Properties

Label 450.2.h.c.361.1
Level 450450
Weight 22
Character 450.361
Analytic conductor 3.5933.593
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(91,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 450=23252 450 = 2 \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 450.h (of order 55, degree 44, 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: 3.593268090963.59326809096
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ10)\Q(\zeta_{10})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3+x2x+1 x^{4} - x^{3} + x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 361.1
Root 0.809017+0.587785i0.809017 + 0.587785i of defining polynomial
Character χ\chi == 450.361
Dual form 450.2.h.c.91.1

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+(0.8090170.587785i)q2+(0.3090170.951057i)q4+(1.80902+1.31433i)q5+2.61803q7+(0.3090170.951057i)q8+(0.690983+2.12663i)q10+(2.927052.12663i)q11+(5.23607+3.80423i)q13+(2.118031.53884i)q14+(0.8090170.587785i)q16+(0.3819661.17557i)q17+(1.763935.42882i)q19+(0.690983+2.12663i)q20+(1.118033.44095i)q22+(3.618032.62866i)q23+(1.545084.75528i)q25+6.47214q26+(0.8090172.48990i)q28+(2.61803+8.05748i)q29+(2.04508+6.29412i)q311.00000q32+(1.000000.726543i)q34+(4.73607+3.44095i)q35+(6.472144.70228i)q37+(4.618033.35520i)q38+(1.80902+1.31433i)q40+(4.61803+3.35520i)q417.70820q43+(1.118033.44095i)q44+(1.381974.25325i)q46+(0.527864+1.62460i)q470.145898q49+(1.545084.75528i)q50+(5.236073.80423i)q52+(0.6458981.98787i)q53+(2.50000+7.69421i)q55+(0.8090172.48990i)q56+(2.61803+8.05748i)q58+(2.927052.12663i)q59+(2.23607+1.62460i)q61+(5.35410+3.88998i)q62+(0.809017+0.587785i)q6414.4721q65+(0.4721361.45309i)q671.23607q68+(1.80902+5.56758i)q70+(1.70820+5.25731i)q71+(2.85410+2.07363i)q738.00000q745.70820q76+(7.663125.56758i)q77+(1.73607+5.34307i)q79+2.23607q80+5.70820q82+(0.6631192.04087i)q83+(2.23607+1.62460i)q85+(6.23607+4.53077i)q86+(2.927052.12663i)q88+(2.854102.07363i)q89+(13.7082+9.95959i)q91+(1.381974.25325i)q92+(0.527864+1.62460i)q94+(10.3262+7.50245i)q95+(1.04508+3.21644i)q97+(0.118034+0.0857567i)q98+O(q100)q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(2.92705 - 2.12663i) q^{11} +(5.23607 + 3.80423i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.381966 - 1.17557i) q^{17} +(-1.76393 - 5.42882i) q^{19} +(0.690983 + 2.12663i) q^{20} +(1.11803 - 3.44095i) q^{22} +(3.61803 - 2.62866i) q^{23} +(1.54508 - 4.75528i) q^{25} +6.47214 q^{26} +(0.809017 - 2.48990i) q^{28} +(-2.61803 + 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000 q^{32} +(-1.00000 - 0.726543i) q^{34} +(-4.73607 + 3.44095i) q^{35} +(-6.47214 - 4.70228i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(1.80902 + 1.31433i) q^{40} +(4.61803 + 3.35520i) q^{41} -7.70820 q^{43} +(-1.11803 - 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-0.527864 + 1.62460i) q^{47} -0.145898 q^{49} +(-1.54508 - 4.75528i) q^{50} +(5.23607 - 3.80423i) q^{52} +(0.645898 - 1.98787i) q^{53} +(-2.50000 + 7.69421i) q^{55} +(-0.809017 - 2.48990i) q^{56} +(2.61803 + 8.05748i) q^{58} +(-2.92705 - 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(5.35410 + 3.88998i) q^{62} +(-0.809017 + 0.587785i) q^{64} -14.4721 q^{65} +(-0.472136 - 1.45309i) q^{67} -1.23607 q^{68} +(-1.80902 + 5.56758i) q^{70} +(-1.70820 + 5.25731i) q^{71} +(-2.85410 + 2.07363i) q^{73} -8.00000 q^{74} -5.70820 q^{76} +(7.66312 - 5.56758i) q^{77} +(-1.73607 + 5.34307i) q^{79} +2.23607 q^{80} +5.70820 q^{82} +(-0.663119 - 2.04087i) q^{83} +(2.23607 + 1.62460i) q^{85} +(-6.23607 + 4.53077i) q^{86} +(-2.92705 - 2.12663i) q^{88} +(2.85410 - 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(-1.38197 - 4.25325i) q^{92} +(0.527864 + 1.62460i) q^{94} +(10.3262 + 7.50245i) q^{95} +(-1.04508 + 3.21644i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+q2q45q5+6q7+q85q10+5q11+12q13+4q14q166q1716q19+5q20+10q235q25+8q26+q286q293q31++4q98+O(q100) 4 q + q^{2} - q^{4} - 5 q^{5} + 6 q^{7} + q^{8} - 5 q^{10} + 5 q^{11} + 12 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 16 q^{19} + 5 q^{20} + 10 q^{23} - 5 q^{25} + 8 q^{26} + q^{28} - 6 q^{29} - 3 q^{31}+ \cdots + 4 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/450Z)×\left(\mathbb{Z}/450\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 11 e(45)e\left(\frac{4}{5}\right)

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 0.809017 0.587785i 0.572061 0.415627i
33 0 0
44 0.309017 0.951057i 0.154508 0.475528i
55 −1.80902 + 1.31433i −0.809017 + 0.587785i
66 0 0
77 2.61803 0.989524 0.494762 0.869029i 0.335255π-0.335255\pi
0.494762 + 0.869029i 0.335255π0.335255\pi
88 −0.309017 0.951057i −0.109254 0.336249i
99 0 0
1010 −0.690983 + 2.12663i −0.218508 + 0.672499i
1111 2.92705 2.12663i 0.882539 0.641202i −0.0513829 0.998679i 0.516363π-0.516363\pi
0.933922 + 0.357477i 0.116363π0.116363\pi
1212 0 0
1313 5.23607 + 3.80423i 1.45222 + 1.05510i 0.985305 + 0.170802i 0.0546359π0.0546359\pi
0.466919 + 0.884300i 0.345364π0.345364\pi
1414 2.11803 1.53884i 0.566068 0.411273i
1515 0 0
1616 −0.809017 0.587785i −0.202254 0.146946i
1717 −0.381966 1.17557i −0.0926404 0.285118i 0.893991 0.448085i 0.147894π-0.147894\pi
−0.986632 + 0.162967i 0.947894π0.947894\pi
1818 0 0
1919 −1.76393 5.42882i −0.404674 1.24546i −0.921167 0.389167i 0.872763π-0.872763\pi
0.516494 0.856291i 0.327237π-0.327237\pi
2020 0.690983 + 2.12663i 0.154508 + 0.475528i
2121 0 0
2222 1.11803 3.44095i 0.238366 0.733614i
2323 3.61803 2.62866i 0.754412 0.548113i −0.142779 0.989755i 0.545604π-0.545604\pi
0.897191 + 0.441642i 0.145604π0.145604\pi
2424 0 0
2525 1.54508 4.75528i 0.309017 0.951057i
2626 6.47214 1.26929
2727 0 0
2828 0.809017 2.48990i 0.152890 0.470547i
2929 −2.61803 + 8.05748i −0.486157 + 1.49624i 0.344142 + 0.938918i 0.388170π0.388170\pi
−0.830299 + 0.557319i 0.811830π0.811830\pi
3030 0 0
3131 2.04508 + 6.29412i 0.367308 + 1.13046i 0.948523 + 0.316708i 0.102578π0.102578\pi
−0.581215 + 0.813750i 0.697422π0.697422\pi
3232 −1.00000 −0.176777
3333 0 0
3434 −1.00000 0.726543i −0.171499 0.124601i
3535 −4.73607 + 3.44095i −0.800542 + 0.581628i
3636 0 0
3737 −6.47214 4.70228i −1.06401 0.773050i −0.0891861 0.996015i 0.528427π-0.528427\pi
−0.974827 + 0.222965i 0.928427π0.928427\pi
3838 −4.61803 3.35520i −0.749144 0.544285i
3939 0 0
4040 1.80902 + 1.31433i 0.286031 + 0.207813i
4141 4.61803 + 3.35520i 0.721216 + 0.523994i 0.886772 0.462206i 0.152942π-0.152942\pi
