Properties

Label 841.2.a.k.1.11
Level 841841
Weight 22
Character 841.1
Self dual yes
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(1,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.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: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 1212
Coefficient field: 12.12.32268092290502656.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1215x10+78x8169x6+148x436x2+1 x^{12} - 15x^{10} + 78x^{8} - 169x^{6} + 148x^{4} - 36x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 29)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.11
Root 0.572821-0.572821 of defining polynomial
Character χ\chi == 841.1

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) == q+2.26775q2+2.84057q3+3.14268q4+0.0578828q5+6.44169q61.56196q7+2.59131q8+5.06883q9+0.131264q103.97289q11+8.92699q12+0.404986q133.54213q14+0.164420q150.408929q16+5.16843q17+11.4948q183.45088q19+0.181907q204.43685q219.00950q22+0.230185q23+7.36078q244.99665q25+0.918405q26+5.87665q274.90874q28+0.372863q30+4.31832q316.10996q3211.2853q33+11.7207q340.0904106q35+15.9297q36+5.37070q377.82573q38+1.15039q39+0.149992q401.46294q4110.0617q42+6.48316q4312.4855q44+0.293398q45+0.522001q469.57399q471.16159q484.56028q4911.3311q50+14.6813q51+1.27274q521.78879q53+13.3268q540.229962q554.04752q569.80247q571.05216q59+0.516719q603.18937q61+9.79287q627.91731q6313.0380q64+0.0234417q6525.5921q66+10.8726q67+16.2427q68+0.653856q690.205028q70+13.4529q71+13.1349q727.01563q73+12.1794q7414.1933q7510.8450q76+6.20549q77+2.60879q78+4.78464q790.0236700q80+1.48654q813.31758q82+8.42345q8313.9436q84+0.299163q85+14.7022q8610.2950q881.13267q89+0.665353q900.632571q91+0.723397q92+12.2665q9321.7114q940.199747q9517.3558q9617.2131q9710.3416q9820.1379q99+O(q100)q+2.26775 q^{2} +2.84057 q^{3} +3.14268 q^{4} +0.0578828 q^{5} +6.44169 q^{6} -1.56196 q^{7} +2.59131 q^{8} +5.06883 q^{9} +0.131264 q^{10} -3.97289 q^{11} +8.92699 q^{12} +0.404986 q^{13} -3.54213 q^{14} +0.164420 q^{15} -0.408929 q^{16} +5.16843 q^{17} +11.4948 q^{18} -3.45088 q^{19} +0.181907 q^{20} -4.43685 q^{21} -9.00950 q^{22} +0.230185 q^{23} +7.36078 q^{24} -4.99665 q^{25} +0.918405 q^{26} +5.87665 q^{27} -4.90874 q^{28} +0.372863 q^{30} +4.31832 q^{31} -6.10996 q^{32} -11.2853 q^{33} +11.7207 q^{34} -0.0904106 q^{35} +15.9297 q^{36} +5.37070 q^{37} -7.82573 q^{38} +1.15039 q^{39} +0.149992 q^{40} -1.46294 q^{41} -10.0617 q^{42} +6.48316 q^{43} -12.4855 q^{44} +0.293398 q^{45} +0.522001 q^{46} -9.57399 q^{47} -1.16159 q^{48} -4.56028 q^{49} -11.3311 q^{50} +14.6813 q^{51} +1.27274 q^{52} -1.78879 q^{53} +13.3268 q^{54} -0.229962 q^{55} -4.04752 q^{56} -9.80247 q^{57} -1.05216 q^{59} +0.516719 q^{60} -3.18937 q^{61} +9.79287 q^{62} -7.91731 q^{63} -13.0380 q^{64} +0.0234417 q^{65} -25.5921 q^{66} +10.8726 q^{67} +16.2427 q^{68} +0.653856 q^{69} -0.205028 q^{70} +13.4529 q^{71} +13.1349 q^{72} -7.01563 q^{73} +12.1794 q^{74} -14.1933 q^{75} -10.8450 q^{76} +6.20549 q^{77} +2.60879 q^{78} +4.78464 q^{79} -0.0236700 q^{80} +1.48654 q^{81} -3.31758 q^{82} +8.42345 q^{83} -13.9436 q^{84} +0.299163 q^{85} +14.7022 q^{86} -10.2950 q^{88} -1.13267 q^{89} +0.665353 q^{90} -0.632571 q^{91} +0.723397 q^{92} +12.2665 q^{93} -21.7114 q^{94} -0.199747 q^{95} -17.3558 q^{96} -17.2131 q^{97} -10.3416 q^{98} -20.1379 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+8q4+8q5+24q6+10q7+10q9+12q13+16q16+24q2038q22+30q23+10q248q2512q28+2q304q33+6q34+44q35+16q36+58q96+O(q100) 12 q + 8 q^{4} + 8 q^{5} + 24 q^{6} + 10 q^{7} + 10 q^{9} + 12 q^{13} + 16 q^{16} + 24 q^{20} - 38 q^{22} + 30 q^{23} + 10 q^{24} - 8 q^{25} - 12 q^{28} + 2 q^{30} - 4 q^{33} + 6 q^{34} + 44 q^{35} + 16 q^{36}+ \cdots - 58 q^{96}+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 2.26775 1.60354 0.801770 0.597633i 0.203892π-0.203892\pi
0.801770 + 0.597633i 0.203892π0.203892\pi
33 2.84057 1.64000 0.820001 0.572361i 0.193973π-0.193973\pi
0.820001 + 0.572361i 0.193973π0.193973\pi
44 3.14268 1.57134
55 0.0578828 0.0258860 0.0129430 0.999916i 0.495880π-0.495880\pi
0.0129430 + 0.999916i 0.495880π0.495880\pi
66 6.44169 2.62981
77 −1.56196 −0.590365 −0.295183 0.955441i 0.595381π-0.595381\pi
−0.295183 + 0.955441i 0.595381π0.595381\pi
88 2.59131 0.916165
99 5.06883 1.68961
1010 0.131264 0.0415092
1111 −3.97289 −1.19787 −0.598935 0.800798i 0.704409π-0.704409\pi
−0.598935 + 0.800798i 0.704409π0.704409\pi
1212 8.92699 2.57700
1313 0.404986 0.112323 0.0561614 0.998422i 0.482114π-0.482114\pi
0.0561614 + 0.998422i 0.482114π0.482114\pi
1414 −3.54213 −0.946674
1515 0.164420 0.0424531
1616 −0.408929 −0.102232
1717 5.16843 1.25353 0.626764 0.779209i 0.284379π-0.284379\pi
0.626764 + 0.779209i 0.284379π0.284379\pi
1818 11.4948 2.70936
1919 −3.45088 −0.791687 −0.395844 0.918318i 0.629548π-0.629548\pi
−0.395844 + 0.918318i 0.629548π0.629548\pi
2020 0.181907 0.0406757
2121 −4.43685 −0.968201
2222 −9.00950 −1.92083
2323 0.230185 0.0479968 0.0239984 0.999712i 0.492360π-0.492360\pi
0.0239984 + 0.999712i 0.492360π0.492360\pi
2424 7.36078 1.50251
2525 −4.99665 −0.999330
2626 0.918405 0.180114
2727 5.87665 1.13096
2828 −4.90874 −0.927664
2929 0 0
3030 0.372863 0.0680752
3131 4.31832 0.775594 0.387797 0.921745i 0.373236π-0.373236\pi
0.387797 + 0.921745i 0.373236π0.373236\pi
3232 −6.10996 −1.08010
3333 −11.2853 −1.96451
3434 11.7207 2.01008
3535 −0.0904106 −0.0152822
3636 15.9297 2.65495
3737 5.37070 0.882937 0.441469 0.897277i 0.354458π-0.354458\pi
0.441469 + 0.897277i 0.354458π0.354458\pi
3838 −7.82573 −1.26950
3939 1.15039 0.184210
4040 0.149992 0.0237158
4141 −1.46294 −0.228473 −0.114237 0.993454i 0.536442π-0.536442\pi
−0.114237 + 0.993454i 0.536442π0.536442\pi
