Properties

Label 775.2.ck.a.524.2
Level 775775
Weight 22
Character 775.524
Analytic conductor 6.1886.188
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [775,2,Mod(49,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 775=5231 775 = 5^{2} \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 775.ck (of order 3030, degree 88, 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: 6.188406156656.18840615665
Analytic rank: 00
Dimension: 3232
Relative dimension: 44 over Q(ζ30)\Q(\zeta_{30})
Twist minimal: no (minimal twist has level 31)
Sato-Tate group: SU(2)[C30]\mathrm{SU}(2)[C_{30}]

Embedding invariants

Embedding label 524.2
Character χ\chi == 775.524
Dual form 775.2.ck.a.599.2

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+(0.2065670.284315i)q2+(2.877440.302431i)q3+(0.5798691.78465i)q4+(0.508398+0.880572i)q6+(0.224987+1.05848i)q7+(1.29565+0.420982i)q8+(5.25377+1.11672i)q9+(1.626901.80686i)q11+(2.20827+4.95987i)q12+(1.168822.62521i)q13+(0.2544660.282614i)q14+(2.648901.92454i)q16+(1.356061.22101i)q17+(0.7677531.72440i)q18+(1.935140.861580i)q19+(0.3272693.11375i)q21+(0.177653+0.835790i)q22+(0.420572+0.136652i)q23+(3.855470.819506i)q24+(0.504947+0.874594i)q26+(6.524622.11998i)q27+(2.01948+0.212256i)q28+(2.55579+1.85689i)q29+(1.15354+5.44696i)q31+3.87532iq32+(4.13487+5.69116i)q33+(0.0670322+0.637769i)q34+(5.039468.72860i)q36+(2.725171.57338i)q37+(0.154776+0.728163i)q38+(2.56926+7.90738i)q39+(0.726079+6.90818i)q41+(0.817684+0.736246i)q42+(3.42162+7.68509i)q43+(4.16801+1.85572i)q44+(0.125728+0.0913471i)q46+(4.67998+6.44144i)q47+(7.04003+6.33887i)q48+(5.325062.37087i)q49+(3.53273+3.92349i)q51+(5.36285+0.563659i)q52+(1.034784.86824i)q53+(0.745029+2.29296i)q54+(0.7371041.27670i)q56+(5.30768+3.06439i)q57+(1.05588+0.343078i)q58+(1.25580+11.9481i)q5914.4351q61+(1.310371.45313i)q62+5.81225iq63+(4.19600+3.04857i)q64+(0.7639552.35121i)q66+(5.57511+3.21879i)q67+(2.96541+1.71208i)q68+(1.251500.266015i)q69+(1.641210.348850i)q71+(7.27716+0.764860i)q72+(10.67179.60883i)q73+(1.010260.449798i)q74+(2.65975+2.95395i)q76+(1.546492.12856i)q77+(1.717462.36388i)q78+(2.306922.56210i)q79+(3.41274+1.51945i)q81+(1.814121.63344i)q82+(12.7832+1.34357i)q83+(5.746741.22151i)q84+(2.891780.614667i)q86+(7.915734.57015i)q87+(2.86855+1.65616i)q88+(0.698188+2.14880i)q89+(2.515761.82781i)q91+0.829816iq92+(1.6719016.0222i)q93+2.79812q94+(1.1720211.1510i)q96+(3.24582+1.05463i)q97+(1.774051.02425i)q98+(6.5296111.3096i)q99+O(q100)q+(-0.206567 - 0.284315i) q^{2} +(-2.87744 - 0.302431i) q^{3} +(0.579869 - 1.78465i) q^{4} +(0.508398 + 0.880572i) q^{6} +(0.224987 + 1.05848i) q^{7} +(-1.29565 + 0.420982i) q^{8} +(5.25377 + 1.11672i) q^{9} +(-1.62690 - 1.80686i) q^{11} +(-2.20827 + 4.95987i) q^{12} +(-1.16882 - 2.62521i) q^{13} +(0.254466 - 0.282614i) q^{14} +(-2.64890 - 1.92454i) q^{16} +(-1.35606 - 1.22101i) q^{17} +(-0.767753 - 1.72440i) q^{18} +(-1.93514 - 0.861580i) q^{19} +(-0.327269 - 3.11375i) q^{21} +(-0.177653 + 0.835790i) q^{22} +(-0.420572 + 0.136652i) q^{23} +(3.85547 - 0.819506i) q^{24} +(-0.504947 + 0.874594i) q^{26} +(-6.52462 - 2.11998i) q^{27} +(2.01948 + 0.212256i) q^{28} +(-2.55579 + 1.85689i) q^{29} +(1.15354 + 5.44696i) q^{31} +3.87532i q^{32} +(4.13487 + 5.69116i) q^{33} +(-0.0670322 + 0.637769i) q^{34} +(5.03946 - 8.72860i) q^{36} +(2.72517 - 1.57338i) q^{37} +(0.154776 + 0.728163i) q^{38} +(2.56926 + 7.90738i) q^{39} +(0.726079 + 6.90818i) q^{41} +(-0.817684 + 0.736246i) q^{42} +(-3.42162 + 7.68509i) q^{43} +(-4.16801 + 1.85572i) q^{44} +(0.125728 + 0.0913471i) q^{46} +(-4.67998 + 6.44144i) q^{47} +(7.04003 + 6.33887i) q^{48} +(5.32506 - 2.37087i) q^{49} +(3.53273 + 3.92349i) q^{51} +(-5.36285 + 0.563659i) q^{52} +(1.03478 - 4.86824i) q^{53} +(0.745029 + 2.29296i) q^{54} +(-0.737104 - 1.27670i) q^{56} +(5.30768 + 3.06439i) q^{57} +(1.05588 + 0.343078i) q^{58} +(-1.25580 + 11.9481i) q^{59} -14.4351 q^{61} +(1.31037 - 1.45313i) q^{62} +5.81225i q^{63} +(-4.19600 + 3.04857i) q^{64} +(0.763955 - 2.35121i) q^{66} +(5.57511 + 3.21879i) q^{67} +(-2.96541 + 1.71208i) q^{68} +(1.25150 - 0.266015i) q^{69} +(-1.64121 - 0.348850i) q^{71} +(-7.27716 + 0.764860i) q^{72} +(10.6717 - 9.60883i) q^{73} +(-1.01026 - 0.449798i) q^{74} +(-2.65975 + 2.95395i) q^{76} +(1.54649 - 2.12856i) q^{77} +(1.71746 - 2.36388i) q^{78} +(2.30692 - 2.56210i) q^{79} +(3.41274 + 1.51945i) q^{81} +(1.81412 - 1.63344i) q^{82} +(-12.7832 + 1.34357i) q^{83} +(-5.74674 - 1.22151i) q^{84} +(2.89178 - 0.614667i) q^{86} +(7.91573 - 4.57015i) q^{87} +(2.86855 + 1.65616i) q^{88} +(-0.698188 + 2.14880i) q^{89} +(2.51576 - 1.82781i) q^{91} +0.829816i q^{92} +(-1.67190 - 16.0222i) q^{93} +2.79812 q^{94} +(1.17202 - 11.1510i) q^{96} +(3.24582 + 1.05463i) q^{97} +(-1.77405 - 1.02425i) q^{98} +(-6.52961 - 11.3096i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+28q4+22q6+20q914q11+12q144q1632q19+18q21+40q24+18q26+28q29+30q31+64q34+2q36+6q3916q4178q44+12q99+O(q100) 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/775Z)×\left(\mathbb{Z}/775\mathbb{Z}\right)^\times.

nn 251251 652652
χ(n)\chi(n) e(815)e\left(\frac{8}{15}\right) 1-1

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 −0.206567 0.284315i −0.146065 0.201041i 0.729715 0.683751i 0.239653π-0.239653\pi
−0.875780 + 0.482710i 0.839653π0.839653\pi
33 −2.87744 0.302431i −1.66129 0.174609i −0.773164 0.634206i 0.781327π-0.781327\pi
−0.888128 + 0.459597i 0.847994π0.847994\pi
44 0.579869 1.78465i 0.289934 0.892327i
55 0 0
66 0.508398 + 0.880572i 0.207553 + 0.359492i
77 0.224987 + 1.05848i 0.0850369 + 0.400067i 0.999994 0.00348400i 0.00110899π-0.00110899\pi
−0.914957 + 0.403551i 0.867776π0.867776\pi
88 −1.29565 + 0.420982i −0.458081 + 0.148840i
99 5.25377 + 1.11672i 1.75126 + 0.372241i
1010 0 0
1111 −1.62690 1.80686i −0.490530 0.544789i 0.446158 0.894954i 0.352792π-0.352792\pi
−0.936688 + 0.350165i 0.886125π0.886125\pi
1212 −2.20827 + 4.95987i −0.637474 + 1.43179i
1313 −1.16882 2.62521i −0.324172 0.728103i 0.675787 0.737097i 0.263804π-0.263804\pi
−0.999960 + 0.00899389i 0.997137π0.997137\pi
1414 0.254466 0.282614i 0.0680090 0.0755317i
1515 0 0
1616 −2.64890 1.92454i −0.662226 0.481135i
1717 −1.35606 1.22101i −0.328894 0.296137i 0.488095 0.872790i 0.337692π-0.337692\pi
−0.816989 + 0.576653i 0.804359π0.804359\pi
1818 −0.767753 1.72440i −0.180961 0.406445i
1919 −1.93514 0.861580i −0.443951 0.197660i 0.172571 0.984997i 0.444792π-0.444792\pi
−0.616523 + 0.787337i 0.711459π0.711459\pi
2020 0 0
2121 −0.327269 3.11375i −0.0714159 0.679477i
2222 −0.177653 + 0.835790i −0.0378757 + 0.178191i
2323 −0.420572 + 0.136652i −0.0876953 + 0.0284939i −0.352536 0.935798i 0.614681π-0.614681\pi
0.264841 + 0.964292i 0.414681π0.414681\pi
2424 3.85547 0.819506i 0.786995 0.167281i
2525 0 0
2626 −0.504947 + 0.874594i −0.0990283 + 0.171522i
2727 −6.52462 2.11998i −1.25566 0.407990i
2828 2.01948 + 0.212256i 0.381646 + 0.0401126i
2929 −2.55579 + 1.85689i −0.474599 + 0.344816i −0.799231 0.601024i 0.794760π-0.794760\pi
0.324632 + 0.945840i 0.394760π0.394760\pi
3030 0 0
3131 1.15354 + 5.44696i 0.207181 + 0.978303i
3232 3.87532i 0.685067i
3333 4.13487 + 5.69116i 0.719789 + 0.990704i
3434 −0.0670322 + 0.637769i −0.0114959 + 0.109376i
3535 0 0
3636 5.03946 8.72860i 0.839910 1.45477i
3737 2.72517 1.57338i 0.448015 0.258661i −0.258977 0.965884i 0.583385π-0.583385\pi
0.706991 + 0.707222i 0.250052π0.250052\pi
3838 0.154776 + 0.728163i 0.0251079 + 0.118124i
3939 2.56926 + 7.90738i 0.411412 + 1.26619i
4040 0 0
4141 0.726079 + 6.90818i 0.113395 + 1.07888i 0.892209 + 0.451623i 0.149155π0.149155\pi
−0.778814 + 0.627254i 0.784179π0.784179\pi
