Properties

Label 1920.2.b.h.191.3
Level 19201920
Weight 22
Character 1920.191
Analytic conductor 15.33115.331
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1920,2,Mod(191,1920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 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("1920.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1920=2735 1920 = 2^{7} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1920.b (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: 15.331277188115.3312771881
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x5+14x48x3+2x2+2x+1 x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25 2^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 191.3
Root 0.5611030.561103i0.561103 - 0.561103i of defining polynomial
Character χ\chi == 1920.191
Dual form 1920.2.b.h.191.4

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+(0.3299981.70032i)q3+1.00000q52.66000iq7+(2.78220+1.12221i)q92.24441iq11+2.74065iq13+(0.3299981.70032i)q15+0.496238iq178.30506q19+(4.52285+0.877793i)q213.15623q23+1.00000q25+(2.82624+4.36032i)q276.55688q291.50376iq31+(3.81623+0.740652i)q332.66000iq359.38064iq37+(4.660000.904410i)q39+10.3657iq41+2.14130q43+(2.78220+1.12221i)q45+8.96505q470.0755782q49+(0.8437660.163758i)q5110.1213q532.24441iq55+(2.74065+14.1213i)q570.435595iq595.87687iq61+(2.98507+7.40065i)q63+2.74065iq6510.1413q67+(1.04155+5.36662i)q694.32752q7110.6101q73+(0.3299981.70032i)q755.97013q7713.2975iq79+(6.481306.24441i)q81+6.08066iq83+0.496238iq85+(2.16376+11.1488i)q87+8.12129iq89+7.29012q91+(2.55688+0.496238i)q938.30506q95+7.48130q97+(2.51870+6.24441i)q99+O(q100)q+(-0.329998 - 1.70032i) q^{3} +1.00000 q^{5} -2.66000i q^{7} +(-2.78220 + 1.12221i) q^{9} -2.24441i q^{11} +2.74065i q^{13} +(-0.329998 - 1.70032i) q^{15} +0.496238i q^{17} -8.30506 q^{19} +(-4.52285 + 0.877793i) q^{21} -3.15623 q^{23} +1.00000 q^{25} +(2.82624 + 4.36032i) q^{27} -6.55688 q^{29} -1.50376i q^{31} +(-3.81623 + 0.740652i) q^{33} -2.66000i q^{35} -9.38064i q^{37} +(4.66000 - 0.904410i) q^{39} +10.3657i q^{41} +2.14130 q^{43} +(-2.78220 + 1.12221i) q^{45} +8.96505 q^{47} -0.0755782 q^{49} +(0.843766 - 0.163758i) q^{51} -10.1213 q^{53} -2.24441i q^{55} +(2.74065 + 14.1213i) q^{57} -0.435595i q^{59} -5.87687i q^{61} +(2.98507 + 7.40065i) q^{63} +2.74065i q^{65} -10.1413 q^{67} +(1.04155 + 5.36662i) q^{69} -4.32752 q^{71} -10.6101 q^{73} +(-0.329998 - 1.70032i) q^{75} -5.97013 q^{77} -13.2975i q^{79} +(6.48130 - 6.24441i) q^{81} +6.08066i q^{83} +0.496238i q^{85} +(2.16376 + 11.1488i) q^{87} +8.12129i q^{89} +7.29012 q^{91} +(-2.55688 + 0.496238i) q^{93} -8.30506 q^{95} +7.48130 q^{97} +(2.51870 + 6.24441i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q3+8q54q9+2q158q19+4q2112q23+8q25+14q278q298q33+28q3936q434q45+4q47+20q5116q6328q67++64q99+O(q100) 8 q + 2 q^{3} + 8 q^{5} - 4 q^{9} + 2 q^{15} - 8 q^{19} + 4 q^{21} - 12 q^{23} + 8 q^{25} + 14 q^{27} - 8 q^{29} - 8 q^{33} + 28 q^{39} - 36 q^{43} - 4 q^{45} + 4 q^{47} + 20 q^{51} - 16 q^{63} - 28 q^{67}+ \cdots + 64 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1920Z)×\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times.

nn 511511 641641 901901 15371537
χ(n)\chi(n) 1-1 1-1 1-1 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 −0.329998 1.70032i −0.190524 0.981682i
44 0 0
55 1.00000 0.447214
66 0 0
77 2.66000i 1.00538i −0.864466 0.502692i 0.832343π-0.832343\pi
0.864466 0.502692i 0.167657π-0.167657\pi
88 0 0
99 −2.78220 + 1.12221i −0.927401 + 0.374069i
1010 0 0
1111 2.24441i 0.676716i −0.941017 0.338358i 0.890128π-0.890128\pi
0.941017 0.338358i 0.109872π-0.109872\pi
1212 0 0
1313 2.74065i 0.760120i 0.924962 + 0.380060i 0.124097π0.124097\pi
−0.924962 + 0.380060i 0.875903π0.875903\pi
1414 0 0
1515 −0.329998 1.70032i −0.0852051 0.439022i
1616 0 0
1717 0.496238i 0.120355i 0.998188 + 0.0601777i 0.0191667π0.0191667\pi
−0.998188 + 0.0601777i 0.980833π0.980833\pi
1818 0 0
1919 −8.30506 −1.90531 −0.952655 0.304052i 0.901660π-0.901660\pi
−0.952655 + 0.304052i 0.901660π0.901660\pi
2020 0 0
2121 −4.52285 + 0.877793i −0.986968 + 0.191550i
2222 0 0
2323 −3.15623 −0.658120 −0.329060 0.944309i 0.606732π-0.606732\pi
−0.329060 + 0.944309i 0.606732π0.606732\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 2.82624 + 4.36032i 0.543909 + 0.839144i
2828 0 0
2929 −6.55688 −1.21758 −0.608791 0.793330i 0.708345π-0.708345\pi
−0.608791 + 0.793330i 0.708345π0.708345\pi
3030 0 0
3131 1.50376i 0.270084i −0.990840 0.135042i 0.956883π-0.956883\pi
0.990840 0.135042i 0.0431169π-0.0431169\pi
3232 0 0
3333 −3.81623 + 0.740652i −0.664320 + 0.128931i
3434 0 0
3535 2.66000i 0.449621i
3636 0 0
3737 9.38064i 1.54217i −0.636734 0.771083i 0.719715π-0.719715\pi
0.636734 0.771083i 0.280285π-0.280285\pi
3838 0 0
3939 4.66000 0.904410i 0.746197 0.144821i
4040 0 0
4141 10.3657i 1.61885i 0.587223 + 0.809425i 0.300221π0.300221\pi
−0.587223 + 0.809425i 0.699779π0.699779\pi
4242 0 0
4343 2.14130 0.326545 0.163273 0.986581i 0.447795π-0.447795\pi
