Properties

Label 930.2.j.h.497.12
Level 930930
Weight 22
Character 930.497
Analytic conductor 7.4267.426
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(497,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.497");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 930=23531 930 = 2 \cdot 3 \cdot 5 \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 930.j (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: 7.426087387987.42608738798
Analytic rank: 00
Dimension: 4040
Relative dimension: 2020 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 497.12
Character χ\chi == 930.497
Dual form 930.2.j.h.683.12

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+(0.7071070.707107i)q2+(1.493530.877144i)q31.00000iq4+(1.98408+1.03122i)q5+(1.67632+0.435847i)q6+(2.39520+2.39520i)q7+(0.7071070.707107i)q8+(1.46124+2.62007i)q9+(2.132140.673776i)q100.0383198iq11+(0.877144+1.49353i)q12+(2.42230+2.42230i)q13+3.38733q14+(2.058753.28048i)q151.00000q16+(3.70534+3.70534i)q17+(2.88592+0.819423i)q18+7.16937iq19+(1.031221.98408i)q20+(1.476365.67823i)q21+(0.02709620.0270962i)q22+(3.94658+3.94658i)q23+(0.435847+1.67632i)q24+(2.87317+4.09205i)q25+3.42565iq26+(0.1157915.19486i)q27+(2.395202.39520i)q283.49394q29+(3.775410.863894i)q301.00000q31+(0.707107+0.707107i)q32+(0.0336120+0.0572316i)q33+5.24015iq34+(2.28230+7.22226i)q35+(2.620071.46124i)q36+(4.898234.89823i)q37+(5.06951+5.06951i)q38+(5.742471.49306i)q39+(0.6737762.13214i)q4010.1701iq41+(5.059062.97117i)q42+(6.93875+6.93875i)q430.0383198q44+(0.197341+6.70530i)q45+5.58130q46+(7.356197.35619i)q47+(1.49353+0.877144i)q48+4.47399iq49+(4.92516+0.861878i)q50+(8.784152.28390i)q51+(2.42230+2.42230i)q52+(0.287477+0.287477i)q53+(3.591453.75520i)q54+(0.03951620.0760297i)q553.38733iq56+(6.2885710.7076i)q57+(2.47059+2.47059i)q58+15.0023q59+(3.28048+2.05875i)q60+5.16656q61+(0.707107+0.707107i)q62+(2.77565+9.77556i)q63+1.00000iq64+(7.30396+2.30812i)q65+(0.0167016+0.0642362i)q66+(5.80813+5.80813i)q67+(3.70534+3.70534i)q68+(2.432599.35603i)q69+(6.72074+3.49308i)q709.58222iq71+(0.8194232.88592i)q72+(9.969119.96911i)q736.92715q74+(0.7018368.63177i)q75+7.16937q76+(0.09178370.0917837i)q77+(3.004795.11629i)q7816.7308iq79+(1.984081.03122i)q80+(4.72958+7.65709i)q81+(7.191337.19133i)q82+(8.18895+8.18895i)q83+(5.67823+1.47636i)q84+(11.1727+3.53069i)q85+9.81288iq86+(5.21829+3.06469i)q87+(0.0270962+0.0270962i)q883.51450q89+(4.88090+4.60182i)q9011.6038q91+(3.946583.94658i)q92+(1.49353+0.877144i)q9310.4032iq94+(7.39319+14.2246i)q95+(1.676320.435847i)q96+(2.475872.47587i)q97+(3.16359+3.16359i)q98+(0.1004010.0559943i)q99+O(q100)q+(0.707107 - 0.707107i) q^{2} +(-1.49353 - 0.877144i) q^{3} -1.00000i q^{4} +(1.98408 + 1.03122i) q^{5} +(-1.67632 + 0.435847i) q^{6} +(2.39520 + 2.39520i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.46124 + 2.62007i) q^{9} +(2.13214 - 0.673776i) q^{10} -0.0383198i q^{11} +(-0.877144 + 1.49353i) q^{12} +(-2.42230 + 2.42230i) q^{13} +3.38733 q^{14} +(-2.05875 - 3.28048i) q^{15} -1.00000 q^{16} +(-3.70534 + 3.70534i) q^{17} +(2.88592 + 0.819423i) q^{18} +7.16937i q^{19} +(1.03122 - 1.98408i) q^{20} +(-1.47636 - 5.67823i) q^{21} +(-0.0270962 - 0.0270962i) q^{22} +(3.94658 + 3.94658i) q^{23} +(0.435847 + 1.67632i) q^{24} +(2.87317 + 4.09205i) q^{25} +3.42565i q^{26} +(0.115791 - 5.19486i) q^{27} +(2.39520 - 2.39520i) q^{28} -3.49394 q^{29} +(-3.77541 - 0.863894i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0336120 + 0.0572316i) q^{33} +5.24015i q^{34} +(2.28230 + 7.22226i) q^{35} +(2.62007 - 1.46124i) q^{36} +(-4.89823 - 4.89823i) q^{37} +(5.06951 + 5.06951i) q^{38} +(5.74247 - 1.49306i) q^{39} +(-0.673776 - 2.13214i) q^{40} -10.1701i q^{41} +(-5.05906 - 2.97117i) q^{42} +(-6.93875 + 6.93875i) q^{43} -0.0383198 q^{44} +(0.197341 + 6.70530i) q^{45} +5.58130 q^{46} +(7.35619 - 7.35619i) q^{47} +(1.49353 + 0.877144i) q^{48} +4.47399i q^{49} +(4.92516 + 0.861878i) q^{50} +(8.78415 - 2.28390i) q^{51} +(2.42230 + 2.42230i) q^{52} +(0.287477 + 0.287477i) q^{53} +(-3.59145 - 3.75520i) q^{54} +(0.0395162 - 0.0760297i) q^{55} -3.38733i q^{56} +(6.28857 - 10.7076i) q^{57} +(-2.47059 + 2.47059i) q^{58} +15.0023 q^{59} +(-3.28048 + 2.05875i) q^{60} +5.16656 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-2.77565 + 9.77556i) q^{63} +1.00000i q^{64} +(-7.30396 + 2.30812i) q^{65} +(0.0167016 + 0.0642362i) q^{66} +(5.80813 + 5.80813i) q^{67} +(3.70534 + 3.70534i) q^{68} +(-2.43259 - 9.35603i) q^{69} +(6.72074 + 3.49308i) q^{70} -9.58222i q^{71} +(0.819423 - 2.88592i) q^{72} +(9.96911 - 9.96911i) q^{73} -6.92715 q^{74} +(-0.701836 - 8.63177i) q^{75} +7.16937 q^{76} +(0.0917837 - 0.0917837i) q^{77} +(3.00479 - 5.11629i) q^{78} -16.7308i q^{79} +(-1.98408 - 1.03122i) q^{80} +(-4.72958 + 7.65709i) q^{81} +(-7.19133 - 7.19133i) q^{82} +(8.18895 + 8.18895i) q^{83} +(-5.67823 + 1.47636i) q^{84} +(-11.1727 + 3.53069i) q^{85} +9.81288i q^{86} +(5.21829 + 3.06469i) q^{87} +(-0.0270962 + 0.0270962i) q^{88} -3.51450 q^{89} +(4.88090 + 4.60182i) q^{90} -11.6038 q^{91} +(3.94658 - 3.94658i) q^{92} +(1.49353 + 0.877144i) q^{93} -10.4032i q^{94} +(-7.39319 + 14.2246i) q^{95} +(1.67632 - 0.435847i) q^{96} +(-2.47587 - 2.47587i) q^{97} +(3.16359 + 3.16359i) q^{98} +(0.100401 - 0.0559943i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q4q3+8q68q7+4q12+24q1312q1540q1656q21+16q2248q25+8q278q28+4q3040q3120q338q378q40+12q42++24q97+O(q100) 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/930Z)×\left(\mathbb{Z}/930\mathbb{Z}\right)^\times.

