Properties

Label 300.2.j.d.43.2
Level 300300
Weight 22
Character 300.43
Analytic conductor 2.3962.396
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [300,2,Mod(7,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) 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("300.7"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 300=22352 300 = 2^{2} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 300.j (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.395512060642.39551206064
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(i)\Q(i)
Coefficient field: 12.0.426337261060096.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x124x93x8+4x7+8x6+8x512x432x3+64 x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 43.2
Root 0.7601981.19252i-0.760198 - 1.19252i of defining polynomial
Character χ\chi == 300.43
Dual form 300.2.j.d.7.2

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+(0.7601981.19252i)q2+(0.7071070.707107i)q3+(0.844199+1.81310i)q4+(1.380780.305697i)q6+(0.6113930.611393i)q7+(2.803910.371591i)q81.00000iq95.12822iq11+(0.685116+1.87899i)q12+(1.761561.76156i)q13+(0.264318+1.19388i)q14+(2.574663.06123i)q16+(3.761563.76156i)q17+(1.19252+0.760198i)q181.22279q190.864641q21+(6.11549+3.89846i)q22+(1.077001.07700i)q23+(1.719912.24542i)q24+(0.761557+3.43982i)q26+(0.7071070.707107i)q27+(1.624650.592379i)q28+0.864641iq29+7.81086iq31+(1.69333+5.39747i)q32+(3.626203.62620i)q33+(7.345251.62620i)q34+(1.81310+0.844199i)q36+(1.761561.76156i)q37+(0.929560+1.45820i)q382.49122q39+5.52311q41+(0.657298+1.03110i)q42+(6.20522+6.20522i)q43+(9.29797+4.32924i)q44+(2.103080.465611i)q46+(2.299792.29979i)q47+(3.985180.344061i)q486.25240iq495.31965iq51+(4.680981.70677i)q52+(2.62620+2.62620i)q53+(0.305697+1.38078i)q54+(1.941481.48710i)q56+(0.864641+0.864641i)q57+(1.031100.657298i)q580.528636q59+4.98168q61+(9.314605.93780i)q62+(0.611393+0.611393i)q63+(7.723842.08382i)q64+(1.56768+7.08093i)q66+(6.20522+6.20522i)q67+(3.64457+9.99558i)q681.52311iq69+8.10243iq71+(0.3715912.80391i)q72+(2.25240+2.25240i)q73+(3.439820.761557i)q74+(1.032282.21703i)q76+(3.13536+3.13536i)q77+(1.89382+2.97082i)q78+15.9133q791.00000q81+(4.198666.58641i)q82+(7.956657.95665i)q83+(0.7299291.56768i)q84+(12.1170+2.68264i)q86+(0.611393+0.611393i)q87+(1.9056014.3791i)q88+7.25240iq89+2.15401iq91+(1.04351+2.86192i)q92+(5.52311+5.52311i)q93+(0.994247+4.49084i)q94+(2.61922+5.01395i)q96+(0.793833+0.793833i)q97+(7.45610+4.75306i)q985.12822q99+O(q100)q+(-0.760198 - 1.19252i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(-1.38078 - 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(2.80391 - 0.371591i) q^{8} -1.00000i q^{9} -5.12822i q^{11} +(0.685116 + 1.87899i) q^{12} +(-1.76156 - 1.76156i) q^{13} +(-0.264318 + 1.19388i) q^{14} +(-2.57466 - 3.06123i) q^{16} +(3.76156 - 3.76156i) q^{17} +(-1.19252 + 0.760198i) q^{18} -1.22279 q^{19} -0.864641 q^{21} +(-6.11549 + 3.89846i) q^{22} +(1.07700 - 1.07700i) q^{23} +(1.71991 - 2.24542i) q^{24} +(-0.761557 + 3.43982i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.62465 - 0.592379i) q^{28} +0.864641i q^{29} +7.81086i q^{31} +(-1.69333 + 5.39747i) q^{32} +(-3.62620 - 3.62620i) q^{33} +(-7.34525 - 1.62620i) q^{34} +(1.81310 + 0.844199i) q^{36} +(1.76156 - 1.76156i) q^{37} +(0.929560 + 1.45820i) q^{38} -2.49122 q^{39} +5.52311 q^{41} +(0.657298 + 1.03110i) q^{42} +(-6.20522 + 6.20522i) q^{43} +(9.29797 + 4.32924i) q^{44} +(-2.10308 - 0.465611i) q^{46} +(-2.29979 - 2.29979i) q^{47} +(-3.98518 - 0.344061i) q^{48} -6.25240i q^{49} -5.31965i q^{51} +(4.68098 - 1.70677i) q^{52} +(2.62620 + 2.62620i) q^{53} +(-0.305697 + 1.38078i) q^{54} +(-1.94148 - 1.48710i) q^{56} +(-0.864641 + 0.864641i) q^{57} +(1.03110 - 0.657298i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(9.31460 - 5.93780i) q^{62} +(-0.611393 + 0.611393i) q^{63} +(7.72384 - 2.08382i) q^{64} +(-1.56768 + 7.08093i) q^{66} +(6.20522 + 6.20522i) q^{67} +(3.64457 + 9.99558i) q^{68} -1.52311i q^{69} +8.10243i q^{71} +(-0.371591 - 2.80391i) q^{72} +(2.25240 + 2.25240i) q^{73} +(-3.43982 - 0.761557i) q^{74} +(1.03228 - 2.21703i) q^{76} +(-3.13536 + 3.13536i) q^{77} +(1.89382 + 2.97082i) q^{78} +15.9133 q^{79} -1.00000 q^{81} +(-4.19866 - 6.58641i) q^{82} +(7.95665 - 7.95665i) q^{83} +(0.729929 - 1.56768i) q^{84} +(12.1170 + 2.68264i) q^{86} +(0.611393 + 0.611393i) q^{87} +(-1.90560 - 14.3791i) q^{88} +7.25240i q^{89} +2.15401i q^{91} +(1.04351 + 2.86192i) q^{92} +(5.52311 + 5.52311i) q^{93} +(-0.994247 + 4.49084i) q^{94} +(2.61922 + 5.01395i) q^{96} +(-0.793833 + 0.793833i) q^{97} +(-7.45610 + 4.75306i) q^{98} -5.12822 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q4q6+12q8+8q12+4q13+12q16+20q1712q22+16q26+4q2820q328q33+4q364q3716q38+16q4120q4240q4616q48+24q98+O(q100) 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48}+ \cdots - 24 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/300Z)×\left(\mathbb{Z}/300\mathbb{Z}\right)^\times.

nn 101101 151151 277277
χ(n)\chi(n) 11 1-1 e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.760198 1.19252i −0.537541 0.843238i
33 0.707107 0.707107i 0.408248 0.408248i
44 −0.844199 + 1.81310i −0.422099 + 0.906550i
55 0 0
66 −1.38078 0.305697i −0.563700 0.124800i
77 −0.611393 0.611393i −0.231085 0.231085i 0.582060 0.813145i 0.302247π-0.302247\pi
−0.813145 + 0.582060i 0.802247π0.802247\pi
88 2.80391 0.371591i 0.991332 0.131377i
99 1.00000i 0.333333i
1010 0 0
1111 5.12822i 1.54622i −0.634274 0.773108i 0.718701π-0.718701\pi
0.634274 0.773108i 0.281299π-0.281299\pi
1212 0.685116 + 1.87899i 0.197776 + 0.542419i
1313 −1.76156 1.76156i −0.488568 0.488568i 0.419286 0.907854i 0.362280π-0.362280\pi
−0.907854 + 0.419286i 0.862280π0.862280\pi
1414 −0.264318 + 1.19388i −0.0706419 + 0.319077i
1515 0 0
1616 −2.57466 3.06123i −0.643664 0.765308i
1717 3.76156 3.76156i 0.912312 0.912312i −0.0841421 0.996454i 0.526815π-0.526815\pi
0.996454 + 0.0841421i 0.0268150π0.0268150\pi
1818 −1.19252 + 0.760198i −0.281079 + 0.179180i
1919 −1.22279 −0.280527 −0.140263 0.990114i 0.544795π-0.544795\pi
−0.140263 + 0.990114i 0.544795π0.544795\pi
2020 0 0
2121 −0.864641 −0.188680
2222 −6.11549 + 3.89846i −1.30383 + 0.831154i
2323 1.07700 1.07700i 0.224571 0.224571i −0.585849 0.810420i 0.699239π-0.699239\pi
0.810420 + 0.585849i 0.199239π0.199239\pi
2424 1.71991 2.24542i 0.351075 0.458344i
2525 0 0
2626 −0.761557 + 3.43982i −0.149354 + 0.674604i
2727 −0.707107 0.707107i −0.136083 0.136083i
2828 1.62465 0.592379i 0.307031 0.111949i
2929 0.864641i 0.160560i 0.996772 + 0.0802799i 0.0255814π0.0255814\pi
−0.996772 + 0.0802799i 0.974419π0.974419\pi
3030 0 0
3131 7.81086i 1.40287i 0.712732 + 0.701436i 0.247457π0.247457\pi
−0.712732 + 0.701436i 0.752543π0.752543\pi
3232 −1.69333 + 5.39747i −0.299341 + 0.954146i
3333 −3.62620 3.62620i −0.631240 0.631240i
3434 −7.34525 1.62620i −1.25970 0.278891i
3535 0 0
3636 1.81310 + 0.844199i 0.302183 + 0.140700i
3737 1.76156 1.76156i 0.289598 0.289598i −0.547323 0.836921i 0.684353π-0.684353\pi
