Properties

Label 128.2.k.a.109.4
Level 128128
Weight 22
Character 128.109
Analytic conductor 1.0221.022
Analytic rank 00
Dimension 240240
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 128=27 128 = 2^{7}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 128.k (of order 3232, degree 1616, 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: 1.022085145871.02208514587
Analytic rank: 00
Dimension: 240240
Relative dimension: 1515 over Q(ζ32)\Q(\zeta_{32})
Twist minimal: yes
Sato-Tate group: SU(2)[C32]\mathrm{SU}(2)[C_{32}]

Embedding invariants

Embedding label 109.4
Character χ\chi == 128.109
Dual form 128.2.k.a.101.4

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+(0.9570901.04114i)q2+(2.863111.53036i)q3+(0.167958+1.99294i)q4+(0.865631+1.05477i)q5+(1.14693+4.44560i)q6+(0.162245+0.108408i)q7+(2.235681.73255i)q8+(4.18867+6.26879i)q9+(1.926660.108268i)q10+(0.1441270.0437204i)q11+(3.530805.44896i)q12+(3.75158+3.07884i)q13+(0.04241410.272677i)q14+(4.092581.69520i)q15+(3.943580.669457i)q16+(0.2234630.0925613i)q17+(2.5177710.3608i)q18+(0.742006+7.53372i)q19+(1.956711.90230i)q20+(0.2986200.558679i)q21+(0.0924232+0.191901i)q22+(6.740551.34078i)q23+(9.05243+1.53908i)q24+(0.612220+3.07784i)q25+(6.79611+0.959202i)q26+(1.4444714.6660i)q27+(0.243301+0.305135i)q28+(1.921356.33383i)q29+(5.681922.63850i)q30+(2.37838+2.37838i)q31+(3.07736+4.74656i)q32+(0.345743+0.345743i)q33+(0.117504+0.321246i)q34+(0.254791+0.0772899i)q35+(13.1968+7.29486i)q36+(3.517130.346407i)q37+(8.553846.43791i)q38+(15.45293.07378i)q39+(0.107825+3.85789i)q40+(0.4569362.29717i)q41+(0.295858+0.845612i)q42+(4.588702.45271i)q43+(0.1113390.279892i)q44+(10.23801.00836i)q45+(5.05537+8.30112i)q46+(3.90401+9.42513i)q47+(10.2664+7.95184i)q48+(2.664216.43198i)q49+(2.618523.58317i)q50+(0.498146+0.606993i)q51+(5.505827.99376i)q52+(0.703882+2.32039i)q53+(13.8869+15.5406i)q54+(0.1708760.114176i)q55+(0.5505510.0387305i)q56+(13.653820.4343i)q57+(4.75552+8.06244i)q58+(1.338001.09807i)q59+(2.69105+8.44098i)q60+(3.57815+6.69426i)q61+(4.75256+0.199910i)q62+1.47117iq63+(1.996547.74686i)q646.62221iq65+(0.02906070.690875i)q66+(1.303592.43884i)q67+(0.2220010.429801i)q68+(17.2471+14.1543i)q69+(0.324327+0.191300i)q70+(3.30056+4.93964i)q71+(20.2255+6.75793i)q72+(8.33969+5.57240i)q73+(3.726873.33030i)q74+(2.957369.74910i)q75+(14.88962.74411i)q76+(0.01864420.0227180i)q77+(17.990113.1468i)q78+(0.3333600.804803i)q79+(4.119813.58008i)q80+(9.65299+23.3044i)q81+(2.82902+1.72287i)q82+(1.717960.169204i)q83+(1.163570.501296i)q84+(0.2910680.155579i)q85+(6.945432.43003i)q86+(4.19204+21.0748i)q87+(0.397970+0.151962i)q88+(8.776061.74567i)q89+(8.74885+11.6243i)q90+(0.942446+0.0928229i)q91+(3.8042113.2083i)q92+(10.44943.16978i)q93+(13.54944.95606i)q94+(7.304077.30407i)q95+(1.5468618.2994i)q96+(5.194475.19447i)q97+(4.14672+8.92981i)q98+(0.3296261.08663i)q99+O(q100)q+(-0.957090 - 1.04114i) q^{2} +(-2.86311 - 1.53036i) q^{3} +(-0.167958 + 1.99294i) q^{4} +(-0.865631 + 1.05477i) q^{5} +(1.14693 + 4.44560i) q^{6} +(0.162245 + 0.108408i) q^{7} +(2.23568 - 1.73255i) q^{8} +(4.18867 + 6.26879i) q^{9} +(1.92666 - 0.108268i) q^{10} +(-0.144127 - 0.0437204i) q^{11} +(3.53080 - 5.44896i) q^{12} +(-3.75158 + 3.07884i) q^{13} +(-0.0424141 - 0.272677i) q^{14} +(4.09258 - 1.69520i) q^{15} +(-3.94358 - 0.669457i) q^{16} +(-0.223463 - 0.0925613i) q^{17} +(2.51777 - 10.3608i) q^{18} +(-0.742006 + 7.53372i) q^{19} +(-1.95671 - 1.90230i) q^{20} +(-0.298620 - 0.558679i) q^{21} +(0.0924232 + 0.191901i) q^{22} +(-6.74055 - 1.34078i) q^{23} +(-9.05243 + 1.53908i) q^{24} +(0.612220 + 3.07784i) q^{25} +(6.79611 + 0.959202i) q^{26} +(-1.44447 - 14.6660i) q^{27} +(-0.243301 + 0.305135i) q^{28} +(-1.92135 - 6.33383i) q^{29} +(-5.68192 - 2.63850i) q^{30} +(-2.37838 + 2.37838i) q^{31} +(3.07736 + 4.74656i) q^{32} +(0.345743 + 0.345743i) q^{33} +(0.117504 + 0.321246i) q^{34} +(-0.254791 + 0.0772899i) q^{35} +(-13.1968 + 7.29486i) q^{36} +(3.51713 - 0.346407i) q^{37} +(8.55384 - 6.43791i) q^{38} +(15.4529 - 3.07378i) q^{39} +(-0.107825 + 3.85789i) q^{40} +(0.456936 - 2.29717i) q^{41} +(-0.295858 + 0.845612i) q^{42} +(4.58870 - 2.45271i) q^{43} +(0.111339 - 0.279892i) q^{44} +(-10.2380 - 1.00836i) q^{45} +(5.05537 + 8.30112i) q^{46} +(-3.90401 + 9.42513i) q^{47} +(10.2664 + 7.95184i) q^{48} +(-2.66421 - 6.43198i) q^{49} +(2.61852 - 3.58317i) q^{50} +(0.498146 + 0.606993i) q^{51} +(-5.50582 - 7.99376i) q^{52} +(-0.703882 + 2.32039i) q^{53} +(-13.8869 + 15.5406i) q^{54} +(0.170876 - 0.114176i) q^{55} +(0.550551 - 0.0387305i) q^{56} +(13.6538 - 20.4343i) q^{57} +(-4.75552 + 8.06244i) q^{58} +(-1.33800 - 1.09807i) q^{59} +(2.69105 + 8.44098i) q^{60} +(-3.57815 + 6.69426i) q^{61} +(4.75256 + 0.199910i) q^{62} +1.47117i q^{63} +(1.99654 - 7.74686i) q^{64} -6.62221i q^{65} +(0.0290607 - 0.690875i) q^{66} +(1.30359 - 2.43884i) q^{67} +(0.222001 - 0.429801i) q^{68} +(17.2471 + 14.1543i) q^{69} +(0.324327 + 0.191300i) q^{70} +(-3.30056 + 4.93964i) q^{71} +(20.2255 + 6.75793i) q^{72} +(-8.33969 + 5.57240i) q^{73} +(-3.72687 - 3.33030i) q^{74} +(2.95736 - 9.74910i) q^{75} +(-14.8896 - 2.74411i) q^{76} +(-0.0186442 - 0.0227180i) q^{77} +(-17.9901 - 13.1468i) q^{78} +(-0.333360 - 0.804803i) q^{79} +(4.11981 - 3.58008i) q^{80} +(-9.65299 + 23.3044i) q^{81} +(-2.82902 + 1.72287i) q^{82} +(-1.71796 - 0.169204i) q^{83} +(1.16357 - 0.501296i) q^{84} +(0.291068 - 0.155579i) q^{85} +(-6.94543 - 2.43003i) q^{86} +(-4.19204 + 21.0748i) q^{87} +(-0.397970 + 0.151962i) q^{88} +(8.77606 - 1.74567i) q^{89} +(8.74885 + 11.6243i) q^{90} +(-0.942446 + 0.0928229i) q^{91} +(3.80421 - 13.2083i) q^{92} +(10.4494 - 3.16978i) q^{93} +(13.5494 - 4.95606i) q^{94} +(-7.30407 - 7.30407i) q^{95} +(-1.54686 - 18.2994i) q^{96} +(5.19447 - 5.19447i) q^{97} +(-4.14672 + 8.92981i) q^{98} +(-0.329626 - 1.08663i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q16q216q316q416q516q616q716q816q916q1016q1116q1216q1316q1416q1516q1616q1716q18+16q99+O(q100) 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/128Z)×\left(\mathbb{Z}/128\mathbb{Z}\right)^\times.

