Properties

Label 600.6.f.i.49.2
Level 600600
Weight 66
Character 600.49
Analytic conductor 96.23096.230
Analytic rank 00
Dimension 22
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] = [600,6,Mod(49,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.49"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 600=23352 600 = 2^{3} \cdot 3 \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 600.f (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,0,0,0,0,-162,0,1368] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 96.230291887896.2302918878
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 49.2
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 600.49
Dual form 600.6.f.i.49.1

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+9.00000iq380.0000iq781.0000q9+684.000q11+978.000iq13862.000iq17916.000q19+720.000q21+1552.00iq23729.000iq27+7314.00q299312.00q31+6156.00iq338826.00iq378802.00q393286.00q417556.00iq435960.00iq47+10407.0q49+7758.00q51+8698.00iq538244.00iq57+42036.0q59+37518.0q61+6480.00iq63+29324.0iq6713968.0q69+84408.0q71+46550.0iq7354720.0iq7726752.0q79+6561.00q81+7956.00iq83+65826.0iq8759674.0q89+78240.0q9183808.0iq93+136898.iq9755404.0q99+O(q100)q+9.00000i q^{3} -80.0000i q^{7} -81.0000 q^{9} +684.000 q^{11} +978.000i q^{13} -862.000i q^{17} -916.000 q^{19} +720.000 q^{21} +1552.00i q^{23} -729.000i q^{27} +7314.00 q^{29} -9312.00 q^{31} +6156.00i q^{33} -8826.00i q^{37} -8802.00 q^{39} -3286.00 q^{41} -7556.00i q^{43} -5960.00i q^{47} +10407.0 q^{49} +7758.00 q^{51} +8698.00i q^{53} -8244.00i q^{57} +42036.0 q^{59} +37518.0 q^{61} +6480.00i q^{63} +29324.0i q^{67} -13968.0 q^{69} +84408.0 q^{71} +46550.0i q^{73} -54720.0i q^{77} -26752.0 q^{79} +6561.00 q^{81} +7956.00i q^{83} +65826.0i q^{87} -59674.0 q^{89} +78240.0 q^{91} -83808.0i q^{93} +136898. i q^{97} -55404.0 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q162q9+1368q111832q19+1440q21+14628q2918624q3117604q396572q41+20814q49+15516q51+84072q59+75036q6127936q69+168816q71+110808q99+O(q100) 2 q - 162 q^{9} + 1368 q^{11} - 1832 q^{19} + 1440 q^{21} + 14628 q^{29} - 18624 q^{31} - 17604 q^{39} - 6572 q^{41} + 20814 q^{49} + 15516 q^{51} + 84072 q^{59} + 75036 q^{61} - 27936 q^{69} + 168816 q^{71}+ \cdots - 110808 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/600Z)×\left(\mathbb{Z}/600\mathbb{Z}\right)^\times.

nn 151151 301301 401401 577577
χ(n)\chi(n) 11 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 9.00000i 0.577350i
44 0 0
55 0 0
66 0 0
77 − 80.0000i − 0.617085i −0.951211 0.308542i 0.900159π-0.900159\pi
0.951211 0.308542i 0.0998412π-0.0998412\pi
88 0 0
99 −81.0000 −0.333333
1010 0 0
1111 684.000 1.70441 0.852206 0.523207i 0.175265π-0.175265\pi
0.852206 + 0.523207i 0.175265π0.175265\pi
1212 0 0
1313 978.000i 1.60502i 0.596639 + 0.802510i 0.296503π0.296503\pi
−0.596639 + 0.802510i 0.703497π0.703497\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 862.000i − 0.723411i −0.932292 0.361705i 0.882195π-0.882195\pi
0.932292 0.361705i 0.117805π-0.117805\pi
1818 0 0
1919 −916.000 −0.582119 −0.291059 0.956705i 0.594008π-0.594008\pi
−0.291059 + 0.956705i 0.594008π0.594008\pi
2020 0 0
2121 720.000 0.356274
2222 0 0
2323 1552.00i 0.611747i 0.952072 + 0.305874i 0.0989485π0.0989485\pi
−0.952072 + 0.305874i 0.901051π0.901051\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 729.000i − 0.192450i
2828 0 0
2929 7314.00 1.61495 0.807477 0.589900i 0.200833π-0.200833\pi
0.807477 + 0.589900i 0.200833π0.200833\pi
3030 0 0
3131 −9312.00 −1.74036 −0.870179 0.492735i 0.835997π-0.835997\pi
−0.870179 + 0.492735i 0.835997π0.835997\pi
3232 0 0
3333 6156.00i 0.984042i
3434 0 0
3535 0 0
3636 0 0
3737 − 8826.00i − 1.05989i −0.848033 0.529944i 0.822213π-0.822213\pi
0.848033 0.529944i 0.177787π-0.177787\pi
3838 0 0
3939 −8802.00 −0.926659
4040 0 0
4141 −3286.00 −0.305287 −0.152643 0.988281i 0.548779π-0.548779\pi
−0.152643 + 0.988281i 0.548779π0.548779\pi
4242 0 0
4343 − 7556.00i − 0.623190i −0.950215 0.311595i 0.899137π-0.899137\pi
0.950215 0.311595i 0.100863π-0.100863\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 5960.00i − 0.393552i −0.980449 0.196776i 0.936953π-0.936953\pi
0.980449 0.196776i 0.0630471π-0.0630471\pi
4848 0 0
4949 10407.0 0.619206
5050 0 0
5151 7758.00 0.417661
5252 0 0
5353 8698.00i 0.425334i 0.977125 + 0.212667i 0.0682149π0.0682149\pi