nn 187187 311311 871871
χ(n)\chi(n) e(14)e\left(\frac{1}{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 0.707107 0.707107i 0.500000 0.500000i
33 −1.49353 0.877144i −0.862287 0.506420i
44 1.00000i 0.500000i
55 1.98408 + 1.03122i 0.887309 + 0.461175i
66 −1.67632 + 0.435847i −0.684353 + 0.177934i
77 2.39520 + 2.39520i 0.905301 + 0.905301i 0.995889 0.0905872i 0.0288744π-0.0288744\pi
−0.0905872 + 0.995889i 0.528874π0.528874\pi
88 −0.707107 0.707107i −0.250000 0.250000i
99 1.46124 + 2.62007i 0.487079 + 0.873358i
1010 2.13214 0.673776i 0.674242 0.213067i
1111 0.0383198i 0.0115539i −0.999983 0.00577693i 0.998161π-0.998161\pi
0.999983 0.00577693i 0.00183886π-0.00183886\pi
1212 −0.877144 + 1.49353i −0.253210 + 0.431144i
1313 −2.42230 + 2.42230i −0.671825 + 0.671825i −0.958136 0.286312i 0.907571π-0.907571\pi
0.286312 + 0.958136i 0.407571π0.407571\pi
1414 3.38733 0.905301
1515 −2.05875 3.28048i −0.531567 0.847016i
1616 −1.00000 −0.250000
1717 −3.70534 + 3.70534i −0.898678 + 0.898678i −0.995319 0.0966412i 0.969190π-0.969190\pi
0.0966412 + 0.995319i 0.469190π0.469190\pi
1818 2.88592 + 0.819423i 0.680218 + 0.193140i
1919 7.16937i 1.64477i 0.568934 + 0.822383i 0.307356π0.307356\pi
−0.568934 + 0.822383i 0.692644π0.692644\pi
2020 1.03122 1.98408i 0.230588 0.443654i
2121 −1.47636 5.67823i −0.322168 1.23909i
2222 −0.0270962 0.0270962i −0.00577693 0.00577693i
2323 3.94658 + 3.94658i 0.822918 + 0.822918i 0.986525 0.163608i 0.0523131π-0.0523131\pi
−0.163608 + 0.986525i 0.552313π0.552313\pi
2424 0.435847 + 1.67632i 0.0889669 + 0.342177i
2525 2.87317 + 4.09205i 0.574634 + 0.818410i
2626 3.42565i 0.671825i
2727 0.115791 5.19486i 0.0222840 0.999752i
2828 2.39520 2.39520i 0.452651 0.452651i
2929 −3.49394 −0.648809 −0.324404 0.945919i 0.605164π-0.605164\pi
−0.324404 + 0.945919i 0.605164π0.605164\pi
3030 −3.77541 0.863894i −0.689292 0.157725i
3131 −1.00000 −0.179605
3232 −0.707107 + 0.707107i −0.125000 + 0.125000i
3333 −0.0336120 + 0.0572316i −0.00585110 + 0.00996275i
3434 5.24015i 0.898678i
3535 2.28230 + 7.22226i 0.385779 + 1.22078i
3636 2.62007 1.46124i 0.436679 0.243539i
3737 −4.89823 4.89823i −0.805265 0.805265i 0.178648 0.983913i 0.442828π-0.442828\pi
−0.983913 + 0.178648i 0.942828π0.942828\pi
3838 5.06951 + 5.06951i 0.822383 + 0.822383i
3939 5.74247 1.49306i 0.919531 0.239081i
4040 −0.673776 2.13214i −0.106533 0.337121i
4141 10.1701i 1.58830i −0.607723 0.794149i 0.707917π-0.707917\pi
0.607723 0.794149i 0.292083π-0.292083\pi
4242 −5.05906 2.97117i −0.780630 0.458462i
4343 −6.93875 + 6.93875i −1.05815 + 1.05815i −0.0599483 + 0.998201i 0.519094π0.519094\pi
−0.998201 + 0.0599483i 0.980906π0.980906\pi
4444 −0.0383198 −0.00577693
4545 0.197341 + 6.70530i 0.0294178 + 0.999567i
4646 5.58130 0.822918
4747 7.35619 7.35619i 1.07301 1.07301i 0.0758955 0.997116i 0.475818π-0.475818\pi
0.997116 0.0758955i 0.0241815π-0.0241815\pi
4848 1.49353 + 0.877144i 0.215572 + 0.126605i
4949 4.47399i 0.639141i
5050 4.92516 + 0.861878i 0.696522 + 0.121888i
5151 8.78415 2.28390i 1.23003 0.319811i
5252 2.42230 + 2.42230i 0.335912 + 0.335912i
5353 0.287477 + 0.287477i 0.0394880 + 0.0394880i 0.726575 0.687087i 0.241111π-0.241111\pi
−0.687087 + 0.726575i 0.741111π0.741111\pi
5454 −3.59145 3.75520i −0.488734 0.511018i
5555 0.0395162 0.0760297i 0.00532836 0.0102518i
5656 3.38733i 0.452651i
5757 6.28857 10.7076i 0.832942 1.41826i
5858 −2.47059 + 2.47059i −0.324404 + 0.324404i
5959 15.0023 1.95314 0.976568 0.215211i 0.0690439π-0.0690439\pi
0.976568 + 0.215211i 0.0690439π0.0690439\pi
6060 −3.28048 + 2.05875i −0.423508 + 0.265783i
6161 5.16656 0.661511 0.330755 0.943717i 0.392697π-0.392697\pi
0.330755 + 0.943717i 0.392697π0.392697\pi
6262 −0.707107 + 0.707107i −0.0898027 + 0.0898027i
6363 −2.77565 + 9.77556i −0.349699 + 1.23161i
6464 1.00000i 0.125000i
6565 −7.30396 + 2.30812i −0.905945 + 0.286287i
6666 0.0167016 + 0.0642362i 0.00205582 + 0.00790693i
6767 5.80813 + 5.80813i 0.709576 + 0.709576i 0.966446 0.256870i 0.0826912π-0.0826912\pi
−0.256870 + 0.966446i 0.582691π0.582691\pi
6868 3.70534 + 3.70534i 0.449339 + 0.449339i
6969 −2.43259 9.35603i −0.292850 1.12633i
7070 6.72074 + 3.49308i 0.803282 + 0.417503i
7171 9.58222i 1.13720i −0.822614 0.568600i 0.807485π-0.807485\pi
0.822614 0.568600i 0.192515π-0.192515\pi
7272 0.819423 2.88592i 0.0965699 0.340109i
7373 9.96911 9.96911i 1.16680 1.16680i 0.183840 0.982956i 0.441147π-0.441147\pi
0.982956 0.183840i 0.0588529π-0.0588529\pi
7474 −6.92715 −0.805265
7575 −0.701836 8.63177i −0.0810410 0.996711i
7676 7.16937 0.822383
7777 0.0917837 0.0917837i 0.0104597 0.0104597i
7878 3.00479 5.11629i 0.340225 0.579306i
7979 16.7308i 1.88236i −0.337908 0.941179i 0.609719π-0.609719\pi
0.337908 0.941179i 0.390281π-0.390281\pi
8080 −1.98408 1.03122i −0.221827 0.115294i
8181 −4.72958 + 7.65709i −0.525509 + 0.850788i
8282 −7.19133 7.19133i −0.794149 0.794149i
8383 8.18895 + 8.18895i 0.898855 + 0.898855i 0.995335 0.0964803i 0.0307585π-0.0307585\pi
−0.0964803 + 0.995335i 0.530758π0.530758\pi
8484 −5.67823 + 1.47636i −0.619546 + 0.161084i
8585 −11.1727 + 3.53069i −1.21185 + 0.382957i
8686 9.81288i 1.05815i
8787 5.21829 + 3.06469i 0.559459 + 0.328569i
8888 −0.0270962 + 0.0270962i −0.00288847 + 0.00288847i
8989 −3.51450 −0.372536 −0.186268 0.982499i 0.559639π-0.559639\pi
−0.186268 + 0.982499i 0.559639π0.559639\pi
9090 4.88090 + 4.60182i 0.514493 + 0.485075i
9191 −11.6038 −1.21641
9292 3.94658 3.94658i 0.411459 0.411459i
9393 1.49353 + 0.877144i 0.154871 + 0.0909556i
9494 10.4032i 1.07301i
9595 −7.39319 + 14.2246i −0.758526 + 1.45942i
9696 1.67632 0.435847i 0.171088 0.0444835i
9797 −2.47587 2.47587i −0.251386 0.251386i 0.570153 0.821539i 0.306884π-0.306884\pi
−0.821539 + 0.570153i 0.806884π0.806884\pi
9898 3.16359 + 3.16359i 0.319570 + 0.319570i
9999 0.100401 0.0559943i 0.0100907 0.00562764i
100100 4.09205 2.87317i 0.409205 0.287317i
101101 7.43842i 0.740150i −0.929002 0.370075i 0.879332π-0.879332\pi
0.929002 0.370075i 0.120668π-0.120668\pi
102102 4.59637 7.82630i 0.455108 0.774919i
103103 −3.85645 + 3.85645i −0.379987 + 0.379987i −0.871097 0.491110i 0.836591π-0.836591\pi
0.491110 + 0.871097i 0.336591π0.336591\pi
104104 3.42565 0.335912
105105 2.92629 12.7885i 0.285577 1.24803i
106106 0.406553 0.0394880
107107 −12.8902 + 12.8902i −1.24614 + 1.24614i −0.288732 + 0.957410i 0.593234π0.593234\pi
−0.957410 + 0.288732i 0.906766π0.906766\pi
108108 −5.19486 0.115791i −0.499876 0.0111420i
109109 0.836888i 0.0801593i 0.999196 + 0.0400796i 0.0127612π0.0127612\pi
−0.999196 + 0.0400796i 0.987239π0.987239\pi
110110 −0.0258190 0.0817033i −0.00246174 0.00779010i
111111 3.01918 + 11.6121i 0.286568 + 1.10217i
112112 −2.39520 2.39520i −0.226325 0.226325i
113113 −12.2848 12.2848i −1.15566 1.15566i −0.985400 0.170256i 0.945540π-0.945540\pi
−0.170256 0.985400i 0.554460π-0.554460\pi
114114 −3.12475 12.0181i −0.292660 1.12560i
115115 3.76055 + 11.9001i 0.350673 + 1.10969i
116116 3.49394i 0.324404i
117117 −9.88615 2.80705i −0.913975 0.259512i
118118 10.6082 10.6082i 0.976568 0.976568i
119119 −17.7501 −1.62715
120120 −0.863894 + 3.77541i −0.0788623 + 0.344646i
121121 10.9985 0.999867
122122 3.65331 3.65331i 0.330755 0.330755i
123123 −8.92062 + 15.1893i −0.804345 + 1.36957i
124124 1.00000i 0.0898027i
125125 1.48081 + 11.0818i 0.132448 + 0.991190i
126126 4.94968 + 8.87505i 0.440953 + 0.790652i
127127 7.40826 + 7.40826i 0.657377 + 0.657377i 0.954759 0.297382i 0.0961135π-0.0961135\pi
−0.297382 + 0.954759i 0.596113π0.596113\pi
128128 0.707107 + 0.707107i 0.0625000 + 0.0625000i
129129 16.4495 4.27691i 1.44830 0.376561i
130130 −3.53259 + 6.79677i −0.309829 + 0.596116i
131131 16.8454i 1.47179i −0.677098 0.735893i 0.736763π-0.736763\pi
0.677098 0.735893i 0.263237π-0.263237\pi
132132 0.0572316 + 0.0336120i 0.00498137 + 0.00292555i
133133 −17.1721 + 17.1721i −1.48901 + 1.48901i
134134 8.21393 0.709576
135135 5.58678 10.1876i 0.480834 0.876812i
136136 5.24015 0.449339