nn 55 127127
χ(n)\chi(n) e(2332)e\left(\frac{23}{32}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.957090 1.04114i −0.676765 0.736199i
33 −2.86311 1.53036i −1.65302 0.883556i −0.990968 0.134095i 0.957187π-0.957187\pi
−0.662049 0.749461i 0.730313π-0.730313\pi
44 −0.167958 + 1.99294i −0.0839788 + 0.996468i
55 −0.865631 + 1.05477i −0.387122 + 0.471709i −0.929712 0.368288i 0.879944π-0.879944\pi
0.542590 + 0.839998i 0.317444π0.317444\pi
66 1.14693 + 4.44560i 0.468231 + 1.81491i
77 0.162245 + 0.108408i 0.0613228 + 0.0409746i 0.585854 0.810417i 0.300759π-0.300759\pi
−0.524531 + 0.851391i 0.675759π0.675759\pi
88 2.23568 1.73255i 0.790433 0.612549i
99 4.18867 + 6.26879i 1.39622 + 2.08960i
1010 1.92666 0.108268i 0.609263 0.0342375i
1111 −0.144127 0.0437204i −0.0434559 0.0131822i 0.268482 0.963285i 0.413478π-0.413478\pi
−0.311938 + 0.950103i 0.600978π0.600978\pi
1212 3.53080 5.44896i 1.01925 1.57298i
1313 −3.75158 + 3.07884i −1.04050 + 0.853917i −0.989464 0.144780i 0.953752π-0.953752\pi
−0.0510365 + 0.998697i 0.516252π0.516252\pi
1414 −0.0424141 0.272677i −0.0113356 0.0728759i
1515 4.09258 1.69520i 1.05670 0.437700i
1616 −3.94358 0.669457i −0.985895 0.167364i
1717 −0.223463 0.0925613i −0.0541977 0.0224494i 0.355420 0.934707i 0.384338π-0.384338\pi
−0.409618 + 0.912257i 0.634338π0.634338\pi
1818 2.51777 10.3608i 0.593445 2.44207i
1919 −0.742006 + 7.53372i −0.170228 + 1.72835i 0.408436 + 0.912787i 0.366074π0.366074\pi
−0.578664 + 0.815566i 0.696426π0.696426\pi
2020 −1.95671 1.90230i −0.437533 0.425368i
2121 −0.298620 0.558679i −0.0651643 0.121914i
2222 0.0924232 + 0.191901i 0.0197047 + 0.0409135i
2323 −6.74055 1.34078i −1.40550 0.279572i −0.566662 0.823950i 0.691766π-0.691766\pi
−0.838840 + 0.544378i 0.816766π0.816766\pi
2424 −9.05243 + 1.53908i −1.84782 + 0.314163i
2525 0.612220 + 3.07784i 0.122444 + 0.615567i
2626 6.79611 + 0.959202i 1.33283 + 0.188115i
2727 −1.44447 14.6660i −0.277989 2.82247i
2828 −0.243301 + 0.305135i −0.0459796 + 0.0576651i
2929 −1.92135 6.33383i −0.356785 1.17616i −0.933307 0.359081i 0.883090π-0.883090\pi
0.576522 0.817082i 0.304410π-0.304410\pi
3030 −5.68192 2.63850i −1.03737 0.481723i
3131 −2.37838 + 2.37838i −0.427170 + 0.427170i −0.887663 0.460493i 0.847673π-0.847673\pi
0.460493 + 0.887663i 0.347673π0.347673\pi
3232 3.07736 + 4.74656i 0.544006 + 0.839082i
3333 0.345743 + 0.345743i 0.0601861 + 0.0601861i
3434 0.117504 + 0.321246i 0.0201518 + 0.0550933i
3535 −0.254791 + 0.0772899i −0.0430675 + 0.0130644i
3636 −13.1968 + 7.29486i −2.19947 + 1.21581i
3737 3.51713 0.346407i 0.578213 0.0569490i 0.195317 0.980740i 0.437427π-0.437427\pi
0.382897 + 0.923791i 0.374927π0.374927\pi
3838 8.55384 6.43791i 1.38762 1.04437i
3939 15.4529 3.07378i 2.47445 0.492198i
4040 −0.107825 + 3.85789i −0.0170486 + 0.609986i
4141 0.456936 2.29717i 0.0713615 0.358758i −0.928561 0.371179i 0.878954π-0.878954\pi
0.999923 + 0.0124205i 0.00395366π0.00395366\pi
4242 −0.295858 + 0.845612i −0.0456519 + 0.130481i
4343 4.58870 2.45271i 0.699771 0.374035i −0.0828263 0.996564i 0.526395π-0.526395\pi
0.782597 + 0.622529i 0.213895π0.213895\pi
4444 0.111339 0.279892i 0.0167850 0.0421954i
4545 −10.2380 1.00836i −1.52619 0.150317i
4646 5.05537 + 8.30112i 0.745374 + 1.22393i
4747 −3.90401 + 9.42513i −0.569459 + 1.37480i 0.332553 + 0.943085i 0.392090π0.392090\pi
−0.902012 + 0.431711i 0.857910π0.857910\pi
4848 10.2664 + 7.95184i 1.48183 + 1.14775i
4949 −2.66421 6.43198i −0.380602 0.918854i
5050 2.61852 3.58317i 0.370314 0.506737i
5151 0.498146 + 0.606993i 0.0697544 + 0.0849960i
5252 −5.50582 7.99376i −0.763520 1.10854i
5353 −0.703882 + 2.32039i −0.0966856 + 0.318730i −0.991920 0.126866i 0.959508π-0.959508\pi
0.895234 + 0.445596i 0.147008π0.147008\pi
5454 −13.8869 + 15.5406i −1.88977 + 2.11480i
5555 0.170876 0.114176i 0.0230409 0.0153954i
5656 0.550551 0.0387305i 0.0735704 0.00517558i
5757 13.6538 20.4343i 1.80849 2.70659i
5858 −4.75552 + 8.06244i −0.624430 + 1.05865i
5959 −1.33800 1.09807i −0.174193 0.142956i 0.543257 0.839566i 0.317191π-0.317191\pi
−0.717450 + 0.696610i 0.754691π0.754691\pi
6060 2.69105 + 8.44098i 0.347413 + 1.08973i
6161 −3.57815 + 6.69426i −0.458136 + 0.857112i 0.541727 + 0.840554i 0.317771π0.317771\pi
−0.999863 + 0.0165573i 0.994729π0.994729\pi
6262 4.75256 + 0.199910i 0.603576 + 0.0253886i
6363 1.47117i 0.185350i
6464 1.99654 7.74686i 0.249567 0.968357i
6565 6.62221i 0.821384i
6666 0.0290607 0.690875i 0.00357713 0.0850408i
6767 1.30359 2.43884i 0.159259 0.297952i −0.789618 0.613599i 0.789721π-0.789721\pi
0.948877 + 0.315646i 0.102221π0.102221\pi
6868 0.222001 0.429801i 0.0269216 0.0521210i
6969 17.2471 + 14.1543i 2.07630 + 1.70398i
7070 0.324327 + 0.191300i 0.0387645 + 0.0228647i
7171 −3.30056 + 4.93964i −0.391704 + 0.586227i −0.973944 0.226790i 0.927177π-0.927177\pi
0.582239 + 0.813018i 0.302177π0.302177\pi
7272 20.2255 + 6.75793i 2.38360 + 0.796430i
7373 −8.33969 + 5.57240i −0.976086 + 0.652200i −0.937840 0.347068i 0.887177π-0.887177\pi
−0.0382465 + 0.999268i 0.512177π0.512177\pi
7474 −3.72687 3.33030i −0.433240 0.387139i
7575 2.95736 9.74910i 0.341486 1.12573i
7676 −14.8896 2.74411i −1.70795 0.314772i
7777 −0.0186442 0.0227180i −0.00212470 0.00258896i
7878 −17.9901 13.1468i −2.03698 1.48858i
7979 −0.333360 0.804803i −0.0375060 0.0905474i 0.904017 0.427497i 0.140605π-0.140605\pi
−0.941523 + 0.336950i 0.890605π0.890605\pi
8080 4.11981 3.58008i 0.460609 0.400266i
8181 −9.65299 + 23.3044i −1.07255 + 2.58938i
8282 −2.82902 + 1.72287i −0.312413 + 0.190259i
8383 −1.71796 0.169204i −0.188571 0.0185726i 0.00329100 0.999995i 0.498952π-0.498952\pi
−0.191862 + 0.981422i 0.561452π0.561452\pi
8484 1.16357 0.501296i 0.126956 0.0546959i
8585 0.291068 0.155579i 0.0315707 0.0168749i
8686 −6.94543 2.43003i −0.748945 0.262037i
8787 −4.19204 + 21.0748i −0.449434 + 2.25946i
8888 −0.397970 + 0.151962i −0.0424237 + 0.0161992i
8989 8.77606 1.74567i 0.930260 0.185040i 0.293374 0.955998i 0.405222π-0.405222\pi
0.636886 + 0.770958i 0.280222π0.280222\pi
9090 8.74885 + 11.6243i 0.922210 + 1.22531i
9191 −0.942446 + 0.0928229i −0.0987952 + 0.00973048i
9292 3.80421 13.2083i 0.396616 1.37706i
9393 10.4494 3.16978i 1.08355 0.328691i
9494 13.5494 4.95606i 1.39751 0.511178i
9595 −7.30407 7.30407i −0.749381 0.749381i
9696 −1.54686 18.2994i −0.157875 1.86768i
9797 5.19447 5.19447i 0.527418 0.527418i −0.392383 0.919802i 0.628349π-0.628349\pi
0.919802 + 0.392383i 0.128349π0.128349\pi
9898 −4.14672 + 8.92981i −0.418882 + 0.902047i
9999 −0.329626 1.08663i −0.0331287 0.109211i
100100 −6.23675 + 0.703168i −0.623675 + 0.0703168i
101101 −0.0387557 0.393493i −0.00385634 0.0391540i 0.993064 0.117575i 0.0375121π-0.0375121\pi
−0.996920 + 0.0784211i 0.975012π0.975012\pi
102102 0.155196 1.09959i 0.0153667 0.108875i
103103 −1.46072 7.34354i −0.143929 0.723580i −0.983583 0.180458i 0.942242π-0.942242\pi
0.839654 0.543122i 0.182758π-0.182758\pi
104104 −3.05308 + 13.3831i −0.299380 + 1.31232i
105105 0.847775 + 0.168633i 0.0827344 + 0.0164569i
106106 3.08953 1.48798i 0.300082 0.144525i
107107 7.44829 + 13.9348i 0.720053 + 1.34712i 0.929323 + 0.369267i 0.120391π0.120391\pi
−0.209270 + 0.977858i 0.567109π0.567109\pi
108108 29.4710 0.415479i 2.83585 0.0399795i
109109 1.12348 11.4069i 0.107610 1.09258i −0.778036 0.628220i 0.783784π-0.783784\pi
0.885645 0.464362i 0.153716π-0.153716\pi
110110 −0.282417 0.0686299i −0.0269274 0.00654360i
111111 −10.6001 4.39069i −1.00611 0.416746i
112112 −0.567251 0.536134i −0.0536001 0.0506599i
113113 2.62802 1.08856i 0.247224 0.102403i −0.255631 0.966774i 0.582283π-0.582283\pi
0.502854 + 0.864371i 0.332283π0.332283\pi
114114 −34.3429 + 5.34195i −3.21651 + 0.500319i
115115 7.24905 5.94914i 0.675977 0.554760i
116116 12.9456 2.76530i 1.20197 0.256752i
117117 −35.0147 10.6216i −3.23711 0.981968i
118118 0.137340 + 2.44400i 0.0126432 + 0.224988i
119119 −0.0262212 0.0392429i −0.00240370 0.00359739i
120120 6.21269 10.8805i 0.567138 0.993253i
121121 −9.12730 6.09867i −0.829755 0.554425i
122122 10.3943 2.68163i 0.941055 0.242784i
123123 −4.82377 + 5.87778i −0.434945 + 0.529982i
124124 −4.34049 5.13943i −0.389788 0.461534i
125125 −9.79329 5.23463i −0.875939 0.468199i
126126 1.53169 1.40804i 0.136454 0.125438i
127127 −1.79922 −0.159655 −0.0798275 0.996809i 0.525437π-0.525437\pi
−0.0798275 + 0.996809i 0.525437π0.525437\pi
128128 −9.97646 + 5.33576i −0.881802 + 0.471619i
129129 −16.8915 −1.48721
130130 −6.89466 + 6.33805i −0.604702 + 0.555884i
131131 −7.98472 4.26792i −0.697628 0.372890i 0.0841445 0.996454i 0.473184π-0.473184\pi
−0.781773 + 0.623564i 0.785684π0.785684\pi
132132 −0.747114 + 0.630973i −0.0650279 + 0.0549192i
133133 −0.937106 + 1.14187i −0.0812574 + 0.0990124i
134134 −3.78684 + 0.976970i −0.327133 + 0.0843974i
