Properties

Label 875.2.bb.c.607.12
Level 875875
Weight 22
Character 875.607
Analytic conductor 6.9876.987
Analytic rank 00
Dimension 288288
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [875,2,Mod(82,875)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(875, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([27, 50]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("875.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 875=537 875 = 5^{3} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 875.bb (of order 6060, degree 1616, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.986910176866.98691017686
Analytic rank: 00
Dimension: 288288
Relative dimension: 1818 over Q(ζ60)\Q(\zeta_{60})
Twist minimal: no (minimal twist has level 175)
Sato-Tate group: SU(2)[C60]\mathrm{SU}(2)[C_{60}]

Embedding invariants

Embedding label 607.12
Character χ\chi == 875.607
Dual form 875.2.bb.c.493.12

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+(0.423319+0.651855i)q2+(0.4025071.04857i)q3+(0.5677581.27521i)q4+(0.5131230.706254i)q6+(1.244042.33503i)q7+(2.606950.412900i)q8+(1.291961.16328i)q9+(0.888306+0.986564i)q11+(1.565660.0820529i)q12+(1.79077+0.912442i)q13+(0.9954781.79939i)q14+(0.4953380.550128i)q16+(0.585165+0.722619i)q17+(1.30520+0.349728i)q18+(4.814552.14358i)q19+(1.94770+2.24432i)q21+(1.019130.161415i)q22+(0.9606540.623856i)q23+(1.482272.56736i)q24+(1.352850.781066i)q26+(4.742042.41619i)q27+(3.68396+0.260667i)q28+(4.040605.56140i)q29+(9.744921.02423i)q31+(1.515195.65478i)q32+(1.39203+0.534349i)q33+(0.223331+0.687341i)q34+(0.7499062.30797i)q36+(0.401079+7.65304i)q37+(3.43539+2.23097i)q38+(1.67755+1.51047i)q39+(0.0622653+0.0202312i)q41+(2.287470.319555i)q42+(3.343313.34331i)q43+(0.753729+1.69290i)q44+(0.813327+0.362116i)q46+(0.145063+0.117470i)q47+(0.377469+0.740824i)q48+(3.90475+5.80972i)q49+(0.5221800.904443i)q51+(0.146828+2.80164i)q52+(10.42784.00284i)q53+(0.4323934.11394i)q54+(4.207275.57365i)q56+(4.185574.18557i)q57+(1.914764.98813i)q58+(4.71962+1.00319i)q59+(0.9510264.47423i)q61+(3.457566.78585i)q62+(4.323541.56960i)q63+(2.919430.948580i)q64+(0.240954+1.13360i)q66+(6.60139+5.34570i)q67+(1.253720.335933i)q68+(1.040820.756203i)q69+(8.724916.33902i)q71+(2.887743.56607i)q72+(1.64457+0.0861882i)q73+(5.15845+2.97823i)q747.35658iq76+(3.40874+0.846904i)q77+(0.274469+1.73293i)q78+(10.37871.09084i)q79+(0.0796638+0.757950i)q81+(0.0131703+0.0491522i)q82+(0.9785996.17863i)q83+(1.75614+3.75795i)q84+(3.59464+0.764065i)q86+(4.20513+6.47533i)q87+(1.90842+2.93870i)q88+(15.3519+3.26314i)q89+(4.35836+3.04639i)q91+(0.2501261.57923i)q92+(2.84842+10.6304i)q93+(0.0151652+0.144287i)q94+(6.53929+0.687307i)q96+(2.72136+17.1820i)q97+(5.440050.0859631i)q98+2.30795iq99+O(q100)q+(0.423319 + 0.651855i) q^{2} +(-0.402507 - 1.04857i) q^{3} +(0.567758 - 1.27521i) q^{4} +(0.513123 - 0.706254i) q^{6} +(-1.24404 - 2.33503i) q^{7} +(2.60695 - 0.412900i) q^{8} +(1.29196 - 1.16328i) q^{9} +(-0.888306 + 0.986564i) q^{11} +(-1.56566 - 0.0820529i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(0.995478 - 1.79939i) q^{14} +(-0.495338 - 0.550128i) q^{16} +(0.585165 + 0.722619i) q^{17} +(1.30520 + 0.349728i) q^{18} +(4.81455 - 2.14358i) q^{19} +(-1.94770 + 2.24432i) q^{21} +(-1.01913 - 0.161415i) q^{22} +(0.960654 - 0.623856i) q^{23} +(-1.48227 - 2.56736i) q^{24} +(-1.35285 - 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.68396 + 0.260667i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-9.74492 - 1.02423i) q^{31} +(1.51519 - 5.65478i) q^{32} +(1.39203 + 0.534349i) q^{33} +(-0.223331 + 0.687341i) q^{34} +(-0.749906 - 2.30797i) q^{36} +(-0.401079 + 7.65304i) q^{37} +(3.43539 + 2.23097i) q^{38} +(1.67755 + 1.51047i) q^{39} +(0.0622653 + 0.0202312i) q^{41} +(-2.28747 - 0.319555i) q^{42} +(3.34331 - 3.34331i) q^{43} +(0.753729 + 1.69290i) q^{44} +(0.813327 + 0.362116i) q^{46} +(0.145063 + 0.117470i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(-3.90475 + 5.80972i) q^{49} +(0.522180 - 0.904443i) q^{51} +(0.146828 + 2.80164i) q^{52} +(10.4278 - 4.00284i) q^{53} +(-0.432393 - 4.11394i) q^{54} +(-4.20727 - 5.57365i) q^{56} +(-4.18557 - 4.18557i) q^{57} +(1.91476 - 4.98813i) q^{58} +(-4.71962 + 1.00319i) q^{59} +(0.951026 - 4.47423i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-4.32354 - 1.56960i) q^{63} +(2.91943 - 0.948580i) q^{64} +(0.240954 + 1.13360i) q^{66} +(-6.60139 + 5.34570i) q^{67} +(1.25372 - 0.335933i) q^{68} +(-1.04082 - 0.756203i) q^{69} +(8.72491 - 6.33902i) q^{71} +(2.88774 - 3.56607i) q^{72} +(-1.64457 + 0.0861882i) q^{73} +(-5.15845 + 2.97823i) q^{74} -7.35658i q^{76} +(3.40874 + 0.846904i) q^{77} +(-0.274469 + 1.73293i) q^{78} +(10.3787 - 1.09084i) q^{79} +(-0.0796638 + 0.757950i) q^{81} +(0.0131703 + 0.0491522i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(1.75614 + 3.75795i) q^{84} +(3.59464 + 0.764065i) q^{86} +(-4.20513 + 6.47533i) q^{87} +(-1.90842 + 2.93870i) q^{88} +(15.3519 + 3.26314i) q^{89} +(4.35836 + 3.04639i) q^{91} +(-0.250126 - 1.57923i) q^{92} +(2.84842 + 10.6304i) q^{93} +(-0.0151652 + 0.144287i) q^{94} +(-6.53929 + 0.687307i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(-5.44005 - 0.0859631i) q^{98} +2.30795i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 288q+8q2+24q310q4+10q7+36q810q96q11+36q1220q1430q16+42q17+14q1830q1912q2132q22+40q2348q26+222q98+O(q100) 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/875Z)×\left(\mathbb{Z}/875\mathbb{Z}\right)^\times.

nn 127127 626626
χ(n)\chi(n) e(1320)e\left(\frac{13}{20}\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 0.423319 + 0.651855i 0.299332 + 0.460931i 0.956049 0.293206i 0.0947222π-0.0947222\pi
−0.656717 + 0.754137i 0.728056π0.728056\pi
33 −0.402507 1.04857i −0.232387 0.605390i 0.766953 0.641703i 0.221772π-0.221772\pi
−0.999340 + 0.0363135i 0.988439π0.988439\pi
44 0.567758 1.27521i 0.283879 0.637603i
55 0 0
66 0.513123 0.706254i 0.209482 0.288327i
77 −1.24404 2.33503i −0.470201 0.882559i
88 2.60695 0.412900i 0.921695 0.145982i
99 1.29196 1.16328i 0.430652 0.387761i
1010 0 0
1111 −0.888306 + 0.986564i −0.267834 + 0.297460i −0.862027 0.506863i 0.830805π-0.830805\pi
0.594192 + 0.804323i 0.297472π0.297472\pi
1212 −1.56566 0.0820529i −0.451968 0.0236866i
1313 −1.79077 + 0.912442i −0.496670 + 0.253066i −0.684336 0.729167i 0.739908π-0.739908\pi
0.187666 + 0.982233i 0.439908π0.439908\pi
1414 0.995478 1.79939i 0.266053 0.480908i
1515 0 0
1616 −0.495338 0.550128i −0.123834 0.137532i
1717 0.585165 + 0.722619i 0.141923 + 0.175261i 0.843151 0.537676i 0.180698π-0.180698\pi
−0.701228 + 0.712937i 0.747364π0.747364\pi
1818 1.30520 + 0.349728i 0.307639 + 0.0824316i
1919 4.81455 2.14358i 1.10453 0.491770i 0.228268 0.973598i 0.426694π-0.426694\pi
0.876266 + 0.481828i 0.160027π0.160027\pi
2020 0 0
2121 −1.94770 + 2.24432i −0.425023 + 0.489750i
2222 −1.01913 0.161415i −0.217280 0.0344138i
2323 0.960654 0.623856i 0.200310 0.130083i −0.440586 0.897710i 0.645229π-0.645229\pi
0.640897 + 0.767627i 0.278563π0.278563\pi
2424 −1.48227 2.56736i −0.302566 0.524060i
2525 0 0
2626 −1.35285 0.781066i −0.265315 0.153180i
2727 −4.74204 2.41619i −0.912607 0.464996i
2828 −3.68396 + 0.260667i −0.696202 + 0.0492614i
2929 −4.04060 5.56140i −0.750320 1.03273i −0.997958 0.0638742i 0.979654π-0.979654\pi
0.247638 0.968853i 0.420346π-0.420346\pi
3030 0 0
3131 −9.74492 1.02423i −1.75024 0.183958i −0.825460 0.564461i 0.809084π-0.809084\pi
−0.924780 + 0.380503i 0.875751π0.875751\pi
3232 1.51519 5.65478i 0.267851 0.999634i
3333 1.39203 + 0.534349i 0.242321 + 0.0930182i
