Properties

Label 1274.2.f.q.1145.1
Level 12741274
Weight 22
Character 1274.1145
Analytic conductor 10.17310.173
Analytic rank 00
Dimension 22
Inner twists 22

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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] = [1274,2,Mod(79,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 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("1274.79"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1274=27213 1274 = 2 \cdot 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1274.f (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,1,0,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.172941217510.1729412175
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 1145.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 1274.1145
Dual form 1274.2.f.q.79.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.500000+0.866025i)q2+(0.500000+0.866025i)q41.00000q8+(1.50000+2.59808i)q9+(0.500000+0.866025i)q11+1.00000q13+(0.5000000.866025i)q16+(0.500000+0.866025i)q17+(1.50000+2.59808i)q18+(2.50000+4.33013i)q191.00000q22+(1.000001.73205i)q23+(2.500004.33013i)q25+(0.500000+0.866025i)q265.00000q29+(4.00000+6.92820i)q31+(0.5000000.866025i)q321.00000q343.00000q36+(4.00000+6.92820i)q37+(2.50000+4.33013i)q386.00000q43+(0.5000000.866025i)q44+(1.000001.73205i)q46+(5.50000+9.52628i)q47+5.00000q50+(0.500000+0.866025i)q52+(2.50000+4.33013i)q53+(2.500004.33013i)q58+(1.50000+2.59808i)q59+(0.500000+0.866025i)q618.00000q62+1.00000q64+(3.500006.06218i)q67+(0.5000000.866025i)q689.00000q71+(1.500002.59808i)q72+(1.00000+1.73205i)q73+(4.00000+6.92820i)q745.00000q76+(7.00000+12.1244i)q79+(4.50000+7.79423i)q81+8.00000q83+(3.000005.19615i)q86+(0.5000000.866025i)q88+(8.0000013.8564i)q89+2.00000q92+(5.50000+9.52628i)q942.00000q973.00000q99+O(q100)q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} -1.00000 q^{22} +(-1.00000 - 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} -5.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.00000 q^{34} -3.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(-2.50000 + 4.33013i) q^{38} -6.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{46} +(5.50000 + 9.52628i) q^{47} +5.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-2.50000 - 4.33013i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(3.50000 - 6.06218i) q^{67} +(-0.500000 - 0.866025i) q^{68} -9.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} -5.00000 q^{76} +(7.00000 + 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +8.00000 q^{83} +(-3.00000 - 5.19615i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-8.00000 - 13.8564i) q^{89} +2.00000 q^{92} +(-5.50000 + 9.52628i) q^{94} -2.00000 q^{97} -3.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2q42q8+3q9q11+2q13q16q173q18+5q192q222q23+5q25+q2610q298q31+q322q346q36+6q99+O(q100) 2 q + q^{2} - q^{4} - 2 q^{8} + 3 q^{9} - q^{11} + 2 q^{13} - q^{16} - q^{17} - 3 q^{18} + 5 q^{19} - 2 q^{22} - 2 q^{23} + 5 q^{25} + q^{26} - 10 q^{29} - 8 q^{31} + q^{32} - 2 q^{34} - 6 q^{36}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1274Z)×\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times.

nn 197197 885885
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.500000 + 0.866025i 0.353553 + 0.612372i
33 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
44 −0.500000 + 0.866025i −0.250000 + 0.433013i
55 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
66 0 0
77 0 0
88 −1.00000 −0.353553
99 1.50000 + 2.59808i 0.500000 + 0.866025i
1010 0 0
1111 −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i 0.881504π-0.881504\pi
0.780750 + 0.624844i 0.214837π0.214837\pi
1212 0 0
1313 1.00000 0.277350
1414 0 0
1515 0 0
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −0.500000 + 0.866025i −0.121268 + 0.210042i −0.920268 0.391289i 0.872029π-0.872029\pi
0.799000 + 0.601331i 0.205363π0.205363\pi
1818 −1.50000 + 2.59808i −0.353553 + 0.612372i
1919 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i 0.0277634π0.0277634\pi
−0.422659 + 0.906289i 0.638903π0.638903\pi
2020 0 0
2121 0 0
2222 −1.00000 −0.213201
2323 −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i 0.233529π-0.233529\pi
−0.951247 + 0.308431i 0.900196π0.900196\pi
2424 0 0
2525 2.50000 4.33013i 0.500000 0.866025i
2626 0.500000 + 0.866025i 0.0980581 + 0.169842i
2727 0 0
2828 0 0
2929 −5.00000 −0.928477 −0.464238 0.885710i 0.653672π-0.653672\pi
−0.464238 + 0.885710i 0.653672π0.653672\pi
3030 0 0
3131 −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i 0.421802π0.421802\pi
−0.961625 + 0.274367i 0.911532π0.911532\pi
3232 0.500000 0.866025i 0.0883883 0.153093i
3333 0 0
3434 −1.00000 −0.171499
3535 0 0
3636 −3.00000 −0.500000
3737 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i 0.0617599π0.0617599\pi
−0.323640 + 0.946180i 0.604907π0.604907\pi
3838 −2.50000 + 4.33013i −0.405554 + 0.702439i
3939 0 0
4040 0 0
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 −6.00000 −0.914991 −0.457496 0.889212i 0.651253π-0.651253\pi
−0.457496 + 0.889212i 0.651253π0.651253\pi
4444 −0.500000 0.866025i −0.0753778 0.130558i
4545 0 0
4646 1.00000 1.73205i 0.147442 0.255377i
4747 5.50000 + 9.52628i 0.802257 + 1.38955i 0.918127 + 0.396286i 0.129701π0.129701\pi
−0.115870 + 0.993264i 0.536965π0.536965\pi
4848 0 0
4949 0 0
5050 5.00000 0.707107
5151 0 0
5252 −0.500000 + 0.866025i −0.0693375 + 0.120096i
