Properties

Label 1040.2.f.g.129.1
Level 10401040
Weight 22
Character 1040.129
Analytic conductor 8.3048.304
Analytic rank 00
Dimension 1010
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] = [1040,2,Mod(129,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.129"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1040=24513 1040 = 2^{4} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1040.f (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [10,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 8.304441810218.30444181021
Analytic rank: 00
Dimension: 1010
Coefficient field: Q[x]/(x10+)\mathbb{Q}[x]/(x^{10} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x10+11x8+36x6+42x4+13x2+1 x^{10} + 11x^{8} + 36x^{6} + 42x^{4} + 13x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 520)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 129.1
Root 1.35685i-1.35685i of defining polynomial
Character χ\chi == 1040.129
Dual form 1040.2.f.g.129.10

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) == q3.22659iq3+(0.589653+2.15692i)q5+1.65488q77.41088q9+4.44624iq11+(2.04103+2.97224i)q13+(6.95950+1.90257i)q15+5.33962iq170.472457iq195.33962iq21+1.08725iq23+(4.304622.54367i)q25+14.2321iq27+5.50812q29+5.47201iq31+14.3462q33+(0.975805+3.56945i)q353.65488q37+(9.590186.58557i)q39+10.4270iq418.14528iq43+(4.3698515.9847i)q451.65488q474.26137q49+17.2288q514.14520iq53+(9.590182.62174i)q551.52443q572.52401iq59+0.160253q6112.2641q63+(7.61438+2.64976i)q65+8.26412q67+3.50812q6912.9861iq7110.2641q73+(8.20738+13.8892i)q75+7.35799iq778.65763q79+23.6885q81+14.0696q83+(11.51713.14852i)q8517.7724iq87+7.61027iq89+(3.37766+4.91869i)q91+17.6559q93+(1.01905+0.278586i)q95+16.7397q9732.9505iq99+O(q100)q-3.22659i q^{3} +(-0.589653 + 2.15692i) q^{5} +1.65488 q^{7} -7.41088 q^{9} +4.44624i q^{11} +(2.04103 + 2.97224i) q^{13} +(6.95950 + 1.90257i) q^{15} +5.33962i q^{17} -0.472457i q^{19} -5.33962i q^{21} +1.08725i q^{23} +(-4.30462 - 2.54367i) q^{25} +14.2321i q^{27} +5.50812 q^{29} +5.47201i q^{31} +14.3462 q^{33} +(-0.975805 + 3.56945i) q^{35} -3.65488 q^{37} +(9.59018 - 6.58557i) q^{39} +10.4270i q^{41} -8.14528i q^{43} +(4.36985 - 15.9847i) q^{45} -1.65488 q^{47} -4.26137 q^{49} +17.2288 q^{51} -4.14520i q^{53} +(-9.59018 - 2.62174i) q^{55} -1.52443 q^{57} -2.52401i q^{59} +0.160253 q^{61} -12.2641 q^{63} +(-7.61438 + 2.64976i) q^{65} +8.26412 q^{67} +3.50812 q^{69} -12.9861i q^{71} -10.2641 q^{73} +(-8.20738 + 13.8892i) q^{75} +7.35799i q^{77} -8.65763 q^{79} +23.6885 q^{81} +14.0696 q^{83} +(-11.5171 - 3.14852i) q^{85} -17.7724i q^{87} +7.61027i q^{89} +(3.37766 + 4.91869i) q^{91} +17.6559 q^{93} +(1.01905 + 0.278586i) q^{95} +16.7397 q^{97} -32.9505i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+3q5+2q78q9+2q13+13q15q25+8q29+8q33+3q3522q37+12q394q452q47+12q49+30q5112q5512q5716q61++72q97+O(q100) 10 q + 3 q^{5} + 2 q^{7} - 8 q^{9} + 2 q^{13} + 13 q^{15} - q^{25} + 8 q^{29} + 8 q^{33} + 3 q^{35} - 22 q^{37} + 12 q^{39} - 4 q^{45} - 2 q^{47} + 12 q^{49} + 30 q^{51} - 12 q^{55} - 12 q^{57} - 16 q^{61}+ \cdots + 72 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1040Z)×\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times.

nn 261261 417417 561561 911911
χ(n)\chi(n) 11 1-1 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 3.22659i 1.86287i −0.363905 0.931436i 0.618557π-0.618557\pi
0.363905 0.931436i 0.381443π-0.381443\pi
44 0 0
55 −0.589653 + 2.15692i −0.263701 + 0.964605i
66 0 0
77 1.65488 0.625486 0.312743 0.949838i 0.398752π-0.398752\pi
0.312743 + 0.949838i 0.398752π0.398752\pi
88 0 0
99 −7.41088 −2.47029
1010 0 0
1111 4.44624i 1.34059i 0.742094 + 0.670296i 0.233833π0.233833\pi
−0.742094 + 0.670296i 0.766167π0.766167\pi
1212 0 0
1313 2.04103 + 2.97224i 0.566081 + 0.824350i
1414 0 0
1515 6.95950 + 1.90257i 1.79693 + 0.491241i
1616 0 0
1717 5.33962i 1.29505i 0.762045 + 0.647524i 0.224195π0.224195\pi
−0.762045 + 0.647524i 0.775805π0.775805\pi
1818 0 0
1919 0.472457i 0.108389i −0.998530 0.0541946i 0.982741π-0.982741\pi
0.998530 0.0541946i 0.0172591π-0.0172591\pi
2020 0 0
2121 5.33962i 1.16520i
2222 0 0
2323 1.08725i 0.226708i 0.993555 + 0.113354i 0.0361594π0.0361594\pi
−0.993555 + 0.113354i 0.963841π0.963841\pi
2424 0 0
2525 −4.30462 2.54367i −0.860924 0.508734i
2626 0 0
2727 14.2321i 2.73897i
2828 0 0
2929 5.50812 1.02283 0.511416 0.859333i 0.329121π-0.329121\pi
0.511416 + 0.859333i 0.329121π0.329121\pi
3030 0 0
3131 5.47201i 0.982803i 0.870933 + 0.491401i 0.163515π0.163515\pi
−0.870933 + 0.491401i 0.836485π0.836485\pi
3232 0 0
3333 14.3462 2.49735
3434 0 0
3535 −0.975805 + 3.56945i −0.164941 + 0.603347i
3636 0 0
3737 −3.65488 −0.600859 −0.300429 0.953804i 0.597130π-0.597130\pi
−0.300429 + 0.953804i 0.597130π0.597130\pi
3838 0 0
3939 9.59018 6.58557i 1.53566 1.05454i
4040 0 0
4141 10.4270i 1.62842i 0.580572 + 0.814209i 0.302829π0.302829\pi
