Properties

Label 525.3.s.c.199.2
Level 525525
Weight 33
Character 525.199
Analytic conductor 14.30514.305
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(124,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.124");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 525=3527 525 = 3 \cdot 5^{2} \cdot 7
Weight: k k == 3 3
Character orbit: [χ][\chi] == 525.s (of order 66, degree 22, not 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: 14.305213878914.3052138789
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 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 21)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 199.2
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 525.199
Dual form 525.3.s.c.124.2

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+(0.8660250.500000i)q2+(0.8660251.50000i)q3+(1.50000+2.59808i)q41.73205iq6+(6.062183.50000i)q7+7.00000iq8+(1.500002.59808i)q9+(5.500009.52628i)q11+(2.59808+4.50000i)q126.92820q137.00000q14+(2.500004.33013i)q16+(12.1244+21.0000i)q17+(2.598081.50000i)q18+(3.000001.73205i)q19+(10.5000+6.06218i)q2111.0000iq22+(24.2487+14.0000i)q23+(10.5000+6.06218i)q24+(6.00000+3.46410i)q265.19615q27+(18.186510.5000i)q2825.0000q29+(28.500016.4545i)q31+(28.578816.5000i)q32+(9.5262816.5000i)q33+24.2487iq34+9.00000q36+(50.2295+29.0000i)q37+(1.732053.00000i)q38+(6.00000+10.3923i)q393.46410iq41+(6.06218+10.5000i)q4226.0000iq43+(16.5000+28.5788i)q44+(14.0000+24.2487i)q46+(38.105166.0000i)q478.66025q48+(24.5000+42.4352i)q49+(21.0000+36.3731i)q51+(10.392318.0000i)q52+(26.8468+15.5000i)q53+(4.50000+2.59808i)q54+(24.500042.4352i)q566.00000iq57+(21.6506+12.5000i)q58+(7.50000+4.33013i)q59+(12.00006.92820i)q6132.9090q62+21.0000iq6313.0000q64+(16.50009.52628i)q66+(45.0333+26.0000i)q67+(36.373163.0000i)q68+48.4974iq69+64.0000q71+(18.186510.5000i)q72+(3.464106.00000i)q73+(29.0000+50.2295i)q74+10.3923iq76+(66.6840+38.5000i)q77+12.0000iq78+(8.50000+14.7224i)q79+(4.50000+7.79423i)q81+(1.732053.00000i)q8253.6936q8336.3731iq84+(13.000022.5167i)q86+(21.6506+37.5000i)q87+(66.6840+38.5000i)q88+(69.000039.8372i)q89+(42.0000+24.2487i)q9184.0000iq92+(49.3634+28.5000i)q93+(66.000038.1051i)q94+(49.5000+28.5788i)q96+91.7987q97+(42.4352+24.5000i)q9833.0000q99+O(q100)q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.50000 + 2.59808i) q^{4} -1.73205i q^{6} +(-6.06218 - 3.50000i) q^{7} +7.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.50000 - 9.52628i) q^{11} +(2.59808 + 4.50000i) q^{12} -6.92820 q^{13} -7.00000 q^{14} +(-2.50000 - 4.33013i) q^{16} +(-12.1244 + 21.0000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-10.5000 + 6.06218i) q^{21} -11.0000i q^{22} +(-24.2487 + 14.0000i) q^{23} +(10.5000 + 6.06218i) q^{24} +(-6.00000 + 3.46410i) q^{26} -5.19615 q^{27} +(18.1865 - 10.5000i) q^{28} -25.0000 q^{29} +(-28.5000 - 16.4545i) q^{31} +(-28.5788 - 16.5000i) q^{32} +(-9.52628 - 16.5000i) q^{33} +24.2487i q^{34} +9.00000 q^{36} +(-50.2295 + 29.0000i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-6.00000 + 10.3923i) q^{39} -3.46410i q^{41} +(-6.06218 + 10.5000i) q^{42} -26.0000i q^{43} +(16.5000 + 28.5788i) q^{44} +(-14.0000 + 24.2487i) q^{46} +(-38.1051 - 66.0000i) q^{47} -8.66025 q^{48} +(24.5000 + 42.4352i) q^{49} +(21.0000 + 36.3731i) q^{51} +(10.3923 - 18.0000i) q^{52} +(26.8468 + 15.5000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(24.5000 - 42.4352i) q^{56} -6.00000i q^{57} +(-21.6506 + 12.5000i) q^{58} +(7.50000 + 4.33013i) q^{59} +(12.0000 - 6.92820i) q^{61} -32.9090 q^{62} +21.0000i q^{63} -13.0000 q^{64} +(-16.5000 - 9.52628i) q^{66} +(45.0333 + 26.0000i) q^{67} +(-36.3731 - 63.0000i) q^{68} +48.4974i q^{69} +64.0000 q^{71} +(18.1865 - 10.5000i) q^{72} +(3.46410 - 6.00000i) q^{73} +(-29.0000 + 50.2295i) q^{74} +10.3923i q^{76} +(-66.6840 + 38.5000i) q^{77} +12.0000i q^{78} +(8.50000 + 14.7224i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.73205 - 3.00000i) q^{82} -53.6936 q^{83} -36.3731i q^{84} +(-13.0000 - 22.5167i) q^{86} +(-21.6506 + 37.5000i) q^{87} +(66.6840 + 38.5000i) q^{88} +(69.0000 - 39.8372i) q^{89} +(42.0000 + 24.2487i) q^{91} -84.0000i q^{92} +(-49.3634 + 28.5000i) q^{93} +(-66.0000 - 38.1051i) q^{94} +(-49.5000 + 28.5788i) q^{96} +91.7987 q^{97} +(42.4352 + 24.5000i) q^{98} -33.0000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q46q9+22q1128q1410q16+12q1942q21+42q2424q26100q29114q31+36q3624q39+66q4456q46+98q49+84q51+132q99+O(q100) 4 q - 6 q^{4} - 6 q^{9} + 22 q^{11} - 28 q^{14} - 10 q^{16} + 12 q^{19} - 42 q^{21} + 42 q^{24} - 24 q^{26} - 100 q^{29} - 114 q^{31} + 36 q^{36} - 24 q^{39} + 66 q^{44} - 56 q^{46} + 98 q^{49} + 84 q^{51}+ \cdots - 132 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/525Z)×\left(\mathbb{Z}/525\mathbb{Z}\right)^\times.

nn 127127 176176 451451
χ(n)\chi(n) 1-1 11 e(16)e\left(\frac{1}{6}\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 0.866025 0.500000i 0.433013 0.250000i −0.267617 0.963525i 0.586236π-0.586236\pi
0.700629 + 0.713525i 0.252903π0.252903\pi
33 0.866025 1.50000i 0.288675 0.500000i
44 −1.50000 + 2.59808i −0.375000 + 0.649519i
55 0 0
66 1.73205i 0.288675i
77 −6.06218 3.50000i −0.866025 0.500000i
88 7.00000i 0.875000i
99 −1.50000 2.59808i −0.166667 0.288675i
1010 0 0
1111 5.50000 9.52628i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
1212 2.59808 + 4.50000i 0.216506 + 0.375000i
1313 −6.92820 −0.532939 −0.266469 0.963843i 0.585857π-0.585857\pi
−0.266469 + 0.963843i 0.585857π0.585857\pi
1414 −7.00000 −0.500000
1515 0 0
1616 −2.50000 4.33013i −0.156250 0.270633i
1717 −12.1244 + 21.0000i −0.713197 + 1.23529i 0.250453 + 0.968129i 0.419420π0.419420\pi
−0.963651 + 0.267165i 0.913913π0.913913\pi
1818 −2.59808 1.50000i −0.144338 0.0833333i
1919 3.00000 1.73205i 0.157895 0.0911606i −0.418971 0.908000i 0.637609π-0.637609\pi
0.576865 + 0.816839i 0.304276π0.304276\pi
2020 0 0
2121 −10.5000 + 6.06218i −0.500000 + 0.288675i
2222 11.0000i 0.500000i
2323 −24.2487 + 14.0000i −1.05429 + 0.608696i −0.923848 0.382760i 0.874974π-0.874974\pi
−0.130444 + 0.991456i 0.541640π0.541640\pi
2424 10.5000 + 6.06218i 0.437500 + 0.252591i
2525 0 0
2626 −6.00000 + 3.46410i −0.230769 + 0.133235i
2727 −5.19615 −0.192450
2828 18.1865 10.5000i 0.649519 0.375000i
2929 −25.0000 −0.862069 −0.431034 0.902335i 0.641851π-0.641851\pi
−0.431034 + 0.902335i 0.641851π0.641851\pi
3030 0 0
3131 −28.5000 16.4545i −0.919355 0.530790i −0.0359257 0.999354i 0.511438π-0.511438\pi
−0.883429 + 0.468565i 0.844771π0.844771\pi
3232 −28.5788 16.5000i −0.893089 0.515625i
3333 −9.52628 16.5000i −0.288675 0.500000i
3434 24.2487i 0.713197i
3535 0 0
3636 9.00000 0.250000
3737 −50.2295 + 29.0000i −1.35755 + 0.783784i −0.989294 0.145939i 0.953380π-0.953380\pi
−0.368260 + 0.929723i 0.620046π0.620046\pi
