Properties

Label 845.2.f.f.408.5
Level 845845
Weight 22
Character 845.408
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 7272
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(408,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.408");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.f (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 7272
Relative dimension: 3636 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 408.5
Character χ\chi == 845.408
Dual form 845.2.f.f.437.32

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) == q2.37242iq2+(1.65235+1.65235i)q33.62837q4+(0.598181+2.15457i)q5+(3.920083.92008i)q63.73834q7+3.86318iq8+2.46055iq9+(5.11155+1.41914i)q10+(1.277261.27726i)q11+(5.995365.99536i)q12+8.86890iq14+(4.54852+2.57171i)q15+1.90834q16+(0.2724350.272435i)q17+5.83745q18+(3.872783.87278i)q19+(2.170427.81759i)q20+(6.177066.17706i)q21+(3.03020+3.03020i)q22+(6.53419+6.53419i)q23+(6.38334+6.38334i)q24+(4.284362.57765i)q25+(0.8913650.891365i)q27+13.5641q280.764574iq29+(6.10117+10.7910i)q30+(3.27268+3.27268i)q31+3.19898iq324.22098iq33+(0.646330+0.646330i)q34+(2.236208.05452i)q358.92778iq36+1.15622q37+(9.18786+9.18786i)q38+(8.323502.31088i)q40+(2.156882.15688i)q41+(14.6546+14.6546i)q42+(1.33870+1.33870i)q43+(4.63438+4.63438i)q44+(5.301431.47185i)q45+(15.5018+15.5018i)q46+1.94248q47+(3.15325+3.15325i)q48+6.97517q49+(6.11526+10.1643i)q500.900318iq51+(1.187151.18715i)q53+(2.114692.11469i)q54+(3.515991.98792i)q5514.4419iq5612.7984iq571.81389q58+(4.50612+4.50612i)q59+(16.50379.33112i)q603.71664q61+(7.76418+7.76418i)q629.19836iq63+11.4060q6410.0139q66+11.0561iq67+(0.988496+0.988496i)q6821.5936q69+(19.10875.30521i)q70+(7.84488+7.84488i)q719.50554q724.49691iq732.74303iq74+(2.8200911.3385i)q75+(14.0519+14.0519i)q76+(4.77484+4.77484i)q77+7.15052iq79+(1.14153+4.11165i)q80+10.3273q81+(5.117025.11702i)q82+11.4388q83+(22.4127+22.4127i)q84+(0.7499460.424015i)q85+(3.17596+3.17596i)q86+(1.263351.26335i)q87+(4.934304.93430i)q88+(1.63827+1.63827i)q89+(3.49185+12.5772i)q90+(23.708523.7085i)q9210.8153q934.60838iq94+(10.66086.02756i)q95+(5.28585+5.28585i)q960.882970iq9716.5480iq98+(3.142773.14277i)q99+O(q100)q-2.37242i q^{2} +(1.65235 + 1.65235i) q^{3} -3.62837 q^{4} +(-0.598181 + 2.15457i) q^{5} +(3.92008 - 3.92008i) q^{6} -3.73834 q^{7} +3.86318i q^{8} +2.46055i q^{9} +(5.11155 + 1.41914i) q^{10} +(-1.27726 - 1.27726i) q^{11} +(-5.99536 - 5.99536i) q^{12} +8.86890i q^{14} +(-4.54852 + 2.57171i) q^{15} +1.90834 q^{16} +(-0.272435 - 0.272435i) q^{17} +5.83745 q^{18} +(-3.87278 - 3.87278i) q^{19} +(2.17042 - 7.81759i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-3.03020 + 3.03020i) q^{22} +(-6.53419 + 6.53419i) q^{23} +(-6.38334 + 6.38334i) q^{24} +(-4.28436 - 2.57765i) q^{25} +(0.891365 - 0.891365i) q^{27} +13.5641 q^{28} -0.764574i q^{29} +(6.10117 + 10.7910i) q^{30} +(-3.27268 + 3.27268i) q^{31} +3.19898i q^{32} -4.22098i q^{33} +(-0.646330 + 0.646330i) q^{34} +(2.23620 - 8.05452i) q^{35} -8.92778i q^{36} +1.15622 q^{37} +(-9.18786 + 9.18786i) q^{38} +(-8.32350 - 2.31088i) q^{40} +(2.15688 - 2.15688i) q^{41} +(-14.6546 + 14.6546i) q^{42} +(-1.33870 + 1.33870i) q^{43} +(4.63438 + 4.63438i) q^{44} +(-5.30143 - 1.47185i) q^{45} +(15.5018 + 15.5018i) q^{46} +1.94248 q^{47} +(3.15325 + 3.15325i) q^{48} +6.97517 q^{49} +(-6.11526 + 10.1643i) q^{50} -0.900318i q^{51} +(-1.18715 - 1.18715i) q^{53} +(-2.11469 - 2.11469i) q^{54} +(3.51599 - 1.98792i) q^{55} -14.4419i q^{56} -12.7984i q^{57} -1.81389 q^{58} +(-4.50612 + 4.50612i) q^{59} +(16.5037 - 9.33112i) q^{60} -3.71664 q^{61} +(7.76418 + 7.76418i) q^{62} -9.19836i q^{63} +11.4060 q^{64} -10.0139 q^{66} +11.0561i q^{67} +(0.988496 + 0.988496i) q^{68} -21.5936 q^{69} +(-19.1087 - 5.30521i) q^{70} +(-7.84488 + 7.84488i) q^{71} -9.50554 q^{72} -4.49691i q^{73} -2.74303i q^{74} +(-2.82009 - 11.3385i) q^{75} +(14.0519 + 14.0519i) q^{76} +(4.77484 + 4.77484i) q^{77} +7.15052i q^{79} +(-1.14153 + 4.11165i) q^{80} +10.3273 q^{81} +(-5.11702 - 5.11702i) q^{82} +11.4388 q^{83} +(22.4127 + 22.4127i) q^{84} +(0.749946 - 0.424015i) q^{85} +(3.17596 + 3.17596i) q^{86} +(1.26335 - 1.26335i) q^{87} +(4.93430 - 4.93430i) q^{88} +(-1.63827 + 1.63827i) q^{89} +(-3.49185 + 12.5772i) q^{90} +(23.7085 - 23.7085i) q^{92} -10.8153 q^{93} -4.60838i q^{94} +(10.6608 - 6.02756i) q^{95} +(-5.28585 + 5.28585i) q^{96} -0.882970i q^{97} -16.5480i q^{98} +(3.14277 - 3.14277i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 72q4q380q412q10+64q12+80q16+8q17+24q22+36q2348q2564q274q30+80q35+28q3824q4056q42+76q4376q48+92q95+O(q100) 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.37242i 1.67755i −0.544475 0.838777i 0.683271π-0.683271\pi
0.544475 0.838777i 0.316729π-0.316729\pi
33 1.65235 + 1.65235i 0.953987 + 0.953987i 0.998987 0.0449999i 0.0143287π-0.0143287\pi
−0.0449999 + 0.998987i 0.514329π0.514329\pi
44 −3.62837 −1.81419
55 −0.598181 + 2.15457i −0.267515 + 0.963554i
66 3.92008 3.92008i 1.60036 1.60036i
77 −3.73834 −1.41296 −0.706479 0.707734i 0.749718π-0.749718\pi
−0.706479 + 0.707734i 0.749718π0.749718\pi
88 3.86318i 1.36584i
99 2.46055i 0.820183i
1010 5.11155 + 1.41914i 1.61641 + 0.448770i
1111 −1.27726 1.27726i −0.385109 0.385109i 0.487830 0.872939i 0.337789π-0.337789\pi
−0.872939 + 0.487830i 0.837789π0.837789\pi
1212 −5.99536 5.99536i −1.73071 1.73071i
1313 0 0
1414 8.86890i 2.37031i
1515 −4.54852 + 2.57171i −1.17442 + 0.664012i
1616 1.90834 0.477085
1717 −0.272435 0.272435i −0.0660752 0.0660752i 0.673297 0.739372i 0.264878π-0.264878\pi
−0.739372 + 0.673297i 0.764878π0.764878\pi
1818 5.83745 1.37590
1919 −3.87278 3.87278i −0.888477 0.888477i 0.105900 0.994377i 0.466228π-0.466228\pi
−0.994377 + 0.105900i 0.966228π0.966228\pi
2020 2.17042 7.81759i 0.485321 1.74807i
2121 −6.17706 6.17706i −1.34794 1.34794i
2222 −3.03020 + 3.03020i −0.646041 + 0.646041i
2323 −6.53419 + 6.53419i −1.36247 + 1.36247i −0.491718 + 0.870755i 0.663631π0.663631\pi
−0.870755 + 0.491718i 0.836369π0.836369\pi
2424 −6.38334 + 6.38334i −1.30299 + 1.30299i
2525 −4.28436 2.57765i −0.856872 0.515529i
2626 0 0
2727 0.891365 0.891365i 0.171543 0.171543i
2828 13.5641 2.56337
2929 0.764574i 0.141978i −0.997477 0.0709889i 0.977385π-0.977385\pi
0.997477 0.0709889i 0.0226155π-0.0226155\pi
3030 6.10117 + 10.7910i 1.11392 + 1.97016i
3131 −3.27268 + 3.27268i −0.587792 + 0.587792i −0.937033 0.349241i 0.886439π-0.886439\pi
0.349241 + 0.937033i 0.386439π0.386439\pi
3232 3.19898i 0.565506i
3333 4.22098i 0.734779i
3434 −0.646330 + 0.646330i −0.110845 + 0.110845i
3535 2.23620 8.05452i 0.377987 1.36146i
3636 8.92778i 1.48796i
3737 1.15622 0.190081 0.0950403 0.995473i 0.469702π-0.469702\pi
0.0950403 + 0.995473i 0.469702π0.469702\pi
3838 −9.18786 + 9.18786i −1.49047 + 1.49047i
3939 0 0
4040 −8.32350 2.31088i −1.31606 0.365382i
4141 2.15688 2.15688i 0.336848 0.336848i −0.518332 0.855180i 0.673447π-0.673447\pi
0.855180 + 0.518332i 0.173447π0.173447\pi
4242 −14.6546 + 14.6546i −2.26125 + 2.26125i
