Properties

Label 147.3.j.a.13.1
Level 147147
Weight 33
Character 147.13
Analytic conductor 4.0054.005
Analytic rank 00
Dimension 108108
Inner twists 22

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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] = [147,3,Mod(13,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.13"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 147=372 147 = 3 \cdot 7^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 147.j (of order 1414, degree 66, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.005459886104.00545988610
Analytic rank: 00
Dimension: 108108
Relative dimension: 1818 over Q(ζ14)\Q(\zeta_{14})
Twist minimal: yes
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 13.1
Character χ\chi == 147.13
Dual form 147.3.j.a.34.1

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+(0.8289713.63196i)q2+(1.354171.07992i)q3+(8.90007+4.28605i)q4+(5.61004+4.47386i)q5+(5.044784.02308i)q6+(3.053506.29890i)q7+(13.6538+17.1213i)q8+(0.6675632.92478i)q9+(20.8995+16.6668i)q10+(2.53997+11.1283i)q11+(7.42365+15.4154i)q12+(7.83503+1.78830i)q13+(20.3461+16.3118i)q14+(2.76557+12.1168i)q15+(26.229132.8902i)q16+(3.00924+6.24875i)q1711.1761q1817.1421iq19+(30.754663.8626i)q20+(10.93725.23227i)q21+(38.312118.4501i)q22+(37.9077+18.2554i)q23+(36.9791+8.44023i)q24+(5.8941425.8239i)q25+(12.9900+26.9741i)q26+(2.254534.68157i)q27+(54.1738+42.9732i)q28+(32.545815.6733i)q29+46.3001q30+5.25973iq31+(62.278029.9915i)q32+(15.4572+12.3267i)q33+(25.1898+5.74940i)q34+(45.3107+21.6762i)q35+(6.59441+28.8920i)q36+(52.536325.3001i)q37+(62.2595+14.2103i)q38+(8.67877+10.8828i)q39+(153.19634.9661i)q40+(46.914737.4132i)q41+(9.93673+44.0611i)q42+(14.4335+18.0990i)q43+(70.302588.1566i)q44+(9.34002+19.3947i)q45+(97.7271+122.546i)q46+(15.07813.44147i)q4772.8642iq48+(30.3523+38.4674i)q4998.6775q50+(2.67310+11.7116i)q51+(62.067649.4973i)q52+(33.3905+16.0800i)q53+(15.1343+12.0692i)q54+(64.036051.0670i)q55+(66.1534138.283i)q56+(18.512023.2134i)q57+(29.9451+131.198i)q58+(48.5283+38.7000i)q59+(27.3192119.693i)q60+(42.875889.0325i)q61+(19.10324.36017i)q62+(20.4613+4.72592i)q63+(19.8572+86.9999i)q64+(35.954345.0853i)q65+(31.956666.3586i)q6637.5577q6768.5120iq68+(31.6192+65.6580i)q69+(41.1657182.535i)q70+(55.5414+26.7473i)q71+(59.190828.5048i)q72+(13.68893.12440i)q73+(48.3380+211.783i)q74+(19.906041.3352i)q75+(73.4719+152.566i)q76+(62.340549.9794i)q77+(46.7205+22.4994i)q78+146.675q79+301.861iq80+(8.108723.90495i)q81+(174.774139.378i)q82+(122.22327.8966i)q83+(119.7680.310020i)q84+(11.074148.5187i)q85+(77.6997+37.4182i)q86+(60.9985+13.9225i)q87+(155.851+195.431i)q88+(79.1623+18.0683i)q89+(62.698450.0003i)q90+(35.1886+43.8915i)q91+(259.137324.948i)q92+(5.68007+7.12258i)q93+(24.998651.9101i)q94+(76.6914+96.1680i)q95+(116.724+26.6414i)q96+140.459iq97+(164.873+78.3499i)q98+34.2436q99+O(q100)q+(-0.828971 - 3.63196i) q^{2} +(1.35417 - 1.07992i) q^{3} +(-8.90007 + 4.28605i) q^{4} +(-5.61004 + 4.47386i) q^{5} +(-5.04478 - 4.02308i) q^{6} +(-3.05350 - 6.29890i) q^{7} +(13.6538 + 17.1213i) q^{8} +(0.667563 - 2.92478i) q^{9} +(20.8995 + 16.6668i) q^{10} +(2.53997 + 11.1283i) q^{11} +(-7.42365 + 15.4154i) q^{12} +(-7.83503 + 1.78830i) q^{13} +(-20.3461 + 16.3118i) q^{14} +(-2.76557 + 12.1168i) q^{15} +(26.2291 - 32.8902i) q^{16} +(-3.00924 + 6.24875i) q^{17} -11.1761 q^{18} -17.1421i q^{19} +(30.7546 - 63.8626i) q^{20} +(-10.9372 - 5.23227i) q^{21} +(38.3121 - 18.4501i) q^{22} +(-37.9077 + 18.2554i) q^{23} +(36.9791 + 8.44023i) q^{24} +(5.89414 - 25.8239i) q^{25} +(12.9900 + 26.9741i) q^{26} +(-2.25453 - 4.68157i) q^{27} +(54.1738 + 42.9732i) q^{28} +(-32.5458 - 15.6733i) q^{29} +46.3001 q^{30} +5.25973i q^{31} +(-62.2780 - 29.9915i) q^{32} +(15.4572 + 12.3267i) q^{33} +(25.1898 + 5.74940i) q^{34} +(45.3107 + 21.6762i) q^{35} +(6.59441 + 28.8920i) q^{36} +(-52.5363 - 25.3001i) q^{37} +(-62.2595 + 14.2103i) q^{38} +(-8.67877 + 10.8828i) q^{39} +(-153.196 - 34.9661i) q^{40} +(46.9147 - 37.4132i) q^{41} +(-9.93673 + 44.0611i) q^{42} +(-14.4335 + 18.0990i) q^{43} +(-70.3025 - 88.1566i) q^{44} +(9.34002 + 19.3947i) q^{45} +(97.7271 + 122.546i) q^{46} +(15.0781 - 3.44147i) q^{47} -72.8642i q^{48} +(-30.3523 + 38.4674i) q^{49} -98.6775 q^{50} +(2.67310 + 11.7116i) q^{51} +(62.0676 - 49.4973i) q^{52} +(-33.3905 + 16.0800i) q^{53} +(-15.1343 + 12.0692i) q^{54} +(-64.0360 - 51.0670i) q^{55} +(66.1534 - 138.283i) q^{56} +(-18.5120 - 23.2134i) q^{57} +(-29.9451 + 131.198i) q^{58} +(48.5283 + 38.7000i) q^{59} +(-27.3192 - 119.693i) q^{60} +(42.8758 - 89.0325i) q^{61} +(19.1032 - 4.36017i) q^{62} +(-20.4613 + 4.72592i) q^{63} +(-19.8572 + 86.9999i) q^{64} +(35.9543 - 45.0853i) q^{65} +(31.9566 - 66.3586i) q^{66} -37.5577 q^{67} -68.5120i q^{68} +(-31.6192 + 65.6580i) q^{69} +(41.1657 - 182.535i) q^{70} +(-55.5414 + 26.7473i) q^{71} +(59.1908 - 28.5048i) q^{72} +(-13.6889 - 3.12440i) q^{73} +(-48.3380 + 211.783i) q^{74} +(-19.9060 - 41.3352i) q^{75} +(73.4719 + 152.566i) q^{76} +(62.3405 - 49.9794i) q^{77} +(46.7205 + 22.4994i) q^{78} +146.675 q^{79} +301.861i q^{80} +(-8.10872 - 3.90495i) q^{81} +(-174.774 - 139.378i) q^{82} +(-122.223 - 27.8966i) q^{83} +(119.768 - 0.310020i) q^{84} +(-11.0741 - 48.5187i) q^{85} +(77.6997 + 37.4182i) q^{86} +(-60.9985 + 13.9225i) q^{87} +(-155.851 + 195.431i) q^{88} +(79.1623 + 18.0683i) q^{89} +(62.6984 - 50.0003i) q^{90} +(35.1886 + 43.8915i) q^{91} +(259.137 - 324.948i) q^{92} +(5.68007 + 7.12258i) q^{93} +(-24.9986 - 51.9101i) q^{94} +(76.6914 + 96.1680i) q^{95} +(-116.724 + 26.6414i) q^{96} +140.459i q^{97} +(164.873 + 78.3499i) q^{98} +34.2436 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 108q32q42q7+12q8+54q9+66q112q14+60q1596q1698q17112q20+24q21116q22+64q23+126q24+130q25+224q26204q28++12q99+O(q100) 108 q - 32 q^{4} - 2 q^{7} + 12 q^{8} + 54 q^{9} + 66 q^{11} - 2 q^{14} + 60 q^{15} - 96 q^{16} - 98 q^{17} - 112 q^{20} + 24 q^{21} - 116 q^{22} + 64 q^{23} + 126 q^{24} + 130 q^{25} + 224 q^{26} - 204 q^{28}+ \cdots + 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/147Z)×\left(\mathbb{Z}/147\mathbb{Z}\right)^\times.

