Properties

Label 74.2.f.a.9.1
Level 7474
Weight 22
Character 74.9
Analytic conductor 0.5910.591
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,2,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 74=237 74 = 2 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 74.f (of order 99, degree 66, 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: 0.5908929749570.590892974957
Analytic rank: 00
Dimension: 66
Coefficient field: Q(ζ18)\Q(\zeta_{18})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x3+1 x^{6} - x^{3} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 9.1
Root 0.766044+0.642788i-0.766044 + 0.642788i of defining polynomial
Character χ\chi == 74.9
Dual form 74.2.f.a.33.1

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+(0.1736480.984808i)q2+(0.2660441.50881i)q3+(0.939693+0.342020i)q4+(1.798131.50881i)q51.53209q6+(1.93969+1.62760i)q7+(0.500000+0.866025i)q8+(0.613341+0.223238i)q9+(1.17365+2.03282i)q10+(0.5603070.970481i)q11+(0.266044+1.50881i)q12+(1.705740.620838i)q13+(1.266042.19285i)q14+(2.75490+2.31164i)q15+(0.7660440.642788i)q16+(2.81908+1.02606i)q17+(0.1133410.642788i)q18+(0.971782+5.51125i)q19+(2.20574+0.802823i)q20+(2.971782.49362i)q21+(0.858441+0.720317i)q22+(4.55303+7.88609i)q23+(1.439690.524005i)q24+(0.0885259+0.502055i)q25+(0.9076041.57202i)q26+(2.798134.84651i)q27+(2.379390.866025i)q28+(4.524817.83721i)q29+(2.75490+2.31164i)q304.53209q31+(0.7660440.642788i)q32+(1.61334+0.587208i)q33+(0.5209452.95442i)q34+(1.032095.85327i)q350.652704q36+(2.33750+5.61570i)q37+5.59627q38+(0.4829262.73881i)q39+(0.4076042.31164i)q40+(6.985452.54250i)q41+(2.971782.49362i)q428.92902q43+(0.858441+0.720317i)q44+(0.7660441.32683i)q45+(8.55690+3.11446i)q46+(0.1945930.337044i)q47+(0.7660441.32683i)q48+(0.1021960.579585i)q49+(0.4790550.174362i)q50+(2.298133.98048i)q51+(1.39053+1.16679i)q52+(9.23055+7.74535i)q53+(5.258771.91404i)q54+(0.456767+2.59045i)q55+(0.439693+2.49362i)q56+(8.05690+2.93247i)q57+(6.93242+5.81699i)q58+(6.415345.38311i)q59+(1.798133.11446i)q60+(2.453360.892951i)q61+(0.786989+4.46324i)q62+(0.826352+1.43128i)q63+(0.500000+0.866025i)q64+(4.003871.45729i)q65+(0.858441+1.48686i)q66+(5.62836+4.72275i)q673.00000q68+(10.6873+8.96773i)q69+(5.58512+2.03282i)q70+(0.448311+2.54250i)q71+(0.113341+0.642788i)q720.709141q73+(5.124493.27714i)q74+0.781059q75+(0.9717825.51125i)q76+(0.4927262.79439i)q77+(2.61334+0.951178i)q78+(3.39646+2.84997i)q792.34730q80+(5.068054.25260i)q81+(3.716886.43783i)q82+(6.81180+2.47929i)q83+(1.93969+3.35965i)q84+(3.520946.09845i)q85+(1.55051+8.79336i)q86+(13.0287+4.74205i)q87+(0.5603070.970481i)q88+(9.95336+8.35186i)q89+(1.17365+0.984808i)q90+(4.31908+1.57202i)q91+(1.581258.96773i)q92+(1.20574+6.83807i)q93+(0.3657150.133109i)q94+(10.06288.44372i)q95+(1.17365+0.984808i)q96+(7.3473012.7259i)q97+(0.553033+0.201288i)q98+(0.1270110.720317i)q99+O(q100)q+(-0.173648 - 0.984808i) q^{2} +(0.266044 - 1.50881i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.79813 - 1.50881i) q^{5} -1.53209 q^{6} +(1.93969 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +(-1.17365 + 2.03282i) q^{10} +(-0.560307 - 0.970481i) q^{11} +(0.266044 + 1.50881i) q^{12} +(1.70574 - 0.620838i) q^{13} +(1.26604 - 2.19285i) q^{14} +(-2.75490 + 2.31164i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.81908 + 1.02606i) q^{17} +(0.113341 - 0.642788i) q^{18} +(-0.971782 + 5.51125i) q^{19} +(2.20574 + 0.802823i) q^{20} +(2.97178 - 2.49362i) q^{21} +(-0.858441 + 0.720317i) q^{22} +(-4.55303 + 7.88609i) q^{23} +(1.43969 - 0.524005i) q^{24} +(0.0885259 + 0.502055i) q^{25} +(-0.907604 - 1.57202i) q^{26} +(2.79813 - 4.84651i) q^{27} +(-2.37939 - 0.866025i) q^{28} +(-4.52481 - 7.83721i) q^{29} +(2.75490 + 2.31164i) q^{30} -4.53209 q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.61334 + 0.587208i) q^{33} +(0.520945 - 2.95442i) q^{34} +(-1.03209 - 5.85327i) q^{35} -0.652704 q^{36} +(2.33750 + 5.61570i) q^{37} +5.59627 q^{38} +(-0.482926 - 2.73881i) q^{39} +(0.407604 - 2.31164i) q^{40} +(6.98545 - 2.54250i) q^{41} +(-2.97178 - 2.49362i) q^{42} -8.92902 q^{43} +(0.858441 + 0.720317i) q^{44} +(-0.766044 - 1.32683i) q^{45} +(8.55690 + 3.11446i) q^{46} +(0.194593 - 0.337044i) q^{47} +(-0.766044 - 1.32683i) q^{48} +(-0.102196 - 0.579585i) q^{49} +(0.479055 - 0.174362i) q^{50} +(2.29813 - 3.98048i) q^{51} +(-1.39053 + 1.16679i) q^{52} +(-9.23055 + 7.74535i) q^{53} +(-5.25877 - 1.91404i) q^{54} +(-0.456767 + 2.59045i) q^{55} +(-0.439693 + 2.49362i) q^{56} +(8.05690 + 2.93247i) q^{57} +(-6.93242 + 5.81699i) q^{58} +(6.41534 - 5.38311i) q^{59} +(1.79813 - 3.11446i) q^{60} +(2.45336 - 0.892951i) q^{61} +(0.786989 + 4.46324i) q^{62} +(0.826352 + 1.43128i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.00387 - 1.45729i) q^{65} +(0.858441 + 1.48686i) q^{66} +(5.62836 + 4.72275i) q^{67} -3.00000 q^{68} +(10.6873 + 8.96773i) q^{69} +(-5.58512 + 2.03282i) q^{70} +(-0.448311 + 2.54250i) q^{71} +(0.113341 + 0.642788i) q^{72} -0.709141 q^{73} +(5.12449 - 3.27714i) q^{74} +0.781059 q^{75} +(-0.971782 - 5.51125i) q^{76} +(0.492726 - 2.79439i) q^{77} +(-2.61334 + 0.951178i) q^{78} +(3.39646 + 2.84997i) q^{79} -2.34730 q^{80} +(-5.06805 - 4.25260i) q^{81} +(-3.71688 - 6.43783i) q^{82} +(6.81180 + 2.47929i) q^{83} +(-1.93969 + 3.35965i) q^{84} +(-3.52094 - 6.09845i) q^{85} +(1.55051 + 8.79336i) q^{86} +(-13.0287 + 4.74205i) q^{87} +(0.560307 - 0.970481i) q^{88} +(-9.95336 + 8.35186i) q^{89} +(-1.17365 + 0.984808i) q^{90} +(4.31908 + 1.57202i) q^{91} +(1.58125 - 8.96773i) q^{92} +(-1.20574 + 6.83807i) q^{93} +(-0.365715 - 0.133109i) q^{94} +(10.0628 - 8.44372i) q^{95} +(-1.17365 + 0.984808i) q^{96} +(7.34730 - 12.7259i) q^{97} +(-0.553033 + 0.201288i) q^{98} +(-0.127011 - 0.720317i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q3+3q5+6q7+3q83q96q109q113q12+3q1418q156q18+9q19+3q20+3q21+3q2215q23+3q24+21q259q26++27q99+O(q100) 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{10} - 9 q^{11} - 3 q^{12} + 3 q^{14} - 18 q^{15} - 6 q^{18} + 9 q^{19} + 3 q^{20} + 3 q^{21} + 3 q^{22} - 15 q^{23} + 3 q^{24} + 21 q^{25} - 9 q^{26}+ \cdots + 27 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/74Z)×\left(\mathbb{Z}/74\mathbb{Z}\right)^\times.

