Properties

Label 1008.2.v.e.323.2
Level 10081008
Weight 22
Character 1008.323
Analytic conductor 8.0498.049
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(323,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1008=24327 1008 = 2^{4} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1008.v (of order 44, degree 22, 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: 8.048920523758.04892052375
Analytic rank: 00
Dimension: 4040
Relative dimension: 2020 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 323.2
Character χ\chi == 1008.323
Dual form 1008.2.v.e.827.2

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+(1.39680+0.221233i)q2+(1.902110.618037i)q4+(2.515042.51504i)q5+1.00000q7+(2.52014+1.28408i)q8+(4.06942+2.95660i)q10+(0.984548+0.984548i)q11+(3.260863.26086i)q13+(1.39680+0.221233i)q14+(3.236062.35115i)q16+5.50927iq17+(1.21444+1.21444i)q19+(6.338263.22950i)q20+(1.157401.59303i)q228.62021iq23+7.65081iq25+(5.27618+3.83336i)q26+(1.902110.618037i)q28+(2.04663+2.04663i)q29+0.164437iq31+(3.99999+4.00001i)q32+(1.218837.69536i)q34+(2.515042.51504i)q35+(8.31105+8.31105i)q37+(1.427661.96501i)q38+(9.56777+3.10874i)q40+9.56578q41+(5.01867+5.01867i)q43+(1.26423+2.48121i)q44+(1.90707+12.0407i)q46+3.37837q47+1.00000q49+(1.6926110.6867i)q50+(8.217844.18719i)q52+(3.72717+3.72717i)q53+4.95235q55+(2.52014+1.28408i)q56+(2.405963.31153i)q58+(10.0781+10.0781i)q59+(1.070421.07042i)q61+(0.03637880.229686i)q62+(4.702266.47216i)q64+16.4023iq65+(3.12073+3.12073i)q67+(3.40493+10.4793i)q68+(4.06942+2.95660i)q70+7.66257iq718.40588iq73+(9.7702113.4476i)q74+(1.55944+3.06058i)q76+(0.984548+0.984548i)q77+13.8712iq79+(14.05202.22559i)q80+(13.3615+2.11626i)q82+(7.312147.31214i)q83+(13.856013.8560i)q85+(8.120385.89979i)q86+(1.216963.74545i)q88+7.49158q89+(3.260863.26086i)q91+(5.3276016.3966i)q92+(4.71891+0.747406i)q94+6.10874q957.84085q97+(1.39680+0.221233i)q98+O(q100)q+(-1.39680 + 0.221233i) q^{2} +(1.90211 - 0.618037i) q^{4} +(-2.51504 - 2.51504i) q^{5} +1.00000 q^{7} +(-2.52014 + 1.28408i) q^{8} +(4.06942 + 2.95660i) q^{10} +(-0.984548 + 0.984548i) q^{11} +(-3.26086 - 3.26086i) q^{13} +(-1.39680 + 0.221233i) q^{14} +(3.23606 - 2.35115i) q^{16} +5.50927i q^{17} +(-1.21444 + 1.21444i) q^{19} +(-6.33826 - 3.22950i) q^{20} +(1.15740 - 1.59303i) q^{22} -8.62021i q^{23} +7.65081i q^{25} +(5.27618 + 3.83336i) q^{26} +(1.90211 - 0.618037i) q^{28} +(-2.04663 + 2.04663i) q^{29} +0.164437i q^{31} +(-3.99999 + 4.00001i) q^{32} +(-1.21883 - 7.69536i) q^{34} +(-2.51504 - 2.51504i) q^{35} +(-8.31105 + 8.31105i) q^{37} +(1.42766 - 1.96501i) q^{38} +(9.56777 + 3.10874i) q^{40} +9.56578 q^{41} +(5.01867 + 5.01867i) q^{43} +(-1.26423 + 2.48121i) q^{44} +(1.90707 + 12.0407i) q^{46} +3.37837 q^{47} +1.00000 q^{49} +(-1.69261 - 10.6867i) q^{50} +(-8.21784 - 4.18719i) q^{52} +(3.72717 + 3.72717i) q^{53} +4.95235 q^{55} +(-2.52014 + 1.28408i) q^{56} +(2.40596 - 3.31153i) q^{58} +(-10.0781 + 10.0781i) q^{59} +(-1.07042 - 1.07042i) q^{61} +(-0.0363788 - 0.229686i) q^{62} +(4.70226 - 6.47216i) q^{64} +16.4023i q^{65} +(-3.12073 + 3.12073i) q^{67} +(3.40493 + 10.4793i) q^{68} +(4.06942 + 2.95660i) q^{70} +7.66257i q^{71} -8.40588i q^{73} +(9.77021 - 13.4476i) q^{74} +(-1.55944 + 3.06058i) q^{76} +(-0.984548 + 0.984548i) q^{77} +13.8712i q^{79} +(-14.0520 - 2.22559i) q^{80} +(-13.3615 + 2.11626i) q^{82} +(-7.31214 - 7.31214i) q^{83} +(13.8560 - 13.8560i) q^{85} +(-8.12038 - 5.89979i) q^{86} +(1.21696 - 3.74545i) q^{88} +7.49158 q^{89} +(-3.26086 - 3.26086i) q^{91} +(-5.32760 - 16.3966i) q^{92} +(-4.71891 + 0.747406i) q^{94} +6.10874 q^{95} -7.84085 q^{97} +(-1.39680 + 0.221233i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q+40q7+48q1024q13+12q1632q198q2256q348q37+32q4352q46+40q498q52+48q55+56q5824q61+48q64+48q70++64q97+O(q100) 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1008Z)×\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times.

nn 127127 577577 757757 785785
χ(n)\chi(n) 1-1 11 e(34)e\left(\frac{3}{4}\right) 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 −1.39680 + 0.221233i −0.987688 + 0.156435i
33 0 0
44 1.90211 0.618037i 0.951056 0.309018i
55 −2.51504 2.51504i −1.12476 1.12476i −0.991016 0.133742i 0.957301π-0.957301\pi
−0.133742 0.991016i 0.542699π-0.542699\pi
66 0 0
77 1.00000 0.377964
88 −2.52014 + 1.28408i −0.891006 + 0.453992i
99 0 0
1010 4.06942 + 2.95660i 1.28686 + 0.934959i
1111 −0.984548 + 0.984548i −0.296852 + 0.296852i −0.839780 0.542927i 0.817316π-0.817316\pi
0.542927 + 0.839780i 0.317316π0.317316\pi
1212 0 0
1313 −3.26086 3.26086i −0.904399 0.904399i 0.0914142 0.995813i 0.470861π-0.470861\pi
−0.995813 + 0.0914142i 0.970861π0.970861\pi
1414 −1.39680 + 0.221233i −0.373311 + 0.0591269i
1515 0 0
1616 3.23606 2.35115i 0.809015 0.587787i
1717 5.50927i 1.33619i 0.744074 + 0.668097i 0.232891π0.232891\pi
−0.744074 + 0.668097i 0.767109π0.767109\pi
1818 0 0
1919 −1.21444 + 1.21444i −0.278613 + 0.278613i −0.832555 0.553942i 0.813123π-0.813123\pi
0.553942 + 0.832555i 0.313123π0.313123\pi
2020 −6.33826 3.22950i −1.41728 0.722137i
2121 0 0
2222 1.15740 1.59303i 0.246759 0.339636i
2323 8.62021i 1.79744i −0.438526 0.898719i 0.644499π-0.644499\pi
0.438526 0.898719i 0.355501π-0.355501\pi
2424 0 0
2525 7.65081i 1.53016i
2626 5.27618 + 3.83336i 1.03474 + 0.751784i
2727 0 0
2828 1.90211 0.618037i 0.359465 0.116798i
2929 −2.04663 + 2.04663i −0.380050 + 0.380050i −0.871120 0.491070i 0.836606π-0.836606\pi
0.491070 + 0.871120i 0.336606π0.336606\pi
3030 0 0
3131 0.164437i 0.0295337i 0.999891 + 0.0147669i 0.00470061π0.00470061\pi
−0.999891 + 0.0147669i 0.995299π0.995299\pi
3232 −3.99999 + 4.00001i −0.707104 + 0.707109i
3333 0 0
3434 −1.21883 7.69536i −0.209028 1.31974i
3535 −2.51504 2.51504i −0.425119 0.425119i
3636 0 0
3737 −8.31105 + 8.31105i −1.36633 + 1.36633i −0.500717 + 0.865611i 0.666930π0.666930\pi
−0.865611 + 0.500717i 0.833070π0.833070\pi
3838 1.42766 1.96501i 0.231598 0.318767i
3939 0 0
4040 9.56777 + 3.10874i 1.51280 + 0.491534i
4141 9.56578 1.49392 0.746962 0.664867i 0.231512π-0.231512\pi
0.746962 + 0.664867i 0.231512π0.231512\pi
4242 0 0
4343 5.01867 + 5.01867i 0.765340 + 0.765340i 0.977282 0.211942i 0.0679789π-0.0679789\pi
−0.211942 + 0.977282i 0.567979π0.567979\pi
