Properties

Label 684.2.r.a.487.5
Level 684684
Weight 22
Character 684.487
Analytic conductor 5.4625.462
Analytic rank 00
Dimension 1616
Inner twists 44

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [684,2,Mod(487,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.487"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 684=223219 684 = 2^{2} \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 684.r (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.461767498265.46176749826
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x163x15+6x149x13+12x129x11+3x10+6x910x8++256 x^{16} - 3 x^{15} + 6 x^{14} - 9 x^{13} + 12 x^{12} - 9 x^{11} + 3 x^{10} + 6 x^{9} - 10 x^{8} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a19]\Z[a_1, \ldots, a_{19}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 487.5
Root 0.5704431.29406i0.570443 - 1.29406i of defining polynomial
Character χ\chi == 684.487
Dual form 684.2.r.a.559.5

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.570443+1.29406i)q2+(1.34919+1.47638i)q4+(1.60333+2.77705i)q5+1.25044iq7+(2.680160.903746i)q8+(2.67906+3.65895i)q10+2.11093iq11+(2.12978+1.22963i)q13+(1.61815+0.713305i)q14+(0.3593743.98382i)q16+(0.7650261.32506i)q17+(3.763072.19984i)q19+(6.263161.37965i)q20+(2.73167+1.20416i)q22+(7.619514.39913i)q23+(2.64132+4.57491i)q25+(0.376297+3.45750i)q26+(1.846121.68708i)q28+(5.20937+3.00763i)q297.78947q31+(4.950312.73760i)q32+(1.278311.74586i)q34+(3.47253+2.00487i)q35+9.97599iq37+(4.99335+3.61476i)q38+(1.787438.89192i)q40+(1.09450+0.631908i)q41+(5.046192.91342i)q43+(3.116532.84804i)q44+(1.3462412.3696i)q46+(6.12910+3.53864i)q47+5.43640q49+(7.426930.808311i)q50+(4.68887+1.48535i)q52+(6.189883.57373i)q53+(5.86215+3.38451i)q55+(1.130083.35138i)q56+(0.920411+8.45692i)q58+(2.835414.91107i)q59+(2.809984.86704i)q61+(4.4434510.0801i)q62+(6.36649+4.84436i)q64+7.88599iq65+(0.02358350.0408478i)q67+(2.98846+0.658296i)q68+(4.575303.35000i)q70+(3.125955.41430i)q71+(0.658098+1.13986i)q73+(12.9095+5.69073i)q74+(1.82930+8.52371i)q762.63959q77+(3.77194+6.53320i)q79+(10.48717.38538i)q80+(1.442081.05588i)q82+7.84164iq83+(2.453174.24902i)q85+(6.64871+4.86814i)q86+(1.907745.65762i)q88+(6.02458+3.47830i)q89+(1.53758+2.66316i)q91+(16.77495.31401i)q92+(1.08291+9.95003i)q94+(12.1425+6.92315i)q95+(8.519354.91865i)q97+(3.10116+7.03503i)q98+O(q100)q+(0.570443 + 1.29406i) q^{2} +(-1.34919 + 1.47638i) q^{4} +(1.60333 + 2.77705i) q^{5} +1.25044i q^{7} +(-2.68016 - 0.903746i) q^{8} +(-2.67906 + 3.65895i) q^{10} +2.11093i q^{11} +(2.12978 + 1.22963i) q^{13} +(-1.61815 + 0.713305i) q^{14} +(-0.359374 - 3.98382i) q^{16} +(-0.765026 - 1.32506i) q^{17} +(3.76307 - 2.19984i) q^{19} +(-6.26316 - 1.37965i) q^{20} +(-2.73167 + 1.20416i) q^{22} +(-7.61951 - 4.39913i) q^{23} +(-2.64132 + 4.57491i) q^{25} +(-0.376297 + 3.45750i) q^{26} +(-1.84612 - 1.68708i) q^{28} +(5.20937 + 3.00763i) q^{29} -7.78947 q^{31} +(4.95031 - 2.73760i) q^{32} +(1.27831 - 1.74586i) q^{34} +(-3.47253 + 2.00487i) q^{35} +9.97599i q^{37} +(4.99335 + 3.61476i) q^{38} +(-1.78743 - 8.89192i) q^{40} +(-1.09450 + 0.631908i) q^{41} +(5.04619 - 2.91342i) q^{43} +(-3.11653 - 2.84804i) q^{44} +(1.34624 - 12.3696i) q^{46} +(6.12910 + 3.53864i) q^{47} +5.43640 q^{49} +(-7.42693 - 0.808311i) q^{50} +(-4.68887 + 1.48535i) q^{52} +(-6.18988 - 3.57373i) q^{53} +(-5.86215 + 3.38451i) q^{55} +(1.13008 - 3.35138i) q^{56} +(-0.920411 + 8.45692i) q^{58} +(-2.83541 - 4.91107i) q^{59} +(2.80998 - 4.86704i) q^{61} +(-4.44345 - 10.0801i) q^{62} +(6.36649 + 4.84436i) q^{64} +7.88599i q^{65} +(0.0235835 - 0.0408478i) q^{67} +(2.98846 + 0.658296i) q^{68} +(-4.57530 - 3.35000i) q^{70} +(-3.12595 - 5.41430i) q^{71} +(0.658098 + 1.13986i) q^{73} +(-12.9095 + 5.69073i) q^{74} +(-1.82930 + 8.52371i) q^{76} -2.63959 q^{77} +(3.77194 + 6.53320i) q^{79} +(10.4871 - 7.38538i) q^{80} +(-1.44208 - 1.05588i) q^{82} +7.84164i q^{83} +(2.45317 - 4.24902i) q^{85} +(6.64871 + 4.86814i) q^{86} +(1.90774 - 5.65762i) q^{88} +(6.02458 + 3.47830i) q^{89} +(-1.53758 + 2.66316i) q^{91} +(16.7749 - 5.31401i) q^{92} +(-1.08291 + 9.95003i) q^{94} +(12.1425 + 6.92315i) q^{95} +(8.51935 - 4.91865i) q^{97} +(3.10116 + 7.03503i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+3q23q4+2q56q1018q13+6q143q162q174q20+3q222q25+24q264q28+6q2927q32+36q34+24q38+48q40+51q98+O(q100) 16 q + 3 q^{2} - 3 q^{4} + 2 q^{5} - 6 q^{10} - 18 q^{13} + 6 q^{14} - 3 q^{16} - 2 q^{17} - 4 q^{20} + 3 q^{22} - 2 q^{25} + 24 q^{26} - 4 q^{28} + 6 q^{29} - 27 q^{32} + 36 q^{34} + 24 q^{38} + 48 q^{40}+ \cdots - 51 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/684Z)×\left(\mathbb{Z}/684\mathbb{Z}\right)^\times.

nn 325325 343343 533533
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1 11

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 0.570443 + 1.29406i 0.403364 + 0.915040i
33 0 0
44 −1.34919 + 1.47638i −0.674595 + 0.738188i
55 1.60333 + 2.77705i 0.717030 + 1.24193i 0.962171 + 0.272445i 0.0878324π0.0878324\pi
−0.245141 + 0.969487i 0.578834π0.578834\pi
66 0 0
77 1.25044i 0.472622i 0.971677 + 0.236311i 0.0759384π0.0759384\pi
−0.971677 + 0.236311i 0.924062π0.924062\pi
88 −2.68016 0.903746i −0.947579 0.319522i
99 0 0
1010 −2.67906 + 3.65895i −0.847193 + 1.15706i
1111 2.11093i 0.636469i 0.948012 + 0.318234i 0.103090π0.103090\pi
−0.948012 + 0.318234i 0.896910π0.896910\pi
1212 0 0
1313 2.12978 + 1.22963i 0.590695 + 0.341038i 0.765372 0.643588i 0.222555π-0.222555\pi
−0.174678 + 0.984626i 0.555888π0.555888\pi
1414 −1.61815 + 0.713305i −0.432468 + 0.190639i
1515 0 0
1616 −0.359374 3.98382i −0.0898436 0.995956i
1717 −0.765026 1.32506i −0.185546 0.321375i 0.758214 0.652005i 0.226072π-0.226072\pi
−0.943760 + 0.330630i 0.892739π0.892739\pi
1818 0 0
1919 3.76307 2.19984i 0.863308 0.504678i
2020 −6.26316 1.37965i −1.40048 0.308498i
2121 0 0
2222 −2.73167 + 1.20416i −0.582394 + 0.256729i
2323 −7.61951 4.39913i −1.58878 0.917282i −0.993509 0.113756i 0.963712π-0.963712\pi
−0.595270 0.803526i 0.702955π-0.702955\pi
2424 0 0
2525 −2.64132 + 4.57491i −0.528265 + 0.914981i
2626 −0.376297 + 3.45750i −0.0737980 + 0.678071i
2727 0 0
2828 −1.84612 1.68708i −0.348884 0.318828i
2929 5.20937 + 3.00763i 0.967356 + 0.558503i 0.898429 0.439119i 0.144709π-0.144709\pi
0.0689265 + 0.997622i 0.478043π0.478043\pi
3030 0 0
3131 −7.78947 −1.39903 −0.699515 0.714618i 0.746601π-0.746601\pi
−0.699515 + 0.714618i 0.746601π0.746601\pi
3232 4.95031 2.73760i 0.875099 0.483943i
3333 0 0
3434 1.27831 1.74586i 0.219228 0.299413i
3535 −3.47253 + 2.00487i −0.586965 + 0.338884i
