Properties

Label 1470.2.g.b.589.2
Level 14701470
Weight 22
Character 1470.589
Analytic conductor 11.73811.738
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(589,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, 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("1470.589");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1470=23572 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1470.g (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: 11.738009097111.7380090971
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 210)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 589.2
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1470.589
Dual form 1470.2.g.b.589.1

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+1.00000iq2+1.00000iq31.00000q4+(1.00000+2.00000i)q51.00000q61.00000iq81.00000q9+(2.000001.00000i)q10+2.00000q111.00000iq12+6.00000iq13+(2.000001.00000i)q15+1.00000q164.00000iq171.00000iq186.00000q19+(1.000002.00000i)q20+2.00000iq22+8.00000iq23+1.00000q24+(3.000004.00000i)q256.00000q261.00000iq276.00000q29+(1.000002.00000i)q30+2.00000q31+1.00000iq32+2.00000iq33+4.00000q34+1.00000q36+4.00000iq376.00000iq386.00000q39+(2.00000+1.00000i)q402.00000q414.00000iq432.00000q44+(1.000002.00000i)q458.00000q468.00000iq47+1.00000iq48+(4.000003.00000i)q50+4.00000q516.00000iq526.00000iq53+1.00000q54+(2.00000+4.00000i)q556.00000iq576.00000iq588.00000q59+(2.00000+1.00000i)q60+10.0000q61+2.00000iq621.00000q64+(12.00006.00000i)q652.00000q66+8.00000iq67+4.00000iq688.00000q696.00000q71+1.00000iq7214.0000iq734.00000q74+(4.000003.00000i)q75+6.00000q766.00000iq78+12.0000q79+(1.00000+2.00000i)q80+1.00000q812.00000iq828.00000iq83+(8.00000+4.00000i)q85+4.00000q866.00000iq872.00000iq8810.0000q89+(2.00000+1.00000i)q908.00000iq92+2.00000iq93+8.00000q94+(6.0000012.0000i)q951.00000q96+10.0000iq972.00000q99+O(q100)q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} +2.00000 q^{11} -1.00000i q^{12} +6.00000i q^{13} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} -4.00000i q^{17} -1.00000i q^{18} -6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +8.00000i q^{23} +1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} -6.00000 q^{26} -1.00000i q^{27} -6.00000 q^{29} +(1.00000 - 2.00000i) q^{30} +2.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} +4.00000 q^{34} +1.00000 q^{36} +4.00000i q^{37} -6.00000i q^{38} -6.00000 q^{39} +(2.00000 + 1.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} -2.00000 q^{44} +(1.00000 - 2.00000i) q^{45} -8.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} -6.00000i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(-2.00000 + 4.00000i) q^{55} -6.00000i q^{57} -6.00000i q^{58} -8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} +10.0000 q^{61} +2.00000i q^{62} -1.00000 q^{64} +(-12.0000 - 6.00000i) q^{65} -2.00000 q^{66} +8.00000i q^{67} +4.00000i q^{68} -8.00000 q^{69} -6.00000 q^{71} +1.00000i q^{72} -14.0000i q^{73} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +6.00000 q^{76} -6.00000i q^{78} +12.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +4.00000 q^{86} -6.00000i q^{87} -2.00000i q^{88} -10.0000 q^{89} +(2.00000 + 1.00000i) q^{90} -8.00000i q^{92} +2.00000i q^{93} +8.00000 q^{94} +(6.00000 - 12.0000i) q^{95} -1.00000 q^{96} +10.0000i q^{97} -2.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q42q52q62q94q10+4q114q15+2q1612q19+2q20+2q246q2512q2612q29+2q30+4q31+8q34+2q3612q39+4q99+O(q100) 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{15} + 2 q^{16} - 12 q^{19} + 2 q^{20} + 2 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{29} + 2 q^{30} + 4 q^{31} + 8 q^{34} + 2 q^{36} - 12 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1470Z)×\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times.

nn 491491 10811081 11771177
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 1.00000i 0.577350i
44 −1.00000 −0.500000
55 −1.00000 + 2.00000i −0.447214 + 0.894427i
66 −1.00000 −0.408248
77 0 0
88 1.00000i 0.353553i
99 −1.00000 −0.333333
1010 −2.00000 1.00000i −0.632456 0.316228i
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 1.00000i 0.288675i
1313 6.00000i 1.66410i 0.554700 + 0.832050i 0.312833π0.312833\pi
−0.554700 + 0.832050i 0.687167π0.687167\pi
1414 0 0
1515 −2.00000 1.00000i −0.516398 0.258199i
1616 1.00000 0.250000
1717 4.00000i 0.970143i −0.874475 0.485071i 0.838794π-0.838794\pi
0.874475 0.485071i 0.161206π-0.161206\pi
1818 1.00000i 0.235702i
1919 −6.00000 −1.37649 −0.688247 0.725476i 0.741620π-0.741620\pi
−0.688247 + 0.725476i 0.741620π0.741620\pi
2020 1.00000 2.00000i 0.223607 0.447214i
2121 0 0
2222 2.00000i 0.426401i
2323 8.00000i 1.66812i 0.551677 + 0.834058i 0.313988π0.313988\pi
−0.551677 + 0.834058i 0.686012π0.686012\pi
2424 1.00000 0.204124
2525 −3.00000 4.00000i −0.600000 0.800000i
2626 −6.00000 −1.17670
2727 1.00000i 0.192450i
2828 0 0
2929 −6.00000 −1.11417 −0.557086 0.830455i 0.688081π-0.688081\pi
−0.557086 + 0.830455i 0.688081π0.688081\pi
3030 1.00000 2.00000i 0.182574 0.365148i
3131 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 1.00000i 0.176777i
3333 2.00000i 0.348155i
3434 4.00000 0.685994
3535 0 0
3636 1.00000 0.166667
3737 4.00000i 0.657596i 0.944400 + 0.328798i 0.106644π0.106644\pi
−0.944400 + 0.328798i 0.893356π0.893356\pi
3838 6.00000i 0.973329i
3939 −6.00000 −0.960769
4040 2.00000 + 1.00000i 0.316228 + 0.158114i
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 4.00000i 0.609994i −0.952353 0.304997i 0.901344π-0.901344\pi
0.952353 0.304997i 0.0986555π-0.0986555\pi
4444 −2.00000 −0.301511
4545 1.00000 2.00000i 0.149071 0.298142i
4646 −8.00000 −1.17954