nn 5050 5252
χ(n)\chi(n) 11 e(1114)e\left(\frac{11}{14}\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 −0.828971 3.63196i −0.414486 1.81598i −0.562261 0.826960i 0.690069π-0.690069\pi
0.147776 0.989021i 0.452789π-0.452789\pi
33 1.35417 1.07992i 0.451391 0.359972i
44 −8.90007 + 4.28605i −2.22502 + 1.07151i
55 −5.61004 + 4.47386i −1.12201 + 0.894772i −0.995268 0.0971639i 0.969023π-0.969023\pi
−0.126740 + 0.991936i 0.540451π0.540451\pi
66 −5.04478 4.02308i −0.840797 0.670513i
77 −3.05350 6.29890i −0.436214 0.899843i
88 13.6538 + 17.1213i 1.70672 + 2.14016i
99 0.667563 2.92478i 0.0741736 0.324976i
1010 20.8995 + 16.6668i 2.08995 + 1.66668i
1111 2.53997 + 11.1283i 0.230906 + 1.01167i 0.948890 + 0.315607i 0.102208π0.102208\pi
−0.717984 + 0.696060i 0.754935π0.754935\pi
1212 −7.42365 + 15.4154i −0.618638 + 1.28461i
1313 −7.83503 + 1.78830i −0.602695 + 0.137561i −0.512972 0.858406i 0.671455π-0.671455\pi
−0.0897232 + 0.995967i 0.528598π0.528598\pi
1414 −20.3461 + 16.3118i −1.45329 + 1.16513i
1515 −2.76557 + 12.1168i −0.184371 + 0.807783i
1616 26.2291 32.8902i 1.63932 2.05564i
1717 −3.00924 + 6.24875i −0.177014 + 0.367573i −0.970532 0.240974i 0.922533π-0.922533\pi
0.793518 + 0.608547i 0.208247π0.208247\pi
1818 −11.1761 −0.620894
1919 17.1421i 0.902217i −0.892469 0.451108i 0.851029π-0.851029\pi
0.892469 0.451108i 0.148971π-0.148971\pi
2020 30.7546 63.8626i 1.53773 3.19313i
2121 −10.9372 5.23227i −0.520821 0.249156i
2222 38.3121 18.4501i 1.74146 0.838643i
2323 −37.9077 + 18.2554i −1.64816 + 0.793712i −0.648692 + 0.761051i 0.724684π0.724684\pi
−0.999466 + 0.0326608i 0.989602π0.989602\pi
2424 36.9791 + 8.44023i 1.54079 + 0.351676i
2525 5.89414 25.8239i 0.235766 1.03296i
2626 12.9900 + 26.9741i 0.499617 + 1.03746i
2727 −2.25453 4.68157i −0.0835010 0.173392i
2828 54.1738 + 42.9732i 1.93478 + 1.53476i
2929 −32.5458 15.6733i −1.12227 0.540457i −0.221677 0.975120i 0.571153π-0.571153\pi
−0.900593 + 0.434663i 0.856867π0.856867\pi
3030 46.3001 1.54334
3131 5.25973i 0.169669i 0.996395 + 0.0848344i 0.0270361π0.0270361\pi
−0.996395 + 0.0848344i 0.972964π0.972964\pi
3232 −62.2780 29.9915i −1.94619 0.937235i
3333 15.4572 + 12.3267i 0.468401 + 0.373537i
3434 25.1898 + 5.74940i 0.740876 + 0.169100i
3535 45.3107 + 21.6762i 1.29459 + 0.619319i
3636 6.59441 + 28.8920i 0.183178 + 0.802555i
3737 −52.5363 25.3001i −1.41990 0.683787i −0.442810 0.896616i 0.646018π-0.646018\pi
−0.977090 + 0.212828i 0.931733π0.931733\pi
3838 −62.2595 + 14.2103i −1.63841 + 0.373956i
3939 −8.67877 + 10.8828i −0.222533 + 0.279047i
4040 −153.196 34.9661i −3.82991 0.874152i
4141 46.9147 37.4132i 1.14426 0.912518i 0.147199 0.989107i 0.452974π-0.452974\pi
0.997063 + 0.0765888i 0.0244029π0.0244029\pi
4242 −9.93673 + 44.0611i −0.236589 + 1.04907i
4343 −14.4335 + 18.0990i −0.335662 + 0.420907i −0.920805 0.390023i 0.872467π-0.872467\pi
0.585143 + 0.810930i 0.301038π0.301038\pi
4444 −70.3025 88.1566i −1.59778 2.00356i
4545 9.34002 + 19.3947i 0.207556 + 0.430994i
4646 97.7271 + 122.546i 2.12450 + 2.66404i
4747 15.0781 3.44147i 0.320810 0.0732229i −0.0590833 0.998253i 0.518818π-0.518818\pi
0.379894 + 0.925030i 0.375961π0.375961\pi
4848 72.8642i 1.51800i
4949 −30.3523 + 38.4674i −0.619434 + 0.785049i
5050 −98.6775 −1.97355
5151 2.67310 + 11.7116i 0.0524137 + 0.229639i
5252 62.0676 49.4973i 1.19361 0.951871i
5353 −33.3905 + 16.0800i −0.630010 + 0.303397i −0.721505 0.692409i 0.756549π-0.756549\pi
0.0914958 + 0.995805i 0.470835π0.470835\pi
5454 −15.1343 + 12.0692i −0.280266 + 0.223504i
5555 −64.0360 51.0670i −1.16429 0.928491i
5656 66.1534 138.283i 1.18131 2.46935i
5757 −18.5120 23.2134i −0.324773 0.407252i
5858 −29.9451 + 131.198i −0.516294 + 2.26203i
5959 48.5283 + 38.7000i 0.822513 + 0.655932i 0.941518 0.336962i 0.109399π-0.109399\pi
−0.119006 + 0.992894i 0.537971π0.537971\pi
6060 −27.3192 119.693i −0.455320 1.99489i
6161 42.8758 89.0325i 0.702882 1.45955i −0.176928 0.984224i 0.556616π-0.556616\pi
0.879810 0.475326i 0.157670π-0.157670\pi
6262 19.1032 4.36017i 0.308115 0.0703253i
6363 −20.4613 + 4.72592i −0.324783 + 0.0750146i
6464 −19.8572 + 86.9999i −0.310268 + 1.35937i
6565 35.9543 45.0853i 0.553143 0.693619i
6666 31.9566 66.3586i 0.484191 1.00543i
6767 −37.5577 −0.560562 −0.280281 0.959918i 0.590428π-0.590428\pi
−0.280281 + 0.959918i 0.590428π0.590428\pi
6868 68.5120i 1.00753i
6969 −31.6192 + 65.6580i −0.458250 + 0.951565i
7070 41.1657 182.535i 0.588082 2.60765i
7171 −55.5414 + 26.7473i −0.782273 + 0.376723i −0.782001 0.623277i 0.785801π-0.785801\pi
−0.000272220 1.00000i 0.500087π0.500087\pi
7272 59.1908 28.5048i 0.822094 0.395900i
7373 −13.6889 3.12440i −0.187519 0.0428000i 0.127730 0.991809i 0.459231π-0.459231\pi
−0.315249 + 0.949009i 0.602088π0.602088\pi
7474 −48.3380 + 211.783i −0.653217 + 2.86193i
7575 −19.9060 41.3352i −0.265413 0.551136i
7676 73.4719 + 152.566i 0.966736 + 2.00745i
7777 62.3405 49.9794i 0.809617 0.649083i
7878 46.7205 + 22.4994i 0.598981 + 0.288454i
7979 146.675 1.85664 0.928322 0.371778i 0.121252π-0.121252\pi
0.928322 + 0.371778i 0.121252π0.121252\pi
8080 301.861i 3.77326i
8181 −8.10872 3.90495i −0.100108 0.0482093i
8282 −174.774 139.378i −2.13140 1.69973i
8383 −122.223 27.8966i −1.47256 0.336103i −0.590425 0.807092i 0.701040π-0.701040\pi
−0.882139 + 0.470989i 0.843897π0.843897\pi
8484 119.768 0.310020i 1.42581 0.00369071i
8585 −11.0741 48.5187i −0.130283 0.570808i
8686 77.6997 + 37.4182i 0.903485 + 0.435096i
8787 −60.9985 + 13.9225i −0.701132 + 0.160029i
8888 −155.851 + 195.431i −1.77104 + 2.22081i
8989 79.1623 + 18.0683i 0.889464 + 0.203014i 0.642752 0.766075i 0.277793π-0.277793\pi
0.246712 + 0.969089i 0.420650π0.420650\pi
9090 62.6984 50.0003i 0.696648 0.555559i
9191 35.1886 + 43.8915i 0.386688 + 0.482324i
9292 259.137 324.948i 2.81671 3.53204i
9393 5.68007 + 7.12258i 0.0610760 + 0.0765869i
9494 −24.9986 51.9101i −0.265943 0.552235i
9595 76.6914 + 96.1680i 0.807278 + 1.01229i
9696 −116.724 + 26.6414i −1.21587 + 0.277514i
9797 140.459i 1.44803i 0.689786 + 0.724014i 0.257705π0.257705\pi
−0.689786 + 0.724014i 0.742295π0.742295\pi
9898 164.873 + 78.3499i 1.68238 + 0.799488i
9999 34.2436 0.345895
100100 58.2243 + 255.097i 0.582243 + 2.55097i
101101 53.5661 42.7175i 0.530357 0.422946i −0.321353 0.946960i 0.604137π-0.604137\pi
0.851710 + 0.524014i 0.175566π0.175566\pi
102102 40.3202 19.4172i 0.395296 0.190364i
103103 29.5626 23.5754i 0.287015 0.228887i −0.469389 0.882992i 0.655526π-0.655526\pi
0.756404 + 0.654104i 0.226954π0.226954\pi
104104 −137.596 109.729i −1.32303 1.05508i
105105 84.7669 19.5785i 0.807303 0.186462i
106106 86.0818 + 107.943i 0.812092 + 1.01833i
107107 8.72916 38.2449i 0.0815809 0.357429i −0.917617 0.397465i 0.869890π-0.869890\pi
0.999198 + 0.0400356i 0.0127471π0.0127471\pi
108108 40.1309 + 32.0033i 0.371582 + 0.296327i
109109 −16.5121 72.3444i −0.151488 0.663710i −0.992453 0.122622i 0.960870π-0.960870\pi
0.840966 0.541088i 0.181987π-0.181987\pi
110110 −132.389 + 274.909i −1.20354 + 2.49918i
111111 −98.4652 + 22.4740i −0.887074 + 0.202469i
112112 −287.263 64.7839i −2.56484 0.578428i
113113 9.37711 41.0838i 0.0829833 0.363574i −0.916338 0.400405i 0.868869π-0.868869\pi
0.999321 + 0.0368316i 0.0117265π0.0117265\pi
114114 −68.9641 + 86.4782i −0.604948 + 0.758581i
115115 130.992 272.007i 1.13906 2.36528i
116116 356.837 3.07618
117117 24.1096i 0.206065i
118118 100.328 208.334i 0.850240 1.76554i
119119 48.5489 0.125669i 0.407974 0.00105604i
120120 −245.215 + 118.089i −2.04346 + 0.984076i
121121 −8.37125 + 4.03138i −0.0691839 + 0.0333172i
122122 −358.906 81.9178i −2.94185 0.671458i
123123 23.1274 101.328i 0.188028 0.823804i
124124 −22.5435 46.8120i −0.181802 0.377516i
125125 4.63269 + 9.61988i 0.0370615 + 0.0769591i
126126 34.1262 + 70.3971i 0.270843 + 0.558707i
127127 −31.6600 15.2467i −0.249292 0.120052i 0.305066 0.952331i 0.401322π-0.401322\pi
−0.554357 + 0.832279i 0.687036π0.687036\pi
128128 55.9476 0.437091
129129 40.0961i 0.310822i
130130 −193.553 93.2102i −1.48887 0.717002i
131131 −165.402 131.904i −1.26261 1.00690i −0.999107 0.0422399i 0.986551π-0.986551\pi
−0.263503 0.964659i 0.584878π-0.584878\pi
132132 −190.403 43.4583i −1.44245 0.329230i
133133 −107.976 + 52.3435i −0.811853 + 0.393560i
134134 31.1342 + 136.408i 0.232345 + 1.01797i
135135 33.5927 + 16.1774i 0.248835 + 0.119832i
