Properties

Label 585.2.c.b.469.2
Level 585585
Weight 22
Character 585.469
Analytic conductor 4.6714.671
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(469,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, 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("585.469");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 585=32513 585 = 3^{2} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 585.c (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: 4.671248518244.67124851824
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+2x4+2x3+4x24x+2 x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 469.2
Root 0.854638+0.854638i-0.854638 + 0.854638i of defining polynomial
Character χ\chi == 585.469
Dual form 585.2.c.b.469.5

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) == q1.53919iq20.369102q4+(0.5391892.17009i)q51.70928iq72.51026iq8+(3.34017+0.829914i)q10+2.53919q11+1.00000iq132.63090q144.60197q160.921622iq17+0.539189q19+(0.199016+0.800984i)q203.90829iq22+2.82991iq23+(4.41855+2.34017i)q25+1.53919q26+0.630898iq285.12783q29+0.879362q31+2.06278iq321.41855q34+(3.70928+0.921622i)q356.04945iq370.829914iq38+(5.44748+1.35350i)q401.26180q416.43188iq430.937221q44+4.35577q465.70928iq47+4.07838q49+(3.60197+6.80098i)q500.369102iq52+8.49693iq53+(1.369105.51026i)q554.29072q56+7.89269iq584.72261q59+8.04945q611.35350iq626.02893q64+(2.170090.539189i)q65+7.86603iq67+0.340173iq68+(1.41855+5.70928i)q70+14.4813q71+1.95055iq739.31124q740.199016q764.34017iq770.496928q79+(2.48133+9.98667i)q80+1.94214iq82+8.63090iq83+(2.00000+0.496928i)q859.89988q866.37402iq88+12.8371q89+1.70928q911.04453iq928.78765q94+(0.2907251.17009i)q95+5.91548iq976.27739iq98+O(q100)q-1.53919i q^{2} -0.369102 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.70928i q^{7} -2.51026i q^{8} +(-3.34017 + 0.829914i) q^{10} +2.53919 q^{11} +1.00000i q^{13} -2.63090 q^{14} -4.60197 q^{16} -0.921622i q^{17} +0.539189 q^{19} +(0.199016 + 0.800984i) q^{20} -3.90829i q^{22} +2.82991i q^{23} +(-4.41855 + 2.34017i) q^{25} +1.53919 q^{26} +0.630898i q^{28} -5.12783 q^{29} +0.879362 q^{31} +2.06278i q^{32} -1.41855 q^{34} +(-3.70928 + 0.921622i) q^{35} -6.04945i q^{37} -0.829914i q^{38} +(-5.44748 + 1.35350i) q^{40} -1.26180 q^{41} -6.43188i q^{43} -0.937221 q^{44} +4.35577 q^{46} -5.70928i q^{47} +4.07838 q^{49} +(3.60197 + 6.80098i) q^{50} -0.369102i q^{52} +8.49693i q^{53} +(-1.36910 - 5.51026i) q^{55} -4.29072 q^{56} +7.89269i q^{58} -4.72261 q^{59} +8.04945 q^{61} -1.35350i q^{62} -6.02893 q^{64} +(2.17009 - 0.539189i) q^{65} +7.86603i q^{67} +0.340173i q^{68} +(1.41855 + 5.70928i) q^{70} +14.4813 q^{71} +1.95055i q^{73} -9.31124 q^{74} -0.199016 q^{76} -4.34017i q^{77} -0.496928 q^{79} +(2.48133 + 9.98667i) q^{80} +1.94214i q^{82} +8.63090i q^{83} +(-2.00000 + 0.496928i) q^{85} -9.89988 q^{86} -6.37402i q^{88} +12.8371 q^{89} +1.70928 q^{91} -1.04453i q^{92} -8.78765 q^{94} +(-0.290725 - 1.17009i) q^{95} +5.91548i q^{97} -6.27739i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q10q4+2q10+12q118q14+10q16+20q20+2q25+6q26+12q2920q31+20q348q3534q40+8q4140q44+32q46+18q4916q50+16q95+O(q100) 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50}+ \cdots - 16 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/585Z)×\left(\mathbb{Z}/585\mathbb{Z}\right)^\times.

nn 326326 352352 496496
χ(n)\chi(n) 11 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 1.53919i 1.08837i −0.838965 0.544185i 0.816839π-0.816839\pi
0.838965 0.544185i 0.183161π-0.183161\pi
33 0 0
44 −0.369102 −0.184551
55 −0.539189 2.17009i −0.241133 0.970492i
66 0 0
77 1.70928i 0.646045i −0.946391 0.323023i 0.895301π-0.895301\pi
0.946391 0.323023i 0.104699π-0.104699\pi
88 2.51026i 0.887511i
99 0 0
1010 −3.34017 + 0.829914i −1.05626 + 0.262442i
1111 2.53919 0.765594 0.382797 0.923832i 0.374961π-0.374961\pi
0.382797 + 0.923832i 0.374961π0.374961\pi
1212 0 0
1313 1.00000i 0.277350i
1414 −2.63090 −0.703137
1515 0 0
1616 −4.60197 −1.15049
1717 0.921622i 0.223526i −0.993735 0.111763i 0.964350π-0.964350\pi
0.993735 0.111763i 0.0356498π-0.0356498\pi
1818 0 0
1919 0.539189 0.123698 0.0618492 0.998086i 0.480300π-0.480300\pi
0.0618492 + 0.998086i 0.480300π0.480300\pi
2020 0.199016 + 0.800984i 0.0445013 + 0.179105i
2121 0 0
2222 3.90829i 0.833250i
2323 2.82991i 0.590078i 0.955485 + 0.295039i 0.0953326π0.0953326\pi
−0.955485 + 0.295039i 0.904667π0.904667\pi
2424 0 0
2525 −4.41855 + 2.34017i −0.883710 + 0.468035i
2626 1.53919 0.301860
2727 0 0
2828 0.630898i 0.119228i
2929 −5.12783 −0.952213 −0.476107 0.879388i 0.657952π-0.657952\pi
−0.476107 + 0.879388i 0.657952π0.657952\pi
3030 0 0
3131 0.879362 0.157938 0.0789690 0.996877i 0.474837π-0.474837\pi
0.0789690 + 0.996877i 0.474837π0.474837\pi
3232 2.06278i 0.364651i
3333 0 0
3434 −1.41855 −0.243279
3535 −3.70928 + 0.921622i −0.626982 + 0.155783i
3636 0 0
3737 6.04945i 0.994523i −0.867601 0.497262i 0.834339π-0.834339\pi
0.867601 0.497262i 0.165661π-0.165661\pi
3838 0.829914i 0.134630i
3939 0 0
4040 −5.44748 + 1.35350i −0.861322 + 0.214008i
4141 −1.26180 −0.197059 −0.0985297 0.995134i 0.531414π-0.531414\pi
−0.0985297 + 0.995134i 0.531414π0.531414\pi
4242 0 0
4343 6.43188i 0.980853i −0.871483 0.490426i 0.836841π-0.836841\pi
0.871483 0.490426i 0.163159π-0.163159\pi
4444 −0.937221 −0.141291
4545 0 0
4646 4.35577 0.642223
4747 5.70928i 0.832783i −0.909185 0.416392i 0.863295π-0.863295\pi
