Properties

Label 154.4.a.g.1.2
Level 154154
Weight 44
Character 154.1
Self dual yes
Analytic conductor 9.0869.086
Analytic rank 00
Dimension 22
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] = [154,4,Mod(1,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 154=2711 154 = 2 \cdot 7 \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 154.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: 9.086294140889.08629414088
Analytic rank: 00
Dimension: 22
Coefficient field: Q(37)\Q(\sqrt{37})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x9 x^{2} - x - 9 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 3.541383.54138 of defining polynomial
Character χ\chi == 154.1

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) == q2.00000q2+9.08276q3+4.00000q4+6.91724q518.1655q6+7.00000q78.00000q8+55.4966q913.8345q10+11.0000q11+36.3311q12+7.08276q1314.0000q14+62.8276q15+16.0000q1668.3311q17110.993q1894.5725q19+27.6689q20+63.5793q2122.0000q22+104.331q2372.6621q2477.1518q2514.1655q26+258.828q27+28.0000q28+48.4966q29125.655q30+38.8413q3132.0000q32+99.9104q33+136.662q34+48.4207q35+221.986q36+144.317q37+189.145q38+64.3311q3955.3379q40+409.986q41127.159q4216.8413q43+44.0000q44+383.883q45208.662q46535.449q47+145.324q48+49.0000q49+154.304q50620.635q51+28.3311q52155.807q53517.655q54+76.0896q5556.0000q56858.979q5796.9932q58+449.235q59+251.311q60529.096q6177.6826q62+388.476q63+64.0000q64+48.9932q65199.821q66296.814q67273.324q68+947.614q6996.8413q70942.414q71443.973q7287.1587q73288.635q74700.752q75378.290q76+77.0000q77128.662q781328.97q79+110.676q80+852.462q81819.973q82+611.001q83+254.317q84472.662q85+33.6826q86+440.483q8788.0000q88+1195.21q89767.766q90+49.5793q91+417.324q92+352.787q93+1070.90q94654.180q95290.648q961854.79q9798.0000q98+610.462q99+O(q100)q-2.00000 q^{2} +9.08276 q^{3} +4.00000 q^{4} +6.91724 q^{5} -18.1655 q^{6} +7.00000 q^{7} -8.00000 q^{8} +55.4966 q^{9} -13.8345 q^{10} +11.0000 q^{11} +36.3311 q^{12} +7.08276 q^{13} -14.0000 q^{14} +62.8276 q^{15} +16.0000 q^{16} -68.3311 q^{17} -110.993 q^{18} -94.5725 q^{19} +27.6689 q^{20} +63.5793 q^{21} -22.0000 q^{22} +104.331 q^{23} -72.6621 q^{24} -77.1518 q^{25} -14.1655 q^{26} +258.828 q^{27} +28.0000 q^{28} +48.4966 q^{29} -125.655 q^{30} +38.8413 q^{31} -32.0000 q^{32} +99.9104 q^{33} +136.662 q^{34} +48.4207 q^{35} +221.986 q^{36} +144.317 q^{37} +189.145 q^{38} +64.3311 q^{39} -55.3379 q^{40} +409.986 q^{41} -127.159 q^{42} -16.8413 q^{43} +44.0000 q^{44} +383.883 q^{45} -208.662 q^{46} -535.449 q^{47} +145.324 q^{48} +49.0000 q^{49} +154.304 q^{50} -620.635 q^{51} +28.3311 q^{52} -155.807 q^{53} -517.655 q^{54} +76.0896 q^{55} -56.0000 q^{56} -858.979 q^{57} -96.9932 q^{58} +449.235 q^{59} +251.311 q^{60} -529.096 q^{61} -77.6826 q^{62} +388.476 q^{63} +64.0000 q^{64} +48.9932 q^{65} -199.821 q^{66} -296.814 q^{67} -273.324 q^{68} +947.614 q^{69} -96.8413 q^{70} -942.414 q^{71} -443.973 q^{72} -87.1587 q^{73} -288.635 q^{74} -700.752 q^{75} -378.290 q^{76} +77.0000 q^{77} -128.662 q^{78} -1328.97 q^{79} +110.676 q^{80} +852.462 q^{81} -819.973 q^{82} +611.001 q^{83} +254.317 q^{84} -472.662 q^{85} +33.6826 q^{86} +440.483 q^{87} -88.0000 q^{88} +1195.21 q^{89} -767.766 q^{90} +49.5793 q^{91} +417.324 q^{92} +352.787 q^{93} +1070.90 q^{94} -654.180 q^{95} -290.648 q^{96} -1854.79 q^{97} -98.0000 q^{98} +610.462 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q4q2+6q3+8q4+26q512q6+14q716q8+38q952q10+22q11+24q12+2q1328q14+4q15+32q1688q1776q18+42q19++418q99+O(q100) 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} + 14 q^{7} - 16 q^{8} + 38 q^{9} - 52 q^{10} + 22 q^{11} + 24 q^{12} + 2 q^{13} - 28 q^{14} + 4 q^{15} + 32 q^{16} - 88 q^{17} - 76 q^{18} + 42 q^{19}+ \cdots + 418 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 −2.00000 −0.707107
33 9.08276 1.74798 0.873989 0.485945i 0.161525π-0.161525\pi
0.873989 + 0.485945i 0.161525π0.161525\pi
44 4.00000 0.500000
55 6.91724 0.618697 0.309348 0.950949i 0.399889π-0.399889\pi
0.309348 + 0.950949i 0.399889π0.399889\pi
66 −18.1655 −1.23601
77 7.00000 0.377964
88 −8.00000 −0.353553
99 55.4966 2.05543
1010 −13.8345 −0.437485
1111 11.0000 0.301511
1212 36.3311 0.873989
1313 7.08276 0.151108 0.0755540 0.997142i 0.475927π-0.475927\pi
0.0755540 + 0.997142i 0.475927π0.475927\pi
1414 −14.0000 −0.267261
1515 62.8276 1.08147
1616 16.0000 0.250000
1717 −68.3311 −0.974866 −0.487433 0.873161i 0.662067π-0.662067\pi
−0.487433 + 0.873161i 0.662067π0.662067\pi
1818 −110.993 −1.45341
1919 −94.5725 −1.14192 −0.570958 0.820979i 0.693428π-0.693428\pi
−0.570958 + 0.820979i 0.693428π0.693428\pi
2020 27.6689 0.309348
2121 63.5793 0.660674
2222 −22.0000 −0.213201
2323 104.331 0.945849 0.472925 0.881103i 0.343198π-0.343198\pi
0.472925 + 0.881103i 0.343198π0.343198\pi
2424 −72.6621 −0.618004
2525 −77.1518 −0.617215
2626 −14.1655 −0.106850
2727 258.828 1.84487
2828 28.0000 0.188982
2929 48.4966 0.310538 0.155269 0.987872i 0.450376π-0.450376\pi
0.155269 + 0.987872i 0.450376π0.450376\pi
3030 −125.655 −0.764714
3131 38.8413 0.225036 0.112518 0.993650i 0.464108π-0.464108\pi
0.112518 + 0.993650i 0.464108π0.464108\pi
3232 −32.0000 −0.176777
3333 99.9104 0.527035
3434 136.662 0.689334
3535 48.4207 0.233845
3636 221.986 1.02771
3737 144.317 0.641233 0.320617 0.947209i 0.396110π-0.396110\pi
0.320617 + 0.947209i 0.396110π0.396110\pi
3838 189.145 0.807457
