Properties

Label 368.2.s.b.15.5
Level 368368
Weight 22
Character 368.15
Analytic conductor 2.9382.938
Analytic rank 00
Dimension 8080
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,2,Mod(15,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 0, 17]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.15");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 368=2423 368 = 2^{4} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 368.s (of order 2222, degree 1010, 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: 2.938494794382.93849479438
Analytic rank: 00
Dimension: 8080
Relative dimension: 88 over Q(ζ22)\Q(\zeta_{22})
Twist minimal: yes
Sato-Tate group: SU(2)[C22]\mathrm{SU}(2)[C_{22}]

Embedding invariants

Embedding label 15.5
Character χ\chi == 368.15
Dual form 368.2.s.b.319.5

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+(0.1068770.0488093i)q3+(1.32017+1.14393i)q5+(2.886241.85487i)q7+(1.95554+2.25682i)q9+(0.293255+2.03963i)q11+(3.33277+2.14184i)q13+(0.0852617+0.186697i)q15+(0.842757+2.87017i)q17+(2.262140.664224i)q19+(0.3990090.0573688i)q21+(0.4290864.77660i)q23+(0.277311+1.92874i)q25+(0.198156+0.674859i)q27+(1.508460.442925i)q29+(7.016543.20435i)q31+(0.130895+0.203677i)q33+(5.932170.852917i)q35+(6.47012+5.60639i)q37+(0.251656+0.391585i)q39+(7.675208.85765i)q41+(4.27491+9.36074i)q435.21639iq45+3.80368iq47+(1.98191+4.33978i)q49+(0.230163+0.265622i)q51+(2.116633.29354i)q53+(2.720352.35720i)q55+(0.274192+0.0394228i)q57+(2.94726+4.58603i)q59+(1.752780.800468i)q61+(9.830262.88643i)q63+(1.949706.64007i)q65+(0.3997332.78020i)q67+(0.1872830.531454i)q69+(8.826771.26910i)q71+(7.48818+2.19873i)q73+(0.0645021+0.219674i)q75+(2.936866.43082i)q77+(2.97137+1.90958i)q79+(1.263188.78560i)q81+(6.577357.59066i)q83+(4.395862.82505i)q85+(0.1396020.120966i)q87+(7.444783.39992i)q89+13.5920q910.906312q93+(3.746231.71085i)q95+(0.136456+0.118240i)q97+(5.176553.32677i)q99+O(q100)q+(0.106877 - 0.0488093i) q^{3} +(-1.32017 + 1.14393i) q^{5} +(-2.88624 - 1.85487i) q^{7} +(-1.95554 + 2.25682i) q^{9} +(0.293255 + 2.03963i) q^{11} +(-3.33277 + 2.14184i) q^{13} +(-0.0852617 + 0.186697i) q^{15} +(0.842757 + 2.87017i) q^{17} +(-2.26214 - 0.664224i) q^{19} +(-0.399009 - 0.0573688i) q^{21} +(0.429086 - 4.77660i) q^{23} +(-0.277311 + 1.92874i) q^{25} +(-0.198156 + 0.674859i) q^{27} +(1.50846 - 0.442925i) q^{29} +(-7.01654 - 3.20435i) q^{31} +(0.130895 + 0.203677i) q^{33} +(5.93217 - 0.852917i) q^{35} +(6.47012 + 5.60639i) q^{37} +(-0.251656 + 0.391585i) q^{39} +(-7.67520 - 8.85765i) q^{41} +(4.27491 + 9.36074i) q^{43} -5.21639i q^{45} +3.80368i q^{47} +(1.98191 + 4.33978i) q^{49} +(0.230163 + 0.265622i) q^{51} +(2.11663 - 3.29354i) q^{53} +(-2.72035 - 2.35720i) q^{55} +(-0.274192 + 0.0394228i) q^{57} +(2.94726 + 4.58603i) q^{59} +(-1.75278 - 0.800468i) q^{61} +(9.83026 - 2.88643i) q^{63} +(1.94970 - 6.64007i) q^{65} +(0.399733 - 2.78020i) q^{67} +(-0.187283 - 0.531454i) q^{69} +(-8.82677 - 1.26910i) q^{71} +(7.48818 + 2.19873i) q^{73} +(0.0645021 + 0.219674i) q^{75} +(2.93686 - 6.43082i) q^{77} +(-2.97137 + 1.90958i) q^{79} +(-1.26318 - 8.78560i) q^{81} +(6.57735 - 7.59066i) q^{83} +(-4.39586 - 2.82505i) q^{85} +(0.139602 - 0.120966i) q^{87} +(7.44478 - 3.39992i) q^{89} +13.5920 q^{91} -0.906312 q^{93} +(3.74623 - 1.71085i) q^{95} +(-0.136456 + 0.118240i) q^{97} +(-5.17655 - 3.32677i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 80q+4q9+12q13+22q17+66q21+36q25+34q29+22q33+12q4156q4966q5788q61154q6566q6916q73158q77248q81116q85+22q97+O(q100) 80 q + 4 q^{9} + 12 q^{13} + 22 q^{17} + 66 q^{21} + 36 q^{25} + 34 q^{29} + 22 q^{33} + 12 q^{41} - 56 q^{49} - 66 q^{57} - 88 q^{61} - 154 q^{65} - 66 q^{69} - 16 q^{73} - 158 q^{77} - 248 q^{81} - 116 q^{85}+ \cdots - 22 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/368Z)×\left(\mathbb{Z}/368\mathbb{Z}\right)^\times.

nn 4747 9797 277277
χ(n)\chi(n) 1-1 e(1722)e\left(\frac{17}{22}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.106877 0.0488093i 0.0617057 0.0281801i −0.384323 0.923199i 0.625565π-0.625565\pi
0.446029 + 0.895019i 0.352838π0.352838\pi
44 0 0
55 −1.32017 + 1.14393i −0.590398 + 0.511582i −0.898037 0.439921i 0.855007π-0.855007\pi
0.307639 + 0.951503i 0.400461π0.400461\pi
66 0 0
77 −2.88624 1.85487i −1.09090 0.701076i −0.133846 0.991002i 0.542733π-0.542733\pi
−0.957049 + 0.289926i 0.906369π0.906369\pi
88 0 0
99 −1.95554 + 2.25682i −0.651847 + 0.752272i
1010 0 0
1111 0.293255 + 2.03963i 0.0884197 + 0.614973i 0.985060 + 0.172213i 0.0550916π0.0550916\pi
−0.896640 + 0.442760i 0.853999π0.853999\pi
1212 0 0
1313 −3.33277 + 2.14184i −0.924345 + 0.594041i −0.913915 0.405905i 0.866956π-0.866956\pi
−0.0104299 + 0.999946i 0.503320π0.503320\pi
1414 0 0
1515 −0.0852617 + 0.186697i −0.0220145 + 0.0482050i
1616 0 0
1717 0.842757 + 2.87017i 0.204399 + 0.696118i 0.996337 + 0.0855166i 0.0272541π0.0272541\pi
−0.791938 + 0.610601i 0.790928π0.790928\pi
1818 0 0
1919 −2.26214 0.664224i −0.518970 0.152383i 0.0117492 0.999931i 0.496260π-0.496260\pi
−0.530719 + 0.847548i 0.678078π0.678078\pi
2020 0 0
2121 −0.399009 0.0573688i −0.0870708 0.0125189i
2222 0 0
2323 0.429086 4.77660i 0.0894706 0.995989i
2424 0 0
2525 −0.277311 + 1.92874i −0.0554621 + 0.385748i
2626 0 0
2727 −0.198156 + 0.674859i −0.0381352 + 0.129877i
2828 0 0
2929 1.50846 0.442925i 0.280114 0.0822490i −0.138658 0.990340i 0.544279π-0.544279\pi
0.418772 + 0.908091i 0.362461π0.362461\pi
3030 0 0
3131 −7.01654 3.20435i −1.26021 0.575518i −0.330497 0.943807i 0.607216π-0.607216\pi
−0.929711 + 0.368289i 0.879944π0.879944\pi
3232 0 0
3333 0.130895 + 0.203677i 0.0227860 + 0.0354557i
3434 0 0
3535 5.93217 0.852917i 1.00272 0.144169i
3636 0 0
3737 6.47012 + 5.60639i 1.06368 + 0.921685i 0.997100 0.0760963i 0.0242456π-0.0242456\pi
0.0665804 + 0.997781i 0.478791π0.478791\pi
3838 0 0
