Properties

Label 1805.2.a.g.1.1
Level 18051805
Weight 22
Character 1805.1
Self dual yes
Analytic conductor 14.41314.413
Analytic rank 00
Dimension 33
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] = [1805,2,Mod(1,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1805=5192 1805 = 5 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1805.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: 14.412997564814.4129975648
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.361.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x26x+7 x^{3} - x^{2} - 6x + 7 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 95)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.285142.28514 of defining polynomial
Character χ\chi == 1805.1

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) == q2.28514q2+2.50702q3+3.22188q41.00000q55.72889q6+3.50702q72.79216q8+3.28514q9+2.28514q104.50702q11+8.07730q12+5.00000q138.01404q142.50702q150.0632663q16+0.158610q177.50702q183.22188q20+8.79216q21+10.2992q22+1.15861q237.00000q24+1.00000q2511.4257q26+0.714858q27+11.2992q28+3.50702q29+5.72889q30+2.28514q31+5.72889q3211.2992q330.362446q343.50702q35+10.5843q36+10.9648q37+12.5351q39+2.79216q406.07730q4120.0913q423.34841q4314.5211q443.28514q452.64759q46+3.06327q470.158610q48+5.29918q492.28514q50+0.397638q51+16.1094q52+5.74293q531.63355q54+4.50702q559.79216q568.01404q583.06327q598.07730q600.873467q615.22188q62+11.5211q6312.9648q645.00000q65+25.8202q66+8.44375q67+0.511021q68+2.90466q69+8.01404q70+16.2359q719.17265q727.15861q7325.0561q74+2.50702q7515.8062q7728.6445q78+10.1265q79+0.0632663q808.06327q81+13.8875q82+4.85543q83+28.3273q840.158610q85+7.65159q86+8.79216q87+12.5843q88+1.11250q89+7.50702q90+17.5351q91+3.73290q92+5.72889q937.00000q94+14.3624q961.61951q9712.1094q9814.8062q99+O(q100)q-2.28514 q^{2} +2.50702 q^{3} +3.22188 q^{4} -1.00000 q^{5} -5.72889 q^{6} +3.50702 q^{7} -2.79216 q^{8} +3.28514 q^{9} +2.28514 q^{10} -4.50702 q^{11} +8.07730 q^{12} +5.00000 q^{13} -8.01404 q^{14} -2.50702 q^{15} -0.0632663 q^{16} +0.158610 q^{17} -7.50702 q^{18} -3.22188 q^{20} +8.79216 q^{21} +10.2992 q^{22} +1.15861 q^{23} -7.00000 q^{24} +1.00000 q^{25} -11.4257 q^{26} +0.714858 q^{27} +11.2992 q^{28} +3.50702 q^{29} +5.72889 q^{30} +2.28514 q^{31} +5.72889 q^{32} -11.2992 q^{33} -0.362446 q^{34} -3.50702 q^{35} +10.5843 q^{36} +10.9648 q^{37} +12.5351 q^{39} +2.79216 q^{40} -6.07730 q^{41} -20.0913 q^{42} -3.34841 q^{43} -14.5211 q^{44} -3.28514 q^{45} -2.64759 q^{46} +3.06327 q^{47} -0.158610 q^{48} +5.29918 q^{49} -2.28514 q^{50} +0.397638 q^{51} +16.1094 q^{52} +5.74293 q^{53} -1.63355 q^{54} +4.50702 q^{55} -9.79216 q^{56} -8.01404 q^{58} -3.06327 q^{59} -8.07730 q^{60} -0.873467 q^{61} -5.22188 q^{62} +11.5211 q^{63} -12.9648 q^{64} -5.00000 q^{65} +25.8202 q^{66} +8.44375 q^{67} +0.511021 q^{68} +2.90466 q^{69} +8.01404 q^{70} +16.2359 q^{71} -9.17265 q^{72} -7.15861 q^{73} -25.0561 q^{74} +2.50702 q^{75} -15.8062 q^{77} -28.6445 q^{78} +10.1265 q^{79} +0.0632663 q^{80} -8.06327 q^{81} +13.8875 q^{82} +4.85543 q^{83} +28.3273 q^{84} -0.158610 q^{85} +7.65159 q^{86} +8.79216 q^{87} +12.5843 q^{88} +1.11250 q^{89} +7.50702 q^{90} +17.5351 q^{91} +3.73290 q^{92} +5.72889 q^{93} -7.00000 q^{94} +14.3624 q^{96} -1.61951 q^{97} -12.1094 q^{98} -14.8062 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3qq2q3+7q43q56q6+2q7+6q8+4q9+q105q11+4q12+15q137q14+q15+3q16+q1714q187q20+12q21+13q99+O(q100) 3 q - q^{2} - q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} + 6 q^{8} + 4 q^{9} + q^{10} - 5 q^{11} + 4 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} + 3 q^{16} + q^{17} - 14 q^{18} - 7 q^{20} + 12 q^{21}+ \cdots - 13 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 −2.28514 −1.61584 −0.807920 0.589292i 0.799407π-0.799407\pi
−0.807920 + 0.589292i 0.799407π0.799407\pi
33 2.50702 1.44743 0.723714 0.690100i 0.242434π-0.242434\pi
0.723714 + 0.690100i 0.242434π0.242434\pi
44 3.22188 1.61094
55 −1.00000 −0.447214
66 −5.72889 −2.33881
77 3.50702 1.32553 0.662764 0.748828i 0.269383π-0.269383\pi
0.662764 + 0.748828i 0.269383π0.269383\pi
88 −2.79216 −0.987178
99 3.28514 1.09505
1010 2.28514 0.722626
1111 −4.50702 −1.35892 −0.679459 0.733714i 0.737785π-0.737785\pi
−0.679459 + 0.733714i 0.737785π0.737785\pi
1212 8.07730 2.33172
1313 5.00000 1.38675 0.693375 0.720577i 0.256123π-0.256123\pi
0.693375 + 0.720577i 0.256123π0.256123\pi
1414 −8.01404 −2.14184
1515 −2.50702 −0.647309
1616 −0.0632663 −0.0158166
1717 0.158610 0.0384685 0.0192343 0.999815i 0.493877π-0.493877\pi
0.0192343 + 0.999815i 0.493877π0.493877\pi
1818 −7.50702 −1.76942
1919 0 0
2020 −3.22188 −0.720433
2121 8.79216 1.91861
2222 10.2992 2.19579
2323 1.15861 0.241587 0.120793 0.992678i 0.461456π-0.461456\pi
0.120793 + 0.992678i 0.461456π0.461456\pi
2424 −7.00000 −1.42887
2525 1.00000 0.200000
2626 −11.4257 −2.24077
2727 0.714858 0.137574
2828 11.2992 2.13534
2929 3.50702 0.651237 0.325619 0.945501i 0.394427π-0.394427\pi
0.325619 + 0.945501i 0.394427π0.394427\pi
3030 5.72889 1.04595
3131 2.28514 0.410424 0.205212 0.978718i 0.434212π-0.434212\pi
0.205212 + 0.978718i 0.434212π0.434212\pi
3232 5.72889 1.01274
3333 −11.2992 −1.96693
3434 −0.362446 −0.0621590
3535 −3.50702 −0.592794
3636 10.5843 1.76405
3737 10.9648 1.80260 0.901302 0.433192i 0.142613π-0.142613\pi
0.901302 + 0.433192i 0.142613π0.142613\pi
