Properties

Label 165.2.k.c.23.8
Level 165165
Weight 22
Character 165.23
Analytic conductor 1.3181.318
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(23,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 165=3511 165 = 3 \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 165.k (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.317531633351.31753163335
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x15+8x14+19x1280x11+168x10+28x9+119x8432x7++16 x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + \cdots + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 23.8
Root 1.31757+1.31757i-1.31757 + 1.31757i of defining polynomial
Character χ\chi == 165.23
Dual form 165.2.k.c.122.8

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.31757+1.31757i)q2+(1.52275+0.825374i)q3+1.47196iq4+(1.492191.66534i)q5+(0.918834+3.09381i)q6+(2.09381+2.09381i)q7+(0.6957240.695724i)q8+(1.63751+2.51367i)q9+(0.2281364.16026i)q101.00000iq11+(1.21492+2.24143i)q12+(0.161681+0.161681i)q135.51746q14+(0.8977003.76751i)q15+4.77725q16+(3.375183.37518i)q17+(1.15440+5.46946i)q188.52083iq19+(2.451322.19645i)q20+(4.91651+1.46016i)q21+(1.317571.31757i)q22+(3.15119+3.15119i)q23+(1.633640.485178i)q24+(0.546726+4.97002i)q25+0.426051iq26+(0.418798+5.17925i)q27+(3.082003.08200i)q283.01631q29+(3.781176.14672i)q30+5.01096q31+(4.90290+4.90290i)q32+(0.8253741.52275i)q338.89405iq34+(6.61126+0.362542i)q35+(3.70003+2.41036i)q36+(4.74287+4.74287i)q37+(11.226811.2268i)q38+(0.112752+0.379646i)q39+(2.196770.120464i)q40+4.49923iq41+(8.401694.55397i)q42+(0.336036+0.336036i)q43+1.47196q44+(1.742646.47790i)q458.30379q46+(6.15190+6.15190i)q47+(7.27454+3.94302i)q481.76804iq49+(7.26868+5.82798i)q50+(2.353767.92533i)q51+(0.237988+0.237988i)q52+(1.62043+1.62043i)q53+(6.27221+7.37580i)q54+(1.66534+1.49219i)q55+2.91342iq56+(7.0328712.9751i)q57+(3.974193.97419i)q585.16965q59+(5.545641.32138i)q603.39049q61+(6.60228+6.60228i)q62+(8.691781.83450i)q63+3.36529iq64+(0.02799500.510513i)q65+(3.093810.918834i)q66+(9.749169.74916i)q67+(4.968144.96814i)q68+(7.39937+2.19755i)q69+(8.23310+9.18845i)q702.23272iq71+(2.88808+0.609564i)q72+(5.43376+5.43376i)q7312.4981q74+(4.93465+7.11683i)q75+12.5423q76+(2.09381+2.09381i)q77+(0.351651+0.648767i)q78+5.93637iq79+(7.128587.95576i)q80+(3.63710+8.23235i)q81+(5.92804+5.92804i)q82+(0.365862+0.365862i)q83+(2.149307.23692i)q84+(0.584411+10.6572i)q85+0.885499iq86+(4.593072.48958i)q87+(0.6957240.695724i)q88+3.70157q89+(10.83116.23903i)q900.677057q91+(4.638434.63843i)q92+(7.63043+4.13592i)q93+16.2111iq94+(14.1901+12.7147i)q95+(3.41914+11.5126i)q96+(4.942874.94287i)q97+(2.329512.32951i)q98+(2.513671.63751i)q99+O(q100)q+(1.31757 + 1.31757i) q^{2} +(1.52275 + 0.825374i) q^{3} +1.47196i q^{4} +(-1.49219 - 1.66534i) q^{5} +(0.918834 + 3.09381i) q^{6} +(-2.09381 + 2.09381i) q^{7} +(0.695724 - 0.695724i) q^{8} +(1.63751 + 2.51367i) q^{9} +(0.228136 - 4.16026i) q^{10} -1.00000i q^{11} +(-1.21492 + 2.24143i) q^{12} +(0.161681 + 0.161681i) q^{13} -5.51746 q^{14} +(-0.897700 - 3.76751i) q^{15} +4.77725 q^{16} +(-3.37518 - 3.37518i) q^{17} +(-1.15440 + 5.46946i) q^{18} -8.52083i q^{19} +(2.45132 - 2.19645i) q^{20} +(-4.91651 + 1.46016i) q^{21} +(1.31757 - 1.31757i) q^{22} +(-3.15119 + 3.15119i) q^{23} +(1.63364 - 0.485178i) q^{24} +(-0.546726 + 4.97002i) q^{25} +0.426051i q^{26} +(0.418798 + 5.17925i) q^{27} +(-3.08200 - 3.08200i) q^{28} -3.01631 q^{29} +(3.78117 - 6.14672i) q^{30} +5.01096 q^{31} +(4.90290 + 4.90290i) q^{32} +(0.825374 - 1.52275i) q^{33} -8.89405i q^{34} +(6.61126 + 0.362542i) q^{35} +(-3.70003 + 2.41036i) q^{36} +(-4.74287 + 4.74287i) q^{37} +(11.2268 - 11.2268i) q^{38} +(0.112752 + 0.379646i) q^{39} +(-2.19677 - 0.120464i) q^{40} +4.49923i q^{41} +(-8.40169 - 4.55397i) q^{42} +(0.336036 + 0.336036i) q^{43} +1.47196 q^{44} +(1.74264 - 6.47790i) q^{45} -8.30379 q^{46} +(6.15190 + 6.15190i) q^{47} +(7.27454 + 3.94302i) q^{48} -1.76804i q^{49} +(-7.26868 + 5.82798i) q^{50} +(-2.35376 - 7.92533i) q^{51} +(-0.237988 + 0.237988i) q^{52} +(-1.62043 + 1.62043i) q^{53} +(-6.27221 + 7.37580i) q^{54} +(-1.66534 + 1.49219i) q^{55} +2.91342i q^{56} +(7.03287 - 12.9751i) q^{57} +(-3.97419 - 3.97419i) q^{58} -5.16965 q^{59} +(5.54564 - 1.32138i) q^{60} -3.39049 q^{61} +(6.60228 + 6.60228i) q^{62} +(-8.69178 - 1.83450i) q^{63} +3.36529i q^{64} +(0.0279950 - 0.510513i) q^{65} +(3.09381 - 0.918834i) q^{66} +(9.74916 - 9.74916i) q^{67} +(4.96814 - 4.96814i) q^{68} +(-7.39937 + 2.19755i) q^{69} +(8.23310 + 9.18845i) q^{70} -2.23272i q^{71} +(2.88808 + 0.609564i) q^{72} +(5.43376 + 5.43376i) q^{73} -12.4981 q^{74} +(-4.93465 + 7.11683i) q^{75} +12.5423 q^{76} +(2.09381 + 2.09381i) q^{77} +(-0.351651 + 0.648767i) q^{78} +5.93637i q^{79} +(-7.12858 - 7.95576i) q^{80} +(-3.63710 + 8.23235i) q^{81} +(-5.92804 + 5.92804i) q^{82} +(-0.365862 + 0.365862i) q^{83} +(-2.14930 - 7.23692i) q^{84} +(-0.584411 + 10.6572i) q^{85} +0.885499i q^{86} +(-4.59307 - 2.48958i) q^{87} +(-0.695724 - 0.695724i) q^{88} +3.70157 q^{89} +(10.8311 - 6.23903i) q^{90} -0.677057 q^{91} +(-4.63843 - 4.63843i) q^{92} +(7.63043 + 4.13592i) q^{93} +16.2111i q^{94} +(-14.1901 + 12.7147i) q^{95} +(3.41914 + 11.5126i) q^{96} +(4.94287 - 4.94287i) q^{97} +(2.32951 - 2.32951i) q^{98} +(2.51367 - 1.63751i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q4q22q38q54q6+8q7+16q8+6q94q104q1224q14+8q154q16+8q1732q1820q208q214q22+14q23+12q24+4q99+O(q100) 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/165Z)×\left(\mathbb{Z}/165\mathbb{Z}\right)^\times.