−0.165557 + 0.986200i 0.552942π0.552942\pi
4242 0 0
4343 −7.70820 −1.17549 −0.587745 0.809046i 0.699984π-0.699984\pi
−0.587745 + 0.809046i 0.699984π0.699984\pi
4444 −1.11803 3.44095i −0.168550 0.518743i
4545 0 0
4646 1.38197 4.25325i 0.203760 0.627108i
4747 −0.527864 + 1.62460i −0.0769969 + 0.236972i −0.982145 0.188123i 0.939759π-0.939759\pi
0.905149 + 0.425096i 0.139759π0.139759\pi
4848 0 0
4949 −0.145898 −0.0208426
5050 −1.54508 4.75528i −0.218508 0.672499i
5151 0 0
5252 5.23607 3.80423i 0.726112 0.527551i
5353 0.645898 1.98787i 0.0887209 0.273055i −0.896846 0.442344i 0.854147π-0.854147\pi
0.985566 + 0.169289i 0.0541471π0.0541471\pi
5454 0 0
5555 −2.50000 + 7.69421i −0.337100 + 1.03749i
5656 −0.809017 2.48990i −0.108109 0.332727i
5757 0 0
5858 2.61803 + 8.05748i 0.343765 + 1.05800i
5959 −2.92705 2.12663i −0.381070 0.276863i 0.380717 0.924692i 0.375677π-0.375677\pi
−0.761786 + 0.647829i 0.775677π0.775677\pi
6060 0 0
6161 −2.23607 + 1.62460i −0.286299 + 0.208009i −0.721660 0.692247i 0.756621π-0.756621\pi
0.435361 + 0.900256i 0.356621π0.356621\pi
6262 5.35410 + 3.88998i 0.679972 + 0.494028i
6363 0 0
6464 −0.809017 + 0.587785i −0.101127 + 0.0734732i
6565 −14.4721 −1.79505
6666 0 0
6767 −0.472136 1.45309i −0.0576806 0.177523i 0.918065 0.396430i 0.129751π-0.129751\pi
−0.975746 + 0.218907i 0.929751π0.929751\pi
6868 −1.23607 −0.149895
6969 0 0
7070 −1.80902 + 5.56758i −0.216219 + 0.665453i
7171 −1.70820 + 5.25731i −0.202727 + 0.623928i 0.797073 + 0.603884i 0.206381π0.206381\pi
−0.999799 + 0.0200445i 0.993619π0.993619\pi
7272 0 0
7373 −2.85410 + 2.07363i −0.334047 + 0.242700i −0.742146 0.670238i 0.766192π-0.766192\pi
0.408099 + 0.912938i 0.366192π0.366192\pi
7474 −8.00000 −0.929981
7575 0 0
7676 −5.70820 −0.654776
7777 7.66312 5.56758i 0.873293 0.634485i
7878 0 0
7979 −1.73607 + 5.34307i −0.195323 + 0.601142i 0.804650 + 0.593750i 0.202353π0.202353\pi
−0.999973 + 0.00739236i 0.997647π0.997647\pi
8080 2.23607 0.250000
8181 0 0
8282 5.70820 0.630366
8383 −0.663119 2.04087i −0.0727868 0.224015i 0.908044 0.418874i 0.137575π-0.137575\pi
−0.980831 + 0.194859i 0.937575π0.937575\pi
8484 0 0
8585 2.23607 + 1.62460i 0.242536 + 0.176212i
8686 −6.23607 + 4.53077i −0.672453 + 0.488565i
8787 0 0
8888 −2.92705 2.12663i −0.312025 0.226699i
8989 2.85410 2.07363i 0.302534 0.219804i −0.426152 0.904651i 0.640131π-0.640131\pi
0.728686 + 0.684848i 0.240131π0.240131\pi
9090 0 0
9191 13.7082 + 9.95959i 1.43701 + 1.04405i
9292 −1.38197 4.25325i −0.144080 0.443432i
9393 0 0
9494 0.527864 + 1.62460i 0.0544450 + 0.167565i
9595 10.3262 + 7.50245i 1.05945 + 0.769735i
9696 0 0
9797 −1.04508 + 3.21644i −0.106112 + 0.326580i −0.989990 0.141138i 0.954924π-0.954924\pi
0.883878 + 0.467718i 0.154924π0.154924\pi
9898 −0.118034 + 0.0857567i −0.0119232 + 0.00866274i
9999 0 0
100100 −4.04508 2.93893i −0.404508 0.293893i
101101 −4.38197 −0.436022 −0.218011 0.975946i 0.569957π-0.569957\pi
−0.218011 + 0.975946i 0.569957π0.569957\pi
102102 0 0
103103 4.42705 13.6251i 0.436210 1.34252i −0.455631 0.890169i 0.650586π-0.650586\pi
0.891841 0.452348i 0.149414π-0.149414\pi
104104 2.00000 6.15537i 0.196116 0.603583i
105105 0 0
106106 −0.645898 1.98787i −0.0627352 0.193079i
107107 11.6180 1.12316 0.561579 0.827423i 0.310194π-0.310194\pi
0.561579 + 0.827423i 0.310194π0.310194\pi
108108 0 0
109109 −13.9443 10.1311i −1.33562 0.970384i −0.999593 0.0285313i 0.990917π-0.990917\pi
−0.336026 0.941853i 0.609083π-0.609083\pi
110110 2.50000 + 7.69421i 0.238366 + 0.733614i
111111 0 0
112112 −2.11803 1.53884i −0.200135 0.145407i
113113 −15.5623 11.3067i −1.46398 1.06364i −0.982304 0.187292i 0.940029π-0.940029\pi
−0.481674 0.876350i 0.659971π-0.659971\pi
114114 0 0
115115 −3.09017 + 9.51057i −0.288160 + 0.886865i
116116 6.85410 + 4.97980i 0.636387 + 0.462363i
117117 0 0
118118 −3.61803 −0.333067
119119 −1.00000 3.07768i −0.0916698 0.282131i
120120 0 0
121121 0.645898 1.98787i 0.0587180 0.180715i
122122 −0.854102 + 2.62866i −0.0773268 + 0.237987i
123123 0 0
124124 6.61803 0.594317
125125 3.45492 + 10.6331i 0.309017 + 0.951057i
126126 0 0
127127 −11.0172 + 8.00448i −0.977620 + 0.710283i −0.957176 0.289508i 0.906508π-0.906508\pi
−0.0204448 + 0.999791i 0.506508π0.506508\pi
128128 −0.309017 + 0.951057i −0.0273135 + 0.0840623i
129129 0 0
130130 −11.7082 + 8.50651i −1.02688 + 0.746070i
131131 5.52786 + 17.0130i 0.482972 + 1.48643i 0.834897 + 0.550406i 0.185527π0.185527\pi
−0.351925 + 0.936028i 0.614473π0.614473\pi
132132 0 0
133133 −4.61803 14.2128i −0.400434 1.23241i
134134 −1.23607 0.898056i −0.106780 0.0775802i
135135 0 0
136136 −1.00000 + 0.726543i −0.0857493 + 0.0623005i
137137 −9.85410 7.15942i −0.841893 0.611671i 0.0810060 0.996714i 0.474187π-0.474187\pi
−0.922899 + 0.385043i 0.874187π0.874187\pi
138138 0 0
139139 −8.47214 + 6.15537i −0.718597 + 0.522091i −0.885936 0.463808i 0.846483π-0.846483\pi
0.167339 + 0.985899i 0.446483π0.446483\pi
140140 1.80902 + 5.56758i 0.152890 + 0.470547i
141141 0 0
142142 1.70820 + 5.25731i 0.143349 + 0.441184i
143143 23.4164 1.95818
144144 0 0
145145 −5.85410 18.0171i −0.486157 1.49624i
146146 −1.09017 + 3.35520i −0.0902231 + 0.277678i
147147 0 0
148148 −6.47214 + 4.70228i −0.532006 + 0.386525i
149149 −22.0902 −1.80970 −0.904849 0.425733i 0.860016π-0.860016\pi
−0.904849 + 0.425733i 0.860016π0.860016\pi
150150 0 0
151151 18.3262 1.49137 0.745684 0.666300i 0.232123π-0.232123\pi
0.745684 + 0.666300i 0.232123π0.232123\pi
152152 −4.61803 + 3.35520i −0.374572 + 0.272143i
153153 0 0
154154 2.92705 9.00854i 0.235868 0.725929i
155155 −11.9721 8.69827i −0.961625 0.698662i
156156 0 0
157157 8.65248 0.690543 0.345271 0.938503i 0.387787π-0.387787\pi
0.345271 + 0.938503i 0.387787π0.387787\pi
158158 1.73607 + 5.34307i 0.138114 + 0.425072i
159159 0 0
160160 1.80902 1.31433i 0.143015 0.103907i
161161 9.47214 6.88191i 0.746509 0.542370i
162162 0 0
163163 0.381966 + 0.277515i 0.0299179 + 0.0217366i 0.602644 0.798010i 0.294114π-0.294114\pi
−0.572726 + 0.819747i 0.694114π0.694114\pi
164164 4.61803 3.35520i 0.360608 0.261997i
165165 0 0
166166 −1.73607 1.26133i −0.134745 0.0978980i
167167 −3.61803 11.1352i −0.279972 0.861665i −0.987861 0.155341i 0.950352π-0.950352\pi
0.707889 0.706324i 0.249648π-0.249648\pi
168168 0 0
169169 8.92705 + 27.4746i 0.686696 + 2.11343i
170170 2.76393 0.211984
171171 0 0
172172 −2.38197 + 7.33094i −0.181623 + 0.558979i
