Properties

Label 416.2.bf.a.53.7
Level 416416
Weight 22
Character 416.53
Analytic conductor 3.3223.322
Analytic rank 00
Dimension 192192
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(53,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 416=2513 416 = 2^{5} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 416.bf (of order 88, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.321776724093.32177672409
Analytic rank: 00
Dimension: 192192
Relative dimension: 4848 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 53.7
Character χ\chi == 416.53
Dual form 416.2.bf.a.157.7

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.282830.595266i)q2+(1.29613+0.536874i)q3+(1.29132+1.52725i)q4+(0.0161519+0.0389942i)q5+(1.98230+0.0828216i)q6+(1.325351.32535i)q7+(0.7474232.72789i)q8+(0.729605+0.729605i)q9+(0.04393210.0404083i)q10+(1.89557+0.785171i)q11+(2.493661.28624i)q12+(0.3826830.923880i)q13+(0.911266+2.48914i)q140.0592130iq15+(0.664999+3.94433i)q16+1.34055iq17+(1.370270.501652i)q18+(2.703606.52708i)q19+(0.0804113+0.0256858i)q20+(2.42937+1.00628i)q21+(1.964312.13561i)q22+(5.882885.88288i)q23+(2.43329+3.13442i)q24+(3.53427+3.53427i)q25+(0.0590352+1.41298i)q26+(2.164585.22575i)q27+(0.3126963.73559i)q28+(4.579601.89693i)q29+(0.0352475+0.0759604i)q3010.5676q31+(3.201014.66407i)q322.87844q33+(0.7979841.71970i)q34+(0.07308790.0302740i)q35+(2.056440.172139i)q36+(3.957879.55514i)q37+(0.417075+9.98251i)q38+(0.992014+0.992014i)q39+(0.118444+0.0149155i)q40+(0.8324560.832456i)q41+(2.517472.73701i)q42+(5.453702.25900i)q43+(1.24863+3.90892i)q44+(0.01666580.0402349i)q45+(11.0486+4.04487i)q469.83174iq47+(1.255695.46938i)q483.48690iq49+(2.430056.63771i)q50+(0.7197061.73753i)q51+(0.9168311.77748i)q52+(1.231670.510176i)q53+(5.88750+5.41527i)q54+(0.0612342+0.0612342i)q55+(2.62481+4.60600i)q56+(7.00844+7.00844i)q57+(7.004040.292633i)q58+(1.137362.74583i)q59+(0.09043330.0764628i)q60+(1.89068+0.783145i)q61+(13.5564+6.29052i)q62+1.93396q63+(6.88272+4.07777i)q64+0.0422070q65+(3.69256+1.71344i)q66+(6.959162.88258i)q67+(2.04736+1.73108i)q68+(4.46660+10.7833i)q69+(0.1117810.00467026i)q70+(11.2976+11.2976i)q71+(2.53560+1.44496i)q72+(8.14583+8.14583i)q73+(10.7651+9.90165i)q74+(6.478332.68341i)q75+(6.4772812.5576i)q76+(1.471673.55292i)q77+(0.6820751.86310i)q78+8.18759iq79+(0.1430650.0896397i)q80+4.83990iq81+(1.56343+0.572369i)q82+(2.920687.05114i)q83+(1.60025+5.00968i)q84+(0.05227370.0216525i)q85+(5.65148+6.14432i)q86+(4.91734+4.91734i)q87+(0.7250645.75775i)q88+(8.00087+8.00087i)q89+(0.00257098+0.0615353i)q90+(0.717274+1.73165i)q91+(16.5813+1.38798i)q92+(13.69695.67346i)q93+(5.85250+12.6125i)q94+0.298187q95+(1.64490+7.76377i)q96+7.38415q97+(2.07563+4.47310i)q98+(1.95588+0.810153i)q99+O(q100)q+(-1.28283 - 0.595266i) q^{2} +(-1.29613 + 0.536874i) q^{3} +(1.29132 + 1.52725i) q^{4} +(-0.0161519 + 0.0389942i) q^{5} +(1.98230 + 0.0828216i) q^{6} +(-1.32535 - 1.32535i) q^{7} +(-0.747423 - 2.72789i) q^{8} +(-0.729605 + 0.729605i) q^{9} +(0.0439321 - 0.0404083i) q^{10} +(1.89557 + 0.785171i) q^{11} +(-2.49366 - 1.28624i) q^{12} +(-0.382683 - 0.923880i) q^{13} +(0.911266 + 2.48914i) q^{14} -0.0592130i q^{15} +(-0.664999 + 3.94433i) q^{16} +1.34055i q^{17} +(1.37027 - 0.501652i) q^{18} +(-2.70360 - 6.52708i) q^{19} +(-0.0804113 + 0.0256858i) q^{20} +(2.42937 + 1.00628i) q^{21} +(-1.96431 - 2.13561i) q^{22} +(5.88288 - 5.88288i) q^{23} +(2.43329 + 3.13442i) q^{24} +(3.53427 + 3.53427i) q^{25} +(-0.0590352 + 1.41298i) q^{26} +(2.16458 - 5.22575i) q^{27} +(0.312696 - 3.73559i) q^{28} +(4.57960 - 1.89693i) q^{29} +(-0.0352475 + 0.0759604i) q^{30} -10.5676 q^{31} +(3.20101 - 4.66407i) q^{32} -2.87844 q^{33} +(0.797984 - 1.71970i) q^{34} +(0.0730879 - 0.0302740i) q^{35} +(-2.05644 - 0.172139i) q^{36} +(3.95787 - 9.55514i) q^{37} +(-0.417075 + 9.98251i) q^{38} +(0.992014 + 0.992014i) q^{39} +(0.118444 + 0.0149155i) q^{40} +(0.832456 - 0.832456i) q^{41} +(-2.51747 - 2.73701i) q^{42} +(-5.45370 - 2.25900i) q^{43} +(1.24863 + 3.90892i) q^{44} +(-0.0166658 - 0.0402349i) q^{45} +(-11.0486 + 4.04487i) q^{46} -9.83174i q^{47} +(-1.25569 - 5.46938i) q^{48} -3.48690i q^{49} +(-2.43005 - 6.63771i) q^{50} +(-0.719706 - 1.73753i) q^{51} +(0.916831 - 1.77748i) q^{52} +(-1.23167 - 0.510176i) q^{53} +(-5.88750 + 5.41527i) q^{54} +(-0.0612342 + 0.0612342i) q^{55} +(-2.62481 + 4.60600i) q^{56} +(7.00844 + 7.00844i) q^{57} +(-7.00404 - 0.292633i) q^{58} +(1.13736 - 2.74583i) q^{59} +(0.0904333 - 0.0764628i) q^{60} +(-1.89068 + 0.783145i) q^{61} +(13.5564 + 6.29052i) q^{62} +1.93396 q^{63} +(-6.88272 + 4.07777i) q^{64} +0.0422070 q^{65} +(3.69256 + 1.71344i) q^{66} +(6.95916 - 2.88258i) q^{67} +(-2.04736 + 1.73108i) q^{68} +(-4.46660 + 10.7833i) q^{69} +(-0.111781 - 0.00467026i) q^{70} +(11.2976 + 11.2976i) q^{71} +(2.53560 + 1.44496i) q^{72} +(-8.14583 + 8.14583i) q^{73} +(-10.7651 + 9.90165i) q^{74} +(-6.47833 - 2.68341i) q^{75} +(6.47728 - 12.5576i) q^{76} +(-1.47167 - 3.55292i) q^{77} +(-0.682075 - 1.86310i) q^{78} +8.18759i q^{79} +(-0.143065 - 0.0896397i) q^{80} +4.83990i q^{81} +(-1.56343 + 0.572369i) q^{82} +(-2.92068 - 7.05114i) q^{83} +(1.60025 + 5.00968i) q^{84} +(-0.0522737 - 0.0216525i) q^{85} +(5.65148 + 6.14432i) q^{86} +(-4.91734 + 4.91734i) q^{87} +(0.725064 - 5.75775i) q^{88} +(8.00087 + 8.00087i) q^{89} +(-0.00257098 + 0.0615353i) q^{90} +(-0.717274 + 1.73165i) q^{91} +(16.5813 + 1.38798i) q^{92} +(13.6969 - 5.67346i) q^{93} +(-5.85250 + 12.6125i) q^{94} +0.298187 q^{95} +(-1.64490 + 7.76377i) q^{96} +7.38415 q^{97} +(-2.07563 + 4.47310i) q^{98} +(-1.95588 + 0.810153i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 192q16q1016q1240q1640q188q2216q23+24q24+80q3048q3148q35+80q3656q3864q4016q4380q44+24q50+32q51++56q98+O(q100) 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/416Z)×\left(\mathbb{Z}/416\mathbb{Z}\right)^\times.