4242 −10.0617 −1.55255
4343 6.48316 0.988672 0.494336 0.869271i 0.335411π-0.335411\pi
0.494336 + 0.869271i 0.335411π0.335411\pi
4444 −12.4855 −1.88226
4545 0.293398 0.0437372
4646 0.522001 0.0769648
4747 −9.57399 −1.39651 −0.698255 0.715849i 0.746040π-0.746040\pi
−0.698255 + 0.715849i 0.746040π0.746040\pi
4848 −1.16159 −0.167661
4949 −4.56028 −0.651469
5050 −11.3311 −1.60247
5151 14.6813 2.05579
5252 1.27274 0.176497
5353 −1.78879 −0.245710 −0.122855 0.992425i 0.539205π-0.539205\pi
−0.122855 + 0.992425i 0.539205π0.539205\pi
5454 13.3268 1.81354
5555 −0.229962 −0.0310080
5656 −4.04752 −0.540872
5757 −9.80247 −1.29837
5858 0 0
5959 −1.05216 −0.136980 −0.0684900 0.997652i 0.521818π-0.521818\pi
−0.0684900 + 0.997652i 0.521818π0.521818\pi
6060 0.516719 0.0667082
6161 −3.18937 −0.408357 −0.204178 0.978934i 0.565452π-0.565452\pi
−0.204178 + 0.978934i 0.565452π0.565452\pi
6262 9.79287 1.24370
6363 −7.91731 −0.997487
6464 −13.0380 −1.62975
6565 0.0234417 0.00290759
6666 −25.5921 −3.15017
6767 10.8726 1.32830 0.664148 0.747601i 0.268795π-0.268795\pi
0.664148 + 0.747601i 0.268795π0.268795\pi
6868 16.2427 1.96972
6969 0.653856 0.0787150
7070 −0.205028 −0.0245056
7171 13.4529 1.59656 0.798281 0.602285i 0.205743π-0.205743\pi
0.798281 + 0.602285i 0.205743π0.205743\pi
7272 13.1349 1.54796
7373 −7.01563 −0.821118 −0.410559 0.911834i 0.634666π-0.634666\pi
−0.410559 + 0.911834i 0.634666π0.634666\pi
7474 12.1794 1.41582
7575 −14.1933 −1.63890
7676 −10.8450 −1.24401
7777 6.20549 0.707181
7878 2.60879 0.295388
7979 4.78464 0.538314 0.269157 0.963096i 0.413255π-0.413255\pi
0.269157 + 0.963096i 0.413255π0.413255\pi
8080 −0.0236700 −0.00264638
8181 1.48654 0.165171
8282 −3.31758 −0.366366
8383 8.42345 0.924594 0.462297 0.886725i 0.347025π-0.347025\pi
0.462297 + 0.886725i 0.347025π0.347025\pi
8484 −13.9436 −1.52137
8585 0.299163 0.0324488
8686 14.7022 1.58537
8787 0 0
8888 −10.2950 −1.09745
8989 −1.13267 −0.120063 −0.0600314 0.998196i 0.519120π-0.519120\pi
−0.0600314 + 0.998196i 0.519120π0.519120\pi
9090 0.665353 0.0701343
9191 −0.632571 −0.0663115
9292 0.723397 0.0754193
9393 12.2665 1.27198
9494 −21.7114 −2.23936
9595 −0.199747 −0.0204936
9696 −17.3558 −1.77136
9797 −17.2131 −1.74773 −0.873864 0.486170i 0.838393π-0.838393\pi
−0.873864 + 0.486170i 0.838393π0.838393\pi
9898 −10.3416 −1.04466
9999 −20.1379 −2.02393
100100 −15.7029 −1.57029
101101 −6.23958 −0.620862 −0.310431 0.950596i 0.600473π-0.600473\pi
−0.310431 + 0.950596i 0.600473π0.600473\pi
102102 33.2934 3.29654
103103 13.2105 1.30167 0.650833 0.759221i 0.274420π-0.274420\pi
0.650833 + 0.759221i 0.274420π0.274420\pi
104104 1.04944 0.102906
105105 −0.256818 −0.0250628
106106 −4.05653 −0.394005
107107 9.26822 0.895993 0.447996 0.894035i 0.352138π-0.352138\pi
0.447996 + 0.894035i 0.352138π0.352138\pi
108108 18.4684 1.77712
109109 −5.75542 −0.551269 −0.275634 0.961263i 0.588888π-0.588888\pi
−0.275634 + 0.961263i 0.588888π0.588888\pi
110110 −0.521495 −0.0497226
111111 15.2558 1.44802
112112 0.638731 0.0603544
113113 8.06227 0.758434 0.379217 0.925308i 0.376193π-0.376193\pi
0.379217 + 0.925308i 0.376193π0.376193\pi
114114 −22.2295 −2.08199
115115 0.0133237 0.00124245
116116 0 0
117117 2.05280 0.189782
118118 −2.38604 −0.219653
119119 −8.07288 −0.740039
120120 0.426063 0.0388940
121121 4.78382 0.434893
122122 −7.23268 −0.654816
123123 −4.15559 −0.374697
124124 13.5711 1.21872
125125 −0.578634 −0.0517546
126126 −17.9545 −1.59951
127127 17.5737 1.55941 0.779706 0.626146i 0.215369π-0.215369\pi
0.779706 + 0.626146i 0.215369π0.215369\pi
128128 −17.3469 −1.53327
129129 18.4158 1.62143
130130 0.0531599 0.00466243
131131 3.34792 0.292509 0.146255 0.989247i 0.453278π-0.453278\pi
0.146255 + 0.989247i 0.453278π0.453278\pi
132132 −35.4659 −3.08691
133133 5.39014 0.467385
134134 24.6562 2.12997
135135 0.340157 0.0292760
136136 13.3930 1.14844
137137 −5.52060 −0.471657 −0.235828 0.971795i 0.575780π-0.575780\pi
−0.235828 + 0.971795i 0.575780π0.575780\pi
138138 1.48278 0.126223
139139 −0.597509 −0.0506801 −0.0253400 0.999679i 0.508067π-0.508067\pi
−0.0253400 + 0.999679i 0.508067π0.508067\pi
140140 −0.284132 −0.0240135
141141 −27.1956 −2.29028
142142 30.5077 2.56015
143143 −1.60896 −0.134548
144144 −2.07279 −0.172733
145145 0 0
146146 −15.9097 −1.31669
147147 −12.9538 −1.06841
148148 16.8784 1.38739
149149 5.10908 0.418552 0.209276 0.977857i 0.432889π-0.432889\pi
0.209276 + 0.977857i 0.432889π0.432889\pi
150150 −32.1869 −2.62805
151151 −7.80026 −0.634776 −0.317388 0.948296i 0.602806π-0.602806\pi
−0.317388 + 0.948296i 0.602806π0.602806\pi
152152 −8.94230 −0.725316
153153 26.1979 2.11797
154154 14.0725 1.13399
155155 0.249957 0.0200770
156156 3.61530 0.289456
157157 18.8577 1.50501 0.752504 0.658588i 0.228846π-0.228846\pi
0.752504 + 0.658588i 0.228846π0.228846\pi
158158 10.8504 0.863208
159159 −5.08119 −0.402965
160160 −0.353662 −0.0279594
161161 −0.359539 −0.0283357
162162 3.37109 0.264858
163163 −2.26200 −0.177173 −0.0885867 0.996068i 0.528235π-0.528235\pi
−0.0885867 + 0.996068i 0.528235π0.528235\pi
164164 −4.59756 −0.359009
165165 −0.653222 −0.0508533
166166 19.1023 1.48262
167167 11.7349 0.908075 0.454037 0.890983i 0.349983π-0.349983\pi
0.454037 + 0.890983i 0.349983π0.349983\pi
168168 −11.4972 −0.887032
169169 −12.8360 −0.987384
170170 0.678426 0.0520329
171171 −17.4919 −1.33764
172172 20.3745 1.55354
173173 19.2889 1.46651 0.733254 0.679954i 0.238000π-0.238000\pi
0.733254 + 0.679954i 0.238000π0.238000\pi
174174 0 0
175175 7.80457 0.589970
176176 1.62463 0.122461
177177 −2.98874 −0.224648
178178 −2.56861 −0.192526
179179 0.910387 0.0680455 0.0340228 0.999421i 0.489168π-0.489168\pi
