Properties

Label 357.2.a.h.1.1
Level 357357
Weight 22
Character 357.1
Self dual yes
Analytic conductor 2.8512.851
Analytic rank 00
Dimension 44
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [357,2,Mod(1,357)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(357, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("357.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 357=3717 357 = 3 \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 357.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 2.850659352162.85065935216
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.7232.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x42x35x2+4x+4 x^{4} - 2x^{3} - 5x^{2} + 4x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 0.652223-0.652223 of defining polynomial
Character χ\chi == 357.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q2.06644q21.00000q3+2.27016q40.238009q5+2.06644q6+1.00000q70.558268q8+1.00000q9+0.491831q105.40303q112.27016q12+0.238009q132.06644q14+0.238009q153.38669q161.00000q172.06644q18+7.89486q190.540319q201.00000q21+11.1650q22+6.38669q23+0.558268q244.94335q250.491831q261.00000q27+2.27016q28+4.13287q290.491831q30+6.18136q31+8.11492q32+5.40303q33+2.06644q340.238009q35+2.27016q36+5.64104q3716.3142q380.238009q39+0.132873q406.30231q41+2.06644q42+10.8627q4312.2657q440.238009q4513.1977q46+6.18136q47+3.38669q48+1.00000q49+10.2151q50+1.00000q51+0.540319q52+12.1814q53+2.06644q54+1.28597q550.558268q567.89486q578.54032q584.14869q59+0.540319q602.55613q6112.7734q62+1.00000q639.99559q640.0566484q6511.1650q66+5.45968q672.27016q686.38669q69+0.491831q70+9.72543q710.558268q7214.9389q7311.6569q74+4.94335q75+17.9226q765.40303q77+0.491831q7816.8904q79+0.806065q80+1.00000q81+13.0233q82+5.45968q832.27016q84+0.238009q8522.4471q864.13287q87+3.01634q886.47602q89+0.491831q90+0.238009q91+14.4988q926.18136q9312.7734q941.87905q958.11492q962.06857q972.06644q985.40303q99+O(q100)q-2.06644 q^{2} -1.00000 q^{3} +2.27016 q^{4} -0.238009 q^{5} +2.06644 q^{6} +1.00000 q^{7} -0.558268 q^{8} +1.00000 q^{9} +0.491831 q^{10} -5.40303 q^{11} -2.27016 q^{12} +0.238009 q^{13} -2.06644 q^{14} +0.238009 q^{15} -3.38669 q^{16} -1.00000 q^{17} -2.06644 q^{18} +7.89486 q^{19} -0.540319 q^{20} -1.00000 q^{21} +11.1650 q^{22} +6.38669 q^{23} +0.558268 q^{24} -4.94335 q^{25} -0.491831 q^{26} -1.00000 q^{27} +2.27016 q^{28} +4.13287 q^{29} -0.491831 q^{30} +6.18136 q^{31} +8.11492 q^{32} +5.40303 q^{33} +2.06644 q^{34} -0.238009 q^{35} +2.27016 q^{36} +5.64104 q^{37} -16.3142 q^{38} -0.238009 q^{39} +0.132873 q^{40} -6.30231 q^{41} +2.06644 q^{42} +10.8627 q^{43} -12.2657 q^{44} -0.238009 q^{45} -13.1977 q^{46} +6.18136 q^{47} +3.38669 q^{48} +1.00000 q^{49} +10.2151 q^{50} +1.00000 q^{51} +0.540319 q^{52} +12.1814 q^{53} +2.06644 q^{54} +1.28597 q^{55} -0.558268 q^{56} -7.89486 q^{57} -8.54032 q^{58} -4.14869 q^{59} +0.540319 q^{60} -2.55613 q^{61} -12.7734 q^{62} +1.00000 q^{63} -9.99559 q^{64} -0.0566484 q^{65} -11.1650 q^{66} +5.45968 q^{67} -2.27016 q^{68} -6.38669 q^{69} +0.491831 q^{70} +9.72543 q^{71} -0.558268 q^{72} -14.9389 q^{73} -11.6569 q^{74} +4.94335 q^{75} +17.9226 q^{76} -5.40303 q^{77} +0.491831 q^{78} -16.8904 q^{79} +0.806065 q^{80} +1.00000 q^{81} +13.0233 q^{82} +5.45968 q^{83} -2.27016 q^{84} +0.238009 q^{85} -22.4471 q^{86} -4.13287 q^{87} +3.01634 q^{88} -6.47602 q^{89} +0.491831 q^{90} +0.238009 q^{91} +14.4988 q^{92} -6.18136 q^{93} -12.7734 q^{94} -1.87905 q^{95} -8.11492 q^{96} -2.06857 q^{97} -2.06644 q^{98} -5.40303 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q24q3+6q42q52q6+4q7+6q8+4q9+4q10+2q116q12+2q13+2q14+2q15+6q164q17+2q18+10q19+4q20++2q99+O(q100) 4 q + 2 q^{2} - 4 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 6 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 4 q^{17} + 2 q^{18} + 10 q^{19} + 4 q^{20}+ \cdots + 2 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 −2.06644 −1.46119 −0.730596 0.682810i 0.760757π-0.760757\pi
−0.730596 + 0.682810i 0.760757π0.760757\pi
33 −1.00000 −0.577350
44 2.27016 1.13508
55 −0.238009 −0.106441 −0.0532205 0.998583i 0.516949π-0.516949\pi
−0.0532205 + 0.998583i 0.516949π0.516949\pi
66 2.06644 0.843619
77 1.00000 0.377964
88 −0.558268 −0.197377
99 1.00000 0.333333
1010 0.491831 0.155531
1111 −5.40303 −1.62908 −0.814538 0.580110i 0.803009π-0.803009\pi
−0.814538 + 0.580110i 0.803009π0.803009\pi
1212 −2.27016 −0.655339
1313 0.238009 0.0660119 0.0330060 0.999455i 0.489492π-0.489492\pi
0.0330060 + 0.999455i 0.489492π0.489492\pi
1414 −2.06644 −0.552278
1515 0.238009 0.0614537
1616 −3.38669 −0.846674
1717 −1.00000 −0.242536
1818 −2.06644 −0.487064
1919 7.89486 1.81121 0.905603 0.424126i 0.139419π-0.139419\pi
0.905603 + 0.424126i 0.139419π0.139419\pi
2020 −0.540319 −0.120819
2121 −1.00000 −0.218218
2222 11.1650 2.38039
2323 6.38669 1.33172 0.665859 0.746078i 0.268065π-0.268065\pi
0.665859 + 0.746078i 0.268065π0.268065\pi
2424 0.558268 0.113956
2525 −4.94335 −0.988670
2626 −0.491831 −0.0964560
2727 −1.00000 −0.192450
2828 2.27016 0.429020
2929 4.13287 0.767455 0.383728 0.923446i 0.374640π-0.374640\pi
0.383728 + 0.923446i 0.374640π0.374640\pi
3030 −0.491831 −0.0897957
3131 6.18136 1.11021 0.555103 0.831782i 0.312679π-0.312679\pi
0.555103 + 0.831782i 0.312679π0.312679\pi
3232 8.11492 1.43453
3333 5.40303 0.940547
3434 2.06644 0.354391
3535 −0.238009 −0.0402309
3636 2.27016 0.378360
3737 5.64104 0.927382 0.463691 0.885997i 0.346525π-0.346525\pi