3939 −0.251656 + 0.391585i −0.0402973 + 0.0627038i
4040 0 0
4141 −7.67520 8.85765i −1.19866 1.38333i −0.903889 0.427767i 0.859301π-0.859301\pi
−0.294776 0.955567i 0.595245π-0.595245\pi
4242 0 0
4343 4.27491 + 9.36074i 0.651917 + 1.42750i 0.889866 + 0.456222i 0.150798π0.150798\pi
−0.237949 + 0.971278i 0.576475π0.576475\pi
4444 0 0
4545 5.21639i 0.777613i
4646 0 0
4747 3.80368i 0.554824i 0.960751 + 0.277412i 0.0894767π0.0894767\pi
−0.960751 + 0.277412i 0.910523π0.910523\pi
4848 0 0
4949 1.98191 + 4.33978i 0.283130 + 0.619969i
5050 0 0
5151 0.230163 + 0.265622i 0.0322292 + 0.0371945i
5252 0 0
5353 2.11663 3.29354i 0.290741 0.452402i −0.664901 0.746931i 0.731526π-0.731526\pi
0.955643 + 0.294529i 0.0951627π0.0951627\pi
5454 0 0
5555 −2.72035 2.35720i −0.366812 0.317844i
5656 0 0
5757 −0.274192 + 0.0394228i −0.0363176 + 0.00522168i
5858 0 0
5959 2.94726 + 4.58603i 0.383701 + 0.597050i 0.978355 0.206931i 0.0663477π-0.0663477\pi
−0.594655 + 0.803981i 0.702711π0.702711\pi
6060 0 0
6161 −1.75278 0.800468i −0.224421 0.102489i 0.300032 0.953929i 0.403003π-0.403003\pi
−0.524452 + 0.851440i 0.675730π0.675730\pi
6262 0 0
6363 9.83026 2.88643i 1.23850 0.363655i
6464 0 0
6565 1.94970 6.64007i 0.241830 0.823599i
6666 0 0
6767 0.399733 2.78020i 0.0488351 0.339656i −0.950726 0.310032i 0.899660π-0.899660\pi
0.999561 0.0296233i 0.00943078π-0.00943078\pi
6868 0 0
6969 −0.187283 0.531454i −0.0225462 0.0639795i
7070 0 0
7171 −8.82677 1.26910i −1.04755 0.150614i −0.403015 0.915193i 0.632038π-0.632038\pi
−0.644530 + 0.764579i 0.722947π0.722947\pi
7272 0 0
7373 7.48818 + 2.19873i 0.876425 + 0.257342i 0.688846 0.724908i 0.258118π-0.258118\pi
0.187579 + 0.982249i 0.439936π0.439936\pi
7474 0 0
7575 0.0645021 + 0.219674i 0.00744806 + 0.0253658i
7676 0 0
7777 2.93686 6.43082i 0.334686 0.732860i
7878 0 0
7979 −2.97137 + 1.90958i −0.334305 + 0.214845i −0.697014 0.717058i 0.745488π-0.745488\pi
0.362709 + 0.931903i 0.381852π0.381852\pi
8080 0 0
8181 −1.26318 8.78560i −0.140353 0.976178i
8282 0 0
8383 6.57735 7.59066i 0.721958 0.833184i −0.269583 0.962977i 0.586886π-0.586886\pi
0.991541 + 0.129793i 0.0414314π0.0414314\pi
8484 0 0
8585 −4.39586 2.82505i −0.476798 0.306420i
8686 0 0
8787 0.139602 0.120966i 0.0149669 0.0129689i
8888 0 0
8989 7.44478 3.39992i 0.789145 0.360390i 0.0202741 0.999794i 0.493546π-0.493546\pi
0.768871 + 0.639404i 0.220819π0.220819\pi
9090 0 0
9191 13.5920 1.42483
9292 0 0
9393 −0.906312 −0.0939802
9494 0 0
9595 3.74623 1.71085i 0.384355 0.175529i
9696 0 0
9797 −0.136456 + 0.118240i −0.0138550 + 0.0120054i −0.661761 0.749715i 0.730191π-0.730191\pi
0.647906 + 0.761721i 0.275645π0.275645\pi
9898 0 0
9999 −5.17655 3.32677i −0.520263 0.334353i
100100 0 0
101101 0.0767173 0.0885364i 0.00763365 0.00880970i −0.751920 0.659254i 0.770872π-0.770872\pi
0.759554 + 0.650445i 0.225417π0.225417\pi
102102 0 0
103103 2.11055 + 14.6792i 0.207959 + 1.44638i 0.779805 + 0.626023i 0.215318π0.215318\pi
−0.571846 + 0.820361i 0.693773π0.693773\pi
104104 0 0
105105 0.592385 0.380703i 0.0578108 0.0371528i
106106 0 0
107107 −6.90224 + 15.1138i −0.667265 + 1.46111i 0.208329 + 0.978059i 0.433198π0.433198\pi
−0.875594 + 0.483048i 0.839530π0.839530\pi
108108 0 0
109109 3.28732 + 11.1956i 0.314868 + 1.07234i 0.953140 + 0.302531i 0.0978315π0.0978315\pi
−0.638271 + 0.769811i 0.720350π0.720350\pi
110110 0 0
111111 0.965154 + 0.283395i 0.0916083 + 0.0268986i
112112 0 0
113113 −2.47103 0.355281i −0.232455 0.0334220i 0.0251028 0.999685i 0.492009π-0.492009\pi
−0.257558 + 0.966263i 0.582918π0.582918\pi
114114 0 0
115115 4.89764 + 6.79676i 0.456707 + 0.633801i
116116 0 0
117117 1.68363 11.7099i 0.155652 1.08258i
118118 0 0
119119 2.89140 9.84719i 0.265054 0.902691i
120120 0 0
121121 6.48032 1.90279i 0.589120 0.172981i
122122 0 0
123123 −1.25264 0.572062i −0.112947 0.0515811i
124124 0 0
125125 −6.56230 10.2111i −0.586950 0.913312i
126126 0 0
127127 −5.88243 + 0.845766i −0.521981 + 0.0750496i −0.398269 0.917269i 0.630389π-0.630389\pi
−0.123712 + 0.992318i 0.539480π0.539480\pi
128128 0 0
129129 0.913782 + 0.791797i 0.0804540 + 0.0697138i
130130 0 0
131131 1.89584 2.94999i 0.165641 0.257742i −0.748504 0.663130i 0.769227π-0.769227\pi
0.914144 + 0.405389i 0.132864π0.132864\pi
132132 0 0
133133 5.29702 + 6.11309i 0.459310 + 0.530072i
134134 0 0
135135 −0.510393 1.11761i −0.0439277 0.0961882i
136136 0 0
137137 14.5442i 1.24260i 0.783573 + 0.621299i 0.213395π0.213395\pi
−0.783573 + 0.621299i 0.786605π0.786605\pi
138138 0 0
139139 4.46279i 0.378529i 0.981926 + 0.189265i 0.0606104π0.0606104\pi
−0.981926 + 0.189265i 0.939390π0.939390\pi
140140 0 0
141141 0.185655 + 0.406528i 0.0156350 + 0.0342358i
142142 0 0
143143 −5.34593 6.16953i −0.447049 0.515922i
144144 0 0
145145 −1.48475 + 2.31032i −0.123302 + 0.191861i
146146 0 0
147147 0.423643 + 0.367089i 0.0349415 + 0.0302770i
148148 0 0
149149 −5.20979 + 0.749055i −0.426803 + 0.0613650i −0.352369 0.935861i 0.614624π-0.614624\pi
−0.0744334 + 0.997226i 0.523715π0.523715\pi
150150 0 0
151151 −8.90169 13.8513i −0.724409 1.12720i −0.986753 0.162229i 0.948132π-0.948132\pi
0.262344 0.964974i 0.415505π-0.415505\pi
152152 0 0
153153 −8.12549 3.71079i −0.656907 0.299999i
154154 0 0
155155 12.9286 3.79617i 1.03845 0.304916i
156156 0 0
157157 −2.26692 + 7.72043i −0.180920 + 0.616158i 0.818228 + 0.574894i 0.194957π0.194957\pi
−0.999148 + 0.0412639i 0.986862π0.986862\pi
158158 0 0
159159 0.0654646 0.455316i 0.00519168 0.0361089i
160160 0 0
161161 −10.0984 + 12.9905i −0.795867 + 1.02379i
162162 0 0
163163 −22.2514 3.19928i −1.74287 0.250587i −0.803942 0.594707i 0.797268π-0.797268\pi
−0.938925 + 0.344121i 0.888177π0.888177\pi
164164 0 0
165165 −0.405797 0.119153i −0.0315913 0.00927603i
166166 0 0
167167 −5.02153 17.1018i −0.388578 1.32337i −0.889125 0.457665i 0.848686π-0.848686\pi
0.500547 0.865710i 0.333132π-0.333132\pi