0.0340228 + 0.999421i 0.489168π0.489168\pi
180180 0.922056 0.0687260
181181 5.26219 0.391136 0.195568 0.980690i 0.437345π-0.437345\pi
0.195568 + 0.980690i 0.437345π0.437345\pi
182182 −1.43451 −0.106333
183183 −9.05962 −0.669706
184184 0.596479 0.0439730
185185 0.310871 0.0228557
186186 27.8173 2.03966
187187 −20.5336 −1.50156
188188 −30.0880 −2.19439
189189 −9.17909 −0.667680
190190 −0.452975 −0.0328623
191191 −10.3088 −0.745920 −0.372960 0.927847i 0.621657π-0.621657\pi
−0.372960 + 0.927847i 0.621657π0.621657\pi
192192 −37.0353 −2.67279
193193 −2.70997 −0.195068 −0.0975340 0.995232i 0.531095π-0.531095\pi
−0.0975340 + 0.995232i 0.531095π0.531095\pi
194194 −39.0350 −2.80255
195195 0.0665878 0.00476845
196196 −14.3315 −1.02368
197197 −14.7786 −1.05293 −0.526466 0.850196i 0.676483π-0.676483\pi
−0.526466 + 0.850196i 0.676483π0.676483\pi
198198 −45.6676 −3.24546
199199 15.0031 1.06354 0.531770 0.846889i 0.321527π-0.321527\pi
0.531770 + 0.846889i 0.321527π0.321527\pi
200200 −12.9478 −0.915551
201201 30.8843 2.17841
202202 −14.1498 −0.995577
203203 0 0
204204 46.1385 3.23034
205205 −0.0846792 −0.00591425
206206 29.9580 2.08727
207207 1.16677 0.0810959
208208 −0.165611 −0.0114830
209209 13.7100 0.948338
210210 −0.582397 −0.0401892
211211 −11.9730 −0.824257 −0.412128 0.911126i 0.635214π-0.635214\pi
−0.412128 + 0.911126i 0.635214π0.635214\pi
212212 −5.62161 −0.386093
213213 38.2138 2.61837
214214 21.0180 1.43676
215215 0.375263 0.0255927
216216 15.2282 1.03615
217217 −6.74505 −0.457884
218218 −13.0518 −0.883981
219219 −19.9284 −1.34664
220220 −0.722696 −0.0487241
221221 2.09314 0.140800
222222 34.5964 2.32196
223223 13.3713 0.895406 0.447703 0.894182i 0.352242π-0.352242\pi
0.447703 + 0.894182i 0.352242π0.352242\pi
224224 9.54351 0.637653
225225 −25.3272 −1.68848
226226 18.2832 1.21618
227227 −2.12231 −0.140862 −0.0704312 0.997517i 0.522438π-0.522438\pi
−0.0704312 + 0.997517i 0.522438π0.522438\pi
228228 −30.8060 −2.04018
229229 −27.3896 −1.80996 −0.904979 0.425456i 0.860114π-0.860114\pi
−0.904979 + 0.425456i 0.860114π0.860114\pi
230230 0.0302149 0.00199231
231231 17.6271 1.15978
232232 0 0
233233 17.4774 1.14498 0.572492 0.819910i 0.305977π-0.305977\pi
0.572492 + 0.819910i 0.305977π0.305977\pi
234234 4.65524 0.304322
235235 −0.554169 −0.0361500
236236 −3.30661 −0.215242
237237 13.5911 0.882837
238238 −18.3072 −1.18668
239239 17.2524 1.11597 0.557984 0.829852i 0.311575π-0.311575\pi
0.557984 + 0.829852i 0.311575π0.311575\pi
240240 −0.0672362 −0.00434008
241241 21.9867 1.41629 0.708143 0.706069i 0.249533π-0.249533\pi
0.708143 + 0.706069i 0.249533π0.249533\pi
242242 10.8485 0.697368
243243 −13.4073 −0.860081
244244 −10.0232 −0.641667
245245 −0.263962 −0.0168639
246246 −9.42382 −0.600841
247247 −1.39756 −0.0889245
248248 11.1901 0.710572
249249 23.9274 1.51634
250250 −1.31220 −0.0829906
251251 −9.77072 −0.616722 −0.308361 0.951269i 0.599781π-0.599781\pi
−0.308361 + 0.951269i 0.599781π0.599781\pi
252252 −24.8815 −1.56739
253253 −0.914498 −0.0574940
254254 39.8526 2.50058
255255 0.849793 0.0532161
256256 −13.2625 −0.828907
257257 −15.4022 −0.960766 −0.480383 0.877059i 0.659502π-0.659502\pi
−0.480383 + 0.877059i 0.659502π0.659502\pi
258258 41.7625 2.60002
259259 −8.38881 −0.521256
260260 0.0736698 0.00456880
261261 0 0
262262 7.59225 0.469050
263263 −30.9933 −1.91113 −0.955564 0.294784i 0.904752π-0.904752\pi
−0.955564 + 0.294784i 0.904752π0.904752\pi
264264 −29.2435 −1.79982
265265 −0.103540 −0.00636044
266266 12.2235 0.749470
267267 −3.21743 −0.196903
268268 34.1690 2.08720
269269 −13.8549 −0.844751 −0.422375 0.906421i 0.638804π-0.638804\pi
−0.422375 + 0.906421i 0.638804π0.638804\pi
270270 0.771390 0.0469453
271271 −26.8382 −1.63030 −0.815152 0.579247i 0.803347π-0.803347\pi
−0.815152 + 0.579247i 0.803347π0.803347\pi
272272 −2.11352 −0.128151
273273 −1.79686 −0.108751
274274 −12.5193 −0.756320
275275 19.8511 1.19707
276276 2.05486 0.123688
277277 −22.5563 −1.35528 −0.677639 0.735395i 0.736997π-0.736997\pi
−0.677639 + 0.735395i 0.736997π0.736997\pi
278278 −1.35500 −0.0812675
279279 21.8888 1.31045
280280 −0.234282 −0.0140010
281281 −3.30007 −0.196866 −0.0984328 0.995144i 0.531383π-0.531383\pi
−0.0984328 + 0.995144i 0.531383π0.531383\pi
282282 −61.6727 −3.67255
283283 −17.6686 −1.05029 −0.525144 0.851013i 0.675989π-0.675989\pi
−0.525144 + 0.851013i 0.675989π0.675989\pi
284284 42.2780 2.50874
285285 −0.567395 −0.0336096
286286 −3.64872 −0.215753
287287 2.28506 0.134883
288288 −30.9703 −1.82494
289289 9.71265 0.571332
290290 0 0
291291 −48.8951 −2.86628
292292 −22.0479 −1.29025
293293 13.5342 0.790675 0.395338 0.918536i 0.370628π-0.370628\pi
0.395338 + 0.918536i 0.370628π0.370628\pi
294294 −29.3759 −1.71324
295295 −0.0609022 −0.00354586
296296 13.9171 0.808916
297297 −23.3472 −1.35474
298298 11.5861 0.671165
299299 0.0932216 0.00539114
300300 −44.6051 −2.57527
301301 −10.1264 −0.583678
302302 −17.6890 −1.01789
303303 −17.7240 −1.01822
304304 1.41117 0.0809360
305305 −0.184610 −0.0105707
306306 59.4102 3.39625
307307 6.51865 0.372039 0.186020 0.982546i 0.440441π-0.440441\pi
0.186020 + 0.982546i 0.440441π0.440441\pi
308308 19.5019 1.11122
309309 37.5252 2.13474
310310 0.566839 0.0321943
311311 24.5460 1.39187 0.695937 0.718102i 0.254989π-0.254989\pi
0.695937 + 0.718102i 0.254989π0.254989\pi
312312 2.98101 0.168767
313313 1.97447 0.111604 0.0558018 0.998442i 0.482229π-0.482229\pi
0.0558018 + 0.998442i 0.482229π0.482229\pi
314314 42.7645 2.41334
315315 −0.458276 −0.0258209
316316 15.0366 0.845875
317317 −29.6808 −1.66704 −0.833519 0.552491i 0.813678π-0.813678\pi
−0.833519 + 0.552491i 0.813678π0.813678\pi
318318 −11.5229 −0.646170