4444 −1.26423 + 2.48121i −0.190590 + 0.374056i
4545 0 0
4646 1.90707 + 12.0407i 0.281182 + 1.77531i
4747 3.37837 0.492786 0.246393 0.969170i 0.420755π-0.420755\pi
0.246393 + 0.969170i 0.420755π0.420755\pi
4848 0 0
4949 1.00000 0.142857
5050 −1.69261 10.6867i −0.239371 1.51132i
5151 0 0
5252 −8.21784 4.18719i −1.13961 0.580658i
5353 3.72717 + 3.72717i 0.511966 + 0.511966i 0.915129 0.403162i 0.132089π-0.132089\pi
−0.403162 + 0.915129i 0.632089π0.632089\pi
5454 0 0
5555 4.95235 0.667774
5656 −2.52014 + 1.28408i −0.336768 + 0.171593i
5757 0 0
5858 2.40596 3.31153i 0.315918 0.434825i
5959 −10.0781 + 10.0781i −1.31206 + 1.31206i −0.392162 + 0.919896i 0.628273π0.628273\pi
−0.919896 + 0.392162i 0.871727π0.871727\pi
6060 0 0
6161 −1.07042 1.07042i −0.137054 0.137054i 0.635252 0.772305i 0.280896π-0.280896\pi
−0.772305 + 0.635252i 0.780896π0.780896\pi
6262 −0.0363788 0.229686i −0.00462011 0.0291701i
6363 0 0
6464 4.70226 6.47216i 0.587782 0.809019i
6565 16.4023i 2.03446i
6666 0 0
6767 −3.12073 + 3.12073i −0.381258 + 0.381258i −0.871555 0.490297i 0.836888π-0.836888\pi
0.490297 + 0.871555i 0.336888π0.336888\pi
6868 3.40493 + 10.4793i 0.412909 + 1.27080i
6969 0 0
7070 4.06942 + 2.95660i 0.486388 + 0.353381i
7171 7.66257i 0.909380i 0.890650 + 0.454690i 0.150250π0.150250\pi
−0.890650 + 0.454690i 0.849750π0.849750\pi
7272 0 0
7373 8.40588i 0.983834i −0.870642 0.491917i 0.836296π-0.836296\pi
0.870642 0.491917i 0.163704π-0.163704\pi
7474 9.77021 13.4476i 1.13576 1.56325i
7575 0 0
7676 −1.55944 + 3.06058i −0.178880 + 0.351073i
7777 −0.984548 + 0.984548i −0.112200 + 0.112200i
7878 0 0
7979 13.8712i 1.56063i 0.625387 + 0.780315i 0.284941π0.284941\pi
−0.625387 + 0.780315i 0.715059π0.715059\pi
8080 −14.0520 2.22559i −1.57107 0.248828i
8181 0 0
8282 −13.3615 + 2.11626i −1.47553 + 0.233702i
8383 −7.31214 7.31214i −0.802611 0.802611i 0.180892 0.983503i 0.442102π-0.442102\pi
−0.983503 + 0.180892i 0.942102π0.942102\pi
8484 0 0
8585 13.8560 13.8560i 1.50290 1.50290i
8686 −8.12038 5.89979i −0.875643 0.636191i
8787 0 0
8888 1.21696 3.74545i 0.129728 0.399266i
8989 7.49158 0.794106 0.397053 0.917796i 0.370033π-0.370033\pi
0.397053 + 0.917796i 0.370033π0.370033\pi
9090 0 0
9191 −3.26086 3.26086i −0.341831 0.341831i
9292 −5.32760 16.3966i −0.555441 1.70946i
9393 0 0
9494 −4.71891 + 0.747406i −0.486719 + 0.0770890i
9595 6.10874 0.626744
9696 0 0
9797 −7.84085 −0.796118 −0.398059 0.917360i 0.630316π-0.630316\pi
−0.398059 + 0.917360i 0.630316π0.630316\pi
9898 −1.39680 + 0.221233i −0.141098 + 0.0223479i
9999 0 0
100100 4.72848 + 14.5527i 0.472848 + 1.45527i
101101 0.748257 + 0.748257i 0.0744543 + 0.0744543i 0.743353 0.668899i 0.233234π-0.233234\pi
−0.668899 + 0.743353i 0.733234π0.733234\pi
102102 0 0
103103 −11.8161 −1.16428 −0.582140 0.813089i 0.697784π-0.697784\pi
−0.582140 + 0.813089i 0.697784π0.697784\pi
104104 12.4050 + 4.03061i 1.21641 + 0.395234i
105105 0 0
106106 −6.03069 4.38155i −0.585753 0.425574i
107107 −4.41189 + 4.41189i −0.426514 + 0.426514i −0.887439 0.460925i 0.847518π-0.847518\pi
0.460925 + 0.887439i 0.347518π0.347518\pi
108108 0 0
109109 −0.128743 0.128743i −0.0123314 0.0123314i 0.700914 0.713246i 0.252776π-0.252776\pi
−0.713246 + 0.700914i 0.752776π0.752776\pi
110110 −6.91745 + 1.09562i −0.659553 + 0.104463i
111111 0 0
112112 3.23606 2.35115i 0.305779 0.222163i
113113 14.3042i 1.34563i 0.739811 + 0.672815i 0.234915π0.234915\pi
−0.739811 + 0.672815i 0.765085π0.765085\pi
114114 0 0
115115 −21.6801 + 21.6801i −2.02168 + 2.02168i
116116 −2.62803 + 5.15782i −0.244007 + 0.478892i
117117 0 0
118118 11.8475 16.3067i 1.09065 1.50116i
119119 5.50927i 0.505034i
120120 0 0
121121 9.06133i 0.823757i
122122 1.73198 + 1.25836i 0.156806 + 0.113926i
123123 0 0
124124 0.101628 + 0.312777i 0.00912646 + 0.0280882i
125125 6.66689 6.66689i 0.596304 0.596304i
126126 0 0
127127 1.31914i 0.117055i 0.998286 + 0.0585274i 0.0186405π0.0186405\pi
−0.998286 + 0.0585274i 0.981359π0.981359\pi
128128 −5.13627 + 10.0806i −0.453986 + 0.891009i
129129 0 0
130130 −3.62873 22.9108i −0.318261 2.00941i
131131 −3.84141 3.84141i −0.335626 0.335626i 0.519093 0.854718i 0.326270π-0.326270\pi
−0.854718 + 0.519093i 0.826270π0.826270\pi
132132 0 0
133133 −1.21444 + 1.21444i −0.105306 + 0.105306i
134134 3.66863 5.04945i 0.316922 0.436206i
135135 0 0
136136 −7.07437 13.8842i −0.606622 1.19056i
137137 −11.8262 −1.01038 −0.505191 0.863008i 0.668578π-0.668578\pi
−0.505191 + 0.863008i 0.668578π0.668578\pi
138138 0 0
139139 −10.6322 10.6322i −0.901814 0.901814i 0.0937788 0.995593i 0.470105π-0.470105\pi
−0.995593 + 0.0937788i 0.970105π0.970105\pi
140140 −6.33826 3.22950i −0.535681 0.272942i
141141 0 0
142142 −1.69521 10.7031i −0.142259 0.898184i
143143 6.42094 0.536946
144144 0 0
145145 10.2947 0.854930
146146 1.85966 + 11.7413i 0.153906 + 0.971721i
147147 0 0
148148 −10.6720 + 20.9451i −0.877234 + 1.72167i
149149 9.66703 + 9.66703i 0.791954 + 0.791954i 0.981812 0.189858i 0.0608027π-0.0608027\pi
−0.189858 + 0.981812i 0.560803π0.560803\pi
150150 0 0
151151 −5.05132 −0.411070 −0.205535 0.978650i 0.565893π-0.565893\pi
−0.205535 + 0.978650i 0.565893π0.565893\pi
152152 1.50113 4.62002i 0.121757 0.374733i
153153 0 0
154154 1.15740 1.59303i 0.0932663 0.128370i
155155 0.413565 0.413565i 0.0332183 0.0332183i
156156 0 0
157157 11.1102 + 11.1102i 0.886692 + 0.886692i 0.994204 0.107512i 0.0342884π-0.0342884\pi
−0.107512 + 0.994204i 0.534288π0.534288\pi
158158 −3.06876 19.3753i −0.244137 1.54142i
159159 0 0
160160 20.1203 6.79865e-5i 1.59065 5.37480e-6i
161161 8.62021i 0.679367i
162162 0 0
163163 0.936756 0.936756i 0.0733724 0.0733724i −0.669468 0.742841i 0.733478π-0.733478\pi
0.742841 + 0.669468i 0.233478π0.233478\pi
164164 18.1952 5.91200i 1.42080 0.461650i
165165 0 0
166166 11.8313 + 8.59592i 0.918286 + 0.667173i
167167 17.9147i 1.38628i −0.720804 0.693139i 0.756227π-0.756227\pi
0.720804 0.693139i 0.243773π-0.243773\pi
168168 0 0
169169 8.26636i 0.635874i
170170 −16.2887 + 22.4195i −1.24929 + 1.71950i
171171 0 0
172172 12.6478 + 6.44435i 0.964385 + 0.491377i
173173 −1.95689 + 1.95689i −0.148780 + 0.148780i −0.777573 0.628793i 0.783549π-0.783549\pi
0.628793 + 0.777573i 0.283549π0.283549\pi
174174 0 0
175175 7.65081i 0.578347i
