Properties

Label 197.14.a.b.1.6
Level 197197
Weight 1414
Character 197.1
Self dual yes
Analytic conductor 211.245211.245
Analytic rank 00
Dimension 109109
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] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: N N == 197 197
Weight: k k == 14 14
Character orbit: [χ][\chi] == 197.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: 211.244930035211.244930035
Analytic rank: 00
Dimension: 109109
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Character χ\chi == 197.1

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) == q168.643q2+977.710q3+20248.6q4+23282.0q5164884.q6126937.q72.03327e6q8638407.q93.92635e6q108.23416e6q11+1.97973e7q12+1.69965e7q13+2.14071e7q14+2.27630e7q15+1.77021e8q168.40289e7q17+1.07663e8q18+2.16492e8q19+4.71428e8q201.24107e8q21+1.38864e9q226.93845e8q231.98795e9q246.78653e8q252.86635e9q262.18296e9q272.57029e9q281.45113e9q293.83883e9q302.27203e9q311.31969e10q328.05062e9q33+1.41709e10q342.95534e9q351.29268e10q36+1.70009e10q373.65099e10q38+1.66177e10q394.73385e10q404.86955e9q41+2.09299e10q42+2.01234e10q431.66730e11q441.48634e10q45+1.17012e11q461.42493e11q47+1.73075e11q488.07761e10q49+1.14450e11q508.21559e10q51+3.44156e11q52+3.00267e10q53+3.68142e11q541.91707e11q55+2.58097e11q56+2.11666e11q57+2.44724e11q583.86530e11q59+4.60919e11q60+4.31426e11q61+3.83163e11q62+8.10373e10q63+7.75410e11q64+3.95712e11q65+1.35768e12q66+1.10450e12q671.70147e12q686.78379e11q69+4.98398e11q70+1.43288e11q71+1.29805e12q721.28575e12q732.86709e12q746.63526e11q75+4.38365e12q76+1.04522e12q772.80246e12q78+4.04290e12q79+4.12139e12q801.11648e12q81+8.21218e11q82+4.40239e12q832.51300e12q841.95636e12q853.39368e12q861.41879e12q87+1.67423e13q88+2.64544e12q89+2.50661e12q902.15748e12q911.40494e13q922.22139e12q93+2.40306e13q94+5.04035e12q951.29027e13q961.19515e13q97+1.36224e13q98+5.25674e12q99+O(q100)q-168.643 q^{2} +977.710 q^{3} +20248.6 q^{4} +23282.0 q^{5} -164884. q^{6} -126937. q^{7} -2.03327e6 q^{8} -638407. q^{9} -3.92635e6 q^{10} -8.23416e6 q^{11} +1.97973e7 q^{12} +1.69965e7 q^{13} +2.14071e7 q^{14} +2.27630e7 q^{15} +1.77021e8 q^{16} -8.40289e7 q^{17} +1.07663e8 q^{18} +2.16492e8 q^{19} +4.71428e8 q^{20} -1.24107e8 q^{21} +1.38864e9 q^{22} -6.93845e8 q^{23} -1.98795e9 q^{24} -6.78653e8 q^{25} -2.86635e9 q^{26} -2.18296e9 q^{27} -2.57029e9 q^{28} -1.45113e9 q^{29} -3.83883e9 q^{30} -2.27203e9 q^{31} -1.31969e10 q^{32} -8.05062e9 q^{33} +1.41709e10 q^{34} -2.95534e9 q^{35} -1.29268e10 q^{36} +1.70009e10 q^{37} -3.65099e10 q^{38} +1.66177e10 q^{39} -4.73385e10 q^{40} -4.86955e9 q^{41} +2.09299e10 q^{42} +2.01234e10 q^{43} -1.66730e11 q^{44} -1.48634e10 q^{45} +1.17012e11 q^{46} -1.42493e11 q^{47} +1.73075e11 q^{48} -8.07761e10 q^{49} +1.14450e11 q^{50} -8.21559e10 q^{51} +3.44156e11 q^{52} +3.00267e10 q^{53} +3.68142e11 q^{54} -1.91707e11 q^{55} +2.58097e11 q^{56} +2.11666e11 q^{57} +2.44724e11 q^{58} -3.86530e11 q^{59} +4.60919e11 q^{60} +4.31426e11 q^{61} +3.83163e11 q^{62} +8.10373e10 q^{63} +7.75410e11 q^{64} +3.95712e11 q^{65} +1.35768e12 q^{66} +1.10450e12 q^{67} -1.70147e12 q^{68} -6.78379e11 q^{69} +4.98398e11 q^{70} +1.43288e11 q^{71} +1.29805e12 q^{72} -1.28575e12 q^{73} -2.86709e12 q^{74} -6.63526e11 q^{75} +4.38365e12 q^{76} +1.04522e12 q^{77} -2.80246e12 q^{78} +4.04290e12 q^{79} +4.12139e12 q^{80} -1.11648e12 q^{81} +8.21218e11 q^{82} +4.40239e12 q^{83} -2.51300e12 q^{84} -1.95636e12 q^{85} -3.39368e12 q^{86} -1.41879e12 q^{87} +1.67423e13 q^{88} +2.64544e12 q^{89} +2.50661e12 q^{90} -2.15748e12 q^{91} -1.40494e13 q^{92} -2.22139e12 q^{93} +2.40306e13 q^{94} +5.04035e12 q^{95} -1.29027e13 q^{96} -1.19515e13 q^{97} +1.36224e13 q^{98} +5.25674e12 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 109q+192q2+8018q3+471040q4+88496q5+383232q6+1680731q7+1820859q8+59521391q9+16373653q10+21199298q11+63225856q12+59695238q13+37888529q14++12084396239183q99+O(q100) 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 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 −168.643 −1.86326 −0.931632 0.363403i 0.881615π-0.881615\pi
−0.931632 + 0.363403i 0.881615π0.881615\pi
33 977.710 0.774322 0.387161 0.922012i 0.373456π-0.373456\pi
0.387161 + 0.922012i 0.373456π0.373456\pi
44 20248.6 2.47175
55 23282.0 0.666369 0.333184 0.942862i 0.391877π-0.391877\pi
0.333184 + 0.942862i 0.391877π0.391877\pi
66 −164884. −1.44277
77 −126937. −0.407803 −0.203901 0.978991i 0.565362π-0.565362\pi
−0.203901 + 0.978991i 0.565362π0.565362\pi
88 −2.03327e6 −2.74227
99 −638407. −0.400425
1010 −3.92635e6 −1.24162
1111 −8.23416e6 −1.40142 −0.700708 0.713448i 0.747132π-0.747132\pi
−0.700708 + 0.713448i 0.747132π0.747132\pi
1212 1.97973e7 1.91393
1313 1.69965e7 0.976626 0.488313 0.872669i 0.337612π-0.337612\pi
0.488313 + 0.872669i 0.337612π0.337612\pi
1414 2.14071e7 0.759845
1515 2.27630e7 0.515984
1616 1.77021e8 2.63782
1717 −8.40289e7 −0.844327 −0.422163 0.906520i 0.638729π-0.638729\pi
−0.422163 + 0.906520i 0.638729π0.638729\pi
1818 1.07663e8 0.746097
1919 2.16492e8 1.05570 0.527852 0.849336i 0.322997π-0.322997\pi
0.527852 + 0.849336i 0.322997π0.322997\pi
2020 4.71428e8 1.64710
2121 −1.24107e8 −0.315771
2222 1.38864e9 2.61121
2323 −6.93845e8 −0.977308 −0.488654 0.872478i 0.662512π-0.662512\pi
−0.488654 + 0.872478i 0.662512π0.662512\pi
2424 −1.98795e9 −2.12340
2525 −6.78653e8 −0.555953
2626 −2.86635e9 −1.81971
2727 −2.18296e9 −1.08438
2828 −2.57029e9 −1.00799
2929 −1.45113e9 −0.453022 −0.226511 0.974009i 0.572732π-0.572732\pi
−0.226511 + 0.974009i 0.572732π0.572732\pi
3030 −3.83883e9 −0.961415
3131 −2.27203e9 −0.459794 −0.229897 0.973215i 0.573839π-0.573839\pi
−0.229897 + 0.973215i 0.573839π0.573839\pi
3232 −1.31969e10 −2.17268
3333 −8.05062e9 −1.08515
