Properties

Label 117.3.k.a.113.13
Level 117117
Weight 33
Character 117.113
Analytic conductor 3.1883.188
Analytic rank 00
Dimension 5252
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,3,Mod(29,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 117=3213 117 = 3^{2} \cdot 13
Weight: k k == 3 3
Character orbit: [χ][\chi] == 117.k (of order 66, 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: 3.188019093023.18801909302
Analytic rank: 00
Dimension: 5252
Relative dimension: 2626 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 113.13
Character χ\chi == 117.113
Dual form 117.3.k.a.29.14

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+0.376029iq2+(2.92720+0.656887i)q3+3.85860q4+(0.994641+0.574256i)q5+(0.2470091.10071i)q6+(2.57212+4.45503i)q7+2.95506iq8+(8.137003.84568i)q9+(0.215937+0.374014i)q10+15.0728iq11+(11.2949+2.53467i)q12+(12.9040+1.57671i)q13+(1.675220.967190i)q14+(3.288731.02760i)q15+14.3232q16+(24.4307+14.1051i)q17+(1.44609+3.05975i)q18+(10.6901+18.5158i)q19+(3.83792+2.21583i)q20+(4.6026414.7304i)q215.66781q22+(12.59287.27045i)q23+(1.941148.65006i)q24+(11.840520.5083i)q25+(0.592890+4.85229i)q26+(21.2924+16.6022i)q27+(9.92477+17.1902i)q2853.9734iq29+(0.3864061.23666i)q30+(20.694035.8431i)q31+17.2062iq32+(9.9011344.1211i)q33+(5.303919.18664i)q34+(5.11666+2.95411i)q35+(31.397414.8390i)q36+(26.547045.9807i)q37+(6.96249+4.01980i)q38+(38.8084+3.86114i)q39+(1.69696+2.93923i)q40+(24.9941+14.4303i)q41+(5.53904+1.73073i)q42+(21.0292+36.4236i)q43+58.1599iq44+(10.3018+0.847651i)q45+(2.73390+4.73525i)q46+(3.483402.01114i)q47+(41.9269+9.40874i)q48+(11.2684+19.5175i)q49+(7.711714.45236i)q50+(62.248057.3365i)q51+(49.7915+6.08391i)q52+12.6540iq53+(6.242908.00658i)q54+(8.65564+14.9920i)q55+(13.16497.60076i)q56+(43.454947.1774i)q57+20.2956q5822.0040iq59+(12.68993.96508i)q60+(5.17426+8.96208i)q61+(13.4780+7.78155i)q62+(3.79666+46.1421i)q63+50.8229q64+(11.9294+8.97848i)q65+(16.59083.72311i)q66+(37.011564.1058i)q67+(94.2683+54.4258i)q68+(32.0857+29.5541i)q69+(1.110831.92401i)q70+(34.190819.7401i)q71+(11.3642+24.0453i)q7265.2913q73+(17.2901+9.98243i)q74+(48.1310+52.2540i)q75+(41.2489+71.4453i)q76+(67.149838.7690i)q77+(1.4519014.5931i)q78+(9.7802516.9399i)q79+(14.2465+8.22520i)q80+(51.421562.5846i)q81+(5.426229.39850i)q82+(71.711241.4025i)q83+(17.759856.8386i)q8432.3997q85+(13.69637.90758i)q86+(35.4544+157.991i)q8744.5410q88+(134.830+77.8441i)q89+(0.318741+3.87377i)q90+(40.2150+53.4324i)q91+(48.590528.0538i)q92+(37.0306+118.513i)q93+(0.756247+1.30986i)q94+24.5555iq95+(11.302550.3660i)q96+(9.71984+16.8353i)q97+(7.33915+4.23726i)q98+(57.9651+122.647i)q99+O(q100)q+0.376029i q^{2} +(-2.92720 + 0.656887i) q^{3} +3.85860 q^{4} +(0.994641 + 0.574256i) q^{5} +(-0.247009 - 1.10071i) q^{6} +(-2.57212 + 4.45503i) q^{7} +2.95506i q^{8} +(8.13700 - 3.84568i) q^{9} +(-0.215937 + 0.374014i) q^{10} +15.0728i q^{11} +(-11.2949 + 2.53467i) q^{12} +(12.9040 + 1.57671i) q^{13} +(-1.67522 - 0.967190i) q^{14} +(-3.28873 - 1.02760i) q^{15} +14.3232 q^{16} +(-24.4307 + 14.1051i) q^{17} +(1.44609 + 3.05975i) q^{18} +(10.6901 + 18.5158i) q^{19} +(3.83792 + 2.21583i) q^{20} +(4.60264 - 14.7304i) q^{21} -5.66781 q^{22} +(12.5928 - 7.27045i) q^{23} +(-1.94114 - 8.65006i) q^{24} +(-11.8405 - 20.5083i) q^{25} +(-0.592890 + 4.85229i) q^{26} +(-21.2924 + 16.6022i) q^{27} +(-9.92477 + 17.1902i) q^{28} -53.9734i q^{29} +(0.386406 - 1.23666i) q^{30} +(20.6940 - 35.8431i) q^{31} +17.2062i q^{32} +(-9.90113 - 44.1211i) q^{33} +(-5.30391 - 9.18664i) q^{34} +(-5.11666 + 2.95411i) q^{35} +(31.3974 - 14.8390i) q^{36} +(26.5470 - 45.9807i) q^{37} +(-6.96249 + 4.01980i) q^{38} +(-38.8084 + 3.86114i) q^{39} +(-1.69696 + 2.93923i) q^{40} +(-24.9941 + 14.4303i) q^{41} +(5.53904 + 1.73073i) q^{42} +(-21.0292 + 36.4236i) q^{43} +58.1599i q^{44} +(10.3018 + 0.847651i) q^{45} +(2.73390 + 4.73525i) q^{46} +(3.48340 - 2.01114i) q^{47} +(-41.9269 + 9.40874i) q^{48} +(11.2684 + 19.5175i) q^{49} +(7.71171 - 4.45236i) q^{50} +(62.2480 - 57.3365i) q^{51} +(49.7915 + 6.08391i) q^{52} +12.6540i q^{53} +(-6.24290 - 8.00658i) q^{54} +(-8.65564 + 14.9920i) q^{55} +(-13.1649 - 7.60076i) q^{56} +(-43.4549 - 47.1774i) q^{57} +20.2956 q^{58} -22.0040i q^{59} +(-12.6899 - 3.96508i) q^{60} +(-5.17426 + 8.96208i) q^{61} +(13.4780 + 7.78155i) q^{62} +(-3.79666 + 46.1421i) q^{63} +50.8229 q^{64} +(11.9294 + 8.97848i) q^{65} +(16.5908 - 3.72311i) q^{66} +(-37.0115 - 64.1058i) q^{67} +(-94.2683 + 54.4258i) q^{68} +(-32.0857 + 29.5541i) q^{69} +(-1.11083 - 1.92401i) q^{70} +(34.1908 - 19.7401i) q^{71} +(11.3642 + 24.0453i) q^{72} -65.2913 q^{73} +(17.2901 + 9.98243i) q^{74} +(48.1310 + 52.2540i) q^{75} +(41.2489 + 71.4453i) q^{76} +(-67.1498 - 38.7690i) q^{77} +(-1.45190 - 14.5931i) q^{78} +(-9.78025 - 16.9399i) q^{79} +(14.2465 + 8.22520i) q^{80} +(51.4215 - 62.5846i) q^{81} +(-5.42622 - 9.39850i) q^{82} +(71.7112 - 41.4025i) q^{83} +(17.7598 - 56.8386i) q^{84} -32.3997 q^{85} +(-13.6963 - 7.90758i) q^{86} +(35.4544 + 157.991i) q^{87} -44.5410 q^{88} +(134.830 + 77.8441i) q^{89} +(-0.318741 + 3.87377i) q^{90} +(-40.2150 + 53.4324i) q^{91} +(48.5905 - 28.0538i) q^{92} +(-37.0306 + 118.513i) q^{93} +(0.756247 + 1.30986i) q^{94} +24.5555i q^{95} +(-11.3025 - 50.3660i) q^{96} +(-9.71984 + 16.8353i) q^{97} +(-7.33915 + 4.23726i) q^{98} +(57.9651 + 122.647i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 52qq398q46q5+12q6q73q96q1039q12+4q136q1425q15+166q16+34q18+5q19+21q2091q21+30q2275q23++522q99+O(q100) 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/117Z)×\left(\mathbb{Z}/117\mathbb{Z}\right)^\times.

