Properties

Label 40.3.i.a.13.9
Level 4040
Weight 33
Character 40.13
Analytic conductor 1.0901.090
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,3,Mod(13,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 40.i (of order 44, degree 22, 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: 1.089921057441.08992105744
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20x183x16+11x14+x1240x10+4x8+176x6192x4256x2+1024 x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 220 2^{20}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 13.9
Root 0.5418281.30630i-0.541828 - 1.30630i of defining polynomial
Character χ\chi == 40.13
Dual form 40.3.i.a.37.9

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.848130.764474i)q2+(0.1307910.130791i)q3+(2.831162.82569i)q4+(4.38731+2.39823i)q5+(0.1417330.341706i)q6+(1.59713+1.59713i)q7+(3.072187.38659i)q8+8.96579iq9+(6.27494+7.78621i)q1011.9427iq11+(0.0007153500.739867i)q12+(9.59714+9.59714i)q13+(1.73074+4.17267i)q14+(0.260155+0.887490i)q15+(0.030939616.0000i)q16+(0.8572880.857288i)q17+(6.85411+16.5699i)q18+20.5611q19+(5.64454+19.1870i)q20+0.417782iq21+(9.1298622.0716i)q22+(22.156022.1560i)q23+(0.5642871.36792i)q24+(13.497021.0435i)q25+(10.4000+25.0735i)q26+(2.34977+2.34977i)q27+(0.00873536+9.03474i)q28+27.3404q29+(0.197662+1.83908i)q30+40.0267q31+(12.174429.5937i)q32+(1.562001.56200i)q33+(0.9290052.23975i)q34+(3.1768410.8374i)q35+(25.3345+25.3836i)q36+(1.57131+1.57131i)q37+(37.999615.7184i)q38+2.51044iq39+(4.23607+39.7751i)q4037.5504q41+(0.319383+0.772115i)q42+(49.2602+49.2602i)q43+(33.746333.8116i)q44+(21.502039.3357i)q45+(57.884924.0095i)q46+(34.0876+34.0876i)q47+(2.088612.09670i)q48+43.8983iq49+(8.8570349.2093i)q500.224252iq51+(0.0524906+54.2896i)q52+(28.800228.8002i)q53+(6.13901+2.54634i)q54+(28.6412+52.3962i)q55+(6.89068+16.7040i)q56+(2.689212.68921i)q57+(50.528520.9010i)q5892.7071q59+(1.77123+3.24774i)q60+4.82618iq61+(73.974430.5993i)q62+(14.319614.3196i)q63+(45.123445.3859i)q64+(19.089565.1217i)q65+(4.080881.69267i)q66+(54.6048+54.6048i)q67+(0.004688854.84955i)q685.79564q69+(2.4137122.4575i)q70+59.2198q71+(66.2266+27.5445i)q72+(34.1124+34.1124i)q73+(4.10520+1.70275i)q74+(0.9870174.51761i)q75+(58.211858.0993i)q76+(19.0740+19.0740i)q77+(1.91917+4.63963i)q7896.2455iq79+(38.2358+70.2711i)q8080.0774q81+(69.3980+28.7063i)q82+(63.695963.6959i)q83+(1.18052+1.18281i)q84+(1.70522+5.81716i)q85+(53.3810+128.697i)q86+(3.575883.57588i)q87+(88.215636.6901i)q883.68406iq89+(69.809556.2598i)q9030.6558iq91+(125.3330.121180i)q92+(5.235145.23514i)q93+(36.9392+89.0574i)q94+(90.2080+49.3101i)q95+(5.462902.27829i)q96+(46.041046.0410i)q97+(33.5591+81.1298i)q98+107.075q99+O(q100)q+(1.84813 - 0.764474i) q^{2} +(0.130791 - 0.130791i) q^{3} +(2.83116 - 2.82569i) q^{4} +(-4.38731 + 2.39823i) q^{5} +(0.141733 - 0.341706i) q^{6} +(-1.59713 + 1.59713i) q^{7} +(3.07218 - 7.38659i) q^{8} +8.96579i q^{9} +(-6.27494 + 7.78621i) q^{10} -11.9427i q^{11} +(0.000715350 - 0.739867i) q^{12} +(-9.59714 + 9.59714i) q^{13} +(-1.73074 + 4.17267i) q^{14} +(-0.260155 + 0.887490i) q^{15} +(0.0309396 - 16.0000i) q^{16} +(0.857288 - 0.857288i) q^{17} +(6.85411 + 16.5699i) q^{18} +20.5611 q^{19} +(-5.64454 + 19.1870i) q^{20} +0.417782i q^{21} +(-9.12986 - 22.0716i) q^{22} +(-22.1560 - 22.1560i) q^{23} +(-0.564287 - 1.36792i) q^{24} +(13.4970 - 21.0435i) q^{25} +(-10.4000 + 25.0735i) q^{26} +(2.34977 + 2.34977i) q^{27} +(-0.00873536 + 9.03474i) q^{28} +27.3404 q^{29} +(0.197662 + 1.83908i) q^{30} +40.0267 q^{31} +(-12.1744 - 29.5937i) q^{32} +(-1.56200 - 1.56200i) q^{33} +(0.929005 - 2.23975i) q^{34} +(3.17684 - 10.8374i) q^{35} +(25.3345 + 25.3836i) q^{36} +(1.57131 + 1.57131i) q^{37} +(37.9996 - 15.7184i) q^{38} +2.51044i q^{39} +(4.23607 + 39.7751i) q^{40} -37.5504 q^{41} +(0.319383 + 0.772115i) q^{42} +(-49.2602 + 49.2602i) q^{43} +(-33.7463 - 33.8116i) q^{44} +(-21.5020 - 39.3357i) q^{45} +(-57.8849 - 24.0095i) q^{46} +(-34.0876 + 34.0876i) q^{47} +(-2.08861 - 2.09670i) q^{48} +43.8983i q^{49} +(8.85703 - 49.2093i) q^{50} -0.224252i q^{51} +(-0.0524906 + 54.2896i) q^{52} +(28.8002 - 28.8002i) q^{53} +(6.13901 + 2.54634i) q^{54} +(28.6412 + 52.3962i) q^{55} +(6.89068 + 16.7040i) q^{56} +(2.68921 - 2.68921i) q^{57} +(50.5285 - 20.9010i) q^{58} -92.7071 q^{59} +(1.77123 + 3.24774i) q^{60} +4.82618i q^{61} +(73.9744 - 30.5993i) q^{62} +(-14.3196 - 14.3196i) q^{63} +(-45.1234 - 45.3859i) q^{64} +(19.0895 - 65.1217i) q^{65} +(-4.08088 - 1.69267i) q^{66} +(54.6048 + 54.6048i) q^{67} +(0.00468885 - 4.84955i) q^{68} -5.79564 q^{69} +(-2.41371 - 22.4575i) q^{70} +59.2198 q^{71} +(66.2266 + 27.5445i) q^{72} +(34.1124 + 34.1124i) q^{73} +(4.10520 + 1.70275i) q^{74} +(-0.987017 - 4.51761i) q^{75} +(58.2118 - 58.0993i) q^{76} +(19.0740 + 19.0740i) q^{77} +(1.91917 + 4.63963i) q^{78} -96.2455i q^{79} +(38.2358 + 70.2711i) q^{80} -80.0774 q^{81} +(-69.3980 + 28.7063i) q^{82} +(63.6959 - 63.6959i) q^{83} +(1.18052 + 1.18281i) q^{84} +(-1.70522 + 5.81716i) q^{85} +(-53.3810 + 128.697i) q^{86} +(3.57588 - 3.57588i) q^{87} +(-88.2156 - 36.6901i) q^{88} -3.68406i q^{89} +(-69.8095 - 56.2598i) q^{90} -30.6558i q^{91} +(-125.333 - 0.121180i) q^{92} +(5.23514 - 5.23514i) q^{93} +(-36.9392 + 89.0574i) q^{94} +(-90.2080 + 49.3101i) q^{95} +(-5.46290 - 2.27829i) q^{96} +(46.0410 - 46.0410i) q^{97} +(33.5591 + 81.1298i) q^{98} +107.075 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q2q216q64q7+4q8+6q1044q124q1556q1612q17+10q1824q20+92q224q2328q25+100q26+68q28+100q30136q31++546q98+O(q100) 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/40Z)×\left(\mathbb{Z}/40\mathbb{Z}\right)^\times.