nn 261261 287287 353353
χ(n)\chi(n) e(58)e\left(\frac{5}{8}\right) 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.28283 0.595266i −0.907099 0.420916i
33 −1.29613 + 0.536874i −0.748320 + 0.309964i −0.724056 0.689741i 0.757724π-0.757724\pi
−0.0242641 + 0.999706i 0.507724π0.507724\pi
44 1.29132 + 1.52725i 0.645659 + 0.763626i
55 −0.0161519 + 0.0389942i −0.00722336 + 0.0174387i −0.927450 0.373947i 0.878004π-0.878004\pi
0.920227 + 0.391386i 0.128004π0.128004\pi
66 1.98230 + 0.0828216i 0.809270 + 0.0338118i
77 −1.32535 1.32535i −0.500935 0.500935i 0.410793 0.911728i 0.365252π-0.365252\pi
−0.911728 + 0.410793i 0.865252π0.865252\pi
88 −0.747423 2.72789i −0.264254 0.964453i
99 −0.729605 + 0.729605i −0.243202 + 0.243202i
1010 0.0439321 0.0404083i 0.0138926 0.0127782i
1111 1.89557 + 0.785171i 0.571536 + 0.236738i 0.649685 0.760204i 0.274901π-0.274901\pi
−0.0781487 + 0.996942i 0.524901π0.524901\pi
1212 −2.49366 1.28624i −0.719856 0.371306i
1313 −0.382683 0.923880i −0.106137 0.256238i
1414 0.911266 + 2.48914i 0.243546 + 0.665250i
1515 0.0592130i 0.0152887i
1616 −0.664999 + 3.94433i −0.166250 + 0.986084i
1717 1.34055i 0.325131i 0.986698 + 0.162566i 0.0519769π0.0519769\pi
−0.986698 + 0.162566i 0.948023π0.948023\pi
1818 1.37027 0.501652i 0.322976 0.118241i
1919 −2.70360 6.52708i −0.620249 1.49741i −0.851411 0.524499i 0.824253π-0.824253\pi
0.231162 0.972915i 0.425747π-0.425747\pi
2020 −0.0804113 + 0.0256858i −0.0179805 + 0.00574353i
2121 2.42937 + 1.00628i 0.530132 + 0.219588i
2222 −1.96431 2.13561i −0.418793 0.455314i
2323 5.88288 5.88288i 1.22666 1.22666i 0.261446 0.965218i 0.415801π-0.415801\pi
0.965218 0.261446i 0.0841995π-0.0841995\pi
2424 2.43329 + 3.13442i 0.496693 + 0.639810i
2525 3.53427 + 3.53427i 0.706855 + 0.706855i
2626 −0.0590352 + 1.41298i −0.0115777 + 0.277108i
2727 2.16458 5.22575i 0.416573 1.00570i
2828 0.312696 3.73559i 0.0590940 0.705960i
2929 4.57960 1.89693i 0.850411 0.352252i 0.0854609 0.996342i 0.472764π-0.472764\pi
0.764950 + 0.644090i 0.222764π0.222764\pi
3030 −0.0352475 + 0.0759604i −0.00643528 + 0.0138684i
3131 −10.5676 −1.89799 −0.948996 0.315287i 0.897899π-0.897899\pi
−0.948996 + 0.315287i 0.897899π0.897899\pi
3232 3.20101 4.66407i 0.565864 0.824499i
3333 −2.87844 −0.501072
3434 0.797984 1.71970i 0.136853 0.294926i
3535 0.0730879 0.0302740i 0.0123541 0.00511724i
3636 −2.05644 0.172139i −0.342741 0.0286899i
3737 3.95787 9.55514i 0.650669 1.57085i −0.161140 0.986932i 0.551517π-0.551517\pi
0.811809 0.583923i 0.198483π-0.198483\pi
3838 −0.417075 + 9.98251i −0.0676585 + 1.61938i
3939 0.992014 + 0.992014i 0.158849 + 0.158849i
4040 0.118444 + 0.0149155i 0.0187276 + 0.00235834i
4141 0.832456 0.832456i 0.130008 0.130008i −0.639109 0.769116i 0.720697π-0.720697\pi
0.769116 + 0.639109i 0.220697π0.220697\pi
4242 −2.51747 2.73701i −0.388454 0.422329i
4343 −5.45370 2.25900i −0.831682 0.344494i −0.0741135 0.997250i 0.523613π-0.523613\pi
−0.757568 + 0.652756i 0.773613π0.773613\pi
4444 1.24863 + 3.90892i 0.188238 + 0.589292i
4545 −0.0166658 0.0402349i −0.00248440 0.00599787i
4646 −11.0486 + 4.04487i −1.62903 + 0.596383i
4747 9.83174i 1.43411i −0.697018 0.717053i 0.745490π-0.745490\pi
0.697018 0.717053i 0.254510π-0.254510\pi
4848 −1.25569 5.46938i −0.181243 0.789438i
4949 3.48690i 0.498128i
5050 −2.43005 6.63771i −0.343661 0.938714i
5151 −0.719706 1.73753i −0.100779 0.243302i
5252 0.916831 1.77748i 0.127142 0.246492i
5353 −1.23167 0.510176i −0.169183 0.0700780i 0.296484 0.955038i 0.404186π-0.404186\pi
−0.465668 + 0.884960i 0.654186π0.654186\pi
5454 −5.88750 + 5.41527i −0.801188 + 0.736924i
5555 −0.0612342 + 0.0612342i −0.00825682 + 0.00825682i
5656 −2.62481 + 4.60600i −0.350754 + 0.615503i
5757 7.00844 + 7.00844i 0.928290 + 0.928290i
5858 −7.00404 0.292633i −0.919676 0.0384246i
5959 1.13736 2.74583i 0.148072 0.357477i −0.832389 0.554192i 0.813027π-0.813027\pi
0.980461 + 0.196715i 0.0630273π0.0630273\pi
6060 0.0904333 0.0764628i 0.0116749 0.00987131i
6161 −1.89068 + 0.783145i −0.242077 + 0.100272i −0.500423 0.865781i 0.666822π-0.666822\pi
0.258347 + 0.966052i 0.416822π0.416822\pi
6262 13.5564 + 6.29052i 1.72167 + 0.798896i
6363 1.93396 0.243657
6464 −6.88272 + 4.07777i −0.860340 + 0.509721i
6565 0.0422070 0.00523514
6666 3.69256 + 1.71344i 0.454522 + 0.210910i
6767 6.95916 2.88258i 0.850196 0.352163i 0.0853308 0.996353i 0.472805π-0.472805\pi
0.764866 + 0.644190i 0.222805π0.222805\pi
6868 −2.04736 + 1.73108i −0.248279 + 0.209924i
6969 −4.46660 + 10.7833i −0.537715 + 1.29816i
7070 −0.111781 0.00467026i −0.0133603 0.000558203i
7171 11.2976 + 11.2976i 1.34078 + 1.34078i 0.895283 + 0.445498i 0.146973π0.146973\pi
0.445498 + 0.895283i 0.353027π0.353027\pi
7272 2.53560 + 1.44496i 0.298824 + 0.170290i
7373 −8.14583 + 8.14583i −0.953398 + 0.953398i −0.998961 0.0455638i 0.985492π-0.985492\pi
0.0455638 + 0.998961i 0.485492π0.485492\pi
7474 −10.7651 + 9.90165i −1.25142 + 1.15104i
7575 −6.47833 2.68341i −0.748053 0.309854i
7676 6.47728 12.5576i 0.742995 1.44046i
7777 −1.47167 3.55292i −0.167712 0.404893i
7878 −0.682075 1.86310i −0.0772298 0.210954i
7979 8.18759i 0.921176i 0.887614 + 0.460588i 0.152361π0.152361\pi
−0.887614 + 0.460588i 0.847639π0.847639\pi
8080 −0.143065 0.0896397i −0.0159952 0.0100220i
8181 4.83990i 0.537767i
8282 −1.56343 + 0.572369i −0.172652 + 0.0632076i
8383 −2.92068 7.05114i −0.320586 0.773963i −0.999220 0.0394868i 0.987428π-0.987428\pi
0.678634 0.734477i 0.262572π-0.262572\pi
8484 1.60025 + 5.00968i 0.174601 + 0.546601i
8585 −0.0522737 0.0216525i −0.00566988 0.00234854i
8686 5.65148 + 6.14432i 0.609415 + 0.662559i
8787 −4.91734 + 4.91734i −0.527194 + 0.527194i
8888 0.725064 5.75775i 0.0772921 0.613779i
8989 8.00087 + 8.00087i 0.848090 + 0.848090i 0.989895 0.141804i 0.0452904π-0.0452904\pi
−0.141804 + 0.989895i 0.545290π0.545290\pi
9090 −0.00257098 + 0.0615353i −0.000271005 + 0.00648639i
9191 −0.717274 + 1.73165i −0.0751908 + 0.181527i
9292 16.5813 + 1.38798i 1.72872 + 0.144706i
9393 13.6969 5.67346i 1.42031 0.588310i
9494 −5.85250 + 12.6125i −0.603639 + 1.30088i
9595 0.298187 0.0305933
9696 −1.64490 + 7.76377i −0.167882 + 0.792387i
9797 7.38415 0.749747 0.374873 0.927076i 0.377686π-0.377686\pi
0.374873 + 0.927076i 0.377686π0.377686\pi
9898 −2.07563 + 4.47310i −0.209670 + 0.451852i
9999 −1.95588 + 0.810153i −0.196574 + 0.0814235i
100100 −0.833858 + 9.96160i −0.0833858 + 0.996160i
101101 0.580319 1.40101i 0.0577439 0.139406i −0.892374 0.451296i 0.850962π-0.850962\pi
0.950118 + 0.311890i 0.100962π0.100962\pi
102102 −0.111026 + 2.65737i −0.0109933 + 0.263119i
103103 2.65966 + 2.65966i 0.262064 + 0.262064i 0.825892 0.563828i 0.190672π-0.190672\pi
−0.563828 + 0.825892i 0.690672π0.690672\pi
104104 −2.23421 + 1.73445i −0.219082 + 0.170076i
105105 −0.0784780 + 0.0784780i −0.00765867 + 0.00765867i
106106 1.27634 + 1.38764i 0.123969 + 0.134780i
107107 −1.97123 0.816508i −0.190566 0.0789348i 0.285360 0.958420i 0.407887π-0.407887\pi
−0.475926 + 0.879486i 0.657887π0.657887\pi
108108 10.7762 3.44225i 1.03694 0.331231i
109109 −5.04573 12.1815i −0.483293 1.16677i −0.958036 0.286648i 0.907459π-0.907459\pi
0.474743 0.880125i 0.342541π-0.342541\pi
110110 0.115004 0.0421026i 0.0109652 0.00401433i
111111 14.5096i 1.37719i
112112 6.10898 4.34627i 0.577244 0.410684i
113113 1.72305i 0.162091i 0.996710 + 0.0810453i 0.0258259π0.0258259\pi
−0.996710 + 0.0810453i 0.974174π0.974174\pi
114114 −4.81877 13.1625i −0.451319 1.23278i
115115 0.134378 + 0.324418i 0.0125308 + 0.0302521i
116116 8.81082 + 4.54466i 0.818064 + 0.421962i
117117 0.953275 + 0.394860i 0.0881303 + 0.0365048i
118118 −3.09355 + 2.84541i −0.284784 + 0.261941i
119119 1.77670 1.77670i 0.162870 0.162870i
120120 −0.161526 + 0.0442572i −0.0147453 + 0.00404011i
121121 −4.80148 4.80148i −0.436498 0.436498i
122122 2.89161 + 0.120813i 0.261794 + 0.0109379i
123123 −0.632046 + 1.52589i −0.0569897 + 0.137585i
124124 −13.6461 16.1394i −1.22546 1.44936i
125125 −0.389873 + 0.161491i −0.0348713 + 0.0144442i
126126 −2.48095 1.15122i −0.221021 0.102559i
127127 −9.54264 −0.846772 −0.423386 0.905949i 0.639159π-0.639159\pi
−0.423386 + 0.905949i 0.639159π0.639159\pi
128128 11.2567 1.13405i 0.994964 0.100236i
129129 8.28149 0.729145
130130 −0.0541445 0.0251244i −0.00474879 0.00220356i
131131 −20.0972 + 8.32454i −1.75590 + 0.727319i −0.758794 + 0.651331i 0.774211π0.774211\pi
−0.997109 + 0.0759882i 0.975789π0.975789\pi
132132 −3.71698 4.39610i −0.323522 0.382632i
133133 −5.06744 + 12.2339i −0.439403 + 1.06081i
