Properties

Label 225.2.q.a.106.28
Level 225225
Weight 22
Character 225.106
Analytic conductor 1.7971.797
Analytic rank 00
Dimension 224224
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 225=3252 225 = 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 225.q (of order 1515, degree 88, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.796634045481.79663404548
Analytic rank: 00
Dimension: 224224
Relative dimension: 2828 over Q(ζ15)\Q(\zeta_{15})
Twist minimal: yes
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 106.28
Character χ\chi == 225.106
Dual form 225.2.q.a.121.28

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+(2.68409+0.570520i)q2+(1.72549+0.150630i)q3+(5.05174+2.24918i)q4+(0.4206152.19615i)q5+(4.717300.580123i)q6+(0.931182+1.61286i)q7+(7.83615+5.69329i)q8+(2.954620.519820i)q9+(2.381925.65469i)q10+(2.702640.574464i)q11+(9.055523.11999i)q12+(1.65646+0.352091i)q13+(3.41954+3.79779i)q14+(0.394961+3.85279i)q15+(10.3844+11.5331i)q16+(5.114643.71600i)q17+(8.22703+0.290429i)q18+(1.23445+0.896882i)q19+(7.0643810.1484i)q20+(1.363802.92323i)q21+(6.926393.08383i)q22+(0.3274610.363683i)q23+(14.37888.64335i)q24+(4.646171.84747i)q254.64695q26+(5.01986+1.34200i)q27+(8.33169+6.05333i)q28+(0.1891221.79938i)q29+(3.25821+10.1159i)q30+(0.2857582.71880i)q31+(11.6068+20.1036i)q32+(4.74991+0.584133i)q33+(11.608112.8921i)q34+(3.15040+2.72341i)q35+(16.0952+4.01948i)q36+(1.303184.01076i)q37+(2.80169+3.11159i)q38+(2.805160.857041i)q39+(15.799314.8147i)q40+(3.716700.790010i)q41+(5.328327.06812i)q42+(5.30871+9.19495i)q43+(12.36108.98078i)q44+(0.1011556.70744i)q45+(1.086420.789333i)q46+(0.670718+6.38145i)q47+(19.655418.3360i)q48+(1.76580+3.05845i)q49+(11.41677.60951i)q50+(9.38499+5.64150i)q51+(9.159921.94700i)q52+(4.808813.49380i)q53+(14.2394+0.738105i)q54+(2.39838+5.69379i)q55+(16.4793+7.33707i)q56+(2.265131.36161i)q57+(0.5189614.93758i)q58+(9.935882.11194i)q59+(10.6609+18.5750i)q60+(7.130901.51572i)q61+(2.318137.13448i)q62+(1.91290+5.24942i)q63+(10.0928+31.0624i)q64+(0.0765136+3.78593i)q65+(12.4159+4.27779i)q66+(0.9140058.69618i)q67+(17.479930.2760i)q68+(0.510249+0.676856i)q69+(6.90220+9.10724i)q70+(2.742921.99285i)q71+(26.1123+12.7481i)q72+(4.80018+14.7734i)q73+(5.7860610.0218i)q74+(8.29519+2.48794i)q75+(4.21888+7.30732i)q76+(3.443183.82404i)q77+(8.018270.699970i)q78+(1.34121+12.7607i)q79+(29.696217.9548i)q80+(8.459573.07174i)q81+10.4267q82+(0.803423+0.357707i)q83+(13.464411.7000i)q84+(10.3122+9.66951i)q85+(19.4950+21.6513i)q86+(0.597368+3.07632i)q87+(17.907719.8885i)q88+(1.51233+4.65447i)q89+(4.0982417.9456i)q90+(0.9745932.99949i)q91+(2.472241.10071i)q92+(0.0835387+4.73431i)q93+(1.84048+17.5110i)q94+(2.488922.33380i)q95+(23.055732.9402i)q96+(0.396958+3.77680i)q97+(2.99465+9.21658i)q98+(8.283900.292436i)q99+O(q100)q+(2.68409 + 0.570520i) q^{2} +(-1.72549 + 0.150630i) q^{3} +(5.05174 + 2.24918i) q^{4} +(0.420615 - 2.19615i) q^{5} +(-4.71730 - 0.580123i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 + 5.69329i) q^{8} +(2.95462 - 0.519820i) q^{9} +(2.38192 - 5.65469i) q^{10} +(-2.70264 - 0.574464i) q^{11} +(-9.05552 - 3.11999i) q^{12} +(-1.65646 + 0.352091i) q^{13} +(-3.41954 + 3.79779i) q^{14} +(-0.394961 + 3.85279i) q^{15} +(10.3844 + 11.5331i) q^{16} +(-5.11464 - 3.71600i) q^{17} +(8.22703 + 0.290429i) q^{18} +(1.23445 + 0.896882i) q^{19} +(7.06438 - 10.1484i) q^{20} +(1.36380 - 2.92323i) q^{21} +(-6.92639 - 3.08383i) q^{22} +(0.327461 - 0.363683i) q^{23} +(-14.3788 - 8.64335i) q^{24} +(-4.64617 - 1.84747i) q^{25} -4.64695 q^{26} +(-5.01986 + 1.34200i) q^{27} +(-8.33169 + 6.05333i) q^{28} +(-0.189122 - 1.79938i) q^{29} +(-3.25821 + 10.1159i) q^{30} +(0.285758 - 2.71880i) q^{31} +(11.6068 + 20.1036i) q^{32} +(4.74991 + 0.584133i) q^{33} +(-11.6081 - 12.8921i) q^{34} +(3.15040 + 2.72341i) q^{35} +(16.0952 + 4.01948i) q^{36} +(1.30318 - 4.01076i) q^{37} +(2.80169 + 3.11159i) q^{38} +(2.80516 - 0.857041i) q^{39} +(15.7993 - 14.8147i) q^{40} +(3.71670 - 0.790010i) q^{41} +(5.32832 - 7.06812i) q^{42} +(-5.30871 + 9.19495i) q^{43} +(-12.3610 - 8.98078i) q^{44} +(0.101155 - 6.70744i) q^{45} +(1.08642 - 0.789333i) q^{46} +(0.670718 + 6.38145i) q^{47} +(-19.6554 - 18.3360i) q^{48} +(1.76580 + 3.05845i) q^{49} +(-11.4167 - 7.60951i) q^{50} +(9.38499 + 5.64150i) q^{51} +(-9.15992 - 1.94700i) q^{52} +(4.80881 - 3.49380i) q^{53} +(-14.2394 + 0.738105i) q^{54} +(-2.39838 + 5.69379i) q^{55} +(-16.4793 + 7.33707i) q^{56} +(-2.26513 - 1.36161i) q^{57} +(0.518961 - 4.93758i) q^{58} +(9.93588 - 2.11194i) q^{59} +(-10.6609 + 18.5750i) q^{60} +(-7.13090 - 1.51572i) q^{61} +(2.31813 - 7.13448i) q^{62} +(-1.91290 + 5.24942i) q^{63} +(10.0928 + 31.0624i) q^{64} +(0.0765136 + 3.78593i) q^{65} +(12.4159 + 4.27779i) q^{66} +(0.914005 - 8.69618i) q^{67} +(-17.4799 - 30.2760i) q^{68} +(-0.510249 + 0.676856i) q^{69} +(6.90220 + 9.10724i) q^{70} +(2.74292 - 1.99285i) q^{71} +(26.1123 + 12.7481i) q^{72} +(4.80018 + 14.7734i) q^{73} +(5.78606 - 10.0218i) q^{74} +(8.29519 + 2.48794i) q^{75} +(4.21888 + 7.30732i) q^{76} +(3.44318 - 3.82404i) q^{77} +(8.01827 - 0.699970i) q^{78} +(1.34121 + 12.7607i) q^{79} +(29.6962 - 17.9548i) q^{80} +(8.45957 - 3.07174i) q^{81} +10.4267 q^{82} +(-0.803423 + 0.357707i) q^{83} +(13.4644 - 11.7000i) q^{84} +(-10.3122 + 9.66951i) q^{85} +(-19.4950 + 21.6513i) q^{86} +(0.597368 + 3.07632i) q^{87} +(-17.9077 - 19.8885i) q^{88} +(1.51233 + 4.65447i) q^{89} +(4.09824 - 17.9456i) q^{90} +(0.974593 - 2.99949i) q^{91} +(2.47224 - 1.10071i) q^{92} +(-0.0835387 + 4.73431i) q^{93} +(-1.84048 + 17.5110i) q^{94} +(2.48892 - 2.33380i) q^{95} +(-23.0557 - 32.9402i) q^{96} +(0.396958 + 3.77680i) q^{97} +(2.99465 + 9.21658i) q^{98} +(-8.28390 - 0.292436i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 224q3q28q3+23q48q510q68q720q88q920q1011q114q123q13+q1448q15+23q1624q1712q19+q20+20q99+O(q100) 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/225Z)×\left(\mathbb{Z}/225\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(25)e\left(\frac{2}{5}\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 2.68409 + 0.570520i 1.89794 + 0.403419i 0.999372 0.0354233i 0.0112779π-0.0112779\pi
0.898564 + 0.438842i 0.144611π0.144611\pi
33 −1.72549 + 0.150630i −0.996211 + 0.0869662i
44 5.05174 + 2.24918i 2.52587 + 1.12459i
55 0.420615 2.19615i 0.188105 0.982149i
66 −4.71730 0.580123i −1.92583 0.236834i
77 −0.931182 + 1.61286i −0.351954 + 0.609602i −0.986592 0.163208i 0.947816π-0.947816\pi
0.634638 + 0.772810i 0.281149π0.281149\pi
88 7.83615 + 5.69329i 2.77050 + 2.01288i
99 2.95462 0.519820i 0.984874 0.173273i
1010 2.38192 5.65469i 0.753229 1.78817i
1111 −2.70264 0.574464i −0.814878 0.173208i −0.218423 0.975854i 0.570091π-0.570091\pi
−0.596455 + 0.802647i 0.703424π0.703424\pi
1212 −9.05552 3.11999i −2.61410 0.900664i
1313 −1.65646 + 0.352091i −0.459419 + 0.0976525i −0.431807 0.901966i 0.642124π-0.642124\pi
−0.0276122 + 0.999619i 0.508790π0.508790\pi
1414 −3.41954 + 3.79779i −0.913911 + 1.01500i
1515 −0.394961 + 3.85279i −0.101978 + 0.994787i
1616 10.3844 + 11.5331i 2.59610 + 2.88327i
1717 −5.11464 3.71600i −1.24048 0.901263i −0.242851 0.970064i 0.578083π-0.578083\pi
−0.997630 + 0.0688008i 0.978083π0.978083\pi
1818 8.22703 + 0.290429i 1.93913 + 0.0684547i
1919 1.23445 + 0.896882i 0.283203 + 0.205759i 0.720313 0.693649i 0.243998π-0.243998\pi
−0.437110 + 0.899408i 0.643998π0.643998\pi
2020 7.06438 10.1484i 1.57964 2.26924i
2121 1.36380 2.92323i 0.297606 0.637900i
2222 −6.92639 3.08383i −1.47671 0.657474i
2323 0.327461 0.363683i 0.0682804 0.0758331i −0.708037 0.706176i 0.750419π-0.750419\pi
0.776317 + 0.630343i 0.217086π0.217086\pi
2424 −14.3788 8.64335i −2.93505 1.76432i
2525 −4.64617 1.84747i −0.929233 0.369494i
2626 −4.64695 −0.911343
2727 −5.01986 + 1.34200i −0.966073 + 0.258268i
2828 −8.33169 + 6.05333i −1.57454 + 1.14397i
2929 −0.189122 1.79938i −0.0351191 0.334136i −0.997948 0.0640249i 0.979606π-0.979606\pi
0.962829 0.270111i 0.0870604π-0.0870604\pi
3030 −3.25821 + 10.1159i −0.594864 + 1.84690i
3131 0.285758 2.71880i 0.0513236 0.488312i −0.938424 0.345485i 0.887714π-0.887714\pi
0.989748 0.142826i 0.0456190π-0.0456190\pi
3232 11.6068 + 20.1036i 2.05182 + 3.55385i
3333 4.74991 + 0.584133i 0.826853 + 0.101685i
3434 −11.6081 12.8921i −1.99077 2.21097i