168168 0 0
169169 1.11949 2.45135i 0.0861148 0.188565i
170170 0 0
171171 5.92274 3.80631i 0.452923 0.291076i
172172 0 0
173173 3.18949 + 22.1834i 0.242493 + 1.68657i 0.639527 + 0.768769i 0.279130π0.279130\pi
−0.397034 + 0.917804i 0.629961π0.629961\pi
174174 0 0
175175 4.37795 5.05242i 0.330942 0.381927i
176176 0 0
177177 0.538836 + 0.346289i 0.0405014 + 0.0260287i
178178 0 0
179179 −17.7381 + 15.3701i −1.32581 + 1.14882i −0.348423 + 0.937337i 0.613283π0.613283\pi
−0.977382 + 0.211480i 0.932172π0.932172\pi
180180 0 0
181181 −21.7001 + 9.91012i −1.61296 + 0.736614i −0.998624 0.0524324i 0.983303π-0.983303\pi
−0.614334 + 0.789046i 0.710575π0.710575\pi
182182 0 0
183183 −0.226403 −0.0167362
184184 0 0
185185 −14.9550 −1.09951
186186 0 0
187187 −5.60695 + 2.56061i −0.410021 + 0.187250i
188188 0 0
189189 1.82370 1.58025i 0.132655 0.114946i
190190 0 0
191191 17.3800 + 11.1694i 1.25757 + 0.808192i 0.987950 0.154775i 0.0494653π-0.0494653\pi
0.269621 + 0.962967i 0.413102π0.413102\pi
192192 0 0
193193 0.929480 1.07268i 0.0669055 0.0772130i −0.721310 0.692612i 0.756460π-0.756460\pi
0.788216 + 0.615399i 0.211005π0.211005\pi
194194 0 0
195195 −0.115718 0.804837i −0.00828674 0.0576355i
196196 0 0
197197 10.5825 6.80094i 0.753970 0.484547i −0.106333 0.994331i 0.533911π-0.533911\pi
0.860303 + 0.509784i 0.170275π0.170275\pi
198198 0 0
199199 −4.46040 + 9.76691i −0.316189 + 0.692358i −0.999279 0.0379768i 0.987909π-0.987909\pi
0.683089 + 0.730335i 0.260636π0.260636\pi
200200 0 0
201201 −0.0929772 0.316651i −0.00655811 0.0223349i
202202 0 0
203203 −5.17535 1.51962i −0.363238 0.106656i
204204 0 0
205205 20.2651 + 2.91368i 1.41538 + 0.203501i
206206 0 0
207207 9.94080 + 10.3092i 0.690934 + 0.716539i
208208 0 0
209209 0.691390 4.80872i 0.0478244 0.332626i
210210 0 0
211211 3.22656 10.9887i 0.222126 0.756491i −0.770729 0.637163i 0.780108π-0.780108\pi
0.992855 0.119328i 0.0380740π-0.0380740\pi
212212 0 0
213213 −1.00533 + 0.295191i −0.0688838 + 0.0202261i
214214 0 0
215215 −16.3517 7.46755i −1.11517 0.509283i
216216 0 0
217217 14.3078 + 22.2633i 0.971274 + 1.51133i
218218 0 0
219219 0.907636 0.130498i 0.0613323 0.00881826i
220220 0 0
221221 −8.95617 7.76057i −0.602457 0.522032i
222222 0 0
223223 −13.6521 + 21.2431i −0.914212 + 1.42254i −0.00788217 + 0.999969i 0.502509π0.502509\pi
−0.906329 + 0.422572i 0.861127π0.861127\pi
224224 0 0
225225 −3.81051 4.39757i −0.254034 0.293171i
226226 0 0
227227 −2.36847 5.18623i −0.157201 0.344222i 0.814600 0.580022i 0.196956π-0.196956\pi
−0.971802 + 0.235800i 0.924229π0.924229\pi
228228 0 0
229229 13.6778i 0.903852i 0.892055 + 0.451926i 0.149263π0.149263\pi
−0.892055 + 0.451926i 0.850737π0.850737\pi
230230 0 0
231231 0.830655i 0.0546531i
232232 0 0
233233 −2.23268 4.88888i −0.146268 0.320281i 0.822291 0.569067i 0.192696π-0.192696\pi
−0.968558 + 0.248786i 0.919968π0.919968\pi
234234 0 0
235235 −4.35115 5.02150i −0.283838 0.327567i
236236 0 0
237237 −0.224367 + 0.349122i −0.0145742 + 0.0226779i
238238 0 0
239239 19.9940 + 17.3249i 1.29330 + 1.12065i 0.985586 + 0.169175i 0.0541103π0.0541103\pi
0.307716 + 0.951478i 0.400435π0.400435\pi
240240 0 0
241241 −20.8629 + 2.99963i −1.34390 + 0.193223i −0.776445 0.630185i 0.782979π-0.782979\pi
−0.567450 + 0.823408i 0.692070π0.692070\pi
242242 0 0
243243 −1.70460 2.65241i −0.109350 0.170152i
244244 0 0
245245 −7.58088 3.46207i −0.484324 0.221184i
246246 0 0
247247 8.96186 2.63144i 0.570229 0.167434i
248248 0 0
249249 0.332475 1.13231i 0.0210698 0.0717570i
250250 0 0
251251 3.92078 27.2696i 0.247478 1.72124i −0.365215 0.930923i 0.619004π-0.619004\pi
0.612692 0.790321i 0.290086π-0.290086\pi
252252 0 0
253253 9.86834 0.525584i 0.620417 0.0330432i
254254 0 0
255255 −0.607707 0.0873751i −0.0380561 0.00547164i
256256 0 0
257257 6.46197 + 1.89741i 0.403087 + 0.118357i 0.476991 0.878908i 0.341728π-0.341728\pi
−0.0739038 + 0.997265i 0.523546π0.523546\pi
258258 0 0
259259 −8.27516 28.1826i −0.514194 1.75118i
260260 0 0
261261 −1.95026 + 4.27048i −0.120718 + 0.264336i
262262 0 0
263263 1.97785 1.27109i 0.121960 0.0783787i −0.478239 0.878230i 0.658725π-0.658725\pi
0.600198 + 0.799851i 0.295088π0.295088\pi
264264 0 0
265265 0.973280 + 6.76931i 0.0597881 + 0.415835i
266266 0 0
267267 0.629731 0.726749i 0.0385389 0.0444763i
268268 0 0
269269 −7.41974 4.76838i −0.452390 0.290733i 0.294536 0.955640i 0.404835π-0.404835\pi
−0.746926 + 0.664907i 0.768471π0.768471\pi
270270 0 0
271271 −6.14891 + 5.32806i −0.373520 + 0.323657i −0.821310 0.570482i 0.806757π-0.806757\pi
0.447790 + 0.894139i 0.352211π0.352211\pi
272272 0 0
273273 1.45268 0.663417i 0.0879202 0.0401518i
274274 0 0
275275 −4.01524 −0.242128
276276 0 0
277277 0.0850459 0.00510991 0.00255496 0.999997i 0.499187π-0.499187\pi
0.00255496 + 0.999997i 0.499187π0.499187\pi
278278 0 0
279279 20.9528 9.56881i 1.25441 0.572870i
280280 0 0
281281 13.7750 11.9361i 0.821748 0.712049i −0.138752 0.990327i 0.544309π-0.544309\pi
0.960501 + 0.278278i 0.0897637π0.0897637\pi
282282 0 0
283283 −16.5423 10.6311i −0.983341 0.631955i −0.0529781 0.998596i 0.516871π-0.516871\pi
−0.930362 + 0.366641i 0.880508π0.880508\pi
284284 0 0
285285 0.316882 0.365702i 0.0187705 0.0216623i
286286 0 0
287287 5.72264 + 39.8018i 0.337797 + 2.34943i
288288 0 0
289289 6.77368 4.35318i 0.398452 0.256070i
290290 0 0
291291 −0.00881286 + 0.0192975i −0.000516619 + 0.00113124i
292292 0 0
293293 −2.95593 10.0670i −0.172687 0.588118i −0.999665 0.0258837i 0.991760π-0.991760\pi
0.826978 0.562234i 0.190058π-0.190058\pi
294294 0 0
295295 −9.13699 2.68286i −0.531976 0.156202i
296296 0 0
297297 −1.43458 0.206261i −0.0832425 0.0119685i
298298 0 0
299299 8.80068 + 16.8384i 0.508956 + 0.973787i
300300 0 0
301301 5.02458 34.9467i 0.289612 2.01430i
302302 0 0
303303 0.00387794 0.0132071i 0.000222782 0.000758726i
304304 0 0