−0.580572 + 0.814209i 0.697171π0.697171\pi
4242 0 0
4343 8.14528i 1.24214i −0.783753 0.621072i 0.786697π-0.786697\pi
0.783753 0.621072i 0.213303π-0.213303\pi
4444 0 0
4545 4.36985 15.9847i 0.651418 2.38286i
4646 0 0
4747 −1.65488 −0.241389 −0.120695 0.992690i 0.538512π-0.538512\pi
−0.120695 + 0.992690i 0.538512π0.538512\pi
4848 0 0
4949 −4.26137 −0.608767
5050 0 0
5151 17.2288 2.41251
5252 0 0
5353 4.14520i 0.569387i −0.958619 0.284693i 0.908108π-0.908108\pi
0.958619 0.284693i 0.0918918π-0.0918918\pi
5454 0 0
5555 −9.59018 2.62174i −1.29314 0.353515i
5656 0 0
5757 −1.52443 −0.201915
5858 0 0
5959 2.52401i 0.328598i −0.986411 0.164299i 0.947464π-0.947464\pi
0.986411 0.164299i 0.0525362π-0.0525362\pi
6060 0 0
6161 0.160253 0.0205183 0.0102591 0.999947i 0.496734π-0.496734\pi
0.0102591 + 0.999947i 0.496734π0.496734\pi
6262 0 0
6363 −12.2641 −1.54513
6464 0 0
6565 −7.61438 + 2.64976i −0.944448 + 0.328662i
6666 0 0
6767 8.26412 1.00962 0.504811 0.863230i 0.331562π-0.331562\pi
0.504811 + 0.863230i 0.331562π0.331562\pi
6868 0 0
6969 3.50812 0.422328
7070 0 0
7171 12.9861i 1.54117i −0.637336 0.770586i 0.719964π-0.719964\pi
0.637336 0.770586i 0.280036π-0.280036\pi
7272 0 0
7373 −10.2641 −1.20132 −0.600662 0.799503i 0.705096π-0.705096\pi
−0.600662 + 0.799503i 0.705096π0.705096\pi
7474 0 0
7575 −8.20738 + 13.8892i −0.947706 + 1.60379i
7676 0 0
7777 7.35799i 0.838521i
7878 0 0
7979 −8.65763 −0.974059 −0.487030 0.873385i 0.661920π-0.661920\pi
−0.487030 + 0.873385i 0.661920π0.661920\pi
8080 0 0
8181 23.6885 2.63205
8282 0 0
8383 14.0696 1.54434 0.772172 0.635414i 0.219171π-0.219171\pi
0.772172 + 0.635414i 0.219171π0.219171\pi
8484 0 0
8585 −11.5171 3.14852i −1.24921 0.341505i
8686 0 0
8787 17.7724i 1.90541i
8888 0 0
8989 7.61027i 0.806687i 0.915049 + 0.403344i 0.132152π0.132152\pi
−0.915049 + 0.403344i 0.867848π0.867848\pi
9090 0 0
9191 3.37766 + 4.91869i 0.354075 + 0.515619i
9292 0 0
9393 17.6559 1.83084
9494 0 0
9595 1.01905 + 0.278586i 0.104553 + 0.0285823i
9696 0 0
9797 16.7397 1.69966 0.849829 0.527058i 0.176705π-0.176705\pi
0.849829 + 0.527058i 0.176705π0.176705\pi
9898 0 0
9999 32.9505i 3.31165i
100100 0 0
101101 15.7729 1.56946 0.784731 0.619836i 0.212801π-0.212801\pi
0.784731 + 0.619836i 0.212801π0.212801\pi
102102 0 0
103103 1.60432i 0.158079i −0.996871 0.0790393i 0.974815π-0.974815\pi
0.996871 0.0790393i 0.0251853π-0.0251853\pi
104104 0 0
105105 11.5171 + 3.14852i 1.12396 + 0.307264i
106106 0 0
107107 1.34368i 0.129898i −0.997889 0.0649492i 0.979311π-0.979311\pi
0.997889 0.0649492i 0.0206885π-0.0206885\pi
108108 0 0
109109 5.33126i 0.510642i −0.966856 0.255321i 0.917819π-0.917819\pi
0.966856 0.255321i 0.0821811π-0.0821811\pi
110110 0 0
111111 11.7928i 1.11932i
112112 0 0
113113 14.7760i 1.39001i 0.719007 + 0.695003i 0.244597π0.244597\pi
−0.719007 + 0.695003i 0.755403π0.755403\pi
114114 0 0
115115 −2.34512 0.641102i −0.218684 0.0597831i
116116 0 0
117117 −15.1258 22.0269i −1.39838 2.03639i
118118 0 0
119119 8.83643i 0.810034i
120120 0 0
121121 −8.76903 −0.797185
122122 0 0
123123 33.6435 3.03353
124124 0 0
125125 8.02473 7.78484i 0.717753 0.696297i
126126 0 0
127127 3.15132i 0.279634i −0.990177 0.139817i 0.955349π-0.955349\pi
0.990177 0.139817i 0.0446515π-0.0446515\pi
128128 0 0
129129 −26.2815 −2.31396
130130 0 0
131131 −21.0724 −1.84110 −0.920551 0.390622i 0.872260π-0.872260\pi
−0.920551 + 0.390622i 0.872260π0.872260\pi
132132 0 0
133133 0.781860i 0.0677959i
134134 0 0
135135 −30.6975 8.39200i −2.64202 0.722268i
136136 0 0
137137 5.58631 0.477270 0.238635 0.971109i 0.423300π-0.423300\pi
0.238635 + 0.971109i 0.423300π0.423300\pi
138138 0 0
139139 7.85391 0.666160 0.333080 0.942899i 0.391912π-0.391912\pi
0.333080 + 0.942899i 0.391912π0.391912\pi
140140 0 0
141141 5.33962i 0.449677i
142142 0 0
143143 −13.2153 + 9.07492i −1.10512 + 0.758883i
144144 0 0
145145 −3.24788 + 11.8806i −0.269722 + 0.986629i
146146 0 0
147147 13.7497i 1.13406i
148148 0 0
149149 15.7314i 1.28877i 0.764702 + 0.644384i 0.222886π0.222886\pi
−0.764702 + 0.644384i 0.777114π0.777114\pi
150150 0 0
151151 18.2097i 1.48189i 0.671568 + 0.740943i 0.265621π0.265621\pi
−0.671568 + 0.740943i 0.734379π0.734379\pi
152152 0 0
153153 39.5713i 3.19915i
154154 0 0
155155 −11.8027 3.22659i −0.948016 0.259166i
156156 0 0
157157 0.385754i 0.0307865i 0.999882 + 0.0153933i 0.00490002π0.00490002\pi
−0.999882 + 0.0153933i 0.995100π0.995100\pi
158158 0 0
159159 −13.3749 −1.06069
160160 0 0
161161 1.79927i 0.141803i
162162 0 0
163163 −6.85666 −0.537055 −0.268527 0.963272i 0.586537π-0.586537\pi
−0.268527 + 0.963272i 0.586537π0.586537\pi
164164 0 0
165165 −8.45927 + 30.9436i −0.658553 + 2.40896i
166166 0 0
167167 −10.8836 −0.842201 −0.421101 0.907014i 0.638356π-0.638356\pi
−0.421101 + 0.907014i 0.638356π0.638356\pi
168168 0 0
169169 −4.66837 + 12.1329i −0.359106 + 0.933297i
170170 0 0
171171 3.50132i 0.267753i
