Properties

Label 350.2.j.a.249.2
Level 350350
Weight 22
Character 350.249
Analytic conductor 2.7952.795
Analytic rank 00
Dimension 44
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,2,Mod(149,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 350=2527 350 = 2 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 350.j (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: 2.794764070742.79476407074
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 70)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 249.2
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 350.249
Dual form 350.2.j.a.149.2

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+(1.732051.00000i)q3+(0.5000000.866025i)q42.00000q6+(1.732052.00000i)q71.00000iq8+(0.500000+0.866025i)q9+(1.50000+2.59808i)q11+(1.73205+1.00000i)q125.00000iq13+(0.5000002.59808i)q14+(0.5000000.866025i)q16+(5.196153.00000i)q17+(0.866025+0.500000i)q18+(0.5000000.866025i)q19+(5.00000+1.73205i)q21+3.00000iq22+(2.59808+1.50000i)q23+(1.00000+1.73205i)q24+(2.500004.33013i)q26+4.00000iq27+(0.8660252.50000i)q28+6.00000q29+(2.000003.46410i)q31+(0.8660250.500000i)q32+(5.196153.00000i)q336.00000q34+1.00000q36+(9.526285.50000i)q37+(0.8660250.500000i)q38+(5.00000+8.66025i)q39+3.00000q41+(3.46410+4.00000i)q42+10.0000iq43+(1.50000+2.59808i)q44+(1.50000+2.59808i)q46+(2.598081.50000i)q47+2.00000iq48+(1.000006.92820i)q49+(6.00000+10.3923i)q51+(4.330132.50000i)q52+(2.59808+1.50000i)q53+(2.00000+3.46410i)q54+(2.000001.73205i)q56+2.00000iq57+(5.196153.00000i)q58+(2.00000+3.46410i)q614.00000iq62+(2.59808+0.500000i)q631.00000q64+(3.000005.19615i)q66+(3.46410+2.00000i)q67+(5.19615+3.00000i)q68+6.00000q69+12.0000q71+(0.8660250.500000i)q72+(3.464102.00000i)q73+(5.500009.52628i)q741.00000q76+(2.59808+7.50000i)q77+10.0000iq78+(5.000008.66025i)q79+(5.500009.52628i)q81+(2.598081.50000i)q82+12.0000iq83+(1.00000+5.19615i)q84+(5.00000+8.66025i)q86+(10.39236.00000i)q87+(2.59808+1.50000i)q88+(3.00000+5.19615i)q89+(10.00008.66025i)q91+3.00000iq92+(6.92820+4.00000i)q93+(1.500002.59808i)q94+(1.00000+1.73205i)q96+14.0000iq97+(4.330135.50000i)q983.00000q99+O(q100)q+(0.866025 - 0.500000i) q^{2} +(-1.73205 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000 q^{6} +(1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-1.73205 + 1.00000i) q^{12} -5.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-5.00000 + 1.73205i) q^{21} +3.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-2.50000 - 4.33013i) q^{26} +4.00000i q^{27} +(-0.866025 - 2.50000i) q^{28} +6.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(9.52628 - 5.50000i) q^{37} +(-0.866025 - 0.500000i) q^{38} +(-5.00000 + 8.66025i) q^{39} +3.00000 q^{41} +(-3.46410 + 4.00000i) q^{42} +10.0000i q^{43} +(1.50000 + 2.59808i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(2.59808 - 1.50000i) q^{47} +2.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-4.33013 - 2.50000i) q^{52} +(2.59808 + 1.50000i) q^{53} +(2.00000 + 3.46410i) q^{54} +(-2.00000 - 1.73205i) q^{56} +2.00000i q^{57} +(5.19615 - 3.00000i) q^{58} +(2.00000 + 3.46410i) q^{61} -4.00000i q^{62} +(2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +(3.46410 + 2.00000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(5.50000 - 9.52628i) q^{74} -1.00000 q^{76} +(2.59808 + 7.50000i) q^{77} +10.0000i q^{78} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +(2.59808 - 1.50000i) q^{82} +12.0000i q^{83} +(-1.00000 + 5.19615i) q^{84} +(5.00000 + 8.66025i) q^{86} +(-10.3923 - 6.00000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 - 8.66025i) q^{91} +3.00000i q^{92} +(-6.92820 + 4.00000i) q^{93} +(1.50000 - 2.59808i) q^{94} +(1.00000 + 1.73205i) q^{96} +14.0000i q^{97} +(-4.33013 - 5.50000i) q^{98} -3.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q48q6+2q96q11+2q142q162q1920q214q2410q26+24q29+8q3124q34+4q3620q39+12q41+6q446q46+12q99+O(q100) 4 q + 2 q^{4} - 8 q^{6} + 2 q^{9} - 6 q^{11} + 2 q^{14} - 2 q^{16} - 2 q^{19} - 20 q^{21} - 4 q^{24} - 10 q^{26} + 24 q^{29} + 8 q^{31} - 24 q^{34} + 4 q^{36} - 20 q^{39} + 12 q^{41} + 6 q^{44} - 6 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/350Z)×\left(\mathbb{Z}/350\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.866025 0.500000i 0.612372 0.353553i
33 −1.73205 1.00000i −1.00000 0.577350i −0.0917517 0.995782i 0.529247π-0.529247\pi
−0.908248 + 0.418432i 0.862580π0.862580\pi
44 0.500000 0.866025i 0.250000 0.433013i
55 0 0
66 −2.00000 −0.816497
77 1.73205 2.00000i 0.654654 0.755929i
88 1.00000i 0.353553i
99 0.500000 + 0.866025i 0.166667 + 0.288675i
1010 0 0
1111 −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i 0.982718π-0.982718\pi
0.546259 + 0.837616i 0.316051π0.316051\pi
1212 −1.73205 + 1.00000i −0.500000 + 0.288675i
1313 5.00000i 1.38675i −0.720577 0.693375i 0.756123π-0.756123\pi
0.720577 0.693375i 0.243877π-0.243877\pi
1414 0.500000 2.59808i 0.133631 0.694365i
1515 0 0
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −5.19615 3.00000i −1.26025 0.727607i −0.287129 0.957892i 0.592701π-0.592701\pi
−0.973123 + 0.230285i 0.926034π0.926034\pi
1818 0.866025 + 0.500000i 0.204124 + 0.117851i
1919 −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i 0.203260π-0.203260\pi
−0.917663 + 0.397360i 0.869927π0.869927\pi
2020 0 0
2121 −5.00000 + 1.73205i −1.09109 + 0.377964i
2222 3.00000i 0.639602i
2323 −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i 0.767924π-0.767924\pi
0.204046 + 0.978961i 0.434591π0.434591\pi
2424 −1.00000 + 1.73205i −0.204124 + 0.353553i
2525 0 0
2626 −2.50000 4.33013i −0.490290 0.849208i
2727 4.00000i 0.769800i
2828 −0.866025 2.50000i −0.163663 0.472456i
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i 0.716379π-0.716379\pi
0.987829 + 0.155543i 0.0497126π0.0497126\pi
3232 −0.866025 0.500000i −0.153093 0.0883883i
3333 5.19615 3.00000i 0.904534 0.522233i
3434 −6.00000 −1.02899
3535 0 0
3636 1.00000 0.166667
3737 9.52628 5.50000i 1.56611 0.904194i 0.569495 0.821995i 0.307139π-0.307139\pi
0.996616 0.0821995i 0.0261945π-0.0261945\pi
3838 −0.866025 0.500000i −0.140488 0.0811107i
3939 −5.00000 + 8.66025i −0.800641 + 1.38675i
4040 0 0
4141 3.00000 0.468521 0.234261 0.972174i 0.424733π-0.424733\pi
0.234261 + 0.972174i 0.424733π0.424733\pi
4242 −3.46410 + 4.00000i −0.534522 + 0.617213i
4343 10.0000i 1.52499i 0.646997 + 0.762493i 0.276025π0.276025\pi
−0.646997 + 0.762493i 0.723975π0.723975\pi
4444 1.50000 + 2.59808i 0.226134 + 0.391675i
4545 0 0
4646 −1.50000 + 2.59808i −0.221163 + 0.383065i
4747 2.59808 1.50000i 0.378968 0.218797i −0.298401 0.954441i 0.596453π-0.596453\pi
0.677369 + 0.735643i 0.263120π0.263120\pi
4848 2.00000i 0.288675i
4949 −1.00000 6.92820i −0.142857 0.989743i