3434 1.41709e10 1.57320
3535 −2.95534e9 −0.271747
3636 −1.29268e10 −0.989752
3737 1.70009e10 1.08933 0.544667 0.838653i 0.316656π-0.316656\pi
0.544667 + 0.838653i 0.316656π0.316656\pi
3838 −3.65099e10 −1.96706
3939 1.66177e10 0.756223
4040 −4.73385e10 −1.82736
4141 −4.86955e9 −0.160101 −0.0800505 0.996791i 0.525508π-0.525508\pi
−0.0800505 + 0.996791i 0.525508π0.525508\pi
4242 2.09299e10 0.588365
4343 2.01234e10 0.485463 0.242731 0.970094i 0.421957π-0.421957\pi
0.242731 + 0.970094i 0.421957π0.421957\pi
4444 −1.66730e11 −3.46395
4545 −1.48634e10 −0.266831
4646 1.17012e11 1.82098
4747 −1.42493e11 −1.92823 −0.964114 0.265487i 0.914467π-0.914467\pi
−0.964114 + 0.265487i 0.914467π0.914467\pi
4848 1.73075e11 2.04252
4949 −8.07761e10 −0.833697
5050 1.14450e11 1.03589
5151 −8.21559e10 −0.653781
5252 3.44156e11 2.41398
5353 3.00267e10 0.186086 0.0930432 0.995662i 0.470341π-0.470341\pi
0.0930432 + 0.995662i 0.470341π0.470341\pi
5454 3.68142e11 2.02049
5555 −1.91707e11 −0.933859
5656 2.58097e11 1.11830
5757 2.11666e11 0.817456
5858 2.44724e11 0.844100
5959 −3.86530e11 −1.19301 −0.596507 0.802608i 0.703445π-0.703445\pi
−0.596507 + 0.802608i 0.703445π0.703445\pi
6060 4.60919e11 1.27539
6161 4.31426e11 1.07217 0.536084 0.844165i 0.319903π-0.319903\pi
0.536084 + 0.844165i 0.319903π0.319903\pi
6262 3.83163e11 0.856717
6363 8.10373e10 0.163294
6464 7.75410e11 1.41046
6565 3.95712e11 0.650793
6666 1.35768e12 2.02192
6767 1.10450e12 1.49169 0.745846 0.666118i 0.232045π-0.232045\pi
0.745846 + 0.666118i 0.232045π0.232045\pi
6868 −1.70147e12 −2.08697
6969 −6.78379e11 −0.756751
7070 4.98398e11 0.506337
7171 1.43288e11 0.132749 0.0663743 0.997795i 0.478857π-0.478857\pi
0.0663743 + 0.997795i 0.478857π0.478857\pi
7272 1.29805e12 1.09807
7373 −1.28575e12 −0.994395 −0.497198 0.867637i 0.665638π-0.665638\pi
−0.497198 + 0.867637i 0.665638π0.665638\pi
7474 −2.86709e12 −2.02972
7575 −6.63526e11 −0.430487
7676 4.38365e12 2.60944
7777 1.04522e12 0.571501
7878 −2.80246e12 −1.40904
7979 4.04290e12 1.87119 0.935594 0.353078i 0.114865π-0.114865\pi
0.935594 + 0.353078i 0.114865π0.114865\pi
8080 4.12139e12 1.75776
8181 −1.11648e12 −0.439235
8282 8.21218e11 0.298310
8383 4.40239e12 1.47802 0.739010 0.673694i 0.235294π-0.235294\pi
0.739010 + 0.673694i 0.235294π0.235294\pi
8484 −2.51300e12 −0.780508
8585 −1.95636e12 −0.562633
8686 −3.39368e12 −0.904545
8787 −1.41879e12 −0.350785
8888 1.67423e13 3.84306
8989 2.64544e12 0.564240 0.282120 0.959379i 0.408962π-0.408962\pi
0.282120 + 0.959379i 0.408962π0.408962\pi
9090 2.50661e12 0.497176
9191 −2.15748e12 −0.398271
9292 −1.40494e13 −2.41567
9393 −2.22139e12 −0.356028
9494 2.40306e13 3.59280
9595 5.04035e12 0.703489
9696 −1.29027e13 −1.68236
9797 −1.19515e13 −1.45682 −0.728411 0.685140i 0.759741π-0.759741\pi
−0.728411 + 0.685140i 0.759741π0.759741\pi
9898 1.36224e13 1.55340
9999 5.25674e12 0.561162
100100 −1.37418e13 −1.37418
101101 −8.86561e12 −0.831036 −0.415518 0.909585i 0.636400π-0.636400\pi
−0.415518 + 0.909585i 0.636400π0.636400\pi
102102 1.38550e13 1.21817
103103 −8.84075e12 −0.729537 −0.364769 0.931098i 0.618852π-0.618852\pi
−0.364769 + 0.931098i 0.618852π0.618852\pi
104104 −3.45585e13 −2.67817
105105 −2.88946e12 −0.210420
106106 −5.06381e12 −0.346728
107107 −2.31071e12 −0.148851 −0.0744253 0.997227i 0.523712π-0.523712\pi
−0.0744253 + 0.997227i 0.523712π0.523712\pi
108108 −4.42019e13 −2.68032
109109 8.23338e12 0.470225 0.235113 0.971968i 0.424454π-0.424454\pi
0.235113 + 0.971968i 0.424454π0.424454\pi
110110 3.23302e13 1.74003
111111 1.66220e13 0.843495
112112 −2.24705e13 −1.07571
113113 2.01925e13 0.912388 0.456194 0.889880i 0.349212π-0.349212\pi
0.456194 + 0.889880i 0.349212π0.349212\pi
114114 −3.56961e13 −1.52314
115115 −1.61541e13 −0.651248
116116 −2.93834e13 −1.11976
117117 −1.08507e13 −0.391065
118118 6.51858e13 2.22290
119119 1.06664e13 0.344319
120120 −4.62833e13 −1.41497
121121 3.32787e13 0.963965
122122 −7.27572e13 −1.99773
123123 −4.76101e12 −0.123970
124124 −4.60054e13 −1.13650
125125 −4.42207e13 −1.03684
126126 −1.36664e13 −0.304261
127127 7.03521e12 0.148783 0.0743914 0.997229i 0.476299π-0.476299\pi
0.0743914 + 0.997229i 0.476299π0.476299\pi
128128 −2.26591e13 −0.455384
129129 1.96748e13 0.375905
130130 −6.67343e13 −1.21260
131131 6.10944e13 1.05618 0.528090 0.849188i 0.322908π-0.322908\pi
0.528090 + 0.849188i 0.322908π0.322908\pi
132132 −1.63014e14 −2.68222
133133 −2.74807e13 −0.430520
134134 −1.86267e14 −2.77942
135135 −5.08236e13 −0.722597
136136 1.70853e14 2.31537
137137 −2.39957e12 −0.0310062 −0.0155031 0.999880i 0.504935π-0.504935\pi
−0.0155031 + 0.999880i 0.504935π0.504935\pi
138138 1.14404e14 1.41003
139139 −1.35358e14 −1.59180 −0.795898 0.605431i 0.793001π-0.793001\pi
−0.795898 + 0.605431i 0.793001π0.793001\pi
140140 −5.98415e13 −0.671692
141141 −1.39317e14 −1.49307
142142 −2.41645e13 −0.247346
143143 −1.39952e14 −1.36866
144144 −1.13011e14 −1.05625
145145 −3.37852e13 −0.301880
146146 2.16834e14 1.85282
147147 −7.89755e13 −0.645550
148148 3.44245e14 2.69256
149149 2.20203e14 1.64859 0.824296 0.566159i 0.191571π-0.191571\pi
0.824296 + 0.566159i 0.191571π0.191571\pi
150150 1.11899e14 0.802110
151151 −1.04073e14 −0.714479 −0.357240 0.934013i 0.616282π-0.616282\pi
−0.357240 + 0.934013i 0.616282π0.616282\pi
152152 −4.40186e14 −2.89503
153153 5.36446e13 0.338089
154154 −1.76269e14 −1.06486
155155 −5.28973e13 −0.306392
156156 3.36485e14 1.86920
157157 3.51596e14 1.87368 0.936842 0.349753i 0.113735π-0.113735\pi
0.936842 + 0.349753i 0.113735π0.113735\pi
158158 −6.81809e14 −3.48652
159159 2.93574e13 0.144091
160160 −3.07249e14 −1.44781
161161 8.80745e13 0.398549
162162 1.88286e14 0.818411
163163 4.20751e14 1.75714 0.878568 0.477617i 0.158499π-0.158499\pi