3636 0 0
3737 9.97599i 1.64004i 0.572334 + 0.820021i 0.306038π0.306038\pi
−0.572334 + 0.820021i 0.693962π0.693962\pi
3838 4.99335 + 3.61476i 0.810028 + 0.586391i
3939 0 0
4040 −1.78743 8.89192i −0.282617 1.40594i
4141 −1.09450 + 0.631908i −0.170932 + 0.0986875i −0.583025 0.812454i 0.698131π-0.698131\pi
0.412093 + 0.911142i 0.364798π0.364798\pi
4242 0 0
4343 5.04619 2.91342i 0.769537 0.444292i −0.0631725 0.998003i 0.520122π-0.520122\pi
0.832709 + 0.553710i 0.186789π0.186789\pi
4444 −3.11653 2.84804i −0.469834 0.429359i
4545 0 0
4646 1.34624 12.3696i 0.198493 1.82379i
4747 6.12910 + 3.53864i 0.894022 + 0.516164i 0.875256 0.483660i 0.160693π-0.160693\pi
0.0187658 + 0.999824i 0.494026π0.494026\pi
4848 0 0
4949 5.43640 0.776629
5050 −7.42693 0.808311i −1.05033 0.114312i
5151 0 0
5252 −4.68887 + 1.48535i −0.650230 + 0.205982i
5353 −6.18988 3.57373i −0.850246 0.490890i 0.0104881 0.999945i 0.496661π-0.496661\pi
−0.860734 + 0.509055i 0.829995π0.829995\pi
5454 0 0
5555 −5.86215 + 3.38451i −0.790452 + 0.456367i
5656 1.13008 3.35138i 0.151013 0.447846i
5757 0 0
5858 −0.920411 + 8.45692i −0.120856 + 1.11045i
5959 −2.83541 4.91107i −0.369138 0.639367i 0.620293 0.784371i 0.287014π-0.287014\pi
−0.989431 + 0.145004i 0.953681π0.953681\pi
6060 0 0
6161 2.80998 4.86704i 0.359782 0.623160i −0.628142 0.778098i 0.716185π-0.716185\pi
0.987924 + 0.154938i 0.0495178π0.0495178\pi
6262 −4.44345 10.0801i −0.564319 1.28017i
6363 0 0
6464 6.36649 + 4.84436i 0.795811 + 0.605545i
6565 7.88599i 0.978137i
6666 0 0
6767 0.0235835 0.0408478i 0.00288118 0.00499036i −0.864581 0.502493i 0.832416π-0.832416\pi
0.867462 + 0.497503i 0.165750π0.165750\pi
6868 2.98846 + 0.658296i 0.362404 + 0.0798301i
6969 0 0
7070 −4.57530 3.35000i −0.546853 0.400402i
7171 −3.12595 5.41430i −0.370982 0.642559i 0.618735 0.785600i 0.287645π-0.287645\pi
−0.989717 + 0.143041i 0.954312π0.954312\pi
7272 0 0
7373 0.658098 + 1.13986i 0.0770245 + 0.133410i 0.901965 0.431809i 0.142125π-0.142125\pi
−0.824940 + 0.565220i 0.808791π0.808791\pi
7474 −12.9095 + 5.69073i −1.50070 + 0.661534i
7575 0 0
7676 −1.82930 + 8.52371i −0.209835 + 0.977737i
7777 −2.63959 −0.300809
7878 0 0
7979 3.77194 + 6.53320i 0.424377 + 0.735042i 0.996362 0.0852216i 0.0271598π-0.0271598\pi
−0.571985 + 0.820264i 0.693826π0.693826\pi
8080 10.4871 7.38538i 1.17249 0.825710i
8181 0 0
8282 −1.44208 1.05588i −0.159251 0.116602i
8383 7.84164i 0.860732i 0.902655 + 0.430366i 0.141615π0.141615\pi
−0.902655 + 0.430366i 0.858385π0.858385\pi
8484 0 0
8585 2.45317 4.24902i 0.266084 0.460871i
8686 6.64871 + 4.86814i 0.716949 + 0.524945i
8787 0 0
8888 1.90774 5.65762i 0.203366 0.603104i
8989 6.02458 + 3.47830i 0.638605 + 0.368699i 0.784077 0.620664i 0.213137π-0.213137\pi
−0.145472 + 0.989362i 0.546470π0.546470\pi
9090 0 0
9191 −1.53758 + 2.66316i −0.161182 + 0.279175i
9292 16.7749 5.31401i 1.74891 0.554024i
9393 0 0
9494 −1.08291 + 9.95003i −0.111694 + 1.02627i
9595 12.1425 + 6.92315i 1.24579 + 0.710300i
9696 0 0
9797 8.51935 4.91865i 0.865009 0.499413i −0.000677265 1.00000i 0.500216π-0.500216\pi
0.865687 + 0.500586i 0.166882π0.166882\pi
9898 3.10116 + 7.03503i 0.313264 + 0.710646i
9999 0 0
100100 −3.19064 10.0720i −0.319064 1.00720i
101101 3.13338 5.42717i 0.311783 0.540024i −0.666965 0.745089i 0.732407π-0.732407\pi
0.978748 + 0.205065i 0.0657405π0.0657405\pi
102102 0 0
103103 −0.526662 −0.0518936 −0.0259468 0.999663i 0.508260π-0.508260\pi
−0.0259468 + 0.999663i 0.508260π0.508260\pi
104104 −4.59687 5.22038i −0.450760 0.511900i
105105 0 0
106106 1.09365 10.0487i 0.106225 0.976016i
107107 6.91564 0.668560 0.334280 0.942474i 0.391507π-0.391507\pi
0.334280 + 0.942474i 0.391507π0.391507\pi
108108 0 0
109109 −10.4902 + 6.05651i −1.00478 + 0.580109i −0.909658 0.415357i 0.863657π-0.863657\pi
−0.0951195 + 0.995466i 0.530323π0.530323\pi
110110 −7.72379 5.65531i −0.736434 0.539212i
111111 0 0
112112 4.98153 0.449376i 0.470711 0.0424621i
113113 4.95424i 0.466056i 0.972470 + 0.233028i 0.0748633π0.0748633\pi
−0.972470 + 0.233028i 0.925137π0.925137\pi
114114 0 0
115115 28.2130i 2.63087i
116116 −11.4688 + 3.63313i −1.06485 + 0.337327i
117117 0 0
118118 4.73779 6.47067i 0.436149 0.595674i
119119 1.65691 0.956619i 0.151889 0.0876931i
120120 0 0
121121 6.54398 0.594907
122122 7.90118 + 0.859926i 0.715339 + 0.0778541i
123123 0 0
124124 10.5095 11.5002i 0.943779 1.03275i
125125 −0.906349 −0.0810663
126126 0 0
127127 −2.86262 + 4.95820i −0.254016 + 0.439969i −0.964628 0.263616i 0.915085π-0.915085\pi
0.710612 + 0.703584i 0.248418π0.248418\pi
128128 −2.63718 + 11.0021i −0.233096 + 0.972454i
129129 0 0
130130 −10.2050 + 4.49851i −0.895034 + 0.394545i
131131 16.1689 9.33512i 1.41268 0.815613i 0.417043 0.908887i 0.363067π-0.363067\pi
0.995640 + 0.0932738i 0.0297332π0.0297332\pi
132132 0 0
133133 2.75077 + 4.70549i 0.238522 + 0.408018i
134134 0.0663126 + 0.00721715i 0.00572854 + 0.000623466i
135135 0 0
136136 0.852869 + 4.24277i 0.0731329 + 0.363814i
137137 9.96622 17.2620i 0.851471 1.47479i −0.0284092 0.999596i 0.509044π-0.509044\pi
0.879880 0.475195i 0.157623π-0.157623\pi
138138 0 0
139139 9.04013 + 5.21932i 0.766774 + 0.442697i 0.831723 0.555191i 0.187355π-0.187355\pi
−0.0649485 + 0.997889i 0.520688π0.520688\pi
140140 1.72516 7.83170i 0.145803 0.661900i
141141 0 0
142142 5.22326 7.13372i 0.438326 0.598648i
143143 −2.59566 + 4.49581i −0.217060 + 0.375959i
144144 0 0
145145 19.2889i 1.60185i
146146 −1.09964 + 1.50184i −0.0910068 + 0.124293i
147147 0 0
148148 −14.7283 13.4595i −1.21066 1.10636i
149149 4.83307 + 8.37113i 0.395941 + 0.685789i 0.993221 0.116243i 0.0370853π-0.0370853\pi
−0.597280 + 0.802033i 0.703752π0.703752\pi
150150 0 0
151151 11.1033 0.903573 0.451787 0.892126i 0.350787π-0.350787\pi
0.451787 + 0.892126i 0.350787π0.350787\pi
152152 −12.0737 + 2.49506i −0.979308 + 0.202376i
153153 0 0
154154 −1.50574 3.41579i −0.121336 0.275252i
155155 −12.4891 21.6317i −1.00315 1.73750i
156156 0 0
157157 −5.65983 9.80311i −0.451704 0.782374i 0.546788 0.837271i 0.315850π-0.315850\pi
−0.998492 + 0.0548972i 0.982517π0.982517\pi
158158 −6.30268 + 8.60795i −0.501414 + 0.684811i
159159 0 0
160160 15.5394 + 9.35797i 1.22850 + 0.739813i
161161 5.50085 9.52774i 0.433527 0.750891i
162162 0 0
163163 15.6778i 1.22798i 0.789312 + 0.613992i 0.210437π0.210437\pi
−0.789312 + 0.613992i 0.789563π0.789563\pi
164164 0.543750 2.46845i 0.0424597 0.192754i
165165 0 0
166166 −10.1476 + 4.47321i −0.787603 + 0.347188i
167167 −1.80453 + 3.12555i −0.139639 + 0.241862i −0.927360 0.374170i 0.877928π-0.877928\pi
