Properties

Label 2420.3.f.c.241.16
Level 24202420
Weight 33
Character 2420.241
Analytic conductor 65.94065.940
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2420,3,Mod(241,2420)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2420, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2420.241"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 2420=225112 2420 = 2^{2} \cdot 5 \cdot 11^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 2420.f (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 65.940223975265.9402239752
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x162x15+5x14+36x13+396x12+1918x11+8573x10+28624x9++121 x^{16} - 2 x^{15} + 5 x^{14} + 36 x^{13} + 396 x^{12} + 1918 x^{11} + 8573 x^{10} + 28624 x^{9} + \cdots + 121 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 285112 2^{8}\cdot 5\cdot 11^{2}
Twist minimal: no (minimal twist has level 220)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 241.16
Root 0.0370387+0.0269102i-0.0370387 + 0.0269102i of defining polynomial
Character χ\chi == 2420.241
Dual form 2420.3.f.c.241.15

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+5.15878q3+2.23607q5+10.1572iq7+17.6130q93.34439iq13+11.5354q15+20.1864iq175.53109iq19+52.3990iq21+34.6484q23+5.00000q25+44.4328q27+44.8670iq2943.3440q31+22.7123iq3559.4002q3717.2530iq39+33.0912iq4165.3574iq43+39.3839q45+68.8573q4754.1697q49+104.137iq513.21911q5328.5337iq57+66.0207q59+47.3889iq61+178.900iq637.47829iq6531.6113q67+178.744q69+3.76017q7122.4126iq73+25.7939q7578.2156iq79+70.7017q8122.1936iq83+45.1381iq85+231.459iq87+68.2014q89+33.9698q91223.602q9312.3679iq95+61.4375q97+O(q100)q+5.15878 q^{3} +2.23607 q^{5} +10.1572i q^{7} +17.6130 q^{9} -3.34439i q^{13} +11.5354 q^{15} +20.1864i q^{17} -5.53109i q^{19} +52.3990i q^{21} +34.6484 q^{23} +5.00000 q^{25} +44.4328 q^{27} +44.8670i q^{29} -43.3440 q^{31} +22.7123i q^{35} -59.4002 q^{37} -17.2530i q^{39} +33.0912i q^{41} -65.3574i q^{43} +39.3839 q^{45} +68.8573 q^{47} -54.1697 q^{49} +104.137i q^{51} -3.21911 q^{53} -28.5337i q^{57} +66.0207 q^{59} +47.3889i q^{61} +178.900i q^{63} -7.47829i q^{65} -31.6113 q^{67} +178.744 q^{69} +3.76017 q^{71} -22.4126i q^{73} +25.7939 q^{75} -78.2156i q^{79} +70.7017 q^{81} -22.1936i q^{83} +45.1381i q^{85} +231.459i q^{87} +68.2014 q^{89} +33.9698 q^{91} -223.602 q^{93} -12.3679i q^{95} +61.4375 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+14q3+46q9+10q15+72q23+80q25+50q27+50q3116q37+30q45+232q47188q49+132q53+78q59+152q67+748q69+230q71+70q75++854q97+O(q100) 16 q + 14 q^{3} + 46 q^{9} + 10 q^{15} + 72 q^{23} + 80 q^{25} + 50 q^{27} + 50 q^{31} - 16 q^{37} + 30 q^{45} + 232 q^{47} - 188 q^{49} + 132 q^{53} + 78 q^{59} + 152 q^{67} + 748 q^{69} + 230 q^{71} + 70 q^{75}+ \cdots + 854 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2420Z)×\left(\mathbb{Z}/2420\mathbb{Z}\right)^\times.

nn 12111211 19371937 23012301
χ(n)\chi(n) 11 11 1-1

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 5.15878 1.71959 0.859797 0.510636i 0.170590π-0.170590\pi
0.859797 + 0.510636i 0.170590π0.170590\pi
44 0 0
55 2.23607 0.447214
66 0 0
77 10.1572i 1.45104i 0.688204 + 0.725518i 0.258400π0.258400\pi
−0.688204 + 0.725518i 0.741600π0.741600\pi
88 0 0
99 17.6130 1.95700
1010 0 0
1111 0 0
1212 0 0
1313 − 3.34439i − 0.257261i −0.991693 0.128630i 0.958942π-0.958942\pi
0.991693 0.128630i 0.0410581π-0.0410581\pi
1414 0 0
1515 11.5354 0.769026
1616 0 0
1717 20.1864i 1.18743i 0.804674 + 0.593717i 0.202340π0.202340\pi
−0.804674 + 0.593717i 0.797660π0.797660\pi
1818 0 0
1919 − 5.53109i − 0.291110i −0.989350 0.145555i 0.953503π-0.953503\pi
0.989350 0.145555i 0.0464968π-0.0464968\pi
2020 0 0
2121 52.3990i 2.49519i
2222 0 0
2323 34.6484 1.50645 0.753227 0.657761i 0.228496π-0.228496\pi
0.753227 + 0.657761i 0.228496π0.228496\pi
2424 0 0
2525 5.00000 0.200000
2626 0 0
2727 44.4328 1.64566
2828 0 0
2929 44.8670i 1.54714i 0.633712 + 0.773569i 0.281530π0.281530\pi
−0.633712 + 0.773569i 0.718470π0.718470\pi
3030 0 0
3131 −43.3440 −1.39819 −0.699097 0.715027i 0.746415π-0.746415\pi
−0.699097 + 0.715027i 0.746415π0.746415\pi
3232 0 0
3333 0 0
3434 0 0
3535 22.7123i 0.648923i
3636 0 0
3737 −59.4002 −1.60541 −0.802706 0.596375i 0.796607π-0.796607\pi
−0.802706 + 0.596375i 0.796607π0.796607\pi
3838 0 0
3939 − 17.2530i − 0.442384i
4040 0 0
4141 33.0912i 0.807102i 0.914957 + 0.403551i 0.132224π0.132224\pi