5050 0 0
5151 6.00000 + 10.3923i 0.840168 + 1.45521i
5252 −4.33013 2.50000i −0.600481 0.346688i
5353 2.59808 + 1.50000i 0.356873 + 0.206041i 0.667708 0.744423i 0.267275π-0.267275\pi
−0.310835 + 0.950464i 0.600609π0.600609\pi
5454 2.00000 + 3.46410i 0.272166 + 0.471405i
5555 0 0
5656 −2.00000 1.73205i −0.267261 0.231455i
5757 2.00000i 0.264906i
5858 5.19615 3.00000i 0.682288 0.393919i
5959 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
6060 0 0
6161 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i 0.0842377π-0.0842377\pi
−0.709113 + 0.705095i 0.750904π0.750904\pi
6262 4.00000i 0.508001i
6363 2.59808 + 0.500000i 0.327327 + 0.0629941i
6464 −1.00000 −0.125000
6565 0 0
6666 3.00000 5.19615i 0.369274 0.639602i
6767 3.46410 + 2.00000i 0.423207 + 0.244339i 0.696449 0.717607i 0.254762π-0.254762\pi
−0.273241 + 0.961946i 0.588096π0.588096\pi
6868 −5.19615 + 3.00000i −0.630126 + 0.363803i
6969 6.00000 0.722315
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 0.866025 0.500000i 0.102062 0.0589256i
7373 −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i 0.408542π-0.408542\pi
−0.688830 + 0.724923i 0.741875π0.741875\pi
7474 5.50000 9.52628i 0.639362 1.10741i
7575 0 0
7676 −1.00000 −0.114708
7777 2.59808 + 7.50000i 0.296078 + 0.854704i
7878 10.0000i 1.13228i
7979 −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i 0.976489π-0.976489\pi
0.434730 0.900561i 0.356844π-0.356844\pi
8080 0 0
8181 5.50000 9.52628i 0.611111 1.05848i
8282 2.59808 1.50000i 0.286910 0.165647i
8383 12.0000i 1.31717i 0.752506 + 0.658586i 0.228845π0.228845\pi
−0.752506 + 0.658586i 0.771155π0.771155\pi
8484 −1.00000 + 5.19615i −0.109109 + 0.566947i
8585 0 0
8686 5.00000 + 8.66025i 0.539164 + 0.933859i
8787 −10.3923 6.00000i −1.11417 0.643268i
8888 2.59808 + 1.50000i 0.276956 + 0.159901i
8989 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i 0.0636557π-0.0636557\pi
−0.662071 + 0.749441i 0.730322π0.730322\pi
9090 0 0
9191 −10.0000 8.66025i −1.04828 0.907841i
9292 3.00000i 0.312772i
9393 −6.92820 + 4.00000i −0.718421 + 0.414781i
9494 1.50000 2.59808i 0.154713 0.267971i
9595 0 0
9696 1.00000 + 1.73205i 0.102062 + 0.176777i
9797 14.0000i 1.42148i 0.703452 + 0.710742i 0.251641π0.251641\pi
−0.703452 + 0.710742i 0.748359π0.748359\pi
9898 −4.33013 5.50000i −0.437409 0.555584i
9999 −3.00000 −0.301511
100100 0 0
101101 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i 0.629684π-0.629684\pi
0.993258 0.115924i 0.0369830π-0.0369830\pi
102102 10.3923 + 6.00000i 1.02899 + 0.594089i
103103 3.46410 2.00000i 0.341328 0.197066i −0.319531 0.947576i 0.603525π-0.603525\pi
0.660859 + 0.750510i 0.270192π0.270192\pi
104104 −5.00000 −0.490290
105105 0 0
106106 3.00000 0.291386
107107 −10.3923 + 6.00000i −1.00466 + 0.580042i −0.909624 0.415432i 0.863630π-0.863630\pi
−0.0950377 + 0.995474i 0.530297π0.530297\pi
108108 3.46410 + 2.00000i 0.333333 + 0.192450i
109109 −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i 0.894690π-0.894690\pi
0.754204 + 0.656640i 0.228023π0.228023\pi
110110 0 0
111111 −22.0000 −2.08815
112112 −2.59808 0.500000i −0.245495 0.0472456i
113113 12.0000i 1.12887i −0.825479 0.564433i 0.809095π-0.809095\pi
0.825479 0.564433i 0.190905π-0.190905\pi
114114 1.00000 + 1.73205i 0.0936586 + 0.162221i
115115 0 0
116116 3.00000 5.19615i 0.278543 0.482451i
117117 4.33013 2.50000i 0.400320 0.231125i
118118 0 0
119119 −15.0000 + 5.19615i −1.37505 + 0.476331i
120120 0 0
121121 1.00000 + 1.73205i 0.0909091 + 0.157459i
122122 3.46410 + 2.00000i 0.313625 + 0.181071i
123123 −5.19615 3.00000i −0.468521 0.270501i
124124 −2.00000 3.46410i −0.179605 0.311086i
125125 0 0
126126 2.50000 0.866025i 0.222718 0.0771517i
127127 19.0000i 1.68598i −0.537931 0.842989i 0.680794π-0.680794\pi
0.537931 0.842989i 0.319206π-0.319206\pi
128128 −0.866025 + 0.500000i −0.0765466 + 0.0441942i
129129 10.0000 17.3205i 0.880451 1.52499i
130130 0 0
131131 −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i 0.208503π-0.208503\pi
−0.924084 + 0.382190i 0.875170π0.875170\pi
132132 6.00000i 0.522233i
133133 −2.59808 0.500000i −0.225282 0.0433555i
134134 4.00000 0.345547
135135 0 0
136136 −3.00000 + 5.19615i −0.257248 + 0.445566i
137137 −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i 0.504656π-0.504656\pi
−0.873247 + 0.487278i 0.837990π0.837990\pi
138138 5.19615 3.00000i 0.442326 0.255377i
139139 4.00000 0.339276 0.169638 0.985506i 0.445740π-0.445740\pi
0.169638 + 0.985506i 0.445740π0.445740\pi
140140 0 0
141141 −6.00000 −0.505291
142142 10.3923 6.00000i 0.872103 0.503509i
143143 12.9904 + 7.50000i 1.08631 + 0.627182i
144144 0.500000 0.866025i 0.0416667 0.0721688i
145145 0 0
146146 −4.00000 −0.331042
147147 −5.19615 + 13.0000i −0.428571 + 1.07222i
148148 11.0000i 0.904194i
149149 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i 0.0972370π0.0972370\pi
−0.216394 + 0.976306i 0.569430π0.569430\pi
150150 0 0
151151 −7.00000 + 12.1244i −0.569652 + 0.986666i 0.426948 + 0.904276i 0.359589π0.359589\pi
−0.996600 + 0.0823900i 0.973745π0.973745\pi
152152 −0.866025 + 0.500000i −0.0702439 + 0.0405554i
153153 6.00000i 0.485071i
154154 6.00000 + 5.19615i 0.483494 + 0.418718i
155155 0 0
156156 5.00000 + 8.66025i 0.400320 + 0.693375i
157157 −4.33013 2.50000i −0.345582 0.199522i 0.317156 0.948373i 0.397272π-0.397272\pi
−0.662738 + 0.748852i 0.730606π0.730606\pi
158158 −8.66025 5.00000i −0.688973 0.397779i
159159 −3.00000 5.19615i −0.237915 0.412082i
160160 0 0
161161 −1.50000 + 7.79423i −0.118217 + 0.614271i
162162 11.0000i 0.864242i
163163 3.46410 2.00000i 0.271329 0.156652i −0.358162 0.933659i 0.616597π-0.616597\pi
0.629492 + 0.777007i 0.283263π0.283263\pi
164164 1.50000 2.59808i 0.117130 0.202876i
165165 0 0
166166 6.00000 + 10.3923i 0.465690 + 0.806599i
167167 9.00000i 0.696441i 0.937413 + 0.348220i 0.113214π0.113214\pi
−0.937413 + 0.348220i 0.886786π0.886786\pi
168168 1.73205 + 5.00000i 0.133631 + 0.385758i
169169 −12.0000 −0.923077
170170 0 0
171171 0.500000 0.866025i 0.0382360 0.0662266i
172172 8.66025 + 5.00000i 0.660338 + 0.381246i
173173 −2.59808 + 1.50000i −0.197528 + 0.114043i −0.595502 0.803354i 0.703047π-0.703047\pi
0.397974 + 0.917397i 0.369713π0.369713\pi
174174 −12.0000 −0.909718
175175 0 0
176176 3.00000 0.226134
177177 0 0
178178 5.19615 + 3.00000i 0.389468 + 0.224860i
179179 −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i 0.869096π-0.869096\pi
0.804508 + 0.593942i 0.202429π0.202429\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 −12.9904 2.50000i −0.962911 0.185312i
183183 8.00000i 0.591377i
184184 1.50000 + 2.59808i 0.110581 + 0.191533i
185185 0 0
186186 −4.00000 + 6.92820i −0.293294 + 0.508001i
