Properties

Label 1728.2.z.a.1583.22
Level 17281728
Weight 22
Character 1728.1583
Analytic conductor 13.79813.798
Analytic rank 00
Dimension 8888
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1728,2,Mod(143,1728)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1728, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1728.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1728=2633 1728 = 2^{6} \cdot 3^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1728.z (of order 1212, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 13.798149469313.7981494693
Analytic rank: 00
Dimension: 8888
Relative dimension: 2222 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 1583.22
Character χ\chi == 1728.1583
Dual form 1728.2.z.a.143.22

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(3.813961.02195i)q5+(1.467152.54117i)q7+(2.650060.710081i)q11+(2.34729+0.628955i)q132.89808iq17+(1.999061.99906i)q19+(2.071411.19593i)q23+(9.171805.29534i)q25+(8.462182.26743i)q29+(0.439075+0.253500i)q31+(8.192588.19258i)q35+(1.364071.36407i)q37+(0.745739+1.29166i)q41+(1.271364.74478i)q43+(3.258025.64306i)q47+(0.805035+1.39436i)q49+(5.17979+5.17979i)q5310.8329q55+(0.664781+2.48100i)q59+(2.9965711.1833i)q61+(8.30972+4.79762i)q65+(2.53505+9.46095i)q67+4.65399iq71+4.91897iq73+(2.08358+7.77604i)q77+(3.612632.08575i)q79+(3.37411+12.5924i)q83+(2.9616911.0532i)q857.33327q89+(5.04210+5.04210i)q91+(5.581399.66725i)q95+(2.50134+4.33245i)q97+O(q100)q+(3.81396 - 1.02195i) q^{5} +(-1.46715 - 2.54117i) q^{7} +(-2.65006 - 0.710081i) q^{11} +(-2.34729 + 0.628955i) q^{13} -2.89808i q^{17} +(1.99906 - 1.99906i) q^{19} +(-2.07141 - 1.19593i) q^{23} +(9.17180 - 5.29534i) q^{25} +(-8.46218 - 2.26743i) q^{29} +(0.439075 + 0.253500i) q^{31} +(-8.19258 - 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(-0.745739 + 1.29166i) q^{41} +(1.27136 - 4.74478i) q^{43} +(-3.25802 - 5.64306i) q^{47} +(-0.805035 + 1.39436i) q^{49} +(5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(0.664781 + 2.48100i) q^{59} +(2.99657 - 11.1833i) q^{61} +(-8.30972 + 4.79762i) q^{65} +(2.53505 + 9.46095i) q^{67} +4.65399i q^{71} +4.91897i q^{73} +(2.08358 + 7.77604i) q^{77} +(3.61263 - 2.08575i) q^{79} +(-3.37411 + 12.5924i) q^{83} +(-2.96169 - 11.0532i) q^{85} -7.33327 q^{89} +(5.04210 + 5.04210i) q^{91} +(5.58139 - 9.66725i) q^{95} +(2.50134 + 4.33245i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 88q+6q5+4q76q112q13+8q1912q23+6q298q37+2q4324q49+16q5542q592q61+12q65+2q67+6q77+54q83+8q85+4q97+O(q100) 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1728Z)×\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times.

nn 325325 703703 12171217
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 e(56)e\left(\frac{5}{6}\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 0
44 0 0
55 3.81396 1.02195i 1.70566 0.457029i 0.731302 0.682053i 0.238913π-0.238913\pi
0.974353 + 0.225024i 0.0722462π0.0722462\pi
66 0 0
77 −1.46715 2.54117i −0.554529 0.960473i −0.997940 0.0641541i 0.979565π-0.979565\pi
0.443411 0.896318i 0.353768π-0.353768\pi
88 0 0
99 0 0
1010 0 0
1111 −2.65006 0.710081i −0.799022 0.214097i −0.163868 0.986482i 0.552397π-0.552397\pi
−0.635155 + 0.772385i 0.719064π0.719064\pi
1212 0 0
1313 −2.34729 + 0.628955i −0.651021 + 0.174441i −0.569191 0.822206i 0.692743π-0.692743\pi
−0.0818307 + 0.996646i 0.526077π0.526077\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.89808i 0.702889i −0.936209 0.351444i 0.885691π-0.885691\pi
0.936209 0.351444i 0.114309π-0.114309\pi
1818 0 0
1919 1.99906 1.99906i 0.458615 0.458615i −0.439586 0.898201i 0.644875π-0.644875\pi
0.898201 + 0.439586i 0.144875π0.144875\pi
2020 0 0
2121 0 0
2222 0 0
2323 −2.07141 1.19593i −0.431918 0.249368i 0.268245 0.963351i 0.413556π-0.413556\pi
−0.700163 + 0.713983i 0.746890π0.746890\pi
2424 0 0
2525 9.17180 5.29534i 1.83436 1.05907i
2626 0 0
2727 0 0
2828 0 0
2929 −8.46218 2.26743i −1.57139 0.421052i −0.635141 0.772396i 0.719058π-0.719058\pi
−0.936246 + 0.351344i 0.885725π0.885725\pi
3030 0 0
3131 0.439075 + 0.253500i 0.0788602 + 0.0455300i 0.538912 0.842362i 0.318836π-0.318836\pi
−0.460051 + 0.887892i 0.652169π0.652169\pi
3232 0 0
3333 0 0
3434 0 0
3535 −8.19258 8.19258i −1.38480 1.38480i
3636 0 0
3737 1.36407 1.36407i 0.224251 0.224251i −0.586035 0.810286i 0.699312π-0.699312\pi
0.810286 + 0.586035i 0.199312π0.199312\pi
3838 0 0
3939 0 0
4040 0 0
4141 −0.745739 + 1.29166i −0.116465 + 0.201723i −0.918364 0.395736i 0.870490π-0.870490\pi
0.801899 + 0.597459i 0.203823π0.203823\pi
4242 0 0
4343 1.27136 4.74478i 0.193881 0.723572i −0.798673 0.601765i 0.794464π-0.794464\pi
0.992554 0.121807i 0.0388690π-0.0388690\pi
4444 0 0
4545 0 0
4646 0 0
4747 −3.25802 5.64306i −0.475231 0.823124i 0.524367 0.851493i 0.324302π-0.324302\pi
−0.999598 + 0.0283684i 0.990969π0.990969\pi
4848 0 0
4949 −0.805035 + 1.39436i −0.115005 + 0.199195i
5050 0 0
5151 0 0
5252 0 0
5353 5.17979 + 5.17979i 0.711499 + 0.711499i 0.966849 0.255349i 0.0821905π-0.0821905\pi