3939 64.3311 0.264134
4040 −55.3379 −0.218742
4141 409.986 1.56169 0.780843 0.624728i 0.214790π-0.214790\pi
0.780843 + 0.624728i 0.214790π0.214790\pi
4242 −127.159 −0.467167
4343 −16.8413 −0.0597274 −0.0298637 0.999554i 0.509507π-0.509507\pi
−0.0298637 + 0.999554i 0.509507π0.509507\pi
4444 44.0000 0.150756
4545 383.883 1.27169
4646 −208.662 −0.668816
4747 −535.449 −1.66177 −0.830885 0.556444i 0.812165π-0.812165\pi
−0.830885 + 0.556444i 0.812165π0.812165\pi
4848 145.324 0.436995
4949 49.0000 0.142857
5050 154.304 0.436437
5151 −620.635 −1.70404
5252 28.3311 0.0755540
5353 −155.807 −0.403807 −0.201903 0.979405i 0.564713π-0.564713\pi
−0.201903 + 0.979405i 0.564713π0.564713\pi
5454 −517.655 −1.30452
5555 76.0896 0.186544
5656 −56.0000 −0.133631
5757 −858.979 −1.99605
5858 −96.9932 −0.219583
5959 449.235 0.991277 0.495639 0.868529i 0.334934π-0.334934\pi
0.495639 + 0.868529i 0.334934π0.334934\pi
6060 251.311 0.540734
6161 −529.096 −1.11056 −0.555278 0.831665i 0.687388π-0.687388\pi
−0.555278 + 0.831665i 0.687388π0.687388\pi
6262 −77.6826 −0.159124
6363 388.476 0.776879
6464 64.0000 0.125000
6565 48.9932 0.0934900
6666 −199.821 −0.372670
6767 −296.814 −0.541218 −0.270609 0.962689i 0.587225π-0.587225\pi
−0.270609 + 0.962689i 0.587225π0.587225\pi
6868 −273.324 −0.487433
6969 947.614 1.65332
7070 −96.8413 −0.165354
7171 −942.414 −1.57527 −0.787634 0.616144i 0.788694π-0.788694\pi
−0.787634 + 0.616144i 0.788694π0.788694\pi
7272 −443.973 −0.726704
7373 −87.1587 −0.139742 −0.0698709 0.997556i 0.522259π-0.522259\pi
−0.0698709 + 0.997556i 0.522259π0.522259\pi
7474 −288.635 −0.453420
7575 −700.752 −1.07888
7676 −378.290 −0.570958
7777 77.0000 0.113961
7878 −128.662 −0.186771
7979 −1328.97 −1.89266 −0.946331 0.323198i 0.895242π-0.895242\pi
−0.946331 + 0.323198i 0.895242π0.895242\pi
8080 110.676 0.154674
8181 852.462 1.16936
8282 −819.973 −1.10428
8383 611.001 0.808024 0.404012 0.914754i 0.367615π-0.367615\pi
0.404012 + 0.914754i 0.367615π0.367615\pi
8484 254.317 0.330337
8585 −472.662 −0.603146
8686 33.6826 0.0422336
8787 440.483 0.542813
8888 −88.0000 −0.106600
8989 1195.21 1.42351 0.711756 0.702427i 0.247900π-0.247900\pi
0.711756 + 0.702427i 0.247900π0.247900\pi
9090 −767.766 −0.899218
9191 49.5793 0.0571135
9292 417.324 0.472925
9393 352.787 0.393358
9494 1070.90 1.17505
9595 −654.180 −0.706500
9696 −290.648 −0.309002
9797 −1854.79 −1.94150 −0.970748 0.240102i 0.922819π-0.922819\pi
−0.970748 + 0.240102i 0.922819π0.922819\pi
9898 −98.0000 −0.101015
9999 610.462 0.619735
100100 −308.607 −0.308607
101101 −1434.95 −1.41369 −0.706844 0.707370i 0.749882π-0.749882\pi
−0.706844 + 0.707370i 0.749882π0.749882\pi
102102 1241.27 1.20494
103103 568.745 0.544079 0.272040 0.962286i 0.412302π-0.412302\pi
0.272040 + 0.962286i 0.412302π0.412302\pi
104104 −56.6621 −0.0534248
105105 439.793 0.408757
106106 311.614 0.285534
107107 1783.71 1.61157 0.805784 0.592209i 0.201744π-0.201744\pi
0.805784 + 0.592209i 0.201744π0.201744\pi
108108 1035.31 0.922433
109109 −529.587 −0.465369 −0.232684 0.972552i 0.574751π-0.574751\pi
−0.232684 + 0.972552i 0.574751π0.574751\pi
110110 −152.179 −0.131907
111111 1310.80 1.12086
112112 112.000 0.0944911
113113 1995.09 1.66091 0.830453 0.557089i 0.188082π-0.188082\pi
0.830453 + 0.557089i 0.188082π0.188082\pi
114114 1717.96 1.41142
115115 721.683 0.585194
116116 193.986 0.155269
117117 393.069 0.310592
118118 −898.469 −0.700939
119119 −478.317 −0.368465
120120 −502.621 −0.382357
121121 121.000 0.0909091
122122 1058.19 0.785281
123123 3723.81 2.72979
124124 155.365 0.112518
125125 −1398.33 −1.00057
126126 −776.952 −0.549336
127127 −1150.65 −0.803965 −0.401982 0.915647i 0.631679π-0.631679\pi
−0.401982 + 0.915647i 0.631679π0.631679\pi
128128 −128.000 −0.0883883
129129 −152.966 −0.104402
130130 −97.9863 −0.0661074
131131 −2230.85 −1.48786 −0.743932 0.668255i 0.767041π-0.767041\pi
−0.743932 + 0.668255i 0.767041π0.767041\pi
132132 399.642 0.263518
133133 −662.007 −0.431604
134134 593.628 0.382699
135135 1790.37 1.14141
136136 546.648 0.344667
137137 656.594 0.409464 0.204732 0.978818i 0.434368π-0.434368\pi
0.204732 + 0.978818i 0.434368π0.434368\pi
138138 −1895.23 −1.16908
139139 1012.17 0.617636 0.308818 0.951121i 0.400067π-0.400067\pi
0.308818 + 0.951121i 0.400067π0.400067\pi
140140 193.683 0.116923
141141 −4863.35 −2.90474
142142 1884.83 1.11388
143143 77.9104 0.0455608
144144 887.945 0.513857
145145 335.462 0.192128
146146 174.317 0.0988124
147147 445.055 0.249711
148148 577.269 0.320617
149149 −786.677 −0.432531 −0.216265 0.976335i 0.569388π-0.569388\pi
−0.216265 + 0.976335i 0.569388π0.569388\pi
150150 1401.50 0.762882
151151 205.573 0.110790 0.0553950 0.998465i 0.482358π-0.482358\pi
0.0553950 + 0.998465i 0.482358π0.482358\pi
152152 756.580 0.403729
153153 −3792.14 −2.00377
154154 −154.000 −0.0805823
155155 268.675 0.139229
156156 257.324 0.132067
157157 −3284.08 −1.66941 −0.834707 0.550695i 0.814363π-0.814363\pi
−0.834707 + 0.550695i 0.814363π0.814363\pi
158158 2657.93 1.33831
159159 −1415.16 −0.705845
160160 −221.352 −0.109371
161161 730.317 0.357497
162162 −1704.92 −0.826861
163163 −1403.88 −0.674601 −0.337301 0.941397i 0.609514π-0.609514\pi
−0.337301 + 0.941397i 0.609514π0.609514\pi
164164 1639.95 0.780843
165165 691.104 0.326075
166166 −1222.00 −0.571360
167167 4161.31 1.92822 0.964108 0.265512i 0.0855409π-0.0855409\pi