0.878568 + 0.477617i 0.158499π0.158499\pi
164164 −9.86017e13 −0.395730
165165 −1.87434e14 −0.723108
166166 −7.42433e14 −2.75394
167167 −3.34789e14 −1.19430 −0.597152 0.802128i 0.703701π-0.703701\pi
−0.597152 + 0.802128i 0.703701π0.703701\pi
168168 2.52344e14 0.865928
169169 −1.39934e13 −0.0462018
170170 3.29927e14 1.04833
171171 −1.38210e14 −0.422731
172172 4.07470e14 1.19994
173173 2.84525e13 0.0806903 0.0403452 0.999186i 0.487154π-0.487154\pi
0.0403452 + 0.999186i 0.487154π0.487154\pi
174174 2.39269e14 0.653606
175175 8.61461e13 0.226719
176176 −1.45762e15 −3.69668
177177 −3.77914e14 −0.923777
178178 −4.46137e14 −1.05133
179179 6.60949e14 1.50184 0.750920 0.660393i 0.229610π-0.229610\pi
0.750920 + 0.660393i 0.229610π0.229610\pi
180180 −3.00962e14 −0.659540
181181 6.24507e14 1.32016 0.660080 0.751196i 0.270523π-0.270523\pi
0.660080 + 0.751196i 0.270523π0.270523\pi
182182 3.63846e14 0.742084
183183 4.21810e14 0.830204
184184 1.41077e15 2.68004
185185 3.95814e14 0.725898
186186 3.74622e14 0.663375
187187 6.91907e14 1.18325
188188 −2.88529e15 −4.76611
189189 2.77098e14 0.442213
190190 −8.50022e14 −1.31079
191191 4.85135e14 0.723012 0.361506 0.932370i 0.382263π-0.382263\pi
0.361506 + 0.932370i 0.382263π0.382263\pi
192192 7.58126e14 1.09215
193193 −6.81300e14 −0.948890 −0.474445 0.880285i 0.657351π-0.657351\pi
−0.474445 + 0.880285i 0.657351π0.657351\pi
194194 2.01554e15 2.71444
195195 3.86892e14 0.503924
196196 −1.63560e15 −2.06069
197197 5.84517e13 0.0712470
198198 −8.86515e14 −1.04559
199199 −6.99058e14 −0.797937 −0.398968 0.916965i 0.630632π-0.630632\pi
−0.398968 + 0.916965i 0.630632π0.630632\pi
200200 1.37988e15 1.52457
201201 1.07988e15 1.15505
202202 1.49513e15 1.54844
203203 1.84202e14 0.184744
204204 −1.66354e15 −1.61599
205205 −1.13373e14 −0.106686
206206 1.49094e15 1.35932
207207 4.42955e14 0.391338
208208 3.00874e15 2.57616
209209 −1.78263e15 −1.47948
210210 4.87289e14 0.392068
211211 −1.16834e14 −0.0911450 −0.0455725 0.998961i 0.514511π-0.514511\pi
−0.0455725 + 0.998961i 0.514511π0.514511\pi
212212 6.07999e14 0.459960
213213 1.40094e14 0.102790
214214 3.89686e14 0.277348
215215 4.68512e14 0.323497
216216 4.43855e15 2.97366
217217 2.88404e14 0.187505
218218 −1.38851e15 −0.876154
219219 −1.25709e15 −0.769982
220220 −3.88181e15 −2.30827
221221 −1.42820e15 −0.824592
222222 −2.80318e15 −1.57165
223223 1.83327e15 0.998261 0.499130 0.866527i 0.333653π-0.333653\pi
0.499130 + 0.866527i 0.333653π0.333653\pi
224224 1.67517e15 0.886025
225225 4.33257e14 0.222617
226226 −3.40533e15 −1.70002
227227 −2.16336e15 −1.04945 −0.524724 0.851272i 0.675831π-0.675831\pi
−0.524724 + 0.851272i 0.675831π0.675831\pi
228228 4.28594e15 2.02055
229229 −2.13339e15 −0.977550 −0.488775 0.872410i 0.662556π-0.662556\pi
−0.488775 + 0.872410i 0.662556π0.662556\pi
230230 2.72428e15 1.21345
231231 1.02192e15 0.442526
232232 2.95054e15 1.24231
233233 −1.87987e14 −0.0769688 −0.0384844 0.999259i 0.512253π-0.512253\pi
−0.0384844 + 0.999259i 0.512253π0.512253\pi
234234 1.82990e15 0.728658
235235 −3.31753e15 −1.28491
236236 −7.82670e15 −2.94884
237237 3.95279e15 1.44890
238238 −1.79881e15 −0.641557
239239 −4.75777e15 −1.65127 −0.825633 0.564208i 0.809182π-0.809182\pi
−0.825633 + 0.564208i 0.809182π0.809182\pi
240240 4.02953e15 1.36107
241241 −1.43440e15 −0.471586 −0.235793 0.971803i 0.575769π-0.575769\pi
−0.235793 + 0.971803i 0.575769π0.575769\pi
242242 −5.61223e15 −1.79612
243243 2.38876e15 0.744271
244244 8.73579e15 2.65014
245245 −1.88063e15 −0.555550
246246 8.02913e14 0.230988
247247 3.67960e15 1.03103
248248 4.61965e15 1.26088
249249 4.30425e15 1.14446
250250 7.45754e15 1.93190
251251 1.42140e15 0.358787 0.179393 0.983777i 0.442587π-0.442587\pi
0.179393 + 0.983777i 0.442587π0.442587\pi
252252 1.64089e15 0.403624
253253 5.71323e15 1.36961
254254 −1.18644e15 −0.277222
255255 −1.91275e15 −0.435659
256256 −2.53085e15 −0.561961
257257 4.96896e15 1.07572 0.537861 0.843034i 0.319233π-0.319233\pi
0.537861 + 0.843034i 0.319233π0.319233\pi
258258 −3.31803e15 −0.700410
259259 −2.15804e15 −0.444233
260260 8.01263e15 1.60860
261261 9.26412e14 0.181401
262262 −1.03032e16 −1.96794
263263 6.85544e15 1.27739 0.638694 0.769461i 0.279475π-0.279475\pi
0.638694 + 0.769461i 0.279475π0.279475\pi
264264 1.63691e16 2.97576
265265 6.99081e14 0.124002
266266 4.63445e15 0.802172
267267 2.58648e15 0.436903
268268 2.23646e16 3.68710
269269 2.11302e15 0.340028 0.170014 0.985442i 0.445619π-0.445619\pi
0.170014 + 0.985442i 0.445619π0.445619\pi
270270 8.57107e15 1.34639
271271 3.88890e15 0.596385 0.298192 0.954506i 0.403616π-0.403616\pi
0.298192 + 0.954506i 0.403616π0.403616\pi
272272 −1.48749e16 −2.22718
273273 −2.10939e15 −0.308390
274274 4.04671e14 0.0577728
275275 5.58814e15 0.779121
276276 −1.37362e16 −1.87050
277277 −4.65652e15 −0.619360 −0.309680 0.950841i 0.600222π-0.600222\pi
−0.309680 + 0.950841i 0.600222π0.600222\pi
278278 2.28272e16 2.96594
279279 1.45048e15 0.184113
280280 6.00900e15 0.745203
281281 8.50499e15 1.03058 0.515291 0.857015i 0.327684π-0.327684\pi
0.515291 + 0.857015i 0.327684π0.327684\pi
282282 2.34949e16 2.78199
283283 −5.02144e15 −0.581054 −0.290527 0.956867i 0.593831π-0.593831\pi
−0.290527 + 0.956867i 0.593831π0.593831\pi
284284 2.90138e15 0.328122
285285 4.92800e15 0.544727
286286 2.36020e16 2.55017
287287 6.18125e14 0.0652896
288288 8.42496e15 0.869995
289289 −2.84372e15 −0.287112
290290 5.69765e15 0.562482
291291 −1.16851e16 −1.12805
292292 −2.60347e16 −2.45790
293293 −1.47381e15 −0.136082 −0.0680412 0.997683i 0.521675π-0.521675\pi
−0.0680412 + 0.997683i 0.521675π0.521675\pi
294294 1.33187e16 1.20283
295295 −8.99919e15 −0.794987
296296 −3.45674e16 −2.98724
297297 1.79749e16 1.51967
298298 −3.71358e16 −3.07176
299299 −1.17929e16 −0.954464