4343 −1.33870 + 1.33870i −0.204150 + 0.204150i −0.801775 0.597626i 0.796111π-0.796111\pi
0.597626 + 0.801775i 0.296111π0.296111\pi
4444 4.63438 + 4.63438i 0.698660 + 0.698660i
4545 −5.30143 1.47185i −0.790290 0.219411i
4646 15.5018 + 15.5018i 2.28562 + 2.28562i
4747 1.94248 0.283340 0.141670 0.989914i 0.454753π-0.454753\pi
0.141670 + 0.989914i 0.454753π0.454753\pi
4848 3.15325 + 3.15325i 0.455133 + 0.455133i
4949 6.97517 0.996453
5050 −6.11526 + 10.1643i −0.864828 + 1.43745i
5151 0.900318i 0.126070i
5252 0 0
5353 −1.18715 1.18715i −0.163068 0.163068i 0.620856 0.783924i 0.286785π-0.286785\pi
−0.783924 + 0.620856i 0.786785π0.786785\pi
5454 −2.11469 2.11469i −0.287773 0.287773i
5555 3.51599 1.98792i 0.474096 0.268051i
5656 14.4419i 1.92988i
5757 12.7984i 1.69519i
5858 −1.81389 −0.238175
5959 −4.50612 + 4.50612i −0.586647 + 0.586647i −0.936722 0.350075i 0.886156π-0.886156\pi
0.350075 + 0.936722i 0.386156π0.386156\pi
6060 16.5037 9.33112i 2.13062 1.20464i
6161 −3.71664 −0.475867 −0.237933 0.971281i 0.576470π-0.576470\pi
−0.237933 + 0.971281i 0.576470π0.576470\pi
6262 7.76418 + 7.76418i 0.986052 + 0.986052i
6363 9.19836i 1.15888i
6464 11.4060 1.42575
6565 0 0
6666 −10.0139 −1.23263
6767 11.0561i 1.35072i 0.737487 + 0.675361i 0.236012π0.236012\pi
−0.737487 + 0.675361i 0.763988π0.763988\pi
6868 0.988496 + 0.988496i 0.119873 + 0.119873i
6969 −21.5936 −2.59956
7070 −19.1087 5.30521i −2.28393 0.634094i
7171 −7.84488 + 7.84488i −0.931016 + 0.931016i −0.997770 0.0667534i 0.978736π-0.978736\pi
0.0667534 + 0.997770i 0.478736π0.478736\pi
7272 −9.50554 −1.12024
7373 4.49691i 0.526323i −0.964752 0.263161i 0.915235π-0.915235\pi
0.964752 0.263161i 0.0847652π-0.0847652\pi
7474 2.74303i 0.318870i
7575 −2.82009 11.3385i −0.325636 1.30925i
7676 14.0519 + 14.0519i 1.61186 + 1.61186i
7777 4.77484 + 4.77484i 0.544144 + 0.544144i
7878 0 0
7979 7.15052i 0.804496i 0.915531 + 0.402248i 0.131771π0.131771\pi
−0.915531 + 0.402248i 0.868229π0.868229\pi
8080 −1.14153 + 4.11165i −0.127627 + 0.459697i
8181 10.3273 1.14748
8282 −5.11702 5.11702i −0.565080 0.565080i
8383 11.4388 1.25557 0.627783 0.778388i 0.283962π-0.283962\pi
0.627783 + 0.778388i 0.283962π0.283962\pi
8484 22.4127 + 22.4127i 2.44542 + 2.44542i
8585 0.749946 0.424015i 0.0813431 0.0459909i
8686 3.17596 + 3.17596i 0.342472 + 0.342472i
8787 1.26335 1.26335i 0.135445 0.135445i
8888 4.93430 4.93430i 0.525998 0.525998i
8989 −1.63827 + 1.63827i −0.173656 + 0.173656i −0.788584 0.614927i 0.789185π-0.789185\pi
0.614927 + 0.788584i 0.289185π0.289185\pi
9090 −3.49185 + 12.5772i −0.368074 + 1.32575i
9191 0 0
9292 23.7085 23.7085i 2.47178 2.47178i
9393 −10.8153 −1.12149
9494 4.60838i 0.475318i
9595 10.6608 6.02756i 1.09378 0.618415i
9696 −5.28585 + 5.28585i −0.539485 + 0.539485i
9797 0.882970i 0.0896520i −0.998995 0.0448260i 0.985727π-0.985727\pi
0.998995 0.0448260i 0.0142733π-0.0142733\pi
9898 16.5480i 1.67160i
9999 3.14277 3.14277i 0.315860 0.315860i
100100 15.5452 + 9.35266i 1.55452 + 0.935266i
101101 7.94189i 0.790248i −0.918628 0.395124i 0.870702π-0.870702\pi
0.918628 0.395124i 0.129298π-0.129298\pi
102102 −2.13593 −0.211489
103103 10.7428 10.7428i 1.05852 1.05852i 0.0603388 0.998178i 0.480782π-0.480782\pi
0.998178 0.0603388i 0.0192181π-0.0192181\pi
104104 0 0
105105 17.0039 9.61392i 1.65941 0.938222i
106106 −2.81643 + 2.81643i −0.273556 + 0.273556i
107107 7.38827 7.38827i 0.714251 0.714251i −0.253170 0.967422i 0.581473π-0.581473\pi
0.967422 + 0.253170i 0.0814733π0.0814733\pi
108108 −3.23420 + 3.23420i −0.311211 + 0.311211i
109109 4.13475 + 4.13475i 0.396037 + 0.396037i 0.876833 0.480796i 0.159652π-0.159652\pi
−0.480796 + 0.876833i 0.659652π0.659652\pi
110110 −4.71618 8.34140i −0.449670 0.795321i
111111 1.91048 + 1.91048i 0.181334 + 0.181334i
112112 −7.13401 −0.674101
113113 −10.3692 10.3692i −0.975452 0.975452i 0.0242536 0.999706i 0.492279π-0.492279\pi
−0.999706 + 0.0242536i 0.992279π0.992279\pi
114114 −30.3632 −2.84377
115115 −10.1698 17.9870i −0.948334 1.67730i
116116 2.77416i 0.257574i
117117 0 0
118118 10.6904 + 10.6904i 0.984132 + 0.984132i
119119 1.01845 + 1.01845i 0.0933616 + 0.0933616i
120120 −9.93497 17.5718i −0.906935 1.60407i
121121 7.73720i 0.703382i
122122 8.81743i 0.798292i
123123 7.12785 0.642697
124124 11.8745 11.8745i 1.06636 1.06636i
125125 8.11655 7.68906i 0.725966 0.687730i
126126 −21.8224 −1.94409
127127 4.97319 + 4.97319i 0.441300 + 0.441300i 0.892449 0.451149i 0.148986π-0.148986\pi
−0.451149 + 0.892449i 0.648986π0.648986\pi
128128 20.6619i 1.82627i
129129 −4.42401 −0.389513
130130 0 0
131131 −9.34748 −0.816693 −0.408347 0.912827i 0.633895π-0.633895\pi
−0.408347 + 0.912827i 0.633895π0.633895\pi
132132 15.3153i 1.33302i
133133 14.4778 + 14.4778i 1.25538 + 1.25538i
134134 26.2298 2.26591
135135 1.38731 + 2.45371i 0.119401 + 0.211181i
136136 1.05247 1.05247i 0.0902482 0.0902482i
137137 13.6982 1.17032 0.585158 0.810919i 0.301032π-0.301032\pi
0.585158 + 0.810919i 0.301032π0.301032\pi
138138 51.2290i 4.36090i
139139 8.98600i 0.762182i 0.924537 + 0.381091i 0.124452π0.124452\pi
−0.924537 + 0.381091i 0.875548π0.875548\pi
140140 −8.11377 + 29.2248i −0.685739 + 2.46994i
141141 3.20967 + 3.20967i 0.270303 + 0.270303i
142142 18.6113 + 18.6113i 1.56183 + 1.56183i
143143 0 0
144144 4.69556i 0.391297i
145145 1.64733 + 0.457353i 0.136803 + 0.0379811i
146146 −10.6685 −0.882935
147147 11.5255 + 11.5255i 0.950603 + 0.950603i
148148 −4.19518 −0.344842
149149 −8.98770 8.98770i −0.736301 0.736301i 0.235559 0.971860i 0.424308π-0.424308\pi
−0.971860 + 0.235559i 0.924308π0.924308\pi
150150 −26.8996 + 6.69044i −2.19634 + 0.546272i
151151 −2.96123 2.96123i −0.240981 0.240981i 0.576275 0.817256i 0.304506π-0.304506\pi
−0.817256 + 0.576275i 0.804506π0.804506\pi
152152 14.9612 14.9612i 1.21352 1.21352i
153153 0.670340 0.670340i 0.0541938 0.0541938i
154154 11.3279 11.3279i 0.912830 0.912830i
155155 −5.09358 9.00889i −0.409126 0.723612i
156156 0 0
157157 −13.0366 + 13.0366i −1.04044 + 1.04044i −0.0412907 + 0.999147i 0.513147π0.513147\pi
−0.999147 + 0.0412907i 0.986853π0.986853\pi
158158 16.9640 1.34959
159159 3.92320i 0.311130i
160160 −6.89244 1.91357i −0.544895 0.151281i
161161 24.4270 24.4270i 1.92512 1.92512i
162162 24.5008i 1.92496i
163163 15.8438i 1.24098i 0.784213 + 0.620492i 0.213067π0.213067\pi
−0.784213 + 0.620492i 0.786933π0.786933\pi
164164 −7.82595 + 7.82595i −0.611104 + 0.611104i
165165 9.09441 + 2.52491i 0.707999 + 0.196564i
166166 27.1375i 2.10628i
167167 12.4834 0.965991 0.482996 0.875623i 0.339549π-0.339549\pi
0.482996 + 0.875623i 0.339549π0.339549\pi
168168 23.8631 23.8631i 1.84108 1.84108i
169169 0 0
170170 −1.00594 1.77919i −0.0771523 0.136457i
171171 9.52916 9.52916i 0.728713 0.728713i
172172 4.85730 4.85730i 0.370366 0.370366i
173173 −11.4282 + 11.4282i −0.868870 + 0.868870i −0.992347 0.123477i 0.960595π-0.960595\pi
0.123477 + 0.992347i 0.460595π0.460595\pi
174174 −2.99719 2.99719i −0.227216 0.227216i
175175 16.0164 + 9.63612i 1.21072 + 0.728422i
176176 −2.43745 2.43745i −0.183730 0.183730i
177177 −14.8914 −1.11931
