Properties

Label 325.6.a.f.1.3
Level 325325
Weight 66
Character 325.1
Self dual yes
Analytic conductor 52.12552.125
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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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] = [325,6,Mod(1,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) 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("325.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 325.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 52.124741439252.1247414392
Analytic rank: 00
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5161x4+328x3+6584x210688x47440 x^{6} - 2x^{5} - 161x^{4} + 328x^{3} + 6584x^{2} - 10688x - 47440 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 65)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 4.153494.15349 of defining polynomial
Character χ\chi == 325.1

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) == q4.15349q229.2293q314.7485q4+121.404q642.5171q7+194.170q8+611.349q9+434.431q11+431.087q12+169.000q13+176.594q14334.530q16+424.475q172539.24q182203.44q19+1242.74q211804.41q22+1176.65q235675.43q24701.940q2610766.6q27+627.063q283074.40q29+6242.41q314823.96q3212698.1q331763.05q349016.48q36+10102.1q37+9151.97q384939.74q397026.52q415161.73q42+21517.8q436407.20q444887.22q463086.13q47+9778.08q4814999.3q4912407.1q512492.49q5238178.9q53+44718.9q548255.53q56+64404.9q57+12769.5q5817513.0q5912844.5q6125927.8q6225992.8q63+30741.2q64+52741.5q66+46496.3q676260.37q6834392.7q69+55843.2q71+118705.q7249566.9q7341958.9q74+32497.4q7618470.8q77+20517.2q78+8611.37q79+166141.q81+29184.6q82+1635.95q8318328.6q8489374.2q86+89862.3q87+84353.3q88+26554.2q897185.39q9117353.9q92182461.q93+12818.2q94+141001.q96181767.q97+62299.5q98+265589.q99+O(q100)q-4.15349 q^{2} -29.2293 q^{3} -14.7485 q^{4} +121.404 q^{6} -42.5171 q^{7} +194.170 q^{8} +611.349 q^{9} +434.431 q^{11} +431.087 q^{12} +169.000 q^{13} +176.594 q^{14} -334.530 q^{16} +424.475 q^{17} -2539.24 q^{18} -2203.44 q^{19} +1242.74 q^{21} -1804.41 q^{22} +1176.65 q^{23} -5675.43 q^{24} -701.940 q^{26} -10766.6 q^{27} +627.063 q^{28} -3074.40 q^{29} +6242.41 q^{31} -4823.96 q^{32} -12698.1 q^{33} -1763.05 q^{34} -9016.48 q^{36} +10102.1 q^{37} +9151.97 q^{38} -4939.74 q^{39} -7026.52 q^{41} -5161.73 q^{42} +21517.8 q^{43} -6407.20 q^{44} -4887.22 q^{46} -3086.13 q^{47} +9778.08 q^{48} -14999.3 q^{49} -12407.1 q^{51} -2492.49 q^{52} -38178.9 q^{53} +44718.9 q^{54} -8255.53 q^{56} +64404.9 q^{57} +12769.5 q^{58} -17513.0 q^{59} -12844.5 q^{61} -25927.8 q^{62} -25992.8 q^{63} +30741.2 q^{64} +52741.5 q^{66} +46496.3 q^{67} -6260.37 q^{68} -34392.7 q^{69} +55843.2 q^{71} +118705. q^{72} -49566.9 q^{73} -41958.9 q^{74} +32497.4 q^{76} -18470.8 q^{77} +20517.2 q^{78} +8611.37 q^{79} +166141. q^{81} +29184.6 q^{82} +1635.95 q^{83} -18328.6 q^{84} -89374.2 q^{86} +89862.3 q^{87} +84353.3 q^{88} +26554.2 q^{89} -7185.39 q^{91} -17353.9 q^{92} -182461. q^{93} +12818.2 q^{94} +141001. q^{96} -181767. q^{97} +62299.5 q^{98} +265589. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q2q220q3+134q452q6172q7+138q8+1034q9+800q11+832q12+1014q13+2108q14+322q164396q176142q18+5304q19+1072q21++301264q99+O(q100) 6 q - 2 q^{2} - 20 q^{3} + 134 q^{4} - 52 q^{6} - 172 q^{7} + 138 q^{8} + 1034 q^{9} + 800 q^{11} + 832 q^{12} + 1014 q^{13} + 2108 q^{14} + 322 q^{16} - 4396 q^{17} - 6142 q^{18} + 5304 q^{19} + 1072 q^{21}+ \cdots + 301264 q^{99}+O(q^{100}) Copy content Toggle raw display

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 −4.15349 −0.734241 −0.367120 0.930173i 0.619656π-0.619656\pi
−0.367120 + 0.930173i 0.619656π0.619656\pi
33 −29.2293 −1.87506 −0.937529 0.347908i 0.886892π-0.886892\pi
−0.937529 + 0.347908i 0.886892π0.886892\pi
44 −14.7485 −0.460890
55 0 0
66 121.404 1.37674
77 −42.5171 −0.327958 −0.163979 0.986464i 0.552433π-0.552433\pi
−0.163979 + 0.986464i 0.552433π0.552433\pi
88 194.170 1.07265
99 611.349 2.51584
1010 0 0
1111 434.431 1.08253 0.541264 0.840853i 0.317946π-0.317946\pi
0.541264 + 0.840853i 0.317946π0.317946\pi
1212 431.087 0.864196
1313 169.000 0.277350
1414 176.594 0.240800
1515 0 0
1616 −334.530 −0.326690
1717 424.475 0.356229 0.178115 0.984010i 0.443000π-0.443000\pi
0.178115 + 0.984010i 0.443000π0.443000\pi
1818 −2539.24 −1.84723
1919 −2203.44 −1.40029 −0.700143 0.714003i 0.746880π-0.746880\pi
−0.700143 + 0.714003i 0.746880π0.746880\pi
2020 0 0
2121 1242.74 0.614940
2222 −1804.41 −0.794837
2323 1176.65 0.463798 0.231899 0.972740i 0.425506π-0.425506\pi
0.231899 + 0.972740i 0.425506π0.425506\pi
2424 −5675.43 −2.01127
2525 0 0
2626 −701.940 −0.203642
2727 −10766.6 −2.84229
2828 627.063 0.151153
2929 −3074.40 −0.678836 −0.339418 0.940636i 0.610230π-0.610230\pi
−0.339418 + 0.940636i 0.610230π0.610230\pi
3030 0 0
3131 6242.41 1.16667 0.583335 0.812231i 0.301747π-0.301747\pi
0.583335 + 0.812231i 0.301747π0.301747\pi
3232 −4823.96 −0.832776
3333 −12698.1 −2.02980
3434 −1763.05 −0.261558
3535 0 0
3636 −9016.48 −1.15953
3737 10102.1 1.21313 0.606563 0.795035i 0.292548π-0.292548\pi
0.606563 + 0.795035i 0.292548π0.292548\pi
3838 9151.97 1.02815
