Properties

Label 560.2.cp.a.221.11
Level 560560
Weight 22
Character 560.221
Analytic conductor 4.4724.472
Analytic rank 00
Dimension 256256
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [560,2,Mod(221,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 8])) 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("560.221"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 560=2457 560 = 2^{4} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 560.cp (of order 1212, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.471622513194.47162251319
Analytic rank: 00
Dimension: 256256
Relative dimension: 6464 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 221.11
Character χ\chi == 560.221
Dual form 560.2.cp.a.261.11

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+(1.19222+0.760664i)q2+(0.450503+0.120712i)q3+(0.8427821.81376i)q4+(0.965926+0.258819i)q5+(0.4452780.486597i)q6+(2.07294+1.64406i)q7+(0.374878+2.80347i)q8+(2.40969+1.39124i)q9+(1.34847+0.426175i)q10+(0.3232441.20636i)q11+(0.160734+0.918838i)q12+(1.23263+1.23263i)q13+(3.721980.383271i)q140.466395q15+(2.579443.05720i)q16+(1.559772.70159i)q17+(1.814623.49163i)q18+(1.58134+5.90166i)q19+(1.283501.53383i)q20+(1.132320.490425i)q21+(1.30302+1.19237i)q22+(3.663162.11493i)q23+(0.5072971.21772i)q24+(0.866025+0.500000i)q25+(2.407190.531952i)q26+(1.907011.90701i)q27+(4.728962.37423i)q28+(3.80964+3.80964i)q29+(0.5560460.354770i)q30+(4.59589+7.96031i)q31+(5.40076+1.68278i)q32+(0.291245+0.504452i)q33+(0.195418+4.40735i)q34+(1.57679+2.12455i)q35+(0.492522+5.54311i)q36+(3.30794+0.886360i)q37+(2.603868.23895i)q38+(0.7040980.406511i)q39+(0.363488+2.80497i)q407.11538iq41+(1.723030.276622i)q42+(7.58075+7.58075i)q43+(2.460480.430415i)q44+(2.68766+0.720158i)q45+(2.75855+5.30790i)q46+(2.11545+3.66407i)q47+(1.53109+1.06591i)q48+(1.59415+6.81606i)q49+(1.41283+0.0626435i)q50+(0.376565+1.40536i)q51+(3.274541.19686i)q52+(0.467566+1.74498i)q53+(0.822984+3.72417i)q541.24892iq55+(3.83197+6.42775i)q562.84960iq57+(7.439791.64408i)q58+(2.20962+8.24641i)q59+(0.393069+0.845928i)q60+(1.072714.00341i)q61+(0.57580512.9864i)q62+(7.282421.07773i)q63+(7.71893+2.10192i)q64+(0.871603+1.50966i)q65+(0.7309470.379878i)q66+(7.21849+1.93419i)q67+(3.585495.10589i)q68+(1.39497+1.39497i)q69+(3.495951.33353i)q70+2.26299iq71+(4.803646.23397i)q72+(2.83312+1.63570i)q73+(4.61802+1.45949i)q74+(0.4505030.120712i)q75+(9.37145+7.84198i)q76+(1.313273.03215i)q77+(1.148660.0509306i)q78+(0.6276781.08717i)q79+(1.700283.62064i)q80+(3.544806.13977i)q81+(5.41241+8.48310i)q82+(3.33449+3.33449i)q83+(1.84381+1.64044i)q84+(2.205842.20584i)q85+(3.2715314.8043i)q86+(2.176121.25639i)q87+(3.260831.35845i)q88+(2.259621.30459i)q89+(2.656492.90300i)q90+(0.528653+4.58169i)q91+(0.7487218.42651i)q92+(1.109564.14092i)q93+(5.309212.75923i)q94+(3.05492+5.29128i)q95+(2.636190.106161i)q96+8.90510q97+(7.085316.91364i)q98+(2.45726+2.45726i)q99+O(q100)q+(-1.19222 + 0.760664i) q^{2} +(-0.450503 + 0.120712i) q^{3} +(0.842782 - 1.81376i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.445278 - 0.486597i) q^{6} +(2.07294 + 1.64406i) q^{7} +(0.374878 + 2.80347i) q^{8} +(-2.40969 + 1.39124i) q^{9} +(-1.34847 + 0.426175i) q^{10} +(-0.323244 - 1.20636i) q^{11} +(-0.160734 + 0.918838i) q^{12} +(1.23263 + 1.23263i) q^{13} +(-3.72198 - 0.383271i) q^{14} -0.466395 q^{15} +(-2.57944 - 3.05720i) q^{16} +(1.55977 - 2.70159i) q^{17} +(1.81462 - 3.49163i) q^{18} +(-1.58134 + 5.90166i) q^{19} +(1.28350 - 1.53383i) q^{20} +(-1.13232 - 0.490425i) q^{21} +(1.30302 + 1.19237i) q^{22} +(3.66316 - 2.11493i) q^{23} +(-0.507297 - 1.21772i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.40719 - 0.531952i) q^{26} +(1.90701 - 1.90701i) q^{27} +(4.72896 - 2.37423i) q^{28} +(3.80964 + 3.80964i) q^{29} +(0.556046 - 0.354770i) q^{30} +(-4.59589 + 7.96031i) q^{31} +(5.40076 + 1.68278i) q^{32} +(0.291245 + 0.504452i) q^{33} +(0.195418 + 4.40735i) q^{34} +(1.57679 + 2.12455i) q^{35} +(0.492522 + 5.54311i) q^{36} +(3.30794 + 0.886360i) q^{37} +(-2.60386 - 8.23895i) q^{38} +(-0.704098 - 0.406511i) q^{39} +(-0.363488 + 2.80497i) q^{40} -7.11538i q^{41} +(1.72303 - 0.276622i) q^{42} +(-7.58075 + 7.58075i) q^{43} +(-2.46048 - 0.430415i) q^{44} +(-2.68766 + 0.720158i) q^{45} +(-2.75855 + 5.30790i) q^{46} +(2.11545 + 3.66407i) q^{47} +(1.53109 + 1.06591i) q^{48} +(1.59415 + 6.81606i) q^{49} +(-1.41283 + 0.0626435i) q^{50} +(-0.376565 + 1.40536i) q^{51} +(3.27454 - 1.19686i) q^{52} +(0.467566 + 1.74498i) q^{53} +(-0.822984 + 3.72417i) q^{54} -1.24892i q^{55} +(-3.83197 + 6.42775i) q^{56} -2.84960i q^{57} +(-7.43979 - 1.64408i) q^{58} +(2.20962 + 8.24641i) q^{59} +(-0.393069 + 0.845928i) q^{60} +(1.07271 - 4.00341i) q^{61} +(-0.575805 - 12.9864i) q^{62} +(-7.28242 - 1.07773i) q^{63} +(-7.71893 + 2.10192i) q^{64} +(0.871603 + 1.50966i) q^{65} +(-0.730947 - 0.379878i) q^{66} +(-7.21849 + 1.93419i) q^{67} +(-3.58549 - 5.10589i) q^{68} +(-1.39497 + 1.39497i) q^{69} +(-3.49595 - 1.33353i) q^{70} +2.26299i q^{71} +(-4.80364 - 6.23397i) q^{72} +(2.83312 + 1.63570i) q^{73} +(-4.61802 + 1.45949i) q^{74} +(-0.450503 - 0.120712i) q^{75} +(9.37145 + 7.84198i) q^{76} +(1.31327 - 3.03215i) q^{77} +(1.14866 - 0.0509306i) q^{78} +(-0.627678 - 1.08717i) q^{79} +(-1.70028 - 3.62064i) q^{80} +(3.54480 - 6.13977i) q^{81} +(5.41241 + 8.48310i) q^{82} +(3.33449 + 3.33449i) q^{83} +(-1.84381 + 1.64044i) q^{84} +(2.20584 - 2.20584i) q^{85} +(3.27153 - 14.8043i) q^{86} +(-2.17612 - 1.25639i) q^{87} +(3.26083 - 1.35845i) q^{88} +(2.25962 - 1.30459i) q^{89} +(2.65649 - 2.90300i) q^{90} +(0.528653 + 4.58169i) q^{91} +(-0.748721 - 8.42651i) q^{92} +(1.10956 - 4.14092i) q^{93} +(-5.30921 - 2.75923i) q^{94} +(-3.05492 + 5.29128i) q^{95} +(-2.63619 - 0.106161i) q^{96} +8.90510 q^{97} +(-7.08531 - 6.91364i) q^{98} +(2.45726 + 2.45726i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 256q+4q4+8q11+16q1420q1640q1816q20+56q2240q24+4q2832q2920q32+16q3740q3860q42+16q43+32q4420q46+80q99+O(q100) 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/560Z)×\left(\mathbb{Z}/560\mathbb{Z}\right)^\times.