5353 −2.50000 + 4.33013i −0.343401 + 0.594789i −0.985062 0.172200i 0.944912π-0.944912\pi
0.641661 + 0.766989i 0.278246π0.278246\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 −2.50000 4.33013i −0.328266 0.568574i
5959 −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i 0.895896π-0.895896\pi
0.751710 + 0.659494i 0.229229π0.229229\pi
6060 0 0
6161 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i 0.146275π-0.146275\pi
−0.832240 + 0.554416i 0.812942π0.812942\pi
6262 −8.00000 −1.01600
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i 0.692695π-0.692695\pi
0.996659 + 0.0816792i 0.0260283π0.0260283\pi
6868 −0.500000 0.866025i −0.0606339 0.105021i
6969 0 0
7070 0 0
7171 −9.00000 −1.06810 −0.534052 0.845452i 0.679331π-0.679331\pi
−0.534052 + 0.845452i 0.679331π0.679331\pi
7272 −1.50000 2.59808i −0.176777 0.306186i
7373 −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i 0.870674π-0.870674\pi
0.801553 + 0.597924i 0.204008π0.204008\pi
7474 −4.00000 + 6.92820i −0.464991 + 0.805387i
7575 0 0
7676 −5.00000 −0.573539
7777 0 0
7878 0 0
7979 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i 0.121990π0.121990\pi
−0.139895 + 0.990166i 0.544677π0.544677\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 8.00000 0.878114 0.439057 0.898459i 0.355313π-0.355313\pi
0.439057 + 0.898459i 0.355313π0.355313\pi
8484 0 0
8585 0 0
8686 −3.00000 5.19615i −0.323498 0.560316i
8787 0 0
8888 0.500000 0.866025i 0.0533002 0.0923186i
8989 −8.00000 13.8564i −0.847998 1.46878i −0.882992 0.469389i 0.844474π-0.844474\pi
0.0349934 0.999388i 0.488859π-0.488859\pi
9090 0 0
9191 0 0
9292 2.00000 0.208514
9393 0 0
9494 −5.50000 + 9.52628i −0.567282 + 0.982561i
9595 0 0
9696 0 0
9797 −2.00000 −0.203069 −0.101535 0.994832i 0.532375π-0.532375\pi
−0.101535 + 0.994832i 0.532375π0.532375\pi
9898 0 0
9999 −3.00000 −0.301511
100100 2.50000 + 4.33013i 0.250000 + 0.433013i
101101 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i 0.480128π-0.480128\pi
0.833143 0.553058i 0.186539π-0.186539\pi
102102 0 0
103103 3.00000 + 5.19615i 0.295599 + 0.511992i 0.975124 0.221660i 0.0711475π-0.0711475\pi
−0.679525 + 0.733652i 0.737814π0.737814\pi
104104 −1.00000 −0.0980581
105105 0 0
106106 −5.00000 −0.485643
107107 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i 0.0402834π-0.0402834\pi
−0.605308 + 0.795991i 0.706950π0.706950\pi
108108 0 0
109109 6.00000 10.3923i 0.574696 0.995402i −0.421379 0.906885i 0.638454π-0.638454\pi
0.996075 0.0885176i 0.0282129π-0.0282129\pi
110110 0 0
111111 0 0
112112 0 0
113113 1.00000 0.0940721 0.0470360 0.998893i 0.485022π-0.485022\pi
0.0470360 + 0.998893i 0.485022π0.485022\pi
114114 0 0
115115 0 0
116116 2.50000 4.33013i 0.232119 0.402042i
117117 1.50000 + 2.59808i 0.138675 + 0.240192i
118118 −3.00000 −0.276172
119119 0 0
120120 0 0
121121 5.00000 + 8.66025i 0.454545 + 0.787296i
122122 −0.500000 + 0.866025i −0.0452679 + 0.0784063i
123123 0 0
124124 −4.00000 6.92820i −0.359211 0.622171i
125125 0 0
126126 0 0
127127 −6.00000 −0.532414 −0.266207 0.963916i 0.585770π-0.585770\pi
−0.266207 + 0.963916i 0.585770π0.585770\pi
128128 0.500000 + 0.866025i 0.0441942 + 0.0765466i
129129 0 0
130130 0 0
131131 −5.00000 8.66025i −0.436852 0.756650i 0.560593 0.828092i 0.310573π-0.310573\pi
−0.997445 + 0.0714417i 0.977240π0.977240\pi
132132 0 0
133133 0 0
134134 7.00000 0.604708
135135 0 0
136136 0.500000 0.866025i 0.0428746 0.0742611i
137137 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i 0.662010π-0.662010\pi
0.999893 0.0146279i 0.00465636π-0.00465636\pi
138138 0 0
139139 −16.0000 −1.35710 −0.678551 0.734553i 0.737392π-0.737392\pi
−0.678551 + 0.734553i 0.737392π0.737392\pi
140140 0 0
141141 0 0
142142 −4.50000 7.79423i −0.377632 0.654077i
143143 −0.500000 + 0.866025i −0.0418121 + 0.0724207i
144144 1.50000 2.59808i 0.125000 0.216506i
145145 0 0
146146 −2.00000 −0.165521
147147 0 0
148148 −8.00000 −0.657596
149149 −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i 0.301004π-0.301004\pi
−0.994847 + 0.101391i 0.967671π0.967671\pi
150150 0 0
151151 7.50000 12.9904i 0.610341 1.05714i −0.380841 0.924640i 0.624366π-0.624366\pi
0.991183 0.132502i 0.0423010π-0.0423010\pi
152152 −2.50000 4.33013i −0.202777 0.351220i
153153 −3.00000 −0.242536
154154 0 0
155155 0 0
156156 0 0
157157 3.50000 6.06218i 0.279330 0.483814i −0.691888 0.722005i 0.743221π-0.743221\pi
0.971219 + 0.238190i 0.0765542π0.0765542\pi
158158 −7.00000 + 12.1244i −0.556890 + 0.964562i
159159 0 0
160160 0 0
161161 0 0
162162 −9.00000 −0.707107
163163 −3.50000 6.06218i −0.274141 0.474826i 0.695777 0.718258i 0.255060π-0.255060\pi
−0.969918 + 0.243432i 0.921727π0.921727\pi
164164 0 0
165165 0 0
166166 4.00000 + 6.92820i 0.310460 + 0.537733i
167167 19.0000 1.47026 0.735132 0.677924i 0.237120π-0.237120\pi
0.735132 + 0.677924i 0.237120π0.237120\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 −7.50000 + 12.9904i −0.573539 + 0.993399i
172172 3.00000 5.19615i 0.228748 0.396203i
173173 7.50000 + 12.9904i 0.570214 + 0.987640i 0.996544 + 0.0830722i 0.0264732π0.0264732\pi
−0.426329 + 0.904568i 0.640193π0.640193\pi
174174 0 0
175175 0 0
176176 1.00000 0.0753778
177177 0 0
178178 8.00000 13.8564i 0.599625 1.03858i
179179 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i 0.809520π-0.809520\pi
0.900975 + 0.433872i 0.142853π0.142853\pi
180180 0 0
181181 23.0000 1.70958 0.854788 0.518977i 0.173687π-0.173687\pi