3939 −4939.74 −0.520047
4040 0 0
4141 −7026.52 −0.652801 −0.326400 0.945232i 0.605836π-0.605836\pi
−0.326400 + 0.945232i 0.605836π0.605836\pi
4242 −5161.73 −0.451514
4343 21517.8 1.77471 0.887355 0.461086i 0.152540π-0.152540\pi
0.887355 + 0.461086i 0.152540π0.152540\pi
4444 −6407.20 −0.498927
4545 0 0
4646 −4887.22 −0.340539
4747 −3086.13 −0.203784 −0.101892 0.994795i 0.532490π-0.532490\pi
−0.101892 + 0.994795i 0.532490π0.532490\pi
4848 9778.08 0.612562
4949 −14999.3 −0.892443
5050 0 0
5151 −12407.1 −0.667951
5252 −2492.49 −0.127828
5353 −38178.9 −1.86695 −0.933477 0.358638i 0.883241π-0.883241\pi
−0.933477 + 0.358638i 0.883241π0.883241\pi
5454 44718.9 2.08693
5555 0 0
5656 −8255.53 −0.351783
5757 64404.9 2.62562
5858 12769.5 0.498429
5959 −17513.0 −0.654984 −0.327492 0.944854i 0.606203π-0.606203\pi
−0.327492 + 0.944854i 0.606203π0.606203\pi
6060 0 0
6161 −12844.5 −0.441969 −0.220984 0.975277i 0.570927π-0.570927\pi
−0.220984 + 0.975277i 0.570927π0.570927\pi
6262 −25927.8 −0.856617
6363 −25992.8 −0.825091
6464 30741.2 0.938148
6565 0 0
6666 52741.5 1.49036
6767 46496.3 1.26541 0.632705 0.774393i 0.281945π-0.281945\pi
0.632705 + 0.774393i 0.281945π0.281945\pi
6868 −6260.37 −0.164183
6969 −34392.7 −0.869648
7070 0 0
7171 55843.2 1.31469 0.657346 0.753589i 0.271679π-0.271679\pi
0.657346 + 0.753589i 0.271679π0.271679\pi
7272 118705. 2.69861
7373 −49566.9 −1.08864 −0.544320 0.838878i 0.683212π-0.683212\pi
−0.544320 + 0.838878i 0.683212π0.683212\pi
7474 −41958.9 −0.890727
7575 0 0
7676 32497.4 0.645378
7777 −18470.8 −0.355024
7878 20517.2 0.381840
7979 8611.37 0.155240 0.0776202 0.996983i 0.475268π-0.475268\pi
0.0776202 + 0.996983i 0.475268π0.475268\pi
8080 0 0
8181 166141. 2.81362
8282 29184.6 0.479313
8383 1635.95 0.0260660 0.0130330 0.999915i 0.495851π-0.495851\pi
0.0130330 + 0.999915i 0.495851π0.495851\pi
8484 −18328.6 −0.283420
8585 0 0
8686 −89374.2 −1.30307
8787 89862.3 1.27286
8888 84353.3 1.16117
8989 26554.2 0.355351 0.177676 0.984089i 0.443142π-0.443142\pi
0.177676 + 0.984089i 0.443142π0.443142\pi
9090 0 0
9191 −7185.39 −0.0909592
9292 −17353.9 −0.213760
9393 −182461. −2.18757
9494 12818.2 0.149627
9595 0 0
9696 141001. 1.56150
9797 −181767. −1.96149 −0.980745 0.195292i 0.937435π-0.937435\pi
−0.980745 + 0.195292i 0.937435π0.937435\pi
9898 62299.5 0.655268
9999 265589. 2.72347
100100 0 0
101101 30120.5 0.293805 0.146902 0.989151i 0.453070π-0.453070\pi
0.146902 + 0.989151i 0.453070π0.453070\pi
102102 51532.8 0.490437
103103 16097.4 0.149507 0.0747535 0.997202i 0.476183π-0.476183\pi
0.0747535 + 0.997202i 0.476183π0.476183\pi
104104 32814.7 0.297498
105105 0 0
106106 158576. 1.37079
107107 215209. 1.81719 0.908597 0.417674i 0.137155π-0.137155\pi
0.908597 + 0.417674i 0.137155π0.137155\pi
108108 158791. 1.30998
109109 122039. 0.983856 0.491928 0.870636i 0.336292π-0.336292\pi
0.491928 + 0.870636i 0.336292π0.336292\pi
110110 0 0
111111 −295276. −2.27468
112112 14223.3 0.107141
113113 −127320. −0.937993 −0.468997 0.883200i 0.655384π-0.655384\pi
−0.468997 + 0.883200i 0.655384π0.655384\pi
114114 −267505. −1.92784
115115 0 0
116116 45342.7 0.312869
117117 103318. 0.697769
118118 72740.2 0.480916
119119 −18047.4 −0.116828
120120 0 0
121121 27679.5 0.171868
122122 53349.4 0.324511
123123 205380. 1.22404
124124 −92066.2 −0.537707
125125 0 0
126126 107961. 0.605815
127127 −327564. −1.80213 −0.901067 0.433680i 0.857215π-0.857215\pi
−0.901067 + 0.433680i 0.857215π0.857215\pi
128128 26683.0 0.143949
129129 −628951. −3.32769
130130 0 0
131131 86617.2 0.440987 0.220494 0.975388i 0.429233π-0.429233\pi
0.220494 + 0.975388i 0.429233π0.429233\pi
132132 187278. 0.935517
133133 93683.8 0.459235
134134 −193122. −0.929116
135135 0 0
136136 82420.1 0.382108
137137 −223125. −1.01565 −0.507827 0.861459i 0.669551π-0.669551\pi
−0.507827 + 0.861459i 0.669551π0.669551\pi
138138 142850. 0.638531
139139 −268128. −1.17708 −0.588539 0.808469i 0.700297π-0.700297\pi
−0.588539 + 0.808469i 0.700297π0.700297\pi
140140 0 0
141141 90205.4 0.382107
142142 −231944. −0.965301
143143 73418.9 0.300239
144144 −204515. −0.821900
145145 0 0
146146 205876. 0.799324
147147 438418. 1.67338
148148 −148990. −0.559118
149149 −22314.5 −0.0823420 −0.0411710 0.999152i 0.513109π-0.513109\pi
−0.0411710 + 0.999152i 0.513109π0.513109\pi
150150 0 0
151151 438136. 1.56375 0.781874 0.623437i 0.214264π-0.214264\pi
0.781874 + 0.623437i 0.214264π0.214264\pi
152152 −427841. −1.50201
153153 259503. 0.896217
154154 76718.2 0.260673
155155 0 0
156156 72853.8 0.239685
157157 452703. 1.46577 0.732883 0.680355i 0.238174π-0.238174\pi
0.732883 + 0.680355i 0.238174π0.238174\pi
158158 −35767.3 −0.113984
159159 1.11594e6 3.50065
160160 0 0
161161 −50027.9 −0.152106
162162 −690066. −2.06587
163163 −367437. −1.08321 −0.541606 0.840632i 0.682183π-0.682183\pi
−0.541606 + 0.840632i 0.682183π0.682183\pi
164164 103631. 0.300869
165165 0 0
166166 −6794.91 −0.0191388
167167 −29002.0 −0.0804706 −0.0402353 0.999190i 0.512811π-0.512811\pi
−0.0402353 + 0.999190i 0.512811π0.512811\pi
168168 241303. 0.659613
169169 28561.0 0.0769231
170170 0 0
171171 −1.34707e6 −3.52290
172172 −317356. −0.817947