136136 −148.074 + 33.7969i −1.08878 + 0.248507i
137137 −100.472 + 125.988i −0.733374 + 0.919622i −0.999012 0.0444508i 0.985846π-0.985846\pi
0.265637 + 0.964073i 0.414418π0.414418\pi
138138 264.679 + 60.4112i 1.91796 + 0.437762i
139139 23.8778 19.0419i 0.171782 0.136992i −0.533825 0.845595i 0.679246π-0.679246\pi
0.705607 + 0.708603i 0.250674π0.250674\pi
140140 −496.173 + 1.28435i −3.54409 + 0.00917390i
141141 16.7018 20.9434i 0.118453 0.148535i
142142 143.188 + 179.551i 1.00836 + 1.26445i
143143 −39.8015 82.6487i −0.278332 0.577963i
144144 −78.6872 98.6706i −0.546439 0.685213i
145145 252.704 57.6779i 1.74278 0.397779i
146146 52.3076i 0.358271i
147147 0.439372 + 84.8694i 0.00298893 + 0.577343i
148148 576.014 3.89199
149149 14.2647 + 62.4976i 0.0957360 + 0.419447i 0.999971 0.00758793i 0.00241534π-0.00241534\pi
−0.904235 + 0.427035i 0.859558π0.859558\pi
150150 −133.626 + 106.563i −0.890842 + 0.710423i
151151 −37.6436 + 18.1282i −0.249296 + 0.120054i −0.554359 0.832278i 0.687037π-0.687037\pi
0.305063 + 0.952332i 0.401322π0.401322\pi
152152 293.495 234.054i 1.93089 1.53983i
153153 16.2674 + 12.9728i 0.106323 + 0.0847896i
154154 −233.202 184.987i −1.51430 1.20121i
155155 −23.5313 29.5073i −0.151815 0.190370i
156156 30.5973 134.056i 0.196137 0.859331i
157157 −5.34984 4.26635i −0.0340754 0.0271742i 0.606304 0.795233i 0.292651π-0.292651\pi
−0.640379 + 0.768059i 0.721223π0.721223\pi
158158 −121.589 532.717i −0.769552 3.37163i
159159 −27.8514 + 57.8341i −0.175166 + 0.363736i
160160 483.560 110.370i 3.02225 0.689809i
161161 230.740 + 183.034i 1.43317 + 1.13686i
162162 −7.46074 + 32.6876i −0.0460540 + 0.201776i
163163 7.69130 9.64458i 0.0471859 0.0591692i −0.757679 0.652628i 0.773667π-0.773667\pi
0.804864 + 0.593459i 0.202238π0.202238\pi
164164 −257.189 + 534.059i −1.56823 + 3.25646i
165165 −141.864 −0.859781
166166 467.034i 2.81346i
167167 −56.9897 + 118.340i −0.341256 + 0.708625i −0.999004 0.0446127i 0.985795π-0.985795\pi
0.657749 + 0.753238i 0.271509π0.271509\pi
168168 −59.7515 258.700i −0.355664 1.53988i
169169 −94.0740 + 45.3036i −0.556651 + 0.268069i
170170 −167.038 + 80.4412i −0.982575 + 0.473183i
171171 −50.1370 11.4434i −0.293199 0.0669207i
172172 50.8857 222.945i 0.295847 1.29619i
173173 98.2242 + 203.965i 0.567770 + 1.17899i 0.965238 + 0.261371i 0.0841746π0.0841746\pi
−0.397468 + 0.917616i 0.630111π0.630111\pi
174174 101.132 + 210.003i 0.581218 + 1.20691i
175175 −180.660 + 41.7267i −1.03234 + 0.238439i
176176 432.634 + 208.346i 2.45815 + 1.18378i
177177 107.508 0.607392
178178 302.492i 1.69940i
179179 −225.959 108.816i −1.26234 0.607911i −0.321548 0.946893i 0.604203π-0.604203\pi
−0.940793 + 0.338982i 0.889917π0.889917\pi
180180 −166.254 132.583i −0.923631 0.736571i
181181 −72.5265 16.5537i −0.400699 0.0914569i 0.0174222 0.999848i 0.494454π-0.494454\pi
−0.418121 + 0.908391i 0.637311π0.637311\pi
182182 130.242 164.188i 0.715615 0.902134i
183183 −38.0864 166.868i −0.208123 0.911845i
184184 −830.137 399.773i −4.51161 2.17268i
185185 407.920 93.1051i 2.20497 0.503271i
186186 21.1603 26.5342i 0.113765 0.142657i
187187 −77.1816 17.6162i −0.412736 0.0942042i
188188 −119.446 + 95.2548i −0.635349 + 0.506674i
189189 −22.6045 + 28.4962i −0.119601 + 0.150774i
190190 285.703 358.261i 1.50370 1.88558i
191191 −1.51962 1.90554i −0.00795610 0.00997664i 0.777838 0.628465i 0.216317π-0.216317\pi
−0.785794 + 0.618489i 0.787745π0.787745\pi
192192 67.0626 + 139.257i 0.349284 + 0.725296i
193193 151.044 + 189.404i 0.782613 + 0.981366i 0.999986 + 0.00527705i 0.00167974π0.00167974\pi
−0.217373 + 0.976089i 0.569749π0.569749\pi
194194 510.140 116.436i 2.62959 0.600187i
195195 99.8808i 0.512209i
196196 105.264 472.454i 0.537062 2.41048i
197197 141.990 0.720759 0.360380 0.932806i 0.382647π-0.382647\pi
0.360380 + 0.932806i 0.382647π0.382647\pi
198198 −28.3869 124.371i −0.143368 0.628138i
199199 −114.494 + 91.3056i −0.575344 + 0.458822i −0.867422 0.497573i 0.834225π-0.834225\pi
0.292078 + 0.956395i 0.405653π0.405653\pi
200200 522.615 251.678i 2.61308 1.25839i
201201 −50.8595 + 40.5591i −0.253032 + 0.201787i
202202 −199.553 159.138i −0.987887 0.787813i
203203 0.654532 + 252.861i 0.00322430 + 1.24562i
204204 −73.9872 92.7771i −0.362683 0.454790i
205205 −95.8120 + 419.780i −0.467376 + 2.04771i
206206 −110.131 87.8268i −0.534618 0.426344i
207207 28.0873 + 123.058i 0.135687 + 0.594485i
208208 −146.688 + 304.601i −0.705232 + 1.46443i
209209 190.763 43.5405i 0.912743 0.208328i
210210 −141.378 291.640i −0.673226 1.38876i
211211 −44.4701 + 194.836i −0.210759 + 0.923395i 0.753294 + 0.657684i 0.228464π0.228464\pi
−0.964053 + 0.265711i 0.914393π0.914393\pi
212212 228.258 286.227i 1.07669 1.35013i
213213 −46.3277 + 96.2005i −0.217501 + 0.451646i
214214 −146.140 −0.682899
215215 166.109i 0.772602i
216216 49.3717 102.521i 0.228573 0.474636i
217217 33.1305 16.0606i 0.152675 0.0740120i
218218 −249.064 + 119.943i −1.14250 + 0.550197i
219219 −21.9112 + 10.5519i −0.100051 + 0.0481821i
220220 788.800 + 180.039i 3.58546 + 0.818357i
221221 12.4029 54.3405i 0.0561216 0.245885i
222222 163.250 + 338.991i 0.735359 + 1.52699i
223223 40.8793 + 84.8867i 0.183315 + 0.380658i 0.972294 0.233763i 0.0751040π-0.0751040\pi
−0.788978 + 0.614421i 0.789390π0.789390\pi
224224 1.25248 + 483.862i 0.00559142 + 2.16010i
225225 −71.5946 34.4782i −0.318198 0.153236i
226226 −156.988 −0.694638
227227 105.940i 0.466696i 0.972393 + 0.233348i 0.0749681π0.0749681\pi
−0.972393 + 0.233348i 0.925032π0.925032\pi
228228 264.252 + 127.257i 1.15900 + 0.558145i
229229 −47.0733 37.5397i −0.205560 0.163929i 0.515299 0.857011i 0.327681π-0.327681\pi
−0.720859 + 0.693082i 0.756252π0.756252\pi
230230 −1096.51 250.271i −4.76742 1.08813i
231231 30.4462 135.003i 0.131802 0.584429i
232232 −176.027 771.225i −0.758738 3.32425i
233233 189.268 + 91.1467i 0.812310 + 0.391188i 0.793451 0.608635i 0.208282π-0.208282\pi
0.0188588 + 0.999822i 0.493997π0.493997\pi
234234 87.5650 19.9861i 0.374210 0.0854109i
235235 −69.1920 + 86.7641i −0.294434 + 0.369209i
236236 −597.775 136.438i −2.53294 0.578128i
237237 198.623 158.396i 0.838071 0.668340i
238238 −40.7021 176.224i −0.171017 0.740436i
239239 −148.270 + 185.925i −0.620377 + 0.777929i −0.988398 0.151889i 0.951464π-0.951464\pi
0.368020 + 0.929818i 0.380036π0.380036\pi
240240 325.984 + 408.771i 1.35827 + 1.70321i
241241 22.1430 + 45.9805i 0.0918798 + 0.190790i 0.941844 0.336050i 0.109091π-0.109091\pi
−0.849965 + 0.526840i 0.823377π0.823377\pi
242242 21.5813 + 27.0621i 0.0891791 + 0.111827i
243243 −15.1976 + 3.46876i −0.0625417 + 0.0142747i
244244 976.164i 4.00067i
245245 −1.82022 351.596i −0.00742949 1.43508i
246246 −387.191 −1.57395
247247 30.6552 + 134.309i 0.124110 + 0.543761i
248248 −90.0534 + 71.8152i −0.363118 + 0.289577i
249249 −195.637 + 94.2137i −0.785690 + 0.378368i
250250 31.0987 24.8004i 0.124395 0.0992014i
251251 57.2727 + 45.6735i 0.228178 + 0.181966i 0.730905 0.682479i 0.239098π-0.239098\pi
−0.502727 + 0.864445i 0.667670π0.667670\pi
252252 161.852 129.759i 0.642269 0.514918i
253253 −299.436 375.481i −1.18354 1.48412i
254254 −29.1300 + 127.627i −0.114685 + 0.502469i
255255 −67.3923 53.7435i −0.264283 0.210759i
256256 33.0497 + 144.800i 0.129100 + 0.565625i
257257 35.4102 73.5299i 0.137783 0.286109i −0.820648 0.571434i 0.806387π-0.806387\pi
0.958431 + 0.285325i 0.0921016π0.0921016\pi
258258 145.627 33.2385i 0.564447 0.128831i
259259 1.05656 + 408.175i 0.00407939 + 1.57596i
260260 −126.758 + 555.364i −0.487531 + 2.13601i
261261 −67.5673 + 84.7267i −0.258878 + 0.324623i
262262 −341.956 + 710.078i −1.30517 + 2.71022i
263263 −298.480 −1.13490 −0.567452 0.823407i 0.692071π-0.692071\pi
−0.567452 + 0.823407i 0.692071π0.692071\pi
264264 432.954i 1.63998i
265265 115.382 239.594i 0.435405 0.904129i
266266 279.619 + 348.775i 1.05120 + 1.31118i
267267 126.712 61.0211i 0.474575 0.228543i
268268 334.266 160.974i 1.24726 0.600649i
269269 −147.015 33.5553i −0.546526 0.124741i −0.0596616 0.998219i 0.519002π-0.519002\pi
−0.486864 + 0.873478i 0.661859π0.661859\pi
270270 30.9083 135.418i 0.114475 0.501548i
271271 −43.0463 89.3866i −0.158842 0.329840i 0.806325 0.591473i 0.201453π-0.201453\pi
−0.965167 + 0.261633i 0.915739π0.915739\pi
272272 126.593 + 262.873i 0.465416 + 0.966446i
273273 95.0505 + 21.4360i 0.348170 + 0.0785200i