0.163273 + 0.986581i 0.447795π0.447795\pi
4444 0 0
4545 −2.78220 + 1.12221i −0.414746 + 0.167289i
4646 0 0
4747 8.96505 1.30769 0.653844 0.756630i 0.273155π-0.273155\pi
0.653844 + 0.756630i 0.273155π0.273155\pi
4848 0 0
4949 −0.0755782 −0.0107969
5050 0 0
5151 0.843766 0.163758i 0.118151 0.0229307i
5252 0 0
5353 −10.1213 −1.39027 −0.695133 0.718881i 0.744654π-0.744654\pi
−0.695133 + 0.718881i 0.744654π0.744654\pi
5454 0 0
5555 2.24441i 0.302637i
5656 0 0
5757 2.74065 + 14.1213i 0.363008 + 1.87041i
5858 0 0
5959 0.435595i 0.0567096i −0.999598 0.0283548i 0.990973π-0.990973\pi
0.999598 0.0283548i 0.00902682π-0.00902682\pi
6060 0 0
6161 5.87687i 0.752457i −0.926527 0.376228i 0.877221π-0.877221\pi
0.926527 0.376228i 0.122779π-0.122779\pi
6262 0 0
6363 2.98507 + 7.40065i 0.376083 + 0.932394i
6464 0 0
6565 2.74065i 0.339936i
6666 0 0
6767 −10.1413 −1.23896 −0.619478 0.785014i 0.712656π-0.712656\pi
−0.619478 + 0.785014i 0.712656π0.712656\pi
6868 0 0
6969 1.04155 + 5.36662i 0.125388 + 0.646065i
7070 0 0
7171 −4.32752 −0.513582 −0.256791 0.966467i 0.582665π-0.582665\pi
−0.256791 + 0.966467i 0.582665π0.582665\pi
7272 0 0
7373 −10.6101 −1.24182 −0.620910 0.783882i 0.713237π-0.713237\pi
−0.620910 + 0.783882i 0.713237π0.713237\pi
7474 0 0
7575 −0.329998 1.70032i −0.0381049 0.196336i
7676 0 0
7777 −5.97013 −0.680360
7878 0 0
7979 13.2975i 1.49609i −0.663648 0.748045i 0.730993π-0.730993\pi
0.663648 0.748045i 0.269007π-0.269007\pi
8080 0 0
8181 6.48130 6.24441i 0.720145 0.693824i
8282 0 0
8383 6.08066i 0.667439i 0.942672 + 0.333719i 0.108304π0.108304\pi
−0.942672 + 0.333719i 0.891696π0.891696\pi
8484 0 0
8585 0.496238i 0.0538246i
8686 0 0
8787 2.16376 + 11.1488i 0.231979 + 1.19528i
8888 0 0
8989 8.12129i 0.860855i 0.902625 + 0.430427i 0.141637π0.141637\pi
−0.902625 + 0.430427i 0.858363π0.858363\pi
9090 0 0
9191 7.29012 0.764213
9292 0 0
9393 −2.55688 + 0.496238i −0.265136 + 0.0514575i
9494 0 0
9595 −8.30506 −0.852081
9696 0 0
9797 7.48130 0.759611 0.379806 0.925066i 0.375991π-0.375991\pi
0.379806 + 0.925066i 0.375991π0.375991\pi
9898 0 0
9999 2.51870 + 6.24441i 0.253138 + 0.627587i
100100 0 0
101101 0.0831016 0.00826892 0.00413446 0.999991i 0.498684π-0.498684\pi
0.00413446 + 0.999991i 0.498684π0.498684\pi
102102 0 0
103103 0.851177i 0.0838690i −0.999120 0.0419345i 0.986648π-0.986648\pi
0.999120 0.0419345i 0.0133521π-0.0133521\pi
104104 0 0
105105 −4.52285 + 0.877793i −0.441385 + 0.0856638i
106106 0 0
107107 9.04815i 0.874718i 0.899287 + 0.437359i 0.144086π0.144086\pi
−0.899287 + 0.437359i 0.855914π0.855914\pi
108108 0 0
109109 9.37322i 0.897792i −0.893584 0.448896i 0.851817π-0.851817\pi
0.893584 0.448896i 0.148183π-0.148183\pi
110110 0 0
111111 −15.9501 + 3.09559i −1.51392 + 0.293820i
112112 0 0
113113 14.4664i 1.36088i 0.732803 + 0.680441i 0.238212π0.238212\pi
−0.732803 + 0.680441i 0.761788π0.761788\pi
114114 0 0
115115 −3.15623 −0.294320
116116 0 0
117117 −3.07558 7.62505i −0.284337 0.704936i
118118 0 0
119119 1.31999 0.121003
120120 0 0
121121 5.96261 0.542055
122122 0 0
123123 17.6250 3.42066i 1.58920 0.308431i
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 11.2701i 1.00006i 0.866008 + 0.500030i 0.166678π0.166678\pi
−0.866008 + 0.500030i 0.833322π0.833322\pi
128128 0 0
129129 −0.706625 3.64090i −0.0622148 0.320564i
130130 0 0
131131 17.0057i 1.48579i −0.669406 0.742897i 0.733451π-0.733451\pi
0.669406 0.742897i 0.266549π-0.266549\pi
132132 0 0
133133 22.0914i 1.91557i
134134 0 0
135135 2.82624 + 4.36032i 0.243244 + 0.375277i
136136 0 0
137137 7.01493i 0.599326i −0.954045 0.299663i 0.903126π-0.903126\pi
0.954045 0.299663i 0.0968743π-0.0968743\pi
138138 0 0
139139 7.93752 0.673251 0.336626 0.941639i 0.390714π-0.390714\pi
0.336626 + 0.941639i 0.390714π0.390714\pi
140140 0 0
141141 −2.95845 15.2435i −0.249146 1.28373i
142142 0 0
143143 6.15116 0.514386
144144 0 0
145145 −6.55688 −0.544519
146146 0 0
147147 0.0249407 + 0.128507i 0.00205707 + 0.0105991i
148148 0 0
149149 −17.6176 −1.44329 −0.721647 0.692262i 0.756614π-0.756614\pi
−0.721647 + 0.692262i 0.756614π0.756614\pi
150150 0 0
151151 8.34508i 0.679113i −0.940586 0.339557i 0.889723π-0.889723\pi
0.940586 0.339557i 0.110277π-0.110277\pi
152152 0 0
153153 −0.556882 1.38064i −0.0450212 0.111618i
154154 0 0
155155 1.50376i 0.120785i
156156 0 0
157157 16.3882i 1.30792i 0.756530 + 0.653959i 0.226893π0.226893\pi
−0.756530 + 0.653959i 0.773107π0.773107\pi
158158 0 0
159159 3.34000 + 17.2095i 0.264880 + 1.36480i
160160 0 0
161161 8.39557i 0.661664i
162162 0 0
163163 −11.6226 −0.910353 −0.455176 0.890401i 0.650424π-0.650424\pi
−0.455176 + 0.890401i 0.650424π0.650424\pi
164164 0 0
165165 −3.81623 + 0.740652i −0.297093 + 0.0576597i
166166 0 0
167167 −4.63754 −0.358863 −0.179432 0.983770i 0.557426π-0.557426\pi
−0.179432 + 0.983770i 0.557426π0.557426\pi
168168 0 0
169169 5.48883 0.422217
170170 0 0
171171 23.1064 9.31999i 1.76699 0.712718i
172172 0 0
