Properties

Label 637.2.a.l.1.2
Level 637637
Weight 22
Character 637.1
Self dual yes
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 55
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] = [637,2,Mod(1,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,4,0,8,2,-5,0,9,3,-5,11,5,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 55
Coefficient field: 5.5.746052.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x5x47x3+8x+2 x^{5} - x^{4} - 7x^{3} + 8x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.195661.19566 of defining polynomial
Character χ\chi == 637.1

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) == q0.195656q20.259788q31.96172q4+3.93251q5+0.0508292q6+0.775135q82.93251q90.769420q10+4.50627q11+0.509632q12+1.00000q131.02162q15+3.77178q162.28141q17+0.573764q181.78768q197.71448q200.881681q22+1.74021q230.201371q24+10.4646q250.195656q26+1.54120q27+1.65110q29+0.199886q30+5.60523q312.28824q321.17068q33+0.446372q34+5.75276q36+7.14407q37+0.349771q380.259788q39+3.04823q408.11574q41+6.81353q438.84004q4411.5321q450.340483q46+3.54543q470.979864q482.04747q50+0.592684q511.96172q52+3.28965q530.301545q54+17.7210q55+0.464419q570.323048q58+4.50627q59+2.00413q60+7.54467q611.09670q627.09585q64+3.93251q65+0.229050q6612.6653q67+4.47548q680.452087q69+9.54869q712.27309q72+1.08004q731.39778q742.71859q75+3.50693q76+0.0508292q78+0.791698q79+14.8326q80+8.39714q81+1.58789q827.14643q838.97166q851.33311q860.428937q87+3.49297q8811.2656q89+2.25633q903.41381q921.45617q930.693685q947.03008q95+0.594459q968.81353q9713.2147q99+O(q100)q-0.195656 q^{2} -0.259788 q^{3} -1.96172 q^{4} +3.93251 q^{5} +0.0508292 q^{6} +0.775135 q^{8} -2.93251 q^{9} -0.769420 q^{10} +4.50627 q^{11} +0.509632 q^{12} +1.00000 q^{13} -1.02162 q^{15} +3.77178 q^{16} -2.28141 q^{17} +0.573764 q^{18} -1.78768 q^{19} -7.71448 q^{20} -0.881681 q^{22} +1.74021 q^{23} -0.201371 q^{24} +10.4646 q^{25} -0.195656 q^{26} +1.54120 q^{27} +1.65110 q^{29} +0.199886 q^{30} +5.60523 q^{31} -2.28824 q^{32} -1.17068 q^{33} +0.446372 q^{34} +5.75276 q^{36} +7.14407 q^{37} +0.349771 q^{38} -0.259788 q^{39} +3.04823 q^{40} -8.11574 q^{41} +6.81353 q^{43} -8.84004 q^{44} -11.5321 q^{45} -0.340483 q^{46} +3.54543 q^{47} -0.979864 q^{48} -2.04747 q^{50} +0.592684 q^{51} -1.96172 q^{52} +3.28965 q^{53} -0.301545 q^{54} +17.7210 q^{55} +0.464419 q^{57} -0.323048 q^{58} +4.50627 q^{59} +2.00413 q^{60} +7.54467 q^{61} -1.09670 q^{62} -7.09585 q^{64} +3.93251 q^{65} +0.229050 q^{66} -12.6653 q^{67} +4.47548 q^{68} -0.452087 q^{69} +9.54869 q^{71} -2.27309 q^{72} +1.08004 q^{73} -1.39778 q^{74} -2.71859 q^{75} +3.50693 q^{76} +0.0508292 q^{78} +0.791698 q^{79} +14.8326 q^{80} +8.39714 q^{81} +1.58789 q^{82} -7.14643 q^{83} -8.97166 q^{85} -1.33311 q^{86} -0.428937 q^{87} +3.49297 q^{88} -11.2656 q^{89} +2.25633 q^{90} -3.41381 q^{92} -1.45617 q^{93} -0.693685 q^{94} -7.03008 q^{95} +0.594459 q^{96} -8.81353 q^{97} -13.2147 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q+4q2+8q4+2q55q6+9q8+3q95q10+11q11+5q12+5q13+10q165q17+9q18+9q19+q20+8q22+10q23+9q25+4q26++11q99+O(q100) 5 q + 4 q^{2} + 8 q^{4} + 2 q^{5} - 5 q^{6} + 9 q^{8} + 3 q^{9} - 5 q^{10} + 11 q^{11} + 5 q^{12} + 5 q^{13} + 10 q^{16} - 5 q^{17} + 9 q^{18} + 9 q^{19} + q^{20} + 8 q^{22} + 10 q^{23} + 9 q^{25} + 4 q^{26}+ \cdots + 11 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 −0.195656 −0.138350 −0.0691749 0.997605i 0.522037π-0.522037\pi
−0.0691749 + 0.997605i 0.522037π0.522037\pi
33 −0.259788 −0.149989 −0.0749945 0.997184i 0.523894π-0.523894\pi
−0.0749945 + 0.997184i 0.523894π0.523894\pi
44 −1.96172 −0.980859
55 3.93251 1.75867 0.879336 0.476202i 0.157987π-0.157987\pi
0.879336 + 0.476202i 0.157987π0.157987\pi
66 0.0508292 0.0207509
77 0 0
88 0.775135 0.274052
99 −2.93251 −0.977503
1010 −0.769420 −0.243312
1111 4.50627 1.35869 0.679346 0.733818i 0.262263π-0.262263\pi
0.679346 + 0.733818i 0.262263π0.262263\pi
1212 0.509632 0.147118
1313 1.00000 0.277350
1414 0 0
1515 −1.02162 −0.263781
1616 3.77178 0.942944
1717 −2.28141 −0.553323 −0.276661 0.960967i 0.589228π-0.589228\pi
−0.276661 + 0.960967i 0.589228π0.589228\pi
1818 0.573764 0.135237
1919 −1.78768 −0.410123 −0.205061 0.978749i 0.565739π-0.565739\pi
−0.205061 + 0.978749i 0.565739π0.565739\pi
2020 −7.71448 −1.72501
2121 0 0
2222 −0.881681 −0.187975
2323 1.74021 0.362859 0.181430 0.983404i 0.441928π-0.441928\pi
0.181430 + 0.983404i 0.441928π0.441928\pi
2424 −0.201371 −0.0411047
2525 10.4646 2.09293
2626 −0.195656 −0.0383714
2727 1.54120 0.296604
2828 0 0
2929 1.65110 0.306602 0.153301 0.988180i 0.451010π-0.451010\pi
0.153301 + 0.988180i 0.451010π0.451010\pi
3030 0.199886 0.0364941
3131 5.60523 1.00673 0.503365 0.864074i 0.332095π-0.332095\pi
0.503365 + 0.864074i 0.332095π0.332095\pi
3232 −2.28824 −0.404508
3333 −1.17068 −0.203789
3434 0.446372 0.0765522
3535 0 0
3636 5.75276 0.958793
3737 7.14407 1.17448 0.587239 0.809414i 0.300215π-0.300215\pi
0.587239 + 0.809414i 0.300215π0.300215\pi
3838 0.349771 0.0567404
3939 −0.259788 −0.0415994
4040 3.04823 0.481967
4141 −8.11574 −1.26746 −0.633732 0.773552i 0.718478π-0.718478\pi
−0.633732 + 0.773552i 0.718478π0.718478\pi
4242 0 0
4343 6.81353 1.03905 0.519527 0.854454i 0.326108π-0.326108\pi
