Properties

Label 845.2.a.n.1.3
Level 845845
Weight 22
Character 845.1
Self dual yes
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 99
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [845,2,Mod(1,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [9,-3,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 99
Coefficient field: Q[x]/(x9)\mathbb{Q}[x]/(x^{9} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x917x79x6+59x5+32x444x323x2+x+1 x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 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 1.3
Root 1.760521.76052 of defining polynomial
Character χ\chi == 845.1

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) == q2.20556q20.0130567q3+2.86449q41.00000q5+0.0287972q64.60897q71.90669q82.99983q9+2.20556q102.93232q110.0374007q12+10.1654q14+0.0130567q151.52367q163.35206q17+6.61630q18+2.46021q192.86449q20+0.0601778q21+6.46741q221.58329q23+0.0248950q24+1.00000q25+0.0783378q2713.2024q28+8.26322q290.0287972q30+9.77959q31+7.17392q32+0.0382863q33+7.39317q34+4.60897q358.59299q364.12917q375.42613q38+1.90669q407.26508q410.132726q420.705329q438.39961q44+2.99983q45+3.49204q468.57322q47+0.0198940q48+14.2426q492.20556q50+0.0437667q5112.4639q530.172779q54+2.93232q55+8.78787q560.0321221q5718.2250q58+5.33445q59+0.0374007q60+1.92092q6121.5695q62+13.8261q6312.7752q640.0844427q66+7.29793q679.60195q68+0.0206725q6910.1654q70+6.68083q71+5.71974q72+12.4541q73+9.10713q740.0130567q75+7.04724q76+13.5150q77+0.984840q79+1.52367q80+8.99847q81+16.0236q82+7.84405q83+0.172379q84+3.35206q85+1.55565q860.107890q87+5.59102q88+0.412834q896.61630q904.53532q920.127689q93+18.9087q942.46021q950.0936675q96+3.38416q9731.4129q98+8.79646q99+O(q100)q-2.20556 q^{2} -0.0130567 q^{3} +2.86449 q^{4} -1.00000 q^{5} +0.0287972 q^{6} -4.60897 q^{7} -1.90669 q^{8} -2.99983 q^{9} +2.20556 q^{10} -2.93232 q^{11} -0.0374007 q^{12} +10.1654 q^{14} +0.0130567 q^{15} -1.52367 q^{16} -3.35206 q^{17} +6.61630 q^{18} +2.46021 q^{19} -2.86449 q^{20} +0.0601778 q^{21} +6.46741 q^{22} -1.58329 q^{23} +0.0248950 q^{24} +1.00000 q^{25} +0.0783378 q^{27} -13.2024 q^{28} +8.26322 q^{29} -0.0287972 q^{30} +9.77959 q^{31} +7.17392 q^{32} +0.0382863 q^{33} +7.39317 q^{34} +4.60897 q^{35} -8.59299 q^{36} -4.12917 q^{37} -5.42613 q^{38} +1.90669 q^{40} -7.26508 q^{41} -0.132726 q^{42} -0.705329 q^{43} -8.39961 q^{44} +2.99983 q^{45} +3.49204 q^{46} -8.57322 q^{47} +0.0198940 q^{48} +14.2426 q^{49} -2.20556 q^{50} +0.0437667 q^{51} -12.4639 q^{53} -0.172779 q^{54} +2.93232 q^{55} +8.78787 q^{56} -0.0321221 q^{57} -18.2250 q^{58} +5.33445 q^{59} +0.0374007 q^{60} +1.92092 q^{61} -21.5695 q^{62} +13.8261 q^{63} -12.7752 q^{64} -0.0844427 q^{66} +7.29793 q^{67} -9.60195 q^{68} +0.0206725 q^{69} -10.1654 q^{70} +6.68083 q^{71} +5.71974 q^{72} +12.4541 q^{73} +9.10713 q^{74} -0.0130567 q^{75} +7.04724 q^{76} +13.5150 q^{77} +0.984840 q^{79} +1.52367 q^{80} +8.99847 q^{81} +16.0236 q^{82} +7.84405 q^{83} +0.172379 q^{84} +3.35206 q^{85} +1.55565 q^{86} -0.107890 q^{87} +5.59102 q^{88} +0.412834 q^{89} -6.61630 q^{90} -4.53532 q^{92} -0.127689 q^{93} +18.9087 q^{94} -2.46021 q^{95} -0.0936675 q^{96} +3.38416 q^{97} -31.4129 q^{98} +8.79646 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 9q3q2+7q3+17q49q5+2q67q712q8+16q9+3q10+9q11+12q122q147q15+37q16q17+10q18+4q1917q20+q21++q99+O(q100) 9 q - 3 q^{2} + 7 q^{3} + 17 q^{4} - 9 q^{5} + 2 q^{6} - 7 q^{7} - 12 q^{8} + 16 q^{9} + 3 q^{10} + 9 q^{11} + 12 q^{12} - 2 q^{14} - 7 q^{15} + 37 q^{16} - q^{17} + 10 q^{18} + 4 q^{19} - 17 q^{20} + q^{21}+ \cdots + 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 −2.20556 −1.55957 −0.779783 0.626050i 0.784671π-0.784671\pi
−0.779783 + 0.626050i 0.784671π0.784671\pi
33 −0.0130567 −0.00753827 −0.00376913 0.999993i 0.501200π-0.501200\pi
−0.00376913 + 0.999993i 0.501200π0.501200\pi
44 2.86449 1.43225
55 −1.00000 −0.447214
66 0.0287972 0.0117564
77 −4.60897 −1.74203 −0.871013 0.491259i 0.836537π-0.836537\pi
−0.871013 + 0.491259i 0.836537π0.836537\pi
88 −1.90669 −0.674116
99 −2.99983 −0.999943
1010 2.20556 0.697459
1111 −2.93232 −0.884128 −0.442064 0.896984i 0.645754π-0.645754\pi
−0.442064 + 0.896984i 0.645754π0.645754\pi
1212 −0.0374007 −0.0107967
1313 0 0
1414 10.1654 2.71681
1515 0.0130567 0.00337122
1616 −1.52367 −0.380917
1717 −3.35206 −0.812994 −0.406497 0.913652i 0.633250π-0.633250\pi
−0.406497 + 0.913652i 0.633250π0.633250\pi
1818 6.61630 1.55948
1919 2.46021 0.564410 0.282205 0.959354i 0.408934π-0.408934\pi
0.282205 + 0.959354i 0.408934π0.408934\pi
2020 −2.86449 −0.640520
2121 0.0601778 0.0131319
2222 6.46741 1.37886
2323 −1.58329 −0.330139 −0.165069 0.986282i 0.552785π-0.552785\pi
−0.165069 + 0.986282i 0.552785π0.552785\pi
2424 0.0248950 0.00508167
2525 1.00000 0.200000
2626 0 0
2727 0.0783378 0.0150761
2828 −13.2024 −2.49501
2929 8.26322 1.53444 0.767221 0.641383i 0.221639π-0.221639\pi
0.767221 + 0.641383i 0.221639π0.221639\pi
3030 −0.0287972 −0.00525763
3131 9.77959 1.75647 0.878233 0.478233i 0.158723π-0.158723\pi
0.878233 + 0.478233i 0.158723π0.158723\pi
3232 7.17392 1.26818
3333 0.0382863 0.00666479
3434 7.39317 1.26792
3535 4.60897 0.779058
3636 −8.59299 −1.43216
3737 −4.12917 −0.678831 −0.339416 0.940637i 0.610229π-0.610229\pi
−0.339416 + 0.940637i 0.610229π0.610229\pi
3838 −5.42613 −0.880235
3939 0 0
4040 1.90669 0.301474
4141 −7.26508 −1.13462 −0.567308 0.823506i 0.692015π-0.692015\pi
