Properties

Label 3330.2.d.d.1999.1
Level 33303330
Weight 22
Character 3330.1999
Analytic conductor 26.59026.590
Analytic rank 00
Dimension 22
Inner twists 22

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3330,2,Mod(1999,3330)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3330.1999");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3330=232537 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3330.d (of order 22, degree 11, 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: 26.590183873126.5901838731
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 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 1110)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1999.1
Root 1.00000i1.00000i of defining polynomial
Character χ\chi == 3330.1999
Dual form 3330.2.d.d.1999.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000iq21.00000q4+(1.00000+2.00000i)q5+1.00000iq7+1.00000iq8+(2.00000+1.00000i)q105.00000q11+1.00000q14+1.00000q161.00000iq17+(1.000002.00000i)q20+5.00000iq22+4.00000iq23+(3.000004.00000i)q251.00000iq283.00000q29+1.00000q311.00000iq321.00000q34+(2.000001.00000i)q351.00000iq37+(2.000001.00000i)q40+1.00000q417.00000iq43+5.00000q44+4.00000q46+4.00000iq47+6.00000q49+(4.00000+3.00000i)q50+3.00000iq53+(5.0000010.0000i)q551.00000q56+3.00000iq588.00000q59+5.00000q611.00000iq621.00000q644.00000iq67+1.00000iq68+(1.00000+2.00000i)q70+6.00000q7110.0000iq731.00000q745.00000iq77+(1.00000+2.00000i)q801.00000iq828.00000iq83+(2.00000+1.00000i)q857.00000q865.00000iq88+8.00000q894.00000iq92+4.00000q941.00000iq976.00000iq98+O(q100)q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +1.00000i q^{7} +1.00000i q^{8} +(2.00000 + 1.00000i) q^{10} -5.00000 q^{11} +1.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +(1.00000 - 2.00000i) q^{20} +5.00000i q^{22} +4.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -1.00000i q^{28} -3.00000 q^{29} +1.00000 q^{31} -1.00000i q^{32} -1.00000 q^{34} +(-2.00000 - 1.00000i) q^{35} -1.00000i q^{37} +(-2.00000 - 1.00000i) q^{40} +1.00000 q^{41} -7.00000i q^{43} +5.00000 q^{44} +4.00000 q^{46} +4.00000i q^{47} +6.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +3.00000i q^{53} +(5.00000 - 10.0000i) q^{55} -1.00000 q^{56} +3.00000i q^{58} -8.00000 q^{59} +5.00000 q^{61} -1.00000i q^{62} -1.00000 q^{64} -4.00000i q^{67} +1.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} +6.00000 q^{71} -10.0000i q^{73} -1.00000 q^{74} -5.00000i q^{77} +(-1.00000 + 2.00000i) q^{80} -1.00000i q^{82} -8.00000i q^{83} +(2.00000 + 1.00000i) q^{85} -7.00000 q^{86} -5.00000i q^{88} +8.00000 q^{89} -4.00000i q^{92} +4.00000 q^{94} -1.00000i q^{97} -6.00000i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q42q5+4q1010q11+2q14+2q16+2q206q256q29+2q312q344q354q40+2q41+10q44+8q46+12q498q50++8q94+O(q100) 2 q - 2 q^{4} - 2 q^{5} + 4 q^{10} - 10 q^{11} + 2 q^{14} + 2 q^{16} + 2 q^{20} - 6 q^{25} - 6 q^{29} + 2 q^{31} - 2 q^{34} - 4 q^{35} - 4 q^{40} + 2 q^{41} + 10 q^{44} + 8 q^{46} + 12 q^{49} - 8 q^{50}+ \cdots + 8 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3330Z)×\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times.

nn 371371 631631 667667
χ(n)\chi(n) 11 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000i 0.707107i
33 0 0
44 −1.00000 −0.500000
55 −1.00000 + 2.00000i −0.447214 + 0.894427i
66 0 0
77 1.00000i 0.377964i 0.981981 + 0.188982i 0.0605189π0.0605189\pi
−0.981981 + 0.188982i 0.939481π0.939481\pi
88 1.00000i 0.353553i
99 0 0
1010 2.00000 + 1.00000i 0.632456 + 0.316228i
1111 −5.00000 −1.50756 −0.753778 0.657129i 0.771771π-0.771771\pi
−0.753778 + 0.657129i 0.771771π0.771771\pi
1212 0 0
1313 0 0 1.00000 00
−1.00000 π\pi
1414 1.00000 0.267261
1515 0 0
1616 1.00000 0.250000
1717 1.00000i 0.242536i −0.992620 0.121268i 0.961304π-0.961304\pi
0.992620 0.121268i 0.0386960π-0.0386960\pi
1818 0 0
1919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2020 1.00000 2.00000i 0.223607 0.447214i
2121 0 0
2222 5.00000i 1.06600i
2323 4.00000i 0.834058i 0.908893 + 0.417029i 0.136929π0.136929\pi
−0.908893 + 0.417029i 0.863071π0.863071\pi
2424 0 0
2525 −3.00000 4.00000i −0.600000 0.800000i
2626 0 0
2727 0 0
2828 1.00000i 0.188982i
2929 −3.00000 −0.557086 −0.278543 0.960424i 0.589851π-0.589851\pi
−0.278543 + 0.960424i 0.589851π0.589851\pi
3030 0 0
3131 1.00000 0.179605 0.0898027 0.995960i 0.471376π-0.471376\pi
0.0898027 + 0.995960i 0.471376π0.471376\pi
3232 1.00000i 0.176777i
3333 0 0
3434 −1.00000 −0.171499
3535 −2.00000 1.00000i −0.338062 0.169031i
3636 0 0
3737 1.00000i 0.164399i
3838 0 0
3939 0 0
4040 −2.00000 1.00000i −0.316228 0.158114i
4141 1.00000 0.156174 0.0780869 0.996947i 0.475119π-0.475119\pi
0.0780869 + 0.996947i 0.475119π0.475119\pi
4242 0 0
4343 7.00000i 1.06749i −0.845645 0.533745i 0.820784π-0.820784\pi
0.845645 0.533745i 0.179216π-0.179216\pi
4444 5.00000 0.753778
4545 0 0
