Properties

Label 352.2.m.e.225.2
Level 352352
Weight 22
Character 352.225
Analytic conductor 2.8112.811
Analytic rank 00
Dimension 1212
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [352,2,Mod(97,352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(352, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("352.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 352=2511 352 = 2^{5} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 352.m (of order 55, degree 44, 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: 2.810734151152.81073415115
Analytic rank: 00
Dimension: 1212
Relative dimension: 33 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x122x11+11x1011x9+39x843x7+99x6+36x5+431x4++25 x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 225.2
Root 0.2891420.889888i0.289142 - 0.889888i of defining polynomial
Character χ\chi == 352.225
Dual form 352.2.m.e.97.2

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+(0.05203310.0378043i)q3+(0.7147602.19980i)q5+(1.319230.958478i)q7+(0.9257732.84924i)q9+(1.79704+2.78759i)q11+(0.3573601.09984i)q13+(0.120353+0.0874418i)q15+(1.038473.19609i)q17+(4.720443.42960i)q190.104878q21+7.86209q23+(0.2831720.205736i)q25+(0.119167+0.366759i)q27+(4.794973.48375i)q29+(1.11571+3.43382i)q31+(0.1988880.0771113i)q33+(1.165533.58713i)q35+(0.2931460.212983i)q37+(0.0229842+0.0707380i)q39+(3.56752+2.59196i)q415.15478q436.92946q45+(0.9372660.680964i)q47+(1.34143+4.12849i)q49+(0.174861+0.127044i)q51+(1.89864+5.84340i)q53+(4.84770+5.94559i)q55+(0.115966+0.356906i)q57+(6.57117+4.77424i)q59+(2.72739+8.39403i)q61+(3.952242.87147i)q632.67486q65+12.6763q67+(0.4090890.297221i)q69+(4.6374914.2727i)q71+(10.5190+7.64250i)q73+(0.00695661+0.0214102i)q75+(0.301134+5.39990i)q77+(0.6416231.97471i)q79+(7.25105+5.26819i)q81+(2.76546+8.51121i)q83+(6.288514.56887i)q850.381198q87+13.9653q89+(1.525621.10842i)q91+(0.07175890.220851i)q93+(10.9184+7.93270i)q95+(0.00246842+0.00759703i)q97+(9.60615+2.53951i)q99+O(q100)q+(-0.0520331 - 0.0378043i) q^{3} +(0.714760 - 2.19980i) q^{5} +(1.31923 - 0.958478i) q^{7} +(-0.925773 - 2.84924i) q^{9} +(-1.79704 + 2.78759i) q^{11} +(-0.357360 - 1.09984i) q^{13} +(-0.120353 + 0.0874418i) q^{15} +(1.03847 - 3.19609i) q^{17} +(-4.72044 - 3.42960i) q^{19} -0.104878 q^{21} +7.86209 q^{23} +(-0.283172 - 0.205736i) q^{25} +(-0.119167 + 0.366759i) q^{27} +(4.79497 - 3.48375i) q^{29} +(1.11571 + 3.43382i) q^{31} +(0.198888 - 0.0771113i) q^{33} +(-1.16553 - 3.58713i) q^{35} +(0.293146 - 0.212983i) q^{37} +(-0.0229842 + 0.0707380i) q^{39} +(3.56752 + 2.59196i) q^{41} -5.15478 q^{43} -6.92946 q^{45} +(-0.937266 - 0.680964i) q^{47} +(-1.34143 + 4.12849i) q^{49} +(-0.174861 + 0.127044i) q^{51} +(1.89864 + 5.84340i) q^{53} +(4.84770 + 5.94559i) q^{55} +(0.115966 + 0.356906i) q^{57} +(-6.57117 + 4.77424i) q^{59} +(-2.72739 + 8.39403i) q^{61} +(-3.95224 - 2.87147i) q^{63} -2.67486 q^{65} +12.6763 q^{67} +(-0.409089 - 0.297221i) q^{69} +(4.63749 - 14.2727i) q^{71} +(-10.5190 + 7.64250i) q^{73} +(0.00695661 + 0.0214102i) q^{75} +(0.301134 + 5.39990i) q^{77} +(-0.641623 - 1.97471i) q^{79} +(-7.25105 + 5.26819i) q^{81} +(-2.76546 + 8.51121i) q^{83} +(-6.28851 - 4.56887i) q^{85} -0.381198 q^{87} +13.9653 q^{89} +(-1.52562 - 1.10842i) q^{91} +(0.0717589 - 0.220851i) q^{93} +(-10.9184 + 7.93270i) q^{95} +(0.00246842 + 0.00759703i) q^{97} +(9.60615 + 2.53951i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q6q7q9+11q112q134q15+12q175q19+24q21+12q23+13q253q2716q317q33+28q354q3746q394q41+22q43++65q99+O(q100) 12 q - 6 q^{7} - q^{9} + 11 q^{11} - 2 q^{13} - 4 q^{15} + 12 q^{17} - 5 q^{19} + 24 q^{21} + 12 q^{23} + 13 q^{25} - 3 q^{27} - 16 q^{31} - 7 q^{33} + 28 q^{35} - 4 q^{37} - 46 q^{39} - 4 q^{41} + 22 q^{43}+ \cdots + 65 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/352Z)×\left(\mathbb{Z}/352\mathbb{Z}\right)^\times.

nn 133133 287287 321321
χ(n)\chi(n) 11 11 e(25)e\left(\frac{2}{5}\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 −0.0520331 0.0378043i −0.0300414 0.0218263i 0.572663 0.819791i 0.305910π-0.305910\pi
−0.602705 + 0.797964i 0.705910π0.705910\pi
44 0 0
55 0.714760 2.19980i 0.319650 0.983782i −0.654148 0.756367i 0.726972π-0.726972\pi
0.973798 0.227415i 0.0730275π-0.0730275\pi
66 0 0
77 1.31923 0.958478i 0.498623 0.362271i −0.309868 0.950780i 0.600285π-0.600285\pi
0.808491 + 0.588509i 0.200285π0.200285\pi
88 0 0
99 −0.925773 2.84924i −0.308591 0.949745i
1010 0 0
1111 −1.79704 + 2.78759i −0.541827 + 0.840490i
1212 0 0
1313 −0.357360 1.09984i −0.0991139 0.305041i 0.889190 0.457538i 0.151269π-0.151269\pi
−0.988304 + 0.152497i 0.951269π0.951269\pi
1414 0 0
1515 −0.120353 + 0.0874418i −0.0310751 + 0.0225774i
1616 0 0
1717 1.03847 3.19609i 0.251866 0.775165i −0.742565 0.669774i 0.766391π-0.766391\pi
0.994431 0.105390i 0.0336092π-0.0336092\pi
1818 0 0
1919 −4.72044 3.42960i −1.08294 0.786804i −0.104749 0.994499i 0.533404π-0.533404\pi
−0.978194 + 0.207695i 0.933404π0.933404\pi
2020 0 0
2121 −0.104878 −0.0228863
2222 0 0
2323 7.86209 1.63936 0.819680 0.572822i 0.194152π-0.194152\pi
0.819680 + 0.572822i 0.194152π0.194152\pi
2424 0 0
2525 −0.283172 0.205736i −0.0566344 0.0411473i
2626 0 0
2727 −0.119167 + 0.366759i −0.0229337 + 0.0705828i
2828 0 0
2929 4.79497 3.48375i 0.890403 0.646916i −0.0455797 0.998961i 0.514513π-0.514513\pi
0.935983 + 0.352045i 0.114513π0.114513\pi
3030 0 0
3131 1.11571 + 3.43382i 0.200388 + 0.616732i 0.999871 + 0.0160430i 0.00510687π0.00510687\pi
−0.799483 + 0.600689i 0.794893π0.794893\pi
3232 0 0
3333 0.198888 0.0771113i 0.0346220 0.0134234i
3434 0 0
3535 −1.16553 3.58713i −0.197011 0.606336i
3636 0 0
3737 0.293146 0.212983i 0.0481929 0.0350142i −0.563428 0.826165i 0.690518π-0.690518\pi
0.611621 + 0.791151i 0.290518π0.290518\pi
3838 0 0
3939 −0.0229842 + 0.0707380i −0.00368041 + 0.0113271i
