Properties

Label 627.2.r.c.100.6
Level 627627
Weight 22
Character 627.100
Analytic conductor 5.0075.007
Analytic rank 00
Dimension 5454
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] = [627,2,Mod(100,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 16])) 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("627.100"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 627=31119 627 = 3 \cdot 11 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 627.r (of order 99, degree 66, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [54] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.006620206735.00662020673
Analytic rank: 00
Dimension: 5454
Relative dimension: 99 over Q(ζ9)\Q(\zeta_{9})
Twist minimal: yes
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 100.6
Character χ\chi == 627.100
Dual form 627.2.r.c.232.6

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+(1.146050.417129i)q2+(0.1736480.984808i)q3+(0.392648+0.329471i)q4+(1.919691.61081i)q5+(0.2117821.20108i)q6+(0.6276511.08712i)q7+(1.53217+2.65379i)q8+(0.9396930.342020i)q9+(2.871981.04531i)q10+(0.5000000.866025i)q11+(0.256283+0.443895i)q12+(0.4988972.82939i)q13+(1.172790.984089i)q14+(1.91969+1.61081i)q15+(0.470959+2.67094i)q16+(5.25098+1.91120i)q171.21960q18+(4.33060+0.495920i)q19+1.28448q20+(1.17960+0.429338i)q21+(0.2117821.20108i)q22+(0.572409+0.480308i)q23+(2.34742+1.96972i)q24+(0.222251+1.26045i)q25+(1.751983.03452i)q26+(0.500000+0.866025i)q27+(0.604621+0.220064i)q28+(4.02109+1.46356i)q29+(1.52815+2.64683i)q30+(4.144917.17919i)q31+(0.4898492.77807i)q32+(0.7660440.642788i)q33+(5.22068+4.38067i)q34+(0.546254+3.09796i)q35+(0.4816540.175308i)q367.13754q37+(4.75623+2.37477i)q382.87303q39+(7.216032.62642i)q40+(0.138834+0.787365i)q41+(1.17279+0.984089i)q42+(0.668091+0.560595i)q43+(0.0890061+0.504779i)q44+(1.25299+2.17024i)q45+(0.455660+0.789227i)q46+(10.0214+3.64748i)q47+(2.54858+0.927608i)q48+(2.712114.69751i)q49+(0.780482+1.35183i)q50+(0.970341+5.50308i)q51+(1.12809+0.946581i)q52+(8.773327.36169i)q53+(0.211782+1.20108i)q54+(2.35484+0.857093i)q55+3.84667q56+(0.263614+4.35092i)q57+5.21887q58+(1.338980.487350i)q59+(0.2230471.26496i)q60+(1.172220.983611i)q61+(7.744936.49877i)q62+(0.217981+1.23623i)q63+(4.432357.67706i)q64+(3.59987+6.23516i)q65+(1.146050.417129i)q66+(1.88620+0.686521i)q67+(1.432102.48047i)q68+(0.373613+0.647117i)q69+(0.666213+3.77828i)q70+(5.89580+4.94716i)q71+(2.347421.96972i)q72+(1.669029.46548i)q73+(8.18000+2.97728i)q74+1.27989q75+(1.537011.62153i)q761.25530q77+(3.29265+1.19843i)q78+(0.5715653.24151i)q79+(5.206464.36874i)q80+(0.766044+0.642788i)q81+(0.169322+0.960274i)q82+(8.0074913.8694i)q83+(0.3217120.557222i)q84+(13.1588+4.78941i)q85+(0.999509+0.363791i)q86+(2.139583.70585i)q87+(1.53217+2.65379i)q88+(1.32646+7.52272i)q89+(2.34126+1.96455i)q90+(2.76276+2.31823i)q91+(0.06650780.377184i)q92+(7.78987+2.83528i)q93+13.0065q94+(9.11221+6.02375i)q952.82093q96+(6.23168+2.26814i)q97+(1.148756.51490i)q98+(0.766044+0.642788i)q99+O(q100)q+(1.14605 - 0.417129i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.392648 + 0.329471i) q^{4} +(-1.91969 - 1.61081i) q^{5} +(-0.211782 - 1.20108i) q^{6} +(-0.627651 - 1.08712i) q^{7} +(-1.53217 + 2.65379i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-2.87198 - 1.04531i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.256283 + 0.443895i) q^{12} +(-0.498897 - 2.82939i) q^{13} +(-1.17279 - 0.984089i) q^{14} +(-1.91969 + 1.61081i) q^{15} +(-0.470959 + 2.67094i) q^{16} +(-5.25098 + 1.91120i) q^{17} -1.21960 q^{18} +(-4.33060 + 0.495920i) q^{19} +1.28448 q^{20} +(-1.17960 + 0.429338i) q^{21} +(0.211782 - 1.20108i) q^{22} +(-0.572409 + 0.480308i) q^{23} +(2.34742 + 1.96972i) q^{24} +(0.222251 + 1.26045i) q^{25} +(-1.75198 - 3.03452i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.604621 + 0.220064i) q^{28} +(4.02109 + 1.46356i) q^{29} +(-1.52815 + 2.64683i) q^{30} +(-4.14491 - 7.17919i) q^{31} +(-0.489849 - 2.77807i) q^{32} +(-0.766044 - 0.642788i) q^{33} +(-5.22068 + 4.38067i) q^{34} +(-0.546254 + 3.09796i) q^{35} +(0.481654 - 0.175308i) q^{36} -7.13754 q^{37} +(-4.75623 + 2.37477i) q^{38} -2.87303 q^{39} +(7.21603 - 2.62642i) q^{40} +(-0.138834 + 0.787365i) q^{41} +(-1.17279 + 0.984089i) q^{42} +(0.668091 + 0.560595i) q^{43} +(0.0890061 + 0.504779i) q^{44} +(1.25299 + 2.17024i) q^{45} +(-0.455660 + 0.789227i) q^{46} +(10.0214 + 3.64748i) q^{47} +(2.54858 + 0.927608i) q^{48} +(2.71211 - 4.69751i) q^{49} +(0.780482 + 1.35183i) q^{50} +(0.970341 + 5.50308i) q^{51} +(1.12809 + 0.946581i) q^{52} +(8.77332 - 7.36169i) q^{53} +(-0.211782 + 1.20108i) q^{54} +(-2.35484 + 0.857093i) q^{55} +3.84667 q^{56} +(-0.263614 + 4.35092i) q^{57} +5.21887 q^{58} +(1.33898 - 0.487350i) q^{59} +(0.223047 - 1.26496i) q^{60} +(1.17222 - 0.983611i) q^{61} +(-7.74493 - 6.49877i) q^{62} +(0.217981 + 1.23623i) q^{63} +(-4.43235 - 7.67706i) q^{64} +(-3.59987 + 6.23516i) q^{65} +(-1.14605 - 0.417129i) q^{66} +(1.88620 + 0.686521i) q^{67} +(1.43210 - 2.48047i) q^{68} +(0.373613 + 0.647117i) q^{69} +(0.666213 + 3.77828i) q^{70} +(5.89580 + 4.94716i) q^{71} +(2.34742 - 1.96972i) q^{72} +(1.66902 - 9.46548i) q^{73} +(-8.18000 + 2.97728i) q^{74} +1.27989 q^{75} +(1.53701 - 1.62153i) q^{76} -1.25530 q^{77} +(-3.29265 + 1.19843i) q^{78} +(0.571565 - 3.24151i) q^{79} +(5.20646 - 4.36874i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.169322 + 0.960274i) q^{82} +(-8.00749 - 13.8694i) q^{83} +(0.321712 - 0.557222i) q^{84} +(13.1588 + 4.78941i) q^{85} +(0.999509 + 0.363791i) q^{86} +(2.13958 - 3.70585i) q^{87} +(1.53217 + 2.65379i) q^{88} +(1.32646 + 7.52272i) q^{89} +(2.34126 + 1.96455i) q^{90} +(-2.76276 + 2.31823i) q^{91} +(0.0665078 - 0.377184i) q^{92} +(-7.78987 + 2.83528i) q^{93} +13.0065 q^{94} +(9.11221 + 6.02375i) q^{95} -2.82093 q^{96} +(-6.23168 + 2.26814i) q^{97} +(1.14875 - 6.51490i) q^{98} +(-0.766044 + 0.642788i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 54q+3q2+3q4+3q618q712q8+30q10+27q1133q12+9q1421q1624q17+6q18+3q19+30q203q22+12q2339q24+30q25+54q98+O(q100) 54 q + 3 q^{2} + 3 q^{4} + 3 q^{6} - 18 q^{7} - 12 q^{8} + 30 q^{10} + 27 q^{11} - 33 q^{12} + 9 q^{14} - 21 q^{16} - 24 q^{17} + 6 q^{18} + 3 q^{19} + 30 q^{20} - 3 q^{22} + 12 q^{23} - 39 q^{24} + 30 q^{25}+ \cdots - 54 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/627Z)×\left(\mathbb{Z}/627\mathbb{Z}\right)^\times.