nn 3939
χ(n)\chi(n) e(49)e\left(\frac{4}{9}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.173648 0.984808i −0.122788 0.696364i
33 0.266044 1.50881i 0.153601 0.871114i −0.806453 0.591298i 0.798616π-0.798616\pi
0.960054 0.279815i 0.0902733π-0.0902733\pi
44 −0.939693 + 0.342020i −0.469846 + 0.171010i
55 −1.79813 1.50881i −0.804150 0.674762i 0.145054 0.989424i 0.453664π-0.453664\pi
−0.949204 + 0.314662i 0.898109π0.898109\pi
66 −1.53209 −0.625473
77 1.93969 + 1.62760i 0.733135 + 0.615173i 0.930984 0.365059i 0.118951π-0.118951\pi
−0.197849 + 0.980232i 0.563396π0.563396\pi
88 0.500000 + 0.866025i 0.176777 + 0.306186i
99 0.613341 + 0.223238i 0.204447 + 0.0744126i
1010 −1.17365 + 2.03282i −0.371140 + 0.642834i
1111 −0.560307 0.970481i −0.168939 0.292611i 0.769108 0.639119i 0.220701π-0.220701\pi
−0.938047 + 0.346508i 0.887367π0.887367\pi
1212 0.266044 + 1.50881i 0.0768004 + 0.435557i
1313 1.70574 0.620838i 0.473086 0.172189i −0.0944636 0.995528i 0.530114π-0.530114\pi
0.567550 + 0.823339i 0.307891π0.307891\pi
1414 1.26604 2.19285i 0.338365 0.586065i
1515 −2.75490 + 2.31164i −0.711312 + 0.596862i
1616 0.766044 0.642788i 0.191511 0.160697i
1717 2.81908 + 1.02606i 0.683727 + 0.248856i 0.660447 0.750873i 0.270367π-0.270367\pi
0.0232799 + 0.999729i 0.492589π0.492589\pi
1818 0.113341 0.642788i 0.0267147 0.151506i
1919 −0.971782 + 5.51125i −0.222942 + 1.26437i 0.643639 + 0.765330i 0.277424π0.277424\pi
−0.866581 + 0.499037i 0.833687π0.833687\pi
2020 2.20574 + 0.802823i 0.493218 + 0.179517i
2121 2.97178 2.49362i 0.648496 0.544153i
2222 −0.858441 + 0.720317i −0.183020 + 0.153572i
2323 −4.55303 + 7.88609i −0.949373 + 1.64436i −0.202624 + 0.979257i 0.564947π0.564947\pi
−0.746749 + 0.665106i 0.768386π0.768386\pi
2424 1.43969 0.524005i 0.293876 0.106962i
2525 0.0885259 + 0.502055i 0.0177052 + 0.100411i
2626 −0.907604 1.57202i −0.177996 0.308298i
2727 2.79813 4.84651i 0.538501 0.932711i
2828 −2.37939 0.866025i −0.449662 0.163663i
2929 −4.52481 7.83721i −0.840237 1.45533i −0.889694 0.456557i 0.849082π-0.849082\pi
0.0494571 0.998776i 0.484251π-0.484251\pi
3030 2.75490 + 2.31164i 0.502974 + 0.422045i
3131 −4.53209 −0.813987 −0.406994 0.913431i 0.633423π-0.633423\pi
−0.406994 + 0.913431i 0.633423π0.633423\pi
3232 −0.766044 0.642788i −0.135419 0.113630i
3333 −1.61334 + 0.587208i −0.280847 + 0.102220i
3434 0.520945 2.95442i 0.0893413 0.506679i
3535 −1.03209 5.85327i −0.174455 0.989383i
3636 −0.652704 −0.108784
3737 2.33750 + 5.61570i 0.384282 + 0.923216i
3838 5.59627 0.907834
3939 −0.482926 2.73881i −0.0773300 0.438560i
4040 0.407604 2.31164i 0.0644478 0.365502i
4141 6.98545 2.54250i 1.09094 0.397071i 0.266974 0.963704i 0.413976π-0.413976\pi
0.823971 + 0.566633i 0.191754π0.191754\pi
4242 −2.97178 2.49362i −0.458556 0.384774i
4343 −8.92902 −1.36166 −0.680831 0.732441i 0.738381π-0.738381\pi
−0.680831 + 0.732441i 0.738381π0.738381\pi
4444 0.858441 + 0.720317i 0.129415 + 0.108592i
4545 −0.766044 1.32683i −0.114195 0.197792i
4646 8.55690 + 3.11446i 1.26165 + 0.459202i
4747 0.194593 0.337044i 0.0283843 0.0491630i −0.851484 0.524380i 0.824297π-0.824297\pi
0.879869 + 0.475217i 0.157630π0.157630\pi
4848 −0.766044 1.32683i −0.110569 0.191511i
4949 −0.102196 0.579585i −0.0145995 0.0827978i
5050 0.479055 0.174362i 0.0677487 0.0246585i
5151 2.29813 3.98048i 0.321803 0.557379i
5252 −1.39053 + 1.16679i −0.192832 + 0.161805i
5353 −9.23055 + 7.74535i −1.26791 + 1.06391i −0.273122 + 0.961979i 0.588056π0.588056\pi
−0.994792 + 0.101927i 0.967499π0.967499\pi
5454 −5.25877 1.91404i −0.715628 0.260467i
5555 −0.456767 + 2.59045i −0.0615904 + 0.349297i
5656 −0.439693 + 2.49362i −0.0587564 + 0.333224i
5757 8.05690 + 2.93247i 1.06716 + 0.388416i
5858 −6.93242 + 5.81699i −0.910271 + 0.763808i
5959 6.41534 5.38311i 0.835207 0.700822i −0.121273 0.992619i 0.538698π-0.538698\pi
0.956480 + 0.291797i 0.0942533π0.0942533\pi
6060 1.79813 3.11446i 0.232138 0.402075i
6161 2.45336 0.892951i 0.314121 0.114331i −0.180149 0.983639i 0.557658π-0.557658\pi
0.494269 + 0.869309i 0.335436π0.335436\pi
6262 0.786989 + 4.46324i 0.0999477 + 0.566832i
6363 0.826352 + 1.43128i 0.104111 + 0.180325i
6464 −0.500000 + 0.866025i −0.0625000 + 0.108253i
6565 −4.00387 1.45729i −0.496619 0.180755i
6666 0.858441 + 1.48686i 0.105667 + 0.183020i
6767 5.62836 + 4.72275i 0.687613 + 0.576976i 0.918220 0.396071i 0.129627π-0.129627\pi
−0.230607 + 0.973047i 0.574071π0.574071\pi
6868 −3.00000 −0.363803
6969 10.6873 + 8.96773i 1.28660 + 1.07959i
7070 −5.58512 + 2.03282i −0.667550 + 0.242968i
7171 −0.448311 + 2.54250i −0.0532047 + 0.301739i −0.999785 0.0207290i 0.993401π-0.993401\pi
0.946580 + 0.322468i 0.104512π0.104512\pi
7272 0.113341 + 0.642788i 0.0133573 + 0.0757532i
7373 −0.709141 −0.0829986 −0.0414993 0.999139i 0.513213π-0.513213\pi
−0.0414993 + 0.999139i 0.513213π0.513213\pi
7474 5.12449 3.27714i 0.595709 0.380960i
7575 0.781059 0.0901889
7676 −0.971782 5.51125i −0.111471 0.632183i
7777 0.492726 2.79439i 0.0561513 0.318450i
7878 −2.61334 + 0.951178i −0.295903 + 0.107700i
7979 3.39646 + 2.84997i 0.382132 + 0.320646i 0.813539 0.581511i 0.197538π-0.197538\pi
−0.431407 + 0.902157i 0.641983π0.641983\pi
8080 −2.34730 −0.262436
8181 −5.06805 4.25260i −0.563116 0.472511i
8282 −3.71688 6.43783i −0.410461 0.710939i
8383 6.81180 + 2.47929i 0.747693 + 0.272138i 0.687634 0.726057i 0.258649π-0.258649\pi
0.0600581 + 0.998195i 0.480871π0.480871\pi
8484 −1.93969 + 3.35965i −0.211638 + 0.366567i
8585 −3.52094 6.09845i −0.381900 0.661470i
8686 1.55051 + 8.79336i 0.167195 + 0.948213i
8787 −13.0287 + 4.74205i −1.39682 + 0.508402i
8888 0.560307 0.970481i 0.0597290 0.103454i
8989 −9.95336 + 8.35186i −1.05505 + 0.885296i −0.993616 0.112815i 0.964013π-0.964013\pi
−0.0614384 + 0.998111i 0.519569π0.519569\pi
9090 −1.17365 + 0.984808i −0.123713 + 0.103808i
9191 4.31908 + 1.57202i 0.452762 + 0.164792i
9292 1.58125 8.96773i 0.164857 0.934950i
9393 −1.20574 + 6.83807i −0.125029 + 0.709075i
9494 −0.365715 0.133109i −0.0377206 0.0137292i
9595 10.0628 8.44372i 1.03242 0.866307i
9696 −1.17365 + 0.984808i −0.119785 + 0.100512i
9797 7.34730 12.7259i 0.746005 1.29212i −0.203719 0.979029i 0.565303π-0.565303\pi
0.949724 0.313089i 0.101364π-0.101364\pi
9898 −0.553033 + 0.201288i −0.0558648 + 0.0203331i
9999 −0.127011 0.720317i −0.0127651 0.0723946i
100100 −0.254900 0.441500i −0.0254900 0.0441500i
101101 −1.51367 + 2.62175i −0.150616 + 0.260874i −0.931454 0.363859i 0.881459π-0.881459\pi
0.780838 + 0.624733i 0.214792π0.214792\pi
102102 −4.31908 1.57202i −0.427652 0.155653i
103103 −4.20826 7.28893i −0.414653 0.718199i 0.580739 0.814090i 0.302764π-0.302764\pi
−0.995392 + 0.0958903i 0.969430π0.969430\pi
104104 1.39053 + 1.16679i 0.136353 + 0.114413i
105105 −9.10607 −0.888661
106106 9.23055 + 7.74535i 0.896550 + 0.752295i
107107 −5.67752 + 2.06645i −0.548866 + 0.199771i −0.601543 0.798841i 0.705447π-0.705447\pi
0.0526763 + 0.998612i 0.483225π0.483225\pi
108108 −0.971782 + 5.51125i −0.0935097 + 0.530320i
109109 −3.47906 19.7307i −0.333233 1.88986i −0.444024 0.896015i 0.646449π-0.646449\pi
0.110791 0.993844i 0.464662π-0.464662\pi
110110 2.63041 0.250800
111111 9.09492 2.03282i 0.863252 0.192947i
112112 2.53209 0.239260
113113 −0.442219 2.50795i −0.0416004 0.235928i 0.956917 0.290362i 0.0937757π-0.0937757\pi
−0.998517 + 0.0544340i 0.982665π0.982665\pi
114114 1.48886 8.44372i 0.139444 0.790827i
115115 20.0856 7.31056i 1.87299 0.681713i
116116 6.93242 + 5.81699i 0.643659 + 0.540094i
117117 1.18479 0.109534
118118 −6.41534 5.38311i −0.590580 0.495556i
119119 3.79813 + 6.57856i 0.348174 + 0.603056i
120120 −3.37939 1.23000i −0.308494 0.112283i
121121 4.87211 8.43874i 0.442919 0.767159i
122122 −1.30541 2.26103i −0.118186 0.204704i
123123 −1.97771 11.2162i −0.178324 1.01133i
124124 4.25877 1.55007i 0.382449 0.139200i
125125 −5.26991 + 9.12776i −0.471356 + 0.816412i
126126 1.26604 1.06234i 0.112788 0.0946405i
127127 −5.38326 + 4.51709i −0.477687 + 0.400827i −0.849589 0.527445i 0.823150π-0.823150\pi
0.371902 + 0.928272i 0.378706π0.378706\pi
128128 0.939693 + 0.342020i 0.0830579 + 0.0302306i
129129 −2.37551 + 13.4722i −0.209152 + 1.18616i
130130 −0.739885 + 4.19610i −0.0648922 + 0.368022i
131131 0.852044 + 0.310119i 0.0744434 + 0.0270952i 0.378973 0.925408i 0.376277π-0.376277\pi
−0.304530 + 0.952503i 0.598499π0.598499\pi
132132 1.31521 1.10359i 0.114474 0.0960552i
133133 −10.8550 + 9.10846i −0.941251 + 0.789803i
134134 3.67365 6.36295i 0.317355 0.549675i
135135 −12.3439 + 4.49281i −1.06239 + 0.386679i
