Properties

Label 1156.2.h.e.757.4
Level 11561156
Weight 22
Character 1156.757
Analytic conductor 9.2319.231
Analytic rank 00
Dimension 1616
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1156,2,Mod(733,1156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1156, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1156.733");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1156=22172 1156 = 2^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1156.h (of order 88, 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: 9.230706473669.23070647366
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ8)\Q(\zeta_{8})
Coefficient field: 16.0.229607785695641627262976.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+799x8+6561 x^{16} + 799x^{8} + 6561 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 68)
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 757.4
Root 2.127490.881234i2.12749 - 0.881234i of defining polynomial
Character χ\chi == 1156.757
Dual form 1156.2.h.e.733.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(3.00872+1.24625i)q3+(0.5411961.30656i)q5+(1.246253.00872i)q7+(5.37794+5.37794i)q9+(0.395595+0.163861i)q112.60555iq13+(3.256623.25662i)q15+(0.4281890.428189i)q1910.6056iq21+(5.621852.32865i)q23+(2.12132+2.12132i)q25+(5.73968+13.8568i)q27+(0.868918+2.09775i)q29+(5.62185+2.32865i)q311.39445q334.60555q35+(3.919691.62359i)q37+(3.247187.83938i)q39+(0.5411961.30656i)q41+(2.40024+2.40024i)q43+(9.937134.11609i)q45+4.00000iq47+(2.54951+2.54951i)q49+(3.68481+3.68481i)q53+0.605551iq55+(1.821940.754670i)q57+(6.085046.08504i)q59+(3.361428.11520i)q61+(9.4784422.8830i)q63+(3.404321.41011i)q659.21110q67+19.8167q69+(3.799911.57398i)q71+(3.788379.14594i)q73+(3.73876+9.02616i)q75+(0.986024+0.986024i)q77+(0.395595+0.163861i)q79+26.0278iq81+(12.5983+12.5983i)q83+(5.22866+5.22866i)q87+7.81665iq89+(7.83938+3.24718i)q91+(14.0125+14.0125i)q93+(0.3277220.791191i)q95+(4.11609+9.93713i)q97+(3.008721.24625i)q99+O(q100)q+(3.00872 + 1.24625i) q^{3} +(0.541196 - 1.30656i) q^{5} +(-1.24625 - 3.00872i) q^{7} +(5.37794 + 5.37794i) q^{9} +(-0.395595 + 0.163861i) q^{11} -2.60555i q^{13} +(3.25662 - 3.25662i) q^{15} +(0.428189 - 0.428189i) q^{19} -10.6056i q^{21} +(5.62185 - 2.32865i) q^{23} +(2.12132 + 2.12132i) q^{25} +(5.73968 + 13.8568i) q^{27} +(-0.868918 + 2.09775i) q^{29} +(5.62185 + 2.32865i) q^{31} -1.39445 q^{33} -4.60555 q^{35} +(-3.91969 - 1.62359i) q^{37} +(3.24718 - 7.83938i) q^{39} +(-0.541196 - 1.30656i) q^{41} +(2.40024 + 2.40024i) q^{43} +(9.93713 - 4.11609i) q^{45} +4.00000i q^{47} +(-2.54951 + 2.54951i) q^{49} +(-3.68481 + 3.68481i) q^{53} +0.605551i q^{55} +(1.82194 - 0.754670i) q^{57} +(-6.08504 - 6.08504i) q^{59} +(-3.36142 - 8.11520i) q^{61} +(9.47844 - 22.8830i) q^{63} +(-3.40432 - 1.41011i) q^{65} -9.21110 q^{67} +19.8167 q^{69} +(-3.79991 - 1.57398i) q^{71} +(3.78837 - 9.14594i) q^{73} +(3.73876 + 9.02616i) q^{75} +(0.986024 + 0.986024i) q^{77} +(-0.395595 + 0.163861i) q^{79} +26.0278i q^{81} +(-12.5983 + 12.5983i) q^{83} +(-5.22866 + 5.22866i) q^{87} +7.81665i q^{89} +(-7.83938 + 3.24718i) q^{91} +(14.0125 + 14.0125i) q^{93} +(-0.327722 - 0.791191i) q^{95} +(-4.11609 + 9.93713i) q^{97} +(-3.00872 - 1.24625i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q80q3316q3532q67+144q69+O(q100) 16 q - 80 q^{33} - 16 q^{35} - 32 q^{67} + 144 q^{69}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1156Z)×\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times.

nn 579579 581581
χ(n)\chi(n) 11 e(18)e\left(\frac{1}{8}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 3.00872 + 1.24625i 1.73709 + 0.719525i 0.998995 + 0.0448236i 0.0142726π0.0142726\pi
0.738091 + 0.674701i 0.235727π0.235727\pi
44 0 0
55 0.541196 1.30656i 0.242030 0.584313i −0.755454 0.655202i 0.772584π-0.772584\pi
0.997484 + 0.0708890i 0.0225836π0.0225836\pi
66 0 0
77 −1.24625 3.00872i −0.471039 1.13719i −0.963705 0.266971i 0.913977π-0.913977\pi
0.492665 0.870219i 0.336023π-0.336023\pi
88 0 0
99 5.37794 + 5.37794i 1.79265 + 1.79265i
1010 0 0
1111 −0.395595 + 0.163861i −0.119277 + 0.0494059i −0.441524 0.897250i 0.645562π-0.645562\pi
0.322247 + 0.946656i 0.395562π0.395562\pi
1212 0 0
1313 2.60555i 0.722650i −0.932440 0.361325i 0.882325π-0.882325\pi
0.932440 0.361325i 0.117675π-0.117675\pi
1414 0 0
1515 3.25662 3.25662i 0.840855 0.840855i
1616 0 0
1717 0 0
1818 0 0
1919 0.428189 0.428189i 0.0982334 0.0982334i −0.656282 0.754516i 0.727872π-0.727872\pi
0.754516 + 0.656282i 0.227872π0.227872\pi
2020 0 0
2121 10.6056i 2.31432i
2222 0 0
2323 5.62185 2.32865i 1.17224 0.485556i 0.290305 0.956934i 0.406243π-0.406243\pi
0.881931 + 0.471378i 0.156243π0.156243\pi
2424 0 0
2525 2.12132 + 2.12132i 0.424264 + 0.424264i
2626 0 0
2727 5.73968 + 13.8568i 1.10460 + 2.66675i
2828 0 0
2929 −0.868918 + 2.09775i −0.161354 + 0.389543i −0.983792 0.179311i 0.942613π-0.942613\pi
0.822438 + 0.568854i 0.192613π0.192613\pi
3030 0 0
3131 5.62185 + 2.32865i 1.00971 + 0.418237i 0.825350 0.564621i 0.190978π-0.190978\pi
0.184363 + 0.982858i 0.440978π0.440978\pi
3232 0 0
3333 −1.39445 −0.242742
3434 0 0
3535 −4.60555 −0.778480
3636 0 0
3737 −3.91969 1.62359i −0.644393 0.266916i 0.0364615 0.999335i 0.488391π-0.488391\pi
−0.680854 + 0.732419i 0.738391π0.738391\pi
3838 0 0
3939 3.24718 7.83938i 0.519964 1.25531i
4040 0 0
4141 −0.541196 1.30656i −0.0845206 0.204051i 0.875969 0.482368i 0.160223π-0.160223\pi
−0.960489 + 0.278317i 0.910223π0.910223\pi
4242 0 0
4343 2.40024 + 2.40024i 0.366033 + 0.366033i 0.866028 0.499995i 0.166665π-0.166665\pi
−0.499995 + 0.866028i 0.666665π0.666665\pi
4444 0 0
4545 9.93713 4.11609i 1.48134 0.613591i
4646 0 0