−0.255349 + 0.966849i 0.582191π0.582191\pi
5454 0 0
5555 −10.8329 −1.46071
5656 0 0
5757 0 0
5858 0 0
5959 0.664781 + 2.48100i 0.0865472 + 0.322998i 0.995603 0.0936766i 0.0298620π-0.0298620\pi
−0.909056 + 0.416675i 0.863195π0.863195\pi
6060 0 0
6161 2.99657 11.1833i 0.383671 1.43188i −0.456580 0.889682i 0.650926π-0.650926\pi
0.840251 0.542198i 0.182408π-0.182408\pi
6262 0 0
6363 0 0
6464 0 0
6565 −8.30972 + 4.79762i −1.03069 + 0.595071i
6666 0 0
6767 2.53505 + 9.46095i 0.309706 + 1.15584i 0.928818 + 0.370536i 0.120826π0.120826\pi
−0.619112 + 0.785303i 0.712507π0.712507\pi
6868 0 0
6969 0 0
7070 0 0
7171 4.65399i 0.552327i 0.961111 + 0.276164i 0.0890632π0.0890632\pi
−0.961111 + 0.276164i 0.910937π0.910937\pi
7272 0 0
7373 4.91897i 0.575722i 0.957672 + 0.287861i 0.0929441π0.0929441\pi
−0.957672 + 0.287861i 0.907056π0.907056\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.08358 + 7.77604i 0.237446 + 0.886162i
7878 0 0
7979 3.61263 2.08575i 0.406453 0.234666i −0.282812 0.959175i 0.591267π-0.591267\pi
0.689264 + 0.724510i 0.257934π0.257934\pi
8080 0 0
8181 0 0
8282 0 0
8383 −3.37411 + 12.5924i −0.370357 + 1.38219i 0.489654 + 0.871917i 0.337123π0.337123\pi
−0.860011 + 0.510275i 0.829544π0.829544\pi
8484 0 0
8585 −2.96169 11.0532i −0.321241 1.19889i
8686 0 0
8787 0 0
8888 0 0
8989 −7.33327 −0.777325 −0.388662 0.921380i 0.627063π-0.627063\pi
−0.388662 + 0.921380i 0.627063π0.627063\pi
9090 0 0
9191 5.04210 + 5.04210i 0.528556 + 0.528556i
9292 0 0
9393 0 0
9494 0 0
9595 5.58139 9.66725i 0.572639 0.991839i
9696 0 0
9797 2.50134 + 4.33245i 0.253973 + 0.439893i 0.964616 0.263659i 0.0849294π-0.0849294\pi
−0.710643 + 0.703552i 0.751596π0.751596\pi
9898 0 0
9999 0 0
100100 0 0
101101 2.82933 10.5592i 0.281529 1.05068i −0.669810 0.742533i 0.733624π-0.733624\pi
0.951339 0.308147i 0.0997090π-0.0997090\pi
102102 0 0
103103 0.321949 0.557632i 0.0317226 0.0549451i −0.849728 0.527221i 0.823234π-0.823234\pi
0.881451 + 0.472276i 0.156567π0.156567\pi
104104 0 0
105105 0 0
106106 0 0
107107 3.74155 3.74155i 0.361709 0.361709i −0.502733 0.864442i 0.667672π-0.667672\pi
0.864442 + 0.502733i 0.167672π0.167672\pi
108108 0 0
109109 6.00859 + 6.00859i 0.575518 + 0.575518i 0.933665 0.358147i 0.116591π-0.116591\pi
−0.358147 + 0.933665i 0.616591π0.616591\pi
110110 0 0
111111 0 0
112112 0 0
113113 −14.4387 8.33620i −1.35828 0.784204i −0.368889 0.929474i 0.620262π-0.620262\pi
−0.989392 + 0.145270i 0.953595π0.953595\pi
114114 0 0
115115 −9.12244 2.44435i −0.850672 0.227937i
116116 0 0
117117 0 0
118118 0 0
119119 −7.36453 + 4.25191i −0.675105 + 0.389772i
120120 0 0
121121 −3.00769 1.73649i −0.273426 0.157863i
122122 0 0
123123 0 0
124124 0 0
125125 15.6093 15.6093i 1.39613 1.39613i
126126 0 0
127127 17.9975i 1.59702i −0.601983 0.798509i 0.705623π-0.705623\pi
0.601983 0.798509i 0.294377π-0.294377\pi
128128 0 0
129129 0 0
130130 0 0
131131 17.4121 4.66555i 1.52130 0.407631i 0.601131 0.799151i 0.294717π-0.294717\pi
0.920170 + 0.391520i 0.128051π0.128051\pi
132132 0 0
133133 −8.01285 2.14704i −0.694802 0.186172i
134134 0 0
135135 0 0
136136 0 0
137137 0.396155 + 0.686161i 0.0338458 + 0.0586227i 0.882452 0.470402i 0.155891π-0.155891\pi
−0.848606 + 0.529025i 0.822558π0.822558\pi
138138 0 0
139139 20.5134 5.49654i 1.73992 0.466211i 0.757492 0.652844i 0.226424π-0.226424\pi
0.982430 + 0.186633i 0.0597576π0.0597576\pi
140140 0 0
141141 0 0
142142 0 0
143143 6.66706 0.557528
144144 0 0
145145 −34.5916 −2.87268
146146 0 0
147147 0 0
148148 0 0
149149 11.3030 3.02863i 0.925977 0.248115i 0.235839 0.971792i 0.424216π-0.424216\pi
0.690139 + 0.723677i 0.257550π0.257550\pi
150150 0 0
151151 4.24025 + 7.34432i 0.345066 + 0.597673i 0.985366 0.170453i 0.0545230π-0.0545230\pi
−0.640299 + 0.768125i 0.721190π0.721190\pi
152152 0 0
153153 0 0
154154 0 0
155155 1.93368 + 0.518128i 0.155317 + 0.0416170i
156156 0 0
157157 3.53516 0.947242i 0.282136 0.0755981i −0.114976 0.993368i 0.536679π-0.536679\pi
0.397112 + 0.917770i 0.370012π0.370012\pi
158158 0 0
159159 0 0
160160 0 0
161161 7.01840i 0.553127i
162162 0 0
163163 3.86060 3.86060i 0.302385 0.302385i −0.539561 0.841946i 0.681410π-0.681410\pi
0.841946 + 0.539561i 0.181410π0.181410\pi
164164 0 0
165165 0 0
166166 0 0
167167 −5.98224 3.45385i −0.462920 0.267267i 0.250351 0.968155i 0.419454π-0.419454\pi
−0.713271 + 0.700888i 0.752787π0.752787\pi
168168 0 0
169169 −6.14414 + 3.54732i −0.472626 + 0.272871i
170170 0 0
171171 0 0
172172 0 0
173173 −3.86859 1.03659i −0.294123 0.0788101i 0.108740 0.994070i 0.465318π-0.465318\pi
−0.402863 + 0.915260i 0.631985π0.631985\pi
174174 0 0
175175 −26.9127 15.5381i −2.03441 1.17457i
176176 0 0
177177 0 0
178178 0 0
179179 10.0625 + 10.0625i 0.752109 + 0.752109i 0.974872 0.222764i 0.0715078π-0.0715078\pi
−0.222764 + 0.974872i 0.571508π0.571508\pi
180180 0 0
181181 15.0346 15.0346i 1.11751 1.11751i 0.125405 0.992106i 0.459977π-0.459977\pi