nn 1717 2121 3131
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.84813 0.764474i 0.924064 0.382237i
33 0.130791 0.130791i 0.0435971 0.0435971i −0.684972 0.728569i 0.740186π-0.740186\pi
0.728569 + 0.684972i 0.240186π0.240186\pi
44 2.83116 2.82569i 0.707790 0.706423i
55 −4.38731 + 2.39823i −0.877463 + 0.479645i
66 0.141733 0.341706i 0.0236221 0.0569510i
77 −1.59713 + 1.59713i −0.228162 + 0.228162i −0.811924 0.583763i 0.801580π-0.801580\pi
0.583763 + 0.811924i 0.301580π0.301580\pi
88 3.07218 7.38659i 0.384023 0.923324i
99 8.96579i 0.996199i
1010 −6.27494 + 7.78621i −0.627494 + 0.778621i
1111 11.9427i 1.08570i −0.839831 0.542849i 0.817346π-0.817346\pi
0.839831 0.542849i 0.182654π-0.182654\pi
1212 0.000715350 0.739867i 5.96125e−5 0.0616556i
1313 −9.59714 + 9.59714i −0.738241 + 0.738241i −0.972238 0.233996i 0.924820π-0.924820\pi
0.233996 + 0.972238i 0.424820π0.424820\pi
1414 −1.73074 + 4.17267i −0.123624 + 0.298048i
1515 −0.260155 + 0.887490i −0.0173437 + 0.0591660i
1616 0.0309396 16.0000i 0.00193372 0.999998i
1717 0.857288 0.857288i 0.0504287 0.0504287i −0.681443 0.731871i 0.738647π-0.738647\pi
0.731871 + 0.681443i 0.238647π0.238647\pi
1818 6.85411 + 16.5699i 0.380784 + 0.920552i
1919 20.5611 1.08216 0.541082 0.840970i 0.318015π-0.318015\pi
0.541082 + 0.840970i 0.318015π0.318015\pi
2020 −5.64454 + 19.1870i −0.282227 + 0.959348i
2121 0.417782i 0.0198944i
2222 −9.12986 22.0716i −0.414993 1.00325i
2323 −22.1560 22.1560i −0.963306 0.963306i 0.0360441 0.999350i 0.488524π-0.488524\pi
−0.999350 + 0.0360441i 0.988524π0.988524\pi
2424 −0.564287 1.36792i −0.0235119 0.0569965i
2525 13.4970 21.0435i 0.539881 0.841741i
2626 −10.4000 + 25.0735i −0.400000 + 0.964366i
2727 2.34977 + 2.34977i 0.0870285 + 0.0870285i
2828 −0.00873536 + 9.03474i −0.000311977 + 0.322669i
2929 27.3404 0.942771 0.471385 0.881927i 0.343754π-0.343754\pi
0.471385 + 0.881927i 0.343754π0.343754\pi
3030 0.197662 + 1.83908i 0.00658872 + 0.0613026i
3131 40.0267 1.29118 0.645591 0.763683i 0.276611π-0.276611\pi
0.645591 + 0.763683i 0.276611π0.276611\pi
3232 −12.1744 29.5937i −0.380449 0.924802i
3333 −1.56200 1.56200i −0.0473333 0.0473333i
3434 0.929005 2.23975i 0.0273237 0.0658751i
3535 3.17684 10.8374i 0.0907668 0.309640i
3636 25.3345 + 25.3836i 0.703737 + 0.705100i
3737 1.57131 + 1.57131i 0.0424677 + 0.0424677i 0.728022 0.685554i 0.240440π-0.240440\pi
−0.685554 + 0.728022i 0.740440π0.740440\pi
3838 37.9996 15.7184i 0.999988 0.413642i
3939 2.51044i 0.0643704i
4040 4.23607 + 39.7751i 0.105902 + 0.994377i
4141 −37.5504 −0.915864 −0.457932 0.888987i 0.651410π-0.651410\pi
−0.457932 + 0.888987i 0.651410π0.651410\pi
4242 0.319383 + 0.772115i 0.00760437 + 0.0183837i
4343 −49.2602 + 49.2602i −1.14558 + 1.14558i −0.158174 + 0.987411i 0.550561π0.550561\pi
−0.987411 + 0.158174i 0.949439π0.949439\pi
4444 −33.7463 33.8116i −0.766961 0.768446i
4545 −21.5020 39.3357i −0.477822 0.874127i
4646 −57.8849 24.0095i −1.25837 0.521946i
4747 −34.0876 + 34.0876i −0.725268 + 0.725268i −0.969673 0.244405i 0.921407π-0.921407\pi
0.244405 + 0.969673i 0.421407π0.421407\pi
4848 −2.08861 2.09670i −0.0435127 0.0436813i
4949 43.8983i 0.895884i
5050 8.85703 49.2093i 0.177141 0.984186i
5151 0.224252i 0.00439709i
5252 −0.0524906 + 54.2896i −0.00100943 + 1.04403i
5353 28.8002 28.8002i 0.543401 0.543401i −0.381124 0.924524i 0.624463π-0.624463\pi
0.924524 + 0.381124i 0.124463π0.124463\pi
5454 6.13901 + 2.54634i 0.113685 + 0.0471544i
5555 28.6412 + 52.3962i 0.520749 + 0.952659i
5656 6.89068 + 16.7040i 0.123048 + 0.298287i
5757 2.68921 2.68921i 0.0471792 0.0471792i
5858 50.5285 20.9010i 0.871181 0.360362i
5959 −92.7071 −1.57131 −0.785653 0.618667i 0.787673π-0.787673\pi
−0.785653 + 0.618667i 0.787673π0.787673\pi
6060 1.77123 + 3.24774i 0.0295205 + 0.0541291i
6161 4.82618i 0.0791176i 0.999217 + 0.0395588i 0.0125952π0.0125952\pi
−0.999217 + 0.0395588i 0.987405π0.987405\pi
6262 73.9744 30.5993i 1.19314 0.493537i
6363 −14.3196 14.3196i −0.227294 0.227294i
6464 −45.1234 45.3859i −0.705053 0.709155i
6565 19.0895 65.1217i 0.293685 1.00187i
6666 −4.08088 1.69267i −0.0618315 0.0256465i
6767 54.6048 + 54.6048i 0.814997 + 0.814997i 0.985378 0.170381i 0.0544998π-0.0544998\pi
−0.170381 + 0.985378i 0.554500π0.554500\pi
6868 0.00468885 4.84955i 6.89537e−5 0.0713169i
6969 −5.79564 −0.0839947
7070 −2.41371 22.4575i −0.0344815 0.320822i
7171 59.2198 0.834082 0.417041 0.908888i 0.363067π-0.363067\pi
0.417041 + 0.908888i 0.363067π0.363067\pi
7272 66.2266 + 27.5445i 0.919814 + 0.382563i
7373 34.1124 + 34.1124i 0.467293 + 0.467293i 0.901037 0.433743i 0.142807π-0.142807\pi
−0.433743 + 0.901037i 0.642807π0.642807\pi
7474 4.10520 + 1.70275i 0.0554756 + 0.0230102i
7575 −0.987017 4.51761i −0.0131602 0.0602347i
7676 58.2118 58.0993i 0.765944 0.764465i
7777 19.0740 + 19.0740i 0.247715 + 0.247715i
7878 1.91917 + 4.63963i 0.0246047 + 0.0594824i
7979 96.2455i 1.21830i −0.793056 0.609149i 0.791511π-0.791511\pi
0.793056 0.609149i 0.208489π-0.208489\pi
8080 38.2358 + 70.2711i 0.477947 + 0.878388i
8181 −80.0774 −0.988610
8282 −69.3980 + 28.7063i −0.846317 + 0.350077i
8383 63.6959 63.6959i 0.767421 0.767421i −0.210231 0.977652i 0.567422π-0.567422\pi
0.977652 + 0.210231i 0.0674216π0.0674216\pi
8484 1.18052 + 1.18281i 0.0140539 + 0.0140811i
8585 −1.70522 + 5.81716i −0.0200614 + 0.0684372i
8686 −53.3810 + 128.697i −0.620710 + 1.49648i
8787 3.57588 3.57588i 0.0411021 0.0411021i
8888 −88.2156 36.6901i −1.00245 0.416933i
8989 3.68406i 0.0413939i −0.999786 0.0206970i 0.993411π-0.993411\pi
0.999786 0.0206970i 0.00658852π-0.00658852\pi
9090 −69.8095 56.2598i −0.775662 0.625109i
9191 30.6558i 0.336877i
9292 −125.333 0.121180i −1.36232 0.00131718i
9393 5.23514 5.23514i 0.0562918 0.0562918i
9494 −36.9392 + 89.0574i −0.392970 + 0.947419i
9595 −90.2080 + 49.3101i −0.949558 + 0.519054i
9696 −5.46290 2.27829i −0.0569052 0.0237322i
9797 46.0410 46.0410i 0.474650 0.474650i −0.428766 0.903416i 0.641051π-0.641051\pi
0.903416 + 0.428766i 0.141051π0.141051\pi
9898 33.5591 + 81.1298i 0.342440 + 0.827855i
9999 107.075 1.08157
100100 −21.2503 97.7160i −0.212503 0.977160i
101101 108.173i 1.07102i 0.844529 + 0.535510i 0.179880π0.179880\pi
−0.844529 + 0.535510i 0.820120π0.820120\pi
102102 −0.171434 0.414446i −0.00168073 0.00406320i
103103 −50.9112 50.9112i −0.494284 0.494284i 0.415369 0.909653i 0.363652π-0.363652\pi
−0.909653 + 0.415369i 0.863652π0.863652\pi
104104 41.4059 + 100.374i 0.398134 + 0.965137i
105105 −1.00194 1.83294i −0.00954225 0.0174566i
106106 31.2095 75.2435i 0.294429 0.709845i
107107 −95.4147 95.4147i −0.891726 0.891726i 0.102960 0.994686i 0.467169π-0.467169\pi
−0.994686 + 0.102960i 0.967169π0.967169\pi
108108 13.2923 + 0.0128518i 0.123077 + 0.000118998i
109109 −46.5432 −0.427002 −0.213501 0.976943i 0.568487π-0.568487\pi
−0.213501 + 0.976943i 0.568487π0.568487\pi
110110 92.9882 + 74.9395i 0.845347 + 0.681269i
111111 0.411026 0.00370294
112112 25.5047 + 25.6035i 0.227720 + 0.228603i
113113 88.0400 + 88.0400i 0.779115 + 0.779115i 0.979680 0.200565i 0.0642779π-0.0642779\pi
−0.200565 + 0.979680i 0.564278π0.564278\pi
114114 2.91418 7.02585i 0.0255630 0.0616302i
115115 150.341 + 44.0703i 1.30731 + 0.383220i
116116 77.4049 77.2554i 0.667284 0.665995i
117117 −86.0459 86.0459i −0.735435 0.735435i
118118 −171.335 + 70.8721i −1.45199 + 0.600611i
119119 2.73841i 0.0230118i
120120 5.75628 + 4.64819i 0.0479690 + 0.0387349i
121121 −21.6274 −0.178739
122122 3.68948 + 8.91939i 0.0302417 + 0.0731098i
123123 −4.91127 + 4.91127i −0.0399290 + 0.0399290i
124124 113.322 113.103i 0.913886 0.912121i
125125 −8.74856 + 124.693i −0.0699885 + 0.997548i
126126 −37.4113 15.5175i −0.296915 0.123154i
127127 44.3246 44.3246i 0.349012 0.349012i −0.510729 0.859742i 0.670625π-0.670625\pi
0.859742 + 0.510729i 0.170625π0.170625\pi
128128 −118.090 49.3834i −0.922579 0.385808i
129129 12.8856i 0.0998884i
130130 −14.5039 134.947i −0.111569 1.03805i
131131 82.8025i 0.632080i −0.948746 0.316040i 0.897647π-0.897647\pi
0.948746 0.316040i 0.102353π-0.102353\pi
132132 −8.83599 0.00854319i −0.0669393 6.47212e-5i
133133 −32.8388 + 32.8388i −0.246908 + 0.246908i
134134 142.661 + 59.1728i 1.06463 + 0.441588i
135135 −15.9444 4.67390i −0.118107 0.0346215i
136136 −3.69869 8.96618i −0.0271962 0.0659278i
137137 25.0030 25.0030i 0.182503 0.182503i −0.609942 0.792446i 0.708807π-0.708807\pi