4747 4.00000i 0.583460i 0.956501 + 0.291730i 0.0942309π0.0942309\pi
−0.956501 + 0.291730i 0.905769π0.905769\pi
4848 0 0
4949 −2.54951 + 2.54951i −0.364216 + 0.364216i
5050 0 0
5151 0 0
5252 0 0
5353 −3.68481 + 3.68481i −0.506147 + 0.506147i −0.913341 0.407194i 0.866507π-0.866507\pi
0.407194 + 0.913341i 0.366507π0.366507\pi
5454 0 0
5555 0.605551i 0.0816525i
5656 0 0
5757 1.82194 0.754670i 0.241321 0.0999585i
5858 0 0
5959 −6.08504 6.08504i −0.792205 0.792205i 0.189647 0.981852i 0.439266π-0.439266\pi
−0.981852 + 0.189647i 0.939266π0.939266\pi
6060 0 0
6161 −3.36142 8.11520i −0.430386 1.03904i −0.979163 0.203076i 0.934906π-0.934906\pi
0.548777 0.835969i 0.315094π-0.315094\pi
6262 0 0
6363 9.47844 22.8830i 1.19417 2.88299i
6464 0 0
6565 −3.40432 1.41011i −0.422254 0.174903i
6666 0 0
6767 −9.21110 −1.12532 −0.562658 0.826690i 0.690221π-0.690221\pi
−0.562658 + 0.826690i 0.690221π0.690221\pi
6868 0 0
6969 19.8167 2.38564
7070 0 0
7171 −3.79991 1.57398i −0.450967 0.186796i 0.145628 0.989339i 0.453480π-0.453480\pi
−0.596594 + 0.802543i 0.703480π0.703480\pi
7272 0 0
7373 3.78837 9.14594i 0.443395 1.07045i −0.531354 0.847150i 0.678317π-0.678317\pi
0.974749 0.223301i 0.0716834π-0.0716834\pi
7474 0 0
7575 3.73876 + 9.02616i 0.431715 + 1.04225i
7676 0 0
7777 0.986024 + 0.986024i 0.112368 + 0.112368i
7878 0 0
7979 −0.395595 + 0.163861i −0.0445080 + 0.0184358i −0.404826 0.914394i 0.632668π-0.632668\pi
0.360318 + 0.932829i 0.382668π0.382668\pi
8080 0 0
8181 26.0278i 2.89197i
8282 0 0
8383 −12.5983 + 12.5983i −1.38284 + 1.38284i −0.543305 + 0.839535i 0.682827π0.682827\pi
−0.839535 + 0.543305i 0.817173π0.817173\pi
8484 0 0
8585 0 0
8686 0 0
8787 −5.22866 + 5.22866i −0.560572 + 0.560572i
8888 0 0
8989 7.81665i 0.828564i 0.910149 + 0.414282i 0.135967π0.135967\pi
−0.910149 + 0.414282i 0.864033π0.864033\pi
9090 0 0
9191 −7.83938 + 3.24718i −0.821790 + 0.340397i
9292 0 0
9393 14.0125 + 14.0125i 1.45303 + 1.45303i
9494 0 0
9595 −0.327722 0.791191i −0.0336236 0.0811745i
9696 0 0
9797 −4.11609 + 9.93713i −0.417926 + 1.00896i 0.565021 + 0.825076i 0.308868π0.308868\pi
−0.982947 + 0.183887i 0.941132π0.941132\pi
9898 0 0
9999 −3.00872 1.24625i −0.302388 0.125253i
100100 0 0
101101 −10.6056 −1.05529 −0.527646 0.849464i 0.676925π-0.676925\pi
−0.527646 + 0.849464i 0.676925π0.676925\pi
102102 0 0
103103 −13.2111 −1.30173 −0.650864 0.759194i 0.725593π-0.725593\pi
−0.650864 + 0.759194i 0.725593π0.725593\pi
104104 0 0
105105 −13.8568 5.73968i −1.35229 0.560136i
106106 0 0
107107 −3.08332 + 7.44378i −0.298075 + 0.719618i 0.701898 + 0.712278i 0.252336π0.252336\pi
−0.999973 + 0.00733983i 0.997664π0.997664\pi
108108 0 0
109109 3.36142 + 8.11520i 0.321966 + 0.777295i 0.999140 + 0.0414716i 0.0132046π0.0132046\pi
−0.677174 + 0.735823i 0.736795π0.736795\pi
110110 0 0
111111 −9.76985 9.76985i −0.927313 0.927313i
112112 0 0
113113 12.5503 5.19849i 1.18063 0.489033i 0.295936 0.955208i 0.404368π-0.404368\pi
0.884692 + 0.466175i 0.154368π0.154368\pi
114114 0 0
115115 8.60555i 0.802472i
116116 0 0
117117 14.0125 14.0125i 1.29546 1.29546i
118118 0 0
119119 0 0
120120 0 0
121121 −7.64853 + 7.64853i −0.695321 + 0.695321i
122122 0 0
123123 4.60555i 0.415269i
124124 0 0
125125 10.4525 4.32957i 0.934900 0.387248i
126126 0 0
127127 −0.428189 0.428189i −0.0379957 0.0379957i 0.687854 0.725849i 0.258553π-0.258553\pi
−0.725849 + 0.687854i 0.758553π0.758553\pi
128128 0 0
129129 4.23034 + 10.2130i 0.372461 + 0.899200i
130130 0 0
131131 −3.41104 + 8.23497i −0.298024 + 0.719493i 0.701950 + 0.712226i 0.252313π0.252313\pi
−0.999974 + 0.00726659i 0.997687π0.997687\pi
132132 0 0
133133 −1.82194 0.754670i −0.157982 0.0654382i
134134 0 0
135135 21.2111 1.82556
136136 0 0
137137 −2.60555 −0.222607 −0.111304 0.993786i 0.535503π-0.535503\pi
−0.111304 + 0.993786i 0.535503π0.535503\pi
138138 0 0
139139 −0.395595 0.163861i −0.0335540 0.0138985i 0.365843 0.930676i 0.380781π-0.380781\pi
−0.399397 + 0.916778i 0.630781π0.630781\pi
140140 0 0
141141 −4.98501 + 12.0349i −0.419814 + 1.01352i
142142 0 0
143143 0.426948 + 1.03074i 0.0357032 + 0.0861952i
144144 0 0
145145 2.27059 + 2.27059i 0.188562 + 0.188562i
146146 0 0
147147 −10.8481 + 4.49343i −0.894736 + 0.370612i
148148 0 0
149149 8.42221i 0.689974i −0.938607 0.344987i 0.887883π-0.887883\pi
0.938607 0.344987i 0.112117π-0.112117\pi
150150 0 0
151151 −3.25662 + 3.25662i −0.265020 + 0.265020i −0.827090 0.562070i 0.810005π-0.810005\pi
0.562070 + 0.827090i 0.310005π0.310005\pi
152152 0 0
153153 0 0
154154 0 0
155155 6.08504 6.08504i 0.488762 0.488762i
156156 0 0
157157 8.42221i 0.672165i −0.941833 0.336083i 0.890898π-0.890898\pi
0.941833 0.336083i 0.109102π-0.109102\pi
158158 0 0
159159 −15.6788 + 6.49435i −1.24341 + 0.515036i
160160 0 0
161161 −14.0125 14.0125i −1.10434 1.10434i
162162 0 0
163163 −2.32865 5.62185i −0.182394 0.440337i 0.806065 0.591827i 0.201593π-0.201593\pi
−0.988459 + 0.151490i 0.951593π0.951593\pi
164164 0 0
165165 −0.754670 + 1.82194i −0.0587510 + 0.141837i
166166 0 0
167167 19.4787 + 8.06833i 1.50730 + 0.624346i 0.975000 0.222207i 0.0713260π-0.0713260\pi
0.532305 + 0.846553i 0.321326π0.321326\pi
168168 0 0
169169 6.21110 0.477777
170170 0 0
171171 4.60555 0.352195
172172 0 0
173173 19.3589 + 8.01872i 1.47183 + 0.609652i 0.967275 0.253729i 0.0816570π-0.0816570\pi
0.504554 + 0.863380i 0.331657π0.331657\pi
174174 0 0
175175 3.73876 9.02616i 0.282624 0.682314i
176176 0 0
177177 −10.7247 25.8917i −0.806117 1.94614i
178178 0 0
179179 10.6262 + 10.6262i 0.794242 + 0.794242i 0.982181 0.187939i 0.0601808π-0.0601808\pi
−0.187939 + 0.982181i 0.560181π0.560181\pi
180180 0 0
181181 −16.9853 + 7.03555i −1.26251 + 0.522948i −0.910679 0.413116i 0.864441π-0.864441\pi