−0.567308 + 0.823506i 0.692015π0.692015\pi
4242 −0.132726 −0.0204800
4343 −0.705329 −0.107562 −0.0537809 0.998553i 0.517127π-0.517127\pi
−0.0537809 + 0.998553i 0.517127π0.517127\pi
4444 −8.39961 −1.26629
4545 2.99983 0.447188
4646 3.49204 0.514873
4747 −8.57322 −1.25053 −0.625266 0.780411i 0.715010π-0.715010\pi
−0.625266 + 0.780411i 0.715010π0.715010\pi
4848 0.0198940 0.00287146
4949 14.2426 2.03466
5050 −2.20556 −0.311913
5151 0.0437667 0.00612857
5252 0 0
5353 −12.4639 −1.71204 −0.856022 0.516940i 0.827071π-0.827071\pi
−0.856022 + 0.516940i 0.827071π0.827071\pi
5454 −0.172779 −0.0235122
5555 2.93232 0.395394
5656 8.78787 1.17433
5757 −0.0321221 −0.00425467
5858 −18.2250 −2.39306
5959 5.33445 0.694487 0.347243 0.937775i 0.387118π-0.387118\pi
0.347243 + 0.937775i 0.387118π0.387118\pi
6060 0.0374007 0.00482841
6161 1.92092 0.245949 0.122974 0.992410i 0.460757π-0.460757\pi
0.122974 + 0.992410i 0.460757π0.460757\pi
6262 −21.5695 −2.73932
6363 13.8261 1.74193
6464 −12.7752 −1.59690
6565 0 0
6666 −0.0844427 −0.0103942
6767 7.29793 0.891584 0.445792 0.895137i 0.352922π-0.352922\pi
0.445792 + 0.895137i 0.352922π0.352922\pi
6868 −9.60195 −1.16441
6969 0.0206725 0.00248867
7070 −10.1654 −1.21499
7171 6.68083 0.792868 0.396434 0.918063i 0.370248π-0.370248\pi
0.396434 + 0.918063i 0.370248π0.370248\pi
7272 5.71974 0.674078
7373 12.4541 1.45765 0.728824 0.684702i 0.240067π-0.240067\pi
0.728824 + 0.684702i 0.240067π0.240067\pi
7474 9.10713 1.05868
7575 −0.0130567 −0.00150765
7676 7.04724 0.808374
7777 13.5150 1.54017
7878 0 0
7979 0.984840 0.110803 0.0554016 0.998464i 0.482356π-0.482356\pi
0.0554016 + 0.998464i 0.482356π0.482356\pi
8080 1.52367 0.170351
8181 8.99847 0.999830
8282 16.0236 1.76951
8383 7.84405 0.860997 0.430498 0.902591i 0.358338π-0.358338\pi
0.430498 + 0.902591i 0.358338π0.358338\pi
8484 0.172379 0.0188081
8585 3.35206 0.363582
8686 1.55565 0.167750
8787 −0.107890 −0.0115670
8888 5.59102 0.596005
8989 0.412834 0.0437604 0.0218802 0.999761i 0.493035π-0.493035\pi
0.0218802 + 0.999761i 0.493035π0.493035\pi
9090 −6.61630 −0.697419
9191 0 0
9292 −4.53532 −0.472840
9393 −0.127689 −0.0132407
9494 18.9087 1.95029
9595 −2.46021 −0.252412
9696 −0.0936675 −0.00955989
9797 3.38416 0.343609 0.171805 0.985131i 0.445040π-0.445040\pi
0.171805 + 0.985131i 0.445040π0.445040\pi
9898 −31.4129 −3.17318
9999 8.79646 0.884077
100100 2.86449 0.286449
101101 −10.5432 −1.04909 −0.524545 0.851383i 0.675765π-0.675765\pi
−0.524545 + 0.851383i 0.675765π0.675765\pi
102102 −0.0965301 −0.00955790
103103 14.1152 1.39081 0.695404 0.718619i 0.255226π-0.255226\pi
0.695404 + 0.718619i 0.255226π0.255226\pi
104104 0 0
105105 −0.0601778 −0.00587275
106106 27.4898 2.67004
107107 −3.97165 −0.383954 −0.191977 0.981399i 0.561490π-0.561490\pi
−0.191977 + 0.981399i 0.561490π0.561490\pi
108108 0.224398 0.0215927
109109 −10.1737 −0.974460 −0.487230 0.873274i 0.661993π-0.661993\pi
−0.487230 + 0.873274i 0.661993π0.661993\pi
110110 −6.46741 −0.616643
111111 0.0539132 0.00511721
112112 7.02254 0.663568
113113 −2.59984 −0.244572 −0.122286 0.992495i 0.539023π-0.539023\pi
−0.122286 + 0.992495i 0.539023π0.539023\pi
114114 0.0708472 0.00663545
115115 1.58329 0.147642
116116 23.6699 2.19770
117117 0 0
118118 −11.7655 −1.08310
119119 15.4495 1.41626
120120 −0.0248950 −0.00227259
121121 −2.40150 −0.218318
122122 −4.23670 −0.383573
123123 0.0948578 0.00855304
124124 28.0135 2.51569
125125 −1.00000 −0.0894427
126126 −30.4943 −2.71665
127127 19.9719 1.77222 0.886109 0.463476i 0.153398π-0.153398\pi
0.886109 + 0.463476i 0.153398π0.153398\pi
128128 13.8286 1.22228
129129 0.00920925 0.000810829 0
130130 0 0
131131 −11.4400 −0.999514 −0.499757 0.866166i 0.666577π-0.666577\pi
−0.499757 + 0.866166i 0.666577π0.666577\pi
132132 0.109671 0.00954562
133133 −11.3390 −0.983217
134134 −16.0960 −1.39048
135135 −0.0783378 −0.00674224
136136 6.39133 0.548052
137137 −3.12520 −0.267004 −0.133502 0.991049i 0.542622π-0.542622\pi
−0.133502 + 0.991049i 0.542622π0.542622\pi
138138 −0.0455944 −0.00388125
139139 6.09526 0.516993 0.258497 0.966012i 0.416773π-0.416773\pi
0.258497 + 0.966012i 0.416773π0.416773\pi
140140 13.2024 1.11580
141141 0.111938 0.00942685
142142 −14.7350 −1.23653
143143 0 0
144144 4.57075 0.380896
145145 −8.26322 −0.686223
146146 −27.4684 −2.27330
147147 −0.185961 −0.0153378
148148 −11.8280 −0.972253
149149 14.6196 1.19769 0.598844 0.800866i 0.295627π-0.295627\pi
0.598844 + 0.800866i 0.295627π0.295627\pi
150150 0.0287972 0.00235129
151151 −12.2510 −0.996973 −0.498487 0.866897i 0.666111π-0.666111\pi
−0.498487 + 0.866897i 0.666111π0.666111\pi
152152 −4.69085 −0.380478
153153 10.0556 0.812948
154154 −29.8081 −2.40200
155155 −9.77959 −0.785515
156156 0 0
157157 7.13991 0.569827 0.284914 0.958553i 0.408035π-0.408035\pi
0.284914 + 0.958553i 0.408035π0.408035\pi
158158 −2.17212 −0.172805
159159 0.162736 0.0129058
160160 −7.17392 −0.567148
161161 7.29733 0.575110
162162 −19.8467 −1.55930
163163 −2.39002 −0.187201 −0.0936004 0.995610i 0.529838π-0.529838\pi
−0.0936004 + 0.995610i 0.529838π0.529838\pi
164164 −20.8108 −1.62505
165165 −0.0382863 −0.00298059
166166 −17.3005 −1.34278
167167 7.43841 0.575601 0.287801 0.957690i 0.407076π-0.407076\pi
0.287801 + 0.957690i 0.407076π0.407076\pi
168168 −0.114740 −0.00885240
169169 0 0
170170 −7.39317 −0.567030
171171 −7.38020 −0.564378
172172 −2.02041 −0.154055
