Properties

Label 396.2.c.a.287.2
Level 396396
Weight 22
Character 396.287
Analytic conductor 3.1623.162
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [396,2,Mod(287,396)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(396, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("396.287");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 396=223211 396 = 2^{2} \cdot 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 396.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: 3.162075920043.16207592004
Analytic rank: 00
Dimension: 1010
Coefficient field: 10.0.5236158660608.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x84x7+3x6+8x5+6x416x316x2+32 x^{10} - 2x^{8} - 4x^{7} + 3x^{6} + 8x^{5} + 6x^{4} - 16x^{3} - 16x^{2} + 32 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 23 2^{3}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 287.2
Root 1.408570.126175i1.40857 - 0.126175i of defining polynomial
Character χ\chi == 396.287
Dual form 396.2.c.a.287.1

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+(1.40857+0.126175i)q2+(1.968160.355453i)q4+0.450958iq54.60354iq7+(2.72745+0.749014i)q8+(0.05689950.635207i)q101.00000q115.39122q13+(0.580851+6.48443i)q14+(3.747311.39918i)q165.39826iq17+4.38126iq19+(0.160294+0.887557i)q20+(1.408570.126175i)q226.03971q23+4.79664q25+(7.593930.680236i)q26+(1.636349.06050i)q283.31081iq294.57881iq31+(5.10182+2.44366i)q32+(0.681125+7.60385i)q34+2.07600q356.27205q37+(0.5528056.17133i)q38+(0.3377741.22996i)q4011.2722iq410.650922iq43+(1.96816+0.355453i)q44+(8.507380.762060i)q46+5.79062q4714.1926q49+(6.75642+0.605215i)q50+(10.6108+1.91633i)q521.46036iq530.450958iq55+(3.44812+12.5559i)q56+(0.417741+4.66353i)q58+4.71375q59+1.28023q61+(0.577730+6.44958i)q62+(6.877964.08580i)q642.43121iq656.54628iq67+(1.9188310.6246i)q68+(2.92420+0.261939i)q70+4.27806q71+9.86189q73+(8.834640.791374i)q74+(1.55733+8.62303i)q76+4.60354iq77+8.84129iq79+(0.630970+1.68988i)q80+(1.42227+15.8777i)q820.627004q83+2.43439q85+(0.0821299+0.916871i)q86+(2.727450.749014i)q88+10.6365iq89+24.8187iq91+(11.8871+2.14684i)q92+(8.15652+0.730631i)q941.97576q95+1.59931q97+(19.99131.79075i)q98+O(q100)q+(-1.40857 + 0.126175i) q^{2} +(1.96816 - 0.355453i) q^{4} +0.450958i q^{5} -4.60354i q^{7} +(-2.72745 + 0.749014i) q^{8} +(-0.0568995 - 0.635207i) q^{10} -1.00000 q^{11} -5.39122 q^{13} +(0.580851 + 6.48443i) q^{14} +(3.74731 - 1.39918i) q^{16} -5.39826i q^{17} +4.38126i q^{19} +(0.160294 + 0.887557i) q^{20} +(1.40857 - 0.126175i) q^{22} -6.03971 q^{23} +4.79664 q^{25} +(7.59393 - 0.680236i) q^{26} +(-1.63634 - 9.06050i) q^{28} -3.31081i q^{29} -4.57881i q^{31} +(-5.10182 + 2.44366i) q^{32} +(0.681125 + 7.60385i) q^{34} +2.07600 q^{35} -6.27205 q^{37} +(-0.552805 - 6.17133i) q^{38} +(-0.337774 - 1.22996i) q^{40} -11.2722i q^{41} -0.650922i q^{43} +(-1.96816 + 0.355453i) q^{44} +(8.50738 - 0.762060i) q^{46} +5.79062 q^{47} -14.1926 q^{49} +(-6.75642 + 0.605215i) q^{50} +(-10.6108 + 1.91633i) q^{52} -1.46036i q^{53} -0.450958i q^{55} +(3.44812 + 12.5559i) q^{56} +(0.417741 + 4.66353i) q^{58} +4.71375 q^{59} +1.28023 q^{61} +(0.577730 + 6.44958i) q^{62} +(6.87796 - 4.08580i) q^{64} -2.43121i q^{65} -6.54628i q^{67} +(-1.91883 - 10.6246i) q^{68} +(-2.92420 + 0.261939i) q^{70} +4.27806 q^{71} +9.86189 q^{73} +(8.83464 - 0.791374i) q^{74} +(1.55733 + 8.62303i) q^{76} +4.60354i q^{77} +8.84129i q^{79} +(0.630970 + 1.68988i) q^{80} +(1.42227 + 15.8777i) q^{82} -0.627004 q^{83} +2.43439 q^{85} +(0.0821299 + 0.916871i) q^{86} +(2.72745 - 0.749014i) q^{88} +10.6365i q^{89} +24.8187i q^{91} +(-11.8871 + 2.14684i) q^{92} +(-8.15652 + 0.730631i) q^{94} -1.97576 q^{95} +1.59931 q^{97} +(19.9913 - 1.79075i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+4q412q8+4q1010q11+8q13+8q144q1624q208q2310q25+16q26+16q28+8q34+16q354q37+32q384q44+20q46++60q98+O(q100) 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/396Z)×\left(\mathbb{Z}/396\mathbb{Z}\right)^\times.

nn 145145 199199 353353
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 −1.40857 + 0.126175i −0.996012 + 0.0892191i
33 0 0
44 1.96816 0.355453i 0.984080 0.177727i
55 0.450958i 0.201674i 0.994903 + 0.100837i 0.0321521π0.0321521\pi
−0.994903 + 0.100837i 0.967848π0.967848\pi
66 0 0
77 4.60354i 1.73997i −0.493074 0.869987i 0.664127π-0.664127\pi
0.493074 0.869987i 0.335873π-0.335873\pi
88 −2.72745 + 0.749014i −0.964299 + 0.264816i
99 0 0
1010 −0.0568995 0.635207i −0.0179932 0.200870i
1111 −1.00000 −0.301511
1212 0 0
1313 −5.39122 −1.49525 −0.747627 0.664118i 0.768807π-0.768807\pi
−0.747627 + 0.664118i 0.768807π0.768807\pi
1414 0.580851 + 6.48443i 0.155239 + 1.73304i
1515 0 0
1616 3.74731 1.39918i 0.936827 0.349794i
1717 5.39826i 1.30927i −0.755945 0.654635i 0.772822π-0.772822\pi
0.755945 0.654635i 0.227178π-0.227178\pi
1818 0 0
1919 4.38126i 1.00513i 0.864539 + 0.502565i 0.167610π0.167610\pi
−0.864539 + 0.502565i 0.832390π0.832390\pi
2020 0.160294 + 0.887557i 0.0358429 + 0.198464i
2121 0 0
2222 1.40857 0.126175i 0.300309 0.0269006i
2323 −6.03971 −1.25937 −0.629684 0.776852i 0.716816π-0.716816\pi
−0.629684 + 0.776852i 0.716816π0.716816\pi
2424 0 0
2525 4.79664 0.959327
2626 7.59393 0.680236i 1.48929 0.133405i
2727 0 0
2828 −1.63634 9.06050i −0.309240 1.71227i
2929 3.31081i 0.614803i −0.951580 0.307401i 0.900541π-0.900541\pi
0.951580 0.307401i 0.0994594π-0.0994594\pi
3030 0 0
3131 4.57881i 0.822378i −0.911550 0.411189i 0.865114π-0.865114\pi
0.911550 0.411189i 0.134886π-0.134886\pi
3232 −5.10182 + 2.44366i −0.901882 + 0.431982i
3333 0 0
3434 0.681125 + 7.60385i 0.116812 + 1.30405i
3535 2.07600 0.350908
3636 0 0
3737 −6.27205 −1.03112 −0.515559 0.856854i 0.672416π-0.672416\pi
−0.515559 + 0.856854i 0.672416π0.672416\pi
3838 −0.552805 6.17133i −0.0896769 1.00112i
3939 0 0
4040 −0.337774 1.22996i −0.0534067 0.194474i