300300 −1.34355e16 −1.06406
301301 −2.55440e15 −0.197973
302302 1.75513e16 1.33126
303303 −8.66800e15 −0.643490
304304 3.83235e16 2.78476
305305 1.00445e16 0.714459
306306 −9.04681e15 −0.629950
307307 −1.24139e16 −0.846269 −0.423134 0.906067i 0.639070π-0.639070\pi
−0.423134 + 0.906067i 0.639070π0.639070\pi
308308 2.11642e16 1.41261
309309 −8.64369e15 −0.564897
310310 8.92078e15 0.570889
311311 4.99006e15 0.312726 0.156363 0.987700i 0.450023π-0.450023\pi
0.156363 + 0.987700i 0.450023π0.450023\pi
312312 −3.37882e16 −2.07377
313313 1.01680e14 0.00611218 0.00305609 0.999995i 0.499027π-0.499027\pi
0.00305609 + 0.999995i 0.499027π0.499027\pi
314314 −5.92944e16 −3.49117
315315 1.88671e15 0.108814
316316 8.18632e16 4.62512
317317 −1.22078e16 −0.675700 −0.337850 0.941200i 0.609700π-0.609700\pi
−0.337850 + 0.941200i 0.609700π0.609700\pi
318318 −4.95093e15 −0.268479
319319 1.19488e16 0.634873
320320 1.80531e16 0.939888
321321 −2.25920e15 −0.115258
322322 −1.48532e16 −0.742602
323323 −1.81915e16 −0.891360
324324 −2.26071e16 −1.08568
325325 −1.15347e16 −0.542958
326326 −7.09569e16 −3.27401
327327 8.04986e15 0.364106
328328 9.90111e15 0.439040
329329 1.80877e16 0.786337
330330 3.16096e16 1.34734
331331 2.84055e16 1.18719 0.593595 0.804764i 0.297708π-0.297708\pi
0.593595 + 0.804764i 0.297708π0.297708\pi
332332 8.91422e16 3.65330
333333 −1.08535e16 −0.436196
334334 5.64601e16 2.22530
335335 2.57149e16 0.994017
336336 −2.19696e16 −0.832945
337337 −4.27689e16 −1.59050 −0.795250 0.606282i 0.792660π-0.792660\pi
−0.795250 + 0.606282i 0.792660π0.792660\pi
338338 2.35989e15 0.0860862
339339 1.97424e16 0.706482
340340 −3.96135e16 −1.39069
341341 1.87083e16 0.644362
342342 2.33081e16 0.787659
343343 2.25522e16 0.747787
344344 −4.09162e16 −1.33127
345345 −1.57940e16 −0.504276
346346 −4.79834e15 −0.150347
347347 1.49991e16 0.461238 0.230619 0.973044i 0.425925π-0.425925\pi
0.230619 + 0.973044i 0.425925π0.425925\pi
348348 −2.87284e16 −0.867055
349349 8.84743e15 0.262091 0.131045 0.991376i 0.458167π-0.458167\pi
0.131045 + 0.991376i 0.458167π0.458167\pi
350350 −1.45280e16 −0.422438
351351 −3.71028e16 −1.05903
352352 1.08665e17 3.04483
353353 −4.66735e16 −1.28391 −0.641955 0.766742i 0.721877π-0.721877\pi
−0.641955 + 0.766742i 0.721877π0.721877\pi
354354 6.37328e16 1.72124
355355 3.33602e15 0.0884595
356356 5.35666e16 1.39466
357357 1.04286e16 0.266614
358358 −1.11465e17 −2.79832
359359 5.38973e16 1.32878 0.664390 0.747386i 0.268691π-0.268691\pi
0.664390 + 0.747386i 0.268691π0.268691\pi
360360 3.02212e16 0.731721
361361 4.81561e15 0.114513
362362 −1.05319e17 −2.45981
363363 3.25369e16 0.746420
364364 −4.36861e16 −0.984428
365365 −2.99349e16 −0.662634
366366 −7.11355e16 −1.54689
367367 −4.87652e16 −1.04179 −0.520895 0.853621i 0.674402π-0.674402\pi
−0.520895 + 0.853621i 0.674402π0.674402\pi
368368 −1.22825e17 −2.57796
369369 3.10875e15 0.0641084
370370 −6.67515e16 −1.35254
371371 −3.81149e15 −0.0758866
372372 −4.49800e16 −0.880015
373373 5.97019e16 1.14784 0.573920 0.818912i 0.305422π-0.305422\pi
0.573920 + 0.818912i 0.305422π0.305422\pi
374374 −1.16686e17 −2.20471
375375 −4.32351e16 −0.802847
376376 2.89727e17 5.28772
377377 −2.46642e16 −0.442433
378378 −4.67308e16 −0.823961
379379 4.52310e16 0.783937 0.391969 0.919979i 0.371794π-0.371794\pi
0.391969 + 0.919979i 0.371794π0.371794\pi
380380 1.02060e17 1.73885
381381 6.87839e15 0.115206
382382 −8.18148e16 −1.34716
383383 6.60843e15 0.106981 0.0534904 0.998568i 0.482965π-0.482965\pi
0.0534904 + 0.998568i 0.482965π0.482965\pi
384384 −2.21540e16 −0.352614
385385 2.43347e16 0.380831
386386 1.14897e17 1.76803
387387 −1.28469e16 −0.194391
388388 −2.42001e17 −3.60091
389389 −9.26328e16 −1.35548 −0.677739 0.735303i 0.737040π-0.737040\pi
−0.677739 + 0.735303i 0.737040π0.737040\pi
390390 −6.52468e16 −0.938943
391391 5.83030e16 0.825167
392392 1.64239e17 2.28622
393393 5.97326e16 0.817824
394394 −9.85750e15 −0.132752
395395 9.41268e16 1.24690
396396 1.06442e17 1.38705
397397 −2.77565e16 −0.355817 −0.177908 0.984047i 0.556933π-0.556933\pi
−0.177908 + 0.984047i 0.556933π0.556933\pi
398398 1.17892e17 1.48677
399399 −2.68682e16 −0.333361
400400 −1.20136e17 −1.46650
401401 −4.95716e16 −0.595380 −0.297690 0.954663i 0.596216π-0.596216\pi
−0.297690 + 0.954663i 0.596216π0.596216\pi
402402 −1.82115e17 −2.15216
403403 −3.86166e16 −0.449046
404404 −1.79516e17 −2.05412
405405 −2.59938e16 −0.292693
406406 −3.10644e16 −0.344227
407407 −1.39988e17 −1.52661
408408 1.67045e17 1.79284
409409 1.31500e16 0.138907 0.0694534 0.997585i 0.477874π-0.477874\pi
0.0694534 + 0.997585i 0.477874π0.477874\pi
410410 1.91196e16 0.198785
411411 −2.34608e15 −0.0240088
412412 −1.79013e17 −1.80324
413413 4.90649e16 0.486515
414414 −7.47015e16 −0.729167
415415 1.02496e17 0.984907
416416 −2.24301e17 −2.12190
417417 −1.32341e17 −1.23256
418418 3.00628e17 2.75666
419419 −1.50811e17 −1.36157 −0.680786 0.732482i 0.738362π-0.738362\pi
−0.680786 + 0.732482i 0.738362π0.738362\pi
420420 −5.85076e16 −0.520106
421421 8.33826e15 0.0729864 0.0364932 0.999334i 0.488381π-0.488381\pi
0.0364932 + 0.999334i 0.488381π0.488381\pi
422422 1.97033e16 0.169827
423423 9.09687e16 0.772111
424424 −6.10524e16 −0.510299
425425 5.70265e16 0.469406
426426 −2.36259e16 −0.191525
427427 −5.47639e16 −0.437233
428428 −4.67886e16 −0.367922
429429 −1.36833e17 −1.05978
430430 −7.90114e16 −0.602761
431431 3.93492e16 0.295688 0.147844 0.989011i 0.452767π-0.452767\pi
0.147844 + 0.989011i 0.452767π0.452767\pi
432432 −3.86430e17 −2.86040
433433 1.27757e17 0.931566 0.465783 0.884899i 0.345773π-0.345773\pi
0.465783 + 0.884899i 0.345773π0.345773\pi
434434 −4.86375e16 −0.349372
435435 −3.30321e16 −0.233752
436436 1.66715e17 1.16228
437437 −1.50212e17 −1.03175
