Properties

Label 425.2.m.e.376.2
Level 425425
Weight 22
Character 425.376
Analytic conductor 3.3943.394
Analytic rank 00
Dimension 2424
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [425,2,Mod(26,425)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(425, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("425.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 425=5217 425 = 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 425.m (of order 88, degree 44, 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: 3.393642085903.39364208590
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: no (minimal twist has level 85)
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 376.2
Character χ\chi == 425.376
Dual form 425.2.m.e.26.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.6729810.672981i)q2+(2.286450.947078i)q31.09419iq4+(2.176100.901371i)q6+(0.2041150.492777i)q7+(2.08233+2.08233i)q8+(2.209572.20957i)q9+(4.31906+1.78902i)q11+(1.036292.50182i)q123.92573iq13+(0.468995+0.194264i)q14+0.614355q16+(0.8671924.03088i)q172.97399q18+(0.7085480.708548i)q191.32002iq21+(1.702684.11062i)q22+(5.301292.19587i)q23+(2.78902+6.73328i)q24+(2.64194+2.64194i)q26+(0.1181960.285350i)q27+(0.5391930.223341i)q28+(3.17120+7.65596i)q29+(2.29036+0.948699i)q31+(3.75122+3.75122i)q32+11.5697q33+(3.29631+2.12910i)q34+(2.417692.41769i)q36+(3.78211+1.56660i)q37+0.953679iq38+(3.717978.97598i)q39+(0.311708+0.752530i)q41+(0.888349+0.888349i)q42+(4.55216+4.55216i)q43+(1.957534.72589i)q44+(2.08989+5.04545i)q461.70505iq47+(1.404690.581842i)q48+(4.74858+4.74858i)q49+(1.8347710.0377i)q514.29551q52+(5.77230+5.77230i)q53+(0.271578+0.112491i)q54+(0.601090+1.45116i)q56+(2.291110.949008i)q57+(3.018167.28648i)q58+(4.283044.28304i)q59+(0.432837+1.04496i)q61+(2.17983+0.902914i)q62+(0.6378181.53983i)q636.27771iq64+(7.786167.78616i)q66+7.68603q67+(4.410560.948875i)q6814.2008q69+(6.414242.65686i)q71+9.20211iq72+(4.6252111.1662i)q73+(3.59958+1.49100i)q74+(0.775289+0.775289i)q76+(1.763171.76317i)q77+(3.53854+8.54279i)q78+(1.36830+0.566769i)q79+8.61002iq81+(0.7162120.296665i)q82+(11.4464+11.4464i)q831.44436q84+6.12703q86+(14.5016+14.5016i)q87+(12.7191+5.26841i)q8812.0717iq89+(1.934510.801300i)q91+(2.40270+5.80064i)q92+(4.33830+4.33830i)q93+(1.14747+1.14747i)q94+(12.1297+5.02427i)q96+(0.08726800.210684i)q976.39141iq98+(13.49625.59031i)q99+O(q100)q+(-0.672981 - 0.672981i) q^{2} +(2.28645 - 0.947078i) q^{3} -1.09419i q^{4} +(-2.17610 - 0.901371i) q^{6} +(0.204115 - 0.492777i) q^{7} +(-2.08233 + 2.08233i) q^{8} +(2.20957 - 2.20957i) q^{9} +(4.31906 + 1.78902i) q^{11} +(-1.03629 - 2.50182i) q^{12} -3.92573i q^{13} +(-0.468995 + 0.194264i) q^{14} +0.614355 q^{16} +(0.867192 - 4.03088i) q^{17} -2.97399 q^{18} +(-0.708548 - 0.708548i) q^{19} -1.32002i q^{21} +(-1.70268 - 4.11062i) q^{22} +(-5.30129 - 2.19587i) q^{23} +(-2.78902 + 6.73328i) q^{24} +(-2.64194 + 2.64194i) q^{26} +(0.118196 - 0.285350i) q^{27} +(-0.539193 - 0.223341i) q^{28} +(3.17120 + 7.65596i) q^{29} +(-2.29036 + 0.948699i) q^{31} +(3.75122 + 3.75122i) q^{32} +11.5697 q^{33} +(-3.29631 + 2.12910i) q^{34} +(-2.41769 - 2.41769i) q^{36} +(-3.78211 + 1.56660i) q^{37} +0.953679i q^{38} +(-3.71797 - 8.97598i) q^{39} +(-0.311708 + 0.752530i) q^{41} +(-0.888349 + 0.888349i) q^{42} +(-4.55216 + 4.55216i) q^{43} +(1.95753 - 4.72589i) q^{44} +(2.08989 + 5.04545i) q^{46} -1.70505i q^{47} +(1.40469 - 0.581842i) q^{48} +(4.74858 + 4.74858i) q^{49} +(-1.83477 - 10.0377i) q^{51} -4.29551 q^{52} +(5.77230 + 5.77230i) q^{53} +(-0.271578 + 0.112491i) q^{54} +(0.601090 + 1.45116i) q^{56} +(-2.29111 - 0.949008i) q^{57} +(3.01816 - 7.28648i) q^{58} +(4.28304 - 4.28304i) q^{59} +(-0.432837 + 1.04496i) q^{61} +(2.17983 + 0.902914i) q^{62} +(-0.637818 - 1.53983i) q^{63} -6.27771i q^{64} +(-7.78616 - 7.78616i) q^{66} +7.68603 q^{67} +(-4.41056 - 0.948875i) q^{68} -14.2008 q^{69} +(6.41424 - 2.65686i) q^{71} +9.20211i q^{72} +(-4.62521 - 11.1662i) q^{73} +(3.59958 + 1.49100i) q^{74} +(-0.775289 + 0.775289i) q^{76} +(1.76317 - 1.76317i) q^{77} +(-3.53854 + 8.54279i) q^{78} +(1.36830 + 0.566769i) q^{79} +8.61002i q^{81} +(0.716212 - 0.296665i) q^{82} +(11.4464 + 11.4464i) q^{83} -1.44436 q^{84} +6.12703 q^{86} +(14.5016 + 14.5016i) q^{87} +(-12.7191 + 5.26841i) q^{88} -12.0717i q^{89} +(-1.93451 - 0.801300i) q^{91} +(-2.40270 + 5.80064i) q^{92} +(-4.33830 + 4.33830i) q^{93} +(-1.14747 + 1.14747i) q^{94} +(12.1297 + 5.02427i) q^{96} +(-0.0872680 - 0.210684i) q^{97} -6.39141i q^{98} +(13.4962 - 5.59031i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+8q9+24q14+8q16+24q1932q2416q2624q2924q318q34+8q36+24q3948q4172q4416q4648q4932q54+24q56++80q99+O(q100) 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/425Z)×\left(\mathbb{Z}/425\mathbb{Z}\right)^\times.

nn 5252 326326
χ(n)\chi(n) 11 e(78)e\left(\frac{7}{8}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.672981 0.672981i −0.475869 0.475869i 0.427938 0.903808i 0.359240π-0.359240\pi
−0.903808 + 0.427938i 0.859240π0.859240\pi
33 2.28645 0.947078i 1.32008 0.546796i 0.392272 0.919849i 0.371689π-0.371689\pi
0.927810 + 0.373054i 0.121689π0.121689\pi
44 1.09419i 0.547097i
55 0 0
66 −2.17610 0.901371i −0.888390 0.367983i
77 0.204115 0.492777i 0.0771481 0.186252i −0.880600 0.473860i 0.842860π-0.842860\pi
0.957748 + 0.287608i 0.0928601π0.0928601\pi
88 −2.08233 + 2.08233i −0.736216 + 0.736216i
99 2.20957 2.20957i 0.736523 0.736523i
1010 0 0
1111 4.31906 + 1.78902i 1.30225 + 0.539408i 0.922612 0.385728i 0.126050π-0.126050\pi
0.379634 + 0.925137i 0.376050π0.376050\pi
1212 −1.03629 2.50182i −0.299150 0.722212i
1313 3.92573i 1.08880i −0.838825 0.544401i 0.816757π-0.816757\pi
0.838825 0.544401i 0.183243π-0.183243\pi
1414 −0.468995 + 0.194264i −0.125344 + 0.0519192i
1515 0 0
1616 0.614355 0.153589
1717 0.867192 4.03088i 0.210325 0.977632i
1818 −2.97399 −0.700977
1919 −0.708548 0.708548i −0.162552 0.162552i 0.621144 0.783696i 0.286668π-0.286668\pi
−0.783696 + 0.621144i 0.786668π0.786668\pi
2020 0 0
2121 1.32002i 0.288052i
2222 −1.70268 4.11062i −0.363012 0.876387i
2323 −5.30129 2.19587i −1.10540 0.457870i −0.246046 0.969258i 0.579132π-0.579132\pi
−0.859350 + 0.511388i 0.829132π0.829132\pi
2424 −2.78902 + 6.73328i −0.569305 + 1.37442i
2525 0 0
2626 −2.64194 + 2.64194i −0.518128 + 0.518128i
2727 0.118196 0.285350i 0.0227468 0.0549156i
2828 −0.539193 0.223341i −0.101898 0.0422075i
2929 3.17120 + 7.65596i 0.588878 + 1.42168i 0.884576 + 0.466395i 0.154448π0.154448\pi
−0.295699 + 0.955281i 0.595552π0.595552\pi
3030 0 0
3131 −2.29036 + 0.948699i −0.411361 + 0.170391i −0.578760 0.815498i 0.696463π-0.696463\pi
0.167399 + 0.985889i 0.446463π0.446463\pi
3232 3.75122 + 3.75122i 0.663128 + 0.663128i
3333 11.5697 2.01402
3434 −3.29631 + 2.12910i −0.565312 + 0.365138i
3535 0 0
3636 −2.41769 2.41769i −0.402949 0.402949i
3737 −3.78211 + 1.56660i −0.621775 + 0.257548i −0.671254 0.741227i 0.734244π-0.734244\pi
0.0494786 + 0.998775i 0.484244π0.484244\pi
3838 0.953679i 0.154707i