4646 4.00000 0.589768
4747 4.00000i 0.583460i 0.956501 + 0.291730i 0.0942309π0.0942309\pi
−0.956501 + 0.291730i 0.905769π0.905769\pi
4848 0 0
4949 6.00000 0.857143
5050 −4.00000 + 3.00000i −0.565685 + 0.424264i
5151 0 0
5252 0 0
5353 3.00000i 0.412082i 0.978543 + 0.206041i 0.0660580π0.0660580\pi
−0.978543 + 0.206041i 0.933942π0.933942\pi
5454 0 0
5555 5.00000 10.0000i 0.674200 1.34840i
5656 −1.00000 −0.133631
5757 0 0
5858 3.00000i 0.393919i
5959 −8.00000 −1.04151 −0.520756 0.853706i 0.674350π-0.674350\pi
−0.520756 + 0.853706i 0.674350π0.674350\pi
6060 0 0
6161 5.00000 0.640184 0.320092 0.947386i 0.396286π-0.396286\pi
0.320092 + 0.947386i 0.396286π0.396286\pi
6262 1.00000i 0.127000i
6363 0 0
6464 −1.00000 −0.125000
6565 0 0
6666 0 0
6767 4.00000i 0.488678i −0.969690 0.244339i 0.921429π-0.921429\pi
0.969690 0.244339i 0.0785709π-0.0785709\pi
6868 1.00000i 0.121268i
6969 0 0
7070 −1.00000 + 2.00000i −0.119523 + 0.239046i
7171 6.00000 0.712069 0.356034 0.934473i 0.384129π-0.384129\pi
0.356034 + 0.934473i 0.384129π0.384129\pi
7272 0 0
7373 10.0000i 1.17041i −0.810885 0.585206i 0.801014π-0.801014\pi
0.810885 0.585206i 0.198986π-0.198986\pi
7474 −1.00000 −0.116248
7575 0 0
7676 0 0
7777 5.00000i 0.569803i
7878 0 0
7979 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8080 −1.00000 + 2.00000i −0.111803 + 0.223607i
8181 0 0
8282 1.00000i 0.110432i
8383 8.00000i 0.878114i −0.898459 0.439057i 0.855313π-0.855313\pi
0.898459 0.439057i 0.144687π-0.144687\pi
8484 0 0
8585 2.00000 + 1.00000i 0.216930 + 0.108465i
8686 −7.00000 −0.754829
8787 0 0
8888 5.00000i 0.533002i
8989 8.00000 0.847998 0.423999 0.905663i 0.360626π-0.360626\pi
0.423999 + 0.905663i 0.360626π0.360626\pi
9090 0 0
9191 0 0
9292 4.00000i 0.417029i
9393 0 0
9494 4.00000 0.412568
9595 0 0
9696 0 0
9797 1.00000i 0.101535i −0.998711 0.0507673i 0.983833π-0.983833\pi
0.998711 0.0507673i 0.0161667π-0.0161667\pi
9898 6.00000i 0.606092i
9999 0 0
100100 3.00000 + 4.00000i 0.300000 + 0.400000i
101101 −10.0000 −0.995037 −0.497519 0.867453i 0.665755π-0.665755\pi
−0.497519 + 0.867453i 0.665755π0.665755\pi
102102 0 0
103103 8.00000i 0.788263i −0.919054 0.394132i 0.871045π-0.871045\pi
0.919054 0.394132i 0.128955π-0.128955\pi
104104 0 0
105105 0 0
106106 3.00000 0.291386
107107 6.00000i 0.580042i −0.957020 0.290021i 0.906338π-0.906338\pi
0.957020 0.290021i 0.0936623π-0.0936623\pi
108108 0 0
109109 −1.00000 −0.0957826 −0.0478913 0.998853i 0.515250π-0.515250\pi
−0.0478913 + 0.998853i 0.515250π0.515250\pi
110110 −10.0000 5.00000i −0.953463 0.476731i
111111 0 0
112112 1.00000i 0.0944911i
113113 21.0000i 1.97551i −0.156001 0.987757i 0.549860π-0.549860\pi
0.156001 0.987757i 0.450140π-0.450140\pi
114114 0 0
115115 −8.00000 4.00000i −0.746004 0.373002i
116116 3.00000 0.278543
117117 0 0
118118 8.00000i 0.736460i
119119 1.00000 0.0916698
120120 0 0
121121 14.0000 1.27273
122122 5.00000i 0.452679i
123123 0 0
124124 −1.00000 −0.0898027
125125 11.0000 2.00000i 0.983870 0.178885i
126126 0 0
127127 8.00000i 0.709885i −0.934888 0.354943i 0.884500π-0.884500\pi
0.934888 0.354943i 0.115500π-0.115500\pi
128128 1.00000i 0.0883883i
129129 0 0
130130 0 0
131131 6.00000 0.524222 0.262111 0.965038i 0.415581π-0.415581\pi
0.262111 + 0.965038i 0.415581π0.415581\pi
132132 0 0
133133 0 0
134134 −4.00000 −0.345547
135135 0 0
136136 1.00000 0.0857493
137137 18.0000i 1.53784i −0.639343 0.768922i 0.720793π-0.720793\pi
0.639343 0.768922i 0.279207π-0.279207\pi
138138 0 0
139139 11.0000 0.933008 0.466504 0.884519i 0.345513π-0.345513\pi
0.466504 + 0.884519i 0.345513π0.345513\pi
140140 2.00000 + 1.00000i 0.169031 + 0.0845154i
141141 0 0
142142 6.00000i 0.503509i
143143 0 0
144144 0 0
145145 3.00000 6.00000i 0.249136 0.498273i
146146 −10.0000 −0.827606
147147 0 0
148148 1.00000i 0.0821995i
149149 4.00000 0.327693 0.163846 0.986486i 0.447610π-0.447610\pi
0.163846 + 0.986486i 0.447610π0.447610\pi
150150 0 0
151151 −2.00000 −0.162758 −0.0813788 0.996683i 0.525932π-0.525932\pi
−0.0813788 + 0.996683i 0.525932π0.525932\pi
152152 0 0
153153 0 0
154154 −5.00000 −0.402911
155155 −1.00000 + 2.00000i −0.0803219 + 0.160644i
156156 0 0
157157 23.0000i 1.83560i 0.397043 + 0.917800i 0.370036π0.370036\pi
−0.397043 + 0.917800i 0.629964π0.629964\pi
158158 0 0
159159 0 0
160160 2.00000 + 1.00000i 0.158114 + 0.0790569i
161161 −4.00000 −0.315244
162162 0 0
163163 1.00000i 0.0783260i 0.999233 + 0.0391630i 0.0124692π0.0124692\pi
−0.999233 + 0.0391630i 0.987531π0.987531\pi
164164 −1.00000 −0.0780869
165165 0 0
166166 −8.00000 −0.620920
167167 6.00000i 0.464294i 0.972681 + 0.232147i 0.0745750π0.0745750\pi
−0.972681 + 0.232147i 0.925425π0.925425\pi
168168 0 0
169169 13.0000 1.00000
170170 1.00000 2.00000i 0.0766965 0.153393i
171171 0 0
172172 7.00000i 0.533745i
173173 13.0000i 0.988372i −0.869356 0.494186i 0.835466π-0.835466\pi
0.869356 0.494186i 0.164534π-0.164534\pi
174174 0 0