137137 −2.39174 + 2.39174i −0.204340 + 0.204340i −0.801856 0.597517i 0.796154π-0.796154\pi
0.597517 + 0.801856i 0.296154π0.296154\pi
138138 −8.33581 4.89561i −0.709592 0.416742i
139139 4.41411i 0.374400i 0.982322 + 0.187200i 0.0599412π0.0599412\pi
−0.982322 + 0.187200i 0.940059π0.940059\pi
140140 7.22226 2.28230i 0.610392 0.192890i
141141 −17.4391 + 4.53422i −1.46864 + 0.381850i
142142 −6.77566 6.77566i −0.568600 0.568600i
143143 0.0928221 + 0.0928221i 0.00776217 + 0.00776217i
144144 −1.46124 2.62007i −0.121770 0.218340i
145145 −6.93227 3.60302i −0.575694 0.299215i
146146 14.0985i 1.16680i
147147 3.92433 6.68201i 0.323673 0.551123i
148148 −4.89823 + 4.89823i −0.402632 + 0.402632i
149149 −5.68468 −0.465707 −0.232853 0.972512i 0.574806π-0.574806\pi
−0.232853 + 0.972512i 0.574806π0.574806\pi
150150 −6.59985 5.60731i −0.538876 0.457835i
151151 6.13286 0.499085 0.249542 0.968364i 0.419720π-0.419720\pi
0.249542 + 0.968364i 0.419720π0.419720\pi
152152 5.06951 5.06951i 0.411191 0.411191i
153153 −15.1227 4.29390i −1.22259 0.347141i
154154 0.129802i 0.0104597i
155155 −1.98408 1.03122i −0.159365 0.0828296i
156156 −1.49306 5.74247i −0.119540 0.459765i
157157 −1.92479 1.92479i −0.153615 0.153615i 0.626116 0.779730i 0.284644π-0.284644\pi
−0.779730 + 0.626116i 0.784644π0.784644\pi
158158 −11.8304 11.8304i −0.941179 0.941179i
159159 −0.177195 0.681512i −0.0140525 0.0540474i
160160 −2.13214 + 0.673776i −0.168561 + 0.0532667i
161161 18.9057i 1.48998i
162162 2.07006 + 8.75870i 0.162640 + 0.688149i
163163 −8.59083 + 8.59083i −0.672886 + 0.672886i −0.958380 0.285494i 0.907842π-0.907842\pi
0.285494 + 0.958380i 0.407842π0.407842\pi
164164 −10.1701 −0.794149
165165 −0.125707 + 0.0788910i −0.00978631 + 0.00614165i
166166 11.5809 0.898855
167167 −1.68138 + 1.68138i −0.130109 + 0.130109i −0.769163 0.639053i 0.779326π-0.779326\pi
0.639053 + 0.769163i 0.279326π0.279326\pi
168168 −2.97117 + 5.05906i −0.229231 + 0.390315i
169169 1.26494i 0.0973032i
170170 −5.40374 + 10.3969i −0.414448 + 0.797405i
171171 −18.7843 + 10.4761i −1.43647 + 0.801130i
172172 6.93875 + 6.93875i 0.529075 + 0.529075i
173173 0.350482 + 0.350482i 0.0266466 + 0.0266466i 0.720305 0.693658i 0.244002π-0.244002\pi
−0.693658 + 0.720305i 0.744002π0.744002\pi
174174 5.85695 1.52282i 0.444014 0.115445i
175175 −2.91946 + 16.6831i −0.220691 + 1.26113i
176176 0.0383198i 0.00288847i
177177 −22.4063 13.1592i −1.68416 0.989106i
178178 −2.48513 + 2.48513i −0.186268 + 0.186268i
179179 1.82086 0.136097 0.0680486 0.997682i 0.478323π-0.478323\pi
0.0680486 + 0.997682i 0.478323π0.478323\pi
180180 6.70530 0.197341i 0.499784 0.0147089i
181181 18.7741 1.39547 0.697733 0.716358i 0.254192π-0.254192\pi
0.697733 + 0.716358i 0.254192π0.254192\pi
182182 −8.20512 + 8.20512i −0.608204 + 0.608204i
183183 −7.71639 4.53182i −0.570412 0.335002i
184184 5.58130i 0.411459i
185185 −4.66735 14.7697i −0.343150 1.08589i
186186 1.67632 0.435847i 0.122913 0.0319579i
187187 0.141988 + 0.141988i 0.0103832 + 0.0103832i
188188 −7.35619 7.35619i −0.536506 0.536506i
189189 12.7201 12.1654i 0.925250 0.884903i
190190 4.83055 + 15.2861i 0.350445 + 1.10897i
191191 5.71872i 0.413792i −0.978363 0.206896i 0.933664π-0.933664\pi
0.978363 0.206896i 0.0663362π-0.0663362\pi
192192 0.877144 1.49353i 0.0633024 0.107786i
193193 2.43627 2.43627i 0.175366 0.175366i −0.613966 0.789332i 0.710427π-0.710427\pi
0.789332 + 0.613966i 0.210427π0.210427\pi
194194 −3.50140 −0.251386
195195 12.9332 + 2.95939i 0.926166 + 0.211927i
196196 4.47399 0.319570
197197 1.37187 1.37187i 0.0977414 0.0977414i −0.656545 0.754287i 0.727983π-0.727983\pi
0.754287 + 0.656545i 0.227983π0.227983\pi
198198 0.0314001 0.110588i 0.00223151 0.00785915i
199199 5.04179i 0.357403i −0.983903 0.178701i 0.942810π-0.942810\pi
0.983903 0.178701i 0.0571896π-0.0571896\pi
200200 0.861878 4.92516i 0.0609440 0.348261i
201201 −3.58002 13.7692i −0.252515 0.971201i
202202 −5.25975 5.25975i −0.370075 0.370075i
203203 −8.36870 8.36870i −0.587367 0.587367i
204204 −2.28390 8.78415i −0.159905 0.615013i
205205 10.4876 20.1783i 0.732484 1.40931i
206206 5.45384i 0.379987i
207207 −4.57344 + 16.1072i −0.317876 + 1.11953i
208208 2.42230 2.42230i 0.167956 0.167956i
209209 0.274729 0.0190034
210210 −6.97366 11.1121i −0.481228 0.766805i
211211 25.9870 1.78902 0.894510 0.447049i 0.147525π-0.147525\pi
0.894510 + 0.447049i 0.147525π0.147525\pi
212212 0.287477 0.287477i 0.0197440 0.0197440i
213213 −8.40499 + 14.3113i −0.575901 + 0.980594i
214214 18.2295i 1.24614i
215215 −20.9224 + 6.61168i −1.42690 + 0.450913i
216216 −3.75520 + 3.59145i −0.255509 + 0.244367i
217217 −2.39520 2.39520i −0.162597 0.162597i
218218 0.591769 + 0.591769i 0.0400796 + 0.0400796i
219219 −23.6335 + 6.14477i −1.59700 + 0.415225i
220220 −0.0760297 0.0395162i −0.00512592 0.00266418i
221221 17.9509i 1.20751i
222222 10.3459 + 6.07611i 0.694369 + 0.407802i
223223 −4.78005 + 4.78005i −0.320096 + 0.320096i −0.848804 0.528708i 0.822677π-0.822677\pi
0.528708 + 0.848804i 0.322677π0.322677\pi
224224 −3.38733 −0.226325
225225 −6.52310 + 13.5074i −0.434873 + 0.900492i
226226 −17.3733 −1.15566
227227 7.48071 7.48071i 0.496512 0.496512i −0.413838 0.910350i 0.635812π-0.635812\pi
0.910350 + 0.413838i 0.135812π0.135812\pi
228228 −10.7076 6.28857i −0.709130 0.416471i
229229 1.28796i 0.0851107i 0.999094 + 0.0425553i 0.0135499π0.0135499\pi
−0.999094 + 0.0425553i 0.986450π0.986450\pi
230230 11.0738 + 5.75555i 0.730182 + 0.379510i
231231 −0.217589 + 0.0565738i −0.0143163 + 0.00372228i
232232 2.47059 + 2.47059i 0.162202 + 0.162202i
233233 −2.55890 2.55890i −0.167639 0.167639i 0.618302 0.785941i 0.287821π-0.287821\pi
−0.785941 + 0.618302i 0.787821π0.787821\pi
234234 −8.97545 + 5.00568i −0.586744 + 0.327231i
235235 22.1812 7.00945i 1.44694 0.457246i
236236 15.0023i 0.976568i
237237 −14.6753 + 24.9878i −0.953263 + 1.62313i
238238 −12.5512 + 12.5512i −0.813574 + 0.813574i
239239 −11.0066 −0.711956 −0.355978 0.934494i 0.615852π-0.615852\pi
−0.355978 + 0.934494i 0.615852π0.615852\pi
240240 2.05875 + 3.28048i 0.132892 + 0.211754i
241241 5.18138 0.333762 0.166881 0.985977i 0.446630π-0.446630\pi
0.166881 + 0.985977i 0.446630π0.446630\pi
242242 7.77714 7.77714i 0.499933 0.499933i
243243 13.7801 7.28754i 0.883995 0.467496i
244244 5.16656i 0.330755i
245245 −4.61366 + 8.87676i −0.294756 + 0.567115i
246246 4.43260 + 17.0483i 0.282612 + 1.08696i
247247 −17.3663 17.3663i −1.10499 1.10499i
248248 0.707107 + 0.707107i 0.0449013 + 0.0449013i
249249 −5.04752 19.4133i −0.319873 1.23027i
250250 8.88313 + 6.78896i 0.561819 + 0.429371i
251251 10.9548i 0.691460i −0.938334 0.345730i 0.887631π-0.887631\pi
0.938334 0.345730i 0.112369π-0.112369\pi
252252 9.77556 + 2.77565i 0.615803 + 0.174850i
253253 0.151232 0.151232i 0.00950788 0.00950788i
254254 10.4769 0.657377
255255 19.7837 + 4.52693i 1.23890 + 0.283487i
256256 1.00000 0.0625000
257257 −2.60182 + 2.60182i −0.162297 + 0.162297i −0.783583 0.621286i 0.786610π-0.786610\pi
0.621286 + 0.783583i 0.286610π0.286610\pi
258258 8.60731 14.6558i 0.535868 0.912429i
259259 23.4645i 1.45801i
260260 2.30812 + 7.30396i 0.143144 + 0.452973i
261261 −5.10547 9.15439i −0.316021 0.566642i
262262 −11.9115 11.9115i −0.735893 0.735893i
263263 12.9412 + 12.9412i 0.797990 + 0.797990i 0.982778 0.184788i 0.0591599π-0.0591599\pi
−0.184788 + 0.982778i 0.559160π0.559160\pi
264264 0.0642362 0.0167016i 0.00395346 0.00102791i
265265 0.273926 + 0.866829i 0.0168271 + 0.0532489i
266266 24.2850i 1.48901i
267267 5.24899 + 3.08272i 0.321233 + 0.188660i
268268 5.80813 5.80813i 0.354788 0.354788i
269269 −9.27758 −0.565664 −0.282832 0.959169i 0.591274π-0.591274\pi
−0.282832 + 0.959169i 0.591274π0.591274\pi
270270 −3.25329 11.1542i −0.197989 0.678823i
271271 30.1199 1.82965 0.914826 0.403847i 0.132327π-0.132327\pi
0.914826 + 0.403847i 0.132327π0.132327\pi
272272 3.70534 3.70534i 0.224670 0.224670i
273273 17.3306 + 10.1782i 1.04889 + 0.616012i
274274 3.38243i 0.204340i
275275 0.156807 0.110099i 0.00945580 0.00663925i
276276 −9.35603 + 2.43259i −0.563167 + 0.146425i
