Properties

Label 325.6.a.e.1.3
Level 325325
Weight 66
Character 325.1
Self dual yes
Analytic conductor 52.12552.125
Analytic rank 00
Dimension 44
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 = [4,9] 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: 44
Coefficient field: 4.4.1878612.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x42x316x2+16x+49 x^{4} - 2x^{3} - 16x^{2} + 16x + 49 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 23 2^{3}
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 3.13795-3.13795 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) == q+8.75180q2+26.2145q3+44.5940q4+229.424q68.06989q7+110.220q8+444.199q9+591.993q11+1169.01q12+169.000q1370.6260q14462.381q16+936.856q17+3887.54q18560.050q19211.548q21+5181.00q222970.19q23+2889.37q24+1479.05q26+5274.32q27359.869q28+802.996q294511.01q317573.72q32+15518.8q33+8199.18q34+19808.6q369143.29q374901.45q38+4430.25q39+15224.1q411851.42q42+20927.4q43+26399.3q4425994.5q46+20002.7q4712121.1q4816741.9q49+24559.2q51+7536.39q5219701.8q53+46159.8q54889.467q5614681.4q57+7027.66q5841769.8q59+41527.5q6139479.5q623584.63q6351487.5q64+135817.q66+8814.24q67+41778.2q6877862.0q6911984.8q71+48959.8q72+59144.1q7380020.3q7424974.9q764777.31q77+38772.6q7869794.0q79+30323.3q81+133238.q82+17957.2q839433.77q84+183152.q86+21050.1q87+65249.7q88110432.q891363.81q91132453.q92118254.q93+175060.q94198541.q96136379.q97146522.q98+262962.q99+O(q100)q+8.75180 q^{2} +26.2145 q^{3} +44.5940 q^{4} +229.424 q^{6} -8.06989 q^{7} +110.220 q^{8} +444.199 q^{9} +591.993 q^{11} +1169.01 q^{12} +169.000 q^{13} -70.6260 q^{14} -462.381 q^{16} +936.856 q^{17} +3887.54 q^{18} -560.050 q^{19} -211.548 q^{21} +5181.00 q^{22} -2970.19 q^{23} +2889.37 q^{24} +1479.05 q^{26} +5274.32 q^{27} -359.869 q^{28} +802.996 q^{29} -4511.01 q^{31} -7573.72 q^{32} +15518.8 q^{33} +8199.18 q^{34} +19808.6 q^{36} -9143.29 q^{37} -4901.45 q^{38} +4430.25 q^{39} +15224.1 q^{41} -1851.42 q^{42} +20927.4 q^{43} +26399.3 q^{44} -25994.5 q^{46} +20002.7 q^{47} -12121.1 q^{48} -16741.9 q^{49} +24559.2 q^{51} +7536.39 q^{52} -19701.8 q^{53} +46159.8 q^{54} -889.467 q^{56} -14681.4 q^{57} +7027.66 q^{58} -41769.8 q^{59} +41527.5 q^{61} -39479.5 q^{62} -3584.63 q^{63} -51487.5 q^{64} +135817. q^{66} +8814.24 q^{67} +41778.2 q^{68} -77862.0 q^{69} -11984.8 q^{71} +48959.8 q^{72} +59144.1 q^{73} -80020.3 q^{74} -24974.9 q^{76} -4777.31 q^{77} +38772.6 q^{78} -69794.0 q^{79} +30323.3 q^{81} +133238. q^{82} +17957.2 q^{83} -9433.77 q^{84} +183152. q^{86} +21050.1 q^{87} +65249.7 q^{88} -110432. q^{89} -1363.81 q^{91} -132453. q^{92} -118254. q^{93} +175060. q^{94} -198541. q^{96} -136379. q^{97} -146522. q^{98} +262962. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+9q2+4q3+93q474q6+136q7+447q8+644q9516q11+710q12+676q13+1604q14719q16344q17+6905q185012q194448q21++290668q99+O(q100) 4 q + 9 q^{2} + 4 q^{3} + 93 q^{4} - 74 q^{6} + 136 q^{7} + 447 q^{8} + 644 q^{9} - 516 q^{11} + 710 q^{12} + 676 q^{13} + 1604 q^{14} - 719 q^{16} - 344 q^{17} + 6905 q^{18} - 5012 q^{19} - 4448 q^{21}+ \cdots + 290668 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 8.75180 1.54711 0.773557 0.633726i 0.218475π-0.218475\pi
0.773557 + 0.633726i 0.218475π0.218475\pi
33 26.2145 1.68166 0.840830 0.541300i 0.182068π-0.182068\pi
0.840830 + 0.541300i 0.182068π0.182068\pi
44 44.5940 1.39356
55 0 0
66 229.424 2.60172
77 −8.06989 −0.0622476 −0.0311238 0.999516i 0.509909π-0.509909\pi
−0.0311238 + 0.999516i 0.509909π0.509909\pi
88 110.220 0.608888
99 444.199 1.82798
1010 0 0
1111 591.993 1.47514 0.737572 0.675268i 0.235972π-0.235972\pi
0.737572 + 0.675268i 0.235972π0.235972\pi
1212 1169.01 2.34350
1313 169.000 0.277350
1414 −70.6260 −0.0963041
1515 0 0
1616 −462.381 −0.451544
1717 936.856 0.786232 0.393116 0.919489i 0.371397π-0.371397\pi
0.393116 + 0.919489i 0.371397π0.371397\pi
1818 3887.54 2.82809
1919 −560.050 −0.355912 −0.177956 0.984038i 0.556949π-0.556949\pi
−0.177956 + 0.984038i 0.556949π0.556949\pi
2020 0 0
2121 −211.548 −0.104679
2222 5181.00 2.28222
2323 −2970.19 −1.17075 −0.585376 0.810762i 0.699053π-0.699053\pi
−0.585376 + 0.810762i 0.699053π0.699053\pi
2424 2889.37 1.02394
2525 0 0
2626 1479.05 0.429092
2727 5274.32 1.39238
2828 −359.869 −0.0867459
2929 802.996 0.177304 0.0886520 0.996063i 0.471744π-0.471744\pi
0.0886520 + 0.996063i 0.471744π0.471744\pi
3030 0 0
3131 −4511.01 −0.843082 −0.421541 0.906809i 0.638511π-0.638511\pi
−0.421541 + 0.906809i 0.638511π0.638511\pi
3232 −7573.72 −1.30748
3333 15518.8 2.48069
3434 8199.18 1.21639
3535 0 0
3636 19808.6 2.54740
3737 −9143.29 −1.09799 −0.548995 0.835826i 0.684989π-0.684989\pi
−0.548995 + 0.835826i 0.684989π0.684989\pi
3838 −4901.45 −0.550637
3939 4430.25 0.466408
4040 0 0
4141 15224.1 1.41440 0.707199 0.707014i 0.249958π-0.249958\pi
0.707199 + 0.707014i 0.249958π0.249958\pi
4242 −1851.42 −0.161951
4343 20927.4 1.72601 0.863006 0.505193i 0.168579π-0.168579\pi
0.863006 + 0.505193i 0.168579π0.168579\pi
4444 26399.3 2.05571
4545 0 0
4646 −25994.5 −1.81129
4747 20002.7 1.32082 0.660411 0.750904i 0.270382π-0.270382\pi
