Properties

Label 576.3.q.h.257.1
Level 576576
Weight 33
Character 576.257
Analytic conductor 15.69515.695
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,3,Mod(65,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.65");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 576=2632 576 = 2^{6} \cdot 3^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 576.q (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.694863227215.6948632272
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(2,3)\Q(\sqrt{-2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x42x2+4 x^{4} - 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 257.1
Root 1.224740.707107i-1.22474 - 0.707107i of defining polynomial
Character χ\chi == 576.257
Dual form 576.3.q.h.65.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+3.00000q3+(6.398983.69445i)q5+(3.39898+5.88721i)q7+9.00000q9+(5.29796+3.05878i)q11+(8.3989814.5475i)q13+(19.196911.0834i)q1525.1701iq17+17.5959q19+(10.1969+17.6616i)q21+(12.3990+7.15855i)q23+(14.7980+25.6308i)q25+27.0000q27+(16.1969+9.35131i)q29+(23.399040.5282i)q31+(15.8939+9.17633i)q3350.2295iq35+49.5959q37+(25.196943.6424i)q39+(34.500019.9186i)q41+(22.095938.2713i)q43+(57.590833.2501i)q45+(28.803116.6295i)q47+(1.393882.41427i)q4975.5103iq51+10.1708iq53+45.2020q55+52.7878q57+(14.2980+8.25493i)q59+(10.6010+18.3615i)q61+(30.5908+52.9848i)q63+(107.490+62.0593i)q65+(43.4898+75.3265i)q67+(37.1969+21.4757i)q69+30.2555iq7148.7878q73+(44.3939+76.8925i)q75+(36.015320.7934i)q77+(55.792996.6361i)q79+81.0000q81+(85.085749.1243i)q83+(92.9898+161.063i)q85+(48.5908+28.0539i)q8775.5103iq89+114.192q91+(70.1969121.585i)q93+(112.59665.0073i)q95+(70.2980+121.760i)q97+(47.6816+27.5290i)q99+O(q100)q+3.00000 q^{3} +(-6.39898 - 3.69445i) q^{5} +(3.39898 + 5.88721i) q^{7} +9.00000 q^{9} +(-5.29796 + 3.05878i) q^{11} +(8.39898 - 14.5475i) q^{13} +(-19.1969 - 11.0834i) q^{15} -25.1701i q^{17} +17.5959 q^{19} +(10.1969 + 17.6616i) q^{21} +(12.3990 + 7.15855i) q^{23} +(14.7980 + 25.6308i) q^{25} +27.0000 q^{27} +(-16.1969 + 9.35131i) q^{29} +(23.3990 - 40.5282i) q^{31} +(-15.8939 + 9.17633i) q^{33} -50.2295i q^{35} +49.5959 q^{37} +(25.1969 - 43.6424i) q^{39} +(-34.5000 - 19.9186i) q^{41} +(-22.0959 - 38.2713i) q^{43} +(-57.5908 - 33.2501i) q^{45} +(28.8031 - 16.6295i) q^{47} +(1.39388 - 2.41427i) q^{49} -75.5103i q^{51} +10.1708i q^{53} +45.2020 q^{55} +52.7878 q^{57} +(14.2980 + 8.25493i) q^{59} +(10.6010 + 18.3615i) q^{61} +(30.5908 + 52.9848i) q^{63} +(-107.490 + 62.0593i) q^{65} +(-43.4898 + 75.3265i) q^{67} +(37.1969 + 21.4757i) q^{69} +30.2555i q^{71} -48.7878 q^{73} +(44.3939 + 76.8925i) q^{75} +(-36.0153 - 20.7934i) q^{77} +(-55.7929 - 96.6361i) q^{79} +81.0000 q^{81} +(85.0857 - 49.1243i) q^{83} +(-92.9898 + 161.063i) q^{85} +(-48.5908 + 28.0539i) q^{87} -75.5103i q^{89} +114.192 q^{91} +(70.1969 - 121.585i) q^{93} +(-112.596 - 65.0073i) q^{95} +(70.2980 + 121.760i) q^{97} +(-47.6816 + 27.5290i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+12q36q56q7+36q9+18q11+14q1318q158q1918q21+30q23+20q25+108q276q29+74q31+54q33+120q37+42q39++162q99+O(q100) 4 q + 12 q^{3} - 6 q^{5} - 6 q^{7} + 36 q^{9} + 18 q^{11} + 14 q^{13} - 18 q^{15} - 8 q^{19} - 18 q^{21} + 30 q^{23} + 20 q^{25} + 108 q^{27} - 6 q^{29} + 74 q^{31} + 54 q^{33} + 120 q^{37} + 42 q^{39}+ \cdots + 162 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/576Z)×\left(\mathbb{Z}/576\mathbb{Z}\right)^\times.

nn 6565 127127 325325
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 3.00000 1.00000
44 0 0
55 −6.39898 3.69445i −1.27980 0.738891i −0.302985 0.952995i 0.597983π-0.597983\pi
−0.976811 + 0.214105i 0.931317π0.931317\pi
66 0 0
77 3.39898 + 5.88721i 0.485568 + 0.841029i 0.999862 0.0165847i 0.00527930π-0.00527930\pi
−0.514294 + 0.857614i 0.671946π0.671946\pi
88 0 0
99 9.00000 1.00000
1010 0 0
1111 −5.29796 + 3.05878i −0.481633 + 0.278071i −0.721097 0.692835i 0.756362π-0.756362\pi
0.239464 + 0.970905i 0.423028π0.423028\pi
1212 0 0
1313 8.39898 14.5475i 0.646075 1.11904i −0.337977 0.941154i 0.609743π-0.609743\pi
0.984052 0.177881i 0.0569242π-0.0569242\pi
1414 0 0
1515 −19.1969 11.0834i −1.27980 0.738891i
1616 0 0
1717 25.1701i 1.48059i −0.672279 0.740297i 0.734685π-0.734685\pi
0.672279 0.740297i 0.265315π-0.265315\pi
1818 0 0
1919 17.5959 0.926101 0.463050 0.886332i 0.346755π-0.346755\pi
0.463050 + 0.886332i 0.346755π0.346755\pi
2020 0 0
2121 10.1969 + 17.6616i 0.485568 + 0.841029i
2222 0 0
2323 12.3990 + 7.15855i 0.539086 + 0.311241i 0.744708 0.667390i 0.232589π-0.232589\pi
−0.205622 + 0.978631i 0.565922π0.565922\pi
2424 0 0
2525 14.7980 + 25.6308i 0.591918 + 1.02523i
2626 0 0
2727 27.0000 1.00000
2828 0 0
2929 −16.1969 + 9.35131i −0.558515 + 0.322459i −0.752549 0.658536i 0.771176π-0.771176\pi
0.194034 + 0.980995i 0.437843π0.437843\pi
3030 0 0
3131 23.3990 40.5282i 0.754806 1.30736i −0.190665 0.981655i 0.561064π-0.561064\pi
0.945471 0.325707i 0.105602π-0.105602\pi
3232 0 0
3333 −15.8939 + 9.17633i −0.481633 + 0.278071i
3434 0 0
3535 50.2295i 1.43513i
3636 0 0
3737 49.5959 1.34043 0.670215 0.742167i 0.266202π-0.266202\pi
0.670215 + 0.742167i 0.266202π0.266202\pi
3838 0 0
3939 25.1969 43.6424i 0.646075 1.11904i
4040 0 0
4141 −34.5000 19.9186i −0.841463 0.485819i 0.0162980 0.999867i 0.494812π-0.494812\pi
−0.857761 + 0.514048i 0.828145π0.828145\pi
4242 0 0
4343 −22.0959 38.2713i −0.513859 0.890029i −0.999871 0.0160771i 0.994882π-0.994882\pi
0.486012 0.873952i 0.338451π-0.338451\pi