−0.977125 + 0.212667i 0.931785π0.931785\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 8244.00i − 0.336086i
5858 0 0
5959 42036.0 1.57214 0.786070 0.618137i 0.212112π-0.212112\pi
0.786070 + 0.618137i 0.212112π0.212112\pi
6060 0 0
6161 37518.0 1.29097 0.645483 0.763774i 0.276656π-0.276656\pi
0.645483 + 0.763774i 0.276656π0.276656\pi
6262 0 0
6363 6480.00i 0.205695i
6464 0 0
6565 0 0
6666 0 0
6767 29324.0i 0.798061i 0.916938 + 0.399031i 0.130653π0.130653\pi
−0.916938 + 0.399031i 0.869347π0.869347\pi
6868 0 0
6969 −13968.0 −0.353193
7070 0 0
7171 84408.0 1.98718 0.993591 0.113033i 0.0360566π-0.0360566\pi
0.993591 + 0.113033i 0.0360566π0.0360566\pi
7272 0 0
7373 46550.0i 1.02238i 0.859468 + 0.511190i 0.170795π0.170795\pi
−0.859468 + 0.511190i 0.829205π0.829205\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 54720.0i − 1.05177i
7878 0 0
7979 −26752.0 −0.482268 −0.241134 0.970492i 0.577519π-0.577519\pi
−0.241134 + 0.970492i 0.577519π0.577519\pi
8080 0 0
8181 6561.00 0.111111
8282 0 0
8383 7956.00i 0.126765i 0.997989 + 0.0633825i 0.0201888π0.0201888\pi
−0.997989 + 0.0633825i 0.979811π0.979811\pi
8484 0 0
8585 0 0
8686 0 0
8787 65826.0i 0.932394i
8888 0 0
8989 −59674.0 −0.798565 −0.399282 0.916828i 0.630741π-0.630741\pi
−0.399282 + 0.916828i 0.630741π0.630741\pi
9090 0 0
9191 78240.0 0.990434
9292 0 0
9393 − 83808.0i − 1.00480i
9494 0 0
9595 0 0
9696 0 0
9797 136898.i 1.47730i 0.674091 + 0.738648i 0.264536π0.264536\pi
−0.674091 + 0.738648i 0.735464π0.735464\pi
9898 0 0
9999 −55404.0 −0.568137
100100 0 0
101101 −202858. −1.97874 −0.989370 0.145421i 0.953546π-0.953546\pi
−0.989370 + 0.145421i 0.953546π0.953546\pi
102102 0 0
103103 8576.00i 0.0796511i 0.999207 + 0.0398255i 0.0126802π0.0126802\pi
−0.999207 + 0.0398255i 0.987320π0.987320\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 19948.0i − 0.168438i −0.996447 0.0842190i 0.973160π-0.973160\pi
0.996447 0.0842190i 0.0268395π-0.0268395\pi
108108 0 0
109109 −37598.0 −0.303109 −0.151554 0.988449i 0.548428π-0.548428\pi
−0.151554 + 0.988449i 0.548428π0.548428\pi
110110 0 0
111111 79434.0 0.611926
112112 0 0
113113 191838.i 1.41331i 0.707556 + 0.706657i 0.249797π0.249797\pi
−0.707556 + 0.706657i 0.750203π0.750203\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 79218.0i − 0.535007i
118118 0 0
119119 −68960.0 −0.446406
120120 0 0
121121 306805. 1.90502
122122 0 0
123123 − 29574.0i − 0.176257i
124124 0 0
125125 0 0
126126 0 0
127127 98888.0i 0.544044i 0.962291 + 0.272022i 0.0876924π0.0876924\pi
−0.962291 + 0.272022i 0.912308π0.912308\pi
128128 0 0
129129 68004.0 0.359799
130130 0 0
131131 29636.0 0.150883 0.0754417 0.997150i 0.475963π-0.475963\pi
0.0754417 + 0.997150i 0.475963π0.475963\pi
132132 0 0
133133 73280.0i 0.359217i
134134 0 0
135135 0 0
136136 0 0
137137 − 4614.00i − 0.0210028i −0.999945 0.0105014i 0.996657π-0.996657\pi
0.999945 0.0105014i 0.00334275π-0.00334275\pi
138138 0 0
139139 254292. 1.11634 0.558169 0.829727i 0.311504π-0.311504\pi
0.558169 + 0.829727i 0.311504π0.311504\pi
140140 0 0
141141 53640.0 0.227217
142142 0 0
143143 668952.i 2.73561i
144144 0 0
145145 0 0
146146 0 0
147147 93663.0i 0.357499i
148148 0 0
149149 83226.0 0.307110 0.153555 0.988140i 0.450928π-0.450928\pi
0.153555 + 0.988140i 0.450928π0.450928\pi
150150 0 0
151151 −212616. −0.758846 −0.379423 0.925223i 0.623877π-0.623877\pi
−0.379423 + 0.925223i 0.623877π0.623877\pi
152152 0 0
153153 69822.0i 0.241137i
154154 0 0
155155 0 0
156156 0 0
157157 112702.i 0.364907i 0.983214 + 0.182454i 0.0584039π0.0584039\pi
−0.983214 + 0.182454i 0.941596π0.941596\pi
158158 0 0
159159 −78282.0 −0.245566
160160 0 0
161161 124160. 0.377500
162162 0 0
163163 411172.i 1.21214i 0.795409 + 0.606072i 0.207256π0.207256\pi
−0.795409 + 0.606072i 0.792744π0.792744\pi
164164 0 0
165165 0 0
166166 0 0
167167 258896.i 0.718347i 0.933271 + 0.359173i 0.116941π0.116941\pi
−0.933271 + 0.359173i 0.883059π0.883059\pi
168168 0 0
169169 −585191. −1.57609
170170 0 0
171171 74196.0 0.194040
172172 0 0
173173 397026.i 1.00856i 0.863539 + 0.504282i 0.168243π0.168243\pi
−0.863539 + 0.504282i 0.831757π0.831757\pi
174174 0 0
175175 0 0
176176 0 0
177177 378324.i 0.907676i
178178 0 0
179179 473468. 1.10448 0.552240 0.833685i 0.313773π-0.313773\pi
0.552240 + 0.833685i 0.313773π0.313773\pi
180180 0 0
181181 −79834.0 −0.181130 −0.0905652 0.995891i 0.528867π-0.528867\pi
