Properties

Label 72.4.i.a.25.4
Level 7272
Weight 44
Character 72.25
Analytic conductor 4.2484.248
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,4,Mod(25,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.25");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 72=2332 72 = 2^{3} \cdot 3^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 72.i (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.248137520414.24813752041
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 8.0.5206055409.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x83x7+x6+9x523x4+27x3+9x281x+81 x^{8} - 3x^{7} + x^{6} + 9x^{5} - 23x^{4} + 27x^{3} + 9x^{2} - 81x + 81 Copy content Toggle raw display
Coefficient ring: Z[a1,,a23]\Z[a_1, \ldots, a_{23}]
Coefficient ring index: 2634 2^{6}\cdot 3^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 25.4
Root 1.35516+1.07868i1.35516 + 1.07868i of defining polynomial
Character χ\chi == 72.25
Dual form 72.4.i.a.49.4

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+(3.96518+3.35817i)q3+(4.00813+6.94228i)q5+(0.468615+0.811666i)q7+(4.44536+26.6315i)q9+(2.66835+4.62171i)q11+(1.55794+2.69842i)q13+(7.42041+40.9874i)q15+132.704q1786.6565q19+(4.58386+1.64471i)q21+(20.621235.7170i)q23+(30.369852.6021i)q25+(71.8066+120.527i)q27+(101.397175.625i)q29+(159.367276.031i)q31+(26.1010+9.36517i)q337.51308q35363.510q37+(2.88427+15.9316i)q39+(4.917298.51700i)q41+(181.230313.899i)q43+(167.066+137.604i)q45+(37.588065.1043i)q47+(171.061+296.286i)q49+(526.197+445.644i)q51+403.981q5342.7803q55+(343.609291.007i)q57+(215.351+372.999i)q59+(160.783+278.484i)q61+(23.69918.87180i)q63+(12.4888+21.6313i)q65+(363.324+629.296i)q67+(38.1769210.874i)q69829.702q71160.106q73+(297.069106.590i)q75+(2.500864.33161i)q77+(462.314800.752i)q79+(689.478+236.773i)q81+(255.843+443.134i)q83+(531.896+921.271i)q85+(991.838355.876i)q87320.459q892.92029q91+(295.0421629.69i)q93+(347.330601.594i)q95+(300.821521.038i)q97+(134.94550.5170i)q99+O(q100)q+(3.96518 + 3.35817i) q^{3} +(4.00813 + 6.94228i) q^{5} +(-0.468615 + 0.811666i) q^{7} +(4.44536 + 26.6315i) q^{9} +(-2.66835 + 4.62171i) q^{11} +(1.55794 + 2.69842i) q^{13} +(-7.42041 + 40.9874i) q^{15} +132.704 q^{17} -86.6565 q^{19} +(-4.58386 + 1.64471i) q^{21} +(-20.6212 - 35.7170i) q^{23} +(30.3698 - 52.6021i) q^{25} +(-71.8066 + 120.527i) q^{27} +(101.397 - 175.625i) q^{29} +(-159.367 - 276.031i) q^{31} +(-26.1010 + 9.36517i) q^{33} -7.51308 q^{35} -363.510 q^{37} +(-2.88427 + 15.9316i) q^{39} +(-4.91729 - 8.51700i) q^{41} +(181.230 - 313.899i) q^{43} +(-167.066 + 137.604i) q^{45} +(37.5880 - 65.1043i) q^{47} +(171.061 + 296.286i) q^{49} +(526.197 + 445.644i) q^{51} +403.981 q^{53} -42.7803 q^{55} +(-343.609 - 291.007i) q^{57} +(215.351 + 372.999i) q^{59} +(-160.783 + 278.484i) q^{61} +(-23.6991 - 8.87180i) q^{63} +(-12.4888 + 21.6313i) q^{65} +(363.324 + 629.296i) q^{67} +(38.1769 - 210.874i) q^{69} -829.702 q^{71} -160.106 q^{73} +(297.069 - 106.590i) q^{75} +(-2.50086 - 4.33161i) q^{77} +(462.314 - 800.752i) q^{79} +(-689.478 + 236.773i) q^{81} +(-255.843 + 443.134i) q^{83} +(531.896 + 921.271i) q^{85} +(991.838 - 355.876i) q^{87} -320.459 q^{89} -2.92029 q^{91} +(295.042 - 1629.69i) q^{93} +(-347.330 - 601.594i) q^{95} +(300.821 - 521.038i) q^{97} +(-134.945 - 50.5170i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q3q35q5+3q715q9+16q11+29q13+141q1534q17218q19+27q21+37q23+97q25216q273q29+331q31+468q33342q35+5133q99+O(q100) 8 q - 3 q^{3} - 5 q^{5} + 3 q^{7} - 15 q^{9} + 16 q^{11} + 29 q^{13} + 141 q^{15} - 34 q^{17} - 218 q^{19} + 27 q^{21} + 37 q^{23} + 97 q^{25} - 216 q^{27} - 3 q^{29} + 331 q^{31} + 468 q^{33} - 342 q^{35}+ \cdots - 5133 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/72Z)×\left(\mathbb{Z}/72\mathbb{Z}\right)^\times.

nn 3737 5555 6565
χ(n)\chi(n) 11 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 3.96518 + 3.35817i 0.763100 + 0.646281i
44 0 0
55 4.00813 + 6.94228i 0.358498 + 0.620937i 0.987710 0.156297i 0.0499557π-0.0499557\pi
−0.629212 + 0.777234i 0.716622π0.716622\pi
66 0 0
77 −0.468615 + 0.811666i −0.0253028 + 0.0438258i −0.878400 0.477927i 0.841388π-0.841388\pi
0.853097 + 0.521753i 0.174722π0.174722\pi
88 0 0
99 4.44536 + 26.6315i 0.164643 + 0.986353i
1010 0 0
1111 −2.66835 + 4.62171i −0.0731397 + 0.126682i −0.900276 0.435320i 0.856635π-0.856635\pi
0.827136 + 0.562002i 0.189969π0.189969\pi
1212 0 0
1313 1.55794 + 2.69842i 0.0332380 + 0.0575699i 0.882166 0.470939i 0.156085π-0.156085\pi
−0.848928 + 0.528509i 0.822751π0.822751\pi
1414 0 0
1515 −7.42041 + 40.9874i −0.127730 + 0.705527i
1616 0 0
1717 132.704 1.89327 0.946634 0.322311i 0.104460π-0.104460\pi
0.946634 + 0.322311i 0.104460π0.104460\pi
1818 0 0
1919 −86.6565 −1.04634 −0.523168 0.852230i 0.675250π-0.675250\pi
−0.523168 + 0.852230i 0.675250π0.675250\pi
2020 0 0
2121 −4.58386 + 1.64471i −0.0476324 + 0.0170907i
2222 0 0
2323 −20.6212 35.7170i −0.186949 0.323805i 0.757283 0.653087i 0.226526π-0.226526\pi
−0.944231 + 0.329282i 0.893193π0.893193\pi
2424 0 0
2525 30.3698 52.6021i 0.242959 0.420817i
2626 0 0
2727 −71.8066 + 120.527i −0.511822 + 0.859092i
2828 0 0
2929 101.397 175.625i 0.649275 1.12458i −0.334021 0.942566i 0.608406π-0.608406\pi
0.983296 0.182012i 0.0582610π-0.0582610\pi
3030 0 0
3131 −159.367 276.031i −0.923325 1.59925i −0.794233 0.607614i 0.792127π-0.792127\pi
−0.129093 0.991633i 0.541206π-0.541206\pi
3232 0 0
3333 −26.1010 + 9.36517i −0.137685 + 0.0494020i
3434 0 0
3535 −7.51308 −0.0362841
3636 0 0
3737 −363.510 −1.61515 −0.807577 0.589762i 0.799222π-0.799222\pi
−0.807577 + 0.589762i 0.799222π0.799222\pi
3838 0 0
3939 −2.88427 + 15.9316i −0.0118424 + 0.0654126i