4444 0 0
4545 −57.5908 33.2501i −1.27980 0.738891i
4646 0 0
4747 28.8031 16.6295i 0.612831 0.353818i −0.161242 0.986915i 0.551550π-0.551550\pi
0.774073 + 0.633097i 0.218216π0.218216\pi
4848 0 0
4949 1.39388 2.41427i 0.0284465 0.0492707i
5050 0 0
5151 75.5103i 1.48059i
5252 0 0
5353 10.1708i 0.191902i 0.995386 + 0.0959509i 0.0305892π0.0305892\pi
−0.995386 + 0.0959509i 0.969411π0.969411\pi
5454 0 0
5555 45.2020 0.821855
5656 0 0
5757 52.7878 0.926101
5858 0 0
5959 14.2980 + 8.25493i 0.242338 + 0.139914i 0.616251 0.787550i 0.288651π-0.288651\pi
−0.373913 + 0.927464i 0.621984π0.621984\pi
6060 0 0
6161 10.6010 + 18.3615i 0.173787 + 0.301008i 0.939741 0.341887i 0.111066π-0.111066\pi
−0.765954 + 0.642896i 0.777733π0.777733\pi
6262 0 0
6363 30.5908 + 52.9848i 0.485568 + 0.841029i
6464 0 0
6565 −107.490 + 62.0593i −1.65369 + 0.954758i
6666 0 0
6767 −43.4898 + 75.3265i −0.649101 + 1.12428i 0.334236 + 0.942489i 0.391522π0.391522\pi
−0.983338 + 0.181787i 0.941812π0.941812\pi
6868 0 0
6969 37.1969 + 21.4757i 0.539086 + 0.311241i
7070 0 0
7171 30.2555i 0.426134i 0.977038 + 0.213067i 0.0683453π0.0683453\pi
−0.977038 + 0.213067i 0.931655π0.931655\pi
7272 0 0
7373 −48.7878 −0.668325 −0.334163 0.942515i 0.608454π-0.608454\pi
−0.334163 + 0.942515i 0.608454π0.608454\pi
7474 0 0
7575 44.3939 + 76.8925i 0.591918 + 1.02523i
7676 0 0
7777 −36.0153 20.7934i −0.467731 0.270045i
7878 0 0
7979 −55.7929 96.6361i −0.706239 1.22324i −0.966243 0.257634i 0.917057π-0.917057\pi
0.260004 0.965608i 0.416276π-0.416276\pi
8080 0 0
8181 81.0000 1.00000
8282 0 0
8383 85.0857 49.1243i 1.02513 0.591859i 0.109544 0.993982i 0.465061π-0.465061\pi
0.915585 + 0.402123i 0.131728π0.131728\pi
8484 0 0
8585 −92.9898 + 161.063i −1.09400 + 1.89486i
8686 0 0
8787 −48.5908 + 28.0539i −0.558515 + 0.322459i
8888 0 0
8989 75.5103i 0.848431i −0.905561 0.424215i 0.860550π-0.860550\pi
0.905561 0.424215i 0.139450π-0.139450\pi
9090 0 0
9191 114.192 1.25486
9292 0 0
9393 70.1969 121.585i 0.754806 1.30736i
9494 0 0
9595 −112.596 65.0073i −1.18522 0.684287i
9696 0 0
9797 70.2980 + 121.760i 0.724721 + 1.25525i 0.959089 + 0.283106i 0.0913648π0.0913648\pi
−0.234367 + 0.972148i 0.575302π0.575302\pi
9898 0 0
9999 −47.6816 + 27.5290i −0.481633 + 0.278071i
100100 0 0
101101 −28.1969 + 16.2795i −0.279178 + 0.161183i −0.633051 0.774110i 0.718198π-0.718198\pi
0.353873 + 0.935293i 0.384864π0.384864\pi
102102 0 0
103103 −67.7929 + 117.421i −0.658183 + 1.14001i 0.322903 + 0.946432i 0.395341π0.395341\pi
−0.981086 + 0.193574i 0.937992π0.937992\pi
104104 0 0
105105 150.688i 1.43513i
106106 0 0
107107 35.3409i 0.330289i 0.986269 + 0.165144i 0.0528090π0.0528090\pi
−0.986269 + 0.165144i 0.947191π0.947191\pi
108108 0 0
109109 −53.5959 −0.491706 −0.245853 0.969307i 0.579068π-0.579068\pi
−0.245853 + 0.969307i 0.579068π0.579068\pi
110110 0 0
111111 148.788 1.34043
112112 0 0
113113 143.076 + 82.6047i 1.26615 + 0.731015i 0.974258 0.225435i 0.0723803π-0.0723803\pi
0.291897 + 0.956450i 0.405714π0.405714\pi
114114 0 0
115115 −52.8939 91.6149i −0.459947 0.796651i
116116 0 0
117117 75.5908 130.927i 0.646075 1.11904i
118118 0 0
119119 148.182 85.5527i 1.24522 0.718930i
120120 0 0
121121 −41.7878 + 72.3785i −0.345353 + 0.598170i
122122 0 0
123123 −103.500 59.7558i −0.841463 0.485819i
124124 0 0
125125 33.9588i 0.271670i
126126 0 0
127127 11.9796 0.0943275 0.0471637 0.998887i 0.484982π-0.484982\pi
0.0471637 + 0.998887i 0.484982π0.484982\pi
128128 0 0
129129 −66.2878 114.814i −0.513859 0.890029i
130130 0 0
131131 13.3082 + 7.68347i 0.101589 + 0.0586525i 0.549934 0.835208i 0.314653π-0.314653\pi
−0.448345 + 0.893861i 0.647986π0.647986\pi
132132 0 0
133133 59.8082 + 103.591i 0.449685 + 0.778878i
134134 0 0
135135 −172.772 99.7502i −1.27980 0.738891i
136136 0 0
137137 −47.7122 + 27.5467i −0.348265 + 0.201071i −0.663921 0.747803i 0.731109π-0.731109\pi
0.315656 + 0.948874i 0.397775π0.397775\pi
138138 0 0
139139 50.4898 87.4509i 0.363236 0.629143i −0.625255 0.780420i 0.715005π-0.715005\pi
0.988491 + 0.151277i 0.0483386π0.0483386\pi
140140 0 0
141141 86.4092 49.8884i 0.612831 0.353818i
142142 0 0
143143 102.762i 0.718619i
144144 0 0
145145 138.192 0.953047
146146 0 0
147147 4.18163 7.24280i 0.0284465 0.0492707i
148148 0 0
149149 −187.389 108.189i −1.25764 0.726100i −0.285027 0.958519i 0.592003π-0.592003\pi
−0.972616 + 0.232419i 0.925336π0.925336\pi
150150 0 0
151151 76.7929 + 133.009i 0.508562 + 0.880855i 0.999951 + 0.00991488i 0.00315606π0.00315606\pi
−0.491389 + 0.870940i 0.663511π0.663511\pi
152152 0 0
153153 226.531i 1.48059i
154154 0 0
155155 −299.459 + 172.893i −1.93199 + 1.11544i
156156 0 0
157157 40.9847 70.9876i 0.261049 0.452150i −0.705472 0.708738i 0.749265π-0.749265\pi
0.966521 + 0.256588i 0.0825983π0.0825983\pi
158158 0 0
159159 30.5124i 0.191902i
160160 0 0
161161 97.3271i 0.604516i
162162 0 0
163163 −55.2122 −0.338725 −0.169363 0.985554i 0.554171π-0.554171\pi
−0.169363 + 0.985554i 0.554171π0.554171\pi
164164 0 0
165165 135.606 0.821855
166166 0 0
167167 −133.803 77.2512i −0.801216 0.462582i 0.0426802 0.999089i 0.486410π-0.486410\pi
−0.843896 + 0.536507i 0.819744π0.819744\pi
168168 0 0
169169 −56.5857 98.0093i −0.334827 0.579937i
170170 0 0
171171 158.363 0.926101
172172 0 0
173173 −22.8031 + 13.1654i −0.131810 + 0.0761003i −0.564455 0.825464i 0.690914π-0.690914\pi
0.432645 + 0.901564i 0.357580π0.357580\pi
174174 0 0
175175 −100.596 + 174.237i −0.574834 + 0.995641i
176176 0 0
177177 42.8939 + 24.7648i 0.242338 + 0.139914i