176176 −0.871238 + 5.50088i −0.0656720 + 0.414644i
177177 0 0
178178 −10.4643 + 1.65738i −0.784329 + 0.124226i
179179 16.4536 + 16.4536i 1.22980 + 1.22980i 0.964039 + 0.265760i 0.0856230π0.0856230\pi
0.265760 + 0.964039i 0.414377π0.414377\pi
180180 0 0
181181 2.01639 2.01639i 0.149877 0.149877i −0.628186 0.778063i 0.716202π-0.716202\pi
0.778063 + 0.628186i 0.216202π0.216202\pi
182182 5.27618 + 3.83336i 0.391096 + 0.284148i
183183 0 0
184184 11.0691 + 21.7242i 0.816023 + 1.60153i
185185 41.8052 3.07358
186186 0 0
187187 −5.42414 5.42414i −0.396653 0.396653i
188188 6.42604 2.08796i 0.468667 0.152280i
189189 0 0
190190 −8.53270 + 1.35145i −0.619027 + 0.0980447i
191191 −6.72330 −0.486481 −0.243240 0.969966i 0.578210π-0.578210\pi
−0.243240 + 0.969966i 0.578210π0.578210\pi
192192 0 0
193193 1.37543 0.0990058 0.0495029 0.998774i 0.484236π-0.484236\pi
0.0495029 + 0.998774i 0.484236π0.484236\pi
194194 10.9521 1.73465i 0.786316 0.124541i
195195 0 0
196196 1.90211 0.618037i 0.135865 0.0441455i
197197 −10.2035 10.2035i −0.726967 0.726967i 0.243048 0.970014i 0.421853π-0.421853\pi
−0.970014 + 0.243048i 0.921853π0.921853\pi
198198 0 0
199199 −14.9391 −1.05900 −0.529501 0.848309i 0.677621π-0.677621\pi
−0.529501 + 0.848309i 0.677621π0.677621\pi
200200 −9.82429 19.2811i −0.694682 1.36338i
201201 0 0
202202 −1.21071 0.879628i −0.0851849 0.0618904i
203203 −2.04663 + 2.04663i −0.143646 + 0.143646i
204204 0 0
205205 −24.0583 24.0583i −1.68030 1.68030i
206206 16.5048 2.61412i 1.14994 0.182134i
207207 0 0
208208 −18.2191 2.88557i −1.26327 0.200078i
209209 2.39136i 0.165414i
210210 0 0
211211 4.93531 4.93531i 0.339761 0.339761i −0.516516 0.856277i 0.672772π-0.672772\pi
0.856277 + 0.516516i 0.172772π0.172772\pi
212212 9.39303 + 4.78597i 0.645116 + 0.328702i
213213 0 0
214214 5.18648 7.13859i 0.354541 0.487984i
215215 25.2443i 1.72164i
216216 0 0
217217 0.164437i 0.0111627i
218218 0.208311 + 0.151347i 0.0141086 + 0.0102505i
219219 0 0
220220 9.41992 3.06073i 0.635091 0.206354i
221221 17.9649 17.9649i 1.20845 1.20845i
222222 0 0
223223 5.25747i 0.352066i −0.984384 0.176033i 0.943673π-0.943673\pi
0.984384 0.176033i 0.0563266π-0.0563266\pi
224224 −3.99999 + 4.00001i −0.267260 + 0.267262i
225225 0 0
226226 −3.16456 19.9802i −0.210504 1.32906i
227227 −6.30931 6.30931i −0.418763 0.418763i 0.466014 0.884777i 0.345690π-0.345690\pi
−0.884777 + 0.466014i 0.845690π0.845690\pi
228228 0 0
229229 19.1785 19.1785i 1.26735 1.26735i 0.319899 0.947452i 0.396351π-0.396351\pi
0.947452 0.319899i 0.103649π-0.103649\pi
230230 25.4865 35.0792i 1.68053 2.31305i
231231 0 0
232232 2.52976 7.78586i 0.166087 0.511167i
233233 −0.555029 −0.0363611 −0.0181806 0.999835i 0.505787π-0.505787\pi
−0.0181806 + 0.999835i 0.505787π0.505787\pi
234234 0 0
235235 −8.49672 8.49672i −0.554265 0.554265i
236236 −12.9411 + 25.3983i −0.842391 + 1.65329i
237237 0 0
238238 −1.21883 7.69536i −0.0790051 0.498816i
239239 −23.0408 −1.49039 −0.745194 0.666848i 0.767643π-0.767643\pi
−0.745194 + 0.666848i 0.767643π0.767643\pi
240240 0 0
241241 −7.47827 −0.481718 −0.240859 0.970560i 0.577429π-0.577429\pi
−0.240859 + 0.970560i 0.577429π0.577429\pi
242242 −2.00466 12.6569i −0.128865 0.813615i
243243 0 0
244244 −2.69762 1.37450i −0.172698 0.0879936i
245245 −2.51504 2.51504i −0.160680 0.160680i
246246 0 0
247247 7.92026 0.503954
248248 −0.211151 0.414405i −0.0134081 0.0263147i
249249 0 0
250250 −7.83739 + 10.7873i −0.495680 + 0.682246i
251251 18.7049 18.7049i 1.18064 1.18064i 0.201066 0.979578i 0.435559π-0.435559\pi
0.979578 0.201066i 0.0644407π-0.0644407\pi
252252 0 0
253253 8.48701 + 8.48701i 0.533574 + 0.533574i
254254 −0.291837 1.84258i −0.0183115 0.115614i
255255 0 0
256256 4.94419 15.2169i 0.309012 0.951058i
257257 18.3076i 1.14200i −0.820951 0.570998i 0.806556π-0.806556\pi
0.820951 0.570998i 0.193444π-0.193444\pi
258258 0 0
259259 −8.31105 + 8.31105i −0.516423 + 0.516423i
260260 10.1372 + 31.1991i 0.628685 + 1.93489i
261261 0 0
262262 6.21554 + 4.51584i 0.383997 + 0.278990i
263263 20.1306i 1.24130i −0.784086 0.620652i 0.786868π-0.786868\pi
0.784086 0.620652i 0.213132π-0.213132\pi
264264 0 0
265265 18.7479i 1.15168i
266266 1.42766 1.96501i 0.0875357 0.120483i
267267 0 0
268268 −4.00725 + 7.86470i −0.244782 + 0.480413i
269269 −8.69779 + 8.69779i −0.530313 + 0.530313i −0.920666 0.390352i 0.872353π-0.872353\pi
0.390352 + 0.920666i 0.372353π0.372353\pi
270270 0 0
271271 11.6299i 0.706466i 0.935535 + 0.353233i 0.114918π0.114918\pi
−0.935535 + 0.353233i 0.885082π0.885082\pi
272272 12.9531 + 17.8283i 0.785399 + 1.08100i
273273 0 0
274274 16.5189 2.61635i 0.997942 0.158059i
275275 −7.53259 7.53259i −0.454232 0.454232i
276276 0 0
277277 22.9876 22.9876i 1.38119 1.38119i 0.538679 0.842511i 0.318923π-0.318923\pi
0.842511 0.538679i 0.181077π-0.181077\pi
278278 17.2033 + 12.4989i 1.03179 + 0.749636i
279279 0 0
280280 9.56777 + 3.10874i 0.571784 + 0.185783i
281281 11.5187 0.687148 0.343574 0.939126i 0.388362π-0.388362\pi
0.343574 + 0.939126i 0.388362π0.388362\pi
282282 0 0
283283 −15.6255 15.6255i −0.928839 0.928839i 0.0687924 0.997631i 0.478085π-0.478085\pi
−0.997631 + 0.0687924i 0.978085π0.978085\pi
284284 4.73575 + 14.5751i 0.281015 + 0.864872i
285285 0 0
286286 −8.96878 + 1.42052i −0.530335 + 0.0839972i
287287 9.56578 0.564650
288288 0 0
289289 −13.3521 −0.785417
290290 −14.3797 + 2.27753i −0.844404 + 0.133741i
291291 0 0
292292 −5.19514 15.9889i −0.304023 0.935681i
293293 −3.77816 3.77816i −0.220722 0.220722i 0.588080 0.808803i 0.299884π-0.299884\pi
−0.808803 + 0.588080i 0.799884π0.799884\pi
294294 0 0
295295 50.6936 2.95150
296296 10.2730 31.6171i 0.597104 1.83771i
297297 0 0
298298 −15.6416 11.3643i −0.906093 0.658314i
299299 −28.1093 + 28.1093i −1.62560 + 1.62560i
300300 0 0
301301 5.01867 + 5.01867i 0.289271 + 0.289271i
302302 7.05569 1.11752i 0.406009 0.0643058i
303303 0 0
304304 −1.07468 + 6.78536i −0.0616369 + 0.389167i
305305 5.38430i 0.308304i
306306 0 0
307307 0.708546 0.708546i 0.0404389 0.0404389i −0.686598 0.727037i 0.740897π-0.740897\pi
0.727037 + 0.686598i 0.240897π0.240897\pi
308308 −1.26423 + 2.48121i −0.0720364 + 0.141380i
309309 0 0
310310 −0.486174 + 0.669162i −0.0276128 + 0.0380058i