173173 4.11803 2.99193i 0.313088 0.227472i −0.420132 0.907463i 0.638016π-0.638016\pi
0.733221 + 0.679991i 0.238016π0.238016\pi
174174 0 0
175175 4.04508 12.4495i 0.305780 0.941093i
176176 −3.61803 −0.272720
177177 0 0
178178 1.09017 3.35520i 0.0817117 0.251483i
179179 −3.04508 + 9.37181i −0.227600 + 0.700482i 0.770417 + 0.637540i 0.220048π0.220048\pi
−0.998017 + 0.0629414i 0.979952π0.979952\pi
180180 0 0
181181 −2.05573 6.32688i −0.152801 0.470273i 0.845130 0.534560i 0.179523π-0.179523\pi
−0.997931 + 0.0642869i 0.979523π0.979523\pi
182182 16.9443 1.25599
183183 0 0
184184 −3.61803 2.62866i −0.266725 0.193787i
185185 17.8885 1.31519
186186 0 0
187187 −3.61803 2.62866i −0.264577 0.192226i
188188 1.38197 + 1.00406i 0.100790 + 0.0732284i
189189 0 0
190190 12.7639 0.925993
191191 3.47214 + 2.52265i 0.251235 + 0.182533i 0.706274 0.707939i 0.250375π-0.250375\pi
−0.455039 + 0.890472i 0.650375π0.650375\pi
192192 0 0
193193 17.8541 1.28517 0.642583 0.766216i 0.277863π-0.277863\pi
0.642583 + 0.766216i 0.277863π0.277863\pi
194194 1.04508 + 3.21644i 0.0750327 + 0.230927i
195195 0 0
196196 −0.0450850 + 0.138757i −0.00322036 + 0.00991123i
197197 5.28115 16.2537i 0.376267 1.15803i −0.566354 0.824162i 0.691646π-0.691646\pi
0.942620 0.333867i 0.108354π-0.108354\pi
198198 0 0
199199 19.5066 1.38278 0.691392 0.722480i 0.256998π-0.256998\pi
0.691392 + 0.722480i 0.256998π0.256998\pi
200200 −5.00000 −0.353553
201201 0 0
202202 −3.54508 + 2.57565i −0.249431 + 0.181222i
203203 −6.85410 + 21.0948i −0.481064 + 1.48056i
204204 0 0
205205 −12.7639 −0.891472
206206 −4.42705 13.6251i −0.308447 0.949303i
207207 0 0
208208 −2.00000 6.15537i −0.138675 0.426798i
209209 −16.7082 12.1392i −1.15573 0.839687i
210210 0 0
211211 2.76393 2.00811i 0.190277 0.138244i −0.488568 0.872526i 0.662481π-0.662481\pi
0.678845 + 0.734281i 0.262481π0.262481\pi
212212 −1.69098 1.22857i −0.116137 0.0843786i
213213 0 0
214214 9.39919 6.82891i 0.642515 0.466815i
215215 13.9443 10.1311i 0.950991 0.690936i
216216 0 0
217217 5.35410 + 16.4782i 0.363460 + 1.11862i
218218 −17.2361 −1.16737
219219 0 0
220220 6.54508 + 4.75528i 0.441270 + 0.320601i
221221 2.47214 7.60845i 0.166294 0.511800i
222222 0 0
223223 6.54508 4.75528i 0.438291 0.318437i −0.346664 0.937989i 0.612686π-0.612686\pi
0.784956 + 0.619552i 0.212686π0.212686\pi
224224 −2.61803 −0.174925
225225 0 0
226226 −19.2361 −1.27956
227227 −18.0172 + 13.0903i −1.19584 + 0.868832i −0.993870 0.110558i 0.964736π-0.964736\pi
−0.201975 + 0.979391i 0.564736π0.564736\pi
228228 0 0
229229 −1.70820 + 5.25731i −0.112881 + 0.347413i −0.991499 0.130113i 0.958466π-0.958466\pi
0.878618 + 0.477525i 0.158466π0.158466\pi
230230 3.09017 + 9.51057i 0.203760 + 0.627108i
231231 0 0
232232 8.47214 0.556223
233233 −5.76393 17.7396i −0.377608 1.16216i −0.941702 0.336447i 0.890775π-0.890775\pi
0.564095 0.825710i 0.309225π-0.309225\pi
234234 0 0
235235 −1.18034 3.63271i −0.0769969 0.236972i
236236 −2.92705 + 2.12663i −0.190535 + 0.138432i
237237 0 0
238238 −2.61803 1.90211i −0.169702 0.123296i
239239 9.94427 7.22494i 0.643241 0.467342i −0.217721 0.976011i 0.569862π-0.569862\pi
0.860962 + 0.508669i 0.169862π0.169862\pi
240240 0 0
241241 −7.73607 5.62058i −0.498324 0.362054i 0.310052 0.950719i 0.399653π-0.399653\pi
−0.808376 + 0.588666i 0.799653π0.799653\pi
242242 −0.645898 1.98787i −0.0415199 0.127785i
243243 0 0
244244 0.854102 + 2.62866i 0.0546783 + 0.168282i
245245 0.263932 0.191758i 0.0168620 0.0122510i
246246 0 0
247247 11.4164 35.1361i 0.726409 2.23566i
248248 5.35410 3.88998i 0.339986 0.247014i
249249 0 0
250250 9.04508 + 6.57164i 0.572061 + 0.415627i
251251 −13.5623 −0.856045 −0.428023 0.903768i 0.640790π-0.640790\pi
−0.428023 + 0.903768i 0.640790π0.640790\pi
252252 0 0
253253 5.00000 15.3884i 0.314347 0.967462i
254254 −4.20820 + 12.9515i −0.264046 + 0.812651i
255255 0 0
256256 0.309017 + 0.951057i 0.0193136 + 0.0594410i
257257 22.0000 1.37232 0.686161 0.727450i 0.259294π-0.259294\pi
0.686161 + 0.727450i 0.259294π0.259294\pi
258258 0 0
259259 −16.9443 12.3107i −1.05287 0.764952i
260260 −4.47214 + 13.7638i −0.277350 + 0.853596i
261261 0 0
262262 14.4721 + 10.5146i 0.894092 + 0.649596i
263263 −9.47214 6.88191i −0.584077 0.424357i 0.256115 0.966646i 0.417558π-0.417558\pi
−0.840192 + 0.542290i 0.817558π0.817558\pi
264264 0 0
265265 1.44427 + 4.44501i 0.0887209 + 0.273055i
266266 −12.0902 8.78402i −0.741296 0.538583i
267267 0 0
268268 −1.52786 −0.0933292
269269 2.80902 + 8.64527i 0.171269 + 0.527111i 0.999443 0.0333590i 0.0106205π-0.0106205\pi
−0.828175 + 0.560470i 0.810620π0.810620\pi
270270 0 0
271271 −5.57295 + 17.1518i −0.338533 + 1.04190i 0.626423 + 0.779483i 0.284518π0.284518\pi
−0.964956 + 0.262413i 0.915482π0.915482\pi
272272 −0.381966 + 1.17557i −0.0231601 + 0.0712794i
273273 0 0
274274 −12.1803 −0.735841
275275 −5.59017 17.2048i −0.337100 1.03749i
276276 0 0
277277 −13.7082 + 9.95959i −0.823646 + 0.598414i −0.917755 0.397148i 0.870000π-0.870000\pi
0.0941084 + 0.995562i 0.470000π0.470000\pi
278278 −3.23607 + 9.95959i −0.194086 + 0.597337i
279279 0 0
280280 4.73607 + 3.44095i 0.283034 + 0.205636i
281281 −1.81966 5.60034i −0.108552 0.334088i 0.881996 0.471257i 0.156200π-0.156200\pi
−0.990548 + 0.137169i 0.956200π0.956200\pi
282282 0 0
283283 1.41641 + 4.35926i 0.0841967 + 0.259131i 0.984288 0.176571i 0.0565004π-0.0565004\pi
−0.900091 + 0.435701i 0.856500π0.856500\pi
284284 4.47214 + 3.24920i 0.265372 + 0.192804i
285285 0 0
286286 18.9443 13.7638i 1.12020 0.813872i
287287 12.0902 + 8.78402i 0.713660 + 0.518504i
288288 0 0
289289 12.5172 9.09429i 0.736307 0.534958i
290290 −15.3262 11.1352i −0.899988 0.653879i
291291 0 0
292292 1.09017 + 3.35520i 0.0637974 + 0.196348i
293293 22.0902 1.29052 0.645261 0.763962i 0.276749π-0.276749\pi
0.645261 + 0.763962i 0.276749π0.276749\pi
294294 0 0
295295 8.09017 0.471028
296296 −2.47214 + 7.60845i −0.143690 + 0.442232i
297297 0 0
298298 −17.8713 + 12.9843i −1.03526 + 0.752159i
299299 28.9443 1.67389
300300 0 0
301301 −20.1803 −1.16318
302302 14.8262 10.7719i 0.853154 0.619853i
303303 0 0
304304 −1.76393 + 5.42882i −0.101168 + 0.311364i
305305 1.90983 5.87785i 0.109357 0.336565i
306306 0 0
307307 10.0000 0.570730 0.285365 0.958419i 0.407885π-0.407885\pi
0.285365 + 0.958419i 0.407885π0.407885\pi
308308 −2.92705 9.00854i −0.166784 0.513309i
309309 0 0
310310 −14.7984 −0.840491
