Properties

Label 224.6.p.a.31.11
Level 224224
Weight 66
Character 224.31
Analytic conductor 35.92635.926
Analytic rank 00
Dimension 8080
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,6,Mod(31,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.31");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 224=257 224 = 2^{5} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 224.p (of order 66, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 35.925975638135.9259756381
Analytic rank: 00
Dimension: 8080
Relative dimension: 4040 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 31.11
Character χ\chi == 224.31
Dual form 224.6.p.a.159.11

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(8.16376+14.1401i)q3+(19.245211.1112i)q5+(103.00478.7217i)q7+(11.794120.4280i)q9+(230.097132.846i)q1131.5899iq13+362.837iq15+(110.876+64.0143i)q17+(1375.262382.02i)q19+(272.226+2099.15i)q21+(2222.74+1283.30i)q23+(1315.58+2278.66i)q253582.45q27+1603.73q29+(349.938+606.110i)q31+(3756.912169.05i)q33+(1107.642659.51i)q35+(2421.844194.76i)q37+(446.683+257.893i)q395910.34iq4115217.5iq43+(453.959262.093i)q45+(49.583885.8817i)q47+(4412.7916217.4i)q49+(1810.33+1045.20i)q51+(17857.430929.9i)q535904.34q55+44909.2q57+(3443.805964.84i)q59+(3111.85+1796.62i)q61+(2822.971175.72i)q63+(351.002607.953i)q65+(42290.424416.4i)q6741906.2iq6931698.2iq71+(27063.6+15625.2i)q73+(21480.237204.8i)q75+(34158.9+4429.84i)q77+(20637.0+11914.8i)q79+(32112.355620.1i)q81+18288.6q83+2845.11q85+(13092.5+22676.8i)q87+(60686.835037.5i)q89+(2486.813253.90i)q91+(5713.629896.28i)q93+(52934.230561.6i)q95+122256.iq97+6267.22iq99+O(q100)q+(-8.16376 + 14.1401i) q^{3} +(19.2452 - 11.1112i) q^{5} +(103.004 - 78.7217i) q^{7} +(-11.7941 - 20.4280i) q^{9} +(-230.097 - 132.846i) q^{11} -31.5899i q^{13} +362.837i q^{15} +(110.876 + 64.0143i) q^{17} +(-1375.26 - 2382.02i) q^{19} +(272.226 + 2099.15i) q^{21} +(-2222.74 + 1283.30i) q^{23} +(-1315.58 + 2278.66i) q^{25} -3582.45 q^{27} +1603.73 q^{29} +(-349.938 + 606.110i) q^{31} +(3756.91 - 2169.05i) q^{33} +(1107.64 - 2659.51i) q^{35} +(-2421.84 - 4194.76i) q^{37} +(446.683 + 257.893i) q^{39} -5910.34i q^{41} -15217.5i q^{43} +(-453.959 - 262.093i) q^{45} +(-49.5838 - 85.8817i) q^{47} +(4412.79 - 16217.4i) q^{49} +(-1810.33 + 1045.20i) q^{51} +(17857.4 - 30929.9i) q^{53} -5904.34 q^{55} +44909.2 q^{57} +(3443.80 - 5964.84i) q^{59} +(-3111.85 + 1796.62i) q^{61} +(-2822.97 - 1175.72i) q^{63} +(-351.002 - 607.953i) q^{65} +(-42290.4 - 24416.4i) q^{67} -41906.2i q^{69} -31698.2i q^{71} +(27063.6 + 15625.2i) q^{73} +(-21480.2 - 37204.8i) q^{75} +(-34158.9 + 4429.84i) q^{77} +(-20637.0 + 11914.8i) q^{79} +(32112.3 - 55620.1i) q^{81} +18288.6 q^{83} +2845.11 q^{85} +(-13092.5 + 22676.8i) q^{87} +(60686.8 - 35037.5i) q^{89} +(-2486.81 - 3253.90i) q^{91} +(-5713.62 - 9896.28i) q^{93} +(-52934.2 - 30561.6i) q^{95} +122256. i q^{97} +6267.22i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 80q3240q9+6856q21+27728q2515920q2928296q332152q37+35400q45+29280q4917512q53108368q57+37704q61+18216q65+157704q73+28224q77++39400q93+O(q100) 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/224Z)×\left(\mathbb{Z}/224\mathbb{Z}\right)^\times.

nn 127127 129129 197197
χ(n)\chi(n) 1-1 e(16)e\left(\frac{1}{6}\right) 11

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 0
33 −8.16376 + 14.1401i −0.523706 + 0.907085i 0.475913 + 0.879492i 0.342118π0.342118\pi
−0.999619 + 0.0275929i 0.991216π0.991216\pi
44 0 0
55 19.2452 11.1112i 0.344268 0.198763i −0.317890 0.948128i 0.602974π-0.602974\pi
0.662158 + 0.749364i 0.269641π0.269641\pi
66 0 0
77 103.004 78.7217i 0.794530 0.607224i
88 0 0
99 −11.7941 20.4280i −0.0485354 0.0840658i
1010 0 0
1111 −230.097 132.846i −0.573362 0.331031i 0.185129 0.982714i 0.440730π-0.440730\pi
−0.758491 + 0.651684i 0.774063π0.774063\pi
1212 0 0
1313 31.5899i 0.0518430i −0.999664 0.0259215i 0.991748π-0.991748\pi
0.999664 0.0259215i 0.00825199π-0.00825199\pi
1414 0 0
1515 362.837i 0.416374i
1616 0 0
1717 110.876 + 64.0143i 0.0930498 + 0.0537223i 0.545803 0.837914i 0.316225π-0.316225\pi
−0.452753 + 0.891636i 0.649558π0.649558\pi
1818 0 0
1919 −1375.26 2382.02i −0.873979 1.51378i −0.857847 0.513905i 0.828198π-0.828198\pi
−0.0161318 0.999870i 0.505135π-0.505135\pi
2020 0 0
2121 272.226 + 2099.15i 0.134704 + 1.03871i
2222 0 0
2323 −2222.74 + 1283.30i −0.876130 + 0.505834i −0.869381 0.494143i 0.835482π-0.835482\pi
−0.00674965 + 0.999977i 0.502148π0.502148\pi
2424 0 0
2525 −1315.58 + 2278.66i −0.420986 + 0.729170i
2626 0 0
2727 −3582.45 −0.945738
2828 0 0
2929 1603.73 0.354108 0.177054 0.984201i 0.443343π-0.443343\pi
0.177054 + 0.984201i 0.443343π0.443343\pi
3030 0 0
3131 −349.938 + 606.110i −0.0654014 + 0.113278i −0.896872 0.442290i 0.854166π-0.854166\pi
0.831471 + 0.555569i 0.187499π0.187499\pi
3232 0 0
3333 3756.91 2169.05i 0.600546 0.346725i
3434 0 0
3535 1107.64 2659.51i 0.152838 0.366971i
3636 0 0
3737 −2421.84 4194.76i −0.290832 0.503735i 0.683175 0.730255i 0.260599π-0.260599\pi
−0.974007 + 0.226519i 0.927265π0.927265\pi
3838 0 0
3939 446.683 + 257.893i 0.0470260 + 0.0271505i
4040 0 0
4141 5910.34i 0.549101i −0.961573 0.274551i 0.911471π-0.911471\pi
0.961573 0.274551i 0.0885291π-0.0885291\pi
4242 0 0
4343 15217.5i 1.25508i −0.778585 0.627540i 0.784062π-0.784062\pi
0.778585 0.627540i 0.215938π-0.215938\pi
4444 0 0
4545 −453.959 262.093i −0.0334184 0.0192941i
4646 0 0
4747 −49.5838 85.8817i −0.00327413 0.00567095i 0.864384 0.502833i 0.167709π-0.167709\pi
−0.867658 + 0.497162i 0.834376π0.834376\pi
4848 0 0