nn 4646 5656 6767
χ(n)\chi(n) 11 1-1 e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.31757 + 1.31757i 0.931660 + 0.931660i 0.997810 0.0661495i 0.0210714π-0.0210714\pi
−0.0661495 + 0.997810i 0.521071π0.521071\pi
33 1.52275 + 0.825374i 0.879158 + 0.476530i
44 1.47196i 0.735981i
55 −1.49219 1.66534i −0.667329 0.744763i
66 0.918834 + 3.09381i 0.375112 + 1.26304i
77 −2.09381 + 2.09381i −0.791384 + 0.791384i −0.981719 0.190335i 0.939043π-0.939043\pi
0.190335 + 0.981719i 0.439043π0.439043\pi
88 0.695724 0.695724i 0.245976 0.245976i
99 1.63751 + 2.51367i 0.545838 + 0.837891i
1010 0.228136 4.16026i 0.0721430 1.31559i
1111 1.00000i 0.301511i
1212 −1.21492 + 2.24143i −0.350717 + 0.647044i
1313 0.161681 + 0.161681i 0.0448422 + 0.0448422i 0.729172 0.684330i 0.239905π-0.239905\pi
−0.684330 + 0.729172i 0.739905π0.739905\pi
1414 −5.51746 −1.47460
1515 −0.897700 3.76751i −0.231785 0.972767i
1616 4.77725 1.19431
1717 −3.37518 3.37518i −0.818602 0.818602i 0.167304 0.985905i 0.446494π-0.446494\pi
−0.985905 + 0.167304i 0.946494π0.946494\pi
1818 −1.15440 + 5.46946i −0.272094 + 1.28917i
1919 8.52083i 1.95481i −0.211371 0.977406i 0.567793π-0.567793\pi
0.211371 0.977406i 0.432207π-0.432207\pi
2020 2.45132 2.19645i 0.548132 0.491141i
2121 −4.91651 + 1.46016i −1.07287 + 0.318633i
2222 1.31757 1.31757i 0.280906 0.280906i
2323 −3.15119 + 3.15119i −0.657068 + 0.657068i −0.954685 0.297617i 0.903808π-0.903808\pi
0.297617 + 0.954685i 0.403808π0.403808\pi
2424 1.63364 0.485178i 0.333466 0.0990366i
2525 −0.546726 + 4.97002i −0.109345 + 0.994004i
2626 0.426051i 0.0835555i
2727 0.418798 + 5.17925i 0.0805978 + 0.996747i
2828 −3.08200 3.08200i −0.582444 0.582444i
2929 −3.01631 −0.560114 −0.280057 0.959983i 0.590353π-0.590353\pi
−0.280057 + 0.959983i 0.590353π0.590353\pi
3030 3.78117 6.14672i 0.690343 1.12223i
3131 5.01096 0.899996 0.449998 0.893030i 0.351425π-0.351425\pi
0.449998 + 0.893030i 0.351425π0.351425\pi
3232 4.90290 + 4.90290i 0.866718 + 0.866718i
3333 0.825374 1.52275i 0.143679 0.265076i
3434 8.89405i 1.52532i
3535 6.61126 + 0.362542i 1.11751 + 0.0612807i
3636 −3.70003 + 2.41036i −0.616672 + 0.401727i
3737 −4.74287 + 4.74287i −0.779722 + 0.779722i −0.979783 0.200061i 0.935886π-0.935886\pi
0.200061 + 0.979783i 0.435886π0.435886\pi
3838 11.2268 11.2268i 1.82122 1.82122i
3939 0.112752 + 0.379646i 0.0180547 + 0.0607921i
4040 −2.19677 0.120464i −0.347340 0.0190471i
4141 4.49923i 0.702662i 0.936251 + 0.351331i 0.114271π0.114271\pi
−0.936251 + 0.351331i 0.885729π0.885729\pi
4242 −8.40169 4.55397i −1.29641 0.702692i
4343 0.336036 + 0.336036i 0.0512450 + 0.0512450i 0.732265 0.681020i 0.238463π-0.238463\pi
−0.681020 + 0.732265i 0.738463π0.738463\pi
4444 1.47196 0.221907
4545 1.74264 6.47790i 0.259777 0.965669i
4646 −8.30379 −1.22433
4747 6.15190 + 6.15190i 0.897346 + 0.897346i 0.995201 0.0978543i 0.0311979π-0.0311979\pi
−0.0978543 + 0.995201i 0.531198π0.531198\pi
4848 7.27454 + 3.94302i 1.04999 + 0.569126i
4949 1.76804i 0.252578i
5050 −7.26868 + 5.82798i −1.02795 + 0.824201i
5151 −2.35376 7.92533i −0.329592 1.10977i
5252 −0.237988 + 0.237988i −0.0330031 + 0.0330031i
5353 −1.62043 + 1.62043i −0.222583 + 0.222583i −0.809585 0.587002i 0.800308π-0.800308\pi
0.587002 + 0.809585i 0.300308π0.300308\pi
5454 −6.27221 + 7.37580i −0.853540 + 1.00372i
5555 −1.66534 + 1.49219i −0.224555 + 0.201207i
5656 2.91342i 0.389322i
5757 7.03287 12.9751i 0.931527 1.71859i
5858 −3.97419 3.97419i −0.521836 0.521836i
5959 −5.16965 −0.673032 −0.336516 0.941678i 0.609249π-0.609249\pi
−0.336516 + 0.941678i 0.609249π0.609249\pi
6060 5.54564 1.32138i 0.715939 0.170590i
6161 −3.39049 −0.434108 −0.217054 0.976160i 0.569645π-0.569645\pi
−0.217054 + 0.976160i 0.569645π0.569645\pi
6262 6.60228 + 6.60228i 0.838490 + 0.838490i
6363 −8.69178 1.83450i −1.09506 0.231126i
6464 3.36529i 0.420661i
6565 0.0279950 0.510513i 0.00347235 0.0633214i
6666 3.09381 0.918834i 0.380821 0.113101i
6767 9.74916 9.74916i 1.19105 1.19105i 0.214276 0.976773i 0.431261π-0.431261\pi
0.976773 0.214276i 0.0687392π-0.0687392\pi
6868 4.96814 4.96814i 0.602476 0.602476i
6969 −7.39937 + 2.19755i −0.890779 + 0.264554i
7070 8.23310 + 9.18845i 0.984044 + 1.09823i
7171 2.23272i 0.264975i −0.991185 0.132488i 0.957704π-0.957704\pi
0.991185 0.132488i 0.0422965π-0.0422965\pi
7272 2.88808 + 0.609564i 0.340363 + 0.0718378i
7373 5.43376 + 5.43376i 0.635973 + 0.635973i 0.949560 0.313586i 0.101531π-0.101531\pi
−0.313586 + 0.949560i 0.601531π0.601531\pi
7474 −12.4981 −1.45287
7575 −4.93465 + 7.11683i −0.569804 + 0.821780i
7676 12.5423 1.43871
7777 2.09381 + 2.09381i 0.238611 + 0.238611i
7878 −0.351651 + 0.648767i −0.0398167 + 0.0734585i
7979 5.93637i 0.667894i 0.942592 + 0.333947i 0.108381π0.108381\pi
−0.942592 + 0.333947i 0.891619π0.891619\pi
8080 −7.12858 7.95576i −0.796999 0.889480i
8181 −3.63710 + 8.23235i −0.404122 + 0.914705i
8282 −5.92804 + 5.92804i −0.654642 + 0.654642i
8383 −0.365862 + 0.365862i −0.0401586 + 0.0401586i −0.726901 0.686742i 0.759040π-0.759040\pi
0.686742 + 0.726901i 0.259040π0.259040\pi
8484 −2.14930 7.23692i −0.234508 0.789613i
8585 −0.584411 + 10.6572i −0.0633883 + 1.15594i
8686 0.885499i 0.0954858i
8787 −4.59307 2.48958i −0.492429 0.266911i
8888 −0.695724 0.695724i −0.0741644 0.0741644i
8989 3.70157 0.392366 0.196183 0.980567i 0.437145π-0.437145\pi
0.196183 + 0.980567i 0.437145π0.437145\pi
9090 10.8311 6.23903i 1.14170 0.657651i
9191 −0.677057 −0.0709749
9292 −4.63843 4.63843i −0.483590 0.483590i
9393 7.63043 + 4.13592i 0.791239 + 0.428875i
9494 16.2111i 1.67204i
9595 −14.1901 + 12.7147i −1.45587 + 1.30450i
9696 3.41914 + 11.5126i 0.348965 + 1.17500i
9797 4.94287 4.94287i 0.501872 0.501872i −0.410147 0.912019i 0.634523π-0.634523\pi
0.912019 + 0.410147i 0.134523π0.134523\pi
9898 2.32951 2.32951i 0.235317 0.235317i
9999 2.51367 1.63751i 0.252634 0.164576i
100100 −7.31568 0.804760i −0.731568 0.0804760i
101101 9.91691i 0.986770i −0.869811 0.493385i 0.835759π-0.835759\pi
0.869811 0.493385i 0.164241π-0.164241\pi
102102 7.34092 13.5434i 0.726860 1.34100i
103103 −5.76598 5.76598i −0.568139 0.568139i 0.363468 0.931607i 0.381593π-0.381593\pi
−0.931607 + 0.363468i 0.881593π0.881593\pi
104104 0.224971 0.0220602
105105 9.76804 + 6.00883i 0.953263 + 0.586401i
106106 −4.27004 −0.414743
107107 −0.481439 0.481439i −0.0465425 0.0465425i 0.683453 0.729995i 0.260478π-0.260478\pi
−0.729995 + 0.683453i 0.760478π0.760478\pi
108108 −7.62366 + 0.616456i −0.733587 + 0.0593185i
109109 2.88151i 0.275999i 0.990432 + 0.137999i 0.0440672π0.0440672\pi
−0.990432 + 0.137999i 0.955933π0.955933\pi
110110 −4.16026 0.228136i −0.396665 0.0217519i
111111 −11.1368 + 3.30754i −1.05706 + 0.313938i
112112 −10.0026 + 10.0026i −0.945160 + 0.945160i
113113 −5.89425 + 5.89425i −0.554485 + 0.554485i −0.927732 0.373247i 0.878244π-0.878244\pi
0.373247 + 0.927732i 0.378244π0.378244\pi
114114 26.3618 7.82923i 2.46901 0.733274i
115115 9.94998 + 0.545627i 0.927840 + 0.0508799i
116116 4.43989i 0.412234i
117117 −0.141658 + 0.671168i −0.0130963 + 0.0620495i
118118 −6.81136 6.81136i −0.627037 0.627037i
119119 14.1339 1.29566
120120 −3.24570 1.99660i −0.296290 0.182263i
121121 −1.00000 −0.0909091
122122 −4.46720 4.46720i −0.404441 0.404441i
123123 −3.71355 + 6.85119i −0.334840 + 0.617751i
124124 7.37595i 0.662380i
125125 9.09260 6.50574i 0.813267 0.581891i
126126 −9.03491 13.8691i −0.804894 1.23556i
127127 0.541796 0.541796i 0.0480766 0.0480766i −0.682660 0.730736i 0.739177π-0.739177\pi
0.730736 + 0.682660i 0.239177π0.239177\pi
128128 5.37181 5.37181i 0.474805 0.474805i
129129 0.234342 + 0.789052i 0.0206327 + 0.0694722i
130130 0.709520 0.635750i 0.0622290 0.0557589i
131131 20.1139i 1.75736i −0.477413 0.878679i 0.658425π-0.658425\pi
0.477413 0.878679i 0.341575π-0.341575\pi
132132 2.24143 + 1.21492i 0.195091 + 0.105745i
133133 17.8410 + 17.8410i 1.54701 + 1.54701i
134134 25.6903 2.21931
135135 8.00029 8.42587i 0.688555 0.725184i
136136 −4.69639 −0.402712