3535 3.15040 + 2.72341i 0.532516 + 0.460340i
3636 16.0952 + 4.01948i 2.68253 + 0.669913i
3737 1.30318 4.01076i 0.214241 0.659366i −0.784966 0.619539i 0.787319π-0.787319\pi
0.999207 0.0398264i 0.0126805π-0.0126805\pi
3838 2.80169 + 3.11159i 0.454494 + 0.504766i
3939 2.80516 0.857041i 0.449186 0.137236i
4040 15.7993 14.8147i 2.49809 2.34241i
4141 3.71670 0.790010i 0.580452 0.123379i 0.0916768 0.995789i 0.470777π-0.470777\pi
0.488775 + 0.872410i 0.337444π0.337444\pi
4242 5.32832 7.06812i 0.822178 1.09063i
4343 −5.30871 + 9.19495i −0.809571 + 1.40222i 0.103591 + 0.994620i 0.466967π0.466967\pi
−0.913162 + 0.407597i 0.866367π0.866367\pi
4444 −12.3610 8.98078i −1.86349 1.35390i
4545 0.101155 6.70744i 0.0150793 0.999886i
4646 1.08642 0.789333i 0.160184 0.116381i
4747 0.670718 + 6.38145i 0.0978342 + 0.930831i 0.927816 + 0.373039i 0.121684π0.121684\pi
−0.829981 + 0.557791i 0.811649π0.811649\pi
4848 −19.6554 18.3360i −2.83702 2.64657i
4949 1.76580 + 3.05845i 0.252257 + 0.436922i
5050 −11.4167 7.60951i −1.61456 1.07615i
5151 9.38499 + 5.64150i 1.31416 + 0.789968i
5252 −9.15992 1.94700i −1.27025 0.270000i
5353 4.80881 3.49380i 0.660540 0.479911i −0.206305 0.978488i 0.566144π-0.566144\pi
0.866845 + 0.498577i 0.166144π0.166144\pi
5454 −14.2394 + 0.738105i −1.93774 + 0.100443i
5555 −2.39838 + 5.69379i −0.323398 + 0.767750i
5656 −16.4793 + 7.33707i −2.20214 + 0.980458i
5757 −2.26513 1.36161i −0.300024 0.180350i
5858 0.518961 4.93758i 0.0681429 0.648336i
5959 9.93588 2.11194i 1.29354 0.274951i 0.490797 0.871274i 0.336706π-0.336706\pi
0.802744 + 0.596323i 0.203372π0.203372\pi
6060 −10.6609 + 18.5750i −1.37631 + 2.39802i
6161 −7.13090 1.51572i −0.913019 0.194068i −0.272630 0.962119i 0.587893π-0.587893\pi
−0.640389 + 0.768051i 0.721227π0.721227\pi
6262 2.31813 7.13448i 0.294403 0.906079i
6363 −1.91290 + 5.24942i −0.241002 + 0.661365i
6464 10.0928 + 31.0624i 1.26160 + 3.88280i
6565 0.0765136 + 3.78593i 0.00949034 + 0.469587i
6666 12.4159 + 4.27779i 1.52829 + 0.526559i
6767 0.914005 8.69618i 0.111664 1.06241i −0.784939 0.619572i 0.787306π-0.787306\pi
0.896603 0.442835i 0.146027π-0.146027\pi
6868 −17.4799 30.2760i −2.11975 3.67151i
6969 −0.510249 + 0.676856i −0.0614268 + 0.0814839i
7070 6.90220 + 9.10724i 0.824971 + 1.08852i
7171 2.74292 1.99285i 0.325524 0.236507i −0.413005 0.910729i 0.635521π-0.635521\pi
0.738529 + 0.674222i 0.235521π0.235521\pi
7272 26.1123 + 12.7481i 3.07737 + 1.50238i
7373 4.80018 + 14.7734i 0.561818 + 1.72910i 0.677221 + 0.735780i 0.263184π0.263184\pi
−0.115403 + 0.993319i 0.536816π0.536816\pi
7474 5.78606 10.0218i 0.672616 1.16501i
7575 8.29519 + 2.48794i 0.957846 + 0.287282i
7676 4.21888 + 7.30732i 0.483939 + 0.838207i
7777 3.44318 3.82404i 0.392387 0.435790i
7878 8.01827 0.699970i 0.907890 0.0792560i
7979 1.34121 + 12.7607i 0.150898 + 1.43570i 0.763757 + 0.645503i 0.223352π0.223352\pi
−0.612860 + 0.790192i 0.709981π0.709981\pi
8080 29.6962 17.9548i 3.32014 2.00740i
8181 8.45957 3.07174i 0.939953 0.341305i
8282 10.4267 1.15143
8383 −0.803423 + 0.357707i −0.0881871 + 0.0392634i −0.450356 0.892849i 0.648703π-0.648703\pi
0.362169 + 0.932112i 0.382036π0.382036\pi
8484 13.4644 11.7000i 1.46909 1.27657i
8585 −10.3122 + 9.66951i −1.11851 + 1.04881i
8686 −19.4950 + 21.6513i −2.10219 + 2.33472i
8787 0.597368 + 3.07632i 0.0640446 + 0.329816i
8888 −17.9077 19.8885i −1.90897 2.12012i
8989 1.51233 + 4.65447i 0.160306 + 0.493372i 0.998660 0.0517547i 0.0164814π-0.0164814\pi
−0.838353 + 0.545127i 0.816481π0.816481\pi
9090 4.09824 17.9456i 0.431993 1.89164i
9191 0.974593 2.99949i 0.102165 0.314432i
9292 2.47224 1.10071i 0.257749 0.114757i
9393 −0.0835387 + 4.73431i −0.00866256 + 0.490925i
9494 −1.84048 + 17.5110i −0.189831 + 1.80613i
9595 2.48892 2.33380i 0.255358 0.239443i
9696 −23.0557 32.9402i −2.35311 3.36195i
9797 0.396958 + 3.77680i 0.0403049 + 0.383476i 0.996016 + 0.0891705i 0.0284216π0.0284216\pi
−0.955711 + 0.294305i 0.904912π0.904912\pi
9898 2.99465 + 9.21658i 0.302505 + 0.931015i
9999 −8.28390 0.292436i −0.832564 0.0293910i
100100 −19.3159 19.7830i −1.93159 1.97830i
101101 3.33145 5.77025i 0.331492 0.574161i −0.651313 0.758810i 0.725781π-0.725781\pi
0.982805 + 0.184648i 0.0591146π0.0591146\pi
102102 21.9715 + 20.4966i 2.17551 + 2.02947i
103103 −1.40438 0.625269i −0.138377 0.0616096i 0.336380 0.941726i 0.390797π-0.390797\pi
−0.474757 + 0.880117i 0.657464π0.657464\pi
104104 −14.9848 6.67167i −1.46938 0.654211i
105105 −5.84621 4.22467i −0.570532 0.412285i
106106 14.9005 6.63415i 1.44727 0.644366i
107107 −14.6327 −1.41460 −0.707299 0.706914i 0.750087π-0.750087\pi
−0.707299 + 0.706914i 0.750087π0.750087\pi
108108 −28.3775 4.51115i −2.73062 0.434086i
109109 0.620591 1.90998i 0.0594418 0.182943i −0.916927 0.399056i 0.869338π-0.869338\pi
0.976368 + 0.216113i 0.0693379π0.0693379\pi
110110 −9.68590 + 13.9143i −0.923514 + 1.32668i
111111 −1.64447 + 7.11683i −0.156087 + 0.675499i
112112 −28.2709 + 6.00918i −2.67135 + 0.567814i
113113 13.0613 2.77626i 1.22870 0.261169i 0.452565 0.891732i 0.350509π-0.350509\pi
0.776138 + 0.630563i 0.217176π0.217176\pi
114114 −5.30298 4.94699i −0.496669 0.463328i
115115 −0.660967 0.872125i −0.0616355 0.0813261i
116116 3.09173 9.51536i 0.287060 0.883479i
117117 −4.71118 + 1.90136i −0.435549 + 0.175780i
118118 27.8737 2.56598
119119 10.7560 4.78889i 0.986004 0.438997i
120120 −25.0300 + 27.9424i −2.28492 + 2.55078i
121121 −3.07473 1.36896i −0.279521 0.124451i
122122 −18.2752 8.13665i −1.65456 0.736658i
123123 −6.29413 + 1.92300i −0.567523 + 0.173391i
124124 7.55865 13.0920i 0.678787 1.17569i
125125 −6.01157 + 9.42661i −0.537692 + 0.843142i
126126 −8.12928 + 12.9986i −0.724214 + 1.15800i
127127 1.59486 + 4.90847i 0.141521 + 0.435556i 0.996547 0.0830282i 0.0264591π-0.0264591\pi
−0.855026 + 0.518585i 0.826459π0.826459\pi
128128 4.51521 + 42.9594i 0.399092 + 3.79711i
129129 7.77508 16.6654i 0.684558 1.46731i
130130 −1.95458 + 10.2054i −0.171428 + 0.895074i
131131 1.24905 11.8839i 0.109130 1.03830i −0.793701 0.608307i 0.791849π-0.791849\pi
0.902831 0.429995i 0.141485π-0.141485\pi
132132 22.6815 + 13.6343i 1.97417 + 1.18671i
133133 −2.59604 + 1.15583i −0.225105 + 0.100223i
134134 7.41462 22.8199i 0.640526 1.97134i
135135 0.835799 + 11.5888i 0.0719342 + 0.997409i
136136 −18.9228 58.2383i −1.62261 4.99389i
137137 −2.90001 3.22078i −0.247764 0.275170i 0.606415 0.795148i 0.292607π-0.292607\pi
−0.854180 + 0.519978i 0.825940π0.825940\pi
138138 −1.75571 + 1.52563i −0.149456 + 0.129870i
139139 8.91270 9.89856i 0.755966 0.839585i −0.235237 0.971938i 0.575587π-0.575587\pi
0.991203 + 0.132353i 0.0422533π0.0422533\pi
140140 9.78959 + 20.8438i 0.827372 + 1.76162i
141141 −2.11855 10.9101i −0.178414 0.918796i
142142 8.49919 3.78408i 0.713236 0.317553i
143143 4.67908 0.391284
144144 36.6771 + 28.6778i 3.05643 + 2.38982i
145145 −4.03125 0.341505i −0.334777 0.0283604i
146146 4.45555 + 42.3918i 0.368744 + 3.50837i
147147 −3.50756 5.01134i −0.289299 0.413329i
148148 15.6042 17.3303i 1.28266 1.42454i
149149 −1.42735 2.47225i −0.116933 0.202535i 0.801618 0.597837i 0.203973π-0.203973\pi
−0.918551 + 0.395303i 0.870640π0.870640\pi
150150 20.8456 + 11.4104i 1.70204 + 0.931657i
151151 5.61232 9.72082i 0.456724 0.791069i −0.542062 0.840339i 0.682356π-0.682356\pi
0.998786 + 0.0492697i 0.0156894π0.0156894\pi
152152 4.56713 + 14.0562i 0.370443 + 1.14011i
153153 −17.0435 8.32068i −1.37788 0.672688i
154154 11.4235 8.29965i 0.920531 0.668805i
155155 −5.85071 1.77114i −0.469940 0.142261i
156156 16.0986 + 1.97977i 1.28892 + 0.158508i
157157 −7.23692 12.5347i −0.577569 1.00038i −0.995757 0.0920188i 0.970668π-0.970668\pi
0.418188 0.908360i 0.362665π-0.362665\pi
158158 −3.68034 + 35.0161i −0.292792 + 2.78573i
159159 −7.77127 + 6.75287i −0.616302 + 0.535537i
160160 49.0326 17.0345i 3.87637 1.34669i
161161 0.281641 + 0.866803i 0.0221964 + 0.0683136i
162162 24.4587 3.41847i 1.92166 0.268580i
163163 2.58162 7.94542i 0.202208 0.622333i −0.797608 0.603176i 0.793902π-0.793902\pi
0.999816 0.0191571i 0.00609828π-0.00609828\pi
164164 20.5527 + 4.36861i 1.60490 + 0.341131i
165165 3.28073 10.1858i 0.255405 0.792966i
166166 −2.36054 + 0.501747i −0.183213 + 0.0389432i
167167 −1.18258 + 11.2515i −0.0915109 + 0.870668i 0.848425 + 0.529316i 0.177551π0.177551\pi
−0.939936 + 0.341352i 0.889115π0.889115\pi