−0.351830 + 0.936064i 0.614441π0.614441\pi
182182 0 0
183183 28.6056i 2.11458i
184184 0 0
185185 −4.24264 + 4.24264i −0.311925 + 0.311925i
186186 0 0
187187 0 0
188188 0 0
189189 34.5382 34.5382i 2.51229 2.51229i
190190 0 0
191191 6.78890i 0.491227i 0.969368 + 0.245614i 0.0789895π0.0789895\pi
−0.969368 + 0.245614i 0.921011π0.921011\pi
192192 0 0
193193 10.7283 4.44382i 0.772242 0.319873i 0.0384615 0.999260i 0.487754π-0.487754\pi
0.733780 + 0.679387i 0.237754π0.237754\pi
194194 0 0
195195 −8.48528 8.48528i −0.607644 0.607644i
196196 0 0
197197 −9.52806 23.0028i −0.678846 1.63888i −0.766122 0.642695i 0.777816π-0.777816\pi
0.0872765 0.996184i 0.472184π-0.472184\pi
198198 0 0
199199 −5.47660 + 13.2217i −0.388226 + 0.937259i 0.602090 + 0.798428i 0.294335π0.294335\pi
−0.990316 + 0.138832i 0.955665π0.955665\pi
200200 0 0
201201 −27.7136 11.4794i −1.95477 0.809692i
202202 0 0
203203 7.39445 0.518989
204204 0 0
205205 −2.00000 −0.139686
206206 0 0
207207 42.7572 + 17.7106i 2.97183 + 1.23097i
208208 0 0
209209 −0.0992262 + 0.239553i −0.00686362 + 0.0165702i
210210 0 0
211211 −8.39605 20.2699i −0.578008 1.39543i −0.894598 0.446872i 0.852538π-0.852538\pi
0.316590 0.948563i 0.397462π-0.397462\pi
212212 0 0
213213 −9.47131 9.47131i −0.648963 0.648963i
214214 0 0
215215 4.43506 1.83706i 0.302469 0.125287i
216216 0 0
217217 19.8167i 1.34524i
218218 0 0
219219 22.7963 22.7963i 1.54043 1.54043i
220220 0 0
221221 0 0
222222 0 0
223223 −12.5983 + 12.5983i −0.843643 + 0.843643i −0.989331 0.145688i 0.953461π-0.953461\pi
0.145688 + 0.989331i 0.453461π0.453461\pi
224224 0 0
225225 22.8167i 1.52111i
226226 0 0
227227 0.395595 0.163861i 0.0262566 0.0108758i −0.369516 0.929224i 0.620477π-0.620477\pi
0.395773 + 0.918348i 0.370477π0.370477\pi
228228 0 0
229229 3.25662 + 3.25662i 0.215203 + 0.215203i 0.806474 0.591270i 0.201373π-0.201373\pi
−0.591270 + 0.806474i 0.701373π0.701373\pi
230230 0 0
231231 1.73784 + 4.19551i 0.114341 + 0.276044i
232232 0 0
233233 3.03370 7.32401i 0.198744 0.479812i −0.792815 0.609462i 0.791386π-0.791386\pi
0.991560 + 0.129650i 0.0413855π0.0413855\pi
234234 0 0
235235 5.22625 + 2.16478i 0.340923 + 0.141215i
236236 0 0
237237 −1.39445 −0.0905792
238238 0 0
239239 −14.7889 −0.956614 −0.478307 0.878193i 0.658749π-0.658749\pi
−0.478307 + 0.878193i 0.658749π0.658749\pi
240240 0 0
241241 −11.7591 4.87076i −0.757468 0.313754i −0.0296835 0.999559i 0.509450π-0.509450\pi
−0.727785 + 0.685806i 0.759450π0.759450\pi
242242 0 0
243243 −15.2181 + 36.7398i −0.976243 + 2.35686i
244244 0 0
245245 1.95131 + 4.71088i 0.124665 + 0.300967i
246246 0 0
247247 −1.11567 1.11567i −0.0709883 0.0709883i
248248 0 0
249249 −53.6053 + 22.2041i −3.39710 + 1.40713i
250250 0 0
251251 12.0000i 0.757433i 0.925513 + 0.378717i 0.123635π0.123635\pi
−0.925513 + 0.378717i 0.876365π0.876365\pi
252252 0 0
253253 −1.84240 + 1.84240i −0.115831 + 0.115831i
254254 0 0
255255 0 0
256256 0 0
257257 13.7139 13.7139i 0.855452 0.855452i −0.135346 0.990798i 0.543215π-0.543215\pi
0.990798 + 0.135346i 0.0432146π0.0432146\pi
258258 0 0
259259 13.8167i 0.858525i
260260 0 0
261261 −15.9546 + 6.60860i −0.987563 + 0.409062i
262262 0 0
263263 16.2831 + 16.2831i 1.00406 + 1.00406i 0.999992 + 0.00406616i 0.00129430π0.00129430\pi
0.00406616 + 0.999992i 0.498706π0.498706\pi
264264 0 0
265265 2.82023 + 6.80863i 0.173245 + 0.418251i
266266 0 0
267267 −9.74153 + 23.5181i −0.596172 + 1.43929i
268268 0 0
269269 22.7632 + 9.42883i 1.38790 + 0.574886i 0.946581 0.322466i 0.104512π-0.104512\pi
0.441316 + 0.897352i 0.354512π0.354512\pi
270270 0 0
271271 −1.21110 −0.0735692 −0.0367846 0.999323i 0.511712π-0.511712\pi
−0.0367846 + 0.999323i 0.511712π0.511712\pi
272272 0 0
273273 −27.6333 −1.67244
274274 0 0
275275 −1.18679 0.491583i −0.0715659 0.0296436i
276276 0 0
277277 −1.95131 + 4.71088i −0.117243 + 0.283049i −0.971597 0.236642i 0.923953π-0.923953\pi
0.854354 + 0.519691i 0.173953π0.173953\pi
278278 0 0
279279 17.7106 + 42.7572i 1.06031 + 2.55981i
280280 0 0
281281 −13.0265 13.0265i −0.777094 0.777094i 0.202242 0.979336i 0.435177π-0.435177\pi
−0.979336 + 0.202242i 0.935177π0.935177\pi
282282 0 0
283283 2.76917 1.14703i 0.164610 0.0681837i −0.298857 0.954298i 0.596605π-0.596605\pi
0.463467 + 0.886114i 0.346605π0.346605\pi
284284 0 0
285285 2.78890i 0.165200i
286286 0 0
287287 −3.25662 + 3.25662i −0.192232 + 0.192232i
288288 0 0
289289 0 0
290290 0 0
291291 −24.7684 + 24.7684i −1.45195 + 1.45195i
292292 0 0
293293 21.6333i 1.26383i −0.775037 0.631916i 0.782269π-0.782269\pi
0.775037 0.631916i 0.217731π-0.217731\pi
294294 0 0
295295 −11.2437 + 4.65729i −0.654633 + 0.271158i
296296 0 0
297297 −4.54118 4.54118i −0.263506 0.263506i
298298 0 0
299299 −6.06740 14.6480i −0.350887 0.847116i
300300 0 0
301301 4.23034 10.2130i 0.243833 0.588665i
302302 0 0
303303 −31.9091 13.2172i −1.83313 0.759308i
304304 0 0
305305 −12.4222 −0.711293
306306 0 0
307307 21.2111 1.21058 0.605291 0.796004i 0.293057π-0.293057\pi
0.605291 + 0.796004i 0.293057π0.293057\pi
308308 0 0
309309 −39.7485 16.4644i −2.26121 0.936626i
310310 0 0
311311 −10.2331 + 24.7049i −0.580267 + 1.40089i 0.312305 + 0.949982i 0.398899π0.398899\pi
−0.892572 + 0.450906i 0.851101π0.851101\pi
312312 0 0
313313 −3.36142 8.11520i −0.189999 0.458698i 0.799960 0.600053i 0.204854π-0.204854\pi
−0.989959 + 0.141355i 0.954854π0.954854\pi
314314 0 0
315315 −24.7684 24.7684i −1.39554 1.39554i
316316 0 0
317317 25.6159 10.6104i 1.43873 0.595942i 0.479241 0.877683i 0.340912π-0.340912\pi
0.959490 + 0.281741i 0.0909119π0.0909119\pi
318318 0 0
319319 0.972244i 0.0544352i
320320 0 0
321321 −18.5537 + 18.5537i −1.03557 + 1.03557i
