Properties

Label 9610.2.a.be.1.2
Level 96109610
Weight 22
Character 9610.1
Self dual yes
Analytic conductor 76.73676.736
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9610,2,Mod(1,9610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9610, 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("9610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9610=25312 9610 = 2 \cdot 5 \cdot 31^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9610.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: 76.736236342576.7362363425
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,5)\Q(\sqrt{2}, \sqrt{5})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x46x2+4 x^{4} - 6x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.874032-0.874032 of defining polynomial
Character χ\chi == 9610.1

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) == q1.00000q20.874032q3+1.00000q41.00000q5+0.874032q6+3.23607q71.00000q82.23607q9+1.00000q10+5.11667q110.874032q12+2.28825q133.23607q14+0.874032q15+1.00000q166.32456q17+2.23607q187.23607q191.00000q202.82843q215.11667q22+3.16228q23+0.874032q24+1.00000q252.28825q26+4.57649q27+3.23607q282.62210q290.874032q301.00000q324.47214q33+6.32456q343.23607q352.23607q36+2.28825q37+7.23607q382.00000q39+1.00000q40+3.23607q41+2.82843q42+0.206331q43+5.11667q44+2.23607q453.16228q4611.7082q470.874032q48+3.47214q491.00000q50+5.52786q51+2.28825q521.62054q534.57649q545.11667q553.23607q56+6.32456q57+2.62210q58+9.70820q59+0.874032q608.94665q617.23607q63+1.00000q642.28825q65+4.47214q66+5.23607q676.32456q682.76393q69+3.23607q70+8.94427q71+2.23607q72+3.90879q732.28825q740.874032q757.23607q76+16.5579q77+2.00000q78+3.90879q791.00000q80+2.70820q813.23607q8212.8554q832.82843q84+6.32456q850.206331q86+2.29180q875.11667q88+16.2241q892.23607q90+7.40492q91+3.16228q92+11.7082q94+7.23607q95+0.874032q9611.4164q973.47214q9811.4412q99+O(q100)q-1.00000 q^{2} -0.874032 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.874032 q^{6} +3.23607 q^{7} -1.00000 q^{8} -2.23607 q^{9} +1.00000 q^{10} +5.11667 q^{11} -0.874032 q^{12} +2.28825 q^{13} -3.23607 q^{14} +0.874032 q^{15} +1.00000 q^{16} -6.32456 q^{17} +2.23607 q^{18} -7.23607 q^{19} -1.00000 q^{20} -2.82843 q^{21} -5.11667 q^{22} +3.16228 q^{23} +0.874032 q^{24} +1.00000 q^{25} -2.28825 q^{26} +4.57649 q^{27} +3.23607 q^{28} -2.62210 q^{29} -0.874032 q^{30} -1.00000 q^{32} -4.47214 q^{33} +6.32456 q^{34} -3.23607 q^{35} -2.23607 q^{36} +2.28825 q^{37} +7.23607 q^{38} -2.00000 q^{39} +1.00000 q^{40} +3.23607 q^{41} +2.82843 q^{42} +0.206331 q^{43} +5.11667 q^{44} +2.23607 q^{45} -3.16228 q^{46} -11.7082 q^{47} -0.874032 q^{48} +3.47214 q^{49} -1.00000 q^{50} +5.52786 q^{51} +2.28825 q^{52} -1.62054 q^{53} -4.57649 q^{54} -5.11667 q^{55} -3.23607 q^{56} +6.32456 q^{57} +2.62210 q^{58} +9.70820 q^{59} +0.874032 q^{60} -8.94665 q^{61} -7.23607 q^{63} +1.00000 q^{64} -2.28825 q^{65} +4.47214 q^{66} +5.23607 q^{67} -6.32456 q^{68} -2.76393 q^{69} +3.23607 q^{70} +8.94427 q^{71} +2.23607 q^{72} +3.90879 q^{73} -2.28825 q^{74} -0.874032 q^{75} -7.23607 q^{76} +16.5579 q^{77} +2.00000 q^{78} +3.90879 q^{79} -1.00000 q^{80} +2.70820 q^{81} -3.23607 q^{82} -12.8554 q^{83} -2.82843 q^{84} +6.32456 q^{85} -0.206331 q^{86} +2.29180 q^{87} -5.11667 q^{88} +16.2241 q^{89} -2.23607 q^{90} +7.40492 q^{91} +3.16228 q^{92} +11.7082 q^{94} +7.23607 q^{95} +0.874032 q^{96} -11.4164 q^{97} -3.47214 q^{98} -11.4412 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q2+4q44q5+4q74q8+4q104q14+4q1620q194q20+4q25+4q284q324q35+20q388q39+4q40+4q4120q47++4q98+O(q100) 4 q - 4 q^{2} + 4 q^{4} - 4 q^{5} + 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{14} + 4 q^{16} - 20 q^{19} - 4 q^{20} + 4 q^{25} + 4 q^{28} - 4 q^{32} - 4 q^{35} + 20 q^{38} - 8 q^{39} + 4 q^{40} + 4 q^{41} - 20 q^{47}+ \cdots + 4 q^{98}+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 −1.00000 −0.707107
33 −0.874032 −0.504623 −0.252311 0.967646i 0.581191π-0.581191\pi
−0.252311 + 0.967646i 0.581191π0.581191\pi
44 1.00000 0.500000
55 −1.00000 −0.447214
66 0.874032 0.356822
77 3.23607 1.22312 0.611559 0.791199i 0.290543π-0.290543\pi
0.611559 + 0.791199i 0.290543π0.290543\pi
88 −1.00000 −0.353553
99 −2.23607 −0.745356
1010 1.00000 0.316228
1111 5.11667 1.54273 0.771367 0.636390i 0.219573π-0.219573\pi
0.771367 + 0.636390i 0.219573π0.219573\pi
1212 −0.874032 −0.252311
1313 2.28825 0.634645 0.317323 0.948318i 0.397216π-0.397216\pi
0.317323 + 0.948318i 0.397216π0.397216\pi
1414 −3.23607 −0.864876
1515 0.874032 0.225674
1616 1.00000 0.250000
1717 −6.32456 −1.53393 −0.766965 0.641689i 0.778234π-0.778234\pi
−0.766965 + 0.641689i 0.778234π0.778234\pi
1818 2.23607 0.527046
1919 −7.23607 −1.66007 −0.830034 0.557713i 0.811679π-0.811679\pi
−0.830034 + 0.557713i 0.811679π0.811679\pi
2020 −1.00000 −0.223607
2121 −2.82843 −0.617213
2222 −5.11667 −1.09088
2323 3.16228 0.659380 0.329690 0.944089i 0.393056π-0.393056\pi
0.329690 + 0.944089i 0.393056π0.393056\pi
2424 0.874032 0.178411
2525 1.00000 0.200000
2626 −2.28825 −0.448762
2727 4.57649 0.880746
2828 3.23607 0.611559
2929 −2.62210 −0.486911 −0.243456 0.969912i 0.578281π-0.578281\pi
−0.243456 + 0.969912i 0.578281π0.578281\pi
3030 −0.874032 −0.159576
3131 0 0
3232 −1.00000 −0.176777
3333 −4.47214 −0.778499
3434 6.32456 1.08465
3535 −3.23607 −0.546995