0.660411 + 0.750904i 0.270382π0.270382\pi
4848 −12121.1 −0.759344
4949 −16741.9 −0.996125
5050 0 0
5151 24559.2 1.32217
5252 7536.39 0.386505
5353 −19701.8 −0.963423 −0.481711 0.876330i 0.659985π-0.659985\pi
−0.481711 + 0.876330i 0.659985π0.659985\pi
5454 46159.8 2.15417
5555 0 0
5656 −889.467 −0.0379018
5757 −14681.4 −0.598523
5858 7027.66 0.274310
5959 −41769.8 −1.56218 −0.781092 0.624416i 0.785337π-0.785337\pi
−0.781092 + 0.624416i 0.785337π0.785337\pi
6060 0 0
6161 41527.5 1.42893 0.714466 0.699670i 0.246670π-0.246670\pi
0.714466 + 0.699670i 0.246670π0.246670\pi
6262 −39479.5 −1.30434
6363 −3584.63 −0.113787
6464 −51487.5 −1.57127
6565 0 0
6666 135817. 3.83791
6767 8814.24 0.239882 0.119941 0.992781i 0.461729π-0.461729\pi
0.119941 + 0.992781i 0.461729π0.461729\pi
6868 41778.2 1.09566
6969 −77862.0 −1.96881
7070 0 0
7171 −11984.8 −0.282152 −0.141076 0.989999i 0.545056π-0.545056\pi
−0.141076 + 0.989999i 0.545056π0.545056\pi
7272 48959.8 1.11303
7373 59144.1 1.29899 0.649493 0.760368i 0.274981π-0.274981\pi
0.649493 + 0.760368i 0.274981π0.274981\pi
7474 −80020.3 −1.69872
7575 0 0
7676 −24974.9 −0.495986
7777 −4777.31 −0.0918241
7878 38772.6 0.721587
7979 −69794.0 −1.25820 −0.629101 0.777323i 0.716577π-0.716577\pi
−0.629101 + 0.777323i 0.716577π0.716577\pi
8080 0 0
8181 30323.3 0.513527
8282 133238. 2.18824
8383 17957.2 0.286117 0.143058 0.989714i 0.454306π-0.454306\pi
0.143058 + 0.989714i 0.454306π0.454306\pi
8484 −9433.77 −0.145877
8585 0 0
8686 183152. 2.67034
8787 21050.1 0.298165
8888 65249.7 0.898198
8989 −110432. −1.47781 −0.738907 0.673807i 0.764658π-0.764658\pi
−0.738907 + 0.673807i 0.764658π0.764658\pi
9090 0 0
9191 −1363.81 −0.0172644
9292 −132453. −1.63152
9393 −118254. −1.41778
9494 175060. 2.04346
9595 0 0
9696 −198541. −2.19873
9797 −136379. −1.47170 −0.735850 0.677144i 0.763217π-0.763217\pi
−0.735850 + 0.677144i 0.763217π0.763217\pi
9898 −146522. −1.54112
9999 262962. 2.69653
100100 0 0
101101 −65451.1 −0.638430 −0.319215 0.947682i 0.603419π-0.603419\pi
−0.319215 + 0.947682i 0.603419π0.603419\pi
102102 214937. 2.04556
103103 101771. 0.945215 0.472607 0.881273i 0.343313π-0.343313\pi
0.472607 + 0.881273i 0.343313π0.343313\pi
104104 18627.3 0.168875
105105 0 0
106106 −172427. −1.49053
107107 −179471. −1.51543 −0.757715 0.652586i 0.773684π-0.773684\pi
−0.757715 + 0.652586i 0.773684π0.773684\pi
108108 235203. 1.94037
109109 −40851.4 −0.329337 −0.164669 0.986349i 0.552655π-0.552655\pi
−0.164669 + 0.986349i 0.552655π0.552655\pi
110110 0 0
111111 −239687. −1.84644
112112 3731.36 0.0281075
113113 −227150. −1.67347 −0.836733 0.547612i 0.815537π-0.815537\pi
−0.836733 + 0.547612i 0.815537π0.815537\pi
114114 −128489. −0.925984
115115 0 0
116116 35808.8 0.247084
117117 75069.6 0.506990
118118 −365561. −2.41688
119119 −7560.32 −0.0489410
120120 0 0
121121 189404. 1.17605
122122 363441. 2.21072
123123 399092. 2.37854
124124 −201164. −1.17489
125125 0 0
126126 −31372.0 −0.176042
127127 −38400.2 −0.211263 −0.105632 0.994405i 0.533686π-0.533686\pi
−0.105632 + 0.994405i 0.533686π0.533686\pi
128128 −208249. −1.12346
129129 548601. 2.90257
130130 0 0
131131 114414. 0.582509 0.291254 0.956646i 0.405927π-0.405927\pi
0.291254 + 0.956646i 0.405927π0.405927\pi
132132 692045. 3.45700
133133 4519.54 0.0221547
134134 77140.5 0.371125
135135 0 0
136136 103261. 0.478727
137137 299097. 1.36148 0.680739 0.732526i 0.261659π-0.261659\pi
0.680739 + 0.732526i 0.261659π0.261659\pi
138138 −681433. −3.04597
139139 −148537. −0.652074 −0.326037 0.945357i 0.605713π-0.605713\pi
−0.326037 + 0.945357i 0.605713π0.605713\pi
140140 0 0
141141 524361. 2.22117
142142 −104888. −0.436522
143143 100047. 0.409132
144144 −205389. −0.825413
145145 0 0
146146 517618. 2.00968
147147 −438880. −1.67514
148148 −407736. −1.53012
149149 −295183. −1.08924 −0.544622 0.838682i 0.683327π-0.683327\pi
−0.544622 + 0.838682i 0.683327π0.683327\pi
150150 0 0
151151 −406812. −1.45195 −0.725974 0.687722i 0.758611π-0.758611\pi
−0.725974 + 0.687722i 0.758611π0.758611\pi
152152 −61729.0 −0.216711
153153 416150. 1.43722
154154 −41810.1 −0.142062
155155 0 0
156156 197563. 0.649970
157157 103767. 0.335978 0.167989 0.985789i 0.446273π-0.446273\pi
0.167989 + 0.985789i 0.446273π0.446273\pi
158158 −610824. −1.94658
159159 −516473. −1.62015
160160 0 0
161161 23969.1 0.0728765
162162 265383. 0.794485
163163 520351. 1.53401 0.767004 0.641642i 0.221747π-0.221747\pi
0.767004 + 0.641642i 0.221747π0.221747\pi
164164 678904. 1.97105
165165 0 0
166166 157158. 0.442655
167167 225112. 0.624609 0.312305 0.949982i 0.398899π-0.398899\pi
0.312305 + 0.949982i 0.398899π0.398899\pi
168168 −23316.9 −0.0637379
169169 28561.0 0.0769231
170170 0 0
171171 −248774. −0.650600
172172 933237. 2.40531
173173 −326742. −0.830023 −0.415011 0.909816i 0.636222π-0.636222\pi
−0.415011 + 0.909816i 0.636222π0.636222\pi
174174 184227. 0.461295
175175 0 0
176176 −273726. −0.666093
177177 −1.09497e6 −2.62706
178178 −966479. −2.28635
179179 312278. 0.728465 0.364232 0.931308i 0.381331π-0.381331\pi
0.364232 + 0.931308i 0.381331π0.381331\pi
