Properties

Label 867.4.a.w.1.10
Level 867867
Weight 44
Character 867.1
Self dual yes
Analytic conductor 51.15551.155
Analytic rank 00
Dimension 2020
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [867,4,Mod(1,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 867=3172 867 = 3 \cdot 17^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 867.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,0,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 51.154655975051.1546559750
Analytic rank: 00
Dimension: 2020
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20128x18+6848x16198916x141344x13+3410877x12+96960x11+2228224 x^{20} - 128 x^{18} + 6848 x^{16} - 198916 x^{14} - 1344 x^{13} + 3410877 x^{12} + 96960 x^{11} + \cdots - 2228224 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25176 2^{5}\cdot 17^{6}
Twist minimal: no (minimal twist has level 51)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.10
Root 0.0209109-0.0209109 of defining polynomial
Character χ\chi == 867.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+0.0209109q2+3.00000q37.99956q4+20.5423q5+0.0627328q6+6.44826q70.334566q8+9.00000q9+0.429559q10+18.2513q1123.9987q12+63.8416q13+0.134839q14+61.6270q15+63.9895q16+0.188198q1861.3281q19164.330q20+19.3448q21+0.381651q22+106.234q231.00370q24+296.987q25+1.33499q26+27.0000q2751.5833q28112.532q29+1.28868q30220.179q31+4.01460q32+54.7538q33+132.462q3571.9961q36187.746q371.28243q38+191.525q396.87276q40+198.268q41+0.404517q42+139.548q43146.002q44+184.881q45+2.22145q46+575.652q47+191.969q48301.420q49+6.21027q50510.705q52276.624q53+0.564595q54+374.923q552.15737q56183.984q572.35315q58+48.2675q59492.989q60+421.765q614.60415q62+58.0344q63511.832q64+1311.46q65+1.14495q66269.737q67+318.702q69+2.76991q70+699.900q713.01109q72816.421q733.92594q74+890.961q75+490.598q76+117.689q77+4.00496q781116.41q79+1314.49q80+81.0000q81+4.14597q82465.803q83154.750q84+2.91808q86337.597q876.10624q8892.3664q89+3.86603q90+411.667q91849.827q92660.538q93+12.0374q941259.82q95+12.0438q96+1668.15q976.30297q98+164.261q99+O(q100)q+0.0209109 q^{2} +3.00000 q^{3} -7.99956 q^{4} +20.5423 q^{5} +0.0627328 q^{6} +6.44826 q^{7} -0.334566 q^{8} +9.00000 q^{9} +0.429559 q^{10} +18.2513 q^{11} -23.9987 q^{12} +63.8416 q^{13} +0.134839 q^{14} +61.6270 q^{15} +63.9895 q^{16} +0.188198 q^{18} -61.3281 q^{19} -164.330 q^{20} +19.3448 q^{21} +0.381651 q^{22} +106.234 q^{23} -1.00370 q^{24} +296.987 q^{25} +1.33499 q^{26} +27.0000 q^{27} -51.5833 q^{28} -112.532 q^{29} +1.28868 q^{30} -220.179 q^{31} +4.01460 q^{32} +54.7538 q^{33} +132.462 q^{35} -71.9961 q^{36} -187.746 q^{37} -1.28243 q^{38} +191.525 q^{39} -6.87276 q^{40} +198.268 q^{41} +0.404517 q^{42} +139.548 q^{43} -146.002 q^{44} +184.881 q^{45} +2.22145 q^{46} +575.652 q^{47} +191.969 q^{48} -301.420 q^{49} +6.21027 q^{50} -510.705 q^{52} -276.624 q^{53} +0.564595 q^{54} +374.923 q^{55} -2.15737 q^{56} -183.984 q^{57} -2.35315 q^{58} +48.2675 q^{59} -492.989 q^{60} +421.765 q^{61} -4.60415 q^{62} +58.0344 q^{63} -511.832 q^{64} +1311.46 q^{65} +1.14495 q^{66} -269.737 q^{67} +318.702 q^{69} +2.76991 q^{70} +699.900 q^{71} -3.01109 q^{72} -816.421 q^{73} -3.92594 q^{74} +890.961 q^{75} +490.598 q^{76} +117.689 q^{77} +4.00496 q^{78} -1116.41 q^{79} +1314.49 q^{80} +81.0000 q^{81} +4.14597 q^{82} -465.803 q^{83} -154.750 q^{84} +2.91808 q^{86} -337.597 q^{87} -6.10624 q^{88} -92.3664 q^{89} +3.86603 q^{90} +411.667 q^{91} -849.827 q^{92} -660.538 q^{93} +12.0374 q^{94} -1259.82 q^{95} +12.0438 q^{96} +1668.15 q^{97} -6.30297 q^{98} +164.261 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+60q3+96q4+32q5+56q7+180q9+80q10+152q11+288q12+56q13+112q14+96q15+512q16+328q19+192q20+168q21104q22+576q23++1368q99+O(q100) 20 q + 60 q^{3} + 96 q^{4} + 32 q^{5} + 56 q^{7} + 180 q^{9} + 80 q^{10} + 152 q^{11} + 288 q^{12} + 56 q^{13} + 112 q^{14} + 96 q^{15} + 512 q^{16} + 328 q^{19} + 192 q^{20} + 168 q^{21} - 104 q^{22} + 576 q^{23}+ \cdots + 1368 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.0209109 0.00739313 0.00369656 0.999993i 0.498823π-0.498823\pi
0.00369656 + 0.999993i 0.498823π0.498823\pi
33 3.00000 0.577350
44 −7.99956 −0.999945
55 20.5423 1.83736 0.918681 0.395001i 0.129256π-0.129256\pi
0.918681 + 0.395001i 0.129256π0.129256\pi
66 0.0627328 0.00426842
77 6.44826 0.348173 0.174087 0.984730i 0.444303π-0.444303\pi
0.174087 + 0.984730i 0.444303π0.444303\pi
88 −0.334566 −0.0147859
99 9.00000 0.333333
1010 0.429559 0.0135838
1111 18.2513 0.500269 0.250135 0.968211i 0.419525π-0.419525\pi
0.250135 + 0.968211i 0.419525π0.419525\pi
1212 −23.9987 −0.577319
1313 63.8416 1.36204 0.681018 0.732266i 0.261537π-0.261537\pi
0.681018 + 0.732266i 0.261537π0.261537\pi
1414 0.134839 0.00257409
1515 61.6270 1.06080
1616 63.9895 0.999836
1717 0 0
1818 0.188198 0.00246438
1919 −61.3281 −0.740507 −0.370254 0.928931i 0.620729π-0.620729\pi
−0.370254 + 0.928931i 0.620729π0.620729\pi
2020 −164.330 −1.83726
2121 19.3448 0.201018
2222 0.381651 0.00369855
2323 106.234 0.963102 0.481551 0.876418i 0.340074π-0.340074\pi
0.481551 + 0.876418i 0.340074π0.340074\pi
2424 −1.00370 −0.00853661
2525 296.987 2.37590
2626 1.33499 0.0100697
2727 27.0000 0.192450
2828 −51.5833 −0.348154
2929 −112.532 −0.720577 −0.360288 0.932841i 0.617322π-0.617322\pi
−0.360288 + 0.932841i 0.617322π0.617322\pi
3030 1.28868 0.00784264
3131 −220.179 −1.27566 −0.637829 0.770178i 0.720167π-0.720167\pi