0.854788 + 0.518977i 0.173687π0.173687\pi
182182 0 0
183183 0 0
184184 1.00000 + 1.73205i 0.0737210 + 0.127688i
185185 0 0
186186 0 0
187187 −0.500000 0.866025i −0.0365636 0.0633300i
188188 −11.0000 −0.802257
189189 0 0
190190 0 0
191191 2.00000 + 3.46410i 0.144715 + 0.250654i 0.929267 0.369410i 0.120440π-0.120440\pi
−0.784552 + 0.620063i 0.787107π0.787107\pi
192192 0 0
193193 −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i 0.879318π-0.879318\pi
0.785022 + 0.619467i 0.212651π0.212651\pi
194194 −1.00000 1.73205i −0.0717958 0.124354i
195195 0 0
196196 0 0
197197 18.0000 1.28245 0.641223 0.767354i 0.278427π-0.278427\pi
0.641223 + 0.767354i 0.278427π0.278427\pi
198198 −1.50000 2.59808i −0.106600 0.184637i
199199 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i 0.718005π-0.718005\pi
0.987022 + 0.160585i 0.0513380π0.0513380\pi
200200 −2.50000 + 4.33013i −0.176777 + 0.306186i
201201 0 0
202202 18.0000 1.26648
203203 0 0
204204 0 0
205205 0 0
206206 −3.00000 + 5.19615i −0.209020 + 0.362033i
207207 3.00000 5.19615i 0.208514 0.361158i
208208 −0.500000 0.866025i −0.0346688 0.0600481i
209209 −5.00000 −0.345857
210210 0 0
211211 −2.00000 −0.137686 −0.0688428 0.997628i 0.521931π-0.521931\pi
−0.0688428 + 0.997628i 0.521931π0.521931\pi
212212 −2.50000 4.33013i −0.171701 0.297394i
213213 0 0
214214 −4.00000 + 6.92820i −0.273434 + 0.473602i
215215 0 0
216216 0 0
217217 0 0
218218 12.0000 0.812743
219219 0 0
220220 0 0
221221 −0.500000 + 0.866025i −0.0336336 + 0.0582552i
222222 0 0
223223 15.0000 1.00447 0.502237 0.864730i 0.332510π-0.332510\pi
0.502237 + 0.864730i 0.332510π0.332510\pi
224224 0 0
225225 15.0000 1.00000
226226 0.500000 + 0.866025i 0.0332595 + 0.0576072i
227227 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i 0.702957π-0.702957\pi
0.993508 + 0.113761i 0.0362899π0.0362899\pi
228228 0 0
229229 −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i 0.187717π-0.187717\pi
−0.897173 + 0.441679i 0.854383π0.854383\pi
230230 0 0
231231 0 0
232232 5.00000 0.328266
233233 −10.5000 18.1865i −0.687878 1.19144i −0.972523 0.232806i 0.925209π-0.925209\pi
0.284645 0.958633i 0.408124π-0.408124\pi
234234 −1.50000 + 2.59808i −0.0980581 + 0.169842i
235235 0 0
236236 −1.50000 2.59808i −0.0976417 0.169120i
237237 0 0
238238 0 0
239239 9.00000 0.582162 0.291081 0.956698i 0.405985π-0.405985\pi
0.291081 + 0.956698i 0.405985π0.405985\pi
240240 0 0
241241 6.00000 10.3923i 0.386494 0.669427i −0.605481 0.795860i 0.707019π-0.707019\pi
0.991975 + 0.126432i 0.0403527π0.0403527\pi
242242 −5.00000 + 8.66025i −0.321412 + 0.556702i
243243 0 0
244244 −1.00000 −0.0640184
245245 0 0
246246 0 0
247247 2.50000 + 4.33013i 0.159071 + 0.275519i
248248 4.00000 6.92820i 0.254000 0.439941i
249249 0 0
250250 0 0
251251 −26.0000 −1.64111 −0.820553 0.571571i 0.806334π-0.806334\pi
−0.820553 + 0.571571i 0.806334π0.806334\pi
252252 0 0
253253 2.00000 0.125739
254254 −3.00000 5.19615i −0.188237 0.326036i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i 0.310501π-0.310501\pi
−0.997429 + 0.0716680i 0.977168π0.977168\pi
258258 0 0
259259 0 0
260260 0 0
261261 −7.50000 12.9904i −0.464238 0.804084i
262262 5.00000 8.66025i 0.308901 0.535032i
263263 −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i 0.431818π0.431818\pi
−0.952517 + 0.304487i 0.901515π0.901515\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 3.50000 + 6.06218i 0.213797 + 0.370306i
269269 −2.50000 + 4.33013i −0.152428 + 0.264013i −0.932119 0.362151i 0.882042π-0.882042\pi
0.779692 + 0.626164i 0.215376π0.215376\pi
270270 0 0
271271 −9.50000 16.4545i −0.577084 0.999539i −0.995812 0.0914269i 0.970857π-0.970857\pi
0.418728 0.908112i 0.362476π-0.362476\pi
272272 1.00000 0.0606339
273273 0 0
274274 12.0000 0.724947
275275 2.50000 + 4.33013i 0.150756 + 0.261116i
276276 0 0
277277 −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i 0.409482π0.409482\pi
−0.971521 + 0.236953i 0.923851π0.923851\pi
278278 −8.00000 13.8564i −0.479808 0.831052i
279279 −24.0000 −1.43684
280280 0 0
281281 20.0000 1.19310 0.596550 0.802576i 0.296538π-0.296538\pi
0.596550 + 0.802576i 0.296538π0.296538\pi
282282 0 0
283283 −3.00000 + 5.19615i −0.178331 + 0.308879i −0.941309 0.337546i 0.890403π-0.890403\pi
0.762978 + 0.646425i 0.223737π0.223737\pi
284284 4.50000 7.79423i 0.267026 0.462502i
285285 0 0
286286 −1.00000 −0.0591312
287287 0 0
288288 3.00000 0.176777
289289 8.00000 + 13.8564i 0.470588 + 0.815083i
290290 0 0
291291 0 0
292292 −1.00000 1.73205i −0.0585206 0.101361i
293293 18.0000 1.05157 0.525786 0.850617i 0.323771π-0.323771\pi
0.525786 + 0.850617i 0.323771π0.323771\pi
294294 0 0
295295 0 0
296296 −4.00000 6.92820i −0.232495 0.402694i
297297 0 0
298298 5.00000 8.66025i 0.289642 0.501675i
299299 −1.00000 1.73205i −0.0578315 0.100167i
300300 0 0
301301 0 0
302302 15.0000 0.863153
303303 0 0
304304 2.50000 4.33013i 0.143385 0.248350i
305305 0 0
306306 −1.50000 2.59808i −0.0857493 0.148522i
307307 7.00000 0.399511 0.199756 0.979846i 0.435985π-0.435985\pi
0.199756 + 0.979846i 0.435985π0.435985\pi
308308 0 0
309309 0 0
310310 0 0
311311 16.0000 27.7128i 0.907277 1.57145i 0.0894452 0.995992i 0.471491π-0.471491\pi
0.817832 0.575458i 0.195176π-0.195176\pi
312312 0 0
313313 9.00000 + 15.5885i 0.508710 + 0.881112i 0.999949 + 0.0100869i 0.00321082π0.00321082\pi
−0.491239 + 0.871025i 0.663456π0.663456\pi
314314 7.00000 0.395033
315315 0 0
316316 −14.0000 −0.787562