0.792446 + 0.609942i 0.208807π0.208807\pi
138138 −10.7111 + 4.43061i −0.0776165 + 0.0321059i
139139 −104.684 −0.753121 −0.376561 0.926392i 0.622893π-0.622893\pi
−0.376561 + 0.926392i 0.622893π0.622893\pi
140140 −21.6290 39.6592i −0.154493 0.283280i
141141 8.91673i 0.0632392i
142142 109.446 45.2720i 0.770745 0.318817i
143143 114.615 + 114.615i 0.801507 + 0.801507i
144144 143.452 + 0.277398i 0.996197 + 0.00192637i
145145 −119.951 + 65.5683i −0.827246 + 0.452195i
146146 89.1222 + 36.9661i 0.610426 + 0.253193i
147147 5.74152 + 5.74152i 0.0390580 + 0.0390580i
148148 8.88864 + 0.00859410i 0.0600584 + 5.80682e-5i
149149 49.3481 0.331196 0.165598 0.986193i 0.447045π-0.447045\pi
0.165598 + 0.986193i 0.447045π0.447045\pi
150150 −5.27772 7.59457i −0.0351848 0.0506305i
151151 −22.1078 −0.146409 −0.0732047 0.997317i 0.523323π-0.523323\pi
−0.0732047 + 0.997317i 0.523323π0.523323\pi
152152 63.1675 151.876i 0.415575 0.999187i
153153 7.68626 + 7.68626i 0.0502370 + 0.0502370i
154154 49.8329 + 20.6697i 0.323590 + 0.134219i
155155 −175.609 + 95.9930i −1.13296 + 0.619309i
156156 7.09374 + 7.10747i 0.0454727 + 0.0455607i
157157 −64.7264 64.7264i −0.412270 0.412270i 0.470258 0.882529i 0.344161π-0.344161\pi
−0.882529 + 0.470258i 0.844161π0.844161\pi
158158 −73.5771 177.874i −0.465678 1.12579i
159159 7.53364i 0.0473814i
160160 124.385 + 100.640i 0.777407 + 0.628998i
161161 70.7723 0.439579
162162 −147.993 + 61.2171i −0.913540 + 0.377883i
163163 25.7888 25.7888i 0.158213 0.158213i −0.623561 0.781775i 0.714315π-0.714315\pi
0.781775 + 0.623561i 0.214315π0.214315\pi
164164 −106.311 + 106.106i −0.648240 + 0.646987i
165165 10.5990 + 3.10695i 0.0642363 + 0.0188300i
166166 69.0244 166.412i 0.415810 1.00248i
167167 −56.4754 + 56.4754i −0.338176 + 0.338176i −0.855681 0.517504i 0.826861π-0.826861\pi
0.517504 + 0.855681i 0.326861π0.326861\pi
168168 3.08599 + 1.28350i 0.0183690 + 0.00763990i
169169 15.2101i 0.0900005i
170170 1.29560 + 12.0545i 0.00762116 + 0.0709086i
171171 184.346i 1.07805i
172172 −0.269424 + 278.657i −0.00156642 + 1.62010i
173173 135.496 135.496i 0.783216 0.783216i −0.197156 0.980372i 0.563171π-0.563171\pi
0.980372 + 0.197156i 0.0631706π0.0631706\pi
174174 3.87502 9.34236i 0.0222702 0.0536917i
175175 12.0528 + 55.1659i 0.0688729 + 0.315233i
176176 −191.082 0.369501i −1.08570 0.00209944i
177177 −12.1253 + 12.1253i −0.0685044 + 0.0685044i
178178 −2.81636 6.80861i −0.0158223 0.0382506i
179179 15.5036 0.0866121 0.0433061 0.999062i 0.486211π-0.486211\pi
0.0433061 + 0.999062i 0.486211π0.486211\pi
180180 −172.026 50.6078i −0.955701 0.281154i
181181 263.672i 1.45675i −0.685179 0.728375i 0.740276π-0.740276\pi
0.685179 0.728375i 0.259724π-0.259724\pi
182182 −23.4355 56.6559i −0.128767 0.311296i
183183 0.631222 + 0.631222i 0.00344930 + 0.00344930i
184184 −231.725 + 95.5901i −1.25937 + 0.519512i
185185 −10.6622 3.12546i −0.0576333 0.0168944i
186186 5.67309 13.6773i 0.0305005 0.0735341i
187187 −10.2383 10.2383i −0.0547503 0.0547503i
188188 −0.186439 + 192.829i −0.000991696 + 1.02568i
189189 −7.50579 −0.0397132
190190 −129.020 + 160.093i −0.679051 + 0.842595i
191191 −120.714 −0.632010 −0.316005 0.948758i 0.602342π-0.602342\pi
−0.316005 + 0.948758i 0.602342π0.602342\pi
192192 −11.8378 0.0343368i −0.0616554 0.000178837i
193193 −182.404 182.404i −0.945098 0.945098i 0.0534716 0.998569i 0.482971π-0.482971\pi
−0.998569 + 0.0534716i 0.982971π0.982971\pi
194194 49.8926 120.287i 0.257178 0.620036i
195195 −6.02061 11.0141i −0.0308749 0.0564826i
196196 124.043 + 124.283i 0.632873 + 0.634098i
197197 224.288 + 224.288i 1.13852 + 1.13852i 0.988716 + 0.149799i 0.0478626π0.0478626\pi
0.149799 + 0.988716i 0.452137π0.452137\pi
198198 197.889 81.8563i 0.999441 0.413416i
199199 87.9089i 0.441753i 0.975302 + 0.220877i 0.0708918π0.0708918\pi
−0.975302 + 0.220877i 0.929108π0.929108\pi
200200 −113.975 164.347i −0.569873 0.821733i
201201 14.2837 0.0710631
202202 82.6954 + 199.918i 0.409383 + 0.989691i
203203 −43.6662 + 43.6662i −0.215104 + 0.215104i
204204 −0.633666 0.634892i −0.00310621 0.00311222i
205205 164.745 90.0544i 0.803636 0.439290i
206206 −133.011 55.1702i −0.645684 0.267817i
207207 198.646 198.646i 0.959644 0.959644i
208208 153.257 + 153.851i 0.736812 + 0.739667i
209209 245.554i 1.17490i
210210 −3.25294 2.62156i −0.0154902 0.0124836i
211211 119.117i 0.564534i 0.959336 + 0.282267i 0.0910864π0.0910864\pi
−0.959336 + 0.282267i 0.908914π0.908914\pi
212212 0.157520 162.919i 0.000743019 0.768484i
213213 7.74544 7.74544i 0.0363636 0.0363636i
214214 −249.281 103.397i −1.16486 0.483162i
215215 97.9828 334.257i 0.455734 1.55468i
216216 24.5757 10.1379i 0.113776 0.0469345i
217217 −63.9279 + 63.9279i −0.294599 + 0.294599i
218218 −86.0179 + 35.5811i −0.394577 + 0.163216i
219219 8.92322 0.0407453
220220 229.143 + 67.4109i 1.04156 + 0.306413i
221221 16.4550i 0.0744571i
222222 0.759629 0.314219i 0.00342175 0.00141540i
223223 111.993 + 111.993i 0.502212 + 0.502212i 0.912125 0.409913i 0.134441π-0.134441\pi
−0.409913 + 0.912125i 0.634441π0.634441\pi
224224 66.7091 + 27.8209i 0.297808 + 0.124200i
225225 188.672 + 121.011i 0.838541 + 0.537829i
226226 230.013 + 95.4050i 1.01776 + 0.422146i
227227 85.8837 + 85.8837i 0.378342 + 0.378342i 0.870504 0.492162i 0.163793π-0.163793\pi
−0.492162 + 0.870504i 0.663793π0.663793\pi
228228 0.0147084 15.2125i 6.45105e−5 0.0667214i
229229 −26.5156 −0.115789 −0.0578943 0.998323i 0.518439π-0.518439\pi
−0.0578943 + 0.998323i 0.518439π0.518439\pi
230230 311.540 33.4839i 1.35452 0.145582i
231231 4.98944 0.0215993
232232 83.9946 201.952i 0.362046 0.870482i
233233 −71.6569 71.6569i −0.307541 0.307541i 0.536414 0.843955i 0.319778π-0.319778\pi
−0.843955 + 0.536414i 0.819778π0.819778\pi
234234 −224.804 93.2441i −0.960700 0.398479i
235235 67.8033 231.303i 0.288524 0.984267i
236236 −262.469 + 261.962i −1.11215 + 1.11001i
237237 −12.5881 12.5881i −0.0531143 0.0531143i
238238 2.09344 + 5.06093i 0.00879596 + 0.0212644i
239239 114.913i 0.480809i 0.970673 + 0.240405i 0.0772801π0.0772801\pi
−0.970673 + 0.240405i 0.922720π0.922720\pi
240240 14.1918 + 4.18994i 0.0591323 + 0.0174581i
241241 219.080 0.909045 0.454522 0.890735i 0.349810π-0.349810\pi
0.454522 + 0.890735i 0.349810π0.349810\pi
242242 −39.9702 + 16.5336i −0.165166 + 0.0683205i
243243 −31.6214 + 31.6214i −0.130129 + 0.130129i
244244 13.6373 + 13.6637i 0.0558905 + 0.0559987i
245245 −105.278 192.596i −0.429707 0.786105i
246246 −5.32212 + 12.8312i −0.0216347 + 0.0521593i
247247 −197.328 + 197.328i −0.798897 + 0.798897i
248248 122.969 295.660i 0.495844 1.19218i
249249 16.6618i 0.0669147i
250250 79.1564 + 237.138i 0.316626 + 0.948551i
251251 95.0552i 0.378706i −0.981909 0.189353i 0.939361π-0.939361\pi
0.981909 0.189353i 0.0606390π-0.0606390\pi
252252 −81.0036 0.0783194i −0.321443 0.000310791i
253253 −264.602 + 264.602i −1.04586 + 1.04586i
254254 48.0326 115.802i 0.189105 0.455915i
255255 0.537806 + 0.983862i 0.00210904 + 0.00385828i
256256 −255.998 0.990065i −0.999993 0.00386744i
257257 −249.128 + 249.128i −0.969369 + 0.969369i −0.999545 0.0301755i 0.990393π-0.990393\pi
0.0301755 + 0.999545i 0.490393π0.490393\pi
258258 9.85070 + 23.8143i 0.0381810 + 0.0923033i
259259 −5.01917 −0.0193790
260260 −129.968 238.311i −0.499878 0.916582i
261261 245.128i 0.939187i
262262 −63.3003 153.030i −0.241604 0.584082i
263263 −85.6095 85.6095i −0.325511 0.325511i 0.525365 0.850877i 0.323929π-0.323929\pi
−0.850877 + 0.525365i 0.823929π0.823929\pi
264264 −16.3366 + 6.73909i −0.0618810 + 0.0255269i
265265 −57.2862 + 195.425i −0.216174 + 0.737453i
266266 −35.5859 + 85.7947i −0.133782 + 0.322537i
267267 −0.481843 0.481843i −0.00180465 0.00180465i
268268 308.891 + 0.298656i 1.15258 + 0.00111439i
269269 −192.119 −0.714196 −0.357098 0.934067i 0.616234π-0.616234\pi
−0.357098 + 0.934067i 0.616234π0.616234\pi
270270 −33.0405 + 3.55115i −0.122372 + 0.0131524i
271271 −485.780 −1.79255 −0.896274 0.443501i 0.853736π-0.853736\pi
−0.896274 + 0.443501i 0.853736π0.853736\pi
272272 −13.6901 13.7431i −0.0503311 0.0505261i
273273 −4.00951 4.00951i −0.0146869 0.0146869i
274274 27.0946 65.3228i 0.0988853 0.238404i
275275 −251.316 161.191i −0.913876 0.586148i
276276 −16.4084 + 16.3767i −0.0594506 + 0.0593358i
277277 −88.8551 88.8551i −0.320777 0.320777i 0.528288 0.849065i 0.322834π-0.322834\pi
−0.849065 + 0.528288i 0.822834π0.822834\pi
278278 −193.469 + 80.0280i −0.695933 + 0.287871i