135135 16.7197 + 11.1717i 1.43900 + 0.961510i
136136 −0.659959 + 0.180223i −0.0565910 + 0.0154540i
137137 −0.528159 0.790446i −0.0451237 0.0675323i 0.808222 0.588878i 0.200430π-0.200430\pi
−0.853346 + 0.521346i 0.825430π0.825430\pi
138138 −1.77034 31.5036i −0.150701 2.68176i
139139 15.2367 + 4.62199i 1.29236 + 0.392032i 0.860288 0.509809i 0.170284π-0.170284\pi
0.432068 + 0.901841i 0.357784π0.357784\pi
140140 −0.111240 0.520763i −0.00940147 0.0440125i
141141 25.6015 21.0106i 2.15603 1.76941i
142142 8.30180 1.29132i 0.696672 0.108365i
143143 0.675311 0.279723i 0.0564724 0.0233916i
144144 −12.3217 27.5256i −1.02681 2.29380i
145145 8.34394 + 3.45617i 0.692926 + 0.287019i
146146 13.7835 + 3.34952i 1.14073 + 0.277208i
147147 −2.21534 + 22.4927i −0.182718 + 1.85516i
148148 0.0996385 + 7.06760i 0.00819023 + 0.580953i
149149 6.11873 + 11.4473i 0.501266 + 0.937803i 0.997571 + 0.0696548i 0.0221898π0.0221898\pi
−0.496305 + 0.868148i 0.665310π0.665310\pi
150150 −12.9807 + 6.25174i −1.05987 + 0.510452i
151151 6.96948 + 1.38632i 0.567169 + 0.112817i 0.470342 0.882484i 0.344131π-0.344131\pi
0.0968269 + 0.995301i 0.469131π0.469131\pi
152152 11.3937 + 18.1286i 0.924147 + 1.47042i
153153 −0.355765 1.78855i −0.0287619 0.144596i
154154 −0.00580853 + 0.0411544i −0.000468064 + 0.00331632i
155155 −0.449855 4.56746i −0.0361332 0.366867i
156156 3.53040 + 31.3129i 0.282659 + 2.50704i
157157 4.80591 + 15.8430i 0.383553 + 1.26441i 0.910146 + 0.414288i 0.135969π0.135969\pi
−0.526593 + 0.850118i 0.676531π0.676531\pi
158158 −0.518859 + 1.11734i −0.0412782 + 0.0888912i
159159 5.56633 5.56633i 0.441439 0.441439i
160160 −7.67041 0.862849i −0.606399 0.0682142i
161161 −0.948267 0.948267i −0.0747339 0.0747339i
162162 33.5020 12.2543i 2.63216 0.962785i
163163 6.28708 1.90716i 0.492442 0.149381i −0.0342903 0.999412i 0.510917π-0.510917\pi
0.526732 + 0.850031i 0.323417π0.323417\pi
164164 4.50137 + 1.29647i 0.351498 + 0.101237i
165165 −0.663967 + 0.0653950i −0.0516897 + 0.00509099i
166166 1.46808 + 1.95058i 0.113945 + 0.151395i
167167 3.04803 0.606292i 0.235864 0.0469163i −0.0757428 0.997127i 0.524133π-0.524133\pi
0.311607 + 0.950211i 0.399133π0.399133\pi
168168 −1.63556 0.731654i −0.126186 0.0564483i
169169 2.05890 10.3508i 0.158377 0.796216i
170170 −0.440558 0.154140i −0.0337892 0.0118220i
171171 −50.3353 + 26.9048i −3.84924 + 2.05746i
172172 4.11739 + 9.55694i 0.313948 + 0.728710i
173173 −15.4705 1.52371i −1.17620 0.115845i −0.509027 0.860751i 0.669995π-0.669995\pi
−0.667170 + 0.744905i 0.732495π0.732495\pi
174174 25.9540 15.8060i 1.96757 1.19825i
175175 −0.234334 + 0.565733i −0.0177140 + 0.0427654i
176176 0.539107 + 0.268902i 0.0406367 + 0.0202692i
177177 2.15039 + 5.19151i 0.161634 + 0.390218i
178178 −10.2170 7.46637i −0.765794 0.559628i
179179 7.82280 + 9.53211i 0.584703 + 0.712463i 0.978387 0.206783i 0.0662994π-0.0662994\pi
−0.393683 + 0.919246i 0.628799π0.628799\pi
180180 3.72914 20.2343i 0.277953 1.50818i
181181 −0.181651 + 0.598824i −0.0135020 + 0.0445102i −0.963433 0.267951i 0.913653π-0.913653\pi
0.949930 + 0.312461i 0.101153π0.101153\pi
182182 0.998648 + 0.892382i 0.0740247 + 0.0661477i
183183 20.4893 13.6905i 1.51461 1.01203i
184184 −17.3927 + 8.68079i −1.28221 + 0.639956i
185185 −2.67916 + 4.00964i −0.196976 + 0.294795i
186186 −13.3012 7.84551i −0.975289 0.575261i
187187 0.0281602 + 0.0231105i 0.00205928 + 0.00169000i
188188 −18.1280 9.36347i −1.32212 0.682901i
189189 1.35556 2.53607i 0.0986025 0.184472i
190190 −0.613929 + 14.5952i −0.0445391 + 1.05885i
191191 23.7786i 1.72056i 0.509822 + 0.860280i 0.329711π0.329711\pi
−0.509822 + 0.860280i 0.670289π0.670289\pi
192192 −17.5718 + 19.1247i −1.26814 + 1.38020i
193193 19.6161i 1.41200i 0.708214 + 0.705998i 0.249501π0.249501\pi
−0.708214 + 0.705998i 0.750499π0.750499\pi
194194 −10.3798 0.436611i −0.745223 0.0313468i
195195 −10.1344 + 18.9601i −0.725738 + 1.35776i
196196 13.2660 4.22930i 0.947571 0.302093i
197197 −6.21590 5.10126i −0.442865 0.363450i 0.386376 0.922341i 0.373727π-0.373727\pi
−0.829241 + 0.558892i 0.811227π0.811227\pi
198198 −0.815857 + 1.38319i −0.0579805 + 0.0982992i
199199 12.4091 18.5716i 0.879659 1.31650i −0.0681530 0.997675i 0.521711π-0.521711\pi
0.947812 0.318828i 0.103289π-0.103289\pi
200200 6.70123 + 5.82036i 0.473849 + 0.411561i
201201 −7.46464 + 4.98771i −0.526515 + 0.351806i
202202 −0.372590 + 0.416959i −0.0262153 + 0.0293371i
203203 0.374913 1.23592i 0.0263137 0.0867446i
204204 −1.29336 + 0.890824i −0.0905536 + 0.0623701i
205205 2.02746 + 2.47047i 0.141604 + 0.172545i
206206 −6.24763 + 8.54925i −0.435293 + 0.595654i
207207 −19.8289 47.8712i −1.37820 3.32728i
208208 16.8558 9.63013i 1.16874 0.667730i
209209 0.436320 1.05337i 0.0301809 0.0728632i
210210 −0.635826 1.04405i −0.0438762 0.0720464i
211211 −1.26380 0.124474i −0.0870038 0.00856913i 0.0544215 0.998518i 0.482669π-0.482669\pi
−0.141425 + 0.989949i 0.545169π0.545169\pi
212212 −4.50616 1.79252i −0.309484 0.123111i
213213 17.0093 9.09167i 1.16546 0.622951i
214214 7.37940 21.0916i 0.504446 1.44179i
215215 −1.38506 + 6.96319i −0.0944606 + 0.474886i
216216 −28.6390 30.2859i −1.94863 2.06069i
217217 −0.643717 + 0.128043i −0.0436983 + 0.00869214i
218218 −12.9515 + 9.74772i −0.877185 + 0.660199i
219219 32.4052 3.19164i 2.18974 0.215671i
220220 0.198845 + 0.359721i 0.0134061 + 0.0242524i
221221 1.12332 0.340755i 0.0755627 0.0229217i
222222 5.57388 + 15.2385i 0.374094 + 1.02274i
223223 3.40850 + 3.40850i 0.228250 + 0.228250i 0.811961 0.583711i 0.198400π-0.198400\pi
−0.583711 + 0.811961i 0.698400π0.698400\pi
224224 −0.0152819 + 1.10372i −0.00102106 + 0.0737452i
225225 −16.7299 + 16.7299i −1.11533 + 1.11533i
226226 −3.64860 1.69429i −0.242701 0.112703i
227227 −3.52798 11.6302i −0.234160 0.771923i −0.992733 0.120335i 0.961603π-0.961603\pi
0.758573 0.651588i 0.225897π-0.225897\pi
228228 38.4310 + 30.6432i 2.54516 + 2.02939i
229229 1.04627 + 10.6230i 0.0691394 + 0.701984i 0.965804 + 0.259274i 0.0834832π0.0834832\pi
−0.896664 + 0.442711i 0.854017π0.854017\pi
230230 −13.1319 1.85343i −0.865892 0.122212i
231231 0.0186135 + 0.0935765i 0.00122468 + 0.00615688i
232232 −15.2692 10.8316i −1.00247 0.711129i
233233 0.564171 + 0.112221i 0.0369600 + 0.00735181i 0.213536 0.976935i 0.431502π-0.431502\pi
−0.176576 + 0.984287i 0.556502π0.556502\pi
234234 22.4536 + 46.6212i 1.46784 + 3.04772i
235235 −6.56194 12.2765i −0.428054 0.800833i
236236 2.41310 2.48212i 0.157080 0.161572i
237237 −0.277194 + 2.81440i −0.0180057 + 0.182815i
238238 −0.0157613 + 0.0648590i −0.00102166 + 0.00420419i
239239 −8.23481 3.41097i −0.532665 0.220637i 0.100105 0.994977i 0.468082π-0.468082\pi
−0.632770 + 0.774340i 0.718082π0.718082\pi
240240 −17.2743 + 3.94536i −1.11505 + 0.254672i
241241 13.1850 5.46139i 0.849319 0.351799i 0.0847977 0.996398i 0.472976π-0.472976\pi
0.764521 + 0.644599i 0.222976π0.222976\pi
242242 2.38606 + 15.3398i 0.153382 + 0.986080i
243243 29.1263 23.9034i 1.86845 1.53340i
244244 −12.7402 8.25538i −0.815610 0.528497i
245245 9.09051 + 2.75758i 0.580771 + 0.176175i
246246 10.7364 0.603331i 0.684528 0.0384670i
247247 −20.4114 30.5478i −1.29875 1.94371i
248248 −1.19664 + 9.43797i −0.0759865 + 0.599311i
249249 4.65976 + 3.11355i 0.295300 + 0.197313i
250250 3.92307 + 15.2062i 0.248117 + 0.961726i
251251 10.0256 12.2162i 0.632811 0.771082i −0.353597 0.935398i 0.615042π-0.615042\pi
0.986408 + 0.164316i 0.0525416π0.0525416\pi
252252 −2.93194 0.247093i −0.184695 0.0155654i
253253 0.912875 + 0.487942i 0.0573920 + 0.0306767i
254254 1.72202 + 1.87325i 0.108049 + 0.117538i
255255 −1.07145 −0.0670969
256256 15.1037 + 5.28011i 0.943978 + 0.330007i
257257 3.04880 0.190179 0.0950894 0.995469i 0.469686π-0.469686\pi
0.0950894 + 0.995469i 0.469686π0.469686\pi
258258 16.1667 + 17.5865i 1.00649 + 1.09489i
259259 0.608190 + 0.325084i 0.0377911 + 0.0201998i
260260 13.1976 + 1.11225i 0.818482 + 0.0689788i
261261 31.6576 38.5749i 1.95955 2.38772i
262262 3.19858 + 12.3980i 0.197609 + 0.765952i
263263 −18.0928 12.0892i −1.11565 0.745454i −0.145839 0.989308i 0.546588π-0.546588\pi
−0.969812 + 0.243854i 0.921588π0.921588\pi
264264 1.37199 + 0.173954i 0.0844400 + 0.0107061i
265265 −1.83818 2.75104i −0.112919 0.168995i
266266 2.08574 0.117208i 0.127885 0.00718648i
267267 −27.7983 8.43253i −1.70123 0.516062i
268268 4.64151 + 3.00759i 0.283525 + 0.183718i
269269 14.0961 11.5684i 0.859456 0.705338i −0.0976042 0.995225i 0.531118π-0.531118\pi
0.957061 + 0.289888i 0.0936179π0.0936179\pi
270270 −4.37087 28.1000i −0.266003 1.71011i
271271 18.5319 7.67617i 1.12573 0.466294i 0.259405 0.965769i 0.416473π-0.416473\pi
0.866329 + 0.499474i 0.166473π0.166473\pi
272272 0.819278 + 0.514622i 0.0496760 + 0.0312035i
273273 2.84038 + 1.17652i 0.171908 + 0.0712065i