311311 21.6074i 1.22525i 0.790376 + 0.612623i 0.209885π0.209885\pi
−0.790376 + 0.612623i 0.790115π0.790115\pi
312312 0 0
313313 5.11637i 0.289194i 0.989491 + 0.144597i 0.0461886π0.0461886\pi
−0.989491 + 0.144597i 0.953811π0.953811\pi
314314 −17.9767 13.0608i −1.01448 0.737065i
315315 0 0
316316 8.57290 + 26.3845i 0.482263 + 1.48425i
317317 −7.88622 + 7.88622i −0.442934 + 0.442934i −0.892997 0.450063i 0.851402π-0.851402\pi
0.450063 + 0.892997i 0.351402π0.351402\pi
318318 0 0
319319 4.03002i 0.225638i
320320 −28.1040 + 4.45136i −1.57106 + 0.248839i
321321 0 0
322322 1.90707 + 12.0407i 0.106277 + 0.671003i
323323 −6.69070 6.69070i −0.372281 0.372281i
324324 0 0
325325 24.9482 24.9482i 1.38388 1.38388i
326326 −1.10122 + 1.51570i −0.0609911 + 0.0839471i
327327 0 0
328328 −24.1071 + 12.2833i −1.33109 + 0.678230i
329329 3.37837 0.186256
330330 0 0
331331 0.144453 + 0.144453i 0.00793985 + 0.00793985i 0.711066 0.703126i 0.248213π-0.248213\pi
−0.703126 + 0.711066i 0.748213π0.748213\pi
332332 −18.4277 9.38934i −1.01135 0.515307i
333333 0 0
334334 3.96331 + 25.0232i 0.216862 + 1.36921i
335335 15.6975 0.857646
336336 0 0
337337 −18.3255 −0.998256 −0.499128 0.866528i 0.666346π-0.666346\pi
−0.499128 + 0.866528i 0.666346π0.666346\pi
338338 −1.82879 11.5465i −0.0994731 0.628045i
339339 0 0
340340 17.7922 34.9192i 0.964916 1.89376i
341341 −0.161896 0.161896i −0.00876716 0.00876716i
342342 0 0
343343 1.00000 0.0539949
344344 −19.0922 6.20338i −1.02938 0.334464i
345345 0 0
346346 2.30046 3.16632i 0.123674 0.170222i
347347 −7.70010 + 7.70010i −0.413363 + 0.413363i −0.882908 0.469545i 0.844418π-0.844418\pi
0.469545 + 0.882908i 0.344418π0.344418\pi
348348 0 0
349349 9.23902 + 9.23902i 0.494553 + 0.494553i 0.909737 0.415184i 0.136283π-0.136283\pi
−0.415184 + 0.909737i 0.636283π0.636283\pi
350350 −1.69261 10.6867i −0.0904738 0.571226i
351351 0 0
352352 −2.66143e−5 7.87638i −1.41855e−6 0.419813i
353353 13.9051i 0.740092i 0.929013 + 0.370046i 0.120658π0.120658\pi
−0.929013 + 0.370046i 0.879342π0.879342\pi
354354 0 0
355355 19.2716 19.2716i 1.02283 1.02283i
356356 14.2498 4.63007i 0.755239 0.245393i
357357 0 0
358358 −26.6225 19.3423i −1.40704 1.02227i
359359 20.3979i 1.07656i −0.842766 0.538281i 0.819074π-0.819074\pi
0.842766 0.538281i 0.180926π-0.180926\pi
360360 0 0
361361 16.0503i 0.844750i
362362 −2.37041 + 3.26259i −0.124586 + 0.171478i
363363 0 0
364364 −8.21784 4.18719i −0.430732 0.219468i
365365 −21.1411 + 21.1411i −1.10658 + 1.10658i
366366 0 0
367367 21.2755i 1.11057i 0.831660 + 0.555285i 0.187391π0.187391\pi
−0.831660 + 0.555285i 0.812609π0.812609\pi
368368 −20.2674 27.8955i −1.05651 1.45415i
369369 0 0
370370 −58.3936 + 9.24867i −3.03574 + 0.480815i
371371 3.72717 + 3.72717i 0.193505 + 0.193505i
372372 0 0
373373 14.6527 14.6527i 0.758688 0.758688i −0.217396 0.976084i 0.569756π-0.569756\pi
0.976084 + 0.217396i 0.0697562π0.0697562\pi
374374 8.77645 + 6.37646i 0.453820 + 0.329719i
375375 0 0
376376 −8.51398 + 4.33811i −0.439075 + 0.223721i
377377 13.3476 0.687434
378378 0 0
379379 −8.85565 8.85565i −0.454884 0.454884i 0.442088 0.896972i 0.354238π-0.354238\pi
−0.896972 + 0.442088i 0.854238π0.854238\pi
380380 11.6195 3.77543i 0.596068 0.193675i
381381 0 0
382382 9.39111 1.48741i 0.480491 0.0761027i
383383 −33.3573 −1.70448 −0.852238 0.523154i 0.824755π-0.824755\pi
−0.852238 + 0.523154i 0.824755π0.824755\pi
384384 0 0
385385 4.95235 0.252395
386386 −1.92121 + 0.304291i −0.0977869 + 0.0154880i
387387 0 0
388388 −14.9142 + 4.84593i −0.757153 + 0.246015i
389389 2.00738 + 2.00738i 0.101778 + 0.101778i 0.756162 0.654384i 0.227072π-0.227072\pi
−0.654384 + 0.756162i 0.727072π0.727072\pi
390390 0 0
391391 47.4911 2.40173
392392 −2.52014 + 1.28408i −0.127287 + 0.0648560i
393393 0 0
394394 16.5096 + 11.9949i 0.831739 + 0.604293i
395395 34.8865 34.8865i 1.75533 1.75533i
396396 0 0
397397 −2.43985 2.43985i −0.122453 0.122453i 0.643225 0.765677i 0.277596π-0.277596\pi
−0.765677 + 0.643225i 0.777596π0.777596\pi
398398 20.8669 3.30501i 1.04596 0.165665i
399399 0 0
400400 17.9882 + 24.7585i 0.899410 + 1.23792i
401401 11.6798i 0.583263i 0.956531 + 0.291632i 0.0941981π0.0941981\pi
−0.956531 + 0.291632i 0.905802π0.905802\pi
402402 0 0
403403 0.536205 0.536205i 0.0267103 0.0267103i
404404 1.88572 + 0.960818i 0.0938180 + 0.0478025i
405405 0 0
406406 2.40596 3.31153i 0.119406 0.164348i
407407 16.3653i 0.811195i
408408 0 0
409409 15.2951i 0.756292i 0.925746 + 0.378146i 0.123438π0.123438\pi
−0.925746 + 0.378146i 0.876562π0.876562\pi
410410 38.9271 + 28.2822i 1.92247 + 1.39676i
411411 0 0
412412 −22.4756 + 7.30281i −1.10729 + 0.359784i
413413 −10.0781 + 10.0781i −0.495911 + 0.495911i
414414 0 0
415415 36.7806i 1.80549i
416416 26.0868 8.81475e-5i 1.27901 4.32179e-6i
417417 0 0
418418 0.529046 + 3.34025i 0.0258765 + 0.163377i
419419 13.1833 + 13.1833i 0.644045 + 0.644045i 0.951547 0.307502i 0.0994932π-0.0994932\pi
−0.307502 + 0.951547i 0.599493π0.599493\pi
420420 0 0
421421 −22.2574 + 22.2574i −1.08476 + 1.08476i −0.0887017 + 0.996058i 0.528272π0.528272\pi
−0.996058 + 0.0887017i 0.971728π0.971728\pi
422422 −5.80180 + 7.98550i −0.282427 + 0.388728i
423423 0 0
424424 −14.1790 4.60701i −0.688594 0.223736i
425425 −42.1504 −2.04459
426426 0 0
427427 −1.07042 1.07042i −0.0518014 0.0518014i
428428 −5.66520 + 11.1186i −0.273838 + 0.537439i
429429 0 0
430430 5.58486 + 35.2612i 0.269326 + 1.70045i
431431 −19.0326 −0.916769 −0.458385 0.888754i 0.651572π-0.651572\pi
−0.458385 + 0.888754i 0.651572π0.651572\pi
432432 0 0
433433 −31.7120 −1.52398 −0.761992 0.647587i 0.775778π-0.775778\pi
−0.761992 + 0.647587i 0.775778π0.775778\pi
434434 −0.0363788 0.229686i −0.00174624 0.0110253i
435435 0 0
436436 −0.324452 0.165316i −0.0155384 0.00791720i
437437 10.4688 + 10.4688i 0.500789 + 0.500789i
438438 0 0
439439 32.9521 1.57272 0.786359 0.617770i 0.211964π-0.211964\pi
0.786359 + 0.617770i 0.211964π0.211964\pi
440440 −12.4806 + 6.35923i −0.594991 + 0.303164i
441441 0 0
442442 −21.1190 + 29.0679i −1.00453 + 1.38262i
443443 −4.94776 + 4.94776i −0.235075 + 0.235075i −0.814807 0.579732i 0.803157π-0.803157\pi
0.579732 + 0.814807i 0.303157π0.303157\pi
444444 0 0
445445 −18.8416 18.8416i −0.893177 0.893177i
446446 1.16312 + 7.34365i 0.0550755 + 0.347732i