nn 241241 337337 351351 421421
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11 11 e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.19222 + 0.760664i −0.843028 + 0.537870i
33 −0.450503 + 0.120712i −0.260098 + 0.0696931i −0.386512 0.922285i 0.626320π-0.626320\pi
0.126413 + 0.991978i 0.459653π0.459653\pi
44 0.842782 1.81376i 0.421391 0.906879i
55 0.965926 + 0.258819i 0.431975 + 0.115747i
66 0.445278 0.486597i 0.181784 0.198652i
77 2.07294 + 1.64406i 0.783497 + 0.621395i
88 0.374878 + 2.80347i 0.132539 + 0.991178i
99 −2.40969 + 1.39124i −0.803231 + 0.463746i
1010 −1.34847 + 0.426175i −0.426424 + 0.134768i
1111 −0.323244 1.20636i −0.0974618 0.363732i 0.899919 0.436056i 0.143625π-0.143625\pi
−0.997381 + 0.0723238i 0.976958π0.976958\pi
1212 −0.160734 + 0.918838i −0.0463998 + 0.265246i
1313 1.23263 + 1.23263i 0.341871 + 0.341871i 0.857070 0.515200i 0.172282π-0.172282\pi
−0.515200 + 0.857070i 0.672282π0.672282\pi
1414 −3.72198 0.383271i −0.994740 0.102433i
1515 −0.466395 −0.120423
1616 −2.57944 3.05720i −0.644859 0.764301i
1717 1.55977 2.70159i 0.378299 0.655233i −0.612516 0.790458i 0.709843π-0.709843\pi
0.990815 + 0.135226i 0.0431759π0.0431759\pi
1818 1.81462 3.49163i 0.427711 0.822985i
1919 −1.58134 + 5.90166i −0.362785 + 1.35393i 0.507613 + 0.861585i 0.330528π0.330528\pi
−0.870399 + 0.492348i 0.836139π0.836139\pi
2020 1.28350 1.53383i 0.286999 0.342974i
2121 −1.13232 0.490425i −0.247093 0.107019i
2222 1.30302 + 1.19237i 0.277804 + 0.254215i
2323 3.66316 2.11493i 0.763822 0.440993i −0.0668442 0.997763i 0.521293π-0.521293\pi
0.830666 + 0.556770i 0.187960π0.187960\pi
2424 −0.507297 1.21772i −0.103551 0.248566i
2525 0.866025 + 0.500000i 0.173205 + 0.100000i
2626 −2.40719 0.531952i −0.472089 0.104324i
2727 1.90701 1.90701i 0.367004 0.367004i
2828 4.72896 2.37423i 0.893689 0.448687i
2929 3.80964 + 3.80964i 0.707432 + 0.707432i 0.965995 0.258562i 0.0832488π-0.0832488\pi
−0.258562 + 0.965995i 0.583249π0.583249\pi
3030 0.556046 0.354770i 0.101520 0.0647718i
3131 −4.59589 + 7.96031i −0.825445 + 1.42971i 0.0761330 + 0.997098i 0.475743π0.475743\pi
−0.901578 + 0.432616i 0.857591π0.857591\pi
3232 5.40076 + 1.68278i 0.954729 + 0.297476i
3333 0.291245 + 0.504452i 0.0506993 + 0.0878137i
3434 0.195418 + 4.40735i 0.0335140 + 0.755855i
3535 1.57679 + 2.12455i 0.266526 + 0.359115i
3636 0.492522 + 5.54311i 0.0820871 + 0.923852i
3737 3.30794 + 0.886360i 0.543822 + 0.145717i 0.520264 0.854006i 0.325834π-0.325834\pi
0.0235587 + 0.999722i 0.492500π0.492500\pi
3838 −2.60386 8.23895i −0.422402 1.33653i
3939 −0.704098 0.406511i −0.112746 0.0650939i
4040 −0.363488 + 2.80497i −0.0574726 + 0.443505i
4141 7.11538i 1.11123i −0.831438 0.555617i 0.812482π-0.812482\pi
0.831438 0.555617i 0.187518π-0.187518\pi
4242 1.72303 0.276622i 0.265869 0.0426838i
4343 −7.58075 + 7.58075i −1.15605 + 1.15605i −0.170738 + 0.985317i 0.554615π0.554615\pi
−0.985317 + 0.170738i 0.945385π0.945385\pi
4444 −2.46048 0.430415i −0.370931 0.0648875i
4545 −2.68766 + 0.720158i −0.400653 + 0.107355i
4646 −2.75855 + 5.30790i −0.406726 + 0.782607i
4747 2.11545 + 3.66407i 0.308570 + 0.534459i 0.978050 0.208371i 0.0668162π-0.0668162\pi
−0.669480 + 0.742830i 0.733483π0.733483\pi
4848 1.53109 + 1.06591i 0.220993 + 0.153851i
4949 1.59415 + 6.81606i 0.227736 + 0.973723i
5050 −1.41283 + 0.0626435i −0.199804 + 0.00885913i
5151 −0.376565 + 1.40536i −0.0527296 + 0.196790i
5252 3.27454 1.19686i 0.454097 0.165974i
5353 0.467566 + 1.74498i 0.0642251 + 0.239691i 0.990575 0.136973i 0.0437375π-0.0437375\pi
−0.926350 + 0.376665i 0.877071π0.877071\pi
5454 −0.822984 + 3.72417i −0.111994 + 0.506795i
5555 1.24892i 0.168404i
5656 −3.83197 + 6.42775i −0.512069 + 0.858944i
5757 2.84960i 0.377439i
5858 −7.43979 1.64408i −0.976892 0.215878i
5959 2.20962 + 8.24641i 0.287668 + 1.07359i 0.946868 + 0.321623i 0.104229π0.104229\pi
−0.659200 + 0.751968i 0.729105π0.729105\pi
6060 −0.393069 + 0.845928i −0.0507451 + 0.109209i
6161 1.07271 4.00341i 0.137346 0.512584i −0.862631 0.505834i 0.831185π-0.831185\pi
0.999977 0.00674971i 0.00214852π-0.00214852\pi
6262 −0.575805 12.9864i −0.0731273 1.64927i
6363 −7.28242 1.07773i −0.917499 0.135781i
6464 −7.71893 + 2.10192i −0.964867 + 0.262740i
6565 0.871603 + 1.50966i 0.108109 + 0.187250i
6666 −0.730947 0.379878i −0.0899733 0.0467598i
6767 −7.21849 + 1.93419i −0.881879 + 0.236299i −0.671218 0.741260i 0.734228π-0.734228\pi
−0.210661 + 0.977559i 0.567562π0.567562\pi
6868 −3.58549 5.10589i −0.434805 0.619180i
6969 −1.39497 + 1.39497i −0.167935 + 0.167935i
7070 −3.49595 1.33353i −0.417847 0.159387i
7171 2.26299i 0.268567i 0.990943 + 0.134284i 0.0428733π0.0428733\pi
−0.990943 + 0.134284i 0.957127π0.957127\pi
7272 −4.80364 6.23397i −0.566114 0.734681i
7373 2.83312 + 1.63570i 0.331592 + 0.191445i 0.656548 0.754285i 0.272016π-0.272016\pi
−0.324956 + 0.945729i 0.605349π0.605349\pi
7474 −4.61802 + 1.45949i −0.536834 + 0.169663i
7575 −0.450503 0.120712i −0.0520196 0.0139386i
7676 9.37145 + 7.84198i 1.07498 + 0.899537i
7777 1.31327 3.03215i 0.149661 0.345546i
7878 1.14866 0.0509306i 0.130060 0.00576676i
7979 −0.627678 1.08717i −0.0706193 0.122316i 0.828554 0.559910i 0.189164π-0.189164\pi
−0.899173 + 0.437594i 0.855831π0.855831\pi
8080 −1.70028 3.62064i −0.190097 0.404800i
8181 3.54480 6.13977i 0.393866 0.682197i
8282 5.41241 + 8.48310i 0.597700 + 0.936802i
8383 3.33449 + 3.33449i 0.366008 + 0.366008i 0.866019 0.500011i 0.166671π-0.166671\pi
−0.500011 + 0.866019i 0.666671π0.666671\pi
8484 −1.84381 + 1.64044i −0.201177 + 0.178987i
8585 2.20584 2.20584i 0.239257 0.239257i
8686 3.27153 14.8043i 0.352778 1.59639i
8787 −2.17612 1.25639i −0.233305 0.134699i
8888 3.26083 1.35845i 0.347606 0.144811i
8989 2.25962 1.30459i 0.239519 0.138286i −0.375437 0.926848i 0.622507π-0.622507\pi
0.614956 + 0.788562i 0.289174π0.289174\pi
9090 2.65649 2.90300i 0.280019 0.306003i
9191 0.528653 + 4.58169i 0.0554179 + 0.480292i
9292 −0.748721 8.42651i −0.0780596 0.878525i
9393 1.10956 4.14092i 0.115056 0.429394i
9494 −5.30921 2.75923i −0.547603 0.284593i
9595 −3.05492 + 5.29128i −0.313428 + 0.542874i
9696 −2.63619 0.106161i −0.269055 0.0108350i
9797 8.90510 0.904176 0.452088 0.891973i 0.350679π-0.350679\pi
0.452088 + 0.891973i 0.350679π0.350679\pi
9898 −7.08531 6.91364i −0.715724 0.698383i
9999 2.45726 + 2.45726i 0.246964 + 0.246964i
100100 1.63675 1.14937i 0.163675 0.114937i
101101 −2.89317 10.7975i −0.287881 1.07439i −0.946708 0.322093i 0.895614π-0.895614\pi
0.658827 0.752295i 0.271053π-0.271053\pi
102102 −0.620057 1.96194i −0.0613948 0.194261i
103103 12.2408 7.06723i 1.20612 0.696355i 0.244212 0.969722i 0.421471π-0.421471\pi
0.961910 + 0.273367i 0.0881373π0.0881373\pi
104104 −2.99357 + 3.91774i −0.293543 + 0.384166i
105105 −0.966809 0.766781i −0.0943509 0.0748301i
106106 −1.88478 1.72474i −0.183066 0.167522i
107107 3.38837 + 0.907910i 0.327566 + 0.0877710i 0.418854 0.908054i 0.362432π-0.362432\pi
−0.0912884 + 0.995824i 0.529099π0.529099\pi
108108 −1.85166 5.06605i −0.178176 0.487481i
109109 −18.8170 + 5.04200i −1.80234 + 0.482936i −0.994340 0.106245i 0.966117π-0.966117\pi
−0.808001 + 0.589181i 0.799451π0.799451\pi
110110 0.950008 + 1.48899i 0.0905797 + 0.141970i
111111 −1.59723 −0.151603
112112 −0.320796 10.5781i −0.0303124 0.999540i
113113 15.1657 1.42667 0.713334 0.700825i 0.247184π-0.247184\pi
0.713334 + 0.700825i 0.247184π0.247184\pi
114114 2.16759 + 3.39736i 0.203013 + 0.318192i
115115 4.08573 1.09477i 0.380996 0.102088i
116116 10.1205 3.69907i 0.939661 0.343450i
117117 −4.68515 1.25538i −0.433142 0.116060i
118118 −8.90710 8.15077i −0.819965 0.750339i
119119 7.67487 3.03589i 0.703554 0.278300i
120120 −0.174841 1.30753i −0.0159607 0.119360i
121121 8.17545 4.72010i 0.743223 0.429100i
122122 1.76634 + 5.58892i 0.159917 + 0.505997i
123123 0.858911 + 3.20550i 0.0774454 + 0.289030i
124124 10.5647 + 15.0446i 0.948742 + 1.35105i
125125 0.707107 + 0.707107i 0.0632456 + 0.0632456i
126126 9.50204 4.25459i 0.846509 0.379029i
127127 3.18169 0.282329 0.141164 0.989986i 0.454915π-0.454915\pi
0.141164 + 0.989986i 0.454915π0.454915\pi
128128 7.60382 8.37746i 0.672089 0.740470i
129129 2.50007 4.33024i 0.220119 0.381257i
130130 −2.18749 1.13685i −0.191855 0.0997085i
131131 1.23059 4.59262i 0.107517 0.401259i −0.891101 0.453804i 0.850067π-0.850067\pi
0.998619 + 0.0525447i 0.0167332π0.0167332\pi
132132 1.16041 0.103106i 0.101001 0.00897421i
133133 −12.9807 + 9.63395i −1.12557 + 0.835369i
134134 7.13477 7.79682i 0.616350 0.673543i
135135 2.33560 1.34846i 0.201017 0.116057i
136136 8.15857 + 3.36000i 0.699591 + 0.288117i