−0.914957 + 0.403551i 0.867776π0.867776\pi
4242 0 0
4343 − 65.3574i − 1.51994i −0.649958 0.759970i 0.725213π-0.725213\pi
0.649958 0.759970i 0.274787π-0.274787\pi
4444 0 0
4545 39.3839 0.875199
4646 0 0
4747 68.8573 1.46505 0.732524 0.680741i 0.238342π-0.238342\pi
0.732524 + 0.680741i 0.238342π0.238342\pi
4848 0 0
4949 −54.1697 −1.10550
5050 0 0
5151 104.137i 2.04190i
5252 0 0
5353 −3.21911 −0.0607379 −0.0303689 0.999539i 0.509668π-0.509668\pi
−0.0303689 + 0.999539i 0.509668π0.509668\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 28.5337i − 0.500591i
5858 0 0
5959 66.0207 1.11899 0.559497 0.828832i 0.310994π-0.310994\pi
0.559497 + 0.828832i 0.310994π0.310994\pi
6060 0 0
6161 47.3889i 0.776867i 0.921477 + 0.388434i 0.126984π0.126984\pi
−0.921477 + 0.388434i 0.873016π0.873016\pi
6262 0 0
6363 178.900i 2.83968i
6464 0 0
6565 − 7.47829i − 0.115051i
6666 0 0
6767 −31.6113 −0.471810 −0.235905 0.971776i 0.575805π-0.575805\pi
−0.235905 + 0.971776i 0.575805π0.575805\pi
6868 0 0
6969 178.744 2.59049
7070 0 0
7171 3.76017 0.0529601 0.0264801 0.999649i 0.491570π-0.491570\pi
0.0264801 + 0.999649i 0.491570π0.491570\pi
7272 0 0
7373 − 22.4126i − 0.307022i −0.988147 0.153511i 0.950942π-0.950942\pi
0.988147 0.153511i 0.0490580π-0.0490580\pi
7474 0 0
7575 25.7939 0.343919
7676 0 0
7777 0 0
7878 0 0
7979 − 78.2156i − 0.990071i −0.868873 0.495036i 0.835155π-0.835155\pi
0.868873 0.495036i 0.164845π-0.164845\pi
8080 0 0
8181 70.7017 0.872860
8282 0 0
8383 − 22.1936i − 0.267392i −0.991022 0.133696i 0.957315π-0.957315\pi
0.991022 0.133696i 0.0426846π-0.0426846\pi
8484 0 0
8585 45.1381i 0.531037i
8686 0 0
8787 231.459i 2.66045i
8888 0 0
8989 68.2014 0.766308 0.383154 0.923684i 0.374838π-0.374838\pi
0.383154 + 0.923684i 0.374838π0.374838\pi
9090 0 0
9191 33.9698 0.373295
9292 0 0
9393 −223.602 −2.40433
9494 0 0
9595 − 12.3679i − 0.130188i
9696 0 0
9797 61.4375 0.633376 0.316688 0.948530i 0.397429π-0.397429\pi
0.316688 + 0.948530i 0.397429π0.397429\pi
9898 0 0
9999 0 0
100100 0 0
101101 − 7.47252i − 0.0739854i −0.999316 0.0369927i 0.988222π-0.988222\pi
0.999316 0.0369927i 0.0117778π-0.0117778\pi
102102 0 0
103103 −82.6449 −0.802378 −0.401189 0.915995i 0.631403π-0.631403\pi
−0.401189 + 0.915995i 0.631403π0.631403\pi
104104 0 0
105105 117.168i 1.11588i
106106 0 0
107107 158.077i 1.47735i 0.674059 + 0.738677i 0.264549π0.264549\pi
−0.674059 + 0.738677i 0.735451π0.735451\pi
108108 0 0
109109 − 79.1292i − 0.725956i −0.931798 0.362978i 0.881760π-0.881760\pi
0.931798 0.362978i 0.118240π-0.118240\pi
110110 0 0
111111 −306.433 −2.76066
112112 0 0
113113 28.2244 0.249774 0.124887 0.992171i 0.460143π-0.460143\pi
0.124887 + 0.992171i 0.460143π0.460143\pi
114114 0 0
115115 77.4763 0.673707
116116 0 0
117117 − 58.9049i − 0.503461i
118118 0 0
119119 −205.038 −1.72301
120120 0 0
121121 0 0
122122 0 0
123123 170.710i 1.38789i
124124 0 0
125125 11.1803 0.0894427
126126 0 0
127127 92.9080i 0.731559i 0.930702 + 0.365779i 0.119198π0.119198\pi
−0.930702 + 0.365779i 0.880802π0.880802\pi
128128 0 0
129129 − 337.165i − 2.61368i
130130 0 0
131131 − 156.944i − 1.19804i −0.800733 0.599021i 0.795556π-0.795556\pi
0.800733 0.599021i 0.204444π-0.204444\pi
132132 0 0
133133 56.1806 0.422411
134134 0 0
135135 99.3547 0.735961
136136 0 0
137137 3.42211 0.0249789 0.0124894 0.999922i 0.496024π-0.496024\pi
0.0124894 + 0.999922i 0.496024π0.496024\pi
138138 0 0
139139 112.664i 0.810534i 0.914198 + 0.405267i 0.132821π0.132821\pi
−0.914198 + 0.405267i 0.867179π0.867179\pi
140140 0 0
141141 355.220 2.51929
142142 0 0
143143 0 0
144144 0 0
145145 100.326i 0.691901i
146146 0 0
147147 −279.449 −1.90102
148148 0 0
149149 − 133.406i − 0.895345i −0.894198 0.447673i 0.852253π-0.852253\pi
0.894198 0.447673i 0.147747π-0.147747\pi
150150 0 0
151151 251.184i 1.66347i 0.555172 + 0.831736i 0.312653π0.312653\pi
−0.555172 + 0.831736i 0.687347π0.687347\pi
152152 0 0
153153 355.543i 2.32381i
154154 0 0
155155 −96.9202 −0.625292
156156 0 0
157157 −236.581 −1.50688 −0.753442 0.657515i 0.771608π-0.771608\pi
−0.753442 + 0.657515i 0.771608π0.771608\pi
158158 0 0
159159 −16.6067 −0.104444
160160 0 0
161161 351.933i 2.18592i
162162 0 0
163163 197.746 1.21317 0.606583 0.795021i 0.292540π-0.292540\pi
0.606583 + 0.795021i 0.292540π0.292540\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 4.16634i − 0.0249481i −0.999922 0.0124741i 0.996029π-0.996029\pi
0.999922 0.0124741i 0.00397072π-0.00397072\pi