317317 −13.0000 22.5167i −0.730153 1.26466i −0.956818 0.290689i 0.906116π-0.906116\pi
0.226665 0.973973i 0.427218π-0.427218\pi
318318 0 0
319319 2.50000 4.33013i 0.139973 0.242441i
320320 0 0
321321 0 0
322322 0 0
323323 −5.00000 −0.278207
324324 −4.50000 7.79423i −0.250000 0.433013i
325325 2.50000 4.33013i 0.138675 0.240192i
326326 3.50000 6.06218i 0.193847 0.335753i
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 6.00000 + 10.3923i 0.329790 + 0.571213i 0.982470 0.186421i 0.0596888π-0.0596888\pi
−0.652680 + 0.757634i 0.726355π0.726355\pi
332332 −4.00000 + 6.92820i −0.219529 + 0.380235i
333333 −12.0000 + 20.7846i −0.657596 + 1.13899i
334334 9.50000 + 16.4545i 0.519817 + 0.900349i
335335 0 0
336336 0 0
337337 15.0000 0.817102 0.408551 0.912735i 0.366034π-0.366034\pi
0.408551 + 0.912735i 0.366034π0.366034\pi
338338 0.500000 + 0.866025i 0.0271964 + 0.0471056i
339339 0 0
340340 0 0
341341 −4.00000 6.92820i −0.216612 0.375183i
342342 −15.0000 −0.811107
343343 0 0
344344 6.00000 0.323498
345345 0 0
346346 −7.50000 + 12.9904i −0.403202 + 0.698367i
347347 −2.00000 + 3.46410i −0.107366 + 0.185963i −0.914702 0.404128i 0.867575π-0.867575\pi
0.807337 + 0.590091i 0.200908π0.200908\pi
348348 0 0
349349 34.0000 1.81998 0.909989 0.414632i 0.136090π-0.136090\pi
0.909989 + 0.414632i 0.136090π0.136090\pi
350350 0 0
351351 0 0
352352 0.500000 + 0.866025i 0.0266501 + 0.0461593i
353353 −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i 0.992342π-0.992342\pi
0.520689 + 0.853746i 0.325675π0.325675\pi
354354 0 0
355355 0 0
356356 16.0000 0.847998
357357 0 0
358358 2.00000 0.105703
359359 8.00000 + 13.8564i 0.422224 + 0.731313i 0.996157 0.0875892i 0.0279163π-0.0279163\pi
−0.573933 + 0.818902i 0.694583π0.694583\pi
360360 0 0
361361 −3.00000 + 5.19615i −0.157895 + 0.273482i
362362 11.5000 + 19.9186i 0.604427 + 1.04690i
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 −5.00000 + 8.66025i −0.260998 + 0.452062i −0.966507 0.256639i 0.917385π-0.917385\pi
0.705509 + 0.708700i 0.250718π0.250718\pi
368368 −1.00000 + 1.73205i −0.0521286 + 0.0902894i
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 −15.5000 26.8468i −0.802560 1.39007i −0.917926 0.396751i 0.870138π-0.870138\pi
0.115367 0.993323i 0.463196π-0.463196\pi
374374 0.500000 0.866025i 0.0258544 0.0447811i
375375 0 0
376376 −5.50000 9.52628i −0.283641 0.491280i
377377 −5.00000 −0.257513
378378 0 0
379379 −4.00000 −0.205466 −0.102733 0.994709i 0.532759π-0.532759\pi
−0.102733 + 0.994709i 0.532759π0.532759\pi
380380 0 0
381381 0 0
382382 −2.00000 + 3.46410i −0.102329 + 0.177239i
383383 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i 0.0434398π0.0434398\pi
−0.377531 + 0.925997i 0.623227π0.623227\pi
384384 0 0
385385 0 0
386386 −4.00000 −0.203595
387387 −9.00000 15.5885i −0.457496 0.792406i
388388 1.00000 1.73205i 0.0507673 0.0879316i
389389 9.50000 16.4545i 0.481669 0.834275i −0.518110 0.855314i 0.673364π-0.673364\pi
0.999779 + 0.0210389i 0.00669738π0.00669738\pi
390390 0 0
391391 2.00000 0.101144
392392 0 0
393393 0 0
394394 9.00000 + 15.5885i 0.453413 + 0.785335i
395395 0 0
396396 1.50000 2.59808i 0.0753778 0.130558i
397397 −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i 0.315848π-0.315848\pi
−0.998492 + 0.0549046i 0.982515π0.982515\pi
398398 10.0000 0.501255
399399 0 0
400400 −5.00000 −0.250000
401401 −19.0000 32.9090i −0.948815 1.64340i −0.747927 0.663781i 0.768951π-0.768951\pi
−0.200888 0.979614i 0.564383π-0.564383\pi
402402 0 0
403403 −4.00000 + 6.92820i −0.199254 + 0.345118i
404404 9.00000 + 15.5885i 0.447767 + 0.775555i
405405 0 0
406406 0 0
407407 −8.00000 −0.396545
408408 0 0
409409 18.0000 31.1769i 0.890043 1.54160i 0.0502202 0.998738i 0.484008π-0.484008\pi
0.839823 0.542861i 0.182659π-0.182659\pi
410410 0 0
411411 0 0
412412 −6.00000 −0.295599
413413 0 0
414414 6.00000 0.294884
415415 0 0
416416 0.500000 0.866025i 0.0245145 0.0424604i
417417 0 0
418418 −2.50000 4.33013i −0.122279 0.211793i
419419 −6.00000 −0.293119 −0.146560 0.989202i 0.546820π-0.546820\pi
−0.146560 + 0.989202i 0.546820π0.546820\pi
420420 0 0
421421 −2.00000 −0.0974740 −0.0487370 0.998812i 0.515520π-0.515520\pi
−0.0487370 + 0.998812i 0.515520π0.515520\pi
422422 −1.00000 1.73205i −0.0486792 0.0843149i
423423 −16.5000 + 28.5788i −0.802257 + 1.38955i
424424 2.50000 4.33013i 0.121411 0.210290i
425425 2.50000 + 4.33013i 0.121268 + 0.210042i
426426 0 0
427427 0 0
428428 −8.00000 −0.386695
429429 0 0
430430 0 0
431431 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
432432 0 0
433433 −5.00000 −0.240285 −0.120142 0.992757i 0.538335π-0.538335\pi
−0.120142 + 0.992757i 0.538335π0.538335\pi
434434 0 0
435435 0 0
436436 6.00000 + 10.3923i 0.287348 + 0.497701i
437437 5.00000 8.66025i 0.239182 0.414276i
438438 0 0
439439 11.0000 + 19.0526i 0.525001 + 0.909329i 0.999576 + 0.0291138i 0.00926853π0.00926853\pi
−0.474575 + 0.880215i 0.657398π0.657398\pi
440440 0 0
441441 0 0
442442 −1.00000 −0.0475651
443443 −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i 0.258683π-0.258683\pi
−0.972626 + 0.232377i 0.925350π0.925350\pi
444444 0 0
445445 0 0
446446 7.50000 + 12.9904i 0.355135 + 0.615112i
447447 0 0
448448 0 0
449449 36.0000 1.69895 0.849473 0.527633i 0.176920π-0.176920\pi
0.849473 + 0.527633i 0.176920π0.176920\pi
450450 7.50000 + 12.9904i 0.353553 + 0.612372i
451451 0 0
452452 −0.500000 + 0.866025i −0.0235180 + 0.0407344i
453453 0 0
454454 12.0000 0.563188