0.909185 0.416392i 0.136705π-0.136705\pi
4848 0 0
4949 4.07838 0.582625
5050 3.60197 + 6.80098i 0.509395 + 0.961804i
5151 0 0
5252 0.369102i 0.0511853i
5353 8.49693i 1.16714i 0.812062 + 0.583571i 0.198345π0.198345\pi
−0.812062 + 0.583571i 0.801655π0.801655\pi
5454 0 0
5555 −1.36910 5.51026i −0.184610 0.743003i
5656 −4.29072 −0.573372
5757 0 0
5858 7.89269i 1.03636i
5959 −4.72261 −0.614831 −0.307415 0.951575i 0.599464π-0.599464\pi
−0.307415 + 0.951575i 0.599464π0.599464\pi
6060 0 0
6161 8.04945 1.03063 0.515313 0.857002i 0.327676π-0.327676\pi
0.515313 + 0.857002i 0.327676π0.327676\pi
6262 1.35350i 0.171895i
6363 0 0
6464 −6.02893 −0.753616
6565 2.17009 0.539189i 0.269166 0.0668781i
6666 0 0
6767 7.86603i 0.960989i 0.876998 + 0.480494i 0.159543π0.159543\pi
−0.876998 + 0.480494i 0.840457π0.840457\pi
6868 0.340173i 0.0412520i
6969 0 0
7070 1.41855 + 5.70928i 0.169549 + 0.682389i
7171 14.4813 1.71862 0.859309 0.511457i 0.170894π-0.170894\pi
0.859309 + 0.511457i 0.170894π0.170894\pi
7272 0 0
7373 1.95055i 0.228295i 0.993464 + 0.114147i 0.0364136π0.0364136\pi
−0.993464 + 0.114147i 0.963586π0.963586\pi
7474 −9.31124 −1.08241
7575 0 0
7676 −0.199016 −0.0228287
7777 4.34017i 0.494609i
7878 0 0
7979 −0.496928 −0.0559088 −0.0279544 0.999609i 0.508899π-0.508899\pi
−0.0279544 + 0.999609i 0.508899π0.508899\pi
8080 2.48133 + 9.98667i 0.277421 + 1.11654i
8181 0 0
8282 1.94214i 0.214474i
8383 8.63090i 0.947364i 0.880696 + 0.473682i 0.157075π0.157075\pi
−0.880696 + 0.473682i 0.842925π0.842925\pi
8484 0 0
8585 −2.00000 + 0.496928i −0.216930 + 0.0538995i
8686 −9.89988 −1.06753
8787 0 0
8888 6.37402i 0.679473i
8989 12.8371 1.36073 0.680365 0.732873i 0.261821π-0.261821\pi
0.680365 + 0.732873i 0.261821π0.261821\pi
9090 0 0
9191 1.70928 0.179181
9292 1.04453i 0.108900i
9393 0 0
9494 −8.78765 −0.906377
9595 −0.290725 1.17009i −0.0298277 0.120048i
9696 0 0
9797 5.91548i 0.600626i 0.953841 + 0.300313i 0.0970911π0.0970911\pi
−0.953841 + 0.300313i 0.902909π0.902909\pi
9898 6.27739i 0.634113i
9999 0 0
100100 1.63090 0.863763i 0.163090 0.0863763i
101101 16.4391 1.63575 0.817874 0.575397i 0.195152π-0.195152\pi
0.817874 + 0.575397i 0.195152π0.195152\pi
102102 0 0
103103 10.1906i 1.00411i 0.864836 + 0.502055i 0.167423π0.167423\pi
−0.864836 + 0.502055i 0.832577π0.832577\pi
104104 2.51026 0.246151
105105 0 0
106106 13.0784 1.27028
107107 9.75154i 0.942717i −0.881942 0.471358i 0.843764π-0.843764\pi
0.881942 0.471358i 0.156236π-0.156236\pi
108108 0 0
109109 16.8638 1.61526 0.807628 0.589693i 0.200751π-0.200751\pi
0.807628 + 0.589693i 0.200751π0.200751\pi
110110 −8.48133 + 2.10731i −0.808663 + 0.200924i
111111 0 0
112112 7.86603i 0.743270i
113113 11.7587i 1.10617i −0.833126 0.553084i 0.813451π-0.813451\pi
0.833126 0.553084i 0.186549π-0.186549\pi
114114 0 0
115115 6.14116 1.52586i 0.572666 0.142287i
116116 1.89269 0.175732
117117 0 0
118118 7.26898i 0.669164i
119119 −1.57531 −0.144408
120120 0 0
121121 −4.55252 −0.413865
122122 12.3896i 1.12170i
123123 0 0
124124 −0.324575 −0.0291477
125125 7.46081 + 8.32684i 0.667315 + 0.744775i
126126 0 0
127127 18.0072i 1.59788i −0.601411 0.798940i 0.705395π-0.705395\pi
0.601411 0.798940i 0.294605π-0.294605\pi
128128 13.4052i 1.18487i
129129 0 0
130130 −0.829914 3.34017i −0.0727882 0.292953i
131131 −14.2557 −1.24552 −0.622761 0.782412i 0.713989π-0.713989\pi
−0.622761 + 0.782412i 0.713989π0.713989\pi
132132 0 0
133133 0.921622i 0.0799148i
134134 12.1073 1.04591
135135 0 0
136136 −2.31351 −0.198382
137137 13.7854i 1.17776i −0.808219 0.588882i 0.799568π-0.799568\pi
0.808219 0.588882i 0.200432π-0.200432\pi
138138 0 0
139139 6.65368 0.564358 0.282179 0.959362i 0.408943π-0.408943\pi
0.282179 + 0.959362i 0.408943π0.408943\pi
140140 1.36910 0.340173i 0.115710 0.0287499i
141141 0 0
142142 22.2895i 1.87049i
143143 2.53919i 0.212338i
144144 0 0
145145 2.76487 + 11.1278i 0.229610 + 0.924116i
146146 3.00227 0.248469
147147 0 0
148148 2.23287i 0.183540i
149149 −9.07838 −0.743730 −0.371865 0.928287i 0.621282π-0.621282\pi
−0.371865 + 0.928287i 0.621282π0.621282\pi
150150 0 0
151151 3.27739 0.266711 0.133355 0.991068i 0.457425π-0.457425\pi
0.133355 + 0.991068i 0.457425π0.457425\pi
152152 1.35350i 0.109784i
153153 0 0
154154 −6.68035 −0.538318
155155 −0.474142 1.90829i −0.0380840 0.153278i
156156 0 0
157157 12.8371i 1.02451i 0.858833 + 0.512256i 0.171190π0.171190\pi
−0.858833 + 0.512256i 0.828810π0.828810\pi
158158 0.764867i 0.0608495i
159159 0 0
160160 4.47641 1.11223i 0.353891 0.0879293i
161161 4.83710 0.381217
162162 0 0
163163 12.0494i 0.943786i −0.881656 0.471893i 0.843571π-0.843571\pi
0.881656 0.471893i 0.156429π-0.156429\pi
164164 0.465732 0.0363675
165165 0 0
166166 13.2846 1.03108
167167 8.72979i 0.675532i −0.941230 0.337766i 0.890329π-0.890329\pi
0.941230 0.337766i 0.109671π-0.109671\pi
168168 0 0
169169 −1.00000 −0.0769231
170170 0.764867 + 3.07838i 0.0586626 + 0.236101i
171171 0 0
172172 2.37402i 0.181018i
173173 0.863763i 0.0656707i 0.999461 + 0.0328354i 0.0104537π0.0104537\pi
−0.999461 + 0.0328354i 0.989546π0.989546\pi
174174 0 0
175175 4.00000 + 7.55252i 0.302372 + 0.570917i
176176 −11.6853 −0.880810
177177 0 0
178178 19.7587i 1.48098i
179179 19.9155 1.48855 0.744276 0.667872i 0.232795π-0.232795\pi
0.744276 + 0.667872i 0.232795π0.232795\pi
180180 0 0
181181 14.3896 1.06957 0.534786 0.844987i 0.320392π-0.320392\pi
0.534786 + 0.844987i 0.320392π0.320392\pi
182182 2.63090i 0.195015i
183183 0 0