0.787721 + 0.616032i 0.211261π0.211261\pi
168168 0 0
169169 −3.47603 6.02065i −0.267387 0.463127i
170170 6.89789 + 0.750733i 0.529044 + 0.0575786i
171171 0 0
172172 −2.50696 + 11.3808i −0.191154 + 0.867780i
173173 4.46906 2.58021i 0.339776 0.196170i −0.320397 0.947283i 0.603816π-0.603816\pi
0.660173 + 0.751113i 0.270483π0.270483\pi
174174 0 0
175175 −5.72065 3.30282i −0.432440 0.249669i
176176 8.40957 0.758614i 0.633895 0.0571827i
177177 0 0
178178 −1.06445 + 9.78035i −0.0797836 + 0.733068i
179179 2.76216 0.206454 0.103227 0.994658i 0.467083π-0.467083\pi
0.103227 + 0.994658i 0.467083π0.467083\pi
180180 0 0
181181 2.07870 + 1.20014i 0.154509 + 0.0892056i 0.575261 0.817970i 0.304901π-0.304901\pi
−0.420752 + 0.907176i 0.638234π0.638234\pi
182182 −4.32339 0.470537i −0.320471 0.0348785i
183183 0 0
184184 16.4458 + 18.6765i 1.21240 + 1.37685i
185185 −27.7038 + 15.9948i −2.03682 + 1.17596i
186186 0 0
187187 2.79711 1.61491i 0.204545 0.118094i
188188 −13.4937 + 4.27457i −0.984128 + 0.311755i
189189 0 0
190190 −2.03238 + 19.6624i −0.147444 + 1.42646i
191191 4.38525i 0.317305i 0.987334 + 0.158653i 0.0507150π0.0507150\pi
−0.987334 + 0.158653i 0.949285π0.949285\pi
192192 0 0
193193 −7.76503 + 4.48314i −0.558939 + 0.322703i −0.752719 0.658341i 0.771258π-0.771258\pi
0.193781 + 0.981045i 0.437925π0.437925\pi
194194 11.2248 + 8.21876i 0.805897 + 0.590072i
195195 0 0
196196 −7.33473 + 8.02617i −0.523910 + 0.573298i
197197 −1.39218 −0.0991890 −0.0495945 0.998769i 0.515793π-0.515793\pi
−0.0495945 + 0.998769i 0.515793π0.515793\pi
198198 0 0
199199 0.241956 + 0.139694i 0.0171518 + 0.00990261i 0.508551 0.861032i 0.330181π-0.330181\pi
−0.491400 + 0.870934i 0.663515π0.663515\pi
200200 11.2137 9.87438i 0.792929 0.698224i
201201 0 0
202202 8.81051 + 0.958893i 0.619905 + 0.0674675i
203203 −3.76086 + 6.51400i −0.263961 + 0.457193i
204204 0 0
205205 −3.50968 2.02631i −0.245126 0.141524i
206206 −0.300431 0.681533i −0.0209320 0.0474847i
207207 0 0
208208 4.13324 8.92656i 0.286588 0.618946i
209209 4.64371 + 7.94357i 0.321212 + 0.549468i
210210 0 0
211211 −0.0832510 0.144195i −0.00573123 0.00992679i 0.863146 0.504955i 0.168491π-0.168491\pi
−0.868877 + 0.495028i 0.835158π0.835158\pi
212212 13.6275 4.31696i 0.935940 0.296490i
213213 0 0
214214 3.94498 + 8.94926i 0.269673 + 0.611759i
215215 16.1814 + 9.34234i 1.10356 + 0.637142i
216216 0 0
217217 9.74027i 0.661212i
218218 −13.8216 10.1201i −0.936114 0.685417i
219219 0 0
220220 2.91233 13.2211i 0.196350 0.891365i
221221 3.76279i 0.253113i
222222 0 0
223223 −5.86577 10.1598i −0.392801 0.680352i 0.600017 0.799987i 0.295161π-0.295161\pi
−0.992818 + 0.119636i 0.961827π0.961827\pi
224224 3.42320 + 6.19007i 0.228722 + 0.413591i
225225 0 0
226226 −6.41109 + 2.82611i −0.426459 + 0.187990i
227227 8.78264 0.582924 0.291462 0.956582i 0.405858π-0.405858\pi
0.291462 + 0.956582i 0.405858π0.405858\pi
228228 0 0
229229 −6.53352 −0.431747 −0.215874 0.976421i 0.569260π-0.569260\pi
−0.215874 + 0.976421i 0.569260π0.569260\pi
230230 36.5093 16.0939i 2.40735 1.06120i
231231 0 0
232232 −11.2438 12.7689i −0.738191 0.838317i
233233 −13.1315 22.7444i −0.860274 1.49004i −0.871664 0.490103i 0.836959π-0.836959\pi
0.0113904 0.999935i 0.496374π-0.496374\pi
234234 0 0
235235 22.6944i 1.48042i
236236 11.0761 + 2.43984i 0.720992 + 0.158820i
237237 0 0
238238 2.18310 + 1.59845i 0.141509 + 0.103612i
239239 23.5704i 1.52464i 0.647198 + 0.762322i 0.275941π0.275941\pi
−0.647198 + 0.762322i 0.724059π0.724059\pi
240240 0 0
241241 −13.5642 7.83128i −0.873746 0.504457i −0.00515448 0.999987i 0.501641π-0.501641\pi
−0.868591 + 0.495529i 0.834974π0.834974\pi
242242 3.73297 + 8.46831i 0.239964 + 0.544364i
243243 0 0
244244 3.39438 + 10.7152i 0.217303 + 0.685967i
245245 8.71633 + 15.0971i 0.556866 + 0.964520i
246246 0 0
247247 10.7195 0.0579979i 0.682065 0.00369032i
248248 20.8770 + 7.03970i 1.32569 + 0.447022i
249249 0 0
250250 −0.517020 1.17287i −0.0326992 0.0741789i
251251 −22.1575 12.7926i −1.39857 0.807463i −0.404324 0.914616i 0.632493π-0.632493\pi
−0.994243 + 0.107153i 0.965827π0.965827\pi
252252 0 0
253253 9.28625 16.0842i 0.583821 1.01121i
254254 −8.04917 0.876033i −0.505050 0.0549672i
255255 0 0
256256 −15.7417 + 2.86337i −0.983856 + 0.178961i
257257 −17.4440 10.0713i −1.08813 0.628229i −0.155049 0.987907i 0.549553π-0.549553\pi
−0.933077 + 0.359677i 0.882887π0.882887\pi
258258 0 0
259259 −12.4744 −0.775120
260260 −11.6427 10.6397i −0.722049 0.659846i
261261 0 0
262262 21.3037 + 15.5984i 1.31614 + 0.963672i
263263 −3.14828 + 1.81766i −0.194131 + 0.112082i −0.593915 0.804528i 0.702419π-0.702419\pi
0.399784 + 0.916609i 0.369085π0.369085\pi
264264 0 0
265265 22.9194i 1.40793i
266266 −4.52004 + 6.24388i −0.277141 + 0.382837i
267267 0 0
268268 0.0284881 + 0.0899296i 0.00174019 + 0.00549332i
269269 −15.9194 + 9.19106i −0.970622 + 0.560389i −0.899426 0.437073i 0.856015π-0.856015\pi
−0.0711964 + 0.997462i 0.522682π0.522682\pi
270270 0 0
271271 16.7304 9.65930i 1.01630 0.586761i 0.103269 0.994653i 0.467070π-0.467070\pi
0.913030 + 0.407893i 0.133736π0.133736\pi
272272 −5.00389 + 3.52392i −0.303405 + 0.213669i
273273 0 0
274274 28.0232 + 3.04991i 1.69295 + 0.184252i
275275 −9.65730 5.57564i −0.582357 0.336224i
276276 0 0
277277 −16.5581 −0.994879 −0.497440 0.867499i 0.665726π-0.665726\pi
−0.497440 + 0.867499i 0.665726π0.665726\pi
278278 −1.59724 + 14.6758i −0.0957964 + 0.880197i
279279 0 0
280280 11.1188 2.23507i 0.664476 0.133571i
281281 −3.45491 1.99469i −0.206103 0.118993i 0.393396 0.919369i 0.371300π-0.371300\pi
−0.599499 + 0.800376i 0.704633π0.704633\pi
282282 0 0
283283 −12.8457 + 7.41645i −0.763596 + 0.440862i −0.830585 0.556892i 0.811994π-0.811994\pi
0.0669896 + 0.997754i 0.478661π0.478661\pi
284284 12.2110 + 2.68984i 0.724592 + 0.159613i
285285 0 0
286286 −7.29853 0.794337i −0.431571 0.0469701i
287287 −0.790163 1.36860i −0.0466419 0.0807861i
288288 0 0
289289 7.32947 12.6950i 0.431145 0.746766i
290290 −24.9610 + 11.0032i −1.46576 + 0.646130i
291291 0 0
292292 −2.57076 0.566285i −0.150442 0.0331394i
293293 22.9900i 1.34309i −0.740963 0.671546i 0.765631π-0.765631\pi
0.740963 0.671546i 0.234369π-0.234369\pi
294294 0 0
295295 9.09217 15.7481i 0.529367 0.916890i
296296 9.01575 26.7372i 0.524030 1.55407i
297297 0 0
298298 −8.07576 + 11.0295i −0.467816 + 0.638924i
299299 −10.8186 18.7383i −0.625655 1.08367i
300300 0 0
301301 3.64306 + 6.30996i 0.209982 + 0.363700i
302302 6.33380 + 14.3683i 0.364469 + 0.826805i
303303 0 0
304304 −10.1161 14.2008i −0.580200 0.814474i