447447 0 0
448448 4.70226 6.47216i 0.222161 0.305781i
449449 31.5258i 1.48779i −0.668294 0.743897i 0.732975π-0.732975\pi
0.668294 0.743897i 0.267025π-0.267025\pi
450450 0 0
451451 −9.41796 + 9.41796i −0.443475 + 0.443475i
452452 8.84054 + 27.2083i 0.415824 + 1.27977i
453453 0 0
454454 10.2087 + 7.41703i 0.479117 + 0.348098i
455455 16.4023i 0.768954i
456456 0 0
457457 35.2517i 1.64901i 0.565857 + 0.824503i 0.308545π0.308545\pi
−0.565857 + 0.824503i 0.691455π0.691455\pi
458458 −22.5456 + 31.0315i −1.05349 + 1.45001i
459459 0 0
460460 −27.8389 + 54.6372i −1.29800 + 2.54747i
461461 −15.8769 + 15.8769i −0.739462 + 0.739462i −0.972474 0.233012i 0.925142π-0.925142\pi
0.233012 + 0.972474i 0.425142π0.425142\pi
462462 0 0
463463 15.9217i 0.739946i −0.929043 0.369973i 0.879367π-0.879367\pi
0.929043 0.369973i 0.120633π-0.120633\pi
464464 −1.81109 + 11.4350i −0.0840778 + 0.530855i
465465 0 0
466466 0.775265 0.122790i 0.0359135 0.00568816i
467467 −6.52420 6.52420i −0.301904 0.301904i 0.539854 0.841758i 0.318479π-0.318479\pi
−0.841758 + 0.539854i 0.818479π0.818479\pi
468468 0 0
469469 −3.12073 + 3.12073i −0.144102 + 0.144102i
470470 13.7480 + 9.98848i 0.634147 + 0.460734i
471471 0 0
472472 12.4572 38.3394i 0.573387 1.76472i
473473 −9.88224 −0.454386
474474 0 0
475475 −9.29148 9.29148i −0.426323 0.426323i
476476 3.40493 + 10.4793i 0.156065 + 0.480316i
477477 0 0
478478 32.1835 5.09738i 1.47204 0.233149i
479479 −31.5891 −1.44334 −0.721671 0.692237i 0.756625π-0.756625\pi
−0.721671 + 0.692237i 0.756625π0.756625\pi
480480 0 0
481481 54.2023 2.47141
482482 10.4457 1.65444i 0.475787 0.0753576i
483483 0 0
484484 5.60023 + 17.2357i 0.254556 + 0.783439i
485485 19.7200 + 19.7200i 0.895440 + 0.895440i
486486 0 0
487487 −29.4810 −1.33591 −0.667955 0.744202i 0.732830π-0.732830\pi
−0.667955 + 0.744202i 0.732830π0.732830\pi
488488 4.07213 + 1.32311i 0.184337 + 0.0598942i
489489 0 0
490490 4.06942 + 2.95660i 0.183837 + 0.133566i
491491 −6.06862 + 6.06862i −0.273873 + 0.273873i −0.830657 0.556784i 0.812035π-0.812035\pi
0.556784 + 0.830657i 0.312035π0.312035\pi
492492 0 0
493493 −11.2755 11.2755i −0.507821 0.507821i
494494 −11.0630 + 1.75222i −0.497749 + 0.0788361i
495495 0 0
496496 0.386616 + 0.532128i 0.0173596 + 0.0238932i
497497 7.66257i 0.343713i
498498 0 0
499499 15.8968 15.8968i 0.711638 0.711638i −0.255240 0.966878i 0.582154π-0.582154\pi
0.966878 + 0.255240i 0.0821544π0.0821544\pi
500500 8.56079 16.8015i 0.382850 0.751388i
501501 0 0
502502 −21.9889 + 30.2652i −0.981414 + 1.35080i
503503 17.1978i 0.766813i 0.923580 + 0.383406i 0.125249π0.125249\pi
−0.923580 + 0.383406i 0.874751π0.874751\pi
504504 0 0
505505 3.76379i 0.167486i
506506 −13.7323 9.97707i −0.610474 0.443535i
507507 0 0
508508 0.815278 + 2.50916i 0.0361721 + 0.111326i
509509 0.959431 0.959431i 0.0425260 0.0425260i −0.685524 0.728050i 0.740427π-0.740427\pi
0.728050 + 0.685524i 0.240427π0.240427\pi
510510 0 0
511511 8.40588i 0.371854i
512512 −3.53957 + 22.3489i −0.156428 + 0.987689i
513513 0 0
514514 4.05024 + 25.5721i 0.178648 + 1.12794i
515515 29.7180 + 29.7180i 1.30953 + 1.30953i
516516 0 0
517517 −3.32617 + 3.32617i −0.146285 + 0.146285i
518518 9.77021 13.4476i 0.429279 0.590852i
519519 0 0
520520 −21.0620 41.3363i −0.923629 1.81272i
521521 −9.04026 −0.396061 −0.198030 0.980196i 0.563454π-0.563454\pi
−0.198030 + 0.980196i 0.563454π0.563454\pi
522522 0 0
523523 −5.32615 5.32615i −0.232896 0.232896i 0.581004 0.813901i 0.302660π-0.302660\pi
−0.813901 + 0.581004i 0.802660π0.802660\pi
524524 −9.68093 4.93266i −0.422913 0.215484i
525525 0 0
526526 4.45354 + 28.1184i 0.194184 + 1.22602i
527527 −0.905927 −0.0394628
528528 0 0
529529 −51.3080 −2.23078
530530 4.14766 + 26.1872i 0.180163 + 1.13750i
531531 0 0
532532 −1.55944 + 3.06058i −0.0676102 + 0.132693i
533533 −31.1926 31.1926i −1.35110 1.35110i
534534 0 0
535535 22.1921 0.959449
536536 3.85741 11.8720i 0.166615 0.512791i
537537 0 0
538538 10.2249 14.0733i 0.440825 0.606744i
539539 −0.984548 + 0.984548i −0.0424075 + 0.0424075i
540540 0 0
541541 12.7082 + 12.7082i 0.546367 + 0.546367i 0.925388 0.379021i 0.123739π-0.123739\pi
−0.379021 + 0.925388i 0.623739π0.623739\pi
542542 −2.57291 16.2447i −0.110516 0.697768i
543543 0 0
544544 −22.0372 22.0370i −0.944836 0.944829i
545545 0.647588i 0.0277396i
546546 0 0
547547 19.7217 19.7217i 0.843239 0.843239i −0.146040 0.989279i 0.546653π-0.546653\pi
0.989279 + 0.146040i 0.0466527π0.0466527\pi
548548 −22.4948 + 7.30904i −0.960930 + 0.312227i
549549 0 0
550550 12.1880 + 8.85508i 0.519698 + 0.377582i
551551 4.97105i 0.211774i
552552 0 0
553553 13.8712i 0.589863i
554554 −27.0235 + 37.1947i −1.14812 + 1.58025i
555555 0 0
556556 −26.7948 13.6526i −1.13635 0.578999i
557557 32.2571 32.2571i 1.36678 1.36678i 0.501789 0.864990i 0.332675π-0.332675\pi
0.864990 0.501789i 0.167325π-0.167325\pi
558558 0 0
559559 32.7303i 1.38434i
560560 −14.0520 2.22559i −0.593807 0.0940481i
561561 0 0
562562 −16.0893 + 2.54831i −0.678688 + 0.107494i
563563 −27.0814 27.0814i −1.14134 1.14134i −0.988205 0.153138i 0.951062π-0.951062\pi
−0.153138 0.988205i 0.548938π-0.548938\pi
564564 0 0
565565 35.9757 35.9757i 1.51351 1.51351i
566566 25.2826 + 18.3688i 1.06271 + 0.772100i
567567 0 0
568568 −9.83939 19.3108i −0.412852 0.810263i
569569 28.4823 1.19404 0.597020 0.802226i 0.296351π-0.296351\pi
0.597020 + 0.802226i 0.296351π0.296351\pi
570570 0 0
571571 15.8844 + 15.8844i 0.664743 + 0.664743i 0.956494 0.291751i 0.0942380π-0.0942380\pi
−0.291751 + 0.956494i 0.594238π0.594238\pi
572572 12.2133 3.96837i 0.510666 0.165926i
573573 0 0
574574 −13.3615 + 2.11626i −0.557698 + 0.0883311i
575575 65.9516 2.75037
576576 0 0
577577 4.65713 0.193879 0.0969395 0.995290i 0.469095π-0.469095\pi
0.0969395 + 0.995290i 0.469095π0.469095\pi
578578 18.6502 2.95392i 0.775747 0.122867i
579579 0 0
580580 19.5817 6.36251i 0.813086 0.264189i
581581 −7.31214 7.31214i −0.303359 0.303359i
582582 0 0
583583 −7.33916 −0.303957
584584 10.7939 + 21.1840i 0.446653 + 0.876601i
585585 0 0
586586 6.11319 + 4.44149i 0.252534 + 0.183476i
587587 −13.2034 + 13.2034i −0.544963 + 0.544963i −0.924980 0.380017i 0.875918π-0.875918\pi
0.380017 + 0.924980i 0.375918π0.375918\pi
588588 0 0
589589 −0.199699 0.199699i −0.00822847 0.00822847i