305305 3.22965 0.948310i 0.184929 0.0543001i
306306 0 0
307307 3.16545 + 1.44561i 0.180662 + 0.0825056i 0.503693 0.863883i 0.331974π-0.331974\pi
−0.323031 + 0.946389i 0.604702π0.604702\pi
308308 0 0
309309 0.942051 + 1.46586i 0.0535914 + 0.0833899i
310310 0 0
311311 23.9759 3.44721i 1.35955 0.195473i 0.576328 0.817219i 0.304485π-0.304485\pi
0.783219 + 0.621745i 0.213576π0.213576\pi
312312 0 0
313313 0.954438 + 0.827025i 0.0539480 + 0.0467462i 0.681417 0.731895i 0.261364π-0.261364\pi
−0.627469 + 0.778641i 0.715909π0.715909\pi
314314 0 0
315315 −9.67573 + 15.0557i −0.545166 + 0.848294i
316316 0 0
317317 15.7072 + 18.1271i 0.882205 + 1.01812i 0.999686 + 0.0250439i 0.00797257π0.00797257\pi
−0.117481 + 0.993075i 0.537482π0.537482\pi
318318 0 0
319319 1.34577 + 2.94682i 0.0753486 + 0.164990i
320320 0 0
321321 1.95222i 0.108962i
322322 0 0
323323 7.05250i 0.392411i
324324 0 0
325325 −3.20684 7.02200i −0.177884 0.389511i
326326 0 0
327327 0.897789 + 1.03610i 0.0496478 + 0.0572966i
328328 0 0
329329 7.05534 10.9783i 0.388974 0.605255i
330330 0 0
331331 23.1969 + 20.1002i 1.27501 + 1.10481i 0.989208 + 0.146520i 0.0468071π0.0468071\pi
0.285807 + 0.958287i 0.407738π0.407738\pi
332332 0 0
333333 −25.3052 + 3.63833i −1.38671 + 0.199380i
334334 0 0
335335 2.65265 + 4.12760i 0.144930 + 0.225515i
336336 0 0
337337 2.98910 + 1.36508i 0.162827 + 0.0743605i 0.495161 0.868801i 0.335109π-0.335109\pi
−0.332334 + 0.943162i 0.607836π0.607836\pi
338338 0 0
339339 −0.281438 + 0.0826378i −0.0152856 + 0.00448827i
340340 0 0
341341 4.47806 15.2509i 0.242501 0.825881i
342342 0 0
343343 −1.08838 + 7.56986i −0.0587671 + 0.408734i
344344 0 0
345345 0.855192 + 0.487370i 0.0460420 + 0.0262391i
346346 0 0
347347 −16.8716 2.42577i −0.905713 0.130222i −0.326310 0.945263i 0.605805π-0.605805\pi
−0.579403 + 0.815041i 0.696714π0.696714\pi
348348 0 0
349349 −13.3777 3.92804i −0.716090 0.210263i −0.0966630 0.995317i 0.530817π-0.530817\pi
−0.619427 + 0.785054i 0.712635π0.712635\pi
350350 0 0
351351 −0.785032 2.67357i −0.0419019 0.142705i
352352 0 0
353353 12.7876 28.0010i 0.680616 1.49034i −0.181373 0.983414i 0.558054π-0.558054\pi
0.861989 0.506927i 0.169219π-0.169219\pi
354354 0 0
355355 13.1046 8.42181i 0.695520 0.446983i
356356 0 0
357357 −0.171609 1.19357i −0.00908254 0.0631704i
358358 0 0
359359 13.3442 15.4001i 0.704282 0.812784i −0.285043 0.958515i 0.592008π-0.592008\pi
0.989324 + 0.145731i 0.0465533π0.0465533\pi
360360 0 0
361361 −11.3077 7.26704i −0.595144 0.382476i
362362 0 0
363363 0.599726 0.519665i 0.0314774 0.0272753i
364364 0 0
365365 −12.4009 + 5.66328i −0.649091 + 0.296430i
366366 0 0
367367 12.9167 0.674247 0.337124 0.941460i 0.390546π-0.390546\pi
0.337124 + 0.941460i 0.390546π0.390546\pi
368368 0 0
369369 34.9993 1.82199
370370 0 0
371371 −12.2182 + 5.57986i −0.634337 + 0.289692i
372372 0 0
373373 16.0991 13.9499i 0.833579 0.722300i −0.129483 0.991582i 0.541332π-0.541332\pi
0.963062 + 0.269281i 0.0867862π0.0867862\pi
374374 0 0
375375 −1.19976 0.771039i −0.0619553 0.0398163i
376376 0 0
377377 −4.07869 + 4.70706i −0.210063 + 0.242426i
378378 0 0
379379 3.11878 + 21.6916i 0.160201 + 1.11422i 0.898253 + 0.439479i 0.144837π0.144837\pi
−0.738051 + 0.674744i 0.764254π0.764254\pi
380380 0 0
381381 −0.587418 + 0.377511i −0.0300943 + 0.0193405i
382382 0 0
383383 4.48093 9.81186i 0.228965 0.501363i −0.759926 0.650010i 0.774765π-0.774765\pi
0.988890 + 0.148647i 0.0474920π0.0474920\pi
384384 0 0
385385 3.47928 + 11.8493i 0.177320 + 0.603898i
386386 0 0
387387 −29.4852 8.65764i −1.49882 0.440093i
388388 0 0
389389 26.1130 + 3.75449i 1.32398 + 0.190360i 0.767795 0.640696i 0.221354π-0.221354\pi
0.556189 + 0.831056i 0.312263π0.312263\pi
390390 0 0
391391 14.0713 2.79397i 0.711614 0.141297i
392392 0 0
393393 0.0586359 0.407822i 0.00295779 0.0205719i
394394 0 0
395395 1.73827 5.92002i 0.0874620 0.297868i
396396 0 0
397397 33.1789 9.74221i 1.66520 0.488947i 0.692580 0.721341i 0.256474π-0.256474\pi
0.972622 + 0.232394i 0.0746558π0.0746558\pi
398398 0 0
399399 0.864507 + 0.394807i 0.0432795 + 0.0197651i
400400 0 0
401401 −7.97618 12.4112i −0.398311 0.619784i 0.582941 0.812515i 0.301902π-0.301902\pi
−0.981252 + 0.192731i 0.938266π0.938266\pi
402402 0 0
403403 30.2478 4.34897i 1.50675 0.216638i
404404 0 0
405405 11.7177 + 10.1535i 0.582260 + 0.504531i
406406 0 0
407407 −9.53759 + 14.8408i −0.472761 + 0.735630i
408408 0 0
409409 −22.8572 26.3786i −1.13022 1.30434i −0.946988 0.321268i 0.895891π-0.895891\pi
−0.183228 0.983071i 0.558655π-0.558655\pi
410410 0 0
411411 0.709894 + 1.55445i 0.0350165 + 0.0766754i
412412 0 0
413413 18.7032i 0.920322i
414414 0 0
415415 17.5450i 0.861250i
416416 0 0
417417 0.217826 + 0.476972i 0.0106670 + 0.0233574i
418418 0 0
419419 −25.0836 28.9481i −1.22542 1.41421i −0.879472 0.475950i 0.842104π-0.842104\pi
−0.345944 0.938255i 0.612441π-0.612441\pi
420420 0 0
421421 −6.85029 + 10.6593i −0.333863 + 0.519501i −0.967080 0.254474i 0.918098π-0.918098\pi
0.633217 + 0.773974i 0.281734π0.281734\pi
422422 0 0
423423 −8.58420 7.43826i −0.417378 0.361660i
424424 0 0
425425 −5.76951 + 0.829530i −0.279862 + 0.0402381i
426426 0 0
427427 3.57417 + 5.56152i 0.172966 + 0.269141i
428428 0 0
429429 −0.872490 0.398453i −0.0421242 0.0192375i
430430 0 0
431431 19.3748 5.68896i 0.933252 0.274028i 0.220455 0.975397i 0.429246π-0.429246\pi
0.712798 + 0.701370i 0.247428π0.247428\pi
432432 0 0
433433 −5.17013 + 17.6078i −0.248460 + 0.846178i 0.736945 + 0.675953i 0.236268π0.236268\pi
−0.985405 + 0.170225i 0.945550π0.945550\pi
434434 0 0
435435 −0.0459214 + 0.319390i −0.00220176 + 0.0153136i
436436 0 0
437437 −4.14338 + 10.5203i −0.198205 + 0.503255i
438438 0 0
439439 −17.7035 2.54538i −0.844941 0.121484i −0.293769 0.955876i 0.594910π-0.594910\pi
−0.551171 + 0.834392i 0.685819π0.685819\pi
440440 0 0
441441 −13.6698 4.01381i −0.650943 0.191134i
