Properties

Label 185.2.a.e.1.4
Level 185185
Weight 22
Character 185.1
Self dual yes
Analytic conductor 1.4771.477
Analytic rank 00
Dimension 55
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] = [185,2,Mod(1,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 185=537 185 = 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 185.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 1.477232437391.47723243739
Analytic rank: 00
Dimension: 55
Coefficient field: 5.5.973904.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x52x48x3+6x2+19x+6 x^{5} - 2x^{4} - 8x^{3} + 6x^{2} + 19x + 6 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 0.383115-0.383115 of defining polynomial
Character χ\chi == 185.1

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+2.15510q2+1.38311q3+2.64446q41.00000q5+2.98075q62.62521q7+1.38887q81.08699q92.15510q101.64446q11+3.65759q12+2.44254q135.65759q141.38311q152.29576q160.578749q172.34258q18+5.20156q192.64446q203.63096q213.54397q22+8.22913q23+1.92097q24+1.00000q25+5.26391q265.65278q276.94225q28+0.766229q292.98075q30+4.21452q317.72533q322.27447q331.24726q34+2.62521q352.87451q36+1.00000q37+11.2099q38+3.37831q391.38887q401.64446q417.82509q421.91893q434.34870q44+1.08699q45+17.7346q469.56543q473.17530q480.108279q49+2.15510q500.800477q51+6.45918q52+7.74217q5312.1823q54+1.64446q553.64608q56+7.19435q57+1.65130q5813.0359q593.65759q603.86379q61+9.08272q62+2.85359q6312.0574q642.44254q654.90172q66+11.4566q671.53048q68+11.3818q69+5.65759q702.54690q711.50969q729.79732q73+2.15510q74+1.38311q75+13.7553q76+4.31704q77+7.28059q781.81364q79+2.29576q804.55746q813.54397q82+10.9822q839.60193q84+0.578749q854.13549q86+1.05978q872.28394q888.85915q89+2.34258q906.41217q91+21.7616q92+5.82917q9320.6145q945.20156q9510.6850q9610.5605q970.233352q98+1.78751q99+O(q100)q+2.15510 q^{2} +1.38311 q^{3} +2.64446 q^{4} -1.00000 q^{5} +2.98075 q^{6} -2.62521 q^{7} +1.38887 q^{8} -1.08699 q^{9} -2.15510 q^{10} -1.64446 q^{11} +3.65759 q^{12} +2.44254 q^{13} -5.65759 q^{14} -1.38311 q^{15} -2.29576 q^{16} -0.578749 q^{17} -2.34258 q^{18} +5.20156 q^{19} -2.64446 q^{20} -3.63096 q^{21} -3.54397 q^{22} +8.22913 q^{23} +1.92097 q^{24} +1.00000 q^{25} +5.26391 q^{26} -5.65278 q^{27} -6.94225 q^{28} +0.766229 q^{29} -2.98075 q^{30} +4.21452 q^{31} -7.72533 q^{32} -2.27447 q^{33} -1.24726 q^{34} +2.62521 q^{35} -2.87451 q^{36} +1.00000 q^{37} +11.2099 q^{38} +3.37831 q^{39} -1.38887 q^{40} -1.64446 q^{41} -7.82509 q^{42} -1.91893 q^{43} -4.34870 q^{44} +1.08699 q^{45} +17.7346 q^{46} -9.56543 q^{47} -3.17530 q^{48} -0.108279 q^{49} +2.15510 q^{50} -0.800477 q^{51} +6.45918 q^{52} +7.74217 q^{53} -12.1823 q^{54} +1.64446 q^{55} -3.64608 q^{56} +7.19435 q^{57} +1.65130 q^{58} -13.0359 q^{59} -3.65759 q^{60} -3.86379 q^{61} +9.08272 q^{62} +2.85359 q^{63} -12.0574 q^{64} -2.44254 q^{65} -4.90172 q^{66} +11.4566 q^{67} -1.53048 q^{68} +11.3818 q^{69} +5.65759 q^{70} -2.54690 q^{71} -1.50969 q^{72} -9.79732 q^{73} +2.15510 q^{74} +1.38311 q^{75} +13.7553 q^{76} +4.31704 q^{77} +7.28059 q^{78} -1.81364 q^{79} +2.29576 q^{80} -4.55746 q^{81} -3.54397 q^{82} +10.9822 q^{83} -9.60193 q^{84} +0.578749 q^{85} -4.13549 q^{86} +1.05978 q^{87} -2.28394 q^{88} -8.85915 q^{89} +2.34258 q^{90} -6.41217 q^{91} +21.7616 q^{92} +5.82917 q^{93} -20.6145 q^{94} -5.20156 q^{95} -10.6850 q^{96} -10.5605 q^{97} -0.233352 q^{98} +1.78751 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q+2q2+3q3+10q45q56q6+11q7+6q8+6q92q105q112q12+4q138q143q15+16q16+2q184q1910q20+3q21+10q99+O(q100) 5 q + 2 q^{2} + 3 q^{3} + 10 q^{4} - 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} - 5 q^{11} - 2 q^{12} + 4 q^{13} - 8 q^{14} - 3 q^{15} + 16 q^{16} + 2 q^{18} - 4 q^{19} - 10 q^{20} + 3 q^{21}+ \cdots - 10 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 2.15510 1.52389 0.761943 0.647644i 0.224246π-0.224246\pi
0.761943 + 0.647644i 0.224246π0.224246\pi
33 1.38311 0.798542 0.399271 0.916833i 0.369263π-0.369263\pi
0.399271 + 0.916833i 0.369263π0.369263\pi
44 2.64446 1.32223
55 −1.00000 −0.447214
66 2.98075 1.21689
77 −2.62521 −0.992236 −0.496118 0.868255i 0.665242π-0.665242\pi
−0.496118 + 0.868255i 0.665242π0.665242\pi
88 1.38887 0.491040
99 −1.08699 −0.362331
1010 −2.15510 −0.681503
1111 −1.64446 −0.495823 −0.247911 0.968783i 0.579744π-0.579744\pi
−0.247911 + 0.968783i 0.579744π0.579744\pi
1212 3.65759 1.05585
1313 2.44254 0.677438 0.338719 0.940888i 0.390006π-0.390006\pi
0.338719 + 0.940888i 0.390006π0.390006\pi
1414 −5.65759 −1.51205
1515 −1.38311 −0.357119
1616 −2.29576 −0.573940
1717 −0.578749 −0.140367 −0.0701837 0.997534i 0.522359π-0.522359\pi
−0.0701837 + 0.997534i 0.522359π0.522359\pi
1818 −2.34258 −0.552151
1919 5.20156 1.19332 0.596660 0.802494i 0.296494π-0.296494\pi
0.596660 + 0.802494i 0.296494π0.296494\pi
2020 −2.64446 −0.591319
2121 −3.63096 −0.792341
2222 −3.54397 −0.755577
2323 8.22913 1.71589 0.857946 0.513739i 0.171740π-0.171740\pi
0.857946 + 0.513739i 0.171740π0.171740\pi
2424 1.92097 0.392116
2525 1.00000 0.200000
2626 5.26391 1.03234
2727 −5.65278 −1.08788
2828 −6.94225 −1.31196
2929 0.766229 0.142285 0.0711426 0.997466i 0.477335π-0.477335\pi
0.0711426 + 0.997466i 0.477335π0.477335\pi
3030 −2.98075 −0.544208
3131 4.21452 0.756950 0.378475 0.925611i 0.376449π-0.376449\pi
0.378475 + 0.925611i 0.376449π0.376449\pi
3232 −7.72533 −1.36566
3333 −2.27447 −0.395935
3434 −1.24726 −0.213904
3535 2.62521 0.443741