4242 −0.817684 + 0.736246i −0.126171 + 0.113605i
4343 −3.42162 + 7.68509i −0.521793 + 1.17197i 0.439953 + 0.898021i 0.354995π0.354995\pi
−0.961746 + 0.273944i 0.911672π0.911672\pi
4444 −4.16801 + 1.85572i −0.628351 + 0.279760i
4545 0 0
4646 0.125728 + 0.0913471i 0.0185377 + 0.0134684i
4747 −4.67998 + 6.44144i −0.682645 + 0.939580i −0.999962 0.00873953i 0.997218π-0.997218\pi
0.317317 + 0.948320i 0.397218π0.397218\pi
4848 7.04003 + 6.33887i 1.01614 + 0.914937i
4949 5.32506 2.37087i 0.760723 0.338696i
5050 0 0
5151 3.53273 + 3.92349i 0.494681 + 0.549399i
5252 −5.36285 + 0.563659i −0.743694 + 0.0781654i
5353 1.03478 4.86824i 0.142137 0.668704i −0.848160 0.529740i 0.822289π-0.822289\pi
0.990297 0.138964i 0.0443772π-0.0443772\pi
5454 0.745029 + 2.29296i 0.101386 + 0.312033i
5555 0 0
5656 −0.737104 1.27670i −0.0984997 0.170606i
5757 5.30768 + 3.06439i 0.703020 + 0.405889i
5858 1.05588 + 0.343078i 0.138644 + 0.0450483i
5959 −1.25580 + 11.9481i −0.163491 + 1.55551i 0.538068 + 0.842902i 0.319154π0.319154\pi
−0.701559 + 0.712612i 0.747512π0.747512\pi
6060 0 0
6161 −14.4351 −1.84823 −0.924115 0.382115i 0.875196π-0.875196\pi
−0.924115 + 0.382115i 0.875196π0.875196\pi
6262 1.31037 1.45313i 0.166417 0.184548i
6363 5.81225i 0.732274i
6464 −4.19600 + 3.04857i −0.524499 + 0.381071i
6565 0 0
6666 0.763955 2.35121i 0.0940363 0.289414i
6767 5.57511 + 3.21879i 0.681108 + 0.393238i 0.800273 0.599636i 0.204688π-0.204688\pi
−0.119164 + 0.992875i 0.538021π0.538021\pi
6868 −2.96541 + 1.71208i −0.359609 + 0.207620i
6969 1.25150 0.266015i 0.150663 0.0320244i
7070 0 0
7171 −1.64121 0.348850i −0.194776 0.0414009i 0.109491 0.993988i 0.465078π-0.465078\pi
−0.304266 + 0.952587i 0.598411π0.598411\pi
7272 −7.27716 + 0.764860i −0.857621 + 0.0901396i
7373 10.6717 9.60883i 1.24903 1.12463i 0.261830 0.965114i 0.415674π-0.415674\pi
0.987196 0.159514i 0.0509928π-0.0509928\pi
7474 −1.01026 0.449798i −0.117441 0.0522880i
7575 0 0
7676 −2.65975 + 2.95395i −0.305094 + 0.338841i
7777 1.54649 2.12856i 0.176239 0.242572i
7878 1.71746 2.36388i 0.194464 0.267657i
7979 2.30692 2.56210i 0.259549 0.288259i −0.599260 0.800555i 0.704538π-0.704538\pi
0.858809 + 0.512296i 0.171205π0.171205\pi
8080 0 0
8181 3.41274 + 1.51945i 0.379194 + 0.168828i
8282 1.81412 1.63344i 0.200336 0.180383i
8383 −12.7832 + 1.34357i −1.40314 + 0.147476i −0.775657 0.631155i 0.782581π-0.782581\pi
−0.627482 + 0.778631i 0.715914π0.715914\pi
8484 −5.74674 1.22151i −0.627021 0.133277i
8585 0 0
8686 2.89178 0.614667i 0.311829 0.0662812i
8787 7.91573 4.57015i 0.848656 0.489972i
8888 2.86855 + 1.65616i 0.305789 + 0.176547i
8989 −0.698188 + 2.14880i −0.0740078 + 0.227773i −0.981217 0.192907i 0.938208π-0.938208\pi
0.907209 + 0.420680i 0.138208π0.138208\pi
9090 0 0
9191 2.51576 1.82781i 0.263724 0.191606i
9292 0.829816i 0.0865143i
9393 −1.67190 16.0222i −0.173368 1.66142i
9494 2.79812 0.288604
9595 0 0
9696 1.17202 11.1510i 0.119619 1.13810i
9797 3.24582 + 1.05463i 0.329563 + 0.107082i 0.469125 0.883132i 0.344569π-0.344569\pi
−0.139562 + 0.990213i 0.544569π0.544569\pi
9898 −1.77405 1.02425i −0.179207 0.103465i
9999 −6.52961 11.3096i −0.656251 1.13666i
100100 0 0
101101 5.47495 + 16.8502i 0.544778 + 1.67665i 0.721518 + 0.692395i 0.243445π0.243445\pi
−0.176741 + 0.984257i 0.556555π0.556555\pi
102102 0.385763 1.81487i 0.0381962 0.179699i
103103 −8.02962 + 0.843947i −0.791182 + 0.0831566i −0.491494 0.870881i 0.663549π-0.663549\pi
−0.299688 + 0.954037i 0.596882π0.596882\pi
104104 2.61955 + 2.90930i 0.256868 + 0.285281i
105105 0 0
106106 −1.59786 + 0.711414i −0.155198 + 0.0690987i
107107 −9.03010 8.13074i −0.872972 0.786028i 0.105063 0.994466i 0.466495π-0.466495\pi
−0.978036 + 0.208438i 0.933162π0.933162\pi
108108 −7.56685 + 10.4149i −0.728121 + 1.00217i
109109 −0.511381 0.371540i −0.0489815 0.0355871i 0.563025 0.826440i 0.309637π-0.309637\pi
−0.612007 + 0.790853i 0.709637π0.709637\pi
110110 0 0
111111 −8.31735 + 3.70312i −0.789448 + 0.351485i
112112 1.44112 3.23680i 0.136173 0.305849i
113113 −8.39779 + 7.56140i −0.789998 + 0.711317i −0.961782 0.273818i 0.911714π-0.911714\pi
0.171784 + 0.985135i 0.445047π0.445047\pi
114114 −0.225139 2.14205i −0.0210862 0.200622i
115115 0 0
116116 1.83188 + 5.63796i 0.170086 + 0.523472i
117117 −3.20907 15.0975i −0.296679 1.39576i
118118 3.65643 2.11104i 0.336602 0.194337i
119119 0.987313 1.71008i 0.0905068 0.156762i
120120 0 0
121121 0.531887 5.06056i 0.0483533 0.460051i
122122 2.98182 + 4.10412i 0.269961 + 0.371570i
123123 20.0975i 1.81213i
124124 10.3898 + 1.09986i 0.933034 + 0.0987702i
125125 0 0
126126 1.65251 1.20062i 0.147217 0.106960i
127127 −0.117161 0.0123141i −0.0103963 0.00109270i 0.0993289 0.995055i 0.468330π-0.468330\pi
−0.109725 + 0.993962i 0.534997π0.534997\pi
128128 9.10481 + 2.95833i 0.804759 + 0.261482i
129129 12.1697 21.0786i 1.07149 1.85587i
130130 0 0
131131 −5.65756 + 1.20255i −0.494303 + 0.105067i −0.448317 0.893875i 0.647976π-0.647976\pi
−0.0459863 + 0.998942i 0.514643π0.514643\pi
132132 12.5544 4.07918i 1.09272 0.355047i
133133 0.476583 2.24215i 0.0413250 0.194419i
134134 −0.236483 2.24998i −0.0204290 0.194369i
135135 0 0
136136 2.27101 + 1.01112i 0.194737 + 0.0867026i
137137 4.80170 + 10.7848i 0.410237 + 0.921407i 0.993990 + 0.109475i 0.0349171π0.0349171\pi
−0.583753 + 0.811931i 0.698416π0.698416\pi
138138 −0.334150 0.300870i −0.0284448 0.0256118i
139139 −12.4767 9.06482i −1.05826 0.768868i −0.0844915 0.996424i 0.526927π-0.526927\pi
−0.973765 + 0.227556i 0.926927π0.926927\pi
140140 0 0
141141 15.4145 17.1195i 1.29813 1.44172i
142142 0.239836 + 0.538681i 0.0201266 + 0.0452051i
143143 −2.84183 + 6.38286i −0.237646 + 0.533762i
144144 −11.7675 13.0692i −0.980628 1.08910i
145145 0 0
146146 −4.93635 1.04925i −0.408535 0.0868368i
147147 −16.0396 + 5.21157i −1.32292 + 0.429843i
148148 −1.22769 5.77583i −0.100916 0.474770i
149149 −5.97511 10.3492i −0.489500 0.847840i 0.510427 0.859921i 0.329488π-0.329488\pi
−0.999927 + 0.0120817i 0.996154π0.996154\pi
150150 0 0
151151 −1.33561 + 4.11059i −0.108691 + 0.334515i −0.990579 0.136943i 0.956272π-0.956272\pi
0.881888 + 0.471458i 0.156272π0.156272\pi
152152 2.86997 + 0.301646i 0.232785 + 0.0244667i
153153 −5.76092 7.92923i −0.465743 0.641040i
154154 −0.924636 −0.0745093
155155 0 0
156156 15.6018 1.24914
157157 5.11634 + 7.04204i 0.408328 + 0.562016i 0.962810 0.270180i 0.0870833π-0.0870833\pi
−0.554481 + 0.832196i 0.687083π0.687083\pi
158158 −1.20498 0.126648i −0.0958628 0.0100756i
159159 −4.44982 + 13.6951i −0.352893 + 1.08609i
160160 0 0
161161 −0.239267 0.414422i −0.0188568 0.0326610i
162162 −0.272957 1.28416i −0.0214455 0.100893i
163163 2.97481 0.966575i 0.233005 0.0757080i −0.190187 0.981748i 0.560909π-0.560909\pi
0.423192 + 0.906040i 0.360909π0.360909\pi
164164 12.7497 + 2.71004i 0.995588 + 0.211619i
165165 0 0
166166 3.02258 + 3.35692i 0.234598 + 0.260547i
167167 5.43194 12.2003i 0.420336 0.944090i −0.571969 0.820275i 0.693820π-0.693820\pi
0.992305 0.123815i 0.0395130π-0.0395130\pi
168168 1.73486 + 3.89656i 0.133847 + 0.300626i
169169 3.17310 3.52408i 0.244085 0.271083i
170170 0 0
171171 −9.20462 6.68755i −0.703895 0.511410i
172172 11.7311 + 10.5628i 0.894490 + 0.805402i
173173 −7.74619 17.3982i −0.588932 1.32276i −0.924656 0.380803i 0.875648π-0.875648\pi
0.335724 0.941960i 0.391019π-0.391019\pi
174174 −2.93449 1.30652i −0.222463 0.0990469i
175175 0 0
176176 0.832136 + 7.91724i 0.0627246 + 0.596785i
177177 7.22697 34.0002i 0.543213 2.55561i
178178 0.755159 0.245366i 0.0566016 0.0183910i
179179 −0.0775964 + 0.0164936i −0.00579983 + 0.00123279i −0.210811 0.977527i 0.567610π-0.567610\pi