0.992106 0.125405i 0.0400229π-0.0400229\pi
182182 0 0
183183 0 0
184184 0 0
185185 3.80849 6.59651i 0.280006 0.484985i
186186 0 0
187187 −2.05787 + 7.68009i −0.150487 + 0.561624i
188188 0 0
189189 0 0
190190 0 0
191191 −10.9007 18.8806i −0.788749 1.36615i −0.926734 0.375719i 0.877396π-0.877396\pi
0.137984 0.990434i 0.455938π-0.455938\pi
192192 0 0
193193 −2.34723 + 4.06553i −0.168958 + 0.292643i −0.938054 0.346490i 0.887373π-0.887373\pi
0.769096 + 0.639133i 0.220707π0.220707\pi
194194 0 0
195195 0 0
196196 0 0
197197 −14.3226 14.3226i −1.02044 1.02044i −0.999787 0.0206566i 0.993424π-0.993424\pi
−0.0206566 0.999787i 0.506576π-0.506576\pi
198198 0 0
199199 14.4965 1.02763 0.513816 0.857901i 0.328232π-0.328232\pi
0.513816 + 0.857901i 0.328232π0.328232\pi
200200 0 0
201201 0 0
202202 0 0
203203 6.65332 + 24.8305i 0.466971 + 1.74276i
204204 0 0
205205 −1.52421 + 5.68844i −0.106456 + 0.397298i
206206 0 0
207207 0 0
208208 0 0
209209 −6.71710 + 3.87812i −0.464632 + 0.268255i
210210 0 0
211211 1.71268 + 6.39179i 0.117905 + 0.440029i 0.999488 0.0320010i 0.0101880π-0.0101880\pi
−0.881582 + 0.472030i 0.843521π0.843521\pi
212212 0 0
213213 0 0
214214 0 0
215215 19.3957i 1.32277i
216216 0 0
217217 1.48769i 0.100991i
218218 0 0
219219 0 0
220220 0 0
221221 1.82276 + 6.80265i 0.122612 + 0.457596i
222222 0 0
223223 −1.59599 + 0.921443i −0.106875 + 0.0617044i −0.552485 0.833523i 0.686320π-0.686320\pi
0.445610 + 0.895227i 0.352987π0.352987\pi
224224 0 0
225225 0 0
226226 0 0
227227 −0.184084 + 0.687012i −0.0122181 + 0.0455986i −0.971766 0.235948i 0.924181π-0.924181\pi
0.959548 + 0.281546i 0.0908473π0.0908473\pi
228228 0 0
229229 1.98433 + 7.40562i 0.131128 + 0.489377i 0.999984 0.00568843i 0.00181069π-0.00181069\pi
−0.868856 + 0.495066i 0.835144π0.835144\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1.36925 −0.0897024 −0.0448512 0.998994i 0.514281π-0.514281\pi
−0.0448512 + 0.998994i 0.514281π0.514281\pi
234234 0 0
235235 −18.1929 18.1929i −1.18677 1.18677i
236236 0 0
237237 0 0
238238 0 0
239239 −0.773627 + 1.33996i −0.0500418 + 0.0866749i −0.889961 0.456036i 0.849269π-0.849269\pi
0.839919 + 0.542711i 0.182602π0.182602\pi
240240 0 0
241241 3.83660 + 6.64519i 0.247137 + 0.428054i 0.962730 0.270463i 0.0871769π-0.0871769\pi
−0.715593 + 0.698517i 0.753844π0.753844\pi
242242 0 0
243243 0 0
244244 0 0
245245 −1.64541 + 6.14075i −0.105121 + 0.392318i
246246 0 0
247247 −3.43505 + 5.94968i −0.218567 + 0.378569i
248248 0 0
249249 0 0
250250 0 0
251251 −5.46632 + 5.46632i −0.345031 + 0.345031i −0.858255 0.513224i 0.828451π-0.828451\pi
0.513224 + 0.858255i 0.328451π0.328451\pi
252252 0 0
253253 4.64014 + 4.64014i 0.291723 + 0.291723i
254254 0 0
255255 0 0
256256 0 0
257257 20.5918 + 11.8887i 1.28448 + 0.741596i 0.977664 0.210172i 0.0674025π-0.0674025\pi
0.306818 + 0.951768i 0.400736π0.400736\pi
258258 0 0
259259 −5.46761 1.46504i −0.339741 0.0910333i
260260 0 0
261261 0 0
262262 0 0
263263 −6.13704 + 3.54322i −0.378426 + 0.218484i −0.677133 0.735860i 0.736778π-0.736778\pi
0.298707 + 0.954345i 0.403445π0.403445\pi
264264 0 0
265265 25.0490 + 14.4621i 1.53875 + 0.888397i
266266 0 0
267267 0 0
268268 0 0
269269 −20.6616 + 20.6616i −1.25976 + 1.25976i −0.308553 + 0.951207i 0.599845π0.599845\pi
−0.951207 + 0.308553i 0.900155π0.900155\pi
270270 0 0
271271 16.6901i 1.01385i 0.861989 + 0.506927i 0.169218π0.169218\pi
−0.861989 + 0.506927i 0.830782π0.830782\pi
272272 0 0
273273 0 0
274274 0 0
275275 −28.0659 + 7.52024i −1.69244 + 0.453487i
276276 0 0
277277 4.49217 + 1.20367i 0.269908 + 0.0723217i 0.391235 0.920291i 0.372048π-0.372048\pi
−0.121326 + 0.992613i 0.538715π0.538715\pi
278278 0 0
279279 0 0
280280 0 0
281281 11.4153 + 19.7719i 0.680979 + 1.17949i 0.974682 + 0.223594i 0.0717790π0.0717790\pi
−0.293703 + 0.955897i 0.594888π0.594888\pi
282282 0 0
283283 24.9438 6.68368i 1.48276 0.397303i 0.575472 0.817822i 0.304818π-0.304818\pi
0.907284 + 0.420518i 0.138152π0.138152\pi
284284 0 0
285285 0 0
286286 0 0
287287 4.37643 0.258333
288288 0 0
289289 8.60110 0.505947
290290 0 0
291291 0 0
292292 0 0
293293 2.76706 0.741431i 0.161653 0.0433149i −0.177085 0.984196i 0.556667π-0.556667\pi
0.338738 + 0.940881i 0.390000π0.390000\pi
294294 0 0
295295 5.07090 + 8.78306i 0.295239 + 0.511370i
296296 0 0
297297 0 0
298298 0 0
299299 5.61438 + 1.50437i 0.324688 + 0.0869998i
300300 0 0
301301 −13.9226 + 3.73054i −0.802484 + 0.215025i
302302 0 0
303303 0 0
304304 0 0
305305 45.7152i 2.61764i
306306 0 0
307307 7.67329 7.67329i 0.437938 0.437938i −0.453380 0.891317i 0.649782π-0.649782\pi
0.891317 + 0.453380i 0.149782π0.149782\pi
308308 0 0
309309 0 0
310310 0 0
311311 15.0777 + 8.70513i 0.854980 + 0.493623i 0.862328 0.506350i 0.169006π-0.169006\pi
−0.00734815 + 0.999973i 0.502339π0.502339\pi
312312 0 0
313313 −21.3027 + 12.2991i −1.20410 + 0.695189i −0.961465 0.274928i 0.911346π-0.911346\pi
−0.242638 + 0.970117i 0.578013π0.578013\pi
314314 0 0
315315 0 0
316316 0 0