178178 3.88666 + 3.88666i 0.291318 + 0.291318i
179179 −18.4481 −1.37888 −0.689438 0.724345i 0.742142π-0.742142\pi
−0.689438 + 0.724345i 0.742142π0.742142\pi
180180 19.2356 + 5.34043i 1.43373 + 0.398052i
181181 2.18983i 0.162769i −0.996683 0.0813844i 0.974066π-0.974066\pi
0.996683 0.0813844i 0.0259342π-0.0259342\pi
182182 0 0
183183 −6.14120 6.14120i −0.453971 0.453971i
184184 −25.2427 25.2427i −1.86092 1.86092i
185185 −0.691626 + 2.49115i −0.0508493 + 0.183153i
186186 25.6583i 1.88136i
187187 0.695942i 0.0508923i
188188 −7.04805 −0.514032
189189 −3.33222 + 3.33222i −0.242384 + 0.242384i
190190 −14.2999 25.2919i −1.03742 1.83487i
191191 8.14632 0.589447 0.294724 0.955583i 0.404772π-0.404772\pi
0.294724 + 0.955583i 0.404772π0.404772\pi
192192 18.8468 + 18.8468i 1.36015 + 1.36015i
193193 23.2471i 1.67336i 0.547691 + 0.836681i 0.315507π0.315507\pi
−0.547691 + 0.836681i 0.684493π0.684493\pi
194194 −2.09477 −0.150396
195195 0 0
196196 −25.3085 −1.80775
197197 22.0689i 1.57234i −0.618008 0.786172i 0.712060π-0.712060\pi
0.618008 0.786172i 0.287940π-0.287940\pi
198198 −7.45596 7.45596i −0.529872 0.529872i
199199 8.13701 0.576817 0.288409 0.957507i 0.406874π-0.406874\pi
0.288409 + 0.957507i 0.406874π0.406874\pi
200200 9.95792 16.5513i 0.704131 1.17035i
201201 −18.2687 + 18.2687i −1.28857 + 1.28857i
202202 −18.8415 −1.32568
203203 2.85823i 0.200609i
204204 3.26669i 0.228714i
205205 3.35694 + 5.93735i 0.234459 + 0.414683i
206206 −25.4864 25.4864i −1.77572 1.77572i
207207 −16.0777 16.0777i −1.11748 1.11748i
208208 0 0
209209 9.89312i 0.684321i
210210 −22.8082 40.3404i −1.57392 2.78375i
211211 −24.7734 −1.70547 −0.852737 0.522340i 0.825059π-0.825059\pi
−0.852737 + 0.522340i 0.825059π0.825059\pi
212212 4.30744 + 4.30744i 0.295836 + 0.295836i
213213 −25.9250 −1.77635
214214 −17.5281 17.5281i −1.19819 1.19819i
215215 −2.08354 3.68511i −0.142096 0.251322i
216216 3.44350 + 3.44350i 0.234301 + 0.234301i
217217 12.2344 12.2344i 0.830525 0.830525i
218218 9.80935 9.80935i 0.664373 0.664373i
219219 7.43048 7.43048i 0.502105 0.502105i
220220 −12.7573 + 7.21291i −0.860098 + 0.486295i
221221 0 0
222222 4.53245 4.53245i 0.304198 0.304198i
223223 −29.5220 −1.97694 −0.988469 0.151425i 0.951614π-0.951614\pi
−0.988469 + 0.151425i 0.951614π0.951614\pi
224224 11.9589i 0.799036i
225225 6.34243 10.5419i 0.422828 0.702792i
226226 −24.6001 + 24.6001i −1.63637 + 1.63637i
227227 7.86679i 0.522137i 0.965320 + 0.261068i 0.0840748π0.0840748\pi
−0.965320 + 0.261068i 0.915925π0.915925\pi
228228 46.4374i 3.07539i
229229 −12.4410 + 12.4410i −0.822125 + 0.822125i −0.986412 0.164288i 0.947467π-0.947467\pi
0.164288 + 0.986412i 0.447467π0.447467\pi
230230 −42.6727 + 24.1269i −2.81376 + 1.59088i
231231 15.7795i 1.03821i
232232 2.95369 0.193919
233233 −1.52992 + 1.52992i −0.100228 + 0.100228i −0.755443 0.655214i 0.772578π-0.772578\pi
0.655214 + 0.755443i 0.272578π0.272578\pi
234234 0 0
235235 −1.16196 + 4.18522i −0.0757976 + 0.273013i
236236 16.3499 16.3499i 1.06429 1.06429i
237237 −11.8152 + 11.8152i −0.767479 + 0.767479i
238238 2.41620 2.41620i 0.156619 0.156619i
239239 −7.05936 7.05936i −0.456632 0.456632i 0.440916 0.897548i 0.354654π-0.354654\pi
−0.897548 + 0.440916i 0.854654π0.854654\pi
240240 −8.68012 + 4.90769i −0.560299 + 0.316790i
241241 −10.2476 10.2476i −0.660104 0.660104i 0.295300 0.955405i 0.404580π-0.404580\pi
−0.955405 + 0.295300i 0.904580π0.904580\pi
242242 −18.3559 −1.17996
243243 14.3903 + 14.3903i 0.923141 + 0.923141i
244244 13.4854 0.863311
245245 −4.17241 + 15.0285i −0.266566 + 0.960136i
246246 16.9102i 1.07816i
247247 0 0
248248 −12.6430 12.6430i −0.802829 0.802829i
249249 18.9009 + 18.9009i 1.19779 + 1.19779i
250250 −18.2417 19.2559i −1.15370 1.21785i
251251 17.7643i 1.12127i −0.828062 0.560636i 0.810557π-0.810557\pi
0.828062 0.560636i 0.189443π-0.189443\pi
252252 33.3751i 2.10243i
253253 16.6918 1.04940
254254 11.7985 11.7985i 0.740304 0.740304i
255255 1.93980 + 0.538553i 0.121475 + 0.0337255i
256256 −26.2066 −1.63791
257257 6.37449 + 6.37449i 0.397630 + 0.397630i 0.877396 0.479767i 0.159279π-0.159279\pi
−0.479767 + 0.877396i 0.659279π0.659279\pi
258258 10.4956i 0.653428i
259259 −4.32232 −0.268576
260260 0 0
261261 1.88127 0.116448
262262 22.1761i 1.37005i
263263 −3.01414 3.01414i −0.185860 0.185860i 0.608044 0.793904i 0.291955π-0.291955\pi
−0.793904 + 0.608044i 0.791955π0.791955\pi
264264 16.3064 1.00359
265265 3.26794 1.84768i 0.200748 0.113502i
266266 34.3473 34.3473i 2.10597 2.10597i
267267 −5.41401 −0.331332
268268 40.1158i 2.45046i
269269 1.79761i 0.109602i 0.998497 + 0.0548011i 0.0174525π0.0174525\pi
−0.998497 + 0.0548011i 0.982548π0.982548\pi
270270 5.82122 3.29129i 0.354268 0.200301i
271271 2.08531 + 2.08531i 0.126674 + 0.126674i 0.767601 0.640928i 0.221450π-0.221450\pi
−0.640928 + 0.767601i 0.721450π0.721450\pi
272272 −0.519898 0.519898i −0.0315235 0.0315235i
273273 0 0
274274 32.4979i 1.96327i
275275 2.17992 + 8.76459i 0.131454 + 0.528524i
276276 78.3496 4.71609
277277 20.1491 + 20.1491i 1.21064 + 1.21064i 0.970815 + 0.239829i 0.0770914π0.0770914\pi
0.239829 + 0.970815i 0.422909π0.422909\pi
278278 21.3186 1.27860
279279 −8.05260 8.05260i −0.482097 0.482097i
280280 31.1161 + 8.63885i 1.85954 + 0.516270i
281281 2.57874 + 2.57874i 0.153835 + 0.153835i 0.779828 0.625993i 0.215306π-0.215306\pi
−0.625993 + 0.779828i 0.715306π0.715306\pi
282282 7.61468 7.61468i 0.453447 0.453447i
283283 5.52077 5.52077i 0.328176 0.328176i −0.523717 0.851892i 0.675455π-0.675455\pi
0.851892 + 0.523717i 0.175455π0.175455\pi
284284 28.4641 28.4641i 1.68904 1.68904i
285285 27.5751 + 7.65576i 1.63341 + 0.453488i
286286 0 0
287287 −8.06314 + 8.06314i −0.475952 + 0.475952i
288288 −7.87125 −0.463818
289289 16.8516i 0.991268i
290290 1.08503 3.90815i 0.0637154 0.229495i
291291 1.45898 1.45898i 0.0855269 0.0855269i
292292 16.3164i 0.954848i
293293 22.5598i 1.31796i −0.752161 0.658979i 0.770988π-0.770988\pi
0.752161 0.658979i 0.229012π-0.229012\pi
294294 27.3432 27.3432i 1.59469 1.59469i
295295 −7.01329 12.4042i −0.408329 0.722203i
296296 4.46667i 0.259620i
297297 −2.27701 −0.132126
298298 −21.3226 + 21.3226i −1.23518 + 1.23518i
299299 0 0
300300 10.2323 + 41.1402i 0.590765 + 2.37523i
301301 5.00451 5.00451i 0.288455 0.288455i
302302 −7.02528 + 7.02528i −0.404259 + 0.404259i
303303 13.1228 13.1228i 0.753886 0.753886i
304304 −7.39057 7.39057i −0.423878 0.423878i
305305 2.22322 8.00777i 0.127301 0.458523i
306306 −1.59033 1.59033i −0.0909129 0.0909129i
307307 −20.4085 −1.16477 −0.582387 0.812912i 0.697881π-0.697881\pi
−0.582387 + 0.812912i 0.697881π0.697881\pi
308308 −17.3249 17.3249i −0.987177 0.987177i
309309 35.5017 2.01962
310310 −21.3729 + 12.0841i −1.21390 + 0.686331i
311311 21.3762i 1.21213i 0.795413 + 0.606067i 0.207254π0.207254\pi
−0.795413 + 0.606067i 0.792746π0.792746\pi
312312 0 0
313313 −5.22723 5.22723i −0.295461 0.295461i 0.543772 0.839233i 0.316996π-0.316996\pi
−0.839233 + 0.543772i 0.816996π0.816996\pi
314314 30.9284 + 30.9284i 1.74539 + 1.74539i