184184 7.10382 0.523700
185185 −13.1278 + 3.26180i −0.965177 + 0.239812i
186186 0 0
187187 2.34017i 0.171130i
188188 2.10731i 0.153691i
189189 0 0
190190 −1.80098 + 0.447480i −0.130657 + 0.0324636i
191191 −1.47641 −0.106829 −0.0534146 0.998572i 0.517010π-0.517010\pi
−0.0534146 + 0.998572i 0.517010π0.517010\pi
192192 0 0
193193 17.7321i 1.27638i 0.769878 + 0.638191i 0.220317π0.220317\pi
−0.769878 + 0.638191i 0.779683π0.779683\pi
194194 9.10504 0.653704
195195 0 0
196196 −1.50534 −0.107524
197197 2.00000i 0.142494i −0.997459 0.0712470i 0.977302π-0.977302\pi
0.997459 0.0712470i 0.0226979π-0.0226979\pi
198198 0 0
199199 5.39189 0.382221 0.191110 0.981569i 0.438791π-0.438791\pi
0.191110 + 0.981569i 0.438791π0.438791\pi
200200 5.87444 + 11.0917i 0.415386 + 0.784302i
201201 0 0
202202 25.3028i 1.78030i
203203 8.76487i 0.615173i
204204 0 0
205205 0.680346 + 2.73820i 0.0475174 + 0.191245i
206206 15.6853 1.09284
207207 0 0
208208 4.60197i 0.319089i
209209 1.36910 0.0947028
210210 0 0
211211 −22.7526 −1.56635 −0.783176 0.621800i 0.786402π-0.786402\pi
−0.783176 + 0.621800i 0.786402π0.786402\pi
212212 3.13624i 0.215398i
213213 0 0
214214 −15.0095 −1.02603
215215 −13.9577 + 3.46800i −0.951910 + 0.236516i
216216 0 0
217217 1.50307i 0.102035i
218218 25.9565i 1.75800i
219219 0 0
220220 0.505339 + 2.03385i 0.0340699 + 0.137122i
221221 0.921622 0.0619950
222222 0 0
223223 8.76099i 0.586679i −0.956008 0.293340i 0.905233π-0.905233\pi
0.956008 0.293340i 0.0947667π-0.0947667\pi
224224 3.52586 0.235581
225225 0 0
226226 −18.0989 −1.20392
227227 17.2267i 1.14338i 0.820470 + 0.571689i 0.193712π0.193712\pi
−0.820470 + 0.571689i 0.806288π0.806288\pi
228228 0 0
229229 −3.07838 −0.203425 −0.101712 0.994814i 0.532432π-0.532432\pi
−0.101712 + 0.994814i 0.532432π0.532432\pi
230230 −2.34858 9.45240i −0.154861 0.623273i
231231 0 0
232232 12.8722i 0.845100i
233233 18.9360i 1.24054i 0.784389 + 0.620269i 0.212977π0.212977\pi
−0.784389 + 0.620269i 0.787023π0.787023\pi
234234 0 0
235235 −12.3896 + 3.07838i −0.808210 + 0.200811i
236236 1.74313 0.113468
237237 0 0
238238 2.42469i 0.157170i
239239 6.63809 0.429382 0.214691 0.976682i 0.431126π-0.431126\pi
0.214691 + 0.976682i 0.431126π0.431126\pi
240240 0 0
241241 −9.47641 −0.610429 −0.305215 0.952284i 0.598728π-0.598728\pi
−0.305215 + 0.952284i 0.598728π0.598728\pi
242242 7.00719i 0.450439i
243243 0 0
244244 −2.97107 −0.190203
245245 −2.19902 8.85043i −0.140490 0.565433i
246246 0 0
247247 0.539189i 0.0343078i
248248 2.20743i 0.140172i
249249 0 0
250250 12.8166 11.4836i 0.810592 0.726286i
251251 −29.4596 −1.85947 −0.929736 0.368226i 0.879965π-0.879965\pi
−0.929736 + 0.368226i 0.879965π0.879965\pi
252252 0 0
253253 7.18568i 0.451760i
254254 −27.7165 −1.73909
255255 0 0
256256 8.57531 0.535957
257257 20.4657i 1.27662i 0.769781 + 0.638309i 0.220366π0.220366\pi
−0.769781 + 0.638309i 0.779634π0.779634\pi
258258 0 0
259259 −10.3402 −0.642507
260260 −0.800984 + 0.199016i −0.0496749 + 0.0123424i
261261 0 0
262262 21.9421i 1.35559i
263263 9.14342i 0.563808i 0.959443 + 0.281904i 0.0909659π0.0909659\pi
−0.959443 + 0.281904i 0.909034π0.909034\pi
264264 0 0
265265 18.4391 4.58145i 1.13270 0.281436i
266266 −1.41855 −0.0869769
267267 0 0
268268 2.90337i 0.177352i
269269 11.3919 0.694576 0.347288 0.937759i 0.387103π-0.387103\pi
0.347288 + 0.937759i 0.387103π0.387103\pi
270270 0 0
271271 −21.1350 −1.28386 −0.641930 0.766763i 0.721866π-0.721866\pi
−0.641930 + 0.766763i 0.721866π0.721866\pi
272272 4.24128i 0.257165i
273273 0 0
274274 −21.2183 −1.28185
275275 −11.2195 + 5.94214i −0.676563 + 0.358325i
276276 0 0
277277 13.0784i 0.785804i −0.919580 0.392902i 0.871471π-0.871471\pi
0.919580 0.392902i 0.128529π-0.128529\pi
278278 10.2413i 0.614231i
279279 0 0
280280 2.31351 + 9.31124i 0.138259 + 0.556453i
281281 0.680346 0.0405860 0.0202930 0.999794i 0.493540π-0.493540\pi
0.0202930 + 0.999794i 0.493540π0.493540\pi
282282 0 0
283283 19.2956i 1.14701i 0.819203 + 0.573504i 0.194416π0.194416\pi
−0.819203 + 0.573504i 0.805584π0.805584\pi
284284 −5.34509 −0.317173
285285 0 0
286286 3.90829 0.231102
287287 2.15676i 0.127309i
288288 0 0
289289 16.1506 0.950036
290290 17.1278 4.25565i 1.00578 0.249900i
291291 0 0
292292 0.719953i 0.0421321i
293293 9.46800i 0.553126i −0.960996 0.276563i 0.910804π-0.910804\pi
0.960996 0.276563i 0.0891955π-0.0891955\pi
294294 0 0
295295 2.54638 + 10.2485i 0.148256 + 0.596689i
296296 −15.1857 −0.882650
297297 0 0
298298 13.9733i 0.809454i
299299 −2.82991 −0.163658
300300 0 0
301301 −10.9939 −0.633675
302302 5.04453i 0.290280i
303303 0 0
304304 −2.48133 −0.142314
305305 −4.34017 17.4680i −0.248518 1.00021i
306306 0 0
307307 0.264063i 0.0150709i −0.999972 0.00753543i 0.997601π-0.997601\pi
0.999972 0.00753543i 0.00239862π-0.00239862\pi
308308 1.60197i 0.0912806i
309309 0 0
310310 −2.93722 + 0.729794i −0.166823 + 0.0414495i
311311 −13.0472 −0.739838 −0.369919 0.929064i 0.620615π-0.620615\pi
−0.369919 + 0.929064i 0.620615π0.620615\pi
312312 0 0
313313 33.7009i 1.90489i 0.304718 + 0.952443i 0.401438π0.401438\pi
−0.304718 + 0.952443i 0.598562π0.598562\pi
314314 19.7587 1.11505
315315 0 0
316316 0.183417 0.0103180
317317 13.9506i 0.783541i 0.920063 + 0.391771i 0.128137π0.128137\pi
−0.920063 + 0.391771i 0.871863π0.871863\pi
318318 0 0
319319 −13.0205 −0.729009
320320 3.25073 + 13.0833i 0.181721 + 0.731379i
321321 0 0
322322 7.44521i 0.414905i
323323 0.496928i 0.0276498i