3636 −2.87451 −0.479085
3737 1.00000 0.164399
3838 11.2099 1.81848
3939 3.37831 0.540962
4040 −1.38887 −0.219600
4141 −1.64446 −0.256821 −0.128411 0.991721i 0.540988π-0.540988\pi
−0.128411 + 0.991721i 0.540988π0.540988\pi
4242 −7.82509 −1.20744
4343 −1.91893 −0.292634 −0.146317 0.989238i 0.546742π-0.546742\pi
−0.146317 + 0.989238i 0.546742π0.546742\pi
4444 −4.34870 −0.655591
4545 1.08699 0.162039
4646 17.7346 2.61482
4747 −9.56543 −1.39526 −0.697630 0.716458i 0.745762π-0.745762\pi
−0.697630 + 0.716458i 0.745762π0.745762\pi
4848 −3.17530 −0.458315
4949 −0.108279 −0.0154684
5050 2.15510 0.304777
5151 −0.800477 −0.112089
5252 6.45918 0.895728
5353 7.74217 1.06347 0.531735 0.846911i 0.321540π-0.321540\pi
0.531735 + 0.846911i 0.321540π0.321540\pi
5454 −12.1823 −1.65780
5555 1.64446 0.221739
5656 −3.64608 −0.487227
5757 7.19435 0.952915
5858 1.65130 0.216827
5959 −13.0359 −1.69713 −0.848565 0.529092i 0.822533π-0.822533\pi
−0.848565 + 0.529092i 0.822533π0.822533\pi
6060 −3.65759 −0.472193
6161 −3.86379 −0.494707 −0.247354 0.968925i 0.579561π-0.579561\pi
−0.247354 + 0.968925i 0.579561π0.579561\pi
6262 9.08272 1.15351
6363 2.85359 0.359518
6464 −12.0574 −1.50717
6565 −2.44254 −0.302959
6666 −4.90172 −0.603360
6767 11.4566 1.39965 0.699824 0.714315i 0.253262π-0.253262\pi
0.699824 + 0.714315i 0.253262π0.253262\pi
6868 −1.53048 −0.185598
6969 11.3818 1.37021
7070 5.65759 0.676211
7171 −2.54690 −0.302261 −0.151131 0.988514i 0.548291π-0.548291\pi
−0.151131 + 0.988514i 0.548291π0.548291\pi
7272 −1.50969 −0.177919
7373 −9.79732 −1.14669 −0.573345 0.819314i 0.694354π-0.694354\pi
−0.573345 + 0.819314i 0.694354π0.694354\pi
7474 2.15510 0.250525
7575 1.38311 0.159708
7676 13.7553 1.57784
7777 4.31704 0.491973
7878 7.28059 0.824365
7979 −1.81364 −0.204050 −0.102025 0.994782i 0.532532π-0.532532\pi
−0.102025 + 0.994782i 0.532532π0.532532\pi
8080 2.29576 0.256674
8181 −4.55746 −0.506385
8282 −3.54397 −0.391366
8383 10.9822 1.20546 0.602728 0.797947i 0.294080π-0.294080\pi
0.602728 + 0.797947i 0.294080π0.294080\pi
8484 −9.60193 −1.04766
8585 0.578749 0.0627742
8686 −4.13549 −0.445941
8787 1.05978 0.113621
8888 −2.28394 −0.243469
8989 −8.85915 −0.939068 −0.469534 0.882914i 0.655578π-0.655578\pi
−0.469534 + 0.882914i 0.655578π0.655578\pi
9090 2.34258 0.246930
9191 −6.41217 −0.672178
9292 21.7616 2.26880
9393 5.82917 0.604456
9494 −20.6145 −2.12622
9595 −5.20156 −0.533669
9696 −10.6850 −1.09054
9797 −10.5605 −1.07225 −0.536126 0.844138i 0.680113π-0.680113\pi
−0.536126 + 0.844138i 0.680113π0.680113\pi
9898 −0.233352 −0.0235721
9999 1.78751 0.179652
100100 2.64446 0.264446
101101 0.908368 0.0903860 0.0451930 0.998978i 0.485610π-0.485610\pi
0.0451930 + 0.998978i 0.485610π0.485610\pi
102102 −1.72511 −0.170811
103103 18.9017 1.86244 0.931221 0.364455i 0.118745π-0.118745\pi
0.931221 + 0.364455i 0.118745π0.118745\pi
104104 3.39237 0.332649
105105 3.63096 0.354346
106106 16.6852 1.62061
107107 9.67742 0.935552 0.467776 0.883847i 0.345055π-0.345055\pi
0.467776 + 0.883847i 0.345055π0.345055\pi
108108 −14.9485 −1.43842
109109 10.9954 1.05316 0.526582 0.850124i 0.323473π-0.323473\pi
0.526582 + 0.850124i 0.323473π0.323473\pi
110110 3.54397 0.337904
111111 1.38311 0.131279
112112 6.02685 0.569483
113113 −2.26855 −0.213407 −0.106704 0.994291i 0.534030π-0.534030\pi
−0.106704 + 0.994291i 0.534030π0.534030\pi
114114 15.5046 1.45213
115115 −8.22913 −0.767371
116116 2.02626 0.188134
117117 −2.65502 −0.245457
118118 −28.0937 −2.58623
119119 1.51934 0.139278
120120 −1.92097 −0.175360
121121 −8.29576 −0.754160
122122 −8.32685 −0.753877
123123 −2.27447 −0.205082
124124 11.1451 1.00086
125125 −1.00000 −0.0894427
126126 6.14976 0.547864
127127 20.5147 1.82038 0.910192 0.414186i 0.135934π-0.135934\pi
0.910192 + 0.414186i 0.135934π0.135934\pi
128128 −10.5341 −0.931095
129129 −2.65410 −0.233681
130130 −5.26391 −0.461675
131131 −12.9339 −1.13004 −0.565021 0.825076i 0.691132π-0.691132\pi
−0.565021 + 0.825076i 0.691132π0.691132\pi
132132 −6.01475 −0.523517
133133 −13.6552 −1.18405
134134 24.6902 2.13290
135135 5.65278 0.486514
136136 −0.803808 −0.0689260
137137 13.2882 1.13529 0.567643 0.823275i 0.307855π-0.307855\pi
0.567643 + 0.823275i 0.307855π0.307855\pi
138138 24.5290 2.08805
139139 12.0833 1.02489 0.512446 0.858719i 0.328739π-0.328739\pi
0.512446 + 0.858719i 0.328739π0.328739\pi
140140 6.94225 0.586727
141141 −13.2301 −1.11417
142142 −5.48883 −0.460612
143143 −4.01665 −0.335889
144144 2.49548 0.207956
145145 −0.766229 −0.0636319
146146 −21.1142 −1.74742
147147 −0.149762 −0.0123522
148148 2.64446 0.217373
149149 −20.2139 −1.65599 −0.827995 0.560736i 0.810518π-0.810518\pi
−0.827995 + 0.560736i 0.810518π0.810518\pi
150150 2.98075 0.243377
151151 15.8330 1.28847 0.644237 0.764826i 0.277175π-0.277175\pi
0.644237 + 0.764826i 0.277175π0.277175\pi
152152 7.22429 0.585968
153153 0.629097 0.0508595
154154 9.30366 0.749711
155155 −4.21452 −0.338519
156156 8.93379 0.715276
157157 17.0862 1.36363 0.681815 0.731525i 0.261191π-0.261191\pi
0.681815 + 0.731525i 0.261191π0.261191\pi
158158 −3.90857 −0.310949
159159 10.7083 0.849225
160160 7.72533 0.610741
161161 −21.6032 −1.70257
162162 −9.82179 −0.771673
163163 6.82137 0.534291 0.267146 0.963656i 0.413920π-0.413920\pi
0.267146 + 0.963656i 0.413920π0.413920\pi
164164 −4.34870 −0.339576
165165 2.27447 0.177068
166166 23.6678 1.83698
167167 −4.90916 −0.379882 −0.189941 0.981796i 0.560830π-0.560830\pi