173173 −7.27997 −0.553486 −0.276743 0.960944i 0.589255π-0.589255\pi
−0.276743 + 0.960944i 0.589255π0.589255\pi
174174 0 0
175175 2.66000i 0.201077i
176176 0 0
177177 −0.740652 + 0.143745i −0.0556708 + 0.0108046i
178178 0 0
179179 3.07558i 0.229880i −0.993372 0.114940i 0.963332π-0.963332\pi
0.993372 0.114940i 0.0366675π-0.0366675\pi
180180 0 0
181181 17.6026i 1.30839i −0.756326 0.654195i 0.773007π-0.773007\pi
0.756326 0.654195i 0.226993π-0.226993\pi
182182 0 0
183183 −9.99259 + 1.93936i −0.738673 + 0.143361i
184184 0 0
185185 9.38064i 0.689678i
186186 0 0
187187 1.11376 0.0814465
188188 0 0
189189 11.5984 7.51778i 0.843662 0.546838i
190190 0 0
191191 −17.5626 −1.27078 −0.635391 0.772190i 0.719161π-0.719161\pi
−0.635391 + 0.772190i 0.719161π0.719161\pi
192192 0 0
193193 −27.7239 −1.99561 −0.997804 0.0662324i 0.978902π-0.978902\pi
−0.997804 + 0.0662324i 0.978902π0.978902\pi
194194 0 0
195195 4.66000 0.904410i 0.333709 0.0647661i
196196 0 0
197197 12.1363 0.864678 0.432339 0.901711i 0.357688π-0.357688\pi
0.432339 + 0.901711i 0.357688π0.357688\pi
198198 0 0
199199 9.78636i 0.693737i 0.937914 + 0.346868i 0.112755π0.112755\pi
−0.937914 + 0.346868i 0.887245π0.887245\pi
200200 0 0
201201 3.34661 + 17.2435i 0.236052 + 1.21626i
202202 0 0
203203 17.4413i 1.22414i
204204 0 0
205205 10.3657i 0.723972i
206206 0 0
207207 8.78128 3.54195i 0.610341 0.246182i
208208 0 0
209209 18.6400i 1.28935i
210210 0 0
211211 −19.6100 −1.35001 −0.675004 0.737814i 0.735858π-0.735858\pi
−0.675004 + 0.737814i 0.735858π0.735858\pi
212212 0 0
213213 1.42807 + 7.35818i 0.0978498 + 0.504174i
214214 0 0
215215 2.14130 0.146035
216216 0 0
217217 −4.00000 −0.271538
218218 0 0
219219 3.50132 + 18.0406i 0.236597 + 1.21907i
220220 0 0
221221 −1.36002 −0.0914846
222222 0 0
223223 8.34753i 0.558992i −0.960147 0.279496i 0.909833π-0.909833\pi
0.960147 0.279496i 0.0901673π-0.0901673\pi
224224 0 0
225225 −2.78220 + 1.12221i −0.185480 + 0.0748138i
226226 0 0
227227 15.8895i 1.05462i 0.849673 + 0.527311i 0.176800π0.176800\pi
−0.849673 + 0.527311i 0.823200π0.823200\pi
228228 0 0
229229 5.64751i 0.373198i 0.982436 + 0.186599i 0.0597465π0.0597465\pi
−0.982436 + 0.186599i 0.940254π0.940254\pi
230230 0 0
231231 1.97013 + 10.1512i 0.129625 + 0.667897i
232232 0 0
233233 22.7539i 1.49065i −0.666699 0.745327i 0.732293π-0.732293\pi
0.666699 0.745327i 0.267707π-0.267707\pi
234234 0 0
235235 8.96505 0.584816
236236 0 0
237237 −22.6101 + 4.38816i −1.46868 + 0.285042i
238238 0 0
239239 0.610115 0.0394650 0.0197325 0.999805i 0.493719π-0.493719\pi
0.0197325 + 0.999805i 0.493719π0.493719\pi
240240 0 0
241241 10.1893 0.656353 0.328177 0.944616i 0.393566π-0.393566\pi
0.328177 + 0.944616i 0.393566π0.393566\pi
242242 0 0
243243 −12.7563 8.95967i −0.818320 0.574763i
244244 0 0
245245 −0.0755782 −0.00482851
246246 0 0
247247 22.7613i 1.44826i
248248 0 0
249249 10.3391 2.00660i 0.655213 0.127163i
250250 0 0
251251 2.24441i 0.141666i −0.997488 0.0708331i 0.977434π-0.977434\pi
0.997488 0.0708331i 0.0225658π-0.0225658\pi
252252 0 0
253253 7.08389i 0.445361i
254254 0 0
255255 0.843766 0.163758i 0.0528387 0.0102549i
256256 0 0
257257 2.51129i 0.156650i 0.996928 + 0.0783248i 0.0249571π0.0249571\pi
−0.996928 + 0.0783248i 0.975043π0.975043\pi
258258 0 0
259259 −24.9525 −1.55047
260260 0 0
261261 18.2426 7.35818i 1.12919 0.455460i
262262 0 0
263263 23.6451 1.45802 0.729008 0.684505i 0.239981π-0.239981\pi
0.729008 + 0.684505i 0.239981π0.239981\pi
264264 0 0
265265 −10.1213 −0.621746
266266 0 0
267267 13.8088 2.68001i 0.845086 0.164014i
268268 0 0
269269 24.5802 1.49868 0.749342 0.662183i 0.230370π-0.230370\pi
0.749342 + 0.662183i 0.230370π0.230370\pi
270270 0 0
271271 29.8676i 1.81433i −0.420776 0.907164i 0.638242π-0.638242\pi
0.420776 0.907164i 0.361758π-0.361758\pi
272272 0 0
273273 −2.40573 12.3956i −0.145601 0.750214i
274274 0 0
275275 2.24441i 0.135343i
276276 0 0
277277 22.8471i 1.37275i −0.727248 0.686375i 0.759201π-0.759201\pi
0.727248 0.686375i 0.240799π-0.240799\pi
278278 0 0
279279 1.68753 + 4.18377i 0.101030 + 0.250476i
280280 0 0
281281 28.2145i 1.68314i −0.540149 0.841569i 0.681632π-0.681632\pi
0.540149 0.841569i 0.318368π-0.318368\pi
282282 0 0
283283 −22.4688 −1.33563 −0.667816 0.744326i 0.732771π-0.732771\pi
−0.667816 + 0.744326i 0.732771π0.732771\pi
284284 0 0
285285 2.74065 + 14.1213i 0.162342 + 0.836473i
286286 0 0
287287 27.5727 1.62757
288288 0 0
289289 16.7537 0.985515
290290 0 0
291291 −2.46881 12.7206i −0.144724 0.745697i
292292 0 0
293293 16.9626 0.990966 0.495483 0.868618i 0.334991π-0.334991\pi
0.495483 + 0.868618i 0.334991π0.334991\pi
294294 0 0
295295 0.435595i 0.0253613i
296296 0 0
297297 9.78636 6.34324i 0.567862 0.368072i
298298 0 0
299299 8.65014i 0.500250i
300300 0 0
301301 5.69585i 0.328303i
302302 0 0
303303 −0.0274234 0.141300i −0.00157543 0.00811745i
304304 0 0
305305 5.87687i 0.336509i
306306 0 0
307307 −10.9576 −0.625386 −0.312693 0.949854i 0.601231π-0.601231\pi
−0.312693 + 0.949854i 0.601231π0.601231\pi