0.519527 + 0.854454i 0.326108π0.326108\pi
4444 −8.84004 −1.33269
4545 −11.5321 −1.71911
4646 −0.340483 −0.0502015
4747 3.54543 0.517154 0.258577 0.965991i 0.416746π-0.416746\pi
0.258577 + 0.965991i 0.416746π0.416746\pi
4848 −0.979864 −0.141431
4949 0 0
5050 −2.04747 −0.289556
5151 0.592684 0.0829923
5252 −1.96172 −0.272041
5353 3.28965 0.451869 0.225934 0.974143i 0.427457π-0.427457\pi
0.225934 + 0.974143i 0.427457π0.427457\pi
5454 −0.301545 −0.0410351
5555 17.7210 2.38949
5656 0 0
5757 0.464419 0.0615138
5858 −0.323048 −0.0424183
5959 4.50627 0.586667 0.293333 0.956010i 0.405235π-0.405235\pi
0.293333 + 0.956010i 0.405235π0.405235\pi
6060 2.00413 0.258732
6161 7.54467 0.965996 0.482998 0.875621i 0.339548π-0.339548\pi
0.482998 + 0.875621i 0.339548π0.339548\pi
6262 −1.09670 −0.139281
6363 0 0
6464 −7.09585 −0.886981
6565 3.93251 0.487768
6666 0.229050 0.0281942
6767 −12.6653 −1.54731 −0.773653 0.633609i 0.781573π-0.781573\pi
−0.773653 + 0.633609i 0.781573π0.781573\pi
6868 4.47548 0.542732
6969 −0.452087 −0.0544249
7070 0 0
7171 9.54869 1.13322 0.566610 0.823986i 0.308254π-0.308254\pi
0.566610 + 0.823986i 0.308254π0.308254\pi
7272 −2.27309 −0.267886
7373 1.08004 0.126409 0.0632044 0.998001i 0.479868π-0.479868\pi
0.0632044 + 0.998001i 0.479868π0.479868\pi
7474 −1.39778 −0.162489
7575 −2.71859 −0.313916
7676 3.50693 0.402273
7777 0 0
7878 0.0508292 0.00575528
7979 0.791698 0.0890730 0.0445365 0.999008i 0.485819π-0.485819\pi
0.0445365 + 0.999008i 0.485819π0.485819\pi
8080 14.8326 1.65833
8181 8.39714 0.933016
8282 1.58789 0.175354
8383 −7.14643 −0.784422 −0.392211 0.919875i 0.628290π-0.628290\pi
−0.392211 + 0.919875i 0.628290π0.628290\pi
8484 0 0
8585 −8.97166 −0.973114
8686 −1.33311 −0.143753
8787 −0.428937 −0.0459869
8888 3.49297 0.372352
8989 −11.2656 −1.19415 −0.597077 0.802184i 0.703671π-0.703671\pi
−0.597077 + 0.802184i 0.703671π0.703671\pi
9090 2.25633 0.237838
9191 0 0
9292 −3.41381 −0.355914
9393 −1.45617 −0.150998
9494 −0.693685 −0.0715482
9595 −7.03008 −0.721271
9696 0.594459 0.0606717
9797 −8.81353 −0.894879 −0.447439 0.894314i 0.647664π-0.647664\pi
−0.447439 + 0.894314i 0.647664π0.647664\pi
9898 0 0
9999 −13.2147 −1.32813
100100 −20.5287 −2.05287
101101 −14.3171 −1.42461 −0.712303 0.701872i 0.752348π-0.752348\pi
−0.712303 + 0.701872i 0.752348π0.752348\pi
102102 −0.115962 −0.0114820
103103 −7.49214 −0.738223 −0.369111 0.929385i 0.620338π-0.620338\pi
−0.369111 + 0.929385i 0.620338π0.620338\pi
104104 0.775135 0.0760082
105105 0 0
106106 −0.643641 −0.0625160
107107 10.9784 1.06132 0.530660 0.847585i 0.321944π-0.321944\pi
0.530660 + 0.847585i 0.321944π0.321944\pi
108108 −3.02340 −0.290926
109109 −12.4463 −1.19214 −0.596068 0.802934i 0.703271π-0.703271\pi
−0.596068 + 0.802934i 0.703271π0.703271\pi
110110 −3.46722 −0.330586
111111 −1.85595 −0.176159
112112 0 0
113113 −1.65110 −0.155323 −0.0776613 0.996980i 0.524745π-0.524745\pi
−0.0776613 + 0.996980i 0.524745π0.524745\pi
114114 −0.0908666 −0.00851043
115115 6.84340 0.638150
116116 −3.23900 −0.300733
117117 −2.93251 −0.271111
118118 −0.881681 −0.0811653
119119 0 0
120120 −0.791894 −0.0722897
121121 9.30650 0.846046
122122 −1.47616 −0.133645
123123 2.10837 0.190106
124124 −10.9959 −0.987460
125125 21.4897 1.92210
126126 0 0
127127 −4.49297 −0.398687 −0.199343 0.979930i 0.563881π-0.563881\pi
−0.199343 + 0.979930i 0.563881π0.563881\pi
128128 5.96483 0.527222
129129 −1.77008 −0.155847
130130 −0.769420 −0.0674826
131131 −12.6567 −1.10582 −0.552911 0.833240i 0.686483π-0.686483\pi
−0.552911 + 0.833240i 0.686483π0.686483\pi
132132 2.29654 0.199888
133133 0 0
134134 2.47804 0.214070
135135 6.06077 0.521628
136136 −1.76840 −0.151639
137137 −9.28641 −0.793392 −0.396696 0.917950i 0.629843π-0.629843\pi
−0.396696 + 0.917950i 0.629843π0.629843\pi
138138 0.0884536 0.00752967
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 0 0
141141 −0.921061 −0.0775673
142142 −1.86826 −0.156781
143143 4.50627 0.376834
144144 −11.0608 −0.921731
145145 6.49297 0.539212
146146 −0.211316 −0.0174887
147147 0 0
148148 −14.0147 −1.15200
149149 −15.1649 −1.24235 −0.621177 0.783670i 0.713345π-0.713345\pi
−0.621177 + 0.783670i 0.713345π0.713345\pi
150150 0.531909 0.0434302
151151 5.14159 0.418416 0.209208 0.977871i 0.432911π-0.432911\pi
0.209208 + 0.977871i 0.432911π0.432911\pi
152152 −1.38570 −0.112395
153153 6.69025 0.540875
154154 0 0
155155 22.0426 1.77051
156156 0.509632 0.0408032
157157 −10.7311 −0.856438 −0.428219 0.903675i 0.640859π-0.640859\pi
−0.428219 + 0.903675i 0.640859π0.640859\pi
158158 −0.154901 −0.0123232
159159 −0.854614 −0.0677753
160160 −8.99853 −0.711397
161161 0 0
162162 −1.64295 −0.129083
163163 2.37239 0.185820 0.0929101 0.995675i 0.470383π-0.470383\pi
0.0929101 + 0.995675i 0.470383π0.470383\pi
164164 15.9208 1.24320
165165 −4.60370 −0.358398
166166 1.39824 0.108525
167167 12.0784 0.934653 0.467327 0.884085i 0.345217π-0.345217\pi
0.467327 + 0.884085i 0.345217π0.345217\pi
168168 0 0
169169 1.00000 0.0769231
170170 1.75536 0.134630
171171 5.24240 0.400896
172172 −13.3662 −1.01917
173173 −19.4097 −1.47569 −0.737846 0.674969i 0.764157π-0.764157\pi
−0.737846 + 0.674969i 0.764157π0.764157\pi
174174 0.0839242 0.00636228