187187 15.5885 9.00000i 1.13994 0.658145i
188188 3.00000i 0.218797i
189189 8.00000 + 6.92820i 0.581914 + 0.503953i
190190 0 0
191191 −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i 0.309616π-0.309616\pi
−0.997225 + 0.0744412i 0.976283π0.976283\pi
192192 1.73205 + 1.00000i 0.125000 + 0.0721688i
193193 −3.46410 2.00000i −0.249351 0.143963i 0.370116 0.928986i 0.379318π-0.379318\pi
−0.619467 + 0.785022i 0.712651π0.712651\pi
194194 7.00000 + 12.1244i 0.502571 + 0.870478i
195195 0 0
196196 −6.50000 2.59808i −0.464286 0.185577i
197197 3.00000i 0.213741i −0.994273 0.106871i 0.965917π-0.965917\pi
0.994273 0.106871i 0.0340831π-0.0340831\pi
198198 −2.59808 + 1.50000i −0.184637 + 0.106600i
199199 −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i 0.878615π-0.878615\pi
0.786389 + 0.617731i 0.211948π0.211948\pi
200200 0 0
201201 −4.00000 6.92820i −0.282138 0.488678i
202202 12.0000i 0.844317i
203203 10.3923 12.0000i 0.729397 0.842235i
204204 12.0000 0.840168
205205 0 0
206206 2.00000 3.46410i 0.139347 0.241355i
207207 −2.59808 1.50000i −0.180579 0.104257i
208208 −4.33013 + 2.50000i −0.300240 + 0.173344i
209209 3.00000 0.207514
210210 0 0
211211 −1.00000 −0.0688428 −0.0344214 0.999407i 0.510959π-0.510959\pi
−0.0344214 + 0.999407i 0.510959π0.510959\pi
212212 2.59808 1.50000i 0.178437 0.103020i
213213 −20.7846 12.0000i −1.42414 0.822226i
214214 −6.00000 + 10.3923i −0.410152 + 0.710403i
215215 0 0
216216 4.00000 0.272166
217217 −3.46410 10.0000i −0.235159 0.678844i
218218 4.00000i 0.270914i
219219 4.00000 + 6.92820i 0.270295 + 0.468165i
220220 0 0
221221 −15.0000 + 25.9808i −1.00901 + 1.74766i
222222 −19.0526 + 11.0000i −1.27872 + 0.738272i
223223 8.00000i 0.535720i −0.963458 0.267860i 0.913684π-0.913684\pi
0.963458 0.267860i 0.0863164π-0.0863164\pi
224224 −2.50000 + 0.866025i −0.167038 + 0.0578638i
225225 0 0
226226 −6.00000 10.3923i −0.399114 0.691286i
227227 20.7846 + 12.0000i 1.37952 + 0.796468i 0.992102 0.125435i 0.0400326π-0.0400326\pi
0.387421 + 0.921903i 0.373366π0.373366\pi
228228 1.73205 + 1.00000i 0.114708 + 0.0662266i
229229 −14.0000 24.2487i −0.925146 1.60240i −0.791326 0.611394i 0.790609π-0.790609\pi
−0.133820 0.991006i 0.542724π-0.542724\pi
230230 0 0
231231 3.00000 15.5885i 0.197386 1.02565i
232232 6.00000i 0.393919i
233233 5.19615 3.00000i 0.340411 0.196537i −0.320043 0.947403i 0.603697π-0.603697\pi
0.660454 + 0.750867i 0.270364π0.270364\pi
234234 2.50000 4.33013i 0.163430 0.283069i
235235 0 0
236236 0 0
237237 20.0000i 1.29914i
238238 −10.3923 + 12.0000i −0.673633 + 0.777844i
239239 −6.00000 −0.388108 −0.194054 0.980991i 0.562164π-0.562164\pi
−0.194054 + 0.980991i 0.562164π0.562164\pi
240240 0 0
241241 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i 0.535394π-0.535394\pi
0.916159 0.400815i 0.131273π-0.131273\pi
242242 1.73205 + 1.00000i 0.111340 + 0.0642824i
243243 −8.66025 + 5.00000i −0.555556 + 0.320750i
244244 4.00000 0.256074
245245 0 0
246246 −6.00000 −0.382546
247247 −4.33013 + 2.50000i −0.275519 + 0.159071i
248248 −3.46410 2.00000i −0.219971 0.127000i
249249 12.0000 20.7846i 0.760469 1.31717i
250250 0 0
251251 −15.0000 −0.946792 −0.473396 0.880850i 0.656972π-0.656972\pi
−0.473396 + 0.880850i 0.656972π0.656972\pi
252252 1.73205 2.00000i 0.109109 0.125988i
253253 9.00000i 0.565825i
254254 −9.50000 16.4545i −0.596083 1.03245i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −10.3923 + 6.00000i −0.648254 + 0.374270i −0.787787 0.615948i 0.788773π-0.788773\pi
0.139533 + 0.990217i 0.455440π0.455440\pi
258258 20.0000i 1.24515i
259259 5.50000 28.5788i 0.341753 1.77580i
260260 0 0
261261 3.00000 + 5.19615i 0.185695 + 0.321634i
262262 −2.59808 1.50000i −0.160510 0.0926703i
263263 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
264264 −3.00000 5.19615i −0.184637 0.319801i
265265 0 0
266266 −2.50000 + 0.866025i −0.153285 + 0.0530994i
267267 12.0000i 0.734388i
268268 3.46410 2.00000i 0.211604 0.122169i
269269 −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i 0.952547π-0.952547\pi
0.623082 + 0.782157i 0.285880π0.285880\pi
270270 0 0
271271 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i 0.00513477π-0.00513477\pi
−0.513905 + 0.857847i 0.671801π0.671801\pi
272272 6.00000i 0.363803i
273273 8.66025 + 25.0000i 0.524142 + 1.51307i
274274 −12.0000 −0.724947
275275 0 0
276276 3.00000 5.19615i 0.180579 0.312772i
277277 −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i 0.352470π-0.352470\pi
−0.551131 + 0.834419i 0.685804π0.685804\pi
278278 3.46410 2.00000i 0.207763 0.119952i
279279 4.00000 0.239474
280280 0 0
281281 −3.00000 −0.178965 −0.0894825 0.995988i 0.528521π-0.528521\pi
−0.0894825 + 0.995988i 0.528521π0.528521\pi
282282 −5.19615 + 3.00000i −0.309426 + 0.178647i
283283 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i 0.0522041π-0.0522041\pi
0.351895 + 0.936039i 0.385537π0.385537\pi
284284 6.00000 10.3923i 0.356034 0.616670i
285285 0 0
286286 15.0000 0.886969
287287 5.19615 6.00000i 0.306719 0.354169i
288288 1.00000i 0.0589256i
289289 9.50000 + 16.4545i 0.558824 + 0.967911i
290290 0 0
291291 14.0000 24.2487i 0.820695 1.42148i
292292 −3.46410 + 2.00000i −0.202721 + 0.117041i
293293 27.0000i 1.57736i 0.614806 + 0.788678i 0.289234π0.289234\pi
−0.614806 + 0.788678i 0.710766π0.710766\pi
294294 2.00000 + 13.8564i 0.116642 + 0.808122i
295295 0 0
296296 −5.50000 9.52628i −0.319681 0.553704i
297297 −10.3923 6.00000i −0.603023 0.348155i
298298 15.5885 + 9.00000i 0.903015 + 0.521356i
299299 7.50000 + 12.9904i 0.433736 + 0.751253i
300300 0 0
301301 20.0000 + 17.3205i 1.15278 + 0.998337i
302302 14.0000i 0.805609i
303303 −20.7846 + 12.0000i −1.19404 + 0.689382i
304304 −0.500000 + 0.866025i −0.0286770 + 0.0496700i
305305 0 0
306306 −3.00000 5.19615i −0.171499 0.297044i
307307 2.00000i 0.114146i 0.998370 + 0.0570730i 0.0181768π0.0181768\pi
−0.998370 + 0.0570730i 0.981823π0.981823\pi
308308 7.79423 + 1.50000i 0.444117 + 0.0854704i
309309 −8.00000 −0.455104
310310 0 0
311311 −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i 0.943838π-0.943838\pi
0.644246 + 0.764818i 0.277171π0.277171\pi
312312 8.66025 + 5.00000i 0.490290 + 0.283069i
313313 −6.92820 + 4.00000i −0.391605 + 0.226093i −0.682855 0.730554i 0.739262π-0.739262\pi
0.291250 + 0.956647i 0.405929π0.405929\pi
314314 −5.00000 −0.282166
315315 0 0
316316 −10.0000 −0.562544
317317 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i 0.497978π-0.497978\pi
0.869184 + 0.494489i 0.164645π0.164645\pi
318318 −5.19615 3.00000i −0.291386 0.168232i
319319 −9.00000 + 15.5885i −0.503903 + 0.872786i
320320 0 0
321321 24.0000 1.33955
322322 2.59808 + 7.50000i 0.144785 + 0.417959i
323323 6.00000i 0.333849i
324324 −5.50000 9.52628i −0.305556 0.529238i