nn 343343 419419 496496
χ(n)\chi(n) 11 11 e(89)e\left(\frac{8}{9}\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 1.14605 0.417129i 0.810382 0.294955i 0.0966003 0.995323i 0.469203π-0.469203\pi
0.713782 + 0.700368i 0.246981π0.246981\pi
33 0.173648 0.984808i 0.100256 0.568579i
44 −0.392648 + 0.329471i −0.196324 + 0.164735i
55 −1.91969 1.61081i −0.858510 0.720375i 0.103137 0.994667i 0.467112π-0.467112\pi
−0.961646 + 0.274292i 0.911556π0.911556\pi
66 −0.211782 1.20108i −0.0864597 0.490337i
77 −0.627651 1.08712i −0.237230 0.410894i 0.722689 0.691174i 0.242906π-0.242906\pi
−0.959918 + 0.280280i 0.909573π0.909573\pi
88 −1.53217 + 2.65379i −0.541703 + 0.938257i
99 −0.939693 0.342020i −0.313231 0.114007i
1010 −2.87198 1.04531i −0.908199 0.330557i
1111 0.500000 0.866025i 0.150756 0.261116i
1212 0.256283 + 0.443895i 0.0739825 + 0.128141i
1313 −0.498897 2.82939i −0.138369 0.784730i −0.972454 0.233094i 0.925115π-0.925115\pi
0.834085 0.551636i 0.185996π-0.185996\pi
1414 −1.17279 0.984089i −0.313442 0.263009i
1515 −1.91969 + 1.61081i −0.495661 + 0.415909i
1616 −0.470959 + 2.67094i −0.117740 + 0.667735i
1717 −5.25098 + 1.91120i −1.27355 + 0.463534i −0.888294 0.459276i 0.848109π-0.848109\pi
−0.385255 + 0.922810i 0.625887π0.625887\pi
1818 −1.21960 −0.287463
1919 −4.33060 + 0.495920i −0.993507 + 0.113772i
2020 1.28448 0.287217
2121 −1.17960 + 0.429338i −0.257409 + 0.0936893i
2222 0.211782 1.20108i 0.0451521 0.256070i
2323 −0.572409 + 0.480308i −0.119356 + 0.100151i −0.700512 0.713641i 0.747045π-0.747045\pi
0.581156 + 0.813792i 0.302600π0.302600\pi
2424 2.34742 + 1.96972i 0.479165 + 0.402067i
2525 0.222251 + 1.26045i 0.0444502 + 0.252090i
2626 −1.75198 3.03452i −0.343592 0.595119i
2727 −0.500000 + 0.866025i −0.0962250 + 0.166667i
2828 0.604621 + 0.220064i 0.114263 + 0.0415882i
2929 4.02109 + 1.46356i 0.746697 + 0.271776i 0.687215 0.726454i 0.258833π-0.258833\pi
0.0594818 + 0.998229i 0.481055π0.481055\pi
3030 −1.52815 + 2.64683i −0.279000 + 0.483242i
3131 −4.14491 7.17919i −0.744447 1.28942i −0.950453 0.310869i 0.899380π-0.899380\pi
0.206006 0.978551i 0.433953π-0.433953\pi
3232 −0.489849 2.77807i −0.0865939 0.491098i
3333 −0.766044 0.642788i −0.133351 0.111895i
3434 −5.22068 + 4.38067i −0.895339 + 0.751279i
3535 −0.546254 + 3.09796i −0.0923337 + 0.523651i
3636 0.481654 0.175308i 0.0802757 0.0292180i
3737 −7.13754 −1.17340 −0.586702 0.809803i 0.699574π-0.699574\pi
−0.586702 + 0.809803i 0.699574π0.699574\pi
3838 −4.75623 + 2.37477i −0.771562 + 0.385238i
3939 −2.87303 −0.460054
4040 7.21603 2.62642i 1.14095 0.415273i
4141 −0.138834 + 0.787365i −0.0216822 + 0.122966i −0.993728 0.111827i 0.964330π-0.964330\pi
0.972046 + 0.234792i 0.0754410π0.0754410\pi
4242 −1.17279 + 0.984089i −0.180966 + 0.151848i
4343 0.668091 + 0.560595i 0.101883 + 0.0854900i 0.692306 0.721604i 0.256595π-0.256595\pi
−0.590423 + 0.807094i 0.701039π0.701039\pi
4444 0.0890061 + 0.504779i 0.0134182 + 0.0760983i
4545 1.25299 + 2.17024i 0.186784 + 0.323520i
4646 −0.455660 + 0.789227i −0.0671835 + 0.116365i
4747 10.0214 + 3.64748i 1.46177 + 0.532039i 0.945851 0.324600i 0.105230π-0.105230\pi
0.515915 + 0.856640i 0.327452π0.327452\pi
4848 2.54858 + 0.927608i 0.367856 + 0.133889i
4949 2.71211 4.69751i 0.387444 0.671073i
5050 0.780482 + 1.35183i 0.110377 + 0.191178i
5151 0.970341 + 5.50308i 0.135875 + 0.770585i
5252 1.12809 + 0.946581i 0.156438 + 0.131267i
5353 8.77332 7.36169i 1.20511 1.01121i 0.205639 0.978628i 0.434073π-0.434073\pi
0.999469 0.0325775i 0.0103716π-0.0103716\pi
5454 −0.211782 + 1.20108i −0.0288199 + 0.163446i
5555 −2.35484 + 0.857093i −0.317527 + 0.115570i
5656 3.84667 0.514032
5757 −0.263614 + 4.35092i −0.0349166 + 0.576293i
5858 5.21887 0.685271
5959 1.33898 0.487350i 0.174321 0.0634476i −0.253385 0.967365i 0.581544π-0.581544\pi
0.427706 + 0.903918i 0.359322π0.359322\pi
6060 0.223047 1.26496i 0.0287952 0.163306i
6161 1.17222 0.983611i 0.150088 0.125939i −0.564652 0.825329i 0.690990π-0.690990\pi
0.714740 + 0.699391i 0.246545π0.246545\pi
6262 −7.74493 6.49877i −0.983607 0.825344i
6363 0.217981 + 1.23623i 0.0274630 + 0.155750i
6464 −4.43235 7.67706i −0.554044 0.959632i
6565 −3.59987 + 6.23516i −0.446509 + 0.773376i
6666 −1.14605 0.417129i −0.141069 0.0513451i
6767 1.88620 + 0.686521i 0.230436 + 0.0838718i 0.454657 0.890666i 0.349762π-0.349762\pi
−0.224221 + 0.974538i 0.571984π0.571984\pi
6868 1.43210 2.48047i 0.173668 0.300802i
6969 0.373613 + 0.647117i 0.0449778 + 0.0779038i
7070 0.666213 + 3.77828i 0.0796277 + 0.451591i
7171 5.89580 + 4.94716i 0.699703 + 0.587120i 0.921689 0.387930i 0.126810π-0.126810\pi
−0.221986 + 0.975050i 0.571254π0.571254\pi
7272 2.34742 1.96972i 0.276646 0.232133i
7373 1.66902 9.46548i 0.195344 1.10785i −0.716584 0.697500i 0.754296π-0.754296\pi
0.911928 0.410350i 0.134593π-0.134593\pi
7474 −8.18000 + 2.97728i −0.950905 + 0.346101i
7575 1.27989 0.147789
7676 1.53701 1.62153i 0.176307 0.186002i
7777 −1.25530 −0.143055
7878 −3.29265 + 1.19843i −0.372819 + 0.135695i
7979 0.571565 3.24151i 0.0643061 0.364698i −0.935625 0.352994i 0.885163π-0.885163\pi
0.999932 0.0117035i 0.00372541π-0.00372541\pi
8080 5.20646 4.36874i 0.582100 0.488440i
8181 0.766044 + 0.642788i 0.0851160 + 0.0714208i
8282 0.169322 + 0.960274i 0.0186985 + 0.106044i
8383 −8.00749 13.8694i −0.878936 1.52236i −0.852510 0.522711i 0.824921π-0.824921\pi
−0.0264258 0.999651i 0.508413π-0.508413\pi
8484 0.321712 0.557222i 0.0351017 0.0607979i
8585 13.1588 + 4.78941i 1.42727 + 0.519485i
8686 0.999509 + 0.363791i 0.107780 + 0.0392286i
8787 2.13958 3.70585i 0.229387 0.397309i
8888 1.53217 + 2.65379i 0.163330 + 0.282895i
8989 1.32646 + 7.52272i 0.140604 + 0.797406i 0.970792 + 0.239922i 0.0771220π0.0771220\pi
−0.830188 + 0.557484i 0.811767π0.811767\pi
9090 2.34126 + 1.96455i 0.246790 + 0.207081i
9191 −2.76276 + 2.31823i −0.289616 + 0.243016i
9292 0.0665078 0.377184i 0.00693391 0.0393242i
9393 −7.78987 + 2.83528i −0.807772 + 0.294005i
9494 13.0065 1.34152
9595 9.11221 + 6.02375i 0.934894 + 0.618023i
9696 −2.82093 −0.287910
9797 −6.23168 + 2.26814i −0.632731 + 0.230295i −0.638419 0.769689i 0.720411π-0.720411\pi
0.00568863 + 0.999984i 0.498189π0.498189\pi
9898 1.14875 6.51490i 0.116041 0.658104i
9999 −0.766044 + 0.642788i −0.0769904 + 0.0646026i
100100 −0.502548 0.421688i −0.0502548 0.0421688i
101101 −1.98990 11.2853i −0.198002 1.12293i −0.908078 0.418801i 0.862450π-0.862450\pi
0.710076 0.704125i 0.248661π-0.248661\pi
102102 3.40756 + 5.90206i 0.337398 + 0.584391i
103103 −2.50253 + 4.33450i −0.246581 + 0.427091i −0.962575 0.271015i 0.912641π-0.912641\pi
0.715994 + 0.698107i 0.245974π0.245974\pi
104104 8.27300 + 3.01112i 0.811234 + 0.295265i
105105 2.95604 + 1.07591i 0.288480 + 0.104998i
106106 6.98391 12.0965i 0.678337 1.17491i
107107 4.93566 + 8.54882i 0.477148 + 0.826445i 0.999657 0.0261888i 0.00833710π-0.00833710\pi
−0.522509 + 0.852634i 0.675004π0.675004\pi
108108 −0.0890061 0.504779i −0.00856462 0.0485724i
109109 2.58969 + 2.17301i 0.248047 + 0.208136i 0.758331 0.651870i 0.226015π-0.226015\pi
−0.510284 + 0.860006i 0.670460π0.670460\pi
110110 −2.34126 + 1.96455i −0.223230 + 0.187312i
111111 −1.23942 + 7.02910i −0.117641 + 0.667173i
112112 3.19924 1.16443i 0.302300 0.110028i
113113 −8.77811 −0.825776 −0.412888 0.910782i 0.635480π-0.635480\pi
−0.412888 + 0.910782i 0.635480π0.635480\pi
114114 1.51278 + 5.09635i 0.141685 + 0.477317i
115115 1.87253 0.174614
116116 −2.06107 + 0.750169i −0.191366 + 0.0696514i
117117 −0.498897 + 2.82939i −0.0461230 + 0.261577i
118118 1.33126 1.11706i 0.122552 0.102834i
119119 5.37349 + 4.50889i 0.492587 + 0.413329i
120120 −1.33347 7.56247i −0.121728 0.690356i
121121 −0.500000 0.866025i −0.0454545 0.0787296i
122122 0.933136 1.61624i 0.0844821 0.146327i
123123 0.751295 + 0.273449i 0.0677420 + 0.0246561i
124124 3.99282 + 1.45327i 0.358566 + 0.130507i
125125 −4.66124 + 8.07350i −0.416914 + 0.722116i
126126 0.765485 + 1.32586i 0.0681949 + 0.118117i
127127 0.231828 + 1.31476i 0.0205714 + 0.116666i 0.993364 0.115010i 0.0366901π-0.0366901\pi
−0.972793 + 0.231676i 0.925579π0.925579\pi
128128 −3.96012 3.32294i −0.350029 0.293709i
129129 0.668091 0.560595i 0.0588222 0.0493577i
130130 −1.52478 + 8.64743i −0.133732 + 0.758430i
131131 −12.4360 + 4.52632i −1.08653 + 0.395466i −0.822336 0.569002i 0.807330π-0.807330\pi
−0.264199 + 0.964468i 0.585107π0.585107\pi
132132 0.512566 0.0446131
133133 3.25723 + 4.39663i 0.282437 + 0.381236i
134134 2.44805 0.211480