137137 −4.24657 2.45176i −0.362809 0.209468i 0.307503 0.951547i 0.400506π-0.400506\pi
−0.670312 + 0.742079i 0.733840π0.733840\pi
138138 0.602010 2.72421i 0.0512465 0.231901i
139139 1.05524 1.05524i 0.0895041 0.0895041i −0.660937 0.750441i 0.729841π-0.729841\pi
0.750441 + 0.660937i 0.229841π0.229841\pi
140140 5.18232 1.06938i 0.437986 0.0903794i
141141 −1.39531 1.39531i −0.117507 0.117507i
142142 −1.72137 2.69798i −0.144454 0.226409i
143143 1.08856 1.88544i 0.0910301 0.157669i
144144 10.4690 + 3.77832i 0.872413 + 0.314860i
145145 2.69382 + 4.66584i 0.223710 + 0.387477i
146146 −4.62193 + 0.204933i −0.382514 + 0.0169603i
147147 −1.54095 2.87822i −0.127095 0.237392i
148148 4.39552 5.25280i 0.361309 0.431777i
149149 −21.9082 5.87029i −1.79479 0.480913i −0.801647 0.597797i 0.796043π-0.796043\pi
−0.993146 + 0.116884i 0.962709π0.962709\pi
150150 0.628921 0.198766i 0.0513512 0.0162292i
151151 −12.3743 7.14429i −1.00700 0.581394i −0.0966912 0.995314i 0.530826π-0.530826\pi
−0.910313 + 0.413920i 0.864159π0.864159\pi
152152 −17.1379 2.22086i −1.39007 0.180135i
153153 8.68002i 0.701738i
154154 0.740743 + 4.61395i 0.0596908 + 0.371803i
155155 −6.49956 + 6.49956i −0.522058 + 0.522058i
156156 −1.33071 + 0.934464i −0.106542 + 0.0748170i
157157 6.60385 1.76950i 0.527045 0.141221i 0.0145215 0.999895i 0.495377π-0.495377\pi
0.512523 + 0.858673i 0.328711π0.328711\pi
158158 1.57530 + 0.818695i 0.125324 + 0.0651319i
159159 −0.421280 0.729678i −0.0334097 0.0578672i
160160 4.78120 + 3.02326i 0.377987 + 0.239010i
161161 11.0706 + 1.63833i 0.872484 + 0.129119i
162162 0.444117 + 10.0164i 0.0348931 + 0.786960i
163163 2.27289 8.48255i 0.178027 0.664405i −0.817990 0.575233i 0.804911π-0.804911\pi
0.996016 0.0891716i 0.0284220π-0.0284220\pi
164164 −12.9056 5.99671i −1.00776 0.468264i
165165 0.150760 + 0.562643i 0.0117366 + 0.0438017i
166166 −6.51188 1.43903i −0.505420 0.111690i
167167 24.1332i 1.86749i −0.357944 0.933743i 0.616522π-0.616522\pi
0.357944 0.933743i 0.383478π-0.383478\pi
168168 0.950410 3.35829i 0.0733257 0.259098i
169169 9.96123i 0.766249i
170170 −0.951947 + 4.30775i −0.0730110 + 0.330390i
171171 −4.40005 16.4212i −0.336480 1.25576i
172172 7.36073 + 20.1386i 0.561251 + 1.53555i
173173 3.16981 11.8299i 0.240996 0.899411i −0.734357 0.678763i 0.762516π-0.762516\pi
0.975354 0.220648i 0.0708171π-0.0708171\pi
174174 3.55011 0.157409i 0.269133 0.0119331i
175175 0.973189 + 2.46026i 0.0735662 + 0.185979i
176176 −2.85431 + 4.09997i −0.215152 + 0.309047i
177177 −1.99088 3.44831i −0.149644 0.259191i
178178 −1.70161 + 3.27417i −0.127541 + 0.245409i
179179 −15.7485 + 4.21979i −1.17710 + 0.315402i −0.793774 0.608213i 0.791887π-0.791887\pi
−0.383322 + 0.923615i 0.625220π0.625220\pi
180180 −0.958923 + 5.48171i −0.0714739 + 0.408583i
181181 17.3039 17.3039i 1.28619 1.28619i 0.349108 0.937083i 0.386485π-0.386485\pi
0.937083 0.349108i 0.113515π-0.113515\pi
182182 −4.11540 5.06026i −0.305053 0.375091i
183183 1.93304i 0.142894i
184184 7.30238 + 9.47674i 0.538339 + 0.698635i
185185 2.96582 + 1.71232i 0.218051 + 0.125892i
186186 1.82701 + 5.78090i 0.133963 + 0.423876i
187187 −3.76329 1.00837i −0.275199 0.0737394i
188188 8.42860 0.748906i 0.614719 0.0546196i
189189 7.08835 0.817881i 0.515602 0.0594921i
190190 −0.382742 8.63214i −0.0277670 0.626241i
191191 −12.9895 22.4985i −0.939887 1.62793i −0.765679 0.643223i 0.777597π-0.777597\pi
−0.174208 0.984709i 0.555736π-0.555736\pi
192192 3.22368 1.87869i 0.232649 0.135583i
193193 −0.620168 + 1.07416i −0.0446407 + 0.0773199i −0.887482 0.460842i 0.847548π-0.847548\pi
0.842842 + 0.538162i 0.180881π0.180881\pi
194194 −10.6169 + 6.77379i −0.762246 + 0.486330i
195195 −0.574894 0.574894i −0.0411690 0.0411690i
196196 13.7062 + 2.85305i 0.979015 + 0.203789i
197197 −12.3942 + 12.3942i −0.883049 + 0.883049i −0.993843 0.110794i 0.964660π-0.964660\pi
0.110794 + 0.993843i 0.464660π0.464660\pi
198198 −4.79874 1.06045i −0.341032 0.0753628i
199199 −6.71638 3.87770i −0.476112 0.274883i 0.242683 0.970106i 0.421973π-0.421973\pi
−0.718795 + 0.695222i 0.755306π0.755306\pi
200200 −1.07708 + 2.61532i −0.0761613 + 0.184931i
201201 3.01847 1.74272i 0.212907 0.122922i
202202 11.6625 + 10.6722i 0.820574 + 0.750896i
203203 1.63388 + 14.1604i 0.114676 + 0.993866i
204204 2.23162 + 1.86741i 0.156245 + 0.130745i
205205 1.84159 6.87292i 0.128623 0.480026i
206206 −9.21796 + 17.7368i −0.642245 + 1.23578i
207207 −5.88474 + 10.1927i −0.409017 + 0.708439i
208208 0.588911 6.94791i 0.0408336 0.481751i
209209 7.63071 0.527827
210210 1.73591 + 0.178756i 0.119789 + 0.0123353i
211211 19.0920 + 19.0920i 1.31435 + 1.31435i 0.918178 + 0.396167i 0.129660π0.129660\pi
0.396167 + 0.918178i 0.370340π0.370340\pi
212212 3.55903 + 0.622585i 0.244435 + 0.0427593i
213213 −0.273170 1.01948i −0.0187173 0.0698538i
214214 −4.73030 + 1.49498i −0.323356 + 0.102195i
215215 −9.28449 + 5.36040i −0.633197 + 0.365576i
216216 6.06115 + 4.63136i 0.412409 + 0.315124i
217217 −22.6142 + 8.94533i −1.53515 + 0.607249i
218218 18.5988 20.3246i 1.25967 1.37655i
219219 −1.47378 0.394898i −0.0995889 0.0266848i
220220 −2.26524 1.05257i −0.152722 0.0709641i
221221 5.25269 1.40745i 0.353334 0.0946756i
222222 1.90425 1.21496i 0.127805 0.0815426i
223223 1.35416 0.0906813 0.0453406 0.998972i 0.485563π-0.485563\pi
0.0453406 + 0.998972i 0.485563π0.485563\pi
224224 8.42887 + 12.3675i 0.563177 + 0.826336i
225225 −2.78248 −0.185498
226226 −18.0808 + 11.5360i −1.20272 + 0.767362i
227227 11.3610 3.04417i 0.754057 0.202049i 0.138740 0.990329i 0.455695π-0.455695\pi
0.615317 + 0.788280i 0.289028π0.289028\pi
228228 −5.16849 2.40159i −0.342292 0.159049i
229229 2.42789 + 0.650551i 0.160439 + 0.0429896i 0.338145 0.941094i 0.390201π-0.390201\pi
−0.177705 + 0.984084i 0.556867π0.556867\pi
230230 −4.03834 + 4.41307i −0.266280 + 0.290989i
231231 −0.225614 + 1.52452i −0.0148443 + 0.100306i
232232 −9.25208 + 12.1084i −0.607428 + 0.794954i
233233 −0.780664 + 0.450717i −0.0511430 + 0.0295274i −0.525353 0.850884i 0.676067π-0.676067\pi
0.474210 + 0.880412i 0.342734π0.342734\pi
234234 6.54066 2.06713i 0.427576 0.135133i
235235 1.09504 + 4.08674i 0.0714324 + 0.266589i
236236 16.8192 + 2.94221i 1.09484 + 0.191522i
237237 0.414006 + 0.414006i 0.0268925 + 0.0268925i
238238 −6.84085 + 9.45745i −0.443427 + 0.613036i
239239 −7.01137 −0.453528 −0.226764 0.973950i 0.572815π-0.572815\pi
−0.226764 + 0.973950i 0.572815π0.572815\pi
240240 1.20304 + 1.42587i 0.0776558 + 0.0920393i
241241 0.423683 0.733841i 0.0272918 0.0472708i −0.852057 0.523449i 0.824645π-0.824645\pi
0.879349 + 0.476178i 0.157978π0.157978\pi
242242 −6.15654 + 11.8462i −0.395757 + 0.761501i
243243 −2.94984 + 11.0090i −0.189232 + 0.706225i
244244 −6.35715 5.31963i −0.406975 0.340555i
245245 −0.224295 + 6.99641i −0.0143297 + 0.446984i
246246 −3.46232 3.16832i −0.220749 0.202005i
247247 −9.22379 + 5.32536i −0.586896 + 0.338844i
248248 −24.0394 9.90030i −1.52650 0.628670i
249249 −1.90471 1.09969i −0.120706 0.0696898i
250250 −1.38090 0.305157i −0.0873357 0.0192998i
251251 −11.3975 + 11.3975i −0.719403 + 0.719403i −0.968483 0.249080i 0.919872π-0.919872\pi
0.249080 + 0.968483i 0.419872π0.419872\pi
252252 −8.09223 + 12.3003i −0.509762 + 0.774844i
253253 −3.73547 3.73547i −0.234847 0.234847i
254254 −3.79327 + 2.42019i −0.238011 + 0.151856i
255255 −0.727467 + 1.26001i −0.0455558 + 0.0789049i
256256 −2.69300 + 15.7717i −0.168313 + 0.985734i
257257 −11.8133 20.4612i −0.736891 1.27633i −0.953889 0.300161i 0.902960π-0.902960\pi
0.216998 0.976172i 0.430374π-0.430374\pi
258258 0.313226 + 7.06432i 0.0195006 + 0.439805i
259259 5.39993 + 7.27582i 0.335536 + 0.452097i
260260 3.47273 0.308562i 0.215370 0.0191362i
261261 −14.4802 3.87995i −0.896301 0.240163i
262262 2.02631 + 6.41149i 0.125186 + 0.396103i
263263 16.3732 + 9.45306i 1.00961 + 0.582901i 0.911079 0.412233i 0.135251π-0.135251\pi
0.0985352 + 0.995134i 0.468584π0.468584\pi
264264 −1.30504 + 1.00561i −0.0803194 + 0.0618908i
265265 1.80654i 0.110975i
266266 8.14765 21.3597i 0.499565 1.30965i
267267 −0.860486 + 0.860486i −0.0526609 + 0.0526609i
268268 −2.57546 + 14.7227i −0.157321 + 0.899332i
269269 17.9130 4.79978i 1.09218 0.292648i 0.332601 0.943068i 0.392074π-0.392074\pi
0.759575 + 0.650420i 0.225407π0.225407\pi
270270 −1.75883 + 3.38427i −0.107039 + 0.205960i
271271 −0.374243 0.648207i −0.0227336 0.0393758i 0.854435 0.519559i 0.173904π-0.173904\pi
−0.877168 + 0.480183i 0.840570π0.840570\pi
272272 −12.2826 + 2.20007i −0.744745 + 0.133399i
273273 −0.791225 2.00025i −0.0478871 0.121061i
274274 6.92781 0.307173i 0.418525 0.0185570i