180180 0 0
181181 −34110.0 −0.0773901 −0.0386951 0.999251i 0.512320π-0.512320\pi
−0.0386951 + 0.999251i 0.512320π0.512320\pi
182182 −11935.8 −0.0267100
183183 1.08862e6 2.40298
184184 −327376. −0.712857
185185 0 0
186186 −1.03493e6 −2.19346
187187 554612. 1.15981
188188 892002. 1.84065
189189 −42563.2 −0.0866721
190190 0 0
191191 −232313. −0.460776 −0.230388 0.973099i 0.574000π-0.574000\pi
−0.230388 + 0.973099i 0.574000π0.574000\pi
192192 −1.34972e6 −2.64235
193193 493813. 0.954265 0.477132 0.878831i 0.341676π-0.341676\pi
0.477132 + 0.878831i 0.341676π0.341676\pi
194194 −1.19357e6 −2.27689
195195 0 0
196196 −746588. −1.38816
197197 172838. 0.317302 0.158651 0.987335i 0.449286π-0.449286\pi
0.158651 + 0.987335i 0.449286π0.449286\pi
198198 2.30139e6 4.17185
199199 382327. 0.684388 0.342194 0.939629i 0.388830π-0.388830\pi
0.342194 + 0.939629i 0.388830π0.388830\pi
200200 0 0
201201 231061. 0.403400
202202 −572815. −0.987725
203203 −6480.09 −0.0110367
204204 1.09519e6 1.84253
205205 0 0
206206 890679. 1.46236
207207 −1.31936e6 −2.14011
208208 −78142.5 −0.125236
209209 −331546. −0.525022
210210 0 0
211211 789495. 1.22080 0.610398 0.792095i 0.291009π-0.291009\pi
0.610398 + 0.792095i 0.291009π0.291009\pi
212212 −878584. −1.34259
213213 −314174. −0.474484
214214 −1.57070e6 −2.34454
215215 0 0
216216 581338. 0.847802
217217 36403.4 0.0524798
218218 −357524. −0.509523
219219 1.55043e6 2.18445
220220 0 0
221221 158329. 0.218062
222222 −2.09769e6 −2.85666
223223 −898082. −1.20936 −0.604678 0.796470i 0.706698π-0.706698\pi
−0.604678 + 0.796470i 0.706698π0.706698\pi
224224 61119.1 0.0813873
225225 0 0
226226 −1.98797e6 −2.58904
227227 426009. 0.548725 0.274362 0.961626i 0.411533π-0.411533\pi
0.274362 + 0.961626i 0.411533π0.411533\pi
228228 −654704. −0.834080
229229 −221579. −0.279216 −0.139608 0.990207i 0.544584π-0.544584\pi
−0.139608 + 0.990207i 0.544584π0.544584\pi
230230 0 0
231231 −125235. −0.154417
232232 88506.6 0.107958
233233 1.48218e6 1.78859 0.894296 0.447475i 0.147677π-0.147677\pi
0.894296 + 0.447475i 0.147677π0.147677\pi
234234 656994. 0.784372
235235 0 0
236236 −1.86268e6 −2.17700
237237 −1.82961e6 −2.11587
238238 −66166.4 −0.0757174
239239 −698853. −0.791391 −0.395695 0.918382i 0.629496π-0.629496\pi
−0.395695 + 0.918382i 0.629496π0.629496\pi
240240 0 0
241241 −367154. −0.407198 −0.203599 0.979054i 0.565264π-0.565264\pi
−0.203599 + 0.979054i 0.565264π0.565264\pi
242242 1.65763e6 1.81949
243243 −486752. −0.528800
244244 1.85188e6 1.99131
245245 0 0
246246 3.49277e6 3.67987
247247 −94648.5 −0.0987123
248248 −497206. −0.513342
249249 470738. 0.481151
250250 0 0
251251 469145. 0.470027 0.235013 0.971992i 0.424487π-0.424487\pi
0.235013 + 0.971992i 0.424487π0.424487\pi
252252 −159853. −0.158570
253253 −1.75833e6 −1.72703
254254 −336071. −0.326849
255255 0 0
256256 −174957. −0.166852
257257 1.28756e6 1.21600 0.607999 0.793938i 0.291972π-0.291972\pi
0.607999 + 0.793938i 0.291972π0.291972\pi
258258 4.80124e6 4.49060
259259 73785.3 0.0683472
260260 0 0
261261 356690. 0.324108
262262 1.00133e6 0.901208
263263 470260. 0.419227 0.209613 0.977784i 0.432779π-0.432779\pi
0.209613 + 0.977784i 0.432779π0.432779\pi
264264 1.71049e6 1.51046
265265 0 0
266266 39554.1 0.0342758
267267 −2.89492e6 −2.48518
268268 393062. 0.334291
269269 −1.19043e6 −1.00305 −0.501525 0.865143i 0.667227π-0.667227\pi
−0.501525 + 0.865143i 0.667227π0.667227\pi
270270 0 0
271271 205159. 0.169694 0.0848472 0.996394i 0.472960π-0.472960\pi
0.0848472 + 0.996394i 0.472960π0.472960\pi
272272 −433185. −0.355019
273273 −35751.6 −0.0290328
274274 2.61764e6 2.10636
275275 0 0
276276 −3.47218e6 −2.74366
277277 −1.35799e6 −1.06340 −0.531702 0.846932i 0.678447π-0.678447\pi
−0.531702 + 0.846932i 0.678447π0.678447\pi
278278 −1.29996e6 −1.00883
279279 −2.00379e6 −1.54114
280280 0 0
281281 1.13136e6 0.854745 0.427372 0.904076i 0.359439π-0.359439\pi
0.427372 + 0.904076i 0.359439π0.359439\pi
282282 4.58910e6 3.43641
283283 896684. 0.665539 0.332769 0.943008i 0.392017π-0.392017\pi
0.332769 + 0.943008i 0.392017π0.392017\pi
284284 −534449. −0.393197
285285 0 0
286286 875589. 0.632973
287287 −122857. −0.0880429
288288 −3.36424e6 −2.39004
289289 −542157. −0.381839
290290 0 0
291291 −3.57512e6 −2.47490
292292 2.63747e6 1.81022
293293 732944. 0.498772 0.249386 0.968404i 0.419771π-0.419771\pi
0.249386 + 0.968404i 0.419771π0.419771\pi
294294 −3.84099e6 −2.59164
295295 0 0
296296 −1.00778e6 −0.668552
297297 3.12236e6 2.05396
298298 −2.58338e6 −1.68519
299299 −501963. −0.324708
300300 0 0
301301 −168882. −0.107440
302302 −3.56033e6 −2.24633
303303 −1.71577e6 −1.07362
304304 258957. 0.160710
305305 0 0
306306 3.64207e6 2.22354
307307 1.12669e6 0.682275 0.341138 0.940013i 0.389188π-0.389188\pi
0.341138 + 0.940013i 0.389188π0.389188\pi
308308 −213040. −0.127963
309309 2.66787e6 1.58953
310310 0 0
311311 −1.97792e6 −1.15960 −0.579799 0.814760i 0.696869π-0.696869\pi
−0.579799 + 0.814760i 0.696869π0.696869\pi
312312 488304. 0.283990
313313 −2.48485e6 −1.43364 −0.716818 0.697261i 0.754402π-0.754402\pi
−0.716818 + 0.697261i 0.754402π0.754402\pi