−0.189941 + 0.981796i 0.560830π0.560830\pi
168168 −5.04294 −0.389071
169169 −7.03402 −0.541078
170170 1.24726 0.0956607
171171 −5.65406 −0.432377
172172 −5.07453 −0.386929
173173 −21.2573 −1.61616 −0.808080 0.589073i 0.799493π-0.799493\pi
−0.808080 + 0.589073i 0.799493π0.799493\pi
174174 2.28394 0.173145
175175 −2.62521 −0.198447
176176 3.77528 0.284572
177177 −18.0301 −1.35523
178178 −19.0924 −1.43103
179179 −7.66910 −0.573215 −0.286608 0.958048i 0.592528π-0.592528\pi
−0.286608 + 0.958048i 0.592528π0.592528\pi
180180 2.87451 0.214253
181181 −10.3972 −0.772817 −0.386409 0.922328i 0.626285π-0.626285\pi
−0.386409 + 0.922328i 0.626285π0.626285\pi
182182 −13.8189 −1.02432
183183 −5.34406 −0.395044
184184 11.4292 0.842572
185185 −1.00000 −0.0735215
186186 12.5624 0.921123
187187 0.951729 0.0695973
188188 −25.2954 −1.84485
189189 14.8397 1.07943
190190 −11.2099 −0.813250
191191 −14.0187 −1.01436 −0.507178 0.861841i 0.669311π-0.669311\pi
−0.507178 + 0.861841i 0.669311π0.669311\pi
192192 −16.6767 −1.20354
193193 −16.5915 −1.19428 −0.597142 0.802136i 0.703697π-0.703697\pi
−0.597142 + 0.802136i 0.703697π0.703697\pi
194194 −22.7589 −1.63399
195195 −3.37831 −0.241926
196196 −0.286339 −0.0204528
197197 −20.3482 −1.44975 −0.724873 0.688882i 0.758102π-0.758102\pi
−0.724873 + 0.688882i 0.758102π0.758102\pi
198198 3.85227 0.273769
199199 −11.5118 −0.816047 −0.408024 0.912971i 0.633782π-0.633782\pi
−0.408024 + 0.912971i 0.633782π0.633782\pi
200200 1.38887 0.0982080
201201 15.8458 1.11768
202202 1.95762 0.137738
203203 −2.01151 −0.141180
204204 −2.11683 −0.148208
205205 1.64446 0.114854
206206 40.7351 2.83815
207207 −8.94501 −0.621721
208208 −5.60747 −0.388808
209209 −8.55374 −0.591675
210210 7.82509 0.539983
211211 −1.51976 −0.104624 −0.0523122 0.998631i 0.516659π-0.516659\pi
−0.0523122 + 0.998631i 0.516659π0.516659\pi
212212 20.4738 1.40615
213213 −3.52266 −0.241368
214214 20.8558 1.42567
215215 1.91893 0.130870
216216 −7.85098 −0.534192
217217 −11.0640 −0.751073
218218 23.6961 1.60490
219219 −13.5508 −0.915679
220220 4.34870 0.293189
221221 −1.41362 −0.0950901
222222 2.98075 0.200055
223223 6.89820 0.461938 0.230969 0.972961i 0.425810π-0.425810\pi
0.230969 + 0.972961i 0.425810π0.425810\pi
224224 20.2806 1.35506
225225 −1.08699 −0.0724662
226226 −4.88895 −0.325208
227227 −26.8277 −1.78062 −0.890308 0.455359i 0.849511π-0.849511\pi
−0.890308 + 0.455359i 0.849511π0.849511\pi
228228 19.0252 1.25997
229229 26.0120 1.71892 0.859462 0.511200i 0.170799π-0.170799\pi
0.859462 + 0.511200i 0.170799π0.170799\pi
230230 −17.7346 −1.16939
231231 5.97097 0.392861
232232 1.06419 0.0698677
233233 11.3141 0.741212 0.370606 0.928790i 0.379150π-0.379150\pi
0.370606 + 0.928790i 0.379150π0.379150\pi
234234 −5.72184 −0.374048
235235 9.56543 0.623980
236236 −34.4729 −2.24399
237237 −2.50847 −0.162943
238238 3.27433 0.212243
239239 21.2819 1.37661 0.688306 0.725420i 0.258355π-0.258355\pi
0.688306 + 0.725420i 0.258355π0.258355\pi
240240 3.17530 0.204965
241241 21.1975 1.36545 0.682726 0.730675i 0.260794π-0.260794\pi
0.682726 + 0.730675i 0.260794π0.260794\pi
242242 −17.8782 −1.14925
243243 10.6548 0.683509
244244 −10.2176 −0.654116
245245 0.108279 0.00691770
246246 −4.90172 −0.312522
247247 12.7050 0.808400
248248 5.85343 0.371693
249249 15.1897 0.962607
250250 −2.15510 −0.136301
251251 −6.06998 −0.383134 −0.191567 0.981480i 0.561357π-0.561357\pi
−0.191567 + 0.981480i 0.561357π0.561357\pi
252252 7.54619 0.475365
253253 −13.5325 −0.850778
254254 44.2112 2.77406
255255 0.800477 0.0501278
256256 1.41258 0.0882866
257257 11.2639 0.702623 0.351312 0.936259i 0.385736π-0.385736\pi
0.351312 + 0.936259i 0.385736π0.385736\pi
258258 −5.71986 −0.356103
259259 −2.62521 −0.163123
260260 −6.45918 −0.400582
261261 −0.832887 −0.0515544
262262 −27.8739 −1.72206
263263 27.5622 1.69956 0.849780 0.527137i 0.176735π-0.176735\pi
0.849780 + 0.527137i 0.176735π0.176735\pi
264264 −3.15895 −0.194420
265265 −7.74217 −0.475598
266266 −29.4283 −1.80436
267267 −12.2532 −0.749885
268268 30.2965 1.85066
269269 −22.9078 −1.39672 −0.698358 0.715749i 0.746085π-0.746085\pi
−0.698358 + 0.715749i 0.746085π0.746085\pi
270270 12.1823 0.741392
271271 5.89472 0.358079 0.179039 0.983842i 0.442701π-0.442701\pi
0.179039 + 0.983842i 0.442701π0.442701\pi
272272 1.32867 0.0805624
273273 −8.86876 −0.536762
274274 28.6374 1.73005
275275 −1.64446 −0.0991645
276276 30.0988 1.81173
277277 20.8630 1.25354 0.626769 0.779205i 0.284377π-0.284377\pi
0.626769 + 0.779205i 0.284377π0.284377\pi
278278 26.0407 1.56182
279279 −4.58116 −0.274267
280280 3.64608 0.217895
281281 −0.481953 −0.0287509 −0.0143754 0.999897i 0.504576π-0.504576\pi
−0.0143754 + 0.999897i 0.504576π0.504576\pi
282282 −28.5122 −1.69787
283283 0.890931 0.0529603 0.0264802 0.999649i 0.491570π-0.491570\pi
0.0264802 + 0.999649i 0.491570π0.491570\pi
284284 −6.73517 −0.399659
285285 −7.19435 −0.426157
286286 −8.65628 −0.511856
287287 4.31704 0.254827
288288 8.39739 0.494821
289289 −16.6650 −0.980297
290290 −1.65130 −0.0969678
291291 −14.6063 −0.856238
292292 −25.9086 −1.51619
293293 −16.5945 −0.969460 −0.484730 0.874664i 0.661082π-0.661082\pi
−0.484730 + 0.874664i 0.661082π0.661082\pi
294294 −0.322753 −0.0188233
295295 13.0359 0.758979
296296 1.38887 0.0807265
297297 9.29576 0.539395
298298 −43.5630 −2.52354
299299 20.1000 1.16241
300300 3.65759 0.211171
301301 5.03760 0.290362
302302 34.1218 1.96349