275275 0.323244 1.20636i 0.0194924 0.0727465i
276276 1.35448 + 3.70579i 0.0815303 + 0.223063i
277277 3.40625 + 12.7123i 0.204661 + 0.763807i 0.989552 + 0.144173i 0.0460522π0.0460522\pi
−0.784891 + 0.619634i 0.787281π0.787281\pi
278278 −0.455395 + 2.06076i −0.0273128 + 0.123596i
279279 25.5759i 1.53119i
280280 −5.36503 + 5.21694i −0.320622 + 0.311772i
281281 10.3017i 0.614549i −0.951621 0.307275i 0.900583π-0.900583\pi
0.951621 0.307275i 0.0994170π-0.0994170\pi
282282 2.72489 + 0.602158i 0.162265 + 0.0358580i
283283 −3.67907 13.7305i −0.218698 0.816191i −0.984832 0.173511i 0.944489π-0.944489\pi
0.766134 0.642681i 0.222178π-0.222178\pi
284284 4.10451 + 1.90720i 0.243558 + 0.113172i
285285 0.737531 2.75250i 0.0436876 0.163044i
286286 0.136383 + 3.07590i 0.00806448 + 0.181882i
287287 11.6981 14.7497i 0.690516 0.870649i
288288 −15.3553 + 3.45876i −0.904822 + 0.203810i
289289 3.63426 + 6.29473i 0.213780 + 0.370278i
290290 −6.76076 3.51362i −0.397006 0.206327i
291291 −4.01178 + 1.07495i −0.235175 + 0.0630149i
292292 5.35448 3.76006i 0.313347 0.220041i
293293 −20.4080 + 20.4080i −1.19225 + 1.19225i −0.215812 + 0.976435i 0.569240π0.569240\pi
−0.976435 + 0.215812i 0.930760π0.930760\pi
294294 4.02651 + 2.25934i 0.234831 + 0.131767i
295295 8.53731i 0.497062i
296296 −1.24481 + 9.60601i −0.0723534 + 0.558338i
297297 −2.91698 1.68412i −0.169260 0.0977225i
298298 30.5848 9.66611i 1.77173 0.559943i
299299 7.12226 + 1.90840i 0.411891 + 0.110366i
300300 −0.598618 + 0.715370i −0.0345612 + 0.0413019i
301301 −28.1776 + 3.25124i −1.62413 + 0.187399i
302302 20.1873 0.895087i 1.16165 0.0515065i
303303 2.60677 + 4.51505i 0.149755 + 0.259383i
304304 22.1215 10.3885i 1.26876 0.595819i
305305 2.07232 3.58936i 0.118660 0.205526i
306306 −6.60257 10.3485i −0.377444 0.591584i
307307 10.3474 + 10.3474i 0.590555 + 0.590555i 0.937781 0.347227i 0.112877π-0.112877\pi
−0.347227 + 0.937781i 0.612877π0.612877\pi
308308 −4.39279 4.93739i −0.250303 0.281334i
309309 −4.66142 + 4.66142i −0.265179 + 0.265179i
310310 2.80493 12.6929i 0.159310 0.720908i
311311 12.1434 + 7.01098i 0.688588 + 0.397556i 0.803083 0.595867i 0.203192π-0.203192\pi
−0.114495 + 0.993424i 0.536525π0.536525\pi
312312 0.875693 2.12631i 0.0495764 0.120379i
313313 25.5865 14.7724i 1.44623 0.834983i 0.447978 0.894044i 0.352144π-0.352144\pi
0.998254 + 0.0590616i 0.0188109π0.0188109\pi
314314 −6.52726 + 7.13294i −0.368355 + 0.402535i
315315 −6.75535 2.92583i −0.380621 0.164852i
316316 −2.50086 + 0.222209i −0.140684 + 0.0125002i
317317 −2.70202 + 10.0841i −0.151761 + 0.566378i 0.847600 + 0.530635i 0.178046π0.178046\pi
−0.999361 + 0.0357431i 0.988620π0.988620\pi
318318 1.05730 + 0.549485i 0.0592903 + 0.0308136i
319319 3.36437 5.82726i 0.188368 0.326264i
320320 −7.99993 + 0.0324919i −0.447210 + 0.00181635i
321321 −1.63607 −0.0913163
322322 −14.4448 + 6.46773i −0.804977 + 0.360432i
323323 13.4773 + 13.4773i 0.749900 + 0.749900i
324324 −8.14857 11.6039i −0.452698 0.644661i
325325 0.451175 + 1.68381i 0.0250267 + 0.0934008i
326326 3.74258 + 11.8420i 0.207282 + 0.655867i
327327 7.86849 4.54287i 0.435128 0.251222i
328328 19.9478 2.66740i 1.10143 0.147282i
329329 −1.63874 + 11.0733i −0.0903466 + 0.610492i
330330 −0.607721 0.556117i −0.0334539 0.0306132i
331331 −20.6215 5.52552i −1.13346 0.303710i −0.357142 0.934050i 0.616249π-0.616249\pi
−0.776319 + 0.630340i 0.782916π0.782916\pi
332332 8.85822 3.23772i 0.486158 0.177693i
333333 −9.20427 + 2.46628i −0.504391 + 0.135151i
334334 18.3573 + 28.7722i 1.00447 + 1.57434i
335335 −7.47313 −0.408301
336336 1.42143 + 4.72676i 0.0775453 + 0.257866i
337337 7.38944 0.402528 0.201264 0.979537i 0.435495π-0.435495\pi
0.201264 + 0.979537i 0.435495π0.435495\pi
338338 7.57715 + 11.8760i 0.412143 + 0.645969i
339339 −6.83219 + 1.83068i −0.371074 + 0.0994289i
340340 −2.14182 5.85991i −0.116157 0.317798i
341341 11.0886 + 2.97119i 0.600483 + 0.160899i
342342 17.7368 + 16.2308i 0.959099 + 0.877659i
343343 −7.90142 + 16.7502i −0.426637 + 0.904423i
344344 −24.0943 18.4106i −1.29908 0.992632i
345345 −1.70848 + 0.986393i −0.0919816 + 0.0531056i
346346 5.21946 + 16.5150i 0.280600 + 0.887853i
347347 −7.15391 26.6988i −0.384042 1.43326i −0.839671 0.543095i 0.817252π-0.817252\pi
0.455629 0.890170i 0.349414π-0.349414\pi
348348 −4.11278 + 2.88810i −0.220468 + 0.154819i
349349 0.943208 + 0.943208i 0.0504888 + 0.0504888i 0.731900 0.681412i 0.238634π-0.238634\pi
−0.681412 + 0.731900i 0.738634π0.738634\pi
350350 −3.03169 2.19291i −0.162051 0.117216i
351351 4.70128 0.250936
352352 0.284278 7.05924i 0.0151521 0.376259i
353353 −4.29150 + 7.43310i −0.228414 + 0.395624i −0.957338 0.288970i 0.906687π-0.906687\pi
0.728924 + 0.684594i 0.240021π0.240021\pi
354354 4.99657 + 2.59675i 0.265565 + 0.138016i
355355 −0.585704 + 2.18588i −0.0310859 + 0.116014i
356356 −0.461848 5.19789i −0.0244779 0.275487i
357357 −3.09109 + 2.29413i −0.163598 + 0.121418i
358358 15.5658 17.0102i 0.822679 0.899018i
359359 3.17739 1.83447i 0.167696 0.0968195i −0.413803 0.910367i 0.635800π-0.635800\pi
0.581499 + 0.813547i 0.302466π0.302466\pi
360360 −3.02649 7.26483i −0.159510 0.382890i
361361 −15.8744 9.16509i −0.835495 0.482373i
362362 −7.46763 + 33.7926i −0.392490 + 1.77610i
363363 −3.11330 + 3.11330i −0.163406 + 0.163406i
364364 8.75562 + 2.90252i 0.458919 + 0.152133i
365365 2.31324 + 2.31324i 0.121080 + 0.121080i
366366 −1.47039 2.30461i −0.0768586 0.120464i
367367 −5.57346 + 9.65351i −0.290932 + 0.503909i −0.974030 0.226417i 0.927299π-0.927299\pi
0.683098 + 0.730327i 0.260632π0.260632\pi
368368 −15.9147 5.74371i −0.829609 0.299412i
369369 9.89918 + 17.1459i 0.515331 + 0.892579i
370370 −4.83841 + 0.214531i −0.251537 + 0.0111529i
371371 −1.89961 + 4.38594i −0.0986229 + 0.227707i
372372 −6.57552 5.50236i −0.340925 0.285284i
373373 −1.95270 0.523224i −0.101107 0.0270915i 0.207911 0.978148i 0.433334π-0.433334\pi
−0.309018 + 0.951056i 0.600000π0.600000\pi
374374 5.25370 1.66040i 0.271663 0.0858571i
375375 −0.403910 0.233198i −0.0208578 0.0120423i
376376 −9.47909 + 7.30419i −0.488847 + 0.376685i
377377 9.39177i 0.483701i
378378 −7.82875 + 6.36694i −0.402667 + 0.327480i
379379 9.38741 9.38741i 0.482199 0.482199i −0.423634 0.905833i 0.639246π-0.639246\pi
0.905833 + 0.423634i 0.139246π0.139246\pi
380380 7.02247 + 10.0003i 0.360245 + 0.513004i
381381 −1.43336 + 0.384068i −0.0734333 + 0.0196764i
382382 32.6001 + 16.9425i 1.66797 + 0.866854i
383383 −13.2963 23.0299i −0.679409 1.17677i −0.975159 0.221505i 0.928903π-0.928903\pi
0.295750 0.955265i 0.404430π-0.404430\pi
384384 −2.41429 + 4.69195i −0.123203 + 0.239435i
385385 2.05330 2.58893i 0.104646 0.131944i
386386 −0.0776990 1.75238i −0.00395478 0.0891937i
387387 7.72067 28.8139i 0.392464 1.46469i
388388 7.50506 16.1517i 0.381012 0.819979i
389389 −3.73629 13.9440i −0.189437 0.706990i −0.993637 0.112630i 0.964072π-0.964072\pi
0.804200 0.594359i 0.202594π-0.202594\pi
390390 1.12270 + 0.248100i 0.0568502 + 0.0125630i
391391 13.1952i 0.667308i
392392 −18.5110 + 7.02435i −0.934949 + 0.354783i
393393 2.21754i 0.111860i
394394 5.34880 24.2044i 0.269469 1.21940i
395395 −0.324910 1.21258i −0.0163480 0.0610116i
396396 6.52781 2.38594i 0.328035 0.119898i
397397 6.38514 23.8297i 0.320461 1.19598i −0.598335 0.801246i 0.704171π-0.704171\pi
0.918797 0.394731i 0.129162π-0.129162\pi
398398 10.9570 0.485826i 0.549227 0.0243523i
399399 4.68491 5.90705i 0.234539 0.295722i
400400 −0.705256 3.93734i −0.0352628 0.196867i
401401 15.8268 + 27.4128i 0.790351 + 1.36893i 0.925749 + 0.378138i 0.123435π0.123435\pi
−0.135398 + 0.990791i 0.543231π0.543231\pi
402402 −2.27307 + 4.37375i −0.113370 + 0.218143i
403403 −15.4772 + 4.14710i −0.770973 + 0.206582i
404404 −22.0223 3.85239i −1.09565 0.191664i
405405 5.01310 5.01310i 0.249103 0.249103i
406406 −12.7193 15.6395i −0.631246 0.776176i
407407 4.27709i 0.212008i
408408 −4.08105 0.528852i −0.202042 0.0261821i
409409 23.3489 + 13.4805i 1.15453 + 0.666567i 0.949986 0.312291i 0.101096π-0.101096\pi
0.204541 + 0.978858i 0.434430π0.434430\pi
410410 3.03240 + 9.59488i 0.149759 + 0.473857i
411411 2.20905 + 0.591913i 0.108964 + 0.0291969i
412412 −2.50192 28.1580i −0.123261 1.38724i
413413 −8.97717 + 20.7270i −0.441738 + 1.01991i
414414 −0.737281 16.6282i −0.0362354 0.817232i
415415 2.35784 + 4.08390i 0.115742 + 0.200471i
416416 4.58291 + 8.73140i 0.224696 + 0.428092i
417417 −0.348008 + 0.602768i −0.0170420 + 0.0295177i
418418 −9.09749 + 5.80440i −0.444973 + 0.283902i
419419 20.4105 + 20.4105i 0.997116 + 0.997116i 0.999996 0.00287947i 0.000916564π-0.000916564\pi