314314 908148. 0.519796
315315 0 0
316316 −3.11240e6 −1.75339
317317 −953844. −0.533125 −0.266563 0.963818i 0.585888π-0.585888\pi
−0.266563 + 0.963818i 0.585888π0.585888\pi
318318 −4.52007e6 −2.50656
319319 475368. 0.261549
320320 0 0
321321 −4.70475e6 −2.54844
322322 209773. 0.112748
323323 −524687. −0.279830
324324 1.35224e6 0.715633
325325 0 0
326326 4.55401e6 2.37329
327327 −1.07090e6 −0.553833
328328 1.67801e6 0.861210
329329 −161420. −0.0822179
330330 0 0
331331 21507.4 0.0107899 0.00539496 0.999985i 0.498283π-0.498283\pi
0.00539496 + 0.999985i 0.498283π0.498283\pi
332332 800783. 0.398722
333333 −4.06144e6 −2.00710
334334 1.97014e6 0.966342
335335 0 0
336336 97815.8 0.0472673
337337 3.16342e6 1.51734 0.758668 0.651477i 0.225850π-0.225850\pi
0.758668 + 0.651477i 0.225850π0.225850\pi
338338 249960. 0.119009
339339 −5.95462e6 −2.81420
340340 0 0
341341 −2.67049e6 −1.24367
342342 −2.17722e6 −1.00655
343343 270736. 0.124254
344344 2.30663e6 1.05095
345345 0 0
346346 −2.85958e6 −1.28414
347347 2.20243e6 0.981927 0.490963 0.871180i 0.336645π-0.336645\pi
0.490963 + 0.871180i 0.336645π0.336645\pi
348348 938710. 0.415512
349349 4.44911e6 1.95528 0.977642 0.210276i 0.0674361π-0.0674361\pi
0.977642 + 0.210276i 0.0674361π0.0674361\pi
350350 0 0
351351 891360. 0.386176
352352 −4.48359e6 −1.92872
353353 23142.7 0.00988501 0.00494251 0.999988i 0.498427π-0.498427\pi
0.00494251 + 0.999988i 0.498427π0.498427\pi
354354 −9.58298e6 −4.06436
355355 0 0
356356 −4.92461e6 −2.05943
357357 −198190. −0.0823021
358358 2.73299e6 1.12702
359359 852005. 0.348904 0.174452 0.984666i 0.444185π-0.444185\pi
0.174452 + 0.984666i 0.444185π0.444185\pi
360360 0 0
361361 −2.16244e6 −0.873326
362362 −298524. −0.119731
363363 4.96513e6 1.97772
364364 −60817.8 −0.0240590
365365 0 0
366366 9.52741e6 3.71768
367367 2.60560e6 1.00982 0.504908 0.863173i 0.331526π-0.331526\pi
0.504908 + 0.863173i 0.331526π0.331526\pi
368368 1.37336e6 0.528647
369369 6.76253e6 2.58549
370370 0 0
371371 158992. 0.0599707
372372 −5.27342e6 −1.97576
373373 2.33488e6 0.868947 0.434473 0.900685i 0.356935π-0.356935\pi
0.434473 + 0.900685i 0.356935π0.356935\pi
374374 4.85385e6 1.79435
375375 0 0
376376 2.20471e6 0.804232
377377 135706. 0.0491753
378378 −372504. −0.134092
379379 −2.67829e6 −0.957767 −0.478883 0.877878i 0.658958π-0.658958\pi
−0.478883 + 0.877878i 0.658958π0.658958\pi
380380 0 0
381381 −1.00664e6 −0.355273
382382 −2.03316e6 −0.712874
383383 2.37423e6 0.827038 0.413519 0.910496i 0.364300π-0.364300\pi
0.413519 + 0.910496i 0.364300π0.364300\pi
384384 −5.45915e6 −1.88928
385385 0 0
386386 4.32175e6 1.47636
387387 9.29592e6 3.15511
388388 −6.08171e6 −2.05091
389389 1.87573e6 0.628487 0.314244 0.949342i 0.398249π-0.398249\pi
0.314244 + 0.949342i 0.398249π0.398249\pi
390390 0 0
391391 −2.78264e6 −0.920483
392392 −1.84530e6 −0.606528
393393 2.99931e6 0.979582
394394 1.51264e6 0.490902
395395 0 0
396396 1.17266e7 3.75779
397397 4.12523e6 1.31363 0.656814 0.754053i 0.271904π-0.271904\pi
0.656814 + 0.754053i 0.271904π0.271904\pi
398398 3.34605e6 1.05883
399399 118477. 0.0372566
400400 0 0
401401 4.32492e6 1.34313 0.671564 0.740947i 0.265623π-0.265623\pi
0.671564 + 0.740947i 0.265623π0.265623\pi
402402 2.02220e6 0.624106
403403 −762361. −0.233829
404404 −2.91873e6 −0.889693
405405 0 0
406406 −56712.5 −0.0170751
407407 −5.41276e6 −1.61969
408408 2.70693e6 0.805056
409409 3.45008e6 1.01981 0.509907 0.860229i 0.329680π-0.329680\pi
0.509907 + 0.860229i 0.329680π0.329680\pi
410410 0 0
411411 7.84067e6 2.28954
412412 4.53837e6 1.31722
413413 337077. 0.0972421
414414 −1.15467e7 −3.31100
415415 0 0
416416 −1.27996e6 −0.362629
417417 −3.89381e6 −1.09657
418418 −2.90162e6 −0.812269
419419 −1.56769e6 −0.436238 −0.218119 0.975922i 0.569992π-0.569992\pi
−0.218119 + 0.975922i 0.569992π0.569992\pi
420420 0 0
421421 6.01650e6 1.65439 0.827196 0.561913i 0.189935π-0.189935\pi
0.827196 + 0.561913i 0.189935π0.189935\pi
422422 6.90950e6 1.88871
423423 8.88518e6 2.41443
424424 −2.17155e6 −0.586616
425425 0 0
426426 −2.74959e6 −0.734081
427427 −335122. −0.0889475
428428 −8.00335e6 −2.11185
429429 2.62267e6 0.688020
430430 0 0
431431 −4.41465e6 −1.14473 −0.572365 0.819999i 0.693974π-0.693974\pi
−0.572365 + 0.819999i 0.693974π0.693974\pi
432432 −2.43875e6 −0.628720
433433 −264873. −0.0678919 −0.0339460 0.999424i 0.510807π-0.510807\pi
−0.0339460 + 0.999424i 0.510807π0.510807\pi
434434 318595. 0.0811923
435435 0 0
436436 −1.82173e6 −0.458953
437437 1.66346e6 0.416685
438438 1.35691e7 3.37960
439439 2.43360e6 0.602682 0.301341 0.953516i 0.402566π-0.402566\pi
0.301341 + 0.953516i 0.402566π0.402566\pi
440440 0 0
441441 −7.43672e6 −1.82090
442442 1.38566e6 0.337366
443443 −6.67033e6 −1.61487 −0.807436 0.589955i 0.799145π-0.799145\pi
−0.807436 + 0.589955i 0.799145π0.799145\pi
444444 −1.06886e7 −2.57314
445445 0 0
446446 −7.85984e6 −1.87101
447447 −7.73806e6 −1.83174
448448 415499. 0.0978080
449449 1.86259e6 0.436014 0.218007 0.975947i 0.430044π-0.430044\pi
0.218007 + 0.975947i 0.430044π0.430044\pi
450450 0 0
451451 9.01255e6 2.08644