3838 0 0
3939 12.5351 2.00722
4040 2.79216 0.441479
4141 −6.07730 −0.949115 −0.474558 0.880224i 0.657392π-0.657392\pi
−0.474558 + 0.880224i 0.657392π0.657392\pi
4242 −20.0913 −3.10016
4343 −3.34841 −0.510628 −0.255314 0.966858i 0.582179π-0.582179\pi
−0.255314 + 0.966858i 0.582179π0.582179\pi
4444 −14.5211 −2.18913
4545 −3.28514 −0.489720
4646 −2.64759 −0.390366
4747 3.06327 0.446823 0.223412 0.974724i 0.428281π-0.428281\pi
0.223412 + 0.974724i 0.428281π0.428281\pi
4848 −0.158610 −0.0228934
4949 5.29918 0.757026
5050 −2.28514 −0.323168
5151 0.397638 0.0556804
5252 16.1094 2.23397
5353 5.74293 0.788852 0.394426 0.918928i 0.370943π-0.370943\pi
0.394426 + 0.918928i 0.370943π0.370943\pi
5454 −1.63355 −0.222298
5555 4.50702 0.607726
5656 −9.79216 −1.30853
5757 0 0
5858 −8.01404 −1.05229
5959 −3.06327 −0.398803 −0.199402 0.979918i 0.563900π-0.563900\pi
−0.199402 + 0.979918i 0.563900π0.563900\pi
6060 −8.07730 −1.04278
6161 −0.873467 −0.111836 −0.0559180 0.998435i 0.517809π-0.517809\pi
−0.0559180 + 0.998435i 0.517809π0.517809\pi
6262 −5.22188 −0.663179
6363 11.5211 1.45152
6464 −12.9648 −1.62060
6565 −5.00000 −0.620174
6666 25.8202 3.17825
6767 8.44375 1.03157 0.515784 0.856719i 0.327501π-0.327501\pi
0.515784 + 0.856719i 0.327501π0.327501\pi
6868 0.511021 0.0619704
6969 2.90466 0.349680
7070 8.01404 0.957861
7171 16.2359 1.92685 0.963424 0.267981i 0.0863564π-0.0863564\pi
0.963424 + 0.267981i 0.0863564π0.0863564\pi
7272 −9.17265 −1.08101
7373 −7.15861 −0.837852 −0.418926 0.908020i 0.637593π-0.637593\pi
−0.418926 + 0.908020i 0.637593π0.637593\pi
7474 −25.0561 −2.91272
7575 2.50702 0.289486
7676 0 0
7777 −15.8062 −1.80128
7878 −28.6445 −3.24335
7979 10.1265 1.13932 0.569662 0.821879i 0.307074π-0.307074\pi
0.569662 + 0.821879i 0.307074π0.307074\pi
8080 0.0632663 0.00707339
8181 −8.06327 −0.895918
8282 13.8875 1.53362
8383 4.85543 0.532952 0.266476 0.963841i 0.414141π-0.414141\pi
0.266476 + 0.963841i 0.414141π0.414141\pi
8484 28.3273 3.09076
8585 −0.158610 −0.0172037
8686 7.65159 0.825092
8787 8.79216 0.942619
8888 12.5843 1.34149
8989 1.11250 0.117924 0.0589621 0.998260i 0.481221π-0.481221\pi
0.0589621 + 0.998260i 0.481221π0.481221\pi
9090 7.50702 0.791309
9191 17.5351 1.83818
9292 3.73290 0.389181
9393 5.72889 0.594059
9494 −7.00000 −0.721995
9595 0 0
9696 14.3624 1.46586
9797 −1.61951 −0.164437 −0.0822184 0.996614i 0.526200π-0.526200\pi
−0.0822184 + 0.996614i 0.526200π0.526200\pi
9898 −12.1094 −1.22323
9999 −14.8062 −1.48808
100100 3.22188 0.322188
101101 12.3132 1.22521 0.612605 0.790389i 0.290121π-0.290121\pi
0.612605 + 0.790389i 0.290121π0.290121\pi
102102 −0.908659 −0.0899707
103103 −10.6164 −1.04606 −0.523032 0.852313i 0.675199π-0.675199\pi
−0.523032 + 0.852313i 0.675199π0.675199\pi
104104 −13.9608 −1.36897
105105 −8.79216 −0.858027
106106 −13.1234 −1.27466
107107 2.17265 0.210038 0.105019 0.994470i 0.466510π-0.466510\pi
0.105019 + 0.994470i 0.466510π0.466510\pi
108108 2.30318 0.221624
109109 −15.8202 −1.51530 −0.757652 0.652659i 0.773653π-0.773653\pi
−0.757652 + 0.652659i 0.773653π0.773653\pi
110110 −10.2992 −0.981988
111111 27.4890 2.60914
112112 −0.221876 −0.0209653
113113 −9.83828 −0.925507 −0.462754 0.886487i 0.653139π-0.653139\pi
−0.462754 + 0.886487i 0.653139π0.653139\pi
114114 0 0
115115 −1.15861 −0.108041
116116 11.2992 1.04910
117117 16.4257 1.51856
118118 7.00000 0.644402
119119 0.556248 0.0509911
120120 7.00000 0.639010
121121 9.31322 0.846656
122122 1.99600 0.180709
123123 −15.2359 −1.37378
124124 7.36245 0.661167
125125 −1.00000 −0.0894427
126126 −26.3273 −2.34542
127127 −15.7109 −1.39411 −0.697056 0.717016i 0.745507π-0.745507\pi
−0.697056 + 0.717016i 0.745507π0.745507\pi
128128 18.1686 1.60590
129129 −8.39452 −0.739097
130130 11.4257 1.00210
131131 −11.5351 −1.00783 −0.503913 0.863754i 0.668107π-0.668107\pi
−0.503913 + 0.863754i 0.668107π0.668107\pi
132132 −36.4046 −3.16861
133133 0 0
134134 −19.2952 −1.66685
135135 −0.714858 −0.0615251
136136 −0.442864 −0.0379753
137137 0.109381 0.00934503 0.00467252 0.999989i 0.498513π-0.498513\pi
0.00467252 + 0.999989i 0.498513π0.498513\pi
138138 −6.63755 −0.565026
139139 1.44375 0.122457 0.0612287 0.998124i 0.480498π-0.480498\pi
0.0612287 + 0.998124i 0.480498π0.480498\pi
140140 −11.2992 −0.954955
141141 7.67967 0.646745
142142 −37.1014 −3.11348
143143 −22.5351 −1.88448
144144 −0.207839 −0.0173199
145145 −3.50702 −0.291242
146146 16.3584 1.35383
147147 13.2851 1.09574
148148 35.3273 2.90388
149149 1.72889 0.141637 0.0708183 0.997489i 0.477439π-0.477439\pi
0.0708183 + 0.997489i 0.477439π0.477439\pi
150150 −5.72889 −0.467762
151151 20.1406 1.63902 0.819508 0.573068i 0.194247π-0.194247\pi
0.819508 + 0.573068i 0.194247π0.194247\pi
152152 0 0
153153 0.521056 0.0421249
154154 36.1194 2.91059
155155 −2.28514 −0.183547
156156 40.3865 3.23351
157157 3.77812 0.301527 0.150764 0.988570i 0.451827π-0.451827\pi
0.150764 + 0.988570i 0.451827π0.451827\pi
158158 −23.1406 −1.84096
159159 14.3976 1.14181
160160 −5.72889 −0.452909
161161 4.06327 0.320230
162162 18.4257 1.44766
163163 −1.61640 −0.126606 −0.0633031 0.997994i 0.520163π-0.520163\pi
−0.0633031 + 0.997994i 0.520163π0.520163\pi
164164 −19.5803 −1.52897
165165 11.2992 0.879640
166166 −11.0953 −0.861166
167167 −6.49298 −0.502442 −0.251221 0.967930i 0.580832π-0.580832\pi
−0.251221 + 0.967930i 0.580832π0.580832\pi
168168 −24.5491 −1.89401