315315 19.8185 + 5.50228i 1.11665 + 0.310019i
316316 25.9447i 1.45951i
317317 25.8830i 1.45373i 0.686779 + 0.726867i 0.259024π0.259024\pi
−0.686779 + 0.726867i 0.740976π0.740976\pi
318318 −9.30747 −0.521937
319319 −0.976562 + 0.976562i −0.0546770 + 0.0546770i
320320 −6.82285 + 24.5751i −0.381409 + 1.37379i
321321 24.4161 1.36277
322322 −57.9511 57.9511i −3.22949 3.22949i
323323 2.11016i 0.117413i
324324 −37.4715 −2.08175
325325 0 0
326326 37.5882 2.08182
327327 13.6641i 0.755628i
328328 8.33241 + 8.33241i 0.460080 + 0.460080i
329329 −7.26165 −0.400348
330330 5.99015 21.5757i 0.329747 1.18771i
331331 −7.44156 + 7.44156i −0.409025 + 0.409025i −0.881398 0.472374i 0.843397π-0.843397\pi
0.472374 + 0.881398i 0.343397π0.343397\pi
332332 −41.5041 −2.27783
333333 2.84492i 0.155901i
334334 29.6158i 1.62050i
335335 −23.8212 6.61357i −1.30149 0.361338i
336336 −11.7879 11.7879i −0.643084 0.643084i
337337 −6.67935 6.67935i −0.363847 0.363847i 0.501380 0.865227i 0.332826π-0.332826\pi
−0.865227 + 0.501380i 0.832826π0.832826\pi
338338 0 0
339339 34.2672i 1.86114i
340340 −2.72108 + 1.53849i −0.147572 + 0.0834361i
341341 8.36016 0.452728
342342 −22.6072 22.6072i −1.22246 1.22246i
343343 0.0928245 0.00501205
344344 −5.17164 5.17164i −0.278836 0.278836i
345345 12.9169 46.5249i 0.695421 2.50482i
346346 27.1125 + 27.1125i 1.45758 + 1.45758i
347347 −5.03872 + 5.03872i −0.270492 + 0.270492i −0.829298 0.558806i 0.811260π-0.811260\pi
0.558806 + 0.829298i 0.311260π0.311260\pi
348348 −4.58389 + 4.58389i −0.245722 + 0.245722i
349349 −23.0603 + 23.0603i −1.23439 + 1.23439i −0.272125 + 0.962262i 0.587726π0.587726\pi
−0.962262 + 0.272125i 0.912274π0.912274\pi
350350 22.8609 37.9976i 1.22197 2.03106i
351351 0 0
352352 4.08594 4.08594i 0.217781 0.217781i
353353 12.9205 0.687688 0.343844 0.939027i 0.388271π-0.388271\pi
0.343844 + 0.939027i 0.388271π0.388271\pi
354354 35.3287i 1.87770i
355355 −12.2097 21.5950i −0.648024 1.14614i
356356 5.94425 5.94425i 0.315045 0.315045i
357357 3.36569i 0.178131i
358358 43.7666i 2.31314i
359359 12.5304 12.5304i 0.661330 0.661330i −0.294364 0.955693i 0.595108π-0.595108\pi
0.955693 + 0.294364i 0.0951077π0.0951077\pi
360360 5.68603 20.4804i 0.299680 1.07941i
361361 10.9968i 0.578781i
362362 −5.19520 −0.273053
363363 12.7846 12.7846i 0.671017 0.671017i
364364 0 0
365365 9.68891 + 2.68996i 0.507140 + 0.140799i
366366 −14.5695 + 14.5695i −0.761561 + 0.761561i
367367 −24.6452 + 24.6452i −1.28647 + 1.28647i −0.349552 + 0.936917i 0.613666π0.613666\pi
−0.936917 + 0.349552i 0.886334π0.886334\pi
368368 −12.4694 + 12.4694i −0.650015 + 0.650015i
369369 5.30710 + 5.30710i 0.276277 + 0.276277i
370370 5.91005 + 1.64083i 0.307249 + 0.0853025i
371371 4.43799 + 4.43799i 0.230409 + 0.230409i
372372 39.2418 2.03459
373373 10.5600 + 10.5600i 0.546778 + 0.546778i 0.925507 0.378730i 0.123639π-0.123639\pi
−0.378730 + 0.925507i 0.623639π0.623639\pi
374374 1.65107 0.0853746
375375 26.1165 + 0.706362i 1.34865 + 0.0364764i
376376 7.50416i 0.386997i
377377 0 0
378378 7.90543 + 7.90543i 0.406611 + 0.406611i
379379 −22.9029 22.9029i −1.17644 1.17644i −0.980645 0.195796i 0.937271π-0.937271\pi
−0.195796 0.980645i 0.562729π-0.562729\pi
380380 −38.6814 + 21.8702i −1.98431 + 1.12192i
381381 16.4350i 0.841988i
382382 19.3265i 0.988829i
383383 32.2292 1.64684 0.823418 0.567435i 0.192064π-0.192064\pi
0.823418 + 0.567435i 0.192064π0.192064\pi
384384 34.1407 34.1407i 1.74224 1.74224i
385385 −13.1440 + 7.43152i −0.669878 + 0.378745i
386386 55.1518 2.80715
387387 −3.29394 3.29394i −0.167440 0.167440i
388388 3.20374i 0.162645i
389389 11.7818 0.597359 0.298679 0.954354i 0.403454π-0.403454\pi
0.298679 + 0.954354i 0.403454π0.403454\pi
390390 0 0
391391 3.56028 0.180051
392392 26.9463i 1.36100i
393393 −15.4454 15.4454i −0.779115 0.779115i
394394 −52.3567 −2.63769
395395 −15.4063 4.27730i −0.775175 0.215214i
396396 −11.4031 + 11.4031i −0.573029 + 0.573029i
397397 8.14777 0.408925 0.204462 0.978874i 0.434455π-0.434455\pi
0.204462 + 0.978874i 0.434455π0.434455\pi
398398 19.3044i 0.967642i
399399 47.8448i 2.39523i
400400 −8.17601 4.91902i −0.408800 0.245951i
401401 −11.6766 11.6766i −0.583101 0.583101i 0.352653 0.935754i 0.385280π-0.385280\pi
−0.935754 + 0.352653i 0.885280π0.885280\pi
402402 43.3409 + 43.3409i 2.16165 + 2.16165i
403403 0 0
404404 28.8161i 1.43366i
405405 −6.17762 + 22.2510i −0.306968 + 1.10566i
406406 6.78093 0.336532
407407 −1.47679 1.47679i −0.0732018 0.0732018i
408408 3.47809 0.172191
409409 2.98672 + 2.98672i 0.147684 + 0.147684i 0.777082 0.629399i 0.216699π-0.216699\pi
−0.629399 + 0.777082i 0.716699π0.716699\pi
410410 14.0859 7.96408i 0.695652 0.393318i
411411 22.6343 + 22.6343i 1.11647 + 1.11647i
412412 −38.9788 + 38.9788i −1.92035 + 1.92035i
413413 16.8454 16.8454i 0.828908 0.828908i
414414 −38.1430 + 38.1430i −1.87463 + 1.87463i
415415 −6.84245 + 24.6456i −0.335882 + 1.20981i
416416 0 0
417417 −14.8481 + 14.8481i −0.727112 + 0.727112i
418418 23.4706 1.14799
419419 17.0792i 0.834371i −0.908821 0.417186i 0.863017π-0.863017\pi
0.908821 0.417186i 0.136983π-0.136983\pi
420420 −61.6965 + 34.8829i −3.01048 + 1.70211i
421421 9.26544 9.26544i 0.451570 0.451570i −0.444305 0.895875i 0.646549π-0.646549\pi
0.895875 + 0.444305i 0.146549π0.146549\pi
422422 58.7730i 2.86102i
423423 4.77957i 0.232391i
424424 4.58619 4.58619i 0.222725 0.222725i
425425 0.464968 + 1.86945i 0.0225543 + 0.0906817i
426426 61.5051i 2.97993i
427427 13.8941 0.672380
428428 −26.8074 + 26.8074i −1.29578 + 1.29578i
429429 0 0
430430 −8.74262 + 4.94303i −0.421607 + 0.238374i
431431 −7.57641 + 7.57641i −0.364943 + 0.364943i −0.865629 0.500686i 0.833081π-0.833081\pi
0.500686 + 0.865629i 0.333081π0.333081\pi
432432 1.70103 1.70103i 0.0818406 0.0818406i
433433 −3.61077 + 3.61077i −0.173522 + 0.173522i −0.788525 0.615003i 0.789155π-0.789155\pi
0.615003 + 0.788525i 0.289155π0.289155\pi
434434 −29.0251 29.0251i −1.39325 1.39325i
435435 1.96626 + 3.47768i 0.0942750 + 0.166742i
436436 −15.0024 15.0024i −0.718485 0.718485i
437437 50.6109 2.42105
438438 −17.6282 17.6282i −0.842309 0.842309i
439439 −20.2393 −0.965969 −0.482985 0.875629i 0.660447π-0.660447\pi
−0.482985 + 0.875629i 0.660447π0.660447\pi
440440 7.67969 + 13.5829i 0.366115 + 0.647539i
441441 17.1627i 0.817273i
442442 0 0
443443 2.66083 + 2.66083i 0.126420 + 0.126420i 0.767486 0.641066i 0.221508π-0.221508\pi
−0.641066 + 0.767486i 0.721508π0.721508\pi
444444 −6.93192 6.93192i −0.328974 0.328974i
445445 −2.54979 4.50975i −0.120872 0.213783i
446446 70.0385i 3.31642i
447447 29.7017i 1.40484i
448448 −42.6395 −2.01453
449449 −21.7913 + 21.7913i −1.02839 + 1.02839i −0.0288081 + 0.999585i 0.509171π0.509171\pi
−0.999585 + 0.0288081i 0.990829π0.990829\pi
450450 −25.0097 15.0469i −1.17897 0.709317i
451451 −5.50980 −0.259446
452452 37.6233 + 37.6233i 1.76965 + 1.76965i
453453 9.78600i 0.459786i
454454 18.6633 0.875913
455455 0 0
456456 49.4426 2.31536
457457 10.1798i 0.476191i −0.971242 0.238096i 0.923477π-0.923477\pi
0.971242 0.238096i 0.0765232π-0.0765232\pi