452452 −1.01295e7 −2.33208
453453 −1.06644e7 −2.44168
454454 3.72835e6 0.848940
455455 0 0
456456 −1.61819e6 −0.364433
457457 4.66486e6 1.04484 0.522418 0.852690i 0.325030π-0.325030\pi
0.522418 + 0.852690i 0.325030π0.325030\pi
458458 −1.93922e6 −0.431979
459459 4.94128e6 1.09473
460460 0 0
461461 5.59911e6 1.22706 0.613531 0.789670i 0.289748π-0.289748\pi
0.613531 + 0.789670i 0.289748π0.289748\pi
462462 −1.09603e6 −0.238901
463463 6.71396e6 1.45555 0.727773 0.685818i 0.240555π-0.240555\pi
0.727773 + 0.685818i 0.240555π0.240555\pi
464464 −371291. −0.0800606
465465 0 0
466466 1.29718e7 2.76716
467467 −2.57048e6 −0.545409 −0.272704 0.962098i 0.587918π-0.587918\pi
−0.272704 + 0.962098i 0.587918π0.587918\pi
468468 3.34766e6 0.706523
469469 −71129.9 −0.0149321
470470 0 0
471471 2.72020e6 0.565000
472472 −4.60388e6 −0.951194
473473 1.23889e7 2.54612
474474 −1.60124e7 −3.27349
475475 0 0
476476 −337145. −0.0682024
477477 −8.75153e6 −1.76112
478478 −6.11622e6 −1.22437
479479 1.24698e6 0.248325 0.124163 0.992262i 0.460376π-0.460376\pi
0.124163 + 0.992262i 0.460376π0.460376\pi
480480 0 0
481481 −1.54522e6 −0.304528
482482 −3.21326e6 −0.629981
483483 628338. 0.122553
484484 8.44630e6 1.63890
485485 0 0
486486 −4.25995e6 −0.818115
487487 8.90535e6 1.70149 0.850743 0.525582i 0.176152π-0.176152\pi
0.850743 + 0.525582i 0.176152π0.176152\pi
488488 4.57718e6 0.870059
489489 1.36407e7 2.57968
490490 0 0
491491 −4.97397e6 −0.931107 −0.465553 0.885020i 0.654145π-0.654145\pi
−0.465553 + 0.885020i 0.654145π0.654145\pi
492492 1.77971e7 3.31464
493493 752292. 0.139402
494494 −828345. −0.152719
495495 0 0
496496 2.08581e6 0.380689
497497 96715.7 0.0175633
498498 4.11981e6 0.744395
499499 −3.44325e6 −0.619038 −0.309519 0.950893i 0.600168π-0.600168\pi
−0.309519 + 0.950893i 0.600168π0.600168\pi
500500 0 0
501501 5.90121e6 1.05038
502502 4.10586e6 0.727185
503503 3.02775e6 0.533580 0.266790 0.963755i 0.414037π-0.414037\pi
0.266790 + 0.963755i 0.414037π0.414037\pi
504504 −395100. −0.0692836
505505 0 0
506506 −1.53886e7 −2.67191
507507 748712. 0.129358
508508 −1.71242e6 −0.294409
509509 4.45477e6 0.762134 0.381067 0.924547i 0.375557π-0.375557\pi
0.381067 + 0.924547i 0.375557π0.375557\pi
510510 0 0
511511 −477286. −0.0808587
512512 5.13279e6 0.865324
513513 −2.95388e6 −0.495564
514514 1.12684e7 1.88129
515515 0 0
516516 2.44643e7 4.04491
517517 1.18415e7 1.94840
518518 645754. 0.105741
519519 −8.56538e6 −1.39582
520520 0 0
521521 −3.88354e6 −0.626806 −0.313403 0.949620i 0.601469π-0.601469\pi
−0.313403 + 0.949620i 0.601469π0.601469\pi
522522 3.12168e6 0.501432
523523 −1.09959e7 −1.75783 −0.878913 0.476983i 0.841730π-0.841730\pi
−0.878913 + 0.476983i 0.841730π0.841730\pi
524524 5.10220e6 0.811763
525525 0 0
526526 4.11563e6 0.648592
527527 −4.22617e6 −0.662858
528528 −7.17559e6 −1.12014
529529 2.38570e6 0.370661
530530 0 0
531531 −1.85541e7 −2.85564
532532 201545. 0.0308739
533533 2.57287e6 0.392284
534534 −2.53357e7 −3.84486
535535 0 0
536536 971510. 0.146061
537537 8.18620e6 1.22503
538538 −1.04184e7 −1.55183
539539 −9.91107e6 −1.46943
540540 0 0
541541 2.61308e6 0.383848 0.191924 0.981410i 0.438527π-0.438527\pi
0.191924 + 0.981410i 0.438527π0.438527\pi
542542 1.79551e6 0.262537
543543 −894176. −0.130144
544544 −7.09549e6 −1.02798
545545 0 0
546546 −312891. −0.0449170
547547 −3.49357e6 −0.499230 −0.249615 0.968345i 0.580304π-0.580304\pi
−0.249615 + 0.968345i 0.580304π0.580304\pi
548548 1.33379e7 1.89731
549549 1.84465e7 2.61206
550550 0 0
551551 −449718. −0.0631047
552552 −8.58199e6 −1.19878
553553 563230. 0.0783200
554554 −1.18849e7 −1.64521
555555 0 0
556556 −6.62385e6 −0.908706
557557 7.52693e6 1.02797 0.513984 0.857800i 0.328169π-0.328169\pi
0.513984 + 0.857800i 0.328169π0.328169\pi
558558 −1.75367e7 −2.38431
559559 3.53673e6 0.478710
560560 0 0
561561 1.45389e7 1.95040
562562 9.90147e6 1.32239
563563 8.11431e6 1.07890 0.539450 0.842018i 0.318632π-0.318632\pi
0.539450 + 0.842018i 0.318632π0.318632\pi
564564 2.33834e7 3.09534
565565 0 0
566566 7.84760e6 1.02966
567567 −244705. −0.0319658
568568 −1.32097e6 −0.171799
569569 3.42992e6 0.444123 0.222061 0.975033i 0.428721π-0.428721\pi
0.222061 + 0.975033i 0.428721π0.428721\pi
570570 0 0
571571 1.17647e7 1.51005 0.755026 0.655695i 0.227624π-0.227624\pi
0.755026 + 0.655695i 0.227624π0.227624\pi
572572 4.46149e6 0.570151
573573 −6.08997e6 −0.774869
574574 −1.07522e6 −0.136212
575575 0 0
576576 −2.28707e7 −2.87226
577577 −8.73061e6 −1.09170 −0.545852 0.837882i 0.683794π-0.683794\pi
−0.545852 + 0.837882i 0.683794π0.683794\pi
578578 −4.74485e6 −0.590749
579579 1.29450e7 1.60475
580580 0 0
581581 −144912. −0.0178101
582582 −3.12887e7 −3.82895
583583 −1.16633e7 −1.42119
584584 6.51889e6 0.790936
585585 0 0
586586 6.41458e6 0.771657
587587 −6.33682e6 −0.759060 −0.379530 0.925179i 0.623914π-0.623914\pi
−0.379530 + 0.925179i 0.623914π0.623914\pi
588588 −1.95714e7 −2.33442
589589 2.52639e6 0.300063
590590 0 0
591591 4.53085e6 0.533593
592592 4.22769e6 0.495791
593593 −1.23132e6 −0.143792 −0.0718960 0.997412i 0.522905π-0.522905\pi