322322 0 0
323323 0 0
324324 0 0
325325 5.52721 5.52721i 0.306594 0.306594i
326326 0 0
327327 28.6056i 1.58189i
328328 0 0
329329 12.0349 4.98501i 0.663505 0.274833i
330330 0 0
331331 −2.40024 2.40024i −0.131929 0.131929i 0.638059 0.769988i 0.279738π-0.279738\pi
−0.769988 + 0.638059i 0.779738π0.779738\pi
332332 0 0
333333 −12.3483 29.8114i −0.676682 1.63365i
334334 0 0
335335 −4.98501 + 12.0349i −0.272360 + 0.657536i
336336 0 0
337337 −21.1808 8.77339i −1.15379 0.477917i −0.277989 0.960584i 0.589668π-0.589668\pi
−0.875804 + 0.482667i 0.839668π0.839668\pi
338338 0 0
339339 44.2389 2.40273
340340 0 0
341341 −2.60555 −0.141099
342342 0 0
343343 −10.2130 4.23034i −0.551447 0.228417i
344344 0 0
345345 10.7247 25.8917i 0.577398 1.39396i
346346 0 0
347347 2.98409 + 7.20423i 0.160194 + 0.386743i 0.983513 0.180836i 0.0578802π-0.0578802\pi
−0.823319 + 0.567579i 0.807880π0.807880\pi
348348 0 0
349349 −16.7113 16.7113i −0.894534 0.894534i 0.100412 0.994946i 0.467984π-0.467984\pi
−0.994946 + 0.100412i 0.967984π0.967984\pi
350350 0 0
351351 36.1047 14.9550i 1.92712 0.798241i
352352 0 0
353353 31.2111i 1.66120i 0.556870 + 0.830600i 0.312002π0.312002\pi
−0.556870 + 0.830600i 0.687998π0.687998\pi
354354 0 0
355355 −4.11300 + 4.11300i −0.218295 + 0.218295i
356356 0 0
357357 0 0
358358 0 0
359359 11.7419 11.7419i 0.619714 0.619714i −0.325744 0.945458i 0.605615π-0.605615\pi
0.945458 + 0.325744i 0.105615π0.105615\pi
360360 0 0
361361 18.6333i 0.980700i
362362 0 0
363363 −32.5443 + 13.4803i −1.70813 + 0.707532i
364364 0 0
365365 −9.89949 9.89949i −0.518163 0.518163i
366366 0 0
367367 −3.73876 9.02616i −0.195162 0.471162i 0.795758 0.605614i 0.207073π-0.207073\pi
−0.990920 + 0.134452i 0.957073π0.957073\pi
368368 0 0
369369 4.11609 9.93713i 0.214275 0.517306i
370370 0 0
371371 15.6788 + 6.49435i 0.814000 + 0.337170i
372372 0 0
373373 −21.0278 −1.08878 −0.544388 0.838834i 0.683238π-0.683238\pi
−0.544388 + 0.838834i 0.683238π0.683238\pi
374374 0 0
375375 36.8444 1.90264
376376 0 0
377377 5.46581 + 2.26401i 0.281503 + 0.116602i
378378 0 0
379379 11.2163 27.0785i 0.576142 1.39093i −0.320109 0.947381i 0.603720π-0.603720\pi
0.896251 0.443548i 0.146280π-0.146280\pi
380380 0 0
381381 −0.754670 1.82194i −0.0386629 0.0933406i
382382 0 0
383383 13.7139 + 13.7139i 0.700750 + 0.700750i 0.964571 0.263822i 0.0849830π-0.0849830\pi
−0.263822 + 0.964571i 0.584983π0.584983\pi
384384 0 0
385385 1.82194 0.754670i 0.0928544 0.0384616i
386386 0 0
387387 25.8167i 1.31233i
388388 0 0
389389 −7.20071 + 7.20071i −0.365091 + 0.365091i −0.865683 0.500592i 0.833116π-0.833116\pi
0.500592 + 0.865683i 0.333116π0.333116\pi
390390 0 0
391391 0 0
392392 0 0
393393 −20.5257 + 20.5257i −1.03539 + 1.03539i
394394 0 0
395395 0.605551i 0.0304686i
396396 0 0
397397 11.7591 4.87076i 0.590171 0.244457i −0.0675534 0.997716i 0.521519π-0.521519\pi
0.657724 + 0.753259i 0.271519π0.271519\pi
398398 0 0
399399 −4.54118 4.54118i −0.227344 0.227344i
400400 0 0
401401 −3.78837 9.14594i −0.189182 0.456726i 0.800620 0.599172i 0.204503π-0.204503\pi
−0.989803 + 0.142445i 0.954503π0.954503\pi
402402 0 0
403403 6.06740 14.6480i 0.302239 0.729669i
404404 0 0
405405 34.0069 + 14.0861i 1.68982 + 0.699945i
406406 0 0
407407 1.81665 0.0900482
408408 0 0
409409 23.2111 1.14772 0.573858 0.818955i 0.305446π-0.305446\pi
0.573858 + 0.818955i 0.305446π0.305446\pi
410410 0 0
411411 −7.83938 3.24718i −0.386688 0.160171i
412412 0 0
413413 −10.7247 + 25.8917i −0.527728 + 1.27405i
414414 0 0
415415 9.64230 + 23.2786i 0.473322 + 1.14270i
416416 0 0
417417 −0.986024 0.986024i −0.0482858 0.0482858i
418418 0 0
419419 3.00872 1.24625i 0.146986 0.0608835i −0.307978 0.951394i 0.599652π-0.599652\pi
0.454964 + 0.890510i 0.349652π0.349652\pi
420420 0 0
421421 18.6056i 0.906779i −0.891312 0.453390i 0.850215π-0.850215\pi
0.891312 0.453390i 0.149785π-0.149785\pi
422422 0 0
423423 −21.5117 + 21.5117i −1.04594 + 1.04594i
424424 0 0
425425 0 0
426426 0 0
427427 −20.2272 + 20.2272i −0.978862 + 0.978862i
428428 0 0
429429 3.63331i 0.175418i
430430 0 0
431431 2.45708 1.01776i 0.118354 0.0490237i −0.322721 0.946494i 0.604597π-0.604597\pi
0.441074 + 0.897471i 0.354597π0.354597\pi
432432 0 0
433433 −10.6262 10.6262i −0.510664 0.510664i 0.404066 0.914730i 0.367597π-0.367597\pi
−0.914730 + 0.404066i 0.867597π0.867597\pi
434434 0 0
435435 4.00185 + 9.66131i 0.191874 + 0.463224i
436436 0 0
437437 1.41011 3.40432i 0.0674549 0.162851i
438438 0 0
439439 −34.3662 14.2350i −1.64021 0.679398i −0.643891 0.765117i 0.722681π-0.722681\pi
−0.996319 + 0.0857193i 0.972681π0.972681\pi
440440 0 0
441441 −27.4222 −1.30582
442442 0 0
443443 −17.2111 −0.817724 −0.408862 0.912596i 0.634074π-0.634074\pi
−0.408862 + 0.912596i 0.634074π0.634074\pi
444444 0 0
445445 10.2130 + 4.23034i 0.484140 + 0.200537i
446446 0 0
447447 10.4962 25.3401i 0.496453 1.19854i
448448 0 0
449449 9.10111 + 21.9720i 0.429508 + 1.03692i 0.979444 + 0.201717i 0.0646521π0.0646521\pi
−0.549936 + 0.835207i 0.685348π0.685348\pi
450450 0 0
451451 0.428189 + 0.428189i 0.0201627 + 0.0201627i
452452 0 0
453453 −13.8568 + 5.73968i −0.651050 + 0.269674i
454454 0 0
455455 12.0000i 0.562569i
456456 0 0
457457 25.8840 25.8840i 1.21080 1.21080i 0.240041 0.970763i 0.422839π-0.422839\pi
0.970763 0.240041i 0.0771610π-0.0771610\pi
458458 0 0
459459 0 0
460460 0 0
461461 20.6554 20.6554i 0.962016 0.962016i −0.0372881 0.999305i 0.511872π-0.511872\pi
0.999305 + 0.0372881i 0.0118719π0.0118719\pi
462462 0 0
463463 39.6333i 1.84192i −0.389662 0.920958i 0.627408π-0.627408\pi
0.389662 0.920958i 0.372592π-0.372592\pi
464464 0 0
465465 25.8917 10.7247i 1.20070 0.497346i