nn 2828 9292
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.376029i 0.188014i 0.995572 + 0.0940072i 0.0299677π0.0299677\pi
−0.995572 + 0.0940072i 0.970032π0.970032\pi
33 −2.92720 + 0.656887i −0.975733 + 0.218962i
44 3.85860 0.964651
55 0.994641 + 0.574256i 0.198928 + 0.114851i 0.596155 0.802869i 0.296694π-0.296694\pi
−0.397227 + 0.917720i 0.630028π0.630028\pi
66 −0.247009 1.10071i −0.0411681 0.183452i
77 −2.57212 + 4.45503i −0.367445 + 0.636434i −0.989165 0.146806i 0.953101π-0.953101\pi
0.621720 + 0.783239i 0.286434π0.286434\pi
88 2.95506i 0.369383i
99 8.13700 3.84568i 0.904111 0.427298i
1010 −0.215937 + 0.374014i −0.0215937 + 0.0374014i
1111 15.0728i 1.37025i 0.728424 + 0.685127i 0.240253π0.240253\pi
−0.728424 + 0.685127i 0.759747π0.759747\pi
1212 −11.2949 + 2.53467i −0.941242 + 0.211222i
1313 12.9040 + 1.57671i 0.992618 + 0.121286i
1414 −1.67522 0.967190i −0.119659 0.0690850i
1515 −3.28873 1.02760i −0.219249 0.0685064i
1616 14.3232 0.895201
1717 −24.4307 + 14.1051i −1.43710 + 0.829709i −0.997647 0.0685572i 0.978160π-0.978160\pi
−0.439451 + 0.898266i 0.644827π0.644827\pi
1818 1.44609 + 3.05975i 0.0803382 + 0.169986i
1919 10.6901 + 18.5158i 0.562638 + 0.974518i 0.997265 + 0.0739073i 0.0235469π0.0235469\pi
−0.434627 + 0.900611i 0.643120π0.643120\pi
2020 3.83792 + 2.21583i 0.191896 + 0.110791i
2121 4.60264 14.7304i 0.219173 0.701446i
2222 −5.66781 −0.257628
2323 12.5928 7.27045i 0.547512 0.316106i −0.200606 0.979672i 0.564291π-0.564291\pi
0.748118 + 0.663566i 0.230958π0.230958\pi
2424 −1.94114 8.65006i −0.0808809 0.360419i
2525 −11.8405 20.5083i −0.473618 0.820331i
2626 −0.592890 + 4.85229i −0.0228035 + 0.186627i
2727 −21.2924 + 16.6022i −0.788609 + 0.614895i
2828 −9.92477 + 17.1902i −0.354456 + 0.613936i
2929 53.9734i 1.86115i −0.366100 0.930576i 0.619307π-0.619307\pi
0.366100 0.930576i 0.380693π-0.380693\pi
3030 0.386406 1.23666i 0.0128802 0.0412220i
3131 20.6940 35.8431i 0.667549 1.15623i −0.311039 0.950397i 0.600677π-0.600677\pi
0.978588 0.205831i 0.0659897π-0.0659897\pi
3232 17.2062i 0.537694i
3333 −9.90113 44.1211i −0.300034 1.33700i
3434 −5.30391 9.18664i −0.155997 0.270195i
3535 −5.11666 + 2.95411i −0.146190 + 0.0844030i
3636 31.3974 14.8390i 0.872151 0.412193i
3737 26.5470 45.9807i 0.717486 1.24272i −0.244507 0.969647i 0.578626π-0.578626\pi
0.961993 0.273074i 0.0880405π-0.0880405\pi
3838 −6.96249 + 4.01980i −0.183223 + 0.105784i
3939 −38.8084 + 3.86114i −0.995087 + 0.0990035i
4040 −1.69696 + 2.93923i −0.0424241 + 0.0734806i
4141 −24.9941 + 14.4303i −0.609612 + 0.351959i −0.772813 0.634633i 0.781151π-0.781151\pi
0.163202 + 0.986593i 0.447818π0.447818\pi
4242 5.53904 + 1.73073i 0.131882 + 0.0412078i
4343 −21.0292 + 36.4236i −0.489050 + 0.847060i −0.999921 0.0125977i 0.995990π-0.995990\pi
0.510870 + 0.859658i 0.329323π0.329323\pi
4444 58.1599i 1.32182i
4545 10.3018 + 0.847651i 0.228929 + 0.0188367i
4646 2.73390 + 4.73525i 0.0594326 + 0.102940i
4747 3.48340 2.01114i 0.0741148 0.0427902i −0.462485 0.886627i 0.653042π-0.653042\pi
0.536599 + 0.843837i 0.319709π0.319709\pi
4848 −41.9269 + 9.40874i −0.873478 + 0.196015i
4949 11.2684 + 19.5175i 0.229968 + 0.398317i
5050 7.71171 4.45236i 0.154234 0.0890471i
5151 62.2480 57.3365i 1.22055 1.12425i
5252 49.7915 + 6.08391i 0.957529 + 0.116998i
5353 12.6540i 0.238755i 0.992849 + 0.119378i 0.0380899π0.0380899\pi
−0.992849 + 0.119378i 0.961910π0.961910\pi
5454 −6.24290 8.00658i −0.115609 0.148270i
5555 −8.65564 + 14.9920i −0.157375 + 0.272582i
5656 −13.1649 7.60076i −0.235088 0.135728i
5757 −43.4549 47.1774i −0.762368 0.827673i
5858 20.2956 0.349923
5959 22.0040i 0.372948i −0.982460 0.186474i 0.940294π-0.940294\pi
0.982460 0.186474i 0.0597061π-0.0597061\pi
6060 −12.6899 3.96508i −0.211499 0.0660847i
6161 −5.17426 + 8.96208i −0.0848239 + 0.146919i −0.905316 0.424738i 0.860366π-0.860366\pi
0.820492 + 0.571658i 0.193699π0.193699\pi
6262 13.4780 + 7.78155i 0.217388 + 0.125509i
6363 −3.79666 + 46.1421i −0.0602644 + 0.732415i
6464 50.8229 0.794107
6565 11.9294 + 8.97848i 0.183530 + 0.138130i
6666 16.5908 3.72311i 0.251376 0.0564108i
6767 −37.0115 64.1058i −0.552410 0.956802i −0.998100 0.0616149i 0.980375π-0.980375\pi
0.445690 0.895187i 0.352958π-0.352958\pi
6868 −94.2683 + 54.4258i −1.38630 + 0.800379i
6969 −32.0857 + 29.5541i −0.465011 + 0.428320i
7070 −1.11083 1.92401i −0.0158690 0.0274859i
7171 34.1908 19.7401i 0.481561 0.278029i −0.239506 0.970895i 0.576985π-0.576985\pi
0.721067 + 0.692865i 0.243652π0.243652\pi
7272 11.3642 + 24.0453i 0.157836 + 0.333963i
7373 −65.2913 −0.894402 −0.447201 0.894434i 0.647579π-0.647579\pi
−0.447201 + 0.894434i 0.647579π0.647579\pi
7474 17.2901 + 9.98243i 0.233650 + 0.134898i
7575 48.1310 + 52.2540i 0.641747 + 0.696720i
7676 41.2489 + 71.4453i 0.542749 + 0.940069i
7777 −67.1498 38.7690i −0.872076 0.503493i
7878 −1.45190 14.5931i −0.0186141 0.187091i
7979 −9.78025 16.9399i −0.123801 0.214429i 0.797463 0.603368i 0.206175π-0.206175\pi
−0.921263 + 0.388939i 0.872842π0.872842\pi
8080 14.2465 + 8.22520i 0.178081 + 0.102815i
8181 51.4215 62.5846i 0.634833 0.772649i
8282 −5.42622 9.39850i −0.0661735 0.114616i
8383 71.7112 41.4025i 0.863991 0.498825i −0.00135589 0.999999i 0.500432π-0.500432\pi
0.865347 + 0.501174i 0.167098π0.167098\pi
8484 17.7598 56.8386i 0.211426 0.676650i
8585 −32.3997 −0.381172
8686 −13.6963 7.90758i −0.159260 0.0919486i
8787 35.4544 + 157.991i 0.407522 + 1.81599i
8888 −44.5410 −0.506148
8989 134.830 + 77.8441i 1.51494 + 0.874653i 0.999846 + 0.0175212i 0.00557746π0.00557746\pi
0.515097 + 0.857132i 0.327756π0.327756\pi
9090 −0.318741 + 3.87377i −0.00354157 + 0.0430419i
9191 −40.2150 + 53.4324i −0.441923 + 0.587169i
9292 48.5905 28.0538i 0.528158 0.304932i
9393 −37.0306 + 118.513i −0.398179 + 1.27434i
9494 0.756247 + 1.30986i 0.00804518 + 0.0139347i
9595 24.5555i 0.258479i
9696 −11.3025 50.3660i −0.117735 0.524646i
9797 −9.71984 + 16.8353i −0.100205 + 0.173559i −0.911769 0.410704i 0.865283π-0.865283\pi
0.811564 + 0.584263i 0.198616π0.198616\pi
9898 −7.33915 + 4.23726i −0.0748893 + 0.0432374i
9999 57.9651 + 122.647i 0.585507 + 1.23886i
100100 −45.6876 79.1333i −0.456876 0.791333i
101101 82.8944i 0.820737i −0.911920 0.410369i 0.865400π-0.865400\pi
0.911920 0.410369i 0.134600π-0.134600\pi
102102 21.5602 + 23.4071i 0.211374 + 0.229481i
103103 −38.2718 + 66.2886i −0.371571 + 0.643579i −0.989807 0.142413i 0.954514π-0.954514\pi
0.618237 + 0.785992i 0.287847π0.287847\pi
104104 −4.65929 + 38.1322i −0.0448008 + 0.366656i
105105 13.0370 12.0083i 0.124162 0.114365i
106106 −4.75828 −0.0448894
107107 20.6786 + 11.9388i 0.193258 + 0.111578i 0.593507 0.804829i 0.297743π-0.297743\pi
−0.400249 + 0.916407i 0.631076π0.631076\pi
108108 −82.1591 + 64.0612i −0.760732 + 0.593159i
109109 5.84222 0.0535983 0.0267992 0.999641i 0.491469π-0.491469\pi
0.0267992 + 0.999641i 0.491469π0.491469\pi
110110 −5.63743 3.25477i −0.0512494 0.0295888i
111111 −47.5042 + 152.033i −0.427965 + 1.36967i
112112 −36.8410 + 63.8104i −0.328937 + 0.569736i
113113 133.419i 1.18070i −0.807146 0.590351i 0.798989π-0.798989\pi
0.807146 0.590351i 0.201011π-0.201011\pi
114114 17.7401 16.3403i 0.155615 0.143336i
115115 16.7004 0.145221
116116 208.262i 1.79536i
117117 111.064 36.7951i 0.949262 0.314488i
118118 8.27412 0.0701197
119119 145.119i 1.21949i
120120 3.03661 9.71841i 0.0253051 0.0809868i
121121 −106.189 −0.877596
122122 −3.37000 1.94567i −0.0276230 0.0159481i
123123 63.6835 58.6588i 0.517752 0.476900i
124124 79.8499 138.304i 0.643951 1.11536i
125125 55.9106i 0.447285i
126126 −17.3508 1.42765i −0.137705 0.0113306i
127127 5.22700 9.05343i 0.0411575 0.0712869i −0.844713 0.535220i 0.820229π-0.820229\pi
0.885870 + 0.463933i 0.153562π0.153562\pi
128128 87.9356i 0.686997i
129129 37.6304 120.433i 0.291708 0.933588i
130130 −3.37617 + 4.48581i −0.0259705 + 0.0345063i
131131 −74.2522 42.8695i −0.566811 0.327248i 0.189064 0.981965i 0.439455π-0.439455\pi
−0.755875 + 0.654716i 0.772788π0.772788\pi
132132 −38.2045 170.246i −0.289428 1.28974i
133133 −109.985 −0.826954
134134 24.1056 13.9174i 0.179893 0.103861i
135135 −30.7122 + 4.28587i −0.227498 + 0.0317472i
136136 −41.6813 72.1942i −0.306480 0.530839i