4040 0 0
4141 −4.91729 8.51700i −0.0187305 0.0324423i 0.856508 0.516133i 0.172629π-0.172629\pi
−0.875239 + 0.483691i 0.839296π0.839296\pi
4242 0 0
4343 181.230 313.899i 0.642728 1.11324i −0.342094 0.939666i 0.611136π-0.611136\pi
0.984821 0.173571i 0.0555307π-0.0555307\pi
4444 0 0
4545 −167.066 + 137.604i −0.553439 + 0.455838i
4646 0 0
4747 37.5880 65.1043i 0.116655 0.202052i −0.801785 0.597612i 0.796116π-0.796116\pi
0.918440 + 0.395560i 0.129450π0.129450\pi
4848 0 0
4949 171.061 + 296.286i 0.498720 + 0.863808i
5050 0 0
5151 526.197 + 445.644i 1.44475 + 1.22358i
5252 0 0
5353 403.981 1.04700 0.523501 0.852025i 0.324626π-0.324626\pi
0.523501 + 0.852025i 0.324626π0.324626\pi
5454 0 0
5555 −42.7803 −0.104882
5656 0 0
5757 −343.609 291.007i −0.798458 0.676226i
5858 0 0
5959 215.351 + 372.999i 0.475192 + 0.823057i 0.999596 0.0284128i 0.00904529π-0.00904529\pi
−0.524404 + 0.851469i 0.675712π0.675712\pi
6060 0 0
6161 −160.783 + 278.484i −0.337477 + 0.584527i −0.983957 0.178403i 0.942907π-0.942907\pi
0.646480 + 0.762931i 0.276240π0.276240\pi
6262 0 0
6363 −23.6991 8.87180i −0.0473937 0.0177419i
6464 0 0
6565 −12.4888 + 21.6313i −0.0238315 + 0.0412774i
6666 0 0
6767 363.324 + 629.296i 0.662494 + 1.14747i 0.979958 + 0.199203i 0.0638353π0.0638353\pi
−0.317464 + 0.948270i 0.602831π0.602831\pi
6868 0 0
6969 38.1769 210.874i 0.0666081 0.367917i
7070 0 0
7171 −829.702 −1.38687 −0.693433 0.720521i 0.743903π-0.743903\pi
−0.693433 + 0.720521i 0.743903π0.743903\pi
7272 0 0
7373 −160.106 −0.256699 −0.128349 0.991729i 0.540968π-0.540968\pi
−0.128349 + 0.991729i 0.540968π0.540968\pi
7474 0 0
7575 297.069 106.590i 0.457367 0.164106i
7676 0 0
7777 −2.50086 4.33161i −0.00370129 0.00641081i
7878 0 0
7979 462.314 800.752i 0.658410 1.14040i −0.322617 0.946530i 0.604563π-0.604563\pi
0.981027 0.193870i 0.0621041π-0.0621041\pi
8080 0 0
8181 −689.478 + 236.773i −0.945785 + 0.324792i
8282 0 0
8383 −255.843 + 443.134i −0.338343 + 0.586027i −0.984121 0.177498i 0.943200π-0.943200\pi
0.645778 + 0.763525i 0.276533π0.276533\pi
8484 0 0
8585 531.896 + 921.271i 0.678732 + 1.17560i
8686 0 0
8787 991.838 355.876i 1.22225 0.438551i
8888 0 0
8989 −320.459 −0.381669 −0.190835 0.981622i 0.561119π-0.561119\pi
−0.190835 + 0.981622i 0.561119π0.561119\pi
9090 0 0
9191 −2.92029 −0.00336406
9292 0 0
9393 295.042 1629.69i 0.328972 1.81711i
9494 0 0
9595 −347.330 601.594i −0.375109 0.649708i
9696 0 0
9797 300.821 521.038i 0.314884 0.545396i −0.664529 0.747263i 0.731368π-0.731368\pi
0.979413 + 0.201867i 0.0647009π0.0647009\pi
9898 0 0
9999 −134.945 50.5170i −0.136995 0.0512843i
100100 0 0
101101 −438.162 + 758.920i −0.431671 + 0.747676i −0.997017 0.0771773i 0.975409π-0.975409\pi
0.565346 + 0.824854i 0.308743π0.308743\pi
102102 0 0
103103 111.719 + 193.502i 0.106873 + 0.185110i 0.914502 0.404581i 0.132583π-0.132583\pi
−0.807629 + 0.589691i 0.799249π0.799249\pi
104104 0 0
105105 −29.7907 25.2302i −0.0276884 0.0234497i
106106 0 0
107107 −1265.34 −1.14322 −0.571612 0.820524i 0.693682π-0.693682\pi
−0.571612 + 0.820524i 0.693682π0.693682\pi
108108 0 0
109109 −213.009 −0.187180 −0.0935898 0.995611i 0.529834π-0.529834\pi
−0.0935898 + 0.995611i 0.529834π0.529834\pi
110110 0 0
111111 −1441.39 1220.73i −1.23252 1.04384i
112112 0 0
113113 −806.988 1397.74i −0.671814 1.16362i −0.977389 0.211449i 0.932182π-0.932182\pi
0.305575 0.952168i 0.401151π-0.401151\pi
114114 0 0
115115 165.305 286.317i 0.134041 0.232167i
116116 0 0
117117 −64.9376 + 53.4857i −0.0513118 + 0.0422629i
118118 0 0
119119 −62.1873 + 107.712i −0.0479051 + 0.0829740i
120120 0 0
121121 651.260 + 1128.02i 0.489301 + 0.847494i
122122 0 0
123123 9.10359 50.2846i 0.00667352 0.0368619i
124124 0 0
125125 1488.94 1.06540
126126 0 0
127127 −1234.19 −0.862333 −0.431167 0.902272i 0.641898π-0.641898\pi
−0.431167 + 0.902272i 0.641898π0.641898\pi
128128 0 0
129129 1772.74 636.067i 1.20993 0.434129i
130130 0 0
131131 723.720 + 1253.52i 0.482685 + 0.836034i 0.999802 0.0198800i 0.00632843π-0.00632843\pi
−0.517118 + 0.855914i 0.672995π0.672995\pi
132132 0 0
133133 40.6086 70.3361i 0.0264753 0.0458565i
134134 0 0
135135 −1124.54 15.4133i −0.716928 0.00982643i
136136 0 0
137137 −276.891 + 479.589i −0.172674 + 0.299081i −0.939354 0.342949i 0.888574π-0.888574\pi
0.766680 + 0.642030i 0.221907π0.221907\pi
138138 0 0
139139 794.528 + 1376.16i 0.484827 + 0.839745i 0.999848 0.0174326i 0.00554925π-0.00554925\pi
−0.515021 + 0.857178i 0.672216π0.672216\pi
140140 0 0
141141 367.675 131.924i 0.219601 0.0787941i
142142 0 0
143143 −16.6285 −0.00972406
144144 0 0
145145 1625.65 0.931055
146146 0 0
147147 −316.692 + 1749.28i −0.177689 + 0.981484i
148148 0 0
149149 606.406 + 1050.33i 0.333414 + 0.577490i 0.983179 0.182645i 0.0584660π-0.0584660\pi
−0.649765 + 0.760135i 0.725133π0.725133\pi
150150 0 0
151151 −265.929 + 460.603i −0.143318 + 0.248234i −0.928744 0.370721i 0.879110π-0.879110\pi
0.785426 + 0.618955i 0.212444π0.212444\pi
152152 0 0
153153 589.919 + 3534.12i 0.311713 + 1.86743i
154154 0 0
155155 1277.52 2212.74i 0.662020 1.14665i
156156 0 0
157157 −1081.47 1873.16i −0.549749 0.952194i −0.998291 0.0584320i 0.981390π-0.981390\pi
0.448542 0.893762i 0.351943π-0.351943\pi
158158 0 0
159159 1601.86 + 1356.64i 0.798967 + 0.676657i
160160 0 0
161161 38.6537 0.0189213
162162 0 0
163163 −1602.11 −0.769859 −0.384930 0.922946i 0.625774π-0.625774\pi
−0.384930 + 0.922946i 0.625774π0.625774\pi
164164 0 0
165165 −169.632 143.664i −0.0800352 0.0677830i
166166 0 0
167167 866.800 + 1501.34i 0.401647 + 0.695673i 0.993925 0.110061i 0.0351046π-0.0351046\pi
−0.592278 + 0.805734i 0.701771π0.701771\pi
168168 0 0
169169 1093.65 1894.25i 0.497790 0.862198i