311311 −0.854102 + 0.620541i −0.0484317 + 0.0351877i −0.611738 0.791061i 0.709529π-0.709529\pi
0.563306 + 0.826248i 0.309529π0.309529\pi
312312 0 0
313313 13.1631 + 9.56357i 0.744023 + 0.540565i 0.893969 0.448130i 0.147910π-0.147910\pi
−0.149945 + 0.988694i 0.547910π0.547910\pi
314314 7.00000 5.08580i 0.395033 0.287008i
315315 0 0
316316 4.54508 + 3.30220i 0.255681 + 0.185763i
317317 6.35410 + 19.5559i 0.356882 + 1.09837i 0.954910 + 0.296895i 0.0959510π0.0959510\pi
−0.598028 + 0.801475i 0.704049π0.704049\pi
318318 0 0
319319 9.47214 + 29.1522i 0.530338 + 1.63221i
320320 0.690983 2.12663i 0.0386271 0.118882i
321321 0 0
322322 3.61803 11.1352i 0.201625 0.620538i
323323 −5.70820 + 4.14725i −0.317613 + 0.230759i
324324 0 0
325325 26.1803 19.0211i 1.45222 1.05510i
326326 0.472136 0.0261492
327327 0 0
328328 1.76393 5.42882i 0.0973969 0.299757i
329329 −1.38197 + 4.25325i −0.0761903 + 0.234489i
330330 0 0
331331 −5.56231 17.1190i −0.305732 0.940946i −0.979403 0.201915i 0.935284π-0.935284\pi
0.673671 0.739031i 0.264716π-0.264716\pi
332332 −2.14590 −0.117771
333333 0 0
334334 −9.47214 6.88191i −0.518292 0.376561i
335335 2.76393 + 2.00811i 0.151010 + 0.109715i
336336 0 0
337337 −0.736068 0.534785i −0.0400962 0.0291316i 0.567557 0.823334i 0.307889π-0.307889\pi
−0.607653 + 0.794203i 0.707889π0.707889\pi
338338 23.3713 + 16.9803i 1.27123 + 0.923604i
339339 0 0
340340 2.23607 1.62460i 0.121268 0.0881062i
341341 19.3713 + 14.0741i 1.04902 + 0.762155i
342342 0 0
343343 −18.7082 −1.01015
344344 2.38197 + 7.33094i 0.128427 + 0.395258i
345345 0 0
346346 1.57295 4.84104i 0.0845623 0.260256i
347347 −6.35410 + 19.5559i −0.341106 + 1.04982i 0.622529 + 0.782596i 0.286105π0.286105\pi
−0.963636 + 0.267220i 0.913895π0.913895\pi
348348 0 0
349349 −27.8885 −1.49284 −0.746420 0.665475i 0.768229π-0.768229\pi
−0.746420 + 0.665475i 0.768229π0.768229\pi
350350 −4.04508 12.4495i −0.216219 0.665453i
351351 0 0
352352 −2.92705 + 2.12663i −0.156012 + 0.113350i
353353 4.09017 12.5882i 0.217698 0.670005i −0.781253 0.624214i 0.785419π-0.785419\pi
0.998951 0.0457907i 0.0145807π-0.0145807\pi
354354 0 0
355355 −3.81966 11.7557i −0.202727 0.623928i
356356 −1.09017 3.35520i −0.0577789 0.177825i
357357 0 0
358358 3.04508 + 9.37181i 0.160938 + 0.495315i
359359 17.9443 + 13.0373i 0.947062 + 0.688081i 0.950110 0.311914i 0.100970π-0.100970\pi
−0.00304782 + 0.999995i 0.500970π0.500970\pi
360360 0 0
361361 −10.9894 + 7.98424i −0.578387 + 0.420223i
362362 −5.38197 3.91023i −0.282870 0.205517i
363363 0 0
364364 13.7082 9.95959i 0.718505 0.522025i
365365 2.43769 7.50245i 0.127595 0.392696i
366366 0 0
367367 −9.46149 29.1195i −0.493886 1.52002i −0.818686 0.574242i 0.805297π-0.805297\pi
0.324800 0.945783i 0.394703π-0.394703\pi
368368 −4.47214 −0.233126
369369 0 0
370370 14.4721 10.5146i 0.752371 0.546629i
371371 1.69098 5.20431i 0.0877915 0.270194i
372372 0 0
373373 9.32624 6.77591i 0.482894 0.350843i −0.319551 0.947569i 0.603532π-0.603532\pi
0.802445 + 0.596726i 0.203532π0.203532\pi
374374 −4.47214 −0.231249
375375 0 0
376376 1.70820 0.0880939
377377 −44.3607 + 32.2299i −2.28469 + 1.65993i
378378 0 0
379379 −6.23607 + 19.1926i −0.320325 + 0.985860i 0.653181 + 0.757201i 0.273434π0.273434\pi
−0.973507 + 0.228658i 0.926566π0.926566\pi
380380 10.3262 7.50245i 0.529725 0.384868i
381381 0 0
382382 4.29180 0.219587
383383 6.18034 + 19.0211i 0.315801 + 0.971934i 0.975424 + 0.220338i 0.0707160π0.0707160\pi
−0.659623 + 0.751597i 0.729284π0.729284\pi
384384 0 0
385385 −6.54508 + 20.1437i −0.333568 + 1.02662i
386386 14.4443 10.4944i 0.735194 0.534150i
387387 0 0
388388 2.73607 + 1.98787i 0.138903 + 0.100919i
389389 −10.0172 + 7.27794i −0.507893 + 0.369006i −0.812024 0.583624i 0.801634π-0.801634\pi
0.304131 + 0.952630i 0.401634π0.401634\pi
390390 0 0
391391 −4.47214 3.24920i −0.226166 0.164319i
392392 0.0450850 + 0.138757i 0.00227713 + 0.00700830i
393393 0 0
394394 −5.28115 16.2537i −0.266061 0.818850i
395395 −3.88197 11.9475i −0.195323 0.601142i
396396 0 0
397397 −9.50658 + 29.2582i −0.477121 + 1.46843i 0.365954 + 0.930633i 0.380743π0.380743\pi
−0.843075 + 0.537796i 0.819257π0.819257\pi
398398 15.7812 11.4657i 0.791038 0.574723i
399399 0 0
400400 −4.04508 + 2.93893i −0.202254 + 0.146946i
401401 −25.7082 −1.28381 −0.641903 0.766786i 0.721855π-0.721855\pi
−0.641903 + 0.766786i 0.721855π0.721855\pi
402402 0 0
403403 −13.2361 + 40.7364i −0.659336 + 2.02923i
404404 −1.35410 + 4.16750i −0.0673691 + 0.207341i
405405 0 0
406406 6.85410 + 21.0948i 0.340163 + 1.04692i
407407 −28.9443 −1.43471
408408 0 0
409409 −4.69098 3.40820i −0.231954 0.168525i 0.465737 0.884923i 0.345789π-0.345789\pi
−0.697691 + 0.716399i 0.745789π0.745789\pi
410410 −10.3262 + 7.50245i −0.509977 + 0.370520i
411411 0 0
412412 −11.5902 8.42075i −0.571007 0.414861i
413413 −7.66312 5.56758i −0.377077 0.273963i
414414 0 0
415415 3.88197 + 2.82041i 0.190558 + 0.138449i
416416 −5.23607 3.80423i −0.256719 0.186518i
417417 0 0
418418 −20.6525 −1.01015
419419 0.954915 + 2.93893i 0.0466507 + 0.143576i 0.971669 0.236347i 0.0759504π-0.0759504\pi
−0.925018 + 0.379923i 0.875950π0.875950\pi
420420 0 0
421421 −7.03444 + 21.6498i −0.342838 + 1.05515i 0.619893 + 0.784686i 0.287176π0.287176\pi
−0.962731 + 0.270460i 0.912824π0.912824\pi
422422 1.05573 3.24920i 0.0513920 0.158168i
423423 0 0
424424 −2.09017 −0.101508
425425 −6.18034 −0.299791
426426 0 0
427427 −5.85410 + 4.25325i −0.283300 + 0.205829i
428428 3.59017 11.0494i 0.173537 0.534093i
429429 0 0
430430 5.32624 16.3925i 0.256854 0.790515i
431431 −5.20163 16.0090i −0.250554 0.771124i −0.994673 0.103078i 0.967131π-0.967131\pi
0.744120 0.668046i 0.232869π-0.232869\pi
432432 0 0
433433 4.79180 + 14.7476i 0.230279 + 0.708726i 0.997713 + 0.0675976i 0.0215334π0.0215334\pi
−0.767434 + 0.641128i 0.778467π0.778467\pi
434434 14.0172 + 10.1841i 0.672848 + 0.488853i
435435 0 0
436436 −13.9443 + 10.1311i −0.667810 + 0.485192i
437437 −20.6525 15.0049i −0.987942 0.717782i
438438 0 0
439439 19.0172 13.8168i 0.907642 0.659441i −0.0327751 0.999463i 0.510434π-0.510434\pi
0.940418 + 0.340022i 0.110434π0.110434\pi
440440 8.09017 0.385684
441441 0 0
442442 −2.47214 7.60845i −0.117588 0.361897i
443443 −16.6180 −0.789547 −0.394773 0.918779i 0.629177π-0.629177\pi
−0.394773 + 0.918779i 0.629177π0.629177\pi
444444 0 0
445445 −2.43769 + 7.50245i −0.115558 + 0.355650i
446446 2.50000 7.69421i 0.118378 0.364331i
447447 0 0