305305 18.0213 1.03190
306306 0 0
307307 −10.3144 17.8650i −0.588673 1.01961i −0.994407 0.105620i 0.966317π-0.966317\pi
0.405734 0.913991i 0.367016π-0.367016\pi
308308 3.56131 3.89703i 0.202924 0.222054i
309309 0 0
310310 20.8685 28.5013i 1.18525 1.61876i
311311 3.16368i 0.179396i 0.995969 + 0.0896978i 0.0285901π0.0285901\pi
−0.995969 + 0.0896978i 0.971410π0.971410\pi
312312 0 0
313313 −7.67203 + 13.2883i −0.433649 + 0.751101i −0.997184 0.0749904i 0.976107π-0.976107\pi
0.563536 + 0.826092i 0.309441π0.309441\pi
314314 9.45722 12.9163i 0.533702 0.728908i
315315 0 0
316316 −14.7345 3.24572i −0.828882 0.182586i
317317 2.28007 + 1.31640i 0.128061 + 0.0739362i 0.562662 0.826687i 0.309777π-0.309777\pi
−0.434601 + 0.900623i 0.643111π0.643111\pi
318318 0 0
319319 −6.34889 + 10.9966i −0.355470 + 0.615692i
320320 −3.24545 + 25.4471i −0.181426 + 1.42254i
321321 0 0
322322 15.4674 + 1.68340i 0.861965 + 0.0938121i
323323 −5.79377 3.30337i −0.322374 0.183804i
324324 0 0
325325 −11.2509 + 6.49569i −0.624086 + 0.360316i
326326 −20.2881 + 8.94332i −1.12365 + 0.495324i
327327 0 0
328328 3.50451 0.704466i 0.193504 0.0388977i
329329 −4.42486 + 7.66408i −0.243950 + 0.422534i
330330 0 0
331331 −9.30930 −0.511685 −0.255843 0.966718i 0.582353π-0.582353\pi
−0.255843 + 0.966718i 0.582353π0.582353\pi
332332 −11.5772 10.5799i −0.635382 0.580645i
333333 0 0
334334 −5.07403 0.552233i −0.277639 0.0302168i
335335 0.151248 0.00826358
336336 0 0
337337 −3.28961 + 1.89926i −0.179196 + 0.103459i −0.586915 0.809648i 0.699658π-0.699658\pi
0.407719 + 0.913108i 0.366324π0.366324\pi
338338 5.80822 7.93263i 0.315926 0.431478i
339339 0 0
340340 2.96336 + 9.35455i 0.160711 + 0.507321i
341341 16.4430i 0.890439i
342342 0 0
343343 15.5510i 0.839674i
344344 −16.1576 + 3.24795i −0.871158 + 0.175118i
345345 0 0
346346 5.88830 + 4.31137i 0.316557 + 0.231781i
347347 −3.07657 + 1.77626i −0.165159 + 0.0953546i −0.580301 0.814402i 0.697065π-0.697065\pi
0.415142 + 0.909757i 0.363732π0.363732\pi
348348 0 0
349349 −1.91850 −0.102695 −0.0513475 0.998681i 0.516352π-0.516352\pi
−0.0513475 + 0.998681i 0.516352π0.516352\pi
350350 1.01074 9.28693i 0.0540266 0.496407i
351351 0 0
352352 5.77887 + 10.4498i 0.308015 + 0.556974i
353353 7.11843 0.378876 0.189438 0.981893i 0.439333π-0.439333\pi
0.189438 + 0.981893i 0.439333π0.439333\pi
354354 0 0
355355 10.0238 17.3618i 0.532010 0.921469i
356356 −13.2636 + 4.20167i −0.702968 + 0.222688i
357357 0 0
358358 1.57566 + 3.57441i 0.0832760 + 0.188913i
359359 −7.25210 + 4.18700i −0.382751 + 0.220982i −0.679015 0.734125i 0.737593π-0.737593\pi
0.296263 + 0.955106i 0.404259π0.404259\pi
360360 0 0
361361 9.32139 16.5563i 0.490600 0.871385i
362362 −0.367273 + 3.37458i −0.0193034 + 0.177364i
363363 0 0
364364 −1.85735 5.86315i −0.0973514 0.307313i
365365 −2.11029 + 3.65513i −0.110458 + 0.191318i
366366 0 0
367367 19.7381 + 11.3958i 1.03032 + 0.594857i 0.917077 0.398710i 0.130542π-0.130542\pi
0.113246 + 0.993567i 0.463875π0.463875\pi
368368 −14.7871 + 31.9357i −0.770830 + 1.66477i
369369 0 0
370370 −36.5016 26.7263i −1.89763 1.38943i
371371 4.46874 7.74008i 0.232005 0.401845i
372372 0 0
373373 23.5670i 1.22025i −0.792305 0.610125i 0.791119π-0.791119\pi
0.792305 0.610125i 0.208881π-0.208881\pi
374374 3.68539 + 2.69842i 0.190567 + 0.139532i
375375 0 0
376376 −13.2289 15.0233i −0.682230 0.774766i
377377 7.39654 + 12.8112i 0.380941 + 0.659809i
378378 0 0
379379 −38.1884 −1.96161 −0.980804 0.194995i 0.937531π-0.937531\pi
−0.980804 + 0.194995i 0.937531π0.937531\pi
380380 −26.6037 + 8.58625i −1.36474 + 0.440465i
381381 0 0
382382 −5.67478 + 2.50153i −0.290347 + 0.127990i
383383 10.8906 + 18.8631i 0.556483 + 0.963857i 0.997786 + 0.0664990i 0.0211829π0.0211829\pi
−0.441303 + 0.897358i 0.645484π0.645484\pi
384384 0 0
385385 −4.23213 7.33026i −0.215689 0.373585i
386386 −10.2310 7.49104i −0.520742 0.381284i
387387 0 0
388388 −4.23244 + 19.2140i −0.214870 + 0.975441i
389389 13.4725 23.3351i 0.683084 1.18314i −0.290950 0.956738i 0.593971π-0.593971\pi
0.974035 0.226399i 0.0726952π-0.0726952\pi
390390 0 0
391391 13.4618i 0.680792i
392392 −14.5704 4.91312i −0.735917 0.248150i
393393 0 0
394394 −0.794162 1.80157i −0.0400093 0.0907619i
395395 −12.0953 + 20.9497i −0.608582 + 1.05410i
396396 0 0
397397 2.35770 + 4.08365i 0.118329 + 0.204953i 0.919106 0.394011i 0.128913π-0.128913\pi
−0.800776 + 0.598964i 0.795579π0.795579\pi
398398 −0.0427497 + 0.392794i −0.00214285 + 0.0196890i
399399 0 0
400400 19.1748 + 8.87846i 0.958742 + 0.443923i
401401 −4.16941 + 2.40721i −0.208210 + 0.120210i −0.600479 0.799640i 0.705024π-0.705024\pi
0.392269 + 0.919850i 0.371690π0.371690\pi
402402 0 0
403403 −16.5899 9.57816i −0.826400 0.477122i
404404 3.78503 + 11.9483i 0.188312 + 0.594452i
405405 0 0
406406 −10.5749 1.15092i −0.524822 0.0571191i
407407 −21.0586 −1.04384
408408 0 0
409409 12.2147 + 7.05216i 0.603978 + 0.348707i 0.770605 0.637313i 0.219954π-0.219954\pi
−0.166627 + 0.986020i 0.553288π0.553288\pi
410410 0.620103 5.69763i 0.0306247 0.281386i
411411 0 0
412412 0.710568 0.777552i 0.0350071 0.0383072i
413413 6.14100 3.54551i 0.302179 0.174463i
414414 0 0
415415 −21.7766 + 12.5727i −1.06897 + 0.617171i
416416 13.9093 + 0.256566i 0.681959 + 0.0125792i
417417 0 0
418418 −7.63050 + 10.5406i −0.373220 + 0.515558i
419419 31.5299i 1.54034i −0.637840 0.770169i 0.720172π-0.720172\pi
0.637840 0.770169i 0.279828π-0.279828\pi
420420 0 0
421421 23.2374 13.4161i 1.13252 0.653862i 0.187954 0.982178i 0.439814π-0.439814\pi
0.944568 + 0.328316i 0.106481π0.106481\pi
422422 0.139107 0.189987i 0.00677163 0.00924841i
423423 0 0
424424 13.3601 + 15.1722i 0.648825 + 0.736829i
425425 8.08272 0.392069
426426 0 0
427427 6.08594 + 3.51372i 0.294519 + 0.170041i
428428 −9.33051 + 10.2101i −0.451007 + 0.493523i
429429 0 0
430430 −2.85899 + 26.2690i −0.137873 + 1.26680i
431431 3.89128 6.73989i 0.187436 0.324649i −0.756958 0.653463i 0.773316π-0.773316\pi
0.944395 + 0.328814i 0.106649π0.106649\pi
432432 0 0
433433 −13.2846 7.66988i −0.638418 0.368591i 0.145587 0.989345i 0.453493π-0.453493\pi
−0.784005 + 0.620755i 0.786826π0.786826\pi
434434 12.6045 5.55627i 0.605036 0.266709i
435435 0 0
436436 5.21156 23.6589i 0.249589 1.13305i
437437 −38.3501 + 0.207494i −1.83454 + 0.00992577i
438438 0 0
439439 −12.6149 21.8497i −0.602077 1.04283i −0.992506 0.122195i 0.961007π-0.961007\pi
0.390429 0.920633i 0.372327π-0.372327\pi
440440 18.7702 3.77313i 0.894835 0.179877i
441441 0 0
442442 4.86928 2.14646i 0.231608 0.102097i