170170 0 0
171171 −385.219 2307.80i −0.172272 1.03206i
172172 0 0
173173 −937.323 + 1623.49i −0.411927 + 0.713478i −0.995100 0.0988692i 0.968477π-0.968477\pi
0.583173 + 0.812348i 0.301811π0.301811\pi
174174 0 0
175175 28.4635 + 49.3003i 0.0122951 + 0.0212957i
176176 0 0
177177 −398.688 + 2202.20i −0.169307 + 0.935182i
178178 0 0
179179 2058.01 0.859344 0.429672 0.902985i 0.358629π-0.358629\pi
0.429672 + 0.902985i 0.358629π0.358629\pi
180180 0 0
181181 −3938.45 −1.61736 −0.808681 0.588248i 0.799818π-0.799818\pi
−0.808681 + 0.588248i 0.799818π0.799818\pi
182182 0 0
183183 −1572.73 + 564.303i −0.635297 + 0.227948i
184184 0 0
185185 −1457.00 2523.59i −0.579030 1.00291i
186186 0 0
187187 −354.101 + 613.322i −0.138473 + 0.239842i
188188 0 0
189189 −64.1781 114.764i −0.0246998 0.0441685i
190190 0 0
191191 2232.54 3866.88i 0.845765 1.46491i −0.0391899 0.999232i 0.512478π-0.512478\pi
0.884955 0.465676i 0.154189π-0.154189\pi
192192 0 0
193193 −2075.02 3594.03i −0.773901 1.34044i −0.935410 0.353564i 0.884970π-0.884970\pi
0.161509 0.986871i 0.448364π-0.448364\pi
194194 0 0
195195 −122.162 + 43.8323i −0.0448626 + 0.0160969i
196196 0 0
197197 536.823 0.194148 0.0970738 0.995277i 0.469052π-0.469052\pi
0.0970738 + 0.995277i 0.469052π0.469052\pi
198198 0 0
199199 1953.59 0.695911 0.347956 0.937511i 0.386876π-0.386876\pi
0.347956 + 0.937511i 0.386876π0.386876\pi
200200 0 0
201201 −672.637 + 3715.38i −0.236040 + 1.30379i
202202 0 0
203203 95.0325 + 164.601i 0.0328570 + 0.0569100i
204204 0 0
205205 39.4183 68.2745i 0.0134297 0.0232610i
206206 0 0
207207 859.530 707.950i 0.288606 0.237710i
208208 0 0
209209 231.230 400.501i 0.0765286 0.132551i
210210 0 0
211211 −1613.64 2794.91i −0.526482 0.911894i −0.999524 0.0308540i 0.990177π-0.990177\pi
0.473042 0.881040i 0.343156π-0.343156\pi
212212 0 0
213213 −3289.92 2786.28i −1.05832 0.896305i
214214 0 0
215215 2905.57 0.921666
216216 0 0
217217 298.726 0.0934510
218218 0 0
219219 −634.850 537.664i −0.195887 0.165899i
220220 0 0
221221 206.745 + 358.093i 0.0629284 + 0.108995i
222222 0 0
223223 −2327.99 + 4032.19i −0.699075 + 1.21083i 0.269713 + 0.962941i 0.413071π0.413071\pi
−0.968788 + 0.247892i 0.920262π0.920262\pi
224224 0 0
225225 1535.88 + 574.960i 0.455075 + 0.170359i
226226 0 0
227227 2040.40 3534.08i 0.596592 1.03333i −0.396728 0.917936i 0.629854π-0.629854\pi
0.993320 0.115391i 0.0368122π-0.0368122\pi
228228 0 0
229229 −649.220 1124.48i −0.187344 0.324489i 0.757020 0.653391i 0.226654π-0.226654\pi
−0.944364 + 0.328903i 0.893321π0.893321\pi
230230 0 0
231231 4.62994 25.5739i 0.00131873 0.00728416i
232232 0 0
233233 −3073.26 −0.864103 −0.432052 0.901849i 0.642210π-0.642210\pi
−0.432052 + 0.901849i 0.642210π0.642210\pi
234234 0 0
235235 602.630 0.167282
236236 0 0
237237 4522.22 1622.60i 1.23945 0.444721i
238238 0 0
239239 1787.76 + 3096.49i 0.483852 + 0.838056i 0.999828 0.0185469i 0.00590399π-0.00590399\pi
−0.515976 + 0.856603i 0.672571π0.672571\pi
240240 0 0
241241 1358.79 2353.50i 0.363185 0.629055i −0.625298 0.780386i 0.715023π-0.715023\pi
0.988483 + 0.151331i 0.0483560π0.0483560\pi
242242 0 0
243243 −3529.03 1376.53i −0.931636 0.363394i
244244 0 0
245245 −1371.27 + 2375.10i −0.357580 + 0.619346i
246246 0 0
247247 −135.005 233.836i −0.0347781 0.0602374i
248248 0 0
249249 −2502.59 + 897.941i −0.636928 + 0.228533i
250250 0 0
251251 −4583.36 −1.15259 −0.576293 0.817243i 0.695501π-0.695501\pi
−0.576293 + 0.817243i 0.695501π0.695501\pi
252252 0 0
253253 220.098 0.0546935
254254 0 0
255255 −984.722 + 5439.21i −0.241826 + 1.33575i
256256 0 0
257257 −2987.71 5174.87i −0.725169 1.25603i −0.958904 0.283730i 0.908428π-0.908428\pi
0.233735 0.972300i 0.424905π-0.424905\pi
258258 0 0
259259 170.346 295.049i 0.0408680 0.0707855i
260260 0 0
261261 5127.91 + 1919.65i 1.21613 + 0.455261i
262262 0 0
263263 −3087.59 + 5347.86i −0.723912 + 1.25385i 0.235509 + 0.971872i 0.424324π0.424324\pi
−0.959420 + 0.281980i 0.909009π0.909009\pi
264264 0 0
265265 1619.21 + 2804.55i 0.375348 + 0.650121i
266266 0 0
267267 −1270.68 1076.16i −0.291252 0.246665i
268268 0 0
269269 6580.02 1.49142 0.745708 0.666273i 0.232111π-0.232111\pi
0.745708 + 0.666273i 0.232111π0.232111\pi
270270 0 0
271271 5817.31 1.30397 0.651986 0.758231i 0.273936π-0.273936\pi
0.651986 + 0.758231i 0.273936π0.273936\pi
272272 0 0
273273 −11.5795 9.80684i −0.00256712 0.00217413i
274274 0 0
275275 162.074 + 280.721i 0.0355398 + 0.0615568i
276276 0 0
277277 −4325.53 + 7492.03i −0.938252 + 1.62510i −0.169521 + 0.985527i 0.554222π0.554222\pi
−0.768730 + 0.639573i 0.779111π0.779111\pi
278278 0 0
279279 6642.69 5471.23i 1.42540 1.17403i
280280 0 0
281281 −3648.14 + 6318.76i −0.774483 + 1.34144i 0.160602 + 0.987019i 0.448656π0.448656\pi
−0.935085 + 0.354424i 0.884677π0.884677\pi
282282 0 0
283283 405.958 + 703.140i 0.0852710 + 0.147694i 0.905507 0.424332i 0.139491π-0.139491\pi
−0.820236 + 0.572026i 0.806158π0.806158\pi
284284 0 0
285285 643.027 3551.82i 0.133648 0.738217i
286286 0 0
287287 9.21728 0.00189574
288288 0 0
289289 12697.5 2.58446
290290 0 0
291291 2942.55 1055.80i 0.592767 0.212688i
292292 0 0
293293 2400.96 + 4158.58i 0.478722 + 0.829170i 0.999702 0.0243984i 0.00776702π-0.00776702\pi
−0.520981 + 0.853568i 0.674434π0.674434\pi
294294 0 0
295295 −1726.31 + 2990.06i −0.340711 + 0.590128i
296296 0 0
297297 −365.437 653.478i −0.0713967 0.127672i
298298 0 0
299299 64.2531 111.290i 0.0124276 0.0215252i
300300 0 0
301301 169.854 + 294.196i 0.0325257 + 0.0563361i
302302 0 0
303303 −4285.98 + 1537.83i −0.812617 + 0.291571i
304304 0 0
305305 −2577.75 −0.483939
306306 0 0
307307 −755.147 −0.140386 −0.0701930 0.997533i 0.522362π-0.522362\pi