466466 0 0
467467 11.4826 + 11.4826i 0.531352 + 0.531352i 0.920975 0.389623i 0.127395π-0.127395\pi
−0.389623 + 0.920975i 0.627395π0.627395\pi
468468 0 0
469469 11.4794 + 27.7136i 0.530068 + 1.27970i
470470 0 0
471471 10.4962 25.3401i 0.483639 1.16761i
472472 0 0
473473 −1.34283 0.556218i −0.0617433 0.0255749i
474474 0 0
475475 1.81665 0.0833538
476476 0 0
477477 −39.6333 −1.81468
478478 0 0
479479 −16.0744 6.65821i −0.734456 0.304222i −0.0160742 0.999871i 0.505117π-0.505117\pi
−0.718382 + 0.695649i 0.755117π0.755117\pi
480480 0 0
481481 −4.23034 + 10.2130i −0.192887 + 0.465670i
482482 0 0
483483 −24.6966 59.6228i −1.12373 2.71293i
484484 0 0
485485 10.7559 + 10.7559i 0.488399 + 0.488399i
486486 0 0
487487 −22.6434 + 9.37922i −1.02607 + 0.425013i −0.831293 0.555834i 0.812399π-0.812399\pi
−0.194779 + 0.980847i 0.562399π0.562399\pi
488488 0 0
489489 19.8167i 0.896140i
490490 0 0
491491 6.94142 6.94142i 0.313262 0.313262i −0.532910 0.846172i 0.678902π-0.678902\pi
0.846172 + 0.532910i 0.178902π0.178902\pi
492492 0 0
493493 0 0
494494 0 0
495495 −3.25662 + 3.25662i −0.146374 + 0.146374i
496496 0 0
497497 13.3944i 0.600823i
498498 0 0
499499 −13.4612 + 5.57582i −0.602607 + 0.249608i −0.663064 0.748563i 0.730744π-0.730744\pi
0.0604568 + 0.998171i 0.480744π0.480744\pi
500500 0 0
501501 48.5507 + 48.5507i 2.16909 + 2.16909i
502502 0 0
503503 14.8904 + 35.9486i 0.663930 + 1.60287i 0.791591 + 0.611052i 0.209253π0.209253\pi
−0.127661 + 0.991818i 0.540747π0.540747\pi
504504 0 0
505505 −5.73968 + 13.8568i −0.255413 + 0.616620i
506506 0 0
507507 18.6875 + 7.74061i 0.829940 + 0.343772i
508508 0 0
509509 3.21110 0.142330 0.0711648 0.997465i 0.477328π-0.477328\pi
0.0711648 + 0.997465i 0.477328π0.477328\pi
510510 0 0
511511 −32.2389 −1.42616
512512 0 0
513513 8.39102 + 3.47567i 0.370472 + 0.153455i
514514 0 0
515515 −7.14980 + 17.2611i −0.315058 + 0.760617i
516516 0 0
517517 −0.655444 1.58238i −0.0288264 0.0695931i
518518 0 0
519519 48.2522 + 48.2522i 2.11803 + 2.11803i
520520 0 0
521521 16.9853 7.03555i 0.744140 0.308233i 0.0217921 0.999763i 0.493063π-0.493063\pi
0.722348 + 0.691530i 0.243063π0.243063\pi
522522 0 0
523523 12.0000i 0.524723i 0.964970 + 0.262362i 0.0845013π0.0845013\pi
−0.964970 + 0.262362i 0.915499π0.915499\pi
524524 0 0
525525 22.4978 22.4978i 0.981883 0.981883i
526526 0 0
527527 0 0
528528 0 0
529529 9.91912 9.91912i 0.431266 0.431266i
530530 0 0
531531 65.4500i 2.84029i
532532 0 0
533533 −3.40432 + 1.41011i −0.147457 + 0.0610788i
534534 0 0
535535 8.05709 + 8.05709i 0.348338 + 0.348338i
536536 0 0
537537 18.7284 + 45.2143i 0.808190 + 1.95114i
538538 0 0
539539 0.590809 1.42634i 0.0254480 0.0614368i
540540 0 0
541541 3.91969 + 1.62359i 0.168521 + 0.0698035i 0.465349 0.885127i 0.345929π-0.345929\pi
−0.296828 + 0.954931i 0.595929π0.595929\pi
542542 0 0
543543 −59.8722 −2.56936
544544 0 0
545545 12.4222 0.532109
546546 0 0
547547 15.0436 + 6.23127i 0.643218 + 0.266430i 0.680357 0.732880i 0.261825π-0.261825\pi
−0.0371393 + 0.999310i 0.511825π0.511825\pi
548548 0 0
549549 25.5655 61.7205i 1.09111 2.63417i
550550 0 0
551551 0.526174 + 1.27030i 0.0224158 + 0.0541165i
552552 0 0
553553 0.986024 + 0.986024i 0.0419300 + 0.0419300i
554554 0 0
555555 −18.0523 + 7.47752i −0.766279 + 0.317403i
556556 0 0
557557 21.3944i 0.906512i 0.891380 + 0.453256i 0.149738π0.149738\pi
−0.891380 + 0.453256i 0.850262π0.850262\pi
558558 0 0
559559 6.25394 6.25394i 0.264514 0.264514i
560560 0 0
561561 0 0
562562 0 0
563563 14.5703 14.5703i 0.614066 0.614066i −0.329937 0.944003i 0.607028π-0.607028\pi
0.944003 + 0.329937i 0.107028π0.107028\pi
564564 0 0
565565 19.2111i 0.808217i
566566 0 0
567567 78.3103 32.4372i 3.28872 1.36223i
568568 0 0
569569 −21.5117 21.5117i −0.901819 0.901819i 0.0937741 0.995593i 0.470107π-0.470107\pi
−0.995593 + 0.0937741i 0.970107π0.970107\pi
570570 0 0
571571 1.24625 + 3.00872i 0.0521541 + 0.125911i 0.947809 0.318838i 0.103293π-0.103293\pi
−0.895655 + 0.444749i 0.853293π0.853293\pi
572572 0 0
573573 −8.46069 + 20.4259i −0.353450 + 0.853304i
574574 0 0
575575 16.8655 + 6.98594i 0.703342 + 0.291334i
576576 0 0
577577 31.4500 1.30928 0.654640 0.755941i 0.272820π-0.272820\pi
0.654640 + 0.755941i 0.272820π0.272820\pi
578578 0 0
579579 37.8167 1.57161
580580 0 0
581581 53.6053 + 22.2041i 2.22392 + 0.921180i
582582 0 0
583583 0.853896 2.06149i 0.0353648 0.0853781i
584584 0 0
585585 −10.7247 25.8917i −0.443412 1.07049i
586586 0 0
587587 3.25662 + 3.25662i 0.134415 + 0.134415i 0.771113 0.636698i 0.219700π-0.219700\pi
−0.636698 + 0.771113i 0.719700π0.719700\pi
588588 0 0
589589 3.40432 1.41011i 0.140272 0.0581027i
590590 0 0
591591 81.0833i 3.33532i
592592 0 0
593593 −1.11567 + 1.11567i −0.0458151 + 0.0458151i −0.729643 0.683828i 0.760314π-0.760314\pi
0.683828 + 0.729643i 0.260314π0.260314\pi
594594 0 0
595595 0 0
596596 0 0
597597 −32.9551 + 32.9551i −1.34876 + 1.34876i
598598 0 0
599599 26.0555i 1.06460i 0.846556 + 0.532300i 0.178672π0.178672\pi
−0.846556 + 0.532300i 0.821328π0.821328\pi
600600 0 0
601601 5.50207 2.27903i 0.224434 0.0929637i −0.267633 0.963521i 0.586241π-0.586241\pi
0.492067 + 0.870557i 0.336241π0.336241\pi
602602 0 0
603603 −49.5367 49.5367i −2.01729 2.01729i
604604 0 0
605605 5.85393 + 14.1326i 0.237996 + 0.574573i
606606 0 0
607607 5.14887 12.4305i 0.208986 0.504538i −0.784278 0.620410i 0.786966π-0.786966\pi
0.993264 + 0.115872i 0.0369663π0.0369663\pi
608608 0 0
609609 22.2478 + 9.21536i 0.901528 + 0.373425i
610610 0 0
611611 10.4222 0.421637
612612 0 0
613613 40.4222 1.63264 0.816319 0.577602i 0.196011π-0.196011\pi
0.816319 + 0.577602i 0.196011π0.196011\pi
614614 0 0
615615 −6.01744 2.49251i −0.242647 0.100508i