3838 1.73205 3.00000i 0.0455803 0.0789474i
3939 −6.00000 + 10.3923i −0.153846 + 0.266469i
4040 0 0
4141 3.46410i 0.0844903i −0.999107 0.0422451i 0.986549π-0.986549\pi
0.999107 0.0422451i 0.0134510π-0.0134510\pi
4242 −6.06218 + 10.5000i −0.144338 + 0.250000i
4343 26.0000i 0.604651i −0.953205 0.302326i 0.902237π-0.902237\pi
0.953205 0.302326i 0.0977630π-0.0977630\pi
4444 16.5000 + 28.5788i 0.375000 + 0.649519i
4545 0 0
4646 −14.0000 + 24.2487i −0.304348 + 0.527146i
4747 −38.1051 66.0000i −0.810747 1.40426i −0.912342 0.409429i 0.865728π-0.865728\pi
0.101595 0.994826i 0.467606π-0.467606\pi
4848 −8.66025 −0.180422
4949 24.5000 + 42.4352i 0.500000 + 0.866025i
5050 0 0
5151 21.0000 + 36.3731i 0.411765 + 0.713197i
5252 10.3923 18.0000i 0.199852 0.346154i
5353 26.8468 + 15.5000i 0.506543 + 0.292453i 0.731412 0.681936i 0.238862π-0.238862\pi
−0.224868 + 0.974389i 0.572195π0.572195\pi
5454 −4.50000 + 2.59808i −0.0833333 + 0.0481125i
5555 0 0
5656 24.5000 42.4352i 0.437500 0.757772i
5757 6.00000i 0.105263i
5858 −21.6506 + 12.5000i −0.373287 + 0.215517i
5959 7.50000 + 4.33013i 0.127119 + 0.0733920i 0.562211 0.826994i 0.309951π-0.309951\pi
−0.435092 + 0.900386i 0.643284π0.643284\pi
6060 0 0
6161 12.0000 6.92820i 0.196721 0.113577i −0.398404 0.917210i 0.630436π-0.630436\pi
0.595125 + 0.803633i 0.297102π0.297102\pi
6262 −32.9090 −0.530790
6363 21.0000i 0.333333i
6464 −13.0000 −0.203125
6565 0 0
6666 −16.5000 9.52628i −0.250000 0.144338i
6767 45.0333 + 26.0000i 0.672139 + 0.388060i 0.796887 0.604129i 0.206479π-0.206479\pi
−0.124748 + 0.992189i 0.539812π0.539812\pi
6868 −36.3731 63.0000i −0.534898 0.926471i
6969 48.4974i 0.702861i
7070 0 0
7171 64.0000 0.901408 0.450704 0.892673i 0.351173π-0.351173\pi
0.450704 + 0.892673i 0.351173π0.351173\pi
7272 18.1865 10.5000i 0.252591 0.145833i
7373 3.46410 6.00000i 0.0474534 0.0821918i −0.841323 0.540533i 0.818223π-0.818223\pi
0.888777 + 0.458341i 0.151556π0.151556\pi
7474 −29.0000 + 50.2295i −0.391892 + 0.678777i
7575 0 0
7676 10.3923i 0.136741i
7777 −66.6840 + 38.5000i −0.866025 + 0.500000i
7878 12.0000i 0.153846i
7979 8.50000 + 14.7224i 0.107595 + 0.186360i 0.914795 0.403917i 0.132352π-0.132352\pi
−0.807200 + 0.590277i 0.799018π0.799018\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.0555556 + 0.0962250i
8282 −1.73205 3.00000i −0.0211226 0.0365854i
8383 −53.6936 −0.646911 −0.323455 0.946243i 0.604845π-0.604845\pi
−0.323455 + 0.946243i 0.604845π0.604845\pi
8484 36.3731i 0.433013i
8585 0 0
8686 −13.0000 22.5167i −0.151163 0.261822i
8787 −21.6506 + 37.5000i −0.248858 + 0.431034i
8888 66.6840 + 38.5000i 0.757772 + 0.437500i
8989 69.0000 39.8372i 0.775281 0.447609i −0.0594743 0.998230i 0.518942π-0.518942\pi
0.834755 + 0.550621i 0.185609π0.185609\pi
9090 0 0
9191 42.0000 + 24.2487i 0.461538 + 0.266469i
9292 84.0000i 0.913043i
9393 −49.3634 + 28.5000i −0.530790 + 0.306452i
9494 −66.0000 38.1051i −0.702128 0.405374i
9595 0 0
9696 −49.5000 + 28.5788i −0.515625 + 0.297696i
9797 91.7987 0.946378 0.473189 0.880961i 0.343103π-0.343103\pi
0.473189 + 0.880961i 0.343103π0.343103\pi
9898 42.4352 + 24.5000i 0.433013 + 0.250000i
9999 −33.0000 −0.333333
100100 0 0
101101 −18.0000 10.3923i −0.178218 0.102894i 0.408237 0.912876i 0.366144π-0.366144\pi
−0.586455 + 0.809982i 0.699477π0.699477\pi
102102 36.3731 + 21.0000i 0.356599 + 0.205882i
103103 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
104104 48.4974i 0.466321i
105105 0 0
106106 31.0000 0.292453
107107 26.8468 15.5000i 0.250905 0.144860i −0.369274 0.929321i 0.620394π-0.620394\pi
0.620178 + 0.784461i 0.287060π0.287060\pi
108108 7.79423 13.5000i 0.0721688 0.125000i
109109 −68.0000 + 117.779i −0.623853 + 1.08055i 0.364908 + 0.931043i 0.381100π0.381100\pi
−0.988761 + 0.149502i 0.952233π0.952233\pi
110110 0 0
111111 100.459i 0.905036i
112112 35.0000i 0.312500i
113113 74.0000i 0.654867i 0.944874 + 0.327434i 0.106184π0.106184\pi
−0.944874 + 0.327434i 0.893816π0.893816\pi
114114 −3.00000 5.19615i −0.0263158 0.0455803i
115115 0 0
116116 37.5000 64.9519i 0.323276 0.559930i
117117 10.3923 + 18.0000i 0.0888231 + 0.153846i
118118 8.66025 0.0733920
119119 147.000 84.8705i 1.23529 0.713197i
120120 0 0
121121 0 0
122122 6.92820 12.0000i 0.0567886 0.0983607i
123123 −5.19615 3.00000i −0.0422451 0.0243902i
124124 85.5000 49.3634i 0.689516 0.398092i
125125 0 0
126126 10.5000 + 18.1865i 0.0833333 + 0.144338i
127127 1.00000i 0.00787402i −0.999992 0.00393701i 0.998747π-0.998747\pi
0.999992 0.00393701i 0.00125319π-0.00125319\pi
128128 103.057 59.5000i 0.805133 0.464844i
129129 −39.0000 22.5167i −0.302326 0.174548i
130130 0 0
131131 157.500 90.9327i 1.20229 0.694142i 0.241226 0.970469i 0.422450π-0.422450\pi
0.961064 + 0.276326i 0.0891171π0.0891171\pi
132132 57.1577 0.433013
133133 −24.2487 −0.182321
134134 52.0000 0.388060
135135 0 0
136136 −147.000 84.8705i −1.08088 0.624048i
137137 −76.2102 44.0000i −0.556279 0.321168i 0.195372 0.980729i 0.437409π-0.437409\pi
−0.751651 + 0.659561i 0.770742π0.770742\pi
138138 24.2487 + 42.0000i 0.175715 + 0.304348i
139139 190.526i 1.37069i −0.728220 0.685344i 0.759652π-0.759652\pi
0.728220 0.685344i 0.240348π-0.240348\pi
140140 0 0
141141 −132.000 −0.936170
142142 55.4256 32.0000i 0.390321 0.225352i
143143 −38.1051 + 66.0000i −0.266469 + 0.461538i
144144 −7.50000 + 12.9904i −0.0520833 + 0.0902110i
145145 0 0
146146 6.92820i 0.0474534i
147147 84.8705 0.577350
148148 174.000i 1.17568i
149149 −115.000 199.186i −0.771812 1.33682i −0.936569 0.350484i 0.886017π-0.886017\pi
0.164757 0.986334i 0.447316π-0.447316\pi
150150 0 0
151151 −113.500 + 196.588i −0.751656 + 1.30191i 0.195364 + 0.980731i 0.437411π0.437411\pi
−0.947020 + 0.321175i 0.895922π0.895922\pi
152152 12.1244 + 21.0000i 0.0797655 + 0.138158i
153153 72.7461 0.475465
154154 −38.5000 + 66.6840i −0.250000 + 0.433013i
155155 0 0
156156 −18.0000 31.1769i −0.115385 0.199852i
157157 24.2487 42.0000i 0.154450 0.267516i −0.778408 0.627758i 0.783973π-0.783973\pi
0.932859 + 0.360242i 0.117306π0.117306\pi
158158 14.7224 + 8.50000i 0.0931799 + 0.0537975i
159159 46.5000 26.8468i 0.292453 0.168848i
160160 0 0
161161 196.000 1.21739
162162 9.00000i 0.0555556i
163163 −183.597 + 106.000i −1.12636 + 0.650307i −0.943018 0.332742i 0.892026π-0.892026\pi
−0.183346 + 0.983048i 0.558693π0.558693\pi
164164 9.00000 + 5.19615i 0.0548780 + 0.0316839i
165165 0 0
166166 −46.5000 + 26.8468i −0.280120 + 0.161728i
167167 96.9948 0.580807 0.290404 0.956904i 0.406210π-0.406210\pi
0.290404 + 0.956904i 0.406210π0.406210\pi
168168 −42.4352 73.5000i −0.252591 0.437500i
169169 −121.000 −0.715976
170170 0 0
171171 −9.00000 5.19615i −0.0526316 0.0303869i
172172 67.5500 + 39.0000i 0.392732 + 0.226744i
173173 −107.387 186.000i −0.620735 1.07514i −0.989349 0.145562i 0.953501π-0.953501\pi