4040 0 0
4141 3.56752 + 2.59196i 0.557153 + 0.404795i 0.830416 0.557144i 0.188103π-0.188103\pi
−0.273263 + 0.961939i 0.588103π0.588103\pi
4242 0 0
4343 −5.15478 −0.786097 −0.393049 0.919518i 0.628580π-0.628580\pi
−0.393049 + 0.919518i 0.628580π0.628580\pi
4444 0 0
4545 −6.92946 −1.03298
4646 0 0
4747 −0.937266 0.680964i −0.136714 0.0993288i 0.517326 0.855788i 0.326927π-0.326927\pi
−0.654040 + 0.756460i 0.726927π0.726927\pi
4848 0 0
4949 −1.34143 + 4.12849i −0.191632 + 0.589784i
5050 0 0
5151 −0.174861 + 0.127044i −0.0244854 + 0.0177897i
5252 0 0
5353 1.89864 + 5.84340i 0.260798 + 0.802653i 0.992632 + 0.121170i 0.0386646π0.0386646\pi
−0.731834 + 0.681483i 0.761335π0.761335\pi
5454 0 0
5555 4.84770 + 5.94559i 0.653664 + 0.801703i
5656 0 0
5757 0.115966 + 0.356906i 0.0153600 + 0.0472733i
5858 0 0
5959 −6.57117 + 4.77424i −0.855494 + 0.621553i −0.926655 0.375912i 0.877329π-0.877329\pi
0.0711616 + 0.997465i 0.477329π0.477329\pi
6060 0 0
6161 −2.72739 + 8.39403i −0.349206 + 1.07475i 0.610087 + 0.792334i 0.291134π0.291134\pi
−0.959293 + 0.282411i 0.908866π0.908866\pi
6262 0 0
6363 −3.95224 2.87147i −0.497935 0.361771i
6464 0 0
6565 −2.67486 −0.331776
6666 0 0
6767 12.6763 1.54865 0.774326 0.632787i 0.218089π-0.218089\pi
0.774326 + 0.632787i 0.218089π0.218089\pi
6868 0 0
6969 −0.409089 0.297221i −0.0492486 0.0357812i
7070 0 0
7171 4.63749 14.2727i 0.550368 1.69386i −0.157503 0.987518i 0.550344π-0.550344\pi
0.707872 0.706341i 0.249656π-0.249656\pi
7272 0 0
7373 −10.5190 + 7.64250i −1.23116 + 0.894487i −0.996976 0.0777068i 0.975240π-0.975240\pi
−0.234179 + 0.972193i 0.575240π0.575240\pi
7474 0 0
7575 0.00695661 + 0.0214102i 0.000803280 + 0.00247224i
7676 0 0
7777 0.301134 + 5.39990i 0.0343174 + 0.615376i
7878 0 0
7979 −0.641623 1.97471i −0.0721882 0.222172i 0.908453 0.417988i 0.137265π-0.137265\pi
−0.980641 + 0.195816i 0.937265π0.937265\pi
8080 0 0
8181 −7.25105 + 5.26819i −0.805672 + 0.585355i
8282 0 0
8383 −2.76546 + 8.51121i −0.303549 + 0.934227i 0.676666 + 0.736290i 0.263424π0.263424\pi
−0.980215 + 0.197937i 0.936576π0.936576\pi
8484 0 0
8585 −6.28851 4.56887i −0.682084 0.495563i
8686 0 0
8787 −0.381198 −0.0408687
8888 0 0
8989 13.9653 1.48032 0.740160 0.672431i 0.234750π-0.234750\pi
0.740160 + 0.672431i 0.234750π0.234750\pi
9090 0 0
9191 −1.52562 1.10842i −0.159928 0.116195i
9292 0 0
9393 0.0717589 0.220851i 0.00744105 0.0229012i
9494 0 0
9595 −10.9184 + 7.93270i −1.12021 + 0.813878i
9696 0 0
9797 0.00246842 + 0.00759703i 0.000250630 + 0.000771361i 0.951182 0.308631i 0.0998709π-0.0998709\pi
−0.950931 + 0.309403i 0.899871π0.899871\pi
9898 0 0
9999 9.60615 + 2.53951i 0.965454 + 0.255230i
100100 0 0
101101 3.10740 + 9.56358i 0.309197 + 0.951612i 0.978077 + 0.208242i 0.0667740π0.0667740\pi
−0.668880 + 0.743370i 0.733226π0.733226\pi
102102 0 0
103103 −3.94477 + 2.86604i −0.388690 + 0.282400i −0.764918 0.644127i 0.777221π-0.777221\pi
0.376229 + 0.926527i 0.377221π0.377221\pi
104104 0 0
105105 −0.0749628 + 0.230712i −0.00731562 + 0.0225152i
106106 0 0
107107 −4.57351 3.32285i −0.442138 0.321232i 0.344346 0.938843i 0.388101π-0.388101\pi
−0.786484 + 0.617611i 0.788101π0.788101\pi
108108 0 0
109109 8.01561 0.767756 0.383878 0.923384i 0.374588π-0.374588\pi
0.383878 + 0.923384i 0.374588π0.374588\pi
110110 0 0
111111 −0.0233050 −0.00221201
112112 0 0
113113 7.78627 + 5.65706i 0.732471 + 0.532171i 0.890344 0.455288i 0.150464π-0.150464\pi
−0.157873 + 0.987459i 0.550464π0.550464\pi
114114 0 0
115115 5.61951 17.2951i 0.524022 1.61277i
116116 0 0
117117 −2.80287 + 2.03641i −0.259126 + 0.188266i
118118 0 0
119119 −1.69339 5.21173i −0.155233 0.477759i
120120 0 0
121121 −4.54131 10.0188i −0.412846 0.910801i
122122 0 0
123123 −0.0876423 0.269735i −0.00790244 0.0243212i
124124 0 0
125125 8.70135 6.32190i 0.778272 0.565448i
126126 0 0
127127 −6.38611 + 19.6544i −0.566676 + 1.74405i 0.0962444 + 0.995358i 0.469317π0.469317\pi
−0.662920 + 0.748690i 0.730683π0.730683\pi
128128 0 0
129129 0.268220 + 0.194873i 0.0236154 + 0.0171576i
130130 0 0
131131 17.9382 1.56727 0.783633 0.621224i 0.213364π-0.213364\pi
0.783633 + 0.621224i 0.213364π0.213364\pi
132132 0 0
133133 −9.51455 −0.825016
134134 0 0
135135 0.721622 + 0.524289i 0.0621073 + 0.0451236i
136136 0 0
137137 −1.37467 + 4.23081i −0.117446 + 0.361463i −0.992449 0.122655i 0.960859π-0.960859\pi
0.875003 + 0.484117i 0.160859π0.160859\pi
138138 0 0
139139 −4.46850 + 3.24655i −0.379013 + 0.275369i −0.760938 0.648824i 0.775261π-0.775261\pi
0.381925 + 0.924193i 0.375261π0.375261\pi
140140 0 0
141141 0.0230256 + 0.0708654i 0.00193910 + 0.00596794i
142142 0 0
143143 3.70810 + 0.980284i 0.310087 + 0.0819755i
144144 0 0
145145 −4.23632 13.0380i −0.351807 1.08275i
146146 0 0
147147 0.225873 0.164106i 0.0186297 0.0135353i
148148 0 0
149149 3.74860 11.5370i 0.307097 0.945149i −0.671789 0.740743i 0.734474π-0.734474\pi
0.978886 0.204406i 0.0655262π-0.0655262\pi
150150 0 0
151151 −12.2528 8.90220i −0.997121 0.724451i −0.0356524 0.999364i 0.511351π-0.511351\pi
−0.961469 + 0.274913i 0.911351π0.911351\pi
152152 0 0
153153 −10.0678 −0.813933
154154 0 0
155155 8.35119 0.670784
156156 0 0
157157 −13.3128 9.67231i −1.06248 0.771934i −0.0879313 0.996127i 0.528026π-0.528026\pi
−0.974545 + 0.224192i 0.928026π0.928026\pi
158158 0 0
159159 0.122114 0.375827i 0.00968424 0.0298050i
160160 0 0
161161 10.3719 7.53564i 0.817422 0.593892i
162162 0 0
163163 −3.84634 11.8378i −0.301268 0.927208i −0.981043 0.193788i 0.937923π-0.937923\pi
0.679775 0.733420i 0.262077π-0.262077\pi
164164 0 0
165165 −0.0274724 0.492632i −0.00213872 0.0383513i
166166 0 0
167167 −4.88568 15.0366i −0.378065 1.16356i −0.941387 0.337328i 0.890477π-0.890477\pi
0.563322 0.826237i 0.309523π-0.309523\pi
168168 0 0
169169 9.43527 6.85513i 0.725790 0.527318i
170170 0 0
171171 −5.40168 + 16.6247i −0.413077 + 1.27132i