169169 12.0000 0.923077
170170 0.362446 0.0277983
171171 0 0
172172 −10.7882 −0.822589
173173 −8.52106 −0.647844 −0.323922 0.946084i 0.605002π-0.605002\pi
−0.323922 + 0.946084i 0.605002π0.605002\pi
174174 −20.0913 −1.52312
175175 3.50702 0.265106
176176 0.285142 0.0214934
177177 −7.67967 −0.577239
178178 −2.54221 −0.190547
179179 10.2711 0.767698 0.383849 0.923396i 0.374598π-0.374598\pi
0.383849 + 0.923396i 0.374598π0.374598\pi
180180 −10.5843 −0.788909
181181 −12.2671 −0.911807 −0.455903 0.890029i 0.650684π-0.650684\pi
−0.455903 + 0.890029i 0.650684π0.650684\pi
182182 −40.0702 −2.97020
183183 −2.18980 −0.161875
184184 −3.23503 −0.238489
185185 −10.9648 −0.806149
186186 −13.0913 −0.959904
187187 −0.714858 −0.0522756
188188 9.86946 0.719805
189189 2.50702 0.182359
190190 0 0
191191 5.71085 0.413223 0.206611 0.978423i 0.433756π-0.433756\pi
0.206611 + 0.978423i 0.433756π0.433756\pi
192192 −32.5030 −2.34570
193193 10.1586 0.731233 0.365616 0.930766i 0.380858π-0.380858\pi
0.365616 + 0.930766i 0.380858π0.380858\pi
194194 3.70082 0.265703
195195 −12.5351 −0.897657
196196 17.0733 1.21952
197197 16.2038 1.15448 0.577238 0.816576i 0.304131π-0.304131\pi
0.577238 + 0.816576i 0.304131π0.304131\pi
198198 33.8343 2.40450
199199 0.334372 0.0237030 0.0118515 0.999930i 0.496227π-0.496227\pi
0.0118515 + 0.999930i 0.496227π0.496227\pi
200200 −2.79216 −0.197436
201201 21.1686 1.49312
202202 −28.1375 −1.97974
203203 12.2992 0.863233
204204 1.28114 0.0896977
205205 6.07730 0.424457
206206 24.2600 1.69027
207207 3.80620 0.264549
208208 −0.316332 −0.0219336
209209 0 0
210210 20.0913 1.38643
211211 −2.02807 −0.139618 −0.0698092 0.997560i 0.522239π-0.522239\pi
−0.0698092 + 0.997560i 0.522239π0.522239\pi
212212 18.5030 1.27079
213213 40.7037 2.78897
214214 −4.96481 −0.339387
215215 3.34841 0.228360
216216 −1.99600 −0.135810
217217 8.01404 0.544028
218218 36.1515 2.44849
219219 −17.9468 −1.21273
220220 14.5211 0.979009
221221 0.793049 0.0533463
222222 −62.8162 −4.21595
223223 19.2319 1.28786 0.643932 0.765083i 0.277302π-0.277302\pi
0.643932 + 0.765083i 0.277302π0.277302\pi
224224 20.0913 1.34241
225225 3.28514 0.219009
226226 22.4819 1.49547
227227 −4.00000 −0.265489 −0.132745 0.991150i 0.542379π-0.542379\pi
−0.132745 + 0.991150i 0.542379π0.542379\pi
228228 0 0
229229 −12.9788 −0.857666 −0.428833 0.903384i 0.641075π-0.641075\pi
−0.428833 + 0.903384i 0.641075π0.641075\pi
230230 2.64759 0.174577
231231 −39.6264 −2.60723
232232 −9.79216 −0.642887
233233 27.0733 1.77363 0.886815 0.462124i 0.152912π-0.152912\pi
0.886815 + 0.462124i 0.152912π0.152912\pi
234234 −37.5351 −2.45375
235235 −3.06327 −0.199825
236236 −9.86946 −0.642447
237237 25.3874 1.64909
238238 −1.27111 −0.0823935
239239 20.0602 1.29758 0.648792 0.760966i 0.275275π-0.275275\pi
0.648792 + 0.760966i 0.275275π0.275275\pi
240240 0.158610 0.0102382
241241 21.5843 1.39037 0.695184 0.718832i 0.255323π-0.255323\pi
0.695184 + 0.718832i 0.255323π0.255323\pi
242242 −21.2820 −1.36806
243243 −22.3593 −1.43435
244244 −2.81420 −0.180161
245245 −5.29918 −0.338552
246246 34.8162 2.21980
247247 0 0
248248 −6.38049 −0.405161
249249 12.1726 0.771410
250250 2.28514 0.144525
251251 −7.26799 −0.458752 −0.229376 0.973338i 0.573668π-0.573668\pi
−0.229376 + 0.973338i 0.573668π0.573668\pi
252252 37.1194 2.33830
253253 −5.22188 −0.328297
254254 35.9015 2.25266
255255 −0.397638 −0.0249010
256256 −15.5883 −0.974270
257257 −15.0773 −0.940496 −0.470248 0.882534i 0.655836π-0.655836\pi
−0.470248 + 0.882534i 0.655836π0.655836\pi
258258 19.1827 1.19426
259259 38.4538 2.38940
260260 −16.1094 −0.999061
261261 11.5211 0.713135
262262 26.3593 1.62848
263263 20.1546 1.24279 0.621393 0.783499i 0.286567π-0.286567\pi
0.621393 + 0.783499i 0.286567π0.286567\pi
264264 31.5491 1.94171
265265 −5.74293 −0.352786
266266 0 0
267267 2.78905 0.170687
268268 27.2047 1.66179
269269 7.72489 0.470995 0.235497 0.971875i 0.424328π-0.424328\pi
0.235497 + 0.971875i 0.424328π0.424328\pi
270270 1.63355 0.0994148
271271 −5.28514 −0.321050 −0.160525 0.987032i 0.551319π-0.551319\pi
−0.160525 + 0.987032i 0.551319π0.551319\pi
272272 −0.0100347 −0.000608441 0
273273 43.9608 2.66063
274274 −0.249951 −0.0151001
275275 −4.50702 −0.271783
276276 9.35844 0.563312
277277 30.6264 1.84016 0.920082 0.391726i 0.128122π-0.128122\pi
0.920082 + 0.391726i 0.128122π0.128122\pi
278278 −3.29918 −0.197872
279279 7.50702 0.449433
280280 9.79216 0.585194
281281 −13.3624 −0.797137 −0.398568 0.917139i 0.630493π-0.630493\pi
−0.398568 + 0.917139i 0.630493π0.630493\pi
282282 −17.5491 −1.04504
283283 4.09534 0.243443 0.121721 0.992564i 0.461159π-0.461159\pi
0.121721 + 0.992564i 0.461159π0.461159\pi
284284 52.3101 3.10403
285285 0 0
286286 51.4959 3.04502
287287 −21.3132 −1.25808
288288 18.8202 1.10899
289289 −16.9748 −0.998520
290290 8.01404 0.470600
291291 −4.06015 −0.238010
292292 −23.0642 −1.34973
293293 −12.1726 −0.711134 −0.355567 0.934651i 0.615712π-0.615712\pi
−0.355567 + 0.934651i 0.615712π0.615712\pi
294294 −30.3584 −1.77054
295295 3.06327 0.178350
296296 −30.6155 −1.77949
297297 −3.22188 −0.186952
298298 −3.95077 −0.228862
299299 5.79305 0.335021
300300 8.07730 0.466343
301301 −11.7429 −0.676851
302302 −46.0241 −2.64839
303303 30.8695 1.77340
304304 0 0
305305 0.873467 0.0500146
306306 −1.19069 −0.0680670
307307 −24.5351 −1.40029 −0.700146 0.714000i 0.746882π-0.746882\pi
−0.700146 + 0.714000i 0.746882π0.746882\pi