443443 2.05095 + 1.18412i 0.0974435 + 0.0562590i 0.547930 0.836524i 0.315416π-0.315416\pi
−0.450486 + 0.892783i 0.648749π0.648749\pi
444444 0 0
445445 22.3074i 1.05747i
446446 9.80134 13.3863i 0.464107 0.633858i
447447 0 0
448448 −6.05758 + 7.96091i −0.286194 + 0.376118i
449449 11.6774i 0.551093i 0.961288 + 0.275546i 0.0888587π0.0888587\pi
−0.961288 + 0.275546i 0.911141π0.911141\pi
450450 0 0
451451 −1.33391 2.31041i −0.0628115 0.108793i
452452 −7.31432 6.68421i −0.344037 0.314399i
453453 0 0
454454 5.00999 + 11.3653i 0.235131 + 0.533399i
455455 −9.86096 −0.462289
456456 0 0
457457 −8.71735 −0.407781 −0.203890 0.978994i 0.565359π-0.565359\pi
−0.203890 + 0.978994i 0.565359π0.565359\pi
458458 −3.72700 8.45477i −0.174151 0.395066i
459459 0 0
460460 41.6530 + 38.0647i 1.94208 + 1.77477i
461461 10.5590 + 18.2887i 0.491781 + 0.851789i 0.999955 0.00946495i 0.00301283π-0.00301283\pi
−0.508174 + 0.861254i 0.669679π0.669679\pi
462462 0 0
463463 0.355651i 0.0165285i 0.999966 + 0.00826426i 0.00263062π0.00263062\pi
−0.999966 + 0.00826426i 0.997369π0.997369\pi
464464 10.1098 21.8341i 0.469334 1.01362i
465465 0 0
466466 21.9419 29.9674i 1.01644 1.38821i
467467 4.47951i 0.207287i −0.994615 0.103643i 0.966950π-0.966950\pi
0.994615 0.103643i 0.0330501π-0.0330501\pi
468468 0 0
469469 0.0510778 + 0.0294898i 0.00235855 + 0.00136171i
470470 −29.3679 + 12.9459i −1.35464 + 0.597148i
471471 0 0
472472 3.16098 + 15.7249i 0.145496 + 0.723798i
473473 6.15002 + 10.6521i 0.282778 + 0.489786i
474474 0 0
475475 0.124583 + 23.0262i 0.00571627 + 1.05651i
476476 −0.823159 + 3.73689i −0.0377295 + 0.171280i
477477 0 0
478478 −30.5016 + 13.4456i −1.39511 + 0.614987i
479479 21.4965 + 12.4110i 0.982199 + 0.567073i 0.902933 0.429781i 0.141409π-0.141409\pi
0.0792655 + 0.996854i 0.474743π0.474743\pi
480480 0 0
481481 −12.2668 + 21.2466i −0.559316 + 0.968764i
482482 2.39657 22.0202i 0.109161 1.00299i
483483 0 0
484484 −8.82907 + 9.66138i −0.401321 + 0.439154i
485485 27.3186 + 15.7724i 1.24048 + 0.716189i
486486 0 0
487487 36.2102 1.64084 0.820420 0.571761i 0.193739π-0.193739\pi
0.820420 + 0.571761i 0.193739π0.193739\pi
488488 −11.9298 + 10.5049i −0.540035 + 0.475535i
489489 0 0
490490 −14.5644 + 19.8915i −0.657955 + 0.898607i
491491 5.16077 2.97957i 0.232902 0.134466i −0.379008 0.925393i 0.623735π-0.623735\pi
0.611910 + 0.790927i 0.290401π0.290401\pi
492492 0 0
493493 9.20366i 0.414512i
494494 6.18992 + 13.8386i 0.278497 + 0.622628i
495495 0 0
496496 2.79934 + 31.0319i 0.125694 + 1.39337i
497497 6.77026 3.90881i 0.303688 0.175334i
498498 0 0
499499 20.1581 11.6383i 0.902402 0.521002i 0.0244234 0.999702i 0.492225π-0.492225\pi
0.877979 + 0.478700i 0.158892π0.158892\pi
500500 1.22284 1.33811i 0.0546869 0.0598422i
501501 0 0
502502 3.91486 35.9706i 0.174729 1.60545i
503503 16.4493 + 9.49702i 0.733439 + 0.423451i 0.819679 0.572823i 0.194152π-0.194152\pi
−0.0862401 + 0.996274i 0.527485π0.527485\pi
504504 0 0
505505 20.0953 0.894231
506506 26.1113 + 2.84183i 1.16079 + 0.126335i
507507 0 0
508508 −3.45795 10.9158i −0.153422 0.484312i
509509 −11.3577 6.55740i −0.503423 0.290652i 0.226703 0.973964i 0.427205π-0.427205\pi
−0.730126 + 0.683312i 0.760539π0.760539\pi
510510 0 0
511511 −1.42532 + 0.822911i −0.0630526 + 0.0364035i
512512 −12.6851 18.7373i −0.560608 0.828081i
513513 0 0
514514 3.08207 28.3187i 0.135944 1.24908i
515515 −0.844413 1.46257i −0.0372093 0.0644483i
516516 0 0
517517 −7.46982 + 12.9381i −0.328522 + 0.569017i
518518 −7.11592 16.1426i −0.312655 0.709265i
519519 0 0
520520 7.12693 21.1357i 0.312537 0.926862i
521521 24.9294i 1.09218i 0.837727 + 0.546089i 0.183884π0.183884\pi
−0.837727 + 0.546089i 0.816116π0.816116\pi
522522 0 0
523523 −15.1705 + 26.2761i −0.663359 + 1.14897i 0.316368 + 0.948636i 0.397536π0.397536\pi
−0.979727 + 0.200335i 0.935797π0.935797\pi
524524 −8.03276 + 36.4662i −0.350913 + 1.59303i
525525 0 0
526526 −4.14808 3.03720i −0.180865 0.132428i
527527 5.95915 + 10.3215i 0.259584 + 0.449613i
528528 0 0
529529 27.2047 + 47.1198i 1.18281 + 2.04869i
530530 29.6592 13.0742i 1.28831 0.567909i
531531 0 0
532532 −10.6584 2.28743i −0.462100 0.0991727i
533533 −3.10805 −0.134625
534534 0 0
535535 11.0880 + 19.2051i 0.479378 + 0.830307i
536536 −0.100124 + 0.0881651i −0.00432468 + 0.00380815i
537537 0 0
538538 −20.9749 15.3577i −0.904292 0.662117i
539539 11.4759i 0.494300i
540540 0 0
541541 12.1933 21.1195i 0.524233 0.907998i −0.475369 0.879787i 0.657685π-0.657685\pi
0.999602 0.0282117i 0.00898124π-0.00898124\pi
542542 22.0435 + 16.1401i 0.946848 + 0.693276i
543543 0 0
544544 −7.41460 4.46514i −0.317898 0.191441i
545545 −33.6384 19.4212i −1.44091 0.831911i
546546 0 0
547547 18.7226 32.4286i 0.800522 1.38655i −0.118751 0.992924i 0.537889π-0.537889\pi
0.919273 0.393621i 0.128778π-0.128778\pi
548548 12.0389 + 38.0036i 0.514276 + 1.62343i
549549 0 0
550550 1.70629 15.6777i 0.0727564 0.668500i
551551 26.2195 0.141861i 1.11699 0.00604348i
552552 0 0
553553 −8.16937 + 4.71659i −0.347397 + 0.200570i
554554 −9.44545 21.4272i −0.401299 0.910354i
555555 0 0
556556 −19.9025 + 6.30478i −0.844056 + 0.267382i
557557 7.69507 13.3283i 0.326051 0.564736i −0.655674 0.755044i 0.727615π-0.727615\pi
0.981724 + 0.190308i 0.0609487π0.0609487\pi
558558 0 0
559559 14.3297 0.606082
560560 9.23497 + 13.1134i 0.390249 + 0.554144i
561561 0 0
562562 0.610426 5.60872i 0.0257493 0.236590i
563563 −25.2567 −1.06444 −0.532222 0.846605i 0.678643π-0.678643\pi
−0.532222 + 0.846605i 0.678643π0.678643\pi
564564 0 0
565565 −13.7582 + 7.94327i −0.578810 + 0.334176i
566566 −16.9251 12.3924i −0.711413 0.520892i
567567 0 0
568568 3.48488 + 17.3362i 0.146222 + 0.727412i
569569 46.3413i 1.94273i −0.237599 0.971363i 0.576361π-0.576361\pi
0.237599 0.971363i 0.423639π-0.423639\pi
570570 0 0
571571 32.1609i 1.34589i −0.739692 0.672946i 0.765029π-0.765029\pi
0.739692 0.672946i 0.234971π-0.234971\pi
572572 −3.13548 9.89787i −0.131101 0.413851i
573573 0 0
574574 1.32031 1.80323i 0.0551088 0.0752654i
575575 40.2512 23.2390i 1.67859 0.969135i
576576 0 0
577577 −39.2983 −1.63601 −0.818004 0.575212i 0.804919π-0.804919\pi
−0.818004 + 0.575212i 0.804919π0.804919\pi
578578 20.6092 + 2.24300i 0.857229 + 0.0932966i
579579 0 0
580580 −28.4776 26.0244i −1.18247 1.08060i
581581 −9.80550 −0.406801
582582 0 0
583583 7.54389 13.0664i 0.312436 0.541155i
584584 −0.733663 3.64975i −0.0303592 0.151028i
585585 0 0
586586 29.7505 13.1145i 1.22898 0.541755i
587587 −15.4560 + 8.92352i −0.637937 + 0.368313i −0.783819 0.620989i 0.786731π-0.786731\pi
0.145883 + 0.989302i 0.453398π0.453398\pi
588588 0 0