−0.637829 + 0.770178i 0.720167π0.720167\pi
3232 4.01460 0.0221778
3333 54.7538 0.288831
3434 0 0
3535 132.462 0.639720
3636 −71.9961 −0.333315
3737 −187.746 −0.834195 −0.417098 0.908862i 0.636953π-0.636953\pi
−0.417098 + 0.908862i 0.636953π0.636953\pi
3838 −1.28243 −0.00547467
3939 191.525 0.786372
4040 −6.87276 −0.0271670
4141 198.268 0.755226 0.377613 0.925964i 0.376745π-0.376745\pi
0.377613 + 0.925964i 0.376745π0.376745\pi
4242 0.404517 0.00148615
4343 139.548 0.494905 0.247452 0.968900i 0.420407π-0.420407\pi
0.247452 + 0.968900i 0.420407π0.420407\pi
4444 −146.002 −0.500242
4545 184.881 0.612454
4646 2.22145 0.00712034
4747 575.652 1.78654 0.893271 0.449519i 0.148405π-0.148405\pi
0.893271 + 0.449519i 0.148405π0.148405\pi
4848 191.969 0.577256
4949 −301.420 −0.878775
5050 6.21027 0.0175653
5151 0 0
5252 −510.705 −1.36196
5353 −276.624 −0.716928 −0.358464 0.933544i 0.616699π-0.616699\pi
−0.358464 + 0.933544i 0.616699π0.616699\pi
5454 0.564595 0.00142281
5555 374.923 0.919175
5656 −2.15737 −0.00514804
5757 −183.984 −0.427532
5858 −2.35315 −0.00532732
5959 48.2675 0.106507 0.0532533 0.998581i 0.483041π-0.483041\pi
0.0532533 + 0.998581i 0.483041π0.483041\pi
6060 −492.989 −1.06074
6161 421.765 0.885271 0.442636 0.896702i 0.354044π-0.354044\pi
0.442636 + 0.896702i 0.354044π0.354044\pi
6262 −4.60415 −0.00943110
6363 58.0344 0.116058
6464 −511.832 −0.999672
6565 1311.46 2.50255
6666 1.14495 0.00213536
6767 −269.737 −0.491846 −0.245923 0.969289i 0.579091π-0.579091\pi
−0.245923 + 0.969289i 0.579091π0.579091\pi
6868 0 0
6969 318.702 0.556047
7070 2.76991 0.00472953
7171 699.900 1.16990 0.584949 0.811070i 0.301114π-0.301114\pi
0.584949 + 0.811070i 0.301114π0.301114\pi
7272 −3.01109 −0.00492862
7373 −816.421 −1.30897 −0.654485 0.756075i 0.727115π-0.727115\pi
−0.654485 + 0.756075i 0.727115π0.727115\pi
7474 −3.92594 −0.00616731
7575 890.961 1.37172
7676 490.598 0.740467
7777 117.689 0.174180
7878 4.00496 0.00581375
7979 −1116.41 −1.58994 −0.794971 0.606648i 0.792514π-0.792514\pi
−0.794971 + 0.606648i 0.792514π0.792514\pi
8080 1314.49 1.83706
8181 81.0000 0.111111
8282 4.14597 0.00558348
8383 −465.803 −0.616007 −0.308003 0.951385i 0.599661π-0.599661\pi
−0.308003 + 0.951385i 0.599661π0.599661\pi
8484 −154.750 −0.201007
8585 0 0
8686 2.91808 0.00365889
8787 −337.597 −0.416025
8888 −6.10624 −0.00739691
8989 −92.3664 −0.110009 −0.0550046 0.998486i 0.517517π-0.517517\pi
−0.0550046 + 0.998486i 0.517517π0.517517\pi
9090 3.86603 0.00452795
9191 411.667 0.474225
9292 −849.827 −0.963050
9393 −660.538 −0.736501
9494 12.0374 0.0132081
9595 −1259.82 −1.36058
9696 12.0438 0.0128043
9797 1668.15 1.74613 0.873066 0.487601i 0.162128π-0.162128\pi
0.873066 + 0.487601i 0.162128π0.162128\pi
9898 −6.30297 −0.00649690
9999 164.261 0.166756
100100 −2375.77 −2.37577
101101 669.102 0.659190 0.329595 0.944122i 0.393088π-0.393088\pi
0.329595 + 0.944122i 0.393088π0.393088\pi
102102 0 0
103103 −692.734 −0.662690 −0.331345 0.943510i 0.607502π-0.607502\pi
−0.331345 + 0.943510i 0.607502π0.607502\pi
104104 −21.3592 −0.0201389
105105 397.387 0.369343
106106 −5.78446 −0.00530034
107107 156.994 0.141843 0.0709215 0.997482i 0.477406π-0.477406\pi
0.0709215 + 0.997482i 0.477406π0.477406\pi
108108 −215.988 −0.192440
109109 1166.37 1.02493 0.512466 0.858708i 0.328732π-0.328732\pi
0.512466 + 0.858708i 0.328732π0.328732\pi
110110 7.83999 0.00679558
111111 −563.238 −0.481623
112112 412.621 0.348116
113113 512.772 0.426881 0.213441 0.976956i 0.431533π-0.431533\pi
0.213441 + 0.976956i 0.431533π0.431533\pi
114114 −3.84728 −0.00316080
115115 2182.30 1.76957
116116 900.209 0.720537
117117 574.575 0.454012
118118 1.00932 0.000787417 0
119119 0 0
120120 −20.6183 −0.0156848
121121 −997.892 −0.749731
122122 8.81950 0.00654492
123123 594.804 0.436030
124124 1761.34 1.27559
125125 3533.02 2.52802
126126 1.21355 0.000858030 0
127127 2060.12 1.43942 0.719708 0.694277i 0.244276π-0.244276\pi
0.719708 + 0.694277i 0.244276π0.244276\pi
128128 −42.8197 −0.0295685
129129 418.645 0.285733
130130 27.4237 0.0185017
131131 273.048 0.182110 0.0910548 0.995846i 0.470976π-0.470976\pi
0.0910548 + 0.995846i 0.470976π0.470976\pi
132132 −438.006 −0.288815
133133 −395.460 −0.257825
134134 −5.64046 −0.00363628
135135 554.643 0.353600
136136 0 0
137137 2175.28 1.35654 0.678272 0.734811i 0.262729π-0.262729\pi
0.678272 + 0.734811i 0.262729π0.262729\pi
138138 6.66436 0.00411093
139139 −732.040 −0.446696 −0.223348 0.974739i 0.571699π-0.571699\pi
−0.223348 + 0.974739i 0.571699π0.571699\pi
140140 −1059.64 −0.639685
141141 1726.96 1.03146
142142 14.6355 0.00864921
143143 1165.19 0.681385
144144 575.906 0.333279
145145 −2311.68 −1.32396
146146 −17.0721 −0.00967739
147147 −904.260 −0.507361
148148 1501.88 0.834150
149149 3003.88 1.65159 0.825796 0.563969i 0.190726π-0.190726\pi
0.825796 + 0.563969i 0.190726π0.190726\pi
150150 18.6308 0.0101413
151151 3176.88 1.71212 0.856061 0.516874i 0.172905π-0.172905\pi
0.856061 + 0.516874i 0.172905π0.172905\pi
152152 20.5183 0.0109490
153153 0 0
154154 2.46098 0.00128774
155155 −4523.00 −2.34384
156156 −1532.11 −0.786329
157157 −623.642 −0.317019 −0.158510 0.987357i 0.550669π-0.550669\pi
−0.158510 + 0.987357i 0.550669π0.550669\pi
158158 −23.3451 −0.0117546
159159 −829.871 −0.413919
160160 82.4693 0.0407486
161161 685.026 0.335327
162162 1.69378 0.000821459 0
163163 −2247.34 −1.07991 −0.539954 0.841694i 0.681559π-0.681559\pi