277277 13.4595 + 13.4595i 0.808703 + 0.808703i 0.984438 0.175735i 0.0562302π-0.0562302\pi
−0.175735 + 0.984438i 0.556230π0.556230\pi
278278 3.12125 + 3.12125i 0.187200 + 0.187200i
279279 −1.46124 2.62007i −0.0874819 0.156860i
280280 3.49308 6.72074i 0.208751 0.401641i
281281 0.798668i 0.0476445i −0.999716 0.0238223i 0.992416π-0.992416\pi
0.999716 0.0238223i 0.00758358π-0.00758358\pi
282282 −9.12513 + 15.5375i −0.543394 + 0.925244i
283283 7.42997 7.42997i 0.441666 0.441666i −0.450906 0.892572i 0.648899π-0.648899\pi
0.892572 + 0.450906i 0.148899π0.148899\pi
284284 −9.58222 −0.568600
285285 23.5190 14.7599i 1.39314 0.874303i
286286 0.131270 0.00776217
287287 24.3594 24.3594i 1.43789 1.43789i
288288 −2.88592 0.819423i −0.170055 0.0482850i
289289 10.4592i 0.615245i
290290 −7.44958 + 2.35413i −0.437454 + 0.138240i
291291 1.52608 + 5.86946i 0.0894602 + 0.344074i
292292 −9.96911 9.96911i −0.583398 0.583398i
293293 9.23580 + 9.23580i 0.539561 + 0.539561i 0.923400 0.383839i 0.125398π-0.125398\pi
−0.383839 + 0.923400i 0.625398π0.625398\pi
294294 −1.94997 7.49982i −0.113725 0.437398i
295295 29.7658 + 15.4707i 1.73303 + 0.900738i
296296 6.92715i 0.402632i
297297 −0.199066 0.00443709i −0.0115510 0.000257466i
298298 −4.01967 + 4.01967i −0.232853 + 0.232853i
299299 −19.1196 −1.10571
300300 −8.63177 + 0.701836i −0.498355 + 0.0405205i
301301 −33.2394 −1.91589
302302 4.33659 4.33659i 0.249542 0.249542i
303303 −6.52456 + 11.1095i −0.374826 + 0.638222i
304304 7.16937i 0.411191i
305305 10.2509 + 5.32786i 0.586964 + 0.305072i
306306 −13.7296 + 7.65709i −0.784868 + 0.437727i
307307 12.8688 + 12.8688i 0.734461 + 0.734461i 0.971500 0.237039i 0.0761769π-0.0761769\pi
−0.237039 + 0.971500i 0.576177π0.576177\pi
308308 −0.0917837 0.0917837i −0.00522986 0.00522986i
309309 9.14236 2.37704i 0.520091 0.135225i
310310 −2.13214 + 0.673776i −0.121097 + 0.0382679i
311311 23.7802i 1.34845i 0.738526 + 0.674226i 0.235522π0.235522\pi
−0.738526 + 0.674226i 0.764478π0.764478\pi
312312 −5.11629 3.00479i −0.289653 0.170113i
313313 2.99407 2.99407i 0.169235 0.169235i −0.617408 0.786643i 0.711817π-0.711817\pi
0.786643 + 0.617408i 0.211817π0.211817\pi
314314 −2.72206 −0.153615
315315 −15.5879 + 16.5332i −0.878277 + 0.931541i
316316 −16.7308 −0.941179
317317 −18.9997 + 18.9997i −1.06713 + 1.06713i −0.0695500 + 0.997578i 0.522156π0.522156\pi
−0.997578 + 0.0695500i 0.977844π0.977844\pi
318318 −0.607198 0.356606i −0.0340500 0.0199975i
319319 0.133887i 0.00749625i
320320 −1.03122 + 1.98408i −0.0576469 + 0.110914i
321321 30.5584 7.94527i 1.70560 0.443462i
322322 13.3683 + 13.3683i 0.744989 + 0.744989i
323323 −26.5650 26.5650i −1.47812 1.47812i
324324 7.65709 + 4.72958i 0.425394 + 0.262754i
325325 −16.8718 2.95249i −0.935882 0.163775i
326326 12.1493i 0.672886i
327327 0.734071 1.24991i 0.0405942 0.0691203i
328328 −7.19133 + 7.19133i −0.397075 + 0.397075i
329329 35.2391 1.94280
330330 −0.0331043 + 0.144673i −0.00182233 + 0.00796398i
331331 −3.70761 −0.203789 −0.101894 0.994795i 0.532490π-0.532490\pi
−0.101894 + 0.994795i 0.532490π0.532490\pi
332332 8.18895 8.18895i 0.449427 0.449427i
333333 5.67626 19.9912i 0.311057 1.09551i
334334 2.37783i 0.130109i
335335 5.53435 + 17.5133i 0.302374 + 0.956852i
336336 1.47636 + 5.67823i 0.0805419 + 0.309773i
337337 −6.75125 6.75125i −0.367764 0.367764i 0.498897 0.866661i 0.333738π-0.333738\pi
−0.866661 + 0.498897i 0.833738π0.833738\pi
338338 0.894449 + 0.894449i 0.0486516 + 0.0486516i
339339 7.57211 + 29.1232i 0.411261 + 1.58175i
340340 3.53069 + 11.1727i 0.191478 + 0.605927i
341341 0.0383198i 0.00207514i
342342 −5.87474 + 20.6902i −0.317670 + 1.11880i
343343 6.05031 6.05031i 0.326686 0.326686i
344344 9.81288 0.529075
345345 4.82165 21.0717i 0.259589 1.13446i
346346 0.495656 0.0266466
347347 6.23364 6.23364i 0.334640 0.334640i −0.519706 0.854345i 0.673958π-0.673958\pi
0.854345 + 0.519706i 0.173958π0.173958\pi
348348 3.06469 5.21829i 0.164285 0.279730i
349349 21.2431i 1.13712i 0.822643 + 0.568558i 0.192498π0.192498\pi
−0.822643 + 0.568558i 0.807502π0.807502\pi
350350 9.73237 + 13.8611i 0.520217 + 0.740908i
351351 12.3030 + 12.8640i 0.656687 + 0.686629i
352352 0.0270962 + 0.0270962i 0.00144423 + 0.00144423i
353353 −17.2207 17.2207i −0.916566 0.916566i 0.0802115 0.996778i 0.474440π-0.474440\pi
−0.996778 + 0.0802115i 0.974440π0.974440\pi
354354 −25.1486 + 6.53872i −1.33663 + 0.347529i
355355 9.88138 19.0119i 0.524449 1.00905i
356356 3.51450i 0.186268i
357357 26.5102 + 15.5694i 1.40307 + 0.824020i
358358 1.28754 1.28754i 0.0680486 0.0680486i
359359 9.65176 0.509400 0.254700 0.967020i 0.418023π-0.418023\pi
0.254700 + 0.967020i 0.418023π0.418023\pi
360360 4.60182 4.88090i 0.242537 0.257246i
361361 −32.3998 −1.70526
362362 13.2753 13.2753i 0.697733 0.697733i
363363 −16.4266 9.64730i −0.862172 0.506352i
364364 11.6038i 0.608204i
365365 30.0599 9.49920i 1.57341 0.497211i
366366 −8.66080 + 2.25183i −0.452707 + 0.117705i
367367 −8.60226 8.60226i −0.449034 0.449034i 0.445999 0.895033i 0.352848π-0.352848\pi
−0.895033 + 0.445999i 0.852848π0.852848\pi
368368 −3.94658 3.94658i −0.205729 0.205729i
369369 26.6464 14.8609i 1.38715 0.773626i
370370 −13.7440 7.14341i −0.714519 0.371368i
371371 1.37713i 0.0714970i
372372 0.877144 1.49353i 0.0454778 0.0774357i
373373 −4.18624 + 4.18624i −0.216756 + 0.216756i −0.807130 0.590374i 0.798980π-0.798980\pi
0.590374 + 0.807130i 0.298980π0.298980\pi
374374 0.200802 0.0103832
375375 7.50875 17.8499i 0.387750 0.921765i
376376 −10.4032 −0.536506
377377 8.46337 8.46337i 0.435886 0.435886i
378378 0.392222 17.5967i 0.0201737 0.905076i
379379 16.0997i 0.826988i −0.910507 0.413494i 0.864308π-0.864308\pi
0.910507 0.413494i 0.135692π-0.135692\pi
380380 14.2246 + 7.39319i 0.729708 + 0.379263i
381381 −4.56631 17.5625i −0.233939 0.899756i
382382 −4.04375 4.04375i −0.206896 0.206896i
383383 3.06182 + 3.06182i 0.156452 + 0.156452i 0.780992 0.624541i 0.214714π-0.214714\pi
−0.624541 + 0.780992i 0.714714π0.714714\pi
384384 −0.435847 1.67632i −0.0222417 0.0855442i
385385 0.276756 0.0874574i 0.0141048 0.00445724i
386386 3.44540i 0.175366i
387387 −28.3192 8.04090i −1.43955 0.408742i
388388 −2.47587 + 2.47587i −0.125693 + 0.125693i
389389 −3.48655 −0.176775 −0.0883874 0.996086i 0.528171π-0.528171\pi
−0.0883874 + 0.996086i 0.528171π0.528171\pi
390390 11.2378 7.05255i 0.569046 0.357120i
391391 −29.2468 −1.47908
392392 3.16359 3.16359i 0.159785 0.159785i
393393 −14.7758 + 25.1590i −0.745341 + 1.26910i
394394 1.94011i 0.0977414i
395395 17.2531 33.1952i 0.868097 1.67023i
396396 −0.0559943 0.100401i −0.00281382 0.00504533i
397397 −19.3189 19.3189i −0.969587 0.969587i 0.0299644 0.999551i 0.490461π-0.490461\pi
−0.999551 + 0.0299644i 0.990461π0.990461\pi
398398 −3.56508 3.56508i −0.178701 0.178701i
399399 40.7093 10.5845i 2.03802 0.529890i
400400 −2.87317 4.09205i −0.143659 0.204603i
401401 9.08809i 0.453837i −0.973914 0.226919i 0.927135π-0.927135\pi
0.973914 0.226919i 0.0728652π-0.0728652\pi
402402 −12.2677 7.20481i −0.611858 0.359343i
403403 2.42230 2.42230i 0.120663 0.120663i
404404 −7.43842 −0.370075
405405 −17.2800 + 10.3151i −0.858651 + 0.512560i
406406 −11.8351 −0.587367
407407 −0.187699 + 0.187699i −0.00930392 + 0.00930392i
408408 −7.82630 4.59637i −0.387459 0.227554i
409409 15.9929i 0.790800i 0.918509 + 0.395400i 0.129394π0.129394\pi
−0.918509 + 0.395400i 0.870606π0.870606\pi
410410 −6.85235 21.6840i −0.338414 1.07090i
411411 5.67002 1.47422i 0.279681 0.0727179i
412412 3.85645 + 3.85645i 0.189994 + 0.189994i
413413 35.9336 + 35.9336i 1.76818 + 1.76818i
414414 8.15560 + 14.6234i 0.400826 + 0.718702i
415415 7.80296 + 24.6922i 0.383032 + 1.21209i
416416 3.42565i 0.167956i
417417 3.87181 6.59258i 0.189603 0.322840i
418418 0.194263 0.194263i 0.00950170 0.00950170i
419419 −22.1030 −1.07980 −0.539900 0.841729i 0.681538π-0.681538\pi
−0.539900 + 0.841729i 0.681538π0.681538\pi
420420 −12.7885 2.92629i −0.624017 0.142788i
421421 −23.3654 −1.13876 −0.569381 0.822074i 0.692817π-0.692817\pi