134134 −10.6433 0.444685i −0.919444 0.0384149i
135135 0.168812 + 0.168812i 0.0145290 + 0.0145290i
136136 3.65687 1.00196i 0.313574 0.0859172i
137137 −11.9526 + 11.9526i −1.02118 + 1.02118i −0.0214118 + 0.999771i 0.506816π0.506816\pi
−0.999771 + 0.0214118i 0.993184π0.993184\pi
138138 12.1488 11.1744i 1.03418 0.951227i
139139 −6.36772 2.63760i −0.540103 0.223718i 0.0959185 0.995389i 0.469421π-0.469421\pi
−0.636022 + 0.771671i 0.719421π0.719421\pi
140140 0.140616 + 0.0725303i 0.0118842 + 0.00612993i
141141 5.27841 + 12.7432i 0.444522 + 1.07317i
142142 −7.76787 21.2180i −0.651865 1.78058i
143143 2.05175i 0.171576i
144144 −2.39262 3.36299i −0.199385 0.280249i
145145 0.209217i 0.0173745i
146146 15.2987 5.60080i 1.26613 0.463526i
147147 1.87202 + 4.51946i 0.154402 + 0.372759i
148148 19.7040 6.29405i 1.61966 0.517368i
149149 1.05874 + 0.438544i 0.0867352 + 0.0359269i 0.425629 0.904898i 0.360053π-0.360053\pi
−0.338894 + 0.940825i 0.610053π0.610053\pi
150150 6.71327 + 7.29870i 0.548136 + 0.595936i
151151 13.7039 13.7039i 1.11521 1.11521i 0.122777 0.992434i 0.460820π-0.460820\pi
0.992434 0.122777i 0.0391800π-0.0391800\pi
152152 −15.7844 + 12.2536i −1.28028 + 0.993899i
153153 −0.978073 0.978073i −0.0790725 0.0790725i
154154 −0.227029 + 5.43383i −0.0182945 + 0.437871i
155155 0.170687 0.412074i 0.0137099 0.0330986i
156156 −0.234051 + 2.79606i −0.0187390 + 0.223864i
157157 11.5135 4.76907i 0.918881 0.380613i 0.127431 0.991847i 0.459327π-0.459327\pi
0.791450 + 0.611234i 0.209327π0.209327\pi
158158 4.87379 10.5033i 0.387738 0.835598i
159159 1.87031 0.148325
160160 0.130169 + 0.200155i 0.0102908 + 0.0158236i
161161 −15.5937 −1.22896
162162 2.88103 6.20878i 0.226355 0.487808i
163163 −17.9956 + 7.45403i −1.40953 + 0.583845i −0.952206 0.305457i 0.901191π-0.901191\pi
−0.457320 + 0.889302i 0.651191π0.651191\pi
164164 2.34634 + 0.196405i 0.183218 + 0.0153367i
165165 0.0464924 0.112243i 0.00361943 0.00873807i
166166 −0.450562 + 10.7840i −0.0349704 + 0.837002i
167167 2.12801 + 2.12801i 0.164670 + 0.164670i 0.784632 0.619962i 0.212852π-0.212852\pi
−0.619962 + 0.784632i 0.712852π0.712852\pi
168168 0.929244 7.37916i 0.0716928 0.569314i
169169 −0.707107 + 0.707107i −0.0543928 + 0.0543928i
170170 0.0541694 + 0.0588932i 0.00415460 + 0.00451690i
171171 6.73475 + 2.78963i 0.515019 + 0.213328i
172172 −3.59240 11.2463i −0.273918 0.857519i
173173 −4.16552 10.0565i −0.316698 0.764578i −0.999425 0.0339039i 0.989206π-0.989206\pi
0.682727 0.730674i 0.260794π-0.260794\pi
174174 9.23524 3.38100i 0.700122 0.256313i
175175 9.36830i 0.708177i
176176 −4.35753 + 6.95463i −0.328461 + 0.524225i
177177 4.16957i 0.313404i
178178 −5.50113 15.0264i −0.412327 1.12628i
179179 2.98859 + 7.21510i 0.223378 + 0.539282i 0.995344 0.0963813i 0.0307268π-0.0307268\pi
−0.771967 + 0.635663i 0.780727π0.780727\pi
180180 0.0399280 0.0774090i 0.00297605 0.00576973i
181181 16.3307 + 6.76440i 1.21385 + 0.502794i 0.895450 0.445162i 0.146854π-0.146854\pi
0.318402 + 0.947956i 0.396854π0.396854\pi
182182 1.95094 1.79445i 0.144613 0.133014i
183183 2.03011 2.03011i 0.150070 0.150070i
184184 −20.4448 11.6508i −1.50721 0.858910i
185185 0.308668 + 0.308668i 0.0226937 + 0.0226937i
186186 −20.9481 0.875223i −1.53599 0.0641745i
187187 −1.05256 + 2.54111i −0.0769709 + 0.185824i
188188 15.0155 12.6959i 1.09512 0.925943i
189189 −9.79477 + 4.05713i −0.712465 + 0.295113i
190190 −0.382523 0.177500i −0.0277512 0.0128772i
191191 −2.70165 −0.195484 −0.0977421 0.995212i 0.531162π-0.531162\pi
−0.0977421 + 0.995212i 0.531162π0.531162\pi
192192 6.73164 8.98046i 0.485814 0.648109i
193193 −25.3193 −1.82252 −0.911262 0.411827i 0.864891π-0.864891\pi
−0.911262 + 0.411827i 0.864891π0.864891\pi
194194 −9.47263 4.39553i −0.680095 0.315581i
195195 −0.0547057 + 0.0226599i −0.00391756 + 0.00162271i
196196 5.32537 4.50269i 0.380383 0.321621i
197197 7.75694 18.7269i 0.552659 1.33424i −0.362816 0.931861i 0.618185π-0.618185\pi
0.915475 0.402376i 0.131815π-0.131815\pi
198198 2.99133 + 0.124979i 0.212584 + 0.00888190i
199199 5.61537 + 5.61537i 0.398063 + 0.398063i 0.877549 0.479486i 0.159177π-0.159177\pi
−0.479486 + 0.877549i 0.659177π0.659177\pi
200200 6.99950 12.2827i 0.494939 0.868518i
201201 −7.47238 + 7.47238i −0.527061 + 0.527061i
202202 −1.57843 + 1.45182i −0.111058 + 0.102150i
203203 −8.58368 3.55547i −0.602456 0.249545i
204204 1.72427 3.34287i 0.120723 0.234048i
205205 0.0190152 + 0.0459067i 0.00132808 + 0.00320627i
206206 −1.82869 4.99510i −0.127411 0.348025i
207207 8.58435i 0.596654i
208208 3.89857 0.895053i 0.270317 0.0620608i
209209 14.4953i 1.00266i
210210 0.147389 0.0539589i 0.0101708 0.00372351i
211211 0.583737 + 1.40926i 0.0401861 + 0.0970178i 0.942698 0.333647i 0.108279π-0.108279\pi
−0.902512 + 0.430664i 0.858279π0.858279\pi
212212 −0.811314 2.53987i −0.0557213 0.174439i
213213 −20.7086 8.57777i −1.41893 0.587739i
214214 2.04271 + 2.22085i 0.139637 + 0.151814i
215215 0.176176 0.176176i 0.0120151 0.0120151i
216216 −15.8731 1.99887i −1.08003 0.136006i
217217 14.0057 + 14.0057i 0.950771 + 0.950771i
218218 −0.778386 + 18.6303i −0.0527189 + 1.26180i
219219 6.18476 14.9313i 0.417927 1.00897i
220220 −0.172593 0.0144473i −0.0116362 0.000974036i
221221 1.23851 0.513006i 0.0833110 0.0345085i
222222 8.63704 18.6133i 0.579680 1.24924i
223223 8.84032 0.591992 0.295996 0.955189i 0.404349π-0.404349\pi
0.295996 + 0.955189i 0.404349π0.404349\pi
224224 −10.4240 + 1.93907i −0.696481 + 0.129559i
225225 −5.15725 −0.343817
226226 1.02567 2.21038i 0.0682266 0.147032i
227227 18.3475 7.59977i 1.21776 0.504414i 0.321066 0.947057i 0.395959π-0.395959\pi
0.896698 + 0.442643i 0.145959π0.145959\pi
228228 −1.65353 + 19.7538i −0.109508 + 1.30822i
229229 −4.77667 + 11.5319i −0.315651 + 0.762049i 0.683824 + 0.729647i 0.260316π0.260316\pi
−0.999475 + 0.0324021i 0.989684π0.989684\pi
230230 0.0207300 0.496165i 0.00136690 0.0327161i
231231 3.81494 + 3.81494i 0.251005 + 0.251005i
232232 −8.59752 11.0748i −0.564455 0.727097i
233233 6.10499 6.10499i 0.399951 0.399951i −0.478265 0.878216i 0.658734π-0.658734\pi
0.878216 + 0.478265i 0.158734π0.158734\pi
234234 −0.987846 1.07399i −0.0645775 0.0702090i
235235 0.383381 + 0.158802i 0.0250090 + 0.0103591i
236236 5.66228 1.80871i 0.368583 0.117737i
237237 −4.39570 10.6122i −0.285532 0.689334i
238238 −3.33681 + 1.22160i −0.216293 + 0.0791845i
239239 1.77849i 0.115041i 0.998344 + 0.0575205i 0.0183194π0.0183194\pi
−0.998344 + 0.0575205i 0.981681π0.981681\pi
240240 0.233556 + 0.0393766i 0.0150760 + 0.00254175i
241241 14.6732i 0.945182i −0.881282 0.472591i 0.843319π-0.843319\pi
0.881282 0.472591i 0.156681π-0.156681\pi
242242 3.30134 + 9.01765i 0.212218 + 0.579677i
243243 3.89532 + 9.40413i 0.249885 + 0.603275i
244244 −3.63753 1.87626i −0.232869 0.120115i
245245 0.135969 + 0.0563201i 0.00868672 + 0.00359816i
246246 1.71912 1.58123i 0.109607 0.100816i
247247 −4.99561 + 4.99561i −0.317863 + 0.317863i
248248 7.89845 + 28.8271i 0.501552 + 1.83052i
249249 7.57115 + 7.57115i 0.479802 + 0.479802i
250250 0.596271 + 0.0249125i 0.0377115 + 0.00157561i
251251 7.62041 18.3973i 0.480996 1.16123i −0.478141 0.878283i 0.658689π-0.658689\pi
0.959137 0.282943i 0.0913109π-0.0913109\pi
252252 2.49736 + 2.95365i 0.157319 + 0.186063i
253253 15.7705 6.53234i 0.991481 0.410685i
254254 12.2416 + 5.68040i 0.768107 + 0.356420i
255255 0.0793781 0.00497085
256256 −15.1156 5.24595i −0.944722 0.327872i
257257 −17.4429 −1.08806 −0.544030 0.839066i 0.683102π-0.683102\pi
−0.544030 + 0.839066i 0.683102π0.683102\pi
258258 −10.6238 4.92969i −0.661407 0.306909i
259259 −17.9095 + 7.41834i −1.11284 + 0.460953i
260260 0.0545027 + 0.0644608i 0.00338011 + 0.00399769i
261261 −1.95729 + 4.72531i −0.121153 + 0.292490i
262262 30.7367 + 1.28420i 1.89892 + 0.0793379i
263263 4.25638 + 4.25638i 0.262460 + 0.262460i 0.826053 0.563593i 0.190581π-0.190581\pi
−0.563593 + 0.826053i 0.690581π0.690581\pi
264264 2.15141 + 7.85206i 0.132410 + 0.483261i
265265 0.0397878 0.0397878i 0.00244414 0.00244414i
266266 13.7831 12.6775i 0.845095 0.777310i
267267 −14.6656 6.07469i −0.897521 0.371765i
268268 13.3889 + 6.90607i 0.817858 + 0.421855i
269269 −4.37648 10.5658i −0.266839 0.644206i 0.732492 0.680775i 0.238357π-0.238357\pi
−0.999331 + 0.0365693i 0.988357π0.988357\pi
270270 −0.116069 0.317045i −0.00706376 0.0192948i
271271 14.4536i 0.877994i −0.898489 0.438997i 0.855334π-0.855334\pi
0.898489 0.438997i 0.144666π-0.144666\pi
272272 −5.28758 0.891464i −0.320607 0.0540529i
273273 2.62953i 0.159146i