135135 2.35484 0.857093i 0.202673 0.0737668i
136136 2.97345 16.8633i 0.254971 1.44601i
137137 −7.44578 + 6.24775i −0.636136 + 0.533782i −0.902829 0.430000i 0.858514π-0.858514\pi
0.266693 + 0.963782i 0.414069π0.414069\pi
138138 0.698112 + 0.585786i 0.0594273 + 0.0498654i
139139 −3.63256 20.6013i −0.308110 1.74738i −0.608494 0.793558i 0.708226π-0.708226\pi
0.300384 0.953818i 0.402885π-0.402885\pi
140140 −0.806202 1.39638i −0.0681365 0.118016i
141141 5.33226 9.23574i 0.449057 0.777790i
142142 8.82050 + 3.21040i 0.740200 + 0.269411i
143143 −2.69977 0.982635i −0.225766 0.0821721i
144144 1.35607 2.34879i 0.113006 0.195732i
145145 −5.36172 9.28676i −0.445266 0.771224i
146146 −2.03554 11.5441i −0.168463 0.955399i
147147 −4.15519 3.48662i −0.342714 0.287572i
148148 2.80254 2.35161i 0.230368 0.193301i
149149 −2.53115 + 14.3549i −0.207360 + 1.17600i 0.686323 + 0.727297i 0.259224π0.259224\pi
−0.893683 + 0.448699i 0.851887π0.851887\pi
150150 1.46683 0.533881i 0.119766 0.0435912i
151151 −19.6797 −1.60151 −0.800757 0.598989i 0.795569π-0.795569\pi
−0.800757 + 0.598989i 0.795569π0.795569\pi
152152 5.31913 12.2523i 0.431439 0.993796i
153153 5.58797 0.451761
154154 −1.43864 + 0.523623i −0.115929 + 0.0421947i
155155 −3.60737 + 20.4584i −0.289751 + 1.64326i
156156 1.12809 0.946581i 0.0903196 0.0757871i
157157 0.450640 + 0.378132i 0.0359650 + 0.0301782i 0.660593 0.750744i 0.270305π-0.270305\pi
−0.624628 + 0.780922i 0.714749π0.714749\pi
158158 −0.697083 3.95335i −0.0554569 0.314512i
159159 −5.72638 9.91837i −0.454131 0.786578i
160160 −3.53458 + 6.12208i −0.279433 + 0.483993i
161161 0.881427 + 0.320813i 0.0694662 + 0.0252836i
162162 1.14605 + 0.417129i 0.0900424 + 0.0327728i
163163 8.85457 15.3366i 0.693544 1.20125i −0.277126 0.960834i 0.589382π-0.589382\pi
0.970669 0.240419i 0.0772849π-0.0772849\pi
164164 −0.204901 0.354899i −0.0160001 0.0277130i
165165 0.435157 + 2.46790i 0.0338770 + 0.192126i
166166 −14.9623 12.5549i −1.16130 0.974448i
167167 −1.25451 + 1.05266i −0.0970771 + 0.0814574i −0.690035 0.723776i 0.742405π-0.742405\pi
0.592957 + 0.805234i 0.297960π0.297960\pi
168168 0.667966 3.78823i 0.0515347 0.292268i
169169 4.45948 1.62312i 0.343037 0.124855i
170170 17.0785 1.30986
171171 4.23904 + 1.01514i 0.324168 + 0.0776296i
172172 −0.447025 −0.0340853
173173 −2.76148 + 1.00510i −0.209951 + 0.0764160i −0.444855 0.895603i 0.646745π-0.646745\pi
0.234904 + 0.972019i 0.424523π0.424523\pi
174174 0.906247 5.13958i 0.0687024 0.389631i
175175 1.23077 1.03274i 0.0930373 0.0780675i
176176 2.07762 + 1.74333i 0.156607 + 0.131409i
177177 −0.247434 1.40327i −0.0185983 0.105476i
178178 4.65814 + 8.06813i 0.349142 + 0.604732i
179179 4.24187 7.34713i 0.317052 0.549151i −0.662819 0.748779i 0.730640π-0.730640\pi
0.979872 + 0.199629i 0.0639736π0.0639736\pi
180180 −1.20701 0.439316i −0.0899654 0.0327447i
181181 16.2668 + 5.92062i 1.20910 + 0.440076i 0.866392 0.499365i 0.166433π-0.166433\pi
0.342709 + 0.939442i 0.388656π0.388656\pi
182182 −2.19927 + 3.80924i −0.163020 + 0.282360i
183183 −0.765114 1.32522i −0.0565588 0.0979628i
184184 −0.397612 2.25497i −0.0293123 0.166238i
185185 13.7018 + 11.4972i 1.00738 + 0.845291i
186186 −7.74493 + 6.49877i −0.567886 + 0.476513i
187187 −0.970341 + 5.50308i −0.0709584 + 0.402425i
188188 −5.13661 + 1.86957i −0.374626 + 0.136353i
189189 1.25530 0.0913098
190190 12.9558 + 3.10256i 0.939910 + 0.225084i
191191 13.7533 0.995150 0.497575 0.867421i 0.334224π-0.334224\pi
0.497575 + 0.867421i 0.334224π0.334224\pi
192192 −8.33010 + 3.03191i −0.601173 + 0.218809i
193193 −0.966625 + 5.48200i −0.0695792 + 0.394603i 0.930052 + 0.367429i 0.119762π0.119762\pi
−0.999631 + 0.0271740i 0.991349π0.991349\pi
194194 −6.19572 + 5.19883i −0.444827 + 0.373254i
195195 5.51532 + 4.62790i 0.394960 + 0.331411i
196196 0.482789 + 2.73803i 0.0344849 + 0.195574i
197197 2.41477 + 4.18251i 0.172045 + 0.297991i 0.939135 0.343549i 0.111629π-0.111629\pi
−0.767089 + 0.641540i 0.778296π0.778296\pi
198198 −0.609802 + 1.05621i −0.0433367 + 0.0750614i
199199 −23.2949 8.47864i −1.65133 0.601035i −0.662364 0.749182i 0.730447π-0.730447\pi
−0.988965 + 0.148148i 0.952669π0.952669\pi
200200 −3.68550 1.34141i −0.260604 0.0948521i
201201 1.00363 1.73833i 0.0707903 0.122612i
202202 −6.98795 12.1035i −0.491670 0.851598i
203203 −0.932773 5.29002i −0.0654678 0.371286i
204204 −2.19411 1.84107i −0.153618 0.128901i
205205 1.53481 1.28786i 0.107196 0.0899480i
206206 −1.05998 + 6.01145i −0.0738524 + 0.418838i
207207 0.702163 0.255567i 0.0488037 0.0177631i
208208 7.79208 0.540284
209209 −1.73582 + 3.99837i −0.120069 + 0.276573i
210210 3.83657 0.264748
211211 17.4850 6.36401i 1.20371 0.438116i 0.339195 0.940716i 0.389845π-0.389845\pi
0.864519 + 0.502600i 0.167623π0.167623\pi
212212 −1.01937 + 5.78111i −0.0700103 + 0.397048i
213213 5.89580 4.94716i 0.403973 0.338974i
214214 9.22249 + 7.73859i 0.630436 + 0.528999i
215215 −0.379514 2.15233i −0.0258827 0.146788i
216216 −1.53217 2.65379i −0.104251 0.180568i
217217 −5.20311 + 9.01204i −0.353210 + 0.611777i
218218 3.87435 + 1.41015i 0.262404 + 0.0955072i
219219 −9.03185 3.28733i −0.610316 0.222137i
220220 0.642238 1.11239i 0.0432997 0.0749972i
221221 8.02722 + 13.9035i 0.539969 + 0.935254i
222222 1.51160 + 8.57272i 0.101452 + 0.575363i
223223 −20.3103 17.0424i −1.36008 1.14124i −0.975958 0.217958i 0.930060π-0.930060\pi
−0.384120 0.923283i 0.625495π-0.625495\pi
224224 −2.71265 + 2.27619i −0.181247 + 0.152084i
225225 0.222251 1.26045i 0.0148167 0.0840300i
226226 −10.0602 + 3.66161i −0.669194 + 0.243567i
227227 11.7161 0.777623 0.388811 0.921317i 0.372886π-0.372886\pi
0.388811 + 0.921317i 0.372886π0.372886\pi
228228 −1.32999 1.79523i −0.0880810 0.118892i
229229 11.2574 0.743910 0.371955 0.928251i 0.378688π-0.378688\pi
0.371955 + 0.928251i 0.378688π0.378688\pi
230230 2.14602 0.781087i 0.141504 0.0515033i
231231 −0.217981 + 1.23623i −0.0143421 + 0.0813380i
232232 −10.0450 + 8.42872i −0.659483 + 0.553372i
233233 −0.215867 0.181134i −0.0141419 0.0118665i 0.635689 0.771945i 0.280716π-0.280716\pi
−0.649831 + 0.760079i 0.725160π0.725160\pi
234234 0.608457 + 3.45073i 0.0397761 + 0.225581i
235235 −13.3625 23.1445i −0.871672 1.50978i
236236 −0.365182 + 0.632513i −0.0237713 + 0.0411731i
237237 −3.09301 1.12576i −0.200912 0.0731262i
238238 8.03909 + 2.92599i 0.521097 + 0.189664i
239239 −11.7070 + 20.2771i −0.757264 + 1.31162i 0.186978 + 0.982364i 0.440131π0.440131\pi
−0.944241 + 0.329255i 0.893203π0.893203\pi
240240 −3.39828 5.88599i −0.219358 0.379939i
241241 1.44446 + 8.19194i 0.0930459 + 0.527690i 0.995329 + 0.0965447i 0.0307791π0.0307791\pi
−0.902283 + 0.431145i 0.858110π0.858110\pi
242242 −0.934271 0.783946i −0.0600572 0.0503940i
243243 0.766044 0.642788i 0.0491418 0.0412348i
244244 −0.136200 + 0.772426i −0.00871929 + 0.0494495i
245245 −12.7732 + 4.64906i −0.816049 + 0.297017i
246246 0.975088 0.0621693
247247 3.56367 + 12.0055i 0.226751 + 0.763893i
248248 25.4028 1.61308
249249 −15.0492 + 5.47744i −0.953701 + 0.347119i
250250 −1.97433 + 11.1970i −0.124868 + 0.708161i
251251 −0.289866 + 0.243227i −0.0182962 + 0.0153523i −0.651890 0.758314i 0.726024π-0.726024\pi
0.633594 + 0.773666i 0.281579π0.281579\pi
252252 −0.492892 0.413585i −0.0310493 0.0260534i
253253 0.129755 + 0.735875i 0.00815760 + 0.0462640i
254254 0.814112 + 1.41008i 0.0510819 + 0.0884764i
255255 7.00165 12.1272i 0.438460 0.759436i
256256 10.7356 + 3.90744i 0.670974 + 0.244215i
257257 −11.7975 4.29395i −0.735909 0.267849i −0.0532451 0.998581i 0.516956π-0.516956\pi
−0.682664 + 0.730733i 0.739179π0.739179\pi
258258 0.531828 0.921152i 0.0331101 0.0573484i
259259 4.47988 + 7.75938i 0.278366 + 0.482145i
260260 −0.640821 3.63428i −0.0397420 0.225388i
261261 −3.27802 2.75059i −0.202904 0.170257i
262262 −12.3642 + 10.3748i −0.763863 + 0.640957i
263263 1.56537 8.87768i 0.0965251 0.547421i −0.897744 0.440517i 0.854795π-0.854795\pi
0.994269 0.106904i 0.0340938π-0.0340938\pi
264264 2.87953 1.04806i 0.177223 0.0645039i
265265 −28.7003 −1.76304
266266 5.56692 + 3.68008i 0.341330 + 0.225640i
267267 7.63877 0.467485
268268 −0.966802 + 0.351887i −0.0590568 + 0.0214949i
269269 4.84085 27.4538i 0.295152 1.67389i −0.371434 0.928459i 0.621134π-0.621134\pi
0.666586 0.745429i 0.267755π-0.267755\pi
270270 2.34126 1.96455i 0.142484 0.119559i
271271 21.2191 + 17.8049i 1.28897 + 1.08157i 0.991941 + 0.126701i 0.0404389π0.0404389\pi
0.297025 + 0.954870i 0.404006π0.404006\pi
272272 −2.63171 14.9251i −0.159571 0.904970i