0.463691 + 0.885997i 0.346525π0.346525\pi
3838 −16.3142 −2.64652
3939 −0.238009 −0.0381120
4040 0.132873 0.0210090
4141 −6.30231 −0.984255 −0.492128 0.870523i 0.663781π-0.663781\pi
−0.492128 + 0.870523i 0.663781π0.663781\pi
4242 2.06644 0.318858
4343 10.8627 1.65655 0.828274 0.560323i 0.189323π-0.189323\pi
0.828274 + 0.560323i 0.189323π0.189323\pi
4444 −12.2657 −1.84913
4545 −0.238009 −0.0354803
4646 −13.1977 −1.94589
4747 6.18136 0.901644 0.450822 0.892614i 0.351131π-0.351131\pi
0.450822 + 0.892614i 0.351131π0.351131\pi
4848 3.38669 0.488827
4949 1.00000 0.142857
5050 10.2151 1.44464
5151 1.00000 0.140028
5252 0.540319 0.0749288
5353 12.1814 1.67324 0.836619 0.547785i 0.184529π-0.184529\pi
0.836619 + 0.547785i 0.184529π0.184529\pi
5454 2.06644 0.281206
5555 1.28597 0.173400
5656 −0.558268 −0.0746016
5757 −7.89486 −1.04570
5858 −8.54032 −1.12140
5959 −4.14869 −0.540113 −0.270056 0.962845i 0.587042π-0.587042\pi
−0.270056 + 0.962845i 0.587042π0.587042\pi
6060 0.540319 0.0697549
6161 −2.55613 −0.327279 −0.163640 0.986520i 0.552323π-0.552323\pi
−0.163640 + 0.986520i 0.552323π0.552323\pi
6262 −12.7734 −1.62222
6363 1.00000 0.125988
6464 −9.99559 −1.24945
6565 −0.0566484 −0.00702637
6666 −11.1650 −1.37432
6767 5.45968 0.667006 0.333503 0.942749i 0.391769π-0.391769\pi
0.333503 + 0.942749i 0.391769π0.391769\pi
6868 −2.27016 −0.275297
6969 −6.38669 −0.768868
7070 0.491831 0.0587851
7171 9.72543 1.15420 0.577098 0.816675i 0.304185π-0.304185\pi
0.577098 + 0.816675i 0.304185π0.304185\pi
7272 −0.558268 −0.0657925
7373 −14.9389 −1.74847 −0.874235 0.485503i 0.838637π-0.838637\pi
−0.874235 + 0.485503i 0.838637π0.838637\pi
7474 −11.6569 −1.35508
7575 4.94335 0.570809
7676 17.9226 2.05586
7777 −5.40303 −0.615733
7878 0.491831 0.0556889
7979 −16.8904 −1.90032 −0.950162 0.311756i 0.899083π-0.899083\pi
−0.950162 + 0.311756i 0.899083π0.899083\pi
8080 0.806065 0.0901208
8181 1.00000 0.111111
8282 13.0233 1.43819
8383 5.45968 0.599278 0.299639 0.954053i 0.403134π-0.403134\pi
0.299639 + 0.954053i 0.403134π0.403134\pi
8484 −2.27016 −0.247695
8585 0.238009 0.0258157
8686 −22.4471 −2.42053
8787 −4.13287 −0.443090
8888 3.01634 0.321543
8989 −6.47602 −0.686457 −0.343228 0.939252i 0.611520π-0.611520\pi
−0.343228 + 0.939252i 0.611520π0.611520\pi
9090 0.491831 0.0518436
9191 0.238009 0.0249502
9292 14.4988 1.51161
9393 −6.18136 −0.640977
9494 −12.7734 −1.31747
9595 −1.87905 −0.192787
9696 −8.11492 −0.828226
9797 −2.06857 −0.210032 −0.105016 0.994471i 0.533489π-0.533489\pi
−0.105016 + 0.994471i 0.533489π0.533489\pi
9898 −2.06644 −0.208742
9999 −5.40303 −0.543025
100100 −11.2222 −1.12222
101101 9.43077 0.938397 0.469198 0.883093i 0.344543π-0.344543\pi
0.469198 + 0.883093i 0.344543π0.344543\pi
102102 −2.06644 −0.204608
103103 −8.46786 −0.834363 −0.417181 0.908823i 0.636982π-0.636982\pi
−0.417181 + 0.908823i 0.636982π0.636982\pi
104104 −0.132873 −0.0130293
105105 0.238009 0.0232273
106106 −25.1720 −2.44492
107107 15.4673 1.49528 0.747642 0.664102i 0.231186π-0.231186\pi
0.747642 + 0.664102i 0.231186π0.231186\pi
108108 −2.27016 −0.218446
109109 1.37530 0.131729 0.0658647 0.997829i 0.479019π-0.479019\pi
0.0658647 + 0.997829i 0.479019π0.479019\pi
110110 −2.65738 −0.253371
111111 −5.64104 −0.535424
112112 −3.38669 −0.320013
113113 10.6165 0.998720 0.499360 0.866394i 0.333568π-0.333568\pi
0.499360 + 0.866394i 0.333568π0.333568\pi
114114 16.3142 1.52797
115115 −1.52009 −0.141749
116116 9.38228 0.871123
117117 0.238009 0.0220040
118118 8.57299 0.789208
119119 −1.00000 −0.0916698
120120 −0.132873 −0.0121296
121121 18.1928 1.65389
122122 5.28208 0.478217
123123 6.30231 0.568260
124124 14.0327 1.26017
125125 2.36661 0.211676
126126 −2.06644 −0.184093
127127 −2.38669 −0.211785 −0.105892 0.994378i 0.533770π-0.533770\pi
−0.105892 + 0.994378i 0.533770π0.533770\pi
128128 4.42539 0.391153
129129 −10.8627 −0.956409
130130 0.117060 0.0102669
131131 −13.0757 −1.14243 −0.571215 0.820801i 0.693528π-0.693528\pi
−0.571215 + 0.820801i 0.693528π0.693528\pi
132132 12.2657 1.06760
133133 7.89486 0.684571
134134 −11.2821 −0.974624
135135 0.238009 0.0204846
136136 0.558268 0.0478710
137137 −6.24566 −0.533603 −0.266801 0.963752i 0.585967π-0.585967\pi
−0.266801 + 0.963752i 0.585967π0.585967\pi
138138 13.1977 1.12346
139139 12.6046 1.06911 0.534555 0.845134i 0.320479π-0.320479\pi
0.534555 + 0.845134i 0.320479π0.320479\pi
140140 −0.540319 −0.0456653
141141 −6.18136 −0.520564
142142 −20.0970 −1.68650
143143 −1.28597 −0.107538
144144 −3.38669 −0.282225
145145 −0.983662 −0.0816887
146146 30.8704 2.55485
147147 −1.00000 −0.0824786
148148 12.8061 1.05265
149149 −2.09698 −0.171791 −0.0858955 0.996304i 0.527375π-0.527375\pi
−0.0858955 + 0.996304i 0.527375π0.527375\pi
150150 −10.2151 −0.834061
151151 8.60462 0.700234 0.350117 0.936706i 0.386142π-0.386142\pi
0.350117 + 0.936706i 0.386142π0.386142\pi
152152 −4.40745 −0.357491
153153 −1.00000 −0.0808452
154154 11.1650 0.899703
155155 −1.47122 −0.118171
156156 −0.540319 −0.0432602
157157 13.1084 1.04616 0.523081 0.852283i 0.324782π-0.324782\pi
0.523081 + 0.852283i 0.324782π0.324782\pi
158158 34.9030 2.77674
159159 −12.1814 −0.966045
160160 −1.93143 −0.152693
161161 6.38669 0.503342
162162 −2.06644 −0.162355
163163 −2.54032 −0.198973 −0.0994866 0.995039i 0.531720π-0.531720\pi
−0.0994866 + 0.995039i 0.531720π0.531720\pi
164164 −14.3072 −1.11721
165165 −1.28597 −0.100113
166166 −11.2821 −0.875660
