Properties

Label 3330.2.e.f.739.6
Level 33303330
Weight 22
Character 3330.739
Analytic conductor 26.59026.590
Analytic rank 00
Dimension 1616
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3330,2,Mod(739,3330)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3330.739");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3330=232537 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3330.e (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 26.590183873126.5901838731
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x162x15+2x14+8x13+138x12220x11+196x10+744x9+4241x8++64 x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a37]\Z[a_1, \ldots, a_{37}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 1110)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 739.6
Root 1.288171.28817i-1.28817 - 1.28817i of defining polynomial
Character χ\chi == 3330.739
Dual form 3330.2.e.f.739.5

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) == q+1.00000q2+1.00000q4+(1.28817+1.82773i)q51.25548iq7+1.00000q8+(1.28817+1.82773i)q10+5.46829q11+4.70887q131.25548iq14+1.00000q161.19309q171.22179iq19+(1.28817+1.82773i)q20+5.46829q221.91577q23+(1.681224.70887i)q25+4.70887q261.25548iq28+5.08822iq293.43275iq31+1.00000q321.19309q34+(2.29468+1.61728i)q35+(4.584733.99753i)q371.22179iq38+(1.28817+1.82773i)q40+4.46326q41+1.34271q43+5.46829q441.91577q461.90301iq47+5.42377q49+(1.681224.70887i)q50+4.70887q52+1.11671iq53+(7.04410+9.99458i)q551.25548iq56+5.08822iq58+8.99577iq596.21190iq613.43275iq62+1.00000q64+(6.06585+8.60657i)q65+4.21117iq671.19309q68+(2.29468+1.61728i)q70+12.4170q7110.2834iq73+(4.584733.99753i)q741.22179iq766.86533iq77+1.00691iq79+(1.28817+1.82773i)q80+4.46326q82+0.754493iq83+(1.536912.18065i)q85+1.34271q86+5.46829q88+11.4743iq895.91190iq911.91577q921.90301iq94+(2.23311+1.57388i)q95+16.6814q97+5.42377q98+O(q100)q+1.00000 q^{2} +1.00000 q^{4} +(-1.28817 + 1.82773i) q^{5} -1.25548i q^{7} +1.00000 q^{8} +(-1.28817 + 1.82773i) q^{10} +5.46829 q^{11} +4.70887 q^{13} -1.25548i q^{14} +1.00000 q^{16} -1.19309 q^{17} -1.22179i q^{19} +(-1.28817 + 1.82773i) q^{20} +5.46829 q^{22} -1.91577 q^{23} +(-1.68122 - 4.70887i) q^{25} +4.70887 q^{26} -1.25548i q^{28} +5.08822i q^{29} -3.43275i q^{31} +1.00000 q^{32} -1.19309 q^{34} +(2.29468 + 1.61728i) q^{35} +(-4.58473 - 3.99753i) q^{37} -1.22179i q^{38} +(-1.28817 + 1.82773i) q^{40} +4.46326 q^{41} +1.34271 q^{43} +5.46829 q^{44} -1.91577 q^{46} -1.90301i q^{47} +5.42377 q^{49} +(-1.68122 - 4.70887i) q^{50} +4.70887 q^{52} +1.11671i q^{53} +(-7.04410 + 9.99458i) q^{55} -1.25548i q^{56} +5.08822i q^{58} +8.99577i q^{59} -6.21190i q^{61} -3.43275i q^{62} +1.00000 q^{64} +(-6.06585 + 8.60657i) q^{65} +4.21117i q^{67} -1.19309 q^{68} +(2.29468 + 1.61728i) q^{70} +12.4170 q^{71} -10.2834i q^{73} +(-4.58473 - 3.99753i) q^{74} -1.22179i q^{76} -6.86533i q^{77} +1.00691i q^{79} +(-1.28817 + 1.82773i) q^{80} +4.46326 q^{82} +0.754493i q^{83} +(1.53691 - 2.18065i) q^{85} +1.34271 q^{86} +5.46829 q^{88} +11.4743i q^{89} -5.91190i q^{91} -1.91577 q^{92} -1.90301i q^{94} +(2.23311 + 1.57388i) q^{95} +16.6814 q^{97} +5.42377 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+16q2+16q4+2q5+16q8+2q102q11+16q16+38q17+2q202q22+20q234q25+16q32+38q34+10q354q37+2q40+6q41+18q98+O(q100) 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} + 2 q^{10} - 2 q^{11} + 16 q^{16} + 38 q^{17} + 2 q^{20} - 2 q^{22} + 20 q^{23} - 4 q^{25} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 4 q^{37} + 2 q^{40} + 6 q^{41}+ \cdots - 18 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 371371 631631 667667
χ(n)\chi(n) 11 1-1 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 1.00000 0.707107
33 0 0
44 1.00000 0.500000
55 −1.28817 + 1.82773i −0.576089 + 0.817387i
66 0 0
77 1.25548i 0.474527i −0.971445 0.237263i 0.923750π-0.923750\pi
0.971445 0.237263i 0.0762505π-0.0762505\pi
88 1.00000 0.353553
99 0 0
1010 −1.28817 + 1.82773i −0.407356 + 0.577980i
1111 5.46829 1.64875 0.824376 0.566043i 0.191526π-0.191526\pi
0.824376 + 0.566043i 0.191526π0.191526\pi
1212 0 0
1313 4.70887 1.30601 0.653003 0.757355i 0.273509π-0.273509\pi
0.653003 + 0.757355i 0.273509π0.273509\pi
1414 1.25548i 0.335541i
1515 0 0
1616 1.00000 0.250000
1717 −1.19309 −0.289367 −0.144684 0.989478i 0.546216π-0.546216\pi
−0.144684 + 0.989478i 0.546216π0.546216\pi
1818 0 0
1919 1.22179i 0.280298i −0.990130 0.140149i 0.955242π-0.955242\pi
0.990130 0.140149i 0.0447582π-0.0447582\pi
2020 −1.28817 + 1.82773i −0.288044 + 0.408694i
2121 0 0
2222 5.46829 1.16584
2323 −1.91577 −0.399466 −0.199733 0.979850i 0.564007π-0.564007\pi
−0.199733 + 0.979850i 0.564007π0.564007\pi
2424 0 0
2525 −1.68122 4.70887i −0.336244 0.941775i
2626 4.70887 0.923486
2727 0 0
2828 1.25548i 0.237263i
2929 5.08822i 0.944858i 0.881369 + 0.472429i 0.156623π0.156623\pi
−0.881369 + 0.472429i 0.843377π0.843377\pi
3030 0 0
3131 3.43275i 0.616540i −0.951299 0.308270i 0.900250π-0.900250\pi
0.951299 0.308270i 0.0997501π-0.0997501\pi
3232 1.00000 0.176777
3333 0 0
3434 −1.19309 −0.204613
3535 2.29468 + 1.61728i 0.387872 + 0.273370i
3636 0 0
3737 −4.58473 3.99753i −0.753725 0.657190i
3838 1.22179i 0.198201i
3939 0 0
4040 −1.28817 + 1.82773i −0.203678 + 0.288990i