173173 2.54119 0.193203 0.0966015 0.995323i 0.469203π-0.469203\pi
0.0966015 + 0.995323i 0.469203π0.469203\pi
174174 0.237958 0.0180396
175175 −4.60897 −0.348405
176176 4.46788 0.336779
177177 −0.0696502 −0.00523523
178178 −0.910531 −0.0682472
179179 −10.6913 −0.799105 −0.399553 0.916710i 0.630835π-0.630835\pi
−0.399553 + 0.916710i 0.630835π0.630835\pi
180180 8.59299 0.640484
181181 −11.7908 −0.876402 −0.438201 0.898877i 0.644384π-0.644384\pi
−0.438201 + 0.898877i 0.644384π0.644384\pi
182182 0 0
183183 −0.0250808 −0.00185403
184184 3.01884 0.222552
185185 4.12917 0.303583
186186 0.281625 0.0206498
187187 9.82931 0.718790
188188 −24.5579 −1.79107
189189 −0.361056 −0.0262630
190190 5.42613 0.393653
191191 13.4746 0.974990 0.487495 0.873126i 0.337911π-0.337911\pi
0.487495 + 0.873126i 0.337911π0.337911\pi
192192 0.166801 0.0120378
193193 −6.98737 −0.502962 −0.251481 0.967862i 0.580918π-0.580918\pi
−0.251481 + 0.967862i 0.580918π0.580918\pi
194194 −7.46397 −0.535882
195195 0 0
196196 40.7978 2.91413
197197 −1.43795 −0.102450 −0.0512248 0.998687i 0.516313π-0.516313\pi
−0.0512248 + 0.998687i 0.516313π0.516313\pi
198198 −19.4011 −1.37878
199199 −2.42852 −0.172153 −0.0860765 0.996289i 0.527433π-0.527433\pi
−0.0860765 + 0.996289i 0.527433π0.527433\pi
200200 −1.90669 −0.134823
201201 −0.0952866 −0.00672100
202202 23.2537 1.63613
203203 −38.0849 −2.67304
204204 0.125369 0.00877761
205205 7.26508 0.507415
206206 −31.1318 −2.16906
207207 4.74960 0.330120
208208 0 0
209209 −7.21411 −0.499011
210210 0.132726 0.00915894
211211 18.2640 1.25735 0.628674 0.777669i 0.283598π-0.283598\pi
0.628674 + 0.777669i 0.283598π0.283598\pi
212212 −35.7026 −2.45207
213213 −0.0872293 −0.00597685
214214 8.75970 0.598801
215215 0.705329 0.0481031
216216 −0.149366 −0.0101631
217217 −45.0738 −3.05981
218218 22.4386 1.51973
219219 −0.162610 −0.0109881
220220 8.39961 0.566301
221221 0 0
222222 −0.118909 −0.00798063
223223 −15.5841 −1.04359 −0.521793 0.853072i 0.674737π-0.674737\pi
−0.521793 + 0.853072i 0.674737π0.674737\pi
224224 −33.0644 −2.20921
225225 −2.99983 −0.199989
226226 5.73409 0.381426
227227 4.03380 0.267733 0.133866 0.990999i 0.457261π-0.457261\pi
0.133866 + 0.990999i 0.457261π0.457261\pi
228228 −0.0920135 −0.00609374
229229 −22.5147 −1.48781 −0.743906 0.668284i 0.767029π-0.767029\pi
−0.743906 + 0.668284i 0.767029π0.767029\pi
230230 −3.49204 −0.230258
231231 −0.176460 −0.0116102
232232 −15.7554 −1.03439
233233 −7.69759 −0.504286 −0.252143 0.967690i 0.581135π-0.581135\pi
−0.252143 + 0.967690i 0.581135π0.581135\pi
234234 0 0
235235 8.57322 0.559255
236236 15.2805 0.994676
237237 −0.0128587 −0.000835264 0
238238 −34.0749 −2.20875
239239 −18.7203 −1.21092 −0.605459 0.795877i 0.707010π-0.707010\pi
−0.605459 + 0.795877i 0.707010π0.707010\pi
240240 −0.0198940 −0.00128415
241241 22.6183 1.45697 0.728486 0.685061i 0.240225π-0.240225\pi
0.728486 + 0.685061i 0.240225π0.240225\pi
242242 5.29665 0.340482
243243 −0.352503 −0.0226131
244244 5.50246 0.352259
245245 −14.2426 −0.909926
246246 −0.209214 −0.0133390
247247 0 0
248248 −18.6466 −1.18406
249249 −0.102417 −0.00649042
250250 2.20556 0.139492
251251 1.78412 0.112612 0.0563062 0.998414i 0.482068π-0.482068\pi
0.0563062 + 0.998414i 0.482068π0.482068\pi
252252 39.6048 2.49487
253253 4.64271 0.291885
254254 −44.0492 −2.76389
255255 −0.0437667 −0.00274078
256256 −4.94936 −0.309335
257257 −4.59847 −0.286845 −0.143422 0.989662i 0.545811π-0.545811\pi
−0.143422 + 0.989662i 0.545811π0.545811\pi
258258 −0.0203115 −0.00126454
259259 19.0312 1.18254
260260 0 0
261261 −24.7883 −1.53435
262262 25.2315 1.55881
263263 18.8127 1.16004 0.580022 0.814601i 0.303044π-0.303044\pi
0.580022 + 0.814601i 0.303044π0.303044\pi
264264 −0.0730001 −0.00449284
265265 12.4639 0.765649
266266 25.0089 1.53339
267267 −0.00539024 −0.000329877 0
268268 20.9049 1.27697
269269 1.85412 0.113048 0.0565238 0.998401i 0.481998π-0.481998\pi
0.0565238 + 0.998401i 0.481998π0.481998\pi
270270 0.172779 0.0105150
271271 −0.149698 −0.00909352 −0.00454676 0.999990i 0.501447π-0.501447\pi
−0.00454676 + 0.999990i 0.501447π0.501447\pi
272272 5.10743 0.309683
273273 0 0
274274 6.89281 0.416410
275275 −2.93232 −0.176826
276276 0.0592161 0.00356439
277277 22.0184 1.32296 0.661478 0.749965i 0.269929π-0.269929\pi
0.661478 + 0.749965i 0.269929π0.269929\pi
278278 −13.4435 −0.806285
279279 −29.3371 −1.75637
280280 −8.78787 −0.525176
281281 0.438029 0.0261306 0.0130653 0.999915i 0.495841π-0.495841\pi
0.0130653 + 0.999915i 0.495841π0.495841\pi
282282 −0.246885 −0.0147018
283283 13.8290 0.822049 0.411025 0.911624i 0.365171π-0.365171\pi
0.411025 + 0.911624i 0.365171π0.365171\pi
284284 19.1372 1.13558
285285 0.0321221 0.00190275
286286 0 0
287287 33.4845 1.97653
288288 −21.5205 −1.26811
289289 −5.76370 −0.339041
290290 18.2250 1.07021
291291 −0.0441858 −0.00259022
292292 35.6748 2.08771
293293 −14.5656 −0.850929 −0.425464 0.904975i 0.639889π-0.639889\pi
−0.425464 + 0.904975i 0.639889π0.639889\pi
294294 0.410148 0.0239203
295295 −5.33445 −0.310584
296296 7.87304 0.457611
297297 −0.229711 −0.0133292
298298 −32.2445 −1.86787
299299 0 0
300300 −0.0374007 −0.00215933
301301 3.25084 0.187375
302302 27.0203 1.55485
303303 0.137659 0.00790833
304304 −3.74854 −0.214994
305305 −1.92092 −0.109992
306306 −22.1782 −1.26785
307307 9.05062 0.516546 0.258273 0.966072i 0.416847π-0.416847\pi
0.258273 + 0.966072i 0.416847π0.416847\pi
308308 38.7135 2.20591
309309 −0.184297 −0.0104843