325325 0 0
326326 2.00000 3.46410i 0.110770 0.191859i
327327 6.92820 4.00000i 0.383131 0.221201i
328328 3.00000i 0.165647i
329329 1.50000 7.79423i 0.0826977 0.429710i
330330 0 0
331331 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i 0.105047π-0.105047\pi
−0.753660 + 0.657264i 0.771714π0.771714\pi
332332 10.3923 + 6.00000i 0.570352 + 0.329293i
333333 9.52628 + 5.50000i 0.522037 + 0.301398i
334334 4.50000 + 7.79423i 0.246229 + 0.426481i
335335 0 0
336336 4.00000 + 3.46410i 0.218218 + 0.188982i
337337 14.0000i 0.762629i 0.924445 + 0.381314i 0.124528π0.124528\pi
−0.924445 + 0.381314i 0.875472π0.875472\pi
338338 −10.3923 + 6.00000i −0.565267 + 0.326357i
339339 −12.0000 + 20.7846i −0.651751 + 1.12887i
340340 0 0
341341 6.00000 + 10.3923i 0.324918 + 0.562775i
342342 1.00000i 0.0540738i
343343 −15.5885 10.0000i −0.841698 0.539949i
344344 10.0000 0.539164
345345 0 0
346346 −1.50000 + 2.59808i −0.0806405 + 0.139673i
347347 −20.7846 12.0000i −1.11578 0.644194i −0.175457 0.984487i 0.556140π-0.556140\pi
−0.940319 + 0.340293i 0.889474π0.889474\pi
348348 −10.3923 + 6.00000i −0.557086 + 0.321634i
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 0 0
351351 20.0000 1.06752
352352 2.59808 1.50000i 0.138478 0.0799503i
353353 10.3923 + 6.00000i 0.553127 + 0.319348i 0.750382 0.661004i 0.229870π-0.229870\pi
−0.197256 + 0.980352i 0.563203π0.563203\pi
354354 0 0
355355 0 0
356356 6.00000 0.317999
357357 31.1769 + 6.00000i 1.65006 + 0.317554i
358358 3.00000i 0.158555i
359359 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i 0.116054π-0.116054\pi
−0.775934 + 0.630814i 0.782721π0.782721\pi
360360 0 0
361361 9.00000 15.5885i 0.473684 0.820445i
362362 1.73205 1.00000i 0.0910346 0.0525588i
363363 4.00000i 0.209946i
364364 −12.5000 + 4.33013i −0.655178 + 0.226960i
365365 0 0
366366 −4.00000 6.92820i −0.209083 0.362143i
367367 0.866025 + 0.500000i 0.0452062 + 0.0260998i 0.522433 0.852680i 0.325025π-0.325025\pi
−0.477227 + 0.878780i 0.658358π0.658358\pi
368368 2.59808 + 1.50000i 0.135434 + 0.0781929i
369369 1.50000 + 2.59808i 0.0780869 + 0.135250i
370370 0 0
371371 7.50000 2.59808i 0.389381 0.134885i
372372 8.00000i 0.414781i
373373 29.4449 17.0000i 1.52460 0.880227i 0.525022 0.851089i 0.324057π-0.324057\pi
0.999575 0.0291379i 0.00927619π-0.00927619\pi
374374 9.00000 15.5885i 0.465379 0.806060i
375375 0 0
376376 −1.50000 2.59808i −0.0773566 0.133986i
377377 30.0000i 1.54508i
378378 10.3923 + 2.00000i 0.534522 + 0.102869i
379379 25.0000 1.28416 0.642082 0.766636i 0.278071π-0.278071\pi
0.642082 + 0.766636i 0.278071π0.278071\pi
380380 0 0
381381 −19.0000 + 32.9090i −0.973399 + 1.68598i
382382 −10.3923 6.00000i −0.531717 0.306987i
383383 −12.9904 + 7.50000i −0.663777 + 0.383232i −0.793715 0.608290i 0.791856π-0.791856\pi
0.129937 + 0.991522i 0.458522π0.458522\pi
384384 2.00000 0.102062
385385 0 0
386386 −4.00000 −0.203595
387387 −8.66025 + 5.00000i −0.440225 + 0.254164i
388388 12.1244 + 7.00000i 0.615521 + 0.355371i
389389 −12.0000 + 20.7846i −0.608424 + 1.05382i 0.383076 + 0.923717i 0.374865π0.374865\pi
−0.991500 + 0.130105i 0.958469π0.958469\pi
390390 0 0
391391 18.0000 0.910299
392392 −6.92820 + 1.00000i −0.349927 + 0.0505076i
393393 6.00000i 0.302660i
394394 −1.50000 2.59808i −0.0755689 0.130889i
395395 0 0
396396 −1.50000 + 2.59808i −0.0753778 + 0.130558i
397397 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i 0.650684π-0.650684\pi
0.542834 + 0.839840i 0.317351π0.317351\pi
398398 4.00000i 0.200502i
399399 4.00000 + 3.46410i 0.200250 + 0.173422i
400400 0 0
401401 −10.5000 18.1865i −0.524345 0.908192i −0.999598 0.0283431i 0.990977π-0.990977\pi
0.475253 0.879849i 0.342356π-0.342356\pi
402402 −6.92820 4.00000i −0.345547 0.199502i
403403 −17.3205 10.0000i −0.862796 0.498135i
404404 −6.00000 10.3923i −0.298511 0.517036i
405405 0 0
406406 3.00000 15.5885i 0.148888 0.773642i
407407 33.0000i 1.63575i
408408 10.3923 6.00000i 0.514496 0.297044i
409409 −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i 0.349725π0.349725\pi
−0.998674 + 0.0514740i 0.983608π0.983608\pi
410410 0 0
411411 12.0000 + 20.7846i 0.591916 + 1.02523i
412412 4.00000i 0.197066i
413413 0 0
414414 −3.00000 −0.147442
415415 0 0
416416 −2.50000 + 4.33013i −0.122573 + 0.212302i
417417 −6.92820 4.00000i −0.339276 0.195881i
418418 2.59808 1.50000i 0.127076 0.0733674i
419419 −15.0000 −0.732798 −0.366399 0.930458i 0.619409π-0.619409\pi
−0.366399 + 0.930458i 0.619409π0.619409\pi
420420 0 0
421421 −34.0000 −1.65706 −0.828529 0.559946i 0.810822π-0.810822\pi
−0.828529 + 0.559946i 0.810822π0.810822\pi
422422 −0.866025 + 0.500000i −0.0421575 + 0.0243396i
423423 2.59808 + 1.50000i 0.126323 + 0.0729325i
424424 1.50000 2.59808i 0.0728464 0.126174i
425425 0 0
426426 −24.0000 −1.16280
427427 10.3923 + 2.00000i 0.502919 + 0.0967868i
428428 12.0000i 0.580042i
429429 −15.0000 25.9808i −0.724207 1.25436i
430430 0 0
431431 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
432432 3.46410 2.00000i 0.166667 0.0962250i
433433 16.0000i 0.768911i 0.923144 + 0.384455i 0.125611π0.125611\pi
−0.923144 + 0.384455i 0.874389π0.874389\pi
434434 −8.00000 6.92820i −0.384012 0.332564i
435435 0 0
436436 2.00000 + 3.46410i 0.0957826 + 0.165900i
437437 2.59808 + 1.50000i 0.124283 + 0.0717547i
438438 6.92820 + 4.00000i 0.331042 + 0.191127i
439439 −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i 0.243367π-0.243367\pi
−0.960323 + 0.278889i 0.910034π0.910034\pi
440440 0 0
441441 5.50000 4.33013i 0.261905 0.206197i
442442 30.0000i 1.42695i
443443 20.7846 12.0000i 0.987507 0.570137i 0.0829786 0.996551i 0.473557π-0.473557\pi
0.904528 + 0.426414i 0.140223π0.140223\pi
444444 −11.0000 + 19.0526i −0.522037 + 0.904194i
445445 0 0
446446 −4.00000 6.92820i −0.189405 0.328060i
447447 36.0000i 1.70274i
448448 −1.73205 + 2.00000i −0.0818317 + 0.0944911i
449449 3.00000 0.141579 0.0707894 0.997491i 0.477448π-0.477448\pi
0.0707894 + 0.997491i 0.477448π0.477448\pi
450450 0 0
451451 −4.50000 + 7.79423i −0.211897 + 0.367016i
452452 −10.3923 6.00000i −0.488813 0.282216i
453453 24.2487 14.0000i 1.13930 0.657777i
454454 24.0000 1.12638
455455 0 0
456456 2.00000 0.0936586
457457 −19.0526 + 11.0000i −0.891241 + 0.514558i −0.874348 0.485299i 0.838711π-0.838711\pi
−0.0168929 + 0.999857i 0.505377π0.505377\pi
458458 −24.2487 14.0000i −1.13307 0.654177i
459459 12.0000 20.7846i 0.560112 0.970143i
460460 0 0
461461 6.00000 0.279448 0.139724 0.990190i 0.455378π-0.455378\pi
0.139724 + 0.990190i 0.455378π0.455378\pi
462462 −5.19615 15.0000i −0.241747 0.697863i
463463 19.0000i 0.883005i 0.897260 + 0.441502i 0.145554π0.145554\pi
−0.897260 + 0.441502i 0.854446π0.854446\pi
464464 −3.00000 5.19615i −0.139272 0.241225i