175175 4.00000 3.00000i 0.302372 0.226779i
176176 −5.00000 −0.376889
177177 0 0
178178 8.00000i 0.599625i
179179 10.0000 0.747435 0.373718 0.927543i 0.378083π-0.378083\pi
0.373718 + 0.927543i 0.378083π0.378083\pi
180180 0 0
181181 −16.0000 −1.18927 −0.594635 0.803996i 0.702704π-0.702704\pi
−0.594635 + 0.803996i 0.702704π0.702704\pi
182182 0 0
183183 0 0
184184 −4.00000 −0.294884
185185 2.00000 + 1.00000i 0.147043 + 0.0735215i
186186 0 0
187187 5.00000i 0.365636i
188188 4.00000i 0.291730i
189189 0 0
190190 0 0
191191 −3.00000 −0.217072 −0.108536 0.994092i 0.534616π-0.534616\pi
−0.108536 + 0.994092i 0.534616π0.534616\pi
192192 0 0
193193 10.0000i 0.719816i −0.932988 0.359908i 0.882808π-0.882808\pi
0.932988 0.359908i 0.117192π-0.117192\pi
194194 −1.00000 −0.0717958
195195 0 0
196196 −6.00000 −0.428571
197197 26.0000i 1.85242i −0.377004 0.926212i 0.623046π-0.623046\pi
0.377004 0.926212i 0.376954π-0.376954\pi
198198 0 0
199199 −24.0000 −1.70131 −0.850657 0.525720i 0.823796π-0.823796\pi
−0.850657 + 0.525720i 0.823796π0.823796\pi
200200 4.00000 3.00000i 0.282843 0.212132i
201201 0 0
202202 10.0000i 0.703598i
203203 3.00000i 0.210559i
204204 0 0
205205 −1.00000 + 2.00000i −0.0698430 + 0.139686i
206206 −8.00000 −0.557386
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −21.0000 −1.44570 −0.722850 0.691005i 0.757168π-0.757168\pi
−0.722850 + 0.691005i 0.757168π0.757168\pi
212212 3.00000i 0.206041i
213213 0 0
214214 −6.00000 −0.410152
215215 14.0000 + 7.00000i 0.954792 + 0.477396i
216216 0 0
217217 1.00000i 0.0678844i
218218 1.00000i 0.0677285i
219219 0 0
220220 −5.00000 + 10.0000i −0.337100 + 0.674200i
221221 0 0
222222 0 0
223223 5.00000i 0.334825i 0.985887 + 0.167412i 0.0535411π0.0535411\pi
−0.985887 + 0.167412i 0.946459π0.946459\pi
224224 1.00000 0.0668153
225225 0 0
226226 −21.0000 −1.39690
227227 1.00000i 0.0663723i −0.999449 0.0331862i 0.989435π-0.989435\pi
0.999449 0.0331862i 0.0105654π-0.0105654\pi
228228 0 0
229229 16.0000 1.05731 0.528655 0.848837i 0.322697π-0.322697\pi
0.528655 + 0.848837i 0.322697π0.322697\pi
230230 −4.00000 + 8.00000i −0.263752 + 0.527504i
231231 0 0
232232 3.00000i 0.196960i
233233 10.0000i 0.655122i −0.944830 0.327561i 0.893773π-0.893773\pi
0.944830 0.327561i 0.106227π-0.106227\pi
234234 0 0
235235 −8.00000 4.00000i −0.521862 0.260931i
236236 8.00000 0.520756
237237 0 0
238238 1.00000i 0.0648204i
239239 11.0000 0.711531 0.355765 0.934575i 0.384220π-0.384220\pi
0.355765 + 0.934575i 0.384220π0.384220\pi
240240 0 0
241241 −2.00000 −0.128831 −0.0644157 0.997923i 0.520518π-0.520518\pi
−0.0644157 + 0.997923i 0.520518π0.520518\pi
242242 14.0000i 0.899954i
243243 0 0
244244 −5.00000 −0.320092
245245 −6.00000 + 12.0000i −0.383326 + 0.766652i
246246 0 0
247247 0 0
248248 1.00000i 0.0635001i
249249 0 0
250250 −2.00000 11.0000i −0.126491 0.695701i
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 20.0000i 1.25739i
254254 −8.00000 −0.501965
255255 0 0
256256 1.00000 0.0625000
257257 6.00000i 0.374270i −0.982334 0.187135i 0.940080π-0.940080\pi
0.982334 0.187135i 0.0599201π-0.0599201\pi
258258 0 0
259259 1.00000 0.0621370
260260 0 0
261261 0 0
262262 6.00000i 0.370681i
263263 19.0000i 1.17159i 0.810459 + 0.585795i 0.199218π0.199218\pi
−0.810459 + 0.585795i 0.800782π0.800782\pi
264264 0 0
265265 −6.00000 3.00000i −0.368577 0.184289i
266266 0 0
267267 0 0
268268 4.00000i 0.244339i
269269 −12.0000 −0.731653 −0.365826 0.930683i 0.619214π-0.619214\pi
−0.365826 + 0.930683i 0.619214π0.619214\pi
270270 0 0
271271 −14.0000 −0.850439 −0.425220 0.905090i 0.639803π-0.639803\pi
−0.425220 + 0.905090i 0.639803π0.639803\pi
272272 1.00000i 0.0606339i
273273 0 0
274274 −18.0000 −1.08742
275275 15.0000 + 20.0000i 0.904534 + 1.20605i
276276 0 0
277277 8.00000i 0.480673i −0.970690 0.240337i 0.922742π-0.922742\pi
0.970690 0.240337i 0.0772579π-0.0772579\pi
278278 11.0000i 0.659736i
279279 0 0
280280 1.00000 2.00000i 0.0597614 0.119523i
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 0 0
283283 16.0000i 0.951101i 0.879688 + 0.475551i 0.157751π0.157751\pi
−0.879688 + 0.475551i 0.842249π0.842249\pi
284284 −6.00000 −0.356034
285285 0 0
286286 0 0
287287 1.00000i 0.0590281i
288288 0 0
289289 16.0000 0.941176
290290 −6.00000 3.00000i −0.352332 0.176166i
291291 0 0
292292 10.0000i 0.585206i
293293 9.00000i 0.525786i 0.964825 + 0.262893i 0.0846766π0.0846766\pi
−0.964825 + 0.262893i 0.915323π0.915323\pi
294294 0 0
295295 8.00000 16.0000i 0.465778 0.931556i
296296 1.00000 0.0581238
297297 0 0
298298 4.00000i 0.231714i
299299 0 0
300300 0 0
301301 7.00000 0.403473
302302 2.00000i 0.115087i
303303 0 0
304304 0 0
305305 −5.00000 + 10.0000i −0.286299 + 0.572598i
306306 0 0
307307 0 0 1.00000 00
−1.00000 π\pi
308308 5.00000i 0.284901i
309309 0 0
310310 2.00000 + 1.00000i 0.113592 + 0.0567962i
311311 −15.0000 −0.850572 −0.425286 0.905059i 0.639826π-0.639826\pi