4141 11.2722i 1.76042i −0.474580 0.880212i 0.657400π-0.657400\pi
0.474580 0.880212i 0.342600π-0.342600\pi
4242 0 0
4343 0.650922i 0.0992646i −0.998768 0.0496323i 0.984195π-0.984195\pi
0.998768 0.0496323i 0.0158049π-0.0158049\pi
4444 −1.96816 + 0.355453i −0.296711 + 0.0535866i
4545 0 0
4646 8.50738 0.762060i 1.25435 0.112360i
4747 5.79062 0.844649 0.422325 0.906445i 0.361214π-0.361214\pi
0.422325 + 0.906445i 0.361214π0.361214\pi
4848 0 0
4949 −14.1926 −2.02751
5050 −6.75642 + 0.605215i −0.955502 + 0.0855903i
5151 0 0
5252 −10.6108 + 1.91633i −1.47145 + 0.265746i
5353 1.46036i 0.200595i −0.994957 0.100298i 0.968020π-0.968020\pi
0.994957 0.100298i 0.0319795π-0.0319795\pi
5454 0 0
5555 0.450958i 0.0608071i
5656 3.44812 + 12.5559i 0.460774 + 1.67786i
5757 0 0
5858 0.417741 + 4.66353i 0.0548521 + 0.612351i
5959 4.71375 0.613678 0.306839 0.951761i 0.400729π-0.400729\pi
0.306839 + 0.951761i 0.400729π0.400729\pi
6060 0 0
6161 1.28023 0.163917 0.0819586 0.996636i 0.473882π-0.473882\pi
0.0819586 + 0.996636i 0.473882π0.473882\pi
6262 0.577730 + 6.44958i 0.0733718 + 0.819098i
6363 0 0
6464 6.87796 4.08580i 0.859744 0.510724i
6565 2.43121i 0.301555i
6666 0 0
6767 6.54628i 0.799756i −0.916568 0.399878i 0.869053π-0.869053\pi
0.916568 0.399878i 0.130947π-0.130947\pi
6868 −1.91883 10.6246i −0.232692 1.28843i
6969 0 0
7070 −2.92420 + 0.261939i −0.349509 + 0.0313077i
7171 4.27806 0.507712 0.253856 0.967242i 0.418301π-0.418301\pi
0.253856 + 0.967242i 0.418301π0.418301\pi
7272 0 0
7373 9.86189 1.15425 0.577124 0.816657i 0.304175π-0.304175\pi
0.577124 + 0.816657i 0.304175π0.304175\pi
7474 8.83464 0.791374i 1.02701 0.0919954i
7575 0 0
7676 1.55733 + 8.62303i 0.178638 + 0.989129i
7777 4.60354i 0.524622i
7878 0 0
7979 8.84129i 0.994723i 0.867543 + 0.497362i 0.165698π0.165698\pi
−0.867543 + 0.497362i 0.834302π0.834302\pi
8080 0.630970 + 1.68988i 0.0705446 + 0.188934i
8181 0 0
8282 1.42227 + 15.8777i 0.157063 + 1.75340i
8383 −0.627004 −0.0688226 −0.0344113 0.999408i 0.510956π-0.510956\pi
−0.0344113 + 0.999408i 0.510956π0.510956\pi
8484 0 0
8585 2.43439 0.264046
8686 0.0821299 + 0.916871i 0.00885630 + 0.0988688i
8787 0 0
8888 2.72745 0.749014i 0.290747 0.0798452i
8989 10.6365i 1.12747i 0.825957 + 0.563733i 0.190635π0.190635\pi
−0.825957 + 0.563733i 0.809365π0.809365\pi
9090 0 0
9191 24.8187i 2.60171i
9292 −11.8871 + 2.14684i −1.23932 + 0.223823i
9393 0 0
9494 −8.15652 + 0.730631i −0.841281 + 0.0753588i
9595 −1.97576 −0.202709
9696 0 0
9797 1.59931 0.162386 0.0811928 0.996698i 0.474127π-0.474127\pi
0.0811928 + 0.996698i 0.474127π0.474127\pi
9898 19.9913 1.79075i 2.01943 0.180893i
9999 0 0
100100 9.44055 1.70498i 0.944055 0.170498i
101101 5.90296i 0.587367i 0.955903 + 0.293683i 0.0948811π0.0948811\pi
−0.955903 + 0.293683i 0.905119π0.905119\pi
102102 0 0
103103 7.11963i 0.701518i 0.936466 + 0.350759i 0.114076π0.114076\pi
−0.936466 + 0.350759i 0.885924π0.885924\pi
104104 14.7043 4.03810i 1.44187 0.395968i
105105 0 0
106106 0.184260 + 2.05702i 0.0178969 + 0.199795i
107107 12.9205 1.24908 0.624538 0.780994i 0.285287π-0.285287\pi
0.624538 + 0.780994i 0.285287π0.285287\pi
108108 0 0
109109 −7.40196 −0.708980 −0.354490 0.935060i 0.615345π-0.615345\pi
−0.354490 + 0.935060i 0.615345π0.615345\pi
110110 0.0568995 + 0.635207i 0.00542516 + 0.0605646i
111111 0 0
112112 −6.44117 17.2509i −0.608633 1.63005i
113113 13.2201i 1.24365i 0.783158 + 0.621823i 0.213608π0.213608\pi
−0.783158 + 0.621823i 0.786392π0.786392\pi
114114 0 0
115115 2.72366i 0.253982i
116116 −1.17684 6.51621i −0.109267 0.605015i
117117 0 0
118118 −6.63967 + 0.594757i −0.611231 + 0.0547518i
119119 −24.8511 −2.27810
120120 0 0
121121 1.00000 0.0909091
122122 −1.80330 + 0.161533i −0.163263 + 0.0146245i
123123 0 0
124124 −1.62755 9.01182i −0.146158 0.809285i
125125 4.41787i 0.395146i
126126 0 0
127127 14.9079i 1.32286i −0.750008 0.661429i 0.769950π-0.769950\pi
0.750008 0.661429i 0.230050π-0.230050\pi
128128 −9.17258 + 6.62297i −0.810749 + 0.585393i
129129 0 0
130130 0.306758 + 3.42454i 0.0269044 + 0.300352i
131131 −5.69955 −0.497972 −0.248986 0.968507i 0.580097π-0.580097\pi
−0.248986 + 0.968507i 0.580097π0.580097\pi
132132 0 0
133133 20.1693 1.74890
134134 0.825976 + 9.22092i 0.0713535 + 0.796566i
135135 0 0
136136 4.04337 + 14.7235i 0.346716 + 1.26253i
137137 3.67780i 0.314215i −0.987581 0.157108i 0.949783π-0.949783\pi
0.987581 0.157108i 0.0502170π-0.0502170\pi
138138 0 0
139139 11.3998i 0.966917i 0.875367 + 0.483459i 0.160620π0.160620\pi
−0.875367 + 0.483459i 0.839380π0.839380\pi
140140 4.08590 0.737921i 0.345322 0.0623657i
141141 0 0
142142 −6.02596 + 0.539783i −0.505687 + 0.0452976i
143143 5.39122 0.450836
144144 0 0
145145 1.49304 0.123990
146146 −13.8912 + 1.24432i −1.14964 + 0.102981i
147147 0 0
148148 −12.3444 + 2.22942i −1.01470 + 0.183257i
149149 19.7575i 1.61860i −0.587397 0.809299i 0.699847π-0.699847\pi
0.587397 0.809299i 0.300153π-0.300153\pi
150150 0 0
151151 4.51126i 0.367121i −0.983008 0.183560i 0.941238π-0.941238\pi
0.983008 0.183560i 0.0587623π-0.0587623\pi
152152 −3.28163 11.9497i −0.266175 0.969247i
153153 0 0
154154 −0.580851 6.48443i −0.0468063 0.522530i
155155 2.06485 0.165853
156156 0 0
157157 −2.46466 −0.196701 −0.0983507 0.995152i 0.531357π-0.531357\pi
−0.0983507 + 0.995152i 0.531357π0.531357\pi
158158 −1.11555 12.4536i −0.0887483 0.990756i
159159 0 0
160160 −1.10199 2.30070i −0.0871197 0.181887i
161161 27.8041i 2.19127i
162162 0 0
163163 22.2074i 1.73941i −0.493568 0.869707i 0.664307π-0.664307\pi
0.493568 0.869707i 0.335693π-0.335693\pi
164164 −4.00674 22.1855i −0.312874 1.73240i
165165 0 0
166166 0.883181 0.0791121i 0.0685482 0.00614029i
167167 11.8748 0.918898 0.459449 0.888204i 0.348047π-0.348047\pi
0.459449 + 0.888204i 0.348047π0.348047\pi
168168 0 0
169169 16.0652 1.23579