−0.569381 + 0.822074i 0.692817π0.692817\pi
422422 18.3756 18.3756i 0.894510 0.894510i
423423 30.0229 + 8.52464i 1.45976 + 0.414482i
424424 0.406553i 0.0197440i
425425 −25.8086 4.51637i −1.25190 0.219076i
426426 4.17639 + 16.0628i 0.202347 + 0.778247i
427427 12.3750 + 12.3750i 0.598866 + 0.598866i
428428 12.8902 + 12.8902i 0.623071 + 0.623071i
429429 −0.0572138 0.220050i −0.00276231 0.0106241i
430430 −10.1192 + 19.4696i −0.487993 + 0.938906i
431431 5.05677i 0.243576i 0.992556 + 0.121788i 0.0388628π0.0388628\pi
−0.992556 + 0.121788i 0.961137π0.961137\pi
432432 −0.115791 + 5.19486i −0.00557100 + 0.249938i
433433 14.4819 14.4819i 0.695955 0.695955i −0.267581 0.963535i 0.586224π-0.586224\pi
0.963535 + 0.267581i 0.0862242π0.0862242\pi
434434 −3.38733 −0.162597
435435 7.19315 + 11.4618i 0.344885 + 0.549551i
436436 0.836888 0.0400796
437437 −28.2945 + 28.2945i −1.35351 + 1.35351i
438438 −12.3664 + 21.0564i −0.590888 + 1.00611i
439439 29.8494i 1.42463i −0.701858 0.712317i 0.747646π-0.747646\pi
0.701858 0.712317i 0.252354π-0.252354\pi
440440 −0.0817033 + 0.0258190i −0.00389505 + 0.00123087i
441441 −11.7222 + 6.53755i −0.558199 + 0.311312i
442442 −12.6932 12.6932i −0.603754 0.603754i
443443 6.49714 + 6.49714i 0.308688 + 0.308688i 0.844401 0.535712i 0.179957π-0.179957\pi
−0.535712 + 0.844401i 0.679957π0.679957\pi
444444 11.6121 3.01918i 0.551086 0.143284i
445445 −6.97306 3.62422i −0.330555 0.171805i
446446 6.76001i 0.320096i
447447 8.49021 + 4.98628i 0.401573 + 0.235843i
448448 −2.39520 + 2.39520i −0.113163 + 0.113163i
449449 15.1932 0.717012 0.358506 0.933527i 0.383286π-0.383286\pi
0.358506 + 0.933527i 0.383286π0.383286\pi
450450 4.93863 + 14.1637i 0.232809 + 0.667682i
451451 −0.389716 −0.0183510
452452 −12.2848 + 12.2848i −0.577828 + 0.577828i
453453 −9.15958 5.37940i −0.430355 0.252746i
454454 10.5793i 0.496512i
455455 −23.0229 11.9661i −1.07933 0.560977i
456456 −12.0181 + 3.12475i −0.562801 + 0.146330i
457457 −8.92437 8.92437i −0.417464 0.417464i 0.466864 0.884329i 0.345384π-0.345384\pi
−0.884329 + 0.466864i 0.845384π0.845384\pi
458458 0.910724 + 0.910724i 0.0425553 + 0.0425553i
459459 18.8197 + 19.6778i 0.878429 + 0.918481i
460460 11.9001 3.76055i 0.554846 0.175336i
461461 9.87377i 0.459867i −0.973206 0.229934i 0.926149π-0.926149\pi
0.973206 0.229934i 0.0738509π-0.0738509\pi
462462 −0.113855 + 0.193862i −0.00529701 + 0.00901929i
463463 −10.7503 + 10.7503i −0.499609 + 0.499609i −0.911316 0.411707i 0.864933π-0.864933\pi
0.411707 + 0.911316i 0.364933π0.364933\pi
464464 3.49394 0.162202
465465 2.05875 + 3.28048i 0.0954722 + 0.152129i
466466 −3.61884 −0.167639
467467 7.08525 7.08525i 0.327866 0.327866i −0.523908 0.851775i 0.675527π-0.675527\pi
0.851775 + 0.523908i 0.175527π0.175527\pi
468468 −2.80705 + 9.88615i −0.129756 + 0.456987i
469469 27.8233i 1.28476i
470470 10.7280 20.6409i 0.494846 0.952093i
471471 1.18640 + 4.56303i 0.0546665 + 0.210253i
472472 −10.6082 10.6082i −0.488284 0.488284i
473473 0.265892 + 0.265892i 0.0122257 + 0.0122257i
474474 7.29206 + 28.0461i 0.334935 + 1.28820i
475475 −29.3374 + 20.5988i −1.34609 + 0.945139i
476476 17.7501i 0.813574i
477477 −0.333139 + 1.17328i −0.0152534 + 0.0537209i
478478 −7.78283 + 7.78283i −0.355978 + 0.355978i
479479 −39.1461 −1.78863 −0.894316 0.447436i 0.852337π-0.852337\pi
−0.894316 + 0.447436i 0.852337π0.852337\pi
480480 3.77541 + 0.863894i 0.172323 + 0.0394312i
481481 23.7300 1.08199
482482 3.66379 3.66379i 0.166881 0.166881i
483483 16.5830 28.2361i 0.754554 1.28479i
484484 10.9985i 0.499933i
485485 −2.35916 7.46548i −0.107124 0.338990i
486486 4.59095 14.8971i 0.208250 0.675746i
487487 −8.33574 8.33574i −0.377729 0.377729i 0.492554 0.870282i 0.336064π-0.336064\pi
−0.870282 + 0.492554i 0.836064π0.836064\pi
488488 −3.65331 3.65331i −0.165378 0.165378i
489489 20.3660 5.29523i 0.920984 0.239458i
490490 3.01447 + 9.53917i 0.136180 + 0.430936i
491491 18.7400i 0.845722i −0.906195 0.422861i 0.861026π-0.861026\pi
0.906195 0.422861i 0.138974π-0.138974\pi
492492 15.1893 + 8.92062i 0.684785 + 0.402173i
493493 12.9463 12.9463i 0.583070 0.583070i
494494 −24.5597 −1.10499
495495 0.256946 0.00756206i 0.0115489 0.000339890i
496496 1.00000 0.0449013
497497 22.9514 22.9514i 1.02951 1.02951i
498498 −17.2964 10.1581i −0.775071 0.455197i
499499 26.7204i 1.19617i 0.801433 + 0.598084i 0.204071π0.204071\pi
−0.801433 + 0.598084i 0.795929π0.795929\pi
500500 11.0818 1.48081i 0.495595 0.0662238i
501501 3.98600 1.03637i 0.178081 0.0463017i
502502 −7.74621 7.74621i −0.345730 0.345730i
503503 2.30936 + 2.30936i 0.102969 + 0.102969i 0.756715 0.653745i 0.226803π-0.226803\pi
−0.653745 + 0.756715i 0.726803π0.726803\pi
504504 8.87505 4.94968i 0.395326 0.220476i
505505 7.67064 14.7584i 0.341339 0.656742i
506506 0.213874i 0.00950788i
507507 1.10954 1.88922i 0.0492763 0.0839033i
508508 7.40826 7.40826i 0.328688 0.328688i
509509 −8.19351 −0.363171 −0.181586 0.983375i 0.558123π-0.558123\pi
−0.181586 + 0.983375i 0.558123π0.558123\pi
510510 17.1902 10.7882i 0.761195 0.477708i
511511 47.7561 2.11260
512512 0.707107 0.707107i 0.0312500 0.0312500i
513513 37.2439 + 0.830149i 1.64436 + 0.0366520i
514514 3.67953i 0.162297i
515515 −11.6284 + 3.67467i −0.512407 + 0.161925i
516516 −4.27691 16.4495i −0.188281 0.724148i
517517 −0.281888 0.281888i −0.0123974 0.0123974i
518518 −16.5919 16.5919i −0.729007 0.729007i
519519 −0.216030 0.830877i −0.00948268 0.0364714i
520520 6.79677 + 3.53259i 0.298058 + 0.154915i
521521 8.17200i 0.358022i 0.983847 + 0.179011i 0.0572897π0.0572897\pi
−0.983847 + 0.179011i 0.942710π0.942710\pi
522522 −10.0832 2.86302i −0.441332 0.125311i
523523 −15.3859 + 15.3859i −0.672777 + 0.672777i −0.958355 0.285578i 0.907814π-0.907814\pi
0.285578 + 0.958355i 0.407814π0.407814\pi
524524 −16.8454 −0.735893
525525 18.9938 22.3559i 0.828957 0.975690i
526526 18.3017 0.797990
527527 3.70534 3.70534i 0.161407 0.161407i
528528 0.0336120 0.0572316i 0.00146278 0.00249069i
529529 8.15092i 0.354388i
530530 0.806636 + 0.419246i 0.0350380 + 0.0182109i
531531 21.9219 + 39.3072i 0.951330 + 1.70579i
532532 17.1721 + 17.1721i 0.744504 + 0.744504i
533533 24.6350 + 24.6350i 1.06706 + 1.06706i
534534 5.89141 1.53178i 0.254946 0.0662868i
535535 −38.8678 + 12.2826i −1.68040 + 0.531023i
536536 8.21393i 0.354788i
537537 −2.71949 1.59715i −0.117355 0.0689222i
538538 −6.56024 + 6.56024i −0.282832 + 0.282832i
539539 0.171442 0.00738455
540540 −10.1876 5.58678i −0.438406 0.240417i
541541 21.4116 0.920558 0.460279 0.887774i 0.347749π-0.347749\pi
0.460279 + 0.887774i 0.347749π0.347749\pi
542542 21.2980 21.2980i 0.914826 0.914826i
543543 −28.0396 16.4676i −1.20329 0.706691i
544544 5.24015i 0.224670i
545545 −0.863015 + 1.66045i −0.0369675 + 0.0711261i
546546 19.4516 5.05748i 0.832453 0.216440i
547547 −21.2857 21.2857i −0.910110 0.910110i 0.0861708 0.996280i 0.472537π-0.472537\pi
−0.996280 + 0.0861708i 0.972537π0.972537\pi
548548 2.39174 + 2.39174i 0.102170 + 0.102170i
549549 7.54957 + 13.5368i 0.322208 + 0.577736i
550550 0.0330270 0.188731i 0.00140828 0.00804752i
551551 25.0494i 1.06714i
552552 −4.89561 + 8.33581i −0.208371 + 0.354796i
553553 40.0736 40.0736i 1.70410 1.70410i
554554 19.0346 0.808703
555555 −5.98432 + 26.1528i −0.254020 + 1.11012i
556556 4.41411 0.187200
557557 −5.01845 + 5.01845i −0.212639 + 0.212639i −0.805387 0.592749i 0.798043π-0.798043\pi
0.592749 + 0.805387i 0.298043π0.298043\pi
558558 −2.88592 0.819423i −0.122171 0.0346889i
559559 33.6155i 1.42178i
560560 −2.28230 7.22226i −0.0964448 0.305196i
561561 −0.0875188 0.336607i −0.00369505 0.0142116i
562562 −0.564744 0.564744i −0.0238223 0.0238223i
563563 15.0576 + 15.0576i 0.634603 + 0.634603i 0.949219 0.314616i 0.101876π-0.101876\pi
−0.314616 + 0.949219i 0.601876π0.601876\pi
564564 4.53422 + 17.4391i 0.190925 + 0.734319i
565565 −11.7057 37.0424i −0.492464 1.55838i
566566 10.5076i 0.441666i
567567 −29.6686 + 7.01198i −1.24596 + 0.294476i
568568 −6.77566 + 6.77566i −0.284300 + 0.284300i
