Properties

Label 859.2.f.a.100.4
Level 859859
Weight 22
Character 859.100
Analytic conductor 6.8596.859
Analytic rank 00
Dimension 840840
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] = [859,2,Mod(100,859)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(859, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([22])) 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("859.100"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 859 859
Weight: k k == 2 2
Character orbit: [χ][\chi] == 859.f (of order 1313, degree 1212, 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: 6.859149533636.85914953363
Analytic rank: 00
Dimension: 840840
Relative dimension: 7070 over Q(ζ13)\Q(\zeta_{13})
Twist minimal: yes
Sato-Tate group: SU(2)[C13]\mathrm{SU}(2)[C_{13}]

Embedding invariants

Embedding label 100.4
Character χ\chi == 859.100
Dual form 859.2.f.a.524.4

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+(2.20441+1.15696i)q2+(1.297391.87959i)q3+(2.384743.45489i)q4+(0.1799520.260706i)q5+(0.685356+5.64442i)q6+(0.00469214+0.0386433i)q7+(0.659588+5.43220i)q8+(0.7858262.07205i)q9+(0.698316+0.366504i)q10+(0.2488692.04962i)q11+(3.399848.96465i)q121.98457q13+(0.05505230.0797571i)q140.723486q15+(1.853604.88753i)q16+(7.44131+1.83412i)q17+(4.12958+3.65849i)q184.18117q191.32985q20+(0.0787210+0.0413160i)q21+(2.91995+4.23028i)q22+(2.750531.44359i)q23+(9.35456+8.28741i)q24+(1.737444.58125i)q25+(4.374802.29607i)q26+(1.73839+0.428474i)q27+(0.144698+0.0759432i)q28+(0.6462731.70408i)q29+(1.594860.837048i)q30+(0.477445+0.422979i)q31+(1.54894+1.37224i)q32+(4.175332.19138i)q33+(14.281712.6525i)q34+(0.009230160.00817721i)q35+(9.032702.22636i)q36+(0.4177281.10146i)q37+(9.217024.83747i)q38+(2.57475+3.73017i)q39+(1.534900.805577i)q40+(2.47468+3.58519i)q410.221335q42+0.328996q43+(7.674714.02800i)q44+(0.398785+0.577740i)q45+7.73349q46+(8.82036+7.81416i)q47+(11.59142.85702i)q48+(6.795121.67485i)q49+(1.47031+12.1091i)q50+(6.20686+16.3662i)q51+(4.73267+6.85646i)q52+(0.8513140.209830i)q53+(4.32785+1.06672i)q54+(0.489564+0.433716i)q550.213013q56+(5.42459+7.85888i)q57+(0.546910+4.50421i)q58+(2.74074+1.43845i)q59+(1.72532+2.49956i)q604.46186q61+(1.541860.380034i)q62+(0.07638370.0400893i)q63+(5.14850+1.26899i)q64+(0.357127+0.517388i)q65+11.7395q66+(3.412498.99799i)q67+(11.4089+30.0828i)q68+(6.28186+3.29697i)q69+(0.0108863+0.0287049i)q70+(4.788831.18034i)q71+(11.77412.90206i)q72+(0.1066900.878674i)q73+(2.19519+1.94477i)q74+(6.356749.20932i)q75+(9.97099+14.4455i)q76+(0.07803650.0192343i)q77+(1.3601411.2017i)q78+(2.73870+3.96769i)q79+(0.940648+1.36276i)q80+(8.036957.12012i)q81+(1.3072710.7663i)q82+(0.2481512.04371i)q83+(0.3304710.173444i)q84+(1.81724+1.60994i)q85+(0.725242+0.380636i)q86+(2.364513.42558i)q87+11.2981q88+(0.781030+0.192507i)q89+(0.2106621.73496i)q90+(0.009311880.0766902i)q91+(11.5467+6.06020i)q92+(1.414460.348632i)q93+(10.403027.4305i)q94+(0.752410+1.09005i)q95+(4.588831.13104i)q96+(4.56478+1.12512i)q97+(13.0415+11.5538i)q98+(4.05136+2.12632i)q99+O(q100)q+(-2.20441 + 1.15696i) q^{2} +(1.29739 - 1.87959i) q^{3} +(2.38474 - 3.45489i) q^{4} +(-0.179952 - 0.260706i) q^{5} +(-0.685356 + 5.64442i) q^{6} +(0.00469214 + 0.0386433i) q^{7} +(-0.659588 + 5.43220i) q^{8} +(-0.785826 - 2.07205i) q^{9} +(0.698316 + 0.366504i) q^{10} +(-0.248869 - 2.04962i) q^{11} +(-3.39984 - 8.96465i) q^{12} -1.98457 q^{13} +(-0.0550523 - 0.0797571i) q^{14} -0.723486 q^{15} +(-1.85360 - 4.88753i) q^{16} +(-7.44131 + 1.83412i) q^{17} +(4.12958 + 3.65849i) q^{18} -4.18117 q^{19} -1.32985 q^{20} +(0.0787210 + 0.0413160i) q^{21} +(2.91995 + 4.23028i) q^{22} +(-2.75053 - 1.44359i) q^{23} +(9.35456 + 8.28741i) q^{24} +(1.73744 - 4.58125i) q^{25} +(4.37480 - 2.29607i) q^{26} +(1.73839 + 0.428474i) q^{27} +(0.144698 + 0.0759432i) q^{28} +(0.646273 - 1.70408i) q^{29} +(1.59486 - 0.837048i) q^{30} +(0.477445 + 0.422979i) q^{31} +(1.54894 + 1.37224i) q^{32} +(-4.17533 - 2.19138i) q^{33} +(14.2817 - 12.6525i) q^{34} +(0.00923016 - 0.00817721i) q^{35} +(-9.03270 - 2.22636i) q^{36} +(-0.417728 - 1.10146i) q^{37} +(9.21702 - 4.83747i) q^{38} +(-2.57475 + 3.73017i) q^{39} +(1.53490 - 0.805577i) q^{40} +(-2.47468 + 3.58519i) q^{41} -0.221335 q^{42} +0.328996 q^{43} +(-7.67471 - 4.02800i) q^{44} +(-0.398785 + 0.577740i) q^{45} +7.73349 q^{46} +(-8.82036 + 7.81416i) q^{47} +(-11.5914 - 2.85702i) q^{48} +(6.79512 - 1.67485i) q^{49} +(1.47031 + 12.1091i) q^{50} +(-6.20686 + 16.3662i) q^{51} +(-4.73267 + 6.85646i) q^{52} +(-0.851314 - 0.209830i) q^{53} +(-4.32785 + 1.06672i) q^{54} +(-0.489564 + 0.433716i) q^{55} -0.213013 q^{56} +(-5.42459 + 7.85888i) q^{57} +(0.546910 + 4.50421i) q^{58} +(-2.74074 + 1.43845i) q^{59} +(-1.72532 + 2.49956i) q^{60} -4.46186 q^{61} +(-1.54186 - 0.380034i) q^{62} +(0.0763837 - 0.0400893i) q^{63} +(5.14850 + 1.26899i) q^{64} +(0.357127 + 0.517388i) q^{65} +11.7395 q^{66} +(-3.41249 - 8.99799i) q^{67} +(-11.4089 + 30.0828i) q^{68} +(-6.28186 + 3.29697i) q^{69} +(-0.0108863 + 0.0287049i) q^{70} +(-4.78883 - 1.18034i) q^{71} +(11.7741 - 2.90206i) q^{72} +(0.106690 - 0.878674i) q^{73} +(2.19519 + 1.94477i) q^{74} +(-6.35674 - 9.20932i) q^{75} +(-9.97099 + 14.4455i) q^{76} +(0.0780365 - 0.0192343i) q^{77} +(1.36014 - 11.2017i) q^{78} +(-2.73870 + 3.96769i) q^{79} +(-0.940648 + 1.36276i) q^{80} +(8.03695 - 7.12012i) q^{81} +(1.30727 - 10.7663i) q^{82} +(-0.248151 - 2.04371i) q^{83} +(0.330471 - 0.173444i) q^{84} +(1.81724 + 1.60994i) q^{85} +(-0.725242 + 0.380636i) q^{86} +(-2.36451 - 3.42558i) q^{87} +11.2981 q^{88} +(0.781030 + 0.192507i) q^{89} +(0.210662 - 1.73496i) q^{90} +(-0.00931188 - 0.0766902i) q^{91} +(-11.5467 + 6.06020i) q^{92} +(1.41446 - 0.348632i) q^{93} +(10.4030 - 27.4305i) q^{94} +(0.752410 + 1.09005i) q^{95} +(4.58883 - 1.13104i) q^{96} +(-4.56478 + 1.12512i) q^{97} +(-13.0415 + 11.5538i) q^{98} +(-4.05136 + 2.12632i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 840q10q25q374q420q5+5q63q7+2q869q9+7q1025q1158q1210q13+9q14148q1540q16q17+5q1838q19+121q99+O(q100) 840 q - 10 q^{2} - 5 q^{3} - 74 q^{4} - 20 q^{5} + 5 q^{6} - 3 q^{7} + 2 q^{8} - 69 q^{9} + 7 q^{10} - 25 q^{11} - 58 q^{12} - 10 q^{13} + 9 q^{14} - 148 q^{15} - 40 q^{16} - q^{17} + 5 q^{18} - 38 q^{19}+ \cdots - 121 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/859Z)×\left(\mathbb{Z}/859\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1113)e\left(\frac{11}{13}\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 −2.20441 + 1.15696i −1.55875 + 0.818098i −0.999937 0.0111929i 0.996437π-0.996437\pi
−0.558818 + 0.829291i 0.688745π0.688745\pi
33 1.29739 1.87959i 0.749046 1.08518i −0.244265 0.969709i 0.578547π-0.578547\pi
0.993311 0.115472i 0.0368381π-0.0368381\pi
44 2.38474 3.45489i 1.19237 1.72744i
55 −0.179952 0.260706i −0.0804770 0.116591i 0.780678 0.624933i 0.214874π-0.214874\pi
−0.861155 + 0.508342i 0.830258π0.830258\pi
66 −0.685356 + 5.64442i −0.279796 + 2.30432i
77 0.00469214 + 0.0386433i 0.00177346 + 0.0146058i 0.993569 0.113231i 0.0361199π-0.0361199\pi
−0.991795 + 0.127836i 0.959197π0.959197\pi
88 −0.659588 + 5.43220i −0.233200 + 1.92057i
99 −0.785826 2.07205i −0.261942 0.690685i
1010 0.698316 + 0.366504i 0.220827 + 0.115899i
1111 −0.248869 2.04962i −0.0750369 0.617985i −0.980914 0.194443i 0.937710π-0.937710\pi
0.905877 0.423541i 0.139213π-0.139213\pi
1212 −3.39984 8.96465i −0.981450 2.58787i
1313 −1.98457 −0.550420 −0.275210 0.961384i 0.588747π-0.588747\pi
−0.275210 + 0.961384i 0.588747π0.588747\pi
1414 −0.0550523 0.0797571i −0.0147134 0.0213160i
1515 −0.723486 −0.186803
1616 −1.85360 4.88753i −0.463399 1.22188i
1717 −7.44131 + 1.83412i −1.80478 + 0.444839i −0.990718 0.135935i 0.956596π-0.956596\pi
−0.814065 + 0.580774i 0.802750π0.802750\pi
1818 4.12958 + 3.65849i 0.973351 + 0.862314i
1919 −4.18117 −0.959226 −0.479613 0.877480i 0.659223π-0.659223\pi
−0.479613 + 0.877480i 0.659223π0.659223\pi
2020 −1.32985 −0.297363
2121 0.0787210 + 0.0413160i 0.0171783 + 0.00901588i
2222 2.91995 + 4.23028i 0.622536 + 0.901899i
2323 −2.75053 1.44359i −0.573526 0.301009i 0.152914 0.988239i 0.451134π-0.451134\pi
−0.726440 + 0.687230i 0.758826π0.758826\pi
2424 9.35456 + 8.28741i 1.90949 + 1.69166i
2525 1.73744 4.58125i 0.347488 0.916250i
2626 4.37480 2.29607i 0.857970 0.450297i
2727 1.73839 + 0.428474i 0.334553 + 0.0824598i