137137 96.1691 + 55.5233i 0.701964 + 0.405279i 0.808079 0.589075i 0.200508π-0.200508\pi
−0.106114 + 0.994354i 0.533841π0.533841\pi
138138 −11.1132 12.0652i −0.0805304 0.0874287i
139139 −202.843 −1.45930 −0.729652 0.683818i 0.760318π-0.760318\pi
−0.729652 + 0.683818i 0.760318π0.760318\pi
140140 −19.7432 + 11.3987i −0.141023 + 0.0814194i
141141 −8.87550 + 8.17520i −0.0629468 + 0.0579802i
142142 7.42285 + 12.8567i 0.0522736 + 0.0905405i
143143 −23.7655 + 194.500i −0.166192 + 1.36014i
144144 116.548 55.0825i 0.809361 0.382518i
145145 30.9945 53.6841i 0.213755 0.370235i
146146 24.5514i 0.168161i
147147 −45.8058 49.7296i −0.311604 0.338296i
148148 102.434 177.421i 0.692123 1.19879i
149149 235.223i 1.57868i −0.613957 0.789340i 0.710423π-0.710423\pi
0.613957 0.789340i 0.289577π-0.289577\pi
150150 −19.6490 + 18.0987i −0.130993 + 0.120658i
151151 133.267 + 230.825i 0.882561 + 1.52864i 0.848483 + 0.529222i 0.177516π0.177516\pi
0.0340779 + 0.999419i 0.489151π0.489151\pi
152152 −54.7155 + 31.5900i −0.359970 + 0.207829i
153153 −144.549 + 208.725i −0.944764 + 1.36422i
154154 14.5783 25.2503i 0.0946640 0.163963i
155155 41.1662 23.7673i 0.265588 0.153338i
156156 −149.746 + 14.8986i −0.959911 + 0.0955038i
157157 29.0426 50.3033i 0.184985 0.320403i −0.758587 0.651572i 0.774110π-0.774110\pi
0.943571 + 0.331169i 0.107443π0.107443\pi
158158 6.36989 3.67766i 0.0403158 0.0232763i
159159 −8.31226 37.0408i −0.0522784 0.232961i
160160 −9.88076 + 17.1140i −0.0617548 + 0.106962i
161161 74.8017i 0.464607i
162162 23.5336 + 19.3360i 0.145269 + 0.119358i
163163 −8.10087 14.0311i −0.0496986 0.0860805i 0.840106 0.542422i 0.182493π-0.182493\pi
−0.889805 + 0.456342i 0.849159π0.849159\pi
164164 −96.4422 + 55.6809i −0.588062 + 0.339518i
165165 15.4887 49.5704i 0.0938711 0.300427i
166166 15.5685 + 26.9655i 0.0937864 + 0.162443i
167167 −27.0940 + 15.6427i −0.162240 + 0.0936691i −0.578922 0.815383i 0.696526π-0.696526\pi
0.416682 + 0.909052i 0.363193π0.363193\pi
168168 43.5291 + 13.6011i 0.259102 + 0.0809589i
169169 164.028 + 40.6919i 0.970580 + 0.240781i
170170 12.1832i 0.0716659i
171171 158.192 + 109.553i 0.925097 + 0.640658i
172172 −81.1432 + 140.544i −0.471763 + 0.817117i
173173 3.74325 + 2.16116i 0.0216373 + 0.0124923i 0.510780 0.859712i 0.329357π-0.329357\pi
−0.489142 + 0.872204i 0.662690π0.662690\pi
174174 −59.4092 + 13.3319i −0.341432 + 0.0766201i
175175 121.820 0.696115
176176 215.891i 1.22665i
177177 14.4541 + 64.4100i 0.0816617 + 0.363898i
178178 −29.2716 + 50.7000i −0.164447 + 0.284831i
179179 −1.59962 0.923541i −0.00893642 0.00515945i 0.495525 0.868594i 0.334976π-0.334976\pi
−0.504462 + 0.863434i 0.668309π0.668309\pi
180180 39.7505 + 3.27075i 0.220836 + 0.0181708i
181181 −10.7339 −0.0593032 −0.0296516 0.999560i 0.509440π-0.509440\pi
−0.0296516 + 0.999560i 0.509440π0.509440\pi
182182 −20.0921 15.1220i −0.110396 0.0830879i
183183 9.25901 29.6327i 0.0505957 0.161927i
184184 21.4846 + 37.2125i 0.116764 + 0.202242i
185185 52.8094 30.4895i 0.285456 0.164808i
186186 −44.5645 13.9246i −0.239594 0.0748634i
187187 −212.603 368.239i −1.13691 1.96919i
188188 13.4410 7.76019i 0.0714949 0.0412776i
189189 −19.1966 137.561i −0.101569 0.727837i
190190 −9.23357 −0.0485977
191191 57.0922 + 32.9622i 0.298912 + 0.172577i 0.641954 0.766743i 0.278124π-0.278124\pi
−0.343042 + 0.939320i 0.611457π0.611457\pi
192192 −148.769 + 33.3849i −0.774837 + 0.173880i
193193 55.9292 + 96.8723i 0.289789 + 0.501929i 0.973759 0.227581i 0.0730816π-0.0730816\pi
−0.683970 + 0.729510i 0.739748π0.739748\pi
194194 −6.33055 3.65494i −0.0326317 0.0188399i
195195 −40.8177 18.4455i −0.209322 0.0945924i
196196 43.4804 + 75.3103i 0.221839 + 0.384236i
197197 10.1710 + 5.87226i 0.0516297 + 0.0298084i 0.525593 0.850736i 0.323844π-0.323844\pi
−0.473963 + 0.880545i 0.657177π0.657177\pi
198198 −46.1189 + 21.7966i −0.232924 + 0.110084i
199199 9.23826 + 16.0011i 0.0464234 + 0.0804077i 0.888303 0.459257i 0.151884π-0.151884\pi
−0.841880 + 0.539665i 0.818551π0.818551\pi
200200 60.6032 34.9893i 0.303016 0.174946i
201201 150.450 + 163.338i 0.748509 + 0.812627i
202202 31.1707 0.154310
203203 240.453 + 138.826i 1.18450 + 0.683871i
204204 240.190 221.239i 1.17740 1.08450i
205205 −33.1468 −0.161692
206206 −24.9265 14.3913i −0.121002 0.0698607i
207207 74.5076 107.587i 0.359940 0.519746i
208208 184.827 + 22.5836i 0.888593 + 0.108575i
209209 −279.085 + 161.130i −1.33534 + 0.770957i
210210 4.51548 + 4.90228i 0.0215023 + 0.0233442i
211211 −13.0910 22.6743i −0.0620426 0.107461i 0.833336 0.552767i 0.186428π-0.186428\pi
−0.895378 + 0.445306i 0.853095π0.853095\pi
212212 48.8268i 0.230315i
213213 −87.1164 + 80.2427i −0.408997 + 0.376726i
214214 −4.48934 + 7.77577i −0.0209782 + 0.0363354i
215215 −41.8329 + 24.1523i −0.194572 + 0.112336i
216216 −49.0604 62.9205i −0.227132 0.291299i
217217 106.455 + 184.385i 0.490575 + 0.849701i
218218 2.19684i 0.0100773i
219219 191.121 42.8890i 0.872698 0.195840i
220220 −33.3987 + 57.8482i −0.151812 + 0.262946i
221221 −337.494 + 143.492i −1.52712 + 0.649285i
222222 −57.1688 17.8629i −0.257517 0.0804637i
223223 −322.919 −1.44807 −0.724033 0.689765i 0.757714π-0.757714\pi
−0.724033 + 0.689765i 0.757714π0.757714\pi
224224 −76.6542 44.2563i −0.342206 0.197573i
225225 −175.214 121.341i −0.778729 0.539294i
226226 50.1696 0.221989
227227 219.554 + 126.760i 0.967200 + 0.558413i 0.898382 0.439216i 0.144744π-0.144744\pi
0.0688188 + 0.997629i 0.478077π0.478077\pi
228228 −167.675 182.039i −0.735418 0.798415i
229229 119.446 206.887i 0.521600 0.903437i −0.478085 0.878314i 0.658669π-0.658669\pi
0.999684 0.0251232i 0.00799781π-0.00799781\pi
230230 6.27983i 0.0273036i
231231 222.028 + 69.3747i 0.961159 + 0.300323i
232232 159.495 0.687477
233233 42.9145i 0.184182i −0.995751 0.0920912i 0.970645π-0.970645\pi
0.995751 0.0920912i 0.0293551π-0.0293551\pi
234234 13.8360 + 41.7631i 0.0591282 + 0.178475i
235235 4.61964 0.0196580
236236 84.9045i 0.359765i
237237 39.7563 + 43.1619i 0.167748 + 0.182118i
238238 54.5691 0.229282
239239 67.0524 + 38.7127i 0.280554 + 0.161978i 0.633674 0.773600i 0.281546π-0.281546\pi
−0.353120 + 0.935578i 0.614879π0.614879\pi
240240 −47.1053 14.7185i −0.196272 0.0613270i
241241 47.8848 82.9389i 0.198692 0.344145i −0.749412 0.662103i 0.769664π-0.769664\pi
0.948105 + 0.317959i 0.102997π0.102997\pi
242242 39.9302i 0.165001i
243243 −109.410 + 216.976i −0.450247 + 0.892904i
244244 −19.9654 + 34.5811i −0.0818254 + 0.141726i
245245 25.8839i 0.105649i
246246 22.0574 + 23.9469i 0.0896642 + 0.0973450i
247247 108.752 + 255.784i 0.440290 + 1.03556i
248248 105.919 + 61.1521i 0.427091 + 0.246581i
249249 −182.716 + 168.300i −0.733801 + 0.675902i
250250 21.0240 0.0840961
251251 −365.360 + 210.940i −1.45562 + 0.840400i −0.998791 0.0491566i 0.984347π-0.984347\pi
−0.456825 + 0.889557i 0.651013π0.651013\pi
252252 −14.6498 + 178.044i −0.0581341 + 0.706524i
253253 109.586 + 189.808i 0.433146 + 0.750231i
254254 3.40435 + 1.96550i 0.0134030 + 0.00773820i
255255 94.8403 21.2829i 0.371923 0.0834624i
256256 170.225 0.664942
257257 336.324 194.177i 1.30865 0.755552i 0.326783 0.945100i 0.394035π-0.394035\pi
0.981872 + 0.189548i 0.0607022π0.0607022\pi
258258 45.2863 + 14.1501i 0.175528 + 0.0548454i
259259 136.564 + 236.535i 0.527273 + 0.913264i
260260 46.0309 + 34.6444i 0.177042 + 0.133248i
261261 −207.564 439.181i −0.795266 1.68269i
262262 16.1202 27.9210i 0.0615275 0.106569i
263263 159.385i 0.606027i −0.952986 0.303014i 0.902007π-0.902007\pi
0.952986 0.303014i 0.0979928π-0.0979928\pi
264264 130.381 29.2584i 0.493866 0.110827i
265265 −7.26665 + 12.5862i −0.0274213 + 0.0474951i
266266 41.3575i 0.155479i
267267 −445.809 139.297i −1.66970 0.521712i
268268 −142.813 247.359i −0.532883 0.922980i
269269 −138.125 + 79.7468i −0.513478 + 0.296456i −0.734262 0.678866i 0.762472π-0.762472\pi
0.220784 + 0.975323i 0.429138π0.429138\pi
270270 −1.61161 11.5487i −0.00596894 0.0427729i
271271 −96.7532 + 167.581i −0.357023 + 0.618382i −0.987462 0.157857i 0.949542π-0.949542\pi
0.630439 + 0.776239i 0.282875π0.282875\pi
272272 −349.926 + 202.030i −1.28649 + 0.742757i
273273 82.6182 182.824i 0.302631 0.669685i
274274 −20.8784 + 36.1624i −0.0761984 + 0.131979i
275275 309.117 178.469i 1.12406 0.648977i