168168 27.3297 15.1423i 2.10853 1.16826i
169169 −9.25621 + 4.12113i −0.712016 + 0.317010i
170170 −33.1955 + 20.0705i −2.54598 + 1.53934i
171171 4.11355 + 2.00825i 0.314571 + 0.153575i
172172 −47.4993 + 34.5103i −3.62179 + 2.63139i
173173 −6.21968 1.32203i −0.472874 0.100512i −0.0346904 0.999398i 0.511045π-0.511045\pi
−0.438183 + 0.898886i 0.644378π0.644378\pi
174174 −0.151713 + 8.59791i −0.0115014 + 0.651806i
175175 7.30613 5.77326i 0.552291 0.436417i
176176 −21.4400 37.1352i −1.61610 2.79917i
177177 −16.8261 + 5.14076i −1.26473 + 0.386403i
178178 1.40375 + 13.3558i 0.105216 + 1.00106i
179179 5.40088 3.92397i 0.403681 0.293291i −0.367358 0.930080i 0.619738π-0.619738\pi
0.771039 + 0.636788i 0.219738π0.219738\pi
180180 15.5973 33.6567i 1.16255 2.50863i
181181 5.85623 + 4.25480i 0.435290 + 0.316257i 0.783761 0.621063i 0.213299π-0.213299\pi
−0.348470 + 0.937320i 0.613299π0.613299\pi
182182 4.32716 7.49486i 0.320751 0.555556i
183183 12.5326 + 1.54123i 0.926437 + 0.113931i
184184 4.63659 0.985537i 0.341814 0.0726547i
185185 −8.26011 4.54896i −0.607295 0.334446i
186186 −2.92524 + 12.6596i −0.214489 + 0.928250i
187187 11.6883 + 12.9812i 0.854735 + 0.949280i
188188 −10.9647 + 33.7460i −0.799686 + 2.46118i
189189 2.50996 9.34596i 0.182573 0.679818i
190190 8.01195 4.84415i 0.581248 0.351431i
191191 0.759730 + 0.843766i 0.0549721 + 0.0610527i 0.770004 0.638039i 0.220254π-0.220254\pi
−0.715032 + 0.699092i 0.753588π0.753588\pi
192192 −22.0939 52.0776i −1.59449 3.75837i
193193 1.53746 + 2.66296i 0.110669 + 0.191684i 0.916040 0.401087i 0.131367π-0.131367\pi
−0.805371 + 0.592771i 0.798034π0.798034\pi
194194 −1.08927 + 10.3637i −0.0782052 + 0.744073i
195195 −0.702297 6.52105i −0.0502926 0.466982i
196196 2.04135 + 19.4221i 0.145811 + 1.38729i
197197 18.8592 13.7020i 1.34366 0.976227i 0.344360 0.938838i 0.388096π-0.388096\pi
0.999301 0.0373893i 0.0119042π-0.0119042\pi
198198 −22.0679 5.51106i −1.56830 0.391654i
199199 −18.6167 −1.31970 −0.659851 0.751396i 0.729381π-0.729381\pi
−0.659851 + 0.751396i 0.729381π0.729381\pi
200200 −25.8898 40.9290i −1.83069 2.89412i
201201 −0.267201 + 15.1428i −0.0188469 + 1.06809i
202202 12.2340 13.5872i 0.860778 0.955991i
203203 3.07824 + 1.37052i 0.216050 + 0.0961917i
204204 34.7218 + 49.6079i 2.43101 + 3.47325i
205205 −0.171679 8.49473i −0.0119905 0.593298i
206206 −3.41274 2.47950i −0.237777 0.172755i
207207 0.778475 1.24477i 0.0541077 0.0865172i
208208 −21.2620 15.4478i −1.47426 1.07111i
209209 −2.82106 3.13310i −0.195136 0.216721i
210210 −13.2815 14.6748i −0.916510 1.01265i
211211 −7.70340 + 8.55549i −0.530324 + 0.588984i −0.947466 0.319857i 0.896365π-0.896365\pi
0.417142 + 0.908841i 0.363032π0.363032\pi
212212 32.1510 6.83391i 2.20814 0.469355i
213213 −4.43269 + 3.85180i −0.303723 + 0.263921i
214214 −39.2755 8.34827i −2.68482 0.570676i
215215 17.9606 + 15.5263i 1.22490 + 1.05888i
216216 −46.9768 18.0635i −3.19637 1.22906i
217217 4.11894 + 2.99259i 0.279612 + 0.203150i
218218 2.75541 4.77250i 0.186620 0.323235i
219219 −10.5080 24.7683i −0.710063 1.67369i
220220 −24.9224 + 23.3691i −1.68027 + 1.57555i
221221 9.78055 + 4.35458i 0.657911 + 0.292921i
222222 −8.47421 + 18.1640i −0.568752 + 1.21909i
223223 2.00257 + 0.425659i 0.134102 + 0.0285043i 0.274474 0.961595i 0.411496π-0.411496\pi
−0.140372 + 0.990099i 0.544830π0.544830\pi
224224 −43.2323 −2.88858
225225 −14.6880 3.04340i −0.979201 0.202894i
226226 36.6416 2.43736
227227 −14.8654 3.15974i −0.986653 0.209720i −0.313795 0.949491i 0.601600π-0.601600\pi
−0.672858 + 0.739771i 0.734934π0.734934\pi
228228 −8.38034 11.9732i −0.555001 0.792945i
229229 −0.192216 0.0855802i −0.0127020 0.00565530i 0.400376 0.916351i 0.368880π-0.368880\pi
−0.413078 + 0.910696i 0.635546π0.635546\pi
230230 −1.27653 2.71796i −0.0841718 0.179217i
231231 −5.36515 + 7.11698i −0.353001 + 0.468263i
232232 8.76239 15.1769i 0.575279 0.996413i
233233 −13.5683 9.85792i −0.888887 0.645814i 0.0467009 0.998909i 0.485129π-0.485129\pi
−0.935587 + 0.353095i 0.885129π0.885129\pi
234234 −13.7300 + 2.41558i −0.897557 + 0.157911i
235235 14.2968 + 1.21114i 0.932617 + 0.0790060i
236236 54.9436 + 11.6786i 3.57653 + 0.760214i
237237 −4.23639 21.8165i −0.275183 1.41713i
238238 31.6023 6.71727i 2.04847 0.435416i
239239 −16.5230 + 18.3506i −1.06878 + 1.18700i −0.0871544 + 0.996195i 0.527777π0.527777\pi
−0.981627 + 0.190808i 0.938889π0.938889\pi
240240 −48.5359 + 35.4539i −3.13298 + 2.28854i
241241 −2.03608 2.26129i −0.131155 0.145663i 0.673990 0.738741i 0.264579π-0.264579\pi
−0.805145 + 0.593078i 0.797913π0.797913\pi
242242 −7.47183 5.42860i −0.480307 0.348964i
243243 −14.1342 + 6.57452i −0.906709 + 0.421756i
244244 −32.6144 23.6957i −2.08792 1.51696i
245245 7.45955 2.59153i 0.476573 0.165567i
246246 −17.9911 + 1.57057i −1.14707 + 0.100136i
247247 −2.36060 1.05101i −0.150201 0.0668740i
248248 17.7182 19.6780i 1.12511 1.24956i
249249 1.33242 0.738238i 0.0844384 0.0467840i
250250 −21.5137 + 21.8721i −1.36064 + 1.38331i
251251 −24.9480 −1.57470 −0.787352 0.616504i 0.788548π-0.788548\pi
−0.787352 + 0.616504i 0.788548π0.788548\pi
252252 −21.4704 + 22.2163i −1.35251 + 1.39949i
253253 −1.09393 + 0.794789i −0.0687750 + 0.0499680i
254254 1.48036 + 14.0847i 0.0928859 + 0.883751i
255255 16.3371 18.2380i 1.02307 1.14211i
256256 −5.56198 + 52.9187i −0.347624 + 3.30742i
257257 −2.15283 3.72881i −0.134290 0.232597i 0.791036 0.611770i 0.209542π-0.209542\pi
−0.925326 + 0.379172i 0.876209π0.876209\pi
258258 30.3770 40.2957i 1.89119 2.50870i
259259 5.25529 + 5.83659i 0.326548 + 0.362668i
260260 −8.12871 + 19.2976i −0.504121 + 1.19679i
261261 −1.49414 5.21817i −0.0924848 0.322996i
262262 10.1326 31.1849i 0.625992 1.92661i
263263 −8.56916 9.51702i −0.528397 0.586844i 0.418566 0.908186i 0.362533π-0.362533\pi
−0.946963 + 0.321342i 0.895866π0.895866\pi
264264 33.8954 + 31.6200i 2.08611 + 1.94608i
265265 −5.65026 12.0304i −0.347093 0.739023i
266266 −7.62742 + 1.62126i −0.467667 + 0.0994058i
267267 −3.31061 7.80343i −0.202606 0.477562i
268268 24.1766 41.8751i 1.47682 2.55793i
269269 16.3393 + 11.8712i 0.996227 + 0.723801i 0.961276 0.275588i 0.0888724π-0.0888724\pi
0.0349513 + 0.999389i 0.488872π0.488872\pi
270270 −4.36832 + 31.5823i −0.265847 + 1.92204i
271271 6.40204 4.65136i 0.388897 0.282550i −0.376107 0.926576i 0.622737π-0.622737\pi
0.765003 + 0.644027i 0.222737π0.222737\pi
272272 −10.2556 97.5760i −0.621840 5.91641i
273273 −1.22984 + 5.32238i −0.0744331 + 0.322125i
274274 −5.94635 10.2994i −0.359232 0.622208i
275275 11.4956 + 7.66211i 0.693212 + 0.462043i
276276 −4.10002 + 2.27166i −0.246792 + 0.136738i
277277 −0.176092 0.0374296i −0.0105804 0.00224892i 0.202618 0.979258i 0.435055π-0.435055\pi
−0.213199 + 0.977009i 0.568388π0.568388\pi
278278 29.5698 21.4837i 1.77348 1.28851i
279279 −0.568983 8.18158i −0.0340641 0.489818i
280280 9.18186 + 39.2772i 0.548721 + 2.34726i
281281 −1.48639 + 0.661783i −0.0886705 + 0.0394786i −0.450593 0.892730i 0.648787π-0.648787\pi
0.361922 + 0.932208i 0.382121π0.382121\pi
282282 0.538049 30.4923i 0.0320403 1.81579i
283283 0.382272 3.63707i 0.0227237 0.216201i −0.977268 0.212010i 0.931999π-0.931999\pi
0.999991 0.00419159i 0.00133423π-0.00133423\pi
284284 18.3388 3.89803i 1.08821 0.231305i
285285 −3.94306 + 4.40185i −0.233567 + 0.260743i
286286 12.5591 + 2.66951i 0.742633 + 0.157851i
287287 −2.18676 + 6.73015i −0.129080 + 0.397268i
288288 44.7441 + 53.3651i 2.63657 + 3.14457i
289289 7.09756 + 21.8440i 0.417503 + 1.28494i
290290 −10.6254 3.21654i −0.623945 0.188882i
291291 −1.25384 6.45703i −0.0735017 0.378518i
292292 −8.97884 + 85.4280i −0.525447 + 4.99929i
293293 12.2406 + 21.2013i 0.715101 + 1.23859i 0.962921 + 0.269785i 0.0869525π0.0869525\pi
−0.247820 + 0.968806i 0.579714π0.579714\pi
294294 −6.55553 15.4520i −0.382326 0.901180i
295295 −0.458949 22.7090i −0.0267210 1.32217i
296296 33.0463 24.0096i 1.92078 1.39553i
297297 14.3378 0.743208i 0.831965 0.0431253i
298298 −2.42067 7.45007i −0.140226 0.431571i
299299 −0.414377 + 0.717721i −0.0239640 + 0.0415069i
300300 36.3093 + 31.2258i 2.09632 + 1.80282i
301301 −9.88675 17.1244i −0.569863 0.987032i
302302 20.6099 22.8896i 1.18597 1.31715i
303303 −4.87921 + 10.4583i −0.280304 + 0.600814i
304304 2.47527 + 23.5506i 0.141966 + 1.35072i
305305 −6.32812 + 15.0230i −0.362347 + 0.860215i