273273 1.80326 + 3.12334i 0.109138 + 0.189033i
274274 −5.92714 + 10.2661i −0.358072 + 0.620198i
275275 1.20271 + 0.437749i 0.0725259 + 0.0263973i
276276 −0.359905 0.130995i −0.0216637 0.00788496i
277277 −7.75580 + 13.4334i −0.466001 + 0.807137i −0.999246 0.0388234i 0.987639π-0.987639\pi
0.533245 + 0.845961i 0.320972π0.320972\pi
278278 −12.7565 22.0949i −0.765084 1.32516i
279279 1.43951 + 8.16387i 0.0861812 + 0.488758i
280280 −7.38439 6.19624i −0.441302 0.370296i
281281 −11.6311 + 9.75962i −0.693851 + 0.582210i −0.920017 0.391879i 0.871825π-0.871825\pi
0.226166 + 0.974089i 0.427381π0.427381\pi
282282 2.25855 12.8089i 0.134495 0.762758i
283283 −6.91298 + 2.51612i −0.410934 + 0.149568i −0.539211 0.842171i 0.681278π-0.681278\pi
0.128277 + 0.991738i 0.459055π0.459055\pi
284284 −3.94492 −0.234088
285285 7.51455 7.92777i 0.445124 0.469600i
286286 −3.50396 −0.207194
287287 0.943102 0.343261i 0.0556695 0.0202621i
288288 −0.489849 + 2.77807i −0.0288646 + 0.163699i
289289 10.8973 9.14394i 0.641019 0.537879i
290290 −10.0186 8.40660i −0.588312 0.493652i
291291 1.15157 + 6.53086i 0.0675061 + 0.382846i
292292 2.46326 + 4.26650i 0.144152 + 0.249678i
293293 −8.96686 + 15.5311i −0.523849 + 0.907334i 0.475765 + 0.879572i 0.342171π0.342171\pi
−0.999615 + 0.0277614i 0.991162π0.991162\pi
294294 −6.21644 2.26260i −0.362550 0.131957i
295295 −3.35545 1.22129i −0.195362 0.0711060i
296296 10.9359 18.9415i 0.635637 1.10095i
297297 0.500000 + 0.866025i 0.0290129 + 0.0502519i
298298 3.08700 + 17.5073i 0.178825 + 1.01417i
299299 1.64455 + 1.37994i 0.0951068 + 0.0798041i
300300 −0.502548 + 0.421688i −0.0290146 + 0.0243462i
301301 0.190108 1.07816i 0.0109576 0.0621439i
302302 −22.5540 + 8.20899i −1.29784 + 0.472374i
303303 −11.4594 −0.658324
304304 0.714960 11.8003i 0.0410058 0.676795i
305305 −3.83471 −0.219575
306306 6.40411 2.33091i 0.366099 0.133249i
307307 −0.284278 + 1.61222i −0.0162246 + 0.0920142i −0.991845 0.127451i 0.959320π-0.959320\pi
0.975620 + 0.219466i 0.0704314π0.0704314\pi
308308 0.492892 0.413585i 0.0280851 0.0235662i
309309 3.83409 + 3.21719i 0.218114 + 0.183019i
310310 4.39957 + 24.9512i 0.249879 + 1.41713i
311311 −14.0959 24.4149i −0.799307 1.38444i −0.920068 0.391759i 0.871867π-0.871867\pi
0.120760 0.992682i 0.461467π-0.461467\pi
312312 4.40197 7.62443i 0.249212 0.431649i
313313 −8.33537 3.03383i −0.471143 0.171482i 0.0955272 0.995427i 0.469546π-0.469546\pi
−0.566670 + 0.823945i 0.691769π0.691769\pi
314314 0.674187 + 0.245384i 0.0380466 + 0.0138478i
315315 1.57288 2.72430i 0.0886215 0.153497i
316316 0.843558 + 1.46109i 0.0474538 + 0.0821925i
317317 3.75332 + 21.2861i 0.210808 + 1.19555i 0.888035 + 0.459775i 0.152070π0.152070\pi
−0.677228 + 0.735773i 0.736819π0.736819\pi
318318 −10.7000 8.97834i −0.600025 0.503481i
319319 3.27802 2.75059i 0.183534 0.154003i
320320 −3.85754 + 21.8772i −0.215643 + 1.22297i
321321 9.27601 3.37619i 0.517736 0.188441i
322322 1.14398 0.0637517
323323 21.7921 10.8807i 1.21254 0.605418i
324324 −0.512566 −0.0284759
325325 3.45542 1.25767i 0.191672 0.0697629i
326326 3.75048 21.2700i 0.207720 1.17804i
327327 2.58969 2.17301i 0.143210 0.120168i
328328 −1.87679 1.57481i −0.103628 0.0869544i
329329 −2.32466 13.1838i −0.128163 0.726846i
330330 1.52815 + 2.64683i 0.0841217 + 0.145703i
331331 13.3176 23.0667i 0.731999 1.26786i −0.224028 0.974583i 0.571921π-0.571921\pi
0.956028 0.293277i 0.0947458π-0.0947458\pi
332332 7.71368 + 2.80755i 0.423343 + 0.154084i
333333 6.70709 + 2.44118i 0.367546 + 0.133776i
334334 −0.998642 + 1.72970i −0.0546433 + 0.0946449i
335335 −2.51506 4.35621i −0.137412 0.238005i
336336 −0.591196 3.35284i −0.0322524 0.182912i
337337 −19.4868 16.3514i −1.06151 0.890715i −0.0672559 0.997736i 0.521424π-0.521424\pi
−0.994257 + 0.107021i 0.965869π0.965869\pi
338338 4.43375 3.72036i 0.241164 0.202361i
339339 −1.52430 + 8.64476i −0.0827888 + 0.469519i
340340 −6.74475 + 2.45489i −0.365786 + 0.133135i
341341 −8.28981 −0.448918
342342 5.28161 0.604826i 0.285597 0.0327052i
343343 −15.5961 −0.842112
344344 −2.51133 + 0.914050i −0.135402 + 0.0492823i
345345 0.325161 1.84408i 0.0175061 0.0992820i
346346 −2.74554 + 2.30378i −0.147601 + 0.123852i
347347 −23.2906 19.5431i −1.25030 1.04913i −0.996646 0.0818365i 0.973921π-0.973921\pi
−0.253659 0.967294i 0.581634π-0.581634\pi
348348 0.380871 + 2.16002i 0.0204168 + 0.115789i
349349 7.10004 + 12.2976i 0.380056 + 0.658277i 0.991070 0.133343i 0.0425713π-0.0425713\pi
−0.611014 + 0.791620i 0.709238π0.709238\pi
350350 0.979740 1.69696i 0.0523693 0.0907063i
351351 2.69977 + 0.982635i 0.144103 + 0.0524492i
352352 −2.65081 0.964814i −0.141288 0.0514248i
353353 −8.53272 + 14.7791i −0.454151 + 0.786613i −0.998639 0.0521560i 0.983391π-0.983391\pi
0.544488 + 0.838769i 0.316724π0.316724\pi
354354 −0.868917 1.50501i −0.0461824 0.0799903i
355355 −3.34915 18.9940i −0.177755 1.00810i
356356 −2.99935 2.51675i −0.158965 0.133388i
357357 5.37349 4.50889i 0.284395 0.238636i
358358 1.79670 10.1896i 0.0949587 0.538538i
359359 6.38837 2.32518i 0.337165 0.122718i −0.167888 0.985806i 0.553695π-0.553695\pi
0.505054 + 0.863088i 0.331473π0.331473\pi
360360 −7.67914 −0.404726
361361 18.5081 4.29526i 0.974112 0.226066i
362362 21.1123 1.10964
363363 −0.939693 + 0.342020i −0.0493211 + 0.0179514i
364364 0.321003 1.82050i 0.0168251 0.0954200i
365365 −18.4511 + 15.4823i −0.965772 + 0.810379i
366366 −1.42965 1.19962i −0.0747288 0.0627049i
367367 5.07881 + 28.8034i 0.265112 + 1.50352i 0.768716 + 0.639590i 0.220896π0.220896\pi
−0.503604 + 0.863935i 0.667993π0.667993\pi
368368 −1.01329 1.75508i −0.0528216 0.0914897i
369369 0.399756 0.692397i 0.0208105 0.0360448i
370370 20.4988 + 7.46097i 1.06568 + 0.387877i
371371 −13.5096 4.91711i −0.701386 0.255283i
372372 2.12454 3.67981i 0.110152 0.190789i
373373 2.35615 + 4.08097i 0.121997 + 0.211305i 0.920555 0.390613i 0.127737π-0.127737\pi
−0.798558 + 0.601918i 0.794404π0.794404\pi
374374 1.18343 + 6.71158i 0.0611938 + 0.347047i
375375 7.14143 + 5.99237i 0.368782 + 0.309445i
376376 −25.0341 + 21.0061i −1.29103 + 1.08331i
377377 2.13486 12.1074i 0.109951 0.623561i
378378 1.43864 0.523623i 0.0739958 0.0269323i
379379 −15.9670 −0.820171 −0.410086 0.912047i 0.634501π-0.634501\pi
−0.410086 + 0.912047i 0.634501π0.634501\pi
380380 −5.56254 + 0.636997i −0.285353 + 0.0326773i
381381 1.33504 0.0683963
382382 15.7620 5.73688i 0.806452 0.293524i
383383 3.58942 20.3566i 0.183411 1.04018i −0.744569 0.667545i 0.767345π-0.767345\pi
0.927980 0.372630i 0.121544π-0.121544\pi
384384 −3.96012 + 3.32294i −0.202089 + 0.169573i
385385 2.40978 + 2.02205i 0.122814 + 0.103053i
386386 1.17890 + 6.68587i 0.0600044 + 0.340302i
387387 −0.436066 0.755288i −0.0221665 0.0383934i
388388 1.69957 2.94374i 0.0862825 0.149446i
389389 6.67462 + 2.42936i 0.338417 + 0.123174i 0.505638 0.862746i 0.331257π-0.331257\pi
−0.167221 + 0.985919i 0.553479π0.553479\pi
390390 8.25128 + 3.00322i 0.417820 + 0.152074i
391391 2.08774 3.61607i 0.105582 0.182873i
392392 8.31081 + 14.3947i 0.419759 + 0.727045i
393393 2.29807 + 13.0330i 0.115922 + 0.657429i
394394 4.51210 + 3.78610i 0.227316 + 0.190741i
395395 −6.31867 + 5.30199i −0.317927 + 0.266772i
396396 0.0890061 0.504779i 0.00447273 0.0253661i
397397 −8.13670 + 2.96152i −0.408369 + 0.148634i −0.538033 0.842924i 0.680832π-0.680832\pi
0.129664 + 0.991558i 0.458610π0.458610\pi
398398 −30.2338 −1.51549
399399 4.89544 2.44428i 0.245079 0.122367i
400400 −3.47126 −0.173563
401401 −1.74876 + 0.636496i −0.0873288 + 0.0317851i −0.385315 0.922785i 0.625907π-0.625907\pi
0.297986 + 0.954570i 0.403685π0.403685\pi
402402 0.425100 2.41086i 0.0212021 0.120243i
403403 −18.2448 + 15.3092i −0.908839 + 0.762606i
404404 4.49950 + 3.77553i 0.223859 + 0.187840i
405405 −0.435157 2.46790i −0.0216231 0.122631i
406406 −3.27563 5.67355i −0.162567 0.281574i
407407 −3.56877 + 6.18129i −0.176897 + 0.306395i
408408 −16.0908 5.85656i −0.796611 0.289943i
409409 −6.58062 2.39515i −0.325391 0.118433i 0.174159 0.984717i 0.444279π-0.444279\pi
−0.499550 + 0.866285i 0.666501π0.666501\pi
410410 1.22177 2.11617i 0.0603390 0.104510i
411411 4.85989 + 8.41758i 0.239721 + 0.415208i
412412 −0.445481 2.52645i −0.0219473 0.124469i
413413 −1.37022 1.14975i −0.0674243 0.0565757i
414414 0.698112 0.585786i 0.0343103 0.0287898i
415415 −6.96903 + 39.5234i −0.342096 + 1.94013i
416416 −7.61585 + 2.77194i −0.373398 + 0.135906i
417417 −20.9191 −1.02441
418418 −0.321505 + 5.30640i −0.0157253 + 0.259545i