324324 0 0
325325 −2.34017 4.41855i −0.129809 0.245097i
326326 −18.5464 −1.02719
327327 0 0
328328 3.16743i 0.174892i
329329 −9.75872 −0.538016
330330 0 0
331331 −18.4547 −1.01436 −0.507180 0.861840i 0.669312π-0.669312\pi
−0.507180 + 0.861840i 0.669312π0.669312\pi
332332 3.18568i 0.174837i
333333 0 0
334334 −13.4368 −0.735229
335335 17.0700 4.24128i 0.932632 0.231726i
336336 0 0
337337 15.8576i 0.863820i −0.901917 0.431910i 0.857840π-0.857840\pi
0.901917 0.431910i 0.142160π-0.142160\pi
338338 1.53919i 0.0837208i
339339 0 0
340340 0.738205 0.183417i 0.0400348 0.00994721i
341341 2.23287 0.120916
342342 0 0
343343 18.9360i 1.02245i
344344 −16.1457 −0.870517
345345 0 0
346346 1.32950 0.0714741
347347 9.72487i 0.522059i −0.965331 0.261029i 0.915938π-0.915938\pi
0.965331 0.261029i 0.0840619π-0.0840619\pi
348348 0 0
349349 30.9093 1.65454 0.827269 0.561805i 0.189893π-0.189893\pi
0.827269 + 0.561805i 0.189893π0.189893\pi
350350 11.6248 6.15676i 0.621369 0.329092i
351351 0 0
352352 5.23779i 0.279175i
353353 5.95055i 0.316716i 0.987382 + 0.158358i 0.0506200π0.0506200\pi
−0.987382 + 0.158358i 0.949380π0.949380\pi
354354 0 0
355355 −7.80817 31.4257i −0.414415 1.66791i
356356 −4.73820 −0.251124
357357 0 0
358358 30.6537i 1.62010i
359359 10.9783 0.579410 0.289705 0.957116i 0.406443π-0.406443\pi
0.289705 + 0.957116i 0.406443π0.406443\pi
360360 0 0
361361 −18.7093 −0.984699
362362 22.1483i 1.16409i
363363 0 0
364364 −0.630898 −0.0330680
365365 4.23287 1.05172i 0.221558 0.0550493i
366366 0 0
367367 10.3740i 0.541520i 0.962647 + 0.270760i 0.0872749π0.0872749\pi
−0.962647 + 0.270760i 0.912725π0.912725\pi
368368 13.0232i 0.678880i
369369 0 0
370370 5.02052 + 20.2062i 0.261004 + 1.05047i
371371 14.5236 0.754027
372372 0 0
373373 23.9877i 1.24204i −0.783796 0.621018i 0.786719π-0.786719\pi
0.783796 0.621018i 0.213281π-0.213281\pi
374374 −3.60197 −0.186253
375375 0 0
376376 −14.3318 −0.739104
377377 5.12783i 0.264096i
378378 0 0
379379 −29.7575 −1.52854 −0.764270 0.644896i 0.776901π-0.776901\pi
−0.764270 + 0.644896i 0.776901π0.776901\pi
380380 0.107307 + 0.431882i 0.00550474 + 0.0221551i
381381 0 0
382382 2.27247i 0.116270i
383383 12.4163i 0.634442i 0.948352 + 0.317221i 0.102750π0.102750\pi
−0.948352 + 0.317221i 0.897250π0.897250\pi
384384 0 0
385385 −9.41855 + 2.34017i −0.480014 + 0.119266i
386386 27.2930 1.38918
387387 0 0
388388 2.18342i 0.110846i
389389 −16.8371 −0.853675 −0.426837 0.904328i 0.640372π-0.640372\pi
−0.426837 + 0.904328i 0.640372π0.640372\pi
390390 0 0
391391 2.60811 0.131898
392392 10.2378i 0.517086i
393393 0 0
394394 −3.07838 −0.155086
395395 0.267938 + 1.07838i 0.0134814 + 0.0542591i
396396 0 0
397397 3.89269i 0.195369i −0.995217 0.0976843i 0.968856π-0.968856\pi
0.995217 0.0976843i 0.0311436π-0.0311436\pi
398398 8.29914i 0.415998i
399399 0 0
400400 20.3340 10.7694i 1.01670 0.538470i
401401 9.10504 0.454684 0.227342 0.973815i 0.426996π-0.426996\pi
0.227342 + 0.973815i 0.426996π0.426996\pi
402402 0 0
403403 0.879362i 0.0438041i
404404 −6.06770 −0.301879
405405 0 0
406406 13.4908 0.669536
407407 15.3607i 0.761401i
408408 0 0
409409 19.4186 0.960186 0.480093 0.877218i 0.340603π-0.340603\pi
0.480093 + 0.877218i 0.340603π0.340603\pi
410410 4.21461 1.04718i 0.208145 0.0517166i
411411 0 0
412412 3.76138i 0.185310i
413413 8.07223i 0.397209i
414414 0 0
415415 18.7298 4.65368i 0.919409 0.228440i
416416 −2.06278 −0.101136
417417 0 0
418418 2.10731i 0.103072i
419419 −16.7792 −0.819720 −0.409860 0.912149i 0.634422π-0.634422\pi
−0.409860 + 0.912149i 0.634422π0.634422\pi
420420 0 0
421421 −19.0205 −0.927003 −0.463502 0.886096i 0.653407π-0.653407\pi
−0.463502 + 0.886096i 0.653407π0.653407\pi
422422 35.0205i 1.70477i
423423 0 0
424424 21.3295 1.03585
425425 2.15676 + 4.07223i 0.104618 + 0.197532i
426426 0 0
427427 13.7587i 0.665831i
428428 3.59932i 0.173979i
429429 0 0
430430 5.33791 + 21.4836i 0.257417 + 1.03603i
431431 −8.02997 −0.386790 −0.193395 0.981121i 0.561950π-0.561950\pi
−0.193395 + 0.981121i 0.561950π0.561950\pi
432432 0 0
433433 13.0472i 0.627008i −0.949587 0.313504i 0.898497π-0.898497\pi
0.949587 0.313504i 0.101503π-0.101503\pi
434434 −2.31351 −0.111052
435435 0 0
436436 −6.22446 −0.298097
437437 1.52586i 0.0729917i
438438 0 0
439439 7.70086 0.367542 0.183771 0.982969i 0.441169π-0.441169\pi
0.183771 + 0.982969i 0.441169π0.441169\pi
440440 −13.8322 + 3.43680i −0.659423 + 0.163843i
441441 0 0
442442 1.41855i 0.0674736i
443443 6.39084i 0.303638i 0.988408 + 0.151819i 0.0485131π0.0485131\pi
−0.988408 + 0.151819i 0.951487π0.951487\pi
444444 0 0
445445 −6.92162 27.8576i −0.328116 1.32058i
446446 −13.4848 −0.638525
447447 0 0
448448 10.3051i 0.486870i
449449 31.6163 1.49207 0.746034 0.665908i 0.231956π-0.231956\pi
0.746034 + 0.665908i 0.231956π0.231956\pi
450450 0 0
451451 −3.20394 −0.150867
452452 4.34017i 0.204145i
453453 0 0
454454 26.5152 1.24442
455455 −0.921622 3.70928i −0.0432063 0.173894i
456456 0 0
457457 35.6430i 1.66731i 0.552286 + 0.833655i 0.313756π0.313756\pi
−0.552286 + 0.833655i 0.686244π0.686244\pi
458458 4.73820i 0.221402i
459459 0 0
460460 −2.26672 + 0.563198i −0.105686 + 0.0262592i
461461 14.9795 0.697664 0.348832 0.937185i 0.386578π-0.386578\pi
0.348832 + 0.937185i 0.386578π0.386578\pi
462462 0 0
463463 9.09663i 0.422756i −0.977404 0.211378i 0.932205π-0.932205\pi
0.977404 0.211378i 0.0677951π-0.0677951\pi
464464 23.5981 1.09551
465465 0 0
466466 29.1461 1.35017