0.964108 + 0.265512i 0.0855409π0.0855409\pi
168168 −508.635 −0.233583
169169 −2146.83 −0.977166
170170 945.324 0.426489
171171 −5248.45 −2.34713
172172 −67.3653 −0.0298637
173173 −2693.66 −1.18379 −0.591894 0.806016i 0.701620π-0.701620\pi
−0.591894 + 0.806016i 0.701620π0.701620\pi
174174 −880.966 −0.383827
175175 −540.063 −0.233285
176176 176.000 0.0753778
177177 4080.29 1.73273
178178 −2390.43 −1.00657
179179 1877.74 0.784071 0.392035 0.919950i 0.371771π-0.371771\pi
0.392035 + 0.919950i 0.371771π0.371771\pi
180180 1535.53 0.635843
181181 639.291 0.262531 0.131265 0.991347i 0.458096π-0.458096\pi
0.131265 + 0.991347i 0.458096π0.458096\pi
182182 −99.1587 −0.0403853
183183 −4805.66 −1.94123
184184 −834.648 −0.334408
185185 998.277 0.396729
186186 −705.573 −0.278146
187187 −751.642 −0.293933
188188 −2141.79 −0.830885
189189 1811.79 0.697294
190190 1308.36 0.499571
191191 3705.56 1.40379 0.701897 0.712278i 0.252337π-0.252337\pi
0.701897 + 0.712278i 0.252337π0.252337\pi
192192 581.297 0.218497
193193 2147.38 0.800891 0.400445 0.916321i 0.368855π-0.368855\pi
0.400445 + 0.916321i 0.368855π0.368855\pi
194194 3709.57 1.37284
195195 444.993 0.163419
196196 196.000 0.0714286
197197 2356.98 0.852426 0.426213 0.904623i 0.359847π-0.359847\pi
0.426213 + 0.904623i 0.359847π0.359847\pi
198198 −1220.92 −0.438219
199199 5191.26 1.84924 0.924619 0.380893i 0.124383π-0.124383\pi
0.924619 + 0.380893i 0.124383π0.124383\pi
200200 617.215 0.218218
201201 −2695.89 −0.946037
202202 2869.89 0.999628
203203 339.476 0.117372
204204 −2482.54 −0.852022
205205 2835.97 0.966209
206206 −1137.49 −0.384722
207207 5790.02 1.94413
208208 113.324 0.0377770
209209 −1040.30 −0.344301
210210 −879.587 −0.289035
211211 4020.35 1.31172 0.655858 0.754884i 0.272307π-0.272307\pi
0.655858 + 0.754884i 0.272307π0.272307\pi
212212 −623.228 −0.201903
213213 −8559.73 −2.75353
214214 −3567.42 −1.13955
215215 −116.495 −0.0369531
216216 −2070.62 −0.652259
217217 271.889 0.0850555
218218 1059.17 0.329066
219219 −791.642 −0.244266
220220 304.358 0.0932720
221221 −483.973 −0.147310
222222 −2621.60 −0.792569
223223 −444.758 −0.133557 −0.0667785 0.997768i 0.521272π-0.521272\pi
−0.0667785 + 0.997768i 0.521272π0.521272\pi
224224 −224.000 −0.0668153
225225 −4281.66 −1.26864
226226 −3990.18 −1.17444
227227 4757.40 1.39101 0.695506 0.718520i 0.255180π-0.255180\pi
0.695506 + 0.718520i 0.255180π0.255180\pi
228228 −3435.92 −0.998023
229229 1032.94 0.298073 0.149037 0.988832i 0.452383π-0.452383\pi
0.149037 + 0.988832i 0.452383π0.452383\pi
230230 −1443.37 −0.413794
231231 699.373 0.199201
232232 −387.973 −0.109792
233233 −2952.57 −0.830168 −0.415084 0.909783i 0.636248π-0.636248\pi
−0.415084 + 0.909783i 0.636248π0.636248\pi
234234 −786.138 −0.219622
235235 −3703.83 −1.02813
236236 1796.94 0.495639
237237 −12070.7 −3.30833
238238 956.635 0.260544
239239 5382.65 1.45680 0.728399 0.685154i 0.240265π-0.240265\pi
0.728399 + 0.685154i 0.240265π0.240265\pi
240240 1005.24 0.270367
241241 2758.35 0.737265 0.368632 0.929575i 0.379826π-0.379826\pi
0.368632 + 0.929575i 0.379826π0.379826\pi
242242 −242.000 −0.0642824
243243 754.367 0.199147
244244 −2116.39 −0.555278
245245 338.945 0.0883852
246246 −7447.62 −1.93025
247247 −669.834 −0.172553
248248 −310.731 −0.0795621
249249 5549.57 1.41241
250250 2796.66 0.707506
251251 −3814.42 −0.959220 −0.479610 0.877482i 0.659222π-0.659222\pi
−0.479610 + 0.877482i 0.659222π0.659222\pi
252252 1553.90 0.388440
253253 1147.64 0.285184
254254 2301.30 0.568489
255255 −4293.08 −1.05429
256256 256.000 0.0625000
257257 −6959.85 −1.68927 −0.844637 0.535339i 0.820184π-0.820184\pi
−0.844637 + 0.535339i 0.820184π0.820184\pi
258258 305.932 0.0738235
259259 1010.22 0.242363
260260 195.973 0.0467450
261261 2691.39 0.638288
262262 4461.70 1.05208
263263 956.774 0.224324 0.112162 0.993690i 0.464222π-0.464222\pi
0.112162 + 0.993690i 0.464222π0.464222\pi
264264 −799.283 −0.186335
265265 −1077.75 −0.249834
266266 1324.01 0.305190
267267 10855.9 2.48827
268268 −1187.26 −0.270609
269269 −974.888 −0.220966 −0.110483 0.993878i 0.535240π-0.535240\pi
−0.110483 + 0.993878i 0.535240π0.535240\pi
270270 −3580.74 −0.807101
271271 3520.03 0.789027 0.394514 0.918890i 0.370913π-0.370913\pi
0.394514 + 0.918890i 0.370913π0.370913\pi
272272 −1093.30 −0.243716
273273 450.317 0.0998331
274274 −1313.19 −0.289535
275275 −848.670 −0.186097
276276 3790.46 0.826662
277277 2310.59 0.501192 0.250596 0.968092i 0.419374π-0.419374\pi
0.250596 + 0.968092i 0.419374π0.419374\pi
278278 −2024.35 −0.436735
279279 2155.56 0.462545
280280 −387.365 −0.0826768
281281 5616.65 1.19239 0.596194 0.802840i 0.296679π-0.296679\pi
0.596194 + 0.802840i 0.296679π0.296679\pi
282282 9726.71 2.05396
283283 −1065.17 −0.223737 −0.111869 0.993723i 0.535684π-0.535684\pi
−0.111869 + 0.993723i 0.535684π0.535684\pi
284284 −3769.66 −0.787634
285285 −5941.76 −1.23495
286286 −155.821 −0.0322163
287287 2869.90 0.590262
288288 −1775.89 −0.363352
289289 −243.868 −0.0496372
290290 −670.925 −0.135855
291291 −16846.6 −3.39369
292292 −348.635 −0.0698709
293293 3453.14 0.688514 0.344257 0.938875i 0.388131π-0.388131\pi
0.344257 + 0.938875i 0.388131π0.388131\pi
294294 −890.111 −0.176572
295295 3107.46 0.613300
296296 −1154.54 −0.226710
297297 2847.10 0.556248
298298 1573.35 0.305845
299299 738.952 0.142925
300300 −2803.01 −0.539439
301301 −117.889 −0.0225748
302302 −411.146 −0.0783404