4141 4.46326 0.697043 0.348522 0.937301i 0.386684π-0.386684\pi
0.348522 + 0.937301i 0.386684π0.386684\pi
4242 0 0
4343 1.34271 0.204761 0.102380 0.994745i 0.467354π-0.467354\pi
0.102380 + 0.994745i 0.467354π0.467354\pi
4444 5.46829 0.824376
4545 0 0
4646 −1.91577 −0.282465
4747 1.90301i 0.277583i −0.990322 0.138791i 0.955678π-0.955678\pi
0.990322 0.138791i 0.0443217π-0.0443217\pi
4848 0 0
4949 5.42377 0.774824
5050 −1.68122 4.70887i −0.237760 0.665935i
5151 0 0
5252 4.70887 0.653003
5353 1.11671i 0.153392i 0.997055 + 0.0766959i 0.0244370π0.0244370\pi
−0.997055 + 0.0766959i 0.975563π0.975563\pi
5454 0 0
5555 −7.04410 + 9.99458i −0.949827 + 1.34767i
5656 1.25548i 0.167771i
5757 0 0
5858 5.08822i 0.668116i
5959 8.99577i 1.17115i 0.810618 + 0.585575i 0.199131π0.199131\pi
−0.810618 + 0.585575i 0.800869π0.800869\pi
6060 0 0
6161 6.21190i 0.795352i −0.917526 0.397676i 0.869817π-0.869817\pi
0.917526 0.397676i 0.130183π-0.130183\pi
6262 3.43275i 0.435960i
6363 0 0
6464 1.00000 0.125000
6565 −6.06585 + 8.60657i −0.752376 + 1.06751i
6666 0 0
6767 4.21117i 0.514476i 0.966348 + 0.257238i 0.0828125π0.0828125\pi
−0.966348 + 0.257238i 0.917188π0.917188\pi
6868 −1.19309 −0.144684
6969 0 0
7070 2.29468 + 1.61728i 0.274267 + 0.193301i
7171 12.4170 1.47363 0.736815 0.676094i 0.236329π-0.236329\pi
0.736815 + 0.676094i 0.236329π0.236329\pi
7272 0 0
7373 10.2834i 1.20359i −0.798652 0.601793i 0.794453π-0.794453\pi
0.798652 0.601793i 0.205547π-0.205547\pi
7474 −4.58473 3.99753i −0.532964 0.464703i
7575 0 0
7676 1.22179i 0.140149i
7777 6.86533i 0.782377i
7878 0 0
7979 1.00691i 0.113286i 0.998394 + 0.0566431i 0.0180397π0.0180397\pi
−0.998394 + 0.0566431i 0.981960π0.981960\pi
8080 −1.28817 + 1.82773i −0.144022 + 0.204347i
8181 0 0
8282 4.46326 0.492884
8383 0.754493i 0.0828164i 0.999142 + 0.0414082i 0.0131844π0.0131844\pi
−0.999142 + 0.0414082i 0.986816π0.986816\pi
8484 0 0
8585 1.53691 2.18065i 0.166701 0.236525i
8686 1.34271 0.144788
8787 0 0
8888 5.46829 0.582922
8989 11.4743i 1.21627i 0.793832 + 0.608137i 0.208083π0.208083\pi
−0.793832 + 0.608137i 0.791917π0.791917\pi
9090 0 0
9191 5.91190i 0.619735i
9292 −1.91577 −0.199733
9393 0 0
9494 1.90301i 0.196281i
9595 2.23311 + 1.57388i 0.229112 + 0.161477i
9696 0 0
9797 16.6814 1.69374 0.846868 0.531803i 0.178485π-0.178485\pi
0.846868 + 0.531803i 0.178485π0.178485\pi
9898 5.42377 0.547883
9999 0 0
100100 −1.68122 4.70887i −0.168122 0.470887i
101101 −3.26214 −0.324595 −0.162298 0.986742i 0.551890π-0.551890\pi
−0.162298 + 0.986742i 0.551890π0.551890\pi
102102 0 0
103103 5.19330 0.511711 0.255856 0.966715i 0.417643π-0.417643\pi
0.255856 + 0.966715i 0.417643π0.417643\pi
104104 4.70887 0.461743
105105 0 0
106106 1.11671i 0.108464i
107107 8.65950i 0.837146i 0.908183 + 0.418573i 0.137470π0.137470\pi
−0.908183 + 0.418573i 0.862530π0.862530\pi
108108 0 0
109109 2.54677i 0.243936i 0.992534 + 0.121968i 0.0389205π0.0389205\pi
−0.992534 + 0.121968i 0.961079π0.961079\pi
110110 −7.04410 + 9.99458i −0.671629 + 0.952945i
111111 0 0
112112 1.25548i 0.118632i
113113 4.72781 0.444755 0.222378 0.974961i 0.428618π-0.428618\pi
0.222378 + 0.974961i 0.428618π0.428618\pi
114114 0 0
115115 2.46784 3.50152i 0.230128 0.326518i
116116 5.08822i 0.472429i
117117 0 0
118118 8.99577i 0.828128i
119119 1.49790i 0.137312i
120120 0 0
121121 18.9022 1.71838
122122 6.21190i 0.562399i
123123 0 0
124124 3.43275i 0.308270i
125125 10.7723 + 2.99303i 0.963501 + 0.267704i
126126 0 0
127127 8.05067i 0.714381i 0.934031 + 0.357191i 0.116265π0.116265\pi
−0.934031 + 0.357191i 0.883735π0.883735\pi
128128 1.00000 0.0883883
129129 0 0
130130 −6.06585 + 8.60657i −0.532010 + 0.754846i
131131 12.9999i 1.13581i 0.823094 + 0.567905i 0.192246π0.192246\pi
−0.823094 + 0.567905i 0.807754π0.807754\pi
132132 0 0
133133 −1.53393 −0.133009
134134 4.21117i 0.363790i
135135 0 0
136136 −1.19309 −0.102307
137137 13.5487i 1.15754i −0.815490 0.578772i 0.803532π-0.803532\pi
0.815490 0.578772i 0.196468π-0.196468\pi
138138 0 0
139139 15.3257 1.29991 0.649955 0.759972i 0.274788π-0.274788\pi
0.649955 + 0.759972i 0.274788π0.274788\pi
140140 2.29468 + 1.61728i 0.193936 + 0.136685i
141141 0 0
142142 12.4170 1.04201
143143 25.7495 2.15328
144144 0 0
145145 −9.29991 6.55451i −0.772315 0.544322i
146146 10.2834i 0.851064i
147147 0 0
148148 −4.58473 3.99753i −0.376863 0.328595i
149149 −13.4684 −1.10337 −0.551686 0.834052i 0.686015π-0.686015\pi
−0.551686 + 0.834052i 0.686015π0.686015\pi
150150 0 0
151151 −10.3930 −0.845767 −0.422883 0.906184i 0.638982π-0.638982\pi
−0.422883 + 0.906184i 0.638982π0.638982\pi
152152 1.22179i 0.0991003i
153153 0 0
154154 6.86533i 0.553224i
155155 6.27415 + 4.42198i 0.503952 + 0.355182i
156156 0 0
157157 14.2297i 1.13565i 0.823148 + 0.567827i 0.192216π0.192216\pi
−0.823148 + 0.567827i 0.807784π0.807784\pi
158158 1.00691i 0.0801054i
159159 0 0
160160 −1.28817 + 1.82773i −0.101839 + 0.144495i
161161 2.40521i 0.189557i
162162 0 0
163163 0.455364 0.0356669 0.0178334 0.999841i 0.494323π-0.494323\pi
0.0178334 + 0.999841i 0.494323π0.494323\pi
164164 4.46326 0.348522
165165 0 0
166166 0.754493i 0.0585600i
167167 −0.755752 −0.0584819 −0.0292409 0.999572i 0.509309π-0.509309\pi
−0.0292409 + 0.999572i 0.509309π0.509309\pi
168168 0 0
169169 9.17350 0.705654
170170 1.53691 2.18065i 0.117875 0.167248i