308308 −50.9256 −2.90176
309309 −26.6155 −1.51410
310310 5.22188 0.296583
311311 −10.2038 −0.578606 −0.289303 0.957238i 0.593424π-0.593424\pi
−0.289303 + 0.957238i 0.593424π0.593424\pi
312312 −35.0000 −1.98148
313313 −31.9820 −1.80773 −0.903864 0.427821i 0.859281π-0.859281\pi
−0.903864 + 0.427821i 0.859281π0.859281\pi
314314 −8.63355 −0.487219
315315 −11.5211 −0.649138
316316 32.6264 1.83538
317317 −2.23591 −0.125581 −0.0627907 0.998027i 0.520000π-0.520000\pi
−0.0627907 + 0.998027i 0.520000π0.520000\pi
318318 −32.9007 −1.84498
319319 −15.8062 −0.884977
320320 12.9648 0.724755
321321 5.44687 0.304014
322322 −9.28514 −0.517441
323323 0 0
324324 −25.9788 −1.44327
325325 5.00000 0.277350
326326 3.69370 0.204575
327327 −39.6616 −2.19329
328328 16.9688 0.936946
329329 10.7429 0.592277
330330 −25.8202 −1.42136
331331 10.0913 0.554670 0.277335 0.960773i 0.410549π-0.410549\pi
0.277335 + 0.960773i 0.410549π0.410549\pi
332332 15.6436 0.858553
333333 36.0210 1.97394
334334 14.8374 0.811866
335335 −8.44375 −0.461331
336336 −0.556248 −0.0303458
337337 −5.61240 −0.305727 −0.152863 0.988247i 0.548849π-0.548849\pi
−0.152863 + 0.988247i 0.548849π0.548849\pi
338338 −27.4217 −1.49154
339339 −24.6647 −1.33960
340340 −0.511021 −0.0277140
341341 −10.2992 −0.557732
342342 0 0
343343 −5.96481 −0.322069
344344 9.34930 0.504080
345345 −2.90466 −0.156381
346346 19.4718 1.04681
347347 5.47494 0.293910 0.146955 0.989143i 0.453053π-0.453053\pi
0.146955 + 0.989143i 0.453053π0.453053\pi
348348 28.3273 1.51850
349349 −18.8202 −1.00742 −0.503712 0.863872i 0.668033π-0.668033\pi
−0.503712 + 0.863872i 0.668033π0.668033\pi
350350 −8.01404 −0.428368
351351 3.57429 0.190781
352352 −25.8202 −1.37622
353353 −12.7008 −0.675996 −0.337998 0.941147i 0.609750π-0.609750\pi
−0.337998 + 0.941147i 0.609750π0.609750\pi
354354 17.5491 0.932726
355355 −16.2359 −0.861713
356356 3.58432 0.189969
357357 1.39452 0.0738060
358358 −23.4709 −1.24048
359359 −11.0804 −0.584802 −0.292401 0.956296i 0.594454π-0.594454\pi
−0.292401 + 0.956296i 0.594454π0.594454\pi
360360 9.17265 0.483441
361361 0 0
362362 28.0321 1.47333
363363 23.3484 1.22547
364364 56.4959 2.96119
365365 7.15861 0.374699
366366 5.00400 0.261563
367367 −20.6405 −1.07742 −0.538712 0.842490i 0.681089π-0.681089\pi
−0.538712 + 0.842490i 0.681089π0.681089\pi
368368 −0.0733010 −0.00382108
369369 −19.9648 −1.03933
370370 25.0561 1.30261
371371 20.1406 1.04565
372372 18.4578 0.956992
373373 −4.55313 −0.235752 −0.117876 0.993028i 0.537609π-0.537609\pi
−0.117876 + 0.993028i 0.537609π0.537609\pi
374374 1.63355 0.0844689
375375 −2.50702 −0.129462
376376 −8.55313 −0.441094
377377 17.5351 0.903103
378378 −5.72889 −0.294663
379379 19.9187 1.02315 0.511577 0.859237i 0.329061π-0.329061\pi
0.511577 + 0.859237i 0.329061π0.329061\pi
380380 0 0
381381 −39.3874 −2.01788
382382 −13.0501 −0.667702
383383 19.9748 1.02067 0.510333 0.859977i 0.329522π-0.329522\pi
0.510333 + 0.859977i 0.329522π0.329522\pi
384384 45.5491 2.32442
385385 15.8062 0.805558
386386 −23.2139 −1.18155
387387 −11.0000 −0.559161
388388 −5.21787 −0.264897
389389 13.8022 0.699799 0.349900 0.936787i 0.386216π-0.386216\pi
0.349900 + 0.936787i 0.386216π0.386216\pi
390390 28.6445 1.45047
391391 0.183767 0.00929349
392392 −14.7962 −0.747319
393393 −28.9187 −1.45876
394394 −37.0281 −1.86545
395395 −10.1265 −0.509521
396396 −47.7037 −2.39720
397397 −16.5491 −0.830577 −0.415289 0.909690i 0.636319π-0.636319\pi
−0.415289 + 0.909690i 0.636319π0.636319\pi
398398 −0.764087 −0.0383002
399399 0 0
400400 −0.0632663 −0.00316332
401401 −8.52506 −0.425721 −0.212861 0.977083i 0.568278π-0.568278\pi
−0.212861 + 0.977083i 0.568278π0.568278\pi
402402 −48.3734 −2.41264
403403 11.4257 0.569155
404404 39.6717 1.97374
405405 8.06327 0.400667
406406 −28.1054 −1.39485
407407 −49.4186 −2.44959
408408 −1.11027 −0.0549665
409409 11.5663 0.571916 0.285958 0.958242i 0.407688π-0.407688\pi
0.285958 + 0.958242i 0.407688π0.407688\pi
410410 −13.8875 −0.685855
411411 0.274220 0.0135263
412412 −34.2047 −1.68515
413413 −10.7429 −0.528625
414414 −8.69771 −0.427469
415415 −4.85543 −0.238344
416416 28.6445 1.40441
417417 3.61951 0.177248
418418 0 0
419419 −21.7149 −1.06084 −0.530420 0.847735i 0.677966π-0.677966\pi
−0.530420 + 0.847735i 0.677966π0.677966\pi
420420 −28.3273 −1.38223
421421 6.92270 0.337392 0.168696 0.985668i 0.446044π-0.446044\pi
0.168696 + 0.985668i 0.446044π0.446044\pi
422422 4.63444 0.225601
423423 10.0633 0.489293
424424 −16.0352 −0.778738
425425 0.158610 0.00769371
426426 −93.0138 −4.50654
427427 −3.06327 −0.148242
428428 7.00000 0.338358
429429 −56.4959 −2.72765
430430 −7.65159 −0.368992
431431 27.9788 1.34769 0.673847 0.738871i 0.264641π-0.264641\pi
0.673847 + 0.738871i 0.264641π0.264641\pi
432432 −0.0452264 −0.00217596
433433 −6.25395 −0.300546 −0.150273 0.988645i 0.548015π-0.548015\pi
−0.150273 + 0.988645i 0.548015π0.548015\pi
434434 −18.3132 −0.879063
435435 −8.79216 −0.421552
436436 −50.9708 −2.44106
437437 0 0
438438 41.0109 1.95958
439439 −31.1976 −1.48898 −0.744490 0.667633i 0.767307π-0.767307\pi
−0.744490 + 0.667633i 0.767307π0.767307\pi
440440 −12.5843 −0.599934
441441 17.4086 0.828979
442442 −1.81223 −0.0861990
443443 −32.7037 −1.55380 −0.776901 0.629623i 0.783209π-0.783209\pi
−0.776901 + 0.629623i 0.783209π0.783209\pi
444444 88.5661 4.20316
445445 −1.11250 −0.0527373
446446 −43.9477 −2.08098