3636 −2.23607 −0.372678
3737 2.28825 0.376185 0.188093 0.982151i 0.439769π-0.439769\pi
0.188093 + 0.982151i 0.439769π0.439769\pi
3838 7.23607 1.17385
3939 −2.00000 −0.320256
4040 1.00000 0.158114
4141 3.23607 0.505389 0.252694 0.967546i 0.418683π-0.418683\pi
0.252694 + 0.967546i 0.418683π0.418683\pi
4242 2.82843 0.436436
4343 0.206331 0.0314652 0.0157326 0.999876i 0.494992π-0.494992\pi
0.0157326 + 0.999876i 0.494992π0.494992\pi
4444 5.11667 0.771367
4545 2.23607 0.333333
4646 −3.16228 −0.466252
4747 −11.7082 −1.70782 −0.853909 0.520423i 0.825774π-0.825774\pi
−0.853909 + 0.520423i 0.825774π0.825774\pi
4848 −0.874032 −0.126156
4949 3.47214 0.496019
5050 −1.00000 −0.141421
5151 5.52786 0.774056
5252 2.28825 0.317323
5353 −1.62054 −0.222599 −0.111299 0.993787i 0.535501π-0.535501\pi
−0.111299 + 0.993787i 0.535501π0.535501\pi
5454 −4.57649 −0.622782
5555 −5.11667 −0.689932
5656 −3.23607 −0.432438
5757 6.32456 0.837708
5858 2.62210 0.344298
5959 9.70820 1.26390 0.631950 0.775009i 0.282255π-0.282255\pi
0.631950 + 0.775009i 0.282255π0.282255\pi
6060 0.874032 0.112837
6161 −8.94665 −1.14550 −0.572751 0.819730i 0.694124π-0.694124\pi
−0.572751 + 0.819730i 0.694124π0.694124\pi
6262 0 0
6363 −7.23607 −0.911659
6464 1.00000 0.125000
6565 −2.28825 −0.283822
6666 4.47214 0.550482
6767 5.23607 0.639688 0.319844 0.947470i 0.396370π-0.396370\pi
0.319844 + 0.947470i 0.396370π0.396370\pi
6868 −6.32456 −0.766965
6969 −2.76393 −0.332738
7070 3.23607 0.386784
7171 8.94427 1.06149 0.530745 0.847532i 0.321912π-0.321912\pi
0.530745 + 0.847532i 0.321912π0.321912\pi
7272 2.23607 0.263523
7373 3.90879 0.457489 0.228745 0.973486i 0.426538π-0.426538\pi
0.228745 + 0.973486i 0.426538π0.426538\pi
7474 −2.28825 −0.266003
7575 −0.874032 −0.100925
7676 −7.23607 −0.830034
7777 16.5579 1.88695
7878 2.00000 0.226455
7979 3.90879 0.439773 0.219887 0.975525i 0.429431π-0.429431\pi
0.219887 + 0.975525i 0.429431π0.429431\pi
8080 −1.00000 −0.111803
8181 2.70820 0.300912
8282 −3.23607 −0.357364
8383 −12.8554 −1.41107 −0.705534 0.708676i 0.749293π-0.749293\pi
−0.705534 + 0.708676i 0.749293π0.749293\pi
8484 −2.82843 −0.308607
8585 6.32456 0.685994
8686 −0.206331 −0.0222492
8787 2.29180 0.245706
8888 −5.11667 −0.545439
8989 16.2241 1.71975 0.859873 0.510508i 0.170543π-0.170543\pi
0.859873 + 0.510508i 0.170543π0.170543\pi
9090 −2.23607 −0.235702
9191 7.40492 0.776246
9292 3.16228 0.329690
9393 0 0
9494 11.7082 1.20761
9595 7.23607 0.742405
9696 0.874032 0.0892055
9797 −11.4164 −1.15916 −0.579580 0.814915i 0.696783π-0.696783\pi
−0.579580 + 0.814915i 0.696783π0.696783\pi
9898 −3.47214 −0.350739
9999 −11.4412 −1.14989
100100 1.00000 0.100000
101101 18.9443 1.88503 0.942513 0.334170i 0.108456π-0.108456\pi
0.942513 + 0.334170i 0.108456π0.108456\pi
102102 −5.52786 −0.547340
103103 −4.00000 −0.394132 −0.197066 0.980390i 0.563141π-0.563141\pi
−0.197066 + 0.980390i 0.563141π0.563141\pi
104104 −2.28825 −0.224381
105105 2.82843 0.276026
106106 1.62054 0.157401
107107 16.9443 1.63806 0.819032 0.573747i 0.194511π-0.194511\pi
0.819032 + 0.573747i 0.194511π0.194511\pi
108108 4.57649 0.440373
109109 −17.7082 −1.69614 −0.848069 0.529886i 0.822235π-0.822235\pi
−0.848069 + 0.529886i 0.822235π0.822235\pi
110110 5.11667 0.487856
111111 −2.00000 −0.189832
112112 3.23607 0.305780
113113 9.52786 0.896306 0.448153 0.893957i 0.352082π-0.352082\pi
0.448153 + 0.893957i 0.352082π0.352082\pi
114114 −6.32456 −0.592349
115115 −3.16228 −0.294884
116116 −2.62210 −0.243456
117117 −5.11667 −0.473037
118118 −9.70820 −0.893713
119119 −20.4667 −1.87618
120120 −0.874032 −0.0797878
121121 15.1803 1.38003
122122 8.94665 0.809992
123123 −2.82843 −0.255031
124124 0 0
125125 −1.00000 −0.0894427
126126 7.23607 0.644640
127127 3.16228 0.280607 0.140303 0.990109i 0.455192π-0.455192\pi
0.140303 + 0.990109i 0.455192π0.455192\pi
128128 −1.00000 −0.0883883
129129 −0.180340 −0.0158780
130130 2.28825 0.200692
131131 −1.70820 −0.149246 −0.0746232 0.997212i 0.523775π-0.523775\pi
−0.0746232 + 0.997212i 0.523775π0.523775\pi
132132 −4.47214 −0.389249
133133 −23.4164 −2.03046
134134 −5.23607 −0.452327
135135 −4.57649 −0.393882
136136 6.32456 0.542326
137137 14.1421 1.20824 0.604122 0.796892i 0.293524π-0.293524\pi
0.604122 + 0.796892i 0.293524π0.293524\pi
138138 2.76393 0.235282
139139 −12.1089 −1.02707 −0.513533 0.858070i 0.671664π-0.671664\pi
−0.513533 + 0.858070i 0.671664π0.671664\pi
140140 −3.23607 −0.273498
141141 10.2333 0.861803
142142 −8.94427 −0.750587
143143 11.7082 0.979089
144144 −2.23607 −0.186339
145145 2.62210 0.217753
146146 −3.90879 −0.323494
147147 −3.03476 −0.250303
148148 2.28825 0.188093
149149 11.2361 0.920495 0.460247 0.887791i 0.347761π-0.347761\pi
0.460247 + 0.887791i 0.347761π0.347761\pi
150150 0.874032 0.0713644
151151 −13.0618 −1.06295 −0.531476 0.847073i 0.678362π-0.678362\pi
−0.531476 + 0.847073i 0.678362π0.678362\pi
152152 7.23607 0.586923
153153 14.1421 1.14332
154154 −16.5579 −1.33427
155155 0 0
156156 −2.00000 −0.160128
157157 6.94427 0.554213 0.277107 0.960839i 0.410624π-0.410624\pi
0.277107 + 0.960839i 0.410624π0.410624\pi
158158 −3.90879 −0.310967
159159 1.41641 0.112328
160160 1.00000 0.0790569
161161 10.2333 0.806501
162162 −2.70820 −0.212777
163163 14.1803 1.11069 0.555345 0.831620i 0.312586π-0.312586\pi
0.555345 + 0.831620i 0.312586π0.312586\pi