2828 0.144698 + 0.0759432i 0.0273453 + 0.0143519i
2929 0.646273 1.70408i 0.120010 0.316440i −0.861527 0.507711i 0.830492π-0.830492\pi
0.981537 + 0.191271i 0.0612610π0.0612610\pi
3030 1.59486 0.837048i 0.291181 0.152823i
3131 0.477445 + 0.422979i 0.0857517 + 0.0759693i 0.704910 0.709297i 0.250988π-0.250988\pi
−0.619158 + 0.785266i 0.712526π0.712526\pi
3232 1.54894 + 1.37224i 0.273817 + 0.242581i
3333 −4.17533 2.19138i −0.726831 0.381471i
3434 14.2817 12.6525i 2.44929 2.16988i
3535 0.00923016 0.00817721i 0.00156018 0.00138220i
3636 −9.03270 2.22636i −1.50545 0.371060i
3737 −0.417728 1.10146i −0.0686741 0.181079i 0.896285 0.443478i 0.146256π-0.146256\pi
−0.964959 + 0.262399i 0.915486π0.915486\pi
3838 9.21702 4.83747i 1.49520 0.784741i
3939 −2.57475 + 3.73017i −0.412290 + 0.597305i
4040 1.53490 0.805577i 0.242689 0.127373i
4141 −2.47468 + 3.58519i −0.386479 + 0.559912i −0.967143 0.254231i 0.918178π-0.918178\pi
0.580664 + 0.814143i 0.302793π0.302793\pi
4242 −0.221335 −0.0341527
4343 0.328996 0.0501714 0.0250857 0.999685i 0.492014π-0.492014\pi
0.0250857 + 0.999685i 0.492014π0.492014\pi
4444 −7.67471 4.02800i −1.15701 0.607243i
4545 −0.398785 + 0.577740i −0.0594473 + 0.0861243i
4646 7.73349 1.14024
4747 −8.82036 + 7.81416i −1.28658 + 1.13981i −0.304265 + 0.952587i 0.598411π0.598411\pi
−0.982317 + 0.187225i 0.940051π0.940051\pi
4848 −11.5914 2.85702i −1.67307 0.412375i
4949 6.79512 1.67485i 0.970732 0.239264i
5050 1.47031 + 12.1091i 0.207934 + 1.71249i
5151 −6.20686 + 16.3662i −0.869135 + 2.29172i
5252 −4.73267 + 6.85646i −0.656303 + 0.950819i
5353 −0.851314 0.209830i −0.116937 0.0288224i 0.180413 0.983591i 0.442257π-0.442257\pi
−0.297350 + 0.954769i 0.596103π0.596103\pi
5454 −4.32785 + 1.06672i −0.588946 + 0.145162i
5555 −0.489564 + 0.433716i −0.0660128 + 0.0584822i
5656 −0.213013 −0.0284650
5757 −5.42459 + 7.85888i −0.718505 + 1.04093i
5858 0.546910 + 4.50421i 0.0718129 + 0.591432i
5959 −2.74074 + 1.43845i −0.356814 + 0.187271i −0.633600 0.773661i 0.718423π-0.718423\pi
0.276785 + 0.960932i 0.410731π0.410731\pi
6060 −1.72532 + 2.49956i −0.222738 + 0.322692i
6161 −4.46186 −0.571282 −0.285641 0.958337i 0.592207π-0.592207\pi
−0.285641 + 0.958337i 0.592207π0.592207\pi
6262 −1.54186 0.380034i −0.195816 0.0482643i
6363 0.0763837 0.0400893i 0.00962345 0.00505077i
6464 5.14850 + 1.26899i 0.643562 + 0.158624i
6565 0.357127 + 0.517388i 0.0442962 + 0.0641741i
6666 11.7395 1.44503
6767 −3.41249 8.99799i −0.416902 1.09928i −0.964858 0.262772i 0.915363π-0.915363\pi
0.547956 0.836507i 0.315406π-0.315406\pi
6868 −11.4089 + 30.0828i −1.38353 + 3.64807i
6969 −6.28186 + 3.29697i −0.756247 + 0.396909i
7070 −0.0108863 + 0.0287049i −0.00130117 + 0.00343089i
7171 −4.78883 1.18034i −0.568329 0.140081i −0.0553278 0.998468i 0.517620π-0.517620\pi
−0.513002 + 0.858388i 0.671467π0.671467\pi
7272 11.7741 2.90206i 1.38759 0.342011i
7373 0.106690 0.878674i 0.0124872 0.102841i −0.985133 0.171795i 0.945043π-0.945043\pi
0.997620 + 0.0689543i 0.0219663π0.0219663\pi
7474 2.19519 + 1.94477i 0.255186 + 0.226075i
7575 −6.35674 9.20932i −0.734013 1.06340i
7676 −9.97099 + 14.4455i −1.14375 + 1.65701i
7777 0.0780365 0.0192343i 0.00889308 0.00219195i
7878 1.36014 11.2017i 0.154005 1.26835i
7979 −2.73870 + 3.96769i −0.308128 + 0.446400i −0.946203 0.323574i 0.895116π-0.895116\pi
0.638075 + 0.769974i 0.279731π0.279731\pi
8080 −0.940648 + 1.36276i −0.105168 + 0.152362i
8181 8.03695 7.12012i 0.892995 0.791124i
8282 1.30727 10.7663i 0.144364 1.18894i
8383 −0.248151 2.04371i −0.0272381 0.224326i 0.972733 0.231928i 0.0745034π-0.0745034\pi
−0.999971 + 0.00760169i 0.997580π0.997580\pi
8484 0.330471 0.173444i 0.0360573 0.0189243i
8585 1.81724 + 1.60994i 0.197108 + 0.174622i
8686 −0.725242 + 0.380636i −0.0782048 + 0.0410451i
8787 −2.36451 3.42558i −0.253502 0.367260i
8888 11.2981 1.20438
8989 0.781030 + 0.192507i 0.0827890 + 0.0204057i 0.280493 0.959856i 0.409502π-0.409502\pi
−0.197704 + 0.980262i 0.563348π0.563348\pi
9090 0.210662 1.73496i 0.0222057 0.182880i
9191 −0.00931188 0.0766902i −0.000976150 0.00803932i
9292 −11.5467 + 6.06020i −1.20383 + 0.631819i
9393 1.41446 0.348632i 0.146672 0.0361515i
9494 10.4030 27.4305i 1.07299 2.82924i
9595 0.752410 + 1.09005i 0.0771956 + 0.111837i
9696 4.58883 1.13104i 0.468345 0.115437i
9797 −4.56478 + 1.12512i −0.463484 + 0.114238i −0.464141 0.885761i 0.653637π-0.653637\pi
0.000657384 1.00000i 0.499791π0.499791\pi
9898 −13.0415 + 11.5538i −1.31739 + 1.16711i
9999 −4.05136 + 2.12632i −0.407177 + 0.213703i
100100 −11.6844 16.9277i −1.16844 1.69277i
101101 −4.58603 1.13036i −0.456327 0.112475i 0.00445048 0.999990i 0.498583π-0.498583\pi
−0.460778 + 0.887515i 0.652430π0.652430\pi
102102 −5.25258 43.2589i −0.520083 4.28327i
103103 6.20417 + 5.49641i 0.611315 + 0.541578i 0.910971 0.412469i 0.135334π-0.135334\pi
−0.299657 + 0.954047i 0.596872π0.596872\pi
104104 1.30900 10.7806i 0.128358 1.05712i
105105 −0.00339470 0.0279579i −0.000331289 0.00272841i
106106 2.11941 0.522388i 0.205856 0.0507388i
107107 −10.0993 5.30051i −0.976335 0.512420i −0.100451 0.994942i 0.532029π-0.532029\pi
−0.875884 + 0.482522i 0.839721π0.839721\pi
108108 5.62592 4.98413i 0.541355 0.479598i
109109 −2.34774 19.3354i −0.224873 1.85199i −0.470209 0.882555i 0.655821π-0.655821\pi
0.245336 0.969438i 0.421102π-0.421102\pi
110110 0.577407 1.52250i 0.0550536 0.145164i
111111 −2.61224 0.643860i −0.247943 0.0611125i
112112 0.180173 0.0945620i 0.0170247 0.00893527i
113113 11.0753 + 5.81278i 1.04188 + 0.546821i 0.896725 0.442588i 0.145940π-0.145940\pi
0.145155 + 0.989409i 0.453632π0.453632\pi
114114 2.86559 23.6003i 0.268387 2.21037i
115115 0.118612 + 0.976856i 0.0110606 + 0.0910923i
116116 −4.34622 6.29658i −0.403536 0.584623i
117117 1.55953 + 4.11213i 0.144178 + 0.380167i
118118 4.37749 6.34189i 0.402981 0.583818i
119119 −0.105792 0.278951i −0.00969794 0.0255714i
120120 0.477203 3.93012i 0.0435625 0.358769i
121121 6.54134 1.61230i 0.594667 0.146572i
122122 9.83577 5.16221i 0.890489 0.467365i
123123 3.52806 + 9.30274i 0.318115 + 0.838800i
124124 2.59993 0.640824i 0.233480 0.0575477i
125125 −3.04489 + 0.750499i −0.272344 + 0.0671266i
126126 −0.121999 + 0.176747i −0.0108686 + 0.0157458i
127127 −2.99992 7.91014i −0.266200 0.701912i −0.999752 0.0222781i 0.992908π-0.992908\pi
0.733552 0.679633i 0.237861π-0.237861\pi
128128 −16.8361 + 4.14972i −1.48811 + 0.366786i
129129 0.426834 0.618376i 0.0375807 0.0544450i
130130 −1.38585 0.727353i −0.121547 0.0637930i
131131 −0.283622 −0.0247802 −0.0123901 0.999923i 0.503944π-0.503944\pi
−0.0123901 + 0.999923i 0.503944π0.503944\pi
132132 −17.5280 + 9.19942i −1.52562 + 0.800707i
133133 −0.0196186 0.161574i −0.00170115 0.0140103i
134134 17.9329 + 15.8872i 1.54917 + 1.37244i
135135 −0.201121 0.530312i −0.0173097 0.0456420i
136136 −5.05509 41.6324i −0.433471 3.56995i
137137 5.50144 2.88738i 0.470019 0.246685i −0.213046 0.977042i 0.568339π-0.568339\pi
0.683066 + 0.730357i 0.260646π0.260646\pi
138138 10.0333 14.5358i 0.854093 1.23737i
139139 −2.09970 0.517529i −0.178094 0.0438963i 0.149260 0.988798i 0.452311π-0.452311\pi
−0.327354 + 0.944902i 0.606157π0.606157\pi
140140 −0.00623983 0.0513896i −0.000527362 0.00434322i
141141 3.24399 + 26.7166i 0.273193 + 2.24995i
142142 11.9222 2.93855i 1.00049 0.246598i
143143 0.493898 + 4.06762i 0.0413018 + 0.340151i
144144 −8.67062 + 7.68150i −0.722552 + 0.640125i
145145 −0.560562 + 0.138166i −0.0465521 + 0.0114741i
146146 0.781406 + 2.06040i 0.0646696 + 0.170520i
147147 5.66787 14.9450i 0.467478 1.23264i
148148 −4.80159 1.18349i −0.394688 0.0972819i
149149 −13.1433 11.6439i −1.07674 0.953906i −0.0776652 0.996979i 0.524747π-0.524747\pi
−0.999072 + 0.0430737i 0.986285π0.986285\pi
150150 24.6677 + 12.9466i 2.01411 + 1.05709i
151151 11.4728 + 10.1640i 0.933640 + 0.827133i 0.985177 0.171539i 0.0548738π-0.0548738\pi
−0.0515378 + 0.998671i 0.516412π0.516412\pi
152152 2.75785 22.7129i 0.223691 1.84226i
153153 9.64797 + 13.9775i 0.779992 + 1.13001i
154154 −0.149771 + 0.132686i −0.0120689 + 0.0106921i
155155 0.0243559 0.200589i 0.00195631 0.0161117i
156156 6.74721 + 17.7909i 0.540209 + 1.42442i
157157 −15.5728 + 3.83836i −1.24285 + 0.306334i −0.805304 0.592863i 0.797998π-0.797998\pi
−0.437544 + 0.899197i 0.644152π0.644152\pi
158158 1.44674 11.9150i 0.115097 0.947907i
159159 −1.49888 + 1.32789i −0.118869 + 0.105308i