−0.425286 + 0.905059i 0.639826π0.639826\pi
312312 0 0
313313 10.0000i 0.565233i −0.959233 0.282617i 0.908798π-0.908798\pi
0.959233 0.282617i 0.0912024π-0.0912024\pi
314314 23.0000 1.29797
315315 0 0
316316 0 0
317317 5.00000i 0.280828i 0.990093 + 0.140414i 0.0448433π0.0448433\pi
−0.990093 + 0.140414i 0.955157π0.955157\pi
318318 0 0
319319 15.0000 0.839839
320320 1.00000 2.00000i 0.0559017 0.111803i
321321 0 0
322322 4.00000i 0.222911i
323323 0 0
324324 0 0
325325 0 0
326326 1.00000 0.0553849
327327 0 0
328328 1.00000i 0.0552158i
329329 −4.00000 −0.220527
330330 0 0
331331 −26.0000 −1.42909 −0.714545 0.699590i 0.753366π-0.753366\pi
−0.714545 + 0.699590i 0.753366π0.753366\pi
332332 8.00000i 0.439057i
333333 0 0
334334 6.00000 0.328305
335335 8.00000 + 4.00000i 0.437087 + 0.218543i
336336 0 0
337337 16.0000i 0.871576i 0.900049 + 0.435788i 0.143530π0.143530\pi
−0.900049 + 0.435788i 0.856470π0.856470\pi
338338 13.0000i 0.707107i
339339 0 0
340340 −2.00000 1.00000i −0.108465 0.0542326i
341341 −5.00000 −0.270765
342342 0 0
343343 13.0000i 0.701934i
344344 7.00000 0.377415
345345 0 0
346346 −13.0000 −0.698884
347347 12.0000i 0.644194i −0.946707 0.322097i 0.895612π-0.895612\pi
0.946707 0.322097i 0.104388π-0.104388\pi
348348 0 0
349349 2.00000 0.107058 0.0535288 0.998566i 0.482953π-0.482953\pi
0.0535288 + 0.998566i 0.482953π0.482953\pi
350350 −3.00000 4.00000i −0.160357 0.213809i
351351 0 0
352352 5.00000i 0.266501i
353353 31.0000i 1.64996i −0.565159 0.824982i 0.691185π-0.691185\pi
0.565159 0.824982i 0.308815π-0.308815\pi
354354 0 0
355355 −6.00000 + 12.0000i −0.318447 + 0.636894i
356356 −8.00000 −0.423999
357357 0 0
358358 10.0000i 0.528516i
359359 6.00000 0.316668 0.158334 0.987386i 0.449388π-0.449388\pi
0.158334 + 0.987386i 0.449388π0.449388\pi
360360 0 0
361361 −19.0000 −1.00000
362362 16.0000i 0.840941i
363363 0 0
364364 0 0
365365 20.0000 + 10.0000i 1.04685 + 0.523424i
366366 0 0
367367 13.0000i 0.678594i 0.940679 + 0.339297i 0.110189π0.110189\pi
−0.940679 + 0.339297i 0.889811π0.889811\pi
368368 4.00000i 0.208514i
369369 0 0
370370 1.00000 2.00000i 0.0519875 0.103975i
371371 −3.00000 −0.155752
372372 0 0
373373 6.00000i 0.310668i −0.987862 0.155334i 0.950355π-0.950355\pi
0.987862 0.155334i 0.0496454π-0.0496454\pi
374374 5.00000 0.258544
375375 0 0
376376 −4.00000 −0.206284
377377 0 0
378378 0 0
379379 −20.0000 −1.02733 −0.513665 0.857991i 0.671713π-0.671713\pi
−0.513665 + 0.857991i 0.671713π0.671713\pi
380380 0 0
381381 0 0
382382 3.00000i 0.153493i
383383 8.00000i 0.408781i 0.978889 + 0.204390i 0.0655212π0.0655212\pi
−0.978889 + 0.204390i 0.934479π0.934479\pi
384384 0 0
385385 10.0000 + 5.00000i 0.509647 + 0.254824i
386386 −10.0000 −0.508987
387387 0 0
388388 1.00000i 0.0507673i
389389 23.0000 1.16615 0.583073 0.812420i 0.301850π-0.301850\pi
0.583073 + 0.812420i 0.301850π0.301850\pi
390390 0 0
391391 4.00000 0.202289
392392 6.00000i 0.303046i
393393 0 0
394394 −26.0000 −1.30986
395395 0 0
396396 0 0
397397 22.0000i 1.10415i 0.833795 + 0.552074i 0.186163π0.186163\pi
−0.833795 + 0.552074i 0.813837π0.813837\pi
398398 24.0000i 1.20301i
399399 0 0
400400 −3.00000 4.00000i −0.150000 0.200000i
401401 −10.0000 −0.499376 −0.249688 0.968326i 0.580328π-0.580328\pi
−0.249688 + 0.968326i 0.580328π0.580328\pi
402402 0 0
403403 0 0
404404 10.0000 0.497519
405405 0 0
406406 −3.00000 −0.148888
407407 5.00000i 0.247841i
408408 0 0
409409 40.0000 1.97787 0.988936 0.148340i 0.0473931π-0.0473931\pi
0.988936 + 0.148340i 0.0473931π0.0473931\pi
410410 2.00000 + 1.00000i 0.0987730 + 0.0493865i
411411 0 0
412412 8.00000i 0.394132i
413413 8.00000i 0.393654i
414414 0 0
415415 16.0000 + 8.00000i 0.785409 + 0.392705i
416416 0 0
417417 0 0
418418 0 0
419419 20.0000 0.977064 0.488532 0.872546i 0.337533π-0.337533\pi
0.488532 + 0.872546i 0.337533π0.337533\pi
420420 0 0
421421 −38.0000 −1.85201 −0.926003 0.377515i 0.876779π-0.876779\pi
−0.926003 + 0.377515i 0.876779π0.876779\pi
422422 21.0000i 1.02226i
423423 0 0
424424 −3.00000 −0.145693
425425 −4.00000 + 3.00000i −0.194029 + 0.145521i
426426 0 0
427427 5.00000i 0.241967i
428428 6.00000i 0.290021i
429429 0 0
430430 7.00000 14.0000i 0.337570 0.675140i
431431 13.0000 0.626188 0.313094 0.949722i 0.398635π-0.398635\pi
0.313094 + 0.949722i 0.398635π0.398635\pi
432432 0 0
433433 20.0000i 0.961139i 0.876957 + 0.480569i 0.159570π0.159570\pi
−0.876957 + 0.480569i 0.840430π0.840430\pi
434434 1.00000 0.0480015
435435 0 0
436436 1.00000 0.0478913
437437 0 0
438438 0 0
439439 33.0000 1.57500 0.787502 0.616312i 0.211374π-0.211374\pi
0.787502 + 0.616312i 0.211374π0.211374\pi
440440 10.0000 + 5.00000i 0.476731 + 0.238366i
441441 0 0
442442 0 0
443443 6.00000i 0.285069i −0.989790 0.142534i 0.954475π-0.954475\pi
0.989790 0.142534i 0.0455251π-0.0455251\pi
444444 0 0
445445 −8.00000 + 16.0000i −0.379236 + 0.758473i
446446 5.00000 0.236757
447447 0 0