310310 21.5695 1.22506
311311 7.28812 0.413272 0.206636 0.978418i 0.433748π-0.433748\pi
0.206636 + 0.978418i 0.433748π0.433748\pi
312312 0 0
313313 12.9725 0.733250 0.366625 0.930369i 0.380513π-0.380513\pi
0.366625 + 0.930369i 0.380513π0.380513\pi
314314 −15.7475 −0.888683
315315 −13.8261 −0.779014
316316 2.82107 0.158697
317317 −15.5048 −0.870838 −0.435419 0.900228i 0.643400π-0.643400\pi
−0.435419 + 0.900228i 0.643400π0.643400\pi
318318 −0.358925 −0.0201275
319319 −24.2304 −1.35664
320320 12.7752 0.714154
321321 0.0518565 0.00289434
322322 −16.0947 −0.896922
323323 −8.24676 −0.458862
324324 25.7760 1.43200
325325 0 0
326326 5.27133 0.291952
327327 0.132834 0.00734574
328328 13.8523 0.764863
329329 39.5137 2.17846
330330 0.0844427 0.00464842
331331 −26.0853 −1.43378 −0.716890 0.697186i 0.754435π-0.754435\pi
−0.716890 + 0.697186i 0.754435π0.754435\pi
332332 22.4692 1.23316
333333 12.3868 0.678793
334334 −16.4058 −0.897688
335335 −7.29793 −0.398728
336336 −0.0916910 −0.00500215
337337 −14.4785 −0.788697 −0.394348 0.918961i 0.629030π-0.629030\pi
−0.394348 + 0.918961i 0.629030π0.629030\pi
338338 0 0
339339 0.0339452 0.00184365
340340 9.60195 0.520739
341341 −28.6769 −1.55294
342342 16.2775 0.880185
343343 −33.3809 −1.80240
344344 1.34484 0.0725091
345345 −0.0206725 −0.00111297
346346 −5.60474 −0.301313
347347 6.81412 0.365801 0.182901 0.983131i 0.441451π-0.441451\pi
0.182901 + 0.983131i 0.441451π0.441451\pi
348348 −0.309050 −0.0165668
349349 33.7357 1.80583 0.902915 0.429818i 0.141422π-0.141422\pi
0.902915 + 0.429818i 0.141422π0.141422\pi
350350 10.1654 0.543361
351351 0 0
352352 −21.0362 −1.12123
353353 18.7215 0.996447 0.498223 0.867049i 0.333986π-0.333986\pi
0.498223 + 0.867049i 0.333986π0.333986\pi
354354 0.153618 0.00816468
355355 −6.68083 −0.354581
356356 1.18256 0.0626756
357357 −0.201719 −0.0106761
358358 23.5803 1.24626
359359 27.9262 1.47389 0.736945 0.675952i 0.236268π-0.236268\pi
0.736945 + 0.675952i 0.236268π0.236268\pi
360360 −5.71974 −0.301457
361361 −12.9474 −0.681441
362362 26.0053 1.36681
363363 0.0313556 0.00164574
364364 0 0
365365 −12.4541 −0.651880
366366 0.0553172 0.00289148
367367 2.50988 0.131015 0.0655074 0.997852i 0.479133π-0.479133\pi
0.0655074 + 0.997852i 0.479133π0.479133\pi
368368 2.41241 0.125755
369369 21.7940 1.13455
370370 −9.10713 −0.473457
371371 57.4456 2.98243
372372 −0.365763 −0.0189640
373373 22.1779 1.14833 0.574165 0.818739i 0.305327π-0.305327\pi
0.574165 + 0.818739i 0.305327π0.305327\pi
374374 −21.6791 −1.12100
375375 0.0130567 0.000674243 0
376376 16.3465 0.843005
377377 0 0
378378 0.796331 0.0409589
379379 1.42116 0.0730001 0.0365001 0.999334i 0.488379π-0.488379\pi
0.0365001 + 0.999334i 0.488379π0.488379\pi
380380 −7.04724 −0.361516
381381 −0.260766 −0.0133595
382382 −29.7191 −1.52056
383383 −21.0733 −1.07679 −0.538397 0.842691i 0.680970π-0.680970\pi
−0.538397 + 0.842691i 0.680970π0.680970\pi
384384 −0.180555 −0.00921390
385385 −13.5150 −0.688787
386386 15.4111 0.784402
387387 2.11587 0.107556
388388 9.69390 0.492133
389389 13.4713 0.683021 0.341511 0.939878i 0.389061π-0.389061\pi
0.341511 + 0.939878i 0.389061π0.389061\pi
390390 0 0
391391 5.30728 0.268401
392392 −27.1562 −1.37160
393393 0.149368 0.00753461
394394 3.17148 0.159777
395395 −0.984840 −0.0495527
396396 25.1974 1.26622
397397 −27.1859 −1.36442 −0.682210 0.731156i 0.738981π-0.738981\pi
−0.682210 + 0.731156i 0.738981π0.738981\pi
398398 5.35624 0.268484
399399 0.148050 0.00741176
400400 −1.52367 −0.0761834
401401 3.27520 0.163556 0.0817779 0.996651i 0.473940π-0.473940\pi
0.0817779 + 0.996651i 0.473940π0.473940\pi
402402 0.210160 0.0104818
403403 0 0
404404 −30.2010 −1.50256
405405 −8.99847 −0.447137
406406 83.9986 4.16878
407407 12.1080 0.600173
408408 −0.0834495 −0.00413137
409409 19.1677 0.947782 0.473891 0.880583i 0.342849π-0.342849\pi
0.473891 + 0.880583i 0.342849π0.342849\pi
410410 −16.0236 −0.791348
411411 0.0408047 0.00201275
412412 40.4327 1.99198
413413 −24.5863 −1.20981
414414 −10.4755 −0.514844
415415 −7.84405 −0.385049
416416 0 0
417417 −0.0795837 −0.00389723
418418 15.9112 0.778240
419419 0.392463 0.0191731 0.00958653 0.999954i 0.496948π-0.496948\pi
0.00958653 + 0.999954i 0.496948π0.496948\pi
420420 −0.172379 −0.00841122
421421 −35.1816 −1.71465 −0.857323 0.514779i 0.827874π-0.827874\pi
−0.857323 + 0.514779i 0.827874π0.827874\pi
422422 −40.2824 −1.96092
423423 25.7182 1.25046
424424 23.7647 1.15412
425425 −3.35206 −0.162599
426426 0.192389 0.00932130
427427 −8.85346 −0.428449
428428 −11.3768 −0.549916
429429 0 0
430430 −1.55565 −0.0750199
431431 −2.27454 −0.109561 −0.0547803 0.998498i 0.517446π-0.517446\pi
−0.0547803 + 0.998498i 0.517446π0.517446\pi
432432 −0.119361 −0.00574275
433433 11.8827 0.571048 0.285524 0.958372i 0.407832π-0.407832\pi
0.285524 + 0.958372i 0.407832π0.407832\pi
434434 99.4130 4.77197
435435 0.107890 0.00517293
436436 −29.1424 −1.39567
437437 −3.89522 −0.186334
438438 0.358645 0.0171367
439439 −35.7273 −1.70517 −0.852585 0.522588i 0.824967π-0.824967\pi
−0.852585 + 0.522588i 0.824967π0.824967\pi
440440 −5.59102 −0.266541
441441 −42.7254 −2.03454
442442 0 0
443443 4.98904 0.237036 0.118518 0.992952i 0.462186π-0.462186\pi
0.118518 + 0.992952i 0.462186π0.462186\pi
444444 0.154434 0.00732911
445445 −0.412834 −0.0195702
446446 34.3716 1.62754
447447 −0.190884 −0.00902849
448448 58.8804 2.78184
449449 23.4886 1.10850 0.554248 0.832352i 0.313006π-0.313006\pi