175175 0 0
176176 16.9967 1.28117
177177 −1.17068 −0.0879935
178178 2.20419 0.165211
179179 14.6444 1.09457 0.547286 0.836945i 0.315661π-0.315661\pi
0.547286 + 0.836945i 0.315661π0.315661\pi
180180 22.6228 1.68620
181181 −9.44627 −0.702136 −0.351068 0.936350i 0.614181π-0.614181\pi
−0.351068 + 0.936350i 0.614181π0.614181\pi
182182 0 0
183183 −1.96002 −0.144889
184184 1.34890 0.0994422
185185 28.0941 2.06552
186186 0.284910 0.0208906
187187 −10.2807 −0.751796
188188 −6.95513 −0.507255
189189 0 0
190190 1.37548 0.0997878
191191 12.5537 0.908357 0.454179 0.890911i 0.349933π-0.349933\pi
0.454179 + 0.890911i 0.349933π0.349933\pi
192192 1.84342 0.133037
193193 −9.36859 −0.674366 −0.337183 0.941439i 0.609474π-0.609474\pi
−0.337183 + 0.941439i 0.609474π0.609474\pi
194194 1.72442 0.123806
195195 −1.02162 −0.0731598
196196 0 0
197197 −7.62276 −0.543099 −0.271550 0.962424i 0.587536π-0.587536\pi
−0.271550 + 0.962424i 0.587536π0.587536\pi
198198 2.58554 0.183746
199199 13.5289 0.959036 0.479518 0.877532i 0.340812π-0.340812\pi
0.479518 + 0.877532i 0.340812π0.340812\pi
200200 8.11151 0.573570
201201 3.29029 0.232079
202202 2.80123 0.197094
203203 0 0
204204 −1.16268 −0.0814038
205205 −31.9152 −2.22906
206206 1.46588 0.102133
207207 −5.10319 −0.354696
208208 3.77178 0.261526
209209 −8.05579 −0.557231
210210 0 0
211211 −15.7995 −1.08768 −0.543840 0.839189i 0.683030π-0.683030\pi
−0.543840 + 0.839189i 0.683030π0.683030\pi
212212 −6.45338 −0.443220
213213 −2.48064 −0.169971
214214 −2.14799 −0.146833
215215 26.7943 1.82736
216216 1.19464 0.0812847
217217 0 0
218218 2.43519 0.164932
219219 −0.280581 −0.0189599
220220 −34.7636 −2.34376
221221 −2.28141 −0.153464
222222 0.363128 0.0243715
223223 22.4737 1.50495 0.752474 0.658622i 0.228861π-0.228861\pi
0.752474 + 0.658622i 0.228861π0.228861\pi
224224 0 0
225225 −30.6876 −2.04584
226226 0.323048 0.0214889
227227 −9.20249 −0.610791 −0.305395 0.952226i 0.598789π-0.598789\pi
−0.305395 + 0.952226i 0.598789π0.598789\pi
228228 −0.911060 −0.0603364
229229 15.2922 1.01054 0.505269 0.862962i 0.331393π-0.331393\pi
0.505269 + 0.862962i 0.331393π0.331393\pi
230230 −1.33895 −0.0882880
231231 0 0
232232 1.27983 0.0840247
233233 −8.05579 −0.527752 −0.263876 0.964557i 0.585001π-0.585001\pi
−0.263876 + 0.964557i 0.585001π0.585001\pi
234234 0.573764 0.0375081
235235 13.9424 0.909504
236236 −8.84004 −0.575438
237237 −0.205674 −0.0133600
238238 0 0
239239 21.7258 1.40533 0.702663 0.711523i 0.251994π-0.251994\pi
0.702663 + 0.711523i 0.251994π0.251994\pi
240240 −3.85333 −0.248731
241241 −20.4980 −1.32039 −0.660195 0.751094i 0.729527π-0.729527\pi
−0.660195 + 0.751094i 0.729527π0.729527\pi
242242 −1.82088 −0.117050
243243 −6.80507 −0.436546
244244 −14.8005 −0.947507
245245 0 0
246246 −0.412517 −0.0263011
247247 −1.78768 −0.113748
248248 4.34481 0.275896
249249 1.85656 0.117655
250250 −4.20460 −0.265922
251251 2.60871 0.164660 0.0823301 0.996605i 0.473764π-0.473764\pi
0.0823301 + 0.996605i 0.473764π0.473764\pi
252252 0 0
253253 7.84187 0.493014
254254 0.879078 0.0551583
255255 2.33073 0.145956
256256 13.0246 0.814040
257257 −8.99676 −0.561202 −0.280601 0.959824i 0.590534π-0.590534\pi
−0.280601 + 0.959824i 0.590534π0.590534\pi
258258 0.346327 0.0215614
259259 0 0
260260 −7.71448 −0.478432
261261 −4.84187 −0.299704
262262 2.47637 0.152990
263263 1.43392 0.0884194 0.0442097 0.999022i 0.485923π-0.485923\pi
0.0442097 + 0.999022i 0.485923π0.485923\pi
264264 −0.907433 −0.0558487
265265 12.9366 0.794689
266266 0 0
267267 2.92668 0.179110
268268 24.8457 1.51769
269269 −8.16832 −0.498031 −0.249016 0.968499i 0.580107π-0.580107\pi
−0.249016 + 0.968499i 0.580107π0.580107\pi
270270 −1.18583 −0.0721672
271271 −0.212317 −0.0128973 −0.00644867 0.999979i 0.502053π-0.502053\pi
−0.00644867 + 0.999979i 0.502053π0.502053\pi
272272 −8.60497 −0.521753
273273 0 0
274274 1.81695 0.109766
275275 47.1565 2.84364
276276 0.886867 0.0533831
277277 22.9749 1.38043 0.690215 0.723604i 0.257516π-0.257516\pi
0.690215 + 0.723604i 0.257516π0.257516\pi
278278 0.782625 0.0469387
279279 −16.4374 −0.984081
280280 0 0
281281 −0.345228 −0.0205946 −0.0102973 0.999947i 0.503278π-0.503278\pi
−0.0102973 + 0.999947i 0.503278π0.503278\pi
282282 0.180211 0.0107314
283283 −28.9715 −1.72217 −0.861087 0.508457i 0.830216π-0.830216\pi
−0.861087 + 0.508457i 0.830216π0.830216\pi
284284 −18.7318 −1.11153
285285 1.82633 0.108183
286286 −0.881681 −0.0521349
287287 0 0
288288 6.71029 0.395408
289289 −11.7952 −0.693834
290290 −1.27039 −0.0745999
291291 2.28965 0.134222
292292 −2.11873 −0.123989
293293 31.5427 1.84274 0.921372 0.388682i 0.127070π-0.127070\pi
0.921372 + 0.388682i 0.127070π0.127070\pi
294294 0 0
295295 17.7210 1.03175
296296 5.53762 0.321868
297297 6.94506 0.402993
298298 2.96710 0.171880
299299 1.74021 0.100639
300300 5.33311 0.307907
301301 0 0
302302 −1.00598 −0.0578879
303303 3.71942 0.213675
304304 −6.74274 −0.386723
305305 29.6695 1.69887
306306 −1.30899 −0.0748300
307307 −18.1941 −1.03839 −0.519197 0.854655i 0.673769π-0.673769\pi
−0.519197 + 0.854655i 0.673769π0.673769\pi
308308 0 0
309309 1.94637 0.110725
310310 −4.31278 −0.244949
311311 −0.376623 −0.0213563 −0.0106782 0.999943i 0.503399π-0.503399\pi