0.368614 0.929582i 0.379832π-0.379832\pi
174174 43.3013i 0.248858i
175175 0 0
176176 −55.0000 −0.312500
177177 12.9904 7.50000i 0.0733920 0.0423729i
178178 39.8372 69.0000i 0.223804 0.387640i
179179 23.0000 39.8372i 0.128492 0.222554i −0.794601 0.607132i 0.792320π-0.792320\pi
0.923092 + 0.384578i 0.125653π0.125653\pi
180180 0 0
181181 31.1769i 0.172248i 0.996284 + 0.0861241i 0.0274481π0.0274481\pi
−0.996284 + 0.0861241i 0.972552π0.972552\pi
182182 48.4974 0.266469
183183 24.0000i 0.131148i
184184 −98.0000 169.741i −0.532609 0.922505i
185185 0 0
186186 −28.5000 + 49.3634i −0.153226 + 0.265395i
187187 133.368 + 231.000i 0.713197 + 1.23529i
188188 228.631 1.21612
189189 31.5000 + 18.1865i 0.166667 + 0.0962250i
190190 0 0
191191 −104.000 180.133i −0.544503 0.943106i −0.998638 0.0521735i 0.983385π-0.983385\pi
0.454135 0.890933i 0.349948π-0.349948\pi
192192 −11.2583 + 19.5000i −0.0586371 + 0.101562i
193193 206.980 + 119.500i 1.07244 + 0.619171i 0.928846 0.370466i 0.120802π-0.120802\pi
0.143590 + 0.989637i 0.454135π0.454135\pi
194194 79.5000 45.8993i 0.409794 0.236595i
195195 0 0
196196 −147.000 −0.750000
197197 26.0000i 0.131980i −0.997820 0.0659898i 0.978980π-0.978980\pi
0.997820 0.0659898i 0.0210205π-0.0210205\pi
198198 −28.5788 + 16.5000i −0.144338 + 0.0833333i
199199 210.000 + 121.244i 1.05528 + 0.609264i 0.924122 0.382098i 0.124798π-0.124798\pi
0.131155 + 0.991362i 0.458132π0.458132\pi
200200 0 0
201201 78.0000 45.0333i 0.388060 0.224046i
202202 −20.7846 −0.102894
203203 151.554 + 87.5000i 0.746574 + 0.431034i
204204 −126.000 −0.617647
205205 0 0
206206 0 0
207207 72.7461 + 42.0000i 0.351431 + 0.202899i
208208 17.3205 + 30.0000i 0.0832717 + 0.144231i
209209 38.1051i 0.182321i
210210 0 0
211211 −52.0000 −0.246445 −0.123223 0.992379i 0.539323π-0.539323\pi
−0.123223 + 0.992379i 0.539323π0.539323\pi
212212 −80.5404 + 46.5000i −0.379907 + 0.219340i
213213 55.4256 96.0000i 0.260214 0.450704i
214214 15.5000 26.8468i 0.0724299 0.125452i
215215 0 0
216216 36.3731i 0.168394i
217217 115.181 + 199.500i 0.530790 + 0.919355i
218218 136.000i 0.623853i
219219 −6.00000 10.3923i −0.0273973 0.0474534i
220220 0 0
221221 84.0000 145.492i 0.380090 0.658336i
222222 50.2295 + 87.0000i 0.226259 + 0.391892i
223223 22.5167 0.100972 0.0504858 0.998725i 0.483923π-0.483923\pi
0.0504858 + 0.998725i 0.483923π0.483923\pi
224224 115.500 + 200.052i 0.515625 + 0.893089i
225225 0 0
226226 37.0000 + 64.0859i 0.163717 + 0.283566i
227227 −33.7750 + 58.5000i −0.148789 + 0.257709i −0.930780 0.365580i 0.880871π-0.880871\pi
0.781991 + 0.623289i 0.214204π0.214204\pi
228228 15.5885 + 9.00000i 0.0683704 + 0.0394737i
229229 27.0000 15.5885i 0.117904 0.0680719i −0.439888 0.898053i 0.644982π-0.644982\pi
0.557792 + 0.829981i 0.311649π0.311649\pi
230230 0 0
231231 133.368i 0.577350i
232232 175.000i 0.754310i
233233 −226.899 + 131.000i −0.973814 + 0.562232i −0.900397 0.435070i 0.856724π-0.856724\pi
−0.0734171 + 0.997301i 0.523390π0.523390\pi
234234 18.0000 + 10.3923i 0.0769231 + 0.0444116i
235235 0 0
236236 −22.5000 + 12.9904i −0.0953390 + 0.0550440i
237237 29.4449 0.124240
238238 84.8705 147.000i 0.356599 0.617647i
239239 −160.000 −0.669456 −0.334728 0.942315i 0.608644π-0.608644\pi
−0.334728 + 0.942315i 0.608644π0.608644\pi
240240 0 0
241241 409.500 + 236.425i 1.69917 + 0.981016i 0.946548 + 0.322564i 0.104545π0.104545\pi
0.752622 + 0.658452i 0.228789π0.228789\pi
242242 0 0
243243 7.79423 + 13.5000i 0.0320750 + 0.0555556i
244244 41.5692i 0.170366i
245245 0 0
246246 −6.00000 −0.0243902
247247 −20.7846 + 12.0000i −0.0841482 + 0.0485830i
248248 115.181 199.500i 0.464441 0.804435i
249249 −46.5000 + 80.5404i −0.186747 + 0.323455i
250250 0 0
251251 67.5500i 0.269123i 0.990905 + 0.134562i 0.0429626π0.0429626\pi
−0.990905 + 0.134562i 0.957037π0.957037\pi
252252 −54.5596 31.5000i −0.216506 0.125000i
253253 308.000i 1.21739i
254254 −0.500000 0.866025i −0.00196850 0.00340955i
255255 0 0
256256 85.5000 148.090i 0.333984 0.578478i
257257 −202.650 351.000i −0.788521 1.36576i −0.926873 0.375376i 0.877514π-0.877514\pi
0.138352 0.990383i 0.455820π-0.455820\pi
258258 −45.0333 −0.174548
259259 406.000 1.56757
260260 0 0
261261 37.5000 + 64.9519i 0.143678 + 0.248858i
262262 90.9327 157.500i 0.347071 0.601145i
263263 91.7987 + 53.0000i 0.349044 + 0.201521i 0.664264 0.747498i 0.268745π-0.268745\pi
−0.315220 + 0.949019i 0.602078π0.602078\pi
264264 115.500 66.6840i 0.437500 0.252591i
265265 0 0
266266 −21.0000 + 12.1244i −0.0789474 + 0.0455803i
267267 138.000i 0.516854i
268268 −135.100 + 78.0000i −0.504104 + 0.291045i
269269 −376.500 217.372i −1.39963 0.808076i −0.405275 0.914195i 0.632824π-0.632824\pi
−0.994353 + 0.106119i 0.966158π0.966158\pi
270270 0 0
271271 109.500 63.2199i 0.404059 0.233284i −0.284175 0.958772i 0.591720π-0.591720\pi
0.688234 + 0.725489i 0.258386π0.258386\pi
272272 121.244 0.445748
273273 72.7461 42.0000i 0.266469 0.153846i
274274 −88.0000 −0.321168
275275 0 0
276276 −126.000 72.7461i −0.456522 0.263573i
277277 −204.382 118.000i −0.737841 0.425993i 0.0834427 0.996513i 0.473408π-0.473408\pi
−0.821284 + 0.570520i 0.806742π0.806742\pi
278278 −95.2628 165.000i −0.342672 0.593525i
279279 98.7269i 0.353860i
280280 0 0
281281 −116.000 −0.412811 −0.206406 0.978466i 0.566177π-0.566177\pi
−0.206406 + 0.978466i 0.566177π0.566177\pi
282282 −114.315 + 66.0000i −0.405374 + 0.234043i
283283 −185.329 + 321.000i −0.654874 + 1.13428i 0.327051 + 0.945007i 0.393945π0.393945\pi
−0.981925 + 0.189269i 0.939388π0.939388\pi
284284 −96.0000 + 166.277i −0.338028 + 0.585482i
285285 0 0
286286 76.2102i 0.266469i
287287 −12.1244 + 21.0000i −0.0422451 + 0.0731707i
288288 99.0000i 0.343750i
289289 −149.500 258.942i −0.517301 0.895992i
290290 0 0
291291 79.5000 137.698i 0.273196 0.473189i
292292 10.3923 + 18.0000i 0.0355901 + 0.0616438i
293293 −19.0526 −0.0650258 −0.0325129 0.999471i 0.510351π-0.510351\pi
−0.0325129 + 0.999471i 0.510351π0.510351\pi
294294 73.5000 42.4352i 0.250000 0.144338i
295295 0 0
296296 −203.000 351.606i −0.685811 1.18786i
297297 −28.5788 + 49.5000i −0.0962250 + 0.166667i
298298 −199.186 115.000i −0.668409 0.385906i
299299 168.000 96.9948i 0.561873 0.324397i
300300 0 0
301301 −91.0000 + 157.617i −0.302326 + 0.523643i
302302 227.000i 0.751656i
303303 −31.1769 + 18.0000i −0.102894 + 0.0594059i
304304 −15.0000 8.66025i −0.0493421 0.0284877i
305305 0 0
306306 63.0000 36.3731i 0.205882 0.118866i
307307 −457.261 −1.48945 −0.744725 0.667371i 0.767420π-0.767420\pi
−0.744725 + 0.667371i 0.767420π0.767420\pi
308308 231.000i 0.750000i
309309 0 0
310310 0 0
311311 285.000 + 164.545i 0.916399 + 0.529083i 0.882484 0.470342i 0.155869π-0.155869\pi
0.0339143 + 0.999425i 0.489203π0.489203\pi
312312 −72.7461 42.0000i −0.233161 0.134615i