442442 0 0
443443 3.42704 + 11.6714i 0.162824 + 0.554527i 0.999971 + 0.00754993i 0.00240324π0.00240324\pi
−0.837148 + 0.546977i 0.815779π0.815779\pi
444444 0 0
445445 −5.93909 + 13.0048i −0.281540 + 0.616486i
446446 0 0
447447 −0.520248 + 0.334343i −0.0246069 + 0.0158139i
448448 0 0
449449 3.57335 + 24.8532i 0.168637 + 1.17290i 0.881705 + 0.471801i 0.156396π0.156396\pi
−0.713068 + 0.701095i 0.752695π0.752695\pi
450450 0 0
451451 15.8156 18.2521i 0.744726 0.859460i
452452 0 0
453453 −1.62746 1.04591i −0.0764648 0.0491410i
454454 0 0
455455 −17.9438 + 15.5484i −0.841217 + 0.728919i
456456 0 0
457457 12.6576 5.78055i 0.592100 0.270403i −0.0967481 0.995309i 0.530844π-0.530844\pi
0.688848 + 0.724906i 0.258117π0.258117\pi
458458 0 0
459459 −2.10396 −0.0982043
460460 0 0
461461 −36.7453 −1.71140 −0.855701 0.517471i 0.826874π-0.826874\pi
−0.855701 + 0.517471i 0.826874π0.826874\pi
462462 0 0
463463 −10.6743 + 4.87477i −0.496075 + 0.226550i −0.647710 0.761887i 0.724273π-0.724273\pi
0.151635 + 0.988436i 0.451546π0.451546\pi
464464 0 0
465465 1.19649 1.03676i 0.0554857 0.0480786i
466466 0 0
467467 10.2099 + 6.56148i 0.472456 + 0.303629i 0.755116 0.655591i 0.227580π-0.227580\pi
−0.282660 + 0.959220i 0.591217π0.591217\pi
468468 0 0
469469 −6.31064 + 7.28287i −0.291398 + 0.336292i
470470 0 0
471471 0.134546 + 0.935787i 0.00619955 + 0.0431188i
472472 0 0
473473 −17.8388 + 11.4643i −0.820231 + 0.527130i
474474 0 0
475475 1.90843 4.17888i 0.0875647 0.191740i
476476 0 0
477477 3.29375 + 11.2175i 0.150811 + 0.513614i
478478 0 0
479479 15.0197 + 4.41019i 0.686269 + 0.201507i 0.606235 0.795285i 0.292679π-0.292679\pi
0.0800338 + 0.996792i 0.474497π0.474497\pi
480480 0 0
481481 −33.5715 4.82685i −1.53073 0.220085i
482482 0 0
483483 −0.445237 + 1.88129i −0.0202590 + 0.0856016i
484484 0 0
485485 0.0448866 0.312193i 0.00203819 0.0141759i
486486 0 0
487487 0.234925 0.800081i 0.0106455 0.0362551i −0.953999 0.299810i 0.903077π-0.903077\pi
0.964644 + 0.263555i 0.0848949π0.0848949\pi
488488 0 0
489489 −2.53433 + 0.744147i −0.114606 + 0.0336515i
490490 0 0
491491 −25.1086 11.4667i −1.13314 0.517486i −0.241573 0.970383i 0.577663π-0.577663\pi
−0.891563 + 0.452897i 0.850391π0.850391\pi
492492 0 0
493493 2.54254 + 3.95626i 0.114510 + 0.178181i
494494 0 0
495495 10.6395 1.52973i 0.478211 0.0687563i
496496 0 0
497497 23.1221 + 20.0355i 1.03717 + 0.898713i
498498 0 0
499499 −20.0953 + 31.2689i −0.899588 + 1.39979i 0.0169575 + 0.999856i 0.494602π0.494602\pi
−0.916546 + 0.399930i 0.869034π0.869034\pi
500500 0 0
501501 −1.37141 1.58270i −0.0612703 0.0707096i
502502 0 0
503503 3.39112 + 7.42551i 0.151202 + 0.331087i 0.970043 0.242934i 0.0781099π-0.0781099\pi
−0.818840 + 0.574021i 0.805383π0.805383\pi
504504 0 0
505505 0.204642i 0.00910647i
506506 0 0
507507 0.316635i 0.0140623i
508508 0 0
509509 7.92945 + 17.3631i 0.351467 + 0.769604i 0.999965 + 0.00838826i 0.00267010π0.00267010\pi
−0.648498 + 0.761216i 0.724603π0.724603\pi
510510 0 0
511511 −17.5343 20.2357i −0.775672 0.895173i
512512 0 0
513513 0.896515 1.39500i 0.0395821 0.0615909i
514514 0 0
515515 −19.5783 16.9647i −0.862723 0.747553i
516516 0 0
517517 −7.75811 + 1.11545i −0.341201 + 0.0490574i
518518 0 0
519519 1.42364 + 2.21523i 0.0624909 + 0.0972377i
520520 0 0
521521 13.5591 + 6.19221i 0.594033 + 0.271286i 0.689662 0.724131i 0.257759π-0.257759\pi
−0.0956292 + 0.995417i 0.530486π0.530486\pi
522522 0 0
523523 27.5519 8.08998i 1.20476 0.353750i 0.383090 0.923711i 0.374860π-0.374860\pi
0.821672 + 0.569961i 0.193042π0.193042\pi
524524 0 0
525525 0.221299 0.753674i 0.00965827 0.0328930i
526526 0 0
527527 3.28377 22.8392i 0.143043 0.994889i
528528 0 0
529529 −22.6318 4.09914i −0.983990 0.178223i
530530 0 0
531531 −16.1133 2.31674i −0.699258 0.100538i
532532 0 0
533533 44.5514 + 13.0815i 1.92974 + 0.566622i
534534 0 0
535535 −8.17705 27.8485i −0.353525 1.20399i
536536 0 0
537537 −1.14559 + 2.50850i −0.0494361 + 0.108250i
538538 0 0
539539 −8.27036 + 5.31504i −0.356229 + 0.228935i
540540 0 0
541541 −2.99096 20.8026i −0.128592 0.894374i −0.947342 0.320224i 0.896242π-0.896242\pi
0.818750 0.574150i 0.194667π-0.194667\pi
542542 0 0
543543 −1.83555 + 2.11834i −0.0787710 + 0.0909065i
544544 0 0
545545 −17.1468 11.0196i −0.734489 0.472027i
546546 0 0
547547 19.7118 17.0804i 0.842818 0.730306i −0.122196 0.992506i 0.538994π-0.538994\pi
0.965013 + 0.262200i 0.0844481π0.0844481\pi
548548 0 0
549549 5.23414 2.39035i 0.223388 0.102018i
550550 0 0
551551 −3.70655 −0.157904
552552 0 0
553553 12.1181 0.515314
554554 0 0
555555 −1.59835 + 0.729942i −0.0678462 + 0.0309843i
556556 0 0
557557 −7.58689 + 6.57408i −0.321467 + 0.278553i −0.800612 0.599183i 0.795492π-0.795492\pi
0.479145 + 0.877736i 0.340947π0.340947\pi
558558 0 0
559559 −34.2965 22.0410i −1.45059 0.932237i
560560 0 0
561561 −0.474275 + 0.547342i −0.0200239 + 0.0231088i
562562 0 0
563563 3.73863 + 26.0027i 0.157564 + 1.09588i 0.903104 + 0.429423i 0.141283π0.141283\pi
−0.745539 + 0.666462i 0.767808π0.767808\pi
564564 0 0
565565 3.66860 2.35766i 0.154339 0.0991876i
566566 0 0
567567 −12.6503 + 27.7004i −0.531264 + 1.16331i
568568 0 0
569569 12.9112 + 43.9715i 0.541266 + 1.84338i 0.537303 + 0.843389i 0.319443π0.319443\pi
0.00396223 + 0.999992i 0.498739π0.498739\pi
570570 0 0
571571 11.4841 + 3.37204i 0.480595 + 0.141115i 0.513052 0.858358i 0.328515π-0.328515\pi
−0.0324565 + 0.999473i 0.510333π0.510333\pi
572572 0 0
573573 2.40270 + 0.345456i 0.100374 + 0.0144316i
574574 0 0
575575 9.09381 + 2.15219i 0.379238 + 0.0897527i
576576 0 0
577577 −3.29784 + 22.9369i −0.137291 + 0.954878i 0.798418 + 0.602104i 0.205671π0.205671\pi
−0.935709 + 0.352774i 0.885238π0.885238\pi
578578 0 0
579579 0.0469838 0.160012i 0.00195258 0.00664988i
580580 0 0
581581 −33.0635 + 9.70832i −1.37171 + 0.402769i
582582 0 0