173173 105419. 0.267797 0.133898 0.990995i 0.457250π-0.457250\pi
0.133898 + 0.990995i 0.457250π0.457250\pi
174174 −373243. −0.934584
175175 0 0
176176 −145330. −0.353651
177177 511892. 1.22813
178178 −110293. −0.260913
179179 −299749. −0.699237 −0.349619 0.936892i 0.613689π-0.613689\pi
−0.349619 + 0.936892i 0.613689π0.613689\pi
180180 0 0
181181 490770. 1.11348 0.556739 0.830688i 0.312052π-0.312052\pi
0.556739 + 0.830688i 0.312052π0.312052\pi
182182 29844.5 0.0667860
183183 375434. 0.828717
184184 228470. 0.497491
185185 0 0
186186 757851. 1.60621
187187 184405. 0.385629
188188 45515.8 0.0939221
189189 457764. 0.932152
190190 0 0
191191 −691134. −1.37082 −0.685408 0.728160i 0.740376π-0.740376\pi
−0.685408 + 0.728160i 0.740376π0.740376\pi
192192 −898544. −1.75908
193193 −166093. −0.320966 −0.160483 0.987039i 0.551305π-0.551305\pi
−0.160483 + 0.987039i 0.551305π0.551305\pi
194194 754969. 1.44021
195195 0 0
196196 221217. 0.411318
197197 656522. 1.20527 0.602634 0.798018i 0.294118π-0.294118\pi
0.602634 + 0.798018i 0.294118π0.294118\pi
198198 −1.10312e6 −1.99968
199199 793002. 1.41952 0.709760 0.704443i 0.248803π-0.248803\pi
0.709760 + 0.704443i 0.248803π0.248803\pi
200200 0 0
201201 −1.35905e6 −2.37272
202202 −125105. −0.215723
203203 130714. 0.222630
204204 182986. 0.307852
205205 0 0
206206 −66860.3 −0.109774
207207 719346. 1.16684
208208 −56535.6 −0.0906075
209209 −957242. −1.51585
210210 0 0
211211 728395. 1.12632 0.563159 0.826349i 0.309586π-0.309586\pi
0.563159 + 0.826349i 0.309586π0.309586\pi
212212 563081. 0.860461
213213 −1.63225e6 −2.46512
214214 −893870. −1.33426
215215 0 0
216216 −2.09054e6 −3.04877
217217 −265409. −0.382619
218218 −506887. −0.722387
219219 1.44880e6 2.04126
220220 0 0
221221 71736.3 0.0988003
222222 1.22643e6 1.67016
223223 −133554. −0.179844 −0.0899221 0.995949i 0.528662π-0.528662\pi
−0.0899221 + 0.995949i 0.528662π0.528662\pi
224224 205101. 0.273116
225225 0 0
226226 528822. 0.688713
227227 −1.14153e6 −1.47035 −0.735176 0.677876i 0.762901π-0.762901\pi
−0.735176 + 0.677876i 0.762901π0.762901\pi
228228 −949874. −1.21012
229229 −765463. −0.964573 −0.482287 0.876013i 0.660194π-0.660194\pi
−0.482287 + 0.876013i 0.660194π0.660194\pi
230230 0 0
231231 539886. 0.665691
232232 −596954. −0.728151
233233 1.07854e6 1.30151 0.650755 0.759288i 0.274453π-0.274453\pi
0.650755 + 0.759288i 0.274453π0.274453\pi
234234 −429131. −0.512330
235235 0 0
236236 258290. 0.301876
237237 −251704. −0.291085
238238 74960.0 0.0857802
239239 16098.4 0.0182300 0.00911501 0.999958i 0.497099π-0.497099\pi
0.00911501 + 0.999958i 0.497099π0.497099\pi
240240 0 0
241241 −76424.5 −0.0847598 −0.0423799 0.999102i 0.513494π-0.513494\pi
−0.0423799 + 0.999102i 0.513494π0.513494\pi
242242 −114967. −0.126193
243243 −2.23990e6 −2.43340
244244 189436. 0.203699
245245 0 0
246246 −853044. −0.898739
247247 −372381. −0.388370
248248 1.21209e6 1.25142
249249 −47817.6 −0.0488753
250250 0 0
251251 −816629. −0.818164 −0.409082 0.912498i 0.634151π-0.634151\pi
−0.409082 + 0.912498i 0.634151π0.634151\pi
252252 383355. 0.380276
253253 511175. 0.502075
254254 1.36054e6 1.32320
255255 0 0
256256 −1.09455e6 −1.04384
257257 1.18641e6 1.12047 0.560237 0.828332i 0.310710π-0.310710\pi
0.560237 + 0.828332i 0.310710π0.310710\pi
258258 2.61234e6 2.44332
259259 −429510. −0.397855
260260 0 0
261261 −1.87953e6 −1.70784
262262 −359764. −0.323791
263263 1.72216e6 1.53527 0.767635 0.640887i 0.221433π-0.221433\pi
0.767635 + 0.640887i 0.221433π0.221433\pi
264264 −2.46559e6 −2.17726
265265 0 0
266266 −389115. −0.337189
267267 −776158. −0.666304
268268 −685750. −0.583215
269269 932022. 0.785318 0.392659 0.919684i 0.371555π-0.371555\pi
0.392659 + 0.919684i 0.371555π0.371555\pi
270270 0 0
271271 −157100. −0.129943 −0.0649714 0.997887i 0.520696π-0.520696\pi
−0.0649714 + 0.997887i 0.520696π0.520696\pi
272272 −142000. −0.116377
273273 210024. 0.170554
274274 926746. 0.745735
275275 0 0
276276 507240. 0.400812
277277 −432798. −0.338911 −0.169456 0.985538i 0.554201π-0.554201\pi
−0.169456 + 0.985538i 0.554201π0.554201\pi
278278 1.11367e6 0.864259
279279 3.81630e6 2.93516
280280 0 0
281281 −544542. −0.411401 −0.205701 0.978615i 0.565947π-0.565947\pi
−0.205701 + 0.978615i 0.565947π0.565947\pi
282282 −374668. −0.280558
283283 1.57849e6 1.17159 0.585796 0.810458i 0.300782π-0.300782\pi
0.585796 + 0.810458i 0.300782π0.300782\pi
284284 −823602. −0.605929
285285 0 0
286286 −304945. −0.220448
287287 298747. 0.214091
288288 −2.94912e6 −2.09513
289289 −1.23968e6 −0.873101
290290 0 0
291291 5.31292e6 3.67791
292292 731036. 0.501743
293293 −47169.2 −0.0320989 −0.0160494 0.999871i 0.505109π-0.505109\pi
−0.0160494 + 0.999871i 0.505109π0.505109\pi
294294 −1.82097e6 −1.22867
295295 0 0
296296 1.96151e6 1.30125
297297 −4.67734e6 −3.07686
298298 92683.2 0.0604589
299299 198854. 0.128634
300300 0 0
301301 −914876. −0.582031
302302 −1.81979e6 −1.14817
303303 −880399. −0.550900
304304 737117. 0.457459
305305 0 0
306306 −1.07784e6 −0.658039
307307 −1.21647e6 −0.736639 −0.368320 0.929699i 0.620067π-0.620067\pi
−0.368320 + 0.929699i 0.620067π0.620067\pi
308308 272416. 0.163627
309309 −470514. −0.280334