172172 0 0
173173 20.6501i 1.57000i −0.619497 0.784999i 0.712663π-0.712663\pi
0.619497 0.784999i 0.287337π-0.287337\pi
174174 0 0
175175 −7.12363 4.20947i −0.538496 0.318206i
176176 0 0
177177 −8.14395 −0.612137
178178 0 0
179179 −1.89201 −0.141416 −0.0707079 0.997497i 0.522526π-0.522526\pi
−0.0707079 + 0.997497i 0.522526π0.522526\pi
180180 0 0
181181 4.69412 0.348911 0.174455 0.984665i 0.444183π-0.444183\pi
0.174455 + 0.984665i 0.444183π0.444183\pi
182182 0 0
183183 0.517070i 0.0382229i
184184 0 0
185185 2.15511 7.88329i 0.158447 0.579591i
186186 0 0
187187 −23.7412 −1.73613
188188 0 0
189189 23.5524i 1.71319i
190190 0 0
191191 −11.3367 −0.820298 −0.410149 0.912019i 0.634523π-0.634523\pi
−0.410149 + 0.912019i 0.634523π0.634523\pi
192192 0 0
193193 −16.4462 −1.18382 −0.591911 0.806004i 0.701626π-0.701626\pi
−0.591911 + 0.806004i 0.701626π0.701626\pi
194194 0 0
195195 8.54968 + 24.5685i 0.612256 + 1.75939i
196196 0 0
197197 16.8858 1.20306 0.601531 0.798849i 0.294558π-0.294558\pi
0.601531 + 0.798849i 0.294558π0.294558\pi
198198 0 0
199199 19.0240 1.34858 0.674288 0.738469i 0.264451π-0.264451\pi
0.674288 + 0.738469i 0.264451π0.264451\pi
200200 0 0
201201 26.6649i 1.88080i
202202 0 0
203203 9.11528 0.639767
204204 0 0
205205 −22.4901 6.14829i −1.57078 0.429415i
206206 0 0
207207 8.05750i 0.560035i
208208 0 0
209209 2.10066 0.145305
210210 0 0
211211 1.89201 0.130252 0.0651258 0.997877i 0.479255π-0.479255\pi
0.0651258 + 0.997877i 0.479255π0.479255\pi
212212 0 0
213213 −41.9009 −2.87101
214214 0 0
215215 17.5687 + 4.80289i 1.19818 + 0.327554i
216216 0 0
217217 9.05553i 0.614729i
218218 0 0
219219 33.1181i 2.23791i
220220 0 0
221221 −15.8706 + 10.8983i −1.06757 + 0.733101i
222222 0 0
223223 14.3721 0.962427 0.481214 0.876603i 0.340196π-0.340196\pi
0.481214 + 0.876603i 0.340196π0.340196\pi
224224 0 0
225225 31.9010 + 18.8508i 2.12673 + 1.25672i
226226 0 0
227227 −6.94886 −0.461212 −0.230606 0.973047i 0.574071π-0.574071\pi
−0.230606 + 0.973047i 0.574071π0.574071\pi
228228 0 0
229229 15.3506i 1.01440i 0.861830 + 0.507198i 0.169319π0.169319\pi
−0.861830 + 0.507198i 0.830681π0.830681\pi
230230 0 0
231231 23.7412 1.56206
232232 0 0
233233 4.06993i 0.266630i −0.991074 0.133315i 0.957438π-0.957438\pi
0.991074 0.133315i 0.0425622π-0.0425622\pi
234234 0 0
235235 0.975805 3.56945i 0.0636545 0.232845i
236236 0 0
237237 27.9346i 1.81455i
238238 0 0
239239 6.89047i 0.445707i 0.974852 + 0.222854i 0.0715372π0.0715372\pi
−0.974852 + 0.222854i 0.928463π0.928463\pi
240240 0 0
241241 0.781860i 0.0503640i −0.999683 0.0251820i 0.991983π-0.991983\pi
0.999683 0.0251820i 0.00801653π-0.00801653\pi
242242 0 0
243243 33.7367i 2.16421i
244244 0 0
245245 2.51273 9.19144i 0.160532 0.587220i
246246 0 0
247247 1.40425 0.964301i 0.0893506 0.0613570i
248248 0 0
249249 45.3969i 2.87691i
250250 0 0
251251 −8.56085 −0.540356 −0.270178 0.962810i 0.587083π-0.587083\pi
−0.270178 + 0.962810i 0.587083π0.587083\pi
252252 0 0
253253 −4.83419 −0.303923
254254 0 0
255255 −10.1590 + 37.1611i −0.636181 + 2.32712i
256256 0 0
257257 0.279087i 0.0174090i −0.999962 0.00870448i 0.997229π-0.997229\pi
0.999962 0.00870448i 0.00277076π-0.00277076\pi
258258 0 0
259259 −6.04839 −0.375829
260260 0 0
261261 −40.8200 −2.52670
262262 0 0
263263 2.67435i 0.164907i 0.996595 + 0.0824537i 0.0262757π0.0262757\pi
−0.996595 + 0.0824537i 0.973724π0.973724\pi
264264 0 0
265265 8.94087 + 2.44423i 0.549233 + 0.150148i
266266 0 0
267267 24.5552 1.50276
268268 0 0
269269 26.5878 1.62109 0.810544 0.585677i 0.199171π-0.199171\pi
0.810544 + 0.585677i 0.199171π0.199171\pi
270270 0 0
271271 25.3879i 1.54221i −0.636710 0.771104i 0.719705π-0.719705\pi
0.636710 0.771104i 0.280295π-0.280295\pi
272272 0 0
273273 15.8706 10.8983i 0.960533 0.659597i
274274 0 0
275275 11.3098 19.1394i 0.682004 1.15415i
276276 0 0
277277 6.37232i 0.382875i 0.981505 + 0.191438i 0.0613150π0.0613150\pi
−0.981505 + 0.191438i 0.938685π0.938685\pi
278278 0 0
279279 40.5524i 2.42781i
280280 0 0
281281 0.765134i 0.0456441i −0.999740 0.0228220i 0.992735π-0.992735\pi
0.999740 0.0228220i 0.00726511π-0.00726511\pi
282282 0 0
283283 9.38817i 0.558069i −0.960281 0.279034i 0.909986π-0.909986\pi
0.960281 0.279034i 0.0900144π-0.0900144\pi
284284 0 0
285285 0.898882 3.28807i 0.0532452 0.194768i
286286 0 0
287287 17.2554i 1.01855i
288288 0 0
289289 −11.5115 −0.677149
290290 0 0
291291 54.0121i 3.16625i
292292 0 0
293293 13.4874 0.787941 0.393971 0.919123i 0.371101π-0.371101\pi
0.393971 + 0.919123i 0.371101π0.371101\pi
294294 0 0
295295 5.44409 + 1.48829i 0.316967 + 0.0866516i
296296 0 0
297297 −63.2793 −3.67184
298298 0 0
299299 −3.23157 + 2.21912i −0.186887 + 0.128335i
300300 0 0
301301 13.4795i 0.776944i
302302 0 0
303303 50.8927i 2.92371i
304304 0 0
305305 −0.0944935 + 0.345653i −0.00541068 + 0.0197920i
306306 0 0
307307 −25.4064 −1.45002 −0.725009 0.688739i 0.758165π-0.758165\pi