−0.0718960 + 0.997412i 0.522905π0.522905\pi
594594 2.73263e7 3.17771
595595 0 0
596596 −1.31634e7 −1.51793
597597 1.00225e7 1.15091
598598 −4.39308e6 −0.502361
599599 −6.75482e6 −0.769213 −0.384607 0.923081i 0.625663π-0.625663\pi
−0.384607 + 0.923081i 0.625663π0.625663\pi
600600 0 0
601601 −20587.5 −0.00232497 −0.00116248 0.999999i 0.500370π-0.500370\pi
−0.00116248 + 0.999999i 0.500370π0.500370\pi
602602 −1.47802e6 −0.166222
603603 3.91527e6 0.438499
604604 −1.81414e7 −2.02338
605605 0 0
606606 −1.50160e7 −1.66102
607607 −6.97910e6 −0.768826 −0.384413 0.923161i 0.625596π-0.625596\pi
−0.384413 + 0.923161i 0.625596π0.625596\pi
608608 4.24167e6 0.465348
609609 −169872. −0.0185600
610610 0 0
611611 3.38046e6 0.366330
612612 1.85578e7 2.00285
613613 3.83537e6 0.412246 0.206123 0.978526i 0.433915π-0.433915\pi
0.206123 + 0.978526i 0.433915π0.433915\pi
614614 9.86059e6 1.05556
615615 0 0
616616 −526558. −0.0559106
617617 −1.16850e7 −1.23571 −0.617853 0.786293i 0.711997π-0.711997\pi
−0.617853 + 0.786293i 0.711997π0.711997\pi
618618 2.33487e7 2.45918
619619 −8.33735e6 −0.874583 −0.437292 0.899320i 0.644062π-0.644062\pi
−0.437292 + 0.899320i 0.644062π0.644062\pi
620620 0 0
621621 −1.56658e7 −1.63013
622622 −1.73103e7 −1.79403
623623 891174. 0.0919903
624624 −2.04846e6 −0.210604
625625 0 0
626626 −2.17469e7 −2.21800
627627 −8.69129e6 −0.882908
628628 4.62739e6 0.468206
629629 −8.56595e6 −0.863274
630630 0 0
631631 −1.66983e7 −1.66955 −0.834775 0.550591i 0.814402π-0.814402\pi
−0.834775 + 0.550591i 0.814402π0.814402\pi
632632 −7.69273e6 −0.766104
633633 2.06962e7 2.05296
634634 −8.34785e6 −0.824805
635635 0 0
636636 −2.30316e7 −2.25778
637637 −2.82938e6 −0.276275
638638 4.16033e6 0.404646
639639 −5.32362e6 −0.515768
640640 0 0
641641 −1.69010e7 −1.62468 −0.812340 0.583184i 0.801807π-0.801807\pi
−0.812340 + 0.583184i 0.801807π0.801807\pi
642642 −4.11750e7 −3.94272
643643 1.01899e7 0.971947 0.485974 0.873974i 0.338465π-0.338465\pi
0.485974 + 0.873974i 0.338465π0.338465\pi
644644 1.06888e6 0.101558
645645 0 0
646646 −4.59195e6 −0.432928
647647 −6.44562e6 −0.605347 −0.302673 0.953094i 0.597879π-0.597879\pi
−0.302673 + 0.953094i 0.597879π0.597879\pi
648648 3.34224e6 0.312680
649649 −2.47274e7 −2.30445
650650 0 0
651651 954295. 0.0882531
652652 2.32046e7 2.13774
653653 −1.82109e7 −1.67128 −0.835640 0.549277i 0.814903π-0.814903\pi
−0.835640 + 0.549277i 0.814903π0.814903\pi
654654 −9.37229e6 −0.856844
655655 0 0
656656 −7.03934e6 −0.638664
657657 2.62717e7 2.37452
658658 −1.41271e6 −0.127201
659659 4.70706e6 0.422217 0.211109 0.977463i 0.432293π-0.432293\pi
0.211109 + 0.977463i 0.432293π0.432293\pi
660660 0 0
661661 −5.15844e6 −0.459213 −0.229607 0.973284i 0.573744π-0.573744\pi
−0.229607 + 0.973284i 0.573744π0.573744\pi
662662 188229. 0.0166932
663663 4.15050e6 0.366705
664664 1.97925e6 0.174213
665665 0 0
666666 −3.55449e7 −3.10522
667667 −2.38505e6 −0.207579
668668 1.00387e7 0.870433
669669 −2.35428e7 −2.03372
670670 0 0
671671 2.45840e7 2.10788
672672 1.60221e6 0.136866
673673 −8.41092e6 −0.715823 −0.357911 0.933756i 0.616511π-0.616511\pi
−0.357911 + 0.933756i 0.616511π0.616511\pi
674674 2.76856e7 2.34749
675675 0 0
676676 1.27365e6 0.107197
677677 1.05108e7 0.881378 0.440689 0.897660i 0.354734π-0.354734\pi
0.440689 + 0.897660i 0.354734π0.354734\pi
678678 −5.21136e7 −4.35389
679679 1.10057e6 0.0916098
680680 0 0
681681 1.11676e7 0.922768
682682 −2.33716e7 −1.92410
683683 −1.27854e7 −1.04873 −0.524364 0.851494i 0.675697π-0.675697\pi
−0.524364 + 0.851494i 0.675697π0.675697\pi
684684 −1.10938e7 −0.906652
685685 0 0
686686 2.36942e6 0.192235
687687 −5.80858e6 −0.469546
688688 −9.67644e6 −0.779371
689689 −3.32961e6 −0.267205
690690 0 0
691691 1.46556e7 1.16764 0.583818 0.811884i 0.301558π-0.301558\pi
0.583818 + 0.811884i 0.301558π0.301558\pi
692692 −1.45708e7 −1.15669
693693 −2.12208e6 −0.167853
694694 1.92753e7 1.51915
695695 0 0
696696 2.32015e6 0.181549
697697 1.42628e7 1.11205
698698 3.89378e7 3.02505
699699 3.88546e7 3.00780
700700 0 0
701701 1.62766e7 1.25103 0.625517 0.780210i 0.284888π-0.284888\pi
0.625517 + 0.780210i 0.284888π0.284888\pi
702702 7.80101e6 0.597459
703703 5.12070e6 0.390788
704704 −3.04802e7 −2.31786
705705 0 0
706706 202540. 0.0152932
707707 528183. 0.0397407
708708 −4.88292e7 −3.66098
709709 −1.32627e7 −0.990873 −0.495436 0.868644i 0.664992π-0.664992\pi
−0.495436 + 0.868644i 0.664992π0.664992\pi
710710 0 0
711711 −3.10024e7 −2.29997
712712 −1.21719e7 −0.899823
713713 1.33986e7 0.987040
714714 −1.73452e6 −0.127331
715715 0 0
716716 1.39257e7 1.01516
717717 −1.83201e7 −1.33085
718718 7.45658e6 0.539794
719719 1.58913e7 1.14640 0.573201 0.819415i 0.305701π-0.305701\pi
0.573201 + 0.819415i 0.305701π0.305701\pi
720720 0 0
721721 −821280. −0.0588373
722722 −1.89253e7 −1.35114
723723 −9.62474e6 −0.684768
724724 −1.52110e6 −0.107848
725725 0 0
726726 4.34539e7 3.05976
727727 −1.21979e7 −0.855950 −0.427975 0.903791i 0.640773π-0.640773\pi
−0.427975 + 0.903791i 0.640773π0.640773\pi
728728 −150320. −0.0105121
729729 −2.01285e7 −1.40279
730730 0 0