3939 −3.71797 8.97598i −0.595352 1.43731i
4040 0 0
4141 −0.311708 + 0.752530i −0.0486806 + 0.117525i −0.946349 0.323146i 0.895260π-0.895260\pi
0.897669 + 0.440671i 0.145260π0.145260\pi
4242 −0.888349 + 0.888349i −0.137075 + 0.137075i
4343 −4.55216 + 4.55216i −0.694197 + 0.694197i −0.963153 0.268955i 0.913322π-0.913322\pi
0.268955 + 0.963153i 0.413322π0.413322\pi
4444 1.95753 4.72589i 0.295108 0.712455i
4545 0 0
4646 2.08989 + 5.04545i 0.308138 + 0.743911i
4747 1.70505i 0.248707i −0.992238 0.124354i 0.960314π-0.960314\pi
0.992238 0.124354i 0.0396857π-0.0396857\pi
4848 1.40469 0.581842i 0.202750 0.0839817i
4949 4.74858 + 4.74858i 0.678369 + 0.678369i
5050 0 0
5151 −1.83477 10.0377i −0.256919 1.40556i
5252 −4.29551 −0.595680
5353 5.77230 + 5.77230i 0.792887 + 0.792887i 0.981962 0.189076i 0.0605492π-0.0605492\pi
−0.189076 + 0.981962i 0.560549π0.560549\pi
5454 −0.271578 + 0.112491i −0.0369571 + 0.0153081i
5555 0 0
5656 0.601090 + 1.45116i 0.0803240 + 0.193919i
5757 −2.29111 0.949008i −0.303465 0.125699i
5858 3.01816 7.28648i 0.396304 0.956761i
5959 4.28304 4.28304i 0.557605 0.557605i −0.371020 0.928625i 0.620992π-0.620992\pi
0.928625 + 0.371020i 0.120992π0.120992\pi
6060 0 0
6161 −0.432837 + 1.04496i −0.0554192 + 0.133794i −0.949164 0.314782i 0.898069π-0.898069\pi
0.893745 + 0.448576i 0.148069π0.148069\pi
6262 2.17983 + 0.902914i 0.276838 + 0.114670i
6363 −0.637818 1.53983i −0.0803575 0.194000i
6464 6.27771i 0.784713i
6565 0 0
6666 −7.78616 7.78616i −0.958410 0.958410i
6767 7.68603 0.938998 0.469499 0.882933i 0.344435π-0.344435\pi
0.469499 + 0.882933i 0.344435π0.344435\pi
6868 −4.41056 0.948875i −0.534859 0.115068i
6969 −14.2008 −1.70957
7070 0 0
7171 6.41424 2.65686i 0.761230 0.315312i 0.0319156 0.999491i 0.489839π-0.489839\pi
0.729314 + 0.684179i 0.239839π0.239839\pi
7272 9.20211i 1.08448i
7373 −4.62521 11.1662i −0.541340 1.30691i −0.923778 0.382929i 0.874915π-0.874915\pi
0.382438 0.923981i 0.375085π-0.375085\pi
7474 3.59958 + 1.49100i 0.418443 + 0.173325i
7575 0 0
7676 −0.775289 + 0.775289i −0.0889317 + 0.0889317i
7777 1.76317 1.76317i 0.200932 0.200932i
7878 −3.53854 + 8.54279i −0.400661 + 0.967281i
7979 1.36830 + 0.566769i 0.153946 + 0.0637666i 0.458326 0.888784i 0.348449π-0.348449\pi
−0.304380 + 0.952551i 0.598449π0.598449\pi
8080 0 0
8181 8.61002i 0.956669i
8282 0.716212 0.296665i 0.0790924 0.0327611i
8383 11.4464 + 11.4464i 1.25640 + 1.25640i 0.952798 + 0.303606i 0.0981905π0.0981905\pi
0.303606 + 0.952798i 0.401810π0.401810\pi
8484 −1.44436 −0.157592
8585 0 0
8686 6.12703 0.660694
8787 14.5016 + 14.5016i 1.55473 + 1.55473i
8888 −12.7191 + 5.26841i −1.35586 + 0.561614i
8989 12.0717i 1.27960i −0.768542 0.639800i 0.779017π-0.779017\pi
0.768542 0.639800i 0.220983π-0.220983\pi
9090 0 0
9191 −1.93451 0.801300i −0.202792 0.0839991i
9292 −2.40270 + 5.80064i −0.250499 + 0.604758i
9393 −4.33830 + 4.33830i −0.449861 + 0.449861i
9494 −1.14747 + 1.14747i −0.118352 + 0.118352i
9595 0 0
9696 12.1297 + 5.02427i 1.23798 + 0.512787i
9797 −0.0872680 0.210684i −0.00886072 0.0213917i 0.919387 0.393354i 0.128685π-0.128685\pi
−0.928248 + 0.371962i 0.878685π0.878685\pi
9898 6.39141i 0.645630i
9999 13.4962 5.59031i 1.35642 0.561848i
100100 0 0
101101 −6.66539 −0.663231 −0.331616 0.943415i 0.607594π-0.607594\pi
−0.331616 + 0.943415i 0.607594π0.607594\pi
102102 −5.52041 + 7.98994i −0.546602 + 0.791122i
103103 −0.350456 −0.0345315 −0.0172657 0.999851i 0.505496π-0.505496\pi
−0.0172657 + 0.999851i 0.505496π0.505496\pi
104104 8.17468 + 8.17468i 0.801594 + 0.801594i
105105 0 0
106106 7.76930i 0.754621i
107107 2.98446 + 7.20512i 0.288518 + 0.696545i 0.999981 0.00617913i 0.00196689π-0.00196689\pi
−0.711463 + 0.702724i 0.751967π0.751967\pi
108108 −0.312228 0.129329i −0.0300441 0.0124447i
109109 −4.66038 + 11.2511i −0.446383 + 1.07766i 0.527284 + 0.849689i 0.323210π0.323210\pi
−0.973667 + 0.227975i 0.926790π0.926790\pi
110110 0 0
111111 −7.16391 + 7.16391i −0.679968 + 0.679968i
112112 0.125399 0.302740i 0.0118491 0.0286062i
113113 16.5171 + 6.84161i 1.55380 + 0.643604i 0.983998 0.178179i 0.0570205π-0.0570205\pi
0.569800 + 0.821783i 0.307020π0.307020\pi
114114 0.903208 + 2.18054i 0.0845932 + 0.204226i
115115 0 0
116116 8.37710 3.46991i 0.777794 0.322173i
117117 −8.67417 8.67417i −0.801927 0.801927i
118118 −5.76481 −0.530694
119119 −1.80932 1.25009i −0.165860 0.114596i
120120 0 0
121121 7.67557 + 7.67557i 0.697779 + 0.697779i
122122 0.994531 0.411948i 0.0900406 0.0372960i
123123 2.01583i 0.181762i
124124 1.03806 + 2.50610i 0.0932205 + 0.225054i
125125 0 0
126126 −0.607036 + 1.46551i −0.0540791 + 0.130558i
127127 −8.76596 + 8.76596i −0.777853 + 0.777853i −0.979465 0.201612i 0.935382π-0.935382\pi
0.201612 + 0.979465i 0.435382π0.435382\pi
128128 3.27766 3.27766i 0.289707 0.289707i
129129 −6.09702 + 14.7195i −0.536813 + 1.29598i
130130 0 0
131131 −3.83884 9.26779i −0.335401 0.809730i −0.998145 0.0608839i 0.980608π-0.980608\pi
0.662744 0.748846i 0.269392π-0.269392\pi
132132 12.6594i 1.10186i
133133 −0.493781 + 0.204531i −0.0428163 + 0.0177351i
134134 −5.17255 5.17255i −0.446841 0.446841i
135135 0 0
136136 6.58785 + 10.1994i 0.564903 + 0.874593i
137137 −3.06808 −0.262124 −0.131062 0.991374i 0.541839π-0.541839\pi
−0.131062 + 0.991374i 0.541839π0.541839\pi
138138 9.55686 + 9.55686i 0.813534 + 0.813534i
139139 −11.3389 + 4.69672i −0.961753 + 0.398371i −0.807636 0.589682i 0.799253π-0.799253\pi
−0.154117 + 0.988053i 0.549253π0.549253\pi
140140 0 0
141141 −1.61482 3.89851i −0.135992 0.328314i
142142 −6.10468 2.52864i −0.512293 0.212199i
143143 7.02320 16.9555i 0.587309 1.41789i
144144 1.35746 1.35746i 0.113122 0.113122i
145145 0 0
146146 −4.40199 + 10.6274i −0.364312 + 0.879526i
147147 15.3547 + 6.36011i 1.26643 + 0.524573i
148148 1.71417 + 4.13836i 0.140904 + 0.340171i
149149 5.46544i 0.447747i 0.974618 + 0.223873i 0.0718702π0.0718702\pi
−0.974618 + 0.223873i 0.928130π0.928130\pi
150150 0 0
151151 3.54105 + 3.54105i 0.288167 + 0.288167i 0.836355 0.548188i 0.184682π-0.184682\pi
−0.548188 + 0.836355i 0.684682π0.684682\pi
152152 2.95087 0.239347
153153 −6.99038 10.8226i −0.565139 0.874957i
154154 −2.37316 −0.191235
155155 0 0
156156 −9.82146 + 4.06818i −0.786346 + 0.325715i
157157 10.9442i 0.873443i −0.899597 0.436721i 0.856140π-0.856140\pi
0.899597 0.436721i 0.143860π-0.143860\pi
158158 −0.539417 1.30227i −0.0429137 0.103603i
159159 18.6649 + 7.73125i 1.48022 + 0.613128i
160160 0 0
161161 −2.16414 + 2.16414i −0.170558 + 0.170558i
162162 5.79438 5.79438i 0.455250 0.455250i
163163 2.82785 6.82704i 0.221495 0.534735i −0.773599 0.633676i 0.781545π-0.781545\pi
0.995093 + 0.0989404i 0.0315453π0.0315453\pi
164164 0.823413 + 0.341069i 0.0642978 + 0.0266330i
165165 0 0
166166 15.4064i 1.19577i
167167 −18.0137 + 7.46152i −1.39394 + 0.577390i −0.948172 0.317758i 0.897070π-0.897070\pi
−0.445770 + 0.895147i 0.647070π0.647070\pi
168168 2.74872 + 2.74872i 0.212069 + 0.212069i
169169 −2.41138 −0.185491
170170 0 0
171171 −3.13117 −0.239447
172172 4.98094 + 4.98094i 0.379793 + 0.379793i