171171 0 0
172172 1.34271 0.102380
173173 4.41375i 0.335571i −0.985823 0.167786i 0.946338π-0.946338\pi
0.985823 0.167786i 0.0536617π-0.0536617\pi
174174 0 0
175175 −5.91190 + 2.11074i −0.446898 + 0.159557i
176176 5.46829 0.412188
177177 0 0
178178 11.4743i 0.860036i
179179 12.6883i 0.948368i −0.880426 0.474184i 0.842743π-0.842743\pi
0.880426 0.474184i 0.157257π-0.157257\pi
180180 0 0
181181 13.2444 0.984445 0.492223 0.870469i 0.336185π-0.336185\pi
0.492223 + 0.870469i 0.336185π0.336185\pi
182182 5.91190i 0.438219i
183183 0 0
184184 −1.91577 −0.141233
185185 13.2123 3.23016i 0.971391 0.237486i
186186 0 0
187187 −6.52417 −0.477094
188188 1.90301i 0.138791i
189189 0 0
190190 2.23311 + 1.57388i 0.162007 + 0.114181i
191191 7.03990i 0.509389i 0.967022 + 0.254695i 0.0819749π0.0819749\pi
−0.967022 + 0.254695i 0.918025π0.918025\pi
192192 0 0
193193 −0.635749 −0.0457622 −0.0228811 0.999738i 0.507284π-0.507284\pi
−0.0228811 + 0.999738i 0.507284π0.507284\pi
194194 16.6814 1.19765
195195 0 0
196196 5.42377 0.387412
197197 5.18937i 0.369727i −0.982764 0.184864i 0.940816π-0.940816\pi
0.982764 0.184864i 0.0591843π-0.0591843\pi
198198 0 0
199199 23.8852i 1.69318i 0.532247 + 0.846589i 0.321348π0.321348\pi
−0.532247 + 0.846589i 0.678652π0.678652\pi
200200 −1.68122 4.70887i −0.118880 0.332968i
201201 0 0
202202 −3.26214 −0.229523
203203 6.38816 0.448361
204204 0 0
205205 −5.74945 + 8.15764i −0.401559 + 0.569754i
206206 5.19330 0.361834
207207 0 0
208208 4.70887 0.326502
209209 6.68111i 0.462142i
210210 0 0
211211 −26.6260 −1.83301 −0.916505 0.400022i 0.869002π-0.869002\pi
−0.916505 + 0.400022i 0.869002π0.869002\pi
212212 1.11671i 0.0766959i
213213 0 0
214214 8.65950i 0.591952i
215215 −1.72964 + 2.45411i −0.117960 + 0.167369i
216216 0 0
217217 −4.30975 −0.292565
218218 2.54677i 0.172489i
219219 0 0
220220 −7.04410 + 9.99458i −0.474913 + 0.673834i
221221 −5.61812 −0.377915
222222 0 0
223223 20.0982i 1.34588i −0.739698 0.672938i 0.765032π-0.765032\pi
0.739698 0.672938i 0.234968π-0.234968\pi
224224 1.25548i 0.0838853i
225225 0 0
226226 4.72781 0.314489
227227 −15.1621 −1.00635 −0.503173 0.864186i 0.667834π-0.667834\pi
−0.503173 + 0.864186i 0.667834π0.667834\pi
228228 0 0
229229 −2.54527 −0.168196 −0.0840980 0.996457i 0.526801π-0.526801\pi
−0.0840980 + 0.996457i 0.526801π0.526801\pi
230230 2.46784 3.50152i 0.162725 0.230883i
231231 0 0
232232 5.08822i 0.334058i
233233 13.9212i 0.912008i 0.889978 + 0.456004i 0.150720π0.150720\pi
−0.889978 + 0.456004i 0.849280π0.849280\pi
234234 0 0
235235 3.47820 + 2.45141i 0.226892 + 0.159912i
236236 8.99577i 0.585575i
237237 0 0
238238 1.49790i 0.0970945i
239239 28.8753i 1.86779i −0.357546 0.933895i 0.616387π-0.616387\pi
0.357546 0.933895i 0.383613π-0.383613\pi
240240 0 0
241241 6.84853i 0.441152i −0.975370 0.220576i 0.929206π-0.929206\pi
0.975370 0.220576i 0.0707938π-0.0707938\pi
242242 18.9022 1.21508
243243 0 0
244244 6.21190i 0.397676i
245245 −6.98676 + 9.91321i −0.446367 + 0.633331i
246246 0 0
247247 5.75326i 0.366071i
248248 3.43275i 0.217980i
249249 0 0
250250 10.7723 + 2.99303i 0.681298 + 0.189296i
251251 18.7459i 1.18323i 0.806221 + 0.591615i 0.201509π0.201509\pi
−0.806221 + 0.591615i 0.798491π0.798491\pi
252252 0 0
253253 −10.4760 −0.658620
254254 8.05067i 0.505144i
255255 0 0
256256 1.00000 0.0625000
257257 −17.3509 −1.08232 −0.541158 0.840921i 0.682014π-0.682014\pi
−0.541158 + 0.840921i 0.682014π0.682014\pi
258258 0 0
259259 −5.01882 + 5.75604i −0.311854 + 0.357663i
260260 −6.06585 + 8.60657i −0.376188 + 0.533757i
261261 0 0
262262 12.9999i 0.803139i
263263 31.3436i 1.93273i −0.257176 0.966364i 0.582792π-0.582792\pi
0.257176 0.966364i 0.417208π-0.417208\pi
264264 0 0
265265 −2.04105 1.43851i −0.125380 0.0883672i
266266 −1.53393 −0.0940516
267267 0 0
268268 4.21117i 0.257238i
269269 −20.8503 −1.27126 −0.635631 0.771993i 0.719260π-0.719260\pi
−0.635631 + 0.771993i 0.719260π0.719260\pi
270270 0 0
271271 −0.977182 −0.0593596 −0.0296798 0.999559i 0.509449π-0.509449\pi
−0.0296798 + 0.999559i 0.509449π0.509449\pi
272272 −1.19309 −0.0723418
273273 0 0
274274 13.5487i 0.818507i
275275 −9.19339 25.7495i −0.554383 1.55275i
276276 0 0
277277 −28.0775 −1.68701 −0.843506 0.537120i 0.819512π-0.819512\pi
−0.843506 + 0.537120i 0.819512π0.819512\pi
278278 15.3257 0.919176
279279 0 0
280280 2.29468 + 1.61728i 0.137134 + 0.0966507i
281281 20.9112i 1.24746i −0.781640 0.623730i 0.785617π-0.785617\pi
0.781640 0.623730i 0.214383π-0.214383\pi
282282 0 0
283283 −11.7273 −0.697116 −0.348558 0.937287i 0.613329π-0.613329\pi
−0.348558 + 0.937287i 0.613329π0.613329\pi
284284 12.4170 0.736815
285285 0 0
286286 25.7495 1.52260
287287 5.60353i 0.330766i
288288 0 0
289289 −15.5765 −0.916267
290290 −9.29991 6.55451i −0.546109 0.384894i
291291 0 0
292292 10.2834i 0.601793i
293293 19.0944i 1.11550i −0.830007 0.557752i 0.811664π-0.811664\pi
0.830007 0.557752i 0.188336π-0.188336\pi
294294 0 0
295295 −16.4419 11.5881i −0.957283 0.674686i
296296 −4.58473 3.99753i −0.266482 0.232352i
297297 0 0
298298 −13.4684 −0.780202
299299 −9.02113 −0.521705
300300 0 0
301301 1.68574i 0.0971645i
302302 −10.3930 −0.598048
303303 0 0
304304 1.22179i 0.0700745i
305305 11.3537 + 8.00200i 0.650111 + 0.458193i
306306 0 0