303303 −13033.3 −2.47110
304304 −1513.16 −0.285479
305305 −3659.89 −0.687097
306306 7584.28 1.41688
307307 4864.91 0.904413 0.452207 0.891913i 0.350637π-0.350637\pi
0.452207 + 0.891913i 0.350637π0.350637\pi
308308 308.000 0.0569803
309309 5165.78 0.951039
310310 −537.349 −0.0984496
311311 378.550 0.0690213 0.0345106 0.999404i 0.489013π-0.489013\pi
0.0345106 + 0.999404i 0.489013π0.489013\pi
312312 −514.648 −0.0933853
313313 1912.52 0.345375 0.172687 0.984977i 0.444755π-0.444755\pi
0.172687 + 0.984977i 0.444755π0.444755\pi
314314 6568.15 1.18045
315315 2687.18 0.480652
316316 −5315.86 −0.946331
317317 −6640.27 −1.17651 −0.588256 0.808674i 0.700185π-0.700185\pi
−0.588256 + 0.808674i 0.700185π0.700185\pi
318318 2830.32 0.499108
319319 533.462 0.0936306
320320 442.703 0.0773371
321321 16201.0 2.81699
322322 −1460.63 −0.252789
323323 6462.24 1.11322
324324 3409.85 0.584679
325325 −546.448 −0.0932661
326326 2807.75 0.477015
327327 −4810.11 −0.813455
328328 −3279.89 −0.552139
329329 −3748.14 −0.628090
330330 −1382.21 −0.230570
331331 −5342.84 −0.887218 −0.443609 0.896220i 0.646302π-0.646302\pi
−0.443609 + 0.896220i 0.646302π0.646302\pi
332332 2444.00 0.404012
333333 8009.12 1.31801
334334 −8322.62 −1.36345
335335 −2053.13 −0.334850
336336 1017.27 0.165168
337337 4264.37 0.689303 0.344652 0.938731i 0.387997π-0.387997\pi
0.344652 + 0.938731i 0.387997π0.387997\pi
338338 4293.67 0.690961
339339 18120.9 2.90323
340340 −1890.65 −0.301573
341341 427.255 0.0678508
342342 10496.9 1.65967
343343 343.000 0.0539949
344344 134.731 0.0211168
345345 6554.87 1.02291
346346 5387.32 0.837064
347347 −3767.11 −0.582792 −0.291396 0.956602i 0.594120π-0.594120\pi
−0.291396 + 0.956602i 0.594120π0.594120\pi
348348 1761.93 0.271406
349349 5616.88 0.861503 0.430752 0.902471i 0.358249π-0.358249\pi
0.430752 + 0.902471i 0.358249π0.358249\pi
350350 1080.13 0.164958
351351 1833.21 0.278774
352352 −352.000 −0.0533002
353353 −1338.83 −0.201866 −0.100933 0.994893i 0.532183π-0.532183\pi
−0.100933 + 0.994893i 0.532183π0.532183\pi
354354 −8160.58 −1.22523
355355 −6518.90 −0.974613
356356 4780.86 0.711756
357357 −4344.44 −0.644068
358358 −3755.47 −0.554422
359359 −3323.84 −0.488650 −0.244325 0.969693i 0.578566π-0.578566\pi
−0.244325 + 0.969693i 0.578566π0.578566\pi
360360 −3071.06 −0.449609
361361 2084.96 0.303974
362362 −1278.58 −0.185637
363363 1099.01 0.158907
364364 198.317 0.0285567
365365 −602.897 −0.0864578
366366 9611.32 1.37265
367367 612.596 0.0871315 0.0435657 0.999051i 0.486128π-0.486128\pi
0.0435657 + 0.999051i 0.486128π0.486128\pi
368368 1669.30 0.236462
369369 22752.8 3.20993
370370 −1996.55 −0.280530
371371 −1090.65 −0.152625
372372 1411.15 0.196679
373373 −11858.9 −1.64619 −0.823094 0.567905i 0.807754π-0.807754\pi
−0.823094 + 0.567905i 0.807754π0.807754\pi
374374 1503.28 0.207842
375375 −12700.7 −1.74897
376376 4283.59 0.587525
377377 343.490 0.0469247
378378 −3623.59 −0.493061
379379 6906.97 0.936114 0.468057 0.883698i 0.344954π-0.344954\pi
0.468057 + 0.883698i 0.344954π0.344954\pi
380380 −2616.72 −0.353250
381381 −10451.1 −1.40531
382382 −7411.12 −0.992633
383383 −5189.68 −0.692377 −0.346189 0.938165i 0.612524π-0.612524\pi
−0.346189 + 0.938165i 0.612524π0.612524\pi
384384 −1162.59 −0.154501
385385 532.627 0.0705070
386386 −4294.76 −0.566315
387387 −934.636 −0.122765
388388 −7419.15 −0.970748
389389 4600.72 0.599654 0.299827 0.953994i 0.403071π-0.403071\pi
0.299827 + 0.953994i 0.403071π0.403071\pi
390390 −889.986 −0.115554
391391 −7129.05 −0.922076
392392 −392.000 −0.0505076
393393 −20262.3 −2.60075
394394 −4713.96 −0.602756
395395 −9192.77 −1.17098
396396 2441.85 0.309868
397397 −5313.96 −0.671788 −0.335894 0.941900i 0.609038π-0.609038\pi
−0.335894 + 0.941900i 0.609038π0.609038\pi
398398 −10382.5 −1.30761
399399 −6012.86 −0.754434
400400 −1234.43 −0.154304
401401 15051.5 1.87440 0.937199 0.348794i 0.113409π-0.113409\pi
0.937199 + 0.348794i 0.113409π0.113409\pi
402402 5391.78 0.668949
403403 275.104 0.0340047
404404 −5739.78 −0.706844
405405 5896.68 0.723478
406406 −678.952 −0.0829946
407407 1587.49 0.193339
408408 4965.08 0.602471
409409 9547.20 1.15423 0.577113 0.816664i 0.304179π-0.304179\pi
0.577113 + 0.816664i 0.304179π0.304179\pi
410410 −5671.95 −0.683213
411411 5963.68 0.715734
412412 2274.98 0.272040
413413 3144.64 0.374668
414414 −11580.0 −1.37470
415415 4226.44 0.499922
416416 −226.648 −0.0267124
417417 9193.33 1.07961
418418 2080.59 0.243457
419419 −643.721 −0.0750545 −0.0375272 0.999296i 0.511948π-0.511948\pi
−0.0375272 + 0.999296i 0.511948π0.511948\pi
420420 1759.17 0.204378
421421 12480.4 1.44479 0.722396 0.691480i 0.243041π-0.243041\pi
0.722396 + 0.691480i 0.243041π0.243041\pi
422422 −8040.69 −0.927523
423423 −29715.6 −3.41565
424424 1246.46 0.142767
425425 5271.87 0.601701
426426 17119.5 1.94704
427427 −3703.68 −0.419750
428428 7134.84 0.805784
429429 707.642 0.0796393
430430 232.991 0.0261298
431431 −5652.33 −0.631701 −0.315850 0.948809i 0.602290π-0.602290\pi
−0.315850 + 0.948809i 0.602290π0.602290\pi
432432 4141.24 0.461217
433433 −2179.80 −0.241928 −0.120964 0.992657i 0.538599π-0.538599\pi
−0.120964 + 0.992657i 0.538599π0.538599\pi
434434 −543.779 −0.0601433
435435 3046.92 0.335836
436436 −2118.35 −0.232684
437437 −9866.85 −1.08008
438438 1583.28 0.172722
439439 −3515.01 −0.382146 −0.191073 0.981576i 0.561197π-0.561197\pi
−0.191073 + 0.981576i 0.561197π0.561197\pi
