Properties

Label 784.2.x.o.165.12
Level 784784
Weight 22
Character 784.165
Analytic conductor 6.2606.260
Analytic rank 00
Dimension 4848
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 784.x (of order 1212, degree 44, not 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: 6.260271518476.26027151847
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 165.12
Character χ\chi == 784.165
Dual form 784.2.x.o.765.12

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+(1.409440.116052i)q2+(0.312249+1.16533i)q3+(1.973060.327139i)q4+(0.2628430.980942i)q5+(0.575337+1.60623i)q6+(2.742960.690063i)q8+(1.337580.772254i)q9+(0.2566211.41309i)q10+(2.36993+0.635020i)q11+(0.997312+2.19712i)q12+(2.657862.65786i)q13+1.22519q15+(3.785961.29093i)q16+(0.5091280.881836i)q17+(1.795631.24368i)q18+(0.09365610.0250951i)q19+(0.1977012.02145i)q20+(3.26658+1.17006i)q22+(1.67238+0.965551i)q23+(1.66064+2.98098i)q24+(3.43697+1.98433i)q25+(3.437654.05455i)q26+(3.87683+3.87683i)q27+(5.05325+5.05325i)q29+(1.726840.142187i)q30+(4.28249+7.41749i)q31+(5.186282.25887i)q32+(1.480012.56346i)q33+(0.6152481.30198i)q34+(2.386501.96128i)q36+(2.067047.71428i)q37+(0.1349150.0245011i)q38+(3.92719+2.26737i)q39+(0.04405452.87206i)q40+8.51782iq41+(4.479504.47950i)q43+(4.46828+2.02823i)q44+(0.4059631.51507i)q45+(2.24507+1.55497i)q46+(6.0299510.4442i)q47+(2.68652+4.00880i)q48+(5.07450+2.39794i)q50+(1.18660+0.317949i)q51+(4.374646.11361i)q52+(1.42191+0.381000i)q53+(5.91409+5.01426i)q54+2.49167iq550.116976iq57+(6.53583+7.70871i)q58+(6.96158+1.86535i)q59+(2.417380.400808i)q60+(4.426541.18609i)q61+(5.17511+10.9515i)q62+(7.047633.78563i)q64+(1.908613.30580i)q65+(2.383493.44129i)q66+(0.907543+3.38700i)q67+(0.7160591.90647i)q68+(1.647381.64738i)q69+5.43131iq71+(3.136033.04128i)q72+(7.34303+4.23950i)q73+(2.0181111.1127i)q74+(1.23921+4.62480i)q75+(0.1929990.0188756i)q76+(5.79829+2.73996i)q78+(0.4335950.751008i)q79+(0.2712174.05312i)q80+(0.990483+1.71557i)q81+(0.988514+12.0054i)q82+(5.443185.44318i)q83+(0.7312090.731209i)q85+(6.833455.79374i)q86+(7.466574.31083i)q87+(6.06240+3.37723i)q88+(3.931552.26988i)q89+(0.7480102.08830i)q90+(2.98385+2.45219i)q92+(9.981022.67441i)q93+(9.7109514.0207i)q94+(0.0492336+0.0852752i)q95+(4.25173+5.33840i)q9616.4025q97+(2.67958+2.67958i)q99+O(q100)q+(1.40944 - 0.116052i) q^{2} +(0.312249 + 1.16533i) q^{3} +(1.97306 - 0.327139i) q^{4} +(0.262843 - 0.980942i) q^{5} +(0.575337 + 1.60623i) q^{6} +(2.74296 - 0.690063i) q^{8} +(1.33758 - 0.772254i) q^{9} +(0.256621 - 1.41309i) q^{10} +(-2.36993 + 0.635020i) q^{11} +(0.997312 + 2.19712i) q^{12} +(2.65786 - 2.65786i) q^{13} +1.22519 q^{15} +(3.78596 - 1.29093i) q^{16} +(0.509128 - 0.881836i) q^{17} +(1.79563 - 1.24368i) q^{18} +(-0.0936561 - 0.0250951i) q^{19} +(0.197701 - 2.02145i) q^{20} +(-3.26658 + 1.17006i) q^{22} +(-1.67238 + 0.965551i) q^{23} +(1.66064 + 2.98098i) q^{24} +(3.43697 + 1.98433i) q^{25} +(3.43765 - 4.05455i) q^{26} +(3.87683 + 3.87683i) q^{27} +(-5.05325 + 5.05325i) q^{29} +(1.72684 - 0.142187i) q^{30} +(-4.28249 + 7.41749i) q^{31} +(5.18628 - 2.25887i) q^{32} +(-1.48001 - 2.56346i) q^{33} +(0.615248 - 1.30198i) q^{34} +(2.38650 - 1.96128i) q^{36} +(2.06704 - 7.71428i) q^{37} +(-0.134915 - 0.0245011i) q^{38} +(3.92719 + 2.26737i) q^{39} +(0.0440545 - 2.87206i) q^{40} +8.51782i q^{41} +(-4.47950 - 4.47950i) q^{43} +(-4.46828 + 2.02823i) q^{44} +(-0.405963 - 1.51507i) q^{45} +(-2.24507 + 1.55497i) q^{46} +(-6.02995 - 10.4442i) q^{47} +(2.68652 + 4.00880i) q^{48} +(5.07450 + 2.39794i) q^{50} +(1.18660 + 0.317949i) q^{51} +(4.37464 - 6.11361i) q^{52} +(-1.42191 + 0.381000i) q^{53} +(5.91409 + 5.01426i) q^{54} +2.49167i q^{55} -0.116976i q^{57} +(-6.53583 + 7.70871i) q^{58} +(-6.96158 + 1.86535i) q^{59} +(2.41738 - 0.400808i) q^{60} +(-4.42654 - 1.18609i) q^{61} +(-5.17511 + 10.9515i) q^{62} +(7.04763 - 3.78563i) q^{64} +(-1.90861 - 3.30580i) q^{65} +(-2.38349 - 3.44129i) q^{66} +(0.907543 + 3.38700i) q^{67} +(0.716059 - 1.90647i) q^{68} +(-1.64738 - 1.64738i) q^{69} +5.43131i q^{71} +(3.13603 - 3.04128i) q^{72} +(7.34303 + 4.23950i) q^{73} +(2.01811 - 11.1127i) q^{74} +(-1.23921 + 4.62480i) q^{75} +(-0.192999 - 0.0188756i) q^{76} +(5.79829 + 2.73996i) q^{78} +(-0.433595 - 0.751008i) q^{79} +(-0.271217 - 4.05312i) q^{80} +(-0.990483 + 1.71557i) q^{81} +(0.988514 + 12.0054i) q^{82} +(5.44318 - 5.44318i) q^{83} +(-0.731209 - 0.731209i) q^{85} +(-6.83345 - 5.79374i) q^{86} +(-7.46657 - 4.31083i) q^{87} +(-6.06240 + 3.37723i) q^{88} +(3.93155 - 2.26988i) q^{89} +(-0.748010 - 2.08830i) q^{90} +(-2.98385 + 2.45219i) q^{92} +(-9.98102 - 2.67441i) q^{93} +(-9.71095 - 14.0207i) q^{94} +(-0.0492336 + 0.0852752i) q^{95} +(4.25173 + 5.33840i) q^{96} -16.4025 q^{97} +(-2.67958 + 2.67958i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q4q24q44q5+4q64q8+2q104q112q12+24q1340q15+16q168q17+18q18+4q19+16q2018q24+10q26+24q27+24q99+O(q100) 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/784Z)×\left(\mathbb{Z}/784\mathbb{Z}\right)^\times.

nn 197197 687687 689689
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.40944 0.116052i 0.996627 0.0820615i
33 0.312249 + 1.16533i 0.180277 + 0.672803i 0.995592 + 0.0937859i 0.0298969π0.0298969\pi
−0.815315 + 0.579017i 0.803436π0.803436\pi
44 1.97306 0.327139i 0.986532 0.163569i
55 0.262843 0.980942i 0.117547 0.438691i −0.881918 0.471403i 0.843748π-0.843748\pi
0.999465 + 0.0327122i 0.0104145π0.0104145\pi
66 0.575337 + 1.60623i 0.234880 + 0.655740i
77 0 0
88 2.74296 0.690063i 0.969782 0.243974i
99 1.33758 0.772254i 0.445861 0.257418i
1010 0.256621 1.41309i 0.0811507 0.446857i
1111 −2.36993 + 0.635020i −0.714560 + 0.191466i −0.597743 0.801688i 0.703936π-0.703936\pi
−0.116817 + 0.993153i 0.537269π0.537269\pi
1212 0.997312 + 2.19712i 0.287899 + 0.634254i
1313 2.65786 2.65786i 0.737157 0.737157i −0.234870 0.972027i 0.575466π-0.575466\pi
0.972027 + 0.234870i 0.0754663π0.0754663\pi
1414 0 0
1515 1.22519 0.316343
1616 3.78596 1.29093i 0.946490 0.322733i
1717 0.509128 0.881836i 0.123482 0.213877i −0.797657 0.603112i 0.793927π-0.793927\pi
0.921138 + 0.389235i 0.127261π0.127261\pi
1818 1.79563 1.24368i 0.423233 0.293138i
1919 −0.0936561 0.0250951i −0.0214862 0.00575721i 0.248060 0.968745i 0.420207π-0.420207\pi
−0.269546 + 0.962987i 0.586874π0.586874\pi
2020 0.197701 2.02145i 0.0442073 0.452009i
2121 0 0
2222 −3.26658 + 1.17006i −0.696438 + 0.249458i
2323 −1.67238 + 0.965551i −0.348716 + 0.201331i −0.664120 0.747626i 0.731193π-0.731193\pi
0.315404 + 0.948958i 0.397860π0.397860\pi
2424 1.66064 + 2.98098i 0.338976 + 0.608489i
2525 3.43697 + 1.98433i 0.687393 + 0.396867i
2626 3.43765 4.05455i 0.674179 0.795163i
2727 3.87683 + 3.87683i 0.746096 + 0.746096i
2828 0 0
2929 −5.05325 + 5.05325i −0.938365 + 0.938365i −0.998208 0.0598432i 0.980940π-0.980940\pi
0.0598432 + 0.998208i 0.480940π0.480940\pi
3030 1.72684 0.142187i 0.315276 0.0259596i
3131 −4.28249 + 7.41749i −0.769158 + 1.33222i 0.168862 + 0.985640i 0.445991π0.445991\pi
−0.938020 + 0.346581i 0.887343π0.887343\pi
3232 5.18628 2.25887i 0.916814 0.399315i
3333 −1.48001 2.56346i −0.257637 0.446241i
3434 0.615248 1.30198i 0.105514 0.223288i
3535 0 0
3636 2.38650 1.96128i 0.397751 0.326880i
3737 2.06704 7.71428i 0.339818 1.26822i −0.558732 0.829349i 0.688712π-0.688712\pi
0.898550 0.438871i 0.144622π-0.144622\pi
3838 −0.134915 0.0245011i −0.0218862 0.00397460i
3939 3.92719 + 2.26737i 0.628854 + 0.363069i
4040 0.0440545 2.87206i 0.00696562 0.454113i
4141 8.51782i 1.33026i 0.746728 + 0.665130i 0.231624π0.231624\pi
−0.746728 + 0.665130i 0.768376π0.768376\pi
4242 0 0
4343 −4.47950 4.47950i −0.683117 0.683117i 0.277584 0.960701i 0.410466π-0.410466\pi