168168 0 0
169169 157.815 0.933817
170170 0 0
171171 − 97.4192i − 0.569703i
172172 0 0
173173 − 221.308i − 1.27923i −0.768694 0.639617i 0.779093π-0.779093\pi
0.768694 0.639617i 0.220907π-0.220907\pi
174174 0 0
175175 50.7862i 0.290207i
176176 0 0
177177 340.586 1.92422
178178 0 0
179179 −24.0936 −0.134601 −0.0673006 0.997733i 0.521439π-0.521439\pi
−0.0673006 + 0.997733i 0.521439π0.521439\pi
180180 0 0
181181 −54.8750 −0.303177 −0.151589 0.988444i 0.548439π-0.548439\pi
−0.151589 + 0.988444i 0.548439π0.548439\pi
182182 0 0
183183 244.469i 1.33590i
184184 0 0
185185 −132.823 −0.717962
186186 0 0
187187 0 0
188188 0 0
189189 451.315i 2.38791i
190190 0 0
191191 228.706 1.19741 0.598706 0.800969i 0.295682π-0.295682\pi
0.598706 + 0.800969i 0.295682π0.295682\pi
192192 0 0
193193 − 140.392i − 0.727421i −0.931512 0.363711i 0.881510π-0.881510\pi
0.931512 0.363711i 0.118490π-0.118490\pi
194194 0 0
195195 − 38.5789i − 0.197840i
196196 0 0
197197 301.867i 1.53232i 0.642651 + 0.766159i 0.277834π0.277834\pi
−0.642651 + 0.766159i 0.722166π0.722166\pi
198198 0 0
199199 169.860 0.853570 0.426785 0.904353i 0.359646π-0.359646\pi
0.426785 + 0.904353i 0.359646π0.359646\pi
200200 0 0
201201 −163.076 −0.811322
202202 0 0
203203 −455.725 −2.24495
204204 0 0
205205 73.9941i 0.360947i
206206 0 0
207207 610.264 2.94814
208208 0 0
209209 0 0
210210 0 0
211211 87.0263i 0.412447i 0.978505 + 0.206224i 0.0661174π0.0661174\pi
−0.978505 + 0.206224i 0.933883π0.933883\pi
212212 0 0
213213 19.3979 0.0910699
214214 0 0
215215 − 146.144i − 0.679738i
216216 0 0
217217 − 440.256i − 2.02883i
218218 0 0
219219 − 115.622i − 0.527952i
220220 0 0
221221 67.5112 0.305480
222222 0 0
223223 −23.3059 −0.104511 −0.0522553 0.998634i 0.516641π-0.516641\pi
−0.0522553 + 0.998634i 0.516641π0.516641\pi
224224 0 0
225225 88.0652 0.391401
226226 0 0
227227 − 394.768i − 1.73907i −0.493875 0.869533i 0.664420π-0.664420\pi
0.493875 0.869533i 0.335580π-0.335580\pi
228228 0 0
229229 429.708 1.87645 0.938227 0.346022i 0.112468π-0.112468\pi
0.938227 + 0.346022i 0.112468π0.112468\pi
230230 0 0
231231 0 0
232232 0 0
233233 − 119.958i − 0.514841i −0.966300 0.257420i 0.917127π-0.917127\pi
0.966300 0.257420i 0.0828725π-0.0828725\pi
234234 0 0
235235 153.969 0.655189
236236 0 0
237237 − 403.497i − 1.70252i
238238 0 0
239239 − 206.753i − 0.865076i −0.901616 0.432538i 0.857618π-0.857618\pi
0.901616 0.432538i 0.142382π-0.142382\pi
240240 0 0
241241 − 314.829i − 1.30634i −0.757209 0.653172i 0.773438π-0.773438\pi
0.757209 0.653172i 0.226562π-0.226562\pi
242242 0 0
243243 −35.1603 −0.144693
244244 0 0
245245 −121.127 −0.494396
246246 0 0
247247 −18.4981 −0.0748912
248248 0 0
249249 − 114.492i − 0.459806i
250250 0 0
251251 −85.3576 −0.340070 −0.170035 0.985438i 0.554388π-0.554388\pi
−0.170035 + 0.985438i 0.554388π0.554388\pi
252252 0 0
253253 0 0
254254 0 0
255255 232.858i 0.913167i
256256 0 0
257257 −295.270 −1.14891 −0.574455 0.818536i 0.694786π-0.694786\pi
−0.574455 + 0.818536i 0.694786π0.694786\pi
258258 0 0
259259 − 603.343i − 2.32951i
260260 0 0
261261 790.244i 3.02775i
262262 0 0
263263 264.881i 1.00715i 0.863951 + 0.503577i 0.167983π0.167983\pi
−0.863951 + 0.503577i 0.832017π0.832017\pi
264264 0 0
265265 −7.19814 −0.0271628
266266 0 0
267267 351.836 1.31774
268268 0 0
269269 89.8558 0.334036 0.167018 0.985954i 0.446586π-0.446586\pi
0.167018 + 0.985954i 0.446586π0.446586\pi
270270 0 0
271271 − 101.229i − 0.373538i −0.982404 0.186769i 0.940198π-0.940198\pi
0.982404 0.186769i 0.0598016π-0.0598016\pi
272272 0 0
273273 175.243 0.641915
274274 0 0
275275 0 0
276276 0 0
277277 258.444i 0.933010i 0.884518 + 0.466505i 0.154487π0.154487\pi
−0.884518 + 0.466505i 0.845513π0.845513\pi
278278 0 0
279279 −763.420 −2.73627
280280 0 0
281281 − 383.628i − 1.36523i −0.730780 0.682613i 0.760844π-0.760844\pi
0.730780 0.682613i 0.239156π-0.239156\pi
282282 0 0
283283 94.3964i 0.333556i 0.985994 + 0.166778i 0.0533364π0.0533364\pi
−0.985994 + 0.166778i 0.946664π0.946664\pi
284284 0 0
285285 − 63.8032i − 0.223871i
286286 0 0
287287 −336.115 −1.17113
288288 0 0
289289 −118.490 −0.410000
290290 0 0
291291 316.943 1.08915
292292 0 0
293293 6.58908i 0.0224883i 0.999937 + 0.0112442i 0.00357921π0.00357921\pi
−0.999937 + 0.0112442i 0.996421π0.996421\pi
294294 0 0
295295 147.627 0.500430
296296 0 0
297297 0 0
298298 0 0
299299 − 115.878i − 0.387552i
300300 0 0
301301 663.852 2.20549
302302 0 0