160160 0.0790160 0.650756i 0.00624677 0.0514468i
161161 0.0428792 0.113063i 0.00337935 0.00891062i
162162 −9.47903 + 24.9941i −0.744743 + 1.96373i
163163 −0.793566 + 0.416496i −0.0621569 + 0.0326224i −0.495515 0.868599i 0.665021π-0.665021\pi
0.433358 + 0.901222i 0.357328π0.357328\pi
164164 6.48497 + 17.0995i 0.506391 + 1.33524i
165165 0.180054 + 1.48287i 0.0140172 + 0.115442i
166166 2.91153 + 4.21808i 0.225978 + 0.327386i
167167 −13.8283 + 3.40838i −1.07007 + 0.263748i −0.734738 0.678352i 0.762695π-0.762695\pi
−0.335332 + 0.942100i 0.608849π0.608849\pi
168168 −0.276360 + 0.400377i −0.0213216 + 0.0308897i
169169 −9.06149 −0.697038
170170 −5.86860 1.44648i −0.450101 0.110940i
171171 3.28567 + 8.66361i 0.251262 + 0.662523i
172172 0.784568 1.13664i 0.0598227 0.0866682i
173173 13.9008 + 12.3151i 1.05686 + 0.936298i 0.998078 0.0619729i 0.0197392π-0.0197392\pi
0.0587839 + 0.998271i 0.481278π0.481278\pi
174174 9.17562 + 4.81574i 0.695602 + 0.365080i
175175 0.185187 + 0.0456445i 0.0139988 + 0.00345040i
176176 −9.55629 + 5.01553i −0.720333 + 0.378060i
177177 −0.852103 + 7.01770i −0.0640480 + 0.527482i
178178 −1.94444 + 0.479260i −0.145742 + 0.0359221i
179179 7.89490 6.99427i 0.590092 0.522776i −0.314386 0.949295i 0.601799π-0.601799\pi
0.904479 + 0.426519i 0.140260π0.140260\pi
180180 1.04503 + 2.75551i 0.0778918 + 0.205384i
181181 1.13113 1.63872i 0.0840760 0.121805i −0.778689 0.627410i 0.784115π-0.784115\pi
0.862765 + 0.505605i 0.168731π0.168731\pi
182182 0.109255 + 0.158283i 0.00809852 + 0.0117327i
183183 −5.78875 + 8.38645i −0.427917 + 0.619944i
184184 9.65609 13.9893i 0.711857 1.03130i
185185 −0.211985 + 0.307114i −0.0155855 + 0.0225795i
186186 −2.71469 + 2.40501i −0.199051 + 0.176344i
187187 5.61117 + 14.7954i 0.410329 + 1.08195i
188188 5.96280 + 49.1081i 0.434882 + 3.58157i
189189 −0.00840088 + 0.0691874i −0.000611074 + 0.00503265i
190190 −2.91978 1.53242i −0.211823 0.111173i
191191 1.73146 4.56548i 0.125284 0.330346i −0.857670 0.514201i 0.828088π-0.828088\pi
0.982953 + 0.183855i 0.0588577π0.0588577\pi
192192 9.06477 8.03069i 0.654193 0.579565i
193193 −7.39796 + 19.5068i −0.532517 + 1.40413i 0.351284 + 0.936269i 0.385745π0.385745\pi
−0.883801 + 0.467863i 0.845024π0.845024\pi
194194 8.76094 7.76152i 0.628999 0.557245i
195195 1.43581 0.102820
196196 10.4182 27.4704i 0.744155 1.96217i
197197 −4.18400 11.0323i −0.298098 0.786019i −0.997458 0.0712503i 0.977301π-0.977301\pi
0.699361 0.714769i 0.253468π-0.253468\pi
198198 6.47080 9.37457i 0.459860 0.666222i
199199 2.34500 + 1.23075i 0.166232 + 0.0872454i 0.545787 0.837924i 0.316231π-0.316231\pi
−0.379555 + 0.925169i 0.623923π0.623923\pi
200200 23.7403 + 12.4599i 1.67869 + 0.881045i
201201 −21.3398 5.25979i −1.50520 0.370997i
202202 11.4173 2.81411i 0.803318 0.198000i
203203 0.0688837 + 0.0169783i 0.00483469 + 0.00119164i
204204 41.7415 + 60.4730i 2.92249 + 4.23396i
205205 1.38000 0.0963835
206206 −20.0357 4.93836i −1.39595 0.344072i
207207 −0.829757 + 6.83366i −0.0576721 + 0.474972i
208208 3.67859 + 9.69963i 0.255064 + 0.672548i
209209 1.04057 + 8.56982i 0.0719774 + 0.592787i
210210 0.0398296 + 0.0577032i 0.00274850 + 0.00398190i
211211 −1.30491 1.89048i −0.0898335 0.130146i 0.775490 0.631359i 0.217503π-0.217503\pi
−0.865324 + 0.501213i 0.832887π0.832887\pi
212212 −2.75510 + 2.44080i −0.189221 + 0.167635i
213213 −8.43151 + 7.46967i −0.577718 + 0.511813i
214214 28.3955 1.94108
215215 −0.0592034 0.0857710i −0.00403764 0.00584953i
216216 −3.47418 + 9.16065i −0.236388 + 0.623303i
217217 −0.0141051 + 0.0204347i −0.000957515 + 0.00138720i
218218 27.5457 + 39.9069i 1.86563 + 2.70284i
219219 −1.51313 1.34051i −0.102248 0.0905835i
220220 0.330958 + 2.72569i 0.0223132 + 0.183766i
221221 14.7678 3.63993i 0.993388 0.244848i
222222 6.50339 1.60294i 0.436479 0.107582i
223223 −2.01256 16.5749i −0.134771 1.10994i −0.890477 0.455028i 0.849629π-0.849629\pi
0.755706 0.654911i 0.227294π-0.227294\pi
224224 −0.0457601 + 0.0662950i −0.00305748 + 0.00442952i
225225 −10.8579 −0.723862
226226 −31.1398 −2.07139
227227 −7.02250 6.22139i −0.466100 0.412928i 0.397112 0.917770i 0.370012π-0.370012\pi
−0.863212 + 0.504842i 0.831551π0.831551\pi
228228 14.2153 + 37.4827i 0.941432 + 2.48235i
229229 11.0936 0.733086 0.366543 0.930401i 0.380541π-0.380541\pi
0.366543 + 0.930401i 0.380541π0.380541\pi
230230 −1.39166 2.01616i −0.0917632 0.132942i
231231 0.0650909 0.171631i 0.00428267 0.0112925i
232232 8.83064 + 4.63468i 0.579760 + 0.304281i
233233 26.8245 14.0786i 1.75733 0.922317i 0.821215 0.570618i 0.193296π-0.193296\pi
0.936113 0.351699i 0.114396π-0.114396\pi
234234 −8.19543 7.26051i −0.535752 0.474635i
235235 3.62444 + 0.893344i 0.236432 + 0.0582753i
236236 −1.56626 + 12.8993i −0.101955 + 0.839672i
237237 3.90447 + 10.2953i 0.253623 + 0.668749i
238238 0.555945 + 0.492525i 0.0360366 + 0.0319256i
239239 21.7197 + 19.2420i 1.40493 + 1.24466i 0.931458 + 0.363850i 0.118538π0.118538\pi
0.473472 + 0.880809i 0.343001π0.343001\pi
240240 1.34105 + 3.53606i 0.0865645 + 0.228252i
241241 10.2774 9.10500i 0.662027 0.586505i −0.263743 0.964593i 0.584957π-0.584957\pi
0.925769 + 0.378089i 0.123419π0.123419\pi
242242 −12.5544 + 11.1223i −0.807030 + 0.714966i
243243 −2.30843 19.0116i −0.148086 1.21960i
244244 −10.6404 + 15.4152i −0.681179 + 0.986858i
245245 −1.65944 1.47013i −0.106018 0.0939234i
246246 −18.5403 16.4252i −1.18208 1.04723i
247247 8.29781 0.527977
248248 −2.61263 + 2.31458i −0.165902 + 0.146976i
249249 −4.16328 2.18506i −0.263837 0.138472i
250250 5.84390 5.17724i 0.369601 0.327438i
251251 −10.3241 9.14634i −0.651650 0.577312i 0.271175 0.962530i 0.412588π-0.412588\pi
−0.922825 + 0.385218i 0.874126π0.874126\pi
252252 0.0436512 0.359500i 0.00274976 0.0226463i
253253 −2.27429 + 5.99682i −0.142984 + 0.377017i
254254 15.7648 + 13.9664i 0.989173 + 0.876331i
255255 5.38369 1.32696i 0.337140 0.0830974i
256256 24.3745 21.5939i 1.52340 1.34962i
257257 −4.27307 6.19060i −0.266546 0.386159i 0.666741 0.745290i 0.267689π-0.267689\pi
−0.933287 + 0.359130i 0.883073π0.883073\pi
258258 −0.225479 + 1.85699i −0.0140377 + 0.115611i
259259 0.0406040 0.0213106i 0.00252301 0.00132418i
260260 2.63917 0.163674
261261 −4.03881 −0.249996
262262 0.625221 0.328141i 0.0386263 0.0202726i
263263 −15.8070 + 3.89607i −0.974700 + 0.240242i −0.694335 0.719652i 0.744302π-0.744302\pi
−0.280365 + 0.959894i 0.590455π0.590455\pi
264264 14.6580 21.2358i 0.902139 1.30697i
265265 0.0984918 + 0.259702i 0.00605030 + 0.0159533i
266266 0.230183 + 0.333478i 0.0141134 + 0.0204468i
267267 1.37513 1.21826i 0.0841566 0.0745563i
268268 −39.2249 9.66808i −2.39604 0.590572i
269269 27.4629 1.67444 0.837220 0.546866i 0.184179π-0.184179\pi
0.837220 + 0.546866i 0.184179π0.184179\pi
270270 1.05691 + 0.936337i 0.0643212 + 0.0569836i
271271 −6.01212 8.71006i −0.365210 0.529099i 0.596700 0.802465i 0.296478π-0.296478\pi
−0.961910 + 0.273366i 0.911863π0.911863\pi
272272 22.7575 + 32.9699i 1.37988 + 1.99909i
273273 −0.156227 0.0819943i −0.00945529 0.00496252i
274274 −8.78684 + 12.7299i −0.530832 + 0.769043i
275275 −9.82224 2.42096i −0.592303 0.145990i
276276 −3.58991 + 29.5655i −0.216087 + 1.77964i
277277 2.82524 + 23.2679i 0.169752 + 1.39803i 0.789749 + 0.613430i 0.210211π0.210211\pi
−0.619997 + 0.784604i 0.712866π0.712866\pi
278278 5.22737 1.28843i 0.313517 0.0772749i
279279 0.501247 1.32168i 0.0300089 0.0791269i
280280 0.0383321 + 0.0555337i 0.00229078 + 0.00331877i
281281 0.330685 0.479081i 0.0197270 0.0285796i −0.812996 0.582269i 0.802165π-0.802165\pi
0.832723 + 0.553689i 0.186780π0.186780\pi
282282 −38.0613 55.1413i −2.26652 3.28362i
283283 −1.92753 15.8747i −0.114580 0.943651i −0.930704 0.365774i 0.880804π-0.880804\pi
0.816124 0.577877i 0.196119π-0.196119\pi
284284 −15.4980 + 13.7301i −0.919639 + 0.814729i
285285 3.02502 0.179187
286286 −5.79484 8.39528i −0.342656 0.496423i
287287 −0.150155 0.0788074i −0.00886336 0.00465185i
288288 1.62616 4.28783i 0.0958225 0.252663i
289289 36.9564 19.3962i 2.17390 1.14095i
290290 1.07586 0.953125i 0.0631764 0.0559694i
291291 −3.80753 + 10.0396i −0.223201 + 0.588533i
292292 −2.78129 2.46401i −0.162763 0.144195i
293293 −5.94415 8.61158i −0.347261 0.503094i 0.609968 0.792426i 0.291182π-0.291182\pi
−0.957229 + 0.289332i 0.906567π0.906567\pi
294294 4.79646 + 39.5024i 0.279735 + 2.30382i