455455 0 0
456456 0 0
457457 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i 0.00537742π0.00537742\pi
−0.485299 + 0.874348i 0.661289π0.661289\pi
458458 1.00000 1.73205i 0.0467269 0.0809334i
459459 0 0
460460 0 0
461461 −36.0000 −1.67669 −0.838344 0.545142i 0.816476π-0.816476\pi
−0.838344 + 0.545142i 0.816476π0.816476\pi
462462 0 0
463463 24.0000 1.11537 0.557687 0.830051i 0.311689π-0.311689\pi
0.557687 + 0.830051i 0.311689π0.311689\pi
464464 2.50000 + 4.33013i 0.116060 + 0.201021i
465465 0 0
466466 10.5000 18.1865i 0.486403 0.842475i
467467 −21.0000 36.3731i −0.971764 1.68314i −0.690225 0.723595i 0.742488π-0.742488\pi
−0.281539 0.959550i 0.590845π-0.590845\pi
468468 −3.00000 −0.138675
469469 0 0
470470 0 0
471471 0 0
472472 1.50000 2.59808i 0.0690431 0.119586i
473473 3.00000 5.19615i 0.137940 0.238919i
474474 0 0
475475 25.0000 1.14708
476476 0 0
477477 −15.0000 −0.686803
478478 4.50000 + 7.79423i 0.205825 + 0.356500i
479479 −18.5000 + 32.0429i −0.845287 + 1.46408i 0.0400855 + 0.999196i 0.487237π0.487237\pi
−0.885372 + 0.464883i 0.846096π0.846096\pi
480480 0 0
481481 4.00000 + 6.92820i 0.182384 + 0.315899i
482482 12.0000 0.546585
483483 0 0
484484 −10.0000 −0.454545
485485 0 0
486486 0 0
487487 −18.5000 + 32.0429i −0.838315 + 1.45200i 0.0529875 + 0.998595i 0.483126π0.483126\pi
−0.891303 + 0.453409i 0.850208π0.850208\pi
488488 −0.500000 0.866025i −0.0226339 0.0392031i
489489 0 0
490490 0 0
491491 −26.0000 −1.17336 −0.586682 0.809818i 0.699566π-0.699566\pi
−0.586682 + 0.809818i 0.699566π0.699566\pi
492492 0 0
493493 2.50000 4.33013i 0.112594 0.195019i
494494 −2.50000 + 4.33013i −0.112480 + 0.194822i
495495 0 0
496496 8.00000 0.359211
497497 0 0
498498 0 0
499499 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i 0.0874801π0.0874801\pi
−0.246214 + 0.969216i 0.579187π0.579187\pi
500500 0 0
501501 0 0
502502 −13.0000 22.5167i −0.580218 1.00497i
503503 −20.0000 −0.891756 −0.445878 0.895094i 0.647108π-0.647108\pi
−0.445878 + 0.895094i 0.647108π0.647108\pi
504504 0 0
505505 0 0
506506 1.00000 + 1.73205i 0.0444554 + 0.0769991i
507507 0 0
508508 3.00000 5.19615i 0.133103 0.230542i
509509 −6.00000 10.3923i −0.265945 0.460631i 0.701866 0.712309i 0.252351π-0.252351\pi
−0.967811 + 0.251679i 0.919017π0.919017\pi
510510 0 0
511511 0 0
512512 −1.00000 −0.0441942
513513 0 0
514514 7.00000 12.1244i 0.308757 0.534782i
515515 0 0
516516 0 0
517517 −11.0000 −0.483779
518518 0 0
519519 0 0
520520 0 0
521521 −7.00000 + 12.1244i −0.306676 + 0.531178i −0.977633 0.210318i 0.932550π-0.932550\pi
0.670957 + 0.741496i 0.265883π0.265883\pi
522522 7.50000 12.9904i 0.328266 0.568574i
523523 13.0000 + 22.5167i 0.568450 + 0.984585i 0.996719 + 0.0809336i 0.0257902π0.0257902\pi
−0.428269 + 0.903651i 0.640876π0.640876\pi
524524 10.0000 0.436852
525525 0 0
526526 −24.0000 −1.04645
527527 −4.00000 6.92820i −0.174243 0.301797i
528528 0 0
529529 9.50000 16.4545i 0.413043 0.715412i
530530 0 0
531531 −9.00000 −0.390567
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 −3.50000 + 6.06218i −0.151177 + 0.261846i
537537 0 0
538538 −5.00000 −0.215565
539539 0 0
540540 0 0
541541 12.0000 + 20.7846i 0.515920 + 0.893600i 0.999829 + 0.0184818i 0.00588327π0.00588327\pi
−0.483909 + 0.875118i 0.660783π0.660783\pi
542542 9.50000 16.4545i 0.408060 0.706781i
543543 0 0
544544 0.500000 + 0.866025i 0.0214373 + 0.0371305i
545545 0 0
546546 0 0
547547 −38.0000 −1.62476 −0.812381 0.583127i 0.801829π-0.801829\pi
−0.812381 + 0.583127i 0.801829π0.801829\pi
548548 6.00000 + 10.3923i 0.256307 + 0.443937i
549549 −1.50000 + 2.59808i −0.0640184 + 0.110883i
550550 −2.50000 + 4.33013i −0.106600 + 0.184637i
551551 −12.5000 21.6506i −0.532518 0.922348i
552552 0 0
553553 0 0
554554 −23.0000 −0.977176
555555 0 0
556556 8.00000 13.8564i 0.339276 0.587643i
557557 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i 0.614098π-0.614098\pi
0.986394 0.164399i 0.0525683π-0.0525683\pi
558558 −12.0000 20.7846i −0.508001 0.879883i
559559 −6.00000 −0.253773
560560 0 0
561561 0 0
562562 10.0000 + 17.3205i 0.421825 + 0.730622i
563563 −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i 0.860196π-0.860196\pi
0.820798 + 0.571218i 0.193529π0.193529\pi
564564 0 0
565565 0 0
566566 −6.00000 −0.252199
567567 0 0
568568 9.00000 0.377632
569569 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i 0.0648579π-0.0648579\pi
−0.664897 + 0.746935i 0.731525π0.731525\pi
570570 0 0
571571 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i 0.460975π-0.460975\pi
0.798379 0.602155i 0.205691π-0.205691\pi
572572 −0.500000 0.866025i −0.0209061 0.0362103i
573573 0 0
574574 0 0
575575 −10.0000 −0.417029
576576 1.50000 + 2.59808i 0.0625000 + 0.108253i
577577 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i 0.739208π-0.739208\pi
0.974144 + 0.225927i 0.0725410π0.0725410\pi
578578 −8.00000 + 13.8564i −0.332756 + 0.576351i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 −2.50000 4.33013i −0.103539 0.179336i
584584 1.00000 1.73205i 0.0413803 0.0716728i
585585 0 0
586586 9.00000 + 15.5885i 0.371787 + 0.643953i
587587 −33.0000 −1.36206 −0.681028 0.732257i 0.738467π-0.738467\pi
−0.681028 + 0.732257i 0.738467π0.738467\pi
588588 0 0
589589 −40.0000 −1.64817
590590 0 0
591591 0 0
592592 4.00000 6.92820i 0.164399 0.284747i
593593 −8.00000 13.8564i −0.328521 0.569014i 0.653698 0.756756i 0.273217π-0.273217\pi
−0.982219 + 0.187741i 0.939883π0.939883\pi