448448 −2.11803 + 1.53884i −0.100068 + 0.0727034i
449449 27.7082 1.30763 0.653815 0.756654i 0.273167π-0.273167\pi
0.653815 + 0.756654i 0.273167π0.273167\pi
450450 0 0
451451 20.6525 0.972487
452452 −15.5623 + 11.3067i −0.731989 + 0.531821i
453453 0 0
454454 −6.88197 + 21.1805i −0.322987 + 0.994051i
455455 −37.8885 −1.77624
456456 0 0
457457 −4.09017 −0.191330 −0.0956650 0.995414i 0.530498π-0.530498\pi
−0.0956650 + 0.995414i 0.530498π0.530498\pi
458458 1.70820 + 5.25731i 0.0798191 + 0.245658i
459459 0 0
460460 8.09017 + 5.87785i 0.377206 + 0.274056i
461461 6.11803 4.44501i 0.284945 0.207025i −0.436126 0.899885i 0.643650π-0.643650\pi
0.721072 + 0.692861i 0.243650π0.243650\pi
462462 0 0
463463 18.4721 + 13.4208i 0.858473 + 0.623717i 0.927469 0.373900i 0.121980π-0.121980\pi
−0.0689961 + 0.997617i 0.521980π0.521980\pi
464464 6.85410 4.97980i 0.318194 0.231181i
465465 0 0
466466 −15.0902 10.9637i −0.699039 0.507881i
467467 −3.29837 10.1514i −0.152631 0.469749i 0.845283 0.534320i 0.179432π-0.179432\pi
−0.997913 + 0.0645710i 0.979432π0.979432\pi
468468 0 0
469469 −1.23607 3.80423i −0.0570763 0.175663i
470470 −3.09017 2.24514i −0.142539 0.103561i
471471 0 0
472472 −1.11803 + 3.44095i −0.0514617 + 0.158383i
473473 −22.5623 + 16.3925i −1.03742 + 0.753727i
474474 0 0
475475 −28.5410 −1.30955
476476 −3.23607 −0.148325
477477 0 0
478478 3.79837 11.6902i 0.173734 0.534697i
479479 9.00000 27.6992i 0.411220 1.26561i −0.504368 0.863489i 0.668274π-0.668274\pi
0.915588 0.402117i 0.131726π-0.131726\pi
480480 0 0
481481 −16.0000 49.2429i −0.729537 2.24528i
482482 −9.56231 −0.435551
483483 0 0
484484 −1.69098 1.22857i −0.0768629 0.0558441i
485485 −2.33688 7.19218i −0.106112 0.326580i
486486 0 0
487487 −14.3992 10.4616i −0.652489 0.474061i 0.211629 0.977350i 0.432123π-0.432123\pi
−0.864118 + 0.503289i 0.832123π0.832123\pi
488488 2.23607 + 1.62460i 0.101222 + 0.0735421i
489489 0 0
490490 0.100813 0.310271i 0.00455427 0.0140166i
491491 −20.4443 14.8536i −0.922637 0.670335i 0.0215419 0.999768i 0.493142π-0.493142\pi
−0.944179 + 0.329433i 0.893142π0.893142\pi
492492 0 0
493493 10.4721 0.471641
494494 −11.4164 35.1361i −0.513648 1.58085i
495495 0 0
496496 2.04508 6.29412i 0.0918270 0.282615i
497497 −4.47214 + 13.7638i −0.200603 + 0.617392i
498498 0 0
499499 35.5967 1.59353 0.796765 0.604290i 0.206543π-0.206543\pi
0.796765 + 0.604290i 0.206543π0.206543\pi
500500 11.1803 0.500000
501501 0 0
502502 −10.9721 + 7.97172i −0.489710 + 0.355795i
503503 −7.38197 + 22.7194i −0.329146 + 1.01301i 0.640389 + 0.768051i 0.278773π0.278773\pi
−0.969534 + 0.244955i 0.921227π0.921227\pi
504504 0 0
505505 7.92705 5.75934i 0.352749 0.256287i
506506 −5.00000 15.3884i −0.222277 0.684099i
507507 0 0
508508 4.20820 + 12.9515i 0.186709 + 0.574631i
509509 −14.1631 10.2901i −0.627769 0.456101i 0.227857 0.973694i 0.426828π-0.426828\pi
−0.855627 + 0.517593i 0.826828π0.826828\pi
510510 0 0
511511 −7.47214 + 5.42882i −0.330548 + 0.240157i
512512 0.809017 + 0.587785i 0.0357538 + 0.0259767i
513513 0 0
514514 17.7984 12.9313i 0.785053 0.570374i
515515 9.89919 + 30.4666i 0.436210 + 1.34252i
516516 0 0
517517 1.90983 + 5.87785i 0.0839942 + 0.258508i
518518 −20.9443 −0.920238
519519 0 0
520520 4.47214 + 13.7638i 0.196116 + 0.603583i
521521 −4.38197 + 13.4863i −0.191977 + 0.590846i 0.808021 + 0.589153i 0.200539π0.200539\pi
−0.999999 + 0.00169226i 0.999461π0.999461\pi
522522 0 0
523523 −8.94427 + 6.49839i −0.391106 + 0.284155i −0.765908 0.642950i 0.777710π-0.777710\pi
0.374803 + 0.927105i 0.377710π0.377710\pi
524524 17.8885 0.781465
525525 0 0
526526 −11.7082 −0.510502
527527 6.61803 4.80828i 0.288286 0.209452i
528528 0 0
529529 −0.927051 + 2.85317i −0.0403066 + 0.124051i
530530 3.78115 + 2.74717i 0.164243 + 0.119329i
531531 0 0
532532 −14.9443 −0.647916
533533 11.4164 + 35.1361i 0.494500 + 1.52191i
534534 0 0
535535 −21.0172 + 15.2699i −0.908654 + 0.660176i
536536 −1.23607 + 0.898056i −0.0533900 + 0.0387901i
537537 0 0
538538 7.35410 + 5.34307i 0.317058 + 0.230356i
539539 −0.427051 + 0.310271i −0.0183944 + 0.0133643i
540540 0 0
541541 21.1803 + 15.3884i 0.910614 + 0.661600i 0.941170 0.337933i 0.109728π-0.109728\pi
−0.0305561 + 0.999533i 0.509728π0.509728\pi
542542 5.57295 + 17.1518i 0.239379 + 0.736732i
543543 0 0
544544 0.381966 + 1.17557i 0.0163767 + 0.0504022i
545545 38.5410 1.65092
546546 0 0
547547 3.00000 9.23305i 0.128271 0.394777i −0.866212 0.499677i 0.833452π-0.833452\pi
0.994483 + 0.104900i 0.0334522π0.0334522\pi
548548 −9.85410 + 7.15942i −0.420946 + 0.305835i
549549 0 0
550550 −14.6353 10.6331i −0.624049 0.453398i
551551 48.3607 2.06023
552552 0 0
553553 −4.54508 + 13.9883i −0.193277 + 0.594844i
554554 −5.23607 + 16.1150i −0.222459 + 0.684659i
555555 0 0
556556 3.23607 + 9.95959i 0.137240 + 0.422381i
557557 18.3262 0.776508 0.388254 0.921552i 0.373078π-0.373078\pi
0.388254 + 0.921552i 0.373078π0.373078\pi
558558 0 0
559559 −40.3607 29.3238i −1.70707 1.24026i
560560 5.85410 0.247381
561561 0 0
562562 −4.76393 3.46120i −0.200954 0.146002i
563563 17.2082 + 12.5025i 0.725239 + 0.526917i 0.888054 0.459739i 0.152057π-0.152057\pi
−0.162815 + 0.986657i 0.552057π0.552057\pi
564564 0 0
565565 43.0132 1.80958
566566 3.70820 + 2.69417i 0.155867 + 0.113244i
567567 0 0
568568 5.52786 0.231944
569569 8.58359 + 26.4176i 0.359843 + 1.10748i 0.953148 + 0.302505i 0.0978228π0.0978228\pi
−0.593305 + 0.804978i 0.702177π0.702177\pi
570570 0 0
571571 2.43769 7.50245i 0.102014 0.313968i −0.887004 0.461762i 0.847217π-0.847217\pi
0.989018 + 0.147794i 0.0472174π0.0472174\pi
572572 7.23607 22.2703i 0.302555 0.931169i
573573 0 0
574574 14.9443 0.623762
575575 −6.90983 21.2663i −0.288160 0.886865i
576576 0 0
577577 −7.26393 + 5.27756i −0.302401 + 0.219708i −0.728629 0.684908i 0.759842π-0.759842\pi
0.426228 + 0.904616i 0.359842π0.359842\pi
578578 4.78115 14.7149i 0.198870 0.612058i
579579 0 0
580580 −18.9443 −0.786618
581581 −1.73607 5.34307i −0.0720242 0.221668i
582582 0 0
583583 −2.33688 7.19218i −0.0967837 0.297870i
584584 2.85410 + 2.07363i 0.118104 + 0.0858073i
585585 0 0
586586 17.8713 12.9843i 0.738258 0.536376i
587587 −0.781153 0.567541i −0.0322416 0.0234249i 0.571548 0.820569i 0.306343π-0.306343\pi
−0.603789 + 0.797144i 0.706343π0.706343\pi
588588 0 0
589589 30.5623 22.2048i 1.25930 0.914933i
590590 6.54508 4.75528i 0.269457 0.195772i
591591 0 0
592592 2.47214 + 7.60845i 0.101604 + 0.312705i