448448 1.00000i 0.0472456i
449449 −24.0000 −1.13263 −0.566315 0.824189i 0.691631π-0.691631\pi
−0.566315 + 0.824189i 0.691631π0.691631\pi
450450 0 0
451451 −5.00000 −0.235441
452452 21.0000i 0.987757i
453453 0 0
454454 −1.00000 −0.0469323
455455 0 0
456456 0 0
457457 19.0000i 0.888783i 0.895833 + 0.444391i 0.146580π0.146580\pi
−0.895833 + 0.444391i 0.853420π0.853420\pi
458458 16.0000i 0.747631i
459459 0 0
460460 8.00000 + 4.00000i 0.373002 + 0.186501i
461461 −3.00000 −0.139724 −0.0698620 0.997557i 0.522256π-0.522256\pi
−0.0698620 + 0.997557i 0.522256π0.522256\pi
462462 0 0
463463 24.0000i 1.11537i 0.830051 + 0.557687i 0.188311π0.188311\pi
−0.830051 + 0.557687i 0.811689π0.811689\pi
464464 −3.00000 −0.139272
465465 0 0
466466 −10.0000 −0.463241
467467 27.0000i 1.24941i −0.780860 0.624705i 0.785219π-0.785219\pi
0.780860 0.624705i 0.214781π-0.214781\pi
468468 0 0
469469 4.00000 0.184703
470470 −4.00000 + 8.00000i −0.184506 + 0.369012i
471471 0 0
472472 8.00000i 0.368230i
473473 35.0000i 1.60930i
474474 0 0
475475 0 0
476476 −1.00000 −0.0458349
477477 0 0
478478 11.0000i 0.503128i
479479 −28.0000 −1.27935 −0.639676 0.768644i 0.720932π-0.720932\pi
−0.639676 + 0.768644i 0.720932π0.720932\pi
480480 0 0
481481 0 0
482482 2.00000i 0.0910975i
483483 0 0
484484 −14.0000 −0.636364
485485 2.00000 + 1.00000i 0.0908153 + 0.0454077i
486486 0 0
487487 12.0000i 0.543772i −0.962329 0.271886i 0.912353π-0.912353\pi
0.962329 0.271886i 0.0876473π-0.0876473\pi
488488 5.00000i 0.226339i
489489 0 0
490490 12.0000 + 6.00000i 0.542105 + 0.271052i
491491 −12.0000 −0.541552 −0.270776 0.962642i 0.587280π-0.587280\pi
−0.270776 + 0.962642i 0.587280π0.587280\pi
492492 0 0
493493 3.00000i 0.135113i
494494 0 0
495495 0 0
496496 1.00000 0.0449013
497497 6.00000i 0.269137i
498498 0 0
499499 30.0000 1.34298 0.671492 0.741012i 0.265654π-0.265654\pi
0.671492 + 0.741012i 0.265654π0.265654\pi
500500 −11.0000 + 2.00000i −0.491935 + 0.0894427i
501501 0 0
502502 0 0
503503 6.00000i 0.267527i 0.991013 + 0.133763i 0.0427062π0.0427062\pi
−0.991013 + 0.133763i 0.957294π0.957294\pi
504504 0 0
505505 10.0000 20.0000i 0.444994 0.889988i
506506 −20.0000 −0.889108
507507 0 0
508508 8.00000i 0.354943i
509509 −42.0000 −1.86162 −0.930809 0.365507i 0.880896π-0.880896\pi
−0.930809 + 0.365507i 0.880896π0.880896\pi
510510 0 0
511511 10.0000 0.442374
512512 1.00000i 0.0441942i
513513 0 0
514514 −6.00000 −0.264649
515515 16.0000 + 8.00000i 0.705044 + 0.352522i
516516 0 0
517517 20.0000i 0.879599i
518518 1.00000i 0.0439375i
519519 0 0
520520 0 0
521521 35.0000 1.53338 0.766689 0.642019i 0.221903π-0.221903\pi
0.766689 + 0.642019i 0.221903π0.221903\pi
522522 0 0
523523 20.0000i 0.874539i −0.899331 0.437269i 0.855946π-0.855946\pi
0.899331 0.437269i 0.144054π-0.144054\pi
524524 −6.00000 −0.262111
525525 0 0
526526 19.0000 0.828439
527527 1.00000i 0.0435607i
528528 0 0
529529 7.00000 0.304348
530530 −3.00000 + 6.00000i −0.130312 + 0.260623i
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 12.0000 + 6.00000i 0.518805 + 0.259403i
536536 4.00000 0.172774
537537 0 0
538538 12.0000i 0.517357i
539539 −30.0000 −1.29219
540540 0 0
541541 34.0000 1.46177 0.730887 0.682498i 0.239107π-0.239107\pi
0.730887 + 0.682498i 0.239107π0.239107\pi
542542 14.0000i 0.601351i
543543 0 0
544544 −1.00000 −0.0428746
545545 1.00000 2.00000i 0.0428353 0.0856706i
546546 0 0
547547 41.0000i 1.75303i −0.481371 0.876517i 0.659861π-0.659861\pi
0.481371 0.876517i 0.340139π-0.340139\pi
548548 18.0000i 0.768922i
549549 0 0
550550 20.0000 15.0000i 0.852803 0.639602i
551551 0 0
552552 0 0
553553 0 0
554554 −8.00000 −0.339887
555555 0 0
556556 −11.0000 −0.466504
557557 6.00000i 0.254228i −0.991888 0.127114i 0.959429π-0.959429\pi
0.991888 0.127114i 0.0405714π-0.0405714\pi
558558 0 0
559559 0 0
560560 −2.00000 1.00000i −0.0845154 0.0422577i
561561 0 0
562562 18.0000i 0.759284i
563563 19.0000i 0.800755i −0.916350 0.400377i 0.868879π-0.868879\pi
0.916350 0.400377i 0.131121π-0.131121\pi
564564 0 0
565565 42.0000 + 21.0000i 1.76695 + 0.883477i
566566 16.0000 0.672530
567567 0 0
568568 6.00000i 0.251754i
569569 −10.0000 −0.419222 −0.209611 0.977785i 0.567220π-0.567220\pi
−0.209611 + 0.977785i 0.567220π0.567220\pi
570570 0 0
571571 −29.0000 −1.21361 −0.606806 0.794850i 0.707550π-0.707550\pi
−0.606806 + 0.794850i 0.707550π0.707550\pi
572572 0 0
573573 0 0
574574 1.00000 0.0417392
575575 16.0000 12.0000i 0.667246 0.500435i
576576 0 0
577577 22.0000i 0.915872i 0.888985 + 0.457936i 0.151411π0.151411\pi
−0.888985 + 0.457936i 0.848589π0.848589\pi
578578 16.0000i 0.665512i
579579 0 0
580580 −3.00000 + 6.00000i −0.124568 + 0.249136i
581581 8.00000 0.331896
582582 0 0
583583 15.0000i 0.621237i
584584 10.0000 0.413803
585585 0 0
586586 9.00000 0.371787
587587 33.0000i 1.36206i 0.732257 + 0.681028i 0.238467π0.238467\pi
−0.732257 + 0.681028i 0.761533π0.761533\pi
588588 0 0
589589 0 0