−0.00287947 + 0.999996i 0.500917π0.500917\pi
420420 −2.20556 + 1.10733i −0.107620 + 0.0540321i
421421 10.2151 10.2151i 0.497855 0.497855i −0.412915 0.910770i 0.635489π-0.635489\pi
0.910770 + 0.412915i 0.135489π0.135489\pi
422422 −37.2844 8.23928i −1.81498 0.401082i
423423 −10.1952 5.88619i −0.495707 0.286196i
424424 −4.71672 + 1.96496i −0.229064 + 0.0954270i
425425 2.70159 1.55977i 0.131047 0.0756597i
426426 1.10116 + 1.00766i 0.0533515 + 0.0488212i
427427 8.80549 6.53522i 0.426128 0.316262i
428428 4.50238 5.38051i 0.217631 0.260077i
429429 −0.262805 + 0.980802i −0.0126883 + 0.0473536i
430430 6.99170 13.4532i 0.337170 0.648769i
431431 7.38631 12.7935i 0.355786 0.616240i −0.631466 0.775404i 0.717546π-0.717546\pi
0.987252 + 0.159164i 0.0508798π0.0508798\pi
432432 −10.7491 0.911106i −0.517168 0.0438356i
433433 −20.9602 −1.00728 −0.503642 0.863913i 0.668007π-0.668007\pi
−0.503642 + 0.863913i 0.668007π0.668007\pi
434434 20.1567 27.8666i 0.967554 1.33764i
435435 −1.77680 1.77680i −0.0851909 0.0851909i
436436 −6.71365 + 38.3788i −0.321526 + 1.83801i
437437 6.68886 + 24.9632i 0.319971 + 1.19415i
438438 2.05746 0.650245i 0.0983091 0.0310699i
439439 20.6155 11.9024i 0.983924 0.568069i 0.0804713 0.996757i 0.474357π-0.474357\pi
0.903452 + 0.428688i 0.141024π0.141024\pi
440440 3.50132 0.468192i 0.166919 0.0223202i
441441 −13.3242 14.2068i −0.634485 0.676513i
442442 −5.19177 + 5.67352i −0.246947 + 0.269862i
443443 35.2525 + 9.44588i 1.67490 + 0.448787i 0.966424 0.256951i 0.0827180π-0.0827180\pi
0.708472 + 0.705739i 0.249385π0.249385\pi
444444 −1.34612 + 2.89699i −0.0638840 + 0.137485i
445445 2.52028 0.675306i 0.119473 0.0320126i
446446 −1.61446 + 1.03006i −0.0764468 + 0.0487748i
447447 10.5783 0.500339
448448 −19.4566 8.33322i −0.919236 0.393708i
449449 −32.8650 −1.55100 −0.775498 0.631350i 0.782501π-0.782501\pi
−0.775498 + 0.631350i 0.782501π0.782501\pi
450450 3.31733 2.11653i 0.156380 0.0997741i
451451 −8.58373 + 2.30000i −0.404192 + 0.108303i
452452 12.7814 27.5069i 0.601185 1.29381i
453453 6.43705 + 1.72480i 0.302439 + 0.0810383i
454454 −11.2292 + 12.2712i −0.527014 + 0.575917i
455455 −0.675189 + 4.56240i −0.0316533 + 0.213889i
456456 7.98879 1.06825i 0.374109 0.0500255i
457457 −32.6490 + 18.8499i −1.52725 + 0.881760i −0.527778 + 0.849382i 0.676975π0.676975\pi
−0.999476 + 0.0323780i 0.989692π0.989692\pi
458458 −3.38943 + 1.07121i −0.158378 + 0.0500542i
459459 −2.17748 8.12645i −0.101636 0.379310i
460460 1.45773 8.33317i 0.0679672 0.388536i
461461 −4.45270 4.45270i −0.207383 0.207383i 0.595771 0.803154i 0.296846π-0.296846\pi
−0.803154 + 0.595771i 0.796846π0.796846\pi
462462 −0.890666 1.98918i −0.0414375 0.0925451i
463463 12.0300 0.559084 0.279542 0.960133i 0.409817π-0.409817\pi
0.279542 + 0.960133i 0.409817π0.409817\pi
464464 1.82012 21.4736i 0.0844969 0.996886i
465465 2.14350 3.71265i 0.0994024 0.172170i
466466 0.587881 1.13118i 0.0272330 0.0524008i
467467 3.55437 13.2651i 0.164477 0.613836i −0.833630 0.552324i 0.813741π-0.813741\pi
0.998106 0.0615118i 0.0195922π-0.0195922\pi
468468 −6.22552 + 7.43972i −0.287775 + 0.343901i
469469 −18.1434 7.85816i −0.837785 0.362856i
470470 −4.41416 4.03934i −0.203610 0.186321i
471471 −2.76146 + 1.59433i −0.127241 + 0.0734628i
472472 −22.2903 + 9.28601i −1.02599 + 0.427423i
473473 11.5956 + 6.69471i 0.533166 + 0.307823i
474474 −0.808505 0.178667i −0.0371359 0.00820645i
475475 −4.32031 + 4.32031i −0.198229 + 0.198229i
476476 0.961867 16.4790i 0.0440871 0.755312i
477477 −3.55437 3.55437i −0.162743 0.162743i
478478 8.35911 5.33330i 0.382337 0.243939i
479479 15.4266 26.7196i 0.704859 1.22085i −0.261884 0.965099i 0.584344π-0.584344\pi
0.966743 0.255751i 0.0823229π-0.0823229\pi
480480 −2.51889 0.784840i −0.114971 0.0358229i
481481 2.98492 + 5.17003i 0.136101 + 0.235733i
482482 0.0530820 + 1.19718i 0.00241782 + 0.0545301i
483483 −5.18510 + 0.598276i −0.235930 + 0.0272225i
484484 −1.67100 18.8063i −0.0759544 0.854832i
485485 8.60167 + 2.30481i 0.390582 + 0.104656i
486486 −4.85725 15.3689i −0.220329 0.697150i
487487 −14.0115 8.08952i −0.634920 0.366571i 0.147735 0.989027i 0.452802π-0.452802\pi
−0.782655 + 0.622456i 0.786135π0.786135\pi
488488 11.6256 + 1.50653i 0.526265 + 0.0681972i
489489 4.09578i 0.185218i
490490 −5.05450 8.51188i −0.228339 0.384527i
491491 −13.9530 + 13.9530i −0.629689 + 0.629689i −0.947990 0.318300i 0.896888π-0.896888\pi
0.318300 + 0.947990i 0.396888π0.396888\pi
492492 6.53788 + 1.14368i 0.294750 + 0.0515611i
493493 16.2342 4.34995i 0.731153 0.195912i
494494 6.94599 13.3652i 0.312515 0.601329i
495495 1.73754 + 3.00952i 0.0780968 + 0.135268i
496496 36.1911 6.48255i 1.62503 0.291075i
497497 −3.72048 + 4.69103i −0.166886 + 0.210422i
498498 3.10733 0.137777i 0.139243 0.00617391i
499499 6.70565 25.0258i 0.300186 1.12031i −0.636824 0.771009i 0.719752π-0.719752\pi
0.937011 0.349301i 0.113581π-0.113581\pi
500500 1.87846 0.686584i 0.0840072 0.0307050i
501501 2.91317 + 10.8721i 0.130151 + 0.485730i
502502 4.91867 22.2580i 0.219531 0.993422i
503503 16.5689i 0.738773i −0.929276 0.369386i 0.879568π-0.879568\pi
0.929276 0.369386i 0.120432π-0.120432\pi
504504 0.291357 20.8201i 0.0129781 0.927401i
505505 11.1784i 0.497431i
506506 7.29494 + 1.61207i 0.324300 + 0.0716652i
507507 1.20244 + 4.48757i 0.0534023 + 0.199300i
508508 2.68147 5.77081i 0.118971 0.256038i
509509 −6.59685 + 24.6198i −0.292400 + 1.09125i 0.650860 + 0.759198i 0.274408π0.274408\pi
−0.943260 + 0.332054i 0.892258π0.892258\pi
510510 −0.0911422 2.05557i −0.00403585 0.0910221i
511511 3.18370 + 8.04853i 0.140839 + 0.356046i
512512 −8.78633 20.8519i −0.388305 0.921531i
513513 8.23888 + 14.2702i 0.363755 + 0.630043i
514514 29.6481 + 15.4083i 1.30772 + 0.679632i
515515 13.6528 3.65827i 0.601616 0.161203i
516516 −5.74700 8.18397i −0.252998 0.360279i
517517 3.73639 3.73639i 0.164326 0.164326i
518518 −11.9724 4.56685i −0.526035 0.200656i
519519 5.71204i 0.250731i
520520 −3.90555 + 3.00945i −0.171270 + 0.131973i
521521 35.2372 + 20.3442i 1.54377 + 0.891295i 0.998596 + 0.0529716i 0.0168693π0.0168693\pi
0.545173 + 0.838324i 0.316464π0.316464\pi
522522 20.2149 6.38878i 0.884783 0.279630i
523523 8.61533 + 2.30847i 0.376722 + 0.100942i 0.442211 0.896911i 0.354194π-0.354194\pi
−0.0654891 + 0.997853i 0.520861π0.520861\pi
524524 −7.29279 6.10257i −0.318587 0.266592i
525525 −0.735408 0.990882i −0.0320958 0.0432456i
526526 −26.7111 + 1.18435i −1.16466 + 0.0516399i
527527 14.3370 + 24.8324i 0.624530 + 1.08172i
528528 0.790963 2.19160i 0.0344222 0.0953771i
529529 −2.55416 + 4.42393i −0.111050 + 0.192345i
530530 −1.37417 2.15379i −0.0596899 0.0935546i
531531 −16.7972 16.7972i −0.728937 0.728937i
532532 6.53377 + 31.6631i 0.283275 + 1.37277i
533533 8.77064 8.77064i 0.379899 0.379899i
534534 0.371349 1.68043i 0.0160698 0.0727193i
535535 3.03793 + 1.75395i 0.131341 + 0.0758298i
536536 −8.12850 19.5118i −0.351098 0.842780i
537537 6.58536 3.80206i 0.284179 0.164071i
538538 −17.7053 + 19.3482i −0.763328 + 0.834159i
539539 7.70735 4.12638i 0.331979 0.177736i
540540 −0.477378 5.37267i −0.0205431 0.231203i
541541 2.81676 10.5123i 0.121102 0.451958i −0.878569 0.477615i 0.841501π-0.841501\pi
0.999671 + 0.0256574i 0.00816789π0.00816789\pi
542542 0.939247 + 0.488133i 0.0403441 + 0.0209671i
543543 −5.70668 + 9.88426i −0.244897 + 0.424174i
544544 12.9701 11.9659i 0.556089 0.513035i
545545 −19.4808 −0.834465
546546 2.46483 + 1.78289i 0.105485 + 0.0763005i
547547 −10.6250 10.6250i −0.454294 0.454294i 0.442483 0.896777i 0.354098π-0.354098\pi
−0.896777 + 0.442483i 0.854098π0.854098\pi
548548 −8.02583 + 5.63595i −0.342846 + 0.240756i
549549 2.98479 + 11.1394i 0.127388 + 0.475417i
550550 0.532259 + 1.68413i 0.0226956 + 0.0718117i
551551 −28.5075 + 16.4588i −1.21446 + 0.701170i
552552 −4.43370 3.38782i −0.188711 0.144195i
553553 0.486232 3.28558i 0.0206767 0.139717i
554554 −13.7308 12.5648i −0.583364 0.533829i
555555 −1.54281 0.413394i −0.0654886 0.0175476i
556556 −1.02461 2.80328i −0.0434532 0.118886i
557557 −8.59765 + 2.30373i −0.364294 + 0.0976123i −0.436323 0.899790i 0.643719π-0.643719\pi
0.0720286 + 0.997403i 0.477053π0.477053\pi
558558 19.4546 + 30.4921i 0.823581 + 1.29083i
559559 −18.6886 −0.790442
560560 2.42796 10.3007i 0.102600 0.435285i
561561 1.81710 0.0767179
562562 7.83614 + 12.2819i 0.330548 + 0.518082i
563563 −21.5129 + 5.76435i −0.906659 + 0.242939i −0.681874 0.731470i 0.738835π-0.738835\pi
−0.224785 + 0.974408i 0.572168π0.572168\pi
564564 −3.70671 + 1.35482i −0.156081 + 0.0570481i
565565 14.6489 + 3.92517i 0.616285 + 0.165133i
566566 14.8305 + 13.5712i 0.623373 + 0.570441i