0.205011 + 0.978760i 0.434277π0.434277\pi
180180 0 0
181181 −1.08143 + 1.87308i −0.0803817 + 0.139225i −0.903414 0.428769i 0.858947π-0.858947\pi
0.823032 + 0.567995i 0.192281π0.192281\pi
182182 −1.03935 0.337704i −0.0770415 0.0250323i
183183 41.5363 + 4.36564i 3.07045 + 0.322717i
184184 0.487386 0.354107i 0.0359306 0.0261051i
185185 0 0
186186 −4.20998 + 3.78500i −0.308691 + 0.277529i
187187 4.43668i 0.324442i
188188 8.78195 + 12.0873i 0.640490 + 0.881559i
189189 0.776000 7.38314i 0.0564457 0.537045i
190190 0 0
191191 2.67085 4.62604i 0.193256 0.334729i −0.753072 0.657939i 0.771429π-0.771429\pi
0.946327 + 0.323210i 0.104762π0.104762\pi
192192 12.9957 7.50308i 0.937885 0.541488i
193193 −0.443616 2.08705i −0.0319322 0.150229i 0.959293 0.282412i 0.0911346π-0.0911346\pi
−0.991225 + 0.132183i 0.957801π0.957801\pi
194194 −0.370632 1.14069i −0.0266098 0.0818966i
195195 0 0
196196 −1.14334 10.8782i −0.0816673 0.777013i
197197 4.36652 3.93163i 0.311102 0.280117i −0.498758 0.866742i 0.666210π-0.666210\pi
0.809859 + 0.586624i 0.199544π0.199544\pi
198198 −1.86669 + 4.19266i −0.132660 + 0.297959i
199199 −6.32901 + 2.81786i −0.448652 + 0.199753i −0.618609 0.785699i 0.712304π-0.712304\pi
0.169958 + 0.985451i 0.445637π0.445637\pi
200200 0 0
201201 −15.0686 10.9480i −1.06286 0.772211i
202202 3.65981 5.03729i 0.257503 0.354423i
203203 −2.54050 2.28748i −0.178308 0.160549i
204204 9.05059 4.02958i 0.633668 0.282127i
205205 0 0
206206 1.89860 + 2.10861i 0.132282 + 0.146914i
207207 −2.36219 + 0.248276i −0.164184 + 0.0172564i
208208 −1.95624 + 9.20337i −0.135641 + 0.638139i
209209 1.59153 + 4.89823i 0.110089 + 0.338818i
210210 0 0
211211 −8.35437 14.4702i −0.575139 0.996170i −0.996027 0.0890568i 0.971615π-0.971615\pi
0.420888 0.907113i 0.361719π-0.361719\pi
212212 −8.08808 4.66966i −0.555492 0.320713i
213213 4.61698 + 1.50015i 0.316350 + 0.102788i
214214 −0.446370 + 4.24693i −0.0305133 + 0.290314i
215215 0 0
216216 9.34610 0.635921
217217 −5.50596 + 2.44649i −0.373769 + 0.166078i
218218 0.222141i 0.0150453i
219219 −33.6132 + 24.4214i −2.27137 + 1.65024i
220220 0 0
221221 −1.62040 + 4.98709i −0.109000 + 0.335468i
222222 2.77094 + 1.59980i 0.185973 + 0.107372i
223223 5.42267 3.13078i 0.363129 0.209653i −0.307323 0.951605i 0.599433π-0.599433\pi
0.670453 + 0.741952i 0.266100π0.266100\pi
224224 −4.10195 + 0.871895i −0.274073 + 0.0582560i
225225 0 0
226226 3.88452 + 0.825681i 0.258395 + 0.0549235i
227227 −7.80452 + 0.820289i −0.518004 + 0.0544445i −0.359924 0.932982i 0.617197π-0.617197\pi
−0.158081 + 0.987426i 0.550531π0.550531\pi
228228 8.54664 7.69543i 0.566015 0.509642i
229229 −11.6687 5.19524i −0.771089 0.343311i −0.0168049 0.999859i 0.505349π-0.505349\pi
−0.754285 + 0.656548i 0.772016π0.772016\pi
230230 0 0
231231 −5.09368 + 5.65711i −0.335140 + 0.372210i
232232 2.52969 3.48183i 0.166083 0.228593i
233233 −7.47514 + 10.2887i −0.489713 + 0.674032i −0.980335 0.197340i 0.936770π-0.936770\pi
0.490622 + 0.871373i 0.336770π0.336770\pi
234234 −3.62955 + 4.03103i −0.237271 + 0.263517i
235235 0 0
236236 20.5951 + 9.16951i 1.34062 + 0.596884i
237237 −7.41290 + 6.67460i −0.481520 + 0.433562i
238238 −0.690146 + 0.0725373i −0.0447355 + 0.00470189i
239239 −24.8690 5.28607i −1.60864 0.341928i −0.686006 0.727596i 0.740638π-0.740638\pi
−0.922638 + 0.385668i 0.873971π0.873971\pi
240240 0 0
241241 −2.30939 + 0.490876i −0.148761 + 0.0316201i −0.281690 0.959505i 0.590895π-0.590895\pi
0.132929 + 0.991126i 0.457562π0.457562\pi
242242 −1.54866 + 0.894121i −0.0995519 + 0.0574763i
243243 8.46339 + 4.88634i 0.542927 + 0.313459i
244244 −8.37048 + 25.7617i −0.535865 + 1.64922i
245245 0 0
246246 −5.71401 + 4.15147i −0.364312 + 0.264688i
247247 6.08718i 0.387318i
248248 −3.78765 6.57173i −0.240516 0.417305i
249249 37.1893 2.35677
250250 0 0
251251 −0.246336 + 2.34373i −0.0155486 + 0.147935i −0.999542 0.0302716i 0.990363π-0.990363\pi
0.983993 + 0.178206i 0.0570294π0.0570294\pi
252252 10.3728 + 3.37034i 0.653428 + 0.212312i
253253 0.931142 + 0.537595i 0.0585404 + 0.0337983i
254254 0.0207005 + 0.0358542i 0.00129886 + 0.00224970i
255255 0 0
256256 2.16580 + 6.66565i 0.135363 + 0.416603i
257257 −5.40862 + 25.4455i −0.337380 + 1.58725i 0.403090 + 0.915160i 0.367936π0.367936\pi
−0.740470 + 0.672089i 0.765397π0.765397\pi
258258 −8.50682 + 0.894103i −0.529612 + 0.0556644i
259259 2.27851 + 2.53054i 0.141580 + 0.157240i
260260 0 0
261261 −15.5012 + 6.90157i −0.959499 + 0.427196i
262262 1.51057 + 1.36012i 0.0933232 + 0.0840285i
263263 −13.4812 + 18.5552i −0.831285 + 1.14417i 0.156398 + 0.987694i 0.450012π0.450012\pi
−0.987683 + 0.156471i 0.949988π0.949988\pi
264264 −7.75322 5.63304i −0.477178 0.346690i
265265 0 0
266266 −0.735922 + 0.327654i −0.0451223 + 0.0200897i
267267 2.65886 5.97190i 0.162720 0.365474i
268268 8.97726 8.08316i 0.548374 0.493758i
269269 −1.78193 16.9539i −0.108646 1.03370i −0.903994 0.427546i 0.859378π-0.859378\pi
0.795347 0.606154i 0.207288π-0.207288\pi
270270 0 0
271271 2.23929 + 6.89184i 0.136027 + 0.418649i 0.995748 0.0921146i 0.0293626π-0.0293626\pi
−0.859721 + 0.510764i 0.829363π0.829363\pi
272272 1.24221 + 5.84413i 0.0753199 + 0.354352i
273273 −7.79175 + 4.49857i −0.471578 + 0.272266i
274274 2.07440 3.59297i 0.125319 0.217059i
275275 0 0
276276 0.250962 2.38775i 0.0151062 0.143725i
277277 −8.87748 12.2188i −0.533396 0.734157i 0.454247 0.890876i 0.349908π-0.349908\pi
−0.987643 + 0.156719i 0.949908π0.949908\pi
278278 5.41979i 0.325058i
279279 −0.0223278 + 29.9052i −0.00133673 + 1.79038i
280280 0 0
281281 2.01209 1.46187i 0.120031 0.0872078i −0.526150 0.850392i 0.676365π-0.676365\pi
0.646181 + 0.763184i 0.276365π0.276365\pi
282282 −8.05144 0.846240i −0.479456 0.0503929i
283283 4.49503 + 1.46052i 0.267202 + 0.0868192i 0.439554 0.898216i 0.355137π-0.355137\pi
−0.172352 + 0.985035i 0.555137π0.555137\pi
284284 −1.57426 + 2.72670i −0.0934153 + 0.161800i
285285 0 0
286286 2.40177 0.510512i 0.142020 0.0301872i
287287 −7.14881 + 2.32279i −0.421981 + 0.137110i
288288 −4.32766 + 20.3600i −0.255010 + 1.19973i
289289 −1.42893 13.5953i −0.0840546 0.799726i
290290 0 0
291291 −9.02071 4.01628i −0.528804 0.235439i
292292 −10.9602 24.6171i −0.641400 1.44061i
293293 7.83935 + 7.05858i 0.457980 + 0.412367i 0.865562 0.500802i 0.166961π-0.166961\pi
−0.407582 + 0.913169i 0.633628π0.633628\pi
294294 4.79497 + 3.48375i 0.279648 + 0.203177i
295295 0 0
296296 −2.86850 + 3.18579i −0.166728 + 0.185170i
297297 6.78443 + 15.2381i 0.393673 + 0.884203i
298298 −1.70817 + 3.83662i −0.0989517 + 0.222249i
299299 0.850314 + 0.944369i 0.0491749 + 0.0546143i
300300 0 0
301301 −8.90432 1.89267i −0.513237 0.109092i
302302 1.44459 0.469377i 0.0831271 0.0270096i
303303 −10.6578 50.1411i −0.612276 2.88053i
304304 3.46785 + 6.00650i 0.198895 + 0.344496i
305305 0 0
306306 −1.06438 + 3.27583i −0.0608467 + 0.187267i
307307 −2.63399 0.276844i −0.150330 0.0158003i 0.0290645 0.999578i 0.490747π-0.490747\pi
−0.179394 + 0.983777i 0.557414π0.557414\pi
308308 −2.90198 3.99424i −0.165356 0.227593i
309309 23.3600 1.32890
310310 0 0
311311 5.51283 0.312604 0.156302 0.987709i 0.450043π-0.450043\pi
0.156302 + 0.987709i 0.450043π0.450043\pi
312312 −6.65773 9.16358i −0.376920 0.518786i
313313 −26.5293 2.78834i −1.49953 0.157607i −0.681088 0.732201i 0.738493π-0.738493\pi
−0.818438 + 0.574595i 0.805160π0.805160\pi
314314 0.945290 2.90930i 0.0533458 0.164181i
315315 0 0
316316 −3.23474 5.60274i −0.181969 0.315179i
317317 −2.23302 10.5055i −0.125419 0.590050i −0.995304 0.0967957i 0.969141π-0.969141\pi
0.869885 0.493254i 0.164193π-0.164193\pi
318318 4.81291 1.56381i 0.269895 0.0876941i