295295 0.868215 + 0.455674i 0.0505494 + 0.0265304i
296296 6.25887 1.54267i 0.363790 0.0896661i
297297 0.445579 3.66967i 0.0258551 0.212936i
298298 42.4447 + 10.4617i 2.45876 + 0.606029i
299299 5.45862 + 2.86490i 0.315680 + 0.165682i
300300 −46.9763 −2.71218
301301 0.00154369 + 0.0127135i 8.89771e−5 + 0.000732792i
302302 −37.0500 9.13202i −2.13199 0.525488i
303303 −8.07446 + 7.15335i −0.463866 + 0.410949i
304304 7.75020 + 20.4356i 0.444504 + 1.17206i
305305 0.802920 + 1.16323i 0.0459751 + 0.0666064i
306306 −37.4396 19.6498i −2.14028 1.12330i
307307 5.32175 + 14.0323i 0.303728 + 0.800865i 0.996795 + 0.0799924i 0.0254896π0.0254896\pi
−0.693067 + 0.720873i 0.743741π0.743741\pi
308308 0.119644 0.315476i 0.00681736 0.0179759i
309309 18.3802 4.53031i 1.04561 0.257720i
310310 0.178384 + 0.470359i 0.0101315 + 0.0267146i
311311 0.768531 6.32942i 0.0435794 0.358909i −0.954564 0.298005i 0.903679π-0.903679\pi
0.998144 0.0609035i 0.0193982π-0.0193982\pi
312312 −18.5647 16.4469i −1.05102 0.931124i
313313 3.12101 0.176410 0.0882049 0.996102i 0.471887π-0.471887\pi
0.0882049 + 0.996102i 0.471887π0.471887\pi
314314 29.8881 26.4785i 1.68668 1.49427i
315315 −0.0241969 0.0126995i −0.00136334 0.000715537i
316316 7.17685 + 18.9238i 0.403729 + 1.06455i
317317 16.2088 + 8.50702i 0.910375 + 0.477802i 0.853803 0.520597i 0.174290π-0.174290\pi
0.0565726 + 0.998398i 0.481983π0.481983\pi
318318 1.76782 4.66136i 0.0991345 0.261396i
319319 −3.65356 0.900522i −0.204560 0.0504196i
320320 −0.595650 1.57060i −0.0332978 0.0877992i
321321 −23.0655 + 12.1057i −1.28739 + 0.675673i
322322 0.0362867 + 0.298847i 0.00202218 + 0.0166541i
323323 31.1134 7.66876i 1.73119 0.426701i
324324 −5.43319 44.7464i −0.301844 2.48591i
325325 −3.44807 + 9.09180i −0.191264 + 0.504322i
326326 1.26748 1.83626i 0.0701990 0.101701i
327327 −39.3885 20.6727i −2.17819 1.14320i
328328 −17.8432 15.8077i −0.985225 0.872833i
329329 −0.343351 0.304183i −0.0189296 0.0167701i
330330 −2.11255 3.06055i −0.116292 0.168478i
331331 0.843596 6.94764i 0.0463682 0.381877i −0.950989 0.309224i 0.899931π-0.899931\pi
0.997357 0.0726524i 0.0231464π-0.0231464\pi
332332 −7.65256 4.01637i −0.419989 0.220427i
333333 −1.95402 + 1.73111i −0.107080 + 0.0948643i
334334 26.5400 23.5124i 1.45220 1.28654i
335335 −1.73174 + 2.50886i −0.0946152 + 0.137074i
336336 0.0560161 0.461334i 0.00305593 0.0251678i
337337 10.4806 5.50062i 0.570913 0.299638i −0.154455 0.988000i 0.549362π-0.549362\pi
0.725368 + 0.688362i 0.241670π0.241670\pi
338338 19.9753 10.4838i 1.08651 0.570245i
339339 25.2946 13.2756i 1.37382 0.721034i
340340 9.89580 2.43910i 0.536675 0.132279i
341341 0.748127 1.08385i 0.0405134 0.0586937i
342342 −17.2665 15.2968i −0.933664 0.827154i
343343 0.193231 + 0.509509i 0.0104335 + 0.0275109i
344344 −0.217002 + 1.78717i −0.0116999 + 0.0963577i
345345 1.98997 + 1.04442i 0.107137 + 0.0562296i
346346 −44.8913 11.0647i −2.41337 0.594843i
347347 0.938442 2.47447i 0.0503782 0.132836i −0.907465 0.420127i 0.861985π-0.861985\pi
0.957843 + 0.287291i 0.0927546π0.0927546\pi
348348 −17.4737 −0.936689
349349 −3.44258 + 3.04986i −0.184277 + 0.163255i −0.750218 0.661191i 0.770051π-0.770051\pi
0.565941 + 0.824446i 0.308513π0.308513\pi
350350 −0.461037 + 0.113636i −0.0246435 + 0.00607407i
351351 −3.44995 0.850335i −0.184144 0.0453875i
352352 2.42710 3.51626i 0.129365 0.187417i
353353 −0.112198 0.924033i −0.00597169 0.0491813i 0.989418 0.145090i 0.0463473π-0.0463473\pi
−0.995390 + 0.0959090i 0.969424π0.969424\pi
354354 −6.24084 16.4558i −0.331697 0.874613i
355355 0.554038 + 1.46088i 0.0294053 + 0.0775354i
356356 2.52764 2.23929i 0.133965 0.118682i
357357 −0.661566 0.163061i −0.0350138 0.00863012i
358358 −9.31148 + 24.5524i −0.492127 + 1.29763i
359359 1.62493 4.28459i 0.0857606 0.226132i −0.885275 0.465069i 0.846030π-0.846030\pi
0.971035 + 0.238937i 0.0767988π0.0767988\pi
360360 −2.87536 2.54735i −0.151545 0.134257i
361361 −1.51782 −0.0798855
362362 −0.597529 + 4.92109i −0.0314054 + 0.258647i
363363 5.45619 14.3868i 0.286376 0.755111i
364364 −0.287162 0.150714i −0.0150514 0.00789958i
365365 −0.248274 + 0.130304i −0.0129953 + 0.00682045i
366366 3.05796 25.1846i 0.159842 1.31642i
367367 −17.2120 4.24237i −0.898457 0.221450i −0.237068 0.971493i 0.576186π-0.576186\pi
−0.661389 + 0.750043i 0.730033π0.730033\pi
368368 −1.95722 + 16.1191i −0.102027 + 0.840268i
369369 9.37336 + 2.31033i 0.487958 + 0.120271i
370370 0.111983 0.922266i 0.00582173 0.0479463i
371371 0.00411403 0.0338821i 0.000213590 0.00175907i
372372 2.16862 5.71819i 0.112438 0.296474i
373373 −16.1496 23.3967i −0.836192 1.21143i −0.975240 0.221148i 0.929020π-0.929020\pi
0.139048 0.990286i 0.455596π-0.455596\pi
374374 −29.4871 26.1233i −1.52474 1.35080i
375375 −2.53977 + 6.69683i −0.131153 + 0.345823i
376376 −36.6303 53.0681i −1.88906 2.73678i
377377 −1.28257 + 3.38186i −0.0660558 + 0.174175i
378378 −0.0615284 0.162237i −0.00316468 0.00834458i
379379 10.6184 + 9.40705i 0.545429 + 0.483208i 0.890257 0.455458i 0.150524π-0.150524\pi
−0.344828 + 0.938666i 0.612063π0.612063\pi
380380 5.56031 0.285238
381381 −18.7599 4.62389i −0.961097 0.236889i
382382 1.46525 + 12.0674i 0.0749688 + 0.617423i
383383 −17.8209 4.39245i −0.910603 0.224443i −0.243929 0.969793i 0.578436π-0.578436\pi
−0.666674 + 0.745350i 0.732283π0.732283\pi
384384 −14.0431 + 37.0286i −0.716634 + 1.88961i
385385 −0.0190573 0.0168833i −0.000971250 0.000860452i
386386 −6.26055 51.5603i −0.318654 2.62435i
387387 −0.258533 0.681696i −0.0131420 0.0346526i
388388 −6.99865 + 18.4539i −0.355303 + 0.936856i
389389 7.69866 1.89755i 0.390338 0.0962096i −0.0392623 0.999229i 0.512501π-0.512501\pi
0.429600 + 0.903019i 0.358655π0.358655\pi
390390 −3.16511 + 1.66118i −0.160272 + 0.0841171i
391391 23.1153 + 5.69741i 1.16899 + 0.288130i
392392 4.61612 + 38.0172i 0.233149 + 1.92016i
393393 −0.367968 + 0.533093i −0.0185615 + 0.0268910i
394394 21.9873 + 19.4790i 1.10770 + 0.981338i
395395 1.52723 0.0768435
396396 −2.31524 + 19.0677i −0.116345 + 0.958189i
397397 2.50621 + 20.6405i 0.125783 + 1.03592i 0.909762 + 0.415130i 0.136264π0.136264\pi
−0.783979 + 0.620787i 0.786813π0.786813\pi
398398 −6.59327 −0.330491
399399 −0.329146 0.172749i −0.0164779 0.00864827i
400400 −25.6115 −1.28058
401401 16.1205 8.46072i 0.805022 0.422508i −0.0114207 0.999935i 0.503635π-0.503635\pi
0.816443 + 0.577427i 0.195943π0.195943\pi
402402 53.1272 13.0947i 2.64974 0.653103i
403403 −0.947522 0.839431i −0.0471994 0.0418150i
404404 −14.8417 + 13.1486i −0.738404 + 0.654169i
405405 −3.30252 0.813998i −0.164104 0.0404479i
406406 −0.171491 + 0.0422688i −0.00851097 + 0.00209777i
407407 −2.15362 + 1.13031i −0.106751 + 0.0560272i
408408 −84.8103 44.5119i −4.19873 2.20367i
409409 −30.9413 + 16.2392i −1.52995 + 0.802978i −0.999012 0.0444344i 0.985851π-0.985851\pi
−0.530935 + 0.847413i 0.678159π0.678159\pi
410410 −3.04209 + 1.59661i −0.150238 + 0.0788511i
411411 1.71041 14.0865i 0.0843682 0.694834i
412412 33.7848 8.32720i 1.66446 0.410252i
413413 −0.0684465 0.0991619i −0.00336803 0.00487944i
414414 −6.07718 16.0242i −0.298677 0.787547i
415415 −0.488151 + 0.432464i −0.0239624 + 0.0212288i
416416 −3.07398 2.72331i −0.150714 0.133521i
417417 −3.69686 + 3.27513i −0.181036 + 0.160384i
418418 −12.2088 17.6875i −0.597153 0.865125i
419419 −17.1211 24.8043i −0.836423 1.21177i −0.975174 0.221440i 0.928924π-0.928924\pi
0.138751 0.990327i 0.455691π-0.455691\pi
420420 −0.104687 0.0549439i −0.00510819 0.00268099i
421421 10.0981 + 2.48897i 0.492153 + 0.121305i 0.477579 0.878589i 0.341515π-0.341515\pi
0.0145742 + 0.999894i 0.495361π0.495361\pi
422422 5.06378 + 2.65768i 0.246501 + 0.129374i
423423 23.1226 + 12.1357i 1.12426 + 0.590058i
424424 1.70136 4.48610i 0.0826251 0.217864i
425425 −4.52627 + 37.2772i −0.219556 + 1.80821i
426426 9.94439 26.2212i 0.481807 1.27042i
427427 −0.0209357 0.172421i −0.00101315 0.00834403i
428428 −42.3968 + 22.2516i −2.04933 + 1.07557i
429429 8.28622 + 4.34894i 0.400062 + 0.209969i
430430 0.229743 + 0.120578i 0.0110792 + 0.00581480i
431431 31.2233 16.3872i 1.50397 0.789346i 0.506627 0.862165i 0.330892π-0.330892\pi
0.997345 + 0.0728197i 0.0231998π0.0231998\pi
432432 −1.12809 9.29064i −0.0542751 0.446996i
433433 6.10513 16.0979i 0.293394 0.773616i −0.704558 0.709646i 0.748855π-0.748855\pi
0.997952 0.0639693i 0.0203760π-0.0203760\pi
