586 + 0.0287585i 0.00915538π0.00915538\pi
−0.999586 + 0.0287585i 0.990845π0.990845\pi
614614 −1.36864 −0.0552338
615615 0 0
616616 28.6419i 1.15402i
617617 46.5266i 1.87309i −0.350548 0.936545i 0.614005π-0.614005\pi
0.350548 0.936545i 0.385995π-0.385995\pi
618618 2.60232i 0.104681i
619619 34.2818i 1.37790i −0.724809 0.688950i 0.758072π-0.758072\pi
0.724809 0.688950i 0.241928π-0.241928\pi
620620 0 0
621621 6.04485 0.242571
622622 2.02904i 0.0813569i
623623 −20.4033 −0.817442
624624 1.44252 2.97758i 0.0577472 0.119198i
625625 0 0
626626 2.84811i 0.113833i
627627 13.6336 0.544474
628628 16.4527 0.656534
629629 17.7859i 0.709171i
630630 0 0
631631 2.32322i 0.0924861i 0.998930 + 0.0462430i 0.0147249π0.0147249\pi
−0.998930 + 0.0462430i 0.985275π0.985275\pi
632632 7.63362i 0.303649i
633633 10.3249 0.410379
634634 10.6359 0.422405
635635 0 0
636636 3.00830 0.119287
637637 −0.226346 + 0.467210i −0.00896815 + 0.0185115i
638638 −7.79834 −0.308739
639639 17.5905i 0.695868i
640640 0 0
641641 28.1312 1.11111 0.555557 0.831478i 0.312505π-0.312505\pi
0.555557 + 0.831478i 0.312505π0.312505\pi
642642 0.0342826i 0.00135303i
643643 14.1338i 0.557383i −0.960381 0.278692i 0.910099π-0.910099\pi
0.960381 0.278692i 0.0899008π-0.0899008\pi
644644 10.8560i 0.427787i
645645 0 0
646646 19.0946 0.751268
647647 −45.8969 −1.80439 −0.902197 0.431325i 0.858046π-0.858046\pi
−0.902197 + 0.431325i 0.858046π0.858046\pi
648648 15.5143i 0.609460i
649649 4.58651 0.180036
650650 0 0
651651 −0.280067 −0.0109767
652652 20.7177i 0.811367i
653653 −50.4482 −1.97419 −0.987095 0.160137i 0.948806π-0.948806\pi
−0.987095 + 0.160137i 0.948806π0.948806\pi
654654 2.21747 0.0867100
655655 0 0
656656 13.9137i 0.543238i
657657 30.8745i 1.20453i
658658 4.08631i 0.159301i
659659 −45.8722 −1.78693 −0.893464 0.449135i 0.851732π-0.851732\pi
−0.893464 + 0.449135i 0.851732π0.851732\pi
660660 0 0
661661 25.8432i 1.00518i −0.864524 0.502592i 0.832380π-0.832380\pi
0.864524 0.502592i 0.167620π-0.167620\pi
662662 3.38614 0.131606
663663 3.59668 7.42405i 0.139683 0.288326i
664664 −20.6235 −0.800345
665665 0 0
666666 −5.36073 −0.207724
667667 −6.48963 −0.251280
668668 14.2326i 0.550674i
669669 2.45269i 0.0948265i
670670 0 0
671671 29.6706i 1.14542i
672672 −6.20957 −0.239539
673673 4.97927 0.191937 0.0959683 0.995384i 0.469405π-0.469405\pi
0.0959683 + 0.995384i 0.469405π0.469405\pi
674674 7.96306i 0.306726i
675675 0 0
676676 −13.4791 17.0656i −0.518426 0.656368i
677677 35.8353 1.37726 0.688631 0.725112i 0.258212π-0.258212\pi
0.688631 + 0.725112i 0.258212π0.258212\pi
678678 3.17755i 0.122033i
679679 30.3249 1.16376
680680 0 0
681681 1.26386i 0.0484311i