167167 14.5038 1.12233 0.561167 0.827703i 0.310352π-0.310352\pi
0.561167 + 0.827703i 0.310352π0.310352\pi
168168 0.558268 0.0430713
169169 −12.9434 −0.995642
170170 −0.491831 −0.0377217
171171 7.89486 0.603735
172172 24.6601 1.88031
173173 −9.58439 −0.728688 −0.364344 0.931264i 0.618707π-0.618707\pi
−0.364344 + 0.931264i 0.618707π0.618707\pi
174174 8.54032 0.647440
175175 −4.94335 −0.373682
176176 18.2984 1.37930
177177 4.14869 0.311834
178178 13.3823 1.00304
179179 −10.3986 −0.777229 −0.388615 0.921400i 0.627046π-0.627046\pi
−0.388615 + 0.921400i 0.627046π0.627046\pi
180180 −0.540319 −0.0402730
181181 −18.9389 −1.40772 −0.703860 0.710339i 0.748542π-0.748542\pi
−0.703860 + 0.710339i 0.748542π0.748542\pi
182182 −0.491831 −0.0364569
183183 2.55613 0.188955
184184 −3.56548 −0.262851
185185 −1.34262 −0.0987114
186186 12.7734 0.936590
187187 5.40303 0.395109
188188 14.0327 1.02344
189189 −1.00000 −0.0727393
190190 3.88294 0.281698
191191 −11.2451 −0.813669 −0.406835 0.913502i 0.633368π-0.633368\pi
−0.406835 + 0.913502i 0.633368π0.633368\pi
192192 9.99559 0.721369
193193 3.10072 0.223195 0.111597 0.993753i 0.464403π-0.464403\pi
0.111597 + 0.993753i 0.464403π0.464403\pi
194194 4.27457 0.306896
195195 0.0566484 0.00405668
196196 2.27016 0.162154
197197 6.51957 0.464500 0.232250 0.972656i 0.425391π-0.425391\pi
0.232250 + 0.972656i 0.425391π0.425391\pi
198198 11.1650 0.793464
199199 −7.64104 −0.541659 −0.270830 0.962627i 0.587298π-0.587298\pi
−0.270830 + 0.962627i 0.587298π0.587298\pi
200200 2.75971 0.195141
201201 −5.45968 −0.385096
202202 −19.4881 −1.37118
203203 4.13287 0.290071
204204 2.27016 0.158943
205205 1.50001 0.104765
206206 17.4983 1.21916
207207 6.38669 0.443906
208208 −0.806065 −0.0558905
209209 −42.6562 −2.95059
210210 −0.491831 −0.0339396
211211 −2.29466 −0.157971 −0.0789854 0.996876i 0.525168π-0.525168\pi
−0.0789854 + 0.996876i 0.525168π0.525168\pi
212212 27.6536 1.89926
213213 −9.72543 −0.666375
214214 −31.9623 −2.18490
215215 −2.58543 −0.176325
216216 0.558268 0.0379853
217217 6.18136 0.419618
218218 −2.84196 −0.192482
219219 14.9389 1.00948
220220 2.91936 0.196823
221221 −0.238009 −0.0160102
222222 11.6569 0.782357
223223 −17.2729 −1.15668 −0.578339 0.815797i 0.696299π-0.696299\pi
−0.578339 + 0.815797i 0.696299π0.696299\pi
224224 8.11492 0.542201
225225 −4.94335 −0.329557
226226 −21.9384 −1.45932
227227 12.7783 0.848127 0.424064 0.905632i 0.360603π-0.360603\pi
0.424064 + 0.905632i 0.360603π0.360603\pi
228228 −17.9226 −1.18695
229229 18.8704 1.24699 0.623494 0.781828i 0.285712π-0.285712\pi
0.623494 + 0.781828i 0.285712π0.285712\pi
230230 3.14118 0.207123
231231 5.40303 0.355493
232232 −2.30725 −0.151478
233233 −9.09151 −0.595605 −0.297802 0.954628i 0.596254π-0.596254\pi
−0.297802 + 0.954628i 0.596254π0.596254\pi
234234 −0.491831 −0.0321520
235235 −1.47122 −0.0959719
236236 −9.41818 −0.613071
237237 16.8904 1.09715
238238 2.06644 0.133947
239239 16.8219 1.08812 0.544058 0.839047i 0.316887π-0.316887\pi
0.544058 + 0.839047i 0.316887π0.316887\pi
240240 −0.806065 −0.0520313
241241 −8.10125 −0.521847 −0.260924 0.965359i 0.584027π-0.584027\pi
−0.260924 + 0.965359i 0.584027π0.584027\pi
242242 −37.5942 −2.41665
243243 −1.00000 −0.0641500
244244 −5.80283 −0.371488
245245 −0.238009 −0.0152059
246246 −13.0233 −0.830337
247247 1.87905 0.119561
248248 −3.45085 −0.219129
249249 −5.45968 −0.345993
250250 −4.89045 −0.309299
251251 −2.68900 −0.169728 −0.0848642 0.996393i 0.527046π-0.527046\pi
−0.0848642 + 0.996393i 0.527046π0.527046\pi
252252 2.27016 0.143007
253253 −34.5075 −2.16947
254254 4.93195 0.309458
255255 −0.238009 −0.0149047
256256 10.8464 0.677898
257257 −20.5441 −1.28150 −0.640752 0.767748i 0.721377π-0.721377\pi
−0.640752 + 0.767748i 0.721377π0.721377\pi
258258 22.4471 1.39750
259259 5.64104 0.350517
260260 −0.128601 −0.00797549
261261 4.13287 0.255818
262262 27.0201 1.66931
263263 11.4554 0.706371 0.353185 0.935553i 0.385098π-0.385098\pi
0.353185 + 0.935553i 0.385098π0.385098\pi
264264 −3.01634 −0.185643
265265 −2.89928 −0.178101
266266 −16.3142 −1.00029
267267 6.47602 0.396326
268268 12.3943 0.757105
269269 −23.5201 −1.43405 −0.717023 0.697050i 0.754496π-0.754496\pi
−0.717023 + 0.697050i 0.754496π0.754496\pi
270270 −0.491831 −0.0299319
271271 27.4743 1.66895 0.834473 0.551049i 0.185772π-0.185772\pi
0.834473 + 0.551049i 0.185772π0.185772\pi
272272 3.38669 0.205349
273273 −0.238009 −0.0144050
274274 12.9063 0.779696
275275 26.7091 1.61062
276276 −14.4988 −0.872726
277277 9.01634 0.541739 0.270870 0.962616i 0.412689π-0.412689\pi
0.270870 + 0.962616i 0.412689π0.412689\pi
278278 −26.0466 −1.56217
279279 6.18136 0.370068
280280 0.132873 0.00794067
281281 9.78973 0.584006 0.292003 0.956417i 0.405678π-0.405678\pi
0.292003 + 0.956417i 0.405678π0.405678\pi
282282 12.7734 0.760644
283283 −12.1487 −0.722164 −0.361082 0.932534i 0.617593π-0.617593\pi
−0.361082 + 0.932534i 0.617593π0.617593\pi
284284 22.0783 1.31010
285285 1.87905 0.111305
286286 2.65738 0.157134
287287 −6.30231 −0.372014
288288 8.11492 0.478177
289289 1.00000 0.0588235
290290 2.03268 0.119363
291291 2.06857 0.121262
292292 −33.9138 −1.98465
293293 −27.7254 −1.61974 −0.809868 0.586612i 0.800462π-0.800462\pi
−0.809868 + 0.586612i 0.800462π0.800462\pi
294294 2.06644 0.120517
295295 0.987426 0.0574902
296296 −3.14921 −0.183044
297297 5.40303 0.313516
298298 4.33327 0.251019
299299 1.52009 0.0879092
300300 11.2222 0.647914
301301 10.8627 0.626116