274274 22.4482 8.21823i 1.35615 0.496482i
275275 3.92446 + 9.47448i 0.236654 + 0.571332i
276276 −22.2367 + 7.10307i −1.33849 + 0.427555i
277277 13.9658 + 5.78484i 0.839125 + 0.347577i 0.760509 0.649328i 0.224950π-0.224950\pi
0.0786167 + 0.996905i 0.474950π0.474950\pi
278278 6.59865 + 7.17408i 0.395761 + 0.430273i
279279 7.71016 7.71016i 0.461595 0.461595i
280280 −0.137212 0.176748i −0.00819996 0.0105627i
281281 1.25022 + 1.25022i 0.0745818 + 0.0745818i 0.743414 0.668832i 0.233205π-0.233205\pi
−0.668832 + 0.743414i 0.733205π0.733205\pi
282282 0.814280 19.4894i 0.0484897 1.16058i
283283 −2.05770 + 4.96773i −0.122318 + 0.295301i −0.973164 0.230114i 0.926090π-0.926090\pi
0.850846 + 0.525415i 0.176090π0.176090\pi
284284 −2.66550 + 31.8431i −0.158168 + 1.88954i
285285 −0.386488 + 0.160089i −0.0228936 + 0.00948283i
286286 −1.22134 + 2.63205i −0.0722192 + 0.155637i
287287 −2.20659 −0.130251
288288 1.06746 + 5.73840i 0.0629005 + 0.338139i
289289 15.2029 0.894290
290290 0.124540 0.268390i 0.00731323 0.0157604i
291291 −9.57081 + 3.96436i −0.561051 + 0.232395i
292292 −22.9596 1.92189i −1.34361 0.112470i
293293 −7.98903 + 19.2872i −0.466724 + 1.12677i 0.498860 + 0.866682i 0.333752π0.333752\pi
−0.965584 + 0.260090i 0.916248π0.916248\pi
294294 0.288790 6.91207i 0.0168426 0.403120i
295295 0.0887010 + 0.0887010i 0.00516437 + 0.00516437i
296296 −29.0235 3.65488i −1.68696 0.212436i
297297 8.20622 8.20622i 0.476173 0.476173i
298298 −1.09713 1.19281i −0.0635552 0.0690975i
299299 −7.68635 3.18379i −0.444513 0.184123i
300300 −4.26734 13.3592i −0.246375 0.771293i
301301 4.23410 + 10.2220i 0.244050 + 0.589188i
302302 −25.7374 + 9.42237i −1.48102 + 0.542197i
303303 2.12745i 0.122219i
304304 27.5429 6.32342i 1.57969 0.362673i
305305 0.0863749i 0.00494581i
306306 0.672490 + 1.83692i 0.0384437 + 0.105010i
307307 4.55614 + 10.9995i 0.260032 + 0.627774i 0.998940 0.0460331i 0.0146580π-0.0146580\pi
−0.738908 + 0.673807i 0.764658π0.764658\pi
308308 3.52582 6.83556i 0.200902 0.389492i
309309 −4.87516 2.01936i −0.277338 0.114877i
310310 −0.464256 + 0.427018i −0.0263680 + 0.0242530i
311311 17.7608 17.7608i 1.00712 1.00712i 0.00714590 0.999974i 0.497725π-0.497725\pi
0.999974 0.00714590i 0.00227463π-0.00227463\pi
312312 1.96465 3.44755i 0.111226 0.195179i
313313 −17.2201 17.2201i −0.973338 0.973338i 0.0263154 0.999654i 0.491623π-0.491623\pi
−0.999654 + 0.0263154i 0.991623π0.991623\pi
314314 −17.6088 0.735706i −0.993723 0.0415183i
315315 −0.0312373 + 0.0754134i −0.00176002 + 0.00424906i
316316 −12.5045 + 10.5728i −0.703434 + 0.594765i
317317 20.3875 8.44477i 1.14508 0.474306i 0.272196 0.962242i 0.412250π-0.412250\pi
0.872879 + 0.487936i 0.162250π0.162250\pi
318318 −2.39929 1.11333i −0.134545 0.0624324i
319319 10.1704 0.569432
320320 −0.0478401 0.334250i −0.00267434 0.0186851i
321321 2.99332 0.167071
322322 20.0041 + 9.28242i 1.11479 + 0.517289i
323323 8.74987 3.62432i 0.486856 0.201662i
324324 −7.39175 + 6.24985i −0.410653 + 0.347214i
325325 1.91274 4.61775i 0.106099 0.256147i
326326 27.5225 + 1.14991i 1.52433 + 0.0636874i
327327 13.0798 + 13.0798i 0.723316 + 0.723316i
328328 −2.89304 1.64865i −0.159741 0.0910314i
329329 −13.0305 + 13.0305i −0.718394 + 0.718394i
330330 −0.126456 + 0.116313i −0.00696118 + 0.00640282i
331331 12.3611 + 5.12015i 0.679430 + 0.281429i 0.695589 0.718440i 0.255144π-0.255144\pi
−0.0161586 + 0.999869i 0.505144π0.505144\pi
332332 6.99735 13.5659i 0.384029 0.744524i
333333 4.08380 + 9.85916i 0.223791 + 0.540279i
334334 −1.46315 3.99661i −0.0800600 0.218685i
335335 0.317926i 0.0173702i
336336 −5.58462 + 8.91307i −0.304666 + 0.486248i
337337 20.7391i 1.12973i −0.825184 0.564865i 0.808928π-0.808928\pi
0.825184 0.564865i 0.191072π-0.191072\pi
338338 1.32802 0.486183i 0.0722345 0.0264449i
339339 −0.925059 2.23329i −0.0502423 0.121296i
340340 −0.0344331 0.107795i −0.00186740 0.00584602i
341341 −20.0316 8.29735i −1.08477 0.449327i
342342 −6.97899 7.58759i −0.377381 0.410290i
343343 −13.8988 + 13.8988i −0.750465 + 0.750465i
344344 −2.08606 + 16.5655i −0.112473 + 0.893152i
345345 −0.348343 0.348343i −0.0187542 0.0187542i
346346 −0.642599 + 15.3803i −0.0345463 + 0.826852i
347347 −4.33031 + 10.4543i −0.232463 + 0.561216i −0.996466 0.0839972i 0.973231π-0.973231\pi
0.764003 + 0.645213i 0.223231π0.223231\pi
348348 −13.8599 1.16017i −0.742966 0.0621917i
349349 −0.672908 + 0.278728i −0.0360199 + 0.0149200i −0.400621 0.916244i 0.631205π-0.631205\pi
0.364601 + 0.931164i 0.381205π0.381205\pi
350350 −5.57663 + 12.0180i −0.298083 + 0.642387i
351351 −5.65631 −0.301912
352352 9.72983 6.32773i 0.518602 0.337269i
353353 −0.797848 −0.0424652 −0.0212326 0.999775i 0.506759π-0.506759\pi
−0.0212326 + 0.999775i 0.506759π0.506759\pi
354354 2.48200 5.34886i 0.131917 0.284289i
355355 −0.623020 + 0.258063i −0.0330665 + 0.0136966i
356356 −1.88768 + 22.5510i −0.100047 + 1.19520i
357357 −1.34897 + 3.25669i −0.0713948 + 0.172362i
358358 0.461039 11.0348i 0.0243667 0.583205i
359359 2.98085 + 2.98085i 0.157323 + 0.157323i 0.781379 0.624056i 0.214516π-0.214516\pi
−0.624056 + 0.781379i 0.714516π0.714516\pi
360360 −0.0972998 + 0.0755350i −0.00512815 + 0.00398104i
361361 −21.8582 + 21.8582i −1.15043 + 1.15043i
362362 −16.9229 18.3987i −0.889450 0.967014i
363363 8.80112 + 3.64555i 0.461939 + 0.191342i
364364 −3.57090 + 1.14066i −0.187166 + 0.0597866i
365365 −0.186069 0.449211i −0.00973932 0.0235128i
366366 −3.81275 + 1.39584i −0.199296 + 0.0729617i
367367 10.9768i 0.572982i 0.958083 + 0.286491i 0.0924888π0.0924888\pi
−0.958083 + 0.286491i 0.907511π0.907511\pi
368368 19.2919 + 27.1161i 1.00566 + 1.41353i
369369 1.21473i 0.0632362i
370370 −0.212230 0.579708i −0.0110333 0.0301376i
371371 0.956236 + 2.30856i 0.0496453 + 0.119854i
372372 26.3519 + 13.5924i 1.36628 + 0.704735i
373373 2.18035 + 0.903129i 0.112894 + 0.0467623i 0.438416 0.898772i 0.355540π-0.355540\pi
−0.325521 + 0.945535i 0.605540π0.605540\pi
374374 2.86289 2.63326i 0.148037 0.136163i
375375 0.418625 0.418625i 0.0216177 0.0216177i
376376 −26.8199 + 7.34847i −1.38313 + 0.378968i
377377 −3.50508 3.50508i −0.180521 0.180521i
378378 14.9801 + 0.625878i 0.770494 + 0.0321917i
379379 2.55877 6.17741i 0.131435 0.317312i −0.844437 0.535655i 0.820065π-0.820065\pi
0.975872 + 0.218342i 0.0700649π0.0700649\pi
380380 0.385054 + 0.455406i 0.0197528 + 0.0233618i
381381 12.3685 5.12319i 0.633657 0.262469i
382382 3.46576 + 1.60820i 0.177324 + 0.0822825i
383383 −20.4733 −1.04613 −0.523067 0.852291i 0.675212π-0.675212\pi
−0.523067 + 0.852291i 0.675212π0.675212\pi
384384 −13.9813 + 7.51331i −0.713482 + 0.383412i
385385 0.162314 0.00827227
386386 32.4804 + 15.0717i 1.65321 + 0.767130i
387387 5.62723 2.33087i 0.286048 0.118485i
388388 9.53528 + 11.2775i 0.484081 + 0.572526i
389389 6.02332 14.5416i 0.305394 0.737287i −0.694448 0.719543i 0.744351π-0.744351\pi
0.999843 0.0177445i 0.00564854π-0.00564854\pi
390390 0.0836669 + 0.00349565i 0.00423664 + 0.000177009i
391391 7.88629 + 7.88629i 0.398827 + 0.398827i
392392 −9.51185 + 2.60619i −0.480421 + 0.131632i
393393 21.5794 21.5794i 1.08853 1.08853i
394394 −21.0983 + 19.4060i −1.06292 + 0.977662i
395395 −0.319269 0.132245i −0.0160641 0.00665399i
396396 −3.76297 1.94096i −0.189097 0.0975370i
397397 −1.40608 3.39458i −0.0705692 0.170369i 0.884659 0.466238i 0.154391π-0.154391\pi
−0.955229 + 0.295869i 0.904391π0.904391\pi
398398 −3.86094 10.5462i −0.193531 0.528634i
399399 18.5773i 0.930026i
400400 −16.2906 + 11.5901i −0.814532 + 0.579504i
401401 14.2356i 0.710893i 0.934697 + 0.355446i 0.115671π0.115671\pi
−0.934697 + 0.355446i 0.884329π0.884329\pi
402402 14.0339 5.13776i 0.699946 0.256248i
403403 4.04404 + 9.76317i 0.201448 + 0.486338i
404404 2.88908 0.922860i 0.143737 0.0459140i
405405 −0.188728 0.0781737i −0.00937797 0.00388448i
406406 8.89496 + 9.67065i 0.441450 + 0.479946i
407407 15.0048 15.0048i 0.743762 0.743762i
408408 −4.20184 + 3.26194i −0.208022 + 0.161490i
409409 14.6882 + 14.6882i 0.726285 + 0.726285i 0.969878 0.243592i 0.0783259π-0.0783259\pi
−0.243592 + 0.969878i 0.578326π0.578326\pi
410410 0.00293340 0.0702097i 0.000144870 0.00346741i
411411 9.07509 21.9092i 0.447641 1.08070i
412412 −0.627506 + 7.49644i −0.0309150 + 0.369323i
413413 −5.14659 + 2.13179i −0.253247 + 0.104898i
414414 5.10997 11.0123i 0.251141 0.541224i
415415 0.322128 0.0158127
416416 −5.53401 1.17248i −0.271327 0.0574858i
417417 9.66944 0.473515
418418 −8.62857 + 18.5951i −0.422037 + 0.909515i
419419 −16.7156 + 6.92384i −0.816612 + 0.338252i −0.751589 0.659632i 0.770712π-0.770712\pi