317317 7.99342 + 2.14183i 0.448955 + 0.120297i 0.476211 0.879331i 0.342010π-0.342010\pi
−0.0272552 + 0.999629i 0.508677π0.508677\pi
318318 0 0
319319 20.8152 + 12.0177i 1.16543 + 0.672860i
320320 0 0
321321 0 0
322322 0 0
323323 −5.79343 5.79343i −0.322355 0.322355i
324324 0 0
325325 −18.1983 + 18.1983i −1.00946 + 1.00946i
326326 0 0
327327 0 0
328328 0 0
329329 −9.55998 + 16.5584i −0.527059 + 0.912893i
330330 0 0
331331 −6.84245 + 25.5364i −0.376095 + 1.40361i 0.475643 + 0.879639i 0.342216π0.342216\pi
−0.851738 + 0.523968i 0.824451π0.824451\pi
332332 0 0
333333 0 0
334334 0 0
335335 19.3372 + 33.4930i 1.05650 + 1.82992i
336336 0 0
337337 12.3368 21.3679i 0.672026 1.16398i −0.305302 0.952256i 0.598757π-0.598757\pi
0.977329 0.211728i 0.0679092π-0.0679092\pi
338338 0 0
339339 0 0
340340 0 0
341341 −0.983569 0.983569i −0.0532632 0.0532632i
342342 0 0
343343 −15.8156 −0.853964
344344 0 0
345345 0 0
346346 0 0
347347 6.16895 + 23.0228i 0.331166 + 1.23593i 0.907966 + 0.419044i 0.137635π0.137635\pi
−0.576799 + 0.816886i 0.695699π0.695699\pi
348348 0 0
349349 6.94337 25.9130i 0.371670 1.38709i −0.486479 0.873692i 0.661719π-0.661719\pi
0.858149 0.513400i 0.171614π-0.171614\pi
350350 0 0
351351 0 0
352352 0 0
353353 −5.54075 + 3.19895i −0.294904 + 0.170263i −0.640151 0.768249i 0.721128π-0.721128\pi
0.345247 + 0.938512i 0.387795π0.387795\pi
354354 0 0
355355 4.75614 + 17.7502i 0.252430 + 0.942080i
356356 0 0
357357 0 0
358358 0 0
359359 17.2363i 0.909697i −0.890569 0.454849i 0.849693π-0.849693\pi
0.890569 0.454849i 0.150307π-0.150307\pi
360360 0 0
361361 11.0076i 0.579345i
362362 0 0
363363 0 0
364364 0 0
365365 5.02693 + 18.7608i 0.263121 + 0.981983i
366366 0 0
367367 1.26366 0.729575i 0.0659625 0.0380835i −0.466656 0.884439i 0.654541π-0.654541\pi
0.532619 + 0.846355i 0.321208π0.321208\pi
368368 0 0
369369 0 0
370370 0 0
371371 5.56323 20.7623i 0.288829 1.07792i
372372 0 0
373373 −2.08247 7.77189i −0.107826 0.402413i 0.890824 0.454348i 0.150128π-0.150128\pi
−0.998650 + 0.0519349i 0.983461π0.983461\pi
374374 0 0
375375 0 0
376376 0 0
377377 21.2893 1.09646
378378 0 0
379379 16.4748 + 16.4748i 0.846255 + 0.846255i 0.989664 0.143409i 0.0458063π-0.0458063\pi
−0.143409 + 0.989664i 0.545806π0.545806\pi
380380 0 0
381381 0 0
382382 0 0
383383 −5.19654 + 9.00067i −0.265531 + 0.459913i −0.967703 0.252095i 0.918881π-0.918881\pi
0.702172 + 0.712008i 0.252214π0.252214\pi
384384 0 0
385385 15.8934 + 27.5282i 0.810004 + 1.40297i
386386 0 0
387387 0 0
388388 0 0
389389 −6.24292 + 23.2989i −0.316529 + 1.18130i 0.606029 + 0.795442i 0.292761π0.292761\pi
−0.922558 + 0.385859i 0.873905π0.873905\pi
390390 0 0
391391 −3.46590 + 6.00311i −0.175278 + 0.303590i
392392 0 0
393393 0 0
394394 0 0
395395 11.6469 11.6469i 0.586019 0.586019i
396396 0 0
397397 8.37131 + 8.37131i 0.420144 + 0.420144i 0.885253 0.465109i 0.153985π-0.153985\pi
−0.465109 + 0.885253i 0.653985π0.653985\pi
398398 0 0
399399 0 0
400400 0 0
401401 3.16266 + 1.82596i 0.157936 + 0.0911842i 0.576885 0.816825i 0.304268π-0.304268\pi
−0.418949 + 0.908010i 0.637601π0.637601\pi
402402 0 0
403403 −1.19008 0.318880i −0.0592820 0.0158846i
404404 0 0
405405 0 0
406406 0 0
407407 −4.58345 + 2.64626i −0.227193 + 0.131170i
408408 0 0
409409 −12.1263 7.00113i −0.599607 0.346184i 0.169280 0.985568i 0.445856π-0.445856\pi
−0.768887 + 0.639385i 0.779189π0.779189\pi
410410 0 0
411411 0 0
412412 0 0
413413 5.32931 5.32931i 0.262238 0.262238i
414414 0 0
415415 51.4750i 2.52681i
416416 0 0
417417 0 0
418418 0 0
419419 0.601258 0.161107i 0.0293734 0.00787057i −0.244102 0.969749i 0.578493π-0.578493\pi
0.273476 + 0.961879i 0.411827π0.411827\pi
420420 0 0
421421 17.3705 + 4.65440i 0.846585 + 0.226842i 0.655936 0.754816i 0.272274π-0.272274\pi
0.190649 + 0.981658i 0.438941π0.438941\pi
422422 0 0
423423 0 0
424424 0 0
425425 −15.3463 26.5806i −0.744407 1.28935i
426426 0 0
427427 −32.8152 + 8.79280i −1.58804 + 0.425514i
428428 0 0
429429 0 0
430430 0 0
431431 6.34380 0.305570 0.152785 0.988259i 0.451176π-0.451176\pi
0.152785 + 0.988259i 0.451176π0.451176\pi
432432 0 0
433433 26.7319 1.28465 0.642327 0.766430i 0.277969π-0.277969\pi
0.642327 + 0.766430i 0.277969π0.277969\pi
434434 0 0
435435 0 0
436436 0 0
437437 −6.53158 + 1.75013i −0.312448 + 0.0837202i
438438 0 0
439439 −0.347800 0.602407i −0.0165996 0.0287513i 0.857606 0.514307i 0.171951π-0.171951\pi
−0.874206 + 0.485555i 0.838617π0.838617\pi
440440 0 0
441441 0 0
442442 0 0
443443 −15.8656 4.25119i −0.753800 0.201980i −0.138597 0.990349i 0.544259π-0.544259\pi
−0.615203 + 0.788369i 0.710926π0.710926\pi
444444 0 0
445445 −27.9688 + 7.49422i −1.32585 + 0.355260i
446446 0 0
447447 0 0
448448 0 0
449449 12.0759i 0.569896i 0.958543 + 0.284948i 0.0919763π0.0919763\pi
−0.958543 + 0.284948i 0.908024π0.908024\pi
450450 0 0
451451 2.89343 2.89343i 0.136247 0.136247i
452452 0 0
453453 0 0
454454 0 0
455455 24.3831 + 14.0776i 1.14310 + 0.659969i
456456 0 0