136136 0.520945 + 2.95442i 0.0446706 + 0.253340i
137137 −0.979055 1.69577i −0.0836464 0.144880i 0.821167 0.570688i 0.193323π-0.193323\pi
−0.904814 + 0.425808i 0.859990π0.859990\pi
138138 6.97565 12.0822i 0.593807 1.02850i
139139 −12.7811 4.65193i −1.08408 0.394571i −0.262652 0.964891i 0.584597π-0.584597\pi
−0.821423 + 0.570319i 0.806819π0.806819\pi
140140 2.97178 + 5.14728i 0.251161 + 0.435024i
141141 −0.456767 0.383273i −0.0384667 0.0322774i
142142 2.58172 0.216653
143143 −1.55825 1.30753i −0.130307 0.109341i
144144 0.613341 0.223238i 0.0511117 0.0186031i
145145 −3.68866 + 20.9194i −0.306327 + 1.73727i
146146 0.123141 + 0.698367i 0.0101912 + 0.0577973i
147147 −0.901674 −0.0743688
148148 −4.11721 4.47756i −0.338433 0.368053i
149149 −6.73648 −0.551874 −0.275937 0.961176i 0.588988π-0.588988\pi
−0.275937 + 0.961176i 0.588988π0.588988\pi
150150 −0.135630 0.769193i −0.0110741 0.0628044i
151151 0.832748 4.72275i 0.0677681 0.384332i −0.931993 0.362476i 0.881931π-0.881931\pi
0.999761 0.0218558i 0.00695748π-0.00695748\pi
152152 −5.25877 + 1.91404i −0.426543 + 0.155249i
153153 1.50000 + 1.25865i 0.121268 + 0.101756i
154154 −2.83750 −0.228652
155155 8.14930 + 6.83807i 0.654568 + 0.549247i
156156 1.39053 + 2.40847i 0.111331 + 0.192832i
157157 13.5954 + 4.94832i 1.08503 + 0.394919i 0.821778 0.569808i 0.192983π-0.192983\pi
0.263253 + 0.964727i 0.415205π0.415205\pi
158158 2.21688 3.83975i 0.176366 0.305474i
159159 9.23055 + 15.9878i 0.732030 + 1.26791i
160160 0.407604 + 2.31164i 0.0322239 + 0.182751i
161161 −21.6668 + 7.88609i −1.70759 + 0.621511i
162162 −3.30793 + 5.72951i −0.259896 + 0.450153i
163163 7.69846 6.45978i 0.602990 0.505969i −0.289415 0.957204i 0.593461π-0.593461\pi
0.892405 + 0.451235i 0.149016π0.149016\pi
164164 −5.69459 + 4.77833i −0.444673 + 0.373125i
165165 3.78699 + 1.37835i 0.294817 + 0.107305i
166166 1.25877 7.13884i 0.0976995 0.554082i
167167 1.81315 10.2829i 0.140306 0.795713i −0.830712 0.556703i 0.812066π-0.812066\pi
0.971017 0.239010i 0.0768228π-0.0768228\pi
168168 3.64543 + 1.32683i 0.281251 + 0.102367i
169169 −7.43448 + 6.23827i −0.571883 + 0.479867i
170170 −5.39440 + 4.52644i −0.413732 + 0.347162i
171171 −1.82635 + 3.16333i −0.139665 + 0.241906i
172172 8.39053 3.05390i 0.639772 0.232858i
173173 0.182266 + 1.03368i 0.0138575 + 0.0785895i 0.990952 0.134215i 0.0428513π-0.0428513\pi
−0.977095 + 0.212805i 0.931740π0.931740\pi
174174 6.93242 + 12.0073i 0.525545 + 0.910271i
175175 −0.645430 + 1.11792i −0.0487899 + 0.0845066i
176176 −1.05303 0.383273i −0.0793754 0.0288903i
177177 −6.41534 11.1117i −0.482207 0.835207i
178178 9.95336 + 8.35186i 0.746036 + 0.625999i
179179 9.15570 0.684329 0.342164 0.939640i 0.388840π-0.388840\pi
0.342164 + 0.939640i 0.388840π0.388840\pi
180180 1.17365 + 0.984808i 0.0874786 + 0.0734032i
181181 21.2408 7.73103i 1.57882 0.574643i 0.603871 0.797082i 0.293624π-0.293624\pi
0.974947 + 0.222439i 0.0714019π0.0714019\pi
182182 0.798133 4.52644i 0.0591616 0.335522i
183183 −0.694593 3.93923i −0.0513458 0.291196i
184184 −9.10607 −0.671308
185185 4.26991 13.6246i 0.313930 1.00170i
186186 6.94356 0.509127
187187 −0.583778 3.31077i −0.0426901 0.242108i
188188 −0.0675813 + 0.383273i −0.00492888 + 0.0279530i
189189 13.3157 4.84651i 0.968573 0.352532i
190190 −10.0628 8.44372i −0.730035 0.612572i
191191 −19.1334 −1.38444 −0.692222 0.721684i 0.743368π-0.743368\pi
−0.692222 + 0.721684i 0.743368π0.743368\pi
192192 1.17365 + 0.984808i 0.0847008 + 0.0710724i
193193 9.50640 + 16.4656i 0.684285 + 1.18522i 0.973661 + 0.228001i 0.0732191π0.0732191\pi
−0.289375 + 0.957216i 0.593448π0.593448\pi
194194 −13.8084 5.02585i −0.991385 0.360835i
195195 −3.26399 + 5.65339i −0.233739 + 0.404848i
196196 0.294263 + 0.509678i 0.0210188 + 0.0364056i
197197 3.20914 + 18.1999i 0.228642 + 1.29669i 0.855599 + 0.517639i 0.173189π0.173189\pi
−0.626958 + 0.779053i 0.715700π0.715700\pi
198198 −0.687319 + 0.250164i −0.0488456 + 0.0177784i
199199 2.78699 4.82721i 0.197564 0.342192i −0.750174 0.661241i 0.770030π-0.770030\pi
0.947738 + 0.319049i 0.103364π0.103364\pi
200200 −0.390530 + 0.327693i −0.0276146 + 0.0231714i
201201 8.62314 7.23567i 0.608229 0.510365i
202202 2.84477 + 1.03541i 0.200157 + 0.0728513i
203203 3.97906 22.5663i 0.279275 1.58385i
204204 −0.798133 + 4.52644i −0.0558805 + 0.316914i
205205 −16.3969 5.96799i −1.14521 0.416823i
206206 −6.44743 + 5.41004i −0.449214 + 0.376935i
207207 −4.55303 + 3.82045i −0.316458 + 0.265540i
208208 0.907604 1.57202i 0.0629310 0.109000i
209209 5.89306 2.14490i 0.407631 0.148366i
210210 1.58125 + 8.96773i 0.109117 + 0.618832i
211211 −10.8550 18.8015i −0.747292 1.29435i −0.949116 0.314925i 0.898021π-0.898021\pi
0.201825 0.979422i 0.435313π-0.435313\pi
212212 6.02481 10.4353i 0.413786 0.716698i
213213 3.71688 + 1.35283i 0.254677 + 0.0926947i
214214 3.02094 + 5.23243i 0.206508 + 0.357682i
215215 16.0556 + 13.4722i 1.09498 + 0.918797i
216216 5.59627 0.380778
217217 −8.79086 7.37641i −0.596762 0.500743i
218218 −18.8268 + 6.85240i −1.27511 + 0.464103i
219219 −0.188663 + 1.06996i −0.0127487 + 0.0723012i
220220 −0.456767 2.59045i −0.0307952 0.174648i
221221 5.44562 0.366312
222222 −3.58125 8.60375i −0.240358 0.577446i
223223 −10.1429 −0.679219 −0.339610 0.940567i 0.610295π-0.610295\pi
−0.339610 + 0.940567i 0.610295π0.610295\pi
224224 −0.439693 2.49362i −0.0293782 0.166612i
225225 −0.0577812 + 0.327693i −0.00385208 + 0.0218462i
226226 −2.39306 + 0.871001i −0.159184 + 0.0579381i
227227 −3.34524 2.80699i −0.222031 0.186306i 0.524986 0.851111i 0.324070π-0.324070\pi
−0.747017 + 0.664804i 0.768515π0.768515\pi
228228 −8.57398 −0.567826
229229 −9.01889 7.56774i −0.595985 0.500091i 0.294167 0.955754i 0.404958π-0.404958\pi
−0.890152 + 0.455663i 0.849402π0.849402\pi
230230 −10.6873 18.5110i −0.704701 1.22058i
231231 −4.08512 1.48686i −0.268781 0.0978284i
232232 4.52481 7.83721i 0.297069 0.514538i
233233 −8.13816 14.0957i −0.533148 0.923440i −0.999251 0.0387091i 0.987675π-0.987675\pi
0.466102 0.884731i 0.345658π-0.345658\pi
234234 −0.205737 1.16679i −0.0134495 0.0762756i
235235 −0.858441 + 0.312447i −0.0559985 + 0.0203818i
236236 −4.18732 + 7.25265i −0.272571 + 0.472107i
237237 5.20368 4.36640i 0.338015 0.283628i
238238 5.81908 4.88279i 0.377195 0.316504i
239239 14.6493 + 5.33191i 0.947584 + 0.344893i 0.769157 0.639060i 0.220677π-0.220677\pi
0.178428 + 0.983953i 0.442899π0.442899\pi
240240 −0.624485 + 3.54163i −0.0403103 + 0.228611i
241241 −0.151826 + 0.861050i −0.00977999 + 0.0554651i −0.989307 0.145847i 0.953409π-0.953409\pi
0.979527 + 0.201312i 0.0645205π0.0645205\pi
242242 −9.15657 3.33272i −0.588607 0.214235i
243243 5.09627 4.27628i 0.326926 0.274323i
244244 −2.00000 + 1.67820i −0.128037 + 0.107436i
245245 −0.690722 + 1.19637i −0.0441286 + 0.0764330i
246246 −10.7023 + 3.89533i −0.682356 + 0.248357i
247247 1.76399 + 10.0041i 0.112240 + 0.636543i
248248 −2.26604 3.92490i −0.143894 0.249232i
249249 5.55303 9.61814i 0.351909 0.609525i
250250 9.90420 + 3.60483i 0.626397 + 0.227990i
251251 1.26991 + 2.19956i 0.0801563 + 0.138835i 0.903317 0.428974i 0.141125π-0.141125\pi
−0.823161 + 0.567809i 0.807791π0.807791\pi
252252 −1.26604 1.06234i −0.0797533 0.0669210i
253253 10.2044 0.641545
254254 5.38326 + 4.51709i 0.337775 + 0.283427i
255255 −10.1382 + 3.68999i −0.634876 + 0.231076i
256256 0.173648 0.984808i 0.0108530 0.0615505i
257257 2.89187 + 16.4006i 0.180390 + 1.02304i 0.931736 + 0.363135i 0.118294π0.118294\pi
−0.751346 + 0.659908i 0.770595π0.770595\pi
258258 13.6800 0.851682
259259 −4.60607 + 14.6972i −0.286207 + 0.913242i
260260 4.26083 0.264245
261261 −1.02569 5.81699i −0.0634888 0.360063i
262262 0.157451 0.892951i 0.00972738 0.0551667i
263263 6.14068 2.23503i 0.378651 0.137818i −0.145681 0.989332i 0.546537π-0.546537\pi
0.524332 + 0.851514i 0.324315π0.324315\pi
264264 −1.31521 1.10359i −0.0809454 0.0679213i
265265 28.2841 1.73748
266266 10.8550 + 9.10846i 0.665565 + 0.558475i
267267 9.95336 + 17.2397i 0.609136 + 1.05505i
268268 −6.90420 2.51292i −0.421741 0.153501i
269269 4.42902 7.67128i 0.270042 0.467726i −0.698830 0.715287i 0.746296π-0.746296\pi
0.968872 + 0.247561i 0.0796291π0.0796291\pi
270270 6.56805 + 11.3762i 0.399719 + 0.692333i
271271 1.64930 + 9.35365i 0.100188 + 0.568194i 0.993034 + 0.117831i 0.0375941π0.0375941\pi
−0.892846 + 0.450362i 0.851295π0.851295\pi
272272 2.81908 1.02606i 0.170932 0.0622141i
273273 3.52094 6.09845i 0.213097 0.369095i
274274 −1.50000 + 1.25865i −0.0906183 + 0.0760378i