583583 7.33833 + 3.35130i 0.303922 + 0.138797i
584584 0 0
585585 11.1727 + 17.3850i 0.461934 + 0.718783i
586586 0 0
587587 −11.2753 + 1.62114i −0.465381 + 0.0669117i −0.371017 0.928626i 0.620991π-0.620991\pi
−0.0943641 + 0.995538i 0.530082π0.530082\pi
588588 0 0
589589 13.7440 + 11.9092i 0.566311 + 0.490712i
590590 0 0
591591 0.799078 1.24339i 0.0328697 0.0511462i
592592 0 0
593593 −3.92550 4.53027i −0.161201 0.186036i 0.669403 0.742900i 0.266550π-0.266550\pi
−0.830604 + 0.556864i 0.812005π0.812005\pi
594594 0 0
595595 7.44740 + 16.3075i 0.305314 + 0.668543i
596596 0 0
597597 1.26157i 0.0516327i
598598 0 0
599599 8.44243i 0.344948i −0.985014 0.172474i 0.944824π-0.944824\pi
0.985014 0.172474i 0.0551761π-0.0551761\pi
600600 0 0
601601 −7.27392 15.9277i −0.296709 0.649703i 0.701293 0.712873i 0.252606π-0.252606\pi
−0.998003 + 0.0631699i 0.979879π0.979879\pi
602602 0 0
603603 5.49271 + 6.33892i 0.223680 + 0.258141i
604604 0 0
605605 −6.37844 + 9.92505i −0.259321 + 0.403511i
606606 0 0
607607 −5.93429 5.14209i −0.240865 0.208711i 0.526060 0.850448i 0.323669π-0.323669\pi
−0.766925 + 0.641737i 0.778214π0.778214\pi
608608 0 0
609609 −0.627300 + 0.0901921i −0.0254195 + 0.00365477i
610610 0 0
611611 −8.14689 12.6768i −0.329588 0.512849i
612612 0 0
613613 −41.3412 18.8799i −1.66975 0.762551i −0.999797 0.0201509i 0.993585π-0.993585\pi
−0.669957 0.742400i 0.733687π-0.733687\pi
614614 0 0
615615 2.30810 0.677719i 0.0930715 0.0273283i
616616 0 0
617617 8.52953 29.0489i 0.343386 1.16947i −0.589040 0.808104i 0.700494π-0.700494\pi
0.932426 0.361362i 0.117688π-0.117688\pi
618618 0 0
619619 −1.27237 + 8.84949i −0.0511407 + 0.355691i 0.948143 + 0.317844i 0.102959π0.102959\pi
−0.999284 + 0.0378468i 0.987950π0.987950\pi
620620 0 0
621621 3.13850 + 1.23609i 0.125944 + 0.0496024i
622622 0 0
623623 −27.7938 3.99615i −1.11354 0.160102i
624624 0 0
625625 10.9960 + 3.22872i 0.439840 + 0.129149i
626626 0 0
627627 −0.160816 0.547690i −0.00642238 0.0218726i
628628 0 0
629629 −10.6385 + 23.2952i −0.424186 + 0.928839i
630630 0 0
631631 −13.2886 + 8.54007i −0.529011 + 0.339975i −0.777728 0.628601i 0.783628π-0.783628\pi
0.248716 + 0.968576i 0.419991π0.419991\pi
632632 0 0
633633 −0.191502 1.33193i −0.00761152 0.0529393i
634634 0 0
635635 6.79830 7.84566i 0.269782 0.311346i
636636 0 0
637637 −15.9004 10.2186i −0.629996 0.404874i
638638 0 0
639639 20.1252 17.4386i 0.796142 0.689861i
640640 0 0
641641 12.0461 5.50126i 0.475791 0.217287i −0.163061 0.986616i 0.552137π-0.552137\pi
0.638852 + 0.769329i 0.279409π0.279409\pi
642642 0 0
643643 34.1878 1.34824 0.674119 0.738623i 0.264524π-0.264524\pi
0.674119 + 0.738623i 0.264524π0.264524\pi
644644 0 0
645645 −2.11211 −0.0831642
646646 0 0
647647 −18.0980 + 8.26507i −0.711505 + 0.324933i −0.738080 0.674713i 0.764267π-0.764267\pi
0.0265749 + 0.999647i 0.491540π0.491540\pi
648648 0 0
649649 −8.48951 + 7.35621i −0.333243 + 0.288756i
650650 0 0
651651 2.61583 + 1.68109i 0.102523 + 0.0658872i
652652 0 0
653653 −23.0306 + 26.5787i −0.901257 + 1.04011i 0.0977351 + 0.995212i 0.468840π0.468840\pi
−0.998992 + 0.0448932i 0.985705π0.985705\pi
654654 0 0
655655 0.871756 + 6.06320i 0.0340623 + 0.236909i
656656 0 0
657657 −19.6056 + 12.5997i −0.764886 + 0.491562i
658658 0 0
659659 −14.8013 + 32.4104i −0.576578 + 1.26253i 0.366642 + 0.930362i 0.380507π0.380507\pi
−0.943220 + 0.332168i 0.892220π0.892220\pi
660660 0 0
661661 −2.85669 9.72901i −0.111113 0.378415i 0.885096 0.465408i 0.154092π-0.154092\pi
−0.996209 + 0.0869932i 0.972274π0.972274\pi
662662 0 0
663663 −1.33600 0.392285i −0.0518860 0.0152351i
664664 0 0
665665 −13.9859 2.01087i −0.542351 0.0779783i
666666 0 0
667667 −1.46841 7.39537i −0.0568572 0.286350i
668668 0 0
669669 −0.422241 + 2.93675i −0.0163248 + 0.113541i
670670 0 0
671671 1.11865 3.80977i 0.0431850 0.147075i
672672 0 0
673673 32.3571 9.50091i 1.24728 0.366233i 0.409531 0.912296i 0.365692π-0.365692\pi
0.837744 + 0.546063i 0.183874π0.183874\pi
674674 0 0
675675 −1.24667 0.569337i −0.0479845 0.0219138i
676676 0 0
677677 −10.6410 16.5578i −0.408969 0.636368i 0.574275 0.818662i 0.305284π-0.305284\pi
−0.983244 + 0.182295i 0.941648π0.941648\pi
678678 0 0
679679 0.613164 0.0881596i 0.0235311 0.00338326i
680680 0 0
681681 −0.506273 0.438688i −0.0194004 0.0168106i
682682 0 0
683683 15.7767 24.5490i 0.603678 0.939342i −0.396099 0.918208i 0.629636π-0.629636\pi
0.999777 0.0211335i 0.00672751π-0.00672751\pi
684684 0 0
685685 −16.6376 19.2009i −0.635692 0.733627i
686686 0 0
687687 0.667602 + 1.46184i 0.0254706 + 0.0557728i
688688 0 0
689689 15.5101i 0.590888i
690690 0 0
691691 3.82254i 0.145416i −0.997353 0.0727082i 0.976836π-0.976836\pi
0.997353 0.0727082i 0.0231642π-0.0231642\pi
692692 0 0
693693 8.77002 + 19.2037i 0.333146 + 0.729487i
694694 0 0
695695 −5.10514 5.89164i −0.193649 0.223483i
696696 0 0
697697 18.9546 29.4940i 0.717958 1.11716i
698698 0 0
699699 −0.477245 0.413536i −0.0180511 0.0156414i
700700 0 0
701701 41.0831 5.90686i 1.55169 0.223099i 0.687469 0.726214i 0.258722π-0.258722\pi
0.864220 + 0.503115i 0.167813π0.167813\pi
702702 0 0
703703 −10.9124 16.9800i −0.411569 0.640414i
704704 0 0
705705 −0.710136 0.324308i −0.0267453 0.0122142i
706706 0 0
707707 −0.385648 + 0.113236i −0.0145038 + 0.00425870i
708708 0 0
709709 8.92143 30.3836i 0.335051 1.14108i −0.603909 0.797054i 0.706391π-0.706391\pi
0.938960 0.344027i 0.111791π-0.111791\pi
710710 0 0
711711 1.50106 10.4401i 0.0562941 0.391534i
712712 0 0
713713 −18.3166 + 32.1403i −0.685961 + 1.20366i
714714 0 0
715715 14.1151 + 2.02944i 0.527873 + 0.0758967i
716716 0 0
717717 2.98252 + 0.875747i 0.111384 + 0.0327054i
718718 0 0
719719 5.56102 + 18.9391i 0.207391 + 0.706309i 0.995833 + 0.0911993i 0.0290700π0.0290700\pi
−0.788442 + 0.615110i 0.789112π0.789112\pi
720720 0 0
721721 21.1365 46.2824i 0.787164 1.72365i
722722 0 0