467467 1.87709i 0.0868616i 0.999056 + 0.0434308i 0.0138288π0.0138288\pi
−0.999056 + 0.0434308i 0.986171π0.986171\pi
468468 0 0
469469 13.4452 0.620842
470470 4.73820 + 19.0700i 0.218557 + 0.879632i
471471 0 0
472472 11.8550i 0.545669i
473473 16.3318i 0.750935i
474474 0 0
475475 −2.38243 + 1.26180i −0.109314 + 0.0578951i
476476 0.581449 0.0266507
477477 0 0
478478 10.2173i 0.467327i
479479 −15.7431 −0.719322 −0.359661 0.933083i 0.617108π-0.617108\pi
−0.359661 + 0.933083i 0.617108π0.617108\pi
480480 0 0
481481 6.04945 0.275831
482482 14.5860i 0.664373i
483483 0 0
484484 1.68035 0.0763794
485485 12.8371 3.18956i 0.582903 0.144830i
486486 0 0
487487 4.94441i 0.224053i −0.993705 0.112026i 0.964266π-0.964266\pi
0.993705 0.112026i 0.0357341π-0.0357341\pi
488488 20.2062i 0.914692i
489489 0 0
490490 −13.6225 + 3.38470i −0.615401 + 0.152905i
491491 −39.4863 −1.78199 −0.890995 0.454014i 0.849992π-0.849992\pi
−0.890995 + 0.454014i 0.849992π0.849992\pi
492492 0 0
493493 4.72592i 0.212845i
494494 0.829914 0.0373396
495495 0 0
496496 −4.04680 −0.181706
497497 24.7526i 1.11030i
498498 0 0
499499 −1.67089 −0.0747993 −0.0373997 0.999300i 0.511907π-0.511907\pi
−0.0373997 + 0.999300i 0.511907π0.511907\pi
500500 −2.75380 3.07346i −0.123154 0.137449i
501501 0 0
502502 45.3439i 2.02380i
503503 9.08557i 0.405105i −0.979271 0.202553i 0.935076π-0.935076\pi
0.979271 0.202553i 0.0649237π-0.0649237\pi
504504 0 0
505505 −8.86376 35.6742i −0.394432 1.58748i
506506 11.0601 0.491683
507507 0 0
508508 6.64650i 0.294891i
509509 −19.5441 −0.866277 −0.433139 0.901327i 0.642594π-0.642594\pi
−0.433139 + 0.901327i 0.642594π0.642594\pi
510510 0 0
511511 3.33403 0.147489
512512 13.6114i 0.601546i
513513 0 0
514514 31.5006 1.38943
515515 22.1145 5.49466i 0.974481 0.242124i
516516 0 0
517517 14.4969i 0.637574i
518518 15.9155i 0.699286i
519519 0 0
520520 −1.35350 5.44748i −0.0593551 0.238888i
521521 −6.50534 −0.285004 −0.142502 0.989795i 0.545515π-0.545515\pi
−0.142502 + 0.989795i 0.545515π0.545515\pi
522522 0 0
523523 36.5452i 1.59801i 0.601326 + 0.799004i 0.294639π0.294639\pi
−0.601326 + 0.799004i 0.705361π0.705361\pi
524524 5.26180 0.229863
525525 0 0
526526 14.0735 0.613632
527527 0.810439i 0.0353033i
528528 0 0
529529 14.9916 0.651808
530530 −7.05172 28.3812i −0.306307 1.23280i
531531 0 0
532532 0.340173i 0.0147484i
533533 1.26180i 0.0546544i
534534 0 0
535535 −21.1617 + 5.25792i −0.914899 + 0.227320i
536536 19.7458 0.852888
537537 0 0
538538 17.5343i 0.755956i
539539 10.3558 0.446055
540540 0 0
541541 20.3402 0.874492 0.437246 0.899342i 0.355954π-0.355954\pi
0.437246 + 0.899342i 0.355954π0.355954\pi
542542 32.5308i 1.39732i
543543 0 0
544544 1.90110 0.0815091
545545 −9.09275 36.5958i −0.389491 1.56759i
546546 0 0
547547 11.5948i 0.495757i 0.968791 + 0.247879i 0.0797334π0.0797334\pi
−0.968791 + 0.247879i 0.920267π0.920267\pi
548548 5.08822i 0.217358i
549549 0 0
550550 9.14608 + 17.2690i 0.389990 + 0.736352i
551551 −2.76487 −0.117787
552552 0 0
553553 0.849388i 0.0361196i
554554 −20.1301 −0.855246
555555 0 0
556556 −2.45589 −0.104153
557557 10.7298i 0.454636i 0.973821 + 0.227318i 0.0729957π0.0729957\pi
−0.973821 + 0.227318i 0.927004π0.927004\pi
558558 0 0
559559 6.43188 0.272040
560560 17.0700 4.24128i 0.721338 0.179227i
561561 0 0
562562 1.04718i 0.0441727i
563563 10.2485i 0.431921i −0.976402 0.215961i 0.930712π-0.930712\pi
0.976402 0.215961i 0.0692883π-0.0692883\pi
564564 0 0
565565 −25.5174 + 6.34017i −1.07353 + 0.266733i
566566 29.6996 1.24837
567567 0 0
568568 36.3519i 1.52529i
569569 −8.84551 −0.370823 −0.185412 0.982661i 0.559362π-0.559362\pi
−0.185412 + 0.982661i 0.559362π0.559362\pi
570570 0 0
571571 9.29299 0.388900 0.194450 0.980912i 0.437708π-0.437708\pi
0.194450 + 0.980912i 0.437708π0.437708\pi
572572 0.937221i 0.0391872i
573573 0 0
574574 3.31965 0.138560
575575 −6.62249 12.5041i −0.276177 0.521458i
576576 0 0
577577 19.5259i 0.812872i 0.913679 + 0.406436i 0.133229π0.133229\pi
−0.913679 + 0.406436i 0.866771π0.866771\pi
578578 24.8588i 1.03399i
579579 0 0
580580 −1.02052 4.10731i −0.0423747 0.170547i
581581 14.7526 0.612040
582582 0 0
583583 21.5753i 0.893558i
584584 4.89639 0.202614
585585 0 0
586586 −14.5730 −0.602007
587587 22.5029i 0.928794i 0.885627 + 0.464397i 0.153729π0.153729\pi
−0.885627 + 0.464397i 0.846271π0.846271\pi
588588 0 0
589589 0.474142 0.0195367
590590 15.7743 3.91935i 0.649419 0.161357i
591591 0 0
592592 27.8394i 1.14419i
593593 4.43907i 0.182291i −0.995838 0.0911454i 0.970947π-0.970947\pi
0.995838 0.0911454i 0.0290528π-0.0290528\pi
594594 0 0
595595 0.849388 + 3.41855i 0.0348215 + 0.140147i
596596 3.35085 0.137256
597597 0 0
598598 4.35577i 0.178121i
599599 33.3607 1.36308 0.681540 0.731780i 0.261310π-0.261310\pi
0.681540 + 0.731780i 0.261310π0.261310\pi
600600 0 0
601601 13.3197 0.543320 0.271660 0.962393i 0.412427π-0.412427\pi
0.271660 + 0.962393i 0.412427π0.412427\pi
602602 16.9216i 0.689674i
603603 0 0
604604 −1.20969 −0.0492217
605605 2.45467 + 9.87936i 0.0997964 + 0.401653i
606606 0 0
607607 14.1184i 0.573047i −0.958073 0.286523i 0.907500π-0.907500\pi
0.958073 0.286523i 0.0924996π-0.0924996\pi
608608 1.11223i 0.0451068i
609609 0 0
610610 −26.8865 + 6.68035i −1.08860 + 0.270479i
611611 5.70928 0.230973
612612 0 0
613613 26.8104i 1.08286i −0.840745 0.541432i 0.817882π-0.817882\pi
0.840745 0.541432i 0.182118π-0.182118\pi
614614 −0.406442 −0.0164027
615615 0 0
616616 −10.8950 −0.438970