172172 0 0
173173 −0.670473 0.487127i −0.0509751 0.0370356i 0.562006 0.827133i 0.310030π-0.310030\pi
−0.612981 + 0.790098i 0.710030π0.710030\pi
174174 0 0
175175 −0.570764 −0.0431457
176176 0 0
177177 0.522405 0.0392664
178178 0 0
179179 13.6719 + 9.93323i 1.02189 + 0.742444i 0.966669 0.256030i 0.0824146π-0.0824146\pi
0.0552180 + 0.998474i 0.482415π0.482415\pi
180180 0 0
181181 3.47869 10.7063i 0.258569 0.795794i −0.734536 0.678569i 0.762600π-0.762600\pi
0.993105 0.117225i 0.0373997π-0.0373997\pi
182182 0 0
183183 0.459245 0.333661i 0.0339484 0.0246649i
184184 0 0
185185 −0.258992 0.797095i −0.0190415 0.0586036i
186186 0 0
187187 7.04320 + 8.63832i 0.515050 + 0.631697i
188188 0 0
189189 0.194321 + 0.598059i 0.0141348 + 0.0435024i
190190 0 0
191191 −21.0000 + 15.2574i −1.51951 + 1.10399i −0.557778 + 0.829990i 0.688346π0.688346\pi
−0.961730 + 0.273998i 0.911654π0.911654\pi
192192 0 0
193193 0.194760 0.599410i 0.0140191 0.0431465i −0.943802 0.330511i 0.892779π-0.892779\pi
0.957821 + 0.287364i 0.0927790π0.0927790\pi
194194 0 0
195195 0.139182 + 0.101121i 0.00996700 + 0.00724145i
196196 0 0
197197 22.7866 1.62348 0.811741 0.584018i 0.198520π-0.198520\pi
0.811741 + 0.584018i 0.198520π0.198520\pi
198198 0 0
199199 17.6443 1.25077 0.625386 0.780316i 0.284942π-0.284942\pi
0.625386 + 0.780316i 0.284942π0.284942\pi
200200 0 0
201201 −0.659586 0.479217i −0.0465236 0.0338014i
202202 0 0
203203 2.98658 9.19175i 0.209617 0.645134i
204204 0 0
205205 8.25171 5.99522i 0.576325 0.418724i
206206 0 0
207207 −7.27851 22.4009i −0.505891 1.55697i
208208 0 0
209209 18.0431 6.99552i 1.24807 0.483890i
210210 0 0
211211 −2.69949 8.30817i −0.185840 0.571958i 0.814121 0.580695i 0.197219π-0.197219\pi
−0.999962 + 0.00873682i 0.997219π0.997219\pi
212212 0 0
213213 −0.780873 + 0.567337i −0.0535045 + 0.0388733i
214214 0 0
215215 −3.68443 + 11.3395i −0.251276 + 0.773349i
216216 0 0
217217 4.76313 + 3.46061i 0.323342 + 0.234922i
218218 0 0
219219 0.836256 0.0565089
220220 0 0
221221 −3.88630 −0.261421
222222 0 0
223223 6.66560 + 4.84284i 0.446361 + 0.324301i 0.788158 0.615474i 0.211035π-0.211035\pi
−0.341796 + 0.939774i 0.611035π0.611035\pi
224224 0 0
225225 −0.324039 + 0.997289i −0.0216026 + 0.0664859i
226226 0 0
227227 −2.56318 + 1.86226i −0.170124 + 0.123603i −0.669589 0.742731i 0.733530π-0.733530\pi
0.499465 + 0.866334i 0.333530π0.333530\pi
228228 0 0
229229 −2.47730 7.62433i −0.163704 0.503830i 0.835234 0.549894i 0.185332π-0.185332\pi
−0.998938 + 0.0460643i 0.985332π0.985332\pi
230230 0 0
231231 0.188470 0.292358i 0.0124004 0.0192357i
232232 0 0
233233 −5.67269 17.4588i −0.371631 1.14376i −0.945724 0.324971i 0.894645π-0.894645\pi
0.574093 0.818790i 0.305355π-0.305355\pi
234234 0 0
235235 −2.16791 + 1.57508i −0.141419 + 0.102747i
236236 0 0
237237 −0.0412669 + 0.127007i −0.00268058 + 0.00824996i
238238 0 0
239239 −12.0977 8.78948i −0.782534 0.568544i 0.123204 0.992381i 0.460683π-0.460683\pi
−0.905739 + 0.423837i 0.860683π0.860683\pi
240240 0 0
241241 −24.4586 −1.57552 −0.787758 0.615984i 0.788758π-0.788758\pi
−0.787758 + 0.615984i 0.788758π0.788758\pi
242242 0 0
243243 1.73335 0.111195
244244 0 0
245245 8.12306 + 5.90175i 0.518963 + 0.377049i
246246 0 0
247247 −2.08512 + 6.41734i −0.132673 + 0.408326i
248248 0 0
249249 0.465656 0.338319i 0.0295098 0.0214401i
250250 0 0
251251 2.19108 + 6.74344i 0.138300 + 0.425642i 0.996089 0.0883595i 0.0281624π-0.0281624\pi
−0.857789 + 0.514002i 0.828162π0.828162\pi
252252 0 0
253253 −14.1285 + 21.9163i −0.888250 + 1.37786i
254254 0 0
255255 0.154488 + 0.475465i 0.00967441 + 0.0297748i
256256 0 0
257257 −15.4384 + 11.2167i −0.963023 + 0.699677i −0.953851 0.300281i 0.902920π-0.902920\pi
−0.00917198 + 0.999958i 0.502920π0.502920\pi
258258 0 0
259259 0.182588 0.561947i 0.0113455 0.0349177i
260260 0 0
261261 −14.3651 10.4368i −0.889176 0.646024i
262262 0 0
263263 16.3340 1.00720 0.503598 0.863938i 0.332009π-0.332009\pi
0.503598 + 0.863938i 0.332009π0.332009\pi
264264 0 0
265265 14.2114 0.873000
266266 0 0
267267 −0.726659 0.527949i −0.0444708 0.0323099i
268268 0 0
269269 5.47241 16.8423i 0.333659 1.02690i −0.633720 0.773562i 0.718473π-0.718473\pi
0.967379 0.253333i 0.0815269π-0.0815269\pi
270270 0 0
271271 7.45427 5.41585i 0.452815 0.328989i −0.337891 0.941185i 0.609714π-0.609714\pi
0.790706 + 0.612196i 0.209714π0.209714\pi
272272 0 0
273273 0.0374794 + 0.115350i 0.00226836 + 0.00698128i
274274 0 0
275275 1.08238 0.419651i 0.0652699 0.0253059i
276276 0 0
277277 9.18452 + 28.2671i 0.551845 + 1.69840i 0.704134 + 0.710067i 0.251335π0.251335\pi
−0.152290 + 0.988336i 0.548665π0.548665\pi
278278 0 0
279279 8.75085 6.35787i 0.523900 0.380636i
280280 0 0
281281 −4.47453 + 13.7712i −0.266928 + 0.821520i 0.724315 + 0.689469i 0.242156π0.242156\pi
−0.991243 + 0.132050i 0.957844π0.957844\pi
282282 0 0
283283 −18.1000 13.1504i −1.07594 0.781713i −0.0989659 0.995091i 0.531553π-0.531553\pi
−0.976970 + 0.213378i 0.931553π0.931553\pi
284284 0 0
285285 0.868010 0.0514165
286286 0 0
287287 7.19072 0.424455
288288 0 0
289289 4.61674 + 3.35426i 0.271573 + 0.197309i
290290 0 0
291291 0.000158760 0 0.000488614i 9.30670e−6 0 2.86431e-5i
292292 0 0
293293 −18.8358 + 13.6850i −1.10040 + 0.799487i −0.981125 0.193374i 0.938057π-0.938057\pi
−0.119274 + 0.992861i 0.538057π0.538057\pi
294294 0 0
295295 5.80557 + 17.8677i 0.338014 + 1.04030i
296296 0 0
297297 −0.808225 0.991269i −0.0468980 0.0575192i
298298 0 0
299299 −2.80960 8.64706i −0.162483 0.500072i
300300 0 0
301301 −6.80036 + 4.94075i −0.391966 + 0.284780i
302302 0 0
303303 0.199857 0.615096i 0.0114815 0.0353364i
304304 0 0
305305 16.5158 + 11.9994i 0.945692 + 0.687085i
306306 0 0
307307 −23.0645 −1.31636 −0.658179 0.752861i 0.728673π-0.728673\pi
−0.658179 + 0.752861i 0.728673π0.728673\pi
308308 0 0