170170 −3.42901 + 0.307158i −0.262993 + 0.0235580i
171171 0 0
172172 −0.231372 1.28112i −0.0176420 0.0976843i
173173 12.9026i 0.980968i 0.871450 + 0.490484i 0.163180π0.163180\pi
−0.871450 + 0.490484i 0.836820π0.836820\pi
174174 0 0
175175 22.0815i 1.66921i
176176 −3.74731 + 1.39918i −0.282464 + 0.105467i
177177 0 0
178178 −1.34206 14.9823i −0.100591 1.12297i
179179 14.2207 1.06290 0.531452 0.847088i 0.321647π-0.321647\pi
0.531452 + 0.847088i 0.321647π0.321647\pi
180180 0 0
181181 15.1818 1.12846 0.564229 0.825619i 0.309174π-0.309174\pi
0.564229 + 0.825619i 0.309174π0.309174\pi
182182 −3.13149 34.9590i −0.232122 2.59133i
183183 0 0
184184 16.4730 4.52383i 1.21441 0.333501i
185185 2.82843i 0.207950i
186186 0 0
187187 5.39826i 0.394760i
188188 11.3969 2.05830i 0.831202 0.150117i
189189 0 0
190190 2.78301 0.249292i 0.201901 0.0180855i
191191 −13.7056 −0.991700 −0.495850 0.868408i 0.665143π-0.665143\pi
−0.495850 + 0.868408i 0.665143π0.665143\pi
192192 0 0
193193 −15.7345 −1.13260 −0.566298 0.824200i 0.691625π-0.691625\pi
−0.566298 + 0.824200i 0.691625π0.691625\pi
194194 −2.25275 + 0.201793i −0.161738 + 0.0144879i
195195 0 0
196196 −27.9333 + 5.04480i −1.99523 + 0.360343i
197197 12.5112i 0.891386i −0.895186 0.445693i 0.852957π-0.852957\pi
0.895186 0.445693i 0.147043π-0.147043\pi
198198 0 0
199199 11.9736i 0.848783i −0.905479 0.424391i 0.860488π-0.860488\pi
0.905479 0.424391i 0.139512π-0.139512\pi
200200 −13.0826 + 3.59275i −0.925078 + 0.254046i
201201 0 0
202202 −0.744805 8.31476i −0.0524043 0.585024i
203203 −15.2415 −1.06974
204204 0 0
205205 5.08329 0.355033
206206 −0.898319 10.0285i −0.0625888 0.698721i
207207 0 0
208208 −20.2025 + 7.54327i −1.40079 + 0.523032i
209209 4.38126i 0.303058i
210210 0 0
211211 22.8088i 1.57022i 0.619354 + 0.785112i 0.287395π0.287395\pi
−0.619354 + 0.785112i 0.712605π0.712605\pi
212212 −0.519088 2.87421i −0.0356511 0.197402i
213213 0 0
214214 −18.1995 + 1.63025i −1.24409 + 0.111441i
215215 0.293538 0.0200191
216216 0 0
217217 −21.0787 −1.43092
218218 10.4262 0.933942i 0.706152 0.0632545i
219219 0 0
220220 −0.160294 0.887557i −0.0108070 0.0598391i
221221 29.1032i 1.95769i
222222 0 0
223223 7.05369i 0.472350i 0.971710 + 0.236175i 0.0758939π0.0758939\pi
−0.971710 + 0.236175i 0.924106π0.924106\pi
224224 11.2495 + 23.4864i 0.751638 + 1.56925i
225225 0 0
226226 −1.66805 18.6215i −0.110957 1.23869i
227227 −17.1425 −1.13779 −0.568894 0.822411i 0.692629π-0.692629\pi
−0.568894 + 0.822411i 0.692629π0.692629\pi
228228 0 0
229229 −0.206790 −0.0136650 −0.00683252 0.999977i 0.502175π-0.502175\pi
−0.00683252 + 0.999977i 0.502175π0.502175\pi
230230 0.343657 + 3.83647i 0.0226601 + 0.252969i
231231 0 0
232232 2.47985 + 9.03008i 0.162810 + 0.592854i
233233 7.61451i 0.498843i −0.968395 0.249421i 0.919760π-0.919760\pi
0.968395 0.249421i 0.0802404π-0.0802404\pi
234234 0 0
235235 2.61133i 0.170344i
236236 9.27742 1.67552i 0.603909 0.109067i
237237 0 0
238238 35.0046 3.13559i 2.26901 0.203250i
239239 −11.7859 −0.762366 −0.381183 0.924500i 0.624483π-0.624483\pi
−0.381183 + 0.924500i 0.624483π0.624483\pi
240240 0 0
241241 5.78630 0.372728 0.186364 0.982481i 0.440330π-0.440330\pi
0.186364 + 0.982481i 0.440330π0.440330\pi
242242 −1.40857 + 0.126175i −0.0905465 + 0.00811083i
243243 0 0
244244 2.51970 0.455063i 0.161308 0.0291324i
245245 6.40026i 0.408897i
246246 0 0
247247 23.6203i 1.50293i
248248 3.42959 + 12.4885i 0.217779 + 0.793018i
249249 0 0
250250 −0.557424 6.22289i −0.0352546 0.393570i
251251 22.0592 1.39237 0.696183 0.717865i 0.254880π-0.254880\pi
0.696183 + 0.717865i 0.254880π0.254880\pi
252252 0 0
253253 6.03971 0.379714
254254 1.88100 + 20.9988i 0.118024 + 1.31758i
255255 0 0
256256 12.0846 10.4863i 0.755288 0.655393i
257257 8.51467i 0.531130i 0.964093 + 0.265565i 0.0855586π0.0855586\pi
−0.964093 + 0.265565i 0.914441π0.914441\pi
258258 0 0
259259 28.8736i 1.79412i
260260 −0.864182 4.78501i −0.0535943 0.296754i
261261 0 0
262262 8.02824 0.719140i 0.495986 0.0444286i
263263 −5.07086 −0.312682 −0.156341 0.987703i 0.549970π-0.549970\pi
−0.156341 + 0.987703i 0.549970π0.549970\pi
264264 0 0
265265 0.658559 0.0404550
266266 −28.4100 + 2.54486i −1.74193 + 0.156035i
267267 0 0
268268 −2.32690 12.8841i −0.142138 0.787024i
269269 25.5790i 1.55958i −0.626040 0.779791i 0.715326π-0.715326\pi
0.626040 0.779791i 0.284674π-0.284674\pi
270270 0 0
271271 29.2394i 1.77617i −0.459682 0.888084i 0.652037π-0.652037\pi
0.459682 0.888084i 0.347963π-0.347963\pi
272272 −7.55312 20.2289i −0.457975 1.22656i
273273 0 0
274274 0.464045 + 5.18045i 0.0280340 + 0.312962i
275275 −4.79664 −0.289248
276276 0 0
277277 32.1011 1.92877 0.964383 0.264508i 0.0852097π-0.0852097\pi
0.964383 + 0.264508i 0.0852097π0.0852097\pi
278278 −1.43837 16.0574i −0.0862675 0.963061i
279279 0 0
280280 −5.66219 + 1.55495i −0.338381 + 0.0929263i
281281 19.4654i 1.16121i 0.814186 + 0.580604i 0.197183π0.197183\pi
−0.814186 + 0.580604i 0.802817π0.802817\pi
282282 0 0
283283 14.3357i 0.852169i 0.904683 + 0.426084i 0.140107π0.140107\pi
−0.904683 + 0.426084i 0.859893π0.859893\pi
284284 8.41990 1.52065i 0.499629 0.0902339i
285285 0 0
286286 −7.59393 + 0.680236i −0.449038 + 0.0402232i
287287 −51.8921 −3.06309
288288 0 0
289289 −12.1412 −0.714190
290290 −2.10305 + 0.188384i −0.123496 + 0.0110623i
291291 0 0
292292 19.4098 3.50544i 1.13587 0.205140i
293293 21.2956i 1.24410i 0.782976 + 0.622052i 0.213701π0.213701\pi
−0.782976 + 0.622052i 0.786299π0.786299\pi
294294 0 0
295295 2.12570i 0.123763i
296296 17.1067 4.69785i 0.994306 0.273057i
297297 0 0
298298 2.49290 + 27.8299i 0.144410 + 1.61214i
299299 32.5614 1.88308
300300 0 0
301301 −2.99654 −0.172718
302302 0.569207 + 6.35444i 0.0327542 + 0.365657i
303303 0 0
304304 6.13016 + 16.4179i 0.351589 + 0.941633i
305305 0.577331i 0.0330579i
306306 0 0