−0.0701930 + 0.997533i 0.522362π0.522362\pi
308308 0 0
309309 −206.829 + 1142.44i −0.0380780 + 0.210328i
310310 0 0
311311 −2633.03 4560.55i −0.480082 0.831527i 0.519657 0.854375i 0.326060π-0.326060\pi
−0.999739 + 0.0228482i 0.992727π0.992727\pi
312312 0 0
313313 −697.053 + 1207.33i −0.125878 + 0.218027i −0.922076 0.387009i 0.873508π-0.873508\pi
0.796198 + 0.605036i 0.206841π0.206841\pi
314314 0 0
315315 −33.3983 200.085i −0.00597391 0.0357889i
316316 0 0
317317 2558.55 4431.55i 0.453321 0.785175i −0.545269 0.838261i 0.683572π-0.683572\pi
0.998590 + 0.0530862i 0.0169058π0.0169058\pi
318318 0 0
319319 541.126 + 937.257i 0.0949756 + 0.164503i
320320 0 0
321321 −5017.30 4249.23i −0.872394 0.738843i
322322 0 0
323323 −11499.7 −1.98099
324324 0 0
325325 189.257 0.0323018
326326 0 0
327327 −844.620 715.321i −0.142837 0.120970i
328328 0 0
329329 35.2286 + 61.0177i 0.00590339 + 0.0102250i
330330 0 0
331331 121.400 210.271i 0.0201593 0.0349170i −0.855770 0.517357i 0.826916π-0.826916\pi
0.875929 + 0.482440i 0.160249π0.160249\pi
332332 0 0
333333 −1615.93 9680.84i −0.265924 1.59311i
334334 0 0
335335 −2912.50 + 5044.59i −0.475005 + 0.822733i
336336 0 0
337337 25.6472 + 44.4223i 0.00414568 + 0.00718052i 0.868091 0.496405i 0.165347π-0.165347\pi
−0.863945 + 0.503586i 0.832014π0.832014\pi
338338 0 0
339339 1494.01 8252.31i 0.239361 1.32214i
340340 0 0
341341 1700.98 0.270127
342342 0 0
343343 −642.117 −0.101082
344344 0 0
345345 1616.96 580.175i 0.252332 0.0905379i
346346 0 0
347347 430.722 + 746.032i 0.0666350 + 0.115415i 0.897418 0.441181i 0.145440π-0.145440\pi
−0.830783 + 0.556596i 0.812107π0.812107\pi
348348 0 0
349349 −1562.68 + 2706.64i −0.239680 + 0.415138i −0.960623 0.277857i 0.910376π-0.910376\pi
0.720942 + 0.692995i 0.243709π0.243709\pi
350350 0 0
351351 −437.104 5.99107i −0.0664697 0.000911053i
352352 0 0
353353 4162.36 7209.43i 0.627593 1.08702i −0.360440 0.932782i 0.617374π-0.617374\pi
0.988033 0.154241i 0.0492931π-0.0492931\pi
354354 0 0
355355 −3325.55 5760.02i −0.497189 0.861156i
356356 0 0
357357 −608.298 + 218.261i −0.0901808 + 0.0323573i
358358 0 0
359359 −5819.46 −0.855542 −0.427771 0.903887i 0.640701π-0.640701\pi
−0.427771 + 0.903887i 0.640701π0.640701\pi
360360 0 0
361361 650.350 0.0948170
362362 0 0
363363 −1205.70 + 6659.83i −0.174334 + 0.962949i
364364 0 0
365365 −641.725 1111.50i −0.0920259 0.159393i
366366 0 0
367367 3129.64 5420.69i 0.445138 0.771002i −0.552924 0.833232i 0.686488π-0.686488\pi
0.998062 + 0.0622299i 0.0198212π0.0198212\pi
368368 0 0
369369 204.962 168.816i 0.0289157 0.0238163i
370370 0 0
371371 −189.312 + 327.898i −0.0264921 + 0.0458857i
372372 0 0
373373 −240.335 416.273i −0.0333622 0.0577850i 0.848862 0.528614i 0.177288π-0.177288\pi
−0.882224 + 0.470829i 0.843955π0.843955\pi
374374 0 0
375375 5903.91 + 5000.11i 0.813004 + 0.688545i
376376 0 0
377377 631.881 0.0863224
378378 0 0
379379 7321.57 0.992305 0.496152 0.868235i 0.334746π-0.334746\pi
0.496152 + 0.868235i 0.334746π0.334746\pi
380380 0 0
381381 −4893.77 4144.61i −0.658046 0.557309i
382382 0 0
383383 −1323.45 2292.28i −0.176567 0.305823i 0.764135 0.645056i 0.223166π-0.223166\pi
−0.940702 + 0.339233i 0.889833π0.889833\pi
384384 0 0
385385 20.0475 34.7233i 0.00265381 0.00459653i
386386 0 0
387387 9165.25 + 3431.03i 1.20387 + 0.450670i
388388 0 0
389389 −2430.72 + 4210.12i −0.316818 + 0.548745i −0.979822 0.199871i 0.935948π-0.935948\pi
0.663004 + 0.748616i 0.269281π0.269281\pi
390390 0 0
391391 −2736.53 4739.80i −0.353944 0.613049i
392392 0 0
393393 −1339.85 + 7400.81i −0.171976 + 0.949927i
394394 0 0
395395 7412.06 0.944155
396396 0 0
397397 −7253.21 −0.916948 −0.458474 0.888708i 0.651604π-0.651604\pi
−0.458474 + 0.888708i 0.651604π0.651604\pi
398398 0 0
399399 397.221 142.525i 0.0498394 0.0178826i
400400 0 0
401401 1150.69 + 1993.05i 0.143298 + 0.248200i 0.928737 0.370740i 0.120896π-0.120896\pi
−0.785438 + 0.618940i 0.787562π0.787562\pi
402402 0 0
403403 496.566 860.078i 0.0613789 0.106311i
404404 0 0
405405 −4407.26 3837.53i −0.540737 0.470835i
406406 0 0
407407 969.971 1680.04i 0.118132 0.204611i
408408 0 0
409409 902.216 + 1562.68i 0.109075 + 0.188924i 0.915396 0.402555i 0.131878π-0.131878\pi
−0.806321 + 0.591479i 0.798544π0.798544\pi
410410 0 0
411411 −2708.47 + 971.811i −0.325058 + 0.116632i
412412 0 0
413413 −403.667 −0.0480948
414414 0 0
415415 −4101.81 −0.485181
416416 0 0
417417 −1470.94 + 8124.90i −0.172739 + 0.954143i
418418 0 0
419419 3738.18 + 6474.71i 0.435852 + 0.754917i 0.997365 0.0725506i 0.0231139π-0.0231139\pi
−0.561513 + 0.827468i 0.689781π0.689781\pi
420420 0 0
421421 −6443.01 + 11159.6i −0.745875 + 1.29189i 0.203910 + 0.978990i 0.434635π0.434635\pi
−0.949785 + 0.312903i 0.898698π0.898698\pi
422422 0 0
423423 1900.92 + 711.614i 0.218501 + 0.0817963i
424424 0 0
425425 4030.21 6980.53i 0.459986 0.796718i
426426 0 0
427427 −150.690 261.003i −0.0170783 0.0295804i
428428 0 0
429429 −65.9349 55.8412i −0.00742043 0.00628447i
430430 0 0
431431 13065.8 1.46022 0.730110 0.683329i 0.239469π-0.239469\pi
0.730110 + 0.683329i 0.239469π0.239469\pi
432432 0 0
433433 −6190.38 −0.687046 −0.343523 0.939144i 0.611620π-0.611620\pi
−0.343523 + 0.939144i 0.611620π0.611620\pi
434434 0 0
435435 6446.01 + 5459.22i 0.710488 + 0.601723i
436436 0 0
437437 1786.96 + 3095.11i 0.195611 + 0.338808i
438438 0 0
439439 7271.78 12595.1i 0.790576 1.36932i −0.135034 0.990841i 0.543114π-0.543114\pi
0.925610 0.378478i 0.123552π-0.123552\pi
440440 0 0
441441 −7130.13 + 5872.71i −0.769909 + 0.634133i
442442 0 0
443443 426.857 739.339i 0.0457802 0.0792935i −0.842227 0.539123i 0.818756π-0.818756\pi
0.888007 + 0.459829i 0.152089π0.152089\pi