434434 0.00745114 0.0613656i 0.000357666 0.00294564i
435435 −0.467570 + 1.23288i −0.0224182 + 0.0591121i
436436 −72.4003 37.9986i −3.46735 1.81980i
437437 11.5004 + 6.03590i 0.550141 + 0.288736i
438438 4.88648 + 1.20441i 0.233485 + 0.0575489i
439439 21.9020 + 11.4951i 1.04533 + 0.548629i 0.897788 0.440427i 0.145173π-0.145173\pi
0.147537 + 0.989056i 0.452865π0.452865\pi
440440 −2.03312 2.94548i −0.0969252 0.140420i
441441 −8.81016 12.7637i −0.419531 0.607796i
442442 −28.3430 + 25.1097i −1.34814 + 1.19435i
443443 −19.4470 17.2285i −0.923955 0.818553i 0.0597740 0.998212i 0.480962π-0.480962\pi
−0.983729 + 0.179659i 0.942500π0.942500\pi
444444 −8.45398 + 7.48957i −0.401208 + 0.355439i
445445 −0.0903605 0.238261i −0.00428350 0.0112947i
446446 23.6131 + 34.2095i 1.11811 + 1.61987i
447447 −38.9376 + 9.59726i −1.84169 + 0.453935i
448448 −0.0248805 + 0.204909i −0.00117549 + 0.00968105i
449449 −10.4214 + 5.46956i −0.491815 + 0.258124i −0.692350 0.721562i 0.743424π-0.743424\pi
0.200535 + 0.979687i 0.435732π0.435732\pi
450450 23.9353 12.5622i 1.12832 0.592190i
451451 7.96415 + 4.17991i 0.375017 + 0.196824i
452452 46.4943 24.4021i 2.18691 1.14778i
453453 33.9887 8.37746i 1.59693 0.393607i
454454 22.6784 + 5.58973i 1.06435 + 0.262339i
455455 −0.0183179 + 0.0162282i −0.000858755 + 0.000760791i
456456 −39.1130 34.6511i −1.83163 1.62269i
457457 −6.32752 + 1.55959i −0.295989 + 0.0729547i −0.384514 0.923119i 0.625631π-0.625631\pi
0.0885248 + 0.996074i 0.471785π0.471785\pi
458458 −24.4549 + 12.8349i −1.14270 + 0.599736i
459459 −13.7217 −0.640476
460460 3.65779 + 1.91975i 0.170545 + 0.0895090i
461461 3.03680 0.141438 0.0707190 0.997496i 0.477471π-0.477471\pi
0.0707190 + 0.997496i 0.477471π0.477471\pi
462462 0.0550834 + 0.453653i 0.00256271 + 0.0211058i
463463 −1.90316 + 15.6739i −0.0884473 + 0.728429i 0.879258 + 0.476346i 0.158039π0.158039\pi
−0.967705 + 0.252084i 0.918884π0.918884\pi
464464 −9.52668 −0.442265
465465 −0.345425 0.306020i −0.0160187 0.0141913i
466466 −42.8438 + 62.0699i −1.98470 + 2.87533i
467467 −0.761124 6.26842i −0.0352206 0.290068i −0.999667 0.0257906i 0.991790π-0.991790\pi
0.964447 0.264277i 0.0851334π-0.0851334\pi
468468 17.9260 + 4.41836i 0.828630 + 0.204239i
469469 0.331700 0.174090i 0.0153165 0.00803871i
470470 −9.02332 + 2.22405i −0.416215 + 0.102588i
471471 −12.9894 + 34.2503i −0.598522 + 1.57817i
472472 −6.00620 15.8371i −0.276458 0.728959i
473473 −0.0818769 0.674317i −0.00376470 0.0310051i
474474 −20.5183 18.1776i −0.942438 0.834927i
475475 −7.26453 + 19.1550i −0.333319 + 0.878891i
476476 −1.21603 0.299724i −0.0557366 0.0137378i
477477 0.234206 + 1.92886i 0.0107235 + 0.0883163i
478478 −70.1414 17.2883i −3.20819 0.790749i
479479 26.8997 1.22908 0.614539 0.788886i 0.289342π-0.289342\pi
0.614539 + 0.788886i 0.289342π0.289342\pi
480480 −1.12064 0.992799i −0.0511499 0.0453149i
481481 0.829010 + 2.18592i 0.0377996 + 0.0996694i
482482 −12.1215 + 31.9618i −0.552120 + 1.45582i
483483 −0.156881 0.227282i −0.00713834 0.0103417i
484484 10.0291 26.4445i 0.455867 1.20202i
485485 1.11477 + 0.987597i 0.0506190 + 0.0448445i
486486 27.0845 + 39.2387i 1.22858 + 1.77990i
487487 2.58988 6.82896i 0.117359 0.309450i −0.863446 0.504441i 0.831699π-0.831699\pi
0.980805 + 0.194991i 0.0624678π0.0624678\pi
488488 2.94299 24.2377i 0.133223 1.09719i
489489 −0.246721 + 2.03193i −0.0111571 + 0.0918872i
490490 5.35898 + 1.32087i 0.242094 + 0.0596708i
491491 2.53902 20.9107i 0.114584 0.943685i −0.816112 0.577893i 0.803875π-0.803875\pi
0.930697 0.365792i 0.119202π-0.119202\pi
492492 40.5534 + 9.99552i 1.82829 + 0.450633i
493493 −1.68363 + 13.8659i −0.0758269 + 0.624490i
494494 −18.2918 + 9.60028i −0.822987 + 0.431937i
495495 1.28339 + 0.673577i 0.0576843 + 0.0302750i
496496 1.18233 3.11756i 0.0530884 0.139983i
497497 0.0231423 0.190594i 0.00103808 0.00854933i
498498 11.7056 0.524541
499499 −17.8047 15.7735i −0.797046 0.706121i 0.162797 0.986660i 0.447948π-0.447948\pi
−0.959843 + 0.280539i 0.909487π0.909487\pi
500500 −4.66838 + 12.3095i −0.208776 + 0.550498i
501501 −11.5344 + 30.4136i −0.515317 + 1.35878i
502502 33.3405 + 8.21770i 1.48806 + 0.366774i
503503 17.3001 15.3266i 0.771375 0.683379i −0.182626 0.983183i 0.558460π-0.558460\pi
0.954001 + 0.299804i 0.0969211π0.0969211\pi
504504 0.167391 + 0.441374i 0.00745619 + 0.0196604i
505505 0.530576 + 1.39901i 0.0236103 + 0.0622553i
506506 −1.92463 15.8507i −0.0855602 0.704652i
507507 −11.7563 + 17.0319i −0.522114 + 0.756412i
508508 −34.4827 8.49921i −1.52992 0.377092i
509509 26.1327 6.44112i 1.15831 0.285498i 0.387075 0.922048i 0.373486π-0.373486\pi
0.771235 + 0.636551i 0.219639π0.219639\pi
510510 −10.3326 + 9.15390i −0.457536 + 0.405342i
511511 0.0344555 0.00152422
512512 −16.4503 + 43.3760i −0.727009 + 1.91697i
513513 −7.26849 1.79152i −0.320912 0.0790976i
514514 16.5819 + 8.70286i 0.731397 + 0.383867i
515515 0.316493 2.60655i 0.0139463 0.114858i
516516 −1.11853 2.94933i −0.0492407 0.129837i
517517 18.2112 + 16.1337i 0.800928 + 0.709560i
518518 −0.0648522 + 0.0939547i −0.00284944 + 0.00412813i
519519 41.1820 10.1505i 1.80769 0.445556i
520520 −3.04611 + 1.59872i −0.133581 + 0.0701086i
521521 18.0905 9.49464i 0.792560 0.415968i −0.0193044 0.999814i 0.506145π-0.506145\pi
0.811864 + 0.583846i 0.198453π0.198453\pi
522522 8.90319 4.67276i 0.389682 0.204521i
523523 3.62655 29.8673i 0.158578 1.30601i −0.668413 0.743791i 0.733026π-0.733026\pi
0.826990 0.562216i 0.190051π-0.190051\pi
524524 −0.676365 + 0.979883i −0.0295471 + 0.0428064i
525525 0.326052 0.288857i 0.0142301 0.0126067i
526526 30.3375 26.8767i 1.32278 1.17188i
527527 −4.32861 2.27183i −0.188557 0.0989625i
528528 −2.97107 + 24.4690i −0.129299 + 1.06488i
529529 −7.58401 10.9873i −0.329740 0.477711i
530530 −0.517582 0.458538i −0.0224823 0.0199176i
531531 5.13430 + 4.54859i 0.222810 + 0.197392i
532532 −0.605006 0.317531i −0.0262303 0.0137667i
533533 4.91116 7.11504i 0.212726 0.308187i
534534 −1.62187 + 4.27653i −0.0701853 + 0.185063i
535535 0.435514 + 3.58678i 0.0188289 + 0.155070i
536536 51.1297 12.6023i 2.20847 0.544338i
537537 −2.90361 23.9134i −0.125300 1.03194i
538538 −60.5395 + 31.7736i −2.61004 + 1.36986i
539539 −5.12390 13.5106i −0.220702 0.581944i
540540 −2.31179 0.569805i −0.0994835 0.0245205i
541541 2.42211 6.38658i 0.104135 0.274580i −0.872815 0.488052i 0.837708π-0.837708\pi
0.976949 + 0.213471i 0.0684770π0.0684770\pi
542542 23.3304 + 12.2448i 1.00213 + 0.525957i
543543 −1.61261 4.25211i −0.0692038 0.182475i
544544 −14.0430 7.37034i −0.602089 0.316001i
545545 −4.61836 + 4.09151i −0.197829 + 0.175261i
546546 0.439253 0.0187983
547547 10.3692 + 9.18631i 0.443355 + 0.392778i 0.855052 0.518543i 0.173525π-0.173525\pi
−0.411697 + 0.911321i 0.635064π0.635064\pi
548548 3.14392 25.8925i 0.134301 1.10607i
549549 3.50624 + 9.24521i 0.149643 + 0.394576i
550550 24.4532 6.02718i 1.04269 0.257000i
551551 −2.70218 + 7.12505i −0.115117 + 0.303537i
552552 −13.7664 36.2990i −0.585936 1.54499i
553553 −0.166175 0.0872154i −0.00706648 0.00370877i
554554 −33.1482 48.0234i −1.40833 2.04032i
555555 0.302221 + 0.796891i 0.0128286 + 0.0338261i
556556 −6.79524 + 6.02005i −0.288182 + 0.255307i
557557 9.97275 + 2.45806i 0.422559 + 0.104151i 0.444861 0.895600i 0.353253π-0.353253\pi
−0.0223015 + 0.999751i 0.507099π0.507099\pi
558558 0.424182 + 3.49345i 0.0179571 + 0.147890i
559559 −0.652914 −0.0276153
560560 −0.0570753 0.0299554i −0.00241187 0.00126585i
561561 35.0892 + 8.64870i 1.48147 + 0.365149i
562562 −0.174688 + 1.43868i −0.00736876 + 0.0606872i
563563 −6.09011 + 1.50108i −0.256667 + 0.0632628i −0.365550 0.930792i 0.619119π-0.619119\pi
0.108882 + 0.994055i 0.465273π0.465273\pi
564564 100.039 + 52.5045i 4.21240 + 2.21084i
565565 −0.477604 3.93342i −0.0200930 0.165480i
566566 22.6155 + 32.7642i 0.950600 + 1.37718i
567567 0.312855 + 0.277166i 0.0131387 + 0.0116399i
568568 9.57050 25.2353i 0.401569 1.05885i
569569 11.6007 10.2773i 0.486326 0.430847i −0.383993 0.923336i 0.625451π-0.625451\pi
0.870319 + 0.492489i 0.163913π0.163913\pi
570570 −6.66839 + 3.49984i −0.279308 + 0.146592i
571571 11.7089 30.8738i 0.490002 1.29203i −0.430959 0.902372i 0.641824π-0.641824\pi
0.920960 0.389657i 0.127406π-0.127406\pi
572572 15.2310 + 7.99383i 0.636839 + 0.334239i
573573 −6.33485 9.17761i −0.264642 0.383400i
574574 0.422181 0.0176215
575575 −11.3923 + 10.0927i −0.475093 + 0.420896i
