Properties

Label 700.2.t.c.299.10
Level 700700
Weight 22
Character 700.299
Analytic conductor 5.5905.590
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [700,2,Mod(199,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.199"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 700=22527 700 = 2^{2} \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 700.t (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,0,0,2,0,0,0,0,16,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.589528141495.58952814149
Analytic rank: 00
Dimension: 3232
Relative dimension: 1616 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 299.10
Character χ\chi == 700.299
Dual form 700.2.t.c.199.10

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.334637+1.37405i)q2+(0.963833+0.556469i)q3+(1.77604+0.919616i)q4+(1.087151.13814i)q6+(1.264332.32410i)q7+(1.857932.13263i)q8+(0.880685+1.52539i)q9+(1.48417+0.856885i)q11+(1.200061.87467i)q12+2.45950q13+(2.770352.51499i)q14+(2.308613.26654i)q16+(3.109465.38574i)q17+(2.390670.699655i)q18+(0.108256+0.187505i)q19+(2.51190+1.53648i)q21+(1.674061.75258i)q22+(3.283285.68681i)q23+(2.97747+1.02162i)q24+(0.823038+3.37948i)q265.29911iq27+(4.38279+2.96499i)q28+2.47123q29+(0.08191310.141878i)q31+(5.26095+2.07905i)q32+(0.9536591.65179i)q33+(6.359756.07482i)q34+(0.1613543.51904i)q36+(6.665623.84840i)q37+(0.2938690.0860036i)q38+(2.37054+1.36863i)q398.34130iq41+(1.27063+3.96564i)q421.89449q43+(1.847932.88672i)q44+(8.91268+2.60838i)q46+(10.1364+5.85225i)q47+(0.407385+4.43307i)q48+(3.80292+5.87689i)q49+(5.99399+3.46063i)q51+(4.36816+2.26179i)q52+(11.2823+6.51382i)q53+(7.281251.77328i)q54+(2.60741+7.01437i)q560.240965iq57+(0.826965+3.39560i)q58+(2.143793.71315i)q59+(6.06251+3.50019i)q61+(0.1675360.160030i)q62+(4.65865+0.118198i)q63+(1.09621+7.92454i)q64+(2.58877+0.757629i)q66+(2.587084.48095i)q67+(10.4753+6.70576i)q68+7.30818iq695.04201iq71+(4.889340.955891i)q72+(3.807596.59493i)q73+(3.0573410.4467i)q74+(0.01983410.432571i)q76+(3.86797+2.36597i)q77+(2.673842.79925i)q78+(13.81257.97463i)q79+(0.306736+0.531282i)q81+(11.46142.79131i)q82+5.47827iq83+(5.874200.418869i)q84+(0.6339672.60313i)q86+(2.38185+1.37516i)q87+(4.58489+1.57315i)q88+(1.54471+0.891838i)q89+(3.109635.71612i)q91+(0.601545+13.1193i)q92+(0.157901+0.0911642i)q93+(4.64929+15.8863i)q94+(6.22760+0.923701i)q9610.5305q97+(9.347753.25878i)q983.01858iq99+O(q100)q+(0.334637 + 1.37405i) q^{2} +(-0.963833 + 0.556469i) q^{3} +(-1.77604 + 0.919616i) q^{4} +(-1.08715 - 1.13814i) q^{6} +(-1.26433 - 2.32410i) q^{7} +(-1.85793 - 2.13263i) q^{8} +(-0.880685 + 1.52539i) q^{9} +(-1.48417 + 0.856885i) q^{11} +(1.20006 - 1.87467i) q^{12} +2.45950 q^{13} +(2.77035 - 2.51499i) q^{14} +(2.30861 - 3.26654i) q^{16} +(-3.10946 - 5.38574i) q^{17} +(-2.39067 - 0.699655i) q^{18} +(-0.108256 + 0.187505i) q^{19} +(2.51190 + 1.53648i) q^{21} +(-1.67406 - 1.75258i) q^{22} +(3.28328 - 5.68681i) q^{23} +(2.97747 + 1.02162i) q^{24} +(0.823038 + 3.37948i) q^{26} -5.29911i q^{27} +(4.38279 + 2.96499i) q^{28} +2.47123 q^{29} +(-0.0819131 - 0.141878i) q^{31} +(5.26095 + 2.07905i) q^{32} +(0.953659 - 1.65179i) q^{33} +(6.35975 - 6.07482i) q^{34} +(0.161354 - 3.51904i) q^{36} +(-6.66562 - 3.84840i) q^{37} +(-0.293869 - 0.0860036i) q^{38} +(-2.37054 + 1.36863i) q^{39} -8.34130i q^{41} +(-1.27063 + 3.96564i) q^{42} -1.89449 q^{43} +(1.84793 - 2.88672i) q^{44} +(8.91268 + 2.60838i) q^{46} +(10.1364 + 5.85225i) q^{47} +(-0.407385 + 4.43307i) q^{48} +(-3.80292 + 5.87689i) q^{49} +(5.99399 + 3.46063i) q^{51} +(-4.36816 + 2.26179i) q^{52} +(-11.2823 + 6.51382i) q^{53} +(7.28125 - 1.77328i) q^{54} +(-2.60741 + 7.01437i) q^{56} -0.240965i q^{57} +(0.826965 + 3.39560i) q^{58} +(-2.14379 - 3.71315i) q^{59} +(6.06251 + 3.50019i) q^{61} +(0.167536 - 0.160030i) q^{62} +(4.65865 + 0.118198i) q^{63} +(-1.09621 + 7.92454i) q^{64} +(2.58877 + 0.757629i) q^{66} +(-2.58708 - 4.48095i) q^{67} +(10.4753 + 6.70576i) q^{68} +7.30818i q^{69} -5.04201i q^{71} +(4.88934 - 0.955891i) q^{72} +(-3.80759 - 6.59493i) q^{73} +(3.05734 - 10.4467i) q^{74} +(0.0198341 - 0.432571i) q^{76} +(3.86797 + 2.36597i) q^{77} +(-2.67384 - 2.79925i) q^{78} +(-13.8125 - 7.97463i) q^{79} +(0.306736 + 0.531282i) q^{81} +(11.4614 - 2.79131i) q^{82} +5.47827i q^{83} +(-5.87420 - 0.418869i) q^{84} +(-0.633967 - 2.60313i) q^{86} +(-2.38185 + 1.37516i) q^{87} +(4.58489 + 1.57315i) q^{88} +(1.54471 + 0.891838i) q^{89} +(-3.10963 - 5.71612i) q^{91} +(-0.601545 + 13.1193i) q^{92} +(0.157901 + 0.0911642i) q^{93} +(-4.64929 + 15.8863i) q^{94} +(-6.22760 + 0.923701i) q^{96} -10.5305 q^{97} +(-9.34775 - 3.25878i) q^{98} -3.01858i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+2q4+16q914q128q132q1414q16+54q1812q2136q24+30q26+32q28+40q29+60q3224q33+60q3660q3746q38+124q98+O(q100) 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/700Z)×\left(\mathbb{Z}/700\mathbb{Z}\right)^\times.

nn 101101 351351 477477
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1 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 0.334637 + 1.37405i 0.236624 + 0.971601i
33 −0.963833 + 0.556469i −0.556469 + 0.321278i −0.751727 0.659474i 0.770779π-0.770779\pi
0.195258 + 0.980752i 0.437446π0.437446\pi
44 −1.77604 + 0.919616i −0.888018 + 0.459808i
55 0 0
66 −1.08715 1.13814i −0.443827 0.464644i
77 −1.26433 2.32410i −0.477874 0.878429i
88 −1.85793 2.13263i −0.656876 0.753998i
99 −0.880685 + 1.52539i −0.293562 + 0.508463i
1010 0 0
1111 −1.48417 + 0.856885i −0.447493 + 0.258360i −0.706771 0.707442i 0.749849π-0.749849\pi
0.259278 + 0.965803i 0.416516π0.416516\pi
1212 1.20006 1.87467i 0.346429 0.541169i
1313 2.45950 0.682142 0.341071 0.940038i 0.389210π-0.389210\pi
0.341071 + 0.940038i 0.389210π0.389210\pi
1414 2.77035 2.51499i 0.740406 0.672160i
1515 0 0
1616 2.30861 3.26654i 0.577153 0.816636i
1717 −3.10946 5.38574i −0.754155 1.30623i −0.945794 0.324768i 0.894714π-0.894714\pi
0.191639 0.981465i 0.438620π-0.438620\pi
1818 −2.39067 0.699655i −0.563487 0.164910i
1919 −0.108256 + 0.187505i −0.0248357 + 0.0430167i −0.878176 0.478337i 0.841240π-0.841240\pi
0.853340 + 0.521354i 0.174573π0.174573\pi
2020 0 0
2121 2.51190 + 1.53648i 0.548141 + 0.335288i
2222 −1.67406 1.75258i −0.356911 0.373651i
2323 3.28328 5.68681i 0.684612 1.18578i −0.288947 0.957345i 0.593305π-0.593305\pi
0.973559 0.228437i 0.0733615π-0.0733615\pi
2424 2.97747 + 1.02162i 0.607774 + 0.208537i
2525 0 0
2626 0.823038 + 3.37948i 0.161411 + 0.662770i
2727 5.29911i 1.01981i
2828 4.38279 + 2.96499i 0.828269 + 0.560331i
2929 2.47123 0.458896 0.229448 0.973321i 0.426308π-0.426308\pi
0.229448 + 0.973321i 0.426308π0.426308\pi
3030 0 0
3131 −0.0819131 0.141878i −0.0147120 0.0254820i 0.858576 0.512687i 0.171350π-0.171350\pi
−0.873288 + 0.487205i 0.838016π0.838016\pi
3232 5.26095 + 2.07905i 0.930013 + 0.367527i
3333 0.953659 1.65179i 0.166011 0.287539i
3434 6.35975 6.07482i 1.09069 1.04182i
3535 0 0
3636 0.161354 3.51904i 0.0268924 0.586507i
3737 −6.66562 3.84840i −1.09582 0.632673i −0.160701 0.987003i 0.551375π-0.551375\pi
−0.935120 + 0.354331i 0.884709π0.884709\pi
3838 −0.293869 0.0860036i −0.0476718 0.0139516i
3939 −2.37054 + 1.36863i −0.379591 + 0.219157i
4040 0 0
4141 8.34130i 1.30269i −0.758781 0.651346i 0.774205π-0.774205\pi