440440 −608.717 −0.0659533
441441 2719.33 0.293633
442442 967.945 0.104164
443443 6329.77 0.678863 0.339432 0.940631i 0.389765π-0.389765\pi
0.339432 + 0.940631i 0.389765π0.389765\pi
444444 5243.20 0.560431
445445 8267.58 0.880721
446446 889.516 0.0944390
447447 −7145.20 −0.756054
448448 448.000 0.0472456
449449 −10624.6 −1.11672 −0.558361 0.829598i 0.688570π-0.688570\pi
−0.558361 + 0.829598i 0.688570π0.688570\pi
450450 8563.32 0.897064
451451 4509.85 0.470866
452452 7980.36 0.830453
453453 1867.17 0.193659
454454 −9514.80 −0.983595
455455 342.952 0.0353359
456456 6871.84 0.705709
457457 −11373.9 −1.16422 −0.582110 0.813110i 0.697773π-0.697773\pi
−0.582110 + 0.813110i 0.697773π0.697773\pi
458458 −2065.89 −0.210770
459459 −17686.0 −1.79850
460460 2886.73 0.292597
461461 −8473.86 −0.856111 −0.428055 0.903753i 0.640801π-0.640801\pi
−0.428055 + 0.903753i 0.640801π0.640801\pi
462462 −1398.75 −0.140856
463463 9796.71 0.983352 0.491676 0.870778i 0.336385π-0.336385\pi
0.491676 + 0.870778i 0.336385π0.336385\pi
464464 775.945 0.0776344
465465 2440.31 0.243369
466466 5905.13 0.587017
467467 −3000.81 −0.297347 −0.148674 0.988886i 0.547500π-0.547500\pi
−0.148674 + 0.988886i 0.547500π0.547500\pi
468468 1572.28 0.155296
469469 −2077.70 −0.204561
470470 7407.65 0.726999
471471 −29828.5 −2.91810
472472 −3593.88 −0.350469
473473 −185.255 −0.0180085
474474 24141.4 2.33934
475475 7296.44 0.704808
476476 −1913.27 −0.184232
477477 −8646.76 −0.829996
478478 −10765.3 −1.03011
479479 14384.2 1.37209 0.686047 0.727557i 0.259345π-0.259345\pi
0.686047 + 0.727557i 0.259345π0.259345\pi
480480 −2010.48 −0.191178
481481 1022.17 0.0968955
482482 −5516.69 −0.521325
483483 6633.30 0.624898
484484 484.000 0.0454545
485485 −12830.0 −1.20120
486486 −1508.73 −0.140818
487487 −19562.5 −1.82025 −0.910126 0.414332i 0.864015π-0.864015\pi
−0.910126 + 0.414332i 0.864015π0.864015\pi
488488 4232.77 0.392641
489489 −12751.1 −1.17919
490490 −677.889 −0.0624978
491491 1724.88 0.158539 0.0792697 0.996853i 0.474741π-0.474741\pi
0.0792697 + 0.996853i 0.474741π0.474741\pi
492492 14895.2 1.36490
493493 −3313.82 −0.302732
494494 1339.67 0.122013
495495 4222.71 0.383428
496496 621.461 0.0562589
497497 −6596.90 −0.595395
498498 −11099.1 −0.998724
499499 20898.7 1.87486 0.937430 0.348173i 0.113198π-0.113198\pi
0.937430 + 0.348173i 0.113198π0.113198\pi
500500 −5593.33 −0.500283
501501 37796.2 3.37048
502502 7628.84 0.678271
503503 −6062.13 −0.537369 −0.268685 0.963228i 0.586589π-0.586589\pi
−0.268685 + 0.963228i 0.586589π0.586589\pi
504504 −3107.81 −0.274668
505505 −9925.86 −0.874644
506506 −2295.28 −0.201656
507507 −19499.2 −1.70807
508508 −4602.59 −0.401982
509509 310.270 0.0270186 0.0135093 0.999909i 0.495700π-0.495700\pi
0.0135093 + 0.999909i 0.495700π0.495700\pi
510510 8586.16 0.745493
511511 −610.111 −0.0528174
512512 −512.000 −0.0441942
513513 −24478.0 −2.10668
514514 13919.7 1.19450
515515 3934.15 0.336620
516516 −611.863 −0.0522011
517517 −5889.93 −0.501043
518518 −2020.44 −0.171377
519519 −24465.9 −2.06924
520520 −391.945 −0.0330537
521521 −6406.10 −0.538688 −0.269344 0.963044i 0.586807π-0.586807\pi
−0.269344 + 0.963044i 0.586807π0.586807\pi
522522 −5382.79 −0.451338
523523 21061.8 1.76094 0.880468 0.474106i 0.157229π-0.157229\pi
0.880468 + 0.474106i 0.157229π0.157229\pi
524524 −8923.39 −0.743932
525525 −4905.26 −0.407777
526526 −1913.55 −0.158621
527527 −2654.07 −0.219380
528528 1598.57 0.131759
529529 −1282.03 −0.105370
530530 2155.51 0.176659
531531 24931.0 2.03750
532532 −2648.03 −0.215802
533533 2903.84 0.235983
534534 −21711.7 −1.75947
535535 12338.4 0.997072
536536 2374.51 0.191349
537537 17055.0 1.37054
538538 1949.78 0.156247
539539 539.000 0.0430730
540540 7161.49 0.570706
541541 −6597.32 −0.524290 −0.262145 0.965029i 0.584430π-0.584430\pi
−0.262145 + 0.965029i 0.584430π0.584430\pi
542542 −7040.05 −0.557927
543543 5806.52 0.458898
544544 2186.59 0.172334
545545 −3663.28 −0.287922
546546 −900.635 −0.0705927
547547 13719.3 1.07238 0.536192 0.844096i 0.319862π-0.319862\pi
0.536192 + 0.844096i 0.319862π0.319862\pi
548548 2626.37 0.204732
549549 −29363.0 −2.28267
550550 1697.34 0.131591
551551 −4586.44 −0.354608
552552 −7580.91 −0.584538
553553 −9302.76 −0.715359
554554 −4621.18 −0.354396
555555 9067.12 0.693473
556556 4048.69 0.308818
557557 9528.54 0.724842 0.362421 0.932014i 0.381950π-0.381950\pi
0.362421 + 0.932014i 0.381950π0.381950\pi
558558 −4311.12 −0.327069
559559 −119.283 −0.00902529
560560 774.731 0.0584613
561561 −6826.98 −0.513789
562562 −11233.3 −0.843146
563563 −12164.1 −0.910576 −0.455288 0.890344i 0.650464π-0.650464\pi
−0.455288 + 0.890344i 0.650464π0.650464\pi
564564 −19453.4 −1.45237
565565 13800.5 1.02760
566566 2130.34 0.158206
567567 5967.24 0.441976
568568 7539.32 0.556941
569569 7553.23 0.556499 0.278249 0.960509i 0.410246π-0.410246\pi
0.278249 + 0.960509i 0.410246π0.410246\pi
570570 11883.5 0.873239
571571 18632.0 1.36555 0.682773 0.730631i 0.260774π-0.260774\pi
0.682773 + 0.730631i 0.260774π0.260774\pi
572572 311.642 0.0227804
573573 33656.7 2.45380
574574 −5739.81 −0.417378
575575 −8049.33 −0.583792
576576 3551.78 0.256929
577577 −8150.64 −0.588069 −0.294034 0.955795i 0.594998π-0.594998\pi
−0.294034 + 0.955795i 0.594998π0.594998\pi
578578 487.735 0.0350988
579579 19504.2 1.39994
580580 1341.85 0.0960642
581581 4277.00 0.305405
582582 33693.2 2.39970