457457 −10.6069 + 6.12391i −0.496171 + 0.286464i −0.727131 0.686499i 0.759147π-0.759147\pi
0.230960 + 0.972963i 0.425813π0.425813\pi
458458 0 0
459459 0 0
460460 0 0
461461 30.3154 + 8.12298i 1.41193 + 0.378325i 0.882613 0.470101i 0.155783π-0.155783\pi
0.529314 + 0.848426i 0.322449π0.322449\pi
462462 0 0
463463 −30.9163 17.8495i −1.43680 0.829538i −0.439176 0.898401i 0.644729π-0.644729\pi
−0.997626 + 0.0688633i 0.978063π0.978063\pi
464464 0 0
465465 0 0
466466 0 0
467467 −7.64586 7.64586i −0.353808 0.353808i 0.507716 0.861524i 0.330490π-0.330490\pi
−0.861524 + 0.507716i 0.830490π0.830490\pi
468468 0 0
469469 20.3226 20.3226i 0.938411 0.938411i
470470 0 0
471471 0 0
472472 0 0
473473 −6.73836 + 11.6712i −0.309830 + 0.536641i
474474 0 0
475475 7.74926 28.9206i 0.355560 1.32697i
476476 0 0
477477 0 0
478478 0 0
479479 −3.03628 5.25898i −0.138731 0.240289i 0.788286 0.615310i 0.210969π-0.210969\pi
−0.927017 + 0.375020i 0.877636π0.877636\pi
480480 0 0
481481 −2.34393 + 4.05980i −0.106874 + 0.185111i
482482 0 0
483483 0 0
484484 0 0
485485 13.9675 + 13.9675i 0.634234 + 0.634234i
486486 0 0
487487 7.15811 0.324365 0.162183 0.986761i 0.448147π-0.448147\pi
0.162183 + 0.986761i 0.448147π0.448147\pi
488488 0 0
489489 0 0
490490 0 0
491491 −7.24226 27.0285i −0.326838 1.21978i −0.912451 0.409187i 0.865813π-0.865813\pi
0.585612 0.810591i 0.300854π-0.300854\pi
492492 0 0
493493 −6.57122 + 24.5241i −0.295953 + 1.10451i
494494 0 0
495495 0 0
496496 0 0
497497 11.8266 6.82809i 0.530495 0.306282i
498498 0 0
499499 −11.4708 42.8097i −0.513505 1.91643i −0.378568 0.925573i 0.623584π-0.623584\pi
−0.134937 0.990854i 0.543083π-0.543083\pi
500500 0 0
501501 0 0
502502 0 0
503503 3.93000i 0.175230i 0.996154 + 0.0876151i 0.0279245π0.0279245\pi
−0.996154 + 0.0876151i 0.972075π0.972075\pi
504504 0 0
505505 43.1638i 1.92077i
506506 0 0
507507 0 0
508508 0 0
509509 −10.8415 40.4609i −0.480539 1.79340i −0.599358 0.800481i 0.704577π-0.704577\pi
0.118819 0.992916i 0.462089π-0.462089\pi
510510 0 0
511511 12.4999 7.21684i 0.552965 0.319254i
512512 0 0
513513 0 0
514514 0 0
515515 0.658030 2.45580i 0.0289963 0.108216i
516516 0 0
517517 4.62691 + 17.2679i 0.203491 + 0.759441i
518518 0 0
519519 0 0
520520 0 0
521521 26.1826 1.14708 0.573540 0.819178i 0.305570π-0.305570\pi
0.573540 + 0.819178i 0.305570π0.305570\pi
522522 0 0
523523 −7.29036 7.29036i −0.318785 0.318785i 0.529515 0.848300i 0.322374π-0.322374\pi
−0.848300 + 0.529515i 0.822374π0.822374\pi
524524 0 0
525525 0 0
526526 0 0
527527 0.734665 1.27248i 0.0320025 0.0554300i
528528 0 0
529529 −8.63952 14.9641i −0.375631 0.650612i
530530 0 0
531531 0 0
532532 0 0
533533 0.938073 3.50093i 0.0406324 0.151642i
534534 0 0
535535 10.4465 18.0938i 0.451640 0.782263i
536536 0 0
537537 0 0
538538 0 0
539539 3.12350 3.12350i 0.134539 0.134539i
540540 0 0
541541 13.6906 + 13.6906i 0.588607 + 0.588607i 0.937254 0.348647i 0.113359π-0.113359\pi
−0.348647 + 0.937254i 0.613359π0.613359\pi
542542 0 0
543543 0 0
544544 0 0
545545 29.0570 + 16.7761i 1.24466 + 0.718607i
546546 0 0
547547 −29.0133 7.77408i −1.24052 0.332396i −0.421851 0.906665i 0.638620π-0.638620\pi
−0.818666 + 0.574269i 0.805286π0.805286\pi
548548 0 0
549549 0 0
550550 0 0
551551 −21.4491 + 12.3836i −0.913762 + 0.527561i
552552 0 0
553553 −10.6005 6.12021i −0.450780 0.260258i
554554 0 0
555555 0 0
556556 0 0
557557 1.85284 1.85284i 0.0785074 0.0785074i −0.666763 0.745270i 0.732321π-0.732321\pi
0.745270 + 0.666763i 0.232321π0.232321\pi
558558 0 0
559559 11.9370i 0.504882i
560560 0 0
561561 0 0
562562 0 0
563563 26.1400 7.00420i 1.10167 0.295192i 0.338226 0.941065i 0.390173π-0.390173\pi
0.763445 + 0.645873i 0.223506π0.223506\pi
564564 0 0
565565 −63.5879 17.0383i −2.67516 0.716808i
566566 0 0
567567 0 0
568568 0 0
569569 −5.84691 10.1271i −0.245115 0.424552i 0.717049 0.697023i 0.245492π-0.245492\pi
−0.962164 + 0.272471i 0.912159π0.912159\pi
570570 0 0
571571 −44.1127 + 11.8200i −1.84606 + 0.494650i −0.999303 0.0373319i 0.988114π-0.988114\pi
−0.846756 + 0.531982i 0.821447π0.821447\pi
572572 0 0
573573 0 0
574574 0 0
575575 −25.3314 −1.05639
576576 0 0
577577 −32.6884 −1.36083 −0.680417 0.732825i 0.738202π-0.738202\pi
−0.680417 + 0.732825i 0.738202π0.738202\pi
578578 0 0
579579 0 0
580580 0 0
581581 36.9497 9.90064i 1.53293 0.410748i
582582 0 0
583583 −10.0487 17.4048i −0.416174 0.720834i
584584 0 0
585585 0 0
586586 0 0
587587 28.3101 + 7.58567i 1.16848 + 0.313094i 0.790349 0.612657i 0.209899π-0.209899\pi
0.378134 + 0.925751i 0.376566π0.376566\pi
588588 0 0
589589 1.38450 0.370975i 0.0570472 0.0152858i
590590 0 0
591591 0 0
592592 0 0
593593 43.9681i 1.80555i 0.430111 + 0.902776i 0.358474π0.358474\pi
−0.430111 + 0.902776i 0.641526π0.641526\pi
594594 0 0
595595 −23.7428 + 23.7428i −0.973360 + 0.973360i
596596 0 0
597597 0 0
598598 0 0
599599 2.81411 + 1.62473i 0.114982 + 0.0663846i 0.556388 0.830923i 0.312187π-0.312187\pi
−0.441406 + 0.897307i 0.645520π0.645520\pi
600600 0 0