274274 −0.317471 + 1.30642i −0.0191791 + 0.0789235i
275275 0.0463270 0.470366i 0.00279362 0.0283641i
276276 −31.1054 + 31.9949i −1.87232 + 1.92587i
277277 10.3694 + 19.3997i 0.623035 + 1.16562i 0.973423 + 0.229012i 0.0735497π0.0735497\pi
−0.350388 + 0.936605i 0.613950π0.613950\pi
278278 −9.77070 20.2872i −0.586008 1.21675i
279279 −24.8718 4.94732i −1.48904 0.296188i
280280 −0.435722 + 0.614233i −0.0260394 + 0.0367074i
281281 3.85751 + 19.3930i 0.230120 + 1.15689i 0.907108 + 0.420897i 0.138285π0.138285\pi
−0.676988 + 0.735994i 0.736715π0.736715\pi
282282 −46.3780 6.54578i −2.76177 0.389795i
283283 1.31008 + 13.3014i 0.0778760 + 0.790688i 0.952226 + 0.305393i 0.0987878π0.0987878\pi
−0.874350 + 0.485295i 0.838712π0.838712\pi
284284 −9.29002 7.40745i −0.551262 0.439551i
285285 9.73446 + 32.0902i 0.576620 + 1.90086i
286286 −0.937566 0.435376i −0.0554394 0.0257443i
287287 0.323169 0.323169i 0.0190761 0.0190761i
288288 −16.8651 + 39.1731i −0.993788 + 2.30830i
289289 −11.9794 11.9794i −0.704673 0.704673i
290290 −4.38753 11.9951i −0.257645 0.704376i
291291 −22.8218 + 6.92290i −1.33784 + 0.405828i
292292 −9.70472 17.5564i −0.567926 1.02741i
293293 −16.6050 + 1.63545i −0.970072 + 0.0955437i −0.570623 0.821212i 0.693298π-0.693298\pi
−0.399448 + 0.916756i 0.630798π0.630798\pi
294294 25.5384 19.2210i 1.48943 1.12099i
295295 2.31643 0.460766i 0.134867 0.0268268i
296296 7.26302 6.86807i 0.422154 0.399198i
297297 −0.433016 + 2.17692i −0.0251261 + 0.126318i
298298 6.06214 17.3266i 0.351171 1.00370i
299299 29.4157 15.7230i 1.70116 0.909287i
300300 18.9326 + 7.53126i 1.09308 + 0.434817i
301301 1.01039 + 0.0995145i 0.0582378 + 0.00573592i
302302 −5.22707 8.58306i −0.300784 0.493900i
303303 −0.491226 + 1.18592i −0.0282202 + 0.0681296i
304304 7.96966 29.2131i 0.457091 1.67548i
305305 −3.96357 9.56890i −0.226953 0.547914i
306306 −1.52164 + 2.08221i −0.0869863 + 0.119032i
307307 −3.74974 4.56907i −0.214009 0.260771i 0.654930 0.755689i 0.272698π-0.272698\pi
−0.868939 + 0.494918i 0.835198π0.835198\pi
308308 0.0484069 0.0333410i 0.00275824 0.00189978i
309309 −7.05608 + 23.2608i −0.401407 + 1.32326i
310310 −4.32482 + 4.83983i −0.245633 + 0.274884i
311311 −16.3214 + 10.9056i −0.925499 + 0.618399i −0.924327 0.381601i 0.875373π-0.875373\pi
−0.00117166 + 0.999999i 0.500373π0.500373\pi
312312 29.2223 33.6450i 1.65439 1.90477i
313313 −8.80698 + 13.1806i −0.497800 + 0.745011i −0.992258 0.124191i 0.960367π-0.960367\pi
0.494458 + 0.869201i 0.335367π0.335367\pi
314314 11.8951 20.1668i 0.671279 1.13808i
315315 −1.55175 1.27349i −0.0874311 0.0717529i
316316 1.65991 0.529193i 0.0933773 0.0297694i
317317 −2.36221 + 4.41939i −0.132675 + 0.248218i −0.939483 0.342597i 0.888694π-0.888694\pi
0.806807 + 0.590815i 0.201194π0.201194\pi
318318 −11.1228 0.467867i −0.623737 0.0262367i
319319 0.996877i 0.0558144i
320320 6.44292 + 8.81182i 0.360170 + 0.492596i
321321 51.2954i 2.86303i
322322 −0.0797047 + 1.89486i −0.00444177 + 0.105596i
323323 0.863142 1.61482i 0.0480265 0.0898512i
324324 −44.8228 23.1519i −2.49016 1.28622i
325325 −11.7730 9.66181i −0.653046 0.535941i
326326 −8.00293 4.72042i −0.443241 0.261440i
327327 −20.6733 + 30.9399i −1.14324 + 1.71098i
328328 −2.95841 5.92741i −0.163351 0.327287i
329329 −1.65517 + 1.10595i −0.0912525 + 0.0609729i
330330 0.703561 + 0.628695i 0.0387298 + 0.0346085i
331331 −0.0486908 + 0.160512i −0.00267629 + 0.00882254i −0.958268 0.285870i 0.907717π-0.907717\pi
0.955592 + 0.294693i 0.0952173π0.0952173\pi
332332 0.625757 3.39536i 0.0343429 0.186345i
333333 16.9037 + 20.5972i 0.926316 + 1.12872i
334334 −3.54848 2.59316i −0.194164 0.141892i
335335 1.44400 + 3.48613i 0.0788943 + 0.190468i
336336 0.803621 + 2.40311i 0.0438411 + 0.131100i
337337 −0.0500988 + 0.120949i −0.00272906 + 0.00658852i −0.925238 0.379387i 0.876135π-0.876135\pi
0.922509 + 0.385975i 0.126135π0.126135\pi
338338 −12.7472 + 7.76304i −0.693358 + 0.422254i
339339 −9.19021 0.905157i −0.499144 0.0491614i
340340 0.261172 + 0.606210i 0.0141640 + 0.0328763i
341341 0.446773 0.238805i 0.0241941 0.0129320i
342342 76.1872 + 26.6560i 4.11973 + 1.44139i
343343 0.531503 2.67204i 0.0286984 0.144277i
344344 6.00943 13.4336i 0.324007 0.724293i
345345 −29.8592 + 5.93936i −1.60756 + 0.319764i
346346 13.2202 + 17.5653i 0.710723 + 0.944315i
347347 11.1775 1.10089i 0.600041 0.0590989i 0.206564 0.978433i 0.433772π-0.433772\pi
0.393477 + 0.919334i 0.371272π0.371272\pi
348348 −41.2966 11.8941i −2.21373 0.637593i
349349 −30.0494 + 9.11537i −1.60851 + 0.487935i −0.961558 0.274601i 0.911454π-0.911454\pi
−0.646947 + 0.762535i 0.723954π0.723954\pi
350350 0.813287 0.297482i 0.0434720 0.0159011i
351351 50.5733 + 50.5733i 2.69940 + 2.69940i
352352 −0.236009 0.818651i −0.0125793 0.0436342i
353353 4.28714 4.28714i 0.228182 0.228182i −0.583751 0.811933i 0.698416π-0.698416\pi
0.811933 + 0.583751i 0.198416π0.198416\pi
354354 3.34698 7.20761i 0.177890 0.383080i
355355 −2.35314 7.75725i −0.124891 0.411712i
356356 2.00499 + 17.7833i 0.106264 + 0.942513i
357357 0.0150184 + 0.152485i 0.000794860 + 0.00807034i
358358 2.43717 17.2677i 0.128808 0.912628i
359359 −3.28081 16.4938i −0.173155 0.870507i −0.965494 0.260426i 0.916137π-0.916137\pi
0.792339 0.610081i 0.208863π-0.208863\pi
360360 −24.6359 + 15.4835i −1.29843 + 0.816052i
361361 −37.5714 7.47342i −1.97744 0.393338i
362362 0.797318 0.384003i 0.0419061 0.0201828i
363363 16.7993 + 31.4293i 0.881734 + 1.64961i
364364 −0.0266990 1.89382i −0.00139941 0.0992634i
365365 1.34147 13.6201i 0.0702155 0.712910i
366366 −33.8639 8.22924i −1.77009 0.430149i
367367 20.2741 + 8.39780i 1.05830 + 0.438362i 0.842847 0.538153i 0.180878π-0.180878\pi
0.215452 + 0.976515i 0.430878π0.430878\pi
368368 25.6843 + 9.79998i 1.33889 + 0.510859i
369369 16.3145 6.75767i 0.849297 0.351790i
370370 6.73881 1.04820i 0.350334 0.0544935i
371371 −0.365751 + 0.300164i −0.0189888 + 0.0155837i
372372 4.56211 + 21.3573i 0.236535 + 1.10732i
373373 2.60073 + 0.788923i 0.134661 + 0.0408489i 0.356896 0.934144i 0.383835π-0.383835\pi
−0.222235 + 0.974993i 0.571335π0.571335\pi
374374 −0.00289053 0.0514376i −0.000149466 0.00265977i
375375 20.0284 + 29.9746i 1.03426 + 1.54788i
376376 7.60137 + 27.8355i 0.392011 + 1.43550i
377377 26.7089 + 17.8463i 1.37558 + 0.919133i
378378 −3.93781 + 1.01592i −0.202539 + 0.0522533i
379379 −4.18516 + 5.09963i −0.214977 + 0.261950i −0.869322 0.494246i 0.835444π-0.835444\pi
0.654345 + 0.756196i 0.272944π0.272944\pi
380380 15.7833 13.3298i 0.809666 0.683802i
381381 5.15137 + 2.75346i 0.263913 + 0.141064i
382382 24.7569 22.7583i 1.26667 1.16441i
383383 −13.8834 −0.709410 −0.354705 0.934978i 0.615419π-0.615419\pi
−0.354705 + 0.934978i 0.615419π0.615419\pi
384384 36.7293 0.00925813i 1.87434 0.000472452i
385385 0.0401013 0.00204375
386386 20.4231 18.7743i 1.03951 0.955589i
387387 34.5961 + 18.4920i 1.75862 + 0.940002i
388388 9.47979 + 11.2247i 0.481263 + 0.569847i
389389 −15.9507 + 19.4360i −0.808733 + 0.985445i 0.191259 + 0.981540i 0.438743π0.438743\pi
−0.999992 + 0.00390496i 0.998757π0.998757\pi
390390 29.4397 7.59518i 1.49074 0.384597i
391391 1.38216 + 0.923529i 0.0698988 + 0.0467049i
392392 −17.1001 9.76397i −0.863683 0.493155i
393393 16.3297 + 24.4391i 0.823722 + 1.23279i
394394 0.638037 + 11.3540i 0.0321439 + 0.572007i
395395 1.13745 + 0.345042i 0.0572315 + 0.0173610i
396396 2.22095 0.474416i 0.111607 0.0238403i
397397 −17.5168 + 14.3757i −0.879145 + 0.721496i −0.961411 0.275114i 0.911284π-0.911284\pi
0.0822661 + 0.996610i 0.473784π0.473784\pi
398398 −31.2123 + 4.85499i −1.56453 + 0.243359i
399399 4.43051 1.83518i 0.221803 0.0918737i
400400 −0.353859 12.5475i −0.0176929 0.627377i
401401 24.4143 + 10.1127i 1.21919 + 0.505005i 0.897152 0.441721i 0.145632π-0.145632\pi
0.322038 + 0.946727i 0.395632π0.395632\pi
402402 12.3373 + 2.99807i 0.615326 + 0.149530i
403403 1.60003 16.2453i 0.0797030 0.809238i
404404 0.790716 0.0111474i 0.0393396 0.000554606i
405405 −16.2249 30.3547i −0.806224 1.50834i
406406 −1.64560 + 0.792550i −0.0816695 + 0.0393336i
407407 −0.522059 0.103844i −0.0258775 0.00514735i
408408 2.16534 + 0.493979i 0.107200 + 0.0244556i
409409 2.28299 + 11.4774i 0.112886 + 0.567519i 0.995283 + 0.0970124i 0.0309287π0.0309287\pi
−0.882397 + 0.470506i 0.844071π0.844071\pi
410410 0.631649 4.47534i 0.0311949 0.221021i
411411 0.302507 + 3.07141i 0.0149216 + 0.151501i
412412 14.8805 1.67772i 0.733111 0.0826553i
413413 −0.0980435 0.323206i −0.00482440 0.0159039i
414414 −30.8627 + 66.4618i −1.51682 + 3.26642i
415415 1.66559 1.66559i 0.0817606 0.0817606i
416416 −26.1589 8.33239i −1.28254 0.408529i
417417 −36.5509 36.5509i −1.78990 1.78990i
418418 −1.51431 + 0.553898i −0.0740672 + 0.0270921i