303303 1.25638 0.0721770
304304 −11.9415 −0.684894
305305 3.86379 0.221240
306306 1.35577 0.0775041
307307 24.7733 1.41389 0.706943 0.707271i 0.250074π-0.250074\pi
0.706943 + 0.707271i 0.250074π0.250074\pi
308308 11.4162 0.650501
309309 26.1432 1.48724
310310 −9.08272 −0.515864
311311 27.1396 1.53895 0.769473 0.638680i 0.220519π-0.220519\pi
0.769473 + 0.638680i 0.220519π0.220519\pi
312312 4.69203 0.265634
313313 −8.71332 −0.492506 −0.246253 0.969206i 0.579199π-0.579199\pi
−0.246253 + 0.969206i 0.579199π0.579199\pi
314314 36.8225 2.07802
315315 −2.85359 −0.160781
316316 −4.79609 −0.269801
317317 7.50140 0.421321 0.210660 0.977559i 0.432439π-0.432439\pi
0.210660 + 0.977559i 0.432439π0.432439\pi
318318 23.0775 1.29412
319319 −1.26003 −0.0705482
320320 12.0574 0.674026
321321 13.3850 0.747077
322322 −46.5570 −2.59452
323323 −3.01040 −0.167503
324324 −12.0520 −0.669557
325325 2.44254 0.135488
326326 14.7007 0.814199
327327 15.2078 0.840996
328328 −2.28394 −0.126109
329329 25.1112 1.38443
330330 4.90172 0.269831
331331 −10.4401 −0.573841 −0.286921 0.957954i 0.592632π-0.592632\pi
−0.286921 + 0.957954i 0.592632π0.592632\pi
332332 29.0420 1.59389
333333 −1.08699 −0.0595669
334334 −10.5797 −0.578897
335335 −11.4566 −0.625942
336336 8.33582 0.454756
337337 −11.4990 −0.626389 −0.313194 0.949689i 0.601399π-0.601399\pi
−0.313194 + 0.949689i 0.601399π0.601399\pi
338338 −15.1590 −0.824542
339339 −3.13766 −0.170414
340340 1.53048 0.0830019
341341 −6.93060 −0.375313
342342 −12.1851 −0.658893
343343 18.6607 1.00758
344344 −2.66515 −0.143695
345345 −11.3818 −0.612777
346346 −45.8115 −2.46284
347347 19.6061 1.05251 0.526257 0.850326i 0.323595π-0.323595\pi
0.526257 + 0.850326i 0.323595π0.323595\pi
348348 2.80255 0.150233
349349 −21.9395 −1.17439 −0.587196 0.809445i 0.699768π-0.699768\pi
−0.587196 + 0.809445i 0.699768π0.699768\pi
350350 −5.65759 −0.302411
351351 −13.8071 −0.736970
352352 12.7040 0.677125
353353 2.11029 0.112319 0.0561597 0.998422i 0.482114π-0.482114\pi
0.0561597 + 0.998422i 0.482114π0.482114\pi
354354 −38.8568 −2.06521
355355 2.54690 0.135175
356356 −23.4276 −1.24166
357357 2.10142 0.111219
358358 −16.5277 −0.873515
359359 −6.97594 −0.368176 −0.184088 0.982910i 0.558933π-0.558933\pi
−0.184088 + 0.982910i 0.558933π0.558933\pi
360360 1.50969 0.0795678
361361 8.05622 0.424012
362362 −22.4070 −1.17769
363363 −11.4740 −0.602228
364364 −16.9567 −0.888773
365365 9.79732 0.512815
366366 −11.5170 −0.602002
367367 9.57842 0.499989 0.249995 0.968247i 0.419571π-0.419571\pi
0.249995 + 0.968247i 0.419571π0.419571\pi
368368 −18.8921 −0.984819
369369 1.78751 0.0930543
370370 −2.15510 −0.112038
371371 −20.3248 −1.05521
372372 15.4150 0.799230
373373 5.34611 0.276811 0.138405 0.990376i 0.455802π-0.455802\pi
0.138405 + 0.990376i 0.455802π0.455802\pi
374374 2.05107 0.106058
375375 −1.38311 −0.0714237
376376 −13.2851 −0.685129
377377 1.87154 0.0963894
378378 31.9811 1.64493
379379 −30.8519 −1.58476 −0.792378 0.610031i 0.791157π-0.791157\pi
−0.792378 + 0.610031i 0.791157π0.791157\pi
380380 −13.7553 −0.705632
381381 28.3742 1.45365
382382 −30.2117 −1.54576
383383 −9.29595 −0.475001 −0.237500 0.971387i 0.576328π-0.576328\pi
−0.237500 + 0.971387i 0.576328π0.576328\pi
384384 −14.5699 −0.743518
385385 −4.31704 −0.220017
386386 −35.7564 −1.81995
387387 2.08587 0.106031
388388 −27.9267 −1.41776
389389 19.0668 0.966726 0.483363 0.875420i 0.339415π-0.339415\pi
0.483363 + 0.875420i 0.339415π0.339415\pi
390390 −7.28059 −0.368667
391391 −4.76261 −0.240855
392392 −0.150386 −0.00759562
393393 −17.8891 −0.902386
394394 −43.8523 −2.20925
395395 1.81364 0.0912540
396396 4.72701 0.237541
397397 −8.23564 −0.413335 −0.206667 0.978411i 0.566262π-0.566262\pi
−0.206667 + 0.978411i 0.566262π0.566262\pi
398398 −24.8090 −1.24356
399399 −18.8867 −0.945517
400400 −2.29576 −0.114788
401401 11.2408 0.561339 0.280669 0.959804i 0.409444π-0.409444\pi
0.280669 + 0.959804i 0.409444π0.409444\pi
402402 34.1493 1.70321
403403 10.2941 0.512787
404404 2.40214 0.119511
405405 4.55746 0.226462
406406 −4.33501 −0.215143
407407 −1.64446 −0.0815127
408408 −1.11176 −0.0550403
409409 22.0826 1.09191 0.545957 0.837813i 0.316166π-0.316166\pi
0.545957 + 0.837813i 0.316166π0.316166\pi
410410 3.54397 0.175024
411411 18.3791 0.906574
412412 49.9848 2.46257
413413 34.2219 1.68395
414414 −19.2774 −0.947433
415415 −10.9822 −0.539097
416416 −18.8694 −0.925149
417417 16.7126 0.818419
418418 −18.4342 −0.901645
419419 −15.6870 −0.766361 −0.383181 0.923673i 0.625171π-0.625171\pi
−0.383181 + 0.923673i 0.625171π0.625171\pi
420420 9.60193 0.468526
421421 2.52196 0.122913 0.0614564 0.998110i 0.480425π-0.480425\pi
0.0614564 + 0.998110i 0.480425π0.480425\pi
422422 −3.27523 −0.159436
423423 10.3976 0.505546
424424 10.7529 0.522206
425425 −0.578749 −0.0280735
426426 −7.59168 −0.367818
427427 10.1432 0.490866
428428 25.5915 1.23701
429429 −5.55548 −0.268221
430430 4.13549 0.199431
431431 24.9936 1.20390 0.601951 0.798533i 0.294390π-0.294390\pi
0.601951 + 0.798533i 0.294390π0.294390\pi
432432 12.9774 0.624377
433433 −18.0649 −0.868146 −0.434073 0.900878i 0.642924π-0.642924\pi
−0.434073 + 0.900878i 0.642924π0.642924\pi
434434 −23.8440 −1.14455
435435 −1.05978 −0.0508127
436436 29.0768 1.39252
437437 42.8043 2.04761
438438 −29.2034 −1.39539
439439 −11.2220 −0.535595 −0.267798 0.963475i 0.586296π-0.586296\pi
−0.267798 + 0.963475i 0.586296π0.586296\pi
440440 2.28394 0.108883