0.758781 0.651346i 0.225795π-0.225795\pi
4242 −1.27063 + 3.96564i −0.196063 + 0.611912i
4343 −1.89449 −0.288907 −0.144454 0.989512i 0.546142π-0.546142\pi
−0.144454 + 0.989512i 0.546142π0.546142\pi
4444 1.84793 2.88672i 0.278586 0.435190i
4545 0 0
4646 8.91268 + 2.60838i 1.31410 + 0.384585i
4747 10.1364 + 5.85225i 1.47855 + 0.853639i 0.999706 0.0242630i 0.00772390π-0.00772390\pi
0.478840 + 0.877902i 0.341057π0.341057\pi
4848 −0.407385 + 4.43307i −0.0588010 + 0.639859i
4949 −3.80292 + 5.87689i −0.543274 + 0.839556i
5050 0 0
5151 5.99399 + 3.46063i 0.839327 + 0.484586i
5252 −4.36816 + 2.26179i −0.605754 + 0.313654i
5353 −11.2823 + 6.51382i −1.54974 + 0.894743i −0.551579 + 0.834123i 0.685974π0.685974\pi
−0.998161 + 0.0606196i 0.980692π0.980692\pi
5454 7.28125 1.77328i 0.990853 0.241312i
5555 0 0
5656 −2.60741 + 7.01437i −0.348430 + 0.937335i
5757 0.240965i 0.0319166i
5858 0.826965 + 3.39560i 0.108586 + 0.445864i
5959 −2.14379 3.71315i −0.279098 0.483411i 0.692063 0.721837i 0.256702π-0.256702\pi
−0.971161 + 0.238426i 0.923369π0.923369\pi
6060 0 0
6161 6.06251 + 3.50019i 0.776225 + 0.448154i 0.835091 0.550112i 0.185415π-0.185415\pi
−0.0588657 + 0.998266i 0.518748π0.518748\pi
6262 0.167536 0.160030i 0.0212771 0.0203239i
6363 4.65865 + 0.118198i 0.586934 + 0.0148916i
6464 −1.09621 + 7.92454i −0.137027 + 0.990567i
6565 0 0
6666 2.58877 + 0.757629i 0.318656 + 0.0932577i
6767 −2.58708 4.48095i −0.316062 0.547435i 0.663601 0.748087i 0.269027π-0.269027\pi
−0.979663 + 0.200652i 0.935694π0.935694\pi
6868 10.4753 + 6.70576i 1.27032 + 0.813193i
6969 7.30818i 0.879801i
7070 0 0
7171 5.04201i 0.598376i −0.954194 0.299188i 0.903284π-0.903284\pi
0.954194 0.299188i 0.0967158π-0.0967158\pi
7272 4.88934 0.955891i 0.576214 0.112653i
7373 −3.80759 6.59493i −0.445644 0.771878i 0.552453 0.833544i 0.313692π-0.313692\pi
−0.998097 + 0.0616659i 0.980359π0.980359\pi
7474 3.05734 10.4467i 0.355408 1.21441i
7575 0 0
7676 0.0198341 0.432571i 0.00227513 0.0496193i
7777 3.86797 + 2.36597i 0.440797 + 0.269627i
7878 −2.67384 2.79925i −0.302753 0.316953i
7979 −13.8125 7.97463i −1.55402 0.897216i −0.997808 0.0661781i 0.978919π-0.978919\pi
−0.556216 0.831038i 0.687747π-0.687747\pi
8080 0 0
8181 0.306736 + 0.531282i 0.0340817 + 0.0590313i
8282 11.4614 2.79131i 1.26570 0.308248i
8383 5.47827i 0.601318i 0.953732 + 0.300659i 0.0972066π0.0972066\pi
−0.953732 + 0.300659i 0.902793π0.902793\pi
8484 −5.87420 0.418869i −0.640928 0.0457024i
8585 0 0
8686 −0.633967 2.60313i −0.0683624 0.280703i
8787 −2.38185 + 1.37516i −0.255362 + 0.147433i
8888 4.58489 + 1.57315i 0.488751 + 0.167698i
8989 1.54471 + 0.891838i 0.163739 + 0.0945347i 0.579630 0.814880i 0.303197π-0.303197\pi
−0.415891 + 0.909414i 0.636530π0.636530\pi
9090 0 0
9191 −3.10963 5.71612i −0.325977 0.599213i
9292 −0.601545 + 13.1193i −0.0627154 + 1.36779i
9393 0.157901 + 0.0911642i 0.0163736 + 0.00945329i
9494 −4.64929 + 15.8863i −0.479537 + 1.63855i
9595 0 0
9696 −6.22760 + 0.923701i −0.635601 + 0.0942748i
9797 −10.5305 −1.06921 −0.534606 0.845101i 0.679540π-0.679540\pi
−0.534606 + 0.845101i 0.679540π0.679540\pi
9898 −9.34775 3.25878i −0.944265 0.329187i
9999 3.01858i 0.303379i
100100 0 0
101101 −0.389513 + 0.224885i −0.0387580 + 0.0223769i −0.519254 0.854620i 0.673790π-0.673790\pi
0.480496 + 0.876997i 0.340457π0.340457\pi
102102 −2.74928 + 9.39411i −0.272219 + 0.930156i
103103 −8.03841 4.64098i −0.792048 0.457289i 0.0486348 0.998817i 0.484513π-0.484513\pi
−0.840683 + 0.541527i 0.817846π0.817846\pi
104104 −4.56957 5.24519i −0.448083 0.514334i
105105 0 0
106106 −12.7258 13.3227i −1.23604 1.29401i
107107 9.26201 16.0423i 0.895392 1.55086i 0.0620738 0.998072i 0.480229π-0.480229\pi
0.833318 0.552793i 0.186438π-0.186438\pi
108108 4.87315 + 9.41141i 0.468919 + 0.905613i
109109 −3.48557 6.03718i −0.333857 0.578257i 0.649408 0.760441i 0.275017π-0.275017\pi
−0.983265 + 0.182183i 0.941684π0.941684\pi
110110 0 0
111111 8.56605 0.813054
112112 −10.5106 1.23545i −0.993163 0.116739i
113113 0.333646i 0.0313868i −0.999877 0.0156934i 0.995004π-0.995004\pi
0.999877 0.0156934i 0.00499557π-0.00499557\pi
114114 0.331098 0.0806358i 0.0310102 0.00755223i
115115 0 0
116116 −4.38900 + 2.27259i −0.407508 + 0.211004i
117117 −2.16604 + 3.75169i −0.200251 + 0.346844i
118118 4.38467 4.18824i 0.403642 0.385558i
119119 −8.58562 + 14.0361i −0.787043 + 1.28669i
120120 0 0
121121 −4.03150 + 6.98276i −0.366500 + 0.634796i
122122 −2.78071 + 9.50150i −0.251753 + 0.860225i
123123 4.64168 + 8.03962i 0.418526 + 0.724908i
124124 0.275954 + 0.176651i 0.0247814 + 0.0158638i
125125 0 0
126126 1.39654 + 6.44077i 0.124414 + 0.573790i
127127 −15.8806 −1.40918 −0.704589 0.709616i 0.748869π-0.748869\pi
−0.704589 + 0.709616i 0.748869π0.748869\pi
128128 −11.2556 + 1.14559i −0.994860 + 0.101257i
129129 1.82597 1.05423i 0.160768 0.0928195i
130130 0 0
131131 −1.60328 + 2.77697i −0.140080 + 0.242625i −0.927526 0.373758i 0.878069π-0.878069\pi
0.787447 + 0.616383i 0.211402π0.211402\pi
132132 −0.174724 + 3.81063i −0.0152078 + 0.331673i
133133 0.572654 + 0.0145293i 0.0496554 + 0.00125985i
134134 5.29133 5.05427i 0.457101 0.436622i
135135 0 0
136136 −5.70864 + 16.6376i −0.489512 + 1.42667i
137137 1.12893 0.651787i 0.0964508 0.0556859i −0.450999 0.892525i 0.648932π-0.648932\pi
0.547450 + 0.836839i 0.315599π0.315599\pi
138138 −10.0418 + 2.44558i −0.854816 + 0.208182i
139139 20.8813 1.77113 0.885563 0.464519i 0.153773π-0.153773\pi
0.885563 + 0.464519i 0.153773π0.153773\pi
140140 0 0
141141 −13.0264 −1.09702
142142 6.92798 1.68724i 0.581383 0.141590i
143143 −3.65031 + 2.10750i −0.305254 + 0.176238i
144144 2.94960 + 6.39833i 0.245800 + 0.533194i
145145 0 0
146146 7.78762 7.43873i 0.644508 0.615633i
147147 0.395068 7.78054i 0.0325846 0.641728i
148148 15.3774 + 0.705083i 1.26402 + 0.0579574i
149149 4.86747 8.43071i 0.398759 0.690670i −0.594814 0.803863i 0.702774π-0.702774\pi
0.993573 + 0.113193i 0.0361078π0.0361078\pi
150150 0 0
151151 −12.9360 + 7.46858i −1.05271 + 0.607784i −0.923408 0.383821i 0.874608π-0.874608\pi
−0.129306 + 0.991605i 0.541275π0.541275\pi
152152 0.601012 0.117501i 0.0487485 0.00953058i
153153 10.9538 0.885563
154154 −1.95660 + 6.10654i −0.157667 + 0.492079i
155155 0 0
156156 2.95155 4.61073i 0.236313 0.369154i
157157 4.11231 + 7.12273i 0.328198 + 0.568456i 0.982154 0.188076i 0.0602252π-0.0602252\pi
−0.653956 + 0.756532i 0.726892π0.726892\pi
158158 6.33540 21.6476i 0.504017 1.72219i
159159 7.24948 12.5565i 0.574921 0.995793i
160160 0 0
161161 −17.3679 0.440656i −1.36878 0.0347285i
162162 −0.627364 + 0.599257i −0.0492903 + 0.0470821i
163163 5.99330 10.3807i 0.469431 0.813079i −0.529958 0.848024i 0.677792π-0.677792\pi
0.999389 + 0.0349450i 0.0111256π0.0111256\pi
164164 7.67080 + 14.8145i 0.598989 + 1.15681i
165165 0 0
166166 −7.52742 + 1.83323i −0.584241 + 0.142286i
167167 14.8103i 1.14606i 0.819535 + 0.573029i 0.194232π0.194232\pi
−0.819535 + 0.573029i 0.805768π0.805768\pi
168168 −1.39017 8.21162i −0.107254 0.633540i
169169 −6.95088 −0.534683
170170 0 0
171171 −0.190679 0.330266i −0.0145816 0.0252561i
172172 3.36469 1.74221i 0.256555 0.132842i
173173 7.81044 13.5281i 0.593817 1.02852i −0.399896 0.916561i 0.630954π-0.630954\pi
0.993713 0.111960i 0.0357129π-0.0357129\pi
174174 −2.68660 2.81261i −0.203671 0.213224i