306306 −40.9990 32.0571i −2.34376 1.83258i
307307 3.80945 0.217417 0.108708 0.994074i 0.465329π-0.465329\pi
0.108708 + 0.994074i 0.465329π0.465329\pi
308308 25.9950 11.5737i 1.48120 0.659474i
309309 2.51742 + 0.867354i 0.143211 + 0.0493420i
310310 −14.6934 8.09184i −0.834526 0.459586i
311311 −16.8714 + 18.7375i −0.956687 + 1.06251i 0.0413039 + 0.999147i 0.486849π0.486849\pi
−0.997991 + 0.0633616i 0.979818π0.979818\pi
312312 26.8611 + 9.25472i 1.52071 + 0.523945i
313313 17.3585 + 19.2786i 0.981161 + 1.08969i 0.995960 + 0.0897989i 0.0286224π0.0286224\pi
−0.0147991 + 0.999890i 0.504711π0.504711\pi
314314 −12.2732 37.7731i −0.692618 2.13166i
315315 10.7239 + 6.40900i 0.604225 + 0.361106i
316316 −21.9258 + 67.4806i −1.23342 + 3.79608i
317317 −20.9744 + 9.33841i −1.17804 + 0.524497i −0.899923 0.436050i 0.856377π-0.856377\pi
−0.278118 + 0.960547i 0.589711π0.589711\pi
318318 −24.7114 + 13.6916i −1.38575 + 0.767788i
319319 −0.522549 + 4.97172i −0.0292571 + 0.278363i
320320 72.4630 9.09997i 4.05080 0.508704i
321321 25.2486 2.20413i 1.40924 0.123022i
322322 0.261421 + 2.48726i 0.0145684 + 0.138609i
323323 −2.98096 9.17445i −0.165865 0.510480i
324324 49.6445 + 3.50945i 2.75803 + 0.194969i
325325 8.34666 + 1.42438i 0.462989 + 0.0790106i
326326 11.4623 19.8533i 0.634839 1.09957i
327327 −0.783122 + 3.38913i −0.0433068 + 0.187420i
328328 33.6224 + 14.9697i 1.85649 + 0.826561i
329329 −10.9169 4.86053i −0.601869 0.267969i
330330 14.6170 25.4679i 0.804639 1.40196i
331331 5.62038 2.50235i 0.308924 0.137542i −0.246419 0.969163i 0.579254π-0.579254\pi
0.555343 + 0.831622i 0.312587π0.312587\pi
332332 −4.86323 −0.266904
333333 1.76552 12.5277i 0.0967497 0.686514i
334334 −9.59337 + 29.5254i −0.524926 + 1.61556i
335335 −18.7137 5.66504i −1.02244 0.309514i
336336 47.8760 14.6272i 2.61185 0.797980i
337337 14.7319 3.13136i 0.802498 0.170576i 0.211636 0.977349i 0.432121π-0.432121\pi
0.590862 + 0.806772i 0.298788π0.298788\pi
338338 −27.1957 + 5.78061i −1.47925 + 0.314424i
339339 −22.1189 + 6.75783i −1.20133 + 0.367035i
340340 −73.8430 + 25.6539i −4.00470 + 1.39128i
341341 −2.33416 + 7.18380i −0.126402 + 0.389024i
342342 9.89539 + 7.73719i 0.535082 + 0.418380i
343343 −19.6137 −1.05904
344344 −93.9494 + 41.8290i −5.06541 + 2.25527i
345345 1.27186 + 1.40528i 0.0684746 + 0.0756578i
346346 −15.9399 7.09691i −0.856935 0.381532i
347347 −15.3731 6.84453i −0.825269 0.367434i −0.0497533 0.998762i 0.515844π-0.515844\pi
−0.775516 + 0.631328i 0.782510π0.782510\pi
348348 −3.90144 + 16.8843i −0.209139 + 0.905096i
349349 −7.75462 + 13.4314i −0.415096 + 0.718967i −0.995438 0.0954057i 0.969585π-0.969585\pi
0.580343 + 0.814372i 0.302919π0.302919\pi
350350 22.9041 11.3276i 1.22427 0.605488i
351351 7.84269 3.99041i 0.418612 0.212993i
352352 −19.8203 61.0006i −1.05643 3.25134i
353353 −0.982184 9.34486i −0.0522764 0.497377i −0.989065 0.147481i 0.952884π-0.952884\pi
0.936789 0.349896i 0.113783π-0.113783\pi
354354 −48.0957 + 4.19861i −2.55626 + 0.223154i
355355 −3.22288 6.86209i −0.171053 0.364202i
356356 −2.82885 + 26.9147i −0.149928 + 1.42647i
357357 −17.8381 + 9.88336i −0.944090 + 0.523083i
358358 16.7351 7.45097i 0.884480 0.393796i
359359 −2.47394 + 7.61399i −0.130569 + 0.401851i −0.994875 0.101116i 0.967759π-0.967759\pi
0.864305 + 0.502968i 0.167759π0.167759\pi
360360 38.9801 51.9846i 2.05443 2.73983i
361361 −5.15185 15.8558i −0.271150 0.834514i
362362 13.2912 + 14.7614i 0.698569 + 0.775840i
363363 5.51162 + 1.89898i 0.289285 + 0.0996704i
364364 11.6698 12.9606i 0.611663 0.679320i
365365 34.4637 4.32799i 1.80391 0.226537i
366366 32.7593 + 11.2869i 1.71236 + 0.589976i
367367 24.1256 10.7414i 1.25935 0.560698i 0.334990 0.942222i 0.391267π-0.391267\pi
0.924359 + 0.381524i 0.124601π0.124601\pi
368368 7.59487 0.395910
369369 10.5708 4.26620i 0.550293 0.222089i
370370 −19.5756 16.9224i −1.01769 0.879752i
371371 1.15712 + 11.0093i 0.0600747 + 0.571573i
372372 −11.0703 + 23.7286i −0.573970 + 1.23027i
373373 −13.8997 + 15.4372i −0.719700 + 0.799308i −0.986381 0.164477i 0.947406π-0.947406\pi
0.266681 + 0.963785i 0.414073π0.414073\pi
374374 23.9665 + 41.5111i 1.23928 + 2.14649i
375375 8.95297 17.1710i 0.462330 0.886708i
376376 −31.0756 + 53.8246i −1.60260 + 2.77579i
377377 0.946817 + 2.91400i 0.0487636 + 0.150079i
378378 12.0690 23.6534i 0.620763 1.21660i
379379 15.5059 11.2657i 0.796485 0.578680i −0.113396 0.993550i 0.536173π-0.536173\pi
0.909881 + 0.414870i 0.136173π0.136173\pi
380380 17.8225 6.19174i 0.914276 0.317629i
381381 −3.49127 8.22928i −0.178863 0.421599i
382382 1.55780 + 2.69818i 0.0797038 + 0.138051i
383383 2.52616 24.0348i 0.129081 1.22812i −0.717765 0.696285i 0.754835π-0.754835\pi
0.846846 0.531838i 0.178498π-0.178498\pi
384384 −14.2619 73.4458i −0.727800 3.74802i
385385 −6.94992 9.17020i −0.354201 0.467357i
386386 2.60740 + 8.02476i 0.132713 + 0.408449i
387387 −10.9055 + 29.9272i −0.554358 + 1.52128i
388388 −6.48938 + 19.9722i −0.329448 + 1.01394i
389389 36.8855 + 7.84025i 1.87017 + 0.397517i 0.996096 0.0882786i 0.0281366π-0.0281366\pi
0.874073 + 0.485795i 0.161470π0.161470\pi
390390 1.83537 17.9037i 0.0929373 0.906591i
391391 −3.02629 + 0.643258i −0.153046 + 0.0325310i
392392 −3.57561 + 34.0197i −0.180596 + 1.71825i
393393 −0.365148 + 20.6937i −0.0184193 + 1.04386i
394394 58.4370 26.0178i 2.94401 1.31076i
395395 28.5887 + 2.42187i 1.43845 + 0.121857i
396396 −41.1904 20.1093i −2.06990 1.01053i
397397 22.7545 16.5321i 1.14202 0.829724i 0.154618 0.987974i 0.450585π-0.450585\pi
0.987399 + 0.158251i 0.0505855π0.0505855\pi
398398 −49.9688 10.6212i −2.50471 0.532393i
399399 4.30533 2.38542i 0.215536 0.119420i
400400 −26.9407 72.7694i −1.34704 3.63847i
401401 −11.7822 20.4073i −0.588373 1.01909i −0.994446 0.105251i 0.966435π-0.966435\pi
0.406073 0.913841i 0.366898π-0.366898\pi
402402 −9.35649 + 40.4923i −0.466659 + 2.01957i
403403 0.483921 + 4.60420i 0.0241058 + 0.229351i
404404 29.8080 21.6568i 1.48300 1.07746i
405405 −3.18779 19.8705i −0.158403 0.987375i
406406 7.48036 + 5.43480i 0.371244 + 0.269725i
407407 −5.82606 + 10.0910i −0.288787 + 0.500194i
408408 41.4234 + 97.6391i 2.05077 + 4.83386i
409409 −10.2783 + 2.18473i −0.508231 + 0.108028i −0.454888 0.890548i 0.650321π-0.650321\pi
−0.0533426 + 0.998576i 0.516988π0.516988\pi
410410 4.38562 22.8986i 0.216590 1.13088i
411411 5.48908 + 5.12060i 0.270756 + 0.252581i
412412 −5.68821 6.31740i −0.280238 0.311236i
413413 −5.84587 + 17.9917i −0.287656 + 0.885315i
414414 2.79966 2.89692i 0.137596 0.142376i
415415 0.447647 + 1.91490i 0.0219741 + 0.0939985i
416416 −26.3045 29.2141i −1.28969 1.43234i
417417 −13.8877 + 18.4224i −0.680086 + 0.902147i
418418 −5.78446 10.0190i −0.282927 0.490045i
419419 −0.989526 + 9.41471i −0.0483415 + 0.459939i 0.943397 + 0.331665i 0.107610π0.107610\pi
−0.991739 + 0.128274i 0.959056π0.959056\pi
420420 −20.0315 34.4911i −0.977439 1.68299i
421421 0.707686 + 6.73319i 0.0344905 + 0.328155i 0.998139 + 0.0609816i 0.0194231π0.0194231\pi
−0.963648 + 0.267174i 0.913910π0.913910\pi
422422 −25.5577 + 18.5687i −1.24413 + 0.903912i
423423 5.29893 + 18.5061i 0.257643 + 0.899799i
424424 57.5737 2.79603
425425 16.8982 + 26.7143i 0.819685 + 1.29583i
426426 −14.0953 + 7.80963i −0.682918 + 0.378378i
427427 9.08481 10.0897i 0.439645 0.488275i
428428 −73.9207 32.9116i −3.57309 1.59084i
429429 −8.07370 + 0.704809i −0.389802 + 0.0340285i
430430 39.3497 + 51.9208i 1.89761 + 2.50384i
431431 −20.0354 14.5565i −0.965069 0.701164i −0.0107465 0.999942i 0.503421π-0.503421\pi
−0.954322 + 0.298779i 0.903421π0.903421\pi
432432 −67.6057 43.9586i −3.25268 2.11496i
433433 5.18591 + 3.76779i 0.249219 + 0.181068i 0.705381 0.708829i 0.250776π-0.250776\pi
−0.456162 + 0.889897i 0.650776π0.650776\pi
434434 9.34827 + 10.3823i 0.448731 + 0.498367i
435435 7.00732 0.0179646i 0.335975 0.000861339i
436436 7.43096 8.25292i 0.355879 0.395243i
437437 0.730416 0.155255i 0.0349405 0.00742684i
438438 −14.0735 72.4754i −0.672457 3.46301i
439439 0.251052 + 0.0533628i 0.0119821 + 0.00254687i 0.213899 0.976856i 0.431384π-0.431384\pi
−0.201917 + 0.979403i 0.564717π0.564717\pi
440440 −51.2105 + 30.9626i −2.44136 + 1.47609i
441441 6.80711 + 8.11867i 0.324148 + 0.386604i
442442 23.7675 + 17.2681i 1.13050 + 0.821359i