275275 0.437633 0.367218i 0.0263903 0.0221441i
276276 −13.1099 4.77163i −0.789125 0.287218i
277277 −5.11040 + 28.9825i −0.307054 + 1.74139i 0.306619 + 0.951832i 0.400802π0.400802\pi
−0.613674 + 0.789560i 0.710309π0.710309\pi
278278 −2.36184 + 13.3947i −0.141654 + 0.803360i
279279 −2.77972 1.01173i −0.166417 0.0605709i
280280 4.55303 3.82045i 0.272096 0.228315i
281281 4.54323 3.81223i 0.271027 0.227418i −0.497137 0.867672i 0.665615π-0.665615\pi
0.768163 + 0.640254i 0.221171π0.221171\pi
282282 −0.298133 + 0.516382i −0.0177536 + 0.0307501i
283283 −21.2062 + 7.71843i −1.26058 + 0.458813i −0.883963 0.467557i 0.845134π-0.845134\pi
−0.376615 + 0.926370i 0.622912π0.622912\pi
284284 −0.448311 2.54250i −0.0266023 0.150869i
285285 −10.0628 17.4293i −0.596071 1.03242i
286286 −1.01707 + 1.76162i −0.0601409 + 0.104167i
287287 17.6878 + 6.43783i 1.04408 + 0.380013i
288288 −0.326352 0.565258i −0.0192305 0.0333081i
289289 −6.12836 5.14230i −0.360492 0.302488i
290290 21.2422 1.24738
291291 −17.2463 14.4713i −1.01099 0.848325i
292292 0.666374 0.242540i 0.0389966 0.0141936i
293293 −0.705737 + 4.00243i −0.0412296 + 0.233825i −0.998458 0.0555078i 0.982322π-0.982322\pi
0.957229 + 0.289333i 0.0934333π0.0934333\pi
294294 0.156574 + 0.887975i 0.00913158 + 0.0517878i
295295 −19.6578 −1.14452
296296 −3.69459 + 4.83218i −0.214744 + 0.280865i
297297 −6.27126 −0.363895
298298 1.16978 + 6.63414i 0.0677634 + 0.384305i
299299 −2.87030 + 16.2783i −0.165994 + 0.941397i
300300 −0.733956 + 0.267138i −0.0423749 + 0.0154232i
301301 −17.3195 14.5328i −0.998282 0.837658i
302302 −4.79561 −0.275956
303303 3.55303 + 2.98135i 0.204116 + 0.171274i
304304 2.79813 + 4.84651i 0.160484 + 0.277966i
305305 −5.75877 2.09602i −0.329746 0.120018i
306306 0.979055 1.69577i 0.0559689 0.0969409i
307307 5.59240 + 9.68631i 0.319175 + 0.552827i 0.980316 0.197434i 0.0632609π-0.0632609\pi
−0.661141 + 0.750261i 0.729928π0.729928\pi
308308 0.492726 + 2.79439i 0.0280757 + 0.159225i
309309 −12.1172 + 4.41030i −0.689324 + 0.250893i
310310 5.31908 9.21291i 0.302103 0.523258i
311311 6.32501 5.30731i 0.358658 0.300950i −0.445597 0.895233i 0.647009π-0.647009\pi
0.804256 + 0.594283i 0.202564π0.202564\pi
312312 2.13041 1.78763i 0.120611 0.101205i
313313 11.0633 + 4.02671i 0.625335 + 0.227603i 0.635199 0.772348i 0.280918π-0.280918\pi
−0.00986477 + 0.999951i 0.503140π0.503140\pi
314314 2.51233 14.2481i 0.141779 0.804067i
315315 0.673648 3.82045i 0.0379558 0.215258i
316316 −4.16637 1.51644i −0.234377 0.0853062i
317317 10.1441 8.51190i 0.569749 0.478076i −0.311814 0.950143i 0.600937π-0.600937\pi
0.881562 + 0.472067i 0.156492π0.156492\pi
318318 14.1420 11.8666i 0.793045 0.665444i
319319 −5.07057 + 8.78249i −0.283898 + 0.491725i
320320 2.20574 0.802823i 0.123304 0.0448791i
321321 1.60741 + 9.11608i 0.0897169 + 0.508810i
322322 11.5287 + 19.9683i 0.642469 + 1.11279i
323323 −8.39440 + 14.5395i −0.467077 + 0.809001i
324324 6.21688 + 2.26276i 0.345382 + 0.125709i
325325 0.462697 + 0.801414i 0.0256658 + 0.0444544i
326326 −7.69846 6.45978i −0.426378 0.357774i
327327 −30.6955 −1.69747
328328 5.69459 + 4.77833i 0.314431 + 0.263839i
329329 0.926022 0.337044i 0.0510532 0.0185819i
330330 0.699807 3.96880i 0.0385231 0.218475i
331331 4.26217 + 24.1720i 0.234270 + 1.32861i 0.844145 + 0.536115i 0.180109π0.180109\pi
−0.609875 + 0.792498i 0.708780π0.708780\pi
332332 −7.24897 −0.397839
333333 0.180045 + 3.96616i 0.00986639 + 0.217344i
334334 −10.4415 −0.571334
335335 −2.99479 16.9843i −0.163623 0.927950i
336336 0.673648 3.82045i 0.0367505 0.208423i
337337 −11.3576 + 4.13381i −0.618686 + 0.225183i −0.632299 0.774724i 0.717889π-0.717889\pi
0.0136136 + 0.999907i 0.495667π0.495667\pi
338338 7.43448 + 6.23827i 0.404382 + 0.339317i
339339 −3.90167 −0.211910
340340 5.39440 + 4.52644i 0.292552 + 0.245481i
341341 2.53936 + 4.39831i 0.137514 + 0.238182i
342342 3.43242 + 1.24930i 0.185604 + 0.0675543i
343343 9.60741 16.6405i 0.518751 0.898504i
344344 −4.46451 7.73275i −0.240710 0.416922i
345345 −5.68660 32.2503i −0.306156 1.73630i
346346 0.986329 0.358995i 0.0530254 0.0192997i
347347 0.904200 1.56612i 0.0485400 0.0840738i −0.840735 0.541447i 0.817876π-0.817876\pi
0.889275 + 0.457374i 0.151210π0.151210\pi
348348 10.6211 8.91215i 0.569350 0.477741i
349349 3.95677 3.32012i 0.211801 0.177722i −0.530715 0.847550i 0.678077π-0.678077\pi
0.742516 + 0.669828i 0.233632π0.233632\pi
350350 1.21301 + 0.441500i 0.0648382 + 0.0235992i
351351 1.76399 10.0041i 0.0941546 0.533977i
352352 −0.194593 + 1.10359i −0.0103718 + 0.0588216i
353353 29.1570 + 10.6123i 1.55187 + 0.564835i 0.968856 0.247625i 0.0796500π-0.0796500\pi
0.583017 + 0.812460i 0.301872π0.301872\pi
354354 −9.82888 + 8.24741i −0.522399 + 0.438345i
355355 4.64227 3.89533i 0.246386 0.206743i
356356 6.49660 11.2524i 0.344319 0.596378i
357357 10.9363 3.98048i 0.578810 0.210670i
358358 −1.58987 9.01660i −0.0840272 0.476542i
359359 −1.51367 2.62175i −0.0798885 0.138371i 0.823313 0.567587i 0.192123π-0.192123\pi
−0.903202 + 0.429216i 0.858790π0.858790\pi
360360 0.766044 1.32683i 0.0403741 0.0699300i
361361 −11.5753 4.21307i −0.609227 0.221741i
362362 −11.3020 19.5756i −0.594020 1.02887i
363363 −11.4363 9.59619i −0.600250 0.503669i
364364 −4.59627 −0.240910
365365 1.27513 + 1.06996i 0.0667433 + 0.0560043i
366366 −3.75877 + 1.36808i −0.196474 + 0.0715107i
367367 4.82651 27.3725i 0.251942 1.42883i −0.551860 0.833937i 0.686082π-0.686082\pi
0.803802 0.594897i 0.202807π-0.202807\pi
368368 1.58125 + 8.96773i 0.0824285 + 0.467475i
369369 4.85204 0.252587
370370 −14.1591 1.83915i −0.736097 0.0956131i
371371 −30.5107 −1.58404
372372 −1.20574 6.83807i −0.0625146 0.354538i
373373 0.898681 5.09667i 0.0465319 0.263896i −0.952662 0.304030i 0.901668π-0.901668\pi
0.999194 + 0.0401346i 0.0127787π0.0127787\pi
374374 −3.15910 + 1.14982i −0.163353 + 0.0594557i
375375 12.3701 + 10.3797i 0.638787 + 0.536006i
376376 0.389185 0.0200707
377377 −12.5838 10.5590i −0.648098 0.543818i
378378 −7.08512 12.2718i −0.364419 0.631193i
379379 19.8195 + 7.21372i 1.01806 + 0.370544i 0.796523 0.604608i 0.206670π-0.206670\pi
0.221538 + 0.975152i 0.428892π0.428892\pi
380380 −6.56805 + 11.3762i −0.336934 + 0.583586i
381381 5.38326 + 9.32407i 0.275793 + 0.477687i
382382 3.32248 + 18.8427i 0.169993 + 0.964078i
383383 36.6771 13.3494i 1.87411 0.682121i 0.911455 0.411400i 0.134960π-0.134960\pi
0.962658 0.270721i 0.0872621π-0.0872621\pi
384384 0.766044 1.32683i 0.0390920 0.0677094i
385385 −5.10220 + 4.28125i −0.260032 + 0.218193i
386386 14.5646 12.2212i 0.741321 0.622042i
387387 −5.47653 1.99329i −0.278388 0.101325i
388388 −2.55169 + 14.4713i −0.129542 + 0.734671i
389389 2.78312 15.7838i 0.141110 0.800273i −0.829299 0.558805i 0.811260π-0.811260\pi
0.970409 0.241468i 0.0776289π-0.0776289\pi
390390 6.13429 + 2.23270i 0.310622 + 0.113057i
391391 −20.9270 + 17.5598i −1.05832 + 0.888037i
392392 0.450837 0.378297i 0.0227707 0.0191069i
393393 0.694593 1.20307i 0.0350376 0.0606868i
394394 17.3662 6.32077i 0.874896 0.318436i
395395 −1.80722 10.2492i −0.0909310 0.515695i
396396 0.365715 + 0.633436i 0.0183779 + 0.0318314i
397397 −7.32042 + 12.6793i −0.367401 + 0.636358i −0.989158 0.146852i 0.953086π-0.953086\pi
0.621757 + 0.783210i 0.286419π0.286419\pi
398398 −5.23783 1.90641i −0.262548 0.0955598i
399399 10.8550 + 18.8015i 0.543432 + 0.941251i
400400 0.390530 + 0.327693i 0.0195265 + 0.0163847i
401401 11.8075 0.589637 0.294818 0.955553i 0.404741π-0.404741\pi
0.294818 + 0.955553i 0.404741π0.404741\pi
402402 −8.62314 7.23567i −0.430083 0.360883i
403403 −7.73055 + 2.81369i −0.385086 + 0.140160i
404404 0.525692 2.98135i 0.0261542 0.148328i
405405 2.69665 + 15.2935i 0.133998 + 0.759939i
406406 −22.9145 −1.13723
407407 4.14022 5.41501i 0.205223 0.268412i
408408 4.59627 0.227549
409409 0.975652 + 5.53320i 0.0482429 + 0.273599i 0.999382 0.0351652i 0.0111957π-0.0111957\pi
−0.951139 + 0.308764i 0.900085π0.900085\pi
410410 −3.03003 + 17.1842i −0.149642 + 0.848665i
411411 −2.81908 + 1.02606i −0.139055 + 0.0506118i
412412 6.44743 + 5.41004i 0.317642 + 0.266533i
413413 21.2053 1.04345
414414 4.55303 + 3.82045i 0.223769 + 0.187765i
415415 −8.50774 14.7358i −0.417629 0.723354i
416416 −1.70574 0.620838i −0.0836306 0.0304391i
417417 −10.4192 + 18.0466i −0.510231 + 0.883746i
418418 −3.13563 5.43107i −0.153369 0.265642i
419419 −1.76171 9.99114i −0.0860650 0.488099i −0.997122 0.0758179i 0.975843π-0.975843\pi
0.911057 0.412281i 0.135268π-0.135268\pi
420420 8.55690 3.11446i 0.417534 0.151970i