4747 8.00000i 1.16692i −0.812142 0.583460i 0.801699π-0.801699\pi
0.812142 0.583460i 0.198301π-0.198301\pi
4848 1.00000i 0.144338i
4949 0 0
5050 4.00000 3.00000i 0.565685 0.424264i
5151 4.00000 0.560112
5252 6.00000i 0.832050i
5353 6.00000i 0.824163i −0.911147 0.412082i 0.864802π-0.864802\pi
0.911147 0.412082i 0.135198π-0.135198\pi
5454 1.00000 0.136083
5555 −2.00000 + 4.00000i −0.269680 + 0.539360i
5656 0 0
5757 6.00000i 0.794719i
5858 6.00000i 0.787839i
5959 −8.00000 −1.04151 −0.520756 0.853706i 0.674350π-0.674350\pi
−0.520756 + 0.853706i 0.674350π0.674350\pi
6060 2.00000 + 1.00000i 0.258199 + 0.129099i
6161 10.0000 1.28037 0.640184 0.768221i 0.278858π-0.278858\pi
0.640184 + 0.768221i 0.278858π0.278858\pi
6262 2.00000i 0.254000i
6363 0 0
6464 −1.00000 −0.125000
6565 −12.0000 6.00000i −1.48842 0.744208i
6666 −2.00000 −0.246183
6767 8.00000i 0.977356i 0.872464 + 0.488678i 0.162521π0.162521\pi
−0.872464 + 0.488678i 0.837479π0.837479\pi
6868 4.00000i 0.485071i
6969 −8.00000 −0.963087
7070 0 0
7171 −6.00000 −0.712069 −0.356034 0.934473i 0.615871π-0.615871\pi
−0.356034 + 0.934473i 0.615871π0.615871\pi
7272 1.00000i 0.117851i
7373 14.0000i 1.63858i −0.573382 0.819288i 0.694369π-0.694369\pi
0.573382 0.819288i 0.305631π-0.305631\pi
7474 −4.00000 −0.464991
7575 4.00000 3.00000i 0.461880 0.346410i
7676 6.00000 0.688247
7777 0 0
7878 6.00000i 0.679366i
7979 12.0000 1.35011 0.675053 0.737769i 0.264121π-0.264121\pi
0.675053 + 0.737769i 0.264121π0.264121\pi
8080 −1.00000 + 2.00000i −0.111803 + 0.223607i
8181 1.00000 0.111111
8282 2.00000i 0.220863i
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 8.00000 + 4.00000i 0.867722 + 0.433861i
8686 4.00000 0.431331
8787 6.00000i 0.643268i
8888 2.00000i 0.213201i
8989 −10.0000 −1.06000 −0.529999 0.847998i 0.677808π-0.677808\pi
−0.529999 + 0.847998i 0.677808π0.677808\pi
9090 2.00000 + 1.00000i 0.210819 + 0.105409i
9191 0 0
9292 8.00000i 0.834058i
9393 2.00000i 0.207390i
9494 8.00000 0.825137
9595 6.00000 12.0000i 0.615587 1.23117i
9696 −1.00000 −0.102062
9797 10.0000i 1.01535i 0.861550 + 0.507673i 0.169494π0.169494\pi
−0.861550 + 0.507673i 0.830506π0.830506\pi
9898 0 0
9999 −2.00000 −0.201008
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 4.00000i 0.396059i
103103 8.00000i 0.788263i 0.919054 + 0.394132i 0.128955π0.128955\pi
−0.919054 + 0.394132i 0.871045π0.871045\pi
104104 6.00000 0.588348
105105 0 0
106106 6.00000 0.582772
107107 12.0000i 1.16008i 0.814587 + 0.580042i 0.196964π0.196964\pi
−0.814587 + 0.580042i 0.803036π0.803036\pi
108108 1.00000i 0.0962250i
109109 14.0000 1.34096 0.670478 0.741929i 0.266089π-0.266089\pi
0.670478 + 0.741929i 0.266089π0.266089\pi
110110 −4.00000 2.00000i −0.381385 0.190693i
111111 −4.00000 −0.379663
112112 0 0
113113 6.00000i 0.564433i −0.959351 0.282216i 0.908930π-0.908930\pi
0.959351 0.282216i 0.0910696π-0.0910696\pi
114114 6.00000 0.561951
115115 −16.0000 8.00000i −1.49201 0.746004i
116116 6.00000 0.557086
117117 6.00000i 0.554700i
118118 8.00000i 0.736460i
119119 0 0
120120 −1.00000 + 2.00000i −0.0912871 + 0.182574i
121121 −7.00000 −0.636364
122122 10.0000i 0.905357i
123123 2.00000i 0.180334i
124124 −2.00000 −0.179605
125125 11.0000 2.00000i 0.983870 0.178885i
126126 0 0
127127 4.00000i 0.354943i 0.984126 + 0.177471i 0.0567917π0.0567917\pi
−0.984126 + 0.177471i 0.943208π0.943208\pi
128128 1.00000i 0.0883883i
129129 4.00000 0.352180
130130 6.00000 12.0000i 0.526235 1.05247i
131131 12.0000 1.04844 0.524222 0.851581i 0.324356π-0.324356\pi
0.524222 + 0.851581i 0.324356π0.324356\pi
132132 2.00000i 0.174078i
133133 0 0
134134 −8.00000 −0.691095
135135 2.00000 + 1.00000i 0.172133 + 0.0860663i
136136 −4.00000 −0.342997
137137 6.00000i 0.512615i −0.966595 0.256307i 0.917494π-0.917494\pi
0.966595 0.256307i 0.0825059π-0.0825059\pi
138138 8.00000i 0.681005i
139139 −14.0000 −1.18746 −0.593732 0.804663i 0.702346π-0.702346\pi
−0.593732 + 0.804663i 0.702346π0.702346\pi
140140 0 0
141141 8.00000 0.673722
142142 6.00000i 0.503509i
143143 12.0000i 1.00349i
144144 −1.00000 −0.0833333
145145 6.00000 12.0000i 0.498273 0.996546i
146146 14.0000 1.15865
147147 0 0
148148 4.00000i 0.328798i
149149 −10.0000 −0.819232 −0.409616 0.912258i 0.634337π-0.634337\pi
−0.409616 + 0.912258i 0.634337π0.634337\pi
150150 3.00000 + 4.00000i 0.244949 + 0.326599i
151151 −8.00000 −0.651031 −0.325515 0.945537i 0.605538π-0.605538\pi
−0.325515 + 0.945537i 0.605538π0.605538\pi
152152 6.00000i 0.486664i
153153 4.00000i 0.323381i
154154 0 0
155155 −2.00000 + 4.00000i −0.160644 + 0.321288i
156156 6.00000 0.480384
157157 22.0000i 1.75579i 0.478852 + 0.877896i 0.341053π0.341053\pi
−0.478852 + 0.877896i 0.658947π0.658947\pi
158158 12.0000i 0.954669i
159159 6.00000 0.475831
160160 −2.00000 1.00000i −0.158114 0.0790569i
161161 0 0
162162 1.00000i 0.0785674i
163163 4.00000i 0.313304i 0.987654 + 0.156652i 0.0500701π0.0500701\pi
−0.987654 + 0.156652i 0.949930π0.949930\pi
164164 2.00000 0.156174
165165 −4.00000 2.00000i −0.311400 0.155700i
166166 8.00000 0.620920
167167 12.0000i 0.928588i 0.885681 + 0.464294i 0.153692π0.153692\pi
−0.885681 + 0.464294i 0.846308π0.846308\pi
168168 0 0
169169 −23.0000 −1.76923
170170 −4.00000 + 8.00000i −0.306786 + 0.613572i
171171 6.00000 0.458831
172172 4.00000i 0.304997i
173173 8.00000i 0.608229i 0.952636 + 0.304114i 0.0983605π0.0983605\pi
−0.952636 + 0.304114i 0.901639π0.901639\pi
174174 6.00000 0.454859
175175 0 0
176176 2.00000 0.150756
177177 8.00000i 0.601317i
178178 10.0000i 0.749532i
179179 −10.0000 −0.747435 −0.373718 0.927543i 0.621917π-0.621917\pi
−0.373718 + 0.927543i 0.621917π0.621917\pi
180180 −1.00000 + 2.00000i −0.0745356 + 0.149071i