308308 0 0
309309 −1.44728 + 0.280887i −0.0823327 + 0.0159791i
310310 0 0
311311 30.5550 1.73262 0.866309 0.499509i 0.166486π-0.166486\pi
0.866309 + 0.499509i 0.166486π0.166486\pi
312312 0 0
313313 −10.9476 −0.618793 −0.309396 0.950933i 0.600127π-0.600127\pi
−0.309396 + 0.950933i 0.600127π0.600127\pi
314314 0 0
315315 2.98507 + 7.40065i 0.168189 + 0.416979i
316316 0 0
317317 22.3639 1.25608 0.628040 0.778181i 0.283857π-0.283857\pi
0.628040 + 0.778181i 0.283857π0.283857\pi
318318 0 0
319319 14.7164i 0.823958i
320320 0 0
321321 15.3848 2.98587i 0.858695 0.166655i
322322 0 0
323323 4.12129i 0.229315i
324324 0 0
325325 2.74065i 0.152024i
326326 0 0
327327 −15.9375 + 3.09314i −0.881347 + 0.171051i
328328 0 0
329329 23.8470i 1.31473i
330330 0 0
331331 −20.6326 −1.13407 −0.567034 0.823694i 0.691909π-0.691909\pi
−0.567034 + 0.823694i 0.691909π0.691909\pi
332332 0 0
333333 10.5270 + 26.0988i 0.576877 + 1.43021i
334334 0 0
335335 −10.1413 −0.554078
336336 0 0
337337 3.11376 0.169618 0.0848088 0.996397i 0.472972π-0.472972\pi
0.0848088 + 0.996397i 0.472972π0.472972\pi
338338 0 0
339339 24.5975 4.77387i 1.33595 0.259281i
340340 0 0
341341 −3.37506 −0.182770
342342 0 0
343343 18.4189i 0.994529i
344344 0 0
345345 1.04155 + 5.36662i 0.0560752 + 0.288929i
346346 0 0
347347 11.7282i 0.629601i −0.949158 0.314800i 0.898062π-0.898062\pi
0.949158 0.314800i 0.101938π-0.101938\pi
348348 0 0
349349 20.1213i 1.07707i −0.842604 0.538534i 0.818978π-0.818978\pi
0.842604 0.538534i 0.181022π-0.181022\pi
350350 0 0
351351 −11.9501 + 7.74573i −0.637850 + 0.413436i
352352 0 0
353353 1.22764i 0.0653407i −0.999466 0.0326703i 0.989599π-0.989599\pi
0.999466 0.0326703i 0.0104011π-0.0104011\pi
354354 0 0
355355 −4.32752 −0.229681
356356 0 0
357357 −0.435595 2.24441i −0.0230541 0.118787i
358358 0 0
359359 −37.2351 −1.96519 −0.982595 0.185759i 0.940526π-0.940526\pi
−0.982595 + 0.185759i 0.940526π0.940526\pi
360360 0 0
361361 49.9740 2.63021
362362 0 0
363363 −1.96765 10.1384i −0.103275 0.532126i
364364 0 0
365365 −10.6101 −0.555359
366366 0 0
367367 18.9826i 0.990885i −0.868641 0.495442i 0.835006π-0.835006\pi
0.868641 0.495442i 0.164994π-0.164994\pi
368368 0 0
369369 −11.6325 28.8395i −0.605562 1.50132i
370370 0 0
371371 26.9226i 1.39775i
372372 0 0
373373 33.6232i 1.74094i 0.492218 + 0.870472i 0.336186π0.336186\pi
−0.492218 + 0.870472i 0.663814π0.663814\pi
374374 0 0
375375 −0.329998 1.70032i −0.0170410 0.0878043i
376376 0 0
377377 17.9701i 0.925509i
378378 0 0
379379 16.3051 0.837535 0.418767 0.908094i 0.362462π-0.362462\pi
0.418767 + 0.908094i 0.362462π0.362462\pi
380380 0 0
381381 19.1628 3.71911i 0.981742 0.190536i
382382 0 0
383383 −3.44372 −0.175966 −0.0879831 0.996122i 0.528042π-0.528042\pi
−0.0879831 + 0.996122i 0.528042π0.528042\pi
384384 0 0
385385 −5.97013 −0.304266
386386 0 0
387387 −5.95753 + 2.40298i −0.302838 + 0.122150i
388388 0 0
389389 22.2426 1.12774 0.563872 0.825862i 0.309311π-0.309311\pi
0.563872 + 0.825862i 0.309311π0.309311\pi
390390 0 0
391391 1.56624i 0.0792084i
392392 0 0
393393 −28.9152 + 5.61184i −1.45858 + 0.283080i
394394 0 0
395395 13.2975i 0.669072i
396396 0 0
397397 8.23678i 0.413392i −0.978405 0.206696i 0.933729π-0.933729\pi
0.978405 0.206696i 0.0662711π-0.0662711\pi
398398 0 0
399399 37.5626 7.29012i 1.88048 0.364963i
400400 0 0
401401 4.16620i 0.208050i 0.994575 + 0.104025i 0.0331722π0.0331722\pi
−0.994575 + 0.104025i 0.966828π0.966828\pi
402402 0 0
403403 4.12129 0.205296
404404 0 0
405405 6.48130 6.24441i 0.322059 0.310287i
406406 0 0
407407 −21.0540 −1.04361
408408 0 0
409409 −11.4132 −0.564349 −0.282174 0.959363i 0.591056π-0.591056\pi
−0.282174 + 0.959363i 0.591056π0.591056\pi
410410 0 0
411411 −11.9277 + 2.31491i −0.588348 + 0.114186i
412412 0 0
413413 −1.15868 −0.0570149
414414 0 0
415415 6.08066i 0.298488i
416416 0 0
417417 −2.61936 13.4964i −0.128271 0.660919i
418418 0 0
419419 15.9319i 0.778326i −0.921169 0.389163i 0.872764π-0.872764\pi
0.921169 0.389163i 0.127236π-0.127236\pi
420420 0 0
421421 20.3507i 0.991830i −0.868371 0.495915i 0.834833π-0.834833\pi
0.868371 0.495915i 0.165167π-0.165167\pi
422422 0 0
423423 −24.9426 + 10.0606i −1.21275 + 0.489165i
424424 0 0
425425 0.496238i 0.0240711i
426426 0 0
427427 −15.6325 −0.756508
428428 0 0
429429 −2.02987 10.4590i −0.0980030 0.504963i
430430 0 0
431431 −20.2377 −0.974815 −0.487407 0.873175i 0.662057π-0.662057\pi
−0.487407 + 0.873175i 0.662057π0.662057\pi
432432 0 0
433433 −6.44391 −0.309675 −0.154837 0.987940i 0.549485π-0.549485\pi
−0.154837 + 0.987940i 0.549485π0.549485\pi
434434 0 0
435435 2.16376 + 11.1488i 0.103744 + 0.534545i
436436 0 0
437437 26.2127 1.25392
438438 0 0
439439 36.0588i 1.72099i −0.509456 0.860496i 0.670154π-0.670154\pi
0.509456 0.860496i 0.329846π-0.329846\pi
440440 0 0
441441 0.210274 0.0848144i 0.0100130 0.00403878i
442442 0 0
443443 11.3157i 0.537625i −0.963192 0.268813i 0.913369π-0.913369\pi
0.963192 0.268813i 0.0866313π-0.0866313\pi
444444 0 0