309309 0.313608 0.0178405
310310 0 0
311311 2.11848 + 1.53917i 0.120128 + 0.0872780i 0.646227 0.763145i 0.276346π-0.276346\pi
−0.526099 + 0.850423i 0.676346π0.676346\pi
312312 0 0
313313 −9.76216 + 30.0448i −0.551790 + 1.69823i 0.152484 + 0.988306i 0.451273π0.451273\pi
−0.704274 + 0.709928i 0.748727π0.748727\pi
314314 0 0
315315 −9.14157 + 6.64174i −0.515069 + 0.374220i
316316 0 0
317317 −3.53064 10.8662i −0.198301 0.610307i −0.999922 0.0124749i 0.996029π-0.996029\pi
0.801621 0.597832i 0.203971π-0.203971\pi
318318 0 0
319319 1.09452 + 19.6268i 0.0612814 + 1.09889i
320320 0 0
321321 0.112356 + 0.345796i 0.00627110 + 0.0193005i
322322 0 0
323323 −15.8633 + 11.5254i −0.882660 + 0.641290i
324324 0 0
325325 −0.125083 + 0.384967i −0.00693837 + 0.0213541i
326326 0 0
327327 −0.417077 0.303024i −0.0230644 0.0167573i
328328 0 0
329329 −1.88916 −0.104153
330330 0 0
331331 19.5632 1.07529 0.537645 0.843171i 0.319314π-0.319314\pi
0.537645 + 0.843171i 0.319314π0.319314\pi
332332 0 0
333333 −0.878224 0.638067i −0.0481264 0.0349659i
334334 0 0
335335 9.06048 27.8853i 0.495027 1.52354i
336336 0 0
337337 3.20368 2.32761i 0.174516 0.126793i −0.497099 0.867694i 0.665601π-0.665601\pi
0.671614 + 0.740901i 0.265601π0.265601\pi
338338 0 0
339339 −0.191283 0.588709i −0.0103891 0.0319743i
340340 0 0
341341 −11.5771 3.06054i −0.626933 0.165738i
342342 0 0
343343 5.71472 + 17.5881i 0.308566 + 0.949669i
344344 0 0
345345 −0.946228 + 0.687475i −0.0509432 + 0.0370124i
346346 0 0
347347 0.585635 1.80240i 0.0314385 0.0967578i −0.934106 0.356996i 0.883801π-0.883801\pi
0.965544 + 0.260238i 0.0838010π0.0838010\pi
348348 0 0
349349 22.2674 + 16.1782i 1.19195 + 0.866001i 0.993469 0.114104i 0.0363997π-0.0363997\pi
0.198479 + 0.980105i 0.436400π0.436400\pi
350350 0 0
351351 0.445962 0.0238037
352352 0 0
353353 −17.3853 −0.925325 −0.462663 0.886534i 0.653106π-0.653106\pi
−0.462663 + 0.886534i 0.653106π0.653106\pi
354354 0 0
355355 −28.0825 20.4031i −1.49046 1.08289i
356356 0 0
357357 −0.108913 + 0.335200i −0.00576430 + 0.0177407i
358358 0 0
359359 0.780494 0.567062i 0.0411929 0.0299284i −0.566998 0.823719i 0.691895π-0.691895\pi
0.608191 + 0.793791i 0.291895π0.291895\pi
360360 0 0
361361 4.64906 + 14.3083i 0.244688 + 0.753071i
362362 0 0
363363 −0.142455 + 0.692991i −0.00747697 + 0.0363726i
364364 0 0
365365 9.29344 + 28.6023i 0.486441 + 1.49711i
366366 0 0
367367 16.8081 12.2118i 0.877378 0.637452i −0.0551785 0.998477i 0.517573π-0.517573\pi
0.932556 + 0.361024i 0.117573π0.117573\pi
368368 0 0
369369 4.08238 12.5643i 0.212520 0.654070i
370370 0 0
371371 8.10551 + 5.88900i 0.420817 + 0.305742i
372372 0 0
373373 −2.62662 −0.136001 −0.0680006 0.997685i 0.521662π-0.521662\pi
−0.0680006 + 0.997685i 0.521662π0.521662\pi
374374 0 0
375375 −0.691753 −0.0357220
376376 0 0
377377 −5.54511 4.02876i −0.285588 0.207491i
378378 0 0
379379 1.48316 4.56471i 0.0761850 0.234473i −0.905711 0.423897i 0.860662π-0.860662\pi
0.981895 + 0.189424i 0.0606619π0.0606619\pi
380380 0 0
381381 1.07531 0.781259i 0.0550899 0.0400251i
382382 0 0
383383 5.29843 + 16.3069i 0.270737 + 0.833244i 0.990316 + 0.138833i 0.0443351π0.0443351\pi
−0.719578 + 0.694411i 0.755665π0.755665\pi
384384 0 0
385385 12.0940 + 3.19720i 0.616365 + 0.162944i
386386 0 0
387387 4.77216 + 14.6872i 0.242582 + 0.746592i
388388 0 0
389389 12.5318 9.10485i 0.635385 0.461634i −0.222877 0.974847i 0.571545π-0.571545\pi
0.858262 + 0.513212i 0.171545π0.171545\pi
390390 0 0
391391 8.16456 25.1279i 0.412899 1.27077i
392392 0 0
393393 −0.933380 0.678140i −0.0470828 0.0342076i
394394 0 0
395395 −4.80258 −0.241644
396396 0 0
397397 −15.5364 −0.779750 −0.389875 0.920868i 0.627482π-0.627482\pi
−0.389875 + 0.920868i 0.627482π0.627482\pi
398398 0 0
399399 0.495072 + 0.359691i 0.0247846 + 0.0180071i
400400 0 0
401401 −5.79452 + 17.8337i −0.289365 + 0.890572i 0.695692 + 0.718340i 0.255098π0.255098\pi
−0.985056 + 0.172232i 0.944902π0.944902\pi
402402 0 0
403403 3.37794 2.45422i 0.168267 0.122253i
404404 0 0
405405 6.40624 + 19.7164i 0.318329 + 0.979715i
406406 0 0
407407 0.0669147 + 1.19991i 0.00331684 + 0.0594772i
408408 0 0
409409 −11.3705 34.9949i −0.562237 1.73039i −0.676020 0.736883i 0.736297π-0.736297\pi
0.113783 0.993506i 0.463703π-0.463703\pi
410410 0 0
411411 0.231472 0.168174i 0.0114177 0.00829541i
412412 0 0
413413 −4.09290 + 12.5966i −0.201398 + 0.619841i
414414 0 0
415415 16.7464 + 12.1669i 0.822047 + 0.597252i
416416 0 0
417417 0.355244 0.0173964
418418 0 0
419419 −18.6797 −0.912565 −0.456283 0.889835i 0.650819π-0.650819\pi
−0.456283 + 0.889835i 0.650819π0.650819\pi
420420 0 0
421421 1.46645 + 1.06544i 0.0714702 + 0.0519261i 0.622947 0.782264i 0.285935π-0.285935\pi
−0.551476 + 0.834190i 0.685935π0.685935\pi
422422 0 0
423423 −1.07253 + 3.30091i −0.0521482 + 0.160496i
424424 0 0
425425 −0.951618 + 0.691391i −0.0461602 + 0.0335374i
426426 0 0
427427 4.44744 + 13.6878i 0.215227 + 0.662400i
428428 0 0
429429 −0.155885 0.191189i −0.00752620 0.00923071i
430430 0 0
431431 −6.13475 18.8808i −0.295500 0.909457i −0.983053 0.183322i 0.941315π-0.941315\pi
0.687552 0.726135i 0.258685π-0.258685\pi
432432 0 0
433433 −13.5039 + 9.81114i −0.648955 + 0.471493i −0.862915 0.505349i 0.831364π-0.831364\pi
0.213960 + 0.976842i 0.431364π0.431364\pi
434434 0 0
435435 −0.272465 + 0.838561i −0.0130637 + 0.0402059i
436436 0 0
437437 −37.1125 26.9638i −1.77533 1.28985i
438438 0 0
439439 −33.3999 −1.59409 −0.797044 0.603921i 0.793604π-0.793604\pi
−0.797044 + 0.603921i 0.793604π0.793604\pi
440440 0 0
441441 13.0049 0.619280
442442 0 0
443443 −7.35442 5.34330i −0.349419 0.253868i 0.399206 0.916861i 0.369286π-0.369286\pi
−0.748625 + 0.662993i 0.769286π0.769286\pi
444444 0 0
445445 9.98184 30.7209i 0.473185 1.45631i
446446 0 0
447447 −0.631200 + 0.458594i −0.0298547 + 0.0216907i
448448 0 0