274274 540.873 + 260.471i 1.97399 + 0.950623i
275275 302.348 1.09945
276276 719.882i 2.60827i
277277 176.081 + 84.7963i 0.635672 + 0.306124i 0.723825 0.689983i 0.242382π-0.242382\pi
−0.0881529 + 0.996107i 0.528096π0.528096\pi
278278 −88.9534 70.9379i −0.319976 0.255172i
279279 15.3836 + 3.51120i 0.0551383 + 0.0125850i
280280 247.538 + 1071.74i 0.884063 + 3.82763i
281281 −95.8034 419.742i −0.340937 1.49374i −0.797100 0.603847i 0.793634π-0.793634\pi
0.456163 0.889896i 0.349223π-0.349223\pi
282282 −89.9110 43.2988i −0.318833 0.153542i
283283 37.1168 8.47167i 0.131155 0.0299352i −0.156440 0.987688i 0.550002π-0.550002\pi
0.287594 + 0.957752i 0.407144π0.407144\pi
284284 379.682 476.106i 1.33691 1.67643i
285285 207.707 + 47.4077i 0.728796 + 0.166343i
286286 −267.183 + 213.071i −0.934205 + 0.745003i
287287 −378.916 181.270i −1.32027 0.631602i
288288 −129.293 + 162.129i −0.448935 + 0.562946i
289289 150.197 + 188.341i 0.519714 + 0.651700i
290290 −418.968 869.996i −1.44472 2.99999i
291291 151.684 + 190.205i 0.521249 + 0.653626i
292292 135.224 30.8639i 0.463094 0.105698i
293293 41.5141i 0.141686i 0.997487 + 0.0708432i 0.0225690π0.0225690\pi
−0.997487 + 0.0708432i 0.977431π0.977431\pi
294294 307.878 71.9500i 1.04720 0.244728i
295295 −445.384 −1.50978
296296 −284.147 1244.93i −0.959957 4.20584i
297297 46.3717 36.9802i 0.156134 0.124512i
298298 215.164 103.617i 0.722026 0.347709i
299299 264.362 210.821i 0.884153 0.705089i
300300 354.329 + 282.568i 1.18110 + 0.941894i
301301 158.076 + 35.6496i 0.525170 + 0.118437i
302302 97.0465 + 121.692i 0.321346 + 0.402955i
303303 26.4063 115.694i 0.0871496 0.381827i
304304 −563.808 449.622i −1.85463 1.47902i
305305 157.784 + 691.297i 0.517325 + 2.26655i
306306 33.6315 69.8366i 0.109907 0.228224i
307307 −164.395 + 37.5221i −0.535488 + 0.122222i −0.481709 0.876331i 0.659984π-0.659984\pi
−0.0537791 + 0.998553i 0.517127π0.517127\pi
308308 −340.621 + 712.015i −1.10591 + 2.31174i
309309 14.5734 63.8502i 0.0471631 0.206635i
310310 −87.6627 + 109.926i −0.282783 + 0.354599i
311311 211.522 439.230i 0.680135 1.41232i −0.219473 0.975618i 0.570434π-0.570434\pi
0.899609 0.436697i 0.143852π-0.143852\pi
312312 −304.826 −0.977006
313313 388.301i 1.24058i −0.784373 0.620289i 0.787015π-0.787015\pi
0.784373 0.620289i 0.212985π-0.212985\pi
314314 −11.0604 + 22.9671i −0.0352241 + 0.0731436i
315315 93.6458 118.054i 0.297288 0.374774i
316316 −1305.42 + 628.655i −4.13106 + 1.98942i
317317 79.6326 38.3491i 0.251207 0.120975i −0.304043 0.952658i 0.598337π-0.598337\pi
0.555250 + 0.831683i 0.312622π0.312622\pi
318318 233.139 + 53.2125i 0.733142 + 0.167335i
319319 91.7518 401.991i 0.287623 1.26016i
320320 −277.826 576.911i −0.868206 1.80285i
321321 −29.4805 61.2170i −0.0918397 0.190707i
322322 473.495 989.768i 1.47048 3.07381i
323323 107.117 + 51.5847i 0.331631 + 0.159705i
324324 88.9050 0.274398
325325 212.872i 0.654990i
326326 −41.4046 19.9394i −0.127008 0.0611638i
327327 −100.486 80.1351i −0.307297 0.245061i
328328 1281.12 + 292.408i 3.90587 + 0.891489i
329329 −67.7184 84.4668i −0.205831 0.256738i
330330 117.601 + 515.244i 0.356367 + 1.56134i
331331 −410.594 197.732i −1.24046 0.597376i −0.305525 0.952184i 0.598832π-0.598832\pi
−0.934939 + 0.354807i 0.884546π0.884546\pi
332332 1207.36 275.572i 3.63662 0.830035i
333333 −109.069 + 136.768i −0.327534 + 0.410714i
334334 477.050 + 108.884i 1.42829 + 0.325999i
335335 210.700 168.028i 0.628956 0.501575i
336336 −458.964 + 222.491i −1.36596 + 0.662175i
337337 −30.2720 + 37.9599i −0.0898280 + 0.112641i −0.824714 0.565550i 0.808664π-0.808664\pi
0.734886 + 0.678190i 0.237236π0.237236\pi
338338 242.526 + 304.118i 0.717532 + 0.899756i
339339 −31.6689 65.7610i −0.0934184 0.193985i
340340 306.513 + 384.355i 0.901510 + 1.13046i
341341 −58.5321 + 13.3596i −0.171648 + 0.0391776i
342342 191.582i 0.560181i
343343 334.983 + 73.7256i 0.976626 + 0.214944i
344344 −506.949 −1.47369
345345 −116.359 509.804i −0.337274 1.47769i
346346 659.367 525.827i 1.90568 1.51973i
347347 20.2104 9.73282i 0.0582433 0.0280485i −0.404535 0.914522i 0.632567π-0.632567\pi
0.462779 + 0.886474i 0.346852π0.346852\pi
348348 483.218 385.354i 1.38856 1.10734i
349349 −34.5312 27.5377i −0.0989434 0.0789047i 0.572769 0.819717i 0.305869π-0.305869\pi
−0.671712 + 0.740812i 0.734441π0.734441\pi
350350 301.312 + 621.560i 0.860891 + 1.77588i
351351 26.0363 + 32.6485i 0.0741775 + 0.0930157i
352352 175.571 769.229i 0.498783 2.18531i
353353 −137.132 109.359i −0.388476 0.309799i 0.409704 0.912219i 0.365632π-0.365632\pi
−0.798180 + 0.602419i 0.794203π0.794203\pi
354354 −89.1213 390.466i −0.251755 1.10301i
355355 191.926 398.538i 0.540636 1.12264i
356356 −781.991 + 178.484i −2.19660 + 0.501361i
357357 65.6079 52.5990i 0.183776 0.147336i
358358 −207.902 + 910.879i −0.580733 + 2.54436i
359359 −162.217 + 203.414i −0.451858 + 0.566612i −0.954625 0.297810i 0.903744π-0.903744\pi
0.502767 + 0.864422i 0.332315π0.332315\pi
360360 −204.536 + 424.724i −0.568157 + 1.17979i
361361 67.1479 0.186005
362362 277.136i 0.765569i
363363 −6.98256 + 14.4994i −0.0192357 + 0.0399433i
364364 −501.302 239.818i −1.37720 0.658840i
365365 90.7735 43.7142i 0.248694 0.119765i
366366 −574.484 + 276.657i −1.56963 + 0.755893i
367367 490.050 + 111.851i 1.33529 + 0.304770i 0.829798 0.558064i 0.188455π-0.188455\pi
0.505488 + 0.862834i 0.331313π0.331313\pi
368368 −393.860 + 1725.61i −1.07027 + 4.68916i
369369 −78.1071 162.191i −0.211672 0.439542i
370370 −676.308 1404.37i −1.82786 3.79559i
371371 203.244 + 161.223i 0.547829 + 0.434564i
372372 −81.0808 39.0464i −0.217959 0.104964i
373373 −154.202 −0.413410 −0.206705 0.978403i 0.566274π-0.566274\pi
−0.206705 + 0.978403i 0.566274π0.566274\pi
374374 294.924i 0.788566i
375375 16.6621 + 8.02406i 0.0444323 + 0.0213975i
376376 264.795 + 211.167i 0.704242 + 0.561614i
377377 283.026 + 64.5989i 0.750733 + 0.171350i
378378 122.236 + 58.4763i 0.323375 + 0.154699i
379379 118.511 + 519.230i 0.312693 + 1.37000i 0.850076 + 0.526661i 0.176556π0.176556\pi
−0.537382 + 0.843339i 0.680587π0.680587\pi
380380 −1094.74 527.199i −2.88089 1.38737i
381381 −59.3382 + 13.5436i −0.155743 + 0.0355474i
382382 −5.66112 + 7.09882i −0.0148197 + 0.0185833i
383383 −463.661 105.828i −1.21060 0.276312i −0.430864 0.902417i 0.641791π-0.641791\pi
−0.779739 + 0.626105i 0.784648π0.784648\pi
384384 75.7627 60.4187i 0.197299 0.157340i
385385 −126.132 + 559.289i −0.327615 + 1.45270i
386386 562.695 705.597i 1.45776 1.82797i
387387 43.3004 + 54.2970i 0.111887 + 0.140302i
388388 −602.013 1250.09i −1.55158 3.22189i
389389 −362.871 455.026i −0.932831 1.16973i −0.985252 0.171108i 0.945265π-0.945265\pi
0.0524216 0.998625i 0.483306π-0.483306\pi
390390 −362.763 + 82.7983i −0.930162 + 0.212303i
391391 291.810i 0.746317i
392392 −1073.03 + 5.55514i −2.73733 + 0.0141713i
393393 −366.428 −0.932386
394394 −117.705 515.701i −0.298744 1.30889i
395395 −822.852 + 656.203i −2.08317 + 1.66127i
396396 −304.770 + 146.770i −0.769622 + 0.370630i
397397 −505.418 + 403.058i −1.27309 + 1.01526i −0.274535 + 0.961577i 0.588524π0.588524\pi
−0.998558 + 0.0536813i 0.982905π0.982905\pi
398398 426.530 + 340.146i 1.07168 + 0.854639i
399399 −89.6921 + 187.488i −0.224792 + 0.469894i
400400 −694.756 871.196i −1.73689 2.17799i
401401 −7.80404 + 34.1917i −0.0194614 + 0.0852661i −0.983726 0.179675i 0.942495π-0.942495\pi
0.964265 + 0.264941i 0.0853525π0.0853525\pi
402402 189.470 + 151.097i 0.471319 + 0.375864i
403403 −9.40596 41.2102i −0.0233398 0.102259i
404404 −293.653 + 609.776i −0.726863 + 1.50935i
405405 62.9605 14.3703i 0.155458 0.0354823i
406406 917.840 211.992i 2.26069 0.522148i
407407 148.108 648.903i 0.363901 1.59436i
408408 −164.020 + 205.674i −0.402009 + 0.504103i
409409 149.521 310.483i 0.365577 0.759128i −0.634326 0.773066i 0.718722π-0.718722\pi
0.999903 + 0.0139374i 0.00443657π0.00443657\pi
410410 1604.05 3.91232
411411 279.111i 0.679103i
412412 −162.064 + 336.529i −0.393359 + 0.816818i
413413 95.5863 423.845i 0.231444 1.02626i
414414 423.659 204.024i 1.02333 0.492811i
415415 810.481 390.307i 1.95297 0.940499i
416416 541.584 + 123.613i 1.30189 + 0.297147i
417417 11.7710 51.5720i 0.0282277 0.123674i
418418 −316.275 656.751i −0.756638 1.57117i
419419 182.812 + 379.612i 0.436305 + 0.905996i 0.996958 + 0.0779452i 0.0248359π0.0248359\pi