−0.0905652 + 0.995891i 0.528867π0.528867\pi
182182 0 0
183183 337662.i 0.745340i
184184 0 0
185185 0 0
186186 0 0
187187 − 589608.i − 1.23299i
188188 0 0
189189 −58320.0 −0.118758
190190 0 0
191191 397360. 0.788135 0.394068 0.919081i 0.371068π-0.371068\pi
0.394068 + 0.919081i 0.371068π0.371068\pi
192192 0 0
193193 − 777858.i − 1.50317i −0.659638 0.751583i 0.729291π-0.729291\pi
0.659638 0.751583i 0.270709π-0.270709\pi
194194 0 0
195195 0 0
196196 0 0
197197 254678.i 0.467548i 0.972291 + 0.233774i 0.0751075π0.0751075\pi
−0.972291 + 0.233774i 0.924892π0.924892\pi
198198 0 0
199199 540264. 0.967104 0.483552 0.875316i 0.339346π-0.339346\pi
0.483552 + 0.875316i 0.339346π0.339346\pi
200200 0 0
201201 −263916. −0.460761
202202 0 0
203203 − 585120.i − 0.996563i
204204 0 0
205205 0 0
206206 0 0
207207 − 125712.i − 0.203916i
208208 0 0
209209 −626544. −0.992169
210210 0 0
211211 1.05690e6 1.63428 0.817142 0.576436i 0.195557π-0.195557\pi
0.817142 + 0.576436i 0.195557π0.195557\pi
212212 0 0
213213 759672.i 1.14730i
214214 0 0
215215 0 0
216216 0 0
217217 744960.i 1.07395i
218218 0 0
219219 −418950. −0.590272
220220 0 0
221221 843036. 1.16109
222222 0 0
223223 1.09063e6i 1.46864i 0.678802 + 0.734321i 0.262499π0.262499\pi
−0.678802 + 0.734321i 0.737501π0.737501\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 2772.00i − 0.00357050i −0.999998 0.00178525i 0.999432π-0.999432\pi
0.999998 0.00178525i 0.000568262π-0.000568262\pi
228228 0 0
229229 304458. 0.383653 0.191827 0.981429i 0.438559π-0.438559\pi
0.191827 + 0.981429i 0.438559π0.438559\pi
230230 0 0
231231 492480. 0.607238
232232 0 0
233233 329990.i 0.398209i 0.979978 + 0.199104i 0.0638033π0.0638033\pi
−0.979978 + 0.199104i 0.936197π0.936197\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 240768.i − 0.278438i
238238 0 0
239239 −721584. −0.817132 −0.408566 0.912729i 0.633971π-0.633971\pi
−0.408566 + 0.912729i 0.633971π0.633971\pi
240240 0 0
241241 271538. 0.301154 0.150577 0.988598i 0.451887π-0.451887\pi
0.150577 + 0.988598i 0.451887π0.451887\pi
242242 0 0
243243 59049.0i 0.0641500i
244244 0 0
245245 0 0
246246 0 0
247247 − 895848.i − 0.934312i
248248 0 0
249249 −71604.0 −0.0731878
250250 0 0
251251 1.34534e6 1.34787 0.673935 0.738791i 0.264603π-0.264603\pi
0.673935 + 0.738791i 0.264603π0.264603\pi
252252 0 0
253253 1.06157e6i 1.04267i
254254 0 0
255255 0 0
256256 0 0
257257 1.62290e6i 1.53270i 0.642421 + 0.766352i 0.277930π0.277930\pi
−0.642421 + 0.766352i 0.722070π0.722070\pi
258258 0 0
259259 −706080. −0.654040
260260 0 0
261261 −592434. −0.538318
262262 0 0
263263 − 472128.i − 0.420892i −0.977606 0.210446i 0.932508π-0.932508\pi
0.977606 0.210446i 0.0674916π-0.0674916\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 537066.i − 0.461052i
268268 0 0
269269 −2430.00 −0.00204751 −0.00102375 0.999999i 0.500326π-0.500326\pi
−0.00102375 + 0.999999i 0.500326π0.500326\pi
270270 0 0
271271 1.65157e6 1.36607 0.683035 0.730385i 0.260659π-0.260659\pi
0.683035 + 0.730385i 0.260659π0.260659\pi
272272 0 0
273273 704160.i 0.571827i
274274 0 0
275275 0 0
276276 0 0
277277 2.21129e6i 1.73159i 0.500397 + 0.865796i 0.333187π0.333187\pi
−0.500397 + 0.865796i 0.666813π0.666813\pi
278278 0 0
279279 754272. 0.580120
280280 0 0
281281 −423014. −0.319587 −0.159793 0.987150i 0.551083π-0.551083\pi
−0.159793 + 0.987150i 0.551083π0.551083\pi
282282 0 0
283283 487052.i 0.361501i 0.983529 + 0.180750i 0.0578526π0.0578526\pi
−0.983529 + 0.180750i 0.942147π0.942147\pi
284284 0 0
285285 0 0
286286 0 0
287287 262880.i 0.188388i
288288 0 0
289289 676813. 0.476677
290290 0 0
291291 −1.23208e6 −0.852918
292292 0 0
293293 1.02692e6i 0.698825i 0.936969 + 0.349412i 0.113619π0.113619\pi
−0.936969 + 0.349412i 0.886381π0.886381\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 498636.i − 0.328014i
298298 0 0
299299 −1.51786e6 −0.981867
300300 0 0
301301 −604480. −0.384561
302302 0 0
303303 − 1.82572e6i − 1.14243i
304304 0 0
305305 0 0
306306 0 0
307307 − 1.07133e6i − 0.648751i −0.945928 0.324376i 0.894846π-0.894846\pi
0.945928 0.324376i 0.105154π-0.105154\pi
308308 0 0
309309 −77184.0 −0.0459866
310310 0 0
311311 1.87422e6 1.09880 0.549400 0.835559i 0.314856π-0.314856\pi
0.549400 + 0.835559i 0.314856π0.314856\pi
312312 0 0
313313 − 2.92883e6i − 1.68979i −0.534932 0.844895i 0.679663π-0.679663\pi