567567 17.4423 6.89952i 0.732507 0.289752i
568568 −6.34422 + 0.848343i −0.266198 + 0.0355957i
569569 29.2554 16.8906i 1.22645 0.708090i 0.260163 0.965565i 0.416224π-0.416224\pi
0.966285 + 0.257474i 0.0828902π0.0828902\pi
570570 1.21443 + 3.84261i 0.0508669 + 0.160949i
571571 −2.17214 8.10652i −0.0909011 0.339247i 0.905465 0.424421i 0.139522π-0.139522\pi
−0.996366 + 0.0851734i 0.972856π0.972856\pi
572572 −2.50232 3.56341i −0.104627 0.148994i
573573 8.56764 + 8.56764i 0.357918 + 0.357918i
574574 −2.72712 + 26.4833i −0.113828 + 1.10539i
575575 4.22986 0.176397
576576 15.6760 15.8039i 0.653167 0.658494i
577577 −19.2193 + 33.2888i −0.800111 + 1.38583i 0.119432 + 0.992842i 0.461893π0.461893\pi
−0.919543 + 0.392990i 0.871441π0.871441\pi
578578 −9.12102 4.74026i −0.379384 0.197169i
579579 0.149723 0.558776i 0.00622230 0.0232219i
580580 10.7330 0.953660i 0.445664 0.0395986i
581581 1.43010 + 12.3943i 0.0593306 + 0.514202i
582582 3.96525 4.33320i 0.164365 0.179617i
583583 1.95394 1.12811i 0.0809240 0.0467215i
584584 −3.52358 + 8.55578i −0.145807 + 0.354041i
585585 −4.20059 2.42521i −0.173673 0.100270i
586586 8.80721 39.8544i 0.363823 1.64637i
587587 11.9589 11.9589i 0.493598 0.493598i −0.415840 0.909438i 0.636512π-0.636512\pi
0.909438 + 0.415840i 0.136512π0.136512\pi
588588 −6.51909 + 0.369196i −0.268843 + 0.0152254i
589589 −39.7113 39.7113i −1.63628 1.63628i
590590 −6.49402 10.1784i −0.267355 0.419037i
591591 4.08749 7.07975i 0.168137 0.291222i
592592 −5.82285 12.3994i −0.239317 0.509611i
593593 1.68846 + 2.92450i 0.0693367 + 0.120095i 0.898609 0.438749i 0.144578π-0.144578\pi
−0.829273 + 0.558844i 0.811245π0.811245\pi
594594 4.75873 0.210998i 0.195253 0.00865736i
595595 8.19910 0.946044i 0.336131 0.0387840i
596596 −29.1112 + 34.7889i −1.19244 + 1.42501i
597597 3.49384 + 0.936171i 0.142993 + 0.0383149i
598598 −9.94296 + 3.14241i −0.406598 + 0.128503i
599599 −3.84522 2.22004i −0.157111 0.0907083i 0.419383 0.907809i 0.362246π-0.362246\pi
−0.576494 + 0.817101i 0.695580π0.695580\pi
600600 0.169529 1.30823i 0.00692100 0.0534081i
601601 45.0884i 1.83919i −0.392862 0.919597i 0.628515π-0.628515\pi
0.392862 0.919597i 0.371485π-0.371485\pi
602602 31.1209 25.3099i 1.26839 1.03155i
603603 14.7034 14.7034i 0.598770 0.598770i
604604 −23.3868 + 16.4229i −0.951597 + 0.668237i
605605 9.11853 2.44330i 0.370721 0.0993344i
606606 −6.54228 3.40007i −0.265762 0.138118i
607607 22.5465 + 39.0517i 0.915134 + 1.58506i 0.806704 + 0.590955i 0.201249π0.201249\pi
0.108430 + 0.994104i 0.465418π0.465418\pi
608608 −18.4716 + 29.2124i −0.749124 + 1.18472i
609609 −2.44540 6.18208i −0.0990927 0.250511i
610610 0.259634 + 5.85564i 0.0105123 + 0.237088i
611611 −1.90888 + 7.12402i −0.0772249 + 0.288207i
612612 15.7435 + 7.31536i 0.636391 + 0.295706i
613613 1.67997 + 6.26974i 0.0678534 + 0.253233i 0.991518 0.129970i 0.0414880π-0.0414880\pi
−0.923665 + 0.383202i 0.874821π0.874821\pi
614614 −20.2072 4.46548i −0.815496 0.180212i
615615 3.31858i 0.133818i
616616 8.99287 + 2.54502i 0.362333 + 0.102542i
617617 29.2448i 1.17735i 0.808369 + 0.588676i 0.200351π0.200351\pi
−0.808369 + 0.588676i 0.799649π0.799649\pi
618618 2.01167 9.10322i 0.0809213 0.366185i
619619 −1.15901 4.32550i −0.0465847 0.173856i 0.938714 0.344697i 0.112018π-0.112018\pi
−0.985299 + 0.170841i 0.945352π0.945352\pi
620620 6.31092 + 17.2664i 0.253453 + 0.693433i
621621 2.95250 11.0189i 0.118480 0.442172i
622622 −19.8106 + 0.878385i −0.794333 + 0.0352200i
623623 6.82887 + 1.01060i 0.273593 + 0.0404890i
624624 0.573389 + 3.20114i 0.0229539 + 0.128148i
625625 0.500000 + 0.866025i 0.0200000 + 0.0346410i
626626 −19.2679 + 37.0746i −0.770101 + 1.48180i
627627 −3.43766 + 0.921118i −0.137287 + 0.0367859i
628628 2.35617 13.4691i 0.0940213 0.537475i
629629 7.55420 7.55420i 0.301206 0.301206i
630630 10.2794 1.65031i 0.409543 0.0657498i
631631 40.2497i 1.60232i 0.598453 + 0.801158i 0.295782π0.295782\pi
−0.598453 + 0.801158i 0.704218π0.704218\pi
632632 2.81255 2.16724i 0.111877 0.0862080i
633633 −10.9056 6.29637i −0.433460 0.250258i
634634 −4.44918 14.0778i −0.176700 0.559100i
635635 3.07327 + 0.823481i 0.121959 + 0.0326788i
636636 −1.67851 + 0.149140i −0.0665571 + 0.00591380i
637637 −6.43670 + 10.3667i −0.255031 + 0.410744i
638638 0.421512 + 9.50653i 0.0166878 + 0.376367i
639639 −3.14835 5.45311i −0.124547 0.215722i
640640 9.51297 6.12400i 0.376033 0.242072i
641641 12.0907 20.9417i 0.477555 0.827149i −0.522114 0.852876i 0.674857π-0.674857\pi
0.999669 + 0.0257265i 0.00818989π0.00818989\pi
642642 1.95055 1.24450i 0.0769822 0.0491163i
643643 −3.10495 3.10495i −0.122447 0.122447i 0.643228 0.765675i 0.277595π-0.277595\pi
−0.765675 + 0.643228i 0.777595π0.777595\pi
644644 12.3016 18.6986i 0.484752 0.736828i
645645 3.53563 3.53563i 0.139215 0.139215i
646646 −26.3197 5.81625i −1.03553 0.228837i
647647 −35.8726 20.7111i −1.41030 0.814236i −0.414881 0.909876i 0.636177π-0.636177\pi
−0.995416 + 0.0956400i 0.969510π0.969510\pi
648648 18.5416 + 7.63609i 0.728381 + 0.299974i
649649 9.23393 5.33121i 0.362463 0.209268i
650650 −1.81871 1.66428i −0.0713357 0.0652784i
651651 9.10796 6.75970i 0.356969 0.264934i
652652 −13.4697 11.2714i −0.527516 0.441423i
653653 −9.31728 + 34.7725i −0.364613 + 1.36075i 0.503331 + 0.864094i 0.332108π0.332108\pi
−0.867944 + 0.496661i 0.834559π0.834559\pi
654654 −5.92538 + 11.4014i −0.231701 + 0.445829i
655655 2.37732 4.11763i 0.0928895 0.160889i
656656 −21.7532 + 18.3537i −0.849318 + 0.716590i
657657 −9.10262 −0.355127
658658 −6.46933 14.4484i −0.252201 0.563256i
659659 14.2006 + 14.2006i 0.553175 + 0.553175i 0.927356 0.374181i 0.122076π-0.122076\pi
−0.374181 + 0.927356i 0.622076π0.622076\pi
660660 1.14756 + 0.200743i 0.0446685 + 0.00781393i
661661 8.05927 + 30.0776i 0.313469 + 1.16988i 0.925406 + 0.378977i 0.123724π0.123724\pi
−0.611937 + 0.790907i 0.709609π0.709609\pi
662662 28.7885 9.09840i 1.11890 0.353619i
663663 −2.19646 + 1.26813i −0.0853033 + 0.0492499i
664664 −8.09814 + 10.5982i −0.314269 + 0.411290i
665665 −15.0318 + 5.94603i −0.582909 + 0.230577i
666666 9.09751 9.94170i 0.352522 0.385233i
667667 22.0124 + 5.89822i 0.852325 + 0.228380i
668668 −43.7719 20.3391i −1.69358 0.786942i
669669 −0.610054 + 0.163463i −0.0235860 + 0.00631986i
670670 8.90962 5.68454i 0.344209 0.219613i
671671 −5.17631 −0.199829
672672 −5.29013 4.55412i −0.204071 0.175679i
673673 −39.1372 −1.50863 −0.754313 0.656515i 0.772030π-0.772030\pi
−0.754313 + 0.656515i 0.772030π0.772030\pi
674674 −8.80984 + 5.62088i −0.339343 + 0.216508i
675675 2.60502 0.698014i 0.100267 0.0268666i
676676 −18.0673 8.39515i −0.694895 0.322890i
677677 11.9359 + 3.19823i 0.458735 + 0.122918i 0.480784 0.876839i 0.340352π-0.340352\pi
−0.0220485 + 0.999757i 0.507019π0.507019\pi
678678 6.75295 7.37957i 0.259345 0.283411i
679679 18.4597 + 14.6405i 0.708420 + 0.561851i
680680 7.01094 + 5.35710i 0.268857 + 0.205435i
681681 −4.75070 + 2.74282i −0.182047 + 0.105105i
682682 −15.4802 + 4.89240i −0.592766 + 0.187340i
683683 −3.04910 11.3794i −0.116671 0.435421i 0.882736 0.469870i 0.155699π-0.155699\pi
−0.999406 + 0.0344487i 0.989032π0.989032\pi
684684 −33.4924 5.85887i −1.28061 0.224019i
685685 −3.46731 3.46731i −0.132479 0.132479i
686686 −3.32099 25.9802i −0.126796 0.991929i
687687 −1.17230 −0.0447261
688688 42.7300 + 3.62183i 1.62907 + 0.138081i
689689 −1.57458 + 2.72725i −0.0599868 + 0.103900i
690690 1.28658 2.47558i 0.0489791 0.0942436i
691691 −6.05702 + 22.6051i −0.230420 + 0.859939i 0.749740 + 0.661732i 0.230178π0.230178\pi
−0.980160 + 0.198207i 0.936488π0.936488\pi
692692 −18.7851 15.7193i −0.714103 0.597558i
693693 1.05387 + 9.13362i 0.0400333 + 0.346958i
694694 28.8378 + 26.3891i 1.09467 + 1.00172i
695695 1.29240 0.746165i 0.0490234 0.0283037i
696696 2.70646 6.57170i 0.102588 0.249100i
697697 −19.2228 11.0983i −0.728117 0.420379i
698698 −1.84198 0.407049i −0.0697199 0.0154070i
699699 0.297285 0.297285i 0.0112443 0.0112443i
700700 5.28251 + 0.308337i 0.199660 + 0.0116540i
701701 14.2281 + 14.2281i 0.537390 + 0.537390i 0.922761 0.385372i 0.125927π-0.125927\pi
−0.385372 + 0.922761i 0.625927π0.625927\pi
702702 −5.60497 + 3.57610i −0.211546 + 0.134971i
703703 −10.4620 + 18.1207i −0.394581 + 0.683435i
704704 5.03078 + 8.63241i 0.189605 + 0.325346i
705705 −0.986637 1.70890i −0.0371589 0.0643611i
706706 −0.537670 12.1263i −0.0202355 0.456379i
707707 11.7543 27.1390i 0.442065 1.02067i
708708 −7.93228 + 0.704807i −0.298113 + 0.0264883i
709709 −44.7577 11.9928i −1.68091 0.450399i −0.712892 0.701273i 0.752615π-0.752615\pi
−0.968020 + 0.250874i 0.919282π0.919282\pi