303303 − 38.5491i − 0.127225i
304304 0 0
305305 105.965i 0.347426i
306306 0 0
307307 − 598.880i − 1.95075i −0.220557 0.975374i 0.570787π-0.570787\pi
0.220557 0.975374i 0.429213π-0.429213\pi
308308 0 0
309309 −426.347 −1.37976
310310 0 0
311311 367.259 1.18090 0.590449 0.807075i 0.298951π-0.298951\pi
0.590449 + 0.807075i 0.298951π0.298951\pi
312312 0 0
313313 372.762 1.19093 0.595466 0.803380i 0.296967π-0.296967\pi
0.595466 + 0.803380i 0.296967π0.296967\pi
314314 0 0
315315 400.032i 1.26994i
316316 0 0
317317 −385.788 −1.21700 −0.608499 0.793555i 0.708228π-0.708228\pi
−0.608499 + 0.793555i 0.708228π0.708228\pi
318318 0 0
319319 0 0
320320 0 0
321321 815.485i 2.54045i
322322 0 0
323323 111.653 0.345674
324324 0 0
325325 − 16.7220i − 0.0514522i
326326 0 0
327327 − 408.210i − 1.24835i
328328 0 0
329329 699.400i 2.12584i
330330 0 0
331331 −617.568 −1.86576 −0.932882 0.360182i 0.882715π-0.882715\pi
−0.932882 + 0.360182i 0.882715π0.882715\pi
332332 0 0
333333 −1046.22 −3.14180
334334 0 0
335335 −70.6850 −0.211000
336336 0 0
337337 170.873i 0.507042i 0.967330 + 0.253521i 0.0815887π0.0815887\pi
−0.967330 + 0.253521i 0.918411π0.918411\pi
338338 0 0
339339 145.604 0.429509
340340 0 0
341341 0 0
342342 0 0
343343 − 52.5095i − 0.153089i
344344 0 0
345345 399.683 1.15850
346346 0 0
347347 − 423.730i − 1.22112i −0.791969 0.610562i 0.790944π-0.790944\pi
0.791969 0.610562i 0.209056π-0.209056\pi
348348 0 0
349349 286.057i 0.819647i 0.912165 + 0.409823i 0.134410π0.134410\pi
−0.912165 + 0.409823i 0.865590π0.865590\pi
350350 0 0
351351 − 148.601i − 0.423364i
352352 0 0
353353 124.306 0.352142 0.176071 0.984377i 0.443661π-0.443661\pi
0.176071 + 0.984377i 0.443661π0.443661\pi
354354 0 0
355355 8.40799 0.0236845
356356 0 0
357357 −1057.75 −2.96288
358358 0 0
359359 − 284.135i − 0.791463i −0.918366 0.395732i 0.870491π-0.870491\pi
0.918366 0.395732i 0.129509π-0.129509\pi
360360 0 0
361361 330.407 0.915255
362362 0 0
363363 0 0
364364 0 0
365365 − 50.1160i − 0.137304i
366366 0 0
367367 −268.901 −0.732700 −0.366350 0.930477i 0.619393π-0.619393\pi
−0.366350 + 0.930477i 0.619393π0.619393\pi
368368 0 0
369369 582.836i 1.57950i
370370 0 0
371371 − 32.6973i − 0.0881328i
372372 0 0
373373 − 556.864i − 1.49293i −0.665423 0.746466i 0.731749π-0.731749\pi
0.665423 0.746466i 0.268251π-0.268251\pi
374374 0 0
375375 57.6769 0.153805
376376 0 0
377377 150.053 0.398018
378378 0 0
379379 −606.719 −1.60084 −0.800421 0.599438i 0.795391π-0.795391\pi
−0.800421 + 0.599438i 0.795391π0.795391\pi
380380 0 0
381381 479.292i 1.25798i
382382 0 0
383383 681.707 1.77991 0.889957 0.456044i 0.150734π-0.150734\pi
0.889957 + 0.456044i 0.150734π0.150734\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 1151.14i − 2.97453i
388388 0 0
389389 −130.409 −0.335241 −0.167620 0.985852i 0.553608π-0.553608\pi
−0.167620 + 0.985852i 0.553608π0.553608\pi
390390 0 0
391391 699.427i 1.78882i
392392 0 0
393393 − 809.638i − 2.06015i
394394 0 0
395395 − 174.895i − 0.442773i
396396 0 0
397397 47.4096 0.119420 0.0597098 0.998216i 0.480982π-0.480982\pi
0.0597098 + 0.998216i 0.480982π0.480982\pi
398398 0 0
399399 289.824 0.726375
400400 0 0
401401 −378.577 −0.944082 −0.472041 0.881577i 0.656483π-0.656483\pi
−0.472041 + 0.881577i 0.656483π0.656483\pi
402402 0 0
403403 144.959i 0.359701i
404404 0 0
405405 158.094 0.390355
406406 0 0
407407 0 0
408408 0 0
409409 − 1.66384i − 0.00406807i −0.999998 0.00203403i 0.999353π-0.999353\pi
0.999998 0.00203403i 0.000647453π-0.000647453\pi
410410 0 0
411411 17.6539 0.0429536
412412 0 0
413413 670.589i 1.62370i
414414 0 0
415415 − 49.6263i − 0.119581i
416416 0 0
417417 581.210i 1.39379i
418418 0 0
419419 230.024 0.548983 0.274491 0.961590i 0.411491π-0.411491\pi
0.274491 + 0.961590i 0.411491π0.411491\pi
420420 0 0
421421 184.393 0.437987 0.218994 0.975726i 0.429723π-0.429723\pi
0.218994 + 0.975726i 0.429723π0.429723\pi
422422 0 0
423423 1212.79 2.86710
424424 0 0
425425 100.932i 0.237487i
426426 0 0
427427 −481.341 −1.12726
428428 0 0
429429 0 0
430430 0 0
431431 − 97.4064i − 0.226001i −0.993595 0.113000i 0.963954π-0.963954\pi
0.993595 0.113000i 0.0360462π-0.0360462\pi
432432 0 0
433433 310.412 0.716887 0.358444 0.933551i 0.383308π-0.383308\pi
0.358444 + 0.933551i 0.383308π0.383308\pi
434434 0 0
435435 517.558i 1.18979i
436436 0 0
437437 − 191.644i − 0.438544i
438438 0 0
439439 124.229i 0.282982i 0.989940 + 0.141491i 0.0451896π0.0451896\pi