617617 14.8950i 0.599649i 0.953994 + 0.299824i 0.0969280π0.0969280\pi
−0.953994 + 0.299824i 0.903072π0.903072\pi
618618 0 0
619619 −45.3184 −1.82150 −0.910751 0.412956i 0.864496π-0.864496\pi
−0.910751 + 0.412956i 0.864496π0.864496\pi
620620 0.175007 + 0.704355i 0.00702845 + 0.0282876i
621621 0 0
622622 20.0821i 0.805218i
623623 21.9421i 0.879093i
624624 0 0
625625 14.0472 20.6803i 0.561887 0.827214i
626626 51.8720 2.07322
627627 0 0
628628 4.73820i 0.189075i
629629 −5.57531 −0.222302
630630 0 0
631631 37.8876 1.50828 0.754141 0.656713i 0.228054π-0.228054\pi
0.754141 + 0.656713i 0.228054π0.228054\pi
632632 1.24742i 0.0496197i
633633 0 0
634634 21.4725 0.852783
635635 −39.0772 + 9.70928i −1.55073 + 0.385301i
636636 0 0
637637 4.07838i 0.161591i
638638 20.0410i 0.793432i
639639 0 0
640640 29.0905 7.22795i 1.14990 0.285710i
641641 8.47027 0.334555 0.167278 0.985910i 0.446502π-0.446502\pi
0.167278 + 0.985910i 0.446502π0.446502\pi
642642 0 0
643643 34.1750i 1.34773i 0.738854 + 0.673865i 0.235367π0.235367\pi
−0.738854 + 0.673865i 0.764633π0.764633\pi
644644 −1.78539 −0.0703541
645645 0 0
646646 −0.764867 −0.0300933
647647 13.8238i 0.543468i −0.962372 0.271734i 0.912403π-0.912403\pi
0.962372 0.271734i 0.0875972π-0.0875972\pi
648648 0 0
649649 −11.9916 −0.470711
650650 −6.80098 + 3.60197i −0.266757 + 0.141281i
651651 0 0
652652 4.44748i 0.174177i
653653 42.8781i 1.67795i 0.544169 + 0.838976i 0.316845π0.316845\pi
−0.544169 + 0.838976i 0.683155π0.683155\pi
654654 0 0
655655 7.68649 + 30.9360i 0.300336 + 1.20877i
656656 5.80674 0.226715
657657 0 0
658658 15.0205i 0.585561i
659659 −23.2495 −0.905672 −0.452836 0.891594i 0.649588π-0.649588\pi
−0.452836 + 0.891594i 0.649588π0.649588\pi
660660 0 0
661661 27.0661 1.05275 0.526374 0.850253i 0.323551π-0.323551\pi
0.526374 + 0.850253i 0.323551π0.323551\pi
662662 28.4052i 1.10400i
663663 0 0
664664 21.6658 0.840796
665665 −2.00000 + 0.496928i −0.0775567 + 0.0192701i
666666 0 0
667667 14.5113i 0.561880i
668668 3.22219i 0.124670i
669669 0 0
670670 −6.52813 26.2739i −0.252203 1.01505i
671671 20.4391 0.789042
672672 0 0
673673 16.1711i 0.623351i 0.950189 + 0.311676i 0.100890π0.100890\pi
−0.950189 + 0.311676i 0.899110π0.899110\pi
674674 −24.4079 −0.940156
675675 0 0
676676 0.369102 0.0141962
677677 43.1194i 1.65721i 0.559831 + 0.828607i 0.310866π0.310866\pi
−0.559831 + 0.828607i 0.689134π0.689134\pi
678678 0 0
679679 10.1112 0.388032
680680 1.24742 + 5.02052i 0.0478363 + 0.192528i
681681 0 0
682682 3.43680i 0.131602i
683683 17.7093i 0.677627i 0.940854 + 0.338813i 0.110026π0.110026\pi
−0.940854 + 0.338813i 0.889974π0.889974\pi
684684 0 0
685685 −29.9155 + 7.43293i −1.14301 + 0.283998i
686686 −29.1461 −1.11280
687687 0 0
688688 29.5993i 1.12846i
689689 −8.49693 −0.323707
690690 0 0
691691 −24.8794 −0.946456 −0.473228 0.880940i 0.656911π-0.656911\pi
−0.473228 + 0.880940i 0.656911π0.656911\pi
692692 0.318817i 0.0121196i
693693 0 0
694694 −14.9684 −0.568193
695695 −3.58759 14.4391i −0.136085 0.547705i
696696 0 0
697697 1.16290i 0.0440479i
698698 47.5753i 1.80075i
699699 0 0
700700 −1.47641 2.78765i −0.0558030 0.105363i
701701 −33.0661 −1.24889 −0.624445 0.781069i 0.714675π-0.714675\pi
−0.624445 + 0.781069i 0.714675π0.714675\pi
702702 0 0
703703 3.26180i 0.123021i
704704 −15.3086 −0.576964
705705 0 0
706706 9.15902 0.344704
707707 28.0989i 1.05677i
708708 0 0
709709 −2.18342 −0.0820000 −0.0410000 0.999159i 0.513054π-0.513054\pi
−0.0410000 + 0.999159i 0.513054π0.513054\pi
710710 −48.3701 + 12.0183i −1.81530 + 0.451037i
711711 0 0
712712 32.2245i 1.20766i
713713 2.48852i 0.0931957i
714714 0 0
715715 5.51026 1.36910i 0.206072 0.0512015i
716716 −7.35085 −0.274714
717717 0 0
718718 16.8976i 0.630613i
719719 5.20847 0.194243 0.0971216 0.995273i 0.469036π-0.469036\pi
0.0971216 + 0.995273i 0.469036π0.469036\pi
720720 0 0
721721 17.4186 0.648701
722722 28.7971i 1.07172i
723723 0 0
724724 −5.31124 −0.197391
725725 22.6576 12.0000i 0.841481 0.445669i
726726 0 0
727727 3.52464i 0.130721i 0.997862 + 0.0653607i 0.0208198π0.0208198\pi
−0.997862 + 0.0653607i 0.979180π0.979180\pi
728728 4.29072i 0.159025i
729729 0 0
730730 −1.61879 6.51518i −0.0599141 0.241138i
731731 −5.92777 −0.219246
732732 0 0
733733 21.8310i 0.806345i −0.915124 0.403172i 0.867907π-0.867907\pi
0.915124 0.403172i 0.132093π-0.132093\pi
734734 15.9676 0.589374
735735 0 0
736736 −5.83749 −0.215173
737737 19.9733i 0.735727i
738738 0 0
739739 −50.3533 −1.85228 −0.926139 0.377184i 0.876893π-0.876893\pi
−0.926139 + 0.377184i 0.876893π0.876893\pi
740740 4.84551 1.20394i 0.178125 0.0442576i
741741 0 0
742742 22.3545i 0.820661i
743743 30.7877i 1.12949i −0.825266 0.564745i 0.808975π-0.808975\pi
0.825266 0.564745i 0.191025π-0.191025\pi
744744 0 0
745745 4.89496 + 19.7009i 0.179337 + 0.721784i
746746 −36.9216 −1.35180
747747 0 0
748748 0.863763i 0.0315823i
749749 −16.6681 −0.609038
750750 0 0
751751 −10.6225 −0.387620 −0.193810 0.981039i 0.562085π-0.562085\pi
−0.193810 + 0.981039i 0.562085π0.562085\pi
752752 26.2739i 0.958111i
753753 0 0
754754 −7.89269 −0.287435
755755 −1.76713 7.11223i −0.0643126 0.258840i
756756 0 0
757757 7.98562i 0.290242i 0.989414 + 0.145121i 0.0463572π0.0463572\pi
−0.989414 + 0.145121i 0.953643π0.953643\pi
758758 45.8024i 1.66362i
759759 0 0
760760 −2.93722 + 0.729794i −0.106544 + 0.0264724i
761761 48.9360 1.77393 0.886964 0.461838i 0.152810π-0.152810\pi