421421 −5.48158 + 9.49438i −0.267156 + 0.462728i −0.968126 0.250463i 0.919417π-0.919417\pi
0.700970 + 0.713190i 0.252751π0.252751\pi
422422 −16.6309 + 13.9550i −0.809579 + 0.679317i
423423 0.194593 0.163283i 0.00946142 0.00793908i
424424 −11.3229 4.12122i −0.549891 0.200144i
425425 −0.265578 + 1.50617i −0.0128824 + 0.0730598i
426426 0.686852 3.89533i 0.0332781 0.188729i
427427 6.21213 + 2.26103i 0.300626 + 0.109419i
428428 4.62836 3.88365i 0.223720 0.187723i
429429 −2.38737 + 2.00324i −0.115264 + 0.0967176i
430430 10.4795 18.1511i 0.505367 0.875322i
431431 −4.80066 + 1.74730i −0.231240 + 0.0841643i −0.455041 0.890470i 0.650375π-0.650375\pi
0.223802 + 0.974635i 0.428153π0.428153\pi
432432 −0.971782 5.51125i −0.0467549 0.265160i
433433 13.8712 + 24.0257i 0.666609 + 1.15460i 0.978846 + 0.204596i 0.0655882π0.0655882\pi
−0.312237 + 0.950004i 0.601078π0.601078\pi
434434 −5.73783 + 9.93821i −0.275424 + 0.477049i
435435 30.5822 + 11.1310i 1.46630 + 0.533691i
436436 10.0175 + 17.3509i 0.479753 + 0.830957i
437437 −39.0376 32.7564i −1.86742 1.56695i
438438 1.08647 0.0519134
439439 −22.3214 18.7298i −1.06534 0.893927i −0.0707180 0.997496i 0.522529π-0.522529\pi
−0.994622 + 0.103570i 0.966973π0.966973\pi
440440 −2.47178 + 0.899655i −0.117838 + 0.0428894i
441441 0.0667040 0.378297i 0.00317638 0.0180141i
442442 −0.945622 5.36289i −0.0449787 0.255087i
443443 6.97864 0.331565 0.165783 0.986162i 0.446985π-0.446985\pi
0.165783 + 0.986162i 0.446985π0.446985\pi
444444 −7.85117 + 5.02087i −0.372600 + 0.238280i
445445 30.4989 1.44579
446446 1.76130 + 9.98881i 0.0833998 + 0.472984i
447447 −1.79220 + 10.1641i −0.0847683 + 0.480745i
448448 −2.37939 + 0.866025i −0.112415 + 0.0409159i
449449 13.9834 + 11.7335i 0.659917 + 0.553736i 0.910062 0.414472i 0.136034π-0.136034\pi
−0.250145 + 0.968208i 0.580478π0.580478\pi
450450 0.332748 0.0156859
451451 −6.38144 5.35467i −0.300490 0.252141i
452452 1.27332 + 2.20545i 0.0598919 + 0.103736i
453453 −6.90420 2.51292i −0.324388 0.118067i
454454 −2.18345 + 3.78184i −0.102474 + 0.177491i
455455 −5.39440 9.34337i −0.252893 0.438024i
456456 1.48886 + 8.44372i 0.0697221 + 0.395413i
457457 21.4209 7.79656i 1.00203 0.364708i 0.211660 0.977343i 0.432113π-0.432113\pi
0.790365 + 0.612636i 0.209891π0.209891\pi
458458 −5.88666 + 10.1960i −0.275066 + 0.476427i
459459 12.8610 10.7916i 0.600299 0.503710i
460460 −16.3739 + 13.7394i −0.763438 + 0.640601i
461461 −8.17277 2.97465i −0.380644 0.138543i 0.144610 0.989489i 0.453807π-0.453807\pi
−0.525254 + 0.850946i 0.676030π0.676030\pi
462462 −0.754900 + 4.28125i −0.0351211 + 0.199182i
463463 0.592701 3.36137i 0.0275451 0.156216i −0.967933 0.251209i 0.919172π-0.919172\pi
0.995478 + 0.0949930i 0.0302829π0.0302829\pi
464464 −8.50387 3.09516i −0.394782 0.143689i
465465 12.4855 10.4765i 0.578999 0.485838i
466466 −12.4684 + 10.4622i −0.577586 + 0.484653i
467467 −18.3170 + 31.7260i −0.847611 + 1.46810i 0.0357242 + 0.999362i 0.488626π0.488626\pi
−0.883335 + 0.468743i 0.844707π0.844707\pi
468468 −1.11334 + 0.405223i −0.0514642 + 0.0187314i
469469 3.23055 + 18.3214i 0.149173 + 0.846002i
470470 0.456767 + 0.791143i 0.0210691 + 0.0364927i
471471 11.0831 19.1964i 0.510681 0.884525i
472472 7.86959 + 2.86429i 0.362227 + 0.131840i
473473 5.00299 + 8.66544i 0.230038 + 0.398437i
474474 −5.20368 4.36640i −0.239013 0.200556i
475475 −2.85298 −0.130904
476476 −5.81908 4.88279i −0.266717 0.223802i
477477 −7.39053 + 2.68993i −0.338389 + 0.123164i
478478 2.70708 15.3526i 0.123819 0.702213i
479479 −3.57832 20.2936i −0.163497 0.927240i −0.950600 0.310418i 0.899531π-0.899531\pi
0.787103 0.616822i 0.211580π-0.211580\pi
480480 3.59627 0.164146
481481 7.47359 + 8.12771i 0.340766 + 0.370592i
482482 0.874333 0.0398248
483483 6.13429 + 34.7893i 0.279120 + 1.58297i
484484 −1.69207 + 9.59619i −0.0769121 + 0.436190i
485485 −32.4124 + 11.7972i −1.47177 + 0.535681i
486486 −5.09627 4.27628i −0.231171 0.193976i
487487 42.2867 1.91620 0.958098 0.286442i 0.0924726π-0.0924726\pi
0.958098 + 0.286442i 0.0924726π0.0924726\pi
488488 2.00000 + 1.67820i 0.0905357 + 0.0759685i
489489 −7.69846 13.3341i −0.348137 0.602990i
490490 1.29813 + 0.472482i 0.0586437 + 0.0213446i
491491 −16.5560 + 28.6759i −0.747163 + 1.29412i 0.202014 + 0.979383i 0.435251π0.435251\pi
−0.949177 + 0.314742i 0.898082π0.898082\pi
492492 5.69459 + 9.86332i 0.256732 + 0.444673i
493493 −4.71436 26.7364i −0.212324 1.20415i
494494 9.54576 3.47437i 0.429484 0.156319i
495495 −0.858441 + 1.48686i −0.0385840 + 0.0668295i
496496 −3.47178 + 2.91317i −0.155888 + 0.130805i
497497 −5.00774 + 4.20199i −0.224628 + 0.188485i
498498 −10.4363 3.79850i −0.467661 0.170215i
499499 −1.73577 + 9.84402i −0.0777036 + 0.440679i 0.920990 + 0.389586i 0.127382π0.127382\pi
−0.998694 + 0.0510934i 0.983729π0.983729\pi
500500 1.83022 10.3797i 0.0818500 0.464195i
501501 −15.0326 5.47140i −0.671605 0.244444i
502502 1.94562 1.63257i 0.0868374 0.0728652i
503503 25.5023 21.3990i 1.13709 0.954132i 0.137751 0.990467i 0.456013π-0.456013\pi
0.999340 + 0.0363348i 0.0115683π0.0115683\pi
504504 −0.826352 + 1.43128i −0.0368086 + 0.0637544i
505505 6.67752 2.43042i 0.297146 0.108152i
506506 −1.77197 10.0494i −0.0787739 0.446749i
507507 7.43448 + 12.8769i 0.330177 + 0.571883i
508508 3.51367 6.08586i 0.155894 0.270016i
509509 −19.3751 7.05196i −0.858786 0.312573i −0.125169 0.992135i 0.539947π-0.539947\pi
−0.733617 + 0.679563i 0.762170π0.762170\pi
510510 5.39440 + 9.34337i 0.238868 + 0.413732i
511511 −1.37551 1.15419i −0.0608492 0.0510585i
512512 −1.00000 −0.0441942
513513 23.9911 + 20.1310i 1.05923 + 0.888803i
514514 15.6493 5.69588i 0.690261 0.251234i
515515 −3.43061 + 19.4559i −0.151171 + 0.857331i
516516 −2.37551 13.4722i −0.104576 0.593081i
517517 −0.436127 −0.0191808
518518 15.2738 + 1.98394i 0.671092 + 0.0871694i
519519 1.60813 0.0705889
520520 −0.739885 4.19610i −0.0324461 0.184011i
521521 −4.53121 + 25.6978i −0.198516 + 1.12584i 0.708806 + 0.705404i 0.249234π0.249234\pi
−0.907322 + 0.420437i 0.861877π0.861877\pi
522522 −5.55051 + 2.02022i −0.242939 + 0.0884226i
523523 1.10535 + 0.927500i 0.0483337 + 0.0405567i 0.666634 0.745385i 0.267734π-0.267734\pi
−0.618301 + 0.785942i 0.712179π0.712179\pi
524524 −0.906726 −0.0396105
525525 1.51501 + 1.27125i 0.0661207 + 0.0554818i
526526 −3.26739 5.65928i −0.142465 0.246756i
527527 −12.7763 4.65020i −0.556545 0.202566i
528528 −0.858441 + 1.48686i −0.0373588 + 0.0647074i
529529 −29.9602 51.8926i −1.30262 2.25620i
530530 −4.91147 27.8544i −0.213341 1.20992i
531531 5.13651 1.86954i 0.222905 0.0811309i
532532 7.08512 12.2718i 0.307179 0.532050i
533533 10.3369 8.67366i 0.447739 0.375698i
534534 15.2494 12.7958i 0.659908 0.553728i
535535 13.3268 + 4.85057i 0.576169 + 0.209708i
536536 −1.27584 + 7.23567i −0.0551081 + 0.312534i
537537 2.43582 13.8142i 0.105113 0.596128i
538538 −8.32383 3.02962i −0.358866 0.130616i
539539 −0.505215 + 0.423925i −0.0217611 + 0.0182598i
540540 10.0628 8.44372i 0.433035 0.363360i
541541 2.72921 4.72713i 0.117338 0.203235i −0.801374 0.598164i 0.795897π-0.795897\pi
0.918712 + 0.394929i 0.129231π0.129231\pi
542542 8.92514 3.24849i 0.383368 0.139534i
543543 −6.01367 34.1052i −0.258071 1.46360i
544544 −1.50000 2.59808i −0.0643120 0.111392i
545545 −23.5141 + 40.7277i −1.00723 + 1.74458i
546546 −6.61721 2.40847i −0.283190 0.103073i
547547 −20.1086 34.8291i −0.859781 1.48918i −0.872137 0.489261i 0.837266π-0.837266\pi
0.0123559 0.999924i 0.496067π-0.496067\pi
548548 1.50000 + 1.25865i 0.0640768 + 0.0537668i
549549 1.70409 0.0727287
550550 −0.437633 0.367218i −0.0186607 0.0156582i
551551 47.5899 17.3213i 2.02740 0.737913i
552552 −2.42262 + 13.7394i −0.103113 + 0.584786i
553553 1.94949 + 11.0561i 0.0829009 + 0.470154i
554554 29.4296 1.25035
555555 −19.4210 10.0673i −0.824377 0.427331i
556556 13.6013 0.576824
557557 −3.06640 17.3904i −0.129928 0.736856i −0.978259 0.207389i 0.933503π-0.933503\pi
0.848331 0.529466i 0.177608π-0.177608\pi
558558 −0.513671 + 2.91317i −0.0217454 + 0.123324i
559559 −15.2306 + 5.54347i −0.644184 + 0.234464i
560560 −4.55303 3.82045i −0.192401 0.161443i
561561 −5.15064 −0.217460
562562 −4.54323 3.81223i −0.191645 0.160809i
563563 −1.15523 2.00092i −0.0486871 0.0843286i 0.840655 0.541571i 0.182170π-0.182170\pi
−0.889342 + 0.457243i 0.848837π0.848837\pi
564564 0.560307 + 0.203935i 0.0235932 + 0.00858722i
565565 −2.98886 + 5.17685i −0.125742 + 0.217792i
566566 11.2836 + 19.5437i 0.474284 + 0.821485i
567567 −2.90895 16.4975i −0.122164 0.692828i
568568 −2.42602 + 0.883000i −0.101794 + 0.0370498i