441441 0.117699 0.00560470
442442 −3.04649 −0.144907
443443 −38.4723 −1.82788 −0.913938 0.405854i 0.866974π-0.866974\pi
−0.913938 + 0.405854i 0.866974π0.866974\pi
444444 3.65759 0.173581
445445 8.85915 0.419964
446446 14.8663 0.703941
447447 −27.9582 −1.32238
448448 31.6531 1.49547
449449 39.8327 1.87982 0.939910 0.341423i 0.110909π-0.110909\pi
0.939910 + 0.341423i 0.110909π0.110909\pi
450450 −2.34258 −0.110430
451451 2.70424 0.127338
452452 −5.99908 −0.282173
453453 21.8989 1.02890
454454 −57.8163 −2.71346
455455 6.41217 0.300607
456456 9.99203 0.467920
457457 −11.8205 −0.552939 −0.276470 0.961023i 0.589165π-0.589165\pi
−0.276470 + 0.961023i 0.589165π0.589165\pi
458458 56.0586 2.61944
459459 3.27154 0.152703
460460 −21.7616 −1.01464
461461 12.7422 0.593464 0.296732 0.954961i 0.404103π-0.404103\pi
0.296732 + 0.954961i 0.404103π0.404103\pi
462462 12.8680 0.598675
463463 −0.694775 −0.0322889 −0.0161445 0.999870i 0.505139π-0.505139\pi
−0.0161445 + 0.999870i 0.505139π0.505139\pi
464464 −1.75908 −0.0816632
465465 −5.82917 −0.270321
466466 24.3831 1.12952
467467 2.28132 0.105567 0.0527834 0.998606i 0.483191π-0.483191\pi
0.0527834 + 0.998606i 0.483191π0.483191\pi
468468 −7.02109 −0.324550
469469 −30.0760 −1.38878
470470 20.6145 0.950874
471471 23.6322 1.08892
472472 −18.1052 −0.833358
473473 3.15560 0.145095
474474 −5.40600 −0.248306
475475 5.20156 0.238664
476476 4.01783 0.184157
477477 −8.41569 −0.385328
478478 45.8646 2.09780
479479 −25.7331 −1.17578 −0.587888 0.808942i 0.700041π-0.700041\pi
−0.587888 + 0.808942i 0.700041π0.700041\pi
480480 10.6850 0.487702
481481 2.44254 0.111370
482482 45.6828 2.08079
483483 −29.8797 −1.35957
484484 −21.9378 −0.997172
485485 10.5605 0.479526
486486 22.9623 1.04159
487487 −18.7007 −0.847412 −0.423706 0.905800i 0.639271π-0.639271\pi
−0.423706 + 0.905800i 0.639271π0.639271\pi
488488 −5.36630 −0.242921
489489 9.43474 0.426654
490490 0.233352 0.0105418
491491 18.5675 0.837939 0.418970 0.908000i 0.362391π-0.362391\pi
0.418970 + 0.908000i 0.362391π0.362391\pi
492492 −6.01475 −0.271166
493493 −0.443455 −0.0199722
494494 27.3805 1.23191
495495 −1.78751 −0.0803428
496496 −9.67553 −0.434444
497497 6.68615 0.299915
498498 32.7353 1.46690
499499 −9.35537 −0.418804 −0.209402 0.977830i 0.567152π-0.567152\pi
−0.209402 + 0.977830i 0.567152π0.567152\pi
500500 −2.64446 −0.118264
501501 −6.78993 −0.303352
502502 −13.0814 −0.583853
503503 −25.6072 −1.14177 −0.570885 0.821030i 0.693400π-0.693400\pi
−0.570885 + 0.821030i 0.693400π0.693400\pi
504504 3.96326 0.176538
505505 −0.908368 −0.0404218
506506 −29.1638 −1.29649
507507 −9.72885 −0.432074
508508 54.2502 2.40696
509509 −32.5502 −1.44276 −0.721382 0.692537i 0.756493π-0.756493\pi
−0.721382 + 0.692537i 0.756493π0.756493\pi
510510 1.72511 0.0763891
511511 25.7200 1.13779
512512 24.1125 1.06563
513513 −29.4033 −1.29819
514514 24.2749 1.07072
515515 −18.9017 −0.832909
516516 −7.01866 −0.308979
517517 15.7299 0.691802
518518 −5.65759 −0.248580
519519 −29.4012 −1.29057
520520 −3.39237 −0.148765
521521 3.09643 0.135657 0.0678285 0.997697i 0.478393π-0.478393\pi
0.0678285 + 0.997697i 0.478393π0.478393\pi
522522 −1.79495 −0.0785630
523523 24.9299 1.09011 0.545054 0.838401i 0.316509π-0.316509\pi
0.545054 + 0.838401i 0.316509π0.316509\pi
524524 −34.2032 −1.49418
525525 −3.63096 −0.158468
526526 59.3994 2.58994
527527 −2.43915 −0.106251
528528 5.22164 0.227243
529529 44.7186 1.94429
530530 −16.6852 −0.724757
531531 14.1699 0.614923
532532 −36.1105 −1.56559
533533 −4.01665 −0.173980
534534 −26.4069 −1.14274
535535 −9.67742 −0.418392
536536 15.9118 0.687283
537537 −10.6072 −0.457736
538538 −49.3687 −2.12843
539539 0.178060 0.00766960
540540 14.9485 0.643283
541541 −37.4914 −1.61188 −0.805940 0.591997i 0.798340π-0.798340\pi
−0.805940 + 0.591997i 0.798340π0.798340\pi
542542 12.7037 0.545671
543543 −14.3805 −0.617127
544544 4.47103 0.191694
545545 −10.9954 −0.470990
546546 −19.1131 −0.817964
547547 −8.33942 −0.356568 −0.178284 0.983979i 0.557055π-0.557055\pi
−0.178284 + 0.983979i 0.557055π0.557055\pi
548548 35.1401 1.50111
549549 4.19991 0.179248
550550 −3.54397 −0.151115
551551 3.98559 0.169792
552552 15.8079 0.672829
553553 4.76118 0.202466
554554 44.9619 1.91025
555555 −1.38311 −0.0587100
556556 31.9538 1.35514
557557 −28.8556 −1.22265 −0.611327 0.791378i 0.709364π-0.709364\pi
−0.611327 + 0.791378i 0.709364π0.709364\pi
558558 −9.87286 −0.417951
559559 −4.68706 −0.198241
560560 −6.02685 −0.254681
561561 1.31635 0.0555764
562562 −1.03866 −0.0438131
563563 16.2728 0.685815 0.342908 0.939369i 0.388588π-0.388588\pi
0.342908 + 0.939369i 0.388588π0.388588\pi
564564 −34.9864 −1.47319
565565 2.26855 0.0954386
566566 1.92005 0.0807055
567567 11.9643 0.502453
568568 −3.53732 −0.148422
569569 35.5680 1.49109 0.745544 0.666457i 0.232190π-0.232190\pi
0.745544 + 0.666457i 0.232190π0.232190\pi
570570 −15.5046 −0.649414
571571 11.0308 0.461623 0.230812 0.972998i 0.425862π-0.425862\pi
0.230812 + 0.972998i 0.425862π0.425862\pi
572572 −10.6219 −0.444122
573573 −19.3894 −0.810006
574574 9.30366 0.388327
575575 8.22913 0.343179
576576 13.1063 0.546094
577577 −33.6759 −1.40195 −0.700973 0.713188i 0.747251π-0.747251\pi
−0.700973 + 0.713188i 0.747251π0.747251\pi
578578 −35.9149 −1.49386
579579 −22.9480 −0.953685
580580 −2.02626 −0.0841359
581581 −28.8306 −1.19610
582582 −31.4781 −1.30481
583583 −12.7317 −0.527292
584584 −13.6072 −0.563070
585585 2.65502 0.109772