−0.0650233 + 0.997884i 0.520712π0.520712\pi
420420 −0.221196 0.0185157i −0.0107932 0.000903473i
421421 1.81037 4.37063i 0.0882322 0.213011i −0.873604 0.486638i 0.838223π-0.838223\pi
0.961836 + 0.273626i 0.0882232π0.0882232\pi
422422 0.0900509 2.15533i 0.00438361 0.104920i
423423 7.17329 + 7.17329i 0.348777 + 0.348777i
424424 −0.471120 + 3.74118i −0.0228796 + 0.181688i
425425 −4.73787 + 4.73787i −0.229821 + 0.229821i
426426 21.4596 + 23.3309i 1.03972 + 1.13039i
427427 3.54375 + 1.46787i 0.171494 + 0.0710353i
428428 −1.29846 4.06493i −0.0627636 0.196486i
429429 1.10153 + 2.65933i 0.0531824 + 0.128394i
430430 −0.330875 + 0.121132i −0.0159562 + 0.00584153i
431431 21.2512i 1.02363i 0.859095 + 0.511816i 0.171027π0.171027\pi
−0.859095 + 0.511816i 0.828973π0.828973\pi
432432 19.1727 + 12.0129i 0.922446 + 0.577973i
433433 11.0925i 0.533072i 0.963825 + 0.266536i 0.0858791π0.0858791\pi
−0.963825 + 0.266536i 0.914121π0.914121\pi
434434 −9.62987 26.3041i −0.462249 1.26264i
435435 −0.112323 0.271172i −0.00538549 0.0130017i
436436 12.0885 23.4362i 0.578936 1.12239i
437437 −54.3029 22.4930i −2.59766 1.07599i
438438 −16.8221 + 15.4728i −0.803792 + 0.739320i
439439 −18.6925 + 18.6925i −0.892145 + 0.892145i −0.994725 0.102580i 0.967290π-0.967290\pi
0.102580 + 0.994725i 0.467290π0.467290\pi
440440 0.212808 + 0.121272i 0.0101452 + 0.00578142i
441441 2.54406 + 2.54406i 0.121146 + 0.121146i
442442 −1.89417 0.0791396i −0.0900966 0.00376429i
443443 −3.76977 + 9.10102i −0.179107 + 0.432403i −0.987780 0.155856i 0.950186π-0.950186\pi
0.808673 + 0.588259i 0.200186π0.200186\pi
444444 −22.1598 + 18.7364i −1.05166 + 0.889192i
445445 −0.441217 + 0.182758i −0.0209157 + 0.00866356i
446446 −11.3406 5.26234i −0.536995 0.249179i
447447 −1.60770 −0.0760418
448448 14.5265 + 3.71754i 0.686312 + 0.175637i
449449 −19.4836 −0.919490 −0.459745 0.888051i 0.652059π-0.652059\pi
−0.459745 + 0.888051i 0.652059π0.652059\pi
450450 6.61589 + 3.06993i 0.311876 + 0.144718i
451451 2.23160 0.924359i 0.105082 0.0435264i
452452 −2.63153 + 2.22500i −0.123777 + 0.104655i
453453 −10.4048 + 25.1194i −0.488859 + 1.18021i
454454 −28.0606 1.17239i −1.31695 0.0550229i
455455 −0.0559391 0.0559391i −0.00262246 0.00262246i
456456 13.8799 24.3565i 0.649988 1.14060i
457457 22.9769 22.9769i 1.07481 1.07481i 0.0778468 0.996965i 0.475195π-0.475195\pi
0.996965 0.0778468i 0.0248045π-0.0248045\pi
458458 12.9922 11.9501i 0.607086 0.558392i
459459 7.00538 + 2.90173i 0.326983 + 0.135441i
460460 −0.321943 + 0.624156i −0.0150107 + 0.0291014i
461461 −7.62051 18.3975i −0.354922 0.856858i −0.995998 0.0893803i 0.971511π-0.971511\pi
0.641075 0.767478i 0.278489π-0.278489\pi
462462 −2.62303 7.16483i −0.122034 0.333338i
463463 11.2437i 0.522539i −0.965266 0.261270i 0.915859π-0.915859\pi
0.965266 0.261270i 0.0841411π-0.0841411\pi
464464 4.43671 + 19.3249i 0.205969 + 0.897138i
465465 0.625738i 0.0290179i
466466 −11.4658 + 4.19759i −0.531142 + 0.194450i
467467 12.2312 + 29.5287i 0.565991 + 1.36642i 0.904908 + 0.425607i 0.139939π0.139939\pi
−0.338917 + 0.940816i 0.610061π0.610061\pi
468468 0.627931 + 1.96578i 0.0290261 + 0.0908682i
469469 −13.0437 5.40290i −0.602304 0.249483i
470470 −0.397284 0.431929i −0.0183254 0.0199234i
471471 −12.3626 + 12.3626i −0.569641 + 0.569641i
472472 −8.34041 1.05029i −0.383899 0.0483437i
473473 −8.56418 8.56418i −0.393781 0.393781i
474474 −0.678109 + 16.2302i −0.0311466 + 0.745480i
475475 13.5132 32.6238i 0.620028 1.49688i
476476 5.00775 + 0.419185i 0.229530 + 0.0192133i
477477 1.27086 0.526408i 0.0581888 0.0241026i
478478 1.05867 2.28150i 0.0484226 0.104354i
479479 −16.6958 −0.762851 −0.381425 0.924400i 0.624567π-0.624567\pi
−0.381425 + 0.924400i 0.624567π0.624567\pi
480480 −0.276174 0.189542i −0.0126055 0.00865135i
481481 −10.3424 −0.471573
482482 −8.73444 + 18.8232i −0.397843 + 0.857374i
483483 20.2115 8.37187i 0.919654 0.380933i
484484 1.13284 13.5333i 0.0514926 0.615150i
485485 −0.119268 + 0.287939i −0.00541569 + 0.0130746i
486486 0.600916 14.3827i 0.0272581 0.652411i
487487 −13.1576 13.1576i −0.596227 0.596227i 0.343079 0.939306i 0.388530π-0.388530\pi
−0.939306 + 0.343079i 0.888530π0.888530\pi
488488 3.54947 + 4.57222i 0.160677 + 0.206975i
489489 19.3228 19.3228i 0.873805 0.873805i
490490 −0.140900 0.153187i −0.00636520 0.00692027i
491491 21.8280 + 9.04146i 0.985084 + 0.408035i 0.816307 0.577619i 0.196018π-0.196018\pi
0.168778 + 0.985654i 0.446018π0.446018\pi
492492 −3.14660 + 1.00512i −0.141860 + 0.0453143i
493493 2.54293 + 6.13919i 0.114528 + 0.276495i
494494 9.38224 3.43481i 0.422127 0.154540i
495495 0.0893537i 0.00401615i
496496 7.02742 41.6821i 0.315541 1.87158i
497497 29.9466i 1.34329i
498498 −5.20567 14.2194i −0.233272 0.637185i
499499 2.50674 + 6.05180i 0.112217 + 0.270916i 0.970004 0.243090i 0.0781610π-0.0781610\pi
−0.857787 + 0.514006i 0.828161π0.828161\pi
500500 −0.750086 0.386898i −0.0335449 0.0173026i
501501 −3.90065 1.61570i −0.174268 0.0721842i
502502 −20.7270 + 19.0645i −0.925090 + 0.850889i
503503 1.96926 1.96926i 0.0878048 0.0878048i −0.661840 0.749645i 0.730224π-0.730224\pi
0.749645 + 0.661840i 0.230224π0.230224\pi
504504 −1.44549 5.27563i −0.0643872 0.234995i
505505 0.0452581 + 0.0452581i 0.00201396 + 0.00201396i
506506 −24.1193 1.00772i −1.07224 0.0447986i
507507 0.536874 1.29613i 0.0238434 0.0575631i
508508 −12.3226 14.5740i −0.546726 0.646617i
509509 28.0705 11.6272i 1.24421 0.515367i 0.339179 0.940722i 0.389851π-0.389851\pi
0.905026 + 0.425355i 0.139851π0.139851\pi
510510 −0.101829 0.0472510i −0.00450905 0.00209231i
511511 21.5922 0.955181
512512 16.2680 + 15.7275i 0.718950 + 0.695062i
513513 −39.9611 −1.76432
514514 22.3764 + 10.3832i 0.986979 + 0.457983i
515515 −0.146670 + 0.0607527i −0.00646305 + 0.00267708i
516516 10.6940 + 12.6479i 0.470779 + 0.556794i
517517 7.71960 18.6368i 0.339508 0.819644i
518518 27.3907 + 1.14440i 1.20348 + 0.0502820i
519519 10.7981 + 10.7981i 0.473984 + 0.473984i
520520 −0.0315465 0.115136i −0.00138341 0.00504904i
521521 24.9407 24.9407i 1.09267 1.09267i 0.0974287 0.995243i 0.468938π-0.468938\pi
0.995243 0.0974287i 0.0310618π-0.0310618\pi
522522 5.32369 4.89668i 0.233012 0.214322i
523523 −5.48560 2.27221i −0.239868 0.0993567i 0.259511 0.965740i 0.416439π-0.416439\pi
−0.499379 + 0.866383i 0.666439π0.666439\pi
524524 −38.6656 19.9439i −1.68911 0.871254i
525525 5.02960 + 12.1425i 0.219510 + 0.529943i
526526 −2.92654 7.99390i −0.127603 0.348551i
527527 14.1664i 0.617097i
528528 1.91416 11.3535i 0.0833031 0.494099i
529529 46.2165i 2.00941i
530530 −0.0747254 + 0.0273568i −0.00324586 + 0.00118830i
531531 1.17355 + 2.83320i 0.0509277 + 0.122950i
532532 −25.2279 + 8.05857i −1.09377 + 0.349383i
533533 −1.08766 0.450522i −0.0471116 0.0195143i
534534 15.1975 + 16.5227i 0.657658 + 0.715009i
535535 0.0636782 0.0636782i 0.00275305 0.00275305i
536536 −13.0648 16.8293i −0.564312 0.726914i
537537 −7.74719 7.74719i −0.334316 0.334316i
538538 −0.675144 + 16.1593i −0.0291075 + 0.696676i
539539 2.73781 6.60966i 0.117926 0.284698i
540540 −0.0398286 + 0.475808i −0.00171395 + 0.0204755i
541541 −37.2615 + 15.4342i −1.60200 + 0.663569i −0.991697 0.128600i 0.958952π-0.958952\pi
−0.610302 + 0.792169i 0.708952π0.708952\pi
542542 −8.60373 + 18.5415i −0.369562 + 0.796428i
543543 −24.7983 −1.06420
544544 6.25242 + 4.29111i 0.268070 + 0.183980i
545545 0.556505 0.0238380
546546 −1.56527 + 3.37325i −0.0669873 + 0.144362i
547547 0.454932 0.188439i 0.0194515 0.00805707i −0.372936 0.927857i 0.621649π-0.621649\pi
0.392388 + 0.919800i 0.371649π0.371649\pi
548548 −33.6893 2.82004i −1.43914 0.120466i
549549 0.808063 1.95084i 0.0344873 0.0832597i
550550 0.605411 14.4903i 0.0258148 0.617867i
551551 −24.7629 24.7629i −1.05493 1.05493i
552552 32.7541 + 4.12467i 1.39411 + 0.175558i
553553 10.8514 10.8514i 0.461449 0.461449i
554554 −14.4723 15.7344i −0.614869 0.668489i
555555 −0.565789 0.234357i −0.0240164 0.00994792i
556556 −4.19448 13.1311i −0.177885 0.556882i
557557 −10.5604 25.4951i −0.447460 1.08026i −0.973270 0.229662i 0.926238π-0.926238\pi
0.525810 0.850602i 0.323762π-0.323762\pi
558558 −14.4804 + 5.30125i −0.613006 + 0.224420i
559559 5.90304i 0.249672i
560560 0.0708075 + 0.308415i 0.00299216 + 0.0130329i
561561 3.85869i 0.162914i
562562 −0.859609 2.34803i −0.0362604 0.0990459i
563563 −12.0391 29.0650i −0.507388 1.22494i −0.945382 0.325964i 0.894311π-0.894311\pi
0.437995 0.898978i 0.355689π-0.355689\pi
564564 −12.6460 + 24.5170i −0.532492 + 1.03235i