164164 3.23607 0.252694
165165 4.47214 0.348155
166166 12.8554 0.997776
167167 22.9613 1.77680 0.888398 0.459074i 0.151819π-0.151819\pi
0.888398 + 0.459074i 0.151819π0.151819\pi
168168 2.82843 0.218218
169169 −7.76393 −0.597226
170170 −6.32456 −0.485071
171171 16.1803 1.23734
172172 0.206331 0.0157326
173173 9.41641 0.715916 0.357958 0.933738i 0.383473π-0.383473\pi
0.357958 + 0.933738i 0.383473π0.383473\pi
174174 −2.29180 −0.173741
175175 3.23607 0.244624
176176 5.11667 0.385684
177177 −8.48528 −0.637793
178178 −16.2241 −1.21604
179179 −11.4412 −0.855158 −0.427579 0.903978i 0.640633π-0.640633\pi
−0.427579 + 0.903978i 0.640633π0.640633\pi
180180 2.23607 0.166667
181181 16.7642 1.24608 0.623038 0.782192i 0.285898π-0.285898\pi
0.623038 + 0.782192i 0.285898π0.285898\pi
182182 −7.40492 −0.548889
183183 7.81966 0.578046
184184 −3.16228 −0.233126
185185 −2.28825 −0.168235
186186 0 0
187187 −32.3607 −2.36645
188188 −11.7082 −0.853909
189189 14.8098 1.07726
190190 −7.23607 −0.524960
191191 17.4164 1.26021 0.630104 0.776511i 0.283012π-0.283012\pi
0.630104 + 0.776511i 0.283012π0.283012\pi
192192 −0.874032 −0.0630778
193193 2.94427 0.211933 0.105967 0.994370i 0.466206π-0.466206\pi
0.105967 + 0.994370i 0.466206π0.466206\pi
194194 11.4164 0.819650
195195 2.00000 0.143223
196196 3.47214 0.248010
197197 −11.8539 −0.844555 −0.422277 0.906467i 0.638769π-0.638769\pi
−0.422277 + 0.906467i 0.638769π0.638769\pi
198198 11.4412 0.813093
199199 −13.3168 −0.944004 −0.472002 0.881598i 0.656468π-0.656468\pi
−0.472002 + 0.881598i 0.656468π0.656468\pi
200200 −1.00000 −0.0707107
201201 −4.57649 −0.322801
202202 −18.9443 −1.33291
203203 −8.48528 −0.595550
204204 5.52786 0.387028
205205 −3.23607 −0.226017
206206 4.00000 0.278693
207207 −7.07107 −0.491473
208208 2.28825 0.158661
209209 −37.0246 −2.56104
210210 −2.82843 −0.195180
211211 10.4721 0.720932 0.360466 0.932772i 0.382618π-0.382618\pi
0.360466 + 0.932772i 0.382618π0.382618\pi
212212 −1.62054 −0.111299
213213 −7.81758 −0.535652
214214 −16.9443 −1.15829
215215 −0.206331 −0.0140717
216216 −4.57649 −0.311391
217217 0 0
218218 17.7082 1.19935
219219 −3.41641 −0.230859
220220 −5.11667 −0.344966
221221 −14.4721 −0.973501
222222 2.00000 0.134231
223223 −3.82998 −0.256474 −0.128237 0.991744i 0.540932π-0.540932\pi
−0.128237 + 0.991744i 0.540932π0.540932\pi
224224 −3.23607 −0.216219
225225 −2.23607 −0.149071
226226 −9.52786 −0.633784
227227 −21.5967 −1.43343 −0.716713 0.697368i 0.754354π-0.754354\pi
−0.716713 + 0.697368i 0.754354π0.754354\pi
228228 6.32456 0.418854
229229 −7.86629 −0.519819 −0.259909 0.965633i 0.583693π-0.583693\pi
−0.259909 + 0.965633i 0.583693π0.583693\pi
230230 3.16228 0.208514
231231 −14.4721 −0.952197
232232 2.62210 0.172149
233233 29.8885 1.95806 0.979032 0.203707i 0.0652991π-0.0652991\pi
0.979032 + 0.203707i 0.0652991π0.0652991\pi
234234 5.11667 0.334487
235235 11.7082 0.763759
236236 9.70820 0.631950
237237 −3.41641 −0.221920
238238 20.4667 1.32666
239239 −13.0618 −0.844896 −0.422448 0.906387i 0.638829π-0.638829\pi
−0.422448 + 0.906387i 0.638829π0.638829\pi
240240 0.874032 0.0564185
241241 −21.8809 −1.40947 −0.704736 0.709469i 0.748935π-0.748935\pi
−0.704736 + 0.709469i 0.748935π0.748935\pi
242242 −15.1803 −0.975829
243243 −16.0965 −1.03259
244244 −8.94665 −0.572751
245245 −3.47214 −0.221827
246246 2.82843 0.180334
247247 −16.5579 −1.05355
248248 0 0
249249 11.2361 0.712057
250250 1.00000 0.0632456
251251 −17.3531 −1.09532 −0.547660 0.836701i 0.684481π-0.684481\pi
−0.547660 + 0.836701i 0.684481π0.684481\pi
252252 −7.23607 −0.455829
253253 16.1803 1.01725
254254 −3.16228 −0.198419
255255 −5.52786 −0.346168
256256 1.00000 0.0625000
257257 5.41641 0.337866 0.168933 0.985628i 0.445968π-0.445968\pi
0.168933 + 0.985628i 0.445968π0.445968\pi
258258 0.180340 0.0112275
259259 7.40492 0.460119
260260 −2.28825 −0.141911
261261 5.86319 0.362922
262262 1.70820 0.105533
263263 −24.2967 −1.49820 −0.749098 0.662459i 0.769513π-0.769513\pi
−0.749098 + 0.662459i 0.769513π0.769513\pi
264264 4.47214 0.275241
265265 1.62054 0.0995493
266266 23.4164 1.43575
267267 −14.1803 −0.867823
268268 5.23607 0.319844
269269 14.1908 0.865231 0.432616 0.901579i 0.357591π-0.357591\pi
0.432616 + 0.901579i 0.357591π0.357591\pi
270270 4.57649 0.278516
271271 −18.0509 −1.09652 −0.548258 0.836309i 0.684709π-0.684709\pi
−0.548258 + 0.836309i 0.684709π0.684709\pi
272272 −6.32456 −0.383482
273273 −6.47214 −0.391711
274274 −14.1421 −0.854358
275275 5.11667 0.308547
276276 −2.76393 −0.166369
277277 2.70091 0.162282 0.0811409 0.996703i 0.474144π-0.474144\pi
0.0811409 + 0.996703i 0.474144π0.474144\pi
278278 12.1089 0.726245
279279 0 0
280280 3.23607 0.193392
281281 −26.0000 −1.55103 −0.775515 0.631329i 0.782510π-0.782510\pi
−0.775515 + 0.631329i 0.782510π0.782510\pi
282282 −10.2333 −0.609387
283283 −1.23607 −0.0734766 −0.0367383 0.999325i 0.511697π-0.511697\pi
−0.0367383 + 0.999325i 0.511697π0.511697\pi
284284 8.94427 0.530745
285285 −6.32456 −0.374634
286286 −11.7082 −0.692321
287287 10.4721 0.618151
288288 2.23607 0.131762
289289 23.0000 1.35294
290290 −2.62210 −0.153975
291291 9.97831 0.584939
292292 3.90879 0.228745
293293 −8.65248 −0.505483 −0.252742 0.967534i 0.581332π-0.581332\pi
−0.252742 + 0.967534i 0.581332π0.581332\pi
294294 3.03476 0.176991
295295 −9.70820 −0.565233
296296 −2.28825 −0.133002