173173 −12.2873 + 5.08958i −0.934189 + 0.386954i −0.797266 0.603628i 0.793721π-0.793721\pi
−0.136923 + 0.990582i 0.543721π0.543721\pi
174174 19.5186i 1.47970i
175175 0 0
176176 2.65344 + 1.09909i 0.200011 + 0.0828471i
177177 5.73658 13.8493i 0.431188 1.04098i
178178 −8.12404 + 8.12404i −0.608922 + 0.608922i
179179 −7.18598 + 7.18598i −0.537105 + 0.537105i −0.922678 0.385572i 0.874004π-0.874004\pi
0.385572 + 0.922678i 0.374004π0.374004\pi
180180 0 0
181181 −18.1259 7.50798i −1.34728 0.558064i −0.411750 0.911297i 0.635082π-0.635082\pi
−0.935535 + 0.353233i 0.885082π0.885082\pi
182182 0.762628 + 1.84115i 0.0565298 + 0.136475i
183183 2.79918i 0.206921i
184184 15.6116 6.46653i 1.15090 0.476719i
185185 0 0
186186 5.83919 0.428150
187187 10.9568 15.8582i 0.801238 1.15967i
188188 −1.86566 −0.136067
189189 −0.116488 0.116488i −0.00847327 0.00847327i
190190 0 0
191191 8.81287i 0.637677i −0.947809 0.318838i 0.896707π-0.896707\pi
0.947809 0.318838i 0.103293π-0.103293\pi
192192 −5.94548 14.3536i −0.429078 1.03589i
193193 −14.2854 5.91720i −1.02829 0.425930i −0.196192 0.980566i 0.562858π-0.562858\pi
−0.832093 + 0.554636i 0.812858π0.812858\pi
194194 −0.0830564 + 0.200516i −0.00596310 + 0.0143962i
195195 0 0
196196 5.19587 5.19587i 0.371133 0.371133i
197197 −0.0880736 + 0.212628i −0.00627498 + 0.0151491i −0.926986 0.375096i 0.877610π-0.877610\pi
0.920711 + 0.390245i 0.127610π0.127610\pi
198198 −12.8449 5.32052i −0.912845 0.378113i
199199 −8.21298 19.8279i −0.582203 1.40556i −0.890812 0.454372i 0.849864π-0.849864\pi
0.308609 0.951189i 0.400136π-0.400136\pi
200200 0 0
201201 17.5737 7.27927i 1.23955 0.513440i
202202 4.48568 + 4.48568i 0.315611 + 0.315611i
203203 4.41997 0.310221
204204 −10.9832 + 2.00759i −0.768976 + 0.140559i
205205 0 0
206206 0.235850 + 0.235850i 0.0164325 + 0.0164325i
207207 −16.5655 + 6.86165i −1.15138 + 0.476918i
208208 2.41179i 0.167228i
209209 −1.79266 4.32787i −0.124001 0.299365i
210210 0 0
211211 −5.94870 + 14.3614i −0.409525 + 0.988682i 0.575738 + 0.817635i 0.304715π0.304715\pi
−0.985263 + 0.171047i 0.945285π0.945285\pi
212212 6.31601 6.31601i 0.433786 0.433786i
213213 12.1496 12.1496i 0.832474 0.832474i
214214 2.84042 6.85739i 0.194167 0.468761i
215215 0 0
216216 0.348070 + 0.840316i 0.0236832 + 0.0571763i
217217 1.32228i 0.0897622i
218218 10.7081 4.43546i 0.725247 0.300407i
219219 −21.1506 21.1506i −1.42923 1.42923i
220220 0 0
221221 −15.8242 3.40436i −1.06445 0.229002i
222222 9.64235 0.647152
223223 −0.756286 0.756286i −0.0506447 0.0506447i 0.681331 0.731976i 0.261401π-0.261401\pi
−0.731976 + 0.681331i 0.761401π0.761401\pi
224224 2.61419 1.08283i 0.174668 0.0723498i
225225 0 0
226226 −6.51143 15.7200i −0.433134 1.04568i
227227 1.91049 + 0.791349i 0.126803 + 0.0525237i 0.445183 0.895440i 0.353139π-0.353139\pi
−0.318380 + 0.947963i 0.603139π0.603139\pi
228228 −1.03840 + 2.50692i −0.0687696 + 0.166025i
229229 9.06042 9.06042i 0.598730 0.598730i −0.341245 0.939974i 0.610849π-0.610849\pi
0.939974 + 0.341245i 0.110849π0.110849\pi
230230 0 0
231231 2.36154 5.70125i 0.155378 0.375115i
232232 −22.5458 9.33876i −1.48020 0.613120i
233233 2.48129 + 5.99035i 0.162554 + 0.392441i 0.984079 0.177732i 0.0568761π-0.0568761\pi
−0.821524 + 0.570173i 0.806876π0.806876\pi
234234 11.6751i 0.763226i
235235 0 0
236236 −4.68648 4.68648i −0.305064 0.305064i
237237 3.66533 0.238089
238238 0.376346 + 2.05892i 0.0243949 + 0.133460i
239239 −1.26828 −0.0820381 −0.0410190 0.999158i 0.513060π-0.513060\pi
−0.0410190 + 0.999158i 0.513060π0.513060\pi
240240 0 0
241241 −2.30585 + 0.955116i −0.148533 + 0.0615244i −0.455712 0.890127i 0.650615π-0.650615\pi
0.307178 + 0.951652i 0.400615π0.400615\pi
242242 10.3310i 0.664103i
243243 8.50895 + 20.5424i 0.545849 + 1.31780i
244244 1.14339 + 0.473608i 0.0731981 + 0.0303196i
245245 0 0
246246 1.35662 1.35662i 0.0864947 0.0864947i
247247 −2.78157 + 2.78157i −0.176987 + 0.176987i
248248 2.79379 6.74480i 0.177406 0.428296i
249249 37.0122 + 15.3309i 2.34555 + 0.971559i
250250 0 0
251251 17.3565i 1.09553i 0.836632 + 0.547765i 0.184521π0.184521\pi
−0.836632 + 0.547765i 0.815479π0.815479\pi
252252 −1.68487 + 0.697896i −0.106137 + 0.0439633i
253253 −18.9682 18.9682i −1.19252 1.19252i
254254 11.7987 0.740313
255255 0 0
256256 −16.9670 −1.06044
257257 −10.9991 10.9991i −0.686105 0.686105i 0.275264 0.961369i 0.411235π-0.411235\pi
−0.961369 + 0.275264i 0.911235π0.911235\pi
258258 14.0091 5.80277i 0.872170 0.361265i
259259 2.18350i 0.135676i
260260 0 0
261261 23.9234 + 9.90938i 1.48082 + 0.613375i
262262 −3.65358 + 8.82051i −0.225719 + 0.544933i
263263 −6.39290 + 6.39290i −0.394203 + 0.394203i −0.876183 0.481979i 0.839918π-0.839918\pi
0.481979 + 0.876183i 0.339918π0.339918\pi
264264 −24.0919 + 24.0919i −1.48275 + 1.48275i
265265 0 0
266266 0.469951 + 0.194660i 0.0288145 + 0.0119354i
267267 −11.4329 27.6014i −0.699680 1.68918i
268268 8.41000i 0.513723i
269269 2.79002 1.15566i 0.170110 0.0704620i −0.296003 0.955187i 0.595654π-0.595654\pi
0.466113 + 0.884725i 0.345654π0.345654\pi
270270 0 0
271271 13.1638 0.799642 0.399821 0.916593i 0.369072π-0.369072\pi
0.399821 + 0.916593i 0.369072π0.369072\pi
272272 0.532764 2.47639i 0.0323035 0.150153i
273273 −5.18205 −0.313632
274274 2.06476 + 2.06476i 0.124737 + 0.124737i
275275 0 0
276276 15.5384i 0.935302i
277277 −1.55039 3.74298i −0.0931540 0.224894i 0.870434 0.492285i 0.163838π-0.163838\pi
−0.963588 + 0.267392i 0.913838π0.913838\pi
278278 10.7917 + 4.47006i 0.647241 + 0.268096i
279279 −2.96450 + 7.15692i −0.177480 + 0.428474i
280280 0 0
281281 10.0869 10.0869i 0.601731 0.601731i −0.339041 0.940772i 0.610102π-0.610102\pi
0.940772 + 0.339041i 0.110102π0.110102\pi
282282 −1.53688 + 3.71037i −0.0915201 + 0.220949i
283283 −5.14980 2.13312i −0.306124 0.126801i 0.224333 0.974513i 0.427980π-0.427980\pi
−0.530457 + 0.847712i 0.677980π0.677980\pi
284284 −2.90712 7.01841i −0.172506 0.416466i
285285 0 0
286286 −16.1372 + 6.68425i −0.954213 + 0.395248i
287287 0.307205 + 0.307205i 0.0181337 + 0.0181337i
288288 16.5771 0.976817
289289 −15.4960 6.99109i −0.911527 0.411241i
290290 0 0
291291 −0.399068 0.399068i −0.0233938 0.0233938i
292292 −12.2180 + 5.06088i −0.715006 + 0.296165i
293293 1.97120i 0.115159i 0.998341 + 0.0575795i 0.0183383π0.0183383\pi
−0.998341 + 0.0575795i 0.981662π0.981662\pi
294294 −6.05316 14.6136i −0.353028 0.852284i
295295 0 0
296296 4.61343 11.1378i 0.268150 0.647372i
297297 1.02099 1.02099i 0.0592438 0.0592438i
298298 3.67814 3.67814i 0.213069 0.213069i
299299 −8.62039 + 20.8115i −0.498530 + 1.20356i
300300 0 0
301301 1.31403 + 3.17236i 0.0757396 + 0.182852i
302302 4.76612i 0.274260i
303303 −15.2401 + 6.31264i −0.875519 + 0.362652i
304304 −0.435300 0.435300i −0.0249662 0.0249662i
305305 0 0
306306 −2.57902 + 11.9878i −0.147433 + 0.685297i
307307 −1.69613 −0.0968034 −0.0484017 0.998828i 0.515413π-0.515413\pi
−0.0484017 + 0.998828i 0.515413π0.515413\pi
308308 −1.92925 1.92925i −0.109929 0.109929i
309309 −0.801300 + 0.331909i −0.0455844 + 0.0188817i
310310 0 0