307307 31.2854i 1.78555i 0.450500 + 0.892777i 0.351246π0.351246\pi
−0.450500 + 0.892777i 0.648754π0.648754\pi
308308 6.86533i 0.391188i
309309 0 0
310310 6.27415 + 4.42198i 0.356348 + 0.251151i
311311 7.52409i 0.426652i 0.976981 + 0.213326i 0.0684296π0.0684296\pi
−0.976981 + 0.213326i 0.931570π0.931570\pi
312312 0 0
313313 −0.0900227 −0.00508838 −0.00254419 0.999997i 0.500810π-0.500810\pi
−0.00254419 + 0.999997i 0.500810π0.500810\pi
314314 14.2297i 0.803029i
315315 0 0
316316 1.00691i 0.0566431i
317317 7.86659i 0.441832i −0.975293 0.220916i 0.929095π-0.929095\pi
0.975293 0.220916i 0.0709046π-0.0709046\pi
318318 0 0
319319 27.8239i 1.55784i
320320 −1.28817 + 1.82773i −0.0720111 + 0.102173i
321321 0 0
322322 2.40521i 0.134037i
323323 1.45771i 0.0811090i
324324 0 0
325325 −7.91665 22.1735i −0.439137 1.22996i
326326 0.455364 0.0252203
327327 0 0
328328 4.46326 0.246442
329329 −2.38919 −0.131720
330330 0 0
331331 21.5849i 1.18641i 0.805051 + 0.593205i 0.202138π0.202138\pi
−0.805051 + 0.593205i 0.797862π0.797862\pi
332332 0.754493i 0.0414082i
333333 0 0
334334 −0.755752 −0.0413529
335335 −7.69690 5.42472i −0.420526 0.296384i
336336 0 0
337337 24.3782i 1.32796i 0.747748 + 0.663982i 0.231135π0.231135\pi
−0.747748 + 0.663982i 0.768865π0.768865\pi
338338 9.17350 0.498973
339339 0 0
340340 1.53691 2.18065i 0.0833505 0.118262i
341341 18.7713i 1.01652i
342342 0 0
343343 15.5978i 0.842202i
344344 1.34271 0.0723939
345345 0 0
346346 4.41375i 0.237285i
347347 −25.4950 −1.36864 −0.684321 0.729181i 0.739901π-0.739901\pi
−0.684321 + 0.729181i 0.739901π0.739901\pi
348348 0 0
349349 2.69761 0.144400 0.0721999 0.997390i 0.476998π-0.476998\pi
0.0721999 + 0.997390i 0.476998π0.476998\pi
350350 −5.91190 + 2.11074i −0.316004 + 0.112824i
351351 0 0
352352 5.46829 0.291461
353353 21.7179 1.15592 0.577962 0.816063i 0.303848π-0.303848\pi
0.577962 + 0.816063i 0.303848π0.303848\pi
354354 0 0
355355 −15.9953 + 22.6950i −0.848942 + 1.20453i
356356 11.4743i 0.608137i
357357 0 0
358358 12.6883i 0.670597i
359359 20.3716 1.07517 0.537585 0.843210i 0.319337π-0.319337\pi
0.537585 + 0.843210i 0.319337π0.319337\pi
360360 0 0
361361 17.5072 0.921433
362362 13.2444 0.696108
363363 0 0
364364 5.91190i 0.309868i
365365 18.7954 + 13.2469i 0.983796 + 0.693372i
366366 0 0
367367 31.0972i 1.62326i −0.584172 0.811630i 0.698581π-0.698581\pi
0.584172 0.811630i 0.301419π-0.301419\pi
368368 −1.91577 −0.0998665
369369 0 0
370370 13.2123 3.23016i 0.686877 0.167928i
371371 1.40201 0.0727885
372372 0 0
373373 33.4131i 1.73006i −0.501716 0.865032i 0.667298π-0.667298\pi
0.501716 0.865032i 0.332702π-0.332702\pi
374374 −6.52417 −0.337357
375375 0 0
376376 1.90301i 0.0981403i
377377 23.9598i 1.23399i
378378 0 0
379379 −24.6191 −1.26460 −0.632298 0.774725i 0.717888π-0.717888\pi
−0.632298 + 0.774725i 0.717888π0.717888\pi
380380 2.23311 + 1.57388i 0.114556 + 0.0807383i
381381 0 0
382382 7.03990i 0.360192i
383383 −17.5596 −0.897252 −0.448626 0.893720i 0.648086π-0.648086\pi
−0.448626 + 0.893720i 0.648086π0.648086\pi
384384 0 0
385385 12.5480 + 8.84373i 0.639505 + 0.450718i
386386 −0.635749 −0.0323587
387387 0 0
388388 16.6814 0.846868
389389 19.6417i 0.995875i 0.867213 + 0.497937i 0.165909π0.165909\pi
−0.867213 + 0.497937i 0.834091π0.834091\pi
390390 0 0
391391 2.28569 0.115592
392392 5.42377 0.273942
393393 0 0
394394 5.18937i 0.261437i
395395 −1.84036 1.29707i −0.0925987 0.0652629i
396396 0 0
397397 4.31480i 0.216554i −0.994121 0.108277i 0.965467π-0.965467\pi
0.994121 0.108277i 0.0345333π-0.0345333\pi
398398 23.8852i 1.19726i
399399 0 0
400400 −1.68122 4.70887i −0.0840610 0.235444i
401401 9.64980i 0.481888i −0.970539 0.240944i 0.922543π-0.922543\pi
0.970539 0.240944i 0.0774570π-0.0774570\pi
402402 0 0
403403 16.1644i 0.805206i
404404 −3.26214 −0.162298
405405 0 0
406406 6.38816 0.317039
407407 −25.0706 21.8596i −1.24271 1.08354i
408408 0 0
409409 25.5235i 1.26206i −0.775760 0.631029i 0.782633π-0.782633\pi
0.775760 0.631029i 0.217367π-0.217367\pi
410410 −5.74945 + 8.15764i −0.283945 + 0.402877i
411411 0 0
412412 5.19330 0.255856
413413 11.2940 0.555742
414414 0 0
415415 −1.37901 0.971918i −0.0676930 0.0477096i
416416 4.70887 0.230872
417417 0 0
418418 6.68111i 0.326784i
419419 22.0969 1.07950 0.539751 0.841824i 0.318518π-0.318518\pi
0.539751 + 0.841824i 0.318518π0.318518\pi
420420 0 0
421421 8.20101i 0.399693i −0.979827 0.199846i 0.935956π-0.935956\pi
0.979827 0.199846i 0.0640443π-0.0640443\pi
422422 −26.6260 −1.29613
423423 0 0
424424 1.11671i 0.0542322i
425425 2.00585 + 5.61812i 0.0972979 + 0.272519i
426426 0 0
427427 −7.79891 −0.377416
428428 8.65950i 0.418573i
429429 0 0
430430 −1.72964 + 2.45411i −0.0834106 + 0.118348i
431431 9.83076i 0.473531i −0.971567 0.236765i 0.923913π-0.923913\pi
0.971567 0.236765i 0.0760873π-0.0760873\pi
432432 0 0
433433 1.61024i 0.0773832i 0.999251 + 0.0386916i 0.0123190π0.0123190\pi
−0.999251 + 0.0386916i 0.987681π0.987681\pi
434434 −4.30975 −0.206875
435435 0 0
436436 2.54677i 0.121968i
437437 2.34067i 0.111970i
438438 0 0
439439 32.2443i 1.53894i 0.638684 + 0.769469i 0.279479π0.279479\pi
−0.638684 + 0.769469i 0.720521π0.720521\pi
440440 −7.04410 + 9.99458i −0.335815 + 0.476473i
441441 0 0
442442 −5.61812 −0.267226
443443 19.0730i 0.906186i −0.891463 0.453093i 0.850321π-0.850321\pi