302302 −17.7809 −1.02318
303303 −9.43077 −0.541784
304304 −26.7375 −1.53350
305305 0.608383 0.0348359
306306 2.06644 0.118130
307307 3.29518 0.188066 0.0940330 0.995569i 0.470024π-0.470024\pi
0.0940330 + 0.995569i 0.470024π0.470024\pi
308308 −12.2657 −0.698906
309309 8.46786 0.481720
310310 3.04019 0.172671
311311 7.18511 0.407430 0.203715 0.979030i 0.434698π-0.434698\pi
0.203715 + 0.979030i 0.434698π0.434698\pi
312312 0.132873 0.00752245
313313 −30.3697 −1.71660 −0.858299 0.513150i 0.828478π-0.828478\pi
−0.858299 + 0.513150i 0.828478π0.828478\pi
314314 −27.0876 −1.52864
315315 −0.238009 −0.0134103
316316 −38.3440 −2.15702
317317 −16.8746 −0.947774 −0.473887 0.880586i 0.657149π-0.657149\pi
−0.473887 + 0.880586i 0.657149π0.657149\pi
318318 25.1720 1.41158
319319 −22.3300 −1.25024
320320 2.37904 0.132993
321321 −15.4673 −0.863302
322322 −13.1977 −0.735479
323323 −7.89486 −0.439282
324324 2.27016 0.126120
325325 −1.17656 −0.0652640
326326 5.24941 0.290738
327327 −1.37530 −0.0760540
328328 3.51838 0.194270
329329 6.18136 0.340789
330330 2.65738 0.146284
331331 30.1764 1.65865 0.829323 0.558769i 0.188726π-0.188726\pi
0.829323 + 0.558769i 0.188726π0.188726\pi
332332 12.3943 0.680228
333333 5.64104 0.309127
334334 −29.9711 −1.63994
335335 −1.29945 −0.0709968
336336 3.38669 0.184759
337337 0.478732 0.0260782 0.0130391 0.999915i 0.495849π-0.495849\pi
0.0130391 + 0.999915i 0.495849π0.495849\pi
338338 26.7466 1.45482
339339 −10.6165 −0.576611
340340 0.540319 0.0293029
341341 −33.3981 −1.80861
342342 −16.3142 −0.882173
343343 1.00000 0.0539949
344344 −6.06430 −0.326965
345345 1.52009 0.0818390
346346 19.8055 1.06475
347347 −5.82240 −0.312563 −0.156281 0.987713i 0.549951π-0.549951\pi
−0.156281 + 0.987713i 0.549951π0.549951\pi
348348 −9.38228 −0.502943
349349 −0.416657 −0.0223031 −0.0111516 0.999938i 0.503550π-0.503550\pi
−0.0111516 + 0.999938i 0.503550π0.503550\pi
350350 10.2151 0.546021
351351 −0.238009 −0.0127040
352352 −43.8452 −2.33696
353353 1.37530 0.0731996 0.0365998 0.999330i 0.488347π-0.488347\pi
0.0365998 + 0.999330i 0.488347π0.488347\pi
354354 −8.57299 −0.455650
355355 −2.31474 −0.122854
356356 −14.7016 −0.779183
357357 1.00000 0.0529256
358358 21.4881 1.13568
359359 −5.41119 −0.285592 −0.142796 0.989752i 0.545609π-0.545609\pi
−0.142796 + 0.989752i 0.545609π0.545609\pi
360360 0.132873 0.00700302
361361 43.3289 2.28047
362362 39.1361 2.05695
363363 −18.1928 −0.954872
364364 0.540319 0.0283204
365365 3.55561 0.186109
366366 −5.28208 −0.276099
367367 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
368368 −21.6298 −1.12753
369369 −6.30231 −0.328085
370370 2.77444 0.144236
371371 12.1814 0.632425
372372 −14.0327 −0.727560
373373 16.8061 0.870185 0.435093 0.900386i 0.356716π-0.356716\pi
0.435093 + 0.900386i 0.356716π0.356716\pi
374374 −11.1650 −0.577330
375375 −2.36661 −0.122211
376376 −3.45085 −0.177964
377377 0.983662 0.0506612
378378 2.06644 0.106286
379379 −13.9673 −0.717453 −0.358727 0.933443i 0.616789π-0.616789\pi
−0.358727 + 0.933443i 0.616789π0.616789\pi
380380 −4.26575 −0.218828
381381 2.38669 0.122274
382382 23.2374 1.18893
383383 −19.7696 −1.01018 −0.505091 0.863066i 0.668541π-0.668541\pi
−0.505091 + 0.863066i 0.668541π0.668541\pi
384384 −4.42539 −0.225832
385385 1.28597 0.0655392
386386 −6.40745 −0.326130
387387 10.8627 0.552183
388388 −4.69599 −0.238403
389389 19.8224 1.00504 0.502518 0.864567i 0.332407π-0.332407\pi
0.502518 + 0.864567i 0.332407π0.332407\pi
390390 −0.117060 −0.00592758
391391 −6.38669 −0.322989
392392 −0.558268 −0.0281968
393393 13.0757 0.659582
394394 −13.4723 −0.678723
395395 4.02008 0.202272
396396 −12.2657 −0.616377
397397 34.2411 1.71851 0.859256 0.511546i 0.170927π-0.170927\pi
0.859256 + 0.511546i 0.170927π0.170927\pi
398398 15.7897 0.791468
399399 −7.89486 −0.395238
400400 16.7416 0.837081
401401 2.96396 0.148013 0.0740066 0.997258i 0.476421π-0.476421\pi
0.0740066 + 0.997258i 0.476421π0.476421\pi
402402 11.2821 0.562699
403403 1.47122 0.0732868
404404 21.4094 1.06515
405405 −0.238009 −0.0118268
406406 −8.54032 −0.423849
407407 −30.4787 −1.51077
408408 −0.558268 −0.0276384
409409 35.2128 1.74116 0.870582 0.492024i 0.163743π-0.163743\pi
0.870582 + 0.492024i 0.163743π0.163743\pi
410410 −3.09967 −0.153082
411411 6.24566 0.308076
412412 −19.2234 −0.947068
413413 −4.14869 −0.204143
414414 −13.1977 −0.648632
415415 −1.29945 −0.0637877
416416 1.93143 0.0946960
417417 −12.6046 −0.617251
418418 88.1463 4.31138
419419 −13.0391 −0.637003 −0.318502 0.947922i 0.603180π-0.603180\pi
−0.318502 + 0.947922i 0.603180π0.603180\pi
420420 0.540319 0.0263649
421421 −24.6763 −1.20265 −0.601324 0.799005i 0.705360π-0.705360\pi
−0.601324 + 0.799005i 0.705360π0.705360\pi
422422 4.74176 0.230825
423423 6.18136 0.300548
424424 −6.80046 −0.330259
425425 4.94335 0.239788
426426 20.0970 0.973702
427427 −2.55613 −0.123700
428428 35.1133 1.69727
429429 1.28597 0.0620873
430430 5.34262 0.257644
431431 0.265746 0.0128005 0.00640026 0.999980i 0.497963π-0.497963\pi
0.00640026 + 0.999980i 0.497963π0.497963\pi
432432 3.38669 0.162942
433433 15.9961 0.768724 0.384362 0.923182i 0.374421π-0.374421\pi
0.384362 + 0.923182i 0.374421π0.374421\pi
434434 −12.7734 −0.613142
435435 0.983662 0.0471630
436436 3.12214 0.149523
437437 50.4221 2.41202
438438 −30.8704 −1.47504
439439 6.82615 0.325794 0.162897 0.986643i 0.447916π-0.447916\pi
0.162897 + 0.986643i 0.447916π0.447916\pi
440440 −0.717916 −0.0342253