447447 4.33437 0.205009
448448 −45.4678 −2.14815
449449 −25.6304 −1.20958 −0.604788 0.796387i 0.706742π-0.706742\pi
−0.604788 + 0.796387i 0.706742π0.706742\pi
450450 −7.50702 −0.353884
451451 27.3905 1.28977
452452 −31.6977 −1.49093
453453 50.4928 2.37236
454454 9.14057 0.428988
455455 −17.5351 −0.822058
456456 0 0
457457 33.1646 1.55138 0.775688 0.631116i 0.217403π-0.217403\pi
0.775688 + 0.631116i 0.217403π0.217403\pi
458458 29.6585 1.38585
459459 0.113383 0.00529229
460460 −3.73290 −0.174047
461461 2.17576 0.101335 0.0506677 0.998716i 0.483865π-0.483865\pi
0.0506677 + 0.998716i 0.483865π0.483865\pi
462462 90.5520 4.21286
463463 −6.20072 −0.288172 −0.144086 0.989565i 0.546024π-0.546024\pi
−0.144086 + 0.989565i 0.546024π0.546024\pi
464464 −0.221876 −0.0103003
465465 −5.72889 −0.265671
466466 −61.8664 −2.86590
467467 −17.1546 −0.793821 −0.396910 0.917857i 0.629918π-0.629918\pi
−0.396910 + 0.917857i 0.629918π0.629918\pi
468468 52.9216 2.44630
469469 29.6124 1.36737
470470 7.00000 0.322886
471471 9.47183 0.436439
472472 8.55313 0.393690
473473 15.0913 0.693901
474474 −58.0138 −2.66466
475475 0 0
476476 1.79216 0.0821436
477477 18.8664 0.863831
478478 −45.8403 −2.09669
479479 −35.7781 −1.63474 −0.817372 0.576110i 0.804570π-0.804570\pi
−0.817372 + 0.576110i 0.804570π0.804570\pi
480480 −14.3624 −0.655553
481481 54.8240 2.49976
482482 −49.3233 −2.24661
483483 10.1867 0.463510
484484 30.0060 1.36391
485485 1.61951 0.0735383
486486 51.0943 2.31768
487487 23.7149 1.07462 0.537311 0.843384i 0.319440π-0.319440\pi
0.537311 + 0.843384i 0.319440π0.319440\pi
488488 2.43886 0.110402
489489 −4.05234 −0.183253
490490 12.1094 0.547046
491491 −39.1867 −1.76847 −0.884235 0.467042i 0.845320π-0.845320\pi
−0.884235 + 0.467042i 0.845320π0.845320\pi
492492 −49.0882 −2.21307
493493 0.556248 0.0250521
494494 0 0
495495 14.8062 0.665489
496496 −0.144573 −0.00649150
497497 56.9397 2.55409
498498 −27.8162 −1.24648
499499 −9.37648 −0.419749 −0.209875 0.977728i 0.567306π-0.567306\pi
−0.209875 + 0.977728i 0.567306π0.567306\pi
500500 −3.22188 −0.144087
501501 −16.2780 −0.727249
502502 16.6084 0.741269
503503 13.4930 0.601622 0.300811 0.953684i 0.402743π-0.402743\pi
0.300811 + 0.953684i 0.402743π0.402743\pi
504504 −32.1686 −1.43291
505505 −12.3132 −0.547931
506506 11.9327 0.530475
507507 30.0842 1.33609
508508 −50.6184 −2.24583
509509 −25.7069 −1.13944 −0.569718 0.821840i 0.692948π-0.692948\pi
−0.569718 + 0.821840i 0.692948π0.692948\pi
510510 0.908659 0.0402361
511511 −25.1054 −1.11060
512512 −0.715746 −0.0316318
513513 0 0
514514 34.4538 1.51969
515515 10.6164 0.467814
516516 −27.0461 −1.19064
517517 −13.8062 −0.607196
518518 −87.8724 −3.86089
519519 −21.3624 −0.937707
520520 13.9608 0.612222
521521 37.7358 1.65324 0.826618 0.562763i 0.190262π-0.190262\pi
0.826618 + 0.562763i 0.190262π0.190262\pi
522522 −26.3273 −1.15231
523523 −38.4006 −1.67914 −0.839570 0.543252i 0.817193π-0.817193\pi
−0.839570 + 0.543252i 0.817193π0.817193\pi
524524 −37.1646 −1.62354
525525 8.79216 0.383721
526526 −46.0561 −2.00814
527527 0.362446 0.0157884
528528 0.714858 0.0311102
529529 −21.6576 −0.941636
530530 13.1234 0.570045
531531 −10.0633 −0.436709
532532 0 0
533533 −30.3865 −1.31619
534534 −6.37337 −0.275803
535535 −2.17265 −0.0939317
536536 −23.5763 −1.01834
537537 25.7499 1.11119
538538 −17.6525 −0.761052
539539 −23.8835 −1.02874
540540 −2.30318 −0.0991132
541541 −12.8062 −0.550581 −0.275291 0.961361i 0.588774π-0.588774\pi
−0.275291 + 0.961361i 0.588774π0.588774\pi
542542 12.0773 0.518765
543543 −30.7539 −1.31977
544544 0.908659 0.0389584
545545 15.8202 0.677664
546546 −100.457 −4.29915
547547 18.2571 0.780616 0.390308 0.920684i 0.372369π-0.372369\pi
0.390308 + 0.920684i 0.372369π0.372369\pi
548548 0.352411 0.0150543
549549 −2.86946 −0.122466
550550 10.2992 0.439159
551551 0 0
552552 −8.11027 −0.345196
553553 35.5139 1.51021
554554 −69.9858 −2.97341
555555 −27.4890 −1.16684
556556 4.65159 0.197271
557557 14.9047 0.631531 0.315765 0.948837i 0.397739π-0.397739\pi
0.315765 + 0.948837i 0.397739π0.397739\pi
558558 −17.1546 −0.726212
559559 −16.7420 −0.708113
560560 0.221876 0.00937598
561561 −1.79216 −0.0756651
562562 30.5351 1.28805
563563 −45.7810 −1.92944 −0.964720 0.263276i 0.915197π-0.915197\pi
−0.964720 + 0.263276i 0.915197π0.915197\pi
564564 24.7429 1.04187
565565 9.83828 0.413899
566566 −9.35844 −0.393365
567567 −28.2780 −1.18757
568568 −45.3333 −1.90214
569569 −0.379598 −0.0159136 −0.00795679 0.999968i 0.502533π-0.502533\pi
−0.00795679 + 0.999968i 0.502533π0.502533\pi
570570 0 0
571571 −15.8514 −0.663361 −0.331681 0.943392i 0.607616π-0.607616\pi
−0.331681 + 0.943392i 0.607616π0.607616\pi
572572 −72.6053 −3.03578
573573 14.3172 0.598110
574574 48.7037 2.03285
575575 1.15861 0.0483174
576576 −42.5912 −1.77464
577577 −19.2350 −0.800765 −0.400382 0.916348i 0.631123π-0.631123\pi
−0.400382 + 0.916348i 0.631123π0.631123\pi
578578 38.7899 1.61345
579579 25.4678 1.05841
580580 −11.2992 −0.469173
581581 17.0281 0.706444
582582 9.27803 0.384587
583583 −25.8835 −1.07199
584584 19.9880 0.827109
585585 −16.4257 −0.679120
586586 27.8162 1.14908
587587 40.8483 1.68599 0.842995 0.537921i 0.180790π-0.180790\pi
0.842995 + 0.537921i 0.180790π0.180790\pi
588588 42.8031 1.76517
589589 0 0
590590 −7.00000 −0.288185
591591 40.6233 1.67102
592592 −0.693703 −0.0285110