449449 −1.58559 4.87996i −0.0748288 0.230299i 0.906645 0.421893i 0.138634π-0.138634\pi
−0.981474 + 0.191594i 0.938634π0.938634\pi
450450 0 0
451451 −13.6363 + 5.28694i −0.642107 + 0.248952i
452452 0 0
453453 0.301012 + 0.926419i 0.0141428 + 0.0435270i
454454 0 0
455455 −3.52877 + 2.56380i −0.165431 + 0.120193i
456456 0 0
457457 −1.15130 + 3.54335i −0.0538557 + 0.165751i −0.974367 0.224966i 0.927773π-0.927773\pi
0.920511 + 0.390717i 0.127773π0.127773\pi
458458 0 0
459459 1.04844 + 0.761737i 0.0489370 + 0.0355548i
460460 0 0
461461 −0.439230 −0.0204570 −0.0102285 0.999948i 0.503256π-0.503256\pi
−0.0102285 + 0.999948i 0.503256π0.503256\pi
462462 0 0
463463 26.8109 1.24601 0.623003 0.782219i 0.285912π-0.285912\pi
0.623003 + 0.782219i 0.285912π0.285912\pi
464464 0 0
465465 −0.434539 0.315711i −0.0201513 0.0146407i
466466 0 0
467467 −5.23362 + 16.1074i −0.242183 + 0.745362i 0.753904 + 0.656984i 0.228168π0.228168\pi
−0.996087 + 0.0883778i 0.971832π0.971832\pi
468468 0 0
469469 16.7229 12.1499i 0.772193 0.561031i
470470 0 0
471471 0.327052 + 1.00656i 0.0150697 + 0.0463799i
472472 0 0
473473 9.26334 14.3694i 0.425929 0.660707i
474474 0 0
475475 0.631102 + 1.94233i 0.0289570 + 0.0891203i
476476 0 0
477477 14.8915 10.8193i 0.681836 0.495383i
478478 0 0
479479 1.10066 3.38748i 0.0502903 0.154778i −0.922758 0.385381i 0.874070π-0.874070\pi
0.973048 + 0.230603i 0.0740700π0.0740700\pi
480480 0 0
481481 −0.339006 0.246302i −0.0154574 0.0112304i
482482 0 0
483483 −0.824563 −0.0375189
484484 0 0
485485 0.0184763 0.000838966
486486 0 0
487487 −14.5377 10.5623i −0.658766 0.478622i 0.207480 0.978239i 0.433474π-0.433474\pi
−0.866246 + 0.499618i 0.833474π0.833474\pi
488488 0 0
489489 −0.247383 + 0.761366i −0.0111870 + 0.0344302i
490490 0 0
491491 9.91237 7.20176i 0.447339 0.325011i −0.341205 0.939989i 0.610835π-0.610835\pi
0.788544 + 0.614978i 0.210835π0.210835\pi
492492 0 0
493493 −6.15493 18.9429i −0.277204 0.853146i
494494 0 0
495495 12.4525 19.3165i 0.559699 0.868212i
496496 0 0
497497 −7.56217 23.2740i −0.339209 1.04398i
498498 0 0
499499 16.3463 11.8763i 0.731762 0.531656i −0.158358 0.987382i 0.550620π-0.550620\pi
0.890120 + 0.455725i 0.150620π0.150620\pi
500500 0 0
501501 −0.314230 + 0.967100i −0.0140388 + 0.0432068i
502502 0 0
503503 13.2493 + 9.62615i 0.590755 + 0.429209i 0.842586 0.538563i 0.181032π-0.181032\pi
−0.251830 + 0.967771i 0.581032π0.581032\pi
504504 0 0
505505 23.2590 1.03501
506506 0 0
507507 −0.750100 −0.0333131
508508 0 0
509509 −3.73628 2.71456i −0.165608 0.120321i 0.501895 0.864929i 0.332637π-0.332637\pi
−0.667502 + 0.744608i 0.732637π0.732637\pi
510510 0 0
511511 −6.55183 + 20.1645i −0.289836 + 0.892023i
512512 0 0
513513 1.82036 1.32257i 0.0803707 0.0583927i
514514 0 0
515515 3.48517 + 10.7263i 0.153575 + 0.472655i
516516 0 0
517517 3.58255 1.38900i 0.157560 0.0610879i
518518 0 0
519519 0.0164713 + 0.0506935i 0.000723011 + 0.00222520i
520520 0 0
521521 9.37691 6.81272i 0.410810 0.298471i −0.363120 0.931742i 0.618288π-0.618288\pi
0.773930 + 0.633272i 0.218288π0.218288\pi
522522 0 0
523523 9.21116 28.3490i 0.402776 1.23962i −0.519962 0.854189i 0.674054π-0.674054\pi
0.922738 0.385428i 0.125946π-0.125946\pi
524524 0 0
525525 0.0296986 + 0.0215773i 0.00129615 + 0.000941711i
526526 0 0
527527 12.1334 0.528540
528528 0 0
529529 38.8125 1.68750
530530 0 0
531531 19.6863 + 14.3030i 0.854314 + 0.620695i
532532 0 0
533533 1.57585 4.84997i 0.0682577 0.210076i
534534 0 0
535535 −10.5786 + 7.68578i −0.457351 + 0.332285i
536536 0 0
537537 −0.335874 1.03371i −0.0144940 0.0446081i
538538 0 0
539539 −9.09793 11.1584i −0.391876 0.480626i
540540 0 0
541541 −0.747789 2.30146i −0.0321500 0.0989474i 0.933694 0.358072i 0.116566π-0.116566\pi
−0.965844 + 0.259125i 0.916566π0.916566\pi
542542 0 0
543543 −0.585752 + 0.425574i −0.0251370 + 0.0182631i
544544 0 0
545545 5.72923 17.6328i 0.245413 0.755305i
546546 0 0
547547 −10.8486 7.88196i −0.463852 0.337008i 0.331189 0.943565i 0.392550π-0.392550\pi
−0.795040 + 0.606556i 0.792550π0.792550\pi
548548 0 0
549549 26.4415 1.12850
550550 0 0
551551 −34.5822 −1.47325
552552 0 0
553553 −2.73917 1.99012i −0.116481 0.0846286i
554554 0 0
555555 −0.0166574 + 0.0512663i −0.000707069 + 0.00217614i
556556 0 0
557557 −6.10060 + 4.43235i −0.258491 + 0.187805i −0.709481 0.704724i 0.751071π-0.751071\pi
0.450991 + 0.892529i 0.351071π0.351071\pi
558558 0 0
559559 1.84212 + 5.66945i 0.0779132 + 0.239792i
560560 0 0
561561 −0.0399145 0.715742i −0.00168519 0.0302187i
562562 0 0
563563 0.379457 + 1.16785i 0.0159922 + 0.0492190i 0.958734 0.284304i 0.0917625π-0.0917625\pi
−0.942742 + 0.333523i 0.891763π0.891763\pi
564564 0 0
565565 18.0097 13.0848i 0.757675 0.550483i
566566 0 0
567567 −4.51636 + 13.8999i −0.189669 + 0.583743i
568568 0 0
569569 −10.8958 7.91626i −0.456775 0.331867i 0.335490 0.942044i 0.391098π-0.391098\pi
−0.792265 + 0.610177i 0.791098π0.791098\pi
570570 0 0
571571 11.8746 0.496935 0.248467 0.968640i 0.420073π-0.420073\pi
0.248467 + 0.968640i 0.420073π0.420073\pi
572572 0 0
573573 1.66949 0.0697441
574574 0 0
575575 −2.22632 1.61752i −0.0928441 0.0674552i
576576 0 0
577577 6.29752 19.3818i 0.262169 0.806874i −0.730163 0.683273i 0.760556π-0.760556\pi
0.992332 0.123601i 0.0394441π-0.0394441\pi
578578 0 0
579579 −0.0327943 + 0.0238264i −0.00136288 + 0.000990192i
580580 0 0
581581 4.50953 + 13.8789i 0.187087 + 0.575794i
582582 0 0
583583 −19.7009 5.20819i −0.815929 0.215701i
584584 0 0
585585 2.47632 + 7.62132i 0.102383 + 0.315103i
586586 0 0
587587 19.1775 13.9333i 0.791541 0.575088i −0.116879 0.993146i 0.537289π-0.537289\pi
0.908420 + 0.418058i 0.137289π0.137289\pi
588588 0 0
589589 6.50995 20.0356i 0.268238 0.825551i
590590 0 0
591591 −1.18566 0.861433i −0.0487716 0.0354346i
592592 0 0
593593 −40.7647 −1.67400 −0.837002 0.547199i 0.815694π-0.815694\pi