319319 7.51318 + 1.59698i 0.420657 + 0.0894135i
320320 0 0
321321 23.5246 + 26.1267i 1.31301 + 1.45825i
322322 −0.0684017 + 0.153633i −0.00381188 + 0.00856162i
323323 1.57218 + 3.53117i 0.0874784 + 0.196480i
324324 4.69064 5.20948i 0.260591 0.289416i
325325 0 0
326326 −0.889309 0.646121i −0.0492543 0.0357853i
327327 1.35911 + 1.22374i 0.0751587 + 0.0676732i
328328 −3.84897 8.64492i −0.212524 0.477336i
329329 −7.87106 3.50442i −0.433945 0.193205i
330330 0 0
331331 −2.05373 19.5400i −0.112883 1.07401i −0.893518 0.449027i 0.851771π-0.851771\pi
0.780635 0.624987i 0.214896π-0.214896\pi
332332 −5.01478 + 23.5927i −0.275222 + 1.29482i
333333 16.0744 5.22289i 0.880872 0.286213i
334334 −4.59080 + 0.975804i −0.251197 + 0.0533936i
335335 0 0
336336 −5.12565 + 8.87788i −0.279627 + 0.484328i
337337 18.2401 + 5.92655i 0.993599 + 0.322840i 0.760305 0.649566i 0.225050π-0.225050\pi
0.233294 + 0.972406i 0.425050π0.425050\pi
338338 −1.65741 0.174200i −0.0901510 0.00947525i
339339 26.4510 19.2178i 1.43662 1.04376i
340340 0 0
341341 7.96520 10.9460i 0.431340 0.592757i
342342 3.99844i 0.216211i
343343 8.15999 + 11.2313i 0.440598 + 0.606431i
344344 1.19794 11.3976i 0.0645885 0.614519i
345345 0 0
346346 −3.34647 + 5.79626i −0.179907 + 0.311609i
347347 9.23180 5.32998i 0.495589 0.286128i −0.231301 0.972882i 0.574298π-0.574298\pi
0.726890 + 0.686754i 0.240965π0.240965\pi
348348 −3.56605 16.7769i −0.191160 0.899338i
349349 5.77910 + 17.7862i 0.309348 + 0.952075i 0.978019 + 0.208517i 0.0668636π0.0668636\pi
−0.668671 + 0.743559i 0.733136π0.733136\pi
350350 0 0
351351 2.06072 + 19.6064i 0.109993 + 1.04651i
352352 7.00216 6.30478i 0.373217 0.336046i
353353 −5.15020 + 11.5675i −0.274117 + 0.615678i −0.997175 0.0751097i 0.976069π-0.976069\pi
0.723058 + 0.690787i 0.242736π0.242736\pi
354354 −11.1596 + 4.96859i −0.593127 + 0.264077i
355355 0 0
356356 3.43001 + 2.49205i 0.181790 + 0.132078i
357357 −3.35812 + 4.62205i −0.177730 + 0.244625i
358358 0.0207182 + 0.0186548i 0.00109499 + 0.000985936i
359359 20.7175 9.22402i 1.09343 0.486825i 0.220853 0.975307i 0.429116π-0.429116\pi
0.872574 + 0.488482i 0.162449π0.162449\pi
360360 0 0
361361 −9.71104 10.7852i −0.511107 0.567642i
362362 0.755932 0.0794517i 0.0397309 0.00417589i
363363 −3.06095 + 14.4006i −0.160658 + 0.755837i
364364 −1.80319 5.54965i −0.0945129 0.290881i
365365 0 0
366366 −7.33880 12.7112i −0.383605 0.664424i
367367 −7.55147 4.35984i −0.394183 0.227582i 0.289788 0.957091i 0.406415π-0.406415\pi
−0.683971 + 0.729509i 0.739749π0.739749\pi
368368 1.37705 + 0.447430i 0.0717836 + 0.0233239i
369369 −3.89987 + 37.1048i −0.203019 + 1.93160i
370370 0 0
371371 5.38574 0.279614
372372 −29.5635 6.30699i −1.53280 0.327002i
373373 25.4134i 1.31586i −0.753081 0.657928i 0.771433π-0.771433\pi
0.753081 0.657928i 0.228567π-0.228567\pi
374374 1.26141 0.916471i 0.0652262 0.0473896i
375375 0 0
376376 3.35188 10.3160i 0.172860 0.532009i
377377 7.86200 + 4.53913i 0.404914 + 0.233777i
378378 −2.25943 + 1.30448i −0.116213 + 0.0670954i
379379 21.6150 4.59441i 1.11029 0.235999i 0.383961 0.923349i 0.374560π-0.374560\pi
0.726326 + 0.687350i 0.241226π0.241226\pi
380380 0 0
381381 0.333399 + 0.0708662i 0.0170806 + 0.00363059i
382382 −1.86696 + 0.196226i −0.0955220 + 0.0100398i
383383 −19.7993 + 17.8274i −1.01170 + 0.910938i −0.996037 0.0889398i 0.971652π-0.971652\pi
−0.0156617 + 0.999877i 0.504985π0.504985\pi
384384 −25.3039 11.2660i −1.29128 0.574916i
385385 0 0
386386 −0.501743 + 0.557242i −0.0255380 + 0.0283629i
387387 −26.5585 + 36.5547i −1.35005 + 1.85818i
388388 3.76430 5.18112i 0.191104 0.263032i
389389 8.66862 9.62748i 0.439517 0.488133i −0.482165 0.876081i 0.660149π-0.660149\pi
0.921681 + 0.387948i 0.126816π0.126816\pi
390390 0 0
391391 0.737176 + 0.328212i 0.0372806 + 0.0165984i
392392 −5.90132 + 5.31357i −0.298062 + 0.268376i
393393 16.6430 1.74925i 0.839528 0.0882379i
394394 −2.01980 0.429321i −0.101756 0.0216289i
395395 0 0
396396 −23.9701 + 5.09500i −1.20454 + 0.256033i
397397 −2.53508 + 1.46363i −0.127232 + 0.0734574i −0.562265 0.826957i 0.690070π-0.690070\pi
0.435033 + 0.900414i 0.356737π0.356737\pi
398398 2.10852 + 1.21736i 0.105691 + 0.0610205i
399399 −2.04944 + 6.30752i −0.102600 + 0.315771i
400400 0 0
401401 9.93025 7.21475i 0.495893 0.360287i −0.311553 0.950229i 0.600849π-0.600849\pi
0.807446 + 0.589942i 0.200849π0.200849\pi
402402 6.54572i 0.326471i
403403 12.9511 9.39479i 0.645142 0.467988i
404404 33.2464 1.65407
405405 0 0
406406 −0.125581 + 1.19482i −0.00623246 + 0.0592979i
407407 −7.27645 2.36426i −0.360680 0.117192i
408408 −6.22889 3.59625i −0.308376 0.178041i
409409 −8.59861 14.8932i −0.425174 0.736423i 0.571263 0.820767i 0.306454π-0.306454\pi
−0.996437 + 0.0843442i 0.973120π0.973120\pi
410410 0 0
411411 −10.5549 32.4848i −0.520637 1.60236i
412412 −3.14997 + 14.8195i −0.155188 + 0.730102i
413413 −12.9294 + 1.35893i −0.636213 + 0.0668687i
414414 0.558539 + 0.620320i 0.0274507 + 0.0304871i
415415 0 0
416416 10.1735 4.52955i 0.498799 0.222080i
417417 33.1594 + 29.8568i 1.62382 + 1.46210i
418418 1.06388 1.46431i 0.0520362 0.0716217i
419419 18.7251 + 13.6046i 0.914782 + 0.664628i 0.942220 0.334996i 0.108735π-0.108735\pi
−0.0274378 + 0.999624i 0.508735π0.508735\pi
420420 0 0
421421 26.6593 11.8695i 1.29929 0.578483i 0.363686 0.931522i 0.381518π-0.381518\pi
0.935609 + 0.353038i 0.114851π0.114851\pi
422422 −2.38836 + 5.36434i −0.116263 + 0.261132i
423423 −31.7808 + 28.6156i −1.54524 + 1.39134i
424424 0.708734 + 6.74315i 0.0344192 + 0.327476i
425425 0 0
426426 −0.527201 1.62256i −0.0255430 0.0786132i
427427 −3.24771 15.2793i −0.157168 0.739416i
428428 −19.7468 + 11.4008i −0.954498 + 0.551080i
429429 10.1076 17.5069i 0.487999 0.845239i
430430 0 0
431431 −3.17267 + 30.1859i −0.152822 + 1.45401i 0.602220 + 0.798330i 0.294283π0.294283\pi
−0.755042 + 0.655676i 0.772384π0.772384\pi
432432 13.2031 + 18.1725i 0.635235 + 0.874326i
433433 13.8400i 0.665107i 0.943084 + 0.332553i 0.107910π0.107910\pi
−0.943084 + 0.332553i 0.892090π0.892090\pi
434434 1.83292 + 1.06006i 0.0879830 + 0.0508846i
435435 0 0
436436 −0.959605 + 0.697194i −0.0459567 + 0.0333895i
437437 0.931602 + 0.0979154i 0.0445646 + 0.00468393i
438438 13.8867 + 4.51207i 0.663534 + 0.215595i
439439 6.46006 11.1892i 0.308322 0.534029i −0.669674 0.742656i 0.733566π-0.733566\pi
0.977995 + 0.208626i 0.0668993π0.0668993\pi
440440 0 0
441441 30.6242 6.50938i 1.45830 0.309970i
442442 1.75263 0.569463i 0.0833639 0.0270866i
443443 −4.93962 + 23.2391i −0.234688 + 1.10412i 0.690122 + 0.723693i 0.257557π0.257557\pi
−0.924810 + 0.380429i 0.875776π0.875776\pi
444444 1.78582 + 16.9909i 0.0847511 + 0.806353i
445445 0 0
446446 −2.01027 0.895031i −0.0951892 0.0423809i
447447 14.0631 + 31.5863i 0.665163 + 1.49398i
448448 −4.17089 3.75549i −0.197056 0.177430i
449449 −15.7054 11.4106i −0.741181 0.538500i 0.151900 0.988396i 0.451461π-0.451461\pi
−0.893081 + 0.449896i 0.851461π0.851461\pi
450450 0 0
451451 11.3009 12.5509i 0.532137 0.590998i
452452 8.62487 + 19.3718i 0.405680 + 0.911171i
453453 5.08632 11.4241i 0.238976 0.536749i
454454 1.84538 + 2.04950i 0.0866078 + 0.0961877i
455455 0 0
456456 −8.16695 1.73594i −0.382452 0.0812928i
457457 −23.1506 + 7.52208i −1.08294 + 0.351868i −0.795514 0.605935i 0.792799π-0.792799\pi
−0.287424 + 0.957803i 0.592799π0.592799\pi
458458 0.933283 + 4.39075i 0.0436094 + 0.205166i
459459 6.25931 + 10.8414i 0.292159 + 0.506035i
460460 0 0
461461 −11.8487 + 36.4665i −0.551848 + 1.69841i 0.152279 + 0.988338i 0.451339π0.451339\pi
−0.704126 + 0.710075i 0.748661π0.748661\pi
462462 2.66059 + 0.279639i 0.123782 + 0.0130100i