−0.725009 + 0.688739i 0.758165π0.758165\pi
308308 0 0
309309 −5.17649 −0.294480
310310 0 0
311311 12.4250 0.704559 0.352280 0.935895i 0.385407π-0.385407\pi
0.352280 + 0.935895i 0.385407π0.385407\pi
312312 0 0
313313 23.9664i 1.35466i −0.735678 0.677331i 0.763136π-0.763136\pi
0.735678 0.677331i 0.236864π-0.236864\pi
314314 0 0
315315 7.23157 26.4527i 0.407453 1.49044i
316316 0 0
317317 −20.3618 −1.14363 −0.571817 0.820381i 0.693761π-0.693761\pi
−0.571817 + 0.820381i 0.693761π0.693761\pi
318318 0 0
319319 24.4904i 1.37120i
320320 0 0
321321 −4.33550 −0.241984
322322 0 0
323323 2.52274 0.140369
324324 0 0
325325 −1.22548 17.9861i −0.0679774 0.997687i
326326 0 0
327327 −17.2018 −0.951260
328328 0 0
329329 −2.73863 −0.150986
330330 0 0
331331 30.0834i 1.65353i 0.562546 + 0.826766i 0.309822π0.309822\pi
−0.562546 + 0.826766i 0.690178π0.690178\pi
332332 0 0
333333 27.0859 1.48430
334334 0 0
335335 −4.87296 + 17.8251i −0.266238 + 0.973887i
336336 0 0
337337 10.8983i 0.593670i −0.954929 0.296835i 0.904069π-0.904069\pi
0.954929 0.296835i 0.0959312π-0.0959312\pi
338338 0 0
339339 47.6760 2.58940
340340 0 0
341341 −24.3299 −1.31754
342342 0 0
343343 −18.6362 −1.00626
344344 0 0
345345 −2.06857 + 7.56674i −0.111368 + 0.407379i
346346 0 0
347347 11.9236i 0.640093i 0.947402 + 0.320047i 0.103699π0.103699\pi
−0.947402 + 0.320047i 0.896301π0.896301\pi
348348 0 0
349349 3.38144i 0.181004i 0.995896 + 0.0905021i 0.0288472π0.0288472\pi
−0.995896 + 0.0905021i 0.971153π0.971153\pi
350350 0 0
351351 −42.3011 + 29.0482i −2.25787 + 1.55048i
352352 0 0
353353 13.4771 0.717314 0.358657 0.933469i 0.383235π-0.383235\pi
0.358657 + 0.933469i 0.383235π0.383235\pi
354354 0 0
355355 28.0101 + 7.65732i 1.48662 + 0.406408i
356356 0 0
357357 28.5115 1.50899
358358 0 0
359359 4.74277i 0.250314i −0.992137 0.125157i 0.960057π-0.960057\pi
0.992137 0.125157i 0.0399434π-0.0399434\pi
360360 0 0
361361 18.7768 0.988252
362362 0 0
363363 28.2941i 1.48505i
364364 0 0
365365 6.05227 22.1389i 0.316790 1.15880i
366366 0 0
367367 31.4288i 1.64057i −0.571956 0.820284i 0.693815π-0.693815\pi
0.571956 0.820284i 0.306185π-0.306185\pi
368368 0 0
369369 77.2729i 4.02267i
370370 0 0
371371 6.85981i 0.356143i
372372 0 0
373373 25.7810i 1.33489i −0.744660 0.667444i 0.767388π-0.767388\pi
0.744660 0.667444i 0.232612π-0.232612\pi
374374 0 0
375375 −25.1185 25.8925i −1.29711 1.33708i
376376 0 0
377377 11.2423 + 16.3714i 0.579005 + 0.843172i
378378 0 0
379379 14.7011i 0.755146i 0.925980 + 0.377573i 0.123241π0.123241\pi
−0.925980 + 0.377573i 0.876759π0.876759\pi
380380 0 0
381381 −10.1680 −0.520923
382382 0 0
383383 1.62790 0.0831816 0.0415908 0.999135i 0.486757π-0.486757\pi
0.0415908 + 0.999135i 0.486757π0.486757\pi
384384 0 0
385385 −15.8706 4.33866i −0.808841 0.221119i
386386 0 0
387387 60.3637i 3.06846i
388388 0 0
389389 28.3607 1.43795 0.718973 0.695038i 0.244612π-0.244612\pi
0.718973 + 0.695038i 0.244612π0.244612\pi
390390 0 0
391391 −5.80552 −0.293598
392392 0 0
393393 67.9919i 3.42974i
394394 0 0
395395 5.10500 18.6738i 0.256860 0.939582i
396396 0 0
397397 −1.54689 −0.0776364 −0.0388182 0.999246i 0.512359π-0.512359\pi
−0.0388182 + 0.999246i 0.512359π0.512359\pi
398398 0 0
399399 −2.52274 −0.126295
400400 0 0
401401 5.55872i 0.277589i 0.990321 + 0.138795i 0.0443228π0.0443228\pi
−0.990321 + 0.138795i 0.955677π0.955677\pi
402402 0 0
403403 −16.2641 + 11.1686i −0.810173 + 0.556346i
404404 0 0
405405 −13.9680 + 51.0942i −0.694075 + 2.53889i
406406 0 0
407407 16.2505i 0.805506i
408408 0 0
409409 4.70652i 0.232722i 0.993207 + 0.116361i 0.0371230π0.0371230\pi
−0.993207 + 0.116361i 0.962877π0.962877\pi
410410 0 0
411411 18.0247i 0.889094i
412412 0 0
413413 4.17694i 0.205534i
414414 0 0
415415 −8.29620 + 30.3471i −0.407245 + 1.48968i
416416 0 0
417417 25.3413i 1.24097i
418418 0 0
419419 17.4613 0.853043 0.426521 0.904478i 0.359739π-0.359739\pi
0.426521 + 0.904478i 0.359739π0.359739\pi
420420 0 0
421421 23.1162i 1.12662i −0.826247 0.563308i 0.809529π-0.809529\pi
0.826247 0.563308i 0.190471π-0.190471\pi
422422 0 0
423423 12.2641 0.596302
424424 0 0
425425 13.5822 22.9850i 0.658835 1.11494i
426426 0 0
427427 0.265199 0.0128339
428428 0 0
429429 29.2810 + 42.6402i 1.41370 + 2.05869i
430430 0 0
431431 19.8860i 0.957877i −0.877848 0.478939i 0.841022π-0.841022\pi
0.877848 0.478939i 0.158978π-0.158978\pi
432432 0 0
433433 2.09858i 0.100851i −0.998728 0.0504255i 0.983942π-0.983942\pi
0.998728 0.0504255i 0.0160578π-0.0160578\pi
434434 0 0
435435 38.3338 + 10.4796i 1.83796 + 0.502457i
436436 0 0
437437 0.513681 0.0245727
438438 0 0
439439 14.7553 0.704233 0.352117 0.935956i 0.385462π-0.385462\pi
0.352117 + 0.935956i 0.385462π0.385462\pi
440440 0 0
441441 31.5805 1.50383
442442 0 0
443443 12.8191i 0.609053i 0.952504 + 0.304526i 0.0984982π0.0984982\pi
−0.952504 + 0.304526i 0.901502π0.901502\pi
444444 0 0
445445 −16.4148 4.48742i −0.778134 0.212724i