723723 −2.08336 + 1.33889i −0.0774810 + 0.0497940i
724724 0 0
725725 0.435973 + 3.03226i 0.0161916 + 0.112615i
726726 0 0
727727 7.98857 9.21930i 0.296280 0.341925i −0.588019 0.808847i 0.700092π-0.700092\pi
0.884298 + 0.466922i 0.154637π0.154637\pi
728728 0 0
729729 22.0891 + 14.1958i 0.818115 + 0.525771i
730730 0 0
731731 −23.2642 + 20.1585i −0.860457 + 0.745590i
732732 0 0
733733 −0.521302 + 0.238070i −0.0192547 + 0.00879333i −0.425019 0.905184i 0.639733π-0.639733\pi
0.405764 + 0.913978i 0.367005π0.367005\pi
734734 0 0
735735 −0.979206 −0.0361185
736736 0 0
737737 5.78782 0.213197
738738 0 0
739739 28.6453 13.0819i 1.05373 0.481224i 0.188229 0.982125i 0.439725π-0.439725\pi
0.865505 + 0.500901i 0.166998π0.166998\pi
740740 0 0
741741 0.829382 0.718663i 0.0304681 0.0264008i
742742 0 0
743743 20.6339 + 13.2606i 0.756983 + 0.486483i 0.861323 0.508058i 0.169637π-0.169637\pi
−0.104340 + 0.994542i 0.533273π0.533273\pi
744744 0 0
745745 6.02094 6.94853i 0.220590 0.254575i
746746 0 0
747747 4.26845 + 29.6877i 0.156174 + 1.08622i
748748 0 0
749749 47.9557 30.8193i 1.75226 1.12611i
750750 0 0
751751 −2.51237 + 5.50132i −0.0916777 + 0.200746i −0.949916 0.312505i 0.898832π-0.898832\pi
0.858238 + 0.513251i 0.171559π0.171559\pi
752752 0 0
753753 −0.911969 3.10588i −0.0332340 0.113185i
754754 0 0
755755 27.5967 + 8.10312i 1.00435 + 0.294903i
756756 0 0
757757 29.1174 + 4.18645i 1.05829 + 0.152159i 0.649418 0.760432i 0.275013π-0.275013\pi
0.408873 + 0.912591i 0.365922π0.365922\pi
758758 0 0
759759 1.02905 0.537840i 0.0373521 0.0195223i
760760 0 0
761761 1.70128 11.8326i 0.0616712 0.428933i −0.935472 0.353401i 0.885025π-0.885025\pi
0.997143 0.0755323i 0.0240656π-0.0240656\pi
762762 0 0
763763 11.2784 38.4107i 0.408305 1.39056i
764764 0 0
765765 14.9719 4.39615i 0.541310 0.158943i
766766 0 0
767767 −19.6451 8.97162i −0.709344 0.323946i
768768 0 0
769769 −21.4693 33.4068i −0.774201 1.20468i −0.974377 0.224921i 0.927788π-0.927788\pi
0.200176 0.979760i 0.435849π-0.435849\pi
770770 0 0
771771 0.783250 0.112614i 0.0282081 0.00405571i
772772 0 0
773773 0.683625 + 0.592365i 0.0245883 + 0.0213059i 0.667068 0.744997i 0.267549π-0.267549\pi
−0.642480 + 0.766303i 0.722094π0.722094\pi
774774 0 0
775775 8.12611 12.6445i 0.291898 0.454203i
776776 0 0
777777 −2.26000 2.60818i −0.0810771 0.0935680i
778778 0 0
779779 11.4789 + 25.1353i 0.411274 + 0.900565i
780780 0 0
781781 18.3756i 0.657529i
782782 0 0
783783 1.10577i 0.0395169i
784784 0 0
785785 −5.83894 12.7855i −0.208401 0.456334i
786786 0 0
787787 35.4591 + 40.9219i 1.26398 + 1.45871i 0.829977 + 0.557798i 0.188354π0.188354\pi
0.434003 + 0.900912i 0.357101π0.357101\pi
788788 0 0
789789 0.149347 0.232388i 0.00531689 0.00827324i
790790 0 0
791791 6.47298 + 5.60887i 0.230153 + 0.199428i
792792 0 0
793793 7.55610 1.08640i 0.268325 0.0385793i
794794 0 0
795795 0.434427 + 0.675981i 0.0154075 + 0.0239746i
796796 0 0
797797 12.3929 + 5.65963i 0.438978 + 0.200474i 0.622629 0.782517i 0.286065π-0.286065\pi
−0.183652 + 0.982991i 0.558792π0.558792\pi
798798 0 0
799799 −10.9172 + 3.20558i −0.386223 + 0.113405i
800800 0 0
801801 −6.88559 + 23.4502i −0.243290 + 0.828571i
802802 0 0
803803 −2.28865 + 15.9179i −0.0807648 + 0.561731i
804804 0 0
805805 −1.52863 28.7016i −0.0538773 1.01160i
806806 0 0
807807 −1.02574 0.147480i −0.0361079 0.00519153i
808808 0 0
809809 −14.6083 4.28939i −0.513601 0.150807i 0.0146541 0.999893i 0.495335π-0.495335\pi
−0.528255 + 0.849086i 0.677153π0.677153\pi
810810 0 0
811811 −2.78682 9.49103i −0.0978585 0.333275i 0.895983 0.444089i 0.146473π-0.146473\pi
−0.993841 + 0.110814i 0.964654π0.964654\pi
812812 0 0
813813 −0.397121 + 0.869574i −0.0139276 + 0.0304973i
814814 0 0
815815 33.0354 21.2306i 1.15718 0.743675i
816816 0 0
817817 −3.45280 24.0148i −0.120798 0.840171i
818818 0 0
819819 −26.5798 + 30.6747i −0.928772 + 1.07186i
820820 0 0
821821 2.23257 + 1.43479i 0.0779173 + 0.0500744i 0.579019 0.815314i 0.303436π-0.303436\pi
−0.501102 + 0.865388i 0.667072π0.667072\pi
822822 0 0
823823 −25.7224 + 22.2886i −0.896628 + 0.776933i −0.975511 0.219951i 0.929410π-0.929410\pi
0.0788827 + 0.996884i 0.474865π0.474865\pi
824824 0 0
825825 −0.429139 + 0.195981i −0.0149407 + 0.00682318i
826826 0 0
827827 −10.0459 −0.349329 −0.174664 0.984628i 0.555884π-0.555884\pi
−0.174664 + 0.984628i 0.555884π0.555884\pi
828828 0 0
829829 −17.5669 −0.610125 −0.305062 0.952332i 0.598677π-0.598677\pi
−0.305062 + 0.952332i 0.598677π0.598677\pi
830830 0 0
831831 0.00908949 0.00415103i 0.000315311 0.000143998i
832832 0 0
833833 −10.7856 + 9.34580i −0.373700 + 0.323813i
834834 0 0
835835 26.1926 + 16.8329i 0.906431 + 0.582528i
836836 0 0
837837 3.55286 4.10021i 0.122805 0.141724i
838838 0 0
839839 −6.36234 44.2510i −0.219652 1.52772i −0.739324 0.673350i 0.764855π-0.764855\pi
0.519672 0.854366i 0.326054π-0.326054\pi
840840 0 0
841841 −22.3171 + 14.3423i −0.769554 + 0.494563i
842842 0 0
843843 0.889645 1.94805i 0.0306410 0.0670944i
844844 0 0
845845 1.32626 + 4.51681i 0.0456246 + 0.155383i
846846 0 0
847847 −22.2332 6.52825i −0.763941 0.224313i
848848 0 0
849849 −2.28690 0.328807i −0.0784862 0.0112846i
850850 0 0
851851 29.5557 28.4995i 1.01316 0.976951i
852852 0 0
853853 2.14980 14.9522i 0.0736079 0.511954i −0.919346 0.393451i 0.871281π-0.871281\pi
0.992954 0.118504i 0.0378097π-0.0378097\pi
854854 0 0
855855 −3.46485 + 11.8002i −0.118495 + 0.403558i
856856 0 0
857857 12.4399 3.65269i 0.424939 0.124773i −0.0622685 0.998059i 0.519834π-0.519834\pi
0.487208 + 0.873286i 0.338015π0.338015\pi
858858 0 0
859859 −17.0018 7.76444i −0.580093 0.264919i 0.103685 0.994610i 0.466937π-0.466937\pi
−0.683777 + 0.729691i 0.739664π0.739664\pi
860860 0 0
861861 2.55432 + 3.97460i 0.0870509 + 0.135454i
862862 0 0
863863 −15.3396 + 2.20550i −0.522166 + 0.0750762i −0.398358 0.917230i 0.630420π-0.630420\pi