593593 −14.2468 −0.585047 −0.292524 0.956258i 0.594495π-0.594495\pi
−0.292524 + 0.956258i 0.594495π0.594495\pi
594594 7.36245 0.302085
595595 −0.556248 −0.0228039
596596 5.57028 0.228168
597597 0.838276 0.0343083
598598 −13.2379 −0.541340
599599 15.8514 0.647672 0.323836 0.946113i 0.395027π-0.395027\pi
0.323836 + 0.946113i 0.395027π0.395027\pi
600600 −7.00000 −0.285774
601601 −16.4718 −0.671900 −0.335950 0.941880i 0.609057π-0.609057\pi
−0.335950 + 0.941880i 0.609057π0.609057\pi
602602 26.8343 1.09368
603603 27.7389 1.12962
604604 64.8904 2.64035
605605 −9.31322 −0.378636
606606 −70.5411 −2.86554
607607 10.3914 0.421774 0.210887 0.977510i 0.432365π-0.432365\pi
0.210887 + 0.977510i 0.432365π0.432365\pi
608608 0 0
609609 30.8343 1.24947
610610 −1.99600 −0.0808156
611611 15.3163 0.619632
612612 1.67878 0.0678606
613613 −21.7850 −0.879890 −0.439945 0.898025i 0.645002π-0.645002\pi
−0.439945 + 0.898025i 0.645002π0.645002\pi
614614 56.0662 2.26265
615615 15.2359 0.614371
616616 44.1335 1.77819
617617 −42.7710 −1.72190 −0.860948 0.508693i 0.830129π-0.830129\pi
−0.860948 + 0.508693i 0.830129π0.830129\pi
618618 60.8202 2.44655
619619 28.7882 1.15709 0.578547 0.815649i 0.303620π-0.303620\pi
0.578547 + 0.815649i 0.303620π0.303620\pi
620620 −7.36245 −0.295683
621621 0.828241 0.0332362
622622 23.3172 0.934935
623623 3.90154 0.156312
624624 −0.793049 −0.0317474
625625 1.00000 0.0400000
626626 73.0833 2.92100
627627 0 0
628628 12.1726 0.485742
629629 1.73913 0.0693435
630630 26.3273 1.04890
631631 −19.3874 −0.771800 −0.385900 0.922541i 0.626109π-0.626109\pi
−0.385900 + 0.922541i 0.626109π0.626109\pi
632632 −28.2749 −1.12472
633633 −5.08442 −0.202088
634634 5.10938 0.202919
635635 15.7109 0.623466
636636 46.3874 1.83938
637637 26.4959 1.04981
638638 36.1194 1.42998
639639 53.3373 2.10999
640640 −18.1686 −0.718179
641641 −40.6866 −1.60702 −0.803512 0.595289i 0.797038π-0.797038\pi
−0.803512 + 0.595289i 0.797038π0.797038\pi
642642 −12.4469 −0.491239
643643 −34.1054 −1.34498 −0.672492 0.740104i 0.734776π-0.734776\pi
−0.672492 + 0.740104i 0.734776π0.734776\pi
644644 13.0913 0.515871
645645 8.39452 0.330534
646646 0 0
647647 −48.0029 −1.88719 −0.943595 0.331103i 0.892579π-0.892579\pi
−0.943595 + 0.331103i 0.892579π0.892579\pi
648648 22.5139 0.884431
649649 13.8062 0.541941
650650 −11.4257 −0.448153
651651 20.0913 0.787442
652652 −5.20784 −0.203955
653653 3.90866 0.152958 0.0764788 0.997071i 0.475632π-0.475632\pi
0.0764788 + 0.997071i 0.475632π0.475632\pi
654654 90.6325 3.54401
655655 11.5351 0.450713
656656 0.384489 0.0150118
657657 −23.5171 −0.917488
658658 −24.5491 −0.957025
659659 −13.0882 −0.509845 −0.254922 0.966961i 0.582050π-0.582050\pi
−0.254922 + 0.966961i 0.582050π0.582050\pi
660660 36.4046 1.41705
661661 23.9428 0.931266 0.465633 0.884978i 0.345827π-0.345827\pi
0.465633 + 0.884978i 0.345827π0.345827\pi
662662 −23.0602 −0.896258
663663 1.98819 0.0772149
664664 −13.5571 −0.526119
665665 0 0
666666 −82.3130 −3.18956
667667 4.06327 0.157330
668668 −20.9196 −0.809403
669669 48.2148 1.86409
670670 19.2952 0.745438
671671 3.93673 0.151976
672672 50.3694 1.94304
673673 11.3304 0.436754 0.218377 0.975865i 0.429924π-0.429924\pi
0.218377 + 0.975865i 0.429924π0.429924\pi
674674 12.8251 0.494005
675675 0.714858 0.0275149
676676 38.6625 1.48702
677677 −8.90466 −0.342234 −0.171117 0.985251i 0.554738π-0.554738\pi
−0.171117 + 0.985251i 0.554738π0.554738\pi
678678 56.3624 2.16459
679679 −5.67967 −0.217966
680680 0.442864 0.0169831
681681 −10.0281 −0.384277
682682 23.5351 0.901205
683683 26.6977 1.02156 0.510780 0.859712i 0.329357π-0.329357\pi
0.510780 + 0.859712i 0.329357π0.329357\pi
684684 0 0
685685 −0.109381 −0.00417923
686686 13.6304 0.520412
687687 −32.5382 −1.24141
688688 0.211842 0.00807638
689689 28.7147 1.09394
690690 6.63755 0.252687
691691 35.9708 1.36840 0.684198 0.729297i 0.260153π-0.260153\pi
0.684198 + 0.729297i 0.260153π0.260153\pi
692692 −27.4538 −1.04364
693693 −51.9256 −1.97249
694694 −12.5110 −0.474912
695695 −1.44375 −0.0547646
696696 −24.5491 −0.930532
697697 −0.963920 −0.0365111
698698 43.0069 1.62784
699699 67.8733 2.56720
700700 11.2992 0.427069
701701 2.45087 0.0925681 0.0462840 0.998928i 0.485262π-0.485262\pi
0.0462840 + 0.998928i 0.485262π0.485262\pi
702702 −8.16776 −0.308272
703703 0 0
704704 58.4326 2.20226
705705 −7.67967 −0.289233
706706 29.0232 1.09230
707707 43.1827 1.62405
708708 −24.7429 −0.929896
709709 −50.2881 −1.88861 −0.944304 0.329075i 0.893263π-0.893263\pi
−0.944304 + 0.329075i 0.893263π0.893263\pi
710710 37.1014 1.39239
711711 33.2671 1.24761
712712 −3.10627 −0.116412
713713 2.64759 0.0991530
714714 −3.18668 −0.119259
715715 22.5351 0.842765
716716 33.0922 1.23671
717717 50.2912 1.87816
718718 25.3203 0.944946
719719 −48.0983 −1.79376 −0.896881 0.442271i 0.854173π-0.854173\pi
−0.896881 + 0.442271i 0.854173π0.854173\pi
720720 0.207839 0.00774570
721721 −37.2319 −1.38659
722722 0 0
723723 54.1123 2.01246
724724 −39.5231 −1.46886
725725 3.50702 0.130247
726726 −53.3544 −1.98017
727727 −16.6797 −0.618615 −0.309307 0.950962i 0.600097π-0.600097\pi
−0.309307 + 0.950962i 0.600097π0.600097\pi
728728 −48.9608 −1.81461
729729 −31.8655 −1.18020
730730 −16.3584 −0.605453
731731 −0.531091 −0.0196431
732732 −7.05526 −0.260770
733733 −4.13365 −0.152680 −0.0763399 0.997082i 0.524323π-0.524323\pi
−0.0763399 + 0.997082i 0.524323π0.524323\pi
734734 47.1664 1.74094