616616 0 0
617617 −0.868918 + 2.09775i −0.0349813 + 0.0844524i −0.940405 0.340057i 0.889554π-0.889554\pi
0.905423 + 0.424510i 0.139554π0.139554\pi
618618 0 0
619619 −7.83983 18.9270i −0.315109 0.760742i −0.999500 0.0316257i 0.989932π-0.989932\pi
0.684390 0.729116i 0.260068π-0.260068\pi
620620 0 0
621621 64.5352 + 64.5352i 2.58971 + 2.58971i
622622 0 0
623623 23.5181 9.74153i 0.942234 0.390286i
624624 0 0
625625 1.00000i 0.0400000i
626626 0 0
627627 −0.597088 + 0.597088i −0.0238454 + 0.0238454i
628628 0 0
629629 0 0
630630 0 0
631631 17.1395 17.1395i 0.682311 0.682311i −0.278209 0.960520i 0.589741π-0.589741\pi
0.960520 + 0.278209i 0.0897409π0.0897409\pi
632632 0 0
633633 71.4500i 2.83988i
634634 0 0
635635 −0.791191 + 0.327722i −0.0313975 + 0.0130053i
636636 0 0
637637 6.64288 + 6.64288i 0.263200 + 0.263200i
638638 0 0
639639 −11.9709 28.9004i −0.473563 1.14328i
640640 0 0
641641 16.6779 40.2639i 0.658736 1.59033i −0.141023 0.990006i 0.545039π-0.545039\pi
0.799758 0.600322i 0.204961π-0.204961\pi
642642 0 0
643643 5.38229 + 2.22942i 0.212257 + 0.0879197i 0.486279 0.873804i 0.338354π-0.338354\pi
−0.274022 + 0.961724i 0.588354π0.588354\pi
644644 0 0
645645 15.6333 0.615561
646646 0 0
647647 −17.2111 −0.676638 −0.338319 0.941031i 0.609858π-0.609858\pi
−0.338319 + 0.941031i 0.609858π0.609858\pi
648648 0 0
649649 3.40432 + 1.41011i 0.133631 + 0.0553518i
650650 0 0
651651 24.6966 59.6228i 0.967935 2.33680i
652652 0 0
653653 −13.4307 32.4245i −0.525583 1.26887i −0.934391 0.356249i 0.884055π-0.884055\pi
0.408808 0.912620i 0.365945π-0.365945\pi
654654 0 0
655655 8.91347 + 8.91347i 0.348278 + 0.348278i
656656 0 0
657657 69.5599 28.8127i 2.71379 1.12409i
658658 0 0
659659 32.0000i 1.24654i 0.782006 + 0.623272i 0.214197π0.214197\pi
−0.782006 + 0.623272i 0.785803π0.785803\pi
660660 0 0
661661 0.856379 0.856379i 0.0333093 0.0333093i −0.690256 0.723565i 0.742502π-0.742502\pi
0.723565 + 0.690256i 0.242502π0.242502\pi
662662 0 0
663663 0 0
664664 0 0
665665 −1.97205 + 1.97205i −0.0764728 + 0.0764728i
666666 0 0
667667 13.8167i 0.534983i
668668 0 0
669669 −53.6053 + 22.2041i −2.07250 + 0.858459i
670670 0 0
671671 2.65953 + 2.65953i 0.102670 + 0.102670i
672672 0 0
673673 3.03370 + 7.32401i 0.116941 + 0.282320i 0.971502 0.237030i 0.0761741π-0.0761741\pi
−0.854562 + 0.519350i 0.826174π0.826174\pi
674674 0 0
675675 −17.2190 + 41.5705i −0.662762 + 1.60005i
676676 0 0
677677 −20.9413 8.67416i −0.804838 0.333375i −0.0579459 0.998320i 0.518455π-0.518455\pi
−0.746893 + 0.664945i 0.768455π0.768455\pi
678678 0 0
679679 35.0278 1.34424
680680 0 0
681681 1.39445 0.0534354
682682 0 0
683683 0.947233 + 0.392357i 0.0362449 + 0.0150131i 0.400732 0.916195i 0.368756π-0.368756\pi
−0.364487 + 0.931208i 0.618756π0.618756\pi
684684 0 0
685685 −1.41011 + 3.40432i −0.0538777 + 0.130072i
686686 0 0
687687 5.73968 + 13.8568i 0.218983 + 0.528671i
688688 0 0
689689 9.60095 + 9.60095i 0.365767 + 0.365767i
690690 0 0
691691 −7.20423 + 2.98409i −0.274062 + 0.113520i −0.515482 0.856901i 0.672387π-0.672387\pi
0.241420 + 0.970421i 0.422387π0.422387\pi
692692 0 0
693693 10.6056i 0.402872i
694694 0 0
695695 −0.428189 + 0.428189i −0.0162422 + 0.0162422i
696696 0 0
697697 0 0
698698 0 0
699699 18.2551 18.2551i 0.690472 0.690472i
700700 0 0
701701 7.81665i 0.295231i −0.989045 0.147615i 0.952840π-0.952840\pi
0.989045 0.147615i 0.0471598π-0.0471598\pi
702702 0 0
703703 −2.37357 + 0.983166i −0.0895210 + 0.0370808i
704704 0 0
705705 13.0265 + 13.0265i 0.490605 + 0.490605i
706706 0 0
707707 13.2172 + 31.9091i 0.497084 + 1.20007i
708708 0 0
709709 7.79022 18.8073i 0.292568 0.706321i −0.707432 0.706781i 0.750146π-0.750146\pi
1.00000 0.000460118i 0.000146460π0.000146460\pi
710710 0 0
711711 −3.00872 1.24625i −0.112836 0.0467381i
712712 0 0
713713 37.0278 1.38670
714714 0 0
715715 1.57779 0.0590062
716716 0 0
717717 −44.4957 18.4307i −1.66172 0.688308i
718718 0 0
719719 2.55714 6.17348i 0.0953653 0.230232i −0.868997 0.494817i 0.835235π-0.835235\pi
0.964362 + 0.264585i 0.0852350π0.0852350\pi
720720 0 0
721721 16.4644 + 39.7485i 0.613166 + 1.48031i
722722 0 0
723723 −29.3095 29.3095i −1.09003 1.09003i
724724 0 0
725725 −6.29326 + 2.60675i −0.233726 + 0.0968124i
726726 0 0
727727 6.42221i 0.238186i 0.992883 + 0.119093i 0.0379987π0.0379987\pi
−0.992883 + 0.119093i 0.962001π0.962001\pi
728728 0 0
729729 −36.3610 + 36.3610i −1.34670 + 1.34670i
730730 0 0
731731 0 0
732732 0 0
733733 −32.5662 + 32.5662i −1.20286 + 1.20286i −0.229566 + 0.973293i 0.573731π0.573731\pi
−0.973293 + 0.229566i 0.926269π0.926269\pi
734734 0 0
735735 16.6056i 0.612505i
736736 0 0
737737 3.64387 1.50934i 0.134224 0.0555973i
738738 0 0
739739 24.5091 + 24.5091i 0.901581 + 0.901581i 0.995573 0.0939921i 0.0299628π-0.0299628\pi
−0.0939921 + 0.995573i 0.529963π0.529963\pi
740740 0 0
741741 −1.96633 4.74715i −0.0722350 0.174391i
742742 0 0
743743 7.96910 19.2391i 0.292358 0.705815i −0.707642 0.706571i 0.750241π-0.750241\pi
1.00000 0.000756791i 0.000240894π0.000240894\pi
744744 0 0
745745 −11.0041 4.55806i −0.403161 0.166995i
746746 0 0
747747 −135.505 −4.95789
748748 0 0
749749 26.2389 0.958747
750750 0 0
751751 −2.21753 0.918531i −0.0809188 0.0335177i 0.341857 0.939752i 0.388944π-0.388944\pi
−0.422776 + 0.906234i 0.638944π0.638944\pi
752752 0 0
753753 −14.9550 + 36.1047i −0.544992 + 1.31573i
754754 0 0
755755 2.49251 + 6.01744i 0.0907116 + 0.218997i
756756 0 0
757757 −27.5968 27.5968i −1.00302 1.00302i −0.999995 0.00302702i 0.999036π-0.999036\pi
−0.00302702 0.999995i 0.500964π-0.500964\pi
758758 0 0
759759 −7.83938 + 3.24718i −0.284551 + 0.117865i
760760 0 0