569569 28.8741 1.21046 0.605232 0.796049i 0.293080π-0.293080\pi
0.605232 + 0.796049i 0.293080π0.293080\pi
570570 6.19357 27.0673i 0.259420 1.13372i
571571 −32.0685 −1.34203 −0.671013 0.741445i 0.734141π-0.734141\pi
−0.671013 + 0.741445i 0.734141π0.734141\pi
572572 0.0928221 0.0928221i 0.00388109 0.00388109i
573573 −5.01615 + 8.54106i −0.209552 + 0.356808i
574574 34.4494i 1.43789i
575575 −4.81040 + 27.4888i −0.200607 + 1.14636i
576576 −2.62007 + 1.46124i −0.109170 + 0.0608848i
577577 −17.0551 17.0551i −0.710014 0.710014i 0.256524 0.966538i 0.417423π-0.417423\pi
−0.966538 + 0.256524i 0.917423π0.917423\pi
578578 −7.39574 7.39574i −0.307622 0.307622i
579579 −5.77559 + 1.50167i −0.240025 + 0.0624073i
580580 −3.60302 + 6.93227i −0.149607 + 0.287847i
581581 39.2284i 1.62747i
582582 5.22943 + 3.07124i 0.216767 + 0.127307i
583583 0.0110161 0.0110161i 0.000456238 0.000456238i
584584 −14.0985 −0.583398
585585 −16.7203 15.7642i −0.691298 0.651770i
586586 13.0614 0.539561
587587 13.9394 13.9394i 0.575340 0.575340i −0.358275 0.933616i 0.616635π-0.616635\pi
0.933616 + 0.358275i 0.116635π0.116635\pi
588588 −6.68201 3.92433i −0.275562 0.161837i
589589 7.16937i 0.295409i
590590 31.9871 10.1082i 1.31689 0.416148i
591591 −3.25224 + 0.845592i −0.133779 + 0.0347830i
592592 4.89823 + 4.89823i 0.201316 + 0.201316i
593593 4.85911 + 4.85911i 0.199540 + 0.199540i 0.799803 0.600263i 0.204937π-0.204937\pi
−0.600263 + 0.799803i 0.704937π0.704937\pi
594594 −0.143899 + 0.137624i −0.00590423 + 0.00564676i
595595 −35.2177 18.3043i −1.44378 0.750401i
596596 5.68468i 0.232853i
597597 −4.42238 + 7.53004i −0.180996 + 0.308184i
598598 −13.5196 + 13.5196i −0.552857 + 0.552857i
599599 1.68745 0.0689475 0.0344738 0.999406i 0.489024π-0.489024\pi
0.0344738 + 0.999406i 0.489024π0.489024\pi
600600 −5.60731 + 6.59985i −0.228917 + 0.269438i
601601 34.0778 1.39006 0.695032 0.718979i 0.255390π-0.255390\pi
0.695032 + 0.718979i 0.255390π0.255390\pi
602602 −23.5038 + 23.5038i −0.957944 + 0.957944i
603603 −6.73069 + 23.7048i −0.274095 + 0.965333i
604604 6.13286i 0.249542i
605605 21.8220 + 11.3419i 0.887191 + 0.461114i
606606 3.24201 + 12.4691i 0.131698 + 0.506524i
607607 28.6914 + 28.6914i 1.16455 + 1.16455i 0.983469 + 0.181079i 0.0579589π0.0579589\pi
0.181079 + 0.983469i 0.442041π0.442041\pi
608608 −5.06951 5.06951i −0.205596 0.205596i
609609 5.15830 + 19.8394i 0.209025 + 0.803934i
610610 11.0158 3.48111i 0.446018 0.140946i
611611 35.6378i 1.44175i
612612 −4.29390 + 15.1227i −0.173571 + 0.611297i
613613 13.7211 13.7211i 0.554190 0.554190i −0.373458 0.927647i 0.621828π-0.621828\pi
0.927647 + 0.373458i 0.121828π0.121828\pi
614614 18.1992 0.734461
615615 −33.3627 + 20.9376i −1.34531 + 0.844287i
616616 −0.129802 −0.00522986
617617 −25.0384 + 25.0384i −1.00801 + 1.00801i −0.00804029 + 0.999968i 0.502559π0.502559\pi
−0.999968 + 0.00804029i 0.997441π0.997441\pi
618618 4.78381 8.14545i 0.192433 0.327658i
619619 31.7434i 1.27587i 0.770088 + 0.637937i 0.220212π0.220212\pi
−0.770088 + 0.637937i 0.779788π0.779788\pi
620620 −1.03122 + 1.98408i −0.0414148 + 0.0796827i
621621 20.9589 20.0449i 0.841051 0.804376i
622622 16.8151 + 16.8151i 0.674226 + 0.674226i
623623 −8.41794 8.41794i −0.337257 0.337257i
624624 −5.74247 + 1.49306i −0.229883 + 0.0597702i
625625 −8.48977 + 23.5143i −0.339591 + 0.940573i
626626 4.23426i 0.169235i
627627 −0.410315 0.240977i −0.0163864 0.00962369i
628628 −1.92479 + 1.92479i −0.0768073 + 0.0768073i
629629 36.2993 1.44735
630630 0.668458 + 22.7130i 0.0266320 + 0.904909i
631631 15.1458 0.602945 0.301472 0.953475i 0.402522π-0.402522\pi
0.301472 + 0.953475i 0.402522π0.402522\pi
632632 −11.8304 + 11.8304i −0.470590 + 0.470590i
633633 −38.8122 22.7944i −1.54265 0.905994i
634634 26.8696i 1.06713i
635635 7.05906 + 22.3381i 0.280130 + 0.886462i
636636 −0.681512 + 0.177195i −0.0270237 + 0.00702624i
637637 −10.8373 10.8373i −0.429391 0.429391i
638638 0.0946726 + 0.0946726i 0.00374812 + 0.00374812i
639639 25.1061 14.0019i 0.993184 0.553906i
640640 0.673776 + 2.13214i 0.0266333 + 0.0842803i
641641 9.65606i 0.381392i 0.981649 + 0.190696i 0.0610744π0.0610744\pi
−0.981649 + 0.190696i 0.938926π0.938926\pi
642642 15.9899 27.2262i 0.631071 1.07453i
643643 −9.67454 + 9.67454i −0.381526 + 0.381526i −0.871652 0.490125i 0.836951π-0.836951\pi
0.490125 + 0.871652i 0.336951π0.336951\pi
644644 18.9057 0.744989
645645 37.0476 + 8.47728i 1.45875 + 0.333793i
646646 −37.5686 −1.47812
647647 27.1946 27.1946i 1.06913 1.06913i 0.0717042 0.997426i 0.477156π-0.477156\pi
0.997426 0.0717042i 0.0228438π-0.0228438\pi
648648 8.75870 2.07006i 0.344074 0.0813198i
649649 0.574886i 0.0225663i
650650 −14.0179 + 9.84247i −0.549828 + 0.386054i
651651 1.47636 + 5.67823i 0.0578630 + 0.222547i
652652 8.59083 + 8.59083i 0.336443 + 0.336443i
653653 21.3008 + 21.3008i 0.833566 + 0.833566i 0.988003 0.154437i 0.0493562π-0.0493562\pi
−0.154437 + 0.988003i 0.549356π0.549356\pi
654654 −0.364755 1.40289i −0.0142631 0.0548573i
655655 17.3713 33.4226i 0.678752 1.30593i
656656 10.1701i 0.397075i
657657 40.6870 + 11.5526i 1.58735 + 0.450710i
658658 24.9178 24.9178i 0.971398 0.971398i
659659 −30.2780 −1.17946 −0.589731 0.807600i 0.700766π-0.700766\pi
−0.589731 + 0.807600i 0.700766π0.700766\pi
660660 0.0788910 + 0.125707i 0.00307083 + 0.00489316i
661661 −12.9343 −0.503087 −0.251544 0.967846i 0.580938π-0.580938\pi
−0.251544 + 0.967846i 0.580938π0.580938\pi
662662 −2.62168 + 2.62168i −0.101894 + 0.101894i
663663 −15.7455 + 26.8101i −0.611506 + 1.04122i
664664 11.5809i 0.449427i
665665 −51.7790 + 16.3627i −2.00791 + 0.634517i
666666 −10.1222 18.1496i −0.392227 0.703284i
667667 −13.7891 13.7891i −0.533916 0.533916i
668668 1.68138 + 1.68138i 0.0650546 + 0.0650546i
669669 11.3319 2.94633i 0.438117 0.113912i
670670 16.2971 + 8.47037i 0.629613 + 0.327239i
671671 0.197982i 0.00764300i
672672 5.05906 + 2.97117i 0.195157 + 0.114616i
673673 3.82947 3.82947i 0.147615 0.147615i −0.629437 0.777052i 0.716714π-0.716714\pi
0.777052 + 0.629437i 0.216714π0.216714\pi
674674 −9.54770 −0.367764
675675 21.5903 14.4519i 0.831012 0.556254i
676676 1.26494 0.0486516
677677 2.79395 2.79395i 0.107380 0.107380i −0.651375 0.758756i 0.725808π-0.725808\pi
0.758756 + 0.651375i 0.225808π0.225808\pi
678678 25.9475 + 15.2389i 0.996507 + 0.585247i
679679 11.8604i 0.455160i
680680 10.3969 + 5.40374i 0.398703 + 0.207224i
681681 −17.7343 + 4.61097i −0.679580 + 0.176693i
682682 0.0270962 + 0.0270962i 0.00103757 + 0.00103757i
683683 −17.3883 17.3883i −0.665345 0.665345i 0.291290 0.956635i 0.405916π-0.405916\pi
−0.956635 + 0.291290i 0.905916π0.905916\pi
684684 10.4761 + 18.7843i 0.400565 + 0.718235i
685685 −7.21181 + 2.27900i −0.275549 + 0.0870760i
686686 8.55644i 0.326686i
687687 1.12973 1.92360i 0.0431017 0.0733899i
688688 6.93875 6.93875i 0.264537 0.264537i
689689 −1.39271 −0.0530580
690690 −11.4905 18.3093i −0.437436 0.697025i
691691 6.95698 0.264656 0.132328 0.991206i 0.457755π-0.457755\pi
0.132328 + 0.991206i 0.457755π0.457755\pi
692692 0.350482 0.350482i 0.0133233 0.0133233i
693693 0.374598 + 0.106363i 0.0142298 + 0.00404038i
694694 8.81570i 0.334640i
695695 −4.55192 + 8.75796i −0.172664 + 0.332208i
696696 −1.52282 5.85695i −0.0577225 0.222007i
697697 37.6836 + 37.6836i 1.42737 + 1.42737i
698698 15.0211 + 15.0211i 0.568558 + 0.568558i
699699 1.57726 + 6.06631i 0.0596574 + 0.229449i
700700 16.6831 + 2.91946i 0.630563 + 0.110345i
701701 30.4250i 1.14914i 0.818456 + 0.574569i 0.194830π0.194830\pi
−0.818456 + 0.574569i 0.805170π0.805170\pi
702702 17.7958 + 0.396659i 0.671658 + 0.0149709i
703703 35.1172 35.1172i 1.32447 1.32447i
704704 0.0383198 0.00144423
705705 −39.2764 8.98728i −1.47924 0.338481i
706706 −24.3538 −0.916566
707707 17.8165 17.8165i 0.670059 0.670059i
708708 −13.1592 + 22.4063i −0.494553 + 0.842082i
709709 43.7876i 1.64448i −0.569143 0.822238i 0.692725π-0.692725\pi
0.569143 0.822238i 0.307275π-0.307275\pi
710710 −6.45627 20.4307i −0.242300 0.766749i