0.891463 0.453093i 0.149679π-0.149679\pi
444444 0 0
445445 −20.9720 14.7809i −0.994168 0.700682i
446446 20.0982i 0.951679i
447447 0 0
448448 1.25548i 0.0593159i
449449 30.6914i 1.44841i −0.689582 0.724207i 0.742206π-0.742206\pi
0.689582 0.724207i 0.257794π-0.257794\pi
450450 0 0
451451 24.4064 1.14925
452452 4.72781 0.222378
453453 0 0
454454 −15.1621 −0.711593
455455 10.8054 + 7.61555i 0.506564 + 0.357022i
456456 0 0
457457 22.4560 1.05045 0.525223 0.850965i 0.323982π-0.323982\pi
0.525223 + 0.850965i 0.323982π0.323982\pi
458458 −2.54527 −0.118932
459459 0 0
460460 2.46784 3.50152i 0.115064 0.163259i
461461 7.37800i 0.343628i 0.985129 + 0.171814i 0.0549628π0.0549628\pi
−0.985129 + 0.171814i 0.945037π0.945037\pi
462462 0 0
463463 −6.16145 −0.286347 −0.143173 0.989698i 0.545731π-0.545731\pi
−0.143173 + 0.989698i 0.545731π0.545731\pi
464464 5.08822i 0.236215i
465465 0 0
466466 13.9212i 0.644887i
467467 −5.37297 −0.248631 −0.124316 0.992243i 0.539674π-0.539674\pi
−0.124316 + 0.992243i 0.539674π0.539674\pi
468468 0 0
469469 5.28704 0.244133
470470 3.47820 + 2.45141i 0.160437 + 0.113075i
471471 0 0
472472 8.99577i 0.414064i
473473 7.34231 0.337600
474474 0 0
475475 −5.75326 + 2.05410i −0.263978 + 0.0942485i
476476 1.49790i 0.0686562i
477477 0 0
478478 28.8753i 1.32073i
479479 21.5810i 0.986062i 0.870012 + 0.493031i 0.164111π0.164111\pi
−0.870012 + 0.493031i 0.835889π0.835889\pi
480480 0 0
481481 −21.5889 18.8239i −0.984370 0.858294i
482482 6.84853i 0.311942i
483483 0 0
484484 18.9022 0.859191
485485 −21.4885 + 30.4891i −0.975742 + 1.38444i
486486 0 0
487487 −0.346315 −0.0156930 −0.00784652 0.999969i 0.502498π-0.502498\pi
−0.00784652 + 0.999969i 0.502498π0.502498\pi
488488 6.21190i 0.281199i
489489 0 0
490490 −6.98676 + 9.91321i −0.315629 + 0.447833i
491491 −10.6278 −0.479624 −0.239812 0.970819i 0.577086π-0.577086\pi
−0.239812 + 0.970819i 0.577086π0.577086\pi
492492 0 0
493493 6.07071i 0.273411i
494494 5.75326i 0.258851i
495495 0 0
496496 3.43275i 0.154135i
497497 15.5893i 0.699277i
498498 0 0
499499 12.0121i 0.537736i −0.963177 0.268868i 0.913350π-0.913350\pi
0.963177 0.268868i 0.0866496π-0.0866496\pi
500500 10.7723 + 2.99303i 0.481751 + 0.133852i
501501 0 0
502502 18.7459i 0.836669i
503503 4.15447 0.185239 0.0926194 0.995702i 0.470476π-0.470476\pi
0.0926194 + 0.995702i 0.470476π0.470476\pi
504504 0 0
505505 4.20220 5.96232i 0.186996 0.265320i
506506 −10.4760 −0.465715
507507 0 0
508508 8.05067i 0.357191i
509509 8.30223 0.367990 0.183995 0.982927i 0.441097π-0.441097\pi
0.183995 + 0.982927i 0.441097π0.441097\pi
510510 0 0
511511 −12.9107 −0.571134
512512 1.00000 0.0441942
513513 0 0
514514 −17.3509 −0.765313
515515 −6.68987 + 9.49197i −0.294791 + 0.418266i
516516 0 0
517517 10.4062i 0.457665i
518518 −5.01882 + 5.75604i −0.220514 + 0.252906i
519519 0 0
520520 −6.06585 + 8.60657i −0.266005 + 0.377423i
521521 −14.0992 −0.617698 −0.308849 0.951111i 0.599944π-0.599944\pi
−0.308849 + 0.951111i 0.599944π0.599944\pi
522522 0 0
523523 29.0802 1.27159 0.635794 0.771858i 0.280673π-0.280673\pi
0.635794 + 0.771858i 0.280673π0.280673\pi
524524 12.9999i 0.567905i
525525 0 0
526526 31.3436i 1.36665i
527527 4.09558i 0.178406i
528528 0 0
529529 −19.3298 −0.840427
530530 −2.04105 1.43851i −0.0886574 0.0624851i
531531 0 0
532532 −1.53393 −0.0665045
533533 21.0169 0.910344
534534 0 0
535535 −15.8273 11.1549i −0.684272 0.482270i
536536 4.21117i 0.181895i
537537 0 0
538538 −20.8503 −0.898918
539539 29.6587 1.27749
540540 0 0
541541 10.2446i 0.440450i 0.975449 + 0.220225i 0.0706791π0.0706791\pi
−0.975449 + 0.220225i 0.929321π0.929321\pi
542542 −0.977182 −0.0419736
543543 0 0
544544 −1.19309 −0.0511533
545545 −4.65481 3.28068i −0.199390 0.140529i
546546 0 0
547547 36.6360 1.56644 0.783220 0.621744i 0.213576π-0.213576\pi
0.783220 + 0.621744i 0.213576π0.213576\pi
548548 13.5487i 0.578772i
549549 0 0
550550 −9.19339 25.7495i −0.392008 1.09796i
551551 6.21674 0.264842
552552 0 0
553553 1.26415 0.0537573
554554 −28.0775 −1.19290
555555 0 0
556556 15.3257 0.649955
557557 3.19892 0.135543 0.0677714 0.997701i 0.478411π-0.478411\pi
0.0677714 + 0.997701i 0.478411π0.478411\pi
558558 0 0
559559 6.32264 0.267419
560560 2.29468 + 1.61728i 0.0969680 + 0.0683424i
561561 0 0
562562 20.9112i 0.882087i
563563 −43.0080 −1.81257 −0.906285 0.422668i 0.861094π-0.861094\pi
−0.906285 + 0.422668i 0.861094π0.861094\pi
564564 0 0
565565 −6.09024 + 8.64118i −0.256218 + 0.363537i
566566 −11.7273 −0.492936
567567 0 0
568568 12.4170 0.521007
569569 19.8692i 0.832960i −0.909145 0.416480i 0.863264π-0.863264\pi
0.909145 0.416480i 0.136736π-0.136736\pi
570570 0 0
571571 −16.6100 −0.695105 −0.347553 0.937660i 0.612987π-0.612987\pi
−0.347553 + 0.937660i 0.612987π0.612987\pi
572572 25.7495 1.07664
573573 0 0
574574 5.60353i 0.233887i
575575 3.22083 + 9.02113i 0.134318 + 0.376207i
576576 0 0
577577 −36.4851 −1.51890 −0.759448 0.650568i 0.774531π-0.774531\pi
−0.759448 + 0.650568i 0.774531π0.774531\pi
578578 −15.5765 −0.647898
579579 0 0
580580 −9.29991 6.55451i −0.386158 0.272161i
581581 0.947251 0.0392986
582582 0 0
583583 6.10649i 0.252905i
584584 10.2834i 0.425532i
585585 0 0
586586 19.0944i 0.788781i
587587 −14.3652 −0.592917 −0.296458 0.955046i 0.595806π-0.595806\pi