458458 29.5153 + 29.5153i 1.37916 + 1.37916i
459459 −0.485678 −0.0226695
460460 36.8996 + 65.2635i 1.72045 + 3.04293i
461461 13.6308 13.6308i 0.634848 0.634848i −0.314432 0.949280i 0.601814π-0.601814\pi
0.949280 + 0.314432i 0.101814π0.101814\pi
462462 37.4355 1.74166
463463 16.7929i 0.780432i −0.920723 0.390216i 0.872400π-0.872400\pi
0.920723 0.390216i 0.127600π-0.127600\pi
464464 1.45907i 0.0677354i
465465 6.46949 23.3023i 0.300015 1.08062i
466466 3.62961 + 3.62961i 0.168139 + 0.168139i
467467 −9.75781 9.75781i −0.451538 0.451538i 0.444327 0.895865i 0.353443π-0.353443\pi
−0.895865 + 0.444327i 0.853443π0.853443\pi
468468 0 0
469469 41.3316i 1.90851i
470470 9.92909 + 2.75665i 0.457995 + 0.127155i
471471 −43.0823 −1.98513
472472 −17.4080 17.4080i −0.801266 0.801266i
473473 3.41974 0.157240
474474 28.0306 + 28.0306i 1.28749 + 1.28749i
475475 6.60972 + 26.5750i 0.303275 + 1.21935i
476476 −3.69533 3.69533i −0.169375 0.169375i
477477 2.92105 2.92105i 0.133746 0.133746i
478478 −16.7478 + 16.7478i −0.766025 + 0.766025i
479479 −9.77217 + 9.77217i −0.446502 + 0.446502i −0.894190 0.447688i 0.852248π-0.852248\pi
0.447688 + 0.894190i 0.352248π0.352248\pi
480480 −8.22685 14.5506i −0.375503 0.664143i
481481 0 0
482482 −24.3115 + 24.3115i −1.10736 + 1.10736i
483483 80.7241 3.67307
484484 28.0734i 1.27607i
485485 1.90242 + 0.528176i 0.0863846 + 0.0239832i
486486 34.1399 34.1399i 1.54862 1.54862i
487487 20.4592i 0.927095i 0.886072 + 0.463547i 0.153424π0.153424\pi
−0.886072 + 0.463547i 0.846576π0.846576\pi
488488 14.3580i 0.649958i
489489 −26.1796 + 26.1796i −1.18388 + 1.18388i
490490 35.6539 + 9.89871i 1.61068 + 0.447178i
491491 10.1889i 0.459817i −0.973212 0.229908i 0.926157π-0.926157\pi
0.973212 0.229908i 0.0738427π-0.0738427\pi
492492 −25.8625 −1.16597
493493 −0.208297 + 0.208297i −0.00938121 + 0.00938121i
494494 0 0
495495 4.89137 + 8.65126i 0.219851 + 0.388845i
496496 −6.24539 + 6.24539i −0.280426 + 0.280426i
497497 29.3268 29.3268i 1.31549 1.31549i
498498 44.8408 44.8408i 2.00936 2.00936i
499499 7.90149 + 7.90149i 0.353719 + 0.353719i 0.861491 0.507772i 0.169531π-0.169531\pi
−0.507772 + 0.861491i 0.669531π0.669531\pi
500500 −29.4499 + 27.8988i −1.31704 + 1.24767i
501501 20.6269 + 20.6269i 0.921543 + 0.921543i
502502 −42.1443 −1.88099
503503 10.0106 + 10.0106i 0.446349 + 0.446349i 0.894139 0.447790i 0.147789π-0.147789\pi
−0.447790 + 0.894139i 0.647789π0.647789\pi
504504 35.5349 1.58285
505505 17.1114 + 4.75069i 0.761446 + 0.211403i
506506 39.5998i 1.76043i
507507 0 0
508508 −18.0446 18.0446i −0.800600 0.800600i
509509 −16.3943 16.3943i −0.726665 0.726665i 0.243289 0.969954i 0.421774π-0.421774\pi
−0.969954 + 0.243289i 0.921774π0.921774\pi
510510 1.27767 4.60202i 0.0565764 0.203781i
511511 16.8110i 0.743673i
512512 20.8492i 0.921415i
513513 −6.90412 −0.304824
514514 15.1230 15.1230i 0.667045 0.667045i
515515 16.7200 + 29.5722i 0.736769 + 1.30311i
516516 16.0520 0.706648
517517 −2.48106 2.48106i −0.109117 0.109117i
518518 10.2544i 0.450551i
519519 −37.7669 −1.65778
520520 0 0
521521 −35.0306 −1.53472 −0.767359 0.641218i 0.778429π-0.778429\pi
−0.767359 + 0.641218i 0.778429π0.778429\pi
522522 4.46316i 0.195347i
523523 28.5551 + 28.5551i 1.24863 + 1.24863i 0.956327 + 0.292298i 0.0944199π0.0944199\pi
0.292298 + 0.956327i 0.405580π0.405580\pi
524524 33.9161 1.48163
525525 10.5425 + 42.3870i 0.460111 + 1.84992i
526526 −7.15081 + 7.15081i −0.311790 + 0.311790i
527527 1.78319 0.0776769
528528 8.05506i 0.350551i
529529 62.3912i 2.71266i
530530 −4.38346 7.75293i −0.190405 0.336766i
531531 −11.0875 11.0875i −0.481158 0.481158i
532532 −52.5307 52.5307i −2.27749 2.27749i
533533 0 0
534534 12.8443i 0.555827i
535535 11.4990 + 20.3381i 0.497147 + 0.879292i
536536 −42.7118 −1.84487
537537 −30.4828 30.4828i −1.31543 1.31543i
538538 4.26468 0.183864
539539 −8.90912 8.90912i −0.383743 0.383743i
540540 −5.03368 8.90296i −0.216615 0.383122i
541541 16.7846 + 16.7846i 0.721626 + 0.721626i 0.968936 0.247310i 0.0795467π-0.0795467\pi
−0.247310 + 0.968936i 0.579547π0.579547\pi
542542 4.94723 4.94723i 0.212502 0.212502i
543543 3.61838 3.61838i 0.155279 0.155279i
544544 0.871515 0.871515i 0.0373659 0.0373659i
545545 −11.3819 + 6.43528i −0.487549 + 0.275657i
546546 0 0
547547 10.0151 10.0151i 0.428216 0.428216i −0.459804 0.888020i 0.652080π-0.652080\pi
0.888020 + 0.459804i 0.152080π0.152080\pi
548548 −49.7022 −2.12317
549549 9.14497i 0.390298i
550550 20.7933 5.17168i 0.886628 0.220521i
551551 −2.96103 + 2.96103i −0.126144 + 0.126144i
552552 83.4199i 3.55059i
553553 26.7310i 1.13672i
554554 47.8022 47.8022i 2.03092 2.03092i
555555 −5.25907 + 2.97345i −0.223235 + 0.126216i
556556 32.6045i 1.38274i
557557 −17.9619 −0.761072 −0.380536 0.924766i 0.624260π-0.624260\pi
−0.380536 + 0.924766i 0.624260π0.624260\pi
558558 −19.1041 + 19.1041i −0.808743 + 0.808743i
559559 0 0
560560 4.26743 15.3707i 0.180332 0.649532i
561561 −1.14994 + 1.14994i −0.0485506 + 0.0485506i
562562 6.11785 6.11785i 0.258066 0.258066i
563563 10.6362 10.6362i 0.448262 0.448262i −0.446514 0.894777i 0.647335π-0.647335\pi
0.894777 + 0.446514i 0.147335π0.147335\pi
564564 −11.6459 11.6459i −0.490380 0.490380i
565565 28.5438 16.1385i 1.20085 0.678953i
566566 −13.0976 13.0976i −0.550532 0.550532i
567567 −38.6071 −1.62135
568568 −30.3062 30.3062i −1.27162 1.27162i
569569 −21.9520 −0.920277 −0.460138 0.887847i 0.652200π-0.652200\pi
−0.460138 + 0.887847i 0.652200π0.652200\pi
570570 18.1627 65.4197i 0.760751 2.74013i
571571 12.0101i 0.502606i −0.967908 0.251303i 0.919141π-0.919141\pi
0.967908 0.251303i 0.0808590π-0.0808590\pi
572572 0 0
573573 13.4606 + 13.4606i 0.562325 + 0.562325i
574574 19.1291 + 19.1291i 0.798435 + 0.798435i
575575 44.8376 11.1520i 1.86986 0.465070i
576576 28.0650i 1.16938i
577577 21.1801i 0.881741i 0.897571 + 0.440870i 0.145330π0.145330\pi
−0.897571 + 0.440870i 0.854670π0.854670\pi
578578 −39.9790 −1.66291
579579 −38.4124 + 38.4124i −1.59637 + 1.59637i
580580 −5.97712 1.65945i −0.248186 0.0689048i
581581 −42.7619 −1.77406
582582 −3.46131 3.46131i −0.143476 0.143476i
583583 3.03262i 0.125598i
584584 17.3724 0.718873
585585 0 0
586586 −53.5214 −2.21095
587587 34.5014i 1.42403i −0.702166 0.712013i 0.747784π-0.747784\pi
0.702166 0.712013i 0.252216π-0.252216\pi
588588 −41.8186 41.8186i −1.72457 1.72457i
589589 25.3488 1.04448
590590 −29.4280 + 16.6385i −1.21153 + 0.684994i
591591 36.4656 36.4656i 1.50000 1.50000i
592592 2.20645 0.0906845
593593 28.3656i 1.16483i −0.812890 0.582417i 0.802107π-0.802107\pi
0.812890 0.582417i 0.197893π-0.197893\pi
594594 5.40203i 0.221648i
595595 −2.80355 + 1.58511i −0.114934 + 0.0649833i
596596 32.6107 + 32.6107i 1.33579 + 1.33579i
597597 13.4452 + 13.4452i 0.550276 + 0.550276i
598598 0 0
599599 3.01612i 0.123235i 0.998100 + 0.0616176i 0.0196259π0.0196259\pi
−0.998100 + 0.0616176i 0.980374π0.980374\pi
600600 43.8025 10.8945i 1.78823 0.444767i
601601 13.5808 0.553973 0.276986 0.960874i 0.410664π-0.410664\pi
0.276986 + 0.960874i 0.410664π0.410664\pi