178178 0 0
179179 266.700i 1.48995i 0.667094 + 0.744973i 0.267538π0.267538\pi
−0.667094 + 0.744973i 0.732462π0.732462\pi
180180 0 0
181181 58.4041 0.322674 0.161337 0.986899i 0.448419π-0.448419\pi
0.161337 + 0.986899i 0.448419π0.448419\pi
182182 0 0
183183 31.8031 + 55.0845i 0.173787 + 0.301008i
184184 0 0
185185 −317.363 183.230i −1.71548 0.990431i
186186 0 0
187187 76.9898 + 133.350i 0.411710 + 0.713103i
188188 0 0
189189 91.7724 + 158.955i 0.485568 + 0.841029i
190190 0 0
191191 −99.5602 + 57.4811i −0.521258 + 0.300948i −0.737449 0.675403i 0.763970π-0.763970\pi
0.216191 + 0.976351i 0.430636π0.430636\pi
192192 0 0
193193 −108.490 + 187.910i −0.562123 + 0.973626i 0.435188 + 0.900340i 0.356682π0.356682\pi
−0.997311 + 0.0732863i 0.976651π0.976651\pi
194194 0 0
195195 −322.469 + 186.178i −1.65369 + 0.954758i
196196 0 0
197197 171.105i 0.868555i 0.900779 + 0.434278i 0.142996π0.142996\pi
−0.900779 + 0.434278i 0.857004π0.857004\pi
198198 0 0
199199 −62.0000 −0.311558 −0.155779 0.987792i 0.549789π-0.549789\pi
−0.155779 + 0.987792i 0.549789π0.549789\pi
200200 0 0
201201 −130.469 + 225.980i −0.649101 + 1.12428i
202202 0 0
203203 −110.106 63.5698i −0.542395 0.313152i
204204 0 0
205205 147.177 + 254.917i 0.717934 + 1.24350i
206206 0 0
207207 111.591 + 64.4270i 0.539086 + 0.311241i
208208 0 0
209209 −93.2225 + 53.8220i −0.446040 + 0.257522i
210210 0 0
211211 −64.7020 + 112.067i −0.306645 + 0.531124i −0.977626 0.210350i 0.932540π-0.932540\pi
0.670981 + 0.741474i 0.265873π0.265873\pi
212212 0 0
213213 90.7665i 0.426134i
214214 0 0
215215 326.529i 1.51874i
216216 0 0
217217 318.131 1.46604
218218 0 0
219219 −146.363 −0.668325
220220 0 0
221221 −366.161 211.403i −1.65684 0.956576i
222222 0 0
223223 −49.1867 85.1939i −0.220568 0.382036i 0.734412 0.678704i 0.237458π-0.237458\pi
−0.954981 + 0.296668i 0.904125π0.904125\pi
224224 0 0
225225 133.182 + 230.677i 0.591918 + 1.02523i
226226 0 0
227227 383.651 221.501i 1.69009 0.975775i 0.735659 0.677352i 0.236873π-0.236873\pi
0.954434 0.298423i 0.0964607π-0.0964607\pi
228228 0 0
229229 −56.0051 + 97.0037i −0.244564 + 0.423597i −0.962009 0.273018i 0.911978π-0.911978\pi
0.717445 + 0.696615i 0.245311π0.245311\pi
230230 0 0
231231 −108.046 62.3803i −0.467731 0.270045i
232232 0 0
233233 80.8526i 0.347007i −0.984833 0.173503i 0.944491π-0.944491\pi
0.984833 0.173503i 0.0555088π-0.0555088\pi
234234 0 0
235235 −245.747 −1.04573
236236 0 0
237237 −167.379 289.908i −0.706239 1.22324i
238238 0 0
239239 37.3888 + 21.5864i 0.156438 + 0.0903197i 0.576176 0.817326i 0.304544π-0.304544\pi
−0.419737 + 0.907646i 0.637878π0.637878\pi
240240 0 0
241241 140.904 + 244.053i 0.584664 + 1.01267i 0.994917 + 0.100696i 0.0321071π0.0321071\pi
−0.410253 + 0.911972i 0.634560π0.634560\pi
242242 0 0
243243 243.000 1.00000
244244 0 0
245245 −17.8388 + 10.2992i −0.0728113 + 0.0420376i
246246 0 0
247247 147.788 255.976i 0.598331 1.03634i
248248 0 0
249249 255.257 147.373i 1.02513 0.591859i
250250 0 0
251251 15.5131i 0.0618050i 0.999522 + 0.0309025i 0.00983814π0.00983814\pi
−0.999522 + 0.0309025i 0.990162π0.990162\pi
252252 0 0
253253 −87.5857 −0.346189
254254 0 0
255255 −278.969 + 483.189i −1.09400 + 1.89486i
256256 0 0
257257 −312.035 180.153i −1.21414 0.700986i −0.250484 0.968121i 0.580590π-0.580590\pi
−0.963659 + 0.267135i 0.913923π0.913923\pi
258258 0 0
259259 168.576 + 291.981i 0.650871 + 1.12734i
260260 0 0
261261 −145.772 + 84.1618i −0.558515 + 0.322459i
262262 0 0
263263 −42.4296 + 24.4967i −0.161329 + 0.0931435i −0.578491 0.815689i 0.696358π-0.696358\pi
0.417162 + 0.908832i 0.363025π0.363025\pi
264264 0 0
265265 37.5755 65.0827i 0.141794 0.245595i
266266 0 0
267267 226.531i 0.848431i
268268 0 0
269269 281.700i 1.04721i −0.851961 0.523606i 0.824587π-0.824587\pi
0.851961 0.523606i 0.175413π-0.175413\pi
270270 0 0
271271 −89.5959 −0.330612 −0.165306 0.986242i 0.552861π-0.552861\pi
−0.165306 + 0.986242i 0.552861π0.552861\pi
272272 0 0
273273 342.576 1.25486
274274 0 0
275275 −156.798 90.5273i −0.570174 0.329190i
276276 0 0
277277 42.1969 + 73.0872i 0.152336 + 0.263853i 0.932086 0.362238i 0.117987π-0.117987\pi
−0.779750 + 0.626091i 0.784654π0.784654\pi
278278 0 0
279279 210.591 364.754i 0.754806 1.30736i
280280 0 0
281281 −23.2673 + 13.4334i −0.0828019 + 0.0478057i −0.540829 0.841132i 0.681890π-0.681890\pi
0.458027 + 0.888938i 0.348556π0.348556\pi
282282 0 0
283283 90.4898 156.733i 0.319752 0.553827i −0.660684 0.750664i 0.729734π-0.729734\pi
0.980436 + 0.196837i 0.0630671π0.0630671\pi
284284 0 0
285285 −337.788 195.022i −1.18522 0.684287i
286286 0 0
287287 270.811i 0.943594i
288288 0 0
289289 −344.535 −1.19216
290290 0 0
291291 210.894 + 365.279i 0.724721 + 1.25525i
292292 0 0
293293 407.985 + 235.550i 1.39244 + 0.803925i 0.993585 0.113089i 0.0360746π-0.0360746\pi
0.398854 + 0.917014i 0.369408π0.369408\pi
294294 0 0
295295 −60.9949 105.646i −0.206762 0.358123i
296296 0 0
297297 −143.045 + 82.5870i −0.481633 + 0.278071i
298298 0 0
299299 208.278 120.249i 0.696580 0.402171i
300300 0 0
301301 150.207 260.166i 0.499027 0.864340i
302302 0 0
303303 −84.5908 + 48.8385i −0.279178 + 0.161183i
304304 0 0
305305 156.660i 0.513639i
306306 0 0
307307 −464.747 −1.51383 −0.756917 0.653511i 0.773295π-0.773295\pi
−0.756917 + 0.653511i 0.773295π0.773295\pi
308308 0 0
309309 −203.379 + 352.262i −0.658183 + 1.14001i
310310 0 0
311311 −218.348 126.063i −0.702083 0.405348i 0.106039 0.994362i 0.466183π-0.466183\pi
−0.808123 + 0.589014i 0.799516π0.799516\pi
312312 0 0