−0.960701 + 0.277584i 0.910466π0.910466\pi
4444 −4.46828 + 2.02823i −0.673618 + 0.305767i
4545 −0.405963 1.51507i −0.0605174 0.225854i
4646 −2.24507 + 1.55497i −0.331018 + 0.229268i
4747 −6.02995 10.4442i −0.879559 1.52344i −0.851826 0.523825i 0.824505π-0.824505\pi
−0.0277324 0.999615i 0.508829π-0.508829\pi
4848 2.68652 + 4.00880i 0.387766 + 0.578620i
4949 0 0
5050 5.07450 + 2.39794i 0.717642 + 0.339120i
5151 1.18660 + 0.317949i 0.166158 + 0.0445218i
5252 4.37464 6.11361i 0.606653 0.847806i
5353 −1.42191 + 0.381000i −0.195315 + 0.0523344i −0.355150 0.934809i 0.615570π-0.615570\pi
0.159836 + 0.987144i 0.448904π0.448904\pi
5454 5.91409 + 5.01426i 0.804806 + 0.682354i
5555 2.49167i 0.335977i
5656 0 0
5757 0.116976i 0.0154939i
5858 −6.53583 + 7.70871i −0.858196 + 1.01220i
5959 −6.96158 + 1.86535i −0.906320 + 0.242848i −0.681729 0.731605i 0.738771π-0.738771\pi
−0.224592 + 0.974453i 0.572105π0.572105\pi
6060 2.41738 0.400808i 0.312083 0.0517441i
6161 −4.42654 1.18609i −0.566760 0.151863i −0.0359500 0.999354i 0.511446π-0.511446\pi
−0.530810 + 0.847491i 0.678112π0.678112\pi
6262 −5.17511 + 10.9515i −0.657240 + 1.39085i
6363 0 0
6464 7.04763 3.78563i 0.880953 0.473203i
6565 −1.90861 3.30580i −0.236734 0.410034i
6666 −2.38349 3.44129i −0.293388 0.423594i
6767 0.907543 + 3.38700i 0.110874 + 0.413787i 0.998945 0.0459185i 0.0146215π-0.0146215\pi
−0.888071 + 0.459706i 0.847955π0.847955\pi
6868 0.716059 1.90647i 0.0868350 0.231194i
6969 −1.64738 1.64738i −0.198322 0.198322i
7070 0 0
7171 5.43131i 0.644578i 0.946641 + 0.322289i 0.104452π0.104452\pi
−0.946641 + 0.322289i 0.895548π0.895548\pi
7272 3.13603 3.04128i 0.369585 0.358418i
7373 7.34303 + 4.23950i 0.859436 + 0.496196i 0.863824 0.503795i 0.168063π-0.168063\pi
−0.00438712 + 0.999990i 0.501396π0.501396\pi
7474 2.01811 11.1127i 0.234600 1.29183i
7575 −1.23921 + 4.62480i −0.143092 + 0.534026i
7676 −0.192999 0.0188756i −0.0221385 0.00216518i
7777 0 0
7878 5.79829 + 2.73996i 0.656527 + 0.310240i
7979 −0.433595 0.751008i −0.0487832 0.0844950i 0.840603 0.541652i 0.182201π-0.182201\pi
−0.889386 + 0.457157i 0.848868π0.848868\pi
8080 −0.271217 4.05312i −0.0303230 0.453153i
8181 −0.990483 + 1.71557i −0.110054 + 0.190619i
8282 0.988514 + 12.0054i 0.109163 + 1.32577i
8383 5.44318 5.44318i 0.597466 0.597466i −0.342171 0.939638i 0.611162π-0.611162\pi
0.939638 + 0.342171i 0.111162π0.111162\pi
8484 0 0
8585 −0.731209 0.731209i −0.0793108 0.0793108i
8686 −6.83345 5.79374i −0.736870 0.624755i
8787 −7.46657 4.31083i −0.800500 0.462169i
8888 −6.06240 + 3.37723i −0.646254 + 0.360014i
8989 3.93155 2.26988i 0.416744 0.240607i −0.276939 0.960887i 0.589320π-0.589320\pi
0.693683 + 0.720280i 0.255987π0.255987\pi
9090 −0.748010 2.08830i −0.0788471 0.220126i
9191 0 0
9292 −2.98385 + 2.45219i −0.311088 + 0.255659i
9393 −9.98102 2.67441i −1.03498 0.277323i
9494 −9.71095 14.0207i −1.00161 1.44612i
9595 −0.0492336 + 0.0852752i −0.00505126 + 0.00874905i
9696 4.25173 + 5.33840i 0.433941 + 0.544848i
9797 −16.4025 −1.66542 −0.832712 0.553706i 0.813213π-0.813213\pi
−0.832712 + 0.553706i 0.813213π0.813213\pi
9898 0 0
9999 −2.67958 + 2.67958i −0.269308 + 0.269308i
100100 7.43051 + 2.79085i 0.743051 + 0.279085i
101101 8.88412 2.38049i 0.884003 0.236868i 0.211870 0.977298i 0.432045π-0.432045\pi
0.672134 + 0.740430i 0.265378π0.265378\pi
102102 1.70935 + 0.310424i 0.169251 + 0.0307365i
103103 6.69469 3.86518i 0.659647 0.380848i −0.132495 0.991184i 0.542299π-0.542299\pi
0.792143 + 0.610336i 0.208966π0.208966\pi
104104 5.45630 9.12448i 0.535034 0.894729i
105105 0 0
106106 −1.95989 + 0.702015i −0.190361 + 0.0681857i
107107 −4.89154 + 18.2555i −0.472883 + 1.76482i 0.156449 + 0.987686i 0.449995π0.449995\pi
−0.629332 + 0.777137i 0.716671π0.716671\pi
108108 8.91749 + 6.38097i 0.858086 + 0.614009i
109109 −4.23429 15.8026i −0.405571 1.51361i −0.802999 0.595980i 0.796764π-0.796764\pi
0.397428 0.917633i 0.369903π-0.369903\pi
110110 0.289165 + 3.51187i 0.0275708 + 0.334844i
111111 9.63510 0.914524
112112 0 0
113113 −20.1152 −1.89228 −0.946138 0.323765i 0.895051π-0.895051\pi
−0.946138 + 0.323765i 0.895051π0.895051\pi
114114 −0.0135754 0.164871i −0.00127145 0.0154416i
115115 0.507576 + 1.89430i 0.0473317 + 0.176644i
116116 −8.31727 + 11.6235i −0.772239 + 1.07921i
117117 1.50257 5.60765i 0.138912 0.518428i
118118 −9.59547 + 3.43701i −0.883335 + 0.316403i
119119 0 0
120120 3.36065 0.845460i 0.306784 0.0771796i
121121 −4.31298 + 2.49010i −0.392089 + 0.226373i
122122 −6.37661 1.15801i −0.577311 0.104842i
123123 −9.92606 + 2.65968i −0.895003 + 0.239815i
124124 −6.02308 + 16.0361i −0.540888 + 1.44009i
125125 6.44039 6.44039i 0.576046 0.576046i
126126 0 0
127127 −0.988901 −0.0877508 −0.0438754 0.999037i 0.513970π-0.513970\pi
−0.0438754 + 0.999037i 0.513970π0.513970\pi
128128 9.49390 6.15352i 0.839150 0.543899i
129129 3.82137 6.61880i 0.336453 0.582753i
130130 −3.07372 4.43785i −0.269583 0.389225i
131131 −7.60883 2.03878i −0.664786 0.178129i −0.0893811 0.995998i 0.528489π-0.528489\pi
−0.575405 + 0.817869i 0.695156π0.695156\pi
132132 −3.75877 4.57370i −0.327159 0.398089i
133133 0 0
134134 1.67220 + 4.66846i 0.144456 + 0.403293i
135135 4.82194 2.78395i 0.415007 0.239604i
136136 0.787994 2.77017i 0.0675700 0.237540i
137137 9.57893 + 5.53040i 0.818383 + 0.472494i 0.849859 0.527011i 0.176687π-0.176687\pi
−0.0314753 + 0.999505i 0.510021π0.510021\pi
138138 −2.51308 2.13071i −0.213927 0.181378i
139139 −12.4154 12.4154i −1.05306 1.05306i −0.998511 0.0545473i 0.982628π-0.982628\pi
−0.0545473 0.998511i 0.517372π-0.517372\pi
140140 0 0
141141 10.2881 10.2881i 0.866411 0.866411i
142142 0.630317 + 7.65513i 0.0528951 + 0.642404i
143143 −4.61114 + 7.98672i −0.385603 + 0.667883i
144144 4.06711 4.65045i 0.338926 0.387538i
145145 3.62873 + 6.28515i 0.301350 + 0.521954i
146146 10.8416 + 5.12316i 0.897256 + 0.423996i
147147 0 0
148148 1.55475 15.8970i 0.127800 1.30672i
149149 1.35622 5.06147i 0.111106 0.414652i −0.887861 0.460113i 0.847809π-0.847809\pi
0.998966 + 0.0454610i 0.0144757π0.0144757\pi
150150 −1.20988 + 6.66221i −0.0987863 + 0.543967i
151151 −1.18073 0.681693i −0.0960862 0.0554754i 0.451187 0.892429i 0.351001π-0.351001\pi
−0.547273 + 0.836954i 0.684334π0.684334\pi
152152 −0.274212 0.00420613i −0.0222415 0.000341162i
153153 1.57271i 0.127146i
154154 0 0
155155 6.15051 + 6.15051i 0.494021 + 0.494021i
156156 8.49035 + 3.18892i 0.679772 + 0.255318i
157157 0.0822524 + 0.306970i 0.00656446 + 0.0244989i 0.969130 0.246549i 0.0792966π-0.0792966\pi
−0.962566 + 0.271048i 0.912630π0.912630\pi
158158 −0.698284 1.00818i −0.0555525 0.0802068i
159159 −0.887981 1.53803i −0.0704215 0.121974i
160160 −0.852640 5.68117i −0.0674071 0.449136i
161161 0 0
162162 −1.19693 + 2.53294i −0.0940400 + 0.199007i
163163 14.3376 + 3.84175i 1.12301 + 0.300909i 0.772100 0.635501i 0.219206π-0.219206\pi
0.350907 + 0.936410i 0.385873π0.385873\pi
164164 2.78651 + 16.8062i 0.217590 + 1.31234i
165165 −2.90362 + 0.778022i −0.226046 + 0.0605689i
166166 7.04016 8.30354i 0.546422 0.644480i
167167 14.5986i 1.12967i 0.825204 + 0.564836i 0.191060π0.191060\pi
−0.825204 + 0.564836i 0.808940π0.808940\pi
168168 0 0
169169 1.12842i 0.0868018i
170170 −1.11546 0.945740i −0.0855516 0.0725349i
171171 −0.144653 + 0.0387596i −0.0110619 + 0.00296402i
172172 −10.3037 7.37291i −0.785653 0.562179i
173173 −11.9299 3.19660i −0.907011 0.243033i −0.224986 0.974362i 0.572234π-0.572234\pi
−0.682025 + 0.731329i 0.738900π0.738900\pi
174174 −11.0240 5.20935i −0.835727 0.394920i
175175 0 0
176176 −8.15268 + 5.46357i −0.614531 + 0.411832i
177177 −4.34749 7.53008i −0.326777 0.565995i
178178 5.27788 3.65554i 0.395594 0.273994i