175175 0 0
176176 −0.627316 + 6.82631i −0.0472857 + 0.514553i
177177 4.13251 + 2.38591i 0.310618 + 0.179336i
178178 −0.708516 + 2.42095i −0.0531055 + 0.181458i
179179 −5.53306 + 3.19451i −0.413560 + 0.238769i −0.692318 0.721592i 0.743411π-0.743411\pi
0.278758 + 0.960361i 0.410077π0.410077\pi
180180 0 0
181181 1.18770i 0.0882808i −0.999025 0.0441404i 0.985945π-0.985945\pi
0.999025 0.0441404i 0.0140549π-0.0140549\pi
182182 6.81366 6.18561i 0.505062 0.458508i
183183 −7.79100 −0.575927
184184 −18.2280 + 3.56366i −1.34378 + 0.262716i
185185 0 0
186186 −0.0724249 + 0.247471i −0.00531045 + 0.0181455i
187187 9.22992 + 5.32890i 0.674958 + 0.389687i
188188 −23.3844 1.07222i −1.70549 0.0781996i
189189 −12.3157 + 6.69985i −0.895834 + 0.487342i
190190 0 0
191191 −9.14608 5.28049i −0.661787 0.382083i 0.131170 0.991360i 0.458126π-0.458126\pi
−0.792958 + 0.609277i 0.791460π0.791460\pi
192192 −3.35319 8.24794i −0.241996 0.595244i
193193 −4.68353 + 2.70403i −0.337128 + 0.194641i −0.659001 0.752142i 0.729021π-0.729021\pi
0.321874 + 0.946783i 0.395687π0.395687\pi
194194 −3.52390 14.4695i −0.253001 1.03885i
195195 0 0
196196 1.34964 13.9348i 0.0964025 0.995342i
197197 17.9504i 1.27892i 0.768826 + 0.639458i 0.220841π0.220841\pi
−0.768826 + 0.639458i 0.779159π0.779159\pi
198198 4.14769 1.01013i 0.294763 0.0717867i
199199 3.82538 + 6.62575i 0.271174 + 0.469687i 0.969163 0.246422i 0.0792548π-0.0792548\pi
−0.697989 + 0.716109i 0.745921π0.745921\pi
200200 0 0
201201 4.98702 + 2.87926i 0.351757 + 0.203087i
202202 −0.439349 0.459956i −0.0309125 0.0323624i
203203 −3.12447 5.74340i −0.219294 0.403108i
204204 −13.8280 0.634039i −0.968154 0.0443916i
205205 0 0
206206 3.68700 12.5982i 0.256885 0.877761i
207207 5.78307 + 10.0166i 0.401951 + 0.696200i
208208 5.67802 8.03405i 0.393700 0.557061i
209209 0.371053i 0.0256662i
210210 0 0
211211 15.5710i 1.07195i 0.844234 + 0.535975i 0.180056π0.180056\pi
−0.844234 + 0.535975i 0.819944π0.819944\pi
212212 14.0475 21.9442i 0.964787 1.50713i
213213 2.80572 + 4.85965i 0.192245 + 0.332978i
214214 25.1423 + 7.35815i 1.71869 + 0.502993i
215215 0 0
216216 −11.3010 + 9.84536i −0.768938 + 0.669892i
217217 −0.226173 + 0.369755i −0.0153536 + 0.0251006i
218218 7.12900 6.80962i 0.482837 0.461205i
219219 7.33975 + 4.23761i 0.495974 + 0.286351i
220220 0 0
221221 −7.64770 13.2462i −0.514440 0.891036i
222222 2.86652 + 11.7702i 0.192388 + 0.789964i
223223 11.4678i 0.767938i −0.923346 0.383969i 0.874557π-0.874557\pi
0.923346 0.383969i 0.125443π-0.125443\pi
224224 −1.81968 14.8556i −0.121582 0.992581i
225225 0 0
226226 0.458447 0.111650i 0.0304954 0.00742686i
227227 −7.75470 + 4.47718i −0.514697 + 0.297161i −0.734762 0.678325i 0.762706π-0.762706\pi
0.220065 + 0.975485i 0.429373π0.429373\pi
228228 0.221595 + 0.427963i 0.0146755 + 0.0283425i
229229 2.08431 + 1.20337i 0.137735 + 0.0795212i 0.567284 0.823522i 0.307994π-0.307994\pi
−0.429549 + 0.903043i 0.641328π0.641328\pi
230230 0 0
231231 −5.04467 0.127993i −0.331915 0.00842129i
232232 −4.59137 5.27022i −0.301438 0.346007i
233233 −2.21768 1.28038i −0.145285 0.0838803i 0.425595 0.904914i 0.360065π-0.360065\pi
−0.570880 + 0.821033i 0.693398π0.693398\pi
234234 −5.87986 1.72080i −0.384378 0.112492i
235235 0 0
236236 7.22213 + 4.62323i 0.470120 + 0.300947i
237237 17.7505 1.15302
238238 −22.1594 7.10010i −1.43638 0.460231i
239239 6.31200i 0.408289i −0.978941 0.204145i 0.934559π-0.934559\pi
0.978941 0.204145i 0.0654413π-0.0654413\pi
240240 0 0
241241 8.33650 4.81308i 0.537001 0.310038i −0.206862 0.978370i 0.566325π-0.566325\pi
0.743863 + 0.668332i 0.232992π0.232992\pi
242242 −10.9438 3.20280i −0.703491 0.205884i
243243 13.1762 + 7.60728i 0.845254 + 0.488008i
244244 −13.9861 0.641286i −0.895367 0.0410542i
245245 0 0
246246 −9.49358 + 9.06825i −0.605288 + 0.578171i
247247 −0.266256 + 0.461169i −0.0169415 + 0.0293435i
248248 −0.150384 + 0.438289i −0.00954938 + 0.0278314i
249249 −3.04848 5.28013i −0.193190 0.334615i
250250 0 0
251251 24.9508 1.57488 0.787440 0.616391i 0.211406π-0.211406\pi
0.787440 + 0.616391i 0.211406π0.211406\pi
252252 −8.38262 + 4.07424i −0.528056 + 0.256653i
253253 11.2536i 0.707506i
254254 −5.31424 21.8208i −0.333445 1.36916i
255255 0 0
256256 −5.34062 15.0824i −0.333789 0.942648i
257257 8.48813 14.7019i 0.529475 0.917078i −0.469934 0.882702i 0.655722π-0.655722\pi
0.999409 0.0343764i 0.0109445π-0.0109445\pi
258258 2.05960 + 2.15620i 0.128225 + 0.134239i
259259 −0.516501 + 20.3573i −0.0320938 + 1.26494i
260260 0 0
261261 −2.17638 + 3.76960i −0.134714 + 0.233332i
262262 −4.35222 1.27372i −0.268881 0.0786906i
263263 7.51675 + 13.0194i 0.463503 + 0.802810i 0.999133 0.0416428i 0.0132591π-0.0132591\pi
−0.535630 + 0.844453i 0.679926π0.679926\pi
264264 −5.29448 + 1.03510i −0.325853 + 0.0637059i
265265 0 0
266266 0.171667 + 0.791719i 0.0105256 + 0.0485434i
267267 −1.98512 −0.121487
268268 8.71550 + 5.57921i 0.532384 + 0.340805i
269269 27.2203 15.7157i 1.65965 0.958201i 0.686778 0.726867i 0.259025π-0.259025\pi
0.972875 0.231333i 0.0743088π-0.0743088\pi
270270 0 0
271271 1.65885 2.87322i 0.100768 0.174536i −0.811233 0.584723i 0.801203π-0.801203\pi
0.912001 + 0.410187i 0.134537π0.134537\pi
272272 −24.7713 2.27640i −1.50198 0.138027i
273273 6.17800 + 3.77898i 0.373910 + 0.228714i
274274 1.27337 + 1.33309i 0.0769270 + 0.0805351i
275275 0 0
276276 −6.72072 12.9796i −0.404540 0.781280i
277277 12.7703 7.37294i 0.767293 0.442997i −0.0646150 0.997910i 0.520582π-0.520582\pi
0.831908 + 0.554913i 0.187249π0.187249\pi
278278 6.98764 + 28.6919i 0.419091 + 1.72083i
279279 0.288558 0.0172755
280280 0 0
281281 20.5438 1.22554 0.612769 0.790262i 0.290056π-0.290056\pi
0.612769 + 0.790262i 0.290056π0.290056\pi
282282 −4.35911 17.8989i −0.259581 1.06587i
283283 −24.1069 + 13.9181i −1.43301 + 0.827346i −0.997349 0.0727665i 0.976817π-0.976817\pi
−0.435657 + 0.900113i 0.643484π0.643484\pi
284284 4.63671 + 8.95479i 0.275138 + 0.531369i
285285 0 0
286286 −4.11735 4.31046i −0.243464 0.254883i
287287 −19.3861 + 10.5462i −1.14432 + 0.622522i
288288 −7.80459 + 6.19401i −0.459890 + 0.364986i
289289 −10.8375 + 18.7710i −0.637498 + 1.10418i
290290 0 0
291291 10.1497 5.85991i 0.594983 0.343514i
292292 12.8272 + 8.21132i 0.750656 + 0.480531i
293293 4.28428 0.250290 0.125145 0.992138i 0.460060π-0.460060\pi
0.125145 + 0.992138i 0.460060π0.460060\pi
294294 10.8231 2.06081i 0.631214 0.120189i
295295 0 0
296296 4.17703 + 21.3653i 0.242785 + 1.24183i
297297 4.54072 + 7.86477i 0.263480 + 0.456360i
298298 13.2131 + 3.86693i 0.765412 + 0.224005i
299299 8.07522 13.9867i 0.467002 0.808871i
300300 0 0
301301 2.39527 + 4.40300i 0.138061 + 0.253785i
302302 −14.5911 15.2754i −0.839621 0.879001i
303303 0.250283 0.433504i 0.0143784 0.0249041i
304304 0.362573 + 0.786501i 0.0207950 + 0.0451089i
305305 0 0
306306 3.66555 + 15.0511i 0.209545 + 0.860414i
307307 14.3171i 0.817117i 0.912732 + 0.408559i 0.133968π0.133968\pi
−0.912732 + 0.408559i 0.866032π0.866032\pi
308308 −9.04545 0.645000i −0.515412 0.0367523i
309309 10.3302 0.587667
310310 0 0
311311 −12.8315 22.2249i −0.727609 1.26026i −0.957891 0.287132i 0.907298π-0.907298\pi
0.230281 0.973124i 0.426035π-0.426035\pi
312312 7.32308 + 2.51267i 0.414588 + 0.142252i
313313 −16.2527 + 28.1505i −0.918656 + 1.59116i −0.117196 + 0.993109i 0.537391π0.537391\pi