601601 12.6206 7.28651i 0.514806 0.297223i −0.220001 0.975500i 0.570606π-0.570606\pi
0.734807 + 0.678276i 0.237273π0.237273\pi
602602 0 0
603603 0 0
604604 0 0
605605 −13.2458 3.54920i −0.538519 0.144296i
606606 0 0
607607 −32.0317 18.4935i −1.30013 0.750629i −0.319702 0.947518i 0.603583π-0.603583\pi
−0.980426 + 0.196889i 0.936916π0.936916\pi
608608 0 0
609609 0 0
610610 0 0
611611 11.1967 + 11.1967i 0.452972 + 0.452972i
612612 0 0
613613 3.34985 3.34985i 0.135299 0.135299i −0.636214 0.771513i 0.719500π-0.719500\pi
0.771513 + 0.636214i 0.219500π0.219500\pi
614614 0 0
615615 0 0
616616 0 0
617617 4.04358 7.00369i 0.162789 0.281958i −0.773079 0.634309i 0.781285π-0.781285\pi
0.935868 + 0.352352i 0.114618π0.114618\pi
618618 0 0
619619 −11.6692 + 43.5499i −0.469023 + 1.75042i 0.174171 + 0.984715i 0.444275π0.444275\pi
−0.643194 + 0.765703i 0.722391π0.722391\pi
620620 0 0
621621 0 0
622622 0 0
623623 10.7590 + 18.6351i 0.431049 + 0.746599i
624624 0 0
625625 17.1046 29.6260i 0.684182 1.18504i
626626 0 0
627627 0 0
628628 0 0
629629 −3.95318 3.95318i −0.157624 0.157624i
630630 0 0
631631 3.49919 0.139300 0.0696502 0.997571i 0.477812π-0.477812\pi
0.0696502 + 0.997571i 0.477812π0.477812\pi
632632 0 0
633633 0 0
634634 0 0
635635 −18.3925 68.6417i −0.729883 2.72396i
636636 0 0
637637 1.01266 3.77930i 0.0401231 0.149741i
638638 0 0
639639 0 0
640640 0 0
641641 −4.01739 + 2.31944i −0.158677 + 0.0916125i −0.577236 0.816577i 0.695869π-0.695869\pi
0.418559 + 0.908190i 0.362535π0.362535\pi
642642 0 0
643643 10.6535 + 39.7595i 0.420134 + 1.56796i 0.774324 + 0.632789i 0.218090π0.218090\pi
−0.354190 + 0.935173i 0.615243π0.615243\pi
644644 0 0
645645 0 0
646646 0 0
647647 2.08960i 0.0821505i 0.999156 + 0.0410752i 0.0130783π0.0130783\pi
−0.999156 + 0.0410752i 0.986922π0.986922\pi
648648 0 0
649649 7.04684i 0.276613i
650650 0 0
651651 0 0
652652 0 0
653653 −4.75454 17.7442i −0.186059 0.694383i −0.994401 0.105670i 0.966301π-0.966301\pi
0.808342 0.588713i 0.200365π-0.200365\pi
654654 0 0
655655 61.6410 35.5885i 2.40851 1.39056i
656656 0 0
657657 0 0
658658 0 0
659659 −7.84088 + 29.2626i −0.305437 + 1.13991i 0.627131 + 0.778914i 0.284229π0.284229\pi
−0.932568 + 0.360994i 0.882438π0.882438\pi
660660 0 0
661661 12.5011 + 46.6546i 0.486235 + 1.81465i 0.574434 + 0.818551i 0.305222π0.305222\pi
−0.0881985 + 0.996103i 0.528111π0.528111\pi
662662 0 0
663663 0 0
664664 0 0
665665 −32.7549 −1.27018
666666 0 0
667667 14.8169 + 14.8169i 0.573714 + 0.573714i
668668 0 0
669669 0 0
670670 0 0
671671 −15.8822 + 27.5087i −0.613124 + 1.06196i
672672 0 0
673673 8.92590 + 15.4601i 0.344068 + 0.595944i 0.985184 0.171500i 0.0548615π-0.0548615\pi
−0.641116 + 0.767444i 0.721528π0.721528\pi
674674 0 0
675675 0 0
676676 0 0
677677 −0.575049 + 2.14611i −0.0221009 + 0.0824818i −0.976095 0.217342i 0.930261π-0.930261\pi
0.953995 + 0.299824i 0.0969279π0.0969279\pi
678678 0 0
679679 7.33966 12.7127i 0.281670 0.487867i
680680 0 0
681681 0 0
682682 0 0
683683 0.857818 0.857818i 0.0328235 0.0328235i −0.690505 0.723328i 0.742611π-0.742611\pi
0.723328 + 0.690505i 0.242611π0.242611\pi
684684 0 0
685685 2.21214 + 2.21214i 0.0845216 + 0.0845216i
686686 0 0
687687 0 0
688688 0 0
689689 −15.4163 8.90063i −0.587316 0.339087i
690690 0 0
691691 37.8791 + 10.1497i 1.44099 + 0.386112i 0.892880 0.450295i 0.148681π-0.148681\pi
0.548109 + 0.836407i 0.315348π0.315348\pi
692692 0 0
693693 0 0
694694 0 0
695695 72.6201 41.9272i 2.75464 1.59039i
696696 0 0
697697 3.74334 + 2.16122i 0.141789 + 0.0818619i
698698 0 0
699699 0 0
700700 0 0
701701 14.3403 14.3403i 0.541627 0.541627i −0.382379 0.924006i 0.624895π-0.624895\pi
0.924006 + 0.382379i 0.124895π0.124895\pi
702702 0 0
703703 5.45369i 0.205690i
704704 0 0
705705 0 0
706706 0 0
707707 −30.9838 + 8.30208i −1.16527 + 0.312232i
708708 0 0
709709 −4.26177 1.14194i −0.160054 0.0428864i 0.177902 0.984048i 0.443069π-0.443069\pi
−0.337956 + 0.941162i 0.609736π0.609736\pi
710710 0 0
711711 0 0
712712 0 0
713713 −0.606335 1.05020i −0.0227074 0.0393304i
714714 0 0
715715 25.4279 6.81339i 0.950951 0.254806i
716716 0 0
717717 0 0
718718 0 0
719719 −49.2509 −1.83675 −0.918374 0.395714i 0.870497π-0.870497\pi
−0.918374 + 0.395714i 0.870497π0.870497\pi
720720 0 0
721721 −1.88938 −0.0703644
722722 0 0
723723 0 0
724724 0 0
725725 −89.6203 + 24.0137i −3.32841 + 0.891846i
726726 0 0
727727 2.18154 + 3.77855i 0.0809090 + 0.140139i 0.903641 0.428291i 0.140884π-0.140884\pi
−0.822732 + 0.568430i 0.807551π0.807551\pi
728728 0 0
729729 0 0
730730 0 0
731731 −13.7508 3.68451i −0.508591 0.136277i
732732 0 0
733733 30.7314 8.23445i 1.13509 0.304146i 0.358114 0.933678i 0.383420π-0.383420\pi
0.776975 + 0.629532i 0.216753π0.216753\pi
734734 0 0
735735 0 0
736736 0 0
737737 26.8722i 0.989849i
738738 0 0
739739 32.4463 32.4463i 1.19356 1.19356i 0.217495 0.976061i 0.430211π-0.430211\pi
0.976061 0.217495i 0.0697887π-0.0697887\pi
740740 0 0
741741 0 0
742742 0 0