735735 −13.2851 −0.490030
736736 6.63755 0.244663
737737 −38.0561 −1.40182
738738 45.6224 1.67938
739739 46.9740 1.72796 0.863982 0.503522i 0.167963π-0.167963\pi
0.863982 + 0.503522i 0.167963π0.167963\pi
740740 −35.3273 −1.29866
741741 0 0
742742 −46.0241 −1.68960
743743 −41.2139 −1.51199 −0.755995 0.654577i 0.772847π-0.772847\pi
−0.755995 + 0.654577i 0.772847π0.772847\pi
744744 −15.9960 −0.586442
745745 −1.72889 −0.0633418
746746 10.4046 0.380938
747747 15.9508 0.583608
748748 −2.30318 −0.0842127
749749 7.61951 0.278411
750750 5.72889 0.209190
751751 −5.97885 −0.218171 −0.109086 0.994032i 0.534792π-0.534792\pi
−0.109086 + 0.994032i 0.534792π0.534792\pi
752752 −0.193802 −0.00706722
753753 −18.2210 −0.664010
754754 −40.0702 −1.45927
755755 −20.1406 −0.732990
756756 8.07730 0.293769
757757 36.3936 1.32275 0.661375 0.750056i 0.269973π-0.269973\pi
0.661375 + 0.750056i 0.269973π0.269973\pi
758758 −45.5171 −1.65325
759759 −13.0913 −0.475186
760760 0 0
761761 −2.71397 −0.0983813 −0.0491907 0.998789i 0.515664π-0.515664\pi
−0.0491907 + 0.998789i 0.515664π0.515664\pi
762762 90.0058 3.26057
763763 −55.4819 −2.00858
764764 18.3997 0.665677
765765 −0.521056 −0.0188388
766766 −45.6454 −1.64923
767767 −15.3163 −0.553041
768768 −39.0802 −1.41019
769769 39.7991 1.43519 0.717596 0.696460i 0.245243π-0.245243\pi
0.717596 + 0.696460i 0.245243π0.245243\pi
770770 −36.1194 −1.30165
771771 −37.7991 −1.36130
772772 32.7298 1.17797
773773 −44.9748 −1.61763 −0.808816 0.588061i 0.799891π-0.799891\pi
−0.808816 + 0.588061i 0.799891π0.799891\pi
774774 25.1366 0.903515
775775 2.28514 0.0820847
776776 4.52194 0.162328
777777 96.4044 3.45849
778778 −31.5400 −1.13076
779779 0 0
780780 −40.3865 −1.44607
781781 −73.1756 −2.61843
782782 −0.419934 −0.0150168
783783 2.50702 0.0895935
784784 −0.335260 −0.0119736
785785 −3.77812 −0.134847
786786 66.0833 2.35711
787787 17.7149 0.631466 0.315733 0.948848i 0.397750π-0.397750\pi
0.315733 + 0.948848i 0.397750π0.397750\pi
788788 52.2068 1.85979
789789 50.5280 1.79884
790790 23.1406 0.823305
791791 −34.5030 −1.22679
792792 41.3413 1.46900
793793 −4.36734 −0.155089
794794 37.8171 1.34208
795795 −14.3976 −0.510632
796796 1.07730 0.0381840
797797 −25.4930 −0.903008 −0.451504 0.892269i 0.649112π-0.649112\pi
−0.451504 + 0.892269i 0.649112π0.649112\pi
798798 0 0
799799 0.485864 0.0171886
800800 5.72889 0.202547
801801 3.65471 0.129133
802802 19.4810 0.687897
803803 32.2640 1.13857
804804 68.2028 2.40533
805805 −4.06327 −0.143211
806806 −26.1094 −0.919664
807807 19.3664 0.681731
808808 −34.3805 −1.20950
809809 −20.4678 −0.719610 −0.359805 0.933027i 0.617157π-0.617157\pi
−0.359805 + 0.933027i 0.617157π0.617157\pi
810810 −18.4257 −0.647414
811811 22.9015 0.804182 0.402091 0.915600i 0.368284π-0.368284\pi
0.402091 + 0.915600i 0.368284π0.368284\pi
812812 39.6264 1.39062
813813 −13.2500 −0.464696
814814 112.929 3.95814
815815 1.61640 0.0566200
816816 −0.0251571 −0.000880674 0
817817 0 0
818818 −26.4306 −0.924124
819819 57.6053 2.01289
820820 19.5803 0.683774
821821 30.7218 1.07220 0.536099 0.844155i 0.319897π-0.319897\pi
0.536099 + 0.844155i 0.319897π0.319897\pi
822822 −0.626631 −0.0218563
823823 4.19692 0.146295 0.0731476 0.997321i 0.476696π-0.476696\pi
0.0731476 + 0.997321i 0.476696π0.476696\pi
824824 29.6427 1.03265
825825 −11.2992 −0.393387
826826 24.5491 0.854173
827827 21.3304 0.741730 0.370865 0.928687i 0.379061π-0.379061\pi
0.370865 + 0.928687i 0.379061π0.379061\pi
828828 12.2631 0.426172
829829 −34.0390 −1.18222 −0.591112 0.806590i 0.701311π-0.701311\pi
−0.591112 + 0.806590i 0.701311π0.701311\pi
830830 11.0953 0.385125
831831 76.7810 2.66350
832832 −64.8240 −2.24737
833833 0.840502 0.0291217
834834 −8.27111 −0.286405
835835 6.49298 0.224699
836836 0 0
837837 1.63355 0.0564638
838838 49.6215 1.71415
839839 −10.4117 −0.359451 −0.179725 0.983717i 0.557521π-0.557521\pi
−0.179725 + 0.983717i 0.557521π0.557521\pi
840840 24.5491 0.847025
841841 −16.7008 −0.575890
842842 −15.8193 −0.545171
843843 −33.4999 −1.15380
844844 −6.53421 −0.224917
845845 −12.0000 −0.412813
846846 −22.9960 −0.790619
847847 32.6616 1.12227
848848 −0.363334 −0.0124769
849849 10.2671 0.352366
850850 −0.362446 −0.0124318
851851 12.7039 0.435485
852852 131.142 4.49286
853853 −13.1305 −0.449581 −0.224790 0.974407i 0.572170π-0.572170\pi
−0.224790 + 0.974407i 0.572170π0.572170\pi
854854 7.00000 0.239535
855855 0 0
856856 −6.06638 −0.207345
857857 43.2459 1.47725 0.738627 0.674115i 0.235475π-0.235475\pi
0.738627 + 0.674115i 0.235475π0.235475\pi
858858 129.101 4.40744
859859 31.4687 1.07370 0.536849 0.843678i 0.319614π-0.319614\pi
0.536849 + 0.843678i 0.319614π0.319614\pi
860860 10.7882 0.367873
861861 −53.4326 −1.82098
862862 −63.9356 −2.17766
863863 23.7842 0.809622 0.404811 0.914400i 0.367337π-0.367337\pi
0.404811 + 0.914400i 0.367337π0.367337\pi
864864 4.09534 0.139326
865865 8.52106 0.289725
866866 14.2912 0.485634
867867 −42.5562 −1.44529
868868 25.8202 0.876396
869869 −45.6405 −1.54825
870870 20.0913 0.681160
871871 42.2188 1.43053
872872 44.1726 1.49587
873873 −5.32033 −0.180066
874874 0 0
875875 −3.50702 −0.118559
876876 −57.8223 −1.95363
877877 38.1695 1.28889 0.644447 0.764649i 0.277088π-0.277088\pi
0.644447 + 0.764649i 0.277088π0.277088\pi
878878 71.2910 2.40595
879879 −30.5171 −1.02931
880880 −0.285142 −0.00961215
881881 5.49209 0.185033 0.0925167 0.995711i 0.470509π-0.470509\pi