−0.989940 + 0.141491i 0.954810π0.954810\pi
440440 0 0
441441 −954.092 −2.16347
442442 0 0
443443 336.800 0.760270 0.380135 0.924931i 0.375878π-0.375878\pi
0.380135 + 0.924931i 0.375878π0.375878\pi
444444 0 0
445445 152.503 0.342703
446446 0 0
447447 − 688.215i − 1.53963i
448448 0 0
449449 202.686 0.451417 0.225709 0.974195i 0.427530π-0.427530\pi
0.225709 + 0.974195i 0.427530π0.427530\pi
450450 0 0
451451 0 0
452452 0 0
453453 1295.80i 2.86050i
454454 0 0
455455 75.9588 0.166942
456456 0 0
457457 − 817.158i − 1.78809i −0.447976 0.894046i 0.647855π-0.647855\pi
0.447976 0.894046i 0.352145π-0.352145\pi
458458 0 0
459459 896.937i 1.95411i
460460 0 0
461461 − 572.857i − 1.24264i −0.783557 0.621320i 0.786597π-0.786597\pi
0.783557 0.621320i 0.213403π-0.213403\pi
462462 0 0
463463 809.225 1.74779 0.873893 0.486119i 0.161588π-0.161588\pi
0.873893 + 0.486119i 0.161588π0.161588\pi
464464 0 0
465465 −499.990 −1.07525
466466 0 0
467467 −800.542 −1.71422 −0.857111 0.515132i 0.827743π-0.827743\pi
−0.857111 + 0.515132i 0.827743π0.827743\pi
468468 0 0
469469 − 321.084i − 0.684613i
470470 0 0
471471 −1220.47 −2.59123
472472 0 0
473473 0 0
474474 0 0
475475 − 27.6554i − 0.0582220i
476476 0 0
477477 −56.6983 −0.118864
478478 0 0
479479 663.266i 1.38469i 0.721567 + 0.692345i 0.243422π0.243422\pi
−0.721567 + 0.692345i 0.756578π0.756578\pi
480480 0 0
481481 198.658i 0.413010i
482482 0 0
483483 1815.54i 3.75889i
484484 0 0
485485 137.378 0.283255
486486 0 0
487487 −247.807 −0.508843 −0.254422 0.967093i 0.581885π-0.581885\pi
−0.254422 + 0.967093i 0.581885π0.581885\pi
488488 0 0
489489 1020.13 2.08615
490490 0 0
491491 834.509i 1.69961i 0.527096 + 0.849806i 0.323281π0.323281\pi
−0.527096 + 0.849806i 0.676719π0.676719\pi
492492 0 0
493493 −905.702 −1.83712
494494 0 0
495495 0 0
496496 0 0
497497 38.1929i 0.0768470i
498498 0 0
499499 525.408 1.05292 0.526461 0.850199i 0.323518π-0.323518\pi
0.526461 + 0.850199i 0.323518π0.323518\pi
500500 0 0
501501 − 21.4932i − 0.0429006i
502502 0 0
503503 327.969i 0.652026i 0.945365 + 0.326013i 0.105705π0.105705\pi
−0.945365 + 0.326013i 0.894295π0.894295\pi
504504 0 0
505505 − 16.7091i − 0.0330873i
506506 0 0
507507 814.133 1.60579
508508 0 0
509509 −392.787 −0.771683 −0.385842 0.922565i 0.626089π-0.626089\pi
−0.385842 + 0.922565i 0.626089π0.626089\pi
510510 0 0
511511 227.650 0.445499
512512 0 0
513513 − 245.762i − 0.479067i
514514 0 0
515515 −184.800 −0.358834
516516 0 0
517517 0 0
518518 0 0
519519 − 1141.68i − 2.19976i
520520 0 0
521521 −92.8535 −0.178222 −0.0891109 0.996022i 0.528403π-0.528403\pi
−0.0891109 + 0.996022i 0.528403π0.528403\pi
522522 0 0
523523 340.960i 0.651932i 0.945382 + 0.325966i 0.105689π0.105689\pi
−0.945382 + 0.325966i 0.894311π0.894311\pi
524524 0 0
525525 261.995i 0.499038i
526526 0 0
527527 − 874.959i − 1.66026i
528528 0 0
529529 671.515 1.26940
530530 0 0
531531 1162.82 2.18988
532532 0 0
533533 110.670 0.207636
534534 0 0
535535 353.471i 0.660693i
536536 0 0
537537 −124.294 −0.231459
538538 0 0
539539 0 0
540540 0 0
541541 186.702i 0.345104i 0.985000 + 0.172552i 0.0552014π0.0552014\pi
−0.985000 + 0.172552i 0.944799π0.944799\pi
542542 0 0
543543 −283.088 −0.521341
544544 0 0
545545 − 176.938i − 0.324657i
546546 0 0
547547 80.5995i 0.147348i 0.997282 + 0.0736741i 0.0234725π0.0234725\pi
−0.997282 + 0.0736741i 0.976528π0.976528\pi
548548 0 0
549549 834.663i 1.52033i
550550 0 0
551551 248.163 0.450387
552552 0 0
553553 794.455 1.43663
554554 0 0
555555 −685.205 −1.23460
556556 0 0
557557 24.3519i 0.0437198i 0.999761 + 0.0218599i 0.00695878π0.00695878\pi
−0.999761 + 0.0218599i 0.993041π0.993041\pi
558558 0 0
559559 −218.581 −0.391021
560560 0 0
561561 0 0
562562 0 0
563563 319.673i 0.567803i 0.958853 + 0.283902i 0.0916289π0.0916289\pi
−0.958853 + 0.283902i 0.908371π0.908371\pi
564564 0 0
565565 63.1117 0.111702
566566 0 0
567567 718.135i 1.26655i
568568 0 0
569569 − 744.166i − 1.30785i −0.756560 0.653924i 0.773121π-0.773121\pi
0.756560 0.653924i 0.226879π-0.226879\pi
570570 0 0
571571 − 265.828i − 0.465549i −0.972531 0.232774i 0.925220π-0.925220\pi
0.972531 0.232774i 0.0747804π-0.0747804\pi
572572 0 0
573573 1179.84 2.05906
574574 0 0
575575 173.242 0.301291
576576 0 0
577577 220.270 0.381750 0.190875 0.981614i 0.438867π-0.438867\pi
0.190875 + 0.981614i 0.438867π0.438867\pi
578578 0 0
579579 − 724.253i − 1.25087i
580580 0 0
581581 225.425 0.387996
582582 0 0
583583 0 0