445445 8.12129i 0.384986i
446446 0 0
447447 5.81378 + 29.9557i 0.274983 + 1.41686i
448448 0 0
449449 10.2444i 0.483464i 0.970343 + 0.241732i 0.0777154π0.0777154\pi
−0.970343 + 0.241732i 0.922285π0.922285\pi
450450 0 0
451451 23.2649 1.09550
452452 0 0
453453 −14.1893 + 2.75386i −0.666673 + 0.129388i
454454 0 0
455455 7.29012 0.341766
456456 0 0
457457 33.3714 1.56105 0.780524 0.625126i 0.214952π-0.214952\pi
0.780524 + 0.625126i 0.214952π0.214952\pi
458458 0 0
459459 −2.16376 + 1.40249i −0.100996 + 0.0654625i
460460 0 0
461461 23.8368 1.11019 0.555096 0.831786i 0.312681π-0.312681\pi
0.555096 + 0.831786i 0.312681π0.312681\pi
462462 0 0
463463 27.7288i 1.28867i −0.764744 0.644334i 0.777135π-0.777135\pi
0.764744 0.644334i 0.222865π-0.222865\pi
464464 0 0
465465 −2.55688 + 0.496238i −0.118573 + 0.0230125i
466466 0 0
467467 24.4996i 1.13371i −0.823819 0.566853i 0.808161π-0.808161\pi
0.823819 0.566853i 0.191839π-0.191839\pi
468468 0 0
469469 26.9758i 1.24563i
470470 0 0
471471 27.8652 5.40806i 1.28396 0.249190i
472472 0 0
473473 4.80596i 0.220978i
474474 0 0
475475 −8.30506 −0.381062
476476 0 0
477477 28.1595 11.3582i 1.28933 0.520055i
478478 0 0
479479 −0.0449159 −0.00205226 −0.00102613 0.999999i 0.500327π-0.500327\pi
−0.00102613 + 0.999999i 0.500327π0.500327\pi
480480 0 0
481481 25.7091 1.17223
482482 0 0
483483 14.2752 2.77052i 0.649544 0.126063i
484484 0 0
485485 7.48130 0.339709
486486 0 0
487487 24.6301i 1.11610i 0.829808 + 0.558049i 0.188450π0.188450\pi
−0.829808 + 0.558049i 0.811550π0.811550\pi
488488 0 0
489489 3.83544 + 19.7622i 0.173444 + 0.893677i
490490 0 0
491491 26.8545i 1.21193i 0.795492 + 0.605964i 0.207212π0.207212\pi
−0.795492 + 0.605964i 0.792788π0.792788\pi
492492 0 0
493493 3.25378i 0.146543i
494494 0 0
495495 2.51870 + 6.24441i 0.113207 + 0.280666i
496496 0 0
497497 11.5112i 0.516347i
498498 0 0
499499 0.305057 0.0136562 0.00682812 0.999977i 0.497827π-0.497827\pi
0.00682812 + 0.999977i 0.497827π0.497827\pi
500500 0 0
501501 1.53038 + 7.88532i 0.0683722 + 0.352290i
502502 0 0
503503 10.6526 0.474975 0.237488 0.971391i 0.423676π-0.423676\pi
0.237488 + 0.971391i 0.423676π0.423676\pi
504504 0 0
505505 0.0831016 0.00369797
506506 0 0
507507 −1.81130 9.33278i −0.0804427 0.414483i
508508 0 0
509509 −23.0457 −1.02148 −0.510742 0.859734i 0.670629π-0.670629\pi
−0.510742 + 0.859734i 0.670629π0.670629\pi
510510 0 0
511511 28.2229i 1.24851i
512512 0 0
513513 −23.4721 36.2127i −1.03632 1.59883i
514514 0 0
515515 0.851177i 0.0375073i
516516 0 0
517517 20.1213i 0.884933i
518518 0 0
519519 2.40237 + 12.3783i 0.105453 + 0.543347i
520520 0 0
521521 20.9476i 0.917729i −0.888506 0.458865i 0.848256π-0.848256\pi
0.888506 0.458865i 0.151744π-0.151744\pi
522522 0 0
523523 8.68520 0.379777 0.189889 0.981806i 0.439187π-0.439187\pi
0.189889 + 0.981806i 0.439187π0.439187\pi
524524 0 0
525525 −4.52285 + 0.877793i −0.197394 + 0.0383100i
526526 0 0
527527 0.746224 0.0325060
528528 0 0
529529 −13.0382 −0.566878
530530 0 0
531531 0.488827 + 1.21191i 0.0212133 + 0.0525925i
532532 0 0
533533 −28.4088 −1.23052
534534 0 0
535535 9.04815i 0.391186i
536536 0 0
537537 −5.22948 + 1.01493i −0.225669 + 0.0437977i
538538 0 0
539539 0.169629i 0.00730643i
540540 0 0
541541 14.0914i 0.605837i −0.953016 0.302919i 0.902039π-0.902039\pi
0.953016 0.302919i 0.0979611π-0.0979611\pi
542542 0 0
543543 −29.9301 + 5.80882i −1.28442 + 0.249280i
544544 0 0
545545 9.37322i 0.401505i
546546 0 0
547547 7.44647 0.318388 0.159194 0.987247i 0.449110π-0.449110\pi
0.159194 + 0.987247i 0.449110π0.449110\pi
548548 0 0
549549 6.59507 + 16.3507i 0.281471 + 0.697829i
550550 0 0
551551 54.4553 2.31987
552552 0 0
553553 −35.3714 −1.50414
554554 0 0
555555 −15.9501 + 3.09559i −0.677045 + 0.131400i
556556 0 0
557557 −10.1065 −0.428225 −0.214112 0.976809i 0.568686π-0.568686\pi
−0.214112 + 0.976809i 0.568686π0.568686\pi
558558 0 0
559559 5.86856i 0.248214i
560560 0 0
561561 −0.367540 1.89376i −0.0155175 0.0799546i
562562 0 0
563563 17.0482i 0.718494i 0.933243 + 0.359247i 0.116966π0.116966\pi
−0.933243 + 0.359247i 0.883034π0.883034\pi
564564 0 0
565565 14.4664i 0.608605i
566566 0 0
567567 −16.6101 17.2402i −0.697559 0.724022i
568568 0 0
569569 30.8694i 1.29411i −0.762443 0.647055i 0.776000π-0.776000\pi
0.762443 0.647055i 0.224000π-0.224000\pi
570570 0 0
571571 −1.33756 −0.0559751 −0.0279875 0.999608i 0.508910π-0.508910\pi
−0.0279875 + 0.999608i 0.508910π0.508910\pi
572572 0 0
573573 5.79561 + 29.8621i 0.242115 + 1.24751i
574574 0 0
575575 −3.15623 −0.131624
576576 0 0
577577 24.2576 1.00986 0.504929 0.863161i 0.331519π-0.331519\pi
0.504929 + 0.863161i 0.331519π0.331519\pi
578578 0 0
579579 9.14882 + 47.1396i 0.380212 + 1.95905i
580580 0 0
581581 16.1745 0.671032
582582 0 0
583583 22.7164i 0.940815i
584584 0 0
585585 −3.07558 7.62505i −0.127160 0.315257i
586586 0 0
587587 15.2344i 0.628793i 0.949292 + 0.314396i 0.101802π0.101802\pi
−0.949292 + 0.314396i 0.898198π0.898198\pi
588588 0 0
589589 12.4888i 0.514593i