0.886964 + 0.461838i 0.152810π0.152810\pi
762762 0 0
763763 28.8248i 1.04353i
764764 0.544946 0.0197155
765765 0 0
766766 19.1110 0.690509
767767 4.72261i 0.170523i
768768 0 0
769769 7.99547 0.288324 0.144162 0.989554i 0.453951π-0.453951\pi
0.144162 + 0.989554i 0.453951π0.453951\pi
770770 3.60197 + 14.4969i 0.129806 + 0.522433i
771771 0 0
772772 6.54495i 0.235558i
773773 26.6141i 0.957242i −0.878022 0.478621i 0.841137π-0.841137\pi
0.878022 0.478621i 0.158863π-0.158863\pi
774774 0 0
775775 −3.88550 + 2.05786i −0.139571 + 0.0739205i
776776 14.8494 0.533062
777777 0 0
778778 25.9155i 0.929115i
779779 −0.680346 −0.0243759
780780 0 0
781781 36.7708 1.31576
782782 4.01438i 0.143554i
783783 0 0
784784 −18.7686 −0.670306
785785 27.8576 6.92162i 0.994281 0.247043i
786786 0 0
787787 9.25792i 0.330009i −0.986293 0.165005i 0.947236π-0.947236\pi
0.986293 0.165005i 0.0527639π-0.0527639\pi
788788 0.738205i 0.0262975i
789789 0 0
790790 1.65983 0.412408i 0.0590540 0.0146728i
791791 −20.0989 −0.714634
792792 0 0
793793 8.04945i 0.285844i
794794 −5.99159 −0.212634
795795 0 0
796796 −1.99016 −0.0705393
797797 15.9421i 0.564700i 0.959312 + 0.282350i 0.0911139π0.0911139\pi
−0.959312 + 0.282350i 0.908886π0.908886\pi
798798 0 0
799799 −5.26180 −0.186149
800800 −4.82726 9.11450i −0.170669 0.322246i
801801 0 0
802802 14.0144i 0.494865i
803803 4.95282i 0.174781i
804804 0 0
805805 −2.60811 10.4969i −0.0919238 0.369968i
806806 1.35350 0.0476751
807807 0 0
808808 41.2663i 1.45174i
809809 17.9239 0.630170 0.315085 0.949063i 0.397967π-0.397967\pi
0.315085 + 0.949063i 0.397967π0.397967\pi
810810 0 0
811811 7.43415 0.261048 0.130524 0.991445i 0.458334π-0.458334\pi
0.130524 + 0.991445i 0.458334π0.458334\pi
812812 3.23513i 0.113531i
813813 0 0
814814 −23.6430 −0.828687
815815 −26.1483 + 6.49693i −0.915937 + 0.227577i
816816 0 0
817817 3.46800i 0.121330i
818818 29.8888i 1.04504i
819819 0 0
820820 −0.251117 1.01068i −0.00876940 0.0352944i
821821 −20.4801 −0.714761 −0.357380 0.933959i 0.616330π-0.616330\pi
−0.357380 + 0.933959i 0.616330π0.616330\pi
822822 0 0
823823 3.75154i 0.130770i −0.997860 0.0653852i 0.979172π-0.979172\pi
0.997860 0.0653852i 0.0208276π-0.0208276\pi
824824 25.5811 0.891159
825825 0 0
826826 12.4247 0.432310
827827 48.1483i 1.67428i −0.546987 0.837141i 0.684225π-0.684225\pi
0.546987 0.837141i 0.315775π-0.315775\pi
828828 0 0
829829 −36.5608 −1.26981 −0.634904 0.772591i 0.718960π-0.718960\pi
−0.634904 + 0.772591i 0.718960π0.718960\pi
830830 −7.16290 28.8287i −0.248628 1.00066i
831831 0 0
832832 6.02893i 0.209016i
833833 3.75872i 0.130232i
834834 0 0
835835 −18.9444 + 4.70701i −0.655598 + 0.162893i
836836 −0.505339 −0.0174775
837837 0 0
838838 25.8264i 0.892159i
839839 45.2294 1.56149 0.780746 0.624849i 0.214839π-0.214839\pi
0.780746 + 0.624849i 0.214839π0.214839\pi
840840 0 0
841841 −2.70540 −0.0932896
842842 29.2762i 1.00892i
843843 0 0
844844 8.39803 0.289072
845845 0.539189 + 2.17009i 0.0185487 + 0.0746532i
846846 0 0
847847 7.78151i 0.267376i
848848 39.1026i 1.34279i
849849 0 0
850850 6.26794 3.31965i 0.214989 0.113863i
851851 17.1194 0.586846
852852 0 0
853853 37.2534i 1.27553i −0.770230 0.637766i 0.779859π-0.779859\pi
0.770230 0.637766i 0.220141π-0.220141\pi
854854 −21.1773 −0.724671
855855 0 0
856856 −24.4789 −0.836671
857857 10.8371i 0.370188i 0.982721 + 0.185094i 0.0592590π0.0592590\pi
−0.982721 + 0.185094i 0.940741π0.940741\pi
858858 0 0
859859 −14.6081 −0.498422 −0.249211 0.968449i 0.580171π-0.580171\pi
−0.249211 + 0.968449i 0.580171π0.580171\pi
860860 5.15183 1.28005i 0.175676 0.0436492i
861861 0 0
862862 12.3596i 0.420971i
863863 10.3440i 0.352116i 0.984380 + 0.176058i 0.0563345π0.0563345\pi
−0.984380 + 0.176058i 0.943665π0.943665\pi
864864 0 0
865865 1.87444 0.465732i 0.0637329 0.0158354i
866866 −20.0821 −0.682417
867867 0 0
868868 0.554787i 0.0188307i
869869 −1.26180 −0.0428035
870870 0 0
871871 −7.86603 −0.266530
872872 42.3324i 1.43356i
873873 0 0
874874 2.34858 0.0794420
875875 14.2329 12.7526i 0.481159 0.431116i
876876 0 0
877877 38.0677i 1.28545i −0.766095 0.642727i 0.777803π-0.777803\pi
0.766095 0.642727i 0.222197π-0.222197\pi
878878 11.8531i 0.400022i
879879 0 0
880880 6.30057 + 25.3580i 0.212392 + 0.854819i
881881 −12.0494 −0.405956 −0.202978 0.979183i 0.565062π-0.565062\pi
−0.202978 + 0.979183i 0.565062π0.565062\pi
882882 0 0
883883 0.320699i 0.0107924i −0.999985 0.00539619i 0.998282π-0.998282\pi
0.999985 0.00539619i 0.00171767π-0.00171767\pi
884884 −0.340173 −0.0114413
885885 0 0
886886 9.83672 0.330471
887887 3.62144i 0.121596i 0.998150 + 0.0607981i 0.0193646π0.0193646\pi
−0.998150 + 0.0607981i 0.980635π0.980635\pi
888888 0 0
889889 −30.7792 −1.03230
890890 −42.8781 + 10.6537i −1.43728 + 0.357112i
891891 0 0
892892 3.23370i 0.108272i
893893 3.07838i 0.103014i
894894 0 0
895895 −10.7382 43.2183i −0.358939 1.44463i
896896 22.9132 0.765477
897897 0 0
898898 48.6635i 1.62392i
899899 −4.50921 −0.150391
900900 0 0
901901 7.83096 0.260887
902902 4.93146i 0.164200i
903903 0 0
904904 −29.5174 −0.981736
905905 −7.75872 31.2267i −0.257909 1.03801i
906906 0 0
907907 10.9333i 0.363036i −0.983388 0.181518i 0.941899π-0.941899\pi
0.983388 0.181518i 0.0581010π-0.0581010\pi
908908 6.35842i 0.211012i
909909 0 0
910910 −5.70928 + 1.41855i −0.189261 + 0.0470245i
911911 37.5897 1.24540 0.622701 0.782460i 0.286035π-0.286035\pi
0.622701 + 0.782460i 0.286035π0.286035\pi
912912 0 0
913913 21.9155i 0.725297i