682682 0.714288i 0.0273515i
683683 40.4712i 1.54859i −0.632827 0.774293i 0.718106π-0.718106\pi
0.632827 0.774293i 0.281894π-0.281894\pi
684684 29.4257i 1.12512i
685685 0 0
686686 −10.4817 −0.400194
687687 10.8112i 0.412472i
688688 −23.4073 −0.892394
689689 6.60498 13.6336i 0.251630 0.519400i
690690 0 0
691691 12.2448i 0.465815i −0.972499 0.232907i 0.925176π-0.925176\pi
0.972499 0.232907i 0.0748239π-0.0748239\pi
692692 −36.0448 −1.37022
693693 38.4033 1.45882
694694 4.38050i 0.166281i
695695 0 0
696696 2.40332i 0.0910977i
697697 34.6913i 1.31403i
698698 −6.39542 −0.242070
699699 9.99209 0.377936
700700 0 0
701701 −11.8353 −0.447012 −0.223506 0.974703i 0.571750π-0.571750\pi
−0.223506 + 0.974703i 0.571750π0.571750\pi
702702 −4.62079 2.23860i −0.174401 0.0844906i
703703 −20.7776 −0.783642
704704 6.03525i 0.227462i
705705 0 0
706706 5.52093 0.207783
707707 29.0162i 1.09127i
708708 0.643787i 0.0241950i
709709 6.37429i 0.239391i 0.992811 + 0.119696i 0.0381919π0.0381919\pi
−0.992811 + 0.119696i 0.961808π0.961808\pi
710710 0 0
711711 10.2352 0.383851
712712 −16.0369 −0.601010
713713 0.594417i 0.0222611i
714714 −3.49794 −0.130907
715715 0 0
716716 −4.29588 −0.160545
717717 1.62306i 0.0606141i
718718 −5.44083 −0.203050
719719 34.9009 1.30158 0.650791 0.759257i 0.274437π-0.274437\pi
0.650791 + 0.759257i 0.274437π0.274437\pi
720720 0 0
721721 28.4112i 1.05809i
722722 11.4386i 0.425700i
723723 1.46890i 0.0546290i
724724 22.9687 0.853625
725725 0 0
726726 3.67678i 0.136458i
727727 19.8106 0.734734 0.367367 0.930076i 0.380259π-0.380259\pi
0.367367 + 0.930076i 0.380259π0.380259\pi
728728 −8.82698 + 18.2201i −0.327150 + 0.675283i
729729 −17.6050 −0.652036
730730 0 0
731731 −58.3619 −2.15859
732732 −4.16472 −0.153932
733733 12.6050i 0.465576i 0.972528 + 0.232788i 0.0747848π0.0747848\pi
−0.972528 + 0.232788i 0.925215π0.925215\pi
734734 9.72615i 0.358999i
735735 0 0
736736 13.1792i 0.485793i
737737 −11.1361 −0.410203
738738 −10.4561 −0.384893
739739 37.1747i 1.36749i −0.729719 0.683747i 0.760349π-0.760349\pi
0.729719 0.683747i 0.239651π-0.239651\pi
740740 0 0
741741 −8.67282 4.20166i −0.318604 0.154352i
742742 −6.42366 −0.235820
743743 27.9322i 1.02473i −0.858767 0.512366i 0.828769π-0.828769\pi
0.858767 0.512366i 0.171231π-0.171231\pi
744744 −0.220132 −0.00807043
745745 0 0
746746 1.04977i 0.0384348i
747747 27.6521i 1.01174i
748748 45.6133i 1.66779i
749749 0.374285i 0.0136761i
750750 0 0
751751 13.6257 0.497209 0.248605 0.968605i 0.420028π-0.420028\pi
0.248605 + 0.968605i 0.420028π0.420028\pi
752752 5.73050i 0.208970i
753753 −10.9009 −0.397249
754754 4.96080 + 2.40332i 0.180662 + 0.0875238i