0.554248 + 0.832352i 0.313006π0.313006\pi
450450 6.61630 0.311895
451451 21.3035 1.00314
452452 −7.44721 −0.350287
453453 0.159957 0.00751545
454454 −8.89679 −0.417547
455455 0 0
456456 0.0612468 0.00286815
457457 −40.2510 −1.88286 −0.941430 0.337208i 0.890518π-0.890518\pi
−0.941430 + 0.337208i 0.890518π0.890518\pi
458458 49.6575 2.32034
459459 −0.262593 −0.0122568
460460 4.53532 0.211460
461461 31.2140 1.45378 0.726890 0.686754i 0.240965π-0.240965\pi
0.726890 + 0.686754i 0.240965π0.240965\pi
462462 0.389194 0.0181069
463463 17.7491 0.824872 0.412436 0.910987i 0.364678π-0.364678\pi
0.412436 + 0.910987i 0.364678π0.364678\pi
464464 −12.5904 −0.584495
465465 0.127689 0.00592142
466466 16.9775 0.786467
467467 26.6645 1.23389 0.616944 0.787007i 0.288370π-0.288370\pi
0.616944 + 0.787007i 0.288370π0.288370\pi
468468 0 0
469469 −33.6359 −1.55316
470470 −18.9087 −0.872196
471471 −0.0932234 −0.00429551
472472 −10.1711 −0.468165
473473 2.06825 0.0950983
474474 0.0283607 0.00130265
475475 2.46021 0.112882
476476 44.2551 2.02843
477477 37.3895 1.71195
478478 41.2888 1.88851
479479 20.4630 0.934980 0.467490 0.883998i 0.345158π-0.345158\pi
0.467490 + 0.883998i 0.345158π0.345158\pi
480480 0.0936675 0.00427531
481481 0 0
482482 −49.8860 −2.27224
483483 −0.0952788 −0.00433534
484484 −6.87908 −0.312686
485485 −3.38416 −0.153667
486486 0.777467 0.0352666
487487 8.11789 0.367857 0.183928 0.982940i 0.441119π-0.441119\pi
0.183928 + 0.982940i 0.441119π0.441119\pi
488488 −3.66260 −0.165798
489489 0.0312057 0.00141117
490490 31.4129 1.41909
491491 3.26996 0.147571 0.0737857 0.997274i 0.476492π-0.476492\pi
0.0737857 + 0.997274i 0.476492π0.476492\pi
492492 0.271719 0.0122501
493493 −27.6988 −1.24749
494494 0 0
495495 −8.79646 −0.395371
496496 −14.9008 −0.669068
497497 −30.7917 −1.38120
498498 0.225887 0.0101222
499499 8.89340 0.398123 0.199062 0.979987i 0.436211π-0.436211\pi
0.199062 + 0.979987i 0.436211π0.436211\pi
500500 −2.86449 −0.128104
501501 −0.0971208 −0.00433904
502502 −3.93498 −0.175627
503503 −23.7974 −1.06107 −0.530537 0.847662i 0.678010π-0.678010\pi
−0.530537 + 0.847662i 0.678010π0.678010\pi
504504 −26.3621 −1.17426
505505 10.5432 0.469168
506506 −10.2398 −0.455213
507507 0 0
508508 57.2093 2.53825
509509 −1.26770 −0.0561898 −0.0280949 0.999605i 0.508944π-0.508944\pi
−0.0280949 + 0.999605i 0.508944π0.508944\pi
510510 0.0965301 0.00427442
511511 −57.4008 −2.53926
512512 −16.7410 −0.739855
513513 0.192727 0.00850911
514514 10.1422 0.447354
515515 −14.1152 −0.621988
516516 0.0263798 0.00116131
517517 25.1394 1.10563
518518 −41.9745 −1.84425
519519 −0.0331794 −0.00145642
520520 0 0
521521 14.3916 0.630506 0.315253 0.949008i 0.397911π-0.397911\pi
0.315253 + 0.949008i 0.397911π0.397911\pi
522522 54.6720 2.39293
523523 19.0185 0.831622 0.415811 0.909451i 0.363498π-0.363498\pi
0.415811 + 0.909451i 0.363498π0.363498\pi
524524 −32.7697 −1.43155
525525 0.0601778 0.00262637
526526 −41.4926 −1.80916
527527 −32.7818 −1.42800
528528 −0.0583357 −0.00253873
529529 −20.4932 −0.891008
530530 −27.4898 −1.19408
531531 −16.0024 −0.694447
532532 −32.4805 −1.40821
533533 0 0
534534 0.0118885 0.000514465 0
535535 3.97165 0.171709
536536 −13.9149 −0.601031
537537 0.139593 0.00602387
538538 −4.08937 −0.176305
539539 −41.7638 −1.79890
540540 −0.224398 −0.00965655
541541 −13.8969 −0.597475 −0.298738 0.954335i 0.596566π-0.596566\pi
−0.298738 + 0.954335i 0.596566π0.596566\pi
542542 0.330168 0.0141819
543543 0.153948 0.00660656
544544 −24.0474 −1.03102
545545 10.1737 0.435792
546546 0 0
547547 37.0840 1.58560 0.792798 0.609484i 0.208623π-0.208623\pi
0.792798 + 0.609484i 0.208623π0.208623\pi
548548 −8.95211 −0.382415
549549 −5.76243 −0.245935
550550 6.46741 0.275771
551551 20.3292 0.866054
552552 −0.0394160 −0.00167766
553553 −4.53910 −0.193022
554554 −48.5628 −2.06324
555555 −0.0539132 −0.00228849
556556 17.4598 0.740461
557557 −31.8065 −1.34768 −0.673842 0.738875i 0.735357π-0.735357\pi
−0.673842 + 0.738875i 0.735357π0.735357\pi
558558 64.7047 2.73917
559559 0 0
560560 −7.02254 −0.296757
561561 −0.128338 −0.00541843
562562 −0.966100 −0.0407525
563563 26.3595 1.11092 0.555461 0.831543i 0.312542π-0.312542\pi
0.555461 + 0.831543i 0.312542π0.312542\pi
564564 0.320645 0.0135016
565565 2.59984 0.109376
566566 −30.5007 −1.28204
567567 −41.4736 −1.74173
568568 −12.7383 −0.534485
569569 17.7846 0.745569 0.372785 0.927918i 0.378403π-0.378403\pi
0.372785 + 0.927918i 0.378403π0.378403\pi
570570 −0.0708472 −0.00296746
571571 19.6399 0.821903 0.410952 0.911657i 0.365196π-0.365196\pi
0.410952 + 0.911657i 0.365196π0.365196\pi
572572 0 0
573573 −0.175934 −0.00734974
574574 −73.8522 −3.08253
575575 −1.58329 −0.0660277
576576 38.3233 1.59681
577577 −18.1454 −0.755403 −0.377701 0.925927i 0.623285π-0.623285\pi
−0.377701 + 0.925927i 0.623285π0.623285\pi
578578 12.7122 0.528757
579579 0.0912317 0.00379146
580580 −23.6699 −0.982840
581581 −36.1530 −1.49988
582582 0.0974545 0.00403962
583583 36.5480 1.51366
584584 −23.7462 −0.982624
585585 0 0
586586 32.1252 1.32708
587587 0.423843 0.0174939 0.00874694 0.999962i 0.497216π-0.497216\pi
0.00874694 + 0.999962i 0.497216π0.497216\pi
588588 −0.532683 −0.0219675
589589 24.0598 0.991367
590590 11.7655 0.484376
591591 0.0187748 0.000772293 0
592592 6.29149 0.258578
593593 47.5064 1.95085 0.975426 0.220327i 0.0707125π-0.0707125\pi
0.975426 + 0.220327i 0.0707125π0.0707125\pi