583583 −1713.88 −0.121752
584584 697.269 0.0494062
585585 2718.95 0.192162
586586 −6906.28 −0.486853
587587 14337.5 1.00813 0.504065 0.863666i 0.331837π-0.331837\pi
0.504065 + 0.863666i 0.331837π0.331837\pi
588588 1780.22 0.124856
589589 −3673.32 −0.256972
590590 −6214.92 −0.433668
591591 21407.9 1.49002
592592 2309.08 0.160308
593593 −27017.3 −1.87094 −0.935471 0.353402i 0.885025π-0.885025\pi
−0.935471 + 0.353402i 0.885025π0.885025\pi
594594 −5694.21 −0.393327
595595 −3308.63 −0.227968
596596 −3146.71 −0.216265
597597 47151.0 3.23243
598598 −1477.90 −0.101064
599599 18429.3 1.25710 0.628549 0.777770i 0.283649π-0.283649\pi
0.628549 + 0.777770i 0.283649π0.283649\pi
600600 5606.01 0.381441
601601 −4515.02 −0.306442 −0.153221 0.988192i 0.548965π-0.548965\pi
−0.153221 + 0.988192i 0.548965π0.548965\pi
602602 235.779 0.0159628
603603 −16472.2 −1.11243
604604 822.292 0.0553950
605605 836.986 0.0562451
606606 26066.5 1.74733
607607 9714.87 0.649612 0.324806 0.945781i 0.394701π-0.394701\pi
0.324806 + 0.945781i 0.394701π0.394701\pi
608608 3026.32 0.201864
609609 3083.38 0.205164
610610 7319.77 0.485851
611611 −3792.46 −0.251107
612612 −15168.6 −1.00188
613613 10724.5 0.706618 0.353309 0.935507i 0.385056π-0.385056\pi
0.353309 + 0.935507i 0.385056π0.385056\pi
614614 −9729.81 −0.639517
615615 25758.5 1.68891
616616 −616.000 −0.0402911
617617 28206.5 1.84044 0.920219 0.391404i 0.128010π-0.128010\pi
0.920219 + 0.391404i 0.128010π0.128010\pi
618618 −10331.6 −0.672486
619619 156.324 0.0101505 0.00507526 0.999987i 0.498384π-0.498384\pi
0.00507526 + 0.999987i 0.498384π0.498384\pi
620620 1074.70 0.0696144
621621 27003.8 1.74497
622622 −757.100 −0.0488054
623623 8366.50 0.538037
624624 1029.30 0.0660334
625625 −28.6176 −0.00183152
626626 −3825.05 −0.244217
627627 −9448.77 −0.601830
628628 −13136.3 −0.834707
629629 −9861.36 −0.625116
630630 −5374.36 −0.339873
631631 16349.5 1.03148 0.515740 0.856745i 0.327517π-0.327517\pi
0.515740 + 0.856745i 0.327517π0.327517\pi
632632 10631.7 0.669157
633633 36515.8 2.29285
634634 13280.5 0.831920
635635 −7959.31 −0.497410
636636 −5660.63 −0.352923
637637 347.055 0.0215869
638638 −1066.92 −0.0662068
639639 −52300.8 −3.23785
640640 −885.406 −0.0546856
641641 −16933.8 −1.04344 −0.521721 0.853116i 0.674710π-0.674710\pi
−0.521721 + 0.853116i 0.674710π0.674710\pi
642642 −32402.1 −1.99191
643643 14717.7 0.902657 0.451328 0.892358i 0.350950π-0.350950\pi
0.451328 + 0.892358i 0.350950π0.350950\pi
644644 2921.27 0.178749
645645 −1058.10 −0.0645933
646646 −12924.5 −0.787162
647647 −4572.55 −0.277845 −0.138922 0.990303i 0.544364π-0.544364\pi
−0.138922 + 0.990303i 0.544364π0.544364\pi
648648 −6819.70 −0.413431
649649 4941.58 0.298881
650650 1092.90 0.0659491
651651 2469.51 0.148675
652652 −5615.50 −0.337301
653653 400.476 0.0239997 0.0119999 0.999928i 0.496180π-0.496180\pi
0.0119999 + 0.999928i 0.496180π0.496180\pi
654654 9620.22 0.575199
655655 −15431.3 −0.920536
656656 6559.78 0.390421
657657 −4837.01 −0.287229
658658 7496.28 0.444127
659659 1761.23 0.104109 0.0520544 0.998644i 0.483423π-0.483423\pi
0.0520544 + 0.998644i 0.483423π0.483423\pi
660660 2764.42 0.163037
661661 −20410.8 −1.20104 −0.600520 0.799610i 0.705040π-0.705040\pi
−0.600520 + 0.799610i 0.705040π0.705040\pi
662662 10685.7 0.627358
663663 −4395.81 −0.257495
664664 −4888.00 −0.285680
665665 −4579.26 −0.267032
666666 −16018.2 −0.931973
667667 5059.70 0.293722
668668 16645.2 0.964108
669669 −4039.63 −0.233455
670670 4106.26 0.236774
671671 −5820.06 −0.334845
672672 −2034.54 −0.116792
673673 4578.55 0.262244 0.131122 0.991366i 0.458142π-0.458142\pi
0.131122 + 0.991366i 0.458142π0.458142\pi
674674 −8528.74 −0.487411
675675 −19969.0 −1.13868
676676 −8587.34 −0.488583
677677 −16330.1 −0.927057 −0.463528 0.886082i 0.653417π-0.653417\pi
−0.463528 + 0.886082i 0.653417π0.653417\pi
678678 −36241.9 −2.05289
679679 −12983.5 −0.733816
680680 3781.30 0.213244
681681 43210.4 2.43146
682682 −854.509 −0.0479778
683683 −25379.8 −1.42186 −0.710929 0.703263i 0.751725π-0.751725\pi
−0.710929 + 0.703263i 0.751725π0.751725\pi
684684 −20993.8 −1.17356
685685 4541.81 0.253334
686686 −686.000 −0.0381802
687687 9381.98 0.521026
688688 −269.461 −0.0149318
689689 −1103.54 −0.0610184
690690 −13109.7 −0.723304
691691 18557.9 1.02167 0.510837 0.859678i 0.329336π-0.329336\pi
0.510837 + 0.859678i 0.329336π0.329336\pi
692692 −10774.6 −0.591894
693693 4273.24 0.234238
694694 7534.22 0.412096
695695 7001.44 0.382129
696696 −3523.86 −0.191913
697697 −28014.8 −1.52243
698698 −11233.8 −0.609175
699699 −26817.5 −1.45112
700700 −2160.25 −0.116643
701701 25115.0 1.35318 0.676590 0.736360i 0.263457π-0.263457\pi
0.676590 + 0.736360i 0.263457π0.263457\pi
702702 −3666.43 −0.197123
703703 −13648.5 −0.732235
704704 704.000 0.0376889
705705 −33641.0 −1.79715
706706 2677.66 0.142741
707707 −10044.6 −0.534324
708708 16321.2 0.866366
709709 36408.7 1.92857 0.964286 0.264864i 0.0853272π-0.0853272\pi
0.964286 + 0.264864i 0.0853272π0.0853272\pi
710710 13037.8 0.689155
711711 −73753.0 −3.89023
712712 −9561.72 −0.503287
713713 4052.36 0.212850
714714 8688.89 0.455425
715715 538.925 0.0281883
716716 7510.95 0.392035
717717 48889.3 2.54645
718718 6647.67 0.345528
719719 3503.59 0.181727 0.0908637 0.995863i 0.471037π-0.471037\pi
0.0908637 + 0.995863i 0.471037π0.471037\pi
720720 6142.13 0.317922
721721 3981.22 0.205643