279279 358.871i 1.28627i
280280 −70.2916 56.7605i −0.251042 0.202716i
281281 390.006 1.38792 0.693961 0.720012i 0.255864π-0.255864\pi
0.693961 + 0.720012i 0.255864π0.255864\pi
282282 6.81660 + 16.4793i 0.0241724 + 0.0584371i
283283 121.062 121.062i 0.427779 0.427779i −0.460092 0.887871i 0.652184π-0.652184\pi
0.887871 + 0.460092i 0.152184π0.152184\pi
284284 167.661 167.337i 0.590355 0.589214i
285285 −5.34908 + 18.2478i −0.0187687 + 0.0640272i
286286 299.445 + 124.204i 1.04701 + 0.434278i
287287 59.9730 59.9730i 0.208965 0.208965i
288288 265.330 109.153i 0.921286 0.379003i
289289 287.530i 0.994914i
290290 −171.559 + 212.878i −0.591583 + 0.734061i
291291 12.0435i 0.0413867i
292292 192.969 + 0.186575i 0.660852 + 0.000638954i
293293 −244.956 + 244.956i −0.836026 + 0.836026i −0.988333 0.152307i 0.951330π-0.951330\pi
0.152307 + 0.988333i 0.451330π0.451330\pi
294294 15.0003 + 6.22183i 0.0510215 + 0.0211627i
295295 406.735 222.332i 1.37876 0.753669i
296296 16.4339 6.77925i 0.0555200 0.0229029i
297297 28.0625 28.0625i 0.0944866 0.0944866i
298298 91.2017 37.7253i 0.306046 0.126595i
299299 425.269 1.42230
300300 −15.5598 10.0011i −0.0518659 0.0333369i
301301 157.350i 0.522757i
302302 −40.8581 + 16.9008i −0.135292 + 0.0559630i
303303 14.1481 + 14.1481i 0.0466934 + 0.0466934i
304304 0.636152 328.977i 0.00209260 1.08216i
305305 −11.5743 21.1739i −0.0379484 0.0694228i
306306 20.0811 + 8.32926i 0.0656247 + 0.0272198i
307307 −135.324 135.324i −0.440796 0.440796i 0.451483 0.892280i 0.350895π-0.350895\pi
−0.892280 + 0.451483i 0.850895π0.850895\pi
308308 107.899 + 0.104324i 0.350321 + 0.000338713i
309309 −13.3175 −0.0430987
310310 −251.165 + 311.656i −0.810209 + 1.00534i
311311 225.951 0.726531 0.363266 0.931686i 0.381662π-0.381662\pi
0.363266 + 0.931686i 0.381662π0.381662\pi
312312 18.5436 + 7.71255i 0.0594347 + 0.0247197i
313313 −230.622 230.622i −0.736812 0.736812i 0.235148 0.971960i 0.424443π-0.424443\pi
−0.971960 + 0.235148i 0.924443π0.924443\pi
314314 −169.104 70.1411i −0.538549 0.223379i
315315 97.1659 + 28.4828i 0.308463 + 0.0904217i
316316 −271.960 272.486i −0.860633 0.862299i
317317 221.563 + 221.563i 0.698938 + 0.698938i 0.964182 0.265243i 0.0854522π-0.0854522\pi
−0.265243 + 0.964182i 0.585452π0.585452\pi
318318 −5.75927 13.9231i −0.0181109 0.0437835i
319319 326.517i 1.02356i
320320 306.816 + 90.9062i 0.958800 + 0.284082i
321321 −24.9588 −0.0777534
322322 130.796 54.1035i 0.406200 0.168023i
323323 17.6268 17.6268i 0.0545721 0.0545721i
324324 −226.712 + 226.274i −0.699729 + 0.698377i
325325 72.4248 + 331.490i 0.222846 + 1.01997i
326326 27.9462 67.3759i 0.0857244 0.206674i
327327 −6.08745 + 6.08745i −0.0186161 + 0.0186161i
328328 −115.362 + 277.370i −0.351713 + 0.845639i
329329 108.885i 0.330957i
330330 21.9635 2.36061i 0.0665560 0.00715336i
331331 141.212i 0.426624i −0.976984 0.213312i 0.931575π-0.931575\pi
0.976984 0.213312i 0.0684250π-0.0684250\pi
332332 0.348379 360.318i 0.00104933 1.08530i
333333 −14.0880 + 14.0880i −0.0423063 + 0.0423063i
334334 −61.1999 + 147.548i −0.183233 + 0.441760i
335335 −370.523 108.614i −1.10604 0.324220i
336336 6.68450 + 0.0129260i 0.0198944 + 3.84703e-5i
337337 225.465 225.465i 0.669035 0.669035i −0.288458 0.957493i 0.593142π-0.593142\pi
0.957493 + 0.288458i 0.0931424π0.0931424\pi
338338 −11.6277 28.1102i −0.0344015 0.0831663i
339339 23.0297 0.0679343
340340 11.6097 + 21.2877i 0.0341463 + 0.0626110i
341341 478.025i 1.40183i
342342 140.928 + 340.696i 0.412070 + 0.996187i
343343 −148.371 148.371i −0.432568 0.432568i
344344 212.528 + 515.201i 0.617815 + 1.49768i
345345 25.4273 13.8992i 0.0737022 0.0402877i
346346 146.831 353.998i 0.424368 1.02312i
347347 346.013 + 346.013i 0.997155 + 0.997155i 0.999996 0.00284067i 0.000904214π-0.000904214\pi
−0.00284067 + 0.999996i 0.500904π0.500904\pi
348348 0.0195579 20.2282i 5.62009e−5 0.0581271i
349349 428.411 1.22754 0.613769 0.789486i 0.289653π-0.289653\pi
0.613769 + 0.789486i 0.289653π0.289653\pi
350350 64.4479 + 92.7396i 0.184137 + 0.264970i
351351 −45.1021 −0.128496
352352 −353.427 + 145.395i −1.00405 + 0.413053i
353353 25.9724 + 25.9724i 0.0735762 + 0.0735762i 0.742937 0.669361i 0.233432π-0.233432\pi
−0.669361 + 0.742937i 0.733432π0.733432\pi
354354 −13.1396 + 31.6785i −0.0371176 + 0.0894874i
355355 −259.816 + 142.022i −0.731876 + 0.400063i
356356 −10.4100 10.4302i −0.0292416 0.0292982i
357357 0.358160 + 0.358160i 0.00100325 + 0.00100325i
358358 28.6526 11.8521i 0.0800352 0.0331063i
359359 288.043i 0.802348i 0.916002 + 0.401174i 0.131398π0.131398\pi
−0.916002 + 0.401174i 0.868602π0.868602\pi
360360 −356.615 + 37.9797i −0.990597 + 0.105499i
361361 61.7587 0.171077
362362 −201.570 487.299i −0.556823 1.34613i
363363 −2.82868 + 2.82868i −0.00779249 + 0.00779249i
364364 −86.6238 86.7915i −0.237978 0.238438i
365365 −231.471 67.8526i −0.634168 0.185898i
366366 1.64913 + 0.684027i 0.00450583 + 0.00186893i
367367 160.854 160.854i 0.438295 0.438295i −0.453143 0.891438i 0.649697π-0.649697\pi
0.891438 + 0.453143i 0.149697π0.149697\pi
368368 −355.181 + 353.810i −0.965167 + 0.961442i
369369 336.669i 0.912382i
370370 −22.0944 + 2.37467i −0.0597145 + 0.00641804i
371371 91.9956i 0.247966i
372372 0.0286331 29.6144i 7.69706e−5 0.0796086i
373373 360.121 360.121i 0.965471 0.965471i −0.0339529 0.999423i 0.510810π-0.510810\pi
0.999423 + 0.0339529i 0.0108096π0.0108096\pi
374374 −26.7486 11.0948i −0.0715204 0.0296652i
375375 15.1646 + 17.4531i 0.0404389 + 0.0465415i
376376 147.068 + 356.515i 0.391138 + 0.948177i
377377 −262.389 + 262.389i −0.695992 + 0.695992i
378378 −13.8717 + 5.73797i −0.0366975 + 0.0151798i
379379 64.1572 0.169280 0.0846402 0.996412i 0.473026π-0.473026\pi
0.0846402 + 0.996412i 0.473026π0.473026\pi
380380 −116.058 + 394.505i −0.305416 + 1.03817i
381381 11.5945i 0.0304319i
382382 −223.095 + 92.2826i −0.584018 + 0.241577i
383383 376.877 + 376.877i 0.984014 + 0.984014i 0.999874 0.0158604i 0.00504875π-0.00504875\pi
−0.0158604 + 0.999874i 0.505049π0.505049\pi
384384 −21.9041 + 8.98625i −0.0570419 + 0.0234017i
385385 −129.428 37.9399i −0.336175 0.0985452i
386386 −476.549 197.663i −1.23458 0.512080i
387387 −441.656 441.656i −1.14123 1.14123i
388388 0.251817 260.447i 0.000649013 0.671256i
389389 −10.3794 −0.0266823 −0.0133411 0.999911i 0.504247π-0.504247\pi
−0.0133411 + 0.999911i 0.504247π0.504247\pi
390390 −19.5469 15.7529i −0.0501202 0.0403920i
391391 −37.9882 −0.0971566
392392 324.259 + 134.864i 0.827191 + 0.344040i
393393 −10.8298 10.8298i −0.0275569 0.0275569i
394394 585.974 + 243.050i 1.48724 + 0.616879i
395395 230.818 + 422.259i 0.584350 + 1.06901i
396396 303.148 302.562i 0.765525 0.764046i
397397 −184.458 184.458i −0.464630 0.464630i 0.435540 0.900169i 0.356558π-0.356558\pi
−0.900169 + 0.435540i 0.856558π0.856558\pi
398398 67.2040 + 162.467i 0.168854 + 0.408208i
399399 8.59006i 0.0215290i
400400 −336.278 216.603i −0.840696 0.541508i
401401 −262.943 −0.655719 −0.327859 0.944727i 0.606327π-0.606327\pi
−0.327859 + 0.944727i 0.606327π0.606327\pi
402402 26.3981 10.9195i 0.0656669 0.0271629i
403403 −384.141 + 384.141i −0.953204 + 0.953204i
404404 305.663 + 306.255i 0.756593 + 0.758057i
405405 351.325 192.044i 0.867468 0.474182i
406406 −47.3191 + 114.082i −0.116549 + 0.280991i
407407 18.7656 18.7656i 0.0461071 0.0461071i
408408 −1.65645 0.688942i −0.00405994 0.00168858i
409409 245.618i 0.600532i 0.953855 + 0.300266i 0.0970755π0.0970755\pi
−0.953855 + 0.300266i 0.902925π0.902925\pi
410410 235.627 292.376i 0.574699 0.713111i
411411 6.54034i 0.0159132i
412412 −287.997 0.278454i −0.699023 0.000675859i
413413 148.065 148.065i 0.358512 0.358512i
414414 215.264 518.984i 0.519962 1.25358i
415415 −126.697 + 432.211i −0.305293 + 1.04147i
416416 400.854 + 167.175i 0.963590 + 0.401864i
417417 −13.6917 + 13.6917i −0.0328339 + 0.0328339i
418418 −187.720 453.816i −0.449091 1.08568i
419419 −673.011 −1.60623 −0.803116 0.595823i 0.796826π-0.796826\pi
−0.803116 + 0.595823i 0.796826π0.796826\pi
420420 −8.01597 2.35819i −0.0190856 0.00561474i
421421 701.227i 1.66562i 0.553557 + 0.832811i 0.313270π0.313270\pi
−0.553557 + 0.832811i 0.686730π0.686730\pi
422422 91.0615 + 220.143i 0.215786 + 0.521666i
423423 −305.622 305.622i −0.722511 0.722511i
424424 −124.256 301.215i −0.293056 0.710413i
425425 −6.46952 29.6112i −0.0152224 0.0696734i
426426 8.39339 20.2358i 0.0197028 0.0475018i