313313 −274.530 475.500i −0.877093 1.51917i −0.854517 0.519424i 0.826146π-0.826146\pi
−0.0225763 0.999745i 0.507187π-0.507187\pi
314314 48.4974i 0.154450i
315315 0 0
316316 −51.0000 −0.161392
317317 161.947 93.5000i 0.510873 0.294953i −0.222319 0.974974i 0.571363π-0.571363\pi
0.733192 + 0.680021i 0.238029π0.238029\pi
318318 26.8468 46.5000i 0.0844239 0.146226i
319319 −137.500 + 238.157i −0.431034 + 0.746574i
320320 0 0
321321 53.6936i 0.167270i
322322 169.741 98.0000i 0.527146 0.304348i
323323 84.0000i 0.260062i
324324 −13.5000 23.3827i −0.0416667 0.0721688i
325325 0 0
326326 −106.000 + 183.597i −0.325153 + 0.563182i
327327 117.779 + 204.000i 0.360182 + 0.623853i
328328 24.2487 0.0739290
329329 533.472i 1.62149i
330330 0 0
331331 8.00000 + 13.8564i 0.0241692 + 0.0418623i 0.877857 0.478923i 0.158973π-0.158973\pi
−0.853688 + 0.520785i 0.825639π0.825639\pi
332332 80.5404 139.500i 0.242591 0.420181i
333333 150.688 + 87.0000i 0.452518 + 0.261261i
334334 84.0000 48.4974i 0.251497 0.145202i
335335 0 0
336336 52.5000 + 30.3109i 0.156250 + 0.0902110i
337337 83.0000i 0.246291i 0.992389 + 0.123145i 0.0392982π0.0392982\pi
−0.992389 + 0.123145i 0.960702π0.960702\pi
338338 −104.789 + 60.5000i −0.310027 + 0.178994i
339339 111.000 + 64.0859i 0.327434 + 0.189044i
340340 0 0
341341 −313.500 + 180.999i −0.919355 + 0.530790i
342342 −10.3923 −0.0303869
343343 343.000i 1.00000i
344344 182.000 0.529070
345345 0 0
346346 −186.000 107.387i −0.537572 0.310367i
347347 −310.037 179.000i −0.893479 0.515850i −0.0183999 0.999831i 0.505857π-0.505857\pi
−0.875079 + 0.483981i 0.839191π0.839191\pi
348348 −64.9519 112.500i −0.186643 0.323276i
349349 678.964i 1.94546i 0.231950 + 0.972728i 0.425489π0.425489\pi
−0.231950 + 0.972728i 0.574511π0.574511\pi
350350 0 0
351351 36.0000 0.102564
352352 −314.367 + 181.500i −0.893089 + 0.515625i
353353 −322.161 + 558.000i −0.912639 + 1.58074i −0.102317 + 0.994752i 0.532625π0.532625\pi
−0.810322 + 0.585985i 0.800708π0.800708\pi
354354 7.50000 12.9904i 0.0211864 0.0366960i
355355 0 0
356356 239.023i 0.671413i
357357 294.000i 0.823529i
358358 46.0000i 0.128492i
359359 −142.000 245.951i −0.395543 0.685101i 0.597627 0.801774i 0.296110π-0.296110\pi
−0.993170 + 0.116673i 0.962777π0.962777\pi
360360 0 0
361361 −174.500 + 302.243i −0.483380 + 0.837238i
362362 15.5885 + 27.0000i 0.0430620 + 0.0745856i
363363 0 0
364364 −126.000 + 72.7461i −0.346154 + 0.199852i
365365 0 0
366366 −12.0000 20.7846i −0.0327869 0.0567886i
367367 −137.698 + 238.500i −0.375199 + 0.649864i −0.990357 0.138540i 0.955759π-0.955759\pi
0.615158 + 0.788404i 0.289092π0.289092\pi
368368 121.244 + 70.0000i 0.329466 + 0.190217i
369369 −9.00000 + 5.19615i −0.0243902 + 0.0140817i
370370 0 0
371371 −108.500 187.928i −0.292453 0.506543i
372372 171.000i 0.459677i
373373 −43.3013 + 25.0000i −0.116089 + 0.0670241i −0.556920 0.830566i 0.688017π-0.688017\pi
0.440831 + 0.897590i 0.354684π0.354684\pi
374374 231.000 + 133.368i 0.617647 + 0.356599i
375375 0 0
376376 462.000 266.736i 1.22872 0.709404i
377377 173.205 0.459430
378378 36.3731 0.0962250
379379 −458.000 −1.20844 −0.604222 0.796816i 0.706516π-0.706516\pi
−0.604222 + 0.796816i 0.706516π0.706516\pi
380380 0 0
381381 −1.50000 0.866025i −0.00393701 0.00227303i
382382 −180.133 104.000i −0.471553 0.272251i
383383 −202.650 351.000i −0.529112 0.916449i −0.999424 0.0339486i 0.989192π-0.989192\pi
0.470311 0.882501i 0.344142π-0.344142\pi
384384 206.114i 0.536755i
385385 0 0
386386 239.000 0.619171
387387 −67.5500 + 39.0000i −0.174548 + 0.100775i
388388 −137.698 + 238.500i −0.354892 + 0.614691i
389389 −349.000 + 604.486i −0.897172 + 1.55395i −0.0660793 + 0.997814i 0.521049π0.521049\pi
−0.831093 + 0.556134i 0.812284π0.812284\pi
390390 0 0
391391 678.964i 1.73648i
392392 −297.047 + 171.500i −0.757772 + 0.437500i
393393 315.000i 0.801527i
394394 −13.0000 22.5167i −0.0329949 0.0571489i
395395 0 0
396396 49.5000 85.7365i 0.125000 0.216506i
397397 −287.520 498.000i −0.724233 1.25441i −0.959289 0.282426i 0.908861π-0.908861\pi
0.235056 0.971982i 0.424473π-0.424473\pi
398398 242.487 0.609264
399399 −21.0000 + 36.3731i −0.0526316 + 0.0911606i
400400 0 0
401401 142.000 + 245.951i 0.354115 + 0.613345i 0.986966 0.160929i 0.0514489π-0.0514489\pi
−0.632851 + 0.774273i 0.718116π0.718116\pi
402402 45.0333 78.0000i 0.112023 0.194030i
403403 197.454 + 114.000i 0.489960 + 0.282878i
404404 54.0000 31.1769i 0.133663 0.0771706i
405405 0 0
406406 175.000 0.431034
407407 638.000i 1.56757i
408408 −254.611 + 147.000i −0.624048 + 0.360294i
409409 181.500 + 104.789i 0.443765 + 0.256208i 0.705193 0.709015i 0.250860π-0.250860\pi
−0.261428 + 0.965223i 0.584193π0.584193\pi
410410 0 0
411411 −132.000 + 76.2102i −0.321168 + 0.185426i
412412 0 0
413413 −30.3109 52.5000i −0.0733920 0.127119i
414414 84.0000 0.202899
415415 0 0
416416 198.000 + 114.315i 0.475962 + 0.274797i
417417 −285.788 165.000i −0.685344 0.395683i
418418 −19.0526 33.0000i −0.0455803 0.0789474i
419419 131.636i 0.314167i −0.987585 0.157083i 0.949791π-0.949791\pi
0.987585 0.157083i 0.0502091π-0.0502091\pi
420420 0 0
421421 −28.0000 −0.0665083 −0.0332542 0.999447i 0.510587π-0.510587\pi
−0.0332542 + 0.999447i 0.510587π0.510587\pi
422422 −45.0333 + 26.0000i −0.106714 + 0.0616114i
423423 −114.315 + 198.000i −0.270249 + 0.468085i
424424 −108.500 + 187.928i −0.255896 + 0.443225i
425425 0 0
426426 110.851i 0.260214i
427427 −96.9948 −0.227154
428428 93.0000i 0.217290i
429429 66.0000 + 114.315i 0.153846 + 0.266469i
430430 0 0
431431 −59.0000 + 102.191i −0.136891 + 0.237102i −0.926318 0.376742i 0.877044π-0.877044\pi
0.789427 + 0.613844i 0.210378π0.210378\pi
432432 12.9904 + 22.5000i 0.0300703 + 0.0520833i
433433 561.184 1.29604 0.648019 0.761624i 0.275598π-0.275598\pi
0.648019 + 0.761624i 0.275598π0.275598\pi
434434 199.500 + 115.181i 0.459677 + 0.265395i
435435 0 0
436436 −204.000 353.338i −0.467890 0.810409i
437437 −48.4974 + 84.0000i −0.110978 + 0.192220i
438438 −10.3923 6.00000i −0.0237267 0.0136986i
439439 640.500 369.793i 1.45900 0.842353i 0.460036 0.887900i 0.347837π-0.347837\pi
0.998962 + 0.0455478i 0.0145033π0.0145033\pi
440440 0 0
441441 73.5000 127.306i 0.166667 0.288675i
442442 168.000i 0.380090i
443443 134.234 77.5000i 0.303011 0.174944i −0.340784 0.940142i 0.610692π-0.610692\pi
0.643795 + 0.765198i 0.277359π0.277359\pi
444444 −261.000 150.688i −0.587838 0.339388i
445445 0 0
446446 19.5000 11.2583i 0.0437220 0.0252429i
447447 −398.372 −0.891212
448448 78.8083 + 45.5000i 0.175911 + 0.101562i
449449 368.000 0.819599 0.409800 0.912176i 0.365599π-0.365599\pi
0.409800 + 0.912176i 0.365599π0.365599\pi
450450 0 0
451451 −33.0000 19.0526i −0.0731707 0.0422451i
452452 −192.258 111.000i −0.425349 0.245575i
453453 196.588 + 340.500i 0.433969 + 0.751656i