743743 −10.8406 6.25880i −0.397702 0.229613i 0.287790 0.957693i 0.407079π-0.407079\pi
−0.685492 + 0.728080i 0.740413π0.740413\pi
744744 0 0
745745 40.0141 23.1021i 1.46600 0.846397i
746746 0 0
747747 0 0
748748 0 0
749749 −14.9973 4.01852i −0.547990 0.146834i
750750 0 0
751751 34.0479 + 19.6575i 1.24242 + 0.717314i 0.969587 0.244747i 0.0787047π-0.0787047\pi
0.272837 + 0.962060i 0.412038π0.412038\pi
752752 0 0
753753 0 0
754754 0 0
755755 23.6777 + 23.6777i 0.861718 + 0.861718i
756756 0 0
757757 −25.3026 + 25.3026i −0.919640 + 0.919640i −0.997003 0.0773631i 0.975350π-0.975350\pi
0.0773631 + 0.997003i 0.475350π0.475350\pi
758758 0 0
759759 0 0
760760 0 0
761761 −11.0907 + 19.2097i −0.402039 + 0.696352i −0.993972 0.109635i 0.965032π-0.965032\pi
0.591933 + 0.805987i 0.298365π0.298365\pi
762762 0 0
763763 6.45338 24.0843i 0.233628 0.871911i
764764 0 0
765765 0 0
766766 0 0
767767 −3.12087 5.40551i −0.112688 0.195182i
768768 0 0
769769 0.792978 1.37348i 0.0285955 0.0495289i −0.851374 0.524560i 0.824230π-0.824230\pi
0.879969 + 0.475031i 0.157563π0.157563\pi
770770 0 0
771771 0 0
772772 0 0
773773 0.198602 + 0.198602i 0.00714323 + 0.00714323i 0.710669 0.703526i 0.248392π-0.248392\pi
−0.703526 + 0.710669i 0.748392π0.748392\pi
774774 0 0
775775 5.36948 0.192877
776776 0 0
777777 0 0
778778 0 0
779779 1.09132 + 4.07287i 0.0391007 + 0.145926i
780780 0 0
781781 3.30471 12.3334i 0.118252 0.441322i
782782 0 0
783783 0 0
784784 0 0
785785 12.5149 7.22549i 0.446676 0.257889i
786786 0 0
787787 3.76684 + 14.0581i 0.134274 + 0.501116i 1.00000 0.000597888i 0.000190314π0.000190314\pi
−0.865726 + 0.500518i 0.833143π0.833143\pi
788788 0 0
789789 0 0
790790 0 0
791791 48.9217i 1.73946i
792792 0 0
793793 28.1353i 0.999112i
794794 0 0
795795 0 0
796796 0 0
797797 3.12214 + 11.6520i 0.110592 + 0.412734i 0.998919 0.0464762i 0.0147992π-0.0147992\pi
−0.888328 + 0.459210i 0.848132π0.848132\pi
798798 0 0
799799 −16.3541 + 9.44202i −0.578565 + 0.334035i
800800 0 0
801801 0 0
802802 0 0
803803 3.49286 13.0355i 0.123261 0.460015i
804804 0 0
805805 7.17244 + 26.7679i 0.252795 + 0.943445i
806806 0 0
807807 0 0
808808 0 0
809809 5.40097 0.189888 0.0949441 0.995483i 0.469733π-0.469733\pi
0.0949441 + 0.995483i 0.469733π0.469733\pi
810810 0 0
811811 −19.4041 19.4041i −0.681371 0.681371i 0.278938 0.960309i 0.410018π-0.410018\pi
−0.960309 + 0.278938i 0.910018π0.910018\pi
812812 0 0
813813 0 0
814814 0 0
815815 10.7788 18.6695i 0.377566 0.653964i
816816 0 0
817817 −6.94356 12.0266i −0.242924 0.420758i
818818 0 0
819819 0 0
820820 0 0
821821 5.53178 20.6449i 0.193061 0.720512i −0.799700 0.600400i 0.795008π-0.795008\pi
0.992760 0.120112i 0.0383253π-0.0383253\pi
822822 0 0
823823 15.8047 27.3746i 0.550918 0.954217i −0.447291 0.894389i 0.647611π-0.647611\pi
0.998209 0.0598289i 0.0190555π-0.0190555\pi
824824 0 0
825825 0 0
826826 0 0
827827 −11.4058 + 11.4058i −0.396617 + 0.396617i −0.877038 0.480421i 0.840484π-0.840484\pi
0.480421 + 0.877038i 0.340484π0.340484\pi
828828 0 0
829829 −15.8083 15.8083i −0.549043 0.549043i 0.377121 0.926164i 0.376914π-0.376914\pi
−0.926164 + 0.377121i 0.876914π0.876914\pi
830830 0 0
831831 0 0
832832 0 0
833833 4.04098 + 2.33306i 0.140012 + 0.0808357i
834834 0 0
835835 −26.3457 7.05931i −0.911730 0.244297i
836836 0 0
837837 0 0
838838 0 0
839839 −28.2922 + 16.3345i −0.976755 + 0.563930i −0.901289 0.433219i 0.857378π-0.857378\pi
−0.0754662 + 0.997148i 0.524044π0.524044\pi
840840 0 0
841841 41.3525 + 23.8749i 1.42595 + 0.823272i
842842 0 0
843843 0 0
844844 0 0
845845 −19.8083 + 19.8083i −0.681428 + 0.681428i
846846 0 0
847847 10.1907i 0.350158i
848848 0 0
849849 0 0
850850 0 0
851851 −4.45686 + 1.19421i −0.152779 + 0.0409371i
852852 0 0
853853 38.7224 + 10.3756i 1.32583 + 0.355255i 0.851159 0.524907i 0.175900π-0.175900\pi
0.474672 + 0.880163i 0.342567π0.342567\pi
854854 0 0
855855 0 0
856856 0 0
857857 0.0140657 + 0.0243624i 0.000480474 + 0.000832205i 0.866266 0.499584i 0.166514π-0.166514\pi
−0.865785 + 0.500416i 0.833180π0.833180\pi
858858 0 0
859859 −11.7598 + 3.15104i −0.401240 + 0.107512i −0.453795 0.891106i 0.649930π-0.649930\pi
0.0525549 + 0.998618i 0.483264π0.483264\pi
860860 0 0
861861 0 0
862862 0 0
863863 40.1140 1.36550 0.682748 0.730654i 0.260785π-0.260785\pi
0.682748 + 0.730654i 0.260785π0.260785\pi
864864 0 0
865865 −15.8140 −0.537692
866866 0 0
867867 0 0
868868 0 0
869869 −11.0547 + 2.96211i −0.375006 + 0.100483i
870870 0 0
871871 −11.9010 20.6132i −0.403251 0.698451i
872872 0 0
873873 0 0
874874 0 0
875875 −62.5669 16.7647i −2.11515 0.566752i
876876 0 0
877877 −45.8849 + 12.2948i −1.54942 + 0.415167i −0.929297 0.369334i 0.879586π-0.879586\pi
−0.620127 + 0.784501i 0.712919π0.712919\pi
878878 0 0
879879 0 0
880880 0 0
881881 20.6694i 0.696371i 0.937426 + 0.348186i 0.113202π0.113202\pi
−0.937426 + 0.348186i 0.886798π0.886798\pi
882882 0 0
883883 37.7611 37.7611i 1.27076 1.27076i 0.325075 0.945688i 0.394610π-0.394610\pi
0.945688 0.325075i 0.105390π-0.105390\pi