427427 −7.70804 7.70804i −0.0180516 0.0180516i
428428 −539.747 0.521861i −1.26109 0.00121930i
429429 29.9814 0.0698868
430430 −74.4456 692.655i −0.173129 1.61082i
431431 405.559 0.940973 0.470486 0.882407i 0.344078π-0.344078\pi
0.470486 + 0.882407i 0.344078π0.344078\pi
432432 37.6689 37.5235i 0.0871966 0.0868600i
433433 145.764 + 145.764i 0.336638 + 0.336638i 0.855100 0.518462i 0.173495π-0.173495\pi
−0.518462 + 0.855100i 0.673495π0.673495\pi
434434 −69.2758 + 167.018i −0.159622 + 0.384834i
435435 −7.11274 + 24.2643i −0.0163511 + 0.0557800i
436436 −131.771 + 131.517i −0.302228 + 0.301644i
437437 −455.553 455.553i −1.04245 1.04245i
438438 16.4913 6.82156i 0.0376513 0.0155743i
439439 62.3888i 0.142116i −0.997472 0.0710579i 0.977362π-0.977362\pi
0.997472 0.0710579i 0.0226375π-0.0226375\pi
440440 475.020 50.5900i 1.07959 0.114977i
441441 −393.583 −0.892479
442442 12.5794 + 30.4110i 0.0284602 + 0.0688032i
443443 169.632 169.632i 0.382918 0.382918i −0.489235 0.872152i 0.662724π-0.662724\pi
0.872152 + 0.489235i 0.162724π0.162724\pi
444444 1.16368 1.16143i 0.00262090 0.00261584i
445445 8.83520 + 16.1631i 0.0198544 + 0.0363216i
446446 292.594 + 121.362i 0.656040 + 0.272112i
447447 6.45431 6.45431i 0.0144392 0.0144392i
448448 144.555 + 0.419297i 0.322668 + 0.000935930i
449449 17.0056i 0.0378743i −0.999821 0.0189371i 0.993972π-0.993972\pi
0.999821 0.0189371i 0.00602824π-0.00602824\pi
450450 441.200 + 79.4102i 0.980444 + 0.176467i
451451 448.452i 0.994351i
452452 498.029 + 0.481526i 1.10183 + 0.00106532i
453453 −2.89151 + 2.89151i −0.00638303 + 0.00638303i
454454 224.380 + 93.0683i 0.494229 + 0.204996i
455455 73.5195 + 134.497i 0.161581 + 0.295597i
456456 −11.6024 28.1259i −0.0254438 0.0616795i
457457 559.163 559.163i 1.22355 1.22355i 0.257191 0.966360i 0.417203π-0.417203\pi
0.966360 0.257191i 0.0827971π-0.0827971\pi
458458 −49.0042 + 20.2705i −0.106996 + 0.0442586i
459459 4.02886 0.00877747
460460 550.168 300.046i 1.19602 0.652274i
461461 327.625i 0.710683i −0.934737 0.355341i 0.884365π-0.884365\pi
0.934737 0.355341i 0.115635π-0.115635\pi
462462 9.22112 3.81429i 0.0199591 0.00825604i
463463 605.934 + 605.934i 1.30871 + 1.30871i 0.922345 + 0.386367i 0.126270π0.126270\pi
0.386367 + 0.922345i 0.373730π0.373730\pi
464464 0.845899 437.445i 0.00182306 0.942769i
465465 −10.4132 + 35.5232i −0.0223939 + 0.0763941i
466466 −187.211 77.6514i −0.401741 0.166634i
467467 83.9231 + 83.9231i 0.179707 + 0.179707i 0.791228 0.611521i 0.209442π-0.209442\pi
−0.611521 + 0.791228i 0.709442π0.709442\pi
468468 −486.749 0.470619i −1.04006 0.00100560i
469469 −174.422 −0.371903
470470 −51.5157 479.311i −0.109608 1.01981i
471471 −16.9313 −0.0359476
472472 −284.813 + 684.789i −0.603418 + 1.45082i
473473 588.298 + 588.298i 1.24376 + 1.24376i
474474 −32.8876 13.6411i −0.0693832 0.0287788i
475475 277.514 432.678i 0.584239 0.910901i
476476 7.73789 + 7.75286i 0.0162561 + 0.0162875i
477477 258.217 + 258.217i 0.541335 + 0.541335i
478478 87.8483 + 212.375i 0.183783 + 0.444299i
479479 831.992i 1.73694i −0.495746 0.868468i 0.665105π-0.665105\pi
0.495746 0.868468i 0.334895π-0.334895\pi
480480 29.4313 3.10568i 0.0613152 0.00647017i
481481 −30.1601 −0.0627028
482482 404.888 167.481i 0.840016 0.347470i
483483 9.25640 9.25640i 0.0191644 0.0191644i
484484 −61.2306 + 61.1123i −0.126510 + 0.126265i
485485 −91.5797 + 312.413i −0.188824 + 0.644151i
486486 −34.2667 + 82.6140i −0.0705075 + 0.169988i
487487 −373.676 + 373.676i −0.767301 + 0.767301i −0.977631 0.210329i 0.932546π-0.932546\pi
0.210329 + 0.977631i 0.432546π0.432546\pi
488488 35.6490 + 14.8269i 0.0730512 + 0.0303830i
489489 6.74590i 0.0137953i
490490 −341.802 275.459i −0.697555 0.562162i
491491 42.8051i 0.0871795i 0.999050 + 0.0435898i 0.0138794π0.0138794\pi
−0.999050 + 0.0435898i 0.986121π0.986121\pi
492492 −0.0268617 + 27.7823i −5.45970e−5 + 0.0564681i
493493 23.4386 23.4386i 0.0475427 0.0475427i
494494 −213.835 + 515.539i −0.432865 + 1.04360i
495495 −469.773 + 256.791i −0.949037 + 0.518770i
496496 1.23841 640.425i 0.00249679 1.29118i
497497 −94.5819 + 94.5819i −0.190306 + 0.190306i
498498 −12.7375 30.7931i −0.0255772 0.0618335i
499499 −485.100 −0.972143 −0.486072 0.873919i 0.661571π-0.661571\pi
−0.486072 + 0.873919i 0.661571π0.661571\pi
500500 327.577 + 377.748i 0.655153 + 0.755496i
501501 14.7730i 0.0294870i
502502 −72.6672 175.674i −0.144755 0.349949i
503503 −666.926 666.926i −1.32590 1.32590i −0.908916 0.416980i 0.863088π-0.863088\pi
−0.416980 0.908916i 0.636912π-0.636912\pi
504504 −149.765 + 61.7803i −0.297153 + 0.122580i
505505 −259.423 474.589i −0.513709 0.939780i
506506 −286.738 + 691.301i −0.566675 + 1.36621i
507507 −1.98935 1.98935i −0.00392376 0.00392376i
508508 0.242429 250.738i 0.000477222 0.493578i
509509 −779.971 −1.53236 −0.766180 0.642626i 0.777845π-0.777845\pi
−0.766180 + 0.642626i 0.777845π0.777845\pi
510510 1.74607 + 1.40717i 0.00342367 + 0.00275915i
511511 −108.964 −0.213237
512512 −473.874 + 193.874i −0.925536 + 0.378660i
513513 48.3138 + 48.3138i 0.0941790 + 0.0941790i
514514 −269.969 + 650.872i −0.525231 + 1.26629i
515515 345.460 + 101.267i 0.670796 + 0.196635i
516516 36.4107 + 36.4812i 0.0705634 + 0.0707000i
517517 407.097 + 407.097i 0.787422 + 0.787422i
518518 −9.27606 + 3.83702i −0.0179075 + 0.00740737i
519519 35.4435i 0.0682919i
520520 −422.381 341.073i −0.812271 0.655909i
521521 −736.972 −1.41453 −0.707267 0.706947i 0.750072π-0.750072\pi
−0.707267 + 0.706947i 0.750072π0.750072\pi
522522 187.394 + 453.028i 0.358992 + 0.867869i
523523 671.690 671.690i 1.28430 1.28430i 0.346108 0.938195i 0.387503π-0.387503\pi
0.938195 0.346108i 0.112497π-0.112497\pi
524524 −233.974 234.427i −0.446516 0.447380i
525525 8.79161 + 5.63882i 0.0167459 + 0.0107406i
526526 −223.664 92.7712i −0.425216 0.176371i
527527 34.3144 34.3144i 0.0651127 0.0651127i
528528 −25.0402 + 24.9436i −0.0474247 + 0.0472417i
529529 452.780i 0.855917i
530530 43.5250 + 404.964i 0.0821227 + 0.764084i
531531 831.192i 1.56533i
532532 −0.179609 + 185.764i −0.000337610 + 0.349181i
533533 360.377 360.377i 0.676129 0.676129i
534534 −1.25886 0.522152i −0.00235742 0.000977812i
535535 647.440 + 189.788i 1.21017 + 0.354744i
536536 571.099 235.587i 1.06548 0.439529i
537537 2.02773 2.02773i 0.00377604 0.00377604i
538538 −355.060 + 146.870i −0.659963 + 0.272992i
539539 524.263 0.972659
540540 −58.3483 + 31.8215i −0.108052 + 0.0589288i
541541 1039.61i 1.92164i 0.277168 + 0.960822i 0.410604π0.410604\pi
−0.277168 + 0.960822i 0.589396π0.589396\pi
542542 −897.785 + 371.366i −1.65643 + 0.685177i
543543 −34.4860 34.4860i −0.0635101 0.0635101i
544544 −35.8072 14.9333i −0.0658221 0.0274510i
545545 204.200 111.621i 0.374678 0.204809i
546546 −10.4753 4.34493i −0.0191855 0.00795775i
547547 238.506 + 238.506i 0.436026 + 0.436026i 0.890672 0.454646i 0.150234π-0.150234\pi
−0.454646 + 0.890672i 0.650234π0.650234\pi
548548 0.136751 141.438i 0.000249546 0.258099i
549549 −43.2705 −0.0788169
550550 −587.690 105.777i −1.06853 0.192321i
551551 562.148 1.02023
552552 −17.8053 + 42.8100i −0.0322559 + 0.0775543i
553553 153.717 + 153.717i 0.277969 + 0.277969i
554554 −232.143 96.2883i −0.419031 0.173806i
555555 −1.80330 + 0.985734i −0.00324919 + 0.00177610i
556556 −296.377 + 295.804i −0.533052 + 0.532022i
557557 −263.387 263.387i −0.472867 0.472867i 0.429974 0.902841i 0.358523π-0.358523\pi
−0.902841 + 0.429974i 0.858523π0.858523\pi
558558 274.347 + 663.239i 0.491661 + 1.18860i
559559 945.513i 1.69144i
560560 −173.300 51.1646i −0.309464 0.0913653i
561561 −2.67816 −0.00477391
562562 720.782 298.149i 1.28253 0.530515i
563563 160.698 160.698i 0.285431 0.285431i −0.549839 0.835270i 0.685311π-0.685311\pi
0.835270 + 0.549839i 0.185311π0.185311\pi
564564 25.1959 + 25.2447i 0.0446736 + 0.0447601i
565565 −597.399 175.119i −1.05734 0.309946i
566566 131.189 316.286i 0.231783 0.558809i
567567 127.894 127.894i 0.225563 0.225563i
568568 181.934 437.432i 0.320307 0.770127i
569569 407.195i 0.715633i −0.933792 0.357817i 0.883521π-0.883521\pi
0.933792 0.357817i 0.116479π-0.116479\pi
570570 4.06414 + 37.8134i 0.00713007 + 0.0663394i
571571 131.146i 0.229678i 0.993384 + 0.114839i 0.0366351π0.0366351\pi
−0.993384 + 0.114839i 0.963365π0.963365\pi
572572 648.363 + 0.626878i 1.13350 + 0.00109594i
573573 −15.7883 + 15.7883i −0.0275538 + 0.0275538i
574574 64.9901 156.686i 0.113223 0.272971i