137137 10.8866 + 10.8866i 0.930104 + 0.930104i 0.997712 0.0676081i 0.0215368π-0.0215368\pi
−0.0676081 + 0.997712i 0.521537π0.521537\pi
138138 −12.6446 6.85374i −1.07638 0.583429i
139139 18.8256i 1.59677i −0.602150 0.798383i 0.705689π-0.705689\pi
0.602150 0.798383i 0.294311π-0.294311\pi
140140 −0.533648 + 9.73153i −0.0451015 + 0.822465i
141141 4.29016 + 14.4454i 0.361297 + 1.21652i
142142 2.94176 2.94176i 0.246867 0.246867i
143143 0.161681 0.161681i 0.0135204 0.0135204i
144144 7.82282 + 12.0084i 0.651901 + 1.00070i
145145 4.50091 + 5.02318i 0.373780 + 0.417153i
146146 14.3187i 1.18502i
147147 1.45930 2.69228i 0.120361 0.222056i
148148 −6.98132 6.98132i −0.573861 0.573861i
149149 −18.1699 −1.48854 −0.744269 0.667880i 0.767202π-0.767202\pi
−0.744269 + 0.667880i 0.767202π0.767202\pi
150150 −15.8786 + 2.87516i −1.29648 + 0.234756i
151151 −5.16859 −0.420614 −0.210307 0.977635i 0.567446π-0.567446\pi
−0.210307 + 0.977635i 0.567446π0.567446\pi
152152 −5.92814 5.92814i −0.480836 0.480836i
153153 2.95719 14.0110i 0.239075 1.13272i
154154 5.51746i 0.444609i
155155 −7.47732 8.34497i −0.600593 0.670284i
156156 −0.558826 + 0.165966i −0.0447419 + 0.0132880i
157157 0.0693025 0.0693025i 0.00553094 0.00553094i −0.704336 0.709867i 0.748755π-0.748755\pi
0.709867 + 0.704336i 0.248755π0.248755\pi
158158 −7.82156 + 7.82156i −0.622250 + 0.622250i
159159 −3.80496 + 1.13004i −0.301753 + 0.0896181i
160160 0.848935 15.4811i 0.0671142 1.22389i
161161 13.1959i 1.03999i
162162 −15.6388 + 6.05455i −1.22870 + 0.475690i
163163 −12.4108 12.4108i −0.972090 0.972090i 0.0275308 0.999621i 0.491236π-0.491236\pi
−0.999621 + 0.0275308i 0.991236π0.991236\pi
164164 −6.62270 −0.517146
165165 −3.76751 + 0.897700i −0.293300 + 0.0698858i
166166 −0.964095 −0.0748283
167167 −5.06115 5.06115i −0.391644 0.391644i 0.483629 0.875273i 0.339318π-0.339318\pi
−0.875273 + 0.483629i 0.839318π0.839318\pi
168168 −2.40466 + 4.43640i −0.185524 + 0.342276i
169169 12.9477i 0.995978i
170170 −14.8116 + 13.2716i −1.13600 + 1.01789i
171171 21.4186 13.9530i 1.63792 1.06701i
172172 −0.494632 + 0.494632i −0.0377153 + 0.0377153i
173173 −10.2684 + 10.2684i −0.780694 + 0.780694i −0.979948 0.199253i 0.936148π-0.936148\pi
0.199253 + 0.979948i 0.436148π0.436148\pi
174174 −2.77149 9.33187i −0.210106 0.707447i
175175 −9.26152 11.5510i −0.700105 0.873173i
176176 4.77725i 0.360099i
177177 −7.87207 4.26690i −0.591701 0.320720i
178178 4.87707 + 4.87707i 0.365552 + 0.365552i
179179 12.8332 0.959200 0.479600 0.877487i 0.340782π-0.340782\pi
0.479600 + 0.877487i 0.340782π0.340782\pi
180180 9.53523 + 2.56510i 0.710714 + 0.191191i
181181 18.9492 1.40848 0.704242 0.709960i 0.251287π-0.251287\pi
0.704242 + 0.709960i 0.251287π0.251287\pi
182182 −0.892068 0.892068i −0.0661245 0.0661245i
183183 −5.16286 2.79843i −0.381650 0.206866i
184184 4.38471i 0.323245i
185185 14.9758 + 0.821225i 1.10104 + 0.0603777i
186186 4.60425 + 15.5030i 0.337600 + 1.13673i
187187 −3.37518 + 3.37518i −0.246818 + 0.246818i
188188 −9.05537 + 9.05537i −0.660430 + 0.660430i
189189 −11.7212 9.96746i −0.852593 0.725026i
190190 −35.4489 1.94391i −2.57173 0.141026i
191191 15.8333i 1.14566i −0.819675 0.572829i 0.805846π-0.805846\pi
0.819675 0.572829i 0.194154π-0.194154\pi
192192 −2.77762 + 5.12448i −0.200458 + 0.369827i
193193 7.37312 + 7.37312i 0.530729 + 0.530729i 0.920789 0.390061i 0.127546π-0.127546\pi
−0.390061 + 0.920789i 0.627546π0.627546\pi
194194 13.0251 0.935149
195195 0.463994 0.754276i 0.0332273 0.0540148i
196196 2.60249 0.185892
197197 9.03516 + 9.03516i 0.643728 + 0.643728i 0.951470 0.307742i 0.0995733π-0.0995733\pi
−0.307742 + 0.951470i 0.599573π0.599573\pi
198198 5.46946 + 1.15440i 0.388698 + 0.0820394i
199199 11.0729i 0.784936i 0.919766 + 0.392468i 0.128379π0.128379\pi
−0.919766 + 0.392468i 0.871621π0.871621\pi
200200 3.07739 + 3.83813i 0.217604 + 0.271397i
201201 22.8922 6.79879i 1.61469 0.479550i
202202 13.0662 13.0662i 0.919334 0.919334i
203203 6.31556 6.31556i 0.443266 0.443266i
204204 11.6658 3.46464i 0.816769 0.242574i
205205 7.49276 6.71372i 0.523317 0.468906i
206206 15.1941i 1.05862i
207207 −13.0812 2.76094i −0.909204 0.191898i
208208 0.772391 + 0.772391i 0.0535557 + 0.0535557i
209209 −8.52083 −0.589398
210210 4.95302 + 20.7871i 0.341791 + 1.43444i
211211 −2.45739 −0.169174 −0.0845869 0.996416i 0.526957π-0.526957\pi
−0.0845869 + 0.996416i 0.526957π0.526957\pi
212212 −2.38521 2.38521i −0.163817 0.163817i
213213 1.84283 3.39987i 0.126269 0.232955i
214214 1.26866i 0.0867235i
215215 0.0581844 1.06104i 0.00396815 0.0723626i
216216 3.89469 + 3.31196i 0.265000 + 0.225350i
217217 −10.4920 + 10.4920i −0.712242 + 0.712242i
218218 −3.79658 + 3.79658i −0.257137 + 0.257137i
219219 3.78935 + 12.7591i 0.256061 + 0.862181i
220220 −2.19645 2.45132i −0.148085 0.165268i
221221 1.09141i 0.0734159i
222222 −19.0314 10.3156i −1.27730 0.692337i
223223 −2.72361 2.72361i −0.182386 0.182386i 0.610009 0.792395i 0.291166π-0.291166\pi
−0.792395 + 0.610009i 0.791166π0.791166\pi
224224 −20.5314 −1.37181
225225 −13.3883 + 6.76419i −0.892551 + 0.450946i
226226 −15.5321 −1.03318
227227 20.3476 + 20.3476i 1.35052 + 1.35052i 0.885084 + 0.465431i 0.154101π0.154101\pi
0.465431 + 0.885084i 0.345899π0.345899\pi
228228 19.0988 + 10.3521i 1.26485 + 0.685586i
229229 12.4003i 0.819433i 0.912213 + 0.409716i 0.134372π0.134372\pi
−0.912213 + 0.409716i 0.865628π0.865628\pi
230230 12.3909 + 13.8287i 0.817029 + 0.911835i
231231 1.46016 + 4.91651i 0.0960716 + 0.323483i
232232 −2.09852 + 2.09852i −0.137774 + 0.137774i
233233 −1.83100 + 1.83100i −0.119953 + 0.119953i −0.764535 0.644582i 0.777031π-0.777031\pi
0.644582 + 0.764535i 0.277031π0.277031\pi
234234 −1.07095 + 0.697664i −0.0700103 + 0.0456077i
235235 1.06520 19.4248i 0.0694859 1.26714i
236236 7.60954i 0.495339i
237237 −4.89973 + 9.03958i −0.318271 + 0.587184i
238238 18.6224 + 18.6224i 1.20711 + 1.20711i
239239 20.2577 1.31036 0.655182 0.755471i 0.272592π-0.272592\pi
0.655182 + 0.755471i 0.272592π0.272592\pi
240240 −4.28854 17.9983i −0.276824 1.16179i
241241 2.30059 0.148194 0.0740971 0.997251i 0.476393π-0.476393\pi
0.0740971 + 0.997251i 0.476393π0.476393\pi
242242 −1.31757 1.31757i −0.0846964 0.0846964i
243243 −12.3331 + 9.53381i −0.791171 + 0.611594i
244244 4.99068i 0.319496i
245245 −2.94440 + 2.63826i −0.188111 + 0.168552i
246246 −13.9197 + 4.13405i −0.887491 + 0.263577i
247247 1.37766 1.37766i 0.0876581 0.0876581i
248248 3.48625 3.48625i 0.221377 0.221377i
249249 −0.859089 + 0.255142i −0.0544425 + 0.0161690i
250250 20.5518 + 3.40836i 1.29981 + 0.215564i
251251 27.0577i 1.70786i 0.520384 + 0.853932i 0.325789π0.325789\pi
−0.520384 + 0.853932i 0.674211π0.674211\pi
252252 2.70032 12.7940i 0.170104 0.805945i
253253 3.15119 + 3.15119i 0.198113 + 0.198113i
254254 1.42770 0.0895821
255255 −9.68613 + 15.7459i −0.606569 + 0.986048i
256256 20.8860 1.30537
257257 −14.3843 14.3843i −0.897267 0.897267i 0.0979266 0.995194i 0.468779π-0.468779\pi
−0.995194 + 0.0979266i 0.968779π0.968779\pi
258258 −0.730868 + 1.34839i −0.0455018 + 0.0839471i
259259 19.8613i 1.23412i
260260 0.751456 + 0.0412076i 0.0466033 + 0.00255559i
261261 −4.93925 7.58201i −0.305732 0.469315i
262262 26.5014 26.5014i 1.63726 1.63726i
263263 1.11325 1.11325i 0.0686457 0.0686457i −0.671950 0.740596i 0.734543π-0.734543\pi
0.740596 + 0.671950i 0.234543π0.234543\pi
264264 −0.485178 1.63364i −0.0298607 0.100544i
265265 5.11656 + 0.280577i 0.314308 + 0.0172357i
266266 47.0133i 2.88257i
267267 5.63656 + 3.05518i 0.344952 + 0.186974i
268268 14.3504 + 14.3504i 0.876590 + 0.876590i
269269 3.23597 0.197301 0.0986504 0.995122i 0.468547π-0.468547\pi
0.0986504 + 0.995122i 0.468547π0.468547\pi
270270 21.6426 0.560737i 1.31712 0.0341253i
271271 −17.4114 −1.05766 −0.528832 0.848726i 0.677370π-0.677370\pi
−0.528832 + 0.848726i 0.677370π0.677370\pi
272272 −16.1241 16.1241i −0.977666 0.977666i
273273 −1.03099 0.558826i −0.0623981 0.0338217i
274274 28.6876i 1.73308i
275275 4.97002 + 0.546726i 0.299703 + 0.0329688i
276276 −3.23471 10.8916i −0.194707 0.655597i