0.836921 + 0.547323i 0.184353π0.184353\pi
3838 0.929560 + 1.45820i 0.150795 + 0.236551i
3939 −2.49122 −0.398914
4040 0 0
4141 5.52311 0.862566 0.431283 0.902217i 0.358061π-0.358061\pi
0.431283 + 0.902217i 0.358061π0.358061\pi
4242 0.657298 + 1.03110i 0.101423 + 0.159102i
4343 −6.20522 + 6.20522i −0.946288 + 0.946288i −0.998629 0.0523416i 0.983332π-0.983332\pi
0.0523416 + 0.998629i 0.483332π0.483332\pi
4444 9.29797 + 4.32924i 1.40172 + 0.652657i
4545 0 0
4646 −2.10308 0.465611i −0.310083 0.0686506i
4747 −2.29979 2.29979i −0.335459 0.335459i 0.519196 0.854655i 0.326231π-0.326231\pi
−0.854655 + 0.519196i 0.826231π0.826231\pi
4848 −3.98518 0.344061i −0.575210 0.0496610i
4949 6.25240i 0.893199i
5050 0 0
5151 5.31965i 0.744899i
5252 4.68098 1.70677i 0.649135 0.236687i
5353 2.62620 + 2.62620i 0.360736 + 0.360736i 0.864084 0.503348i 0.167899π-0.167899\pi
−0.503348 + 0.864084i 0.667899π0.667899\pi
5454 −0.305697 + 1.38078i −0.0416001 + 0.187900i
5555 0 0
5656 −1.94148 1.48710i −0.259441 0.198723i
5757 −0.864641 + 0.864641i −0.114524 + 0.114524i
5858 1.03110 0.657298i 0.135390 0.0863075i
5959 −0.528636 −0.0688225 −0.0344113 0.999408i 0.510956π-0.510956\pi
−0.0344113 + 0.999408i 0.510956π0.510956\pi
6060 0 0
6161 4.98168 0.637838 0.318919 0.947782i 0.396680π-0.396680\pi
0.318919 + 0.947782i 0.396680π0.396680\pi
6262 9.31460 5.93780i 1.18295 0.754101i
6363 −0.611393 + 0.611393i −0.0770283 + 0.0770283i
6464 7.72384 2.08382i 0.965480 0.260477i
6565 0 0
6666 −1.56768 + 7.08093i −0.192968 + 0.871603i
6767 6.20522 + 6.20522i 0.758089 + 0.758089i 0.975974 0.217886i 0.0699160π-0.0699160\pi
−0.217886 + 0.975974i 0.569916π0.569916\pi
6868 3.64457 + 9.99558i 0.441969 + 1.21214i
6969 1.52311i 0.183361i
7070 0 0
7171 8.10243i 0.961581i 0.876835 + 0.480791i 0.159650π0.159650\pi
−0.876835 + 0.480791i 0.840350π0.840350\pi
7272 −0.371591 2.80391i −0.0437924 0.330444i
7373 2.25240 + 2.25240i 0.263623 + 0.263623i 0.826524 0.562901i 0.190315π-0.190315\pi
−0.562901 + 0.826524i 0.690315π0.690315\pi
7474 −3.43982 0.761557i −0.399871 0.0885292i
7575 0 0
7676 1.03228 2.21703i 0.118410 0.254311i
7777 −3.13536 + 3.13536i −0.357307 + 0.357307i
7878 1.89382 + 2.97082i 0.214433 + 0.336379i
7979 15.9133 1.79039 0.895193 0.445680i 0.147038π-0.147038\pi
0.895193 + 0.445680i 0.147038π0.147038\pi
8080 0 0
8181 −1.00000 −0.111111
8282 −4.19866 6.58641i −0.463664 0.727348i
8383 7.95665 7.95665i 0.873355 0.873355i −0.119481 0.992836i 0.538123π-0.538123\pi
0.992836 + 0.119481i 0.0381231π0.0381231\pi
8484 0.729929 1.56768i 0.0796418 0.171048i
8585 0 0
8686 12.1170 + 2.68264i 1.30661 + 0.289277i
8787 0.611393 + 0.611393i 0.0655483 + 0.0655483i
8888 −1.90560 14.3791i −0.203138 1.53281i
8989 7.25240i 0.768752i 0.923177 + 0.384376i 0.125583π0.125583\pi
−0.923177 + 0.384376i 0.874417π0.874417\pi
9090 0 0
9191 2.15401i 0.225801i
9292 1.04351 + 2.86192i 0.108793 + 0.298376i
9393 5.52311 + 5.52311i 0.572720 + 0.572720i
9494 −0.994247 + 4.49084i −0.102549 + 0.463195i
9595 0 0
9696 2.61922 + 5.01395i 0.267323 + 0.511734i
9797 −0.793833 + 0.793833i −0.0806015 + 0.0806015i −0.746258 0.665657i 0.768152π-0.768152\pi
0.665657 + 0.746258i 0.268152π0.268152\pi
9898 −7.45610 + 4.75306i −0.753179 + 0.480131i
9999 −5.12822 −0.515405
100100 0 0
101101 −10.1170 −1.00668 −0.503341 0.864088i 0.667896π-0.667896\pi
−0.503341 + 0.864088i 0.667896π0.667896\pi
102102 −6.34377 + 4.04398i −0.628127 + 0.400414i
103103 −3.82267 + 3.82267i −0.376659 + 0.376659i −0.869895 0.493236i 0.835814π-0.835814\pi
0.493236 + 0.869895i 0.335814π0.335814\pi
104104 −5.59383 4.28467i −0.548520 0.420147i
105105 0 0
106106 1.13536 5.12822i 0.110276 0.498097i
107107 −5.51107 5.51107i −0.532775 0.532775i 0.388622 0.921397i 0.372951π-0.372951\pi
−0.921397 + 0.388622i 0.872951π0.872951\pi
108108 1.87899 0.685116i 0.180806 0.0659253i
109109 7.31695i 0.700836i 0.936593 + 0.350418i 0.113961π0.113961\pi
−0.936593 + 0.350418i 0.886039π0.886039\pi
110110 0 0
111111 2.49122i 0.236456i
112112 −0.297490 + 3.44575i −0.0281101 + 0.325592i
113113 0.509161 + 0.509161i 0.0478978 + 0.0478978i 0.730650 0.682752i 0.239217π-0.239217\pi
−0.682752 + 0.730650i 0.739217π0.739217\pi
114114 1.68840 + 0.373802i 0.158133 + 0.0350098i
115115 0 0
116116 −1.56768 0.729929i −0.145555 0.0677722i
117117 −1.76156 + 1.76156i −0.162856 + 0.162856i
118118 0.401868 + 0.630408i 0.0369949 + 0.0580337i
119119 −4.59958 −0.421643
120120 0 0
121121 −15.2986 −1.39078
122122 −3.78706 5.94074i −0.342864 0.537849i
123123 3.90543 3.90543i 0.352141 0.352141i
124124 −14.1619 6.59392i −1.27177 0.592152i
125125 0 0
126126 1.19388 + 0.264318i 0.106359 + 0.0235473i
127127 7.49103 + 7.49103i 0.664722 + 0.664722i 0.956489 0.291767i 0.0942433π-0.0942433\pi
−0.291767 + 0.956489i 0.594243π0.594243\pi
128128 −8.35664 7.62671i −0.738629 0.674112i
129129 8.77551i 0.772641i
130130 0 0
131131 13.9964i 1.22287i −0.791296 0.611434i 0.790593π-0.790593\pi
0.791296 0.611434i 0.209407π-0.209407\pi
132132 9.63589 3.51342i 0.838696 0.305804i
133133 0.747604 + 0.747604i 0.0648255 + 0.0648255i
134134 2.68264 12.1170i 0.231745 1.04675i
135135 0 0
136136 9.14931 11.9448i 0.784547 1.02426i
137137 −7.01395 + 7.01395i −0.599242 + 0.599242i −0.940111 0.340869i 0.889279π-0.889279\pi
0.340869 + 0.940111i 0.389279π0.389279\pi
138138 −1.81634 + 1.15787i −0.154617 + 0.0985643i
139139 −2.28006 −0.193392 −0.0966960 0.995314i 0.530827π-0.530827\pi
−0.0966960 + 0.995314i 0.530827π0.530827\pi
140140 0 0
141141 −3.25240 −0.273901
142142 9.66229 6.15945i 0.810842 0.516889i
143143 −9.03365 + 9.03365i −0.755432 + 0.755432i
144144 −3.06123 + 2.57466i −0.255103 + 0.214555i
145145 0 0
146146 0.973757 4.39829i 0.0805887 0.364005i
147147 −4.42111 4.42111i −0.364647 0.364647i
148148 1.70677 + 4.68098i 0.140296 + 0.384774i
149149 10.1170i 0.828820i −0.910090 0.414410i 0.863988π-0.863988\pi
0.910090 0.414410i 0.136012π-0.136012\pi
150150 0 0
151151 7.93691i 0.645897i 0.946417 + 0.322948i 0.104674π0.104674\pi
−0.946417 + 0.322948i 0.895326π0.895326\pi
152152 −3.42859 + 0.454377i −0.278095 + 0.0368548i
153153 −3.76156 3.76156i −0.304104 0.304104i
154154 6.12247 + 1.35548i 0.493362 + 0.109228i
155155 0 0
156156 2.10308 4.51683i 0.168381 0.361635i
157157 −9.01395 + 9.01395i −0.719392 + 0.719392i −0.968481 0.249089i 0.919869π-0.919869\pi
0.249089 + 0.968481i 0.419869π0.419869\pi
158158 −12.0972 18.9769i −0.962405 1.50972i
159159 3.71400 0.294540
160160 0 0
161161 −1.31695 −0.103790
162162 0.760198 + 1.19252i 0.0597268 + 0.0936931i
163163 13.0849 13.0849i 1.02489 1.02489i 0.0252033 0.999682i 0.491977π-0.491977\pi
0.999682 0.0252033i 0.00802331π-0.00802331\pi
164164 −4.66261 + 10.0140i −0.364088 + 0.781958i
165165 0 0
166166 −15.5371 3.43982i −1.20591 0.266982i
167167 11.3334 + 11.3334i 0.877008 + 0.877008i 0.993224 0.116216i 0.0370765π-0.0370765\pi
−0.116216 + 0.993224i 0.537076π0.537076\pi
168168 −2.42438 + 0.321293i −0.187045 + 0.0247883i
169169 6.79383i 0.522603i