722722 −4169.91 −0.214942
723723 25053.4 1.28872
724724 2557.16 0.131265
725725 −3741.60 −0.191668
726726 −2198.03 −0.112364
727727 −18869.2 −0.962613 −0.481306 0.876552i 0.659838π-0.659838\pi
−0.481306 + 0.876552i 0.659838π0.659838\pi
728728 −396.635 −0.0201927
729729 −16164.7 −0.821254
730730 1205.79 0.0611349
731731 1150.79 0.0582262
732732 −19222.6 −0.970613
733733 −26123.3 −1.31635 −0.658176 0.752864i 0.728672π-0.728672\pi
−0.658176 + 0.752864i 0.728672π0.728672\pi
734734 −1225.19 −0.0616112
735735 3078.55 0.154495
736736 −3338.59 −0.167204
737737 −3264.95 −0.163183
738738 −45505.7 −2.26977
739739 −1259.95 −0.0627170 −0.0313585 0.999508i 0.509983π-0.509983\pi
−0.0313585 + 0.999508i 0.509983π0.509983\pi
740740 3993.11 0.198364
741741 −6083.95 −0.301619
742742 2181.30 0.107922
743743 −6987.68 −0.345024 −0.172512 0.985007i 0.555188π-0.555188\pi
−0.172512 + 0.985007i 0.555188π0.555188\pi
744744 −2822.29 −0.139073
745745 −5441.63 −0.267605
746746 23717.7 1.16403
747747 33908.4 1.66084
748748 −3006.57 −0.146967
749749 12486.0 0.609116
750750 25401.4 1.23671
751751 26501.3 1.28768 0.643838 0.765162i 0.277341π-0.277341\pi
0.643838 + 0.765162i 0.277341π0.277341\pi
752752 −8567.18 −0.415443
753753 −34645.5 −1.67670
754754 −686.979 −0.0331808
755755 1422.00 0.0685454
756756 7247.17 0.348647
757757 −18638.9 −0.894905 −0.447453 0.894308i 0.647669π-0.647669\pi
−0.447453 + 0.894308i 0.647669π0.647669\pi
758758 −13813.9 −0.661932
759759 10423.8 0.498496
760760 5233.44 0.249785
761761 10502.8 0.500298 0.250149 0.968207i 0.419520π-0.419520\pi
0.250149 + 0.968207i 0.419520π0.419520\pi
762762 20902.1 0.993707
763763 −3707.11 −0.175893
764764 14822.2 0.701897
765765 −26231.1 −1.23972
766766 10379.4 0.489585
767767 3181.82 0.149790
768768 2325.19 0.109249
769769 −31451.8 −1.47488 −0.737440 0.675413i 0.763965π-0.763965\pi
−0.737440 + 0.675413i 0.763965π0.763965\pi
770770 −1065.25 −0.0498560
771771 −63214.7 −2.95282
772772 8589.53 0.400445
773773 −12785.3 −0.594897 −0.297448 0.954738i 0.596136π-0.596136\pi
−0.297448 + 0.954738i 0.596136π0.596136\pi
774774 1869.27 0.0868082
775775 −2996.68 −0.138895
776776 14838.3 0.686422
777777 9175.60 0.423646
778778 −9201.43 −0.424020
779779 −38773.4 −1.78331
780780 1779.97 0.0817093
781781 −10366.6 −0.474961
782782 14258.1 0.652006
783783 12552.3 0.572900
784784 784.000 0.0357143
785785 −22716.7 −1.03286
786786 40524.5 1.83901
787787 −26171.7 −1.18542 −0.592708 0.805418i 0.701941π-0.701941\pi
−0.592708 + 0.805418i 0.701941π0.701941\pi
788788 9427.93 0.426213
789789 8690.15 0.392114
790790 18385.5 0.828010
791791 13965.6 0.627763
792792 −4883.70 −0.219109
793793 −3747.46 −0.167814
794794 10627.9 0.475026
795795 −9788.99 −0.436704
796796 20765.0 0.924619
797797 −9956.37 −0.442500 −0.221250 0.975217i 0.571014π-0.571014\pi
−0.221250 + 0.975217i 0.571014π0.571014\pi
798798 12025.7 0.533466
799799 36587.8 1.62000
800800 2468.86 0.109109
801801 66330.3 2.92593
802802 −30102.9 −1.32540
803803 −958.745 −0.0421337
804804 −10783.6 −0.473019
805805 5051.78 0.221182
806806 −550.208 −0.0240450
807807 −8854.67 −0.386244
808808 11479.6 0.499814
809809 27460.5 1.19340 0.596699 0.802465i 0.296478π-0.296478\pi
0.596699 + 0.802465i 0.296478π0.296478\pi
810810 −11793.4 −0.511576
811811 13721.5 0.594116 0.297058 0.954859i 0.403994π-0.403994\pi
0.297058 + 0.954859i 0.403994π0.403994\pi
812812 1357.90 0.0586861
813813 31971.6 1.37920
814814 −3174.98 −0.136711
815815 −9710.94 −0.417374
816816 −9930.16 −0.426011
817817 1592.73 0.0682037
818818 −19094.4 −0.816162
819819 2751.48 0.117393
820820 11343.9 0.483105
821821 −7959.34 −0.338347 −0.169173 0.985586i 0.554110π-0.554110\pi
−0.169173 + 0.985586i 0.554110π0.554110\pi
822822 −11927.4 −0.506101
823823 15031.6 0.636659 0.318329 0.947980i 0.396878π-0.396878\pi
0.318329 + 0.947980i 0.396878π0.396878\pi
824824 −4549.96 −0.192361
825825 −7708.27 −0.325294
826826 −6289.28 −0.264930
827827 34367.2 1.44506 0.722531 0.691339i 0.242979π-0.242979\pi
0.722531 + 0.691339i 0.242979π0.242979\pi
828828 23160.1 0.972063
829829 34355.0 1.43932 0.719662 0.694324i 0.244297π-0.244297\pi
0.719662 + 0.694324i 0.244297π0.244297\pi
830830 −8452.87 −0.353498
831831 20986.6 0.876072
832832 453.297 0.0188885
833833 −3348.22 −0.139267
834834 −18386.7 −0.763403
835835 28784.8 1.19298
836836 −4161.19 −0.172150
837837 10053.2 0.415161
838838 1287.44 0.0530715
839839 25095.0 1.03263 0.516314 0.856399i 0.327304π-0.327304\pi
0.516314 + 0.856399i 0.327304π0.327304\pi
840840 −3518.35 −0.144517
841841 −22037.1 −0.903566
842842 −24960.8 −1.02162
843843 51014.7 2.08427
844844 16081.4 0.655858
845845 −14850.2 −0.604569
846846 59431.1 2.41523
847847 847.000 0.0343604
848848 −2492.91 −0.100952
849849 −9674.67 −0.391088
850850 −10543.7 −0.425467
851851 15056.8 0.606510
852852 −34238.9 −1.37677
853853 −8877.88 −0.356357 −0.178179 0.983998i 0.557020π-0.557020\pi
−0.178179 + 0.983998i 0.557020π0.557020\pi
854854 7407.35 0.296808
855855 −36304.8 −1.45216
856856 −14269.7 −0.569776
857857 −28281.8 −1.12729 −0.563646 0.826016i 0.690602π-0.690602\pi
−0.563646 + 0.826016i 0.690602π0.690602\pi
858858 −1415.28 −0.0563135
859859 −25282.1 −1.00421 −0.502104 0.864807i 0.667441π-0.667441\pi
−0.502104 + 0.864807i 0.667441π0.667441\pi
860860 −465.982 −0.0184766
861861 26066.7 1.03176
862862 11304.7 0.446680
863863 −38721.6 −1.52735 −0.763673 0.645603i 0.776606π-0.776606\pi