438438 2.12001e17 1.43468
439439 2.68659e17 1.79135 0.895677 0.444705i 0.146692π-0.146692\pi
0.895677 + 0.444705i 0.146692π0.146692\pi
440440 3.89793e17 2.56089
441441 5.15680e16 0.333833
442442 2.40856e17 1.53643
443443 2.46386e17 1.54879 0.774393 0.632705i 0.218055π-0.218055\pi
0.774393 + 0.632705i 0.218055π0.218055\pi
444444 3.36571e17 2.08491
445445 6.15911e16 0.375992
446446 −3.09168e17 −1.86002
447447 2.15295e17 1.27654
448448 −9.84281e16 −0.575191
449449 2.00826e17 1.15670 0.578349 0.815790i 0.303697π-0.303697\pi
0.578349 + 0.815790i 0.303697π0.303697\pi
450450 −7.30659e16 −0.414795
451451 4.00967e16 0.224368
452452 4.08869e17 2.25520
453453 −1.01754e17 −0.553237
454454 3.64837e17 1.95540
455455 −5.02305e16 −0.265395
456456 −4.30374e17 −2.24168
457457 −2.20923e17 −1.13445 −0.567227 0.823562i 0.691984π-0.691984\pi
−0.567227 + 0.823562i 0.691984π0.691984\pi
458458 3.59782e17 1.82143
459459 1.83432e17 0.915571
460460 −3.27098e17 −1.60972
461461 2.66171e17 1.29153 0.645765 0.763536i 0.276539π-0.276539\pi
0.645765 + 0.763536i 0.276539π0.276539\pi
462462 −1.72340e17 −0.824543
463463 1.86059e17 0.877757 0.438878 0.898547i 0.355376π-0.355376\pi
0.438878 + 0.898547i 0.355376π0.355376\pi
464464 −2.56880e17 −1.19499
465465 −5.17182e16 −0.237246
466466 3.17028e16 0.143413
467467 4.17029e16 0.186040 0.0930200 0.995664i 0.470348π-0.470348\pi
0.0930200 + 0.995664i 0.470348π0.470348\pi
468468 −2.19711e17 −0.966617
469469 −1.40202e17 −0.608316
470470 5.59479e17 2.39413
471471 3.43759e17 1.45084
472472 7.85920e17 3.27156
473473 −1.65699e17 −0.680335
474474 −6.66612e17 −2.69969
475475 −1.46923e17 −0.586922
476476 2.15979e17 0.851072
477477 −1.91692e16 −0.0745136
478478 8.02366e17 3.07674
479479 9.96294e16 0.376883 0.188442 0.982084i 0.439656π-0.439656\pi
0.188442 + 0.982084i 0.439656π0.439656\pi
480480 −3.00400e17 −1.12107
481481 2.88956e17 1.06387
482482 2.41903e17 0.878689
483483 8.61113e16 0.308605
484484 6.73847e17 2.38269
485485 −2.78255e17 −0.970781
486486 −4.02848e17 −1.38677
487487 4.08953e17 1.38911 0.694553 0.719441i 0.255602π-0.255602\pi
0.694553 + 0.719441i 0.255602π0.255602\pi
488488 −8.77206e17 −2.94017
489489 4.11372e17 1.36059
490490 3.17155e17 1.03514
491491 2.83532e17 0.913215 0.456607 0.889668i 0.349064π-0.349064\pi
0.456607 + 0.889668i 0.349064π0.349064\pi
492492 −9.64038e16 −0.306423
493493 1.21937e17 0.382499
494494 −6.20541e17 −1.92108
495495 1.22387e17 0.373941
496496 −4.02196e17 −1.21285
497497 −1.81885e16 −0.0541353
498498 −7.25884e17 −2.13244
499499 −2.26848e17 −0.657781 −0.328891 0.944368i 0.606675π-0.606675\pi
−0.328891 + 0.944368i 0.606675π0.606675\pi
500500 −8.95409e17 −2.56281
501501 −3.27327e17 −0.924776
502502 −2.39709e17 −0.668514
503503 2.79315e17 0.768958 0.384479 0.923134i 0.374381π-0.374381\pi
0.384479 + 0.923134i 0.374381π0.374381\pi
504504 −1.64771e17 −0.447797
505505 −2.06409e17 −0.553776
506506 −9.63499e17 −2.55195
507507 −1.36815e16 −0.0357751
508508 1.42453e17 0.367754
509509 2.57680e17 0.656772 0.328386 0.944544i 0.393495π-0.393495\pi
0.328386 + 0.944544i 0.393495π0.393495\pi
510510 3.22573e17 0.811749
511511 1.63209e17 0.405517
512512 6.12434e17 1.50247
513513 −4.72593e17 −1.14479
514514 −8.37982e17 −2.00435
515515 −2.05830e17 −0.486141
516516 3.98388e17 0.929144
517517 1.17331e18 2.70225
518518 3.63939e17 0.827724
519519 2.78183e16 0.0624803
520520 −8.04590e17 −1.78465
521521 2.39796e17 0.525287 0.262643 0.964893i 0.415406π-0.415406\pi
0.262643 + 0.964893i 0.415406π0.415406\pi
522522 −1.56233e17 −0.337999
523523 4.83508e17 1.03310 0.516551 0.856257i 0.327216π-0.327216\pi
0.516551 + 0.856257i 0.327216π0.327216\pi
524524 1.23708e18 2.61062
525525 8.42259e16 0.175554
526526 −1.15612e18 −2.38011
527527 1.90916e17 0.388216
528528 −1.42513e18 −2.86242
529529 −2.26156e16 −0.0448690
530530 −1.17895e17 −0.231049
531531 2.46763e17 0.477712
532532 −5.56447e17 −1.06414
533533 −8.27654e16 −0.156359
534534 −4.36192e17 −0.814067
535535 −5.37978e16 −0.0991893
536536 −2.24574e18 −4.09062
537537 6.46217e17 1.16291
538538 −3.56347e17 −0.633561
539539 6.65123e17 1.16836
540540 −1.02911e18 −1.78608
541541 1.04736e17 0.179603 0.0898016 0.995960i 0.471377π-0.471377\pi
0.0898016 + 0.995960i 0.471377π0.471377\pi
542542 −6.55838e17 −1.11122
543543 6.10586e17 1.02223
544544 1.10892e18 1.83445
545545 1.91689e17 0.313343
546546 3.55735e17 0.574612
547547 −6.03348e17 −0.963054 −0.481527 0.876431i 0.659918π-0.659918\pi
−0.481527 + 0.876431i 0.659918π0.659918\pi
548548 −4.85879e16 −0.0766398
549549 −2.75425e17 −0.429323
550550 −9.42403e17 −1.45171
551551 −3.14158e17 −0.478258
552552 1.37933e18 2.07522
553553 −5.13193e17 −0.763076
554554 7.85292e17 1.15403
555555 3.86992e17 0.562079
556556 −2.74081e18 −3.93453
557557 1.94030e16 0.0275302 0.0137651 0.999905i 0.495618π-0.495618\pi
0.0137651 + 0.999905i 0.495618π0.495618\pi
558558 −2.44614e17 −0.343051
559559 3.42027e17 0.474115
560560 −5.23156e17 −0.716819
561561 6.76485e17 0.916219
562562 −1.43431e18 −1.92025
563563 7.77947e17 1.02955 0.514773 0.857327i 0.327876π-0.327876\pi
0.514773 + 0.857327i 0.327876π0.327876\pi
564564 −2.82098e18 −3.69050
565565 4.70120e17 0.607987
566566 8.46833e17 1.08266
567567 1.41722e17 0.179121
568568 −2.91343e17 −0.364032
569569 −9.09128e17 −1.12304 −0.561520 0.827463i 0.689783π-0.689783\pi
−0.561520 + 0.827463i 0.689783π0.689783\pi
570570 −8.31075e17 −1.01497
571571 −1.52398e18 −1.84011 −0.920057 0.391784i 0.871858π-0.871858\pi
−0.920057 + 0.391784i 0.871858π0.871858\pi
572572 −2.83384e18 −3.38299
573573 4.74321e17 0.559844
574574 −1.04243e17 −0.121652
575575 4.70880e17 0.543337
576576 −4.95027e17 −0.564784
577577 1.21715e18 1.37309 0.686546 0.727086i 0.259126π-0.259126\pi