755755 0 0
756756 11.1316i 0.404851i
757757 30.8560 1.12148 0.560740 0.827992i 0.310517π-0.310517\pi
0.560740 + 0.827992i 0.310517π0.310517\pi
758758 18.5143 0.672470
759759 5.30080i 0.192407i
760760 0 0
761761 17.0162i 0.616837i 0.951251 + 0.308419i 0.0997997π0.0997997\pi
−0.951251 + 0.308419i 0.900200π0.900200\pi
762762 2.95289i 0.106972i
763763 24.2096 0.876445
764764 −17.8847 −0.647044
765765 0 0
766766 −16.0969 −0.581604
767767 −2.91764 1.41349i −0.105350 0.0510381i
768768 −1.81060 −0.0653343
769769 29.0162i 1.04635i 0.852225 + 0.523176i 0.175253π0.175253\pi
−0.852225 + 0.523176i 0.824747π0.824747\pi
770770 0 0
771771 −3.96644 −0.142848
772772 32.2175i 1.15953i
773773 40.5160i 1.45726i −0.684908 0.728630i 0.740158π-0.740158\pi
0.684908 0.728630i 0.259842π-0.259842\pi
774774 17.5905i 0.632276i
775775 0 0
776776 23.8353 0.855637
777777 3.80624 0.136548
778778 18.2801i 0.655372i
779779 −40.5266 −1.45202
780780 0 0
781781 31.8538 1.13982
782782 7.42405i 0.265484i
783783 −6.65435 −0.237807
784784 −0.308705 −0.0110252
785785 0 0
786786 1.86884i 0.0666593i
787787 34.0264i 1.21291i −0.795118 0.606455i 0.792591π-0.792591\pi
0.795118 0.606455i 0.207409π-0.207409\pi
788788 28.7407i 1.02384i
789789 3.48737 0.124154
790790 0 0
791791 34.6913i 1.23348i
792792 30.1849 1.07257
793793 −9.14399 + 18.8745i −0.324712 + 0.670253i
794794 7.26990 0.257999
795795 0 0
796796 −19.3166 −0.684659
797797 −14.7776 −0.523450 −0.261725 0.965143i 0.584291π-0.584291\pi
−0.261725 + 0.965143i 0.584291π0.584291\pi
798798 4.08631i 0.144654i
799799 14.2880i 0.505472i
800800 0 0
801801 21.5025i 0.759752i
802802 0.560135 0.0197790
803803 55.9092 1.97299
804804 1.56312i 0.0551270i
805805 0 0
806806 −0.220132 + 0.454384i −0.00775382 + 0.0160050i
807807 0.489634 0.0172359
808808 22.8066i 0.802335i
809809 −36.0554 −1.26764 −0.633820 0.773480i 0.718514π-0.718514\pi
−0.633820 + 0.773480i 0.718514π0.718514\pi
810810 0 0
811811 5.31040i 0.186473i 0.995644 + 0.0932366i 0.0297213π0.0297213\pi
−0.995644 + 0.0932366i 0.970279π0.970279\pi
812812 11.9506i 0.419385i
813813 1.36412i 0.0478417i
814814 9.70750i 0.340248i
815815 0 0
816816 4.90538 0.171723
817817 68.1787i 2.38527i
818818 −4.46060 −0.155961
819819 −24.4297 11.8353i −0.853643 0.413558i
820820 0 0
821821 13.6336i 0.475817i 0.971288 + 0.237908i 0.0764618π0.0764618\pi
−0.971288 + 0.237908i 0.923538π0.923538\pi
822822 −0.840202 −0.0293054
823823 39.6459 1.38197 0.690984 0.722870i 0.257177π-0.257177\pi
0.690984 + 0.722870i 0.257177π0.257177\pi
824824 22.3311i 0.777942i
825825 0 0
826826 1.37468i 0.0478314i
827827 23.8952i 0.830918i 0.909612 + 0.415459i 0.136379π0.136379\pi