589589 −29.3123 + 17.1356i −1.20779 + 0.706060i
590590 25.5656 + 2.78243i 1.05252 + 0.114551i
591591 0 0
592592 39.7426 3.58511i 1.63341 0.147347i
593593 −11.7249 + 20.3082i −0.481485 + 0.833957i −0.999774 0.0212488i 0.993236π-0.993236\pi
0.518289 + 0.855205i 0.326569π0.326569\pi
594594 0 0
595595 5.31315 + 3.06755i 0.217818 + 0.125757i
596596 −18.8797 4.15880i −0.773341 0.170351i
597597 0 0
598598 18.0772 24.6891i 0.739231 1.00961i
599599 7.40584 12.8273i 0.302595 0.524109i −0.674128 0.738614i 0.735481π-0.735481\pi
0.976723 + 0.214505i 0.0688138π0.0688138\pi
600600 0 0
601601 4.30046i 0.175419i 0.996146 + 0.0877097i 0.0279548π0.0279548\pi
−0.996146 + 0.0877097i 0.972045π0.972045\pi
602602 −6.08732 + 8.31381i −0.248101 + 0.338846i
603603 0 0
604604 −14.9805 + 16.3926i −0.609546 + 0.667007i
605605 10.4921 + 18.1729i 0.426566 + 0.738835i
606606 0 0
607607 −20.1844 −0.819260 −0.409630 0.912252i 0.634342π-0.634342\pi
−0.409630 + 0.912252i 0.634342π0.634342\pi
608608 12.6061 21.1917i 0.511244 0.859435i
609609 0 0
610610 10.2801 + 23.3207i 0.416230 + 0.944227i
611611 8.70243 + 15.0730i 0.352062 + 0.609790i
612612 0 0
613613 0.467103 + 0.809046i 0.0188661 + 0.0326771i 0.875304 0.483572i 0.160661π-0.160661\pi
−0.856438 + 0.516250i 0.827328π0.827328\pi
614614 17.2347 23.5384i 0.695535 0.949933i
615615 0 0
616616 7.07452 + 2.38552i 0.285040 + 0.0961153i
617617 4.11324 7.12434i 0.165593 0.286815i −0.771273 0.636505i 0.780380π-0.780380\pi
0.936866 + 0.349690i 0.113713π0.113713\pi
618618 0 0
619619 7.04730i 0.283255i 0.989920 + 0.141627i 0.0452335π0.0452335\pi
−0.989920 + 0.141627i 0.954766π0.954766\pi
620620 48.7867 + 10.7467i 1.95932 + 0.431598i
621621 0 0
622622 −4.09399 + 1.80470i −0.164154 + 0.0723618i
623623 −4.34940 + 7.53338i −0.174255 + 0.301819i
624624 0 0
625625 11.7534 + 20.3576i 0.470138 + 0.814302i
626626 −21.5724 2.34783i −0.862206 0.0938383i
627627 0 0
628628 22.1093 + 4.87022i 0.882256 + 0.194343i
629629 13.2188 7.63188i 0.527068 0.304303i
630630 0 0
631631 −17.5204 10.1154i −0.697476 0.402688i 0.108931 0.994049i 0.465257π-0.465257\pi
−0.806407 + 0.591362i 0.798591π0.798591\pi
632632 −4.20505 20.9189i −0.167268 0.832108i
633633 0 0
634634 −0.402851 + 3.70148i −0.0159992 + 0.147004i
635635 −18.3589 −0.728549
636636 0 0
637637 11.5783 + 6.68475i 0.458750 + 0.264860i
638638 −17.8520 1.94292i −0.706766 0.0769210i
639639 0 0
640640 −34.7815 + 10.3163i −1.37486 + 0.407789i
641641 6.91570 3.99278i 0.273154 0.157705i −0.357166 0.934041i 0.616257π-0.616257\pi
0.630320 + 0.776335i 0.282924π0.282924\pi
642642 0 0
643643 9.89926 5.71534i 0.390389 0.225391i −0.291940 0.956437i 0.594301π-0.594301\pi
0.682328 + 0.731046i 0.260967π0.260967\pi
644644 6.64485 + 20.9761i 0.261844 + 0.826572i
645645 0 0
646646 0.969747 9.38188i 0.0381542 0.369125i
647647 48.3776i 1.90192i −0.309312 0.950961i 0.600099π-0.600099\pi
0.309312 0.950961i 0.399901π-0.399901\pi
648648 0 0
649649 10.3669 5.98534i 0.406937 0.234945i
650650 −14.8238 10.8539i −0.581438 0.425725i
651651 0 0
652652 −23.1464 21.1524i −0.906483 0.828391i
653653 −32.2260 −1.26110 −0.630551 0.776148i 0.717171π-0.717171\pi
−0.630551 + 0.776148i 0.717171π0.717171\pi
654654 0 0
655655 51.8481 + 29.9345i 2.02587 + 1.16964i
656656 2.91075 + 4.13319i 0.113646 + 0.161374i
657657 0 0
658658 −12.4419 1.35412i −0.485036 0.0527890i
659659 13.5111 23.4019i 0.526317 0.911608i −0.473213 0.880948i 0.656906π-0.656906\pi
0.999530 0.0306595i 0.00976076π-0.00976076\pi
660660 0 0
661661 23.1686 + 13.3764i 0.901155 + 0.520282i 0.877575 0.479440i 0.159160π-0.159160\pi
0.0235802 + 0.999722i 0.492493π0.492493\pi
662662 −5.31042 12.0468i −0.206396 0.468212i
663663 0 0
664664 7.08685 21.0168i 0.275023 0.815611i
665665 −8.65699 + 15.1835i −0.335703 + 0.588790i
666666 0 0
667667 −26.4619 45.8334i −1.02461 1.77467i
668668 −2.17982 6.88113i −0.0843398 0.266239i
669669 0 0
670670 0.0862786 + 0.195725i 0.00333323 + 0.00756150i
671671 10.2740 + 5.93168i 0.396622 + 0.228990i
672672 0 0
673673 29.5414i 1.13874i −0.822083 0.569368i 0.807188π-0.807188\pi
0.822083 0.569368i 0.192812π-0.192812\pi
674674 −4.33429 3.17354i −0.166951 0.122240i
675675 0 0
676676 13.5786 + 2.99108i 0.522253 + 0.115042i
677677 15.6682i 0.602176i 0.953596 + 0.301088i 0.0973498π0.0973498\pi
−0.953596 + 0.301088i 0.902650π0.902650\pi
678678 0 0
679679 6.15048 + 10.6529i 0.236034 + 0.408822i
680680 −10.4149 + 9.17100i −0.399394 + 0.351692i
681681 0 0
682682 21.2783 9.37980i 0.814787 0.359171i
683683 −29.7127 −1.13693 −0.568463 0.822709i 0.692462π-0.692462\pi
−0.568463 + 0.822709i 0.692462π0.692462\pi
684684 0 0
685685 63.9165 2.44212
686686 −20.1239 + 8.87094i −0.768335 + 0.338694i
687687 0 0
688688 −13.4200 19.0561i −0.511634 0.726508i
689689 −8.78872 15.2225i −0.334824 0.579932i
690690 0 0
691691 32.8555i 1.24988i 0.780671 + 0.624942i 0.214877π0.214877\pi
−0.780671 + 0.624942i 0.785123π0.785123\pi
692692 −2.22024 + 10.0792i −0.0844010 + 0.383154i
693693 0 0
694694 −4.05360 2.96802i −0.153872 0.112664i
695695 33.4732i 1.26971i
696696 0 0
697697 1.67464 + 0.966852i 0.0634314 + 0.0366221i
698698 −1.09440 2.48266i −0.0414235 0.0939701i
699699 0 0
700700 12.5944 3.98970i 0.476025 0.150796i
701701 8.96916 + 15.5350i 0.338761 + 0.586751i 0.984200 0.177061i 0.0566590π-0.0566590\pi
−0.645439 + 0.763812i 0.723326π0.723326\pi
702702 0 0
703703 21.9456 + 37.5403i 0.827693 + 1.41586i
704704 −10.2261 + 13.4392i −0.385411 + 0.506509i
705705 0 0
706706 4.06066 + 9.21169i 0.152825 + 0.346686i
707707 6.78635 + 3.91810i 0.255227 + 0.147355i
708708 0 0
709709 3.51145 6.08201i 0.131875 0.228415i −0.792524 0.609841i 0.791233π-0.791233\pi
0.924399 + 0.381426i 0.124567π0.124567\pi
710710 28.1853 + 3.06755i 1.05777 + 0.115123i
711711 0 0
712712 −13.0033 14.7671i −0.487321 0.553419i
713713 59.3520 + 34.2669i 2.22275 + 1.28330i
714714 0 0
715715 −16.6468 −0.622554
716716 −3.72668 + 4.07799i −0.139273 + 0.152402i
717717 0 0
718718 −9.55515 6.99622i −0.356595 0.261097i
719719 23.4325 13.5288i 0.873886 0.504538i 0.00524853 0.999986i 0.498329π-0.498329\pi
0.868638 + 0.495448i 0.164996π0.164996\pi
720720 0 0
721721 0.658560i 0.0245260i
722722 26.7422 + 2.61802i 0.995242 + 0.0974327i
723723 0 0
724724 −4.57642 + 1.44973i −0.170081 + 0.0538788i
725725 −27.5193 + 15.8882i −1.02204 + 0.590075i
726726 0 0
727727 −23.9684 + 13.8381i −0.888938 + 0.513229i −0.873595 0.486654i 0.838217π-0.838217\pi
−0.0153429 + 0.999882i 0.504884π0.504884\pi
728728 6.52777 5.74811i 0.241935 0.213039i
729729 0 0
730730 −5.93377 0.645803i −0.219619 0.0239022i