593593 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
594594 0 0
595595 5.85410 + 4.25325i 0.239995 + 0.174366i
596596 −6.82624 + 21.0090i −0.279614 + 0.860562i
597597 0 0
598598 23.4164 17.0130i 0.957568 0.695714i
599599 −0.472136 −0.0192910 −0.00964548 0.999953i 0.503070π-0.503070\pi
−0.00964548 + 0.999953i 0.503070π0.503070\pi
600600 0 0
601601 −7.72949 −0.315292 −0.157646 0.987496i 0.550391π-0.550391\pi
−0.157646 + 0.987496i 0.550391π0.550391\pi
602602 −16.3262 + 11.8617i −0.665408 + 0.483447i
603603 0 0
604604 5.66312 17.4293i 0.230429 0.709188i
605605 1.44427 + 4.44501i 0.0587180 + 0.180715i
606606 0 0
607607 6.56231 0.266356 0.133178 0.991092i 0.457482π-0.457482\pi
0.133178 + 0.991092i 0.457482π0.457482\pi
608608 1.76393 + 5.42882i 0.0715369 + 0.220168i
609609 0 0
610610 −1.90983 5.87785i −0.0773268 0.237987i
611611 −8.94427 + 6.49839i −0.361847 + 0.262897i
612612 0 0
613613 −39.0344 28.3602i −1.57659 1.14546i −0.920481 0.390788i 0.872203π-0.872203\pi
−0.656105 0.754669i 0.727797π-0.727797\pi
614614 8.09017 5.87785i 0.326493 0.237211i
615615 0 0
616616 −7.66312 5.56758i −0.308756 0.224324i
617617 −0.652476 2.00811i −0.0262677 0.0808436i 0.937063 0.349160i 0.113533π-0.113533\pi
−0.963331 + 0.268316i 0.913533π0.913533\pi
618618 0 0
619619 −2.90983 8.95554i −0.116956 0.359953i 0.875394 0.483410i 0.160602π-0.160602\pi
−0.992350 + 0.123457i 0.960602π0.960602\pi
620620 −11.9721 + 8.69827i −0.480813 + 0.349331i
621621 0 0
622622 −0.326238 + 1.00406i −0.0130809 + 0.0402590i
623623 7.47214 5.42882i 0.299365 0.217501i
624624 0 0
625625 −20.2254 14.6946i −0.809017 0.587785i
626626 16.2705 0.650300
627627 0 0
628628 2.67376 8.22899i 0.106695 0.328373i
629629 −3.05573 + 9.40456i −0.121840 + 0.374985i
630630 0 0
631631 14.3607 + 44.1976i 0.571690 + 1.75948i 0.647184 + 0.762334i 0.275946π0.275946\pi
−0.0754947 + 0.997146i 0.524054π0.524054\pi
632632 5.61803 0.223473
633633 0 0
634634 16.6353 + 12.0862i 0.660670 + 0.480005i
635635 9.40983 28.9605i 0.373418 1.14926i
636636 0 0
637637 −0.763932 0.555029i −0.0302681 0.0219911i
638638 24.7984 + 18.0171i 0.981777 + 0.713303i
639639 0 0
640640 −0.690983 2.12663i −0.0273135 0.0840623i
641641 −11.1803 8.12299i −0.441597 0.320839i 0.344672 0.938723i 0.387990π-0.387990\pi
−0.786269 + 0.617884i 0.787990π0.787990\pi
642642 0 0
643643 21.8885 0.863200 0.431600 0.902065i 0.357949π-0.357949\pi
0.431600 + 0.902065i 0.357949π0.357949\pi
644644 −3.61803 11.1352i −0.142571 0.438787i
645645 0 0
646646 −2.18034 + 6.71040i −0.0857843 + 0.264017i
647647 7.09017 21.8213i 0.278743 0.857884i −0.709461 0.704744i 0.751062π-0.751062\pi
0.988205 0.153139i 0.0489383π-0.0489383\pi
648648 0 0
649649 −13.0902 −0.513834
650650 10.0000 30.7768i 0.392232 1.20717i
651651 0 0
652652 0.381966 0.277515i 0.0149589 0.0108683i
653653 1.19098 3.66547i 0.0466068 0.143441i −0.925045 0.379858i 0.875973π-0.875973\pi
0.971652 + 0.236417i 0.0759730π0.0759730\pi
654654 0 0
655655 −32.3607 23.5114i −1.26444 0.918667i
656656 −1.76393 5.42882i −0.0688700 0.211960i
657657 0 0
658658 1.38197 + 4.25325i 0.0538746 + 0.165809i
659659 −16.6803 12.1190i −0.649774 0.472088i 0.213420 0.976960i 0.431540π-0.431540\pi
−0.863194 + 0.504872i 0.831540π0.831540\pi
660660 0 0
661661 24.6525 17.9111i 0.958870 0.696660i 0.00598211 0.999982i 0.498096π-0.498096\pi
0.952888 + 0.303322i 0.0980958π0.0980958\pi
662662 −14.5623 10.5801i −0.565980 0.411209i
663663 0 0
664664 −1.73607 + 1.26133i −0.0673725 + 0.0489490i
665665 27.0344 + 19.6417i 1.04835 + 0.761671i
666666 0 0
667667 11.7082 + 36.0341i 0.453343 + 1.39525i
668668 −11.7082 −0.453004
669669 0 0
670670 3.41641 0.131987
671671 −3.09017 + 9.51057i −0.119295 + 0.367151i
672672 0 0
673673 25.4443 18.4863i 0.980805 0.712596i 0.0229163 0.999737i 0.492705π-0.492705\pi
0.957888 + 0.287141i 0.0927049π0.0927049\pi
674674 −0.909830 −0.0350453
675675 0 0
676676 28.8885 1.11110
677677 23.5344 17.0988i 0.904502 0.657159i −0.0351163 0.999383i 0.511180π-0.511180\pi
0.939618 + 0.342224i 0.111180π0.111180\pi
678678 0 0
679679 −2.73607 + 8.42075i −0.105001 + 0.323159i
680680 0.854102 2.62866i 0.0327533 0.100804i
681681 0 0
682682 23.9443 0.916874
683683 −10.3541 31.8666i −0.396189 1.21934i −0.928032 0.372501i 0.878500π-0.878500\pi
0.531843 0.846843i 0.321500π-0.321500\pi
684684 0 0
685685 27.2361 1.04064
686686 −15.1353 + 10.9964i −0.577867 + 0.419845i
687687 0 0
688688 6.23607 + 4.53077i 0.237748 + 0.172734i
689689 10.9443 7.95148i 0.416944 0.302927i
690690 0 0
691691 −9.09017 6.60440i −0.345806 0.251243i 0.401301 0.915946i 0.368558π-0.368558\pi
−0.747108 + 0.664703i 0.768558π0.768558\pi
692692 −1.57295 4.84104i −0.0597945 0.184029i
693693 0 0
694694 6.35410 + 19.5559i 0.241198 + 0.742332i
695695 7.23607 22.2703i 0.274480 0.844762i
696696 0 0
697697 2.18034 6.71040i 0.0825863 0.254174i
698698 −22.5623 + 16.3925i −0.853996 + 0.620464i
699699 0 0
700700 −10.5902 7.69421i −0.400271 0.290814i
701701 −40.8328 −1.54223 −0.771117 0.636693i 0.780302π-0.780302\pi
−0.771117 + 0.636693i 0.780302π0.780302\pi
702702 0 0
703703 −14.1115 + 43.4306i −0.532224 + 1.63802i
704704 −1.11803 + 3.44095i −0.0421375 + 0.129686i
705705 0 0
706706 −4.09017 12.5882i −0.153936 0.473765i
707707 −11.4721 −0.431454
708708 0 0
709709 35.3607 + 25.6910i 1.32800 + 0.964847i 0.999795 + 0.0202400i 0.00644302π0.00644302\pi
0.328203 + 0.944607i 0.393557π0.393557\pi
710710 −10.0000 7.26543i −0.375293 0.272667i
711711 0 0
712712 −2.85410 2.07363i −0.106962 0.0777124i
713713 23.9443 + 17.3965i 0.896720 + 0.651505i
714714 0 0
715715 −42.3607 + 30.7768i −1.58420 + 1.15099i
716716 7.97214 + 5.79210i 0.297933 + 0.216461i
717717 0 0
718718 22.1803 0.827763
719719 5.12461 + 15.7719i 0.191116 + 0.588194i 1.00000 0.000225882i 7.19006e5π7.19006e-5\pi
−0.808884 + 0.587968i 0.799928π0.799928\pi
720720 0 0
721721 11.5902 35.6709i 0.431640 1.32845i
722722 −4.19756 + 12.9188i −0.156217 + 0.480787i
723723 0 0
724724 −6.65248 −0.247237
725725 34.2705 + 24.8990i 1.27277 + 0.924725i
726726 0 0
727727 6.94427 5.04531i 0.257549 0.187120i −0.451517 0.892263i 0.649117π-0.649117\pi
0.709066 + 0.705142i 0.249117π0.249117\pi
728728 5.23607 16.1150i 0.194062 0.597260i
729729 0 0
730730 −2.43769 7.50245i −0.0902231 0.277678i
731731 2.94427 + 9.06154i 0.108898 + 0.335153i
732732 0 0
733733 −11.0902 34.1320i −0.409625 1.26070i −0.916971 0.398953i 0.869374π-0.869374\pi