−0.909612 + 0.415459i 0.863621π0.863621\pi
828828 11.4408 0.397596
829829 27.3562 0.950121 0.475060 0.879953i 0.342426π-0.342426\pi
0.475060 + 0.879953i 0.342426π0.342426\pi
830830 0 0
831831 −3.26386 −0.113222
832832 1.85997 3.83923i 0.0644827 0.133101i
833833 −0.769701 −0.0266686
834834 0.230697i 0.00798839i
835835 0 0
836836 53.2857 1.84292
837837 0.609505i 0.0210676i
838838 5.83528i 0.201576i
839839 29.5411i 1.01987i 0.860212 + 0.509936i 0.170331π0.170331\pi
−0.860212 + 0.509936i 0.829669π0.829669\pi
840840 0 0
841841 −21.8560 −0.753656
842842 −17.8398 −0.614800
843843 8.66226i 0.298344i
844844 40.3540 1.38904
845845 0 0
846846 −4.30644 −0.148059
847847 40.1417i 1.37929i
848848 9.00830 0.309346
849849 −8.51601 −0.292269
850850 0 0
851851 8.07841i 0.276924i
852852 4.47116i 0.153180i
853853 5.61515i 0.192259i 0.995369 + 0.0961295i 0.0306463π0.0306463\pi
−0.995369 + 0.0961295i 0.969354π0.969354\pi
854854 8.89296 0.304311
855855 0 0
856856 0.294187i 0.0100551i
857857 −39.9216 −1.36370 −0.681848 0.731494i 0.738823π-0.738823\pi
−0.681848 + 0.731494i 0.738823π0.738823\pi
858858 −1.96306 + 4.05203i −0.0670177 + 0.138334i
859859 28.6498 0.977520 0.488760 0.872418i 0.337449π-0.337449\pi
0.488760 + 0.872418i 0.337449π0.337449\pi
860860 0 0
861861 7.42405 0.253011
862862 −13.1193 −0.446845
863863 38.5530i 1.31236i 0.754605 + 0.656179i 0.227828π0.227828\pi
−0.754605 + 0.656179i 0.772172π0.772172\pi
864864 13.5137i 0.459747i
865865 0 0
866866 9.31661i 0.316591i
867867 4.95458 0.168266
868868 −1.09462 −0.0371537
869869 18.5345i 0.628739i
870870 0 0
871871 7.08405 + 3.43196i 0.240034 + 0.116288i
872872 19.0286 0.644391
873873 31.9585i 1.08163i
874874 −8.67282 −0.293363
875875 0 0
876876 7.84771i 0.265150i
877877 27.3826i 0.924644i 0.886712 + 0.462322i 0.152984π0.152984\pi
−0.886712 + 0.462322i 0.847016π0.847016\pi
878878 13.5888i 0.458599i
879879 11.1361i 0.375611i
880880 0 0
881881 25.0841 0.845103 0.422552 0.906339i 0.361135π-0.361135\pi
0.422552 + 0.906339i 0.361135π0.361135\pi
882882 0.231991i 0.00781153i
883883 −50.5513 −1.70119 −0.850593 0.525825i 0.823757π-0.823757\pi
−0.850593 + 0.525825i 0.823757π0.823757\pi
884884 14.0573 29.0162i 0.472797 0.975921i
885885 0 0
886886 1.57465i 0.0529015i
887887 19.6583 0.660061 0.330031 0.943970i 0.392941π-0.392941\pi
0.330031 + 0.943970i 0.392941π0.392941\pi
888888 2.99170 0.100395
889889 32.2386i 1.08125i
890890 0 0
891891 37.6689i 1.26195i
892892 9.58611i 0.320967i
893893 −16.6913 −0.558553
894894 −2.77761 −0.0928971
895895 0 0
896896 −30.8251 −1.02979
897897 −1.63362 + 3.37202i −0.0545450 + 0.112589i
898898 15.5025 0.517324