181181 −2.00000 −0.148659 −0.0743294 0.997234i 0.523682π-0.523682\pi
−0.0743294 + 0.997234i 0.523682π0.523682\pi
182182 0 0
183183 10.0000i 0.739221i
184184 8.00000 0.589768
185185 −8.00000 4.00000i −0.588172 0.294086i
186186 −2.00000 −0.146647
187187 8.00000i 0.585018i
188188 8.00000i 0.583460i
189189 0 0
190190 12.0000 + 6.00000i 0.870572 + 0.435286i
191191 −18.0000 −1.30243 −0.651217 0.758891i 0.725741π-0.725741\pi
−0.651217 + 0.758891i 0.725741π0.725741\pi
192192 1.00000i 0.0721688i
193193 8.00000i 0.575853i 0.957653 + 0.287926i 0.0929658π0.0929658\pi
−0.957653 + 0.287926i 0.907034π0.907034\pi
194194 −10.0000 −0.717958
195195 6.00000 12.0000i 0.429669 0.859338i
196196 0 0
197197 2.00000i 0.142494i 0.997459 + 0.0712470i 0.0226979π0.0226979\pi
−0.997459 + 0.0712470i 0.977302π0.977302\pi
198198 2.00000i 0.142134i
199199 6.00000 0.425329 0.212664 0.977125i 0.431786π-0.431786\pi
0.212664 + 0.977125i 0.431786π0.431786\pi
200200 −4.00000 + 3.00000i −0.282843 + 0.212132i
201201 −8.00000 −0.564276
202202 10.0000i 0.703598i
203203 0 0
204204 −4.00000 −0.280056
205205 2.00000 4.00000i 0.139686 0.279372i
206206 −8.00000 −0.557386
207207 8.00000i 0.556038i
208208 6.00000i 0.416025i
209209 −12.0000 −0.830057
210210 0 0
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 6.00000i 0.412082i
213213 6.00000i 0.411113i
214214 −12.0000 −0.820303
215215 8.00000 + 4.00000i 0.545595 + 0.272798i
216216 −1.00000 −0.0680414
217217 0 0
218218 14.0000i 0.948200i
219219 14.0000 0.946032
220220 2.00000 4.00000i 0.134840 0.269680i
221221 24.0000 1.61441
222222 4.00000i 0.268462i
223223 8.00000i 0.535720i −0.963458 0.267860i 0.913684π-0.913684\pi
0.963458 0.267860i 0.0863164π-0.0863164\pi
224224 0 0
225225 3.00000 + 4.00000i 0.200000 + 0.266667i
226226 6.00000 0.399114
227227 8.00000i 0.530979i 0.964114 + 0.265489i 0.0855335π0.0855335\pi
−0.964114 + 0.265489i 0.914466π0.914466\pi
228228 6.00000i 0.397360i
229229 14.0000 0.925146 0.462573 0.886581i 0.346926π-0.346926\pi
0.462573 + 0.886581i 0.346926π0.346926\pi
230230 8.00000 16.0000i 0.527504 1.05501i
231231 0 0
232232 6.00000i 0.393919i
233233 10.0000i 0.655122i 0.944830 + 0.327561i 0.106227π0.106227\pi
−0.944830 + 0.327561i 0.893773π0.893773\pi
234234 6.00000 0.392232
235235 16.0000 + 8.00000i 1.04372 + 0.521862i
236236 8.00000 0.520756
237237 12.0000i 0.779484i
238238 0 0
239239 −26.0000 −1.68180 −0.840900 0.541190i 0.817974π-0.817974\pi
−0.840900 + 0.541190i 0.817974π0.817974\pi
240240 −2.00000 1.00000i −0.129099 0.0645497i
241241 26.0000 1.67481 0.837404 0.546585i 0.184072π-0.184072\pi
0.837404 + 0.546585i 0.184072π0.184072\pi
242242 7.00000i 0.449977i
243243 1.00000i 0.0641500i
244244 −10.0000 −0.640184
245245 0 0
246246 2.00000 0.127515
247247 36.0000i 2.29063i
248248 2.00000i 0.127000i
249249 8.00000 0.506979
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 16.0000i 1.00591i
254254 −4.00000 −0.250982
255255 −4.00000 + 8.00000i −0.250490 + 0.500979i
256256 1.00000 0.0625000
257257 0 0 1.00000 00
−1.00000 π\pi
258258 4.00000i 0.249029i
259259 0 0
260260 12.0000 + 6.00000i 0.744208 + 0.372104i
261261 6.00000 0.371391
262262 12.0000i 0.741362i
263263 16.0000i 0.986602i −0.869859 0.493301i 0.835790π-0.835790\pi
0.869859 0.493301i 0.164210π-0.164210\pi
264264 2.00000 0.123091
265265 12.0000 + 6.00000i 0.737154 + 0.368577i
266266 0 0
267267 10.0000i 0.611990i
268268 8.00000i 0.488678i
269269 18.0000 1.09748 0.548740 0.835993i 0.315108π-0.315108\pi
0.548740 + 0.835993i 0.315108π0.315108\pi
270270 −1.00000 + 2.00000i −0.0608581 + 0.121716i
271271 −10.0000 −0.607457 −0.303728 0.952759i 0.598232π-0.598232\pi
−0.303728 + 0.952759i 0.598232π0.598232\pi
272272 4.00000i 0.242536i
273273 0 0
274274 6.00000 0.362473
275275 −6.00000 8.00000i −0.361814 0.482418i
276276 8.00000 0.481543
277277 28.0000i 1.68236i 0.540758 + 0.841178i 0.318138π0.318138\pi
−0.540758 + 0.841178i 0.681862π0.681862\pi
278278 14.0000i 0.839664i
279279 −2.00000 −0.119737
280280 0 0
281281 30.0000 1.78965 0.894825 0.446417i 0.147300π-0.147300\pi
0.894825 + 0.446417i 0.147300π0.147300\pi
282282 8.00000i 0.476393i
283283 20.0000i 1.18888i 0.804141 + 0.594438i 0.202626π0.202626\pi
−0.804141 + 0.594438i 0.797374π0.797374\pi
284284 6.00000 0.356034
285285 12.0000 + 6.00000i 0.710819 + 0.355409i
286286 −12.0000 −0.709575
287287 0 0
288288 1.00000i 0.0589256i
289289 1.00000 0.0588235
290290 12.0000 + 6.00000i 0.704664 + 0.352332i
291291 −10.0000 −0.586210
292292 14.0000i 0.819288i
293293 0 0 1.00000 00
−1.00000 π\pi
294294 0 0
295295 8.00000 16.0000i 0.465778 0.931556i
296296 4.00000 0.232495
297297 2.00000i 0.116052i
298298 10.0000i 0.579284i
299299 −48.0000 −2.77591
300300 −4.00000 + 3.00000i −0.230940 + 0.173205i
301301 0 0
302302 8.00000i 0.460348i
303303 10.0000i 0.574485i
304304 −6.00000 −0.344124
305305 −10.0000 + 20.0000i −0.572598 + 1.14520i
306306 −4.00000 −0.228665
307307 12.0000i 0.684876i 0.939540 + 0.342438i 0.111253π0.111253\pi
−0.939540 + 0.342438i 0.888747π0.888747\pi
308308 0 0
309309 −8.00000 −0.455104
310310 −4.00000 2.00000i −0.227185 0.113592i
311311 −24.0000 −1.36092 −0.680458 0.732787i 0.738219π-0.738219\pi
−0.680458 + 0.732787i 0.738219π0.738219\pi
312312 6.00000i 0.339683i
313313 2.00000i 0.113047i −0.998401 0.0565233i 0.981998π-0.981998\pi
0.998401 0.0565233i 0.0180015π-0.0180015\pi
314314 −22.0000 −1.24153
315315 0 0
316316 −12.0000 −0.675053
317317 2.00000i 0.112331i −0.998421 0.0561656i 0.982113π-0.982113\pi
0.998421 0.0561656i 0.0178875π-0.0178875\pi
318318 6.00000i 0.336463i
319319 −12.0000 −0.671871
320320 1.00000 2.00000i 0.0559017 0.111803i
321321 −12.0000 −0.669775