313313 −98.1061 169.925i −0.313438 0.542891i 0.665666 0.746250i 0.268147π-0.268147\pi
−0.979104 + 0.203359i 0.934814π0.934814\pi
314314 0 0
315315 452.065i 1.43513i
316316 0 0
317317 −98.9847 + 57.1488i −0.312255 + 0.180280i −0.647935 0.761696i 0.724367π-0.724367\pi
0.335680 + 0.941976i 0.391034π0.391034\pi
318318 0 0
319319 57.2071 99.0857i 0.179333 0.310613i
320320 0 0
321321 106.023i 0.330289i
322322 0 0
323323 442.891i 1.37118i
324324 0 0
325325 497.151 1.52970
326326 0 0
327327 −160.788 −0.491706
328328 0 0
329329 195.802 + 113.046i 0.595143 + 0.343606i
330330 0 0
331331 27.2980 + 47.2815i 0.0824712 + 0.142844i 0.904311 0.426875i 0.140385π-0.140385\pi
−0.821840 + 0.569719i 0.807052π0.807052\pi
332332 0 0
333333 446.363 1.34043
334334 0 0
335335 556.581 321.342i 1.66143 0.959230i
336336 0 0
337337 118.884 205.913i 0.352771 0.611016i −0.633963 0.773363i 0.718573π-0.718573\pi
0.986734 + 0.162347i 0.0519063π0.0519063\pi
338338 0 0
339339 429.227 + 247.814i 1.26615 + 0.731015i
340340 0 0
341341 286.289i 0.839558i
342342 0 0
343343 352.051 1.02639
344344 0 0
345345 −158.682 274.845i −0.459947 0.796651i
346346 0 0
347347 −108.349 62.5553i −0.312245 0.180275i 0.335686 0.941974i 0.391032π-0.391032\pi
−0.647931 + 0.761699i 0.724365π0.724365\pi
348348 0 0
349349 −269.985 467.627i −0.773595 1.33991i −0.935581 0.353113i 0.885123π-0.885123\pi
0.161986 0.986793i 0.448210π-0.448210\pi
350350 0 0
351351 226.772 392.781i 0.646075 1.11904i
352352 0 0
353353 254.490 146.930i 0.720934 0.416232i −0.0941622 0.995557i 0.530017π-0.530017\pi
0.815096 + 0.579325i 0.196684π0.196684\pi
354354 0 0
355355 111.778 193.604i 0.314866 0.545364i
356356 0 0
357357 444.545 256.658i 1.24522 0.718930i
358358 0 0
359359 422.550i 1.17702i 0.808490 + 0.588509i 0.200285π0.200285\pi
−0.808490 + 0.588509i 0.799715π0.799715\pi
360360 0 0
361361 −51.3837 −0.142337
362362 0 0
363363 −125.363 + 217.136i −0.345353 + 0.598170i
364364 0 0
365365 312.192 + 180.244i 0.855320 + 0.493819i
366366 0 0
367367 131.358 + 227.519i 0.357924 + 0.619943i 0.987614 0.156904i 0.0501513π-0.0501513\pi
−0.629690 + 0.776847i 0.716818π0.716818\pi
368368 0 0
369369 −310.500 179.267i −0.841463 0.485819i
370370 0 0
371371 −59.8775 + 34.5703i −0.161395 + 0.0931814i
372372 0 0
373373 60.9847 105.629i 0.163498 0.283187i −0.772623 0.634865i 0.781056π-0.781056\pi
0.936121 + 0.351679i 0.114389π0.114389\pi
374374 0 0
375375 101.876i 0.271670i
376376 0 0
377377 314.166i 0.833331i
378378 0 0
379379 641.151 1.69169 0.845846 0.533428i 0.179096π-0.179096\pi
0.845846 + 0.533428i 0.179096π0.179096\pi
380380 0 0
381381 35.9388 0.0943275
382382 0 0
383383 640.681 + 369.897i 1.67280 + 0.965789i 0.966063 + 0.258308i 0.0831650π0.0831650\pi
0.706733 + 0.707481i 0.250168π0.250168\pi
384384 0 0
385385 153.641 + 266.114i 0.399067 + 0.691204i
386386 0 0
387387 −198.863 344.441i −0.513859 0.890029i
388388 0 0
389389 −75.7520 + 43.7355i −0.194735 + 0.112430i −0.594197 0.804319i 0.702530π-0.702530\pi
0.399462 + 0.916750i 0.369197π0.369197\pi
390390 0 0
391391 180.182 312.084i 0.460823 0.798168i
392392 0 0
393393 39.9245 + 23.0504i 0.101589 + 0.0586525i
394394 0 0
395395 824.496i 2.08733i
396396 0 0
397397 −483.090 −1.21685 −0.608425 0.793611i 0.708199π-0.708199\pi
−0.608425 + 0.793611i 0.708199π0.708199\pi
398398 0 0
399399 179.424 + 310.772i 0.449685 + 0.778878i
400400 0 0
401401 317.682 + 183.414i 0.792224 + 0.457390i 0.840745 0.541432i 0.182118π-0.182118\pi
−0.0485212 + 0.998822i 0.515451π0.515451\pi
402402 0 0
403403 −393.055 680.791i −0.975323 1.68931i
404404 0 0
405405 −518.317 299.251i −1.27980 0.738891i
406406 0 0
407407 −262.757 + 151.703i −0.645595 + 0.372734i
408408 0 0
409409 −267.641 + 463.567i −0.654379 + 1.13342i 0.327671 + 0.944792i 0.393736π0.393736\pi
−0.982049 + 0.188625i 0.939597π0.939597\pi
410410 0 0
411411 −143.137 + 82.6400i −0.348265 + 0.201071i
412412 0 0
413413 112.233i 0.271751i
414414 0 0
415415 −725.949 −1.74927
416416 0 0
417417 151.469 262.353i 0.363236 0.629143i
418418 0 0
419419 −605.620 349.655i −1.44539 0.834499i −0.447193 0.894438i 0.647576π-0.647576\pi
−0.998202 + 0.0599386i 0.980910π0.980910\pi
420420 0 0
421421 −180.772 313.107i −0.429388 0.743722i 0.567431 0.823421i 0.307937π-0.307937\pi
−0.996819 + 0.0796989i 0.974604π0.974604\pi
422422 0 0
423423 259.228 149.665i 0.612831 0.353818i
424424 0 0
425425 645.131 372.466i 1.51795 0.876391i
426426 0 0
427427 −72.0653 + 124.821i −0.168771 + 0.292320i
428428 0 0
429429 308.287i 0.718619i
430430 0 0
431431 463.747i 1.07598i −0.842952 0.537989i 0.819184π-0.819184\pi
0.842952 0.537989i 0.180816π-0.180816\pi
432432 0 0
433433 −689.514 −1.59241 −0.796206 0.605026i 0.793163π-0.793163\pi
−0.796206 + 0.605026i 0.793163π0.793163\pi
434434 0 0
435435 414.576 0.953047
436436 0 0
437437 218.171 + 125.961i 0.499248 + 0.288241i
438438 0 0
439439 310.772 + 538.274i 0.707910 + 1.22614i 0.965631 + 0.259917i 0.0836951π0.0836951\pi
−0.257721 + 0.966219i 0.582972π0.582972\pi
440440 0 0
441441 12.5449 21.7284i 0.0284465 0.0492707i
442442 0 0
443443 698.843 403.477i 1.57752 0.910784i 0.582320 0.812960i 0.302145π-0.302145\pi
0.995204 0.0978236i 0.0311881π-0.0311881\pi
444444 0 0
445445 −278.969 + 483.189i −0.626897 + 1.08582i
446446 0 0
447447 −562.166 324.567i −1.25764 0.726100i
448448 0 0
449449 317.554i 0.707248i 0.935388 + 0.353624i 0.115051π0.115051\pi
−0.935388 + 0.353624i 0.884949π0.884949\pi
450450 0 0
451451 243.706 0.540368
452452 0 0