602602 −11.8728 11.8728i −0.483899 0.483899i
603603 −27.2042 −1.10784
604604 10.7444 + 10.7444i 0.437185 + 0.437185i
605605 16.6704 + 4.62824i 0.677746 + 0.188165i
606606 −31.1328 31.1328i −1.26468 1.26468i
607607 −25.3551 + 25.3551i −1.02913 + 1.02913i −0.0295695 + 0.999563i 0.509414π0.509414\pi
−0.999563 + 0.0295695i 0.990586π0.990586\pi
608608 12.3890 12.3890i 0.502438 0.502438i
609609 −4.72282 + 4.72282i −0.191378 + 0.191378i
610610 −18.9978 5.27442i −0.769198 0.213555i
611611 0 0
612612 −2.43224 + 2.43224i −0.0983175 + 0.0983175i
613613 4.50152 0.181815 0.0909074 0.995859i 0.471023π-0.471023\pi
0.0909074 + 0.995859i 0.471023π0.471023\pi
614614 48.4175i 1.95397i
615615 −4.26374 + 15.3575i −0.171931 + 0.619273i
616616 −18.4461 + 18.4461i −0.743213 + 0.743213i
617617 38.4700i 1.54874i −0.632731 0.774372i 0.718066π-0.718066\pi
0.632731 0.774372i 0.281934π-0.281934\pi
618618 84.2250i 3.38803i
619619 5.85514 5.85514i 0.235338 0.235338i −0.579578 0.814916i 0.696783π-0.696783\pi
0.814916 + 0.579578i 0.196783π0.196783\pi
620620 18.4814 + 32.6876i 0.742230 + 1.31277i
621621 11.6487i 0.467446i
622622 50.7134 2.03342
623623 6.12441 6.12441i 0.245369 0.245369i
624624 0 0
625625 11.7115 + 22.0871i 0.468459 + 0.883485i
626626 −12.4012 + 12.4012i −0.495651 + 0.495651i
627627 −16.3469 + 16.3469i −0.652834 + 0.652834i
628628 47.3018 47.3018i 1.88755 1.88755i
629629 −0.314994 0.314994i −0.0125596 0.0125596i
630630 13.0537 47.0179i 0.520073 1.87324i
631631 −26.4142 26.4142i −1.05153 1.05153i −0.998598 0.0529351i 0.983142π-0.983142\pi
−0.0529351 0.998598i 0.516858π-0.516858\pi
632632 −27.6237 −1.09881
633633 −40.9345 40.9345i −1.62700 1.62700i
634634 61.4053 2.43872
635635 −13.6900 + 7.74023i −0.543270 + 0.307162i
636636 14.2348i 0.564448i
637637 0 0
638638 2.31681 + 2.31681i 0.0917235 + 0.0917235i
639639 −19.3027 19.3027i −0.763603 0.763603i
640640 44.5174 + 12.3595i 1.75971 + 0.488553i
641641 3.43214i 0.135561i −0.997700 0.0677806i 0.978408π-0.978408\pi
0.997700 0.0677806i 0.0215918π-0.0215918\pi
642642 57.9252i 2.28613i
643643 16.4627 0.649227 0.324614 0.945847i 0.394766π-0.394766\pi
0.324614 + 0.945847i 0.394766π0.394766\pi
644644 −88.6302 + 88.6302i −3.49252 + 3.49252i
645645 2.64636 9.53185i 0.104200 0.375316i
646646 5.00619 0.196966
647647 13.4904 + 13.4904i 0.530364 + 0.530364i 0.920681 0.390317i 0.127635π-0.127635\pi
−0.390317 + 0.920681i 0.627635π0.627635\pi
648648 39.8964i 1.56728i
649649 11.5110 0.451846
650650 0 0
651651 40.4311 1.58462
652652 57.4872i 2.25137i
653653 −27.0722 27.0722i −1.05942 1.05942i −0.998120 0.0612973i 0.980476π-0.980476\pi
−0.0612973 0.998120i 0.519524π-0.519524\pi
654654 32.4171 1.26761
655655 5.59149 20.1398i 0.218477 0.786928i
656656 4.11605 4.11605i 0.160705 0.160705i
657657 11.0649 0.431681
658658 17.2277i 0.671605i
659659 39.2882i 1.53045i 0.643763 + 0.765225i 0.277372π0.277372\pi
−0.643763 + 0.765225i 0.722628π0.722628\pi
660660 −32.9979 9.16131i −1.28444 0.356604i
661661 19.1671 + 19.1671i 0.745515 + 0.745515i 0.973633 0.228119i 0.0732574π-0.0732574\pi
−0.228119 + 0.973633i 0.573257π0.573257\pi
662662 17.6545 + 17.6545i 0.686161 + 0.686161i
663663 0 0
664664 44.1900i 1.71490i
665665 −39.8537 + 22.5331i −1.54546 + 0.873794i
666666 6.74935 0.261532
667667 4.99587 + 4.99587i 0.193441 + 0.193441i
668668 −45.2943 −1.75249
669669 −48.7808 48.7808i −1.88597 1.88597i
670670 −15.6902 + 56.5140i −0.606164 + 2.18332i
671671 4.74713 + 4.74713i 0.183261 + 0.183261i
672672 19.7603 19.7603i 0.762270 0.762270i
673673 −5.02239 + 5.02239i −0.193599 + 0.193599i −0.797249 0.603650i 0.793712π-0.793712\pi
0.603650 + 0.797249i 0.293712π0.293712\pi
674674 −15.8462 + 15.8462i −0.610373 + 0.610373i
675675 −6.11655 + 1.52130i −0.235426 + 0.0585550i
676676 0 0
677677 19.2265 19.2265i 0.738933 0.738933i −0.233439 0.972372i 0.574998π-0.574998\pi
0.972372 + 0.233439i 0.0749978π0.0749978\pi
678678 −81.2961 −3.12216
679679 3.30084i 0.126675i
680680 1.63805 + 2.89718i 0.0628163 + 0.111102i
681681 −12.9987 + 12.9987i −0.498112 + 0.498112i
682682 19.8338i 0.759475i
683683 4.61676i 0.176655i −0.996091 0.0883277i 0.971848π-0.971848\pi
0.996091 0.0883277i 0.0281523π-0.0281523\pi
684684 −34.5753 + 34.5753i −1.32202 + 1.32202i
685685 −8.19401 + 29.5138i −0.313077 + 1.12766i
686686 0.220219i 0.00840798i
687687 −41.1139 −1.56859
688688 −2.55469 + 2.55469i −0.0973967 + 0.0973967i
689689 0 0
690690 −110.377 30.6442i −4.20197 1.16661i
691691 7.48635 7.48635i 0.284794 0.284794i −0.550223 0.835018i 0.685457π-0.685457\pi
0.835018 + 0.550223i 0.185457π0.185457\pi
692692 41.4658 41.4658i 1.57629 1.57629i
693693 −11.7487 + 11.7487i −0.446297 + 0.446297i
694694 11.9539 + 11.9539i 0.453766 + 0.453766i
695695 −19.3610 5.37525i −0.734404 0.203895i
696696 4.88054 + 4.88054i 0.184996 + 0.184996i
697697 −1.17522 −0.0445146
698698 54.7086 + 54.7086i 2.07075 + 2.07075i
699699 −5.05594 −0.191233
700700 −58.1134 34.9634i −2.19648 1.32149i
701701 48.9646i 1.84937i −0.380735 0.924684i 0.624329π-0.624329\pi
0.380735 0.924684i 0.375671π-0.375671\pi
702702 0 0
703703 −4.47777 4.47777i −0.168882 0.168882i
704704 −14.5685 14.5685i −0.549070 0.549070i
705705 −8.83542 + 4.99550i −0.332761 + 0.188141i
706706 30.6528i 1.15363i
707707 29.6895i 1.11659i
708708 54.0316 2.03063
709709 17.4186 17.4186i 0.654169 0.654169i −0.299825 0.953994i 0.596928π-0.596928\pi
0.953994 + 0.299825i 0.0969284π0.0969284\pi
710710 −51.2324 + 28.9665i −1.92272 + 1.08709i
711711 −17.5942 −0.659834
712712 −6.32893 6.32893i −0.237187 0.237187i
713713 42.7687i 1.60170i
714714 7.98484 0.298825
715715 0 0
716716 66.9366 2.50154
717717 23.3291i 0.871242i
718718 −29.7274 29.7274i −1.10942 1.10942i
719719 −46.6034 −1.73801 −0.869007 0.494799i 0.835242π-0.835242\pi
−0.869007 + 0.494799i 0.835242π0.835242\pi
720720 −10.1169 2.80879i −0.377035 0.104678i
721721 −40.1601 + 40.1601i −1.49564 + 1.49564i
722722 26.0891 0.970937
723723 33.8652i 1.25946i
724724 7.94552i 0.295293i
725725 −1.97080 + 3.27571i −0.0731937 + 0.121657i
726726 −30.3304 30.3304i −1.12567 1.12567i
727727 16.4412 + 16.4412i 0.609770 + 0.609770i 0.942886 0.333116i 0.108100π-0.108100\pi
−0.333116 + 0.942886i 0.608100π0.608100\pi
728728 0 0
729729 16.5738i 0.613846i
730730 6.38172 22.9861i 0.236198 0.850755i
731731 0.729418 0.0269785
732732 22.2826 + 22.2826i 0.823588 + 0.823588i
733733 −30.6968 −1.13381 −0.566907 0.823782i 0.691860π-0.691860\pi
−0.566907 + 0.823782i 0.691860π0.691860\pi
734734 58.4687 + 58.4687i 2.15812 + 2.15812i
735735 −31.7267 + 17.9381i −1.17026 + 0.661657i
736736 −20.9028 20.9028i −0.770486 0.770486i
737737 14.1216 14.1216i 0.520176 0.520176i
738738 12.5907 12.5907i 0.463469 0.463469i
739739 24.4091 24.4091i 0.897902 0.897902i −0.0973480 0.995250i 0.531036π-0.531036\pi
0.995250 + 0.0973480i 0.0310360π0.0310360\pi
740740 2.50948 9.03881i 0.0922502 0.332273i
741741 0 0
742742 10.5288 10.5288i 0.386523 0.386523i
743743 −0.307988 −0.0112990 −0.00564949 0.999984i 0.501798π-0.501798\pi
−0.00564949 + 0.999984i 0.501798π0.501798\pi