322322 0 0
323323 24.0000i 1.33540i
324324 −1.00000 −0.0555556
325325 24.0000 18.0000i 1.33128 0.998460i
326326 −4.00000 −0.221540
327327 14.0000i 0.774202i
328328 2.00000i 0.110432i
329329 0 0
330330 2.00000 4.00000i 0.110096 0.220193i
331331 −8.00000 −0.439720 −0.219860 0.975531i 0.570560π-0.570560\pi
−0.219860 + 0.975531i 0.570560π0.570560\pi
332332 8.00000i 0.439057i
333333 4.00000i 0.219199i
334334 −12.0000 −0.656611
335335 −16.0000 8.00000i −0.874173 0.437087i
336336 0 0
337337 8.00000i 0.435788i −0.975972 0.217894i 0.930081π-0.930081\pi
0.975972 0.217894i 0.0699187π-0.0699187\pi
338338 23.0000i 1.25104i
339339 6.00000 0.325875
340340 −8.00000 4.00000i −0.433861 0.216930i
341341 4.00000 0.216612
342342 6.00000i 0.324443i
343343 0 0
344344 −4.00000 −0.215666
345345 8.00000 16.0000i 0.430706 0.861411i
346346 −8.00000 −0.430083
347347 36.0000i 1.93258i 0.257454 + 0.966291i 0.417117π0.417117\pi
−0.257454 + 0.966291i 0.582883π0.582883\pi
348348 6.00000i 0.321634i
349349 −26.0000 −1.39175 −0.695874 0.718164i 0.744983π-0.744983\pi
−0.695874 + 0.718164i 0.744983π0.744983\pi
350350 0 0
351351 6.00000 0.320256
352352 2.00000i 0.106600i
353353 20.0000i 1.06449i 0.846590 + 0.532246i 0.178652π0.178652\pi
−0.846590 + 0.532246i 0.821348π0.821348\pi
354354 8.00000 0.425195
355355 6.00000 12.0000i 0.318447 0.636894i
356356 10.0000 0.529999
357357 0 0
358358 10.0000i 0.528516i
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 −2.00000 1.00000i −0.105409 0.0527046i
361361 17.0000 0.894737
362362 2.00000i 0.105118i
363363 7.00000i 0.367405i
364364 0 0
365365 28.0000 + 14.0000i 1.46559 + 0.732793i
366366 −10.0000 −0.522708
367367 32.0000i 1.67039i 0.549957 + 0.835193i 0.314644π0.314644\pi
−0.549957 + 0.835193i 0.685356π0.685356\pi
368368 8.00000i 0.417029i
369369 2.00000 0.104116
370370 4.00000 8.00000i 0.207950 0.415900i
371371 0 0
372372 2.00000i 0.103695i
373373 24.0000i 1.24267i 0.783544 + 0.621336i 0.213410π0.213410\pi
−0.783544 + 0.621336i 0.786590π0.786590\pi
374374 8.00000 0.413670
375375 2.00000 + 11.0000i 0.103280 + 0.568038i
376376 −8.00000 −0.412568
377377 36.0000i 1.85409i
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 −6.00000 + 12.0000i −0.307794 + 0.615587i
381381 −4.00000 −0.204926
382382 18.0000i 0.920960i
383383 20.0000i 1.02195i 0.859595 + 0.510976i 0.170716π0.170716\pi
−0.859595 + 0.510976i 0.829284π0.829284\pi
384384 1.00000 0.0510310
385385 0 0
386386 −8.00000 −0.407189
387387 4.00000i 0.203331i
388388 10.0000i 0.507673i
389389 −2.00000 −0.101404 −0.0507020 0.998714i 0.516146π-0.516146\pi
−0.0507020 + 0.998714i 0.516146π0.516146\pi
390390 12.0000 + 6.00000i 0.607644 + 0.303822i
391391 32.0000 1.61831
392392 0 0
393393 12.0000i 0.605320i
394394 −2.00000 −0.100759
395395 −12.0000 + 24.0000i −0.603786 + 1.20757i
396396 2.00000 0.100504
397397 2.00000i 0.100377i 0.998740 + 0.0501886i 0.0159822π0.0159822\pi
−0.998740 + 0.0501886i 0.984018π0.984018\pi
398398 6.00000i 0.300753i
399399 0 0
400400 −3.00000 4.00000i −0.150000 0.200000i
401401 −14.0000 −0.699127 −0.349563 0.936913i 0.613670π-0.613670\pi
−0.349563 + 0.936913i 0.613670π0.613670\pi
402402 8.00000i 0.399004i
403403 12.0000i 0.597763i
404404 10.0000 0.497519
405405 −1.00000 + 2.00000i −0.0496904 + 0.0993808i
406406 0 0
407407 8.00000i 0.396545i
408408 4.00000i 0.198030i
409409 26.0000 1.28562 0.642809 0.766027i 0.277769π-0.277769\pi
0.642809 + 0.766027i 0.277769π0.277769\pi
410410 4.00000 + 2.00000i 0.197546 + 0.0987730i
411411 6.00000 0.295958
412412 8.00000i 0.394132i
413413 0 0
414414 8.00000 0.393179
415415 16.0000 + 8.00000i 0.785409 + 0.392705i
416416 −6.00000 −0.294174
417417 14.0000i 0.685583i
418418 12.0000i 0.586939i
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 34.0000 1.65706 0.828529 0.559946i 0.189178π-0.189178\pi
0.828529 + 0.559946i 0.189178π0.189178\pi
422422 0 0
423423 8.00000i 0.388973i
424424 −6.00000 −0.291386
425425 −16.0000 + 12.0000i −0.776114 + 0.582086i
426426 6.00000 0.290701
427427 0 0
428428 12.0000i 0.580042i
429429 −12.0000 −0.579365
430430 −4.00000 + 8.00000i −0.192897 + 0.385794i
431431 2.00000 0.0963366 0.0481683 0.998839i 0.484662π-0.484662\pi
0.0481683 + 0.998839i 0.484662π0.484662\pi
432432 1.00000i 0.0481125i
433433 26.0000i 1.24948i −0.780833 0.624740i 0.785205π-0.785205\pi
0.780833 0.624740i 0.214795π-0.214795\pi
434434 0 0
435435 12.0000 + 6.00000i 0.575356 + 0.287678i
436436 −14.0000 −0.670478
437437 48.0000i 2.29615i
438438 14.0000i 0.668946i
439439 −18.0000 −0.859093 −0.429547 0.903045i 0.641327π-0.641327\pi
−0.429547 + 0.903045i 0.641327π0.641327\pi
440440 4.00000 + 2.00000i 0.190693 + 0.0953463i
441441 0 0
442442 24.0000i 1.14156i
443443 12.0000i 0.570137i 0.958507 + 0.285069i 0.0920164π0.0920164\pi
−0.958507 + 0.285069i 0.907984π0.907984\pi
444444 4.00000 0.189832
445445 10.0000 20.0000i 0.474045 0.948091i
446446 8.00000 0.378811
447447 10.0000i 0.472984i
448448 0 0
449449 6.00000 0.283158 0.141579 0.989927i 0.454782π-0.454782\pi
0.141579 + 0.989927i 0.454782π0.454782\pi
450450 −4.00000 + 3.00000i −0.188562 + 0.141421i
451451 −4.00000 −0.188353
452452 6.00000i 0.282216i
453453 8.00000i 0.375873i
454454 −8.00000 −0.375459
455455 0 0
456456 −6.00000 −0.280976
457457 28.0000i 1.30978i 0.755722 + 0.654892i 0.227286π0.227286\pi
−0.755722 + 0.654892i 0.772714π0.772714\pi
458458 14.0000i 0.654177i
459459 −4.00000 −0.186704
460460 16.0000 + 8.00000i 0.746004 + 0.373002i
461461 18.0000 0.838344 0.419172 0.907907i 0.362320π-0.362320\pi
0.419172 + 0.907907i 0.362320π0.362320\pi
462462 0 0
463463 36.0000i 1.67306i −0.547920 0.836531i 0.684580π-0.684580\pi
0.547920 0.836531i 0.315420π-0.315420\pi