297297 23.4164 1.35876
298298 −11.2361 −0.650888
299299 7.23607 0.418473
300300 −0.874032 −0.0504623
301301 0.667701 0.0384856
302302 13.0618 0.751621
303303 −16.5579 −0.951227
304304 −7.23607 −0.415017
305305 8.94665 0.512284
306306 −14.1421 −0.808452
307307 24.0000 1.36975 0.684876 0.728659i 0.259856π-0.259856\pi
0.684876 + 0.728659i 0.259856π0.259856\pi
308308 16.5579 0.943474
309309 3.49613 0.198888
310310 0 0
311311 −7.41641 −0.420546 −0.210273 0.977643i 0.567435π-0.567435\pi
−0.210273 + 0.977643i 0.567435π0.567435\pi
312312 2.00000 0.113228
313313 25.4558 1.43885 0.719425 0.694570i 0.244406π-0.244406\pi
0.719425 + 0.694570i 0.244406π0.244406\pi
314314 −6.94427 −0.391888
315315 7.23607 0.407706
316316 3.90879 0.219887
317317 15.7082 0.882261 0.441130 0.897443i 0.354578π-0.354578\pi
0.441130 + 0.897443i 0.354578π0.354578\pi
318318 −1.41641 −0.0794282
319319 −13.4164 −0.751175
320320 −1.00000 −0.0559017
321321 −14.8098 −0.826604
322322 −10.2333 −0.570282
323323 45.7649 2.54643
324324 2.70820 0.150456
325325 2.28825 0.126929
326326 −14.1803 −0.785376
327327 15.4775 0.855910
328328 −3.23607 −0.178682
329329 −37.8885 −2.08886
330330 −4.47214 −0.246183
331331 22.3423 1.22804 0.614021 0.789290i 0.289551π-0.289551\pi
0.614021 + 0.789290i 0.289551π0.289551\pi
332332 −12.8554 −0.705534
333333 −5.11667 −0.280392
334334 −22.9613 −1.25638
335335 −5.23607 −0.286077
336336 −2.82843 −0.154303
337337 0.412662 0.0224791 0.0112396 0.999937i 0.496422π-0.496422\pi
0.0112396 + 0.999937i 0.496422π0.496422\pi
338338 7.76393 0.422302
339339 −8.32766 −0.452296
340340 6.32456 0.342997
341341 0 0
342342 −16.1803 −0.874933
343343 −11.4164 −0.616428
344344 −0.206331 −0.0111246
345345 2.76393 0.148805
346346 −9.41641 −0.506229
347347 16.7642 0.899951 0.449976 0.893041i 0.351433π-0.351433\pi
0.449976 + 0.893041i 0.351433π0.351433\pi
348348 2.29180 0.122853
349349 −7.23607 −0.387338 −0.193669 0.981067i 0.562039π-0.562039\pi
−0.193669 + 0.981067i 0.562039π0.562039\pi
350350 −3.23607 −0.172975
351351 10.4721 0.558961
352352 −5.11667 −0.272720
353353 −0.255039 −0.0135744 −0.00678718 0.999977i 0.502160π-0.502160\pi
−0.00678718 + 0.999977i 0.502160π0.502160\pi
354354 8.48528 0.450988
355355 −8.94427 −0.474713
356356 16.2241 0.859873
357357 17.8885 0.946762
358358 11.4412 0.604688
359359 −3.88854 −0.205229 −0.102615 0.994721i 0.532721π-0.532721\pi
−0.102615 + 0.994721i 0.532721π0.532721\pi
360360 −2.23607 −0.117851
361361 33.3607 1.75583
362362 −16.7642 −0.881108
363363 −13.2681 −0.696395
364364 7.40492 0.388123
365365 −3.90879 −0.204595
366366 −7.81966 −0.408740
367367 27.9504 1.45900 0.729500 0.683981i 0.239753π-0.239753\pi
0.729500 + 0.683981i 0.239753π0.239753\pi
368368 3.16228 0.164845
369369 −7.23607 −0.376695
370370 2.28825 0.118960
371371 −5.24419 −0.272265
372372 0 0
373373 4.65248 0.240896 0.120448 0.992720i 0.461567π-0.461567\pi
0.120448 + 0.992720i 0.461567π0.461567\pi
374374 32.3607 1.67333
375375 0.874032 0.0451348
376376 11.7082 0.603805
377377 −6.00000 −0.309016
378378 −14.8098 −0.761736
379379 −25.7082 −1.32054 −0.660271 0.751028i 0.729559π-0.729559\pi
−0.660271 + 0.751028i 0.729559π0.729559\pi
380380 7.23607 0.371202
381381 −2.76393 −0.141601
382382 −17.4164 −0.891101
383383 8.81913 0.450637 0.225318 0.974285i 0.427658π-0.427658\pi
0.225318 + 0.974285i 0.427658π0.427658\pi
384384 0.874032 0.0446028
385385 −16.5579 −0.843869
386386 −2.94427 −0.149859
387387 −0.461370 −0.0234528
388388 −11.4164 −0.579580
389389 −21.3407 −1.08202 −0.541009 0.841017i 0.681957π-0.681957\pi
−0.541009 + 0.841017i 0.681957π0.681957\pi
390390 −2.00000 −0.101274
391391 −20.0000 −1.01144
392392 −3.47214 −0.175369
393393 1.49302 0.0753131
394394 11.8539 0.597190
395395 −3.90879 −0.196673
396396 −11.4412 −0.574943
397397 23.1246 1.16059 0.580295 0.814406i 0.302937π-0.302937\pi
0.580295 + 0.814406i 0.302937π0.302937\pi
398398 13.3168 0.667511
399399 20.4667 1.02462
400400 1.00000 0.0500000
401401 6.40337 0.319769 0.159884 0.987136i 0.448888π-0.448888\pi
0.159884 + 0.987136i 0.448888π0.448888\pi
402402 4.57649 0.228255
403403 0 0
404404 18.9443 0.942513
405405 −2.70820 −0.134572
406406 8.48528 0.421117
407407 11.7082 0.580354
408408 −5.52786 −0.273670
409409 37.1034 1.83465 0.917323 0.398145i 0.130346π-0.130346\pi
0.917323 + 0.398145i 0.130346π0.130346\pi
410410 3.23607 0.159818
411411 −12.3607 −0.609707
412412 −4.00000 −0.197066
413413 31.4164 1.54590
414414 7.07107 0.347524
415415 12.8554 0.631049
416416 −2.28825 −0.112190
417417 10.5836 0.518281
418418 37.0246 1.81093
419419 −19.2361 −0.939743 −0.469872 0.882735i 0.655700π-0.655700\pi
−0.469872 + 0.882735i 0.655700π0.655700\pi
420420 2.82843 0.138013
421421 −6.65248 −0.324222 −0.162111 0.986773i 0.551830π-0.551830\pi
−0.162111 + 0.986773i 0.551830π0.551830\pi
422422 −10.4721 −0.509776
423423 26.1803 1.27293
424424 1.62054 0.0787006
425425 −6.32456 −0.306786
426426 7.81758 0.378763
427427 −28.9520 −1.40108
428428 16.9443 0.819032
429429 −10.2333 −0.494071
430430 0.206331 0.00995016
431431 18.0000 0.867029 0.433515 0.901146i 0.357273π-0.357273\pi
0.433515 + 0.901146i 0.357273π0.357273\pi
432432 4.57649 0.220187
433433 25.2982 1.21575 0.607877 0.794031i 0.292021π-0.292021\pi
0.607877 + 0.794031i 0.292021π0.292021\pi
434434 0 0
435435 −2.29180 −0.109883
436436 −17.7082 −0.848069