310310 0 0
311311 745149. 0.436860 0.218430 0.975853i 0.429906π-0.429906\pi
0.218430 + 0.975853i 0.429906π0.429906\pi
312312 −959148. −0.557826
313313 1.98248e6 1.14379 0.571896 0.820326i 0.306208π-0.306208\pi
0.571896 + 0.820326i 0.306208π0.306208\pi
314314 −1.88030e6 −1.07622
315315 0 0
316316 −127005. −0.0715488
317317 191631. 0.107107 0.0535535 0.998565i 0.482945π-0.482945\pi
0.0535535 + 0.998565i 0.482945π0.482945\pi
318318 −4.63505e6 −2.57032
319319 −1.33561e6 −0.734860
320320 0 0
321321 −6.29040e6 −3.40734
322322 207790. 0.111683
323323 −935304. −0.498823
324324 −2.45033e6 −1.29677
325325 0 0
326326 1.52615e6 0.795339
327327 −3.56710e6 −1.84479
328328 −1.36434e6 −0.700224
329329 131213. 0.0668326
330330 0 0
331331 1.37008e6 0.687346 0.343673 0.939089i 0.388329π-0.388329\pi
0.343673 + 0.939089i 0.388329π0.388329\pi
332332 −24127.8 −0.0120136
333333 6.17589e6 3.05203
334334 120460. 0.0590848
335335 0 0
336336 −415735. −0.200895
337337 −2.20098e6 −1.05570 −0.527852 0.849337i 0.677002π-0.677002\pi
−0.527852 + 0.849337i 0.677002π0.677002\pi
338338 −118628. −0.0564801
339339 3.72146e6 1.75879
340340 0 0
341341 2.71190e6 1.26295
342342 5.59505e6 2.58666
343343 1.35231e6 0.620642
344344 4.17811e6 1.90364
345345 0 0
346346 −437859. −0.196627
347347 2.30264e6 1.02660 0.513302 0.858208i 0.328422π-0.328422\pi
0.513302 + 0.858208i 0.328422π0.328422\pi
348348 −1.32533e6 −0.586647
349349 −642226. −0.282244 −0.141122 0.989992i 0.545071π-0.545071\pi
−0.141122 + 0.989992i 0.545071π0.545071\pi
350350 0 0
351351 −1.81955e6 −0.788309
352352 −2.09568e6 −0.901504
353353 3.50057e6 1.49521 0.747604 0.664145i 0.231204π-0.231204\pi
0.747604 + 0.664145i 0.231204π0.231204\pi
354354 −2.12614e6 −0.901746
355355 0 0
356356 −391634. −0.163778
357357 527513. 0.219060
358358 1.24500e6 0.513409
359359 1.77270e6 0.725935 0.362968 0.931802i 0.381764π-0.381764\pi
0.362968 + 0.931802i 0.381764π0.381764\pi
360360 0 0
361361 2.37904e6 0.960802
362362 −2.03841e6 −0.817561
363363 −809052. −0.322263
364364 105974. 0.0419222
365365 0 0
366366 −1.55936e6 −0.608478
367367 509693. 0.197535 0.0987673 0.995111i 0.468510π-0.468510\pi
0.0987673 + 0.995111i 0.468510π0.468510\pi
368368 −393626. −0.151518
369369 −4.29566e6 −1.64234
370370 0 0
371371 1.62326e6 0.612283
372372 2.69103e6 1.00823
373373 2.55346e6 0.950293 0.475147 0.879907i 0.342395π-0.342395\pi
0.475147 + 0.879907i 0.342395π0.342395\pi
374374 −765926. −0.283144
375375 0 0
376376 −599233. −0.218588
377377 −519573. −0.188275
378378 −1.90132e6 −0.684424
379379 1.42480e6 0.509513 0.254757 0.967005i 0.418005π-0.418005\pi
0.254757 + 0.967005i 0.418005π0.418005\pi
380380 0 0
381381 9.57446e6 3.37911
382382 2.87062e6 1.00651
383383 −940463. −0.327601 −0.163800 0.986494i 0.552375π-0.552375\pi
−0.163800 + 0.986494i 0.552375π0.552375\pi
384384 −779924. −0.269913
385385 0 0
386386 689868. 0.235666
387387 1.31549e7 4.46489
388388 2.68079e6 0.904032
389389 5.26222e6 1.76317 0.881586 0.472024i 0.156476π-0.156476\pi
0.881586 + 0.472024i 0.156476π0.156476\pi
390390 0 0
391391 499460. 0.165218
392392 −2.91241e6 −0.957275
393393 −2.53176e6 −0.826877
394394 −2.72686e6 −0.884957
395395 0 0
396396 −3.91704e6 −1.25522
397397 66917.7 0.0213091 0.0106545 0.999943i 0.496608π-0.496608\pi
0.0106545 + 0.999943i 0.496608π0.496608\pi
398398 −3.29373e6 −1.04227
399399 −2.73831e6 −0.861093
400400 0 0
401401 −3.26462e6 −1.01384 −0.506922 0.861992i 0.669217π-0.669217\pi
−0.506922 + 0.861992i 0.669217π0.669217\pi
402402 5.64481e6 1.74215
403403 1.05497e6 0.323576
404404 −444232. −0.135412
405405 0 0
406406 −542922. −0.163464
407407 4.38865e6 1.31324
408408 −2.40908e6 −0.716474
409409 5.49644e6 1.62470 0.812350 0.583171i 0.198188π-0.198188\pi
0.812350 + 0.583171i 0.198188π0.198188\pi
410410 0 0
411411 6.52176e6 1.90441
412412 −237412. −0.0689063
413413 744602. 0.214807
414414 −2.98780e6 −0.856743
415415 0 0
416416 −815249. −0.230971
417417 7.83719e6 2.20709
418418 3.97590e6 1.11300
419419 4.68601e6 1.30397 0.651986 0.758231i 0.273936π-0.273936\pi
0.651986 + 0.758231i 0.273936π0.273936\pi
420420 0 0
421421 4.86774e6 1.33851 0.669256 0.743032i 0.266613π-0.266613\pi
0.669256 + 0.743032i 0.266613π0.266613\pi
422422 −3.02538e6 −0.826989
423423 −1.88671e6 −0.512688
424424 −7.41318e6 −2.00258
425425 0 0
426426 6.77956e6 1.81000
427427 546109. 0.144947
428428 −3.17401e6 −0.837527
429429 −2.14598e6 −0.562966
430430 0 0
431431 3.25405e6 0.843783 0.421892 0.906646i 0.361366π-0.361366\pi
0.421892 + 0.906646i 0.361366π0.361366\pi
432432 3.60175e6 0.928547
433433 693375. 0.177725 0.0888625 0.996044i 0.471677π-0.471677\pi
0.0888625 + 0.996044i 0.471677π0.471677\pi
434434 1.10238e6 0.280935
435435 0 0
436436 −1.79989e6 −0.453450
437437 −2.59268e6 −0.649450
438438 −6.01759e6 −1.49878
439439 −5.29607e6 −1.31157 −0.655787 0.754946i 0.727663π-0.727663\pi
−0.655787 + 0.754946i 0.727663π0.727663\pi
440440 0 0
441441 −9.16981e6 −2.24525
442442 −297956. −0.0725432
443443 −1.05676e6 −0.255838 −0.127919 0.991785i 0.540830π-0.540830\pi
−0.127919 + 0.991785i 0.540830π0.540830\pi
444444 4.35487e6 1.04838
445445 0 0
446446 554718. 0.132049
447447 652236. 0.154396