590590 −70.8090 + 11.2151i −2.91516 + 0.461718i
591591 0 0
592592 −7.35455 + 46.4356i −0.302270 + 1.90849i
593593 8.00745i 0.328827i 0.986392 + 0.164413i 0.0525731π0.0525731\pi
−0.986392 + 0.164413i 0.947427π0.947427\pi
594594 0 0
595595 13.8560 13.8560i 0.568041 0.568041i
596596 24.3624 + 12.4132i 0.997921 + 0.508464i
597597 0 0
598598 33.0444 45.4817i 1.35129 1.85989i
599599 29.8782i 1.22079i −0.792096 0.610396i 0.791010π-0.791010\pi
0.792096 0.610396i 0.208990π-0.208990\pi
600600 0 0
601601 28.4594i 1.16088i −0.814302 0.580441i 0.802880π-0.802880\pi
0.814302 0.580441i 0.197120π-0.197120\pi
602602 −8.12038 5.89979i −0.330962 0.240458i
603603 0 0
604604 −9.60817 + 3.12190i −0.390951 + 0.127028i
605605 22.7896 22.7896i 0.926528 0.926528i
606606 0 0
607607 27.1606i 1.10242i 0.834368 + 0.551208i 0.185833π0.185833\pi
−0.834368 + 0.551208i 0.814167π0.814167\pi
608608 −3.28289e−5 9.71555i −1.33139e−6 0.394018i
609609 0 0
610610 −1.19118 7.52080i −0.0482296 0.304508i
611611 −11.0164 11.0164i −0.445675 0.445675i
612612 0 0
613613 −25.1239 + 25.1239i −1.01474 + 1.01474i −0.0148539 + 0.999890i 0.504728π0.504728\pi
−0.999890 + 0.0148539i 0.995272π0.995272\pi
614614 −0.832946 + 1.14645i −0.0336149 + 0.0462671i
615615 0 0
616616 1.21696 3.74545i 0.0490327 0.150908i
617617 −20.2712 −0.816089 −0.408044 0.912962i 0.633789π-0.633789\pi
−0.408044 + 0.912962i 0.633789π0.633789\pi
618618 0 0
619619 −13.2344 13.2344i −0.531937 0.531937i 0.389211 0.921148i 0.372748π-0.372748\pi
−0.921148 + 0.389211i 0.872748π0.872748\pi
620620 0.531048 1.04224i 0.0213274 0.0418575i
621621 0 0
622622 −4.78027 30.1813i −0.191671 1.21016i
623623 7.49158 0.300144
624624 0 0
625625 4.71914 0.188766
626626 −1.13191 7.14655i −0.0452401 0.285634i
627627 0 0
628628 27.9994 + 14.2664i 1.11730 + 0.569290i
629629 −45.7878 45.7878i −1.82568 1.82568i
630630 0 0
631631 −47.8911 −1.90651 −0.953257 0.302161i 0.902292π-0.902292\pi
−0.953257 + 0.302161i 0.902292π0.902292\pi
632632 −17.8118 34.9574i −0.708514 1.39053i
633633 0 0
634634 9.27080 12.7602i 0.368191 0.506771i
635635 3.31769 3.31769i 0.131658 0.131658i
636636 0 0
637637 −3.26086 3.26086i −0.129200 0.129200i
638638 0.891572 + 5.62914i 0.0352977 + 0.222860i
639639 0 0
640640 38.2710 12.4352i 1.51279 0.491545i
641641 23.5861i 0.931595i 0.884891 + 0.465797i 0.154232π0.154232\pi
−0.884891 + 0.465797i 0.845768π0.845768\pi
642642 0 0
643643 −29.9073 + 29.9073i −1.17943 + 1.17943i −0.199537 + 0.979890i 0.563944π0.563944\pi
−0.979890 + 0.199537i 0.936056π0.936056\pi
644644 −5.32760 16.3966i −0.209937 0.646117i
645645 0 0
646646 10.8258 + 7.86539i 0.425935 + 0.309460i
647647 35.8559i 1.40964i −0.709385 0.704821i 0.751027π-0.751027\pi
0.709385 0.704821i 0.248973π-0.248973\pi
648648 0 0
649649 19.8448i 0.778975i
650650 −29.3283 + 40.3670i −1.15035 + 1.58333i
651651 0 0
652652 1.20287 2.36077i 0.0471079 0.0924547i
653653 −26.7966 + 26.7966i −1.04863 + 1.04863i −0.0498765 + 0.998755i 0.515883π0.515883\pi
−0.998755 + 0.0498765i 0.984117π0.984117\pi
654654 0 0
655655 19.3226i 0.754995i
656656 30.9554 22.4906i 1.20861 0.878109i
657657 0 0
658658 −4.71891 + 0.747406i −0.183962 + 0.0291369i
659659 −19.9220 19.9220i −0.776050 0.776050i 0.203107 0.979157i 0.434896π-0.434896\pi
−0.979157 + 0.203107i 0.934896π0.934896\pi
660660 0 0
661661 3.02969 3.02969i 0.117841 0.117841i −0.645727 0.763568i 0.723446π-0.723446\pi
0.763568 + 0.645727i 0.223446π0.223446\pi
662662 −0.233730 0.169814i −0.00908417 0.00660003i
663663 0 0
664664 27.8170 + 9.03824i 1.07951 + 0.350752i
665665 6.10874 0.236887
666666 0 0
667667 17.6424 + 17.6424i 0.683117 + 0.683117i
668668 −11.0719 34.0757i −0.428385 1.31843i
669669 0 0
670670 −21.9263 + 3.47280i −0.847087 + 0.134166i
671671 2.10776 0.0813693
672672 0 0
673673 41.8102 1.61166 0.805832 0.592144i 0.201718π-0.201718\pi
0.805832 + 0.592144i 0.201718π0.201718\pi
674674 25.5972 4.05421i 0.985965 0.156162i
675675 0 0
676676 5.10892 + 15.7236i 0.196497 + 0.604752i
677677 −11.0622 11.0622i −0.425154 0.425154i 0.461820 0.886974i 0.347197π-0.347197\pi
−0.886974 + 0.461820i 0.847197π0.847197\pi
678678 0 0
679679 −7.84085 −0.300904
680680 −17.1269 + 52.7115i −0.656786 + 2.02139i
681681 0 0
682682 0.261953 + 0.190320i 0.0100307 + 0.00728773i
683683 −25.6844 + 25.6844i −0.982786 + 0.982786i −0.999854 0.0170687i 0.994567π-0.994567\pi
0.0170687 + 0.999854i 0.494567π0.494567\pi
684684 0 0
685685 29.7434 + 29.7434i 1.13644 + 1.13644i
686686 −1.39680 + 0.221233i −0.0533302 + 0.00844670i
687687 0 0
688688 28.0404 + 4.44108i 1.06903 + 0.169315i
689689 24.3075i 0.926044i
690690 0 0
691691 15.7276 15.7276i 0.598306 0.598306i −0.341556 0.939862i 0.610954π-0.610954\pi
0.939862 + 0.341556i 0.110954π0.110954\pi
692692 −2.51280 + 4.93166i −0.0955222 + 0.187474i
693693 0 0
694694 9.05200 12.4590i 0.343609 0.472938i
695695 53.4809i 2.02865i
696696 0 0
697697 52.7005i 1.99617i
698698 −14.9490 10.8611i −0.565830 0.411099i
699699 0 0
700700 4.72848 + 14.5527i 0.178720 + 0.550040i
701701 −4.35804 + 4.35804i −0.164601 + 0.164601i −0.784601 0.620000i 0.787132π-0.787132\pi
0.620000 + 0.784601i 0.287132π0.287132\pi
702702 0 0
703703 20.1866i 0.761352i
704704 1.74255 + 11.0017i 0.0656748 + 0.414644i
705705 0 0
706706 −3.07626 19.4226i −0.115776 0.730981i
707707 0.748257 + 0.748257i 0.0281411 + 0.0281411i
708708 0 0
709709 −2.68056 + 2.68056i −0.100670 + 0.100670i −0.755648 0.654978i 0.772678π-0.772678\pi
0.654978 + 0.755648i 0.272678π0.272678\pi
710710 −22.6552 + 31.1822i −0.850233 + 1.17025i
711711 0 0
712712 −18.8799 + 9.61982i −0.707553 + 0.360518i
713713 1.41748 0.0530850
714714 0 0
715715 −16.1489 16.1489i −0.603934 0.603934i
716716 41.4655 + 21.1277i 1.54964 + 0.789578i
717717 0 0
718718 4.51269 + 28.4919i 0.168412 + 1.06331i
719719 19.9117 0.742581 0.371290 0.928517i 0.378915π-0.378915\pi
0.371290 + 0.928517i 0.378915π0.378915\pi
720720 0 0
721721 −11.8161 −0.440056
722722 −3.55084 22.4190i −0.132149 0.834350i
723723 0 0
724724 2.58920 5.08160i 0.0962268 0.188856i
725725 −15.6584 15.6584i −0.581539 0.581539i
726726 0 0
727727 24.0642 0.892491 0.446246 0.894911i 0.352761π-0.352761\pi
0.446246 + 0.894911i 0.352761π0.352761\pi
728728 12.4050 + 4.03061i 0.459761 + 0.149385i