710710 −0.964428 3.05157i −0.0361944 0.114523i
711711 3.02502 + 1.74650i 0.113447 + 0.0654988i
712712 4.50447 + 5.84572i 0.168812 + 0.219078i
713713 38.8799i 1.45606i
714714 1.94020 5.08639i 0.0726101 0.190353i
715715 1.53946 1.53946i 0.0575725 0.0575725i
716716 −5.61885 + 32.1203i −0.209986 + 1.20039i
717717 3.15865 0.846357i 0.117962 0.0316078i
718718 −2.39274 + 4.60402i −0.0892963 + 0.171820i
719719 −12.7442 22.0736i −0.475279 0.823207i 0.524320 0.851521i 0.324319π-0.324319\pi
−0.999599 + 0.0283142i 0.990986π0.990986\pi
720720 9.13433 + 6.35914i 0.340417 + 0.236991i
721721 36.9934 + 5.47465i 1.37770 + 0.203886i
722722 25.8973 1.14827i 0.963800 0.0427341i
723723 −0.102287 + 0.381741i −0.00380410 + 0.0141971i
724724 −16.8017 45.9686i −0.624430 1.70841i
725725 1.39442 + 5.20406i 0.0517876 + 0.193274i
726726 1.34357 6.07991i 0.0498644 0.225647i
727727 4.26612i 0.158222i 0.996866 + 0.0791109i 0.0252081π0.0252081\pi
−0.996866 + 0.0791109i 0.974792π0.974792\pi
728728 −12.6465 + 3.19964i −0.468709 + 0.118586i
729729 15.9531i 0.590857i
730730 −4.51748 0.998294i −0.167200 0.0369485i
731731 8.65591 + 32.3043i 0.320151 + 1.19482i
732732 3.50606 + 1.62913i 0.129588 + 0.0602143i
733733 −1.63628 + 6.10669i −0.0604375 + 0.225556i −0.989538 0.144271i 0.953916π-0.953916\pi
0.929101 + 0.369827i 0.120583π0.120583\pi
734734 −0.698282 15.7486i −0.0257741 0.581293i
735735 −0.743504 3.17898i −0.0274246 0.117258i
736736 23.3428 5.25793i 0.860428 0.193810i
737737 4.66667 + 8.08291i 0.171899 + 0.297738i
738738 −24.8443 12.9117i −0.914530 0.475287i
739739 −29.4189 + 7.88278i −1.08219 + 0.289973i −0.755494 0.655156i 0.772603π-0.772603\pi
−0.326699 + 0.945129i 0.605936π0.605936\pi
740740 5.60527 3.93617i 0.206054 0.144697i
741741 3.51251 3.51251i 0.129035 0.129035i
742742 −1.07147 6.67397i −0.0393349 0.245009i
743743 27.4086i 1.00553i 0.864425 + 0.502763i 0.167683π0.167683\pi
−0.864425 + 0.502763i 0.832317π0.832317\pi
744744 12.0249 + 1.55827i 0.440855 + 0.0571291i
745745 −19.6424 11.3405i −0.719641 0.415485i
746746 2.72604 0.861547i 0.0998075 0.0315435i
747747 −12.6742 3.39604i −0.463724 0.124255i
748748 −5.00057 + 5.97586i −0.182839 + 0.218499i
749749 5.53122 + 7.45271i 0.202106 + 0.272316i
750750 0.658935 0.0292166i 0.0240609 0.00106684i
751751 13.2890 + 23.0173i 0.484924 + 0.839913i 0.999850 0.0173217i 0.00551395π-0.00551395\pi
−0.514926 + 0.857235i 0.672181π0.672181\pi
752752 5.74513 15.9186i 0.209503 0.580492i
753753 3.75879 6.51042i 0.136978 0.237253i
754754 −7.14398 11.1971i −0.260168 0.407773i
755755 −10.1036 10.1036i −0.367706 0.367706i
756756 4.49049 13.5458i 0.163318 0.492658i
757757 22.5403 22.5403i 0.819243 0.819243i −0.166756 0.985998i 0.553329π-0.553329\pi
0.985998 + 0.166756i 0.0533291π0.0533291\pi
758758 −4.05121 + 18.3325i −0.147146 + 0.665868i
759759 2.13376 + 1.23193i 0.0774505 + 0.0447161i
760760 −15.9792 6.58081i −0.579626 0.238711i
761761 −9.34590 + 5.39586i −0.338789 + 0.195600i −0.659736 0.751497i 0.729332π-0.729332\pi
0.320948 + 0.947097i 0.395999π0.395999\pi
762762 1.41674 1.54820i 0.0513229 0.0560853i
763763 −47.2958 20.4845i −1.71222 0.741587i
764764 −51.7541 + 4.59851i −1.87240 + 0.166368i
765765 −2.24655 + 8.38425i −0.0812243 + 0.303133i
766766 33.3701 + 17.3427i 1.20571 + 0.626616i
767767 −7.44115 + 12.8884i −0.268684 + 0.465375i
768768 −0.690632 7.43030i −0.0249210 0.268118i
769769 −26.1120 −0.941624 −0.470812 0.882234i 0.656039π-0.656039\pi
−0.470812 + 0.882234i 0.656039π0.656039\pi
770770 −0.478675 + 4.64845i −0.0172502 + 0.167519i
771771 7.79182 + 7.79182i 0.280616 + 0.280616i
772772 1.42561 + 2.03012i 0.0513087 + 0.0730656i
773773 −9.39580 35.0656i −0.337943 1.26122i −0.900643 0.434560i 0.856904π-0.856904\pi
0.562699 0.826662i 0.309763π-0.309763\pi
774774 12.7130 + 40.2254i 0.456958 + 1.44587i
775775 −7.96031 + 4.59589i −0.285943 + 0.165089i
776776 3.33833 + 24.9652i 0.119839 + 0.896200i
777777 −3.31097 2.62594i −0.118780 0.0942052i
778778 15.0612 + 13.7823i 0.539970 + 0.494119i
779779 41.9925 + 11.2519i 1.50454 + 0.403140i
780780 −1.52723 + 0.558209i −0.0546836 + 0.0199871i
781781 2.72999 0.731497i 0.0976866 0.0261750i
782782 10.0371 + 15.7316i 0.358925 + 0.562559i
783783 14.5300 0.519261
784784 16.7261 22.4552i 0.597360 0.801973i
785785 6.83681 0.244016
786786 −1.68680 2.64380i −0.0601662 0.0943011i
787787 39.0231 10.4562i 1.39103 0.372724i 0.515912 0.856642i 0.327453π-0.327453\pi
0.875113 + 0.483918i 0.160787π0.160787\pi
788788 12.0345 + 32.9256i 0.428710 + 1.17293i
789789 −8.51727 2.28220i −0.303223 0.0812483i
790790 1.30973 + 1.19852i 0.0465981 + 0.0426413i
791791 31.4375 + 24.9332i 1.11779 + 0.886524i
792792 −5.96769 + 7.81003i −0.212053 + 0.277517i
793793 6.25699 3.61247i 0.222192 0.128283i
794794 10.5139 + 33.2672i 0.373123 + 1.18061i
795795 −0.218070 0.813850i −0.00773416 0.0288643i
796796 −12.6937 + 8.91383i −0.449915 + 0.315942i
797797 21.9467 + 21.9467i 0.777391 + 0.777391i 0.979386 0.201996i 0.0647427π-0.0647427\pi
−0.201996 + 0.979386i 0.564743π0.564743\pi
798798 −1.09217 + 10.6062i −0.0386624 + 0.375454i
799799 13.1984 0.466927
800800 3.83581 + 4.15771i 0.135616 + 0.146997i
801801 −3.62999 + 6.28733i −0.128259 + 0.222152i
802802 −39.7209 20.6432i −1.40259 0.728938i
803803 1.05746 3.94651i 0.0373171 0.139269i
804804 −0.616952 6.94351i −0.0217582 0.244879i
805805 10.2693 + 4.44778i 0.361946 + 0.156764i
806806 15.2977 16.7172i 0.538837 0.588837i
807807 −7.49048 + 4.32463i −0.263677 + 0.152234i
808808 29.1858 12.1587i 1.02675 0.427740i
809809 31.3035 + 18.0731i 1.10057 + 0.635416i 0.936371 0.351011i 0.114162π-0.114162\pi
0.164201 + 0.986427i 0.447495π0.447495\pi
810810 −2.16344 + 9.79001i −0.0760156 + 0.343986i
811811 −7.28087 + 7.28087i −0.255666 + 0.255666i −0.823289 0.567623i 0.807863π-0.807863\pi
0.567623 + 0.823289i 0.307863π0.307863\pi
812812 27.0606 + 8.97067i 0.949640 + 0.314809i
813813 0.246844 + 0.246844i 0.00865719 + 0.00865719i
814814 3.25343 + 5.09924i 0.114033 + 0.178728i
815815 4.39089 7.60525i 0.153806 0.266400i
816816 5.26780 2.47380i 0.184410 0.0866003i
817817 −32.7512 56.7268i −1.14582 1.98462i
818818 −38.0911 + 1.68893i −1.33182 + 0.0590520i
819819 −7.64811 10.3050i −0.267247 0.360086i
820820 −10.9138 9.13258i −0.381125 0.318924i
821821 −2.23549 0.598999i −0.0780193 0.0209052i 0.219598 0.975590i 0.429525π-0.429525\pi
−0.297618 + 0.954685i 0.596192π0.596192\pi
822822 −3.08392 + 0.974653i −0.107564 + 0.0339949i
823823 12.8674 + 7.42901i 0.448530 + 0.258959i 0.707209 0.707004i 0.249954π-0.249954\pi
−0.258679 + 0.965963i 0.583287π0.583287\pi
824824 24.4016 + 31.6674i 0.850070 + 1.10319i
825825 0.582491i 0.0202797i
826826 −5.06354 31.5398i −0.176183 1.09741i
827827 10.4703 10.4703i 0.364089 0.364089i −0.501227 0.865316i 0.667118π-0.667118\pi
0.865316 + 0.501227i 0.167118π0.167118\pi
828828 13.5275 + 19.2637i 0.470112 + 0.669459i
829829 26.1738 7.01325i 0.909054 0.243580i 0.226153 0.974092i 0.427385π-0.427385\pi
0.682901 + 0.730511i 0.260718π0.260718\pi
830830 −5.91755 3.07539i −0.205401 0.106748i
831831 −3.06905 5.31575i −0.106464 0.184401i
832832 −12.1055 6.92371i −0.419683 0.240037i
833833 20.9007 + 6.32471i 0.724167 + 0.219138i
834834 −0.0436009 0.983349i −0.00150978 0.0340506i
835835 6.24614 23.3109i 0.216157 0.806708i
836836 6.43102 13.8403i 0.222421 0.478675i
837837 6.41599 + 23.9448i 0.221769 + 0.827653i
838838 −39.8593 8.80829i −1.37692 0.304277i
839839 4.57635i 0.157993i 0.996875 + 0.0789966i 0.0251716π0.0251716\pi
−0.996875 + 0.0789966i 0.974828π0.974828\pi
840840 1.78721 2.99787i 0.0616648 0.103436i
841841 0.0266983i 0.000920632i
842842 −4.40841 + 19.9490i −0.151924 + 0.687486i
843843 1.24354 + 4.64096i 0.0428298 + 0.159843i
844844 50.7186 18.5379i 1.74581 0.638099i
845845 2.57816 9.62181i 0.0886913 0.331000i
846846 16.6323 0.737463i 0.571831 0.0253545i
847847 24.7073 + 3.65644i 0.848954 + 0.125637i
848848 4.12870 5.93051i 0.141780 0.203655i
849849 3.31486 + 5.74151i 0.113766 + 0.197048i
850850 −2.03444 + 3.91459i −0.0697807 + 0.134269i
851851 13.9921 3.74918i 0.479644 0.128520i
852852 −2.07932 0.363738i −0.0712362 0.0124615i
853853 29.7217 29.7217i 1.01765 1.01765i 0.0178097 0.999841i 0.494331π-0.494331\pi
0.999841 0.0178097i 0.00566931π-0.00566931\pi
854854 −5.52699 + 14.4894i −0.189130 + 0.495819i
855855 17.0005i 0.581404i
856856 −1.27508 + 9.83955i −0.0435813 + 0.336309i
857857 11.4429 + 6.60656i 0.390882 + 0.225676i 0.682542 0.730846i 0.260874π-0.260874\pi
−0.291660 + 0.956522i 0.594208π0.594208\pi
858858 −0.432738 1.36924i −0.0147734 0.0467450i