170170 0 0
171171 1.22279i 0.0935088i
172172 −6.01224 16.4891i −0.458429 1.25728i
173173 −7.96772 7.96772i −0.605775 0.605775i 0.336064 0.941839i 0.390904π-0.390904\pi
−0.941839 + 0.336064i 0.890904π0.890904\pi
174174 0.264318 1.19388i 0.0200379 0.0905076i
175175 0 0
176176 −15.6987 + 13.2034i −1.18333 + 0.995244i
177177 −0.373802 + 0.373802i −0.0280967 + 0.0280967i
178178 8.64861 5.51325i 0.648241 0.413236i
179179 −12.6475 −0.945320 −0.472660 0.881245i 0.656706π-0.656706\pi
−0.472660 + 0.881245i 0.656706π0.656706\pi
180180 0 0
181181 7.72928 0.574513 0.287256 0.957854i 0.407257π-0.407257\pi
0.287256 + 0.957854i 0.407257π0.407257\pi
182182 2.56869 1.63747i 0.190404 0.121378i
183183 3.52258 3.52258i 0.260396 0.260396i
184184 2.61962 3.42003i 0.193121 0.252128i
185185 0 0
186186 2.38776 10.7851i 0.175079 0.790800i
187187 −19.2901 19.2901i −1.41063 1.41063i
188188 6.11123 2.22827i 0.445707 0.162513i
189189 0.864641i 0.0628934i
190190 0 0
191191 7.04516i 0.509770i −0.966971 0.254885i 0.917962π-0.917962\pi
0.966971 0.254885i 0.0820376π-0.0820376\pi
192192 3.98810 6.93506i 0.287816 0.500495i
193193 11.5048 + 11.5048i 0.828133 + 0.828133i 0.987258 0.159125i 0.0508674π-0.0508674\pi
−0.159125 + 0.987258i 0.550867π0.550867\pi
194194 1.55013 + 0.343190i 0.111293 + 0.0246396i
195195 0 0
196196 11.3362 + 5.27827i 0.809730 + 0.377019i
197197 −7.87859 + 7.87859i −0.561327 + 0.561327i −0.929684 0.368358i 0.879920π-0.879920\pi
0.368358 + 0.929684i 0.379920π0.379920\pi
198198 3.89846 + 6.11549i 0.277051 + 0.434609i
199199 −11.4792 −0.813741 −0.406870 0.913486i 0.633380π-0.633380\pi
−0.406870 + 0.913486i 0.633380π0.633380\pi
200200 0 0
201201 8.77551 0.618977
202202 7.69095 + 12.0648i 0.541133 + 0.848873i
203203 0.528636 0.528636i 0.0371030 0.0371030i
204204 9.64504 + 4.49084i 0.675288 + 0.314422i
205205 0 0
206206 7.46460 + 1.65262i 0.520083 + 0.115143i
207207 −1.07700 1.07700i −0.0748570 0.0748570i
208208 −0.857132 + 9.92794i −0.0594314 + 0.688379i
209209 6.27072i 0.433755i
210210 0 0
211211 5.49134i 0.378039i −0.981973 0.189020i 0.939469π-0.939469\pi
0.981973 0.189020i 0.0605310π-0.0605310\pi
212212 −6.97859 + 2.54452i −0.479292 + 0.174759i
213213 5.72928 + 5.72928i 0.392564 + 0.392564i
214214 −2.38255 + 10.7616i −0.162868 + 0.735645i
215215 0 0
216216 −2.24542 1.71991i −0.152781 0.117025i
217217 4.77551 4.77551i 0.324183 0.324183i
218218 8.72559 5.56233i 0.590972 0.376728i
219219 3.18537 0.215247
220220 0 0
221221 −13.2524 −0.891453
222222 −2.97082 + 1.89382i −0.199389 + 0.127105i
223223 −10.8678 + 10.8678i −0.727764 + 0.727764i −0.970174 0.242410i 0.922062π-0.922062\pi
0.242410 + 0.970174i 0.422062π0.422062\pi
224224 4.33526 2.26469i 0.289662 0.151316i
225225 0 0
226226 0.220121 0.994247i 0.0146422 0.0661363i
227227 4.98244 + 4.98244i 0.330696 + 0.330696i 0.852851 0.522155i 0.174872π-0.174872\pi
−0.522155 + 0.852851i 0.674872π0.674872\pi
228228 −0.837751 2.29761i −0.0554814 0.152163i
229229 25.7572i 1.70208i 0.525098 + 0.851041i 0.324028π0.324028\pi
−0.525098 + 0.851041i 0.675972π0.675972\pi
230230 0 0
231231 4.43407i 0.291740i
232232 0.321293 + 2.42438i 0.0210939 + 0.159168i
233233 0.715328 + 0.715328i 0.0468627 + 0.0468627i 0.730150 0.683287i 0.239450π-0.239450\pi
−0.683287 + 0.730150i 0.739450π0.739450\pi
234234 3.43982 + 0.761557i 0.224868 + 0.0497846i
235235 0 0
236236 0.446274 0.958469i 0.0290499 0.0623910i
237237 11.2524 11.2524i 0.730922 0.730922i
238238 3.49659 + 5.48509i 0.226650 + 0.355545i
239239 26.9354 1.74231 0.871154 0.491009i 0.163372π-0.163372\pi
0.871154 + 0.491009i 0.163372π0.163372\pi
240240 0 0
241241 14.0925 0.907775 0.453887 0.891059i 0.350037π-0.350037\pi
0.453887 + 0.891059i 0.350037π0.350037\pi
242242 11.6300 + 18.2439i 0.747603 + 1.17276i
243243 −0.707107 + 0.707107i −0.0453609 + 0.0453609i
244244 −4.20553 + 9.03228i −0.269231 + 0.578232i
245245 0 0
246246 −7.62620 1.68840i −0.486229 0.107648i
247247 2.15401 + 2.15401i 0.137056 + 0.137056i
248248 2.90245 + 21.9010i 0.184306 + 1.39071i
249249 11.2524i 0.713092i
250250 0 0
251251 17.2471i 1.08863i 0.838882 + 0.544314i 0.183210π0.183210\pi
−0.838882 + 0.544314i 0.816790π0.816790\pi
252252 −0.592379 1.62465i −0.0373164 0.102344i
253253 −5.52311 5.52311i −0.347235 0.347235i
254254 3.23853 14.6279i 0.203203 0.917834i
255255 0 0
256256 −2.74229 + 15.7632i −0.171393 + 0.985203i
257257 15.0140 15.0140i 0.936545 0.936545i −0.0615588 0.998103i 0.519607π-0.519607\pi
0.998103 + 0.0615588i 0.0196072π0.0196072\pi
258258 10.4650 6.67112i 0.651520 0.415326i
259259 −2.15401 −0.133844
260260 0 0
261261 0.864641 0.0535199
262262 −16.6909 + 10.6400i −1.03117 + 0.657341i
263263 −6.73386 + 6.73386i −0.415228 + 0.415228i −0.883555 0.468327i 0.844857π-0.844857\pi
0.468327 + 0.883555i 0.344857π0.344857\pi
264264 −11.5150 8.82008i −0.708699 0.542838i
265265 0 0
266266 0.323204 1.45986i 0.0198169 0.0895096i
267267 5.12822 + 5.12822i 0.313842 + 0.313842i
268268 −16.4891 + 6.01224i −1.00723 + 0.367256i
269269 25.7047i 1.56724i −0.621238 0.783622i 0.713370π-0.713370\pi
0.621238 0.783622i 0.286630π-0.286630\pi
270270 0 0
271271 0.931222i 0.0565677i −0.999600 0.0282839i 0.990996π-0.990996\pi
0.999600 0.0282839i 0.00900423π-0.00900423\pi
272272 −21.1997 1.83029i −1.28542 0.110977i
273273 1.52311 + 1.52311i 0.0921831 + 0.0921831i
274274 13.6963 + 3.03228i 0.827421 + 0.183186i
275275 0 0
276276 2.76156 + 1.28581i 0.166226 + 0.0773968i
277277 22.0602 22.0602i 1.32547 1.32547i 0.416190 0.909277i 0.363365π-0.363365\pi
0.909277 0.416190i 0.136635π-0.136635\pi
278278 1.73330 + 2.71901i 0.103956 + 0.163075i
279279 7.81086 0.467624
280280 0 0
281281 8.56934 0.511204 0.255602 0.966782i 0.417726π-0.417726\pi
0.255602 + 0.966782i 0.417726π0.417726\pi
282282 2.47246 + 3.87854i 0.147233 + 0.230964i
283283 11.5705 11.5705i 0.687796 0.687796i −0.273949 0.961744i 0.588330π-0.588330\pi
0.961744 + 0.273949i 0.0883299π0.0883299\pi
284284 −14.6905 6.84006i −0.871721 0.405883i
285285 0 0
286286 17.6402 + 3.90543i 1.04308 + 0.230933i
287287 −3.37680 3.37680i −0.199326 0.199326i
288288 5.39747 + 1.69333i 0.318049 + 0.0997803i
289289 11.2986i 0.664625i
290290 0 0
291291 1.12265i 0.0658108i
292292 −5.98529 + 2.18235i −0.350262 + 0.127712i
293293 −12.8969 12.8969i −0.753446 0.753446i 0.221675 0.975121i 0.428848π-0.428848\pi
−0.975121 + 0.221675i 0.928848π0.928848\pi
294294 −1.91134 + 8.63317i −0.111471 + 0.503497i
295295 0 0
296296 4.28467 5.59383i 0.249041 0.325135i
297297 −3.62620 + 3.62620i −0.210413 + 0.210413i
298298 −12.0648 + 7.69095i −0.698892 + 0.445525i
299299 −3.79441 −0.219436
300300 0 0
301301 7.58767 0.437346
302302 9.46491 6.03362i 0.544644 0.347196i
303303 −7.15383 + 7.15383i −0.410977 + 0.410977i
304304 3.14826 + 3.74324i 0.180565 + 0.214689i
305305 0 0
306306 −1.62620 + 7.34525i −0.0929636 + 0.419900i
307307 1.60564 + 1.60564i 0.0916387 + 0.0916387i 0.751440 0.659801i 0.229360π-0.229360\pi
−0.659801 + 0.751440i 0.729360π0.729360\pi