−0.0106782 + 0.999943i 0.503399π0.503399\pi
312312 −0.201371 −0.0114004
313313 10.9883 0.621095 0.310548 0.950558i 0.399488π-0.399488\pi
0.310548 + 0.950558i 0.399488π0.399488\pi
314314 2.09961 0.118488
315315 0 0
316316 −1.55309 −0.0873680
317317 26.1806 1.47045 0.735225 0.677823i 0.237077π-0.237077\pi
0.735225 + 0.677823i 0.237077π0.237077\pi
318318 0.167211 0.00937670
319319 7.44031 0.416578
320320 −27.9045 −1.55991
321321 −2.85206 −0.159186
322322 0 0
323323 4.07844 0.226930
324324 −16.4728 −0.915158
325325 10.4646 0.580473
326326 −0.464174 −0.0257082
327327 3.23340 0.178807
328328 −6.29079 −0.347351
329329 0 0
330330 0.900743 0.0495843
331331 −34.0932 −1.87393 −0.936967 0.349419i 0.886379π-0.886379\pi
−0.936967 + 0.349419i 0.886379π0.886379\pi
332332 14.0193 0.769408
333333 −20.9501 −1.14806
334334 −2.36321 −0.129309
335335 −49.8062 −2.72120
336336 0 0
337337 14.7532 0.803657 0.401829 0.915715i 0.368375π-0.368375\pi
0.401829 + 0.915715i 0.368375π0.368375\pi
338338 −0.195656 −0.0106423
339339 0.428937 0.0232967
340340 17.5999 0.954487
341341 25.2587 1.36784
342342 −1.02571 −0.0554639
343343 0 0
344344 5.28141 0.284754
345345 −1.77784 −0.0957155
346346 3.79763 0.204162
347347 29.9466 1.60762 0.803809 0.594888i 0.202804π-0.202804\pi
0.803809 + 0.594888i 0.202804π0.202804\pi
348348 0.841454 0.0451066
349349 −13.4793 −0.721532 −0.360766 0.932656i 0.617485π-0.617485\pi
−0.360766 + 0.932656i 0.617485π0.617485\pi
350350 0 0
351351 1.54120 0.0822630
352352 −10.3114 −0.549602
353353 0.163532 0.00870392 0.00435196 0.999991i 0.498615π-0.498615\pi
0.00435196 + 0.999991i 0.498615π0.498615\pi
354354 0.229050 0.0121739
355355 37.5503 1.99296
356356 22.1000 1.17130
357357 0 0
358358 −2.86527 −0.151434
359359 8.92130 0.470848 0.235424 0.971893i 0.424352π-0.424352\pi
0.235424 + 0.971893i 0.424352π0.424352\pi
360360 −8.93895 −0.471124
361361 −15.8042 −0.831799
362362 1.84822 0.0971404
363363 −2.41772 −0.126898
364364 0 0
365365 4.24726 0.222312
366366 0.383490 0.0200453
367367 36.6552 1.91339 0.956693 0.291098i 0.0940207π-0.0940207\pi
0.956693 + 0.291098i 0.0940207π0.0940207\pi
368368 6.56369 0.342156
369369 23.7995 1.23895
370370 −5.49679 −0.285765
371371 0 0
372372 2.85660 0.148108
373373 27.1274 1.40460 0.702302 0.711879i 0.252156π-0.252156\pi
0.702302 + 0.711879i 0.252156π0.252156\pi
374374 2.01147 0.104011
375375 −5.58278 −0.288294
376376 2.74819 0.141727
377377 1.65110 0.0850360
378378 0 0
379379 −15.8943 −0.816434 −0.408217 0.912885i 0.633849π-0.633849\pi
−0.408217 + 0.912885i 0.633849π0.633849\pi
380380 13.7910 0.707465
381381 1.16722 0.0597986
382382 −2.45622 −0.125671
383383 1.15079 0.0588025 0.0294013 0.999568i 0.490640π-0.490640\pi
0.0294013 + 0.999568i 0.490640π0.490640\pi
384384 −1.54959 −0.0790774
385385 0 0
386386 1.83302 0.0932985
387387 −19.9808 −1.01568
388388 17.2897 0.877750
389389 −14.3130 −0.725699 −0.362850 0.931848i 0.618196π-0.618196\pi
−0.362850 + 0.931848i 0.618196π0.618196\pi
390390 0.199886 0.0101216
391391 −3.97013 −0.200778
392392 0 0
393393 3.28807 0.165861
394394 1.49144 0.0751377
395395 3.11336 0.156650
396396 25.9235 1.30271
397397 −25.9176 −1.30077 −0.650383 0.759607i 0.725391π-0.725391\pi
−0.650383 + 0.759607i 0.725391π0.725391\pi
398398 −2.64701 −0.132682
399399 0 0
400400 39.4703 1.97351
401401 −4.29631 −0.214548 −0.107274 0.994230i 0.534212π-0.534212\pi
−0.107274 + 0.994230i 0.534212π0.534212\pi
402402 −0.643765 −0.0321081
403403 5.60523 0.279216
404404 28.0861 1.39734
405405 33.0219 1.64087
406406 0 0
407407 32.1931 1.59575
408408 0.459410 0.0227442
409409 −24.7071 −1.22169 −0.610844 0.791751i 0.709170π-0.709170\pi
−0.610844 + 0.791751i 0.709170π0.709170\pi
410410 6.24441 0.308389
411411 2.41250 0.119000
412412 14.6975 0.724093
413413 0 0
414414 0.998471 0.0490722
415415 −28.1034 −1.37954
416416 −2.28824 −0.112190
417417 1.03915 0.0508876
418418 1.57617 0.0770928
419419 −24.9293 −1.21787 −0.608937 0.793218i 0.708404π-0.708404\pi
−0.608937 + 0.793218i 0.708404π0.708404\pi
420420 0 0
421421 −10.0000 −0.487370 −0.243685 0.969854i 0.578356π-0.578356\pi
−0.243685 + 0.969854i 0.578356π0.578356\pi
422422 3.09127 0.150480
423423 −10.3970 −0.505520
424424 2.54993 0.123835
425425 −23.8741 −1.15806
426426 0.485352 0.0235154
427427 0 0
428428 −21.5365 −1.04101
429429 −1.17068 −0.0565209
430430 −5.24247 −0.252814
431431 −5.68851 −0.274006 −0.137003 0.990571i 0.543747π-0.543747\pi
−0.137003 + 0.990571i 0.543747π0.543747\pi
432432 5.81305 0.279681
433433 12.2598 0.589169 0.294584 0.955625i 0.404819π-0.404819\pi
0.294584 + 0.955625i 0.404819π0.404819\pi
434434 0 0
435435 −1.68680 −0.0808758
436436 24.4161 1.16932
437437 −3.11095 −0.148817
438438 0.0548975 0.00262310
439439 5.02317 0.239743 0.119871 0.992789i 0.461752π-0.461752\pi
0.119871 + 0.992789i 0.461752π0.461752\pi
440440 13.7361 0.654845
441441 0 0
442442 0.446372 0.0212317
443443 0.578803 0.0274997 0.0137499 0.999905i 0.495623π-0.495623\pi
0.0137499 + 0.999905i 0.495623π0.495623\pi
444444 3.64085 0.172787
445445 −44.3022 −2.10012
446446 −4.39711 −0.208209
447447 3.93966 0.186339
448448 0 0
449449 −7.36359 −0.347509 −0.173755 0.984789i 0.555590π-0.555590\pi
−0.173755 + 0.984789i 0.555590π0.555590\pi