4949 4412.79 16217.4i 0.262557 0.964916i
5050 0 0
5151 −1810.33 + 1045.20i −0.0974614 + 0.0562694i
5252 0 0
5353 17857.4 30929.9i 0.873228 1.51248i 0.0145896 0.999894i 0.495356π-0.495356\pi
0.858638 0.512582i 0.171311π-0.171311\pi
5454 0 0
5555 −5904.34 −0.263187
5656 0 0
5757 44909.2 1.83083
5858 0 0
5959 3443.80 5964.84i 0.128798 0.223084i −0.794413 0.607378i 0.792222π-0.792222\pi
0.923211 + 0.384293i 0.125555π0.125555\pi
6060 0 0
6161 −3111.85 + 1796.62i −0.107076 + 0.0618205i −0.552582 0.833459i 0.686357π-0.686357\pi
0.445505 + 0.895279i 0.353024π0.353024\pi
6262 0 0
6363 −2822.97 1175.72i −0.0896097 0.0373209i
6464 0 0
6565 −351.002 607.953i −0.0103045 0.0178479i
6666 0 0
6767 −42290.4 24416.4i −1.15095 0.664499i −0.201829 0.979421i 0.564689π-0.564689\pi
−0.949118 + 0.314921i 0.898022π0.898022\pi
6868 0 0
6969 41906.2i 1.05963i
7070 0 0
7171 31698.2i 0.746257i −0.927780 0.373128i 0.878285π-0.878285\pi
0.927780 0.373128i 0.121715π-0.121715\pi
7272 0 0
7373 27063.6 + 15625.2i 0.594399 + 0.343176i 0.766835 0.641844i 0.221831π-0.221831\pi
−0.172436 + 0.985021i 0.555164π0.555164\pi
7474 0 0
7575 −21480.2 37204.8i −0.440946 0.763741i
7676 0 0
7777 −34158.9 + 4429.84i −0.656563 + 0.0851455i
7878 0 0
7979 −20637.0 + 11914.8i −0.372031 + 0.214792i −0.674345 0.738416i 0.735574π-0.735574\pi
0.302314 + 0.953208i 0.402241π0.402241\pi
8080 0 0
8181 32112.3 55620.1i 0.543824 0.941931i
8282 0 0
8383 18288.6 0.291398 0.145699 0.989329i 0.453457π-0.453457\pi
0.145699 + 0.989329i 0.453457π0.453457\pi
8484 0 0
8585 2845.11 0.0427121
8686 0 0
8787 −13092.5 + 22676.8i −0.185449 + 0.321206i
8888 0 0
8989 60686.8 35037.5i 0.812118 0.468876i −0.0355730 0.999367i 0.511326π-0.511326\pi
0.847691 + 0.530491i 0.177992π0.177992\pi
9090 0 0
9191 −2486.81 3253.90i −0.0314803 0.0411908i
9292 0 0
9393 −5713.62 9896.28i −0.0685021 0.118649i
9494 0 0
9595 −52934.2 30561.6i −0.601766 0.347430i
9696 0 0
9797 122256.i 1.31929i 0.751579 + 0.659644i 0.229293π0.229293\pi
−0.751579 + 0.659644i 0.770707π0.770707\pi
9898 0 0
9999 6267.22i 0.0642668i
100100 0 0
101101 −91505.7 52830.9i −0.892575 0.515329i −0.0177913 0.999842i 0.505663π-0.505663\pi
−0.874784 + 0.484513i 0.838997π0.838997\pi
102102 0 0
103103 −90044.5 155962.i −0.836304 1.44852i −0.892964 0.450127i 0.851379π-0.851379\pi
0.0566605 0.998394i 0.481955π-0.481955\pi
104104 0 0
105105 28563.1 + 37373.8i 0.252832 + 0.330822i
106106 0 0
107107 −130537. + 75365.5i −1.10223 + 0.636375i −0.936807 0.349847i 0.886234π-0.886234\pi
−0.165427 + 0.986222i 0.552900π0.552900\pi
108108 0 0
109109 −39532.1 + 68471.7i −0.318701 + 0.552007i −0.980217 0.197924i 0.936580π-0.936580\pi
0.661516 + 0.749931i 0.269913π0.269913\pi
110110 0 0
111111 79085.5 0.609241
112112 0 0
113113 100179. 0.738040 0.369020 0.929421i 0.379693π-0.379693\pi
0.369020 + 0.929421i 0.379693π0.379693\pi
114114 0 0
115115 −28518.0 + 49394.6i −0.201082 + 0.348285i
116116 0 0
117117 −645.318 + 372.575i −0.00435822 + 0.00251622i
118118 0 0
119119 16460.0 2134.60i 0.106552 0.0138181i
120120 0 0
121121 −45229.2 78339.2i −0.280837 0.486425i
122122 0 0
123123 83572.5 + 48250.6i 0.498082 + 0.287568i
124124 0 0
125125 127916.i 0.732233i
126126 0 0
127127 133657.i 0.735329i −0.929959 0.367664i 0.880158π-0.880158\pi
0.929959 0.367664i 0.119842π-0.119842\pi
128128 0 0
129129 215176. + 124232.i 1.13846 + 0.657292i
130130 0 0
131131 64841.1 + 112308.i 0.330120 + 0.571785i 0.982535 0.186077i 0.0595773π-0.0595773\pi
−0.652415 + 0.757862i 0.726244π0.726244\pi
132132 0 0
133133 −329174. 137096.i −1.61360 0.672039i
134134 0 0
135135 −68944.9 + 39805.4i −0.325588 + 0.187978i
136136 0 0
137137 23507.7 40716.5i 0.107006 0.185340i −0.807550 0.589799i 0.799207π-0.799207\pi
0.914556 + 0.404459i 0.132540π0.132540\pi
138138 0 0
139139 323808. 1.42151 0.710756 0.703439i 0.248353π-0.248353\pi
0.710756 + 0.703439i 0.248353π0.248353\pi
140140 0 0
141141 1619.16 0.00685871
142142 0 0
143143 −4196.61 + 7268.73i −0.0171616 + 0.0297248i
144144 0 0
145145 30864.0 17819.4i 0.121908 0.0703837i
146146 0 0
147147 193289. + 194792.i 0.737759 + 0.743494i
148148 0 0
149149 −88736.6 153696.i −0.327444 0.567150i 0.654560 0.756010i 0.272854π-0.272854\pi
−0.982004 + 0.188860i 0.939521π0.939521\pi
150150 0 0
151151 132002. + 76211.4i 0.471128 + 0.272006i 0.716712 0.697370i 0.245646π-0.245646\pi
−0.245584 + 0.969375i 0.578980π0.578980\pi
152152 0 0
153153 3019.97i 0.0104297i
154154 0 0
155155 15552.9i 0.0519976i
156156 0 0
157157 −269397. 155536.i −0.872254 0.503596i −0.00415732 0.999991i 0.501323π-0.501323\pi
−0.868097 + 0.496395i 0.834657π0.834657\pi
158158 0 0
159159 291567. + 505008.i 0.914629 + 1.58418i
160160 0 0
161161 −127928. + 307163.i −0.388957 + 0.933908i
162162 0 0
163163 152716. 88170.5i 0.450210 0.259929i −0.257709 0.966223i 0.582968π-0.582968\pi
0.707919 + 0.706294i 0.249634π0.249634\pi
164164 0 0
165165 48201.6 83487.6i 0.137832 0.238733i
166166 0 0
167167 469993. 1.30407 0.652035 0.758189i 0.273916π-0.273916\pi
0.652035 + 0.758189i 0.273916π0.273916\pi
168168 0 0
169169 370295. 0.997312
170170 0 0
171171 −32439.9 + 56187.6i −0.0848378 + 0.146943i
172172 0 0
173173 −674698. + 389537.i −1.71393 + 0.989540i −0.784839 + 0.619700i 0.787254π0.787254\pi
−0.929095 + 0.369841i 0.879412π0.879412\pi
174174 0 0
175175 43868.9 + 338276.i 0.108283 + 0.834981i
176176 0 0
177177 56228.8 + 97391.1i 0.134904 + 0.233661i
178178 0 0
179179 −535593. 309225.i −1.24940 0.721343i −0.278412 0.960462i 0.589808π-0.589808\pi
−0.970990 + 0.239119i 0.923141π0.923141\pi
180180 0 0