446446 0 0
447447 50.7588 2.40081
448448 0 0
449449 25.7925i 1.21722i 0.793468 + 0.608612i 0.208273π0.208273\pi
−0.793468 + 0.608612i 0.791727π0.791727\pi
450450 0 0
451451 −46.3607 −2.18304
452452 0 0
453453 58.7553 2.76057
454454 0 0
455455 −12.6009 + 4.38503i −0.590739 + 0.205574i
456456 0 0
457457 9.61892 0.449954 0.224977 0.974364i 0.427769π-0.427769\pi
0.224977 + 0.974364i 0.427769π0.427769\pi
458458 0 0
459459 −75.9940 −3.54709
460460 0 0
461461 18.4899i 0.861160i −0.902552 0.430580i 0.858309π-0.858309\pi
0.902552 0.430580i 0.141691π-0.141691\pi
462462 0 0
463463 4.26412 0.198170 0.0990852 0.995079i 0.468408π-0.468408\pi
0.0990852 + 0.995079i 0.468408π0.468408\pi
464464 0 0
465465 −10.4109 + 38.0825i −0.482793 + 1.76603i
466466 0 0
467467 8.12164i 0.375825i −0.982186 0.187912i 0.939828π-0.939828\pi
0.982186 0.187912i 0.0601721π-0.0601721\pi
468468 0 0
469469 13.6761 0.631505
470470 0 0
471471 1.24467 0.0573514
472472 0 0
473473 36.2159 1.66521
474474 0 0
475475 −1.20178 + 2.03375i −0.0551412 + 0.0933148i
476476 0 0
477477 30.7196i 1.40655i
478478 0 0
479479 9.07748i 0.414761i 0.978260 + 0.207380i 0.0664938π0.0664938\pi
−0.978260 + 0.207380i 0.933506π0.933506\pi
480480 0 0
481481 −7.45973 10.8632i −0.340134 0.495318i
482482 0 0
483483 5.80552 0.264160
484484 0 0
485485 −9.87061 + 36.1062i −0.448201 + 1.63950i
486486 0 0
487487 −0.124845 −0.00565727 −0.00282863 0.999996i 0.500900π-0.500900\pi
−0.00282863 + 0.999996i 0.500900π0.500900\pi
488488 0 0
489489 22.1236i 1.00046i
490490 0 0
491491 31.7515 1.43293 0.716463 0.697626i 0.245760π-0.245760\pi
0.716463 + 0.697626i 0.245760π0.245760\pi
492492 0 0
493493 29.4113i 1.32462i
494494 0 0
495495 71.0717 + 19.4294i 3.19444 + 0.873285i
496496 0 0
497497 21.4905i 0.963981i
498498 0 0
499499 12.3636i 0.553469i 0.960946 + 0.276734i 0.0892522π0.0892522\pi
−0.960946 + 0.276734i 0.910748π0.910748\pi
500500 0 0
501501 35.1170i 1.56891i
502502 0 0
503503 26.5184i 1.18240i −0.806527 0.591198i 0.798655π-0.798655\pi
0.806527 0.591198i 0.201345π-0.201345\pi
504504 0 0
505505 −9.30054 + 34.0209i −0.413869 + 1.51391i
506506 0 0
507507 39.1478 + 15.0629i 1.73861 + 0.668968i
508508 0 0
509509 39.4076i 1.74671i −0.487085 0.873355i 0.661940π-0.661940\pi
0.487085 0.873355i 0.338060π-0.338060\pi
510510 0 0
511511 −16.9859 −0.751411
512512 0 0
513513 6.72406 0.296874
514514 0 0
515515 3.46040 + 0.945994i 0.152483 + 0.0416855i
516516 0 0
517517 7.35799i 0.323604i
518518 0 0
519519 −66.6294 −2.92471
520520 0 0
521521 −30.8042 −1.34956 −0.674779 0.738020i 0.735761π-0.735761\pi
−0.674779 + 0.738020i 0.735761π0.735761\pi
522522 0 0
523523 5.53950i 0.242225i 0.992639 + 0.121113i 0.0386463π0.0386463\pi
−0.992639 + 0.121113i 0.961354π0.961354\pi
524524 0 0
525525 −13.5822 + 22.9850i −0.592777 + 1.00315i
526526 0 0
527527 −29.2185 −1.27278
528528 0 0
529529 21.8179 0.948603
530530 0 0
531531 18.7051i 0.811734i
532532 0 0
533533 −30.9914 + 21.2818i −1.34239 + 0.921815i
534534 0 0
535535 2.89821 + 0.792305i 0.125301 + 0.0342543i
536536 0 0
537537 6.10475i 0.263440i
538538 0 0
539539 18.9471i 0.816108i
540540 0 0
541541 10.7346i 0.461518i −0.973011 0.230759i 0.925879π-0.925879\pi
0.973011 0.230759i 0.0741208π-0.0741208\pi
542542 0 0
543543 15.1460i 0.649976i
544544 0 0
545545 11.4991 + 3.14359i 0.492567 + 0.134657i
546546 0 0
547547 32.6681i 1.39679i −0.715714 0.698393i 0.753899π-0.753899\pi
0.715714 0.698393i 0.246101π-0.246101\pi
548548 0 0
549549 −1.18761 −0.0506861
550550 0 0
551551 2.60235i 0.110864i
552552 0 0
553553 −14.3273 −0.609260
554554 0 0
555555 −25.4361 6.95366i −1.07970 0.295166i
556556 0 0
557557 21.4016 0.906815 0.453407 0.891303i 0.350208π-0.350208\pi
0.453407 + 0.891303i 0.350208π0.350208\pi
558558 0 0
559559 24.2097 16.6248i 1.02396 0.703154i
560560 0 0
561561 76.6032i 3.23419i
562562 0 0
563563 4.68087i 0.197275i 0.995123 + 0.0986376i 0.0314485π0.0314485\pi
−0.995123 + 0.0986376i 0.968552π0.968552\pi
564564 0 0
565565 −31.8706 8.71270i −1.34081 0.366546i
566566 0 0
567567 39.2016 1.64631
568568 0 0
569569 −18.4434 −0.773186 −0.386593 0.922250i 0.626348π-0.626348\pi
−0.386593 + 0.922250i 0.626348π0.626348\pi
570570 0 0
571571 −0.667911 −0.0279512 −0.0139756 0.999902i 0.504449π-0.504449\pi
−0.0139756 + 0.999902i 0.504449π0.504449\pi
572572 0 0
573573 36.5790i 1.52811i
574574 0 0
575575 2.76561 4.68021i 0.115334 0.195178i
576576 0 0
577577 24.6947 1.02805 0.514026 0.857775i 0.328154π-0.328154\pi
0.514026 + 0.857775i 0.328154π0.328154\pi
578578 0 0
579579 53.0650i 2.20531i
580580 0 0
581581 23.2836 0.965965
582582 0 0
583583 18.4305 0.763315
584584 0 0
585585 56.4292 19.6370i 2.33306 0.811892i
586586 0 0
587587 −18.2586 −0.753614 −0.376807 0.926292i 0.622978π-0.622978\pi
−0.376807 + 0.926292i 0.622978π0.622978\pi
588588 0 0
589589 2.58529 0.106525
590590 0 0
591591 54.4835i 2.24115i
592592 0 0