450450 6.00423 0.283042
451451 −36.5717 −1.72210
452452 3.23900 0.152350
453453 −1.33572 −0.0627578
454454 1.80052 0.0845028
455455 0 0
456456 0.359988 0.0168580
457457 7.91824 0.370399 0.185200 0.982701i 0.440707π-0.440707\pi
0.185200 + 0.982701i 0.440707π0.440707\pi
458458 −2.99202 −0.139808
459459 −3.51610 −0.164118
460460 −13.4248 −0.625936
461461 −9.53600 −0.444136 −0.222068 0.975031i 0.571281π-0.571281\pi
−0.222068 + 0.975031i 0.571281π0.571281\pi
462462 0 0
463463 2.16049 0.100406 0.0502032 0.998739i 0.484013π-0.484013\pi
0.0502032 + 0.998739i 0.484013π0.484013\pi
464464 6.22758 0.289108
465465 −5.72642 −0.265556
466466 1.57617 0.0730145
467467 −8.11900 −0.375702 −0.187851 0.982198i 0.560152π-0.560152\pi
−0.187851 + 0.982198i 0.560152π0.560152\pi
468468 5.75276 0.265921
469469 0 0
470470 −2.72792 −0.125830
471471 2.78783 0.128456
472472 3.49297 0.160777
473473 30.7036 1.41176
474474 0.0402414 0.00184835
475475 −18.7074 −0.858357
476476 0 0
477477 −9.64694 −0.441703
478478 −4.25079 −0.194427
479479 14.5533 0.664955 0.332478 0.943111i 0.392115π-0.392115\pi
0.332478 + 0.943111i 0.392115π0.392115\pi
480480 2.33772 0.106702
481481 7.14407 0.325742
482482 4.01056 0.182676
483483 0 0
484484 −18.2567 −0.829852
485485 −34.6593 −1.57380
486486 1.33146 0.0603960
487487 −33.2590 −1.50711 −0.753554 0.657386i 0.771662π-0.771662\pi
−0.753554 + 0.657386i 0.771662π0.771662\pi
488488 5.84814 0.264733
489489 −0.616320 −0.0278710
490490 0 0
491491 −22.5563 −1.01795 −0.508977 0.860780i 0.669976π-0.669976\pi
−0.508977 + 0.860780i 0.669976π0.669976\pi
492492 −4.13604 −0.186467
493493 −3.76684 −0.169650
494494 0.349771 0.0157370
495495 −51.9669 −2.33574
496496 21.1417 0.949290
497497 0 0
498498 −0.363248 −0.0162775
499499 −11.3854 −0.509682 −0.254841 0.966983i 0.582023π-0.582023\pi
−0.254841 + 0.966983i 0.582023π0.582023\pi
500500 −42.1568 −1.88531
501501 −3.13782 −0.140188
502502 −0.510410 −0.0227807
503503 −8.81825 −0.393186 −0.196593 0.980485i 0.562988π-0.562988\pi
−0.196593 + 0.980485i 0.562988π0.562988\pi
504504 0 0
505505 −56.3022 −2.50541
506506 −1.53431 −0.0682084
507507 −0.259788 −0.0115376
508508 8.81394 0.391056
509509 19.2838 0.854738 0.427369 0.904077i 0.359441π-0.359441\pi
0.427369 + 0.904077i 0.359441π0.359441\pi
510510 −0.456023 −0.0201930
511511 0 0
512512 −14.4780 −0.639844
513513 −2.75517 −0.121644
514514 1.76027 0.0776423
515515 −29.4629 −1.29829
516516 3.47239 0.152864
517517 15.9767 0.702653
518518 0 0
519519 5.04241 0.221337
520520 3.04823 0.133674
521521 25.1168 1.10039 0.550193 0.835037i 0.314554π-0.314554\pi
0.550193 + 0.835037i 0.314554π0.314554\pi
522522 0.947342 0.0414640
523523 −29.9648 −1.31027 −0.655134 0.755513i 0.727388π-0.727388\pi
−0.655134 + 0.755513i 0.727388π0.727388\pi
524524 24.8289 1.08466
525525 0 0
526526 −0.280556 −0.0122328
527527 −12.7878 −0.557046
528528 −4.41554 −0.192162
529529 −19.9717 −0.868333
530530 −2.53113 −0.109945
531531 −13.2147 −0.573469
532532 0 0
533533 −8.11574 −0.351532
534534 −0.572623 −0.0247798
535535 43.1726 1.86651
536536 −9.81728 −0.424042
537537 −3.80444 −0.164174
538538 1.59818 0.0689026
539539 0 0
540540 −11.8895 −0.511644
541541 5.09973 0.219255 0.109627 0.993973i 0.465034π-0.465034\pi
0.109627 + 0.993973i 0.465034π0.465034\pi
542542 0.0415412 0.00178435
543543 2.45403 0.105313
544544 5.22042 0.223823
545545 −48.9451 −2.09658
546546 0 0
547547 2.92025 0.124861 0.0624305 0.998049i 0.480115π-0.480115\pi
0.0624305 + 0.998049i 0.480115π0.480115\pi
548548 18.2173 0.778206
549549 −22.1248 −0.944265
550550 −9.22647 −0.393418
551551 −2.95165 −0.125744
552552 −0.350428 −0.0149152
553553 0 0
554554 −4.49519 −0.190982
555555 −7.29853 −0.309805
556556 7.84687 0.332782
557557 25.9874 1.10112 0.550561 0.834795i 0.314414π-0.314414\pi
0.550561 + 0.834795i 0.314414π0.314414\pi
558558 3.21608 0.136148
559559 6.81353 0.288182
560560 0 0
561561 2.67079 0.112761
562562 0.0675460 0.00284925
563563 3.65069 0.153858 0.0769291 0.997037i 0.475488π-0.475488\pi
0.0769291 + 0.997037i 0.475488π0.475488\pi
564564 1.80686 0.0760826
565565 −6.49297 −0.273161
566566 5.66845 0.238263
567567 0 0
568568 7.40152 0.310561
569569 −25.3533 −1.06286 −0.531432 0.847101i 0.678346π-0.678346\pi
−0.531432 + 0.847101i 0.678346π0.678346\pi
570570 −0.357334 −0.0149671
571571 27.7253 1.16027 0.580133 0.814522i 0.303000π-0.303000\pi
0.580133 + 0.814522i 0.303000π0.303000\pi
572572 −8.84004 −0.369621
573573 −3.26132 −0.136244
574574 0 0
575575 18.2107 0.759438
576576 20.8086 0.867027
577577 39.5754 1.64755 0.823773 0.566920i 0.191865π-0.191865\pi
0.823773 + 0.566920i 0.191865π0.191865\pi
578578 2.30780 0.0959918
579579 2.43385 0.101147
580580 −12.7374 −0.528891
581581 0 0
582582 −0.447985 −0.0185696
583583 14.8241 0.613951
584584 0.837175 0.0346426
585585 −11.5321 −0.476795
586586 −6.17153 −0.254943
587587 −8.24177 −0.340174 −0.170087 0.985429i 0.554405π-0.554405\pi
−0.170087 + 0.985429i 0.554405π0.554405\pi
588588 0 0
589589 −10.0204 −0.412882
590590 −3.46722 −0.142743
591591 1.98031 0.0814589
592592 26.9458 1.10747
593593 −11.9230 −0.489618 −0.244809 0.969571i 0.578725π-0.578725\pi
−0.244809 + 0.969571i 0.578725π0.578725\pi
594594 −1.35884 −0.0557540