594594 0 0
595595 0 0
596596 10.0000 0.409616
597597 0 0
598598 1.00000 1.73205i 0.0408930 0.0708288i
599599 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
600600 0 0
601601 −17.0000 −0.693444 −0.346722 0.937968i 0.612705π-0.612705\pi
−0.346722 + 0.937968i 0.612705π0.612705\pi
602602 0 0
603603 21.0000 0.855186
604604 7.50000 + 12.9904i 0.305171 + 0.528571i
605605 0 0
606606 0 0
607607 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i 0.0193454π-0.0193454\pi
−0.551678 + 0.834058i 0.686012π0.686012\pi
608608 5.00000 0.202777
609609 0 0
610610 0 0
611611 5.50000 + 9.52628i 0.222506 + 0.385392i
612612 1.50000 2.59808i 0.0606339 0.105021i
613613 −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i 0.938064π-0.938064\pi
0.658012 + 0.753007i 0.271397π0.271397\pi
614614 3.50000 + 6.06218i 0.141249 + 0.244650i
615615 0 0
616616 0 0
617617 −18.0000 −0.724653 −0.362326 0.932051i 0.618017π-0.618017\pi
−0.362326 + 0.932051i 0.618017π0.618017\pi
618618 0 0
619619 −18.0000 + 31.1769i −0.723481 + 1.25311i 0.236115 + 0.971725i 0.424126π0.424126\pi
−0.959596 + 0.281381i 0.909208π0.909208\pi
620620 0 0
621621 0 0
622622 32.0000 1.28308
623623 0 0
624624 0 0
625625 −12.5000 21.6506i −0.500000 0.866025i
626626 −9.00000 + 15.5885i −0.359712 + 0.623040i
627627 0 0
628628 3.50000 + 6.06218i 0.139665 + 0.241907i
629629 −8.00000 −0.318981
630630 0 0
631631 −8.00000 −0.318475 −0.159237 0.987240i 0.550904π-0.550904\pi
−0.159237 + 0.987240i 0.550904π0.550904\pi
632632 −7.00000 12.1244i −0.278445 0.482281i
633633 0 0
634634 13.0000 22.5167i 0.516296 0.894251i
635635 0 0
636636 0 0
637637 0 0
638638 5.00000 0.197952
639639 −13.5000 23.3827i −0.534052 0.925005i
640640 0 0
641641 −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i 0.949015π-0.949015\pi
0.631721 + 0.775196i 0.282349π0.282349\pi
642642 0 0
643643 −21.0000 −0.828159 −0.414080 0.910241i 0.635896π-0.635896\pi
−0.414080 + 0.910241i 0.635896π0.635896\pi
644644 0 0
645645 0 0
646646 −2.50000 4.33013i −0.0983612 0.170367i
647647 −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i 0.948453π-0.948453\pi
0.633090 + 0.774078i 0.281786π0.281786\pi
648648 4.50000 7.79423i 0.176777 0.306186i
649649 −1.50000 2.59808i −0.0588802 0.101983i
650650 5.00000 0.196116
651651 0 0
652652 7.00000 0.274141
653653 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i 0.129211π-0.129211\pi
−0.801337 + 0.598213i 0.795878π0.795878\pi
654654 0 0
655655 0 0
656656 0 0
657657 −6.00000 −0.234082
658658 0 0
659659 −40.0000 −1.55818 −0.779089 0.626913i 0.784318π-0.784318\pi
−0.779089 + 0.626913i 0.784318π0.784318\pi
660660 0 0
661661 −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i 0.380480π0.380480\pi
−0.989051 + 0.147573i 0.952854π0.952854\pi
662662 −6.00000 + 10.3923i −0.233197 + 0.403908i
663663 0 0
664664 −8.00000 −0.310460
665665 0 0
666666 −24.0000 −0.929981
667667 5.00000 + 8.66025i 0.193601 + 0.335326i
668668 −9.50000 + 16.4545i −0.367566 + 0.636643i
669669 0 0
670670 0 0
671671 −1.00000 −0.0386046
672672 0 0
673673 6.00000 0.231283 0.115642 0.993291i 0.463108π-0.463108\pi
0.115642 + 0.993291i 0.463108π0.463108\pi
674674 7.50000 + 12.9904i 0.288889 + 0.500371i
675675 0 0
676676 −0.500000 + 0.866025i −0.0192308 + 0.0333087i
677677 −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i 0.993028π-0.993028\pi
0.480913 0.876768i 0.340305π-0.340305\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 4.00000 6.92820i 0.153168 0.265295i
683683 24.0000 41.5692i 0.918334 1.59060i 0.116390 0.993204i 0.462868π-0.462868\pi
0.801945 0.597398i 0.203799π-0.203799\pi
684684 −7.50000 12.9904i −0.286770 0.496700i
685685 0 0
686686 0 0
687687 0 0
688688 3.00000 + 5.19615i 0.114374 + 0.198101i
689689 −2.50000 + 4.33013i −0.0952424 + 0.164965i
690690 0 0
691691 7.50000 + 12.9904i 0.285313 + 0.494177i 0.972685 0.232128i 0.0745690π-0.0745690\pi
−0.687372 + 0.726306i 0.741236π0.741236\pi
692692 −15.0000 −0.570214
693693 0 0
694694 −4.00000 −0.151838
695695 0 0
696696 0 0
697697 0 0
698698 17.0000 + 29.4449i 0.643459 + 1.11450i
699699 0 0
700700 0 0
701701 30.0000 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
702702 0 0
703703 −20.0000 + 34.6410i −0.754314 + 1.30651i
704704 −0.500000 + 0.866025i −0.0188445 + 0.0326396i
705705 0 0
706706 −18.0000 −0.677439
707707 0 0
708708 0 0
709709 −1.00000 1.73205i −0.0375558 0.0650485i 0.846637 0.532172i 0.178624π-0.178624\pi
−0.884192 + 0.467123i 0.845291π0.845291\pi
710710 0 0
711711 −21.0000 + 36.3731i −0.787562 + 1.36410i
712712 8.00000 + 13.8564i 0.299813 + 0.519291i
713713 16.0000 0.599205
714714 0 0
715715 0 0
716716 1.00000 + 1.73205i 0.0373718 + 0.0647298i
717717 0 0
718718 −8.00000 + 13.8564i −0.298557 + 0.517116i
719719 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i 0.0223039π0.0223039\pi
−0.438141 + 0.898906i 0.644363π0.644363\pi
720720 0 0
721721 0 0
722722 −6.00000 −0.223297
723723 0 0
724724 −11.5000 + 19.9186i −0.427394 + 0.740268i
725725 −12.5000 + 21.6506i −0.464238 + 0.804084i
726726 0 0
727727 4.00000 0.148352 0.0741759 0.997245i 0.476367π-0.476367\pi
0.0741759 + 0.997245i 0.476367π0.476367\pi
728728 0 0
729729 −27.0000 −1.00000
730730 0 0
731731 3.00000 5.19615i 0.110959 0.192187i
732732 0 0
733733 13.0000 + 22.5167i 0.480166 + 0.831672i 0.999741 0.0227529i 0.00724310π-0.00724310\pi
−0.519575 + 0.854425i 0.673910π0.673910\pi
734734 −10.0000 −0.369107
735735 0 0