319319 0 0
320320 −0.754675 −0.0421876
321321 26.3270 1.46943
322322 −0.815345 −0.0454374
323323 −17.8356 −0.992402
324324 4.67170 0.259539
325325 −2.02357 −0.112248
326326 −5.12964 −0.284105
327327 −16.3486 −0.904082
328328 −3.79093 −0.209319
329329 14.9542 0.824451
330330 −1.48134 −0.0815452
331331 −28.3740 −1.55958 −0.779788 0.626044i 0.784673π-0.784673\pi
−0.779788 + 0.626044i 0.784673π0.784673\pi
332332 26.4722 1.45285
333333 27.2231 1.49182
334334 26.6118 1.45613
335335 0.629335 0.0343842
336336 1.81436 0.0989814
337337 −4.01726 −0.218834 −0.109417 0.993996i 0.534898π-0.534898\pi
−0.109417 + 0.993996i 0.534898π0.534898\pi
338338 −29.1088 −1.58331
339339 22.9014 1.24383
340340 0.940173 0.0509881
341341 −17.1562 −0.929061
342342 −39.6673 −2.14496
343343 18.0567 0.974970
344344 16.7998 0.905787
345345 0.0378470 0.00203761
346346 43.7424 2.35160
347347 −3.55272 −0.190720 −0.0953601 0.995443i 0.530400π-0.530400\pi
−0.0953601 + 0.995443i 0.530400π0.530400\pi
348348 0 0
349349 3.34203 0.178895 0.0894473 0.995992i 0.471490π-0.471490\pi
0.0894473 + 0.995992i 0.471490π0.471490\pi
350350 17.6988 0.946040
351351 2.37996 0.127033
352352 24.2742 1.29382
353353 12.5154 0.666125 0.333063 0.942905i 0.391918π-0.391918\pi
0.333063 + 0.942905i 0.391918π0.391918\pi
354354 −6.77771 −0.360231
355355 0.778690 0.0413286
356356 −3.55962 −0.188659
357357 −22.9316 −1.21367
358358 2.06453 0.109114
359359 18.3959 0.970899 0.485450 0.874265i 0.338656π-0.338656\pi
0.485450 + 0.874265i 0.338656π0.338656\pi
360360 0.760284 0.0400705
361361 −7.09140 −0.373231
362362 11.9333 0.627202
363363 13.5888 0.713225
364364 −1.98797 −0.104198
365365 −0.406084 −0.0212554
366366 −20.5449 −1.07390
367367 9.83019 0.513132 0.256566 0.966527i 0.417409π-0.417409\pi
0.256566 + 0.966527i 0.417409π0.417409\pi
368368 −0.0941293 −0.00490683
369369 −7.41540 −0.386030
370370 0.704977 0.0366500
371371 2.79403 0.145059
372372 38.5496 1.99871
373373 22.1796 1.14842 0.574209 0.818709i 0.305310π-0.305310\pi
0.574209 + 0.818709i 0.305310π0.305310\pi
374374 −46.5650 −2.40782
375375 −1.64365 −0.0848777
376376 −24.8091 −1.27943
377377 0 0
378378 −20.8159 −1.07065
379379 8.70022 0.446900 0.223450 0.974715i 0.428268π-0.428268\pi
0.223450 + 0.974715i 0.428268π0.428268\pi
380380 −0.627740 −0.0322024
381381 49.9192 2.55744
382382 −23.3778 −1.19611
383383 5.08621 0.259893 0.129947 0.991521i 0.458519π-0.458519\pi
0.129947 + 0.991521i 0.458519π0.458519\pi
384384 −49.2752 −2.51456
385385 0.359191 0.0183061
386386 −6.14553 −0.312799
387387 32.8620 1.67047
388388 −54.0953 −2.74627
389389 29.8408 1.51299 0.756494 0.654000i 0.226910π-0.226910\pi
0.756494 + 0.654000i 0.226910π0.226910\pi
390390 0.151004 0.00764640
391391 1.18969 0.0601654
392392 −11.8171 −0.596853
393393 9.51001 0.479716
394394 −33.5142 −1.68842
395395 0.276949 0.0139348
396396 −63.2869 −3.18028
397397 −2.92259 −0.146680 −0.0733402 0.997307i 0.523366π-0.523366\pi
−0.0733402 + 0.997307i 0.523366π0.523366\pi
398398 34.0232 1.70543
399399 15.3111 0.766512
400400 2.04328 0.102164
401401 −20.4408 −1.02076 −0.510382 0.859948i 0.670496π-0.670496\pi
−0.510382 + 0.859948i 0.670496π0.670496\pi
402402 70.0377 3.49316
403403 1.74886 0.0871169
404404 −19.6090 −0.975585
405405 0.0860448 0.00427560
406406 0 0
407407 −21.3372 −1.05764
408408 38.0437 1.88344
409409 −33.6119 −1.66200 −0.831001 0.556271i 0.812232π-0.812232\pi
−0.831001 + 0.556271i 0.812232π0.812232\pi
410410 −0.192031 −0.00948374
411411 −15.6816 −0.773518
412412 41.5163 2.04536
413413 1.64344 0.0808683
414414 2.64593 0.130041
415415 0.487573 0.0239340
416416 −2.47445 −0.121320
417417 −1.69727 −0.0831154
418418 31.0907 1.52070
419419 −7.53000 −0.367865 −0.183932 0.982939i 0.558883π-0.558883\pi
−0.183932 + 0.982939i 0.558883π0.558883\pi
420420 −0.807095 −0.0393822
421421 −20.3755 −0.993041 −0.496521 0.868025i 0.665389π-0.665389\pi
−0.496521 + 0.868025i 0.665389π0.665389\pi
422422 −27.1518 −1.32173
423423 −48.5289 −2.35956
424424 −4.63531 −0.225111
425425 −25.8248 −1.25269
426426 86.6592 4.19865
427427 4.98167 0.241080
428428 29.1270 1.40791
429429 −4.57037 −0.220659
430430 0.851002 0.0410390
431431 11.8352 0.570081 0.285040 0.958516i 0.407993π-0.407993\pi
0.285040 + 0.958516i 0.407993π0.407993\pi
432432 −2.40313 −0.115621
433433 −17.0972 −0.821637 −0.410818 0.911717i 0.634757π-0.634757\pi
−0.410818 + 0.911717i 0.634757π0.634757\pi
434434 −15.2961 −0.734235
435435 0 0
436436 −18.0874 −0.866230
437437 −0.794341 −0.0379985
438438 −45.1925 −2.15938
439439 18.7510 0.894934 0.447467 0.894300i 0.352326π-0.352326\pi
0.447467 + 0.894300i 0.352326π0.352326\pi
440440 −0.595901 −0.0284085
441441 −23.1153 −1.10073
442442 4.74671 0.225778
443443 3.40383 0.161721 0.0808603 0.996725i 0.474233π-0.474233\pi
0.0808603 + 0.996725i 0.474233π0.474233\pi
444444 47.9442 2.27533
445445 −0.0655622 −0.00310794
446446 30.3227 1.43582
447447 14.5127 0.686427
448448 20.3648 0.962147
449449 0.139283 0.00657317 0.00328658 0.999995i 0.498954π-0.498954\pi
0.00328658 + 0.999995i 0.498954π0.498954\pi
450450 −57.4356 −2.70754
451451 5.81210 0.273681
452452 25.3371 1.19176
453453 −22.1572 −1.04104
454454 −4.81285 −0.225878
455455 −0.0366150 −0.00171654
456456 −25.4012 −1.18952
457457 32.0795 1.50062 0.750308 0.661088i 0.229905π-0.229905\pi
0.750308 + 0.661088i 0.229905π0.229905\pi
458458 −62.1128 −2.90234
459459 30.3730 1.41769
460460 0.0418722 0.00195230
461461 −0.725509 −0.0337903 −0.0168952 0.999857i 0.505378π-0.505378\pi
−0.0168952 + 0.999857i 0.505378π0.505378\pi
462462 39.9738 1.85975
463463 −9.14813 −0.425150 −0.212575 0.977145i 0.568185π-0.568185\pi
−0.212575 + 0.977145i 0.568185π0.568185\pi
464464 0 0