586586 −35.7628 −1.47735
587587 4.39536 0.181416 0.0907080 0.995878i 0.471087π-0.471087\pi
0.0907080 + 0.995878i 0.471087π0.471087\pi
588588 −0.396040 −0.0163324
589589 21.9221 0.903284
590590 28.0937 1.15660
591591 −28.1438 −1.15768
592592 −2.29576 −0.0943551
593593 −0.696484 −0.0286012 −0.0143006 0.999898i 0.504552π-0.504552\pi
−0.0143006 + 0.999898i 0.504552π0.504552\pi
594594 20.0333 0.821976
595595 −1.51934 −0.0622868
596596 −53.4549 −2.18960
597597 −15.9221 −0.651648
598598 43.3174 1.77138
599599 31.3890 1.28252 0.641260 0.767324i 0.278412π-0.278412\pi
0.641260 + 0.767324i 0.278412π0.278412\pi
600600 1.92097 0.0784232
601601 41.4460 1.69062 0.845309 0.534278i 0.179417π-0.179417\pi
0.845309 + 0.534278i 0.179417π0.179417\pi
602602 10.8565 0.442479
603603 −12.4533 −0.507136
604604 41.8698 1.70366
605605 8.29576 0.337271
606606 2.70762 0.109989
607607 11.3837 0.462051 0.231026 0.972948i 0.425792π-0.425792\pi
0.231026 + 0.972948i 0.425792π0.425792\pi
608608 −40.1838 −1.62967
609609 −2.78215 −0.112739
610610 8.32685 0.337144
611611 −23.3639 −0.945202
612612 1.66362 0.0672479
613613 −14.4059 −0.581848 −0.290924 0.956746i 0.593963π-0.593963\pi
−0.290924 + 0.956746i 0.593963π0.593963\pi
614614 53.3889 2.15460
615615 2.27447 0.0917156
616616 5.99582 0.241578
617617 −22.8874 −0.921413 −0.460707 0.887552i 0.652404π-0.652404\pi
−0.460707 + 0.887552i 0.652404π0.652404\pi
618618 56.3413 2.26638
619619 −40.5987 −1.63180 −0.815901 0.578192i 0.803758π-0.803758\pi
−0.815901 + 0.578192i 0.803758π0.803758\pi
620620 −11.1451 −0.447599
621621 −46.5175 −1.86668
622622 58.4886 2.34518
623623 23.2571 0.931777
624624 −7.75578 −0.310480
625625 1.00000 0.0400000
626626 −18.7781 −0.750523
627627 −11.8308 −0.472477
628628 45.1838 1.80303
629629 −0.578749 −0.0230763
630630 −6.14976 −0.245012
631631 −31.2970 −1.24592 −0.622958 0.782256i 0.714069π-0.714069\pi
−0.622958 + 0.782256i 0.714069π0.714069\pi
632632 −2.51891 −0.100197
633633 −2.10200 −0.0835469
634634 16.1663 0.642045
635635 −20.5147 −0.814101
636636 28.3177 1.12287
637637 −0.264476 −0.0104789
638638 −2.71550 −0.107507
639639 2.76846 0.109519
640640 10.5341 0.416398
641641 29.7434 1.17479 0.587397 0.809299i 0.300153π-0.300153\pi
0.587397 + 0.809299i 0.300153π0.300153\pi
642642 28.8460 1.13846
643643 −29.2023 −1.15163 −0.575814 0.817581i 0.695315π-0.695315\pi
−0.575814 + 0.817581i 0.695315π0.695315\pi
644644 −57.1287 −2.25119
645645 2.65410 0.104505
646646 −6.48771 −0.255256
647647 0.300586 0.0118173 0.00590863 0.999983i 0.498119π-0.498119\pi
0.00590863 + 0.999983i 0.498119π0.498119\pi
648648 −6.32973 −0.248655
649649 21.4370 0.841475
650650 5.26391 0.206468
651651 −15.3028 −0.599763
652652 18.0388 0.706455
653653 29.4692 1.15322 0.576610 0.817020i 0.304375π-0.304375\pi
0.576610 + 0.817020i 0.304375π0.304375\pi
654654 32.7744 1.28158
655655 12.9339 0.505370
656656 3.77528 0.147400
657657 10.6496 0.415481
658658 54.1172 2.10971
659659 −1.80662 −0.0703757 −0.0351879 0.999381i 0.511203π-0.511203\pi
−0.0351879 + 0.999381i 0.511203π0.511203\pi
660660 6.01475 0.234124
661661 50.0378 1.94624 0.973122 0.230291i 0.0739679π-0.0739679\pi
0.973122 + 0.230291i 0.0739679π0.0739679\pi
662662 −22.4995 −0.874469
663663 −1.95519 −0.0759334
664664 15.2529 0.591927
665665 13.6552 0.529525
666666 −2.34258 −0.0907731
667667 6.30540 0.244146
668668 −12.9821 −0.502291
669669 9.54101 0.368877
670670 −24.6902 −0.953864
671671 6.35383 0.245287
672672 28.0504 1.08207
673673 16.4032 0.632299 0.316149 0.948709i 0.397610π-0.397610\pi
0.316149 + 0.948709i 0.397610π0.397610\pi
674674 −24.7814 −0.954545
675675 −5.65278 −0.217576
676676 −18.6012 −0.715429
677677 −36.3118 −1.39558 −0.697789 0.716304i 0.745833π-0.745833\pi
−0.697789 + 0.716304i 0.745833π0.745833\pi
678678 −6.76198 −0.259692
679679 27.7234 1.06393
680680 0.803808 0.0308246
681681 −37.1058 −1.42190
682682 −14.9361 −0.571934
683683 25.4014 0.971959 0.485980 0.873970i 0.338463π-0.338463\pi
0.485980 + 0.873970i 0.338463π0.338463\pi
684684 −14.9519 −0.571701
685685 −13.2882 −0.507716
686686 40.2157 1.53544
687687 35.9776 1.37263
688688 4.40540 0.167954
689689 18.9105 0.720434
690690 −24.5290 −0.933803
691691 −4.47905 −0.170391 −0.0851956 0.996364i 0.527152π-0.527152\pi
−0.0851956 + 0.996364i 0.527152π0.527152\pi
692692 −56.2139 −2.13693
693693 −4.69260 −0.178257
694694 42.2532 1.60391
695695 −12.0833 −0.458346
696696 1.47190 0.0557923
697697 0.951729 0.0360493
698698 −47.2817 −1.78964
699699 15.6487 0.591889
700700 −6.94225 −0.262393
701701 −20.9639 −0.791795 −0.395898 0.918295i 0.629567π-0.629567\pi
−0.395898 + 0.918295i 0.629567π0.629567\pi
702702 −29.7557 −1.12306
703703 5.20156 0.196181
704704 19.8278 0.747288
705705 13.2301 0.498274
706706 4.54789 0.171162
707707 −2.38466 −0.0896842
708708 −47.6799 −1.79192
709709 −39.5543 −1.48549 −0.742746 0.669573i 0.766477π-0.766477\pi
−0.742746 + 0.669573i 0.766477π0.766477\pi
710710 5.48883 0.205992
711711 1.97141 0.0739337
712712 −12.3042 −0.461120
713713 34.6819 1.29885
714714 4.52877 0.169485
715715 4.01665 0.150214
716716 −20.2806 −0.757922
717717 29.4353 1.09928
718718 −15.0339 −0.561059
719719 −44.0927 −1.64438 −0.822190 0.569213i 0.807248π-0.807248\pi
−0.822190 + 0.569213i 0.807248π0.807248\pi
720720 −2.49548 −0.0930009
721721 −49.6210 −1.84798
722722 17.3620 0.646146
723723 29.3186 1.09037
724724 −27.4949 −1.02184
725725 0.766229 0.0284570
726726 −24.7276 −0.917727