−0.560653 + 0.828051i 0.689450π0.689450\pi
420420 −670.517 + 537.565i −1.59647 + 1.27992i
421421 202.337 + 97.4405i 0.480611 + 0.231450i 0.658472 0.752606i 0.271203π-0.271203\pi
−0.177860 + 0.984056i 0.556918π0.556918\pi
422422 744.502 1.76422
423423 46.3975i 0.109687i
424424 −731.216 352.135i −1.72457 0.830508i
425425 143.630 + 114.541i 0.337953 + 0.269509i
426426 387.801 + 88.5130i 0.910331 + 0.207777i
427427 −691.728 + 1.79054i −1.61997 + 0.00419330i
428428 86.2296 + 377.796i 0.201471 + 0.882702i
429429 −143.152 68.9382i −0.333687 0.160695i
430430 −603.303 + 137.700i −1.40303 + 0.320232i
431431 −76.2920 + 95.6672i −0.177012 + 0.221966i −0.862420 0.506193i 0.831052π-0.831052\pi
0.685408 + 0.728159i 0.259624π0.259624\pi
432432 −213.112 48.6414i −0.493315 0.112596i
433433 236.904 188.925i 0.547122 0.436316i −0.310516 0.950568i 0.600502π-0.600502\pi
0.857639 + 0.514252i 0.171931π0.171931\pi
434434 −85.7958 107.015i −0.197686 0.246578i
435435 279.917 351.004i 0.643487 0.806907i
436436 457.031 + 573.099i 1.04824 + 1.31445i
437437 312.936 + 649.817i 0.716100 + 1.48700i
438438 56.4878 + 70.8335i 0.128968 + 0.161720i
439439 −139.246 + 31.7819i −0.317188 + 0.0723961i −0.378151 0.925744i 0.623440π-0.623440\pi
0.0609629 + 0.998140i 0.480583π0.480583\pi
440440 1793.63i 4.07644i
441441 92.2468 + 114.453i 0.209176 + 0.259531i
442442 −207.644 −0.469784
443443 −102.625 449.631i −0.231660 1.01497i −0.948263 0.317487i 0.897161π-0.897161\pi
0.716603 0.697481i 0.245696π-0.245696\pi
444444 780.022 622.047i 1.75681 1.40101i
445445 −524.939 + 252.797i −1.17964 + 0.568084i
446446 274.417 218.841i 0.615286 0.490674i
447447 86.8089 + 69.2278i 0.194203 + 0.154872i
448448 608.637 140.576i 1.35857 0.313786i
449449 −398.695 499.947i −0.887961 1.11347i −0.992896 0.118989i 0.962035π-0.962035\pi
0.104934 0.994479i 0.466537π-0.466537\pi
450450 −65.8734 + 288.610i −0.146385 + 0.641356i
451451 535.509 + 427.054i 1.18738 + 0.946906i
452452 92.6303 + 405.840i 0.204934 + 0.897875i
453453 −31.3990 + 65.2007i −0.0693135 + 0.143931i
454454 384.770 87.8212i 0.847511 0.193439i
455455 −393.774 88.8046i −0.865437 0.195175i
456456 144.683 633.900i 0.317288 1.39013i
457457 170.200 213.424i 0.372429 0.467011i −0.559933 0.828538i 0.689173π-0.689173\pi
0.932362 + 0.361527i 0.117745π0.117745\pi
458458 −97.3203 + 202.088i −0.212490 + 0.441239i
459459 36.0384 0.0785150
460460 2982.32i 6.48330i
461461 −65.5948 + 136.209i −0.142288 + 0.295464i −0.959919 0.280279i 0.909573π-0.909573\pi
0.817630 + 0.575743i 0.195287π0.195287\pi
462462 −515.565 + 1.33454i −1.11594 + 0.00288862i
463463 −24.7587 + 11.9232i −0.0534745 + 0.0257520i −0.460430 0.887696i 0.652305π-0.652305\pi
0.406955 + 0.913448i 0.366590π0.366590\pi
464464 −1369.14 + 659.345i −2.95074 + 1.42100i
465465 −63.7309 14.5462i −0.137056 0.0312821i
466466 174.143 762.972i 0.373698 1.63728i
467467 28.8886 + 59.9877i 0.0618599 + 0.128453i 0.929607 0.368553i 0.120147π-0.120147\pi
−0.867747 + 0.497007i 0.834432π0.834432\pi
468468 −103.335 214.577i −0.220801 0.458498i
469469 114.682 + 236.572i 0.244525 + 0.504418i
470470 372.482 + 179.378i 0.792515 + 0.381655i
471471 −11.8519 −0.0251633
472472 1359.27i 2.87980i
473473 −238.072 114.650i −0.503324 0.242388i
474474 −739.943 590.084i −1.56106 1.24490i
475475 −442.676 101.038i −0.931950 0.212712i
476476 −431.550 + 209.202i −0.906619 + 0.439499i
477477 24.7403 + 108.394i 0.0518665 + 0.227242i
478478 798.184 + 384.385i 1.66984 + 0.804153i
479479 −143.308 + 32.7091i −0.299182 + 0.0682863i −0.369477 0.929240i 0.620463π-0.620463\pi
0.0702950 + 0.997526i 0.477606π0.477606\pi
480480 535.634 671.664i 1.11590 1.39930i
481481 456.868 + 104.277i 0.949829 + 0.216792i
482482 148.643 118.539i 0.308389 0.245932i
483483 510.122 1.32045i 1.05615 0.00273386i
484484 57.2260 71.7592i 0.118236 0.148263i
485485 −628.392 787.979i −1.29565 1.62470i
486486 25.1968 + 52.3217i 0.0518452 + 0.107658i
487487 −37.3325 46.8135i −0.0766581 0.0961262i 0.742024 0.670374i 0.233866π-0.233866\pi
−0.818682 + 0.574247i 0.805295π0.805295\pi
488488 2109.77 481.540i 4.32329 0.986763i
489489 21.3664i 0.0436940i
490490 −1275.47 + 298.074i −2.60300 + 0.608313i
491491 692.984 1.41137 0.705686 0.708525i 0.250639π-0.250639\pi
0.705686 + 0.708525i 0.250639π0.250639\pi
492492 228.461 + 1000.95i 0.464351 + 2.03445i
493493 195.876 156.206i 0.397315 0.316848i
494494 462.393 222.677i 0.936018 0.450763i
495495 −192.108 + 153.201i −0.388097 + 0.309497i
496496 172.994 + 137.958i 0.348778 + 0.278141i
497497 338.075 + 268.177i 0.680230 + 0.539591i
498498 504.358 + 632.444i 1.01277 + 1.26997i
499499 91.6874 401.709i 0.183742 0.805027i −0.796086 0.605184i 0.793100π-0.793100\pi
0.979828 0.199843i 0.0640433π-0.0640433\pi
500500 −82.4626 65.7617i −0.164925 0.131523i
501501 50.6238 + 221.797i 0.101045 + 0.442709i
502502 118.407 245.874i 0.235870 0.489790i
503503 −569.083 + 129.889i −1.13138 + 0.258229i −0.746920 0.664914i 0.768468π-0.768468\pi
−0.384457 + 0.923143i 0.625611π0.625611\pi
504504 −360.288 285.797i −0.714857 0.567058i
505505 −109.396 + 479.294i −0.216625 + 0.949098i
506506 −1115.51 + 1398.80i −2.20456 + 2.76443i
507507 −78.4682 + 162.941i −0.154770 + 0.321383i
508508 347.124 0.683316
509509 79.0599i 0.155324i 0.996980 + 0.0776620i 0.0247455π0.0247455\pi
−0.996980 + 0.0776620i 0.975255π0.975255\pi
510510 −139.328 + 289.318i −0.273192 + 0.567290i
511511 22.1188 + 95.7654i 0.0432853 + 0.187408i
512512 700.139 337.169i 1.36746 0.658534i
513513 −80.2520 + 38.6473i −0.156437 + 0.0753360i
514514 −296.412 67.6541i −0.576677 0.131623i
515515 −60.3744 + 264.518i −0.117232 + 0.513627i
516516 −171.854 356.858i −0.333050 0.691585i
517517 76.5958 + 159.053i 0.148154 + 0.307646i
518518 1481.60 342.203i 2.86023 0.660623i
519519 353.277 + 170.129i 0.680688 + 0.327802i
520520 1262.83 2.42852
521521 34.5587i 0.0663316i 0.999450 + 0.0331658i 0.0105589π0.0105589\pi
−0.999450 + 0.0331658i 0.989441π0.989441\pi
522522 363.735 + 175.166i 0.696811 + 0.335566i
523523 −734.302 585.586i −1.40402 1.11967i −0.976464 0.215679i 0.930804π-0.930804\pi
−0.427555 0.903989i 0.640625π-0.640625\pi
524524 2037.44 + 465.031i 3.88824 + 0.887464i
525525 −199.583 + 251.603i −0.380158 + 0.479243i
526526 247.431 + 1084.07i 0.470401 + 2.06096i
527527 −32.8668 15.8278i −0.0623658 0.0300338i
528528 810.857 185.073i 1.53571 0.350517i
529529 773.906 970.447i 1.46296 1.83449i
530530 −965.845 220.448i −1.82235 0.415939i
531531 145.585 116.100i 0.274171 0.218644i
532532 736.651 928.653i 1.38468 1.74559i
533533 −300.672 + 377.031i −0.564113 + 0.707376i
534534 −326.666 409.627i −0.611735 0.767091i
535535 122.132 + 253.609i 0.228283 + 0.474035i
536536 −512.803 643.035i −0.956723 1.19969i
537537 −423.499 + 96.6610i −0.788639 + 0.180002i
538538 561.771i 1.04418i
539539 −505.172 240.064i −0.937239 0.445388i
540540 −368.314 −0.682064
541541 103.425 + 453.137i 0.191175 + 0.837591i 0.975982 + 0.217851i 0.0699047π0.0699047\pi
−0.784807 + 0.619740i 0.787238π0.787238\pi
542542 −288.964 + 230.441i −0.533145 + 0.425169i
543543 −116.090 + 55.9060i −0.213794 + 0.102958i
544544 374.819 298.908i 0.689005 0.549463i
545545 416.293 + 331.982i 0.763840 + 0.609142i
546546 −0.939600 362.990i −0.00172088 0.664816i
547547 −326.584 409.523i −0.597045 0.748671i 0.387869 0.921714i 0.373211π-0.373211\pi
−0.984914 + 0.173044i 0.944640π0.944640\pi
548548 354.219 1551.93i 0.646384 2.83200i
549549 −231.779 184.837i −0.422183 0.336680i
550550 −250.638 1098.12i −0.455705 1.99658i
551551 −268.673 + 557.905i −0.487609 + 1.01253i
552552 −1555.87 + 355.117i −2.81860 + 0.643328i
553553 −447.872 923.890i −0.809895 1.67069i
554554 162.010 709.814i 0.292438 1.28125i
555555 451.848 566.600i 0.814141 1.02090i
556556 −130.899 + 271.815i −0.235431 + 0.488877i
557557 −769.420 −1.38136 −0.690682 0.723158i 0.742690π-0.742690\pi
−0.690682 + 0.723158i 0.742690π0.742690\pi
558558 58.7833i 0.105346i
559559 80.7203 167.617i 0.144401 0.299852i
560560 1901.39 921.732i 3.39534 1.64595i
561561 −123.541 + 59.4943i −0.220216 + 0.106050i
562562 −1445.07 + 695.908i −2.57130 + 1.23827i
563563 −516.829 117.963i −0.917990 0.209525i −0.262678 0.964883i 0.584606π-0.584606\pi
−0.655312 + 0.755358i 0.727463π0.727463\pi
564564 −58.8829 + 257.983i −0.104402 + 0.457416i