0.507346 0.861742i 0.330626π-0.330626\pi
734734 −24.7705 17.9968i −0.914296 0.664275i
735735 0 0
736736 −3.61803 + 2.62866i −0.133363 + 0.0968935i
737737 −4.47214 3.24920i −0.164733 0.119686i
738738 0 0
739739 38.9787 28.3197i 1.43386 1.04176i 0.444573 0.895743i 0.353356π-0.353356\pi
0.989283 0.146014i 0.0466444π-0.0466444\pi
740740 5.52786 17.0130i 0.203208 0.625411i
741741 0 0
742742 −1.69098 5.20431i −0.0620779 0.191056i
743743 39.0132 1.43125 0.715627 0.698483i 0.246141π-0.246141\pi
0.715627 + 0.698483i 0.246141π0.246141\pi
744744 0 0
745745 39.9615 29.0337i 1.46408 1.06371i
746746 3.56231 10.9637i 0.130425 0.401408i
747747 0 0
748748 −3.61803 + 2.62866i −0.132288 + 0.0961132i
749749 30.4164 1.11139
750750 0 0
751751 24.7984 0.904906 0.452453 0.891788i 0.350549π-0.350549\pi
0.452453 + 0.891788i 0.350549π0.350549\pi
752752 1.38197 1.00406i 0.0503951 0.0366142i
753753 0 0
754754 −16.9443 + 52.1491i −0.617074 + 1.89916i
755755 −33.1525 + 24.0867i −1.20654 + 0.876604i
756756 0 0
757757 −17.1246 −0.622405 −0.311202 0.950344i 0.600732π-0.600732\pi
−0.311202 + 0.950344i 0.600732π0.600732\pi
758758 6.23607 + 19.1926i 0.226504 + 0.697108i
759759 0 0
760760 3.94427 12.1392i 0.143074 0.440336i
761761 1.14590 0.832544i 0.0415388 0.0301797i −0.566822 0.823840i 0.691827π-0.691827\pi
0.608361 + 0.793661i 0.291827π0.291827\pi
762762 0 0
763763 −36.5066 26.5236i −1.32163 0.960218i
764764 3.47214 2.52265i 0.125617 0.0912664i
765765 0 0
766766 16.1803 + 11.7557i 0.584619 + 0.424751i
767767 −7.23607 22.2703i −0.261279 0.804135i
768768 0 0
769769 7.62868 + 23.4787i 0.275097 + 0.846662i 0.989194 + 0.146615i 0.0468377π0.0468377\pi
−0.714097 + 0.700047i 0.753162π0.753162\pi
770770 6.54508 + 20.1437i 0.235868 + 0.725929i
771771 0 0
772772 5.51722 16.9803i 0.198569 0.611133i
773773 −0.927051 + 0.673542i −0.0333437 + 0.0242256i −0.604332 0.796732i 0.706560π-0.706560\pi
0.570989 + 0.820958i 0.306560π0.306560\pi
774774 0 0
775775 33.0902 1.18863
776776 3.38197 0.121406
777777 0 0
778778 −3.82624 + 11.7759i −0.137177 + 0.422188i
779779 10.0689 30.9888i 0.360755 1.11029i
780780 0 0
781781 6.18034 + 19.0211i 0.221150 + 0.680630i
782782 −5.52786 −0.197676
783783 0 0
784784 0.118034 + 0.0857567i 0.00421550 + 0.00306274i
785785 −15.6525 + 11.3722i −0.558661 + 0.405891i
786786 0 0
787787 −22.7082 16.4985i −0.809460 0.588107i 0.104214 0.994555i 0.466767π-0.466767\pi
−0.913674 + 0.406448i 0.866767π0.866767\pi
788788 −13.8262 10.0453i −0.492539 0.357851i
789789 0 0
790790 −10.1631 7.38394i −0.361588 0.262709i
791791 −40.7426 29.6013i −1.44864 1.05250i
792792 0 0
793793 −17.8885 −0.635241
794794 9.50658 + 29.2582i 0.337376 + 1.03834i
795795 0 0
796796 6.02786 18.5519i 0.213652 0.657553i
797797 −0.465558 + 1.43284i −0.0164909 + 0.0507538i −0.958963 0.283530i 0.908494π-0.908494\pi
0.942472 + 0.334284i 0.108494π0.108494\pi
798798 0 0
799799 2.11146 0.0746979
800800 −1.54508 + 4.75528i −0.0546270 + 0.168125i
801801 0 0
802802 −20.7984 + 15.1109i −0.734416 + 0.533585i
803803 −3.94427 + 12.1392i −0.139190 + 0.428384i
804804 0 0
805805 −8.09017 + 24.8990i −0.285141 + 0.877574i
806806 13.2361 + 40.7364i 0.466221 + 1.43488i
807807 0 0
808808 1.35410 + 4.16750i 0.0476371 + 0.146612i
809809 −24.9443 18.1231i −0.876994 0.637173i 0.0554606 0.998461i 0.482337π-0.482337\pi
−0.932454 + 0.361288i 0.882337π0.882337\pi
810810 0 0
811811 4.61803 3.35520i 0.162161 0.117817i −0.503745 0.863852i 0.668045π-0.668045\pi
0.665906 + 0.746035i 0.268045π0.268045\pi
812812 17.9443 + 13.0373i 0.629720 + 0.457519i
813813 0 0
814814 −23.4164 + 17.0130i −0.820745 + 0.596306i
815815 −1.05573 −0.0369805
816816 0 0
817817 13.5967 + 41.8465i 0.475690 + 1.46402i
818818 −5.79837 −0.202735
819819 0 0
820820 −3.94427 + 12.1392i −0.137740 + 0.423920i
821821 13.9336 42.8833i 0.486287 1.49664i −0.343821 0.939035i 0.611721π-0.611721\pi
0.830108 0.557602i 0.188279π-0.188279\pi
822822 0 0
823823 −2.39919 + 1.74311i −0.0836304 + 0.0607610i −0.628815 0.777555i 0.716460π-0.716460\pi
0.545184 + 0.838316i 0.316460π0.316460\pi
824824 −14.3262 −0.499078
825825 0 0
826826 −9.47214 −0.329578
827827 35.6803 25.9233i 1.24073 0.901441i 0.243080 0.970006i 0.421842π-0.421842\pi
0.997647 + 0.0685652i 0.0218421π0.0218421\pi
828828 0 0
829829 8.00000 24.6215i 0.277851 0.855139i −0.710599 0.703597i 0.751576π-0.751576\pi
0.988451 0.151542i 0.0484239π-0.0484239\pi
830830 4.79837 0.166554
831831 0 0
832832 −6.47214 −0.224381
833833 0.0557281 + 0.171513i 0.00193086 + 0.00594259i
834834 0 0
835835 21.1803 + 15.3884i 0.732976 + 0.532538i
836836 −16.7082 + 12.1392i −0.577865 + 0.419844i
837837 0 0
838838 2.50000 + 1.81636i 0.0863611 + 0.0627450i
839839 5.14590 3.73871i 0.177656 0.129075i −0.495403 0.868663i 0.664980π-0.664980\pi
0.673060 + 0.739588i 0.264980π0.264980\pi
840840 0 0
841841 −34.6074 25.1437i −1.19336 0.867026i
842842 7.03444 + 21.6498i 0.242423 + 0.746101i
843843 0 0
844844 −1.05573 3.24920i −0.0363397 0.111842i
845845 −52.2599 37.9690i −1.79779 1.30617i
846846 0 0
847847 1.69098 5.20431i 0.0581029 0.178822i
848848 −1.69098 + 1.22857i −0.0580686 + 0.0421893i
849849 0 0
850850 −5.00000 + 3.63271i −0.171499 + 0.124601i
851851 −35.7771 −1.22642
852852 0 0
853853 −13.4721 + 41.4630i −0.461277 + 1.41967i 0.402328 + 0.915496i 0.368201π0.368201\pi
−0.863605 + 0.504169i 0.831799π0.831799\pi
854854 −2.23607 + 6.88191i −0.0765167 + 0.235494i
855855 0 0
856856 −3.59017 11.0494i −0.122709 0.377661i
857857 16.0689 0.548903 0.274451 0.961601i 0.411504π-0.411504\pi
0.274451 + 0.961601i 0.411504π0.411504\pi
858858 0 0
859859 1.85410 + 1.34708i 0.0632611 + 0.0459619i 0.618966 0.785417i 0.287552π-0.287552\pi
−0.555705 + 0.831379i 0.687552π0.687552\pi
860860 −5.32624 16.3925i −0.181623 0.558979i
861861 0 0
862862 −13.6180 9.89408i −0.463832 0.336994i
863863 −8.23607 5.98385i −0.280359 0.203693i 0.438715 0.898626i 0.355434π-0.355434\pi
−0.719074 + 0.694934i 0.755434π0.755434\pi
864864 0 0
865865 −3.51722 + 10.8249i −0.119589 + 0.368057i
866866 12.5451 + 9.11454i 0.426299 + 0.309725i
867867 0 0
868868 17.3262 0.588091
869869 6.28115 + 19.3314i 0.213074 + 0.655773i
870870 0 0
871871 3.05573 9.40456i 0.103539 0.318661i
872872 −5.32624 + 16.3925i −0.180369 + 0.555119i
873873 0 0
874874 −25.5279 −0.863493
875875 9.04508 + 27.8379i 0.305780 + 0.941093i
876876 0 0
877877 30.0344 21.8213i 1.01419 0.736853i 0.0491070 0.998794i 0.484362π-0.484362\pi