441441 1.00000 0.0476190
442442 0.491831 0.0233940
443443 21.3295 1.01340 0.506698 0.862124i 0.330866π-0.330866\pi
0.506698 + 0.862124i 0.330866π0.330866\pi
444444 −12.8061 −0.607749
445445 1.54135 0.0730671
446446 35.6933 1.69013
447447 2.09698 0.0991836
448448 −9.99559 −0.472247
449449 4.49559 0.212160 0.106080 0.994358i 0.466170π-0.466170\pi
0.106080 + 0.994358i 0.466170π0.466170\pi
450450 10.2151 0.481545
451451 34.0516 1.60343
452452 24.1012 1.13363
453453 −8.60462 −0.404280
454454 −26.4056 −1.23928
455455 −0.0566484 −0.00265572
456456 4.40745 0.206398
457457 4.69394 0.219573 0.109787 0.993955i 0.464983π-0.464983\pi
0.109787 + 0.993955i 0.464983π0.464983\pi
458458 −38.9944 −1.82209
459459 1.00000 0.0466760
460460 −3.45085 −0.160897
461461 12.9548 0.603363 0.301681 0.953409i 0.402452π-0.402452\pi
0.301681 + 0.953409i 0.402452π0.402452\pi
462462 −11.1650 −0.519444
463463 −22.7744 −1.05842 −0.529209 0.848492i 0.677511π-0.677511\pi
−0.529209 + 0.848492i 0.677511π0.677511\pi
464464 −13.9968 −0.649784
465465 1.47122 0.0682263
466466 18.7870 0.870292
467467 −40.4498 −1.87179 −0.935897 0.352273i 0.885409π-0.885409\pi
−0.935897 + 0.352273i 0.885409π0.885409\pi
468468 0.540319 0.0249763
469469 5.45968 0.252105
470470 3.04019 0.140233
471471 −13.1084 −0.604002
472472 2.31608 0.106606
473473 −58.6916 −2.69864
474474 −34.9030 −1.60315
475475 −39.0271 −1.79069
476476 −2.27016 −0.104053
477477 12.1814 0.557746
478478 −34.7613 −1.58995
479479 7.31865 0.334398 0.167199 0.985923i 0.446528π-0.446528\pi
0.167199 + 0.985923i 0.446528π0.446528\pi
480480 1.93143 0.0881572
481481 1.34262 0.0612182
482482 16.7407 0.762519
483483 −6.38669 −0.290605
484484 41.3005 1.87729
485485 0.492339 0.0223560
486486 2.06644 0.0937355
487487 25.0391 1.13463 0.567316 0.823500i 0.307982π-0.307982\pi
0.567316 + 0.823500i 0.307982π0.307982\pi
488488 1.42701 0.0645975
489489 2.54032 0.114877
490490 0.491831 0.0222187
491491 35.5109 1.60258 0.801292 0.598274i 0.204146π-0.204146\pi
0.801292 + 0.598274i 0.204146π0.204146\pi
492492 14.3072 0.645021
493493 −4.13287 −0.186135
494494 −3.88294 −0.174702
495495 1.28597 0.0578001
496496 −20.9344 −0.939982
497497 9.72543 0.436245
498498 11.2821 0.505562
499499 21.1246 0.945666 0.472833 0.881152i 0.343231π-0.343231\pi
0.472833 + 0.881152i 0.343231π0.343231\pi
500500 5.37258 0.240269
501501 −14.5038 −0.647980
502502 5.55666 0.248006
503503 31.4296 1.40138 0.700688 0.713468i 0.252876π-0.252876\pi
0.700688 + 0.713468i 0.252876π0.252876\pi
504504 −0.558268 −0.0248672
505505 −2.24461 −0.0998839
506506 71.3076 3.17001
507507 12.9434 0.574834
508508 −5.41818 −0.240393
509509 −3.19394 −0.141569 −0.0707843 0.997492i 0.522550π-0.522550\pi
−0.0707843 + 0.997492i 0.522550π0.522550\pi
510510 0.491831 0.0217786
511511 −14.9389 −0.660860
512512 −31.2641 −1.38169
513513 −7.89486 −0.348567
514514 42.4530 1.87252
515515 2.01543 0.0888104
516516 −24.6601 −1.08560
517517 −33.3981 −1.46885
518518 −11.6569 −0.512173
519519 9.58439 0.420708
520520 0.0316250 0.00138685
521521 19.2782 0.844593 0.422297 0.906458i 0.361224π-0.361224\pi
0.422297 + 0.906458i 0.361224π0.361224\pi
522522 −8.54032 −0.373800
523523 6.51192 0.284746 0.142373 0.989813i 0.454527π-0.454527\pi
0.142373 + 0.989813i 0.454527π0.454527\pi
524524 −29.6839 −1.29675
525525 4.94335 0.215746
526526 −23.6719 −1.03214
527527 −6.18136 −0.269264
528528 −18.2984 −0.796337
529529 17.7899 0.773473
530530 5.99117 0.260240
531531 −4.14869 −0.180038
532532 17.9226 0.777043
533533 −1.50001 −0.0649726
534534 −13.3823 −0.579108
535535 −3.68137 −0.159159
536536 −3.04796 −0.131652
537537 10.3986 0.448734
538538 48.6028 2.09541
539539 −5.40303 −0.232725
540540 0.540319 0.0232516
541541 −17.7265 −0.762121 −0.381060 0.924550i 0.624441π-0.624441\pi
−0.381060 + 0.924550i 0.624441π0.624441\pi
542542 −56.7739 −2.43865
543543 18.9389 0.812748
544544 −8.11492 −0.347925
545545 −0.327333 −0.0140214
546546 0.491831 0.0210484
547547 −15.2620 −0.652556 −0.326278 0.945274i 0.605795π-0.605795\pi
−0.326278 + 0.945274i 0.605795π0.605795\pi
548548 −14.1786 −0.605682
549549 −2.55613 −0.109093
550550 −55.1926 −2.35342
551551 32.6285 1.39002
552552 3.56548 0.151757
553553 −16.8904 −0.718255
554554 −18.6317 −0.791585
555555 1.34262 0.0569911
556556 28.6145 1.21353
557557 −33.0102 −1.39869 −0.699344 0.714785i 0.746524π-0.746524\pi
−0.699344 + 0.714785i 0.746524π0.746524\pi
558558 −12.7734 −0.540741
559559 2.58543 0.109352
560560 0.806065 0.0340625
561561 −5.40303 −0.228116
562562 −20.2298 −0.853345
563563 1.49131 0.0628510 0.0314255 0.999506i 0.489995π-0.489995\pi
0.0314255 + 0.999506i 0.489995π0.489995\pi
564564 −14.0327 −0.590882
565565 −2.52684 −0.106305
566566 25.1045 1.05522
567567 1.00000 0.0419961
568568 −5.42939 −0.227812
569569 0.242948 0.0101849 0.00509246 0.999987i 0.498379π-0.498379\pi
0.00509246 + 0.999987i 0.498379π0.498379\pi
570570 −3.88294 −0.162638
571571 −23.2505 −0.973001 −0.486501 0.873680i 0.661727π-0.661727\pi
−0.486501 + 0.873680i 0.661727π0.661727\pi
572572 −2.91936 −0.122065
573573 11.2451 0.469772
574574 13.0233 0.543583
575575 −31.5717 −1.31663
576576 −9.99559 −0.416483
577577 −10.5364 −0.438637 −0.219319 0.975653i 0.570383π-0.570383\pi
−0.219319 + 0.975653i 0.570383π0.570383\pi
578578 −2.06644 −0.0859524
579579 −3.10072 −0.128862
580580 −2.23307 −0.0927232
581581 5.45968 0.226506
582582 −4.27457 −0.177187
583583 −65.8163 −2.72583
584584 8.33992 0.345109
585585 −0.0566484 −0.00234212