465465 0 0
466466 3.00000 5.19615i 0.138972 0.240707i
467467 −15.5885 + 9.00000i −0.721348 + 0.416470i −0.815249 0.579111i 0.803400π-0.803400\pi
0.0939008 + 0.995582i 0.470066π0.470066\pi
468468 5.00000i 0.231125i
469469 10.0000 3.46410i 0.461757 0.159957i
470470 0 0
471471 5.00000 + 8.66025i 0.230388 + 0.399043i
472472 0 0
473473 −25.9808 15.0000i −1.19460 0.689701i
474474 10.0000 + 17.3205i 0.459315 + 0.795557i
475475 0 0
476476 −3.00000 + 15.5885i −0.137505 + 0.714496i
477477 3.00000i 0.137361i
478478 −5.19615 + 3.00000i −0.237666 + 0.137217i
479479 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i 0.648611π-0.648611\pi
0.998392 0.0566937i 0.0180558π-0.0180558\pi
480480 0 0
481481 −27.5000 47.6314i −1.25389 2.17180i
482482 25.0000i 1.13872i
483483 10.3923 12.0000i 0.472866 0.546019i
484484 2.00000 0.0909091
485485 0 0
486486 −5.00000 + 8.66025i −0.226805 + 0.392837i
487487 13.8564 + 8.00000i 0.627894 + 0.362515i 0.779936 0.625859i 0.215252π-0.215252\pi
−0.152042 + 0.988374i 0.548585π0.548585\pi
488488 3.46410 2.00000i 0.156813 0.0905357i
489489 −8.00000 −0.361773
490490 0 0
491491 −12.0000 −0.541552 −0.270776 0.962642i 0.587280π-0.587280\pi
−0.270776 + 0.962642i 0.587280π0.587280\pi
492492 −5.19615 + 3.00000i −0.234261 + 0.135250i
493493 −31.1769 18.0000i −1.40414 0.810679i
494494 −2.50000 + 4.33013i −0.112480 + 0.194822i
495495 0 0
496496 −4.00000 −0.179605
497497 20.7846 24.0000i 0.932317 1.07655i
498498 24.0000i 1.07547i
499499 −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i 0.951061π-0.951061\pi
0.361478 0.932381i 0.382272π-0.382272\pi
500500 0 0
501501 9.00000 15.5885i 0.402090 0.696441i
502502 −12.9904 + 7.50000i −0.579789 + 0.334741i
503503 24.0000i 1.07011i −0.844818 0.535054i 0.820291π-0.820291\pi
0.844818 0.535054i 0.179709π-0.179709\pi
504504 0.500000 2.59808i 0.0222718 0.115728i
505505 0 0
506506 −4.50000 7.79423i −0.200049 0.346496i
507507 20.7846 + 12.0000i 0.923077 + 0.532939i
508508 −16.4545 9.50000i −0.730050 0.421494i
509509 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i 0.124214π-0.124214\pi
−0.791849 + 0.610718i 0.790881π0.790881\pi
510510 0 0
511511 −10.0000 + 3.46410i −0.442374 + 0.153243i
512512 1.00000i 0.0441942i
513513 3.46410 2.00000i 0.152944 0.0883022i
514514 −6.00000 + 10.3923i −0.264649 + 0.458385i
515515 0 0
516516 −10.0000 17.3205i −0.440225 0.762493i
517517 9.00000i 0.395820i
518518 −9.52628 27.5000i −0.418561 1.20828i
519519 6.00000 0.263371
520520 0 0
521521 −16.5000 + 28.5788i −0.722878 + 1.25206i 0.236963 + 0.971519i 0.423848π0.423848\pi
−0.959841 + 0.280543i 0.909485π0.909485\pi
522522 5.19615 + 3.00000i 0.227429 + 0.131306i
523523 −17.3205 + 10.0000i −0.757373 + 0.437269i −0.828352 0.560208i 0.810721π-0.810721\pi
0.0709788 + 0.997478i 0.477388π0.477388\pi
524524 −3.00000 −0.131056
525525 0 0
526526 0 0
527527 −20.7846 + 12.0000i −0.905392 + 0.522728i
528528 −5.19615 3.00000i −0.226134 0.130558i
529529 −7.00000 + 12.1244i −0.304348 + 0.527146i
530530 0 0
531531 0 0
532532 −1.73205 + 2.00000i −0.0750939 + 0.0867110i
533533 15.0000i 0.649722i
534534 −6.00000 10.3923i −0.259645 0.449719i
535535 0 0
536536 2.00000 3.46410i 0.0863868 0.149626i
537537 5.19615 3.00000i 0.224231 0.129460i
538538 12.0000i 0.517357i
539539 19.5000 + 7.79423i 0.839924 + 0.335721i
540540 0 0
541541 −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i 0.221681π-0.221681\pi
−0.939110 + 0.343617i 0.888348π0.888348\pi
542542 13.8564 + 8.00000i 0.595184 + 0.343629i
543543 −3.46410 2.00000i −0.148659 0.0858282i
544544 3.00000 + 5.19615i 0.128624 + 0.222783i
545545 0 0
546546 20.0000 + 17.3205i 0.855921 + 0.741249i
547547 28.0000i 1.19719i −0.801050 0.598597i 0.795725π-0.795725\pi
0.801050 0.598597i 0.204275π-0.204275\pi
548548 −10.3923 + 6.00000i −0.443937 + 0.256307i
549549 −2.00000 + 3.46410i −0.0853579 + 0.147844i
550550 0 0
551551 −3.00000 5.19615i −0.127804 0.221364i
552552 6.00000i 0.255377i
553553 −25.9808 5.00000i −1.10481 0.212622i
554554 −2.00000 −0.0849719
555555 0 0
556556 2.00000 3.46410i 0.0848189 0.146911i
557557 23.3827 + 13.5000i 0.990756 + 0.572013i 0.905500 0.424346i 0.139496π-0.139496\pi
0.0852559 + 0.996359i 0.472829π0.472829\pi
558558 3.46410 2.00000i 0.146647 0.0846668i
559559 50.0000 2.11477
560560 0 0
561561 −36.0000 −1.51992
562562 −2.59808 + 1.50000i −0.109593 + 0.0632737i
563563 −15.5885 9.00000i −0.656975 0.379305i 0.134148 0.990961i 0.457170π-0.457170\pi
−0.791123 + 0.611656i 0.790503π0.790503\pi
564564 −3.00000 + 5.19615i −0.126323 + 0.218797i
565565 0 0
566566 26.0000 1.09286
567567 −9.52628 27.5000i −0.400066 1.15489i
568568 12.0000i 0.503509i
569569 −1.50000 2.59808i −0.0628833 0.108917i 0.832870 0.553469i 0.186696π-0.186696\pi
−0.895753 + 0.444552i 0.853363π0.853363\pi
570570 0 0
571571 −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i 0.970773π-0.970773\pi
0.577301 + 0.816532i 0.304106π0.304106\pi
572572 12.9904 7.50000i 0.543155 0.313591i
573573 24.0000i 1.00261i
574574 1.50000 7.79423i 0.0626088 0.325325i
575575 0 0
576576 −0.500000 0.866025i −0.0208333 0.0360844i
577577 −17.3205 10.0000i −0.721062 0.416305i 0.0940813 0.995565i 0.470009π-0.470009\pi
−0.815144 + 0.579259i 0.803342π0.803342\pi
578578 16.4545 + 9.50000i 0.684416 + 0.395148i
579579 4.00000 + 6.92820i 0.166234 + 0.287926i
580580 0 0
581581 24.0000 + 20.7846i 0.995688 + 0.862291i
582582 28.0000i 1.16064i
583583 −7.79423 + 4.50000i −0.322804 + 0.186371i
584584 −2.00000 + 3.46410i −0.0827606 + 0.143346i
585585 0 0
586586 13.5000 + 23.3827i 0.557680 + 0.965930i
587587 12.0000i 0.495293i 0.968850 + 0.247647i 0.0796572π0.0796572\pi
−0.968850 + 0.247647i 0.920343π0.920343\pi
588588 8.66025 + 11.0000i 0.357143 + 0.453632i
589589 −4.00000 −0.164817
590590 0 0
591591 −3.00000 + 5.19615i −0.123404 + 0.213741i
592592 −9.52628 5.50000i −0.391528 0.226049i
593593 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i 0.401884π-0.401884\pi
0.976900 + 0.213697i 0.0685507π0.0685507\pi
594594 −12.0000 −0.492366
595595 0 0
596596 18.0000 0.737309
597597 6.92820 4.00000i 0.283552 0.163709i
598598 12.9904 + 7.50000i 0.531216 + 0.306698i
599599 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i 0.505017π-0.505017\pi
0.873799 0.486287i 0.161649π-0.161649\pi
600600 0 0
601601 2.00000 0.0815817 0.0407909 0.999168i 0.487012π-0.487012\pi
0.0407909 + 0.999168i 0.487012π0.487012\pi
602602 25.9808 + 5.00000i 1.05890 + 0.203785i
603603 4.00000i 0.162893i
604604 7.00000 + 12.1244i 0.284826 + 0.493333i
605605 0 0
606606 −12.0000 + 20.7846i −0.487467 + 0.844317i
607607 −16.4545 + 9.50000i −0.667867 + 0.385593i −0.795268 0.606258i 0.792670π-0.792670\pi
0.127401 + 0.991851i 0.459336π0.459336\pi