181181 178785.i 0.405635i 0.979217 + 0.202818i 0.0650098π0.0650098\pi
−0.979217 + 0.202818i 0.934990π0.934990\pi
182182 0 0
183183 58668.9i 0.129503i
184184 0 0
185185 −93217.6 53819.2i −0.200248 0.115613i
186186 0 0
187187 −17008.1 29459.0i −0.0355675 0.0616047i
188188 0 0
189189 −369008. + 282017.i −0.751418 + 0.574275i
190190 0 0
191191 9396.44 5425.04i 0.0186372 0.0107602i −0.490652 0.871355i 0.663242π-0.663242\pi
0.509290 + 0.860595i 0.329908π0.329908\pi
192192 0 0
193193 −473563. + 820235.i −0.915133 + 1.58506i −0.108427 + 0.994104i 0.534581π0.534581\pi
−0.806706 + 0.590953i 0.798752π0.798752\pi
194194 0 0
195195 11462.0 0.0215861
196196 0 0
197197 −81454.8 −0.149538 −0.0747689 0.997201i 0.523822π-0.523822\pi
−0.0747689 + 0.997201i 0.523822π0.523822\pi
198198 0 0
199199 −491764. + 851761.i −0.880287 + 1.52470i −0.0292649 + 0.999572i 0.509317π0.509317\pi
−0.851022 + 0.525130i 0.824017π0.824017\pi
200200 0 0
201201 690498. 398659.i 1.20551 0.696004i
202202 0 0
203203 165191. 126248.i 0.281350 0.215023i
204204 0 0
205205 −65671.0 113745.i −0.109141 0.189038i
206206 0 0
207207 52430.4 + 30270.7i 0.0850467 + 0.0491017i
208208 0 0
209209 730793.i 1.15725i
210210 0 0
211211 427608.i 0.661210i −0.943769 0.330605i 0.892747π-0.892747\pi
0.943769 0.330605i 0.107253π-0.107253\pi
212212 0 0
213213 448214. + 258776.i 0.676918 + 0.390819i
214214 0 0
215215 −169084. 292863.i −0.249464 0.432084i
216216 0 0
217217 11668.9 + 89979.7i 0.0168221 + 0.129716i
218218 0 0
219219 −441881. + 255120.i −0.622580 + 0.359447i
220220 0 0
221221 2022.21 3502.56i 0.00278513 0.00482398i
222222 0 0
223223 60238.8 0.0811174 0.0405587 0.999177i 0.487086π-0.487086\pi
0.0405587 + 0.999177i 0.487086π0.487086\pi
224224 0 0
225225 62064.5 0.0817310
226226 0 0
227227 27615.1 47830.8i 0.0355699 0.0616088i −0.847692 0.530488i 0.822009π-0.822009\pi
0.883262 + 0.468879i 0.155342π0.155342\pi
228228 0 0
229229 −3063.24 + 1768.56i −0.00386004 + 0.00222859i −0.501929 0.864909i 0.667376π-0.667376\pi
0.498069 + 0.867138i 0.334043π0.334043\pi
230230 0 0
231231 216227. 519172.i 0.266612 0.640150i
232232 0 0
233233 −599259. 1.03795e6i −0.723143 1.25252i −0.959734 0.280912i 0.909363π-0.909363\pi
0.236590 0.971610i 0.423970π-0.423970\pi
234234 0 0
235235 −1908.50 1101.87i −0.00225435 0.00130155i
236236 0 0
237237 389078.i 0.449952i
238238 0 0
239239 531464.i 0.601837i −0.953650 0.300918i 0.902707π-0.902707\pi
0.953650 0.300918i 0.0972932π-0.0972932\pi
240240 0 0
241241 −487249. 281313.i −0.540391 0.311995i 0.204846 0.978794i 0.434331π-0.434331\pi
−0.745237 + 0.666799i 0.767664π0.767664\pi
242242 0 0
243243 89046.0 + 154232.i 0.0967384 + 0.167556i
244244 0 0
245245 −95269.3 361137.i −0.101400 0.384377i
246246 0 0
247247 −75247.8 + 43444.3i −0.0784786 + 0.0453096i
248248 0 0
249249 −149304. + 258602.i −0.152607 + 0.264323i
250250 0 0
251251 1.06837e6 1.07037 0.535187 0.844734i 0.320241π-0.320241\pi
0.535187 + 0.844734i 0.320241π0.320241\pi
252252 0 0
253253 681926. 0.669786
254254 0 0
255255 −23226.8 + 40229.9i −0.0223686 + 0.0387435i
256256 0 0
257257 1.16285e6 671372.i 1.09822 0.634060i 0.162470 0.986714i 0.448054π-0.448054\pi
0.935754 + 0.352654i 0.114721π0.114721\pi
258258 0 0
259259 −579679. 241427.i −0.536955 0.223633i
260260 0 0
261261 −18914.6 32761.0i −0.0171868 0.0297684i
262262 0 0
263263 −1.39724e6 806697.i −1.24561 0.719153i −0.275378 0.961336i 0.588803π-0.588803\pi
−0.970231 + 0.242183i 0.922136π0.922136\pi
264264 0 0
265265 793667.i 0.694263i
266266 0 0
267267 1.14415e6i 0.982213i
268268 0 0
269269 1.89088e6 + 1.09170e6i 1.59325 + 0.919864i 0.992744 + 0.120245i 0.0383679π0.0383679\pi
0.600507 + 0.799619i 0.294965π0.294965\pi
270270 0 0
271271 203437. + 352363.i 0.168270 + 0.291452i 0.937812 0.347144i 0.112849π-0.112849\pi
−0.769542 + 0.638597i 0.779515π0.779515\pi
272272 0 0
273273 66312.0 8599.58i 0.0538500 0.00698346i
274274 0 0
275275 605422. 349541.i 0.482755 0.278719i
276276 0 0
277277 254717. 441182.i 0.199461 0.345477i −0.748893 0.662691i 0.769414π-0.769414\pi
0.948354 + 0.317215i 0.102748π0.102748\pi
278278 0 0
279279 16508.8 0.0126971
280280 0 0
281281 −1.11878e6 −0.845240 −0.422620 0.906307i 0.638889π-0.638889\pi
−0.422620 + 0.906307i 0.638889π0.638889\pi
282282 0 0
283283 −134959. + 233755.i −0.100169 + 0.173498i −0.911754 0.410736i 0.865272π-0.865272\pi
0.811585 + 0.584234i 0.198605π0.198605\pi
284284 0 0
285285 864285. 498995.i 0.630296 0.363902i
286286 0 0
287287 −465272. 608790.i −0.333428 0.436278i
288288 0 0
289289 −701733. 1.21544e6i −0.494228 0.856028i
290290 0 0
291291 −1.72870e6 998066.i −1.19671 0.690918i
292292 0 0
293293 1.92194e6i 1.30789i −0.756542 0.653945i 0.773113π-0.773113\pi
0.756542 0.653945i 0.226887π-0.226887\pi
294294 0 0
295295 153059.i 0.102401i
296296 0 0
297297 824311. + 475916.i 0.542250 + 0.313068i
298298 0 0
299299 40539.3 + 70216.1i 0.0262239 + 0.0454212i
300300 0 0
301301 −1.19794e6 1.56747e6i −0.762115 0.997199i
302302 0 0
303303 1.49406e6 862597.i 0.934894 0.539761i
304304 0 0
305305 −39925.3 + 69152.7i −0.0245753 + 0.0425657i
306306 0 0
307307 −940708. −0.569651 −0.284825 0.958579i 0.591936π-0.591936\pi
−0.284825 + 0.958579i 0.591936π0.591936\pi
308308 0 0
309309 2.94041e6 1.75191
310310 0 0
311311 365640. 633306.i 0.214364 0.371290i −0.738712 0.674022i 0.764565π-0.764565\pi
0.953076 + 0.302732i 0.0978987π0.0978987\pi
312312 0 0
313313 271139. 156542.i 0.156434 0.0903171i −0.419740 0.907645i 0.637879π-0.637879\pi
0.576173 + 0.817327i 0.304545π0.304545\pi
314314 0 0
315315 −67392.2 + 8739.66i −0.0382678 + 0.00496270i
316316 0 0