444444 0 0
445445 −1284.44 2224.71i −0.136828 0.236992i
446446 0 0
447447 −1122.66 + 6201.15i −0.118792 + 0.656162i
448448 0 0
449449 6187.67 0.650366 0.325183 0.945651i 0.394574π-0.394574\pi
0.325183 + 0.945651i 0.394574π0.394574\pi
450450 0 0
451451 52.4842 0.00547979
452452 0 0
453453 −2601.24 + 933.339i −0.269795 + 0.0968037i
454454 0 0
455455 −11.7049 20.2735i −0.00120601 0.00208887i
456456 0 0
457457 −2389.06 + 4137.98i −0.244542 + 0.423559i −0.962003 0.273040i 0.911971π-0.911971\pi
0.717461 + 0.696599i 0.245304π0.245304\pi
458458 0 0
459459 −9529.06 + 15994.5i −0.969016 + 1.62649i
460460 0 0
461461 4544.60 7871.47i 0.459139 0.795252i −0.539777 0.841808i 0.681491π-0.681491\pi
0.998916 + 0.0465564i 0.0148247π0.0148247\pi
462462 0 0
463463 3674.11 + 6363.74i 0.368791 + 0.638765i 0.989377 0.145374i 0.0464385π-0.0464385\pi
−0.620586 + 0.784139i 0.713105π0.713105\pi
464464 0 0
465465 12496.4 4483.76i 1.24625 0.447160i
466466 0 0
467467 948.436 0.0939794 0.0469897 0.998895i 0.485037π-0.485037\pi
0.0469897 + 0.998895i 0.485037π0.485037\pi
468468 0 0
469469 −681.037 −0.0670519
470470 0 0
471471 2002.17 11059.2i 0.195871 1.08191i
472472 0 0
473473 967.168 + 1675.18i 0.0940178 + 0.162844i
474474 0 0
475475 −2631.74 + 4558.31i −0.254216 + 0.440315i
476476 0 0
477477 1795.84 + 10758.6i 0.172381 + 1.03271i
478478 0 0
479479 −1493.94 + 2587.58i −0.142505 + 0.246826i −0.928439 0.371484i 0.878849π-0.878849\pi
0.785934 + 0.618310i 0.212182π0.212182\pi
480480 0 0
481481 −566.326 980.905i −0.0536845 0.0929843i
482482 0 0
483483 153.269 + 129.806i 0.0144389 + 0.0122285i
484484 0 0
485485 4822.92 0.451542
486486 0 0
487487 −19555.8 −1.81963 −0.909814 0.415017i 0.863776π-0.863776\pi
−0.909814 + 0.415017i 0.863776π0.863776\pi
488488 0 0
489489 −6352.66 5380.16i −0.587479 0.497545i
490490 0 0
491491 −429.064 743.160i −0.0394366 0.0683062i 0.845633 0.533764i 0.179223π-0.179223\pi
−0.885070 + 0.465458i 0.845890π0.845890\pi
492492 0 0
493493 13455.9 23306.2i 1.22925 2.12913i
494494 0 0
495495 −190.174 1139.30i −0.0172680 0.103450i
496496 0 0
497497 388.811 673.440i 0.0350917 0.0607806i
498498 0 0
499499 −1844.70 3195.12i −0.165491 0.286640i 0.771338 0.636425i 0.219588π-0.219588\pi
−0.936830 + 0.349786i 0.886254π0.886254\pi
500500 0 0
501501 −1604.74 + 8863.96i −0.143103 + 0.790444i
502502 0 0
503503 9034.08 0.800814 0.400407 0.916337i 0.368869π-0.368869\pi
0.400407 + 0.916337i 0.368869π0.368869\pi
504504 0 0
505505 −7024.84 −0.619013
506506 0 0
507507 10697.7 3838.40i 0.937086 0.336231i
508508 0 0
509509 3145.21 + 5447.66i 0.273888 + 0.474387i 0.969854 0.243687i 0.0783570π-0.0783570\pi
−0.695966 + 0.718075i 0.745024π0.745024\pi
510510 0 0
511511 75.0281 129.953i 0.00649520 0.0112500i
512512 0 0
513513 6222.51 10444.5i 0.535537 0.898898i
514514 0 0
515515 −895.565 + 1551.16i −0.0766278 + 0.132723i
516516 0 0
517517 200.595 + 347.442i 0.0170642 + 0.0295560i
518518 0 0
519519 −9168.62 + 3289.75i −0.775449 + 0.278235i
520520 0 0
521521 −13010.4 −1.09404 −0.547019 0.837120i 0.684238π-0.684238\pi
−0.547019 + 0.837120i 0.684238π0.684238\pi
522522 0 0
523523 1108.69 0.0926956 0.0463478 0.998925i 0.485242π-0.485242\pi
0.0463478 + 0.998925i 0.485242π0.485242\pi
524524 0 0
525525 −52.6957 + 291.070i −0.00438063 + 0.0241968i
526526 0 0
527527 −21148.7 36630.5i −1.74810 3.02780i
528528 0 0
529529 5233.03 9063.88i 0.430100 0.744956i
530530 0 0
531531 −8976.22 + 7393.25i −0.733588 + 0.604218i
532532 0 0
533533 15.3217 26.5379i 0.00124513 0.00215663i
534534 0 0
535535 −5071.64 8784.34i −0.409843 0.709869i
536536 0 0
537537 8160.37 + 6911.14i 0.655765 + 0.555377i
538538 0 0
539539 −1825.80 −0.145905
540540 0 0
541541 −38.8964 −0.00309110 −0.00154555 0.999999i 0.500492π-0.500492\pi
−0.00154555 + 0.999999i 0.500492π0.500492\pi
542542 0 0
543543 −15616.7 13226.0i −1.23421 1.04527i
544544 0 0
545545 −853.768 1478.77i −0.0671035 0.116227i
546546 0 0
547547 −5014.91 + 8686.08i −0.391997 + 0.678958i −0.992713 0.120504i 0.961549π-0.961549\pi
0.600716 + 0.799462i 0.294882π0.294882\pi
548548 0 0
549549 −8131.18 3043.93i −0.632114 0.236633i
550550 0 0
551551 −8786.73 + 15219.1i −0.679359 + 1.17669i
552552 0 0
553553 433.295 + 750.489i 0.0333193 + 0.0577107i
554554 0 0
555555 2697.40 14899.3i 0.206303 1.13953i
556556 0 0
557557 −7355.74 −0.559556 −0.279778 0.960065i 0.590261π-0.590261\pi
−0.279778 + 0.960065i 0.590261π0.590261\pi
558558 0 0
559559 1129.38 0.0854519
560560 0 0
561561 −3463.72 + 1242.80i −0.260674 + 0.0935312i
562562 0 0
563563 10729.9 + 18584.8i 0.803220 + 1.39122i 0.917486 + 0.397767i 0.130215π0.130215\pi
−0.114267 + 0.993450i 0.536452π0.536452\pi
564564 0 0
565565 6469.02 11204.7i 0.481688 0.834308i
566566 0 0
567567 130.919 670.581i 0.00969678 0.0496680i
568568 0 0
569569 728.962 1262.60i 0.0537077 0.0930245i −0.837922 0.545791i 0.816229π-0.816229\pi
0.891629 + 0.452766i 0.149563π0.149563\pi
570570 0 0
571571 11200.0 + 19399.0i 0.820853 + 1.42176i 0.905048 + 0.425310i 0.139835π0.139835\pi
−0.0841950 + 0.996449i 0.526832π0.526832\pi
572572 0 0
573573 21838.1 7835.62i 1.59215 0.571270i
574574 0 0
575575 −2505.05 −0.181683
576576 0 0
577577 −12833.5 −0.925936 −0.462968 0.886375i 0.653215π-0.653215\pi
−0.462968 + 0.886375i 0.653215π0.653215\pi
578578 0 0
579579 3841.56 21219.3i 0.275734 1.52304i
580580 0 0
581581 −239.784 415.319i −0.0171221 0.0296563i
582582 0 0
583583 −1077.96 + 1867.08i −0.0765774 + 0.132636i
584584 0 0
585585 −631.591 236.438i −0.0446377 0.0167102i
586586 0 0
587587 10377.4 17974.2i 0.729677 1.26384i −0.227343 0.973815i 0.573004π-0.573004\pi
0.957020 0.290023i 0.0936629π-0.0936629\pi
588588 0 0