594594 0.506642 0.0207878
595595 −15.4495 −0.633369
596596 41.8778 1.71538
597597 0.0317083 0.00129774
598598 0 0
599599 25.7871 1.05363 0.526816 0.849979i 0.323386π-0.323386\pi
0.526816 + 0.849979i 0.323386π0.323386\pi
600600 0.0248950 0.00101633
601601 −12.6776 −0.517130 −0.258565 0.965994i 0.583250π-0.583250\pi
−0.258565 + 0.965994i 0.583250π0.583250\pi
602602 −7.16992 −0.292224
603603 −21.8925 −0.891533
604604 −35.0929 −1.42791
605605 2.40150 0.0976349
606606 −0.303616 −0.0123336
607607 −4.40448 −0.178772 −0.0893862 0.995997i 0.528491π-0.528491\pi
−0.0893862 + 0.995997i 0.528491π0.528491\pi
608608 17.6493 0.715775
609609 0.497262 0.0201501
610610 4.23670 0.171539
611611 0 0
612612 28.8042 1.16434
613613 33.3599 1.34739 0.673696 0.739008i 0.264706π-0.264706\pi
0.673696 + 0.739008i 0.264706π0.264706\pi
614614 −19.9617 −0.805588
615615 −0.0948578 −0.00382503
616616 −25.7688 −1.03826
617617 32.5535 1.31055 0.655277 0.755389i 0.272552π-0.272552\pi
0.655277 + 0.755389i 0.272552π0.272552\pi
618618 0.406477 0.0163509
619619 35.5813 1.43013 0.715067 0.699056i 0.246396π-0.246396\pi
0.715067 + 0.699056i 0.246396π0.246396\pi
620620 −28.0135 −1.12505
621621 −0.124031 −0.00497721
622622 −16.0744 −0.644524
623623 −1.90274 −0.0762317
624624 0 0
625625 1.00000 0.0400000
626626 −28.6116 −1.14355
627627 0.0941922 0.00376168
628628 20.4522 0.816133
629629 13.8412 0.551886
630630 30.4943 1.21492
631631 −25.4117 −1.01162 −0.505812 0.862644i 0.668807π-0.668807\pi
−0.505812 + 0.862644i 0.668807π0.668807\pi
632632 −1.87778 −0.0746942
633633 −0.238467 −0.00947822
634634 34.1968 1.35813
635635 −19.9719 −0.792560
636636 0.466157 0.0184843
637637 0 0
638638 53.4416 2.11577
639639 −20.0413 −0.792823
640640 −13.8286 −0.546622
641641 −10.1479 −0.400817 −0.200408 0.979712i 0.564227π-0.564227\pi
−0.200408 + 0.979712i 0.564227π0.564227\pi
642642 −0.114372 −0.00451392
643643 −1.85439 −0.0731298 −0.0365649 0.999331i 0.511642π-0.511642\pi
−0.0365649 + 0.999331i 0.511642π0.511642\pi
644644 20.9032 0.823700
645645 −0.00920925 −0.000362614 0
646646 18.1887 0.715626
647647 −29.6034 −1.16383 −0.581914 0.813250i 0.697696π-0.697696\pi
−0.581914 + 0.813250i 0.697696π0.697696\pi
648648 −17.1573 −0.674001
649649 −15.6423 −0.614015
650650 0 0
651651 0.588514 0.0230657
652652 −6.84619 −0.268118
653653 6.78882 0.265667 0.132834 0.991138i 0.457592π-0.457592\pi
0.132834 + 0.991138i 0.457592π0.457592\pi
654654 −0.292973 −0.0114562
655655 11.4400 0.446996
656656 11.0696 0.432195
657657 −37.3603 −1.45756
658658 −87.1498 −3.39745
659659 7.94959 0.309672 0.154836 0.987940i 0.450515π-0.450515\pi
0.154836 + 0.987940i 0.450515π0.450515\pi
660660 −0.109671 −0.00426893
661661 −40.3832 −1.57072 −0.785361 0.619038i 0.787523π-0.787523\pi
−0.785361 + 0.619038i 0.787523π0.787523\pi
662662 57.5328 2.23607
663663 0 0
664664 −14.9562 −0.580412
665665 11.3390 0.439708
666666 −27.3198 −1.05862
667667 −13.0831 −0.506579
668668 21.3073 0.824402
669669 0.203476 0.00786684
670670 16.0960 0.621843
671671 −5.63275 −0.217450
672672 0.431710 0.0166536
673673 9.63920 0.371564 0.185782 0.982591i 0.440518π-0.440518\pi
0.185782 + 0.982591i 0.440518π0.440518\pi
674674 31.9333 1.23002
675675 0.0783378 0.00301522
676676 0 0
677677 51.1565 1.96610 0.983051 0.183330i 0.0586878π-0.0586878\pi
0.983051 + 0.183330i 0.0586878π0.0586878\pi
678678 −0.0748681 −0.00287529
679679 −15.5975 −0.598577
680680 −6.39133 −0.245097
681681 −0.0526680 −0.00201824
682682 63.2485 2.42191
683683 8.34502 0.319313 0.159657 0.987173i 0.448961π-0.448961\pi
0.159657 + 0.987173i 0.448961π0.448961\pi
684684 −21.1405 −0.808328
685685 3.12520 0.119408
686686 73.6236 2.81096
687687 0.293967 0.0112155
688688 1.07469 0.0409721
689689 0 0
690690 0.0455944 0.00173575
691691 36.1243 1.37423 0.687117 0.726547i 0.258876π-0.258876\pi
0.687117 + 0.726547i 0.258876π0.258876\pi
692692 7.27921 0.276714
693693 −40.5426 −1.54009
694694 −15.0289 −0.570491
695695 −6.09526 −0.231206
696696 0.205713 0.00779753
697697 24.3530 0.922435
698698 −74.4061 −2.81631
699699 0.100505 0.00380144
700700 −13.2024 −0.499002
701701 −45.9823 −1.73673 −0.868364 0.495928i 0.834828π-0.834828\pi
−0.868364 + 0.495928i 0.834828π0.834828\pi
702702 0 0
703703 −10.1586 −0.383139
704704 37.4609 1.41186
705705 −0.111938 −0.00421582
706706 −41.2915 −1.55402
707707 48.5934 1.82754
708708 −0.199512 −0.00749813
709709 −38.0949 −1.43069 −0.715343 0.698774i 0.753729π-0.753729\pi
−0.715343 + 0.698774i 0.753729π0.753729\pi
710710 14.7350 0.552993
711711 −2.95435 −0.110797
712712 −0.787147 −0.0294996
713713 −15.4839 −0.579877
714714 0.444904 0.0166501
715715 0 0
716716 −30.6251 −1.14452
717717 0.244425 0.00912822
718718 −61.5930 −2.29863
719719 −27.8672 −1.03927 −0.519635 0.854388i 0.673932π-0.673932\pi
−0.519635 + 0.854388i 0.673932π0.673932\pi
720720 −4.57075 −0.170342
721721 −65.0563 −2.42282
722722 28.5562 1.06275
723723 −0.295319 −0.0109830
724724 −33.7746 −1.25522
725725 8.26322 0.306888
726726 −0.0691566 −0.00256664
727727 −13.7750 −0.510885 −0.255443 0.966824i 0.582221π-0.582221\pi
−0.255443 + 0.966824i 0.582221π0.582221\pi
728728 0 0
729729 −26.9908 −0.999659
730730 27.4684 1.01665
731731 2.36431 0.0874470
732732 −0.0718438 −0.00265542
733733 6.58392 0.243183 0.121591 0.992580i 0.461200π-0.461200\pi
0.121591 + 0.992580i 0.461200π0.461200\pi
734734 −5.53570 −0.204326
735735 0.185961 0.00685927
736736 −11.3584 −0.418676