437437 −22.8825 −1.09462
438438 3.41641 0.163242
439439 8.47214 0.404353 0.202176 0.979349i 0.435199π-0.435199\pi
0.202176 + 0.979349i 0.435199π0.435199\pi
440440 5.11667 0.243928
441441 −7.76393 −0.369711
442442 14.4721 0.688369
443443 24.0000 1.14027 0.570137 0.821549i 0.306890π-0.306890\pi
0.570137 + 0.821549i 0.306890π0.306890\pi
444444 −2.00000 −0.0949158
445445 −16.2241 −0.769094
446446 3.82998 0.181355
447447 −9.82068 −0.464502
448448 3.23607 0.152890
449449 −1.15917 −0.0547048 −0.0273524 0.999626i 0.508708π-0.508708\pi
−0.0273524 + 0.999626i 0.508708π0.508708\pi
450450 2.23607 0.105409
451451 16.5579 0.779681
452452 9.52786 0.448153
453453 11.4164 0.536390
454454 21.5967 1.01359
455455 −7.40492 −0.347148
456456 −6.32456 −0.296174
457457 −18.9737 −0.887551 −0.443775 0.896138i 0.646361π-0.646361\pi
−0.443775 + 0.896138i 0.646361π0.646361\pi
458458 7.86629 0.367568
459459 −28.9443 −1.35100
460460 −3.16228 −0.147442
461461 13.2681 0.617957 0.308979 0.951069i 0.400013π-0.400013\pi
0.308979 + 0.951069i 0.400013π0.400013\pi
462462 14.4721 0.673305
463463 24.5517 1.14101 0.570507 0.821293i 0.306747π-0.306747\pi
0.570507 + 0.821293i 0.306747π0.306747\pi
464464 −2.62210 −0.121728
465465 0 0
466466 −29.8885 −1.38456
467467 7.05573 0.326500 0.163250 0.986585i 0.447802π-0.447802\pi
0.163250 + 0.986585i 0.447802π0.447802\pi
468468 −5.11667 −0.236518
469469 16.9443 0.782414
470470 −11.7082 −0.540059
471471 −6.06952 −0.279669
472472 −9.70820 −0.446856
473473 1.05573 0.0485424
474474 3.41641 0.156921
475475 −7.23607 −0.332014
476476 −20.4667 −0.938089
477477 3.62365 0.165915
478478 13.0618 0.597432
479479 25.8885 1.18288 0.591439 0.806350i 0.298560π-0.298560\pi
0.591439 + 0.806350i 0.298560π0.298560\pi
480480 −0.874032 −0.0398939
481481 5.23607 0.238744
482482 21.8809 0.996648
483483 −8.94427 −0.406978
484484 15.1803 0.690015
485485 11.4164 0.518392
486486 16.0965 0.730153
487487 8.81913 0.399633 0.199817 0.979833i 0.435965π-0.435965\pi
0.199817 + 0.979833i 0.435965π0.435965\pi
488488 8.94665 0.404996
489489 −12.3941 −0.560479
490490 3.47214 0.156855
491491 −28.2542 −1.27509 −0.637546 0.770412i 0.720051π-0.720051\pi
−0.637546 + 0.770412i 0.720051π0.720051\pi
492492 −2.82843 −0.127515
493493 16.5836 0.746887
494494 16.5579 0.744975
495495 11.4412 0.514245
496496 0 0
497497 28.9443 1.29833
498498 −11.2361 −0.503500
499499 7.53244 0.337198 0.168599 0.985685i 0.446076π-0.446076\pi
0.168599 + 0.985685i 0.446076π0.446076\pi
500500 −1.00000 −0.0447214
501501 −20.0689 −0.896612
502502 17.3531 0.774508
503503 2.11146 0.0941452 0.0470726 0.998891i 0.485011π-0.485011\pi
0.0470726 + 0.998891i 0.485011π0.485011\pi
504504 7.23607 0.322320
505505 −18.9443 −0.843009
506506 −16.1803 −0.719304
507507 6.78593 0.301374
508508 3.16228 0.140303
509509 32.2418 1.42909 0.714546 0.699589i 0.246633π-0.246633\pi
0.714546 + 0.699589i 0.246633π0.246633\pi
510510 5.52786 0.244778
511511 12.6491 0.559564
512512 −1.00000 −0.0441942
513513 −33.1158 −1.46210
514514 −5.41641 −0.238908
515515 4.00000 0.176261
516516 −0.180340 −0.00793902
517517 −59.9070 −2.63471
518518 −7.40492 −0.325353
519519 −8.23024 −0.361268
520520 2.28825 0.100346
521521 −16.3607 −0.716774 −0.358387 0.933573i 0.616673π-0.616673\pi
−0.358387 + 0.933573i 0.616673π0.616673\pi
522522 −5.86319 −0.256625
523523 −21.0857 −0.922013 −0.461006 0.887397i 0.652511π-0.652511\pi
−0.461006 + 0.887397i 0.652511π0.652511\pi
524524 −1.70820 −0.0746232
525525 −2.82843 −0.123443
526526 24.2967 1.05939
527527 0 0
528528 −4.47214 −0.194625
529529 −13.0000 −0.565217
530530 −1.62054 −0.0703920
531531 −21.7082 −0.942056
532532 −23.4164 −1.01523
533533 7.40492 0.320743
534534 14.1803 0.613643
535535 −16.9443 −0.732565
536536 −5.23607 −0.226164
537537 10.0000 0.431532
538538 −14.1908 −0.611811
539539 17.7658 0.765226
540540 −4.57649 −0.196941
541541 42.0689 1.80868 0.904341 0.426810i 0.140363π-0.140363\pi
0.904341 + 0.426810i 0.140363π0.140363\pi
542542 18.0509 0.775354
543543 −14.6525 −0.628798
544544 6.32456 0.271163
545545 17.7082 0.758536
546546 6.47214 0.276982
547547 16.2918 0.696587 0.348293 0.937386i 0.386761π-0.386761\pi
0.348293 + 0.937386i 0.386761π0.386761\pi
548548 14.1421 0.604122
549549 20.0053 0.853806
550550 −5.11667 −0.218176
551551 18.9737 0.808305
552552 2.76393 0.117641
553553 12.6491 0.537895
554554 −2.70091 −0.114751
555555 2.00000 0.0848953
556556 −12.1089 −0.513533
557557 17.7658 0.752760 0.376380 0.926465i 0.377169π-0.377169\pi
0.376380 + 0.926465i 0.377169π0.377169\pi
558558 0 0
559559 0.472136 0.0199692
560560 −3.23607 −0.136749
561561 28.2843 1.19416
562562 26.0000 1.09674
563563 24.6525 1.03898 0.519489 0.854477i 0.326122π-0.326122\pi
0.519489 + 0.854477i 0.326122π0.326122\pi
564564 10.2333 0.430902
565565 −9.52786 −0.400840
566566 1.23607 0.0519558
567567 8.76393 0.368051
568568 −8.94427 −0.375293
569569 37.1034 1.55546 0.777728 0.628601i 0.216372π-0.216372\pi
0.777728 + 0.628601i 0.216372π0.216372\pi
570570 6.32456 0.264906
571571 18.4335 0.771417 0.385709 0.922621i 0.373957π-0.373957\pi
0.385709 + 0.922621i 0.373957π0.373957\pi
572572 11.7082 0.489545
573573 −15.2225 −0.635929
574574 −10.4721 −0.437099
575575 3.16228 0.131876
576576 −2.23607 −0.0931695
577577 −16.0000 −0.666089 −0.333044 0.942911i 0.608076π-0.608076\pi
−0.333044 + 0.942911i 0.608076π0.608076\pi