0.0925167 + 0.995711i 0.470509π0.470509\pi
882882 −39.7810 −1.33950
883883 −34.2983 −1.15423 −0.577115 0.816663i 0.695821π-0.695821\pi
−0.577115 + 0.816663i 0.695821π0.695821\pi
884884 2.55511 0.0859375
885885 7.67967 0.258149
886886 74.7327 2.51069
887887 37.5171 1.25970 0.629850 0.776717i 0.283116π-0.283116\pi
0.629850 + 0.776717i 0.283116π0.283116\pi
888888 −76.7537 −2.57568
889889 −55.0983 −1.84794
890890 2.54221 0.0852151
891891 36.3413 1.21748
892892 61.9628 2.07467
893893 0 0
894894 −9.90466 −0.331261
895895 −10.2711 −0.343325
896896 63.7178 2.12866
897897 14.5233 0.484918
898898 58.5692 1.95448
899899 8.01404 0.267283
900900 10.5843 0.352811
901901 0.910886 0.0303460
902902 −62.5912 −2.08406
903903 −29.4397 −0.979694
904904 27.4701 0.913640
905905 12.2671 0.407772
906906 −115.383 −3.83335
907907 22.2531 0.738901 0.369450 0.929250i 0.379546π-0.379546\pi
0.369450 + 0.929250i 0.379546π0.379546\pi
908908 −12.8875 −0.427687
909909 40.4507 1.34166
910910 40.0702 1.32831
911911 −10.0421 −0.332710 −0.166355 0.986066i 0.553200π-0.553200\pi
−0.166355 + 0.986066i 0.553200π0.553200\pi
912912 0 0
913913 −21.8835 −0.724238
914914 −75.7859 −2.50678
915915 2.18980 0.0723925
916916 −41.8162 −1.38165
917917 −40.4538 −1.33590
918918 −0.259097 −0.00855149
919919 6.06104 0.199935 0.0999676 0.994991i 0.468126π-0.468126\pi
0.0999676 + 0.994991i 0.468126π0.468126\pi
920920 3.23503 0.106656
921921 −61.5099 −2.02682
922922 −4.97193 −0.163742
923923 81.1796 2.67206
924924 −127.671 −4.20008
925925 10.9648 0.360521
926926 14.1695 0.465640
927927 −34.8764 −1.14549
928928 20.0913 0.659531
929929 −51.8764 −1.70201 −0.851004 0.525158i 0.824006π-0.824006\pi
−0.851004 + 0.525158i 0.824006π0.824006\pi
930930 13.0913 0.429282
931931 0 0
932932 87.2268 2.85721
933933 −25.5812 −0.837491
934934 39.2007 1.28269
935935 0.714858 0.0233783
936936 −45.8632 −1.49909
937937 25.1998 0.823243 0.411621 0.911355i 0.364963π-0.364963\pi
0.411621 + 0.911355i 0.364963π0.364963\pi
938938 −67.6685 −2.20946
939939 −80.1794 −2.61655
940940 −9.86946 −0.321906
941941 1.93585 0.0631068 0.0315534 0.999502i 0.489955π-0.489955\pi
0.0315534 + 0.999502i 0.489955π0.489955\pi
942942 −21.6445 −0.705215
943943 −7.04122 −0.229294
944944 0.193802 0.00630770
945945 −2.50702 −0.0815533
946946 −34.4859 −1.12123
947947 31.3624 1.01914 0.509571 0.860428i 0.329804π-0.329804\pi
0.509571 + 0.860428i 0.329804π0.329804\pi
948948 81.7951 2.65658
949949 −35.7930 −1.16189
950950 0 0
951951 −5.60548 −0.181770
952952 −1.55313 −0.0503373
953953 −52.9085 −1.71387 −0.856937 0.515422i 0.827635π-0.827635\pi
−0.856937 + 0.515422i 0.827635π0.827635\pi
954954 −43.1123 −1.39581
955955 −5.71085 −0.184799
956956 64.6313 2.09033
957957 −39.6264 −1.28094
958958 81.7581 2.64148
959959 0.383601 0.0123871
960960 32.5030 1.04903
961961 −25.7781 −0.831552
962962 −125.281 −4.03921
963963 7.13746 0.230001
964964 69.5420 2.23980
965965 −10.1586 −0.327017
966966 −23.2780 −0.748958
967967 −60.0281 −1.93037 −0.965186 0.261563i 0.915762π-0.915762\pi
−0.965186 + 0.261563i 0.915762π0.915762\pi
968968 −26.0040 −0.835800
969969 0 0
970970 −3.70082 −0.118826
971971 −1.75005 −0.0561618 −0.0280809 0.999606i 0.508940π-0.508940\pi
−0.0280809 + 0.999606i 0.508940π0.508940\pi
972972 −72.0390 −2.31065
973973 5.06327 0.162321
974974 −54.1918 −1.73642
975975 12.5351 0.401444
976976 0.0552611 0.00176886
977977 −5.47583 −0.175187 −0.0875937 0.996156i 0.527918π-0.527918\pi
−0.0875937 + 0.996156i 0.527918π0.527918\pi
978978 9.26018 0.296108
979979 −5.01404 −0.160249
980980 −17.0733 −0.545387
981981 −51.9717 −1.65933
982982 89.5472 2.85756
983983 −5.05926 −0.161365 −0.0806827 0.996740i 0.525710π-0.525710\pi
−0.0806827 + 0.996740i 0.525710π0.525710\pi
984984 42.5411 1.35616
985985 −16.2038 −0.516297
986986 −1.27111 −0.0404802
987987 26.9327 0.857278
988988 0 0
989989 −3.87950 −0.123361
990990 −33.8343 −1.07532
991991 −0.0984581 −0.00312762 −0.00156381 0.999999i 0.500498π-0.500498\pi
−0.00156381 + 0.999999i 0.500498π0.500498\pi
992992 13.0913 0.415650
993993 25.2992 0.802845
994994 −130.115 −4.12700
995995 −0.334372 −0.0106003
996996 39.2188 1.24269
997997 18.3593 0.581446 0.290723 0.956807i 0.406104π-0.406104\pi
0.290723 + 0.956807i 0.406104π0.406104\pi
998998 21.4266 0.678247
999999 7.83828 0.247992
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 1805.2.a.g.1.1 3
5.4 even 2 9025.2.a.ba.1.3 3
19.8 odd 6 95.2.e.b.26.1 yes 6
19.12 odd 6 95.2.e.b.11.1 6
19.18 odd 2 1805.2.a.h.1.3 3
57.8 even 6 855.2.k.g.406.3 6
57.50 even 6 855.2.k.g.676.3 6
76.27 even 6 1520.2.q.j.881.1 6
76.31 even 6 1520.2.q.j.961.1 6
95.8 even 12 475.2.j.b.349.2 12
95.12 even 12 475.2.j.b.49.2 12
95.27 even 12 475.2.j.b.349.5 12
95.69 odd 6 475.2.e.d.201.3 6
95.84 odd 6 475.2.e.d.26.3 6
95.88 even 12 475.2.j.b.49.5 12
95.94 odd 2 9025.2.a.z.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.b.11.1 6 19.12 odd 6
95.2.e.b.26.1 yes 6 19.8 odd 6
475.2.e.d.26.3 6 95.84 odd 6
475.2.e.d.201.3 6 95.69 odd 6
475.2.j.b.49.2 12 95.12 even 12
475.2.j.b.49.5 12 95.88 even 12
475.2.j.b.349.2 12 95.8 even 12
475.2.j.b.349.5 12 95.27 even 12
855.2.k.g.406.3 6 57.8 even 6
855.2.k.g.676.3 6 57.50 even 6
1520.2.q.j.881.1 6 76.27 even 6
1520.2.q.j.961.1 6 76.31 even 6
1805.2.a.g.1.1 3 1.1 even 1 trivial
1805.2.a.h.1.3 3 19.18 odd 2
9025.2.a.z.1.1 3 95.94 odd 2
9025.2.a.ba.1.3 3 5.4 even 2