308308 −3.03785 8.33158i −0.173098 0.474736i
309309 5.40608i 0.307541i
310310 0 0
311311 19.4161i 1.10099i 0.834839 + 0.550494i 0.185561π0.185561\pi
−0.834839 + 0.550494i 0.814439π0.814439\pi
312312 −6.98516 + 0.925715i −0.395457 + 0.0524083i
313313 −17.7110 17.7110i −1.00108 1.00108i −0.999999 0.00108322i 0.999655π-0.999655\pi
−0.00108322 0.999999i 0.500345π-0.500345\pi
314314 17.6017 + 3.89692i 0.993321 + 0.219916i
315315 0 0
316316 −13.4340 + 28.8524i −0.755721 + 1.62307i
317317 7.78946 7.78946i 0.437500 0.437500i −0.453670 0.891170i 0.649885π-0.649885\pi
0.891170 + 0.453670i 0.149885π0.149885\pi
318318 −2.82338 4.42902i −0.158327 0.248367i
319319 4.43407 0.248260
320320 0 0
321321 −7.79383 −0.435009
322322 1.00114 + 1.57048i 0.0557914 + 0.0875196i
323323 −4.59958 + 4.59958i −0.255928 + 0.255928i
324324 0.844199 1.81310i 0.0468999 0.100728i
325325 0 0
326326 −25.5510 5.65685i −1.41514 0.313304i
327327 5.17386 + 5.17386i 0.286115 + 0.286115i
328328 15.4863 2.05234i 0.855089 0.113322i
329329 2.81215i 0.155039i
330330 0 0
331331 31.7005i 1.74242i −0.490912 0.871209i 0.663336π-0.663336\pi
0.490912 0.871209i 0.336664π-0.336664\pi
332332 7.70919 + 21.1432i 0.423097 + 1.16038i
333333 −1.76156 1.76156i −0.0965327 0.0965327i
334334 4.89968 22.1310i 0.268098 1.21095i
335335 0 0
336336 2.22615 + 2.64687i 0.121447 + 0.144398i
337337 −18.9634 + 18.9634i −1.03300 + 1.03300i −0.0335632 + 0.999437i 0.510686π0.510686\pi
−0.999437 + 0.0335632i 0.989314π0.989314\pi
338338 −8.10177 + 5.16466i −0.440678 + 0.280920i
339339 0.720062 0.0391084
340340 0 0
341341 40.0558 2.16914
342342 1.45820 0.929560i 0.0788502 0.0502648i
343343 −8.10243 + 8.10243i −0.437490 + 0.437490i
344344 −15.0931 + 19.7047i −0.813765 + 1.06241i
345345 0 0
346346 −3.44461 + 15.5587i −0.185183 + 0.836441i
347347 −7.71957 7.71957i −0.414408 0.414408i 0.468863 0.883271i 0.344664π-0.344664\pi
−0.883271 + 0.468863i 0.844664π0.844664\pi
348348 −1.62465 + 0.592379i −0.0870906 + 0.0317549i
349349 27.0741i 1.44925i −0.689146 0.724623i 0.742014π-0.742014\pi
0.689146 0.724623i 0.257986π-0.257986\pi
350350 0 0
351351 2.49122i 0.132971i
352352 27.6794 + 8.68375i 1.47532 + 0.462846i
353353 9.96772 + 9.96772i 0.530528 + 0.530528i 0.920730 0.390201i 0.127595π-0.127595\pi
−0.390201 + 0.920730i 0.627595π0.627595\pi
354354 0.729929 + 0.161602i 0.0387953 + 0.00858906i
355355 0 0
356356 −13.1493 6.12247i −0.696912 0.324490i
357357 −3.25240 + 3.25240i −0.172135 + 0.172135i
358358 9.61461 + 15.0824i 0.508148 + 0.797129i
359359 −14.2334 −0.751211 −0.375606 0.926780i 0.622565π-0.622565\pi
−0.375606 + 0.926780i 0.622565π0.622565\pi
360360 0 0
361361 −17.5048 −0.921305
362362 −5.87578 9.21731i −0.308824 0.484451i
363363 −10.8178 + 10.8178i −0.567785 + 0.567785i
364364 −3.90543 1.81841i −0.204700 0.0953107i
365365 0 0
366366 −6.87859 1.52288i −0.359550 0.0796023i
367367 2.89145 + 2.89145i 0.150933 + 0.150933i 0.778534 0.627602i 0.215963π-0.215963\pi
−0.627602 + 0.778534i 0.715963π0.715963\pi
368368 −6.06988 0.524045i −0.316414 0.0273177i
369369 5.52311i 0.287522i
370370 0 0
371371 3.21128i 0.166721i
372372 −14.6766 + 5.35135i −0.760944 + 0.277454i
373373 11.2847 + 11.2847i 0.584298 + 0.584298i 0.936081 0.351783i 0.114425π-0.114425\pi
−0.351783 + 0.936081i 0.614425π0.614425\pi
374374 −8.33950 + 37.6681i −0.431225 + 1.94777i
375375 0 0
376376 −7.30299 5.59383i −0.376623 0.288480i
377377 1.52311 1.52311i 0.0784444 0.0784444i
378378 1.03110 0.657298i 0.0530341 0.0338078i
379379 −15.4562 −0.793932 −0.396966 0.917833i 0.629937π-0.629937\pi
−0.396966 + 0.917833i 0.629937π0.629937\pi
380380 0 0
381381 10.5939 0.542743
382382 −8.40148 + 5.35571i −0.429857 + 0.274022i
383383 12.5562 12.5562i 0.641593 0.641593i −0.309354 0.950947i 0.600113π-0.600113\pi
0.950947 + 0.309354i 0.100113π0.100113\pi
384384 −11.3019 + 0.516138i −0.576749 + 0.0263390i
385385 0 0
386386 4.97376 22.4656i 0.253158 1.14347i
387387 6.20522 + 6.20522i 0.315429 + 0.315429i
388388 −0.769144 2.10945i −0.0390474 0.107091i
389389 5.16327i 0.261788i 0.991396 + 0.130894i 0.0417848π0.0417848\pi
−0.991396 + 0.130894i 0.958215π0.958215\pi
390390 0 0
391391 8.10243i 0.409757i
392392 −2.32333 17.5312i −0.117346 0.885458i
393393 −9.89692 9.89692i −0.499233 0.499233i
394394 15.3847 + 3.40608i 0.775068 + 0.171596i
395395 0 0
396396 4.32924 9.29797i 0.217552 0.467240i
397397 3.46293 3.46293i 0.173800 0.173800i −0.614847 0.788646i 0.710782π-0.710782\pi
0.788646 + 0.614847i 0.210782π0.210782\pi
398398 8.72648 + 13.6892i 0.437419 + 0.686177i
399399 1.05727 0.0529298
400400 0 0
401401 3.49521 0.174542 0.0872712 0.996185i 0.472185π-0.472185\pi
0.0872712 + 0.996185i 0.472185π0.472185\pi
402402 −6.67112 10.4650i −0.332725 0.521945i
403403 13.7593 13.7593i 0.685399 0.685399i
404404 8.54079 18.3432i 0.424920 0.912608i
405405 0 0
406406 −1.03228 0.228540i −0.0512310 0.0113423i
407407 −9.03365 9.03365i −0.447781 0.447781i
408408 −1.97673 14.9158i −0.0978629 0.738443i
409409 14.8034i 0.731982i 0.930618 + 0.365991i 0.119270π0.119270\pi
−0.930618 + 0.365991i 0.880730π0.880730\pi
410410 0 0
411411 9.91923i 0.489279i
412412 −3.70379 10.1580i −0.182473 0.500448i
413413 0.323204 + 0.323204i 0.0159039 + 0.0159039i
414414 −0.465611 + 2.10308i −0.0228835 + 0.103361i
415415 0 0
416416 12.4908 6.52505i 0.612414 0.319917i
417417 −1.61224 + 1.61224i −0.0789520 + 0.0789520i
418418 7.47795 4.76699i 0.365758 0.233161i
419419 19.0701 0.931634 0.465817 0.884881i 0.345760π-0.345760\pi
0.465817 + 0.884881i 0.345760π0.345760\pi
420420 0 0
421421 −20.8034 −1.01390 −0.506948 0.861976i 0.669226π-0.669226\pi
−0.506948 + 0.861976i 0.669226π0.669226\pi
422422 −6.54852 + 4.17450i −0.318777 + 0.203212i
423423 −2.29979 + 2.29979i −0.111820 + 0.111820i
424424 8.33950 + 6.38776i 0.405002 + 0.310217i
425425 0 0
426426 2.47689 11.1877i 0.120006 0.542044i
427427 −3.04577 3.04577i −0.147395 0.147395i
428428 14.6446 5.33968i 0.707872 0.258103i
429429 12.7755i 0.616807i
430430 0 0
431431 15.3302i 0.738428i 0.929344 + 0.369214i 0.120373π0.120373\pi
−0.929344 + 0.369214i 0.879627π0.879627\pi
432432 −0.344061 + 3.98518i −0.0165537 + 0.191737i
433433 −16.2803 16.2803i −0.782381 0.782381i 0.197851 0.980232i 0.436604π-0.436604\pi
−0.980232 + 0.197851i 0.936604π0.936604\pi
434434 −9.32521 2.06455i −0.447625 0.0991016i
435435 0 0
436436 −13.2663 6.17696i −0.635343 0.295823i
437437 −1.31695 + 1.31695i −0.0629981 + 0.0629981i
438438 −2.42151 3.79861i −0.115704 0.181505i
439439 −24.6554 −1.17674 −0.588368 0.808593i 0.700230π-0.700230\pi
−0.588368 + 0.808593i 0.700230π0.700230\pi
440440 0 0
441441 −6.25240 −0.297733
442442 10.0744 + 15.8037i 0.479192 + 0.751706i
443443 1.77116 1.77116i 0.0841501 0.0841501i −0.663779 0.747929i 0.731048π-0.731048\pi
0.747929 + 0.663779i 0.231048π0.231048\pi
444444 4.51683 + 2.10308i 0.214359 + 0.0998079i
445445 0 0
446446 21.2218 + 4.69839i 1.00488 + 0.222475i
447447 −7.15383 7.15383i −0.338364 0.338364i
448448 −5.99634 3.44827i −0.283300 0.162916i