761761 31.4500i 1.14006i 0.821624 + 0.570030i 0.193068π0.193068\pi
−0.821624 + 0.570030i 0.806932π0.806932\pi
762762 0 0
763763 20.2272 20.2272i 0.732273 0.732273i
764764 0 0
765765 0 0
766766 0 0
767767 −15.8549 + 15.8549i −0.572487 + 0.572487i
768768 0 0
769769 18.6056i 0.670933i −0.942052 0.335467i 0.891106π-0.891106\pi
0.942052 0.335467i 0.108894π-0.108894\pi
770770 0 0
771771 58.3525 24.1704i 2.10151 0.870475i
772772 0 0
773773 −20.2272 20.2272i −0.727521 0.727521i 0.242604 0.970125i 0.421998π-0.421998\pi
−0.970125 + 0.242604i 0.921998π0.921998\pi
774774 0 0
775775 6.98594 + 16.8655i 0.250942 + 0.605828i
776776 0 0
777777 −17.2190 + 41.5705i −0.617730 + 1.49133i
778778 0 0
779779 −0.791191 0.327722i −0.0283474 0.0117419i
780780 0 0
781781 1.76114 0.0630186
782782 0 0
783783 −34.0555 −1.21704
784784 0 0
785785 −11.0041 4.55806i −0.392755 0.162684i
786786 0 0
787787 −7.96910 + 19.2391i −0.284068 + 0.685800i −0.999923 0.0124489i 0.996037π-0.996037\pi
0.715855 + 0.698249i 0.246037π0.246037\pi
788788 0 0
789789 28.6984 + 69.2841i 1.02169 + 2.46658i
790790 0 0
791791 −31.2816 31.2816i −1.11225 1.11225i
792792 0 0
793793 −21.1446 + 8.75836i −0.750865 + 0.311019i
794794 0 0
795795 24.0000i 0.851192i
796796 0 0
797797 −2.56914 + 2.56914i −0.0910035 + 0.0910035i −0.751143 0.660140i 0.770497π-0.770497\pi
0.660140 + 0.751143i 0.270497π0.270497\pi
798798 0 0
799799 0 0
800800 0 0
801801 −42.0375 + 42.0375i −1.48532 + 1.48532i
802802 0 0
803803 4.23886i 0.149586i
804804 0 0
805805 −25.8917 + 10.7247i −0.912563 + 0.377996i
806806 0 0
807807 56.7374 + 56.7374i 1.99725 + 1.99725i
808808 0 0
809809 −11.2659 27.1983i −0.396088 0.956240i −0.988585 0.150667i 0.951858π-0.951858\pi
0.592497 0.805573i 0.298142π-0.298142\pi
810810 0 0
811811 5.80432 14.0129i 0.203817 0.492058i −0.788610 0.614894i 0.789199π-0.789199\pi
0.992427 + 0.122836i 0.0391988π0.0391988\pi
812812 0 0
813813 −3.64387 1.50934i −0.127796 0.0529349i
814814 0 0
815815 −8.60555 −0.301439
816816 0 0
817817 2.05551 0.0719133
818818 0 0
819819 −59.6228 24.6966i −2.08339 0.862968i
820820 0 0
821821 −6.93632 + 16.7458i −0.242079 + 0.584431i −0.997489 0.0708216i 0.977438π-0.977438\pi
0.755410 + 0.655253i 0.227438π0.227438\pi
822822 0 0
823823 −6.98594 16.8655i −0.243514 0.587896i 0.754113 0.656745i 0.228067π-0.228067\pi
−0.997627 + 0.0688493i 0.978067π0.978067\pi
824824 0 0
825825 −2.95807 2.95807i −0.102987 0.102987i
826826 0 0
827827 8.23497 3.41104i 0.286358 0.118613i −0.234881 0.972024i 0.575470π-0.575470\pi
0.521239 + 0.853411i 0.325470π0.325470\pi
828828 0 0
829829 18.8444i 0.654493i 0.944939 + 0.327247i 0.106121π0.106121\pi
−0.944939 + 0.327247i 0.893879π0.893879\pi
830830 0 0
831831 −11.7419 + 11.7419i −0.407322 + 0.407322i
832832 0 0
833833 0 0
834834 0 0
835835 21.0836 21.0836i 0.729627 0.729627i
836836 0 0
837837 91.2666i 3.15464i
838838 0 0
839839 19.4787 8.06833i 0.672478 0.278550i −0.0202004 0.999796i 0.506430π-0.506430\pi
0.692679 + 0.721246i 0.256430π0.256430\pi
840840 0 0
841841 16.8605 + 16.8605i 0.581398 + 0.581398i
842842 0 0
843843 −22.9587 55.4273i −0.790741 1.90902i
844844 0 0
845845 3.36142 8.11520i 0.115637 0.279171i
846846 0 0
847847 32.5443 + 13.4803i 1.11824 + 0.463188i
848848 0 0
849849 9.76114 0.335001
850850 0 0
851851 −25.8167 −0.884983
852852 0 0
853853 −38.4420 15.9232i −1.31623 0.545199i −0.389532 0.921013i 0.627363π-0.627363\pi
−0.926695 + 0.375813i 0.877363π0.877363\pi
854854 0 0
855855 2.49251 6.01744i 0.0852419 0.205792i
856856 0 0
857857 10.0843 + 24.3456i 0.344472 + 0.831630i 0.997252 + 0.0740819i 0.0236026π0.0236026\pi
−0.652780 + 0.757548i 0.726397π0.726397\pi
858858 0 0
859859 −1.28457 1.28457i −0.0438289 0.0438289i 0.684853 0.728682i 0.259867π-0.259867\pi
−0.728682 + 0.684853i 0.759867π0.759867\pi
860860 0 0
861861 −13.8568 + 5.73968i −0.472239 + 0.195608i
862862 0 0
863863 52.4777i 1.78636i 0.449697 + 0.893181i 0.351532π0.351532\pi
−0.449697 + 0.893181i 0.648468π0.648468\pi
864864 0 0
865865 20.9539 20.9539i 0.712454 0.712454i
866866 0 0
867867 0 0
868868 0 0
869869 0.129645 0.129645i 0.00439792 0.00439792i
870870 0 0
871871 24.0000i 0.813209i
872872 0 0
873873 −75.5774 + 31.3052i −2.55791 + 1.05952i
874874 0 0
875875 −26.0529 26.0529i −0.880750 0.880750i
876876 0 0
877877 0.968144 + 2.33731i 0.0326919 + 0.0789253i 0.939382 0.342872i 0.111400π-0.111400\pi
−0.906690 + 0.421797i 0.861400π0.861400\pi
878878 0 0
879879 26.9606 65.0886i 0.909358 2.19538i
880880 0 0
881881 −31.6333 13.1030i −1.06575 0.441450i −0.220264 0.975440i 0.570692π-0.570692\pi
−0.845490 + 0.533991i 0.820692π0.820692\pi
882882 0 0
883883 −25.5778 −0.860761 −0.430381 0.902647i 0.641621π-0.641621\pi
−0.430381 + 0.902647i 0.641621π0.641621\pi
884884 0 0
885885 −39.6333 −1.33226
886886 0 0
887887 15.2832 + 6.33049i 0.513158 + 0.212557i 0.624209 0.781258i 0.285421π-0.285421\pi
−0.111050 + 0.993815i 0.535421π0.535421\pi
888888 0 0
889889 −0.754670 + 1.82194i −0.0253108 + 0.0611057i
890890 0 0
891891 −4.26493 10.2965i −0.142881 0.344944i
892892 0 0
893893 1.71276 + 1.71276i 0.0573152 + 0.0573152i
894894 0 0
895895 19.6347 8.13296i 0.656316 0.271855i
896896 0 0
897897 51.6333i 1.72399i
898898 0 0
899899 −9.76985 + 9.76985i −0.325843 + 0.325843i
900900 0 0
901901 0 0
902902 0 0
903903 25.4558 25.4558i 0.847117 0.847117i
904904 0 0
905905 26.0000i 0.864269i
906906 0 0
907907 −32.0652 + 13.2818i −1.06471 + 0.441016i −0.845120 0.534577i 0.820471π-0.820471\pi
−0.219587 + 0.975593i 0.570471π0.570471\pi
908908 0 0
909909 −57.0360 57.0360i −1.89176 1.89176i
910910 0 0
911911 2.55714 + 6.17348i 0.0847219 + 0.204537i 0.960563 0.278063i 0.0896925π-0.0896925\pi
−0.875841 + 0.482600i 0.839693π0.839693\pi