276276 −123.806 + 114.037i −0.448573 + 0.413179i
277277 160.981 278.828i 0.581159 1.00660i −0.414183 0.910194i 0.635933π-0.635933\pi
0.995342 0.0964039i 0.0307340π-0.0307340\pi
278278 76.2750i 0.274370i
279279 30.5461 371.238i 0.109484 1.33060i
280280 −8.72957 15.1201i −0.0311770 0.0540002i
281281 −357.552 + 206.433i −1.27243 + 0.734637i −0.975444 0.220246i 0.929314π-0.929314\pi
−0.296984 + 0.954883i 0.595981π0.595981\pi
282282 −3.07411 3.33745i −0.0109011 0.0118349i
283283 −243.879 422.411i −0.861764 1.49262i −0.870225 0.492654i 0.836027π-0.836027\pi
0.00846154 0.999964i 0.497307π-0.497307\pi
284284 131.929 76.1692i 0.464538 0.268201i
285285 −16.1302 71.8788i −0.0565971 0.252206i
286286 −73.1376 8.93651i −0.255726 0.0312465i
287287 148.466i 0.517303i
288288 66.1695 + 140.007i 0.229755 + 0.486135i
289289 253.405 438.911i 0.876835 1.51872i
290290 20.1868 + 11.6548i 0.0696096 + 0.0401891i
291291 17.3931 55.6650i 0.0597700 0.191289i
292292 −251.933 −0.862785
293293 548.637i 1.87248i 0.351360 + 0.936240i 0.385719π0.385719\pi
−0.351360 + 0.936240i 0.614281π0.614281\pi
294294 18.6998 17.2243i 0.0636046 0.0585861i
295295 12.6359 21.8860i 0.0428336 0.0741899i
296296 135.876 + 78.4479i 0.459040 + 0.265027i
297297 −250.241 320.937i −0.842562 1.08059i
298298 88.4508 0.296815
299299 173.961 73.9629i 0.581810 0.247367i
300300 185.718 + 201.627i 0.619062 + 0.672091i
301301 −108.179 187.371i −0.359398 0.622496i
302302 −86.7968 + 50.1122i −0.287407 + 0.165934i
303303 54.4523 + 242.649i 0.179711 + 0.800821i
304304 153.117 + 265.206i 0.503674 + 0.872390i
305305 −10.2931 + 5.94270i −0.0337477 + 0.0194843i
306306 −78.4868 54.3545i −0.256493 0.177629i
307307 78.3446 0.255194 0.127597 0.991826i 0.459274π-0.459274\pi
0.127597 + 0.991826i 0.459274π0.459274\pi
308308 −259.104 149.594i −0.841248 0.485695i
309309 68.4850 219.180i 0.221634 0.709322i
310310 8.93720 + 15.4797i 0.0288297 + 0.0499345i
311311 −390.829 225.645i −1.25668 0.725547i −0.284255 0.958749i 0.591746π-0.591746\pi
−0.972428 + 0.233202i 0.925080π0.925080\pi
312312 −11.4099 114.681i −0.0365702 0.367568i
313313 117.824 + 204.077i 0.376435 + 0.652004i 0.990541 0.137220i 0.0438166π-0.0438166\pi
−0.614106 + 0.789224i 0.710483π0.710483\pi
314314 18.9155 + 10.9209i 0.0602404 + 0.0347798i
315315 −30.2737 + 43.7146i −0.0961070 + 0.138777i
316316 −37.7381 65.3643i −0.119424 0.206849i
317317 107.908 62.3008i 0.340404 0.196532i −0.320047 0.947402i 0.603699π-0.603699\pi
0.660451 + 0.750869i 0.270365π0.270365\pi
318318 13.9284 3.12565i 0.0438001 0.00982909i
319319 813.530 2.55025
320320 50.5505 + 29.1853i 0.157970 + 0.0912042i
321321 −68.3730 21.3638i −0.213000 0.0665538i
322322 −28.1276 −0.0873528
323323 −522.334 301.570i −1.61713 0.933652i
324324 198.415 241.489i 0.612392 0.745337i
325325 −120.454 283.308i −0.370628 0.871718i
326326 5.27611 3.04616i 0.0161844 0.00934406i
327327 −17.1013 + 3.83768i −0.0522977 + 0.0117360i
328328 −42.6425 73.8590i −0.130008 0.225180i
329329 20.6915i 0.0628922i
330330 18.6399 + 5.82421i 0.0564846 + 0.0176491i
331331 −167.292 + 289.758i −0.505413 + 0.875401i 0.494567 + 0.869139i 0.335327π0.335327\pi
−0.999980 + 0.00626172i 0.998007π0.998007\pi
332332 276.705 159.756i 0.833449 0.481192i
333333 39.1856 476.236i 0.117674 1.43014i
334334 −5.88212 10.1881i −0.0176111 0.0305034i
335335 85.0163i 0.253780i
336336 65.9246 210.986i 0.196204 0.627935i
337337 −185.957 + 322.088i −0.551802 + 0.955750i 0.446342 + 0.894862i 0.352726π0.352726\pi
−0.998145 + 0.0608873i 0.980607π0.980607\pi
338338 −15.3013 + 61.6793i −0.0452702 + 0.182483i
339339 87.6415 + 390.545i 0.258530 + 1.15205i
340340 −125.017 −0.367698
341341 540.255 + 311.916i 1.58433 + 0.914711i
342342 −41.1949 + 59.4846i −0.120453 + 0.173932i
343343 −368.002 −1.07289
344344 −107.634 62.1425i −0.312889 0.180647i
345345 −48.8854 + 10.9703i −0.141697 + 0.0317979i
346346 −0.812660 + 1.40757i −0.00234873 + 0.00406812i
347347 170.800i 0.492219i −0.969242 0.246110i 0.920848π-0.920848\pi
0.969242 0.246110i 0.0791523π-0.0791523\pi
348348 136.805 + 609.624i 0.393116 + 1.75179i
349349 134.718 0.386010 0.193005 0.981198i 0.438177π-0.438177\pi
0.193005 + 0.981198i 0.438177π0.438177\pi
350350 45.8079i 0.130880i
351351 −300.935 + 180.663i −0.857365 + 0.514709i
352352 −259.345 −0.736777
353353 126.976i 0.359705i 0.983694 + 0.179853i 0.0575621π0.0575621\pi
−0.983694 + 0.179853i 0.942438π0.942438\pi
354354 −24.2200 + 5.43517i −0.0684181 + 0.0153536i
355355 45.3435 0.127728
356356 520.255 + 300.370i 1.46139 + 0.843735i
357357 95.3270 + 424.793i 0.267023 + 1.18990i
358358 0.347278 0.601503i 0.000970051 0.00168018i
359359 443.856i 1.23637i −0.786034 0.618184i 0.787869π-0.787869\pi
0.786034 0.618184i 0.212131π-0.212131\pi
360360 −2.50486 + 30.4424i −0.00695795 + 0.0845624i
361361 −48.0575 + 83.2381i −0.133123 + 0.230576i
362362 4.03625i 0.0111499i
363363 310.837 69.7543i 0.856300 0.192161i
364364 −155.174 + 206.174i −0.426301 + 0.566413i
365365 −64.9414 37.4939i −0.177922 0.102723i
366366 11.1428 + 3.48166i 0.0304447 + 0.00951272i
367367 −116.173 −0.316547 −0.158274 0.987395i 0.550593π-0.550593\pi
−0.158274 + 0.987395i 0.550593π0.550593\pi
368368 180.369 104.136i 0.490134 0.282979i
369369 −147.882 + 213.539i −0.400765 + 0.578696i
370370 11.4649 + 19.8579i 0.0309863 + 0.0536699i
371371 −56.3741 32.5476i −0.151952 0.0877294i
372372 −142.887 + 457.296i −0.384104 + 1.22929i
373373 210.987 0.565649 0.282825 0.959172i 0.408729π-0.408729\pi
0.282825 + 0.959172i 0.408729π0.408729\pi
374374 138.468 79.9447i 0.370236 0.213756i
375375 36.7270 + 163.662i 0.0979386 + 0.436431i
376376 5.94304 + 10.2936i 0.0158060 + 0.0273767i
377377 85.1006 696.474i 0.225731 1.84741i
378378 51.7270 7.21848i 0.136844 0.0190965i
379379 −190.883 + 330.619i −0.503650 + 0.872347i 0.496341 + 0.868127i 0.334676π0.334676\pi
−0.999991 + 0.00421947i 0.998657π0.998657\pi
380380 94.7498i 0.249342i
381381 −9.35339 + 29.9348i −0.0245496 + 0.0785689i
382382 −12.3947 + 21.4683i −0.0324470 + 0.0561998i
383383 253.952i 0.663061i −0.943445 0.331530i 0.892435π-0.892435\pi
0.943445 0.331530i 0.107565π-0.107565\pi
384384 −57.7638 257.405i −0.150427 0.670326i
385385 −44.5266 77.1224i −0.115654 0.200318i
386386 −36.4268 + 21.0310i −0.0943699 + 0.0544845i
387387 −31.0408 + 377.250i −0.0802089 + 0.974806i
388388 −37.5050 + 64.9606i −0.0966624 + 0.167424i
389389 −291.388 + 168.233i −0.749070 + 0.432476i −0.825358 0.564610i 0.809027π-0.809027\pi
0.0762879 + 0.997086i 0.475693π0.475693\pi
390390 6.93605 15.3486i 0.0177847 0.0393555i
391391 −205.100 + 355.244i −0.524553 + 0.908552i
392392 −57.6755 + 33.2990i −0.147131 + 0.0849463i
393393 245.512 + 76.7124i 0.624711 + 0.195197i
394394 −2.20814 + 3.82461i −0.00560441 + 0.00970713i
395395 22.4655i 0.0568746i
396396 223.664 + 473.247i 0.564809 + 1.19507i
397397 −124.854 216.254i −0.314494 0.544720i 0.664835 0.746990i 0.268502π-0.268502\pi
−0.979330 + 0.202269i 0.935168π0.935168\pi
398398 −6.01689 + 3.47385i −0.0151178 + 0.00872828i
399399 321.948 72.2477i 0.806887 0.181072i
400400 −169.594 293.745i −0.423984 0.734361i
401401 −487.509 + 281.464i −1.21573 + 0.701904i −0.964003 0.265893i 0.914333π-0.914333\pi
−0.251731 + 0.967797i 0.581000π0.581000\pi
402402 −61.4198 + 56.5736i −0.152786 + 0.140730i
403403 323.550 429.892i 0.802854 1.06673i
404404 319.857i 0.791724i
405405 87.0855 32.7201i 0.215026 0.0807903i
406406 −52.2025 + 90.4174i −0.128578 + 0.222703i
407407 693.058 + 400.137i 1.70284 + 0.983138i
408408 169.433 + 183.947i 0.415277 + 0.450850i
409409 −740.437 −1.81036 −0.905179 0.425030i 0.860264π-0.860264\pi
−0.905179 + 0.425030i 0.860264π0.860264\pi
410410 12.4642i 0.0304004i
411411 −317.979 99.3554i −0.773671 0.241741i
412412 −147.676 + 255.782i −0.358436 + 0.620829i
413413 98.0284 + 56.5967i 0.237357 + 0.137038i
414414 40.4560 + 28.0170i 0.0977198 + 0.0676740i
415415 95.1026 0.229163
416416 −27.1292 + 222.029i −0.0652145 + 0.533724i
417417 593.763 133.245i 1.42389 0.319533i
418418 −60.5896 104.944i −0.144951 0.251063i
419419 387.326 223.623i 0.924405 0.533705i 0.0393673 0.999225i 0.487466π-0.487466\pi
0.885038 + 0.465519i 0.154132π0.154132\pi
420420 50.3045 46.3354i 0.119773 0.110322i