453453 230.379 + 399.027i 0.508562 + 0.880855i
454454 0 0
455455 −730.711 421.876i −1.60596 0.927201i
456456 0 0
457457 −285.843 495.094i −0.625477 1.08336i −0.988448 0.151557i 0.951571π-0.951571\pi
0.362972 0.931800i 0.381762π-0.381762\pi
458458 0 0
459459 679.593i 1.48059i
460460 0 0
461461 478.550 276.291i 1.03807 0.599330i 0.118784 0.992920i 0.462101π-0.462101\pi
0.919286 + 0.393591i 0.128767π0.128767\pi
462462 0 0
463463 60.1663 104.211i 0.129949 0.225078i −0.793708 0.608299i 0.791852π-0.791852\pi
0.923657 + 0.383221i 0.125185π0.125185\pi
464464 0 0
465465 −898.378 + 518.679i −1.93199 + 1.11544i
466466 0 0
467467 880.440i 1.88531i 0.333767 + 0.942656i 0.391680π0.391680\pi
−0.333767 + 0.942656i 0.608320π0.608320\pi
468468 0 0
469469 −591.284 −1.26073
470470 0 0
471471 122.954 212.963i 0.261049 0.452150i
472472 0 0
473473 234.127 + 135.173i 0.494982 + 0.285778i
474474 0 0
475475 260.384 + 450.998i 0.548176 + 0.949469i
476476 0 0
477477 91.5371i 0.191902i
478478 0 0
479479 593.793 342.826i 1.23965 0.715713i 0.270628 0.962684i 0.412769π-0.412769\pi
0.969023 + 0.246971i 0.0794353π0.0794353\pi
480480 0 0
481481 416.555 721.495i 0.866019 1.49999i
482482 0 0
483483 291.981i 0.604516i
484484 0 0
485485 1038.85i 2.14196i
486486 0 0
487487 391.131 0.803143 0.401571 0.915828i 0.368464π-0.368464\pi
0.401571 + 0.915828i 0.368464π0.368464\pi
488488 0 0
489489 −165.637 −0.338725
490490 0 0
491491 −166.469 96.1111i −0.339042 0.195746i 0.320807 0.947145i 0.396046π-0.396046\pi
−0.659848 + 0.751399i 0.729379π0.729379\pi
492492 0 0
493493 235.373 + 407.679i 0.477431 + 0.826935i
494494 0 0
495495 406.818 0.821855
496496 0 0
497497 −178.120 + 102.838i −0.358391 + 0.206917i
498498 0 0
499499 304.692 527.742i 0.610605 1.05760i −0.380534 0.924767i 0.624260π-0.624260\pi
0.991139 0.132832i 0.0424070π-0.0424070\pi
500500 0 0
501501 −401.409 231.754i −0.801216 0.462582i
502502 0 0
503503 232.130i 0.461491i 0.973014 + 0.230746i 0.0741165π0.0741165\pi
−0.973014 + 0.230746i 0.925883π0.925883\pi
504504 0 0
505505 240.576 0.476387
506506 0 0
507507 −169.757 294.028i −0.334827 0.579937i
508508 0 0
509509 223.136 + 128.827i 0.438381 + 0.253099i 0.702910 0.711278i 0.251883π-0.251883\pi
−0.264530 + 0.964377i 0.585217π0.585217\pi
510510 0 0
511511 −165.829 287.224i −0.324518 0.562081i
512512 0 0
513513 475.090 0.926101
514514 0 0
515515 867.610 500.915i 1.68468 0.972650i
516516 0 0
517517 −101.732 + 176.204i −0.196773 + 0.340821i
518518 0 0
519519 −68.4092 + 39.4961i −0.131810 + 0.0761003i
520520 0 0
521521 484.088i 0.929152i 0.885533 + 0.464576i 0.153793π0.153793\pi
−0.885533 + 0.464576i 0.846207π0.846207\pi
522522 0 0
523523 644.384 1.23209 0.616046 0.787711i 0.288734π-0.288734\pi
0.616046 + 0.787711i 0.288734π0.288734\pi
524524 0 0
525525 −301.788 + 522.712i −0.574834 + 0.995641i
526526 0 0
527527 −1020.10 588.955i −1.93567 1.11756i
528528 0 0
529529 −162.010 280.610i −0.306257 0.530454i
530530 0 0
531531 128.682 + 74.2944i 0.242338 + 0.139914i
532532 0 0
533533 −579.530 + 334.592i −1.08730 + 0.627752i
534534 0 0
535535 130.565 226.146i 0.244047 0.422702i
536536 0 0
537537 800.101i 1.48995i
538538 0 0
539539 17.0542i 0.0316405i
540540 0 0
541541 332.302 0.614237 0.307118 0.951671i 0.400635π-0.400635\pi
0.307118 + 0.951671i 0.400635π0.400635\pi
542542 0 0
543543 175.212 0.322674
544544 0 0
545545 342.959 + 198.008i 0.629283 + 0.363317i
546546 0 0
547547 −157.329 272.501i −0.287621 0.498174i 0.685621 0.727959i 0.259531π-0.259531\pi
−0.973241 + 0.229785i 0.926198π0.926198\pi
548548 0 0
549549 95.4092 + 165.254i 0.173787 + 0.301008i
550550 0 0
551551 −285.000 + 164.545i −0.517241 + 0.298629i
552552 0 0
553553 379.278 656.928i 0.685855 1.18793i
554554 0 0
555555 −952.090 549.689i −1.71548 0.990431i
556556 0 0
557557 664.080i 1.19224i 0.802894 + 0.596122i 0.203293π0.203293\pi
−0.802894 + 0.596122i 0.796707π0.796707\pi
558558 0 0
559559 −742.333 −1.32797
560560 0 0
561561 230.969 + 400.051i 0.411710 + 0.713103i
562562 0 0
563563 211.024 + 121.835i 0.374821 + 0.216403i 0.675563 0.737302i 0.263901π-0.263901\pi
−0.300741 + 0.953706i 0.597234π0.597234\pi
564564 0 0
565565 −610.358 1057.17i −1.08028 1.87110i
566566 0 0
567567 275.317 + 476.864i 0.485568 + 0.841029i
568568 0 0
569569 −502.155 + 289.919i −0.882522 + 0.509524i −0.871489 0.490415i 0.836845π-0.836845\pi
−0.0110330 + 0.999939i 0.503512π0.503512\pi
570570 0 0
571571 −356.843 + 618.070i −0.624944 + 1.08243i 0.363608 + 0.931552i 0.381545π0.381545\pi
−0.988552 + 0.150882i 0.951789π0.951789\pi
572572 0 0
573573 −298.681 + 172.443i −0.521258 + 0.300948i
574574 0 0
575575 423.728i 0.736918i
576576 0 0
577577 829.433 1.43749 0.718746 0.695273i 0.244717π-0.244717\pi
0.718746 + 0.695273i 0.244717π0.244717\pi
578578 0 0
579579 −325.469 + 563.730i −0.562123 + 0.973626i
580580 0 0
581581 578.409 + 333.945i 0.995541 + 0.574776i
582582 0 0
583583 −31.1102 53.8844i −0.0533623 0.0924261i
584584 0 0
585585 −967.408 + 558.533i −1.65369 + 0.954758i
586586 0 0
587587 −777.480 + 448.878i −1.32450 + 0.764699i −0.984442 0.175707i 0.943779π-0.943779\pi
−0.340054 + 0.940406i 0.610445π0.610445\pi
588588 0 0
589589 411.727 713.131i 0.699026 1.21075i
590590 0 0
591591 513.316i 0.868555i
592592 0 0
593593 378.065i 0.637547i −0.947831 0.318774i 0.896729π-0.896729\pi
0.947831 0.318774i 0.103271π-0.103271\pi
594594 0 0
595595 −1264.28 −2.12484
596596 0 0
597597 −186.000 −0.311558
598598 0 0
599599 822.438 + 474.835i 1.37302 + 0.792712i 0.991307 0.131569i 0.0420016π-0.0420016\pi