277277 −11.1533 + 11.1533i −0.670138 + 0.670138i −0.957748 0.287610i 0.907139π-0.907139\pi
0.287610 + 0.957748i 0.407139π0.407139\pi
278278 24.8040 24.8040i 1.48764 1.48764i
279279 8.20553 + 12.5959i 0.491252 + 0.754098i
280280 4.85184 4.34738i 0.289953 0.259806i
281281 25.9907i 1.55048i 0.631670 + 0.775238i 0.282370π0.282370\pi
−0.631670 + 0.775238i 0.717630π0.717630\pi
282282 −13.3802 + 24.6853i −0.796779 + 1.46999i
283283 13.9756 + 13.9756i 0.830762 + 0.830762i 0.987621 0.156859i 0.0501368π-0.0501368\pi
−0.156859 + 0.987621i 0.550137π0.550137\pi
284284 3.28648 0.195017
285285 −32.1023 + 7.64915i −1.90158 + 0.453096i
286286 0.426051 0.0251929
287287 −9.42052 9.42052i −0.556076 0.556076i
288288 −4.29571 + 20.3528i −0.253127 + 1.19930i
289289 5.78370i 0.340217i
290290 −0.688129 + 12.5486i −0.0404083 + 0.736881i
291291 11.6065 3.44702i 0.680382 0.202068i
292292 −7.99829 + 7.99829i −0.468064 + 0.468064i
293293 14.6351 14.6351i 0.854994 0.854994i −0.135749 0.990743i 0.543344π-0.543344\pi
0.990743 + 0.135749i 0.0433441π0.0433441\pi
294294 5.46998 1.62454i 0.319016 0.0947450i
295295 7.71412 + 8.60924i 0.449133 + 0.501249i
296296 6.59945i 0.383585i
297297 5.17925 0.418798i 0.300530 0.0243011i
298298 −23.9401 23.9401i −1.38681 1.38681i
299299 −1.01897 −0.0589288
300300 −10.4757 7.26362i −0.604815 0.419366i
301301 −1.40719 −0.0811089
302302 −6.80996 6.80996i −0.391869 0.391869i
303303 8.18517 15.1009i 0.470226 0.867527i
304304 40.7061i 2.33466i
305305 5.05927 + 5.64633i 0.289693 + 0.323308i
306306 22.3567 14.5641i 1.27805 0.832576i
307307 −0.137152 + 0.137152i −0.00782767 + 0.00782767i −0.711010 0.703182i 0.751762π-0.751762\pi
0.703182 + 0.711010i 0.251762π0.251762\pi
308308 −3.08200 + 3.08200i −0.175613 + 0.175613i
309309 −4.02103 13.5392i −0.228749 0.770219i
310310 1.14318 20.8469i 0.0649284 1.18403i
311311 18.1688i 1.03026i −0.857113 0.515128i 0.827745π-0.827745\pi
0.857113 0.515128i 0.172255π-0.172255\pi
312312 0.342573 + 0.185685i 0.0193944 + 0.0105123i
313313 −15.5417 15.5417i −0.878466 0.878466i 0.114910 0.993376i 0.463342π-0.463342\pi
−0.993376 + 0.114910i 0.963342π0.963342\pi
314314 0.182621 0.0103059
315315 9.91472 + 17.2122i 0.558631 + 0.969798i
316316 −8.73811 −0.491557
317317 0.878898 + 0.878898i 0.0493638 + 0.0493638i 0.731358 0.681994i 0.238887π-0.238887\pi
−0.681994 + 0.731358i 0.738887π0.738887\pi
318318 −6.50220 3.52439i −0.364625 0.197638i
319319 3.01631i 0.168881i
320320 5.60435 5.02165i 0.313293 0.280719i
321321 −0.335742 1.13048i −0.0187393 0.0630971i
322322 17.3865 17.3865i 0.968914 0.968914i
323323 −28.7593 + 28.7593i −1.60021 + 1.60021i
324324 −12.1177 5.35367i −0.673206 0.297426i
325325 −0.891953 + 0.715162i −0.0494766 + 0.0396701i
326326 32.7042i 1.81132i
327327 −2.37833 + 4.38781i −0.131522 + 0.242646i
328328 3.13022 + 3.13022i 0.172838 + 0.172838i
329329 −25.7618 −1.42029
330330 −6.14672 3.78117i −0.338366 0.208146i
331331 −1.81586 −0.0998088 −0.0499044 0.998754i 0.515892π-0.515892\pi
−0.0499044 + 0.998754i 0.515892π0.515892\pi
332332 −0.538536 0.538536i −0.0295560 0.0295560i
333333 −19.6885 4.15550i −1.07892 0.227720i
334334 13.3368i 0.729757i
335335 −30.7833 1.68806i −1.68187 0.0922287i
336336 −23.4874 + 6.97556i −1.28134 + 0.380548i
337337 −0.824320 + 0.824320i −0.0449036 + 0.0449036i −0.729202 0.684298i 0.760109π-0.760109\pi
0.684298 + 0.729202i 0.260109π0.260109\pi
338338 17.0595 17.0595i 0.927913 0.927913i
339339 −13.8404 + 4.11049i −0.751708 + 0.223251i
340340 −15.6871 0.860232i −0.850751 0.0466526i
341341 5.01096i 0.271359i
342342 46.6044 + 9.83641i 2.52008 + 0.531892i
343343 −10.9547 10.9547i −0.591498 0.591498i
344344 0.467576 0.0252100
345345 14.7009 + 9.04331i 0.791472 + 0.486875i
346346 −27.0587 −1.45468
347347 −10.0480 10.0480i −0.539406 0.539406i 0.383949 0.923354i 0.374564π-0.374564\pi
−0.923354 + 0.383949i 0.874564π0.874564\pi
348348 3.66457 6.76083i 0.196442 0.362419i
349349 1.50331i 0.0804702i −0.999190 0.0402351i 0.987189π-0.987189\pi
0.999190 0.0402351i 0.0128107π-0.0128107\pi
350350 3.01653 27.4219i 0.161241 1.46576i
351351 −0.769674 + 0.905098i −0.0410822 + 0.0483105i
352352 4.90290 4.90290i 0.261325 0.261325i
353353 10.4384 10.4384i 0.555578 0.555578i −0.372467 0.928045i 0.621488π-0.621488\pi
0.928045 + 0.372467i 0.121488π0.121488\pi
354354 −4.75005 15.9939i −0.252463 0.850066i
355355 −3.71824 + 3.33165i −0.197344 + 0.176825i
356356 5.44858i 0.288774i
357357 21.5224 + 11.6658i 1.13909 + 0.617419i
358358 16.9086 + 16.9086i 0.893649 + 0.893649i
359359 −14.3901 −0.759480 −0.379740 0.925093i 0.623987π-0.623987\pi
−0.379740 + 0.925093i 0.623987π0.623987\pi
360360 −3.29444 5.71923i −0.173632 0.301430i
361361 −53.6045 −2.82129
362362 24.9669 + 24.9669i 1.31223 + 1.31223i
363363 −1.52275 0.825374i −0.0799235 0.0433209i
364364 0.996603i 0.0522362i
365365 0.940853 17.1573i 0.0492465 0.898053i
366366 −3.11530 10.4895i −0.162839 0.548296i
367367 −23.9839 + 23.9839i −1.25195 + 1.25195i −0.297104 + 0.954845i 0.596021π0.596021\pi
−0.954845 + 0.297104i 0.903979π0.903979\pi
368368 −15.0540 + 15.0540i −0.784744 + 0.784744i
369369 −11.3096 + 7.36756i −0.588754 + 0.383540i
370370 18.6495 + 20.8136i 0.969543 + 1.08205i
371371 6.78572i 0.352297i
372372 −6.08792 + 11.2317i −0.315644 + 0.582337i
373373 −16.6266 16.6266i −0.860894 0.860894i 0.130548 0.991442i 0.458326π-0.458326\pi
−0.991442 + 0.130548i 0.958326π0.958326\pi
374374 −8.89405 −0.459900
375375 19.2154 2.40179i 0.992279 0.124028i
376376 8.56004 0.441451
377377 −0.487680 0.487680i −0.0251168 0.0251168i
378378 −2.31070 28.5763i −0.118850 1.46980i
379379 27.3979i 1.40733i 0.710530 + 0.703667i 0.248455π0.248455\pi
−0.710530 + 0.703667i 0.751545π0.751545\pi
380380 −18.7156 20.8873i −0.960089 1.07150i
381381 1.27220 0.377833i 0.0651769 0.0193570i
382382 20.8615 20.8615i 1.06736 1.06736i
383383 17.6188 17.6188i 0.900277 0.900277i −0.0951829 0.995460i 0.530344π-0.530344\pi
0.995460 + 0.0951829i 0.0303436π0.0303436\pi
384384 12.6137 3.74615i 0.643688 0.191170i
385385 0.362542 6.61126i 0.0184768 0.336941i
386386 19.4291i 0.988917i
387387 −0.294420 + 1.39495i −0.0149662 + 0.0709091i
388388 7.27572 + 7.27572i 0.369369 + 0.369369i
389389 19.7634 1.00204 0.501022 0.865434i 0.332957π-0.332957\pi
0.501022 + 0.865434i 0.332957π0.332957\pi
390390 1.60515 0.382466i 0.0812800 0.0193669i
391391 21.2716 1.07575
392392 −1.23007 1.23007i −0.0621279 0.0621279i
393393 16.6015 30.6283i 0.837434 1.54500i
394394 23.8088i 1.19947i
395395 9.88608 8.85820i 0.497423 0.445705i
396396 2.41036 + 3.70003i 0.121125 + 0.185934i
397397 −1.41299 + 1.41299i −0.0709160 + 0.0709160i −0.741675 0.670759i 0.765968π-0.765968\pi
0.670759 + 0.741675i 0.265968π0.265968\pi
398398 −14.5893 + 14.5893i −0.731294 + 0.731294i
399399 12.4418 + 41.8927i 0.622868 + 2.09726i
400400 −2.61185 + 23.7430i −0.130592 + 1.18715i
401401 24.4929i 1.22312i 0.791199 + 0.611559i 0.209457π0.209457\pi
−0.791199 + 0.611559i 0.790543π0.790543\pi
402402 39.1199 + 21.2041i 1.95112 + 1.05757i
403403 0.810178 + 0.810178i 0.0403578 + 0.0403578i
404404 14.5973 0.726244
405405 19.1369 6.22724i 0.950921 0.309434i
406406 16.6423 0.825946
407407 4.74287 + 4.74287i 0.235095 + 0.235095i
408408 −7.15141 3.87628i −0.354048 0.191904i
409409 22.4416i 1.10966i −0.831962 0.554832i 0.812782π-0.812782\pi
0.831962 0.554832i 0.187218π-0.187218\pi
410410 18.7180 + 1.02644i 0.924415 + 0.0506921i
411411 7.59200 + 25.5630i 0.374486 + 1.26093i
412412 8.48731 8.48731i 0.418140 0.418140i
413413 10.8242 10.8242i 0.532626 0.532626i
414414 −13.5976 20.8730i −0.668285 1.02585i
415415 1.15522 + 0.0633489i 0.0567076 + 0.00310967i
416416 1.58541i 0.0777312i
417417 15.5382 28.6666i 0.760907 1.40381i
418418 −11.2268 11.2268i −0.549119 0.549119i
419419 2.45688 0.120027 0.0600133 0.998198i 0.480886π-0.480886\pi
0.0600133 + 0.998198i 0.480886π0.480886\pi
420420 −8.84477 + 14.3782i −0.431580 + 0.701584i
421421 −0.919497 −0.0448135 −0.0224068 0.999749i 0.507133π-0.507133\pi