−0.801459 + 0.598049i 0.795943π0.795943\pi
314314 −8.41088 + 8.03406i −0.474653 + 0.453388i
315315 0 0
316316 31.8650 + 1.46107i 1.79255 + 0.0821915i
317317 −2.52937 1.46033i −0.142064 0.0820205i 0.427284 0.904118i 0.359471π-0.359471\pi
−0.569347 + 0.822097i 0.692804π0.692804\pi
318318 19.6792 + 5.75931i 1.10355 + 0.322966i
319319 −3.66772 + 2.11756i −0.205353 + 0.118561i
320320 0 0
321321 20.6161i 1.15068i
322322 −5.20645 24.0119i −0.290144 1.33813i
323323 1.34647 0.0749198
324324 −1.03335 0.661497i −0.0574083 0.0367498i
325325 0 0
326326 16.2692 + 4.76134i 0.901067 + 0.263706i
327327 6.71901 + 3.87922i 0.371562 + 0.214522i
328328 −17.7889 + 15.4975i −0.982228 + 0.855708i
329329 0.785443 30.9573i 0.0433029 1.70673i
330330 0 0
331331 3.41964 + 1.97433i 0.187960 + 0.108519i 0.591027 0.806652i 0.298723π-0.298723\pi
−0.403067 + 0.915170i 0.632056π0.632056\pi
332332 −5.03790 9.72960i −0.276491 0.533981i
333333 11.7406 6.77845i 0.643382 0.371457i
334334 −20.3502 + 4.95608i −1.11351 + 0.271185i
335335 0 0
336336 10.8180 4.65808i 0.590170 0.254119i
337337 10.0467i 0.547280i −0.961832 0.273640i 0.911772π-0.911772\pi
0.961832 0.273640i 0.0882277π-0.0882277\pi
338338 −2.32602 9.55087i −0.126519 0.519499i
339339 0.185664 + 0.321579i 0.0100839 + 0.0174658i
340340 0 0
341341 0.243146 + 0.140380i 0.0131671 + 0.00760201i
342342 0.389995 0.372522i 0.0210885 0.0201437i
343343 18.4667 + 1.40802i 0.997106 + 0.0760258i
344344 3.51983 + 4.04025i 0.189776 + 0.217836i
345345 0 0
346346 21.2019 + 6.20496i 1.13982 + 0.333581i
347347 −0.0100550 0.0174157i −0.000539780 0.000934926i 0.865755 0.500467i 0.166838π-0.166838\pi
−0.866295 + 0.499532i 0.833505π0.833505\pi
348348 2.96564 4.63274i 0.158975 0.248341i
349349 5.60366i 0.299957i 0.988689 + 0.149978i 0.0479204π0.0479204\pi
−0.988689 + 0.149978i 0.952080π0.952080\pi
350350 0 0
351351 13.0331i 0.695657i
352352 −9.58963 + 1.42237i −0.511129 + 0.0758126i
353353 −12.7422 22.0701i −0.678198 1.17467i −0.975523 0.219897i 0.929428π-0.929428\pi
0.297325 0.954776i 0.403905π-0.403905\pi
354354 −1.89547 + 6.47669i −0.100743 + 0.344232i
355355 0 0
356356 −3.56361 0.163398i −0.188871 0.00866007i
357357 0.464459 18.3061i 0.0245818 0.968860i
358358 −6.24099 6.53371i −0.329847 0.345317i
359359 16.7562 + 9.67422i 0.884361 + 0.510586i 0.872094 0.489339i 0.162762π-0.162762\pi
0.0122672 + 0.999925i 0.496095π0.496095\pi
360360 0 0
361361 9.47656 + 16.4139i 0.498766 + 0.863889i
362362 1.63196 0.397447i 0.0857737 0.0208893i
363363 8.97361i 0.470993i
364364 10.7795 + 7.29238i 0.564997 + 0.382225i
365365 0 0
366366 −2.60715 10.7052i −0.136278 0.559571i
367367 −14.9780 + 8.64757i −0.781846 + 0.451399i −0.837084 0.547074i 0.815742π-0.815742\pi
0.0552378 + 0.998473i 0.482408π0.482408\pi
368368 −10.9964 23.8536i −0.573227 1.24346i
369369 12.7237 + 7.34606i 0.662372 + 0.382420i
370370 0 0
371371 29.4034 + 17.9855i 1.52655 + 0.933762i
372372 −0.364274 0.0167026i −0.0188867 0.000865990i
373373 9.62126 + 5.55483i 0.498170 + 0.287618i 0.727957 0.685622i 0.240470π-0.240470\pi
−0.229788 + 0.973241i 0.573803π0.573803\pi
374374 −4.23351 + 14.4656i −0.218910 + 0.748000i
375375 0 0
376376 −6.35201 32.4902i −0.327580 1.67556i
377377 6.07799 0.313032
378378 −13.3272 14.6804i −0.685478 0.755076i
379379 14.3198i 0.735558i 0.929913 + 0.367779i 0.119882π0.119882\pi
−0.929913 + 0.367779i 0.880118π0.880118\pi
380380 0 0
381381 15.3063 8.83707i 0.784164 0.452737i
382382 4.19506 14.3342i 0.214638 0.733403i
383383 9.05330 + 5.22693i 0.462602 + 0.267084i 0.713138 0.701024i 0.247273π-0.247273\pi
−0.250536 + 0.968107i 0.580607π0.580607\pi
384384 10.2110 7.36753i 0.521077 0.375972i
385385 0 0
386386 −5.28276 5.53054i −0.268886 0.281497i
387387 1.66845 2.88984i 0.0848121 0.146899i
388388 18.7026 9.68403i 0.949480 0.491632i
389389 −15.0629 26.0897i −0.763718 1.32280i −0.940922 0.338624i 0.890038π-0.890038\pi
0.177204 0.984174i 0.443295π-0.443295\pi
390390 0 0
391391 −40.8369 −2.06521
392392 19.5988 2.80862i 0.989887 0.141857i
393393 3.56871i 0.180018i
394394 −24.6648 + 6.00688i −1.24260 + 0.302622i
395395 0 0
396396 2.77594 + 5.36111i 0.139496 + 0.269406i
397397 −6.71896 + 11.6376i −0.337215 + 0.584073i −0.983908 0.178677i 0.942818π-0.942818\pi
0.646693 + 0.762750i 0.276151π0.276151\pi
398398 −7.82401 + 7.47349i −0.392182 + 0.374612i
399399 −0.560028 + 0.304660i −0.0280365 + 0.0152521i
400400 0 0
401401 14.4423 25.0149i 0.721216 1.24918i −0.239297 0.970946i 0.576917π-0.576917\pi
0.960513 0.278236i 0.0897497π-0.0897497\pi
402402 −2.28741 + 7.81593i −0.114086 + 0.389823i
403403 −0.201465 0.348948i −0.0100357 0.0173823i
404404 0.484981 0.757607i 0.0241287 0.0376924i
405405 0 0
406406 6.84617 6.21513i 0.339770 0.308452i
407407 13.1905 0.653830
408408 −3.75616 19.2126i −0.185957 0.951164i
409409 22.4328 12.9516i 1.10923 0.640413i 0.170599 0.985341i 0.445430π-0.445430\pi
0.938629 + 0.344927i 0.112096π0.112096\pi
410410 0 0
411411 −0.725398 + 1.25643i −0.0357813 + 0.0619749i
412412 18.5444 + 0.850295i 0.913619 + 0.0418910i
413413 −5.91929 + 9.67706i −0.291269 + 0.476177i
414414 −11.8281 + 11.2982i −0.581318 + 0.555274i
415415 0 0
416416 12.9393 + 5.11341i 0.634400 + 0.250705i
417417 −20.1260 + 11.6198i −0.985577 + 0.569023i
418418 0.509846 0.124168i 0.0249374 0.00607325i
419419 28.1022 1.37288 0.686441 0.727185i 0.259172π-0.259172\pi
0.686441 + 0.727185i 0.259172π0.259172\pi
420420 0 0
421421 15.6269 0.761608 0.380804 0.924656i 0.375647π-0.375647\pi
0.380804 + 0.924656i 0.375647π0.375647\pi
422422 −21.3953 + 5.21062i −1.04151 + 0.253649i
423423 −17.8539 + 10.3080i −0.868088 + 0.501191i
424424 34.8532 + 11.9587i 1.69262 + 0.580765i
425425 0 0
426426 −5.73851 + 5.48142i −0.278032 + 0.265576i
427427 0.469768 18.5153i 0.0227337 0.896019i
428428 −1.69694 + 37.0092i −0.0820245 + 1.78890i
429429 2.34552 4.06256i 0.113243 0.196142i
430430 0 0
431431 −17.2771 + 9.97495i −0.832210 + 0.480477i −0.854609 0.519273i 0.826203π-0.826203\pi
0.0223988 + 0.999749i 0.492870π0.492870\pi
432432 −17.3098 12.2336i −0.832817 0.588589i
433433 11.8294 0.568487 0.284243 0.958752i 0.408258π-0.408258\pi
0.284243 + 0.958752i 0.408258π0.408258\pi
434434 −0.583749 0.187039i −0.0280208 0.00897818i
435435 0 0
436436 11.7424 + 7.51687i 0.562359 + 0.359993i
437437 0.710872 + 1.23127i 0.0340056 + 0.0588995i
438438 −3.36654 + 11.5033i −0.160860 + 0.549647i
439439 13.9474 24.1577i 0.665675 1.15298i −0.313427 0.949612i 0.601477π-0.601477\pi
0.979102 0.203371i 0.0651897π-0.0651897\pi
440440 0 0
441441 −5.61538 10.9766i −0.267399 0.522696i
442442 15.6418 14.9410i 0.744003 0.710671i
443443 −9.59955 + 16.6269i −0.456088 + 0.789968i −0.998750 0.0499830i 0.984083π-0.984083\pi
0.542662 + 0.839951i 0.317417π0.317417\pi
444444 −15.2136 + 7.87748i −0.722007 + 0.373849i
445445 0 0
446446 15.7573 3.83753i 0.746130 0.181713i
447447 10.8344i 0.512449i
448448 19.8034 7.47156i 0.935624 0.352998i
449449 4.94035 0.233150 0.116575 0.993182i 0.462809π-0.462809\pi
0.116575 + 0.993182i 0.462809π0.462809\pi
450450 0 0
451451 7.14753 + 12.3799i 0.336564 + 0.582946i
452452 0.306826 + 0.592568i 0.0144319 + 0.0278720i
453453 8.31206 14.3969i 0.390535 0.676426i
454454 −8.74688 9.15713i −0.410511 0.429765i
455455 0 0