0.534932 0.844895i 0.320337π-0.320337\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 2.94831e6i − 1.64788i −0.566680 0.823938i 0.691773π-0.691773\pi
0.566680 0.823938i 0.308227π-0.308227\pi
318318 0 0
319319 5.00278e6 2.75254
320320 0 0
321321 179532. 0.0972477
322322 0 0
323323 789592.i 0.421111i
324324 0 0
325325 0 0
326326 0 0
327327 − 338382.i − 0.175000i
328328 0 0
329329 −476800. −0.242855
330330 0 0
331331 −856100. −0.429491 −0.214746 0.976670i 0.568892π-0.568892\pi
−0.214746 + 0.976670i 0.568892π0.568892\pi
332332 0 0
333333 714906.i 0.353296i
334334 0 0
335335 0 0
336336 0 0
337337 − 3.11272e6i − 1.49302i −0.665375 0.746509i 0.731728π-0.731728\pi
0.665375 0.746509i 0.268272π-0.268272\pi
338338 0 0
339339 −1.72654e6 −0.815977
340340 0 0
341341 −6.36941e6 −2.96629
342342 0 0
343343 − 2.17712e6i − 0.999188i
344344 0 0
345345 0 0
346346 0 0
347347 − 2.09651e6i − 0.934701i −0.884072 0.467351i 0.845209π-0.845209\pi
0.884072 0.467351i 0.154791π-0.154791\pi
348348 0 0
349349 4.44677e6 1.95425 0.977127 0.212656i 0.0682113π-0.0682113\pi
0.977127 + 0.212656i 0.0682113π0.0682113\pi
350350 0 0
351351 712962. 0.308886
352352 0 0
353353 − 1.80434e6i − 0.770692i −0.922772 0.385346i 0.874082π-0.874082\pi
0.922772 0.385346i 0.125918π-0.125918\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 620640.i − 0.257733i
358358 0 0
359359 −2.84270e6 −1.16411 −0.582055 0.813149i 0.697751π-0.697751\pi
−0.582055 + 0.813149i 0.697751π0.697751\pi
360360 0 0
361361 −1.63704e6 −0.661138
362362 0 0
363363 2.76124e6i 1.09986i
364364 0 0
365365 0 0
366366 0 0
367367 1.65561e6i 0.641641i 0.947140 + 0.320821i 0.103959π0.103959\pi
−0.947140 + 0.320821i 0.896041π0.896041\pi
368368 0 0
369369 266166. 0.101762
370370 0 0
371371 695840. 0.262467
372372 0 0
373373 199690.i 0.0743163i 0.999309 + 0.0371582i 0.0118305π0.0118305\pi
−0.999309 + 0.0371582i 0.988169π0.988169\pi
374374 0 0
375375 0 0
376376 0 0
377377 7.15309e6i 2.59203i
378378 0 0
379379 1.45610e6 0.520707 0.260353 0.965513i 0.416161π-0.416161\pi
0.260353 + 0.965513i 0.416161π0.416161\pi
380380 0 0
381381 −889992. −0.314104
382382 0 0
383383 4.62548e6i 1.61124i 0.592434 + 0.805619i 0.298167π0.298167\pi
−0.592434 + 0.805619i 0.701833π0.701833\pi
384384 0 0
385385 0 0
386386 0 0
387387 612036.i 0.207730i
388388 0 0
389389 −3.51068e6 −1.17630 −0.588149 0.808753i 0.700143π-0.700143\pi
−0.588149 + 0.808753i 0.700143π0.700143\pi
390390 0 0
391391 1.33782e6 0.442545
392392 0 0
393393 266724.i 0.0871125i
394394 0 0
395395 0 0
396396 0 0
397397 4.84773e6i 1.54370i 0.635807 + 0.771848i 0.280667π0.280667\pi
−0.635807 + 0.771848i 0.719333π0.719333\pi
398398 0 0
399399 −659520. −0.207394
400400 0 0
401401 −4.21515e6 −1.30904 −0.654519 0.756046i 0.727129π-0.727129\pi
−0.654519 + 0.756046i 0.727129π0.727129\pi
402402 0 0
403403 − 9.10714e6i − 2.79331i
404404 0 0
405405 0 0
406406 0 0
407407 − 6.03698e6i − 1.80648i
408408 0 0
409409 −4.49535e6 −1.32879 −0.664394 0.747383i 0.731310π-0.731310\pi
−0.664394 + 0.747383i 0.731310π0.731310\pi
410410 0 0
411411 41526.0 0.0121259
412412 0 0
413413 − 3.36288e6i − 0.970144i
414414 0 0
415415 0 0
416416 0 0
417417 2.28863e6i 0.644518i
418418 0 0
419419 4.44571e6 1.23710 0.618552 0.785744i 0.287720π-0.287720\pi
0.618552 + 0.785744i 0.287720π0.287720\pi
420420 0 0
421421 −4.87185e6 −1.33964 −0.669821 0.742523i 0.733629π-0.733629\pi
−0.669821 + 0.742523i 0.733629π0.733629\pi
422422 0 0
423423 482760.i 0.131184i
424424 0 0
425425 0 0
426426 0 0
427427 − 3.00144e6i − 0.796636i
428428 0 0
429429 −6.02057e6 −1.57941
430430 0 0
431431 549152. 0.142397 0.0711983 0.997462i 0.477318π-0.477318\pi
0.0711983 + 0.997462i 0.477318π0.477318\pi
432432 0 0
433433 − 2.37675e6i − 0.609206i −0.952479 0.304603i 0.901476π-0.901476\pi
0.952479 0.304603i 0.0985239π-0.0985239\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 1.42163e6i − 0.356110i
438438 0 0
439439 −1.31188e6 −0.324887 −0.162444 0.986718i 0.551938π-0.551938\pi
−0.162444 + 0.986718i 0.551938π0.551938\pi
440440 0 0
441441 −842967. −0.206402
442442 0 0
443443 − 2.92914e6i − 0.709138i −0.935030 0.354569i 0.884628π-0.884628\pi
0.935030 0.354569i 0.115372π-0.115372\pi
444444 0 0
445445 0 0
446446 0 0
447447 749034.i 0.177310i
448448 0 0
449449 4.30777e6 1.00841 0.504205 0.863584i 0.331786π-0.331786\pi
0.504205 + 0.863584i 0.331786π0.331786\pi
450450 0 0
451451 −2.24762e6 −0.520334
452452 0 0