569569 0.141559 0.245188i 0.00593447 0.0102788i −0.863043 0.505131i 0.831444π-0.831444\pi
0.868977 + 0.494852i 0.164778π0.164778\pi
570570 −15.4172 + 12.9365i −0.645754 + 0.541852i
571571 −8.40420 + 7.05196i −0.351705 + 0.295115i −0.801474 0.598029i 0.795951π-0.795951\pi
0.449769 + 0.893145i 0.351506π0.351506\pi
572572 1.91147 + 0.695720i 0.0799227 + 0.0290895i
573573 −5.09034 + 28.8687i −0.212652 + 1.20601i
574574 3.26857 18.5370i 0.136428 0.773719i
575575 −4.36231 1.58775i −0.181921 0.0662138i
576576 −0.500000 + 0.419550i −0.0208333 + 0.0174812i
577577 −12.1382 + 10.1851i −0.505318 + 0.424012i −0.859478 0.511173i 0.829211π-0.829211\pi
0.354160 + 0.935185i 0.384767π0.384767\pi
578578 −4.00000 + 6.92820i −0.166378 + 0.288175i
579579 27.3726 9.96280i 1.13757 0.414040i
580580 −3.68866 20.9194i −0.153163 0.868633i
581581 9.17752 + 15.8959i 0.380748 + 0.659474i
582582 −11.2567 + 19.4972i −0.466606 + 0.808185i
583583 12.6887 + 4.61830i 0.525511 + 0.191270i
584584 −0.354570 0.614134i −0.0146722 0.0254130i
585585 −2.13041 1.78763i −0.0880818 0.0739094i
586586 4.06418 0.167890
587587 −14.2947 11.9947i −0.590007 0.495074i 0.298209 0.954500i 0.403611π-0.403611\pi
−0.888216 + 0.459426i 0.848055π0.848055\pi
588588 0.847296 0.308391i 0.0349419 0.0127178i
589589 4.40420 24.9775i 0.181472 1.02918i
590590 3.41353 + 19.3591i 0.140533 + 0.797002i
591591 28.3141 1.16469
592592 5.40033 + 2.79936i 0.221952 + 0.115053i
593593 −39.4329 −1.61932 −0.809658 0.586901i 0.800348π-0.800348\pi
−0.809658 + 0.586901i 0.800348π0.800348\pi
594594 1.08899 + 6.17598i 0.0446819 + 0.253404i
595595 3.09627 17.5598i 0.126935 0.719882i
596596 6.33022 2.30401i 0.259296 0.0943760i
597597 −6.54189 5.48930i −0.267742 0.224662i
598598 16.5294 0.675937
599599 5.35710 + 4.49514i 0.218885 + 0.183666i 0.745636 0.666353i 0.232146π-0.232146\pi
−0.526751 + 0.850019i 0.676590π0.676590\pi
600600 0.390530 + 0.676417i 0.0159433 + 0.0276146i
601601 −33.7301 12.2768i −1.37588 0.500780i −0.454954 0.890515i 0.650344π-0.650344\pi
−0.920927 + 0.389735i 0.872567π0.872567\pi
602602 −11.3045 + 19.5800i −0.460738 + 0.798022i
603603 2.39780 + 4.15312i 0.0976461 + 0.169128i
604604 0.832748 + 4.72275i 0.0338841 + 0.192166i
605605 −21.4932 + 7.82288i −0.873823 + 0.318045i
606606 2.31908 4.01676i 0.0942061 0.163170i
607607 8.60788 7.22287i 0.349383 0.293167i −0.451159 0.892443i 0.648989π-0.648989\pi
0.800542 + 0.599276i 0.204545π0.204545\pi
608608 4.28699 3.59721i 0.173860 0.145886i
609609 −32.9898 12.0073i −1.33681 0.486560i
610610 −1.06418 + 6.03525i −0.0430873 + 0.244360i
611611 0.122674 0.695720i 0.00496286 0.0281458i
612612 −1.84002 0.669713i −0.0743785 0.0270716i
613613 0.735767 0.617381i 0.0297173 0.0249358i −0.627808 0.778368i 0.716048π-0.716048\pi
0.657525 + 0.753432i 0.271603π0.271603\pi
614614 8.56805 7.18945i 0.345778 0.290142i
615615 −13.3669 + 23.1521i −0.539005 + 0.933585i
616616 2.66637 0.970481i 0.107431 0.0391018i
617617 −3.71641 21.0768i −0.149617 0.848521i −0.963543 0.267553i 0.913785π-0.913785\pi
0.813926 0.580969i 0.197326π-0.197326\pi
618618 6.44743 + 11.1673i 0.259354 + 0.449214i
619619 −5.72550 + 9.91686i −0.230127 + 0.398592i −0.957845 0.287284i 0.907248π-0.907248\pi
0.727718 + 0.685876i 0.240581π0.240581\pi
620620 −9.99660 3.63846i −0.401473 0.146124i
621621 25.4800 + 44.1326i 1.02248 + 1.77098i
622622 −6.32501 5.30731i −0.253610 0.212804i
623623 −32.8999 −1.31811
624624 −2.13041 1.78763i −0.0852849 0.0715625i
625625 25.6434 9.33342i 1.02573 0.373337i
626626 2.04442 11.5945i 0.0817113 0.463408i
627627 −1.66843 9.46216i −0.0666308 0.377882i
628628 −14.4679 −0.577333
629629 0.827534 + 18.2295i 0.0329959 + 0.726858i
630630 −3.87939 −0.154558
631631 8.35710 + 47.3954i 0.332691 + 1.88678i 0.448938 + 0.893563i 0.351802π0.351802\pi
−0.116247 + 0.993220i 0.537087π0.537087\pi
632632 −0.769915 + 4.36640i −0.0306256 + 0.173686i
633633 −31.2558 + 11.3762i −1.24231 + 0.452163i
634634 −10.1441 8.51190i −0.402873 0.338051i
635635 16.4953 0.654594
636636 −14.1420 11.8666i −0.560768 0.470540i
637637 −0.534148 0.925172i −0.0211637 0.0366566i
638638 9.52956 + 3.46848i 0.377279 + 0.137318i
639639 −0.842549 + 1.45934i −0.0333307 + 0.0577305i
640640 −1.17365 2.03282i −0.0463925 0.0803542i
641641 5.53121 + 31.3691i 0.218470 + 1.23900i 0.874783 + 0.484515i 0.161004π0.161004\pi
−0.656313 + 0.754488i 0.727885π0.727885\pi
642642 8.69846 3.16598i 0.343301 0.124951i
643643 −11.2897 + 19.5543i −0.445221 + 0.771146i −0.998068 0.0621372i 0.980208π-0.980208\pi
0.552846 + 0.833283i 0.313542π0.313542\pi
644644 17.6630 14.8210i 0.696019 0.584029i
645645 24.5985 20.6406i 0.968567 0.812724i
646646 15.7763 + 5.74211i 0.620711 + 0.225920i
647647 5.12954 29.0911i 0.201663 1.14369i −0.700942 0.713218i 0.747237π-0.747237\pi
0.902605 0.430469i 0.141652π-0.141652\pi
648648 1.14883 6.51536i 0.0451304 0.255947i
649649 −8.81877 3.20977i −0.346167 0.125995i
650650 0.708892 0.594831i 0.0278050 0.0233312i
651651 −13.4684 + 11.3013i −0.527867 + 0.442933i
652652 −5.02481 + 8.70323i −0.196787 + 0.340845i
653653 8.71600 3.17237i 0.341084 0.124144i −0.165799 0.986160i 0.553020π-0.553020\pi
0.506882 + 0.862015i 0.330798π0.330798\pi
654654 5.33022 + 30.2292i 0.208428 + 1.18205i
655655 −1.06418 1.84321i −0.0415809 0.0720202i
656656 3.71688 6.43783i 0.145120 0.251355i
657657 −0.434945 0.158307i −0.0169688 0.00617614i
658658 −0.492726 0.853427i −0.0192085 0.0332700i
659659 20.8418 + 17.4884i 0.811883 + 0.681250i 0.951056 0.309018i 0.100000π-0.100000\pi
−0.139174 + 0.990268i 0.544445π0.544445\pi
660660 −4.03003 −0.156869
661661 8.43763 + 7.08001i 0.328186 + 0.275381i 0.791960 0.610573i 0.209061π-0.209061\pi
−0.463774 + 0.885953i 0.653505π0.653505\pi
662662 23.0646 8.39484i 0.896433 0.326275i
663663 1.44878 8.21643i 0.0562659 0.319100i
664664 1.25877 + 7.13884i 0.0488498 + 0.277041i
665665 33.2618 1.28984
666666 3.87464 0.866025i 0.150139 0.0335578i
667667 82.4065 3.19079
668668 1.81315 + 10.2829i 0.0701528 + 0.397856i
669669 −2.69846 + 15.3037i −0.104329 + 0.591677i
670670 −16.2062 + 5.89858i −0.626100 + 0.227882i
671671 −2.24123 1.88061i −0.0865217 0.0726003i
672672 −3.87939 −0.149651
673673 10.1141 + 8.48670i 0.389868 + 0.327138i 0.816562 0.577258i 0.195877π-0.195877\pi
−0.426694 + 0.904396i 0.640322π0.640322\pi
674674 6.04323 + 10.4672i 0.232777 + 0.403181i
675675 2.68092 + 0.975776i 0.103189 + 0.0375576i
676676 4.85251 8.40480i 0.186635 0.323261i
677677 17.7763 + 30.7895i 0.683199 + 1.18334i 0.973999 + 0.226552i 0.0727452π0.0727452\pi
−0.290800 + 0.956784i 0.593921π0.593921\pi
678678 0.677519 + 3.84240i 0.0260199 + 0.147566i
679679 34.9641 12.7259i 1.34180 0.488375i
680680 3.52094 6.09845i 0.135022 0.233865i
681681 −5.12520 + 4.30055i −0.196398 + 0.164798i
682682 3.89053 3.26454i 0.148976 0.125006i
683683 −30.8756 11.2378i −1.18142 0.430002i −0.324717 0.945811i 0.605269π-0.605269\pi
−0.856704 + 0.515809i 0.827491π0.827491\pi
684684 0.634285 3.59721i 0.0242525 0.137543i
685685 −0.798133 + 4.52644i −0.0304951 + 0.172946i
686686 −18.0560 6.57186i −0.689382 0.250915i
687687 −13.8177 + 11.5945i −0.527179 + 0.442356i
688688 −6.84002 + 5.73946i −0.260773 + 0.218815i
689689 −10.9363 + 18.9422i −0.416639 + 0.721641i
690690 −30.7729 + 11.2004i −1.17150 + 0.426393i
691691 −7.38089 41.8591i −0.280782 1.59240i −0.719973 0.694002i 0.755846π-0.755846\pi
0.439191 0.898394i 0.355265π-0.355265\pi
692692 −0.524815 0.909006i −0.0199505 0.0345552i
693693 0.926022 1.60392i 0.0351767 0.0609278i
694694 −1.69934 0.618509i −0.0645061 0.0234783i
695695 15.9632 + 27.6490i 0.605517 + 1.04879i
696696 −10.6211 8.91215i −0.402591 0.337814i
697697 22.3013 0.844722
698698 −3.95677 3.32012i −0.149766 0.125668i
699699 −23.4329 + 8.52887i −0.886313 + 0.322592i
700700 0.224155 1.27125i 0.00847228 0.0480487i
701701 −2.88161 16.3424i −0.108837 0.617244i −0.989618 0.143721i 0.954093π-0.954093\pi
0.880781 0.473523i 0.157018π-0.157018\pi
702702 −10.1584 −0.383404
703703 −33.2211 + 7.42528i −1.25296 + 0.280050i
704704 1.12061 0.0422348
705705 0.243041 + 1.37835i 0.00915344 + 0.0519117i
706706 5.38800 30.5569i 0.202780 1.15002i
707707 −7.20321 + 2.62175i −0.270905 + 0.0986012i
708708 9.82888 + 8.24741i 0.369392 + 0.309957i
709709 5.68779 0.213609 0.106805 0.994280i 0.465938π-0.465938\pi
0.106805 + 0.994280i 0.465938π0.465938\pi
710710 −4.64227 3.89533i −0.174221 0.146189i
711711 1.44697 + 2.50622i 0.0542655 + 0.0939906i
712712 −12.2096 4.44393i −0.457574 0.166543i