448448 −1.30703e6 −0.307673
449449 1.60061e6 0.374687 0.187344 0.982294i 0.440012π-0.440012\pi
0.187344 + 0.982294i 0.440012π0.440012\pi
450450 0 0
451451 −3.05254e6 −0.706675
452452 1.87777e6 0.432312
453453 −1.28064e7 −2.93212
454454 4.74132e6 1.07959
455455 0 0
456456 1.25055e7 2.81636
457457 20508.5 0.00459350 0.00229675 0.999997i 0.499269π-0.499269\pi
0.00229675 + 0.999997i 0.499269π0.499269\pi
458458 3.17934e6 0.708229
459459 −4.57014e6 −1.01251
460460 0 0
461461 −5.97691e6 −1.30986 −0.654930 0.755690i 0.727302π-0.727302\pi
−0.654930 + 0.755690i 0.727302π0.727302\pi
462462 −2.24241e6 −0.488777
463463 758041. 0.164339 0.0821694 0.996618i 0.473815π-0.473815\pi
0.0821694 + 0.996618i 0.473815π0.473815\pi
464464 1.02848e6 0.221769
465465 0 0
466466 −4.47972e6 −0.955621
467467 5.52758e6 1.17285 0.586426 0.810003i 0.300535π-0.300535\pi
0.586426 + 0.810003i 0.300535π0.300535\pi
468468 −1.52379e6 −0.321595
469469 −1.97689e6 −0.415002
470470 0 0
471471 −1.32322e7 −2.74839
472472 −3.40049e6 −0.702566
473473 9.34802e6 1.92118
474474 1.04545e6 0.213726
475475 0 0
476476 266173. 0.0538451
477477 −2.33406e7 −4.69696
478478 −66864.5 −0.0133852
479479 6.18197e6 1.23109 0.615543 0.788103i 0.288937π-0.288937\pi
0.615543 + 0.788103i 0.288937π0.288937\pi
480480 0 0
481481 1.70725e6 0.336461
482482 317429. 0.0622341
483483 1.46228e6 0.285208
484484 −408231. −0.0792123
485485 0 0
486486 9.30343e6 1.78670
487487 −6.33627e6 −1.21063 −0.605315 0.795986i 0.706953π-0.706953\pi
−0.605315 + 0.795986i 0.706953π0.706953\pi
488488 −2.49400e6 −0.474076
489489 1.07399e7 2.03108
490490 0 0
491491 4.76619e6 0.892211 0.446105 0.894980i 0.352811π-0.352811\pi
0.446105 + 0.894980i 0.352811π0.352811\pi
492492 −3.02904e6 −0.564148
493493 −1.30500e6 −0.241821
494494 1.54668e6 0.285157
495495 0 0
496496 −2.08828e6 −0.381140
497497 −2.37429e6 −0.431164
498498 198610. 0.0358863
499499 −6.32136e6 −1.13647 −0.568236 0.822865i 0.692374π-0.692374\pi
−0.568236 + 0.822865i 0.692374π0.692374\pi
500500 0 0
501501 847708. 0.150887
502502 3.39186e6 0.600730
503503 2.42758e6 0.427813 0.213906 0.976854i 0.431381π-0.431381\pi
0.213906 + 0.976854i 0.431381π0.431381\pi
504504 −5.04701e6 −0.885030
505505 0 0
506506 −2.12316e6 −0.368644
507507 −834817. −0.144235
508508 4.83108e6 0.830586
509509 −5.22784e6 −0.894391 −0.447196 0.894436i 0.647577π-0.647577\pi
−0.447196 + 0.894436i 0.647577π0.647577\pi
510510 0 0
511511 2.10744e6 0.357028
512512 3.69234e6 0.622482
513513 2.37235e7 3.98002
514514 −4.92775e6 −0.822698
515515 0 0
516516 9.27607e6 1.53370
517517 −1.34071e6 −0.220602
518518 1.78397e6 0.292121
519519 −3.08133e6 −0.502134
520520 0 0
521521 −1.15960e7 −1.87161 −0.935806 0.352516i 0.885326π-0.885326\pi
−0.935806 + 0.352516i 0.885326π0.885326\pi
522522 7.80662e6 1.25397
523523 −3.49229e6 −0.558285 −0.279143 0.960250i 0.590050π-0.590050\pi
−0.279143 + 0.960250i 0.590050π0.590050\pi
524524 −1.27747e6 −0.203247
525525 0 0
526526 −7.15299e6 −1.12726
527527 2.64975e6 0.415602
528528 4.24790e6 0.663116
529529 −5.05183e6 −0.784891
530530 0 0
531531 −1.07066e7 −1.64784
532532 −1.38169e6 −0.211657
533533 −1.18748e6 −0.181054
534534 3.22377e6 0.489227
535535 0 0
536536 9.02816e6 1.35734
537537 8.76143e6 1.31111
538538 −3.87115e6 −0.576612
539539 −6.51616e6 −0.966095
540540 0 0
541541 216425. 0.0317917 0.0158959 0.999874i 0.494940π-0.494940\pi
0.0158959 + 0.999874i 0.494940π0.494940\pi
542542 652513. 0.0954094
543543 −1.43448e7 −2.08783
544544 −2.04765e6 −0.296659
545545 0 0
546546 −872332. −0.125228
547547 658142. 0.0940484 0.0470242 0.998894i 0.485026π-0.485026\pi
0.0470242 + 0.998894i 0.485026π0.485026\pi
548548 3.29075e6 0.468105
549549 −7.85245e6 −1.11192
550550 0 0
551551 6.77424e6 0.950565
552552 −6.67801e6 −0.932824
553553 −366131. −0.0509124
554554 1.79762e6 0.248842
555555 0 0
556556 3.95448e6 0.542504
557557 6.55817e6 0.895663 0.447831 0.894118i 0.352196π-0.352196\pi
0.447831 + 0.894118i 0.352196π0.352196\pi
558558 −1.58510e7 −2.15511
559559 3.63652e6 0.492216
560560 0 0
561561 −5.39003e6 −0.723076
562562 2.26175e6 0.302068
563563 −9.44685e6 −1.25608 −0.628038 0.778183i 0.716142π-0.716142\pi
−0.628038 + 0.778183i 0.716142π0.716142\pi
564564 −1.33039e6 −0.176109
565565 0 0
566566 −6.55626e6 −0.860231
567567 −7.06384e6 −0.922748
568568 1.08430e7 1.41020
569569 1.98661e6 0.257236 0.128618 0.991694i 0.458946π-0.458946\pi
0.128618 + 0.991694i 0.458946π0.458946\pi
570570 0 0
571571 1.05472e7 1.35378 0.676888 0.736086i 0.263328π-0.263328\pi
0.676888 + 0.736086i 0.263328π0.263328\pi
572572 −1.08282e6 −0.138377
573573 2.02013e7 2.57036
574574 −1.24084e6 −0.157195
575575 0 0
576576 1.87936e7 2.36023
577577 3.57968e6 0.447615 0.223807 0.974633i 0.428151π-0.428151\pi
0.223807 + 0.974633i 0.428151π0.428151\pi
578578 5.14899e6 0.641066
579579 4.85478e6 0.601830
580580 0 0
581581 −69555.9 −0.00854857
582582 −2.20672e7 −2.70047
583583 −1.65861e7 −2.02103
584584 −9.62437e6 −1.16772
585585 0 0
586586 195917. 0.0235683
587587 8.78869e6 1.05276 0.526379 0.850250i 0.323549π-0.323549\pi
0.526379 + 0.850250i 0.323549π0.323549\pi
588588 −6.46601e6 −0.771246
589589 −1.37548e7 −1.63367