584584 0 0
585585 − 131.715i − 0.225154i
586586 0 0
587587 −451.754 −0.769598 −0.384799 0.923000i 0.625729π-0.625729\pi
−0.384799 + 0.923000i 0.625729π0.625729\pi
588588 0 0
589589 239.740i 0.407028i
590590 0 0
591591 1557.26i 2.63496i
592592 0 0
593593 − 337.627i − 0.569353i −0.958624 0.284677i 0.908114π-0.908114\pi
0.958624 0.284677i 0.0918863π-0.0918863\pi
594594 0 0
595595 −458.479 −0.770553
596596 0 0
597597 876.273 1.46779
598598 0 0
599599 −659.439 −1.10090 −0.550450 0.834868i 0.685544π-0.685544\pi
−0.550450 + 0.834868i 0.685544π0.685544\pi
600600 0 0
601601 − 592.806i − 0.986367i −0.869925 0.493183i 0.835833π-0.835833\pi
0.869925 0.493183i 0.164167π-0.164167\pi
602602 0 0
603603 −556.771 −0.923335
604604 0 0
605605 0 0
606606 0 0
607607 − 615.618i − 1.01420i −0.861888 0.507099i 0.830718π-0.830718\pi
0.861888 0.507099i 0.169282π-0.169282\pi
608608 0 0
609609 −2350.99 −3.86040
610610 0 0
611611 − 230.286i − 0.376900i
612612 0 0
613613 − 468.595i − 0.764428i −0.924074 0.382214i 0.875162π-0.875162\pi
0.924074 0.382214i 0.124838π-0.124838\pi
614614 0 0
615615 381.719i 0.620682i
616616 0 0
617617 −94.7516 −0.153568 −0.0767841 0.997048i 0.524465π-0.524465\pi
−0.0767841 + 0.997048i 0.524465π0.524465\pi
618618 0 0
619619 −15.2679 −0.0246655 −0.0123327 0.999924i 0.503926π-0.503926\pi
−0.0123327 + 0.999924i 0.503926π0.503926\pi
620620 0 0
621621 1539.53 2.47911
622622 0 0
623623 692.739i 1.11194i
624624 0 0
625625 25.0000 0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 − 1199.08i − 1.90632i
630630 0 0
631631 961.254 1.52338 0.761691 0.647940i 0.224369π-0.224369\pi
0.761691 + 0.647940i 0.224369π0.224369\pi
632632 0 0
633633 448.950i 0.709241i
634634 0 0
635635 207.749i 0.327163i
636636 0 0
637637 181.165i 0.284403i
638638 0 0
639639 66.2280 0.103643
640640 0 0
641641 157.742 0.246087 0.123044 0.992401i 0.460734π-0.460734\pi
0.123044 + 0.992401i 0.460734π0.460734\pi
642642 0 0
643643 −895.842 −1.39322 −0.696611 0.717449i 0.745310π-0.745310\pi
−0.696611 + 0.717449i 0.745310π0.745310\pi
644644 0 0
645645 − 753.923i − 1.16887i
646646 0 0
647647 −169.006 −0.261215 −0.130608 0.991434i 0.541693π-0.541693\pi
−0.130608 + 0.991434i 0.541693π0.541693\pi
648648 0 0
649649 0 0
650650 0 0
651651 − 2271.18i − 3.48876i
652652 0 0
653653 131.764 0.201783 0.100891 0.994897i 0.467831π-0.467831\pi
0.100891 + 0.994897i 0.467831π0.467831\pi
654654 0 0
655655 − 350.937i − 0.535781i
656656 0 0
657657 − 394.753i − 0.600842i
658658 0 0
659659 − 956.323i − 1.45117i −0.688131 0.725586i 0.741569π-0.741569\pi
0.688131 0.725586i 0.258431π-0.258431\pi
660660 0 0
661661 −649.628 −0.982795 −0.491398 0.870935i 0.663514π-0.663514\pi
−0.491398 + 0.870935i 0.663514π0.663514\pi
662662 0 0
663663 348.275 0.525302
664664 0 0
665665 125.624 0.188908
666666 0 0
667667 1554.57i 2.33069i
668668 0 0
669669 −120.230 −0.179716
670670 0 0
671671 0 0
672672 0 0
673673 − 758.633i − 1.12724i −0.826034 0.563621i 0.809408π-0.809408\pi
0.826034 0.563621i 0.190592π-0.190592\pi
674674 0 0
675675 222.164 0.329132
676676 0 0
677677 − 141.672i − 0.209265i −0.994511 0.104632i 0.966633π-0.966633\pi
0.994511 0.104632i 0.0333666π-0.0333666\pi
678678 0 0
679679 624.036i 0.919052i
680680 0 0
681681 − 2036.52i − 2.99049i
682682 0 0
683683 101.169 0.148124 0.0740621 0.997254i 0.476404π-0.476404\pi
0.0740621 + 0.997254i 0.476404π0.476404\pi
684684 0 0
685685 7.65207 0.0111709
686686 0 0
687687 2216.77 3.22674
688688 0 0
689689 10.7660i 0.0156255i
690690 0 0
691691 −630.444 −0.912364 −0.456182 0.889886i 0.650783π-0.650783\pi
−0.456182 + 0.889886i 0.650783π0.650783\pi
692692 0 0
693693 0 0
694694 0 0
695695 251.925i 0.362482i
696696 0 0
697697 −667.991 −0.958380
698698 0 0
699699 − 618.837i − 0.885317i
700700 0 0
701701 260.870i 0.372140i 0.982536 + 0.186070i 0.0595752π0.0595752\pi
−0.982536 + 0.186070i 0.940425π0.940425\pi
702702 0 0
703703 328.548i 0.467351i
704704 0 0
705705 794.295 1.12666
706706 0 0
707707 75.9003 0.107355
708708 0 0
709709 −638.185 −0.900120 −0.450060 0.892998i 0.648597π-0.648597\pi
−0.450060 + 0.892998i 0.648597π0.648597\pi
710710 0 0
711711 − 1377.61i − 1.93757i
712712 0 0
713713 −1501.80 −2.10632
714714 0 0
715715 0 0
716716 0 0
717717 − 1066.59i − 1.48758i
718718 0 0
719719 900.685 1.25269 0.626345 0.779546i 0.284550π-0.284550\pi
0.626345 + 0.779546i 0.284550π0.284550\pi
720720 0 0
721721 − 839.445i − 1.16428i
722722 0 0