317317 1.65827e6 + 2.87221e6i 0.926846 + 1.60534i 0.788565 + 0.614951i 0.210824π0.210824\pi
0.138281 + 0.990393i 0.455842π0.455842\pi
318318 0 0
319319 −369013. 213050.i −0.203032 0.117221i
320320 0 0
321321 2.46107e6i 1.33309i
322322 0 0
323323 352145.i 0.187809i
324324 0 0
325325 71982.5 + 41559.1i 0.0378023 + 0.0218252i
326326 0 0
327327 −645462. 1.11797e6i −0.333812 0.578179i
328328 0 0
329329 −11868.1 4942.87i −0.00604493 0.00251761i
330330 0 0
331331 908606. 524584.i 0.455833 0.263175i −0.254458 0.967084i 0.581897π-0.581897\pi
0.710290 + 0.703909i 0.248564π0.248564\pi
332332 0 0
333333 −57127.0 + 98946.8i −0.0282313 + 0.0488980i
334334 0 0
335335 −1.08518e6 −0.528312
336336 0 0
337337 −2.90507e6 −1.39342 −0.696710 0.717353i 0.745353π-0.745353\pi
−0.696710 + 0.717353i 0.745353π0.745353\pi
338338 0 0
339339 −817837. + 1.41653e6i −0.386516 + 0.669465i
340340 0 0
341341 161039. 92976.0i 0.0749973 0.0432997i
342342 0 0
343343 −822120. 2.01784e6i −0.377311 0.926086i
344344 0 0
345345 −465628. 806492.i −0.210616 0.364798i
346346 0 0
347347 −391122. 225815.i −0.174377 0.100677i 0.410271 0.911964i 0.365434π-0.365434\pi
−0.584648 + 0.811287i 0.698767π0.698767\pi
348348 0 0
349349 1.27258e6i 0.559269i −0.960107 0.279634i 0.909787π-0.909787\pi
0.960107 0.279634i 0.0902132π-0.0902132\pi
350350 0 0
351351 113169.i 0.0490299i
352352 0 0
353353 1.73409e6 + 1.00118e6i 0.740686 + 0.427636i 0.822319 0.569027i 0.192680π-0.192680\pi
−0.0816324 + 0.996663i 0.526013π0.526013\pi
354354 0 0
355355 −352205. 610037.i −0.148328 0.256912i
356356 0 0
357357 −104193. + 250172.i −0.0432679 + 0.103889i
358358 0 0
359359 −1.09761e6 + 633703.i −0.449480 + 0.259507i −0.707610 0.706603i 0.750227π-0.750227\pi
0.258131 + 0.966110i 0.416893π0.416893\pi
360360 0 0
361361 −2.54463e6 + 4.40743e6i −1.02768 + 1.77999i
362362 0 0
363363 1.47696e6 0.588305
364364 0 0
365365 694457. 0.272843
366366 0 0
367367 −2.18287e6 + 3.78084e6i −0.845985 + 1.46529i 0.0387779 + 0.999248i 0.487654π0.487654\pi
−0.884763 + 0.466041i 0.845680π0.845680\pi
368368 0 0
369369 −120736. + 69707.1i −0.0461607 + 0.0266509i
370370 0 0
371371 −595464. 4.59167e6i −0.224606 1.73195i
372372 0 0
373373 1.74926e6 + 3.02980e6i 0.651001 + 1.12757i 0.982880 + 0.184245i 0.0589840π0.0589840\pi
−0.331879 + 0.943322i 0.607683π0.607683\pi
374374 0 0
375375 −1.80874e6 1.04427e6i −0.664198 0.383475i
376376 0 0
377377 50661.7i 0.0183580i
378378 0 0
379379 4.42455e6i 1.58224i 0.611663 + 0.791118i 0.290501π0.290501\pi
−0.611663 + 0.791118i 0.709499π0.709499\pi
380380 0 0
381381 1.88991e6 + 1.09114e6i 0.667006 + 0.385096i
382382 0 0
383383 2.38842e6 + 4.13686e6i 0.831980 + 1.44103i 0.896466 + 0.443113i 0.146126π0.146126\pi
−0.0644852 + 0.997919i 0.520541π0.520541\pi
384384 0 0
385385 −608172. + 464799.i −0.209110 + 0.159814i
386386 0 0
387387 −310862. + 179476.i −0.105509 + 0.0609158i
388388 0 0
389389 −1.27234e6 + 2.20375e6i −0.426312 + 0.738395i −0.996542 0.0830906i 0.973521π-0.973521\pi
0.570230 + 0.821485i 0.306854π0.306854\pi
390390 0 0
391391 −328598. −0.108698
392392 0 0
393393 −2.11739e6 −0.691544
394394 0 0
395395 −264775. + 458604.i −0.0853856 + 0.147892i
396396 0 0
397397 −988211. + 570544.i −0.314683 + 0.181682i −0.649020 0.760771i 0.724821π-0.724821\pi
0.334337 + 0.942454i 0.391488π0.391488\pi
398398 0 0
399399 4.62584e6 3.53533e6i 1.45465 1.11173i
400400 0 0
401401 −2.23541e6 3.87184e6i −0.694217 1.20242i −0.970444 0.241327i 0.922417π-0.922417\pi
0.276227 0.961093i 0.410916π-0.410916\pi
402402 0 0
403403 19147.0 + 11054.5i 0.00587269 + 0.00339060i
404404 0 0
405405 1.42722e6i 0.432369i
406406 0 0
407407 1.28693e6i 0.385097i
408408 0 0
409409 −497871. 287446.i −0.147167 0.0849666i 0.424609 0.905377i 0.360412π-0.360412\pi
−0.571775 + 0.820410i 0.693745π0.693745\pi
410410 0 0
411411 383823. + 664801.i 0.112080 + 0.194127i
412412 0 0
413413 −114836. 885507.i −0.0331285 0.255456i
414414 0 0
415415 351968. 203209.i 0.100319 0.0579192i
416416 0 0
417417 −2.64349e6 + 4.57866e6i −0.744454 + 1.28943i
418418 0 0
419419 2.06791e6 0.575434 0.287717 0.957715i 0.407104π-0.407104\pi
0.287717 + 0.957715i 0.407104π0.407104\pi
420420 0 0
421421 −4.36685e6 −1.20078 −0.600390 0.799708i 0.704988π-0.704988\pi
−0.600390 + 0.799708i 0.704988π0.704988\pi
422422 0 0
423423 −1169.59 + 2025.80i −0.000317822 + 0.000550484i
424424 0 0
425425 −291733. + 168432.i −0.0783454 + 0.0452327i
426426 0 0
427427 −179100. + 430030.i −0.0475364 + 0.114138i
428428 0 0
429429 −68520.2 118680.i −0.0179753 0.0311341i
430430 0 0
431431 5.19547e6 + 2.99961e6i 1.34720 + 0.777806i 0.987852 0.155398i 0.0496659π-0.0496659\pi
0.359348 + 0.933204i 0.382999π0.382999\pi
432432 0 0
433433 5.69706e6i 1.46026i −0.683307 0.730131i 0.739459π-0.739459\pi
0.683307 0.730131i 0.260541π-0.260541\pi
434434 0 0
435435 581892.i 0.147441i
436436 0 0
437437 6.11368e6 + 3.52974e6i 1.53144 + 0.884176i
438438 0 0
439439 2.73386e6 + 4.73519e6i 0.677042 + 1.17267i 0.975867 + 0.218364i 0.0700718π0.0700718\pi
−0.298825 + 0.954308i 0.596595π0.596595\pi
440440 0 0
441441 −383333. + 101125.i −0.0938598 + 0.0247606i
442442 0 0
443443 5.51411e6 3.18357e6i 1.33495 0.770735i 0.348898 0.937161i 0.386556π-0.386556\pi
0.986054 + 0.166426i 0.0532225π0.0532225\pi
444444 0 0
445445 778618. 1.34861e6i 0.186391 0.322838i
446446 0 0
447447 2.89770e6 0.685938
448448 0 0
449449 4.50171e6 1.05381 0.526904 0.849925i 0.323353π-0.323353\pi
0.526904 + 0.849925i 0.323353π0.323353\pi
450450 0 0
451451 −785167. + 1.35995e6i −0.181769 + 0.314834i
452452 0 0
453453 −2.15527e6 + 1.24434e6i −0.493464 + 0.284902i