307307 2.34785i 0.133999i −0.997753 0.0669993i 0.978657π-0.978657\pi
0.997753 0.0669993i 0.0213425π-0.0213425\pi
308308 1.63634 + 9.06050i 0.0932393 + 0.516270i
309309 0 0
310310 −2.90849 + 0.260532i −0.165191 + 0.0147972i
311311 12.9742 0.735697 0.367848 0.929886i 0.380095π-0.380095\pi
0.367848 + 0.929886i 0.380095π0.380095\pi
312312 0 0
313313 8.66454 0.489749 0.244874 0.969555i 0.421253π-0.421253\pi
0.244874 + 0.969555i 0.421253π0.421253\pi
314314 3.47166 0.310978i 0.195917 0.0175495i
315315 0 0
316316 3.14267 + 17.4011i 0.176789 + 0.978887i
317317 7.51714i 0.422205i −0.977464 0.211102i 0.932295π-0.932295\pi
0.977464 0.211102i 0.0677053π-0.0677053\pi
318318 0 0
319319 3.31081i 0.185370i
320320 1.84252 + 3.10167i 0.103000 + 0.173388i
321321 0 0
322322 −3.50817 39.1641i −0.195503 2.18253i
323323 23.6512 1.31599
324324 0 0
325325 −25.8597 −1.43444
326326 2.80201 + 31.2807i 0.155189 + 1.73248i
327327 0 0
328328 8.44305 + 30.7444i 0.466189 + 1.69758i
329329 26.6574i 1.46967i
330330 0 0
331331 26.1423i 1.43691i −0.695572 0.718456i 0.744849π-0.744849\pi
0.695572 0.718456i 0.255151π-0.255151\pi
332332 −1.23404 + 0.222871i −0.0677270 + 0.0122316i
333333 0 0
334334 −16.7265 + 1.49830i −0.915234 + 0.0819833i
335335 2.95210 0.161290
336336 0 0
337337 7.72064 0.420570 0.210285 0.977640i 0.432561π-0.432561\pi
0.210285 + 0.977640i 0.432561π0.432561\pi
338338 −22.6291 + 2.02703i −1.23086 + 0.110256i
339339 0 0
340340 4.79126 0.865311i 0.259843 0.0469281i
341341 4.57881i 0.247956i
342342 0 0
343343 33.1114i 1.78785i
344344 0.487550 + 1.77536i 0.0262869 + 0.0957208i
345345 0 0
346346 −1.62799 18.1743i −0.0875211 0.977056i
347347 30.6201 1.64377 0.821886 0.569651i 0.192922π-0.192922\pi
0.821886 + 0.569651i 0.192922π0.192922\pi
348348 0 0
349349 −19.2853 −1.03232 −0.516161 0.856492i 0.672639π-0.672639\pi
−0.516161 + 0.856492i 0.672639π0.672639\pi
350350 2.78613 + 31.1034i 0.148925 + 1.66255i
351351 0 0
352352 5.10182 2.44366i 0.271928 0.130248i
353353 24.5083i 1.30444i −0.758028 0.652222i 0.773837π-0.773837\pi
0.758028 0.652222i 0.226163π-0.226163\pi
354354 0 0
355355 1.92922i 0.102393i
356356 3.78077 + 20.9343i 0.200381 + 1.10952i
357357 0 0
358358 −20.0309 + 1.79429i −1.05867 + 0.0948313i
359359 21.6374 1.14198 0.570990 0.820957i 0.306559π-0.306559\pi
0.570990 + 0.820957i 0.306559π0.306559\pi
360360 0 0
361361 −0.195476 −0.0102882
362362 −21.3847 + 1.91557i −1.12396 + 0.100680i
363363 0 0
364364 8.82188 + 48.8471i 0.462392 + 2.56029i
365365 4.44730i 0.232782i
366366 0 0
367367 11.3739i 0.593710i −0.954923 0.296855i 0.904062π-0.904062\pi
0.954923 0.296855i 0.0959379π-0.0959379\pi
368368 −22.6327 + 8.45063i −1.17981 + 0.440520i
369369 0 0
370370 0.356876 + 3.98405i 0.0185531 + 0.207121i
371371 −6.72281 −0.349031
372372 0 0
373373 −22.0678 −1.14263 −0.571313 0.820732i 0.693566π-0.693566\pi
−0.571313 + 0.820732i 0.693566π0.693566\pi
374374 −0.681125 7.60385i −0.0352201 0.393186i
375375 0 0
376376 −15.7936 + 4.33726i −0.814494 + 0.223677i
377377 17.8493i 0.919287i
378378 0 0
379379 11.5928i 0.595480i 0.954647 + 0.297740i 0.0962329π0.0962329\pi
−0.954647 + 0.297740i 0.903767π0.903767\pi
380380 −3.88862 + 0.702292i −0.199482 + 0.0360268i
381381 0 0
382382 19.3053 1.72930i 0.987745 0.0884785i
383383 −8.35063 −0.426697 −0.213349 0.976976i 0.568437π-0.568437\pi
−0.213349 + 0.976976i 0.568437π0.568437\pi
384384 0 0
385385 −2.07600 −0.105803
386386 22.1632 1.98530i 1.12808 0.101049i
387387 0 0
388388 3.14770 0.568481i 0.159800 0.0288602i
389389 21.1897i 1.07436i −0.843467 0.537181i 0.819489π-0.819489\pi
0.843467 0.537181i 0.180511π-0.180511\pi
390390 0 0
391391 32.6040i 1.64885i
392392 38.7096 10.6304i 1.95513 0.536919i
393393 0 0
394394 1.57860 + 17.6230i 0.0795287 + 0.887831i
395395 −3.98705 −0.200610
396396 0 0
397397 −5.63389 −0.282757 −0.141378 0.989956i 0.545153π-0.545153\pi
−0.141378 + 0.989956i 0.545153π0.545153\pi
398398 1.51076 + 16.8656i 0.0757276 + 0.845398i
399399 0 0
400400 17.9745 6.71134i 0.898723 0.335567i
401401 27.1670i 1.35665i −0.734761 0.678327i 0.762705π-0.762705\pi
0.734761 0.678327i 0.237295π-0.237295\pi
402402 0 0
403403 24.6853i 1.22966i
404404 2.09823 + 11.6180i 0.104391 + 0.578016i
405405 0 0
406406 21.4687 1.92309i 1.06548 0.0954413i
407407 6.27205 0.310894
408408 0 0
409409 −35.1236 −1.73675 −0.868374 0.495909i 0.834835π-0.834835\pi
−0.868374 + 0.495909i 0.834835π0.834835\pi
410410 −7.16019 + 0.641384i −0.353617 + 0.0316757i
411411 0 0
412412 2.53070 + 14.0126i 0.124678 + 0.690350i
413413 21.7000i 1.06778i
414414 0 0
415415 0.282752i 0.0138798i
416416 27.5050 13.1743i 1.34854 0.645923i
417417 0 0
418418 0.552805 + 6.17133i 0.0270386 + 0.301850i
419419 5.90419 0.288439 0.144219 0.989546i 0.453933π-0.453933\pi
0.144219 + 0.989546i 0.453933π0.453933\pi
420420 0 0
421421 −4.05579 −0.197667 −0.0988336 0.995104i 0.531511π-0.531511\pi
−0.0988336 + 0.995104i 0.531511π0.531511\pi
422422 −2.87790 32.1279i −0.140094 1.56396i
423423 0 0
424424 1.09383 + 3.98305i 0.0531210 + 0.193434i
425425 25.8935i 1.25602i
426426 0 0
427427 5.89361i 0.285212i
428428 25.4297 4.59265i 1.22919 0.221994i
429429 0 0
430430 −0.413470 + 0.0370371i −0.0199393 + 0.00178609i
431431 −12.5967 −0.606763 −0.303382 0.952869i 0.598116π-0.598116\pi
−0.303382 + 0.952869i 0.598116π0.598116\pi
432432 0 0
433433 7.12665 0.342485 0.171242 0.985229i 0.445222π-0.445222\pi
0.171242 + 0.985229i 0.445222π0.445222\pi
434434 29.6909 2.65960i 1.42521 0.127665i
435435 0 0
436436 −14.5682 + 2.63105i −0.697693 + 0.126004i
437437 26.4616i 1.26583i
438438 0 0
439439 14.7602i 0.704466i −0.935912 0.352233i 0.885422π-0.885422\pi
0.935912 0.352233i 0.114578π-0.114578\pi
440440 0.337774 + 1.22996i 0.0161027 + 0.0586362i
441441 0 0
442442 −3.67209 40.9940i −0.174664 1.94989i
443443 0.00946572 0.000449730 0.000224865 1.00000i 0.499928π-0.499928\pi