453453 − 1.91354e6i − 0.438120i
454454 0 0
455455 0 0
456456 0 0
457457 4.48196e6i 1.00387i 0.864905 + 0.501935i 0.167378π0.167378\pi
−0.864905 + 0.501935i 0.832622π0.832622\pi
458458 0 0
459459 −628398. −0.139220
460460 0 0
461461 −95906.0 −0.0210181 −0.0105091 0.999945i 0.503345π-0.503345\pi
−0.0105091 + 0.999945i 0.503345π0.503345\pi
462462 0 0
463463 − 7.24487e6i − 1.57065i −0.619086 0.785323i 0.712497π-0.712497\pi
0.619086 0.785323i 0.287503π-0.287503\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 1.80528e6i − 0.383048i −0.981488 0.191524i 0.938657π-0.938657\pi
0.981488 0.191524i 0.0613430π-0.0613430\pi
468468 0 0
469469 2.34592e6 0.492471
470470 0 0
471471 −1.01432e6 −0.210679
472472 0 0
473473 − 5.16830e6i − 1.06217i
474474 0 0
475475 0 0
476476 0 0
477477 − 704538.i − 0.141778i
478478 0 0
479479 1.02682e6 0.204481 0.102241 0.994760i 0.467399π-0.467399\pi
0.102241 + 0.994760i 0.467399π0.467399\pi
480480 0 0
481481 8.63183e6 1.70114
482482 0 0
483483 1.11744e6i 0.217950i
484484 0 0
485485 0 0
486486 0 0
487487 − 6.43013e6i − 1.22856i −0.789087 0.614281i 0.789446π-0.789446\pi
0.789087 0.614281i 0.210554π-0.210554\pi
488488 0 0
489489 −3.70055e6 −0.699832
490490 0 0
491491 −6.89637e6 −1.29097 −0.645486 0.763772i 0.723345π-0.723345\pi
−0.645486 + 0.763772i 0.723345π0.723345\pi
492492 0 0
493493 − 6.30467e6i − 1.16827i
494494 0 0
495495 0 0
496496 0 0
497497 − 6.75264e6i − 1.22626i
498498 0 0
499499 8.27403e6 1.48753 0.743765 0.668441i 0.233038π-0.233038\pi
0.743765 + 0.668441i 0.233038π0.233038\pi
500500 0 0
501501 −2.33006e6 −0.414738
502502 0 0
503503 5.83070e6i 1.02755i 0.857926 + 0.513773i 0.171753π0.171753\pi
−0.857926 + 0.513773i 0.828247π0.828247\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 5.26672e6i − 0.909956i
508508 0 0
509509 −3.66421e6 −0.626881 −0.313441 0.949608i 0.601482π-0.601482\pi
−0.313441 + 0.949608i 0.601482π0.601482\pi
510510 0 0
511511 3.72400e6 0.630895
512512 0 0
513513 667764.i 0.112029i
514514 0 0
515515 0 0
516516 0 0
517517 − 4.07664e6i − 0.670774i
518518 0 0
519519 −3.57323e6 −0.582295
520520 0 0
521521 −5.79381e6 −0.935126 −0.467563 0.883960i 0.654868π-0.654868\pi
−0.467563 + 0.883960i 0.654868π0.654868\pi
522522 0 0
523523 − 6.06676e6i − 0.969845i −0.874557 0.484922i 0.838848π-0.838848\pi
0.874557 0.484922i 0.161152π-0.161152\pi
524524 0 0
525525 0 0
526526 0 0
527527 8.02694e6i 1.25899i
528528 0 0
529529 4.02764e6 0.625765
530530 0 0
531531 −3.40492e6 −0.524047
532532 0 0
533533 − 3.21371e6i − 0.489991i
534534 0 0
535535 0 0
536536 0 0
537537 4.26121e6i 0.637672i
538538 0 0
539539 7.11839e6 1.05538
540540 0 0
541541 −2.19330e6 −0.322184 −0.161092 0.986939i 0.551502π-0.551502\pi
−0.161092 + 0.986939i 0.551502π0.551502\pi
542542 0 0
543543 − 718506.i − 0.104576i
544544 0 0
545545 0 0
546546 0 0
547547 1.03263e7i 1.47563i 0.675004 + 0.737814i 0.264142π0.264142\pi
−0.675004 + 0.737814i 0.735858π0.735858\pi
548548 0 0
549549 −3.03896e6 −0.430322
550550 0 0
551551 −6.69962e6 −0.940094
552552 0 0
553553 2.14016e6i 0.297600i
554554 0 0
555555 0 0
556556 0 0
557557 − 4.01187e6i − 0.547910i −0.961742 0.273955i 0.911668π-0.911668\pi
0.961742 0.273955i 0.0883320π-0.0883320\pi
558558 0 0
559559 7.38977e6 1.00023
560560 0 0
561561 5.30647e6 0.711867
562562 0 0
563563 9.59663e6i 1.27599i 0.770040 + 0.637996i 0.220236π0.220236\pi
−0.770040 + 0.637996i 0.779764π0.779764\pi
564564 0 0
565565 0 0
566566 0 0
567567 − 524880.i − 0.0685650i
568568 0 0
569569 −6.76649e6 −0.876159 −0.438079 0.898936i 0.644341π-0.644341\pi
−0.438079 + 0.898936i 0.644341π0.644341\pi
570570 0 0
571571 1.42954e7 1.83488 0.917439 0.397877i 0.130253π-0.130253\pi
0.917439 + 0.397877i 0.130253π0.130253\pi
572572 0 0
573573 3.57624e6i 0.455030i
574574 0 0
575575 0 0
576576 0 0
577577 − 1.38116e7i − 1.72705i −0.504309 0.863523i 0.668253π-0.668253\pi
0.504309 0.863523i 0.331747π-0.331747\pi
578578 0 0
579579 7.00072e6 0.867854
580580 0 0
581581 636480. 0.0782248
582582 0 0
583583 5.94943e6i 0.724943i
584584 0 0
585585 0 0
586586 0 0
587587 − 2.82424e6i − 0.338303i −0.985590 0.169151i 0.945897π-0.945897\pi
0.985590 0.169151i 0.0541027π-0.0541027\pi
588588 0 0
589589 8.52979e6 1.01310
590590 0 0
591591 −2.29210e6 −0.269939
592592 0 0
593593 6.72749e6i 0.785626i 0.919618 + 0.392813i 0.128498π0.128498\pi
−0.919618 + 0.392813i 0.871502π0.871502\pi
594594 0 0
595595 0 0