565565 −0.0671889 0.0278305i −0.00282666 0.00117084i
566566 5.59681 5.14789i 0.235251 0.216382i
567567 6.41456 6.41456i 0.269386 0.269386i
568568 22.3745 39.2627i 0.938814 1.64743i
569569 9.01457 + 9.01457i 0.377910 + 0.377910i 0.870348 0.492437i 0.163894π-0.163894\pi
−0.492437 + 0.870348i 0.663894π0.663894\pi
570570 0.591095 + 0.0246963i 0.0247582 + 0.00103441i
571571 −6.08450 + 14.6893i −0.254628 + 0.614727i −0.998567 0.0535210i 0.982956π-0.982956\pi
0.743938 + 0.668248i 0.232956π0.232956\pi
572572 3.13354 2.64946i 0.131020 0.110780i
573573 3.50168 1.45044i 0.146285 0.0605931i
574574 2.83069 + 1.31351i 0.118151 + 0.0548248i
575575 41.5834 1.73415
576576 2.04651 7.99683i 0.0852711 0.333201i
577577 5.62489 0.234167 0.117084 0.993122i 0.462645π-0.462645\pi
0.117084 + 0.993122i 0.462645π0.462645\pi
578578 −19.5028 9.04978i −0.811210 0.376421i
579579 32.8171 13.5933i 1.36383 0.564917i
580580 −0.319527 + 0.270166i −0.0132676 + 0.0112180i
581581 −5.47431 + 13.2162i −0.227113 + 0.548298i
582582 14.6376 + 0.611567i 0.606748 + 0.0253503i
583583 −1.93415 1.93415i −0.0801042 0.0801042i
584584 28.3093 + 16.1325i 1.17145 + 0.667568i
585585 −0.0307945 + 0.0307945i −0.00127319 + 0.00127319i
586586 21.7296 19.9867i 0.897642 0.825642i
587587 9.51250 + 3.94021i 0.392623 + 0.162630i 0.570256 0.821467i 0.306844π-0.306844\pi
−0.177633 + 0.984097i 0.556844π0.556844\pi
588588 −4.48498 + 8.69511i −0.184958 + 0.358580i
589589 28.5705 + 68.9754i 1.17723 + 2.84208i
590590 −0.0609879 0.166589i −0.00251083 0.00685837i
591591 28.4370i 1.16974i
592592 35.0567 + 21.9653i 1.44082 + 0.902768i
593593 36.9766i 1.51845i 0.650830 + 0.759224i 0.274421π0.274421\pi
−0.650830 + 0.759224i 0.725579π0.725579\pi
594594 −15.4121 + 5.64232i −0.632366 + 0.231507i
595595 0.0405838 + 0.0979780i 0.00166377 + 0.00401671i
596596 0.697400 + 2.18326i 0.0285666 + 0.0894298i
597597 −10.2930 4.26349i −0.421264 0.174493i
598598 7.96509 + 8.65969i 0.325717 + 0.354121i
599599 20.4511 20.4511i 0.835609 0.835609i −0.152668 0.988277i 0.548787π-0.548787\pi
0.988277 + 0.152668i 0.0487867π0.0487867\pi
600600 −2.47799 + 19.6778i −0.101164 + 0.803343i
601601 25.8677 + 25.8677i 1.05517 + 1.05517i 0.998387 + 0.0567784i 0.0180829π0.0180829\pi
0.0567784 + 0.998387i 0.481917π0.481917\pi
602602 0.653179 15.6336i 0.0266216 0.637176i
603603 −2.97429 + 7.18058i −0.121123 + 0.292416i
604604 38.6255 + 3.23324i 1.57165 + 0.131559i
605605 0.264783 0.109677i 0.0107650 0.00445899i
606606 1.26640 2.72916i 0.0514439 0.110865i
607607 −5.96429 −0.242083 −0.121042 0.992647i 0.538623π-0.538623\pi
−0.121042 + 0.992647i 0.538623π0.538623\pi
608608 −39.0970 8.28344i −1.58559 0.335938i
609609 13.0344 0.528180
610610 −0.0514160 + 0.110805i −0.00208177 + 0.00448634i
611611 −9.08334 + 3.76244i −0.367473 + 0.152212i
612612 0.230761 2.75677i 0.00932797 0.111436i
613613 −4.98277 + 12.0295i −0.201252 + 0.485866i −0.991994 0.126284i 0.959695π-0.959695\pi
0.790742 + 0.612150i 0.209695π0.209695\pi
614614 0.702858 16.8226i 0.0283650 0.678905i
615615 −0.0492923 0.0492923i −0.00198766 0.00198766i
616616 −8.59200 + 6.67008i −0.346182 + 0.268745i
617617 17.7974 17.7974i 0.716495 0.716495i −0.251391 0.967886i 0.580888π-0.580888\pi
0.967886 + 0.251391i 0.0808879π0.0808879\pi
618618 5.05196 + 5.49251i 0.203220 + 0.220941i
619619 17.4572 + 7.23102i 0.701665 + 0.290639i 0.704851 0.709356i 0.251014π-0.251014\pi
−0.00318554 + 0.999995i 0.501014π0.501014\pi
620620 0.849752 0.271437i 0.0341269 0.0109012i
621621 −18.0085 43.4764i −0.722657 1.74465i
622622 −33.3565 + 12.2117i −1.33747 + 0.489645i
623623 21.2079i 0.849677i
624624 −4.57252 + 3.25315i −0.183047 + 0.130230i
625625 24.9733i 0.998931i
626626 11.8400 + 32.3411i 0.473221 + 1.29261i
627627 7.78216 + 18.7878i 0.310790 + 0.750313i
628628 22.1512 + 11.4257i 0.883929 + 0.455935i
629629 12.8091 + 5.30572i 0.510734 + 0.211553i
630630 0.0849632 0.0781483i 0.00338501 0.00311350i
631631 −33.8185 + 33.8185i −1.34629 + 1.34629i −0.456644 + 0.889649i 0.650949π0.650949\pi
−0.889649 + 0.456644i 0.849051π0.849051\pi
632632 22.3348 6.11959i 0.888431 0.243424i
633633 −1.51319 1.51319i −0.0601441 0.0601441i
634634 −31.1806 1.30274i −1.23834 0.0517386i
635635 0.154132 0.372108i 0.00611654 0.0147666i
636636 2.41516 + 2.85643i 0.0957673 + 0.113265i
637637 −3.22147 + 1.33438i −0.127639 + 0.0528699i
638638 −13.0469 6.05408i −0.516531 0.239683i
639639 −16.4856 −0.652161
640640 −0.137597 + 0.457264i −0.00543899 + 0.0180750i
641641 18.4797 0.729903 0.364951 0.931027i 0.381086π-0.381086\pi
0.364951 + 0.931027i 0.381086π0.381086\pi
642642 −3.83993 1.78182i −0.151550 0.0703229i
643643 −19.0785 + 7.90259i −0.752385 + 0.311648i −0.725714 0.687996i 0.758490π-0.758490\pi
−0.0266704 + 0.999644i 0.508490π0.508490\pi
644644 −20.1365 23.8156i −0.793488 0.938465i
645645 −0.133762 + 0.322930i −0.00526688 + 0.0127154i
646646 −13.3821 0.559110i −0.526510 0.0219979i
647647 −4.39897 4.39897i −0.172941 0.172941i 0.615329 0.788270i 0.289023π-0.289023\pi
−0.788270 + 0.615329i 0.789023π0.789023\pi
648648 13.2027 3.61745i 0.518651 0.142107i
649649 4.31190 4.31190i 0.169257 0.169257i
650650 −5.20251 + 4.78522i −0.204059 + 0.187692i
651651 −25.6725 10.6339i −1.00619 0.416776i
652652 −34.6222 17.8583i −1.35591 0.699386i
653653 2.02746 + 4.89471i 0.0793405 + 0.191545i 0.958572 0.284849i 0.0919435π-0.0919435\pi
−0.879232 + 0.476394i 0.841944π0.841944\pi
654654 −8.99325 24.5652i −0.351664 0.960575i
655655 0.918133i 0.0358744i
656656 2.72990 + 3.83707i 0.106585 + 0.149812i
657657 11.8865i 0.463736i
658658 24.4725 8.95933i 0.954039 0.349271i
659659 16.8242 + 40.6173i 0.655379 + 1.58222i 0.804863 + 0.593460i 0.202239π0.202239\pi
−0.149484 + 0.988764i 0.547761π0.547761\pi
660660 0.231459 0.0739351i 0.00900953 0.00287792i
661661 −5.30944 2.19924i −0.206513 0.0855405i 0.277029 0.960861i 0.410650π-0.410650\pi
−0.483542 + 0.875321i 0.660650π0.660650\pi
662662 −12.8094 13.9265i −0.497852 0.541267i
663663 −1.32984 + 1.32984i −0.0516469 + 0.0516469i
664664 −17.0517 + 13.2375i −0.661735 + 0.513713i
665665 −0.395202 0.395202i −0.0153253 0.0153253i
666666 0.629992 15.0786i 0.0244117 0.584284i
667667 15.7818 38.1007i 0.611074 1.47526i
668668 −0.502072 + 5.99795i −0.0194257 + 0.232068i
669669 −11.4582 + 4.74614i −0.442999 + 0.183496i
670670 0.189250 0.407846i 0.00731138 0.0157565i
671671 −4.19882 −0.162094
672672 12.4698 8.10964i 0.481032 0.312836i
673673 45.6326 1.75901 0.879503 0.475892i 0.157875π-0.157875\pi
0.879503 + 0.475892i 0.157875π0.157875\pi
674674 −12.3453 + 26.6048i −0.475522 + 1.02478i
675675 26.1195 10.8190i 1.00534 0.416425i
676676 −1.99303 0.166831i −0.0766550 0.00641658i
677677 0.465826 1.12460i 0.0179032 0.0432221i −0.914675 0.404190i 0.867554π-0.867554\pi
0.932578 + 0.360968i 0.117554π0.117554\pi
678678 −0.142705 + 3.41559i −0.00548057 + 0.131175i
679679 −9.78658 9.78658i −0.375575 0.375575i
680680 −0.0199949 + 0.158780i −0.000766770 + 0.00608894i
681681 −19.7005 + 19.7005i −0.754927 + 0.754927i
682682 20.7580 + 22.5682i 0.794866 + 0.864182i
683683 −29.6803 12.2940i −1.13569 0.470416i −0.265976 0.963980i 0.585694π-0.585694\pi
−0.869710 + 0.493563i 0.835694π0.835694\pi
684684 4.43624 + 13.8880i 0.169624 + 0.531019i
685685 −0.273025 0.659142i −0.0104318 0.0251845i
686686 26.1033 9.55635i 0.996629 0.364863i
687687 17.5113i 0.668097i
688688 12.5369 20.0090i 0.477967 0.762836i
689689 1.33315i 0.0507891i
690690 0.239509 + 0.654222i 0.00911795 + 0.0249058i
691691 2.35974 + 5.69691i 0.0897687 + 0.216721i 0.962387 0.271682i 0.0875798π-0.0875798\pi
−0.872618 + 0.488403i 0.837580π0.837580\pi
692692 9.97973 19.3479i 0.379372 0.735496i
693693 3.66597 + 1.51849i 0.139259 + 0.0576828i
694694 11.7781 10.8334i 0.447092 0.411231i
695695 0.205702 0.205702i 0.00780272 0.00780272i
696696 17.0893 + 9.73860i 0.647767 + 0.369141i
697697 1.11595 + 1.11595i 0.0422696 + 0.0422696i
698698 1.02915 + 0.0429983i 0.0389537 + 0.00162751i
699699 −4.63524 + 11.1905i −0.175321 + 0.423262i
700700 14.3078 12.0974i 0.540782 0.457241i
701701 21.4136 8.86979i 0.808779 0.335007i 0.0603125 0.998180i 0.480790π-0.480790\pi
0.748467 + 0.663172i 0.230790π0.230790\pi
702702 7.25610 + 3.36701i 0.273864 + 0.127080i
703703 −73.0676 −2.75580
704704 −16.2484 + 2.32559i −0.612385 + 0.0876488i
705705 −0.582167 −0.0219257
706706 1.02351 + 0.474932i 0.0385201 + 0.0178743i
707707 −2.62596 + 1.08771i −0.0987593 + 0.0409075i
708708 −6.36799 + 5.38424i −0.239324 + 0.202352i