586586 57.2928 2.36675
587587 43.8752 1.81092 0.905461 0.424430i 0.139525π-0.139525\pi
0.905461 + 0.424430i 0.139525π0.139525\pi
588588 −2.27016 −0.0936198
589589 48.8010 2.01081
590590 −2.04045 −0.0840041
591591 −6.51957 −0.268179
592592 −19.1045 −0.785190
593593 45.3175 1.86097 0.930483 0.366336i 0.119388π-0.119388\pi
0.930483 + 0.366336i 0.119388π0.119388\pi
594594 −11.1650 −0.458106
595595 0.238009 0.00975743
596596 −4.76047 −0.194996
597597 7.64104 0.312727
598598 −3.14118 −0.128452
599599 −7.25368 −0.296377 −0.148189 0.988959i 0.547344π-0.547344\pi
−0.148189 + 0.988959i 0.547344π0.547344\pi
600600 −2.75971 −0.112665
601601 −4.18458 −0.170693 −0.0853463 0.996351i 0.527200π-0.527200\pi
−0.0853463 + 0.996351i 0.527200π0.527200\pi
602602 −22.4471 −0.914876
603603 5.45968 0.222335
604604 19.5339 0.794821
605605 −4.33005 −0.176041
606606 19.4881 0.791649
607607 −34.6812 −1.40767 −0.703834 0.710365i 0.748530π-0.748530\pi
−0.703834 + 0.710365i 0.748530π0.748530\pi
608608 64.0662 2.59823
609609 −4.13287 −0.167472
610610 −1.25719 −0.0509019
611611 1.47122 0.0595192
612612 −2.27016 −0.0917658
613613 1.98352 0.0801136 0.0400568 0.999197i 0.487246π-0.487246\pi
0.0400568 + 0.999197i 0.487246π0.487246\pi
614614 −6.80929 −0.274800
615615 −1.50001 −0.0604862
616616 3.01634 0.121532
617617 −11.1808 −0.450123 −0.225062 0.974345i 0.572258π-0.572258\pi
−0.225062 + 0.974345i 0.572258π0.572258\pi
618618 −17.4983 −0.703884
619619 −40.8425 −1.64160 −0.820799 0.571217i 0.806472π-0.806472\pi
−0.820799 + 0.571217i 0.806472π0.806472\pi
620620 −3.33991 −0.134134
621621 −6.38669 −0.256289
622622 −14.8476 −0.595333
623623 −6.47602 −0.259456
624624 0.806065 0.0322684
625625 24.1535 0.966139
626626 62.7571 2.50828
627627 42.6562 1.70352
628628 29.7581 1.18748
629629 −5.64104 −0.224923
630630 0.491831 0.0195950
631631 11.8702 0.472546 0.236273 0.971687i 0.424074π-0.424074\pi
0.236273 + 0.971687i 0.424074π0.424074\pi
632632 9.42939 0.375081
633633 2.29466 0.0912045
634634 34.8704 1.38488
635635 0.568056 0.0225426
636636 −27.6536 −1.09654
637637 0.238009 0.00943027
638638 46.1436 1.82684
639639 9.72543 0.384732
640640 −1.05329 −0.0416348
641641 −37.2440 −1.47105 −0.735524 0.677499i 0.763064π-0.763064\pi
−0.735524 + 0.677499i 0.763064π0.763064\pi
642642 31.9623 1.26145
643643 44.7254 1.76380 0.881900 0.471437i 0.156265π-0.156265\pi
0.881900 + 0.471437i 0.156265π0.156265\pi
644644 14.4988 0.571333
645645 2.58543 0.101801
646646 16.3142 0.641875
647647 −4.67641 −0.183849 −0.0919244 0.995766i 0.529302π-0.529302\pi
−0.0919244 + 0.995766i 0.529302π0.529302\pi
648648 −0.558268 −0.0219308
649649 22.4155 0.879885
650650 2.43129 0.0953632
651651 −6.18136 −0.242267
652652 −5.76693 −0.225850
653653 −35.0511 −1.37165 −0.685827 0.727765i 0.740559π-0.740559\pi
−0.685827 + 0.727765i 0.740559π0.740559\pi
654654 2.84196 0.111129
655655 3.11214 0.121601
656656 21.3440 0.833343
657657 −14.9389 −0.582823
658658 −12.7734 −0.497959
659659 −50.0635 −1.95020 −0.975099 0.221771i 0.928816π-0.928816\pi
−0.975099 + 0.221771i 0.928816π0.928816\pi
660660 −2.91936 −0.113636
661661 −12.4221 −0.483163 −0.241582 0.970381i 0.577666π-0.577666\pi
−0.241582 + 0.970381i 0.577666π0.577666\pi
662662 −62.3577 −2.42360
663663 0.238009 0.00924352
664664 −3.04796 −0.118284
665665 −1.87905 −0.0728665
666666 −11.6569 −0.451694
667667 26.3954 1.02203
668668 32.9258 1.27394
669669 17.2729 0.667808
670670 2.68524 0.103740
671671 13.8109 0.533162
672672 −8.11492 −0.313040
673673 24.4270 0.941593 0.470796 0.882242i 0.343967π-0.343967\pi
0.470796 + 0.882242i 0.343967π0.343967\pi
674674 −0.989268 −0.0381052
675675 4.94335 0.190270
676676 −29.3835 −1.13013
677677 −0.375154 −0.0144183 −0.00720917 0.999974i 0.502295π-0.502295\pi
−0.00720917 + 0.999974i 0.502295π0.502295\pi
678678 21.9384 0.842540
679679 −2.06857 −0.0793845
680680 −0.132873 −0.00509544
681681 −12.7783 −0.489667
682682 69.0150 2.64272
683683 5.26589 0.201494 0.100747 0.994912i 0.467877π-0.467877\pi
0.100747 + 0.994912i 0.467877π0.467877\pi
684684 17.9226 0.685288
685685 1.48653 0.0567972
686686 −2.06644 −0.0788969
687687 −18.8704 −0.719949
688688 −36.7887 −1.40256
689689 2.89928 0.110454
690690 −3.14118 −0.119582
691691 −39.3491 −1.49691 −0.748455 0.663185i 0.769204π-0.769204\pi
−0.748455 + 0.663185i 0.769204π0.769204\pi
692692 −21.7581 −0.827119
693693 −5.40303 −0.205244
694694 12.0316 0.456714
695695 −3.00002 −0.113797
696696 2.30725 0.0874560
697697 6.30231 0.238717
698698 0.860996 0.0325892
699699 9.09151 0.343873
700700 −11.2222 −0.424159
701701 3.68526 0.139190 0.0695951 0.997575i 0.477829π-0.477829\pi
0.0695951 + 0.997575i 0.477829π0.477829\pi
702702 0.491831 0.0185630
703703 44.5353 1.67968
704704 54.0065 2.03545
705705 1.47122 0.0554094
706706 −2.84196 −0.106959
707707 9.43077 0.354681
708708 9.41818 0.353957
709709 15.9673 0.599665 0.299833 0.953992i 0.403069π-0.403069\pi
0.299833 + 0.953992i 0.403069π0.403069\pi
710710 4.78327 0.179513
711711 −16.8904 −0.633441
712712 3.61535 0.135491
713713 39.4785 1.47848
714714 −2.06644 −0.0773344
715715 0.306073 0.0114465
716716 −23.6065 −0.882217
717717 −16.8219 −0.628225
718718 11.1819 0.417304
719719 −24.2206 −0.903277 −0.451639 0.892201i 0.649160π-0.649160\pi
−0.451639 + 0.892201i 0.649160π0.649160\pi
720720 0.806065 0.0300403
721721 −8.46786 −0.315360
722722 −89.5364 −3.33220
723723 8.10125 0.301289
724724 −42.9944 −1.59787
725725 −20.4302 −0.758760