578578 −23.0000 −0.956674
579579 −2.57339 −0.106946
580580 2.62210 0.108877
581581 −41.6011 −1.72590
582582 −9.97831 −0.413614
583583 −8.29180 −0.343411
584584 −3.90879 −0.161747
585585 5.11667 0.211548
586586 8.65248 0.357430
587587 −27.9203 −1.15239 −0.576197 0.817311i 0.695464π-0.695464\pi
−0.576197 + 0.817311i 0.695464π0.695464\pi
588588 −3.03476 −0.125151
589589 0 0
590590 9.70820 0.399680
591591 10.3607 0.426181
592592 2.28825 0.0940463
593593 21.5279 0.884043 0.442022 0.897004i 0.354261π-0.354261\pi
0.442022 + 0.897004i 0.354261π0.354261\pi
594594 −23.4164 −0.960787
595595 20.4667 0.839053
596596 11.2361 0.460247
597597 11.6393 0.476366
598598 −7.23607 −0.295905
599599 33.4164 1.36536 0.682679 0.730719i 0.260815π-0.260815\pi
0.682679 + 0.730719i 0.260815π0.260815\pi
600600 0.874032 0.0356822
601601 −8.81913 −0.359740 −0.179870 0.983690i 0.557568π-0.557568\pi
−0.179870 + 0.983690i 0.557568π0.557568\pi
602602 −0.667701 −0.0272135
603603 −11.7082 −0.476795
604604 −13.0618 −0.531476
605605 −15.1803 −0.617169
606606 16.5579 0.672619
607607 6.94427 0.281859 0.140930 0.990020i 0.454991π-0.454991\pi
0.140930 + 0.990020i 0.454991π0.454991\pi
608608 7.23607 0.293461
609609 7.41641 0.300528
610610 −8.94665 −0.362239
611611 −26.7912 −1.08386
612612 14.1421 0.571662
613613 −26.6637 −1.07694 −0.538469 0.842645i 0.680997π-0.680997\pi
−0.538469 + 0.842645i 0.680997π0.680997\pi
614614 −24.0000 −0.968561
615615 2.82843 0.114053
616616 −16.5579 −0.667137
617617 38.9443 1.56784 0.783919 0.620864i 0.213218π-0.213218\pi
0.783919 + 0.620864i 0.213218π0.213218\pi
618618 −3.49613 −0.140635
619619 −44.9697 −1.80748 −0.903742 0.428077i 0.859191π-0.859191\pi
−0.903742 + 0.428077i 0.859191π0.859191\pi
620620 0 0
621621 14.4721 0.580747
622622 7.41641 0.297371
623623 52.5021 2.10345
624624 −2.00000 −0.0800641
625625 1.00000 0.0400000
626626 −25.4558 −1.01742
627627 32.3607 1.29236
628628 6.94427 0.277107
629629 −14.4721 −0.577042
630630 −7.23607 −0.288292
631631 9.40802 0.374527 0.187264 0.982310i 0.440038π-0.440038\pi
0.187264 + 0.982310i 0.440038π0.440038\pi
632632 −3.90879 −0.155483
633633 −9.15298 −0.363798
634634 −15.7082 −0.623852
635635 −3.16228 −0.125491
636636 1.41641 0.0561642
637637 7.94510 0.314796
638638 13.4164 0.531161
639639 −20.0000 −0.791188
640640 1.00000 0.0395285
641641 25.3770 1.00233 0.501166 0.865351i 0.332905π-0.332905\pi
0.501166 + 0.865351i 0.332905π0.332905\pi
642642 14.8098 0.584498
643643 29.6684 1.17001 0.585003 0.811031i 0.301093π-0.301093\pi
0.585003 + 0.811031i 0.301093π0.301093\pi
644644 10.2333 0.403250
645645 0.180340 0.00710088
646646 −45.7649 −1.80060
647647 −36.5331 −1.43627 −0.718133 0.695906i 0.755003π-0.755003\pi
−0.718133 + 0.695906i 0.755003π0.755003\pi
648648 −2.70820 −0.106388
649649 49.6737 1.94986
650650 −2.28825 −0.0897524
651651 0 0
652652 14.1803 0.555345
653653 40.8328 1.59791 0.798956 0.601390i 0.205386π-0.205386\pi
0.798956 + 0.601390i 0.205386π0.205386\pi
654654 −15.4775 −0.605220
655655 1.70820 0.0667451
656656 3.23607 0.126347
657657 −8.74032 −0.340992
658658 37.8885 1.47705
659659 −27.2361 −1.06097 −0.530483 0.847695i 0.677990π-0.677990\pi
−0.530483 + 0.847695i 0.677990π0.677990\pi
660660 4.47214 0.174078
661661 −14.6525 −0.569915 −0.284958 0.958540i 0.591980π-0.591980\pi
−0.284958 + 0.958540i 0.591980π0.591980\pi
662662 −22.3423 −0.868357
663663 12.6491 0.491251
664664 12.8554 0.498888
665665 23.4164 0.908049
666666 5.11667 0.198267
667667 −8.29180 −0.321060
668668 22.9613 0.888398
669669 3.34752 0.129423
670670 5.23607 0.202287
671671 −45.7771 −1.76720
672672 2.82843 0.109109
673673 16.8129 0.648091 0.324046 0.946041i 0.394957π-0.394957\pi
0.324046 + 0.946041i 0.394957π0.394957\pi
674674 −0.412662 −0.0158951
675675 4.57649 0.176149
676676 −7.76393 −0.298613
677677 −41.3159 −1.58790 −0.793950 0.607983i 0.791979π-0.791979\pi
−0.793950 + 0.607983i 0.791979π0.791979\pi
678678 8.32766 0.319822
679679 −36.9443 −1.41779
680680 −6.32456 −0.242536
681681 18.8762 0.723339
682682 0 0
683683 −2.11146 −0.0807926 −0.0403963 0.999184i 0.512862π-0.512862\pi
−0.0403963 + 0.999184i 0.512862π0.512862\pi
684684 16.1803 0.618671
685685 −14.1421 −0.540343
686686 11.4164 0.435880
687687 6.87539 0.262312
688688 0.206331 0.00786629
689689 −3.70820 −0.141271
690690 −2.76393 −0.105221
691691 47.7771 1.81753 0.908763 0.417313i 0.137028π-0.137028\pi
0.908763 + 0.417313i 0.137028π0.137028\pi
692692 9.41641 0.357958
693693 −37.0246 −1.40645
694694 −16.7642 −0.636362
695695 12.1089 0.459318
696696 −2.29180 −0.0868703
697697 −20.4667 −0.775231
698698 7.23607 0.273889
699699 −26.1235 −0.988083
700700 3.23607 0.122312
701701 5.05573 0.190952 0.0954761 0.995432i 0.469563π-0.469563\pi
0.0954761 + 0.995432i 0.469563π0.469563\pi
702702 −10.4721 −0.395245
703703 −16.5579 −0.624493
704704 5.11667 0.192842
705705 −10.2333 −0.385410
706706 0.255039 0.00959852
707707 61.3050 2.30561
708708 −8.48528 −0.318896
709709 −2.20943 −0.0829770 −0.0414885 0.999139i 0.513210π-0.513210\pi
−0.0414885 + 0.999139i 0.513210π0.513210\pi
710710 8.94427 0.335673
711711 −8.74032 −0.327788
712712 −16.2241 −0.608022
713713 0 0
714714 −17.8885 −0.669462
715715 −11.7082 −0.437862
716716 −11.4412 −0.427579
717717 11.4164 0.426354
718718 3.88854 0.145119
719719 30.2874 1.12953 0.564764 0.825252i 0.308967π-0.308967\pi