914914 54.8613 1.81465
915915 0 0
916916 1.13624 0.0375423
917917 24.3668i 0.804664i
918918 0 0
919919 −33.6742 −1.11081 −0.555405 0.831580i 0.687437π-0.687437\pi
−0.555405 + 0.831580i 0.687437π0.687437\pi
920920 −3.83030 15.4159i −0.126281 0.508247i
921921 0 0
922922 23.0563i 0.759317i
923923 14.4813i 0.476659i
924924 0 0
925925 14.1568 + 26.7298i 0.465471 + 0.878870i
926926 −14.0014 −0.460116
927927 0 0
928928 10.5776i 0.347226i
929929 −43.2039 −1.41748 −0.708738 0.705472i 0.750735π-0.750735\pi
−0.708738 + 0.705472i 0.750735π0.750735\pi
930930 0 0
931931 2.19902 0.0720698
932932 6.98932i 0.228943i
933933 0 0
934934 2.88920 0.0945376
935935 −5.07838 + 1.26180i −0.166081 + 0.0412651i
936936 0 0
937937 27.5630i 0.900445i 0.892916 + 0.450222i 0.148655π0.148655\pi
−0.892916 + 0.450222i 0.851345π0.851345\pi
938938 20.6947i 0.675707i
939939 0 0
940940 4.57304 1.13624i 0.149156 0.0370600i
941941 −58.1666 −1.89618 −0.948088 0.318007i 0.896987π-0.896987\pi
−0.948088 + 0.318007i 0.896987π0.896987\pi
942942 0 0
943943 3.57077i 0.116280i
944944 21.7333 0.707358
945945 0 0
946946 −25.1377 −0.817296
947947 48.5152i 1.57653i −0.615335 0.788266i 0.710979π-0.710979\pi
0.615335 0.788266i 0.289021π-0.289021\pi
948948 0 0
949949 −1.95055 −0.0633176
950950 1.94214 + 3.66701i 0.0630114 + 0.118974i
951951 0 0
952952 3.95443i 0.128164i
953953 23.0349i 0.746173i −0.927796 0.373087i 0.878299π-0.878299\pi
0.927796 0.373087i 0.121701π-0.121701\pi
954954 0 0
955955 0.796064 + 3.20394i 0.0257600 + 0.103677i
956956 −2.45013 −0.0792430
957957 0 0
958958 24.2316i 0.782889i
959959 −23.5630 −0.760890
960960 0 0
961961 −30.2267 −0.975056
962962 9.31124i 0.300207i
963963 0 0
964964 3.49777 0.112655
965965 38.4801 9.56093i 1.23872 0.307777i
966966 0 0
967967 54.9998i 1.76868i 0.466848 + 0.884338i 0.345389π0.345389\pi
−0.466848 + 0.884338i 0.654611π0.654611\pi
968968 11.4280i 0.367310i
969969 0 0
970970 −4.90934 19.7587i −0.157629 0.634414i
971971 −9.70540 −0.311461 −0.155731 0.987800i 0.549773π-0.549773\pi
−0.155731 + 0.987800i 0.549773π0.549773\pi
972972 0 0
973973 11.3730i 0.364601i
974974 −7.61038 −0.243852
975975 0 0
976976 −37.0433 −1.18573
977977 32.2062i 1.03037i −0.857080 0.515184i 0.827724π-0.827724\pi
0.857080 0.515184i 0.172276π-0.172276\pi
978978 0 0
979979 32.5958 1.04177
980980 0.811662 + 3.26672i 0.0259276 + 0.104351i
981981 0 0
982982 60.7768i 1.93947i
983983 44.0782i 1.40588i 0.711251 + 0.702938i 0.248129π0.248129\pi
−0.711251 + 0.702938i 0.751871π0.751871\pi
984984 0 0
985985 −4.34017 + 1.07838i −0.138289 + 0.0343600i
986986 7.27408 0.231654
987987 0 0
988988 0.199016i 0.00633154i
989989 18.2017 0.578779
990990 0 0
991991 12.0677 0.383343 0.191672 0.981459i 0.438609π-0.438609\pi
0.191672 + 0.981459i 0.438609π0.438609\pi
992992 1.81393i 0.0575923i
993993 0 0
994994 −38.0989 −1.20842
995995 −2.90725 11.7009i −0.0921659 0.370942i
996996 0 0
997997 45.7587i 1.44919i 0.689173 + 0.724597i 0.257974π0.257974\pi
−0.689173 + 0.724597i 0.742026π0.742026\pi
998998 2.57182i 0.0814094i
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 585.2.c.b.469.2 6
3.2 odd 2 65.2.b.a.14.5 yes 6
5.2 odd 4 2925.2.a.bj.1.2 3
5.3 odd 4 2925.2.a.bf.1.2 3
5.4 even 2 inner 585.2.c.b.469.5 6
12.11 even 2 1040.2.d.c.209.6 6
15.2 even 4 325.2.a.j.1.2 3
15.8 even 4 325.2.a.k.1.2 3
15.14 odd 2 65.2.b.a.14.2 6
39.2 even 12 845.2.l.d.654.4 12
39.5 even 4 845.2.d.b.844.3 6
39.8 even 4 845.2.d.a.844.3 6
39.11 even 12 845.2.l.e.654.4 12
39.17 odd 6 845.2.n.g.484.2 12
39.20 even 12 845.2.l.e.699.3 12
39.23 odd 6 845.2.n.g.529.5 12
39.29 odd 6 845.2.n.f.529.2 12
39.32 even 12 845.2.l.d.699.3 12
39.35 odd 6 845.2.n.f.484.5 12
39.38 odd 2 845.2.b.c.339.2 6
60.23 odd 4 5200.2.a.cb.1.1 3
60.47 odd 4 5200.2.a.cj.1.3 3
60.59 even 2 1040.2.d.c.209.1 6
195.29 odd 6 845.2.n.f.529.5 12
195.38 even 4 4225.2.a.ba.1.2 3
195.44 even 4 845.2.d.a.844.4 6
195.59 even 12 845.2.l.d.699.4 12
195.74 odd 6 845.2.n.f.484.2 12
195.77 even 4 4225.2.a.bh.1.2 3
195.89 even 12 845.2.l.d.654.3 12
195.119 even 12 845.2.l.e.654.3 12
195.134 odd 6 845.2.n.g.484.5 12
195.149 even 12 845.2.l.e.699.4 12
195.164 even 4 845.2.d.b.844.4 6
195.179 odd 6 845.2.n.g.529.2 12
195.194 odd 2 845.2.b.c.339.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.b.a.14.2 6 15.14 odd 2
65.2.b.a.14.5 yes 6 3.2 odd 2
325.2.a.j.1.2 3 15.2 even 4
325.2.a.k.1.2 3 15.8 even 4
585.2.c.b.469.2 6 1.1 even 1 trivial
585.2.c.b.469.5 6 5.4 even 2 inner
845.2.b.c.339.2 6 39.38 odd 2
845.2.b.c.339.5 6 195.194 odd 2
845.2.d.a.844.3 6 39.8 even 4
845.2.d.a.844.4 6 195.44 even 4
845.2.d.b.844.3 6 39.5 even 4
845.2.d.b.844.4 6 195.164 even 4
845.2.l.d.654.3 12 195.89 even 12
845.2.l.d.654.4 12 39.2 even 12
845.2.l.d.699.3 12 39.32 even 12
845.2.l.d.699.4 12 195.59 even 12
845.2.l.e.654.3 12 195.119 even 12
845.2.l.e.654.4 12 39.11 even 12
845.2.l.e.699.3 12 39.20 even 12
845.2.l.e.699.4 12 195.149 even 12
845.2.n.f.484.2 12 195.74 odd 6
845.2.n.f.484.5 12 39.35 odd 6
845.2.n.f.529.2 12 39.29 odd 6
845.2.n.f.529.5 12 195.29 odd 6
845.2.n.g.484.2 12 39.17 odd 6
845.2.n.g.484.5 12 195.134 odd 6
845.2.n.g.529.2 12 195.179 odd 6
845.2.n.g.529.5 12 39.23 odd 6
1040.2.d.c.209.1 6 60.59 even 2
1040.2.d.c.209.6 6 12.11 even 2
2925.2.a.bf.1.2 3 5.3 odd 4
2925.2.a.bj.1.2 3 5.2 odd 4
4225.2.a.ba.1.2 3 195.38 even 4
4225.2.a.bh.1.2 3 195.77 even 4
5200.2.a.cb.1.1 3 60.23 odd 4
5200.2.a.cj.1.3 3 60.47 odd 4