593593 −6.67326 −0.274038 −0.137019 0.990568i 0.543752π-0.543752\pi
−0.137019 + 0.990568i 0.543752π0.543752\pi
594594 0 0
595595 −19.0595 5.21043i −0.781363 0.213607i
596596 0 0
597597 61.3826i 2.51222i
598598 0 0
599599 −39.4490 −1.61184 −0.805922 0.592022i 0.798330π-0.798330\pi
−0.805922 + 0.592022i 0.798330π0.798330\pi
600600 0 0
601601 −25.9245 −1.05748 −0.528741 0.848783i 0.677336π-0.677336\pi
−0.528741 + 0.848783i 0.677336π0.677336\pi
602602 0 0
603603 −61.2444 −2.49406
604604 0 0
605605 5.17068 18.9141i 0.210218 0.768968i
606606 0 0
607607 4.40112i 0.178636i −0.996003 0.0893181i 0.971531π-0.971531\pi
0.996003 0.0893181i 0.0284688π-0.0284688\pi
608608 0 0
609609 29.4113i 1.19180i
610610 0 0
611611 −3.37766 4.91869i −0.136646 0.198989i
612612 0 0
613613 −14.2573 −0.575848 −0.287924 0.957653i 0.592965π-0.592965\pi
−0.287924 + 0.957653i 0.592965π0.592965\pi
614614 0 0
615615 −19.8380 + 72.5664i −0.799945 + 2.92616i
616616 0 0
617617 −9.58843 −0.386016 −0.193008 0.981197i 0.561824π-0.561824\pi
−0.193008 + 0.981197i 0.561824π0.561824\pi
618618 0 0
619619 41.8263i 1.68114i −0.541703 0.840570i 0.682220π-0.682220\pi
0.541703 0.840570i 0.317780π-0.317780\pi
620620 0 0
621621 −15.4739 −0.620946
622622 0 0
623623 12.5941i 0.504572i
624624 0 0
625625 12.0595 + 21.8991i 0.482379 + 0.875962i
626626 0 0
627627 6.77796i 0.270686i
628628 0 0
629629 19.5157i 0.778141i
630630 0 0
631631 10.7991i 0.429906i −0.976624 0.214953i 0.931040π-0.931040\pi
0.976624 0.214953i 0.0689599π-0.0689599\pi
632632 0 0
633633 6.10475i 0.242642i
634634 0 0
635635 6.79714 + 1.85818i 0.269736 + 0.0737398i
636636 0 0
637637 −8.69760 12.6658i −0.344611 0.501837i
638638 0 0
639639 96.2387i 3.80714i
640640 0 0
641641 −17.0240 −0.672407 −0.336204 0.941789i 0.609143π-0.609143\pi
−0.336204 + 0.941789i 0.609143π0.609143\pi
642642 0 0
643643 −33.9076 −1.33719 −0.668593 0.743628i 0.733103π-0.733103\pi
−0.668593 + 0.743628i 0.733103π0.733103\pi
644644 0 0
645645 15.4970 56.6871i 0.610192 2.23205i
646646 0 0
647647 24.1282i 0.948577i 0.880369 + 0.474288i 0.157295π0.157295\pi
−0.880369 + 0.474288i 0.842705π0.842705\pi
648648 0 0
649649 11.2224 0.440516
650650 0 0
651651 29.2185 1.14516
652652 0 0
653653 6.35210i 0.248577i −0.992246 0.124288i 0.960335π-0.960335\pi
0.992246 0.124288i 0.0396648π-0.0396648\pi
654654 0 0
655655 12.4254 45.4515i 0.485500 1.77594i
656656 0 0
657657 76.0661 2.96762
658658 0 0
659659 19.8436 0.772998 0.386499 0.922290i 0.373684π-0.373684\pi
0.386499 + 0.922290i 0.373684π0.373684\pi
660660 0 0
661661 40.1796i 1.56280i −0.624028 0.781402i 0.714505π-0.714505\pi
0.624028 0.781402i 0.285495π-0.285495\pi
662662 0 0
663663 35.1645 + 51.2079i 1.36567 + 1.98875i
664664 0 0
665665 1.68641 + 0.461026i 0.0653962 + 0.0178778i
666666 0 0
667667 5.98872i 0.231884i
668668 0 0
669669 46.3729i 1.79288i
670670 0 0
671671 0.712522i 0.0275066i
672672 0 0
673673 24.0716i 0.927894i −0.885863 0.463947i 0.846433π-0.846433\pi
0.885863 0.463947i 0.153567π-0.153567\pi
674674 0 0
675675 36.2018 61.2637i 1.39341 2.35804i
676676 0 0
677677 24.0869i 0.925736i 0.886427 + 0.462868i 0.153180π0.153180\pi
−0.886427 + 0.462868i 0.846820π0.846820\pi
678678 0 0
679679 27.7022 1.06311
680680 0 0
681681 22.4211i 0.859179i
682682 0 0
683683 38.1236 1.45876 0.729380 0.684109i 0.239809π-0.239809\pi
0.729380 + 0.684109i 0.239809π0.239809\pi
684684 0 0
685685 −3.29398 + 12.0492i −0.125857 + 0.460377i
686686 0 0
687687 49.5300 1.88969
688688 0 0
689689 12.3205 8.46048i 0.469374 0.322319i
690690 0 0
691691 4.01418i 0.152707i −0.997081 0.0763533i 0.975672π-0.975672\pi
0.997081 0.0763533i 0.0243277π-0.0243277\pi
692692 0 0
693693 54.5292i 2.07139i
694694 0 0
695695 −4.63108 + 16.9403i −0.175667 + 0.642581i
696696 0 0
697697 −55.6760 −2.10888
698698 0 0
699699 −13.1320 −0.496697
700700 0 0
701701 29.3041 1.10680 0.553401 0.832915i 0.313330π-0.313330\pi
0.553401 + 0.832915i 0.313330π0.313330\pi
702702 0 0
703703 1.72677i 0.0651265i
704704 0 0
705705 −11.5171 3.14852i −0.433761 0.118580i
706706 0 0
707707 26.1023 0.981677
708708 0 0
709709 9.99630i 0.375419i 0.982225 + 0.187709i 0.0601063π0.0601063\pi
−0.982225 + 0.187709i 0.939894π0.939894\pi
710710 0 0
711711 64.1606 2.40621
712712 0 0
713713 −5.94947 −0.222809
714714 0 0
715715 −11.7815 33.8553i −0.440602 1.26612i
716716 0 0
717717 22.2327 0.830296
718718 0 0
719719 52.7587 1.96757 0.983783 0.179363i 0.0574035π-0.0574035\pi
0.983783 + 0.179363i 0.0574035π0.0574035\pi
720720 0 0
721721 2.65496i 0.0988760i
722722 0 0
723723 −2.52274 −0.0938218
724724 0 0
725725 −23.7104 14.0108i −0.880581 0.520349i
726726 0 0
727727 14.2257i 0.527601i 0.964577 + 0.263801i 0.0849761π0.0849761\pi
−0.964577 + 0.263801i 0.915024π0.915024\pi
728728 0 0
729729 −37.7891 −1.39960
730730 0 0
731731 43.4927 1.60864
732732 0 0
733733 11.8558 0.437904 0.218952 0.975736i 0.429736π-0.429736\pi