464464 −6.00000 −0.278543
465465 −4.00000 2.00000i −0.185496 0.0927478i
466466 −10.0000 −0.463241
467467 24.0000i 1.11059i 0.831654 + 0.555294i 0.187394π0.187394\pi
−0.831654 + 0.555294i 0.812606π0.812606\pi
468468 6.00000i 0.277350i
469469 0 0
470470 −8.00000 + 16.0000i −0.369012 + 0.738025i
471471 −22.0000 −1.01371
472472 8.00000i 0.368230i
473473 8.00000i 0.367840i
474474 −12.0000 −0.551178
475475 18.0000 + 24.0000i 0.825897 + 1.10120i
476476 0 0
477477 6.00000i 0.274721i
478478 26.0000i 1.18921i
479479 8.00000 0.365529 0.182765 0.983157i 0.441495π-0.441495\pi
0.182765 + 0.983157i 0.441495π0.441495\pi
480480 1.00000 2.00000i 0.0456435 0.0912871i
481481 −24.0000 −1.09431
482482 26.0000i 1.18427i
483483 0 0
484484 7.00000 0.318182
485485 −20.0000 10.0000i −0.908153 0.454077i
486486 −1.00000 −0.0453609
487487 12.0000i 0.543772i 0.962329 + 0.271886i 0.0876473π0.0876473\pi
−0.962329 + 0.271886i 0.912353π0.912353\pi
488488 10.0000i 0.452679i
489489 −4.00000 −0.180886
490490 0 0
491491 −30.0000 −1.35388 −0.676941 0.736038i 0.736695π-0.736695\pi
−0.676941 + 0.736038i 0.736695π0.736695\pi
492492 2.00000i 0.0901670i
493493 24.0000i 1.08091i
494494 36.0000 1.61972
495495 2.00000 4.00000i 0.0898933 0.179787i
496496 2.00000 0.0898027
497497 0 0
498498 8.00000i 0.358489i
499499 12.0000 0.537194 0.268597 0.963253i 0.413440π-0.413440\pi
0.268597 + 0.963253i 0.413440π0.413440\pi
500500 −11.0000 + 2.00000i −0.491935 + 0.0894427i
501501 −12.0000 −0.536120
502502 0 0
503503 12.0000i 0.535054i −0.963550 0.267527i 0.913794π-0.913794\pi
0.963550 0.267527i 0.0862064π-0.0862064\pi
504504 0 0
505505 10.0000 20.0000i 0.444994 0.889988i
506506 −16.0000 −0.711287
507507 23.0000i 1.02147i
508508 4.00000i 0.177471i
509509 30.0000 1.32973 0.664863 0.746965i 0.268490π-0.268490\pi
0.664863 + 0.746965i 0.268490π0.268490\pi
510510 −8.00000 4.00000i −0.354246 0.177123i
511511 0 0
512512 1.00000i 0.0441942i
513513 6.00000i 0.264906i
514514 0 0
515515 −16.0000 8.00000i −0.705044 0.352522i
516516 −4.00000 −0.176090
517517 16.0000i 0.703679i
518518 0 0
519519 −8.00000 −0.351161
520520 −6.00000 + 12.0000i −0.263117 + 0.526235i
521521 26.0000 1.13908 0.569540 0.821963i 0.307121π-0.307121\pi
0.569540 + 0.821963i 0.307121π0.307121\pi
522522 6.00000i 0.262613i
523523 28.0000i 1.22435i −0.790721 0.612177i 0.790294π-0.790294\pi
0.790721 0.612177i 0.209706π-0.209706\pi
524524 −12.0000 −0.524222
525525 0 0
526526 16.0000 0.697633
527527 8.00000i 0.348485i
528528 2.00000i 0.0870388i
529529 −41.0000 −1.78261
530530 −6.00000 + 12.0000i −0.260623 + 0.521247i
531531 8.00000 0.347170
532532 0 0
533533 12.0000i 0.519778i
534534 10.0000 0.432742
535535 −24.0000 12.0000i −1.03761 0.518805i
536536 8.00000 0.345547
537537 10.0000i 0.431532i
538538 18.0000i 0.776035i
539539 0 0
540540 −2.00000 1.00000i −0.0860663 0.0430331i
541541 22.0000 0.945854 0.472927 0.881102i 0.343197π-0.343197\pi
0.472927 + 0.881102i 0.343197π0.343197\pi
542542 10.0000i 0.429537i
543543 2.00000i 0.0858282i
544544 4.00000 0.171499
545545 −14.0000 + 28.0000i −0.599694 + 1.19939i
546546 0 0
547547 40.0000i 1.71028i 0.518400 + 0.855138i 0.326528π0.326528\pi
−0.518400 + 0.855138i 0.673472π0.673472\pi
548548 6.00000i 0.256307i
549549 −10.0000 −0.426790
550550 8.00000 6.00000i 0.341121 0.255841i
551551 36.0000 1.53365
552552 8.00000i 0.340503i
553553 0 0
554554 −28.0000 −1.18961
555555 4.00000 8.00000i 0.169791 0.339581i
556556 14.0000 0.593732
557557 42.0000i 1.77960i −0.456354 0.889799i 0.650845π-0.650845\pi
0.456354 0.889799i 0.349155π-0.349155\pi
558558 2.00000i 0.0846668i
559559 24.0000 1.01509
560560 0 0
561561 8.00000 0.337760
562562 30.0000i 1.26547i
563563 4.00000i 0.168580i −0.996441 0.0842900i 0.973138π-0.973138\pi
0.996441 0.0842900i 0.0268622π-0.0268622\pi
564564 −8.00000 −0.336861
565565 12.0000 + 6.00000i 0.504844 + 0.252422i
566566 −20.0000 −0.840663
567567 0 0
568568 6.00000i 0.251754i
569569 46.0000 1.92842 0.964210 0.265139i 0.0854179π-0.0854179\pi
0.964210 + 0.265139i 0.0854179π0.0854179\pi
570570 −6.00000 + 12.0000i −0.251312 + 0.502625i
571571 4.00000 0.167395 0.0836974 0.996491i 0.473327π-0.473327\pi
0.0836974 + 0.996491i 0.473327π0.473327\pi
572572 12.0000i 0.501745i
573573 18.0000i 0.751961i
574574 0 0
575575 32.0000 24.0000i 1.33449 1.00087i
576576 1.00000 0.0416667
577577 26.0000i 1.08239i 0.840896 + 0.541197i 0.182029π0.182029\pi
−0.840896 + 0.541197i 0.817971π0.817971\pi
578578 1.00000i 0.0415945i
579579 −8.00000 −0.332469
580580 −6.00000 + 12.0000i −0.249136 + 0.498273i
581581 0 0
582582 10.0000i 0.414513i
583583 12.0000i 0.496989i
584584 −14.0000 −0.579324
585585 12.0000 + 6.00000i 0.496139 + 0.248069i
586586 0 0
587587 12.0000i 0.495293i 0.968850 + 0.247647i 0.0796572π0.0796572\pi
−0.968850 + 0.247647i 0.920343π0.920343\pi
588588 0 0
589589 −12.0000 −0.494451
590590 16.0000 + 8.00000i 0.658710 + 0.329355i
591591 −2.00000 −0.0822690
592592 4.00000i 0.164399i
593593 12.0000i 0.492781i 0.969171 + 0.246390i 0.0792446π0.0792446\pi
−0.969171 + 0.246390i 0.920755π0.920755\pi
594594 2.00000 0.0820610
595595 0 0
596596 10.0000 0.409616
597597 6.00000i 0.245564i
598598 48.0000i 1.96287i
599599 −30.0000 −1.22577 −0.612883 0.790173i 0.709990π-0.709990\pi
−0.612883 + 0.790173i 0.709990π0.709990\pi
600600 −3.00000 4.00000i −0.122474 0.163299i
601601 −38.0000 −1.55005 −0.775026 0.631929i 0.782263π-0.782263\pi
−0.775026 + 0.631929i 0.782263π0.782263\pi
602602 0 0
603603 8.00000i 0.325785i
604604 8.00000 0.325515
605605 7.00000 14.0000i 0.284590 0.569181i
606606 10.0000 0.406222
607607 8.00000i 0.324710i −0.986732 0.162355i 0.948091π-0.948091\pi