731731 −7.72093 4.45768i −0.285569 0.164873i
732732 0 0
733733 −2.82689 −0.104414 −0.0522068 0.998636i 0.516626π-0.516626\pi
−0.0522068 + 0.998636i 0.516626π0.516626\pi
734734 −3.48741 + 32.0430i −0.128723 + 1.18273i
735735 0 0
736736 −49.7620 0.917891i −1.83425 0.0338339i
737737 0.0862268 + 0.0497831i 0.00317621 + 0.00183378i
738738 0 0
739739 21.3233 12.3110i 0.784392 0.452869i −0.0535927 0.998563i 0.517067π-0.517067\pi
0.837984 + 0.545694i 0.183734π0.183734\pi
740740 13.7633 62.4812i 0.505950 2.29685i
741741 0 0
742742 12.5653 + 1.36755i 0.461286 + 0.0502042i
743743 3.96328 + 6.86460i 0.145399 + 0.251838i 0.929522 0.368768i 0.120220π-0.120220\pi
−0.784123 + 0.620605i 0.786887π0.786887\pi
744744 0 0
745745 −15.4980 + 26.8433i −0.567803 + 0.983463i
746746 30.4971 13.4436i 1.11658 0.492205i
747747 0 0
748748 −1.38962 + 6.30842i −0.0508094 + 0.230659i
749749 8.64759i 0.315976i
750750 0 0
751751 −7.13985 + 12.3666i −0.260537 + 0.451263i −0.966385 0.257101i 0.917233π-0.917233\pi
0.705848 + 0.708363i 0.250566π0.250566\pi
752752 11.8947 25.6890i 0.433754 0.936780i
753753 0 0
754754 −12.3592 + 16.8796i −0.450094 + 0.614720i
755755 17.8022 + 30.8344i 0.647889 + 1.12218i
756756 0 0
757757 −17.1966 29.7854i −0.625021 1.08257i −0.988537 0.150981i 0.951757π-0.951757\pi
0.363515 0.931588i 0.381576π-0.381576\pi
758758 −21.7843 49.4182i −0.791242 1.79495i
759759 0 0
760760 −26.2870 29.5289i −0.953531 1.07112i
761761 31.6267 1.14647 0.573233 0.819392i 0.305689π-0.305689\pi
0.573233 + 0.819392i 0.305689π0.305689\pi
762762 0 0
763763 −7.57331 13.1174i −0.274172 0.474880i
764764 −6.47428 5.91653i −0.234231 0.214053i
765765 0 0
766766 −18.1975 + 24.8534i −0.657502 + 0.897989i
767767 13.9460i 0.503561i
768768 0 0
769769 11.7685 20.3836i 0.424383 0.735052i −0.571980 0.820268i 0.693824π-0.693824\pi
0.996363 + 0.0852153i 0.0271578π0.0271578\pi
770770 7.07162 9.65813i 0.254844 0.348055i
771771 0 0
772772 3.85769 17.5127i 0.138841 0.630296i
773773 10.5693 + 6.10219i 0.380152 + 0.219481i 0.677884 0.735169i 0.262897π-0.262897\pi
−0.297733 + 0.954649i 0.596230π0.596230\pi
774774 0 0
775775 20.5745 35.6361i 0.739058 1.28009i
776776 −27.2784 + 5.48343i −0.979238 + 0.196844i
777777 0 0
778778 37.8824 + 4.12293i 1.35815 + 0.147814i
779779 −2.72857 + 4.78564i −0.0977612 + 0.171463i
780780 0 0
781781 11.4292 6.59865i 0.408969 0.236118i
782782 −17.4204 + 7.67918i −0.622951 + 0.274607i
783783 0 0
784784 −1.95370 21.6577i −0.0697751 0.773488i
785785 18.1491 31.4352i 0.647770 1.12197i
786786 0 0
787787 −36.6534 −1.30655 −0.653276 0.757120i 0.726606π-0.726606\pi
−0.653276 + 0.757120i 0.726606π0.726606\pi
788788 1.87832 2.05539i 0.0669124 0.0732202i
789789 0 0
790790 −34.0099 3.70148i −1.21002 0.131693i
791791 −6.19498 −0.220268
792792 0 0
793793 11.9693 6.91048i 0.425042 0.245398i
794794 −3.93956 + 5.38050i −0.139810 + 0.190947i
795795 0 0
796796 −0.532685 + 0.168746i −0.0188805 + 0.00598103i
797797 14.7351i 0.521944i 0.965346 + 0.260972i 0.0840430π0.0840430\pi
−0.965346 + 0.260972i 0.915957π0.915957\pi
798798 0 0
799799 10.8286i 0.383088i
800800 −0.551120 + 29.8781i −0.0194850 + 1.05635i
801801 0 0
802802 −5.49348 4.02229i −0.193982 0.142032i
803803 −2.40616 + 1.38920i −0.0849115 + 0.0490237i
804804 0 0
805805 35.2786 1.24341
806806 2.93116 26.9321i 0.103246 0.948642i
807807 0 0
808808 −13.3027 + 11.7139i −0.467989 + 0.412093i
809809 −14.1872 −0.498796 −0.249398 0.968401i 0.580233π-0.580233\pi
−0.249398 + 0.968401i 0.580233π0.580233\pi
810810 0 0
811811 21.0255 36.4173i 0.738307 1.27879i −0.214950 0.976625i 0.568959π-0.568959\pi
0.953257 0.302160i 0.0977077π-0.0977077\pi
812812 −4.54301 14.3411i −0.159428 0.503273i
813813 0 0
814814 −12.0127 27.2511i −0.421046 0.955151i
815815 −43.5381 + 25.1367i −1.52507 + 0.880501i
816816 0 0
817817 12.5801 22.0642i 0.440122 0.771929i
818818 −2.15814 + 19.8294i −0.0754576 + 0.693320i
819819 0 0
820820 7.72682 2.44772i 0.269832 0.0854782i
821821 22.3593 38.7274i 0.780343 1.35159i −0.151398 0.988473i 0.548378π-0.548378\pi
0.931742 0.363122i 0.118289π-0.118289\pi
822822 0 0
823823 −34.6560 20.0087i −1.20803 0.697458i −0.245703 0.969345i 0.579019π-0.579019\pi
−0.962329 + 0.271887i 0.912352π0.912352\pi
824824 1.41154 + 0.475969i 0.0491733 + 0.0165812i
825825 0 0
826826 8.09119 + 5.92432i 0.281529 + 0.206133i
827827 −13.1881 + 22.8424i −0.458594 + 0.794309i −0.998887 0.0471684i 0.984980π-0.984980\pi
0.540293 + 0.841477i 0.318314π0.318314\pi
828828 0 0
829829 39.6736i 1.37792i 0.724798 + 0.688961i 0.241933π0.241933\pi
−0.724798 + 0.688961i 0.758067π0.758067\pi
830830 −28.6922 21.0082i −0.995920 0.729206i
831831 0 0
832832 7.60245 + 18.1458i 0.263567 + 0.629094i
833833 −4.15898 7.20357i −0.144100 0.249589i
834834 0 0
835835 −11.5730 −0.400502
836836 −17.9929 3.86152i −0.622299 0.133554i
837837 0 0
838838 40.8017 17.9860i 1.40947 0.621317i
839839 7.96193 + 13.7905i 0.274876 + 0.476100i 0.970104 0.242690i 0.0780298π-0.0780298\pi
−0.695228 + 0.718790i 0.744696π0.744696\pi
840840 0 0
841841 3.59168 + 6.22098i 0.123851 + 0.214516i
842842 30.6169 + 22.4175i 1.05513 + 0.772558i
843843 0 0
844844 0.325207 + 0.0716365i 0.0111941 + 0.00246583i
845845 11.1464 19.3062i 0.383449 0.664152i
846846 0 0
847847 8.18285i 0.281166i
848848 −12.0126 + 25.9437i −0.412515 + 0.890910i
849849 0 0
850850 4.61073 + 10.4595i 0.158147 + 0.358759i
851851 43.8856 76.0122i 1.50438 2.60566i
852852 0 0
853853 19.4390 + 33.6693i 0.665578 + 1.15281i 0.979128 + 0.203243i 0.0651482π0.0651482\pi
−0.313550 + 0.949572i 0.601518π0.601518\pi
854854 −1.07529 + 9.87995i −0.0367955 + 0.338085i
855855 0 0
856856 −18.5350 6.24998i −0.633513 0.213620i
857857 −28.7983 + 16.6267i −0.983730 + 0.567957i −0.903394 0.428811i 0.858933π-0.858933\pi
−0.0803358 + 0.996768i 0.525599π0.525599\pi
858858 0 0
859859 28.1710 + 16.2645i 0.961183 + 0.554939i 0.896537 0.442969i 0.146075π-0.146075\pi
0.0646461 + 0.997908i 0.479408π0.479408\pi
860860 −35.6246 + 11.2853i −1.21479 + 0.384824i
861861 0 0
862862 10.9416 + 1.19083i 0.372672 + 0.0405598i
863863 20.4964 0.697707 0.348853 0.937177i 0.386571π-0.386571\pi
0.348853 + 0.937177i 0.386571π0.386571\pi
864864 0 0
865865 14.3307 + 8.27386i 0.487260 + 0.281320i
866866 2.34718 21.5663i 0.0797603 0.732854i
867867 0 0
868868 14.3803 + 13.1415i 0.488099 + 0.446050i
869869 −13.7911 + 7.96231i −0.467832 + 0.270103i
870870 0 0
871871 0.100455 0.0579979i 0.00340380 0.00196518i
872872 33.5889 6.75195i 1.13746 0.228650i
873873 0 0
874874 −22.1451 49.5091i −0.749069 1.67467i