3434 −0.223331 + 0.687341i −0.0383009 + 0.117878i
3535 0 0
3636 −0.749906 2.30797i −0.124984 0.384662i
3737 −0.401079 + 7.65304i −0.0659369 + 1.25815i 0.742612 + 0.669722i 0.233587π0.233587\pi
−0.808549 + 0.588430i 0.799746π0.799746\pi
3838 3.43539 + 2.23097i 0.557295 + 0.361911i
3939 1.67755 + 1.51047i 0.268623 + 0.241869i
4040 0 0
4141 0.0622653 + 0.0202312i 0.00972421 + 0.00315959i 0.313875 0.949464i 0.398373π-0.398373\pi
−0.304151 + 0.952624i 0.598373π0.598373\pi
4242 −2.28747 0.319555i −0.352964 0.0493085i
4343 3.34331 3.34331i 0.509850 0.509850i −0.404630 0.914480i 0.632600π-0.632600\pi
0.914480 + 0.404630i 0.132600π0.132600\pi
4444 0.753729 + 1.69290i 0.113629 + 0.255215i
4545 0 0
4646 0.813327 + 0.362116i 0.119919 + 0.0533912i
4747 0.145063 + 0.117470i 0.0211596 + 0.0171347i 0.639842 0.768507i 0.279000π-0.279000\pi
−0.618682 + 0.785641i 0.712333π0.712333\pi
4848 −0.377469 + 0.740824i −0.0544829 + 0.106929i
4949 −3.90475 + 5.80972i −0.557822 + 0.829961i
5050 0 0
5151 0.522180 0.904443i 0.0731199 0.126647i
5252 0.146828 + 2.80164i 0.0203614 + 0.388518i
5353 10.4278 4.00284i 1.43236 0.549832i 0.486292 0.873796i 0.338349π-0.338349\pi
0.946069 + 0.323964i 0.105016π0.105016\pi
5454 −0.432393 4.11394i −0.0588412 0.559837i
5555 0 0
5656 −4.20727 5.57365i −0.562220 0.744810i
5757 −4.18557 4.18557i −0.554392 0.554392i
5858 1.91476 4.98813i 0.251421 0.654974i
5959 −4.71962 + 1.00319i −0.614442 + 0.130604i −0.504612 0.863347i 0.668364π-0.668364\pi
−0.109831 + 0.993950i 0.535031π0.535031\pi
6060 0 0
6161 0.951026 4.47423i 0.121766 0.572866i −0.874386 0.485231i 0.838736π-0.838736\pi
0.996153 0.0876354i 0.0279310π-0.0279310\pi
6262 −3.45756 6.78585i −0.439111 0.861804i
6363 −4.32354 1.56960i −0.544715 0.197750i
6464 2.91943 0.948580i 0.364929 0.118573i
6565 0 0
6666 0.240954 + 1.13360i 0.0296594 + 0.139536i
6767 −6.60139 + 5.34570i −0.806488 + 0.653081i −0.941217 0.337801i 0.890317π-0.890317\pi
0.134730 + 0.990882i 0.456983π0.456983\pi
6868 1.25372 0.335933i 0.152036 0.0407379i
6969 −1.04082 0.756203i −0.125300 0.0910361i
7070 0 0
7171 8.72491 6.33902i 1.03546 0.752303i 0.0660625 0.997815i 0.478956π-0.478956\pi
0.969393 + 0.245513i 0.0789563π0.0789563\pi
7272 2.88774 3.56607i 0.340324 0.420265i
7373 −1.64457 + 0.0861882i −0.192482 + 0.0100876i −0.148333 0.988937i 0.547391π-0.547391\pi
−0.0441488 + 0.999025i 0.514058π0.514058\pi
7474 −5.15845 + 2.97823i −0.599658 + 0.346213i
7575 0 0
7676 7.35658i 0.843857i
7777 3.40874 + 0.846904i 0.388462 + 0.0965136i
7878 −0.274469 + 1.73293i −0.0310775 + 0.196216i
7979 10.3787 1.09084i 1.16769 0.122729i 0.499224 0.866473i 0.333618π-0.333618\pi
0.668465 + 0.743744i 0.266952π0.266952\pi
8080 0 0
8181 −0.0796638 + 0.757950i −0.00885153 + 0.0842167i
8282 0.0131703 + 0.0491522i 0.00145442 + 0.00542796i
8383 −0.978599 6.17863i −0.107415 0.678193i −0.981362 0.192170i 0.938447π-0.938447\pi
0.873946 0.486022i 0.161553π-0.161553\pi
8484 1.75614 + 3.75795i 0.191611 + 0.410026i
8585 0 0
8686 3.59464 + 0.764065i 0.387620 + 0.0823912i
8787 −4.20513 + 6.47533i −0.450837 + 0.694228i
8888 −1.90842 + 2.93870i −0.203438 + 0.313267i
8989 15.3519 + 3.26314i 1.62729 + 0.345892i 0.929046 0.369964i 0.120630π-0.120630\pi
0.698248 + 0.715856i 0.253963π0.253963\pi
9090 0 0
9191 4.35836 + 3.04639i 0.456880 + 0.319349i
9292 −0.250126 1.57923i −0.0260774 0.164646i
9393 2.84842 + 10.6304i 0.295367 + 1.10233i
9494 −0.0151652 + 0.144287i −0.00156417 + 0.0148821i
9595 0 0
9696 −6.53929 + 0.687307i −0.667413 + 0.0701479i
9797 −2.72136 + 17.1820i −0.276312 + 1.74457i 0.325149 + 0.945663i 0.394586π0.394586\pi
−0.601461 + 0.798902i 0.705414π0.705414\pi
9898 −5.44005 0.0859631i −0.549528 0.00868358i
9999 2.30795i 0.231958i
100100 0 0
101101 −3.07011 + 1.77253i −0.305487 + 0.176373i −0.644905 0.764262i 0.723103π-0.723103\pi
0.339418 + 0.940636i 0.389770π0.389770\pi
102102 0.810614 0.0424825i 0.0802628 0.00420639i
103103 4.00546 4.94633i 0.394669 0.487376i −0.540617 0.841269i 0.681809π-0.681809\pi
0.935286 + 0.353893i 0.115142π0.115142\pi
104104 −4.29169 + 3.11810i −0.420835 + 0.305755i
105105 0 0
106106 7.02354 + 5.10290i 0.682186 + 0.495637i
107107 9.52075 2.55108i 0.920406 0.246622i 0.232647 0.972561i 0.425261π-0.425261\pi
0.687759 + 0.725939i 0.258595π0.258595\pi
108108 −5.77347 + 4.67527i −0.555553 + 0.449878i
109109 −2.25184 10.5941i −0.215687 1.01473i −0.944118 0.329609i 0.893083π-0.893083\pi
0.728430 0.685120i 0.240250π-0.240250\pi
110110 0 0
111111 8.18615 2.65984i 0.776995 0.252461i
112112 −0.668350 + 1.84101i −0.0631531 + 0.173959i
113113 3.00115 + 5.89008i 0.282324 + 0.554092i 0.988002 0.154440i 0.0493575π-0.0493575\pi
−0.705678 + 0.708533i 0.749357π0.749357\pi
114114 0.956551 4.50022i 0.0895892 0.421484i
115115 0 0
116116 −9.38601 + 1.99506i −0.871470 + 0.185237i
117117 −1.25217 + 3.26200i −0.115763 + 0.301572i
118118 −2.65184 2.65184i −0.244122 0.244122i
119119 0.959372 2.26534i 0.0879455 0.207664i
120120 0 0
121121 0.965593 + 9.18700i 0.0877811 + 0.835182i
122122 3.31913 1.27410i 0.300500 0.115351i
123123 −0.00384843 0.0734325i −0.000347002 0.00662118i
124124 −6.83886 + 11.8453i −0.614148 + 1.06374i
125125 0 0
126126 −0.807091 3.48276i −0.0719014 0.310269i
127127 8.39463 16.4754i 0.744903 1.46195i −0.137023 0.990568i 0.543754π-0.543754\pi
0.881927 0.471387i 0.156246π-0.156246\pi
128128 −7.24505 5.86692i −0.640378 0.518568i
129129 −4.85139 2.15998i −0.427141 0.190175i
130130 0 0
131131 6.81590 + 15.3088i 0.595508 + 1.33753i 0.920102 + 0.391679i 0.128106π0.128106\pi
−0.324594 + 0.945853i 0.605228π0.605228\pi
132132 1.47174 1.47174i 0.128098 0.128098i
133133 −10.9948 8.57545i −0.953370 0.743586i
134134 −6.27911 2.04021i −0.542433 0.176247i
135135 0 0
136136 1.82386 + 1.64221i 0.156395 + 0.140819i
137137 2.76974 + 1.79869i 0.236635 + 0.153673i 0.657509 0.753446i 0.271610π-0.271610\pi
−0.420874 + 0.907119i 0.638277π0.638277\pi
138138 0.0523334 0.998581i 0.00445492 0.0850048i
139139 2.66592 + 8.20486i 0.226120 + 0.695927i 0.998176 + 0.0603721i 0.0192287π0.0192287\pi
−0.772055 + 0.635555i 0.780771π0.780771\pi
140140 0 0
141141 0.0647859 0.199391i 0.00545596 0.0167917i
142142 7.82554 + 3.00394i 0.656705 + 0.252085i
143143 0.690568 2.57723i 0.0577482 0.215519i
144144 −1.27991 0.134524i −0.106659 0.0112103i
145145 0 0
146146 −0.752360 1.03553i −0.0622658 0.0857015i
147147 7.66357 + 1.75594i 0.632080 + 0.144827i
148148 9.53148 + 4.85653i 0.783483 + 0.399205i
149149 0.0342344 + 0.0197652i 0.00280459 + 0.00161923i 0.501402 0.865215i 0.332818π-0.332818\pi
−0.498597 + 0.866834i 0.666151π0.666151\pi
150150 0 0
151151 4.89690 + 8.48169i 0.398504 + 0.690230i 0.993542 0.113468i 0.0361960π-0.0361960\pi
−0.595037 + 0.803698i 0.702863π0.702863\pi
152152 11.6662 7.57612i 0.946254 0.614505i
153153 1.59662 + 0.252879i 0.129079 + 0.0204441i
154154 0.890929 + 2.58052i 0.0717931 + 0.207944i
155155 0 0
156156 2.87861 1.28164i 0.230473 0.102613i
157157 12.7152 + 3.40702i 1.01478 + 0.271910i 0.727626 0.685974i 0.240624π-0.240624\pi
0.287156 + 0.957884i 0.407290π0.407290\pi
158158 5.10455 + 6.30360i 0.406096 + 0.501487i
159159 −8.39448 9.32301i −0.665725 0.739363i
160160 0 0
161161 −2.65181 1.46706i −0.208992 0.115621i
162162 −0.527797 + 0.268926i −0.0414676 + 0.0211288i
163163 3.48720 + 0.182756i 0.273138 + 0.0143146i 0.188413 0.982090i 0.439666π-0.439666\pi
0.0847249 + 0.996404i 0.472999π0.472999\pi
164164 0.0611506 0.0679147i 0.00477506 0.00530324i
165165 0 0
166166 3.61331 3.25344i 0.280447 0.252516i
167167 −18.9176 + 2.99626i −1.46389 + 0.231857i −0.836979 0.547235i 0.815681π-0.815681\pi