311311 4.16844 + 10.0635i 0.236371 + 0.570649i 0.996902 0.0786518i 0.0250615π-0.0250615\pi
−0.760531 + 0.649301i 0.775062π0.775062\pi
312312 26.4331 + 10.9489i 1.49648 + 0.619861i
313313 −10.0614 + 24.2903i −0.568702 + 1.37297i 0.333947 + 0.942592i 0.391619π0.391619\pi
−0.902649 + 0.430377i 0.858381π0.858381\pi
314314 −7.36524 + 7.36524i −0.415645 + 0.415645i
315315 0 0
316316 0.620155 1.49719i 0.0348865 0.0842234i
317317 23.1074 + 9.57139i 1.29784 + 0.537583i 0.921313 0.388823i 0.127118π-0.127118\pi
0.376527 + 0.926406i 0.377118π0.377118\pi
318318 −7.35813 17.7641i −0.412623 0.996161i
319319 38.7399i 2.16902i
320320 0 0
321321 13.6476 + 13.6476i 0.761735 + 0.761735i
322322 2.91286 0.162327
323323 −3.47052 + 2.24162i −0.193105 + 0.124727i
324324 9.42103 0.523390
325325 0 0
326326 −6.49756 + 2.69138i −0.359867 + 0.149062i
327327 30.1389i 1.66668i
328328 −0.917938 2.21610i −0.0506847 0.122364i
329329 −0.840209 0.348026i −0.0463222 0.0191873i
330330 0 0
331331 22.8306 22.8306i 1.25488 1.25488i 0.301376 0.953505i 0.402554π-0.402554\pi
0.953505 0.301376i 0.0974458π-0.0974458\pi
332332 12.5245 12.5245i 0.687374 0.687374i
333333 −4.89532 + 11.8183i −0.268262 + 0.647641i
334334 17.1443 + 7.10142i 0.938097 + 0.388572i
335335 0 0
336336 0.810961i 0.0442416i
337337 11.8844 4.92267i 0.647383 0.268155i −0.0347353 0.999397i 0.511059π-0.511059\pi
0.682119 + 0.731242i 0.261059π0.261059\pi
338338 1.62281 + 1.62281i 0.0882693 + 0.0882693i
339339 44.2450 2.40306
340340 0 0
341341 −11.5895 −0.627604
342342 2.10722 + 2.10722i 0.113945 + 0.113945i
343343 6.75868 2.79954i 0.364934 0.151161i
344344 18.9582i 1.02216i
345345 0 0
346346 11.6943 + 4.84395i 0.628691 + 0.260412i
347347 −10.3086 + 24.8871i −0.553394 + 1.33601i 0.361521 + 0.932364i 0.382257π0.382257\pi
−0.914915 + 0.403647i 0.867743π0.867743\pi
348348 15.8675 15.8675i 0.850589 0.850589i
349349 10.1253 10.1253i 0.541995 0.541995i −0.382119 0.924113i 0.624805π-0.624805\pi
0.924113 + 0.382119i 0.124805π0.124805\pi
350350 0 0
351351 −1.12021 0.464005i −0.0597922 0.0247667i
352352 9.49076 + 22.9127i 0.505859 + 1.22125i
353353 1.65351i 0.0880076i −0.999031 0.0440038i 0.985989π-0.985989\pi
0.999031 0.0440038i 0.0140114π-0.0140114\pi
354354 −13.1809 + 5.45973i −0.700559 + 0.290181i
355355 0 0
356356 −13.2088 −0.700065
357357 −5.32084 1.14471i −0.281609 0.0605845i
358358 9.67206 0.511184
359359 −12.2781 12.2781i −0.648012 0.648012i 0.304500 0.952512i 0.401511π-0.401511\pi
−0.952512 + 0.304500i 0.901511π0.901511\pi
360360 0 0
361361 17.9959i 0.947154i
362362 7.14564 + 17.2511i 0.375566 + 0.906697i
363363 24.8191 + 10.2804i 1.30267 + 0.539582i
364364 −0.876777 + 2.11673i −0.0459556 + 0.110947i
365365 0 0
366366 1.88380 1.88380i 0.0984676 0.0984676i
367367 3.66265 8.84242i 0.191189 0.461571i −0.798996 0.601337i 0.794635π-0.794635\pi
0.990185 + 0.139766i 0.0446350π0.0446350\pi
368368 −3.25688 1.34904i −0.169776 0.0703237i
369369 0.974026 + 2.35151i 0.0507058 + 0.122415i
370370 0 0
371371 4.02267 1.66624i 0.208846 0.0865070i
372372 4.74694 + 4.74694i 0.246117 + 0.246117i
373373 −14.4236 −0.746828 −0.373414 0.927665i 0.621813π-0.621813\pi
−0.373414 + 0.927665i 0.621813π0.621813\pi
374374 −18.0460 + 3.29858i −0.933134 + 0.170565i
375375 0 0
376376 3.55049 + 3.55049i 0.183102 + 0.183102i
377377 30.0553 12.4493i 1.54793 0.641172i
378378 0.156789i 0.00806434i
379379 −3.64196 8.79246i −0.187075 0.451638i 0.802319 0.596895i 0.203599π-0.203599\pi
−0.989394 + 0.145257i 0.953599π0.953599\pi
380380 0 0
381381 −11.7409 + 28.3450i −0.601503 + 1.45216i
382382 −5.93089 + 5.93089i −0.303451 + 0.303451i
383383 −19.6401 + 19.6401i −1.00356 + 1.00356i −0.00356842 + 0.999994i 0.501136π0.501136\pi
−0.999994 + 0.00356842i 0.998864π0.998864\pi
384384 4.39000 10.5984i 0.224026 0.540847i
385385 0 0
386386 5.63163 + 13.5960i 0.286643 + 0.692016i
387387 20.1166i 1.02258i
388388 −0.230529 + 0.0954881i −0.0117033 + 0.00484767i
389389 −14.8835 14.8835i −0.754624 0.754624i 0.220715 0.975338i 0.429161π-0.429161\pi
−0.975338 + 0.220715i 0.929161π0.929161\pi
390390 0 0
391391 −13.4485 + 19.4646i −0.680121 + 0.984369i
392392 −19.7763 −0.998852
393393 −17.5546 17.5546i −0.885514 0.885514i
394394 0.202367 0.0838230i 0.0101951 0.00422294i
395395 0 0
396396 −6.11688 14.7675i −0.307385 0.742093i
397397 −27.3935 11.3468i −1.37484 0.569478i −0.431744 0.901996i 0.642102π-0.642102\pi
−0.943097 + 0.332518i 0.892102π0.892102\pi
398398 −7.81661 + 18.8710i −0.391811 + 0.945916i
399399 −0.935298 + 0.935298i −0.0468235 + 0.0468235i
400400 0 0
401401 6.33937 15.3046i 0.316573 0.764275i −0.682858 0.730551i 0.739263π-0.739263\pi
0.999431 0.0337238i 0.0107366π-0.0107366\pi
402402 −16.7256 6.92796i −0.834196 0.345535i
403403 3.72434 + 8.99135i 0.185523 + 0.447891i
404404 7.29322i 0.362851i
405405 0 0
406406 −2.97455 2.97455i −0.147625 0.147625i
407407 −19.1379 −0.948629
408408 24.7224 + 17.0812i 1.22394 + 0.845647i
409409 −19.3593 −0.957257 −0.478629 0.878017i 0.658866π-0.658866\pi
−0.478629 + 0.878017i 0.658866π0.658866\pi
410410 0 0
411411 −7.01500 + 2.90571i −0.346024 + 0.143328i
412412 0.383467i 0.0188921i
413413 −1.23635 2.98482i −0.0608369 0.146873i
414414 15.7660 + 6.53050i 0.774857 + 0.320956i
415415 0 0
416416 14.7263 14.7263i 0.722015 0.722015i
417417 −21.4776 + 21.4776i −1.05176 + 1.05176i
418418 −1.70615 + 4.11900i −0.0834503 + 0.201467i
419419 13.3054 + 5.51126i 0.650009 + 0.269243i 0.683228 0.730205i 0.260576π-0.260576\pi
−0.0332183 + 0.999448i 0.510576π0.510576\pi
420420 0 0
421421 26.7439i 1.30342i −0.758468 0.651710i 0.774052π-0.774052\pi
0.758468 0.651710i 0.225948π-0.225948\pi
422422 13.6683 5.66161i 0.665364 0.275603i
423423 −3.76743 3.76743i −0.183179 0.183179i
424424 −24.0397 −1.16747
425425 0 0
426426 −16.3529 −0.792298
427427 0.426584 + 0.426584i 0.0206439 + 0.0206439i
428428 7.88379 3.26557i 0.381077 0.157847i
429429 45.4194i 2.19287i
430430 0 0
431431 −26.4399 10.9518i −1.27356 0.527527i −0.359518 0.933138i 0.617059π-0.617059\pi
−0.914046 + 0.405611i 0.867059π0.867059\pi
432432 0.0726141 0.175306i 0.00349365 0.00843442i
433433 25.5919 25.5919i 1.22987 1.22987i 0.265855 0.964013i 0.414346π-0.414346\pi
0.964013 0.265855i 0.0856542π-0.0856542\pi
434434 0.889869 0.889869i 0.0427151 0.0427151i
435435 0 0
436436 12.3109 + 5.09935i 0.589586 + 0.244215i
437437 2.20034 + 5.31210i 0.105257 + 0.254112i
438438 28.4679i 1.36025i
439439 29.9716 12.4146i 1.43047 0.592519i 0.473000 0.881063i 0.343171π-0.343171\pi
0.957467 + 0.288544i 0.0931711π0.0931711\pi
440440 0 0
441441 20.9846 0.999268
442442 8.35828 + 12.9404i 0.397563 + 0.615513i
443443 1.88468 0.0895437 0.0447719 0.998997i 0.485744π-0.485744\pi
0.0447719 + 0.998997i 0.485744π0.485744\pi
444444 7.83870 + 7.83870i 0.372008 + 0.372008i
445445 0 0
446446 1.01793i 0.0482005i
447447 5.17620 + 12.4965i 0.244826 + 0.591062i
448448 −3.09351 1.28137i −0.146154 0.0605391i
449449 0.766010 1.84931i 0.0361503 0.0872745i −0.904773 0.425894i 0.859960π-0.859960\pi
0.940924 + 0.338619i 0.109960π0.109960\pi
450450 0 0