575575 −765.282 + 167.201i −1.33093 + 0.290784i
576576 406.920 404.567i 0.706459 0.702373i
577577 417.933 417.933i 0.724321 0.724321i −0.245162 0.969482i 0.578841π-0.578841\pi
0.969482 + 0.245162i 0.0788410π0.0788410\pi
578578 219.809 + 531.393i 0.380293 + 0.919365i
579579 −47.7137 −0.0824071
580580 −154.324 + 524.578i −0.266075 + 0.904445i
581581 203.462i 0.350192i
582582 −9.20697 22.2580i −0.0158195 0.0382440i
583583 −343.952 343.952i −0.589969 0.589969i
584584 356.774 147.175i 0.610914 0.252012i
585585 583.868 + 171.153i 0.998064 + 0.292569i
586586 −265.448 + 639.972i −0.452982 + 1.09210i
587587 212.882 + 212.882i 0.362660 + 0.362660i 0.864791 0.502131i 0.167451π-0.167451\pi
−0.502131 + 0.864791i 0.667451π0.667451\pi
588588 32.4789 + 0.0314027i 0.0552363 + 5.34059e-5i
589589 822.992 1.39727
590590 581.731 721.837i 0.985985 1.22345i
591591 58.6697 0.0992720
592592 25.1895 25.0922i 0.0425498 0.0423855i
593593 97.2530 + 97.2530i 0.164002 + 0.164002i 0.784337 0.620335i 0.213003π-0.213003\pi
−0.620335 + 0.784337i 0.713003π0.713003\pi
594594 30.4101 73.3162i 0.0511955 0.123428i
595595 −6.56731 12.0142i −0.0110375 0.0201920i
596596 139.712 139.443i 0.234417 0.233964i
597597 11.4977 + 11.4977i 0.0192592 + 0.0192592i
598598 785.952 325.107i 1.31430 0.543657i
599599 712.479i 1.18945i 0.803930 + 0.594723i 0.202738π0.202738\pi
−0.803930 + 0.594723i 0.797262π0.797262\pi
600600 −36.4020 6.58823i −0.0606700 0.0109804i
601601 217.550 0.361980 0.180990 0.983485i 0.442070π-0.442070\pi
0.180990 + 0.983485i 0.442070π0.442070\pi
602602 −120.290 290.803i −0.199817 0.483062i
603603 −489.575 + 489.575i −0.811899 + 0.811899i
604604 −62.5908 + 62.4699i −0.103627 + 0.103427i
605605 94.8861 51.8674i 0.156837 0.0857312i
606606 36.9633 + 15.3317i 0.0609956 + 0.0252998i
607607 12.6560 12.6560i 0.0208501 0.0208501i −0.696605 0.717455i 0.745307π-0.745307\pi
0.717455 + 0.696605i 0.245307π0.245307\pi
608608 −250.318 608.478i −0.411708 1.00079i
609609 11.4223i 0.0187558i
610610 −37.5776 30.2840i −0.0616027 0.0496458i
611611 654.287i 1.07085i
612612 43.4800 + 0.0420392i 0.0710458 + 6.86916e-5i
613613 −523.841 + 523.841i −0.854552 + 0.854552i −0.990690 0.136138i 0.956531π-0.956531\pi
0.136138 + 0.990690i 0.456531π0.456531\pi
614614 −353.549 146.645i −0.575813 0.238836i
615615 9.76895 33.3256i 0.0158845 0.0541880i
616616 199.491 82.2931i 0.323849 0.133593i
617617 −331.035 + 331.035i −0.536523 + 0.536523i −0.922506 0.385983i 0.873862π-0.873862\pi
0.385983 + 0.922506i 0.373862π0.373862\pi
618618 −24.6125 + 10.1809i −0.0398260 + 0.0164739i
619619 −277.907 −0.448961 −0.224481 0.974479i 0.572069π-0.572069\pi
−0.224481 + 0.974479i 0.572069π0.572069\pi
620620 −225.932 + 767.990i −0.364407 + 1.23869i
621621 104.123i 0.167670i
622622 417.587 172.734i 0.671361 0.277707i
623623 5.88393 + 5.88393i 0.00944451 + 0.00944451i
624624 40.1670 + 0.0776721i 0.0643703 + 0.000124475i
625625 −260.660 568.050i −0.417057 0.908881i
626626 −602.524 249.915i −0.962498 0.399225i
627627 −32.1164 32.1164i −0.0512223 0.0512223i
628628 −366.148 0.354015i −0.583038 0.000563718i
629629 2.69412 0.00428318
630630 201.349 21.6408i 0.319602 0.0343504i
631631 425.237 0.673910 0.336955 0.941521i 0.390603π-0.390603\pi
0.336955 + 0.941521i 0.390603π0.390603\pi
632632 −710.926 295.684i −1.12488 0.467854i
633633 15.5794 + 15.5794i 0.0246121 + 0.0246121i
634634 578.857 + 240.098i 0.913024 + 0.378704i
635635 −88.1655 + 300.766i −0.138843 + 0.473647i
636636 −21.2877 21.3289i −0.0334713 0.0335361i
637637 −421.298 421.298i −0.661379 0.661379i
638638 −249.613 603.445i −0.391244 0.945839i
639639 530.952i 0.830911i
640640 636.531 66.5464i 0.994580 0.103979i
641641 −474.056 −0.739558 −0.369779 0.929120i 0.620567π-0.620567\pi
−0.369779 + 0.929120i 0.620567π0.620567\pi
642642 −46.1271 + 19.0804i −0.0718491 + 0.0297202i
643643 −490.408 + 490.408i −0.762687 + 0.762687i −0.976807 0.214121i 0.931311π-0.931311\pi
0.214121 + 0.976807i 0.431311π0.431311\pi
644644 200.368 199.981i 0.311130 0.310529i
645645 −30.9026 56.5332i −0.0479110 0.0876483i
646646 19.1014 46.0518i 0.0295687 0.0712876i
647647 −319.187 + 319.187i −0.493334 + 0.493334i −0.909355 0.416021i 0.863424π-0.863424\pi
0.416021 + 0.909355i 0.363424π0.363424\pi
648648 −246.013 + 591.499i −0.379649 + 0.912807i
649649 1107.17i 1.70596i
650650 387.266 + 557.270i 0.595794 + 0.857339i
651651 16.7224i 0.0256873i
652652 0.141049 145.883i 0.000216333 0.223747i
653653 95.6351 95.6351i 0.146455 0.146455i −0.630077 0.776532i 0.716977π-0.716977\pi
0.776532 + 0.630077i 0.216977π0.216977\pi
654654 −6.59670 + 15.9041i −0.0100867 + 0.0243182i
655655 198.579 + 363.280i 0.303174 + 0.554626i
656656 −1.16179 + 600.806i −0.00177103 + 0.915862i
657657 −305.845 + 305.845i −0.465517 + 0.465517i
658658 −83.2396 201.233i −0.126504 0.305826i
659659 295.703 0.448715 0.224358 0.974507i 0.427972π-0.427972\pi
0.224358 + 0.974507i 0.427972π0.427972\pi
660660 38.7867 21.1532i 0.0587678 0.0320503i
661661 1223.87i 1.85154i −0.378088 0.925770i 0.623418π-0.623418\pi
0.378088 0.925770i 0.376582π-0.376582\pi
662662 −107.953 260.979i −0.163071 0.394228i
663663 2.15217 + 2.15217i 0.00324611 + 0.00324611i
664664 −274.810 666.181i −0.413871 1.00328i
665665 65.3192 222.829i 0.0982244 0.335081i
666666 −15.2665 + 36.8063i −0.0229227 + 0.0552647i
667667 −605.754 605.754i −0.908177 0.908177i
668668 −0.308887 + 319.473i −0.000462405 + 0.478253i
669669 29.2955 0.0437900
670670 −767.807 + 82.5229i −1.14598 + 0.123168i
671671 57.6374 0.0858978
672672 12.3637 5.08624i 0.0183984 0.00756880i
673673 −95.3663 95.3663i −0.141703 0.141703i 0.632697 0.774400i 0.281948π-0.281948\pi
−0.774400 + 0.632697i 0.781948π0.781948\pi
674674 244.326 589.050i 0.362502 0.873961i
675675 81.1623 17.7325i 0.120241 0.0262704i
676676 −42.9790 43.0622i −0.0635784 0.0637015i
677677 208.006 + 208.006i 0.307247 + 0.307247i 0.843841 0.536594i 0.180289π-0.180289\pi
−0.536594 + 0.843841i 0.680289π0.680289\pi
678678 42.5619 17.6056i 0.0627757 0.0259670i
679679 147.067i 0.216594i
680680 37.7302 + 30.4671i 0.0554856 + 0.0448046i
681681 22.4657 0.0329892
682682 −365.438 883.452i −0.535832 1.29538i
683683 −704.881 + 704.881i −1.03204 + 1.03204i −0.0325668 + 0.999470i 0.510368π0.510368\pi
−0.999470 + 0.0325668i 0.989632π0.989632\pi
684684 520.906 + 521.914i 0.761559 + 0.763033i
685685 −49.7331 + 169.658i −0.0726030 + 0.247677i
686686 −387.634 160.783i −0.565065 0.234378i
687687 −3.46801 + 3.46801i −0.00504805 + 0.00504805i
688688 786.637 + 789.685i 1.14337 + 1.14780i
689689 552.800i 0.802321i
690690 36.3673 45.1261i 0.0527062 0.0654001i
691691 814.437i 1.17864i 0.807901 + 0.589318i 0.200603π0.200603\pi
−0.807901 + 0.589318i 0.799397π0.799397\pi
692692 0.741084 766.483i 0.00107093 1.10763i
693693 −171.014 + 171.014i −0.246773 + 0.246773i
694694 903.994 + 374.959i 1.30259 + 0.540286i
695695 459.281 251.056i 0.660836 0.361231i
696696 −15.4278 37.3993i −0.0221664 0.0537347i
697697 −32.1915 + 32.1915i −0.0461858 + 0.0461858i
698698 791.758 327.509i 1.13432 0.469210i
699699 −18.7442 −0.0268158
700700 190.005 + 122.126i 0.271436 + 0.174466i
701701 39.4607i 0.0562920i −0.999604 0.0281460i 0.991040π-0.991040\pi
0.999604 0.0281460i 0.00896033π-0.00896033\pi
702702 −83.3545 + 34.4794i −0.118739 + 0.0491159i
703703 32.3078 + 32.3078i 0.0459570 + 0.0459570i
704704 −542.029 + 538.894i −0.769928 + 0.765474i
705705 −21.3843 39.1205i −0.0303324 0.0554900i
706706 67.8556 + 28.1451i 0.0961127 + 0.0398656i
707707 −172.767 172.767i −0.244366 0.244366i
708708 −0.0663180 + 68.5909i −9.36695e−5 + 0.0968798i
709709 1177.86 1.66130 0.830648 0.556798i 0.187970π-0.187970\pi
0.830648 + 0.556798i 0.187970π0.187970\pi
710710 −371.601 + 461.098i −0.523381 + 0.649434i
711711 862.917 1.21367
712712 −27.2126 11.3181i −0.0382200 0.0158962i
713713 −886.832 886.832i −1.24380 1.24380i
714714 0.935729 + 0.388122i 0.00131054 + 0.000543588i
715715 −777.728 227.980i −1.08773 0.318853i
716716 43.8931 43.8083i 0.0613032 0.0611848i
717717 15.0297 + 15.0297i 0.0209619 + 0.0209619i
718718 220.201 + 532.341i 0.306687 + 0.741422i
719719 242.835i 0.337740i −0.985638 0.168870i 0.945988π-0.945988\pi
0.985638 0.168870i 0.0540119π-0.0540119\pi
720720 −630.036 + 342.814i −0.875049 + 0.476131i
721721 162.624 0.225553
722722 114.138 47.2129i 0.158086 0.0653918i
723723 28.6537 28.6537i 0.0396317 0.0396317i