−0.539954 + 0.841694i 0.681559π0.681559\pi
164164 −1586.06 −0.755185
165165 1124.77 0.530686
166166 −9.74037 −0.00455422
167167 −1887.30 −0.874511 −0.437256 0.899337i 0.644050π-0.644050\pi
−0.437256 + 0.899337i 0.644050π0.644050\pi
168168 −6.47210 −0.00297222
169169 1878.75 0.855144
170170 0 0
171171 −551.953 −0.246836
172172 −1116.32 −0.494878
173173 −2484.88 −1.09203 −0.546017 0.837774i 0.683856π-0.683856\pi
−0.546017 + 0.837774i 0.683856π0.683856\pi
174174 −7.05946 −0.00307573
175175 1915.05 0.827224
176176 1167.89 0.500187
177177 144.802 0.0614916
178178 −1.93147 −0.000813312 0
179179 1110.51 0.463708 0.231854 0.972751i 0.425521π-0.425521\pi
0.231854 + 0.972751i 0.425521π0.425521\pi
180180 −1478.97 −0.612420
181181 596.594 0.244997 0.122499 0.992469i 0.460909π-0.460909\pi
0.122499 + 0.992469i 0.460909π0.460909\pi
182182 8.60835 0.00350601
183183 1265.30 0.511111
184184 −35.5423 −0.0142403
185185 −3856.74 −1.53272
186186 −13.8125 −0.00544505
187187 0 0
188188 −4604.96 −1.78644
189189 174.103 0.0670060
190190 −26.3441 −0.0100589
191191 −2220.92 −0.841363 −0.420681 0.907209i 0.638209π-0.638209\pi
−0.420681 + 0.907209i 0.638209π0.638209\pi
192192 −1535.50 −0.577161
193193 −1156.23 −0.431229 −0.215615 0.976479i 0.569175π-0.569175\pi
−0.215615 + 0.976479i 0.569175π0.569175\pi
194194 34.8825 0.0129094
195195 3934.37 1.44485
196196 2411.23 0.878727
197197 3490.60 1.26241 0.631205 0.775616i 0.282561π-0.282561\pi
0.631205 + 0.775616i 0.282561π0.282561\pi
198198 3.43486 0.00123285
199199 −2736.58 −0.974831 −0.487415 0.873170i 0.662060π-0.662060\pi
−0.487415 + 0.873170i 0.662060π0.662060\pi
200200 −99.3617 −0.0351297
201201 −809.212 −0.283967
202202 13.9915 0.00487347
203203 −725.638 −0.250886
204204 0 0
205205 4072.89 1.38762
206206 −14.4857 −0.00489935
207207 956.107 0.321034
208208 4085.19 1.36181
209209 −1119.32 −0.370453
210210 8.30973 0.00273060
211211 4456.34 1.45397 0.726984 0.686654i 0.240921π-0.240921\pi
0.726984 + 0.686654i 0.240921π0.240921\pi
212212 2212.87 0.716889
213213 2099.70 0.675441
214214 3.28289 0.00104866
215215 2866.64 0.909319
216216 −9.03327 −0.00284554
217217 −1419.77 −0.444150
218218 24.3898 0.00757745
219219 −2449.26 −0.755735
220220 −2999.22 −0.919125
221221 0 0
222222 −11.7778 −0.00356070
223223 638.518 0.191741 0.0958707 0.995394i 0.469436π-0.469436\pi
0.0958707 + 0.995394i 0.469436π0.469436\pi
224224 25.8872 0.00772171
225225 2672.88 0.791966
226226 10.7225 0.00315599
227227 −1101.58 −0.322090 −0.161045 0.986947i 0.551487π-0.551487\pi
−0.161045 + 0.986947i 0.551487π0.551487\pi
228228 1471.80 0.427509
229229 −3603.12 −1.03974 −0.519871 0.854244i 0.674020π-0.674020\pi
−0.519871 + 0.854244i 0.674020π0.674020\pi
230230 45.6338 0.0130826
231231 353.067 0.100563
232232 37.6494 0.0106543
233233 1977.85 0.556110 0.278055 0.960565i 0.410310π-0.410310\pi
0.278055 + 0.960565i 0.410310π0.410310\pi
234234 12.0149 0.00335657
235235 11825.2 3.28252
236236 −386.119 −0.106501
237237 −3349.22 −0.917953
238238 0 0
239239 −5104.03 −1.38139 −0.690694 0.723147i 0.742695π-0.742695\pi
−0.690694 + 0.723147i 0.742695π0.742695\pi
240240 3943.48 1.06063
241241 −163.071 −0.0435864 −0.0217932 0.999762i 0.506938π-0.506938\pi
−0.0217932 + 0.999762i 0.506938π0.506938\pi
242242 −20.8668 −0.00554285
243243 243.000 0.0641500
244244 −3373.94 −0.885223
245245 −6191.87 −1.61463
246246 12.4379 0.00322362
247247 −3915.29 −1.00860
248248 73.6644 0.0188617
249249 −1397.41 −0.355652
250250 73.8786 0.0186900
251251 −4032.94 −1.01417 −0.507085 0.861896i 0.669277π-0.669277\pi
−0.507085 + 0.861896i 0.669277π0.669277\pi
252252 −464.250 −0.116051
253253 1938.91 0.481810
254254 43.0790 0.0106418
255255 0 0
256256 4093.76 0.999453
257257 −2385.61 −0.579029 −0.289515 0.957174i 0.593494π-0.593494\pi
−0.289515 + 0.957174i 0.593494π0.593494\pi
258258 8.75425 0.00211246
259259 −1210.63 −0.290445
260260 −10491.1 −2.50242
261261 −1012.79 −0.240192
262262 5.70969 0.00134636
263263 −7312.21 −1.71441 −0.857206 0.514974i 0.827802π-0.827802\pi
−0.857206 + 0.514974i 0.827802π0.827802\pi
264264 −18.3187 −0.00427061
265265 −5682.49 −1.31726
266266 −8.26943 −0.00190613
267267 −277.099 −0.0635138
268268 2157.78 0.491819
269269 −1272.89 −0.288511 −0.144255 0.989540i 0.546079π-0.546079\pi
−0.144255 + 0.989540i 0.546079π0.546079\pi
270270 11.5981 0.00261421
271271 269.767 0.0604693 0.0302346 0.999543i 0.490375π-0.490375\pi
0.0302346 + 0.999543i 0.490375π0.490375\pi
272272 0 0
273273 1235.00 0.273794
274274 45.4871 0.0100291
275275 5420.39 1.18859
276276 −2549.48 −0.556017
277277 3470.76 0.752843 0.376422 0.926448i 0.377154π-0.377154\pi
0.376422 + 0.926448i 0.377154π0.377154\pi
278278 −15.3076 −0.00330248
279279 −1981.61 −0.425219
280280 −44.3173 −0.00945881
281281 −721.579 −0.153188 −0.0765940 0.997062i 0.524405π-0.524405\pi
−0.0765940 + 0.997062i 0.524405π0.524405\pi
282282 36.1122 0.00762572
283283 −1017.08 −0.213636 −0.106818 0.994279i 0.534066π-0.534066\pi
−0.106818 + 0.994279i 0.534066π0.534066\pi
284284 −5598.89 −1.16983
285285 −3779.47 −0.785531
286286 24.3652 0.00503757
287287 1278.48 0.262950
288288 36.1314 0.00739259
289289 0 0
290290 −48.3393 −0.00978820
291291 5004.45 1.00813
292292 6531.01 1.30890
293293 2776.30 0.553560 0.276780 0.960933i 0.410733π-0.410733\pi
0.276780 + 0.960933i 0.410733π0.410733\pi
294294 −18.9089 −0.00375099
295295 991.527 0.195691
296296 62.8133 0.0123343