451451 −2.69258 + 2.69258i −0.126788 + 0.126788i
452452 7.48604 18.0729i 0.352114 0.850078i
453453 11.4501 + 4.74278i 0.537972 + 0.222835i
454454 −0.753158 1.81828i −0.0353474 0.0853363i
455455 0 0
456456 6.74700 2.79470i 0.315957 0.130874i
457457 −12.4863 12.4863i −0.584086 0.584086i 0.351938 0.936023i 0.385523π-0.385523\pi
−0.936023 + 0.351938i 0.885523π0.885523\pi
458458 −12.1950 −0.569834
459459 −1.04771 0.723885i −0.0489030 0.0337881i
460460 0 0
461461 −22.5151 22.5151i −1.04863 1.04863i −0.998755 0.0498792i 0.984116π-0.984116\pi
−0.0498792 0.998755i 0.515884π-0.515884\pi
462462 −5.42610 + 2.24757i −0.252445 + 0.104566i
463463 15.7977i 0.734179i −0.930186 0.367090i 0.880354π-0.880354\pi
0.930186 0.367090i 0.119646π-0.119646\pi
464464 1.94825 + 4.70348i 0.0904450 + 0.218354i
465465 0 0
466466 2.36154 5.70125i 0.109396 0.264105i
467467 −6.26872 + 6.26872i −0.290082 + 0.290082i −0.837112 0.547031i 0.815758π-0.815758\pi
0.547031 + 0.837112i 0.315758π0.315758\pi
468468 −9.49122 + 9.49122i −0.438732 + 0.438732i
469469 1.56883 3.78750i 0.0724419 0.174890i
470470 0 0
471471 −10.3650 25.0234i −0.477595 1.15302i
472472 17.8374i 0.821035i
473473 −27.8049 + 11.5172i −1.27847 + 0.529560i
474474 −2.46670 2.46670i −0.113299 0.113299i
475475 0 0
476476 −1.36784 + 1.97974i −0.0626950 + 0.0907413i
477477 25.5086 1.16796
478478 0.853527 + 0.853527i 0.0390394 + 0.0390394i
479479 −11.0031 + 4.55765i −0.502746 + 0.208244i −0.619619 0.784903i 0.712713π-0.712713\pi
0.116873 + 0.993147i 0.462713π0.462713\pi
480480 0 0
481481 6.15006 + 14.8476i 0.280419 + 0.676991i
482482 2.19457 + 0.909021i 0.0999600 + 0.0414048i
483483 −2.89859 + 6.99782i −0.131890 + 0.318412i
484484 8.39855 8.39855i 0.381752 0.381752i
485485 0 0
486486 8.09830 19.5510i 0.367346 0.886852i
487487 24.7378 + 10.2467i 1.12098 + 0.464324i 0.864704 0.502281i 0.167506π-0.167506\pi
0.256272 + 0.966605i 0.417506π0.417506\pi
488488 −1.27465 3.07727i −0.0577006 0.139302i
489489 18.2879i 0.827006i
490490 0 0
491491 16.3477 + 16.3477i 0.737761 + 0.737761i 0.972144 0.234383i 0.0753070π-0.0753070\pi
−0.234383 + 0.972144i 0.575307π0.575307\pi
492492 2.20571 0.0994411
493493 33.6103 6.14355i 1.51373 0.276691i
494494 3.74389 0.168446
495495 0 0
496496 −1.40710 + 0.582838i −0.0631805 + 0.0261702i
497497 3.70309i 0.166106i
498498 −14.5911 35.2259i −0.653841 1.57851i
499499 −4.58831 1.90054i −0.205401 0.0850799i 0.277611 0.960694i 0.410457π-0.410457\pi
−0.483012 + 0.875614i 0.660457π0.660457\pi
500500 0 0
501501 −34.1208 + 34.1208i −1.52440 + 1.52440i
502502 11.6806 11.6806i 0.521330 0.521330i
503503 8.94738 21.6009i 0.398944 0.963136i −0.588973 0.808153i 0.700468π-0.700468\pi
0.987917 0.154983i 0.0495323π-0.0495323\pi
504504 4.53458 + 1.87829i 0.201986 + 0.0836655i
505505 0 0
506506 25.5305i 1.13497i
507507 −5.51349 + 2.28376i −0.244863 + 0.101425i
508508 9.59165 + 9.59165i 0.425561 + 0.425561i
509509 −23.9562 −1.06184 −0.530921 0.847422i 0.678154π-0.678154\pi
−0.530921 + 0.847422i 0.678154π0.678154\pi
510510 0 0
511511 −6.44654 −0.285178
512512 4.86316 + 4.86316i 0.214924 + 0.214924i
513513 −0.285931 + 0.118437i −0.0126242 + 0.00522911i
514514 14.8044i 0.652993i
515515 0 0
516516 16.1060 + 6.67132i 0.709027 + 0.293688i
517517 3.05036 7.36423i 0.134155 0.323878i
518518 1.46946 1.46946i 0.0645642 0.0645642i
519519 −23.2741 + 23.2741i −1.02162 + 1.02162i
520520 0 0
521521 7.00747 + 2.90259i 0.307003 + 0.127165i 0.530866 0.847456i 0.321867π-0.321867\pi
−0.223863 + 0.974621i 0.571867π0.571867\pi
522522 −9.43114 22.7688i −0.412790 0.996563i
523523 17.3848i 0.760185i 0.924948 + 0.380093i 0.124108π0.124108\pi
−0.924948 + 0.380093i 0.875892π0.875892\pi
524524 −10.1407 + 4.20044i −0.443001 + 0.183497i
525525 0 0
526526 8.60461 0.375179
527527 1.83791 + 10.0549i 0.0800605 + 0.437997i
528528 7.10788 0.309331
529529 7.01842 + 7.01842i 0.305149 + 0.305149i
530530 0 0
531531 18.9273i 0.821377i
532532 0.223796 + 0.540292i 0.00970280 + 0.0234246i
533533 2.95423 + 1.22368i 0.127962 + 0.0530036i
534534 −10.8811 + 26.2693i −0.470871 + 1.13678i
535535 0 0
536536 −16.0049 + 16.0049i −0.691305 + 0.691305i
537537 −9.62469 + 23.2361i −0.415336 + 1.00271i
538538 −2.65537 1.09989i −0.114481 0.0474196i
539539 12.0141 + 29.0047i 0.517486 + 1.24932i
540540 0 0
541541 −20.5428 + 8.50911i −0.883204 + 0.365835i −0.777739 0.628588i 0.783633π-0.783633\pi
−0.105466 + 0.994423i 0.533633π0.533633\pi
542542 −8.85896 8.85896i −0.380525 0.380525i
543543 −48.5545 −2.08367
544544 18.3737 11.8677i 0.787767 0.508822i
545545 0 0
546546 3.48742 + 3.48742i 0.149248 + 0.149248i
547547 37.1299 15.3797i 1.58756 0.657589i 0.597972 0.801517i 0.295974π-0.295974\pi
0.989588 + 0.143929i 0.0459736π0.0459736\pi
548548 3.35707i 0.143407i
549549 1.35253 + 3.26530i 0.0577246 + 0.139360i
550550 0 0
551551 3.17767 7.67157i 0.135373 0.326820i
552552 29.5708 29.5708i 1.25862 1.25862i
553553 0.558581 0.558581i 0.0237533 0.0237533i
554554 −1.47557 + 3.56234i −0.0626909 + 0.151349i
555555 0 0
556556 5.13912 + 12.4069i 0.217947 + 0.526172i
557557 6.44000i 0.272872i −0.990649 0.136436i 0.956435π-0.956435\pi
0.990649 0.136436i 0.0435647π-0.0435647\pi
558558 6.81152 2.82143i 0.288355 0.119440i
559559 17.8705 + 17.8705i 0.755844 + 0.755844i
560560 0 0
561561 10.0331 46.6359i 0.423598 1.96897i
562562 −13.5765 −0.572691
563563 −14.0594 14.0594i −0.592532 0.592532i 0.345782 0.938315i 0.387614π-0.387614\pi
−0.938315 + 0.345782i 0.887614π0.887614\pi
564564 −4.26572 + 1.76692i −0.179619 + 0.0744008i
565565 0 0
566566 2.03017 + 4.90127i 0.0853345 + 0.206016i
567567 4.24282 + 1.75743i 0.178182 + 0.0738052i
568568 −7.82410 + 18.8891i −0.328292 + 0.792567i
569569 −4.57941 + 4.57941i −0.191979 + 0.191979i −0.796551 0.604572i 0.793344π-0.793344\pi
0.604572 + 0.796551i 0.293344π0.293344\pi
570570 0 0
571571 −14.0045 + 33.8098i −0.586069 + 1.41490i 0.301164 + 0.953572i 0.402625π0.402625\pi
−0.887232 + 0.461323i 0.847375π0.847375\pi
572572 −18.5526 7.68473i −0.775723 0.321315i
573573 −8.34647 20.1502i −0.348679 0.841785i
574574 0.413486i 0.0172586i
575575 0 0
576576 −13.8710 13.8710i −0.577959 0.577959i
577577 −19.2887 −0.802999 −0.401500 0.915859i 0.631511π-0.631511\pi
−0.401500 + 0.915859i 0.631511π0.631511\pi
578578 5.72361 + 15.1334i 0.238071 + 0.629465i
579579 −38.2669 −1.59032
580580 0 0
581581 7.97688 3.30413i 0.330937 0.137079i
582582 0.537130i 0.0222647i
583583 14.6042 + 35.2577i 0.604845 + 1.46022i
584584 32.8831 + 13.6206i 1.36071 + 0.563625i
585585 0 0
586586 1.32658 1.32658i 0.0548006 0.0548006i
587587 −12.6487 + 12.6487i −0.522068 + 0.522068i −0.918196 0.396127i 0.870354π-0.870354\pi
0.396127 + 0.918196i 0.370354π0.370354\pi
588588 6.95919 16.8010i 0.286992 0.692860i
589589 2.29503 + 0.950633i 0.0945651 + 0.0391702i
590590 0 0
591591 0.569576i 0.0234292i
592592 −2.32356 + 0.962450i −0.0954977 + 0.0395565i
593593 −15.9962 15.9962i −0.656884 0.656884i 0.297757 0.954642i 0.403761π-0.403761\pi
−0.954642 + 0.297757i 0.903761π0.903761\pi
594594 −1.37421 −0.0563847
595595 0 0