736736 −2.00000 −0.0737210
737737 3.50000 + 6.06218i 0.128924 + 0.223303i
738738 0 0
739739 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i 0.809894π-0.809894\pi
0.900464 + 0.434930i 0.143227π0.143227\pi
740740 0 0
741741 0 0
742742 0 0
743743 −27.0000 −0.990534 −0.495267 0.868741i 0.664930π-0.664930\pi
−0.495267 + 0.868741i 0.664930π0.664930\pi
744744 0 0
745745 0 0
746746 15.5000 26.8468i 0.567495 0.982931i
747747 12.0000 + 20.7846i 0.439057 + 0.760469i
748748 1.00000 0.0365636
749749 0 0
750750 0 0
751751 −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i 0.995991π-0.995991\pi
0.489053 0.872254i 0.337342π-0.337342\pi
752752 5.50000 9.52628i 0.200564 0.347388i
753753 0 0
754754 −2.50000 4.33013i −0.0910446 0.157694i
755755 0 0
756756 0 0
757757 33.0000 1.19941 0.599703 0.800223i 0.295286π-0.295286\pi
0.599703 + 0.800223i 0.295286π0.295286\pi
758758 −2.00000 3.46410i −0.0726433 0.125822i
759759 0 0
760760 0 0
761761 −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i 0.830786π-0.830786\pi
−0.00800331 0.999968i 0.502548π-0.502548\pi
762762 0 0
763763 0 0
764764 −4.00000 −0.144715
765765 0 0
766766 −12.0000 + 20.7846i −0.433578 + 0.750978i
767767 −1.50000 + 2.59808i −0.0541619 + 0.0938111i
768768 0 0
769769 46.0000 1.65880 0.829401 0.558653i 0.188682π-0.188682\pi
0.829401 + 0.558653i 0.188682π0.188682\pi
770770 0 0
771771 0 0
772772 −2.00000 3.46410i −0.0719816 0.124676i
773773 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i 0.775776π-0.775776\pi
0.941825 + 0.336104i 0.109109π0.109109\pi
774774 9.00000 15.5885i 0.323498 0.560316i
775775 20.0000 + 34.6410i 0.718421 + 1.24434i
776776 2.00000 0.0717958
777777 0 0
778778 19.0000 0.681183
779779 0 0
780780 0 0
781781 4.50000 7.79423i 0.161023 0.278899i
782782 1.00000 + 1.73205i 0.0357599 + 0.0619380i
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 5.50000 9.52628i 0.196054 0.339575i −0.751192 0.660084i 0.770521π-0.770521\pi
0.947245 + 0.320509i 0.103854π0.103854\pi
788788 −9.00000 + 15.5885i −0.320612 + 0.555316i
789789 0 0
790790 0 0
791791 0 0
792792 3.00000 0.106600
793793 0.500000 + 0.866025i 0.0177555 + 0.0307535i
794794 9.00000 15.5885i 0.319398 0.553214i
795795 0 0
796796 5.00000 + 8.66025i 0.177220 + 0.306955i
797797 −54.0000 −1.91278 −0.956389 0.292096i 0.905647π-0.905647\pi
−0.956389 + 0.292096i 0.905647π0.905647\pi
798798 0 0
799799 −11.0000 −0.389152
800800 −2.50000 4.33013i −0.0883883 0.153093i
801801 24.0000 41.5692i 0.847998 1.46878i
802802 19.0000 32.9090i 0.670913 1.16206i
803803 −1.00000 1.73205i −0.0352892 0.0611227i
804804 0 0
805805 0 0
806806 −8.00000 −0.281788
807807 0 0
808808 −9.00000 + 15.5885i −0.316619 + 0.548400i
809809 −4.50000 + 7.79423i −0.158212 + 0.274030i −0.934224 0.356687i 0.883906π-0.883906\pi
0.776012 + 0.630718i 0.217239π0.217239\pi
810810 0 0
811811 20.0000 0.702295 0.351147 0.936320i 0.385792π-0.385792\pi
0.351147 + 0.936320i 0.385792π0.385792\pi
812812 0 0
813813 0 0
814814 −4.00000 6.92820i −0.140200 0.242833i
815815 0 0
816816 0 0
817817 −15.0000 25.9808i −0.524784 0.908952i
818818 36.0000 1.25871
819819 0 0
820820 0 0
821821 6.00000 + 10.3923i 0.209401 + 0.362694i 0.951526 0.307568i 0.0995151π-0.0995151\pi
−0.742125 + 0.670262i 0.766182π0.766182\pi
822822 0 0
823823 −18.0000 + 31.1769i −0.627441 + 1.08676i 0.360623 + 0.932712i 0.382564π0.382564\pi
−0.988063 + 0.154047i 0.950769π0.950769\pi
824824 −3.00000 5.19615i −0.104510 0.181017i
825825 0 0
826826 0 0
827827 −33.0000 −1.14752 −0.573761 0.819023i 0.694516π-0.694516\pi
−0.573761 + 0.819023i 0.694516π0.694516\pi
828828 3.00000 + 5.19615i 0.104257 + 0.180579i
829829 13.5000 23.3827i 0.468874 0.812114i −0.530493 0.847690i 0.677993π-0.677993\pi
0.999367 + 0.0355753i 0.0113264π0.0113264\pi
830830 0 0
831831 0 0
832832 1.00000 0.0346688
833833 0 0
834834 0 0
835835 0 0
836836 2.50000 4.33013i 0.0864643 0.149761i
837837 0 0
838838 −3.00000 5.19615i −0.103633 0.179498i
839839 37.0000 1.27738 0.638691 0.769463i 0.279476π-0.279476\pi
0.638691 + 0.769463i 0.279476π0.279476\pi
840840 0 0
841841 −4.00000 −0.137931
842842 −1.00000 1.73205i −0.0344623 0.0596904i
843843 0 0
844844 1.00000 1.73205i 0.0344214 0.0596196i
845845 0 0
846846 −33.0000 −1.13456
847847 0 0
848848 5.00000 0.171701
849849 0 0
850850 −2.50000 + 4.33013i −0.0857493 + 0.148522i
851851 8.00000 13.8564i 0.274236 0.474991i
852852 0 0
853853 −38.0000 −1.30110 −0.650548 0.759465i 0.725461π-0.725461\pi
−0.650548 + 0.759465i 0.725461π0.725461\pi
854854 0 0
855855 0 0
856856 −4.00000 6.92820i −0.136717 0.236801i
857857 −21.5000 + 37.2391i −0.734426 + 1.27206i 0.220549 + 0.975376i 0.429215π0.429215\pi
−0.954975 + 0.296687i 0.904118π0.904118\pi
858858 0 0
859859 −20.0000 34.6410i −0.682391 1.18194i −0.974249 0.225475i 0.927607π-0.927607\pi
0.291858 0.956462i 0.405727π-0.405727\pi
860860 0 0
861861 0 0
862862 0 0
863863 6.00000 + 10.3923i 0.204242 + 0.353758i 0.949891 0.312581i 0.101194π-0.101194\pi
−0.745649 + 0.666339i 0.767860π0.767860\pi
864864 0 0
865865 0 0
866866 −2.50000 4.33013i −0.0849535 0.147144i
867867 0 0
868868 0 0
869869 −14.0000 −0.474917
870870 0 0
871871 3.50000 6.06218i 0.118593 0.205409i
872872 −6.00000 + 10.3923i −0.203186 + 0.351928i
873873 −3.00000 5.19615i −0.101535 0.175863i
874874 10.0000 0.338255
875875 0 0
876876 0 0
877877 16.0000 + 27.7128i 0.540282 + 0.935795i 0.998888 + 0.0471555i 0.0150156π0.0150156\pi