419419 34.9701 1.70840 0.854200 0.519945i 0.174048π-0.174048\pi
0.854200 + 0.519945i 0.174048π0.174048\pi
420420 −1.51516 + 0.551475i −0.0739324 + 0.0269092i
421421 −1.92891 + 10.9394i −0.0940094 + 0.533154i 0.901037 + 0.433742i 0.142807π0.142807\pi
−0.995046 + 0.0994117i 0.968304π0.968304\pi
422422 17.3841 14.5870i 0.846244 0.710083i
423423 −8.16949 6.85502i −0.397214 0.333302i
424424 6.09420 + 34.5619i 0.295960 + 1.67847i
425425 −3.57601 6.19382i −0.173462 0.300445i
426426 4.69329 8.12902i 0.227391 0.393852i
427427 −1.80505 0.656985i −0.0873526 0.0317938i
428428 −4.75457 1.73052i −0.229821 0.0836479i
429429 −1.43652 + 2.48812i −0.0693557 + 0.120128i
430430 −1.33274 2.30838i −0.0642707 0.111320i
431431 −6.47368 36.7141i −0.311826 1.76845i −0.589490 0.807776i 0.700671π-0.700671\pi
0.277663 0.960678i 0.410440π-0.410440\pi
432432 −2.07762 1.74333i −0.0999597 0.0838761i
433433 13.1969 11.0735i 0.634203 0.532159i −0.268029 0.963411i 0.586372π-0.586372\pi
0.902232 + 0.431252i 0.141928π0.141928\pi
434434 −2.20385 + 12.4986i −0.105788 + 0.599954i
435435 −10.0767 + 3.66763i −0.483142 + 0.175849i
436436 −1.73278 −0.0829852
437437 2.24068 2.36389i 0.107186 0.113080i
438438 −11.7222 −0.560109
439439 12.4561 4.53364i 0.594496 0.216379i −0.0272099 0.999630i 0.508662π-0.508662\pi
0.621706 + 0.783251i 0.286440π0.286440\pi
440440 1.33347 7.56247i 0.0635706 0.360527i
441441 −4.15519 + 3.48662i −0.197866 + 0.166030i
442442 14.9992 + 12.5858i 0.713439 + 0.598646i
443443 −1.07787 6.11289i −0.0512110 0.290432i 0.948437 0.316966i 0.102664π-0.102664\pi
−0.999648 + 0.0265338i 0.991553π0.991553\pi
444444 −1.82923 3.16832i −0.0868114 0.150362i
445445 9.57127 16.5779i 0.453721 0.785869i
446446 −30.3855 11.0594i −1.43880 0.523679i
447447 13.6973 + 4.98539i 0.647858 + 0.235801i
448448 −5.56394 + 9.63703i −0.262871 + 0.455307i
449449 −14.5112 25.1342i −0.684827 1.18615i −0.973491 0.228724i 0.926545π-0.926545\pi
0.288664 0.957430i 0.406789π-0.406789\pi
450450 −0.271059 1.53725i −0.0127778 0.0724666i
451451 0.612461 + 0.513916i 0.0288397 + 0.0241994i
452452 3.44671 2.89213i 0.162120 0.136035i
453453 −3.41735 + 19.3808i −0.160561 + 0.910587i
454454 13.4272 4.88711i 0.630171 0.229364i
455455 9.03785 0.423701
456456 −11.1425 7.36592i −0.521797 0.344941i
457457 −3.30144 −0.154435 −0.0772175 0.997014i 0.524604π-0.524604\pi
−0.0772175 + 0.997014i 0.524604π0.524604\pi
458458 12.9016 4.69579i 0.602851 0.219420i
459459 0.970341 5.50308i 0.0452917 0.256862i
460460 −0.735245 + 0.616944i −0.0342810 + 0.0287652i
461461 31.7828 + 26.6690i 1.48027 + 1.24210i 0.905891 + 0.423511i 0.139203π0.139203\pi
0.574383 + 0.818586i 0.305242π0.305242\pi
462462 0.265850 + 1.50771i 0.0123685 + 0.0701451i
463463 −13.0644 22.6282i −0.607154 1.05162i −0.991707 0.128519i 0.958978π-0.958978\pi
0.384553 0.923103i 0.374356π-0.374356\pi
464464 −5.80284 + 10.0508i −0.269390 + 0.466597i
465465 19.5212 + 7.10514i 0.905274 + 0.329493i
466466 −0.322952 0.117545i −0.0149605 0.00544516i
467467 6.24557 10.8176i 0.289010 0.500581i −0.684563 0.728953i 0.740007π-0.740007\pi
0.973574 + 0.228373i 0.0733404π0.0733404\pi
468468 −0.736309 1.27533i −0.0340359 0.0589519i
469469 −0.437542 2.48143i −0.0202038 0.114582i
470470 −24.9684 20.9509i −1.15170 0.966395i
471471 0.450640 0.378132i 0.0207644 0.0174234i
472472 −0.758221 + 4.30009i −0.0349000 + 0.197927i
473473 0.819536 0.298287i 0.0376823 0.0137152i
474474 −4.01434 −0.184385
475475 −1.58756 5.34828i −0.0728424 0.245396i
476476 −3.59544 −0.164797
477477 −10.7621 + 3.91707i −0.492761 + 0.179350i
478478 −4.95867 + 28.1220i −0.226804 + 1.28627i
479479 13.6070 11.4177i 0.621721 0.521686i −0.276623 0.960979i 0.589215π-0.589215\pi
0.898344 + 0.439293i 0.144771π0.144771\pi
480480 5.41530 + 4.54397i 0.247173 + 0.207403i
481481 3.56090 + 20.1948i 0.162363 + 0.920806i
482482 5.07253 + 8.78588i 0.231047 + 0.400186i
483483 0.468997 0.812327i 0.0213401 0.0369622i
484484 0.481654 + 0.175308i 0.0218934 + 0.00796854i
485485 15.6164 + 5.68391i 0.709104 + 0.258093i
486486 0.609802 1.05621i 0.0276612 0.0479106i
487487 −5.86342 10.1557i −0.265697 0.460201i 0.702049 0.712129i 0.252269π-0.252269\pi
−0.967746 + 0.251928i 0.918935π0.918935\pi
488488 0.814259 + 4.61789i 0.0368598 + 0.209042i
489489 −13.5660 11.3832i −0.613475 0.514767i
490490 −12.6995 + 10.6561i −0.573704 + 0.481395i
491491 4.07169 23.0917i 0.183753 1.04211i −0.743794 0.668408i 0.766976π-0.766976\pi
0.927547 0.373706i 0.121913π-0.121913\pi
492492 −0.385088 + 0.140161i −0.0173611 + 0.00631893i
493493 −23.9118 −1.07693
494494 9.09200 + 12.2724i 0.409069 + 0.552163i
495495 2.50597 0.112635
496496 21.1273 7.68970i 0.948642 0.345278i
497497 1.67767 9.51455i 0.0752539 0.426786i
498498 −14.9623 + 12.5549i −0.670478 + 0.562598i
499499 7.72602 + 6.48290i 0.345864 + 0.290215i 0.799127 0.601162i 0.205296π-0.205296\pi
−0.453263 + 0.891377i 0.649740π0.649740\pi
500500 −0.829758 4.70579i −0.0371079 0.210449i
501501 0.818825 + 1.41825i 0.0365824 + 0.0633626i
502502 −0.230745 + 0.399663i −0.0102987 + 0.0178378i
503503 −17.5060 6.37165i −0.780552 0.284098i −0.0791491 0.996863i 0.525220π-0.525220\pi
−0.701403 + 0.712765i 0.747443π0.747443\pi
504504 −3.61468 1.31564i −0.161011 0.0586031i
505505 −14.3584 + 24.8695i −0.638942 + 1.10668i
506506 0.455660 + 0.789227i 0.0202566 + 0.0350854i
507507 −0.824078 4.67358i −0.0365986 0.207561i
508508 −0.524202 0.439858i −0.0232577 0.0195155i
509509 −2.82381 + 2.36946i −0.125163 + 0.105025i −0.703221 0.710972i 0.748255π-0.748255\pi
0.578057 + 0.815996i 0.303811π0.303811\pi
510510 2.96565 16.8190i 0.131321 0.744759i
511511 −11.3377 + 4.12658i −0.501550 + 0.182549i
512512 24.2726 1.07271
513513 1.73582 3.99837i 0.0766383 0.176532i
514514 −15.3117 −0.675371
515515 11.7861 4.28980i 0.519358 0.189031i
516516 −0.0776250 + 0.440234i −0.00341725 + 0.0193802i
517517 8.16949 6.85502i 0.359294 0.301483i
518518 8.37085 + 7.02397i 0.367794 + 0.308616i
519519 0.510300 + 2.89406i 0.0223997 + 0.127035i
520520 −11.0312 19.1066i −0.483751 0.837881i
521521 12.6447 21.9013i 0.553976 0.959515i −0.444006 0.896024i 0.646443π-0.646443\pi
0.997982 0.0634910i 0.0202234π-0.0202234\pi
522522 −4.90413 1.78496i −0.214648 0.0781255i
523523 10.7859 + 3.92576i 0.471636 + 0.171661i 0.566893 0.823791i 0.308145π-0.308145\pi
−0.0952573 + 0.995453i 0.530367π0.530367\pi
524524 3.39167 5.87454i 0.148166 0.256630i
525525 −0.803326 1.39140i −0.0350600 0.0607258i
526526 −1.90914 10.8273i −0.0832423 0.472091i
527527 35.4857 + 29.7760i 1.54578 + 1.29706i
528528 2.07762 1.74333i 0.0904169 0.0758688i
529529 −3.89695 + 22.1007i −0.169433 + 0.960901i
530530 −32.8920 + 11.9717i −1.42874 + 0.520018i
531531 −1.42492 −0.0618361
532532 −2.72751 0.653165i −0.118252 0.0283183i
533533 2.29702 0.0994951
534534 8.75443 3.18635i 0.378841 0.137887i
535535 4.29558 24.3614i 0.185714 1.05324i
536536 −4.71186 + 3.95372i −0.203521 + 0.170775i
537537 −6.49892 5.45324i −0.280449 0.235325i
538538 −5.90392 33.4828i −0.254536 1.44354i
539539 −2.71211 4.69751i −0.116819 0.202336i
540540 −0.642238 + 1.11239i −0.0276375 + 0.0478696i
541541 26.3888 + 9.60474i 1.13454 + 0.412940i 0.839940 0.542680i 0.182590π-0.182590\pi
0.294604 + 0.955620i 0.404812π0.404812\pi
542542 31.7451 + 11.5543i 1.36357 + 0.496299i
543543 8.65537 14.9915i 0.371438 0.643349i
544544 7.88164 + 13.6514i 0.337922 + 0.585299i
545545 −1.47109 8.34299i −0.0630147 0.357374i
546546 3.36947 + 2.82732i 0.144200 + 0.120998i
547547 −19.6037 + 16.4495i −0.838195 + 0.703329i −0.957157 0.289570i 0.906488π-0.906488\pi
0.118962 + 0.992899i 0.462043π0.462043\pi
548548 0.865120 4.90634i 0.0369561 0.209588i
549549 −1.43794 + 0.523369i −0.0613699 + 0.0223368i
550550 1.56096 0.0665597
551551 −18.1395 4.34393i −0.772769 0.185058i
552552 −2.28975 −0.0974584
553553 −3.88266 + 1.41317i −0.165107 + 0.0600942i
554554 −3.28508 + 18.6306i −0.139570 + 0.791539i
555555 13.7018 11.4972i 0.581610 0.488029i
556556 8.21384 + 6.89223i 0.348344 + 0.292296i
557557 6.41170 + 36.3626i 0.271673 + 1.54073i 0.749337 + 0.662189i 0.230372π0.230372\pi
−0.477664 + 0.878542i 0.658517π0.658517\pi
558558 5.05514 + 8.75577i 0.214001 + 0.370661i
559559 1.25283 2.16997i 0.0529891 0.0917799i
560560 −8.01720 2.91802i −0.338789 0.123309i
561561 5.25098 + 1.91120i 0.221696 + 0.0806909i
562562 −9.25879 + 16.0367i −0.390558 + 0.676467i
563563 −13.8998 24.0751i −0.585806 1.01465i −0.994774 0.102097i 0.967445π-0.967445\pi
0.408968 0.912549i 0.365889π-0.365889\pi