179179 −0.122083 0.455619i −0.00912489 0.0340545i 0.961213 0.275806i 0.0889448π-0.0889448\pi
−0.970338 + 0.241752i 0.922278π0.922278\pi
180180 −1.29663 2.85653i −0.0966451 0.212913i
181181 −15.4654 15.4654i −1.14953 1.14953i −0.986645 0.162887i 0.947919π-0.947919\pi
−0.162887 0.986645i 0.552081π-0.552081\pi
182182 0 0
183183 5.52873i 0.408696i
184184 −3.92098 + 3.80251i −0.289059 + 0.280325i
185185 −7.02396 4.05528i −0.516412 0.298150i
186186 −14.3781 2.61110i −1.05425 0.191455i
187187 −0.646613 + 2.41319i −0.0472850 + 0.176470i
188188 −15.3142 18.6344i −1.11690 1.35905i
189189 0 0
190190 −0.0594956 + 0.125904i −0.00431627 + 0.00913405i
191191 −3.04108 5.26731i −0.220045 0.381129i 0.734776 0.678309i 0.237287π-0.237287\pi
−0.954821 + 0.297180i 0.903954π0.903954\pi
192192 6.61211 + 7.03075i 0.477188 + 0.507400i
193193 −5.03089 + 8.71375i −0.362131 + 0.627229i −0.988311 0.152449i 0.951284π-0.951284\pi
0.626180 + 0.779678i 0.284617π0.284617\pi
194194 −23.1184 + 1.90355i −1.65981 + 0.136667i
195195 3.25639 3.25639i 0.233195 0.233195i
196196 0 0
197197 −10.0837 10.0837i −0.718432 0.718432i 0.249852 0.968284i 0.419618π-0.419618\pi
−0.968284 + 0.249852i 0.919618π0.919618\pi
198198 −3.46574 + 4.08769i −0.246300 + 0.290499i
199199 10.0980 + 5.83005i 0.715825 + 0.413282i 0.813214 0.581965i 0.197716π-0.197716\pi
−0.0973893 + 0.995246i 0.531049π0.531049\pi
200200 10.7968 + 3.07122i 0.763447 + 0.217168i
201201 −3.66359 + 2.11517i −0.258409 + 0.149193i
202202 12.2454 4.38620i 0.861584 0.308612i
203203 0 0
204204 2.44526 + 0.239150i 0.171202 + 0.0167439i
205205 8.35549 + 2.23885i 0.583572 + 0.156368i
206206 8.98723 6.22469i 0.626170 0.433695i
207207 −1.49130 + 2.58301i −0.103653 + 0.179532i
208208 6.63143 13.4937i 0.459807 0.935617i
209209 0.237894 0.0164555
210210 0 0
211211 6.53423 6.53423i 0.449835 0.449835i −0.445465 0.895300i 0.646962π-0.646962\pi
0.895300 + 0.445465i 0.146962π0.146962\pi
212212 −2.68088 + 1.21690i −0.184124 + 0.0835771i
213213 −6.32927 + 1.69592i −0.433674 + 0.116203i
214214 −4.77576 + 26.2977i −0.326464 + 1.79768i
215215 −5.57153 + 3.21672i −0.379975 + 0.219379i
216216 13.3092 + 7.95872i 0.905579 + 0.541522i
217217 0 0
218218 −7.80192 21.7815i −0.528413 1.47523i
219219 −2.64756 + 9.88082i −0.178905 + 0.667684i
220220 0.815122 + 4.91622i 0.0549555 + 0.331452i
221221 −0.990604 3.69698i −0.0666352 0.248686i
222222 13.5801 1.11818i 0.911439 0.0750472i
223223 23.3350 1.56263 0.781315 0.624137i 0.214549π-0.214549\pi
0.781315 + 0.624137i 0.214549π0.214549\pi
224224 0 0
225225 6.12964 0.408643
226226 −28.3512 + 2.33441i −1.88589 + 0.155283i
227227 4.05036 + 15.1161i 0.268832 + 1.00329i 0.959863 + 0.280468i 0.0904898π0.0904898\pi
−0.691032 + 0.722824i 0.742844π0.742844\pi
228228 −0.0382674 0.230801i −0.00253432 0.0152852i
229229 −6.92092 + 25.8292i −0.457347 + 1.70684i 0.223747 + 0.974647i 0.428171π0.428171\pi
−0.681094 + 0.732196i 0.738496π0.738496\pi
230230 0.935237 + 2.61100i 0.0616677 + 0.172164i
231231 0 0
232232 −10.3738 + 17.3479i −0.681072 + 1.13895i
233233 11.0402 6.37405i 0.723267 0.417578i −0.0926872 0.995695i 0.529546π-0.529546\pi
0.815954 + 0.578117i 0.196212π0.196212\pi
234234 1.46700 8.07805i 0.0959008 0.528078i
235235 −11.8301 + 3.16986i −0.771708 + 0.206779i
236236 −13.1254 + 5.95786i −0.854391 + 0.387823i
237237 0.739782 0.739782i 0.0480540 0.0480540i
238238 0 0
239239 14.9688 0.968253 0.484127 0.874998i 0.339137π-0.339137\pi
0.484127 + 0.874998i 0.339137π0.339137\pi
240240 4.63853 1.58164i 0.299416 0.102094i
241241 9.90526 17.1564i 0.638054 1.10514i −0.347805 0.937567i 0.613073π-0.613073\pi
0.985859 0.167575i 0.0535937π-0.0535937\pi
242242 −5.78992 + 4.01019i −0.372190 + 0.257785i
243243 13.5791 + 3.63850i 0.871098 + 0.233410i
244244 −9.12186 0.892134i −0.583967 0.0571130i
245245 0 0
246246 −13.6816 + 4.90061i −0.872305 + 0.312452i
247247 −0.315624 + 0.182226i −0.0200827 + 0.0115947i
248248 −6.62815 + 23.3010i −0.420888 + 1.47962i
249249 8.04272 + 4.64346i 0.509686 + 0.294268i
250250 8.32995 9.82480i 0.526832 0.621375i
251251 −9.23966 9.23966i −0.583202 0.583202i 0.352580 0.935782i 0.385305π-0.385305\pi
−0.935782 + 0.352580i 0.885305π0.885305\pi
252252 0 0
253253 3.35028 3.35028i 0.210630 0.210630i
254254 −1.39380 + 0.114764i −0.0874548 + 0.00720096i
255255 0.623780 1.08042i 0.0390626 0.0676584i
256256 12.6670 9.77483i 0.791687 0.610927i
257257 11.6109 + 20.1107i 0.724271 + 1.25447i 0.959273 + 0.282479i 0.0911568π0.0911568\pi
−0.235003 + 0.971995i 0.575510π0.575510\pi
258258 4.61788 9.77231i 0.287496 0.608398i
259259 0 0
260260 −4.84726 5.89818i −0.300614 0.365790i
261261 −2.85675 + 10.6615i −0.176828 + 0.659933i
262262 −10.9608 1.99052i −0.677162 0.122975i
263263 3.91454 + 2.26006i 0.241381 + 0.139361i 0.615811 0.787894i 0.288828π-0.288828\pi
−0.374430 + 0.927255i 0.622162π0.622162\pi
264264 −5.82856 6.01016i −0.358723 0.369900i
265265 1.49496i 0.0918345i
266266 0 0
267267 3.87278 + 3.87278i 0.237011 + 0.237011i
268268 2.89866 + 6.38587i 0.177064 + 0.390079i
269269 −0.103258 0.385363i −0.00629574 0.0234960i 0.962707 0.270548i 0.0872049π-0.0872049\pi
−0.969002 + 0.247052i 0.920538π0.920538\pi
270270 6.47317 4.48342i 0.393945 0.272852i
271271 5.31084 + 9.19864i 0.322611 + 0.558778i 0.981026 0.193877i 0.0621063π-0.0621063\pi
−0.658415 + 0.752655i 0.728773π0.728773\pi
272272 0.789149 3.99584i 0.0478492 0.242284i
273273 0 0
274274 14.1428 + 6.68313i 0.854397 + 0.403742i
275275 −9.40545 2.52018i −0.567170 0.151973i
276276 −3.78932 2.71147i −0.228090 0.163211i
277277 11.1219 2.98011i 0.668252 0.179058i 0.0912848 0.995825i 0.470903π-0.470903\pi
0.576967 + 0.816767i 0.304236π0.304236\pi
278278 −18.9396 16.0579i −1.13592 0.963091i
279279 13.2287i 0.791981i
280280 0 0
281281 18.6360i 1.11173i 0.831272 + 0.555866i 0.187613π0.187613\pi
−0.831272 + 0.555866i 0.812387π0.812387\pi
282282 13.3065 15.6944i 0.792390 0.934588i
283283 8.77861 2.35222i 0.521834 0.139825i 0.0117192 0.999931i 0.496270π-0.496270\pi
0.510115 + 0.860106i 0.329603π0.329603\pi
284284 1.77679 + 10.7163i 0.105433 + 0.635897i
285285 −0.114747 0.0307463i −0.00679701 0.00182125i
286286 −5.57226 + 11.7920i −0.329495 + 0.697274i
287287 0 0
288288 5.19267 7.02655i 0.305981 0.414044i
289289 7.98158 + 13.8245i 0.469505 + 0.813206i
290290 5.84390 + 8.43745i 0.343166 + 0.495464i
291291 −5.12167 19.1143i −0.300238 1.12050i
292292 15.8752 + 5.96261i 0.929024 + 0.348935i
293293 12.0193 + 12.0193i 0.702174 + 0.702174i 0.964877 0.262703i 0.0846138π-0.0846138\pi
−0.262703 + 0.964877i 0.584614π0.584614\pi
294294 0 0
295295 7.31920i 0.426140i
296296 0.346451 22.5863i 0.0201371 1.31280i
297297 −11.6497 6.72594i −0.675982 0.390278i
298298 1.32411 7.29125i 0.0767039 0.422371i
299299 −1.87866 + 7.01125i −0.108646 + 0.405471i
300300 −0.932092 + 9.53042i −0.0538143 + 0.550239i
301301 0 0
302302 −1.74328 0.823782i −0.100315 0.0474033i
303303 5.54812 + 9.60962i 0.318731 + 0.552058i
304304 −0.386974 + 0.0258947i −0.0221945 + 0.00148516i
305305 −2.32697 + 4.03043i −0.133242 + 0.230781i
306306 −0.182516 2.21664i −0.0104338 0.126717i
307307 −17.8339 + 17.8339i −1.01784 + 1.01784i −0.0179975 + 0.999838i 0.505729π0.505729\pi
−0.999838 + 0.0179975i 0.994271π0.994271\pi
308308 0 0
309309 6.59462 + 6.59462i 0.375155 + 0.375155i
310310 9.38257 + 7.95501i 0.532894 + 0.451814i
311311 −5.66778 3.27229i −0.321390 0.185555i 0.330622 0.943763i 0.392742π-0.392742\pi
−0.652012 + 0.758209i 0.726075π0.726075\pi
312312 12.3367 + 3.50928i 0.698431 + 0.198674i
313313 16.6047 9.58671i 0.938551 0.541873i 0.0490453 0.998797i 0.484382π-0.484382\pi
0.889506 + 0.456924i 0.151049π0.151049\pi