0.965084 + 0.261941i 0.0843625π0.0843625\pi
878878 7.26393 22.3561i 0.245146 0.754481i
879879 0 0
880880 6.54508 4.75528i 0.220635 0.160301i
881881 7.29180 + 22.4418i 0.245667 + 0.756085i 0.995526 + 0.0944874i 0.0301212π0.0301212\pi
−0.749859 + 0.661597i 0.769879π0.769879\pi
882882 0 0
883883 −9.29180 28.5972i −0.312694 0.962373i −0.976693 0.214640i 0.931142π-0.931142\pi
0.663999 0.747733i 0.268858π-0.268858\pi
884884 −6.47214 4.70228i −0.217681 0.158155i
885885 0 0
886886 −13.4443 + 9.76784i −0.451669 + 0.328157i
887887 18.9443 + 13.7638i 0.636086 + 0.462144i 0.858503 0.512808i 0.171395π-0.171395\pi
−0.222417 + 0.974952i 0.571395π0.571395\pi
888888 0 0
889889 −28.8435 + 20.9560i −0.967379 + 0.702842i
890890 2.43769 + 7.50245i 0.0817117 + 0.251483i
891891 0 0
892892 −2.50000 7.69421i −0.0837062 0.257621i
893893 9.75078 0.326297
894894 0 0
895895 −6.80902 20.9560i −0.227600 0.700482i
896896 −0.809017 + 2.48990i −0.0270274 + 0.0831817i
897897 0 0
898898 22.4164 16.2865i 0.748045 0.543487i
899899 −56.0689 −1.87000
900900 0 0
901901 −2.58359 −0.0860719
902902 16.7082 12.1392i 0.556322 0.404192i
903903 0 0
904904 −5.94427 + 18.2946i −0.197704 + 0.608469i
905905 12.0344 + 8.74353i 0.400038 + 0.290645i
906906 0 0
907907 30.4721 1.01181 0.505905 0.862589i 0.331159π-0.331159\pi
0.505905 + 0.862589i 0.331159π0.331159\pi
908908 6.88197 + 21.1805i 0.228386 + 0.702900i
909909 0 0
910910 −30.6525 + 22.2703i −1.01612 + 0.738254i
911911 14.7082 10.6861i 0.487305 0.354047i −0.316842 0.948478i 0.602623π-0.602623\pi
0.804147 + 0.594431i 0.202623π0.202623\pi
912912 0 0
913913 −6.28115 4.56352i −0.207876 0.151031i
914914 −3.30902 + 2.40414i −0.109453 + 0.0795219i
915915 0 0
916916 4.47214 + 3.24920i 0.147764 + 0.107356i
917917 14.4721 + 44.5407i 0.477912 + 1.47086i
918918 0 0
919919 −12.5836 38.7283i −0.415094 1.27753i −0.912166 0.409820i 0.865592π-0.865592\pi
0.497072 0.867709i 0.334408π-0.334408\pi
920920 10.0000 0.329690
921921 0 0
922922 2.33688 7.19218i 0.0769611 0.236862i
923923 −28.9443 + 21.0292i −0.952712 + 0.692186i
924924 0 0
925925 −32.3607 + 23.5114i −1.06401 + 0.773050i
926926 22.8328 0.750333
927927 0 0
928928 2.61803 8.05748i 0.0859412 0.264500i
929929 5.87539 18.0826i 0.192765 0.593270i −0.807230 0.590237i 0.799034π-0.799034\pi
0.999995 0.00303360i 0.000965627π-0.000965627\pi
930930 0 0
931931 0.257354 + 0.792055i 0.00843444 + 0.0259585i
932932 −18.6525 −0.610982
933933 0 0
934934 −8.63525 6.27388i −0.282554 0.205288i
935935 10.0000 0.327035
936936 0 0
937937 7.02786 + 5.10604i 0.229590 + 0.166807i 0.696633 0.717428i 0.254681π-0.254681\pi
−0.467043 + 0.884235i 0.654681π0.654681\pi
938938 −3.23607 2.35114i −0.105661 0.0767675i
939939 0 0
940940 −3.81966 −0.124584
941941 −3.59017 2.60841i −0.117036 0.0850318i 0.527728 0.849414i 0.323044π-0.323044\pi
−0.644764 + 0.764382i 0.723044π0.723044\pi
942942 0 0
943943 25.5279 0.831302
944944 1.11803 + 3.44095i 0.0363889 + 0.111994i
945945 0 0
946946 −8.61803 + 26.5236i −0.280196 + 0.862356i
947947 10.3713 31.9196i 0.337023 1.03725i −0.628694 0.777652i 0.716410π-0.716410\pi
0.965717 0.259597i 0.0835897π-0.0835897\pi
948948 0 0
949949 −22.8328 −0.741185
950950 −23.0902 + 16.7760i −0.749144 + 0.544285i
951951 0 0
952952 −2.61803 + 1.90211i −0.0848510 + 0.0616478i
953953 −1.63932 + 5.04531i −0.0531028 + 0.163434i −0.974091 0.226157i 0.927384π-0.927384\pi
0.920988 + 0.389591i 0.127384π0.127384\pi
954954 0 0
955955 −9.59675 −0.310543
956956 −3.79837 11.6902i −0.122848 0.378088i
957957 0 0
958958 −9.00000 27.6992i −0.290777 0.894919i
959959 −25.7984 18.7436i −0.833073 0.605263i
960960 0 0
961961 −10.3541 + 7.52270i −0.334003 + 0.242668i
962962 −41.8885 30.4338i −1.35054 0.981225i
963963 0 0
964964 −7.73607 + 5.62058i −0.249162 + 0.181027i
965965 −32.2984 + 23.4661i −1.03972 + 0.755402i
966966 0 0
967967 3.37132 + 10.3759i 0.108414 + 0.333665i 0.990517 0.137393i 0.0438722π-0.0438722\pi
−0.882102 + 0.471058i 0.843872π0.843872\pi
968968 −2.09017 −0.0671806
969969 0 0
970970 −6.11803 4.44501i −0.196438 0.142721i
971971 4.39261 13.5191i 0.140966 0.433847i −0.855505 0.517795i 0.826753π-0.826753\pi
0.996470 + 0.0839479i 0.0267529π0.0267529\pi
972972 0 0
973973 −22.1803 + 16.1150i −0.711069 + 0.516622i
974974 −17.7984 −0.570297
975975 0 0
976976 2.76393 0.0884713
977977 −0.618034 + 0.449028i −0.0197727 + 0.0143657i −0.597628 0.801774i 0.703890π-0.703890\pi
0.577855 + 0.816139i 0.303890π0.303890\pi
978978 0 0
979979 3.94427 12.1392i 0.126059 0.387971i
980980 −0.100813 0.310271i −0.00322036 0.00991123i
981981 0 0
982982 −25.2705 −0.806414
983983 −12.4164 38.2138i −0.396022 1.21883i −0.928163 0.372174i 0.878612π-0.878612\pi
0.532141 0.846656i 0.321388π-0.321388\pi
984984 0 0
985985 11.8090 + 36.3444i 0.376267 + 1.15803i
986986 8.47214 6.15537i 0.269808 0.196027i
987987 0 0
988988 −29.8885 21.7153i −0.950881 0.690856i
989989 −27.8885 + 20.2622i −0.886804 + 0.644301i
990990 0 0
991991 −23.8262 17.3108i −0.756865 0.549895i 0.141082 0.989998i 0.454942π-0.454942\pi
−0.897947 + 0.440103i 0.854942π0.854942\pi
992992 −2.04508 6.29412i −0.0649315 0.199839i
993993 0 0
994994 4.47214 + 13.7638i 0.141848 + 0.436562i
995995 −35.2877 + 25.6380i −1.11870 + 0.812780i
996996 0 0
997997 −1.72949 + 5.32282i −0.0547735 + 0.168576i −0.974701 0.223513i 0.928247π-0.928247\pi
0.919927 + 0.392089i 0.128247π0.128247\pi
998998 28.7984 20.9232i 0.911597 0.662314i
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 450.2.h.c.361.1 4
3.2 odd 2 150.2.g.a.61.1 4
15.2 even 4 750.2.h.b.199.1 8
15.8 even 4 750.2.h.b.199.2 8
15.14 odd 2 750.2.g.b.301.1 4
25.16 even 5 inner 450.2.h.c.91.1 4
75.29 odd 10 3750.2.a.d.1.1 2
75.38 even 20 750.2.h.b.49.1 8
75.41 odd 10 150.2.g.a.91.1 yes 4
75.47 even 20 3750.2.c.b.1249.4 4
75.53 even 20 3750.2.c.b.1249.1 4
75.59 odd 10 750.2.g.b.451.1 4
75.62 even 20 750.2.h.b.49.2 8
75.71 odd 10 3750.2.a.f.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.g.a.61.1 4 3.2 odd 2
150.2.g.a.91.1 yes 4 75.41 odd 10
450.2.h.c.91.1 4 25.16 even 5 inner
450.2.h.c.361.1 4 1.1 even 1 trivial
750.2.g.b.301.1 4 15.14 odd 2
750.2.g.b.451.1 4 75.59 odd 10
750.2.h.b.49.1 8 75.38 even 20
750.2.h.b.49.2 8 75.62 even 20
750.2.h.b.199.1 8 15.2 even 4
750.2.h.b.199.2 8 15.8 even 4
3750.2.a.d.1.1 2 75.29 odd 10
3750.2.a.f.1.2 2 75.71 odd 10
3750.2.c.b.1249.1 4 75.53 even 20
3750.2.c.b.1249.4 4 75.47 even 20