−0.626910 + 0.779092i 0.715681π0.715681\pi
168168 −4.15088 + 6.65503i −0.320247 + 0.513447i
169169 −5.26691 + 7.24928i −0.405147 + 0.557637i
170170 0 0
171171 3.72661 8.37009i 0.284981 0.640077i
172172 −2.36522 6.16160i −0.180346 0.469818i
173173 2.70053 + 4.15845i 0.205317 + 0.316161i 0.926296 0.376796i 0.122974π-0.122974\pi
−0.720979 + 0.692957i 0.756308π0.756308\pi
174174 −6.00109 −0.454941
175175 0 0
176176 0.982748 0.0740774
177177 2.95159 + 4.54504i 0.221855 + 0.341626i
178178 4.37165 + 11.3885i 0.327669 + 0.853607i
179179 8.23757 18.5019i 0.615705 1.38290i −0.289194 0.957270i 0.593387π-0.593387\pi
0.904899 0.425626i 0.139946π-0.139946\pi
180180 0 0
181181 −2.67679 + 3.68429i −0.198965 + 0.273851i −0.896828 0.442380i 0.854134π-0.854134\pi
0.697863 + 0.716231i 0.254134π0.254134\pi
182182 −0.140827 + 4.13061i −0.0104388 + 0.306181i
183183 −5.07431 + 0.803693i −0.375104 + 0.0594107i
184184 2.24679 2.02301i 0.165635 0.149139i
185185 0 0
186186 −5.72372 + 6.35683i −0.419683 + 0.466105i
187187 −1.23272 0.0646039i −0.0901451 0.00472430i
188188 0.232159 0.118291i 0.0169319 0.00862725i
189189 0.257382 + 14.0787i 0.0187218 + 1.02407i
190190 0 0
191191 −10.3573 11.5029i −0.749427 0.832323i 0.240976 0.970531i 0.422532π-0.422532\pi
−0.990403 + 0.138208i 0.955866π0.955866\pi
192192 −2.16974 2.67940i −0.156587 0.193369i
193193 −7.57383 2.02940i −0.545176 0.146080i −0.0242890 0.999705i 0.507732π-0.507732\pi
−0.520887 + 0.853625i 0.674399π0.674399\pi
194194 −12.3522 + 5.49953i −0.886833 + 0.394843i
195195 0 0
196196 5.19164 + 8.27788i 0.370831 + 0.591277i
197197 16.1577 + 2.55912i 1.15119 + 0.182330i 0.702718 0.711469i 0.251970π-0.251970\pi
0.448469 + 0.893799i 0.351970π0.351970\pi
198198 −1.50445 + 0.976999i −0.106916 + 0.0694323i
199199 13.6561 + 23.6530i 0.968053 + 1.67672i 0.701179 + 0.712985i 0.252657π0.252657\pi
0.266874 + 0.963731i 0.414009π0.414009\pi
200200 0 0
201201 8.26242 + 4.77031i 0.582786 + 0.336472i
202202 −2.45507 1.25092i −0.172738 0.0880144i
203203 −7.95942 + 16.3535i −0.558641 + 1.14779i
204204 −0.856878 1.17939i −0.0599935 0.0825739i
205205 0 0
206206 4.91987 + 0.517100i 0.342784 + 0.0360280i
207207 0.515402 1.92351i 0.0358229 0.133693i
208208 1.38899 + 0.533185i 0.0963095 + 0.0369697i
209209 −2.16202 + 6.65402i −0.149550 + 0.460268i
210210 0 0
211211 4.53761 + 13.9653i 0.312382 + 0.961413i 0.976819 + 0.214068i 0.0686715π0.0686715\pi
−0.664437 + 0.747345i 0.731328π0.731328\pi
212212 0.815998 15.5702i 0.0560430 1.06936i
213213 −10.1587 6.59714i −0.696063 0.452029i
214214 5.69325 + 5.12622i 0.389182 + 0.350421i
215215 0 0
216216 −13.3599 4.34090i −0.909027 0.295361i
217217 9.73141 + 24.0289i 0.660611 + 1.63119i
218218 5.95255 5.95255i 0.403158 0.403158i
219219 0.752324 + 1.68975i 0.0508373 + 0.114183i
220220 0 0
221221 −1.70724 0.760113i −0.114842 0.0511307i
222222 5.19919 + 4.21022i 0.348947 + 0.282571i
223223 9.81559 19.2642i 0.657301 1.29003i −0.286046 0.958216i 0.592341π-0.592341\pi
0.943346 0.331809i 0.107659π-0.107659\pi
224224 −15.0891 + 3.49672i −1.00818 + 0.233634i
225225 0 0
226226 −2.56903 + 4.44970i −0.170890 + 0.295989i
227227 −0.492014 9.38818i −0.0326561 0.623116i −0.965113 0.261834i 0.915673π-0.915673\pi
0.932457 0.361281i 0.117661π-0.117661\pi
228228 −7.71385 + 2.96107i −0.510862 + 0.196102i
229229 −0.325389 3.09587i −0.0215023 0.204581i 0.978496 0.206265i 0.0661307π-0.0661307\pi
−0.999999 + 0.00168368i 0.999464π0.999464\pi
230230 0 0
231231 −0.484007 3.91517i −0.0318454 0.257600i
232232 −12.8299 12.8299i −0.842326 0.842326i
233233 −10.4487 + 27.2198i −0.684516 + 1.78323i −0.0654920 + 0.997853i 0.520862π0.520862\pi
−0.619024 + 0.785372i 0.712472π0.712472\pi
234234 −2.65642 + 0.564639i −0.173656 + 0.0369116i
235235 0 0
236236 −1.40033 + 6.58805i −0.0911540 + 0.428846i
237237 −5.32129 10.4436i −0.345655 0.678386i
238238 1.88279 0.333592i 0.122043 0.0216236i
239239 3.05660 0.993150i 0.197715 0.0642416i −0.208485 0.978025i 0.566853π-0.566853\pi
0.406201 + 0.913784i 0.366853π0.366853\pi
240240 0 0
241241 5.57588 + 26.2325i 0.359174 + 1.68978i 0.672469 + 0.740125i 0.265234π0.265234\pi
−0.313295 + 0.949656i 0.601433π0.601433\pi
242242 −5.57983 + 4.51846i −0.358685 + 0.290458i
243243 −14.5955 + 3.91085i −0.936301 + 0.250881i
244244 −5.16561 3.75303i −0.330694 0.240263i
245245 0 0
246246 0.0462382 0.0335940i 0.00294804 0.00214188i
247247 −6.66586 + 8.23165i −0.424138 + 0.523767i
248248 −25.8274 + 1.35356i −1.64004 + 0.0859510i
249249 −6.08480 + 3.51306i −0.385609 + 0.222631i
250250 0 0
251251 13.7541i 0.868150i −0.900877 0.434075i 0.857075π-0.857075\pi
0.900877 0.434075i 0.142925π-0.142925\pi
252252 −4.45628 + 4.62225i −0.280719 + 0.291175i
253253 −0.237881 + 1.50192i −0.0149555 + 0.0944250i
254254 14.2932 1.50227i 0.896833 0.0942610i
255255 0 0
256256 1.39915 13.3120i 0.0874468 0.832000i
257257 −2.39177 8.92621i −0.149195 0.556802i −0.999533 0.0305651i 0.990269π-0.990269\pi
0.850338 0.526237i 0.176397π-0.176397\pi
258258 −0.645695 4.07676i −0.0401992 0.253808i
259259 18.3691 8.58412i 1.14140 0.533391i
260260 0 0
261261 −11.6898 2.48474i −0.723578 0.153801i
262262 −7.09379 + 10.9235i −0.438256 + 0.674854i
263263 4.57051 7.03797i 0.281830 0.433980i −0.669198 0.743084i 0.733362π-0.733362\pi
0.951028 + 0.309104i 0.100029π0.100029\pi
264264 3.84957 + 0.818252i 0.236925 + 0.0503599i
265265 0 0
266266 0.935639 10.7972i 0.0573677 0.662017i
267267 −2.75761 17.4109i −0.168763 1.06553i
268268 3.06887 + 11.4532i 0.187461 + 0.699615i
269269 0.460334 4.37978i 0.0280670 0.267040i −0.971485 0.237102i 0.923802π-0.923802\pi
0.999552 0.0299378i 0.00953093π-0.00953093\pi
270270 0 0
271271 −3.41350 + 0.358773i −0.207355 + 0.0217939i −0.207636 0.978206i 0.566577π-0.566577\pi
0.000281350 1.00000i 0.499910π0.499910\pi
272272 0.107679 0.679856i 0.00652898 0.0412223i
273273 1.44007 5.79622i 0.0871572 0.350803i
274274 2.56689i 0.155072i
275275 0 0
276276 −1.55525 + 0.897924i −0.0936150 + 0.0540487i
277277 7.68850 0.402937i 0.461957 0.0242102i 0.180062 0.983655i 0.442370π-0.442370\pi
0.281895 + 0.959445i 0.409037π0.409037\pi
278278 −4.21984 + 5.21107i −0.253089 + 0.312539i
279279 −13.7815 + 10.0128i −0.825076 + 0.599453i
280280 0 0
281281 19.6291 + 14.2614i 1.17097 + 0.850761i 0.991125 0.132934i 0.0424398π-0.0424398\pi
0.179847 + 0.983695i 0.442440π0.442440\pi
282282 0.157399 0.0421749i 0.00937296 0.00251148i
283283 5.63377 4.56213i 0.334893 0.271191i −0.447093 0.894488i 0.647541π-0.647541\pi
0.781985 + 0.623297i 0.214207π0.214207\pi
284284 −3.12991 14.7251i −0.185726 0.873772i
285285 0 0
286286 1.97231 0.640843i 0.116625 0.0378939i
287287 −0.0302197 0.170560i −0.00178381 0.0100678i
288288 −4.62055 9.06833i −0.272268 0.534357i
289289 3.35474 15.7828i 0.197338 0.928400i
290290 0 0
291291 19.1118 4.06234i 1.12035 0.238138i
292292 −0.823809 + 2.14610i −0.0482098 + 0.125591i
293293 −22.0206 22.0206i −1.28645 1.28645i −0.936925 0.349529i 0.886342π-0.886342\pi
−0.349529 0.936925i 0.613658π-0.613658\pi
294294 2.09952 + 5.73885i 0.122446 + 0.334697i
295295 0 0
296296 2.11435 + 20.1167i 0.122894 + 1.16926i
297297 6.59611 2.53201i 0.382745 0.146922i
298298 0.00160802 + 0.0306828i 9.31501e−5 + 0.00177741i
299299 −1.15108 + 1.99372i −0.0665684 + 0.115300i
300300 0 0
301301 −11.9659 3.64755i −0.689705 0.210241i
302302 −3.45587 + 6.78253i −0.198863 + 0.390291i
303303 3.09435 + 2.50576i 0.177766 + 0.143952i
304304 −3.56407 1.58683i −0.204414 0.0910108i
305305 0 0
306306 0.511039 + 1.14781i 0.0292141 + 0.0656160i