565565 131.197 + 272.434i 0.232208 + 0.482184i
566566 −61.5376 127.784i −0.108724 0.225767i
567567 0.163075 + 62.9998i 0.000287610 + 0.111111i
568568 −1216.30 585.738i −2.14137 1.03123i
569569 −859.498 −1.51054 −0.755271 0.655413i 0.772495π-0.772495\pi
−0.755271 + 0.655413i 0.772495π0.772495\pi
570570 793.682i 1.39243i
571571 −237.852 114.544i −0.416554 0.200602i 0.213854 0.976866i 0.431398π-0.431398\pi
−0.630408 + 0.776264i 0.717112π0.717112\pi
572572 708.473 + 564.988i 1.23859 + 0.987741i
573573 −4.11564 0.939369i −0.00718262 0.00163939i
574574 −344.254 + 1526.48i −0.599745 + 2.65937i
575575 247.992 + 1086.52i 0.431290 + 1.88961i
576576 241.200 + 116.156i 0.418750 + 0.201659i
577577 −697.807 + 159.270i −1.20937 + 0.276031i −0.779234 0.626733i 0.784392π-0.784392\pi
−0.430137 + 0.902764i 0.641535π0.641535\pi
578578 559.539 701.640i 0.968061 1.21391i
579579 409.080 + 93.3698i 0.706528 + 0.161260i
580580 −2001.87 + 1596.44i −3.45150 + 2.75248i
581581 197.490 + 855.052i 0.339914 + 1.47169i
582582 565.076 708.583i 0.970922 1.21750i
583583 −263.755 330.738i −0.452410 0.567304i
584584 −133.411 277.031i −0.228444 0.474369i
585585 −107.863 135.256i −0.184381 0.231206i
586586 150.778 34.4140i 0.257300 0.0587270i
587587 868.739i 1.47996i 0.672626 + 0.739982i 0.265166π0.265166\pi
−0.672626 + 0.739982i 0.734834π0.734834\pi
588588 −367.665 753.460i −0.625280 1.28139i
589589 90.1630 0.153078
590590 369.211 + 1617.62i 0.625781 + 2.74172i
591591 192.278 153.337i 0.325344 0.259453i
592592 −2210.10 + 1064.33i −3.73328 + 1.79785i
593593 736.106 587.025i 1.24133 0.989925i 0.241517 0.970397i 0.422355π-0.422355\pi
0.999809 0.0195280i 0.00621635π-0.00621635\pi
594594 −172.751 137.765i −0.290827 0.231927i
595595 −271.799 + 217.906i −0.456806 + 0.366229i
596596 −394.824 495.094i −0.662457 0.830694i
597597 −56.4416 + 247.287i −0.0945421 + 0.414216i
598598 −984.844 785.387i −1.64690 1.31336i
599599 14.7744 + 64.7311i 0.0246652 + 0.108065i 0.985762 0.168146i 0.0537781π-0.0537781\pi
−0.961097 + 0.276212i 0.910921π0.910921\pi
600600 435.920 905.196i 0.726533 1.50866i
601601 −549.686 + 125.462i −0.914618 + 0.208756i −0.653831 0.756641i 0.726839π-0.726839\pi
−0.260787 + 0.965396i 0.583982π0.583982\pi
602602 −1.56263 603.679i −0.00259572 1.00279i
603603 −25.0721 + 109.848i −0.0415789 + 0.182169i
604604 257.333 322.685i 0.426048 0.534247i
605605 28.9272 60.0680i 0.0478136 0.0992860i
606606 −442.085 −0.729514
607607 627.796i 1.03426i −0.855907 0.517130i 0.827000π-0.827000\pi
0.855907 0.517130i 0.173000π-0.173000\pi
608608 −514.118 + 1067.58i −0.845589 + 1.75588i
609609 273.955 + 341.711i 0.449845 + 0.561102i
610610 2379.96 1146.13i 3.90158 1.87890i
611611 −111.983 + 53.9281i −0.183278 + 0.0882621i
612612 −200.383 45.7361i −0.327423 0.0747322i
613613 145.794 638.763i 0.237836 1.04203i −0.705114 0.709094i 0.749104π-0.749104\pi
0.942950 0.332934i 0.108039π-0.108039\pi
614614 272.557 + 565.971i 0.443904 + 0.921777i
615615 323.581 + 671.923i 0.526148 + 1.09256i
616616 1706.89 + 384.942i 2.77093 + 0.624905i
617617 564.311 + 271.758i 0.914604 + 0.440450i 0.831142 0.556061i 0.187688π-0.187688\pi
0.0834624 + 0.996511i 0.473402π0.473402\pi
618618 −243.982 −0.394794
619619 645.643i 1.04304i 0.853238 + 0.521521i 0.174635π0.174635\pi
−0.853238 + 0.521521i 0.825365π0.825365\pi
620620 335.900 + 161.761i 0.541775 + 0.260905i
621621 170.928 + 136.310i 0.275246 + 0.219501i
622622 −1770.61 404.131i −2.84664 0.649728i
623623 −127.912 553.807i −0.205316 0.888935i
624624 130.303 + 570.893i 0.208818 + 0.914893i
625625 527.594 + 254.076i 0.844151 + 0.406522i
626626 −1410.29 + 321.891i −2.25287 + 0.514202i
627627 211.306 264.970i 0.337011 0.422599i
628628 65.8998 + 15.0412i 0.104936 + 0.0239509i
629629 316.188 252.152i 0.502684 0.400877i
630630 −506.396 242.255i −0.803803 0.384531i
631631 −623.119 + 781.366i −0.987510 + 1.23830i −0.0163512 + 0.999866i 0.505205π0.505205\pi
−0.971159 + 0.238432i 0.923366π0.923366\pi
632632 2002.66 + 2511.26i 3.16877 + 3.97351i
633633 150.187 + 311.866i 0.237262 + 0.492679i
634634 −205.295 257.432i −0.323810 0.406045i
635635 245.826 56.1081i 0.387127 0.0883592i
636636 634.100i 0.997012i
637637 169.020 355.672i 0.265337 0.558355i
638638 −1536.07 −2.40764
639639 41.1528 + 180.302i 0.0644019 + 0.282163i
640640 −313.868 + 250.302i −0.490420 + 0.391097i
641641 −94.5155 + 45.5162i −0.147450 + 0.0710082i −0.506154 0.862443i 0.668933π-0.668933\pi
0.358704 + 0.933451i 0.383219π0.383219\pi
642642 −197.899 + 157.819i −0.308254 + 0.245825i
643643 −37.0867 29.5757i −0.0576776 0.0459964i 0.594227 0.804298i 0.297458π-0.297458\pi
−0.651904 + 0.758301i 0.726030π0.726030\pi
644644 −2838.09 640.051i −4.40697 0.993869i
645645 −179.384 224.941i −0.278115 0.348745i
646646 98.5569 431.806i 0.152565 0.668430i
647647 248.400 + 198.092i 0.383926 + 0.306170i 0.796367 0.604814i 0.206752π-0.206752\pi
−0.412441 + 0.910984i 0.635324π0.635324\pi
648648 −43.8567 192.149i −0.0676801 0.296526i
649649 −307.406 + 638.336i −0.473661 + 0.983568i
650650 773.141 176.464i 1.18945 0.271484i
651651 27.5203 57.5270i 0.0422739 0.0883672i
652652 −27.1159 + 118.803i −0.0415889 + 0.182213i
653653 289.268 362.731i 0.442983 0.555483i −0.509344 0.860563i 0.670112π-0.670112\pi
0.952327 + 0.305080i 0.0986832π0.0986832\pi
654654 −207.747 + 431.392i −0.317656 + 0.659620i
655655 1518.03 2.31760
656656 2524.35i 3.84809i
657657 −18.2764 + 37.9513i −0.0278180 + 0.0577646i
658658 −250.643 + 315.971i −0.380917 + 0.480200i
659659 −587.112 + 282.738i −0.890913 + 0.429041i −0.822598 0.568623i 0.807476π-0.807476\pi
−0.0683146 + 0.997664i 0.521762π0.521762\pi
660660 1262.60 608.035i 1.91303 0.921265i
661661 760.247 + 173.521i 1.15015 + 0.262513i 0.754760 0.656001i 0.227753π-0.227753\pi
0.395387 + 0.918515i 0.370611π0.370611\pi
662662 −377.783 + 1655.17i −0.570669 + 2.50026i
663663 −41.8876 86.9805i −0.0631789 0.131192i
664664 −1191.18 2473.50i −1.79394 3.72516i
665665 371.575 776.721i 0.558760 1.16800i
666666 587.150 + 282.757i 0.881607 + 0.424559i
667667 1519.86 2.27865
668668 1297.50i 1.94236i
669669 147.028 + 70.8050i 0.219773 + 0.105837i
670670 −784.934 625.964i −1.17154 0.934275i
671671 1099.69 + 250.997i 1.63888 + 0.374063i
672672 524.227 + 653.880i 0.780099 + 0.973036i
673673 −158.021 692.336i −0.234801 1.02873i −0.945599 0.325335i 0.894523π-0.894523\pi
0.710798 0.703397i 0.248334π-0.248334\pi
674674 162.964 + 78.4792i 0.241786 + 0.116438i
675675 −134.185 + 30.6268i −0.198793 + 0.0453731i
676676 643.092 806.411i 0.951319 1.19292i
677677 −952.525 217.408i −1.40698 0.321134i −0.549432 0.835538i 0.685156π-0.685156\pi
−0.857548 + 0.514405i 0.828013π0.828013\pi
678678 −212.589 + 169.534i −0.313553 + 0.250050i
679679 884.735 428.891i 1.30300 0.631651i
680680 679.499 852.064i 0.999263 1.25304i
681681 114.406 + 143.461i 0.167997 + 0.210662i
682682 97.0429 + 201.512i 0.142292 + 0.295472i
683683 325.371 + 408.002i 0.476385 + 0.597368i 0.960722 0.277514i 0.0895104π-0.0895104\pi
−0.484337 + 0.874882i 0.660939π0.660939\pi
684684 495.270 113.042i 0.724079 0.165266i
685685 1156.30i 1.68803i
686686 −9.92264 1277.76i −0.0144645 1.86263i
687687 −104.285 −0.151798
688688 216.703 + 949.439i 0.314976 + 1.38000i
689689 232.860 185.700i 0.337968 0.269520i
690690 −1755.13 + 845.226i −2.54367 + 1.22497i
691691 810.433 646.299i 1.17284 0.935309i 0.174063 0.984735i 0.444310π-0.444310\pi
0.998778 + 0.0494256i 0.0157391π0.0157391\pi
692692 −1748.41 1394.31i −2.52660 2.01489i
693693 −104.563 215.697i −0.150884 0.311251i
694694 −52.1031 65.3352i −0.0750765 0.0941430i
695695 −48.7646 + 213.652i −0.0701649 + 0.307412i
696696 −1071.23 854.277i −1.53912 1.22741i
697697 92.6083 + 405.744i 0.132867 + 0.582129i
698698 −71.3906 + 148.244i −0.102279 + 0.212384i
699699 354.732 80.9653i 0.507486 0.115830i
700700 1429.04 1145.69i 2.04149 1.63670i
701701 212.301 930.153i 0.302855 1.32689i −0.562941 0.826497i 0.690330π-0.690330\pi
0.865796 0.500397i 0.166813π-0.166813\pi
702702 96.9948 121.628i 0.138169 0.173259i
703703 −433.698 + 900.583i −0.616924 + 1.28106i
704704 −1018.60 −1.44688
705705 192.215i 0.272645i
706706 −283.509 + 588.713i −0.401571 + 0.833872i
707707 −432.637 206.969i −0.611934 0.292743i
708708 −956.832 + 460.786i −1.35146 + 0.650828i
709709 −1171.86 + 564.340i −1.65284 + 0.795966i −0.653607 + 0.756834i 0.726745π0.726745\pi