465465 0.710019 0.0329263
466466 39.6344 1.83603
467467 30.6641 1.41897 0.709483 0.704722i 0.248928π-0.248928\pi
0.709483 + 0.704722i 0.248928π0.248928\pi
468468 6.45130 0.298211
469469 −16.9825 −0.784180
470470 −1.25672 −0.0579680
471471 53.5666 2.46822
472472 −2.72648 −0.125496
473473 −25.7568 −1.18430
474474 30.8212 1.41566
475475 17.2429 0.791157
476476 −25.3705 −1.16285
477477 −9.06709 −0.415154
478478 39.1242 1.78950
479479 5.29729 0.242039 0.121020 0.992650i 0.461384π-0.461384\pi
0.121020 + 0.992650i 0.461384π0.461384\pi
480480 −1.00460 −0.0458535
481481 2.17506 0.0991740
482482 49.8602 2.27107
483483 −1.02130 −0.0464706
484484 15.0340 0.683364
485485 −0.996344 −0.0452417
486486 −30.4045 −1.37917
487487 −3.48158 −0.157766 −0.0788828 0.996884i 0.525135π-0.525135\pi
−0.0788828 + 0.996884i 0.525135π0.525135\pi
488488 −8.26463 −0.374122
489489 −6.42536 −0.290565
490490 −0.598599 −0.0270419
491491 5.85160 0.264079 0.132039 0.991244i 0.457847π-0.457847\pi
0.132039 + 0.991244i 0.457847π0.457847\pi
492492 −13.0597 −0.588776
493493 0 0
494494 −3.16931 −0.142594
495495 −1.16564 −0.0523915
496496 −1.76589 −0.0792908
497497 −21.0128 −0.942555
498498 54.2613 2.43151
499499 −23.7183 −1.06178 −0.530889 0.847441i 0.678142π-0.678142\pi
−0.530889 + 0.847441i 0.678142π0.678142\pi
500500 −1.81846 −0.0813240
501501 33.3338 1.48924
502502 −22.1575 −0.988939
503503 −19.3361 −0.862154 −0.431077 0.902315i 0.641866π-0.641866\pi
−0.431077 + 0.902315i 0.641866π0.641866\pi
504504 −20.5162 −0.913863
505505 −0.361165 −0.0160716
506506 −2.07385 −0.0921939
507507 −36.4615 −1.61931
508508 55.2284 2.45036
509509 38.8356 1.72136 0.860678 0.509149i 0.170040π-0.170040\pi
0.860678 + 0.509149i 0.170040π0.170040\pi
510510 1.92712 0.0853342
511511 10.9581 0.484759
512512 4.61786 0.204083
513513 −20.2796 −0.895368
514514 −34.9284 −1.54063
515515 0.764659 0.0336949
516516 57.8751 2.54781
517517 38.0364 1.67284
518518 −19.0237 −0.835854
519519 54.7915 2.40508
520520 0.0607446 0.00266383
521521 −33.3472 −1.46097 −0.730484 0.682930i 0.760706π-0.760706\pi
−0.730484 + 0.682930i 0.760706π0.760706\pi
522522 0 0
523523 31.8103 1.39097 0.695484 0.718542i 0.255190π-0.255190\pi
0.695484 + 0.718542i 0.255190π0.255190\pi
524524 10.5214 0.459632
525525 22.1694 0.967552
526526 −70.2849 −3.06457
527527 22.3189 0.972229
528528 4.61487 0.200836
529529 −22.9470 −0.997696
530530 −0.234804 −0.0101992
531531 −5.33324 −0.231443
532532 16.9395 0.734420
533533 −0.592471 −0.0256628
534534 −7.29632 −0.315742
535535 0.536471 0.0231937
536536 28.1741 1.21694
537537 2.58602 0.111595
538538 −31.4195 −1.35459
539539 18.1175 0.780375
540540 1.06900 0.0460026
541541 38.7402 1.66557 0.832785 0.553596i 0.186745π-0.186745\pi
0.832785 + 0.553596i 0.186745π0.186745\pi
542542 −60.8622 −2.61426
543543 14.9476 0.641464
544544 −31.5789 −1.35393
545545 −0.333140 −0.0142701
546546 −4.07483 −0.174387
547547 5.99056 0.256138 0.128069 0.991765i 0.459122π-0.459122\pi
0.128069 + 0.991765i 0.459122π0.459122\pi
548548 −17.3495 −0.741132
549549 −16.1664 −0.689964
550550 45.0173 1.91954
551551 0 0
552552 1.69434 0.0721159
553553 −7.47342 −0.317802
554554 −51.1520 −2.17324
555555 0.883050 0.0374834
556556 −1.87778 −0.0796356
557557 1.87739 0.0795478 0.0397739 0.999209i 0.487336π-0.487336\pi
0.0397739 + 0.999209i 0.487336π0.487336\pi
558558 49.6384 2.10136
559559 2.62559 0.111050
560560 0.0369716 0.00156233
561561 −58.3270 −2.46257
562562 −7.48372 −0.315682
563563 26.4739 1.11574 0.557872 0.829927i 0.311618π-0.311618\pi
0.557872 + 0.829927i 0.311618π0.311618\pi
564564 −85.4669 −3.59881
565565 0.466667 0.0196328
566566 −40.0679 −1.68418
567567 −2.32191 −0.0975110
568568 34.8605 1.46271
569569 −12.7851 −0.535980 −0.267990 0.963422i 0.586359π-0.586359\pi
−0.267990 + 0.963422i 0.586359π0.586359\pi
570570 −1.28671 −0.0538943
571571 −38.0544 −1.59253 −0.796263 0.604951i 0.793193π-0.793193\pi
−0.796263 + 0.604951i 0.793193π0.793193\pi
572572 −5.05645 −0.211421
573573 −29.2829 −1.22331
574574 5.18193 0.216290
575575 −1.15015 −0.0479647
576576 −66.0873 −2.75364
577577 0.102256 0.00425695 0.00212848 0.999998i 0.499322π-0.499322\pi
0.00212848 + 0.999998i 0.499322π0.499322\pi
578578 22.0258 0.916154
579579 −7.69786 −0.319912
580580 0 0
581581 −13.1571 −0.545848
582582 −110.882 −4.59619
583583 7.10668 0.294328
584584 −18.1796 −0.752279
585585 0.118822 0.00491269
586586 30.6921 1.26788
587587 −0.735311 −0.0303495 −0.0151748 0.999885i 0.504830π-0.504830\pi
−0.0151748 + 0.999885i 0.504830π0.504830\pi
588588 −40.7096 −1.67884
589589 −14.9020 −0.614028
590590 −0.138111 −0.00568593
591591 −41.9797 −1.72681
592592 −2.19624 −0.0902647
593593 44.7555 1.83789 0.918944 0.394388i 0.129043π-0.129043\pi
0.918944 + 0.394388i 0.129043π0.129043\pi
594594 −52.9457 −2.17239
595595 −0.467281 −0.0191566
596596 16.0562 0.657687
597597 42.6173 1.74421
598598 0.211403 0.00864491
599599 4.06004 0.165889 0.0829444 0.996554i 0.473568π-0.473568\pi
0.0829444 + 0.996554i 0.473568π0.473568\pi
600600 −36.7792 −1.50151
601601 −44.4331 −1.81246 −0.906232 0.422781i 0.861054π-0.861054\pi
−0.906232 + 0.422781i 0.861054π0.861054\pi
602602 −22.9642 −0.935950
603603 55.1112 2.24430
604604 −24.5137 −0.997449
605605 0.276901 0.0112576
606606 −40.1935 −1.63275
607607 −9.70174 −0.393781 −0.196891 0.980425i 0.563084π-0.563084\pi
−0.196891 + 0.980425i 0.563084π0.563084\pi
608608 21.0848 0.855100
609609 0 0
610610 −0.418648 −0.0169506
611611 −3.87733 −0.156860
612612 82.3315 3.32805
613613 −1.78505 −0.0720975 −0.0360488 0.999350i 0.511477π-0.511477\pi
−0.0360488 + 0.999350i 0.511477π0.511477\pi
614614 14.7827 0.596580
615615 −0.240537 −0.00969939