709709 1.79886 4.34283i 0.0675575 0.163098i −0.886495 0.462739i 0.846867π-0.846867\pi
0.954052 + 0.299641i 0.0968668π0.0968668\pi
710710 0.952847 + 0.0398105i 0.0357597 + 0.00149406i
711711 −5.97371 5.97371i −0.224032 0.224032i
712712 15.8454 27.8055i 0.593832 1.04205i
713713 −62.1677 + 62.1677i −2.32820 + 2.32820i
714714 3.66909 3.37480i 0.137312 0.126299i
715715 0.0800064 + 0.0331397i 0.00299207 + 0.00123936i
716716 −7.16005 + 13.8813i −0.267584 + 0.518769i
717717 −0.954825 2.30515i −0.0356586 0.0860875i
718718 −2.04953 5.59833i −0.0764879 0.208928i
719719 9.07164i 0.338315i −0.985589 0.169158i 0.945895π-0.945895\pi
0.985589 0.169158i 0.0541047π-0.0541047\pi
720720 0.169783 0.0389795i 0.00632743 0.00145268i
721721 7.04996i 0.262554i
722722 41.0519 15.0290i 1.52779 0.559321i
723723 7.87765 + 19.0183i 0.292973 + 0.707299i
724724 10.7572 + 33.6761i 0.399787 + 1.25156i
725725 22.8899 + 9.48129i 0.850108 + 0.352126i
726726 −9.12030 9.91563i −0.338486 0.368004i
727727 −7.72242 + 7.72242i −0.286409 + 0.286409i −0.835658 0.549250i 0.814914π-0.814914\pi
0.549250 + 0.835658i 0.314914π0.314914\pi
728728 5.25986 + 0.662365i 0.194943 + 0.0245489i
729729 −20.3646 20.3646i −0.754246 0.754246i
730730 −0.0287042 + 0.687023i −0.00106239 + 0.0254279i
731731 3.02830 7.31096i 0.112006 0.270406i
732732 5.72202 + 0.478975i 0.211492 + 0.0177034i
733733 −14.2669 + 5.90955i −0.526961 + 0.218274i −0.630272 0.776375i 0.717056π-0.717056\pi
0.103311 + 0.994649i 0.467056π0.467056\pi
734734 6.53409 14.0813i 0.241177 0.519752i
735735 −0.206470 −0.00761575
736736 −8.60700 46.2693i −0.317258 1.70551i
737737 15.4549 0.569288
738738 0.723086 1.55829i 0.0266172 0.0573616i
739739 26.3508 10.9149i 0.969331 0.401510i 0.158868 0.987300i 0.449215π-0.449215\pi
0.810463 + 0.585790i 0.199215π0.199215\pi
740740 −0.0728255 + 0.870002i −0.00267712 + 0.0319819i
741741 3.79294 9.15696i 0.139337 0.336389i
742742 0.147515 3.53071i 0.00541545 0.129616i
743743 −13.0743 13.0743i −0.479651 0.479651i 0.425369 0.905020i 0.360144π-0.360144\pi
−0.905020 + 0.425369i 0.860144π0.860144\pi
744744 −25.7139 33.1232i −0.942719 1.21436i
745745 −0.0342013 + 0.0342013i −0.00125304 + 0.00125304i
746746 −2.25942 2.45645i −0.0827231 0.0899370i
747747 7.27549 + 3.01361i 0.266196 + 0.110262i
748748 −5.24010 + 1.67385i −0.191597 + 0.0612020i
749749 1.53040 + 3.69472i 0.0559198 + 0.135002i
750750 −0.786219 + 0.287832i −0.0287086 + 0.0105102i
751751 5.15515i 0.188114i −0.995567 0.0940570i 0.970016π-0.970016\pi
0.995567 0.0940570i 0.0299836π-0.0299836\pi
752752 38.7797 + 6.53809i 1.41415 + 0.238420i
753753 27.9364i 1.01806i
754754 2.40997 + 6.58288i 0.0877660 + 0.239734i
755755 0.313029 + 0.755720i 0.0113923 + 0.0275035i
756756 −18.8444 9.72005i −0.685365 0.353515i
757757 11.8137 + 4.89341i 0.429378 + 0.177854i 0.586897 0.809662i 0.300349π-0.300349\pi
−0.157519 + 0.987516i 0.550349π0.550349\pi
758758 −6.95967 + 6.40144i −0.252787 + 0.232511i
759759 −16.9335 + 16.9335i −0.614647 + 0.614647i
760760 −0.222871 0.813419i −0.00808440 0.0295058i
761761 −9.86724 9.86724i −0.357687 0.357687i 0.505273 0.862960i 0.331392π-0.331392\pi
−0.862960 + 0.505273i 0.831392π0.831392\pi
762762 −18.9164 0.790336i −0.685267 0.0286309i
763763 −9.45735 + 22.8321i −0.342379 + 0.826576i
764764 −3.48868 4.12610i −0.126216 0.149277i
765765 0.0539369 0.0223414i 0.00195009 0.000807755i
766766 26.2638 + 12.1870i 0.948948 + 0.440335i
767767 −2.97207 −0.107315
768768 22.4081 1.31572i 0.808583 0.0474768i
769769 −3.19833 −0.115335 −0.0576673 0.998336i 0.518366π-0.518366\pi
−0.0576673 + 0.998336i 0.518366π0.518366\pi
770770 −0.208221 0.0966197i −0.00750377 0.00348193i
771771 22.6083 9.36466i 0.814218 0.337260i
772772 −32.6953 38.6690i −1.17673 1.39173i
773773 −15.2248 + 36.7559i −0.547597 + 1.32202i 0.371663 + 0.928368i 0.378788π0.378788\pi
−0.919261 + 0.393650i 0.871212π0.871212\pi
774774 −8.60628 0.359575i −0.309346 0.0129247i
775775 −37.3487 37.3487i −1.34161 1.34161i
776776 −5.51908 20.1431i −0.198124 0.723096i
777777 19.2302 19.2302i 0.689881 0.689881i
778778 −16.3830 + 15.0689i −0.587359 + 0.540247i
779779 −7.68414 3.18287i −0.275313 0.114038i
780780 −0.105250 0.0542884i −0.00376855 0.00194384i
781781 12.5449 + 30.2860i 0.448891 + 1.08372i
782782 −5.42235 14.8112i −0.193903 0.529648i
783783 28.0379i 1.00199i
784784 13.7535 + 2.31878i 0.491196 + 0.0828136i
785785 0.525991i 0.0187734i
786786 −40.5281 + 14.8372i −1.44559 + 0.529227i
787787 −14.9254 36.0330i −0.532031 1.28444i −0.930176 0.367114i 0.880346π-0.880346\pi
0.398145 0.917323i 0.369654π-0.369654\pi
788788 38.6174 12.3356i 1.37569 0.439437i
789789 −7.80196 3.23168i −0.277757 0.115051i
790790 0.330847 + 0.359698i 0.0117710 + 0.0127975i
791791 2.28364 2.28364i 0.0811969 0.0811969i
792792 3.67188 + 4.72990i 0.130474 + 0.168070i
793793 1.44706 + 1.44706i 0.0513868 + 0.0513868i
794794 −0.216911 + 5.19167i −0.00769788 + 0.184245i
795795 −0.0302091 + 0.0729311i −0.00107140 + 0.00258660i
796796 −1.32486 + 15.8273i −0.0469584 + 0.560984i
797797 −38.2905 + 15.8605i −1.35632 + 0.561806i −0.938045 0.346514i 0.887365π-0.887365\pi
−0.418275 + 0.908320i 0.637365π0.637365\pi
798798 −11.0584 + 23.8315i −0.391463 + 0.843626i
799799 13.1799 0.466273
800800 27.7973 5.17086i 0.982784 0.182817i
801801 −11.6750 −0.412514
802802 8.47398 18.2619i 0.299226 0.644850i
803803 −21.8369 + 9.04513i −0.770606 + 0.319196i
804804 −21.0614 1.76299i −0.742779 0.0621760i
805805 0.251869 0.608065i 0.00887721 0.0214315i
806806 0.623858 14.9318i 0.0219745 0.525950i
807807 11.3450 + 11.3450i 0.399362 + 0.399362i
808808 −4.25555 0.535894i −0.149710 0.0188527i
809809 24.6419 24.6419i 0.866364 0.866364i −0.125704 0.992068i 0.540119π-0.540119\pi
0.992068 + 0.125704i 0.0401189π0.0401189\pi
810810 0.195572 + 0.212627i 0.00687171 + 0.00747095i
811811 26.0479 + 10.7894i 0.914665 + 0.378867i 0.789841 0.613312i 0.210163π-0.210163\pi
0.124825 + 0.992179i 0.460163π0.460163\pi
812812 −5.65414 17.7007i −0.198422 0.621172i
813813 7.75976 + 18.7337i 0.272147 + 0.657020i
814814 −28.1805 + 10.3168i −0.987728 + 0.361604i
815815 0.822122i 0.0287977i
816816 7.33198 1.68331i 0.256671 0.0589277i
817817 41.7042i 1.45904i
818818 −10.0991 27.5859i −0.353108 0.964518i
819819 −0.740096 1.78675i −0.0258611 0.0624341i
820820 −0.0455565 + 0.0883212i −0.00159090 + 0.00308431i
821821 8.22241 + 3.40583i 0.286964 + 0.118864i 0.521522 0.853238i 0.325364π-0.325364\pi
−0.234558 + 0.972102i 0.575364π0.575364\pi
822822 −24.6836 + 22.7037i −0.860940 + 0.791884i
823823 −0.137427 + 0.137427i −0.00479042 + 0.00479042i −0.709498 0.704708i 0.751078π-0.751078\pi
0.704708 + 0.709498i 0.251078π0.251078\pi
824824 5.26736 9.24314i 0.183497 0.322000i
825825 −10.1732 10.1732i −0.354185 0.354185i
826826 7.87120 + 0.328863i 0.273874 + 0.0114426i
827827 −11.9383 + 28.8217i −0.415137 + 1.00223i 0.568600 + 0.822614i 0.307485π0.307485\pi
−0.983737 + 0.179615i 0.942515π0.942515\pi
828828 −13.1105 + 11.0851i −0.455620 + 0.385235i
829829 13.6250 5.64365i 0.473215 0.196012i −0.133313 0.991074i 0.542562π-0.542562\pi
0.606528 + 0.795062i 0.292562π0.292562\pi
830830 −0.413237 0.191752i −0.0143437 0.00665581i
831831 −21.2072 −0.735671
832832 6.40127 + 4.79831i 0.221924 + 0.166351i
833833 4.67436 0.161957
834834 −12.4043 5.75589i −0.429525 0.199310i
835835 −0.117352 + 0.0486086i −0.00406112 + 0.00168217i
836836 22.1380 18.7181i 0.765659 0.647378i
837837 −22.8743 + 55.2235i −0.790653 + 1.90880i
838838 25.5649 + 1.06812i 0.883124 + 0.0368974i
839839 21.1436 + 21.1436i 0.729959 + 0.729959i 0.970611 0.240652i 0.0773612π-0.0773612\pi
−0.240652 + 0.970611i 0.577361π0.577361\pi
840840 0.272735 + 0.155423i 0.00941026 + 0.00536259i
841841 −3.13170 + 3.13170i −0.107990 + 0.107990i
842842 −4.92409 + 4.52913i −0.169695 + 0.156084i
843843 −2.29166 0.949235i −0.0789288 0.0326934i
844844 −1.39851 + 2.71132i −0.0481388 + 0.0933275i
845845 −0.0161519 0.0389942i −0.000555643 0.00134144i
846846 −4.93211 13.4721i −0.169570 0.463182i
847847 12.7273i 0.437315i
848848 2.83136 4.51886i 0.0972294 0.155178i
849849 7.54355i 0.258894i
850850 8.89819 3.25760i 0.305205 0.111735i
851851 −32.9280 79.4953i −1.12876 2.72506i
852852 −13.6409 42.7038i −0.467330 1.46301i
853853 31.2010 + 12.9239i 1.06830 + 0.442505i 0.846391 0.532561i 0.178770π-0.178770\pi
0.221911 + 0.975067i 0.428770π0.428770\pi
854854 −3.67227 3.99251i −0.125662 0.136621i
855855 −0.217559 + 0.217559i −0.00744034 + 0.00744034i
856856 −0.754002 + 5.98756i −0.0257713 + 0.204650i