884884 0 0
885885 0 0
886886 0 0
887887 −24.4908 14.1398i −0.822322 0.474768i 0.0288948 0.999582i 0.490801π-0.490801\pi
−0.851216 + 0.524815i 0.824135π0.824135\pi
888888 0 0
889889 −45.7347 + 26.4049i −1.53389 + 0.885593i
890890 0 0
891891 0 0
892892 0 0
893893 −17.7937 4.76782i −0.595445 0.159549i
894894 0 0
895895 48.6615 + 28.0947i 1.62657 + 0.939103i
896896 0 0
897897 0 0
898898 0 0
899899 −3.14074 3.14074i −0.104750 0.104750i
900900 0 0
901901 15.0115 15.0115i 0.500105 0.500105i
902902 0 0
903903 0 0
904904 0 0
905905 41.9767 72.7058i 1.39535 2.41682i
906906 0 0
907907 9.12179 34.0430i 0.302884 1.13038i −0.631867 0.775077i 0.717711π-0.717711\pi
0.934751 0.355302i 0.115622π-0.115622\pi
908908 0 0
909909 0 0
910910 0 0
911911 −8.81619 15.2701i −0.292093 0.505921i 0.682211 0.731155i 0.261018π-0.261018\pi
−0.974305 + 0.225235i 0.927685π0.927685\pi
912912 0 0
913913 17.8832 30.9746i 0.591847 1.02511i
914914 0 0
915915 0 0
916916 0 0
917917 −37.4020 37.4020i −1.23512 1.23512i
918918 0 0
919919 −40.6483 −1.34086 −0.670431 0.741972i 0.733891π-0.733891\pi
−0.670431 + 0.741972i 0.733891π0.733891\pi
920920 0 0
921921 0 0
922922 0 0
923923 −2.92715 10.9243i −0.0963483 0.359577i
924924 0 0
925925 5.28775 19.7341i 0.173860 0.648855i
926926 0 0
927927 0 0
928928 0 0
929929 46.7331 26.9814i 1.53326 0.885230i 0.534055 0.845450i 0.320667π-0.320667\pi
0.999208 0.0397807i 0.0126659π-0.0126659\pi
930930 0 0
931931 1.17810 + 4.39672i 0.0386106 + 0.144097i
932932 0 0
933933 0 0
934934 0 0
935935 31.3946i 1.02671i
936936 0 0
937937 47.0464i 1.53694i −0.639886 0.768470i 0.721018π-0.721018\pi
0.639886 0.768470i 0.278982π-0.278982\pi
938938 0 0
939939 0 0
940940 0 0
941941 −0.645083 2.40748i −0.0210291 0.0784816i 0.954614 0.297846i 0.0962683π-0.0962683\pi
−0.975643 + 0.219365i 0.929602π0.929602\pi
942942 0 0
943943 3.08946 1.78370i 0.100607 0.0580853i
944944 0 0
945945 0 0
946946 0 0
947947 13.4692 50.2676i 0.437689 1.63348i −0.296859 0.954921i 0.595939π-0.595939\pi
0.734548 0.678557i 0.237394π-0.237394\pi
948948 0 0
949949 −3.09381 11.5462i −0.100429 0.374807i
950950 0 0
951951 0 0
952952 0 0
953953 −61.2734 −1.98484 −0.992420 0.122896i 0.960782π-0.960782\pi
−0.992420 + 0.122896i 0.960782π0.960782\pi
954954 0 0
955955 −60.8700 60.8700i −1.96971 1.96971i
956956 0 0
957957 0 0
958958 0 0
959959 1.16244 2.01340i 0.0375370 0.0650160i
960960 0 0
961961 −15.3715 26.6242i −0.495854 0.858844i
962962 0 0
963963 0 0
964964 0 0
965965 −4.79750 + 17.9045i −0.154437 + 0.576367i
966966 0 0
967967 3.75805 6.50913i 0.120851 0.209319i −0.799253 0.600995i 0.794771π-0.794771\pi
0.920103 + 0.391676i 0.128104π0.128104\pi
968968 0 0
969969 0 0
970970 0 0
971971 −20.5494 + 20.5494i −0.659461 + 0.659461i −0.955253 0.295791i 0.904417π-0.904417\pi
0.295791 + 0.955253i 0.404417π0.404417\pi
972972 0 0
973973 −44.0638 44.0638i −1.41262 1.41262i
974974 0 0
975975 0 0
976976 0 0
977977 −48.8661 28.2129i −1.56337 0.902610i −0.996913 0.0785154i 0.974982π-0.974982\pi
−0.566453 0.824094i 0.691685π-0.691685\pi
978978 0 0
979979 19.4336 + 5.20721i 0.621100 + 0.166423i
980980 0 0
981981 0 0
982982 0 0
983983 5.17882 2.98999i 0.165179 0.0953660i −0.415132 0.909761i 0.636265π-0.636265\pi
0.580311 + 0.814395i 0.302931π0.302931\pi
984984 0 0
985985 −69.2628 39.9889i −2.20690 1.27415i
986986 0 0
987987 0 0
988988 0 0
989989 −8.30792 + 8.30792i −0.264176 + 0.264176i
990990 0 0
991991 20.2358i 0.642812i −0.946942 0.321406i 0.895845π-0.895845\pi
0.946942 0.321406i 0.104155π-0.104155\pi
992992 0 0
993993 0 0
994994 0 0
995995 55.2892 14.8147i 1.75278 0.469657i
996996 0 0
997997 0.647795 + 0.173576i 0.0205159 + 0.00549721i 0.269062 0.963123i 0.413286π-0.413286\pi
−0.248547 + 0.968620i 0.579953π0.579953\pi
998998 0 0
999999 0 0
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 1728.2.z.a.1583.22 88
3.2 odd 2 576.2.y.a.239.3 88
4.3 odd 2 432.2.v.a.179.3 88
9.2 odd 6 inner 1728.2.z.a.1007.22 88
9.7 even 3 576.2.y.a.47.9 88
12.11 even 2 144.2.u.a.131.20 yes 88
16.5 even 4 432.2.v.a.395.5 88
16.11 odd 4 inner 1728.2.z.a.719.22 88
36.7 odd 6 144.2.u.a.83.18 yes 88
36.11 even 6 432.2.v.a.35.5 88
48.5 odd 4 144.2.u.a.59.18 yes 88
48.11 even 4 576.2.y.a.527.9 88
144.11 even 12 inner 1728.2.z.a.143.22 88
144.43 odd 12 576.2.y.a.335.3 88
144.101 odd 12 432.2.v.a.251.3 88
144.133 even 12 144.2.u.a.11.20 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.20 88 144.133 even 12
144.2.u.a.59.18 yes 88 48.5 odd 4
144.2.u.a.83.18 yes 88 36.7 odd 6
144.2.u.a.131.20 yes 88 12.11 even 2
432.2.v.a.35.5 88 36.11 even 6
432.2.v.a.179.3 88 4.3 odd 2
432.2.v.a.251.3 88 144.101 odd 12
432.2.v.a.395.5 88 16.5 even 4
576.2.y.a.47.9 88 9.7 even 3
576.2.y.a.239.3 88 3.2 odd 2
576.2.y.a.335.3 88 144.43 odd 12
576.2.y.a.527.9 88 48.11 even 4
1728.2.z.a.143.22 88 144.11 even 12 inner
1728.2.z.a.719.22 88 16.11 odd 4 inner
1728.2.z.a.1007.22 88 9.2 odd 6 inner
1728.2.z.a.1583.22 88 1.1 even 1 trivial