−0.0224068 + 0.999749i 0.507133π0.507133\pi
422422 −3.23778 3.23778i −0.157612 0.157612i
423423 −5.39003 + 25.5377i −0.262072 + 1.24168i
424424 2.25474i 0.109500i
425425 18.6200 14.9294i 0.903203 0.724183i
426426 6.90760 2.05150i 0.334674 0.0993955i
427427 7.09903 7.09903i 0.343546 0.343546i
428428 0.708660 0.708660i 0.0342544 0.0342544i
429429 0.379646 0.112752i 0.0183295 0.00544371i
430430 1.47466 1.32133i 0.0711143 0.0637204i
431431 14.3343i 0.690458i −0.938518 0.345229i 0.887801π-0.887801\pi
0.938518 0.345229i 0.112199π-0.112199\pi
432432 2.00070 + 24.7426i 0.0962589 + 1.19043i
433433 −2.60099 2.60099i −0.124995 0.124995i 0.641842 0.766837i 0.278171π-0.278171\pi
−0.766837 + 0.641842i 0.778171π0.778171\pi
434434 −27.6478 −1.32714
435435 2.70774 + 11.3640i 0.129826 + 0.544861i
436436 −4.24148 −0.203130
437437 26.8507 + 26.8507i 1.28444 + 1.28444i
438438 −11.8183 + 21.8037i −0.564699 + 1.04182i
439439 10.0523i 0.479772i −0.970801 0.239886i 0.922890π-0.922890\pi
0.970801 0.239886i 0.0771101π-0.0771101\pi
440440 −0.120464 + 2.19677i −0.00574291 + 0.104727i
441441 4.44428 2.89520i 0.211632 0.137866i
442442 1.43800 1.43800i 0.0683986 0.0683986i
443443 −10.7107 + 10.7107i −0.508879 + 0.508879i −0.914182 0.405303i 0.867166π-0.867166\pi
0.405303 + 0.914182i 0.367166π0.367166\pi
444444 −4.86858 16.3930i −0.231053 0.777977i
445445 −5.52346 6.16438i −0.261837 0.292220i
446446 7.17706i 0.339844i
447447 −27.6682 14.9970i −1.30866 0.709333i
448448 −7.04626 7.04626i −0.332904 0.332904i
449449 −25.8564 −1.22024 −0.610120 0.792309i 0.708879π-0.708879\pi
−0.610120 + 0.792309i 0.708879π0.708879\pi
450450 −26.5522 8.72767i −1.25168 0.411426i
451451 4.49923 0.211861
452452 −8.67612 8.67612i −0.408090 0.408090i
453453 −7.87045 4.26602i −0.369786 0.200435i
454454 53.6185i 2.51644i
455455 1.01030 + 1.12753i 0.0473636 + 0.0528595i
456456 −4.13412 13.9200i −0.193598 0.651864i
457457 −13.9683 + 13.9683i −0.653409 + 0.653409i −0.953812 0.300403i 0.902879π-0.902879\pi
0.300403 + 0.953812i 0.402879π0.402879\pi
458458 −16.3382 + 16.3382i −0.763433 + 0.763433i
459459 16.0674 18.8944i 0.749961 0.881916i
460460 −0.803142 + 14.6460i −0.0374467 + 0.682873i
461461 0.0529299i 0.00246519i −0.999999 0.00123260i 0.999608π-0.999608\pi
0.999999 0.00123260i 0.000392348π-0.000392348\pi
462462 −4.55397 + 8.40169i −0.211870 + 0.390882i
463463 2.46604 + 2.46604i 0.114607 + 0.114607i 0.762084 0.647478i 0.224176π-0.224176\pi
−0.647478 + 0.762084i 0.724176π0.724176\pi
464464 −14.4097 −0.668952
465465 −4.49834 18.8789i −0.208606 0.875486i
466466 −4.82492 −0.223510
467467 −13.3103 13.3103i −0.615928 0.615928i 0.328557 0.944484i 0.393438π-0.393438\pi
−0.944484 + 0.328557i 0.893438π0.893438\pi
468468 −0.987934 0.208515i −0.0456673 0.00963863i
469469 40.8257i 1.88515i
470470 26.9970 24.1900i 1.24528 1.11580i
471471 0.162731 0.0483296i 0.00749823 0.00222691i
472472 −3.59665 + 3.59665i −0.165549 + 0.165549i
473473 0.336036 0.336036i 0.0154509 0.0154509i
474474 −18.3660 + 5.45454i −0.843577 + 0.250535i
475475 42.3487 + 4.65855i 1.94309 + 0.213749i
476476 20.8046i 0.953579i
477477 −6.72670 1.41975i −0.307994 0.0650059i
478478 26.6909 + 26.6909i 1.22081 + 1.22081i
479479 15.7954 0.721710 0.360855 0.932622i 0.382485π-0.382485\pi
0.360855 + 0.932622i 0.382485π0.382485\pi
480480 14.0704 22.8731i 0.642222 1.04401i
481481 −1.53366 −0.0699290
482482 3.03119 + 3.03119i 0.138067 + 0.138067i
483483 10.8916 20.0941i 0.495585 0.914312i
484484 1.47196i 0.0669074i
485485 −15.6073 0.855855i −0.708690 0.0388624i
486486 −28.8112 3.68830i −1.30690 0.167305i
487487 19.8992 19.8992i 0.901717 0.901717i −0.0938674 0.995585i 0.529923π-0.529923\pi
0.995585 + 0.0938674i 0.0299230π0.0299230\pi
488488 −2.35885 + 2.35885i −0.106780 + 0.106780i
489489 −8.65496 29.1421i −0.391391 1.31785i
490490 −7.35552 0.403354i −0.332289 0.0182217i
491491 15.0149i 0.677611i 0.940856 + 0.338806i 0.110023π0.110023\pi
−0.940856 + 0.338806i 0.889977π0.889977\pi
492492 −10.0847 5.46621i −0.454653 0.246436i
493493 10.1806 + 10.1806i 0.458510 + 0.458510i
494494 3.63031 0.163335
495495 −6.47790 1.74264i −0.291160 0.0783257i
496496 23.9386 1.07488
497497 4.67488 + 4.67488i 0.209697 + 0.209697i
498498 −1.46807 0.795740i −0.0657859 0.0356580i
499499 5.53151i 0.247625i 0.992306 + 0.123812i 0.0395121π0.0395121\pi
−0.992306 + 0.123812i 0.960488π0.960488\pi
500500 9.57621 + 13.3840i 0.428261 + 0.598549i
501501 −3.52950 11.8842i −0.157687 0.530947i
502502 −35.6503 + 35.6503i −1.59115 + 1.59115i
503503 −29.2941 + 29.2941i −1.30616 + 1.30616i −0.381993 + 0.924165i 0.624762π0.624762\pi
−0.924165 + 0.381993i 0.875238π0.875238\pi
504504 −7.32339 + 4.77077i −0.326210 + 0.212507i
505505 −16.5150 + 14.7979i −0.734910 + 0.658500i
506506 8.30379i 0.369149i
507507 10.6867 19.7161i 0.474614 0.875622i
508508 0.797503 + 0.797503i 0.0353835 + 0.0353835i
509509 −12.2904 −0.544763 −0.272382 0.962189i 0.587811π-0.587811\pi
−0.272382 + 0.962189i 0.587811π0.587811\pi
510510 −33.5084 + 7.98419i −1.48378 + 0.353546i
511511 −22.7545 −1.00660
512512 16.7751 + 16.7751i 0.741361 + 0.741361i
513513 44.1315 3.56851i 1.94845 0.157553i
514514 37.9045i 1.67190i
515515 −0.998377 + 18.2063i −0.0439937 + 0.802264i
516516 −1.16146 + 0.344943i −0.0511302 + 0.0151852i
517517 6.15190 6.15190i 0.270560 0.270560i
518518 26.1686 26.1686i 1.14978 1.14978i
519519 −24.1115 + 7.16092i −1.05838 + 0.314329i
520520 −0.335699 0.374653i −0.0147214 0.0164296i
521521 9.03181i 0.395691i −0.980233 0.197845i 0.936606π-0.936606\pi
0.980233 0.197845i 0.0633944π-0.0633944\pi
522522 3.48201 16.4976i 0.152404 0.722080i
523523 −3.54962 3.54962i −0.155214 0.155214i 0.625228 0.780442i 0.285006π-0.285006\pi
−0.780442 + 0.625228i 0.785006π0.785006\pi
524524 29.6069 1.29338
525525 −4.56905 25.2335i −0.199410 1.10128i
526526 2.93355 0.127909
527527 −16.9129 16.9129i −0.736738 0.736738i
528528 3.94302 7.27454i 0.171598 0.316584i
529529 3.14005i 0.136524i
530530 6.37173 + 7.11108i 0.276770 + 0.308886i
531531 −8.46538 12.9948i −0.367366 0.563927i
532532 −26.2612 + 26.2612i −1.13857 + 1.13857i
533533 −0.727440 + 0.727440i −0.0315089 + 0.0315089i
534534 3.40113 + 11.4519i 0.147181 + 0.495574i
535535 −0.0833609 + 1.52016i −0.00360401 + 0.0657222i
536536 13.5654i 0.585938i
537537 19.5417 + 10.5922i 0.843289 + 0.457088i
538538 4.26361 + 4.26361i 0.183817 + 0.183817i
539539 −1.76804 −0.0761550
540540 12.4026 + 11.7761i 0.533722 + 0.506764i
541541 6.29034 0.270443 0.135221 0.990815i 0.456825π-0.456825\pi
0.135221 + 0.990815i 0.456825π0.456825\pi
542542 −22.9406 22.9406i −0.985384 0.985384i
543543 28.8549 + 15.6402i 1.23828 + 0.671185i
544544 33.0963i 1.41899i
545545 4.79870 4.29977i 0.205554 0.184182i
546546 −0.622103 2.09468i −0.0266236 0.0896441i
547547 10.6433 10.6433i 0.455076 0.455076i −0.441959 0.897035i 0.645716π-0.645716\pi
0.897035 + 0.441959i 0.145716π0.145716\pi
548548 −16.0247 + 16.0247i −0.684539 + 0.684539i
549549 −5.55198 8.52259i −0.236953 0.363735i
550550 5.82798 + 7.26868i 0.248506 + 0.309937i
551551 25.7014i 1.09492i
552552 −3.61903 + 6.67680i −0.154036 + 0.284184i
553553 −12.4296 12.4296i −0.528560 0.528560i
554554 −29.3905 −1.24868
555555 22.1265 + 13.6111i 0.939216 + 0.577760i
556556 27.7106 1.17519
557557 7.68611 + 7.68611i 0.325671 + 0.325671i 0.850938 0.525267i 0.176034π-0.176034\pi
−0.525267 + 0.850938i 0.676034π0.676034\pi
558558 −5.78464 + 27.4073i −0.244883 + 1.16024i
559559 0.108661i 0.00459588i
560560 31.5837 + 1.73195i 1.33465 + 0.0731883i
561561 −7.92533 + 2.35376i −0.334608 + 0.0993757i
562562 −34.2445 + 34.2445i −1.44452 + 1.44452i
563563 −0.0543618 + 0.0543618i −0.00229108 + 0.00229108i −0.708251 0.705960i 0.750516π-0.750516\pi
0.705960 + 0.708251i 0.250516π0.250516\pi
564564 −21.2631 + 6.31496i −0.895338 + 0.265908i
565565 18.6113 + 1.02059i 0.782983 + 0.0429364i
566566 36.8275i 1.54798i
567567 −9.62156 24.8523i −0.404068 1.04370i
568568 −1.55336 1.55336i −0.0651774 0.0651774i