454454 0 0
455455 −84013.8 34990.4i −0.0190249 0.00792355i
456456 0 0
457457 718680. + 1.24479e6i 0.160970 + 0.278808i 0.935217 0.354075i 0.115204π-0.115204\pi
−0.774247 + 0.632884i 0.781871π0.781871\pi
458458 0 0
459459 −397208. 229328.i −0.0880008 0.0508073i
460460 0 0
461461 6.30635e6i 1.38206i −0.722828 0.691028i 0.757158π-0.757158\pi
0.722828 0.691028i 0.242842π-0.242842\pi
462462 0 0
463463 9.12301e6i 1.97782i 0.148531 + 0.988908i 0.452545π0.452545\pi
−0.148531 + 0.988908i 0.547455π0.547455\pi
464464 0 0
465465 −219919. 126970.i −0.0471662 0.0272314i
466466 0 0
467467 −664462. 1.15088e6i −0.140987 0.244196i 0.786882 0.617104i 0.211694π-0.211694\pi
−0.927868 + 0.372908i 0.878361π0.878361\pi
468468 0 0
469469 −6.27820e6 + 814179.i −1.31796 + 0.170918i
470470 0 0
471471 4.39858e6 2.53952e6i 0.913609 0.527472i
472472 0 0
473473 −2.02159e6 + 3.50149e6i −0.415470 + 0.719615i
474474 0 0
475475 7.23707e6 1.47173
476476 0 0
477477 −842447. −0.169530
478478 0 0
479479 −2.00910e6 + 3.47987e6i −0.400095 + 0.692985i −0.993737 0.111744i 0.964356π-0.964356\pi
0.593642 + 0.804729i 0.297690π0.297690\pi
480480 0 0
481481 −132512. + 76505.8i −0.0261151 + 0.0150776i
482482 0 0
483483 −3.29892e6 4.31652e6i −0.643435 0.841910i
484484 0 0
485485 1.35841e6 + 2.35283e6i 0.262226 + 0.454188i
486486 0 0
487487 −7.43986e6 4.29540e6i −1.42148 0.820695i −0.425059 0.905166i 0.639747π-0.639747\pi
−0.996426 + 0.0844709i 0.973080π0.973080\pi
488488 0 0
489489 2.87921e6i 0.544505i
490490 0 0
491491 1.57232e6i 0.294332i 0.989112 + 0.147166i 0.0470151π0.0470151\pi
−0.989112 + 0.147166i 0.952985π0.952985\pi
492492 0 0
493493 177815. + 102662.i 0.0329497 + 0.0190235i
494494 0 0
495495 69636.4 + 120614.i 0.0127739 + 0.0221250i
496496 0 0
497497 −2.49533e6 3.26505e6i −0.453145 0.592924i
498498 0 0
499499 −1.25743e6 + 725978.i −0.226065 + 0.130518i −0.608755 0.793358i 0.708331π-0.708331\pi
0.382691 + 0.923877i 0.374998π0.374998\pi
500500 0 0
501501 −3.83692e6 + 6.64573e6i −0.682948 + 1.18290i
502502 0 0
503503 −3.59897e6 −0.634247 −0.317123 0.948384i 0.602717π-0.602717\pi
−0.317123 + 0.948384i 0.602717π0.602717\pi
504504 0 0
505505 −2.34806e6 −0.409714
506506 0 0
507507 −3.02300e6 + 5.23599e6i −0.522298 + 0.904647i
508508 0 0
509509 −1.76938e6 + 1.02155e6i −0.302711 + 0.174770i −0.643660 0.765312i 0.722585π-0.722585\pi
0.340949 + 0.940082i 0.389252π0.389252\pi
510510 0 0
511511 4.01770e6 521030.i 0.680653 0.0882695i
512512 0 0
513513 4.92680e6 + 8.53347e6i 0.826555 + 1.43164i
514514 0 0
515515 −3.46584e6 2.00101e6i −0.575825 0.332453i
516516 0 0
517517 26348.1i 0.00433534i
518518 0 0
519519 1.27204e7i 2.07291i
520520 0 0
521521 6.36726e6 + 3.67614e6i 1.02768 + 0.593332i 0.916320 0.400448i 0.131145π-0.131145\pi
0.111362 + 0.993780i 0.464479π0.464479\pi
522522 0 0
523523 4.56417e6 + 7.90537e6i 0.729638 + 1.26377i 0.957036 + 0.289968i 0.0936445π0.0936445\pi
−0.227399 + 0.973802i 0.573022π0.573022\pi
524524 0 0
525525 −5.14138e6 2.14130e6i −0.814107 0.339062i
526526 0 0
527527 −77599.5 + 44802.1i −0.0121712 + 0.00702703i
528528 0 0
529529 75537.1 130834.i 0.0117360 0.0203274i
530530 0 0
531531 −162466. −0.0250050
532532 0 0
533533 −186707. −0.0284670
534534 0 0
535535 −1.67480e6 + 2.90085e6i −0.252976 + 0.438167i
536536 0 0
537537 8.74491e6 5.04887e6i 1.30864 0.755542i
538538 0 0
539539 −3.16979e6 + 3.14534e6i −0.469957 + 0.466332i
540540 0 0
541541 −5.66666e6 9.81493e6i −0.832403 1.44176i −0.896128 0.443797i 0.853631π-0.853631\pi
0.0637246 0.997968i 0.479702π-0.479702\pi
542542 0 0
543543 −2.52804e6 1.45956e6i −0.367946 0.212433i
544544 0 0
545545 1.75700e6i 0.253385i
546546 0 0
547547 9.79610e6i 1.39986i 0.714211 + 0.699930i 0.246786π0.246786\pi
−0.714211 + 0.699930i 0.753214π0.753214\pi
548548 0 0
549549 73402.9 + 42379.2i 0.0103940 + 0.00600097i
550550 0 0
551551 −2.20555e6 3.82012e6i −0.309483 0.536040i
552552 0 0
553553 −1.18775e6 + 2.85186e6i −0.165163 + 0.396565i
554554 0 0
555555 1.52201e6 878735.i 0.209742 0.121095i
556556 0 0
557557 −3.23228e6 + 5.59847e6i −0.441439 + 0.764595i −0.997797 0.0663481i 0.978865π-0.978865\pi
0.556357 + 0.830943i 0.312199π0.312199\pi
558558 0 0
559559 −480718. −0.0650670
560560 0 0
561561 555402. 0.0745076
562562 0 0
563563 627220. 1.08638e6i 0.0833967 0.144447i −0.821310 0.570482i 0.806756π-0.806756\pi
0.904707 + 0.426035i 0.140090π0.140090\pi
564564 0 0
565565 1.92796e6 1.11311e6i 0.254084 0.146695i
566566 0 0
567567 −1.07080e6 8.25704e6i −0.139879 1.07862i
568568 0 0
569569 −2.77361e6 4.80403e6i −0.359140 0.622050i 0.628677 0.777667i 0.283597π-0.283597\pi
−0.987817 + 0.155617i 0.950263π0.950263\pi
570570 0 0
571571 −5.57019e6 3.21595e6i −0.714956 0.412780i 0.0979373 0.995193i 0.468776π-0.468776\pi
−0.812893 + 0.582412i 0.802109π0.802109\pi
572572 0 0
573573 177155.i 0.0225407i
574574 0 0
575575 6.75314e6i 0.851797i
576576 0 0
577577 9.92482e6 + 5.73010e6i 1.24103 + 0.716510i 0.969304 0.245864i 0.0790715π-0.0790715\pi
0.271728 + 0.962374i 0.412405π0.412405\pi
578578 0 0
579579 −7.73211e6 1.33924e7i −0.958521 1.66021i
580580 0 0
581581 1.88381e6 1.43971e6i 0.231524 0.176944i
582582 0 0
583583 −8.21784e6 + 4.74457e6i −1.00135 + 0.578130i
584584 0 0
585585 −8279.51 + 14340.5i −0.00100026 + 0.00173251i
586586 0 0
587587 1.54952e7 1.85610 0.928052 0.372451i 0.121483π-0.121483\pi
0.928052 + 0.372451i 0.121483π0.121483\pi
588588 0 0
589589 1.92502e6 0.228638
590590 0 0
591591 664978. 1.15178e6i 0.0783138 0.135644i
592592 0 0
593593 7.54037e6 4.35344e6i 0.880554 0.508388i 0.00971325 0.999953i 0.496908π-0.496908\pi