449449 33.1512i 1.56450i 0.622963 + 0.782251i 0.285929π0.285929\pi
−0.622963 + 0.782251i 0.714071π0.714071\pi
450450 0 0
451451 28.3237i 1.33371i
452452 −1.35299 + 0.493326i −0.0636394 + 0.0232041i
453453 5.61224 + 5.61224i 0.263686 + 0.263686i
454454 2.15401 9.72928i 0.101093 0.456618i
455455 0 0
456456 −2.10308 + 2.74567i −0.0984859 + 0.128578i
457457 7.50479 7.50479i 0.351059 0.351059i −0.509444 0.860504i 0.670149π-0.670149\pi
0.860504 + 0.509444i 0.170149π0.170149\pi
458458 30.7159 19.5806i 1.43526 0.914939i
459459 −5.31965 −0.248300
460460 0 0
461461 −27.0216 −1.25852 −0.629262 0.777193i 0.716643π-0.716643\pi
−0.629262 + 0.777193i 0.716643π0.716643\pi
462462 5.28771 3.37077i 0.246006 0.156822i
463463 27.7123 27.7123i 1.28790 1.28790i 0.351843 0.936059i 0.385555π-0.385555\pi
0.936059 0.351843i 0.114445π-0.114445\pi
464464 2.64687 2.22615i 0.122878 0.103347i
465465 0 0
466466 0.309251 1.39683i 0.0143258 0.0647070i
467467 −2.00823 2.00823i −0.0929296 0.0929296i 0.659114 0.752043i 0.270932π-0.270932\pi
−0.752043 + 0.659114i 0.770932π0.770932\pi
468468 −1.70677 4.68098i −0.0788956 0.216378i
469469 7.58767i 0.350366i
470470 0 0
471471 12.7477i 0.587381i
472472 −1.48225 + 0.196436i −0.0682260 + 0.00904172i
473473 31.8217 + 31.8217i 1.46317 + 1.46317i
474474 −21.9727 4.86464i −1.00924 0.223440i
475475 0 0
476476 3.88296 8.33950i 0.177975 0.382240i
477477 2.62620 2.62620i 0.120245 0.120245i
478478 −20.4763 32.1210i −0.936562 1.46918i
479479 13.7593 0.628678 0.314339 0.949311i 0.398217π-0.398217\pi
0.314339 + 0.949311i 0.398217π0.398217\pi
480480 0 0
481481 −6.20617 −0.282977
482482 −10.7131 16.8055i −0.487966 0.765470i
483483 −0.931222 + 0.931222i −0.0423721 + 0.0423721i
484484 12.9151 27.7379i 0.587049 1.26081i
485485 0 0
486486 1.38078 + 0.305697i 0.0626334 + 0.0138667i
487487 −24.3355 24.3355i −1.10275 1.10275i −0.994078 0.108671i 0.965340π-0.965340\pi
−0.108671 0.994078i 0.534660π-0.534660\pi
488488 13.9682 1.85115i 0.632310 0.0837975i
489489 18.5048i 0.836816i
490490 0 0
491491 28.8918i 1.30387i −0.758275 0.651935i 0.773957π-0.773957\pi
0.758275 0.651935i 0.226043π-0.226043\pi
492492 3.78397 + 10.3779i 0.170595 + 0.467872i
493493 3.25240 + 3.25240i 0.146481 + 0.146481i
494494 0.931222 4.20617i 0.0418977 0.189244i
495495 0 0
496496 23.9109 20.1103i 1.07363 0.902979i
497497 4.95377 4.95377i 0.222207 0.222207i
498498 −13.4187 + 8.55405i −0.601306 + 0.383316i
499499 12.5365 0.561211 0.280605 0.959823i 0.409465π-0.409465\pi
0.280605 + 0.959823i 0.409465π0.409465\pi
500500 0 0
501501 16.0279 0.716074
502502 20.5675 13.1112i 0.917972 0.585182i
503503 −9.01392 + 9.01392i −0.401911 + 0.401911i −0.878906 0.476995i 0.841726π-0.841726\pi
0.476995 + 0.878906i 0.341726π0.341726\pi
504504 −1.48710 + 1.94148i −0.0662409 + 0.0864805i
505505 0 0
506506 −2.38776 + 10.7851i −0.106149 + 0.479455i
507507 −4.80397 4.80397i −0.213352 0.213352i
508508 −19.9059 + 7.25806i −0.883182 + 0.322025i
509509 22.5448i 0.999279i 0.866233 + 0.499640i 0.166534π0.166534\pi
−0.866233 + 0.499640i 0.833466π0.833466\pi
510510 0 0
511511 2.75420i 0.121839i
512512 20.8826 8.71295i 0.922891 0.385062i
513513 0.864641 + 0.864641i 0.0381748 + 0.0381748i
514514 −29.3180 6.49084i −1.29316 0.286299i
515515 0 0
516516 −15.9109 7.40828i −0.700437 0.326131i
517517 −11.7938 + 11.7938i −0.518692 + 0.518692i
518518 1.63747 + 2.56869i 0.0719464 + 0.112862i
519519 −11.2681 −0.494613
520520 0 0
521521 −18.9046 −0.828226 −0.414113 0.910225i 0.635908π-0.635908\pi
−0.414113 + 0.910225i 0.635908π0.635908\pi
522522 −0.657298 1.03110i −0.0287692 0.0451300i
523523 −21.8269 + 21.8269i −0.954426 + 0.954426i −0.999006 0.0445800i 0.985805π-0.985805\pi
0.0445800 + 0.999006i 0.485805π0.485805\pi
524524 25.3768 + 11.8157i 1.10859 + 0.516172i
525525 0 0
526526 13.1493 + 2.91118i 0.573337 + 0.126934i
527527 29.3810 + 29.3810i 1.27986 + 1.27986i
528528 −1.76442 + 20.4368i −0.0767866 + 0.889400i
529529 20.6801i 0.899136i
530530 0 0
531531 0.528636i 0.0229408i
532532 −1.98661 + 0.724353i −0.0861303 + 0.0314047i
533533 −9.72928 9.72928i −0.421422 0.421422i
534534 2.21703 10.0140i 0.0959404 0.433346i
535535 0 0
536536 19.7047 + 15.0931i 0.851114 + 0.651922i
537537 −8.94315 + 8.94315i −0.385925 + 0.385925i
538538 −30.6533 + 19.5407i −1.32156 + 0.842457i
539539 −32.0637 −1.38108
540540 0 0
541541 7.85838 0.337858 0.168929 0.985628i 0.445969π-0.445969\pi
0.168929 + 0.985628i 0.445969π0.445969\pi
542542 −1.11050 + 0.707913i −0.0477000 + 0.0304075i
543543 5.46543 5.46543i 0.234544 0.234544i
544544 13.9333 + 26.6724i 0.597387 + 1.14357i
545545 0 0
546546 0.658473 2.97421i 0.0281801 0.127284i
547547 17.8105 + 17.8105i 0.761522 + 0.761522i 0.976597 0.215076i 0.0689998π-0.0689998\pi
−0.215076 + 0.976597i 0.569000π0.569000\pi
548548 −6.79582 18.6382i −0.290303 0.796183i
549549 4.98168i 0.212613i
550550 0 0
551551 1.05727i 0.0450413i
552552 −0.565976 4.27068i −0.0240895 0.181772i
553553 −9.72928 9.72928i −0.413731 0.413731i
554554 −43.0773 9.53707i −1.83018 0.405191i
555555 0 0
556556 1.92482 4.13397i 0.0816307 0.175319i
557557 −23.3372 + 23.3372i −0.988827 + 0.988827i −0.999938 0.0111112i 0.996463π-0.996463\pi
0.0111112 + 0.999938i 0.496463π0.496463\pi
558558 −5.93780 9.31460i −0.251367 0.394318i
559559 21.8617 0.924652
560560 0 0
561561 −27.2803 −1.15178
562562 −6.51439 10.2191i −0.274793 0.431067i
563563 −5.27400 + 5.27400i −0.222273 + 0.222273i −0.809455 0.587182i 0.800237π-0.800237\pi
0.587182 + 0.809455i 0.300237π0.300237\pi
564564 2.74567 5.89692i 0.115614 0.248305i
565565 0 0
566566 −22.5939 5.00217i −0.949693 0.210257i
567567 0.611393 + 0.611393i 0.0256761 + 0.0256761i
568568 3.01079 + 22.7185i 0.126330 + 0.953247i
569569 28.5606i 1.19732i −0.801002 0.598661i 0.795699π-0.795699\pi
0.801002 0.598661i 0.204301π-0.204301\pi
570570 0 0
571571 32.2837i 1.35103i 0.737347 + 0.675515i 0.236078π0.236078\pi
−0.737347 + 0.675515i 0.763922π0.763922\pi
572572 −8.75270 24.0051i −0.365969 1.00370i
573573 −4.98168 4.98168i −0.208113 0.208113i
574574 −1.45986 + 6.59392i −0.0609333 + 0.275225i
575575 0 0
576576 −2.08382 7.72384i −0.0868257 0.321827i
577577 −27.0279 + 27.0279i −1.12519 + 1.12519i −0.134237 + 0.990949i 0.542858π0.542858\pi
−0.990949 + 0.134237i 0.957142π0.957142\pi
578578 −13.4738 + 8.58919i −0.560437 + 0.357263i
579579 16.2702 0.676168
580580 0 0
581581 −9.72928 −0.403639
582582 1.33878 0.853435i 0.0554942 0.0353760i
583583 13.4677 13.4677i 0.557776 0.557776i
584584 7.15249 + 5.47855i 0.295972 + 0.226704i
585585 0 0
586586 −5.57560 + 25.1840i −0.230326 + 1.04034i
587587 17.1558 + 17.1558i 0.708096 + 0.708096i 0.966135 0.258039i 0.0830761π-0.0830761\pi
−0.258039 + 0.966135i 0.583076π0.583076\pi
588588 11.7482 4.28362i 0.484488 0.176653i
589589 9.55102i 0.393543i
590590 0 0
591591 11.1420i 0.458321i
592592 −9.92794 0.857132i −0.408036 0.0352279i
593593 21.5833 + 21.5833i 0.886320 + 0.886320i 0.994167 0.107848i 0.0343959π-0.0343959\pi
−0.107848 + 0.994167i 0.534396π0.534396\pi