590590 0 0
591591 −1.91896e7 −2.25995
592592 −3.37945e6 −0.396316
593593 −6.61381e6 −0.772352 −0.386176 0.922425i 0.626204π-0.626204\pi
−0.386176 + 0.922425i 0.626204π0.626204\pi
594594 1.94273e7 2.25916
595595 0 0
596596 329105. 0.0379506
597597 −2.31789e7 −2.66168
598598 −825940. −0.0944486
599599 1.20269e7 1.36957 0.684787 0.728743i 0.259895π-0.259895\pi
0.684787 + 0.728743i 0.259895π0.259895\pi
600600 0 0
601601 3.83969e6 0.433621 0.216810 0.976214i 0.430435π-0.430435\pi
0.216810 + 0.976214i 0.430435π0.430435\pi
602602 3.79993e6 0.427351
603603 2.84255e7 3.18357
604604 −6.46184e6 −0.720716
605605 0 0
606606 3.65673e6 0.404494
607607 −5.50595e6 −0.606542 −0.303271 0.952904i 0.598079π-0.598079\pi
−0.303271 + 0.952904i 0.598079π0.598079\pi
608608 1.06293e7 1.16613
609609 −3.82069e6 −0.417444
610610 0 0
611611 −521557. −0.0565195
612612 −3.82727e6 −0.413058
613613 −7.77688e6 −0.835899 −0.417950 0.908470i 0.637251π-0.637251\pi
−0.417950 + 0.908470i 0.637251π0.637251\pi
614614 5.05259e6 0.540871
615615 0 0
616616 −3.58646e6 −0.380815
617617 5.24549e6 0.554719 0.277359 0.960766i 0.410541π-0.410541\pi
0.277359 + 0.960766i 0.410541π0.410541\pi
618618 1.95428e6 0.205833
619619 1.53925e7 1.61467 0.807333 0.590096i 0.200910π-0.200910\pi
0.807333 + 0.590096i 0.200910π0.200910\pi
620620 0 0
621621 −1.26685e7 −1.31825
622622 −3.09497e6 −0.320760
623623 −1.12901e6 −0.116540
624624 1.65249e6 0.169894
625625 0 0
626626 −8.23420e6 −0.839819
627627 2.79795e7 2.84231
628628 −6.67669e6 −0.675557
629629 4.28807e6 0.432151
630630 0 0
631631 −959665. −0.0959503 −0.0479752 0.998849i 0.515277π-0.515277\pi
−0.0479752 + 0.998849i 0.515277π0.515277\pi
632632 1.67207e6 0.166518
633633 −2.12904e7 −2.11191
634634 −795939. −0.0786423
635635 0 0
636636 −1.64584e7 −1.61341
637637 −2.53488e6 −0.247519
638638 5.54747e6 0.539564
639639 3.41397e7 3.30756
640640 0 0
641641 −4.04738e6 −0.389071 −0.194536 0.980895i 0.562320π-0.562320\pi
−0.194536 + 0.980895i 0.562320π0.562320\pi
642642 2.61271e7 2.50181
643643 3.34301e6 0.318867 0.159434 0.987209i 0.449033π-0.449033\pi
0.159434 + 0.987209i 0.449033π0.449033\pi
644644 737835. 0.0701043
645645 0 0
646646 3.88478e6 0.366256
647647 −1.60437e6 −0.150676 −0.0753379 0.997158i 0.524004π-0.524004\pi
−0.0753379 + 0.997158i 0.524004π0.524004\pi
648648 3.22596e7 3.01801
649649 −7.60820e6 −0.709039
650650 0 0
651651 7.75771e6 0.717433
652652 5.41913e6 0.499242
653653 −8.15286e6 −0.748216 −0.374108 0.927385i 0.622051π-0.622051\pi
−0.374108 + 0.927385i 0.622051π0.622051\pi
654654 1.48159e7 1.35452
655655 0 0
656656 2.35058e6 0.213263
657657 −3.03027e7 −2.73884
658658 −544994. −0.0490713
659659 −9.64758e6 −0.865376 −0.432688 0.901544i 0.642435π-0.642435\pi
−0.432688 + 0.901544i 0.642435π0.642435\pi
660660 0 0
661661 −1.08154e7 −0.962802 −0.481401 0.876500i 0.659872π-0.659872\pi
−0.481401 + 0.876500i 0.659872π0.659872\pi
662662 −5.69061e6 −0.504677
663663 −2.09680e6 −0.185256
664664 317652. 0.0279596
665665 0 0
666666 −2.56515e7 −2.24093
667667 −3.61750e6 −0.314843
668668 427736. 0.0370881
669669 3.90370e6 0.337218
670670 0 0
671671 −5.58004e6 −0.478444
672672 −5.99494e6 −0.512108
673673 −8.41679e6 −0.716323 −0.358161 0.933660i 0.616596π-0.616596\pi
−0.358161 + 0.933660i 0.616596π0.616596\pi
674674 9.14177e6 0.775141
675675 0 0
676676 −421232. −0.0354531
677677 −1.30052e7 −1.09055 −0.545276 0.838257i 0.683575π-0.683575\pi
−0.545276 + 0.838257i 0.683575π0.683575\pi
678678 −1.54571e7 −1.29138
679679 7.72821e6 0.643287
680680 0 0
681681 3.33660e7 2.75700
682682 −1.12639e7 −0.927313
683683 6.34198e6 0.520204 0.260102 0.965581i 0.416244π-0.416244\pi
0.260102 + 0.965581i 0.416244π0.416244\pi
684684 1.98673e7 1.62367
685685 0 0
686686 −5.61682e6 −0.455701
687687 2.23739e7 1.80863
688688 −7.19837e6 −0.579780
689689 −6.45223e6 −0.517800
690690 0 0
691691 −5.39316e6 −0.429683 −0.214841 0.976649i 0.568923π-0.568923\pi
−0.214841 + 0.976649i 0.568923π0.568923\pi
692692 −1.55478e6 −0.123425
693693 −1.12921e7 −0.893184
694694 −9.56401e6 −0.753774
695695 0 0
696696 1.74485e7 1.36532
697697 −2.98258e6 −0.232547
698698 2.66748e6 0.207235
699699 −3.15250e7 −2.44040
700700 0 0
701701 2.51700e6 0.193459 0.0967293 0.995311i 0.469162π-0.469162\pi
0.0967293 + 0.995311i 0.469162π0.469162\pi
702702 7.55750e6 0.578809
703703 −2.22593e7 −1.69872
704704 1.33550e7 1.01557
705705 0 0
706706 −1.45396e7 −1.09784
707707 −1.28064e6 −0.0963556
708708 −7.54964e6 −0.566035
709709 −7.70344e6 −0.575532 −0.287766 0.957701i 0.592913π-0.592913\pi
−0.287766 + 0.957701i 0.592913π0.592913\pi
710710 0 0
711711 5.26456e6 0.390560
712712 5.15601e6 0.381166
713713 7.34515e6 0.541099
714714 −2.19102e6 −0.160843
715715 0 0
716716 4.42084e6 0.322272
717717 −470544. −0.0341824
718718 −7.36288e6 −0.533012
719719 9.67017e6 0.697609 0.348804 0.937196i 0.386588π-0.386588\pi
0.348804 + 0.937196i 0.386588π0.386588\pi
720720 0 0
721721 −684413. −0.0490321
722722 −9.88133e6 −0.705460
723723 2.23383e6 0.158929
724724 −7.23811e6 −0.513191
725725 0 0
726726 3.36039e6 0.236618
727727 −6.56744e6 −0.460850 −0.230425 0.973090i 0.574012π-0.574012\pi