726726 37.5942 1.39525
727727 31.9869 1.18633 0.593164 0.805081i 0.297878π-0.297878\pi
0.593164 + 0.805081i 0.297878π0.297878\pi
728728 −0.132873 −0.00492460
729729 1.00000 0.0370370
730730 −7.34743 −0.271941
731731 −10.8627 −0.401772
732732 5.80283 0.214479
733733 −13.6850 −0.505466 −0.252733 0.967536i 0.581329π-0.581329\pi
−0.252733 + 0.967536i 0.581329π0.581329\pi
734734 0 0
735735 0.238009 0.00877911
736736 51.8275 1.91039
737737 −29.4988 −1.08660
738738 13.0233 0.479395
739739 5.27443 0.194023 0.0970115 0.995283i 0.469072π-0.469072\pi
0.0970115 + 0.995283i 0.469072π0.469072\pi
740740 −3.04796 −0.112045
741741 −1.87905 −0.0690287
742742 −25.1720 −0.924093
743743 −8.67641 −0.318307 −0.159153 0.987254i 0.550876π-0.550876\pi
−0.159153 + 0.987254i 0.550876π0.550876\pi
744744 3.45085 0.126514
745745 0.499100 0.0182856
746746 −34.7287 −1.27151
747747 5.45968 0.199759
748748 12.2657 0.448480
749749 15.4673 0.565164
750750 4.89045 0.178574
751751 3.27832 0.119628 0.0598138 0.998210i 0.480949π-0.480949\pi
0.0598138 + 0.998210i 0.480949π0.480949\pi
752752 −20.9344 −0.763398
753753 2.68900 0.0979928
754754 −2.03268 −0.0740257
755755 −2.04798 −0.0745336
756756 −2.27016 −0.0825649
757757 0.273398 0.00993681 0.00496841 0.999988i 0.498419π-0.498419\pi
0.00496841 + 0.999988i 0.498419π0.498419\pi
758758 28.8626 1.04834
759759 34.5075 1.25254
760760 1.04901 0.0380517
761761 13.5795 0.492255 0.246127 0.969237i 0.420842π-0.420842\pi
0.246127 + 0.969237i 0.420842π0.420842\pi
762762 −4.93195 −0.178666
763763 1.37530 0.0497891
764764 −25.5283 −0.923580
765765 0.238009 0.00860524
766766 40.8527 1.47607
767767 −0.987426 −0.0356539
768768 −10.8464 −0.391385
769769 19.6072 0.707053 0.353527 0.935424i 0.384982π-0.384982\pi
0.353527 + 0.935424i 0.384982π0.384982\pi
770770 −2.65738 −0.0957653
771771 20.5441 0.739877
772772 7.03914 0.253344
773773 −27.4634 −0.987791 −0.493896 0.869521i 0.664428π-0.664428\pi
−0.493896 + 0.869521i 0.664428π0.664428\pi
774774 −22.4471 −0.806845
775775 −30.5566 −1.09763
776776 1.15482 0.0414555
777777 −5.64104 −0.202371
778778 −40.9617 −1.46855
779779 −49.7559 −1.78269
780780 0.128601 0.00460465
781781 −52.5468 −1.88027
782782 13.1977 0.471949
783783 −4.13287 −0.147697
784784 −3.38669 −0.120953
785785 −3.11992 −0.111355
786786 −27.0201 −0.963775
787787 −32.5754 −1.16119 −0.580594 0.814193i 0.697180π-0.697180\pi
−0.580594 + 0.814193i 0.697180π0.697180\pi
788788 14.8005 0.527245
789789 −11.4554 −0.407823
790790 −8.30725 −0.295559
791791 10.6165 0.377481
792792 3.01634 0.107181
793793 −0.608383 −0.0216043
794794 −70.7571 −2.51107
795795 2.89928 0.102827
796796 −17.3464 −0.614826
797797 −12.4032 −0.439343 −0.219671 0.975574i 0.570499π-0.570499\pi
−0.219671 + 0.975574i 0.570499π0.570499\pi
798798 16.3142 0.577518
799799 −6.18136 −0.218681
800800 −40.1149 −1.41828
801801 −6.47602 −0.228819
802802 −6.12484 −0.216276
803803 80.7156 2.84839
804804 −12.3943 −0.437115
805805 −1.52009 −0.0535762
806806 −3.04019 −0.107086
807807 23.5201 0.827946
808808 −5.26489 −0.185218
809809 −45.1807 −1.58847 −0.794235 0.607611i 0.792128π-0.792128\pi
−0.794235 + 0.607611i 0.792128π0.792128\pi
810810 0.491831 0.0172812
811811 11.6928 0.410588 0.205294 0.978700i 0.434185π-0.434185\pi
0.205294 + 0.978700i 0.434185π0.434185\pi
812812 9.38228 0.329254
813813 −27.4743 −0.963566
814814 62.9824 2.20753
815815 0.604620 0.0211789
816816 −3.38669 −0.118558
817817 85.7596 3.00035
818818 −72.7651 −2.54417
819819 0.238009 0.00831672
820820 3.40526 0.118917
821821 39.1317 1.36571 0.682853 0.730556i 0.260739π-0.260739\pi
0.682853 + 0.730556i 0.260739π0.260739\pi
822822 −12.9063 −0.450158
823823 10.8415 0.377909 0.188955 0.981986i 0.439490π-0.439490\pi
0.188955 + 0.981986i 0.439490π0.439490\pi
824824 4.72733 0.164684
825825 −26.7091 −0.929891
826826 8.57299 0.298293
827827 29.8375 1.03755 0.518777 0.854910i 0.326388π-0.326388\pi
0.518777 + 0.854910i 0.326388π0.326388\pi
828828 14.4988 0.503869
829829 −37.8452 −1.31442 −0.657209 0.753708i 0.728263π-0.728263\pi
−0.657209 + 0.753708i 0.728263π0.728263\pi
830830 2.68524 0.0932061
831831 −9.01634 −0.312773
832832 −2.37904 −0.0824785
833833 −1.00000 −0.0346479
834834 26.0466 0.901922
835835 −3.45203 −0.119462
836836 −96.8364 −3.34916
837837 −6.18136 −0.213659
838838 26.9445 0.930784
839839 −39.4296 −1.36126 −0.680630 0.732627i 0.738294π-0.738294\pi
−0.680630 + 0.732627i 0.738294π0.738294\pi
840840 −0.132873 −0.00458455
841841 −11.9194 −0.411012
842842 50.9920 1.75730
843843 −9.78973 −0.337176
844844 −5.20924 −0.179309
845845 3.08064 0.105977
846846 −12.7734 −0.439158
847847 18.1928 0.625111
848848 −41.2546 −1.41669
849849 12.1487 0.416942
850850 −10.2151 −0.350376
851851 36.0276 1.23501
852852 −22.0783 −0.756389
853853 −2.44283 −0.0836411 −0.0418205 0.999125i 0.513316π-0.513316\pi
−0.0418205 + 0.999125i 0.513316π0.513316\pi
854854 5.28208 0.180749
855855 −1.87905 −0.0642622
856856 −8.63491 −0.295135
857857 32.4018 1.10683 0.553413 0.832907i 0.313325π-0.313325\pi
0.553413 + 0.832907i 0.313325π0.313325\pi
858858 −2.65738 −0.0907214
859859 −49.1414 −1.67668 −0.838342 0.545145i 0.816475π-0.816475\pi
−0.838342 + 0.545145i 0.816475π0.816475\pi
860860 −5.86933 −0.200143
861861 6.30231 0.214782
862862 −0.549147 −0.0187040
863863 12.9842 0.441987 0.220994 0.975275i 0.429070π-0.429070\pi
0.220994 + 0.975275i 0.429070π0.429070\pi
864864 −8.11492 −0.276075
865865 2.28117 0.0775623
866866 −33.0549 −1.12325