297297 492.784 0.0962769
298298 62.8138 0.0122104
299299 6782.16 1.31178
300300 −7127.30 −1.37165
301301 899.844 0.172313
302302 66.4314 0.0126579
303303 2007.31 0.380583
304304 −3924.36 −0.740386
305305 8664.04 1.62656
306306 0 0
307307 −727.432 −0.135234 −0.0676168 0.997711i 0.521540π-0.521540\pi
−0.0676168 + 0.997711i 0.521540π0.521540\pi
308308 −941.460 −0.174171
309309 −2078.20 −0.382604
310310 −94.5800 −0.0173283
311311 −1184.60 −0.215989 −0.107994 0.994152i 0.534443π-0.534443\pi
−0.107994 + 0.994152i 0.534443π0.534443\pi
312312 −64.0776 −0.0116272
313313 254.466 0.0459529 0.0229765 0.999736i 0.492686π-0.492686\pi
0.0229765 + 0.999736i 0.492686π0.492686\pi
314314 −13.0409 −0.00234376
315315 1192.16 0.213240
316316 8930.75 1.58985
317317 8638.25 1.53051 0.765256 0.643726i 0.222612π-0.222612\pi
0.765256 + 0.643726i 0.222612π0.222612\pi
318318 −17.3534 −0.00306015
319319 −2053.86 −0.360482
320320 −10514.2 −1.83676
321321 470.983 0.0818931
322322 14.3245 0.00247911
323323 0 0
324324 −647.965 −0.111105
325325 18960.1 3.23606
326326 −46.9939 −0.00798390
327327 3499.10 0.591744
328328 −66.3337 −0.0111667
329329 3711.95 0.622026
330330 23.5200 0.00392343
331331 931.174 0.154628 0.0773141 0.997007i 0.475366π-0.475366\pi
0.0773141 + 0.997007i 0.475366π0.475366\pi
332332 3726.22 0.615973
333333 −1689.71 −0.278065
334334 −39.4651 −0.00646537
335335 −5541.03 −0.903699
336336 1237.86 0.200985
337337 −8125.43 −1.31341 −0.656707 0.754146i 0.728051π-0.728051\pi
−0.656707 + 0.754146i 0.728051π0.728051\pi
338338 39.2864 0.00632219
339339 1538.32 0.246460
340340 0 0
341341 −4018.55 −0.638172
342342 −11.5419 −0.00182489
343343 −4155.39 −0.654140
344344 −46.6880 −0.00731759
345345 6546.89 1.02166
346346 −51.9611 −0.00807354
347347 −10952.1 −1.69435 −0.847177 0.531310i 0.821700π-0.821700\pi
−0.847177 + 0.531310i 0.821700π0.821700\pi
348348 2700.63 0.416002
349349 −4845.63 −0.743212 −0.371606 0.928391i 0.621193π-0.621193\pi
−0.371606 + 0.928391i 0.621193π0.621193\pi
350350 40.0455 0.00611577
351351 1723.72 0.262124
352352 73.2716 0.0110949
353353 −1814.62 −0.273605 −0.136802 0.990598i 0.543683π-0.543683\pi
−0.136802 + 0.990598i 0.543683π0.543683\pi
354354 3.02795 0.000454616 0
355355 14377.6 2.14953
356356 738.891 0.110003
357357 0 0
358358 23.2219 0.00342825
359359 −10174.2 −1.49575 −0.747874 0.663840i 0.768925π-0.768925\pi
−0.747874 + 0.663840i 0.768925π0.768925\pi
360360 −61.8548 −0.00905565
361361 −3097.86 −0.451649
362362 12.4753 0.00181130
363363 −2993.67 −0.432857
364364 −3293.16 −0.474199
365365 −16771.2 −2.40505
366366 26.4585 0.00377871
367367 −4544.86 −0.646430 −0.323215 0.946326i 0.604764π-0.604764\pi
−0.323215 + 0.946326i 0.604764π0.604764\pi
368368 6797.87 0.962944
369369 1784.41 0.251742
370370 −80.6479 −0.0113316
371371 −1783.74 −0.249615
372372 5284.02 0.736461
373373 −549.941 −0.0763402 −0.0381701 0.999271i 0.512153π-0.512153\pi
−0.0381701 + 0.999271i 0.512153π0.512153\pi
374374 0 0
375375 10599.0 1.45955
376376 −192.593 −0.0264155
377377 −7184.24 −0.981452
378378 3.64066 0.000495384 0
379379 2072.61 0.280905 0.140452 0.990087i 0.455144π-0.455144\pi
0.140452 + 0.990087i 0.455144π0.455144\pi
380380 10078.0 1.36051
381381 6180.35 0.831047
382382 −46.4415 −0.00622030
383383 −12705.2 −1.69506 −0.847530 0.530748i 0.821911π-0.821911\pi
−0.847530 + 0.530748i 0.821911π0.821911\pi
384384 −128.459 −0.0170714
385385 2417.60 0.320032
386386 −24.1778 −0.00318813
387387 1255.93 0.164968
388388 −13344.5 −1.74604
389389 6157.69 0.802589 0.401295 0.915949i 0.368560π-0.368560\pi
0.401295 + 0.915949i 0.368560π0.368560\pi
390390 82.2712 0.0106820
391391 0 0
392392 100.845 0.0129934
393393 819.145 0.105141
394394 72.9916 0.00933316
395395 −22933.6 −2.92130
396396 −1314.02 −0.166747
397397 −7088.92 −0.896178 −0.448089 0.893989i 0.647895π-0.647895\pi
−0.448089 + 0.893989i 0.647895π0.647895\pi
398398 −57.2245 −0.00720705
399399 −1186.38 −0.148855
400400 19004.1 2.37551
401401 877.750 0.109309 0.0546543 0.998505i 0.482594π-0.482594\pi
0.0546543 + 0.998505i 0.482594π0.482594\pi
402402 −16.9214 −0.00209941
403403 −14056.6 −1.73749
404404 −5352.52 −0.659154
405405 1663.93 0.204151
406406 −15.1738 −0.00185483
407407 −3426.60 −0.417322
408408 0 0
409409 7333.73 0.886625 0.443313 0.896367i 0.353803π-0.353803\pi
0.443313 + 0.896367i 0.353803π0.353803\pi
410410 85.1678 0.0102589
411411 6525.84 0.783201
412412 5541.57 0.662654
413413 311.241 0.0370828
414414 19.9931 0.00237345
415415 −9568.68 −1.13183
416416 256.299 0.0302069
417417 −2196.12 −0.257900
418418 −23.4059 −0.00273881
419419 −1047.46 −0.122129 −0.0610643 0.998134i 0.519449π-0.519449\pi
−0.0610643 + 0.998134i 0.519449π0.519449\pi
420420 −3178.92 −0.369323
421421 −15517.0 −1.79632 −0.898162 0.439665i 0.855097π-0.855097\pi
−0.898162 + 0.439665i 0.855097π0.855097\pi
422422 93.1863 0.0107494
423423 5180.87 0.595514
424424 92.5488 0.0106004
425425 0 0
426426 43.9066 0.00499362
427427 2719.65 0.308228
428428 −1255.89 −0.141835
429429 3495.57 0.393398
430430 59.9442 0.00672271
431431 −7274.46 −0.812989 −0.406495 0.913653i 0.633249π-0.633249\pi
−0.406495 + 0.913653i 0.633249π0.633249\pi
432432 1727.72 0.192419
433433 5853.31 0.649635 0.324818 0.945777i 0.394697π-0.394697\pi
0.324818 + 0.945777i 0.394697π0.394697\pi
434434 −29.6888 −0.00328366
435435 −6935.03 −0.764389
436436 −9330.41 −1.02488
437437 −6515.14 −0.713184