314314 0.151555 + 0.423112i 0.00855274 + 0.0238776i
315315 0 0
316316 −1.10119 1.33994i −0.0619470 0.0753776i
317317 −18.1794 4.87115i −1.02106 0.273591i −0.290814 0.956780i 0.593926π-0.593926\pi
−0.730242 + 0.683189i 0.760593π0.760593\pi
318318 −1.43005 2.06471i −0.0801933 0.115783i
319319 8.76691 15.1847i 0.490853 0.850182i
320320 −1.86106 7.90834i −0.104037 0.442089i
321321 −22.8010 −1.27263
322322 0 0
323323 −0.0698127 + 0.0698127i −0.00388448 + 0.00388448i
324324 −1.39306 + 3.70895i −0.0773921 + 0.206053i
325325 14.4090 3.86089i 0.799270 0.214164i
326326 20.6539 + 3.75081i 1.14391 + 0.207738i
327327 17.0931 9.86868i 0.945248 0.545739i
328328 5.87783 + 23.3640i 0.324549 + 1.29006i
329329 0 0
330330 −4.00219 + 1.43355i −0.220313 + 0.0789143i
331331 2.53476 9.45985i 0.139323 0.519960i −0.860620 0.509248i 0.829924π-0.829924\pi
0.999943 0.0107120i 0.00340981π-0.00340981\pi
332332 8.95906 12.5204i 0.491692 0.687147i
333333 −3.19255 11.9148i −0.174951 0.652926i
334334 1.69420 + 20.5759i 0.0927025 + 1.12586i
335335 3.56099 0.194558
336336 0 0
337337 4.91600 0.267792 0.133896 0.990995i 0.457251π-0.457251\pi
0.133896 + 0.990995i 0.457251π0.457251\pi
338338 −0.130956 1.59045i −0.00712308 0.0865090i
339339 −6.28094 23.4408i −0.341134 1.27313i
340340 −1.68193 1.20352i −0.0912154 0.0652698i
341341 5.43893 20.2984i 0.294535 1.09922i
342342 −0.199382 + 0.0714167i −0.0107813 + 0.00386178i
343343 0 0
344344 −15.3782 9.19593i −0.829137 0.495811i
345345 −2.04899 + 1.18299i −0.110314 + 0.0636898i
346346 −17.1854 3.12093i −0.923895 0.167782i
347347 −9.03438 + 2.42076i −0.484991 + 0.129953i −0.493026 0.870015i 0.664109π-0.664109\pi
0.00803463 + 0.999968i 0.497442π0.497442\pi
348348 −16.1423 6.06293i −0.865316 0.325007i
349349 17.2061 17.2061i 0.921021 0.921021i −0.0760810 0.997102i 0.524241π-0.524241\pi
0.997102 + 0.0760810i 0.0242407π0.0242407\pi
350350 0 0
351351 20.6081 1.09998
352352 −10.8567 + 8.64674i −0.578663 + 0.460873i
353353 −4.08472 + 7.07494i −0.217408 + 0.376561i −0.954015 0.299760i 0.903093π-0.903093\pi
0.736607 + 0.676321i 0.236427π0.236427\pi
354354 −7.00143 10.1087i −0.372122 0.537270i
355355 5.32780 + 1.42758i 0.282771 + 0.0757681i
356356 7.01464 5.76479i 0.371775 0.305533i
357357 0 0
358358 −0.224944 0.628001i −0.0118887 0.0331909i
359359 10.0193 5.78465i 0.528799 0.305302i −0.211728 0.977329i 0.567909π-0.567909\pi
0.740527 + 0.672027i 0.234576π0.234576\pi
360360 −2.15903 3.87564i −0.113791 0.204264i
361361 −16.4463 9.49530i −0.865597 0.499753i
362362 −23.5924 20.0028i −1.23999 1.05132i
363363 −4.24851 4.24851i −0.222989 0.222989i
364364 0 0
365365 6.08876 6.08876i 0.318700 0.318700i
366366 −0.641623 7.79244i −0.0335382 0.407317i
367367 4.25356 7.36738i 0.222034 0.384574i −0.733392 0.679807i 0.762064π-0.762064\pi
0.955425 + 0.295232i 0.0953971π0.0953971\pi
368368 −5.08511 + 5.81447i −0.265080 + 0.303100i
369369 6.57792 + 11.3933i 0.342433 + 0.593111i
370370 −10.3705 4.90055i −0.539136 0.254767i
371371 0 0
372372 −20.5681 2.01159i −1.06641 0.104296i
373373 1.35756 5.06649i 0.0702919 0.262333i −0.921833 0.387588i 0.873308π-0.873308\pi
0.992125 + 0.125255i 0.0399749π0.0399749\pi
374374 −0.631308 + 3.47630i −0.0326441 + 0.179755i
375375 9.51618 + 5.49417i 0.491414 + 0.283718i
376376 −23.7470 24.4869i −1.22466 1.26281i
377377 26.8616i 1.38344i
378378 0 0
379379 −3.62966 3.62966i −0.186443 0.186443i 0.607713 0.794156i 0.292087π-0.292087\pi
−0.794156 + 0.607713i 0.792087π0.792087\pi
380380 −0.0692443 + 0.184360i −0.00355216 + 0.00945745i
381381 −0.308783 1.15239i −0.0158194 0.0590390i
382382 −4.89752 7.07105i −0.250579 0.361786i
383383 −3.48127 6.02973i −0.177884 0.308105i 0.763271 0.646078i 0.223592π-0.223592\pi
−0.941156 + 0.337973i 0.890259π0.890259\pi
384384 10.1353 + 9.14209i 0.517217 + 0.466530i
385385 0 0
386386 −6.07950 + 12.8654i −0.309438 + 0.654831i
387387 −9.45101 2.53239i −0.480422 0.128729i
388388 −32.3632 + 5.36590i −1.64299 + 0.272412i
389389 12.7317 3.41145i 0.645523 0.172967i 0.0788190 0.996889i 0.474885π-0.474885\pi
0.566704 + 0.823922i 0.308218π0.308218\pi
390390 4.21178 4.96761i 0.213272 0.251545i
391391 1.96636i 0.0994429i
392392 0 0
393393 9.50339i 0.479383i
394394 −15.3826 13.0421i −0.774964 0.657053i
395395 −0.850663 + 0.227934i −0.0428015 + 0.0114686i
396396 −4.41038 + 6.16357i −0.221630 + 0.309731i
397397 6.02928 + 1.61554i 0.302601 + 0.0810817i 0.406925 0.913462i 0.366601π-0.366601\pi
−0.104324 + 0.994543i 0.533268π0.533268\pi
398398 14.9091 + 7.04524i 0.747325 + 0.353146i
399399 0 0
400400 15.5739 + 3.07572i 0.778693 + 0.153786i
401401 7.95077 + 13.7711i 0.397042 + 0.687697i 0.993360 0.115051i 0.0367033π-0.0367033\pi
−0.596317 + 0.802749i 0.703370π0.703370\pi
402402 −4.91815 + 3.40638i −0.245295 + 0.169895i
403403 8.33239 + 31.0969i 0.415066 + 1.54905i
404404 16.7502 7.60321i 0.833353 0.378274i
405405 1.42253 + 1.42253i 0.0706861 + 0.0706861i
406406 0 0
407407 19.5949i 0.971282i
408408 3.47421 + 0.0532908i 0.171999 + 0.00263829i
409409 4.93864 + 2.85133i 0.244200 + 0.140989i 0.617106 0.786880i 0.288305π-0.288305\pi
−0.372906 + 0.927869i 0.621638π0.621638\pi
410410 12.0364 + 2.18585i 0.594436 + 0.107952i
411411 −3.45372 + 12.8895i −0.170360 + 0.635791i
412412 11.9446 9.81634i 0.588468 0.483616i
413413 0 0
414414 −1.80214 + 3.81368i −0.0885704 + 0.187432i
415415 −3.90874 6.77014i −0.191873 0.332333i
416416 7.78066 19.7881i 0.381478 0.970194i
417417 10.5913 18.3447i 0.518659 0.898343i
418418 0.335298 0.0276082i 0.0164000 0.00135036i
419419 4.57142 4.57142i 0.223328 0.223328i −0.586570 0.809898i 0.699522π-0.699522\pi
0.809898 + 0.586570i 0.199522π0.199522\pi
420420 0 0
421421 0.421252 + 0.421252i 0.0205306 + 0.0205306i 0.717298 0.696767i 0.245379π-0.245379\pi
−0.696767 + 0.717298i 0.745379π0.745379\pi
422422 8.45131 9.96794i 0.411404 0.485232i
423423 −16.1311 9.31331i −0.784322 0.452829i
424424 −3.63733 + 2.02628i −0.176644 + 0.0984047i
425425 3.49971 2.02056i 0.169761 0.0980115i
426426 −8.72393 + 3.12483i −0.422676 + 0.151399i
427427 0 0
428428 −3.67924 + 37.6194i −0.177843 + 1.81840i
429429 −10.7470 2.87964i −0.518869 0.139031i
430430 −7.47945 + 5.18038i −0.360691 + 0.249820i
431431 10.5518 18.2762i 0.508262 0.880336i −0.491692 0.870769i 0.663621π-0.663621\pi
0.999954 0.00956658i 0.00304518π-0.00304518\pi
432432 19.6822 + 9.67280i 0.946963 + 0.465383i
433433 13.9717 0.671436 0.335718 0.941962i 0.391021π-0.391021\pi
0.335718 + 0.941962i 0.391021π0.391021\pi
434434 0 0
435435 −6.19120 + 6.19120i −0.296845 + 0.296845i
436436 −13.5242 29.7943i −0.647690 1.42689i
437437 0.180859 0.0484611i 0.00865168 0.00231821i
438438 −2.58489 + 14.2337i −0.123511 + 0.680113i
439439 4.69322 2.70963i 0.223995 0.129324i −0.383804 0.923415i 0.625386π-0.625386\pi
0.607799 + 0.794091i 0.292053π0.292053\pi
440440 1.71941 + 6.83455i 0.0819696 + 0.325824i
441441 0 0
442442 −1.82525 5.09573i −0.0868181 0.242379i
443443 1.56401 5.83698i 0.0743085 0.277323i −0.918767 0.394800i 0.870814π-0.870814\pi
0.993076 + 0.117477i 0.0374806π0.0374806\pi
444444 19.0107 3.15202i 0.902207 0.149588i
445445 −1.19324 4.45325i −0.0565652 0.211104i
446446 32.8894 2.70809i 1.55736 0.128232i
447447 6.32175 0.299009
448448 0 0
449449 18.4262 0.869587 0.434794 0.900530i 0.356821π-0.356821\pi
0.434794 + 0.900530i 0.356821π0.356821\pi
450450 8.63938 0.711360i 0.407264 0.0335338i
451451 −5.40898 20.1866i −0.254699 0.950550i
452452 −39.6885 + 6.58045i −1.86679 + 0.309518i
453453 0.425716 1.58879i 0.0200019 0.0746480i
454454 7.46301 + 20.8353i 0.350257 + 0.977848i
455455 0 0
456456 −0.0807208 0.320860i −0.00378010 0.0150257i
457457 31.1530 17.9862i 1.45728 0.841358i 0.458399 0.888747i 0.348423π-0.348423\pi