307307 −2.33566 + 2.33566i −0.133303 + 0.133303i −0.770610 0.637307i 0.780048π-0.780048\pi
0.637307 + 0.770610i 0.280048π0.280048\pi
308308 3.01532 3.86601i 0.171814 0.220286i
309309 −6.79877 2.20905i −0.386768 0.125669i
310310 0 0
311311 −4.59090 4.13366i −0.260326 0.234399i 0.528624 0.848856i 0.322708π-0.322708\pi
−0.788950 + 0.614458i 0.789375π0.789375\pi
312312 4.99696 + 3.24507i 0.282897 + 0.183716i
313313 0.586184 11.1851i 0.0331331 0.632216i −0.930712 0.365753i 0.880811π-0.880811\pi
0.963845 0.266463i 0.0858552π-0.0858552\pi
314314 3.16170 + 9.73071i 0.178425 + 0.549136i
315315 0 0
316316 4.50152 13.8542i 0.253230 0.779362i
317317 8.39567 + 3.22280i 0.471548 + 0.181010i 0.582525 0.812813i 0.302065π-0.302065\pi
−0.110977 + 0.993823i 0.535398π0.535398\pi
318318 2.52370 9.41859i 0.141522 0.528168i
319319 9.07597 + 0.953923i 0.508157 + 0.0534094i
320320 0 0
321321 −6.50714 8.95630i −0.363193 0.499892i
322322 −0.166253 2.34963i −0.00926494 0.130940i
323323 4.36630 + 2.22474i 0.242947 + 0.123788i
324324 0.921313 + 0.531920i 0.0511840 + 0.0295511i
325325 0 0
326326 1.35707 + 2.35051i 0.0751610 + 0.130183i
327327 −10.2022 + 6.62539i −0.564183 + 0.366385i
328328 0.170676 + 0.0270324i 0.00942401 + 0.00149262i
329329 0.0938322 0.484864i 0.00517314 0.0267314i
330330 0 0
331331 −6.60155 + 2.93920i −0.362854 + 0.161553i −0.580062 0.814572i 0.696972π-0.696972\pi
0.217208 + 0.976125i 0.430305π0.430305\pi
332332 −8.43463 2.26005i −0.462910 0.124036i
333333 8.38447 + 10.3540i 0.459466 + 0.567394i
334334 −9.96132 11.0632i −0.545059 0.605349i
335335 0 0
336336 2.19943 0.0402094i 0.119989 0.00219360i
337337 −9.03950 + 4.60585i −0.492413 + 0.250897i −0.682521 0.730866i 0.739116π-0.739116\pi
0.190108 + 0.981763i 0.439116π0.439116\pi
338338 −6.95506 0.364499i −0.378305 0.0198261i
339339 4.96815 5.51769i 0.269833 0.299680i
340340 0 0
341341 9.66695 8.70416i 0.523494 0.471356i
342342 7.03363 1.11402i 0.380335 0.0602392i
343343 18.4235 + 1.89023i 0.994778 + 0.102063i
344344 7.33539 10.0963i 0.395498 0.544356i
345345 0 0
346346 −1.56752 + 3.52070i −0.0842703 + 0.189274i
347347 2.87267 + 7.48356i 0.154213 + 0.401738i 0.988821 0.149105i 0.0476393π-0.0476393\pi
−0.834608 + 0.550844i 0.814306π0.814306\pi
348348 5.86988 + 9.03883i 0.314659 + 0.484532i
349349 −8.82065 −0.472158 −0.236079 0.971734i 0.575862π-0.575862\pi
−0.236079 + 0.971734i 0.575862π0.575862\pi
350350 0 0
351351 10.6965 0.570939
352352 4.23285 + 6.51801i 0.225612 + 0.347411i
353353 −6.03343 15.7176i −0.321127 0.836565i −0.995197 0.0978967i 0.968789π-0.968789\pi
0.674070 0.738668i 0.264545π-0.264545\pi
354354 −1.71324 + 3.84801i −0.0910579 + 0.204519i
355355 0 0
356356 12.8773 17.7241i 0.682497 0.939376i
357357 −2.76151 0.0941494i −0.146155 0.00498292i
358358 15.5477 2.46251i 0.821720 0.130148i
359359 −10.2724 + 9.24932i −0.542157 + 0.488161i −0.894104 0.447859i 0.852187π-0.852187\pi
0.351947 + 0.936020i 0.385520π0.385520\pi
360360 0 0
361361 5.87151 6.52098i 0.309027 0.343209i
362362 −3.53476 0.185249i −0.185783 0.00973647i
363363 9.24451 4.71031i 0.485211 0.247227i
364364 6.35927 3.82819i 0.333316 0.200652i
365365 0 0
366366 −2.67195 2.96750i −0.139665 0.155114i
367367 −0.653967 0.807582i −0.0341368 0.0421554i 0.759792 0.650167i 0.225301π-0.225301\pi
−0.793928 + 0.608011i 0.791968π0.791968\pi
368368 −0.819049 0.219464i −0.0426959 0.0114403i
369369 0.103979 0.0462943i 0.00541292 0.00240999i
370370 0 0
371371 −22.3192 19.3695i −1.15876 1.00561i
372372 15.1732 + 2.40320i 0.786695 + 0.124600i
373373 18.4553 11.9850i 0.955577 0.620559i 0.0301748 0.999545i 0.490394π-0.490394\pi
0.925403 + 0.378985i 0.123727π0.123727\pi
374374 −0.479720 0.830899i −0.0248057 0.0429648i
375375 0 0
376376 0.426675 + 0.246341i 0.0220041 + 0.0127041i
377377 12.3102 + 6.27237i 0.634009 + 0.323044i
378378 −9.06828 + 6.12754i −0.466422 + 0.315167i
379379 −17.8299 24.5408i −0.915862 1.26058i −0.965125 0.261790i 0.915687π-0.915687\pi
0.0492625 0.998786i 0.484313π-0.484313\pi
380380 0 0
381381 −20.6544 2.17087i −1.05816 0.111217i
382382 3.11380 11.6209i 0.159316 0.594575i
383383 19.9640 + 7.66347i 1.02011 + 0.391585i 0.810212 0.586137i 0.199352π-0.199352\pi
0.209902 + 0.977722i 0.432685π0.432685\pi
384384 −3.23567 + 9.95838i −0.165120 + 0.508186i
385385 0 0
386386 −1.88327 5.79612i −0.0958562 0.295015i
387387 0.430196 8.20863i 0.0218681 0.417268i
388388 20.3655 + 13.2255i 1.03390 + 0.671423i
389389 15.6392 + 14.0816i 0.792938 + 0.713964i 0.962419 0.271569i 0.0875426π-0.0875426\pi
−0.169481 + 0.985533i 0.554209π0.554209\pi
390390 0 0
391391 1.01295 + 0.329128i 0.0512271 + 0.0166447i
392392 −7.78066 + 16.7579i −0.392982 + 0.846403i
393393 13.3088 13.3088i 0.671340 0.671340i
394394 5.17168 + 11.6158i 0.260545 + 0.585195i
395395 0 0
396396 2.94311 + 1.31036i 0.147897 + 0.0658479i
397397 −3.98282 3.22523i −0.199892 0.161869i 0.524148 0.851627i 0.324384π-0.324384\pi
−0.724040 + 0.689758i 0.757717π0.757717\pi
398398 −9.63744 + 18.9145i −0.483081 + 0.948100i
399399 −4.56645 + 14.9804i −0.228608 + 0.749960i
400400 0 0
401401 −17.1661 + 29.7326i −0.857235 + 1.48477i 0.0173216 + 0.999850i 0.494486π0.494486\pi
−0.874556 + 0.484924i 0.838847π0.838847\pi
402402 0.388093 + 7.40526i 0.0193563 + 0.369341i
403403 18.3854 7.05751i 0.915844 0.351560i
404404 0.517259 + 4.92139i 0.0257346 + 0.244848i
405405 0 0
406406 −14.0295 + 1.73437i −0.696272 + 0.0860755i
407407 −7.19393 7.19393i −0.356590 0.356590i
408408 0.987852 2.57344i 0.0489060 0.127404i
409409 25.6660 5.45549i 1.26910 0.269756i 0.476327 0.879268i 0.341968π-0.341968\pi
0.792777 + 0.609512i 0.208634π0.208634\pi
410410 0 0
411411 0.771207 3.62824i 0.0380408 0.178968i
412412 −4.03345 7.91610i −0.198714 0.389998i
413413 8.21385 + 9.77247i 0.404177 + 0.480872i
414414 1.47203 0.478291i 0.0723462 0.0235067i
415415 0 0
416416 2.44630 + 11.5089i 0.119940 + 0.564272i
417417 7.53028 6.09790i 0.368760 0.298616i
418418 −5.25268 + 1.40745i −0.256917 + 0.0688407i
419419 −20.8379 15.1396i −1.01800 0.739617i −0.0521248 0.998641i 0.516599π-0.516599\pi
−0.965871 + 0.259023i 0.916599π0.916599\pi
420420 0 0
421421 −9.53283 + 6.92601i −0.464602 + 0.337553i −0.795334 0.606172i 0.792704π-0.792704\pi
0.330732 + 0.943725i 0.392704π0.392704\pi
422422 −7.18251 + 8.86966i −0.349639 + 0.431768i
423423 0.324066 0.0169836i 0.0157566 0.000825770i
424424 25.5318 14.7408i 1.23994 0.715877i
425425 0 0
426426 9.41470i 0.456144i
427427 −11.6306 + 3.34542i −0.562843 + 0.161896i
428428 2.15233 13.5893i 0.104037 0.656864i
429429 −2.98036 + 0.313248i −0.143893 + 0.0151238i
430430 0 0
431431 1.62917 15.5005i 0.0784745 0.746635i −0.882559 0.470202i 0.844181π-0.844181\pi
0.961033 0.276433i 0.0891523π-0.0891523\pi
432432 1.01970 + 3.80556i 0.0490602 + 0.183095i
433433 0.121416 + 0.766591i 0.00583489 + 0.0368400i 0.990434 0.137987i 0.0440633π-0.0440633\pi
−0.984599 + 0.174827i 0.944063π0.944063\pi
434434 −11.5439 + 16.5154i −0.554123 + 0.792763i
435435 0 0
436436 −14.7881 3.14331i −0.708223 0.150537i
437437 3.28784 5.06282i 0.157279 0.242188i
438438 −0.782996 + 1.20571i −0.0374130 + 0.0576110i
439439 10.3322 + 2.19617i 0.493128 + 0.104818i 0.447762 0.894153i 0.352221π-0.352221\pi
0.0453661 + 0.998970i 0.485555π0.485555\pi
440440 0 0
441441 1.71358 + 12.0482i 0.0815991 + 0.573726i
442442 −0.227225 1.43464i −0.0108080 0.0682391i
443443 7.03490 + 26.2546i 0.334238 + 1.24739i 0.904693 + 0.426064i 0.140100π0.140100\pi
−0.570455 + 0.821329i 0.693233π0.693233\pi
444444 1.25591 11.9492i 0.0596028 0.567083i
445445 0 0
446446 16.7126 1.75656i 0.791364 0.0831757i