419419 −26.2140 + 7.95192i −1.28064 + 0.388477i −0.856041 0.516907i 0.827083π-0.827083\pi
−0.424594 + 0.905384i 0.639583π0.639583\pi
420420 −0.478465 + 1.66124i −0.0233467 + 0.0810601i
421421 39.8566 3.92553i 1.94249 0.191319i 0.949876 0.312628i 0.101209π-0.101209\pi
0.992615 + 0.121309i 0.0387093π0.0387093\pi
422422 1.07998 + 1.43493i 0.0525725 + 0.0698514i
423423 −75.4368 + 15.0053i −3.66786 + 0.729583i
424424 2.44653 + 6.40716i 0.118814 + 0.311159i
425425 0.148080 0.744450i 0.00718295 0.0361111i
426426 −25.7452 9.00758i −1.24736 0.436419i
427427 −1.30625 + 0.698206i −0.0632139 + 0.0337885i
428428 −29.0221 + 12.5035i −1.40284 + 0.604380i
429429 −2.36157 0.232594i −0.114018 0.0112298i
430430 8.57531 5.22235i 0.413538 0.251844i
431431 −1.00757 + 2.43249i −0.0485330 + 0.117169i −0.946287 0.323329i 0.895198π-0.895198\pi
0.897754 + 0.440498i 0.145198π0.145198\pi
432432 −4.12185 + 58.8035i −0.198313 + 2.82919i
433433 −4.69123 11.3256i −0.225446 0.544275i 0.770167 0.637842i 0.220173π-0.220173\pi
−0.995613 + 0.0935676i 0.970173π0.970173\pi
434434 0.749406 + 0.547652i 0.0359726 + 0.0262881i
435435 −18.6004 22.6647i −0.891821 1.08669i
436436 22.5445 + 4.15490i 1.07969 + 0.198984i
437437 15.1026 49.7865i 0.722454 2.38161i
438438 −34.3377 30.6838i −1.64072 1.46613i
439439 13.1415 8.78085i 0.627208 0.419087i −0.200934 0.979605i 0.564398π-0.564398\pi
0.828143 + 0.560518i 0.189398π0.189398\pi
440440 0.184209 0.551311i 0.00878182 0.0262827i
441441 29.1612 43.6429i 1.38863 2.07823i
442442 −1.42989 0.843403i −0.0680131 0.0401166i
443443 −1.62908 1.33695i −0.0774001 0.0635206i 0.594898 0.803801i 0.297193π-0.297193\pi
−0.672298 + 0.740281i 0.734693π0.734693\pi
444444 10.5307 20.3878i 0.499766 0.967562i
445445 −5.75554 + 10.7679i −0.272839 + 0.510446i
446446 0.286494 6.81097i 0.0135659 0.322509i
447447 42.1389i 1.99310i
448448 1.16375 1.04045i 0.0549822 0.0491564i
449449 36.1725i 1.70709i 0.521023 + 0.853543i 0.325551π0.325551\pi
−0.521023 + 0.853543i 0.674449π0.674449\pi
450450 33.4303 + 1.40620i 1.57592 + 0.0662889i
451451 −0.166290 + 0.311107i −0.00783030 + 0.0146495i
452452 1.72804 + 5.42031i 0.0812801 + 0.254950i
453453 −17.8328 14.6350i −0.837859 0.687613i
454454 −8.73209 + 14.8043i −0.409817 + 0.694799i
455455 0.717903 1.07442i 0.0336558 0.0503695i
456456 −4.87800 69.3405i −0.228433 3.24716i
457457 1.06878 0.714133i 0.0499952 0.0334057i −0.530321 0.847797i 0.677929π-0.677929\pi
0.580317 + 0.814391i 0.302929π0.302929\pi
458458 10.0586 11.2564i 0.470009 0.525979i
459459 −1.03472 + 3.41101i −0.0482965 + 0.159212i
460460 10.6387 + 15.4461i 0.496033 + 0.720177i
461461 −18.2743 22.2673i −0.851117 1.03709i −0.998844 0.0480615i 0.984696π-0.984696\pi
0.147727 0.989028i 0.452804π-0.452804\pi
462462 0.0796117 0.108940i 0.00370387 0.00506837i
463463 13.5855 + 32.7983i 0.631371 + 1.52426i 0.837900 + 0.545824i 0.183783π0.183783\pi
−0.206529 + 0.978440i 0.566217π0.566217\pi
464464 3.33676 + 26.2642i 0.154905 + 1.21929i
465465 −5.70188 + 13.7656i −0.264419 + 0.638363i
466466 −0.423124 0.694787i −0.0196009 0.0321854i
467467 27.8915 + 2.74707i 1.29066 + 0.127119i 0.719948 0.694028i 0.244166π-0.244166\pi
0.570716 + 0.821148i 0.306666π0.306666\pi
468468 27.0492 67.9981i 1.25035 3.14321i
469469 0.475892 0.254370i 0.0219746 0.0117457i
470470 −6.50126 + 18.5817i −0.299881 + 0.857108i
471471 10.4856 52.7149i 0.483153 2.42897i
472472 −4.89379 0.136778i −0.225255 0.00629570i
473473 −0.768589 + 0.152882i −0.0353398 + 0.00702952i
474474 3.19550 2.40504i 0.146774 0.110467i
475475 −23.6418 + 2.32852i −1.08476 + 0.106840i
476476 0.0826125 0.0456661i 0.00378654 0.00209310i
477477 −17.4944 + 5.30685i −0.801011 + 0.242984i
478478 4.33014 + 11.8382i 0.198056 + 0.541467i
479479 12.6269 + 12.6269i 0.576937 + 0.576937i 0.934058 0.357121i 0.116242π-0.116242\pi
−0.357121 + 0.934058i 0.616242π0.616242\pi
480480 20.6408 + 14.2090i 0.942117 + 0.648547i
481481 −12.1283 + 12.1283i −0.553001 + 0.553001i
482482 −18.3053 8.50039i −0.833783 0.387182i
483483 1.26380 + 4.16619i 0.0575049 + 0.189568i
484484 13.6873 17.1658i 0.622148 0.780264i
485485 0.982499 + 9.97548i 0.0446130 + 0.452963i
486486 −52.7633 7.44701i −2.39339 0.337803i
487487 −2.66111 13.3783i −0.120586 0.606229i −0.993064 0.117575i 0.962488π-0.962488\pi
0.872478 0.488654i 0.162512π-0.162512\pi
488488 3.59852 + 21.1656i 0.162898 + 0.958120i
489489 −20.9192 4.16110i −0.946001 0.188171i
490490 −5.82941 12.1038i −0.263346 0.546793i
491491 −4.76807 8.92043i −0.215180 0.402573i 0.751054 0.660241i 0.229546π-0.229546\pi
−0.966234 + 0.257668i 0.917046π0.917046\pi
492492 −10.9039 10.6007i −0.491584 0.477916i
493493 −0.156918 + 1.59322i −0.00706724 + 0.0717549i
494494 −12.2691 + 50.4882i −0.552013 + 2.27157i
495495 1.43149 + 0.592941i 0.0643405 + 0.0266507i
496496 10.9716 7.78711i 0.492638 0.349652i
497497 −1.07100 + 0.443622i −0.0480408 + 0.0198992i
498498 −1.21816 7.83143i −0.0545869 0.350935i
499499 −17.4315 + 14.3057i −0.780342 + 0.640410i −0.937824 0.347112i 0.887162π-0.887162\pi
0.157482 + 0.987522i 0.449662π0.449662\pi
500500 12.0771 18.6382i 0.540105 0.833526i
501501 −9.65471 2.92872i −0.431340 0.130846i
502502 −22.3143 + 1.25395i −0.995934 + 0.0559664i
503503 16.4770 + 24.6595i 0.734672 + 1.09951i 0.991122 + 0.132957i 0.0424473π0.0424473\pi
−0.256450 + 0.966558i 0.582553π0.582553\pi
504504 2.54887 + 3.28906i 0.113536 + 0.146506i
505505 0.448595 + 0.299741i 0.0199622 + 0.0133383i
506506 −0.365686 1.41744i −0.0162567 0.0630128i
507507 −21.7354 + 26.4846i −0.965301 + 1.17622i
508508 0.302193 3.58573i 0.0134076 0.159091i
509509 −18.5335 9.90636i −0.821483 0.439092i 0.00640920 0.999979i 0.497960π-0.497960\pi
−0.827892 + 0.560888i 0.810460π0.810460\pi
510510 1.02547 + 1.11553i 0.0454088 + 0.0493967i
511511 −1.95717 −0.0865799
512512 −8.95820 20.7786i −0.395900 0.918293i
513513 111.561 4.92555
514514 −2.91797 3.17423i −0.128706 0.140009i
515515 9.01022 + 4.81606i 0.397038 + 0.212221i
516516 2.83706 33.6637i 0.124894 1.48196i
517517 0.974744 1.18773i 0.0428692 0.0522363i
518518 −0.243633 0.944348i −0.0107046 0.0414923i
519519 41.9618 + 28.0380i 1.84192 + 1.23073i
520520 −11.4733 14.8051i −0.503138 0.649248i
521521 4.11838 + 6.16359i 0.180429 + 0.270032i 0.910649 0.413181i 0.135582π-0.135582\pi
−0.730220 + 0.683213i 0.760582π0.760582\pi
522522 −70.4611 + 3.95955i −3.08400 + 0.173305i
523523 −22.7413 6.89849i −0.994407 0.301650i −0.249177 0.968458i 0.580160π-0.580160\pi
−0.745230 + 0.666808i 0.767660π0.767660\pi
524524 9.84678 15.1962i 0.430159 0.663849i
525525 1.53670 1.26114i 0.0670671 0.0550406i
526526 4.72983 + 30.4077i 0.206231 + 1.32584i
527527 0.751626 0.311334i 0.0327413 0.0135619i
528528 −1.13201 1.59493i −0.0492642 0.0694102i
529529 22.3881 + 9.27346i 0.973396 + 0.403194i
530530 −1.10491 + 4.54680i −0.0479944 + 0.197500i
531531 1.27912 12.9871i 0.0555089 0.563591i
532532 −2.11827 2.05938i −0.0918387 0.0892853i
533533 5.35840 + 10.0249i 0.232098 + 0.434225i
534534 17.8260 + 37.0127i 0.771407 + 1.60170i
535535 −21.1455 4.20610i −0.914200 0.181846i
536536 −1.31101 7.71101i −0.0566270 0.333065i
537537 −7.80994 39.2632i −0.337024 1.69433i
538538 −25.5356 3.60409i −1.10092 0.155383i
539539 0.102776 + 1.04350i 0.00442687 + 0.0449468i
540540 −25.0728 + 31.4449i −1.07896 + 1.35317i
541541 2.53495 + 8.35660i 0.108986 + 0.359278i 0.994421 0.105485i 0.0336395π-0.0336395\pi
−0.885435 + 0.464763i 0.846139π0.846139\pi
542542 −25.7287 11.9476i −1.10514 0.513193i
543543 1.43651 1.43651i 0.0616464 0.0616464i
544544 −0.248328 1.34552i −0.0106470 0.0576889i
545545 11.0592 + 11.0592i 0.473723 + 0.473723i
546546 −1.49357 4.08328i −0.0639189 0.174748i
547547 −16.0061 + 4.85540i −0.684372 + 0.207602i −0.613277 0.789868i 0.710149π-0.710149\pi
−0.0710944 + 0.997470i 0.522649π0.522649\pi
548548 1.66401 0.919825i 0.0710832 0.0392930i
549549 −56.9526 + 5.60934i −2.43068 + 0.239401i
550550 −0.534057 + 0.401949i −0.0227723 + 0.0171392i
551551 49.1429 9.77514i 2.09356 0.416435i
552552 63.0819 + 1.76309i 2.68495 + 0.0750420i
553553 0.0331615 0.166714i 0.00141017 0.00708941i
554554 10.2735 29.3633i 0.436478 1.24753i
555555 13.8069 7.37996i 0.586072 0.313262i
556556 −11.7704 + 29.5894i −0.499178 + 1.25487i
557557 38.4640 + 3.78837i 1.62977 + 0.160518i 0.871151 0.491015i 0.163374π-0.163374\pi
0.758620 + 0.651534i 0.225874π0.225874\pi
558558 18.6537 + 30.6302i 0.789675 + 1.29668i
559559 −9.66336 + 23.3294i −0.408717 + 0.986729i
560560 1.05653 0.134228i 0.0446465 0.00567215i
561561 −0.0452583 0.109263i −0.00191081 0.00461309i
562562 16.4989 22.5771i 0.695965 0.952357i
563563 −7.38497 8.99862i −0.311240 0.379246i 0.593772 0.804633i 0.297638π-0.297638\pi
−0.905012 + 0.425387i 0.860138π0.860138\pi
564564 37.5728 + 54.5510i 1.58210 + 2.29701i