594594 7.08093 + 1.56768i 0.290534 + 0.0643227i
595595 0 0
596596 18.3432 + 8.54079i 0.751366 + 0.349844i
597597 −8.11704 + 8.11704i −0.332208 + 0.332208i
598598 2.88450 + 4.52490i 0.117956 + 0.185037i
599599 23.7636 0.970955 0.485478 0.874249i 0.338646π-0.338646\pi
0.485478 + 0.874249i 0.338646π0.338646\pi
600600 0 0
601601 22.1695 0.904314 0.452157 0.891938i 0.350655π-0.350655\pi
0.452157 + 0.891938i 0.350655π0.350655\pi
602602 −5.76813 9.04843i −0.235091 0.368786i
603603 6.20522 6.20522i 0.252696 0.252696i
604604 −14.3904 6.70033i −0.585537 0.272633i
605605 0 0
606606 13.9694 + 3.09275i 0.567468 + 0.125634i
607607 9.35348 + 9.35348i 0.379646 + 0.379646i 0.870974 0.491328i 0.163489π-0.163489\pi
−0.491328 + 0.870974i 0.663489π0.663489\pi
608608 2.07058 6.59995i 0.0839731 0.267663i
609609 0.747604i 0.0302944i
610610 0 0
611611 8.10243i 0.327789i
612612 9.99558 3.64457i 0.404047 0.147323i
613613 24.1247 + 24.1247i 0.974389 + 0.974389i 0.999680 0.0252913i 0.00805134π-0.00805134\pi
−0.0252913 + 0.999680i 0.508051π0.508051\pi
614614 0.694151 3.13536i 0.0280137 0.126533i
615615 0 0
616616 −7.62620 + 9.95634i −0.307268 + 0.401152i
617617 −3.82611 + 3.82611i −0.154033 + 0.154033i −0.779917 0.625883i 0.784739π-0.784739\pi
0.625883 + 0.779917i 0.284739π0.284739\pi
618618 6.44685 4.10969i 0.259330 0.165316i
619619 −30.1297 −1.21101 −0.605507 0.795840i 0.707029π-0.707029\pi
−0.605507 + 0.795840i 0.707029π0.707029\pi
620620 0 0
621621 −1.52311 −0.0611205
622622 23.1541 14.7601i 0.928395 0.591826i
623623 4.43407 4.43407i 0.177647 0.177647i
624624 6.41403 + 7.62620i 0.256767 + 0.305292i
625625 0 0
626626 −7.65681 + 34.5845i −0.306028 + 1.38227i
627627 4.43407 + 4.43407i 0.177080 + 0.177080i
628628 −8.73362 23.9528i −0.348509 0.955819i
629629 13.2524i 0.528408i
630630 0 0
631631 21.5701i 0.858694i 0.903140 + 0.429347i 0.141256π0.141256\pi
−0.903140 + 0.429347i 0.858744π0.858744\pi
632632 44.6195 5.91324i 1.77487 0.235216i
633633 −3.88296 3.88296i −0.154334 0.154334i
634634 −15.2106 3.36754i −0.604090 0.133742i
635635 0 0
636636 −3.13536 + 6.73386i −0.124325 + 0.267015i
637637 −11.0140 + 11.0140i −0.436389 + 0.436389i
638638 −3.37077 5.28771i −0.133450 0.209342i
639639 8.10243 0.320527
640640 0 0
641641 48.3911 1.91133 0.955666 0.294452i 0.0951370π-0.0951370\pi
0.955666 + 0.294452i 0.0951370π0.0951370\pi
642642 5.92485 + 9.29429i 0.233835 + 0.366816i
643643 −23.3413 + 23.3413i −0.920491 + 0.920491i −0.997064 0.0765729i 0.975602π-0.975602\pi
0.0765729 + 0.997064i 0.475602π0.475602\pi
644644 1.11177 2.38776i 0.0438097 0.0940907i
645645 0 0
646646 8.98168 + 1.98849i 0.353379 + 0.0782362i
647647 −32.4465 32.4465i −1.27560 1.27560i −0.943103 0.332501i 0.892108π-0.892108\pi
−0.332501 0.943103i 0.607892π-0.607892\pi
648648 −2.80391 + 0.371591i −0.110148 + 0.0145975i
649649 2.71096i 0.106414i
650650 0 0
651651 6.75359i 0.264694i
652652 12.6779 + 34.7704i 0.496506 + 1.36171i
653653 −18.4725 18.4725i −0.722885 0.722885i 0.246307 0.969192i 0.420783π-0.420783\pi
−0.969192 + 0.246307i 0.920783π0.920783\pi
654654 2.23677 10.1031i 0.0874645 0.395062i
655655 0 0
656656 −14.2201 16.9075i −0.555202 0.660128i
657657 2.25240 2.25240i 0.0878743 0.0878743i
658658 3.35355 2.13779i 0.130735 0.0833399i
659659 47.5028 1.85045 0.925223 0.379423i 0.123878π-0.123878\pi
0.925223 + 0.379423i 0.123878π0.123878\pi
660660 0 0
661661 −46.1204 −1.79387 −0.896937 0.442158i 0.854213π-0.854213\pi
−0.896937 + 0.442158i 0.854213π0.854213\pi
662662 −37.8035 + 24.0987i −1.46927 + 0.936621i
663663 −9.37086 + 9.37086i −0.363934 + 0.363934i
664664 19.3531 25.2663i 0.751046 0.980525i
665665 0 0
666666 −0.761557 + 3.43982i −0.0295097 + 0.133290i
667667 0.931222 + 0.931222i 0.0360571 + 0.0360571i
668668 −30.1163 + 10.9810i −1.16524 + 0.424867i
669669 15.3694i 0.594217i
670670 0 0
671671 25.5471i 0.986236i
672672 1.46412 4.66687i 0.0564797 0.180028i
673673 −3.60599 3.60599i −0.139001 0.139001i 0.634183 0.773183i 0.281337π-0.281337\pi
−0.773183 + 0.634183i 0.781337π0.781337\pi
674674 37.0300 + 8.19825i 1.42634 + 0.315785i
675675 0 0
676676 12.3179 + 5.73535i 0.473765 + 0.220590i
677677 8.26635 8.26635i 0.317702 0.317702i −0.530182 0.847884i 0.677876π-0.677876\pi
0.847884 + 0.530182i 0.177876π0.177876\pi
678678 −0.547390 0.858688i −0.0210224 0.0329777i
679679 0.970688 0.0372516
680680 0 0
681681 7.04623 0.270012
682682 −30.4503 47.7673i −1.16600 1.82910i
683683 −8.43079 + 8.43079i −0.322595 + 0.322595i −0.849762 0.527167i 0.823254π-0.823254\pi
0.527167 + 0.849762i 0.323254π0.323254\pi
684684 −2.21703 1.03228i −0.0847704 0.0394700i
685685 0 0
686686 15.8217 + 3.50285i 0.604077 + 0.133739i
687687 18.2131 + 18.2131i 0.694872 + 0.694872i
688688 34.9719 + 3.01932i 1.33329 + 0.115110i
689689 9.25240i 0.352488i
690690 0 0
691691 21.9182i 0.833809i 0.908950 + 0.416905i 0.136885π0.136885\pi
−0.908950 + 0.416905i 0.863115π0.863115\pi
692692 21.1726 7.71993i 0.804862 0.293468i
693693 3.13536 + 3.13536i 0.119102 + 0.119102i
694694 −3.33733 + 15.0741i −0.126683 + 0.572206i
695695 0 0
696696 1.94148 + 1.48710i 0.0735917 + 0.0563686i
697697 20.7755 20.7755i 0.786929 0.786929i
698698 −32.2864 + 20.5817i −1.22206 + 0.779029i
699699 1.01163 0.0382633
700700 0 0
701701 −21.8184 −0.824070 −0.412035 0.911168i 0.635182π-0.635182\pi
−0.412035 + 0.911168i 0.635182π0.635182\pi
702702 2.97082 1.89382i 0.112126 0.0714776i
703703 −2.15401 + 2.15401i −0.0812400 + 0.0812400i
704704 −10.6863 39.6095i −0.402754 1.49284i
705705 0 0
706706 4.30925 19.4641i 0.162181 0.732542i
707707 6.18549 + 6.18549i 0.232629 + 0.232629i
708708 −0.362177 0.993303i −0.0136114 0.0373306i
709709 31.7938i 1.19404i 0.802225 + 0.597021i 0.203649π0.203649\pi
−0.802225 + 0.597021i 0.796351π0.796351\pi
710710 0 0
711711 15.9133i 0.596795i
712712 2.69493 + 20.3351i 0.100997 + 0.762089i
713713 8.41233 + 8.41233i 0.315044 + 0.315044i
714714 6.35101 + 1.40608i 0.237680 + 0.0526211i
715715 0 0
716716 10.6770 22.9312i 0.399019 0.856979i
717717 19.0462 19.0462i 0.711294 0.711294i
718718 10.8202 + 16.9736i 0.403807 + 0.633450i
719719 −52.0874 −1.94253 −0.971265 0.237999i 0.923508π-0.923508\pi
−0.971265 + 0.237999i 0.923508π0.923508\pi
720720 0 0
721721 4.67432 0.174081
722722 13.3071 + 20.8748i 0.495239 + 0.776879i
723723 9.96487 9.96487i 0.370598 0.370598i
724724 −6.52505 + 14.0140i −0.242502 + 0.520824i
725725 0 0
726726 21.1240 + 4.67674i 0.783986 + 0.173570i
727727 −8.13069 8.13069i −0.301551 0.301551i 0.540070 0.841620i 0.318398π-0.318398\pi
−0.841620 + 0.540070i 0.818398π0.818398\pi
728728 0.800411 + 6.03965i 0.0296652 + 0.223844i
729729 1.00000i 0.0370370i
730730 0 0
731731 46.6826i 1.72662i
732732 3.41303 + 9.36054i 0.126149 + 0.345976i
733733 29.9956 + 29.9956i 1.10791 + 1.10791i 0.993424 + 0.114489i 0.0365232π0.0365232\pi
0.114489 + 0.993424i 0.463477π0.463477\pi
734734 1.25003 5.64618i 0.0461396 0.208404i
735735 0 0
736736 3.98937 + 7.63682i 0.147050 + 0.281497i
737737 31.8217 31.8217i 1.17217 1.17217i