713713 20.6348 35.7404i 0.772778 1.33849i
714714 −5.81908 10.0789i −0.217774 0.377195i
715715 0.829126 + 4.70221i 0.0310076 + 0.175853i
716716 −8.60354 + 3.13143i −0.321529 + 0.117027i
717717 11.9422 20.6845i 0.445990 0.772478i
718718 −2.31908 + 1.94594i −0.0865472 + 0.0726217i
719719 9.21735 7.73427i 0.343749 0.288440i −0.454525 0.890734i 0.650191π-0.650191\pi
0.798274 + 0.602294i 0.205747π0.205747\pi
720720 −1.43969 0.524005i −0.0536542 0.0195285i
721721 3.70068 20.9876i 0.137821 0.781620i
722722 −2.13903 + 12.1311i −0.0796066 + 0.451471i
723723 1.25877 + 0.458155i 0.0468142 + 0.0170390i
724724 −17.3157 + 14.5296i −0.643532 + 0.539987i
725725 3.53415 2.96550i 0.131255 0.110136i
726726 −7.46451 + 12.9289i −0.277034 + 0.479837i
727727 −25.5898 + 9.31391i −0.949072 + 0.345434i −0.769742 0.638355i 0.779615π-0.779615\pi
−0.179330 + 0.983789i 0.557393π0.557393\pi
728728 0.798133 + 4.52644i 0.0295808 + 0.167761i
729729 −15.0201 26.0155i −0.556299 0.963538i
730730 0.832282 1.44155i 0.0308041 0.0533543i
731731 −25.1716 9.16171i −0.931005 0.338858i
732732 2.00000 + 3.46410i 0.0739221 + 0.128037i
733733 −16.2324 13.6206i −0.599556 0.503087i 0.291747 0.956496i 0.405764π-0.405764\pi
−0.891303 + 0.453408i 0.850208π0.850208\pi
734734 −27.7948 −1.02592
735735 1.62133 + 1.36046i 0.0598037 + 0.0501812i
736736 8.55690 3.11446i 0.315412 0.114800i
737737 1.42973 8.10840i 0.0526648 0.298677i
738738 −0.842549 4.77833i −0.0310146 0.175893i
739739 −30.6195 −1.12636 −0.563178 0.826336i 0.690421π-0.690421\pi
−0.563178 + 0.826336i 0.690421π0.690421\pi
740740 0.647489 + 14.2634i 0.0238022 + 0.524331i
741741 15.5635 0.571741
742742 5.29813 + 30.0472i 0.194501 + 1.10307i
743743 −2.98798 + 16.9457i −0.109618 + 0.621676i 0.879656 + 0.475610i 0.157772π0.157772\pi
−0.989275 + 0.146067i 0.953339π0.953339\pi
744744 −6.52481 + 2.37484i −0.239211 + 0.0870658i
745745 12.1131 + 10.1641i 0.443789 + 0.372383i
746746 −5.17530 −0.189481
747747 3.62449 + 3.04130i 0.132613 + 0.111275i
748748 1.68092 + 2.91144i 0.0614606 + 0.106453i
749749 −14.3760 5.23243i −0.525287 0.191189i
750750 8.07398 13.9845i 0.294820 0.510643i
751751 13.7506 + 23.8168i 0.501767 + 0.869086i 0.999998 + 0.00204181i 0.000649930π0.000649930\pi
−0.498231 + 0.867045i 0.666017π0.666017\pi
752752 −0.0675813 0.383273i −0.00246444 0.0139765i
753753 3.65657 1.33088i 0.133253 0.0485001i
754754 −8.21348 + 14.2262i −0.299117 + 0.518086i
755755 −8.62314 + 7.23567i −0.313828 + 0.263333i
756756 −10.8550 + 9.10846i −0.394794 + 0.331271i
757757 −18.0753 6.57888i −0.656959 0.239113i −0.00803598 0.999968i 0.502558π-0.502558\pi
−0.648923 + 0.760854i 0.724780π0.724780\pi
758758 3.66250 20.7711i 0.133028 0.754440i
759759 2.71482 15.3965i 0.0985418 0.558858i
760760 12.3439 + 4.49281i 0.447760 + 0.162971i
761761 30.1313 25.2832i 1.09226 0.916515i 0.0953800 0.995441i 0.469593π-0.469593\pi
0.996881 + 0.0789255i 0.0251489π0.0251489\pi
762762 8.24763 6.92058i 0.298780 0.250706i
763763 25.3653 43.9340i 0.918286 1.59052i
764764 17.9795 6.54401i 0.650476 0.236754i
765765 −0.798133 4.52644i −0.0288566 0.163654i
766766 −19.5155 33.8018i −0.705123 1.22131i
767767 7.60085 13.1651i 0.274451 0.475363i
768768 −1.43969 0.524005i −0.0519504 0.0189084i
769769 −6.48087 11.2252i −0.233706 0.404791i 0.725190 0.688549i 0.241752π-0.241752\pi
−0.958896 + 0.283758i 0.908419π0.908419\pi
770770 5.10220 + 4.28125i 0.183870 + 0.154286i
771771 25.5149 0.918895
772772 −14.5646 12.2212i −0.524193 0.439850i
773773 −11.1878 + 4.07202i −0.402397 + 0.146460i −0.535287 0.844670i 0.679796π-0.679796\pi
0.132890 + 0.991131i 0.457574π0.457574\pi
774774 −1.01202 + 5.73946i −0.0363764 + 0.206301i
775775 −0.401207 2.27536i −0.0144118 0.0817333i
776776 14.6946 0.527505
777777 20.9500 + 10.8598i 0.751576 + 0.389594i
778778 −16.0273 −0.574608
779779 7.22399 + 40.9693i 0.258826 + 1.46788i
780780 1.13357 6.42880i 0.0405883 0.230188i
781781 2.71864 0.989503i 0.0972804 0.0354072i
782782 20.9270 + 17.5598i 0.748346 + 0.627937i
783783 −50.6441 −1.80987
784784 −0.450837 0.378297i −0.0161013 0.0135106i
785785 −16.9802 29.4106i −0.606051 1.04971i
786786 −1.30541 0.475129i −0.0465623 0.0169473i
787787 −10.4618 + 18.1204i −0.372924 + 0.645923i −0.990014 0.140970i 0.954978π-0.954978\pi
0.617090 + 0.786892i 0.288311π0.288311\pi
788788 −9.24035 16.0048i −0.329174 0.570146i
789789 −1.73854 9.85976i −0.0618937 0.351017i
790790 −9.77972 + 3.55953i −0.347947 + 0.126642i
791791 3.22416 5.58440i 0.114638 0.198558i
792792 0.560307 0.470154i 0.0199097 0.0167062i
793793 3.63041 3.04628i 0.128920 0.108177i
794794 13.7579 + 5.00746i 0.488249 + 0.177708i
795795 7.52481 42.6753i 0.266878 1.51354i
796796 −0.967911 + 5.48930i −0.0343067 + 0.194563i
797797 3.67752 + 1.33851i 0.130264 + 0.0474124i 0.406330 0.913726i 0.366808π-0.366808\pi
−0.276065 + 0.961139i 0.589031π0.589031\pi
798798 16.6309 13.9550i 0.588727 0.494000i
799799 0.894400 0.750491i 0.0316416 0.0265505i
800800 0.254900 0.441500i 0.00901208 0.0156094i
801801 −7.96926 + 2.90057i −0.281580 + 0.102487i
802802 −2.05035 11.6281i −0.0724002 0.410602i
803803 0.397337 + 0.688207i 0.0140217 + 0.0242863i
804804 −5.62836 + 9.74860i −0.198497 + 0.343807i
805805 50.8585 + 18.5110i 1.79253 + 0.652426i
806806 4.11334 + 7.12452i 0.144886 + 0.250950i
807807 −10.3962 8.72346i −0.365964 0.307080i
808808 −3.02734 −0.106501
809809 11.5921 + 9.72697i 0.407558 + 0.341982i 0.823406 0.567452i 0.192071π-0.192071\pi
−0.415848 + 0.909434i 0.636515π0.636515\pi
810810 14.5929 5.31137i 0.512741 0.186622i
811811 6.99629 39.6779i 0.245673 1.39328i −0.573251 0.819380i 0.694318π-0.694318\pi
0.818924 0.573901i 0.194571π-0.194571\pi
812812 3.97906 + 22.5663i 0.139637 + 0.791923i
813813 14.5517 0.510350
814814 −6.05169 3.13701i −0.212112 0.109952i
815815 −23.5895 −0.826303
816816 −0.798133 4.52644i −0.0279403 0.158457i
817817 8.67705 49.2100i 0.303572 1.72164i
818818 5.27972 1.92166i 0.184601 0.0671892i
819819 2.29813 + 1.92836i 0.0803033 + 0.0673825i
820820 17.4492 0.609354
821821 19.4008 + 16.2792i 0.677092 + 0.568148i 0.915155 0.403102i 0.132068π-0.132068\pi
−0.238063 + 0.971250i 0.576512π0.576512\pi
822822 1.50000 + 2.59808i 0.0523185 + 0.0906183i
823823 −26.7212 9.72573i −0.931443 0.339018i −0.168662 0.985674i 0.553945π-0.553945\pi
−0.762781 + 0.646656i 0.776167π0.776167\pi
824824 4.20826 7.28893i 0.146602 0.253922i
825825 −0.437633 0.758003i −0.0152364 0.0263903i
826826 −3.68227 20.8832i −0.128122 0.726618i
827827 −2.64068 + 0.961130i −0.0918255 + 0.0334218i −0.387524 0.921859i 0.626670π-0.626670\pi
0.295699 + 0.955281i 0.404447π0.404447\pi
828828 2.97178 5.14728i 0.103277 0.178880i
829829 −15.2585 + 12.8034i −0.529950 + 0.444681i −0.868084 0.496417i 0.834649π-0.834649\pi
0.338134 + 0.941098i 0.390204π0.390204\pi
830830 −13.0346 + 10.9373i −0.452438 + 0.379641i
831831 42.3696 + 15.4213i 1.46979 + 0.534959i
832832 −0.315207 + 1.78763i −0.0109279 + 0.0619749i
833833 0.306589 1.73875i 0.0106227 0.0602443i
834834 19.5817 + 7.12716i 0.678059 + 0.246793i
835835 −18.7752 + 15.7543i −0.649743 + 0.545199i
836836 −4.80406 + 4.03109i −0.166152 + 0.139418i
837837 −12.6814 + 21.9648i −0.438333 + 0.759215i
838838 −9.53343 + 3.46989i −0.329327 + 0.119865i
839839 6.48726 + 36.7911i 0.223965 + 1.27017i 0.864654 + 0.502369i 0.167538π0.167538\pi
−0.640688 + 0.767801i 0.721351π0.721351\pi
840840 −4.55303 7.88609i −0.157095 0.272096i
841841 −26.4479 + 45.8091i −0.911997 + 1.57962i
842842 10.3020 + 3.74962i 0.355030 + 0.129221i
843843 −4.54323 7.86911i −0.156477 0.271027i
844844 16.6309 + 13.9550i 0.572459 + 0.480350i
845845 22.7806 0.783675
846846 −0.194593 0.163283i −0.00669024 0.00561377i
847847 23.1853 8.43874i 0.796655 0.289959i
848848 −2.09240 + 11.8666i −0.0718532 + 0.407500i
849849 6.00387 + 34.0496i 0.206052 + 1.16858i
850850 1.52940 0.0524580
851851 −54.9286 7.13479i −1.88293 0.244577i
852852 −3.95542 −0.135511
853853 3.87227 + 21.9608i 0.132584 + 0.751922i 0.976512 + 0.215465i 0.0691266π0.0691266\pi
−0.843928 + 0.536457i 0.819762π0.819762\pi
854854 1.14796 6.51038i 0.0392822 0.222781i
855855 8.05690 2.93247i 0.275540 0.100288i
856856 −4.62836 3.88365i −0.158194 0.132740i
857857 −18.2817 −0.624491 −0.312245 0.950002i 0.601081π-0.601081\pi
−0.312245 + 0.950002i 0.601081π0.601081\pi
858858 2.38737 + 2.00324i 0.0815036 + 0.0683897i
859859 7.59358 + 13.1525i 0.259090 + 0.448756i 0.965998 0.258549i 0.0832442π-0.0832442\pi
−0.706909 + 0.707305i 0.749911π0.749911\pi
860860 −19.6951 7.16842i −0.671596 0.244441i