438438 −51.2164 −0.00558724
439439 −4390.59 −0.477338 −0.238669 0.971101i 0.576711π-0.576711\pi
−0.238669 + 0.971101i 0.576711π0.576711\pi
440440 −125.436 −0.0135908
441441 −2712.78 −0.292925
442442 0 0
443443 −698.038 −0.0748641 −0.0374320 0.999299i 0.511918π-0.511918\pi
−0.0374320 + 0.999299i 0.511918π0.511918\pi
444444 4505.65 0.481597
445445 −1897.42 −0.202127
446446 13.3520 0.00141757
447447 9011.63 0.953547
448448 −3300.43 −0.348059
449449 5550.98 0.583445 0.291723 0.956503i 0.405772π-0.405772\pi
0.291723 + 0.956503i 0.405772π0.405772\pi
450450 55.8925 0.00585510
451451 3618.64 0.377816
452452 −4101.95 −0.426858
453453 9530.63 0.988495
454454 −23.0351 −0.00238126
455455 8456.61 0.871323
456456 61.5549 0.00632143
457457 −6755.97 −0.691534 −0.345767 0.938320i 0.612381π-0.612381\pi
−0.345767 + 0.938320i 0.612381π0.612381\pi
458458 −75.3446 −0.00768695
459459 0 0
460460 −17457.4 −1.76947
461461 1187.20 0.119942 0.0599710 0.998200i 0.480899π-0.480899\pi
0.0599710 + 0.998200i 0.480899π0.480899\pi
462462 7.38295 0.000743476 0
463463 3496.16 0.350930 0.175465 0.984486i 0.443857π-0.443857\pi
0.175465 + 0.984486i 0.443857π0.443857\pi
464464 −7200.89 −0.720459
465465 −13569.0 −1.35322
466466 41.3588 0.00411139
467467 −18552.6 −1.83835 −0.919175 0.393848i 0.871144π-0.871144\pi
−0.919175 + 0.393848i 0.871144π0.871144\pi
468468 −4596.34 −0.453987
469469 −1739.34 −0.171248
470470 247.276 0.0242681
471471 −1870.93 −0.183031
472472 −16.1486 −0.00157479
473473 2546.93 0.247586
474474 −70.0352 −0.00678654
475475 −18213.7 −1.75937
476476 0 0
477477 −2489.61 −0.238976
478478 −106.730 −0.0102128
479479 18512.5 1.76588 0.882941 0.469483i 0.155560π-0.155560\pi
0.882941 + 0.469483i 0.155560π0.155560\pi
480480 247.408 0.0235262
481481 −11986.0 −1.13620
482482 −3.40997 −0.000322240 0
483483 2055.08 0.193601
484484 7982.70 0.749690
485485 34267.7 3.20828
486486 5.08135 0.000474269 0
487487 −13830.9 −1.28693 −0.643466 0.765475i 0.722504π-0.722504\pi
−0.643466 + 0.765475i 0.722504π0.722504\pi
488488 −141.108 −0.0130895
489489 −6742.01 −0.623486
490490 −129.478 −0.0119371
491491 2710.45 0.249126 0.124563 0.992212i 0.460247π-0.460247\pi
0.124563 + 0.992212i 0.460247π0.460247\pi
492492 −4758.17 −0.436006
493493 0 0
494494 −81.8723 −0.00745670
495495 3374.31 0.306392
496496 −14089.2 −1.27545
497497 4513.14 0.407328
498498 −29.2211 −0.00262938
499499 −8787.23 −0.788317 −0.394159 0.919042i 0.628964π-0.628964\pi
−0.394159 + 0.919042i 0.628964π0.628964\pi
500500 −28262.6 −2.52788
501501 −5661.89 −0.504899
502502 −84.3325 −0.00749789
503503 4482.62 0.397356 0.198678 0.980065i 0.436335π-0.436335\pi
0.198678 + 0.980065i 0.436335π0.436335\pi
504504 −19.4163 −0.00171601
505505 13744.9 1.21117
506506 40.5443 0.00356209
507507 5636.25 0.493718
508508 −16480.0 −1.43934
509509 −17537.7 −1.52720 −0.763599 0.645691i 0.776569π-0.776569\pi
−0.763599 + 0.645691i 0.776569π0.776569\pi
510510 0 0
511511 −5264.50 −0.455749
512512 428.162 0.0369576
513513 −1655.86 −0.142511
514514 −49.8854 −0.00428084
515515 −14230.4 −1.21760
516516 −3348.97 −0.285718
517517 10506.4 0.893752
518518 −25.3155 −0.00214729
519519 −7454.63 −0.630486
520520 −438.768 −0.0370024
521521 21557.7 1.81278 0.906390 0.422441i 0.138827π-0.138827\pi
0.906390 + 0.422441i 0.138827π0.138827\pi
522522 −21.1784 −0.00177577
523523 −8765.00 −0.732823 −0.366412 0.930453i 0.619414π-0.619414\pi
−0.366412 + 0.930453i 0.619414π0.619414\pi
524524 −2184.27 −0.182100
525525 5745.15 0.477598
526526 −152.905 −0.0126749
527527 0 0
528528 3503.67 0.288783
529529 −881.307 −0.0724342
530530 −118.826 −0.00973864
531531 434.407 0.0355022
532532 3163.51 0.257811
533533 12657.7 1.02865
534534 −5.79440 −0.000469566 0
535535 3225.03 0.260617
536536 90.2449 0.00727236
537537 3331.54 0.267722
538538 −26.6173 −0.00213300
539539 −5501.29 −0.439624
540540 −4436.90 −0.353581
541541 5971.04 0.474519 0.237260 0.971446i 0.423751π-0.423751\pi
0.237260 + 0.971446i 0.423751π0.423751\pi
542542 5.64107 0.000447057 0
543543 1789.78 0.141449
544544 0 0
545545 23959.9 1.88317
546546 25.8250 0.00202419
547547 17281.6 1.35084 0.675419 0.737434i 0.263963π-0.263963\pi
0.675419 + 0.737434i 0.263963π0.263963\pi
548548 −17401.3 −1.35647
549549 3795.89 0.295090
550550 113.345 0.00878738
551551 6901.40 0.533592
552552 −106.627 −0.00822163
553553 −7198.87 −0.553575
554554 72.5767 0.00556587
555555 −11570.2 −0.884915
556556 5856.00 0.446672
557557 −6265.83 −0.476646 −0.238323 0.971186i 0.576598π-0.576598\pi
−0.238323 + 0.971186i 0.576598π0.576598\pi
558558 −41.4374 −0.00314370
559559 8908.98 0.674078
560560 8476.20 0.639616
561561 0 0
562562 −15.0889 −0.00113254
563563 −3685.25 −0.275870 −0.137935 0.990441i 0.544046π-0.544046\pi
−0.137935 + 0.990441i 0.544046π0.544046\pi
564564 −13814.9 −1.03140
565565 10533.5 0.784335
566566 −21.2680 −0.00157944
567567 522.309 0.0386859
568568 −234.162 −0.0172979
569569 −3570.81 −0.263086 −0.131543 0.991310i 0.541993π-0.541993\pi
−0.131543 + 0.991310i 0.541993π0.541993\pi
570570 −79.0322 −0.00580753
571571 8578.53 0.628722 0.314361 0.949304i 0.398210π-0.398210\pi
0.314361 + 0.949304i 0.398210π0.398210\pi
572572 −9321.01 −0.681348
573573 −6662.76 −0.485761
574574 26.7343 0.00194402
575575 31550.2 2.28823
576576 −4606.49 −0.333224
577577 15119.3 1.09086 0.545429 0.838157i 0.316367π-0.316367\pi
0.545429 + 0.838157i 0.316367π0.316367\pi
578578 0 0
579579 −3468.69 −0.248970