596596 0 0
597597 4.86238e6i 0.558358i
598598 0 0
599599 −1.02563e7 −1.16795 −0.583977 0.811770i 0.698504π-0.698504\pi
−0.583977 + 0.811770i 0.698504π0.698504\pi
600600 0 0
601601 −6.93684e6 −0.783385 −0.391693 0.920096i 0.628110π-0.628110\pi
−0.391693 + 0.920096i 0.628110π0.628110\pi
602602 0 0
603603 − 2.37524e6i − 0.266020i
604604 0 0
605605 0 0
606606 0 0
607607 − 6.04044e6i − 0.665422i −0.943029 0.332711i 0.892037π-0.892037\pi
0.943029 0.332711i 0.107963π-0.107963\pi
608608 0 0
609609 5.26608e6 0.575366
610610 0 0
611611 5.82888e6 0.631658
612612 0 0
613613 − 5.65002e6i − 0.607294i −0.952785 0.303647i 0.901796π-0.901796\pi
0.952785 0.303647i 0.0982043π-0.0982043\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 7.77818e6i − 0.822555i −0.911510 0.411278i 0.865083π-0.865083\pi
0.911510 0.411278i 0.134917π-0.134917\pi
618618 0 0
619619 −5.86584e6 −0.615323 −0.307662 0.951496i 0.599546π-0.599546\pi
−0.307662 + 0.951496i 0.599546π0.599546\pi
620620 0 0
621621 1.13141e6 0.117731
622622 0 0
623623 4.77392e6i 0.492782i
624624 0 0
625625 0 0
626626 0 0
627627 − 5.63890e6i − 0.572829i
628628 0 0
629629 −7.60801e6 −0.766734
630630 0 0
631631 −4.14394e6 −0.414324 −0.207162 0.978307i 0.566423π-0.566423\pi
−0.207162 + 0.978307i 0.566423π0.566423\pi
632632 0 0
633633 9.51210e6i 0.943555i
634634 0 0
635635 0 0
636636 0 0
637637 1.01780e7i 0.993839i
638638 0 0
639639 −6.83705e6 −0.662394
640640 0 0
641641 −8.41769e6 −0.809185 −0.404593 0.914497i 0.632587π-0.632587\pi
−0.404593 + 0.914497i 0.632587π0.632587\pi
642642 0 0
643643 − 1.79931e7i − 1.71625i −0.513444 0.858123i 0.671630π-0.671630\pi
0.513444 0.858123i 0.328370π-0.328370\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 7.92533e6i − 0.744315i −0.928170 0.372157i 0.878618π-0.878618\pi
0.928170 0.372157i 0.121382π-0.121382\pi
648648 0 0
649649 2.87526e7 2.67957
650650 0 0
651651 −6.70464e6 −0.620045
652652 0 0
653653 1.53749e7i 1.41101i 0.708704 + 0.705506i 0.249280π0.249280\pi
−0.708704 + 0.705506i 0.750720π0.750720\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 3.77055e6i − 0.340793i
658658 0 0
659659 −1.46609e7 −1.31507 −0.657534 0.753425i 0.728400π-0.728400\pi
−0.657534 + 0.753425i 0.728400π0.728400\pi
660660 0 0
661661 −3.32825e6 −0.296287 −0.148143 0.988966i 0.547330π-0.547330\pi
−0.148143 + 0.988966i 0.547330π0.547330\pi
662662 0 0
663663 7.58732e6i 0.670355i
664664 0 0
665665 0 0
666666 0 0
667667 1.13513e7i 0.987943i
668668 0 0
669669 −9.81569e6 −0.847921
670670 0 0
671671 2.56623e7 2.20034
672672 0 0
673673 − 2.08463e7i − 1.77415i −0.461621 0.887077i 0.652732π-0.652732\pi
0.461621 0.887077i 0.347268π-0.347268\pi
674674 0 0
675675 0 0
676676 0 0
677677 1.60880e7i 1.34906i 0.738248 + 0.674530i 0.235653π0.235653\pi
−0.738248 + 0.674530i 0.764347π0.764347\pi
678678 0 0
679679 1.09518e7 0.911618
680680 0 0
681681 24948.0 0.00206143
682682 0 0
683683 − 3.93124e6i − 0.322461i −0.986917 0.161231i 0.948454π-0.948454\pi
0.986917 0.161231i 0.0515463π-0.0515463\pi
684684 0 0
685685 0 0
686686 0 0
687687 2.74012e6i 0.221502i
688688 0 0
689689 −8.50664e6 −0.682669
690690 0 0
691691 9.05300e6 0.721269 0.360634 0.932707i 0.382560π-0.382560\pi
0.360634 + 0.932707i 0.382560π0.382560\pi
692692 0 0
693693 4.43232e6i 0.350589i
694694 0 0
695695 0 0
696696 0 0
697697 2.83253e6i 0.220848i
698698 0 0
699699 −2.96991e6 −0.229906
700700 0 0
701701 1.82887e7 1.40568 0.702842 0.711346i 0.251914π-0.251914\pi
0.702842 + 0.711346i 0.251914π0.251914\pi
702702 0 0
703703 8.08462e6i 0.616980i
704704 0 0
705705 0 0
706706 0 0
707707 1.62286e7i 1.22105i
708708 0 0
709709 −1.05416e7 −0.787572 −0.393786 0.919202i 0.628835π-0.628835\pi
−0.393786 + 0.919202i 0.628835π0.628835\pi
710710 0 0
711711 2.16691e6 0.160756
712712 0 0
713713 − 1.44522e7i − 1.06466i
714714 0 0
715715 0 0
716716 0 0
717717 − 6.49426e6i − 0.471771i
718718 0 0
719719 −1.34280e7 −0.968703 −0.484352 0.874873i 0.660944π-0.660944\pi
−0.484352 + 0.874873i 0.660944π0.660944\pi
720720 0 0
721721 686080. 0.0491515
722722 0 0
723723 2.44384e6i 0.173871i
724724 0 0
725725 0 0
726726 0 0
727727 9.97059e6i 0.699657i 0.936814 + 0.349828i 0.113760π0.113760\pi
−0.936814 + 0.349828i 0.886240π0.886240\pi
728728 0 0
729729 −531441. −0.0370370
730730 0 0
731731 −6.51327e6 −0.450823
732732 0 0
733733 2.70572e7i 1.86004i 0.367509 + 0.930020i 0.380211π0.380211\pi