0.998877 + 0.0473884i 0.0150898π0.0150898\pi
458458 −6.75710 + 37.2080i −0.315739 + 1.73862i
459459 5.39253 1.44492i 0.251702 0.0674433i
460460 1.62118 + 3.57152i 0.0755878 + 0.166523i
461461 0.903879 0.903879i 0.0420978 0.0420978i −0.685745 0.727842i 0.740523π-0.740523\pi
0.727842 + 0.685745i 0.240523π0.240523\pi
462462 0 0
463463 −12.5999 −0.585565 −0.292782 0.956179i 0.594581π-0.594581\pi
−0.292782 + 0.956179i 0.594581π0.594581\pi
464464 −12.6080 + 25.6548i −0.585312 + 1.19099i
465465 −5.24687 + 9.08785i −0.243318 + 0.421439i
466466 14.8208 10.2651i 0.686560 0.475522i
467467 −8.00668 2.14538i −0.370505 0.0992765i 0.0687620 0.997633i 0.478095π-0.478095\pi
−0.439267 + 0.898357i 0.644762π0.644762\pi
468468 1.13018 11.5558i 0.0522424 0.534167i
469469 0 0
470470 −16.3059 + 5.84064i −0.752137 + 0.269409i
471471 −0.332038 + 0.191702i −0.0152995 + 0.00883318i
472472 −17.8081 + 9.92050i −0.819684 + 0.456628i
473473 13.4606 + 7.77151i 0.618921 + 0.357334i
474474 0.956828 1.12854i 0.0439486 0.0518353i
475475 −0.272096 0.272096i −0.0124846 0.0124846i
476476 0 0
477477 −1.60770 + 1.60770i −0.0736114 + 0.0736114i
478478 21.0977 1.73717i 0.964987 0.0794563i
479479 4.63918 8.03529i 0.211969 0.367142i −0.740361 0.672209i 0.765346π-0.765346\pi
0.952331 + 0.305067i 0.0986789π0.0986789\pi
480480 6.35419 2.76755i 0.290028 0.126321i
481481 −15.0096 25.9974i −0.684378 1.18538i
482482 11.9699 25.3305i 0.545212 1.15377i
483483 0 0
484484 −7.69517 + 6.32407i −0.349781 + 0.287458i
485485 −4.31128 + 16.0899i −0.195765 + 0.730606i
486486 19.5612 + 3.55238i 0.887314 + 0.161139i
487487 33.5037 + 19.3434i 1.51820 + 0.876533i 0.999771 + 0.0214118i 0.00681612π0.00681612\pi
0.518429 + 0.855121i 0.326517π0.326517\pi
488488 −12.9603 0.198798i −0.586685 0.00899914i
489489 17.9076i 0.809810i
490490 0 0
491491 −29.8086 29.8086i −1.34524 1.34524i −0.890750 0.454494i 0.849820π-0.849820\pi
−0.454494 0.890750i 0.650180π-0.650180\pi
492492 −18.7147 + 8.49492i −0.843722 + 0.382980i
493493 1.88338 + 7.02889i 0.0848234 + 0.316565i
494494 −0.423706 + 0.293466i −0.0190635 + 0.0132036i
495495 1.92420 + 3.33282i 0.0864865 + 0.149799i
496496 −6.63786 + 33.6107i −0.298049 + 1.50917i
497497 0 0
498498 11.8746 + 5.61132i 0.532115 + 0.251449i
499499 10.7993 + 2.89367i 0.483444 + 0.129538i 0.492306 0.870422i 0.336154π-0.336154\pi
−0.00886191 + 0.999961i 0.502821π0.502821\pi
500500 10.6004 14.8142i 0.474064 0.662512i
501501 −17.0121 + 4.55839i −0.760046 + 0.203654i
502502 −14.0951 11.9505i −0.629093 0.533377i
503503 18.1532i 0.809409i −0.914448 0.404704i 0.867374π-0.867374\pi
0.914448 0.404704i 0.132626π-0.132626\pi
504504 0 0
505505 9.34050i 0.415647i
506506 4.33322 5.11084i 0.192635 0.227205i
507507 1.31498 0.352349i 0.0584005 0.0156484i
508508 −1.95116 + 0.323508i −0.0865689 + 0.0143533i
509509 1.97895 + 0.530258i 0.0877154 + 0.0235033i 0.302410 0.953178i 0.402209π-0.402209\pi
−0.214694 + 0.976681i 0.568876π0.568876\pi
510510 0.753798 1.59518i 0.0333787 0.0706358i
511511 0 0
512512 16.7190 15.2471i 0.738883 0.673834i
513513 −0.265799 0.460378i −0.0117353 0.0203262i
514514 18.6989 + 26.9975i 0.824772 + 1.19081i
515515 −2.03187 7.58304i −0.0895348 0.334149i
516516 5.37454 14.3094i 0.236601 0.629938i
517517 20.9228 + 20.9228i 0.920183 + 0.920183i
518518 0 0
519519 14.9004i 0.654053i
520520 −7.51644 7.75062i −0.329618 0.339887i
521521 −2.51905 1.45437i −0.110361 0.0637172i 0.443803 0.896124i 0.353629π-0.353629\pi
−0.554165 + 0.832407i 0.686962π0.686962\pi
522522 −2.78913 + 15.3584i −0.122077 + 0.672218i
523523 −4.28781 + 16.0023i −0.187493 + 0.699732i 0.806590 + 0.591111i 0.201310π0.201310\pi
−0.994083 + 0.108622i 0.965356π0.965356\pi
524524 −15.6797 1.53350i −0.684969 0.0669911i
525525 0 0
526526 5.77962 + 2.73114i 0.252003 + 0.119083i
527527 4.36067 + 7.55290i 0.189954 + 0.329010i
528528 −8.91253 7.79456i −0.387868 0.339215i
529529 −9.63542 + 16.6890i −0.418931 + 0.725611i
530530 0.173493 + 2.10706i 0.00753607 + 0.0915247i
531531 −7.87117 + 7.87117i −0.341580 + 0.341580i
532532 0 0
533533 22.6392 + 22.6392i 0.980611 + 0.980611i
534534 5.90792 + 5.00903i 0.255661 + 0.216762i
535535 16.6219 + 9.59663i 0.718625 + 0.414899i
536536 4.82659 + 8.66412i 0.208477 + 0.374233i
537537 0.492826 0.284533i 0.0212670 0.0122785i
538538 −0.190258 0.531165i −0.00820262 0.0229001i
539539 0 0
540540 8.60326 7.07035i 0.370225 0.304260i
541541 −7.01543 1.87978i −0.301617 0.0808180i 0.104837 0.994489i 0.466568π-0.466568\pi
−0.406453 + 0.913671i 0.633235π0.633235\pi
542542 8.55285 + 12.3486i 0.367377 + 0.530419i
543543 13.1932 22.8513i 0.566174 0.980643i
544544 0.648534 5.72350i 0.0278057 0.245393i
545545 −16.6144 −0.711682
546546 0 0
547547 18.2712 18.2712i 0.781218 0.781218i −0.198818 0.980036i 0.563710π-0.563710\pi
0.980036 + 0.198818i 0.0637103π0.0637103\pi
548548 20.7090 + 7.77819i 0.884647 + 0.332268i
549549 −6.83683 + 1.83192i −0.291789 + 0.0781846i
550550 −13.5489 2.46053i −0.577728 0.104917i
551551 0.600079 0.346456i 0.0255642 0.0147595i
552552 −5.65550 3.38190i −0.240714 0.143943i
553553 0 0
554554 15.3299 5.49103i 0.651305 0.233291i
555555 2.53252 9.45148i 0.107499 0.401193i
556556 −28.5579 20.4348i −1.21112 0.866627i
557557 1.28251 + 4.78640i 0.0543418 + 0.202806i 0.987759 0.155986i 0.0498554π-0.0498554\pi
−0.933417 + 0.358792i 0.883189π0.883189\pi
558558 1.53522 + 18.6451i 0.0649911 + 0.789310i
559559 −23.8117 −1.00713
560560 0 0
561561 −3.01407 −0.127254
562562 2.16276 + 26.2664i 0.0912303 + 1.10798i
563563 6.29301 + 23.4858i 0.265219 + 0.989809i 0.962116 + 0.272639i 0.0878964π0.0878964\pi
−0.696898 + 0.717170i 0.745437π0.745437\pi
564564 16.9334 23.6646i 0.713024 0.996460i
565565 −5.28712 + 19.7318i −0.222431 + 0.830123i
566566 12.1000 4.33410i 0.508600 0.182176i
567567 0 0
568568 3.74795 + 14.8979i 0.157260 + 0.625100i
569569 −2.33865 + 1.35022i −0.0980412 + 0.0566041i −0.548219 0.836335i 0.684694π-0.684694\pi
0.450178 + 0.892939i 0.351361π0.351361\pi
570570 −0.165297 0.0300185i −0.00692354 0.00125734i
571571 12.8196 3.43500i 0.536484 0.143750i 0.0196030 0.999808i 0.493760π-0.493760\pi
0.516881 + 0.856058i 0.327093π0.327093\pi
572572 −6.48530 + 17.2668i −0.271164 + 0.721961i
573573 5.18857 5.18857i 0.216756 0.216756i
574574 0 0
575575 −7.66390 −0.319607
576576 6.50333 10.5062i 0.270972 0.437756i
577577 −12.4461 + 21.5572i −0.518137 + 0.897439i 0.481641 + 0.876369i 0.340041π0.340041\pi
−0.999778 + 0.0210709i 0.993292π0.993292\pi
578578 12.8540 + 18.5586i 0.534654 + 0.771935i
579579 −11.7253 3.14178i −0.487286 0.130568i
580580 9.21584 + 11.2139i 0.382667 + 0.465632i
581581 0 0
582582 −9.43697 26.3462i −0.391175 1.09209i
583583 3.12788 1.80589i 0.129544 0.0747921i
584584 23.0671 + 6.56161i 0.954525 + 0.271522i
585585 −5.10584 2.94786i −0.211101 0.121879i
586586 18.3354 + 15.5456i 0.757427 + 0.642185i
587587 −23.9315 23.9315i −0.987758 0.987758i 0.0121684 0.999926i 0.496127π-0.496127\pi
−0.999926 + 0.0121684i 0.996127π0.996127\pi
588588 0 0
589589 0.587224 0.587224i 0.0241961 0.0241961i
590590 0.849411 + 10.3160i 0.0349697 + 0.424703i
591591 8.60218 14.8994i 0.353846 0.612880i
592592 −2.13290 31.8744i −0.0876615 1.31003i
593593 0.895084 + 1.55033i 0.0367567 + 0.0636645i 0.883819 0.467830i 0.154964π-0.154964\pi
−0.847062 + 0.531494i 0.821631π0.821631\pi
594594 −17.2001 8.12786i −0.705729 0.333490i
595595 0 0
596596 1.02010 10.4303i 0.0417849 0.427241i
597597 −3.64086 + 13.5879i −0.149010 + 0.556114i
598598 −1.83419 + 10.1000i −0.0750057 + 0.413019i
599599 −37.3788 21.5806i −1.52726 0.881761i −0.999476 0.0323796i 0.989691π-0.989691\pi
−0.527779 0.849381i 0.676975π-0.676975\pi