608608 1.00000i 0.0405554i
609609 −30.0000 + 10.3923i −1.21566 + 0.421117i
610610 0 0
611611 −7.50000 12.9904i −0.303418 0.525535i
612612 −5.19615 3.00000i −0.210042 0.121268i
613613 40.7032 + 23.5000i 1.64399 + 0.949156i 0.979396 + 0.201948i 0.0647272π0.0647272\pi
0.664590 + 0.747208i 0.268606π0.268606\pi
614614 1.00000 + 1.73205i 0.0403567 + 0.0698999i
615615 0 0
616616 7.50000 2.59808i 0.302184 0.104679i
617617 6.00000i 0.241551i −0.992680 0.120775i 0.961462π-0.961462\pi
0.992680 0.120775i 0.0385381π-0.0385381\pi
618618 −6.92820 + 4.00000i −0.278693 + 0.160904i
619619 −0.500000 + 0.866025i −0.0200967 + 0.0348085i −0.875899 0.482495i 0.839731π-0.839731\pi
0.855802 + 0.517303i 0.173064π0.173064\pi
620620 0 0
621621 −6.00000 10.3923i −0.240772 0.417029i
622622 12.0000i 0.481156i
623623 15.5885 + 3.00000i 0.624538 + 0.120192i
624624 10.0000 0.400320
625625 0 0
626626 −4.00000 + 6.92820i −0.159872 + 0.276907i
627627 −5.19615 3.00000i −0.207514 0.119808i
628628 −4.33013 + 2.50000i −0.172791 + 0.0997609i
629629 −66.0000 −2.63159
630630 0 0
631631 32.0000 1.27390 0.636950 0.770905i 0.280196π-0.280196\pi
0.636950 + 0.770905i 0.280196π0.280196\pi
632632 −8.66025 + 5.00000i −0.344486 + 0.198889i
633633 1.73205 + 1.00000i 0.0688428 + 0.0397464i
634634 9.00000 15.5885i 0.357436 0.619097i
635635 0 0
636636 −6.00000 −0.237915
637637 −34.6410 + 5.00000i −1.37253 + 0.198107i
638638 18.0000i 0.712627i
639639 6.00000 + 10.3923i 0.237356 + 0.411113i
640640 0 0
641641 22.5000 38.9711i 0.888697 1.53927i 0.0472793 0.998882i 0.484945π-0.484945\pi
0.841417 0.540386i 0.181722π-0.181722\pi
642642 20.7846 12.0000i 0.820303 0.473602i
643643 38.0000i 1.49857i −0.662246 0.749287i 0.730396π-0.730396\pi
0.662246 0.749287i 0.269604π-0.269604\pi
644644 6.00000 + 5.19615i 0.236433 + 0.204757i
645645 0 0
646646 3.00000 + 5.19615i 0.118033 + 0.204440i
647647 18.1865 + 10.5000i 0.714986 + 0.412798i 0.812905 0.582397i 0.197885π-0.197885\pi
−0.0979182 + 0.995194i 0.531218π0.531218\pi
648648 −9.52628 5.50000i −0.374228 0.216060i
649649 0 0
650650 0 0
651651 −4.00000 + 20.7846i −0.156772 + 0.814613i
652652 4.00000i 0.156652i
653653 −18.1865 + 10.5000i −0.711694 + 0.410897i −0.811688 0.584091i 0.801451π-0.801451\pi
0.0999939 + 0.994988i 0.468118π0.468118\pi
654654 4.00000 6.92820i 0.156412 0.270914i
655655 0 0
656656 −1.50000 2.59808i −0.0585652 0.101438i
657657 4.00000i 0.156055i
658658 −2.59808 7.50000i −0.101284 0.292380i
659659 −24.0000 −0.934907 −0.467454 0.884018i 0.654829π-0.654829\pi
−0.467454 + 0.884018i 0.654829π0.654829\pi
660660 0 0
661661 −22.0000 + 38.1051i −0.855701 + 1.48212i 0.0202925 + 0.999794i 0.493540π0.493540\pi
−0.875993 + 0.482323i 0.839793π0.839793\pi
662662 6.06218 + 3.50000i 0.235613 + 0.136031i
663663 51.9615 30.0000i 2.01802 1.16510i
664664 12.0000 0.465690
665665 0 0
666666 11.0000 0.426241
667667 −15.5885 + 9.00000i −0.603587 + 0.348481i
668668 7.79423 + 4.50000i 0.301568 + 0.174110i
669669 −8.00000 + 13.8564i −0.309298 + 0.535720i
670670 0 0
671671 −12.0000 −0.463255
672672 5.19615 + 1.00000i 0.200446 + 0.0385758i
673673 34.0000i 1.31060i 0.755367 + 0.655302i 0.227459π0.227459\pi
−0.755367 + 0.655302i 0.772541π0.772541\pi
674674 7.00000 + 12.1244i 0.269630 + 0.467013i
675675 0 0
676676 −6.00000 + 10.3923i −0.230769 + 0.399704i
677677 −2.59808 + 1.50000i −0.0998522 + 0.0576497i −0.549095 0.835760i 0.685027π-0.685027\pi
0.449242 + 0.893410i 0.351694π0.351694\pi
678678 24.0000i 0.921714i
679679 28.0000 + 24.2487i 1.07454 + 0.930580i
680680 0 0
681681 −24.0000 41.5692i −0.919682 1.59294i
682682 10.3923 + 6.00000i 0.397942 + 0.229752i
683683 −10.3923 6.00000i −0.397650 0.229584i 0.287819 0.957685i 0.407070π-0.407070\pi
−0.685470 + 0.728101i 0.740403π0.740403\pi
684684 −0.500000 0.866025i −0.0191180 0.0331133i
685685 0 0
686686 −18.5000 0.866025i −0.706333 0.0330650i
687687 56.0000i 2.13653i
688688 8.66025 5.00000i 0.330169 0.190623i
689689 7.50000 12.9904i 0.285727 0.494894i
690690 0 0
691691 −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i 0.958371π-0.958371\pi
0.382791 0.923835i 0.374963π-0.374963\pi
692692 3.00000i 0.114043i
693693 −5.19615 + 6.00000i −0.197386 + 0.227921i
694694 −24.0000 −0.911028
695695 0 0
696696 −6.00000 + 10.3923i −0.227429 + 0.393919i
697697 −15.5885 9.00000i −0.590455 0.340899i
698698 8.66025 5.00000i 0.327795 0.189253i
699699 −12.0000 −0.453882
700700 0 0
701701 18.0000 0.679851 0.339925 0.940452i 0.389598π-0.389598\pi
0.339925 + 0.940452i 0.389598π0.389598\pi
702702 17.3205 10.0000i 0.653720 0.377426i
703703 −9.52628 5.50000i −0.359290 0.207436i
704704 1.50000 2.59808i 0.0565334 0.0979187i
705705 0 0
706706 12.0000 0.451626
707707 −10.3923 30.0000i −0.390843 1.12827i
708708 0 0
709709 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i 0.0819909π-0.0819909\pi
−0.704118 + 0.710083i 0.748658π0.748658\pi
710710 0 0
711711 5.00000 8.66025i 0.187515 0.324785i
712712 5.19615 3.00000i 0.194734 0.112430i
713713 12.0000i 0.449404i
714714 30.0000 10.3923i 1.12272 0.388922i
715715 0 0
716716 1.50000 + 2.59808i 0.0560576 + 0.0970947i
717717 10.3923 + 6.00000i 0.388108 + 0.224074i
718718 5.19615 + 3.00000i 0.193919 + 0.111959i
719719 −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i 0.932409π-0.932409\pi
0.306253 0.951950i 0.400925π-0.400925\pi
720720 0 0
721721 2.00000 10.3923i 0.0744839 0.387030i
722722 18.0000i 0.669891i
723723 −43.3013 + 25.0000i −1.61039 + 0.929760i
724724 1.00000 1.73205i 0.0371647 0.0643712i
725725 0 0
726726 −2.00000 3.46410i −0.0742270 0.128565i
727727 29.0000i 1.07555i 0.843088 + 0.537775i 0.180735π0.180735\pi
−0.843088 + 0.537775i 0.819265π0.819265\pi
728728 −8.66025 + 10.0000i −0.320970 + 0.370625i
729729 −13.0000 −0.481481
730730 0 0
731731 30.0000 51.9615i 1.10959 1.92187i
732732 −6.92820 4.00000i −0.256074 0.147844i
733733 −40.7032 + 23.5000i −1.50341 + 0.867992i −0.503415 + 0.864045i 0.667923π0.667923\pi
−0.999992 + 0.00394730i 0.998744π0.998744\pi
734734 1.00000 0.0369107
735735 0 0
736736 3.00000 0.110581
737737 −10.3923 + 6.00000i −0.382805 + 0.221013i
738738 2.59808 + 1.50000i 0.0956365 + 0.0552158i
739739 −18.5000 + 32.0429i −0.680534 + 1.17872i 0.294285 + 0.955718i 0.404919π0.404919\pi
−0.974818 + 0.223001i 0.928415π0.928415\pi
740740 0 0
741741 10.0000 0.367359
742742 5.19615 6.00000i 0.190757 0.220267i
743743 9.00000i 0.330178i −0.986279 0.165089i 0.947209π-0.947209\pi
0.986279 0.165089i 0.0527911π-0.0527911\pi
744744 4.00000 + 6.92820i 0.146647 + 0.254000i
745745 0 0
746746 17.0000 29.4449i 0.622414 1.07805i
747747 −10.3923 + 6.00000i −0.380235 + 0.219529i
748748 18.0000i 0.658145i
749749 −6.00000 + 31.1769i −0.219235 + 1.13918i