−0.367509 + 0.930020i 0.619789π0.619789\pi
734734 0 0
735735 0 0
736736 0 0
737737 2.00576e7i 1.36022i
738738 0 0
739739 −4.87076e6 −0.328084 −0.164042 0.986453i 0.552453π-0.552453\pi
−0.164042 + 0.986453i 0.552453π0.552453\pi
740740 0 0
741741 8.06263e6 0.539425
742742 0 0
743743 − 144288.i − 0.00958867i −0.999989 0.00479433i 0.998474π-0.998474\pi
0.999989 0.00479433i 0.00152609π-0.00152609\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 644436.i − 0.0422550i
748748 0 0
749749 −1.59584e6 −0.103941
750750 0 0
751751 −8.74882e6 −0.566043 −0.283022 0.959114i 0.591337π-0.591337\pi
−0.283022 + 0.959114i 0.591337π0.591337\pi
752752 0 0
753753 1.21081e7i 0.778193i
754754 0 0
755755 0 0
756756 0 0
757757 − 5.58062e6i − 0.353951i −0.984215 0.176975i 0.943369π-0.943369\pi
0.984215 0.176975i 0.0566313π-0.0566313\pi
758758 0 0
759759 −9.55411e6 −0.601985
760760 0 0
761761 273178. 0.0170995 0.00854976 0.999963i 0.497278π-0.497278\pi
0.00854976 + 0.999963i 0.497278π0.497278\pi
762762 0 0
763763 3.00784e6i 0.187044i
764764 0 0
765765 0 0
766766 0 0
767767 4.11112e7i 2.52332i
768768 0 0
769769 2.16358e7 1.31934 0.659672 0.751554i 0.270695π-0.270695\pi
0.659672 + 0.751554i 0.270695π0.270695\pi
770770 0 0
771771 −1.46061e7 −0.884907
772772 0 0
773773 − 5.39836e6i − 0.324947i −0.986713 0.162474i 0.948053π-0.948053\pi
0.986713 0.162474i 0.0519473π-0.0519473\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 6.35472e6i − 0.377610i
778778 0 0
779779 3.00998e6 0.177713
780780 0 0
781781 5.77351e7 3.38698
782782 0 0
783783 − 5.33191e6i − 0.310798i
784784 0 0
785785 0 0
786786 0 0
787787 1.56497e7i 0.900677i 0.892858 + 0.450338i 0.148697π0.148697\pi
−0.892858 + 0.450338i 0.851303π0.851303\pi
788788 0 0
789789 4.24915e6 0.243002
790790 0 0
791791 1.53470e7 0.872134
792792 0 0
793793 3.66926e7i 2.07203i
794794 0 0
795795 0 0
796796 0 0
797797 − 2.43553e7i − 1.35815i −0.734069 0.679074i 0.762381π-0.762381\pi
0.734069 0.679074i 0.237619π-0.237619\pi
798798 0 0
799799 −5.13752e6 −0.284699
800800 0 0
801801 4.83359e6 0.266188
802802 0 0
803803 3.18402e7i 1.74256i
804804 0 0
805805 0 0
806806 0 0
807807 − 21870.0i − 0.00118213i
808808 0 0
809809 2.60329e7 1.39846 0.699231 0.714896i 0.253526π-0.253526\pi
0.699231 + 0.714896i 0.253526π0.253526\pi
810810 0 0
811811 −2.63808e7 −1.40843 −0.704217 0.709985i 0.748702π-0.748702\pi
−0.704217 + 0.709985i 0.748702π0.748702\pi
812812 0 0
813813 1.48641e7i 0.788701i
814814 0 0
815815 0 0
816816 0 0
817817 6.92130e6i 0.362771i
818818 0 0
819819 −6.33744e6 −0.330145
820820 0 0
821821 −7.46105e6 −0.386315 −0.193158 0.981168i 0.561873π-0.561873\pi
−0.193158 + 0.981168i 0.561873π0.561873\pi
822822 0 0
823823 3.34734e6i 0.172266i 0.996284 + 0.0861332i 0.0274511π0.0274511\pi
−0.996284 + 0.0861332i 0.972549π0.972549\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 3.70089e7i − 1.88167i −0.338872 0.940833i 0.610045π-0.610045\pi
0.338872 0.940833i 0.389955π-0.389955\pi
828828 0 0
829829 −2.35921e7 −1.19229 −0.596143 0.802878i 0.703301π-0.703301\pi
−0.596143 + 0.802878i 0.703301π0.703301\pi
830830 0 0
831831 −1.99016e7 −0.999735
832832 0 0
833833 − 8.97083e6i − 0.447940i
834834 0 0
835835 0 0
836836 0 0
837837 6.78845e6i 0.334932i
838838 0 0
839839 3.54805e7 1.74014 0.870071 0.492926i 0.164073π-0.164073\pi
0.870071 + 0.492926i 0.164073π0.164073\pi
840840 0 0
841841 3.29834e7 1.60807
842842 0 0
843843 − 3.80713e6i − 0.184514i
844844 0 0
845845 0 0
846846 0 0
847847 − 2.45444e7i − 1.17556i
848848 0 0
849849 −4.38347e6 −0.208713
850850 0 0
851851 1.36980e7 0.648383
852852 0 0
853853 5.54993e6i 0.261165i 0.991437 + 0.130582i 0.0416847π0.0416847\pi
−0.991437 + 0.130582i 0.958315π0.958315\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 2.21344e7i − 1.02948i −0.857348 0.514738i 0.827889π-0.827889\pi
0.857348 0.514738i 0.172111π-0.172111\pi
858858 0 0
859859 9.65533e6 0.446462 0.223231 0.974766i 0.428340π-0.428340\pi
0.223231 + 0.974766i 0.428340π0.428340\pi
860860 0 0
861861 −2.36592e6 −0.108766
862862 0 0
863863 − 1.43771e7i − 0.657120i −0.944483 0.328560i 0.893437π-0.893437\pi
0.944483 0.328560i 0.106563π-0.106563\pi
864864 0 0
865865 0 0
866866 0 0
867867 6.09132e6i 0.275210i
868868 0 0
869869 −1.82984e7 −0.821983
870870 0 0
871871 −2.86789e7 −1.28090
872872 0 0
873873 − 1.10887e7i − 0.492432i
874874 0 0
875875 0 0
876876 0 0