565565 −1.12671 + 3.71426i −0.0474010 + 0.156260i
566566 12.5948 14.0946i 0.529400 0.592442i
567567 −4.09254 + 2.73455i −0.171871 + 0.114840i
568568 1.17917 + 16.7618i 0.0494769 + 0.703311i
569569 −18.0568 + 27.0239i −0.756979 + 1.13290i 0.230179 + 0.973148i 0.426069π0.426069\pi
−0.987157 + 0.159750i 0.948931π0.948931\pi
570570 24.0938 40.8482i 1.00918 1.71094i
571571 −34.6976 28.4755i −1.45205 1.19166i −0.943828 0.330437i 0.892804π-0.892804\pi
−0.508219 0.861228i 0.669696π-0.669696\pi
572572 0.444046 + 1.39283i 0.0185665 + 0.0582373i
573573 36.3899 68.0808i 1.52021 2.84412i
574574 −0.645767 0.0271633i −0.0269538 0.00113377i
575575 21.5672i 0.899413i
576576 56.9263 19.9332i 2.37193 0.830549i
577577 9.94863i 0.414167i −0.978323 0.207083i 0.933603π-0.933603\pi
0.978323 0.207083i 0.0663971π-0.0663971\pi
578578 −1.00691 + 23.9377i −0.0418819 + 0.995678i
579579 30.0197 56.1630i 1.24758 2.33405i
580580 −8.28935 + 16.0484i −0.344197 + 0.666375i
581581 −0.260387 0.213694i −0.0108027 0.00886552i
582582 29.0502 + 17.1349i 1.20417 + 0.710263i
583583 0.202897 0.303656i 0.00840312 0.0125762i
584584 −8.99041 + 26.9070i −0.372026 + 1.11342i
585585 41.5132 27.7383i 1.71636 1.14684i
586586 17.5952 + 15.7229i 0.726850 + 0.649505i
587587 −2.75765 + 9.09076i −0.113820 + 0.375216i −0.995280 0.0970434i 0.969061π-0.969061\pi
0.881460 + 0.472259i 0.156561π0.156561\pi
588588 −44.4544 8.19283i −1.83327 0.337867i
589589 −16.1533 19.6828i −0.665584 0.811017i
590590 −2.69675 1.97074i −0.111023 0.0811339i
591591 9.99003 + 24.1181i 0.410935 + 0.992084i
592592 −14.1020 0.988484i −0.579589 0.0406264i
593593 10.9497 26.4350i 0.449652 1.08556i −0.522800 0.852455i 0.675113π-0.675113\pi
0.972452 0.233101i 0.0748874π-0.0748874\pi
594594 2.68092 1.63267i 0.109999 0.0669894i
595595 0.0640903 + 0.00631234i 0.00262745 + 0.000258781i
596596 −23.8415 + 10.2716i −0.976586 + 0.420740i
597597 −63.9499 + 34.1820i −2.61730 + 1.39897i
598598 −44.5234 15.5776i −1.82070 0.637017i
599599 −8.41706 + 42.3154i −0.343912 + 1.72896i 0.291307 + 0.956630i 0.405910π0.405910\pi
−0.635219 + 0.772332i 0.719090π0.719090\pi
600600 −10.2791 26.9197i −0.419643 1.09899i
601601 −18.4819 + 3.67629i −0.753894 + 0.149959i −0.557054 0.830477i 0.688068π-0.688068\pi
−0.196841 + 0.980435i 0.563068π0.563068\pi
602602 −0.863423 1.14720i −0.0351905 0.0467565i
603603 20.7489 2.04359i 0.844961 0.0832214i
604604 −3.93342 + 13.6569i −0.160048 + 0.555691i
605605 14.3336 4.34805i 0.582744 0.176773i
606606 1.70487 0.623600i 0.0692554 0.0253320i
607607 −15.4956 15.4956i −0.628947 0.628947i 0.318856 0.947803i 0.396701π-0.396701\pi
−0.947803 + 0.318856i 0.896701π0.896701\pi
608608 −38.0427 + 19.6620i −1.54283 + 0.797399i
609609 −2.96482 + 2.96482i −0.120141 + 0.120141i
610610 −6.16910 + 13.2849i −0.249780 + 0.537891i
611611 −14.3722 47.3789i −0.581439 1.91675i
612612 3.62422 0.408616i 0.146500 0.0165173i
613613 −2.56143 26.0066i −0.103455 1.05040i −0.897044 0.441942i 0.854290π-0.854290\pi
0.793589 0.608455i 0.208210π-0.208210\pi
614614 −1.16822 + 8.27703i −0.0471455 + 0.334034i
615615 −2.02413 10.1760i −0.0816207 0.410335i
616616 −0.0810425 0.0184882i −0.00326530 0.000744911i
617617 15.1008 + 3.00375i 0.607937 + 0.120926i 0.489453 0.872030i 0.337196π-0.337196\pi
0.118484 + 0.992956i 0.462196π0.462196\pi
618618 30.9711 14.9163i 1.24584 0.600021i
619619 13.8857 + 25.9783i 0.558112 + 1.04416i 0.989845 + 0.142153i 0.0454026π0.0454026\pi
−0.431732 + 0.902002i 0.642097π0.642097\pi
620620 9.17820 0.129394i 0.368605 0.00519657i
621621 −9.92730 + 100.794i −0.398369 + 4.04471i
622622 26.9753 + 6.55524i 1.08161 + 0.262841i
623623 1.61311 + 0.668174i 0.0646281 + 0.0267698i
624624 −62.9976 + 1.77662i −2.52192 + 0.0711219i
625625 −0.497564 + 0.206098i −0.0199026 + 0.00824392i
626626 22.1519 3.44567i 0.885370 0.137717i
627627 −2.86127 + 2.34819i −0.114268 + 0.0937775i
628628 −32.3812 + 6.91692i −1.29215 + 0.276015i
629629 −0.818013 0.248141i −0.0326163 0.00989405i
630630 0.159281 + 2.83443i 0.00634590 + 0.112927i
631631 −0.870439 1.30270i −0.0346516 0.0518598i 0.813739 0.581230i 0.197428π-0.197428\pi
−0.848391 + 0.529370i 0.822428π0.822428\pi
632632 −2.13965 1.22172i −0.0851107 0.0485974i
633633 3.42792 + 2.29046i 0.136247 + 0.0910377i
634634 6.86207 1.77035i 0.272528 0.0703097i
635635 1.55746 1.89777i 0.0618060 0.0753108i
636636 10.1584 + 12.0282i 0.402808 + 0.476951i
637637 29.7980 + 15.9274i 1.18064 + 0.631066i
638638 1.03789 0.954101i 0.0410905 0.0377732i
639639 −44.7905 −1.77189
640640 3.00791 15.1417i 0.118898 0.598529i
641641 −0.546606 −0.0215897 −0.0107948 0.999942i 0.503436π-0.503436\pi
−0.0107948 + 0.999942i 0.503436π0.503436\pi
642642 −53.4058 + 49.0943i −2.10776 + 1.93760i
643643 24.9021 + 13.3105i 0.982043 + 0.524913i 0.882597 0.470130i 0.155793π-0.155793\pi
0.0994462 + 0.995043i 0.468293π0.468293\pi
644644 2.04910 1.73057i 0.0807460 0.0681939i
645645 14.6218 17.8167i 0.575733 0.701533i
646646 −2.50737 + 0.646878i −0.0986511 + 0.0254511i
647647 16.1546 + 10.7942i 0.635104 + 0.424363i 0.831008 0.556260i 0.187764π-0.187764\pi
−0.195904 + 0.980623i 0.562764π0.562764\pi
648648 18.7950 + 68.8255i 0.738338 + 2.70372i
649649 0.144834 + 0.216759i 0.00568522 + 0.00850853i
650650 1.20845 + 21.5046i 0.0473992 + 0.843478i
651651 2.03898 + 0.618519i 0.0799141 + 0.0242417i
652652 2.74489 + 12.8501i 0.107498 + 0.503247i
653653 −15.9635 + 13.1009i −0.624701 + 0.512679i −0.892648 0.450755i 0.851155π-0.851155\pi
0.267947 + 0.963434i 0.413655π0.413655\pi
654654 51.9991 8.08831i 2.03332 0.316278i
655655 11.4135 4.72763i 0.445963 0.184724i
656656 −3.33982 + 8.75319i −0.130398 + 0.341755i
657657 −69.8644 28.9388i −2.72567 1.12901i
658658 2.73560 + 0.664776i 0.106645 + 0.0259157i
659659 −0.237451 + 2.41088i −0.00924979 + 0.0939147i −0.998701 0.0509506i 0.983775π-0.983775\pi
0.989451 + 0.144865i 0.0462749π0.0462749\pi
660660 −0.0188098 1.33423i −0.000732171 0.0519347i
661661 −19.0704 35.6782i −0.741752 1.38772i −0.915250 0.402886i 0.868007π-0.868007\pi
0.173498 0.984834i 0.444493π-0.444493\pi
662662 0.213718 0.102930i 0.00830637 0.00400050i
663663 −3.73767 0.743468i −0.145159 0.0288739i
664664 −4.13396 + 2.59816i −0.160429 + 0.100828i
665665 −0.393224 1.97687i −0.0152486 0.0766597i
666666 5.26628 37.3125i 0.204064 1.44583i
667667 4.45867 + 45.2696i 0.172640 + 1.75285i
668668 0.696360 + 6.17637i 0.0269430 + 0.238971i
669669 −4.54266 14.9751i −0.175629 0.578972i
670670 2.24752 4.83995i 0.0868293 0.186984i
671671 0.808384 0.808384i 0.0312073 0.0312073i
672672 1.73284 3.13668i 0.0668458 0.121000i
673673 2.88867 + 2.88867i 0.111350 + 0.111350i 0.760587 0.649237i 0.224911π-0.224911\pi
−0.649237 + 0.760587i 0.724911π0.724911\pi
674674 0.173875 0.0635993i 0.00669740 0.00244975i
675675 44.2552 13.4247i 1.70338 0.516716i
676676 20.2827 + 5.84176i 0.780103 + 0.224683i
677677 −19.5225 + 1.92280i −0.750310 + 0.0738991i −0.465941 0.884816i 0.654284π-0.654284\pi
−0.284369 + 0.958715i 0.591784π0.591784\pi
678678 7.85346 + 10.4346i 0.301610 + 0.400740i
679679 1.40590 0.279651i 0.0539535 0.0107320i
680680 0.381186 0.852114i 0.0146178 0.0326771i
681681 −7.69743 + 38.6976i −0.294966 + 1.48289i
682682 −0.676232 0.236596i −0.0258942 0.00905974i
683683 23.2162 12.4093i 0.888345 0.474830i 0.0369267 0.999318i 0.488243π-0.488243\pi
0.851418 + 0.524488i 0.175743π0.175743\pi
684684 −45.1653 104.834i −1.72694 4.00842i
685685 1.29093 + 0.127146i 0.0493240 + 0.00485799i
686686 −3.29068 + 2.00402i −0.125639 + 0.0765137i
687687 13.2614 32.0159i 0.505954 1.22148i
688688 −19.7379 + 6.60053i −0.752501 + 0.251643i
689689 −4.50343 10.8723i −0.171567 0.414200i
690690 34.7616 + 25.4032i 1.32335 + 0.967082i
691691 30.1714 + 36.7639i 1.14777 + 1.39856i 0.903354 + 0.428895i 0.141097π0.141097\pi
0.244418 + 0.969670i 0.421403π0.421403\pi
692692 5.63503 30.5757i 0.214212 1.16231i
693693 0.0643200 0.212035i 0.00244332 0.00805453i
694694 −11.8441 10.5838i −0.449595 0.401754i
695695 −18.0645 + 12.0703i −0.685224 + 0.457852i
696696 27.1411 + 54.3795i 1.02878 + 2.06125i
697697 −0.314738 + 0.471038i −0.0119215 + 0.0178419i
698698 38.2503 + 22.5614i 1.44780 + 0.853963i
699699 −1.44354 1.18469i −0.0545999 0.0448089i
700700 −1.08811 0.562032i −0.0411267 0.0212428i
701701 20.3759 38.1206i 0.769587 1.43980i −0.124649 0.992201i 0.539781π-0.539781\pi
0.894236 0.447595i 0.147719π-0.147719\pi
702702 4.25084 101.057i 0.160438 3.81416i
703703 26.7541i 1.00905i
704704 −0.626451 + 1.02924i −0.0236103 + 0.0387910i
705705 45.1912i 1.70200i
706706 −8.56671 0.360347i −0.322412 0.0135619i
707707 0.0363701 0.0680437i 0.00136784 0.00255905i
708708 −10.7075 + 3.41364i −0.402413 + 0.128293i
709709 −24.6436 20.2245i −0.925510 0.759546i 0.0454055 0.998969i 0.485542π-0.485542\pi