596596 5.98025 0.244961
597597 −37.5571 37.5571i −1.53711 1.53711i
598598 19.8071 8.20436i 0.809972 0.335501i
599599 17.4019i 0.711023i −0.934672 0.355511i 0.884307π-0.884307\pi
0.934672 0.355511i 0.115693π-0.115693\pi
600600 0 0
601601 19.9088 + 8.24649i 0.812096 + 0.336381i 0.749790 0.661676i 0.230155π-0.230155\pi
0.0623060 + 0.998057i 0.480155π0.480155\pi
602602 1.25062 3.01926i 0.0509713 0.123056i
603603 16.9828 16.9828i 0.691593 0.691593i
604604 3.87460 3.87460i 0.157655 0.157655i
605605 0 0
606606 14.5046 + 6.00799i 0.589208 + 0.244058i
607607 6.14655 + 14.8391i 0.249481 + 0.602300i 0.998160 0.0606323i 0.0193117π-0.0193117\pi
−0.748679 + 0.662932i 0.769312π0.769312\pi
608608 5.31584i 0.215586i
609609 10.1060 4.18605i 0.409517 0.169627i
610610 0 0
611611 −6.69358 −0.270793
612612 −11.8420 + 7.64882i −0.478686 + 0.309185i
613613 15.6440 0.631855 0.315928 0.948783i 0.397684π-0.397684\pi
0.315928 + 0.948783i 0.397684π0.397684\pi
614614 1.14147 + 1.14147i 0.0460658 + 0.0460658i
615615 0 0
616616 7.34301i 0.295858i
617617 −8.96313 21.6389i −0.360842 0.871150i −0.995177 0.0980919i 0.968726π-0.968726\pi
0.634335 0.773058i 0.281274π-0.281274\pi
618618 0.762628 + 0.315891i 0.0306774 + 0.0127070i
619619 −11.0559 + 26.6912i −0.444372 + 1.07281i 0.530026 + 0.847981i 0.322182π0.322182\pi
−0.974398 + 0.224828i 0.927818π0.927818\pi
620620 0 0
621621 −1.25318 + 1.25318i −0.0502884 + 0.0502884i
622622 3.96727 9.57783i 0.159073 0.384036i
623623 −5.94866 2.46402i −0.238328 0.0987187i
624624 −2.28416 5.51444i −0.0914394 0.220754i
625625 0 0
626626 23.1180 9.57580i 0.923982 0.382726i
627627 −8.19766 8.19766i −0.327383 0.327383i
628628 −11.9751 −0.477858
629629 3.03497 + 16.6038i 0.121012 + 0.662036i
630630 0 0
631631 29.7914 + 29.7914i 1.18598 + 1.18598i 0.978169 + 0.207809i 0.0666332π0.0666332\pi
0.207809 + 0.978169i 0.433367π0.433367\pi
632632 −4.02946 + 1.66906i −0.160284 + 0.0663916i
633633 38.4705i 1.52907i
634634 −9.10946 21.9922i −0.361783 0.873421i
635635 0 0
636636 8.45948 20.4230i 0.335440 0.809824i
637637 18.6417 18.6417i 0.738610 0.738610i
638638 26.0712 26.0712i 1.03217 1.03217i
639639 8.30217 20.0432i 0.328429 0.792897i
640640 0 0
641641 7.27533 + 17.5642i 0.287358 + 0.693744i 0.999969 0.00781522i 0.00248769π-0.00248769\pi
−0.712611 + 0.701559i 0.752488π0.752488\pi
642642 18.3692i 0.724973i
643643 18.7908 7.78340i 0.741036 0.306947i 0.0199581 0.999801i 0.493647π-0.493647\pi
0.721078 + 0.692853i 0.243647π0.243647\pi
644644 2.36799 + 2.36799i 0.0933119 + 0.0933119i
645645 0 0
646646 3.84416 + 0.827023i 0.151247 + 0.0325388i
647647 16.7736 0.659440 0.329720 0.944079i 0.393046π-0.393046\pi
0.329720 + 0.944079i 0.393046π0.393046\pi
648648 −17.9289 17.9289i −0.704315 0.704315i
649649 26.1612 10.8363i 1.02692 0.425362i
650650 0 0
651651 1.25230 + 3.02332i 0.0490816 + 0.118493i
652652 −7.47010 3.09422i −0.292552 0.121179i
653653 2.56320 6.18810i 0.100306 0.242159i −0.865758 0.500462i 0.833163π-0.833163\pi
0.966064 + 0.258303i 0.0831633π0.0831633\pi
654654 20.2829 20.2829i 0.793124 0.793124i
655655 0 0
656656 −0.191500 + 0.462321i −0.00747680 + 0.0180506i
657657 −34.8923 14.4529i −1.36128 0.563860i
658658 0.331230 + 0.799660i 0.0129127 + 0.0311740i
659659 36.0525i 1.40440i −0.711978 0.702202i 0.752200π-0.752200\pi
0.711978 0.702202i 0.247800π-0.247800\pi
660660 0 0
661661 −31.6304 31.6304i −1.23028 1.23028i −0.963855 0.266427i 0.914157π-0.914157\pi
−0.266427 0.963855i 0.585843π-0.585843\pi
662662 −30.7291 −1.19432
663663 −39.4053 + 7.20280i −1.53037 + 0.279734i
664664 −47.6704 −1.84997
665665 0 0
666666 11.2480 4.65907i 0.435850 0.180535i
667667 47.5501i 1.84115i
668668 8.16434 + 19.7105i 0.315888 + 0.762621i
669669 −2.44547 1.01295i −0.0945474 0.0391628i
670670 0 0
671671 −3.73891 + 3.73891i −0.144339 + 0.144339i
672672 4.95168 4.95168i 0.191015 0.191015i
673673 −1.88991 + 4.56264i −0.0728506 + 0.175877i −0.956110 0.293007i 0.905344π-0.905344\pi
0.883260 + 0.468884i 0.155344π0.155344\pi
674674 −11.3108 4.68510i −0.435677 0.180463i
675675 0 0
676676 2.63851i 0.101481i
677677 −26.2906 + 10.8899i −1.01043 + 0.418534i −0.825612 0.564238i 0.809170π-0.809170\pi
−0.184819 + 0.982773i 0.559170π0.559170\pi
678678 −29.7761 29.7761i −1.14354 1.14354i
679679 −0.121633 −0.00466783
680680 0 0
681681 5.11770 0.196111
682682 7.79949 + 7.79949i 0.298658 + 0.298658i
683683 30.2745 12.5401i 1.15842 0.479835i 0.281073 0.959686i 0.409310π-0.409310\pi
0.877350 + 0.479852i 0.159310π0.159310\pi
684684 3.42611i 0.131000i
685685 0 0
686686 −6.43250 2.66443i −0.245594 0.101728i
687687 12.1353 29.2971i 0.462989 1.11775i
688688 −2.79664 + 2.79664i −0.106621 + 0.106621i
689689 22.6605 22.6605i 0.863297 0.863297i
690690 0 0
691691 6.13856 + 2.54268i 0.233522 + 0.0967279i 0.496376 0.868108i 0.334664π-0.334664\pi
−0.262854 + 0.964836i 0.584664π0.584664\pi
692692 5.56898 + 13.4447i 0.211701 + 0.511091i
693693 7.79168i 0.295982i
694694 23.6860 9.81108i 0.899110 0.372423i
695695 0 0
696696 −60.3943 −2.28924
697697 2.76305 + 1.90905i 0.104658 + 0.0723103i
698698 −13.6283 −0.515837
699699 11.3467 + 11.3467i 0.429170 + 0.429170i
700700 0 0
701701 24.2220i 0.914852i −0.889248 0.457426i 0.848772π-0.848772\pi
0.889248 0.457426i 0.151228π-0.151228\pi
702702 0.441611 + 1.06614i 0.0166675 + 0.0402390i
703703 3.78982 + 1.56980i 0.142936 + 0.0592060i
704704 11.2309 27.1138i 0.423281 1.02189i
705705 0 0
706706 −1.11278 + 1.11278i −0.0418801 + 0.0418801i
707707 −1.36050 + 3.28455i −0.0511670 + 0.123528i
708708 −15.1538 6.27693i −0.569516 0.235901i
709709 −0.466820 1.12700i −0.0175318 0.0423255i 0.914871 0.403746i 0.132292π-0.132292\pi
−0.932403 + 0.361420i 0.882292π0.882292\pi
710710 0 0
711711 4.27567 1.77104i 0.160350 0.0664192i
712712 25.1373 + 25.1373i 0.942062 + 0.942062i
713713 14.2251 0.532734
714714 2.81046 + 4.35119i 0.105179 + 0.162839i
715715 0 0
716716 7.86285 + 7.86285i 0.293849 + 0.293849i
717717 −2.89985 + 1.20116i −0.108297 + 0.0448581i
718718 16.5258i 0.616738i
719719 6.74904 + 16.2936i 0.251697 + 0.607650i 0.998341 0.0575735i 0.0183364π-0.0183364\pi
−0.746645 + 0.665223i 0.768336π0.768336\pi
720720 0 0
721721 −0.0715333 + 0.172697i −0.00266404 + 0.00643156i
722722 −12.1109 + 12.1109i −0.450721 + 0.450721i
723723 −4.36765 + 4.36765i −0.162435 + 0.162435i
724724 −8.21518 + 19.8332i −0.305315 + 0.737095i
725725 0 0
726726 −9.78428 23.6213i −0.363129 0.876670i
727727 11.3177i 0.419751i 0.977728 + 0.209876i 0.0673059π0.0673059\pi
−0.977728 + 0.209876i 0.932694π0.932694\pi
728728 5.69687 2.35972i 0.211140 0.0874570i
729729 20.6459 + 20.6459i 0.764664 + 0.764664i
730730 0 0
731731 14.4016 + 22.2968i 0.532662 + 0.824676i
732732 3.06285 0.113206
733733 −1.79642 1.79642i −0.0663522 0.0663522i 0.673152 0.739504i 0.264940π-0.264940\pi
−0.739504 + 0.673152i 0.764940π0.764940\pi
734734 −8.41568 + 3.48589i −0.310628 + 0.128666i
735735 0 0
736736 −11.6491 28.1235i −0.429393 1.03665i
737737 33.1965 + 13.7504i 1.22281 + 0.506503i
738738 0.927018 2.23802i 0.0341240 0.0823827i