737737 −21.3999 −0.788274
738738 −48.0680 −1.76941
739739 −5.47501 −0.201401 −0.100701 0.994917i 0.532108π-0.532108\pi
−0.100701 + 0.994917i 0.532108π0.532108\pi
740740 11.8280 0.434805
741741 0 0
742742 −126.700 −4.65129
743743 26.6714 0.978479 0.489239 0.872150i 0.337274π-0.337274\pi
0.489239 + 0.872150i 0.337274π0.337274\pi
744744 0.243463 0.00892578
745745 −14.6196 −0.535622
746746 −48.9148 −1.79090
747747 −23.5308 −0.860948
748748 28.1560 1.02948
749749 18.3052 0.668857
750750 −0.0287972 −0.00105153
751751 21.8067 0.795740 0.397870 0.917442i 0.369750π-0.369750\pi
0.397870 + 0.917442i 0.369750π0.369750\pi
752752 13.0627 0.476349
753753 −0.0232946 −0.000848903 0
754754 0 0
755755 12.2510 0.445860
756756 −1.03424 −0.0376151
757757 −8.33422 −0.302912 −0.151456 0.988464i 0.548396π-0.548396\pi
−0.151456 + 0.988464i 0.548396π0.548396\pi
758758 −3.13446 −0.113849
759759 −0.0606183 −0.00220031
760760 4.69085 0.170155
761761 7.33096 0.265747 0.132874 0.991133i 0.457580π-0.457580\pi
0.132874 + 0.991133i 0.457580π0.457580\pi
762762 0.575135 0.0208350
763763 46.8901 1.69753
764764 38.5980 1.39643
765765 −10.0556 −0.363561
766766 46.4783 1.67933
767767 0 0
768768 0.0646221 0.00233185
769769 22.3346 0.805407 0.402703 0.915331i 0.368071π-0.368071\pi
0.402703 + 0.915331i 0.368071π0.368071\pi
770770 29.8081 1.07421
771771 0.0600407 0.00216231
772772 −20.0153 −0.720365
773773 27.1591 0.976844 0.488422 0.872608i 0.337573π-0.337573\pi
0.488422 + 0.872608i 0.337573π0.337573\pi
774774 −4.66667 −0.167740
775775 9.77959 0.351293
776776 −6.45254 −0.231633
777777 −0.248484 −0.00891432
778778 −29.7117 −1.06522
779779 −17.8736 −0.640388
780780 0 0
781781 −19.5903 −0.700997
782782 −11.7055 −0.418589
783783 0.647322 0.0231334
784784 −21.7010 −0.775036
785785 −7.13991 −0.254834
786786 −0.329440 −0.0117507
787787 −11.5806 −0.412805 −0.206403 0.978467i 0.566176π-0.566176\pi
−0.206403 + 0.978467i 0.566176π0.566176\pi
788788 −4.11899 −0.146733
789789 −0.245632 −0.00874472
790790 2.17212 0.0772807
791791 11.9826 0.426051
792792 −16.7721 −0.595971
793793 0 0
794794 59.9601 2.12790
795795 −0.162736 −0.00577167
796796 −6.95647 −0.246566
797797 −47.7004 −1.68963 −0.844817 0.535055i 0.820291π-0.820291\pi
−0.844817 + 0.535055i 0.820291π0.820291\pi
798798 −0.326532 −0.0115591
799799 28.7379 1.01668
800800 7.17392 0.253636
801801 −1.23843 −0.0437579
802802 −7.22365 −0.255076
803803 −36.5195 −1.28875
804804 −0.272948 −0.00962612
805805 −7.29733 −0.257197
806806 0 0
807807 −0.0242086 −0.000852184 0
808808 20.1027 0.707209
809809 36.3910 1.27944 0.639720 0.768608i 0.279050π-0.279050\pi
0.639720 + 0.768608i 0.279050π0.279050\pi
810810 19.8467 0.697340
811811 36.8088 1.29253 0.646266 0.763112i 0.276330π-0.276330\pi
0.646266 + 0.763112i 0.276330π0.276330\pi
812812 −109.094 −3.82845
813813 0.00195456 6.85494e−5 0
814814 −26.7050 −0.936010
815815 2.39002 0.0837188
816816 −0.0666860 −0.00233448
817817 −1.73526 −0.0607089
818818 −42.2755 −1.47813
819819 0 0
820820 20.8108 0.726744
821821 −33.6668 −1.17498 −0.587491 0.809231i 0.699884π-0.699884\pi
−0.587491 + 0.809231i 0.699884π0.699884\pi
822822 −0.0899971 −0.00313901
823823 31.8809 1.11130 0.555649 0.831417i 0.312470π-0.312470\pi
0.555649 + 0.831417i 0.312470π0.312470\pi
824824 −26.9132 −0.937566
825825 0.0382863 0.00133296
826826 54.2266 1.88678
827827 18.4625 0.642003 0.321002 0.947079i 0.395981π-0.395981\pi
0.321002 + 0.947079i 0.395981π0.395981\pi
828828 13.6052 0.472813
829829 −34.9663 −1.21443 −0.607214 0.794538i 0.707713π-0.707713\pi
−0.607214 + 0.794538i 0.707713π0.707713\pi
830830 17.3005 0.600510
831831 −0.287487 −0.00997280
832832 0 0
833833 −47.7420 −1.65416
834834 0.175527 0.00607799
835835 −7.43841 −0.257417
836836 −20.6648 −0.714706
837837 0.766111 0.0264807
838838 −0.865600 −0.0299017
839839 28.7234 0.991641 0.495820 0.868425i 0.334867π-0.334867\pi
0.495820 + 0.868425i 0.334867π0.334867\pi
840840 0.114740 0.00395892
841841 39.2808 1.35451
842842 77.5951 2.67410
843843 −0.00571920 −0.000196980 0
844844 52.3172 1.80083
845845 0 0
846846 −56.7230 −1.95018
847847 11.0684 0.380316
848848 18.9908 0.652147
849849 −0.180561 −0.00619683
850850 7.39317 0.253584
851851 6.53767 0.224108
852852 −0.249868 −0.00856032
853853 13.7453 0.470629 0.235315 0.971919i 0.424388π-0.424388\pi
0.235315 + 0.971919i 0.424388π0.424388\pi
854854 19.5268 0.668195
855855 7.38020 0.252398
856856 7.57269 0.258829
857857 −12.6495 −0.432099 −0.216049 0.976382i 0.569317π-0.569317\pi
−0.216049 + 0.976382i 0.569317π0.569317\pi
858858 0 0
859859 −11.0929 −0.378485 −0.189243 0.981930i 0.560603π-0.560603\pi
−0.189243 + 0.981930i 0.560603π0.560603\pi
860860 2.02041 0.0688954
861861 −0.437196 −0.0148996
862862 5.01663 0.170867
863863 33.0295 1.12434 0.562169 0.827022i 0.309967π-0.309967\pi
0.562169 + 0.827022i 0.309967π0.309967\pi
864864 0.561989 0.0191192
865865 −2.54119 −0.0864030
866866 −26.2081 −0.890587
867867 0.0752546 0.00255578
868868 −129.114 −4.38240
869869 −2.88787 −0.0979641
870870 −0.237958 −0.00806753
871871 0 0
872872 19.3980 0.656899
873873 −10.1519 −0.343590
874874 8.59114 0.290600
875875 4.60897 0.155812
876876 −0.465794 −0.0157377
877877 −15.4397 −0.521362 −0.260681 0.965425i 0.583947π-0.583947\pi
−0.260681 + 0.965425i 0.583947π0.583947\pi
878878 78.7987 2.65933
879879 0.190178 0.00641453
880880 −4.46788 −0.150612
881881 −16.6260 −0.560143 −0.280072 0.959979i 0.590358π-0.590358\pi