0.000224865 1.00000i 0.499928π0.499928\pi
444444 0 0
445445 −4.79661 −0.227381
446446 −0.889999 9.93565i −0.0421427 0.470467i
447447 0 0
448448 −18.8091 31.6629i −0.888648 1.49593i
449449 3.11056i 0.146796i 0.997303 + 0.0733982i 0.0233844π0.0233844\pi
−0.997303 + 0.0733982i 0.976616π0.976616\pi
450450 0 0
451451 11.2722i 0.530788i
452452 4.69914 + 26.0193i 0.221029 + 1.22385i
453453 0 0
454454 24.1465 2.16295i 1.13325 0.101512i
455455 −11.1922 −0.524697
456456 0 0
457457 7.09532 0.331905 0.165953 0.986134i 0.446930π-0.446930\pi
0.165953 + 0.986134i 0.446930π0.446930\pi
458458 0.291278 0.0260916i 0.0136105 0.00121918i
459459 0 0
460460 −0.968132 5.36059i −0.0451394 0.249939i
461461 30.5522i 1.42296i 0.702708 + 0.711478i 0.251974π0.251974\pi
−0.702708 + 0.711478i 0.748026π0.748026\pi
462462 0 0
463463 25.8995i 1.20365i −0.798628 0.601825i 0.794441π-0.794441\pi
0.798628 0.601825i 0.205559π-0.205559\pi
464464 −4.63241 12.4066i −0.215054 0.575963i
465465 0 0
466466 0.960759 + 10.7256i 0.0445063 + 0.496854i
467467 −30.1266 −1.39409 −0.697047 0.717026i 0.745503π-0.745503\pi
−0.697047 + 0.717026i 0.745503π0.745503\pi
468468 0 0
469469 −30.1361 −1.39156
470470 −0.329484 3.67825i −0.0151979 0.169665i
471471 0 0
472472 −12.8565 + 3.53067i −0.591769 + 0.162512i
473473 0.650922i 0.0299294i
474474 0 0
475475 21.0153i 0.964250i
476476 −48.9110 + 8.83341i −2.24183 + 0.404879i
477477 0 0
478478 16.6013 1.48708i 0.759326 0.0680176i
479479 35.2644 1.61127 0.805636 0.592411i 0.201824π-0.201824\pi
0.805636 + 0.592411i 0.201824π0.201824\pi
480480 0 0
481481 33.8140 1.54178
482482 −8.15043 + 0.730085i −0.371242 + 0.0332545i
483483 0 0
484484 1.96816 0.355453i 0.0894618 0.0161570i
485485 0.721223i 0.0327490i
486486 0 0
487487 8.15092i 0.369354i 0.982799 + 0.184677i 0.0591238π0.0591238\pi
−0.982799 + 0.184677i 0.940876π0.940876\pi
488488 −3.49177 + 0.958913i −0.158065 + 0.0434080i
489489 0 0
490490 0.807551 + 9.01523i 0.0364814 + 0.407267i
491491 −35.0295 −1.58086 −0.790430 0.612553i 0.790143π-0.790143\pi
−0.790430 + 0.612553i 0.790143π0.790143\pi
492492 0 0
493493 −17.8726 −0.804943
494494 2.98029 + 33.2710i 0.134090 + 1.49693i
495495 0 0
496496 −6.40656 17.1582i −0.287663 0.770425i
497497 19.6942i 0.883406i
498498 0 0
499499 25.0804i 1.12275i −0.827560 0.561377i 0.810272π-0.810272\pi
0.827560 0.561377i 0.189728π-0.189728\pi
500500 1.57035 + 8.69507i 0.0702280 + 0.388855i
501501 0 0
502502 −31.0720 + 2.78332i −1.38681 + 0.124226i
503503 18.9025 0.842820 0.421410 0.906870i 0.361535π-0.361535\pi
0.421410 + 0.906870i 0.361535π0.361535\pi
504504 0 0
505505 −2.66199 −0.118457
506506 −8.50738 + 0.762060i −0.378199 + 0.0338777i
507507 0 0
508508 −5.29904 29.3410i −0.235107 1.30180i
509509 10.9702i 0.486247i −0.969995 0.243124i 0.921828π-0.921828\pi
0.969995 0.243124i 0.0781720π-0.0781720\pi
510510 0 0
511511 45.3996i 2.00836i
512512 −15.6990 + 16.2955i −0.693802 + 0.720165i
513513 0 0
514514 −1.07434 11.9935i −0.0473870 0.529012i
515515 −3.21065 −0.141478
516516 0 0
517517 −5.79062 −0.254671
518518 −3.64312 40.6706i −0.160070 1.78696i
519519 0 0
520520 1.82101 + 6.63100i 0.0798566 + 0.290789i
521521 6.21862i 0.272443i −0.990678 0.136221i 0.956504π-0.956504\pi
0.990678 0.136221i 0.0434959π-0.0434959\pi
522522 0 0
523523 8.06214i 0.352533i 0.984343 + 0.176266i 0.0564020π0.0564020\pi
−0.984343 + 0.176266i 0.943598π0.943598\pi
524524 −11.2176 + 2.02592i −0.490044 + 0.0885029i
525525 0 0
526526 7.14268 0.639815i 0.311435 0.0278972i
527527 −24.7176 −1.07672
528528 0 0
529529 13.4782 0.586007
530530 −0.927629 + 0.0830936i −0.0402936 + 0.00360935i
531531 0 0
532532 39.6965 7.16925i 1.72106 0.310826i
533533 60.7710i 2.63228i
534534 0 0
535535 5.82662i 0.251907i
536536 4.90326 + 17.8547i 0.211789 + 0.771204i
537537 0 0
538538 3.22743 + 36.0300i 0.139144 + 1.55336i
539539 14.1926 0.611318
540540 0 0
541541 −15.5904 −0.670284 −0.335142 0.942168i 0.608784π-0.608784\pi
−0.335142 + 0.942168i 0.608784π0.608784\pi
542542 3.68928 + 41.1859i 0.158468 + 1.76908i
543543 0 0
544544 13.1915 + 27.5409i 0.565582 + 1.18081i
545545 3.33797i 0.142983i
546546 0 0
547547 35.1984i 1.50497i −0.658607 0.752487i 0.728854π-0.728854\pi
0.658607 0.752487i 0.271146π-0.271146\pi
548548 −1.30728 7.23849i −0.0558444 0.309213i
549549 0 0
550550 6.75642 0.605215i 0.288095 0.0258064i
551551 14.5055 0.617957
552552 0 0
553553 40.7013 1.73079
554554 −45.2167 + 4.05035i −1.92107 + 0.172083i
555555 0 0
556556 4.05209 + 22.4366i 0.171847 + 0.951524i
557557 34.1280i 1.44605i −0.690823 0.723024i 0.742752π-0.742752\pi
0.690823 0.723024i 0.257248π-0.257248\pi
558558 0 0
559559 3.50926i 0.148426i
560560 7.77942 2.90469i 0.328740 0.122746i
561561 0 0
562562 −2.45604 27.4184i −0.103602 1.15658i
563563 45.8757 1.93343 0.966716 0.255853i 0.0823562π-0.0823562\pi
0.966716 + 0.255853i 0.0823562π0.0823562\pi
564564 0 0
565565 −5.96172 −0.250812
566566 −1.80880 20.1929i −0.0760297 0.848770i
567567 0 0
568568 −11.6682 + 3.20433i −0.489586 + 0.134451i
569569 6.58959i 0.276250i 0.990415 + 0.138125i 0.0441075π0.0441075\pi
−0.990415 + 0.138125i 0.955892π0.955892\pi
570570 0 0
571571 4.44412i 0.185981i −0.995667 0.0929904i 0.970357π-0.970357\pi
0.995667 0.0929904i 0.0296426π-0.0296426\pi
572572 10.6108 1.91633i 0.443659 0.0801256i
573573 0 0
574574 73.0939 6.54748i 3.05088 0.273286i
575575 −28.9703 −1.20815
576576 0 0
577577 −26.8917 −1.11952 −0.559759 0.828656i 0.689106π-0.689106\pi
−0.559759 + 0.828656i 0.689106π0.689106\pi
578578 17.1018 1.53192i 0.711342 0.0637194i
579579 0 0
580580 2.93854 0.530705i 0.122016 0.0220363i
581581 2.88644i 0.119750i
582582 0 0
583583 1.46036i 0.0604818i
584584 −26.8978 + 7.38670i −1.11304 + 0.305664i
585585 0 0
586586 −2.68697 29.9965i −0.110998 1.23914i