912912 0 0
913913 2.91945 7.04819i 0.0966198 0.233261i
914914 0 0
915915 −37.3750 15.4812i −1.23558 0.511793i
916916 0 0
917917 29.0278 0.958581
918918 0 0
919919 40.8444 1.34733 0.673666 0.739036i 0.264718π-0.264718\pi
0.673666 + 0.739036i 0.264718π0.264718\pi
920920 0 0
921921 63.8183 + 26.4344i 2.10288 + 0.871043i
922922 0 0
923923 −4.10107 + 9.90087i −0.134988 + 0.325891i
924924 0 0
925925 −4.87076 11.7591i −0.160150 0.386636i
926926 0 0
927927 −71.0485 71.0485i −2.33354 2.33354i
928928 0 0
929929 1.30656 0.541196i 0.0428669 0.0177561i −0.361147 0.932509i 0.617615π-0.617615\pi
0.404014 + 0.914753i 0.367615π0.367615\pi
930930 0 0
931931 2.18335i 0.0715563i
932932 0 0
933933 −61.5772 + 61.5772i −2.01595 + 2.01595i
934934 0 0
935935 0 0
936936 0 0
937937 4.54118 4.54118i 0.148354 0.148354i −0.629028 0.777382i 0.716547π-0.716547\pi
0.777382 + 0.629028i 0.216547π0.216547\pi
938938 0 0
939939 28.6056i 0.933507i
940940 0 0
941941 20.9413 8.67416i 0.682666 0.282770i −0.0142749 0.999898i 0.504544π-0.504544\pi
0.696941 + 0.717129i 0.254544π0.254544\pi
942942 0 0
943943 −6.08504 6.08504i −0.198156 0.198156i
944944 0 0
945945 −26.4344 63.8183i −0.859911 2.07601i
946946 0 0
947947 −5.01960 + 12.1184i −0.163115 + 0.393795i −0.984212 0.176994i 0.943363π-0.943363\pi
0.821097 + 0.570789i 0.193363π0.193363\pi
948948 0 0
949949 −23.8302 9.87080i −0.773562 0.320420i
950950 0 0
951951 90.2944 2.92800
952952 0 0
953953 50.2389 1.62740 0.813698 0.581288i 0.197451π-0.197451\pi
0.813698 + 0.581288i 0.197451π0.197451\pi
954954 0 0
955955 8.87012 + 3.67412i 0.287030 + 0.118892i
956956 0 0
957957 1.21166 2.92521i 0.0391675 0.0945586i
958958 0 0
959959 3.24718 + 7.83938i 0.104857 + 0.253147i
960960 0 0
961961 4.26227 + 4.26227i 0.137492 + 0.137492i
962962 0 0
963963 −56.6141 + 23.4503i −1.82436 + 0.755676i
964964 0 0
965965 16.4222i 0.528649i
966966 0 0
967967 −15.4267 + 15.4267i −0.496089 + 0.496089i −0.910218 0.414129i 0.864086π-0.864086\pi
0.414129 + 0.910218i 0.364086π0.364086\pi
968968 0 0
969969 0 0
970970 0 0
971971 38.9105 38.9105i 1.24870 1.24870i 0.292402 0.956296i 0.405546π-0.405546\pi
0.956296 0.292402i 0.0944545π-0.0944545\pi
972972 0 0
973973 1.39445i 0.0447040i
974974 0 0
975975 23.5181 9.74153i 0.753183 0.311979i
976976 0 0
977977 11.9108 + 11.9108i 0.381060 + 0.381060i 0.871484 0.490424i 0.163158π-0.163158\pi
−0.490424 + 0.871484i 0.663158π0.663158\pi
978978 0 0
979979 −1.28084 3.09223i −0.0409360 0.0988282i
980980 0 0
981981 −25.5655 + 61.7205i −0.816243 + 1.97059i
982982 0 0
983983 10.6085 + 4.39420i 0.338360 + 0.140153i 0.545393 0.838181i 0.316381π-0.316381\pi
−0.207033 + 0.978334i 0.566381π0.566381\pi
984984 0 0
985985 −35.2111 −1.12192
986986 0 0
987987 42.4222 1.35031
988988 0 0
989989 19.0831 + 7.90447i 0.606806 + 0.251347i
990990 0 0
991991 12.7256 30.7224i 0.404243 0.975928i −0.582381 0.812916i 0.697879π-0.697879\pi
0.986624 0.163012i 0.0521210π-0.0521210\pi
992992 0 0
993993 −4.23034 10.2130i −0.134246 0.324098i
994994 0 0
995995 14.3110 + 14.3110i 0.453690 + 0.453690i
996996 0 0
997997 51.2680 21.2359i 1.62368 0.672548i 0.629173 0.777265i 0.283394π-0.283394\pi
0.994502 + 0.104717i 0.0333937π0.0333937\pi
998998 0 0
999999 63.6333i 2.01327i
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 1156.2.h.e.757.4 16
17.2 even 8 inner 1156.2.h.e.733.4 16
17.3 odd 16 1156.2.e.c.829.2 4
17.4 even 4 inner 1156.2.h.e.977.4 16
17.5 odd 16 68.2.e.a.21.1 yes 4
17.6 odd 16 1156.2.a.h.1.4 4
17.7 odd 16 1156.2.b.a.577.1 4
17.8 even 8 inner 1156.2.h.e.1001.1 16
17.9 even 8 inner 1156.2.h.e.1001.4 16
17.10 odd 16 1156.2.b.a.577.4 4
17.11 odd 16 1156.2.a.h.1.1 4
17.12 odd 16 1156.2.e.c.905.2 4
17.13 even 4 inner 1156.2.h.e.977.1 16
17.14 odd 16 68.2.e.a.13.1 4
17.15 even 8 inner 1156.2.h.e.733.1 16
17.16 even 2 inner 1156.2.h.e.757.1 16
51.5 even 16 612.2.k.e.361.2 4
51.14 even 16 612.2.k.e.217.2 4
68.11 even 16 4624.2.a.bq.1.4 4
68.23 even 16 4624.2.a.bq.1.1 4
68.31 even 16 272.2.o.g.81.2 4
68.39 even 16 272.2.o.g.225.2 4
85.14 odd 16 1700.2.o.c.1101.2 4
85.22 even 16 1700.2.m.b.1449.2 4
85.39 odd 16 1700.2.o.c.701.2 4
85.48 even 16 1700.2.m.b.149.2 4
85.73 even 16 1700.2.m.a.1449.1 4
85.82 even 16 1700.2.m.a.149.1 4
136.5 odd 16 1088.2.o.t.769.2 4
136.99 even 16 1088.2.o.s.897.1 4
136.107 even 16 1088.2.o.s.769.1 4
136.133 odd 16 1088.2.o.t.897.2 4
204.107 odd 16 2448.2.be.u.1585.1 4
204.167 odd 16 2448.2.be.u.1441.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
68.2.e.a.13.1 4 17.14 odd 16
68.2.e.a.21.1 yes 4 17.5 odd 16
272.2.o.g.81.2 4 68.31 even 16
272.2.o.g.225.2 4 68.39 even 16
612.2.k.e.217.2 4 51.14 even 16
612.2.k.e.361.2 4 51.5 even 16
1088.2.o.s.769.1 4 136.107 even 16
1088.2.o.s.897.1 4 136.99 even 16
1088.2.o.t.769.2 4 136.5 odd 16
1088.2.o.t.897.2 4 136.133 odd 16
1156.2.a.h.1.1 4 17.11 odd 16
1156.2.a.h.1.4 4 17.6 odd 16
1156.2.b.a.577.1 4 17.7 odd 16
1156.2.b.a.577.4 4 17.10 odd 16
1156.2.e.c.829.2 4 17.3 odd 16
1156.2.e.c.905.2 4 17.12 odd 16
1156.2.h.e.733.1 16 17.15 even 8 inner
1156.2.h.e.733.4 16 17.2 even 8 inner
1156.2.h.e.757.1 16 17.16 even 2 inner
1156.2.h.e.757.4 16 1.1 even 1 trivial
1156.2.h.e.977.1 16 17.13 even 4 inner
1156.2.h.e.977.4 16 17.4 even 4 inner
1156.2.h.e.1001.1 16 17.8 even 8 inner
1156.2.h.e.1001.4 16 17.9 even 8 inner
1700.2.m.a.149.1 4 85.82 even 16
1700.2.m.a.1449.1 4 85.73 even 16
1700.2.m.b.149.2 4 85.48 even 16
1700.2.m.b.1449.2 4 85.22 even 16
1700.2.o.c.701.2 4 85.39 odd 16
1700.2.o.c.1101.2 4 85.14 odd 16
2448.2.be.u.1441.1 4 204.167 odd 16
2448.2.be.u.1585.1 4 204.107 odd 16
4624.2.a.bq.1.1 4 68.23 even 16
4624.2.a.bq.1.4 4 68.11 even 16