−0.280072 + 0.959979i 0.590358π0.590358\pi
882882 94.2333 3.17300
883883 57.2845 1.92778 0.963888 0.266309i 0.0858041π-0.0858041\pi
0.963888 + 0.266309i 0.0858041π0.0858041\pi
884884 0 0
885885 0.0696502 0.00234126
886886 −11.0036 −0.369674
887887 18.4657 0.620018 0.310009 0.950734i 0.399668π-0.399668\pi
0.310009 + 0.950734i 0.399668π0.399668\pi
888888 −0.102796 −0.00344960
889889 −92.0498 −3.08725
890890 0.910531 0.0305211
891891 −26.3864 −0.883977
892892 −44.6405 −1.49467
893893 −21.0919 −0.705813
894894 0.421005 0.0140805
895895 10.6913 0.357371
896896 −63.7354 −2.12925
897897 0 0
898898 −51.8055 −1.72877
899899 80.8109 2.69519
900900 −8.59299 −0.286433
901901 41.7796 1.39188
902902 −46.9862 −1.56447
903903 −0.0424451 −0.00141249
904904 4.95708 0.164870
905905 11.7908 0.391939
906906 −0.352795 −0.0117208
907907 44.9489 1.49250 0.746251 0.665664i 0.231852π-0.231852\pi
0.746251 + 0.665664i 0.231852π0.231852\pi
908908 11.5548 0.383459
909909 31.6279 1.04903
910910 0 0
911911 −44.3728 −1.47014 −0.735069 0.677992i 0.762850π-0.762850\pi
−0.735069 + 0.677992i 0.762850π0.762850\pi
912912 0.0489434 0.00162068
913913 −23.0013 −0.761231
914914 88.7759 2.93645
915915 0.0250808 0.000829146 0
916916 −64.4931 −2.13091
917917 52.7264 1.74118
918918 0.579164 0.0191153
919919 25.1680 0.830217 0.415108 0.909772i 0.363744π-0.363744\pi
0.415108 + 0.909772i 0.363744π0.363744\pi
920920 −3.01884 −0.0995282
921921 −0.118171 −0.00389386
922922 −68.8443 −2.26726
923923 0 0
924924 −0.505469 −0.0166287
925925 −4.12917 −0.135766
926926 −39.1468 −1.28644
927927 −42.3430 −1.39073
928928 59.2797 1.94595
929929 37.5601 1.23231 0.616153 0.787626i 0.288690π-0.288690\pi
0.616153 + 0.787626i 0.288690π0.288690\pi
930930 −0.281625 −0.00923485
931931 35.0397 1.14838
932932 −22.0497 −0.722262
933933 −0.0951586 −0.00311535
934934 −58.8102 −1.92433
935935 −9.82931 −0.321453
936936 0 0
937937 −17.1212 −0.559326 −0.279663 0.960098i 0.590223π-0.590223\pi
−0.279663 + 0.960098i 0.590223π0.590223\pi
938938 74.1860 2.42226
939939 −0.169378 −0.00552743
940940 24.5579 0.800991
941941 −0.208568 −0.00679913 −0.00339956 0.999994i 0.501082π-0.501082\pi
−0.00339956 + 0.999994i 0.501082π0.501082\pi
942942 0.205610 0.00669913
943943 11.5027 0.374580
944944 −8.12794 −0.264542
945945 0.361056 0.0117452
946946 −4.56165 −0.148312
947947 0.414059 0.0134551 0.00672755 0.999977i 0.497859π-0.497859\pi
0.00672755 + 0.999977i 0.497859π0.497859\pi
948948 −0.0368337 −0.00119630
949949 0 0
950950 −5.42613 −0.176047
951951 0.202441 0.00656461
952952 −29.4575 −0.954722
953953 −33.8593 −1.09681 −0.548404 0.836213i 0.684765π-0.684765\pi
−0.548404 + 0.836213i 0.684765π0.684765\pi
954954 −82.4647 −2.66989
955955 −13.4746 −0.436029
956956 −53.6243 −1.73433
957957 0.316368 0.0102267
958958 −45.1324 −1.45816
959959 14.4039 0.465128
960960 −0.166801 −0.00538348
961961 64.6403 2.08517
962962 0 0
963963 11.9143 0.383932
964964 64.7899 2.08674
965965 6.98737 0.224931
966966 0.210143 0.00676124
967967 13.2125 0.424885 0.212442 0.977174i 0.431858π-0.431858\pi
0.212442 + 0.977174i 0.431858π0.431858\pi
968968 4.57892 0.147172
969969 0.107675 0.00345902
970970 7.46397 0.239654
971971 −17.6019 −0.564872 −0.282436 0.959286i 0.591142π-0.591142\pi
−0.282436 + 0.959286i 0.591142π0.591142\pi
972972 −1.00974 −0.0323875
973973 −28.0929 −0.900616
974974 −17.9045 −0.573697
975975 0 0
976976 −2.92685 −0.0936861
977977 −11.7812 −0.376913 −0.188457 0.982082i 0.560348π-0.560348\pi
−0.188457 + 0.982082i 0.560348π0.560348\pi
978978 −0.0688260 −0.00220081
979979 −1.21056 −0.0386897
980980 −40.7978 −1.30324
981981 30.5192 0.974404
982982 −7.21210 −0.230147
983983 −45.4985 −1.45118 −0.725589 0.688128i 0.758433π-0.758433\pi
−0.725589 + 0.688128i 0.758433π0.758433\pi
984984 −0.180864 −0.00576574
985985 1.43795 0.0458169
986986 61.0914 1.94555
987987 −0.515917 −0.0164218
988988 0 0
989989 1.11674 0.0355103
990990 19.4011 0.616608
991991 33.2685 1.05681 0.528405 0.848993i 0.322790π-0.322790\pi
0.528405 + 0.848993i 0.322790π0.322790\pi
992992 70.1580 2.22752
993993 0.340588 0.0108082
994994 67.9130 2.15407
995995 2.42852 0.0769892
996996 −0.293373 −0.00929589
997997 −39.7870 −1.26007 −0.630033 0.776568i 0.716959π-0.716959\pi
−0.630033 + 0.776568i 0.716959π0.716959\pi
998998 −19.6149 −0.620899
999999 −0.323470 −0.0102341
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 845.2.a.n.1.3 9
3.2 odd 2 7605.2.a.cs.1.7 9
5.4 even 2 4225.2.a.bt.1.7 9
13.2 odd 12 845.2.m.j.316.5 36
13.3 even 3 845.2.e.p.191.7 18
13.4 even 6 845.2.e.o.146.3 18
13.5 odd 4 845.2.c.h.506.14 18
13.6 odd 12 845.2.m.j.361.14 36
13.7 odd 12 845.2.m.j.361.5 36
13.8 odd 4 845.2.c.h.506.5 18
13.9 even 3 845.2.e.p.146.7 18
13.10 even 6 845.2.e.o.191.3 18
13.11 odd 12 845.2.m.j.316.14 36
13.12 even 2 845.2.a.o.1.7 yes 9
39.38 odd 2 7605.2.a.cp.1.3 9
65.64 even 2 4225.2.a.bs.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.a.n.1.3 9 1.1 even 1 trivial
845.2.a.o.1.7 yes 9 13.12 even 2
845.2.c.h.506.5 18 13.8 odd 4
845.2.c.h.506.14 18 13.5 odd 4
845.2.e.o.146.3 18 13.4 even 6
845.2.e.o.191.3 18 13.10 even 6
845.2.e.p.146.7 18 13.9 even 3
845.2.e.p.191.7 18 13.3 even 3
845.2.m.j.316.5 36 13.2 odd 12
845.2.m.j.316.14 36 13.11 odd 12
845.2.m.j.361.5 36 13.7 odd 12
845.2.m.j.361.14 36 13.6 odd 12
4225.2.a.bs.1.3 9 65.64 even 2
4225.2.a.bt.1.7 9 5.4 even 2
7605.2.a.cp.1.3 9 39.38 odd 2
7605.2.a.cs.1.7 9 3.2 odd 2