421421 −159.450 276.175i −0.378741 0.655999i 0.612138 0.790751i 0.290310π-0.290310\pi
−0.990879 + 0.134752i 0.956976π0.956976\pi
422422 8.52618 4.92259i 0.0202042 0.0116649i
423423 20.6102 29.7607i 0.0487238 0.0703562i
424424 −37.3934 −0.0881920
425425 578.541 + 334.021i 1.36127 + 0.785931i
426426 −30.1736 32.7583i −0.0708300 0.0768974i
427427 −26.6176 46.1030i −0.0623362 0.107970i
428428 79.7906 + 46.0671i 0.186427 + 0.107634i
429429 −58.1981 584.951i −0.135660 1.36352i
430430 −9.08195 15.7304i −0.0211208 0.0365823i
431431 101.578 + 58.6459i 0.235679 + 0.136069i 0.613189 0.789936i 0.289886π-0.289886\pi
−0.377510 + 0.926005i 0.623220π0.623220\pi
432432 −304.976 + 237.796i −0.705964 + 0.550455i
433433 211.520 + 366.363i 0.488498 + 0.846104i 0.999912 0.0132303i 0.00421145π-0.00421145\pi
−0.511414 + 0.859334i 0.670878π0.670878\pi
434434 −69.3341 + 40.0301i −0.159756 + 0.0922352i
435435 −55.4628 + 177.504i −0.127501 + 0.408055i
436436 22.5428 0.0517037
437437 269.237 + 155.444i 0.616103 + 0.355707i
438438 16.1275 + 71.8670i 0.0368208 + 0.164080i
439439 −268.616 −0.611882 −0.305941 0.952050i 0.598971π-0.598971\pi
−0.305941 + 0.952050i 0.598971π0.598971\pi
440440 −44.3023 25.5780i −0.100687 0.0581317i
441441 166.749 + 115.479i 0.378117 + 0.261858i
442442 −53.9571 126.907i −0.122075 0.287121i
443443 33.2832 19.2161i 0.0751314 0.0433771i −0.461964 0.886899i 0.652855π-0.652855\pi
0.537095 + 0.843522i 0.319522π0.319522\pi
444444 −183.300 + 586.635i −0.412837 + 1.32125i
445445 89.4049 + 154.854i 0.200910 + 0.347986i
446446 121.427i 0.272257i
447447 154.515 + 688.546i 0.345672 + 1.54037i
448448 −130.722 + 226.418i −0.291791 + 0.505396i
449449 −521.983 + 301.367i −1.16254 + 0.671196i −0.951913 0.306370i 0.900886π-0.900886\pi
−0.210632 + 0.977565i 0.567552π0.567552\pi
450450 45.6278 65.8856i 0.101395 0.146412i
451451 −217.505 376.730i −0.482274 0.835323i
452452 514.812i 1.13897i
453453 −541.724 588.129i −1.19586 1.29830i
454454 −47.6654 + 82.5589i −0.104990 + 0.181848i
455455 −70.6833 + 30.0524i −0.155348 + 0.0660491i
456456 139.412 128.412i 0.305728 0.281605i
457457 259.602 0.568058 0.284029 0.958816i 0.408329π-0.408329\pi
0.284029 + 0.958816i 0.408329π0.408329\pi
458458 77.7955 + 44.9153i 0.169859 + 0.0980683i
459459 286.014 705.933i 0.623125 1.53798i
460460 64.4402 0.140087
461461 −462.851 267.227i −1.00402 0.579669i −0.0945820 0.995517i 0.530151π-0.530151\pi
−0.909434 + 0.415848i 0.863485π0.863485\pi
462462 −26.0869 + 83.4889i −0.0564651 + 0.180712i
463463 −307.484 + 532.579i −0.664113 + 1.15028i 0.315412 + 0.948955i 0.397857π0.397857\pi
−0.979525 + 0.201323i 0.935476π0.935476\pi
464464 773.073i 1.66610i
465465 −104.889 + 96.6132i −0.225568 + 0.207770i
466466 16.1371 0.0346290
467467 247.090i 0.529100i −0.964372 0.264550i 0.914777π-0.914777\pi
0.964372 0.264550i 0.0852234π-0.0852234\pi
468468 428.550 141.977i 0.915706 0.303371i
469469 380.791 0.811921
470470 1.73712i 0.00369599i
471471 −51.9700 + 166.325i −0.110340 + 0.353133i
472472 65.0230 0.137761
473473 −549.005 316.968i −1.16069 0.670123i
474474 −16.2301 + 14.9495i −0.0342408 + 0.0315391i
475475 253.152 438.472i 0.532952 0.923099i
476476 559.958i 1.17638i
477477 48.6633 + 102.966i 0.102020 + 0.215861i
478478 −14.5571 + 25.2136i −0.0304542 + 0.0527482i
479479 820.294i 1.71251i 0.516550 + 0.856257i 0.327216π0.327216\pi
−0.516550 + 0.856257i 0.672784π0.672784\pi
480480 17.6810 56.5866i 0.0368354 0.117889i
481481 415.061 551.479i 0.862913 1.14653i
482482 31.1874 + 18.0061i 0.0647042 + 0.0373570i
483483 −49.1363 218.960i −0.101731 0.453332i
484484 −409.742 −0.846573
485485 −19.3355 + 11.1634i −0.0398670 + 0.0230172i
486486 −81.5892 41.1413i −0.167879 0.0846529i
487487 −367.489 636.510i −0.754598 1.30700i −0.945574 0.325407i 0.894499π-0.894499\pi
0.190976 0.981595i 0.438835π-0.438835\pi
488488 −26.4835 15.2903i −0.0542695 0.0313325i
489489 32.9297 + 35.7505i 0.0673410 + 0.0731095i
490490 −9.73309 −0.0198635
491491 113.097 65.2966i 0.230340 0.132987i −0.380389 0.924827i 0.624210π-0.624210\pi
0.610729 + 0.791840i 0.290876π0.290876\pi
492492 245.729 226.341i 0.499450 0.460042i
493493 761.298 + 1318.61i 1.54421 + 2.67466i
494494 −96.1823 + 40.8937i −0.194701 + 0.0827808i
495495 −12.7765 + 155.277i −0.0258110 + 0.313691i
496496 296.405 513.388i 0.597590 1.03506i
497497 203.095i 0.408642i
498498 −63.2855 68.7066i −0.127079 0.137965i
499499 −14.4740 + 25.0696i −0.0290059 + 0.0502397i −0.880164 0.474670i 0.842568π-0.842568\pi
0.851158 + 0.524909i 0.175901π0.175901\pi
500500 215.737i 0.431474i
501501 69.0341 63.5871i 0.137793 0.126920i
502502 −79.3197 137.386i −0.158007 0.273677i
503503 −255.144 + 147.308i −0.507245 + 0.292858i −0.731701 0.681626i 0.761273π-0.761273\pi
0.224455 + 0.974484i 0.427940π0.427940\pi
504504 −136.353 11.2194i −0.270541 0.0222606i
505505 47.6026 82.4502i 0.0942627 0.163268i
506506 −71.3735 + 41.2075i −0.141054 + 0.0814377i
507507 −506.873 11.3655i −0.999749 0.0224172i
508508 20.1689 34.9336i 0.0397026 0.0687669i
509509 538.032 310.633i 1.05704 0.610280i 0.132425 0.991193i 0.457724π-0.457724\pi
0.924611 + 0.380913i 0.124390π0.124390\pi
510510 8.00300 + 35.6627i 0.0156921 + 0.0699269i
511511 167.937 290.875i 0.328644 0.569227i
512512 415.752i 0.812016i
513513 −535.022 216.768i −1.04293 0.422550i
514514 73.0161 + 126.468i 0.142055 + 0.246046i
515515 −76.1333 + 43.9556i −0.147832 + 0.0853507i
516516 145.201 464.703i 0.281397 0.900587i
517517 30.3135 + 52.5045i 0.0586334 + 0.101556i
518518 −88.9441 + 51.3519i −0.171707 + 0.0991350i
519519 −12.3769 3.86727i −0.0238475 0.00745138i
520520 −26.5320 + 35.2522i −0.0510230 + 0.0677927i
521521 166.583i 0.319738i 0.987138 + 0.159869i 0.0511071π0.0511071\pi
−0.987138 + 0.159869i 0.948893π0.948893\pi
522522 165.145 78.0502i 0.316370 0.149522i
523523 −51.1561 + 88.6049i −0.0978127 + 0.169417i −0.910779 0.412894i 0.864518π-0.864518\pi
0.812966 + 0.582311i 0.197851π0.197851\pi
524524 −286.510 165.417i −0.546775 0.315680i
525525 −356.592 + 80.0221i −0.679223 + 0.152423i
526526 59.9334 0.113942
527527 1167.56i 2.21548i
528528 −141.816 631.956i −0.268591 1.19689i
529529 −158.781 + 275.017i −0.300153 + 0.519881i
530530 −4.73278 2.73247i −0.00892977 0.00515560i
531531 −84.6202 179.046i −0.159360 0.337187i
532532 −424.388 −0.797722
533533 −345.277 + 146.801i −0.647799 + 0.275424i
534534 52.3798 167.637i 0.0980895 0.313927i
535535 13.7119 + 23.7497i 0.0256297 + 0.0443919i
536536 189.436 109.371i 0.353426 0.204051i
537537 5.28907 + 1.65262i 0.00984929 + 0.00307750i
538538 −29.9871 51.9392i −0.0557381 0.0965412i
539539 −294.184 + 169.847i −0.545795 + 0.315115i
540540 −118.506 + 16.5375i −0.219456 + 0.0306250i
541541 638.732 1.18065 0.590325 0.807166i 0.299000π-0.299000\pi
0.590325 + 0.807166i 0.299000π0.299000\pi
542542 −63.0155 36.3820i −0.116265 0.0671255i
543543 31.4202 7.05095i 0.0578641 0.0129852i
544544 −242.694 420.359i −0.446129 0.772719i
545545 5.81091 + 3.35493i 0.0106622 + 0.00615583i
546546 68.7471 + 31.0668i 0.125911 + 0.0568990i
547547 −250.228 433.408i −0.457456 0.792337i 0.541370 0.840785i 0.317906π-0.317906\pi
−0.998826 + 0.0484477i 0.984573π0.984573\pi
548548 371.078 + 214.242i 0.677150 + 0.390953i
549549 −7.63764 + 92.8229i −0.0139119 + 0.169076i
550550 67.1094 + 116.237i 0.122017 + 0.211340i
551551 999.363 576.982i 1.81373 1.04715i
552552 −87.3342 94.8153i −0.158214 0.171767i
553553 100.624 0.181960
554554 104.847 + 60.5336i 0.189255 + 0.109266i
555555 −134.555 + 123.939i −0.242442 + 0.223313i
556556 −782.692 −1.40772
557557 −217.719 125.700i −0.390877 0.225673i 0.291663 0.956521i 0.405791π-0.405791\pi
−0.682540 + 0.730848i 0.739125π0.739125\pi
558558 139.596 + 11.4862i 0.250172 + 0.0205846i
559559 −328.791 + 436.854i −0.588176 + 0.781492i
560560 −73.2871 + 42.3123i −0.130870 + 0.0755577i
561561 864.221 + 938.252i 1.54050 + 1.67246i
562562 −77.6247 134.450i −0.138122 0.239235i
563563 751.814i 1.33537i −0.744443 0.667685i 0.767285π-0.767285\pi
0.744443 0.667685i 0.232715π-0.232715\pi
564564 −34.2470 + 31.5449i −0.0607217 + 0.0559306i
565565 76.6169 132.704i 0.135605 0.234875i
566566 158.839 91.7056i 0.280634 0.162024i
567567 146.555 + 390.059i 0.258474 + 0.687935i