0.986732 0.162355i 0.0519090π-0.0519090\pi
608608 6.00000i 0.243332i
609609 0 0
610610 −20.0000 10.0000i −0.809776 0.404888i
611611 48.0000 1.94187
612612 4.00000i 0.161690i
613613 28.0000i 1.13091i −0.824779 0.565455i 0.808701π-0.808701\pi
0.824779 0.565455i 0.191299π-0.191299\pi
614614 −12.0000 −0.484281
615615 4.00000 + 2.00000i 0.161296 + 0.0806478i
616616 0 0
617617 26.0000i 1.04672i −0.852111 0.523360i 0.824678π-0.824678\pi
0.852111 0.523360i 0.175322π-0.175322\pi
618618 8.00000i 0.321807i
619619 −22.0000 −0.884255 −0.442127 0.896952i 0.645776π-0.645776\pi
−0.442127 + 0.896952i 0.645776π0.645776\pi
620620 2.00000 4.00000i 0.0803219 0.160644i
621621 8.00000 0.321029
622622 24.0000i 0.962312i
623623 0 0
624624 −6.00000 −0.240192
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 2.00000 0.0799361
627627 12.0000i 0.479234i
628628 22.0000i 0.877896i
629629 16.0000 0.637962
630630 0 0
631631 −4.00000 −0.159237 −0.0796187 0.996825i 0.525370π-0.525370\pi
−0.0796187 + 0.996825i 0.525370π0.525370\pi
632632 12.0000i 0.477334i
633633 0 0
634634 2.00000 0.0794301
635635 −8.00000 4.00000i −0.317470 0.158735i
636636 −6.00000 −0.237915
637637 0 0
638638 12.0000i 0.475085i
639639 6.00000 0.237356
640640 2.00000 + 1.00000i 0.0790569 + 0.0395285i
641641 14.0000 0.552967 0.276483 0.961019i 0.410831π-0.410831\pi
0.276483 + 0.961019i 0.410831π0.410831\pi
642642 12.0000i 0.473602i
643643 12.0000i 0.473234i 0.971603 + 0.236617i 0.0760386π0.0760386\pi
−0.971603 + 0.236617i 0.923961π0.923961\pi
644644 0 0
645645 −4.00000 + 8.00000i −0.157500 + 0.315000i
646646 −24.0000 −0.944267
647647 36.0000i 1.41531i −0.706560 0.707653i 0.749754π-0.749754\pi
0.706560 0.707653i 0.250246π-0.250246\pi
648648 1.00000i 0.0392837i
649649 −16.0000 −0.628055
650650 18.0000 + 24.0000i 0.706018 + 0.941357i
651651 0 0
652652 4.00000i 0.156652i
653653 34.0000i 1.33052i −0.746611 0.665261i 0.768320π-0.768320\pi
0.746611 0.665261i 0.231680π-0.231680\pi
654654 −14.0000 −0.547443
655655 −12.0000 + 24.0000i −0.468879 + 0.937758i
656656 −2.00000 −0.0780869
657657 14.0000i 0.546192i
658658 0 0
659659 26.0000 1.01282 0.506408 0.862294i 0.330973π-0.330973\pi
0.506408 + 0.862294i 0.330973π0.330973\pi
660660 4.00000 + 2.00000i 0.155700 + 0.0778499i
661661 −38.0000 −1.47803 −0.739014 0.673690i 0.764708π-0.764708\pi
−0.739014 + 0.673690i 0.764708π0.764708\pi
662662 8.00000i 0.310929i
663663 24.0000i 0.932083i
664664 −8.00000 −0.310460
665665 0 0
666666 4.00000 0.154997
667667 48.0000i 1.85857i
668668 12.0000i 0.464294i
669669 8.00000 0.309298
670670 8.00000 16.0000i 0.309067 0.618134i
671671 20.0000 0.772091
672672 0 0
673673 12.0000i 0.462566i −0.972887 0.231283i 0.925708π-0.925708\pi
0.972887 0.231283i 0.0742923π-0.0742923\pi
674674 8.00000 0.308148
675675 −4.00000 + 3.00000i −0.153960 + 0.115470i
676676 23.0000 0.884615
677677 40.0000i 1.53732i −0.639655 0.768662i 0.720923π-0.720923\pi
0.639655 0.768662i 0.279077π-0.279077\pi
678678 6.00000i 0.230429i
679679 0 0
680680 4.00000 8.00000i 0.153393 0.306786i
681681 −8.00000 −0.306561
682682 4.00000i 0.153168i
683683 4.00000i 0.153056i −0.997067 0.0765279i 0.975617π-0.975617\pi
0.997067 0.0765279i 0.0243834π-0.0243834\pi
684684 −6.00000 −0.229416
685685 12.0000 + 6.00000i 0.458496 + 0.229248i
686686 0 0
687687 14.0000i 0.534133i
688688 4.00000i 0.152499i
689689 36.0000 1.37149
690690 16.0000 + 8.00000i 0.609110 + 0.304555i
691691 2.00000 0.0760836 0.0380418 0.999276i 0.487888π-0.487888\pi
0.0380418 + 0.999276i 0.487888π0.487888\pi
692692 8.00000i 0.304114i
693693 0 0
694694 −36.0000 −1.36654
695695 14.0000 28.0000i 0.531050 1.06210i
696696 −6.00000 −0.227429
697697 8.00000i 0.303022i
698698 26.0000i 0.984115i
699699 −10.0000 −0.378235
700700 0 0
701701 −34.0000 −1.28416 −0.642081 0.766637i 0.721929π-0.721929\pi
−0.642081 + 0.766637i 0.721929π0.721929\pi
702702 6.00000i 0.226455i
703703 24.0000i 0.905177i
704704 −2.00000 −0.0753778
705705 −8.00000 + 16.0000i −0.301297 + 0.602595i
706706 −20.0000 −0.752710
707707 0 0
708708 8.00000i 0.300658i
709709 6.00000 0.225335 0.112667 0.993633i 0.464061π-0.464061\pi
0.112667 + 0.993633i 0.464061π0.464061\pi
710710 12.0000 + 6.00000i 0.450352 + 0.225176i
711711 −12.0000 −0.450035
712712 10.0000i 0.374766i
713713 16.0000i 0.599205i
714714 0 0
715715 −24.0000 12.0000i −0.897549 0.448775i
716716 10.0000 0.373718
717717 26.0000i 0.970988i
718718 6.00000i 0.223918i
719719 −4.00000 −0.149175 −0.0745874 0.997214i 0.523764π-0.523764\pi
−0.0745874 + 0.997214i 0.523764π0.523764\pi
720720 1.00000 2.00000i 0.0372678 0.0745356i
721721 0 0
722722 17.0000i 0.632674i
723723 26.0000i 0.966950i
724724 2.00000 0.0743294
725725 18.0000 + 24.0000i 0.668503 + 0.891338i
726726 7.00000 0.259794
727727 24.0000i 0.890111i −0.895503 0.445055i 0.853184π-0.853184\pi
0.895503 0.445055i 0.146816π-0.146816\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 −14.0000 + 28.0000i −0.518163 + 1.03633i
731731 −16.0000 −0.591781
732732 10.0000i 0.369611i
733733 14.0000i 0.517102i 0.965998 + 0.258551i 0.0832450π0.0832450\pi
−0.965998 + 0.258551i 0.916755π0.916755\pi
734734 −32.0000 −1.18114
735735 0 0
736736 −8.00000 −0.294884
737737 16.0000i 0.589368i
738738 2.00000i 0.0736210i
739739 44.0000 1.61857 0.809283 0.587419i 0.199856π-0.199856\pi
0.809283 + 0.587419i 0.199856π0.199856\pi
740740 8.00000 + 4.00000i 0.294086 + 0.147043i
741741 36.0000 1.32249
742742 0 0
743743 48.0000i 1.76095i 0.474093 + 0.880475i 0.342776π0.342776\pi
−0.474093 + 0.880475i 0.657224π0.657224\pi
744744 2.00000 0.0733236
745745 10.0000 20.0000i 0.366372 0.732743i
746746 −24.0000 −0.878702
747747 8.00000i 0.292705i
748748 8.00000i 0.292509i