564564 0.949207 + 5.38322i 0.0399688 + 0.226674i
565565 16.8512 + 14.1399i 0.708936 + 0.594868i
566566 −6.87309 + 5.76721i −0.288898 + 0.242414i
567567 0.217981 1.23623i 0.00915433 0.0519168i
568568 −22.1621 + 8.06634i −0.929901 + 0.338456i
569569 45.0113 1.88697 0.943487 0.331411i 0.107525π-0.107525\pi
0.943487 + 0.331411i 0.107525π0.107525\pi
570570 5.30517 12.2202i 0.222209 0.511847i
571571 −17.2748 −0.722928 −0.361464 0.932386i 0.617723π-0.617723\pi
−0.361464 + 0.932386i 0.617723π0.617723\pi
572572 1.38381 0.503665i 0.0578600 0.0210593i
573573 2.38823 13.5443i 0.0997696 0.565822i
574574 0.937661 0.786791i 0.0391372 0.0328400i
575575 −0.732623 0.614743i −0.0305525 0.0256366i
576576 1.53934 + 8.73003i 0.0641392 + 0.363751i
577577 −8.83572 15.3039i −0.367836 0.637111i 0.621391 0.783501i 0.286568π-0.286568\pi
−0.989227 + 0.146390i 0.953235π0.953235\pi
578578 8.67470 15.0250i 0.360820 0.624959i
579579 5.23087 + 1.90388i 0.217387 + 0.0791225i
580580 5.16499 + 1.87990i 0.214464 + 0.0780587i
581581 −10.0518 + 17.4102i −0.417019 + 0.722299i
582582 4.04397 + 7.00436i 0.167628 + 0.290340i
583583 −1.98875 11.2788i −0.0823656 0.467118i
584584 22.5622 + 18.9319i 0.933630 + 0.783409i
585585 5.51532 4.62790i 0.228030 0.191340i
586586 −3.79804 + 21.5397i −0.156896 + 0.889799i
587587 30.3398 11.0428i 1.25226 0.455784i 0.371093 0.928596i 0.378983π-0.378983\pi
0.881164 + 0.472811i 0.156761π0.156761\pi
588588 2.78027 0.114656
589589 21.5102 + 29.0346i 0.886313 + 1.19635i
590590 −4.35496 −0.179291
591591 4.53829 1.65180i 0.186680 0.0679460i
592592 3.36149 19.0639i 0.138156 0.783523i
593593 −20.0248 + 16.8028i −0.822319 + 0.690008i −0.953514 0.301349i 0.902563π-0.902563\pi
0.131195 + 0.991357i 0.458119π0.458119\pi
594594 0.934271 + 0.783946i 0.0383336 + 0.0321657i
595595 −3.05245 17.3113i −0.125138 0.709695i
596596 −3.73566 6.47035i −0.153019 0.265036i
597597 −12.3949 + 21.4687i −0.507291 + 0.878654i
598598 2.46036 + 0.895496i 0.100611 + 0.0366196i
599599 8.65599 + 3.15052i 0.353674 + 0.128727i 0.512746 0.858540i 0.328628π-0.328628\pi
−0.159072 + 0.987267i 0.550850π0.550850\pi
600600 −1.96101 + 3.39657i −0.0800580 + 0.138664i
601601 −19.6932 34.1096i −0.803301 1.39136i −0.917432 0.397892i 0.869742π-0.869742\pi
0.114132 0.993466i 0.463591π-0.463591\pi
602602 −0.231856 1.31492i −0.00944976 0.0535923i
603603 −1.53764 1.29024i −0.0626177 0.0525425i
604604 7.72721 6.48390i 0.314416 0.263826i
605605 −0.435157 + 2.46790i −0.0176917 + 0.100334i
606606 −13.1330 + 4.78004i −0.533493 + 0.194176i
607607 2.65783 0.107878 0.0539389 0.998544i 0.482822π-0.482822\pi
0.0539389 + 0.998544i 0.482822π0.482822\pi
608608 3.49904 + 11.7878i 0.141905 + 0.478058i
609609 −5.37163 −0.217669
610610 −4.39478 + 1.59957i −0.177939 + 0.0647646i
611611 5.32049 30.1740i 0.215244 1.22071i
612612 −2.19411 + 1.84107i −0.0886915 + 0.0744210i
613613 22.2706 + 18.6873i 0.899502 + 0.754772i 0.970093 0.242734i 0.0780441π-0.0780441\pi
−0.0705911 + 0.997505i 0.522489π0.522489\pi
614614 0.346706 + 1.96627i 0.0139919 + 0.0793522i
615615 −1.00178 1.73513i −0.0403955 0.0699671i
616616 1.92333 3.33131i 0.0774933 0.134222i
617617 23.5983 + 8.58909i 0.950033 + 0.345784i 0.770120 0.637899i 0.220196π-0.220196\pi
0.179913 + 0.983683i 0.442418π0.442418\pi
618618 5.73606 + 2.08775i 0.230738 + 0.0839818i
619619 −5.70768 + 9.88598i −0.229411 + 0.397351i −0.957634 0.287989i 0.907013π-0.907013\pi
0.728223 + 0.685340i 0.240347π0.240347\pi
620620 −5.32403 9.22149i −0.213818 0.370344i
621621 −0.129755 0.735875i −0.00520687 0.0295296i
622622 −26.3389 22.1009i −1.05609 0.886166i
623623 7.34557 6.16366i 0.294294 0.246942i
624624 1.35308 7.67370i 0.0541666 0.307194i
625625 27.9665 10.1790i 1.11866 0.407159i
626626 −10.8183 −0.432385
627627 3.63620 + 2.40376i 0.145216 + 0.0959968i
628628 −0.301526 −0.0120322
629629 37.4790 13.6413i 1.49439 0.543913i
630630 0.666213 3.77828i 0.0265426 0.150530i
631631 31.2943 26.2591i 1.24581 1.04536i 0.248760 0.968565i 0.419977π-0.419977\pi
0.997047 0.0767917i 0.0244676π-0.0244676\pi
632632 7.72655 + 6.48334i 0.307346 + 0.257894i
633633 −3.23109 18.3244i −0.128424 0.728331i
634634 13.1806 + 22.8294i 0.523468 + 0.906672i
635635 1.67279 2.89736i 0.0663826 0.114978i
636636 5.51627 + 2.00776i 0.218734 + 0.0796128i
637637 −14.6441 5.33003i −0.580222 0.211183i
638638 2.60944 4.51967i 0.103309 0.178936i
639639 −3.84821 6.66529i −0.152233 0.263675i
640640 2.24958 + 12.7580i 0.0889224 + 0.504304i
641641 14.8592 + 12.4683i 0.586903 + 0.492470i 0.887206 0.461374i 0.152643π-0.152643\pi
−0.300303 + 0.953844i 0.597088π0.597088\pi
642642 9.22249 7.73859i 0.363983 0.305418i
643643 4.46362 25.3145i 0.176028 0.998305i −0.760922 0.648843i 0.775253π-0.775253\pi
0.936950 0.349462i 0.113636π-0.113636\pi
644644 −0.451789 + 0.164438i −0.0178030 + 0.00647976i
645645 −2.18554 −0.0860554
646646 20.4362 21.5600i 0.804051 0.848265i
647647 37.0389 1.45615 0.728075 0.685498i 0.240415π-0.240415\pi
0.728075 + 0.685498i 0.240415π0.240415\pi
648648 −2.87953 + 1.04806i −0.113119 + 0.0411719i
649649 0.247434 1.40327i 0.00971264 0.0550831i
650650 3.43548 2.88271i 0.134751 0.113069i
651651 7.97162 + 6.68898i 0.312432 + 0.262162i
652652 1.57622 + 8.93920i 0.0617296 + 0.350086i
653653 −21.2195 36.7533i −0.830384 1.43827i −0.897734 0.440537i 0.854788π-0.854788\pi
0.0673509 0.997729i 0.478545π-0.478545\pi
654654 2.06150 3.57062i 0.0806109 0.139622i
655655 31.1642 + 11.3428i 1.21768 + 0.443201i
656656 −2.03762 0.741633i −0.0795557 0.0289559i
657657 −4.80575 + 8.32380i −0.187490 + 0.324742i
658658 −8.16353 14.1396i −0.318248 0.551221i
659659 6.86683 + 38.9437i 0.267494 + 1.51703i 0.761839 + 0.647766i 0.224297π0.224297\pi
−0.494346 + 0.869265i 0.664592π0.664592\pi
660660 −0.983965 0.825645i −0.0383008 0.0321382i
661661 34.3266 28.8034i 1.33515 1.12032i 0.352305 0.935885i 0.385398π-0.385398\pi
0.982844 0.184438i 0.0590465π-0.0590465\pi
662662 5.64084 31.9908i 0.219237 1.24336i
663663 15.0862 5.49094i 0.585901 0.213250i
664664 49.0753 1.90449
665665 0.829265 13.6869i 0.0321575 0.530756i
666666 8.70497 0.337311
667667 −3.00466 + 1.09361i −0.116341 + 0.0423447i
668668 0.145761 0.826651i 0.00563966 0.0319841i
669669 −20.3103 + 17.0424i −0.785241 + 0.658896i
670670 −4.69949 3.94334i −0.181557 0.152345i
671671 −0.265721 1.50698i −0.0102581 0.0581763i
672672 1.77056 + 3.06670i 0.0683008 + 0.118300i
673673 9.99114 17.3052i 0.385130 0.667065i −0.606657 0.794964i 0.707490π-0.707490\pi
0.991787 + 0.127899i 0.0408233π0.0408233\pi
674674 −29.1535 10.6110i −1.12295 0.408721i
675675 −1.20271 0.437749i −0.0462922 0.0168490i
676676 −1.21624 + 2.10658i −0.0467783 + 0.0810224i
677677 −1.44899 2.50973i −0.0556893 0.0964566i 0.836837 0.547452i 0.184402π-0.184402\pi
−0.892526 + 0.450996i 0.851069π0.851069\pi
678678 1.85905 + 10.5432i 0.0713963 + 0.404908i
679679 6.37707 + 5.35100i 0.244729 + 0.205352i
680680 −32.8716 + 27.5825i −1.26057 + 1.05774i
681681 2.03447 11.5381i 0.0779612 0.442140i
682682 −9.50056 + 3.45792i −0.363795 + 0.132411i
683683 16.1643 0.618511 0.309255 0.950979i 0.399920π-0.399920\pi
0.309255 + 0.950979i 0.399920π0.399920\pi
684684 −1.99891 + 0.998049i −0.0764303 + 0.0381614i
685685 24.3575 0.930652
686686 −17.8740 + 6.50561i −0.682433 + 0.248385i
687687 1.95483 11.0864i 0.0745813 0.422972i
688688 −1.81196 + 1.52042i −0.0690804 + 0.0579653i
689689 −25.2060 21.1504i −0.960273 0.805765i
690690 −0.396568 2.24905i −0.0150971 0.0856198i
691691 3.31507 + 5.74186i 0.126111 + 0.218431i 0.922167 0.386793i 0.126417π-0.126417\pi
−0.796056 + 0.605223i 0.793084π0.793084\pi
692692 0.753139 1.30448i 0.0286301 0.0495887i
693693 1.17960 + 0.429338i 0.0448092 + 0.0163092i
694694 −34.8443 12.6823i −1.32267 0.481413i
695695 −26.2113 + 45.3993i −0.994251 + 1.72209i
696696 6.55638 + 11.3560i 0.248519 + 0.430447i
697697 −0.775799 4.39978i −0.0293855 0.166653i
698698 13.2667 + 11.1321i 0.502153 + 0.421356i
699699 −0.215867 + 0.181134i −0.00816485 + 0.00685112i
700700 −0.143002 + 0.811004i −0.00540497 + 0.0306531i
701701 −21.0380 + 7.65720i −0.794594 + 0.289208i −0.707244 0.706969i 0.750062π-0.750062\pi
−0.0873494 + 0.996178i 0.527840π0.527840\pi
702702 3.50396 0.132249
703703 30.9098 3.53965i 1.16579 0.133500i
704704 −8.86471 −0.334101
705705 −25.1133 + 9.14048i −0.945820 + 0.344250i
706706 −3.61416 + 20.4969i −0.136021 + 0.771411i
707707 −11.0195 + 9.24648i −0.414432 + 0.347750i
708708 0.559491 + 0.469468i 0.0210269 + 0.0176437i