0.870841 + 0.491564i 0.163575π0.163575\pi
594594 0 0
595595 293058. 223971.i 0.0339361 0.0259358i
596596 0 0
597597 −8.02929e6 1.39071e7i −0.922023 1.59699i
598598 0 0
599599 −9.92434e6 5.72982e6i −1.13015 0.652490i −0.186175 0.982517i 0.559609π-0.559609\pi
−0.943972 + 0.330026i 0.892942π0.892942\pi
600600 0 0
601601 9.83228e6i 1.11037i −0.831727 0.555185i 0.812647π-0.812647\pi
0.831727 0.555185i 0.187353π-0.187353\pi
602602 0 0
603603 1.15188e6i 0.129007i
604604 0 0
605605 −1.74089e6 1.00510e6i −0.193367 0.111640i
606606 0 0
607607 6.70187e6 + 1.16080e7i 0.738286 + 1.27875i 0.953267 + 0.302130i 0.0976977π0.0976977\pi
−0.214981 + 0.976618i 0.568969π0.568969\pi
608608 0 0
609609 436576. + 3.36647e6i 0.0476998 + 0.367817i
610610 0 0
611611 −2712.99 + 1566.35i −0.000293999 + 0.000169740i
612612 0 0
613613 −838947. + 1.45310e6i −0.0901744 + 0.156187i −0.907584 0.419870i 0.862076π-0.862076\pi
0.817410 + 0.576056i 0.195409π0.195409\pi
614614 0 0
615615 2.14449e6 0.228631
616616 0 0
617617 1.48745e7 1.57300 0.786499 0.617592i 0.211891π-0.211891\pi
0.786499 + 0.617592i 0.211891π0.211891\pi
618618 0 0
619619 −3.56661e6 + 6.17755e6i −0.374136 + 0.648022i −0.990197 0.139676i 0.955394π-0.955394\pi
0.616061 + 0.787698i 0.288727π0.288727\pi
620620 0 0
621621 7.96285e6 4.59735e6i 0.828590 0.478387i
622622 0 0
623623 3.49279e6 8.38638e6i 0.360539 0.865674i
624624 0 0
625625 −2.68990e6 4.65904e6i −0.275445 0.477085i
626626 0 0
627627 −1.03335e7 5.96603e6i −1.04973 0.606061i
628628 0 0
629629 620131.i 0.0624967i
630630 0 0
631631 9.49875e6i 0.949715i −0.880063 0.474857i 0.842500π-0.842500\pi
0.880063 0.474857i 0.157500π-0.157500\pi
632632 0 0
633633 6.04639e6 + 3.49089e6i 0.599773 + 0.346279i
634634 0 0
635635 −1.48509e6 2.57225e6i −0.146156 0.253150i
636636 0 0
637637 −512305. 139400.i −0.0500241 0.0136117i
638638 0 0
639639 −647530. + 373852.i −0.0627347 + 0.0362199i
640640 0 0
641641 7.67359e6 1.32910e7i 0.737655 1.27766i −0.215894 0.976417i 0.569266π-0.569266\pi
0.953549 0.301239i 0.0974002π-0.0974002\pi
642642 0 0
643643 −988668. −0.0943025 −0.0471512 0.998888i 0.515014π-0.515014\pi
−0.0471512 + 0.998888i 0.515014π0.515014\pi
644644 0 0
645645 5.52146e6 0.522582
646646 0 0
647647 −5.51747e6 + 9.55655e6i −0.518179 + 0.897512i 0.481598 + 0.876392i 0.340056π0.340056\pi
−0.999777 + 0.0211198i 0.993277π0.993277\pi
648648 0 0
649649 −1.58482e6 + 914994.i −0.147695 + 0.0852720i
650650 0 0
651651 −1.36758e6 569574.i −0.126474 0.0526742i
652652 0 0
653653 2.55762e6 + 4.42993e6i 0.234722 + 0.406550i 0.959192 0.282756i 0.0912488π-0.0912488\pi
−0.724470 + 0.689306i 0.757915π0.757915\pi
654654 0 0
655655 2.49576e6 + 1.44093e6i 0.227300 + 0.131232i
656656 0 0
657657 737139.i 0.0666248i
658658 0 0
659659 1.13694e7i 1.01982i −0.860227 0.509911i 0.829678π-0.829678\pi
0.860227 0.509911i 0.170322π-0.170322\pi
660660 0 0
661661 −1.41836e7 8.18893e6i −1.26265 0.728993i −0.289066 0.957309i 0.593345π-0.593345\pi
−0.973587 + 0.228316i 0.926678π0.926678\pi
662662 0 0
663663 33017.6 + 57188.2i 0.00291717 + 0.00505269i
664664 0 0
665665 −7.85832e6 + 1.01909e6i −0.689089 + 0.0893635i
666666 0 0
667667 −3.56467e6 + 2.05806e6i −0.310245 + 0.179120i
668668 0 0
669669 −491775. + 851779.i −0.0424816 + 0.0735803i
670670 0 0
671671 954701. 0.0818580
672672 0 0
673673 9.53588e6 0.811564 0.405782 0.913970i 0.366999π-0.366999\pi
0.405782 + 0.913970i 0.366999π0.366999\pi
674674 0 0
675675 4.71301e6 8.16317e6i 0.398143 0.689604i
676676 0 0
677677 1.06224e7 6.13284e6i 0.890740 0.514269i 0.0165554 0.999863i 0.494730π-0.494730\pi
0.874184 + 0.485594i 0.161397π0.161397\pi
678678 0 0
679679 9.62416e6 + 1.25929e7i 0.801103 + 1.04821i
680680 0 0
681681 450887. + 780959.i 0.0372563 + 0.0645298i
682682 0 0
683683 −2.91586e6 1.68347e6i −0.239175 0.138088i 0.375623 0.926773i 0.377429π-0.377429\pi
−0.614797 + 0.788685i 0.710762π0.710762\pi
684684 0 0
685685 1.04480e6i 0.0850756i
686686 0 0
687687 57752.4i 0.00466851i
688688 0 0
689689 −977071. 564112.i −0.0784112 0.0452707i
690690 0 0
691691 −2.65246e6 4.59420e6i −0.211327 0.366028i 0.740803 0.671722i 0.234445π-0.234445\pi
−0.952130 + 0.305694i 0.901112π0.901112\pi
692692 0 0
693693 493366. + 645551.i 0.0390244 + 0.0510620i
694694 0 0
695695 6.23174e6 3.59789e6i 0.489381 0.282544i
696696 0 0
697697 378346. 655315.i 0.0294990 0.0510938i
698698 0 0
699699 1.95688e7 1.51486
700700 0 0
701701 3.03260e6 0.233088 0.116544 0.993186i 0.462818π-0.462818\pi
0.116544 + 0.993186i 0.462818π0.462818\pi
702702 0 0
703703 −6.66133e6 + 1.15378e7i −0.508362 + 0.880508i
704704 0 0
705705 31161.1 17990.8i 0.00236124 0.00136326i
706706 0 0
707707 −1.35844e7 + 1.76168e6i −1.02210 + 0.132549i
708708 0 0
709709 −7.72319e6 1.33770e7i −0.577007 0.999406i −0.995820 0.0913332i 0.970887π-0.970887\pi
0.418813 0.908072i 0.362446π-0.362446\pi
710710 0 0
711711 486790. + 281049.i 0.0361134 + 0.0208501i
712712 0 0
713713 1.79630e6i 0.132329i
714714 0 0
715715 186517.i 0.0136444i
716716 0 0
717717 7.51492e6 + 4.33874e6i 0.545917 + 0.315185i
718718 0 0
719719 8.99286e6 + 1.55761e7i 0.648748 + 1.12366i 0.983422 + 0.181330i 0.0580402π0.0580402\pi
−0.334675 + 0.942334i 0.608626π0.608626\pi
720720 0 0
721721 −2.15525e7 8.97627e6i −1.54405 0.643070i
722722 0 0
723723 7.95557e6 4.59315e6i 0.566012 0.326787i
724724 0 0
725725 −2.10984e6 + 3.65435e6i −0.149075 + 0.258205i
726726 0 0
727727 −1.55969e7 −1.09447 −0.547234 0.836980i 0.684319π-0.684319\pi
−0.547234 + 0.836980i 0.684319π0.684319\pi
728728 0 0
729729 1.26988e7 0.884998
730730 0 0