587587 −18.6184 −0.768464 −0.384232 0.923237i 0.625534π-0.625534\pi
−0.384232 + 0.923237i 0.625534π0.625534\pi
588588 0 0
589589 20.0610 0.826597
590590 −0.268210 2.99421i −0.0110420 0.123270i
591591 0 0
592592 −23.5033 + 8.77570i −0.965979 + 0.360679i
593593 24.8200i 1.01924i 0.860401 + 0.509618i 0.170213π0.170213\pi
−0.860401 + 0.509618i 0.829787π0.829787\pi
594594 0 0
595595 11.2068i 0.459434i
596596 −7.02286 38.8859i −0.287668 1.59283i
597597 0 0
598598 −45.8652 + 4.10843i −1.87557 + 0.168006i
599599 −4.54608 −0.185748 −0.0928739 0.995678i 0.529605π-0.529605\pi
−0.0928739 + 0.995678i 0.529605π0.529605\pi
600600 0 0
601601 10.5497 0.430332 0.215166 0.976577i 0.430971π-0.430971\pi
0.215166 + 0.976577i 0.430971π0.430971\pi
602602 4.22085 0.378088i 0.172029 0.0154097i
603603 0 0
604604 −1.60354 8.87887i −0.0652471 0.361276i
605605 0.450958i 0.0183340i
606606 0 0
607607 4.75119i 0.192845i −0.995340 0.0964225i 0.969260π-0.969260\pi
0.995340 0.0964225i 0.0307400π-0.0307400\pi
608608 −10.7063 22.3524i −0.434199 0.906510i
609609 0 0
610610 −0.0728447 0.813214i −0.00294939 0.0329261i
611611 −31.2185 −1.26297
612612 0 0
613613 24.6283 0.994726 0.497363 0.867543i 0.334302π-0.334302\pi
0.497363 + 0.867543i 0.334302π0.334302\pi
614614 0.296239 + 3.30712i 0.0119552 + 0.133464i
615615 0 0
616616 −3.44812 12.5559i −0.138929 0.505893i
617617 14.0774i 0.566736i 0.959011 + 0.283368i 0.0914518π0.0914518\pi
−0.959011 + 0.283368i 0.908548π0.908548\pi
618618 0 0
619619 16.9924i 0.682980i 0.939885 + 0.341490i 0.110932π0.110932\pi
−0.939885 + 0.341490i 0.889068π0.889068\pi
620620 4.06395 0.733956i 0.163212 0.0294764i
621621 0 0
622622 −18.2751 + 1.63701i −0.732763 + 0.0656382i
623623 48.9655 1.96176
624624 0 0
625625 21.9909 0.879637
626626 −12.2046 + 1.09325i −0.487796 + 0.0436949i
627627 0 0
628628 −4.85085 + 0.876072i −0.193570 + 0.0349591i
629629 33.8581i 1.35001i
630630 0 0
631631 11.2451i 0.447659i 0.974628 + 0.223829i 0.0718558π0.0718558\pi
−0.974628 + 0.223829i 0.928144π0.928144\pi
632632 −6.62225 24.1142i −0.263419 0.959211i
633633 0 0
634634 0.948474 + 10.5884i 0.0376687 + 0.420521i
635635 6.72281 0.266787
636636 0 0
637637 76.5153 3.03165
638638 −0.417741 4.66353i −0.0165385 0.184631i
639639 0 0
640640 −2.98668 4.13645i −0.118059 0.163507i
641641 17.6143i 0.695722i −0.937546 0.347861i 0.886908π-0.886908\pi
0.937546 0.347861i 0.113092π-0.113092\pi
642642 0 0
643643 6.03887i 0.238150i −0.992885 0.119075i 0.962007π-0.962007\pi
0.992885 0.119075i 0.0379929π-0.0379929\pi
644644 9.88304 + 54.7229i 0.389446 + 2.15638i
645645 0 0
646646 −33.3145 + 2.98419i −1.31074 + 0.117411i
647647 −48.1430 −1.89270 −0.946349 0.323146i 0.895260π-0.895260\pi
−0.946349 + 0.323146i 0.895260π0.895260\pi
648648 0 0
649649 −4.71375 −0.185031
650650 36.4253 3.26285i 1.42872 0.127979i
651651 0 0
652652 −7.89368 43.7076i −0.309140 1.71172i
653653 20.5620i 0.804655i 0.915496 + 0.402328i 0.131799π0.131799\pi
−0.915496 + 0.402328i 0.868201π0.868201\pi
654654 0 0
655655 2.57026i 0.100428i
656656 −15.7718 42.2404i −0.615786 1.64921i
657657 0 0
658658 3.36349 + 37.5489i 0.131122 + 1.46381i
659659 −33.8196 −1.31742 −0.658712 0.752395i 0.728898π-0.728898\pi
−0.658712 + 0.752395i 0.728898π0.728898\pi
660660 0 0
661661 −18.7893 −0.730821 −0.365410 0.930847i 0.619071π-0.619071\pi
−0.365410 + 0.930847i 0.619071π0.619071\pi
662662 3.29850 + 36.8234i 0.128200 + 1.43118i
663663 0 0
664664 1.71012 0.469635i 0.0663656 0.0182254i
665665 9.09551i 0.352709i
666666 0 0
667667 19.9964i 0.774263i
668668 23.3715 4.22093i 0.904270 0.163313i
669669 0 0
670670 −4.15825 + 0.372480i −0.160647 + 0.0143902i
671671 −1.28023 −0.0494229
672672 0 0
673673 −10.8744 −0.419178 −0.209589 0.977790i 0.567213π-0.567213\pi
−0.209589 + 0.977790i 0.567213π0.567213\pi
674674 −10.8751 + 0.974150i −0.418893 + 0.0375228i
675675 0 0
676676 31.6189 5.71043i 1.21611 0.219632i
677677 49.5233i 1.90333i 0.307133 + 0.951667i 0.400630π0.400630\pi
−0.307133 + 0.951667i 0.599370π0.599370\pi
678678 0 0
679679 7.36250i 0.282547i
680680 −6.63967 + 1.82339i −0.254620 + 0.0699238i
681681 0 0
682682 −0.577730 6.44958i −0.0221224 0.246967i
683683 −8.75966 −0.335179 −0.167590 0.985857i 0.553598π-0.553598\pi
−0.167590 + 0.985857i 0.553598π0.553598\pi
684684 0 0
685685 1.65853 0.0633692
686686 −4.17782 46.6398i −0.159510 1.78072i
687687 0 0
688688 −0.910755 2.43920i −0.0347222 0.0929937i
689689 7.87310i 0.299941i
690690 0 0
691691 9.60042i 0.365217i −0.983186 0.182609i 0.941546π-0.941546\pi
0.983186 0.182609i 0.0584541π-0.0584541\pi
692692 4.58628 + 25.3944i 0.174344 + 0.965351i
693693 0 0
694694 −43.1307 + 3.86349i −1.63722 + 0.146656i
695695 −5.14082 −0.195002
696696 0 0
697697 −60.8504 −2.30487
698698 27.1648 2.43333i 1.02820 0.0921027i
699699 0 0
700700 −7.84894 43.4600i −0.296662 1.64263i
701701 28.5860i 1.07968i −0.841769 0.539839i 0.818485π-0.818485\pi
0.841769 0.539839i 0.181515π-0.181515\pi
702702 0 0
703703 27.4795i 1.03641i
704704 −6.87796 + 4.08580i −0.259223 + 0.153989i
705705 0 0
706706 3.09233 + 34.5217i 0.116381 + 1.29924i
707707 27.1745 1.02200
708708 0 0
709709 −6.19988 −0.232841 −0.116421 0.993200i 0.537142π-0.537142\pi
−0.116421 + 0.993200i 0.537142π0.537142\pi
710710 −0.243419 2.71745i −0.00913537 0.101984i
711711 0 0
712712 −7.96688 29.0105i −0.298572 1.08721i
713713 27.6547i 1.03568i
714714 0 0
715715 2.43121i 0.0909221i
716716 27.9886 5.05479i 1.04598 0.188906i
717717 0 0
718718 −30.4779 + 2.73010i −1.13743 + 0.101886i
719719 −16.1753 −0.603238 −0.301619 0.953428i 0.597527π-0.597527\pi
−0.301619 + 0.953428i 0.597527π0.597527\pi
720720 0 0
721721 32.7755 1.22062
722722 0.275342 0.0246641i 0.0102472 0.000917903i
723723 0 0
724724 29.8803 5.39643i 1.11049 0.200557i
725725 15.8808i 0.589797i
726726 0 0
727727 14.8038i 0.549042i 0.961581 + 0.274521i 0.0885193π0.0885193\pi