−0.999234 + 0.0391320i 0.987541π0.987541\pi
710710 −1606.58 366.691i −2.26278 0.516466i
711711 97.9146 428.992i 0.137714 0.603364i
712712 771.511 + 1602.06i 1.08358 + 2.25008i
713713 −96.0184 199.384i −0.134668 0.279641i
714714 −245.424 194.682i −0.343732 0.272664i
715715 593.047 + 285.596i 0.829436 + 0.399435i
716716 2477.44 3.46011
717717 411.894i 0.574468i
718718 873.264 + 420.542i 1.21625 + 0.585713i
719719 811.071 + 646.807i 1.12805 + 0.899593i 0.995794 0.0916223i 0.0292053π-0.0292053\pi
0.132260 + 0.991215i 0.457777π0.457777\pi
720720 882.877 + 201.511i 1.22622 + 0.279876i
721721 −238.768 114.224i −0.331163 0.158425i
722722 −55.6637 243.879i −0.0770965 0.337782i
723723 79.6405 + 38.3528i 0.110153 + 0.0530468i
724724 716.441 163.523i 0.989559 0.225860i
725725 −596.574 + 748.080i −0.822861 + 1.03184i
726726 58.4497 + 13.3408i 0.0805092 + 0.0183757i
727727 798.146 636.500i 1.09786 0.875516i 0.104963 0.994476i 0.466528π-0.466528\pi
0.992899 + 0.118960i 0.0379561π0.0379561\pi
728728 −271.022 + 1201.76i −0.372284 + 1.65077i
729729 −16.8342 + 21.1095i −0.0230922 + 0.0289567i
730730 −234.017 293.448i −0.320571 0.401983i
731731 −69.6623 144.655i −0.0952972 0.197887i
732732 1054.17 + 1321.89i 1.44013 + 1.80587i
733733 −426.040 + 97.2408i −0.581227 + 0.132661i −0.503019 0.864276i 0.667777π-0.667777\pi
−0.0782089 + 0.996937i 0.524920π0.524920\pi
734734 1872.56i 2.55118i
735735 −382.159 474.155i −0.519944 0.645109i
736736 2908.32 3.95152
737737 −95.3954 417.954i −0.129437 0.567102i
738738 −524.323 + 418.134i −0.710465 + 0.566577i
739739 921.832 443.931i 1.24740 0.600718i 0.310590 0.950544i 0.399473π-0.399473\pi
0.936815 + 0.349826i 0.113759π0.113759\pi
740740 −3231.46 + 2577.01i −4.36684 + 3.48244i
741741 186.555 + 148.773i 0.251761 + 0.200773i
742742 417.072 871.825i 0.562092 1.17497i
743743 276.053 + 346.160i 0.371539 + 0.465895i 0.932091 0.362224i 0.117983π-0.117983\pi
−0.560552 + 0.828119i 0.689411π0.689411\pi
744744 −44.3934 + 194.500i −0.0596685 + 0.261425i
745745 −359.631 286.796i −0.482726 0.384961i
746746 127.829 + 560.056i 0.171353 + 0.750745i
747747 −163.183 + 338.853i −0.218451 + 0.453618i
748748 762.425 174.019i 1.01928 0.232645i
749749 −267.556 + 61.7969i −0.357217 + 0.0825059i
750750 15.3306 67.1679i 0.0204408 0.0895572i
751751 364.166 456.650i 0.484908 0.608056i −0.477843 0.878445i 0.658581π-0.658581\pi
0.962751 + 0.270390i 0.0871525π0.0871525\pi
752752 282.293 586.188i 0.375390 0.779505i
753753 126.881 0.168500
754754 1081.49i 1.43434i
755755 130.079 270.113i 0.172291 0.357765i
756756 79.0459 350.503i 0.104558 0.463628i
757757 514.908 247.966i 0.680195 0.327565i −0.0616867 0.998096i 0.519648π-0.519648\pi
0.741882 + 0.670531i 0.233934π0.233934\pi
758758 1787.58 860.853i 2.35829 1.13569i
759759 −810.976 185.100i −1.06848 0.243874i
760760 −599.392 + 2626.11i −0.788674 + 3.45541i
761761 108.758 + 225.838i 0.142914 + 0.296764i 0.960123 0.279577i 0.0901942π-0.0901942\pi
−0.817209 + 0.576341i 0.804480π0.804480\pi
762762 98.3794 + 204.287i 0.129107 + 0.268093i
763763 −405.270 + 324.912i −0.531154 + 0.425835i
764764 21.6919 + 10.4463i 0.0283926 + 0.0136731i
765765 −149.299 −0.195162
766766 1771.73i 2.31296i
767767 −449.427 216.433i −0.585955 0.282181i
768768 201.127 + 160.393i 0.261884 + 0.208845i
769769 −402.371 91.8385i −0.523239 0.119426i −0.0472601 0.998883i 0.515049π-0.515049\pi
−0.475979 + 0.879457i 0.657906π0.657906\pi
770770 2135.88 5.52872i 2.77387 0.00718016i
771771 −31.4547 137.812i −0.0407973 0.178745i
772772 −2156.10 1038.32i −2.79287 1.34498i
773773 1288.36 294.059i 1.66670 0.380413i 0.717862 0.696186i 0.245121π-0.245121\pi
0.948835 + 0.315773i 0.102264π0.102264\pi
774774 161.310 202.276i 0.208410 0.261338i
775775 135.827 + 31.0016i 0.175260 + 0.0400021i
776776 −2404.83 + 1917.79i −3.09901 + 2.47138i
777777 442.225 + 551.598i 0.569144 + 0.709907i
778778 −1351.83 + 1695.14i −1.73757 + 2.17884i
779779 −641.342 804.218i −0.823289 1.03237i
780780 428.094 + 888.946i 0.548838 + 1.13967i
781781 −438.727 550.146i −0.561750 0.704413i
782782 −1059.84 + 241.902i −1.35530 + 0.309338i
783783 187.701i 0.239721i
784784 469.089 + 2007.26i 0.598328 + 2.56027i
785785 49.0999 0.0625477
786786 303.758 + 1330.85i 0.386461 + 1.69319i
787787 −250.942 + 200.120i −0.318859 + 0.254282i −0.769819 0.638263i 0.779653π-0.779653\pi
0.450959 + 0.892544i 0.351082π0.351082\pi
788788 −1263.72 + 608.574i −1.60370 + 0.772302i
789789 −404.193 + 322.333i −0.512285 + 0.408534i
790790 3065.42 + 2444.59i 3.88028 + 3.09442i
791791 −287.416 + 66.3840i −0.363358 + 0.0839241i
792792 467.554 + 586.294i 0.590345 + 0.740270i
793793 −176.717 + 774.247i −0.222846 + 0.976352i
794794 1882.87 + 1501.54i 2.37137 + 1.89110i
795795 −102.494 449.055i −0.128923 0.564849i
796796 627.661 1303.35i 0.788518 1.63738i
797797 117.682 26.8602i 0.147656 0.0337016i −0.148054 0.988979i 0.547301π-0.547301\pi
0.295710 + 0.955278i 0.404444π0.404444\pi
798798 755.300 + 170.336i 0.946491 + 0.213454i
799799 −23.8686 + 104.575i −0.0298731 + 0.130883i
800800 −1141.57 + 1431.49i −1.42697 + 1.78936i
801801 105.692 219.471i 0.131950 0.273996i
802802 130.652 0.162908
803803 160.271i 0.199590i
804804 278.815 578.965i 0.346785 0.720106i
805805 −2113.33 + 5.47035i −2.62525 + 0.00679547i
806806 −141.877 + 68.3241i −0.176025 + 0.0847694i
807807 −235.321 + 113.325i −0.291600 + 0.140427i
808808 1462.76 + 333.865i 1.81034 + 0.413199i
809809 140.582 615.928i 0.173772 0.761345i −0.810651 0.585530i 0.800887π-0.800887\pi
0.984423 0.175816i 0.0562562π-0.0562562\pi
810810 −104.385 216.757i −0.128870 0.267602i
811811 160.813 + 333.932i 0.198290 + 0.411754i 0.976277 0.216527i 0.0694730π-0.0694730\pi
−0.777986 + 0.628281i 0.783759π0.783759\pi
812812 −1089.60 2247.68i −1.34187 2.76808i
813813 −154.822 74.5584i −0.190433 0.0917078i
814814 −2479.57 −3.04615
815815 88.5163i 0.108609i
816816 455.310 + 219.266i 0.557978 + 0.268708i
817817 310.255 + 247.420i 0.379749 + 0.302840i
818818 −1251.61 285.672i −1.53009 0.349233i
819819 151.864 73.6186i 0.185426 0.0898884i
820820 −946.463 4146.73i −1.15422 5.05698i
821821 −444.201 213.916i −0.541049 0.260556i 0.143339 0.989674i 0.454216π-0.454216\pi
−0.684388 + 0.729118i 0.739930π0.739930\pi
822822 1013.72 231.375i 1.23324 0.281478i
823823 −228.870 + 286.994i −0.278092 + 0.348717i −0.901188 0.433429i 0.857303π-0.857303\pi
0.623095 + 0.782146i 0.285875π0.285875\pi
824824 807.281 + 184.257i 0.979710 + 0.223612i
825825 409.431 326.511i 0.496280 0.395770i
826826 −1618.63 + 4.18982i −1.95960 + 0.00507242i
827827 −635.621 + 797.043i −0.768586 + 0.963776i −0.999959 0.00908888i 0.997107π-0.997107\pi
0.231373 + 0.972865i 0.425678π0.425678\pi
828828 −777.412 974.844i −0.938904 1.17735i
829829 356.065 + 739.377i 0.429511 + 0.891890i 0.997621 + 0.0689368i 0.0219607π0.0219607\pi
−0.568110 + 0.822953i 0.692325π0.692325\pi
830830 −2089.45 2620.08i −2.51740 3.15672i
831831 330.017 75.3243i 0.397133 0.0906429i
832832 717.158i 0.861968i
833833 −149.036 305.421i −0.178915 0.366652i
834834 −197.065 −0.236289
835835 −209.723 918.859i −0.251166 1.10043i
836836 −1511.19 + 1205.13i −1.80764 + 1.44155i
837837 24.6238 11.8582i 0.0294191 0.0141675i
838838 1227.19 978.653i 1.46443 1.16784i
839839 −86.5900 69.0532i −0.103206 0.0823042i 0.570527 0.821279i 0.306739π-0.306739\pi
−0.673733 + 0.738975i 0.735310π0.735310\pi
840840 1492.59 + 1184.00i 1.77690 + 1.40952i
841841 289.226 + 362.678i 0.343908 + 0.431247i
842842 186.168 815.657i 0.221103 0.968714i
843843 −583.020 464.943i −0.691602 0.551534i
844844 −439.291 1924.66i −0.520487 2.28040i
845845 325.077 675.029i 0.384707 0.798851i
846846 −168.514 + 38.4622i −0.199189 + 0.0454636i
847847 50.9549 + 40.4198i 0.0601592 + 0.0477212i
848848 −346.927 + 1519.98i −0.409111 + 1.79243i
849849 41.1139 51.5551i 0.0484262 0.0607245i
850850 296.944 616.611i 0.349346 0.725424i
851851 2453.39 2.88295
852852 1054.75i 1.23797i
853853 95.9902 199.326i 0.112532 0.233676i −0.837095 0.547058i 0.815748π-0.815748\pi
0.949627 + 0.313382i 0.101462π0.101462\pi
854854 579.926 + 2510.85i 0.679070 + 2.94010i
855855 332.467 160.108i 0.388850 0.187260i
856856 773.988 372.733i 0.904192 0.435436i
857857 1164.04 + 265.685i 1.35828 + 0.310017i 0.838787 0.544460i 0.183265π-0.183265\pi