750750 0 0
751751 −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i 0.323993π-0.323993\pi
−0.999570 + 0.0293387i 0.990660π0.990660\pi
752752 −2.59808 1.50000i −0.0947421 0.0546994i
753753 25.9808 + 15.0000i 0.946792 + 0.546630i
754754 −15.0000 25.9808i −0.546268 0.946164i
755755 0 0
756756 10.0000 3.46410i 0.363696 0.125988i
757757 26.0000i 0.944986i 0.881334 + 0.472493i 0.156646π0.156646\pi
−0.881334 + 0.472493i 0.843354π0.843354\pi
758758 21.6506 12.5000i 0.786386 0.454020i
759759 −9.00000 + 15.5885i −0.326679 + 0.565825i
760760 0 0
761761 25.5000 + 44.1673i 0.924374 + 1.60106i 0.792564 + 0.609788i 0.208745π0.208745\pi
0.131810 + 0.991275i 0.457921π0.457921\pi
762762 38.0000i 1.37659i
763763 3.46410 + 10.0000i 0.125409 + 0.362024i
764764 −12.0000 −0.434145
765765 0 0
766766 −7.50000 + 12.9904i −0.270986 + 0.469362i
767767 0 0
768768 1.73205 1.00000i 0.0625000 0.0360844i
769769 49.0000 1.76699 0.883493 0.468445i 0.155186π-0.155186\pi
0.883493 + 0.468445i 0.155186π0.155186\pi
770770 0 0
771771 24.0000 0.864339
772772 −3.46410 + 2.00000i −0.124676 + 0.0719816i
773773 33.7750 + 19.5000i 1.21480 + 0.701366i 0.963802 0.266621i 0.0859071π-0.0859071\pi
0.251000 + 0.967987i 0.419240π0.419240\pi
774774 −5.00000 + 8.66025i −0.179721 + 0.311286i
775775 0 0
776776 14.0000 0.502571
777777 −38.1051 + 44.0000i −1.36701 + 1.57849i
778778 24.0000i 0.860442i
779779 −1.50000 2.59808i −0.0537431 0.0930857i
780780 0 0
781781 −18.0000 + 31.1769i −0.644091 + 1.11560i
782782 15.5885 9.00000i 0.557442 0.321839i
783783 24.0000i 0.857690i
784784 −5.50000 + 4.33013i −0.196429 + 0.154647i
785785 0 0
786786 3.00000 + 5.19615i 0.107006 + 0.185341i
787787 29.4449 + 17.0000i 1.04960 + 0.605985i 0.922536 0.385911i 0.126113π-0.126113\pi
0.127060 + 0.991895i 0.459446π0.459446\pi
788788 −2.59808 1.50000i −0.0925526 0.0534353i
789789 0 0
790790 0 0
791791 −24.0000 20.7846i −0.853342 0.739016i
792792 3.00000i 0.106600i
793793 17.3205 10.0000i 0.615069 0.355110i
794794 1.00000 1.73205i 0.0354887 0.0614682i
795795 0 0
796796 2.00000 + 3.46410i 0.0708881 + 0.122782i
797797 30.0000i 1.06265i −0.847167 0.531327i 0.821693π-0.821693\pi
0.847167 0.531327i 0.178307π-0.178307\pi
798798 5.19615 + 1.00000i 0.183942 + 0.0353996i
799799 −18.0000 −0.636794
800800 0 0
801801 −3.00000 + 5.19615i −0.106000 + 0.183597i
802802 −18.1865 10.5000i −0.642189 0.370768i
803803 10.3923 6.00000i 0.366736 0.211735i
804804 −8.00000 −0.282138
805805 0 0
806806 −20.0000 −0.704470
807807 20.7846 12.0000i 0.731653 0.422420i
808808 −10.3923 6.00000i −0.365600 0.211079i
809809 19.5000 33.7750i 0.685583 1.18747i −0.287670 0.957730i 0.592880π-0.592880\pi
0.973253 0.229736i 0.0737862π-0.0737862\pi
810810 0 0
811811 47.0000 1.65039 0.825197 0.564846i 0.191064π-0.191064\pi
0.825197 + 0.564846i 0.191064π0.191064\pi
812812 −5.19615 15.0000i −0.182349 0.526397i
813813 32.0000i 1.12229i
814814 16.5000 + 28.5788i 0.578325 + 1.00169i
815815 0 0
816816 6.00000 10.3923i 0.210042 0.363803i
817817 8.66025 5.00000i 0.302984 0.174928i
818818 22.0000i 0.769212i
819819 2.50000 12.9904i 0.0873571 0.453921i
820820 0 0
821821 9.00000 + 15.5885i 0.314102 + 0.544041i 0.979246 0.202674i 0.0649632π-0.0649632\pi
−0.665144 + 0.746715i 0.731630π0.731630\pi
822822 20.7846 + 12.0000i 0.724947 + 0.418548i
823823 38.1051 + 22.0000i 1.32826 + 0.766872i 0.985031 0.172379i 0.0551455π-0.0551455\pi
0.343230 + 0.939251i 0.388479π0.388479\pi
824824 −2.00000 3.46410i −0.0696733 0.120678i
825825 0 0
826826 0 0
827827 54.0000i 1.87776i −0.344239 0.938882i 0.611863π-0.611863\pi
0.344239 0.938882i 0.388137π-0.388137\pi
828828 −2.59808 + 1.50000i −0.0902894 + 0.0521286i
829829 7.00000 12.1244i 0.243120 0.421096i −0.718481 0.695546i 0.755162π-0.755162\pi
0.961601 + 0.274450i 0.0884958π0.0884958\pi
830830 0 0
831831 2.00000 + 3.46410i 0.0693792 + 0.120168i
832832 5.00000i 0.173344i
833833 −15.5885 + 39.0000i −0.540108 + 1.35127i
834834 −8.00000 −0.277017
835835 0 0
836836 1.50000 2.59808i 0.0518786 0.0898563i
837837 13.8564 + 8.00000i 0.478947 + 0.276520i
838838 −12.9904 + 7.50000i −0.448745 + 0.259083i
839839 6.00000 0.207143 0.103572 0.994622i 0.466973π-0.466973\pi
0.103572 + 0.994622i 0.466973π0.466973\pi
840840 0 0
841841 7.00000 0.241379
842842 −29.4449 + 17.0000i −1.01474 + 0.585859i
843843 5.19615 + 3.00000i 0.178965 + 0.103325i
844844 −0.500000 + 0.866025i −0.0172107 + 0.0298098i
845845 0 0
846846 3.00000 0.103142
847847 5.19615 + 1.00000i 0.178542 + 0.0343604i
848848 3.00000i 0.103020i
849849 −26.0000 45.0333i −0.892318 1.54554i
850850 0 0
851851 −16.5000 + 28.5788i −0.565613 + 0.979670i
852852 −20.7846 + 12.0000i −0.712069 + 0.411113i
853853 1.00000i 0.0342393i 0.999853 + 0.0171197i 0.00544963π0.00544963\pi
−0.999853 + 0.0171197i 0.994550π0.994550\pi
854854 10.0000 3.46410i 0.342193 0.118539i
855855 0 0
856856 6.00000 + 10.3923i 0.205076 + 0.355202i
857857 15.5885 + 9.00000i 0.532492 + 0.307434i 0.742030 0.670366i 0.233863π-0.233863\pi
−0.209539 + 0.977800i 0.567196π0.567196\pi
858858 −25.9808 15.0000i −0.886969 0.512092i
859859 16.0000 + 27.7128i 0.545913 + 0.945549i 0.998549 + 0.0538535i 0.0171504π0.0171504\pi
−0.452636 + 0.891695i 0.649516π0.649516\pi
860860 0 0
861861 −15.0000 + 5.19615i −0.511199 + 0.177084i
862862 0 0
863863 −33.7750 + 19.5000i −1.14971 + 0.663788i −0.948818 0.315825i 0.897719π-0.897719\pi
−0.200897 + 0.979612i 0.564385π0.564385\pi
864864 2.00000 3.46410i 0.0680414 0.117851i
865865 0 0
866866 8.00000 + 13.8564i 0.271851 + 0.470860i
867867 38.0000i 1.29055i
868868 −10.3923 2.00000i −0.352738 0.0678844i
869869 30.0000 1.01768
870870 0 0
871871 10.0000 17.3205i 0.338837 0.586883i
872872 3.46410 + 2.00000i 0.117309 + 0.0677285i
873873 −12.1244 + 7.00000i −0.410347 + 0.236914i
874874 3.00000 0.101477
875875 0 0
876876 8.00000 0.270295
877877 −6.06218 + 3.50000i −0.204705 + 0.118187i −0.598848 0.800862i 0.704375π-0.704375\pi
0.394143 + 0.919049i 0.371041π0.371041\pi
878878 −8.66025 5.00000i −0.292269 0.168742i
879879 27.0000 46.7654i 0.910687 1.57736i
880880 0 0
881881 33.0000 1.11180 0.555899 0.831250i 0.312374π-0.312374\pi
0.555899 + 0.831250i 0.312374π0.312374\pi
882882 2.59808 6.50000i 0.0874818 0.218866i
883883 8.00000i 0.269221i −0.990899 0.134611i 0.957022π-0.957022\pi
0.990899 0.134611i 0.0429784π-0.0429784\pi
884884 15.0000 + 25.9808i 0.504505 + 0.873828i
885885 0 0
886886 12.0000 20.7846i 0.403148 0.698273i
887887 20.7846 12.0000i 0.697879 0.402921i −0.108678 0.994077i 0.534662π-0.534662\pi
0.806557 + 0.591156i 0.201328π0.201328\pi
888888 22.0000i 0.738272i
889889 −38.0000 32.9090i −1.27448 1.10373i
890890 0 0
891891 16.5000 + 28.5788i 0.552771 + 0.957427i