−0.296458 + 0.955046i 0.595806π0.595806\pi
588588 0 0
589589 −4.19411 −0.172815
590590 −16.4419 11.5881i −0.676901 0.477075i
591591 0 0
592592 −4.58473 3.99753i −0.188431 0.164297i
593593 19.6724i 0.807850i 0.914792 + 0.403925i 0.132354π0.132354\pi
−0.914792 + 0.403925i 0.867646π0.867646\pi
594594 0 0
595595 −2.73777 1.92956i −0.112237 0.0791041i
596596 −13.4684 −0.551686
597597 0 0
598598 −9.02113 −0.368901
599599 −32.9039 −1.34442 −0.672208 0.740362i 0.734654π-0.734654\pi
−0.672208 + 0.740362i 0.734654π0.734654\pi
600600 0 0
601601 43.6508 1.78055 0.890276 0.455422i 0.150512π-0.150512\pi
0.890276 + 0.455422i 0.150512π0.150512\pi
602602 1.68574i 0.0687057i
603603 0 0
604604 −10.3930 −0.422883
605605 −24.3493 + 34.5482i −0.989940 + 1.40458i
606606 0 0
607607 15.4852 0.628523 0.314262 0.949336i 0.398243π-0.398243\pi
0.314262 + 0.949336i 0.398243π0.398243\pi
608608 1.22179i 0.0495502i
609609 0 0
610610 11.3537 + 8.00200i 0.459698 + 0.323992i
611611 8.96104i 0.362525i
612612 0 0
613613 47.5322i 1.91981i 0.280329 + 0.959904i 0.409556π0.409556\pi
−0.280329 + 0.959904i 0.590444π0.590444\pi
614614 31.2854i 1.26258i
615615 0 0
616616 6.86533i 0.276612i
617617 31.3888i 1.26367i 0.775105 + 0.631833i 0.217697π0.217697\pi
−0.775105 + 0.631833i 0.782303π0.782303\pi
618618 0 0
619619 8.12905 0.326734 0.163367 0.986565i 0.447765π-0.447765\pi
0.163367 + 0.986565i 0.447765π0.447765\pi
620620 6.27415 + 4.42198i 0.251976 + 0.177591i
621621 0 0
622622 7.52409i 0.301688i
623623 14.4058 0.577155
624624 0 0
625625 −19.3470 + 15.8333i −0.773880 + 0.633332i
626626 −0.0900227 −0.00359803
627627 0 0
628628 14.2297i 0.567827i
629629 5.47000 + 4.76941i 0.218103 + 0.190169i
630630 0 0
631631 37.9315i 1.51003i −0.655709 0.755014i 0.727630π-0.727630\pi
0.655709 0.755014i 0.272370π-0.272370\pi
632632 1.00691i 0.0400527i
633633 0 0
634634 7.86659i 0.312422i
635635 −14.7145 10.3707i −0.583926 0.411547i
636636 0 0
637637 25.5399 1.01193
638638 27.8239i 1.10156i
639639 0 0
640640 −1.28817 + 1.82773i −0.0509195 + 0.0722475i
641641 36.9793 1.46059 0.730296 0.683130i 0.239382π-0.239382\pi
0.730296 + 0.683130i 0.239382π0.239382\pi
642642 0 0
643643 −8.44944 −0.333213 −0.166607 0.986023i 0.553281π-0.553281\pi
−0.166607 + 0.986023i 0.553281π0.553281\pi
644644 2.40521i 0.0947786i
645645 0 0
646646 1.45771i 0.0573527i
647647 −4.22924 −0.166269 −0.0831343 0.996538i 0.526493π-0.526493\pi
−0.0831343 + 0.996538i 0.526493π0.526493\pi
648648 0 0
649649 49.1915i 1.93093i
650650 −7.91665 22.1735i −0.310517 0.869716i
651651 0 0
652652 0.455364 0.0178334
653653 −40.2219 −1.57400 −0.787002 0.616951i 0.788368π-0.788368\pi
−0.787002 + 0.616951i 0.788368π0.788368\pi
654654 0 0
655655 −23.7604 16.7462i −0.928397 0.654327i
656656 4.46326 0.174261
657657 0 0
658658 −2.38919 −0.0931404
659659 −20.4172 −0.795341 −0.397670 0.917528i 0.630181π-0.630181\pi
−0.397670 + 0.917528i 0.630181π0.630181\pi
660660 0 0
661661 49.8075i 1.93729i −0.248454 0.968644i 0.579923π-0.579923\pi
0.248454 0.968644i 0.420077π-0.420077\pi
662662 21.5849i 0.838919i
663663 0 0
664664 0.754493i 0.0292800i
665665 1.97597 2.80362i 0.0766250 0.108720i
666666 0 0
667667 9.74786i 0.377439i
668668 −0.755752 −0.0292409
669669 0 0
670670 −7.69690 5.42472i −0.297357 0.209575i
671671 33.9685i 1.31134i
672672 0 0
673673 30.7799i 1.18648i 0.805026 + 0.593239i 0.202151π0.202151\pi
−0.805026 + 0.593239i 0.797849π0.797849\pi
674674 24.3782i 0.939013i
675675 0 0
676676 9.17350 0.352827
677677 36.8784i 1.41735i 0.705533 + 0.708677i 0.250708π0.250708\pi
−0.705533 + 0.708677i 0.749292π0.749292\pi
678678 0 0
679679 20.9431i 0.803723i
680680 1.53691 2.18065i 0.0589377 0.0836242i
681681 0 0
682682 18.7713i 0.718789i
683683 −22.1763 −0.848552 −0.424276 0.905533i 0.639471π-0.639471\pi
−0.424276 + 0.905533i 0.639471π0.639471\pi
684684 0 0
685685 24.7634 + 17.4531i 0.946161 + 0.666848i
686686 15.5978i 0.595527i
687687 0 0
688688 1.34271 0.0511902
689689 5.25844i 0.200331i
690690 0 0
691691 15.0935 0.574185 0.287093 0.957903i 0.407311π-0.407311\pi
0.287093 + 0.957903i 0.407311π0.407311\pi
692692 4.41375i 0.167786i
693693 0 0
694694 −25.4950 −0.967776
695695 −19.7422 + 28.0113i −0.748864 + 1.06253i
696696 0 0
697697 −5.32507 −0.201701
698698 2.69761 0.102106
699699 0 0
700700 −5.91190 + 2.11074i −0.223449 + 0.0797784i
701701 31.2390i 1.17988i −0.807447 0.589941i 0.799151π-0.799151\pi
0.807447 0.589941i 0.200849π-0.200849\pi
702702 0 0
703703 −4.88414 + 5.60159i −0.184209 + 0.211268i
704704 5.46829 0.206094
705705 0 0
706706 21.7179 0.817362
707707 4.09555i 0.154029i
708708 0 0
709709 23.2007i 0.871322i −0.900111 0.435661i 0.856515π-0.856515\pi
0.900111 0.435661i 0.143485π-0.143485\pi
710710 −15.9953 + 22.6950i −0.600293 + 0.851729i
711711 0 0
712712 11.4743i 0.430018i
713713 6.57636i 0.246287i
714714 0 0
715715 −33.1698 + 47.0632i −1.24048 + 1.76006i
716716 12.6883i 0.474184i
717717 0 0
718718 20.3716 0.760260
719719 −41.3863 −1.54345 −0.771724 0.635958i 0.780605π-0.780605\pi
−0.771724 + 0.635958i 0.780605π0.780605\pi
720720 0 0
721721 6.52009i 0.242821i
722722 17.5072 0.651552
723723 0 0
724724 13.2444 0.492223
725725 23.9598 8.55441i 0.889844 0.317703i
726726 0 0
727727 −8.02093 −0.297480 −0.148740 0.988876i 0.547522π-0.547522\pi