711711 43.8359 24.4476i 1.64397 0.916856i
712712 2.48513 + 2.48513i 0.0931340 + 0.0931340i
713713 −3.94658 3.94658i −0.147800 0.147800i
714714 29.7548 7.73633i 1.11354 0.289525i
715715 0.0884468 + 0.279887i 0.00330772 + 0.0104672i
716716 1.82086i 0.0680486i
717717 16.4386 + 9.65436i 0.613911 + 0.360549i
718718 6.82483 6.82483i 0.254700 0.254700i
719719 15.8238 0.590130 0.295065 0.955477i 0.404659π-0.404659\pi
0.295065 + 0.955477i 0.404659π0.404659\pi
720720 −0.197341 6.70530i −0.00735446 0.249892i
721721 −18.4739 −0.688006
722722 −22.9102 + 22.9102i −0.852628 + 0.852628i
723723 −7.73852 4.54482i −0.287799 0.169024i
724724 18.7741i 0.697733i
725725 −10.0387 14.2974i −0.372828 0.530992i
726726 −18.4370 + 4.79368i −0.684262 + 0.177910i
727727 −6.35959 6.35959i −0.235864 0.235864i 0.579271 0.815135i 0.303337π-0.303337\pi
−0.815135 + 0.579271i 0.803337π0.803337\pi
728728 8.20512 + 8.20512i 0.304102 + 0.304102i
729729 −26.9732 1.20304i −0.999007 0.0445569i
730730 14.5386 27.9725i 0.538098 1.03531i
731731 51.4209i 1.90187i
732732 −4.53182 + 7.71639i −0.167501 + 0.285206i
733733 −16.6044 + 16.6044i −0.613299 + 0.613299i −0.943804 0.330505i 0.892781π-0.892781\pi
0.330505 + 0.943804i 0.392781π0.392781\pi
734734 −12.1654 −0.449034
735735 14.6768 9.21082i 0.541363 0.339746i
736736 −5.58130 −0.205729
737737 0.222567 0.222567i 0.00819834 0.00819834i
738738 8.33359 29.3500i 0.306764 1.08039i
739739 46.2648i 1.70188i 0.525265 + 0.850939i 0.323966π0.323966\pi
−0.525265 + 0.850939i 0.676034π0.676034\pi
740740 −14.7697 + 4.66735i −0.542943 + 0.171575i
741741 10.7043 + 41.1699i 0.393232 + 1.51241i
742742 0.973778 + 0.973778i 0.0357485 + 0.0357485i
743743 21.0299 + 21.0299i 0.771513 + 0.771513i 0.978371 0.206858i 0.0663237π-0.0663237\pi
−0.206858 + 0.978371i 0.566324π0.566324\pi
744744 −0.435847 1.67632i −0.0159789 0.0614567i
745745 −11.2789 5.86215i −0.413226 0.214773i
746746 5.92024i 0.216756i
747747 −9.48968 + 33.4217i −0.347209 + 1.22283i
748748 0.141988 0.141988i 0.00519160 0.00519160i
749749 −61.7492 −2.25627
750750 −7.31229 17.9313i −0.267007 0.654757i
751751 −15.8787 −0.579421 −0.289710 0.957114i 0.593559π-0.593559\pi
−0.289710 + 0.957114i 0.593559π0.593559\pi
752752 −7.35619 + 7.35619i −0.268253 + 0.268253i
753753 −9.60893 + 16.3613i −0.350169 + 0.596237i
754754 11.9690i 0.435886i
755755 12.1681 + 6.32432i 0.442843 + 0.230166i
756756 −12.1654 12.7201i −0.442451 0.462625i
757757 −9.22666 9.22666i −0.335349 0.335349i 0.519265 0.854613i 0.326206π-0.326206\pi
−0.854613 + 0.519265i 0.826206π0.826206\pi
758758 −11.3842 11.3842i −0.413494 0.413494i
759759 −0.358521 + 0.0932166i −0.0130135 + 0.00338355i
760760 15.2861 4.83055i 0.554485 0.175222i
761761 29.4202i 1.06648i −0.845963 0.533242i 0.820974π-0.820974\pi
0.845963 0.533242i 0.179026π-0.179026\pi
762762 −15.6475 9.18972i −0.566847 0.332908i
763763 −2.00451 + 2.00451i −0.0725683 + 0.0725683i
764764 −5.71872 −0.206896
765765 −25.5767 24.1142i −0.924726 0.871852i
766766 4.33007 0.156452
767767 −36.3401 + 36.3401i −1.31216 + 1.31216i
768768 −1.49353 0.877144i −0.0538930 0.0316512i
769769 42.6183i 1.53686i 0.639937 + 0.768428i 0.278961π0.278961\pi
−0.639937 + 0.768428i 0.721039π0.721039\pi
770770 0.133854 0.257538i 0.00482377 0.00928101i
771771 6.16805 1.60371i 0.222137 0.0577563i
772772 −2.43627 2.43627i −0.0876832 0.0876832i
773773 −7.38044 7.38044i −0.265456 0.265456i 0.561810 0.827266i 0.310105π-0.310105\pi
−0.827266 + 0.561810i 0.810105π0.810105\pi
774774 −25.7105 + 14.3389i −0.924144 + 0.515402i
775775 −2.87317 4.09205i −0.103207 0.146991i
776776 3.50140i 0.125693i
777777 −20.5818 + 35.0449i −0.738367 + 1.25723i
778778 −2.46536 + 2.46536i −0.0883874 + 0.0883874i
779779 72.9130 2.61238
780780 2.95939 12.9332i 0.105963 0.463083i
781781 −0.367189 −0.0131391
782782 −20.6806 + 20.6806i −0.739538 + 0.739538i
783783 −0.404567 + 18.1505i −0.0144580 + 0.648647i
784784 4.47399i 0.159785i
785785 −1.83406 5.80381i −0.0654604 0.207147i
786786 7.34200 + 28.2382i 0.261881 + 1.00722i
787787 10.3895 + 10.3895i 0.370347 + 0.370347i 0.867603 0.497257i 0.165659π-0.165659\pi
−0.497257 + 0.867603i 0.665659π0.665659\pi
788788 −1.37187 1.37187i −0.0488707 0.0488707i
789789 −7.97672 30.6794i −0.283979 1.09221i
790790 −11.2728 35.6724i −0.401068 1.26917i
791791 58.8491i 2.09243i
792792 −0.110588 0.0314001i −0.00392958 0.00111576i
793793 −12.5150 + 12.5150i −0.444419 + 0.444419i
794794 −27.3210 −0.969587
795795 0.351219 1.53490i 0.0124565 0.0544374i
796796 −5.04179 −0.178701
797797 −0.920813 + 0.920813i −0.0326169 + 0.0326169i −0.723227 0.690610i 0.757342π-0.757342\pi
0.690610 + 0.723227i 0.257342π0.257342\pi
798798 21.3014 36.2703i 0.754063 1.28395i
799799 54.5145i 1.92858i
800800 −4.92516 0.861878i −0.174131 0.0304720i
801801 −5.13551 9.20825i −0.181454 0.325358i
802802 −6.42625 6.42625i −0.226919 0.226919i
803803 −0.382015 0.382015i −0.0134810 0.0134810i
804804 −13.7692 + 3.58002i −0.485601 + 0.126258i
805805 −19.4959 + 37.5105i −0.687141 + 1.32207i
806806 3.42565i 0.120663i
807807 13.8563 + 8.13778i 0.487765 + 0.286463i
808808 −5.25975 + 5.25975i −0.185038 + 0.185038i
809809 0.728913 0.0256272 0.0128136 0.999918i 0.495921π-0.495921\pi
0.0128136 + 0.999918i 0.495921π0.495921\pi
810810 −4.92497 + 19.5127i −0.173046 + 0.685606i
811811 −3.76569 −0.132231 −0.0661155 0.997812i 0.521061π-0.521061\pi
−0.0661155 + 0.997812i 0.521061π0.521061\pi
812812 −8.36870 + 8.36870i −0.293684 + 0.293684i
813813 −44.9848 26.4195i −1.57769 0.926572i
814814 0.265447i 0.00930392i
815815 −25.9040 + 8.18589i −0.907376 + 0.286739i
816816 −8.78415 + 2.28390i −0.307507 + 0.0799526i
817817 −49.7465 49.7465i −1.74041 1.74041i
818818 11.3087 + 11.3087i 0.395400 + 0.395400i
819819 −16.9559 30.4028i −0.592486 1.06236i
820820 −20.1783 10.4876i −0.704656 0.366242i
821821 6.66388i 0.232571i 0.993216 + 0.116285i 0.0370987π0.0370987\pi
−0.993216 + 0.116285i 0.962901π0.962901\pi
822822 2.96688 5.05174i 0.103482 0.176200i
823823 4.33761 4.33761i 0.151200 0.151200i −0.627454 0.778654i 0.715903π-0.715903\pi
0.778654 + 0.627454i 0.215903π0.215903\pi
824824 5.45384 0.189994
825825 −0.330768 + 0.0268942i −0.0115159 + 0.000936337i
826826 50.8178 1.76818
827827 17.7402 17.7402i 0.616886 0.616886i −0.327845 0.944731i 0.606322π-0.606322\pi
0.944731 + 0.327845i 0.106322π0.106322\pi
828828 16.1072 + 4.57344i 0.559764 + 0.158938i
829829 18.4718i 0.641554i −0.947155 0.320777i 0.896056π-0.896056\pi
0.947155 0.320777i 0.103944π-0.103944\pi
830830 22.9775 + 11.9425i 0.797562 + 0.414530i
831831 −8.29618 31.9080i −0.287791 1.10688i
832832 −2.42230 2.42230i −0.0839781 0.0839781i
833833 −16.5777 16.5777i −0.574382 0.574382i
834834 −1.92388 7.39944i −0.0666184 0.256222i
835835 −5.06988 + 1.60213i −0.175450 + 0.0554439i
836836 0.274729i 0.00950170i
837837 −0.115791 + 5.19486i −0.00400232 + 0.179561i
838838 −15.6292 + 15.6292i −0.539900 + 0.539900i
839839 −37.1676 −1.28317 −0.641583 0.767053i 0.721722π-0.721722\pi
−0.641583 + 0.767053i 0.721722π0.721722\pi
840840 −11.1121 + 6.97366i −0.383402 + 0.240614i
841841 −16.7924 −0.579047
842842 −16.5218 + 16.5218i −0.569381 + 0.569381i
843843 −0.700547 + 1.19283i −0.0241281 + 0.0410833i
844844 25.9870i 0.894510i
845845 −1.30443 + 2.50975i −0.0448739 + 0.0863380i
846846 27.2572 15.2016i 0.937123 0.522641i
847847 26.3437 + 26.3437i 0.905180 + 0.905180i
848848 −0.287477 0.287477i −0.00987199 0.00987199i
849849 −17.6140 + 4.57969i −0.604511 + 0.157175i
850850 −21.4430 + 15.0558i −0.735487 + 0.516411i
851851 38.6625i 1.32533i
852852 14.3113 + 8.40499i 0.490297 + 0.287950i
853853 7.20464 7.20464i 0.246682 0.246682i −0.572925 0.819608i 0.694192π-0.694192\pi
0.819608 + 0.572925i 0.194192π0.194192\pi
854854 17.5008 0.598866
855855 −48.0728 + 1.41481i −1.64405 + 0.0483854i
856856 18.2295 0.623071
857857 0.0169638 0.0169638i 0.000579472 0.000579472i −0.706817 0.707396i 0.749870π-0.749870\pi
0.707396 + 0.706817i 0.249870π0.249870\pi
858858 −0.196055 0.115143i −0.00669322 0.00393091i