595595 0 0
596596 29.7492 1.21857
597597 −3.51464 −0.143845
598598 −0.340483 −0.0139234
599599 −35.6158 −1.45522 −0.727611 0.685990i 0.759369π-0.759369\pi
−0.727611 + 0.685990i 0.759369π0.759369\pi
600600 −2.10728 −0.0860292
601601 38.9252 1.58779 0.793896 0.608054i 0.208050π-0.208050\pi
0.793896 + 0.608054i 0.208050π0.208050\pi
602602 0 0
603603 37.1410 1.51250
604604 −10.0863 −0.410408
605605 36.5979 1.48792
606606 −0.727728 −0.0295619
607607 −13.6966 −0.555926 −0.277963 0.960592i 0.589659π-0.589659\pi
−0.277963 + 0.960592i 0.589659π0.589659\pi
608608 4.09065 0.165898
609609 0 0
610610 −5.80502 −0.235039
611611 3.54543 0.143433
612612 −13.1244 −0.530522
613613 3.16112 0.127676 0.0638382 0.997960i 0.479666π-0.479666\pi
0.0638382 + 0.997960i 0.479666π0.479666\pi
614614 3.55979 0.143662
615615 8.29120 0.334334
616616 0 0
617617 20.9297 0.842597 0.421299 0.906922i 0.361574π-0.361574\pi
0.421299 + 0.906922i 0.361574π0.361574\pi
618618 −0.380820 −0.0153188
619619 30.9544 1.24416 0.622082 0.782952i 0.286287π-0.286287\pi
0.622082 + 0.782952i 0.286287π0.286287\pi
620620 −43.2414 −1.73662
621621 2.68201 0.107625
622622 0.0736887 0.00295465
623623 0 0
624624 −0.979864 −0.0392260
625625 32.1854 1.28742
626626 −2.14993 −0.0859285
627627 2.09280 0.0835784
628628 21.0515 0.840045
629629 −16.2986 −0.649866
630630 0 0
631631 −15.1218 −0.601988 −0.300994 0.953626i 0.597318π-0.597318\pi
−0.300994 + 0.953626i 0.597318π0.597318\pi
632632 0.613673 0.0244106
633633 4.10452 0.163140
634634 −5.12240 −0.203437
635635 −17.6687 −0.701159
636636 1.67651 0.0664780
637637 0 0
638638 −1.45574 −0.0576335
639639 −28.0016 −1.10773
640640 23.4568 0.927210
641641 −47.2414 −1.86592 −0.932962 0.359976i 0.882785π-0.882785\pi
−0.932962 + 0.359976i 0.882785π0.882785\pi
642642 0.558023 0.0220234
643643 39.9249 1.57448 0.787241 0.616645i 0.211509π-0.211509\pi
0.787241 + 0.616645i 0.211509π0.211509\pi
644644 0 0
645645 −6.96085 −0.274083
646646 −0.797972 −0.0313958
647647 −29.8278 −1.17265 −0.586327 0.810075i 0.699426π-0.699426\pi
−0.586327 + 0.810075i 0.699426π0.699426\pi
648648 6.50892 0.255695
649649 20.3065 0.797100
650650 −2.04747 −0.0803084
651651 0 0
652652 −4.65397 −0.182263
653653 25.1549 0.984387 0.492194 0.870486i 0.336195π-0.336195\pi
0.492194 + 0.870486i 0.336195π0.336195\pi
654654 −0.632635 −0.0247380
655655 −49.7727 −1.94478
656656 −30.6107 −1.19515
657657 −3.16722 −0.123565
658658 0 0
659659 17.3155 0.674517 0.337258 0.941412i 0.390500π-0.390500\pi
0.337258 + 0.941412i 0.390500π0.390500\pi
660660 9.03117 0.351538
661661 −9.20074 −0.357867 −0.178934 0.983861i 0.557265π-0.557265\pi
−0.178934 + 0.983861i 0.557265π0.557265\pi
662662 6.67055 0.259258
663663 0.592684 0.0230179
664664 −5.53945 −0.214972
665665 0 0
666666 4.09901 0.158833
667667 2.87327 0.111253
668668 −23.6944 −0.916763
669669 −5.83840 −0.225725
670670 9.74490 0.376478
671671 33.9984 1.31249
672672 0 0
673673 17.3609 0.669212 0.334606 0.942358i 0.391397π-0.391397\pi
0.334606 + 0.942358i 0.391397π0.391397\pi
674674 −2.88655 −0.111186
675675 16.1281 0.620770
676676 −1.96172 −0.0754507
677677 49.9825 1.92098 0.960492 0.278307i 0.0897733π-0.0897733\pi
0.960492 + 0.278307i 0.0897733π0.0897733\pi
678678 −0.0839242 −0.00322309
679679 0 0
680680 −6.95425 −0.266683
681681 2.39070 0.0916118
682682 −4.94202 −0.189240
683683 33.6153 1.28626 0.643128 0.765759i 0.277636π-0.277636\pi
0.643128 + 0.765759i 0.277636π0.277636\pi
684684 −10.2841 −0.393223
685685 −36.5189 −1.39532
686686 0 0
687687 −3.97274 −0.151570
688688 25.6991 0.979770
689689 3.28965 0.125326
690690 0.347845 0.0132422
691691 −15.1309 −0.575607 −0.287803 0.957689i 0.592925π-0.592925\pi
−0.287803 + 0.957689i 0.592925π0.592925\pi
692692 38.0764 1.44745
693693 0 0
694694 −5.85924 −0.222414
695695 −15.7300 −0.596674
696696 −0.332484 −0.0126028
697697 18.5153 0.701317
698698 2.63731 0.0998238
699699 2.09280 0.0791570
700700 0 0
701701 2.02467 0.0764705 0.0382353 0.999269i 0.487826π-0.487826\pi
0.0382353 + 0.999269i 0.487826π0.487826\pi
702702 −0.301545 −0.0113811
703703 −12.7713 −0.481680
704704 −31.9758 −1.20513
705705 −3.62208 −0.136415
706706 −0.0319960 −0.00120419
707707 0 0
708708 2.29654 0.0863093
709709 −30.4553 −1.14377 −0.571886 0.820333i 0.693788π-0.693788\pi
−0.571886 + 0.820333i 0.693788π0.693788\pi
710710 −7.34695 −0.275726
711711 −2.32166 −0.0870691
712712 −8.73238 −0.327260
713713 9.75429 0.365301
714714 0 0
715715 17.7210 0.662727
716716 −28.7282 −1.07362
717717 −5.64411 −0.210783
718718 −1.74551 −0.0651418
719719 −24.4246 −0.910883 −0.455442 0.890266i 0.650519π-0.650519\pi
−0.455442 + 0.890266i 0.650519π0.650519\pi
720720 −43.4966 −1.62102
721721 0 0
722722 3.09219 0.115079
723723 5.32514 0.198044
724724 18.5309 0.688697
725725 17.2782 0.641695
726726 0.473043 0.0175563
727727 −3.09307 −0.114716 −0.0573578 0.998354i 0.518268π-0.518268\pi
−0.0573578 + 0.998354i 0.518268π0.518268\pi
728728 0 0
729729 −23.4236 −0.867539
730730 −0.831003 −0.0307568
731731 −15.5445 −0.574933
732732 3.84501 0.142115
733733 −8.41427 −0.310788 −0.155394 0.987853i 0.549665π-0.549665\pi
−0.155394 + 0.987853i 0.549665π0.549665\pi
734734 −7.17182 −0.264717
735735 0 0
736736 −3.98203 −0.146779