456456 −0.513889 + 0.447696i −0.0240651 + 0.0209653i
457457 22.6243 + 13.0622i 1.05832 + 0.611022i 0.924967 0.380046i 0.124092π-0.124092\pi
0.133354 + 0.991068i 0.457425π0.457425\pi
458458 −0.956014 + 3.26664i −0.0446716 + 0.152640i
459459 −28.5396 + 16.4774i −1.33212 + 0.769097i
460460 0 0
461461 13.3894i 0.623609i 0.950146 + 0.311804i 0.100933π0.100933\pi
−0.950146 + 0.311804i 0.899067π0.899067\pi
462462 −1.51226 6.97447i −0.0703568 0.324482i
463463 −16.4019 −0.762259 −0.381130 0.924522i 0.624465π-0.624465\pi
−0.381130 + 0.924522i 0.624465π0.624465\pi
464464 5.70512 8.07239i 0.264853 0.374751i
465465 0 0
466466 1.01719 3.47567i 0.0471203 0.161007i
467467 −10.3345 5.96663i −0.478224 0.276103i 0.241452 0.970413i 0.422376π-0.422376\pi
−0.719676 + 0.694310i 0.755710π0.755710\pi
468468 0.396850 8.65507i 0.0183444 0.400081i
469469 −7.14326 + 11.6781i −0.329845 + 0.539242i
470470 0 0
471471 −7.92716 4.57675i −0.365264 0.210885i
472472 −3.93577 + 11.4707i −0.181159 + 0.527981i
473473 2.81175 1.62336i 0.129284 0.0746423i
474474 5.93998 + 24.3902i 0.272832 + 1.12028i
475475 0 0
476476 2.34057 32.8241i 0.107280 1.50449i
477477 22.9465i 1.05065i
478478 8.67301 2.11223i 0.396694 0.0966110i
479479 −18.5889 32.1969i −0.849347 1.47111i −0.881792 0.471639i 0.843663π-0.843663\pi
0.0324444 0.999474i 0.489671π-0.489671\pi
480480 0 0
481481 −16.3941 9.46512i −0.747505 0.431572i
482482 9.40312 + 9.84415i 0.428300 + 0.448389i
483483 16.9850 9.23998i 0.772843 0.420434i
484484 0.738629 16.1091i 0.0335741 0.732230i
485485 0 0
486486 −6.04356 + 20.6505i −0.274142 + 0.936724i
487487 −0.489188 0.847298i −0.0221672 0.0383948i 0.854729 0.519075i 0.173723π-0.173723\pi
−0.876896 + 0.480680i 0.840390π0.840390\pi
488488 −3.79909 19.4322i −0.171977 0.879654i
489489 13.3403i 0.603271i
490490 0 0
491491 18.4167i 0.831132i −0.909563 0.415566i 0.863583π-0.863583\pi
0.909563 0.415566i 0.136417π-0.136417\pi
492492 −15.6372 10.0101i −0.704977 0.451290i
493493 −7.68420 13.3094i −0.346079 0.599426i
494494 −0.722769 0.211525i −0.0325189 0.00951698i
495495 0 0
496496 −0.652555 0.0599677i −0.0293006 0.00269263i
497497 −11.7181 + 6.37478i −0.525631 + 0.285948i
498498 6.23504 5.95570i 0.279399 0.266881i
499499 −16.9167 9.76688i −0.757297 0.437226i 0.0710273 0.997474i 0.477372π-0.477372\pi
−0.828324 + 0.560249i 0.810706π0.810706\pi
500500 0 0
501501 −8.24149 14.2747i −0.368203 0.637746i
502502 8.34945 + 34.2837i 0.372654 + 1.53016i
503503 11.7007i 0.521707i 0.965378 + 0.260853i 0.0840039π0.0840039\pi
−0.965378 + 0.260853i 0.915996π0.915996\pi
504504 −8.40335 10.1548i −0.374315 0.452329i
505505 0 0
506506 −15.4630 + 3.76586i −0.687414 + 0.167413i
507507 6.69948 3.86795i 0.297534 0.171782i
508508 28.2046 14.6041i 1.25138 0.647951i
509509 1.85583 + 1.07147i 0.0822584 + 0.0474919i 0.540565 0.841302i 0.318211π-0.318211\pi
−0.458307 + 0.888794i 0.651544π0.651544\pi
510510 0 0
511511 −10.5132 + 17.1874i −0.465079 + 0.760327i
512512 18.9368 12.3854i 0.836896 0.547363i
513513 0.993611 + 0.573662i 0.0438690 + 0.0253278i
514514 23.0416 + 6.74335i 1.01632 + 0.297436i
515515 0 0
516516 −2.27351 + 3.55154i −0.100086 + 0.156348i
517517 −20.0588 −0.882186
518518 −28.1448 + 6.10258i −1.23661 + 0.268132i
519519 17.3851i 0.763120i
520520 0 0
521521 −11.8399 + 6.83576i −0.518714 + 0.299480i −0.736408 0.676537i 0.763480π-0.763480\pi
0.217694 + 0.976017i 0.430146π0.430146\pi
522522 −5.90792 1.72901i −0.258582 0.0756767i
523523 −32.5328 18.7828i −1.42256 0.821316i −0.426043 0.904703i 0.640093π-0.640093\pi
−0.996517 + 0.0833873i 0.973426π0.973426\pi
524524 0.293745 6.40640i 0.0128323 0.279865i
525525 0 0
526526 −15.3739 + 14.6852i −0.670336 + 0.640304i
527527 −0.509411 + 0.882325i −0.0221903 + 0.0384347i
528528 −3.19400 6.92851i −0.139001 0.301524i
529529 −10.0599 17.4242i −0.437386 0.757575i
530530 0 0
531531 7.55201 0.327729
532532 −1.03042 + 0.500818i −0.0446742 + 0.0217132i
533533 20.5154i 0.888621i
534534 −0.664294 2.72766i −0.0287468 0.118037i
535535 0 0
536536 −4.74960 + 13.8426i −0.205152 + 0.597907i
537537 3.55530 6.15795i 0.153422 0.265735i
538538 30.7030 + 32.1431i 1.32370 + 1.38579i
539539 0.608349 11.9810i 0.0262035 0.516056i
540540 0 0
541541 −13.3052 + 23.0452i −0.572034 + 0.990793i 0.424323 + 0.905511i 0.360512π0.360512\pi
−0.996357 + 0.0852815i 0.972821π0.972821\pi
542542 4.50306 + 1.31787i 0.193423 + 0.0566072i
543543 0.660916 + 1.14474i 0.0283626 + 0.0491255i
544544 −5.16149 34.7988i −0.221297 1.49199i
545545 0 0
546546 −3.12512 + 9.75348i −0.133743 + 0.417411i
547547 24.0582 1.02865 0.514327 0.857594i 0.328042π-0.328042\pi
0.514327 + 0.857594i 0.328042π0.328042\pi
548548 −1.40562 + 2.19578i −0.0600452 + 0.0937990i
549549 −10.6783 + 6.16513i −0.455740 + 0.263121i
550550 0 0
551551 −0.267527 + 0.463370i −0.0113970 + 0.0197402i
552552 15.5856 13.5781i 0.663369 0.577921i
553553 −1.07029 + 42.1842i −0.0455134 + 1.79385i
554554 14.4042 + 15.0798i 0.611976 + 0.640679i
555555 0 0
556556 −37.0859 + 19.2028i −1.57279 + 0.814378i
557557 23.1592 13.3710i 0.981286 0.566546i 0.0786280 0.996904i 0.474946π-0.474946\pi
0.902658 + 0.430358i 0.141613π0.141613\pi
558558 0.0965622 + 0.396494i 0.00408780 + 0.0167849i
559559 −4.65950 −0.197076
560560 0 0
561561 −11.8615 −0.500791
562562 6.87470 + 28.2282i 0.289992 + 1.19073i
563563 15.1306 8.73567i 0.637680 0.368165i −0.146041 0.989279i 0.546653π-0.546653\pi
0.783720 + 0.621114i 0.213320π0.213320\pi
564564 23.1353 11.9793i 0.974174 0.504419i
565565 0 0
566566 −27.1913 28.4666i −1.14293 1.19654i
567567 0.846937 1.38460i 0.0355680 0.0581479i
568568 −10.7527 + 9.36768i −0.451175 + 0.393059i
569569 −10.1792 + 17.6309i −0.426734 + 0.739125i −0.996581 0.0826258i 0.973669π-0.973669\pi
0.569846 + 0.821751i 0.307003π0.307003\pi
570570 0 0
571571 19.2734 11.1275i 0.806565 0.465671i −0.0391963 0.999232i 0.512480π-0.512480\pi
0.845762 + 0.533561i 0.179146π0.179146\pi
572572 4.54498 7.09989i 0.190035 0.296861i
573573 11.7537 0.491019
574574 −20.9783 23.1083i −0.875618 0.964522i
575575 0 0
576576 −11.1226 8.65117i −0.463442 0.360465i
577577 −0.485564 0.841022i −0.0202143 0.0350122i 0.855741 0.517404i 0.173102π-0.173102\pi
−0.875956 + 0.482392i 0.839768π0.839768\pi
578578 −29.4190 8.60976i −1.22367 0.358119i
579579 3.00942 5.21247i 0.125067 0.216623i
580580 0 0
581581 12.7321 6.92636i 0.528215 0.287354i
582582 11.4483 + 11.9852i 0.474546 + 0.496803i
583583 11.1632 19.3352i 0.462332 0.800783i
584584 −6.99033 + 20.3731i −0.289262 + 0.843044i
585585 0 0
586586 1.43368 + 5.88682i 0.0592246 + 0.243182i
587587 17.6042i 0.726602i −0.931672 0.363301i 0.881650π-0.881650\pi
0.931672 0.363301i 0.118350π-0.118350\pi
588588 6.45346 + 14.1818i 0.266136 + 0.584849i
589589 0.0354704 0.00146153
590590 0 0
591591 −9.98887 17.3012i −0.410887 0.711677i
592592 −27.9593 + 12.8891i −1.14912 + 0.529738i
593593 11.1886 19.3792i 0.459461 0.795810i −0.539471 0.842004i 0.681376π-0.681376\pi
0.998932 + 0.0461938i 0.0147092π0.0147092\pi
594594 −9.28710 + 8.87103i −0.381054 + 0.363983i
595595 0 0
596596 −0.891792 + 19.4494i −0.0365292 + 0.796680i
597597 −7.37405 4.25741i −0.301800 0.174244i
598598 21.9207 + 6.41531i 0.896404 + 0.262342i
599599 −15.9061 + 9.18338i −0.649905 + 0.375223i −0.788420 0.615137i 0.789100π-0.789100\pi