859859 1.75493i 0.0598775i −0.999552 0.0299387i 0.990469π-0.990469\pi
0.999552 0.0299387i 0.00953122π-0.00953122\pi
860860 6.61168 + 20.9224i 0.225457 + 0.713449i
861861 −57.7481 + 15.0147i −1.96805 + 0.511698i
862862 3.57568 + 3.57568i 0.121788 + 0.121788i
863863 −18.3540 18.3540i −0.624777 0.624777i 0.321972 0.946749i 0.395654π-0.395654\pi
−0.946749 + 0.321972i 0.895654π0.895654\pi
864864 3.59145 + 3.75520i 0.122183 + 0.127754i
865865 0.333961 + 1.05681i 0.0113550 + 0.0359326i
866866 20.4805i 0.695955i
867867 −9.17419 + 15.6210i −0.311572 + 0.530518i
868868 −2.39520 + 2.39520i −0.0812985 + 0.0812985i
869869 −0.641120 −0.0217485
870870 13.1910 + 3.01839i 0.447218 + 0.102333i
871871 −28.1380 −0.953421
872872 0.591769 0.591769i 0.0200398 0.0200398i
873873 2.86913 10.1048i 0.0971053 0.341995i
874874 40.0144i 1.35351i
875875 −22.9964 + 30.0901i −0.777421 + 1.01723i
876876 6.14477 + 23.6335i 0.207613 + 0.798501i
877877 −18.5647 18.5647i −0.626886 0.626886i 0.320397 0.947283i 0.396184π-0.396184\pi
−0.947283 + 0.320397i 0.896184π0.896184\pi
878878 −21.1067 21.1067i −0.712317 0.712317i
879879 −5.69277 21.8950i −0.192012 0.738501i
880880 −0.0395162 + 0.0760297i −0.00133209 + 0.00256296i
881881 6.58057i 0.221705i −0.993837 0.110853i 0.964642π-0.964642\pi
0.993837 0.110853i 0.0353581π-0.0353581\pi
882882 −3.66609 + 12.9116i −0.123444 + 0.434755i
883883 24.4430 24.4430i 0.822571 0.822571i −0.163905 0.986476i 0.552409π-0.552409\pi
0.986476 + 0.163905i 0.0524091π0.0524091\pi
884884 −17.9509 −0.603754
885885 −30.8860 49.2148i −1.03822 1.65434i
886886 9.18835 0.308688
887887 4.64793 4.64793i 0.156062 0.156062i −0.624757 0.780819i 0.714802π-0.714802\pi
0.780819 + 0.624757i 0.214802π0.214802\pi
888888 6.07611 10.3459i 0.203901 0.347185i
889889 35.4886i 1.19025i
890890 −7.49341 + 2.36799i −0.251180 + 0.0793751i
891891 0.293418 + 0.181237i 0.00982989 + 0.00607166i
892892 4.78005 + 4.78005i 0.160048 + 0.160048i
893893 52.7393 + 52.7393i 1.76485 + 1.76485i
894894 9.52932 2.47765i 0.318708 0.0828650i
895895 3.61273 + 1.87770i 0.120760 + 0.0627646i
896896 3.38733i 0.113163i
897897 28.5556 + 16.7706i 0.953442 + 0.559955i
898898 10.7432 10.7432i 0.358506 0.358506i
899899 3.49394 0.116529
900900 13.5074 + 6.52310i 0.450246 + 0.217437i
901901 −2.13040 −0.0709739
902902 −0.275570 + 0.275570i −0.00917549 + 0.00917549i
903903 49.6439 + 29.1558i 1.65205 + 0.970243i
904904 17.3733i 0.577828i
905905 37.2493 + 19.3602i 1.23821 + 0.643555i
906906 −10.2806 + 2.67299i −0.341550 + 0.0888041i
907907 −25.1449 25.1449i −0.834923 0.834923i 0.153263 0.988186i 0.451022π-0.451022\pi
−0.988186 + 0.153263i 0.951022π0.951022\pi
908908 −7.48071 7.48071i −0.248256 0.248256i
909909 19.4892 10.8693i 0.646416 0.360511i
910910 −24.7409 + 7.81836i −0.820153 + 0.259176i
911911 15.4101i 0.510561i 0.966867 + 0.255280i 0.0821678π0.0821678\pi
−0.966867 + 0.255280i 0.917832π0.917832\pi
912912 −6.28857 + 10.7076i −0.208235 + 0.354565i
913913 0.313799 0.313799i 0.0103852 0.0103852i
914914 −12.6210 −0.417464
915915 −10.6367 16.9488i −0.351637 0.560310i
916916 1.28796 0.0425553
917917 40.3480 40.3480i 1.33241 1.33241i
918918 27.2219 + 0.606762i 0.898455 + 0.0200261i
919919 4.10799i 0.135510i −0.997702 0.0677550i 0.978416π-0.978416\pi
0.997702 0.0677550i 0.0215836π-0.0215836\pi
920920 5.75555 11.0738i 0.189755 0.365091i
921921 −7.93208 30.5077i −0.261371 1.00526i
922922 −6.98181 6.98181i −0.229934 0.229934i
923923 23.2110 + 23.2110i 0.763999 + 0.763999i
924924 0.0565738 + 0.217589i 0.00186114 + 0.00715815i
925925 5.97036 34.1173i 0.196304 1.12177i
926926 15.2032i 0.499609i
927927 −15.7394 4.46900i −0.516948 0.146781i
928928 2.47059 2.47059i 0.0811011 0.0811011i
929929 1.62724 0.0533879 0.0266939 0.999644i 0.491502π-0.491502\pi
0.0266939 + 0.999644i 0.491502π0.491502\pi
930930 3.77541 + 0.863894i 0.123800 + 0.0283282i
931931 −32.0757 −1.05124
932932 −2.55890 + 2.55890i −0.0838197 + 0.0838197i
933933 20.8587 35.5163i 0.682882 1.16275i
934934 10.0201i 0.327866i
935935 0.135295 + 0.428137i 0.00442463 + 0.0140016i
936936 5.00568 + 8.97545i 0.163616 + 0.293372i
937937 19.6327 + 19.6327i 0.641372 + 0.641372i 0.950893 0.309521i 0.100169π-0.100169\pi
−0.309521 + 0.950893i 0.600169π0.600169\pi
938938 19.6740 + 19.6740i 0.642380 + 0.642380i
939939 −7.09796 + 1.84549i −0.231633 + 0.0602253i
940940 −7.00945 22.1812i −0.228623 0.723469i
941941 24.6253i 0.802763i −0.915911 0.401381i 0.868530π-0.868530\pi
0.915911 0.401381i 0.131470π-0.131470\pi
942942 4.06546 + 2.38764i 0.132460 + 0.0777935i
943943 40.1370 40.1370i 1.30704 1.30704i
944944 −15.0023 −0.488284
945945 37.7829 11.0200i 1.22908 0.358479i
946946 0.376028 0.0122257
947947 −30.8926 + 30.8926i −1.00388 + 1.00388i −0.00388328 + 0.999992i 0.501236π0.501236\pi
−0.999992 + 0.00388328i 0.998764π0.998764\pi
948948 24.9878 + 14.6753i 0.811567 + 0.476631i
949949 48.2963i 1.56777i
950950 −6.17912 + 35.3103i −0.200477 + 1.14562i
951951 45.0420 11.7110i 1.46059 0.379757i
952952 12.5512 + 12.5512i 0.406787 + 0.406787i
953953 −37.6776 37.6776i −1.22050 1.22050i −0.967455 0.253044i 0.918568π-0.918568\pi
−0.253044 0.967455i 0.581432π-0.581432\pi
954954 0.594070 + 1.06520i 0.0192337 + 0.0344871i
955955 5.89726 11.3464i 0.190831 0.367162i
956956 11.0066i 0.355978i
957957 0.117438 0.199964i 0.00379625 0.00646392i
958958 −27.6805 + 27.6805i −0.894316 + 0.894316i
959959 −11.4574 −0.369978
960960 3.28048 2.05875i 0.105877 0.0664459i
961961 1.00000 0.0322581
962962 16.7796 16.7796i 0.540997 0.540997i
963963 −52.6089 14.9377i −1.69530 0.481359i
964964 5.18138i 0.166881i
965965 7.34609 2.32143i 0.236479 0.0747295i
966966 −8.23999 31.6919i −0.265117 1.01967i
967967 −25.0874 25.0874i −0.806757 0.806757i 0.177384 0.984142i 0.443236π-0.443236\pi
−0.984142 + 0.177384i 0.943236π0.943236\pi
968968 −7.77714 7.77714i −0.249967 0.249967i
969969 16.3742 + 62.9768i 0.526014 + 2.02311i
970970 −6.94707 3.61072i −0.223057 0.115933i
971971 30.9651i 0.993718i −0.867831 0.496859i 0.834487π-0.834487\pi
0.867831 0.496859i 0.165513π-0.165513\pi
972972 −7.28754 13.7801i −0.233748 0.441998i
973973 −10.5727 + 10.5727i −0.338945 + 0.338945i
974974 −11.7885 −0.377729
975975 22.6088 + 19.2087i 0.724060 + 0.615170i
976976 −5.16656 −0.165378
977977 −19.3792 + 19.3792i −0.619994 + 0.619994i −0.945530 0.325536i 0.894455π-0.894455\pi
0.325536 + 0.945530i 0.394455π0.394455\pi
978978 10.6567 18.1452i 0.340763 0.580221i
979979 0.134675i 0.00430423i
980980 8.87676 + 4.61366i 0.283558 + 0.147378i
981981 −2.19271 + 1.22289i −0.0700078 + 0.0390439i
982982 −13.2511 13.2511i −0.422861 0.422861i
983983 −3.06898 3.06898i −0.0978851 0.0978851i 0.656468 0.754354i 0.272050π-0.272050\pi
−0.754354 + 0.656468i 0.772050π0.772050\pi
984984 17.0483 4.43260i 0.543479 0.141306i
985985 4.13659 1.30720i 0.131803 0.0416509i
986986 18.3088i 0.583070i
987987 −52.6306 30.9098i −1.67525 0.983870i
988988 −17.3663 + 17.3663i −0.552497 + 0.552497i
989989 −54.7686 −1.74154
990990 0.176341 0.187035i 0.00560449 0.00594438i
991991 11.3175 0.359513 0.179756 0.983711i 0.442469π-0.442469\pi
0.179756 + 0.983711i 0.442469π0.442469\pi
992992 0.707107 0.707107i 0.0224507 0.0224507i
993993 5.53741 + 3.25211i 0.175724 + 0.103203i
994994 32.4581i 1.02951i
995995 5.19919 10.0033i 0.164825 0.317127i
996996 −19.4133 + 5.04752i −0.615134 + 0.159937i
997997 6.77107 + 6.77107i 0.214442 + 0.214442i 0.806151 0.591709i 0.201547π-0.201547\pi
−0.591709 + 0.806151i 0.701547π0.701547\pi
998998 18.8942 + 18.8942i 0.598084 + 0.598084i
999999 −26.0128 + 24.8785i −0.823009 + 0.787120i
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 930.2.j.h.497.12 yes 40
3.2 odd 2 inner 930.2.j.h.497.8 40
5.3 odd 4 inner 930.2.j.h.683.8 yes 40
15.8 even 4 inner 930.2.j.h.683.12 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.j.h.497.8 40 3.2 odd 2 inner
930.2.j.h.497.12 yes 40 1.1 even 1 trivial
930.2.j.h.683.8 yes 40 5.3 odd 4 inner
930.2.j.h.683.12 yes 40 15.8 even 4 inner