731731 974136. 1.68725e6i 0.0674258 0.116785i
732732 0 0
733733 −1.11442e7 + 6.43409e6i −0.766104 + 0.442310i −0.831483 0.555550i 0.812508π-0.812508\pi
0.0653790 + 0.997861i 0.479174π0.479174\pi
734734 0 0
735735 5.88426e6 + 1.60113e6i 0.401766 + 0.109322i
736736 0 0
737737 6.48726e6 + 1.12363e7i 0.439939 + 0.761997i
738738 0 0
739739 −1.72415e7 9.95440e6i −1.16135 0.670508i −0.209726 0.977760i 0.567257π-0.567257\pi
−0.951628 + 0.307252i 0.900591π0.900591\pi
740740 0 0
741741 1.41868e6i 0.0949157i
742742 0 0
743743 2.89554e7i 1.92423i −0.272640 0.962116i 0.587897π-0.587897\pi
0.272640 0.962116i 0.412103π-0.412103\pi
744744 0 0
745745 −3.41550e6 1.97194e6i −0.225457 0.130168i
746746 0 0
747747 −215698. 373600.i −0.0141431 0.0244966i
748748 0 0
749749 −7.51297e6 + 1.80391e7i −0.489336 + 1.17492i
750750 0 0
751751 56095.8 32386.9i 0.00362936 0.00209541i −0.498184 0.867071i 0.666000π-0.666000\pi
0.501814 + 0.864976i 0.332666π0.332666\pi
752752 0 0
753753 −8.72188e6 + 1.51067e7i −0.560561 + 0.970920i
754754 0 0
755755 3.38720e6 0.216259
756756 0 0
757757 −1.28686e7 −0.816190 −0.408095 0.912940i 0.633807π-0.633807\pi
−0.408095 + 0.912940i 0.633807π0.633807\pi
758758 0 0
759759 −5.56709e6 + 9.64248e6i −0.350771 + 0.607553i
760760 0 0
761761 −1.58510e7 + 9.15160e6i −0.992193 + 0.572843i −0.905929 0.423429i 0.860826π-0.860826\pi
−0.0862641 + 0.996272i 0.527493π0.527493\pi
762762 0 0
763763 1.31822e6 + 1.01649e7i 0.0819742 + 0.632110i
764764 0 0
765765 −33555.5 58119.8i −0.00207305 0.00359063i
766766 0 0
767767 −188429. 108789.i −0.0115654 0.00667726i
768768 0 0
769769 1.68118e7i 1.02518i 0.858634 + 0.512589i 0.171314π0.171314\pi
−0.858634 + 0.512589i 0.828686π0.828686\pi
770770 0 0
771771 2.19237e7i 1.32824i
772772 0 0
773773 2.16919e7 + 1.25238e7i 1.30571 + 0.753854i 0.981378 0.192088i 0.0615259π-0.0615259\pi
0.324336 + 0.945942i 0.394859π0.394859\pi
774774 0 0
775775 −920744. 1.59478e6i −0.0550662 0.0953774i
776776 0 0
777777 8.14615e6 6.22574e6i 0.484061 0.369946i
778778 0 0
779779 −1.40785e7 + 8.12825e6i −0.831216 + 0.479903i
780780 0 0
781781 −4.21099e6 + 7.29365e6i −0.247034 + 0.427875i
782782 0 0
783783 −5.74528e6 −0.334894
784784 0 0
785785 −6.91278e6 −0.400386
786786 0 0
787787 1.99502e6 3.45547e6i 0.114818 0.198870i −0.802889 0.596128i 0.796705π-0.796705\pi
0.917707 + 0.397258i 0.130038π0.130038\pi
788788 0 0
789789 2.28135e7 1.31714e7i 1.30467 0.753249i
790790 0 0
791791 1.03189e7 7.88625e6i 0.586395 0.448156i
792792 0 0
793793 56755.2 + 98302.9i 0.00320496 + 0.00555115i
794794 0 0
795795 1.12225e7 + 6.47931e6i 0.629755 + 0.363589i
796796 0 0
797797 2.69992e7i 1.50558i 0.658259 + 0.752792i 0.271293π0.271293\pi
−0.658259 + 0.752792i 0.728707π0.728707\pi
798798 0 0
799799 12696.3i 0.000703575i
800800 0 0
801801 −1.43149e6 826473.i −0.0788330 0.0455142i
802802 0 0
803803 −4.15149e6 7.19060e6i −0.227204 0.393528i
804804 0 0
805805 950949. + 7.33284e6i 0.0517211 + 0.398825i
806806 0 0
807807 −3.08735e7 + 1.78248e7i −1.66879 + 0.963476i
808808 0 0
809809 8.61028e6 1.49134e7i 0.462536 0.801136i −0.536550 0.843868i 0.680273π-0.680273\pi
0.999087 + 0.0427321i 0.0136062π0.0136062\pi
810810 0 0
811811 1.90148e7 1.01517 0.507587 0.861601i 0.330538π-0.330538\pi
0.507587 + 0.861601i 0.330538π0.330538\pi
812812 0 0
813813 −6.64325e6 −0.352496
814814 0 0
815815 1.95936e6 3.39371e6i 0.103329 0.178970i
816816 0 0
817817 −3.62483e7 + 2.09280e7i −1.89991 + 1.09691i
818818 0 0
819819 −37140.9 + 89177.3i −0.00193483 + 0.00464563i
820820 0 0
821821 −1.54355e6 2.67352e6i −0.0799216 0.138428i 0.823294 0.567615i 0.192134π-0.192134\pi
−0.903216 + 0.429186i 0.858800π0.858800\pi
822822 0 0
823823 2.03659e7 + 1.17582e7i 1.04810 + 0.605122i 0.922117 0.386910i 0.126458π-0.126458\pi
0.125984 + 0.992032i 0.459791π0.459791\pi
824824 0 0
825825 1.14143e7i 0.583866i
826826 0 0
827827 2.15389e7i 1.09512i 0.836767 + 0.547559i 0.184443π0.184443\pi
−0.836767 + 0.547559i 0.815557π0.815557\pi
828828 0 0
829829 −1.14533e7 6.61258e6i −0.578823 0.334183i 0.181843 0.983328i 0.441794π-0.441794\pi
−0.760665 + 0.649144i 0.775127π0.775127\pi
830830 0 0
831831 4.15889e6 + 7.20342e6i 0.208918 + 0.361856i
832832 0 0
833833 1.52742e6 1.51563e6i 0.0762684 0.0756801i
834834 0 0
835835 9.04510e6 5.22219e6i 0.448949 0.259201i
836836 0 0
837837 1.25364e6 2.17136e6i 0.0618526 0.107132i
838838 0 0
839839 1.67107e7 0.819575 0.409788 0.912181i 0.365603π-0.365603\pi
0.409788 + 0.912181i 0.365603π0.365603\pi
840840 0 0
841841 −1.79392e7 −0.874607
842842 0 0
843843 9.13348e6 1.58196e7i 0.442657 0.766704i
844844 0 0
845845 7.12639e6 4.11442e6i 0.343343 0.198229i
846846 0 0
847847 −1.08258e7 4.50876e6i −0.518503 0.215948i
848848 0 0
849849 −2.20354e6 3.81664e6i −0.104918 0.181724i
850850 0 0
851851 1.07662e7 + 6.21590e6i 0.509613 + 0.294225i
852852 0 0
853853 484559.i 0.0228020i 0.999935 + 0.0114010i 0.00362914π0.00362914\pi
−0.999935 + 0.0114010i 0.996371π0.996371\pi
854854 0 0
855855 1.44179e6i 0.0674506i
856856 0 0
857857 −2.82629e7 1.63176e7i −1.31451 0.758935i −0.331674 0.943394i 0.607613π-0.607613\pi
−0.982840 + 0.184459i 0.940947π0.940947\pi
858858 0 0
859859 −5.10980e6 8.85044e6i −0.236277 0.409243i 0.723366 0.690465i 0.242594π-0.242594\pi
−0.959643 + 0.281221i 0.909261π0.909261\pi
860860 0 0
861861 1.24067e7 1.60894e6i 0.570359 0.0739662i
862862 0 0
863863 2.91512e7 1.68305e7i 1.33239 0.769253i 0.346721 0.937968i 0.387295π-0.387295\pi
0.985665 + 0.168715i 0.0539617π0.0539617\pi
864864 0 0
865865 −8.65645e6 + 1.49934e7i −0.393369 + 0.681334i
866866 0 0
867867 2.29151e7 1.03532
868868 0 0