0.138515 + 0.990360i 0.455767π0.455767\pi
600600 0 0
601601 11.9668i 0.488136i 0.969758 + 0.244068i 0.0784820π0.0784820\pi
−0.969758 + 0.244068i 0.921518π0.921518\pi
602602 −5.24840 + 4.76463i −0.213909 + 0.194192i
603603 9.11360 0.371134
604604 16.1065 25.1606i 0.655365 1.02377i
605605 0 0
606606 0.679410 + 0.198836i 0.0275992 + 0.00807717i
607607 −14.1791 8.18629i −0.575511 0.332271i 0.183837 0.982957i 0.441148π-0.441148\pi
−0.759347 + 0.650686i 0.774482π0.774482\pi
608608 −0.959363 + 0.761386i −0.0389073 + 0.0308783i
609609 6.20749 + 3.79701i 0.251540 + 0.153863i
610610 0 0
611611 24.9304 + 14.3936i 1.00858 + 0.582303i
612612 −19.4544 + 10.0733i −0.786396 + 0.407189i
613613 −39.6151 + 22.8718i −1.60004 + 0.923783i −0.608561 + 0.793507i 0.708253π0.708253\pi
−0.991478 + 0.130276i 0.958414π0.958414\pi
614614 −19.6724 + 4.79101i −0.793912 + 0.193349i
615615 0 0
616616 −2.14068 12.6448i −0.0862503 0.509472i
617617 3.88479i 0.156396i 0.996938 + 0.0781979i 0.0249166π0.0249166\pi
−0.996938 + 0.0781979i 0.975083π0.975083\pi
618618 3.45688 + 14.1943i 0.139056 + 0.570978i
619619 −10.2165 17.6955i −0.410636 0.711242i 0.584323 0.811521i 0.301360π-0.301360\pi
−0.994959 + 0.100278i 0.968027π0.968027\pi
620620 0 0
621621 −30.1350 17.3985i −1.20928 0.698176i
622622 26.2442 25.0684i 1.05230 1.00515i
623623 0.119695 4.71765i 0.00479549 0.189009i
624624 −1.00196 + 10.9031i −0.0401106 + 0.436474i
625625 0 0
626626 −44.1189 12.9118i −1.76335 0.516061i
627627 0.206479 + 0.357633i 0.00824599 + 0.0142825i
628628 −13.8538 8.86849i −0.552827 0.353891i
629629 47.8657i 1.90853i
630630 0 0
631631 23.7070i 0.943762i 0.881662 + 0.471881i 0.156425π0.156425\pi
−0.881662 + 0.471881i 0.843575π0.843575\pi
632632 8.65563 + 44.2731i 0.344302 + 1.76109i
633633 −8.66476 15.0078i −0.344393 0.596507i
634634 1.16015 3.96417i 0.0460756 0.157437i
635635 0 0
636636 −1.32821 + 28.9675i −0.0526670 + 1.14864i
637637 −9.35326 + 14.4542i −0.370590 + 0.572696i
638638 −4.13700 4.33103i −0.163785 0.171467i
639639 7.69103 + 4.44042i 0.304252 + 0.175660i
640640 0 0
641641 −7.19683 12.4653i −0.284258 0.492349i 0.688171 0.725548i 0.258414π-0.258414\pi
−0.972429 + 0.233200i 0.925080π0.925080\pi
642642 −28.3276 + 6.89890i −1.11800 + 0.272278i
643643 47.6127i 1.87766i −0.344380 0.938830i 0.611911π-0.611911\pi
0.344380 0.938830i 0.388089π-0.388089\pi
644644 31.2513 15.1892i 1.23147 0.598538i
645645 0 0
646646 0.450580 + 1.85012i 0.0177278 + 0.0727922i
647647 −0.00937783 + 0.00541429i −0.000368680 + 0.000212858i −0.500184 0.865919i 0.666734π-0.666734\pi
0.499816 + 0.866132i 0.333401π0.333401\pi
648648 0.563134 1.64124i 0.0221220 0.0644738i
649649 6.36349 + 3.67396i 0.249789 + 0.144216i
650650 0 0
651651 0.0122353 0.482240i 0.000479540 0.0189005i
652652 −1.09806 + 23.9480i −0.0430033 + 0.937877i
653653 −9.19915 5.31113i −0.359990 0.207841i 0.309086 0.951034i 0.399977π-0.399977\pi
−0.669077 + 0.743193i 0.733310π0.733310\pi
654654 −3.08183 + 10.5304i −0.120509 + 0.411771i
655655 0 0
656656 −27.2472 19.2568i −1.06383 0.751853i
657657 13.4131 0.523296
658658 42.7997 9.28019i 1.66851 0.361780i
659659 13.3688i 0.520773i 0.965505 + 0.260386i 0.0838499π0.0838499\pi
−0.965505 + 0.260386i 0.916150π0.916150\pi
660660 0 0
661661 −6.49983 + 3.75268i −0.252814 + 0.145962i −0.621052 0.783769i 0.713294π-0.713294\pi
0.368238 + 0.929732i 0.379961π0.379961\pi
662662 −1.56849 + 5.35944i −0.0609612 + 0.208301i
663663 14.7422 + 8.51142i 0.572540 + 0.330556i
664664 11.6831 10.1782i 0.453393 0.394992i
665665 0 0
666666 13.2428 + 13.8639i 0.513147 + 0.537215i
667667 8.11376 14.0534i 0.314166 0.544151i
668668 −13.6198 26.3037i −0.526967 1.01772i
669669 6.38146 + 11.0530i 0.246721 + 0.427334i
670670 0 0
671671 −11.9970 −0.463141
672672 10.0205 + 13.3057i 0.386551 + 0.513279i
673673 19.9107i 0.767501i −0.923437 0.383751i 0.874632π-0.874632\pi
0.923437 0.383751i 0.125368π-0.125368\pi
674674 13.8047 3.36200i 0.531738 0.129500i
675675 0 0
676676 12.3450 6.39214i 0.474808 0.245852i
677677 −13.0027 + 22.5213i −0.499733 + 0.865563i −1.00000 0.000308393i 0.999902π-0.999902\pi
0.500267 + 0.865871i 0.333235π0.333235\pi
678678 −0.379736 + 0.362724i −0.0145837 + 0.0139303i
679679 13.3141 + 24.4740i 0.510948 + 0.939226i
680680 0 0
681681 4.98282 8.63049i 0.190942 0.330721i
682682 −0.111524 + 0.381071i −0.00427048 + 0.0145920i
683683 7.41000 + 12.8345i 0.283536 + 0.491098i 0.972253 0.233932i 0.0751592π-0.0751592\pi
−0.688717 + 0.725030i 0.741826π0.741826\pi
684684 0.642372 + 0.411213i 0.0245617 + 0.0157231i
685685 0 0
686686 4.24493 + 25.8453i 0.162072 + 0.986779i
687687 −2.67856 −0.102194
688688 −4.37365 + 6.18844i −0.166744 + 0.235932i
689689 −27.7487 + 16.0207i −1.05714 + 0.610341i
690690 0 0
691691 13.2455 22.9418i 0.503882 0.872749i −0.496108 0.868261i 0.665238π-0.665238\pi
0.999990 0.00448815i 0.00142863π-0.00142863\pi
692692 −1.43099 + 31.2090i −0.0543980 + 1.18639i
693693 −7.01549 + 3.81650i −0.266497 + 0.144977i
694694 0.0205654 0.0196440i 0.000780651 0.000745677i
695695 0 0
696696 7.35803 + 2.52466i 0.278905 + 0.0956969i
697697 −44.9241 + 25.9369i −1.70162 + 0.982432i
698698 −7.69971 + 1.87519i −0.291438 + 0.0709769i
699699 2.84996 0.107795
700700 0 0
701701 −0.713553 −0.0269505 −0.0134753 0.999909i 0.504289π-0.504289\pi
−0.0134753 + 0.999909i 0.504289π0.504289\pi
702702 17.9082 4.36137i 0.675902 0.164609i
703703 1.44319 0.833226i 0.0544310 0.0314257i
704704 −5.16345 12.7007i −0.194605 0.478675i
705705 0 0
706706 26.0615 24.8939i 0.980836 0.936893i
707707 1.01513 + 0.620938i 0.0381779 + 0.0233528i
708708 −9.53361 0.437133i −0.358295 0.0164285i
709709 −9.56584 + 16.5685i −0.359253 + 0.622244i −0.987836 0.155498i 0.950302π-0.950302\pi
0.628584 + 0.777742i 0.283635π0.283635\pi
710710 0 0
711711 24.3288 14.0463i 0.912403 0.526776i
712712 −0.967997 4.95126i −0.0362772 0.185556i
713713 −1.07578 −0.0402881
714714 25.3089 5.48769i 0.947162 0.205372i
715715 0 0
716716 6.88919 10.7619i 0.257461 0.402190i
717717 3.51243 + 6.08371i 0.131174 + 0.227200i
718718 −7.68563 + 26.2613i −0.286825 + 0.980063i
719719 −20.0286 + 34.6906i −0.746941 + 1.29374i 0.202341 + 0.979315i 0.435145π0.435145\pi
−0.949282 + 0.314425i 0.898188π0.898188\pi
720720 0 0
721721 −0.622875 + 24.5499i −0.0231971 + 0.914284i
722722 −19.3823 + 18.5140i −0.721335 + 0.689019i
723723 −5.35666 + 9.27801i −0.199216 + 0.345053i
724724 1.09222 + 2.10939i 0.0405922 + 0.0783949i
725725 0 0
726726 12.3302 3.00290i 0.457617 0.111448i
727727 14.4074i 0.534341i −0.963649 0.267171i 0.913911π-0.913911\pi
0.963649 0.267171i 0.0860887π-0.0860887\pi
728728 −6.41291 + 17.2518i −0.237678 + 0.639395i
729729 −18.7733 −0.695307
730730 0 0
731731 5.89085 + 10.2032i 0.217881 + 0.377381i
732732 13.8371 7.16473i 0.511434 0.264816i
733733 0.387263 0.670759i 0.0143039 0.0247751i −0.858785 0.512336i 0.828780π-0.828780\pi
0.873089 + 0.487561i 0.162113π0.162113\pi
734734 −16.8944 17.6868i −0.623584 0.652831i
735735 0 0
736736 29.0963 23.0919i 1.07250 0.851179i
737737 7.67931 + 4.43365i 0.282871 + 0.163316i
738738 −5.83603 + 19.9413i −0.214827 + 0.734051i
739739 −7.09915 + 4.09870i −0.261147 + 0.150773i −0.624858 0.780739i 0.714843π-0.714843\pi
0.363711 + 0.931512i 0.381510π0.381510\pi
740740 0 0
741741 0.592653i 0.0217716i