589589 13810.2 + 23919.9i 0.966108 + 1.67335i
590590 0 0
591591 2128.60 + 1802.75i 0.148154 + 0.125474i
592592 0 0
593593 113.272 0.00784406 0.00392203 0.999992i 0.498752π-0.498752\pi
0.00392203 + 0.999992i 0.498752π0.498752\pi
594594 0 0
595595 −997.019 −0.0686955
596596 0 0
597597 7746.34 + 6560.49i 0.531050 + 0.449754i
598598 0 0
599599 5581.01 + 9666.59i 0.380691 + 0.659376i 0.991161 0.132663i 0.0423529π-0.0423529\pi
−0.610470 + 0.792039i 0.709020π0.709020\pi
600600 0 0
601601 939.910 1627.97i 0.0637932 0.110493i −0.832365 0.554228i 0.813014π-0.813014\pi
0.896158 + 0.443735i 0.146347π0.146347\pi
602602 0 0
603603 −15144.0 + 12473.3i −1.02274 + 0.842376i
604604 0 0
605605 −5220.67 + 9042.46i −0.350827 + 0.607650i
606606 0 0
607607 10662.2 + 18467.4i 0.712956 + 1.23488i 0.963743 + 0.266834i 0.0859774π0.0859774\pi
−0.250787 + 0.968042i 0.580689π0.580689\pi
608608 0 0
609609 −175.938 + 971.810i −0.0117067 + 0.0646629i
610610 0 0
611611 234.239 0.0155095
612612 0 0
613613 26096.2 1.71944 0.859720 0.510765i 0.170638π-0.170638\pi
0.859720 + 0.510765i 0.170638π0.170638\pi
614614 0 0
615615 385.578 138.347i 0.0252813 0.00907107i
616616 0 0
617617 9590.63 + 16611.5i 0.625777 + 1.08388i 0.988390 + 0.151937i 0.0485512π0.0485512\pi
−0.362614 + 0.931940i 0.618116π0.618116\pi
618618 0 0
619619 1681.58 2912.58i 0.109190 0.189122i −0.806253 0.591571i 0.798508π-0.798508\pi
0.915442 + 0.402450i 0.131841π0.131841\pi
620620 0 0
621621 5785.61 + 79.2993i 0.373862 + 0.00512427i
622622 0 0
623623 150.172 260.105i 0.00965731 0.0167270i
624624 0 0
625625 2171.62 + 3761.36i 0.138984 + 0.240727i
626626 0 0
627627 2261.82 811.553i 0.144064 0.0516911i
628628 0 0
629629 −48239.4 −3.05792
630630 0 0
631631 1485.04 0.0936900 0.0468450 0.998902i 0.485083π-0.485083\pi
0.0468450 + 0.998902i 0.485083π0.485083\pi
632632 0 0
633633 2987.40 16501.2i 0.187581 1.03612i
634634 0 0
635635 −4946.78 8568.07i −0.309145 0.535454i
636636 0 0
637637 −533.004 + 923.189i −0.0331529 + 0.0574224i
638638 0 0
639639 −3688.32 22096.2i −0.228338 1.36794i
640640 0 0
641641 −8208.10 + 14216.8i −0.505773 + 0.876024i 0.494205 + 0.869345i 0.335459π0.335459\pi
−0.999978 + 0.00667861i 0.997874π0.997874\pi
642642 0 0
643643 10200.0 + 17666.9i 0.625580 + 1.08354i 0.988428 + 0.151688i 0.0484710π0.0484710\pi
−0.362848 + 0.931848i 0.618196π0.618196\pi
644644 0 0
645645 11521.1 + 9757.40i 0.703323 + 0.595655i
646646 0 0
647647 25011.7 1.51980 0.759900 0.650040i 0.225248π-0.225248\pi
0.759900 + 0.650040i 0.225248π0.225248\pi
648648 0 0
649649 −2298.53 −0.139022
650650 0 0
651651 1184.51 + 1003.17i 0.0713125 + 0.0603956i
652652 0 0
653653 −3763.77 6519.03i −0.225555 0.390673i 0.730931 0.682452i 0.239086π-0.239086\pi
−0.956486 + 0.291779i 0.905753π0.905753\pi
654654 0 0
655655 −5801.52 + 10048.5i −0.346083 + 0.599433i
656656 0 0
657657 −711.729 4263.87i −0.0422636 0.253195i
658658 0 0
659659 −14984.0 + 25953.0i −0.885725 + 1.53412i −0.0408452 + 0.999165i 0.513005π0.513005\pi
−0.844880 + 0.534956i 0.820328π0.820328\pi
660660 0 0
661661 −6153.81 10658.7i −0.362111 0.627195i 0.626197 0.779665i 0.284611π-0.284611\pi
−0.988308 + 0.152470i 0.951277π0.951277\pi
662662 0 0
663663 −382.756 + 2114.19i −0.0224208 + 0.123844i
664664 0 0
665665 651.057 0.0379653
666666 0 0
667667 −8363.73 −0.485525
668668 0 0
669669 −22771.7 + 8170.60i −1.31600 + 0.472188i
670670 0 0
671671 −858.047 1486.18i −0.0493659 0.0855043i
672672 0 0
673673 −1385.42 + 2399.61i −0.0793521 + 0.137442i −0.902971 0.429702i 0.858618π-0.858618\pi
0.823618 + 0.567144i 0.191952π0.191952\pi
674674 0 0
675675 4159.23 + 7437.57i 0.237168 + 0.424107i
676676 0 0
677677 11232.5 19455.2i 0.637666 1.10447i −0.348278 0.937391i 0.613233π-0.613233\pi
0.985944 0.167078i 0.0534332π-0.0534332\pi
678678 0 0
679679 281.939 + 488.333i 0.0159349 + 0.0276001i
680680 0 0
681681 19958.6 7161.26i 1.12308 0.402966i
682682 0 0
683683 −7924.28 −0.443945 −0.221972 0.975053i 0.571249π-0.571249\pi
−0.221972 + 0.975053i 0.571249π0.571249\pi
684684 0 0
685685 −4439.25 −0.247613
686686 0 0
687687 1201.93 6638.97i 0.0667488 0.368694i
688688 0 0
689689 629.377 + 1090.11i 0.0348002 + 0.0602757i
690690 0 0
691691 11390.2 19728.4i 0.627067 1.08611i −0.361070 0.932539i 0.617589π-0.617589\pi
0.988137 0.153573i 0.0490780π-0.0490780\pi
692692 0 0
693693 104.240 85.8572i 0.00571394 0.00470627i
694694 0 0
695695 −6369.14 + 11031.7i −0.347619 + 0.602094i
696696 0 0
697697 −652.547 1130.24i −0.0354619 0.0614219i
698698 0 0
699699 −12186.0 10320.5i −0.659397 0.558453i
700700 0 0
701701 −13999.0 −0.754256 −0.377128 0.926161i 0.623088π-0.623088\pi
−0.377128 + 0.926161i 0.623088π0.623088\pi
702702 0 0
703703 31500.5 1.68999
704704 0 0
705705 2389.54 + 2023.73i 0.127653 + 0.108111i
706706 0 0
707707 −410.659 711.283i −0.0218450 0.0378367i
708708 0 0
709709 4513.32 7817.30i 0.239071 0.414083i −0.721377 0.692543i 0.756490π-0.756490\pi
0.960448 + 0.278459i 0.0898238π0.0898238\pi
710710 0 0
711711 23380.4 + 8752.51i 1.23324 + 0.461666i
712712 0 0
713713 −6572.67 + 11384.2i −0.345229 + 0.597954i
714714 0 0
715715 −66.6490 115.439i −0.00348606 0.00603803i
716716 0 0
717717 −3309.76 + 18281.8i −0.172392 + 0.952225i
718718 0 0
719719 18206.9 0.944371 0.472186 0.881499i 0.343465π-0.343465\pi
0.472186 + 0.881499i 0.343465π0.343465\pi
720720 0 0
721721 −209.412 −0.0108168
722722 0 0
723723 13291.3 4768.99i 0.683692 0.245312i
724724 0 0
725725 −6158.83 10667.4i −0.315494 0.546452i
726726 0 0
727727 −5167.05 + 8949.60i −0.263598 + 0.456564i −0.967195 0.254034i 0.918242π-0.918242\pi
0.703598 + 0.710599i 0.251576π0.251576\pi
728728 0 0
729729 −9370.62 17309.3i −0.476077 0.879404i
730730 0 0