729729 0 0
730730 24.8528 34.2070i 0.919844 1.26606i
731731 −27.6492 + 27.6492i −1.02264 + 1.02264i
732732 0 0
733733 −3.18890 3.18890i −0.117785 0.117785i 0.645758 0.763542i 0.276542π-0.276542\pi
−0.763542 + 0.645758i 0.776542π0.776542\pi
734734 −4.70683 29.7176i −0.173732 1.09690i
735735 0 0
736736 34.4809 + 34.4807i 1.27098 + 1.27098i
737737 6.14502i 0.226355i
738738 0 0
739739 20.8311 20.8311i 0.766285 0.766285i −0.211165 0.977450i 0.567726π-0.567726\pi
0.977450 + 0.211165i 0.0677258π0.0677258\pi
740740 79.5181 25.8371i 2.92314 0.949792i
741741 0 0
742742 −6.03069 4.38155i −0.221394 0.160852i
743743 28.6291i 1.05030i 0.851010 + 0.525150i 0.175991π0.175991\pi
−0.851010 + 0.525150i 0.824009π0.824009\pi
744744 0 0
745745 48.6258i 1.78151i
746746 −17.2253 + 23.7086i −0.630662 + 0.868032i
747747 0 0
748748 −13.6696 6.96501i −0.499812 0.254666i
749749 −4.41189 + 4.41189i −0.161207 + 0.161207i
750750 0 0
751751 28.1706i 1.02796i −0.857802 0.513980i 0.828170π-0.828170\pi
0.857802 0.513980i 0.171830π-0.171830\pi
752752 10.9326 7.94305i 0.398671 0.289653i
753753 0 0
754754 −18.6439 + 2.95292i −0.678971 + 0.107539i
755755 12.7042 + 12.7042i 0.462355 + 0.462355i
756756 0 0
757757 −4.64056 + 4.64056i −0.168664 + 0.168664i −0.786392 0.617728i 0.788053π-0.788053\pi
0.617728 + 0.786392i 0.288053π0.288053\pi
758758 14.3287 + 10.4104i 0.520444 + 0.378124i
759759 0 0
760760 −15.3949 + 7.84414i −0.558432 + 0.284537i
761761 6.29768 0.228291 0.114145 0.993464i 0.463587π-0.463587\pi
0.114145 + 0.993464i 0.463587π0.463587\pi
762762 0 0
763763 −0.128743 0.128743i −0.00466082 0.00466082i
764764 −12.7885 + 4.15524i −0.462670 + 0.150331i
765765 0 0
766766 46.5935 7.37972i 1.68349 0.266640i
767767 65.7265 2.37325
768768 0 0
769769 4.73382 0.170706 0.0853529 0.996351i 0.472798π-0.472798\pi
0.0853529 + 0.996351i 0.472798π0.472798\pi
770770 −6.91745 + 1.09562i −0.249288 + 0.0394834i
771771 0 0
772772 2.61623 0.850068i 0.0941601 0.0305946i
773773 −5.44275 5.44275i −0.195762 0.195762i 0.602418 0.798180i 0.294204π-0.294204\pi
−0.798180 + 0.602418i 0.794204π0.794204\pi
774774 0 0
775775 −1.25808 −0.0451914
776776 19.7601 10.0683i 0.709346 0.361431i
777777 0 0
778778 −3.24801 2.35982i −0.116447 0.0846035i
779779 −11.6171 + 11.6171i −0.416226 + 0.416226i
780780 0 0
781781 −7.54417 7.54417i −0.269952 0.269952i
782782 −66.3356 + 10.5066i −2.37216 + 0.375714i
783783 0 0
784784 3.23606 2.35115i 0.115574 0.0839696i
785785 55.8852i 1.99463i
786786 0 0
787787 −27.1082 + 27.1082i −0.966302 + 0.966302i −0.999450 0.0331485i 0.989447π-0.989447\pi
0.0331485 + 0.999450i 0.489447π0.489447\pi
788788 −25.7142 13.1020i −0.916032 0.466740i
789789 0 0
790790 −41.0115 + 56.4476i −1.45912 + 2.00832i
791791 14.3042i 0.508600i
792792 0 0
793793 6.98099i 0.247902i
794794 3.94777 + 2.86822i 0.140101 + 0.101789i
795795 0 0
796796 −28.4158 + 9.23289i −1.00717 + 0.327251i
797797 11.7301 11.7301i 0.415501 0.415501i −0.468149 0.883650i 0.655079π-0.655079\pi
0.883650 + 0.468149i 0.155079π0.155079\pi
798798 0 0
799799 18.6124i 0.658458i
800800 −30.6033 30.6031i −1.08199 1.08198i
801801 0 0
802802 −2.58396 16.3144i −0.0912429 0.576082i
803803 8.27599 + 8.27599i 0.292053 + 0.292053i
804804 0 0
805805 −21.6801 + 21.6801i −0.764124 + 0.764124i
806806 −0.630346 + 0.867598i −0.0222030 + 0.0305598i
807807 0 0
808808 −2.84654 0.924890i −0.100141 0.0325375i
809809 −13.7126 −0.482111 −0.241055 0.970511i 0.577494π-0.577494\pi
−0.241055 + 0.970511i 0.577494π0.577494\pi
810810 0 0
811811 22.2730 + 22.2730i 0.782111 + 0.782111i 0.980187 0.198076i 0.0634692π-0.0634692\pi
−0.198076 + 0.980187i 0.563469π0.563469\pi
812812 −2.62803 + 5.15782i −0.0922259 + 0.181004i
813813 0 0
814814 3.62053 + 22.8590i 0.126899 + 0.801208i
815815 −4.71195 −0.165052
816816 0 0
817817 −12.1898 −0.426467
818818 −3.38377 21.3642i −0.118311 0.746981i
819819 0 0
820820 −60.6304 30.8926i −2.11731 1.07882i
821821 −0.690329 0.690329i −0.0240926 0.0240926i 0.694958 0.719050i 0.255423π-0.255423\pi
−0.719050 + 0.694958i 0.755423π0.755423\pi
822822 0 0
823823 −1.43063 −0.0498688 −0.0249344 0.999689i 0.507938π-0.507938\pi
−0.0249344 + 0.999689i 0.507938π0.507938\pi
824824 29.7784 15.1729i 1.03738 0.528574i
825825 0 0
826826 11.8475 16.3067i 0.412228 0.567384i
827827 −9.59770 + 9.59770i −0.333745 + 0.333745i −0.854007 0.520262i 0.825834π-0.825834\pi
0.520262 + 0.854007i 0.325834π0.325834\pi
828828 0 0
829829 17.0260 + 17.0260i 0.591337 + 0.591337i 0.937992 0.346656i 0.112683π-0.112683\pi
−0.346656 + 0.937992i 0.612683π0.612683\pi
830830 −8.13706 51.3752i −0.282442 1.78326i
831831 0 0
832832 −36.4381 + 5.77139i −1.26327 + 0.200087i
833833 5.50927i 0.190885i
834834 0 0
835835 −45.0560 + 45.0560i −1.55923 + 1.55923i
836836 −1.47795 4.54863i −0.0511158 0.157318i
837837 0 0
838838 −21.3310 15.4979i −0.736867 0.535364i
839839 29.0214i 1.00193i 0.865467 + 0.500965i 0.167022π0.167022\pi
−0.865467 + 0.500965i 0.832978π0.832978\pi
840840 0 0
841841 20.6226i 0.711123i
842842 26.1651 36.0133i 0.901710 1.24110i
843843 0 0
844844 6.33731 12.4377i 0.218139 0.428124i
845845 20.7902 20.7902i 0.715205 0.715205i
846846 0 0
847847 9.06133i 0.311351i
848848 20.8245 + 3.29822i 0.715116 + 0.113261i
849849 0 0
850850 58.8758 9.32505i 2.01942 0.319846i
851851 71.6430 + 71.6430i 2.45589 + 2.45589i
852852 0 0
853853 17.4096 17.4096i 0.596092 0.596092i −0.343178 0.939270i 0.611503π-0.611503\pi
0.939270 + 0.343178i 0.111503π0.111503\pi
854854 1.73198 + 1.25836i 0.0592672 + 0.0430600i
855855 0 0
856856 5.45336 16.7838i 0.186392 0.573660i
857857 17.6637 0.603379 0.301690 0.953406i 0.402449π-0.402449\pi
0.301690 + 0.953406i 0.402449π0.402449\pi
858858 0 0
859859 5.79823 + 5.79823i 0.197833 + 0.197833i 0.799070 0.601237i 0.205325π-0.205325\pi
−0.601237 + 0.799070i 0.705325π0.705325\pi
860860 −15.6019 48.0174i −0.532020 1.63738i
861861 0 0
862862 26.5848 4.21064i 0.905482 0.143415i
863863 39.0789 1.33026 0.665131 0.746727i 0.268376π-0.268376\pi
0.665131 + 0.746727i 0.268376π0.268376\pi
864864 0 0
865865 9.84331 0.334683
866866 44.2954 7.01574i 1.50522 0.238405i
867867 0 0
868868 0.101628 + 0.312777i 0.00344948 + 0.0106164i
869869 −13.6568 13.6568i −0.463277 0.463277i
870870 0 0