447447 0.00694557 0.0438526i 0.000328514 0.00207416i
448448 −5.84684 5.63690i −0.276237 0.266318i
449449 39.0168i 1.84131i −0.390372 0.920657i 0.627654π-0.627654\pi
0.390372 0.920657i 0.372346π-0.372346\pi
450450 0 0
451451 −0.0752701 + 0.0434572i −0.00354433 + 0.00204632i
452452 9.21499 0.482937i 0.433437 0.0227154i
453453 6.92257 8.54866i 0.325251 0.401651i
454454 5.91145 4.29492i 0.277438 0.201571i
455455 0 0
456456 −12.6398 9.18334i −0.591912 0.430049i
457457 −22.2310 + 5.95677i −1.03992 + 0.278646i −0.738080 0.674713i 0.764268π-0.764268\pi
−0.301840 + 0.953359i 0.597601π0.597601\pi
458458 1.88031 1.52265i 0.0878613 0.0711487i
459459 −1.02889 4.84056i −0.0480246 0.225938i
460460 0 0
461461 23.0880 7.50175i 1.07532 0.349391i 0.282760 0.959191i 0.408750π-0.408750\pi
0.792556 + 0.609799i 0.208750π0.208750\pi
462462 2.34724 1.97287i 0.109203 0.0917863i
463463 −2.79874 5.49284i −0.130069 0.255274i 0.816783 0.576945i 0.195755π-0.195755\pi
−0.946851 + 0.321671i 0.895755π0.895755\pi
464464 −1.05803 + 4.97762i −0.0491176 + 0.231080i
465465 0 0
466466 −22.1665 + 4.71162i −1.02684 + 0.218262i
467467 10.5121 27.3851i 0.486444 1.26723i −0.442420 0.896808i 0.645880π-0.645880\pi
0.928864 0.370422i 0.120787π-0.120787\pi
468468 3.44880 + 3.44880i 0.159421 + 0.159421i
469469 20.6947 + 8.76422i 0.955594 + 0.404694i
470470 0 0
471471 −1.54546 14.7041i −0.0712109 0.677527i
472472 −11.8896 + 4.56399i −0.547263 + 0.210075i
473473 0.328506 + 6.26828i 0.0151047 + 0.288216i
474474 4.55512 7.88970i 0.209224 0.362386i
475475 0 0
476476 −2.34409 2.50956i −0.107441 0.115026i
477477 8.81577 17.3019i 0.403646 0.792200i
478478 1.94131 + 1.57204i 0.0887934 + 0.0719035i
479479 8.30871 + 3.69927i 0.379635 + 0.169024i 0.587677 0.809096i 0.300043π-0.300043\pi
−0.208043 + 0.978120i 0.566709π0.566709\pi
480480 0 0
481481 −6.26471 14.0708i −0.285646 0.641572i
482482 −14.7394 + 14.7394i −0.671360 + 0.671360i
483483 −0.470937 + 3.37110i −0.0214284 + 0.153390i
484484 12.2635 + 3.98466i 0.557433 + 0.181121i
485485 0 0
486486 −8.72786 7.85860i −0.395904 0.356473i
487487 0.445473 + 0.289294i 0.0201863 + 0.0131091i 0.554693 0.832055i 0.312836π-0.312836\pi
−0.534506 + 0.845164i 0.679502π0.679502\pi
488488 0.631868 12.0568i 0.0286033 0.545784i
489489 −1.21199 3.73011i −0.0548080 0.168682i
490490 0 0
491491 1.98288 6.10267i 0.0894861 0.275410i −0.896291 0.443466i 0.853749π-0.853749\pi
0.985777 + 0.168056i 0.0537489π0.0537489\pi
492492 −0.0958265 0.0367843i −0.00432019 0.00165837i
493493 1.65436 6.17415i 0.0745086 0.278070i
494494 −8.18762 0.860554i −0.368379 0.0387181i
495495 0 0
496496 4.26357 + 5.86830i 0.191440 + 0.263494i
497497 −25.6559 12.4870i −1.15082 0.560118i
498498 −4.86582 2.47926i −0.218043 0.111098i
499499 −5.43364 3.13711i −0.243243 0.140437i 0.373423 0.927661i 0.378184π-0.378184\pi
−0.616666 + 0.787225i 0.711517π0.711517\pi
500500 0 0
501501 10.7562 + 18.6303i 0.480553 + 0.832343i
502502 8.96567 5.82237i 0.400157 0.259865i
503503 −4.92568 0.780151i −0.219625 0.0347852i 0.0456521 0.998957i 0.485463π-0.485463\pi
−0.265277 + 0.964172i 0.585463π0.585463\pi
504504 −11.9193 2.30666i −0.530929 0.102747i
505505 0 0
506506 −1.07973 + 0.480729i −0.0480001 + 0.0213710i
507507 9.72131 + 2.60482i 0.431739 + 0.115684i
508508 −16.2434 20.0589i −0.720684 0.889971i
509509 −15.1400 16.8147i −0.671070 0.745298i 0.307425 0.951572i 0.400533π-0.400533\pi
−0.978494 + 0.206274i 0.933866π0.933866\pi
510510 0 0
511511 2.24715 + 3.73290i 0.0994082 + 0.165134i
512512 −7.34327 + 3.74158i −0.324530 + 0.165356i
513513 −28.0101 1.46795i −1.23668 0.0648115i
514514 4.80611 5.33772i 0.211988 0.235437i
515515 0 0
516516 −5.50883 + 4.96017i −0.242513 + 0.218359i
517517 −0.244752 + 0.0387649i −0.0107642 + 0.00170488i
518518 13.3716 + 8.34013i 0.587513 + 0.366444i
519519 3.27343 4.50548i 0.143687 0.197769i
520520 0 0
521521 12.5522 28.1927i 0.549921 1.23514i −0.398219 0.917290i 0.630372π-0.630372\pi
0.948140 0.317853i 0.102962π-0.102962\pi
522522 −3.32882 8.67186i −0.145698 0.379557i
523523 16.6846 + 25.6920i 0.729567 + 1.12343i 0.987553 + 0.157286i 0.0502743π0.0502743\pi
−0.257987 + 0.966149i 0.583059π0.583059\pi
524524 23.3916 1.02187
525525 0 0
526526 6.52252 0.284395
527527 −4.96226 7.64121i −0.216159 0.332856i
528528 −0.395563 1.03048i −0.0172147 0.0448457i
529529 −8.82128 + 19.8129i −0.383534 + 0.861432i
530530 0 0
531531 −4.93056 + 6.78633i −0.213968 + 0.294502i
532532 −17.1778 + 9.15184i −0.744754 + 0.396783i
533533 −0.129963 + 0.0205840i −0.00562930 + 0.000891594i
534534 10.1820 9.16792i 0.440619 0.396735i
535535 0 0
536536 −15.0022 + 16.6617i −0.647998 + 0.719675i
537537 −22.7161 1.19050i −0.980273 0.0513739i
538538 3.04985 1.55398i 0.131488 0.0669966i
539539 −2.26305 9.01310i −0.0974764 0.388222i
540540 0 0
541541 26.4951 + 29.4258i 1.13911 + 1.26511i 0.959603 + 0.281356i 0.0907841π0.0907841\pi
0.179509 + 0.983756i 0.442549π0.442549\pi
542542 −1.67887 2.07323i −0.0721135 0.0890528i
543543 4.94065 + 1.32384i 0.212023 + 0.0568115i
544544 4.97289 2.21407i 0.213211 0.0949276i
545545 0 0
546546 4.38790 1.51493i 0.187785 0.0648331i
547547 −37.0235 5.86395i −1.58301 0.250724i −0.697932 0.716164i 0.745896π-0.745896\pi
−0.885079 + 0.465440i 0.845896π0.845896\pi
548548 3.86625 2.51077i 0.165158 0.107255i
549549 −3.97611 6.88682i −0.169696 0.293922i
550550 0 0
551551 −31.3750 18.1143i −1.33662 0.771697i
552552 −3.02561 1.54162i −0.128778 0.0656159i
553553 −15.4586 22.8774i −0.657365 0.972848i
554554 3.51735 + 4.84122i 0.149438 + 0.205684i
555555 0 0
556556 11.9765 + 1.25878i 0.507916 + 0.0533841i
557557 1.55832 5.81572i 0.0660280 0.246420i −0.925021 0.379915i 0.875953π-0.875953\pi
0.991050 + 0.133495i 0.0426200π0.0426200\pi
558558 −12.3609 4.74490i −0.523278 0.200868i
559559 −2.93652 + 9.03767i −0.124201 + 0.382253i
560560 0 0
561561 0.428435 + 1.31859i 0.0180885 + 0.0556708i
562562 −0.986964 + 18.8324i −0.0416326 + 0.794397i
563563 25.3462 + 16.4600i 1.06822 + 0.693708i 0.954018 0.299750i 0.0969033π-0.0969033\pi
0.114199 + 0.993458i 0.463570π0.463570\pi
564564 −0.217481 0.195821i −0.00915761 0.00824555i
565565 0 0
566566 5.35873 + 1.74116i 0.225244 + 0.0731863i
567567 1.86894 0.756899i 0.0784882 0.0317868i
568568 20.1280 20.1280i 0.844552 0.844552i
569569 2.02703 + 4.55278i 0.0849775 + 0.190863i 0.951036 0.309080i 0.100021π-0.100021\pi
−0.866059 + 0.499943i 0.833354π0.833354\pi
570570 0 0
571571 −2.23119 0.993391i −0.0933725 0.0415721i 0.359519 0.933138i 0.382941π-0.382941\pi
−0.452891 + 0.891566i 0.649607π0.649607\pi
572572 −2.89443 2.34386i −0.121022 0.0980018i
573573 −7.89270 + 15.4903i −0.329722 + 0.647117i
574574 0.0983877 0.0919002i 0.00410662 0.00383584i
575575 0 0
576576 2.66831 4.62165i 0.111180 0.192569i
577577 1.27197 + 24.2706i 0.0529527 + 1.01040i 0.887891 + 0.460054i 0.152170π0.152170\pi
−0.834938 + 0.550343i 0.814497π0.814497\pi
578578 11.7082 4.49437i 0.486998 0.186941i
579579 0.920556 + 8.75851i 0.0382570 + 0.363991i
580580 0 0
581581 −13.2099 + 9.97149i −0.548038 + 0.413687i
582582 10.7384 + 10.7384i 0.445123 + 0.445123i
583583 −5.31398 + 13.8434i −0.220083 + 0.573335i
584584 −4.25172 + 0.903731i −0.175937 + 0.0373966i
585585 0 0
586586 5.03247 23.6759i 0.207890 0.978044i
587587 −4.09368 8.03430i −0.168964 0.331611i 0.790961 0.611866i 0.209581π-0.209581\pi
−0.959926 + 0.280255i 0.909581π0.909581\pi
588588 6.59023 8.77567i 0.271777 0.361903i
589589 −49.1130 + 15.9578i −2.02366 + 0.657528i
590590 0 0
591591 −3.82016 17.9724i −0.157140 0.739287i
592592 4.40882 3.57019i 0.181202 0.146734i