576576 −1.41641 11.6652i −0.0590170 0.486049i
577577 6.27686 + 9.09359i 0.261309 + 0.378571i 0.931575 0.363550i 0.118435π-0.118435\pi
−0.670266 + 0.742121i 0.733820π0.733820\pi
578578 −59.0263 + 85.5144i −2.45517 + 3.55693i
579579 27.0668 + 39.2130i 1.12486 + 1.62964i
580580 −0.859444 + 2.26617i −0.0356865 + 0.0940975i
581581 0.0778113 0.0191788i 0.00322816 0.000795669i
582582 −3.22213 26.5367i −0.133562 1.09998i
583583 −0.218207 + 1.79709i −0.00903719 + 0.0744280i
584584 4.70276 + 1.15913i 0.194602 + 0.0479650i
585585 0.791415 1.14656i 0.0327210 0.0474046i
586586 23.0667 + 12.1063i 0.952875 + 0.500107i
587587 −23.3594 33.8420i −0.964147 1.39681i −0.917429 0.397901i 0.869739π-0.869739\pi
−0.0467188 0.998908i 0.514876π-0.514876\pi
588588 −38.1167 55.2216i −1.57191 2.27730i
589589 −1.99628 1.76855i −0.0822552 0.0728718i
590590 −2.44110 −0.100499
591591 −26.1645 6.44896i −1.07626 0.265275i
592592 −4.60911 + 4.08332i −0.189433 + 0.167823i
593593 −16.8446 24.4036i −0.691724 1.00214i −0.998728 0.0504270i 0.983942π-0.983942\pi
0.307004 0.951708i 0.400674π-0.400674\pi
594594 3.26344 + 8.60499i 0.133901 + 0.353067i
595595 −0.0536865 + 0.0777783i −0.00220093 + 0.00318860i
596596 −71.5716 + 17.6408i −2.93169 + 0.722596i
597597 5.35566 2.81087i 0.219193 0.115041i
598598 −15.3476 −0.627611
599599 −19.3017 −0.788646 −0.394323 0.918972i 0.629021π-0.629021\pi
−0.394323 + 0.918972i 0.629021π0.629021\pi
600600 54.2197 28.4567i 2.21351 1.16174i
601601 1.02963 8.47974i 0.0419993 0.345896i −0.956528 0.291641i 0.905799π-0.905799\pi
0.998527 0.0542545i 0.0172782π-0.0172782\pi
602602 −0.0181120 0.0262397i −0.000738189 0.00106945i
603603 −15.9627 + 14.1417i −0.650051 + 0.575895i
604604 62.4749 15.3987i 2.54207 0.626563i
605605 −1.59746 1.41523i −0.0649461 0.0575372i
606606 9.52327 25.1108i 0.386856 1.02006i
607607 2.19441 18.0726i 0.0890685 0.733545i −0.877935 0.478781i 0.841079π-0.841079\pi
0.967003 0.254765i 0.0819980π-0.0819980\pi
608608 −6.47639 5.73758i −0.262652 0.232690i
609609 0.121281 0.107446i 0.00491455 0.00435391i
610610 −3.11578 1.63529i −0.126154 0.0662110i
611611 17.5046 15.5077i 0.708161 0.627375i
612612 71.2985 2.88207
613613 26.8323 + 23.7713i 1.08374 + 0.960114i 0.999340 0.0363175i 0.0115628π-0.0115628\pi
0.0844045 + 0.996432i 0.473101π0.473101\pi
614614 −27.9662 24.7759i −1.12862 0.999873i
615615 1.79039 2.59383i 0.0721957 0.104593i
616616 0.0530124 + 0.436596i 0.00213593 + 0.0175910i
617617 −31.4711 + 27.8809i −1.26698 + 1.12244i −0.280273 + 0.959920i 0.590425π0.590425\pi
−0.986705 + 0.162524i 0.948036π0.948036\pi
618618 −35.2761 + 31.2519i −1.41901 + 1.25714i
619619 0.888727 + 2.34338i 0.0357210 + 0.0941885i 0.951690 0.307061i 0.0993454π-0.0993454\pi
−0.915969 + 0.401249i 0.868576π0.868576\pi
620620 −0.634929 0.562498i −0.0254994 0.0225905i
621621 −4.16295 3.68805i −0.167053 0.147996i
622622 5.62876 + 14.8418i 0.225693 + 0.595103i
623623 −0.00377438 + 0.0310848i −0.000151217 + 0.00124539i
624624 23.0039 + 5.66994i 0.920891 + 0.226979i
625625 −17.5936 15.5866i −0.703744 0.623463i
626626 −6.87999 + 3.61090i −0.274980 + 0.144320i
627627 17.4578 + 9.16254i 0.697196 + 0.365916i
628628 −23.8760 + 62.9559i −0.952757 + 2.51221i
629629 5.12865 + 7.43014i 0.204493 + 0.296259i
630630 0.0680329 0.00271049
631631 6.73178 + 17.7503i 0.267988 + 0.706626i 0.999687 + 0.0249990i 0.00795825π0.00795825\pi
−0.731699 + 0.681627i 0.761273π0.761273\pi
632632 −19.7469 17.4942i −0.785489 0.695882i
633633 −5.24630 −0.208522
634634 −45.5731 −1.80994
635635 −1.52238 + 2.20554i −0.0604137 + 0.0875243i
636636 1.01328 + 8.34511i 0.0401792 + 0.330905i
637637 −13.4854 + 3.32385i −0.534310 + 0.131696i
638638 9.09583 2.24192i 0.360107 0.0887585i
639639 1.31746 + 10.8503i 0.0521179 + 0.429229i
640640 4.11154 + 3.64250i 0.162523 + 0.143983i
641641 −12.6409 18.3135i −0.499284 0.723338i 0.489613 0.871940i 0.337138π-0.337138\pi
−0.988897 + 0.148602i 0.952523π0.952523\pi
642642 36.8399 53.3718i 1.45396 2.10642i
643643 0.631821 1.66597i 0.0249166 0.0656996i −0.921981 0.387236i 0.873430π-0.873430\pi
0.946897 + 0.321536i 0.104199π0.104199\pi
644644 −0.288365 0.417769i −0.0113632 0.0164624i
645645 −0.238024 −0.00937218
646646 −59.7142 + 52.9022i −2.34942 + 2.08141i
647647 −24.0058 + 21.2672i −0.943764 + 0.836102i −0.986630 0.162979i 0.947890π-0.947890\pi
0.0428657 + 0.999081i 0.486351π0.486351\pi
648648 33.3768 + 48.3547i 1.31117 + 1.89955i
649649 3.63037 + 5.25951i 0.142505 + 0.206454i
650650 −2.91794 24.0314i −0.114451 0.942588i
651651 0.0201091 + 0.0530234i 0.000788139 + 0.00207815i
652652 −0.453501 + 3.73491i −0.0177605 + 0.146270i
653653 20.0432 + 4.94020i 0.784351 + 0.193325i 0.611101 0.791553i 0.290727π-0.290727\pi
0.173250 + 0.984878i 0.444573π0.444573\pi
654654 110.746 4.33051
655655 0.0510384 + 0.0739419i 0.00199424 + 0.00288915i
656656 22.1098 + 5.44957i 0.863241 + 0.212770i
657657 −1.90450 + 0.469417i −0.0743016 + 0.0183137i
658658 1.10882 + 0.273299i 0.0432262 + 0.0106543i
659659 33.3277 + 17.4917i 1.29826 + 0.681380i 0.965197 0.261524i 0.0842250π-0.0842250\pi
0.333064 + 0.942904i 0.391917π0.391917\pi
660660 5.55255 + 2.91420i 0.216133 + 0.113435i
661661 −13.4574 + 19.4964i −0.523432 + 0.758322i −0.992154 0.125024i 0.960099π-0.960099\pi
0.468722 + 0.883346i 0.344715π0.344715\pi
662662 6.17854 + 16.2915i 0.240136 + 0.633186i
663663 12.3179 32.4797i 0.478389 1.26141i
664664 11.2655 0.437187
665665 −0.0385929 + 0.0341903i −0.00149657 + 0.00132584i
666666 2.30463 6.07682i 0.0893027 0.235472i
667667 −4.23759 + 3.75418i −0.164080 + 0.145362i
668668 −21.2014 + 55.9035i −0.820306 + 2.16297i
669669 −33.7651 17.7213i −1.30543 0.685145i
670670 0.914809 7.53413i 0.0353422 0.291069i
671671 1.11042 + 9.14513i 0.0428673 + 0.353044i
672672 0.0652387 + 0.172020i 0.00251664 + 0.00663583i
673673 −11.3622 + 10.0660i −0.437979 + 0.388015i −0.853097 0.521752i 0.825279π-0.825279\pi
0.415118 + 0.909767i 0.363740π0.363740\pi
674674 −16.7395 + 24.2513i −0.644780 + 0.934125i
675675 4.98329 7.21954i 0.191807 0.277880i
676676 −21.6093 + 31.3064i −0.831126 + 1.20409i
677677 19.9974 + 28.9713i 0.768564 + 1.11346i 0.990381 + 0.138368i 0.0441858π0.0441858\pi
−0.221817 + 0.975088i 0.571199π0.571199\pi
678678 −40.4003 + 58.5300i −1.55157 + 2.24783i
679679 −0.0648969 0.171119i −0.00249051 0.00656695i
680680 −9.94414 + 8.80974i −0.381340 + 0.337838i
681681 −20.8046 + 5.12786i −0.797232 + 0.196500i
682682 −0.395205 + 3.25481i −0.0151332 + 0.124633i
683683 −36.2333 + 19.0167i −1.38643 + 0.727655i −0.982347 0.187068i 0.940102π-0.940102\pi
−0.404083 + 0.914722i 0.632409π0.632409\pi
684684 37.7673 + 9.30879i 1.44407 + 0.355931i
685685 −1.74275 0.914666i −0.0665870 0.0349476i
686686 −1.01545 0.899607i −0.0387699 0.0343472i
687687 14.3927 20.8514i 0.549115 0.795531i
688688 −0.609825 1.60798i −0.0232493 0.0613035i
689689 1.68949 + 0.416422i 0.0643644 + 0.0158644i
690690 −5.59508 −0.213001
691691 −8.07443 + 11.6978i −0.307166 + 0.445006i −0.945918 0.324406i 0.894836π-0.894836\pi
0.638752 + 0.769413i 0.279451π0.279451\pi
692692 75.6971 18.6576i 2.87757 0.709257i
693693 −0.101178 0.146581i −0.00384342 0.00556815i
694694 0.794159 + 6.54049i 0.0301459 + 0.248274i
695695 0.242922 + 0.640534i 0.00921457 + 0.0242968i
696696 20.1680 10.5850i 0.764467 0.401223i
697697 11.8392 31.2173i 0.448441 1.18244i
698698 4.06028 10.7061i 0.153684 0.405231i
699699 8.33978 68.6843i 0.315439 2.59788i
700700 0.599319 0.530950i 0.0226521 0.0200680i
701701 3.77804 31.1150i 0.142695 1.17520i −0.728777 0.684751i 0.759911π-0.759911\pi
0.871472 0.490446i 0.163166π-0.163166\pi
702702 8.58891 2.11698i 0.324168 0.0799001i
703703 1.74659 + 4.60539i 0.0658740 + 0.173695i
704704 1.31965 10.8683i 0.0497362 0.409614i
705705 6.38141 5.65344i 0.240338 0.212921i
706706 1.31640 + 1.90714i 0.0495435 + 0.0717762i
707707 0.0221623 0.182523i 0.000833500 0.00686449i
708708 22.2133 + 19.6793i 0.834827 + 0.739593i
709709 −31.1906 16.3701i −1.17139 0.614791i −0.237160 0.971471i 0.576217π-0.576217\pi
−0.934227 + 0.356679i 0.883909π0.883909\pi
710710 −2.91152 2.57938i −0.109267 0.0968023i
711711 10.3734 + 2.55682i 0.389033 + 0.0958881i
712712 −1.56089 + 4.11574i −0.0584970 + 0.154244i
713713 −0.702619 1.85265i −0.0263133 0.0693824i
714714 1.64702 0.405954i 0.0616382 0.0151924i