742742 −14.8736 + 46.4204i −0.546027 + 1.70415i
743743 8.66498 0.317887 0.158944 0.987288i 0.449191π-0.449191\pi
0.158944 + 0.987288i 0.449191π0.449191\pi
744744 −0.0989492 0.506121i −0.00362765 0.0185553i
745745 0 0
746746 −4.41301 + 15.0790i −0.161572 + 0.552080i
747747 −8.35649 4.82462i −0.305748 0.176524i
748748 −21.2932 0.976331i −0.778557 0.0356982i
749749 −48.9942 1.24307i −1.79021 0.0454209i
750750 0 0
751751 −6.73208 3.88677i −0.245657 0.141830i 0.372117 0.928186i 0.378632π-0.378632\pi
−0.617774 + 0.786356i 0.711965π0.711965\pi
752752 42.5177 19.6004i 1.55046 0.714754i
753753 −24.0484 + 13.8843i −0.876372 + 0.505974i
754754 2.03392 + 8.35147i 0.0740709 + 0.304143i
755755 0 0
756756 15.7118 23.2249i 0.571433 0.844680i
757757 5.10767i 0.185641i −0.995683 0.0928206i 0.970412π-0.970412\pi
0.995683 0.0928206i 0.0295883π-0.0295883\pi
758758 −19.6761 + 4.79192i −0.714669 + 0.174050i
759759 −6.26227 10.8466i −0.227306 0.393705i
760760 0 0
761761 −4.16241 2.40317i −0.150887 0.0871149i 0.422655 0.906290i 0.361098π-0.361098\pi
−0.573543 + 0.819176i 0.694431π0.694431\pi
762762 17.2646 + 18.0744i 0.625432 + 0.654766i
763763 −9.62411 + 15.7338i −0.348416 + 0.569603i
764764 21.0998 + 0.967463i 0.763364 + 0.0350016i
765765 0 0
766766 −4.15250 + 14.1888i −0.150036 + 0.512663i
767767 −5.27264 9.13249i −0.190384 0.329755i
768768 13.5403 + 11.5650i 0.488595 + 0.417315i
769769 24.7841i 0.893738i −0.894600 0.446869i 0.852539π-0.852539\pi
0.894600 0.446869i 0.147461π-0.147461\pi
770770 0 0
771771 18.8935i 0.680434i
772772 5.83144 9.10951i 0.209878 0.327858i
773773 12.6560 + 21.9209i 0.455205 + 0.788438i 0.998700 0.0509742i 0.0162326π-0.0162326\pi
−0.543495 + 0.839412i 0.682899π0.682899\pi
774774 4.52912 + 1.32549i 0.162796 + 0.0476438i
775775 0 0
776776 19.5649 + 22.4577i 0.702340 + 0.806184i
777777 −10.8304 19.9084i −0.388537 0.714210i
778778 30.8080 29.4277i 1.10452 1.05504i
779779 1.56404 + 0.902999i 0.0560375 + 0.0323533i
780780 0 0
781781 4.32042 + 7.48318i 0.154597 + 0.267769i
782782 −13.6655 56.1120i −0.488678 2.00656i
783783 13.0953i 0.467989i
784784 10.4177 + 25.9899i 0.372059 + 0.928209i
785785 0 0
786786 4.90359 1.19422i 0.174905 0.0425965i
787787 43.2134 24.9493i 1.54039 0.889345i 0.541577 0.840651i 0.317827π-0.317827\pi
0.998814 0.0486943i 0.0155060π-0.0155060\pi
788788 −16.5075 31.8806i −0.588056 1.13570i
789789 −14.4898 8.36567i −0.515850 0.297826i
790790 0 0
791791 −0.775428 + 0.421840i −0.0275711 + 0.0149989i
792792 −6.43751 + 5.60830i −0.228747 + 0.199282i
793793 14.9107 + 8.60871i 0.529495 + 0.305704i
794794 −18.2390 5.33783i −0.647279 0.189433i
795795 0 0
796796 −12.8872 8.24969i −0.456773 0.292403i
797797 −38.2770 −1.35584 −0.677921 0.735135i 0.737119π-0.737119\pi
−0.677921 + 0.735135i 0.737119π0.737119\pi
798798 −0.606025 0.667557i −0.0214531 0.0236313i
799799 72.7894i 2.57510i
800800 0 0
801801 −2.72080 + 1.57086i −0.0961349 + 0.0555035i
802802 39.2046 + 11.4736i 1.38436 + 0.405148i
803803 11.3022 + 6.52532i 0.398846 + 0.230274i
804804 −11.5049 0.527522i −0.405748 0.0186043i
805805 0 0
806806 0.412054 0.393594i 0.0145140 0.0138638i
807807 −17.4906 + 30.2945i −0.615697 + 1.06642i
808808 1.20328 + 0.412866i 0.0423314 + 0.0145246i
809809 4.90151 + 8.48966i 0.172328 + 0.298480i 0.939233 0.343280i 0.111538π-0.111538\pi
−0.766906 + 0.641760i 0.778205π0.778205\pi
810810 0 0
811811 4.75188 0.166861 0.0834305 0.996514i 0.473412π-0.473412\pi
0.0834305 + 0.996514i 0.473412π0.473412\pi
812812 10.8309 + 7.32718i 0.380090 + 0.257134i
813813 3.69240i 0.129498i
814814 4.41404 + 18.1245i 0.154712 + 0.635262i
815815 0 0
816816 25.1421 11.5904i 0.880150 0.405745i
817817 0.205091 0.355228i 0.00717522 0.0124278i
818818 25.3029 + 26.4897i 0.884696 + 0.926191i
819819 11.4579 + 0.290709i 0.400372 + 0.0101582i
820820 0 0
821821 −7.82822 + 13.5589i −0.273207 + 0.473208i −0.969681 0.244374i 0.921418π-0.921418\pi
0.696474 + 0.717582i 0.254751π0.254751\pi
822822 −1.96914 0.576288i −0.0686816 0.0201004i
823823 9.89848 + 17.1447i 0.345039 + 0.597626i 0.985361 0.170481i 0.0545322π-0.0545322\pi
−0.640322 + 0.768107i 0.721199π0.721199\pi
824824 5.03730 + 25.7656i 0.175483 + 0.897586i
825825 0 0
826826 −15.2776 4.89511i −0.531575 0.170323i
827827 13.0808 0.454863 0.227431 0.973794i 0.426967π-0.426967\pi
0.227431 + 0.973794i 0.426967π0.426967\pi
828828 −19.4824 12.4716i −0.677059 0.433418i
829829 21.7092 12.5338i 0.753990 0.435316i −0.0731437 0.997321i 0.523303π-0.523303\pi
0.827134 + 0.562005i 0.189970π0.189970\pi
830830 0 0
831831 −8.20562 + 14.2126i −0.284650 + 0.493028i
832832 −2.69613 + 19.4904i −0.0934715 + 0.675707i
833833 43.4764 + 2.20757i 1.50637 + 0.0764879i
834834 −22.7011 23.7658i −0.786074 0.822943i
835835 0 0
836836 0.341226 + 0.659003i 0.0118015 + 0.0227921i
837837 −0.751825 + 0.434066i −0.0259869 + 0.0150035i
838838 9.40403 + 38.6139i 0.324857 + 1.33389i
839839 −32.1347 −1.10941 −0.554707 0.832046i 0.687170π-0.687170\pi
−0.554707 + 0.832046i 0.687170π0.687170\pi
840840 0 0
841841 −22.8930 −0.789414
842842 5.22933 + 21.4722i 0.180215 + 0.739980i
843843 −19.8007 + 11.4320i −0.681974 + 0.393738i
844844 −14.3193 27.6546i −0.492891 0.951911i
845845 0 0
846846 −20.1383 21.0828i −0.692368 0.724842i
847847 21.3258 + 0.541075i 0.732764 + 0.0185916i
848848 −4.76870 + 51.8919i −0.163758 + 1.78198i
849849 15.4900 26.8295i 0.531616 0.920785i
850850 0 0
851851 −43.7702 + 25.2707i −1.50042 + 0.866270i
852852 −9.45208 6.05073i −0.323823 0.207295i
853853 −45.8238 −1.56898 −0.784489 0.620142i 0.787075π-0.787075\pi
−0.784489 + 0.620142i 0.787075π0.787075\pi
854854 25.5982 5.55042i 0.875953 0.189931i
855855 0 0
856856 −51.4204 + 10.0529i −1.75751 + 0.343603i
857857 −18.6629 32.3250i −0.637512 1.10420i −0.985977 0.166881i 0.946630π-0.946630\pi
0.348465 0.937322i 0.386703π-0.386703\pi
858858 6.36707 + 1.86339i 0.217368 + 0.0636150i
859859 −6.62605 + 11.4767i −0.226078 + 0.391579i −0.956642 0.291265i 0.905924π-0.905924\pi
0.730564 + 0.682844i 0.239257π0.239257\pi
860860 0 0
861861 12.8163 20.9525i 0.436778 0.714059i
862862 −19.4877 20.4017i −0.663752 0.694884i
863863 −3.96707 + 6.87116i −0.135041 + 0.233897i −0.925613 0.378471i 0.876450π-0.876450\pi
0.790572 + 0.612369i 0.209783π0.209783\pi
864864 11.0171 27.8783i 0.374809 0.948440i
865865 0 0
866866 3.95857 + 16.2543i 0.134518 + 0.552342i
867867 24.1229i 0.819255i
868868 0.0616582 0.864691i 0.00209281 0.0293495i
869869 27.3334 0.927221
870870 0 0
871871 −6.36291 11.0209i −0.215599 0.373428i
872872 −6.39914 + 18.6501i −0.216702 + 0.631571i
873873 9.27406 16.0631i 0.313879 0.543655i
874874 −1.45394 + 1.38880i −0.0491803 + 0.0469769i
875875 0 0
876876 −16.9326 0.776391i −0.572101 0.0262318i
877877 −44.8202 25.8770i −1.51347 0.873803i −0.999876 0.0157714i 0.994980π-0.994980\pi
−0.513596 0.858032i 0.671687π-0.671687\pi
878878 37.8612 + 11.0805i 1.27775 + 0.373948i
879879 −4.12932 + 2.38407i −0.139279 + 0.0804126i
880880 0 0
881881 7.69261i 0.259171i 0.991568 + 0.129585i 0.0413646π0.0413646\pi
−0.991568 + 0.129585i 0.958635π0.958635\pi
882882 13.2033 11.3890i 0.444579 0.383488i
883883 35.2766 1.18715 0.593575 0.804778i 0.297716π-0.297716\pi
0.593575 + 0.804778i 0.297716π0.297716\pi
884884 25.7640 + 16.4928i 0.866538 + 0.554713i
885885 0 0