−0.961581 + 0.274521i 0.911481π0.911481\pi
728728 −18.5895 67.6917i −0.688975 2.50882i
729729 0 0
730730 −0.561137 6.26434i −0.0207686 0.231854i
731731 −3.51385 −0.129964
732732 0 0
733733 4.58421 0.169322 0.0846609 0.996410i 0.473019π-0.473019\pi
0.0846609 + 0.996410i 0.473019π0.473019\pi
734734 1.43509 + 16.0209i 0.0529703 + 0.591343i
735735 0 0
736736 30.8135 14.7590i 1.13580 0.544024i
737737 6.54628i 0.241135i
738738 0 0
739739 1.28355i 0.0472163i −0.999721 0.0236081i 0.992485π-0.992485\pi
0.999721 0.0236081i 0.00751540π-0.00751540\pi
740740 −1.00537 5.56680i −0.0369583 0.204640i
741741 0 0
742742 9.46957 0.848249i 0.347639 0.0311402i
743743 −23.9767 −0.879620 −0.439810 0.898091i 0.644954π-0.644954\pi
−0.439810 + 0.898091i 0.644954π0.644954\pi
744744 0 0
745745 8.90980 0.326430
746746 31.0841 2.78440i 1.13807 0.101944i
747747 0 0
748748 1.91883 + 10.6246i 0.0701593 + 0.388475i
749749 59.4802i 2.17336i
750750 0 0
751751 37.2322i 1.35862i 0.733850 + 0.679312i 0.237722π0.237722\pi
−0.733850 + 0.679312i 0.762278π0.762278\pi
752752 21.6992 8.10211i 0.791290 0.295453i
753753 0 0
754754 −2.25213 25.1421i −0.0820179 0.915621i
755755 2.03439 0.0740389
756756 0 0
757757 33.0955 1.20288 0.601438 0.798919i 0.294595π-0.294595\pi
0.601438 + 0.798919i 0.294595π0.294595\pi
758758 −1.46272 16.3293i −0.0531282 0.593106i
759759 0 0
760760 5.38880 1.47988i 0.195472 0.0536807i
761761 14.2090i 0.515077i 0.966268 + 0.257538i 0.0829114π0.0829114\pi
−0.966268 + 0.257538i 0.917089π0.917089\pi
762762 0 0
763763 34.0752i 1.23361i
764764 −26.9747 + 4.87169i −0.975912 + 0.176251i
765765 0 0
766766 11.7625 1.05364i 0.424996 0.0380696i
767767 −25.4129 −0.917605
768768 0 0
769769 −29.1166 −1.04997 −0.524985 0.851111i 0.675929π-0.675929\pi
−0.524985 + 0.851111i 0.675929π0.675929\pi
770770 2.92420 0.261939i 0.105381 0.00943963i
771771 0 0
772772 −30.9681 + 5.59289i −1.11457 + 0.201292i
773773 6.64019i 0.238831i −0.992844 0.119416i 0.961898π-0.961898\pi
0.992844 0.119416i 0.0381021π-0.0381021\pi
774774 0 0
775775 21.9629i 0.788929i
776776 −4.36205 + 1.19791i −0.156588 + 0.0430024i
777777 0 0
778778 2.67361 + 29.8473i 0.0958537 + 1.07008i
779779 49.3866 1.76946
780780 0 0
781781 −4.27806 −0.153081
782782 −4.11380 45.9251i −0.147109 1.64228i
783783 0 0
784784 −53.1840 + 19.8579i −1.89943 + 0.709212i
785785 1.11146i 0.0396696i
786786 0 0
787787 5.12622i 0.182730i −0.995817 0.0913651i 0.970877π-0.970877\pi
0.995817 0.0913651i 0.0291230π-0.0291230\pi
788788 −4.44715 24.6240i −0.158423 0.877195i
789789 0 0
790790 5.61605 0.503065i 0.199810 0.0178983i
791791 60.8594 2.16391
792792 0 0
793793 −6.90202 −0.245098
794794 7.93574 0.710855i 0.281629 0.0252273i
795795 0 0
796796 −4.25604 23.5659i −0.150851 0.835270i
797797 25.6924i 0.910072i 0.890473 + 0.455036i 0.150374π0.150374\pi
−0.890473 + 0.455036i 0.849626π0.849626\pi
798798 0 0
799799 31.2593i 1.10587i
800800 −24.4716 + 11.7213i −0.865200 + 0.414412i
801801 0 0
802802 3.42779 + 38.2667i 0.121039 + 1.35124i
803803 −9.86189 −0.348019
804804 0 0
805805 −12.5385 −0.441923
806806 −3.11467 34.7711i −0.109709 1.22476i
807807 0 0
808808 −4.42140 16.1000i −0.155544 0.566397i
809809 11.1617i 0.392424i 0.980561 + 0.196212i 0.0628641π0.0628641\pi
−0.980561 + 0.196212i 0.937136π0.937136\pi
810810 0 0
811811 25.6391i 0.900309i 0.892951 + 0.450154i 0.148631π0.148631\pi
−0.892951 + 0.450154i 0.851369π0.851369\pi
812812 −29.9976 + 5.41763i −1.05271 + 0.190121i
813813 0 0
814814 −8.83464 + 0.791374i −0.309654 + 0.0277377i
815815 10.0146 0.350795
816816 0 0
817817 2.85186 0.0997739
818818 49.4741 4.43171i 1.72982 0.154951i
819819 0 0
820820 10.0047 1.80687i 0.349380 0.0630987i
821821 32.3388i 1.12863i −0.825559 0.564316i 0.809140π-0.809140\pi
0.825559 0.564316i 0.190860π-0.190860\pi
822822 0 0
823823 10.1239i 0.352896i 0.984310 + 0.176448i 0.0564607π0.0564607\pi
−0.984310 + 0.176448i 0.943539π0.943539\pi
824824 −5.33271 19.4184i −0.185774 0.676473i
825825 0 0
826826 2.73799 + 30.5660i 0.0952668 + 1.06353i
827827 5.77199 0.200712 0.100356 0.994952i 0.468002π-0.468002\pi
0.100356 + 0.994952i 0.468002π0.468002\pi
828828 0 0
829829 46.2848 1.60754 0.803769 0.594942i 0.202825π-0.202825\pi
0.803769 + 0.594942i 0.202825π0.202825\pi
830830 0.0356762 + 0.398277i 0.00123834 + 0.0138244i
831831 0 0
832832 −37.0806 + 22.0274i −1.28554 + 0.763663i
833833 76.6153i 2.65456i
834834 0 0
835835 5.35503i 0.185318i
836836 −1.55733 8.62303i −0.0538615 0.298234i
837837 0 0
838838 −8.31649 + 0.744961i −0.287288 + 0.0257342i
839839 48.0233 1.65795 0.828975 0.559286i 0.188925π-0.188925\pi
0.828975 + 0.559286i 0.188925π0.188925\pi
840840 0 0
841841 18.0385 0.622018
842842 5.71288 0.511739i 0.196879 0.0176357i
843843 0 0
844844 8.10746 + 44.8914i 0.279070 + 1.54523i
845845 7.24474i 0.249227i
846846 0 0
847847 4.60354i 0.158180i
848848 −2.04330 5.47240i −0.0701671 0.187923i
849849 0 0
850850 3.26711 + 36.4729i 0.112061 + 1.25101i
851851 37.8814 1.29856
852852 0 0
853853 33.6945 1.15368 0.576839 0.816858i 0.304286π-0.304286\pi
0.576839 + 0.816858i 0.304286π0.304286\pi
854854 0.743625 + 8.30158i 0.0254463 + 0.284074i
855855 0 0
856856 −35.2401 + 9.67767i −1.20448 + 0.330776i
857857 27.0979i 0.925646i 0.886451 + 0.462823i 0.153164π0.153164\pi
−0.886451 + 0.462823i 0.846836π0.846836\pi
858858 0 0
859859 3.07528i 0.104927i 0.998623 + 0.0524636i 0.0167073π0.0167073\pi
−0.998623 + 0.0524636i 0.983293π0.983293\pi
860860 0.577730 0.104339i 0.0197004 0.00355793i
861861 0 0
862862 17.7434 1.58939i 0.604343 0.0541348i
863863 −4.36829 −0.148698 −0.0743492 0.997232i 0.523688π-0.523688\pi
−0.0743492 + 0.997232i 0.523688π0.523688\pi
864864 0 0
865865 −5.81854 −0.197836
866866 −10.0384 + 0.899204i −0.341119 + 0.0305562i
867867 0 0
868868 −41.4863 + 7.49249i −1.40814 + 0.254312i