737737 −57.0731 −2.10231
738738 −4.65652 −0.171409
739739 −7.22758 −0.265871 −0.132936 0.991125i 0.542440π-0.542440\pi
−0.132936 + 0.991125i 0.542440π0.542440\pi
740740 −55.1128 −2.02599
741741 0.464419 0.0170609
742742 0 0
743743 −53.9092 −1.97774 −0.988869 0.148791i 0.952462π-0.952462\pi
−0.988869 + 0.148791i 0.952462π0.952462\pi
744744 −1.12873 −0.0413813
745745 −59.6360 −2.18489
746746 −5.30765 −0.194327
747747 20.9570 0.766776
748748 20.1678 0.737406
749749 0 0
750750 1.09231 0.0398854
751751 29.2442 1.06714 0.533568 0.845757i 0.320851π-0.320851\pi
0.533568 + 0.845757i 0.320851π0.320851\pi
752752 13.3726 0.487647
753753 −0.677712 −0.0246972
754754 −0.323048 −0.0117647
755755 20.2193 0.735857
756756 0 0
757757 −22.0597 −0.801773 −0.400887 0.916128i 0.631298π-0.631298\pi
−0.400887 + 0.916128i 0.631298π0.631298\pi
758758 3.10981 0.112954
759759 −2.03723 −0.0739467
760760 −5.44926 −0.197666
761761 17.8161 0.645833 0.322917 0.946427i 0.395337π-0.395337\pi
0.322917 + 0.946427i 0.395337π0.395337\pi
762762 −0.228374 −0.00827313
763763 0 0
764764 −24.6269 −0.890971
765765 26.3095 0.951222
766766 −0.225159 −0.00813532
767767 4.50627 0.162712
768768 −3.38365 −0.122097
769769 −11.3069 −0.407738 −0.203869 0.978998i 0.565352π-0.565352\pi
−0.203869 + 0.978998i 0.565352π0.565352\pi
770770 0 0
771771 2.33725 0.0841741
772772 18.3785 0.661458
773773 −1.92821 −0.0693528 −0.0346764 0.999399i 0.511040π-0.511040\pi
−0.0346764 + 0.999399i 0.511040π0.511040\pi
774774 3.90936 0.140519
775775 58.6567 2.10701
776776 −6.83168 −0.245243
777777 0 0
778778 2.80043 0.100400
779779 14.5084 0.519816
780780 2.00413 0.0717594
781781 43.0290 1.53970
782782 0.776782 0.0277777
783783 2.54467 0.0909392
784784 0 0
785785 −42.2003 −1.50619
786786 −0.643331 −0.0229469
787787 5.53155 0.197178 0.0985892 0.995128i 0.468567π-0.468567\pi
0.0985892 + 0.995128i 0.468567π0.468567\pi
788788 14.9537 0.532704
789789 −0.372516 −0.0132619
790790 −0.609148 −0.0216725
791791 0 0
792792 −10.2432 −0.363975
793793 7.54467 0.267919
794794 5.07093 0.179961
795795 −3.36078 −0.119195
796796 −26.5398 −0.940679
797797 −13.8038 −0.488955 −0.244477 0.969655i 0.578616π-0.578616\pi
−0.244477 + 0.969655i 0.578616π0.578616\pi
798798 0 0
799799 −8.08857 −0.286153
800800 −23.9456 −0.846605
801801 33.0365 1.16729
802802 0.840601 0.0296826
803803 4.86695 0.171751
804804 −6.45461 −0.227637
805805 0 0
806806 −1.09670 −0.0386296
807807 2.12204 0.0746992
808808 −11.0977 −0.390415
809809 28.2996 0.994961 0.497480 0.867475i 0.334259π-0.334259\pi
0.497480 + 0.867475i 0.334259π0.334259\pi
810810 −6.46093 −0.227014
811811 −12.2124 −0.428837 −0.214418 0.976742i 0.568786π-0.568786\pi
−0.214418 + 0.976742i 0.568786π0.568786\pi
812812 0 0
813813 0.0551575 0.00193446
814814 −6.29879 −0.220772
815815 9.32946 0.326797
816816 2.23547 0.0782571
817817 −12.1804 −0.426140
818818 4.83410 0.169020
819819 0 0
820820 62.6087 2.18639
821821 −41.4011 −1.44491 −0.722453 0.691420i 0.756986π-0.756986\pi
−0.722453 + 0.691420i 0.756986π0.756986\pi
822822 −0.472021 −0.0164636
823823 47.1752 1.64443 0.822213 0.569180i 0.192739π-0.192739\pi
0.822213 + 0.569180i 0.192739π0.192739\pi
824824 −5.80742 −0.202311
825825 −12.2507 −0.426515
826826 0 0
827827 21.1124 0.734150 0.367075 0.930191i 0.380359π-0.380359\pi
0.367075 + 0.930191i 0.380359π0.380359\pi
828828 10.0110 0.347907
829829 −0.636752 −0.0221153 −0.0110577 0.999939i 0.503520π-0.503520\pi
−0.0110577 + 0.999939i 0.503520π0.503520\pi
830830 5.49861 0.190859
831831 −5.96862 −0.207049
832832 −7.09585 −0.246004
833833 0 0
834834 −0.203317 −0.00704029
835835 47.4983 1.64375
836836 15.8032 0.546565
837837 8.63877 0.298600
838838 4.87757 0.168493
839839 −26.9432 −0.930183 −0.465092 0.885263i 0.653979π-0.653979\pi
−0.465092 + 0.885263i 0.653979π0.653979\pi
840840 0 0
841841 −26.2739 −0.905995
842842 1.95656 0.0674276
843843 0.0896862 0.00308896
844844 30.9941 1.06686
845845 3.93251 0.135282
846846 2.03424 0.0699386
847847 0 0
848848 12.4078 0.426087
849849 7.52645 0.258307
850850 4.67112 0.160218
851851 12.4322 0.426170
852852 4.86631 0.166717
853853 6.74784 0.231042 0.115521 0.993305i 0.463146π-0.463146\pi
0.115521 + 0.993305i 0.463146π0.463146\pi
854854 0 0
855855 20.6158 0.705045
856856 8.50973 0.290856
857857 −45.0268 −1.53809 −0.769043 0.639197i 0.779267π-0.779267\pi
−0.769043 + 0.639197i 0.779267π0.779267\pi
858858 0.229050 0.00781965
859859 −36.7270 −1.25311 −0.626554 0.779378i 0.715535π-0.715535\pi
−0.626554 + 0.779378i 0.715535π0.715535\pi
860860 −52.5629 −1.79238
861861 0 0
862862 1.11299 0.0379087
863863 −43.4275 −1.47829 −0.739144 0.673547i 0.764770π-0.764770\pi
−0.739144 + 0.673547i 0.764770π0.764770\pi
864864 −3.52663 −0.119978
865865 −76.3288 −2.59526
866866 −2.39871 −0.0815114
867867 3.06425 0.104067
868868 0 0
869869 3.56761 0.121023
870870 0.330033 0.0111892
871871 −12.6653 −0.429146
872872 −9.64754 −0.326707
873873 25.8458 0.874747
874874 0.608676 0.0205888
875875 0 0
876876 0.550422 0.0185970
877877 40.0081 1.35098 0.675488 0.737371i 0.263933π-0.263933\pi
0.675488 + 0.737371i 0.263933π0.263933\pi
878878 −0.982815 −0.0331684
879879 −8.19443 −0.276391
880880 66.8395 2.25316
881881 35.4308 1.19370 0.596848 0.802355i 0.296420π-0.296420\pi