899899 0.654353i 0.0218239i
900900 0 0
901901 22.4606 0.748271
902902 18.9344i 0.630447i
903903 12.4896i 0.415629i
904904 27.2672i 0.906895i
905905 0 0
906906 −5.14665 −0.170986
907907 22.0537 0.732282 0.366141 0.930559i 0.380679π-0.380679\pi
0.366141 + 0.930559i 0.380679π0.380679\pi
908908 4.93967i 0.163929i
909909 30.5793 1.01425
910910 0 0
911911 −14.0079 −0.464103 −0.232051 0.972704i 0.574544π-0.574544\pi
−0.232051 + 0.972704i 0.574544π0.574544\pi
912912 5.73050i 0.189756i
913913 −50.0739 −1.65720
914914 −22.9668 −0.759676
915915 0 0
916916 42.2544i 1.39613i
917917 20.4033i 0.673777i
918918 7.61249i 0.251250i
919919 21.8353 0.720279 0.360140 0.932898i 0.382729π-0.382729\pi
0.360140 + 0.932898i 0.382729π0.382729\pi
920920 0 0
921921 1.02412i 0.0337458i
922922 1.14851 0.0378241
923923 −20.2633 9.81681i −0.666974 0.323124i
924924 −9.76140 −0.321126
925925 0 0
926926 1.52884 0.0502407
927927 −29.9418 −0.983416
928928 14.5081i 0.476252i
929929 15.2224i 0.499431i −0.968319 0.249715i 0.919663π-0.919663\pi
0.968319 0.249715i 0.0803370π-0.0803370\pi
930930 0 0
931931 0.899170i 0.0294691i
932932 39.0532 1.27923
933933 1.51827 0.0497060
934934 18.2403i 0.596841i
935935 0 0
936936 −19.2017 9.30249i −0.627626 0.304061i
937937 25.4610 0.831774 0.415887 0.909416i 0.363471π-0.363471\pi
0.415887 + 0.909416i 0.363471π0.363471\pi
938938 3.33774i 0.108981i
939939 −2.13116 −0.0695478
940940 0 0
941941 24.9299i 0.812691i 0.913719 + 0.406346i 0.133197π0.133197\pi
−0.913719 + 0.406346i 0.866803π0.866803\pi
942942 2.40784i 0.0784518i
943943 15.7569i 0.513114i
944944 1.92781i 0.0627448i
945945 0 0
946946 31.8538 1.03565
947947 16.6807i 0.542051i −0.962572 0.271025i 0.912637π-0.912637\pi
0.962572 0.271025i 0.0873628π-0.0873628\pi
948948 −2.60160 −0.0844960
949949 −35.5658 17.2303i −1.15451 0.559319i
950950 0 0
951951 7.95854i 0.258073i
952952 −30.0166 −0.972844
953953 27.1730 0.880221 0.440110 0.897944i 0.354939π-0.354939\pi
0.440110 + 0.897944i 0.354939π0.354939\pi
954954 6.76970i 0.219177i
955955 0 0
956956 6.34356i 0.205165i
957957 5.83528i 0.188628i
958958 3.85206 0.124454
959959 −9.17302 −0.296212
960960 0 0
961961 30.9401 0.998067
962962 2.99170 6.17528i 0.0964561 0.199099i
963963 0.394448 0.0127109
964964 5.74106i 0.184907i
965965 0 0
966966 1.58877 0.0511179
967967 6.75914i 0.217359i −0.994077 0.108680i 0.965338π-0.965338\pi
0.994077 0.108680i 0.0346622π-0.0346622\pi
968968 31.5513i 1.01410i
969969 14.2880i 0.458996i
970970 0 0
971971 46.6419 1.49681 0.748405 0.663242i 0.230820π-0.230820\pi
0.748405 + 0.663242i 0.230820π0.230820\pi
972972 17.7816 0.570344
973973 2.51867i 0.0807449i