590590 −16.0000 8.00000i −0.658710 0.329355i
591591 0 0
592592 1.00000i 0.0410997i
593593 24.0000i 0.985562i −0.870153 0.492781i 0.835980π-0.835980\pi
0.870153 0.492781i 0.164020π-0.164020\pi
594594 0 0
595595 −1.00000 + 2.00000i −0.0409960 + 0.0819920i
596596 −4.00000 −0.163846
597597 0 0
598598 0 0
599599 24.0000 0.980613 0.490307 0.871550i 0.336885π-0.336885\pi
0.490307 + 0.871550i 0.336885π0.336885\pi
600600 0 0
601601 −7.00000 −0.285536 −0.142768 0.989756i 0.545600π-0.545600\pi
−0.142768 + 0.989756i 0.545600π0.545600\pi
602602 7.00000i 0.285299i
603603 0 0
604604 2.00000 0.0813788
605605 −14.0000 + 28.0000i −0.569181 + 1.13836i
606606 0 0
607607 10.0000i 0.405887i −0.979190 0.202944i 0.934949π-0.934949\pi
0.979190 0.202944i 0.0650509π-0.0650509\pi
608608 0 0
609609 0 0
610610 10.0000 + 5.00000i 0.404888 + 0.202444i
611611 0 0
612612 0 0
613613 37.0000i 1.49442i −0.664590 0.747208i 0.731394π-0.731394\pi
0.664590 0.747208i 0.268606π-0.268606\pi
614614 0 0
615615 0 0
616616 5.00000 0.201456
617617 34.0000i 1.36879i −0.729112 0.684394i 0.760067π-0.760067\pi
0.729112 0.684394i 0.239933π-0.239933\pi
618618 0 0
619619 31.0000 1.24600 0.622998 0.782224i 0.285915π-0.285915\pi
0.622998 + 0.782224i 0.285915π0.285915\pi
620620 1.00000 2.00000i 0.0401610 0.0803219i
621621 0 0
622622 15.0000i 0.601445i
623623 8.00000i 0.320513i
624624 0 0
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 −10.0000 −0.399680
627627 0 0
628628 23.0000i 0.917800i
629629 −1.00000 −0.0398726
630630 0 0
631631 5.00000 0.199047 0.0995234 0.995035i 0.468268π-0.468268\pi
0.0995234 + 0.995035i 0.468268π0.468268\pi
632632 0 0
633633 0 0
634634 5.00000 0.198575
635635 16.0000 + 8.00000i 0.634941 + 0.317470i
636636 0 0
637637 0 0
638638 15.0000i 0.593856i
639639 0 0
640640 −2.00000 1.00000i −0.0790569 0.0395285i
641641 37.0000 1.46141 0.730706 0.682692i 0.239191π-0.239191\pi
0.730706 + 0.682692i 0.239191π0.239191\pi
642642 0 0
643643 21.0000i 0.828159i 0.910241 + 0.414080i 0.135896π0.135896\pi
−0.910241 + 0.414080i 0.864104π0.864104\pi
644644 4.00000 0.157622
645645 0 0
646646 0 0
647647 42.0000i 1.65119i −0.564263 0.825595i 0.690840π-0.690840\pi
0.564263 0.825595i 0.309160π-0.309160\pi
648648 0 0
649649 40.0000 1.57014
650650 0 0
651651 0 0
652652 1.00000i 0.0391630i
653653 10.0000i 0.391330i 0.980671 + 0.195665i 0.0626866π0.0626866\pi
−0.980671 + 0.195665i 0.937313π0.937313\pi
654654 0 0
655655 −6.00000 + 12.0000i −0.234439 + 0.468879i
656656 1.00000 0.0390434
657657 0 0
658658 4.00000i 0.155936i
659659 −32.0000 −1.24654 −0.623272 0.782006i 0.714197π-0.714197\pi
−0.623272 + 0.782006i 0.714197π0.714197\pi
660660 0 0
661661 −13.0000 −0.505641 −0.252821 0.967513i 0.581358π-0.581358\pi
−0.252821 + 0.967513i 0.581358π0.581358\pi
662662 26.0000i 1.01052i
663663 0 0
664664 8.00000 0.310460
665665 0 0
666666 0 0
667667 12.0000i 0.464642i
668668 6.00000i 0.232147i
669669 0 0
670670 4.00000 8.00000i 0.154533 0.309067i
671671 −25.0000 −0.965114
672672 0 0
673673 36.0000i 1.38770i −0.720121 0.693849i 0.755914π-0.755914\pi
0.720121 0.693849i 0.244086π-0.244086\pi
674674 16.0000 0.616297
675675 0 0
676676 −13.0000 −0.500000
677677 2.00000i 0.0768662i 0.999261 + 0.0384331i 0.0122367π0.0122367\pi
−0.999261 + 0.0384331i 0.987763π0.987763\pi
678678 0 0
679679 1.00000 0.0383765
680680 −1.00000 + 2.00000i −0.0383482 + 0.0766965i
681681 0 0
682682 5.00000i 0.191460i
683683 37.0000i 1.41577i 0.706330 + 0.707883i 0.250350π0.250350\pi
−0.706330 + 0.707883i 0.749650π0.749650\pi
684684 0 0
685685 36.0000 + 18.0000i 1.37549 + 0.687745i
686686 13.0000 0.496342
687687 0 0
688688 7.00000i 0.266872i
689689 0 0
690690 0 0
691691 −5.00000 −0.190209 −0.0951045 0.995467i 0.530319π-0.530319\pi
−0.0951045 + 0.995467i 0.530319π0.530319\pi
692692 13.0000i 0.494186i
693693 0 0
694694 −12.0000 −0.455514
695695 −11.0000 + 22.0000i −0.417254 + 0.834508i
696696 0 0
697697 1.00000i 0.0378777i
698698 2.00000i 0.0757011i
699699 0 0
700700 −4.00000 + 3.00000i −0.151186 + 0.113389i
701701 −26.0000 −0.982006 −0.491003 0.871158i 0.663370π-0.663370\pi
−0.491003 + 0.871158i 0.663370π0.663370\pi
702702 0 0
703703 0 0
704704 5.00000 0.188445
705705 0 0
706706 −31.0000 −1.16670
707707 10.0000i 0.376089i
708708 0 0
709709 −9.00000 −0.338002 −0.169001 0.985616i 0.554054π-0.554054\pi
−0.169001 + 0.985616i 0.554054π0.554054\pi
710710 12.0000 + 6.00000i 0.450352 + 0.225176i
711711 0 0
712712 8.00000i 0.299813i
713713 4.00000i 0.149801i
714714 0 0
715715 0 0
716716 −10.0000 −0.373718
717717 0 0
718718 6.00000i 0.223918i
719719 −28.0000 −1.04422 −0.522112 0.852877i 0.674856π-0.674856\pi
−0.522112 + 0.852877i 0.674856π0.674856\pi
720720 0 0
721721 8.00000 0.297936
722722 19.0000i 0.707107i
723723 0 0
724724 16.0000 0.594635
725725 9.00000 + 12.0000i 0.334252 + 0.445669i
726726 0 0
727727 42.0000i 1.55769i −0.627214 0.778847i 0.715805π-0.715805\pi