715715 0.971572 0.860738i 0.0363347 0.0321898i
716716 −5.33716 43.9555i −0.199459 1.64269i
717717 64.3458 15.8598i 2.40304 0.592295i
718718 1.37510 + 11.3250i 0.0513184 + 0.422645i
719719 0.351152 + 2.89200i 0.0130958 + 0.107853i 0.997791 0.0664320i 0.0211615π-0.0211615\pi
−0.984695 + 0.174285i 0.944238π0.944238\pi
720720 3.56291 + 0.878177i 0.132782 + 0.0327277i
721721 −0.183289 + 0.265539i −0.00682602 + 0.00988920i
722722 3.34591 1.75607i 0.124522 0.0653541i
723723 −3.77987 31.1300i −0.140575 1.15774i
724724 −2.96415 7.81583i −0.110162 0.290473i
725725 −6.68397 5.92148i −0.248236 0.219918i
726726 4.61732 + 38.0270i 0.171365 + 1.41132i
727727 22.1929 11.6477i 0.823089 0.431990i 6.70287e−5 1.00000i 0.499979π-0.499979\pi
0.823022 + 0.568010i 0.192286π0.192286\pi
728728 0.422738 0.0156677
729729 −10.2068 5.35696i −0.378031 0.198406i
730730 0.396542 0.574490i 0.0146767 0.0212628i
731731 −2.44816 + 0.603417i −0.0905484 + 0.0223182i
732732 15.1696 + 39.9990i 0.560685 + 1.47840i
733733 −8.28254 + 11.9993i −0.305922 + 0.443205i −0.945549 0.325481i 0.894474π-0.894474\pi
0.639626 + 0.768686i 0.279089π0.279089\pi
734734 42.8505 10.5617i 1.58164 0.389840i
735735 −4.91618 + 1.21173i −0.181336 + 0.0446953i
736736 −2.27946 6.01044i −0.0840219 0.221548i
737737 −17.5932 + 9.23364i −0.648055 + 0.340125i
738738 −23.3357 + 5.75174i −0.859000 + 0.211724i
739739 −3.79329 + 31.2406i −0.139539 + 1.14920i 0.739739 + 0.672894i 0.234949π0.234949\pi
−0.879278 + 0.476310i 0.841974π0.841974\pi
740740 0.555515 + 1.46477i 0.0204211 + 0.0538461i
741741 10.7655 15.5965i 0.395479 0.572951i
742742 0.0301314 + 0.0794499i 0.00110616 + 0.00291670i
743743 10.3657 + 15.0174i 0.380282 + 0.550934i 0.965654 0.259831i 0.0836668π-0.0836668\pi
−0.585372 + 0.810765i 0.699051π0.699051\pi
744744 0.960881 + 7.91357i 0.0352276 + 0.290126i
745745 −0.670476 + 5.52186i −0.0245643 + 0.202305i
746746 62.6694 + 32.8914i 2.29449 + 1.20424i
747747 −4.03967 + 2.12018i −0.147804 + 0.0775735i
748748 64.4977 + 15.8973i 2.35827 + 0.581261i
749749 0.157442 0.415140i 0.00575280 0.0151689i
750750 −2.14929 17.7010i −0.0784810 0.646349i
751751 −35.9535 + 31.8520i −1.31196 + 1.16230i −0.336609 + 0.941644i 0.609280π0.609280\pi
−0.975353 + 0.220652i 0.929181π0.929181\pi
752752 54.5413 + 28.6255i 1.98892 + 1.04386i
753753 −30.5857 + 7.53869i −1.11460 + 0.274725i
754754 −1.08538 8.93891i −0.0395272 0.325536i
755755 0.585259 4.82004i 0.0212997 0.175419i
756756 0.219001 + 0.194018i 0.00796499 + 0.00705636i
757757 6.33105 + 52.1409i 0.230106 + 1.89509i 0.411071 + 0.911604i 0.365155π0.365155\pi
−0.180965 + 0.983490i 0.557922π0.557922\pi
758758 −34.2909 8.45195i −1.24550 0.306989i
759759 8.32092 + 12.0549i 0.302030 + 0.437566i
760760 −6.41767 + 3.36825i −0.232793 + 0.122179i
761761 −31.4542 + 27.8660i −1.14021 + 1.01014i −0.140415 + 0.990093i 0.544844π0.544844\pi
−0.999799 + 0.0200490i 0.993618π0.993618\pi
762762 46.7042 11.5115i 1.69191 0.417019i
763763 0.736167 0.181449i 0.0266510 0.00656889i
764764 −11.6441 16.8695i −0.421270 0.610315i
765765 1.90784 5.03056i 0.0689781 0.181880i
766766 44.3664 10.9353i 1.60302 0.395110i
767767 5.43919 2.85471i 0.196398 0.103077i
768768 −8.96453 73.8295i −0.323480 2.66409i
769769 −1.34246 + 11.0561i −0.0484102 + 0.398694i 0.948282 + 0.317428i 0.102819π0.102819\pi
−0.996692 + 0.0812657i 0.974104π0.974104\pi
770770 0.0615435 + 0.0151691i 0.00221787 + 0.000546657i
771771 −17.1796 −0.618708
772772 49.7517 + 72.0778i 1.79060 + 2.59414i
773773 22.0259 11.5601i 0.792217 0.415788i −0.0195207 0.999809i 0.506214π-0.506214\pi
0.811738 + 0.584022i 0.198522π0.198522\pi
774774 1.35861 + 1.20363i 0.0488343 + 0.0432634i
775775 2.76731 1.45239i 0.0994046 0.0521716i
776776 −3.10099 25.5389i −0.111319 0.916794i
777777 0.0126239 0.103967i 0.000452878 0.00372979i
778778 −14.7756 + 13.0901i −0.529732 + 0.469301i
779779 10.3470 14.9903i 0.370721 0.537082i
780780 3.42402 4.96055i 0.122600 0.177616i
781781 −1.22746 + 10.1090i −0.0439220 + 0.361730i
782782 −57.5473 + 14.1841i −2.05789 + 0.507224i
783783 1.85363 2.68544i 0.0662432 0.0959698i
784784 −20.7813 30.1069i −0.742188 1.07525i
785785 3.80305 + 3.36920i 0.135737 + 0.120252i
786786 0.194382 1.60088i 0.00693339 0.0571016i
787787 47.1705 11.6265i 1.68145 0.414439i 0.721006 0.692929i 0.243680π-0.243680\pi
0.960439 + 0.278490i 0.0898338π0.0898338\pi
788788 −48.0931 11.8539i −1.71325 0.422277i
789789 −13.1847 + 34.7653i −0.469389 + 1.23768i
790790 −3.36665 + 1.76696i −0.119780 + 0.0628655i
791791 −0.172658 + 0.455262i −0.00613901 + 0.0161872i
792792 −8.87836 23.4103i −0.315479 0.831849i
793793 8.85485 0.314445
794794 −29.4051 42.6006i −1.04355 1.51184i
795795 0.615914 + 0.151809i 0.0218442 + 0.00538412i
796796 9.84429 5.16668i 0.348922 0.183128i
797797 −37.0905 9.14198i −1.31381 0.323826i −0.480678 0.876897i 0.659609π-0.659609\pi
−0.833134 + 0.553072i 0.813456π0.813456\pi
798798 0.925437 0.0327601
799799 51.3030 74.3252i 1.81497 2.62944i
800800 8.97778 4.71190i 0.317413 0.166591i
801801 −0.214870 1.76961i −0.00759206 0.0625262i
802802 −25.7476 + 37.3018i −0.909179 + 1.31717i
803803 −1.82750 −0.0644912
804804 −69.0619 + 61.1835i −2.43562 + 2.15777i
805805 −0.0371924 + 0.00916710i −0.00131086 + 0.000323098i
806806 3.05992 + 0.754203i 0.107781 + 0.0265657i
807807 35.6299 51.6189i 1.25423 1.81707i
808808 9.16521 24.1667i 0.322431 0.850181i
809809 5.51186 + 45.3942i 0.193787 + 1.59598i 0.687389 + 0.726289i 0.258757π0.258757\pi
−0.493603 + 0.869688i 0.664320π0.664320\pi
810810 8.22188 2.02651i 0.288888 0.0712044i
811811 −27.6633 6.81839i −0.971390 0.239426i −0.278474 0.960444i 0.589828π-0.589828\pi
−0.692917 + 0.721018i 0.743675π0.743675\pi
812812 0.222928 0.197497i 0.00782323 0.00693077i
813813 −24.1714 −0.847727
814814 3.43974 4.98332i 0.120563 0.174665i
815815 0.251387 + 0.131938i 0.00880569 + 0.00462158i
816816 91.4951 3.20297
817817 −1.37559 −0.0481257
818818 49.4191 71.5959i 1.72790 2.50329i
819819 −0.151589 + 0.0795599i −0.00529694 + 0.00278005i
820820 3.29094 4.76775i 0.114925 0.166497i
821821 −31.0366 + 16.2893i −1.08319 + 0.568500i −0.909247 0.416256i 0.863342π-0.863342\pi
−0.173939 + 0.984756i 0.555650π0.555650\pi
822822 12.5271 + 33.0313i 0.436933 + 1.15210i
823823 −45.2723 11.1586i −1.57809 0.388965i −0.649589 0.760285i 0.725059π-0.725059\pi
−0.928505 + 0.371320i 0.878905π0.878905\pi
824824 −33.9498 + 30.0769i −1.18270 + 1.04778i
825825 −17.2937 + 15.3208i −0.602088 + 0.533403i
826826 0.265611 + 0.139403i 0.00924179 + 0.00485047i
827827 −15.6470 13.8620i −0.544100 0.482030i 0.345723 0.938337i 0.387634π-0.387634\pi
−0.889823 + 0.456306i 0.849172π0.849172\pi
828828 21.6308 + 19.1632i 0.751722 + 0.665967i
829829 −48.8147 + 25.6199i −1.69540 + 0.889817i −0.713449 + 0.700707i 0.752868π0.752868\pi
−0.981956 + 0.189110i 0.939440π0.939440\pi
830830 0.575741 1.51810i 0.0199842 0.0526941i
831831 47.3995 + 24.8772i 1.64427 + 0.862980i
832832 −10.2175 2.51840i −0.354230 0.0873097i
833833 −47.4927 + 24.9261i −1.64553 + 0.863639i
834834 4.36019 11.4969i 0.150981 0.398105i
835835 3.37702 + 2.99178i 0.116867 + 0.103535i
836836 32.0893 + 16.8417i 1.10983 + 0.582484i
837837 0.648749 + 0.939875i 0.0224240 + 0.0324868i
838838 66.4397 + 34.8703i 2.29512 + 1.20457i
839839 15.7465 0.543629 0.271815 0.962350i 0.412376π-0.412376\pi
0.271815 + 0.962350i 0.412376π0.412376\pi
840840 0.154112 0.00531737
841841 19.2206 + 17.0280i 0.662779 + 0.587171i
842842 −25.1401 + 6.19648i −0.866385 + 0.213545i
843843 −0.471448 1.24310i −0.0162375 0.0428148i
844844 −9.64327 −0.331935
845845 1.63063 + 2.36238i 0.0560955 + 0.0812684i
846846 −65.0124 −2.23517
847847 0.0929973 + 0.245214i 0.00319542 + 0.00842564i
848848 0.552441 + 4.54976i 0.0189709 + 0.156239i
849849 −32.3386 16.9726i −1.10986 0.582498i
850850 −33.1506 87.4110i −1.13706 2.99817i
851851 −0.441081 + 3.63263i −0.0151201 + 0.124525i
852852 5.69993 + 46.9431i 0.195276 + 1.60824i
853853 −3.21714 + 26.4955i −0.110153 + 0.907189i 0.827943 + 0.560813i 0.189511π0.189511\pi
−0.938095 + 0.346377i 0.887412π0.887412\pi
854854 0.245636 + 0.355865i 0.00840548 + 0.0121774i
855855 1.66739 2.41563i 0.0570234 0.0826127i
856856 35.4548 51.3652i 1.21182 1.75563i
857857 −41.6392 + 21.8539i −1.42237 + 0.746516i −0.988034 0.154236i 0.950708π-0.950708\pi
−0.434333 + 0.900752i 0.643016π0.643016\pi