709709 5.82268 + 33.0221i 0.218675 + 1.24017i 0.874413 + 0.485182i 0.161247π0.161247\pi
−0.655738 + 0.754989i 0.727642π0.727642\pi
710710 −11.7613 20.3711i −0.441392 0.764514i
711711 −1.64576 + 2.85053i −0.0617206 + 0.106903i
712712 −21.9961 8.00592i −0.824338 0.300035i
713713 5.82080 + 2.11860i 0.217991 + 0.0793421i
714714 4.27751 7.40887i 0.160082 0.277270i
715715 3.59987 + 6.23516i 0.134628 + 0.233182i
716716 0.755105 + 4.28241i 0.0282196 + 0.160041i
717717 17.9362 + 15.0502i 0.669839 + 0.562062i
718718 6.35151 5.32955i 0.237036 0.198897i
719719 1.23330 6.99437i 0.0459942 0.260846i −0.953136 0.302542i 0.902165π-0.902165\pi
0.999130 + 0.0416957i 0.0132760π0.0132760\pi
720720 −6.38667 + 2.32456i −0.238017 + 0.0866312i
721721 6.28285 0.233986
722722 19.4196 12.6429i 0.722723 0.470519i
723723 8.31832 0.309362
724724 −8.33779 + 3.03471i −0.309872 + 0.112784i
725725 −0.951047 + 5.39365i −0.0353210 + 0.200315i
726726 −0.934271 + 0.783946i −0.0346740 + 0.0290950i
727727 −15.4956 13.0024i −0.574702 0.482232i 0.308501 0.951224i 0.400173π-0.400173\pi
−0.883202 + 0.468992i 0.844617π0.844617\pi
728728 −1.91909 10.8837i −0.0711262 0.403377i
729729 −0.500000 0.866025i −0.0185185 0.0320750i
730730 −14.6878 + 25.4400i −0.543619 + 0.941576i
731731 −4.57954 1.66682i −0.169380 0.0616495i
732732 0.737041 + 0.268261i 0.0272418 + 0.00991521i
733733 −15.1831 + 26.2979i −0.560800 + 0.971334i 0.436627 + 0.899643i 0.356173π0.356173\pi
−0.997427 + 0.0716911i 0.977160π0.977160\pi
734734 17.8353 + 30.8917i 0.658314 + 1.14023i
735735 2.36039 + 13.3864i 0.0870642 + 0.493766i
736736 1.61472 + 1.35491i 0.0595195 + 0.0499428i
737737 1.53764 1.29024i 0.0566398 0.0475265i
738738 0.169322 0.960274i 0.00623284 0.0353482i
739739 −18.0322 + 6.56319i −0.663326 + 0.241431i −0.651672 0.758501i 0.725932π-0.725932\pi
−0.0116544 + 0.999932i 0.503710π0.503710\pi
740740 −9.16799 −0.337022
741741 12.4419 1.42479i 0.457066 0.0523411i
742742 −17.5338 −0.643687
743743 9.57223 3.48401i 0.351171 0.127816i −0.160411 0.987050i 0.551282π-0.551282\pi
0.511582 + 0.859235i 0.329060π0.329060\pi
744744 4.41114 25.0168i 0.161720 0.917162i
745745 27.9819 23.4796i 1.02518 0.860227i
746746 4.40256 + 3.69419i 0.161189 + 0.135254i
747747 2.78097 + 15.7717i 0.101750 + 0.577055i
748748 −1.43210 2.48047i −0.0523628 0.0906951i
749749 6.19574 10.7313i 0.226388 0.392115i
750750 10.6841 + 3.88868i 0.390127 + 0.141994i
751751 −2.06244 0.750667i −0.0752595 0.0273922i 0.304116 0.952635i 0.401639π-0.401639\pi
−0.379376 + 0.925243i 0.623861π0.623861\pi
752752 −14.4619 + 25.0487i −0.527369 + 0.913431i
753753 0.189197 + 0.327699i 0.00689472 + 0.0119420i
754754 −2.60368 14.7662i −0.0948204 0.537753i
755755 37.7789 + 31.7003i 1.37492 + 1.15369i
756756 −0.492892 + 0.413585i −0.0179263 + 0.0150420i
757757 −4.18042 + 23.7083i −0.151940 + 0.861694i 0.809590 + 0.586995i 0.199689π0.199689\pi
−0.961530 + 0.274699i 0.911422π0.911422\pi
758758 −18.2991 + 6.66032i −0.664652 + 0.241914i
759759 0.747227 0.0271226
760760 −29.9472 + 14.9525i −1.08630 + 0.542386i
761761 −18.2139 −0.660253 −0.330127 0.943937i 0.607091π-0.607091\pi
−0.330127 + 0.943937i 0.607091π0.607091\pi
762762 1.53003 0.556885i 0.0554271 0.0201738i
763763 0.736906 4.17920i 0.0266778 0.151297i
764764 −5.40019 + 4.53130i −0.195372 + 0.163937i
765765 −10.7272 9.00115i −0.387841 0.325437i
766766 −4.37768 24.8270i −0.158172 0.897037i
767767 −2.04692 3.54536i −0.0739098 0.128016i
768768 5.71229 9.89397i 0.206124 0.357018i
769769 9.95947 + 3.62495i 0.359148 + 0.130719i 0.515291 0.857015i 0.327684π-0.327684\pi
−0.156143 + 0.987734i 0.549906π0.549906\pi
770770 3.60520 + 1.31218i 0.129922 + 0.0472878i
771771 −6.27733 + 10.8727i −0.226072 + 0.391569i
772772 −1.42662 2.47097i −0.0513451 0.0889323i
773773 −0.816172 4.62874i −0.0293556 0.166484i 0.966606 0.256269i 0.0824932π-0.0824932\pi
−0.995961 + 0.0897847i 0.971382π0.971382\pi
774774 −0.814807 0.683704i −0.0292876 0.0245752i
775775 8.12779 6.82003i 0.291959 0.244983i
776776 3.52879 20.0128i 0.126676 0.718416i
777777 8.41942 3.06442i 0.302045 0.109935i
778778 8.66282 0.310577
779779 0.210763 3.47861i 0.00755136 0.124634i
780780 −3.69034 −0.132135
781781 7.23227 2.63233i 0.258791 0.0941922i
782782 0.884292 5.01507i 0.0316222 0.179339i
783783 −3.27802 + 2.75059i −0.117147 + 0.0982979i
784784 11.2695 + 9.45622i 0.402481 + 0.337722i
785785 −0.255989 1.45179i −0.00913665 0.0518165i
786786 8.07016 + 13.9779i 0.287853 + 0.498576i
787787 27.5192 47.6647i 0.980954 1.69906i 0.322259 0.946652i 0.395558π-0.395558\pi
0.658695 0.752410i 0.271109π-0.271109\pi
788788 −2.32617 0.846657i −0.0828664 0.0301609i
789789 −8.47098 3.08319i −0.301575 0.109764i
790790 −5.02991 + 8.71206i −0.178956 + 0.309961i
791791 5.50959 + 9.54289i 0.195898 + 0.339306i
792792 −0.532116 3.01778i −0.0189079 0.107232i
793793 −3.36783 2.82595i −0.119595 0.100352i
794794 −8.08976 + 6.78811i −0.287095 + 0.240901i
795795 −4.98375 + 28.2643i −0.176755 + 1.00243i
796796 11.9402 4.34586i 0.423207 0.154035i
797797 −10.8736 −0.385164 −0.192582 0.981281i 0.561686π-0.561686\pi
−0.192582 + 0.981281i 0.561686π0.561686\pi
798798 4.59086 4.84330i 0.162515 0.171451i
799799 −59.5930 −2.10825
800800 3.39275 1.23486i 0.119952 0.0436589i
801801 1.32646 7.52272i 0.0468681 0.265802i
802802 −1.73867 + 1.45892i −0.0613945 + 0.0515161i
803803 −7.36283 6.17815i −0.259829 0.218022i
804804 0.178658 + 1.01322i 0.00630077 + 0.0357335i
805805 −1.17529 2.03567i −0.0414237 0.0717479i
806806 −14.5236 + 25.1556i −0.511572 + 0.886068i
807807 −26.1961 9.53461i −0.922147 0.335634i
808808 32.9976 + 12.0102i 1.16085 + 0.422516i
809809 −6.56793 + 11.3760i −0.230916 + 0.399959i −0.958078 0.286507i 0.907506π-0.907506\pi
0.727162 + 0.686466i 0.240839π0.240839\pi
810810 −1.52815 2.64683i −0.0536936 0.0930000i
811811 2.47373 + 14.0292i 0.0868646 + 0.492633i 0.996939 + 0.0781878i 0.0249134π0.0249134\pi
−0.910074 + 0.414446i 0.863976π0.863976\pi
812812 2.10916 + 1.76979i 0.0740170 + 0.0621076i
813813 21.2191 17.8049i 0.744185 0.624445i
814814 −1.51160 + 8.57272i −0.0529816 + 0.300474i
815815 −41.7023 + 15.1784i −1.46077 + 0.531675i
816816 −15.1554 −0.530545
817817 −3.17124 2.09639i −0.110948 0.0733435i
818818 −8.54083 −0.298623
819819 3.38902 1.23350i 0.118422 0.0431021i
820820 −0.178329 + 1.01135i −0.00622750 + 0.0353179i
821821 −16.5809 + 13.9131i −0.578679 + 0.485569i −0.884513 0.466516i 0.845509π-0.845509\pi
0.305834 + 0.952085i 0.401065π0.401065\pi
822822 9.08091 + 7.61979i 0.316733 + 0.265771i
823823 −4.22828 23.9798i −0.147389 0.835882i −0.965418 0.260706i 0.916045π-0.916045\pi
0.818030 0.575176i 0.195066π-0.195066\pi
824824 −7.66858 13.2824i −0.267148 0.462714i
825825 0.639947 1.10842i 0.0222801 0.0385903i
826826 −2.04994 0.746119i −0.0713267 0.0259608i
827827 −35.2325 12.8236i −1.22516 0.445920i −0.353220 0.935540i 0.614913π-0.614913\pi
−0.871936 + 0.489620i 0.837135π0.837135\pi
828828 −0.191501 + 0.331690i −0.00665514 + 0.0115270i
829829 5.48387 + 9.49834i 0.190463 + 0.329891i 0.945404 0.325902i 0.105668π-0.105668\pi
−0.754941 + 0.655793i 0.772335π0.772335\pi
830830 8.49946 + 48.2028i 0.295021 + 1.67315i
831831 11.8826 + 9.97067i 0.412202 + 0.345879i
832832 −19.5101 + 16.3709i −0.676390 + 0.567559i
833833 −5.26334 + 29.8499i −0.182364 + 1.03424i
834834 −23.9744 + 8.72596i −0.830164 + 0.302155i
835835 4.10390 0.142021
836836 −0.635779 2.14185i −0.0219889 0.0740775i
837837 8.28981 0.286538
838838 40.0775 14.5870i 1.38446 0.503901i
839839 −2.39319 + 13.5725i −0.0826221 + 0.468573i 0.915222 + 0.402949i 0.132015π0.132015\pi
−0.997844 + 0.0656239i 0.979096π0.979096\pi
840840 −7.38439 + 6.19624i −0.254786 + 0.213791i
841841 −8.18815 6.87067i −0.282350 0.236920i
842842 2.35251 + 13.3417i 0.0810728 + 0.459787i
843843 7.59164 + 13.1491i 0.261470 + 0.452879i
844844 −4.76868 + 8.25960i −0.164145 + 0.284307i
845845 −11.1753 4.06749i −0.384443 0.139926i
846846 −12.2221 4.44848i −0.420204 0.152942i
847847 −0.627651 + 1.08712i −0.0215663 + 0.0373540i
848848 15.5308 + 26.9001i 0.533328 + 0.923752i
849849 1.27747 + 7.24488i 0.0438426 + 0.248643i
850850 −6.68192 5.60679i −0.229188 0.192311i
851851 4.08559 3.42822i 0.140052 0.117518i
852852 −0.685028 + 3.88499i −0.0234687 + 0.133098i
853853 30.7242 11.1827i 1.05198 0.382888i 0.242568 0.970134i 0.422010π-0.422010\pi
0.809408 + 0.587246i 0.199788π0.199788\pi
854854 −2.34273 −0.0801667
855855 −6.50244 8.77703i −0.222379 0.300168i
856856 −30.2490 −1.03389