443443 7.32776 12.6920i 0.348152 0.603017i −0.637769 0.770228i 0.720143π-0.720143\pi
0.985921 + 0.167210i 0.0534759π0.0534759\pi
444444 −24.3145 + 32.2536i −1.15391 + 1.53069i
445445 10.8580 1.36356i 0.514720 0.0646390i
446446 5.13223 + 2.28501i 0.243018 + 0.108199i
447447 2.83528 + 4.05084i 0.134104 + 0.191598i
448448 −59.4974 12.6466i −2.81099 0.597494i
449449 15.5412 0.733436 0.366718 0.930332i 0.380481π-0.380481\pi
0.366718 + 0.930332i 0.380481π0.380481\pi
450450 −37.6876 16.5486i −1.77661 0.780107i
451451 −10.4988 −0.494367
452452 72.2266 + 15.3522i 3.39725 + 0.722108i
453453 −8.21974 + 17.6185i −0.386197 + 0.827791i
454454 −38.0974 16.9621i −1.78800 0.796069i
455455 −6.17740 3.40198i −0.289601 0.159487i
456456 −9.99782 23.5659i −0.468191 1.10357i
457457 7.26861 12.5896i 0.340011 0.588916i −0.644423 0.764669i 0.722903π-0.722903\pi
0.984434 + 0.175752i 0.0562358π0.0562358\pi
458458 −0.467100 0.339368i −0.0218262 0.0158576i
459459 30.6617 + 11.7900i 1.43116 + 0.550310i
460460 −1.37747 5.89239i −0.0642248 0.274734i
461461 −3.21841 0.684094i −0.149896 0.0318614i 0.132352 0.991203i 0.457747π-0.457747\pi
−0.282249 + 0.959341i 0.591080π0.591080\pi
462462 −18.4609 + 16.0417i −0.858880 + 0.746326i
463463 37.4109 7.95194i 1.73863 0.369558i 0.774007 0.633177i 0.218249π-0.218249\pi
0.964627 + 0.263619i 0.0849161π0.0849161\pi
464464 18.7884 20.8666i 0.872230 0.968709i
465465 10.3621 + 2.17479i 0.480532 + 0.100853i
466466 −30.7943 34.2005i −1.42652 1.58431i
467467 4.63677 + 3.36881i 0.214564 + 0.155890i 0.689876 0.723927i 0.257665π-0.257665\pi
−0.475312 + 0.879817i 0.657665π0.657665\pi
468468 −28.0762 0.991138i −1.29782 0.0458154i
469469 13.1746 + 9.57189i 0.608345 + 0.441989i
470470 37.6828 + 11.4074i 1.73818 + 0.526184i
471471 14.3753 + 20.5384i 0.662380 + 0.946360i
472472 89.8829 + 40.0184i 4.13720 + 1.84200i
473473 19.6297 21.8010i 0.902576 1.00241i
474474 1.07591 60.9743i 0.0494184 2.80064i
475475 −4.07850 6.44767i −0.187135 0.295840i
476476 65.1078 2.98421
477477 12.3921 12.8226i 0.567393 0.587105i
478478 −54.8185 + 39.8280i −2.50734 + 1.82169i
479479 1.40830 + 13.3991i 0.0643469 + 0.612220i 0.978414 + 0.206656i 0.0662581π0.0662581\pi
−0.914067 + 0.405564i 0.867075π0.867075\pi
480480 −82.0393 + 36.7786i −3.74457 + 1.67870i
481481 −0.746503 + 7.10250i −0.0340376 + 0.323846i
482482 −4.17490 7.23113i −0.190161 0.329369i
483483 −0.616535 1.45323i −0.0280533 0.0661244i
484484 −12.4537 13.8312i −0.566078 0.628693i
485485 8.46139 + 0.716801i 0.384212 + 0.0325483i
486486 −41.6883 + 9.58275i −1.89102 + 0.434682i
487487 −8.88128 + 27.3338i −0.402449 + 1.23861i 0.520557 + 0.853827i 0.325724π0.325724\pi
−0.923006 + 0.384785i 0.874276π0.874276\pi
488488 −47.2494 52.4757i −2.13888 2.37547i
489489 −3.25774 + 14.0986i −0.147320 + 0.637560i
490490 21.5006 2.70007i 0.971299 0.121977i
491491 −15.6203 + 3.32021i −0.704936 + 0.149839i −0.546412 0.837516i 0.684007π-0.684007\pi
−0.158524 + 0.987355i 0.550673π0.550673\pi
492492 −36.1215 4.44214i −1.62848 0.200267i
493493 −5.71920 + 9.90594i −0.257580 + 0.446141i
494494 −5.73644 4.16777i −0.258095 0.187517i
495495 −4.12657 + 18.0697i −0.185476 + 0.812173i
496496 34.3236 24.9375i 1.54117 1.11973i
497497 0.660016 + 6.27963i 0.0296058 + 0.281680i
498498 3.99750 1.22133i 0.179132 0.0547290i
499499 10.4973 + 18.1818i 0.469922 + 0.813929i 0.999409 0.0343894i 0.0109486π-0.0109486\pi
−0.529486 + 0.848318i 0.677615π0.677615\pi
500500 −51.5711 + 34.0997i −2.30633 + 1.52498i
501501 0.345717 19.5925i 0.0154455 0.875328i
502502 −66.9626 14.2333i −2.98869 0.635265i
503503 3.48380 2.53113i 0.155335 0.112857i −0.507403 0.861709i 0.669394π-0.669394\pi
0.662738 + 0.748852i 0.269394π0.269394\pi
504504 −44.8762 + 30.2446i −1.99895 + 1.34720i
505505 −11.2711 9.74344i −0.501557 0.433577i
506506 −3.38966 + 1.50917i −0.150689 + 0.0670909i
507507 15.3507 8.50522i 0.681749 0.377730i
508508 −2.98322 + 28.3835i −0.132359 + 1.25931i
509509 −41.2503 + 8.76803i −1.82839 + 0.388636i −0.988139 0.153562i 0.950925π-0.950925\pi
−0.840251 + 0.542198i 0.817592π0.817592\pi
510510 54.2552 39.6316i 2.40246 1.75492i
511511 −28.2972 6.01476i −1.25180 0.266077i
512512 −18.4234 + 56.7015i −0.814209 + 2.50588i
513513 −7.40039 2.84559i −0.326735 0.125636i
514514 −3.65103 11.2367i −0.161040 0.495630i
515515 −1.96389 + 2.82123i −0.0865393 + 0.124318i
516516 76.7613 66.7019i 3.37923 2.93639i
517517 1.85321 17.6321i 0.0815040 0.775459i
518518 10.7758 + 18.6642i 0.473460 + 0.820056i
519519 10.9311 + 1.34428i 0.479823 + 0.0590075i
520520 −20.9548 + 30.1027i −0.918930 + 1.32009i
521521 −25.2789 + 18.3662i −1.10749 + 0.804637i −0.982266 0.187491i 0.939964π-0.939964\pi
−0.125222 + 0.992129i 0.539964π0.539964\pi
522522 −1.03332 14.8585i −0.0452273 0.650337i
523523 −11.4494 35.2378i −0.500649 1.54084i −0.807964 0.589232i 0.799430π-0.799430\pi
0.307314 0.951608i 0.400570π-0.400570\pi
524524 33.0389 57.2251i 1.44331 2.49989i
525525 −11.7370 + 11.0622i −0.512245 + 0.482795i
526526 −17.5707 30.4334i −0.766120 1.32696i
527527 −11.5646 + 12.8438i −0.503763 + 0.559486i
528528 42.5882 + 60.8469i 1.85341 + 2.64802i
529529 2.37912 + 22.6358i 0.103440 + 0.984166i
530530 −8.30220 35.5143i −0.360625 1.54264i
531531 28.2589 11.4048i 1.22633 0.494928i
532532 −15.7142 −0.681297
533533 −5.87841 + 2.61724i −0.254622 + 0.113365i
534534 −4.43394 22.8338i −0.191875 0.988117i
535535 −6.15475 + 32.1357i −0.266093 + 1.38935i
536536 56.6722 62.9408i 2.44787 2.71863i
537537 −8.72809 + 7.58430i −0.376645 + 0.327287i
538538 37.0834 + 41.1853i 1.59878 + 1.77563i
539539 −3.01535 9.28030i −0.129880 0.399731i
540540 −21.8432 + 60.4237i −0.939980 + 2.60022i
541541 −10.3961 + 31.9960i −0.446965 + 1.37562i 0.433350 + 0.901226i 0.357332π0.357332\pi
−0.880314 + 0.474391i 0.842668π0.842668\pi
542542 19.8373 8.83215i 0.852087 0.379374i
543543 −10.7458 6.45949i −0.461145 0.277203i
544544 15.3404 145.954i 0.657712 6.25771i
545545 −3.93358 2.16628i −0.168496 0.0927933i
546546 −6.33752 + 13.5841i −0.271221 + 0.581346i
547547 −0.581655 5.53408i −0.0248698 0.236620i −0.999895 0.0145239i 0.995377π-0.995377\pi
0.975025 0.222096i 0.0712899π-0.0712899\pi
548548 −7.40596 22.7932i −0.316367 0.973678i
549549 −21.8570 0.771591i −0.932835 0.0329307i
550550 26.4839 + 27.1243i 1.12928 + 1.15658i
551551 1.38037 2.39086i 0.0588056 0.101854i
552552 −7.85193 + 2.39894i −0.334200 + 0.102106i
553553 −21.8301 9.71940i −0.928312 0.413311i
554554 −0.451293 0.200928i −0.0191736 0.00853663i
555555 14.9379 + 6.60496i 0.634080 + 0.280365i
556556 67.2883 29.9587i 2.85366 1.27053i
557557 37.0966 1.57183 0.785917 0.618332i 0.212191π-0.212191\pi
0.785917 + 0.618332i 0.212191π0.212191\pi
558558 3.14056 22.2847i 0.132950 0.943386i
559559 5.55619 17.1002i 0.235002 0.723262i
560560 1.30587 + 64.6148i 0.0551829 + 2.73048i
561561 −22.1234 20.6383i −0.934052 0.871350i
562562 −4.36716 + 0.928268i −0.184217 + 0.0391566i
563563 20.9186 4.44638i 0.881612 0.187392i 0.255203 0.966887i 0.417858π-0.417858\pi
0.626408 + 0.779495i 0.284524π0.284524\pi
564564 13.8364 59.8800i 0.582617 2.52140i
565565 −0.603315 29.8523i −0.0253817 1.25590i
566566 3.10107 9.54412i 0.130348 0.401169i
567567 −2.92313 + 16.5044i −0.122760 + 0.693120i
568568 32.8398 1.37793
569569 −13.8567 + 6.16939i −0.580902 + 0.258634i −0.676083 0.736826i 0.736324π-0.736324\pi
0.0951807 + 0.995460i 0.469657π0.469657\pi
570570 −13.0949 + 9.56536i −0.548483 + 0.400649i
571571 34.7764 + 15.4834i 1.45535 + 0.647962i 0.973582 0.228339i 0.0733296π-0.0733296\pi
0.481764 + 0.876301i 0.339996π0.339996\pi
572572 23.6375 + 10.5241i 0.988333 + 0.440034i
573573 −1.43800 1.34147i −0.0600734 0.0560407i
574574 −9.70913 + 16.8167i −0.405251 + 0.701916i
575575 −2.19333 + 1.08475i −0.0914683 + 0.0452374i
576576 45.9672 + 86.5312i 1.91530 + 3.60547i
577577 2.27456 + 7.00039i 0.0946913 + 0.291430i 0.987173 0.159653i 0.0510377π-0.0510377\pi
−0.892482 + 0.451083i 0.851038π0.851038\pi
578578 6.58800 + 62.6806i 0.274025 + 2.60717i
579579 −3.05399 4.36331i −0.126919 0.181333i
580580 −19.5967 10.7922i −0.813710 0.448122i
581581 0.171204 1.62889i 0.00710273 0.0675779i
582582 0.318439 18.0466i 0.0131997 0.748055i
583583 −15.0036 + 6.68001i −0.621384 + 0.276658i
584584 −46.4946 + 143.096i −1.92396 + 5.92133i
585585 2.19407 + 11.1462i 0.0907137 + 0.460839i