892892 −6.92820 4.00000i −0.231973 0.133930i
893893 −2.59808 1.50000i −0.0869413 0.0501956i
894894 −18.0000 31.1769i −0.602010 1.04271i
895895 0 0
896896 −0.500000 + 2.59808i −0.0167038 + 0.0867956i
897897 30.0000i 1.00167i
898898 2.59808 1.50000i 0.0866989 0.0500556i
899899 12.0000 20.7846i 0.400222 0.693206i
900900 0 0
901901 −9.00000 15.5885i −0.299833 0.519327i
902902 9.00000i 0.299667i
903903 −17.3205 50.0000i −0.576390 1.66390i
904904 −12.0000 −0.399114
905905 0 0
906906 14.0000 24.2487i 0.465119 0.805609i
907907 8.66025 + 5.00000i 0.287559 + 0.166022i 0.636841 0.770996i 0.280241π-0.280241\pi
−0.349281 + 0.937018i 0.613574π0.613574\pi
908908 20.7846 12.0000i 0.689761 0.398234i
909909 12.0000 0.398015
910910 0 0
911911 −30.0000 −0.993944 −0.496972 0.867766i 0.665555π-0.665555\pi
−0.496972 + 0.867766i 0.665555π0.665555\pi
912912 1.73205 1.00000i 0.0573539 0.0331133i
913913 −31.1769 18.0000i −1.03181 0.595713i
914914 −11.0000 + 19.0526i −0.363848 + 0.630203i
915915 0 0
916916 −28.0000 −0.925146
917917 −7.79423 1.50000i −0.257388 0.0495344i
918918 24.0000i 0.792118i
919919 19.0000 + 32.9090i 0.626752 + 1.08557i 0.988199 + 0.153174i 0.0489495π0.0489495\pi
−0.361447 + 0.932393i 0.617717π0.617717\pi
920920 0 0
921921 2.00000 3.46410i 0.0659022 0.114146i
922922 5.19615 3.00000i 0.171126 0.0987997i
923923 60.0000i 1.97492i
924924 −12.0000 10.3923i −0.394771 0.341882i
925925 0 0
926926 9.50000 + 16.4545i 0.312189 + 0.540728i
927927 3.46410 + 2.00000i 0.113776 + 0.0656886i
928928 −5.19615 3.00000i −0.170572 0.0984798i
929929 16.5000 + 28.5788i 0.541347 + 0.937641i 0.998827 + 0.0484211i 0.0154190π0.0154190\pi
−0.457480 + 0.889220i 0.651248π0.651248\pi
930930 0 0
931931 −5.50000 + 4.33013i −0.180255 + 0.141914i
932932 6.00000i 0.196537i
933933 20.7846 12.0000i 0.680458 0.392862i
934934 −9.00000 + 15.5885i −0.294489 + 0.510070i
935935 0 0
936936 −2.50000 4.33013i −0.0817151 0.141535i
937937 2.00000i 0.0653372i 0.999466 + 0.0326686i 0.0104006π0.0104006\pi
−0.999466 + 0.0326686i 0.989599π0.989599\pi
938938 6.92820 8.00000i 0.226214 0.261209i
939939 16.0000 0.522140
940940 0 0
941941 −12.0000 + 20.7846i −0.391189 + 0.677559i −0.992607 0.121376i 0.961269π-0.961269\pi
0.601418 + 0.798935i 0.294603π0.294603\pi
942942 8.66025 + 5.00000i 0.282166 + 0.162909i
943943 −7.79423 + 4.50000i −0.253815 + 0.146540i
944944 0 0
945945 0 0
946946 −30.0000 −0.975384
947947 25.9808 15.0000i 0.844261 0.487435i −0.0144491 0.999896i 0.504599π-0.504599\pi
0.858710 + 0.512461i 0.171266π0.171266\pi
948948 17.3205 + 10.0000i 0.562544 + 0.324785i
949949 −10.0000 + 17.3205i −0.324614 + 0.562247i
950950 0 0
951951 −36.0000 −1.16738
952952 5.19615 + 15.0000i 0.168408 + 0.486153i
953953 12.0000i 0.388718i 0.980930 + 0.194359i 0.0622627π0.0622627\pi
−0.980930 + 0.194359i 0.937737π0.937737\pi
954954 1.50000 + 2.59808i 0.0485643 + 0.0841158i
955955 0 0
956956 −3.00000 + 5.19615i −0.0970269 + 0.168056i
957957 31.1769 18.0000i 1.00781 0.581857i
958958 24.0000i 0.775405i
959959 −30.0000 + 10.3923i −0.968751 + 0.335585i
960960 0 0
961961 7.50000 + 12.9904i 0.241935 + 0.419045i
962962 −47.6314 27.5000i −1.53570 0.886636i
963963 −10.3923 6.00000i −0.334887 0.193347i
964964 −12.5000 21.6506i −0.402598 0.697320i
965965 0 0
966966 3.00000 15.5885i 0.0965234 0.501550i
967967 32.0000i 1.02905i 0.857475 + 0.514525i 0.172032π0.172032\pi
−0.857475 + 0.514525i 0.827968π0.827968\pi
968968 1.73205 1.00000i 0.0556702 0.0321412i
969969 6.00000 10.3923i 0.192748 0.333849i
970970 0 0
971971 −13.5000 23.3827i −0.433236 0.750386i 0.563914 0.825833i 0.309295π-0.309295\pi
−0.997150 + 0.0754473i 0.975962π0.975962\pi
972972 10.0000i 0.320750i
973973 6.92820 8.00000i 0.222108 0.256468i
974974 16.0000 0.512673
975975 0 0
976976 2.00000 3.46410i 0.0640184 0.110883i
977977 25.9808 + 15.0000i 0.831198 + 0.479893i 0.854263 0.519841i 0.174009π-0.174009\pi
−0.0230645 + 0.999734i 0.507342π0.507342\pi
978978 −6.92820 + 4.00000i −0.221540 + 0.127906i
979979 −18.0000 −0.575282
980980 0 0
981981 −4.00000 −0.127710
982982 −10.3923 + 6.00000i −0.331632 + 0.191468i
983983 49.3634 + 28.5000i 1.57445 + 0.909009i 0.995613 + 0.0935651i 0.0298263π0.0298263\pi
0.578836 + 0.815444i 0.303507π0.303507\pi
984984 −3.00000 + 5.19615i −0.0956365 + 0.165647i
985985 0 0
986986 −36.0000 −1.14647
987987 −10.3923 + 12.0000i −0.330791 + 0.381964i
988988 5.00000i 0.159071i
989989 −15.0000 25.9808i −0.476972 0.826140i
990990 0 0
991991 −10.0000 + 17.3205i −0.317660 + 0.550204i −0.979999 0.199000i 0.936231π-0.936231\pi
0.662339 + 0.749204i 0.269564π0.269564\pi
992992 −3.46410 + 2.00000i −0.109985 + 0.0635001i
993993 14.0000i 0.444277i
994994 6.00000 31.1769i 0.190308 0.988872i
995995 0 0
996996 −12.0000 20.7846i −0.380235 0.658586i
997997 −12.1244 7.00000i −0.383982 0.221692i 0.295567 0.955322i 0.404491π-0.404491\pi
−0.679549 + 0.733630i 0.737825π0.737825\pi
998998 −24.2487 14.0000i −0.767580 0.443162i
999999 22.0000 + 38.1051i 0.696049 + 1.20559i
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 350.2.j.a.249.2 4
5.2 odd 4 350.2.e.h.151.1 2
5.3 odd 4 70.2.e.b.11.1 2
5.4 even 2 inner 350.2.j.a.249.1 4
7.2 even 3 inner 350.2.j.a.149.1 4
7.3 odd 6 2450.2.c.p.99.2 2
7.4 even 3 2450.2.c.f.99.2 2
15.8 even 4 630.2.k.e.361.1 2
20.3 even 4 560.2.q.d.81.1 2
35.2 odd 12 350.2.e.h.51.1 2
35.3 even 12 490.2.a.j.1.1 1
35.4 even 6 2450.2.c.f.99.1 2
35.9 even 6 inner 350.2.j.a.149.2 4
35.13 even 4 490.2.e.a.361.1 2
35.17 even 12 2450.2.a.f.1.1 1
35.18 odd 12 490.2.a.g.1.1 1
35.23 odd 12 70.2.e.b.51.1 yes 2
35.24 odd 6 2450.2.c.p.99.1 2
35.32 odd 12 2450.2.a.p.1.1 1
35.33 even 12 490.2.e.a.471.1 2
105.23 even 12 630.2.k.e.541.1 2
105.38 odd 12 4410.2.a.c.1.1 1
105.53 even 12 4410.2.a.m.1.1 1
140.3 odd 12 3920.2.a.g.1.1 1
140.23 even 12 560.2.q.d.401.1 2
140.123 even 12 3920.2.a.be.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.e.b.11.1 2 5.3 odd 4
70.2.e.b.51.1 yes 2 35.23 odd 12
350.2.e.h.51.1 2 35.2 odd 12
350.2.e.h.151.1 2 5.2 odd 4
350.2.j.a.149.1 4 7.2 even 3 inner
350.2.j.a.149.2 4 35.9 even 6 inner
350.2.j.a.249.1 4 5.4 even 2 inner
350.2.j.a.249.2 4 1.1 even 1 trivial
490.2.a.g.1.1 1 35.18 odd 12
490.2.a.j.1.1 1 35.3 even 12
490.2.e.a.361.1 2 35.13 even 4
490.2.e.a.471.1 2 35.33 even 12
560.2.q.d.81.1 2 20.3 even 4
560.2.q.d.401.1 2 140.23 even 12
630.2.k.e.361.1 2 15.8 even 4
630.2.k.e.541.1 2 105.23 even 12
2450.2.a.f.1.1 1 35.17 even 12
2450.2.a.p.1.1 1 35.32 odd 12
2450.2.c.f.99.1 2 35.4 even 6
2450.2.c.f.99.2 2 7.4 even 3
2450.2.c.p.99.1 2 35.24 odd 6
2450.2.c.p.99.2 2 7.3 odd 6
3920.2.a.g.1.1 1 140.3 odd 12
3920.2.a.be.1.1 1 140.123 even 12
4410.2.a.c.1.1 1 105.38 odd 12
4410.2.a.m.1.1 1 105.53 even 12