731731 1.96060e7 1.35705
732732 4.85461e7 3.34870
733733 3.40342e6 0.233968 0.116984 0.993134i 0.462677π-0.462677\pi
0.116984 + 0.993134i 0.462677π0.462677\pi
734734 2.28037e7 1.56230
735735 0 0
736736 2.24954e7 1.53073
737737 5.21796e6 0.353861
738738 5.91843e7 4.00005
739739 −8.97838e6 −0.604765 −0.302383 0.953187i 0.597782π-0.597782\pi
−0.302383 + 0.953187i 0.597782π0.597782\pi
740740 0 0
741741 −2.48116e6 −0.166000
742742 1.39146e6 0.0927816
743743 −1.67949e7 −1.11611 −0.558054 0.829804i 0.688452π-0.688452\pi
−0.558054 + 0.829804i 0.688452π0.688452\pi
744744 −1.30340e7 −0.863267
745745 0 0
746746 2.04344e7 1.34436
747747 7.97656e6 0.523015
748748 2.47324e7 1.61626
749749 1.44831e6 0.0943318
750750 0 0
751751 −1.55176e7 −1.00398 −0.501989 0.864874i 0.667398π-0.667398\pi
−0.501989 + 0.864874i 0.667398π0.667398\pi
752752 −9.24888e6 −0.596410
753753 1.22984e7 0.790425
754754 1.18768e6 0.0760798
755755 0 0
756756 −1.89806e6 −0.120783
757757 1.23231e7 0.781592 0.390796 0.920477i 0.372200π-0.372200\pi
0.390796 + 0.920477i 0.372200π0.372200\pi
758758 −2.34399e7 −1.48178
759759 −4.60938e7 −2.90427
760760 0 0
761761 1.01874e7 0.637677 0.318838 0.947809i 0.396707π-0.396707\pi
0.318838 + 0.947809i 0.396707π0.396707\pi
762762 −8.80992e6 −0.549648
763763 329666. 0.0205004
764764 −1.03598e7 −0.642121
765765 0 0
766766 2.07788e7 1.27952
767767 −7.05909e6 −0.433272
768768 −4.58641e6 −0.280588
769769 5.61745e6 0.342550 0.171275 0.985223i 0.445211π-0.445211\pi
0.171275 + 0.985223i 0.445211π0.445211\pi
770770 0 0
771771 3.37526e7 2.04490
772772 2.20211e7 1.32983
773773 −1.86328e7 −1.12158 −0.560790 0.827958i 0.689502π-0.689502\pi
−0.560790 + 0.827958i 0.689502π0.689502\pi
774774 8.13561e7 4.88132
775775 0 0
776776 −1.50318e7 −0.896101
777777 1.93424e6 0.114937
778778 1.64160e7 0.972342
779779 −8.52626e6 −0.503402
780780 0 0
781781 −7.09489e6 −0.416215
782782 −2.43531e7 −1.42409
783783 4.23526e6 0.246874
784784 7.74113e6 0.449795
785785 0 0
786786 2.62494e7 1.51552
787787 2.13328e7 1.22775 0.613877 0.789402i 0.289609π-0.289609\pi
0.613877 + 0.789402i 0.289609π0.289609\pi
788788 7.70752e6 0.442180
789789 1.23276e7 0.704997
790790 0 0
791791 1.83307e6 0.104169
792792 2.89838e7 1.64189
793793 7.01815e6 0.396314
794794 3.61032e7 2.03233
795795 0 0
796796 1.70495e7 0.953738
797797 −7.53097e6 −0.419957 −0.209979 0.977706i 0.567339π-0.567339\pi
−0.209979 + 0.977706i 0.567339π0.567339\pi
798798 1.03689e6 0.0576402
799799 1.87397e7 1.03847
800800 0 0
801801 −4.90538e7 −2.70141
802802 3.78509e7 2.07797
803803 3.50129e7 1.91619
804804 1.03039e7 0.562163
805805 0 0
806806 −6.67203e6 −0.361760
807807 −3.12064e7 −1.68679
808808 −7.21405e6 −0.388732
809809 2.98814e7 1.60520 0.802601 0.596516i 0.203449π-0.203449\pi
0.802601 + 0.596516i 0.203449π0.203449\pi
810810 0 0
811811 −7.90498e6 −0.422035 −0.211018 0.977482i 0.567678π-0.567678\pi
−0.211018 + 0.977482i 0.567678π0.567678\pi
812812 −288973. −0.0153804
813813 5.37814e6 0.285368
814814 −4.73714e7 −2.50585
815815 0 0
816816 −1.13557e7 −0.597020
817817 −1.17204e7 −0.614309
818818 3.01944e7 1.57777
819819 −605803. −0.0315589
820820 0 0
821821 −1.45139e7 −0.751494 −0.375747 0.926722i 0.622614π-0.622614\pi
−0.375747 + 0.926722i 0.622614π0.622614\pi
822822 6.86200e7 3.54218
823823 6.15126e6 0.316566 0.158283 0.987394i 0.449404π-0.449404\pi
0.158283 + 0.987394i 0.449404π0.449404\pi
824824 1.12172e7 0.575530
825825 0 0
826826 2.95003e6 0.150445
827827 3.97991e6 0.202353 0.101176 0.994869i 0.467739π-0.467739\pi
0.101176 + 0.994869i 0.467739π0.467739\pi
828828 −5.88354e7 −2.98238
829829 4.29025e6 0.216819 0.108409 0.994106i 0.465424π-0.465424\pi
0.108409 + 0.994106i 0.465424π0.465424\pi
830830 0 0
831831 −3.55991e7 −1.78828
832832 −8.70139e6 −0.435793
833833 −1.56847e7 −0.783185
834834 −3.40779e7 −1.69651
835835 0 0
836836 −1.47850e7 −0.731652
837837 −2.37925e7 −1.17389
838838 −1.37201e7 −0.674911
839839 2.83937e7 1.39257 0.696284 0.717766i 0.254835π-0.254835\pi
0.696284 + 0.717766i 0.254835π0.254835\pi
840840 0 0
841841 −1.98663e7 −0.968563
842842 5.26552e7 2.55953
843843 2.96581e7 1.43739
844844 3.52068e7 1.70126
845845 0 0
846846 7.77613e7 3.73541
847847 −1.52847e6 −0.0732063
848848 9.10976e6 0.435028
849849 2.35061e7 1.11921
850850 0 0
851851 2.71573e7 1.28547
852852 −1.40103e7 −0.661224
853853 1.61127e7 0.758222 0.379111 0.925351i 0.376230π-0.376230\pi
0.379111 + 0.925351i 0.376230π0.376230\pi
854854 −2.93292e6 −0.137612
855855 0 0
856856 −1.97814e7 −0.922726
857857 −2.56599e7 −1.19344 −0.596722 0.802448i 0.703531π-0.703531\pi
−0.596722 + 0.802448i 0.703531π0.703531\pi
858858 2.29531e7 1.06445
859859 −1.56669e7 −0.724439 −0.362219 0.932093i 0.617981π-0.617981\pi
−0.362219 + 0.932093i 0.617981π0.617981\pi
860860 0 0
861861 −3.22062e6 −0.148058
862862 −3.86362e7 −1.77103
863863 2.50939e7 1.14694 0.573471 0.819226i 0.305597π-0.305597\pi
0.573471 + 0.819226i 0.305597π0.305597\pi
864864 −3.99463e7 −1.82050
865865 0 0
866866 −2.31812e6 −0.105037
867867 −1.42124e7 −0.642124
868868 1.62337e6 0.0731339
869869 −4.13176e7 −1.85603
870870 0 0