0.381711 + 0.924282i 0.375335π0.375335\pi
600600 0 0
601601 −252.308 437.011i −0.419814 0.727139i 0.576107 0.817375i 0.304571π-0.304571\pi
−0.995920 + 0.0902356i 0.971238π0.971238\pi
602602 0 0
603603 −391.408 + 677.939i −0.649101 + 1.12428i
604604 0 0
605605 534.798 308.766i 0.883964 0.510357i
606606 0 0
607607 −429.954 + 744.702i −0.708326 + 1.22686i 0.257151 + 0.966371i 0.417216π0.417216\pi
−0.965478 + 0.260486i 0.916117π0.916117\pi
608608 0 0
609609 −330.318 190.709i −0.542395 0.313152i
610610 0 0
611611 558.682i 0.914373i
612612 0 0
613613 655.253 1.06893 0.534464 0.845191i 0.320513π-0.320513\pi
0.534464 + 0.845191i 0.320513π0.320513\pi
614614 0 0
615615 441.530 + 764.752i 0.717934 + 1.24350i
616616 0 0
617617 −147.227 85.0013i −0.238617 0.137765i 0.375924 0.926650i 0.377325π-0.377325\pi
−0.614541 + 0.788885i 0.710659π0.710659\pi
618618 0 0
619619 270.531 + 468.573i 0.437045 + 0.756983i 0.997460 0.0712282i 0.0226918π-0.0226918\pi
−0.560415 + 0.828212i 0.689359π0.689359\pi
620620 0 0
621621 334.772 + 193.281i 0.539086 + 0.311241i
622622 0 0
623623 444.545 256.658i 0.713555 0.411971i
624624 0 0
625625 244.490 423.469i 0.391184 0.677550i
626626 0 0
627627 −279.667 + 161.466i −0.446040 + 0.257522i
628628 0 0
629629 1248.33i 1.98463i
630630 0 0
631631 260.788 0.413293 0.206646 0.978416i 0.433745π-0.433745\pi
0.206646 + 0.978416i 0.433745π0.433745\pi
632632 0 0
633633 −194.106 + 336.202i −0.306645 + 0.531124i
634634 0 0
635635 −76.6571 44.2580i −0.120720 0.0696977i
636636 0 0
637637 −23.4143 40.5547i −0.0367571 0.0636652i
638638 0 0
639639 272.300i 0.426134i
640640 0 0
641641 585.418 337.991i 0.913289 0.527288i 0.0318012 0.999494i 0.489876π-0.489876\pi
0.881488 + 0.472206i 0.156542π0.156542\pi
642642 0 0
643643 −378.318 + 655.267i −0.588364 + 1.01908i 0.406082 + 0.913837i 0.366895π0.366895\pi
−0.994447 + 0.105241i 0.966439π0.966439\pi
644644 0 0
645645 979.588i 1.51874i
646646 0 0
647647 554.770i 0.857450i 0.903435 + 0.428725i 0.141037π0.141037\pi
−0.903435 + 0.428725i 0.858963π0.858963\pi
648648 0 0
649649 −101.000 −0.155624
650650 0 0
651651 954.392 1.46604
652652 0 0
653653 −174.499 100.747i −0.267227 0.154283i 0.360400 0.932798i 0.382640π-0.382640\pi
−0.627627 + 0.778514i 0.715974π0.715974\pi
654654 0 0
655655 −56.7724 98.3328i −0.0866755 0.150126i
656656 0 0
657657 −439.090 −0.668325
658658 0 0
659659 89.7122 51.7954i 0.136134 0.0785969i −0.430386 0.902645i 0.641623π-0.641623\pi
0.566520 + 0.824048i 0.308289π0.308289\pi
660660 0 0
661661 109.207 189.152i 0.165215 0.286161i −0.771517 0.636209i 0.780502π-0.780502\pi
0.936732 + 0.350048i 0.113835π0.113835\pi
662662 0 0
663663 −1098.48 634.210i −1.65684 0.956576i
664664 0 0
665665 883.834i 1.32907i
666666 0 0
667667 −267.767 −0.401450
668668 0 0
669669 −147.560 255.582i −0.220568 0.382036i
670670 0 0
671671 −112.328 64.8523i −0.167403 0.0966503i
672672 0 0
673673 −394.429 683.170i −0.586075 1.01511i −0.994740 0.102428i 0.967339π-0.967339\pi
0.408665 0.912684i 0.365994π-0.365994\pi
674674 0 0
675675 399.545 + 692.032i 0.591918 + 1.02523i
676676 0 0
677677 634.550 366.358i 0.937297 0.541149i 0.0481850 0.998838i 0.484656π-0.484656\pi
0.889112 + 0.457690i 0.151323π0.151323\pi
678678 0 0
679679 −477.883 + 827.717i −0.703804 + 1.21902i
680680 0 0
681681 1150.95 664.503i 1.69009 0.975775i
682682 0 0
683683 1353.33i 1.98145i 0.135883 + 0.990725i 0.456613π0.456613\pi
−0.135883 + 0.990725i 0.543387π0.543387\pi
684684 0 0
685685 407.080 0.594277
686686 0 0
687687 −168.015 + 291.011i −0.244564 + 0.423597i
688688 0 0
689689 147.959 + 85.4243i 0.214745 + 0.123983i
690690 0 0
691691 −368.257 637.840i −0.532934 0.923068i −0.999260 0.0384555i 0.987756π-0.987756\pi
0.466327 0.884613i 0.345577π-0.345577\pi
692692 0 0
693693 −324.138 187.141i −0.467731 0.270045i
694694 0 0
695695 −646.166 + 373.064i −0.929736 + 0.536783i
696696 0 0
697697 −501.353 + 868.369i −0.719301 + 1.24587i
698698 0 0
699699 242.558i 0.347007i
700700 0 0
701701 1068.34i 1.52403i 0.647561 + 0.762014i 0.275789π0.275789\pi
−0.647561 + 0.762014i 0.724211π0.724211\pi
702702 0 0
703703 872.686 1.24137
704704 0 0
705705 −737.241 −1.04573
706706 0 0
707707 −191.682 110.667i −0.271120 0.156531i
708708 0 0
709709 136.944 + 237.194i 0.193151 + 0.334547i 0.946293 0.323311i 0.104796π-0.104796\pi
−0.753142 + 0.657858i 0.771463π0.771463\pi
710710 0 0
711711 −502.136 869.725i −0.706239 1.22324i
712712 0 0
713713 580.247 335.006i 0.813811 0.469854i
714714 0 0
715715 379.651 657.575i 0.530980 0.919685i
716716 0 0
717717 112.166 + 64.7593i 0.156438 + 0.0903197i
718718 0 0
719719 654.423i 0.910185i −0.890444 0.455092i 0.849606π-0.849606\pi
0.890444 0.455092i 0.150394π-0.150394\pi
720720 0 0
721721 −921.706 −1.27837
722722 0 0
723723 422.712 + 732.159i 0.584664 + 1.01267i
724724 0 0
725725 −479.363 276.761i −0.661191 0.381739i
726726 0 0
727727 −583.166 1010.07i −0.802155 1.38937i −0.918195 0.396128i 0.870354π-0.870354\pi
0.116041 0.993244i 0.462980π-0.462980\pi
728728 0 0
729729 729.000 1.00000
730730 0 0
731731 −963.292 + 556.157i −1.31777 + 0.760816i
732732 0 0
733733 439.146 760.623i 0.599108 1.03768i −0.393845 0.919177i 0.628855π-0.628855\pi
0.992953 0.118508i 0.0378112π-0.0378112\pi
734734 0 0
735735 −53.5163 + 30.8977i −0.0728113 + 0.0420376i
736736 0 0
737737 532.103i 0.721984i
738738 0 0
739739 593.151 0.802640 0.401320 0.915938i 0.368552π-0.368552\pi
0.401320 + 0.915938i 0.368552π0.368552\pi
740740 0 0
741741 443.363 767.928i 0.598331 1.03634i