590590 0 0
591591 −4.00497 20.6357i −0.164742 0.848839i
592592 0 0
593593 30.5076i 1.25280i −0.779503 0.626399i 0.784528π-0.784528\pi
0.779503 0.626399i 0.215472π-0.215472\pi
594594 0 0
595595 1.31999 0.0541144
596596 0 0
597597 16.6400 3.22948i 0.681029 0.132174i
598598 0 0
599599 −41.5878 −1.69923 −0.849615 0.527403i 0.823166π-0.823166\pi
−0.849615 + 0.527403i 0.823166π0.823166\pi
600600 0 0
601601 −29.6709 −1.21030 −0.605150 0.796111i 0.706887π-0.706887\pi
−0.605150 + 0.796111i 0.706887π0.706887\pi
602602 0 0
603603 28.2152 11.3806i 1.14901 0.463455i
604604 0 0
605605 5.96261 0.242414
606606 0 0
607607 4.87638i 0.197926i −0.995091 0.0989631i 0.968447π-0.968447\pi
0.995091 0.0989631i 0.0315526π-0.0315526\pi
608608 0 0
609609 29.6558 5.75559i 1.20171 0.233228i
610610 0 0
611611 24.5701i 0.993999i
612612 0 0
613613 44.9682i 1.81625i 0.418702 + 0.908124i 0.362485π0.362485\pi
−0.418702 + 0.908124i 0.637515π0.637515\pi
614614 0 0
615615 17.6250 3.42066i 0.710711 0.137934i
616616 0 0
617617 13.7762i 0.554609i 0.960782 + 0.277305i 0.0894411π0.0894411\pi
−0.960782 + 0.277305i 0.910559π0.910559\pi
618618 0 0
619619 −18.6126 −0.748105 −0.374052 0.927408i 0.622032π-0.622032\pi
−0.374052 + 0.927408i 0.622032π0.622032\pi
620620 0 0
621621 −8.92026 13.7622i −0.357958 0.552258i
622622 0 0
623623 21.6026 0.865490
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 31.6940 6.15116i 1.26574 0.245654i
628628 0 0
629629 4.65503 0.185608
630630 0 0
631631 48.0489i 1.91280i 0.292067 + 0.956398i 0.405657π0.405657\pi
−0.292067 + 0.956398i 0.594343π0.594343\pi
632632 0 0
633633 6.47126 + 33.3434i 0.257210 + 1.32528i
634634 0 0
635635 11.2701i 0.447241i
636636 0 0
637637 0.207134i 0.00820693i
638638 0 0
639639 12.0400 4.85637i 0.476296 0.192115i
640640 0 0
641641 22.1995i 0.876827i 0.898773 + 0.438414i 0.144460π0.144460\pi
−0.898773 + 0.438414i 0.855540π0.855540\pi
642642 0 0
643643 20.5751 0.811401 0.405700 0.914006i 0.367028π-0.367028\pi
0.405700 + 0.914006i 0.367028π0.367028\pi
644644 0 0
645645 −0.706625 3.64090i −0.0278233 0.143360i
646646 0 0
647647 −48.7852 −1.91795 −0.958973 0.283498i 0.908505π-0.908505\pi
−0.958973 + 0.283498i 0.908505π0.908505\pi
648648 0 0
649649 −0.977654 −0.0383763
650650 0 0
651651 1.31999 + 6.80130i 0.0517346 + 0.266564i
652652 0 0
653653 46.2278 1.80903 0.904516 0.426440i 0.140232π-0.140232\pi
0.904516 + 0.426440i 0.140232π0.140232\pi
654654 0 0
655655 17.0057i 0.664467i
656656 0 0
657657 29.5195 11.9067i 1.15166 0.464526i
658658 0 0
659659 42.6631i 1.66192i −0.556333 0.830960i 0.687792π-0.687792\pi
0.556333 0.830960i 0.312208π-0.312208\pi
660660 0 0
661661 41.8171i 1.62650i −0.581916 0.813249i 0.697697π-0.697697\pi
0.581916 0.813249i 0.302303π-0.302303\pi
662662 0 0
663663 0.448803 + 2.31247i 0.0174300 + 0.0898088i
664664 0 0
665665 22.0914i 0.856668i
666666 0 0
667667 20.6951 0.801316
668668 0 0
669669 −14.1935 + 2.75467i −0.548752 + 0.106502i
670670 0 0
671671 −13.1901 −0.509200
672672 0 0
673673 −8.76127 −0.337722 −0.168861 0.985640i 0.554009π-0.554009\pi
−0.168861 + 0.985640i 0.554009π0.554009\pi
674674 0 0
675675 2.82624 + 4.36032i 0.108782 + 0.167829i
676676 0 0
677677 −26.2278 −1.00801 −0.504007 0.863699i 0.668142π-0.668142\pi
−0.504007 + 0.863699i 0.668142π0.668142\pi
678678 0 0
679679 19.9002i 0.763701i
680680 0 0
681681 27.0173 5.24349i 1.03530 0.200931i
682682 0 0
683683 25.5469i 0.977525i 0.872417 + 0.488763i 0.162552π0.162552\pi
−0.872417 + 0.488763i 0.837448π0.837448\pi
684684 0 0
685685 7.01493i 0.268027i
686686 0 0
687687 9.60259 1.86367i 0.366362 0.0711033i
688688 0 0
689689 27.7389i 1.05677i
690690 0 0
691691 3.61000 0.137331 0.0686655 0.997640i 0.478126π-0.478126\pi
0.0686655 + 0.997640i 0.478126π0.478126\pi
692692 0 0
693693 16.6101 6.69972i 0.630966 0.254501i
694694 0 0
695695 7.93752 0.301087
696696 0 0
697697 −5.14386 −0.194838
698698 0 0
699699 −38.6889 + 7.50873i −1.46335 + 0.284006i
700700 0 0
701701 −19.9850 −0.754821 −0.377411 0.926046i 0.623185π-0.623185\pi
−0.377411 + 0.926046i 0.623185π0.623185\pi
702702 0 0
703703 77.9067i 2.93831i
704704 0 0
705705 −2.95845 15.2435i −0.111422 0.574103i
706706 0 0
707707 0.221050i 0.00831344i
708708 0 0
709709 15.0839i 0.566488i −0.959048 0.283244i 0.908589π-0.908589\pi
0.959048 0.283244i 0.0914106π-0.0914106\pi
710710 0 0
711711 14.9226 + 36.9964i 0.559641 + 1.38747i
712712 0 0
713713 4.74622i 0.177747i
714714 0 0
715715 6.15116 0.230040
716716 0 0
717717 −0.201337 1.03739i −0.00751905 0.0387421i
718718 0 0
719719 −9.05770 −0.337795 −0.168898 0.985634i 0.554021π-0.554021\pi
−0.168898 + 0.985634i 0.554021π0.554021\pi
720720 0 0
721721 −2.26413 −0.0843205
722722 0 0
723723 −3.36246 17.3252i −0.125051 0.644330i
724724 0 0
725725 −6.55688 −0.243516
726726 0 0
727727 16.2675i 0.603327i −0.953414 0.301664i 0.902458π-0.902458\pi
0.953414 0.301664i 0.0975420π-0.0975420\pi
728728 0 0
729729 −11.0248 + 24.6466i −0.408325 + 0.912837i
730730 0 0