858858 −23.2978 −0.795374
859859 0.962852 29.2929i 0.0328521 0.999460i
860860 −0.437514 −0.0149191
861861 −0.342934 + 0.179986i −0.0116872 + 0.00613390i
862862 −49.8695 + 72.2485i −1.69856 + 2.46079i
863863 −18.6464 + 27.0140i −0.634731 + 0.919567i −0.999935 0.0113608i 0.996384π-0.996384\pi
0.365204 + 0.930927i 0.380999π0.380999\pi
864864 2.10469 + 3.04917i 0.0716030 + 0.103735i
865865 0.709123 5.84015i 0.0241109 0.198571i
866866 5.16648 + 42.5498i 0.175564 + 1.44590i
867867 11.4898 94.6271i 0.390214 3.21370i
868868 0.0369628 + 0.0974629i 0.00125460 + 0.00330811i
869869 8.81385 + 4.62587i 0.298989 + 0.156922i
870870 −0.395682 3.25874i −0.0134149 0.110482i
871871 6.77231 + 17.8571i 0.229471 + 0.605065i
872872 106.582 3.60933
873873 5.91843 + 8.57433i 0.200309 + 0.290197i
874874 −32.3350 −1.09375
875875 −0.0432888 0.114143i −0.00146343 0.00385874i
876876 −8.23973 + 2.03091i −0.278395 + 0.0686182i
877877 −28.6250 25.3595i −0.966598 0.856331i 0.0230667 0.999734i 0.492657π-0.492657\pi
−0.989664 + 0.143403i 0.954195π0.954195\pi
878878 −61.5804 −2.07824
879879 −23.8981 −0.806062
880880 3.02725 + 1.58882i 0.102049 + 0.0535593i
881881 19.7750 + 28.6490i 0.666236 + 0.965210i 0.999748 + 0.0224638i 0.00715104π0.00715104\pi
−0.333511 + 0.942746i 0.608234π0.608234\pi
882882 34.1884 + 17.9435i 1.15118 + 0.604188i
883883 −37.7950 33.4835i −1.27190 1.12681i −0.985677 0.168647i 0.946060π-0.946060\pi
−0.286227 0.958162i 0.592401π-0.592401\pi
884884 22.6417 59.7013i 0.761523 2.00797i
885885 1.98289 1.04070i 0.0666541 0.0349828i
886886 62.8020 + 15.4793i 2.10988 + 0.520038i
887887 −26.7199 14.0237i −0.897166 0.470869i −0.0479110 0.998852i 0.515256π-0.515256\pi
−0.849255 + 0.527982i 0.822949π0.822949\pi
888888 5.22058 13.7655i 0.175191 0.461942i
889889 0.291598 0.153042i 0.00977987 0.00513287i
890890 0.474851 + 0.420681i 0.0159170 + 0.0141013i
891891 −16.5937 14.7007i −0.555910 0.492494i
892892 −62.0639 32.5737i −2.07805 1.09065i
893893 36.8794 32.6723i 1.23412 1.09334i
894894 74.7309 66.2058i 2.49937 2.21425i
895895 −3.24415 0.799610i −0.108440 0.0267280i
896896 −0.239356 0.631129i −0.00799632 0.0210846i
897897 12.4668 6.54307i 0.416253 0.218467i
898898 16.6449 24.1143i 0.555448 0.804705i
899899 1.02935 0.540245i 0.0343308 0.0180182i
900900 −25.8933 + 37.5129i −0.863110 + 1.25043i
901901 6.71974 0.223867
902902 −22.3923 −0.745582
903903 0.0258988 + 0.0135928i 0.000861860 + 0.000452339i
904904 −38.8814 + 56.3294i −1.29317 + 1.87349i
905905 −0.630772 −0.0209676
906906 −65.2326 + 57.7911i −2.16721 + 1.91998i
907907 −1.43575 0.353880i −0.0476732 0.0117504i 0.215407 0.976524i 0.430892π-0.430892\pi
−0.263080 + 0.964774i 0.584738π0.584738\pi
908908 −38.2410 + 9.42557i −1.26907 + 0.312798i
909909 1.26167 + 10.3908i 0.0418469 + 0.344640i
910910 0.0216047 0.0569668i 0.000716188 0.00188843i
911911 30.8030 44.6259i 1.02055 1.47852i 0.148619 0.988895i 0.452517π-0.452517\pi
0.871932 0.489628i 0.162867π-0.162867\pi
912912 48.4655 + 11.9457i 1.60485 + 0.395561i
913913 −4.12708 + 1.01723i −0.136586 + 0.0336655i
914914 12.1441 10.7587i 0.401690 0.355866i
915915 3.22809 0.106717
916916 26.4553 38.3272i 0.874109 1.26636i
917917 −0.00133080 0.0109601i −4.39468e−5 0.000361934i
918918 30.2484 15.8756i 0.998346 0.523972i
919919 −16.9383 + 24.5394i −0.558743 + 0.809479i −0.995953 0.0898806i 0.971351π-0.971351\pi
0.437209 + 0.899360i 0.355967π0.355967\pi
920920 −5.38471 −0.177529
921921 33.2793 + 8.20261i 1.09659 + 0.270285i
922922 −6.69437 + 3.51348i −0.220467 + 0.115710i
923923 9.50375 + 2.34246i 0.312820 + 0.0771032i
924924 −0.437740 0.634176i −0.0144006 0.0208629i
925925 −5.77184 −0.189777
926926 −13.9388 36.7537i −0.458058 1.20780i
927927 6.51346 17.1746i 0.213930 0.564088i
928928 3.33945 1.75268i 0.109623 0.0575345i
929929 −6.14828 + 16.2117i −0.201718 + 0.531888i −0.997257 0.0740150i 0.976419π-0.976419\pi
0.795539 + 0.605903i 0.207188π0.207188\pi
930930 1.11551 + 0.274949i 0.0365791 + 0.00901594i
931931 −28.4116 + 7.00282i −0.931151 + 0.229508i
932932 15.3294 126.249i 0.502132 4.13543i
933933 −10.8996 9.65623i −0.356838 0.316131i
934934 8.93017 + 12.9376i 0.292204 + 0.423331i
935935 2.84751 4.12533i 0.0931235 0.134913i
936936 −23.3666 + 5.75934i −0.763760 + 0.188250i
937937 −2.35361 + 19.3837i −0.0768889 + 0.633237i 0.902419 + 0.430860i 0.141790π0.141790\pi
−0.979308 + 0.202377i 0.935133π0.935133\pi
938938 −0.529788 + 0.767530i −0.0172982 + 0.0250608i
939939 4.04915 5.86621i 0.132139 0.191436i
940940 11.7297 10.3916i 0.382582 0.338938i
941941 −1.30175 + 10.7208i −0.0424357 + 0.349489i 0.955990 + 0.293399i 0.0947865π0.0947865\pi
−0.998426 + 0.0560901i 0.982137π0.982137\pi
942942 −10.9924 90.5302i −0.358150 2.94963i
943943 11.9822 6.28875i 0.390195 0.204790i
944944 12.1107 + 10.7292i 0.394170 + 0.349204i
945945 0.0195493 0.0102603i 0.000635939 0.000333767i
946946 0.960652 + 1.39174i 0.0312335 + 0.0452495i
947947 43.5476 1.41511 0.707553 0.706660i 0.249799π-0.249799\pi
0.707553 + 0.706660i 0.249799π0.249799\pi
948948 44.8801 + 11.0619i 1.45764 + 0.359275i
949949 −0.211734 + 1.74379i −0.00687318 + 0.0566058i
950950 −6.14763 50.6303i −0.199456 1.64266i
951951 37.0187 19.4289i 1.20041 0.630026i
952952 1.58510 0.390691i 0.0513732 0.0126624i
953953 19.3476 51.0155i 0.626731 1.65256i −0.124265 0.992249i 0.539657π-0.539657\pi
0.750997 0.660306i 0.229573π-0.229573\pi
954954 −2.74791 3.98103i −0.0889668 0.128891i
955955 −1.50182 + 0.370167i −0.0485979 + 0.0119783i
956956 118.275 29.1521i 3.82527 0.942845i
957957 −6.43269 + 5.69887i −0.207939 + 0.184218i
958958 −59.2980 + 31.1220i −1.91583 + 1.00551i
959959 0.137391 + 0.199046i 0.00443659 + 0.00642752i
960960 −3.72487 0.918098i −0.120220 0.0296315i
961961 −3.68759 30.3701i −0.118955 0.979680i
962962 −4.35651 3.85953i −0.140460 0.124436i
963963 −3.04667 + 25.0915i −0.0981774 + 0.808564i
964964 −6.94781 57.2204i −0.223774 1.84294i
965965 6.41682 1.58160i 0.206565 0.0509136i
966966 0.608788 + 0.319517i 0.0195874 + 0.0102803i
967967 −6.81606 + 6.03850i −0.219190 + 0.194185i −0.765571 0.643351i 0.777543π-0.777543\pi
0.546381 + 0.837537i 0.316005π0.316005\pi
968968 4.44372 + 36.5973i 0.142826 + 1.17628i
969969 25.9520 68.4297i 0.833697 2.19828i
970970 −3.60002 0.887326i −0.115590 0.0284903i
971971 25.7375 13.5081i 0.825954 0.433494i 0.00189536 0.999998i 0.499397π-0.499397\pi
0.824059 + 0.566504i 0.191704π0.191704\pi
972972 −71.1880 37.3623i −2.28336 1.19840i
973973 0.0101469 0.0835676i 0.000325296 0.00267905i
974974 2.19170 + 18.0502i 0.0702265 + 0.578367i
975975 12.6154 + 18.2765i 0.404015 + 0.585317i
976976 8.27048 + 21.8075i 0.264732 + 0.698040i
977977 −18.7430 + 27.1540i −0.599643 + 0.868732i −0.998841 0.0481323i 0.984673π-0.984673\pi
0.399198 + 0.916865i 0.369288π0.369288\pi
978978 −1.80700 4.76467i −0.0577815 0.152357i
979979 0.200192 1.64873i 0.00639816 0.0526936i
980980 −9.03647 + 2.22729i −0.288659 + 0.0711482i
981981 −38.2190 + 20.0589i −1.22024 + 0.640431i
982982 18.5959 + 49.0333i 0.593418 + 1.56472i
983983 −6.94164 + 1.71096i −0.221404 + 0.0545712i −0.348457 0.937325i 0.613294π-0.613294\pi
0.127053 + 0.991896i 0.459448π0.459448\pi
984984 −52.8614 + 13.0292i −1.68516 + 0.415355i
985985 −2.12326 + 3.07608i −0.0676528 + 0.0980120i
986986 −12.3310 32.5141i −0.392699 1.03546i
987987 −1.01720 + 0.250717i −0.0323777 + 0.00798040i
988988 19.7881 28.6680i 0.629543 0.912051i
989989 −0.904913 0.474935i −0.0287746 0.0151021i
990990 −3.60844 −0.114684
991991 −27.2813 + 14.3184i −0.866620 + 0.454837i −0.838586 0.544770i 0.816617π-0.816617\pi
−0.0280345 + 0.999607i 0.508925π0.508925\pi
992992 0.159104 + 1.31034i 0.00505156 + 0.0416034i
993993 −11.9642 10.5994i −0.379673 0.336361i
994994 0.169496 + 0.446924i 0.00537608 + 0.0141756i
995995 −0.101124 0.832829i −0.00320584 0.0264025i
996996 −17.4775 + 9.17288i −0.553794 + 0.290654i
997997 11.1156 16.1037i 0.352035 0.510011i −0.606462 0.795112i 0.707412π-0.707412\pi
0.958497 + 0.285101i 0.0920273π0.0920273\pi
998998 57.4982 + 14.1720i 1.82008 + 0.448608i
999999 −0.254227 2.09375i −0.00804339 0.0662432i
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 859.2.f.a.100.4 840
859.524 even 13 inner 859.2.f.a.524.4 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
859.2.f.a.100.4 840 1.1 even 1 trivial
859.2.f.a.524.4 yes 840 859.524 even 13 inner