742742 0 0
743743 −47.0561 27.1679i −0.0633326 0.0365651i 0.467999 0.883729i 0.344975π-0.344975\pi
−0.531332 + 0.847164i 0.678308π0.678308\pi
744744 0 0
745745 799.398 + 1384.60i 1.07302 + 1.85852i
746746 0 0
747747 765.771 442.118i 1.02513 0.591859i
748748 0 0
749749 −208.059 + 120.123i −0.277783 + 0.160378i
750750 0 0
751751 −455.570 + 789.071i −0.606618 + 1.05069i 0.385175 + 0.922844i 0.374141π0.374141\pi
−0.991793 + 0.127850i 0.959192π0.959192\pi
752752 0 0
753753 46.5392i 0.0618050i
754754 0 0
755755 1134.83i 1.50309i
756756 0 0
757757 −1272.22 −1.68061 −0.840304 0.542115i 0.817624π-0.817624\pi
−0.840304 + 0.542115i 0.817624π0.817624\pi
758758 0 0
759759 −262.757 −0.346189
760760 0 0
761761 399.480 + 230.640i 0.524940 + 0.303074i 0.738954 0.673756i 0.235320π-0.235320\pi
−0.214013 + 0.976831i 0.568654π0.568654\pi
762762 0 0
763763 −182.171 315.530i −0.238757 0.413539i
764764 0 0
765765 −836.908 + 1449.57i −1.09400 + 1.89486i
766766 0 0
767767 240.177 138.666i 0.313138 0.180790i
768768 0 0
769769 −269.439 + 466.682i −0.350376 + 0.606868i −0.986315 0.164871i 0.947279π-0.947279\pi
0.635940 + 0.771739i 0.280613π0.280613\pi
770770 0 0
771771 −936.104 540.460i −1.21414 0.700986i
772772 0 0
773773 1036.29i 1.34061i 0.742087 + 0.670304i 0.233836π0.233836\pi
−0.742087 + 0.670304i 0.766164π0.766164\pi
774774 0 0
775775 1385.03 1.78713
776776 0 0
777777 505.727 + 875.944i 0.650871 + 1.12734i
778778 0 0
779779 −607.059 350.486i −0.779280 0.449918i
780780 0 0
781781 −92.5449 160.292i −0.118495 0.205240i
782782 0 0
783783 −437.317 + 252.485i −0.558515 + 0.322459i
784784 0 0
785785 −524.520 + 302.832i −0.668179 + 0.385773i
786786 0 0
787787 −706.096 + 1222.99i −0.897199 + 1.55399i −0.0661406 + 0.997810i 0.521069π0.521069\pi
−0.831059 + 0.556185i 0.812265π0.812265\pi
788788 0 0
789789 −127.289 + 73.4902i −0.161329 + 0.0931435i
790790 0 0
791791 1123.09i 1.41983i
792792 0 0
793793 356.151 0.449119
794794 0 0
795795 112.727 195.248i 0.141794 0.245595i
796796 0 0
797797 −60.4602 34.9067i −0.0758597 0.0437976i 0.461590 0.887093i 0.347279π-0.347279\pi
−0.537450 + 0.843296i 0.680612π0.680612\pi
798798 0 0
799799 −418.565 724.976i −0.523861 0.907355i
800800 0 0
801801 679.593i 0.848431i
802802 0 0
803803 258.476 149.231i 0.321887 0.185842i
804804 0 0
805805 359.570 622.794i 0.446671 0.773657i
806806 0 0
807807 845.099i 1.04721i
808808 0 0
809809 1263.33i 1.56160i 0.624781 + 0.780800i 0.285188π0.285188\pi
−0.624781 + 0.780800i 0.714812π0.714812\pi
810810 0 0
811811 442.241 0.545303 0.272652 0.962113i 0.412099π-0.412099\pi
0.272652 + 0.962113i 0.412099π0.412099\pi
812812 0 0
813813 −268.788 −0.330612
814814 0 0
815815 353.302 + 203.979i 0.433499 + 0.250281i
816816 0 0
817817 −388.798 673.418i −0.475885 0.824257i
818818 0 0
819819 1027.73 1.25486
820820 0 0
821821 −498.077 + 287.565i −0.606671 + 0.350261i −0.771661 0.636034i 0.780574π-0.780574\pi
0.164991 + 0.986295i 0.447241π0.447241\pi
822822 0 0
823823 11.6214 20.1289i 0.0141208 0.0244580i −0.858879 0.512179i 0.828838π-0.828838\pi
0.872999 + 0.487721i 0.162172π0.162172\pi
824824 0 0
825825 −470.394 271.582i −0.570174 0.329190i
826826 0 0
827827 790.958i 0.956418i −0.878246 0.478209i 0.841286π-0.841286\pi
0.878246 0.478209i 0.158714π-0.158714\pi
828828 0 0
829829 −1159.78 −1.39901 −0.699503 0.714630i 0.746595π-0.746595\pi
−0.699503 + 0.714630i 0.746595π0.746595\pi
830830 0 0
831831 126.591 + 219.262i 0.152336 + 0.263853i
832832 0 0
833833 −60.7673 35.0840i −0.0729500 0.0421177i
834834 0 0
835835 570.802 + 988.658i 0.683595 + 1.18402i
836836 0 0
837837 631.772 1094.26i 0.754806 1.30736i
838838 0 0
839839 473.470 273.358i 0.564327 0.325814i −0.190553 0.981677i 0.561028π-0.561028\pi
0.754880 + 0.655862i 0.227695π0.227695\pi
840840 0 0
841841 −245.606 + 425.402i −0.292041 + 0.505829i
842842 0 0
843843 −69.8020 + 40.3002i −0.0828019 + 0.0478057i
844844 0 0
845845 836.213i 0.989601i
846846 0 0
847847 −568.143 −0.670771
848848 0 0
849849 271.469 470.199i 0.319752 0.553827i
850850 0 0
851851 614.939 + 355.035i 0.722607 + 0.417197i
852852 0 0
853853 108.317 + 187.611i 0.126984 + 0.219943i 0.922507 0.385981i 0.126137π-0.126137\pi
−0.795523 + 0.605924i 0.792804π0.792804\pi
854854 0 0
855855 −1013.36 585.066i −1.18522 0.684287i
856856 0 0
857857 489.741 282.752i 0.571460 0.329932i −0.186273 0.982498i 0.559641π-0.559641\pi
0.757732 + 0.652566i 0.226307π0.226307\pi
858858 0 0
859859 187.884 325.424i 0.218724 0.378841i −0.735694 0.677314i 0.763144π-0.763144\pi
0.954418 + 0.298473i 0.0964773π0.0964773\pi
860860 0 0
861861 812.434i 0.943594i
862862 0 0
863863 1429.35i 1.65626i 0.560534 + 0.828131i 0.310596π0.310596\pi
−0.560534 + 0.828131i 0.689404π0.689404\pi
864864 0 0
865865 194.555 0.224919
866866 0 0
867867 −1033.60 −1.19216
868868 0 0
869869 591.177 + 341.316i 0.680295 + 0.392769i
870870 0 0
871871 730.540 + 1265.33i 0.838737 + 1.45273i
872872 0 0
873873 632.682 + 1095.84i 0.724721 + 1.25525i
874874 0 0
875875 199.922 115.425i 0.228483 0.131915i
876876 0 0
877877 −420.813 + 728.870i −0.479833 + 0.831095i −0.999732 0.0231327i 0.992636π-0.992636\pi
0.519900 + 0.854227i 0.325969π0.325969\pi
878878 0 0
879879 1223.95 + 706.650i 1.39244 + 0.803925i
880880 0 0
881881 449.261i 0.509944i −0.966948 0.254972i 0.917934π-0.917934\pi
0.966948 0.254972i 0.0820663π-0.0820663\pi
882882 0 0
883883 −122.445 −0.138669 −0.0693346 0.997593i 0.522088π-0.522088\pi
−0.0693346 + 0.997593i 0.522088π0.522088\pi
884884 0 0