−0.970916 + 0.239422i 0.923042π0.923042\pi
710710 −5.82424 + 9.87434i −0.218580 + 0.370577i
711711 3.64881 5.46082i 0.136841 0.204797i
712712 16.5960 19.1077i 0.621962 0.716092i
713713 19.2205 12.8427i 0.719813 0.480964i
714714 0.144384 0.161578i 0.00540345 0.00604690i
715715 −0.289526 + 0.954438i −0.0108276 + 0.0356940i
716716 −20.3108 + 13.9893i −0.759049 + 0.522806i
717717 18.3571 + 22.3682i 0.685560 + 0.835357i
718718 −14.0323 + 19.2018i −0.523682 + 0.716605i
719719 −7.12269 17.1957i −0.265632 0.641291i 0.733637 0.679542i 0.237821π-0.237821\pi
−0.999268 + 0.0382507i 0.987821π0.987821\pi
720720 39.6993 + 10.8304i 1.47951 + 0.403626i
721721 0.559108 1.34981i 0.0208223 0.0502694i
722722 28.1783 + 46.2699i 1.04869 + 1.72199i
723723 −46.1079 4.54124i −1.71477 0.168890i
724724 −1.16291 0.462596i −0.0432191 0.0171922i
725725 18.3182 9.79128i 0.680321 0.363639i
726726 16.6439 47.5711i 0.617714 1.76553i
727727 −6.68420 + 33.6037i −0.247903 + 1.24629i 0.633431 + 0.773799i 0.281646π0.281646\pi
−0.881334 + 0.472494i 0.843354π0.843354\pi
728728 −1.94619 + 1.84036i −0.0721306 + 0.0682082i
729729 −45.7533 + 9.10089i −1.69457 + 0.337070i
730730 −15.4644 + 11.6390i −0.572363 + 0.430780i
731731 −1.25243 + 0.123354i −0.0463228 + 0.00456240i
732732 23.8430 + 43.1333i 0.881261 + 1.59425i
733733 45.8766 13.9165i 1.69449 0.514018i 0.712295 0.701880i 0.247656π-0.247656\pi
0.982195 + 0.187862i 0.0601558π0.0601558\pi
734734 −10.6608 29.1457i −0.393498 1.07579i
735735 −21.8070 21.8070i −0.804365 0.804365i
736736 −14.3790 36.1205i −0.530018 1.33142i
737737 −0.294510 + 0.294510i −0.0108484 + 0.0108484i
738738 −22.6501 10.5180i −0.833762 0.387173i
739739 −11.5396 38.0411i −0.424492 1.39936i −0.865071 0.501649i 0.832727π-0.832727\pi
0.440579 0.897714i 0.354773π-0.354773\pi
740740 −7.54097 6.01284i −0.277212 0.221036i
741741 11.6908 + 118.699i 0.429472 + 4.36051i
742742 0.662570 + 0.0935150i 0.0243237 + 0.00343304i
743743 2.46999 + 12.4175i 0.0906151 + 0.455553i 0.999277 + 0.0380201i 0.0121051π0.0121051\pi
−0.908662 + 0.417533i 0.862895π0.862895\pi
744744 17.8696 25.1906i 0.655132 0.923534i
745745 −17.3709 3.45529i −0.636422 0.126592i
746746 −1.66775 3.46280i −0.0610607 0.126782i
747747 −6.13526 11.4783i −0.224478 0.419968i
748748 −0.0507874 + 0.0522399i −0.00185697 + 0.00191008i
749749 −0.302201 + 3.06830i −0.0110422 + 0.112113i
750750 12.0389 49.5408i 0.439598 1.80898i
751751 17.7882 + 7.36812i 0.649101 + 0.268867i 0.682844 0.730564i 0.260743π-0.260743\pi
−0.0337429 + 0.999431i 0.510743π0.510743\pi
752752 21.7055 34.5552i 0.791519 1.26010i
753753 −47.3997 + 19.6336i −1.72734 + 0.715488i
754754 −6.98226 44.8884i −0.254279 1.63474i
755755 −7.49525 + 6.15119i −0.272780 + 0.223865i
756756 4.82655 + 3.12750i 0.175540 + 0.113746i
757757 33.7719 + 10.2446i 1.22746 + 0.372346i 0.836452 0.548041i 0.184626π-0.184626\pi
0.391009 + 0.920387i 0.372126π0.372126\pi
758758 9.31502 0.523457i 0.338337 0.0190128i
759759 −1.86693 2.79406i −0.0677654 0.101418i
760760 −28.9842 3.67490i −1.05137 0.133303i
761761 −18.9623 12.6702i −0.687384 0.459295i 0.162194 0.986759i 0.448143π-0.448143\pi
−0.849578 + 0.527464i 0.823143π0.823143\pi
762762 −2.06357 7.99862i −0.0747554 0.289760i
763763 1.41888 1.72891i 0.0513670 0.0625909i
764764 −47.3892 3.99380i −1.71448 0.144490i
765765 2.19448 + 1.17297i 0.0793415 + 0.0424089i
766766 13.2877 + 14.4546i 0.480104 + 0.522267i
767767 8.40038 0.303320
768768 −35.1629 38.2316i −1.26883 1.37957i
769769 34.0603 1.22825 0.614123 0.789210i 0.289510π-0.289510\pi
0.614123 + 0.789210i 0.289510π0.289510\pi
770770 −0.0383806 0.0417512i −0.00138314 0.00150461i
771771 −8.72904 4.66577i −0.314369 0.168034i
772772 −39.0936 3.29467i −1.40701 0.118578i
773773 8.79030 10.7110i 0.316165 0.385249i −0.590543 0.807006i 0.701087π-0.701087\pi
0.906709 + 0.421757i 0.138587π0.138587\pi
774774 −13.8588 53.7180i −0.498143 1.93085i
775775 −8.77636 5.86418i −0.315256 0.210647i
776776 2.61350 20.6128i 0.0938190 0.739958i
777777 −1.24382 1.86150i −0.0446217 0.0667811i
778778 35.5019 1.99503i 1.27281 0.0715252i
779779 16.9672 + 5.14695i 0.607913 + 0.184409i
780780 −36.0841 23.3817i −1.29202 0.837198i
781781 0.691663 0.567633i 0.0247496 0.0203115i
782782 −0.361324 2.32292i −0.0129209 0.0830676i
783783 −90.1166 + 37.3275i −3.22050 + 1.33398i
784784 6.20061 + 27.1486i 0.221450 + 0.969593i
785785 −20.8709 8.64500i −0.744914 0.308553i
786786 9.81560 40.3919i 0.350111 1.44073i
787787 1.71371 17.3996i 0.0610872 0.620229i −0.915089 0.403251i 0.867880π-0.867880\pi
0.976177 0.216978i 0.0696199π-0.0696199\pi
788788 11.2105 11.5311i 0.399357 0.410778i
789789 33.3008 + 62.3014i 1.18554 + 2.21799i
790790 −0.729406 1.51449i −0.0259511 0.0538830i
791791 0.544392 + 0.108286i 0.0193564 + 0.00385022i
792792 −2.61958 1.85827i −0.0930829 0.0660307i
793793 −7.18682 36.1306i −0.255211 1.28303i
794794 31.7324 + 4.47870i 1.12614 + 0.158943i
795795 1.05283 + 10.6896i 0.0373402 + 0.379121i
796796 34.9277 + 27.8498i 1.23798 + 0.987110i
797797 7.77476 + 25.6299i 0.275396 + 0.907859i 0.980125 + 0.198382i 0.0635687π0.0635687\pi
−0.704729 + 0.709477i 0.748931π0.748931\pi
798798 −6.15108 2.85636i −0.217746 0.101114i
799799 1.74480 1.74480i 0.0617267 0.0617267i
800800 −12.7251 + 12.3776i −0.449901 + 0.437613i
801801 47.7032 + 47.7032i 1.68551 + 1.68551i
802802 −12.8379 35.0975i −0.453321 1.23934i
803803 1.44560 0.438518i 0.0510141 0.0154750i
804804 −8.68644 15.7143i −0.306347 0.554199i
805805 1.82106 0.179359i 0.0641838 0.00632156i
806806 −18.4451 + 13.8824i −0.649700 + 0.488986i
807807 −58.0626 + 11.5494i −2.04390 + 0.406557i
808808 −0.768392 0.812579i −0.0270320 0.0285864i
809809 5.04354 25.3556i 0.177322 0.891456i −0.784990 0.619508i 0.787332π-0.787332\pi
0.962312 0.271948i 0.0876678π-0.0876678\pi
810810 −16.0749 + 45.9447i −0.564814 + 1.61433i
811811 −12.6496 + 6.76135i −0.444187 + 0.237423i −0.678298 0.734787i 0.737282π-0.737282\pi
0.234111 + 0.972210i 0.424782π0.424782\pi
812812 2.40014 + 0.954759i 0.0842284 + 0.0335055i
813813 −64.8063 6.38286i −2.27286 0.223857i
814814 0.391541 + 0.642926i 0.0137235 + 0.0225345i
815815 −3.43066 + 8.28235i −0.120171 + 0.290118i
816816 −1.55812 2.72721i −0.0545452 0.0954715i
817817 15.0732 + 36.3899i 0.527344 + 1.27312i
818818 9.76454 13.3618i 0.341409 0.467184i
819819 −4.52949 5.51919i −0.158273 0.192856i
820820 −5.26401 + 3.62567i −0.183827 + 0.126614i
821821 0.620931 2.04693i 0.0216706 0.0714385i −0.945438 0.325802i 0.894366π-0.894366\pi
0.967109 + 0.254363i 0.0818658π0.0818658\pi
822822 2.90825 3.25457i 0.101437 0.113516i
823823 25.0522 16.7393i 0.873265 0.583497i −0.0361688 0.999346i 0.511515π-0.511515\pi
0.909434 + 0.415849i 0.136515π0.136515\pi
824824 −15.9888 13.8870i −0.556995 0.483778i
825825 −0.852470 + 1.27581i −0.0296792 + 0.0444180i
826826 −0.242667 + 0.411414i −0.00844347 + 0.0143149i
827827 −17.2781 14.1797i −0.600817 0.493078i 0.284120 0.958789i 0.408299π-0.408299\pi
−0.884937 + 0.465711i 0.845799π0.845799\pi
828828 98.7346 31.4774i 3.43126 1.09391i
829829 −13.3858 + 25.0432i −0.464910 + 0.869785i 0.534783 + 0.844989i 0.320393π0.320393\pi
−0.999693 + 0.0247952i 0.992107π0.992107\pi
830830 −3.32824 0.139998i −0.115525 0.00485940i
831831 71.4125i 2.47727i
832832 16.3612 + 35.2100i 0.567222 + 1.22069i
833833 1.68391i 0.0583441i
834834 −3.07221 + 73.0372i −0.106382 + 2.52907i
835835 −1.99897 + 3.73981i −0.0691773 + 0.129422i
836836 2.02602 + 1.04648i 0.0700712 + 0.0361933i
837837 38.3168 + 31.4458i 1.32442 + 1.08693i
838838 33.3682 + 19.6818i 1.15269 + 0.679896i
839839 26.5008 39.6613i 0.914910 1.36926i −0.0143760 0.999897i 0.504576π-0.504576\pi
0.929285 0.369362i 0.120424π-0.120424\pi
840840 2.18752 1.09180i 0.0754766 0.0376708i
841841 −12.3132 + 8.22742i −0.424593 + 0.283704i
842842 −42.2334 37.7393i −1.45546 1.30058i
843843 18.6339 61.4278i 0.641786 2.11569i
844844 0.460333 2.49777i 0.0158453 0.0859768i
845845 9.13551 + 11.1317i 0.314271 + 0.382941i
846846 87.8225 + 64.1790i 3.01940 + 2.20652i
847847 −0.819710 1.97895i −0.0281656 0.0679977i
848848 4.32921 8.67942i 0.148666 0.298052i
849849 16.6051 40.0883i 0.569887 1.37583i
850850 −0.916805 + 0.558333i −0.0314461 + 0.0191507i
851851 −24.1719 2.38072i −0.828601 0.0816101i
852852 15.2623 + 35.4255i 0.522876 + 1.21366i
853853 18.9420 10.1247i 0.648562 0.346664i −0.114092 0.993470i 0.536396π-0.536396\pi
0.762654 + 0.646807i 0.223896π0.223896\pi
854854 1.97713 + 0.691748i 0.0676561 + 0.0236711i
855855 15.1933 76.3820i 0.519601 2.61221i
856856 40.7947 + 18.2492i 1.39433 + 0.623743i
857857 44.3065 8.81310i 1.51348 0.301050i 0.632633 0.774451i 0.281974π-0.281974\pi
0.880847 + 0.473401i 0.156974π0.156974\pi