569569 8.63090 0.361826 0.180913 0.983499i 0.442095π-0.442095\pi
0.180913 + 0.983499i 0.442095π0.442095\pi
570570 −52.3752 32.2187i −2.19375 1.34949i
571571 44.5130 1.86281 0.931405 0.363984i 0.118584π-0.118584\pi
0.931405 + 0.363984i 0.118584π0.118584\pi
572572 0.237988 + 0.237988i 0.00995080 + 0.00995080i
573573 13.0684 24.1101i 0.545941 1.00722i
574574 24.8243i 1.03615i
575575 −13.9386 17.3843i −0.581281 0.724975i
576576 −8.45923 + 5.51070i −0.352468 + 0.229613i
577577 −20.3357 + 20.3357i −0.846587 + 0.846587i −0.989706 0.143119i 0.954287π-0.954287\pi
0.143119 + 0.989706i 0.454287π0.454287\pi
578578 −7.62041 + 7.62041i −0.316967 + 0.316967i
579579 5.14181 + 17.3130i 0.213686 + 0.719502i
580580 −7.39394 + 6.62517i −0.307017 + 0.275095i
581581 1.53209i 0.0635617i
582582 19.8339 + 10.7506i 0.822144 + 0.445627i
583583 1.62043 + 1.62043i 0.0671113 + 0.0671113i
584584 7.56079 0.312868
585585 1.32910 0.765602i 0.0549517 0.0316538i
586586 38.5655 1.59313
587587 −0.959751 0.959751i −0.0396132 0.0396132i 0.687023 0.726636i 0.258917π-0.258917\pi
−0.726636 + 0.687023i 0.758917π0.758917\pi
588588 3.96294 + 2.14803i 0.163429 + 0.0885834i
589589 42.6976i 1.75932i
590590 −1.17938 + 21.5071i −0.0485545 + 0.885433i
591591 6.30087 + 21.2156i 0.259183 + 0.872695i
592592 −22.6579 + 22.6579i −0.931232 + 0.931232i
593593 −17.7549 + 17.7549i −0.729108 + 0.729108i −0.970442 0.241334i 0.922415π-0.922415\pi
0.241334 + 0.970442i 0.422415π0.422415\pi
594594 7.37580 + 6.27221i 0.302633 + 0.257352i
595595 −21.0906 23.5378i −0.864629 0.964958i
596596 26.7454i 1.09554i
597597 −9.13928 + 16.8612i −0.374046 + 0.690083i
598598 −1.34257 1.34257i −0.0549016 0.0549016i
599599 44.2947 1.80983 0.904915 0.425592i 0.139934π-0.139934\pi
0.904915 + 0.425592i 0.139934π0.139934\pi
600600 1.51819 + 8.38450i 0.0619799 + 0.342296i
601601 −22.9340 −0.935497 −0.467748 0.883862i 0.654935π-0.654935\pi
−0.467748 + 0.883862i 0.654935π0.654935\pi
602602 −1.85406 1.85406i −0.0755659 0.0755659i
603603 40.4706 + 8.54180i 1.64809 + 0.347849i
604604 7.60797i 0.309564i
605605 1.49219 + 1.66534i 0.0606662 + 0.0677058i
606606 30.6810 9.11200i 1.24633 0.370150i
607607 10.8599 10.8599i 0.440790 0.440790i −0.451487 0.892278i 0.649106π-0.649106\pi
0.892278 + 0.451487i 0.149106π0.149106\pi
608608 41.7767 41.7767i 1.69427 1.69427i
609609 14.8297 4.40430i 0.600930 0.178471i
610610 −0.773494 + 14.1053i −0.0313179 + 0.571108i
611611 1.98929i 0.0804780i
612612 20.6237 + 4.35288i 0.833663 + 0.175955i
613613 6.73269 + 6.73269i 0.271931 + 0.271931i 0.829877 0.557946i 0.188410π-0.188410\pi
−0.557946 + 0.829877i 0.688410π0.688410\pi
614614 −0.361414 −0.0145855
615615 16.9509 4.03896i 0.683526 0.162867i
616616 2.91342 0.117385
617617 −14.3232 14.3232i −0.576631 0.576631i 0.357343 0.933973i 0.383683π-0.383683\pi
−0.933973 + 0.357343i 0.883683π0.883683\pi
618618 12.5408 23.1368i 0.504466 0.930698i
619619 17.4592i 0.701743i −0.936424 0.350871i 0.885885π-0.885885\pi
0.936424 0.350871i 0.114115π-0.114115\pi
620620 12.2835 11.0063i 0.493317 0.442025i
621621 −17.6405 15.0011i −0.707888 0.601972i
622622 23.9385 23.9385i 0.959848 0.959848i
623623 −7.75037 + 7.75037i −0.310512 + 0.310512i
624624 0.538644 + 1.81367i 0.0215630 + 0.0726048i
625625 −24.4022 5.43447i −0.976087 0.217379i
626626 40.9543i 1.63686i
627627 −12.9751 7.03287i −0.518174 0.280866i
628628 0.102011 + 0.102011i 0.00407067 + 0.00407067i
629629 32.0161 1.27656
630630 −9.61492 + 35.7415i −0.383068 + 1.42398i
631631 11.4177 0.454532 0.227266 0.973833i 0.427021π-0.427021\pi
0.227266 + 0.973833i 0.427021π0.427021\pi
632632 4.13007 + 4.13007i 0.164286 + 0.164286i
633633 −3.74198 2.02827i −0.148730 0.0806164i
634634 2.31601i 0.0919807i
635635 −1.71074 0.0938117i −0.0678886 0.00372280i
636636 −1.66338 5.60076i −0.0659573 0.222085i
637637 0.285859 0.285859i 0.0113261 0.0113261i
638638 −3.97419 + 3.97419i −0.157340 + 0.157340i
639639 5.61233 3.65611i 0.222020 0.144634i
640640 −16.9617 0.930126i −0.670469 0.0367665i
641641 49.6654i 1.96166i 0.194855 + 0.980832i 0.437576π0.437576\pi
−0.194855 + 0.980832i 0.562424π0.562424\pi
642642 1.04712 1.93184i 0.0413264 0.0762437i
643643 −20.8135 20.8135i −0.820803 0.820803i 0.165420 0.986223i 0.447102π-0.447102\pi
−0.986223 + 0.165420i 0.947102π0.947102\pi
644644 19.4239 0.765410
645645 0.964359 1.56768i 0.0379716 0.0617272i
646646 −75.7847 −2.98171
647647 4.95430 + 4.95430i 0.194774 + 0.194774i 0.797755 0.602982i 0.206021π-0.206021\pi
−0.602982 + 0.797755i 0.706021π0.706021\pi
648648 3.19703 + 8.25785i 0.125591 + 0.324399i
649649 5.16965i 0.202927i
650650 −2.11748 0.232933i −0.0830544 0.00913638i
651651 −24.6365 + 7.31682i −0.965579 + 0.286769i
652652 18.2683 18.2683i 0.715440 0.715440i
653653 −6.32930 + 6.32930i −0.247684 + 0.247684i −0.820020 0.572335i 0.806038π-0.806038\pi
0.572335 + 0.820020i 0.306038π0.306038\pi
654654 −8.91483 + 2.64763i −0.348598 + 0.103531i
655655 −33.4965 + 30.0138i −1.30882 + 1.17274i
656656 21.4940i 0.839198i
657657 −4.76083 + 22.5565i −0.185738 + 0.880014i
658658 −33.9428 33.9428i −1.32323 1.32323i
659659 4.08497 0.159128 0.0795639 0.996830i 0.474647π-0.474647\pi
0.0795639 + 0.996830i 0.474647π0.474647\pi
660660 −1.32138 5.54564i −0.0514347 0.215864i
661661 1.41024 0.0548519 0.0274259 0.999624i 0.491269π-0.491269\pi
0.0274259 + 0.999624i 0.491269π0.491269\pi
662662 −2.39252 2.39252i −0.0929879 0.0929879i
663663 0.900818 1.66193i 0.0349849 0.0645441i
664664 0.509078i 0.0197561i
665665 3.08915 56.3334i 0.119792 2.18452i
666666 −20.4658 31.4161i −0.793033 1.21735i
667667 9.50495 9.50495i 0.368033 0.368033i
668668 7.44983 7.44983i 0.288242 0.288242i
669669 −1.89937 6.39536i −0.0734338 0.247259i
670670 −38.3349 42.7832i −1.48101 1.65286i
671671 3.39049i 0.130889i
672672 −31.2642 16.9461i −1.20604 0.653711i
673673 18.1505 + 18.1505i 0.699650 + 0.699650i 0.964335 0.264685i 0.0852680π-0.0852680\pi
−0.264685 + 0.964335i 0.585268π0.585268\pi
674674 −2.17219 −0.0836698
675675 −25.9699 0.750192i −0.999583 0.0288749i
676676 19.0586 0.733022
677677 −32.0068 32.0068i −1.23012 1.23012i −0.963916 0.266205i 0.914230π-0.914230\pi
−0.266205 0.963916i 0.585770π-0.585770\pi
678678 −23.6515 12.8198i −0.908331 0.492343i
679679 20.6988i 0.794347i
680680 7.00791 + 7.82109i 0.268741 + 0.299925i
681681 14.1898 + 47.7785i 0.543755 + 1.83088i
682682 6.60228 6.60228i 0.252814 0.252814i
683683 −0.422561 + 0.422561i −0.0161689 + 0.0161689i −0.715145 0.698976i 0.753639π-0.753639\pi
0.698976 + 0.715145i 0.253639π0.253639\pi
684684 20.5383 + 31.5273i 0.785300 + 1.20548i
685685 1.88501 34.3748i 0.0720224 1.31339i
686686 28.8671i 1.10215i
687687 −10.2349 + 18.8825i −0.390484 + 0.720411i
688688 1.60533 + 1.60533i 0.0612025 + 0.0612025i
689689 −0.523985 −0.0199622
690690 7.45432 + 31.2846i 0.283781 + 1.19099i
691691 33.4110 1.27101 0.635507 0.772095i 0.280791π-0.280791\pi
0.635507 + 0.772095i 0.280791π0.280791\pi
692692 −15.1148 15.1148i −0.574577 0.574577i
693693 −1.83450 + 8.69178i −0.0696871 + 0.330173i
694694 26.4779i 1.00509i
695695 −31.3510 + 28.0914i −1.18921 + 1.06557i
696696 −4.92757 + 1.46345i −0.186779 + 0.0554718i
697697 15.1857 15.1857i 0.575200 0.575200i
698698 1.98071 1.98071i 0.0749709 0.0749709i
699699 −4.29940 + 1.27689i −0.162618 + 0.0482963i
700700 17.0026 13.6326i 0.642639 0.515264i
701701 5.59359i 0.211267i −0.994405 0.105634i 0.966313π-0.966313\pi
0.994405 0.105634i 0.0336871π-0.0336871\pi
702702 −2.20662 + 0.178429i −0.0832836 + 0.00673438i
703703 40.4131 + 40.4131i 1.52421 + 1.52421i
704704 3.36529 0.126834
705705 17.6548 28.6999i 0.664917 1.08090i
706706 27.5065 1.03522
707707 20.7641 + 20.7641i 0.780914 + 0.780914i
708708 6.28072 11.5874i 0.236044 0.435481i
709709 7.90281i 0.296796i −0.988928 0.148398i 0.952588π-0.952588\pi
0.988928 0.148398i 0.0474117π-0.0474117\pi
710710 −9.28870 0.509364i −0.348599 0.0191161i
711711 −14.9221 + 9.72089i −0.559622 + 0.364562i
712712 2.57527 2.57527i 0.0965124 0.0965124i
713713 −15.7905 + 15.7905i −0.591358 + 0.591358i