731731 24050.0 41655.8i 1.21686 2.10766i
732732 0 0
733733 −11176.3 19358.0i −0.563176 0.975449i −0.997217 0.0745557i 0.976246π-0.976246\pi
0.434041 0.900893i 0.357087π-0.357087\pi
734734 0 0
735735 −13413.3 + 4812.77i −0.673141 + 0.241526i
736736 0 0
737737 −3877.90 −0.193818
738738 0 0
739739 −22423.2 −1.11617 −0.558086 0.829783i 0.688464π-0.688464\pi
−0.558086 + 0.829783i 0.688464π0.688464\pi
740740 0 0
741741 249.941 1380.57i 0.0123911 0.0684435i
742742 0 0
743743 −5827.69 10093.9i −0.287749 0.498395i 0.685523 0.728051i 0.259573π-0.259573\pi
−0.973272 + 0.229655i 0.926240π0.926240\pi
744744 0 0
745745 −4861.10 + 8419.68i −0.239056 + 0.414058i
746746 0 0
747747 −12938.7 4843.62i −0.633736 0.237240i
748748 0 0
749749 592.957 1027.03i 0.0289268 0.0501027i
750750 0 0
751751 −1319.06 2284.68i −0.0640923 0.111011i 0.832199 0.554478i 0.187082π-0.187082\pi
−0.896291 + 0.443466i 0.853749π0.853749\pi
752752 0 0
753753 −18173.9 15391.7i −0.879539 0.744895i
754754 0 0
755755 −4263.51 −0.205517
756756 0 0
757757 −19939.5 −0.957350 −0.478675 0.877992i 0.658883π-0.658883\pi
−0.478675 + 0.877992i 0.658883π0.658883\pi
758758 0 0
759759 872.730 + 739.128i 0.0417366 + 0.0353473i
760760 0 0
761761 13380.7 + 23176.0i 0.637385 + 1.10398i 0.986005 + 0.166719i 0.0533172π0.0533172\pi
−0.348620 + 0.937264i 0.613349π0.613349\pi
762762 0 0
763763 99.8193 172.892i 0.00473618 0.00820330i
764764 0 0
765765 −22170.4 + 18260.6i −1.04781 + 0.863024i
766766 0 0
767767 −671.007 + 1162.22i −0.0315888 + 0.0547135i
768768 0 0
769769 −3788.40 6561.71i −0.177651 0.307700i 0.763425 0.645897i 0.223516π-0.223516\pi
−0.941075 + 0.338197i 0.890183π0.890183\pi
770770 0 0
771771 5531.28 30552.6i 0.258371 1.42714i
772772 0 0
773773 27041.3 1.25823 0.629113 0.777314i 0.283418π-0.283418\pi
0.629113 + 0.777314i 0.283418π0.283418\pi
774774 0 0
775775 −19359.7 −0.897319
776776 0 0
777777 1666.28 597.870i 0.0769337 0.0276042i
778778 0 0
779779 426.116 + 738.054i 0.0195984 + 0.0339455i
780780 0 0
781781 2213.93 3834.64i 0.101435 0.175691i
782782 0 0
783783 13886.6 + 24832.2i 0.633802 + 1.13337i
784784 0 0
785785 8669.33 15015.7i 0.394168 0.682719i
786786 0 0
787787 −16802.1 29102.2i −0.761031 1.31814i −0.942320 0.334714i 0.891360π-0.891360\pi
0.181289 0.983430i 0.441973π-0.441973\pi
788788 0 0
789789 −30201.9 + 10836.6i −1.36276 + 0.488964i
790790 0 0
791791 1512.67 0.0679953
792792 0 0
793793 −1001.96 −0.0448682
794794 0 0
795795 −2997.71 + 16558.1i −0.133733 + 0.738688i
796796 0 0
797797 −21603.1 37417.7i −0.960127 1.66299i −0.722172 0.691714i 0.756856π-0.756856\pi
−0.237955 0.971276i 0.576477π-0.576477\pi
798798 0 0
799799 4988.09 8639.63i 0.220859 0.382538i
800800 0 0
801801 −1424.55 8534.30i −0.0628391 0.376460i
802802 0 0
803803 427.218 739.964i 0.0187749 0.0325190i
804804 0 0
805805 154.929 + 268.345i 0.00678326 + 0.0117490i
806806 0 0
807807 26091.0 + 22096.8i 1.13810 + 0.963873i
808808 0 0
809809 33276.5 1.44616 0.723078 0.690766i 0.242727π-0.242727\pi
0.723078 + 0.690766i 0.242727π0.242727\pi
810810 0 0
811811 21917.4 0.948980 0.474490 0.880261i 0.342633π-0.342633\pi
0.474490 + 0.880261i 0.342633π0.342633\pi
812812 0 0
813813 23066.7 + 19535.5i 0.995061 + 0.842732i
814814 0 0
815815 −6421.47 11122.3i −0.275993 0.478034i
816816 0 0
817817 −15704.7 + 27201.4i −0.672509 + 1.16482i
818818 0 0
819819 −12.9817 77.7718i −0.000553869 0.00331815i
820820 0 0
821821 536.732 929.647i 0.0228162 0.0395188i −0.854392 0.519629i 0.826070π-0.826070\pi
0.877208 + 0.480110i 0.159403π0.159403\pi
822822 0 0
823823 −6229.21 10789.3i −0.263835 0.456976i 0.703422 0.710772i 0.251654π-0.251654\pi
−0.967258 + 0.253796i 0.918321π0.918321\pi
824824 0 0
825825 −300.055 + 1657.38i −0.0126625 + 0.0699427i
826826 0 0
827827 −902.282 −0.0379388 −0.0189694 0.999820i 0.506039π-0.506039\pi
−0.0189694 + 0.999820i 0.506039π0.506039\pi
828828 0 0
829829 29605.8 1.24035 0.620176 0.784462i 0.287061π-0.287061\pi
0.620176 + 0.784462i 0.287061π0.287061\pi
830830 0 0
831831 −42311.0 + 15181.4i −1.76625 + 0.633740i
832832 0 0
833833 22700.5 + 39318.5i 0.944210 + 1.63542i
834834 0 0
835835 −6948.49 + 12035.1i −0.287979 + 0.498794i
836836 0 0
837837 44712.8 + 612.847i 1.84648 + 0.0253084i
838838 0 0
839839 −22726.8 + 39363.9i −0.935178 + 1.61978i −0.160863 + 0.986977i 0.551428π0.551428\pi
−0.774316 + 0.632799i 0.781906π0.781906\pi
840840 0 0
841841 −8368.28 14494.3i −0.343117 0.594296i
842842 0 0
843843 −35685.0 + 12804.0i −1.45796 + 0.523122i
844844 0 0
845845 17533.9 0.713827
846846 0 0
847847 −1220.76 −0.0495229
848848 0 0
849849 −751.567 + 4151.36i −0.0303813 + 0.167814i
850850 0 0
851851 7496.02 + 12983.5i 0.301951 + 0.522995i
852852 0 0
853853 −2795.92 + 4842.68i −0.112228 + 0.194385i −0.916668 0.399649i 0.869132π-0.869132\pi
0.804440 + 0.594034i 0.202465π0.202465\pi
854854 0 0
855855 14477.4 11924.2i 0.579082 0.476960i
856856 0 0
857857 20490.8 35491.1i 0.816747 1.41465i −0.0913204 0.995822i 0.529109π-0.529109\pi
0.908067 0.418825i 0.137558π-0.137558\pi
858858 0 0
859859 −21149.0 36631.2i −0.840040 1.45499i −0.889860 0.456234i 0.849198π-0.849198\pi
0.0498192 0.998758i 0.484135π-0.484135\pi
860860 0 0
861861 36.5482 + 30.9532i 0.00144664 + 0.00122518i
862862 0 0
863863 19236.0 0.758749 0.379374 0.925243i 0.376139π-0.376139\pi
0.379374 + 0.925243i 0.376139π0.376139\pi
864864 0 0
865865 −15027.6 −0.590700
866866 0 0
867867 50347.8 + 42640.3i 1.97220 + 1.67029i
868868 0 0
869869 2467.23 + 4273.36i 0.0963118 + 0.166817i
870870 0 0
871871 −1132.07 + 1960.80i −0.0440399 + 0.0762794i
872872 0 0
873873 15213.3 + 5695.14i 0.589796 + 0.220792i
874874 0 0
875875 −697.738 + 1208.52i −0.0269576 + 0.0466919i