0.686546 + 0.727086i 0.259126π0.259126\pi
578578 4.79575e17 0.534966
579579 −6.66113e17 −0.734746
580580 −6.84103e17 −0.746173
581581 −5.58825e17 −0.602741
582582 1.97062e18 2.10186
583583 −2.47245e17 −0.260784
584584 2.61428e18 2.72690
585585 −2.52625e17 −0.260594
586586 2.48549e17 0.253558
587587 8.69734e17 0.877483 0.438742 0.898613i 0.355424π-0.355424\pi
0.438742 + 0.898613i 0.355424π0.355424\pi
588588 −1.59915e18 −1.59564
589589 −4.91875e17 −0.485406
590590 1.51765e18 1.48127
591591 5.71488e16 0.0551682
592592 3.00951e18 2.87346
593593 −5.90997e17 −0.558123 −0.279061 0.960273i 0.590023π-0.590023\pi
−0.279061 + 0.960273i 0.590023π0.590023\pi
594594 −3.03134e18 −2.83154
595595 2.48334e17 0.229443
596596 4.45881e18 4.07491
597597 −6.83476e17 −0.617860
598598 1.98880e18 1.77842
599599 9.71699e17 0.859523 0.429762 0.902942i 0.358598π-0.358598\pi
0.429762 + 0.902942i 0.358598π0.358598\pi
600600 1.34913e18 1.18051
601601 1.40573e18 1.21680 0.608399 0.793631i 0.291812π-0.291812\pi
0.608399 + 0.793631i 0.291812π0.291812\pi
602602 4.30782e17 0.368876
603603 −7.05120e17 −0.597311
604604 −2.10734e18 −1.76602
605605 7.74793e17 0.642356
606606 1.46180e18 1.19899
607607 −2.00311e18 −1.62547 −0.812734 0.582635i 0.802022π-0.802022\pi
−0.812734 + 0.582635i 0.802022π0.802022\pi
608608 −2.85701e18 −2.29371
609609 1.80096e17 0.143051
610610 −1.69393e18 −1.33123
611611 −2.42189e18 −1.88316
612612 1.08623e18 0.835674
613613 1.42761e18 1.08672 0.543360 0.839500i 0.317152π-0.317152\pi
0.543360 + 0.839500i 0.317152π0.317152\pi
614614 2.09352e18 1.57682
615615 −1.10846e17 −0.0826096
616616 −2.12521e18 −1.56721
617617 −6.56052e17 −0.478724 −0.239362 0.970930i 0.576938π-0.576938\pi
−0.239362 + 0.970930i 0.576938π0.576938\pi
618618 1.45770e18 1.05255
619619 2.07305e18 1.48123 0.740613 0.671932i 0.234535π-0.234535\pi
0.740613 + 0.671932i 0.234535π0.234535\pi
620620 −1.07110e18 −0.757326
621621 1.51464e18 1.05977
622622 −8.41541e17 −0.582690
623623 −3.35804e17 −0.230099
624624 2.94167e18 1.99478
625625 −2.01112e17 −0.134964
626626 −1.71476e16 −0.0113886
627627 −1.74289e18 −1.14560
628628 7.11933e18 4.63129
629629 −1.42857e18 −0.919754
630630 −3.18181e17 −0.202750
631631 −5.78882e17 −0.365089 −0.182545 0.983198i 0.558433π-0.558433\pi
−0.182545 + 0.983198i 0.558433π0.558433\pi
632632 −8.22031e18 −5.13130
633633 −1.14230e17 −0.0705756
634634 2.05877e18 1.25901
635635 1.63793e17 0.0991442
636636 5.94447e17 0.356157
637637 −1.37291e18 −0.814210
638638 −2.01509e18 −1.18294
639639 −9.14759e16 −0.0531558
640640 −5.27549e17 −0.303454
641641 −1.85697e18 −1.05737 −0.528687 0.848817i 0.677315π-0.677315\pi
−0.528687 + 0.848817i 0.677315π0.677315\pi
642642 3.80999e17 0.214757
643643 −9.29050e17 −0.518403 −0.259202 0.965823i 0.583459π-0.583459\pi
−0.259202 + 0.965823i 0.583459π0.583459\pi
644644 1.78339e18 0.985115
645645 4.58069e17 0.250491
646646 3.06788e18 1.66084
647647 2.68373e18 1.43834 0.719170 0.694834i 0.244522π-0.244522\pi
0.719170 + 0.694834i 0.244522π0.244522\pi
648648 2.27010e18 1.20450
649649 3.18275e18 1.67191
650650 1.94526e18 1.01167
651651 2.81976e17 0.145189
652652 8.51962e18 4.34321
653653 9.76106e17 0.492676 0.246338 0.969184i 0.420773π-0.420773\pi
0.246338 + 0.969184i 0.420773π0.420773\pi
654654 −1.35756e18 −0.678426
655655 1.42240e18 0.703805
656656 −8.62012e17 −0.422317
657657 8.20833e17 0.398181
658658 −3.05036e18 −1.46515
659659 −3.05827e18 −1.45452 −0.727261 0.686361i 0.759207π-0.759207\pi
−0.727261 + 0.686361i 0.759207π0.759207\pi
660660 −3.79528e18 −1.78735
661661 4.02652e18 1.87768 0.938838 0.344359i 0.111904π-0.111904\pi
0.938838 + 0.344359i 0.111904π0.111904\pi
662662 −4.79040e18 −2.21205
663663 −1.39636e18 −0.638500
664664 −8.95123e18 −4.05313
665665 −6.39806e17 −0.286885
666666 1.83037e18 0.812749
667667 1.00686e18 0.442742
668668 −6.77902e18 −2.95203
669669 1.79240e18 0.772976
670670 −4.33665e18 −1.85212
671671 −3.55243e18 −1.50255
672672 1.63783e18 0.686069
673673 2.53323e18 1.05094 0.525468 0.850814i 0.323890π-0.323890\pi
0.525468 + 0.850814i 0.323890π0.323890\pi
674674 7.21269e18 2.96352
675675 1.48147e18 0.602864
676676 −2.83347e17 −0.114200
677677 1.77456e18 0.708379 0.354189 0.935174i 0.384757π-0.384757\pi
0.354189 + 0.935174i 0.384757π0.384757\pi
678678 −3.32942e18 −1.31636
679679 1.51709e18 0.594096
680680 3.97780e18 1.54289
681681 −2.11514e18 −0.812611
682682 −3.15502e18 −1.20062
683683 3.40712e18 1.28426 0.642130 0.766596i 0.278051π-0.278051\pi
0.642130 + 0.766596i 0.278051π0.278051\pi
684684 −2.79855e18 −1.04489
685685 −5.58666e16 −0.0206616
686686 −3.80329e18 −1.39332
687687 −2.08583e18 −0.756939
688688 3.56226e18 1.28056
689689 5.10350e17 0.181737
690690 2.66355e18 0.939599
691691 2.47368e18 0.864443 0.432221 0.901768i 0.357730π-0.357730\pi
0.432221 + 0.901768i 0.357730π0.357730\pi
692692 5.76125e17 0.199447
693693 −6.67274e17 −0.228843
694694 −2.52951e18 −0.859408
695695 −3.15140e18 −1.06072
696696 2.88477e18 0.961947
697697 4.09183e17 0.135178
698698 −1.49206e18 −0.488345
699699 −1.83797e17 −0.0595987
700700 1.74434e18 0.560394
701701 −5.59856e18 −1.78201 −0.891003 0.453998i 0.849997π-0.849997\pi
−0.891003 + 0.453998i 0.849997π0.849997\pi
702702 6.25714e18 1.97326
703703 3.68055e18 1.15001
704704 −6.38485e18 −1.97664
705705 −3.24358e18 −0.994936
706706 7.87118e18 2.39226
707707 1.12537e18 0.338899
708708 −7.65224e18 −2.28335
709709 4.84633e18 1.43289 0.716444 0.697644i 0.245768π-0.245768\pi
0.716444 + 0.697644i 0.245768π0.245768\pi
710710 −5.62598e17 −0.164823
711711 −2.58102e18 −0.749270
712712 −5.37890e18 −1.54730
713713 1.57644e18 0.449360
714714 −1.75872e18 −0.496772
715715 −3.25836e18 −0.912031
716716 1.33833e19 3.71218
717717 −4.65172e18 −1.27861
718718 −9.08943e18 −2.47587