871871 1.48961e6 0.0665313
872872 −4.50266e6 −0.200530
873873 −6.05796e7 −2.69024
874874 1.45582e7 0.644660
875875 0 0
876876 6.91400e7 3.04417
877877 −9.38359e6 −0.411974 −0.205987 0.978555i 0.566040π-0.566040\pi
−0.205987 + 0.978555i 0.566040π0.566040\pi
878878 2.12984e7 0.932419
879879 1.92137e7 0.838764
880880 0 0
881881 2.07853e7 0.902227 0.451114 0.892466i 0.351027π-0.351027\pi
0.451114 + 0.892466i 0.351027π0.351027\pi
882882 −6.50847e7 −2.81713
883883 2.64517e6 0.114170 0.0570850 0.998369i 0.481819π-0.481819\pi
0.0570850 + 0.998369i 0.481819π0.481819\pi
884884 7.06052e6 0.303883
885885 0 0
886886 −5.83774e7 −2.49839
887887 1.19650e7 0.510628 0.255314 0.966858i 0.417821π-0.417821\pi
0.255314 + 0.966858i 0.417821π0.417821\pi
888888 −2.64184e7 −1.12428
889889 309885. 0.0131506
890890 0 0
891891 1.79512e7 0.757527
892892 −4.00491e7 −1.68531
893893 −1.12025e7 −0.470097
894894 −6.77220e7 −2.83391
895895 0 0
896896 1.68055e6 0.0699329
897897 −1.31587e7 −0.546049
898898 1.63010e7 0.674563
899899 −3.62233e6 −0.149482
900900 0 0
901901 −1.84578e7 −0.757474
902902 7.88761e7 3.22797
903903 −4.42714e6 −0.180678
904904 −2.50366e7 −1.01895
905905 0 0
906906 −9.33323e7 −3.77756
907907 −9.86913e6 −0.398346 −0.199173 0.979964i 0.563826π-0.563826\pi
−0.199173 + 0.979964i 0.563826π0.563826\pi
908908 1.89975e7 0.764683
909909 −2.90733e7 −1.16704
910910 0 0
911911 1.49818e7 0.598092 0.299046 0.954239i 0.403332π-0.403332\pi
0.299046 + 0.954239i 0.403332π0.403332\pi
912912 6.78842e6 0.270260
913913 1.06305e7 0.422063
914914 4.08259e7 1.61648
915915 0 0
916916 −9.88111e6 −0.389105
917917 −923311. −0.0362598
918918 4.32451e7 1.69368
919919 −3.28227e7 −1.28199 −0.640997 0.767543i 0.721479π-0.721479\pi
−0.640997 + 0.767543i 0.721479π0.721479\pi
920920 0 0
921921 2.95357e7 1.14735
922922 4.90023e7 1.89841
923923 −2.02543e6 −0.0782550
924924 −5.58472e6 −0.215190
925925 0 0
926926 5.87592e7 2.25190
927927 4.52065e7 1.72783
928928 −6.08167e6 −0.231821
929929 2.17184e7 0.825635 0.412818 0.910814i 0.364545π-0.364545\pi
0.412818 + 0.910814i 0.364545π0.364545\pi
930930 0 0
931931 9.37629e6 0.354533
932932 6.60964e7 2.49252
933933 −5.18501e7 −1.95005
934934 −2.24963e7 −0.843810
935935 0 0
936936 8.27421e6 0.308700
937937 2.19377e7 0.816286 0.408143 0.912918i 0.366176π-0.366176\pi
0.408143 + 0.912918i 0.366176π0.366176\pi
938938 −622515. −0.0231016
939939 −6.51390e7 −2.41089
940940 0 0
941941 −3.70200e7 −1.36289 −0.681447 0.731867i 0.738649π-0.738649\pi
−0.681447 + 0.731867i 0.738649π0.738649\pi
942942 2.38066e7 0.874119
943943 −4.52185e7 −1.65591
944944 1.93136e7 0.705395
945945 0 0
946946 1.08425e8 3.93914
947947 2.28075e7 0.826422 0.413211 0.910635i 0.364407π-0.364407\pi
0.413211 + 0.910635i 0.364407π0.364407\pi
948948 −8.15899e7 −2.94860
949949 9.99535e6 0.360274
950950 0 0
951951 −2.50045e7 −0.896535
952952 −833302. −0.0297996
953953 −1.14558e7 −0.408595 −0.204298 0.978909i 0.565491π-0.565491\pi
−0.204298 + 0.978909i 0.565491π0.565491\pi
954954 −7.65917e7 −2.72465
955955 0 0
956956 −3.11647e7 −1.10285
957957 1.24615e7 0.439836
958958 1.09133e7 0.384188
959959 −2.41368e6 −0.0847487
960960 0 0
961961 −8.27991e6 −0.289213
962962 −1.35234e7 −0.471139
963963 −7.97210e7 −2.77017
964964 −1.63729e7 −0.567456
965965 0 0
966966 5.49909e6 0.189604
967967 −2.44915e7 −0.842265 −0.421132 0.906999i 0.638367π-0.638367\pi
−0.421132 + 0.906999i 0.638367π0.638367\pi
968968 2.08762e7 0.716084
969969 −1.37544e7 −0.470578
970970 0 0
971971 −1.10404e6 −0.0375783 −0.0187891 0.999823i 0.505981π-0.505981\pi
−0.0187891 + 0.999823i 0.505981π0.505981\pi
972972 −2.17062e7 −0.736917
973973 1.19867e6 0.0405900
974974 7.79378e7 2.63239
975975 0 0
976976 −1.92016e7 −0.645226
977977 2.44544e7 0.819636 0.409818 0.912167i 0.365592π-0.365592\pi
0.409818 + 0.912167i 0.365592π0.365592\pi
978978 1.19381e8 3.99106
979979 −6.53749e7 −2.17999
980980 0 0
981981 −1.81462e7 −0.602022
982982 −4.35312e7 −1.44053
983983 −7.78582e6 −0.256993 −0.128496 0.991710i 0.541015π-0.541015\pi
−0.128496 + 0.991710i 0.541015π0.541015\pi
984984 4.39881e7 1.44826
985985 0 0
986986 6.58391e6 0.215671
987987 −4.23153e6 −0.138263
988988 −4.22076e6 −0.137562
989989 −6.21584e7 −2.02073
990990 0 0
991991 7.12590e6 0.230492 0.115246 0.993337i 0.463234π-0.463234\pi
0.115246 + 0.993337i 0.463234π0.463234\pi
992992 3.41652e7 1.10231
993993 563805. 0.0181450
994994 846436. 0.0271724
995995 0 0
996996 2.09921e7 0.670514
997997 −4.38741e7 −1.39788 −0.698940 0.715180i 0.746345π-0.746345\pi
−0.698940 + 0.715180i 0.746345π0.746345\pi
998998 −3.01346e7 −0.957722
999999 −4.82247e7 −1.52882
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.e.1.3 4
5.2 odd 4 325.6.b.e.274.7 8
5.3 odd 4 325.6.b.e.274.2 8
5.4 even 2 65.6.a.c.1.2 4
15.14 odd 2 585.6.a.g.1.3 4
20.19 odd 2 1040.6.a.o.1.4 4
65.64 even 2 845.6.a.f.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.6.a.c.1.2 4 5.4 even 2
325.6.a.e.1.3 4 1.1 even 1 trivial
325.6.b.e.274.2 8 5.3 odd 4
325.6.b.e.274.7 8 5.2 odd 4
585.6.a.g.1.3 4 15.14 odd 2
845.6.a.f.1.3 4 65.64 even 2
1040.6.a.o.1.4 4 20.19 odd 2