876876 0 0
877877 12060.4 + 20889.2i 0.464368 + 0.804308i 0.999173 0.0406670i 0.0129483π-0.0129483\pi
−0.534805 + 0.844975i 0.679615π0.679615\pi
878878 0 0
879879 −4444.99 + 24552.4i −0.170564 + 0.942128i
880880 0 0
881881 34292.4 1.31140 0.655698 0.755023i 0.272375π-0.272375\pi
0.655698 + 0.755023i 0.272375π0.272375\pi
882882 0 0
883883 −15818.9 −0.602887 −0.301444 0.953484i 0.597469π-0.597469\pi
−0.301444 + 0.953484i 0.597469π0.597469\pi
884884 0 0
885885 −16886.3 + 6058.87i −0.641384 + 0.230132i
886886 0 0
887887 10381.8 + 17981.8i 0.392995 + 0.680688i 0.992843 0.119426i 0.0381055π-0.0381055\pi
−0.599848 + 0.800114i 0.704772π0.704772\pi
888888 0 0
889889 578.359 1001.75i 0.0218195 0.0377925i
890890 0 0
891891 745.466 3818.36i 0.0280292 0.143569i
892892 0 0
893893 −3257.24 + 5641.71i −0.122060 + 0.211414i
894894 0 0
895895 8248.75 + 14287.3i 0.308073 + 0.533598i
896896 0 0
897897 628.505 225.511i 0.0233948 0.00839419i
898898 0 0
899899 −64637.3 −2.39797
900900 0 0
901901 53610.1 1.98225
902902 0 0
903903 −314.458 + 1736.94i −0.0115886 + 0.0640108i
904904 0 0
905905 −15785.8 27341.8i −0.579821 1.00428i
906906 0 0
907907 6337.77 10977.3i 0.232020 0.401871i −0.726382 0.687291i 0.758800π-0.758800\pi
0.958402 + 0.285420i 0.0921331π0.0921331\pi
908908 0 0
909909 −22159.0 8295.27i −0.808545 0.302681i
910910 0 0
911911 9162.83 15870.5i 0.333236 0.577182i −0.649908 0.760013i 0.725193π-0.725193\pi
0.983144 + 0.182831i 0.0585261π0.0585261\pi
912912 0 0
913913 −1365.36 2364.87i −0.0494926 0.0857237i
914914 0 0
915915 −10221.2 8656.52i −0.369294 0.312760i
916916 0 0
917917 −1356.58 −0.0488532
918918 0 0
919919 2706.30 0.0971409 0.0485705 0.998820i 0.484533π-0.484533\pi
0.0485705 + 0.998820i 0.484533π0.484533\pi
920920 0 0
921921 −2994.30 2535.91i −0.107129 0.0907288i
922922 0 0
923923 −1292.62 2238.89i −0.0460966 0.0798417i
924924 0 0
925925 −11039.7 + 19121.4i −0.392416 + 0.679684i
926926 0 0
927927 −4656.64 + 3835.43i −0.164988 + 0.135892i
928928 0 0
929929 −12442.9 + 21551.7i −0.439437 + 0.761127i −0.997646 0.0685731i 0.978155π-0.978155\pi
0.558209 + 0.829700i 0.311489π0.311489\pi
930930 0 0
931931 −14823.5 25675.1i −0.521828 0.903832i
932932 0 0
933933 4874.64 26925.6i 0.171049 0.944806i
934934 0 0
935935 −5677.13 −0.198569
936936 0 0
937937 −33383.1 −1.16390 −0.581952 0.813223i 0.697711π-0.697711\pi
−0.581952 + 0.813223i 0.697711π0.697711\pi
938938 0 0
939939 −6818.37 + 2446.47i −0.236964 + 0.0850238i
940940 0 0
941941 14589.7 + 25270.1i 0.505431 + 0.875433i 0.999980 + 0.00628300i 0.00199996π0.00199996\pi
−0.494549 + 0.869150i 0.664667π0.664667\pi
942942 0 0
943943 −202.801 + 351.262i −0.00700330 + 0.0121301i
944944 0 0
945945 539.489 905.531i 0.0185710 0.0311713i
946946 0 0
947947 19442.0 33674.6i 0.667140 1.15552i −0.311561 0.950226i 0.600852π-0.600852\pi
0.978700 0.205294i 0.0658149π-0.0658149\pi
948948 0 0
949949 −249.435 432.034i −0.00853214 0.0147781i
950950 0 0
951951 25027.0 8979.83i 0.853372 0.306194i
952952 0 0
953953 −5321.13 −0.180869 −0.0904345 0.995902i 0.528826π-0.528826\pi
−0.0904345 + 0.995902i 0.528826π0.528826\pi
954954 0 0
955955 35793.3 1.21282
956956 0 0
957957 −1001.81 + 5533.59i −0.0338389 + 0.186913i
958958 0 0
959959 −259.511 449.485i −0.00873830 0.0151352i
960960 0 0
961961 −35899.9 + 62180.5i −1.20506 + 2.08722i
962962 0 0
963963 −5624.88 33697.9i −0.188224 1.12762i
964964 0 0
965965 16633.9 28810.7i 0.554884 0.961087i
966966 0 0
967967 −24510.2 42453.0i −0.815094 1.41178i −0.909261 0.416227i 0.863352π-0.863352\pi
0.0941669 0.995556i 0.469981π-0.469981\pi
968968 0 0
969969 −45598.4 38618.0i −1.51170 1.28028i
970970 0 0
971971 −11409.6 −0.377087 −0.188544 0.982065i 0.560377π-0.560377\pi
−0.188544 + 0.982065i 0.560377π0.560377\pi
972972 0 0
973973 −1489.31 −0.0490700
974974 0 0
975975 750.439 + 635.558i 0.0246495 + 0.0208760i
976976 0 0
977977 −9228.33 15983.9i −0.302191 0.523410i 0.674441 0.738329i 0.264385π-0.264385\pi
−0.976632 + 0.214919i 0.931051π0.931051\pi
978978 0 0
979979 855.094 1481.07i 0.0279152 0.0483505i
980980 0 0
981981 −946.902 5672.76i −0.0308178 0.184625i
982982 0 0
983983 −17803.6 + 30836.8i −0.577668 + 1.00055i 0.418078 + 0.908411i 0.362704π0.362704\pi
−0.995746 + 0.0921393i 0.970629π0.970629\pi
984984 0 0
985985 2151.66 + 3726.78i 0.0696015 + 0.120553i
986986 0 0
987987 −65.2202 + 360.250i −0.00210332 + 0.0116179i
988988 0 0
989989 −14948.7 −0.480629
990990 0 0
991991 31299.9 1.00330 0.501652 0.865070i 0.332726π-0.332726\pi
0.501652 + 0.865070i 0.332726π0.332726\pi
992992 0 0
993993 1187.50 426.080i 0.0379497 0.0136166i
994994 0 0
995995 7830.24 + 13562.4i 0.249483 + 0.432117i
996996 0 0
997997 14389.2 24922.9i 0.457083 0.791691i −0.541722 0.840557i 0.682228π-0.682228\pi
0.998805 + 0.0488666i 0.0155609π0.0155609\pi
998998 0 0
999999 26102.4 43812.9i 0.826672 1.38757i
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 72.4.i.a.25.4 8
3.2 odd 2 216.4.i.a.73.1 8
4.3 odd 2 144.4.i.e.97.1 8
9.2 odd 6 648.4.a.h.1.4 4
9.4 even 3 inner 72.4.i.a.49.4 yes 8
9.5 odd 6 216.4.i.a.145.1 8
9.7 even 3 648.4.a.i.1.1 4
12.11 even 2 432.4.i.e.289.1 8
36.7 odd 6 1296.4.a.ba.1.1 4
36.11 even 6 1296.4.a.y.1.4 4
36.23 even 6 432.4.i.e.145.1 8
36.31 odd 6 144.4.i.e.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.4.i.a.25.4 8 1.1 even 1 trivial
72.4.i.a.49.4 yes 8 9.4 even 3 inner
144.4.i.e.49.1 8 36.31 odd 6
144.4.i.e.97.1 8 4.3 odd 2
216.4.i.a.73.1 8 3.2 odd 2
216.4.i.a.145.1 8 9.5 odd 6
432.4.i.e.145.1 8 36.23 even 6
432.4.i.e.289.1 8 12.11 even 2
648.4.a.h.1.4 4 9.2 odd 6
648.4.a.i.1.1 4 9.7 even 3
1296.4.a.y.1.4 4 36.11 even 6
1296.4.a.ba.1.1 4 36.7 odd 6