869869 8.84129i 0.299920i
870870 0 0
871871 35.2924i 1.19584i
872872 20.1885 5.54418i 0.683668 0.187749i
873873 0 0
874874 3.33879 + 37.2731i 0.112936 + 1.26078i
875875 20.3378 0.687544
876876 0 0
877877 5.50220 0.185796 0.0928981 0.995676i 0.470387π-0.470387\pi
0.0928981 + 0.995676i 0.470387π0.470387\pi
878878 1.86237 + 20.7908i 0.0628518 + 0.701656i
879879 0 0
880880 −0.630970 1.68988i −0.0212700 0.0569657i
881881 24.1682i 0.814247i −0.913373 0.407124i 0.866532π-0.866532\pi
0.913373 0.407124i 0.133468π-0.133468\pi
882882 0 0
883883 51.0030i 1.71639i −0.513326 0.858194i 0.671587π-0.671587\pi
0.513326 0.858194i 0.328413π-0.328413\pi
884884 10.3448 + 57.2798i 0.347934 + 1.92653i
885885 0 0
886886 −0.0133332 + 0.00119434i −0.000447936 + 4.01245e-5i
887887 −27.1324 −0.911015 −0.455508 0.890232i 0.650542π-0.650542\pi
−0.455508 + 0.890232i 0.650542π0.650542\pi
888888 0 0
889889 −68.6289 −2.30174
890890 6.75638 0.605211i 0.226474 0.0202867i
891891 0 0
892892 2.50726 + 13.8828i 0.0839492 + 0.464830i
893893 25.3703i 0.848983i
894894 0 0
895895 6.41293i 0.214361i
896896 30.4891 + 42.2264i 1.01857 + 1.41068i
897897 0 0
898898 −0.392475 4.38145i −0.0130970 0.146211i
899899 −15.1596 −0.505600
900900 0 0
901901 −7.88339 −0.262634
902902 −1.42227 15.8777i −0.0473564 0.528671i
903903 0 0
904904 −9.90207 36.0572i −0.329338 1.19925i
905905 6.84637i 0.227581i
906906 0 0
907907 53.1849i 1.76598i 0.469396 + 0.882988i 0.344472π0.344472\pi
−0.469396 + 0.882988i 0.655528π0.655528\pi
908908 −33.7392 + 6.09336i −1.11967 + 0.202215i
909909 0 0
910910 15.7650 1.41217i 0.522605 0.0468130i
911911 29.2194 0.968082 0.484041 0.875045i 0.339169π-0.339169\pi
0.484041 + 0.875045i 0.339169π0.339169\pi
912912 0 0
913913 0.627004 0.0207508
914914 −9.99428 + 0.895251i −0.330581 + 0.0296123i
915915 0 0
916916 −0.406995 + 0.0735040i −0.0134475 + 0.00242864i
917917 26.2381i 0.866459i
918918 0 0
919919 37.4675i 1.23594i 0.786202 + 0.617969i 0.212044π0.212044\pi
−0.786202 + 0.617969i 0.787956π0.787956\pi
920920 2.04006 + 7.42863i 0.0672587 + 0.244915i
921921 0 0
922922 −3.85492 43.0350i −0.126955 1.41728i
923923 −23.0639 −0.759159
924924 0 0
925925 −30.0847 −0.989180
926926 3.26786 + 36.4813i 0.107389 + 1.19885i
927927 0 0
928928 8.09050 + 16.8912i 0.265584 + 0.554480i
929929 7.31585i 0.240025i −0.992772 0.120013i 0.961706π-0.961706\pi
0.992772 0.120013i 0.0382935π-0.0382935\pi
930930 0 0
931931 62.1815i 2.03792i
932932 −2.70660 14.9866i −0.0886576 0.490901i
933933 0 0
934934 42.4356 3.80122i 1.38853 0.124380i
935935 −2.43439 −0.0796130
936936 0 0
937937 35.3106 1.15355 0.576774 0.816904i 0.304311π-0.304311\pi
0.576774 + 0.816904i 0.304311π0.304311\pi
938938 42.4489 3.80242i 1.38601 0.124153i
939939 0 0
940940 0.928204 + 5.13951i 0.0302747 + 0.167632i
941941 3.59895i 0.117323i 0.998278 + 0.0586613i 0.0186832π0.0186832\pi
−0.998278 + 0.0586613i 0.981317π0.981317\pi
942942 0 0
943943 68.0810i 2.21702i
944944 17.6639 6.59537i 0.574910 0.214661i
945945 0 0
946946 −0.0821299 0.916871i −0.00267027 0.0298101i
947947 −43.7091 −1.42036 −0.710178 0.704022i 0.751386π-0.751386\pi
−0.710178 + 0.704022i 0.751386π0.751386\pi
948948 0 0
949949 −53.1676 −1.72589
950950 −2.65161 29.6016i −0.0860295 0.960404i
951951 0 0
952952 67.7802 18.6138i 2.19677 0.603278i
953953 7.81428i 0.253129i 0.991958 + 0.126565i 0.0403951π0.0403951\pi
−0.991958 + 0.126565i 0.959605π0.959605\pi
954954 0 0
955955 6.18063i 0.200000i
956956 −23.1965 + 4.18933i −0.750229 + 0.135493i
957957 0 0
958958 −49.6725 + 4.44948i −1.60485 + 0.143756i
959959 −16.9309 −0.546727
960960 0 0
961961 10.0345 0.323695
962962 −47.6295 + 4.26647i −1.53564 + 0.137557i
963963 0 0
964964 11.3884 2.05676i 0.366794 0.0662437i
965965 7.09561i 0.228416i
966966 0 0
967967 40.7961i 1.31191i 0.754798 + 0.655957i 0.227735π0.227735\pi
−0.754798 + 0.655957i 0.772265π0.772265\pi
968968 −2.72745 + 0.749014i −0.0876635 + 0.0240742i
969969 0 0
970970 −0.0910001 1.01590i −0.00292184 0.0326184i
971971 −17.8775 −0.573717 −0.286859 0.957973i 0.592611π-0.592611\pi
−0.286859 + 0.957973i 0.592611π0.592611\pi
972972 0 0
973973 52.4794 1.68241
974974 −1.02844 11.4812i −0.0329534 0.367881i
975975 0 0
976976 4.79743 1.79127i 0.153562 0.0573373i
977977 26.9702i 0.862854i −0.902148 0.431427i 0.858010π-0.858010\pi
0.902148 0.431427i 0.141990π-0.141990\pi
978978 0 0
979979 10.6365i 0.339944i
980980 −2.27499 12.5967i −0.0726719 0.402388i
981981 0 0
982982 49.3416 4.41984i 1.57455 0.141043i
983983 21.5536 0.687452 0.343726 0.939070i 0.388311π-0.388311\pi
0.343726 + 0.939070i 0.388311π0.388311\pi
984984 0 0
985985 5.64202 0.179770
986986 25.1749 2.25508i 0.801733 0.0718163i
987987 0 0
988988 −8.39593 46.4886i −0.267110 1.47900i
989989 3.93138i 0.125011i
990990 0 0
991991 0.996115i 0.0316426i −0.999875 0.0158213i 0.994964π-0.994964\pi
0.999875 0.0158213i 0.00503629π-0.00503629\pi
992992 11.1890 + 23.3602i 0.355252 + 0.741688i
993993 0 0
994994 2.48491 + 27.7408i 0.0788167 + 0.879883i
995995 5.39957 0.171178
996996 0 0
997997 −17.8333 −0.564787 −0.282394 0.959299i 0.591128π-0.591128\pi
−0.282394 + 0.959299i 0.591128π0.591128\pi
998998 3.16452 + 35.3276i 0.100171 + 1.11828i
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 396.2.c.a.287.2 yes 10
3.2 odd 2 396.2.c.b.287.9 yes 10
4.3 odd 2 396.2.c.b.287.10 yes 10
8.3 odd 2 6336.2.d.g.3455.5 10
8.5 even 2 6336.2.d.h.3455.5 10
12.11 even 2 inner 396.2.c.a.287.1 10
24.5 odd 2 6336.2.d.g.3455.6 10
24.11 even 2 6336.2.d.h.3455.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
396.2.c.a.287.1 10 12.11 even 2 inner
396.2.c.a.287.2 yes 10 1.1 even 1 trivial
396.2.c.b.287.9 yes 10 3.2 odd 2
396.2.c.b.287.10 yes 10 4.3 odd 2
6336.2.d.g.3455.5 10 8.3 odd 2
6336.2.d.g.3455.6 10 24.5 odd 2
6336.2.d.h.3455.5 10 8.5 even 2
6336.2.d.h.3455.6 10 24.11 even 2