600600 −0.207702 + 13.5408i −0.00847938 + 0.552800i
601601 27.6564i 1.12813i −0.825730 0.564065i 0.809237π-0.809237\pi
0.825730 0.564065i 0.190763π-0.190763\pi
602602 0 0
603603 3.82954 + 3.82954i 0.155951 + 0.155951i
604604 −2.55266 0.958762i −0.103866 0.0390115i
605605 1.30901 + 4.88529i 0.0532188 + 0.198615i
606606 8.93498 + 12.9003i 0.362959 + 0.524041i
607607 −10.7968 18.7006i −0.438228 0.759032i 0.559325 0.828948i 0.311060π-0.311060\pi
−0.997553 + 0.0699158i 0.977727π0.977727\pi
608608 −0.542413 + 0.0814064i −0.0219978 + 0.00330147i
609609 0 0
610610 −2.81199 + 5.95071i −0.113854 + 0.240937i
611611 −43.7859 11.7324i −1.77139 0.474642i
612612 −0.514493 3.10305i −0.0207972 0.125433i
613613 9.58708 2.56885i 0.387219 0.103755i −0.0599573 0.998201i 0.519096π-0.519096\pi
0.447176 + 0.894446i 0.352430π0.352430\pi
614614 −23.0662 + 27.2056i −0.930878 + 1.09793i
615615 10.4360i 0.420819i
616616 0 0
617617 14.2458i 0.573515i 0.958003 + 0.286758i 0.0925774π0.0925774\pi
−0.958003 + 0.286758i 0.907423π0.907423\pi
618618 10.0601 + 8.52942i 0.404675 + 0.343104i
619619 35.2895 9.45579i 1.41840 0.380060i 0.533487 0.845808i 0.320881π-0.320881\pi
0.884917 + 0.465748i 0.154215π0.154215\pi
620620 14.1474 + 10.1233i 0.568174 + 0.406560i
621621 −10.2268 2.74027i −0.410388 0.109963i
622622 −8.36817 3.95435i −0.335533 0.158555i
623623 0 0
624624 17.7952 + 3.51442i 0.712379 + 0.140689i
625625 5.29682 + 9.17437i 0.211873 + 0.366975i
626626 22.2908 15.4389i 0.890919 0.617064i
627627 0.0742821 + 0.277225i 0.00296654 + 0.0110713i
628628 0.262711 + 0.578764i 0.0104833 + 0.0230952i
629629 −5.75034 5.75034i −0.229281 0.229281i
630630 0 0
631631 4.87006i 0.193874i −0.995291 0.0969370i 0.969095π-0.969095\pi
0.995291 0.0969370i 0.0309045π-0.0309045\pi
632632 −1.70758 1.76078i −0.0679237 0.0700399i
633633 9.65483 + 5.57422i 0.383745 + 0.221555i
634634 −26.1881 4.75585i −1.04006 0.188879i
635635 −0.259925 + 0.970054i −0.0103148 + 0.0384954i
636636 −2.25519 2.74414i −0.0894242 0.108812i
637637 0 0
638638 10.5942 22.4195i 0.419430 0.887595i
639639 4.19436 + 7.26484i 0.165926 + 0.287393i
640640 −3.54084 10.9304i −0.139964 0.432061i
641641 −17.1939 + 29.7808i −0.679120 + 1.17627i 0.296126 + 0.955149i 0.404305π0.404305\pi
−0.975246 + 0.221121i 0.929028π0.929028\pi
642642 −32.1367 + 2.64611i −1.26834 + 0.104434i
643643 11.9018 11.9018i 0.469361 0.469361i −0.432346 0.901708i 0.642314π-0.642314\pi
0.901708 + 0.432346i 0.142314π0.142314\pi
644644 0 0
645645 −5.48825 5.48825i −0.216099 0.216099i
646646 −0.0902951 + 0.106499i −0.00355261 + 0.00419015i
647647 −4.56190 2.63381i −0.179347 0.103546i 0.407639 0.913143i 0.366352π-0.366352\pi
−0.586986 + 0.809597i 0.699686π0.699686\pi
648648 −1.53300 + 5.38922i −0.0602221 + 0.211709i
649649 15.3139 8.84148i 0.601123 0.347058i
650650 19.8607 7.11392i 0.779000 0.279031i
651651 0 0
652652 29.5458 + 2.88963i 1.15710 + 0.113167i
653653 33.1336 + 8.87812i 1.29662 + 0.347427i 0.840170 0.542323i 0.182455π-0.182455\pi
0.456447 + 0.889751i 0.349122π0.349122\pi
654654 22.9464 15.8930i 0.897276 0.621467i
655655 −3.99985 + 6.92794i −0.156287 + 0.270697i
656656 10.9959 + 32.2481i 0.429319 + 1.25908i
657657 13.0959 0.510919
658658 0 0
659659 −14.4817 + 14.4817i −0.564126 + 0.564126i −0.930477 0.366351i 0.880607π-0.880607\pi
0.366351 + 0.930477i 0.380607π0.380607\pi
660660 −5.47450 + 2.48497i −0.213095 + 0.0967274i
661661 −15.3347 + 4.10893i −0.596452 + 0.159819i −0.544400 0.838826i 0.683243π-0.683243\pi
−0.0520518 + 0.998644i 0.516576π0.516576\pi
662662 2.47476 13.6273i 0.0961843 0.529640i
663663 3.99889 2.30876i 0.155304 0.0896648i
664664 11.1743 18.6865i 0.433646 0.725178i
665665 0 0
666666 −5.88246 16.4227i −0.227941 0.636367i
667667 3.57180 13.3301i 0.138301 0.516145i
668668 4.77576 + 28.8039i 0.184780 + 1.11446i
669669 7.28634 + 27.1930i 0.281706 + 1.05134i
670670 5.01901 0.413261i 0.193901 0.0159657i
671671 11.2438 0.434061
672672 0 0
673673 −8.09831 −0.312167 −0.156083 0.987744i 0.549887π-0.549887\pi
−0.156083 + 0.987744i 0.549887π0.549887\pi
674674 6.92883 0.570514i 0.266889 0.0219754i
675675 5.63161 + 21.0175i 0.216761 + 0.808962i
676676 −0.369151 2.22645i −0.0141981 0.0856327i
677677 5.86138 21.8750i 0.225271 0.840724i −0.757025 0.653386i 0.773348π-0.773348\pi
0.982296 0.187337i 0.0599857π-0.0599857\pi
678678 −11.5730 32.3095i −0.444458 1.24084i
679679 0 0
680680 −2.51026 1.50110i −0.0962639 0.0575644i
681681 −16.3505 + 9.43999i −0.626554 + 0.361741i
682682 5.31019 29.2406i 0.203338 1.11968i
683683 −36.8038 + 9.86156i −1.40826 + 0.377342i −0.881304 0.472550i 0.843334π-0.843334\pi
−0.526956 + 0.849892i 0.676667π0.676667\pi
684684 −0.272729 + 0.123797i −0.0104281 + 0.00473348i
685685 7.94275 7.94275i 0.303477 0.303477i
686686 0 0
687687 −32.2606 −1.23082
688688 −22.7419 11.1765i −0.867027 0.426099i
689689 −2.76660 + 4.79189i −0.105399 + 0.182556i
690690 −2.75065 + 1.90514i −0.104715 + 0.0725275i
691691 23.8952 + 6.40271i 0.909018 + 0.243571i 0.682885 0.730526i 0.260725π-0.260725\pi
0.226133 + 0.974096i 0.427392π0.427392\pi
692692 −24.5841 2.40437i −0.934548 0.0914004i
693693 0 0
694694 −12.4525 + 4.46038i −0.472691 + 0.169314i
695695 −15.4421 + 8.91547i −0.585750 + 0.338183i
696696 −23.4552 6.67201i −0.889068 0.252902i
697697 7.51132 + 4.33666i 0.284511 + 0.164263i
698698 22.2542 26.2478i 0.842334 0.993495i
699699 10.8752 + 10.8752i 0.411336 + 0.411336i
700700 0 0
701701 −10.6300 + 10.6300i −0.401489 + 0.401489i −0.878757 0.477269i 0.841627π-0.841627\pi
0.477269 + 0.878757i 0.341627π0.341627\pi
702702 29.0460 2.39162i 1.09627 0.0902660i
703703 −0.387181 + 0.670617i −0.0146028 + 0.0252928i
704704 −14.2984 + 13.4470i −0.538892 + 0.506804i
705705 −7.38785 12.7961i −0.278242 0.481930i
706706 −4.93612 + 10.4458i −0.185773 + 0.393132i
707707 0 0
708708 −11.0413 13.4351i −0.414956 0.504921i
709709 −0.916878 + 3.42184i −0.0344341 + 0.128510i −0.981003 0.193991i 0.937857π-0.937857\pi
0.946569 + 0.322501i 0.104523π0.104523\pi
710710 7.67492 + 1.39379i 0.288034 + 0.0523080i
711711 −1.15994 0.669691i −0.0435011 0.0251154i
712712 9.21772 8.93921i 0.345449 0.335011i
713713 16.5398i 0.619422i
714714 0 0
715715 6.62251 + 6.62251i 0.247668 + 0.247668i
716716 −0.389927 0.859027i −0.0145723 0.0321033i
717717 4.67400 + 17.4436i 0.174554 + 0.651444i
718718 13.4503 9.31590i 0.501962 0.347666i
719719 8.10598 + 14.0400i 0.302302 + 0.523603i 0.976657 0.214805i 0.0689115π-0.0689115\pi
−0.674355 + 0.738407i 0.735578π0.735578\pi
720720 −3.49282 5.21194i −0.130170 0.194237i
721721 0 0
722722 −24.2821 11.4745i −0.903688 0.427035i
723723 23.0858 + 6.18582i 0.858569 + 0.230053i
724724 −35.5735 25.4548i −1.32208 0.946022i
725725 −27.3952 + 7.34051i −1.01743 + 0.272620i
726726 −6.48108 5.49498i −0.240536 0.203938i
727727 14.2822i 0.529699i −0.964290 0.264849i 0.914678π-0.914678\pi
0.964290 0.264849i 0.0853223π-0.0853223\pi
728728 0 0
729729 22.9031i 0.848263i
730730 7.87515 9.28839i 0.291473 0.343779i
731731 −6.23082 + 1.66954i −0.230455 + 0.0617503i
732732 −1.80866 10.9085i −0.0668501 0.403191i
733733 −33.2603 8.91206i −1.22850 0.329175i −0.414502 0.910048i 0.636044π-0.636044\pi
−0.813994 + 0.580874i 0.802711π0.802711\pi
734734 5.14015 10.8775i 0.189726 0.401497i
735735 0 0
736736 −6.49240 + 8.78531i −0.239313 + 0.323831i
737737 −4.30162 7.45062i −0.158452 0.274447i
738738 10.5934 + 15.2948i 0.389950 + 0.563010i
739739 −5.40009 20.1534i −0.198646 0.741356i −0.991293 0.131675i 0.957964π-0.957964\pi
0.792647 0.609681i 0.208702π-0.208702\pi
740740 −15.1854 5.70352i −0.558225 0.209666i
741741 −0.310906 0.310906i −0.0114214 0.0114214i
742742 0 0