0.596848 + 0.802355i 0.296420π0.296420\pi
882882 0 0
883883 22.6654 0.762751 0.381375 0.924420i 0.375451π-0.375451\pi
0.381375 + 0.924420i 0.375451π0.375451\pi
884884 4.47548 0.150527
885885 −4.60370 −0.154752
886886 −0.113246 −0.00380459
887887 44.6881 1.50048 0.750240 0.661166i 0.229938π-0.229938\pi
0.750240 + 0.661166i 0.229938π0.229938\pi
888888 −1.43861 −0.0482766
889889 0 0
890890 8.66800 0.290552
891891 37.8398 1.26768
892892 −44.0870 −1.47614
893893 −6.33810 −0.212096
894894 −0.770818 −0.0257800
895895 57.5892 1.92499
896896 0 0
897897 −0.452087 −0.0150947
898898 1.44073 0.0480779
899899 9.25480 0.308665
900900 60.2005 2.00668
901901 −7.50505 −0.250029
902902 7.15549 0.238252
903903 0 0
904904 −1.27983 −0.0425664
905905 −37.1476 −1.23483
906906 0.261343 0.00868254
907907 54.4748 1.80881 0.904403 0.426680i 0.140317π-0.140317\pi
0.904403 + 0.426680i 0.140317π0.140317\pi
908908 18.0527 0.599100
909909 41.9851 1.39256
910910 0 0
911911 −27.4793 −0.910431 −0.455215 0.890381i 0.650438π-0.650438\pi
−0.455215 + 0.890381i 0.650438π0.650438\pi
912912 1.75169 0.0580041
913913 −32.2038 −1.06579
914914 −1.54925 −0.0512447
915915 −7.70779 −0.254812
916916 −29.9990 −0.991196
917917 0 0
918918 0.687947 0.0227056
919919 −48.2880 −1.59287 −0.796437 0.604722i 0.793284π-0.793284\pi
−0.796437 + 0.604722i 0.793284π0.793284\pi
920920 5.30456 0.174886
921921 4.72662 0.155747
922922 1.86578 0.0614461
923923 9.54869 0.314299
924924 0 0
925925 74.7601 2.45810
926926 −0.422713 −0.0138912
927927 21.9708 0.721615
928928 −3.77812 −0.124023
929929 43.3154 1.42113 0.710566 0.703631i 0.248439π-0.248439\pi
0.710566 + 0.703631i 0.248439π0.248439\pi
930930 1.12041 0.0367397
931931 0 0
932932 15.8032 0.517651
933933 0.0978423 0.00320321
934934 1.58853 0.0519784
935935 −40.4288 −1.32216
936936 −2.27309 −0.0742983
937937 −37.2211 −1.21596 −0.607980 0.793952i 0.708020π-0.708020\pi
−0.607980 + 0.793952i 0.708020π0.708020\pi
938938 0 0
939939 −2.85463 −0.0931574
940940 −27.3511 −0.892095
941941 15.9751 0.520773 0.260386 0.965504i 0.416150π-0.416150\pi
0.260386 + 0.965504i 0.416150π0.416150\pi
942942 −0.545456 −0.0177719
943943 −14.1231 −0.459911
944944 16.9967 0.553194
945945 0 0
946946 −6.00736 −0.195316
947947 27.7572 0.901988 0.450994 0.892527i 0.351070π-0.351070\pi
0.450994 + 0.892527i 0.351070π0.351070\pi
948948 0.403474 0.0131042
949949 1.08004 0.0350595
950950 3.66023 0.118754
951951 −6.80142 −0.220551
952952 0 0
953953 12.0303 0.389700 0.194850 0.980833i 0.437578π-0.437578\pi
0.194850 + 0.980833i 0.437578π0.437578\pi
954954 1.88748 0.0611096
955955 49.3677 1.59750
956956 −42.6199 −1.37843
957957 −1.93291 −0.0624820
958958 −2.84744 −0.0919965
959959 0 0
960960 7.24926 0.233969
961961 0.418620 0.0135039
962962 −1.39778 −0.0450663
963963 −32.1942 −1.03744
964964 40.2113 1.29512
965965 −36.8421 −1.18599
966966 0 0
967967 5.40788 0.173906 0.0869528 0.996212i 0.472287π-0.472287\pi
0.0869528 + 0.996212i 0.472287π0.472287\pi
968968 7.21380 0.231860
969969 −1.05953 −0.0340370
970970 6.78131 0.217735
971971 42.2752 1.35668 0.678338 0.734750i 0.262700π-0.262700\pi
0.678338 + 0.734750i 0.262700π0.262700\pi
972972 13.3496 0.428190
973973 0 0
974974 6.50733 0.208508
975975 −2.71859 −0.0870646
976976 28.4568 0.910881
977977 −10.8302 −0.346488 −0.173244 0.984879i 0.555425π-0.555425\pi
−0.173244 + 0.984879i 0.555425π0.555425\pi
978978 0.120587 0.00385594
979979 −50.7660 −1.62249
980980 0 0
981981 36.4988 1.16532
982982 4.41329 0.140834
983983 21.5610 0.687688 0.343844 0.939027i 0.388271π-0.388271\pi
0.343844 + 0.939027i 0.388271π0.388271\pi
984984 1.63427 0.0520988
985985 −29.9766 −0.955134
986986 0.737005 0.0234710
987987 0 0
988988 3.50693 0.111570
989989 11.8570 0.377030
990990 10.1677 0.323149
991991 8.62624 0.274022 0.137011 0.990570i 0.456251π-0.456251\pi
0.137011 + 0.990570i 0.456251π0.456251\pi
992992 −12.8261 −0.407230
993993 8.85703 0.281069
994994 0 0
995995 53.2024 1.68663
996996 −3.64205 −0.115403
997997 21.6967 0.687142 0.343571 0.939127i 0.388363π-0.388363\pi
0.343571 + 0.939127i 0.388363π0.388363\pi
998998 2.22763 0.0705144
999999 11.0104 0.348354
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 637.2.a.l.1.2 5
3.2 odd 2 5733.2.a.bl.1.4 5
7.2 even 3 91.2.e.c.53.4 10
7.3 odd 6 637.2.e.m.79.4 10
7.4 even 3 91.2.e.c.79.4 yes 10
7.5 odd 6 637.2.e.m.508.4 10
7.6 odd 2 637.2.a.k.1.2 5
13.12 even 2 8281.2.a.bw.1.4 5
21.2 odd 6 819.2.j.h.235.2 10
21.11 odd 6 819.2.j.h.352.2 10
21.20 even 2 5733.2.a.bm.1.4 5
28.11 odd 6 1456.2.r.p.625.3 10
28.23 odd 6 1456.2.r.p.417.3 10
91.25 even 6 1183.2.e.f.170.2 10
91.51 even 6 1183.2.e.f.508.2 10
91.90 odd 2 8281.2.a.bx.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.4 10 7.2 even 3
91.2.e.c.79.4 yes 10 7.4 even 3
637.2.a.k.1.2 5 7.6 odd 2
637.2.a.l.1.2 5 1.1 even 1 trivial
637.2.e.m.79.4 10 7.3 odd 6
637.2.e.m.508.4 10 7.5 odd 6
819.2.j.h.235.2 10 21.2 odd 6
819.2.j.h.352.2 10 21.11 odd 6
1183.2.e.f.170.2 10 91.25 even 6
1183.2.e.f.508.2 10 91.51 even 6
1456.2.r.p.417.3 10 28.23 odd 6
1456.2.r.p.625.3 10 28.11 odd 6
5733.2.a.bl.1.4 5 3.2 odd 2
5733.2.a.bm.1.4 5 21.20 even 2
8281.2.a.bw.1.4 5 13.12 even 2
8281.2.a.bx.1.4 5 91.90 odd 2