616616 16.0803 0.647894
617617 8.71009 0.350655 0.175327 0.984510i 0.443902π-0.443902\pi
0.175327 + 0.984510i 0.443902π0.443902\pi
618618 85.0978 3.42313
619619 14.2041 0.570911 0.285456 0.958392i 0.407855π-0.407855\pi
0.285456 + 0.958392i 0.407855π0.407855\pi
620620 0.785534 0.0315478
621621 1.35272 0.0542826
622622 55.6641 2.23193
623623 1.76919 0.0708810
624624 −0.470428 −0.0188322
625625 24.9498 0.997990
626626 4.47759 0.178961
627627 38.9441 1.55528
628628 59.2637 2.36488
629629 27.7581 1.10679
630630 −1.03925 −0.0414049
631631 16.5703 0.659653 0.329827 0.944042i 0.393010π-0.393010\pi
0.329827 + 0.944042i 0.393010π0.393010\pi
632632 12.3985 0.493185
633633 −34.0102 −1.35178
634634 −67.3085 −2.67316
635635 1.01721 0.0403669
636636 −15.9686 −0.633194
637637 −1.84685 −0.0731748
638638 0 0
639639 68.1903 2.69757
640640 −1.00409 −0.0396901
641641 −7.29754 −0.288236 −0.144118 0.989561i 0.546034π-0.546034\pi
−0.144118 + 0.989561i 0.546034π0.546034\pi
642642 59.7030 2.35629
643643 −33.8706 −1.33573 −0.667863 0.744284i 0.732791π-0.732791\pi
−0.667863 + 0.744284i 0.732791π0.732791\pi
644644 −1.12992 −0.0445250
645645 1.06596 0.0419722
646646 −40.4467 −1.59136
647647 33.4448 1.31485 0.657425 0.753520i 0.271646π-0.271646\pi
0.657425 + 0.753520i 0.271646π0.271646\pi
648648 3.85207 0.151324
649649 4.18013 0.164084
650650 −4.58895 −0.179993
651651 −19.1598 −0.750931
652652 −7.10874 −0.278400
653653 23.7557 0.929633 0.464817 0.885407i 0.346120π-0.346120\pi
0.464817 + 0.885407i 0.346120π0.346120\pi
654654 −37.0746 −1.44973
655655 0.193787 0.00757189
656656 0.598240 0.0233573
657657 −35.5610 −1.38737
658658 33.9123 1.32204
659659 −4.93124 −0.192094 −0.0960469 0.995377i 0.530620π-0.530620\pi
−0.0960469 + 0.995377i 0.530620π0.530620\pi
660660 −2.05287 −0.0799077
661661 −23.4731 −0.912998 −0.456499 0.889724i 0.650897π-0.650897\pi
−0.456499 + 0.889724i 0.650897π0.650897\pi
662662 −64.3450 −2.50084
663663 5.94571 0.230912
664664 21.8277 0.847081
665665 0.311997 0.0120987
666666 61.7352 2.39219
667667 0 0
668668 36.8790 1.42689
669669 37.9820 1.46847
670670 1.42717 0.0551365
671671 12.6710 0.489158
672672 27.1090 1.04575
673673 29.9293 1.15369 0.576846 0.816853i 0.304283π-0.304283\pi
0.576846 + 0.816853i 0.304283π0.304283\pi
674674 −9.11013 −0.350909
675675 −29.3636 −1.13020
676676 −40.3394 −1.55151
677677 22.0163 0.846154 0.423077 0.906094i 0.360950π-0.360950\pi
0.423077 + 0.906094i 0.360950π0.360950\pi
678678 51.9346 1.99454
679679 26.8862 1.03180
680680 0.775223 0.0297285
681681 −6.02856 −0.231015
682682 −38.9059 −1.48979
683683 −4.61710 −0.176668 −0.0883341 0.996091i 0.528154π-0.528154\pi
−0.0883341 + 0.996091i 0.528154π0.528154\pi
684684 −54.9715 −2.10189
685685 −0.319548 −0.0122093
686686 40.9480 1.56340
687687 −77.8022 −2.96834
688688 −2.65115 −0.101074
689689 −0.724436 −0.0275988
690690 0.0858274 0.00326739
691691 −35.7459 −1.35984 −0.679919 0.733287i 0.737985π-0.737985\pi
−0.679919 + 0.733287i 0.737985π0.737985\pi
692692 60.6188 2.30438
693693 31.4546 1.19486
694694 −8.05668 −0.305827
695695 −0.0345855 −0.00131190
696696 0 0
697697 −7.56111 −0.286398
698698 7.57887 0.286865
699699 49.6458 1.87778
700700 24.5272 0.927043
701701 −3.64465 −0.137656 −0.0688282 0.997629i 0.521926π-0.521926\pi
−0.0688282 + 0.997629i 0.521926π0.521926\pi
702702 5.39714 0.203702
703703 −18.5337 −0.699010
704704 51.7984 1.95223
705705 −1.57416 −0.0592861
706706 28.3817 1.06816
707707 9.74598 0.366535
708708 −9.39266 −0.352998
709709 −20.9910 −0.788334 −0.394167 0.919039i 0.628967π-0.628967\pi
−0.394167 + 0.919039i 0.628967π0.628967\pi
710710 1.76587 0.0662720
711711 24.2525 0.909541
712712 −2.93510 −0.109997
713713 0.994013 0.0372261
714714 −52.0030 −1.94616
715715 −0.0931312 −0.00348291
716716 2.86105 0.106923
717717 49.0067 1.83019
718718 41.7173 1.55688
719719 24.2529 0.904480 0.452240 0.891896i 0.350625π-0.350625\pi
0.452240 + 0.891896i 0.350625π0.350625\pi
720720 −0.119979 −0.00447136
721721 −20.6342 −0.768459
722722 −16.0815 −0.598491
723723 62.4547 2.32271
724724 16.5374 0.614607
725725 0 0
726726 30.8159 1.14368
727727 30.9357 1.14734 0.573672 0.819085i 0.305519π-0.305519\pi
0.573672 + 0.819085i 0.305519π0.305519\pi
728728 −1.63919 −0.0607523
729729 −42.5441 −1.57571
730730 −0.920897 −0.0340839
731731 33.5077 1.23933
732732 −28.4715 −1.05234
733733 −18.5100 −0.683681 −0.341841 0.939758i 0.611050π-0.611050\pi
−0.341841 + 0.939758i 0.611050π0.611050\pi
734734 22.2924 0.822827
735735 −0.749802 −0.0276569
736736 −1.40642 −0.0518413
737737 −43.1955 −1.59113
738738 −16.8163 −0.619015
739739 −34.0491 −1.25251 −0.626257 0.779616i 0.715414π-0.715414\pi
−0.626257 + 0.779616i 0.715414π0.715414\pi
740740 0.976968 0.0359140
741741 −3.96986 −0.145837
742742 6.33614 0.232607
743743 −34.8269 −1.27768 −0.638838 0.769342i 0.720584π-0.720584\pi
−0.638838 + 0.769342i 0.720584π0.720584\pi
744744 31.7862 1.16534
745745 0.295728 0.0108346
746746 50.2978 1.84153
747747 42.6970 1.56220
748748 −64.5304 −2.35947
749749 −14.4766 −0.528963
750750 −3.72738 −0.136105
751751 −48.5887 −1.77303 −0.886513 0.462703i 0.846880π-0.846880\pi
−0.886513 + 0.462703i 0.846880π0.846880\pi
752752 3.91508 0.142768
753753 −27.7544 −1.01143
754754 0 0
755755 −0.451501 −0.0164318
756756 −28.8469 −1.04915
757757 −30.0918 −1.09371 −0.546853 0.837229i 0.684174π-0.684174\pi
−0.546853 + 0.837229i 0.684174π0.684174\pi
758758 19.7299 0.716622
759759 −2.59769 −0.0942903
760760 −0.517605 −0.0187755
761761 −9.82865 −0.356288 −0.178144 0.984004i 0.557009π-0.557009\pi
−0.178144 + 0.984004i 0.557009π0.557009\pi
762762 113.204 4.10095
763763 8.98973 0.325450
764764 −32.3973 −1.17209
765765 1.51641 0.0548258