738738 −6.58641 + 4.19866i −0.242449 + 0.154555i
739739 39.4719 1.45200 0.725999 0.687696i 0.241378π-0.241378\pi
0.725999 + 0.687696i 0.241378π0.241378\pi
740740 0 0
741741 3.04623 0.111906
742742 −3.82951 + 2.44121i −0.140586 + 0.0896196i
743743 12.2252 12.2252i 0.448499 0.448499i −0.446356 0.894855i 0.647279π-0.647279\pi
0.894855 + 0.446356i 0.147279π0.147279\pi
744744 17.5387 + 13.4340i 0.642999 + 0.492514i
745745 0 0
746746 4.87859 22.0358i 0.178618 0.806786i
747747 −7.95665 7.95665i −0.291118 0.291118i
748748 51.2595 18.6902i 1.87423 0.683380i
749749 6.73887i 0.246233i
750750 0 0
751751 28.9069i 1.05483i −0.849609 0.527413i 0.823162π-0.823162\pi
0.849609 0.527413i 0.176838π-0.176838\pi
752752 −1.11902 + 12.9614i −0.0408066 + 0.472652i
753753 12.1955 + 12.1955i 0.444430 + 0.444430i
754754 −2.97421 0.658473i −0.108314 0.0239802i
755755 0 0
756756 −1.56768 0.729929i −0.0570160 0.0265473i
757757 16.2018 16.2018i 0.588864 0.588864i −0.348459 0.937324i 0.613295π-0.613295\pi
0.937324 + 0.348459i 0.113295π0.113295\pi
758758 11.7498 + 18.4318i 0.426771 + 0.669474i
759759 −7.81086 −0.283516
760760 0 0
761761 −6.64641 −0.240932 −0.120466 0.992717i 0.538439π-0.538439\pi
−0.120466 + 0.992717i 0.538439π0.538439\pi
762762 −8.05348 12.6334i −0.291747 0.457661i
763763 4.47353 4.47353i 0.161953 0.161953i
764764 12.7736 + 5.94751i 0.462131 + 0.215173i
765765 0 0
766766 −24.5187 5.42831i −0.885898 0.196133i
767767 0.931222 + 0.931222i 0.0336245 + 0.0336245i
768768 9.20720 + 13.0854i 0.332236 + 0.472178i
769769 29.3449i 1.05820i −0.848559 0.529101i 0.822529π-0.822529\pi
0.848559 0.529101i 0.177471π-0.177471\pi
770770 0 0
771771 21.2329i 0.764686i
772772 −30.5717 + 11.1470i −1.10030 + 0.401189i
773773 −37.5833 37.5833i −1.35178 1.35178i −0.883674 0.468104i 0.844937π-0.844937\pi
−0.468104 0.883674i 0.655063π-0.655063\pi
774774 2.68264 12.1170i 0.0964257 0.435538i
775775 0 0
776776 −1.93086 + 2.52082i −0.0693137 + 0.0904921i
777777 −1.52311 + 1.52311i −0.0546414 + 0.0546414i
778778 6.15729 3.92510i 0.220749 0.140722i
779779 −6.75359 −0.241973
780780 0 0
781781 41.5510 1.48681
782782 −9.66229 + 6.15945i −0.345523 + 0.220261i
783783 0.611393 0.611393i 0.0218494 0.0218494i
784784 −19.1400 + 16.0978i −0.683573 + 0.574920i
785785 0 0
786786 −4.27864 + 19.3259i −0.152614 + 0.689331i
787787 −7.59353 7.59353i −0.270680 0.270680i 0.558694 0.829374i 0.311303π-0.311303\pi
−0.829374 + 0.558694i 0.811303π0.811303\pi
788788 −7.63357 20.9358i −0.271935 0.745806i
789789 9.52311i 0.339032i
790790 0 0
791791 0.622595i 0.0221369i
792792 −14.3791 + 1.90560i −0.510938 + 0.0677126i
793793 −8.77551 8.77551i −0.311628 0.311628i
794794 −6.76212 1.49710i −0.239979 0.0531300i
795795 0 0
796796 9.69075 20.8130i 0.343479 0.737696i
797797 −27.4908 + 27.4908i −0.973775 + 0.973775i −0.999665 0.0258893i 0.991758π-0.991758\pi
0.0258893 + 0.999665i 0.491758π0.491758\pi
798798 −0.803735 1.26082i −0.0284519 0.0446324i
799799 −17.3016 −0.612086
800800 0 0
801801 7.25240 0.256251
802802 −2.65705 4.16810i −0.0938237 0.147181i
803803 11.5508 11.5508i 0.407618 0.407618i
804804 −7.40828 + 15.9109i −0.261270 + 0.561133i
805805 0 0
806806 −26.8680 5.94842i −0.946384 0.209524i
807807 −18.1760 18.1760i −0.639824 0.639824i
808808 −28.3673 + 3.75940i −0.997957 + 0.132255i
809809 47.7205i 1.67776i 0.544313 + 0.838882i 0.316791π0.316791\pi
−0.544313 + 0.838882i 0.683209π0.683209\pi
810810 0 0
811811 37.3179i 1.31041i 0.755451 + 0.655205i 0.227418π0.227418\pi
−0.755451 + 0.655205i 0.772582π0.772582\pi
812812 0.512195 + 1.40474i 0.0179745 + 0.0492968i
813813 −0.658473 0.658473i −0.0230937 0.0230937i
814814 −3.90543 + 17.6402i −0.136885 + 0.618287i
815815 0 0
816816 −16.2847 + 13.6963i −0.570078 + 0.479465i
817817 7.58767 7.58767i 0.265459 0.265459i
818818 17.6533 11.2535i 0.617235 0.393470i
819819 2.15401 0.0752672
820820 0 0
821821 −0.686380 −0.0239548 −0.0119774 0.999928i 0.503813π-0.503813\pi
−0.0119774 + 0.999928i 0.503813π0.503813\pi
822822 11.8289 7.54057i 0.412579 0.263008i
823823 −27.2553 + 27.2553i −0.950059 + 0.950059i −0.998811 0.0487521i 0.984476π-0.984476\pi
0.0487521 + 0.998811i 0.484476π0.484476\pi
824824 −9.29797 + 12.1389i −0.323910 + 0.422879i
825825 0 0
826826 0.139728 0.631126i 0.00486175 0.0219597i
827827 −31.4437 31.4437i −1.09341 1.09341i −0.995162 0.0982432i 0.968678π-0.968678\pi
−0.0982432 0.995162i 0.531322π-0.531322\pi
828828 2.86192 1.04351i 0.0994587 0.0362645i
829829 0.270718i 0.00940243i 0.999989 + 0.00470122i 0.00149645π0.00149645\pi
−0.999989 + 0.00470122i 0.998504π0.998504\pi
830830 0 0
831831 31.1978i 1.08224i
832832 −17.2767 9.93522i −0.598964 0.344442i
833833 −23.5187 23.5187i −0.814876 0.814876i
834834 3.14826 + 0.697006i 0.109015 + 0.0241354i
835835 0 0
836836 −11.3694 5.29373i −0.393220 0.183088i
837837 5.52311 5.52311i 0.190907 0.190907i
838838 −14.4970 22.7414i −0.500792 0.785589i
839839 −31.0214 −1.07098 −0.535489 0.844542i 0.679873π-0.679873\pi
−0.535489 + 0.844542i 0.679873π0.679873\pi
840840 0 0
841841 28.2524 0.974221
842842 15.8147 + 24.8085i 0.545011 + 0.854956i
843843 6.05944 6.05944i 0.208698 0.208698i
844844 9.95634 + 4.63578i 0.342711 + 0.159570i
845845 0 0
846846 4.49084 + 0.994247i 0.154398 + 0.0341829i
847847 9.35348 + 9.35348i 0.321389 + 0.321389i
848848 1.27785 14.8010i 0.0438814 0.508267i
849849 16.3632i 0.561583i
850850 0 0
851851 3.79441i 0.130071i
852852 −15.2244 + 5.55110i −0.521580 + 0.190178i
853853 −3.82611 3.82611i −0.131003 0.131003i 0.638565 0.769568i 0.279528π-0.279528\pi
−0.769568 + 0.638565i 0.779528π0.779528\pi
854854 −1.31675 + 5.94751i −0.0450581 + 0.203520i
855855 0 0
856856 −17.5004 13.4047i −0.598152 0.458163i
857857 −20.7711 + 20.7711i −0.709529 + 0.709529i −0.966436 0.256907i 0.917296π-0.917296\pi
0.256907 + 0.966436i 0.417296π0.417296\pi
858858 15.2350 9.71191i 0.520115 0.331559i
859859 −1.69693 −0.0578985 −0.0289492 0.999581i 0.509216π-0.509216\pi
−0.0289492 + 0.999581i 0.509216π0.509216\pi
860860 0 0
861861 −4.77551 −0.162749
862862 18.2815 11.6540i 0.622670 0.396935i
863863 5.92869 5.92869i 0.201815 0.201815i −0.598962 0.800777i 0.704420π-0.704420\pi
0.800777 + 0.598962i 0.204420π0.204420\pi
864864 5.01395 2.61922i 0.170578 0.0891077i
865865 0 0
866866 −7.03831 + 31.7908i −0.239171 + 1.08030i
867867 −7.98933 7.98933i −0.271332 0.271332i
868868 4.62699 + 12.6900i 0.157050 + 0.430725i
869869 81.6068i 2.76832i
870870 0 0
871871 21.8617i 0.740756i
872872 2.71891 + 20.5161i 0.0920740 + 0.694762i
873873 0.793833 + 0.793833i 0.0268672 + 0.0268672i
874874 2.57162 + 0.569343i 0.0869865 + 0.0192583i
875875 0 0
876876 −2.68909 + 5.77539i −0.0908558 + 0.195132i
877877 10.0323 10.0323i 0.338766 0.338766i −0.517137 0.855903i 0.673002π-0.673002\pi
0.855903 + 0.517137i 0.173002π0.173002\pi
878878 18.7430 + 29.4020i 0.632544 + 0.992269i
879879 −18.2390 −0.615186
880880 0 0
881881 −29.8130 −1.00443 −0.502213 0.864744i 0.667481π-0.667481\pi
−0.502213 + 0.864744i 0.667481π0.667481\pi