714714 12.9868 + 43.7277i 0.486017 + 1.63647i
715715 −0.510513 0.0279950i −0.0190921 0.00104695i
716716 18.8900i 0.705953i
717717 30.8474 + 16.7202i 1.15202 + 0.624428i
718718 −18.9599 18.9599i −0.707577 0.707577i
719719 2.71116 0.101109 0.0505547 0.998721i 0.483901π-0.483901\pi
0.0505547 + 0.998721i 0.483901π0.483901\pi
720720 8.32502 30.9466i 0.310255 1.15331i
721721 24.1457 0.899232
722722 −70.6275 70.6275i −2.62848 2.62848i
723723 3.50322 + 1.89885i 0.130286 + 0.0706190i
724724 27.8926i 1.03662i
725725 1.64909 14.9911i 0.0612458 0.556756i
726726 −0.918834 3.09381i −0.0341011 0.114822i
727727 −28.7249 + 28.7249i −1.06535 + 1.06535i −0.0676395 + 0.997710i 0.521547π0.521547\pi
−0.997710 + 0.0676395i 0.978453π0.978453\pi
728728 −0.471045 + 0.471045i −0.0174581 + 0.0174581i
729729 −26.6492 + 4.33812i −0.987008 + 0.160671i
730730 23.8455 21.3662i 0.882561 0.790799i
731731 2.26836i 0.0838984i
732732 4.11918 7.59954i 0.152249 0.280887i
733733 −28.0365 28.0365i −1.03555 1.03555i −0.999344 0.0362092i 0.988472π-0.988472\pi
−0.0362092 0.999344i 0.511528π-0.511528\pi
734734 −63.2007 −2.33278
735735 −6.66112 + 1.58717i −0.245699 + 0.0585437i
736736 −30.8999 −1.13899
737737 −9.74916 9.74916i −0.359115 0.359115i
738738 −24.6084 5.19390i −0.905847 0.191190i
739739 14.9125i 0.548565i −0.961649 0.274282i 0.911560π-0.911560\pi
0.961649 0.274282i 0.0884403π-0.0884403\pi
740740 −1.20881 + 22.0438i −0.0444368 + 0.810345i
741741 3.23490 0.960739i 0.118837 0.0352936i
742742 8.94064 8.94064i 0.328221 0.328221i
743743 8.00940 8.00940i 0.293836 0.293836i −0.544757 0.838594i 0.683378π-0.683378\pi
0.838594 + 0.544757i 0.183378π0.183378\pi
744744 8.18613 2.43121i 0.300118 0.0891326i
745745 27.1130 + 30.2591i 0.993344 + 1.10861i
746746 43.8133i 1.60412i
747747 −1.51876 0.320553i −0.0555686 0.0117284i
748748 −4.96814 4.96814i −0.181653 0.181653i
749749 2.01608 0.0736659
750750 28.4821 + 22.1530i 1.04002 + 0.808915i
751751 −14.6500 −0.534587 −0.267294 0.963615i 0.586129π-0.586129\pi
−0.267294 + 0.963615i 0.586129π0.586129\pi
752752 29.3892 + 29.3892i 1.07171 + 1.07171i
753753 −22.3327 + 41.2020i −0.813849 + 1.50148i
754754 1.28510i 0.0468006i
755755 7.71253 + 8.60746i 0.280688 + 0.313258i
756756 14.6717 17.2532i 0.533605 0.627493i
757757 28.2615 28.2615i 1.02718 1.02718i 0.0275615 0.999620i 0.491226π-0.491226\pi
0.999620 0.0275615i 0.00877422π-0.00877422\pi
758758 −36.0985 + 36.0985i −1.31116 + 1.31116i
759759 2.19755 + 7.39937i 0.0797660 + 0.268580i
760760 −1.02646 + 18.7183i −0.0372335 + 0.678985i
761761 3.35785i 0.121722i 0.998146 + 0.0608610i 0.0193846π0.0193846\pi
−0.998146 + 0.0608610i 0.980615π0.980615\pi
762762 2.17403 + 1.17839i 0.0787568 + 0.0426886i
763763 −6.03332 6.03332i −0.218421 0.218421i
764764 23.3061 0.843184
765765 −27.7458 + 15.9824i −1.00315 + 0.577844i
766766 46.4278 1.67750
767767 −0.835835 0.835835i −0.0301802 0.0301802i
768768 31.8041 + 17.2388i 1.14763 + 0.622051i
769769 16.5162i 0.595588i 0.954630 + 0.297794i 0.0962508π0.0962508\pi
−0.954630 + 0.297794i 0.903749π0.903749\pi
770770 9.18845 8.23310i 0.331129 0.296700i
771771 −10.0312 33.7760i −0.361265 1.21641i
772772 −10.8530 + 10.8530i −0.390606 + 0.390606i
773773 −18.4182 + 18.4182i −0.662457 + 0.662457i −0.955959 0.293502i 0.905179π-0.905179\pi
0.293502 + 0.955959i 0.405179π0.405179\pi
774774 −2.22585 + 1.45002i −0.0800066 + 0.0521198i
775775 −2.73962 + 24.9046i −0.0984102 + 0.894599i
776776 6.87774i 0.246897i
777777 16.3930 30.2437i 0.588095 1.08499i
778778 26.0396 + 26.0396i 0.933565 + 0.933565i
779779 38.3372 1.37357
780780 1.11027 + 0.682982i 0.0397539 + 0.0244547i
781781 −2.23272 −0.0798930
782782 28.0268 + 28.0268i 1.00224 + 1.00224i
783783 −1.26322 15.6222i −0.0451440 0.558292i
784784 8.44639i 0.301657i
785785 −0.218825 0.0119997i −0.00781020 0.000428287i
786786 62.2284 18.4813i 2.21962 0.659207i
787787 6.14166 6.14166i 0.218926 0.218926i −0.589119 0.808046i 0.700525π-0.700525\pi
0.808046 + 0.589119i 0.200525π0.200525\pi
788788 −13.2994 + 13.2994i −0.473772 + 0.473772i
789789 2.61404 0.776347i 0.0930622 0.0276387i
790790 24.6968 + 1.35430i 0.878674 + 0.0481838i
791791 24.6828i 0.877621i
792792 0.609564 2.88808i 0.0216599 0.102623i
793793 −0.548178 0.548178i −0.0194664 0.0194664i
794794 −3.72342 −0.132139
795795 7.55964 + 4.65032i 0.268113 + 0.164930i
796796 −16.2989 −0.577698
797797 −28.9739 28.9739i −1.02631 1.02631i −0.999644 0.0266641i 0.991512π-0.991512\pi
−0.0266641 0.999644i 0.508488π-0.508488\pi
798798 −38.8036 + 71.5893i −1.37363 + 2.53423i
799799 41.5275i 1.46914i
800800 −27.0480 + 21.6870i −0.956293 + 0.766750i
801801 6.06138 + 9.30454i 0.214168 + 0.328760i
802802 −32.2710 + 32.2710i −1.13953 + 1.13953i
803803 5.43376 5.43376i 0.191753 0.191753i
804804 10.0076 + 33.6965i 0.352940 + 1.18838i
805805 −21.9758 + 19.6909i −0.774544 + 0.694012i
806806 2.13493i 0.0751996i
807807 4.92757 + 2.67089i 0.173459 + 0.0940198i
808808 −6.89943 6.89943i −0.242721 0.242721i
809809 27.5336 0.968031 0.484016 0.875059i 0.339178π-0.339178\pi
0.484016 + 0.875059i 0.339178π0.339178\pi
810810 33.4190 + 17.0094i 1.17422 + 0.597648i
811811 12.6038 0.442580 0.221290 0.975208i 0.428973π-0.428973\pi
0.221290 + 0.975208i 0.428973π0.428973\pi
812812 9.29627 + 9.29627i 0.326235 + 0.326235i
813813 −26.5131 14.3709i −0.929854 0.504009i
814814 12.4981i 0.438057i
815815 −2.14893 + 39.1876i −0.0752737 + 1.37268i
816816 −11.2445 37.8613i −0.393636 1.32541i
817817 2.86330 2.86330i 0.100174 0.100174i
818818 29.5683 29.5683i 1.03383 1.03383i
819819 −1.10869 1.70190i −0.0387408 0.0594692i
820820 9.88235 + 11.0291i 0.345106 + 0.385152i
821821 17.3304i 0.604836i 0.953175 + 0.302418i 0.0977938π0.0977938\pi
−0.953175 + 0.302418i 0.902206π0.902206\pi
822822 −23.6780 + 43.6839i −0.825866 + 1.52365i
823823 −20.4085 20.4085i −0.711397 0.711397i 0.255430 0.966828i 0.417783π-0.417783\pi
−0.966828 + 0.255430i 0.917783π0.917783\pi
824824 −8.02306 −0.279496
825825 7.11683 + 4.93465i 0.247776 + 0.171803i
826826 28.5233 0.992454
827827 −13.1570 13.1570i −0.457513 0.457513i 0.440325 0.897838i 0.354863π-0.354863\pi
−0.897838 + 0.440325i 0.854863π0.854863\pi
828828 4.06400 19.2550i 0.141234 0.669157i
829829 25.7974i 0.895980i −0.894039 0.447990i 0.852140π-0.852140\pi
0.894039 0.447990i 0.147860π-0.147860\pi
830830 1.43862 + 1.60555i 0.0499351 + 0.0557294i
831831 −26.1893 + 7.77801i −0.908498 + 0.269816i
832832 −0.544103 + 0.544103i −0.0188634 + 0.0188634i
833833 −5.96747 + 5.96747i −0.206760 + 0.206760i
834834 58.2427 17.2976i 2.01678 0.598967i
835835 −0.876336 + 15.9808i −0.0303269 + 0.553037i
836836 12.5423i 0.433786i
837837 2.09858 + 25.9530i 0.0725377 + 0.897068i
838838 3.23710 + 3.23710i 0.111824 + 0.111824i
839839 17.9282 0.618949 0.309475 0.950908i 0.399847π-0.399847\pi
0.309475 + 0.950908i 0.399847π0.399847\pi
840840 10.9763 2.61538i 0.378720 0.0902391i
841841 −19.9019 −0.686272
842842 −1.21150 1.21150i −0.0417510 0.0417510i
843843 −21.4521 + 39.5773i −0.738848 + 1.36311i
844844 3.61719i 0.124509i
845845 −21.5624 + 19.3205i −0.741768 + 0.664645i
846846 −40.7493 + 26.5459i −1.40099 + 0.912665i
847847 2.09381 2.09381i 0.0719440 0.0719440i
848848 −7.74119 + 7.74119i −0.265834 + 0.265834i
849849 9.74618 + 32.8164i 0.334488 + 1.12625i
850850 44.2036 + 4.86261i 1.51617 + 0.166786i
851851 29.8913i 1.02466i
852852 5.00448 + 2.71258i 0.171451 + 0.0929314i
853853 −9.62668 9.62668i −0.329611 0.329611i 0.522827 0.852439i 0.324877π-0.324877\pi
−0.852439 + 0.522827i 0.824877π0.824877\pi
854854 18.7069 0.640137
855855 −55.1971 14.8487i −1.88770 0.507815i
856856 −0.669897 −0.0228966
857857 18.5942 + 18.5942i 0.635167 + 0.635167i 0.949359 0.314193i 0.101734π-0.101734\pi
−0.314193 + 0.949359i 0.601734π0.601734\pi
858858 0.648767 + 0.351651i 0.0221486 + 0.0120052i
859859 52.8538i 1.80335i 0.432416 + 0.901674i 0.357661π0.357661\pi
−0.432416 + 0.901674i 0.642339π0.642339\pi
860860 1.56182 + 0.0856453i 0.0532575 + 0.00292048i