857857 1.19804 + 1.19804i 0.0409243 + 0.0409243i 0.727273 0.686349i 0.240788π-0.240788\pi
−0.686349 + 0.727273i 0.740788π0.740788\pi
858858 0.169929 4.06718i 0.00580129 0.138851i
859859 −16.1774 + 39.0557i −0.551966 + 1.33256i 0.364034 + 0.931386i 0.381399π0.381399\pi
−0.916000 + 0.401179i 0.868601π0.868601\pi
860860 0.496563 + 0.0415660i 0.0169327 + 0.00141739i
861861 2.86003 1.18466i 0.0974694 0.0403731i
862862 12.6501 27.2617i 0.430864 0.928536i
863863 24.0375 0.818245 0.409122 0.912479i 0.365835π-0.365835\pi
0.409122 + 0.912479i 0.365835π0.365835\pi
864864 −17.4444 26.8234i −0.593472 0.912551i
865865 0.459424 0.0156209
866866 6.60299 14.2298i 0.224379 0.483549i
867867 −19.7049 + 8.16205i −0.669215 + 0.277198i
868868 −3.30444 + 39.4761i −0.112160 + 1.33991i
869869 −6.42866 + 15.5202i −0.218077 + 0.526485i
870870 −0.0173277 + 0.414731i −0.000587464 + 0.0140607i
871871 −5.32631 5.32631i −0.180475 0.180475i
872872 −29.4583 + 22.8689i −0.997586 + 0.774438i
873873 −5.38752 + 5.38752i −0.182340 + 0.182340i
874874 56.2723 + 61.1795i 1.90344 + 2.06943i
875875 0.730749 + 0.302686i 0.0247038 + 0.0102327i
876876 30.7904 9.83540i 1.04031 0.332307i
877877 19.4012 + 46.8387i 0.655133 + 1.58163i 0.805232 + 0.592959i 0.202040π0.202040\pi
−0.150100 + 0.988671i 0.547960π0.547960\pi
878878 35.1064 12.8523i 1.18478 0.433746i
879879 29.2878i 0.987854i
880880 −0.200808 0.282249i −0.00676923 0.00951461i
881881 34.4908i 1.16203i −0.813895 0.581013i 0.802657π-0.802657\pi
0.813895 0.581013i 0.197343π-0.197343\pi
882882 −1.74921 4.77799i −0.0588989 0.160883i
883883 0.745661 + 1.80019i 0.0250935 + 0.0605811i 0.935930 0.352187i 0.114562π-0.114562\pi
−0.910836 + 0.412768i 0.864562π0.864562\pi
884884 2.38280 + 1.22906i 0.0801421 + 0.0413377i
885885 −0.162589 0.0673467i −0.00546538 0.00226383i
886886 10.2535 9.43107i 0.344473 0.316843i
887887 −2.41435 + 2.41435i −0.0810658 + 0.0810658i −0.746477 0.665411i 0.768256π-0.768256\pi
0.665411 + 0.746477i 0.268256π0.268256\pi
888888 39.5804 10.8448i 1.32823 0.363927i
889889 12.6473 + 12.6473i 0.424178 + 0.424178i
890890 0.674797 + 0.0281934i 0.0226192 + 0.000945045i
891891 −3.80015 + 9.17437i −0.127310 + 0.307353i
892892 11.4157 + 13.5014i 0.382225 + 0.452060i
893893 −64.1725 + 26.5811i −2.14745 + 0.889504i
894894 2.06241 + 0.957011i 0.0689774 + 0.0320072i
895895 −0.329618 −0.0110179
896896 −16.4221 13.4161i −0.548624 0.448200i
897897 11.6718 0.389710
898898 24.9942 + 11.5979i 0.834069 + 0.387028i
899899 −48.3953 + 20.0460i −1.61407 + 0.668571i
900900 −6.65965 7.87642i −0.221988 0.262547i
901901 0.683916 1.65112i 0.0227845 0.0550068i
902902 −3.41301 0.142597i −0.113641 0.00474797i
903903 −10.9759 10.9759i −0.365254 0.365254i
904904 4.70028 1.28785i 0.156329 0.0428331i
905905 −0.527545 + 0.527545i −0.0175362 + 0.0175362i
906906 28.3003 26.0303i 0.940214 0.864799i
907907 25.2022 + 10.4391i 0.836826 + 0.346625i 0.759601 0.650389i 0.225394π-0.225394\pi
0.0772250 + 0.997014i 0.475394π0.475394\pi
908908 35.2992 + 18.2075i 1.17144 + 0.604237i
909909 0.598783 + 1.44559i 0.0198604 + 0.0479472i
910910 0.0384618 + 0.105059i 0.00127500 + 0.00348267i
911911 56.7297i 1.87954i 0.341810 + 0.939769i 0.388960π0.388960\pi
−0.341810 + 0.939769i 0.611040π0.611040\pi
912912 −32.3042 + 22.9830i −1.06970 + 0.761044i
913913 15.6592i 0.518243i
914914 −43.1528 + 15.7981i −1.42737 + 0.522555i
915915 0.0463724 + 0.111953i 0.00153303 + 0.00370105i
916916 −23.7803 + 7.59616i −0.785724 + 0.250984i
917917 37.6688 + 15.6029i 1.24393 + 0.515254i
918918 −7.25944 7.89249i −0.239597 0.260491i
919919 18.1268 18.1268i 0.597948 0.597948i −0.341818 0.939766i 0.611043π-0.611043\pi
0.939766 + 0.341818i 0.111043π0.111043\pi
920920 0.784537 0.609046i 0.0258654 0.0200796i
921921 −11.8107 11.8107i −0.389175 0.389175i
922922 −1.17559 + 28.1372i −0.0387159 + 0.926648i
923923 6.11423 14.7611i 0.201252 0.485866i
924924 −0.900077 + 10.7527i −0.0296104 + 0.353737i
925925 47.7587 19.7823i 1.57029 0.650437i
926926 −6.69299 + 14.4238i −0.219945 + 0.473995i
927927 −3.88100 −0.127469
928928 5.81192 27.4317i 0.190786 0.900489i
929929 −23.9790 −0.786726 −0.393363 0.919383i 0.628688π-0.628688\pi
−0.393363 + 0.919383i 0.628688π0.628688\pi
930930 0.372481 0.802717i 0.0122141 0.0263221i
931931 −22.7592 + 9.42718i −0.745904 + 0.308963i
932932 17.2073 + 1.44038i 0.563645 + 0.0471812i
933933 −13.4849 + 32.5555i −0.441477 + 1.06582i
934934 1.88686 45.1611i 0.0617399 1.47772i
935935 −0.0820876 0.0820876i −0.00268455 0.00268455i
936936 0.364632 2.89555i 0.0119184 0.0946441i
937937 6.41304 6.41304i 0.209505 0.209505i −0.594552 0.804057i 0.702671π-0.702671\pi
0.804057 + 0.594552i 0.202671π0.202671\pi
938938 13.5168 + 14.6955i 0.441338 + 0.479825i
939939 31.5645 + 13.0744i 1.03007 + 0.426668i
940940 0.252536 + 0.790583i 0.00823683 + 0.0257860i
941941 −10.5045 25.3602i −0.342439 0.826720i −0.997468 0.0711164i 0.977344π-0.977344\pi
0.655029 0.755603i 0.272656π-0.272656\pi
942942 23.2183 8.50014i 0.756492 0.276950i
943943 9.79447i 0.318952i
944944 10.0741 + 6.31211i 0.327885 + 0.205442i
945945 0.447470i 0.0145562i
946946 5.88844 + 16.0844i 0.191450 + 0.522948i
947947 −0.374193 0.903381i −0.0121596 0.0293559i 0.917683 0.397313i 0.130057π-0.130057\pi
−0.929843 + 0.367957i 0.880057π0.880057\pi
948948 10.5312 20.4170i 0.342038 0.663114i
949949 10.6430 + 4.40849i 0.345488 + 0.143106i
950950 −36.7550 + 33.8069i −1.19249 + 1.09684i
951951 −21.8910 + 21.8910i −0.709865 + 0.709865i
952952 −6.17457 3.51868i −0.200119 0.114041i
953953 40.0557 + 40.0557i 1.29753 + 1.29753i 0.930018 + 0.367513i 0.119791π0.119791\pi
0.367513 + 0.930018i 0.380209π0.380209\pi
954954 −1.94366 0.0812070i −0.0629282 0.00262918i
955955 0.0436368 0.105349i 0.00141205 0.00340900i
956956 −2.71620 + 2.29660i −0.0878483 + 0.0742772i
957957 −13.1821 + 5.46021i −0.426117 + 0.176504i
958958 21.4179 + 9.93844i 0.691981 + 0.321096i
959959 31.6828 1.02309
960960 0.241457 + 0.407547i 0.00779299 + 0.0131535i
961961 80.6736 2.60238
962962 13.2676 + 6.15648i 0.427764 + 0.198493i
963963 2.03395 0.842488i 0.0655430 0.0271488i
964964 22.4096 18.9477i 0.721766 0.610265i
965965 0.408956 0.987307i 0.0131648 0.0317825i
966966 −30.9114 1.29150i −0.994559 0.0415533i
967967 −19.4546 19.4546i −0.625619 0.625619i 0.321344 0.946963i 0.395865π-0.395865\pi
−0.946963 + 0.321344i 0.895865π0.895865\pi
968968 −9.50915 + 16.6866i −0.305636 + 0.536328i
969969 −9.39516 + 9.39516i −0.301816 + 0.301816i
970970 0.324402 0.298381i 0.0104159 0.00958045i
971971 −24.3758 10.0968i −0.782256 0.324021i −0.0444307 0.999012i 0.514147π-0.514147\pi
−0.737826 + 0.674991i 0.764147π0.764147\pi
972972 −9.33239 + 18.0928i −0.299336 + 0.580328i
973973 4.94372 + 11.9352i 0.158488 + 0.382625i
974974 9.04671 + 24.7112i 0.289875 + 0.791799i
975975 7.01210i 0.224567i
976976 −1.83169 7.97827i −0.0586309 0.255378i
977977 33.9648i 1.08663i 0.839529 + 0.543315i 0.182831π0.182831\pi
−0.839529 + 0.543315i 0.817169π0.817169\pi
978978 −36.2900 + 13.2857i −1.16043 + 0.424829i
979979 8.88416 + 21.4483i 0.283939 + 0.685489i
980980 0.0895638 + 0.280386i 0.00286101 + 0.00895659i
981981 12.5691 + 5.20627i 0.401299 + 0.166223i
982982 −22.6196 24.5921i −0.721820 0.784767i
983983 28.9047 28.9047i 0.921918 0.921918i −0.0752469 0.997165i 0.523974π-0.523974\pi
0.997165 + 0.0752469i 0.0239745π0.0239745\pi
984984 4.63487 + 0.583661i 0.147754 + 0.0186064i
985985 0.604951 + 0.604951i 0.0192754 + 0.0192754i
986986 0.392289 9.38927i 0.0124930 0.299015i
987987 9.89346 23.8849i 0.314912 0.760266i
988988 −14.0805 1.17864i −0.447959 0.0374975i
989989 −45.3729 + 18.7941i −1.44277 + 0.597616i
990990 −0.0531892 + 0.114626i −0.00169046 + 0.00364305i
991991 2.13976 0.0679716 0.0339858 0.999422i 0.489180π-0.489180\pi
0.0339858 + 0.999422i 0.489180π0.489180\pi
992992 −33.8269 + 49.2879i −1.07401 + 1.56489i
993993 −18.7705 −0.595664
994994 −17.8262 + 38.4165i −0.565412 + 1.21850i
995995 −0.309666 + 0.128268i −0.00981706 + 0.00406636i
996996 −1.78630 + 21.3398i −0.0566010 + 0.676178i
997997 18.2315 44.0146i 0.577396 1.39396i −0.317746 0.948176i 0.602926π-0.602926\pi
0.895142 0.445781i 0.147074π-0.147074\pi
998998 0.386705 9.25562i 0.0122409 0.292982i
999999 −41.3657 41.3657i −1.30875 1.30875i
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 416.2.bf.a.53.7 192
32.29 even 8 inner 416.2.bf.a.157.7 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.bf.a.53.7 192 1.1 even 1 trivial
416.2.bf.a.157.7 yes 192 32.29 even 8 inner