−0.837002 + 0.547199i 0.815694π0.815694\pi
594594 0 0
595595 −12.6752 −0.519631
596596 0 0
597597 −0.918089 0.667031i −0.0375749 0.0272998i
598598 0 0
599599 −7.23216 + 22.2583i −0.295498 + 0.909450i 0.687556 + 0.726132i 0.258684π0.258684\pi
−0.983054 + 0.183318i 0.941316π0.941316\pi
600600 0 0
601601 −26.1694 + 19.0132i −1.06747 + 0.775563i −0.975456 0.220195i 0.929331π-0.929331\pi
−0.0920150 + 0.995758i 0.529331π0.529331\pi
602602 0 0
603603 −11.7353 36.1176i −0.477900 1.47082i
604604 0 0
605605 −25.2854 + 2.82895i −1.02800 + 0.115013i
606606 0 0
607607 8.66071 + 26.6549i 0.351527 + 1.08189i 0.957996 + 0.286782i 0.0925855π0.0925855\pi
−0.606469 + 0.795107i 0.707414π0.707414\pi
608608 0 0
609609 −0.502889 + 0.365370i −0.0203781 + 0.0148055i
610610 0 0
611611 −0.414011 + 1.27419i −0.0167491 + 0.0515484i
612612 0 0
613613 −1.91565 1.39180i −0.0773722 0.0562142i 0.548427 0.836199i 0.315227π-0.315227\pi
−0.625799 + 0.779984i 0.715227π0.715227\pi
614614 0 0
615615 −0.656008 −0.0264528
616616 0 0
617617 −10.4196 −0.419477 −0.209738 0.977758i 0.567261π-0.567261\pi
−0.209738 + 0.977758i 0.567261π0.567261\pi
618618 0 0
619619 26.5852 + 19.3153i 1.06855 + 0.776347i 0.975651 0.219329i 0.0703868π-0.0703868\pi
0.0928986 + 0.995676i 0.470387π0.470387\pi
620620 0 0
621621 −0.936903 + 2.88349i −0.0375966 + 0.115710i
622622 0 0
623623 18.4235 13.3854i 0.738121 0.536277i
624624 0 0
625625 −8.22838 25.3243i −0.329135 1.01297i
626626 0 0
627627 −1.20330 0.318108i −0.0480552 0.0127040i
628628 0 0
629629 −0.376288 1.15810i −0.0150036 0.0461763i
630630 0 0
631631 −16.7872 + 12.1966i −0.668289 + 0.485540i −0.869452 0.494017i 0.835528π-0.835528\pi
0.201163 + 0.979558i 0.435528π0.435528\pi
632632 0 0
633633 −0.173622 + 0.534352i −0.00690084 + 0.0212386i
634634 0 0
635635 38.6713 + 28.0964i 1.53463 + 1.11497i
636636 0 0
637637 5.02006 0.198902
638638 0 0
639639 −44.9596 −1.77857
640640 0 0
641641 0.790786 + 0.574539i 0.0312342 + 0.0226929i 0.603293 0.797520i 0.293855π-0.293855\pi
−0.572059 + 0.820213i 0.693855π0.693855\pi
642642 0 0
643643 −11.8078 + 36.3406i −0.465653 + 1.43313i 0.392506 + 0.919749i 0.371608π0.371608\pi
−0.858159 + 0.513384i 0.828392π0.828392\pi
644644 0 0
645645 0.620395 0.450743i 0.0244280 0.0177480i
646646 0 0
647647 −10.8077 33.2625i −0.424893 1.30768i −0.903097 0.429436i 0.858712π-0.858712\pi
0.478205 0.878248i 0.341288π-0.341288\pi
648648 0 0
649649 −1.49996 26.8972i −0.0588787 1.05581i
650650 0 0
651651 −0.117014 0.360133i −0.00458615 0.0141147i
652652 0 0
653653 −28.6326 + 20.8028i −1.12048 + 0.814077i −0.984282 0.176604i 0.943489π-0.943489\pi
−0.136199 + 0.990681i 0.543489π0.543489\pi
654654 0 0
655655 12.8215 39.4605i 0.500977 1.54185i
656656 0 0
657657 31.5135 + 22.8959i 1.22946 + 0.893253i
658658 0 0
659659 23.8852 0.930437 0.465219 0.885196i 0.345976π-0.345976\pi
0.465219 + 0.885196i 0.345976π0.345976\pi
660660 0 0
661661 −28.4658 −1.10719 −0.553596 0.832785i 0.686745π-0.686745\pi
−0.553596 + 0.832785i 0.686745π0.686745\pi
662662 0 0
663663 0.202216 + 0.146919i 0.00785343 + 0.00570585i
664664 0 0
665665 −6.80062 + 20.9301i −0.263717 + 0.811636i
666666 0 0
667667 37.6985 27.3896i 1.45969 1.06053i
668668 0 0
669669 −0.163752 0.503976i −0.00633101 0.0194849i
670670 0 0
671671 −18.4979 22.6872i −0.714103 0.875831i
672672 0 0
673673 13.8277 + 42.5572i 0.533017 + 1.64046i 0.747895 + 0.663817i 0.231065π0.231065\pi
−0.214878 + 0.976641i 0.568935π0.568935\pi
674674 0 0
675675 0.109200 0.0793388i 0.00420313 0.00305375i
676676 0 0
677677 −1.82355 + 5.61231i −0.0700847 + 0.215699i −0.979964 0.199174i 0.936174π-0.936174\pi
0.909879 + 0.414873i 0.136174π0.136174\pi
678678 0 0
679679 0.0105380 + 0.00765631i 0.000404412 + 0.000293822i
680680 0 0
681681 0.203772 0.00780856
682682 0 0
683683 −35.5174 −1.35904 −0.679518 0.733659i 0.737811π-0.737811\pi
−0.679518 + 0.733659i 0.737811π0.737811\pi
684684 0 0
685685 8.32440 + 6.04803i 0.318059 + 0.231083i
686686 0 0
687687 −0.159331 + 0.490371i −0.00607886 + 0.0187088i
688688 0 0
689689 5.74832 4.17640i 0.218994 0.159108i
690690 0 0
691691 6.53766 + 20.1208i 0.248704 + 0.765433i 0.995005 + 0.0998241i 0.0318280π0.0318280\pi
−0.746301 + 0.665609i 0.768172π0.768172\pi
692692 0 0
693693 15.1068 5.85708i 0.573860 0.222492i
694694 0 0
695695 3.94788 + 12.1503i 0.149752 + 0.460888i
696696 0 0
697697 11.9889 8.71043i 0.454111 0.329931i
698698 0 0
699699 −0.364848 + 1.12289i −0.0137998 + 0.0424715i
700700 0 0
701701 15.6462 + 11.3677i 0.590951 + 0.429351i 0.842655 0.538453i 0.180991π-0.180991\pi
−0.251705 + 0.967804i 0.580991π0.580991\pi
702702 0 0
703703 −2.11422 −0.0797394
704704 0 0
705705 0.172348 0.00649099
706706 0 0
707707 13.2659 + 9.63821i 0.498914 + 0.362482i
708708 0 0
709709 −8.22899 + 25.3262i −0.309046 + 0.951146i 0.669090 + 0.743181i 0.266684π0.266684\pi
−0.978136 + 0.207965i 0.933316π0.933316\pi
710710 0 0
711711 −5.03242 + 3.65627i −0.188731 + 0.137121i
712712 0 0
713713 8.77185 + 26.9970i 0.328508 + 1.01104i
714714 0 0
715715 4.80683 7.45642i 0.179765 0.278854i
716716 0 0
717717 0.297200 + 0.914689i 0.0110992 + 0.0341597i
718718 0 0
719719 27.7036 20.1278i 1.03317 0.750641i 0.0642283 0.997935i 0.479541π-0.479541\pi
0.968940 + 0.247294i 0.0795414π0.0795414\pi
720720 0 0
721721 −2.45703 + 7.56195i −0.0915045 + 0.281622i
722722 0 0
723723 1.27266 + 0.924640i 0.0473307 + 0.0343877i
724724 0 0
725725 −2.07454 −0.0770463
726726 0 0
727727 −38.7547 −1.43733 −0.718666 0.695355i 0.755247π-0.755247\pi
−0.718666 + 0.695355i 0.755247π0.755247\pi
728728 0 0
729729 21.6630 + 15.7391i 0.802332 + 0.582928i
730730 0 0
731731 −5.35310 + 16.4751i −0.197991 + 0.609355i
732732 0 0
733733 22.6174 16.4325i 0.835393 0.606949i −0.0856869 0.996322i 0.527308π-0.527308\pi
0.921080 + 0.389374i 0.127308π0.127308\pi
734734 0 0