858858 2.01807 + 2.68134i 0.0688958 + 0.0915396i
859859 −25.1481 + 2.47687i −0.858041 + 0.0845097i −0.517462 0.855706i 0.673123π-0.673123\pi
−0.340579 + 0.940216i 0.610623π0.610623\pi
860860 −13.6446 3.92986i −0.465275 0.134007i
861861 −1.41983 + 0.430702i −0.0483878 + 0.0146783i
862862 3.49691 1.27909i 0.119105 0.0435659i
863863 −4.10853 4.10853i −0.139856 0.139856i 0.633713 0.773569i 0.281530π-0.281530\pi
−0.773569 + 0.633713i 0.781530π0.781530\pi
864864 65.1679 51.9888i 2.21706 1.76870i
865865 14.9989 14.9989i 0.509977 0.509977i
866866 −7.30167 + 15.7239i −0.248121 + 0.534319i
867867 15.9656 + 52.6314i 0.542219 + 1.78746i
868868 −0.147065 1.30439i −0.00499170 0.0442739i
869869 0.0128599 + 0.130568i 0.000436241 + 0.00442923i
870870 −5.79489 + 41.0578i −0.196465 + 1.39199i
871871 2.61829 + 13.1631i 0.0887175 + 0.446013i
872872 −17.2513 27.4487i −0.584202 0.929529i
873873 54.3210 + 10.8051i 1.83849 + 0.365698i
874874 −66.2894 + 31.9262i −2.24227 + 1.07992i
875875 −1.02143 1.91097i −0.0345307 0.0646025i
876876 0.918023 + 65.1176i 0.0310171 + 2.20012i
877877 4.15053 42.1410i 0.140153 1.42300i −0.625739 0.780032i 0.715203π-0.715203\pi
0.765893 0.642968i 0.222297π-0.222297\pi
878878 −21.7197 5.27809i −0.733004 0.178127i
879879 50.0446 + 20.7292i 1.68796 + 0.699177i
880880 −0.750298 + 0.335867i −0.0252926 + 0.0113221i
881881 −47.0203 + 19.4765i −1.58415 + 0.656178i −0.989065 0.147481i 0.952884π-0.952884\pi
−0.595090 + 0.803659i 0.702884π0.702884\pi
882882 −73.3484 + 11.4091i −2.46977 + 0.384166i
883883 −28.1130 + 23.0718i −0.946079 + 0.776427i −0.974782 0.223161i 0.928363π-0.928363\pi
0.0287023 + 0.999588i 0.490863π0.490863\pi
884884 0.490433 + 2.29594i 0.0164951 + 0.0772207i
885885 −7.33732 2.22575i −0.246641 0.0748178i
886886 0.167219 + 2.97569i 0.00561783 + 0.0999704i
887887 −1.48282 2.21919i −0.0497881 0.0745131i 0.805740 0.592269i 0.201768π-0.201768\pi
−0.855529 + 0.517756i 0.826768π0.826768\pi
888888 −31.3055 + 8.54897i −1.05054 + 0.286885i
889889 −0.291914 0.195051i −0.00979049 0.00654180i
890890 16.7195 4.31347i 0.560437 0.144588i
891891 2.41013 2.93676i 0.0807425 0.0983851i
892892 −7.36539 + 6.22043i −0.246612 + 0.208275i
893893 −68.1094 36.4052i −2.27919 1.21825i
894894 −43.8726 + 40.3307i −1.46732 + 1.34886i
895895 −16.8259 −0.562427
896896 −2.19707 0.215833i −0.0733989 0.00721048i
897897 −108.282 −3.61545
898898 37.6607 34.6203i 1.25676 1.15530i
899899 19.6340 + 10.4946i 0.654829 + 0.350013i
900900 −30.5317 36.1516i −1.01772 1.20505i
901901 0.372070 0.453368i 0.0123954 0.0151039i
902902 0.483062 0.124626i 0.0160842 0.00414958i
903903 −2.74056 1.83118i −0.0912001 0.0609379i
904904 3.98943 6.98686i 0.132686 0.232380i
905905 −0.474381 0.709961i −0.0157690 0.0235999i
906906 1.83047 + 32.5736i 0.0608133 + 1.08218i
907907 −22.0926 6.70171i −0.733572 0.222527i −0.0986712 0.995120i 0.531459π-0.531459\pi
−0.634901 + 0.772593i 0.718959π0.718959\pi
908908 23.7708 5.07765i 0.788860 0.168508i
909909 2.30439 1.89117i 0.0764319 0.0627260i
910910 −1.80572 + 0.280875i −0.0598591 + 0.00931091i
911911 4.55436 1.88648i 0.150893 0.0625019i −0.305959 0.952045i 0.598977π-0.598977\pi
0.456852 + 0.889543i 0.348977π0.348977\pi
912912 −67.5247 + 71.4438i −2.23596 + 2.36574i
913913 0.240206 + 0.0994968i 0.00794967 + 0.00329286i
914914 −1.76643 0.429259i −0.0584283 0.0141986i
915915 −3.29577 + 33.4625i −0.108955 + 1.10624i
916916 −21.3466 + 0.300942i −0.705311 + 0.00994342i
917917 −0.832800 1.55806i −0.0275015 0.0514517i
918918 4.54166 2.18735i 0.149897 0.0721933i
919919 12.1036 + 2.40756i 0.399262 + 0.0794181i 0.390637 0.920545i 0.372255π-0.372255\pi
0.00862457 + 0.999963i 0.497255π0.497255\pi
920920 5.89937 25.8597i 0.194497 0.852570i
921921 3.74358 + 18.8202i 0.123355 + 0.620148i
922922 −5.69328 + 40.3379i −0.187498 + 1.32846i
923923 −2.82605 28.6933i −0.0930205 0.944453i
924924 −0.189618 + 0.0213787i −0.00623798 + 0.000703306i
925925 3.21944 + 10.6131i 0.105855 + 0.348956i
926926 21.1451 45.5353i 0.694873 1.49638i
927927 39.9166 39.9166i 1.31103 1.31103i
928928 24.1512 28.6113i 0.792803 0.939211i
929929 −10.7155 10.7155i −0.351566 0.351566i 0.509126 0.860692i 0.329969π-0.329969\pi
−0.860692 + 0.509126i 0.829969π0.829969\pi
930930 19.7891 7.23841i 0.648912 0.237357i
931931 50.4336 15.2989i 1.65289 0.501400i
932932 −0.318405 + 1.10551i −0.0104297 + 0.0362121i
933933 63.4193 6.24626i 2.07626 0.204493i
934934 −23.8346 31.6682i −0.779891 1.03622i
935935 −0.0487527 + 0.00969751i −0.00159438 + 0.000317142i
936936 −96.6842 + 36.9183i −3.16022 + 1.20671i
937937 6.65123 33.4380i 0.217286 1.09237i −0.705986 0.708226i 0.749496π-0.749496\pi
0.923272 0.384146i 0.125504π-0.125504\pi
938938 −0.720306 0.252017i −0.0235188 0.00822865i
939939 45.3865 24.2596i 1.48113 0.791681i
940940 25.5685 11.0156i 0.833951 0.359289i
941941 24.6978 + 2.43252i 0.805124 + 0.0792978i 0.492202 0.870481i 0.336192π-0.336192\pi
0.312922 + 0.949779i 0.398692π0.398692\pi
942942 −64.9194 + 39.5358i −2.11519 + 1.28815i
943943 −6.16001 + 14.8716i −0.200597 + 0.484285i
944944 4.54140 + 5.22605i 0.147810 + 0.170093i
945945 1.50157 + 3.62511i 0.0488461 + 0.117925i
946946 0.894781 + 0.653890i 0.0290918 + 0.0212598i
947947 13.6876 + 16.6784i 0.444787 + 0.541975i 0.946349 0.323147i 0.104741π-0.104741\pi
−0.501562 + 0.865122i 0.667241π0.667241\pi
948948 −5.56236 1.02513i −0.180657 0.0332947i
949949 14.1304 46.5818i 0.458694 1.51211i
950950 25.0517 + 22.3859i 0.812783 + 0.726295i
951951 13.5266 9.03815i 0.438629 0.293082i
952952 −0.126613 0.0423049i −0.00410354 0.00137111i
953953 −33.0015 + 49.3903i −1.06902 + 1.59991i −0.307764 + 0.951463i 0.599581π0.599581\pi
−0.761261 + 0.648446i 0.775419π0.775419\pi
954954 22.2689 + 13.1350i 0.720981 + 0.425261i
955955 −25.0811 20.5835i −0.811604 0.666066i
956956 8.18094 15.8385i 0.264590 0.512255i
957957 1.52559 2.85417i 0.0493152 0.0922622i
958958 1.06133 25.2315i 0.0342900 0.815192i
959959 0.185503i 0.00599019i
960960 −4.96151 35.0892i −0.160132 1.13250i
961961 19.6866i 0.635052i
962962 24.2351 + 1.01942i 0.781371 + 0.0328673i
963963 −56.1557 + 105.060i −1.80959 + 3.38551i
964964 8.66969 + 27.1941i 0.279232 + 0.875862i
965965 −20.6905 16.9803i −0.666052 0.546615i
966966 3.12803 5.30321i 0.100643 0.170628i
967967 −2.51428 + 3.76288i −0.0808537 + 0.121006i −0.869692 0.493594i 0.835683π-0.835683\pi
0.788839 + 0.614600i 0.210683π0.210683\pi
968968 −30.9720 + 2.17884i −0.995478 + 0.0700304i
969969 −4.94254 + 3.30250i −0.158777 + 0.106092i
970970 9.44556 10.5704i 0.303279 0.339394i
971971 −4.47380 + 14.7482i −0.143571 + 0.473291i −0.999004 0.0446232i 0.985791π-0.985791\pi
0.855433 + 0.517914i 0.173291π0.173291\pi
972972 42.7459 + 62.0616i 1.37107 + 1.99063i
973973 1.97100 + 2.40168i 0.0631875 + 0.0769942i
974974 −11.3818 + 15.5748i −0.364697 + 0.499050i
975975 18.9212 + 45.6797i 0.605962 + 1.46292i
976976 18.5923 24.0039i 0.595124 0.768347i
977977 −10.0872 + 24.3526i −0.322717 + 0.779108i 0.676377 + 0.736555i 0.263549π0.263549\pi
−0.999094 + 0.0425525i 0.986451π0.986451\pi
978978 15.6893 + 25.7625i 0.501689 + 0.823793i
979979 −1.34119 0.132095i −0.0428645 0.00422179i
980980 −7.02249 + 17.6536i −0.224325 + 0.563925i
981981 76.2133 40.7369i 2.43330 1.30063i
982982 −4.72397 + 13.5019i −0.150748 + 0.430863i
983983 −1.83343 + 9.21726i −0.0584772 + 0.293985i −0.998946 0.0458944i 0.985386π-0.985386\pi
0.940469 + 0.339879i 0.110386π0.110386\pi
984984 −0.600859 + 21.4983i −0.0191547 + 0.685340i
985985 10.7614 2.14057i 0.342885 0.0682041i
986986 1.80895 1.36148i 0.0576088 0.0433583i
987987 6.43144 0.633441i 0.204715 0.0201627i
988988 64.3081 35.5479i 2.04591 1.13093i
989989 −34.2189 + 10.3802i −1.08810 + 0.330071i
990990 −0.752725 2.05788i −0.0239232 0.0654037i
991991 −29.5439 29.5439i −0.938492 0.938492i 0.0597231 0.998215i 0.480978π-0.480978\pi
−0.998215 + 0.0597231i 0.980978π0.980978\pi
992992 −18.6083 3.97000i −0.590813 0.126047i
993993 0.385049 0.385049i 0.0122192 0.0122192i
994994 1.48691 + 0.690476i 0.0471621 + 0.0219006i
995995 8.84709 + 29.1649i 0.280472 + 0.924591i
996996 −6.98775 + 8.76366i −0.221415 + 0.277687i
997997 −3.80500 38.6328i −0.120506 1.22351i −0.845203 0.534446i 0.820520π-0.820520\pi
0.724697 0.689067i 0.241980π-0.241980\pi
998998 31.5778 + 4.45688i 0.999577 + 0.141080i
999999 −10.1608 51.0819i −0.321474 1.61616i
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 128.2.k.a.109.4 yes 240
4.3 odd 2 512.2.k.a.273.15 240
128.27 odd 32 512.2.k.a.497.15 240
128.101 even 32 inner 128.2.k.a.101.4 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.2.k.a.101.4 240 128.101 even 32 inner
128.2.k.a.109.4 yes 240 1.1 even 1 trivial
512.2.k.a.273.15 240 4.3 odd 2
512.2.k.a.497.15 240 128.27 odd 32