871871 20.3525 0.689618
872872 0.489769 + 0.159134i 0.0165857 + 0.00538897i
873873 0 0
874874 −16.9388 12.3068i −0.572964 0.416282i
875875 6.66689 6.66689i 0.225382 0.225382i
876876 0 0
877877 6.28950 + 6.28950i 0.212381 + 0.212381i 0.805278 0.592897i 0.202016π-0.202016\pi
−0.592897 + 0.805278i 0.702016π0.702016\pi
878878 −46.0276 + 7.29008i −1.55336 + 0.246028i
879879 0 0
880880 16.0261 11.6437i 0.540240 0.392509i
881881 21.5545i 0.726190i 0.931752 + 0.363095i 0.118280π0.118280\pi
−0.931752 + 0.363095i 0.881720π0.881720\pi
882882 0 0
883883 5.85864 5.85864i 0.197159 0.197159i −0.601622 0.798781i 0.705479π-0.705479\pi
0.798781 + 0.601622i 0.205479π0.205479\pi
884884 23.0683 45.2743i 0.775872 1.52274i
885885 0 0
886886 5.81643 8.00565i 0.195407 0.268955i
887887 28.0138i 0.940613i −0.882503 0.470306i 0.844143π-0.844143\pi
0.882503 0.470306i 0.155857π-0.155857\pi
888888 0 0
889889 1.31914i 0.0442426i
890890 30.4863 + 22.1496i 1.02190 + 0.742456i
891891 0 0
892892 −3.24931 10.0003i −0.108795 0.334835i
893893 −4.10284 + 4.10284i −0.137296 + 0.137296i
894894 0 0
895895 82.7628i 2.76645i
896896 −5.13627 + 10.0806i −0.171591 + 0.336770i
897897 0 0
898898 6.97454 + 44.0353i 0.232743 + 1.46948i
899899 −0.336542 0.336542i −0.0112243 0.0112243i
900900 0 0
901901 −20.5340 + 20.5340i −0.684087 + 0.684087i
902902 11.0715 15.2386i 0.368640 0.507390i
903903 0 0
904904 −18.3678 36.0487i −0.610905 1.19896i
905905 −10.1426 −0.337151
906906 0 0
907907 3.74119 + 3.74119i 0.124224 + 0.124224i 0.766486 0.642262i 0.222004π-0.222004\pi
−0.642262 + 0.766486i 0.722004π0.722004\pi
908908 −15.9004 8.10163i −0.527673 0.268862i
909909 0 0
910910 −3.62873 22.9108i −0.120291 0.759486i
911911 46.9910 1.55688 0.778441 0.627718i 0.216011π-0.216011\pi
0.778441 + 0.627718i 0.216011π0.216011\pi
912912 0 0
913913 14.3983 0.476514
914914 −7.79883 49.2397i −0.257963 1.62870i
915915 0 0
916916 24.6266 48.3327i 0.813687 1.59696i
917917 −3.84141 3.84141i −0.126855 0.126855i
918918 0 0
919919 −28.7166 −0.947272 −0.473636 0.880721i 0.657059π-0.657059\pi
−0.473636 + 0.880721i 0.657059π0.657059\pi
920920 26.7979 82.4762i 0.883502 2.71916i
921921 0 0
922922 18.6644 25.6894i 0.614680 0.846035i
923923 24.9866 24.9866i 0.822442 0.822442i
924924 0 0
925925 −63.5863 63.5863i −2.09070 2.09070i
926926 3.52241 + 22.2395i 0.115754 + 0.730836i
927927 0 0
928928 −5.53246e−5 16.3731i −1.81612e−6 0.537472i
929929 39.0905i 1.28252i 0.767325 + 0.641259i 0.221587π0.221587\pi
−0.767325 + 0.641259i 0.778413π0.778413\pi
930930 0 0
931931 −1.21444 + 1.21444i −0.0398018 + 0.0398018i
932932 −1.05573 + 0.343028i −0.0345815 + 0.0112363i
933933 0 0
934934 10.5564 + 7.66965i 0.345416 + 0.250959i
935935 27.2838i 0.892277i
936936 0 0
937937 22.0325i 0.719770i 0.932997 + 0.359885i 0.117184π0.117184\pi
−0.932997 + 0.359885i 0.882816π0.882816\pi
938938 3.66863 5.04945i 0.119785 0.164870i
939939 0 0
940940 −21.4130 10.9104i −0.698415 0.355859i
941941 −28.7845 + 28.7845i −0.938349 + 0.938349i −0.998207 0.0598579i 0.980935π-0.980935\pi
0.0598579 + 0.998207i 0.480935π0.480935\pi
942942 0 0
943943 82.4590i 2.68523i
944944 −8.91824 + 56.3085i −0.290264 + 1.83269i
945945 0 0
946946 13.8035 2.18627i 0.448792 0.0710819i
947947 −8.81984 8.81984i −0.286606 0.286606i 0.549130 0.835737i 0.314959π-0.314959\pi
−0.835737 + 0.549130i 0.814959π0.814959\pi
948948 0 0
949949 −27.4104 + 27.4104i −0.889778 + 0.889778i
950950 15.0339 + 10.9228i 0.487766 + 0.354382i
951951 0 0
952952 −7.07437 13.8842i −0.229282 0.449988i
953953 1.32312 0.0428599 0.0214300 0.999770i 0.493178π-0.493178\pi
0.0214300 + 0.999770i 0.493178π0.493178\pi
954954 0 0
955955 16.9093 + 16.9093i 0.547173 + 0.547173i
956956 −43.8262 + 14.2401i −1.41744 + 0.460557i
957957 0 0
958958 44.1237 6.98853i 1.42557 0.225789i
959959 −11.8262 −0.381889
960960 0 0
961961 30.9730 0.999128
962962 −75.7098 + 11.9913i −2.44098 + 0.386615i
963963 0 0
964964 −14.2245 + 4.62184i −0.458141 + 0.148860i
965965 −3.45926 3.45926i −0.111358 0.111358i
966966 0 0
967967 16.3028 0.524263 0.262132 0.965032i 0.415575π-0.415575\pi
0.262132 + 0.965032i 0.415575π0.415575\pi
968968 −11.6355 22.8359i −0.373979 0.733972i
969969 0 0
970970 −31.9077 23.1823i −1.02449 0.744338i
971971 16.8788 16.8788i 0.541666 0.541666i −0.382351 0.924017i 0.624886π-0.624886\pi
0.924017 + 0.382351i 0.124886π0.124886\pi
972972 0 0
973973 −10.6322 10.6322i −0.340854 0.340854i
974974 41.1791 6.52215i 1.31946 0.208983i
975975 0 0
976976 −5.98068 0.947229i −0.191437 0.0303201i
977977 1.46807i 0.0469676i 0.999724 + 0.0234838i 0.00747581π0.00747581\pi
−0.999724 + 0.0234838i 0.992524π0.992524\pi
978978 0 0
979979 −7.37582 + 7.37582i −0.235732 + 0.235732i
980980 −6.33826 3.22950i −0.202468 0.103162i
981981 0 0
982982 7.13408 9.81923i 0.227658 0.313344i
983983 34.4565i 1.09899i −0.835496 0.549496i 0.814820π-0.814820\pi
0.835496 0.549496i 0.185180π-0.185180\pi
984984 0 0
985985 51.3241i 1.63532i
986986 18.2441 + 13.2551i 0.581010 + 0.422128i
987987 0 0
988988 15.0652 4.89501i 0.479288 0.155731i
989989 43.2620 43.2620i 1.37565 1.37565i
990990 0 0
991991 14.4789i 0.459937i −0.973198 0.229969i 0.926138π-0.926138\pi
0.973198 0.229969i 0.0738624π-0.0738624\pi
992992 −0.657749 0.657745i −0.0208836 0.0208834i
993993 0 0
994994 −1.69521 10.7031i −0.0537689 0.339482i
995995 37.5723 + 37.5723i 1.19112 + 1.19112i
996996 0 0
997997 −32.5498 + 32.5498i −1.03086 + 1.03086i −0.0313557 + 0.999508i 0.509982π0.509982\pi
−0.999508 + 0.0313557i 0.990018π0.990018\pi
998998 −18.6878 + 25.7216i −0.591551 + 0.814202i
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 1008.2.v.e.323.2 40
3.2 odd 2 inner 1008.2.v.e.323.19 yes 40
4.3 odd 2 4032.2.v.e.1583.3 40
12.11 even 2 4032.2.v.e.1583.18 40
16.5 even 4 4032.2.v.e.3599.18 40
16.11 odd 4 inner 1008.2.v.e.827.19 yes 40
48.5 odd 4 4032.2.v.e.3599.3 40
48.11 even 4 inner 1008.2.v.e.827.2 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1008.2.v.e.323.2 40 1.1 even 1 trivial
1008.2.v.e.323.19 yes 40 3.2 odd 2 inner
1008.2.v.e.827.2 yes 40 48.11 even 4 inner
1008.2.v.e.827.19 yes 40 16.11 odd 4 inner
4032.2.v.e.1583.3 40 4.3 odd 2
4032.2.v.e.1583.18 40 12.11 even 2
4032.2.v.e.3599.3 40 48.5 odd 4
4032.2.v.e.3599.18 40 16.5 even 4