−0.148740 + 0.988876i 0.547522π0.547522\pi
728728 5.91190i 0.219110i
729729 0 0
730730 18.7954 + 13.2469i 0.695649 + 0.490288i
731731 −1.60197 −0.0592510
732732 0 0
733733 43.5044i 1.60687i 0.595391 + 0.803436i 0.296997π0.296997\pi
−0.595391 + 0.803436i 0.703003π0.703003\pi
734734 31.0972i 1.14782i
735735 0 0
736736 −1.91577 −0.0706163
737737 23.0279i 0.848244i
738738 0 0
739739 −40.4960 −1.48967 −0.744834 0.667249i 0.767472π-0.767472\pi
−0.744834 + 0.667249i 0.767472π0.767472\pi
740740 13.2123 3.23016i 0.485695 0.118743i
741741 0 0
742742 1.40201 0.0514692
743743 33.7617i 1.23860i 0.785156 + 0.619298i 0.212583π0.212583\pi
−0.785156 + 0.619298i 0.787417π0.787417\pi
744744 0 0
745745 17.3496 24.6166i 0.635640 0.901882i
746746 33.4131i 1.22334i
747747 0 0
748748 −6.52417 −0.238547
749749 10.8718 0.397248
750750 0 0
751751 −16.9597 −0.618867 −0.309434 0.950921i 0.600139π-0.600139\pi
−0.309434 + 0.950921i 0.600139π0.600139\pi
752752 1.90301i 0.0693956i
753753 0 0
754754 23.9598i 0.872564i
755755 13.3879 18.9956i 0.487237 0.691319i
756756 0 0
757757 10.2892 0.373969 0.186984 0.982363i 0.440129π-0.440129\pi
0.186984 + 0.982363i 0.440129π0.440129\pi
758758 −24.6191 −0.894204
759759 0 0
760760 2.23311 + 1.57388i 0.0810034 + 0.0570906i
761761 30.3977 1.10192 0.550959 0.834533i 0.314262π-0.314262\pi
0.550959 + 0.834533i 0.314262π0.314262\pi
762762 0 0
763763 3.19741 0.115754
764764 7.03990i 0.254695i
765765 0 0
766766 −17.5596 −0.634453
767767 42.3600i 1.52953i
768768 0 0
769769 46.4643i 1.67554i 0.546019 + 0.837772i 0.316142π0.316142\pi
−0.546019 + 0.837772i 0.683858π0.683858\pi
770770 12.5480 + 8.84373i 0.452198 + 0.318706i
771771 0 0
772772 −0.635749 −0.0228811
773773 30.6420i 1.10212i 0.834467 + 0.551058i 0.185776π0.185776\pi
−0.834467 + 0.551058i 0.814224π0.814224\pi
774774 0 0
775775 −16.1644 + 5.77121i −0.580642 + 0.207308i
776776 16.6814 0.598826
777777 0 0
778778 19.6417i 0.704190i
779779 5.45317i 0.195380i
780780 0 0
781781 67.8999 2.42965
782782 2.28569 0.0817361
783783 0 0
784784 5.42377 0.193706
785785 −26.0081 18.3303i −0.928270 0.654238i
786786 0 0
787787 8.65409i 0.308485i 0.988033 + 0.154243i 0.0492937π0.0492937\pi
−0.988033 + 0.154243i 0.950706π0.950706\pi
788788 5.18937i 0.184864i
789789 0 0
790790 −1.84036 1.29707i −0.0654772 0.0461478i
791791 5.93567i 0.211048i
792792 0 0
793793 29.2511i 1.03874i
794794 4.31480i 0.153127i
795795 0 0
796796 23.8852i 0.846589i
797797 25.1436 0.890634 0.445317 0.895373i 0.353091π-0.353091\pi
0.445317 + 0.895373i 0.353091π0.353091\pi
798798 0 0
799799 2.27046i 0.0803232i
800800 −1.68122 4.70887i −0.0594401 0.166484i
801801 0 0
802802 9.64980i 0.340746i
803803 56.2328i 1.98441i
804804 0 0
805805 −4.39609 3.09833i −0.154942 0.109202i
806806 16.1644i 0.569367i
807807 0 0
808808 −3.26214 −0.114762
809809 54.4206i 1.91333i −0.291199 0.956663i 0.594054π-0.594054\pi
0.291199 0.956663i 0.405946π-0.405946\pi
810810 0 0
811811 32.8378 1.15309 0.576546 0.817065i 0.304400π-0.304400\pi
0.576546 + 0.817065i 0.304400π0.304400\pi
812812 6.38816 0.224180
813813 0 0
814814 −25.0706 21.8596i −0.878726 0.766180i
815815 −0.586588 + 0.832284i −0.0205473 + 0.0291536i
816816 0 0
817817 1.64051i 0.0573941i
818818 25.5235i 0.892409i
819819 0 0
820820 −5.74945 + 8.15764i −0.200779 + 0.284877i
821821 −25.1041 −0.876138 −0.438069 0.898941i 0.644337π-0.644337\pi
−0.438069 + 0.898941i 0.644337π0.644337\pi
822822 0 0
823823 11.1202i 0.387627i 0.981038 + 0.193814i 0.0620857π0.0620857\pi
−0.981038 + 0.193814i 0.937914π0.937914\pi
824824 5.19330 0.180917
825825 0 0
826826 11.2940 0.392969
827827 −7.01483 −0.243930 −0.121965 0.992534i 0.538920π-0.538920\pi
−0.121965 + 0.992534i 0.538920π0.538920\pi
828828 0 0
829829 12.5028i 0.434240i −0.976145 0.217120i 0.930334π-0.930334\pi
0.976145 0.217120i 0.0696662π-0.0696662\pi
830830 −1.37901 0.971918i −0.0478662 0.0337358i
831831 0 0
832832 4.70887 0.163251
833833 −6.47105 −0.224209
834834 0 0
835835 0.973540 1.38131i 0.0336907 0.0478023i
836836 6.68111i 0.231071i
837837 0 0
838838 22.0969 0.763324
839839 −44.6267 −1.54069 −0.770343 0.637630i 0.779915π-0.779915\pi
−0.770343 + 0.637630i 0.779915π0.779915\pi
840840 0 0
841841 3.11004 0.107243
842842 8.20101i 0.282626i
843843 0 0
844844 −26.6260 −0.916505
845845 −11.8171 + 16.7667i −0.406519 + 0.576793i
846846 0 0
847847 23.7313i 0.815418i
848848 1.11671i 0.0383479i
849849 0 0
850850 2.00585 + 5.61812i 0.0688000 + 0.192700i
851851 8.78330 + 7.65835i 0.301088 + 0.262525i
852852 0 0
853853 3.59757 0.123178 0.0615892 0.998102i 0.480383π-0.480383\pi
0.0615892 + 0.998102i 0.480383π0.480383\pi
854854 −7.79891 −0.266873
855855 0 0
856856 8.65950i 0.295976i
857857 −7.66263 −0.261750 −0.130875 0.991399i 0.541779π-0.541779\pi
−0.130875 + 0.991399i 0.541779π0.541779\pi
858858 0 0
859859 56.3900i 1.92400i −0.273046 0.962001i 0.588031π-0.588031\pi
0.273046 0.962001i 0.411969π-0.411969\pi
860860 −1.72964 + 2.45411i −0.0589802 + 0.0836844i
861861 0 0
862862 9.83076i 0.334837i
863863 12.7800i 0.435037i −0.976056 0.217518i 0.930204π-0.930204\pi
0.976056 0.217518i 0.0697962π-0.0697962\pi
864864 0 0
865865 8.06716 + 5.68568i 0.274292 + 0.193319i
866866 1.61024i 0.0547182i
867867 0 0
868868 −4.30975 −0.146282
869869 5.50607i 0.186781i
870870 0 0