593593 −24.7752 + 6.63849i −1.01740 + 0.272610i −0.728716 0.684816i 0.759883π-0.759883\pi
−0.288679 + 0.957426i 0.593216π0.593216\pi
594594 4.44277 + 3.22786i 0.182289 + 0.132441i
595595 0 0
596596 0.0446416 0.0324340i 0.00182859 0.00132855i
597597 19.3051 23.8398i 0.790104 0.975697i
598598 −1.78689 + 0.0936469i −0.0730714 + 0.00382951i
599599 −23.1803 + 13.3832i −0.947123 + 0.546822i −0.892186 0.451668i 0.850829π-0.850829\pi
−0.0549370 + 0.998490i 0.517496π0.517496\pi
600600 0 0
601601 3.83116i 0.156276i 0.996943 + 0.0781382i 0.0248975π0.0248975\pi
−0.996943 + 0.0781382i 0.975102π0.975102\pi
602602 −2.68775 9.34413i −0.109544 0.380838i
603603 −2.31015 + 14.5857i −0.0940764 + 0.593975i
604604 13.5961 1.42901i 0.553219 0.0581457i
605605 0 0
606606 −0.323490 + 3.07780i −0.0131409 + 0.125027i
607607 8.71399 + 32.5210i 0.353690 + 1.31999i 0.882125 + 0.471015i 0.156112π0.156112\pi
−0.528435 + 0.848974i 0.677221π0.677221\pi
608608 −4.82648 30.4732i −0.195740 1.23585i
609609 20.3514 + 1.76358i 0.824682 + 0.0714637i
610610 0 0
611611 −0.366959 0.0779995i −0.0148456 0.00315552i
612612 1.22897 1.89244i 0.0496780 0.0764974i
613613 −24.1890 + 37.2478i −0.976985 + 1.50442i −0.117622 + 0.993058i 0.537527π0.537527\pi
−0.859363 + 0.511366i 0.829140π0.829140\pi
614614 −2.51124 0.533781i −0.101346 0.0215417i
615615 0 0
616616 9.23610 + 0.800364i 0.372133 + 0.0322476i
617617 5.46815 + 34.5246i 0.220140 + 1.38991i 0.811902 + 0.583794i 0.198432π0.198432\pi
−0.591762 + 0.806112i 0.701568π0.701568\pi
618618 −1.43807 5.36695i −0.0578476 0.215890i
619619 1.39751 13.2964i 0.0561706 0.534427i −0.929866 0.367898i 0.880077π-0.880077\pi
0.986037 0.166529i 0.0532559π-0.0532559\pi
620620 0 0
621621 −6.06282 + 0.637228i −0.243293 + 0.0255711i
622622 0.751132 4.74246i 0.0301176 0.190155i
623623 −11.4787 39.9066i −0.459885 1.59882i
624624 1.67106i 0.0668960i
625625 0 0
626626 7.53917 4.35274i 0.301326 0.173971i
627627 7.84740 0.411265i 0.313395 0.0164243i
628628 11.5638 14.2801i 0.461446 0.569838i
629629 −5.76493 + 4.18846i −0.229863 + 0.167005i
630630 0 0
631631 11.1996 + 8.13699i 0.445849 + 0.323928i 0.787955 0.615733i 0.211140π-0.211140\pi
−0.342106 + 0.939662i 0.611140π0.611140\pi
632632 26.6062 7.12911i 1.05834 0.283581i
633633 12.8171 10.3791i 0.509436 0.412533i
634634 1.45326 + 6.83703i 0.0577162 + 0.271533i
635635 0 0
636636 −16.6548 + 5.41147i −0.660405 + 0.214579i
637637 1.69147 13.9667i 0.0670186 0.553382i
638638 3.22021 + 6.32003i 0.127489 + 0.250212i
639639 3.89813 18.3393i 0.154208 0.725490i
640640 0 0
641641 2.29399 0.487602i 0.0906070 0.0192591i −0.162385 0.986727i 0.551919π-0.551919\pi
0.252992 + 0.967468i 0.418585π0.418585\pi
642642 3.08361 8.03308i 0.121700 0.317041i
643643 −16.5284 16.5284i −0.651816 0.651816i 0.301614 0.953430i 0.402475π-0.402475\pi
−0.953430 + 0.301614i 0.902475π0.902475\pi
644644 −3.37639 + 2.54867i −0.133048 + 0.100432i
645645 0 0
646646 0.398131 + 3.78797i 0.0156643 + 0.149036i
647647 10.9473 4.20226i 0.430381 0.165208i −0.133527 0.991045i 0.542630π-0.542630\pi
0.563909 + 0.825837i 0.309297π0.309297\pi
648648 0.105278 + 2.00883i 0.00413572 + 0.0789143i
649649 3.20276 5.54735i 0.125719 0.217752i
650650 0 0
651651 21.2789 19.8758i 0.833986 0.778994i
652652 2.21293 4.34313i 0.0866652 0.170090i
653653 −16.1758 13.0989i −0.633008 0.512600i 0.258261 0.966075i 0.416851π-0.416851\pi
−0.891269 + 0.453475i 0.850184π0.850184\pi
654654 −8.63758 3.84570i −0.337756 0.150379i
655655 0 0
656656 −0.0197126 0.0442752i −0.000769648 0.00172866i
657657 −2.02445 + 2.02445i −0.0789813 + 0.0789813i
658658 0.355782 0.144087i 0.0138698 0.00561711i
659659 30.5370 + 9.92209i 1.18955 + 0.386510i 0.835908 0.548870i 0.184942π-0.184942\pi
0.353646 + 0.935379i 0.384942π0.384942\pi
660660 0 0
661661 −7.51696 6.76830i −0.292376 0.263256i 0.509868 0.860252i 0.329694π-0.329694\pi
−0.802244 + 0.596996i 0.796361π0.796361\pi
662662 −4.71049 3.05903i −0.183079 0.118893i
663663 −0.109852 + 2.09611i −0.00426631 + 0.0814060i
664664 −5.10231 15.7033i −0.198008 0.609406i
665665 0 0
666666 −3.19997 + 9.84849i −0.123996 + 0.381621i
667667 −7.35113 2.82183i −0.284637 0.109262i
668668 −6.91979 + 25.8250i −0.267735 + 0.999199i
669669 −24.1506 2.53833i −0.933716 0.0981375i
670670 0 0
671671 3.56931 + 4.91273i 0.137792 + 0.189654i
672672 9.73998 + 14.4144i 0.375728 + 0.556048i
673673 −10.0639 5.12781i −0.387935 0.197663i 0.249135 0.968469i 0.419854π-0.419854\pi
−0.637070 + 0.770806i 0.719854π0.719854\pi
674674 −6.82894 3.94269i −0.263041 0.151867i
675675 0 0
676676 6.25399 + 10.8322i 0.240538 + 0.416624i
677677 −20.5086 + 13.3184i −0.788208 + 0.511868i −0.874863 0.484370i 0.839049π-0.839049\pi
0.0866551 + 0.996238i 0.472382π0.472382\pi
678678 5.69985 + 0.902768i 0.218901 + 0.0346706i
679679 43.5059 15.0205i 1.66960 0.576435i
680680 0 0
681681 −9.64609 + 4.29471i −0.369639 + 0.164574i
682682 9.76605 + 2.61681i 0.373961 + 0.100203i
683683 10.3756 + 12.8128i 0.397012 + 0.490269i 0.935978 0.352058i 0.114518π-0.114518\pi
−0.538966 + 0.842328i 0.681185π0.681185\pi
684684 −8.55778 9.50438i −0.327215 0.363409i
685685 0 0
686686 6.56689 + 12.8096i 0.250725 + 0.489074i
687687 −3.11525 + 1.58730i −0.118854 + 0.0605593i
688688 −3.49532 0.183182i −0.133258 0.00698375i
689689 −15.0213 + 16.6829i −0.572267 + 0.635567i
690690 0 0
691691 −20.8963 + 18.8151i −0.794932 + 0.715760i −0.962849 0.270041i 0.912963π-0.912963\pi
0.167917 + 0.985801i 0.446296π0.446296\pi
692692 6.83613 1.08274i 0.259870 0.0411594i
693693 5.38914 2.87117i 0.204716 0.109067i
694694 −3.66214 + 5.04050i −0.139013 + 0.191335i
695695 0 0
696696 −8.28889 + 18.6172i −0.314190 + 0.705681i
697697 0.0218160 + 0.0568327i 0.000826341 + 0.00215269i
698698 −3.73395 5.74978i −0.141332 0.217632i
699699 32.7474 1.23862
700700 0 0
701701 −35.1051 −1.32590 −0.662951 0.748663i 0.730696π-0.730696\pi
−0.662951 + 0.748663i 0.730696π0.730696\pi
702702 4.52805 + 6.97258i 0.170900 + 0.263163i
703703 14.4739 + 37.7057i 0.545892 + 1.42210i
704704 −1.65751 + 3.72283i −0.0624698 + 0.140310i
705705 0 0
706706 7.69154 10.5865i 0.289475 0.398428i
707707 7.95823 + 4.96372i 0.299300 + 0.186680i
708708 7.47165 1.18339i 0.280802 0.0444746i
709709 −39.0403 + 35.1521i −1.46619 + 1.32016i −0.623423 + 0.781885i 0.714258π0.714258\pi
−0.842767 + 0.538278i 0.819075π0.819075\pi
710710 0 0
711711 12.1398 13.4826i 0.455278 0.505638i
712712 41.3689 + 2.16805i 1.55036 + 0.0812511i
713713 −10.0005 + 5.09550i −0.374521 + 0.190828i
714714 −1.10763 1.83996i −0.0414520 0.0688588i
715715 0 0
716716 −18.9168 21.0092i −0.706953 0.785151i
717717 −2.27169 2.80530i −0.0848377 0.104766i
718718 −10.3777 2.78070i −0.387293 0.103775i
719719 −2.53041 + 1.12661i −0.0943685 + 0.0420156i −0.453378 0.891318i 0.649781π-0.649781\pi
0.359009 + 0.933334i 0.383115π0.383115\pi
720720 0 0
721721 −16.5328 3.19947i −0.615712 0.119154i
722722 6.73625 + 1.06692i 0.250697 + 0.0397066i
723723 25.2621 16.4054i 0.939508 0.610124i
724724 3.17846 + 5.50525i 0.118126 + 0.204601i
725725 0 0
726726 6.98382 + 4.03211i 0.259194 + 0.149646i
727727 5.31536 + 2.70831i 0.197136 + 0.100446i 0.549772 0.835315i 0.314715π-0.314715\pi
−0.352636 + 0.935761i 0.614715π0.614715\pi
728728 12.6199 + 6.14222i 0.467724 + 0.227646i
729729 11.3195 + 15.5799i 0.419239 + 0.577033i
730730 0 0
731731 4.37233 + 0.459550i 0.161716 + 0.0169971i
732732 −1.85611 + 6.92710i −0.0686038 + 0.256033i
733733 −28.1255 10.7964i −1.03884 0.398773i −0.221641 0.975128i 0.571141π-0.571141\pi
−0.817199 + 0.576355i 0.804475π0.804475\pi