739739 −12.6407 + 12.6407i −0.464997 + 0.464997i −0.900289 0.435292i 0.856645π-0.856645\pi
0.435292 + 0.900289i 0.356645π0.356645\pi
740740 0 0
741741 −3.72555 + 8.99428i −0.136862 + 0.330413i
742742 −3.82853 1.58583i −0.140550 0.0582176i
743743 −4.57351 11.0414i −0.167786 0.405071i 0.817513 0.575910i 0.195352π-0.195352\pi
−0.985299 + 0.170839i 0.945352π0.945352\pi
744744 18.0676i 0.662390i
745745 0 0
746746 9.70683 + 9.70683i 0.355392 + 0.355392i
747747 50.5831 1.85074
748748 −17.3519 11.9888i −0.634450 0.438354i
749749 4.15968 0.151992
750750 0 0
751751 24.7061 10.2336i 0.901537 0.373429i 0.116726 0.993164i 0.462760π-0.462760\pi
0.784811 + 0.619735i 0.212760π0.212760\pi
752752 1.04751i 0.0381987i
753753 16.4379 + 39.6847i 0.599031 + 1.44619i
754754 −28.6048 11.8485i −1.04172 0.431496i
755755 0 0
756756 −0.127461 + 0.127461i −0.00463569 + 0.00463569i
757757 −0.179229 + 0.179229i −0.00651419 + 0.00651419i −0.710356 0.703842i 0.751466π-0.751466\pi
0.703842 + 0.710356i 0.251466π0.251466\pi
758758 −3.46619 + 8.36813i −0.125898 + 0.303944i
759759 −61.3341 25.4054i −2.22629 0.922159i
760760 0 0
761761 32.3234i 1.17172i 0.810412 + 0.585860i 0.199243π0.199243\pi
−0.810412 + 0.585860i 0.800757π0.800757\pi
762762 26.9770 11.1742i 0.977274 0.404800i
763763 4.59305 + 4.59305i 0.166279 + 0.166279i
764764 −9.64298 −0.348871
765765 0 0
766766 26.4348 0.955129
767767 −16.8141 16.8141i −0.607121 0.607121i
768768 −38.7942 + 16.0691i −1.39986 + 0.579843i
769769 7.23844i 0.261025i −0.991447 0.130512i 0.958338π-0.958338\pi
0.991447 0.130512i 0.0416622π-0.0416622\pi
770770 0 0
771771 −35.5659 14.7319i −1.28087 0.530555i
772772 −6.47456 + 15.6310i −0.233025 + 0.562571i
773773 −5.84658 + 5.84658i −0.210287 + 0.210287i −0.804389 0.594102i 0.797507π-0.797507\pi
0.594102 + 0.804389i 0.297507π0.297507\pi
774774 13.5381 13.5381i 0.486616 0.486616i
775775 0 0
776776 0.620435 + 0.256992i 0.0222723 + 0.00922549i
777777 2.06795 + 4.99247i 0.0741872 + 0.179104i
778778 20.0326i 0.718205i
779779 0.754064 0.312344i 0.0270172 0.0111909i
780780 0 0
781781 32.4567 1.16139
782782 22.1499 4.04873i 0.792080 0.144782i
783783 2.55945 0.0914673
784784 2.91732 + 2.91732i 0.104190 + 0.104190i
785785 0 0
786786 23.6279i 0.842778i
787787 4.08149 + 9.85358i 0.145489 + 0.351242i 0.979779 0.200085i 0.0641217π-0.0641217\pi
−0.834289 + 0.551327i 0.814122π0.814122\pi
788788 0.232657 + 0.0963695i 0.00828805 + 0.00343302i
789789 −8.56247 + 20.6716i −0.304832 + 0.735929i
790790 0 0
791791 6.74277 6.74277i 0.239745 0.239745i
792792 −16.4627 + 39.7445i −0.584977 + 1.41226i
793793 4.10224 + 1.69920i 0.145675 + 0.0603405i
794794 10.7992 + 26.0715i 0.383248 + 0.925242i
795795 0 0
796796 −21.6955 + 8.98658i −0.768978 + 0.318521i
797797 16.0429 + 16.0429i 0.568269 + 0.568269i 0.931643 0.363374i 0.118375π-0.118375\pi
−0.363374 + 0.931643i 0.618375π0.618375\pi
798798 1.25888 0.0445637
799799 −6.87286 1.47861i −0.243144 0.0523093i
800800 0 0
801801 −26.6733 26.6733i −0.942454 0.942454i
802802 −14.5660 + 6.03342i −0.514342 + 0.213048i
803803 56.5023i 1.99392i
804804 −7.96493 19.2290i −0.280901 0.678156i
805805 0 0
806806 3.54460 8.55742i 0.124853 0.301422i
807807 5.28472 5.28472i 0.186031 0.186031i
808808 13.8796 13.8796i 0.488281 0.488281i
809809 −7.24370 + 17.4878i −0.254675 + 0.614840i −0.998570 0.0534567i 0.982976π-0.982976\pi
0.743895 + 0.668296i 0.232976π0.232976\pi
810810 0 0
811811 −10.8154 26.1106i −0.379779 0.916867i −0.992007 0.126186i 0.959726π-0.959726\pi
0.612228 0.790681i 0.290274π-0.290274\pi
812812 4.83630i 0.169721i
813813 30.0983 12.4671i 1.05559 0.437241i
814814 12.8794 + 12.8794i 0.451423 + 0.451423i
815815 0 0
816816 −1.12720 6.16671i −0.0394598 0.215878i
817817 6.45084 0.225686
818818 13.0285 + 13.0285i 0.455530 + 0.455530i
819819 −6.04495 + 2.50390i −0.211228 + 0.0874934i
820820 0 0
821821 5.59227 + 13.5009i 0.195172 + 0.471186i 0.990922 0.134439i 0.0429232π-0.0429232\pi
−0.795750 + 0.605625i 0.792923π0.792923\pi
822822 6.67645 + 2.76548i 0.232868 + 0.0964570i
823823 −7.45453 + 17.9968i −0.259848 + 0.627330i −0.998928 0.0462883i 0.985261π-0.985261\pi
0.739080 + 0.673618i 0.235261π0.235261\pi
824824 0.729767 0.729767i 0.0254226 0.0254226i
825825 0 0
826826 −1.17668 + 2.84076i −0.0409420 + 0.0988428i
827827 −9.01621 3.73464i −0.313524 0.129866i 0.220372 0.975416i 0.429273π-0.429273\pi
−0.533896 + 0.845550i 0.679273π0.679273\pi
828828 7.50797 + 18.1258i 0.260920 + 0.629916i
829829 5.96301i 0.207104i 0.994624 + 0.103552i 0.0330208π0.0330208\pi
−0.994624 + 0.103552i 0.966979π0.966979\pi
830830 0 0
831831 −7.08978 7.08978i −0.245942 0.245942i
832832 −24.6446 −0.854398
833833 23.2589 15.0230i 0.805873 0.520517i
834834 28.9081 1.00100
835835 0 0
836836 −4.73552 + 1.96152i −0.163782 + 0.0678405i
837837 0.765686i 0.0264660i
838838 −5.24528 12.6632i −0.181195 0.437444i
839839 20.9048 + 8.65906i 0.721715 + 0.298944i 0.713142 0.701019i 0.247271π-0.247271\pi
0.00857233 + 0.999963i 0.497271π0.497271\pi
840840 0 0
841841 −28.0511 + 28.0511i −0.967281 + 0.967281i
842842 −17.9982 + 17.9982i −0.620258 + 0.620258i
843843 13.5100 32.6161i 0.465310 1.12336i
844844 15.7142 + 6.50903i 0.540904 + 0.224050i
845845 0 0
846846 5.07081i 0.174338i
847847 5.34904 2.21564i 0.183795 0.0761304i
848848 3.54624 + 3.54624i 0.121779 + 0.121779i
849849 −13.7950 −0.473443
850850 0 0
851851 23.4901 0.805232
852852 −13.2940 13.2940i −0.455444 0.455444i
853853 6.10940 2.53060i 0.209182 0.0866459i −0.275632 0.961263i 0.588887π-0.588887\pi
0.484814 + 0.874617i 0.338887π0.338887\pi
854854 0.574166i 0.0196476i
855855 0 0
856856 −21.2181 8.78882i −0.725219 0.300396i
857857 10.4589 25.2501i 0.357270 0.862526i −0.638412 0.769695i 0.720408π-0.720408\pi
0.995682 0.0928314i 0.0295918π-0.0295918\pi
858858 −30.5664 + 30.5664i −1.04352 + 1.04352i
859859 10.0721 10.0721i 0.343654 0.343654i −0.514085 0.857739i 0.671868π-0.671868\pi
0.857739 + 0.514085i 0.171868π0.171868\pi
860860 0 0
861861 0.993355 + 0.411461i 0.0338534 + 0.0140226i
862862 10.4232 + 25.1639i 0.355016 + 0.857084i
863863 31.4670i 1.07115i 0.844488 + 0.535574i 0.179905π0.179905\pi
−0.844488 + 0.535574i 0.820095π0.820095\pi
864864 1.51379 0.627031i 0.0515001 0.0213320i
865865 0 0
866866 −34.4457 −1.17051
867867 −42.0518 1.30888i −1.42815 0.0444521i
868868 1.44683 0.0491086
869869 4.89583 + 4.89583i 0.166080 + 0.166080i
870870 0 0
871871 30.1733i 1.02238i
872872 −13.7242 33.1331i −0.464759 1.12203i
873873 −0.658344 0.272695i −0.0222816 0.00922933i
874874 2.09415 5.05573i 0.0708358 0.171013i
875875 0 0
876876 −23.1429 + 23.1429i −0.781925 + 0.781925i
877877 2.13245 5.14819i 0.0720078 0.173842i −0.883778 0.467907i 0.845008π-0.845008\pi
0.955785 + 0.294065i 0.0950082π0.0950082\pi
878878 −28.5251 11.8155i −0.962677 0.398754i
879879 1.86688 + 4.50705i 0.0629684 + 0.152019i
880880 0 0
881881 29.7926 12.3405i 1.00374 0.415762i 0.180572 0.983562i 0.442205π-0.442205\pi
0.823167 + 0.567800i 0.192205π0.192205\pi
882882 −14.1223 14.1223i −0.475521 0.475521i