454454 67.5500i 0.148789i
455455 0 0
456456 42.0000 0.0921053
457457 295.315 170.500i 0.646203 0.373085i −0.140797 0.990038i 0.544967π-0.544967\pi
0.787000 + 0.616953i 0.211633π0.211633\pi
458458 15.5885 27.0000i 0.0340359 0.0589520i
459459 63.0000 109.119i 0.137255 0.237732i
460460 0 0
461461 55.4256i 0.120229i 0.998191 + 0.0601146i 0.0191466π0.0191466\pi
−0.998191 + 0.0601146i 0.980853π0.980853\pi
462462 66.6840 + 115.500i 0.144338 + 0.250000i
463463 178.000i 0.384449i 0.981351 + 0.192225i 0.0615702π0.0615702\pi
−0.981351 + 0.192225i 0.938430π0.938430\pi
464464 62.5000 + 108.253i 0.134698 + 0.233304i
465465 0 0
466466 −131.000 + 226.899i −0.281116 + 0.486907i
467467 329.090 + 570.000i 0.704689 + 1.22056i 0.966804 + 0.255520i 0.0822467π0.0822467\pi
−0.262115 + 0.965037i 0.584420π0.584420\pi
468468 −62.3538 −0.133235
469469 −182.000 315.233i −0.388060 0.672139i
470470 0 0
471471 −42.0000 72.7461i −0.0891720 0.154450i
472472 −30.3109 + 52.5000i −0.0642180 + 0.111229i
473473 −247.683 143.000i −0.523643 0.302326i
474474 25.5000 14.7224i 0.0537975 0.0310600i
475475 0 0
476476 509.223i 1.06980i
477477 93.0000i 0.194969i
478478 −138.564 + 80.0000i −0.289883 + 0.167364i
479479 −441.000 254.611i −0.920668 0.531548i −0.0368199 0.999322i 0.511723π-0.511723\pi
−0.883848 + 0.467774i 0.845056π0.845056\pi
480480 0 0
481481 348.000 200.918i 0.723493 0.417709i
482482 472.850 0.981016
483483 169.741 294.000i 0.351431 0.608696i
484484 0 0
485485 0 0
486486 13.5000 + 7.79423i 0.0277778 + 0.0160375i
487487 728.327 + 420.500i 1.49554 + 0.863450i 0.999987 0.00512864i 0.00163251π-0.00163251\pi
0.495552 + 0.868578i 0.334966π0.334966\pi
488488 48.4974 + 84.0000i 0.0993800 + 0.172131i
489489 367.195i 0.750910i
490490 0 0
491491 −959.000 −1.95316 −0.976578 0.215162i 0.930972π-0.930972\pi
−0.976578 + 0.215162i 0.930972π0.930972\pi
492492 15.5885 9.00000i 0.0316839 0.0182927i
493493 303.109 525.000i 0.614825 1.06491i
494494 −12.0000 + 20.7846i −0.0242915 + 0.0420741i
495495 0 0
496496 164.545i 0.331744i
497497 −387.979 224.000i −0.780643 0.450704i
498498 93.0000i 0.186747i
499499 −59.0000 102.191i −0.118236 0.204792i 0.800832 0.598889i 0.204391π-0.204391\pi
−0.919069 + 0.394097i 0.871057π0.871057\pi
500500 0 0
501501 84.0000 145.492i 0.167665 0.290404i
502502 33.7750 + 58.5000i 0.0672809 + 0.116534i
503503 −363.731 −0.723123 −0.361561 0.932348i 0.617756π-0.617756\pi
−0.361561 + 0.932348i 0.617756π0.617756\pi
504504 −147.000 −0.291667
505505 0 0
506506 154.000 + 266.736i 0.304348 + 0.527146i
507507 −104.789 + 181.500i −0.206685 + 0.357988i
508508 2.59808 + 1.50000i 0.00511432 + 0.00295276i
509509 −382.500 + 220.836i −0.751473 + 0.433863i −0.826226 0.563339i 0.809517π-0.809517\pi
0.0747526 + 0.997202i 0.476183π0.476183\pi
510510 0 0
511511 −42.0000 + 24.2487i −0.0821918 + 0.0474534i
512512 305.000i 0.595703i
513513 −15.5885 + 9.00000i −0.0303869 + 0.0175439i
514514 −351.000 202.650i −0.682879 0.394261i
515515 0 0
516516 117.000 67.5500i 0.226744 0.130911i
517517 −838.313 −1.62149
518518 351.606 203.000i 0.678777 0.391892i
519519 −372.000 −0.716763
520520 0 0
521521 −843.000 486.706i −1.61804 0.934177i −0.987426 0.158082i 0.949469π-0.949469\pi
−0.630616 0.776095i 0.717198π-0.717198\pi
522522 64.9519 + 37.5000i 0.124429 + 0.0718391i
523523 235.559 + 408.000i 0.450399 + 0.780115i 0.998411 0.0563562i 0.0179483π-0.0179483\pi
−0.548011 + 0.836471i 0.684615π0.684615\pi
524524 545.596i 1.04121i
525525 0 0
526526 106.000 0.201521
527527 691.088 399.000i 1.31136 0.757116i
528528 −47.6314 + 82.5000i −0.0902110 + 0.156250i
529529 127.500 220.836i 0.241021 0.417460i
530530 0 0
531531 25.9808i 0.0489280i
532532 36.3731 63.0000i 0.0683704 0.118421i
533533 24.0000i 0.0450281i
534534 −69.0000 119.512i −0.129213 0.223804i
535535 0 0
536536 −182.000 + 315.233i −0.339552 + 0.588122i
537537 −39.8372 69.0000i −0.0741847 0.128492i
538538 −434.745 −0.808076
539539 539.000 1.00000
540540 0 0
541541 −403.000 698.016i −0.744917 1.29023i −0.950234 0.311538i 0.899156π-0.899156\pi
0.205317 0.978696i 0.434178π-0.434178\pi
542542 63.2199 109.500i 0.116642 0.202030i
543543 46.7654 + 27.0000i 0.0861241 + 0.0497238i
544544 693.000 400.104i 1.27390 0.735485i
545545 0 0
546546 42.0000 72.7461i 0.0769231 0.133235i
547547 154.000i 0.281536i −0.990043 0.140768i 0.955043π-0.955043\pi
0.990043 0.140768i 0.0449571π-0.0449571\pi
548548 228.631 132.000i 0.417209 0.240876i
549549 −36.0000 20.7846i −0.0655738 0.0378590i
550550 0 0
551551 −75.0000 + 43.3013i −0.136116 + 0.0785867i
552552 −339.482 −0.615004
553553 119.000i 0.215190i
554554 −236.000 −0.425993
555555 0 0
556556 495.000 + 285.788i 0.890288 + 0.514008i
557557 736.988 + 425.500i 1.32314 + 0.763914i 0.984228 0.176905i 0.0566086π-0.0566086\pi
0.338910 + 0.940819i 0.389942π0.389942\pi
558558 49.3634 + 85.5000i 0.0884650 + 0.153226i
559559 180.133i 0.322242i
560560 0 0
561561 462.000 0.823529
562562 −100.459 + 58.0000i −0.178753 + 0.103203i
563563 213.908 370.500i 0.379944 0.658082i −0.611110 0.791546i 0.709277π-0.709277\pi
0.991054 + 0.133464i 0.0426100π0.0426100\pi
564564 198.000 342.946i 0.351064 0.608060i
565565 0 0
566566 370.659i 0.654874i
567567 54.5596 31.5000i 0.0962250 0.0555556i
568568 448.000i 0.788732i
569569 −409.000 708.409i −0.718805 1.24501i −0.961474 0.274897i 0.911356π-0.911356\pi
0.242669 0.970109i 0.421977π-0.421977\pi
570570 0 0
571571 −142.000 + 245.951i −0.248687 + 0.430738i −0.963162 0.268923i 0.913332π-0.913332\pi
0.714475 + 0.699661i 0.246666π0.246666\pi
572572 −114.315 198.000i −0.199852 0.346154i
573573 −360.267 −0.628737
574574 24.2487i 0.0422451i
575575 0 0
576576 19.5000 + 33.7750i 0.0338542 + 0.0586371i
577577 378.453 655.500i 0.655898 1.13605i −0.325770 0.945449i 0.605623π-0.605623\pi
0.981668 0.190599i 0.0610432π-0.0610432\pi
578578 −258.942 149.500i −0.447996 0.258651i
579579 358.500 206.980i 0.619171 0.357479i
580580 0 0
581581 325.500 + 187.928i 0.560241 + 0.323455i
582582 159.000i 0.273196i
583583 295.315 170.500i 0.506543 0.292453i
584584 42.0000 + 24.2487i 0.0719178 + 0.0415218i
585585 0 0
586586 −16.5000 + 9.52628i −0.0281570 + 0.0162564i
587587 947.432 1.61402 0.807012 0.590535i 0.201083π-0.201083\pi
0.807012 + 0.590535i 0.201083π0.201083\pi
588588 −127.306 + 220.500i −0.216506 + 0.375000i
589589 −114.000 −0.193548
590590 0 0
591591 −39.0000 22.5167i −0.0659898 0.0380993i
592592 251.147 + 145.000i 0.424235 + 0.244932i
593593 −204.382 354.000i −0.344658 0.596965i 0.640634 0.767847i 0.278672π-0.278672\pi
−0.985292 + 0.170882i 0.945338π0.945338\pi
594594 57.1577i 0.0962250i
595595 0 0
596596 690.000 1.15772
597597 363.731 210.000i 0.609264 0.351759i
598598 96.9948 168.000i 0.162199 0.280936i
599599 278.000 481.510i 0.464107 0.803857i −0.535054 0.844818i 0.679709π-0.679709\pi