885885 −182.985 316.939i −0.206762 0.358123i
886886 0 0
887887 −1361.09 785.828i −1.53449 0.885940i −0.999147 0.0413069i 0.986848π-0.986848\pi
−0.535346 0.844633i 0.679819π-0.679819\pi
888888 0 0
889889 40.7184 + 70.5263i 0.0458025 + 0.0793322i
890890 0 0
891891 −429.135 + 247.761i −0.481633 + 0.278071i
892892 0 0
893893 506.816 292.611i 0.567543 0.327671i
894894 0 0
895895 985.312 1706.61i 1.10091 1.90683i
896896 0 0
897897 624.833 360.747i 0.696580 0.402171i
898898 0 0
899899 875.244i 0.973575i
900900 0 0
901901 256.000 0.284129
902902 0 0
903903 450.621 780.499i 0.499027 0.864340i
904904 0 0
905905 −373.727 215.771i −0.412957 0.238421i
906906 0 0
907907 −349.288 604.984i −0.385102 0.667017i 0.606681 0.794945i 0.292500π-0.292500\pi
−0.991783 + 0.127929i 0.959167π0.959167\pi
908908 0 0
909909 −253.772 + 146.516i −0.279178 + 0.161183i
910910 0 0
911911 −70.4888 + 40.6967i −0.0773752 + 0.0446726i −0.538188 0.842825i 0.680891π-0.680891\pi
0.460813 + 0.887497i 0.347558π0.347558\pi
912912 0 0
913913 −300.520 + 520.517i −0.329157 + 0.570117i
914914 0 0
915915 469.980i 0.513639i
916916 0 0
917917 104.464i 0.113919i
918918 0 0
919919 −348.665 −0.379396 −0.189698 0.981842i 0.560751π-0.560751\pi
−0.189698 + 0.981842i 0.560751π0.560751\pi
920920 0 0
921921 −1394.24 −1.51383
922922 0 0
923923 440.141 + 254.115i 0.476859 + 0.275315i
924924 0 0
925925 733.918 + 1271.18i 0.793425 + 1.37425i
926926 0 0
927927 −610.136 + 1056.79i −0.658183 + 1.14001i
928928 0 0
929929 −932.298 + 538.262i −1.00355 + 0.579400i −0.909297 0.416148i 0.863380π-0.863380\pi
−0.0942533 + 0.995548i 0.530046π0.530046\pi
930930 0 0
931931 24.5265 42.4812i 0.0263443 0.0456297i
932932 0 0
933933 −655.044 378.190i −0.702083 0.405348i
934934 0 0
935935 1137.74i 1.21683i
936936 0 0
937937 −1437.39 −1.53404 −0.767018 0.641626i 0.778260π-0.778260\pi
−0.767018 + 0.641626i 0.778260π0.778260\pi
938938 0 0
939939 −294.318 509.774i −0.313438 0.542891i
940940 0 0
941941 186.591 + 107.728i 0.198290 + 0.114483i 0.595858 0.803090i 0.296812π-0.296812\pi
−0.397568 + 0.917573i 0.630146π0.630146\pi
942942 0 0
943943 −285.177 493.940i −0.302414 0.523797i
944944 0 0
945945 1356.20i 1.43513i
946946 0 0
947947 407.651 235.357i 0.430466 0.248529i −0.269079 0.963118i 0.586719π-0.586719\pi
0.699545 + 0.714589i 0.253386π0.253386\pi
948948 0 0
949949 −409.767 + 709.738i −0.431789 + 0.747880i
950950 0 0
951951 −296.954 + 171.447i −0.312255 + 0.180280i
952952 0 0
953953 1192.14i 1.25093i 0.780251 + 0.625466i 0.215091π0.215091\pi
−0.780251 + 0.625466i 0.784909π0.784909\pi
954954 0 0
955955 849.445 0.889471
956956 0 0
957957 171.621 297.257i 0.179333 0.310613i
958958 0 0
959959 −324.346 187.261i −0.338213 0.195267i
960960 0 0
961961 −614.524 1064.39i −0.639464 1.10758i
962962 0 0
963963 318.068i 0.330289i
964964 0 0
965965 1388.45 801.621i 1.43881 0.830695i
966966 0 0
967967 96.3888 166.950i 0.0996782 0.172648i −0.811873 0.583834i 0.801552π-0.801552\pi
0.911551 + 0.411186i 0.134885π0.134885\pi
968968 0 0
969969 1328.67i 1.37118i
970970 0 0
971971 202.388i 0.208433i −0.994555 0.104216i 0.966767π-0.966767\pi
0.994555 0.104216i 0.0332335π-0.0332335\pi
972972 0 0
973973 686.455 0.705504
974974 0 0
975975 1491.45 1.52970
976976 0 0
977977 35.1980 + 20.3216i 0.0360266 + 0.0208000i 0.517905 0.855438i 0.326712π-0.326712\pi
−0.481879 + 0.876238i 0.660045π0.660045\pi
978978 0 0
979979 230.969 + 400.051i 0.235924 + 0.408632i
980980 0 0
981981 −482.363 −0.491706
982982 0 0
983983 631.105 364.369i 0.642019 0.370670i −0.143373 0.989669i 0.545795π-0.545795\pi
0.785392 + 0.618999i 0.212461π0.212461\pi
984984 0 0
985985 632.141 1094.90i 0.641767 1.11157i
986986 0 0
987987 587.406 + 339.139i 0.595143 + 0.343606i
988988 0 0
989989 632.699i 0.639736i
990990 0 0
991991 746.527 0.753306 0.376653 0.926354i 0.377075π-0.377075\pi
0.376653 + 0.926354i 0.377075π0.377075\pi
992992 0 0
993993 81.8939 + 141.844i 0.0824712 + 0.142844i
994994 0 0
995995 396.737 + 229.056i 0.398730 + 0.230207i
996996 0 0
997997 119.046 + 206.194i 0.119404 + 0.206814i 0.919532 0.393016i 0.128568π-0.128568\pi
−0.800128 + 0.599830i 0.795235π0.795235\pi
998998 0 0
999999 1339.09 1.34043
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 576.3.q.h.257.1 4
3.2 odd 2 1728.3.q.e.449.2 4
4.3 odd 2 576.3.q.c.257.1 4
8.3 odd 2 144.3.q.d.113.2 4
8.5 even 2 72.3.m.a.41.2 4
9.2 odd 6 inner 576.3.q.h.65.1 4
9.7 even 3 1728.3.q.e.1601.2 4
12.11 even 2 1728.3.q.f.449.2 4
24.5 odd 2 216.3.m.a.17.1 4
24.11 even 2 432.3.q.c.17.1 4
36.7 odd 6 1728.3.q.f.1601.2 4
36.11 even 6 576.3.q.c.65.1 4
72.5 odd 6 648.3.e.b.161.4 4
72.11 even 6 144.3.q.d.65.2 4
72.13 even 6 648.3.e.b.161.1 4
72.29 odd 6 72.3.m.a.65.2 yes 4
72.43 odd 6 432.3.q.c.305.1 4
72.59 even 6 1296.3.e.c.161.4 4
72.61 even 6 216.3.m.a.89.1 4
72.67 odd 6 1296.3.e.c.161.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.m.a.41.2 4 8.5 even 2
72.3.m.a.65.2 yes 4 72.29 odd 6
144.3.q.d.65.2 4 72.11 even 6
144.3.q.d.113.2 4 8.3 odd 2
216.3.m.a.17.1 4 24.5 odd 2
216.3.m.a.89.1 4 72.61 even 6
432.3.q.c.17.1 4 24.11 even 2
432.3.q.c.305.1 4 72.43 odd 6
576.3.q.c.65.1 4 36.11 even 6
576.3.q.c.257.1 4 4.3 odd 2
576.3.q.h.65.1 4 9.2 odd 6 inner
576.3.q.h.257.1 4 1.1 even 1 trivial
648.3.e.b.161.1 4 72.13 even 6
648.3.e.b.161.4 4 72.5 odd 6
1296.3.e.c.161.1 4 72.67 odd 6
1296.3.e.c.161.4 4 72.59 even 6
1728.3.q.e.449.2 4 3.2 odd 2
1728.3.q.e.1601.2 4 9.7 even 3
1728.3.q.f.449.2 4 12.11 even 2
1728.3.q.f.1601.2 4 36.7 odd 6