719719 4.13840e18 1.11711 0.558554 0.829468i 0.311356π-0.311356\pi
0.558554 + 0.829468i 0.311356π0.311356\pi
720720 −2.63112e18 −0.703850
721721 1.12222e18 0.297507
722722 −8.12121e17 −0.213368
723723 −1.40243e18 −0.365159
724724 1.26454e19 3.26311
725725 9.84815e17 0.251859
726726 −5.48714e18 −1.39078
727727 2.30819e18 0.579827 0.289914 0.957053i 0.406373π-0.406373\pi
0.289914 + 0.957053i 0.406373π0.406373\pi
728728 4.38674e18 1.09217
729729 4.11553e18 1.01554
730730 5.04832e18 1.23466
731731 −1.69095e18 −0.409889
732732 8.54106e18 2.05206
733733 9.74851e17 0.232147 0.116073 0.993241i 0.462969π-0.462969\pi
0.116073 + 0.993241i 0.462969π0.462969\pi
734734 8.22392e18 1.94113
735735 −1.83871e18 −0.430174
736736 9.15658e18 2.12338
737737 −9.09462e18 −2.09048
738738 −5.24271e17 −0.119451
739739 −1.83041e18 −0.413390 −0.206695 0.978405i 0.566271π-0.566271\pi
−0.206695 + 0.978405i 0.566271π0.566271\pi
740740 8.01469e18 1.79424
741741 3.59758e18 0.798349
742742 6.42784e17 0.141397
743743 9.61873e17 0.209745 0.104872 0.994486i 0.466557π-0.466557\pi
0.104872 + 0.994486i 0.466557π0.466557\pi
744744 4.51667e18 0.976325
745745 5.12677e18 1.09857
746746 −1.00683e19 −2.13873
747747 −2.81051e18 −0.591836
748748 1.40102e19 2.92471
749749 2.93314e17 0.0607017
750750 7.29131e18 1.49592
751751 −2.27503e16 −0.00462731 −0.00231365 0.999997i 0.500736π-0.500736\pi
−0.00231365 + 0.999997i 0.500736π0.500736\pi
752752 −2.52243e19 −5.08631
753753 1.38971e18 0.277817
754754 4.15945e18 0.824370
755755 −2.42303e18 −0.476107
756756 5.61085e18 1.09304
757757 1.33460e16 0.00257768 0.00128884 0.999999i 0.499590π-0.499590\pi
0.00128884 + 0.999999i 0.499590π0.499590\pi
758758 −7.62791e18 −1.46068
759759 5.58588e18 1.06052
760760 −1.02484e19 −1.92915
761761 −7.44101e18 −1.38877 −0.694387 0.719602i 0.744324π-0.744324\pi
−0.694387 + 0.719602i 0.744324π0.744324\pi
762762 −1.16000e18 −0.214659
763763 −1.04512e18 −0.191759
764764 9.82330e18 1.78711
765765 1.24895e18 0.225292
766766 −1.11447e18 −0.199334
767767 −6.56967e18 −1.16513
768768 −2.47443e18 −0.435139
769769 −5.10767e18 −0.890638 −0.445319 0.895372i 0.646910π-0.646910\pi
−0.445319 + 0.895372i 0.646910π0.646910\pi
770770 −4.10389e18 −0.709588
771771 4.85820e18 0.832955
772772 −1.37954e19 −2.34542
773773 −5.37726e18 −0.906555 −0.453278 0.891369i 0.649745π-0.649745\pi
−0.453278 + 0.891369i 0.649745π0.649745\pi
774774 2.16654e18 0.362202
775775 1.54192e18 0.255623
776776 2.43006e19 3.99500
777777 −2.10994e18 −0.343980
778778 1.56219e19 2.52561
779779 −1.05422e18 −0.169019
780780 7.83402e18 1.24558
781781 −1.17985e18 −0.186036
782782 −9.83242e18 −1.53751
783783 3.16776e18 0.491249
784784 −1.42990e19 −2.19914
785785 8.18585e18 1.24856
786786 −1.00735e19 −1.52382
787787 −7.93261e18 −1.19009 −0.595045 0.803692i 0.702866π-0.702866\pi
−0.595045 + 0.803692i 0.702866π0.702866\pi
788788 1.18357e18 0.176105
789789 6.70263e18 0.989110
790790 −1.58739e19 −2.32331
791791 −2.56317e18 −0.372074
792792 −1.06884e19 −1.53886
793793 7.33275e18 1.04711
794794 4.68095e18 0.662981
795795 6.83498e17 0.0960176
796796 −1.41550e19 −1.97230
797797 −4.94222e18 −0.683035 −0.341517 0.939875i 0.610941π-0.610941\pi
−0.341517 + 0.939875i 0.610941π0.610941\pi
798798 4.53115e18 0.621140
799799 1.19736e19 1.62806
800800 8.95609e18 1.20791
801801 −1.68887e18 −0.225936
802802 8.35992e18 1.10935
803803 1.05871e19 1.39356
804804 2.18661e19 2.85500
805805 2.05055e18 0.265581
806806 6.51244e18 0.836692
807807 2.06592e18 0.263291
808808 1.80262e19 2.27892
809809 9.58960e18 1.20264 0.601319 0.799009i 0.294642π-0.294642\pi
0.601319 + 0.799009i 0.294642π0.294642\pi
810810 4.38368e18 0.545364
811811 1.48266e19 1.82981 0.914905 0.403670i 0.132266π-0.132266\pi
0.914905 + 0.403670i 0.132266π0.132266\pi
812812 3.72983e18 0.456641
813813 3.80222e18 0.461794
814814 2.36081e19 2.84448
815815 9.79591e18 1.17090
816816 −1.45433e19 −1.72455
817817 4.35654e18 0.512505
818818 −2.21766e18 −0.258820
819819 1.37735e18 0.159478
820820 −2.29564e18 −0.263702
821821 −9.00025e18 −1.02571 −0.512854 0.858476i 0.671412π-0.671412\pi
−0.512854 + 0.858476i 0.671412π0.671412\pi
822822 3.95651e17 0.0447348
823823 5.63543e18 0.632162 0.316081 0.948732i 0.397633π-0.397633\pi
0.316081 + 0.948732i 0.397633π0.397633\pi
824824 1.79756e19 2.00059
825825 5.46358e18 0.603291
826826 −8.27448e18 −0.906505
827827 4.31129e18 0.468620 0.234310 0.972162i 0.424717π-0.424717\pi
0.234310 + 0.972162i 0.424717π0.424717\pi
828828 8.96923e18 0.967292
829829 5.67661e17 0.0607413 0.0303707 0.999539i 0.490331π-0.490331\pi
0.0303707 + 0.999539i 0.490331π0.490331\pi
830830 −1.72853e19 −1.83514
831831 −4.55273e18 −0.479585
832832 1.31793e19 1.37749
833833 6.78752e18 0.703913
834834 2.23184e19 2.29659
835835 −7.79456e18 −0.795847
836836 −3.60957e19 −3.65691
837837 4.95975e18 0.498591
838838 2.54332e19 2.53697
839839 −4.18939e18 −0.414666 −0.207333 0.978270i 0.566478π-0.566478\pi
−0.207333 + 0.978270i 0.566478π0.566478\pi
840840 5.87506e18 0.577028
841841 −8.15485e18 −0.794771
842842 −1.40619e18 −0.135993
843843 8.31541e18 0.798003
844844 −2.36572e18 −0.225288
845845 −3.25794e17 −0.0307875
846846 −1.53413e19 −1.43865
847847 −4.22429e18 −0.393108
848848 5.31535e18 0.490862
849849 −4.90951e18 −0.449923
850850 −9.61714e18 −0.874627
851851 −1.17960e19 −1.06461
852852 2.83671e18 0.254072
853853 8.68784e18 0.772224 0.386112 0.922452i 0.373818π-0.373818\pi
0.386112 + 0.922452i 0.373818π0.373818\pi
854854 9.23557e18 0.814681
855855 −3.21779e18 −0.281694
856856 4.69829e18 0.408188
857857 −2.31006e18 −0.199181 −0.0995906 0.995029i 0.531753π-0.531753\pi
−0.0995906 + 0.995029i 0.531753π0.531753\pi
858858 2.30759e19 1.97466
859859 9.12762e18 0.775179 0.387589 0.921832i 0.373308π-0.373308\pi