0.564764 + 0.825252i 0.308967π0.308967\pi
720720 2.23607 0.0833333
721721 −12.9443 −0.482070
722722 −33.3607 −1.24156
723723 19.1246 0.711252
724724 16.7642 0.623038
725725 −2.62210 −0.0973822
726726 13.2681 0.492426
727727 −1.41641 −0.0525317 −0.0262658 0.999655i 0.508362π-0.508362\pi
−0.0262658 + 0.999655i 0.508362π0.508362\pi
728728 −7.40492 −0.274445
729729 5.94427 0.220158
730730 3.90879 0.144671
731731 −1.30495 −0.0482654
732732 7.81966 0.289023
733733 −30.7639 −1.13629 −0.568146 0.822928i 0.692339π-0.692339\pi
−0.568146 + 0.822928i 0.692339π0.692339\pi
734734 −27.9504 −1.03167
735735 3.03476 0.111939
736736 −3.16228 −0.116563
737737 26.7912 0.986868
738738 7.23607 0.266363
739739 −11.0286 −0.405692 −0.202846 0.979211i 0.565019π-0.565019\pi
−0.202846 + 0.979211i 0.565019π0.565019\pi
740740 −2.28825 −0.0841176
741741 14.4721 0.531647
742742 5.24419 0.192520
743743 9.74187 0.357395 0.178697 0.983904i 0.442812π-0.442812\pi
0.178697 + 0.983904i 0.442812π0.442812\pi
744744 0 0
745745 −11.2361 −0.411658
746746 −4.65248 −0.170339
747747 28.7456 1.05175
748748 −32.3607 −1.18322
749749 54.8328 2.00355
750750 −0.874032 −0.0319151
751751 −23.3050 −0.850410 −0.425205 0.905097i 0.639798π-0.639798\pi
−0.425205 + 0.905097i 0.639798π0.639798\pi
752752 −11.7082 −0.426954
753753 15.1672 0.552723
754754 6.00000 0.218507
755755 13.0618 0.475367
756756 14.8098 0.538629
757757 31.4953 1.14471 0.572357 0.820004i 0.306029π-0.306029\pi
0.572357 + 0.820004i 0.306029π0.306029\pi
758758 25.7082 0.933764
759759 −14.1421 −0.513327
760760 −7.23607 −0.262480
761761 −51.5006 −1.86689 −0.933447 0.358715i 0.883215π-0.883215\pi
−0.933447 + 0.358715i 0.883215π0.883215\pi
762762 2.76393 0.100127
763763 −57.3050 −2.07458
764764 17.4164 0.630104
765765 −14.1421 −0.511310
766766 −8.81913 −0.318648
767767 22.2148 0.802128
768768 −0.874032 −0.0315389
769769 −15.3475 −0.553446 −0.276723 0.960950i 0.589248π-0.589248\pi
−0.276723 + 0.960950i 0.589248π0.589248\pi
770770 16.5579 0.596705
771771 −4.73411 −0.170495
772772 2.94427 0.105967
773773 27.0764 0.973870 0.486935 0.873438i 0.338115π-0.338115\pi
0.486935 + 0.873438i 0.338115π0.338115\pi
774774 0.461370 0.0165836
775775 0 0
776776 11.4164 0.409825
777777 −6.47214 −0.232187
778778 21.3407 0.765102
779779 −23.4164 −0.838980
780780 2.00000 0.0716115
781781 45.7649 1.63760
782782 20.0000 0.715199
783783 −12.0000 −0.428845
784784 3.47214 0.124005
785785 −6.94427 −0.247852
786786 −1.49302 −0.0532544
787787 −13.6808 −0.487667 −0.243833 0.969817i 0.578405π-0.578405\pi
−0.243833 + 0.969817i 0.578405π0.578405\pi
788788 −11.8539 −0.422277
789789 21.2361 0.756024
790790 3.90879 0.139069
791791 30.8328 1.09629
792792 11.4412 0.406546
793793 −20.4721 −0.726987
794794 −23.1246 −0.820662
795795 −1.41641 −0.0502348
796796 −13.3168 −0.472002
797797 −12.5216 −0.443538 −0.221769 0.975099i 0.571183π-0.571183\pi
−0.221769 + 0.975099i 0.571183π0.571183\pi
798798 −20.4667 −0.724513
799799 74.0492 2.61967
800800 −1.00000 −0.0353553
801801 −36.2781 −1.28182
802802 −6.40337 −0.226111
803803 20.0000 0.705785
804804 −4.57649 −0.161400
805805 −10.2333 −0.360678
806806 0 0
807807 −12.4033 −0.436615
808808 −18.9443 −0.666457
809809 −36.9458 −1.29894 −0.649472 0.760385i 0.725010π-0.725010\pi
−0.649472 + 0.760385i 0.725010π0.725010\pi
810810 2.70820 0.0951566
811811 56.5410 1.98542 0.992712 0.120512i 0.0384536π-0.0384536\pi
0.992712 + 0.120512i 0.0384536π0.0384536\pi
812812 −8.48528 −0.297775
813813 15.7771 0.553327
814814 −11.7082 −0.410372
815815 −14.1803 −0.496716
816816 5.52786 0.193514
817817 −1.49302 −0.0522343
818818 −37.1034 −1.29729
819819 −16.5579 −0.578580
820820 −3.23607 −0.113008
821821 1.79677 0.0627078 0.0313539 0.999508i 0.490018π-0.490018\pi
0.0313539 + 0.999508i 0.490018π0.490018\pi
822822 12.3607 0.431128
823823 1.25659 0.0438020 0.0219010 0.999760i 0.493028π-0.493028\pi
0.0219010 + 0.999760i 0.493028π0.493028\pi
824824 4.00000 0.139347
825825 −4.47214 −0.155700
826826 −31.4164 −1.09312
827827 −0.874032 −0.0303931 −0.0151965 0.999885i 0.504837π-0.504837\pi
−0.0151965 + 0.999885i 0.504837π0.504837\pi
828828 −7.07107 −0.245737
829829 −37.6436 −1.30742 −0.653708 0.756747i 0.726787π-0.726787\pi
−0.653708 + 0.756747i 0.726787π0.726787\pi
830830 −12.8554 −0.446219
831831 −2.36068 −0.0818911
832832 2.28825 0.0793306
833833 −21.9597 −0.760859
834834 −10.5836 −0.366480
835835 −22.9613 −0.794607
836836 −37.0246 −1.28052
837837 0 0
838838 19.2361 0.664499
839839 30.9443 1.06831 0.534157 0.845385i 0.320629π-0.320629\pi
0.534157 + 0.845385i 0.320629π0.320629\pi
840840 −2.82843 −0.0975900
841841 −22.1246 −0.762918
842842 6.65248 0.229259
843843 22.7248 0.782685
844844 10.4721 0.360466
845845 7.76393 0.267087
846846 −26.1803 −0.900099
847847 49.1246 1.68794
848848 −1.62054 −0.0556497
849849 1.08036 0.0370780
850850 6.32456 0.216930
851851 7.23607 0.248049
852852 −7.81758 −0.267826
853853 14.9443 0.511682 0.255841 0.966719i 0.417648π-0.417648\pi
0.255841 + 0.966719i 0.417648π0.417648\pi
854854 28.9520 0.990716
855855 −16.1803 −0.553356
856856 −16.9443 −0.579143
857857 −7.52786 −0.257147 −0.128573 0.991700i 0.541040π-0.541040\pi
−0.128573 + 0.991700i 0.541040π0.541040\pi
858858 10.2333 0.349361
859859 21.0069 0.716745 0.358373 0.933579i 0.383332π-0.383332\pi
0.358373 + 0.933579i 0.383332π0.383332\pi