734734 0.249589 0.768156i 0.00921250 0.0283532i
735735 0 0
736736 −2.07219 6.37755i −0.0763820 0.235080i
737737 0.590180 11.2613i 0.0217396 0.414816i
738738 0.0741934 + 0.0481817i 0.00273110 + 0.00177359i
739739 −33.5727 30.2290i −1.23499 1.11199i −0.989792 0.142517i 0.954480π-0.954480\pi
−0.245198 0.969473i 0.578853π-0.578853\pi
740740 0 0
741741 11.3145 + 3.67629i 0.415648 + 0.135052i
742742 3.17791 22.7484i 0.116665 0.835119i
743743 −23.4363 + 23.4363i −0.859793 + 0.859793i −0.991313 0.131520i 0.958014π-0.958014\pi
0.131520 + 0.991313i 0.458014π0.458014\pi
744744 11.8150 + 26.5369i 0.433159 + 0.972891i
745745 0 0
746746 15.6249 + 6.95667i 0.572070 + 0.254702i
747747 −8.45180 6.84413i −0.309235 0.250414i
748748 −0.782267 + 1.53529i −0.0286025 + 0.0561356i
749749 −17.8010 19.0576i −0.650434 0.696351i
750750 0 0
751751 19.3994 33.6008i 0.707894 1.22611i −0.257742 0.966214i 0.582979π-0.582979\pi
0.965637 0.259895i 0.0836881π-0.0836881\pi
752752 −0.00723178 0.137991i −0.000263716 0.00503200i
753753 −14.4221 + 5.53611i −0.525569 + 0.201747i
754754 1.12248 + 10.6797i 0.0408784 + 0.388932i
755755 0 0
756756 18.0993 + 7.66505i 0.658265 + 0.278775i
757757 −2.63808 2.63808i −0.0958825 0.0958825i 0.657538 0.753421i 0.271598π-0.271598\pi
−0.753421 + 0.657538i 0.771598π0.771598\pi
758758 8.44928 22.0111i 0.306892 0.799480i
759759 1.67061 0.355100i 0.0606394 0.0128893i
760760 0 0
761761 −8.25480 + 38.8358i −0.299236 + 1.40780i 0.529573 + 0.848265i 0.322352π0.322352\pi
−0.828809 + 0.559532i 0.810981π0.810981\pi
762762 −7.32833 14.3827i −0.265477 0.521029i
763763 −21.9362 + 18.4375i −0.794142 + 0.667483i
764764 −20.5490 + 6.67679i −0.743438 + 0.241558i
765765 0 0
766766 3.45569 + 16.2577i 0.124859 + 0.587416i
767767 7.53640 6.10285i 0.272124 0.220361i
768768 −14.5217 + 3.89107i −0.524006 + 0.140407i
769769 0.563611 + 0.409487i 0.0203243 + 0.0147665i 0.597901 0.801570i 0.296002π-0.296002\pi
−0.577577 + 0.816336i 0.696002π0.696002\pi
770770 0 0
771771 −8.39701 + 6.10079i −0.302411 + 0.219714i
772772 −6.88801 + 8.50598i −0.247905 + 0.306137i
773773 −32.7224 + 1.71491i −1.17694 + 0.0616809i −0.630755 0.775982i 0.717255π-0.717255\pi
−0.546187 + 0.837663i 0.683921π0.683921\pi
774774 5.53295 3.19445i 0.198878 0.114822i
775775 0 0
776776 45.9162i 1.64829i
777777 −16.3947 15.8060i −0.588156 0.567037i
778778 −2.55878 + 16.1555i −0.0917365 + 0.579202i
779779 0.343147 0.0360662i 0.0122945 0.00129221i
780780 0 0
781781 −1.49654 + 14.2387i −0.0535505 + 0.509499i
782782 0.214258 + 0.799623i 0.00766186 + 0.0285945i
783783 5.72327 + 36.1353i 0.204533 + 1.29137i
784784 5.13027 0.729660i 0.183224 0.0260593i
785785 0 0
786786 14.3093 + 3.04153i 0.510395 + 0.108488i
787787 14.5264 22.3687i 0.517810 0.797358i −0.478945 0.877845i 0.658981π-0.658981\pi
0.996756 + 0.0804867i 0.0256474π0.0256474\pi
788788 12.4371 19.1514i 0.443052 0.682240i
789789 −9.21943 1.95965i −0.328221 0.0697654i
790790 0 0
791791 10.0200 14.3352i 0.356270 0.509702i
792792 0.952952 + 6.01670i 0.0338617 + 0.213794i
793793 2.37940 + 8.88006i 0.0844951 + 0.315340i
794794 0.416373 3.96152i 0.0147765 0.140589i
795795 0 0
796796 37.9158 3.98511i 1.34389 0.141248i
797797 −2.59453 + 16.3812i −0.0919030 + 0.580252i 0.898165 + 0.439660i 0.144901π0.144901\pi
−0.990067 + 0.140593i 0.955099π0.955099\pi
798798 −11.6981 + 3.36485i −0.414109 + 0.119114i
799799 0.173565i 0.00614027i
800800 0 0
801801 23.6299 13.6427i 0.834921 0.482042i
802802 −26.6481 + 1.39657i −0.940976 + 0.0493145i
803803 1.37585 1.69903i 0.0485527 0.0599576i
804804 10.7742 7.82790i 0.379976 0.276069i
805805 0 0
806806 12.3834 + 8.99706i 0.436186 + 0.316908i
807807 −4.77777 + 1.28020i −0.168186 + 0.0450652i
808808 −7.27174 + 5.88854i −0.255819 + 0.207158i
809809 8.99442 + 42.3154i 0.316227 + 1.48773i 0.793280 + 0.608857i 0.208372π0.208372\pi
−0.477053 + 0.878874i 0.658295π0.658295\pi
810810 0 0
811811 −24.7816 + 8.05202i −0.870198 + 0.282745i −0.709881 0.704321i 0.751252π-0.751252\pi
−0.160317 + 0.987066i 0.551252π0.551252\pi
812812 16.3351 + 19.4347i 0.573248 + 0.682025i
813813 1.75015 + 3.43487i 0.0613805 + 0.120466i
814814 1.64407 7.73473i 0.0576245 0.271102i
815815 0 0
816816 −0.756215 + 0.160738i −0.0264728 + 0.00562697i
817817 8.92991 23.2632i 0.312418 0.813876i
818818 14.4211 + 14.4211i 0.504223 + 0.504223i
819819 9.17462 1.13420i 0.320587 0.0396321i
820820 0 0
821821 −2.77911 26.4415i −0.0969916 0.922814i −0.929505 0.368809i 0.879766π-0.879766\pi
0.832514 0.554005i 0.186901π-0.186901\pi
822822 2.69155 1.03319i 0.0938787 0.0360367i
823823 −0.126889 2.42118i −0.00442306 0.0843971i 0.995526 0.0944878i 0.0301213π-0.0301213\pi
−0.999949 + 0.0100907i 0.996788π0.996788\pi
824824 8.39968 14.5487i 0.292617 0.506827i
825825 0 0
826826 −2.89315 + 9.49111i −0.100666 + 0.330238i
827827 −2.88877 + 5.66953i −0.100452 + 0.197149i −0.935763 0.352629i 0.885288π-0.885288\pi
0.835311 + 0.549778i 0.185288π0.185288\pi
828828 −2.16024 1.74933i −0.0750736 0.0607934i
829829 −16.1918 7.20907i −0.562365 0.250381i 0.105808 0.994387i 0.466257π-0.466257\pi
−0.668174 + 0.744005i 0.732924π0.732924\pi
830830 0 0
831831 −3.51718 7.89971i −0.122010 0.274038i
832832 −4.36250 + 4.36250i −0.151242 + 0.151242i
833833 −6.48314 + 0.578000i −0.224628 + 0.0200265i
834834 7.16266 + 2.32729i 0.248023 + 0.0805875i
835835 0 0
836836 7.25773 + 6.53489i 0.251014 + 0.226014i
837837 43.7361 + 28.4026i 1.51174 + 0.981736i
838838 1.04774 19.9921i 0.0361937 0.690617i
839839 −7.84911 24.1571i −0.270981 0.833995i −0.990255 0.139268i 0.955525π-0.955525\pi
0.719273 0.694727i 0.244475π-0.244475\pi
840840 0 0
841841 −5.64130 + 17.3621i −0.194528 + 0.598695i
842842 −8.55018 3.28211i −0.294659 0.113109i
843843 7.05313 26.3226i 0.242923 0.906600i
844844 20.3849 + 2.14254i 0.701678 + 0.0737493i
845845 0 0
846846 0.148254 + 0.204054i 0.00509708 + 0.00701553i
847847 20.2507 13.6836i 0.695823 0.470175i
848848 −7.36733 3.75384i −0.252995 0.128908i
849849 −7.05132 4.07108i −0.242001 0.139719i
850850 0 0
851851 4.38910 + 7.60214i 0.150456 + 0.260598i
852852 −14.1804 + 9.20886i −0.485812 + 0.315490i
853853 19.9447 + 3.15894i 0.682895 + 0.108160i 0.488237 0.872711i 0.337640π-0.337640\pi
0.194658 + 0.980871i 0.437640π0.437640\pi
854854 −7.10417 6.16527i −0.243100 0.210971i
855855 0 0
856856 23.7668 10.5816i 0.812331 0.361673i
857857 −3.59245 0.962594i −0.122716 0.0328816i 0.196938 0.980416i 0.436900π-0.436900\pi
−0.319654 + 0.947534i 0.603567π0.603567\pi
858858 −1.46584 1.81016i −0.0500428 0.0617977i
859859 14.7837 + 16.4190i 0.504413 + 0.560208i 0.940542 0.339677i 0.110318π-0.110318\pi
−0.436129 + 0.899884i 0.643651π0.643651\pi
860860 0 0
861861 −0.166680 + 0.100339i −0.00568043 + 0.00341954i
862862 10.7938 5.49970i 0.367637 0.187320i
863863 −39.3355 2.06149i −1.33900 0.0701738i −0.630666 0.776055i 0.717218π-0.717218\pi
−0.708331 + 0.705881i 0.750551π0.750551\pi
864864 −20.8482 + 23.1542i −0.709269 + 0.787723i
865865 0 0
866866 −0.448308 + 0.403659i −0.0152341 + 0.0137169i
867867 −17.8996 + 2.83502i −0.607903 + 0.0962823i
868868 36.1669 + 1.23305i 1.22758 + 0.0418525i
869869 −8.14324 + 11.2082i −0.276240 + 0.380212i
870870 0 0
871871 6.94391 15.5963i 0.235286 0.528460i
872872 −10.2447 26.6884i −0.346930 0.903785i
873873 16.4716 + 25.3641i 0.557480 + 0.858444i
874874 4.69203 0.158710
875875 0 0
876876 2.58191 0.0872347
877877 12.2611 + 18.8804i 0.414027 + 0.637546i 0.982740 0.184990i 0.0592253π-0.0592253\pi
−0.568713 + 0.822536i 0.692559π0.692559\pi
878878 2.94223 + 7.66476i 0.0992953 + 0.258673i