766766 11.5342 0.416749
767767 −0.426111 −0.0153860
768768 −37.6731 −1.35941
769769 29.9752 1.08093 0.540466 0.841366i 0.318248π-0.318248\pi
0.540466 + 0.841366i 0.318248π0.318248\pi
770770 0.814555 0.0293545
771771 −43.7511 −1.57566
772772 −8.51656 −0.306518
773773 −16.9149 −0.608388 −0.304194 0.952610i 0.598387π-0.598387\pi
−0.304194 + 0.952610i 0.598387π0.598387\pi
774774 74.5227 2.67866
775775 −21.5772 −0.775074
776776 −44.6045 −1.60121
777777 −23.8290 −0.854861
778778 67.6714 2.42614
779779 5.04844 0.180879
780780 0.209264 0.00749285
781781 −53.4467 −1.91247
782782 2.69792 0.0964776
783783 0 0
784784 1.86483 0.0666012
785785 1.09154 0.0389586
786786 21.5663 0.769244
787787 −19.9957 −0.712769 −0.356384 0.934339i 0.615991π-0.615991\pi
−0.356384 + 0.934339i 0.615991π0.615991\pi
788788 −46.4444 −1.65451
789789 −88.0386 −3.13426
790790 0.628049 0.0223450
791791 −12.5929 −0.447753
792792 −52.1834 −1.85426
793793 −1.29165 −0.0458678
794794 −6.62769 −0.235208
795795 −0.294114 −0.0104311
796796 47.1499 1.67118
797797 40.3008 1.42753 0.713764 0.700387i 0.246989π-0.246989\pi
0.713764 + 0.700387i 0.246989π0.246989\pi
798798 34.7216 1.22913
799799 −49.4825 −1.75056
800800 30.5293 1.07937
801801 −5.74131 −0.202859
802802 −46.3545 −1.63684
803803 27.8723 0.983592
804804 97.0593 3.42302
805805 −0.0208112 −0.000733497 0
806806 3.96597 0.139695
807807 −39.3559 −1.38539
808808 −16.1687 −0.568812
809809 50.1152 1.76196 0.880978 0.473157i 0.156886π-0.156886\pi
0.880978 + 0.473157i 0.156886π0.156886\pi
810810 0.195128 0.00685610
811811 −24.7764 −0.870017 −0.435009 0.900426i 0.643255π-0.643255\pi
−0.435009 + 0.900426i 0.643255π0.643255\pi
812812 0 0
813813 −76.2357 −2.67370
814814 −48.3873 −1.69597
815815 −0.130931 −0.00458631
816816 −6.00360 −0.210168
817817 −22.3726 −0.782719
818818 −76.2233 −2.66509
819819 −3.20640 −0.112041
820820 −0.266120 −0.00929330
821821 −35.5876 −1.24202 −0.621008 0.783804i 0.713277π-0.713277\pi
−0.621008 + 0.783804i 0.713277π0.713277\pi
822822 −35.5620 −1.24037
823823 −15.4039 −0.536947 −0.268474 0.963287i 0.586519π-0.586519\pi
−0.268474 + 0.963287i 0.586519π0.586519\pi
824824 34.2324 1.19254
825825 56.3885 1.96319
826826 3.72690 0.129675
827827 −41.4272 −1.44056 −0.720282 0.693682i 0.755987π-0.755987\pi
−0.720282 + 0.693682i 0.755987π0.755987\pi
828828 3.66677 0.127429
829829 −4.64043 −0.161169 −0.0805844 0.996748i 0.525679π-0.525679\pi
−0.0805844 + 0.996748i 0.525679π0.525679\pi
830830 1.10569 0.0383791
831831 −64.0728 −2.22266
832832 −5.28020 −0.183058
833833 −23.5695 −0.816634
834834 −3.84897 −0.133279
835835 0.679249 0.0235064
836836 43.0860 1.49016
837837 25.3773 0.877167
838838 −17.0761 −0.589886
839839 35.4256 1.22303 0.611514 0.791233i 0.290561π-0.290561\pi
0.611514 + 0.791233i 0.290561π0.290561\pi
840840 −0.665493 −0.0229617
841841 0 0
842842 −46.2065 −1.59238
843843 −9.37407 −0.322860
844844 −37.6273 −1.29519
845845 −0.742983 −0.0255594
846846 −110.051 −3.78364
847847 −7.47213 −0.256746
848848 0.731490 0.0251195
849849 −50.1888 −1.72248
850850 −58.5642 −2.00873
851851 1.23625 0.0423782
852852 120.094 4.11434
853853 −25.5045 −0.873256 −0.436628 0.899642i 0.643827π-0.643827\pi
−0.436628 + 0.899642i 0.643827π0.643827\pi
854854 11.2972 0.386581
855855 −1.01248 −0.0346262
856856 24.0168 0.820877
857857 −35.7869 −1.22246 −0.611228 0.791455i 0.709324π-0.709324\pi
−0.611228 + 0.791455i 0.709324π0.709324\pi
858858 −10.3644 −0.353836
859859 29.5758 1.00911 0.504556 0.863379i 0.331656π-0.331656\pi
0.504556 + 0.863379i 0.331656π0.331656\pi
860860 1.17933 0.0402149
861861 6.49086 0.221208
862862 26.8392 0.914147
863863 −40.2058 −1.36862 −0.684310 0.729191i 0.739896π-0.739896\pi
−0.684310 + 0.729191i 0.739896π0.739896\pi
864864 −35.9061 −1.22155
865865 1.11650 0.0379620
866866 −38.7720 −1.31753
867867 27.5894 0.936987
868868 −21.1975 −0.719491
869869 −19.0088 −0.644831
870870 0 0
871871 4.40323 0.149198
872872 −14.9140 −0.505053
873873 −87.2504 −2.95298
874874 −1.80137 −0.0609321
875875 0.903803 0.0305541
876876 −62.6285 −2.11602
877877 −52.1025 −1.75938 −0.879688 0.475552i 0.842248π-0.842248\pi
−0.879688 + 0.475552i 0.842248π0.842248\pi
878878 42.5224 1.43506
879879 38.4448 1.29671
880880 0.0940381 0.00317002
881881 −45.2608 −1.52487 −0.762437 0.647063i 0.775997π-0.775997\pi
−0.762437 + 0.647063i 0.775997π0.775997\pi
882882 −52.4196 −1.76506
883883 −33.8980 −1.14076 −0.570379 0.821382i 0.693204π-0.693204\pi
−0.570379 + 0.821382i 0.693204π0.693204\pi
884884 6.57806 0.221244
885885 −0.172997 −0.00581522
886886 7.71902 0.259326
887887 30.4108 1.02110 0.510548 0.859850i 0.329443π-0.329443\pi
0.510548 + 0.859850i 0.329443π0.329443\pi
888888 39.5325 1.32662
889889 −27.4494 −0.920622
890890 −0.148678 −0.00498371
891891 −5.90583 −0.197853
892892 42.0216 1.40699
893893 33.0387 1.10560
894894 32.9111 1.10071
895895 0.0526958 0.00176142
896896 27.0952 0.905188
897897 0.264802 0.00884149
898898 0.315858 0.0105403
899899 0 0
900900 −79.5951 −2.65317
901901 −9.24525 −0.308004
902902 13.1804 0.438859
903903 −28.7648 −0.957233
904904 20.8918 0.694851
905905 0.304591 0.0101249
906906 −50.2469 −1.66934
907907 15.8825 0.527368 0.263684 0.964609i 0.415062π-0.415062\pi
0.263684 + 0.964609i 0.415062π0.415062\pi
908908 −6.66973 −0.221343
909909 −31.6274 −1.04901
910910 −0.0830336 −0.00275254
911911 −24.9672 −0.827199 −0.413600 0.910459i 0.635729π-0.635729\pi
−0.413600 + 0.910459i 0.635729π0.635729\pi
912912 4.00852 0.132735
913913 −33.4654 −1.10754
914914 72.7482 2.40630
915915 −0.524396 −0.0173360
916916 −86.0768 −2.84406
917917 −5.22932 −0.172687
918918 68.8784 2.27332
919919 13.4638 0.444131 0.222065 0.975032i 0.428720π-0.428720\pi