0.999161 + 0.0409613i 0.0130420π0.0130420\pi
600600 0 0
601601 580.237i 0.965453i −0.875771 0.482726i 0.839647π-0.839647\pi
0.875771 0.482726i 0.160353π-0.160353\pi
602602 182.000i 0.302326i
603603 156.000i 0.258706i
604604 −340.500 589.763i −0.563742 0.976429i
605605 0 0
606606 −18.0000 + 31.1769i −0.0297030 + 0.0514471i
607607 329.956 + 571.500i 0.543584 + 0.941516i 0.998695 + 0.0510805i 0.0162665π0.0162665\pi
−0.455110 + 0.890435i 0.650400π0.650400\pi
608608 −114.315 −0.188019
609609 262.500 151.554i 0.431034 0.248858i
610610 0 0
611611 264.000 + 457.261i 0.432079 + 0.748382i
612612 −109.119 + 189.000i −0.178299 + 0.308824i
613613 277.128 + 160.000i 0.452085 + 0.261011i 0.708710 0.705500i 0.249277π-0.249277\pi
−0.256625 + 0.966511i 0.582611π0.582611\pi
614614 −396.000 + 228.631i −0.644951 + 0.372363i
615615 0 0
616616 −269.500 466.788i −0.437500 0.757772i
617617 652.000i 1.05673i 0.849019 + 0.528363i 0.177194π0.177194\pi
−0.849019 + 0.528363i 0.822806π0.822806\pi
618618 0 0
619619 558.000 + 322.161i 0.901454 + 0.520455i 0.877672 0.479262i 0.159096π-0.159096\pi
0.0237823 + 0.999717i 0.492429π0.492429\pi
620620 0 0
621621 126.000 72.7461i 0.202899 0.117144i
622622 329.090 0.529083
623623 −557.720 −0.895217
624624 60.0000 0.0961538
625625 0 0
626626 −475.500 274.530i −0.759585 0.438546i
627627 −57.1577 33.0000i −0.0911606 0.0526316i
628628 72.7461 + 126.000i 0.115838 + 0.200637i
629629 1406.43i 2.23597i
630630 0 0
631631 −97.0000 −0.153724 −0.0768621 0.997042i 0.524490π-0.524490\pi
−0.0768621 + 0.997042i 0.524490π0.524490\pi
632632 −103.057 + 59.5000i −0.163065 + 0.0941456i
633633 −45.0333 + 78.0000i −0.0711427 + 0.123223i
634634 93.5000 161.947i 0.147476 0.255437i
635635 0 0
636636 161.081i 0.253272i
637637 −169.741 294.000i −0.266469 0.461538i
638638 275.000i 0.431034i
639639 −96.0000 166.277i −0.150235 0.260214i
640640 0 0
641641 −350.000 + 606.218i −0.546022 + 0.945738i 0.452520 + 0.891754i 0.350525π0.350525\pi
−0.998542 + 0.0539833i 0.982808π0.982808\pi
642642 −26.8468 46.5000i −0.0418174 0.0724299i
643643 325.626 0.506416 0.253208 0.967412i 0.418514π-0.418514\pi
0.253208 + 0.967412i 0.418514π0.418514\pi
644644 −294.000 + 509.223i −0.456522 + 0.790719i
645645 0 0
646646 42.0000 + 72.7461i 0.0650155 + 0.112610i
647647 180.133 312.000i 0.278413 0.482226i −0.692577 0.721344i 0.743525π-0.743525\pi
0.970991 + 0.239118i 0.0768582π0.0768582\pi
648648 −54.5596 31.5000i −0.0841969 0.0486111i
649649 82.5000 47.6314i 0.127119 0.0733920i
650650 0 0
651651 399.000 0.612903
652652 636.000i 0.975460i
653653 −323.027 + 186.500i −0.494682 + 0.285605i −0.726515 0.687151i 0.758861π-0.758861\pi
0.231833 + 0.972756i 0.425528π0.425528\pi
654654 204.000 + 117.779i 0.311927 + 0.180091i
655655 0 0
656656 −15.0000 + 8.66025i −0.0228659 + 0.0132016i
657657 −20.7846 −0.0316356
658658 266.736 + 462.000i 0.405374 + 0.702128i
659659 818.000 1.24127 0.620637 0.784098i 0.286874π-0.286874\pi
0.620637 + 0.784098i 0.286874π0.286874\pi
660660 0 0
661661 327.000 + 188.794i 0.494705 + 0.285618i 0.726524 0.687141i 0.241134π-0.241134\pi
−0.231819 + 0.972759i 0.574468π0.574468\pi
662662 13.8564 + 8.00000i 0.0209311 + 0.0120846i
663663 −145.492 252.000i −0.219445 0.380090i
664664 375.855i 0.566047i
665665 0 0
666666 174.000 0.261261
667667 606.218 350.000i 0.908872 0.524738i
668668 −145.492 + 252.000i −0.217803 + 0.377246i
669669 19.5000 33.7750i 0.0291480 0.0504858i
670670 0 0
671671 152.420i 0.227154i
672672 400.104 0.595392
673673 1205.00i 1.79049i −0.445574 0.895245i 0.647000π-0.647000\pi
0.445574 0.895245i 0.353000π-0.353000\pi
674674 41.5000 + 71.8801i 0.0615727 + 0.106647i
675675 0 0
676676 181.500 314.367i 0.268491 0.465040i
677677 −269.334 466.500i −0.397834 0.689069i 0.595624 0.803263i 0.296905π-0.296905\pi
−0.993458 + 0.114194i 0.963571π0.963571\pi
678678 128.172 0.189044
679679 −556.500 321.295i −0.819588 0.473189i
680680 0 0
681681 58.5000 + 101.325i 0.0859031 + 0.148789i
682682 −180.999 + 313.500i −0.265395 + 0.459677i
683683 821.858 + 474.500i 1.20331 + 0.694729i 0.961289 0.275543i 0.0888576π-0.0888576\pi
0.242017 + 0.970272i 0.422191π0.422191\pi
684684 27.0000 15.5885i 0.0394737 0.0227901i
685685 0 0
686686 −171.500 297.047i −0.250000 0.433013i
687687 54.0000i 0.0786026i
688688 −112.583 + 65.0000i −0.163639 + 0.0944767i
689689 −186.000 107.387i −0.269956 0.155859i
690690 0 0
691691 −267.000 + 154.153i −0.386397 + 0.223086i −0.680598 0.732657i 0.738280π-0.738280\pi
0.294201 + 0.955744i 0.404946π0.404946\pi
692692 644.323 0.931102
693693 200.052 + 115.500i 0.288675 + 0.166667i
694694 −358.000 −0.515850
695695 0 0
696696 −262.500 151.554i −0.377155 0.217751i
697697 72.7461 + 42.0000i 0.104370 + 0.0602582i
698698 339.482 + 588.000i 0.486364 + 0.842407i
699699 453.797i 0.649209i
700700 0 0
701701 −413.000 −0.589158 −0.294579 0.955627i 0.595179π-0.595179\pi
−0.294579 + 0.955627i 0.595179π0.595179\pi
702702 31.1769 18.0000i 0.0444116 0.0256410i
703703 −100.459 + 174.000i −0.142900 + 0.247511i
704704 −71.5000 + 123.842i −0.101562 + 0.175911i
705705 0 0
706706 644.323i 0.912639i
707707 72.7461 + 126.000i 0.102894 + 0.178218i
708708 45.0000i 0.0635593i
709709 445.000 + 770.763i 0.627645 + 1.08711i 0.988023 + 0.154306i 0.0493142π0.0493142\pi
−0.360379 + 0.932806i 0.617352π0.617352\pi
710710 0 0
711711 25.5000 44.1673i 0.0358650 0.0621200i
712712 278.860 + 483.000i 0.391658 + 0.678371i
713713 921.451 1.29236
714714 −147.000 254.611i −0.205882 0.356599i
715715 0 0
716716 69.0000 + 119.512i 0.0963687 + 0.166916i
717717 −138.564 + 240.000i −0.193255 + 0.334728i
718718 −245.951 142.000i −0.342550 0.197772i
719719 −579.000 + 334.286i −0.805285 + 0.464932i −0.845316 0.534267i 0.820588π-0.820588\pi
0.0400307 + 0.999198i 0.487254π0.487254\pi
720720 0 0
721721 0 0
722722 349.000i 0.483380i
723723 709.275 409.500i 0.981016 0.566390i
724724 −81.0000 46.7654i −0.111878 0.0645931i
725725 0 0
726726 0 0
727727 −417.424 −0.574174 −0.287087 0.957905i 0.592687π-0.592687\pi
−0.287087 + 0.957905i 0.592687π0.592687\pi
728728 −169.741 + 294.000i −0.233161 + 0.403846i
729729 27.0000 0.0370370
730730 0 0
731731 546.000 + 315.233i 0.746922 + 0.431236i
732732 62.3538 + 36.0000i 0.0851828 + 0.0491803i
733733 −98.7269 171.000i −0.134689 0.233288i 0.790790 0.612088i 0.209670π-0.209670\pi
−0.925479 + 0.378800i 0.876337π0.876337\pi
734734 275.396i 0.375199i
735735 0 0
736736 924.000 1.25543
737737 495.367 286.000i 0.672139 0.388060i
738738 −5.19615 + 9.00000i −0.00704086 + 0.0121951i
739739 −155.000 + 268.468i −0.209743 + 0.363285i −0.951633 0.307236i 0.900596π-0.900596\pi
0.741891 + 0.670521i 0.233929π0.233929\pi
740740 0 0
741741 41.5692i 0.0560988i
742742 −187.928 108.500i −0.253272 0.146226i