869869 6.33135e6 0.284411
870870 0 0
871871 −771312. + 1.33595e6i −0.0344496 + 0.0596685i
872872 0 0
873873 2.49744e6 1.44190e6i 0.110907 0.0640322i
874874 0 0
875875 1.00697e7 + 1.31759e7i 0.444630 + 0.581781i
876876 0 0
877877 3.88346e6 + 6.72635e6i 0.170498 + 0.295311i 0.938594 0.345023i 0.112129π-0.112129\pi
−0.768096 + 0.640335i 0.778796π0.778796\pi
878878 0 0
879879 2.71764e7 + 1.56903e7i 1.18637 + 0.684950i
880880 0 0
881881 3.44116e7i 1.49370i −0.664990 0.746852i 0.731564π-0.731564\pi
0.664990 0.746852i 0.268436π-0.268436\pi
882882 0 0
883883 4.33214e7i 1.86982i 0.354880 + 0.934912i 0.384522π0.384522\pi
−0.354880 + 0.934912i 0.615478π0.615478\pi
884884 0 0
885885 2.16427e6 + 1.24954e6i 0.0928865 + 0.0536280i
886886 0 0
887887 −40392.9 69962.6i −0.00172384 0.00298577i 0.865162 0.501492i 0.167215π-0.167215\pi
−0.866886 + 0.498506i 0.833882π0.833882\pi
888888 0 0
889889 −1.05217e7 1.37672e7i −0.446510 0.584241i
890890 0 0
891891 −1.47779e7 + 8.53200e6i −0.623616 + 0.360045i
892892 0 0
893893 −136381. + 236219.i −0.00572303 + 0.00991258i
894894 0 0
895895 −1.37434e7 −0.573506
896896 0 0
897897 −1.32381e6 −0.0549345
898898 0 0
899899 −561206. + 972037.i −0.0231592 + 0.0401129i
900900 0 0
901901 3.95991e6 2.28625e6i 0.162507 0.0938237i
902902 0 0
903903 3.19438e7 4.14258e6i 1.30367 0.169064i
904904 0 0
905905 1.98652e6 + 3.44076e6i 0.0806254 + 0.139647i
906906 0 0
907907 9.05859e6 + 5.22998e6i 0.365630 + 0.211097i 0.671548 0.740961i 0.265630π-0.265630\pi
−0.305917 + 0.952058i 0.598963π0.598963\pi
908908 0 0
909909 2.49237e6i 0.100047i
910910 0 0
911911 1.12503e7i 0.449127i −0.974459 0.224563i 0.927904π-0.927904\pi
0.974459 0.224563i 0.0720956π-0.0720956\pi
912912 0 0
913913 −4.20816e6 2.42958e6i −0.167076 0.0964616i
914914 0 0
915915 −651882. 1.12909e6i −0.0257405 0.0445838i
916916 0 0
917917 1.55200e7 + 6.46383e6i 0.609493 + 0.253844i
918918 0 0
919919 −4.64723e6 + 2.68308e6i −0.181512 + 0.104796i −0.588003 0.808859i 0.700086π-0.700086\pi
0.406491 + 0.913655i 0.366752π0.366752\pi
920920 0 0
921921 7.67972e6 1.33017e7i 0.298329 0.516722i
922922 0 0
923923 −1.00134e6 −0.0386882
924924 0 0
925925 1.27445e7 0.489745
926926 0 0
927927 −2.12399e6 + 3.67886e6i −0.0811807 + 0.140609i
928928 0 0
929929 −2.14406e7 + 1.23787e7i −0.815074 + 0.470583i −0.848715 0.528851i 0.822623π-0.822623\pi
0.0336410 + 0.999434i 0.489290π0.489290\pi
930930 0 0
931931 −4.46988e7 + 1.17917e7i −1.69014 + 0.445864i
932932 0 0
933933 5.96999e6 + 1.03403e7i 0.224527 + 0.388893i
934934 0 0
935935 −654649. 377962.i −0.0244895 0.0141390i
936936 0 0
937937 1.46850e6i 0.0546419i 0.999627 + 0.0273210i 0.00869762π0.00869762\pi
−0.999627 + 0.0273210i 0.991302π0.991302\pi
938938 0 0
939939 5.11189e6i 0.189198i
940940 0 0
941941 5.16498e6 + 2.98200e6i 0.190149 + 0.109783i 0.592052 0.805899i 0.298318π-0.298318\pi
−0.401903 + 0.915682i 0.631651π0.631651\pi
942942 0 0
943943 7.58472e6 + 1.31371e7i 0.277754 + 0.481084i
944944 0 0
945945 −3.96808e6 + 9.52758e6i −0.144544 + 0.347059i
946946 0 0
947947 4.13119e7 2.38514e7i 1.49692 0.864250i 0.496931 0.867790i 0.334460π-0.334460\pi
0.999994 + 0.00353991i 0.00112679π0.00112679\pi
948948 0 0
949949 493597. 854935.i 0.0177913 0.0308154i
950950 0 0
951951 −5.41510e7 −1.94158
952952 0 0
953953 −4.82889e7 −1.72232 −0.861162 0.508330i 0.830263π-0.830263\pi
−0.861162 + 0.508330i 0.830263π0.830263\pi
954954 0 0
955955 120557. 208812.i 0.00427746 0.00740877i
956956 0 0
957957 6.02507e6 3.47858e6i 0.212658 0.122778i
958958 0 0
959959 −783878. 6.04455e6i −0.0275234 0.212235i
960960 0 0
961961 1.40697e7 + 2.43694e7i 0.491445 + 0.851208i
962962 0 0
963963 3.07913e6 + 1.77774e6i 0.106995 + 0.0617735i
964964 0 0
965965 2.10474e7i 0.727580i
966966 0 0
967967 5.23912e7i 1.80174i −0.434089 0.900870i 0.642930π-0.642930\pi
0.434089 0.900870i 0.357070π-0.357070\pi
968968 0 0
969969 4.97935e6 + 2.87483e6i 0.170358 + 0.0983565i
970970 0 0
971971 −1.39434e7 2.41507e7i −0.474592 0.822017i 0.524985 0.851112i 0.324071π-0.324071\pi
−0.999577 + 0.0290944i 0.990738π0.990738\pi
972972 0 0
973973 3.33536e7 2.54907e7i 1.12943 0.863176i
974974 0 0
975975 −1.17530e6 + 678558.i −0.0395946 + 0.0228599i
976976 0 0
977977 2.87737e7 4.98375e7i 0.964405 1.67040i 0.253201 0.967414i 0.418517π-0.418517\pi
0.711204 0.702985i 0.248150π-0.248150\pi
978978 0 0
979979 −1.86184e7 −0.620850
980980 0 0
981981 1.86499e6 0.0618732
982982 0 0
983983 5.32884e6 9.22981e6i 0.175893 0.304656i −0.764577 0.644532i 0.777052π-0.777052\pi
0.940470 + 0.339877i 0.110385π0.110385\pi
984984 0 0
985985 −1.56761e6 + 905061.i −0.0514811 + 0.0297226i
986986 0 0
987987 166781. 127463.i 0.00544946 0.00416478i
988988 0 0
989989 1.95285e7 + 3.38244e7i 0.634862 + 1.09961i
990990 0 0
991991 −5.15687e6 2.97732e6i −0.166802 0.0963034i 0.414275 0.910152i 0.364035π-0.364035\pi
−0.581077 + 0.813848i 0.697369π0.697369\pi
992992 0 0
993993 1.71303e7i 0.551306i
994994 0 0
995995 2.18564e7i 0.699875i
996996 0 0
997997 −3.30824e7 1.91001e7i −1.05404 0.608552i −0.130265 0.991479i 0.541583π-0.541583\pi
−0.923779 + 0.382927i 0.874916π0.874916\pi
998998 0 0
999999 8.67614e6 + 1.50275e7i 0.275051 + 0.476402i
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 224.6.p.a.31.11 80
4.3 odd 2 inner 224.6.p.a.31.30 yes 80
7.5 odd 6 inner 224.6.p.a.159.30 yes 80
28.19 even 6 inner 224.6.p.a.159.11 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.6.p.a.31.11 80 1.1 even 1 trivial
224.6.p.a.31.30 yes 80 4.3 odd 2 inner
224.6.p.a.159.11 yes 80 28.19 even 6 inner
224.6.p.a.159.30 yes 80 7.5 odd 6 inner