568568 58.3332 + 101.036i 0.102699 + 0.177880i
569569 536.258i 0.942456i −0.882011 0.471228i 0.843811π-0.843811\pi
0.882011 0.471228i 0.156189π-0.156189\pi
570570 27.0285 6.06541i 0.0474184 0.0106411i
571571 −50.9656 + 88.2750i −0.0892567 + 0.154597i −0.907197 0.420706i 0.861782π-0.861782\pi
0.817940 + 0.575303i 0.195116π0.195116\pi
572572 −91.7015 + 750.497i −0.160317 + 1.31206i
573573 −188.773 58.9838i −0.329447 0.102939i
574574 55.8275 0.0972605
575575 −298.209 172.171i −0.518624 0.299428i
576576 413.545 195.448i 0.717961 0.339320i
577577 −6.86778 −0.0119026 −0.00595128 0.999982i 0.501894π-0.501894\pi
−0.00595128 + 0.999982i 0.501894π0.501894\pi
578578 165.043 + 95.2877i 0.285542 + 0.164858i
579579 −227.350 246.825i −0.392660 0.426296i
580580 119.596 207.146i 0.206199 0.357148i
581581 425.968i 0.733164i
582582 20.9317 + 6.54029i 0.0359651 + 0.0112376i
583583 −190.731 −0.327155
584584 192.940i 0.330377i
585585 131.598 + 27.1811i 0.224954 + 0.0464634i
586586 −206.303 −0.352054
587587 522.260i 0.889711i −0.895602 0.444855i 0.853255π-0.853255\pi
0.895602 0.444855i 0.146745π-0.146745\pi
588588 −176.746 191.887i −0.300589 0.326338i
589589 884.886 1.50235
590590 8.22978 + 4.75147i 0.0139488 + 0.00805333i
591591 −33.6301 10.5080i −0.0569037 0.0177801i
592592 380.238 658.592i 0.642294 1.11249i
593593 624.635i 1.05335i 0.850068 + 0.526674i 0.176561π0.176561\pi
−0.850068 + 0.526674i 0.823439π0.823439\pi
594594 120.681 94.0979i 0.203167 0.158414i
595595 83.3357 144.342i 0.140060 0.242591i
596596 907.633i 1.52287i
597597 −37.5532 40.7700i −0.0629032 0.0682915i
598598 27.8122 + 65.4144i 0.0465087 + 0.109389i
599599 −472.937 273.050i −0.789544 0.455843i 0.0502581 0.998736i 0.483996π-0.483996\pi
−0.839802 + 0.542893i 0.817329π0.817329\pi
600600 −154.414 + 142.230i −0.257356 + 0.237050i
601601 563.710 0.937953 0.468977 0.883211i 0.344623π-0.344623\pi
0.468977 + 0.883211i 0.344623π0.344623\pi
602602 70.4571 40.6784i 0.117038 0.0675721i
603603 −547.693 379.294i −0.908279 0.629012i
604604 514.223 + 890.661i 0.851363 + 1.47460i
605605 −105.620 60.9797i −0.174579 0.100793i
606606 −91.2429 + 20.4756i −0.150566 + 0.0337882i
607607 201.365 0.331739 0.165869 0.986148i 0.446957π-0.446957\pi
0.165869 + 0.986148i 0.446957π0.446957\pi
608608 −318.587 + 183.936i −0.523992 + 0.302527i
609609 −795.048 248.420i −1.30550 0.407915i
610610 −2.23463 3.87049i −0.00366332 0.00634506i
611611 48.1208 20.4595i 0.0787575 0.0334852i
612612 −557.756 + 805.388i −0.911367 + 1.31599i
613613 −317.568 + 550.044i −0.518055 + 0.897298i 0.481725 + 0.876322i 0.340010π0.340010\pi
−0.999780 + 0.0209752i 0.993323π0.993323\pi
614614 29.4598i 0.0479802i
615615 97.0274 21.7737i 0.157768 0.0354044i
616616 114.565 198.432i 0.185982 0.322130i
617617 64.1839i 0.104026i 0.998646 + 0.0520129i 0.0165637π0.0165637\pi
−0.998646 + 0.0520129i 0.983436π0.983436\pi
618618 82.4182 + 25.7523i 0.133363 + 0.0416704i
619619 3.79581 + 6.57454i 0.00613217 + 0.0106212i 0.869075 0.494680i 0.164715π-0.164715\pi
−0.862943 + 0.505301i 0.831381π0.831381\pi
620620 158.844 91.7086i 0.256200 0.147917i
621621 −147.426 + 363.873i −0.237401 + 0.585947i
622622 84.8491 146.963i 0.136413 0.236275i
623623 −693.597 + 400.448i −1.11332 + 0.642774i
624624 −555.861 + 55.3039i −0.890803 + 0.0886281i
625625 −263.904 + 457.096i −0.422247 + 0.731354i
626626 −76.7389 + 44.3052i −0.122586 + 0.0707752i
627627 711.095 654.987i 1.13412 1.04464i
628628 112.064 194.100i 0.178446 0.309077i
629629 1497.79i 2.38122i
630630 −16.4380 11.3838i −0.0260920 0.0180695i
631631 423.578 + 733.658i 0.671280 + 1.16269i 0.977541 + 0.210743i 0.0675884π0.0675884\pi
−0.306262 + 0.951947i 0.599078π0.599078\pi
632632 50.0584 28.9012i 0.0792064 0.0457298i
633633 53.2144 + 57.7728i 0.0840669 + 0.0912682i
634634 23.4269 + 40.5766i 0.0369509 + 0.0640009i
635635 10.3980 6.00327i 0.0163748 0.00945398i
636636 −32.0737 142.926i −0.0504304 0.224726i
637637 114.635 + 269.622i 0.179960 + 0.423268i
638638 305.911i 0.479484i
639639 202.297 292.112i 0.316583 0.457139i
640640 −50.4976 + 87.4644i −0.0789025 + 0.136663i
641641 928.289 + 535.948i 1.44819 + 0.836112i 0.998374 0.0570099i 0.0181567π-0.0181567\pi
0.449815 + 0.893122i 0.351490π0.351490\pi
642642 8.03340 25.7102i 0.0125131 0.0400471i
643643 411.550 0.640047 0.320023 0.947410i 0.396309π-0.396309\pi
0.320023 + 0.947410i 0.396309π0.396309\pi
644644 288.630i 0.448183i
645645 106.588 98.1780i 0.165253 0.152214i
646646 113.399 196.413i 0.175540 0.304044i
647647 872.018 + 503.460i 1.34779 + 0.778145i 0.987936 0.154865i 0.0494943π-0.0494943\pi
0.359851 + 0.933010i 0.382828π0.382828\pi
648648 184.941 + 151.954i 0.285403 + 0.234496i
649649 331.661 0.511034
650650 106.532 45.2942i 0.163896 0.0696834i
651651 −432.734 469.803i −0.664723 0.721664i
652652 −31.2580 54.1405i −0.0479418 0.0830376i
653653 −999.048 + 576.801i −1.52994 + 0.883309i −0.530573 + 0.847639i 0.678023π0.678023\pi
−0.999364 + 0.0356698i 0.988644π0.988644\pi
654654 −1.44308 6.43060i −0.00220654 0.00983272i
655655 −49.2362 85.2796i −0.0751698 0.130198i
656656 −357.996 + 206.689i −0.545725 + 0.315074i
657657 −531.275 + 251.090i −0.808638 + 0.382176i
658658 −7.78061 −0.0118246
659659 −269.095 155.362i −0.408338 0.235754i 0.281737 0.959492i 0.409089π-0.409089\pi
−0.690076 + 0.723737i 0.742423π0.742423\pi
660660 59.7649 191.272i 0.0905528 0.289807i
661661 257.855 + 446.618i 0.390099 + 0.675670i 0.992462 0.122551i 0.0391076π-0.0391076\pi
−0.602364 + 0.798222i 0.705774π0.705774\pi
662662 −108.957 62.9065i −0.164588 0.0950250i
663663 893.654 641.725i 1.34789 0.967911i
664664 122.347 + 211.911i 0.184257 + 0.319143i
665665 −109.395 63.1595i −0.164505 0.0949767i
666666 179.079 + 14.7349i 0.268887 + 0.0221245i
667667 −392.411 679.675i −0.588322 1.01900i
668668 −104.545 + 60.3591i −0.156505 + 0.0903580i
669669 945.248 212.121i 1.41293 0.317072i
670670 31.9686 0.0477143
671671 −135.084 77.9905i −0.201317 0.116230i
672672 253.454 + 79.1939i 0.377163 + 0.117848i
673673 −209.818 −0.311765 −0.155883 0.987776i 0.549822π-0.549822\pi
−0.155883 + 0.987776i 0.549822π0.549822\pi
674674 −121.114 69.9254i −0.179695 0.103747i
675675 592.594 + 240.094i 0.877917 + 0.355695i
676676 632.919 + 157.014i 0.936270 + 0.232269i
677677 11.9220 6.88315i 0.0176100 0.0101671i −0.491169 0.871064i 0.663430π-0.663430\pi
0.508779 + 0.860897i 0.330097π0.330097\pi
678678 −146.856 + 32.9557i −0.216602 + 0.0486073i
679679 −50.0011 86.6045i −0.0736394 0.127547i
680680 95.7430i 0.140799i
681681 −725.947 226.829i −1.06600 0.333082i
682682 −117.290 + 203.152i −0.171979 + 0.297876i
683683 402.924 232.628i 0.589933 0.340598i −0.175138 0.984544i 0.556037π-0.556037\pi
0.765071 + 0.643946i 0.222704π0.222704\pi
684684 610.398 + 422.720i 0.892395 + 0.618011i
685685 63.7691 + 110.451i 0.0930936 + 0.161243i
686686 138.380i 0.201719i
687687 −213.742 + 684.062i −0.311123 + 0.995724i
688688 −301.205 + 521.703i −0.437799 + 0.758289i
689689 −19.9518 + 163.288i −0.0289576 + 0.236992i
690690 −4.12514 18.3823i −0.00597847 0.0266411i
691691 −518.379 −0.750187 −0.375094 0.926987i 0.622389π-0.622389\pi
−0.375094 + 0.926987i 0.622389π0.622389\pi
692692 14.4437 + 8.33907i 0.0208724 + 0.0120507i
693693 −695.491 57.2263i −1.00359 0.0825776i
694694 64.2258 0.0925443
695695 −201.756 116.484i −0.290297 0.167603i
696696 −466.873 + 104.770i −0.670794 + 0.150532i
697697 407.081 705.086i 0.584048 1.01160i
698698 50.6577i 0.0725755i
699699 28.1900 + 125.619i 0.0403290 + 0.179713i
700700 470.055 0.671508
701701 775.035i 1.10561i 0.833310 + 0.552806i 0.186443π0.186443\pi
−0.833310 + 0.552806i 0.813557π0.813557\pi
702702 −67.9344 113.160i −0.0967727 0.161197i
703703 1135.16 1.61474
704704 766.042i 1.08813i
705705 −13.5226 + 3.03458i −0.0191810 + 0.00430437i
706706 −47.7466 −0.0676298
707707 369.298 + 213.214i 0.522345 + 0.301576i
708708 55.7727 + 248.532i 0.0787750 + 0.351034i
709709 −308.569 + 534.457i −0.435217 + 0.753819i −0.997313 0.0732533i 0.976662π-0.976662\pi
0.562096 + 0.827072i 0.309995π0.309995\pi
710710 17.0505i 0.0240147i
711711 −144.727 100.228i −0.203555 0.140968i
712712 −230.034 + 398.431i −0.323082 + 0.559594i
713713 601.819i 0.844066i