723723 − 1624.13i − 2.24638i
724724 0 0
725725 224.335i 0.309428i
726726 0 0
727727 −356.679 −0.490618 −0.245309 0.969445i 0.578889π-0.578889\pi
−0.245309 + 0.969445i 0.578889π0.578889\pi
728728 0 0
729729 −817.700 −1.12167
730730 0 0
731731 1319.33 1.80483
732732 0 0
733733 183.795i 0.250743i 0.992110 + 0.125371i 0.0400123π0.0400123\pi
−0.992110 + 0.125371i 0.959988π0.959988\pi
734734 0 0
735735 −624.868 −0.850161
736736 0 0
737737 0 0
738738 0 0
739739 625.309i 0.846156i 0.906093 + 0.423078i 0.139050π0.139050\pi
−0.906093 + 0.423078i 0.860950π0.860950\pi
740740 0 0
741741 −95.4278 −0.128782
742742 0 0
743743 478.632i 0.644188i 0.946708 + 0.322094i 0.104387π0.104387\pi
−0.946708 + 0.322094i 0.895613π0.895613\pi
744744 0 0
745745 − 298.306i − 0.400411i
746746 0 0
747747 − 390.896i − 0.523288i
748748 0 0
749749 −1605.63 −2.14369
750750 0 0
751751 −725.136 −0.965560 −0.482780 0.875742i 0.660373π-0.660373\pi
−0.482780 + 0.875742i 0.660373π0.660373\pi
752752 0 0
753753 −440.341 −0.584782
754754 0 0
755755 561.665i 0.743927i
756756 0 0
757757 555.723 0.734112 0.367056 0.930199i 0.380366π-0.380366\pi
0.367056 + 0.930199i 0.380366π0.380366\pi
758758 0 0
759759 0 0
760760 0 0
761761 − 1023.24i − 1.34460i −0.740280 0.672299i 0.765307π-0.765307\pi
0.740280 0.672299i 0.234693π-0.234693\pi
762762 0 0
763763 803.735 1.05339
764764 0 0
765765 795.019i 1.03924i
766766 0 0
767767 − 220.799i − 0.287874i
768768 0 0
769769 − 500.191i − 0.650443i −0.945638 0.325222i 0.894561π-0.894561\pi
0.945638 0.325222i 0.105439π-0.105439\pi
770770 0 0
771771 −1523.23 −1.97566
772772 0 0
773773 −755.149 −0.976907 −0.488453 0.872590i 0.662439π-0.662439\pi
−0.488453 + 0.872590i 0.662439π0.662439\pi
774774 0 0
775775 −216.720 −0.279639
776776 0 0
777777 − 3112.52i − 4.00581i
778778 0 0
779779 183.030 0.234955
780780 0 0
781781 0 0
782782 0 0
783783 1993.56i 2.54606i
784784 0 0
785785 −529.010 −0.673899
786786 0 0
787787 1401.42i 1.78071i 0.455271 + 0.890353i 0.349543π0.349543\pi
−0.455271 + 0.890353i 0.650457π0.650457\pi
788788 0 0
789789 1366.47i 1.73190i
790790 0 0
791791 286.682i 0.362430i
792792 0 0
793793 158.487 0.199858
794794 0 0
795795 −37.1337 −0.0467090
796796 0 0
797797 66.4088 0.0833235 0.0416617 0.999132i 0.486735π-0.486735\pi
0.0416617 + 0.999132i 0.486735π0.486735\pi
798798 0 0
799799 1389.98i 1.73965i
800800 0 0
801801 1201.23 1.49967
802802 0 0
803803 0 0
804804 0 0
805805 786.946i 0.977572i
806806 0 0
807807 463.546 0.574407
808808 0 0
809809 6.37591i 0.00788122i 0.999992 + 0.00394061i 0.00125434π0.00125434\pi
−0.999992 + 0.00394061i 0.998746π0.998746\pi
810810 0 0
811811 − 672.405i − 0.829107i −0.910025 0.414553i 0.863938π-0.863938\pi
0.910025 0.414553i 0.136062π-0.136062\pi
812812 0 0
813813 − 522.217i − 0.642334i
814814 0 0
815815 442.173 0.542544
816816 0 0
817817 −361.498 −0.442470
818818 0 0
819819 598.312 0.730539
820820 0 0
821821 79.6541i 0.0970208i 0.998823 + 0.0485104i 0.0154474π0.0154474\pi
−0.998823 + 0.0485104i 0.984553π0.984553\pi
822822 0 0
823823 −691.951 −0.840766 −0.420383 0.907347i 0.638104π-0.638104\pi
−0.420383 + 0.907347i 0.638104π0.638104\pi
824824 0 0
825825 0 0
826826 0 0
827827 1050.43i 1.27017i 0.772440 + 0.635087i 0.219036π0.219036\pi
−0.772440 + 0.635087i 0.780964π0.780964\pi
828828 0 0
829829 333.117 0.401830 0.200915 0.979609i 0.435608π-0.435608\pi
0.200915 + 0.979609i 0.435608π0.435608\pi
830830 0 0
831831 1333.26i 1.60440i
832832 0 0
833833 − 1093.49i − 1.31271i
834834 0 0
835835 − 9.31621i − 0.0111571i
836836 0 0
837837 −1925.90 −2.30095
838838 0 0
839839 29.8091 0.0355294 0.0177647 0.999842i 0.494345π-0.494345\pi
0.0177647 + 0.999842i 0.494345π0.494345\pi
840840 0 0
841841 −1172.05 −1.39363
842842 0 0
843843 − 1979.05i − 2.34763i
844844 0 0
845845 352.885 0.417616
846846 0 0
847847 0 0
848848 0 0
849849 486.971i 0.573581i
850850 0 0
851851 −2058.13 −2.41848
852852 0 0
853853 − 540.502i − 0.633648i −0.948484 0.316824i 0.897383π-0.897383\pi
0.948484 0.316824i 0.102617π-0.102617\pi
854854 0 0
855855 − 217.836i − 0.254779i
856856 0 0
857857 273.436i 0.319062i 0.987193 + 0.159531i 0.0509981π0.0509981\pi
−0.987193 + 0.159531i 0.949002π0.949002\pi
858858 0 0
859859 −275.966 −0.321264 −0.160632 0.987014i 0.551353π-0.551353\pi
−0.160632 + 0.987014i 0.551353π0.551353\pi
860860 0 0
861861 −1733.95 −2.01387
862862 0 0
863863 −36.8569 −0.0427079 −0.0213539 0.999772i 0.506798π-0.506798\pi