580580 18492.4 1.32389
581581 −3003.62 −0.214477
582582 104.648 0.00745323
583583 −5048.73 −0.358657
584584 273.146 0.0193542
585585 11803.1 0.834185
586586 58.0550 0.00409254
587587 −15700.9 −1.10399 −0.551997 0.833846i 0.686134π-0.686134\pi
−0.551997 + 0.833846i 0.686134π0.686134\pi
588588 7233.68 0.507333
589589 13503.2 0.944634
590590 20.7337 0.00144677
591591 10471.8 0.728853
592592 −12013.8 −0.834059
593593 −12196.6 −0.844614 −0.422307 0.906453i 0.638780π-0.638780\pi
−0.422307 + 0.906453i 0.638780π0.638780\pi
594594 10.3046 0.000711787 0
595595 0 0
596596 −24029.7 −1.65150
597597 −8209.75 −0.562819
598598 141.821 0.00969816
599599 19363.2 1.32080 0.660400 0.750914i 0.270387π-0.270387\pi
0.660400 + 0.750914i 0.270387π0.270387\pi
600600 −298.085 −0.0202821
601601 −12765.4 −0.866406 −0.433203 0.901296i 0.642617π-0.642617\pi
−0.433203 + 0.901296i 0.642617π0.642617\pi
602602 18.8166 0.00127393
603603 −2427.64 −0.163949
604604 −25413.6 −1.71203
605605 −20499.0 −1.37753
606606 41.9746 0.00281370
607607 −15295.8 −1.02279 −0.511397 0.859344i 0.670872π-0.670872\pi
−0.511397 + 0.859344i 0.670872π0.670872\pi
608608 −246.208 −0.0164228
609609 −2176.91 −0.144849
610610 181.173 0.0120254
611611 36750.5 2.43333
612612 0 0
613613 11554.2 0.761291 0.380646 0.924721i 0.375702π-0.375702\pi
0.380646 + 0.924721i 0.375702π0.375702\pi
614614 −15.2113 −0.000999800 0
615615 12218.7 0.801144
616616 −39.3747 −0.00257541
617617 7681.67 0.501220 0.250610 0.968088i 0.419369π-0.419369\pi
0.250610 + 0.968088i 0.419369π0.419369\pi
618618 −43.4571 −0.00282864
619619 18736.0 1.21658 0.608292 0.793713i 0.291855π-0.291855\pi
0.608292 + 0.793713i 0.291855π0.291855\pi
620620 36182.0 2.34372
621621 2868.32 0.185349
622622 −24.7711 −0.00159683
623623 −595.603 −0.0383023
624624 12255.6 0.786243
625625 35453.0 2.26899
626626 5.32112 0.000339736 0
627627 −3357.95 −0.213881
628628 4988.86 0.317002
629629 0 0
630630 24.9292 0.00157651
631631 −15516.0 −0.978892 −0.489446 0.872034i 0.662801π-0.662801\pi
−0.489446 + 0.872034i 0.662801π0.662801\pi
632632 373.511 0.0235086
633633 13369.0 0.839449
634634 180.634 0.0113153
635635 42319.6 2.64473
636636 6638.61 0.413896
637637 −19243.1 −1.19692
638638 −42.9480 −0.00266509
639639 6299.10 0.389966
640640 −879.617 −0.0543280
641641 12592.6 0.775940 0.387970 0.921672i 0.373176π-0.373176\pi
0.387970 + 0.921672i 0.373176π0.373176\pi
642642 9.84868 0.000605446 0
643643 8183.85 0.501928 0.250964 0.967996i 0.419252π-0.419252\pi
0.250964 + 0.967996i 0.419252π0.419252\pi
644644 −5479.91 −0.335308
645645 8599.93 0.524996
646646 0 0
647647 −2042.87 −0.124132 −0.0620661 0.998072i 0.519769π-0.519769\pi
−0.0620661 + 0.998072i 0.519769π0.519769\pi
648648 −27.0998 −0.00164287
649649 880.943 0.0532820
650650 396.474 0.0239246
651651 −4259.32 −0.256430
652652 17977.7 1.07985
653653 −17805.3 −1.06704 −0.533518 0.845789i 0.679130π-0.679130\pi
−0.533518 + 0.845789i 0.679130π0.679130\pi
654654 73.1693 0.00437484
655655 5609.05 0.334601
656656 12687.1 0.755102
657657 −7347.79 −0.436324
658658 77.6204 0.00459872
659659 24705.9 1.46040 0.730202 0.683231i 0.239426π-0.239426\pi
0.730202 + 0.683231i 0.239426π0.239426\pi
660660 −8997.67 −0.530657
661661 14655.1 0.862354 0.431177 0.902267i 0.358098π-0.358098\pi
0.431177 + 0.902267i 0.358098π0.358098\pi
662662 19.4717 0.00114319
663663 0 0
664664 155.842 0.00910818
665665 −8123.67 −0.473718
666666 −35.3335 −0.00205577
667667 −11954.8 −0.693989
668668 15097.5 0.874464
669669 1915.55 0.110702
670670 −115.868 −0.00668116
671671 7697.75 0.442874
672672 77.6617 0.00445813
673673 22375.5 1.28159 0.640797 0.767711i 0.278604π-0.278604\pi
0.640797 + 0.767711i 0.278604π0.278604\pi
674674 −169.910 −0.00971023
675675 8018.65 0.457242
676676 −15029.2 −0.855097
677677 −18940.5 −1.07525 −0.537623 0.843185i 0.680678π-0.680678\pi
−0.537623 + 0.843185i 0.680678π0.680678\pi
678678 32.1676 0.00182211
679679 10756.7 0.607957
680680 0 0
681681 −3304.74 −0.185959
682682 −84.0316 −0.00471809
683683 −9489.30 −0.531622 −0.265811 0.964025i 0.585640π-0.585640\pi
−0.265811 + 0.964025i 0.585640π0.585640\pi
684684 4415.39 0.246822
685685 44685.3 2.49246
686686 −86.8930 −0.00483614
687687 −10809.4 −0.600296
688688 8929.62 0.494824
689689 −17660.1 −0.976482
690690 136.901 0.00755326
691691 4564.16 0.251272 0.125636 0.992076i 0.459903π-0.459903\pi
0.125636 + 0.992076i 0.459903π0.459903\pi
692692 19877.9 1.09197
693693 1059.20 0.0580602
694694 −229.019 −0.0125266
695695 −15037.8 −0.820742
696696 112.948 0.00615129
697697 0 0
698698 −101.327 −0.00549466
699699 5933.56 0.321070
700700 −15319.6 −0.827179
701701 −25637.7 −1.38135 −0.690673 0.723167i 0.742686π-0.742686\pi
−0.690673 + 0.723167i 0.742686π0.742686\pi
702702 36.0446 0.00193792
703703 11514.1 0.617728
704704 −9341.58 −0.500105
705705 35475.7 1.89516
706706 −37.9454 −0.00202279
707707 4314.55 0.229512
708708 −1158.36 −0.0614883
709709 15590.0 0.825804 0.412902 0.910775i 0.364515π-0.364515\pi
0.412902 + 0.910775i 0.364515π0.364515\pi
710710 300.648 0.0158917
711711 −10047.6 −0.529980
712712 30.9026 0.00162658
713713 −23390.6 −1.22859
714714 0 0
715715 23935.7 1.25195
716716 −8883.63 −0.463683
717717 −15312.1 −0.797545
718718 −212.752 −0.0110583
719719 −27501.9 −1.42649 −0.713247 0.700913i 0.752776π-0.752776\pi
−0.713247 + 0.700913i 0.752776π0.752776\pi
720720 11830.4 0.612353
721721 −4466.93 −0.230731
722722 −64.7791 −0.00333910