879879 −14.2266 + 31.9534i −0.479851 + 1.07776i
880880 0 0
881881 −1.48864 + 2.04893i −0.0501535 + 0.0690304i −0.833357 0.552735i 0.813584π-0.813584\pi
0.783204 + 0.621765i 0.213584π0.213584\pi
882882 −7.12831 + 6.21726i −0.240023 + 0.209346i
883883 −41.9699 + 6.64738i −1.41240 + 0.223702i −0.815566 0.578664i 0.803574π-0.803574\pi
−0.596833 + 0.802366i 0.703574π0.703574\pi
884884 −1.93860 + 1.74552i −0.0652022 + 0.0587083i
885885 0 0
886886 −14.1362 + 15.6998i −0.474914 + 0.527445i
887887 31.7581 + 1.66437i 1.06633 + 0.0558841i 0.577418 0.816448i 0.304060π-0.304060\pi
0.488913 + 0.872333i 0.337394π0.337394\pi
888888 20.2426 10.3141i 0.679298 0.346120i
889889 −48.9138 + 0.894227i −1.64052 + 0.0299914i
890890 0 0
891891 −0.677001 0.751885i −0.0226804 0.0251891i
892892 −18.9929 23.4543i −0.635930 0.785308i
893893 0.950220 + 0.254611i 0.0317979 + 0.00852022i
894894 0.0315257 0.0140362i 0.00105438 0.000469440i
895895 0 0
896896 −4.68636 + 24.2161i −0.156560 + 0.809002i
897897 2.55386 + 0.404492i 0.0852710 + 0.0135056i
898898 25.4333 16.5165i 0.848719 0.551164i
899899 33.6791 + 58.3340i 1.12326 + 1.94555i
900900 0 0
901901 8.99448 + 5.19297i 0.299650 + 0.173003i
902902 −0.0601911 0.0306689i −0.00200414 0.00102116i
903903 0.991680 + 14.0152i 0.0330010 + 0.466398i
904904 10.2558 + 14.1160i 0.341104 + 0.469490i
905905 0 0
906906 8.50294 + 0.893695i 0.282491 + 0.0296910i
907907 −5.62950 + 21.0096i −0.186924 + 0.697611i 0.807286 + 0.590160i 0.200936π0.200936\pi
−0.994210 + 0.107451i 0.965731π0.965731\pi
908908 −12.2512 4.70280i −0.406571 0.156068i
909909 −1.90450 + 5.86143i −0.0631681 + 0.194411i
910910 0 0
911911 1.19819 + 3.68765i 0.0396978 + 0.122177i 0.968941 0.247290i 0.0795401π-0.0795401\pi
−0.929244 + 0.369468i 0.879540π0.879540\pi
912912 −0.229330 + 4.37587i −0.00759387 + 0.144900i
913913 6.96491 + 4.52306i 0.230505 + 0.149692i
914914 −13.2937 11.9697i −0.439718 0.395924i
915915 0 0
916916 −4.13261 1.34277i −0.136545 0.0443663i
917917 27.2672 34.9600i 0.900444 1.15448i
918918 2.71979 2.71979i 0.0897665 0.0897665i
919919 3.22781 + 7.24979i 0.106476 + 0.239148i 0.958924 0.283663i 0.0915498π-0.0915498\pi
−0.852448 + 0.522812i 0.824883π0.824883\pi
920920 0 0
921921 3.38921 + 1.50898i 0.111678 + 0.0497224i
922922 14.6637 + 11.8744i 0.482922 + 0.391062i
923923 −9.84030 + 19.3127i −0.323897 + 0.635684i
924924 −5.26745 1.60566i −0.173286 0.0528224i
925925 0 0
926926 2.39577 4.14960i 0.0787299 0.136364i
927927 −0.579102 11.0499i −0.0190202 0.362927i
928928 −37.5708 + 14.4221i −1.23332 + 0.473428i
929929 5.09312 + 48.4578i 0.167100 + 1.58985i 0.681187 + 0.732109i 0.261464π0.261464\pi
−0.514087 + 0.857738i 0.671869π0.671869\pi
930930 0 0
931931 −6.34605 + 36.3414i −0.207983 + 1.19104i
932932 28.7785 + 28.7785i 0.942670 + 0.942670i
933933 −2.48655 + 6.47768i −0.0814060 + 0.212070i
934934 22.3011 4.74024i 0.729713 0.155105i
935935 0 0
936936 −1.91745 + 9.02090i −0.0626738 + 0.294857i
937937 18.7668 + 36.8319i 0.613085 + 1.20325i 0.963765 + 0.266752i 0.0859503π0.0859503\pi
−0.350680 + 0.936495i 0.614050π0.614050\pi
938938 3.04749 + 17.2000i 0.0995039 + 0.561601i
939939 −11.9642 + 3.88740i −0.390437 + 0.126861i
940940 0 0
941941 −9.40997 44.2704i −0.306756 1.44318i −0.813745 0.581222i 0.802575π-0.802575\pi
0.506989 0.861953i 0.330759π-0.330759\pi
942942 8.93068 7.23192i 0.290977 0.235629i
943943 0.0724368 0.0194094i 0.00235887 0.000632057i
944944 2.88969 + 2.09948i 0.0940513 + 0.0683323i
945945 0 0
946946 −3.94694 + 2.86762i −0.128326 + 0.0932344i
947947 −5.03167 + 6.21359i −0.163507 + 0.201915i −0.852314 0.523030i 0.824801π-0.824801\pi
0.688807 + 0.724945i 0.258135π0.258135\pi
948948 −16.3390 + 0.856289i −0.530665 + 0.0278110i
949949 2.86640 1.65492i 0.0930472 0.0537208i
950950 0 0
951951 10.1006i 0.327535i
952952 1.56567 6.30176i 0.0507438 0.204241i
953953 −0.239793 + 1.51399i −0.00776765 + 0.0490430i −0.991268 0.131865i 0.957904π-0.957904\pi
0.983500 + 0.180908i 0.0579035π0.0579035\pi
954954 15.0102 1.57764i 0.485974 0.0510779i
955955 0 0
956956 0.468940 4.46167i 0.0151666 0.144301i
957957 −2.65289 9.90071i −0.0857556 0.320044i
958958 1.10585 + 6.98204i 0.0357283 + 0.225580i
959959 0.754348 8.70508i 0.0243592 0.281102i
960960 0 0
961961 63.5919 + 13.5169i 2.05135 + 0.436028i
962962 6.52013 10.0401i 0.210217 0.323706i
963963 9.33277 14.3712i 0.300744 0.463106i
964964 36.6175 + 7.78329i 1.17937 + 0.250683i
965965 0 0
966966 −2.39682 + 1.12007i −0.0771165 + 0.0360376i
967967 3.11543 + 19.6701i 0.100186 + 0.632547i 0.985774 + 0.168076i 0.0537555π0.0537555\pi
−0.885588 + 0.464471i 0.846245π0.846245\pi
968968 6.31056 + 23.5513i 0.202829 + 0.756969i
969969 0.575322 5.47382i 0.0184820 0.175844i
970970 0 0
971971 −29.5811 + 3.10909i −0.949301 + 0.0997756i −0.566506 0.824058i 0.691705π-0.691705\pi
−0.382795 + 0.923833i 0.625039π0.625039\pi
972972 −3.29957 + 20.8327i −0.105834 + 0.668208i
973973 15.8421 16.4321i 0.507875 0.526791i
974974 0.412847i 0.0132285i
975975 0 0
976976 −2.93248 + 1.69307i −0.0938663 + 0.0541938i
977977 −32.0110 + 1.67762i −1.02412 + 0.0536720i −0.556993 0.830517i 0.688045π-0.688045\pi
−0.467129 + 0.884189i 0.654712π0.654712\pi
978978 1.91843 2.36907i 0.0613448 0.0757545i
979979 −16.8565 + 12.2469i −0.538735 + 0.391414i
980980 0 0
981981 −15.2332 11.0676i −0.486358 0.353360i
982982 4.81745 1.29083i 0.153731 0.0411921i
983983 29.9691 24.2685i 0.955866 0.774045i −0.0183109 0.999832i 0.505829π-0.505829\pi
0.974177 + 0.225788i 0.0724955π0.0724955\pi
984984 −0.0403529 0.189846i −0.00128640 0.00605206i
985985 0 0
986986 4.72497 1.53524i 0.150474 0.0488919i
987987 −0.546180 + 0.0967716i −0.0173851 + 0.00308027i
988988 6.71245 + 13.1739i 0.213551 + 0.419118i
989989 1.12602 5.29751i 0.0358054 0.168451i
990990 0 0
991991 −4.56112 + 0.969496i −0.144889 + 0.0307971i −0.279785 0.960063i 0.590263π-0.590263\pi
0.134896 + 0.990860i 0.456930π0.456930\pi
992992 −20.5573 + 53.5535i −0.652694 + 1.70033i
993993 5.73911 + 5.73911i 0.182125 + 0.182125i
994994 −2.72094 22.0099i −0.0863030 0.698112i
995995 0 0
996996 1.02518 + 9.75395i 0.0324841 + 0.309066i
997997 15.2110 5.83897i 0.481739 0.184922i −0.105365 0.994434i 0.533601π-0.533601\pi
0.587104 + 0.809511i 0.300268π0.300268\pi
998998 −0.255223 4.86995i −0.00807894 0.154155i
999999 20.3931 35.3220i 0.645210 1.11754i
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 875.2.bb.c.607.12 288
5.2 odd 4 875.2.bb.b.768.7 288
5.3 odd 4 875.2.bb.a.768.12 288
5.4 even 2 175.2.x.a.117.7 yes 288
7.3 odd 6 inner 875.2.bb.c.857.7 288
25.3 odd 20 inner 875.2.bb.c.243.7 288
25.4 even 10 875.2.bb.b.257.7 288
25.21 even 5 875.2.bb.a.257.12 288
25.22 odd 20 175.2.x.a.103.12 yes 288
35.3 even 12 875.2.bb.a.143.12 288
35.17 even 12 875.2.bb.b.143.7 288
35.24 odd 6 175.2.x.a.17.12 yes 288
175.3 even 60 inner 875.2.bb.c.493.12 288
175.122 even 60 175.2.x.a.3.7 288
175.129 odd 30 875.2.bb.b.507.7 288
175.171 odd 30 875.2.bb.a.507.12 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.3.7 288 175.122 even 60
175.2.x.a.17.12 yes 288 35.24 odd 6
175.2.x.a.103.12 yes 288 25.22 odd 20
175.2.x.a.117.7 yes 288 5.4 even 2
875.2.bb.a.143.12 288 35.3 even 12
875.2.bb.a.257.12 288 25.21 even 5
875.2.bb.a.507.12 288 175.171 odd 30
875.2.bb.a.768.12 288 5.3 odd 4
875.2.bb.b.143.7 288 35.17 even 12
875.2.bb.b.257.7 288 25.4 even 10
875.2.bb.b.507.7 288 175.129 odd 30
875.2.bb.b.768.7 288 5.2 odd 4
875.2.bb.c.243.7 288 25.3 odd 20 inner
875.2.bb.c.493.12 288 175.3 even 60 inner
875.2.bb.c.607.12 288 1.1 even 1 trivial
875.2.bb.c.857.7 288 7.3 odd 6 inner