886886 −26.0586 7.62631i −0.875456 0.256211i
887887 −10.0685 5.81304i −0.338067 0.195183i 0.321350 0.946960i 0.395863π-0.395863\pi
−0.659417 + 0.751778i 0.729197π0.729197\pi
888888 −15.9151 18.2682i −0.534076 0.613041i
889889 20.0784 + 36.9082i 0.673409 + 1.23786i
890890 0 0
891891 −0.910494 0.525674i −0.0305027 0.0176107i
892892 10.5459 + 20.3672i 0.353104 + 0.681943i
893893 −2.19466 + 1.26709i −0.0734414 + 0.0424014i
894894 −14.8870 + 3.62558i −0.497896 + 0.121258i
895895 0 0
896896 16.8933 + 24.7107i 0.564364 + 0.825526i
897897 17.9744i 0.600149i
898898 1.65322 + 6.78830i 0.0551688 + 0.226529i
899899 −0.202426 0.350613i −0.00675130 0.0116936i
900900 0 0
901901 70.1635 + 40.5089i 2.33749 + 1.34955i
902902 −14.6188 + 13.9638i −0.486752 + 0.464945i
903903 −4.75877 2.91086i −0.158362 0.0968673i
904904 −0.711543 + 0.619890i −0.0236656 + 0.0206172i
905905 0 0
906906 22.5636 + 6.60347i 0.749626 + 0.219386i
907907 −11.5887 20.0723i −0.384798 0.666490i 0.606943 0.794745i 0.292396π-0.292396\pi
−0.991741 + 0.128256i 0.959062π0.959062\pi
908908 9.65534 15.0830i 0.320424 0.500546i
909909 0.792212i 0.0262760i
910910 0 0
911911 43.0818i 1.42737i −0.700469 0.713683i 0.747026π-0.747026\pi
0.700469 0.713683i 0.252974π-0.252974\pi
912912 −0.787123 0.556295i −0.0260642 0.0184208i
913913 −4.69424 8.13067i −0.155357 0.269086i
914914 −10.3772 + 35.4581i −0.343246 + 1.17285i
915915 0 0
916916 −4.80845 0.220476i −0.158876 0.00728473i
917917 8.48105 + 0.215180i 0.280069 + 0.00710587i
918918 −32.1911 33.7010i −1.06247 1.11230i
919919 18.1455 + 10.4763i 0.598564 + 0.345581i 0.768476 0.639878i 0.221015π-0.221015\pi
−0.169912 + 0.985459i 0.554348π0.554348\pi
920920 0 0
921921 −7.96699 13.7992i −0.262521 0.454700i
922922 −18.3978 + 4.48060i −0.605899 + 0.147561i
923923 12.4008i 0.408177i
924924 9.07722 4.41184i 0.298619 0.145139i
925925 0 0
926926 −5.48867 22.5370i −0.180369 0.740612i
927927 14.1586 8.17448i 0.465030 0.268485i
928928 13.0010 + 5.13781i 0.426780 + 0.168657i
929929 8.90058 + 5.13875i 0.292019 + 0.168597i 0.638852 0.769330i 0.279410π-0.279410\pi
−0.346833 + 0.937927i 0.612743π0.612743\pi
930930 0 0
931931 −0.690259 1.34928i −0.0226223 0.0442208i
932932 5.11613 + 0.234584i 0.167585 + 0.00768405i
933933 24.7349 + 14.2807i 0.809784 + 0.467529i
934934 4.74016 16.1968i 0.155103 0.529976i
935935 0 0
936936 12.0253 2.35101i 0.393060 0.0768452i
937937 38.3992 1.25445 0.627224 0.778839i 0.284191π-0.284191\pi
0.627224 + 0.778839i 0.284191π0.284191\pi
938938 −18.4366 5.90730i −0.601978 0.192880i
939939 36.1764i 1.18057i
940940 0 0
941941 −13.2891 + 7.67245i −0.433211 + 0.250115i −0.700714 0.713443i 0.747135π-0.747135\pi
0.267502 + 0.963557i 0.413802π0.413802\pi
942942 3.63597 12.4239i 0.118466 0.404792i
943943 −47.4354 27.3869i −1.54471 0.891839i
944944 −17.0784 1.56945i −0.555853 0.0510811i
945945 0 0
946946 3.17150 + 3.32025i 0.103114 + 0.107951i
947947 −13.3114 + 23.0560i −0.432562 + 0.749219i −0.997093 0.0761928i 0.975724π-0.975724\pi
0.564531 + 0.825412i 0.309057π0.309057\pi
948948 −31.5256 + 16.3237i −1.02390 + 0.530169i
949949 −9.36474 16.2202i −0.303992 0.526530i
950950 0 0
951951 3.25052 0.105405
952952 45.8852 7.76807i 1.48715 0.251765i
953953 5.39146i 0.174646i −0.996180 0.0873232i 0.972169π-0.972169\pi
0.996180 0.0873232i 0.0278313π-0.0278313\pi
954954 31.5297 7.67874i 1.02081 0.248608i
955955 0 0
956956 5.80462 + 11.2103i 0.187735 + 0.362568i
957957 2.35672 4.08195i 0.0761818 0.131951i
958958 38.0197 36.3163i 1.22836 1.17333i
959959 −2.94216 1.79967i −0.0950074 0.0581143i
960960 0 0
961961 15.4866 26.8235i 0.499567 0.865276i
962962 7.51951 25.6937i 0.242439 0.828397i
963963 16.3138 + 28.2564i 0.525705 + 0.910548i
964964 −10.3797 + 16.2146i −0.334309 + 0.522237i
965965 0 0
966966 18.3800 + 20.2462i 0.591367 + 0.651410i
967967 6.14901 0.197739 0.0988694 0.995100i 0.468477π-0.468477\pi
0.0988694 + 0.995100i 0.468477π0.468477\pi
968968 22.3819 4.37577i 0.719380 0.140643i
969969 −1.29778 + 0.749271i −0.0416906 + 0.0240701i
970970 0 0
971971 15.6816 27.1613i 0.503247 0.871649i −0.496746 0.867896i 0.665472π-0.665472\pi
0.999993 0.00375309i 0.00119465π-0.00119465\pi
972972 −30.3972 1.39377i −0.974991 0.0447051i
973973 −26.4009 48.5302i −0.846374 1.55581i
974974 1.00053 0.955707i 0.0320591 0.0306228i
975975 0 0
976976 25.4295 11.7229i 0.813979 0.375240i
977977 34.0446 19.6557i 1.08918 0.628841i 0.155825 0.987785i 0.450196π-0.450196\pi
0.933359 + 0.358944i 0.116863π0.116863\pi
978978 −18.3303 + 4.46417i −0.586139 + 0.142748i
979979 −3.05681 −0.0976961
980980 0 0
981981 12.2787 0.392030
982982 25.3054 6.16289i 0.807529 0.196666i
983983 26.4013 15.2428i 0.842072 0.486170i −0.0158960 0.999874i 0.505060π-0.505060\pi
0.857968 + 0.513703i 0.171727π0.171727\pi
984984 8.52163 24.8360i 0.271660 0.791743i
985985 0 0
986986 15.7164 15.0123i 0.500513 0.478089i
987987 16.4697 + 30.2747i 0.524237 + 0.963654i
988988 0.0487820 1.06391i 0.00155196 0.0338474i
989989 −6.22015 + 10.7736i −0.197789 + 0.342581i
990990 0 0
991991 −11.3870 + 6.57431i −0.361721 + 0.208840i −0.669835 0.742510i 0.733635π-0.733635\pi
0.308114 + 0.951349i 0.400302π0.400302\pi
992992 −0.135970 0.916712i −0.00431706 0.0291056i
993993 −4.39461 −0.139459
994994 −12.6806 13.9681i −0.402204 0.443041i
995995 0 0
996996 10.2699 + 6.57427i 0.325415 + 0.208314i
997997 5.65950 + 9.80253i 0.179238 + 0.310449i 0.941620 0.336678i 0.109303π-0.109303\pi
−0.762382 + 0.647128i 0.775970π0.775970\pi
998998 7.75924 26.5128i 0.245615 0.839249i
999999 −20.3931 + 35.3218i −0.645208 + 1.11753i
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 700.2.t.c.299.10 32
4.3 odd 2 inner 700.2.t.c.299.15 32
5.2 odd 4 700.2.p.c.551.2 32
5.3 odd 4 140.2.o.a.131.15 yes 32
5.4 even 2 700.2.t.d.299.7 32
7.3 odd 6 700.2.t.d.199.2 32
20.3 even 4 140.2.o.a.131.7 yes 32
20.7 even 4 700.2.p.c.551.10 32
20.19 odd 2 700.2.t.d.299.2 32
28.3 even 6 700.2.t.d.199.7 32
35.3 even 12 140.2.o.a.31.7 32
35.13 even 4 980.2.o.f.411.15 32
35.17 even 12 700.2.p.c.451.10 32
35.18 odd 12 980.2.o.f.31.7 32
35.23 odd 12 980.2.g.a.391.10 32
35.24 odd 6 inner 700.2.t.c.199.15 32
35.33 even 12 980.2.g.a.391.9 32
140.3 odd 12 140.2.o.a.31.15 yes 32
140.23 even 12 980.2.g.a.391.11 32
140.59 even 6 inner 700.2.t.c.199.10 32
140.83 odd 4 980.2.o.f.411.7 32
140.87 odd 12 700.2.p.c.451.2 32
140.103 odd 12 980.2.g.a.391.12 32
140.123 even 12 980.2.o.f.31.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.7 32 35.3 even 12
140.2.o.a.31.15 yes 32 140.3 odd 12
140.2.o.a.131.7 yes 32 20.3 even 4
140.2.o.a.131.15 yes 32 5.3 odd 4
700.2.p.c.451.2 32 140.87 odd 12
700.2.p.c.451.10 32 35.17 even 12
700.2.p.c.551.2 32 5.2 odd 4
700.2.p.c.551.10 32 20.7 even 4
700.2.t.c.199.10 32 140.59 even 6 inner
700.2.t.c.199.15 32 35.24 odd 6 inner
700.2.t.c.299.10 32 1.1 even 1 trivial
700.2.t.c.299.15 32 4.3 odd 2 inner
700.2.t.d.199.2 32 7.3 odd 6
700.2.t.d.199.7 32 28.3 even 6
700.2.t.d.299.2 32 20.19 odd 2
700.2.t.d.299.7 32 5.4 even 2
980.2.g.a.391.9 32 35.33 even 12
980.2.g.a.391.10 32 35.23 odd 12
980.2.g.a.391.11 32 140.23 even 12
980.2.g.a.391.12 32 140.103 odd 12
980.2.o.f.31.7 32 35.18 odd 12
980.2.o.f.31.15 32 140.123 even 12
980.2.o.f.411.7 32 140.83 odd 4
980.2.o.f.411.15 32 35.13 even 4