724724 −745.054 746.497i −1.02908 1.03107i
725725 369.014 575.338i 0.508984 0.793569i
726726 −3.06531 + 7.39020i −0.00422219 + 0.0101793i
727727 −619.622 + 619.622i −0.852300 + 0.852300i −0.990416 0.138116i 0.955895π-0.955895\pi
0.138116 + 0.990416i 0.455895π0.455895\pi
728728 −226.442 94.1802i −0.311046 0.129368i
729729 712.425i 0.977264i
730730 −479.660 + 51.5532i −0.657069 + 0.0706209i
731731 84.4603i 0.115541i
732732 3.57073 + 0.00345241i 0.00487804 + 4.71640e-6i
733733 281.127 281.127i 0.383529 0.383529i −0.488843 0.872372i 0.662581π-0.662581\pi
0.872372 + 0.488843i 0.162581π0.162581\pi
734734 174.310 420.248i 0.237480 0.572545i
735735 −38.9593 11.4204i −0.0530059 0.0155379i
736736 −385.942 + 925.414i −0.524378 + 1.25736i
737737 652.127 652.127i 0.884841 0.884841i
738738 −257.375 622.208i −0.348746 0.843100i
739739 1109.74 1.50168 0.750839 0.660485i 0.229649π-0.229649\pi
0.750839 + 0.660485i 0.229649π0.229649\pi
740740 −39.0179 + 21.2793i −0.0527268 + 0.0287558i
741741 51.6175i 0.0696592i
742742 70.3282 + 170.020i 0.0947819 + 0.229137i
743743 −339.850 339.850i −0.457403 0.457403i 0.440399 0.897802i 0.354837π-0.354837\pi
−0.897802 + 0.440399i 0.854837π0.854837\pi
744744 −22.5865 54.7531i −0.0303582 0.0735929i
745745 −216.506 + 118.348i −0.290612 + 0.158856i
746746 390.247 940.852i 0.523119 1.26120i
747747 571.084 + 571.084i 0.764504 + 0.764504i
748748 −57.9166 0.0559974i −0.0774286 7.48629e-5i
749749 304.780 0.406916
750750 41.3685 + 20.6626i 0.0551580 + 0.0275501i
751751 −980.557 −1.30567 −0.652834 0.757501i 0.726420π-0.726420\pi
−0.652834 + 0.757501i 0.726420π0.726420\pi
752752 544.346 + 546.455i 0.723865 + 0.726670i
753753 −12.4324 12.4324i −0.0165105 0.0165105i
754754 −284.339 + 685.518i −0.377108 + 0.909176i
755755 96.9939 53.0195i 0.128469 0.0702245i
756756 −21.2501 + 21.2090i −0.0281086 + 0.0280543i
757757 −101.564 101.564i −0.134166 0.134166i 0.636834 0.771001i 0.280243π-0.280243\pi
−0.771001 + 0.636834i 0.780243π0.780243\pi
758758 118.571 49.0465i 0.156426 0.0647052i
759759 69.2154i 0.0911929i
760760 87.0983 + 817.819i 0.114603 + 1.07608i
761761 767.675 1.00877 0.504386 0.863478i 0.331719π-0.331719\pi
0.504386 + 0.863478i 0.331719π0.331719\pi
762762 −8.86372 21.4282i −0.0116322 0.0281210i
763763 74.3357 74.3357i 0.0974256 0.0974256i
764764 −341.760 + 341.100i −0.447330 + 0.446466i
765765 −52.1554 15.2886i −0.0681770 0.0199852i
766766 984.630 + 408.405i 1.28542 + 0.533166i
767767 889.722 889.722i 1.16000 1.16000i
768768 −33.6118 + 33.3528i −0.0437654 + 0.0434282i
769769 331.840i 0.431522i −0.976446 0.215761i 0.930777π-0.930777\pi
0.976446 0.215761i 0.0692232π-0.0692232\pi
770770 −268.203 + 28.8261i −0.348315 + 0.0374365i
771771 65.1675i 0.0845234i
772772 −1031.83 0.997640i −1.33657 0.00129228i
773773 −180.328 + 180.328i −0.233283 + 0.233283i −0.814061 0.580779i 0.802748π-0.802748\pi
0.580779 + 0.814061i 0.302748π0.302748\pi
774774 −1153.87 478.603i −1.49079 0.618350i
775775 540.241 842.302i 0.697085 1.08684i
776776 −198.640 481.533i −0.255979 0.620532i
777777 −0.656463 + 0.656463i −0.000844869 + 0.000844869i
778778 −19.1825 + 7.93478i −0.0246561 + 0.0101989i
779779 −772.078 −0.991114
780780 −48.1678 14.1703i −0.0617536 0.0181671i
781781 707.243i 0.905561i
782782 −70.2071 + 29.0410i −0.0897789 + 0.0371368i
783783 64.2435 + 64.2435i 0.0820479 + 0.0820479i
784784 702.372 + 1.35820i 0.895883 + 0.00173239i
785785 439.204 + 128.747i 0.559495 + 0.164008i
786786 −28.2941 11.7358i −0.0359976 0.0149311i
787787 945.029 + 945.029i 1.20080 + 1.20080i 0.973924 + 0.226876i 0.0728513π0.0728513\pi
0.226876 + 0.973924i 0.427149π0.427149\pi
788788 1268.76 + 1.22672i 1.61010 + 0.00155675i
789789 −22.3940 −0.0283827
790790 749.388 + 603.935i 0.948593 + 0.764474i
791791 −281.223 −0.355529
792792 328.955 790.922i 0.415348 0.998639i
793793 −46.3175 46.3175i −0.0584079 0.0584079i
794794 −481.915 199.889i −0.606946 0.251749i
795795 18.0674 + 33.0524i 0.0227263 + 0.0415754i
796796 248.403 + 248.884i 0.312065 + 0.312669i
797797 680.774 + 680.774i 0.854171 + 0.854171i 0.990644 0.136473i 0.0435766π-0.0435766\pi
−0.136473 + 0.990644i 0.543577π0.543577\pi
798798 6.56687 + 15.8755i 0.00822917 + 0.0198942i
799799 58.4458i 0.0731487i
800800 −787.073 143.235i −0.983841 0.179043i
801801 33.0305 0.0412366
802802 −485.953 + 201.013i −0.605926 + 0.250640i
803803 407.393 407.393i 0.507339 0.507339i
804804 40.4394 40.3613i 0.0502977 0.0502006i
805805 −310.500 + 169.728i −0.385714 + 0.210842i
806806 −416.277 + 1003.61i −0.516472 + 1.24517i
807807 −25.1275 + 25.1275i −0.0311369 + 0.0311369i
808808 799.029 + 332.327i 0.988898 + 0.411296i
809809 427.952i 0.528989i −0.964387 0.264495i 0.914795π-0.914795\pi
0.964387 0.264495i 0.0852051π-0.0852051\pi
810810 502.481 623.500i 0.620347 0.769753i
811811 1222.46i 1.50735i −0.657245 0.753677i 0.728278π-0.728278\pi
0.657245 0.753677i 0.271722π-0.271722\pi
812812 −0.238828 + 247.013i −0.000294123 + 0.304203i
813813 −63.5359 + 63.5359i −0.0781499 + 0.0781499i
814814 20.3354 49.0270i 0.0249821 0.0602297i
815815 −51.2962 + 174.991i −0.0629401 + 0.214713i
816816 −3.58802 0.00693825i −0.00439708 8.50276e-6i
817817 −1012.84 + 1012.84i −1.23971 + 1.23971i
818818 187.768 + 453.933i 0.229545 + 0.554930i
819819 274.853 0.335596
820820 211.955 720.478i 0.258482 0.878632i
821821 1019.26i 1.24148i 0.784015 + 0.620742i 0.213169π0.213169\pi
−0.784015 + 0.620742i 0.786831π0.786831\pi
822822 −4.99992 12.0874i −0.00608262 0.0147049i
823823 −158.477 158.477i −0.192560 0.192560i 0.604241 0.796801i 0.293476π-0.293476\pi
−0.796801 + 0.604241i 0.793476π0.793476\pi
824824 −532.469 + 219.652i −0.646200 + 0.266568i
825825 −53.9523 + 11.7876i −0.0653967 + 0.0142880i
826826 160.452 386.836i 0.194252 0.468325i
827827 −573.534 573.534i −0.693511 0.693511i 0.269492 0.963003i 0.413144π-0.413144\pi
−0.963003 + 0.269492i 0.913144π0.913144\pi
828828 1.08648 1123.71i 0.00131217 1.35714i
829829 −1133.71 −1.36756 −0.683782 0.729686i 0.739666π-0.739666\pi
−0.683782 + 0.729686i 0.739666π0.739666\pi
830830 96.2620 + 895.638i 0.115978 + 1.07908i
831831 −23.2430 −0.0279699
832832 868.630 + 2.51955i 1.04403 + 0.00302830i
833833 37.6335 + 37.6335i 0.0451783 + 0.0451783i
834834 −14.8371 + 35.7711i −0.0177903 + 0.0428910i
835835 112.335 383.216i 0.134532 0.458941i
836836 −693.861 695.204i −0.829977 0.831584i
837837 94.0534 + 94.0534i 0.112370 + 0.112370i
838838 −1243.81 + 514.499i −1.48426 + 0.613961i
839839 1109.49i 1.32240i 0.750212 + 0.661198i 0.229952π0.229952\pi
−0.750212 + 0.661198i 0.770048π0.770048\pi
840840 −16.6173 + 1.76976i −0.0197825 + 0.00210685i
841841 −93.5052 −0.111183
842842 536.070 + 1295.96i 0.636662 + 1.53914i
843843 51.0094 51.0094i 0.0605094 0.0605094i
844844 336.587 + 337.238i 0.398800 + 0.399572i
845845 36.4772 + 66.7314i 0.0431683 + 0.0789721i
846846 −798.470 331.189i −0.943817 0.391477i
847847 34.5418 34.5418i 0.0407814 0.0407814i
848848 −459.912 461.694i −0.542349 0.544450i
849849 31.6676i 0.0372999i
850850 −34.5935 49.7795i −0.0406982 0.0585642i
851851 69.6278i 0.0818188i
852852 0.0423629 43.8148i 4.97217e−5 0.0514258i
853853 −1.51055 + 1.51055i −0.00177087 + 0.00177087i −0.707992 0.706221i 0.750399π-0.750399\pi
0.706221 + 0.707992i 0.250399π0.250399\pi
854854 −20.1380 8.35286i −0.0235809 0.00978087i
855855 −442.104 808.785i −0.517081 0.945948i
856856 −997.920 + 411.658i −1.16579 + 0.480908i
857857 −396.892 + 396.892i −0.463118 + 0.463118i −0.899676 0.436558i 0.856197π-0.856197\pi
0.436558 + 0.899676i 0.356197π0.356197\pi
858858 55.4095 22.9200i 0.0645799 0.0267133i
859859 −941.956 −1.09657 −0.548286 0.836291i 0.684720π-0.684720\pi
−0.548286 + 0.836291i 0.684720π0.684720\pi
860860 −667.101 1223.20i −0.775699 1.42233i
861861 15.6879i 0.0182206i
862862 749.526 310.039i 0.869520 0.359674i
863863 833.800 + 833.800i 0.966164 + 0.966164i 0.999446 0.0332818i 0.0105959π-0.0105959\pi
−0.0332818 + 0.999446i 0.510596π0.510596\pi
864864 40.9313 98.1452i 0.0473742 0.113594i
865865 −269.514 + 919.416i −0.311577 + 1.06291i
866866 380.824 + 157.958i 0.439751 + 0.182400i
867867 37.6064 + 37.6064i 0.0433754 + 0.0433754i
868868 −0.349647 + 361.631i −0.000402819 + 0.416625i
869869 −1149.43 −1.32270
870870 5.40414 + 50.2810i 0.00621165 + 0.0577943i
871871 −1048.10 −1.20333
872872 −142.989 + 343.796i −0.163979 + 0.394261i