0.218952 + 0.975736i 0.429736π0.429736\pi
734734 0 0
735735 −29.6570 8.10755i −1.09392 0.299051i
736736 0 0
737737 36.7442i 1.35349i
738738 0 0
739739 12.4740i 0.458864i 0.973325 + 0.229432i 0.0736868π0.0736868\pi
−0.973325 + 0.229432i 0.926313π0.926313\pi
740740 0 0
741741 −3.11140 4.53095i −0.114300 0.166449i
742742 0 0
743743 30.9003 1.13362 0.566812 0.823847i 0.308177π-0.308177\pi
0.566812 + 0.823847i 0.308177π0.308177\pi
744744 0 0
745745 −33.9314 9.27607i −1.24315 0.339849i
746746 0 0
747747 −104.268 −3.81498
748748 0 0
749749 2.22363i 0.0812497i
750750 0 0
751751 −11.2456 −0.410358 −0.205179 0.978725i 0.565778π-0.565778\pi
−0.205179 + 0.978725i 0.565778π0.565778\pi
752752 0 0
753753 27.6223i 1.00661i
754754 0 0
755755 −39.2769 10.7374i −1.42943 0.390775i
756756 0 0
757757 4.81148i 0.174876i −0.996170 0.0874381i 0.972132π-0.972132\pi
0.996170 0.0874381i 0.0278680π-0.0278680\pi
758758 0 0
759759 15.5979i 0.566169i
760760 0 0
761761 7.77200i 0.281735i −0.990028 0.140867i 0.955011π-0.955011\pi
0.990028 0.140867i 0.0449891π-0.0449891\pi
762762 0 0
763763 8.82259i 0.319399i
764764 0 0
765765 85.3521 + 23.3333i 3.08591 + 0.843618i
766766 0 0
767767 7.50196 5.15159i 0.270880 0.186013i
768768 0 0
769769 28.5345i 1.02898i 0.857496 + 0.514491i 0.172019π0.172019\pi
−0.857496 + 0.514491i 0.827981π0.827981\pi
770770 0 0
771771 −0.900499 −0.0324307
772772 0 0
773773 −31.8056 −1.14397 −0.571984 0.820264i 0.693826π-0.693826\pi
−0.571984 + 0.820264i 0.693826π0.693826\pi
774774 0 0
775775 13.9190 23.5549i 0.499985 0.846118i
776776 0 0
777777 19.5157i 0.700121i
778778 0 0
779779 4.92629 0.176503
780780 0 0
781781 57.7395 2.06608
782782 0 0
783783 78.3921i 2.80150i
784784 0 0
785785 −0.832042 0.227461i −0.0296968 0.00811844i
786786 0 0
787787 −33.8537 −1.20675 −0.603376 0.797457i 0.706178π-0.706178\pi
−0.603376 + 0.797457i 0.706178π0.706178\pi
788788 0 0
789789 8.62903 0.307201
790790 0 0
791791 24.4525i 0.869430i
792792 0 0
793793 0.327081 + 0.476309i 0.0116150 + 0.0169142i
794794 0 0
795795 7.88652 28.8485i 0.279706 1.02315i
796796 0 0
797797 37.4776i 1.32753i 0.747943 + 0.663763i 0.231042π0.231042\pi
−0.747943 + 0.663763i 0.768958π0.768958\pi
798798 0 0
799799 8.83643i 0.312610i
800800 0 0
801801 56.3988i 1.99275i
802802 0 0
803803 45.6367i 1.61048i
804804 0 0
805805 −3.88089 1.06095i −0.136783 0.0373935i
806806 0 0
807807 85.7880i 3.01988i
808808 0 0
809809 8.64480 0.303935 0.151968 0.988385i 0.451439π-0.451439\pi
0.151968 + 0.988385i 0.451439π0.451439\pi
810810 0 0
811811 15.4230i 0.541574i 0.962639 + 0.270787i 0.0872840π0.0872840\pi
−0.962639 + 0.270787i 0.912716π0.912716\pi
812812 0 0
813813 −81.9165 −2.87294
814814 0 0
815815 4.04305 14.7893i 0.141622 0.518045i
816816 0 0
817817 −3.84830 −0.134635
818818 0 0
819819 −25.0315 36.4519i −0.874670 1.27373i
820820 0 0
821821 24.9107i 0.869389i 0.900578 + 0.434694i 0.143144π0.143144\pi
−0.900578 + 0.434694i 0.856856π0.856856\pi
822822 0 0
823823 3.47743i 0.121215i −0.998162 0.0606077i 0.980696π-0.980696\pi
0.998162 0.0606077i 0.0193039π-0.0193039\pi
824824 0 0
825825 −61.7549 36.4920i −2.15003 1.27049i
826826 0 0
827827 −32.6194 −1.13429 −0.567143 0.823619i 0.691951π-0.691951\pi
−0.567143 + 0.823619i 0.691951π0.691951\pi
828828 0 0
829829 36.8123 1.27854 0.639271 0.768981i 0.279236π-0.279236\pi
0.639271 + 0.768981i 0.279236π0.279236\pi
830830 0 0
831831 20.5608 0.713248
832832 0 0
833833 22.7541i 0.788383i
834834 0 0
835835 6.41757 23.4752i 0.222089 0.812391i
836836 0 0
837837 −77.8782 −2.69187
838838 0 0
839839 23.6723i 0.817259i −0.912700 0.408629i 0.866007π-0.866007\pi
0.912700 0.408629i 0.133993π-0.133993\pi
840840 0 0
841841 1.33938 0.0461856
842842 0 0
843843 −2.46877 −0.0850291
844844 0 0
845845 −23.4169 17.2235i −0.805566 0.592506i
846846 0 0
847847 −14.5117 −0.498628
848848 0 0
849849 −30.2918 −1.03961
850850 0 0
851851 3.97378i 0.136219i
852852 0 0
853853 1.82238 0.0623970 0.0311985 0.999513i 0.490068π-0.490068\pi
0.0311985 + 0.999513i 0.490068π0.490068\pi
854854 0 0
855855 −7.55208 2.06457i −0.258276 0.0706066i
856856 0 0
857857 34.1031i 1.16494i 0.812852 + 0.582470i 0.197914π0.197914\pi
−0.812852 + 0.582470i 0.802086π0.802086\pi
858858 0 0
859859 18.6350 0.635819 0.317910 0.948121i 0.397019π-0.397019\pi
0.317910 + 0.948121i 0.397019π0.397019\pi
860860 0 0
861861 55.6760 1.89743
862862 0 0
863863 5.16462 0.175806 0.0879028 0.996129i 0.471984π-0.471984\pi
0.0879028 + 0.996129i 0.471984π0.471984\pi
864864 0 0
865865 44.5406 + 12.1764i 1.51443 + 0.414010i
866866 0 0
867867 37.1430i 1.26144i
868868 0 0
869869 38.4939i 1.30582i
870870 0 0
871871 16.8673 + 24.5629i 0.571528 + 0.832282i
872872 0 0
873873 −124.056 −4.19865
874874 0 0
875875 13.2800 12.8830i 0.448945 0.435524i
876876 0 0
877877 −20.1381 −0.680015 −0.340007 0.940423i 0.610430π-0.610430\pi
−0.340007 + 0.940423i 0.610430π0.610430\pi
878878 0 0
879879 43.5182i 1.46783i