−0.123808 + 0.992306i 0.539511π0.539511\pi
864864 0 0
865865 −29.5870 25.6373i −1.00599 0.871694i
866866 0 0
867867 0.511478 0.795876i 0.0173707 0.0270294i
868868 0 0
869869 −4.76622 5.50051i −0.161683 0.186592i
870870 0 0
871871 4.62254 + 10.1219i 0.156629 + 0.342969i
872872 0 0
873873 0.539179i 0.0182484i
874874 0 0
875875 41.6440i 1.40782i
876876 0 0
877877 10.0439 + 21.9931i 0.339160 + 0.742656i 0.999969 0.00789806i 0.00251406π-0.00251406\pi
−0.660809 + 0.750554i 0.729787π0.729787\pi
878878 0 0
879879 −0.807283 0.931654i −0.0272290 0.0314239i
880880 0 0
881881 −14.5573 + 22.6517i −0.490449 + 0.763154i −0.994962 0.100250i 0.968036π-0.968036\pi
0.504513 + 0.863404i 0.331672π0.331672\pi
882882 0 0
883883 17.6976 + 15.3351i 0.595573 + 0.516067i 0.899668 0.436575i 0.143809π-0.143809\pi
−0.304095 + 0.952642i 0.598354π0.598354\pi
884884 0 0
885885 −1.10749 + 0.159233i −0.0372277 + 0.00535254i
886886 0 0
887887 6.33778 + 9.86178i 0.212802 + 0.331126i 0.931202 0.364504i 0.118762π-0.118762\pi
−0.718400 + 0.695630i 0.755125π0.755125\pi
888888 0 0
889889 18.5469 + 8.47008i 0.622042 + 0.284077i
890890 0 0
891891 17.5490 5.15284i 0.587913 0.172627i
892892 0 0
893893 2.52649 8.60445i 0.0845459 0.287937i
894894 0 0
895895 5.83486 40.5823i 0.195038 1.35652i
896896 0 0
897897 1.76246 + 1.37009i 0.0588469 + 0.0457458i
898898 0 0
899899 −12.0035 1.72584i −0.400338 0.0575600i
900900 0 0
901901 11.2368 + 3.29943i 0.374353 + 0.109920i
902902 0 0
903903 −1.16871 3.98026i −0.0388923 0.132455i
904904 0 0
905905 17.3113 37.9065i 0.575448 1.26006i
906906 0 0
907907 7.47865 4.80624i 0.248325 0.159588i −0.410558 0.911835i 0.634666π-0.634666\pi
0.658882 + 0.752246i 0.271030π0.271030\pi
908908 0 0
909909 0.0497866 + 0.346273i 0.00165132 + 0.0114852i
910910 0 0
911911 −4.09127 + 4.72158i −0.135550 + 0.156433i −0.819466 0.573128i 0.805730π-0.805730\pi
0.683916 + 0.729561i 0.260275π0.260275\pi
912912 0 0
913913 17.4110 + 11.1894i 0.576221 + 0.370314i
914914 0 0
915915 0.298890 0.258990i 0.00988100 0.00856194i
916916 0 0
917917 −10.9437 + 4.99782i −0.361393 + 0.165043i
918918 0 0
919919 44.4385 1.46589 0.732945 0.680288i 0.238145π-0.238145\pi
0.732945 + 0.680288i 0.238145π0.238145\pi
920920 0 0
921921 0.408875 0.0134729
922922 0 0
923923 32.1358 14.6759i 1.05776 0.483065i
924924 0 0
925925 −12.6075 + 10.9244i −0.414532 + 0.359194i
926926 0 0
927927 −37.2555 23.9427i −1.22363 0.786380i
928928 0 0
929929 31.2517 36.0664i 1.02534 1.18330i 0.0424483 0.999099i 0.486484π-0.486484\pi
0.982888 0.184203i 0.0589703π-0.0589703\pi
930930 0 0
931931 −1.60077 11.1336i −0.0524632 0.364890i
932932 0 0
933933 2.39422 1.53867i 0.0783834 0.0503739i
934934 0 0
935935 4.47296 9.79441i 0.146281 0.320311i
936936 0 0
937937 −6.33560 21.5771i −0.206975 0.704892i −0.995905 0.0904086i 0.971183π-0.971183\pi
0.788930 0.614483i 0.210635π-0.210635\pi
938938 0 0
939939 0.142374 + 0.0418049i 0.00464621 + 0.00136425i
940940 0 0
941941 3.89577 + 0.560127i 0.126998 + 0.0182596i 0.205521 0.978653i 0.434111π-0.434111\pi
−0.0785225 + 0.996912i 0.525020π0.525020\pi
942942 0 0
943943 −45.6028 + 32.8607i −1.48503 + 1.07009i
944944 0 0
945945 −0.599899 + 4.17239i −0.0195147 + 0.135728i
946946 0 0
947947 −14.6947 + 50.0455i −0.477513 + 1.62626i 0.270602 + 0.962691i 0.412777π0.412777\pi
−0.748115 + 0.663569i 0.769041π0.769041\pi
948948 0 0
949949 −29.6657 + 8.71065i −0.962990 + 0.282760i
950950 0 0
951951 2.56352 + 1.17072i 0.0831278 + 0.0379632i
952952 0 0
953953 27.2605 + 42.4182i 0.883054 + 1.37406i 0.927014 + 0.375026i 0.122366π0.122366\pi
−0.0439598 + 0.999033i 0.513997π0.513997\pi
954954 0 0
955955 −35.7216 + 5.13599i −1.15592 + 0.166197i
956956 0 0
957957 0.287665 + 0.249263i 0.00929887 + 0.00805752i
958958 0 0
959959 26.9777 41.9781i 0.871156 1.35555i
960960 0 0
961961 18.6634 + 21.5387i 0.602044 + 0.694796i
962962 0 0
963963 −20.6114 45.1328i −0.664194 1.45438i
964964 0 0
965965 2.47938i 0.0798140i
966966 0 0
967967 3.03743i 0.0976771i −0.998807 0.0488385i 0.984448π-0.984448\pi
0.998807 0.0488385i 0.0155520π-0.0155520\pi
968968 0 0
969969 −0.344227 0.753753i −0.0110582 0.0242140i
970970 0 0
971971 0.183013 + 0.211208i 0.00587316 + 0.00677798i 0.758679 0.651465i 0.225845π-0.225845\pi
−0.752805 + 0.658243i 0.771300π0.771300\pi
972972 0 0
973973 8.27791 12.8807i 0.265378 0.412936i
974974 0 0
975975 −0.685478 0.593970i −0.0219529 0.0190223i
976976 0 0
977977 −31.1017 + 4.47175i −0.995033 + 0.143064i −0.620547 0.784169i 0.713090π-0.713090\pi
−0.374485 + 0.927233i 0.622180π0.622180\pi
978978 0 0
979979 9.11780 + 14.1876i 0.291406 + 0.453437i
980980 0 0
981981 −31.6949 14.4746i −1.01194 0.462137i
982982 0 0
983983 −18.0776 + 5.30806i −0.576585 + 0.169301i −0.557007 0.830508i 0.688050π-0.688050\pi
−0.0195781 + 0.999808i 0.506232π0.506232\pi
984984 0 0
985985 −6.19083 + 21.0840i −0.197256 + 0.671793i
986986 0 0
987987 0.218213 1.51770i 0.00694578 0.0483090i
988988 0 0
989989 46.5468 16.4029i 1.48010 0.521583i
990990 0 0
991991 19.6292 + 2.82225i 0.623541 + 0.0896516i 0.446841 0.894613i 0.352549π-0.352549\pi
0.176699 + 0.984265i 0.443458π0.443458\pi
992992 0 0
993993 3.46030 + 1.01604i 0.109809 + 0.0322429i
994994 0 0
995995 −5.28421 17.9964i −0.167521 0.570523i
996996 0 0
997997 −18.6659 + 40.8727i −0.591156 + 1.29445i 0.343586 + 0.939121i 0.388358π0.388358\pi
−0.934741 + 0.355329i 0.884369π0.884369\pi
998998 0 0
999999 −5.06562 + 3.25547i −0.160269 + 0.102999i
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 368.2.s.b.15.5 yes 80
4.3 odd 2 inner 368.2.s.b.15.4 80
23.20 odd 22 inner 368.2.s.b.319.4 yes 80
92.43 even 22 inner 368.2.s.b.319.5 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.2.s.b.15.4 80 4.3 odd 2 inner
368.2.s.b.15.5 yes 80 1.1 even 1 trivial
368.2.s.b.319.4 yes 80 23.20 odd 22 inner
368.2.s.b.319.5 yes 80 92.43 even 22 inner