0.627214 0.778847i 0.284195π-0.284195\pi
728728 0 0
729729 0 0
730730 10.0000 20.0000i 0.370117 0.740233i
731731 −7.00000 −0.258904
732732 0 0
733733 19.0000i 0.701781i 0.936416 + 0.350891i 0.114121π0.114121\pi
−0.936416 + 0.350891i 0.885879π0.885879\pi
734734 13.0000 0.479839
735735 0 0
736736 4.00000 0.147442
737737 20.0000i 0.736709i
738738 0 0
739739 −37.0000 −1.36107 −0.680534 0.732717i 0.738252π-0.738252\pi
−0.680534 + 0.732717i 0.738252π0.738252\pi
740740 −2.00000 1.00000i −0.0735215 0.0367607i
741741 0 0
742742 3.00000i 0.110133i
743743 15.0000i 0.550297i 0.961402 + 0.275148i 0.0887270π0.0887270\pi
−0.961402 + 0.275148i 0.911273π0.911273\pi
744744 0 0
745745 −4.00000 + 8.00000i −0.146549 + 0.293097i
746746 −6.00000 −0.219676
747747 0 0
748748 5.00000i 0.182818i
749749 6.00000 0.219235
750750 0 0
751751 20.0000 0.729810 0.364905 0.931045i 0.381101π-0.381101\pi
0.364905 + 0.931045i 0.381101π0.381101\pi
752752 4.00000i 0.145865i
753753 0 0
754754 0 0
755755 2.00000 4.00000i 0.0727875 0.145575i
756756 0 0
757757 20.0000i 0.726912i −0.931611 0.363456i 0.881597π-0.881597\pi
0.931611 0.363456i 0.118403π-0.118403\pi
758758 20.0000i 0.726433i
759759 0 0
760760 0 0
761761 21.0000 0.761249 0.380625 0.924730i 0.375709π-0.375709\pi
0.380625 + 0.924730i 0.375709π0.375709\pi
762762 0 0
763763 1.00000i 0.0362024i
764764 3.00000 0.108536
765765 0 0
766766 8.00000 0.289052
767767 0 0
768768 0 0
769769 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
770770 5.00000 10.0000i 0.180187 0.360375i
771771 0 0
772772 10.0000i 0.359908i
773773 27.0000i 0.971123i −0.874203 0.485561i 0.838615π-0.838615\pi
0.874203 0.485561i 0.161385π-0.161385\pi
774774 0 0
775775 −3.00000 4.00000i −0.107763 0.143684i
776776 1.00000 0.0358979
777777 0 0
778778 23.0000i 0.824590i
779779 0 0
780780 0 0
781781 −30.0000 −1.07348
782782 4.00000i 0.143040i
783783 0 0
784784 6.00000 0.214286
785785 −46.0000 23.0000i −1.64181 0.820905i
786786 0 0
787787 10.0000i 0.356462i 0.983989 + 0.178231i 0.0570374π0.0570374\pi
−0.983989 + 0.178231i 0.942963π0.942963\pi
788788 26.0000i 0.926212i
789789 0 0
790790 0 0
791791 21.0000 0.746674
792792 0 0
793793 0 0
794794 22.0000 0.780751
795795 0 0
796796 24.0000 0.850657
797797 8.00000i 0.283375i 0.989911 + 0.141687i 0.0452527π0.0452527\pi
−0.989911 + 0.141687i 0.954747π0.954747\pi
798798 0 0
799799 4.00000 0.141510
800800 −4.00000 + 3.00000i −0.141421 + 0.106066i
801801 0 0
802802 10.0000i 0.353112i
803803 50.0000i 1.76446i
804804 0 0
805805 4.00000 8.00000i 0.140981 0.281963i
806806 0 0
807807 0 0
808808 10.0000i 0.351799i
809809 48.0000 1.68759 0.843795 0.536666i 0.180316π-0.180316\pi
0.843795 + 0.536666i 0.180316π0.180316\pi
810810 0 0
811811 −8.00000 −0.280918 −0.140459 0.990086i 0.544858π-0.544858\pi
−0.140459 + 0.990086i 0.544858π0.544858\pi
812812 3.00000i 0.105279i
813813 0 0
814814 5.00000 0.175250
815815 −2.00000 1.00000i −0.0700569 0.0350285i
816816 0 0
817817 0 0
818818 40.0000i 1.39857i
819819 0 0
820820 1.00000 2.00000i 0.0349215 0.0698430i
821821 50.0000 1.74501 0.872506 0.488603i 0.162493π-0.162493\pi
0.872506 + 0.488603i 0.162493π0.162493\pi
822822 0 0
823823 24.0000i 0.836587i 0.908312 + 0.418294i 0.137372π0.137372\pi
−0.908312 + 0.418294i 0.862628π0.862628\pi
824824 8.00000 0.278693
825825 0 0
826826 −8.00000 −0.278356
827827 35.0000i 1.21707i 0.793527 + 0.608535i 0.208242π0.208242\pi
−0.793527 + 0.608535i 0.791758π0.791758\pi
828828 0 0
829829 −21.0000 −0.729360 −0.364680 0.931133i 0.618822π-0.618822\pi
−0.364680 + 0.931133i 0.618822π0.618822\pi
830830 8.00000 16.0000i 0.277684 0.555368i
831831 0 0
832832 0 0
833833 6.00000i 0.207888i
834834 0 0
835835 −12.0000 6.00000i −0.415277 0.207639i
836836 0 0
837837 0 0
838838 20.0000i 0.690889i
839839 40.0000 1.38095 0.690477 0.723355i 0.257401π-0.257401\pi
0.690477 + 0.723355i 0.257401π0.257401\pi
840840 0 0
841841 −20.0000 −0.689655
842842 38.0000i 1.30957i
843843 0 0
844844 21.0000 0.722850
845845 −13.0000 + 26.0000i −0.447214 + 0.894427i
846846 0 0
847847 14.0000i 0.481046i
848848 3.00000i 0.103020i
849849 0 0
850850 3.00000 + 4.00000i 0.102899 + 0.137199i
851851 4.00000 0.137118
852852 0 0
853853 2.00000i 0.0684787i −0.999414 0.0342393i 0.989099π-0.989099\pi
0.999414 0.0342393i 0.0109009π-0.0109009\pi
854854 5.00000 0.171096
855855 0 0
856856 6.00000 0.205076
857857 27.0000i 0.922302i −0.887322 0.461151i 0.847437π-0.847437\pi
0.887322 0.461151i 0.152563π-0.152563\pi
858858 0 0
859859 −8.00000 −0.272956 −0.136478 0.990643i 0.543578π-0.543578\pi
−0.136478 + 0.990643i 0.543578π0.543578\pi
860860 −14.0000 7.00000i −0.477396 0.238698i
861861 0 0
862862 13.0000i 0.442782i
863863 21.0000i 0.714848i 0.933942 + 0.357424i 0.116345π0.116345\pi
−0.933942 + 0.357424i 0.883655π0.883655\pi
864864 0 0
865865 26.0000 + 13.0000i 0.884027 + 0.442013i
866866 20.0000 0.679628
867867 0 0
868868 1.00000i 0.0339422i