586586 20.7590 + 63.8895i 0.857545 + 2.63925i
587587 −16.6264 18.4655i −0.686247 0.762154i 0.294877 0.955535i 0.404721π-0.404721\pi
−0.981124 + 0.193381i 0.938055π0.938055\pi
588588 −6.44787 33.2052i −0.265906 1.36936i
589589 2.79120 3.09994i 0.115009 0.127731i
590590 11.7241 61.2148i 0.482673 2.52017i
591591 −30.4774 + 26.4834i −1.25367 + 1.08938i
592592 59.7891 26.6198i 2.45732 1.09407i
593593 43.3690 1.78095 0.890476 0.455030i 0.150371π-0.150371\pi
0.890476 + 0.455030i 0.150371π0.150371\pi
594594 38.9080 + 6.18519i 1.59642 + 0.253781i
595595 −5.99299 25.6362i −0.245688 1.05098i
596596 −1.65009 15.6995i −0.0675903 0.643079i
597597 32.1229 2.80423i 1.31470 0.114770i
598598 −1.52170 + 1.69002i −0.0622268 + 0.0691099i
599599 −5.35663 9.27796i −0.218866 0.379087i 0.735596 0.677421i 0.236902π-0.236902\pi
−0.954462 + 0.298334i 0.903569π0.903569\pi
600600 50.8378 + 66.7228i 2.07544 + 2.72395i
601601 8.90717 15.4277i 0.363331 0.629308i −0.625176 0.780484i 0.714973π-0.714973\pi
0.988507 + 0.151176i 0.0483060π0.0483060\pi
602602 −16.7671 51.6039i −0.683377 2.10322i
603603 −1.81991 26.1690i −0.0741125 1.06569i
604604 50.2159 36.4840i 2.04325 1.48451i
605605 −4.29972 + 6.17677i −0.174808 + 0.251121i
606606 −19.0629 + 25.2873i −0.774378 + 1.02723i
607607 21.1667 + 36.6618i 0.859129 + 1.48805i 0.872761 + 0.488148i 0.162327π0.162327\pi
−0.0136324 + 0.999907i 0.504339π0.504339\pi
608608 −3.70250 + 35.2269i −0.150156 + 1.42864i
609609 −5.51791 1.90114i −0.223597 0.0770382i
610610 −25.5562 + 36.7128i −1.03474 + 1.48646i
611611 −3.35787 10.3345i −0.135845 0.418087i
612612 −67.3845 80.3678i −2.72386 3.24868i
613613 13.3402 41.0570i 0.538806 1.65828i −0.196471 0.980510i 0.562948π-0.562948\pi
0.735278 0.677766i 0.237052π-0.237052\pi
614614 10.2249 + 2.17337i 0.412643 + 0.0877100i
615615 1.57579 + 14.6317i 0.0635420 + 0.590007i
616616 48.7527 10.3627i 1.96430 0.417525i
617617 3.95649 37.6435i 0.159282 1.51547i −0.564496 0.825436i 0.690929π-0.690929\pi
0.723778 0.690033i 0.242404π-0.242404\pi
618618 6.26214 + 3.76429i 0.251900 + 0.151422i
619619 −14.5465 + 6.47652i −0.584674 + 0.260313i −0.677686 0.735351i 0.737017π-0.737017\pi
0.0930123 + 0.995665i 0.470350π0.470350\pi
620620 −25.5727 22.1066i −1.02702 0.887824i
621621 −1.15575 + 2.26509i −0.0463787 + 0.0908949i
622622 −55.9743 + 40.6677i −2.24437 + 1.63063i
623623 −8.91523 1.89499i −0.357181 0.0759212i
624624 39.0143 + 23.4523i 1.56182 + 0.938842i
625625 18.1737 + 17.1673i 0.726948 + 0.686692i
626626 35.5929 + 61.6488i 1.42258 + 2.46398i
627627 5.33964 + 4.98119i 0.213245 + 0.198930i
628628 −8.36622 79.5993i −0.333849 3.17636i
629629 −21.5693 + 15.6710i −0.860024 + 0.624844i
630630 25.1275 + 23.3205i 1.00110 + 0.929113i
631631 −11.5984 8.42673i −0.461725 0.335463i 0.332483 0.943109i 0.392114π-0.392114\pi
−0.794208 + 0.607647i 0.792114π0.792114\pi
632632 −62.1407 + 107.631i −2.47183 + 4.28133i
633633 12.0034 15.9228i 0.477093 0.632873i
634634 −61.6249 + 13.0988i −2.44744 + 0.520219i
635635 11.4506 1.43797i 0.454402 0.0570643i
636636 −54.4469 + 16.6347i −2.15896 + 0.659611i
637637 −4.00183 4.44448i −0.158558 0.176097i
638638 −4.23903 + 13.0464i −0.167825 + 0.516512i
639639 7.06836 7.31393i 0.279620 0.289335i
640640 96.2445 + 8.15328i 3.80440 + 0.322287i
641641 −15.0892 16.7583i −0.595989 0.661913i 0.367387 0.930068i 0.380253π-0.380253\pi
−0.963376 + 0.268156i 0.913586π0.913586\pi
642642 69.0269 + 8.48877i 2.72428 + 0.335025i
643643 −21.0243 36.4152i −0.829119 1.43608i −0.898730 0.438502i 0.855509π-0.855509\pi
0.0696109 0.997574i 0.477824π-0.477824\pi
644644 −0.526817 + 5.01232i −0.0207595 + 0.197513i
645645 −33.3295 24.0850i −1.31235 0.948346i
646646 −2.76695 26.3257i −0.108864 1.03577i
647647 9.23613 6.71044i 0.363110 0.263815i −0.391238 0.920289i 0.627953π-0.627953\pi
0.754348 + 0.656475i 0.227953π0.227953\pi
648648 83.7788 + 24.0922i 3.29114 + 0.946431i
649649 −28.0664 −1.10170
650650 21.5905 + 8.58511i 0.846850 + 0.336736i
651651 −7.55796 4.54324i −0.296220 0.178064i
652652 30.9124 34.3317i 1.21062 1.34453i
653653 7.83342 + 3.48766i 0.306545 + 0.136483i 0.554244 0.832354i 0.313008π-0.313008\pi
−0.247698 + 0.968837i 0.579674π0.579674\pi
654654 −4.03554 + 8.64994i −0.157802 + 0.338240i
655655 −25.5735 7.74166i −0.999239 0.302492i
656656 47.7070 + 34.6612i 1.86265 + 1.35329i
657657 21.8622 + 41.1546i 0.852927 + 1.60560i
658658 −26.5289 19.2744i −1.03421 0.751395i
659659 −20.3348 22.5840i −0.792130 0.879749i 0.202913 0.979197i 0.434959π-0.434959\pi
−0.995043 + 0.0994474i 0.968293π0.968293\pi
660660 39.4832 44.0772i 1.53688 1.71570i
661661 −14.3063 + 15.8887i −0.556449 + 0.618000i −0.954082 0.299545i 0.903165π-0.903165\pi
0.397633 + 0.917545i 0.369832π0.369832\pi
662662 16.5132 3.51000i 0.641805 0.136420i
663663 −17.5322 6.04054i −0.680893 0.234595i
664664 −8.33227 1.77108i −0.323355 0.0687312i
665665 1.44645 + 6.18746i 0.0560908 + 0.239939i
666666 11.8861 32.6182i 0.460578 1.26393i
667667 −0.716332 0.520446i −0.0277365 0.0201517i
668668 −31.2808 + 54.1799i −1.21029 + 2.09628i
669669 −3.51953 0.432823i −0.136073 0.0167339i
670670 −46.9972 25.8820i −1.81566 0.999909i
671671 18.4016 + 8.19290i 0.710384 + 0.316284i
672672 74.5968 6.51208i 2.87764 0.251209i
673673 −21.8048 4.63475i −0.840513 0.178657i −0.232513 0.972593i 0.574695π-0.574695\pi
−0.608000 + 0.793937i 0.708028π0.708028\pi
674674 41.3282 1.59190
675675 25.8024 + 3.03891i 0.993136 + 0.116968i
676676 −56.0291 −2.15497
677677 30.7046 + 6.52646i 1.18007 + 0.250832i 0.755862 0.654731i 0.227218π-0.227218\pi
0.424211 + 0.905563i 0.360551π0.360551\pi
678678 −63.2246 + 5.51931i −2.42813 + 0.211968i
679679 −6.46107 2.87665i −0.247953 0.110396i
680680 −135.859 + 17.0613i −5.20996 + 0.654273i
681681 26.1261 + 3.21292i 1.00115 + 0.123120i
682682 −10.3636 + 17.9503i −0.396842 + 0.687351i
683683 −41.1891 29.9257i −1.57606 1.14507i −0.921045 0.389457i 0.872663π-0.872663\pi
−0.655014 0.755617i 0.727337π-0.727337\pi
684684 16.2637 + 19.3973i 0.621858 + 0.741674i
685685 −8.29312 + 5.01414i −0.316864 + 0.191581i
686686 −52.6448 11.1900i −2.00999 0.427236i
687687 0.344558 + 0.118714i 0.0131457 + 0.00452923i
688688 −161.174 + 34.2586i −6.14470 + 1.30610i
689689 −6.73545 + 7.48047i −0.256600 + 0.284983i
690690 2.61204 + 4.49752i 0.0994387 + 0.171218i
691691 −4.76023 5.28677i −0.181088 0.201118i 0.645766 0.763535i 0.276538π-0.276538\pi
−0.826854 + 0.562417i 0.809872π0.809872\pi
692692 −28.4467 20.6678i −1.08138 0.785670i
693693 8.18548 13.0884i 0.310941 0.497188i
694694 −37.3577 27.1420i −1.41808 1.03029i
695695 −17.9899 23.7371i −0.682397 0.900401i
696696 −12.8333 + 27.5075i −0.486445 + 1.04267i
697697 −21.9453 9.77066i −0.831236 0.370090i
698698 −28.4770 + 31.6269i −1.07787 + 1.19710i
699699 24.8968 + 14.9659i 0.941683 + 0.566064i
700700 49.8938 12.7322i 1.88581 0.481232i
701701 −42.2657 −1.59635 −0.798177 0.602423i 0.794202π-0.794202\pi
−0.798177 + 0.602423i 0.794202π0.794202\pi
702702 23.3271 6.23620i 0.880424 0.235370i
703703 5.20589 3.78230i 0.196344 0.142652i
704704 −9.43295 89.7486i −0.355518 3.38253i
705705 −24.8513 + 0.0637112i −0.935955 + 0.00239950i
706706 2.69516 25.6428i 0.101434 0.965079i
707707 6.20438 + 10.7463i 0.233340 + 0.404156i
708708 −96.5638 11.8752i −3.62909 0.446297i
709709 6.41778 + 7.12767i 0.241025 + 0.267685i 0.851505 0.524346i 0.175690π-0.175690\pi
−0.610480 + 0.792031i 0.709024π0.709024\pi
710710 −4.73553 20.2572i −0.177721 0.760238i
711711 10.5961 + 37.0060i 0.397383 + 1.38783i
712712 −14.6484 + 45.0832i −0.548973 + 1.68956i
713713 −0.895207 0.994228i −0.0335258 0.0372341i
714714 −53.5176 + 16.3508i −2.00284 + 0.611914i
715715 1.96809 10.2760i 0.0736025 0.384299i
716716 36.1096 7.67533i 1.34948 0.286840i
717717 25.7460 34.1526i 0.961503 1.27545i
718718 −10.9842 + 19.0252i −0.409927 + 0.710014i
719719 −35.1893 25.5666i −1.31234 0.953472i −0.999994 0.00350360i 0.998885π-0.998885\pi
−0.312347 0.949968i 0.601115π-0.601115\pi
720720 78.4078 68.4863i 2.92209 2.55233i
721721 2.31620 1.68282i 0.0862598 0.0626714i
722722 −4.78198 45.4975i −0.177967 1.69324i
723723 3.85385 + 3.59514i 0.143326 + 0.133705i
724724 20.0144 + 34.6659i 0.743828 + 1.28835i
725725 −2.44560 + 8.70960i −0.0908274 + 0.323466i
726726 13.7103 + 8.24151i 0.508836 + 0.305871i