0.387589 + 0.921832i 0.373308π0.373308\pi
860860 9.48671e18 0.799606
861861 6.04347e17 0.0505552
862862 −6.63599e18 −0.550945
863863 −8.94008e18 −0.736667 −0.368333 0.929694i 0.620072π-0.620072\pi
−0.368333 + 0.929694i 0.620072π0.620072\pi
864864 2.88082e19 2.35601
865865 6.62431e17 0.0537695
866866 −2.15454e19 −1.73575
867867 −2.78034e18 −0.222317
868868 5.83978e18 0.463467
869869 −3.32899e19 −2.62231
870870 5.57065e18 0.435543
871871 1.87726e19 1.45683
872872 −1.67407e19 −1.28948
873873 7.62992e18 0.583348
874874 2.53322e19 1.92242
875875 5.61324e18 0.422826
876876 −2.54544e19 −1.90321
877877 −1.53523e18 −0.113940 −0.0569699 0.998376i 0.518144π-0.518144\pi
−0.0569699 + 0.998376i 0.518144π0.518144\pi
878878 −4.53075e19 −3.33777
879879 −1.44096e18 −0.105372
880880 −3.39362e19 −2.46335
881881 −4.06751e18 −0.293080 −0.146540 0.989205i 0.546814π-0.546814\pi
−0.146540 + 0.989205i 0.546814π0.546814\pi
882882 −8.69660e18 −0.622019
883883 1.66406e18 0.118148 0.0590739 0.998254i 0.481185π-0.481185\pi
0.0590739 + 0.998254i 0.481185π0.481185\pi
884884 −2.89190e19 −2.03819
885885 −8.79859e18 −0.615576
886886 −4.15514e19 −2.88580
887887 −1.40781e19 −0.970598 −0.485299 0.874348i 0.661289π-0.661289\pi
−0.485299 + 0.874348i 0.661289π0.661289\pi
888888 −3.37969e19 −2.31309
889889 −8.93027e17 −0.0606740
890890 −1.03869e19 −0.700572
891891 9.19325e18 0.615551
892892 3.71211e19 2.46746
893893 −3.08486e19 −2.03564
894894 −3.63081e19 −2.37853
895895 1.53882e19 1.00078
896896 2.87628e18 0.185707
897897 −1.15301e19 −0.739063
898898 −3.38681e19 −2.15523
899899 3.29701e18 0.208297
900900 8.77285e18 0.550255
901901 −2.52311e18 −0.157118
902902 −6.76204e18 −0.418057
903903 −2.49746e18 −0.153295
904904 −4.10567e19 −2.50201
905905 1.45397e19 0.879713
906906 1.71601e19 1.03083
907907 1.07645e19 0.642018 0.321009 0.947076i 0.395978π-0.395978\pi
0.321009 + 0.947076i 0.395978π0.395978\pi
908908 −4.38050e19 −2.59398
909909 5.65986e18 0.332767
910910 8.47104e18 0.494502
911911 −5.38036e18 −0.311847 −0.155924 0.987769i 0.549835π-0.549835\pi
−0.155924 + 0.987769i 0.549835π0.549835\pi
912912 3.74693e19 2.15630
913913 −3.62499e19 −2.07132
914914 3.72573e19 2.11379
915915 9.82056e18 0.553222
916916 −4.31981e19 −2.41626
917917 −7.75513e18 −0.430713
918918 −3.09346e19 −1.70595
919919 −3.08489e18 −0.168923 −0.0844614 0.996427i 0.526917π-0.526917\pi
−0.0844614 + 0.996427i 0.526917π0.526917\pi
920920 3.28456e19 1.78590
921921 −1.21372e19 −0.655285
922922 −4.48880e19 −2.40646
923923 2.43539e18 0.129646
924924 2.06925e19 1.09382
925925 −1.15377e19 −0.605618
926926 −3.13776e19 −1.63549
927927 5.64400e18 0.292125
928928 1.91504e19 0.984273
929929 4.76854e18 0.243379 0.121690 0.992568i 0.461169π-0.461169\pi
0.121690 + 0.992568i 0.461169π0.461169\pi
930930 8.72194e18 0.442052
931931 −1.74873e19 −0.880138
932932 −3.80648e18 −0.190248
933933 4.87883e18 0.242150
934934 −7.03292e18 −0.346642
935935 1.61090e19 0.788483
936936 2.20624e19 1.07241
937937 1.56454e19 0.755232 0.377616 0.925962i 0.376744π-0.376744\pi
0.377616 + 0.925962i 0.376744π0.376744\pi
938938 2.36441e19 1.13345
939939 9.94133e16 0.00473280
940940 −6.71753e19 −3.17599
941941 1.99139e19 0.935024 0.467512 0.883987i 0.345150π-0.345150\pi
0.467512 + 0.883987i 0.345150π0.345150\pi
942942 −5.79727e19 −2.70329
943943 3.37871e18 0.156468
944944 −6.84239e19 −3.14695
945945 6.45139e18 0.294677
946946 2.79441e19 1.26764
947947 9.90709e18 0.446346 0.223173 0.974779i 0.428359π-0.428359\pi
0.223173 + 0.974779i 0.428359π0.428359\pi
948948 8.00385e19 3.58133
949949 −2.18533e19 −0.971152
950950 2.47775e19 1.09359
951951 −1.19357e19 −0.523210
952952 −2.16876e19 −0.944215
953953 8.48243e18 0.366789 0.183395 0.983039i 0.441291π-0.441291\pi
0.183395 + 0.983039i 0.441291π0.441291\pi
954954 3.23277e18 0.138839
955955 1.12949e19 0.481792
956956 −9.63382e19 −4.08152
957957 1.16825e19 0.491596
958958 −1.68018e19 −0.702233
959959 3.04593e17 0.0126444
960960 1.76507e19 0.727776
961961 −1.92554e19 −0.788590
962962 −4.87306e19 −1.98227
963963 1.47517e18 0.0596034
964964 −2.90447e19 −1.16564
965965 −1.58620e19 −0.632310
966966 −1.45221e19 −0.575014
967967 1.71826e19 0.675797 0.337898 0.941183i 0.390284π-0.390284\pi
0.337898 + 0.941183i 0.390284π0.390284\pi
968968 −6.76645e19 −2.64345
969969 −1.77861e19 −0.690200
970970 4.69258e19 1.80882
971971 −4.44228e19 −1.70091 −0.850454 0.526050i 0.823673π-0.823673\pi
−0.850454 + 0.526050i 0.823673π0.823673\pi
972972 4.83690e19 1.83965
973973 1.71819e19 0.649139
974974 −6.89673e19 −2.58827
975975 −1.12776e19 −0.420424
976976 7.63715e19 2.82818
977977 1.89917e19 0.698635 0.349317 0.937004i 0.386413π-0.386413\pi
0.349317 + 0.937004i 0.386413π0.386413\pi
978978 −6.93752e19 −2.53514
979979 −2.17830e19 −0.790734
980980 −3.80801e19 −1.37318
981981 −5.25625e18 −0.188290
982982 −4.78159e19 −1.70156
983983 −1.07021e19 −0.378331 −0.189165 0.981945i 0.560578π-0.560578\pi
−0.189165 + 0.981945i 0.560578π0.560578\pi
984984 9.68041e18 0.339958
985985 1.36087e18 0.0474768
986986 −2.05639e19 −0.712697
987987 1.76845e19 0.608879
988988 7.45069e19 2.54845
989989 −1.39625e19 −0.474447
990990 −2.06398e19 −0.696750
991991 −5.41492e18 −0.181599 −0.0907995 0.995869i 0.528942π-0.528942\pi
−0.0907995 + 0.995869i 0.528942π0.528942\pi
992992 2.99837e19 0.998985
993993 2.77723e19 0.919268
994994 3.06737e18 0.100868
995995 −1.62754e19 −0.531720
996996 8.71552e19 2.82883
997997 2.11859e19 0.683169 0.341584 0.939851i 0.389037π-0.389037\pi
0.341584 + 0.939851i 0.389037π0.389037\pi
998998 3.82564e19 1.22562
999999 −3.71123e19 −1.18125
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 197.14.a.b.1.6 109
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.b.1.6 109 1.1 even 1 trivial