744744 41.7813i 1.53178i
745745 24.7409 13.9884i 0.906437 0.512494i
746746 25.0528 25.0528i 0.917249 0.917249i
747747 28.1456i 1.02979i
748748 2.52514i 0.0923282i
749749 −27.6199 + 27.6199i −1.00921 + 1.00921i
750750 1.67579 61.9592i 0.0611911 2.26243i
751751 20.9010i 0.762690i 0.924433 + 0.381345i 0.124539π0.124539\pi
−0.924433 + 0.381345i 0.875461π0.875461\pi
752752 3.70691 0.135177
753753 29.3529 29.3529i 1.06968 1.06968i
754754 0 0
755755 8.15153 4.60883i 0.296665 0.167733i
756756 12.0905 12.0905i 0.439729 0.439729i
757757 −23.7489 + 23.7489i −0.863168 + 0.863168i −0.991705 0.128536i 0.958972π-0.958972\pi
0.128536 + 0.991705i 0.458972π0.458972\pi
758758 −54.3352 + 54.3352i −1.97354 + 1.97354i
759759 27.5807 + 27.5807i 1.00112 + 1.00112i
760760 23.2855 + 41.1846i 0.844656 + 1.49392i
761761 33.9474 + 33.9474i 1.23059 + 1.23059i 0.963736 + 0.266856i 0.0859850π0.0859850\pi
0.266856 + 0.963736i 0.414015π0.414015\pi
762762 38.9906 1.41248
763763 −15.4571 15.4571i −0.559584 0.559584i
764764 −29.5579 −1.06937
765765 1.04331 + 1.84528i 0.0377210 + 0.0667162i
766766 76.4612i 2.76266i
767767 0 0
768768 −43.3025 43.3025i −1.56255 1.56255i
769769 16.5558 + 16.5558i 0.597016 + 0.597016i 0.939517 0.342502i 0.111274π-0.111274\pi
−0.342502 + 0.939517i 0.611274π0.611274\pi
770770 17.6307 + 31.1830i 0.635365 + 1.12376i
771771 21.0658i 0.758667i
772772 84.3490i 3.03579i
773773 −26.8939 −0.967307 −0.483653 0.875260i 0.660690π-0.660690\pi
−0.483653 + 0.875260i 0.660690π0.660690\pi
774774 −7.81460 + 7.81460i −0.280890 + 0.280890i
775775 22.4572 5.58553i 0.806686 0.200638i
776776 3.41107 0.122450
777777 −7.14201 7.14201i −0.256218 0.256218i
778778 27.9513i 1.00210i
779779 −16.7062 −0.598563
780780 0 0
781781 20.0399 0.717086
782782 8.44649i 0.302046i
783783 −0.681514 0.681514i −0.0243553 0.0243553i
784784 13.3110 0.475392
785785 −20.2901 35.8867i −0.724186 1.28085i
786786 −36.6428 + 36.6428i −1.30701 + 1.30701i
787787 1.45463 0.0518521 0.0259261 0.999664i 0.491747π-0.491747\pi
0.0259261 + 0.999664i 0.491747π0.491747\pi
788788 80.0741i 2.85252i
789789 9.96087i 0.354616i
790790 −10.1476 + 36.5502i −0.361034 + 1.30040i
791791 38.7636 + 38.7636i 1.37827 + 1.37827i
792792 12.1411 + 12.1411i 0.431414 + 0.431414i
793793 0 0
794794 19.3299i 0.685994i
795795 8.45282 + 2.34678i 0.299790 + 0.0832318i
796796 −29.5241 −1.04645
797797 8.79879 + 8.79879i 0.311669 + 0.311669i 0.845556 0.533887i 0.179269π-0.179269\pi
−0.533887 + 0.845556i 0.679269π0.679269\pi
798798 113.508 4.01813
799799 −0.529200 0.529200i −0.0187218 0.0187218i
800800 8.24585 13.7056i 0.291535 0.484566i
801801 −4.03104 4.03104i −0.142430 0.142430i
802802 −27.7018 + 27.7018i −0.978183 + 0.978183i
803803 −5.74373 + 5.74373i −0.202692 + 0.202692i
804804 66.2855 66.2855i 2.33771 2.33771i
805805 38.0180 + 67.2415i 1.33996 + 2.36995i
806806 0 0
807807 −2.97029 + 2.97029i −0.104559 + 0.104559i
808808 30.6810 1.07935
809809 7.21727i 0.253746i 0.991919 + 0.126873i 0.0404940π0.0404940\pi
−0.991919 + 0.126873i 0.959506π0.959506\pi
810810 52.7887 + 14.6559i 1.85481 + 0.514956i
811811 −15.0515 + 15.0515i −0.528530 + 0.528530i −0.920134 0.391604i 0.871920π-0.871920\pi
0.391604 + 0.920134i 0.371920π0.371920\pi
812812 10.3707i 0.363942i
813813 6.89134i 0.241690i
814814 −3.50357 + 3.50357i −0.122800 + 0.122800i
815815 −34.1366 9.47747i −1.19575 0.331981i
816816 1.71811i 0.0601460i
817817 10.3690 0.362765
818818 7.08575 7.08575i 0.247747 0.247747i
819819 0 0
820820 −12.1802 21.5429i −0.425352 0.752311i
821821 −12.4012 + 12.4012i −0.432805 + 0.432805i −0.889581 0.456777i 0.849004π-0.849004\pi
0.456777 + 0.889581i 0.349004π0.349004\pi
822822 53.6980 53.6980i 1.87293 1.87293i
823823 −7.74299 + 7.74299i −0.269904 + 0.269904i −0.829061 0.559158i 0.811125π-0.811125\pi
0.559158 + 0.829061i 0.311125π0.311125\pi
824824 41.5013 + 41.5013i 1.44576 + 1.44576i
825825 −10.8802 + 18.0842i −0.378800 + 0.629611i
826826 −39.9644 39.9644i −1.39054 1.39054i
827827 1.86613 0.0648917 0.0324458 0.999473i 0.489670π-0.489670\pi
0.0324458 + 0.999473i 0.489670π0.489670\pi
828828 58.3358 + 58.3358i 2.02731 + 2.02731i
829829 34.7843 1.20811 0.604055 0.796943i 0.293551π-0.293551\pi
0.604055 + 0.796943i 0.293551π0.293551\pi
830830 58.4697 + 16.2331i 2.02951 + 0.563461i
831831 66.5870i 2.30988i
832832 0 0
833833 −1.90028 1.90028i −0.0658408 0.0658408i
834834 35.2258 + 35.2258i 1.21977 + 1.21977i
835835 −7.46731 + 26.8963i −0.258417 + 0.930784i
836836 35.8959i 1.24149i
837837 5.83431i 0.201663i
838838 −40.5189 −1.39970
839839 13.7215 13.7215i 0.473718 0.473718i −0.429397 0.903116i 0.641274π-0.641274\pi
0.903116 + 0.429397i 0.141274π0.141274\pi
840840 37.1403 + 65.6892i 1.28146 + 2.26649i
841841 28.4154 0.979842
842842 −21.9815 21.9815i −0.757533 0.757533i
843843 8.52199i 0.293513i
844844 89.8873 3.09405
845845 0 0
846846 11.3391 0.389848
847847 28.9243i 0.993849i
848848 −2.26549 2.26549i −0.0777973 0.0777973i
849849 18.2445 0.626151
850850 4.43512 1.10310i 0.152123 0.0378360i
851851 −7.55493 + 7.55493i −0.258980 + 0.258980i
852852 94.0657 3.22264
853853 2.67051i 0.0914364i 0.998954 + 0.0457182i 0.0145576π0.0145576\pi
−0.998954 + 0.0457182i 0.985442π0.985442\pi
854854 32.9625i 1.12795i
855855 14.8311 + 26.2314i 0.507213 + 0.897096i
856856 28.5422 + 28.5422i 0.975553 + 0.975553i
857857 −17.5773 17.5773i −0.600430 0.600430i 0.339996 0.940427i 0.389574π-0.389574\pi
−0.940427 + 0.339996i 0.889574π0.889574\pi
858858 0 0
859859 52.8699i 1.80390i 0.431844 + 0.901949i 0.357863π0.357863\pi
−0.431844 + 0.901949i 0.642137π0.642137\pi
860860 7.55986 + 13.3709i 0.257789 + 0.455946i
861861 −26.6463 −0.908104
862862 17.9744 + 17.9744i 0.612211 + 0.612211i
863863 −3.40127 −0.115780 −0.0578902 0.998323i 0.518437π-0.518437\pi
−0.0578902 + 0.998323i 0.518437π0.518437\pi
864864 2.85146 + 2.85146i 0.0970087 + 0.0970087i
865865 −17.7868 31.4590i −0.604768 1.06964i
866866 8.56625 + 8.56625i 0.291093 + 0.291093i
867867 27.8447 27.8447i 0.945657 0.945657i
868868 −44.3910 + 44.3910i −1.50673 + 1.50673i
869869 9.13309 9.13309i 0.309819 0.309819i
870870 8.25052 4.66479i 0.279719 0.158151i
871871 0 0
872872 −15.9733 + 15.9733i −0.540923 + 0.540923i
873873 2.17259 0.0735311
874874 120.070i 4.06144i
875875 −30.3424 + 28.7443i −1.02576 + 0.971735i
876876 −26.9605 + 26.9605i −0.910912 + 0.910912i
877877 19.6750i 0.664379i −0.943213 0.332189i 0.892213π-0.892213\pi
0.943213 0.332189i 0.107787π-0.107787\pi
878878 48.0161i 1.62046i
879879 37.2768 37.2768i 1.25732 1.25732i
880880 6.70970 3.79362i 0.226184 0.127883i
881881 2.38273i 0.0802762i −0.999194 0.0401381i 0.987220π-0.987220\pi
0.999194 0.0401381i 0.0127798π-0.0127798\pi
882882 40.7172 1.37102
883883 −30.4180 + 30.4180i −1.02365 + 1.02365i −0.0239343 + 0.999714i 0.507619π0.507619\pi
−0.999714 + 0.0239343i 0.992381π0.992381\pi
884884 0 0
885885 8.90776 32.0846i 0.299431 1.07851i
886886 6.31260 6.31260i 0.212076 0.212076i
887887 −16.0566 + 16.0566i −0.539127 + 0.539127i −0.923272 0.384146i 0.874496π-0.874496\pi