974974 −22.6807 −0.726737
975975 0 0
976976 −12.4712 −0.399192
977977 52.7467i 1.68752i 0.536723 + 0.843758i 0.319662π0.319662\pi
−0.536723 + 0.843758i 0.680338π0.680338\pi
978978 3.03202 0.0969534
979979 −38.9378 −1.24446
980980 0 0
981981 25.5137i 0.814591i
982982 17.7859i 0.567571i
983983 20.9977i 0.669724i 0.942267 + 0.334862i 0.108690π0.108690\pi
−0.942267 + 0.334862i 0.891310π0.891310\pi
984984 5.83528 0.186022
985985 0 0
986986 8.17262i 0.260269i
987987 3.05767 0.0973268
988988 −33.8969 16.4218i −1.07840 0.522447i
989989 26.5081 0.842909
990990 0 0
991991 −32.3170 −1.02658 −0.513292 0.858214i 0.671574π-0.671574\pi
−0.513292 + 0.858214i 0.671574π0.671574\pi
992992 −1.32887 −0.0421916
993993 2.53376i 0.0804064i
994994 9.54731i 0.302822i
995995 0 0
996996 7.02864i 0.222711i
997997 21.3905 0.677444 0.338722 0.940887i 0.390005π-0.390005\pi
0.338722 + 0.940887i 0.390005π0.390005\pi
998998 7.49811 0.237348
999999 8.28345i 0.262077i
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 325.2.c.g.51.4 6
5.2 odd 4 325.2.d.e.324.3 6
5.3 odd 4 325.2.d.f.324.4 6
5.4 even 2 65.2.c.a.51.3 6
13.5 odd 4 4225.2.a.be.1.2 3
13.8 odd 4 4225.2.a.bc.1.2 3
13.12 even 2 inner 325.2.c.g.51.3 6
15.14 odd 2 585.2.b.g.181.4 6
20.19 odd 2 1040.2.k.d.961.4 6
65.4 even 6 845.2.m.h.361.4 12
65.9 even 6 845.2.m.h.361.3 12
65.12 odd 4 325.2.d.f.324.3 6
65.19 odd 12 845.2.e.k.146.2 6
65.24 odd 12 845.2.e.i.191.2 6
65.29 even 6 845.2.m.h.316.4 12
65.34 odd 4 845.2.a.k.1.2 3
65.38 odd 4 325.2.d.e.324.4 6
65.44 odd 4 845.2.a.i.1.2 3
65.49 even 6 845.2.m.h.316.3 12
65.54 odd 12 845.2.e.k.191.2 6
65.59 odd 12 845.2.e.i.146.2 6
65.64 even 2 65.2.c.a.51.4 yes 6
195.44 even 4 7605.2.a.cc.1.2 3
195.164 even 4 7605.2.a.bs.1.2 3
195.194 odd 2 585.2.b.g.181.3 6
260.259 odd 2 1040.2.k.d.961.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.c.a.51.3 6 5.4 even 2
65.2.c.a.51.4 yes 6 65.64 even 2
325.2.c.g.51.3 6 13.12 even 2 inner
325.2.c.g.51.4 6 1.1 even 1 trivial
325.2.d.e.324.3 6 5.2 odd 4
325.2.d.e.324.4 6 65.38 odd 4
325.2.d.f.324.3 6 65.12 odd 4
325.2.d.f.324.4 6 5.3 odd 4
585.2.b.g.181.3 6 195.194 odd 2
585.2.b.g.181.4 6 15.14 odd 2
845.2.a.i.1.2 3 65.44 odd 4
845.2.a.k.1.2 3 65.34 odd 4
845.2.e.i.146.2 6 65.59 odd 12
845.2.e.i.191.2 6 65.24 odd 12
845.2.e.k.146.2 6 65.19 odd 12
845.2.e.k.191.2 6 65.54 odd 12
845.2.m.h.316.3 12 65.49 even 6
845.2.m.h.316.4 12 65.29 even 6
845.2.m.h.361.3 12 65.9 even 6
845.2.m.h.361.4 12 65.4 even 6
1040.2.k.d.961.3 6 260.259 odd 2
1040.2.k.d.961.4 6 20.19 odd 2
4225.2.a.bc.1.2 3 13.8 odd 4
4225.2.a.be.1.2 3 13.5 odd 4
7605.2.a.bs.1.2 3 195.164 even 4
7605.2.a.cc.1.2 3 195.44 even 4