743743 30.1201i 1.10500i −0.833513 0.552500i 0.813674π-0.813674\pi
0.833513 0.552500i 0.186326π-0.186326\pi
744744 −29.2230 0.448251i −1.07137 0.0164337i
745745 −4.60854 2.66074i −0.168844 0.0974820i
746746 1.32543 7.29848i 0.0485274 0.267216i
747747 3.07719 11.4842i 0.112588 0.420186i
748748 −0.486359 + 4.97291i −0.0177831 + 0.181828i
749749 0 0
750750 14.0501 + 6.63935i 0.513039 + 0.242435i
751751 −22.6093 39.1605i −0.825026 1.42899i −0.901900 0.431946i 0.857827π-0.857827\pi
0.0768741 0.997041i 0.475506π-0.475506\pi
752752 −36.3119 31.7570i −1.32416 1.15806i
753753 7.88217 13.6523i 0.287242 0.497518i
754754 3.11736 + 37.8600i 0.113528 + 1.37878i
755755 −0.979047 + 0.979047i −0.0356312 + 0.0356312i
756756 0 0
757757 −10.1353 10.1353i −0.368375 0.368375i 0.498509 0.866884i 0.333881π-0.333881\pi
−0.866884 + 0.498509i 0.833881π0.833881\pi
758758 −5.53703 4.69457i −0.201114 0.170515i
759759 4.95030 + 2.85806i 0.179684 + 0.103741i
760760 −0.0762005 + 0.267880i −0.00276408 + 0.00971704i
761761 −17.0843 + 9.86363i −0.619306 + 0.357556i −0.776599 0.629996i 0.783057π-0.783057\pi
0.157293 + 0.987552i 0.449723π0.449723\pi
762762 −0.568951 1.58840i −0.0206109 0.0575417i
763763 0 0
764764 −7.72339 9.39788i −0.279422 0.340003i
765765 −1.54273 0.413374i −0.0557776 0.0149456i
766766 −5.60641 8.09456i −0.202568 0.292468i
767767 −13.5451 + 23.4607i −0.489084 + 0.847118i
768768 15.3462 + 11.7090i 0.553756 + 0.422513i
769769 41.2736 1.48837 0.744183 0.667976i 0.232839π-0.232839\pi
0.744183 + 0.667976i 0.232839π0.232839\pi
770770 0 0
771771 −19.8101 + 19.8101i −0.713444 + 0.713444i
772772 −7.07565 + 18.8386i −0.254658 + 0.678015i
773773 −51.5773 + 13.8201i −1.85511 + 0.497074i −0.999779 0.0210159i 0.993310π-0.993310\pi
−0.855326 + 0.518090i 0.826643π0.826643\pi
774774 −13.6146 2.47245i −0.489365 0.0888704i
775775 −29.4375 + 16.9958i −1.05743 + 0.610506i
776776 −44.9914 + 11.3188i −1.61510 + 0.406320i
777777 0 0
778778 17.5487 6.28579i 0.629152 0.225356i
779779 0.213755 0.797746i 0.00765858 0.0285822i
780780 5.35977 7.49035i 0.191911 0.268198i
781781 −3.44899 12.8718i −0.123415 0.460590i
782782 0.228200 + 2.77147i 0.00816043 + 0.0991075i
783783 −39.1812 −1.40022
784784 0 0
785785 0.322740 0.0115191
786786 −1.10289 13.3945i −0.0393389 0.477766i
787787 0.132467 + 0.494375i 0.00472196 + 0.0176226i 0.968247 0.249997i 0.0804296π-0.0804296\pi
−0.963525 + 0.267620i 0.913763π0.913763\pi
788788 −23.1945 16.5970i −0.826269 0.591242i
789789 −1.41140 + 5.26743i −0.0502473 + 0.187526i
790790 −1.17251 + 0.419982i −0.0417160 + 0.0149423i
791791 0 0
792792 −5.50089 + 9.19905i −0.195466 + 0.326874i
793793 −14.9176 + 8.61266i −0.529739 + 0.305845i
794794 8.68542 + 1.57730i 0.308234 + 0.0559763i
795795 −1.74212 + 0.466799i −0.0617865 + 0.0165556i
796796 21.8311 + 8.19964i 0.773784 + 0.290628i
797797 −35.5605 + 35.5605i −1.25962 + 1.25962i −0.308341 + 0.951276i 0.599774π0.599774\pi
−0.951276 + 0.308341i 0.900226π0.900226\pi
798798 0 0
799799 −12.2801 −0.434438
800800 22.3074 + 2.52767i 0.788686 + 0.0893666i
801801 3.50586 6.07232i 0.123873 0.214555i
802802 12.8043 + 18.4869i 0.452137 + 0.652796i
803803 −20.0946 5.38433i −0.709123 0.190009i
804804 −6.53653 + 5.37187i −0.230526 + 0.189451i
805805 0 0
806806 15.3529 + 42.8623i 0.540783 + 1.50976i
807807 0.416833 0.240659i 0.0146732 0.00847158i
808808 22.7261 12.6602i 0.799501 0.445384i
809809 1.17802 + 0.680131i 0.0414170 + 0.0239121i 0.520566 0.853822i 0.325721π-0.325721\pi
−0.479149 + 0.877734i 0.659054π0.659054\pi
810810 2.17006 + 1.83989i 0.0762483 + 0.0646471i
811811 −12.4370 12.4370i −0.436722 0.436722i 0.454186 0.890907i 0.349930π-0.349930\pi
−0.890907 + 0.454186i 0.849930π0.849930\pi
812812 0 0
813813 −9.06114 + 9.06114i −0.317788 + 0.317788i
814814 2.27403 + 27.6179i 0.0797049 + 0.968006i
815815 7.53706 13.0546i 0.264012 0.457282i
816816 4.90288 0.328080i 0.171635 0.0114851i
817817 0.307119 + 0.531945i 0.0107447 + 0.0186104i
818818 7.29164 + 3.44564i 0.254946 + 0.120474i
819819 0 0
820820 17.2183 + 1.68398i 0.601290 + 0.0588072i
821821 −1.42969 + 5.33567i −0.0498965 + 0.186216i −0.986376 0.164506i 0.947397π-0.947397\pi
0.936480 + 0.350722i 0.114064π0.114064\pi
822822 −3.37197 + 18.5678i −0.117611 + 0.647626i
823823 −16.5082 9.53100i −0.575439 0.332230i 0.183880 0.982949i 0.441134π-0.441134\pi
−0.759319 + 0.650719i 0.774468π0.774468\pi
824824 15.6960 15.2218i 0.546797 0.530276i
825825 11.7474i 0.408991i
826826 0 0
827827 3.94521 + 3.94521i 0.137188 + 0.137188i 0.772366 0.635178i 0.219073π-0.219073\pi
−0.635178 + 0.772366i 0.719073π0.719073\pi
828828 −2.09743 + 5.58431i −0.0728907 + 0.194068i
829829 6.94085 + 25.9036i 0.241066 + 0.899669i 0.975320 + 0.220795i 0.0708652π0.0708652\pi
−0.734255 + 0.678874i 0.762468π0.762468\pi
830830 −6.29484 9.08851i −0.218497 0.315467i
831831 6.94562 + 12.0302i 0.240941 + 0.417322i
832832 8.66994 28.7932i 0.300576 0.998226i
833833 0 0
834834 12.7989 27.0850i 0.443190 0.937875i
835835 14.3203 + 3.83713i 0.495576 + 0.132789i
836836 0.469380 0.0778244i 0.0162338 0.00269161i
837837 −45.3588 + 12.1539i −1.56783 + 0.420099i
838838 5.91263 6.97368i 0.204249 0.240902i
839839 5.34140i 0.184406i 0.995740 + 0.0922028i 0.0293908π0.0293908\pi
−0.995740 + 0.0922028i 0.970609π0.970609\pi
840840 0 0
841841 22.0706i 0.761056i
842842 0.642619 + 0.544844i 0.0221461 + 0.0187766i
843843 −21.7171 + 5.81908i −0.747976 + 0.200420i
844844 10.7548 15.0300i 0.370197 0.517356i
845845 −1.10692 0.296598i −0.0380791 0.0102033i
846846 −23.8167 11.2545i −0.818837 0.386939i
847847 0 0
848848 −4.89146 + 3.27804i −0.167973 + 0.112568i
849849 5.48222 + 9.49549i 0.188149 + 0.325884i
850850 4.69816 3.25402i 0.161145 0.111612i
851851 3.99165 + 14.8971i 0.136832 + 0.510664i
852852 −11.9332 + 5.41671i −0.408826 + 0.185574i
853853 −1.42841 1.42841i −0.0489078 0.0489078i 0.682230 0.731138i 0.261010π-0.261010\pi
−0.731138 + 0.682230i 0.761010π0.761010\pi
854854 0 0
855855 0.152084i 0.00520115i
856856 −0.819860 + 53.4494i −0.0280222 + 1.82686i
857857 −22.1543 12.7908i −0.756778 0.436926i 0.0713599 0.997451i 0.477266π-0.477266\pi
−0.828138 + 0.560525i 0.810599π0.810599\pi
858858 −15.4815 2.81148i −0.528528 0.0959825i
859859 11.7968 44.0264i 0.402503 1.50216i −0.406113 0.913823i 0.633116π-0.633116\pi
0.808616 0.588337i 0.200217π-0.200217\pi
860860 −9.94066 + 8.16946i −0.338974 + 0.278576i
861861 0 0
862862 12.7512 26.9839i 0.434306 0.919075i
863863 −19.7223 34.1601i −0.671356 1.16282i −0.977520 0.210843i 0.932379π-0.932379\pi
0.306164 0.951979i 0.400954π-0.400954\pi
864864 28.8636 + 11.3491i 0.981959 + 0.386104i
865865 −6.27135 + 10.8623i −0.213232 + 0.369329i
866866 19.6923 1.62145i 0.669172 0.0550991i
867867 −13.6178 + 13.6178i −0.462486 + 0.462486i
868868 0 0
869869 1.50449 + 1.50449i 0.0510364 + 0.0510364i
870870 −8.00765 + 9.44466i −0.271485 + 0.320204i
871871 11.4143 + 6.59004i 0.386758 + 0.223295i
872872 −22.5193 40.4239i −0.762598 1.36893i
873873 −21.9398 + 12.6669i −0.742548 + 0.428710i
874874 0.249287 0.0892924i 0.00843226 0.00302036i
875875 0 0
876876 −1.99140 + 20.3616i −0.0672832 + 0.687955i
877877 10.1823 + 2.72833i 0.343831 + 0.0921292i 0.426602 0.904439i 0.359710π-0.359710\pi
−0.0827714 + 0.996569i 0.526377π0.526377\pi
878878 6.30037 4.36373i 0.212627 0.147269i
879879 −10.2534 + 17.7594i −0.345839 + 0.599011i
880880 3.21658 + 9.43337i 0.108431 + 0.317999i
881881 15.4426 0.520274 0.260137 0.965572i 0.416232π-0.416232\pi
0.260137 + 0.965572i 0.416232π0.416232\pi
882882 0 0
883883 10.0224 10.0224i 0.337280 0.337280i −0.518063 0.855343i 0.673347π-0.673347\pi
0.855343 + 0.518063i 0.173347π0.173347\pi
884884 −3.16395 6.97032i −0.106415 0.234437i