860860 −0.206331 −0.00703583
861861 −9.15298 −0.311933
862862 −18.0000 −0.613082
863863 −0.491473 −0.0167299 −0.00836497 0.999965i 0.502663π-0.502663\pi
−0.00836497 + 0.999965i 0.502663π0.502663\pi
864864 −4.57649 −0.155695
865865 −9.41641 −0.320167
866866 −25.2982 −0.859669
867867 −20.1027 −0.682725
868868 0 0
869869 20.0000 0.678454
870870 2.29180 0.0776992
871871 11.9814 0.405975
872872 17.7082 0.599675
873873 25.5279 0.863987
874874 22.8825 0.774011
875875 −3.23607 −0.109399
876876 −3.41641 −0.115430
877877 5.23607 0.176809 0.0884047 0.996085i 0.471823π-0.471823\pi
0.0884047 + 0.996085i 0.471823π0.471823\pi
878878 −8.47214 −0.285921
879879 7.56254 0.255078
880880 −5.11667 −0.172483
881881 −36.9458 −1.24473 −0.622367 0.782725i 0.713829π-0.713829\pi
−0.622367 + 0.782725i 0.713829π0.713829\pi
882882 7.76393 0.261425
883883 54.0439 1.81872 0.909360 0.416009i 0.136572π-0.136572\pi
0.909360 + 0.416009i 0.136572π0.136572\pi
884884 −14.4721 −0.486751
885885 8.48528 0.285230
886886 −24.0000 −0.806296
887887 37.2361 1.25026 0.625132 0.780519i 0.285045π-0.285045\pi
0.625132 + 0.780519i 0.285045π0.285045\pi
888888 2.00000 0.0671156
889889 10.2333 0.343215
890890 16.2241 0.543831
891891 13.8570 0.464227
892892 −3.82998 −0.128237
893893 84.7214 2.83509
894894 9.82068 0.328453
895895 11.4412 0.382438
896896 −3.23607 −0.108109
897897 −6.32456 −0.211171
898898 1.15917 0.0386822
899899 0 0
900900 −2.23607 −0.0745356
901901 10.2492 0.341451
902902 −16.5579 −0.551318
903903 −0.583592 −0.0194207
904904 −9.52786 −0.316892
905905 −16.7642 −0.557262
906906 −11.4164 −0.379285
907907 34.4721 1.14463 0.572314 0.820034i 0.306046π-0.306046\pi
0.572314 + 0.820034i 0.306046π0.306046\pi
908908 −21.5967 −0.716713
909909 −42.3607 −1.40502
910910 7.40492 0.245471
911911 −21.9597 −0.727558 −0.363779 0.931485i 0.618514π-0.618514\pi
−0.363779 + 0.931485i 0.618514π0.618514\pi
912912 6.32456 0.209427
913913 −65.7771 −2.17690
914914 18.9737 0.627593
915915 −7.81966 −0.258510
916916 −7.86629 −0.259909
917917 −5.52786 −0.182546
918918 28.9443 0.955303
919919 11.6393 0.383946 0.191973 0.981400i 0.438511π-0.438511\pi
0.191973 + 0.981400i 0.438511π0.438511\pi
920920 3.16228 0.104257
921921 −20.9768 −0.691208
922922 −13.2681 −0.436962
923923 20.4667 0.673669
924924 −14.4721 −0.476098
925925 2.28825 0.0752371
926926 −24.5517 −0.806819
927927 8.94427 0.293768
928928 2.62210 0.0860745
929929 14.7310 0.483309 0.241655 0.970362i 0.422310π-0.422310\pi
0.241655 + 0.970362i 0.422310π0.422310\pi
930930 0 0
931931 −25.1246 −0.823426
932932 29.8885 0.979032
933933 6.48218 0.212217
934934 −7.05573 −0.230870
935935 32.3607 1.05831
936936 5.11667 0.167244
937937 −55.3050 −1.80673 −0.903367 0.428868i 0.858912π-0.858912\pi
−0.903367 + 0.428868i 0.858912π0.858912\pi
938938 −16.9443 −0.553250
939939 −22.2492 −0.726076
940940 11.7082 0.381880
941941 −8.27895 −0.269886 −0.134943 0.990853i 0.543085π-0.543085\pi
−0.134943 + 0.990853i 0.543085π0.543085\pi
942942 6.06952 0.197756
943943 10.2333 0.333244
944944 9.70820 0.315975
945945 −14.8098 −0.481764
946946 −1.05573 −0.0343247
947947 19.5927 0.636676 0.318338 0.947977i 0.396875π-0.396875\pi
0.318338 + 0.947977i 0.396875π0.396875\pi
948948 −3.41641 −0.110960
949949 8.94427 0.290343
950950 7.23607 0.234769
951951 −13.7295 −0.445209
952952 20.4667 0.663329
953953 54.2502 1.75734 0.878668 0.477433i 0.158433π-0.158433\pi
0.878668 + 0.477433i 0.158433π0.158433\pi
954954 −3.62365 −0.117320
955955 −17.4164 −0.563582
956956 −13.0618 −0.422448
957957 11.7264 0.379060
958958 −25.8885 −0.836421
959959 45.7649 1.47783
960960 0.874032 0.0282093
961961 0 0
962962 −5.23607 −0.168818
963963 −37.8885 −1.22094
964964 −21.8809 −0.704736
965965 −2.94427 −0.0947795
966966 8.94427 0.287777
967967 −45.4311 −1.46096 −0.730482 0.682932i 0.760705π-0.760705\pi
−0.730482 + 0.682932i 0.760705π0.760705\pi
968968 −15.1803 −0.487915
969969 −40.0000 −1.28499
970970 −11.4164 −0.366559
971971 −6.83282 −0.219275 −0.109638 0.993972i 0.534969π-0.534969\pi
−0.109638 + 0.993972i 0.534969π0.534969\pi
972972 −16.0965 −0.516296
973973 −39.1853 −1.25622
974974 −8.81913 −0.282583
975975 −2.00000 −0.0640513
976976 −8.94665 −0.286375
977977 −17.4164 −0.557200 −0.278600 0.960407i 0.589870π-0.589870\pi
−0.278600 + 0.960407i 0.589870π0.589870\pi
978978 12.3941 0.396319
979979 83.0132 2.65311
980980 −3.47214 −0.110913
981981 39.5967 1.26423
982982 28.2542 0.901627
983983 −41.0122 −1.30809 −0.654043 0.756457i 0.726928π-0.726928\pi
−0.654043 + 0.756457i 0.726928π0.726928\pi
984984 2.82843 0.0901670
985985 11.8539 0.377696
986986 −16.5836 −0.528129
987987 33.1158 1.05409
988988 −16.5579 −0.526777
989989 0.652476 0.0207475
990990 −11.4412 −0.363626
991991 55.7432 1.77074 0.885371 0.464885i 0.153904π-0.153904\pi
0.885371 + 0.464885i 0.153904π0.153904\pi
992992 0 0
993993 −19.5279 −0.619698
994994 −28.9443 −0.918057
995995 13.3168 0.422171
996996 11.2361 0.356028
997997 12.2918 0.389285 0.194643 0.980874i 0.437645π-0.437645\pi
0.194643 + 0.980874i 0.437645π0.437645\pi
998998 −7.53244 −0.238435
999999 10.4721 0.331324
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 9610.2.a.be.1.2 4
31.30 odd 2 inner 9610.2.a.be.1.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9610.2.a.be.1.2 4 1.1 even 1 trivial
9610.2.a.be.1.3 yes 4 31.30 odd 2 inner