−0.458606 + 0.888640i 0.651651π0.651651\pi
878878 −11.0000 + 19.0526i −0.371232 + 0.642993i
879879 0 0
880880 0 0
881881 −42.0000 −1.41502 −0.707508 0.706705i 0.750181π-0.750181\pi
−0.707508 + 0.706705i 0.750181π0.750181\pi
882882 0 0
883883 24.0000 0.807664 0.403832 0.914833i 0.367678π-0.367678\pi
0.403832 + 0.914833i 0.367678π0.367678\pi
884884 −0.500000 0.866025i −0.0168168 0.0291276i
885885 0 0
886886 6.00000 10.3923i 0.201574 0.349136i
887887 9.00000 + 15.5885i 0.302190 + 0.523409i 0.976632 0.214919i 0.0689488π-0.0689488\pi
−0.674441 + 0.738328i 0.735615π0.735615\pi
888888 0 0
889889 0 0
890890 0 0
891891 −4.50000 7.79423i −0.150756 0.261116i
892892 −7.50000 + 12.9904i −0.251119 + 0.434950i
893893 −27.5000 + 47.6314i −0.920252 + 1.59392i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 18.0000 + 31.1769i 0.600668 + 1.04039i
899899 20.0000 34.6410i 0.667037 1.15534i
900900 −7.50000 + 12.9904i −0.250000 + 0.433013i
901901 −2.50000 4.33013i −0.0832871 0.144257i
902902 0 0
903903 0 0
904904 −1.00000 −0.0332595
905905 0 0
906906 0 0
907907 23.0000 39.8372i 0.763702 1.32277i −0.177227 0.984170i 0.556713π-0.556713\pi
0.940930 0.338602i 0.109954π-0.109954\pi
908908 6.00000 + 10.3923i 0.199117 + 0.344881i
909909 54.0000 1.79107
910910 0 0
911911 34.0000 1.12647 0.563235 0.826297i 0.309557π-0.309557\pi
0.563235 + 0.826297i 0.309557π0.309557\pi
912912 0 0
913913 −4.00000 + 6.92820i −0.132381 + 0.229290i
914914 −11.0000 + 19.0526i −0.363848 + 0.630203i
915915 0 0
916916 2.00000 0.0660819
917917 0 0
918918 0 0
919919 19.0000 + 32.9090i 0.626752 + 1.08557i 0.988199 + 0.153174i 0.0489495π0.0489495\pi
−0.361447 + 0.932393i 0.617717π0.617717\pi
920920 0 0
921921 0 0
922922 −18.0000 31.1769i −0.592798 1.02676i
923923 −9.00000 −0.296239
924924 0 0
925925 40.0000 1.31519
926926 12.0000 + 20.7846i 0.394344 + 0.683025i
927927 −9.00000 + 15.5885i −0.295599 + 0.511992i
928928 −2.50000 + 4.33013i −0.0820665 + 0.142143i
929929 23.0000 + 39.8372i 0.754606 + 1.30702i 0.945570 + 0.325418i 0.105505π0.105505\pi
−0.190965 + 0.981597i 0.561162π0.561162\pi
930930 0 0
931931 0 0
932932 21.0000 0.687878
933933 0 0
934934 21.0000 36.3731i 0.687141 1.19016i
935935 0 0
936936 −1.50000 2.59808i −0.0490290 0.0849208i
937937 41.0000 1.33941 0.669706 0.742627i 0.266420π-0.266420\pi
0.669706 + 0.742627i 0.266420π0.266420\pi
938938 0 0
939939 0 0
940940 0 0
941941 6.00000 10.3923i 0.195594 0.338779i −0.751501 0.659732i 0.770670π-0.770670\pi
0.947095 + 0.320953i 0.104003π0.104003\pi
942942 0 0
943943 0 0
944944 3.00000 0.0976417
945945 0 0
946946 6.00000 0.195077
947947 3.50000 + 6.06218i 0.113735 + 0.196994i 0.917273 0.398258i 0.130385π-0.130385\pi
−0.803539 + 0.595253i 0.797052π0.797052\pi
948948 0 0
949949 −1.00000 + 1.73205i −0.0324614 + 0.0562247i
950950 12.5000 + 21.6506i 0.405554 + 0.702439i
951951 0 0
952952 0 0
953953 9.00000 0.291539 0.145769 0.989319i 0.453434π-0.453434\pi
0.145769 + 0.989319i 0.453434π0.453434\pi
954954 −7.50000 12.9904i −0.242821 0.420579i
955955 0 0
956956 −4.50000 + 7.79423i −0.145540 + 0.252083i
957957 0 0
958958 −37.0000 −1.19542
959959 0 0
960960 0 0
961961 −16.5000 28.5788i −0.532258 0.921898i
962962 −4.00000 + 6.92820i −0.128965 + 0.223374i
963963 −12.0000 + 20.7846i −0.386695 + 0.669775i
964964 6.00000 + 10.3923i 0.193247 + 0.334714i
965965 0 0
966966 0 0
967967 23.0000 0.739630 0.369815 0.929105i 0.379421π-0.379421\pi
0.369815 + 0.929105i 0.379421π0.379421\pi
968968 −5.00000 8.66025i −0.160706 0.278351i
969969 0 0
970970 0 0
971971 −30.0000 51.9615i −0.962746 1.66752i −0.715553 0.698558i 0.753825π-0.753825\pi
−0.247193 0.968966i 0.579508π-0.579508\pi
972972 0 0
973973 0 0
974974 −37.0000 −1.18556
975975 0 0
976976 0.500000 0.866025i 0.0160046 0.0277208i
977977 −5.00000 + 8.66025i −0.159964 + 0.277066i −0.934856 0.355028i 0.884471π-0.884471\pi
0.774891 + 0.632094i 0.217805π0.217805\pi
978978 0 0
979979 16.0000 0.511362
980980 0 0
981981 36.0000 1.14939
982982 −13.0000 22.5167i −0.414847 0.718536i
983983 6.50000 11.2583i 0.207318 0.359085i −0.743551 0.668679i 0.766860π-0.766860\pi
0.950869 + 0.309594i 0.100193π0.100193\pi
984984 0 0
985985 0 0
986986 5.00000 0.159232
987987 0 0
988988 −5.00000 −0.159071
989989 6.00000 + 10.3923i 0.190789 + 0.330456i
990990 0 0
991991 14.0000 24.2487i 0.444725 0.770286i −0.553308 0.832977i 0.686635π-0.686635\pi
0.998033 + 0.0626908i 0.0199682π0.0199682\pi
992992 4.00000 + 6.92820i 0.127000 + 0.219971i
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 −7.50000 + 12.9904i −0.237527 + 0.411409i −0.960004 0.279986i 0.909670π-0.909670\pi
0.722477 + 0.691395i 0.243004π0.243004\pi
998998 −16.0000 + 27.7128i −0.506471 + 0.877234i
999999 0 0
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 1274.2.f.q.1145.1 2
7.2 even 3 inner 1274.2.f.q.79.1 2
7.3 odd 6 1274.2.a.e.1.1 1
7.4 even 3 1274.2.a.f.1.1 1
7.5 odd 6 182.2.f.a.79.1 yes 2
7.6 odd 2 182.2.f.a.53.1 2
21.5 even 6 1638.2.j.c.1171.1 2
21.20 even 2 1638.2.j.c.235.1 2
28.19 even 6 1456.2.r.f.625.1 2
28.27 even 2 1456.2.r.f.417.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.f.a.53.1 2 7.6 odd 2
182.2.f.a.79.1 yes 2 7.5 odd 6
1274.2.a.e.1.1 1 7.3 odd 6
1274.2.a.f.1.1 1 7.4 even 3
1274.2.f.q.79.1 2 7.2 even 3 inner
1274.2.f.q.1145.1 2 1.1 even 1 trivial
1456.2.r.f.417.1 2 28.27 even 2
1456.2.r.f.625.1 2 28.19 even 6
1638.2.j.c.235.1 2 21.20 even 2
1638.2.j.c.1171.1 2 21.5 even 6