885885 −8.52927 + 2.28541i −0.286708 + 0.0768233i
886886 1.52699 8.40840i 0.0513004 0.282486i
887887 −37.9027 + 21.8831i −1.27265 + 0.734763i −0.975485 0.220064i 0.929373π-0.929373\pi
−0.297162 + 0.954827i 0.596040π0.596040\pi
888888 26.4287 6.64883i 0.886888 0.223120i
889889 0 0
890890 −2.19862 6.13812i −0.0736979 0.205750i
891891 1.25795 4.69474i 0.0421430 0.157280i
892892 46.0415 7.63380i 1.54158 0.255598i
893893 0.302644 + 1.12948i 0.0101276 + 0.0377967i
894894 8.91016 0.733655i 0.298000 0.0245371i
895895 −0.479024 −0.0160120
896896 0 0
897897 −8.75703 −0.292389
898898 25.9707 2.13841i 0.866655 0.0713596i
899899 −15.8419 59.1229i −0.528358 1.97186i
900900 12.0942 2.00524i 0.403139 0.0668415i
901901 −0.387956 + 1.44787i −0.0129247 + 0.0482356i
902902 −9.96636 27.8242i −0.331844 0.926443i
903903 0 0
904904 −55.1750 + 13.8807i −1.83509 + 0.461666i
905905 −19.2356 + 11.1057i −0.639413 + 0.369165i
906906 0.415639 2.28872i 0.0138087 0.0760377i
907907 46.8743 12.5599i 1.55643 0.417045i 0.624902 0.780703i 0.285139π-0.285139\pi
0.931533 + 0.363658i 0.118472π0.118472\pi
908908 12.9367 + 28.5001i 0.429319 + 0.945808i
909909 10.0449 10.0449i 0.333169 0.333169i
910910 0 0
911911 −35.2525 −1.16797 −0.583983 0.811766i 0.698507π-0.698507\pi
−0.583983 + 0.811766i 0.698507π0.698507\pi
912912 −0.151008 0.442867i −0.00500038 0.0146648i
913913 −9.44340 + 16.3564i −0.312531 + 0.541319i
914914 41.8210 28.9659i 1.38332 0.958107i
915915 −5.42336 1.45319i −0.179291 0.0480409i
916916 −5.20567 + 53.2268i −0.172000 + 1.75866i
917917 0 0
918918 7.43278 2.66236i 0.245318 0.0878708i
919919 22.1228 12.7726i 0.729763 0.421329i −0.0885726 0.996070i 0.528231π-0.528231\pi
0.818335 + 0.574741i 0.194897π0.194897\pi
920920 2.69944 + 4.84572i 0.0889980 + 0.159759i
921921 −26.3510 15.2138i −0.868295 0.501310i
922922 1.16907 1.37886i 0.0385012 0.0454105i
923923 14.4357 + 14.4357i 0.475156 + 0.475156i
924924 0 0
925925 22.4120 22.4120i 0.736903 0.736903i
926926 −17.7588 + 1.46224i −0.583590 + 0.0480523i
927927 5.96981 10.3400i 0.196074 0.339610i
928928 −14.7930 + 37.6222i −0.485603 + 1.23501i
929929 1.98515 + 3.43838i 0.0651306 + 0.112810i 0.896752 0.442534i 0.145920π-0.145920\pi
−0.831621 + 0.555343i 0.812587π0.812587\pi
930930 −6.34051 + 13.4177i −0.207913 + 0.439985i
931931 0 0
932932 19.6978 16.1881i 0.645222 0.530258i
933933 2.04354 7.62660i 0.0669025 0.249684i
934934 −11.5339 2.09460i −0.377402 0.0685375i
935935 2.19724 + 1.26858i 0.0718576 + 0.0414870i
936936 0.251842 16.4184i 0.00823170 0.536653i
937937 18.3326i 0.598899i −0.954112 0.299450i 0.903197π-0.903197\pi
0.954112 0.299450i 0.0968031π-0.0968031\pi
938938 0 0
939939 16.3565 + 16.3565i 0.533773 + 0.533773i
940940 −22.3045 + 10.1244i −0.727492 + 0.330221i
941941 −7.71512 28.7932i −0.251506 0.938632i −0.970001 0.243100i 0.921836π-0.921836\pi
0.718496 0.695531i 0.244831π-0.244831\pi
942942 −0.445742 + 0.308728i −0.0145230 + 0.0100589i
943943 −8.22438 14.2451i −0.267823 0.463883i
944944 −23.9482 + 16.0491i −0.779448 + 0.522352i
945945 0 0
946946 19.8739 + 9.39136i 0.646157 + 0.305339i
947947 −27.1840 7.28394i −0.883362 0.236696i −0.211505 0.977377i 0.567837π-0.567837\pi
−0.671857 + 0.740681i 0.734503π0.734503\pi
948948 1.21763 1.70165i 0.0395467 0.0552670i
949949 30.7847 8.24874i 0.999314 0.267765i
950950 −0.415081 0.351926i −0.0134670 0.0114180i
951951 22.7060i 0.736291i
952952 0 0
953953 9.54510i 0.309196i −0.987977 0.154598i 0.950592π-0.950592\pi
0.987977 0.154598i 0.0494083π-0.0494083\pi
954954 −2.07938 + 2.45254i −0.0673225 + 0.0794038i
955955 −5.96625 + 1.59865i −0.193063 + 0.0517311i
956956 29.5345 4.89689i 0.955212 0.158377i
957957 20.4327 + 5.47492i 0.660495 + 0.176979i
958958 5.60615 11.8637i 0.181126 0.383298i
959959 0 0
960960 8.63470 4.63812i 0.278684 0.149695i
961961 −21.1794 36.6839i −0.683208 1.18335i
962962 −24.1722 34.8999i −0.779343 1.12522i
963963 7.55502 + 28.1957i 0.243457 + 0.908595i
964964 13.9312 37.0911i 0.448693 1.19462i
965965 7.22535 + 7.22535i 0.232592 + 0.232592i
966966 0 0
967967 54.0255i 1.73734i 0.495388 + 0.868672i 0.335026π0.335026\pi
−0.495388 + 0.868672i 0.664974π0.664974\pi
968968 −10.1120 + 9.80646i −0.325012 + 0.315192i
969969 −0.103154 0.0595558i −0.00331377 0.00191321i
970970 −4.20923 + 23.1782i −0.135150 + 0.744207i
971971 −1.54187 + 5.75433i −0.0494809 + 0.184665i −0.986243 0.165301i 0.947140π-0.947140\pi
0.936762 + 0.349966i 0.113807π0.113807\pi
972972 27.9827 + 2.73675i 0.897544 + 0.0877813i
973973 0 0
974974 49.4665 + 23.3752i 1.58501 + 0.748991i
975975 8.99842 + 15.5857i 0.288180 + 0.499143i
976976 −18.2899 + 1.22388i −0.585444 + 0.0391754i
977977 14.6499 25.3743i 0.468690 0.811795i −0.530669 0.847579i 0.678059π-0.678059\pi
0.999360 + 0.0357835i 0.0113927π0.0113927\pi
978978 2.07822 + 25.2398i 0.0664542 + 0.807078i
979979 −7.87607 + 7.87607i −0.251720 + 0.251720i
980980 0 0
981981 −17.8673 17.8673i −0.570460 0.570460i
982982 −45.4729 38.5542i −1.45110 1.23031i
983983 13.8442 + 7.99296i 0.441562 + 0.254936i 0.704260 0.709942i 0.251279π-0.251279\pi
−0.262698 + 0.964878i 0.584612π0.584612\pi
984984 −25.3914 + 14.1450i −0.809449 + 0.450926i
985985 −12.5419 + 7.24108i −0.399619 + 0.230720i
986986 3.47024 + 9.68825i 0.110515 + 0.308537i
987987 0 0
988988 −0.563133 + 0.462795i −0.0179156 + 0.0147235i
989989 11.8166 + 3.16625i 0.375746 + 0.100681i
990990 3.09884 + 4.47411i 0.0984876 + 0.142197i
991991 −10.3826 + 17.9832i −0.329814 + 0.571255i −0.982475 0.186396i 0.940319π-0.940319\pi
0.652661 + 0.757650i 0.273653π0.273653\pi
992992 −5.45509 + 48.1428i −0.173199 + 1.52853i
993993 11.8153 0.374948
994994 0 0
995995 8.37312 8.37312i 0.265446 0.265446i
996996 17.3878 + 6.53077i 0.550955 + 0.206935i
997997 48.0242 12.8681i 1.52094 0.407535i 0.600890 0.799331i 0.294813π-0.294813\pi
0.920052 + 0.391796i 0.128146π0.128146\pi
998998 15.5568 + 2.82518i 0.492443 + 0.0894294i
999999 37.9205 21.8934i 1.19975 0.692677i
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 784.2.x.o.165.12 48
7.2 even 3 inner 784.2.x.o.373.5 48
7.3 odd 6 784.2.m.j.197.5 24
7.4 even 3 784.2.m.k.197.5 24
7.5 odd 6 112.2.w.c.37.5 48
7.6 odd 2 112.2.w.c.53.12 yes 48
16.13 even 4 inner 784.2.x.o.557.5 48
28.19 even 6 448.2.ba.c.177.4 48
28.27 even 2 448.2.ba.c.305.9 48
56.5 odd 6 896.2.ba.f.737.4 48
56.13 odd 2 896.2.ba.f.865.9 48
56.19 even 6 896.2.ba.e.737.9 48
56.27 even 2 896.2.ba.e.865.4 48
112.5 odd 12 896.2.ba.f.289.9 48
112.13 odd 4 112.2.w.c.109.5 yes 48
112.19 even 12 448.2.ba.c.401.9 48
112.27 even 4 896.2.ba.e.417.9 48
112.45 odd 12 784.2.m.j.589.5 24
112.61 odd 12 112.2.w.c.93.12 yes 48
112.69 odd 4 896.2.ba.f.417.4 48
112.75 even 12 896.2.ba.e.289.4 48
112.83 even 4 448.2.ba.c.81.4 48
112.93 even 12 inner 784.2.x.o.765.12 48
112.109 even 12 784.2.m.k.589.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.5 48 7.5 odd 6
112.2.w.c.53.12 yes 48 7.6 odd 2
112.2.w.c.93.12 yes 48 112.61 odd 12
112.2.w.c.109.5 yes 48 112.13 odd 4
448.2.ba.c.81.4 48 112.83 even 4
448.2.ba.c.177.4 48 28.19 even 6
448.2.ba.c.305.9 48 28.27 even 2
448.2.ba.c.401.9 48 112.19 even 12
784.2.m.j.197.5 24 7.3 odd 6
784.2.m.j.589.5 24 112.45 odd 12
784.2.m.k.197.5 24 7.4 even 3
784.2.m.k.589.5 24 112.109 even 12
784.2.x.o.165.12 48 1.1 even 1 trivial
784.2.x.o.373.5 48 7.2 even 3 inner
784.2.x.o.557.5 48 16.13 even 4 inner
784.2.x.o.765.12 48 112.93 even 12 inner
896.2.ba.e.289.4 48 112.75 even 12
896.2.ba.e.417.9 48 112.27 even 4
896.2.ba.e.737.9 48 56.19 even 6
896.2.ba.e.865.4 48 56.27 even 2
896.2.ba.f.289.9 48 112.5 odd 12
896.2.ba.f.417.4 48 112.69 odd 4
896.2.ba.f.737.4 48 56.5 odd 6
896.2.ba.f.865.9 48 56.13 odd 2