877877 9.01032e6i 0.395586i 0.980244 + 0.197793i 0.0633774π0.0633774\pi
−0.980244 + 0.197793i 0.936623π0.936623\pi
878878 0 0
879879 −9.24230e6 −0.403467
880880 0 0
881881 −1.64420e7 −0.713700 −0.356850 0.934162i 0.616149π-0.616149\pi
−0.356850 + 0.934162i 0.616149π0.616149\pi
882882 0 0
883883 − 6.06516e6i − 0.261783i −0.991397 0.130891i 0.958216π-0.958216\pi
0.991397 0.130891i 0.0417839π-0.0417839\pi
884884 0 0
885885 0 0
886886 0 0
887887 2.85746e7i 1.21947i 0.792605 + 0.609735i 0.208724π0.208724\pi
−0.792605 + 0.609735i 0.791276π0.791276\pi
888888 0 0
889889 7.91104e6 0.335722
890890 0 0
891891 4.48772e6 0.189379
892892 0 0
893893 5.45936e6i 0.229094i
894894 0 0
895895 0 0
896896 0 0
897897 − 1.36607e7i − 0.566881i
898898 0 0
899899 −6.81080e7 −2.81060
900900 0 0
901901 7.49768e6 0.307691
902902 0 0
903903 − 5.44032e6i − 0.222027i
904904 0 0
905905 0 0
906906 0 0
907907 − 1.47466e7i − 0.595215i −0.954688 0.297607i 0.903811π-0.903811\pi
0.954688 0.297607i 0.0961887π-0.0961887\pi
908908 0 0
909909 1.64315e7 0.659580
910910 0 0
911911 −2.61222e6 −0.104283 −0.0521416 0.998640i 0.516605π-0.516605\pi
−0.0521416 + 0.998640i 0.516605π0.516605\pi
912912 0 0
913913 5.44190e6i 0.216060i
914914 0 0
915915 0 0
916916 0 0
917917 − 2.37088e6i − 0.0931078i
918918 0 0
919919 4.66079e7 1.82042 0.910208 0.414152i 0.135922π-0.135922\pi
0.910208 + 0.414152i 0.135922π0.135922\pi
920920 0 0
921921 9.64199e6 0.374557
922922 0 0
923923 8.25510e7i 3.18947i
924924 0 0
925925 0 0
926926 0 0
927927 − 694656.i − 0.0265504i
928928 0 0
929929 3.16320e7 1.20251 0.601254 0.799058i 0.294668π-0.294668\pi
0.601254 + 0.799058i 0.294668π0.294668\pi
930930 0 0
931931 −9.53281e6 −0.360451
932932 0 0
933933 1.68679e7i 0.634393i
934934 0 0
935935 0 0
936936 0 0
937937 2.57021e7i 0.956355i 0.878263 + 0.478177i 0.158702π0.158702\pi
−0.878263 + 0.478177i 0.841298π0.841298\pi
938938 0 0
939939 2.63594e7 0.975601
940940 0 0
941941 −7.01907e6 −0.258408 −0.129204 0.991618i 0.541242π-0.541242\pi
−0.129204 + 0.991618i 0.541242π0.541242\pi
942942 0 0
943943 − 5.09987e6i − 0.186758i
944944 0 0
945945 0 0
946946 0 0
947947 3.38467e6i 0.122643i 0.998118 + 0.0613213i 0.0195314π0.0195314\pi
−0.998118 + 0.0613213i 0.980469π0.980469\pi
948948 0 0
949949 −4.55259e7 −1.64094
950950 0 0
951951 2.65348e7 0.951401
952952 0 0
953953 9.74473e6i 0.347566i 0.984784 + 0.173783i 0.0555991π0.0555991\pi
−0.984784 + 0.173783i 0.944401π0.944401\pi
954954 0 0
955955 0 0
956956 0 0
957957 4.50250e7i 1.58918i
958958 0 0
959959 −369120. −0.0129605
960960 0 0
961961 5.80842e7 2.02885
962962 0 0
963963 1.61579e6i 0.0561460i
964964 0 0
965965 0 0
966966 0 0
967967 − 1.09405e7i − 0.376244i −0.982146 0.188122i 0.939760π-0.939760\pi
0.982146 0.188122i 0.0602400π-0.0602400\pi
968968 0 0
969969 −7.10633e6 −0.243128
970970 0 0
971971 −2.25329e7 −0.766953 −0.383476 0.923551i 0.625273π-0.625273\pi
−0.383476 + 0.923551i 0.625273π0.625273\pi
972972 0 0
973973 − 2.03434e7i − 0.688875i
974974 0 0
975975 0 0
976976 0 0
977977 − 2.79146e7i − 0.935610i −0.883832 0.467805i 0.845045π-0.845045\pi
0.883832 0.467805i 0.154955π-0.154955\pi
978978 0 0
979979 −4.08170e7 −1.36108
980980 0 0
981981 3.04544e6 0.101036
982982 0 0
983983 3.07607e7i 1.01534i 0.861551 + 0.507670i 0.169493π0.169493\pi
−0.861551 + 0.507670i 0.830507π0.830507\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 4.29120e6i − 0.140212i
988988 0 0
989989 1.17269e7 0.381235
990990 0 0
991991 −4.31296e6 −0.139505 −0.0697527 0.997564i 0.522221π-0.522221\pi
−0.0697527 + 0.997564i 0.522221π0.522221\pi
992992 0 0
993993 − 7.70490e6i − 0.247967i
994994 0 0
995995 0 0
996996 0 0
997997 − 2.85667e7i − 0.910170i −0.890448 0.455085i 0.849609π-0.849609\pi
0.890448 0.455085i 0.150391π-0.150391\pi
998998 0 0
999999 −6.43415e6 −0.203975
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 600.6.f.i.49.2 2
5.2 odd 4 600.6.a.g.1.1 1
5.3 odd 4 120.6.a.c.1.1 1
5.4 even 2 inner 600.6.f.i.49.1 2
15.8 even 4 360.6.a.c.1.1 1
20.3 even 4 240.6.a.n.1.1 1
40.3 even 4 960.6.a.f.1.1 1
40.13 odd 4 960.6.a.o.1.1 1
60.23 odd 4 720.6.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.6.a.c.1.1 1 5.3 odd 4
240.6.a.n.1.1 1 20.3 even 4
360.6.a.c.1.1 1 15.8 even 4
600.6.a.g.1.1 1 5.2 odd 4
600.6.f.i.49.1 2 5.4 even 2 inner
600.6.f.i.49.2 2 1.1 even 1 trivial
720.6.a.g.1.1 1 60.23 odd 4
960.6.a.f.1.1 1 40.3 even 4
960.6.a.o.1.1 1 40.13 odd 4