−0.230425 + 0.973090i 0.574012π0.574012\pi
728728 −1.39518e6 −0.0975670
729729 2.50984e7 1.74915
730730 0 0
731731 9.13379e6 0.632204
732732 −5.53709e6 −0.381947
733733 −1.34964e7 −0.927808 −0.463904 0.885885i 0.653552π-0.653552\pi
−0.463904 + 0.885885i 0.653552π0.653552\pi
734734 −2.11701e6 −0.145038
735735 0 0
736736 −5.67612e6 −0.386240
737737 2.01994e7 1.36984
738738 1.78420e7 1.20588
739739 1.14388e7 0.770492 0.385246 0.922814i 0.374117π-0.374117\pi
0.385246 + 0.922814i 0.374117π0.374117\pi
740740 0 0
741741 1.08844e7 0.728215
742742 −6.74218e6 −0.449563
743743 1.51089e7 1.00406 0.502031 0.864850i 0.332586π-0.332586\pi
0.502031 + 0.864850i 0.332586π0.332586\pi
744744 −3.54284e7 −2.34649
745745 0 0
746746 −1.06058e7 −0.697744
747747 1.00014e6 0.0655780
748748 −2.71970e6 −0.177732
749749 −9.15007e6 −0.595964
750750 0 0
751751 2.10421e6 0.136141 0.0680706 0.997681i 0.478316π-0.478316\pi
0.0680706 + 0.997681i 0.478316π0.478316\pi
752752 1.03241e6 0.0665742
753753 2.38695e7 1.53411
754754 2.15804e6 0.138239
755755 0 0
756756 −6.75132e6 −0.429620
757757 1.09867e7 0.696828 0.348414 0.937341i 0.386720π-0.386720\pi
0.348414 + 0.937341i 0.386720π0.386720\pi
758758 −5.91789e6 −0.374106
759759 −1.49413e7 −0.941419
760760 0 0
761761 −1.14683e7 −0.717859 −0.358929 0.933365i 0.616858π-0.616858\pi
−0.358929 + 0.933365i 0.616858π0.616858\pi
762762 −3.97675e7 −2.48108
763763 −5.18873e6 −0.322664
764764 1.01932e7 0.631795
765765 0 0
766766 3.90621e6 0.240538
767767 −2.95970e6 −0.181660
768768 3.19928e7 1.95726
769769 −2.18586e6 −0.133293 −0.0666464 0.997777i 0.521230π-0.521230\pi
−0.0666464 + 0.997777i 0.521230π0.521230\pi
770770 0 0
771771 −3.46779e7 −2.10095
772772 2.44963e6 0.147930
773773 4.06142e6 0.244472 0.122236 0.992501i 0.460993π-0.460993\pi
0.122236 + 0.992501i 0.460993π0.460993\pi
774774 −5.46389e7 −3.27831
775775 0 0
776776 −3.52937e7 −2.10398
777777 1.25543e7 0.746000
778778 −2.18566e7 −1.29459
779779 1.54825e7 0.914108
780780 0 0
781781 2.42600e7 1.42319
782782 −2.07450e6 −0.121310
783783 3.31007e7 1.92945
784784 5.01772e6 0.291552
785785 0 0
786786 1.05156e7 0.607127
787787 1.97898e7 1.13895 0.569475 0.822008i 0.307146π-0.307146\pi
0.569475 + 0.822008i 0.307146π0.307146\pi
788788 −9.68271e6 −0.555496
789789 −5.03375e7 −2.87872
790790 0 0
791791 5.41327e6 0.307623
792792 5.15694e7 2.92132
793793 −2.17071e6 −0.122580
794794 −277942. −0.0156460
795795 0 0
796796 −1.16956e7 −0.654243
797797 −2.61426e6 −0.145782 −0.0728908 0.997340i 0.523222π-0.523222\pi
−0.0728908 + 0.997340i 0.523222π0.523222\pi
798798 1.13735e7 0.632250
799799 −1.30999e6 −0.0725939
800800 0 0
801801 1.62339e7 0.894007
802802 1.35596e7 0.744406
803803 −2.15334e7 −1.17848
804804 2.00440e7 1.09356
805805 0 0
806806 −4.38180e6 −0.237583
807807 −2.72423e7 −1.47252
808808 5.84848e6 0.315148
809809 −134453. −0.00722267 −0.00361134 0.999993i 0.501150π-0.501150\pi
−0.00361134 + 0.999993i 0.501150π0.501150\pi
810810 0 0
811811 −1.38880e7 −0.741459 −0.370729 0.928741i 0.620892π-0.620892\pi
−0.370729 + 0.928741i 0.620892π0.620892\pi
812812 −1.92784e6 −0.102608
813813 4.59191e6 0.243650
814814 −1.82282e7 −0.964237
815815 0 0
816816 4.15055e6 0.218213
817817 −4.74132e7 −2.48510
818818 −2.28294e7 −1.19292
819819 −4.39278e6 −0.228839
820820 0 0
821821 −2.09003e7 −1.08217 −0.541084 0.840969i 0.681986π-0.681986\pi
−0.541084 + 0.840969i 0.681986π0.681986\pi
822822 −2.70881e7 −1.39830
823823 7.88591e6 0.405837 0.202919 0.979196i 0.434957π-0.434957\pi
0.202919 + 0.979196i 0.434957π0.434957\pi
824824 3.12562e6 0.160368
825825 0 0
826826 −3.09270e6 −0.157720
827827 3.09009e7 1.57111 0.785556 0.618790i 0.212377π-0.212377\pi
0.785556 + 0.618790i 0.212377π0.212377\pi
828828 −1.06093e7 −0.537786
829829 3.72829e7 1.88418 0.942092 0.335356i 0.108856π-0.108856\pi
0.942092 + 0.335356i 0.108856π0.108856\pi
830830 0 0
831831 1.26504e7 0.635478
832832 5.19527e6 0.260196
833833 −6.36683e6 −0.317915
834834 −3.25517e7 −1.62054
835835 0 0
836836 1.41179e7 0.698640
837837 −6.72094e7 −3.31602
838838 −1.94633e7 −0.957429
839839 3.71338e7 1.82123 0.910615 0.413256i 0.135608π-0.135608\pi
0.910615 + 0.413256i 0.135608π0.135608\pi
840840 0 0
841841 −1.10592e7 −0.539181
842842 −2.02181e7 −0.982790
843843 1.59166e7 0.771401
844844 −1.07427e7 −0.519109
845845 0 0
846846 7.83642e6 0.376437
847847 −1.17685e6 −0.0563655
848848 1.27720e7 0.609915
849849 −4.61382e7 −2.19680
850850 0 0
851851 1.18866e7 0.562645
852852 2.40733e7 1.13615
853853 3.69954e7 1.74091 0.870453 0.492252i 0.163826π-0.163826\pi
0.870453 + 0.492252i 0.163826π0.163826\pi
854854 −2.26826e6 −0.106426
855855 0 0
856856 4.17871e7 1.94920
857857 1.25620e7 0.584260 0.292130 0.956379i 0.405636π-0.405636\pi
0.292130 + 0.956379i 0.405636π0.405636\pi
858858 8.91331e6 0.413353
859859 5.95648e6 0.275427 0.137714 0.990472i 0.456025π-0.456025\pi
0.137714 + 0.990472i 0.456025π0.456025\pi
860860 0 0
861861 −8.73216e6 −0.401434
862862 −1.35157e7 −0.619540
863863 1.36218e7 0.622600 0.311300 0.950312i 0.399236π-0.399236\pi
0.311300 + 0.950312i 0.399236π0.399236\pi
864864 5.19375e7 2.36699
865865 0 0
866866 −2.87993e6 −0.130493
867867 3.62349e7 1.63711