882882 4.75306 + 7.45610i 0.160044 + 0.251060i
883883 −5.56557 + 5.56557i −0.187296 + 0.187296i −0.794526 0.607230i 0.792281π-0.792281\pi
0.607230 + 0.794526i 0.292281π0.292281\pi
884884 11.1877 24.0279i 0.376282 0.808146i
885885 0 0
886886 −3.45856 0.765707i −0.116193 0.0257244i
887887 8.59630 + 8.59630i 0.288636 + 0.288636i 0.836541 0.547905i 0.184574π-0.184574\pi
−0.547905 + 0.836541i 0.684574π0.684574\pi
888888 −0.925715 6.98516i −0.0310649 0.234406i
889889 9.15994i 0.307214i
890890 0 0
891891 5.12822i 0.171802i
892892 −10.5298 28.8791i −0.352565 0.966943i
893893 2.81215 + 2.81215i 0.0941052 + 0.0941052i
894894 −3.09275 + 13.9694i −0.103437 + 0.467206i
895895 0 0
896896 0.446274 + 9.77211i 0.0149090 + 0.326463i
897897 −2.68305 + 2.68305i −0.0895845 + 0.0895845i
898898 39.5334 25.2015i 1.31925 0.840984i
899899 −6.75359 −0.225245
900900 0 0
901901 19.7572 0.658207
902902 −33.7766 + 21.5316i −1.12464 + 0.716925i
903903 5.36529 5.36529i 0.178546 0.178546i
904904 1.61684 + 1.23844i 0.0537754 + 0.0411900i
905905 0 0
906906 2.42629 10.9591i 0.0806080 0.364092i
907907 31.6263 + 31.6263i 1.05013 + 1.05013i 0.998675 + 0.0514592i 0.0163872π0.0163872\pi
0.0514592 + 0.998675i 0.483613π0.483613\pi
908908 −13.2398 + 4.82748i −0.439379 + 0.160206i
909909 10.1170i 0.335561i
910910 0 0
911911 42.2656i 1.40032i −0.713985 0.700161i 0.753112π-0.753112\pi
0.713985 0.700161i 0.246888π-0.246888\pi
912912 4.87302 + 0.420714i 0.161362 + 0.0139312i
913913 −40.8034 40.8034i −1.35040 1.35040i
914914 −14.6547 3.24448i −0.484735 0.107318i
915915 0 0
916916 −46.7003 21.7442i −1.54302 0.718448i
917917 −8.55728 + 8.55728i −0.282586 + 0.282586i
918918 4.04398 + 6.34377i 0.133471 + 0.209376i
919919 31.2829 1.03193 0.515964 0.856610i 0.327434π-0.327434\pi
0.515964 + 0.856610i 0.327434π0.327434\pi
920920 0 0
921921 2.27072 0.0748227
922922 20.5418 + 32.2238i 0.676508 + 1.06123i
923923 14.2729 14.2729i 0.469798 0.469798i
924924 −8.03940 3.74324i −0.264477 0.123143i
925925 0 0
926926 −54.1143 11.9806i −1.77831 0.393707i
927927 3.82267 + 3.82267i 0.125553 + 0.125553i
928928 −4.66687 1.46412i −0.153198 0.0480621i
929929 22.1050i 0.725241i −0.931937 0.362620i 0.881882π-0.881882\pi
0.931937 0.362620i 0.118118π-0.118118\pi
930930 0 0
931931 7.64535i 0.250566i
932932 −1.90084 + 0.693082i −0.0622641 + 0.0227026i
933933 13.7293 + 13.7293i 0.449477 + 0.449477i
934934 −0.868197 + 3.92150i −0.0284083 + 0.128315i
935935 0 0
936936 −4.28467 + 5.59383i −0.140049 + 0.182840i
937937 15.2986 15.2986i 0.499784 0.499784i −0.411586 0.911371i 0.635025π-0.635025\pi
0.911371 + 0.411586i 0.135025π0.135025\pi
938938 −9.04843 + 5.76813i −0.295442 + 0.188336i
939939 −25.0471 −0.817381
940940 0 0
941941 25.5264 0.832138 0.416069 0.909333i 0.363407π-0.363407\pi
0.416069 + 0.909333i 0.363407π0.363407\pi
942942 15.2018 9.69074i 0.495302 0.315741i
943943 5.94842 5.94842i 0.193707 0.193707i
944944 1.36106 + 1.61828i 0.0442986 + 0.0526704i
945945 0 0
946946 13.7572 62.1388i 0.447285 2.02031i
947947 11.9881 + 11.9881i 0.389562 + 0.389562i 0.874531 0.484969i 0.161169π-0.161169\pi
−0.484969 + 0.874531i 0.661169π0.661169\pi
948948 10.9024 + 29.9010i 0.354095 + 0.971138i
949949 7.93545i 0.257596i
950950 0 0
951951 11.0160i 0.357217i
952952 −12.8968 + 1.70916i −0.417988 + 0.0553943i
953953 −5.99563 5.99563i −0.194218 0.194218i 0.603298 0.797516i 0.293853π-0.293853\pi
−0.797516 + 0.603298i 0.793853π0.793853\pi
954954 −5.12822 1.13536i −0.166032 0.0367586i
955955 0 0
956956 −22.7389 + 48.8366i −0.735427 + 1.57949i
957957 3.13536 3.13536i 0.101352 0.101352i
958958 −10.4598 16.4082i −0.337940 0.530125i
959959 8.57657 0.276952
960960 0 0
961961 −30.0096 −0.968051
962962 4.71791 + 7.40097i 0.152112 + 0.238617i
963963 −5.51107 + 5.51107i −0.177592 + 0.177592i
964964 −11.8968 + 25.5510i −0.383171 + 0.822943i
965965 0 0
966966 1.81841 + 0.402586i 0.0585065 + 0.0129530i
967967 −1.66866 1.66866i −0.0536606 0.0536606i 0.679767 0.733428i 0.262081π-0.262081\pi
−0.733428 + 0.679767i 0.762081π0.762081\pi
968968 −42.8960 + 5.68483i −1.37873 + 0.182717i
969969 6.50479i 0.208964i
970970 0 0
971971 4.79719i 0.153949i 0.997033 + 0.0769745i 0.0245260π0.0245260\pi
−0.997033 + 0.0769745i 0.975474π0.975474\pi
972972 −0.685116 1.87899i −0.0219751 0.0602687i
973973 1.39401 + 1.39401i 0.0446900 + 0.0446900i
974974 −10.5208 + 47.5204i −0.337107 + 1.52265i
975975 0 0
976976 −12.8261 15.2501i −0.410554 0.488143i
977977 25.0140 25.0140i 0.800267 0.800267i −0.182870 0.983137i 0.558539π-0.558539\pi
0.983137 + 0.182870i 0.0585387π0.0585387\pi
978978 −22.0673 + 14.0673i −0.705634 + 0.449823i
979979 37.1919 1.18866
980980 0 0
981981 7.31695 0.233612
982982 −34.4540 + 21.9635i −1.09947 + 0.700884i
983983 −30.9151 + 30.9151i −0.986038 + 0.986038i −0.999904 0.0138655i 0.995586π-0.995586\pi
0.0138655 + 0.999904i 0.495586π0.495586\pi
984984 9.49926 12.4017i 0.302825 0.395352i
985985 0 0
986986 1.40608 6.35101i 0.0447786 0.202257i
987987 1.98849 + 1.98849i 0.0632945 + 0.0632945i
988988 −5.72384 + 2.08702i −0.182100 + 0.0663969i
989989 13.3661i 0.425017i
990990 0 0
991991 26.5873i 0.844575i −0.906462 0.422287i 0.861227π-0.861227\pi
0.906462 0.422287i 0.138773π-0.138773\pi
992992 −42.1589 13.2264i −1.33855 0.419937i
993993 −22.4157 22.4157i −0.711340 0.711340i
994994 −9.67331 2.14162i −0.306819 0.0679280i
995995 0 0
996996 20.4017 + 9.49926i 0.646453 + 0.300996i
997997 2.47252 2.47252i 0.0783054 0.0783054i −0.666869 0.745175i 0.732366π-0.732366\pi
0.745175 + 0.666869i 0.232366π0.232366\pi
998998 −9.53021 14.9500i −0.301674 0.473234i
999999 −2.49122 −0.0788187
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 300.2.j.d.43.2 12
3.2 odd 2 900.2.k.n.343.5 12
4.3 odd 2 inner 300.2.j.d.43.5 12
5.2 odd 4 inner 300.2.j.d.7.5 12
5.3 odd 4 60.2.j.a.7.2 12
5.4 even 2 60.2.j.a.43.5 yes 12
12.11 even 2 900.2.k.n.343.2 12
15.2 even 4 900.2.k.n.307.2 12
15.8 even 4 180.2.k.e.127.5 12
15.14 odd 2 180.2.k.e.163.2 12
20.3 even 4 60.2.j.a.7.5 yes 12
20.7 even 4 inner 300.2.j.d.7.2 12
20.19 odd 2 60.2.j.a.43.2 yes 12
40.3 even 4 960.2.w.g.127.5 12
40.13 odd 4 960.2.w.g.127.2 12
40.19 odd 2 960.2.w.g.703.2 12
40.29 even 2 960.2.w.g.703.5 12
60.23 odd 4 180.2.k.e.127.2 12
60.47 odd 4 900.2.k.n.307.5 12
60.59 even 2 180.2.k.e.163.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.2.j.a.7.2 12 5.3 odd 4
60.2.j.a.7.5 yes 12 20.3 even 4
60.2.j.a.43.2 yes 12 20.19 odd 2
60.2.j.a.43.5 yes 12 5.4 even 2
180.2.k.e.127.2 12 60.23 odd 4
180.2.k.e.127.5 12 15.8 even 4
180.2.k.e.163.2 12 15.14 odd 2
180.2.k.e.163.5 12 60.59 even 2
300.2.j.d.7.2 12 20.7 even 4 inner
300.2.j.d.7.5 12 5.2 odd 4 inner
300.2.j.d.43.2 12 1.1 even 1 trivial
300.2.j.d.43.5 12 4.3 odd 2 inner
900.2.k.n.307.2 12 15.2 even 4
900.2.k.n.307.5 12 60.47 odd 4
900.2.k.n.343.2 12 12.11 even 2
900.2.k.n.343.5 12 3.2 odd 2
960.2.w.g.127.2 12 40.13 odd 4
960.2.w.g.127.5 12 40.3 even 4
960.2.w.g.703.2 12 40.19 odd 2
960.2.w.g.703.5 12 40.29 even 2