723723 −489.213 −0.0251646
724724 −4772.49 −0.244984
725725 −33420.6 −1.71202
726726 −62.6005 −0.00320017
727727 27457.0 1.40072 0.700360 0.713790i 0.253023π-0.253023\pi
0.700360 + 0.713790i 0.253023π0.253023\pi
728728 −137.730 −0.00701182
729729 729.000 0.0370370
730730 −350.701 −0.0177809
731731 0 0
732732 −10121.8 −0.511084
733733 −22002.0 −1.10868 −0.554340 0.832290i 0.687029π-0.687029\pi
−0.554340 + 0.832290i 0.687029π0.687029\pi
734734 −95.0373 −0.00477914
735735 −18575.6 −0.932206
736736 426.488 0.0213595
737737 −4923.05 −0.246055
738738 37.3137 0.00186116
739739 7294.60 0.363107 0.181554 0.983381i 0.441887π-0.441887\pi
0.181554 + 0.983381i 0.441887π0.441887\pi
740740 30852.2 1.53263
741741 −11745.9 −0.582315
742742 −37.2997 −0.00184544
743743 −2257.31 −0.111457 −0.0557286 0.998446i 0.517748π-0.517748\pi
−0.0557286 + 0.998446i 0.517748π0.517748\pi
744744 220.993 0.0108898
745745 61706.6 3.03457
746746 −11.4998 −0.000564393 0
747747 −4192.23 −0.205336
748748 0 0
749749 1012.34 0.0493860
750750 221.636 0.0107907
751751 −3350.03 −0.162776 −0.0813878 0.996683i 0.525935π-0.525935\pi
−0.0813878 + 0.996683i 0.525935π0.525935\pi
752752 36835.7 1.78625
753753 −12098.8 −0.585532
754754 −150.229 −0.00725600
755755 65260.4 3.14579
756756 −1392.75 −0.0670023
757757 −27564.3 −1.32344 −0.661718 0.749753i 0.730172π-0.730172\pi
−0.661718 + 0.749753i 0.730172π0.730172\pi
758758 43.3402 0.00207676
759759 5816.72 0.278173
760760 421.493 0.0201173
761761 27697.8 1.31937 0.659687 0.751541i 0.270689π-0.270689\pi
0.659687 + 0.751541i 0.270689π0.270689\pi
762762 129.237 0.00614404
763763 7521.03 0.356854
764764 17766.4 0.841317
765765 0 0
766766 −265.678 −0.0125318
767767 3081.47 0.145066
768768 12281.3 0.577035
769769 34530.8 1.61926 0.809632 0.586938i 0.199667π-0.199667\pi
0.809632 + 0.586938i 0.199667π0.199667\pi
770770 50.5543 0.00236604
771771 −7156.84 −0.334303
772772 9249.33 0.431206
773773 −3723.24 −0.173241 −0.0866206 0.996241i 0.527607π-0.527607\pi
−0.0866206 + 0.996241i 0.527607π0.527607\pi
774774 26.2627 0.00121963
775775 −65390.4 −3.03083
776776 −558.105 −0.0258181
777777 −3631.90 −0.167688
778778 128.763 0.00593365
779779 −12159.4 −0.559250
780780 −31473.2 −1.44477
781781 12774.0 0.585264
782782 0 0
783783 −3038.37 −0.138675
784784 −19287.7 −0.878631
785785 −12811.1 −0.582479
786786 17.1291 0.000777321 0
787787 5397.77 0.244485 0.122243 0.992500i 0.460991π-0.460991\pi
0.122243 + 0.992500i 0.460991π0.460991\pi
788788 −27923.3 −1.26234
789789 −21936.6 −0.989816
790790 −479.562 −0.0215975
791791 3306.49 0.148629
792792 −54.9562 −0.00246564
793793 26926.2 1.20577
794794 −148.236 −0.00662556
795795 −17047.5 −0.760518
796796 21891.5 0.974778
797797 −6133.78 −0.272609 −0.136305 0.990667i 0.543523π-0.543523\pi
−0.136305 + 0.990667i 0.543523π0.543523\pi
798798 −24.8083 −0.00110051
799799 0 0
800800 1192.29 0.0526921
801801 −831.298 −0.0366697
802802 18.3546 0.000808133 0
803803 −14900.7 −0.654838
804804 6473.34 0.283952
805805 14072.0 0.616116
806806 −293.937 −0.0128455
807807 −3818.67 −0.166572
808808 −223.859 −0.00974668
809809 2078.87 0.0903453 0.0451726 0.998979i 0.485616π-0.485616\pi
0.0451726 + 0.998979i 0.485616π0.485616\pi
810810 34.7943 0.00150932
811811 29163.4 1.26272 0.631361 0.775489i 0.282497π-0.282497\pi
0.631361 + 0.775489i 0.282497π0.282497\pi
812812 5804.79 0.250872
813813 809.301 0.0349119
814814 −71.6533 −0.00308532
815815 −46165.6 −1.98418
816816 0 0
817817 −8558.23 −0.366481
818818 153.355 0.00655493
819819 3705.01 0.158075
820820 −32581.3 −1.38755
821821 11121.7 0.472775 0.236388 0.971659i 0.424036π-0.424036\pi
0.236388 + 0.971659i 0.424036π0.424036\pi
822822 136.461 0.00579031
823823 38055.6 1.61183 0.805914 0.592033i 0.201674π-0.201674\pi
0.805914 + 0.592033i 0.201674π0.201674\pi
824824 231.765 0.00979844
825825 16261.2 0.686232
826826 6.50835 0.000274158 0
827827 −1391.63 −0.0585146 −0.0292573 0.999572i 0.509314π-0.509314\pi
−0.0292573 + 0.999572i 0.509314π0.509314\pi
828828 −7648.44 −0.321017
829829 −28005.4 −1.17330 −0.586651 0.809840i 0.699554π-0.699554\pi
−0.586651 + 0.809840i 0.699554π0.699554\pi
830830 −200.090 −0.00836774
831831 10412.3 0.434654
832832 −32676.2 −1.36159
833833 0 0
834834 −45.9229 −0.00190669
835835 −38769.5 −1.60679
836836 8954.04 0.370433
837837 −5944.84 −0.245500
838838 −21.9034 −0.000902912 0
839839 −26495.8 −1.09027 −0.545135 0.838348i 0.683521π-0.683521\pi
−0.545135 + 0.838348i 0.683521π0.683521\pi
840840 −132.952 −0.00546105
841841 −11725.5 −0.480769
842842 −324.475 −0.0132804
843843 −2164.74 −0.0884431
844844 −35648.8 −1.45389
845845 38593.9 1.57121
846846 108.337 0.00440271
847847 −6434.67 −0.261036
848848 −17701.0 −0.716811
849849 −3051.24 −0.123343
850850 0 0
851851 −19945.0 −0.803415
852852 −16796.7 −0.675404
853853 47429.5 1.90381 0.951907 0.306386i 0.0991198π-0.0991198\pi
0.951907 + 0.306386i 0.0991198π0.0991198\pi
854854 56.8705 0.00227877
855855 −11338.4 −0.453527
856856 −52.5249 −0.00209727
857857 2113.73 0.0842516 0.0421258 0.999112i 0.486587π-0.486587\pi
0.0421258 + 0.999112i 0.486587π0.486587\pi
858858 73.0956 0.00290844
859859 35271.0 1.40097 0.700483 0.713669i 0.252968π-0.252968\pi
0.700483 + 0.713669i 0.252968π0.252968\pi
860860 −22931.9 −0.909269
861861 3835.45 0.151814
862862 −152.116 −0.00601053
863863 −46110.0 −1.81877 −0.909387 0.415951i 0.863449π-0.863449\pi
−0.909387 + 0.415951i 0.863449π0.863449\pi