873873 412.794 + 412.794i 0.472846 + 0.472846i
874874 −1190.18 493.662i −1.36176 0.564831i
875875 −185.179 213.125i −0.211634 0.243571i
876876 25.2631 25.2143i 0.0288391 0.0287834i
877877 −33.6015 33.6015i −0.0383142 0.0383142i 0.687690 0.726004i 0.258625π-0.258625\pi
−0.726004 + 0.687690i 0.758625π0.758625\pi
878878 −47.6946 115.303i −0.0543219 0.131324i
879879 64.0762i 0.0728967i
880880 839.224 456.638i 0.953664 0.518906i
881881 1084.55 1.23104 0.615521 0.788121i 0.288946π-0.288946\pi
0.615521 + 0.788121i 0.288946π0.288946\pi
882882 −727.392 + 300.884i −0.824708 + 0.341138i
883883 1165.53 1165.53i 1.31997 1.31997i 0.406174 0.913796i 0.366863π-0.366863\pi
0.913796 0.406174i 0.133137π-0.133137\pi
884884 46.4968 + 46.5868i 0.0525982 + 0.0527000i
885885 24.1182 82.2765i 0.0272523 0.0929679i
886886 183.823 443.182i 0.207475 0.500206i
887887 −381.705 + 381.705i −0.430333 + 0.430333i −0.888742 0.458409i 0.848420π-0.848420\pi
0.458409 + 0.888742i 0.348420π0.348420\pi
888888 1.26275 3.03608i 0.00142201 0.00341901i
889889 141.584i 0.159263i
890890 28.6849 + 23.1172i 0.0322302 + 0.0259744i
891891 956.338i 1.07333i
892892 633.529 + 0.612536i 0.710234 + 0.000686699i
893893 −700.879 + 700.879i −0.784859 + 0.784859i
894894 6.99425 16.8625i 0.00782354 0.0188619i
895895 −68.0190 + 37.1811i −0.0759989 + 0.0415431i
896896 267.477 109.734i 0.298524 0.122471i
897897 55.6215 55.6215i 0.0620084 0.0620084i
898898 −13.0003 31.4285i −0.0144769 0.0349983i
899899 1094.34 1.21729
900900 876.101 190.525i 0.973446 0.211695i
901901 49.3802i 0.0548060i
902902 342.830 + 828.798i 0.380078 + 0.918845i
903903 −20.5800 20.5800i −0.0227907 0.0227907i
904904 920.790 379.840i 1.01857 0.420177i
905905 632.344 + 1156.81i 0.698723 + 1.27824i
906906 −3.13340 + 7.55437i −0.00345850 + 0.00833815i
907907 −457.511 457.511i −0.504422 0.504422i 0.408387 0.912809i 0.366092π-0.366092\pi
−0.912809 + 0.408387i 0.866092π0.866092\pi
908908 485.831 + 0.469732i 0.535056 + 0.000517326i
909909 −969.856 −1.06695
910910 238.693 + 192.363i 0.262300 + 0.211388i
911911 −620.530 −0.681152 −0.340576 0.940217i 0.610622π-0.610622\pi
−0.340576 + 0.940217i 0.610622π0.610622\pi
912912 −42.9441 43.1105i −0.0470879 0.0472703i
913913 −760.699 760.699i −0.833187 0.833187i
914914 605.940 1460.87i 0.662954 1.59833i
915915 −4.28318 1.25556i −0.00468107 0.00137219i
916916 −75.0699 + 74.9248i −0.0819540 + 0.0817957i
917917 132.247 + 132.247i 0.144216 + 0.144216i
918918 7.44585 3.07996i 0.00811095 0.00335507i
919919 981.064i 1.06753i −0.845631 0.533767i 0.820776π-0.820776\pi
0.845631 0.533767i 0.179224π-0.179224\pi
920920 787.403 975.113i 0.855873 1.05990i
921921 −35.3985 −0.0384349
922922 −250.460 605.493i −0.271649 0.656717i
923923 −568.341 + 568.341i −0.615754 + 0.615754i
924924 14.1259 14.0986i 0.0152878 0.0152582i
925925 54.2738 11.8579i 0.0586743 0.0128193i
926926 1583.06 + 656.623i 1.70957 + 0.709096i
927927 456.459 456.459i 0.492405 0.492405i
928928 −332.852 809.101i −0.358676 0.871876i
929929 776.484i 0.835827i −0.908487 0.417914i 0.862761π-0.862761\pi
0.908487 0.417914i 0.137239π-0.137239\pi
930930 7.91173 + 73.6121i 0.00850724 + 0.0791528i
931931 902.598i 0.969493i
932932 −405.353 0.391921i −0.434928 0.000420516i
933933 29.5525 29.5525i 0.0316747 0.0316747i
934934 219.258 + 90.9437i 0.234751 + 0.0973701i
935935 69.4724 + 20.3649i 0.0743021 + 0.0217806i
936936 −899.934 + 371.237i −0.961468 + 0.396621i
937937 759.800 759.800i 0.810885 0.810885i −0.173881 0.984767i 0.555631π-0.555631\pi
0.984767 + 0.173881i 0.0556309π0.0556309\pi
938938 −322.355 + 133.341i −0.343662 + 0.142155i
939939 −60.3267 −0.0642457
940940 −461.628 846.446i −0.491094 0.900475i
941941 759.500i 0.807120i 0.914953 + 0.403560i 0.132227π0.132227\pi
−0.914953 + 0.403560i 0.867773π0.867773\pi
942942 −31.2912 + 12.9435i −0.0332179 + 0.0137405i
943943 831.969 + 831.969i 0.882257 + 0.882257i
944944 −2.86832 + 1483.31i −0.00303847 + 1.57130i
945945 32.9302 18.0006i 0.0348468 0.0190482i
946946 1536.99 + 637.512i 1.62472 + 0.673903i
947947 −822.618 822.618i −0.868657 0.868657i 0.123667 0.992324i 0.460535π-0.460535\pi
−0.992324 + 0.123667i 0.960535π0.960535\pi
948948 −71.2089 0.0688492i −0.0751149 7.26258e-5i
949949 −654.763 −0.689951
950950 182.110 1011.80i 0.191695 1.06505i
951951 57.9572 0.0609434
952952 20.2275 + 8.41288i 0.0212473 + 0.00883706i
953953 659.139 + 659.139i 0.691647 + 0.691647i 0.962594 0.270947i 0.0873369π-0.0873369\pi
−0.270947 + 0.962594i 0.587337π0.587337\pi
954954 674.618 + 279.818i 0.707146 + 0.293310i
955955 529.610 289.499i 0.554565 0.303140i
956956 324.710 + 325.338i 0.339655 + 0.340312i
957957 −42.7056 42.7056i −0.0446244 0.0446244i
958958 −636.036 1537.63i −0.663920 1.60504i
959959 79.8661i 0.0832806i
960960 52.0186 28.2391i 0.0541861 0.0294158i
961961 641.133 0.667152
962962 −55.7397 + 23.0566i −0.0579415 + 0.0239673i
963963 855.468 855.468i 0.888336 0.888336i
964964 620.250 619.052i 0.643413 0.642170i
965965 1237.71 + 362.817i 1.28260 + 0.375976i
966966 10.0307 24.1833i 0.0103838 0.0250345i
967967 332.005 332.005i 0.343335 0.343335i −0.514284 0.857620i 0.671942π-0.671942\pi
0.857620 + 0.514284i 0.171942π0.171942\pi
968968 −66.4433 + 159.753i −0.0686398 + 0.165034i
969969 4.61086i 0.00475837i
970970 69.5807 + 647.390i 0.0717326 + 0.667413i
971971 960.961i 0.989661i 0.868989 + 0.494831i 0.164770π0.164770\pi
−0.868989 + 0.494831i 0.835230π0.835230\pi
972972 −0.172950 + 178.877i −0.000177932 + 0.184030i
973973 167.194 167.194i 0.171834 0.171834i
974974 −404.936 + 976.266i −0.415745 + 1.00233i
975975 52.8286 + 33.8835i 0.0541832 + 0.0347524i
976976 77.2187 + 0.149320i 0.0791175 + 0.000152992i
977977 69.4628 69.4628i 0.0710980 0.0710980i −0.670664 0.741762i 0.733991π-0.733991\pi
0.741762 + 0.670664i 0.233991π0.233991\pi
978978 −5.15706 12.4673i −0.00527307 0.0127477i
979979 −43.9975 −0.0449413
980980 −842.275 247.786i −0.859465 0.252843i
981981 417.297i 0.425379i
982982 32.7234 + 79.1094i 0.0333232 + 0.0805595i
983983 234.943 + 234.943i 0.239006 + 0.239006i 0.816438 0.577433i 0.195945π-0.195945\pi
−0.577433 + 0.816438i 0.695945π0.695945\pi
984984 21.1892 + 51.3659i 0.0215338 + 0.0522011i
985985 −1521.91 446.128i −1.54509 0.452921i
986986 25.3993 61.2356i 0.0257600 0.0621051i
987987 −14.2412 14.2412i −0.0144288 0.0144288i
988988 −1.07926 + 1116.25i −0.00109237 + 1.12981i
989989 2182.82 2.20710
990990 −671.892 + 833.712i −0.678679 + 0.842134i
991991 −919.592 −0.927944 −0.463972 0.885850i 0.653576π-0.653576\pi
−0.463972 + 0.885850i 0.653576π0.653576\pi
992992 −487.299 1184.54i −0.491229 1.19409i
993993 −18.4694 18.4694i −0.0185996 0.0185996i
994994 −102.494 + 247.105i −0.103113 + 0.248596i
995995 −210.825 385.684i −0.211885 0.387622i
996996 −47.0810 47.1721i −0.0472700 0.0473615i
997997 −835.935 835.935i −0.838450 0.838450i 0.150205 0.988655i 0.452007π-0.452007\pi
−0.988655 + 0.150205i 0.952007π0.952007\pi
998998 −896.526 + 370.846i −0.898323 + 0.371589i
999999 7.38441i 0.00739180i
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 40.3.i.a.13.9 yes 20
3.2 odd 2 360.3.u.b.253.2 20
4.3 odd 2 160.3.m.a.113.5 20
5.2 odd 4 inner 40.3.i.a.37.7 yes 20
5.3 odd 4 200.3.i.b.157.4 20
5.4 even 2 200.3.i.b.93.2 20
8.3 odd 2 160.3.m.a.113.6 20
8.5 even 2 inner 40.3.i.a.13.7 20
15.2 even 4 360.3.u.b.37.4 20
20.3 even 4 800.3.m.b.657.5 20
20.7 even 4 160.3.m.a.17.6 20
20.19 odd 2 800.3.m.b.593.6 20
24.5 odd 2 360.3.u.b.253.4 20
40.3 even 4 800.3.m.b.657.6 20
40.13 odd 4 200.3.i.b.157.2 20
40.19 odd 2 800.3.m.b.593.5 20
40.27 even 4 160.3.m.a.17.5 20
40.29 even 2 200.3.i.b.93.4 20
40.37 odd 4 inner 40.3.i.a.37.9 yes 20
120.77 even 4 360.3.u.b.37.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.3.i.a.13.7 20 8.5 even 2 inner
40.3.i.a.13.9 yes 20 1.1 even 1 trivial
40.3.i.a.37.7 yes 20 5.2 odd 4 inner
40.3.i.a.37.9 yes 20 40.37 odd 4 inner
160.3.m.a.17.5 20 40.27 even 4
160.3.m.a.17.6 20 20.7 even 4
160.3.m.a.113.5 20 4.3 odd 2
160.3.m.a.113.6 20 8.3 odd 2
200.3.i.b.93.2 20 5.4 even 2
200.3.i.b.93.4 20 40.29 even 2
200.3.i.b.157.2 20 40.13 odd 4
200.3.i.b.157.4 20 5.3 odd 4
360.3.u.b.37.2 20 120.77 even 4
360.3.u.b.37.4 20 15.2 even 4
360.3.u.b.253.2 20 3.2 odd 2
360.3.u.b.253.4 20 24.5 odd 2
800.3.m.b.593.5 20 40.19 odd 2
800.3.m.b.593.6 20 20.19 odd 2
800.3.m.b.657.5 20 20.3 even 4
800.3.m.b.657.6 20 40.3 even 4