749749 0 0
750750 −11.0000 + 2.00000i −0.401663 + 0.0730297i
751751 20.0000 0.729810 0.364905 0.931045i 0.381101π-0.381101\pi
0.364905 + 0.931045i 0.381101π0.381101\pi
752752 8.00000i 0.291730i
753753 0 0
754754 36.0000 1.31104
755755 8.00000 16.0000i 0.291150 0.582300i
756756 0 0
757757 32.0000i 1.16306i −0.813525 0.581530i 0.802454π-0.802454\pi
0.813525 0.581530i 0.197546π-0.197546\pi
758758 20.0000i 0.726433i
759759 −16.0000 −0.580763
760760 −12.0000 6.00000i −0.435286 0.217643i
761761 6.00000 0.217500 0.108750 0.994069i 0.465315π-0.465315\pi
0.108750 + 0.994069i 0.465315π0.465315\pi
762762 4.00000i 0.144905i
763763 0 0
764764 18.0000 0.651217
765765 −8.00000 4.00000i −0.289241 0.144620i
766766 −20.0000 −0.722629
767767 48.0000i 1.73318i
768768 1.00000i 0.0360844i
769769 30.0000 1.08183 0.540914 0.841078i 0.318079π-0.318079\pi
0.540914 + 0.841078i 0.318079π0.318079\pi
770770 0 0
771771 0 0
772772 8.00000i 0.287926i
773773 0 0 1.00000 00
−1.00000 π\pi
774774 −4.00000 −0.143777
775775 −6.00000 8.00000i −0.215526 0.287368i
776776 10.0000 0.358979
777777 0 0
778778 2.00000i 0.0717035i
779779 12.0000 0.429945
780780 −6.00000 + 12.0000i −0.214834 + 0.429669i
781781 −12.0000 −0.429394
782782 32.0000i 1.14432i
783783 6.00000i 0.214423i
784784 0 0
785785 −44.0000 22.0000i −1.57043 0.785214i
786786 −12.0000 −0.428026
787787 28.0000i 0.998092i −0.866575 0.499046i 0.833684π-0.833684\pi
0.866575 0.499046i 0.166316π-0.166316\pi
788788 2.00000i 0.0712470i
789789 16.0000 0.569615
790790 −24.0000 12.0000i −0.853882 0.426941i
791791 0 0
792792 2.00000i 0.0710669i
793793 60.0000i 2.13066i
794794 −2.00000 −0.0709773
795795 −6.00000 + 12.0000i −0.212798 + 0.425596i
796796 −6.00000 −0.212664
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 −32.0000 −1.13208
800800 4.00000 3.00000i 0.141421 0.106066i
801801 10.0000 0.353333
802802 14.0000i 0.494357i
803803 28.0000i 0.988099i
804804 8.00000 0.282138
805805 0 0
806806 −12.0000 −0.422682
807807 18.0000i 0.633630i
808808 10.0000i 0.351799i
809809 −30.0000 −1.05474 −0.527372 0.849635i 0.676823π-0.676823\pi
−0.527372 + 0.849635i 0.676823π0.676823\pi
810810 −2.00000 1.00000i −0.0702728 0.0351364i
811811 14.0000 0.491606 0.245803 0.969320i 0.420948π-0.420948\pi
0.245803 + 0.969320i 0.420948π0.420948\pi
812812 0 0
813813 10.0000i 0.350715i
814814 −8.00000 −0.280400
815815 −8.00000 4.00000i −0.280228 0.140114i
816816 4.00000 0.140028
817817 24.0000i 0.839654i
818818 26.0000i 0.909069i
819819 0 0
820820 −2.00000 + 4.00000i −0.0698430 + 0.139686i
821821 22.0000 0.767805 0.383903 0.923374i 0.374580π-0.374580\pi
0.383903 + 0.923374i 0.374580π0.374580\pi
822822 6.00000i 0.209274i
823823 12.0000i 0.418294i −0.977884 0.209147i 0.932931π-0.932931\pi
0.977884 0.209147i 0.0670687π-0.0670687\pi
824824 8.00000 0.278693
825825 8.00000 6.00000i 0.278524 0.208893i
826826 0 0
827827 20.0000i 0.695468i −0.937593 0.347734i 0.886951π-0.886951\pi
0.937593 0.347734i 0.113049π-0.113049\pi
828828 8.00000i 0.278019i
829829 18.0000 0.625166 0.312583 0.949890i 0.398806π-0.398806\pi
0.312583 + 0.949890i 0.398806π0.398806\pi
830830 −8.00000 + 16.0000i −0.277684 + 0.555368i
831831 −28.0000 −0.971309
832832 6.00000i 0.208013i
833833 0 0
834834 14.0000 0.484780
835835 −24.0000 12.0000i −0.830554 0.415277i
836836 12.0000 0.415029
837837 2.00000i 0.0691301i
838838 20.0000i 0.690889i
839839 −20.0000 −0.690477 −0.345238 0.938515i 0.612202π-0.612202\pi
−0.345238 + 0.938515i 0.612202π0.612202\pi
840840 0 0
841841 7.00000 0.241379
842842 34.0000i 1.17172i
843843 30.0000i 1.03325i
844844 0 0
845845 23.0000 46.0000i 0.791224 1.58245i
846846 −8.00000 −0.275046
847847 0 0
848848 6.00000i 0.206041i
849849 −20.0000 −0.686398
850850 −12.0000 16.0000i −0.411597 0.548795i
851851 −32.0000 −1.09695
852852 6.00000i 0.205557i
853853 38.0000i 1.30110i 0.759465 + 0.650548i 0.225461π0.225461\pi
−0.759465 + 0.650548i 0.774539π0.774539\pi
854854 0 0
855855 −6.00000 + 12.0000i −0.205196 + 0.410391i
856856 12.0000 0.410152
857857 24.0000i 0.819824i −0.912125 0.409912i 0.865559π-0.865559\pi
0.912125 0.409912i 0.134441π-0.134441\pi
858858 12.0000i 0.409673i
859859 −10.0000 −0.341196 −0.170598 0.985341i 0.554570π-0.554570\pi
−0.170598 + 0.985341i 0.554570π0.554570\pi
860860 −8.00000 4.00000i −0.272798 0.136399i
861861 0 0
862862 2.00000i 0.0681203i
863863 48.0000i 1.63394i 0.576681 + 0.816970i 0.304348π0.304348\pi
−0.576681 + 0.816970i 0.695652π0.695652\pi
864864 1.00000 0.0340207
865865 −16.0000 8.00000i −0.544016 0.272008i
866866 26.0000 0.883516
867867 1.00000i 0.0339618i
868868 0 0
869869 24.0000 0.814144
870870 −6.00000 + 12.0000i −0.203419 + 0.406838i
871871 −48.0000 −1.62642
872872 14.0000i 0.474100i
873873 10.0000i 0.338449i
874874 48.0000 1.62362
875875 0 0
876876 −14.0000 −0.473016
877877 28.0000i 0.945493i −0.881199 0.472746i 0.843263π-0.843263\pi
0.881199 0.472746i 0.156737π-0.156737\pi
878878 18.0000i 0.607471i
879879 0 0
880880 −2.00000 + 4.00000i −0.0674200 + 0.134840i
881881 −30.0000 −1.01073 −0.505363 0.862907i 0.668641π-0.668641\pi
−0.505363 + 0.862907i 0.668641π0.668641\pi
882882 0 0
883883 24.0000i 0.807664i −0.914833 0.403832i 0.867678π-0.867678\pi
0.914833 0.403832i 0.132322π-0.132322\pi
884884 −24.0000 −0.807207
885885 16.0000 + 8.00000i 0.537834 + 0.268917i
886886 −12.0000 −0.403148
887887 0 0 1.00000 00
−1.00000 π\pi
888888 4.00000i 0.134231i
889889 0 0
890890 20.0000 + 10.0000i 0.670402 + 0.335201i
891891 2.00000 0.0670025
892892 8.00000i 0.267860i
893893 48.0000i 1.60626i
894894 10.0000 0.334450
895895 10.0000 20.0000i 0.334263 0.668526i
896896 0 0
897897 48.0000i 1.60267i
898898 6.00000i 0.200223i