861861 −6.56961 22.1205i −0.223892 0.753865i
862862 18.8864 18.8864i 0.643273 0.643273i
863863 33.0543 33.0543i 1.12518 1.12518i 0.134233 0.990950i 0.457143π-0.457143\pi
0.990950 0.134233i 0.0428570π-0.0428570\pi
864864 −23.3400 + 27.4466i −0.794043 + 0.933754i
865865 32.4229 + 1.77797i 1.10241 + 0.0604530i
866866 6.85394i 0.232907i
867867 −4.77372 + 8.80710i −0.162124 + 0.299105i
868868 −15.4438 15.4438i −0.524197 0.524197i
869869 5.93637 0.201378
870870 −11.4052 + 18.5404i −0.386671 + 0.628579i
871871 3.15251 0.106819
872872 2.00474 + 2.00474i 0.0678889 + 0.0678889i
873873 20.5188 + 4.33073i 0.694455 + 0.146573i
874874 70.7552i 2.39333i
875875 −5.41638 + 32.6599i −0.183107 + 1.10411i
876876 −18.7810 + 5.57778i −0.634550 + 0.188456i
877877 7.28035 7.28035i 0.245840 0.245840i −0.573421 0.819261i 0.694384π-0.694384\pi
0.819261 + 0.573421i 0.194384π0.194384\pi
878878 13.2446 13.2446i 0.446984 0.446984i
879879 34.3651 10.2061i 1.15911 0.344245i
880880 −7.95576 + 7.12858i −0.268188 + 0.240304i
881881 29.9331i 1.00847i −0.863566 0.504236i 0.831774π-0.831774\pi
0.863566 0.504236i 0.168226π-0.168226\pi
882882 9.67025 + 2.04102i 0.325614 + 0.0687248i
883883 13.3384 + 13.3384i 0.448872 + 0.448872i 0.894979 0.446107i 0.147190π-0.147190\pi
−0.446107 + 0.894979i 0.647190π0.647190\pi
884884 1.60651 0.0540327
885885 4.64080 + 19.4767i 0.155999 + 0.654703i
886886 −28.2240 −0.948205
887887 −18.3918 18.3918i −0.617537 0.617537i 0.327362 0.944899i 0.393840π-0.393840\pi
−0.944899 + 0.327362i 0.893840π0.893840\pi
888888 −5.44702 + 10.0493i −0.182790 + 0.337232i
889889 2.26883i 0.0760941i
890890 0.844462 15.3995i 0.0283064 0.516193i
891891 8.23235 + 3.63710i 0.275794 + 0.121847i
892892 4.00905 4.00905i 0.134233 0.134233i
893893 52.4193 52.4193i 1.75414 1.75414i
894894 −16.6951 56.2142i −0.558369 1.88008i
895895 −19.1496 21.3717i −0.640102 0.714377i
896896 22.4950i 0.751507i
897897 −1.55164 0.841035i −0.0518077 0.0280813i
898898 −34.0676 34.0676i −1.13685 1.13685i
899899 −15.1146 −0.504101
900900 −9.95663 19.7070i −0.331888 0.656901i
901901 10.9385 0.364414
902902 5.92804 + 5.92804i 0.197382 + 0.197382i
903903 −2.14279 1.16146i −0.0713075 0.0386508i
904904 8.20154i 0.272779i
905905 −28.2759 31.5569i −0.939922 1.04899i
906906 −4.74907 15.9906i −0.157777 0.531252i
907907 24.1125 24.1125i 0.800643 0.800643i −0.182553 0.983196i 0.558436π-0.558436\pi
0.983196 + 0.182553i 0.0584360π0.0584360\pi
908908 −29.9509 + 29.9509i −0.993954 + 0.993954i
909909 24.9279 16.2391i 0.826805 0.538616i
910910 −0.154461 + 2.81673i −0.00512034 + 0.0933738i
911911 36.8662i 1.22143i −0.791850 0.610715i 0.790882π-0.790882\pi
0.791850 0.610715i 0.209118π-0.209118\pi
912912 33.5978 61.9851i 1.11253 2.05253i
913913 0.365862 + 0.365862i 0.0121083 + 0.0121083i
914914 −36.8083 −1.21751
915915 3.04365 + 12.7737i 0.100620 + 0.422286i
916916 −18.2527 −0.603087
917917 42.1146 + 42.1146i 1.39075 + 1.39075i
918918 46.0645 3.72481i 1.52035 0.122937i
919919 36.9865i 1.22007i 0.792374 + 0.610035i 0.208845π0.208845\pi
−0.792374 + 0.610035i 0.791155π0.791155\pi
920920 7.30204 6.54283i 0.240741 0.215711i
921921 −0.322049 + 0.0956459i −0.0106119 + 0.00315164i
922922 0.0697387 0.0697387i 0.00229672 0.00229672i
923923 0.360988 0.360988i 0.0118821 0.0118821i
924924 −7.23692 + 2.14930i −0.238077 + 0.0707069i
925925 −20.9791 26.1652i −0.689788 0.860306i
926926 6.49835i 0.213549i
927927 5.05191 23.9356i 0.165926 0.786150i
928928 −14.7886 14.7886i −0.485461 0.485461i
929929 40.7878 1.33820 0.669102 0.743170i 0.266679π-0.266679\pi
0.669102 + 0.743170i 0.266679π0.266679\pi
930930 18.9473 30.8010i 0.621306 1.01001i
931931 −15.0652 −0.493742
932932 −2.69516 2.69516i −0.0882829 0.0882829i
933933 14.9960 27.6664i 0.490948 0.905757i
934934 35.0744i 1.14767i
935935 10.6572 + 0.584411i 0.348529 + 0.0191123i
936936 0.368393 + 0.565502i 0.0120413 + 0.0184840i
937937 −3.15650 + 3.15650i −0.103119 + 0.103119i −0.756784 0.653665i 0.773230π-0.773230\pi
0.653665 + 0.756784i 0.273230π0.273230\pi
938938 −53.7905 + 53.7905i −1.75632 + 1.75632i
939939 −10.8383 36.4937i −0.353695 1.19093i
940940 28.5926 + 1.56793i 0.932588 + 0.0511403i
941941 57.5077i 1.87470i 0.348394 + 0.937348i 0.386727π0.386727\pi
−0.348394 + 0.937348i 0.613273π0.613273\pi
942942 0.278086 + 0.150731i 0.00906053 + 0.00491108i
943943 −14.1779 14.1779i −0.461697 0.461697i
944944 −24.6967 −0.803810
945945 0.891092 + 34.3932i 0.0289872 + 1.11881i
946946 0.885499 0.0287900
947947 27.6497 + 27.6497i 0.898494 + 0.898494i 0.995303 0.0968091i 0.0308636π-0.0308636\pi
−0.0968091 + 0.995303i 0.530864π0.530864\pi
948948 −13.3059 7.21222i −0.432157 0.234242i
949949 1.75707i 0.0570369i
950950 49.6592 + 61.9352i 1.61116 + 2.00944i
951951 0.612919 + 2.06376i 0.0198753 + 0.0669220i
952952 9.83332 9.83332i 0.318700 0.318700i
953953 −1.83684 + 1.83684i −0.0595012 + 0.0595012i −0.736231 0.676730i 0.763396π-0.763396\pi
0.676730 + 0.736231i 0.263396π0.263396\pi
954954 −6.99226 10.7335i −0.226383 0.347510i
955955 −26.3679 + 23.6264i −0.853245 + 0.764531i
956956 29.8186i 0.964403i
957957 −2.48958 + 4.59307i −0.0804768 + 0.148473i
958958 20.8115 + 20.8115i 0.672389 + 0.672389i
959959 −45.5888 −1.47214
960960 12.6788 3.02102i 0.409205 0.0975029i
961961 −5.89023 −0.190007
962962 −2.02070 2.02070i −0.0651500 0.0651500i
963963 0.421817 1.99854i 0.0135928 0.0644021i
964964 3.38639i 0.109068i
965965 1.27665 23.2809i 0.0410969 0.749438i
966966 40.8257 12.1249i 1.31354 0.390112i
967967 5.45469 5.45469i 0.175411 0.175411i −0.613941 0.789352i 0.710417π-0.710417\pi
0.789352 + 0.613941i 0.210417π0.210417\pi
968968 −0.695724 + 0.695724i −0.0223614 + 0.0223614i
969969 −67.5304 + 20.0560i −2.16939 + 0.644290i
970970 −19.4360 21.6913i −0.624051 0.696465i
971971 30.2021i 0.969231i −0.874727 0.484615i 0.838960π-0.838960\pi
0.874727 0.484615i 0.161040π-0.161040\pi
972972 −14.0334 18.1539i −0.450122 0.582288i
973973 39.4171 + 39.4171i 1.26366 + 1.26366i
974974 52.4370 1.68019
975975 −1.94849 + 0.352816i −0.0624018 + 0.0112992i
976976 −16.1972 −0.518461
977977 −21.7515 21.7515i −0.695892 0.695892i 0.267630 0.963522i 0.413760π-0.413760\pi
−0.963522 + 0.267630i 0.913760π0.913760\pi
978978 26.9932 49.8001i 0.863146 1.59243i
979979 3.70157i 0.118303i
980980 −3.88342 4.33404i −0.124051 0.138446i
981981 −7.24317 + 4.71851i −0.231257 + 0.150651i
982982 −19.7831 + 19.7831i −0.631303 + 0.631303i
983983 13.0850 13.0850i 0.417347 0.417347i −0.466941 0.884288i 0.654644π-0.654644\pi
0.884288 + 0.466941i 0.154644π0.154644\pi
984984 2.18293 + 7.35014i 0.0695893 + 0.234314i
985985 1.56443 28.5288i 0.0498470 0.909004i
986986 26.8272i 0.854352i
987987 −39.2286 21.2631i −1.24866 0.676812i
988988 2.02786 + 2.02786i 0.0645148 + 0.0645148i
989989 −2.11782 −0.0673428
990990 −6.23903 10.8311i −0.198289 0.344235i
991991 −40.4113 −1.28371 −0.641853 0.766828i 0.721834π-0.721834\pi
−0.641853 + 0.766828i 0.721834π0.721834\pi
992992 24.5683 + 24.5683i 0.780043 + 0.780043i
993993 −2.76510 1.49877i −0.0877477 0.0475619i
994994 12.3189i 0.390733i
995995 18.4401 16.5229i 0.584592 0.523810i
996996 −0.375560 1.26455i −0.0119001 0.0400687i
997997 9.17711 9.17711i 0.290642 0.290642i −0.546692 0.837334i 0.684113π-0.684113\pi
0.837334 + 0.546692i 0.184113π0.184113\pi
998998 −7.28814 + 7.28814i −0.230702 + 0.230702i
999999 −26.5508 22.5782i −0.840029 0.714342i
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 165.2.k.c.23.8 16
3.2 odd 2 165.2.k.d.23.1 yes 16
5.2 odd 4 165.2.k.d.122.1 yes 16
5.3 odd 4 825.2.k.i.782.8 16
5.4 even 2 825.2.k.j.518.1 16
15.2 even 4 inner 165.2.k.c.122.8 yes 16
15.8 even 4 825.2.k.j.782.1 16
15.14 odd 2 825.2.k.i.518.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.k.c.23.8 16 1.1 even 1 trivial
165.2.k.c.122.8 yes 16 15.2 even 4 inner
165.2.k.d.23.1 yes 16 3.2 odd 2
165.2.k.d.122.1 yes 16 5.2 odd 4
825.2.k.i.518.8 16 15.14 odd 2
825.2.k.i.782.8 16 5.3 odd 4
825.2.k.j.518.1 16 5.4 even 2
825.2.k.j.782.1 16 15.8 even 4