867867 −1.00000 −0.0339618
868868 14.0327 0.476300
869869 91.2596 3.09577
870870 −2.03268 −0.0689142
871871 1.29945 0.0440303
872872 −0.767783 −0.0260004
873873 −2.06857 −0.0700106
874874 −104.194 −3.52442
875875 2.36661 0.0800060
876876 33.9138 1.14584
877877 −20.2130 −0.682544 −0.341272 0.939965i 0.610858π-0.610858\pi
−0.341272 + 0.939965i 0.610858π0.610858\pi
878878 −14.1058 −0.476048
879879 27.7254 0.935155
880880 −4.35519 −0.146814
881881 24.7329 0.833274 0.416637 0.909073i 0.363209π-0.363209\pi
0.416637 + 0.909073i 0.363209π0.363209\pi
882882 −2.06644 −0.0695805
883883 1.87051 0.0629476 0.0314738 0.999505i 0.489980π-0.489980\pi
0.0314738 + 0.999505i 0.489980π0.489980\pi
884884 −0.540319 −0.0181729
885885 −0.987426 −0.0331920
886886 −44.0761 −1.48077
887887 −58.4459 −1.96242 −0.981211 0.192937i 0.938199π-0.938199\pi
−0.981211 + 0.192937i 0.938199π0.938199\pi
888888 3.14921 0.105681
889889 −2.38669 −0.0800472
890890 −3.18511 −0.106765
891891 −5.40303 −0.181008
892892 −39.2122 −1.31292
893893 48.8010 1.63306
894894 −4.33327 −0.144926
895895 2.47497 0.0827291
896896 4.42539 0.147842
897897 −1.52009 −0.0507544
898898 −9.28986 −0.310007
899899 25.5468 0.852033
900900 −11.2222 −0.374073
901901 −12.1814 −0.405820
902902 −70.3654 −2.34291
903903 −10.8627 −0.361488
904904 −5.92687 −0.197125
905905 4.50764 0.149839
906906 17.7809 0.590731
907907 −7.38684 −0.245276 −0.122638 0.992451i 0.539135π-0.539135\pi
−0.122638 + 0.992451i 0.539135π0.539135\pi
908908 29.0088 0.962692
909909 9.43077 0.312799
910910 0.117060 0.00388051
911911 −57.4106 −1.90210 −0.951048 0.309042i 0.899992π-0.899992\pi
−0.951048 + 0.309042i 0.899992π0.899992\pi
912912 26.7375 0.885367
913913 −29.4988 −0.976269
914914 −9.69974 −0.320839
915915 −0.608383 −0.0201125
916916 42.8387 1.41543
917917 −13.0757 −0.431798
918918 −2.06644 −0.0682026
919919 −39.6776 −1.30884 −0.654422 0.756130i 0.727088π-0.727088\pi
−0.654422 + 0.756130i 0.727088π0.727088\pi
920920 0.848619 0.0279781
921921 −3.29518 −0.108580
922922 −26.7702 −0.881629
923923 2.31474 0.0761907
924924 12.2657 0.403513
925925 −27.8857 −0.916875
926926 47.0619 1.54655
927927 −8.46786 −0.278121
928928 33.5380 1.10094
929929 5.89942 0.193554 0.0967768 0.995306i 0.469147π-0.469147\pi
0.0967768 + 0.995306i 0.469147π0.469147\pi
930930 −3.04019 −0.0996916
931931 7.89486 0.258744
932932 −20.6392 −0.676059
933933 −7.18511 −0.235230
934934 83.5870 2.73505
935935 −1.28597 −0.0420558
936936 −0.132873 −0.00434309
937937 −32.4825 −1.06116 −0.530578 0.847636i 0.678025π-0.678025\pi
−0.530578 + 0.847636i 0.678025π0.678025\pi
938938 −11.2821 −0.368373
939939 30.3697 0.991078
940940 −3.33991 −0.108936
941941 −11.2746 −0.367541 −0.183771 0.982969i 0.558830π-0.558830\pi
−0.183771 + 0.982969i 0.558830π0.558830\pi
942942 27.0876 0.882562
943943 −40.2509 −1.31075
944944 14.0503 0.457299
945945 0.238009 0.00774244
946946 121.282 3.94323
947947 17.6199 0.572570 0.286285 0.958145i 0.407580π-0.407580\pi
0.286285 + 0.958145i 0.407580π0.407580\pi
948948 38.3440 1.24536
949949 −3.55561 −0.115420
950950 80.6470 2.61653
951951 16.8746 0.547198
952952 0.558268 0.0180936
953953 −20.5026 −0.664144 −0.332072 0.943254i 0.607748π-0.607748\pi
−0.332072 + 0.943254i 0.607748π0.607748\pi
954954 −25.1720 −0.814974
955955 2.67645 0.0866078
956956 38.1883 1.23510
957957 22.3300 0.721828
958958 −15.1235 −0.488619
959959 −6.24566 −0.201683
960960 −2.37904 −0.0767833
961961 7.20922 0.232556
962962 −2.77444 −0.0894515
963963 15.4673 0.498428
964964 −18.3911 −0.592338
965965 −0.738001 −0.0237571
966966 13.1977 0.424629
967967 −36.0543 −1.15943 −0.579714 0.814820i 0.696836π-0.696836\pi
−0.579714 + 0.814820i 0.696836π0.696836\pi
968968 −10.1564 −0.326440
969969 7.89486 0.253620
970970 −1.01739 −0.0326664
971971 −1.13069 −0.0362854 −0.0181427 0.999835i 0.505775π-0.505775\pi
−0.0181427 + 0.999835i 0.505775π0.505775\pi
972972 −2.27016 −0.0728154
973973 12.6046 0.404086
974974 −51.7418 −1.65791
975975 1.17656 0.0376802
976976 8.65684 0.277099
977977 11.3062 0.361718 0.180859 0.983509i 0.442112π-0.442112\pi
0.180859 + 0.983509i 0.442112π0.442112\pi
978978 −5.24941 −0.167858
979979 34.9901 1.11829
980980 −0.540319 −0.0172599
981981 1.37530 0.0439098
982982 −73.3810 −2.34168
983983 −25.7140 −0.820151 −0.410075 0.912052i 0.634498π-0.634498\pi
−0.410075 + 0.912052i 0.634498π0.634498\pi
984984 −3.51838 −0.112162
985985 −1.55172 −0.0494418
986986 8.54032 0.271979
987987 −6.18136 −0.196755
988988 4.26575 0.135711
989989 69.3768 2.20605
990990 −2.65738 −0.0844571
991991 10.4356 0.331497 0.165748 0.986168i 0.446996π-0.446996\pi
0.165748 + 0.986168i 0.446996π0.446996\pi
992992 50.1613 1.59262
993993 −30.1764 −0.957620
994994 −20.0970 −0.637437
995995 1.81864 0.0576547
996996 −12.3943 −0.392730
997997 28.6480 0.907293 0.453646 0.891182i 0.350123π-0.350123\pi
0.453646 + 0.891182i 0.350123π0.350123\pi
998998 −43.6526 −1.38180
999999 −5.64104 −0.178475
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 357.2.a.h.1.1 4
3.2 odd 2 1071.2.a.j.1.4 4
4.3 odd 2 5712.2.a.bx.1.3 4
5.4 even 2 8925.2.a.bs.1.4 4
7.6 odd 2 2499.2.a.z.1.1 4
17.16 even 2 6069.2.a.s.1.1 4
21.20 even 2 7497.2.a.be.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
357.2.a.h.1.1 4 1.1 even 1 trivial
1071.2.a.j.1.4 4 3.2 odd 2
2499.2.a.z.1.1 4 7.6 odd 2
5712.2.a.bx.1.3 4 4.3 odd 2
6069.2.a.s.1.1 4 17.16 even 2
7497.2.a.be.1.4 4 21.20 even 2
8925.2.a.bs.1.4 4 5.4 even 2