727727 25.6825 + 5.45899i 0.952511 + 0.202463i 0.657858 0.753142i 0.271463π-0.271463\pi
0.294653 + 0.955604i 0.404796π0.404796\pi
728728 24.7140 17.9558i 0.915962 0.665486i
729729 23.3981 13.4733i 0.866596 0.499011i
730730 94.9728 + 8.04556i 3.51510 + 0.297779i
731731 61.3206 27.3017i 2.26802 1.00979i
732732 59.8450 + 35.9740i 2.21193 + 1.32964i
733733 −5.43558 + 51.7161i −0.200768 + 1.91018i 0.176885 + 0.984231i 0.443398π0.443398\pi
−0.377653 + 0.925947i 0.623269π0.623269\pi
734734 70.8836 15.0668i 2.61636 0.556124i
735735 −12.4810 + 5.59529i −0.460369 + 0.206385i
736736 11.1121 + 2.36196i 0.409598 + 0.0870628i
737737 −7.46588 + 22.9776i −0.275009 + 0.846391i
738738 30.8069 5.42000i 1.13402 0.199513i
739739 −7.71260 23.7369i −0.283712 0.873177i −0.986782 0.162056i 0.948188π-0.948188\pi
0.703069 0.711121i 0.251812π-0.251812\pi
740740 −31.4965 41.5587i −1.15783 1.52773i
741741 4.23150 + 1.45792i 0.155448 + 0.0535582i
742742 −3.17520 + 30.2100i −0.116565 + 1.10904i
743743 −0.897873 1.55516i −0.0329398 0.0570534i 0.849086 0.528255i 0.177154π-0.177154\pi
−0.882025 + 0.471202i 0.843820π0.843820\pi
744744 −27.6084 + 36.6231i −1.01217 + 1.34267i
745745 −6.02980 + 2.09482i −0.220915 + 0.0767483i
746746 −46.1153 + 33.5047i −1.68840 + 1.22669i
747747 −2.18787 + 1.47452i −0.0800498 + 0.0539500i
748748 29.8493 + 91.8668i 1.09140 + 3.35898i
749749 13.6257 23.6005i 0.497873 0.862342i
750750 33.8270 40.9807i 1.23519 1.49640i
751751 9.00025 + 15.5889i 0.328424 + 0.568846i 0.982199 0.187842i 0.0601493π-0.0601493\pi
−0.653776 + 0.756688i 0.726816π0.726816\pi
752752 −66.6327 + 74.0031i −2.42984 + 2.69862i
753753 43.0475 3.75791i 1.56874 0.136946i
754754 0.878842 + 8.36162i 0.0320055 + 0.304512i
755755 −18.9878 16.4142i −0.691036 0.597375i
756756 33.7004 41.5680i 1.22567 1.51181i
757757 −9.03751 −0.328474 −0.164237 0.986421i 0.552516π-0.552516\pi
−0.164237 + 0.986421i 0.552516π0.552516\pi
758758 48.0465 21.3917i 1.74513 0.776981i
759759 1.76785 1.53618i 0.0641689 0.0557598i
760760 32.7905 4.11787i 1.18944 0.149371i
761761 26.4976 29.4286i 0.960539 1.06679i −0.0371821 0.999309i 0.511838π-0.511838\pi
0.997721 0.0674778i 0.0214952π-0.0214952\pi
762762 −4.67591 24.0799i −0.169390 0.872324i
763763 2.50264 + 2.77947i 0.0906017 + 0.100623i
764764 1.94018 + 5.97126i 0.0701932 + 0.216032i
765765 −25.4422 + 33.9302i −0.919866 + 1.22675i
766766 20.4928 63.0704i 0.740435 2.27883i
767767 −15.7148 + 6.99667i −0.567428 + 0.252635i
768768 1.62599 92.1484i 0.0586730 3.32512i
769769 −3.52699 + 33.5571i −0.127187 + 1.21010i 0.725703 + 0.688008i 0.241515π0.241515\pi
−0.852890 + 0.522091i 0.825152π0.825152\pi
770770 −13.4224 28.5787i −0.483710 1.02990i
771771 4.27636 + 6.10975i 0.154009 + 0.220037i
772772 1.77737 + 16.9106i 0.0639691 + 0.608625i
773773 8.69380 + 26.7568i 0.312694 + 0.962374i 0.976693 + 0.214640i 0.0688580π0.0688580\pi
−0.663999 + 0.747734i 0.731142π0.731142\pi
774774 −46.3454 + 74.1054i −1.66585 + 2.66366i
775775 −6.35059 + 12.1041i −0.228120 + 0.434791i
776776 −18.3918 + 31.8556i −0.660228 + 1.14355i
777777 −9.94710 9.27936i −0.356850 0.332895i
778778 94.5309 + 42.0879i 3.38910 + 1.50892i
779779 5.29664 + 2.35821i 0.189772 + 0.0844918i
780780 11.1192 34.5223i 0.398131 1.23610i
781781 −8.55795 + 3.81024i −0.306227 + 0.136341i
782782 −8.48982 −0.303595
783783 3.36413 + 8.77883i 0.120224 + 0.313730i
784784 −16.9365 + 52.1253i −0.604877 + 1.86162i
785785 −30.5721 + 10.6211i −1.09117 + 0.379083i
786786 −12.7863 + 55.3354i −0.456071 + 1.97375i
787787 −30.1553 + 6.40972i −1.07492 + 0.228482i −0.711174 0.703016i 0.751836π-0.751836\pi
−0.363748 + 0.931498i 0.618503π0.618503\pi
788788 126.090 26.8013i 4.49177 0.954755i
789789 16.2195 + 15.1307i 0.577431 + 0.538668i
790790 75.3527 + 22.8109i 2.68093 + 0.811576i
791791 −7.68473 + 23.6512i −0.273238 + 0.840939i
792792 −63.2490 49.4543i −2.24745 1.75728i
793793 12.3457 0.438409
794794 70.5070 31.3918i 2.50220 1.11405i
795795 11.5616 + 19.9072i 0.410048 + 0.706037i
796796 −94.0467 41.8723i −3.33340 1.48412i
797797 10.6082 + 4.72307i 0.375761 + 0.167300i 0.585923 0.810367i 0.300732π-0.300732\pi
−0.210161 + 0.977667i 0.567399π0.567399\pi
798798 12.9168 3.94638i 0.457251 0.139700i
799799 20.2830 35.1312i 0.717561 1.24285i
800800 −16.7864 114.848i −0.593489 4.06049i
801801 6.88784 + 12.9660i 0.243370 + 0.458133i
802802 −19.9816 61.4969i −0.705574 2.17153i
803803 −4.48636 42.6848i −0.158320 1.50631i
804804 −35.4088 + 75.8967i −1.24877 + 2.67667i
805805 2.02209 0.253936i 0.0712694 0.00895008i
806806 −1.32790 + 12.6342i −0.0467734 + 0.445019i
807807 −29.9815 18.0225i −1.05540 0.634421i
808808 58.9575 26.2496i 2.07412 0.923456i
809809 11.6688 35.9129i 0.410254 1.26263i −0.506174 0.862432i 0.668941π-0.668941\pi
0.916428 0.400200i 0.131059π-0.131059\pi
810810 2.78024 55.1529i 0.0976876 1.93788i
811811 −1.37548 4.23331i −0.0482998 0.148652i 0.923998 0.382398i 0.124902π-0.124902\pi
−0.972298 + 0.233746i 0.924902π0.924902\pi
812812 12.4679 + 13.8470i 0.437539 + 0.485936i
813813 −10.3460 + 8.99020i −0.362851 + 0.315300i
814814 −21.3948 + 23.7613i −0.749887 + 0.832834i
815815 −16.3635 9.01160i −0.573187 0.315663i
816816 32.3939 + 166.821i 1.13401 + 5.83992i
817817 −14.8001 + 6.58944i −0.517791 + 0.230535i
818818 −28.8344 −1.00817
819819 1.32036 9.36896i 0.0461370 0.327378i
820820 18.2389 43.2993i 0.636931 1.51208i
821821 −0.872620 8.30242i −0.0304546 0.289757i −0.999140 0.0414649i 0.986798π-0.986798\pi
0.968685 0.248292i 0.0798691π-0.0798691\pi
822822 11.8118 + 16.8758i 0.411982 + 0.588610i
823823 −3.06147 + 3.40010i −0.106716 + 0.118520i −0.794136 0.607740i 0.792076π-0.792076\pi
0.687420 + 0.726260i 0.258743π0.258743\pi
824824 −7.44507 12.8952i −0.259361 0.449227i
825825 −20.9897 11.4893i −0.730768 0.400006i
826826 −25.9555 + 44.9562i −0.903106 + 1.56423i
827827 −2.49659 7.68370i −0.0868148 0.267189i 0.898219 0.439547i 0.144861π-0.144861\pi
−0.985034 + 0.172359i 0.944861π0.944861\pi
828828 6.73236 4.53730i 0.233966 0.157682i
829829 −14.9236 + 10.8426i −0.518316 + 0.376579i −0.815969 0.578095i 0.803796π-0.803796\pi
0.297653 + 0.954674i 0.403796π0.403796\pi
830830 0.109036 + 5.39514i 0.00378468 + 0.187268i
831831 0.309483 + 0.0380595i 0.0107358 + 0.00132027i
832832 −27.6551 47.9000i −0.958767 1.66063i
833833 2.33380 22.2046i 0.0808613 0.769344i
834834 −47.7863 + 41.5240i −1.65470 + 1.43786i
835835 24.2126 + 7.32969i 0.837912 + 0.253654i
836836 −7.20434 22.1727i −0.249167 0.766858i
837837 2.21416 + 14.0315i 0.0765327 + 0.485000i
838838 −8.02726 + 24.7054i −0.277297 + 0.853433i
839839 13.0629 + 2.77660i 0.450981 + 0.0958589i 0.427802 0.903872i 0.359288π-0.359288\pi
0.0231787 + 0.999731i 0.492621π0.492621\pi
840840 −21.7595 66.3893i −0.750775 2.29065i
841841 25.1643 5.34884i 0.867734 0.184443i
842842 −1.94193 + 18.4762i −0.0669233 + 0.636732i
843843 2.46506 1.36579i 0.0849012 0.0470404i
844844 −58.1584 + 25.8938i −2.00189 + 0.891301i
845845 5.15732 + 22.0614i 0.177417 + 0.758937i
846846 3.66466 + 52.6952i 0.125994 + 1.81170i
847847 5.07107 3.68435i 0.174244 0.126596i
848848 90.2309 + 19.1792i 3.09854 + 0.658615i
849849 −0.111754 + 6.33331i −0.00383537 + 0.217359i
850850 30.1153 + 81.3443i 1.03295 + 2.79009i
851851 −1.03191 1.78731i −0.0353733 0.0612683i
852852 −31.0562 + 9.48837i −1.06397 + 0.325066i
853853 −5.56890 52.9846i −0.190676 1.81416i −0.503116 0.864219i 0.667813π-0.667813\pi
0.312440 0.949937i 0.398854π-0.398854\pi
854854 30.1408 21.8986i 1.03140 0.749354i
855855 6.14065 8.18929i 0.210006 0.280068i
856856 −114.664 83.3084i −3.91914 2.84742i
857857 −3.75868 + 6.51022i −0.128394 + 0.222385i −0.923054 0.384669i 0.874316π-0.874316\pi
0.794661 + 0.607054i 0.207649π0.207649\pi
858858 −22.0726 2.71444i −0.753547 0.0926694i
859859 23.4780 4.99040i 0.801058 0.170270i 0.210847 0.977519i 0.432378π-0.432378\pi
0.590211 + 0.807249i 0.299044π0.299044\pi
860860 55.8109 + 118.831i 1.90314 + 4.05211i
861861 2.75946 11.9422i 0.0940423 0.406988i
862862 −45.4718 50.5016i −1.54878 1.72009i
863863 −13.5353 + 41.6575i −0.460748 + 1.41804i 0.403504 + 0.914978i 0.367792π0.367792\pi
−0.864252 + 0.503059i 0.832208π0.832208\pi
864864 −85.2437 85.3411i −2.90005 2.90336i
865865 −5.51948 + 13.1033i −0.187668 + 0.445525i
866866 11.7698 + 13.0717i 0.399956 + 0.444196i