880880 0 0
881881 −10.2164 −0.344199 −0.172100 0.985080i 0.555055π-0.555055\pi
−0.172100 + 0.985080i 0.555055π0.555055\pi
882882 0 0
883883 14.6787i 0.493976i 0.969018 + 0.246988i 0.0794409π0.0794409\pi
−0.969018 + 0.246988i 0.920559π0.920559\pi
884884 0 0
885885 4.80210 17.5659i 0.161421 0.590470i
886886 0 0
887887 12.6524i 0.424827i 0.977180 + 0.212413i 0.0681323π0.0681323\pi
−0.977180 + 0.212413i 0.931868π0.931868\pi
888888 0 0
889889 5.21505i 0.174907i
890890 0 0
891891 105.325i 3.52851i
892892 0 0
893893 0.781860i 0.0261640i
894894 0 0
895895 1.11563 4.08093i 0.0372915 0.136410i
896896 0 0
897897 7.16019 + 10.4270i 0.239072 + 0.348146i
898898 0 0
899899 30.1405i 1.00524i
900900 0 0
901901 22.1338 0.737383
902902 0 0
903903 −43.4927 −1.44735
904904 0 0
905905 −2.76790 + 10.1248i −0.0920081 + 0.336561i
906906 0 0
907907 39.2705i 1.30396i −0.758238 0.651978i 0.773940π-0.773940\pi
0.758238 0.651978i 0.226060π-0.226060\pi
908908 0 0
909909 −116.891 −3.87703
910910 0 0
911911 8.32826 0.275928 0.137964 0.990437i 0.455944π-0.455944\pi
0.137964 + 0.990437i 0.455944π0.455944\pi
912912 0 0
913913 62.5569i 2.07033i
914914 0 0
915915 1.11528 + 0.304892i 0.0368700 + 0.0100794i
916916 0 0
917917 −34.8723 −1.15158
918918 0 0
919919 −45.1893 −1.49066 −0.745329 0.666697i 0.767708π-0.767708\pi
−0.745329 + 0.666697i 0.767708π0.767708\pi
920920 0 0
921921 81.9760i 2.70120i
922922 0 0
923923 38.5979 26.5051i 1.27046 0.872427i
924924 0 0
925925 15.7329 + 9.29681i 0.517293 + 0.305677i
926926 0 0
927927 11.8894i 0.390501i
928928 0 0
929929 18.8393i 0.618098i 0.951046 + 0.309049i 0.100011π0.100011\pi
−0.951046 + 0.309049i 0.899989π0.899989\pi
930930 0 0
931931 2.01332i 0.0659837i
932932 0 0
933933 40.0905i 1.31250i
934934 0 0
935935 13.9991 51.2079i 0.457819 1.67468i
936936 0 0
937937 15.8303i 0.517154i −0.965991 0.258577i 0.916746π-0.916746\pi
0.965991 0.258577i 0.0832536π-0.0832536\pi
938938 0 0
939939 −77.3298 −2.52356
940940 0 0
941941 8.41058i 0.274177i −0.990559 0.137088i 0.956226π-0.956226\pi
0.990559 0.137088i 0.0437745π-0.0437745\pi
942942 0 0
943943 −11.3367 −0.369175
944944 0 0
945945 −50.8007 13.8878i −1.65255 0.451769i
946946 0 0
947947 47.9898 1.55946 0.779730 0.626116i 0.215356π-0.215356\pi
0.779730 + 0.626116i 0.215356π0.215356\pi
948948 0 0
949949 −20.9494 30.5074i −0.680046 0.990311i
950950 0 0
951951 65.6992i 2.13044i
952952 0 0
953953 38.6553i 1.25217i −0.779755 0.626084i 0.784657π-0.784657\pi
0.779755 0.626084i 0.215343π-0.215343\pi
954954 0 0
955955 6.68474 24.4525i 0.216313 0.791263i
956956 0 0
957957 79.0205 2.55437
958958 0 0
959959 9.24467 0.298526
960960 0 0
961961 1.05706 0.0340986
962962 0 0
963963 9.95785i 0.320887i
964964 0 0
965965 9.69753 35.4731i 0.312175 1.14192i
966966 0 0
967967 32.5757 1.04756 0.523782 0.851853i 0.324521π-0.324521\pi
0.523782 + 0.851853i 0.324521π0.324521\pi
968968 0 0
969969 8.13985i 0.261490i
970970 0 0
971971 7.75150 0.248758 0.124379 0.992235i 0.460306π-0.460306\pi
0.124379 + 0.992235i 0.460306π0.460306\pi
972972 0 0
973973 12.9973 0.416674
974974 0 0
975975 −58.0336 + 3.95412i −1.85856 + 0.126633i
976976 0 0
977977 −0.0696366 −0.00222787 −0.00111394 0.999999i 0.500355π-0.500355\pi
−0.00111394 + 0.999999i 0.500355π0.500355\pi
978978 0 0
979979 −33.8371 −1.08144
980980 0 0
981981 39.5093i 1.26143i
982982 0 0
983983 −51.0126 −1.62705 −0.813525 0.581530i 0.802454π-0.802454\pi
−0.813525 + 0.581530i 0.802454π0.802454\pi
984984 0 0
985985 −9.95675 + 36.4213i −0.317248 + 1.16048i
986986 0 0
987987 8.83643i 0.281267i
988988 0 0
989989 8.85599 0.281604
990990 0 0
991991 −42.6294 −1.35417 −0.677084 0.735906i 0.736757π-0.736757\pi
−0.677084 + 0.735906i 0.736757π0.736757\pi
992992 0 0
993993 97.0667 3.08032
994994 0 0
995995 −11.2176 + 41.0333i −0.355620 + 1.30084i
996996 0 0
997997 56.5323i 1.79040i −0.445670 0.895198i 0.647034π-0.647034\pi
0.445670 0.895198i 0.352966π-0.352966\pi
998998 0 0
999999 52.0166i 1.64573i
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 1040.2.f.g.129.1 10
4.3 odd 2 520.2.f.b.129.10 yes 10
5.4 even 2 1040.2.f.f.129.10 10
13.12 even 2 1040.2.f.f.129.1 10
20.3 even 4 2600.2.k.f.2001.2 20
20.7 even 4 2600.2.k.f.2001.19 20
20.19 odd 2 520.2.f.a.129.1 10
52.51 odd 2 520.2.f.a.129.10 yes 10
65.64 even 2 inner 1040.2.f.g.129.10 10
260.103 even 4 2600.2.k.f.2001.1 20
260.207 even 4 2600.2.k.f.2001.20 20
260.259 odd 2 520.2.f.b.129.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
520.2.f.a.129.1 10 20.19 odd 2
520.2.f.a.129.10 yes 10 52.51 odd 2
520.2.f.b.129.1 yes 10 260.259 odd 2
520.2.f.b.129.10 yes 10 4.3 odd 2
1040.2.f.f.129.1 10 13.12 even 2
1040.2.f.f.129.10 10 5.4 even 2
1040.2.f.g.129.1 10 1.1 even 1 trivial
1040.2.f.g.129.10 10 65.64 even 2 inner
2600.2.k.f.2001.1 20 260.103 even 4
2600.2.k.f.2001.2 20 20.3 even 4
2600.2.k.f.2001.19 20 20.7 even 4
2600.2.k.f.2001.20 20 260.207 even 4