864864 108.394 0.00426811
865865 −51045.2 −2.00646
866866 122.398 0.00480284
867867 0 0
868868 11357.6 0.444126
869869 −20375.8 −0.795399
870870 −145.018 −0.00565122
871871 −17220.5 −0.669912
872872 −390.226 −0.0151545
873873 15013.3 0.582044
874874 −136.238 −0.00527266
875875 22781.8 0.880189
876876 19593.0 0.755693
877877 20985.3 0.808008 0.404004 0.914757i 0.367618π-0.367618\pi
0.404004 + 0.914757i 0.367618π0.367618\pi
878878 −91.8112 −0.00352902
879879 8328.90 0.319598
880880 23991.2 0.919025
881881 33923.6 1.29729 0.648646 0.761090i 0.275336π-0.275336\pi
0.648646 + 0.761090i 0.275336π0.275336\pi
882882 −56.7267 −0.00216563
883883 −31168.8 −1.18790 −0.593948 0.804503i 0.702432π-0.702432\pi
−0.593948 + 0.804503i 0.702432π0.702432\pi
884884 0 0
885885 2974.58 0.112982
886886 −14.5966 −0.000553480 0
887887 −35032.5 −1.32613 −0.663064 0.748563i 0.730744π-0.730744\pi
−0.663064 + 0.748563i 0.730744π0.730744\pi
888888 188.440 0.00712120
889889 13284.2 0.501167
890890 −39.6768 −0.00149435
891891 1478.35 0.0555855
892892 −5107.87 −0.191731
893893 −35303.7 −1.32295
894894 188.441 0.00704969
895895 22812.5 0.851999
896896 −276.113 −0.0102950
897897 20346.5 0.757357
898898 116.076 0.00431349
899899 24777.3 0.919209
900900 −21381.9 −0.791922
901901 0 0
902902 75.6691 0.00279324
903903 2699.53 0.0994848
904904 −171.556 −0.00631180
905905 12255.4 0.450149
906906 199.294 0.00730807
907907 −23052.2 −0.843921 −0.421960 0.906614i 0.638658π-0.638658\pi
−0.421960 + 0.906614i 0.638658π0.638658\pi
908908 8812.17 0.322073
909909 6021.92 0.219730
910910 176.835 0.00644180
911911 18173.2 0.660927 0.330463 0.943819i 0.392795π-0.392795\pi
0.330463 + 0.943819i 0.392795π0.392795\pi
912912 −11773.1 −0.427462
913913 −8501.50 −0.308169
914914 −141.274 −0.00511260
915915 25992.1 0.939096
916916 28823.4 1.03969
917917 1760.69 0.0634057
918918 0 0
919919 −13457.8 −0.483061 −0.241530 0.970393i 0.577649π-0.577649\pi
−0.241530 + 0.970393i 0.577649π0.577649\pi
920920 −730.121 −0.0261645
921921 −2182.30 −0.0780772
922922 24.8254 0.000886746 0
923923 44682.7 1.59344
924924 −2824.38 −0.100558
925925 −55758.1 −1.98196
926926 73.1080 0.00259447
927927 −6234.61 −0.220897
928928 −451.773 −0.0159808
929929 −33883.2 −1.19663 −0.598316 0.801260i 0.704163π-0.704163\pi
−0.598316 + 0.801260i 0.704163π0.704163\pi
930930 −283.740 −0.0100045
931931 18485.5 0.650740
932932 −15822.0 −0.556079
933933 −3553.80 −0.124701
934934 −387.951 −0.0135912
935935 0 0
936936 −192.233 −0.00671296
937937 21838.9 0.761414 0.380707 0.924696i 0.375681π-0.375681\pi
0.380707 + 0.924696i 0.375681π0.375681\pi
938938 −36.3712 −0.00126606
939939 763.398 0.0265309
940940 −94596.6 −3.28234
941941 −34598.1 −1.19858 −0.599291 0.800531i 0.704551π-0.704551\pi
−0.599291 + 0.800531i 0.704551π0.704551\pi
942942 −39.1228 −0.00135317
943943 21062.8 0.727360
944944 3088.61 0.106489
945945 3576.48 0.123114
946946 53.2587 0.00183043
947947 −7753.79 −0.266066 −0.133033 0.991112i 0.542472π-0.542472\pi
−0.133033 + 0.991112i 0.542472π0.542472\pi
948948 26792.3 0.917903
949949 −52121.6 −1.78287
950950 −380.865 −0.0130072
951951 25914.8 0.883642
952952 0 0
953953 −32189.4 −1.09414 −0.547071 0.837086i 0.684257π-0.684257\pi
−0.547071 + 0.837086i 0.684257π0.684257\pi
954954 −52.0601 −0.00176678
955955 −45622.9 −1.54589
956956 40830.0 1.38131
957957 −6161.57 −0.208125
958958 387.113 0.0130554
959959 14026.8 0.472313
960960 −31542.7 −1.06045
961961 18688.0 0.627302
962962 −250.638 −0.00840011
963963 1412.95 0.0472810
964964 1304.50 0.0435840
965965 −23751.6 −0.792324
966966 42.9736 0.00143132
967967 −8790.83 −0.292341 −0.146171 0.989259i 0.546695π-0.546695\pi
−0.146171 + 0.989259i 0.546695π0.546695\pi
968968 333.860 0.0110854
969969 0 0
970970 716.568 0.0237192
971971 30609.1 1.01163 0.505815 0.862642i 0.331192π-0.331192\pi
0.505815 + 0.862642i 0.331192π0.331192\pi
972972 −1943.89 −0.0641465
973973 −4720.38 −0.155528
974974 −289.216 −0.00951445
975975 56880.4 1.86834
976976 26988.6 0.885126
977977 19095.9 0.625314 0.312657 0.949866i 0.398781π-0.398781\pi
0.312657 + 0.949866i 0.398781π0.398781\pi
978978 −140.982 −0.00460951
979979 −1685.80 −0.0550342
980980 49532.2 1.61454
981981 10497.3 0.341644
982982 56.6780 0.00184182
983983 −2465.89 −0.0800100 −0.0400050 0.999199i 0.512737π-0.512737\pi
−0.0400050 + 0.999199i 0.512737π0.512737\pi
984984 −199.001 −0.00644707
985985 71705.0 2.31950
986986 0 0
987987 11135.9 0.359127
988988 31320.6 1.00854
989989 14824.8 0.476644
990990 70.5599 0.00226519
991991 21369.6 0.684994 0.342497 0.939519i 0.388727π-0.388727\pi
0.342497 + 0.939519i 0.388727π0.388727\pi
992992 −883.933 −0.0282912
993993 2793.52 0.0892747
994994 94.3738 0.00301142
995995 −56215.8 −1.79112
996996 11178.7 0.355632
997997 −25866.7 −0.821670 −0.410835 0.911710i 0.634763π-0.634763\pi
−0.410835 + 0.911710i 0.634763π0.634763\pi
998998 −183.749 −0.00582813
999999 −5069.14 −0.160541
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 867.4.a.w.1.10 20
17.5 odd 16 51.4.h.a.25.5 40
17.7 odd 16 51.4.h.a.49.5 yes 40
17.16 even 2 867.4.a.v.1.10 20
51.5 even 16 153.4.l.c.127.6 40
51.41 even 16 153.4.l.c.100.6 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.4.h.a.25.5 40 17.5 odd 16
51.4.h.a.49.5 yes 40 17.7 odd 16
153.4.l.c.100.6 40 51.41 even 16
153.4.l.c.127.6 40 51.5 even 16
867.4.a.v.1.10 20 17.16 even 2
867.4.a.w.1.10 20 1.1 even 1 trivial