861861 14.4192 24.9748i 0.491406 0.851139i
862862 2.55438 + 4.42431i 0.0870024 + 0.150693i
863863 0.353855 + 2.00681i 0.0120454 + 0.0683127i 0.990238 0.139387i 0.0445133π-0.0445133\pi
−0.978193 + 0.207700i 0.933402π0.933402\pi
864864 −5.25877 + 1.91404i −0.178907 + 0.0651168i
865865 1.23190 2.13371i 0.0418857 0.0725482i
866866 21.2520 17.8325i 0.722171 0.605974i
867867 −9.38919 + 7.87846i −0.318873 + 0.267567i
868868 10.7836 + 3.92490i 0.366019 + 0.133220i
869869 0.862778 4.89306i 0.0292677 0.165986i
870870 5.65136 32.0505i 0.191599 1.08661i
871871 12.5326 + 4.56148i 0.424649 + 0.154560i
872872 15.3478 12.8783i 0.519741 0.436114i
873873 7.34730 6.16511i 0.248668 0.208657i
874874 −25.4800 + 44.1326i −0.861873 + 1.49281i
875875 −25.0783 + 9.12776i −0.847802 + 0.308575i
876876 −0.188663 1.06996i −0.00637433 0.0361506i
877877 −1.13445 1.96492i −0.0383076 0.0663507i 0.846236 0.532808i 0.178863π-0.178863\pi
−0.884544 + 0.466458i 0.845530π0.845530\pi
878878 −14.5692 + 25.2346i −0.491688 + 0.851628i
879879 5.85117 + 2.12965i 0.197355 + 0.0718313i
880880 1.31521 + 2.27801i 0.0443356 + 0.0767916i
881881 23.1616 + 19.4349i 0.780335 + 0.654779i 0.943333 0.331848i 0.107672π-0.107672\pi
−0.162998 + 0.986626i 0.552116π0.552116\pi
882882 −0.384133 −0.0129344
883883 −1.65136 1.38566i −0.0555727 0.0466310i 0.614578 0.788856i 0.289326π-0.289326\pi
−0.670151 + 0.742225i 0.733771π0.733771\pi
884884 −5.11721 + 1.86251i −0.172110 + 0.0626431i
885885 −5.22984 + 29.6599i −0.175799 + 0.997006i
886886 −1.21183 6.87262i −0.0407122 0.230890i
887887 −30.0387 −1.00860 −0.504300 0.863528i 0.668250π-0.668250\pi
−0.504300 + 0.863528i 0.668250π0.668250\pi
888888 6.30793 + 6.86002i 0.211680 + 0.230207i
889889 −17.7939 −0.596787
890890 −5.29607 30.0355i −0.177525 1.00679i
891891 −1.28740 + 7.30121i −0.0431295 + 0.244600i
892892 9.53121 3.46908i 0.319129 0.116153i
893893 1.66843 + 1.39998i 0.0558320 + 0.0468486i
894894 10.3209 0.345182
895895 −16.4632 13.8142i −0.550303 0.461759i
896896 1.26604 + 2.19285i 0.0422956 + 0.0732581i
897897 23.7973 + 8.66149i 0.794567 + 0.289199i
898898 9.12701 15.8084i 0.304572 0.527535i
899899 20.5069 + 35.5189i 0.683942 + 1.18462i
900900 −0.0577812 0.327693i −0.00192604 0.0109231i
901901 −33.9688 + 12.3636i −1.13167 + 0.411893i
902902 −4.16519 + 7.21432i −0.138686 + 0.240211i
903903 −26.5351 + 22.2656i −0.883032 + 0.740952i
904904 1.95084 1.63695i 0.0648839 0.0544440i
905905 −49.8585 18.1470i −1.65735 0.603227i
906906 −1.27584 + 7.23567i −0.0423871 + 0.240389i
907907 −0.218474 + 1.23903i −0.00725431 + 0.0411412i −0.988220 0.153040i 0.951094π-0.951094\pi
0.980966 + 0.194181i 0.0622049π0.0622049\pi
908908 4.10354 + 1.49357i 0.136181 + 0.0495657i
909909 −1.51367 + 1.27012i −0.0502053 + 0.0421272i
910910 −8.26470 + 6.93491i −0.273972 + 0.229890i
911911 22.8371 39.5550i 0.756626 1.31052i −0.187935 0.982181i 0.560180π-0.560180\pi
0.944562 0.328334i 0.106487π-0.106487\pi
912912 8.05690 2.93247i 0.266791 0.0971039i
913913 −1.41060 7.99989i −0.0466839 0.264758i
914914 −11.3978 19.7416i −0.377006 0.652993i
915915 −4.69459 + 8.13127i −0.155198 + 0.268812i
916916 11.0633 + 4.02671i 0.365542 + 0.133046i
917917 1.14796 + 1.98832i 0.0379088 + 0.0656600i
918918 −12.8610 10.7916i −0.424475 0.356177i
919919 −12.5006 −0.412358 −0.206179 0.978514i 0.566103π-0.566103\pi
−0.206179 + 0.978514i 0.566103π0.566103\pi
920920 16.3739 + 13.7394i 0.539832 + 0.452973i
921921 16.1027 5.86089i 0.530601 0.193123i
922922 −1.51027 + 8.56515i −0.0497380 + 0.282078i
923923 0.813777 + 4.61516i 0.0267858 + 0.151910i
924924 4.34730 0.143016
925925 −2.61246 + 1.67069i −0.0858973 + 0.0549318i
926926 −3.41323 −0.112166
927927 −0.953936 5.41004i −0.0313314 0.177689i
928928 −1.57145 + 8.91215i −0.0515854 + 0.292556i
929929 −14.8769 + 5.41473i −0.488094 + 0.177652i −0.574331 0.818623i 0.694738π-0.694738\pi
0.0862374 + 0.996275i 0.472516π0.472516\pi
930930 −12.4855 10.4765i −0.409414 0.343539i
931931 3.29355 0.107942
932932 12.4684 + 10.4622i 0.408415 + 0.342701i
933933 −6.32501 10.9552i −0.207071 0.358658i
934934 34.4247 + 12.5296i 1.12641 + 0.409980i
935935 −3.94562 + 6.83402i −0.129036 + 0.223496i
936936 0.592396 + 1.02606i 0.0193631 + 0.0335378i
937937 7.32454 + 41.5395i 0.239282 + 1.35704i 0.833405 + 0.552663i 0.186388π0.186388\pi
−0.594123 + 0.804375i 0.702501π0.702501\pi
938938 17.4820 6.36295i 0.570809 0.207758i
939939 9.01889 15.6212i 0.294320 0.509778i
940940 0.699807 0.587208i 0.0228252 0.0191526i
941941 40.3469 33.8551i 1.31527 1.10364i 0.327986 0.944683i 0.393630π-0.393630\pi
0.987285 0.158961i 0.0508143π-0.0508143\pi
942942 −20.8293 7.58126i −0.678657 0.247011i
943943 −11.7547 + 66.6639i −0.382784 + 2.17088i
944944 1.45424 8.24741i 0.0473315 0.268430i
945945 −31.2558 11.3762i −1.01675 0.370068i
946946 7.66503 6.43172i 0.249212 0.209113i
947947 3.45929 2.90269i 0.112412 0.0943248i −0.584849 0.811142i 0.698846π-0.698846\pi
0.697261 + 0.716817i 0.254402π0.254402\pi
948948 −3.39646 + 5.88284i −0.110312 + 0.191066i
949949 −1.20961 + 0.440261i −0.0392655 + 0.0142915i
950950 0.495414 + 2.80963i 0.0160734 + 0.0911566i
951951 −10.1441 17.5701i −0.328945 0.569749i
952952 −3.79813 + 6.57856i −0.123098 + 0.213212i
953953 −44.1715 16.0771i −1.43085 0.520789i −0.493678 0.869645i 0.664348π-0.664348\pi
−0.937176 + 0.348856i 0.886570π0.886570\pi
954954 3.93242 + 6.81115i 0.127317 + 0.220519i
955955 34.4044 + 28.8687i 1.11330 + 0.934170i
956956 −15.5895 −0.504199
957957 11.9021 + 9.98708i 0.384742 + 0.322837i
958958 −19.3640 + 7.04791i −0.625621 + 0.227707i
959959 0.860967 4.88279i 0.0278021 0.157673i
960960 −0.624485 3.54163i −0.0201552 0.114306i
961961 −10.4602 −0.337425
962962 6.70645 8.77141i 0.216225 0.282802i
963963 −3.94356 −0.127080
964964 −0.151826 0.861050i −0.00489000 0.0277325i
965965 7.74969 43.9507i 0.249471 1.41482i
966966 33.1955 12.0822i 1.06805 0.388738i
967967 0.149548 + 0.125486i 0.00480915 + 0.00403536i 0.645189 0.764023i 0.276779π-0.276779\pi
−0.640380 + 0.768058i 0.721223π0.721223\pi
968968 9.74422 0.313191
969969 19.7041 + 16.5337i 0.632988 + 0.531140i
970970 17.2463 + 29.8714i 0.553745 + 0.959114i
971971 −0.752679 0.273953i −0.0241546 0.00879156i 0.329915 0.944011i 0.392980π-0.392980\pi
−0.354069 + 0.935219i 0.615202π0.615202\pi
972972 −3.32635 + 5.76141i −0.106693 + 0.184797i
973973 −17.2199 29.8257i −0.552044 0.956168i
974974 −7.34302 41.6443i −0.235285 1.33437i
975975 1.33228 0.484911i 0.0426672 0.0155296i
976976 1.30541 2.26103i 0.0417851 0.0723739i
977977 −12.6438 + 10.6094i −0.404512 + 0.339426i −0.822235 0.569149i 0.807273π-0.807273\pi
0.417722 + 0.908575i 0.362828π0.362828\pi
978978 −11.7947 + 9.89695i −0.377154 + 0.316470i
979979 13.6823 + 4.97994i 0.437287 + 0.159159i
980980 0.239885 1.36046i 0.00766286 0.0434582i
981981 2.27079 12.8783i 0.0725008 0.411173i
982982 31.1152 + 11.3250i 0.992924 + 0.361395i
983983 −22.4466 + 18.8349i −0.715934 + 0.600740i −0.926257 0.376892i 0.876993π-0.876993\pi
0.210323 + 0.977632i 0.432548π0.432548\pi
984984 8.72462 7.32083i 0.278131 0.233379i
985985 21.6898 37.5679i 0.691096 1.19701i
986986 −25.5116 + 9.28547i −0.812455 + 0.295710i
987987 −0.262174 1.48686i −0.00834509 0.0473274i
988988 −5.07919 8.79742i −0.161591 0.279883i
989989 40.6541 70.4150i 1.29273 2.23907i
990990 1.61334 + 0.587208i 0.0512753 + 0.0186627i
991991 6.89393 + 11.9406i 0.218993 + 0.379307i 0.954500 0.298210i 0.0963895π-0.0963895\pi
−0.735507 + 0.677517i 0.763056π0.763056\pi
992992 3.47178 + 2.91317i 0.110229 + 0.0924933i
993993 37.6049 1.19336
994994 5.00774 + 4.20199i 0.158836 + 0.133279i
995995 −12.2947 + 4.47492i −0.389769 + 0.141864i
996996 −1.92855 + 10.9373i −0.0611084 + 0.346563i
997997 3.43170 + 19.4622i 0.108683 + 0.616373i 0.989685 + 0.143260i 0.0457585π0.0457585\pi
−0.881002 + 0.473113i 0.843130π0.843130\pi
998998 9.99588 0.316414
999999 33.7572 + 4.38479i 1.06803 + 0.138729i
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 74.2.f.a.9.1 6
3.2 odd 2 666.2.x.c.379.1 6
4.3 odd 2 592.2.bc.b.305.1 6
37.12 even 9 2738.2.a.m.1.3 3
37.25 even 18 2738.2.a.p.1.3 3
37.33 even 9 inner 74.2.f.a.33.1 yes 6
111.107 odd 18 666.2.x.c.181.1 6
148.107 odd 18 592.2.bc.b.33.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.f.a.9.1 6 1.1 even 1 trivial
74.2.f.a.33.1 yes 6 37.33 even 9 inner
592.2.bc.b.33.1 6 148.107 odd 18
592.2.bc.b.305.1 6 4.3 odd 2
666.2.x.c.181.1 6 111.107 odd 18
666.2.x.c.379.1 6 3.2 odd 2
2738.2.a.m.1.3 3 37.12 even 9
2738.2.a.p.1.3 3 37.25 even 18