868868 3.91439e6 0.176345
869869 3.74105e6 0.168052
870870 0 0
871871 7.85787e6 0.350962
872872 2.36962e7 1.05533
873873 −1.11123e8 −4.93480
874874 1.07687e7 0.476853
875875 0 0
876876 −2.13676e7 −0.940798
877877 2.57256e7 1.12945 0.564725 0.825279i 0.308982π-0.308982\pi
0.564725 + 0.825279i 0.308982π0.308982\pi
878878 2.19972e7 0.963011
879879 1.37872e6 0.0601872
880880 0 0
881881 4.32713e6 0.187828 0.0939140 0.995580i 0.470062π-0.470062\pi
0.0939140 + 0.995580i 0.470062π0.470062\pi
882882 3.80868e7 1.64855
883883 −3.46067e7 −1.49368 −0.746841 0.665003i 0.768430π-0.768430\pi
−0.746841 + 0.665003i 0.768430π0.768430\pi
884884 −1.05800e6 −0.0455361
885885 0 0
886886 4.38923e6 0.187847
887887 −3.18896e7 −1.36094 −0.680472 0.732774i 0.738225π-0.738225\pi
−0.680472 + 0.732774i 0.738225π0.738225\pi
888888 −5.73336e7 −2.43993
889889 1.39271e7 0.591025
890890 0 0
891891 7.21769e7 3.04582
892892 1.96973e6 0.0828884
893893 6.80010e6 0.285356
894894 −2.70906e6 −0.113364
895895 0 0
896896 −1.13448e6 −0.0472094
897897 −5.81236e6 −0.241197
898898 −6.64811e6 −0.275111
899899 −1.91917e7 −0.791978
900900 0 0
901901 −1.62060e7 −0.665064
902902 1.26787e7 0.518870
903903 2.67411e7 1.09134
904904 −2.47216e7 −1.00613
905905 0 0
906906 5.31913e7 2.15288
907907 2.40329e7 0.970035 0.485018 0.874504i 0.338813π-0.338813\pi
0.485018 + 0.874504i 0.338813π0.338813\pi
908908 1.68358e7 0.677671
909909 1.84141e7 0.739166
910910 0 0
911911 −1.88212e6 −0.0751366 −0.0375683 0.999294i 0.511961π-0.511961\pi
−0.0375683 + 0.999294i 0.511961π0.511961\pi
912912 −2.15454e7 −0.857763
913913 710708. 0.0282172
914914 −85182.0 −0.00337274
915915 0 0
916916 1.12894e7 0.444562
917917 −3.68271e6 −0.144625
918918 1.89821e7 0.743424
919919 −2.08679e6 −0.0815061 −0.0407530 0.999169i 0.512976π-0.512976\pi
−0.0407530 + 0.999169i 0.512976π0.512976\pi
920920 0 0
921921 3.55565e7 1.38124
922922 2.48251e7 0.961752
923923 9.43750e6 0.364630
924924 −7.96251e6 −0.306810
925925 0 0
926926 −3.14852e6 −0.120664
927927 9.84111e6 0.376136
928928 1.48308e7 0.565319
929929 4.37732e7 1.66406 0.832030 0.554730i 0.187179π-0.187179\pi
0.832030 + 0.554730i 0.187179π0.187179\pi
930930 0 0
931931 3.30500e7 1.24968
932932 −1.59069e7 −0.599853
933933 −2.17801e7 −0.819137
934934 −2.29588e7 −0.861156
935935 0 0
936936 2.00612e7 0.748458
937937 1.71324e7 0.637484 0.318742 0.947842i 0.396740π-0.396740\pi
0.318742 + 0.947842i 0.396740π0.396740\pi
938938 8.21099e6 0.304711
939939 −5.79463e7 −2.14468
940940 0 0
941941 −2.91171e7 −1.07195 −0.535975 0.844234i 0.680056π-0.680056\pi
−0.535975 + 0.844234i 0.680056π0.680056\pi
942942 5.49598e7 2.01798
943943 −8.26778e6 −0.302768
944944 5.85864e6 0.213977
945945 0 0
946946 −3.88270e7 −1.41061
947947 3.57121e7 1.29402 0.647009 0.762482i 0.276019π-0.276019\pi
0.647009 + 0.762482i 0.276019π0.276019\pi
948948 3.71225e6 0.134158
949949 −8.37680e6 −0.301934
950950 0 0
951951 −5.60123e6 −0.200832
952952 −3.50426e6 −0.125315
953953 1.21150e7 0.432105 0.216053 0.976382i 0.430682π-0.430682\pi
0.216053 + 0.976382i 0.430682π0.430682\pi
954954 9.69452e7 3.44870
955955 0 0
956956 −237427. −0.00840204
957957 3.90390e7 1.37790
958958 −2.56768e7 −0.903913
959959 9.48661e6 0.333092
960960 0 0
961961 1.03386e7 0.361120
962962 −7.09105e6 −0.247043
963963 1.31568e8 4.57177
964964 1.12715e6 0.0390650
965965 0 0
966966 −6.07356e6 −0.209411
967967 1.23685e6 0.0425353 0.0212676 0.999774i 0.493230π-0.493230\pi
0.0212676 + 0.999774i 0.493230π0.493230\pi
968968 5.37452e6 0.184354
969969 2.73383e7 0.935322
970970 0 0
971971 2.65552e7 0.903861 0.451931 0.892053i 0.350735π-0.350735\pi
0.451931 + 0.892053i 0.350735π0.350735\pi
972972 3.30352e7 1.12153
973973 1.14000e7 0.386032
974974 2.63177e7 0.888894
975975 0 0
976976 4.29686e6 0.144387
977977 2.10622e7 0.705939 0.352970 0.935635i 0.385172π-0.385172\pi
0.352970 + 0.935635i 0.385172π0.385172\pi
978978 −4.46081e7 −1.49131
979979 1.15360e7 0.384678
980980 0 0
981981 7.46083e7 2.47523
982982 −1.97963e7 −0.655098
983983 5.95953e7 1.96711 0.983554 0.180615i 0.0578088π-0.0578088\pi
0.983554 + 0.180615i 0.0578088π0.0578088\pi
984984 3.98785e7 1.31296
985985 0 0
986986 5.42033e6 0.177555
987987 −3.83527e6 −0.125315
988988 5.49206e6 0.178996
989989 2.53190e7 0.823107
990990 0 0
991991 7.17026e6 0.231927 0.115963 0.993253i 0.463004π-0.463004\pi
0.115963 + 0.993253i 0.463004π0.463004\pi
992992 −3.01131e7 −0.971576
993993 −4.00464e7 −1.28881
994994 9.86160e6 0.316578
995995 0 0
996996 705238. 0.0225262
997997 5.19624e7 1.65558 0.827791 0.561036i 0.189597π-0.189597\pi
0.827791 + 0.561036i 0.189597π0.189597\pi
998998 2.62557e7 0.834445
999999 −1.08765e8 −3.44805
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 325.6.a.f.1.3 6
5.2 odd 4 325.6.b.f.274.5 12
5.3 odd 4 325.6.b.f.274.8 12
5.4 even 2 65.6.a.e.1.4 6
15.14 odd 2 585.6.a.k.1.3 6
20.19 odd 2 1040.6.a.r.1.1 6
65.64 even 2 845.6.a.g.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.6.a.e.1.4 6 5.4 even 2
325.6.a.f.1.3 6 1.1 even 1 trivial
325.6.b.f.274.5 12 5.2 odd 4
325.6.b.f.274.8 12 5.3 odd 4
585.6.a.k.1.3 6 15.14 odd 2
845.6.a.g.1.3 6 65.64 even 2
1040.6.a.r.1.1 6 20.19 odd 2