0.519489 + 0.854477i 0.326123π0.326123\pi
858858 −131.712 + 577.069i −0.153511 + 0.672575i
859859 −499.864 1037.98i −0.581914 1.20836i −0.959323 0.282310i 0.908899π-0.908899\pi
0.377410 0.926046i 0.376815π-0.376815\pi
860860 711.953 + 1478.39i 0.827852 + 1.71905i
861861 −708.874 + 163.728i −0.823315 + 0.190160i
862862 410.703 + 197.784i 0.476454 + 0.229448i
863863 −1214.35 −1.40713 −0.703563 0.710633i 0.748409π-0.748409\pi
−0.703563 + 0.710633i 0.748409π0.748409\pi
864864 359.176i 0.415713i
865865 −1463.55 704.809i −1.69197 0.814809i
866866 −882.554 703.813i −1.01912 0.812717i
867867 406.786 + 92.8462i 0.469188 + 0.107089i
868868 −226.028 + 284.940i −0.260400 + 0.328271i
869869 372.550 + 1632.25i 0.428711 + 1.87831i
870870 −1506.88 725.674i −1.73204 0.834108i
871871 294.266 67.1642i 0.337848 0.0771116i
872872 1013.18 1270.48i 1.16190 1.45698i
873873 410.811 + 93.7650i 0.470574 + 0.107405i
874874 2100.70 1675.25i 2.40354 1.91676i
875875 46.4487 58.5552i 0.0530843 0.0669202i
876876 149.786 187.825i 0.170988 0.214412i
877877 818.888 + 1026.85i 0.933738 + 1.17087i 0.985064 + 0.172188i 0.0550838π0.0550838\pi
−0.0513262 + 0.998682i 0.516345π0.516345\pi
878878 230.861 + 479.388i 0.262940 + 0.546000i
879879 44.8317 + 56.2172i 0.0510031 + 0.0639559i
880880 −3359.21 + 766.717i −3.81728 + 0.871269i
881881 1003.65i 1.13922i 0.821915 + 0.569610i 0.192906π0.192906\pi
−0.821915 + 0.569610i 0.807094π0.807094\pi
882882 339.220 429.915i 0.384603 0.487432i
883883 1127.54 1.27694 0.638470 0.769647i 0.279568π-0.279568\pi
0.638470 + 0.769647i 0.279568π0.279568\pi
884884 122.520 + 536.794i 0.138597 + 0.607233i
885885 −603.126 + 480.977i −0.681499 + 0.543477i
886886 −1547.97 + 745.462i −1.74714 + 0.841380i
887887 −448.953 + 358.028i −0.506148 + 0.403639i −0.842996 0.537920i 0.819210π-0.819210\pi
0.336848 + 0.941559i 0.390639π0.390639\pi
888888 −1729.20 1378.99i −1.94730 1.55292i
889889 0.636717 + 245.979i 0.000716217 + 0.276692i
890890 1353.31 + 1697.00i 1.52057 + 1.90674i
891891 22.8597 100.155i 0.0256563 0.112407i
892892 −727.657 580.287i −0.815759 0.650546i
893893 −58.9941 258.470i −0.0660629 0.289440i
894894 179.471 372.675i 0.200750 0.416862i
895895 1754.47 400.446i 1.96030 0.447425i
896896 −170.836 352.408i −0.190665 0.393313i
897897 130.322 570.977i 0.145286 0.636541i
898898 −1485.28 + 1862.49i −1.65399 + 2.07404i
899899 82.4372 171.183i 0.0916987 0.190414i
900900 784.972 0.872191
901901 257.037i 0.285280i
902902 1107.12 2298.96i 1.22741 2.54874i
903903 252.561 122.433i 0.279691 0.135585i
904904 831.440 400.400i 0.919735 0.442921i
905905 480.936 231.606i 0.531421 0.255919i
906906 262.835 + 59.9904i 0.290105 + 0.0662146i
907907 −251.876 + 1103.54i −0.277702 + 1.21669i 0.622989 + 0.782231i 0.285918π0.285918\pi
−0.900691 + 0.434461i 0.856939π0.856939\pi
908908 −454.064 942.873i −0.500070 1.03841i
909909 −89.1808 185.186i −0.0981087 0.203725i
910910 3.89256 + 1503.79i 0.00427754 + 1.65251i
911911 −1076.52 518.423i −1.18169 0.569070i −0.263284 0.964718i 0.584806π-0.584806\pi
−0.918402 + 0.395648i 0.870520π0.870520\pi
912912 −1249.05 −1.36957
913913 1430.99i 1.56735i
914914 −916.238 441.237i −1.00245 0.482754i
915915 960.209 + 765.741i 1.04941 + 0.836876i
916916 579.852 + 132.348i 0.633027 + 0.144484i
917917 −325.793 + 1444.62i −0.355281 + 1.57537i
918918 −29.8748 130.890i −0.0325433 0.142582i
919919 916.390 + 441.310i 0.997160 + 0.480207i 0.859974 0.510339i 0.170480π-0.170480\pi
0.137186 + 0.990545i 0.456194π0.456194\pi
920920 6445.63 1471.17i 7.00612 1.59910i
921921 −182.098 + 228.344i −0.197718 + 0.247931i
922922 549.082 + 125.324i 0.595534 + 0.135927i
923923 387.337 308.891i 0.419650 0.334659i
924924 307.657 + 1332.03i 0.332962 + 1.44159i
925925 −963.004 + 1207.57i −1.04109 + 1.30548i
926926 63.8287 + 80.0387i 0.0689295 + 0.0864349i
927927 −49.2180 102.202i −0.0530938 0.110250i
928928 1556.83 + 1952.20i 1.67762 + 2.10366i
929929 −1645.76 + 375.634i −1.77154 + 0.404342i −0.978734 0.205133i 0.934237π-0.934237\pi
−0.792805 + 0.609475i 0.791380π0.791380\pi
930930 243.526i 0.261856i
931931 659.412 + 520.302i 0.708284 + 0.558864i
932932 −2075.16 −2.22657
933933 −187.894 823.219i −0.201387 0.882336i
934934 193.925 154.650i 0.207629 0.165578i
935935 511.804 246.472i 0.547384 0.263606i
936936 −412.787 + 329.186i −0.441011 + 0.351695i
937937 −1208.15 963.470i −1.28938 1.02825i −0.997417 0.0718218i 0.977119π-0.977119\pi
−0.291967 0.956428i 0.594310π-0.594310\pi
938938 764.152 612.633i 0.814661 0.653127i
939939 −419.333 525.827i −0.446574 0.559986i
940940 243.939 1068.77i 0.259510 1.13699i
941941 −27.2728 21.7493i −0.0289828 0.0231130i 0.608891 0.793254i 0.291615π-0.291615\pi
−0.637874 + 0.770141i 0.720186π0.720186\pi
942942 9.82489 + 43.0457i 0.0104298 + 0.0456960i
943943 −1095.43 + 2274.69i −1.16165 + 2.41219i
944944 2545.70 581.040i 2.69672 0.615508i
945945 −0.675585 260.995i −0.000714905 0.276185i
946946 −219.048 + 959.710i −0.231551 + 1.01449i
947947 −288.184 + 361.371i −0.304312 + 0.381596i −0.910349 0.413841i 0.864187π-0.864187\pi
0.606037 + 0.795437i 0.292758π0.292758\pi
948948 −1088.86 + 2261.05i −1.14859 + 2.38507i
949949 112.840 0.118904
950950 1691.54i 1.78057i
951951 66.4225 137.928i 0.0698449 0.145034i
952952 665.027 + 829.504i 0.698558 + 0.871328i
953953 826.063 397.811i 0.866803 0.417430i 0.0530158 0.998594i 0.483117π-0.483117\pi
0.813787 + 0.581164i 0.197402π0.197402\pi
954954 373.175 179.712i 0.391169 0.188377i
955955 17.0502 + 3.89160i 0.0178536 + 0.00407498i
956956 522.732 2290.24i 0.546791 2.39565i
957957 −309.869 643.449i −0.323792 0.672360i
958958 237.597 + 493.374i 0.248013 + 0.515005i
959959 1100.38 + 248.159i 1.14742 + 0.258769i
960960 −999.240 481.209i −1.04087 0.501259i
961961 933.335 0.971212
962962 1745.77i 1.81473i
963963 −106.031 51.0618i −0.110105 0.0530237i
964964 −394.149 314.323i −0.408868 0.326062i
965965 −1694.73 386.811i −1.75620 0.400841i
966966 −427.673 1851.65i −0.442725 1.91682i
967967 −7.55426 33.0974i −0.00781206 0.0342269i 0.970872 0.239600i 0.0770163π-0.0770163\pi
−0.978684 + 0.205373i 0.934159π0.934159\pi
968968 −183.321 88.2829i −0.189382 0.0912014i
969969 200.762 45.8225i 0.207184 0.0472885i
970970 −2340.99 + 2935.51i −2.41339 + 3.02630i
971971 −1512.36 345.185i −1.55752 0.355495i −0.644891 0.764275i 0.723097π-0.723097\pi
−0.912633 + 0.408780i 0.865954π0.865954\pi
972972 120.393 96.0099i 0.123861 0.0987757i
973973 −192.854 92.2592i −0.198205 0.0948193i
974974 −139.077 + 174.397i −0.142790 + 0.179053i
975975 229.883 + 288.265i 0.235778 + 0.295656i
976976 −1803.71 3745.43i −1.84806 3.83753i
977977 −162.223 203.421i −0.166041 0.208209i 0.691849 0.722042i 0.256797π-0.256797\pi
−0.857890 + 0.513833i 0.828225π0.828225\pi
978978 −77.6018 + 17.7121i −0.0793475 + 0.0181105i
979979 926.837i 0.946719i
980980 1523.16 + 3121.42i 1.55424 + 3.18513i
981981 −222.615 −0.226926
982982 −574.464 2516.89i −0.584993 2.56302i
983983 422.924 337.271i 0.430238 0.343103i −0.384305 0.923206i 0.625559π-0.625559\pi
0.814543 + 0.580103i 0.196988π0.196988\pi
984984 2050.64 987.536i 2.08398 1.00359i
985985 −796.568 + 635.242i −0.808698 + 0.644915i
986986 −729.711 581.925i −0.740072 0.590188i
987987 −182.919 41.2523i −0.185329 0.0417957i
988988 −848.488 1063.97i −0.858794 1.07689i
989989 216.735 949.578i 0.219146 0.960140i
990990 715.672 + 570.729i 0.722901 + 0.576494i
991991 283.922 + 1243.94i 0.286501 + 1.25524i 0.889291 + 0.457342i 0.151198π0.151198\pi
−0.602790 + 0.797900i 0.705944π0.705944\pi
992992 157.747 327.566i 0.159020 0.330208i
993993 −769.548 + 175.644i −0.774973 + 0.176883i
994994 693.753 1450.18i 0.697941 1.45894i
995995 233.825 1024.46i 0.235000 1.02960i
996996 1337.38 1677.02i 1.34275 1.68375i
997997 248.532 516.082i 0.249280 0.517635i −0.738354 0.674413i 0.764397π-0.764397\pi
0.987634 + 0.156778i 0.0501109π0.0501109\pi
998998 −1535.00 −1.53807
999999 302.992i 0.303295i
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 147.3.j.a.13.1 108
3.2 odd 2 441.3.v.c.307.18 108
49.34 odd 14 inner 147.3.j.a.34.1 yes 108
147.83 even 14 441.3.v.c.181.18 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.3.j.a.13.1 108 1.1 even 1 trivial
147.3.j.a.34.1 yes 108 49.34 odd 14 inner
441.3.v.c.181.18 108 147.83 even 14
441.3.v.c.307.18 108 3.2 odd 2