0.222065 + 0.975032i 0.428720π0.428720\pi
920920 0.0345259 0.00113828
921921 18.5167 0.610145
922922 −1.64527 −0.0541841
923923 5.44822 0.179330
924924 55.3963 1.82241
925925 −26.8355 −0.882345
926926 −20.7456 −0.681744
927927 66.9616 2.19931
928928 0 0
929929 7.53667 0.247270 0.123635 0.992328i 0.460545π-0.460545\pi
0.123635 + 0.992328i 0.460545π0.460545\pi
930930 1.61014 0.0527987
931931 15.7370 0.515759
932932 54.9259 1.79916
933933 69.7245 2.28268
934934 69.5385 2.27537
935935 −1.18854 −0.0388694
936936 5.31944 0.173871
937937 −36.4635 −1.19121 −0.595605 0.803277i 0.703088π-0.703088\pi
−0.595605 + 0.803277i 0.703088π0.703088\pi
938938 −38.5121 −1.25746
939939 5.60861 0.183030
940940 −1.74158 −0.0568039
941941 −35.1767 −1.14673 −0.573364 0.819301i 0.694362π-0.694362\pi
−0.573364 + 0.819301i 0.694362π0.694362\pi
942942 121.475 3.95788
943943 −0.336747 −0.0109660
944944 0.430261 0.0140038
945945 −0.531311 −0.0172836
946946 −58.4100 −1.89907
947947 −10.3967 −0.337848 −0.168924 0.985629i 0.554029π-0.554029\pi
−0.168924 + 0.985629i 0.554029π0.554029\pi
948948 42.7125 1.38724
949949 −2.84123 −0.0922303
950950 39.1025 1.26865
951951 −84.3103 −2.73395
952952 −20.9193 −0.677998
953953 53.8152 1.74325 0.871623 0.490178i 0.163068π-0.163068\pi
0.871623 + 0.490178i 0.163068π0.163068\pi
954954 −20.5619 −0.665715
955955 −0.596703 −0.0193089
956956 54.2189 1.75356
957957 0 0
958958 12.0129 0.388119
959959 8.62295 0.278450
960960 −2.14371 −0.0691878
961961 −12.3521 −0.398454
962962 4.93248 0.159029
963963 46.9790 1.51388
964964 69.0970 2.22547
965965 −0.156861 −0.00504952
966966 −2.31604 −0.0745174
967967 −11.8947 −0.382508 −0.191254 0.981541i 0.561255π-0.561255\pi
−0.191254 + 0.981541i 0.561255π0.561255\pi
968968 12.3963 0.398433
969969 −50.6634 −1.62754
970970 −2.25946 −0.0725468
971971 −50.0900 −1.60746 −0.803732 0.594991i 0.797156π-0.797156\pi
−0.803732 + 0.594991i 0.797156π0.797156\pi
972972 −42.1350 −1.35148
973973 0.933285 0.0299197
974974 −7.89535 −0.252983
975975 −5.74809 −0.184086
976976 1.30423 0.0417473
977977 13.8116 0.441871 0.220936 0.975288i 0.429089π-0.429089\pi
0.220936 + 0.975288i 0.429089π0.429089\pi
978978 −14.5711 −0.465932
979979 4.49997 0.143820
980980 −0.829547 −0.0264989
981981 −29.1732 −0.931429
982982 13.2699 0.423461
983983 11.6553 0.371746 0.185873 0.982574i 0.440489π-0.440489\pi
0.185873 + 0.982574i 0.440489π0.440489\pi
984984 −10.7684 −0.343284
985985 −0.855428 −0.0272562
986986 0 0
987987 42.4784 1.35210
988988 −4.39208 −0.139731
989989 1.49232 0.0474531
990990 −2.64337 −0.0840118
991991 6.93524 0.220305 0.110153 0.993915i 0.464866π-0.464866\pi
0.110153 + 0.993915i 0.464866π0.464866\pi
992992 −26.3848 −0.837718
993993 −80.5983 −2.55771
994994 −47.6518 −1.51142
995995 0.868420 0.0275308
996996 75.1961 2.38268
997997 23.9700 0.759136 0.379568 0.925164i 0.376073π-0.376073\pi
0.379568 + 0.925164i 0.376073π0.376073\pi
998998 −53.7872 −1.70260
999999 31.5617 0.998568
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 841.2.a.k.1.11 12
3.2 odd 2 7569.2.a.bp.1.2 12
29.2 odd 28 841.2.e.i.236.2 12
29.3 odd 28 841.2.e.h.270.2 12
29.4 even 14 841.2.d.l.190.4 24
29.5 even 14 841.2.d.m.605.4 24
29.6 even 14 841.2.d.m.645.4 24
29.7 even 7 841.2.d.l.571.1 24
29.8 odd 28 841.2.e.e.267.2 12
29.9 even 14 841.2.d.k.574.1 24
29.10 odd 28 841.2.e.h.651.2 12
29.11 odd 28 841.2.e.e.63.2 12
29.12 odd 4 841.2.b.e.840.11 12
29.13 even 14 841.2.d.k.778.1 24
29.14 odd 28 29.2.e.a.22.1 yes 12
29.15 odd 28 841.2.e.i.196.2 12
29.16 even 7 841.2.d.k.778.4 24
29.17 odd 4 841.2.b.e.840.2 12
29.18 odd 28 841.2.e.f.63.1 12
29.19 odd 28 841.2.e.a.651.1 12
29.20 even 7 841.2.d.k.574.4 24
29.21 odd 28 841.2.e.f.267.1 12
29.22 even 14 841.2.d.l.571.4 24
29.23 even 7 841.2.d.m.645.1 24
29.24 even 7 841.2.d.m.605.1 24
29.25 even 7 841.2.d.l.190.1 24
29.26 odd 28 841.2.e.a.270.1 12
29.27 odd 28 29.2.e.a.4.1 12
29.28 even 2 inner 841.2.a.k.1.2 12
87.14 even 28 261.2.o.a.109.2 12
87.56 even 28 261.2.o.a.91.2 12
87.86 odd 2 7569.2.a.bp.1.11 12
116.27 even 28 464.2.y.d.33.2 12
116.43 even 28 464.2.y.d.225.2 12
145.14 odd 28 725.2.q.a.51.2 12
145.27 even 28 725.2.p.a.149.4 24
145.43 even 28 725.2.p.a.399.4 24
145.72 even 28 725.2.p.a.399.1 24
145.114 odd 28 725.2.q.a.526.2 12
145.143 even 28 725.2.p.a.149.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.e.a.4.1 12 29.27 odd 28
29.2.e.a.22.1 yes 12 29.14 odd 28
261.2.o.a.91.2 12 87.56 even 28
261.2.o.a.109.2 12 87.14 even 28
464.2.y.d.33.2 12 116.27 even 28
464.2.y.d.225.2 12 116.43 even 28
725.2.p.a.149.1 24 145.143 even 28
725.2.p.a.149.4 24 145.27 even 28
725.2.p.a.399.1 24 145.72 even 28
725.2.p.a.399.4 24 145.43 even 28
725.2.q.a.51.2 12 145.14 odd 28
725.2.q.a.526.2 12 145.114 odd 28
841.2.a.k.1.2 12 29.28 even 2 inner
841.2.a.k.1.11 12 1.1 even 1 trivial
841.2.b.e.840.2 12 29.17 odd 4
841.2.b.e.840.11 12 29.12 odd 4
841.2.d.k.574.1 24 29.9 even 14
841.2.d.k.574.4 24 29.20 even 7
841.2.d.k.778.1 24 29.13 even 14
841.2.d.k.778.4 24 29.16 even 7
841.2.d.l.190.1 24 29.25 even 7
841.2.d.l.190.4 24 29.4 even 14
841.2.d.l.571.1 24 29.7 even 7
841.2.d.l.571.4 24 29.22 even 14
841.2.d.m.605.1 24 29.24 even 7
841.2.d.m.605.4 24 29.5 even 14
841.2.d.m.645.1 24 29.23 even 7
841.2.d.m.645.4 24 29.6 even 14
841.2.e.a.270.1 12 29.26 odd 28
841.2.e.a.651.1 12 29.19 odd 28
841.2.e.e.63.2 12 29.11 odd 28
841.2.e.e.267.2 12 29.8 odd 28
841.2.e.f.63.1 12 29.18 odd 28
841.2.e.f.267.1 12 29.21 odd 28
841.2.e.h.270.2 12 29.3 odd 28
841.2.e.h.651.2 12 29.10 odd 28
841.2.e.i.196.2 12 29.15 odd 28
841.2.e.i.236.2 12 29.2 odd 28
7569.2.a.bp.1.2 12 3.2 odd 2
7569.2.a.bp.1.11 12 87.86 odd 2