727727 −34.7329 −1.28817 −0.644086 0.764953i 0.722762π-0.722762\pi
−0.644086 + 0.764953i 0.722762π0.722762\pi
728728 −8.90567 −0.330066
729729 28.4093 1.05220
730730 21.1142 0.781472
731731 1.11058 0.0410763
732732 −14.1321 −0.522339
733733 19.7348 0.728921 0.364461 0.931219i 0.381253π-0.381253\pi
0.364461 + 0.931219i 0.381253π0.381253\pi
734734 20.6425 0.761927
735735 0.149762 0.00552407
736736 −63.5728 −2.34332
737737 −18.8399 −0.693977
738738 3.85227 0.141804
739739 26.1822 0.963128 0.481564 0.876411i 0.340069π-0.340069\pi
0.481564 + 0.876411i 0.340069π0.340069\pi
740740 −2.64446 −0.0972122
741741 17.5725 0.645541
742742 −43.8020 −1.60802
743743 38.3253 1.40602 0.703010 0.711180i 0.251839π-0.251839\pi
0.703010 + 0.711180i 0.251839π0.251839\pi
744744 8.09596 0.296812
745745 20.2139 0.740581
746746 11.5214 0.421828
747747 −11.9376 −0.436774
748748 2.51681 0.0920236
749749 −25.4053 −0.928288
750750 −2.98075 −0.108842
751751 24.2638 0.885399 0.442699 0.896670i 0.354021π-0.354021\pi
0.442699 + 0.896670i 0.354021π0.354021\pi
752752 21.9599 0.800796
753753 −8.39549 −0.305948
754754 4.03336 0.146886
755755 −15.8330 −0.576224
756756 39.2430 1.42726
757757 −9.26589 −0.336775 −0.168387 0.985721i 0.553856π-0.553856\pi
−0.168387 + 0.985721i 0.553856π0.553856\pi
758758 −66.4889 −2.41499
759759 −18.7169 −0.679382
760760 −7.22429 −0.262053
761761 15.8829 0.575753 0.287877 0.957667i 0.407051π-0.407051\pi
0.287877 + 0.957667i 0.407051π0.407051\pi
762762 61.1492 2.21520
763763 −28.8651 −1.04499
764764 −37.0718 −1.34121
765765 −0.629097 −0.0227451
766766 −20.0337 −0.723847
767767 −31.8406 −1.14970
768768 1.95377 0.0705005
769769 −16.2832 −0.587188 −0.293594 0.955930i 0.594851π-0.594851\pi
−0.293594 + 0.955930i 0.594851π0.594851\pi
770770 −9.30366 −0.335281
771771 15.5793 0.561074
772772 −43.8756 −1.57912
773773 3.98058 0.143172 0.0715858 0.997434i 0.477194π-0.477194\pi
0.0715858 + 0.997434i 0.477194π0.477194\pi
774774 4.49525 0.161578
775775 4.21452 0.151390
776776 −14.6671 −0.526519
777777 −3.63096 −0.130260
778778 41.0909 1.47318
779779 −8.55374 −0.306470
780780 −8.93379 −0.319881
781781 4.18827 0.149868
782782 −10.2639 −0.367036
783783 −4.33133 −0.154789
784784 0.248583 0.00887795
785785 −17.0862 −0.609834
786786 −38.5528 −1.37513
787787 −5.01650 −0.178819 −0.0894094 0.995995i 0.528498π-0.528498\pi
−0.0894094 + 0.995995i 0.528498π0.528498\pi
788788 −53.8099 −1.91690
789789 38.1217 1.35717
790790 3.90857 0.139061
791791 5.95541 0.211750
792792 2.48263 0.0882163
793793 −9.43744 −0.335133
794794 −17.7486 −0.629875
795795 −10.7083 −0.379785
796796 −30.4424 −1.07900
797797 2.99628 0.106134 0.0530668 0.998591i 0.483100π-0.483100\pi
0.0530668 + 0.998591i 0.483100π0.483100\pi
798798 −40.7027 −1.44086
799799 5.53599 0.195849
800800 −7.72533 −0.273132
801801 9.62984 0.340254
802802 24.2251 0.855417
803803 16.1113 0.568555
804804 41.9036 1.47783
805805 21.6032 0.761412
806806 22.1849 0.781428
807807 −31.6842 −1.11534
808808 1.26161 0.0443831
809809 17.7054 0.622488 0.311244 0.950330i 0.399254π-0.399254\pi
0.311244 + 0.950330i 0.399254π0.399254\pi
810810 9.82179 0.345103
811811 −25.3743 −0.891011 −0.445505 0.895279i 0.646976π-0.646976\pi
−0.445505 + 0.895279i 0.646976π0.646976\pi
812812 −5.31936 −0.186673
813813 8.15307 0.285941
814814 −3.54397 −0.124216
815815 −6.82137 −0.238942
816816 1.83770 0.0643324
817817 −9.98144 −0.349206
818818 47.5902 1.66395
819819 6.96998 0.243551
820820 4.34870 0.151863
821821 15.2958 0.533826 0.266913 0.963721i 0.413996π-0.413996\pi
0.266913 + 0.963721i 0.413996π0.413996\pi
822822 39.6088 1.38152
823823 44.7798 1.56092 0.780462 0.625203i 0.214984π-0.214984\pi
0.780462 + 0.625203i 0.214984π0.214984\pi
824824 26.2520 0.914533
825825 −2.27447 −0.0791870
826826 73.7517 2.56615
827827 −13.6099 −0.473263 −0.236631 0.971600i 0.576043π-0.576043\pi
−0.236631 + 0.971600i 0.576043π0.576043\pi
828828 −23.6547 −0.822058
829829 15.3300 0.532434 0.266217 0.963913i 0.414226π-0.414226\pi
0.266217 + 0.963913i 0.414226π0.414226\pi
830830 −23.6678 −0.821522
831831 28.8560 1.00100
832832 −29.4505 −1.02101
833833 0.0626665 0.00217126
834834 36.0173 1.24718
835835 4.90916 0.169888
836836 −22.6200 −0.782330
837837 −23.8238 −0.823470
838838 −33.8071 −1.16785
839839 23.5040 0.811447 0.405723 0.913996i 0.367020π-0.367020\pi
0.405723 + 0.913996i 0.367020π0.367020\pi
840840 5.04294 0.173998
841841 −28.4129 −0.979755
842842 5.43508 0.187305
843843 −0.666596 −0.0229588
844844 −4.01893 −0.138337
845845 7.03402 0.241978
846846 22.4078 0.770395
847847 21.7781 0.748304
848848 −17.7742 −0.610367
849849 1.23226 0.0422910
850850 −1.24726 −0.0427808
851851 8.22913 0.282091
852852 −9.31551 −0.319144
853853 −16.6766 −0.570996 −0.285498 0.958379i 0.592159π-0.592159\pi
−0.285498 + 0.958379i 0.592159π0.592159\pi
854854 21.8597 0.748024
855855 5.65406 0.193365
856856 13.4407 0.459393
857857 −48.2788 −1.64917 −0.824585 0.565737i 0.808592π-0.808592\pi
−0.824585 + 0.565737i 0.808592π0.808592\pi
858858 −11.9726 −0.408739
859859 −30.5872 −1.04362 −0.521812 0.853061i 0.674744π-0.674744\pi
−0.521812 + 0.853061i 0.674744π0.674744\pi
860860 5.07453 0.173040
861861 5.97097 0.203490
862862 53.8638 1.83461
863863 −30.2802 −1.03075 −0.515374 0.856965i 0.672347π-0.672347\pi
−0.515374 + 0.856965i 0.672347π0.672347\pi
864864 43.6696 1.48567
865865 21.2573 0.722769
866866 −38.9318 −1.32296
867867 −23.0497 −0.782808
868868 −29.2583 −0.993091