869869 0 0
870870 0 0
871871 0 0
872872 1.00000i 0.0338643i
873873 0 0
874874 0 0
875875 2.00000 + 11.0000i 0.0676123 + 0.371868i
876876 0 0
877877 13.0000i 0.438979i −0.975615 0.219489i 0.929561π-0.929561\pi
0.975615 0.219489i 0.0704391π-0.0704391\pi
878878 33.0000i 1.11370i
879879 0 0
880880 5.00000 10.0000i 0.168550 0.337100i
881881 45.0000 1.51609 0.758044 0.652203i 0.226155π-0.226155\pi
0.758044 + 0.652203i 0.226155π0.226155\pi
882882 0 0
883883 33.0000i 1.11054i −0.831671 0.555269i 0.812615π-0.812615\pi
0.831671 0.555269i 0.187385π-0.187385\pi
884884 0 0
885885 0 0
886886 −6.00000 −0.201574
887887 45.0000i 1.51095i 0.655176 + 0.755476i 0.272594π0.272594\pi
−0.655176 + 0.755476i 0.727406π0.727406\pi
888888 0 0
889889 8.00000 0.268311
890890 16.0000 + 8.00000i 0.536321 + 0.268161i
891891 0 0
892892 5.00000i 0.167412i
893893 0 0
894894 0 0
895895 −10.0000 + 20.0000i −0.334263 + 0.668526i
896896 −1.00000 −0.0334077
897897 0 0
898898 24.0000i 0.800890i
899899 −3.00000 −0.100056
900900 0 0
901901 3.00000 0.0999445
902902 5.00000i 0.166482i
903903 0 0
904904 21.0000 0.698450
905905 16.0000 32.0000i 0.531858 1.06372i
906906 0 0
907907 36.0000i 1.19536i 0.801735 + 0.597680i 0.203911π0.203911\pi
−0.801735 + 0.597680i 0.796089π0.796089\pi
908908 1.00000i 0.0331862i
909909 0 0
910910 0 0
911911 −12.0000 −0.397578 −0.198789 0.980042i 0.563701π-0.563701\pi
−0.198789 + 0.980042i 0.563701π0.563701\pi
912912 0 0
913913 40.0000i 1.32381i
914914 19.0000 0.628464
915915 0 0
916916 −16.0000 −0.528655
917917 6.00000i 0.198137i
918918 0 0
919919 −48.0000 −1.58337 −0.791687 0.610927i 0.790797π-0.790797\pi
−0.791687 + 0.610927i 0.790797π0.790797\pi
920920 4.00000 8.00000i 0.131876 0.263752i
921921 0 0
922922 3.00000i 0.0987997i
923923 0 0
924924 0 0
925925 −4.00000 + 3.00000i −0.131519 + 0.0986394i
926926 24.0000 0.788689
927927 0 0
928928 3.00000i 0.0984798i
929929 −3.00000 −0.0984268 −0.0492134 0.998788i 0.515671π-0.515671\pi
−0.0492134 + 0.998788i 0.515671π0.515671\pi
930930 0 0
931931 0 0
932932 10.0000i 0.327561i
933933 0 0
934934 −27.0000 −0.883467
935935 −10.0000 5.00000i −0.327035 0.163517i
936936 0 0
937937 16.0000i 0.522697i −0.965244 0.261349i 0.915833π-0.915833\pi
0.965244 0.261349i 0.0841672π-0.0841672\pi
938938 4.00000i 0.130605i
939939 0 0
940940 8.00000 + 4.00000i 0.260931 + 0.130466i
941941 22.0000 0.717180 0.358590 0.933495i 0.383258π-0.383258\pi
0.358590 + 0.933495i 0.383258π0.383258\pi
942942 0 0
943943 4.00000i 0.130258i
944944 −8.00000 −0.260378
945945 0 0
946946 35.0000 1.13795
947947 27.0000i 0.877382i 0.898638 + 0.438691i 0.144558π0.144558\pi
−0.898638 + 0.438691i 0.855442π0.855442\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 1.00000i 0.0324102i
953953 14.0000i 0.453504i 0.973952 + 0.226752i 0.0728108π0.0728108\pi
−0.973952 + 0.226752i 0.927189π0.927189\pi
954954 0 0
955955 3.00000 6.00000i 0.0970777 0.194155i
956956 −11.0000 −0.355765
957957 0 0
958958 28.0000i 0.904639i
959959 18.0000 0.581250
960960 0 0
961961 −30.0000 −0.967742
962962 0 0
963963 0 0
964964 2.00000 0.0644157
965965 20.0000 + 10.0000i 0.643823 + 0.321911i
966966 0 0
967967 10.0000i 0.321578i −0.986989 0.160789i 0.948596π-0.948596\pi
0.986989 0.160789i 0.0514039π-0.0514039\pi
968968 14.0000i 0.449977i
969969 0 0
970970 1.00000 2.00000i 0.0321081 0.0642161i
971971 −39.0000 −1.25157 −0.625785 0.779996i 0.715221π-0.715221\pi
−0.625785 + 0.779996i 0.715221π0.715221\pi
972972 0 0
973973 11.0000i 0.352644i
974974 −12.0000 −0.384505
975975 0 0
976976 5.00000 0.160046
977977 3.00000i 0.0959785i 0.998848 + 0.0479893i 0.0152813π0.0152813\pi
−0.998848 + 0.0479893i 0.984719π0.984719\pi
978978 0 0
979979 −40.0000 −1.27841
980980 6.00000 12.0000i 0.191663 0.383326i
981981 0 0
982982 12.0000i 0.382935i
983983 7.00000i 0.223265i −0.993750 0.111633i 0.964392π-0.964392\pi
0.993750 0.111633i 0.0356080π-0.0356080\pi
984984 0 0
985985 52.0000 + 26.0000i 1.65686 + 0.828429i
986986 3.00000 0.0955395
987987 0 0
988988 0 0
989989 28.0000 0.890348
990990 0 0
991991 −5.00000 −0.158830 −0.0794151 0.996842i 0.525305π-0.525305\pi
−0.0794151 + 0.996842i 0.525305π0.525305\pi
992992 1.00000i 0.0317500i
993993 0 0
994994 6.00000 0.190308
995995 24.0000 48.0000i 0.760851 1.52170i
996996 0 0
997997 24.0000i 0.760088i −0.924968 0.380044i 0.875909π-0.875909\pi
0.924968 0.380044i 0.124091π-0.124091\pi
998998 30.0000i 0.949633i
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 3330.2.d.d.1999.1 2
3.2 odd 2 1110.2.d.c.889.2 yes 2
5.4 even 2 inner 3330.2.d.d.1999.2 2
15.2 even 4 5550.2.a.d.1.1 1
15.8 even 4 5550.2.a.bo.1.1 1
15.14 odd 2 1110.2.d.c.889.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.d.c.889.1 2 15.14 odd 2
1110.2.d.c.889.2 yes 2 3.2 odd 2
3330.2.d.d.1999.1 2 1.1 even 1 trivial
3330.2.d.d.1999.2 2 5.4 even 2 inner
5550.2.a.d.1.1 1 15.2 even 4
5550.2.a.bo.1.1 1 15.8 even 4