899899 −12.0000 −0.400222
900900 −3.00000 4.00000i −0.100000 0.133333i
901901 −24.0000 −0.799556
902902 4.00000i 0.133185i
903903 0 0
904904 −6.00000 −0.199557
905905 2.00000 4.00000i 0.0664822 0.132964i
906906 8.00000 0.265782
907907 24.0000i 0.796907i 0.917189 + 0.398453i 0.130453π0.130453\pi
−0.917189 + 0.398453i 0.869547π0.869547\pi
908908 8.00000i 0.265489i
909909 10.0000 0.331679
910910 0 0
911911 6.00000 0.198789 0.0993944 0.995048i 0.468309π-0.468309\pi
0.0993944 + 0.995048i 0.468309π0.468309\pi
912912 6.00000i 0.198680i
913913 16.0000i 0.529523i
914914 −28.0000 −0.926158
915915 −20.0000 10.0000i −0.661180 0.330590i
916916 −14.0000 −0.462573
917917 0 0
918918 4.00000i 0.132020i
919919 −60.0000 −1.97922 −0.989609 0.143787i 0.954072π-0.954072\pi
−0.989609 + 0.143787i 0.954072π0.954072\pi
920920 −8.00000 + 16.0000i −0.263752 + 0.527504i
921921 −12.0000 −0.395413
922922 18.0000i 0.592798i
923923 36.0000i 1.18495i
924924 0 0
925925 16.0000 12.0000i 0.526077 0.394558i
926926 36.0000 1.18303
927927 8.00000i 0.262754i
928928 6.00000i 0.196960i
929929 −30.0000 −0.984268 −0.492134 0.870519i 0.663783π-0.663783\pi
−0.492134 + 0.870519i 0.663783π0.663783\pi
930930 2.00000 4.00000i 0.0655826 0.131165i
931931 0 0
932932 10.0000i 0.327561i
933933 24.0000i 0.785725i
934934 −24.0000 −0.785304
935935 16.0000 + 8.00000i 0.523256 + 0.261628i
936936 −6.00000 −0.196116
937937 26.0000i 0.849383i −0.905338 0.424691i 0.860383π-0.860383\pi
0.905338 0.424691i 0.139617π-0.139617\pi
938938 0 0
939939 2.00000 0.0652675
940940 −16.0000 8.00000i −0.521862 0.260931i
941941 10.0000 0.325991 0.162995 0.986627i 0.447884π-0.447884\pi
0.162995 + 0.986627i 0.447884π0.447884\pi
942942 22.0000i 0.716799i
943943 16.0000i 0.521032i
944944 −8.00000 −0.260378
945945 0 0
946946 8.00000 0.260102
947947 12.0000i 0.389948i −0.980808 0.194974i 0.937538π-0.937538\pi
0.980808 0.194974i 0.0624622π-0.0624622\pi
948948 12.0000i 0.389742i
949949 84.0000 2.72676
950950 −24.0000 + 18.0000i −0.778663 + 0.583997i
951951 2.00000 0.0648544
952952 0 0
953953 10.0000i 0.323932i 0.986796 + 0.161966i 0.0517835π0.0517835\pi
−0.986796 + 0.161966i 0.948217π0.948217\pi
954954 −6.00000 −0.194257
955955 18.0000 36.0000i 0.582466 1.16493i
956956 26.0000 0.840900
957957 12.0000i 0.387905i
958958 8.00000i 0.258468i
959959 0 0
960960 2.00000 + 1.00000i 0.0645497 + 0.0322749i
961961 −27.0000 −0.870968
962962 24.0000i 0.773791i
963963 12.0000i 0.386695i
964964 −26.0000 −0.837404
965965 −16.0000 8.00000i −0.515058 0.257529i
966966 0 0
967967 56.0000i 1.80084i 0.435023 + 0.900419i 0.356740π0.356740\pi
−0.435023 + 0.900419i 0.643260π0.643260\pi
968968 7.00000i 0.224989i
969969 −24.0000 −0.770991
970970 10.0000 20.0000i 0.321081 0.642161i
971971 24.0000 0.770197 0.385098 0.922876i 0.374168π-0.374168\pi
0.385098 + 0.922876i 0.374168π0.374168\pi
972972 1.00000i 0.0320750i
973973 0 0
974974 −12.0000 −0.384505
975975 18.0000 + 24.0000i 0.576461 + 0.768615i
976976 10.0000 0.320092
977977 18.0000i 0.575871i −0.957650 0.287936i 0.907031π-0.907031\pi
0.957650 0.287936i 0.0929689π-0.0929689\pi
978978 4.00000i 0.127906i
979979 −20.0000 −0.639203
980980 0 0
981981 −14.0000 −0.446986
982982 30.0000i 0.957338i
983983 16.0000i 0.510321i −0.966899 0.255160i 0.917872π-0.917872\pi
0.966899 0.255160i 0.0821283π-0.0821283\pi
984984 −2.00000 −0.0637577
985985 −4.00000 2.00000i −0.127451 0.0637253i
986986 −24.0000 −0.764316
987987 0 0
988988 36.0000i 1.14531i
989989 32.0000 1.01754
990990 4.00000 + 2.00000i 0.127128 + 0.0635642i
991991 4.00000 0.127064 0.0635321 0.997980i 0.479763π-0.479763\pi
0.0635321 + 0.997980i 0.479763π0.479763\pi
992992 2.00000i 0.0635001i
993993 8.00000i 0.253872i
994994 0 0
995995 −6.00000 + 12.0000i −0.190213 + 0.380426i
996996 −8.00000 −0.253490
997997 42.0000i 1.33015i 0.746775 + 0.665077i 0.231601π0.231601\pi
−0.746775 + 0.665077i 0.768399π0.768399\pi
998998 12.0000i 0.379853i
999999 4.00000 0.126554
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 1470.2.g.b.589.2 2
5.2 odd 4 7350.2.a.bk.1.1 1
5.3 odd 4 7350.2.a.bz.1.1 1
5.4 even 2 inner 1470.2.g.b.589.1 2
7.2 even 3 1470.2.n.f.949.2 4
7.3 odd 6 1470.2.n.b.79.1 4
7.4 even 3 1470.2.n.f.79.1 4
7.5 odd 6 1470.2.n.b.949.2 4
7.6 odd 2 210.2.g.b.169.2 yes 2
21.20 even 2 630.2.g.c.379.1 2
28.27 even 2 1680.2.t.e.1009.2 2
35.4 even 6 1470.2.n.f.79.2 4
35.9 even 6 1470.2.n.f.949.1 4
35.13 even 4 1050.2.a.p.1.1 1
35.19 odd 6 1470.2.n.b.949.1 4
35.24 odd 6 1470.2.n.b.79.2 4
35.27 even 4 1050.2.a.d.1.1 1
35.34 odd 2 210.2.g.b.169.1 2
84.83 odd 2 5040.2.t.h.1009.2 2
105.62 odd 4 3150.2.a.bk.1.1 1
105.83 odd 4 3150.2.a.d.1.1 1
105.104 even 2 630.2.g.c.379.2 2
140.27 odd 4 8400.2.a.bp.1.1 1
140.83 odd 4 8400.2.a.w.1.1 1
140.139 even 2 1680.2.t.e.1009.1 2
420.419 odd 2 5040.2.t.h.1009.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.g.b.169.1 2 35.34 odd 2
210.2.g.b.169.2 yes 2 7.6 odd 2
630.2.g.c.379.1 2 21.20 even 2
630.2.g.c.379.2 2 105.104 even 2
1050.2.a.d.1.1 1 35.27 even 4
1050.2.a.p.1.1 1 35.13 even 4
1470.2.g.b.589.1 2 5.4 even 2 inner
1470.2.g.b.589.2 2 1.1 even 1 trivial
1470.2.n.b.79.1 4 7.3 odd 6
1470.2.n.b.79.2 4 35.24 odd 6
1470.2.n.b.949.1 4 35.19 odd 6
1470.2.n.b.949.2 4 7.5 odd 6
1470.2.n.f.79.1 4 7.4 even 3
1470.2.n.f.79.2 4 35.4 even 6
1470.2.n.f.949.1 4 35.9 even 6
1470.2.n.f.949.2 4 7.2 even 3
1680.2.t.e.1009.1 2 140.139 even 2
1680.2.t.e.1009.2 2 28.27 even 2
3150.2.a.d.1.1 1 105.83 odd 4
3150.2.a.bk.1.1 1 105.62 odd 4
5040.2.t.h.1009.1 2 420.419 odd 2
5040.2.t.h.1009.2 2 84.83 odd 2
7350.2.a.bk.1.1 1 5.2 odd 4
7350.2.a.bz.1.1 1 5.3 odd 4
8400.2.a.w.1.1 1 140.83 odd 4
8400.2.a.bp.1.1 1 140.27 odd 4