−0.0213539 + 0.999772i 0.506798π0.506798\pi
864864 0 0
865865 − 494.859i − 0.572091i
866866 0 0
867867 −611.264 −0.705033
868868 0 0
869869 0 0
870870 0 0
871871 105.721i 0.121378i
872872 0 0
873873 1082.10 1.23952
874874 0 0
875875 113.561i 0.129785i
876876 0 0
877877 448.626i 0.511546i 0.966737 + 0.255773i 0.0823300π0.0823300\pi
−0.966737 + 0.255773i 0.917670π0.917670\pi
878878 0 0
879879 33.9916i 0.0386708i
880880 0 0
881881 710.818 0.806831 0.403415 0.915017i 0.367823π-0.367823\pi
0.403415 + 0.915017i 0.367823π0.367823\pi
882882 0 0
883883 −1282.97 −1.45297 −0.726486 0.687182i 0.758848π-0.758848\pi
−0.726486 + 0.687182i 0.758848π0.758848\pi
884884 0 0
885885 761.574 0.860536
886886 0 0
887887 − 1023.50i − 1.15389i −0.816785 0.576943i 0.804246π-0.804246\pi
0.816785 0.576943i 0.195754π-0.195754\pi
888888 0 0
889889 −943.689 −1.06152
890890 0 0
891891 0 0
892892 0 0
893893 − 380.856i − 0.426490i
894894 0 0
895895 −53.8750 −0.0601955
896896 0 0
897897 − 597.789i − 0.666432i
898898 0 0
899899 − 1944.72i − 2.16320i
900900 0 0
901901 − 64.9821i − 0.0721222i
902902 0 0
903903 3424.67 3.79254
904904 0 0
905905 −122.704 −0.135585
906906 0 0
907907 1544.86 1.70327 0.851633 0.524138i 0.175613π-0.175613\pi
0.851633 + 0.524138i 0.175613π0.175613\pi
908908 0 0
909909 − 131.614i − 0.144790i
910910 0 0
911911 −376.609 −0.413401 −0.206701 0.978404i 0.566273π-0.566273\pi
−0.206701 + 0.978404i 0.566273π0.566273\pi
912912 0 0
913913 0 0
914914 0 0
915915 546.649i 0.597431i
916916 0 0
917917 1594.11 1.73840
918918 0 0
919919 − 1416.00i − 1.54081i −0.637556 0.770404i 0.720054π-0.720054\pi
0.637556 0.770404i 0.279946π-0.279946\pi
920920 0 0
921921 − 3089.49i − 3.35450i
922922 0 0
923923 − 12.5755i − 0.0136246i
924924 0 0
925925 −297.001 −0.321082
926926 0 0
927927 −1455.63 −1.57026
928928 0 0
929929 −800.241 −0.861400 −0.430700 0.902495i 0.641733π-0.641733\pi
−0.430700 + 0.902495i 0.641733π0.641733\pi
930930 0 0
931931 299.617i 0.321823i
932932 0 0
933933 1894.61 2.03067
934934 0 0
935935 0 0
936936 0 0
937937 − 954.407i − 1.01858i −0.860596 0.509288i 0.829909π-0.829909\pi
0.860596 0.509288i 0.170091π-0.170091\pi
938938 0 0
939939 1923.00 2.04792
940940 0 0
941941 − 874.736i − 0.929581i −0.885421 0.464791i 0.846130π-0.846130\pi
0.885421 0.464791i 0.153870π-0.153870\pi
942942 0 0
943943 1146.56i 1.21586i
944944 0 0
945945 1009.17i 1.06790i
946946 0 0
947947 614.074 0.648441 0.324221 0.945982i 0.394898π-0.394898\pi
0.324221 + 0.945982i 0.394898π0.394898\pi
948948 0 0
949949 −74.9564 −0.0789846
950950 0 0
951951 −1990.20 −2.09274
952952 0 0
953953 − 612.752i − 0.642971i −0.946914 0.321486i 0.895818π-0.895818\pi
0.946914 0.321486i 0.104182π-0.104182\pi
954954 0 0
955955 511.401 0.535499
956956 0 0
957957 0 0
958958 0 0
959959 34.7592i 0.0362453i
960960 0 0
961961 917.705 0.954948
962962 0 0
963963 2784.22i 2.89119i
964964 0 0
965965 − 313.927i − 0.325313i
966966 0 0
967967 − 200.077i − 0.206905i −0.994634 0.103452i 0.967011π-0.967011\pi
0.994634 0.103452i 0.0329890π-0.0329890\pi
968968 0 0
969969 575.992 0.594419
970970 0 0
971971 946.128 0.974385 0.487193 0.873295i 0.338021π-0.338021\pi
0.487193 + 0.873295i 0.338021π0.338021\pi
972972 0 0
973973 −1144.36 −1.17611
974974 0 0
975975 − 86.2650i − 0.0884769i
976976 0 0
977977 −343.304 −0.351386 −0.175693 0.984445i 0.556217π-0.556217\pi
−0.175693 + 0.984445i 0.556217π0.556217\pi
978978 0 0
979979 0 0
980980 0 0
981981 − 1393.71i − 1.42070i
982982 0 0
983983 −195.765 −0.199151 −0.0995753 0.995030i 0.531748π-0.531748\pi
−0.0995753 + 0.995030i 0.531748π0.531748\pi
984984 0 0
985985 674.994i 0.685273i
986986 0 0
987987 3608.05i 3.65558i
988988 0 0
989989 − 2264.53i − 2.28972i
990990 0 0
991991 −1157.74 −1.16826 −0.584130 0.811660i 0.698564π-0.698564\pi
−0.584130 + 0.811660i 0.698564π0.698564\pi
992992 0 0
993993 −3185.90 −3.20836
994994 0 0
995995 379.819 0.381728
996996 0 0
997997 1469.14i 1.47356i 0.676133 + 0.736779i 0.263654π0.263654\pi
−0.676133 + 0.736779i 0.736346π0.736346\pi
998998 0 0
999999 −2639.32 −2.64196
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 2420.3.f.c.241.16 16
11.6 odd 10 220.3.p.a.41.4 16
11.9 even 5 220.3.p.a.161.4 yes 16
11.10 odd 2 inner 2420.3.f.c.241.15 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
220.3.p.a.41.4 16 11.6 odd 10
220.3.p.a.161.4 yes 16 11.9 even 5
2420.3.f.c.241.15 16 11.10 odd 2 inner
2420.3.f.c.241.16 16 1.1 even 1 trivial