867867 −15.5371 36.6225i −0.527668 1.24377i
868868 14.0770 + 24.3820i 0.477804 + 0.827580i
869869 3.70579 35.2582i 0.125710 1.19605i
870870 18.8185 + 3.94960i 0.638007 + 0.133904i
871871 1.54784 + 14.7267i 0.0524464 + 0.498994i
872872 15.7371 11.4337i 0.532927 0.387194i
873873 3.13612 + 10.9527i 0.106141 + 0.370692i
874874 2.04908 0.0693110
875875 −9.60588 18.4737i −0.324738 0.624525i
876876 2.62488 148.757i 0.0886866 5.02605i
877877 −17.2909 + 19.2035i −0.583871 + 0.648454i −0.960621 0.277860i 0.910375π-0.910375\pi
0.376750 + 0.926315i 0.377041π0.377041\pi
878878 0.643402 + 0.286461i 0.0217138 + 0.00966759i
879879 −24.3145 34.7387i −0.820107 1.17171i
880880 −90.5726 + 31.4659i −3.05320 + 1.06072i
881881 −8.85610 6.43433i −0.298369 0.216778i 0.428520 0.903532i 0.359035π-0.359035\pi
−0.726890 + 0.686754i 0.759035π0.759035\pi
882882 13.6390 + 25.6748i 0.459250 + 0.864517i
883883 34.4894 + 25.0580i 1.16066 + 0.843270i 0.989862 0.142036i 0.0453648π-0.0453648\pi
0.170800 + 0.985306i 0.445365π0.445365\pi
884884 39.6146 + 43.9965i 1.33238 + 1.47976i
885885 4.21257 + 39.1150i 0.141604 + 1.31484i
886886 26.9094 29.8859i 0.904039 1.00404i
887887 −54.9183 + 11.6733i −1.84398 + 0.391949i −0.991423 0.130690i 0.958281π-0.958281\pi
−0.852554 + 0.522639i 0.824948π0.824948\pi
888888 −53.4045 + 46.4060i −1.79214 + 1.55728i
889889 −9.40176 1.99841i −0.315325 0.0670244i
890890 29.9218 + 2.53481i 1.00298 + 0.0849669i
891891 −24.6278 + 3.44210i −0.825063 + 0.115315i
892892 9.15908 + 6.65446i 0.306669 + 0.222808i
893893 −4.89544 + 8.47915i −0.163820 + 0.283744i
894894 5.29905 + 12.4904i 0.177227 + 0.417741i
895895 −6.34594 13.5116i −0.212121 0.451644i
896896 −73.4917 32.7206i −2.45519 1.09312i
897897 0.606892 1.30084i 0.0202635 0.0434337i
898898 41.7140 + 8.86659i 1.39201 + 0.295882i
899899 −4.94620 −0.164965
900900 −67.3549 48.4105i −2.24516 1.61368i
901901 −37.5783 −1.25191
902902 −28.1796 5.98975i −0.938277 0.199437i
903903 19.6389 + 28.0586i 0.653542 + 0.933733i
904904 118.156 + 52.6066i 3.92982 + 1.74967i
905905 11.8074 11.0715i 0.392492 0.368030i
906906 −32.1143 + 42.6002i −1.06692 + 1.41530i
907907 19.3181 33.4600i 0.641448 1.11102i −0.343662 0.939093i 0.611667π-0.611667\pi
0.985110 0.171927i 0.0549992π-0.0549992\pi
908908 −67.9895 49.3972i −2.25631 1.63931i
909909 6.84369 18.7807i 0.226991 0.622915i
910910 −14.6398 12.6556i −0.485304 0.419528i
911911 21.0207 + 4.46810i 0.696448 + 0.148035i 0.542514 0.840047i 0.317472π-0.317472\pi
0.153934 + 0.988081i 0.450806π0.450806\pi
912912 −7.81847 40.2635i −0.258896 1.33326i
913913 2.37685 0.505216i 0.0786624 0.0167202i
914914 26.6922 29.6447i 0.882900 0.980559i
915915 8.65619 26.8752i 0.286165 0.888468i
916916 −0.778542 0.864658i −0.0257237 0.0285691i
917917 18.0039 + 13.0806i 0.594542 + 0.431960i
918918 75.5721 + 49.1385i 2.49425 + 1.62181i
919919 10.5406 + 7.65821i 0.347703 + 0.252621i 0.747905 0.663806i 0.231060π-0.231060\pi
−0.400202 + 0.916427i 0.631060π0.631060\pi
920920 −0.214169 10.5972i −0.00706094 0.349379i
921921 −6.57316 + 0.573817i −0.216593 + 0.0189079i
922922 −8.24821 3.67234i −0.271640 0.120942i
923923 −3.84187 + 4.26682i −0.126457 + 0.140444i
924924 −43.1108 + 23.8860i −1.41824 + 0.785790i
925925 −13.4645 + 16.2271i −0.442711 + 0.533544i
926926 104.951 3.44890
927927 −4.47443 1.11741i −0.146960 0.0367006i
928928 33.9789 24.6871i 1.11541 0.810394i
929929 2.50268 + 23.8114i 0.0821101 + 0.781226i 0.955656 + 0.294484i 0.0951479π0.0951479\pi
−0.873546 + 0.486741i 0.838185π0.838185\pi
930930 26.5721 + 11.7491i 0.871333 + 0.385269i
931931 −0.563277 + 5.35923i −0.0184607 + 0.175642i
932932 −46.3711 80.3172i −1.51894 2.63088i
933933 26.2889 34.8727i 0.860660 1.14168i
934934 10.5235 + 11.6876i 0.344340 + 0.382429i
935935 33.4250 20.2092i 1.09311 0.660913i
936936 −47.7425 11.9228i −1.56051 0.389710i
937937 5.43437 16.7253i 0.177533 0.546390i −0.822207 0.569188i 0.807257π-0.807257\pi
0.999740 + 0.0227980i 0.00725746π0.00725746\pi
938938 29.9008 + 33.2082i 0.976294 + 1.08428i
939939 −32.8558 30.6502i −1.07221 1.00023i
940940 69.4994 + 38.2743i 2.26682 + 1.24837i
941941 −13.7789 + 2.92879i −0.449179 + 0.0954759i −0.426947 0.904277i 0.640411π-0.640411\pi
−0.0222325 + 0.999753i 0.507077π0.507077\pi
942942 26.8671 + 63.3283i 0.875376 + 2.06335i
943943 0.929764 1.61040i 0.0302773 0.0524418i
944944 127.535 + 92.6599i 4.15093 + 3.01582i
945945 −19.4694 9.44331i −0.633340 0.307191i
946946 65.1258 47.3167i 2.11742 1.53840i
947947 2.31050 + 21.9829i 0.0750810 + 0.714348i 0.965711 + 0.259619i 0.0835971π0.0835971\pi
−0.890630 + 0.454729i 0.849736π0.849736\pi
948948 27.6681 119.740i 0.898617 3.88896i
949949 −13.1529 22.7815i −0.426961 0.739517i
950950 −7.26853 19.6330i −0.235822 0.636978i
951951 34.7845 19.2727i 1.12796 0.624960i
952952 111.550 + 23.7108i 3.61537 + 0.768471i
953953 −25.0086 + 18.1698i −0.810108 + 0.588578i −0.913862 0.406025i 0.866915π-0.866915\pi
0.103754 + 0.994603i 0.466915π0.466915\pi
954954 40.5769 27.3470i 1.31373 0.885392i
955955 2.17259 1.31358i 0.0703034 0.0425065i
956956 −124.744 + 55.5394i −4.03450 + 1.79627i
957957 0.152762 8.65735i 0.00493810 0.279852i
958958 −3.86445 + 36.7678i −0.124855 + 1.18791i
959959 7.89509 1.67815i 0.254946 0.0541904i
960960 −123.663 + 26.6170i −3.99121 + 0.859059i
961961 23.0123 + 4.89142i 0.742334 + 0.157788i
962962 −6.05580 + 18.6378i −0.195247 + 0.600908i
963963 −43.2341 + 7.60638i −1.39320 + 0.245112i
964964 −5.19968 16.0030i −0.167470 0.515421i
965965 6.49493 2.25641i 0.209079 0.0726364i
966966 −0.825734 4.25235i −0.0265676 0.136817i
967967 2.69303 25.6224i 0.0866019 0.823962i −0.861876 0.507119i 0.830711π-0.830711\pi
0.948478 0.316843i 0.102623π-0.102623\pi
968968 −16.3002 28.2327i −0.523907 0.907433i
969969 6.52556 + 15.3814i 0.209631 + 0.494121i
970970 22.3022 + 6.75135i 0.716079 + 0.216773i
971971 27.8824 20.2577i 0.894787 0.650101i −0.0423344 0.999103i 0.513479π-0.513479\pi
0.937122 + 0.349002i 0.113479π0.113479\pi
972972 −86.1896 + 1.42243i −2.76453 + 0.0456245i
973973 7.66559 + 23.5923i 0.245748 + 0.756333i
974974 −39.4326 + 68.2993i −1.26350 + 2.18845i
975975 −14.6166 1.20050i −0.468106 0.0384469i
976976 −56.5694 97.9811i −1.81074 3.13630i
977977 4.17072 4.63205i 0.133433 0.148192i −0.672725 0.739892i 0.734876π-0.734876\pi
0.806158 + 0.591700i 0.201543π0.201543\pi
978978 −16.7876 + 35.9832i −0.536808 + 1.15062i
979979 −1.41346 13.4481i −0.0451743 0.429804i
980980 43.5125 + 3.68613i 1.38996 + 0.117749i
981981 0.840764 5.96587i 0.0268435 0.190476i
982982 −43.8206 −1.39837
983983 −1.85033 + 0.823819i −0.0590163 + 0.0262757i −0.436033 0.899931i 0.643617π-0.643617\pi
0.377016 + 0.926207i 0.376950π0.376950\pi
984984 −60.2699 20.7654i −1.92133 0.661978i
985985 −22.1592 47.1809i −0.706051 1.50331i
986986 −21.0024 + 23.3255i −0.668852 + 0.742835i
987987 19.5692 + 6.74237i 0.622893 + 0.214612i
988988 −9.56125 10.6188i −0.304184 0.337830i
989989 1.60565 + 4.94168i 0.0510566 + 0.157136i
990990 −21.3852 + 46.1464i −0.679667 + 1.46663i
991991 −0.263346 + 0.810497i −0.00836547 + 0.0257463i −0.955152 0.296116i 0.904309π-0.904309\pi
0.946787 + 0.321862i 0.104309π0.104309\pi
992992 57.9745 25.8119i 1.84069 0.819530i
993993 −9.32097 + 5.16438i −0.295792 + 0.163887i
994994 −1.81112 + 17.2316i −0.0574452 + 0.546554i
995995 −7.83047 + 40.8851i −0.248243 + 1.29614i
996996 8.39145 0.732548i 0.265893 0.0232117i
997997 6.02165 + 57.2921i 0.190707 + 1.81446i 0.502793 + 0.864407i 0.332306π0.332306\pi
−0.312086 + 0.950054i 0.601028π0.601028\pi
998998 17.8025 + 54.7904i 0.563528 + 1.73436i
999999 −1.15933 + 21.8824i −0.0366796 + 0.692327i
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 225.2.q.a.106.28 yes 224
3.2 odd 2 675.2.r.a.181.1 224
9.4 even 3 inner 225.2.q.a.31.1 224
9.5 odd 6 675.2.r.a.631.28 224
25.21 even 5 inner 225.2.q.a.196.1 yes 224
75.71 odd 10 675.2.r.a.46.28 224
225.121 even 15 inner 225.2.q.a.121.28 yes 224
225.221 odd 30 675.2.r.a.496.1 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.1 224 9.4 even 3 inner
225.2.q.a.106.28 yes 224 1.1 even 1 trivial
225.2.q.a.121.28 yes 224 225.121 even 15 inner
225.2.q.a.196.1 yes 224 25.21 even 5 inner
675.2.r.a.46.28 224 75.71 odd 10
675.2.r.a.181.1 224 3.2 odd 2
675.2.r.a.496.1 224 225.221 odd 30
675.2.r.a.631.28 224 9.5 odd 6