869869 2.98245 0.101173
870870 −2.28394 −0.0774328
871871 27.9832 0.948174
872872 15.2711 0.517146
873873 11.4792 0.388510
874874 92.2476 3.12032
875875 2.62521 0.0887483
876876 −35.8346 −1.21074
877877 21.4151 0.723137 0.361569 0.932345i 0.382241π-0.382241\pi
0.361569 + 0.932345i 0.382241π0.382241\pi
878878 −24.1845 −0.816186
879879 −22.9521 −0.774154
880880 −3.77528 −0.127265
881881 1.54785 0.0521484 0.0260742 0.999660i 0.491699π-0.491699\pi
0.0260742 + 0.999660i 0.491699π0.491699\pi
882882 0.253652 0.00854092
883883 10.5279 0.354291 0.177146 0.984185i 0.443314π-0.443314\pi
0.177146 + 0.984185i 0.443314π0.443314\pi
884884 −3.73825 −0.125731
885885 18.0301 0.606077
886886 −82.9118 −2.78547
887887 17.9508 0.602730 0.301365 0.953509i 0.402558π-0.402558\pi
0.301365 + 0.953509i 0.402558π0.402558\pi
888888 1.92097 0.0644635
889889 −53.8553 −1.80625
890890 19.0924 0.639977
891891 7.49456 0.251077
892892 18.2420 0.610787
893893 −49.7551 −1.66499
894894 −60.2527 −2.01515
895895 7.66910 0.256350
896896 27.6543 0.923865
897897 27.8005 0.928233
898898 85.8434 2.86463
899899 3.22929 0.107703
900900 −2.87451 −0.0958170
901901 −4.48078 −0.149276
902902 5.82791 0.194048
903903 6.96757 0.231866
904904 −3.15072 −0.104791
905905 10.3972 0.345614
906906 47.1944 1.56793
907907 −20.8340 −0.691782 −0.345891 0.938275i 0.612423π-0.612423\pi
−0.345891 + 0.938275i 0.612423π0.612423\pi
908908 −70.9447 −2.35438
909909 −0.987390 −0.0327497
910910 13.8189 0.458091
911911 29.5904 0.980373 0.490186 0.871618i 0.336929π-0.336929\pi
0.490186 + 0.871618i 0.336929π0.336929\pi
912912 −16.5165 −0.546916
913913 −18.0598 −0.597693
914914 −25.4743 −0.842616
915915 5.34406 0.176669
916916 68.7877 2.27281
917917 33.9543 1.12127
918918 7.05051 0.232701
919919 22.2046 0.732462 0.366231 0.930524i 0.380648π-0.380648\pi
0.366231 + 0.930524i 0.380648π0.380648\pi
920920 −11.4292 −0.376810
921921 34.2643 1.12905
922922 27.4607 0.904371
923923 −6.22090 −0.204763
924924 15.7900 0.519452
925925 1.00000 0.0328798
926926 −1.49731 −0.0492047
927927 −20.5460 −0.674821
928928 −5.91938 −0.194313
929929 −12.6544 −0.415178 −0.207589 0.978216i 0.566562π-0.566562\pi
−0.207589 + 0.978216i 0.566562π0.566562\pi
930930 −12.5624 −0.411939
931931 −0.563220 −0.0184588
932932 29.9197 0.980052
933933 37.5372 1.22891
934934 4.91647 0.160872
935935 −0.951729 −0.0311249
936936 −3.68748 −0.120529
937937 59.1488 1.93231 0.966154 0.257968i 0.0830528π-0.0830528\pi
0.966154 + 0.257968i 0.0830528π0.0830528\pi
938938 −64.8168 −2.11634
939939 −12.0515 −0.393287
940940 25.2954 0.825044
941941 20.7402 0.676110 0.338055 0.941126i 0.390231π-0.390231\pi
0.338055 + 0.941126i 0.390231π0.390231\pi
942942 50.9298 1.65938
943943 −13.5325 −0.440677
944944 29.9273 0.974050
945945 −14.8397 −0.482736
946946 6.80064 0.221108
947947 −48.0626 −1.56182 −0.780912 0.624641i 0.785245π-0.785245\pi
−0.780912 + 0.624641i 0.785245π0.785245\pi
948948 −6.63354 −0.215447
949949 −23.9303 −0.776810
950950 11.2099 0.363697
951951 10.3753 0.336442
952952 2.11016 0.0683908
953953 0.993315 0.0321766 0.0160883 0.999871i 0.494879π-0.494879\pi
0.0160883 + 0.999871i 0.494879π0.494879\pi
954954 −18.1367 −0.587196
955955 14.0187 0.453634
956956 56.2791 1.82020
957957 −1.74277 −0.0563357
958958 −55.4575 −1.79175
959959 −34.8843 −1.12647
960960 16.6767 0.538238
961961 −13.2378 −0.427026
962962 5.26391 0.169715
963963 −10.5193 −0.338980
964964 56.0559 1.80544
965965 16.5915 0.534100
966966 −64.3937 −2.07183
967967 −31.4163 −1.01028 −0.505140 0.863037i 0.668559π-0.668559\pi
−0.505140 + 0.863037i 0.668559π0.668559\pi
968968 −11.5217 −0.370323
969969 −4.16373 −0.133758
970970 22.7589 0.730743
971971 −36.6023 −1.17462 −0.587312 0.809361i 0.699814π-0.699814\pi
−0.587312 + 0.809361i 0.699814π0.699814\pi
972972 28.1763 0.903755
973973 −31.7212 −1.01693
974974 −40.3020 −1.29136
975975 3.37831 0.108192
976976 8.87032 0.283932
977977 4.13108 0.132165 0.0660825 0.997814i 0.478950π-0.478950\pi
0.0660825 + 0.997814i 0.478950π0.478950\pi
978978 20.3328 0.650172
979979 14.5685 0.465611
980980 0.286339 0.00914678
981981 −11.9519 −0.381594
982982 40.0148 1.27692
983983 19.1236 0.609947 0.304974 0.952361i 0.401352π-0.401352\pi
0.304974 + 0.952361i 0.401352π0.401352\pi
984984 −3.15895 −0.100704
985985 20.3482 0.648346
986986 −0.955690 −0.0304354
987987 34.7317 1.10552
988988 33.5978 1.06889
989989 −15.7911 −0.502129
990990 −3.85227 −0.122433
991991 3.96555 0.125970 0.0629850 0.998014i 0.479938π-0.479938\pi
0.0629850 + 0.998014i 0.479938π0.479938\pi
992992 −32.5586 −1.03374
993993 −14.4399 −0.458236
994994 14.4093 0.457036
995995 11.5118 0.364947
996996 40.1685 1.27279
997997 29.1697 0.923813 0.461906 0.886929i 0.347166π-0.347166\pi
0.461906 + 0.886929i 0.347166π0.347166\pi
998998 −20.1618 −0.638210
999999 −5.65278 −0.178846
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 185.2.a.e.1.4 5
3.2 odd 2 1665.2.a.p.1.2 5
4.3 odd 2 2960.2.a.w.1.3 5
5.2 odd 4 925.2.b.f.149.8 10
5.3 odd 4 925.2.b.f.149.3 10
5.4 even 2 925.2.a.f.1.2 5
7.6 odd 2 9065.2.a.k.1.4 5
15.14 odd 2 8325.2.a.ch.1.4 5
37.36 even 2 6845.2.a.f.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
185.2.a.e.1.4 5 1.1 even 1 trivial
925.2.a.f.1.2 5 5.4 even 2
925.2.b.f.149.3 10 5.3 odd 4
925.2.b.f.149.8 10 5.2 odd 4
1665.2.a.p.1.2 5 3.2 odd 2
2960.2.a.w.1.3 5 4.3 odd 2
6845.2.a.f.1.2 5 37.36 even 2
8325.2.a.ch.1.4 5 15.14 odd 2
9065.2.a.k.1.4 5 7.6 odd 2