871871 19.8299i 0.671910i
872872 2.54677i 0.0862444i
873873 0 0
874874 2.34067i 0.0791744i
875875 3.75768 13.5244i 0.127033 0.457207i
876876 0 0
877877 40.4607i 1.36626i −0.730297 0.683130i 0.760618π-0.760618\pi
0.730297 0.683130i 0.239382π-0.239382\pi
878878 32.2443i 1.08819i
879879 0 0
880880 −7.04410 + 9.99458i −0.237457 + 0.336917i
881881 48.2664 1.62614 0.813069 0.582168i 0.197795π-0.197795\pi
0.813069 + 0.582168i 0.197795π0.197795\pi
882882 0 0
883883 −7.33442 −0.246823 −0.123411 0.992356i 0.539383π-0.539383\pi
−0.123411 + 0.992356i 0.539383π0.539383\pi
884884 −5.61812 −0.188958
885885 0 0
886886 19.0730i 0.640770i
887887 28.5353i 0.958120i −0.877782 0.479060i 0.840978π-0.840978\pi
0.877782 0.479060i 0.159022π-0.159022\pi
888888 0 0
889889 10.1075 0.338993
890890 −20.9720 14.7809i −0.702983 0.495457i
891891 0 0
892892 20.0982i 0.672938i
893893 −2.32508 −0.0778059
894894 0 0
895895 23.1908 + 16.3447i 0.775184 + 0.546344i
896896 1.25548i 0.0419426i
897897 0 0
898898 30.6914i 1.02418i
899899 17.4666 0.582543
900900 0 0
901901 1.33233i 0.0443865i
902902 24.4064 0.812643
903903 0 0
904904 4.72781 0.157245
905905 −17.0610 + 24.2072i −0.567128 + 0.804673i
906906 0 0
907907 −31.6207 −1.04995 −0.524974 0.851118i 0.675925π-0.675925\pi
−0.524974 + 0.851118i 0.675925π0.675925\pi
908908 −15.1621 −0.503173
909909 0 0
910910 10.8054 + 7.61555i 0.358195 + 0.252453i
911911 2.67057i 0.0884800i 0.999021 + 0.0442400i 0.0140866π0.0140866\pi
−0.999021 + 0.0442400i 0.985913π0.985913\pi
912912 0 0
913913 4.12579i 0.136544i
914914 22.4560 0.742777
915915 0 0
916916 −2.54527 −0.0840980
917917 16.3212 0.538972
918918 0 0
919919 40.0514i 1.32117i 0.750750 + 0.660587i 0.229692π0.229692\pi
−0.750750 + 0.660587i 0.770308π0.770308\pi
920920 2.46784 3.50152i 0.0813624 0.115442i
921921 0 0
922922 7.37800i 0.242981i
923923 58.4703 1.92457
924924 0 0
925925 −11.1159 + 28.3097i −0.365489 + 0.930816i
926926 −6.16145 −0.202478
927927 0 0
928928 5.08822i 0.167029i
929929 −47.8279 −1.56918 −0.784592 0.620013i 0.787127π-0.787127\pi
−0.784592 + 0.620013i 0.787127π0.787127\pi
930930 0 0
931931 6.62671i 0.217182i
932932 13.9212i 0.456004i
933933 0 0
934934 −5.37297 −0.175809
935935 8.40426 11.9244i 0.274849 0.389971i
936936 0 0
937937 44.7707i 1.46260i 0.682058 + 0.731298i 0.261085π0.261085\pi
−0.682058 + 0.731298i 0.738915π0.738915\pi
938938 5.28704 0.172628
939939 0 0
940940 3.47820 + 2.45141i 0.113446 + 0.0799561i
941941 −38.1052 −1.24219 −0.621097 0.783734i 0.713313π-0.713313\pi
−0.621097 + 0.783734i 0.713313π0.713313\pi
942942 0 0
943943 −8.55058 −0.278445
944944 8.99577i 0.292787i
945945 0 0
946946 7.34231 0.238719
947947 −53.7661 −1.74716 −0.873582 0.486678i 0.838209π-0.838209\pi
−0.873582 + 0.486678i 0.838209π0.838209\pi
948948 0 0
949949 48.4234i 1.57189i
950950 −5.75326 + 2.05410i −0.186660 + 0.0666438i
951951 0 0
952952 1.49790i 0.0485473i
953953 12.7882i 0.414252i −0.978314 0.207126i 0.933589π-0.933589\pi
0.978314 0.207126i 0.0664109π-0.0664109\pi
954954 0 0
955955 −12.8671 9.06861i −0.416368 0.293453i
956956 28.8753i 0.933895i
957957 0 0
958958 21.5810i 0.697251i
959959 −17.0101 −0.549286
960960 0 0
961961 19.2162 0.619878
962962 −21.5889 18.8239i −0.696055 0.606906i
963963 0 0
964964 6.84853i 0.220576i
965965 0.818954 1.16198i 0.0263631 0.0374054i
966966 0 0
967967 −49.4979 −1.59175 −0.795873 0.605463i 0.792988π-0.792988\pi
−0.795873 + 0.605463i 0.792988π0.792988\pi
968968 18.9022 0.607540
969969 0 0
970970 −21.4885 + 30.4891i −0.689954 + 0.978946i
971971 22.7751 0.730887 0.365444 0.930834i 0.380917π-0.380917\pi
0.365444 + 0.930834i 0.380917π0.380917\pi
972972 0 0
973973 19.2411i 0.616843i
974974 −0.346315 −0.0110967
975975 0 0
976976 6.21190i 0.198838i
977977 −7.08386 −0.226633 −0.113316 0.993559i 0.536147π-0.536147\pi
−0.113316 + 0.993559i 0.536147π0.536147\pi
978978 0 0
979979 62.7449i 2.00534i
980980 −6.98676 + 9.91321i −0.223184 + 0.316666i
981981 0 0
982982 −10.6278 −0.339146
983983 50.8277i 1.62115i −0.585634 0.810576i 0.699154π-0.699154\pi
0.585634 0.810576i 0.300846π-0.300846\pi
984984 0 0
985985 9.48478 + 6.68481i 0.302210 + 0.212996i
986986 6.07071i 0.193331i
987987 0 0
988988 5.75326i 0.183036i
989989 −2.57232 −0.0817949
990990 0 0
991991 42.8852i 1.36229i −0.732146 0.681147i 0.761481π-0.761481\pi
0.732146 0.681147i 0.238519π-0.238519\pi
992992 3.43275i 0.108990i
993993 0 0
994994 15.5893i 0.494464i
995995 −43.6558 30.7683i −1.38398 0.975421i
996996 0 0
997997 6.15244 0.194850 0.0974248 0.995243i 0.468939π-0.468939\pi
0.0974248 + 0.995243i 0.468939π0.468939\pi
998998 12.0121i 0.380237i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3330.2.e.f.739.6 16
3.2 odd 2 1110.2.e.c.739.14 yes 16
5.4 even 2 3330.2.e.e.739.12 16
15.14 odd 2 1110.2.e.d.739.3 yes 16
37.36 even 2 3330.2.e.e.739.11 16
111.110 odd 2 1110.2.e.d.739.11 yes 16
185.184 even 2 inner 3330.2.e.f.739.5 16
555.554 odd 2 1110.2.e.c.739.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.e.c.739.6 16 555.554 odd 2
1110.2.e.c.739.14 yes 16 3.2 odd 2
1110.2.e.d.739.3 yes 16 15.14 odd 2
1110.2.e.d.739.11 yes 16 111.110 odd 2
3330.2.e.e.739.11 16 37.36 even 2
3330.2.e.e.739.12 16 5.4 even 2
3330.2.e.f.739.5 16 185.184 even 2 inner
3330.2.e.f.739.6 16 1.1 even 1 trivial