731731 1.06259i 0.0393015i
732732 0 0
733733 4.34324i 0.160421i 0.996778 + 0.0802107i 0.0255593π0.0255593\pi
−0.996778 + 0.0802107i 0.974441π0.974441\pi
734734 0 0
735735 0.0249407 + 0.128507i 0.000919950 + 0.00474007i
736736 0 0
737737 22.7613i 0.838422i
738738 0 0
739739 23.6500 0.869980 0.434990 0.900435i 0.356752π-0.356752\pi
0.434990 + 0.900435i 0.356752π0.356752\pi
740740 0 0
741741 −38.7015 + 7.51117i −1.42174 + 0.275930i
742742 0 0
743743 0.858588 0.0314985 0.0157493 0.999876i 0.494987π-0.494987\pi
0.0157493 + 0.999876i 0.494987π0.494987\pi
744744 0 0
745745 −17.6176 −0.645460
746746 0 0
747747 −6.82375 16.9176i −0.249668 0.618983i
748748 0 0
749749 24.0681 0.879428
750750 0 0
751751 14.0486i 0.512642i −0.966592 0.256321i 0.917490π-0.917490\pi
0.966592 0.256321i 0.0825105π-0.0825105\pi
752752 0 0
753753 −3.81623 + 0.740652i −0.139071 + 0.0269909i
754754 0 0
755755 8.34508i 0.303709i
756756 0 0
757757 1.12324i 0.0408248i 0.999792 + 0.0204124i 0.00649792π0.00649792\pi
−0.999792 + 0.0204124i 0.993502π0.993502\pi
758758 0 0
759759 12.0449 2.33767i 0.437203 0.0848521i
760760 0 0
761761 35.0187i 1.26943i 0.772748 + 0.634713i 0.218882π0.218882\pi
−0.772748 + 0.634713i 0.781118π0.781118\pi
762762 0 0
763763 −24.9327 −0.902626
764764 0 0
765765 −0.556882 1.38064i −0.0201341 0.0499170i
766766 0 0
767767 1.19381 0.0431061
768768 0 0
769769 −23.7688 −0.857125 −0.428562 0.903512i 0.640980π-0.640980\pi
−0.428562 + 0.903512i 0.640980π0.640980\pi
770770 0 0
771771 4.27000 0.828719i 0.153780 0.0298456i
772772 0 0
773773 −3.09894 −0.111461 −0.0557306 0.998446i 0.517749π-0.517749\pi
−0.0557306 + 0.998446i 0.517749π0.517749\pi
774774 0 0
775775 1.50376i 0.0540167i
776776 0 0
777777 8.23426 + 42.4273i 0.295402 + 1.52207i
778778 0 0
779779 86.0877i 3.08441i
780780 0 0
781781 9.71273i 0.347549i
782782 0 0
783783 −18.5313 28.5901i −0.662255 1.02173i
784784 0 0
785785 16.3882i 0.584918i
786786 0 0
787787 47.4828 1.69258 0.846290 0.532723i 0.178831π-0.178831\pi
0.846290 + 0.532723i 0.178831π0.178831\pi
788788 0 0
789789 −7.80282 40.2043i −0.277788 1.43131i
790790 0 0
791791 38.4805 1.36821
792792 0 0
793793 16.1065 0.571957
794794 0 0
795795 3.34000 + 17.2095i 0.118458 + 0.610357i
796796 0 0
797797 −41.3862 −1.46597 −0.732987 0.680242i 0.761875π-0.761875\pi
−0.732987 + 0.680242i 0.761875π0.761875\pi
798798 0 0
799799 4.44880i 0.157387i
800800 0 0
801801 −9.11376 22.5951i −0.322019 0.798357i
802802 0 0
803803 23.8135i 0.840360i
804804 0 0
805805 8.39557i 0.295905i
806806 0 0
807807 −8.11143 41.7944i −0.285536 1.47123i
808808 0 0
809809 26.2127i 0.921590i 0.887507 + 0.460795i 0.152436π0.152436\pi
−0.887507 + 0.460795i 0.847564π0.847564\pi
810810 0 0
811811 −21.4853 −0.754450 −0.377225 0.926122i 0.623122π-0.623122\pi
−0.377225 + 0.926122i 0.623122π0.623122\pi
812812 0 0
813813 −50.7846 + 9.85625i −1.78109 + 0.345674i
814814 0 0
815815 −11.6226 −0.407122
816816 0 0
817817 −17.7836 −0.622170
818818 0 0
819819 −20.2826 + 8.18103i −0.708731 + 0.285868i
820820 0 0
821821 23.9350 0.835337 0.417669 0.908599i 0.362847π-0.362847\pi
0.417669 + 0.908599i 0.362847π0.362847\pi
822822 0 0
823823 5.47611i 0.190885i −0.995435 0.0954427i 0.969573π-0.969573\pi
0.995435 0.0954427i 0.0304267π-0.0304267\pi
824824 0 0
825825 −3.81623 + 0.740652i −0.132864 + 0.0257862i
826826 0 0
827827 22.1022i 0.768568i −0.923215 0.384284i 0.874448π-0.874448\pi
0.923215 0.384284i 0.125552π-0.125552\pi
828828 0 0
829829 17.3732i 0.603397i 0.953403 + 0.301699i 0.0975536π0.0975536\pi
−0.953403 + 0.301699i 0.902446π0.902446\pi
830830 0 0
831831 −38.8475 + 7.53950i −1.34760 + 0.261542i
832832 0 0
833833 0.0375048i 0.00129946i
834834 0 0
835835 −4.63754 −0.160489
836836 0 0
837837 6.55688 4.24999i 0.226639 0.146901i
838838 0 0
839839 −18.2724 −0.630835 −0.315417 0.948953i 0.602145π-0.602145\pi
−0.315417 + 0.948953i 0.602145π0.602145\pi
840840 0 0
841841 13.9927 0.482507
842842 0 0
843843 −47.9739 + 9.31074i −1.65231 + 0.320679i
844844 0 0
845845 5.48883 0.188821
846846 0 0
847847 15.8605i 0.544974i
848848 0 0
849849 7.41466 + 38.2043i 0.254471 + 1.31117i
850850 0 0
851851 29.6075i 1.01493i
852852 0 0
853853 2.49808i 0.0855325i 0.999085 + 0.0427663i 0.0136171π0.0136171\pi
−0.999085 + 0.0427663i 0.986383π0.986383\pi
854854 0 0
855855 23.1064 9.31999i 0.790221 0.318737i
856856 0 0
857857 25.9775i 0.887376i −0.896181 0.443688i 0.853670π-0.853670\pi
0.896181 0.443688i 0.146330π-0.146330\pi
858858 0 0
859859 −32.8351 −1.12032 −0.560160 0.828384i 0.689260π-0.689260\pi
−0.560160 + 0.828384i 0.689260π0.689260\pi
860860 0 0
861861 −9.09894 46.8826i −0.310091 1.59775i
862862 0 0
863863 37.2926 1.26945 0.634727 0.772737i 0.281113π-0.281113\pi
0.634727 + 0.772737i 0.281113π0.281113\pi
864864 0 0
865865 −7.27997 −0.247526
866866 0 0
867867 −5.52870 28.4868i −0.187765 0.967462i
868868 0 0
869869 −29.8452 −1.01243
870870 0 0
871871 27.7938i 0.941756i
872872 0 0
873873 −20.8145 + 8.39557i −0.704464 + 0.284147i
874874 0 0