463463 −3.87603 5.33489i −0.180134 0.247934i 0.709396 0.704810i 0.248968π-0.248968\pi
−0.889530 + 0.456877i 0.848968π0.848968\pi
464464 10.3437 0.480195
465465 0 0
466466 4.46933 0.207038
467467 −22.5718 31.0674i −1.04450 1.43763i −0.893484 0.449096i 0.851746π-0.851746\pi
−0.151014 0.988532i 0.548254π-0.548254\pi
468468 −28.8046 3.02749i −1.33149 0.139946i
469469 −2.15270 + 6.62532i −0.0994024 + 0.305929i
470470 0 0
471471 −12.5922 21.8104i −0.580220 1.00497i
472472 −3.40287 16.0092i −0.156630 0.736885i
473473 19.4525 6.32051i 0.894429 0.290617i
474474 3.42895 + 0.728845i 0.157497 + 0.0334770i
475475 0 0
476476 −2.47938 2.75363i −0.113642 0.126212i
477477 10.8729 24.4210i 0.497838 1.11816i
478478 3.63421 + 8.16256i 0.166225 + 0.373347i
479479 −5.03531 + 5.59228i −0.230069 + 0.255518i −0.847115 0.531409i 0.821663π-0.821663\pi
0.617046 + 0.786927i 0.288329π0.288329\pi
480480 0 0
481481 −7.31567 5.31515i −0.333566 0.242350i
482482 0.616606 + 0.555195i 0.0280856 + 0.0252884i
483483 0.563141 + 1.26484i 0.0256238 + 0.0575520i
484484 −8.72293 3.88370i −0.396497 0.176532i
485485 0 0
486486 −0.358996 3.41562i −0.0162844 0.154936i
487487 5.20450 24.4852i 0.235838 1.10953i −0.687691 0.726004i 0.741375π-0.741375\pi
0.923529 0.383528i 0.125291π-0.125291\pi
488488 18.7029 6.07693i 0.846639 0.275090i
489489 −8.85217 + 1.88159i −0.400309 + 0.0850883i
490490 0 0
491491 19.8550 34.3899i 0.896044 1.55199i 0.0635377 0.997979i 0.479762π-0.479762\pi
0.832507 0.554015i 0.186905π-0.186905\pi
492492 −35.8670 11.6539i −1.61701 0.525399i
493493 5.73310 + 0.602573i 0.258206 + 0.0271385i
494494 1.73068 1.25741i 0.0778668 0.0565735i
495495 0 0
496496 7.42729 16.6485i 0.333495 0.747539i
497497 1.81567i 0.0814440i
498498 −7.68207 10.5735i −0.344242 0.473808i
499499 −2.47252 + 23.5245i −0.110685 + 1.05310i 0.788351 + 0.615226i 0.210935π0.210935\pi
−0.899036 + 0.437875i 0.855731π0.855731\pi
500500 0 0
501501 −19.3199 + 33.4630i −0.863148 + 1.49502i
502502 0.717241 0.414099i 0.0320120 0.0184822i
503503 −4.19699 19.7453i −0.187135 0.880400i −0.967064 0.254532i 0.918078π-0.918078\pi
0.779930 0.625867i 0.215255π-0.215255\pi
504504 −2.44685 7.53063i −0.108991 0.335441i
505505 0 0
506506 −0.0394968 0.375787i −0.00175585 0.0167058i
507507 −10.1962 + 9.18070i −0.452829 + 0.407729i
508508 −0.0899143 + 0.201951i −0.00398930 + 0.00896012i
509509 −10.8155 + 4.81536i −0.479387 + 0.213437i −0.632180 0.774821i 0.717840π-0.717840\pi
0.152793 + 0.988258i 0.451173π0.451173\pi
510510 0 0
511511 12.5717 + 9.13389i 0.556140 + 0.404060i
512512 12.7019 17.4827i 0.561351 0.772633i
513513 10.7995 + 9.72394i 0.476811 + 0.429322i
514514 8.35179 3.71845i 0.368381 0.164014i
515515 0 0
516516 −30.5611 33.9416i −1.34538 1.49419i
517517 19.2526 2.02354i 0.846731 0.0889950i
518518 0.248806 1.17054i 0.0109319 0.0514306i
519519 17.0275 + 52.4051i 0.747422 + 2.30033i
520520 0 0
521521 16.3742 + 28.3610i 0.717368 + 1.24252i 0.962039 + 0.272911i 0.0879865π0.0879865\pi
−0.244672 + 0.969606i 0.578680π0.578680\pi
522522 5.16425 + 2.98158i 0.226033 + 0.130500i
523523 28.0587 + 9.11682i 1.22692 + 0.398651i 0.849598 0.527431i 0.176845π-0.176845\pi
0.377323 + 0.926082i 0.376845π0.376845\pi
524524 −1.13451 + 10.7941i −0.0495611 + 0.471543i
525525 0 0
526526 8.06030 0.351446
527527 5.08650 8.79490i 0.221571 0.383112i
528528 23.0331i 1.00239i
529529 −18.4492 + 13.4041i −0.802138 + 0.582788i
530530 0 0
531531 −19.9404 + 61.3703i −0.865340 + 2.66324i
532532 −3.72510 2.15069i −0.161504 0.0932441i
533533 17.2868 9.98053i 0.748774 0.432305i
534534 −2.24713 + 0.477643i −0.0972430 + 0.0206696i
535535 0 0
536536 −8.57845 1.82340i −0.370532 0.0787591i
537537 0.228267 0.0239919i 0.00985047 0.00103533i
538538 −4.45217 + 4.00875i −0.191947 + 0.172830i
539539 −12.9472 5.76446i −0.557675 0.248293i
540540 0 0
541541 8.87657 9.85843i 0.381634 0.423847i −0.521470 0.853270i 0.674616π-0.674616\pi
0.903104 + 0.429423i 0.141283π0.141283\pi
542542 1.49689 2.06029i 0.0642968 0.0884970i
543543 3.67822 5.06264i 0.157848 0.217258i
544544 4.73179 5.25519i 0.202874 0.225314i
545545 0 0
546546 2.88853 + 1.28605i 0.123618 + 0.0550381i
547547 −28.0640 + 25.2689i −1.19993 + 1.08042i −0.205114 + 0.978738i 0.565756π0.565756\pi
−0.994817 + 0.101684i 0.967577π0.967577\pi
548548 22.0315 2.31560i 0.941137 0.0989175i
549549 −75.8388 16.1200i −3.23672 0.687986i
550550 0 0
551551 6.54568 1.39133i 0.278855 0.0592725i
552552 −1.50952 + 0.871520i −0.0642493 + 0.0370944i
553553 3.23095 + 1.86539i 0.137394 + 0.0793245i
554554 −1.64019 + 5.04800i −0.0696852 + 0.214469i
555555 0 0
556556 −23.4124 + 17.0101i −0.992907 + 0.721389i
557557 11.3637i 0.481496i −0.970588 0.240748i 0.922607π-0.922607\pi
0.970588 0.240748i 0.0773928π-0.0773928\pi
558558 8.50711 6.17108i 0.360135 0.261243i
559559 24.1743 1.02246
560560 0 0
561561 1.34179 12.7663i 0.0566505 0.538993i
562562 −0.831262 0.270094i −0.0350647 0.0113932i
563563 −17.4821 10.0933i −0.736781 0.425381i 0.0841167 0.996456i 0.473193π-0.473193\pi
−0.820898 + 0.571075i 0.806526π0.806526\pi
564564 −21.6140 37.4365i −0.910113 1.57636i
565565 0 0
566566 −0.513276 1.57970i −0.0215746 0.0663998i
567567 −0.840485 + 3.95417i −0.0352971 + 0.166060i
568568 2.27329 0.238933i 0.0953852 0.0100254i
569569 20.7361 + 23.0298i 0.869304 + 0.965460i 0.999662 0.0260074i 0.00827935π-0.00827935\pi
−0.130358 + 0.991467i 0.541613π0.541613\pi
570570 0 0
571571 −9.50060 + 4.22994i −0.397588 + 0.177017i −0.595784 0.803145i 0.703158π-0.703158\pi
0.198196 + 0.980162i 0.436492π0.436492\pi
572572 9.74330 + 8.77291i 0.407388 + 0.366814i
573573 −9.08427 + 12.5034i −0.379501 + 0.522338i
574574 2.13711 + 1.55270i 0.0892012 + 0.0648085i
575575 0 0
576576 −25.4492 + 11.3307i −1.06038 + 0.472113i
577577 −2.20201 + 4.94581i −0.0916711 + 0.205897i −0.953562 0.301197i 0.902614π-0.902614\pi
0.861891 + 0.507094i 0.169280π0.169280\pi
578578 −3.57019 + 3.21461i −0.148500 + 0.133710i
579579 0.645291 + 6.13953i 0.0268174 + 0.255150i
580580 0 0
581581 −4.29819 13.2285i −0.178319 0.548809i
582582 0.721492 + 3.39435i 0.0299068 + 0.140700i
583583 −10.4797 + 6.05046i −0.434025 + 0.250585i
584584 −9.78162 + 16.9423i −0.404766 + 0.701076i
585585 0 0
586586 0.387510 3.68691i 0.0160079 0.152305i
587587 7.38424 + 10.1635i 0.304780 + 0.419494i 0.933744 0.357940i 0.116521π-0.116521\pi
−0.628964 + 0.777434i 0.716521π0.716521\pi
588588 31.6471i 1.30510i
589589 2.46073 11.5345i 0.101393 0.475270i
590590 0 0
591591 −13.7535 + 9.99247i −0.565741 + 0.411035i
592592 −10.2467 1.07697i −0.421138 0.0442634i
593593 −25.7451 8.36510i −1.05723 0.343513i −0.271726 0.962375i 0.587594π-0.587594\pi
−0.785500 + 0.618861i 0.787594π0.787594\pi
594594 2.93098 5.07660i 0.120259 0.208295i
595595 0 0
596596 −21.9345 + 4.66233i −0.898473 + 0.190976i
597597 19.0636 6.19413i 0.780220 0.253509i
598598 0.0928516 0.436832i 0.00379698 0.0178634i
599599 −1.50051 14.2764i −0.0613094 0.583320i −0.981448 0.191727i 0.938591π-0.938591\pi
0.920139 0.391592i 0.128076π-0.128076\pi
600600 0 0
601601 0.584684 + 0.260318i 0.0238498 + 0.0106186i 0.418627 0.908158i 0.362512π-0.362512\pi
−0.394777 + 0.918777i 0.629178π0.629178\pi
602602 1.30122 + 2.92260i 0.0530339 + 0.119116i
603603 25.6958 + 23.1366i 1.04642 + 0.942197i
604604 6.56150 + 4.76721i 0.266984 + 0.193975i
605605 0 0
606606 −12.0543 + 13.3877i −0.489673 + 0.543837i
607607 −2.65104 5.95432i −0.107602 0.241679i 0.851717 0.524002i 0.175562π-0.175562\pi
−0.959319 + 0.282323i 0.908895π0.908895\pi
608608 3.33890 7.49929i 0.135410 0.304136i
609609 6.61834 + 7.35041i 0.268189 + 0.297854i
610610 0 0
611611 22.3802 + 4.75706i 0.905405 + 0.192450i