714714 −159.735 + 35.8457i −0.223718 + 0.0502041i
715715 −135.331 + 179.810i −0.189274 + 0.251482i
716716 −6.17230 3.56358i −0.00862052 0.00497706i
717717 −221.706 69.2740i −0.309213 0.0966165i
718718 166.903 0.232455
719719 −534.714 + 308.717i −0.743692 + 0.429371i −0.823410 0.567447i 0.807931π-0.807931\pi
0.0797184 + 0.996817i 0.474598π0.474598\pi
720720 147.555 + 12.1411i 0.204937 + 0.0168626i
721721 −196.879 341.004i −0.273064 0.472960i
722722 −31.2999 18.0710i −0.0433517 0.0250291i
723723 −85.6869 + 274.234i −0.118516 + 0.379300i
724724 −41.4178 −0.0572069
725725 −1106.90 + 639.070i −1.52676 + 0.881475i
726726 26.2296 + 116.884i 0.0361290 + 0.160997i
727727 −527.853 914.268i −0.726070 1.25759i −0.958532 0.284984i 0.908012π-0.908012\pi
0.232462 0.972605i 0.425322π-0.425322\pi
728728 −157.896 118.838i −0.216890 0.163239i
729729 177.736 707.001i 0.243808 0.969823i
730730 14.0988 24.4199i 0.0193134 0.0334519i
731731 1186.47i 1.62308i
732732 35.7268 114.341i 0.0488072 0.156203i
733733 435.712 754.675i 0.594422 1.02957i −0.399206 0.916861i 0.630714π-0.630714\pi
0.993628 0.112708i 0.0359526π-0.0359526\pi
734734 43.6844i 0.0595155i
735735 −17.0028 75.7673i −0.0231331 0.103085i
736736 125.097 + 216.674i 0.169968 + 0.294394i
737737 966.253 557.866i 1.31106 0.756942i
738738 −80.2968 55.6080i −0.108803 0.0753496i
739739 38.1201 66.0259i 0.0515833 0.0893449i −0.839081 0.544007i 0.816907π-0.816907\pi
0.890664 + 0.454662i 0.150240π0.150240\pi
740740 203.770 117.647i 0.275365 0.158982i
741741 −486.359 677.294i −0.656355 0.914027i
742742 12.2388 21.1983i 0.0164944 0.0285691i
743743 426.534 246.260i 0.574071 0.331440i −0.184703 0.982794i 0.559132π-0.559132\pi
0.758773 + 0.651355i 0.225799π0.225799\pi
744744 −350.215 109.428i −0.470719 0.147080i
745745 135.078 233.963i 0.181313 0.314044i
746746 79.3373i 0.106350i
747747 424.293 612.671i 0.567997 0.820175i
748748 −820.349 1420.89i −1.09672 1.89958i
749749 −106.376 + 61.4160i −0.142024 + 0.0819974i
750750 −61.5415 + 13.8104i −0.0820553 + 0.0184139i
751751 −197.444 341.982i −0.262907 0.455369i 0.704106 0.710095i 0.251348π-0.251348\pi
−0.967013 + 0.254726i 0.918015π0.918015\pi
752752 49.8934 28.8060i 0.0663477 0.0383058i
753753 930.916 857.465i 1.23628 1.13873i
754754 261.894 + 32.0003i 0.347340 + 0.0424407i
755755 306.117i 0.405453i
756756 −74.0720 530.794i −0.0979789 0.702109i
757757 45.1326 78.1720i 0.0596204 0.103266i −0.834675 0.550743i 0.814344π-0.814344\pi
0.894295 + 0.447478i 0.147678π0.147678\pi
758758 −124.323 71.7776i −0.164014 0.0946934i
759759 −445.463 483.622i −0.586907 0.637183i
760760 −72.5630 −0.0954776
761761 749.692i 0.985140i −0.870273 0.492570i 0.836058π-0.836058\pi
0.870273 0.492570i 0.163942π-0.163942\pi
762762 −11.2563 3.51715i −0.0147721 0.00461568i
763763 −15.0269 + 26.0273i −0.0196944 + 0.0341118i
764764 220.296 + 127.188i 0.288346 + 0.166477i
765765 −263.636 + 124.599i −0.344622 + 0.162874i
766766 95.4934 0.124665
767767 34.6939 283.940i 0.0452333 0.370195i
768768 −498.283 + 111.819i −0.648806 + 0.145597i
769769 6.79598 + 11.7710i 0.00883743 + 0.0153069i 0.870410 0.492327i 0.163854π-0.163854\pi
−0.861573 + 0.507634i 0.830520π0.830520\pi
770770 29.0003 16.7433i 0.0376627 0.0217445i
771771 −856.936 + 789.321i −1.11146 + 1.02376i
772772 215.809 + 373.792i 0.279545 + 0.484186i
773773 −20.8183 + 12.0195i −0.0269318 + 0.0155491i −0.513405 0.858146i 0.671616π-0.671616\pi
0.486474 + 0.873695i 0.338283π0.338283\pi
774774 −141.857 11.6723i −0.183278 0.0150804i
775775 −980.106 −1.26465
776776 −49.7493 28.7227i −0.0641099 0.0370138i
777777 −555.126 602.679i −0.714448 0.775649i
778778 −63.2605 109.570i −0.0813117 0.140836i
779779 −534.379 308.524i −0.685981 0.396052i
780780 −157.499 71.1739i −0.201922 0.0912486i
781781 297.538 + 515.351i 0.380971 + 0.659861i
782782 −133.582 77.1236i −0.170821 0.0986235i
783783 896.075 + 1149.23i 1.14441 + 1.46772i
784784 161.400 + 279.554i 0.205868 + 0.356574i
785785 57.7739 33.3558i 0.0735974 0.0424915i
786786 −28.8461 + 92.3195i −0.0366999 + 0.117455i
787787 −564.709 −0.717546 −0.358773 0.933425i 0.616805π-0.616805\pi
−0.358773 + 0.933425i 0.616805π0.616805\pi
788788 39.2460 + 22.6587i 0.0498046 + 0.0287547i
789789 104.698 + 466.552i 0.132697 + 0.591321i
790790 8.44767 0.0106933
791791 594.388 + 343.170i 0.751439 + 0.433843i
792792 −362.430 + 171.291i −0.457614 + 0.216276i
793793 −80.8994 + 107.489i −0.102017 + 0.135547i
794794 81.3178 46.9488i 0.102415 0.0591295i
795795 13.0032 41.6157i 0.0163562 0.0523468i
796796 35.6468 + 61.7420i 0.0447824 + 0.0775654i
797797 410.342i 0.514858i −0.966297 0.257429i 0.917125π-0.917125\pi
0.966297 0.257429i 0.0828754π-0.0828754\pi
798798 27.1672 + 121.062i 0.0340441 + 0.151706i
799799 −56.7345 + 98.2670i −0.0710068 + 0.122987i
800800 352.869 203.729i 0.441087 0.254662i
801801 1396.47 + 114.905i 1.74341 + 0.143451i
802802 −105.838 183.318i −0.131968 0.228576i
803803 984.123i 1.22556i
804804 580.528 + 630.256i 0.722049 + 0.783901i
805805 −42.9553 + 74.4008i −0.0533607 + 0.0924234i
806806 161.652 + 121.664i 0.200560 + 0.150948i
807807 351.936 324.168i 0.436104 0.401695i
808808 244.958 0.303166
809809 −518.289 299.234i −0.640654 0.369882i 0.144212 0.989547i 0.453935π-0.453935\pi
−0.784867 + 0.619665i 0.787269π0.787269\pi
810810 12.3037 + 32.7467i 0.0151898 + 0.0404280i
811811 −427.373 −0.526971 −0.263485 0.964663i 0.584872π-0.584872\pi
−0.263485 + 0.964663i 0.584872π0.584872\pi
812812 927.814 + 535.673i 1.14263 + 0.659696i
813813 173.134 554.100i 0.212957 0.681550i
814814 −150.463 + 260.610i −0.184844 + 0.320159i
815815 18.6079i 0.0228318i
816816 891.592 821.244i 1.09264 1.00643i
817817 −899.218 −1.10063
818818 278.426i 0.340374i
819819 −121.745 + 589.433i −0.148651 + 0.719699i
820820 −127.900 −0.155976
821821 515.147i 0.627463i 0.949512 + 0.313732i 0.101579π0.101579\pi
−0.949512 + 0.313732i 0.898421π0.898421\pi
822822 37.3605 119.569i 0.0454507 0.145461i
823823 −992.582 −1.20605 −0.603026 0.797721i 0.706039π-0.706039\pi
−0.603026 + 0.797721i 0.706039π0.706039\pi
824824 −195.887 113.095i −0.237727 0.137252i
825825 −787.613 + 725.469i −0.954683 + 0.879356i
826826 −21.2820 + 36.8615i −0.0257651 + 0.0446265i
827827 943.762i 1.14119i −0.821233 0.570594i 0.806713π-0.806713\pi
0.821233 0.570594i 0.193287π-0.193287\pi
828828 287.495 415.137i 0.347217 0.501373i
829829 133.486 231.205i 0.161021 0.278896i −0.774214 0.632924i 0.781855π-0.781855\pi
0.935235 + 0.354027i 0.115188π0.115188\pi
830830 35.7613i 0.0430859i
831831 −288.066 + 921.930i −0.346650 + 1.10942i
832832 655.820 + 80.1331i 0.788245 + 0.0963138i
833833 −550.591 317.884i −0.660974 0.381614i
834834 50.1041 + 223.272i 0.0600768 + 0.267712i
835835 −35.9318 −0.0430320
836836 −1076.88 + 621.737i −1.28813 + 0.743704i
837837 154.447 + 1106.75i 0.184524 + 1.32228i
838838 84.0886 + 145.646i 0.100344 + 0.173802i
839839 702.552 + 405.618i 0.837368 + 0.483455i 0.856369 0.516365i 0.172715π-0.172715\pi
−0.0190007 + 0.999819i 0.506048π0.506048\pi
840840 35.4854 + 38.5251i 0.0422445 + 0.0458632i
841841 −2072.13 −2.46388
842842 103.850 59.9578i 0.123337 0.0712088i
843843 911.024 839.142i 1.08069 0.995423i
844844 −50.5129 87.4909i −0.0598494 0.103662i
845845 139.781 + 134.668i 0.165422 + 0.159370i
846846 11.1909 + 7.75003i 0.0132280 + 0.00916079i
847847 273.131 473.076i 0.322468 0.558531i
848848 181.246i 0.213734i
849849 991.359 + 1076.28i 1.16768 + 1.26770i
850850 −125.601 + 217.548i −0.147766 + 0.255939i
851851 772.033i 0.907207i
852852 −336.148 + 309.625i −0.394539 + 0.363409i
853853 294.569 + 510.209i 0.345333 + 0.598135i 0.985414 0.170173i 0.0544326π-0.0544326\pi
−0.640081 + 0.768307i 0.721099π0.721099\pi
854854 17.3361 10.0090i 0.0202998 0.0117201i
855855 94.4325 + 199.808i 0.110447 + 0.233693i
856856 −35.2799 + 61.1067i −0.0412149 + 0.0713863i
857857 1354.80 782.195i 1.58086 0.912713i 0.586131 0.810216i 0.300650π-0.300650\pi
0.994733 0.102496i 0.0326830π-0.0326830\pi
858858 219.959 21.8842i 0.256362 0.0255060i
859859 219.269 379.785i 0.255261 0.442124i −0.709706 0.704498i 0.751172π-0.751172\pi
0.964966 + 0.262374i 0.0845054π0.0845054\pi
860860 −161.417 + 93.1939i −0.187694 + 0.108365i
861861 97.5254 + 434.589i 0.113270 + 0.504750i