857857 8.59406 3.12798i 0.293568 0.106850i −0.191038 0.981583i 0.561185π-0.561185\pi
0.484606 + 0.874733i 0.338963π0.338963\pi
858858 −0.608457 + 3.45073i −0.0207724 + 0.117806i
859859 4.38782 3.68182i 0.149711 0.125622i −0.564856 0.825189i 0.691068π-0.691068\pi
0.714567 + 0.699567i 0.246624π0.246624\pi
860860 0.858147 + 0.720071i 0.0292626 + 0.0245542i
861861 −0.174278 0.988381i −0.00593938 0.0336839i
862862 −22.7337 39.3759i −0.774312 1.34115i
863863 3.84115 6.65306i 0.130754 0.226473i −0.793213 0.608944i 0.791593π-0.791593\pi
0.923968 + 0.382471i 0.124927π0.124927\pi
864864 2.65081 + 0.964814i 0.0901822 + 0.0328237i
865865 6.92018 + 2.51874i 0.235293 + 0.0856397i
866866 10.5053 18.1956i 0.356983 0.618313i
867867 −7.11272 12.3196i −0.241561 0.418395i
868868 −0.926217 5.25284i −0.0314378 0.178293i
869869 −2.52144 2.11574i −0.0855341 0.0717716i
870870 −10.0186 + 8.40660i −0.339662 + 0.285010i
871871 1.00141 5.67929i 0.0339315 0.192435i
872872 −9.73456 + 3.54309i −0.329654 + 0.119984i
873873 6.63161 0.224446
874874 1.58189 3.64379i 0.0535082 0.123253i
875875 11.7025 0.395618
876876 4.62942 1.68497i 0.156414 0.0569299i
877877 4.54125 25.7547i 0.153347 0.869674i −0.806935 0.590641i 0.798875π-0.798875\pi
0.960281 0.279033i 0.0900139π-0.0900139\pi
878878 12.3842 10.3916i 0.417947 0.350699i
879879 13.7380 + 11.5276i 0.463372 + 0.388815i
880880 −1.18021 6.69330i −0.0397849 0.225631i
881881 −3.26808 5.66049i −0.110105 0.190707i 0.805708 0.592313i 0.201785π-0.201785\pi
−0.915812 + 0.401607i 0.868452π0.868452\pi
882882 −3.30770 + 5.72910i −0.111376 + 0.192909i
883883 14.7451 + 5.36678i 0.496213 + 0.180607i 0.577990 0.816044i 0.303837π-0.303837\pi
−0.0817772 + 0.996651i 0.526060π0.526060\pi
884884 −7.73269 2.81447i −0.260078 0.0946608i
885885 −1.78540 + 3.09240i −0.0600155 + 0.103950i
886886 −3.78516 6.55609i −0.127165 0.220256i
887887 4.71281 + 26.7277i 0.158241 + 0.897428i 0.955763 + 0.294138i 0.0950326π0.0950326\pi
−0.797522 + 0.603290i 0.793856π0.793856\pi
888888 −16.7548 14.0589i −0.562254 0.471787i
889889 1.28380 1.07724i 0.0430572 0.0361293i
890890 4.05404 22.9916i 0.135892 0.770681i
891891 0.939693 0.342020i 0.0314809 0.0114581i
892892 13.5898 0.455019
893893 −45.2073 10.8260i −1.51281 0.362277i
894894 17.7773 0.594563
895895 −19.9779 + 7.27135i −0.667787 + 0.243055i
896896 −1.12687 + 6.39079i −0.0376460 + 0.213501i
897897 1.64455 1.37994i 0.0549099 0.0460749i
898898 −27.1148 22.7520i −0.904833 0.759245i
899899 −6.15988 34.9344i −0.205444 1.16513i
900900 0.328015 + 0.568139i 0.0109338 + 0.0189380i
901901 −31.9988 + 55.4236i −1.06604 + 1.84643i
902902 0.916283 + 0.333500i 0.0305089 + 0.0111043i
903903 −1.02876 0.374440i −0.0342351 0.0124606i
904904 13.4495 23.2953i 0.447325 0.774790i
905905 −21.6901 37.5684i −0.721004 1.24882i
906906 4.16781 + 23.6368i 0.138466 + 0.785282i
907907 −32.2853 27.0906i −1.07201 0.899527i −0.0767813 0.997048i 0.524464π-0.524464\pi
−0.995233 + 0.0975208i 0.968909π0.968909\pi
908908 −4.60029 + 3.86011i −0.152666 + 0.128102i
909909 −1.98990 + 11.2853i −0.0660008 + 0.374309i
910910 10.3578 3.76995i 0.343359 0.124973i
911911 −16.2810 −0.539413 −0.269707 0.962943i 0.586927π-0.586927\pi
−0.269707 + 0.962943i 0.586927π0.586927\pi
912912 −11.4969 2.75320i −0.380700 0.0911677i
913913 −16.0150 −0.530018
914914 −3.78363 + 1.37713i −0.125151 + 0.0455513i
915915 −0.665890 + 3.77645i −0.0220136 + 0.124846i
916916 −4.42020 + 3.70899i −0.146048 + 0.122548i
917917 12.7261 + 10.6785i 0.420253 + 0.352634i
918918 −1.18343 6.71158i −0.0390591 0.221515i
919919 −18.7809 32.5294i −0.619524 1.07305i −0.989573 0.144034i 0.953992π-0.953992\pi
0.370049 0.929012i 0.379341π-0.379341\pi
920920 −2.86903 + 4.96930i −0.0945891 + 0.163833i
921921 1.53836 + 0.559918i 0.0506907 + 0.0184499i
922922 47.5492 + 17.3065i 1.56595 + 0.569959i
923923 11.0560 19.1496i 0.363914 0.630317i
924924 −0.321712 0.557222i −0.0105836 0.0183313i
925925 −1.58633 8.99651i −0.0521581 0.295803i
926926 −24.4114 20.4836i −0.802208 0.673132i
927927 3.83409 3.21719i 0.125928 0.105666i
928928 2.09614 11.8878i 0.0688091 0.390236i
929929 −15.5780 + 5.66993i −0.511098 + 0.186024i −0.584679 0.811265i 0.698779π-0.698779\pi
0.0735812 + 0.997289i 0.476557π0.476557\pi
930930 25.3361 0.830803
931931 −9.41546 + 21.6880i −0.308579 + 0.710796i
932932 0.144438 0.00473124
933933 −26.4917 + 9.64219i −0.867299 + 0.315671i
934934 2.64540 15.0028i 0.0865601 0.490907i
935935 10.7272 9.00115i 0.350815 0.294369i
936936 −6.74421 5.65906i −0.220441 0.184972i
937937 3.81937 + 21.6607i 0.124773 + 0.707624i 0.981442 + 0.191758i 0.0614189π0.0614189\pi
−0.856669 + 0.515867i 0.827470π0.827470\pi
938938 −1.53652 2.66133i −0.0501692 0.0868956i
939939 −4.43516 + 7.68192i −0.144736 + 0.250690i
940940 12.8722 + 4.68510i 0.419845 + 0.152811i
941941 1.18598 + 0.431660i 0.0386618 + 0.0140717i 0.361279 0.932458i 0.382340π-0.382340\pi
−0.322617 + 0.946530i 0.604563π0.604563\pi
942942 0.358727 0.621334i 0.0116880 0.0202442i
943943 −0.298708 0.517378i −0.00972728 0.0168481i
944944 0.671077 + 3.80587i 0.0218417 + 0.123870i
945945 −2.40978 2.02205i −0.0783903 0.0657773i
946946 0.814807 0.683704i 0.0264917 0.0222291i
947947 6.24771 35.4325i 0.203023 1.15140i −0.697496 0.716588i 0.745703π-0.745703\pi
0.900520 0.434815i 0.143186π-0.143186\pi
948948 1.58537 0.577028i 0.0514904 0.0187410i
949949 −27.6142 −0.896393
950950 −4.05035 5.46719i −0.131411 0.177379i
951951 21.6145 0.700899
952952 −20.1988 + 7.35174i −0.654645 + 0.238271i
953953 −1.85596 + 10.5256i −0.0601203 + 0.340959i −1.00000 0.000546995i 0.999826π-0.999826\pi
0.939880 + 0.341506i 0.110937π0.110937\pi
954954 −10.7000 + 8.97834i −0.346424 + 0.290685i
955955 −26.4019 22.1538i −0.854346 0.716882i
956956 −2.08399 11.8189i −0.0674011 0.382251i
957957 −2.13958 3.70585i −0.0691627 0.119793i
958958 10.8317 18.7611i 0.349958 0.606145i
959959 11.4654 + 4.17307i 0.370238 + 0.134756i
960960 20.8750 + 7.59787i 0.673737 + 0.245220i
961961 −18.8605 + 32.6673i −0.608403 + 1.05378i
962962 12.5048 + 21.6590i 0.403172 + 0.698315i
963963 −1.71414 9.72135i −0.0552373 0.313266i
964964 −3.26617 2.74064i −0.105196 0.0882702i
965965 10.6861 8.96667i 0.343997 0.288647i
966966 0.198650 1.12660i 0.00639147 0.0362479i
967967 −15.3965 + 5.60386i −0.495117 + 0.180208i −0.577497 0.816393i 0.695970π-0.695970\pi
0.0823794 + 0.996601i 0.473748π0.473748\pi
968968 3.06434 0.0984915
969969 −6.93124 23.3504i −0.222664 0.750123i
970970 20.2681 0.650771
971971 14.4139 5.24622i 0.462563 0.168359i −0.100218 0.994966i 0.531954π-0.531954\pi
0.562780 + 0.826606i 0.309732π0.309732\pi
972972 −0.0890061 + 0.504779i −0.00285487 + 0.0161908i
973973 −20.1161 + 16.8794i −0.644894 + 0.541130i
974974 −10.9561 9.19322i −0.351055 0.294570i
975975 −0.638535 3.62131i −0.0204495 0.115975i
976976 2.07510 + 3.59418i 0.0664223 + 0.115047i
977977 −11.1597 + 19.3292i −0.357031 + 0.618396i −0.987463 0.157848i 0.949544π-0.949544\pi
0.630432 + 0.776244i 0.282878π0.282878\pi
978978 −20.2956 7.38700i −0.648982 0.236210i
979979 7.17809 + 2.61261i 0.229413 + 0.0834994i
980980 3.48364 6.03384i 0.111281 0.192744i
981981 −1.69030 2.92769i −0.0539672 0.0934738i
982982 −4.96585 28.1627i −0.158467 0.898709i
983983 16.2167 + 13.6075i 0.517234 + 0.434011i 0.863666 0.504064i 0.168163π-0.168163\pi
−0.346432 + 0.938075i 0.612607π0.612607\pi
984984 −1.87679 + 1.57481i −0.0598298 + 0.0502032i
985985 2.10161 11.9188i 0.0669629 0.379766i
986986 −27.4042 + 9.97430i −0.872726 + 0.317646i
987987 −13.3872 −0.426119
988988 −5.35474 3.53982i −0.170357 0.112617i
989989 −0.651680 −0.0207222
990990 2.87198 1.04531i 0.0912774 0.0332223i
991991 8.41611 47.7301i 0.267347 1.51620i −0.494922 0.868937i 0.664803π-0.664803\pi
0.762269 0.647261i 0.224086π-0.224086\pi
992992 −17.9139 + 15.0316i −0.568768 + 0.477253i
993993 −20.4037 17.1207i −0.647491 0.543310i
994994 −2.04610 11.6040i −0.0648982 0.368056i
995995 31.0614 + 53.7999i 0.984711 + 1.70557i
996996 4.10436 7.10897i 0.130052 0.225256i
997997 −45.2094 16.4549i −1.43180 0.521131i −0.494351 0.869262i 0.664594π-0.664594\pi
−0.937446 + 0.348131i 0.886816π0.886816\pi
998998 11.5586 + 4.20700i 0.365882 + 0.133170i
999999 3.56877 6.18129i 0.112911 0.195567i
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 627.2.r.c.100.6 54
19.4 even 9 inner 627.2.r.c.232.6 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
627.2.r.c.100.6 54 1.1 even 1 trivial
627.2.r.c.232.6 yes 54 19.4 even 9 inner