612612 −17.4915 + 5.68333i −0.707052 + 0.229735i
613613 2.17170 + 10.2171i 0.0877143 + 0.412663i 0.999995 + 0.00309833i 0.000986230π0.000986230\pi
−0.912281 + 0.409565i 0.865680π0.865680\pi
614614 0.465385 + 0.806070i 0.0187814 + 0.0325303i
615615 0 0
616616 −1.10762 + 3.40892i −0.0446274 + 0.137349i
617617 −21.5845 2.26862i −0.868958 0.0913311i −0.340453 0.940262i 0.610580π-0.610580\pi
−0.528505 + 0.848930i 0.677247π0.677247\pi
618618 −4.82540 6.64159i −0.194106 0.267164i
619619 −28.5478 −1.14743 −0.573716 0.819054i 0.694499π-0.694499\pi
−0.573716 + 0.819054i 0.694499π0.694499\pi
620620 0 0
621621 3.03377 0.121741
622622 −1.13877 1.56738i −0.0456604 0.0628462i
623623 −2.43155 0.255566i −0.0974178 0.0102390i
624624 8.41235 25.8906i 0.336764 1.03645i
625625 0 0
626626 4.68731 + 8.11866i 0.187343 + 0.324487i
627627 −3.09816 14.5757i −0.123729 0.582098i
628628 15.5344 5.04743i 0.619890 0.201414i
629629 −5.61660 1.19385i −0.223949 0.0476018i
630630 0 0
631631 18.2275 + 20.2436i 0.725624 + 0.805887i 0.987232 0.159287i 0.0509196π-0.0509196\pi
−0.261609 + 0.965174i 0.584253π0.584253\pi
632632 −1.91037 + 4.29075i −0.0759903 + 0.170677i
633633 19.6630 + 44.1638i 0.781533 + 1.75535i
634634 −2.52561 + 2.80498i −0.100305 + 0.111400i
635635 0 0
636636 21.8607 + 15.8828i 0.866835 + 0.629792i
637637 −12.4481 11.2083i −0.493210 0.444089i
638638 −1.09793 2.46599i −0.0434675 0.0976295i
639639 −8.23296 3.66555i −0.325691 0.145007i
640640 0 0
641641 −4.30742 40.9824i −0.170133 1.61871i −0.663013 0.748608i 0.730722π-0.730722\pi
0.492880 0.870097i 0.335944π-0.335944\pi
642642 2.56881 12.0853i 0.101383 0.476969i
643643 −29.3044 + 9.52156i −1.15565 + 0.375494i −0.823269 0.567651i 0.807852π-0.807852\pi
−0.332382 + 0.943145i 0.607852π0.607852\pi
644644 −0.878342 + 0.186697i −0.0346115 + 0.00735691i
645645 0 0
646646 0.679205 1.17642i 0.0267230 0.0462855i
647647 8.47978 + 2.75525i 0.333375 + 0.108320i 0.470921 0.882175i 0.343922π-0.343922\pi
−0.137547 + 0.990495i 0.543922π0.543922\pi
648648 −5.06138 0.531973i −0.198830 0.0208979i
649649 23.6317 17.1694i 0.927623 0.673958i
650650 0 0
651651 16.5830 5.37445i 0.649938 0.210641i
652652 5.86949i 0.229867i
653653 23.0655 + 31.7469i 0.902623 + 1.24235i 0.969624 + 0.244601i 0.0786569π0.0786569\pi
−0.0670010 + 0.997753i 0.521343π0.521343\pi
654654 0.0671825 0.639199i 0.00262704 0.0249946i
655655 0 0
656656 11.3718 19.6965i 0.443993 0.769018i
657657 66.7969 38.5652i 2.60600 1.50457i
658658 0.629540 + 2.96175i 0.0245420 + 0.115461i
659659 −10.1832 31.3407i −0.396681 1.22086i −0.927644 0.373465i 0.878170π-0.878170\pi
0.530963 0.847395i 0.321830π-0.321830\pi
660660 0 0
661661 0.0177359 + 0.168746i 0.000689846 + 0.00656345i 0.994861 0.101246i 0.0322830π-0.0322830\pi
−0.994172 + 0.107810i 0.965616π0.965616\pi
662662 −5.13127 + 4.62022i −0.199433 + 0.179570i
663663 6.17087 13.8600i 0.239657 0.538278i
664664 15.9969 7.12229i 0.620801 0.276398i
665665 0 0
666666 −4.80539 3.49132i −0.186205 0.135286i
667667 0.821147 1.13021i 0.0317950 0.0437620i
668668 −18.6236 16.7687i −0.720567 0.648801i
669669 −16.5503 + 7.36866i −0.639871 + 0.284889i
670670 0 0
671671 23.4846 + 26.0823i 0.906612 + 1.00689i
672672 12.0668 1.26827i 0.465487 0.0489246i
673673 3.03267 14.2676i 0.116901 0.549976i −0.880248 0.474514i 0.842624π-0.842624\pi
0.997149 0.0754613i 0.0240429π-0.0240429\pi
674674 −2.08278 6.41015i −0.0802258 0.246910i
675675 0 0
676676 −4.44929 7.70639i −0.171126 0.296400i
677677 −13.6545 7.88341i −0.524784 0.302984i 0.214106 0.976810i 0.431316π-0.431316\pi
−0.738890 + 0.673826i 0.764650π0.764650\pi
678678 −10.9278 3.55065i −0.419679 0.136362i
679679 −0.386039 + 3.67291i −0.0148148 + 0.140953i
680680 0 0
681681 22.7051 0.870063
682682 −4.75744 0.00355200i −0.182172 0.000136013i
683683 20.5935i 0.787988i −0.919113 0.393994i 0.871093π-0.871093\pi
0.919113 0.393994i 0.128907π-0.128907\pi
684684 −17.2724 + 12.5492i −0.660428 + 0.479829i
685685 0 0
686686 1.50763 4.64001i 0.0575616 0.177156i
687687 32.0048 + 18.4780i 1.22106 + 0.704979i
688688 23.8538 13.7720i 0.909418 0.525053i
689689 −13.9896 + 2.97359i −0.532962 + 0.113285i
690690 0 0
691691 5.82165 + 1.23743i 0.221466 + 0.0470741i 0.317308 0.948322i 0.397221π-0.397221\pi
−0.0958421 + 0.995397i 0.530554π0.530554\pi
692692 −35.5416 + 3.73557i −1.35109 + 0.142005i
693693 10.5019 9.45597i 0.398935 0.359203i
694694 −3.42238 1.52374i −0.129912 0.0578404i
695695 0 0
696696 −8.33206 + 9.25369i −0.315826 + 0.350760i
697697 7.45032 10.2545i 0.282201 0.388417i
698698 3.86312 5.31713i 0.146221 0.201256i
699699 24.6209 27.3443i 0.931248 1.03426i
700700 0 0
701701 −24.3281 10.8316i −0.918859 0.409103i −0.107871 0.994165i 0.534403π-0.534403\pi
−0.810988 + 0.585062i 0.801070π0.801070\pi
702702 5.14871 4.63592i 0.194326 0.174972i
703703 −6.62916 + 0.696753i −0.250024 + 0.0262785i
704704 12.3348 + 2.62185i 0.464886 + 0.0988146i
705705 0 0
706706 4.35268 0.925191i 0.163815 0.0348200i
707707 −16.6037 + 9.58617i −0.624448 + 0.360525i
708708 −56.4879 32.6133i −2.12295 1.22568i
709709 0.816662 2.51343i 0.0306704 0.0943938i −0.934550 0.355833i 0.884197π-0.884197\pi
0.965220 + 0.261439i 0.0841971π0.0841971\pi
710710 0 0
711711 14.9812 10.8845i 0.561839 0.408200i
712712 3.07802i 0.115354i
713713 −1.22948 2.13321i −0.0460445 0.0798892i
714714 2.00779 0.0751398
715715 0 0
716716 −0.0155603 + 0.148047i −0.000581518 + 0.00553277i
717717 69.9605 + 22.7315i 2.61272 + 0.848925i
718718 −6.90207 3.98491i −0.257583 0.148716i
719719 2.59912 + 4.50181i 0.0969308 + 0.167889i 0.910413 0.413701i 0.135764π-0.135764\pi
−0.813482 + 0.581590i 0.802431π0.802431\pi
720720 0 0
721721 −2.69986 8.30930i −0.100548 0.309455i
722722 −1.06041 + 4.98886i −0.0394645 + 0.185666i
723723 6.79359 0.714035i 0.252656 0.0265552i
724724 2.71572 + 3.01611i 0.100929 + 0.112093i
725725 0 0
726726 4.72660 2.10442i 0.175421 0.0781023i
727727 17.9889 + 16.1973i 0.667171 + 0.600723i 0.931514 0.363705i 0.118488π-0.118488\pi
−0.264343 + 0.964429i 0.585155π0.585155\pi
728728 −2.49007 + 3.42729i −0.0922882 + 0.127024i
729729 −31.9419 23.2071i −1.18303 0.859524i
730730 0 0
731731 14.0235 6.24366i 0.518677 0.230930i
732732 31.8767 71.5963i 1.17820 2.64628i
733733 29.9954 27.0080i 1.10790 0.997562i 0.107910 0.994161i 0.465584π-0.465584\pi
0.999994 0.00340093i 0.00108255π-0.00108255\pi
734734 0.320315 + 3.04759i 0.0118230 + 0.112489i
735735 0 0
736736 −0.529571 1.62985i −0.0195202 0.0600771i
737737 −3.25427 15.3101i −0.119872 0.563955i
738738 11.3550 6.55583i 0.417985 0.241324i
739739 3.04893 5.28089i 0.112157 0.194261i −0.804483 0.593976i 0.797558π-0.797558\pi
0.916640 + 0.399715i 0.130891π0.130891\pi
740740 0 0
741741 1.84095 17.5155i 0.0676292 0.643449i
742742 −1.11251 1.53125i −0.0408417 0.0562138i
743743 16.2263i 0.595284i −0.954678 0.297642i 0.903800π-0.903800\pi
0.954678 0.297642i 0.0962001π-0.0962001\pi
744744 8.91125 + 20.0553i 0.326702 + 0.735262i
745745 0 0
746746 −7.22540 + 5.24956i −0.264541 + 0.192200i
747747 −68.6603 7.21649i −2.51215 0.264038i
748748 7.91793 + 2.57269i 0.289508 + 0.0940670i
749749 6.57456 11.3875i 0.240229 0.416089i
750750 0 0
751751 −35.6481 + 7.57723i −1.30082 + 0.276497i −0.805697 0.592328i 0.798209π-0.798209\pi
−0.495119 + 0.868825i 0.664876π0.664876\pi
752752 24.7936 8.05593i 0.904130 0.293770i
753753 1.41763 6.66944i 0.0516614 0.243048i
754754 −0.333487 3.17292i −0.0121449 0.115551i
755755 0 0
756756 −12.7264 5.66615i −0.462854 0.206076i
757757 17.7183 + 39.7960i 0.643984 + 1.44641i 0.880148 + 0.474699i 0.157443π0.157443\pi
−0.236164 + 0.971713i 0.575890π0.575890\pi