743743 812.000i 1.09287i 0.837503 + 0.546433i 0.184015π0.184015\pi
−0.837503 + 0.546433i 0.815985π0.815985\pi
744744 −199.500 345.544i −0.268145 0.464441i
745745 0 0
746746 −25.0000 + 43.3013i −0.0335121 + 0.0580446i
747747 80.5404 + 139.500i 0.107818 + 0.186747i
748748 −800.207 −1.06980
749749 −217.000 −0.289720
750750 0 0
751751 537.500 + 930.977i 0.715712 + 1.23965i 0.962684 + 0.270628i 0.0872312π0.0872312\pi
−0.246972 + 0.969023i 0.579435π0.579435\pi
752752 −190.526 + 330.000i −0.253358 + 0.438830i
753753 101.325 + 58.5000i 0.134562 + 0.0776892i
754754 150.000 86.6025i 0.198939 0.114857i
755755 0 0
756756 −94.5000 + 54.5596i −0.125000 + 0.0721688i
757757 484.000i 0.639366i −0.947525 0.319683i 0.896424π-0.896424\pi
0.947525 0.319683i 0.103576π-0.103576\pi
758758 −396.640 + 229.000i −0.523271 + 0.302111i
759759 462.000 + 266.736i 0.608696 + 0.351431i
760760 0 0
761761 144.000 83.1384i 0.189225 0.109249i −0.402395 0.915466i 0.631822π-0.631822\pi
0.591620 + 0.806217i 0.298489π0.298489\pi
762762 −1.73205 −0.00227303
763763 824.456 476.000i 1.08055 0.623853i
764764 624.000 0.816754
765765 0 0
766766 −351.000 202.650i −0.458225 0.264556i
767767 −51.9615 30.0000i −0.0677464 0.0391134i
768768 −148.090 256.500i −0.192826 0.333984i
769769 594.093i 0.772553i 0.922383 + 0.386277i 0.126239π0.126239\pi
−0.922383 + 0.386277i 0.873761π0.873761\pi
770770 0 0
771771 −702.000 −0.910506
772772 −620.940 + 358.500i −0.804327 + 0.464378i
773773 516.151 894.000i 0.667725 1.15653i −0.310814 0.950471i 0.600602π-0.600602\pi
0.978539 0.206062i 0.0660650π-0.0660650\pi
774774 −39.0000 + 67.5500i −0.0503876 + 0.0872739i
775775 0 0
776776 642.591i 0.828081i
777777 351.606 609.000i 0.452518 0.783784i
778778 698.000i 0.897172i
779779 −6.00000 10.3923i −0.00770218 0.0133406i
780780 0 0
781781 352.000 609.682i 0.450704 0.780643i
782782 −339.482 588.000i −0.434120 0.751918i
783783 129.904 0.165905
784784 122.500 212.176i 0.156250 0.270633i
785785 0 0
786786 −157.500 272.798i −0.200382 0.347071i
787787 −204.382 + 354.000i −0.259698 + 0.449809i −0.966161 0.257940i 0.916956π-0.916956\pi
0.706463 + 0.707750i 0.250290π0.250290\pi
788788 67.5500 + 39.0000i 0.0857233 + 0.0494924i
789789 159.000 91.7987i 0.201521 0.116348i
790790 0 0
791791 259.000 448.601i 0.327434 0.567132i
792792 231.000i 0.291667i
793793 −83.1384 + 48.0000i −0.104840 + 0.0605296i
794794 −498.000 287.520i −0.627204 0.362116i
795795 0 0
796796 −630.000 + 363.731i −0.791457 + 0.456948i
797797 −625.270 −0.784530 −0.392265 0.919852i 0.628308π-0.628308\pi
−0.392265 + 0.919852i 0.628308π0.628308\pi
798798 42.0000i 0.0526316i
799799 1848.00 2.31289
800800 0 0
801801 −207.000 119.512i −0.258427 0.149203i
802802 245.951 + 142.000i 0.306672 + 0.177057i
803803 −38.1051 66.0000i −0.0474534 0.0821918i
804804 270.200i 0.336070i
805805 0 0
806806 228.000 0.282878
807807 −652.117 + 376.500i −0.808076 + 0.466543i
808808 72.7461 126.000i 0.0900323 0.155941i
809809 −376.000 + 651.251i −0.464771 + 0.805008i −0.999191 0.0402116i 0.987197π-0.987197\pi
0.534420 + 0.845219i 0.320530π0.320530\pi
810810 0 0
811811 270.200i 0.333169i −0.986027 0.166584i 0.946726π-0.946726\pi
0.986027 0.166584i 0.0532738π-0.0532738\pi
812812 −454.663 + 262.500i −0.559930 + 0.323276i
813813 219.000i 0.269373i
814814 319.000 + 552.524i 0.391892 + 0.678777i
815815 0 0
816816 105.000 181.865i 0.128676 0.222874i
817817 −45.0333 78.0000i −0.0551203 0.0954712i
818818 209.578 0.256208
819819 145.492i 0.177646i
820820 0 0
821821 −441.500 764.700i −0.537759 0.931426i −0.999024 0.0441635i 0.985938π-0.985938\pi
0.461265 0.887262i 0.347396π-0.347396\pi
822822 −76.2102 + 132.000i −0.0927132 + 0.160584i
823823 −424.352 245.000i −0.515617 0.297691i 0.219523 0.975607i 0.429550π-0.429550\pi
−0.735139 + 0.677916i 0.762883π0.762883\pi
824824 0 0
825825 0 0
826826 −52.5000 30.3109i −0.0635593 0.0366960i
827827 1279.00i 1.54655i 0.634068 + 0.773277i 0.281384π0.281384\pi
−0.634068 + 0.773277i 0.718616π0.718616\pi
828828 −218.238 + 126.000i −0.263573 + 0.152174i
829829 −1311.00 756.906i −1.58142 0.913035i −0.994652 0.103283i 0.967065π-0.967065\pi
−0.586771 0.809753i 0.699601π-0.699601\pi
830830 0 0
831831 −354.000 + 204.382i −0.425993 + 0.245947i
832832 90.0666 0.108253
833833 −1188.19 −1.42639
834834 −330.000 −0.395683
835835 0 0
836836 99.0000 + 57.1577i 0.118421 + 0.0683704i
837837 148.090 + 85.5000i 0.176930 + 0.102151i
838838 −65.8179 114.000i −0.0785417 0.136038i
839839 523.079i 0.623456i −0.950171 0.311728i 0.899092π-0.899092\pi
0.950171 0.311728i 0.100908π-0.100908\pi
840840 0 0
841841 −216.000 −0.256837
842842 −24.2487 + 14.0000i −0.0287989 + 0.0166271i
843843 −100.459 + 174.000i −0.119168 + 0.206406i
844844 78.0000 135.100i 0.0924171 0.160071i
845845 0 0
846846 228.631i 0.270249i
847847 0 0
848848 155.000i 0.182783i
849849 321.000 + 555.988i 0.378092 + 0.654874i
850850 0 0
851851 812.000 1406.43i 0.954172 1.65267i
852852 166.277 + 288.000i 0.195161 + 0.338028i
853853 −387.979 −0.454841 −0.227421 0.973797i 0.573029π-0.573029\pi
−0.227421 + 0.973797i 0.573029π0.573029\pi
854854 −84.0000 + 48.4974i −0.0983607 + 0.0567886i
855855 0 0
856856 108.500 + 187.928i 0.126752 + 0.219541i
857857 415.692 720.000i 0.485055 0.840140i −0.514797 0.857312i 0.672133π-0.672133\pi
0.999853 + 0.0171718i 0.00546622π0.00546622\pi
858858 114.315 + 66.0000i 0.133235 + 0.0769231i
859859 −981.000 + 566.381i −1.14203 + 0.659349i −0.946931 0.321436i 0.895835π-0.895835\pi
−0.195094 + 0.980785i 0.562501π0.562501\pi
860860 0 0
861861 21.0000 + 36.3731i 0.0243902 + 0.0422451i
862862 118.000i 0.136891i
863863 −19.0526 + 11.0000i −0.0220771 + 0.0127462i −0.510998 0.859582i 0.670724π-0.670724\pi
0.488921 + 0.872328i 0.337391π0.337391\pi
864864 148.500 + 85.7365i 0.171875 + 0.0992321i
865865 0 0
866866 486.000 280.592i 0.561201 0.324010i
867867 −517.883 −0.597328
868868 −691.088 −0.796185
869869 187.000 0.215190
870870 0 0
871871 −312.000 180.133i −0.358209 0.206812i
872872 −824.456 476.000i −0.945477 0.545872i
873873 −137.698 238.500i −0.157730 0.273196i
874874 96.9948i 0.110978i
875875 0 0
876876 36.0000 0.0410959
877877 −34.6410 + 20.0000i −0.0394994 + 0.0228050i −0.519620 0.854398i 0.673926π-0.673926\pi
0.480120 + 0.877203i 0.340593π0.340593\pi
878878 369.793 640.500i 0.421176 0.729499i
879879 −16.5000 + 28.5788i −0.0187713 + 0.0325129i
880880 0 0
881881 20.7846i 0.0235921i −0.999930 0.0117960i 0.996245π-0.996245\pi
0.999930 0.0117960i 0.00375488π-0.00375488\pi
882882 147.000i 0.166667i
883883 386.000i 0.437146i −0.975821 0.218573i 0.929860π-0.929860\pi
0.975821 0.218573i 0.0701402π-0.0701402\pi
884884 252.000 + 436.477i 0.285068 + 0.493752i
885885 0 0
886886 77.5000 134.234i 0.0874718 0.151506i