−0.763673 + 0.645603i 0.776606π0.776606\pi
864864 −8282.48 −0.326129
865865 −18632.7 −0.732405
866866 4359.61 0.171069
867867 −2214.99 −0.0867648
868868 1087.56 0.0425278
869869 −14618.6 −0.570659
870870 −6093.85 −0.237472
871871 −2102.26 −0.0817824
872872 4236.69 0.164533
873873 −102934. −3.99061
874874 19733.7 0.763732
875875 −9788.33 −0.378178
876876 −3166.57 −0.122133
877877 47198.6 1.81731 0.908656 0.417546i 0.137110π-0.137110\pi
0.908656 + 0.417546i 0.137110π0.137110\pi
878878 7030.02 0.270218
879879 31364.1 1.20351
880880 1217.43 0.0466360
881881 12794.1 0.489266 0.244633 0.969616i 0.421333π-0.421333\pi
0.244633 + 0.969616i 0.421333π0.421333\pi
882882 −5438.66 −0.207630
883883 −22310.6 −0.850295 −0.425148 0.905124i 0.639778π-0.639778\pi
−0.425148 + 0.905124i 0.639778π0.639778\pi
884884 −1935.89 −0.0736550
885885 28224.3 1.07203
886886 −12659.5 −0.480029
887887 −31281.7 −1.18415 −0.592073 0.805884i 0.701690π-0.701690\pi
−0.592073 + 0.805884i 0.701690π0.701690\pi
888888 −10486.4 −0.396284
889889 −8054.54 −0.303870
890890 −16535.2 −0.622764
891891 9377.09 0.352575
892892 −1779.03 −0.0667785
893893 50638.7 1.89760
894894 14290.4 0.534611
895895 12988.8 0.485102
896896 −896.000 −0.0334077
897897 6711.73 0.249831
898898 21249.3 0.789642
899899 1883.67 0.0698820
900900 −17126.6 −0.634320
901901 10646.5 0.393657
902902 −9019.70 −0.332952
903903 −1070.76 −0.0394603
904904 −15960.7 −0.587219
905905 4422.12 0.162427
906906 −3734.34 −0.136937
907907 −31863.9 −1.16651 −0.583255 0.812289i 0.698221π-0.698221\pi
−0.583255 + 0.812289i 0.698221π0.698221\pi
908908 19029.6 0.695506
909909 −79634.6 −2.90573
910910 −685.904 −0.0249863
911911 −38643.5 −1.40540 −0.702698 0.711488i 0.748022π-0.748022\pi
−0.702698 + 0.711488i 0.748022π0.748022\pi
912912 −13743.7 −0.499011
913913 6721.01 0.243629
914914 22747.8 0.823227
915915 −33241.9 −1.20103
916916 4131.77 0.149037
917917 −15615.9 −0.562360
918918 35371.9 1.27173
919919 −22868.7 −0.820857 −0.410428 0.911893i 0.634621π-0.634621\pi
−0.410428 + 0.911893i 0.634621π0.634621\pi
920920 −5773.46 −0.206897
921921 44186.8 1.58090
922922 16947.7 0.605362
923923 −6674.90 −0.238036
924924 2797.49 0.0996003
925925 −11134.3 −0.395778
926926 −19593.4 −0.695335
927927 31563.4 1.11832
928928 −1551.89 −0.0548958
929929 9352.39 0.330293 0.165146 0.986269i 0.447190π-0.447190\pi
0.165146 + 0.986269i 0.447190π0.447190\pi
930930 −4880.62 −0.172088
931931 −4634.05 −0.163131
932932 −11810.3 −0.415084
933933 3438.28 0.120648
934934 6001.63 0.210256
935935 −5199.28 −0.181855
936936 −3144.55 −0.109811
937937 6943.74 0.242094 0.121047 0.992647i 0.461375π-0.461375\pi
0.121047 + 0.992647i 0.461375π0.461375\pi
938938 4155.39 0.144647
939939 17371.0 0.603707
940940 −14815.3 −0.514066
941941 −17294.1 −0.599120 −0.299560 0.954077i 0.596840π-0.596840\pi
−0.299560 + 0.954077i 0.596840π0.596840\pi
942942 59657.0 2.06341
943943 42774.3 1.47712
944944 7187.75 0.247819
945945 12532.6 0.431413
946946 370.509 0.0127339
947947 52139.8 1.78914 0.894570 0.446928i 0.147482π-0.147482\pi
0.894570 + 0.446928i 0.147482π0.147482\pi
948948 −48282.7 −1.65417
949949 −617.324 −0.0211161
950950 −14592.9 −0.498374
951951 −60312.0 −2.05652
952952 3826.54 0.130272
953953 13921.4 0.473197 0.236599 0.971607i 0.423967π-0.423967\pi
0.236599 + 0.971607i 0.423967π0.423967\pi
954954 17293.5 0.586896
955955 25632.2 0.868523
956956 21530.6 0.728399
957957 4845.31 0.163664
958958 −28768.5 −0.970217
959959 4596.16 0.154763
960960 4020.97 0.135184
961961 −28282.4 −0.949359
962962 −2044.33 −0.0685155
963963 98989.9 3.31246
964964 11033.4 0.368632
965965 14853.9 0.495508
966966 −13266.6 −0.441869
967967 −18698.2 −0.621812 −0.310906 0.950441i 0.600632π-0.600632\pi
−0.310906 + 0.950441i 0.600632π0.600632\pi
968968 −968.000 −0.0321412
969969 58695.0 1.94588
970970 25660.0 0.849374
971971 −46060.5 −1.52230 −0.761149 0.648578i 0.775364π-0.775364\pi
−0.761149 + 0.648578i 0.775364π0.775364\pi
972972 3017.47 0.0995734
973973 7085.21 0.233444
974974 39125.0 1.28711
975975 −4963.26 −0.163027
976976 −8465.54 −0.277639
977977 −2625.78 −0.0859839 −0.0429919 0.999075i 0.513689π-0.513689\pi
−0.0429919 + 0.999075i 0.513689π0.513689\pi
978978 25502.1 0.833812
979979 13147.4 0.429205
980980 1355.78 0.0441926
981981 −29390.3 −0.956533
982982 −3449.76 −0.112104
983983 −21740.7 −0.705412 −0.352706 0.935734i 0.614739π-0.614739\pi
−0.352706 + 0.935734i 0.614739π0.614739\pi
984984 −29790.5 −0.965127
985985 16303.8 0.527393
986986 6627.64 0.214064
987987 −34043.5 −1.09789
988988 −2679.34 −0.0862764
989989 −1757.07 −0.0564931
990990 −8445.43 −0.271124
991991 8494.35 0.272282 0.136141 0.990689i 0.456530π-0.456530\pi
0.136141 + 0.990689i 0.456530π0.456530\pi
992992 −1242.92 −0.0397811
993993 −48527.8 −1.55084
994994 13193.8 0.421008
995995 35909.2 1.14412
996996 22198.3 0.706205
997997 −9802.62 −0.311386 −0.155693 0.987805i 0.549761π-0.549761\pi
−0.155693 + 0.987805i 0.549761π0.549761\pi
998998 −41797.5 −1.32573
999999 37353.3 1.18299
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 154.4.a.g.1.2 2
3.2 odd 2 1386.4.a.u.1.2 2
4.3 odd 2 1232.4.a.j.1.1 2
7.6 odd 2 1078.4.a.i.1.1 2
11.10 odd 2 1694.4.a.p.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.g.1.2 2 1.1 even 1 trivial
1078.4.a.i.1.1 2 7.6 odd 2
1232.4.a.j.1.1 2 4.3 odd 2
1386.4.a.u.1.2 2 3.2 odd 2
1694.4.a.p.1.2 2 11.10 odd 2