758758 −5.77120 5.19641i −0.209619 0.188742i
759759 −2.51672 1.82851i −0.0913512 0.0663705i
760760 0 0
761761 2.20765 2.45184i 0.0800272 0.0888792i −0.701801 0.712373i 0.747621π-0.747621\pi
0.781828 + 0.623494i 0.214287π0.214287\pi
762762 −0.0487209 0.109429i −0.00176497 0.00396419i
763763 0.278214 0.624878i 0.0100720 0.0226221i
764764 −6.70714 7.44903i −0.242656 0.269497i
765765 0 0
766766 9.15848 + 1.94669i 0.330909 + 0.0703369i
767767 32.8342 10.6685i 1.18557 0.385216i
768768 −4.21607 19.8350i −0.152134 0.715735i
769769 −22.8568 39.5891i −0.824237 1.42762i −0.902501 0.430688i 0.858271π-0.858271\pi
0.0782634 0.996933i 0.475062π-0.475062\pi
770770 0 0
771771 23.2585 71.5823i 0.837635 2.57798i
772772 −3.98190 0.418515i −0.143312 0.0150627i
773773 17.6339 + 24.2710i 0.634249 + 0.872969i 0.998292 0.0584131i 0.0186041π-0.0186041\pi
−0.364044 + 0.931382i 0.618604π0.618604\pi
774774 15.8791 0.570764
775775 0 0
776776 −4.64943 −0.166905
777777 −5.79097 7.97058i −0.207750 0.285943i
778778 −4.52789 0.475900i −0.162333 0.0170618i
779779 4.54689 13.9939i 0.162909 0.501383i
780780 0 0
781781 2.03977 + 3.53298i 0.0729886 + 0.126420i
782782 −0.0589606 0.277388i −0.00210843 0.00991937i
783783 20.6122 6.69730i 0.736619 0.239342i
784784 −18.6684 3.96809i −0.666729 0.141718i
785785 0 0
786786 −3.93523 4.37051i −0.140365 0.155891i
787787 17.5840 39.4944i 0.626803 1.40782i −0.268899 0.963168i 0.586660π-0.586660\pi
0.895702 0.444654i 0.146673π-0.146673\pi
788788 −4.48459 10.0725i −0.159757 0.358820i
789789 44.4030 49.3145i 1.58079 1.75564i
790790 0 0
791791 −9.89298 7.18767i −0.351754 0.255564i
792792 13.2212 + 11.9045i 0.469796 + 0.423006i
793793 16.8721 + 37.8953i 0.599145 + 1.34570i
794794 0.939794 + 0.418423i 0.0333520 + 0.0148493i
795795 0 0
796796 1.35890 + 12.9291i 0.0481649 + 0.458259i
797797 4.74532 22.3250i 0.168088 0.790792i −0.810626 0.585564i 0.800873π-0.800873\pi
0.978714 0.205228i 0.0657935π-0.0657935\pi
798798 2.21667 0.720239i 0.0784691 0.0254962i
799799 14.2114 3.02072i 0.502763 0.106865i
800800 0 0
801801 −6.06773 + 10.5096i −0.214393 + 0.371339i
802802 −4.10252 1.33299i −0.144865 0.0470695i
803803 −34.7236 3.64960i −1.22537 0.128792i
804804 −28.2762 + 20.5438i −0.997223 + 0.724525i
805805 0 0
806806 −5.34635 1.74155i −0.188317 0.0613435i
807807 49.3229i 1.73625i
808808 −14.1872 19.5270i −0.499105 0.686959i
809809 −2.22002 + 21.1221i −0.0780517 + 0.742613i 0.883582 + 0.468276i 0.155125π0.155125\pi
−0.961634 + 0.274336i 0.911542π0.911542\pi
810810 0 0
811811 −1.06157 + 1.83869i −0.0372767 + 0.0645652i −0.884062 0.467370i 0.845202π-0.845202\pi
0.846785 + 0.531935i 0.178535π0.178535\pi
812812 −5.55551 + 3.20748i −0.194960 + 0.112560i
813813 −4.35913 20.5081i −0.152881 0.719250i
814814 0.830879 + 2.55718i 0.0291223 + 0.0896292i
815815 0 0
816816 −1.80693 17.1918i −0.0632553 0.601834i
817817 13.2426 11.9237i 0.463301 0.417158i
818818 −2.45818 + 5.52116i −0.0859482 + 0.193043i
819819 15.2584 6.79347i 0.533171 0.237383i
820820 0 0
821821 −33.8104 24.5647i −1.17999 0.857313i −0.187819 0.982204i 0.560142π-0.560142\pi
−0.992171 + 0.124891i 0.960142π0.960142\pi
822822 −7.05561 + 9.71121i −0.246093 + 0.338717i
823823 −12.1121 10.9058i −0.422203 0.380153i 0.430464 0.902608i 0.358350π-0.358350\pi
−0.852667 + 0.522454i 0.825016π0.825016\pi
824824 10.0483 4.47378i 0.350049 0.155852i
825825 0 0
826826 3.05714 + 3.39530i 0.106372 + 0.118138i
827827 −30.9192 + 3.24974i −1.07517 + 0.113005i −0.625524 0.780205i 0.715115π-0.715115\pi
−0.449642 + 0.893209i 0.648448π0.648448\pi
828828 −0.926674 + 4.35966i −0.0322041 + 0.151509i
829829 8.66756 + 26.6760i 0.301037 + 0.926496i 0.981126 + 0.193367i 0.0619409π0.0619409\pi
−0.680090 + 0.733129i 0.738059π0.738059\pi
830830 0 0
831831 21.8491 + 37.8437i 0.757936 + 1.31278i
832832 12.9075 + 7.45215i 0.447487 + 0.258357i
833833 −10.1160 3.28688i −0.350498 0.113884i
834834 1.63912 15.5951i 0.0567579 0.540015i
835835 0 0
836836 9.66453 0.334255
837837 4.02104 37.9848i 0.138988 1.31295i
838838 8.13409i 0.280987i
839839 −18.6621 + 13.5588i −0.644287 + 0.468102i −0.861320 0.508062i 0.830362π-0.830362\pi
0.217034 + 0.976164i 0.430362π0.430362\pi
840840 0 0
841841 −5.87746 + 18.0890i −0.202671 + 0.623757i
842842 −8.88160 5.12779i −0.306080 0.176715i
843843 −6.23179 + 3.59793i −0.214634 + 0.123919i
844844 −30.6687 + 6.51884i −1.05566 + 0.224388i
845845 0 0
846846 14.7007 + 3.12473i 0.505420 + 0.107430i
847847 5.47617 0.575568i 0.188163 0.0197768i
848848 −12.1101 + 10.9040i −0.415864 + 0.374446i
849849 −12.4925 5.56202i −0.428741 0.190888i
850850 0 0
851851 −0.931124 + 1.03412i −0.0319185 + 0.0354491i
852852 5.35449 7.36982i 0.183442 0.252486i
853853 −17.6458 + 24.2874i −0.604182 + 0.831585i −0.996083 0.0884221i 0.971818π-0.971818\pi
0.391901 + 0.920007i 0.371818π0.371818\pi
854854 −3.67326 + 4.07957i −0.125696 + 0.139600i
855855 0 0
856856 15.1227 + 6.73307i 0.516884 + 0.230132i
857857 40.5663 36.5261i 1.38572 1.24771i 0.450904 0.892572i 0.351102π-0.351102\pi
0.934815 0.355135i 0.115565π-0.115565\pi
858858 −7.06535 + 0.742598i −0.241207 + 0.0253519i
859859 9.13238 + 1.94115i 0.311593 + 0.0662311i 0.361054 0.932545i 0.382417π-0.382417\pi
−0.0494610 + 0.998776i 0.515750π0.515750\pi
860860 0 0
861861 21.2728 4.52167i 0.724974 0.154098i
862862 9.23768 5.33338i 0.314637 0.181656i
863863 11.5326 + 6.65836i 0.392575 + 0.226653i 0.683275 0.730161i 0.260555π-0.260555\pi
−0.290700 + 0.956814i 0.593888π0.593888\pi
864864 8.21560 25.2850i 0.279500 0.860214i
865865 0 0
866866 3.93491 2.85888i 0.133714 0.0971487i
867867 39.5520i 1.34326i
868868 1.17340 + 11.2449i 0.0398276 + 0.381676i
869869 −8.38250 −0.284357
870870 0 0
871871 1.93371 18.3980i 0.0655213 0.623394i
872872 0.818983 + 0.266104i 0.0277343 + 0.00901141i
873873 15.8751 + 9.16547i 0.537290 + 0.310204i
874874 −0.164599 0.285094i −0.00556766 0.00964346i
875875 0 0
876876 24.0925 + 74.1490i 0.814010 + 2.50526i
877877 −8.84998 + 41.6359i −0.298843 + 1.40594i 0.530728 + 0.847542i 0.321919π0.321919\pi
−0.829571 + 0.558402i 0.811415π0.811415\pi
878878 −4.51568 + 0.474617i −0.152397 + 0.0160175i
879879 −20.4225 22.6815i −0.688835 0.765029i
880880 0 0
881881 −5.27402 + 2.34814i −0.177686 + 0.0791110i −0.493652 0.869660i 0.664338π-0.664338\pi
0.315966 + 0.948771i 0.397672π0.397672\pi
882882 −8.17666 7.36230i −0.275323 0.247902i
883883 −15.9860 + 22.0029i −0.537973 + 0.740457i −0.988319 0.152397i 0.951301π-0.951301\pi
0.450346 + 0.892854i 0.351301π0.351301\pi
884884 7.96061 + 5.78372i 0.267744 + 0.194528i
885885 0 0
886886 7.62758 3.39602i 0.256254 0.114091i
887887 2.99834 6.73437i 0.100674 0.226118i −0.856185 0.516669i 0.827172π-0.827172\pi
0.956860 + 0.290551i 0.0938385π0.0938385\pi
888888 9.21742 8.29940i 0.309316 0.278510i
889889 −0.0133254 0.126783i −0.000446920 0.00425216i
890890 0 0
891891 −2.80677 8.63835i −0.0940304 0.289396i
892892 −2.44292 11.4930i −0.0817950 0.384815i
893893 14.6062 8.43290i 0.488778 0.282196i
894894 6.07548 10.5230i 0.203194 0.351943i
895895 0 0
896896 −1.08287 + 10.3028i −0.0361762 + 0.344193i
897897 −2.16112 2.97453i −0.0721578 0.0993166i
898898 6.82232i 0.227664i
899899 −13.0626 11.7793i −0.435663 0.392862i
900900 0 0
901901 −7.34737 + 5.33818i −0.244776 + 0.177841i
902902 −5.90278 0.620408i −0.196541 0.0206573i
903903 25.0493 + 8.13900i 0.833588 + 0.270849i
904904 7.69738 13.3322i 0.256011 0.443424i
905905 0 0
906906 −4.29869 + 0.913715i −0.142814 + 0.0303562i
907907 −15.6763 + 5.09354i −0.520523 + 0.169128i −0.557482 0.830189i 0.688233π-0.688233\pi
0.0369599 + 0.999317i 0.488233π0.488233\pi
908908 −3.06167 + 14.4040i −0.101605 + 0.478014i