883883 38.2240 1.28634 0.643169 0.765724i 0.277619π-0.277619\pi
0.643169 + 0.765724i 0.277619π0.277619\pi
884884 −3.72503 + 17.3147i −0.125286 + 0.582356i
885885 0 0
886886 −1.26835 1.26835i −0.0426111 0.0426111i
887887 −5.72381 + 2.37088i −0.192187 + 0.0796063i −0.476701 0.879065i 0.658168π-0.658168\pi
0.284515 + 0.958672i 0.408168π0.408168\pi
888888 29.8353i 1.00121i
889889 2.53040 + 6.10892i 0.0848668 + 0.204887i
890890 0 0
891891 −15.4035 + 37.1872i −0.516035 + 1.24582i
892892 −0.827523 + 0.827523i −0.0277075 + 0.0277075i
893893 −1.20811 + 1.20811i −0.0404279 + 0.0404279i
894894 4.92639 11.8934i 0.164763 0.397773i
895895 0 0
896896 −0.946134 2.28417i −0.0316081 0.0763088i
897897 55.7485i 1.86139i
898898 −1.76006 + 0.729042i −0.0587340 + 0.0243284i
899899 −14.5264 14.5264i −0.484483 0.484483i
900900 0 0
901901 28.2731 18.2618i 0.941915 0.608387i
902902 3.62410 0.120669
903903 6.00894 + 6.00894i 0.199965 + 0.199965i
904904 −48.6406 + 20.1476i −1.61776 + 0.670099i
905905 0 0
906906 −4.51389 10.8975i −0.149964 0.362045i
907907 10.0069 + 4.14501i 0.332275 + 0.137633i 0.542583 0.840002i 0.317447π-0.317447\pi
−0.210307 + 0.977635i 0.567447π0.567447\pi
908908 0.865889 2.09044i 0.0287355 0.0693737i
909909 −14.7276 + 14.7276i −0.488485 + 0.488485i
910910 0 0
911911 −15.0373 + 36.3032i −0.498207 + 1.20278i 0.452241 + 0.891896i 0.350625π0.350625\pi
−0.950448 + 0.310882i 0.899375π0.899375\pi
912912 −1.40755 0.583028i −0.0466088 0.0193060i
913913 28.9599 + 69.9154i 0.958433 + 2.31386i
914914 16.8061i 0.555897i
915915 0 0
916916 −9.91385 9.91385i −0.327563 0.327563i
917917 −5.35051 −0.176689
918918 0.217929 + 1.19225i 0.00719272 + 0.0393501i
919919 48.2620 1.59202 0.796008 0.605286i 0.206941π-0.206941\pi
0.796008 + 0.605286i 0.206941π0.206941\pi
920920 0 0
921921 −3.87812 + 1.60637i −0.127788 + 0.0529317i
922922 30.3045i 0.998026i
923923 −10.4301 25.1806i −0.343312 0.828829i
924924 −6.23827 2.58398i −0.205224 0.0850066i
925925 0 0
926926 −10.6315 + 10.6315i −0.349374 + 0.349374i
927927 −0.774357 + 0.774357i −0.0254332 + 0.0254332i
928928 −16.8233 + 40.6151i −0.552252 + 1.33325i
929929 −21.5317 8.91871i −0.706431 0.292613i 0.000395678 1.00000i 0.499874π-0.499874\pi
−0.706827 + 0.707387i 0.749874π0.749874\pi
930930 0 0
931931 6.72920i 0.220541i
932932 6.55460 2.71501i 0.214703 0.0889330i
933933 19.0619 + 19.0619i 0.624057 + 0.624057i
934934 8.43745 0.276082
935935 0 0
936936 36.1250 1.18078
937937 6.87594 + 6.87594i 0.224627 + 0.224627i 0.810444 0.585816i 0.199226π-0.199226\pi
−0.585816 + 0.810444i 0.699226π0.699226\pi
938938 −3.60471 + 1.49312i −0.117698 + 0.0487520i
939939 65.0674i 2.12339i
940940 0 0
941941 13.0919 + 5.42286i 0.426785 + 0.176780i 0.585728 0.810508i 0.300809π-0.300809\pi
−0.158943 + 0.987288i 0.550809π0.550809\pi
942942 −9.86479 + 23.8157i −0.321412 + 0.775958i
943943 3.30491 3.30491i 0.107623 0.107623i
944944 2.63131 2.63131i 0.0856418 0.0856418i
945945 0 0
946946 26.4630 + 10.9613i 0.860387 + 0.356384i
947947 14.7284 + 35.5574i 0.478607 + 1.15546i 0.960262 + 0.279099i 0.0900358π0.0900358\pi
−0.481655 + 0.876361i 0.659964π0.659964\pi
948948 4.01058i 0.130257i
949949 −43.8357 + 18.1573i −1.42297 + 0.589412i
950950 0 0
951951 61.8987 2.00720
952952 6.37071 1.16449i 0.206476 0.0377412i
953953 −37.7984 −1.22441 −0.612206 0.790698i 0.709718π-0.709718\pi
−0.612206 + 0.790698i 0.709718π0.709718\pi
954954 −17.1668 17.1668i −0.555795 0.555795i
955955 0 0
956956 1.38774i 0.0448828i
957957 36.6897 + 88.5768i 1.18601 + 2.86328i
958958 10.4721 + 4.33769i 0.338339 + 0.140145i
959959 −0.626240 + 1.51188i −0.0202223 + 0.0488210i
960960 0 0
961961 −17.5746 + 17.5746i −0.566922 + 0.566922i
962962 5.85325 14.1310i 0.188716 0.455602i
963963 22.5145 + 9.32583i 0.725521 + 0.300521i
964964 1.04508 + 2.52305i 0.0336598 + 0.0812620i
965965 0 0
966966 6.66009 2.75870i 0.214285 0.0887598i
967967 3.39288 + 3.39288i 0.109108 + 0.109108i 0.759553 0.650445i 0.225418π-0.225418\pi
−0.650445 + 0.759553i 0.725418π0.725418\pi
968968 −31.9662 −1.02743
969969 −5.81217 + 8.41221i −0.186714 + 0.270239i
970970 0 0
971971 −25.8080 25.8080i −0.828217 0.828217i 0.159053 0.987270i 0.449156π-0.449156\pi
−0.987270 + 0.159053i 0.949156π0.949156\pi
972972 22.4774 9.31043i 0.720962 0.298632i
973973 6.54621i 0.209862i
974974 −9.75221 23.5439i −0.312481 0.754396i
975975 0 0
976976 −0.265916 + 0.641978i −0.00851176 + 0.0205492i
977977 −44.0684 + 44.0684i −1.40987 + 1.40987i −0.649569 + 0.760303i 0.725051π0.725051\pi
−0.760303 + 0.649569i 0.774949π0.774949\pi
978978 −12.3074 + 12.3074i −0.393547 + 0.393547i
979979 21.5965 52.1385i 0.690227 1.66635i
980980 0 0
981981 14.5627 + 35.1576i 0.464953 + 1.12249i
982982 22.0034i 0.702156i
983983 −37.1141 + 15.3732i −1.18376 + 0.490328i −0.885717 0.464225i 0.846333π-0.846333\pi
−0.298040 + 0.954553i 0.596333π0.596333\pi
984984 −4.19764 4.19764i −0.133816 0.133816i
985985 0 0
986986 −26.7536 18.4846i −0.852008 0.588670i
987987 −2.25070 −0.0716407
988988 3.04358 + 3.04358i 0.0968291 + 0.0968291i
989989 34.1282 14.1364i 1.08521 0.449511i
990990 0 0
991991 9.59778 + 23.1711i 0.304883 + 0.736054i 0.999855 + 0.0170168i 0.00541686π0.00541686\pi
−0.694972 + 0.719037i 0.744583π0.744583\pi
992992 −12.1504 5.03287i −0.385776 0.159794i
993993 30.5786 73.8232i 0.970382 2.34271i
994994 −2.49211 + 2.49211i −0.0790449 + 0.0790449i
995995 0 0
996996 16.7750 40.4985i 0.531536 1.28324i
997997 34.5204 + 14.2988i 1.09327 + 0.452848i 0.855146 0.518387i 0.173467π-0.173467\pi
0.238125 + 0.971235i 0.423467π0.423467\pi
998998 1.80882 + 4.36687i 0.0572571 + 0.138231i
999999 1.26439i 0.0400035i
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 425.2.m.e.376.2 24
5.2 odd 4 85.2.m.a.19.5 yes 24
5.3 odd 4 85.2.m.a.19.2 yes 24
5.4 even 2 inner 425.2.m.e.376.5 24
15.2 even 4 765.2.bh.b.19.2 24
15.8 even 4 765.2.bh.b.19.5 24
17.3 odd 16 7225.2.a.by.1.8 24
17.9 even 8 inner 425.2.m.e.26.2 24
17.14 odd 16 7225.2.a.by.1.7 24
85.3 even 16 1445.2.b.i.579.18 24
85.9 even 8 inner 425.2.m.e.26.5 24
85.14 odd 16 7225.2.a.by.1.18 24
85.37 even 16 1445.2.b.i.579.7 24
85.43 odd 8 85.2.m.a.9.5 yes 24
85.48 even 16 1445.2.b.i.579.17 24
85.54 odd 16 7225.2.a.by.1.17 24
85.77 odd 8 85.2.m.a.9.2 24
85.82 even 16 1445.2.b.i.579.8 24
255.77 even 8 765.2.bh.b.604.5 24
255.128 even 8 765.2.bh.b.604.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.m.a.9.2 24 85.77 odd 8
85.2.m.a.9.5 yes 24 85.43 odd 8
85.2.m.a.19.2 yes 24 5.3 odd 4
85.2.m.a.19.5 yes 24 5.2 odd 4
425.2.m.e.26.2 24 17.9 even 8 inner
425.2.m.e.26.5 24 85.9 even 8 inner
425.2.m.e.376.2 24 1.1 even 1 trivial
425.2.m.e.376.5 24 5.4 even 2 inner
765.2.bh.b.19.2 24 15.2 even 4
765.2.bh.b.19.5 24 15.8 even 4
765.2.bh.b.604.2 24 255.128 even 8
765.2.bh.b.604.5 24 255.77 even 8
1445.2.b.i.579.7 24 85.37 even 16
1445.2.b.i.579.8 24 85.82 even 16
1445.2.b.i.579.17 24 85.48 even 16
1445.2.b.i.579.18 24 85.3 even 16
7225.2.a.by.1.7 24 17.14 odd 16
7225.2.a.by.1.8 24 17.3 odd 16
7225.2.a.by.1.17 24 85.54 odd 16
7225.2.a.by.1.18 24 85.14 odd 16