735735 −0.199557 0.614173i −0.00736077 0.0226541i
736736 0 0
737737 −22.7797 + 35.3362i −0.839102 + 1.30163i
738738 0 0
739739 −0.0121639 0.0374367i −0.000447457 0.00137713i 0.950833 0.309705i 0.100230π-0.100230\pi
−0.951280 + 0.308328i 0.900230π0.900230\pi
740740 0 0
741741 0.351098 0.255088i 0.0128979 0.00937089i
742742 0 0
743743 −8.08821 + 24.8930i −0.296728 + 0.913234i 0.685908 + 0.727688i 0.259405π0.259405\pi
−0.982636 + 0.185546i 0.940595π0.940595\pi
744744 0 0
745745 −22.6998 16.4924i −0.831657 0.604234i
746746 0 0
747747 26.8106 0.980950
748748 0 0
749749 −9.21839 −0.336833
750750 0 0
751751 −15.6085 11.3402i −0.569562 0.413811i 0.265384 0.964143i 0.414501π-0.414501\pi
−0.834946 + 0.550332i 0.814501π0.814501\pi
752752 0 0
753753 0.140922 0.433715i 0.00513550 0.0158054i
754754 0 0
755755 −28.3409 + 20.5909i −1.03143 + 0.749379i
756756 0 0
757757 14.1487 + 43.5453i 0.514244 + 1.58268i 0.784653 + 0.619936i 0.212841π0.212841\pi
−0.270408 + 0.962746i 0.587159π0.587159\pi
758758 0 0
759759 1.56368 0.606256i 0.0567579 0.0220057i
760760 0 0
761761 −4.08236 12.5642i −0.147985 0.455452i 0.849397 0.527754i 0.176966π-0.176966\pi
−0.997383 + 0.0723016i 0.976966π0.976966\pi
762762 0 0
763763 10.5744 7.68278i 0.382821 0.278135i
764764 0 0
765765 −7.19605 + 22.1472i −0.260174 + 0.800733i
766766 0 0
767767 7.59918 + 5.52113i 0.274391 + 0.199356i
768768 0 0
769769 −3.36696 −0.121416 −0.0607078 0.998156i 0.519336π-0.519336\pi
−0.0607078 + 0.998156i 0.519336π0.519336\pi
770770 0 0
771771 1.22735 0.0442019
772772 0 0
773773 −39.0007 28.3357i −1.40276 1.01916i −0.994326 0.106374i 0.966076π-0.966076\pi
−0.408432 0.912789i 0.633924π-0.633924\pi
774774 0 0
775775 0.390522 1.20190i 0.0140280 0.0431737i
776776 0 0
777777 −0.0307446 + 0.0223373i −0.00110296 + 0.000801346i
778778 0 0
779779 −7.95089 24.4703i −0.284870 0.876741i
780780 0 0
781781 31.4527 + 38.5760i 1.12547 + 1.38036i
782782 0 0
783783 0.706293 + 2.17375i 0.0252408 + 0.0776833i
784784 0 0
785785 −30.7926 + 22.3722i −1.09904 + 0.798496i
786786 0 0
787787 7.98685 24.5810i 0.284700 0.876218i −0.701788 0.712386i 0.747615π-0.747615\pi
0.986488 0.163832i 0.0523855π-0.0523855\pi
788788 0 0
789789 −0.849908 0.617494i −0.0302575 0.0219834i
790790 0 0
791791 15.6941 0.558017
792792 0 0
793793 10.2068 0.362453
794794 0 0
795795 −0.739464 0.537252i −0.0262261 0.0190544i
796796 0 0
797797 0.0666498 0.205127i 0.00236086 0.00726597i −0.949869 0.312648i 0.898784π-0.898784\pi
0.952230 + 0.305382i 0.0987841π0.0987841\pi
798798 0 0
799799 −3.14974 + 2.28842i −0.111430 + 0.0809586i
800800 0 0
801801 −12.9287 39.7905i −0.456813 1.40593i
802802 0 0
803803 −2.40111 43.0565i −0.0847334 1.51943i
804804 0 0
805805 −9.16350 28.2024i −0.322971 0.994003i
806806 0 0
807807 −0.921459 + 0.669479i −0.0324369 + 0.0235668i
808808 0 0
809809 −7.30467 + 22.4815i −0.256819 + 0.790406i 0.736647 + 0.676277i 0.236408π0.236408\pi
−0.993466 + 0.114129i 0.963592π0.963592\pi
810810 0 0
811811 30.6038 + 22.2350i 1.07465 + 0.780776i 0.976742 0.214420i 0.0687861π-0.0687861\pi
0.0979043 + 0.995196i 0.468786π0.468786\pi
812812 0 0
813813 −0.592612 −0.0207838
814814 0 0
815815 −28.7901 −1.00847
816816 0 0
817817 24.3328 + 17.6788i 0.851298 + 0.618504i
818818 0 0
819819 −1.74579 + 5.37299i −0.0610028 + 0.187747i
820820 0 0
821821 −21.6139 + 15.7034i −0.754331 + 0.548053i −0.897166 0.441693i 0.854378π-0.854378\pi
0.142835 + 0.989746i 0.454378π0.454378\pi
822822 0 0
823823 6.04233 + 18.5964i 0.210622 + 0.648229i 0.999435 + 0.0335960i 0.0106960π0.0106960\pi
−0.788813 + 0.614633i 0.789304π0.789304\pi
824824 0 0
825825 −0.0721842 0.0190828i −0.00251313 0.000664379i
826826 0 0
827827 8.27460 + 25.4666i 0.287736 + 0.885560i 0.985565 + 0.169296i 0.0541494π0.0541494\pi
−0.697829 + 0.716264i 0.745851π0.745851\pi
828828 0 0
829829 −27.9174 + 20.2832i −0.969612 + 0.704464i −0.955363 0.295434i 0.904536π-0.904536\pi
−0.0142486 + 0.999898i 0.504536π0.504536\pi
830830 0 0
831831 0.590716 1.81804i 0.0204917 0.0630671i
832832 0 0
833833 11.8020 + 8.57463i 0.408914 + 0.297093i
834834 0 0
835835 −36.5696 −1.26554
836836 0 0
837837 −1.39234 −0.0481263
838838 0 0
839839 26.5571 + 19.2948i 0.916851 + 0.666132i 0.942738 0.333533i 0.108241π-0.108241\pi
−0.0258869 + 0.999665i 0.508241π0.508241\pi
840840 0 0
841841 1.89373 5.82831i 0.0653011 0.200976i
842842 0 0
843843 0.753433 0.547401i 0.0259496 0.0188535i
844844 0 0
845845 −8.33599 25.6555i −0.286767 0.882577i
846846 0 0
847847 −15.5938 8.86439i −0.535811 0.304584i
848848 0 0
849849 0.444659 + 1.36852i 0.0152606 + 0.0469674i
850850 0 0
851851 2.30474 1.67449i 0.0790054 0.0574008i
852852 0 0
853853 −9.36132 + 28.8112i −0.320525 + 0.986476i 0.652895 + 0.757449i 0.273554π0.273554\pi
−0.973420 + 0.229027i 0.926446π0.926446\pi
854854 0 0
855855 32.7101 + 23.7653i 1.11866 + 0.812756i
856856 0 0
857857 −22.7328 −0.776538 −0.388269 0.921546i 0.626927π-0.626927\pi
−0.388269 + 0.921546i 0.626927π0.626927\pi
858858 0 0
859859 −18.4958 −0.631068 −0.315534 0.948914i 0.602184π-0.602184\pi
−0.315534 + 0.948914i 0.602184π0.602184\pi
860860 0 0
861861 −0.374156 0.271840i −0.0127512 0.00926429i
862862 0 0
863863 −12.3132 + 37.8961i −0.419146 + 1.29000i 0.489344 + 0.872091i 0.337236π0.337236\pi
−0.908490 + 0.417908i 0.862764π0.862764\pi
864864 0 0
865865 −1.55081 + 1.12673i −0.0527292 + 0.0383100i
866866 0 0
867867 −0.113418 0.349065i −0.00385188 0.0118549i
868868 0 0
869869 6.65770 + 1.76005i 0.225847 + 0.0597056i
870870 0 0
871871 −4.52999 13.9419i −0.153493 0.472403i
872872 0 0
873873 0.0193605 0.0140662i 0.000655254 0.000476070i
874874 0 0
875875 5.41969 16.6801i 0.183219 0.563890i
876876 0 0
877877 −0.146583 0.106498i −0.00494974 0.00359620i 0.585308 0.810811i 0.300974π-0.300974\pi
−0.590257 + 0.807215i 0.700974π0.700974\pi
878878 0 0
879879 1.49744 0.0505073
880880 0 0