875875 2.66000i 0.0899243i
876876 0 0
877877 13.0931i 0.442124i 0.975260 + 0.221062i 0.0709523π0.0709523\pi
−0.975260 + 0.221062i 0.929048π0.929048\pi
878878 0 0
879879 −5.59763 28.8419i −0.188803 0.972814i
880880 0 0
881881 34.6083i 1.16598i 0.812478 + 0.582991i 0.198118π0.198118\pi
−0.812478 + 0.582991i 0.801882π0.801882\pi
882882 0 0
883883 53.9202 1.81456 0.907280 0.420526i 0.138154π-0.138154\pi
0.907280 + 0.420526i 0.138154π0.138154\pi
884884 0 0
885885 −0.740652 + 0.143745i −0.0248967 + 0.00483195i
886886 0 0
887887 −32.8949 −1.10450 −0.552252 0.833677i 0.686231π-0.686231\pi
−0.552252 + 0.833677i 0.686231π0.686231\pi
888888 0 0
889889 29.9784 1.00544
890890 0 0
891891 −14.0150 14.5467i −0.469522 0.487334i
892892 0 0
893893 −74.4553 −2.49155
894894 0 0
895895 3.07558i 0.102805i
896896 0 0
897897 −14.7080 + 2.85453i −0.491087 + 0.0953099i
898898 0 0
899899 9.85999i 0.328849i
900900 0 0
901901 5.02257i 0.167326i
902902 0 0
903903 −9.68479 + 1.87962i −0.322290 + 0.0625498i
904904 0 0
905905 17.6026i 0.585130i
906906 0 0
907907 −35.3615 −1.17416 −0.587080 0.809529i 0.699723π-0.699723\pi
−0.587080 + 0.809529i 0.699723π0.699723\pi
908908 0 0
909909 −0.231206 + 0.0932572i −0.00766860 + 0.00309315i
910910 0 0
911911 −7.61275 −0.252222 −0.126111 0.992016i 0.540249π-0.540249\pi
−0.126111 + 0.992016i 0.540249π0.540249\pi
912912 0 0
913913 13.6475 0.451667
914914 0 0
915915 −9.99259 + 1.93936i −0.330345 + 0.0641131i
916916 0 0
917917 −45.2351 −1.49379
918918 0 0
919919 18.0474i 0.595330i 0.954670 + 0.297665i 0.0962078π0.0962078\pi
−0.954670 + 0.297665i 0.903792π0.903792\pi
920920 0 0
921921 3.61600 + 18.6315i 0.119151 + 0.613930i
922922 0 0
923923 11.8602i 0.390384i
924924 0 0
925925 9.38064i 0.308433i
926926 0 0
927927 0.955196 + 2.36815i 0.0313728 + 0.0777801i
928928 0 0
929929 25.6958i 0.843053i 0.906816 + 0.421527i 0.138506π0.138506\pi
−0.906816 + 0.421527i 0.861494π0.861494\pi
930930 0 0
931931 0.627681 0.0205714
932932 0 0
933933 −10.0831 51.9535i −0.330106 1.70088i
934934 0 0
935935 1.11376 0.0364240
936936 0 0
937937 −22.9124 −0.748516 −0.374258 0.927325i 0.622103π-0.622103\pi
−0.374258 + 0.927325i 0.622103π0.622103\pi
938938 0 0
939939 3.61267 + 18.6144i 0.117895 + 0.607458i
940940 0 0
941941 13.7657 0.448750 0.224375 0.974503i 0.427966π-0.427966\pi
0.224375 + 0.974503i 0.427966π0.427966\pi
942942 0 0
943943 32.7166i 1.06540i
944944 0 0
945945 11.5984 7.51778i 0.377297 0.244553i
946946 0 0
947947 10.3933i 0.337738i −0.985638 0.168869i 0.945988π-0.945988\pi
0.985638 0.168869i 0.0540116π-0.0540116\pi
948948 0 0
949949 29.0786i 0.943932i
950950 0 0
951951 −7.38003 38.0258i −0.239314 1.23307i
952952 0 0
953953 17.4290i 0.564580i 0.959329 + 0.282290i 0.0910940π0.0910940\pi
−0.959329 + 0.282290i 0.908906π0.908906\pi
954954 0 0
955955 −17.5626 −0.568311
956956 0 0
957957 25.0226 4.85637i 0.808865 0.156984i
958958 0 0
959959 −18.6597 −0.602553
960960 0 0
961961 28.7387 0.927055
962962 0 0
963963 −10.1539 25.1738i −0.327205 0.811214i
964964 0 0
965965 −27.7239 −0.892463
966966 0 0
967967 29.7587i 0.956976i 0.878094 + 0.478488i 0.158815π0.158815\pi
−0.878094 + 0.478488i 0.841185π0.841185\pi
968968 0 0
969969 −7.00752 + 1.36002i −0.225114 + 0.0436900i
970970 0 0
971971 8.71819i 0.279780i 0.990167 + 0.139890i 0.0446749π0.0446749\pi
−0.990167 + 0.139890i 0.955325π0.955325\pi
972972 0 0
973973 21.1138i 0.676876i
974974 0 0
975975 4.66000 0.904410i 0.149239 0.0289643i
976976 0 0
977977 12.2500i 0.391912i 0.980613 + 0.195956i 0.0627809π0.0627809\pi
−0.980613 + 0.195956i 0.937219π0.937219\pi
978978 0 0
979979 18.2275 0.582554
980980 0 0
981981 10.5187 + 26.0782i 0.335836 + 0.832613i
982982 0 0
983983 −4.74400 −0.151310 −0.0756551 0.997134i 0.524105π-0.524105\pi
−0.0756551 + 0.997134i 0.524105π0.524105\pi
984984 0 0
985985 12.1363 0.386696
986986 0 0
987987 −40.5476 + 7.86946i −1.29065 + 0.250488i
988988 0 0
989989 −6.75844 −0.214906
990990 0 0
991991 23.7350i 0.753966i 0.926220 + 0.376983i 0.123039π0.123039\pi
−0.926220 + 0.376983i 0.876961π0.876961\pi
992992 0 0
993993 6.80871 + 35.0821i 0.216068 + 1.11330i
994994 0 0
995995 9.78636i 0.310249i
996996 0 0
997997 5.50192i 0.174248i 0.996197 + 0.0871238i 0.0277676π0.0277676\pi
−0.996197 + 0.0871238i 0.972232π0.972232\pi
998998 0 0
999999 40.9026 26.5119i 1.29410 0.838799i
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 1920.2.b.h.191.3 yes 8
3.2 odd 2 1920.2.b.g.191.4 yes 8
4.3 odd 2 1920.2.b.b.191.6 yes 8
8.3 odd 2 1920.2.b.g.191.3 yes 8
8.5 even 2 1920.2.b.a.191.6 yes 8
12.11 even 2 1920.2.b.a.191.5 8
24.5 odd 2 1920.2.b.b.191.5 yes 8
24.11 even 2 inner 1920.2.b.h.191.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.b.a.191.5 8 12.11 even 2
1920.2.b.a.191.6 yes 8 8.5 even 2
1920.2.b.b.191.5 yes 8 24.5 odd 2
1920.2.b.b.191.6 yes 8 4.3 odd 2
1920.2.b.g.191.3 yes 8 8.3 odd 2
1920.2.b.g.191.4 yes 8 3.2 odd 2
1920.2.b.h.191.3 yes 8 1.1 even 1 trivial
1920.2.b.h.191.4 yes 8 24.11 even 2 inner