859859 −35.7695 9.58442i −1.22044 0.327016i −0.409590 0.912270i 0.634328π-0.634328\pi
−0.810850 + 0.585254i 0.800995π0.800995\pi
860860 1.89768 + 21.3575i 0.0647102 + 0.728284i
861861 −3.48956 + 8.05690i −0.118924 + 0.274579i
862862 0.925409 + 20.8711i 0.0315196 + 0.710874i
863863 −2.63376 4.56181i −0.0896543 0.155286i 0.817711 0.575629i 0.195243π-0.195243\pi
−0.907365 + 0.420344i 0.861910π0.861910\pi
864864 13.5084 7.09023i 0.459565 0.241215i
865865 6.12361 10.6064i 0.208209 0.360628i
866866 24.9892 15.9437i 0.849168 0.541788i
867867 −2.39710 2.39710i −0.0814097 0.0814097i
868868 −2.83416 + 48.5556i −0.0961978 + 1.64809i
869869 −1.10863 + 1.10863i −0.0376077 + 0.0376077i
870870 3.46988 + 0.766790i 0.117640 + 0.0259966i
871871 −11.2819 6.51360i −0.382272 0.220705i
872872 −21.1892 50.8628i −0.717556 1.72243i
873873 −21.4586 + 12.3891i −0.726263 + 0.419308i
874874 −26.9632 24.6736i −0.912042 0.834598i
875875 0.303265 + 2.62831i 0.0102522 + 0.0888532i
876876 −1.95833 + 2.34027i −0.0661657 + 0.0790703i
877877 1.60881 6.00415i 0.0543256 0.202746i −0.933429 0.358763i 0.883199π-0.883199\pi
0.987754 + 0.156017i 0.0498654π0.0498654\pi
878878 −15.5245 + 29.8717i −0.523928 + 1.00812i
879879 6.73037 11.6573i 0.227010 0.393193i
880880 −3.81820 + 3.22151i −0.128712 + 0.108597i
881881 −43.4652 −1.46438 −0.732189 0.681101i 0.761501π-0.761501\pi
−0.732189 + 0.681101i 0.761501π0.761501\pi
882882 26.6919 + 6.80241i 0.898764 + 0.229049i
883883 23.6683 + 23.6683i 0.796503 + 0.796503i 0.982542 0.186039i 0.0595651π-0.0595651\pi
−0.186039 + 0.982542i 0.559565π0.559565\pi
884884 1.87409 10.7133i 0.0630325 0.360327i
885885 −1.03056 3.84609i −0.0346418 0.129285i
886886 −49.2139 + 15.5537i −1.65337 + 0.522537i
887887 11.2322 6.48494i 0.377142 0.217743i −0.299432 0.954118i 0.596797π-0.596797\pi
0.676574 + 0.736375i 0.263464π0.263464\pi
888888 −0.598767 4.47780i −0.0200933 0.150265i
889889 6.59544 + 5.23087i 0.221204 + 0.175438i
890890 −2.49105 + 2.72220i −0.0835000 + 0.0912482i
891891 −8.55263 2.29167i −0.286524 0.0767739i
892892 1.14126 2.45612i 0.0382123 0.0822370i
893893 −24.9693 + 6.69051i −0.835567 + 0.223889i
894894 −12.6117 + 8.04656i −0.421799 + 0.269117i
895895 −16.3040 −0.544983
896896 29.5353 4.86485i 0.986705 0.162523i
897897 −3.43897 −0.114824
898898 39.1824 24.9992i 1.30753 0.834235i
899899 −47.8346 + 12.8172i −1.59537 + 0.427479i
900900 −2.34502 + 5.04674i −0.0781673 + 0.168225i
901901 5.44352 + 1.45859i 0.181350 + 0.0485925i
902902 8.48418 9.27145i 0.282492 0.308705i
903903 12.3017 4.86607i 0.409373 0.161933i
904904 5.68528 + 42.5166i 0.189089 + 1.41408i
905905 21.1929 12.2357i 0.704475 0.406729i
906906 −8.98639 + 2.84009i −0.298553 + 0.0943555i
907907 −0.285501 1.06550i −0.00947990 0.0353795i 0.961024 0.276465i 0.0891631π-0.0891631\pi
−0.970504 + 0.241086i 0.922496π0.922496\pi
908908 4.05346 23.1717i 0.134519 0.768980i
909909 21.9935 + 21.9935i 0.729479 + 0.729479i
910910 −2.66548 5.95298i −0.0883597 0.197339i
911911 −23.0712 −0.764382 −0.382191 0.924083i 0.624830π-0.624830\pi
−0.382191 + 0.924083i 0.624830π0.624830\pi
912912 −8.71182 + 7.35037i −0.288477 + 0.243395i
913913 2.94476 5.10047i 0.0974573 0.168801i
914914 24.5863 47.3081i 0.813244 1.56481i
915915 −0.500307 + 1.86717i −0.0165396 + 0.0617267i
916916 3.22612 3.85533i 0.106594 0.127384i
917917 10.1015 7.49707i 0.333580 0.247575i
918918 8.77753 + 8.03220i 0.289702 + 0.265102i
919919 −28.1800 + 16.2697i −0.929573 + 0.536689i −0.886676 0.462390i 0.846992π-0.846992\pi
−0.0428964 + 0.999080i 0.513659π0.513659\pi
920920 4.60080 + 11.0438i 0.151684 + 0.364104i
921921 −5.91057 3.41247i −0.194760 0.112445i
922922 8.69560 + 1.92159i 0.286374 + 0.0632843i
923923 −2.78943 + 2.78943i −0.0918152 + 0.0918152i
924924 2.57497 + 1.69405i 0.0847103 + 0.0557301i
925925 2.42158 + 2.42158i 0.0796211 + 0.0796211i
926926 −14.3425 + 9.15082i −0.471323 + 0.300715i
927927 −19.6644 + 34.0597i −0.645863 + 1.11867i
928928 14.1642 + 26.9857i 0.464962 + 0.885850i
929929 −15.6818 27.1617i −0.514504 0.891148i −0.999858 0.0168299i 0.994643π-0.994643\pi
0.485354 0.874318i 0.338691π-0.338691\pi
930930 0.268553 + 6.05678i 0.00880619 + 0.198610i
931931 −42.7469 1.37041i −1.40097 0.0449134i
932932 0.159562 + 1.79579i 0.00522661 + 0.0588231i
933933 −6.31694 1.69262i −0.206807 0.0554139i
934934 5.85268 + 18.5186i 0.191506 + 0.605948i
935935 −3.37407 1.94802i −0.110344 0.0637071i
936936 1.76307 13.6053i 0.0576279 0.444704i
937937 47.0197i 1.53607i 0.640410 + 0.768033i 0.278764π0.278764\pi
−0.640410 + 0.768033i 0.721236π0.721236\pi
938938 27.6084 4.43237i 0.901445 0.144722i
939939 −9.74359 + 9.74359i −0.317970 + 0.317970i
940940 8.33523 + 1.45809i 0.271865 + 0.0475578i
941941 18.2900 4.90080i 0.596238 0.159762i 0.0519356 0.998650i 0.483461π-0.483461\pi
0.544303 + 0.838889i 0.316794π0.316794\pi
942942 2.07952 4.00133i 0.0677544 0.130370i
943943 −15.0485 26.0648i −0.490047 0.848786i
944944 19.5114 28.0264i 0.635042 0.912180i
945945 7.05850 + 1.04459i 0.229613 + 0.0339804i
946946 −18.9169 + 0.838761i −0.615042 + 0.0272705i
947947 12.5608 46.8775i 0.408171 1.52331i −0.389962 0.920831i 0.627512π-0.627512\pi
0.798132 0.602482i 0.205822π-0.205822\pi
948948 1.09982 0.401990i 0.0357206 0.0130560i
949949 1.47598 + 5.50842i 0.0479122 + 0.178811i
950950 1.86446 8.43707i 0.0604911 0.273735i
951951 4.86908i 0.157891i
952952 11.3882 + 20.3782i 0.369093 + 0.660462i
953953 43.9007i 1.42208i −0.703149 0.711042i 0.748223π-0.748223\pi
0.703149 0.711042i 0.251777π-0.251777\pi
954954 6.94128 + 1.53392i 0.224732 + 0.0496623i
955955 −6.72386 25.0938i −0.217579 0.812016i
956956 −5.90906 + 12.7169i −0.191113 + 0.411295i
957957 −0.812239 + 3.03132i −0.0262560 + 0.0979886i
958958 1.93275 + 43.5901i 0.0624443 + 1.40833i
959959 −4.77205 12.0640i −0.154097 0.389565i
960960 3.60007 0.980326i 0.116192 0.0316399i
961961 −26.7443 46.3225i −0.862720 1.49428i
962962 −7.49134 3.89330i −0.241530 0.125525i
963963 −9.42805 + 2.52624i −0.303815 + 0.0814069i
964964 −0.973937 1.38693i −0.0313684 0.0446699i
965965 −0.877050 + 0.877050i −0.0282332 + 0.0282332i
966966 5.72669 4.65739i 0.184253 0.149849i
967967 47.1575i 1.51648i 0.651974 + 0.758241i 0.273941π0.273941\pi
−0.651974 + 0.758241i 0.726059π0.726059\pi
968968 16.2975 + 21.1502i 0.523821 + 0.679793i
969969 −7.69847 4.44471i −0.247310 0.142785i
970970 −12.0083 + 3.79513i −0.385563 + 0.121854i
971971 10.8615 + 2.91032i 0.348561 + 0.0933966i 0.428852 0.903375i 0.358918π-0.358918\pi
−0.0802908 + 0.996771i 0.525585π0.525585\pi
972972 17.4815 + 14.6284i 0.560720 + 0.469208i
973973 3.92231 0.452572i 0.125744 0.0145088i
974974 22.8582 1.01351i 0.732422 0.0324750i
975975 −0.406511 0.704098i −0.0130188 0.0225492i
976976 −15.0062 + 7.04705i −0.480337 + 0.225570i
977977 27.6146 47.8300i 0.883471 1.53022i 0.0360141 0.999351i 0.488534π-0.488534\pi
0.847457 0.530865i 0.178133π-0.178133\pi
978978 −3.11551 4.88308i −0.0996231 0.156144i
979979 −2.30422 2.30422i −0.0736432 0.0736432i
980980 12.5008 + 6.30326i 0.399322 + 0.201350i
981981 38.3286 38.3286i 1.22374 1.22374i
982982 6.02151 27.2486i 0.192154 0.869537i
983983 −43.0347 24.8461i −1.37259 0.792468i −0.381341 0.924435i 0.624537π-0.624537\pi
−0.991254 + 0.131967i 0.957871π0.957871\pi
984984 −8.66455 + 3.60961i −0.276216 + 0.115070i
985985 −15.1797 + 8.76401i −0.483666 + 0.279245i
986986 −16.0459 + 17.5349i −0.511007 + 0.558425i
987987 −0.598424 5.18638i −0.0190481 0.165084i
988988 1.88527 + 21.2178i 0.0599784 + 0.675029i
989989 −11.7368 + 43.8023i −0.373208 + 1.39283i
990990 −4.36077 2.26632i −0.138594 0.0720284i
991991 26.5894 46.0542i 0.844639 1.46296i −0.0412944 0.999147i 0.513148π-0.513148\pi
0.885934 0.463811i 0.153519π-0.153519\pi
992992 −38.2167 + 35.2579i −1.21338 + 1.11944i
993993 9.95706 0.315978
994994 0.867336 8.42278i 0.0275102 0.267154i
995995 −5.48390 5.48390i −0.173851 0.173851i
996996 −3.59983 + 2.52789i −0.114065 + 0.0800994i
997997 −1.00208 3.73982i −0.0317362 0.118441i 0.948241 0.317553i 0.102861π-0.102861\pi
−0.979977 + 0.199112i 0.936194π0.936194\pi
998998 11.0416 + 34.9371i 0.349516 + 1.10591i
999999 7.99858 4.61798i 0.253064 0.146106i
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 560.2.cp.a.221.11 256
7.2 even 3 inner 560.2.cp.a.541.55 yes 256
16.5 even 4 inner 560.2.cp.a.501.55 yes 256
112.37 even 12 inner 560.2.cp.a.261.11 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.cp.a.221.11 256 1.1 even 1 trivial
560.2.cp.a.261.11 yes 256 112.37 even 12 inner
560.2.cp.a.501.55 yes 256 16.5 even 4 inner
560.2.cp.a.541.55 yes 256 7.2 even 3 inner