0.384146 + 0.923272i 0.374496π0.374496\pi
888888 −7.38052 + 7.38052i −0.247674 + 0.247674i
889889 −18.5915 18.5915i −0.623538 0.623538i
890890 −10.6990 + 6.04917i −0.358632 + 0.202769i
891891 −13.1907 13.1907i −0.441906 0.441906i
892892 107.117 3.58653
893893 −7.52280 7.52280i −0.251741 0.251741i
894894 −70.4649 −2.35670
895895 11.0353 39.7477i 0.368869 1.32862i
896896 77.2410i 2.58044i
897897 0 0
898898 51.6980 + 51.6980i 1.72518 + 1.72518i
899899 2.50221 + 2.50221i 0.0834533 + 0.0834533i
900900 −23.0127 + 38.2498i −0.767089 + 1.27499i
901901 0.646845i 0.0215495i
902902 13.0716i 0.435235i
903903 16.5385 0.550365
904904 40.0581 40.0581i 1.33231 1.33231i
905905 4.71815 + 1.30992i 0.156837 + 0.0435431i
906906 −23.2165 −0.771316
907907 −16.3686 16.3686i −0.543510 0.543510i 0.381046 0.924556i 0.375564π-0.375564\pi
−0.924556 + 0.381046i 0.875564π0.875564\pi
908908 28.5436i 0.947253i
909909 19.5414 0.648147
910910 0 0
911911 −23.7450 −0.786707 −0.393354 0.919387i 0.628685π-0.628685\pi
−0.393354 + 0.919387i 0.628685π0.628685\pi
912912 24.4237i 0.808749i
913913 −14.6103 14.6103i −0.483530 0.483530i
914914 −24.1508 −0.798837
915915 16.9052 9.55812i 0.558869 0.315982i
916916 45.1406 45.1406i 1.49149 1.49149i
917917 34.9440 1.15395
918918 1.15223i 0.0380293i
919919 56.9671i 1.87917i −0.342313 0.939586i 0.611210π-0.611210\pi
0.342313 0.939586i 0.388790π-0.388790\pi
920920 69.4870 39.2876i 2.29092 1.29527i
921921 −33.7221 33.7221i −1.11118 1.11118i
922922 −32.3379 32.3379i −1.06499 1.06499i
923923 0 0
924924 57.2537i 1.88351i
925925 −4.95364 2.98032i −0.162875 0.0979922i
926926 −39.8398 −1.30922
927927 26.4331 + 26.4331i 0.868177 + 0.868177i
928928 2.44586 0.0802892
929929 20.6626 + 20.6626i 0.677918 + 0.677918i 0.959529 0.281611i 0.0908687π-0.0908687\pi
−0.281611 + 0.959529i 0.590869π0.590869\pi
930930 −55.2828 15.3483i −1.81279 0.503292i
931931 −27.0133 27.0133i −0.885325 0.885325i
932932 5.55112 5.55112i 0.181833 0.181833i
933933 −35.3211 + 35.3211i −1.15636 + 1.15636i
934934 −23.1496 + 23.1496i −0.757478 + 0.757478i
935935 −1.49946 0.416299i −0.0490375 0.0136144i
936936 0 0
937937 −1.77191 + 1.77191i −0.0578859 + 0.0578859i −0.735457 0.677571i 0.763033π-0.763033\pi
0.677571 + 0.735457i 0.263033π0.263033\pi
938938 −98.0558 −3.20164
939939 17.2745i 0.563731i
940940 4.21601 15.1855i 0.137511 0.495297i
941941 −15.5682 + 15.5682i −0.507507 + 0.507507i −0.913761 0.406253i 0.866835π-0.866835\pi
0.406253 + 0.913761i 0.366835π0.366835\pi
942942 102.209i 3.33016i
943943 28.1869i 0.917891i
944944 −8.59920 + 8.59920i −0.279880 + 0.279880i
945945 −5.18624 9.17279i −0.168708 0.298391i
946946 8.11306i 0.263778i
947947 0.361869 0.0117591 0.00587957 0.999983i 0.498128π-0.498128\pi
0.00587957 + 0.999983i 0.498128π0.498128\pi
948948 42.8699 42.8699i 1.39235 1.39235i
949949 0 0
950950 63.0471 15.6810i 2.04552 0.508760i
951951 −42.7679 + 42.7679i −1.38684 + 1.38684i
952952 −3.93447 + 3.93447i −0.127517 + 0.127517i
953953 −28.6611 + 28.6611i −0.928423 + 0.928423i −0.997604 0.0691813i 0.977961π-0.977961\pi
0.0691813 + 0.997604i 0.477961π0.477961\pi
954954 −6.92996 6.92996i −0.224366 0.224366i
955955 −4.87298 + 17.5518i −0.157686 + 0.567964i
956956 25.6140 + 25.6140i 0.828415 + 0.828415i
957957 −3.22725 −0.104322
958958 23.1837 + 23.1837i 0.749031 + 0.749031i
959959 −51.2085 −1.65361
960960 −51.8805 + 29.3329i −1.67443 + 0.946716i
961961 9.57907i 0.309002i
962962 0 0
963963 18.1792 + 18.1792i 0.585817 + 0.585817i
964964 37.1820 + 37.1820i 1.19755 + 1.19755i
965965 −50.0875 13.9060i −1.61237 0.447649i
966966 191.511i 6.16178i
967967 12.2654i 0.394430i 0.980360 + 0.197215i 0.0631897π0.0631897\pi
−0.980360 + 0.197215i 0.936810π0.936810\pi
968968 29.8902 0.960707
969969 −3.48674 + 3.48674i −0.112010 + 0.112010i
970970 1.25305 4.51334i 0.0402332 0.144915i
971971 22.6199 0.725907 0.362953 0.931807i 0.381768π-0.381768\pi
0.362953 + 0.931807i 0.381768π0.381768\pi
972972 −52.2135 52.2135i −1.67475 1.67475i
973973 33.5927i 1.07693i
974974 48.5378 1.55525
975975 0 0
976976 −7.09261 −0.227029
977977 35.1692i 1.12516i −0.826742 0.562581i 0.809808π-0.809808\pi
0.826742 0.562581i 0.190192π-0.190192\pi
978978 62.1090 + 62.1090i 1.98603 + 1.98603i
979979 4.18500 0.133753
980980 15.1391 54.5290i 0.483600 1.74186i
981981 −10.1737 + 10.1737i −0.324823 + 0.324823i
982982 −24.1722 −0.771367
983983 12.2764i 0.391555i 0.980648 + 0.195778i 0.0627231π0.0627231\pi
−0.980648 + 0.195778i 0.937277π0.937277\pi
984984 27.5362i 0.877821i
985985 47.5490 + 13.2012i 1.51504 + 0.420625i
986986 0.494167 + 0.494167i 0.0157375 + 0.0157375i
987987 −11.9988 11.9988i −0.381927 0.381927i
988988 0 0
989989 17.4946i 0.556297i
990990 20.5244 11.6044i 0.652309 0.368812i
991991 33.1990 1.05460 0.527301 0.849679i 0.323204π-0.323204\pi
0.527301 + 0.849679i 0.323204π0.323204\pi
992992 −10.4693 10.4693i −0.332399 0.332399i
993993 −24.5922 −0.780409
994994 −69.5755 69.5755i −2.20680 2.20680i
995995 −4.86740 + 17.5318i −0.154307 + 0.555795i
996996 −68.5794 68.5794i −2.17302 2.17302i
997997 −26.5760 + 26.5760i −0.841671 + 0.841671i −0.989076 0.147405i 0.952908π-0.952908\pi
0.147405 + 0.989076i 0.452908π0.452908\pi
998998 18.7456 18.7456i 0.593383 0.593383i
999999 1.03061 1.03061i 0.0326070 0.0326070i
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 845.2.f.f.408.5 72
5.2 odd 4 845.2.k.f.577.32 yes 72
13.2 odd 12 845.2.o.i.488.32 144
13.3 even 3 845.2.t.i.188.32 144
13.4 even 6 845.2.t.i.418.32 144
13.5 odd 4 845.2.k.f.268.5 yes 72
13.6 odd 12 845.2.o.i.258.32 144
13.7 odd 12 845.2.o.i.258.5 144
13.8 odd 4 845.2.k.f.268.32 yes 72
13.9 even 3 845.2.t.i.418.5 144
13.10 even 6 845.2.t.i.188.5 144
13.11 odd 12 845.2.o.i.488.5 144
13.12 even 2 inner 845.2.f.f.408.32 yes 72
65.2 even 12 845.2.t.i.657.32 144
65.7 even 12 845.2.t.i.427.32 144
65.12 odd 4 845.2.k.f.577.5 yes 72
65.17 odd 12 845.2.o.i.587.32 144
65.22 odd 12 845.2.o.i.587.5 144
65.32 even 12 845.2.t.i.427.5 144
65.37 even 12 845.2.t.i.657.5 144
65.42 odd 12 845.2.o.i.357.5 144
65.47 even 4 inner 845.2.f.f.437.32 yes 72
65.57 even 4 inner 845.2.f.f.437.5 yes 72
65.62 odd 12 845.2.o.i.357.32 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.f.f.408.5 72 1.1 even 1 trivial
845.2.f.f.408.32 yes 72 13.12 even 2 inner
845.2.f.f.437.5 yes 72 65.57 even 4 inner
845.2.f.f.437.32 yes 72 65.47 even 4 inner
845.2.k.f.268.5 yes 72 13.5 odd 4
845.2.k.f.268.32 yes 72 13.8 odd 4
845.2.k.f.577.5 yes 72 65.12 odd 4
845.2.k.f.577.32 yes 72 5.2 odd 4
845.2.o.i.258.5 144 13.7 odd 12
845.2.o.i.258.32 144 13.6 odd 12
845.2.o.i.357.5 144 65.42 odd 12
845.2.o.i.357.32 144 65.62 odd 12
845.2.o.i.488.5 144 13.11 odd 12
845.2.o.i.488.32 144 13.2 odd 12
845.2.o.i.587.5 144 65.22 odd 12
845.2.o.i.587.32 144 65.17 odd 12
845.2.t.i.188.5 144 13.10 even 6
845.2.t.i.188.32 144 13.3 even 3
845.2.t.i.418.5 144 13.9 even 3
845.2.t.i.418.32 144 13.4 even 6
845.2.t.i.427.5 144 65.32 even 12
845.2.t.i.427.32 144 65.7 even 12
845.2.t.i.657.5 144 65.37 even 12
845.2.t.i.657.32 144 65.2 even 12