887887 −862.561 1494.00i −0.972448 1.68433i −0.688112 0.725604i 0.741560π-0.741560\pi
−0.284336 0.958725i 0.591773π-0.591773\pi
888888 −703.213 −0.791906
889889 −3.50000 + 6.06218i −0.00393701 + 0.00681910i
890890 0 0
891891 49.5000 + 85.7365i 0.0555556 + 0.0962250i
892892 −33.7750 + 58.5000i −0.0378643 + 0.0655830i
893893 −228.631 132.000i −0.256025 0.147816i
894894 −345.000 + 199.186i −0.385906 + 0.222803i
895895 0 0
896896 −833.000 −0.929688
897897 336.000i 0.374582i
898898 318.697 184.000i 0.354897 0.204900i
899899 712.500 + 411.362i 0.792547 + 0.457577i
900900 0 0
901901 −651.000 + 375.855i −0.722531 + 0.417153i
902902 −38.1051 −0.0422451
903903 157.617 + 273.000i 0.174548 + 0.302326i
904904 −518.000 −0.573009
905905 0 0
906906 340.500 + 196.588i 0.375828 + 0.216984i
907907 512.687 + 296.000i 0.565256 + 0.326351i 0.755252 0.655434i 0.227514π-0.227514\pi
−0.189996 + 0.981785i 0.560848π0.560848\pi
908908 −101.325 175.500i −0.111591 0.193282i
909909 62.3538i 0.0685961i
910910 0 0
911911 −416.000 −0.456641 −0.228321 0.973586i 0.573323π-0.573323\pi
−0.228321 + 0.973586i 0.573323π0.573323\pi
912912 −25.9808 + 15.0000i −0.0284877 + 0.0164474i
913913 −295.315 + 511.500i −0.323455 + 0.560241i
914914 170.500 295.315i 0.186543 0.323101i
915915 0 0
916916 93.5307i 0.102108i
917917 −1273.06 −1.38828
918918 126.000i 0.137255i
919919 25.0000 + 43.3013i 0.0272035 + 0.0471178i 0.879307 0.476256i 0.158006π-0.158006\pi
−0.852103 + 0.523374i 0.824673π0.824673\pi
920920 0 0
921921 −396.000 + 685.892i −0.429967 + 0.744725i
922922 27.7128 + 48.0000i 0.0300573 + 0.0520607i
923923 −443.405 −0.480395
924924 −346.500 200.052i −0.375000 0.216506i
925925 0 0
926926 89.0000 + 154.153i 0.0961123 + 0.166471i
927927 0 0
928928 714.471 + 412.500i 0.769904 + 0.444504i
929929 −357.000 + 206.114i −0.384284 + 0.221867i −0.679681 0.733508i 0.737882π-0.737882\pi
0.295396 + 0.955375i 0.404548π0.404548\pi
930930 0 0
931931 147.000 + 84.8705i 0.157895 + 0.0911606i
932932 786.000i 0.843348i
933933 493.634 285.000i 0.529083 0.305466i
934934 570.000 + 329.090i 0.610278 + 0.352344i
935935 0 0
936936 −126.000 + 72.7461i −0.134615 + 0.0777202i
937937 −1605.61 −1.71357 −0.856783 0.515677i 0.827540π-0.827540\pi
−0.856783 + 0.515677i 0.827540π0.827540\pi
938938 −315.233 182.000i −0.336070 0.194030i
939939 −951.000 −1.01278
940940 0 0
941941 −1150.50 664.241i −1.22264 0.705889i −0.257156 0.966370i 0.582786π-0.582786\pi
−0.965479 + 0.260481i 0.916119π0.916119\pi
942942 −72.7461 42.0000i −0.0772252 0.0445860i
943943 48.4974 + 84.0000i 0.0514289 + 0.0890774i
944944 43.3013i 0.0458700i
945945 0 0
946946 −286.000 −0.302326
947947 −1186.45 + 685.000i −1.25286 + 0.723337i −0.971676 0.236318i 0.924059π-0.924059\pi
−0.281180 + 0.959655i 0.590726π0.590726\pi
948948 −44.1673 + 76.5000i −0.0465900 + 0.0806962i
949949 −24.0000 + 41.5692i −0.0252898 + 0.0438032i
950950 0 0
951951 323.894i 0.340582i
952952 594.093 + 1029.00i 0.624048 + 1.08088i
953953 1150.00i 1.20672i −0.797471 0.603358i 0.793829π-0.793829\pi
0.797471 0.603358i 0.206171π-0.206171\pi
954954 −46.5000 80.5404i −0.0487421 0.0844239i
955955 0 0
956956 240.000 415.692i 0.251046 0.434824i
957957 238.157 + 412.500i 0.248858 + 0.431034i
958958 −509.223 −0.531548
959959 308.000 + 533.472i 0.321168 + 0.556279i
960960 0 0
961961 61.0000 + 105.655i 0.0634755 + 0.109943i
962962 200.918 348.000i 0.208854 0.361746i
963963 −80.5404 46.5000i −0.0836349 0.0482866i
964964 −1228.50 + 709.275i −1.27438 + 0.735762i
965965 0 0
966966 339.482i 0.351431i
967967 5.00000i 0.00517063i 0.999997 + 0.00258532i 0.000822932π0.000822932\pi
−0.999997 + 0.00258532i 0.999177π0.999177\pi
968968 0 0
969969 126.000 + 72.7461i 0.130031 + 0.0750734i
970970 0 0
971971 385.500 222.569i 0.397013 0.229216i −0.288181 0.957576i 0.593051π-0.593051\pi
0.685195 + 0.728360i 0.259717π0.259717\pi
972972 −46.7654 −0.0481125
973973 −666.840 + 1155.00i −0.685344 + 1.18705i
974974 841.000 0.863450
975975 0 0
976976 −60.0000 34.6410i −0.0614754 0.0354928i
977977 −829.652 479.000i −0.849184 0.490276i 0.0111917 0.999937i 0.496437π-0.496437\pi
−0.860375 + 0.509661i 0.829771π0.829771\pi
978978 183.597 + 318.000i 0.187727 + 0.325153i
979979 876.418i 0.895217i
980980 0 0
981981 408.000 0.415902
982982 −830.518 + 479.500i −0.845742 + 0.488289i
983983 140.296 243.000i 0.142722 0.247202i −0.785798 0.618483i 0.787748π-0.787748\pi
0.928521 + 0.371280i 0.121081π0.121081\pi
984984 21.0000 36.3731i 0.0213415 0.0369645i
985985 0 0
986986 606.218i 0.614825i
987987 800.207 + 462.000i 0.810747 + 0.468085i
988988 72.0000i 0.0728745i
989989 364.000 + 630.466i 0.368049 + 0.637479i
990990 0 0
991991 −461.500 + 799.341i −0.465691 + 0.806601i −0.999232 0.0391732i 0.987528π-0.987528\pi
0.533541 + 0.845774i 0.320861π0.320861\pi
992992 542.998 + 940.500i 0.547377 + 0.948085i
993993 27.7128 0.0279082
994994 −448.000 −0.450704
995995 0 0
996996 −139.500 241.621i −0.140060 0.242591i
997997 −10.3923 + 18.0000i −0.0104236 + 0.0180542i −0.871190 0.490946i 0.836651π-0.836651\pi
0.860767 + 0.509000i 0.169985π0.169985\pi
998998 −102.191 59.0000i −0.102396 0.0591182i
999999 261.000 150.688i 0.261261 0.150839i
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 525.3.s.c.199.2 4
5.2 odd 4 525.3.o.g.451.1 2
5.3 odd 4 21.3.f.b.10.1 2
5.4 even 2 inner 525.3.s.c.199.1 4
7.5 odd 6 inner 525.3.s.c.124.1 4
15.8 even 4 63.3.m.c.10.1 2
20.3 even 4 336.3.bh.a.241.1 2
35.3 even 12 147.3.d.b.97.2 2
35.12 even 12 525.3.o.g.376.1 2
35.13 even 4 147.3.f.c.31.1 2
35.18 odd 12 147.3.d.b.97.1 2
35.19 odd 6 inner 525.3.s.c.124.2 4
35.23 odd 12 147.3.f.c.19.1 2
35.33 even 12 21.3.f.b.19.1 yes 2
60.23 odd 4 1008.3.cg.g.577.1 2
105.23 even 12 441.3.m.e.19.1 2
105.38 odd 12 441.3.d.b.244.1 2
105.53 even 12 441.3.d.b.244.2 2
105.68 odd 12 63.3.m.c.19.1 2
105.83 odd 4 441.3.m.e.325.1 2
140.3 odd 12 2352.3.f.d.97.1 2
140.103 odd 12 336.3.bh.a.145.1 2
140.123 even 12 2352.3.f.d.97.2 2
420.383 even 12 1008.3.cg.g.145.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.f.b.10.1 2 5.3 odd 4
21.3.f.b.19.1 yes 2 35.33 even 12
63.3.m.c.10.1 2 15.8 even 4
63.3.m.c.19.1 2 105.68 odd 12
147.3.d.b.97.1 2 35.18 odd 12
147.3.d.b.97.2 2 35.3 even 12
147.3.f.c.19.1 2 35.23 odd 12
147.3.f.c.31.1 2 35.13 even 4
336.3.bh.a.145.1 2 140.103 odd 12
336.3.bh.a.241.1 2 20.3 even 4
441.3.d.b.244.1 2 105.38 odd 12
441.3.d.b.244.2 2 105.53 even 12
441.3.m.e.19.1 2 105.23 even 12
441.3.m.e.325.1 2 105.83 odd 4
525.3.o.g.376.1 2 35.12 even 12
525.3.o.g.451.1 2 5.2 odd 4
525.3.s.c.124.1 4 7.5 odd 6 inner
525.3.s.c.124.2 4 35.19 odd 6 inner
525.3.s.c.199.1 4 5.4 even 2 inner
525.3.s.c.199.2 4 1.1 even 1 trivial
1008.3.cg.g.145.1 2 420.383 even 12
1008.3.cg.g.577.1 2 60.23 odd 4
2352.3.f.d.97.1 2 140.3 odd 12
2352.3.f.d.97.2 2 140.123 even 12