881881 −2.32439 −0.0783108 −0.0391554 0.999233i 0.512467π-0.512467\pi
−0.0391554 + 0.999233i 0.512467π0.512467\pi
882882 0 0
883883 −46.5566 33.8253i −1.56675 1.13831i −0.930184 0.367093i 0.880353π-0.880353\pi
−0.636569 0.771220i 0.719647π-0.719647\pi
884884 0 0
885885 0.373394 1.14919i 0.0125515 0.0386296i
886886 0 0
887887 −7.44033 + 5.40572i −0.249822 + 0.181506i −0.705648 0.708563i 0.749344π-0.749344\pi
0.455826 + 0.890069i 0.349344π0.349344\pi
888888 0 0
889889 10.4136 + 32.0497i 0.349260 + 1.07491i
890890 0 0
891891 −1.65516 29.6801i −0.0554498 0.994320i
892892 0 0
893893 2.08887 + 6.42889i 0.0699015 + 0.215135i
894894 0 0
895895 31.6233 22.9757i 1.05705 0.767992i
896896 0 0
897897 −0.180704 + 0.556149i −0.00603352 + 0.0185693i
898898 0 0
899899 17.3124 + 12.5782i 0.577400 + 0.419506i
900900 0 0
901901 20.6477 0.687874
902902 0 0
903903 0.540626 0.0179909
904904 0 0
905905 −21.0654 15.3049i −0.700236 0.508751i
906906 0 0
907907 −6.60183 + 20.3183i −0.219210 + 0.674659i 0.779618 + 0.626256i 0.215413π0.215413\pi
−0.998828 + 0.0484035i 0.984587π0.984587\pi
908908 0 0
909909 24.3722 17.7074i 0.808373 0.587318i
910910 0 0
911911 −2.43738 7.50147i −0.0807538 0.248535i 0.902526 0.430635i 0.141710π-0.141710\pi
−0.983280 + 0.182100i 0.941710π0.941710\pi
912912 0 0
913913 −18.7561 23.0039i −0.620737 0.761319i
914914 0 0
915915 −0.405739 1.24874i −0.0134133 0.0412820i
916916 0 0
917917 23.6646 17.1933i 0.781474 0.567774i
918918 0 0
919919 13.6579 42.0345i 0.450531 1.38659i −0.425772 0.904831i 0.639997π-0.639997\pi
0.876303 0.481761i 0.160003π-0.160003\pi
920920 0 0
921921 1.20012 + 0.871936i 0.0395452 + 0.0287313i
922922 0 0
923923 −17.3550 −0.571246
924924 0 0
925925 −0.126829 −0.00417011
926926 0 0
927927 11.8180 + 8.58628i 0.388154 + 0.282010i
928928 0 0
929929 11.5674 35.6009i 0.379515 1.16803i −0.560866 0.827906i 0.689532π-0.689532\pi
0.940382 0.340121i 0.110468π-0.110468\pi
930930 0 0
931931 20.4912 14.8877i 0.671571 0.487925i
932932 0 0
933933 −0.0520441 0.160175i −0.00170385 0.00524390i
934934 0 0
935935 24.0368 9.31935i 0.786088 0.304775i
936936 0 0
937937 12.0708 + 37.1502i 0.394337 + 1.21365i 0.929476 + 0.368882i 0.120259π0.120259\pi
−0.535139 + 0.844764i 0.679741π0.679741\pi
938938 0 0
939939 1.64378 1.19428i 0.0536427 0.0389737i
940940 0 0
941941 17.8264 54.8639i 0.581123 1.78851i −0.0331893 0.999449i 0.510566π-0.510566\pi
0.614312 0.789063i 0.289434π-0.289434\pi
942942 0 0
943943 28.0482 + 20.3782i 0.913374 + 0.663605i
944944 0 0
945945 1.45451 0.0473151
946946 0 0
947947 −28.2809 −0.919007 −0.459503 0.888176i 0.651973π-0.651973\pi
−0.459503 + 0.888176i 0.651973π0.651973\pi
948948 0 0
949949 12.1646 + 8.83811i 0.394880 + 0.286897i
950950 0 0
951951 −0.227079 + 0.698876i −0.00736353 + 0.0226626i
952952 0 0
953953 6.31132 4.58544i 0.204444 0.148537i −0.480852 0.876802i 0.659673π-0.659673\pi
0.685296 + 0.728264i 0.259673π0.259673\pi
954954 0 0
955955 18.5533 + 57.1013i 0.600372 + 1.84776i
956956 0 0
957957 0.685027 1.06262i 0.0221438 0.0343497i
958958 0 0
959959 2.24163 + 6.89902i 0.0723859 + 0.222781i
960960 0 0
961961 14.5332 10.5590i 0.468814 0.340614i
962962 0 0
963963 −5.23355 + 16.1072i −0.168649 + 0.519047i
964964 0 0
965965 −1.17938 0.856868i −0.0379655 0.0275836i
966966 0 0
967967 −21.5958 −0.694475 −0.347237 0.937777i 0.612880π-0.612880\pi
−0.347237 + 0.937777i 0.612880π0.612880\pi
968968 0 0
969969 1.26113 0.0405133
970970 0 0
971971 −24.6230 17.8897i −0.790190 0.574107i 0.117830 0.993034i 0.462406π-0.462406\pi
−0.908020 + 0.418927i 0.862406π0.862406\pi
972972 0 0
973973 −2.78324 + 8.56592i −0.0892264 + 0.274611i
974974 0 0
975975 0.0210619 0.0153023i 0.000674520 0.000490067i
976976 0 0
977977 −9.02534 27.7772i −0.288746 0.888670i −0.985251 0.171117i 0.945262π-0.945262\pi
0.696504 0.717553i 0.254738π-0.254738\pi
978978 0 0
979979 −25.0962 + 38.9296i −0.802078 + 1.24419i
980980 0 0
981981 −7.42063 22.8384i −0.236922 0.729172i
982982 0 0
983983 4.38749 3.18770i 0.139939 0.101672i −0.515613 0.856822i 0.672436π-0.672436\pi
0.655552 + 0.755150i 0.272436π0.272436\pi
984984 0 0
985985 16.2870 50.1262i 0.518946 1.59715i
986986 0 0
987987 0.0982990 + 0.0714184i 0.00312889 + 0.00227327i
988988 0 0
989989 −40.5274 −1.28870
990990 0 0
991991 27.9224 0.886985 0.443492 0.896278i 0.353739π-0.353739\pi
0.443492 + 0.896278i 0.353739π0.353739\pi
992992 0 0
993993 −1.01793 0.739572i −0.0323032 0.0234696i
994994 0 0
995995 12.6114 38.8140i 0.399810 1.23049i
996996 0 0
997997 −10.3584 + 7.52580i −0.328053 + 0.238344i −0.739604 0.673042i 0.764987π-0.764987\pi
0.411551 + 0.911387i 0.364987π0.364987\pi
998998 0 0
999999 0.0431800 + 0.132894i 0.00136615 + 0.00420459i
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 352.2.m.e.225.2 yes 12
4.3 odd 2 352.2.m.f.225.2 yes 12
8.3 odd 2 704.2.m.n.577.2 12
8.5 even 2 704.2.m.m.577.2 12
11.3 even 5 3872.2.a.bq.1.3 6
11.8 odd 10 3872.2.a.bp.1.3 6
11.9 even 5 inner 352.2.m.e.97.2 12
44.3 odd 10 3872.2.a.bn.1.4 6
44.19 even 10 3872.2.a.bo.1.4 6
44.31 odd 10 352.2.m.f.97.2 yes 12
88.3 odd 10 7744.2.a.dv.1.3 6
88.19 even 10 7744.2.a.dw.1.3 6
88.53 even 10 704.2.m.m.449.2 12
88.69 even 10 7744.2.a.du.1.4 6
88.75 odd 10 704.2.m.n.449.2 12
88.85 odd 10 7744.2.a.dt.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.2.m.e.97.2 12 11.9 even 5 inner
352.2.m.e.225.2 yes 12 1.1 even 1 trivial
352.2.m.f.97.2 yes 12 44.31 odd 10
352.2.m.f.225.2 yes 12 4.3 odd 2
704.2.m.m.449.2 12 88.53 even 10
704.2.m.m.577.2 12 8.5 even 2
704.2.m.n.449.2 12 88.75 odd 10
704.2.m.n.577.2 12 8.3 odd 2
3872.2.a.bn.1.4 6 44.3 odd 10
3872.2.a.bo.1.4 6 44.19 even 10
3872.2.a.bp.1.3 6 11.8 odd 10
3872.2.a.bq.1.3 6 11.3 even 5
7744.2.a.dt.1.4 6 88.85 odd 10
7744.2.a.du.1.4 6 88.69 even 10
7744.2.a.dv.1.3 6 88.3 odd 10
7744.2.a.dw.1.3 6 88.19 even 10