875875 1.13333i 0.0383137i
876876 0 0
877877 −29.2384 + 16.8808i −0.987312 + 0.570025i −0.904470 0.426538i 0.859733π-0.859733\pi
−0.0828424 + 0.996563i 0.526400π0.526400\pi
878878 21.0787 28.7885i 0.711372 0.971563i
879879 0 0
880880 15.5900 + 22.1374i 0.525539 + 0.746253i
881881 37.8371 1.27476 0.637382 0.770548i 0.280017π-0.280017\pi
0.637382 + 0.770548i 0.280017π0.280017\pi
882882 0 0
883883 23.2555 + 13.4265i 0.782609 + 0.451839i 0.837354 0.546661i 0.184101π-0.184101\pi
−0.0547454 + 0.998500i 0.517435π0.517435\pi
884884 5.55529 + 5.07672i 0.186845 + 0.170748i
885885 0 0
886886 −0.362369 + 3.32952i −0.0121740 + 0.111858i
887887 −4.11911 + 7.13451i −0.138306 + 0.239554i −0.926856 0.375418i 0.877499π-0.877499\pi
0.788549 + 0.614972i 0.210832π0.210832\pi
888888 0 0
889889 −6.19993 3.57953i −0.207939 0.120054i
890890 −28.8671 + 12.7251i −0.967629 + 0.426546i
891891 0 0
892892 22.9138 + 5.04743i 0.767209 + 0.169000i
893893 30.8487 0.166907i 1.03231 0.00558533i
894894 0 0
895895 4.42865 + 7.67065i 0.148033 + 0.256401i
896896 −13.7574 3.29764i −0.459603 0.110166i
897897 0 0
898898 −15.1113 + 6.66132i −0.504272 + 0.222291i
899899 −40.5782 23.4279i −1.35336 0.781363i
900900 0 0
901901 10.9360i 0.364330i
902902 2.22889 3.04412i 0.0742138 0.101358i
903903 0 0
904904 4.47737 13.2781i 0.148915 0.441624i
905905 7.69687i 0.255853i
906906 0 0
907907 12.9847 + 22.4902i 0.431150 + 0.746774i 0.996973 0.0777533i 0.0247747π-0.0247747\pi
−0.565823 + 0.824527i 0.691441π0.691441\pi
908908 −11.8494 + 12.9665i −0.393238 + 0.430308i
909909 0 0
910910 −5.62512 12.7607i −0.186471 0.423013i
911911 −35.0480 −1.16119 −0.580597 0.814191i 0.697181π-0.697181\pi
−0.580597 + 0.814191i 0.697181π0.697181\pi
912912 0 0
913913 −16.5531 −0.547829
914914 −4.97275 11.2808i −0.164484 0.373135i
915915 0 0
916916 8.81495 9.64593i 0.291254 0.318711i
917917 11.6730 + 20.2182i 0.385477 + 0.667665i
918918 0 0
919919 6.29627i 0.207695i 0.994593 + 0.103847i 0.0331153π0.0331153\pi
−0.994593 + 0.103847i 0.966885π0.966885\pi
920920 −25.4974 + 75.6152i −0.840623 + 2.49296i
921921 0 0
922922 −17.6434 + 24.0966i −0.581054 + 0.793580i
923923 15.3750i 0.506075i
924924 0 0
925925 −45.6392 26.3498i −1.50061 0.866376i
926926 −0.460234 + 0.202879i −0.0151242 + 0.00666701i
927927 0 0
928928 34.0217 + 0.627551i 1.11682 + 0.0206004i
929929 1.85864 + 3.21925i 0.0609799 + 0.105620i 0.894904 0.446259i 0.147244π-0.147244\pi
−0.833924 + 0.551880i 0.813911π0.813911\pi
930930 0 0
931931 20.4576 11.9592i 0.670469 0.391948i
932932 51.2963 + 11.2995i 1.68027 + 0.370128i
933933 0 0
934934 5.79675 2.55530i 0.189676 0.0836120i
935935 8.96938 + 5.17848i 0.293330 + 0.169354i
936936 0 0
937937 −21.7674 + 37.7022i −0.711109 + 1.23168i 0.253332 + 0.967379i 0.418473π0.418473\pi
−0.964441 + 0.264298i 0.914860π0.914860\pi
938938 −0.00902461 + 0.0829200i −0.000294664 + 0.00270743i
939939 0 0
940940 −33.5055 30.6191i −1.09283 0.998683i
941941 −34.9810 20.1963i −1.14035 0.658380i −0.193831 0.981035i 0.562091π-0.562091\pi
−0.946517 + 0.322655i 0.895425π0.895425\pi
942942 0 0
943943 11.1194 0.362097
944944 −18.5459 + 13.0607i −0.603616 + 0.425089i
945945 0 0
946946 −10.2763 + 14.0349i −0.334111 + 0.456315i
947947 21.1885 12.2332i 0.688533 0.397525i −0.114529 0.993420i 0.536536π-0.536536\pi
0.803062 + 0.595895i 0.203203π0.203203\pi
948948 0 0
949949 3.23686i 0.105073i
950950 −29.7262 + 13.2963i −0.964446 + 0.431390i
951951 0 0
952952 −5.30533 + 1.06646i −0.171947 + 0.0345642i
953953 43.7145 25.2386i 1.41605 0.817557i 0.420101 0.907477i 0.361994π-0.361994\pi
0.995949 + 0.0899200i 0.0286611π0.0286611\pi
954954 0 0
955955 −12.1780 + 7.03099i −0.394072 + 0.227518i
956956 −34.7988 31.8010i −1.12547 1.02852i
957957 0 0
958958 −3.79808 + 34.8975i −0.122710 + 1.12749i
959959 21.5851 + 12.4622i 0.697019 + 0.402424i
960960 0 0
961961 29.6759 0.957286
962962 −34.4920 3.75394i −1.11207 0.121032i
963963 0 0
964964 29.8626 9.45995i 0.961809 0.304684i
965965 −24.8998 14.3759i −0.801552 0.462776i
966966 0 0
967967 −43.6786 + 25.2179i −1.40461 + 0.810952i −0.994861 0.101246i 0.967717π-0.967717\pi
−0.409749 + 0.912198i 0.634384π0.634384\pi
968968 −17.5389 5.91409i −0.563721 0.190086i
969969 0 0
970970 −4.82676 + 44.3493i −0.154978 + 1.42397i
971971 −5.26456 9.11849i −0.168948 0.292626i 0.769102 0.639126i 0.220704π-0.220704\pi
−0.938050 + 0.346499i 0.887370π0.887370\pi
972972 0 0
973973 −6.52645 + 11.3041i −0.209228 + 0.362394i
974974 20.6559 + 46.8582i 0.661856 + 1.50143i
975975 0 0
976976 −20.3993 9.44539i −0.652964 0.302340i
977977 6.92660i 0.221602i −0.993843 0.110801i 0.964658π-0.964658\pi
0.993843 0.110801i 0.0353415π-0.0353415\pi
978978 0 0
979979 −7.34243 + 12.7175i −0.234665 + 0.406452i
980980 −34.0490 7.50031i −1.08766 0.239588i
981981 0 0
982982 6.79967 + 4.97868i 0.216986 + 0.158876i
983983 17.5996 + 30.4835i 0.561341 + 0.972272i 0.997380 + 0.0723437i 0.0230479π0.0230479\pi
−0.436038 + 0.899928i 0.643619π0.643619\pi
984984 0 0
985985 −2.23213 3.86616i −0.0711215 0.123186i
986986 11.9101 5.25016i 0.379295 0.167199i
987987 0 0
988988 −14.3770 + 15.9043i −0.457394 + 0.505982i
989989 −51.2660 −1.63016
990990 0 0
991991 −24.9524 43.2188i −0.792638 1.37289i −0.924328 0.381599i 0.875374π-0.875374\pi
0.131690 0.991291i 0.457960π-0.457960\pi
992992 −38.5603 + 21.3244i −1.22429 + 0.677051i
993993 0 0
994994 8.92028 + 6.53137i 0.282934 + 0.207163i
995995 0.895899i 0.0284019i
996996 0 0
997997 −2.63314 + 4.56074i −0.0833925 + 0.144440i −0.904705 0.426038i 0.859909π-0.859909\pi
0.821313 + 0.570478i 0.193242π0.193242\pi
998998 26.5598 + 19.4469i 0.840734 + 0.615580i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 684.2.r.a.487.5 16
3.2 odd 2 76.2.f.a.31.4 yes 16
4.3 odd 2 inner 684.2.r.a.487.2 16
12.11 even 2 76.2.f.a.31.7 yes 16
19.8 odd 6 inner 684.2.r.a.559.2 16
24.5 odd 2 1216.2.n.f.639.6 16
24.11 even 2 1216.2.n.f.639.3 16
57.8 even 6 76.2.f.a.27.7 yes 16
76.27 even 6 inner 684.2.r.a.559.5 16
228.179 odd 6 76.2.f.a.27.4 16
456.179 odd 6 1216.2.n.f.255.6 16
456.293 even 6 1216.2.n.f.255.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.2.f.a.27.4 16 228.179 odd 6
76.2.f.a.27.7 yes 16 57.8 even 6
76.2.f.a.31.4 yes 16 3.2 odd 2
76.2.f.a.31.7 yes 16 12.11 even 2
684.2.r.a.487.2 16 4.3 odd 2 inner
684.2.r.a.487.5 16 1.1 even 1 trivial
684.2.r.a.559.2 16 19.8 odd 6 inner
684.2.r.a.559.5 16 76.27 even 6 inner
1216.2.n.f.255.3 16 456.293 even 6
1216.2.n.f.255.6 16 456.179 odd 6
1216.2.n.f.639.3 16 24.11 even 2
1216.2.n.f.639.6 16 24.5 odd 2