862862 −22.0526 + 38.1962i −0.0255830 + 0.0443111i
863863 1057.49i 1.22536i −0.790331 0.612680i 0.790091π-0.790091\pi
0.790331 0.612680i 0.209909π-0.209909\pi
864864 −285.660 366.362i −0.330625 0.424030i
865865 2.48212 + 4.29916i 0.00286951 + 0.00497013i
866866 −137.763 + 79.5376i −0.159080 + 0.0918448i
867867 −453.453 + 1451.24i −0.523014 + 1.67386i
868868 410.767 + 711.468i 0.473233 + 0.819664i
869869 255.331 147.416i 0.293822 0.169638i
870870 −66.7467 20.8556i −0.0767203 0.0239720i
871871 −376.521 885.579i −0.432286 1.01674i
872872 17.2641i 0.0197983i
873873 −14.3473 + 174.368i −0.0164345 + 0.199734i
874874 −58.4514 + 101.241i −0.0668781 + 0.115836i
875875 249.084 + 143.809i 0.284667 + 0.164353i
876876 737.459 165.492i 0.841848 0.188918i
877877 152.759 0.174184 0.0870920 0.996200i 0.472243π-0.472243\pi
0.0870920 + 0.996200i 0.472243π0.472243\pi
878878 101.008i 0.115043i
879879 −360.393 1605.97i −0.410003 1.82704i
880880 −123.977 + 214.734i −0.140883 + 0.244016i
881881 1343.46 + 775.645i 1.52492 + 0.880414i 0.999564 + 0.0295323i 0.00940179π0.00940179\pi
0.525358 + 0.850882i 0.323932π0.323932\pi
882882 −43.4235 + 62.7026i −0.0492330 + 0.0710914i
883883 −613.125 −0.694366 −0.347183 0.937797i 0.612862π-0.612862\pi
−0.347183 + 0.937797i 0.612862π0.612862\pi
884884 −1302.25 + 553.678i −1.47314 + 0.626333i
885885 −22.6112 + 72.3651i −0.0255493 + 0.0817685i
886886 7.22579 + 12.5154i 0.00815552 + 0.0141258i
887887 809.756 467.513i 0.912916 0.527072i 0.0315475 0.999502i 0.489956π-0.489956\pi
0.881368 + 0.472430i 0.156623π0.156623\pi
888888 −449.267 140.378i −0.505932 0.158083i
889889 26.8889 + 46.5729i 0.0302462 + 0.0523880i
890890 −58.2295 + 33.6188i −0.0654265 + 0.0377740i
891891 943.325 + 775.065i 1.05873 + 0.869883i
892892 −1246.02 −1.39688
893893 74.4759 + 42.9987i 0.0833996 + 0.0481508i
894894 −258.913 + 58.1022i −0.289612 + 0.0649913i
895895 −1.06070 1.83718i −0.00118514 0.00205272i
896896 −391.756 226.181i −0.437228 0.252434i
897897 −460.634 + 330.777i −0.513527 + 0.368759i
898898 −113.323 196.281i −0.126195 0.218575i
899899 −1934.57 1116.93i −2.15192 1.24241i
900900 −676.081 468.207i −0.751202 0.520230i
901901 −178.486 309.146i −0.198097 0.343115i
902902 141.662 81.7884i 0.157053 0.0906745i
903903 439.743 + 477.412i 0.486980 + 0.528695i
904904 394.263 0.436131
905905 −10.6764 6.16400i −0.0117971 0.00681105i
906906 221.154 203.704i 0.244099 0.224839i
907907 1149.05 1.26687 0.633433 0.773797i 0.281645π-0.281645\pi
0.633433 + 0.773797i 0.281645π0.281645\pi
908908 847.173 + 489.116i 0.933010 + 0.538674i
909909 −318.786 674.512i −0.350699 0.742037i
910910 −11.3006 26.5790i −0.0124182 0.0292077i
911911 443.854 256.259i 0.487216 0.281294i −0.236203 0.971704i 0.575903π-0.575903\pi
0.723419 + 0.690410i 0.242570π0.242570\pi
912912 −622.415 675.732i −0.682472 0.740934i
913913 624.051 + 1080.89i 0.683517 + 1.18389i
914914 97.6180i 0.106803i
915915 26.2261 24.1568i 0.0286625 0.0264009i
916916 460.896 798.295i 0.503161 0.871501i
917917 381.971 220.531i 0.416544 0.240492i
918918 265.451 + 107.550i 0.289163 + 0.117156i
919919 314.275 + 544.341i 0.341975 + 0.592318i 0.984799 0.173695i 0.0555708π-0.0555708\pi
−0.642824 + 0.766014i 0.722237π0.722237\pi
920920 49.3507i 0.0536421i
921921 −229.330 + 51.4636i −0.249001 + 0.0558779i
922922 100.485 174.046i 0.108986 0.188770i
923923 472.324 200.818i 0.511727 0.217570i
924924 856.717 + 267.689i 0.927183 + 0.289707i
925925 −1257.31 −1.35926
926926 −200.265 115.623i −0.216269 0.124863i
927927 −56.4924 + 686.572i −0.0609411 + 0.740638i
928928 928.677 1.00073
929929 203.102 + 117.261i 0.218625 + 0.126223i 0.605313 0.795987i 0.293048π-0.293048\pi
−0.386689 + 0.922210i 0.626381π0.626381\pi
930930 −36.3294 39.4414i −0.0390639 0.0424101i
931931 −240.922 + 417.289i −0.258778 + 0.448216i
932932 165.590i 0.177672i
933933 1292.26 + 403.778i 1.38506 + 0.432773i
934934 92.9128 0.0994784
935935 488.353i 0.522303i
936936 108.732 + 328.200i 0.116166 + 0.350641i
937937 −598.868 −0.639133 −0.319567 0.947564i 0.603537π-0.603537\pi
−0.319567 + 0.947564i 0.603537π0.603537\pi
938938 143.189i 0.152653i
939939 −478.950 519.978i −0.510064 0.553757i
940940 17.8253 0.0189631
941941 −219.420 126.682i −0.233178 0.134625i 0.378859 0.925454i 0.376316π-0.376316\pi
−0.612037 + 0.790829i 0.709650π0.709650\pi
942942 −62.5432 19.5422i −0.0663941 0.0207454i
943943 −209.830 + 363.436i −0.222513 + 0.385404i
944944 315.167i 0.333864i
945945 59.9017 147.848i 0.0633880 0.156453i
946946 119.189 206.442i 0.125993 0.218226i
947947 1553.39i 1.64033i 0.572130 + 0.820163i 0.306117π0.306117\pi
−0.572130 + 0.820163i 0.693883π0.693883\pi
948948 153.404 + 166.545i 0.161818 + 0.175680i
949949 −842.521 102.946i −0.887799 0.108478i
950950 164.878 + 95.1925i 0.173556 + 0.100203i
951951 −274.944 + 253.250i −0.289110 + 0.266299i
952952 428.837 0.450459
953953 373.494 215.637i 0.391914 0.226272i −0.291075 0.956700i 0.594013π-0.594013\pi
0.682989 + 0.730429i 0.260680π0.260680\pi
954954 −38.7181 + 18.2988i −0.0405850 + 0.0191811i
955955 37.8575 + 65.5711i 0.0396414 + 0.0686609i
956956 258.729 + 149.377i 0.270637 + 0.156252i
957957 −2381.36 + 534.397i −2.48836 + 0.558409i
958958 −308.454 −0.321978
959959 −494.716 + 285.624i −0.515867 + 0.297836i
960960 −167.143 52.2253i −0.174107 0.0544014i
961961 −375.984 651.223i −0.391242 0.677651i
962962 207.372 + 156.075i 0.215564 + 0.162240i
963963 214.175 + 17.6227i 0.222404 + 0.0182998i
964964 184.768 320.028i 0.191668 0.331980i
965965 128.471i 0.133130i
966966 82.3352 18.4767i 0.0852331 0.0191270i
967967 548.133 949.394i 0.566839 0.981794i −0.430037 0.902811i 0.641500π-0.641500\pi
0.996876 0.0789825i 0.0251671π-0.0251671\pi
968968 313.795i 0.324169i
969969 1727.07 + 539.640i 1.78233 + 0.556904i
970970 −4.19775 7.27071i −0.00432757 0.00749558i
971971 88.2684 50.9618i 0.0909046 0.0524838i −0.453859 0.891074i 0.649953π-0.649953\pi
0.544763 + 0.838590i 0.316620π0.316620\pi
972972 −422.169 + 837.223i −0.434331 + 0.861341i
973973 521.736 903.674i 0.536214 0.928750i
974974 239.346 138.187i 0.245735 0.141875i
975975 538.695 + 750.176i 0.552507 + 0.769411i
976976 −74.1120 + 128.366i −0.0759345 + 0.131522i
977977 874.681 504.997i 0.895272 0.516886i 0.0196090 0.999808i 0.493758π-0.493758\pi
0.875663 + 0.482922i 0.160425π0.160425\pi
978978 −13.4432 + 12.3825i −0.0137456 + 0.0126611i
979979 −1173.33 + 2032.26i −1.19850 + 2.07586i
980980 99.8756i 0.101914i
981981 47.5381 22.4673i 0.0484588 0.0229024i
982982 24.5534 + 42.5278i 0.0250035 + 0.0433073i
983983 −1248.07 + 720.573i −1.26965 + 0.733035i −0.974922 0.222546i 0.928563π-0.928563\pi
−0.294731 + 0.955580i 0.595230π0.595230\pi
984984 173.340 + 188.189i 0.176159 + 0.191249i
985985 6.74436 + 11.6816i 0.00684706 + 0.0118595i
986986 −495.834 + 286.270i −0.502874 + 0.290335i
987987 −13.5920 60.5682i −0.0137710 0.0613660i
988988 419.629 + 986.969i 0.424726 + 0.998957i
989989 611.566i 0.618368i
990990 −58.3886 4.80432i −0.0589784 0.00485285i
991991 −698.522 + 1209.87i −0.704865 + 1.22086i 0.261875 + 0.965102i 0.415659π0.415659\pi
−0.966740 + 0.255761i 0.917674π0.917674\pi
992992 616.723 + 356.065i 0.621696 + 0.358937i
993993 299.358 958.071i 0.301468 0.964824i
994994 −76.3697 −0.0768307
995995 21.2205i 0.0213272i
996996 −705.030 + 649.401i −0.707861 + 0.652009i
997997 682.194 1181.60i 0.684247 1.18515i −0.289426 0.957200i 0.593464π-0.593464\pi
0.973673 0.227950i 0.0732023π-0.0732023\pi
998998 −9.42691 5.44263i −0.00944580 0.00545354i
999999 198.129 + 1419.78i 0.198328 + 1.42120i
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 117.3.k.a.113.13 yes 52
3.2 odd 2 351.3.k.a.152.14 52
9.2 odd 6 117.3.u.a.74.14 yes 52
9.7 even 3 351.3.u.a.35.13 52
13.3 even 3 117.3.u.a.68.14 yes 52
39.29 odd 6 351.3.u.a.341.13 52
117.16 even 3 351.3.k.a.224.13 52
117.29 odd 6 inner 117.3.k.a.29.14 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.3.k.a.29.14 52 117.29 odd 6 inner
117.3.k.a.113.13 yes 52 1.1 even 1 trivial
117.3.u.a.68.14 yes 52 13.3 even 3
117.3.u.a.74.14 yes 52 9.2 odd 6
351.3.k.a.152.14 52 3.2 odd 2
351.3.k.a.224.13 52 117.16 even 3
351.3.u.a.35.13 52 9.7 even 3
351.3.u.a.341.13 52 39.29 odd 6