909909 9.94714 + 94.6408i 0.329926 + 3.13904i
910910 0 0
911911 40.9333 + 18.2247i 1.35618 + 0.603810i 0.950648 0.310271i 0.100420π-0.100420\pi
0.405531 + 0.914081i 0.367087π0.367087\pi
912912 −8.16199 18.3321i −0.270271 0.607038i
913913 23.2247 + 20.9116i 0.768625 + 0.692073i
914914 6.92078 + 5.02824i 0.228919 + 0.166319i
915915 0 0
916916 −16.0380 + 17.8120i −0.529911 + 0.588526i
917917 −2.54575 5.71785i −0.0840681 0.188820i
918918 1.78942 4.01909i 0.0590595 0.132650i
919919 6.93006 + 7.69662i 0.228602 + 0.253888i 0.846523 0.532352i 0.178692π-0.178692\pi
−0.617921 + 0.786240i 0.712025π0.712025\pi
920920 0 0
921921 7.49544 + 1.59320i 0.246983 + 0.0524979i
922922 12.8155 4.16401i 0.422056 0.137134i
923923 1.00247 + 4.71626i 0.0329968 + 0.155238i
924924 7.14231 + 12.3708i 0.234965 + 0.406971i
925925 0 0
926926 −0.716131 + 2.20402i −0.0235335 + 0.0724287i
927927 −43.1282 4.53296i −1.41652 0.148882i
928928 −7.19606 9.90452i −0.236222 0.325132i
929929 −44.0624 −1.44564 −0.722820 0.691037i 0.757154π-0.757154\pi
−0.722820 + 0.691037i 0.757154π0.757154\pi
930930 0 0
931931 −12.3474 −0.404671
932932 14.0271 + 19.3066i 0.459472 + 0.632409i
933933 −15.8629 1.66725i −0.519327 0.0545834i
934934 −4.17034 + 12.8350i −0.136458 + 0.419974i
935935 0 0
936936 10.5136 + 18.2101i 0.343648 + 0.595216i
937937 7.18687 + 33.8116i 0.234785 + 1.10458i 0.924703 + 0.380689i 0.124313π0.124313\pi
−0.689918 + 0.723887i 0.742354π0.742354\pi
938938 2.32835 0.756528i 0.0760235 0.0247015i
939939 75.4933 + 16.0466i 2.46363 + 0.523661i
940940 0 0
941941 −14.8206 16.4600i −0.483138 0.536580i 0.451457 0.892293i 0.350905π-0.350905\pi
−0.934595 + 0.355713i 0.884238π0.884238\pi
942942 −3.59988 + 8.08546i −0.117290 + 0.263439i
943943 −1.24939 2.80617i −0.0406856 0.0913814i
944944 26.3211 29.2326i 0.856680 0.951440i
945945 0 0
946946 −5.81526 4.22504i −0.189071 0.137368i
947947 −20.8694 18.7909i −0.678165 0.610622i 0.256334 0.966588i 0.417485π-0.417485\pi
−0.934499 + 0.355966i 0.884152π0.884152\pi
948948 7.61334 + 17.0998i 0.247270 + 0.555377i
949949 −37.6985 16.7844i −1.22374 0.544846i
950950 0 0
951951 3.24818 + 30.9044i 0.105330 + 1.00214i
952952 −0.559300 + 2.63130i −0.0181270 + 0.0852809i
953953 7.29152 2.36916i 0.236196 0.0767446i −0.188527 0.982068i 0.560371π-0.560371\pi
0.424723 + 0.905323i 0.360371π0.360371\pi
954954 −9.18925 + 1.95324i −0.297513 + 0.0632383i
955955 0 0
956956 −23.8546 + 41.3173i −0.771512 + 1.33630i
957957 −21.1358 6.86743i −0.683222 0.221992i
958958 2.63009 + 0.276434i 0.0849745 + 0.00893118i
959959 −10.3352 + 7.50893i −0.333740 + 0.242476i
960960 0 0
961961 −28.3387 + 12.5665i −0.914152 + 0.405372i
962962 3.17789i 0.102459i
963963 −38.3622 52.8011i −1.23621 1.70149i
964964 −0.463100 + 4.40610i −0.0149154 + 0.141911i
965965 0 0
966966 0.243285 0.421383i 0.00782758 0.0135578i
967967 −1.60246 + 0.925182i −0.0515317 + 0.0297518i −0.525545 0.850766i 0.676138π-0.676138\pi
0.474013 + 0.880518i 0.342805π0.342805\pi
968968 1.44127 + 6.78063i 0.0463241 + 0.217938i
969969 −3.45592 10.6362i −0.111020 0.341685i
970970 0 0
971971 −5.16072 49.1010i −0.165615 1.57573i −0.689723 0.724074i 0.742268π-0.742268\pi
0.524107 0.851652i 0.324399π-0.324399\pi
972972 13.6281 12.2708i 0.437121 0.393585i
973973 6.78784 15.2457i 0.217608 0.488756i
974974 −8.03659 + 3.57812i −0.257509 + 0.114650i
975975 0 0
976976 38.2373 + 27.7810i 1.22395 + 0.889248i
977977 −20.9383 + 28.8192i −0.669877 + 0.922007i −0.999758 0.0220160i 0.992992π-0.992992\pi
0.329881 + 0.944023i 0.392992π0.392992\pi
978978 2.36353 + 2.12813i 0.0755773 + 0.0680501i
979979 5.01847 2.23437i 0.160391 0.0714107i
980980 0 0
981981 −2.27177 2.52306i −0.0725321 0.0805550i
982982 −13.8789 + 1.45874i −0.442895 + 0.0465501i
983983 1.32722 6.24409i 0.0423318 0.199156i −0.951900 0.306409i 0.900872π-0.900872\pi
0.994232 + 0.107254i 0.0342057π0.0342057\pi
984984 8.46068 + 26.0393i 0.269717 + 0.830103i
985985 0 0
986986 −1.01295 1.75448i −0.0322588 0.0558739i
987987 21.5887 + 12.4642i 0.687175 + 0.396740i
988988 10.8635 + 3.52977i 0.345614 + 0.112297i
989989 0.388855 3.69971i 0.0123649 0.117644i
990990 0 0
991991 −44.2919 −1.40698 −0.703489 0.710706i 0.748376π-0.748376\pi
−0.703489 + 0.710706i 0.748376π0.748376\pi
992992 −21.1087 + 4.47033i −0.670202 + 0.141933i
993993 56.8463i 1.80396i
994994 −0.516222 + 0.375058i −0.0163736 + 0.0118961i
995995 0 0
996996 21.5649 66.3699i 0.683310 2.10301i
997997 −4.60999 2.66158i −0.146000 0.0842931i 0.425221 0.905090i 0.360197π-0.360197\pi
−0.571220 + 0.820797i 0.693530π0.693530\pi
998998 7.19911 4.15641i 0.227884 0.131569i
999999 −21.1162 + 4.48839i −0.668087 + 0.142006i
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 775.2.ck.a.524.2 32
5.2 odd 4 775.2.bl.a.276.1 16
5.3 odd 4 31.2.g.a.28.2 yes 16
5.4 even 2 inner 775.2.ck.a.524.3 32
15.8 even 4 279.2.y.c.28.1 16
20.3 even 4 496.2.bg.c.369.1 16
31.10 even 15 inner 775.2.ck.a.599.3 32
155.3 even 60 961.2.d.q.531.2 16
155.8 odd 20 961.2.c.j.521.4 16
155.13 even 60 961.2.g.m.547.1 16
155.18 odd 60 961.2.g.s.547.1 16
155.23 even 20 961.2.c.i.521.4 16
155.28 odd 60 961.2.d.p.531.2 16
155.33 odd 20 961.2.g.k.732.2 16
155.38 odd 60 961.2.d.p.628.2 16
155.43 even 60 961.2.d.n.374.3 16
155.48 even 60 961.2.a.j.1.4 8
155.53 even 60 961.2.c.i.439.4 16
155.58 even 20 961.2.g.m.448.1 16
155.68 even 12 961.2.d.n.388.3 16
155.72 odd 60 775.2.bl.a.351.1 16
155.73 even 60 961.2.g.n.846.1 16
155.78 odd 20 961.2.g.t.844.1 16
155.83 even 60 961.2.g.l.816.2 16
155.88 even 12 961.2.g.j.235.2 16
155.98 odd 12 961.2.g.k.235.2 16
155.103 odd 60 31.2.g.a.10.2 16
155.108 even 20 961.2.g.n.844.1 16
155.113 odd 60 961.2.g.t.846.1 16
155.118 odd 12 961.2.d.o.388.3 16
155.123 even 4 961.2.g.l.338.2 16
155.128 odd 20 961.2.g.s.448.1 16
155.133 odd 60 961.2.c.j.439.4 16
155.134 even 30 inner 775.2.ck.a.599.2 32
155.138 odd 60 961.2.a.i.1.4 8
155.143 odd 60 961.2.d.o.374.3 16
155.148 even 60 961.2.d.q.628.2 16
155.153 even 20 961.2.g.j.732.2 16
465.203 odd 60 8649.2.a.be.1.5 8
465.293 even 60 8649.2.a.bf.1.5 8
465.413 even 60 279.2.y.c.10.1 16
620.103 even 60 496.2.bg.c.289.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.g.a.10.2 16 155.103 odd 60
31.2.g.a.28.2 yes 16 5.3 odd 4
279.2.y.c.10.1 16 465.413 even 60
279.2.y.c.28.1 16 15.8 even 4
496.2.bg.c.289.1 16 620.103 even 60
496.2.bg.c.369.1 16 20.3 even 4
775.2.bl.a.276.1 16 5.2 odd 4
775.2.bl.a.351.1 16 155.72 odd 60
775.2.ck.a.524.2 32 1.1 even 1 trivial
775.2.ck.a.524.3 32 5.4 even 2 inner
775.2.ck.a.599.2 32 155.134 even 30 inner
775.2.ck.a.599.3 32 31.10 even 15 inner
961.2.a.i.1.4 8 155.138 odd 60
961.2.a.j.1.4 8 155.48 even 60
961.2.c.i.439.4 16 155.53 even 60
961.2.c.i.521.4 16 155.23 even 20
961.2.c.j.439.4 16 155.133 odd 60
961.2.c.j.521.4 16 155.8 odd 20
961.2.d.n.374.3 16 155.43 even 60
961.2.d.n.388.3 16 155.68 even 12
961.2.d.o.374.3 16 155.143 odd 60
961.2.d.o.388.3 16 155.118 odd 12
961.2.d.p.531.2 16 155.28 odd 60
961.2.d.p.628.2 16 155.38 odd 60
961.2.d.q.531.2 16 155.3 even 60
961.2.d.q.628.2 16 155.148 even 60
961.2.g.j.235.2 16 155.88 even 12
961.2.g.j.732.2 16 155.153 even 20
961.2.g.k.235.2 16 155.98 odd 12
961.2.g.k.732.2 16 155.33 odd 20
961.2.g.l.338.2 16 155.123 even 4
961.2.g.l.816.2 16 155.83 even 60
961.2.g.m.448.1 16 155.58 even 20
961.2.g.m.547.1 16 155.13 even 60
961.2.g.n.844.1 16 155.108 even 20
961.2.g.n.846.1 16 155.73 even 60
961.2.g.s.448.1 16 155.128 odd 20
961.2.g.s.547.1 16 155.18 odd 60
961.2.g.t.844.1 16 155.78 odd 20
961.2.g.t.846.1 16 155.113 odd 60
8649.2.a.be.1.5 8 465.203 odd 60
8649.2.a.bf.1.5 8 465.293 even 60