Properties

Label 684.2.cf.c.127.3
Level 684684
Weight 22
Character 684.127
Analytic conductor 5.4625.462
Analytic rank 00
Dimension 6060
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(91,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 684=223219 684 = 2^{2} \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 684.cf (of order 1818, degree 66, 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: 5.461767498265.46176749826
Analytic rank: 00
Dimension: 6060
Relative dimension: 1010 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: no (minimal twist has level 228)
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 127.3
Character χ\chi == 684.127
Dual form 684.2.cf.c.307.3

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+(1.13356+0.845604i)q2+(0.5699091.91708i)q4+(0.1629080.923898i)q5+(2.27351+1.31261i)q7+(0.975067+2.65504i)q8+(0.965918+0.909537i)q10+(5.141372.96837i)q11+(1.394813.83220i)q13+(3.68710+0.434566i)q14+(3.350412.18512i)q16+(2.94059+2.46745i)q17+(4.313830.625180i)q19+(1.864030.214229i)q20+(3.31798+7.71239i)q22+(0.4013330.0707658i)q23+(3.871411.40908i)q25+(4.82161+3.16457i)q26+(3.812073.61043i)q28+(4.156344.95333i)q29+(3.66403+6.34629i)q31+(5.645630.356152i)q32+(1.246855.28357i)q34+(0.8423452.31432i)q352.51566iq37+(5.418642.93911i)q38+(2.294141.33339i)q40+(1.577094.33302i)q41+(11.30901.99407i)q43+(2.7605011.5481i)q44+(0.5147740.259151i)q46+(2.453542.92401i)q47+(0.05410880.0937192i)q49+(3.19695+4.87096i)q50+(8.14155+0.489954i)q52+(4.84195+0.853766i)q53+(3.580054.26653i)q55+(1.26821+7.31614i)q56+(0.522897+9.12951i)q58+(1.21047+1.01570i)q59+(1.112766.31077i)q61+(1.2130510.2922i)q62+(6.09849+5.17769i)q64+(3.31333+1.91295i)q65+(2.22499+1.86699i)q67+(3.05443+7.04358i)q68+(1.00215+3.33571i)q70+(1.17754+6.67818i)q71+(11.1504+4.05843i)q73+(2.12725+2.85164i)q74+(3.65701+7.91368i)q76+15.5853q77+(4.29071+1.56169i)q79+(1.47302+3.45141i)q80+(1.87629+6.24532i)q82+(0.641515+0.370379i)q83+(2.75872+2.31484i)q85+(11.1332+11.8233i)q86+(12.8943+10.7562i)q88+(5.8751616.1419i)q89+(1.8590810.5434i)q91+(0.364387+0.729058i)q92+(0.308673+5.38926i)q94+(0.125156+4.08739i)q95+(2.43876+2.90640i)q97+(0.140585+0.0604816i)q98+O(q100)q+(-1.13356 + 0.845604i) q^{2} +(0.569909 - 1.91708i) q^{4} +(-0.162908 - 0.923898i) q^{5} +(2.27351 + 1.31261i) q^{7} +(0.975067 + 2.65504i) q^{8} +(0.965918 + 0.909537i) q^{10} +(5.14137 - 2.96837i) q^{11} +(-1.39481 - 3.83220i) q^{13} +(-3.68710 + 0.434566i) q^{14} +(-3.35041 - 2.18512i) q^{16} +(-2.94059 + 2.46745i) q^{17} +(-4.31383 - 0.625180i) q^{19} +(-1.86403 - 0.214229i) q^{20} +(-3.31798 + 7.71239i) q^{22} +(-0.401333 - 0.0707658i) q^{23} +(3.87141 - 1.40908i) q^{25} +(4.82161 + 3.16457i) q^{26} +(3.81207 - 3.61043i) q^{28} +(4.15634 - 4.95333i) q^{29} +(-3.66403 + 6.34629i) q^{31} +(5.64563 - 0.356152i) q^{32} +(1.24685 - 5.28357i) q^{34} +(0.842345 - 2.31432i) q^{35} -2.51566i q^{37} +(5.41864 - 2.93911i) q^{38} +(2.29414 - 1.33339i) q^{40} +(1.57709 - 4.33302i) q^{41} +(11.3090 - 1.99407i) q^{43} +(-2.76050 - 11.5481i) q^{44} +(0.514774 - 0.259151i) q^{46} +(2.45354 - 2.92401i) q^{47} +(-0.0541088 - 0.0937192i) q^{49} +(-3.19695 + 4.87096i) q^{50} +(-8.14155 + 0.489954i) q^{52} +(4.84195 + 0.853766i) q^{53} +(-3.58005 - 4.26653i) q^{55} +(-1.26821 + 7.31614i) q^{56} +(-0.522897 + 9.12951i) q^{58} +(-1.21047 + 1.01570i) q^{59} +(1.11276 - 6.31077i) q^{61} +(-1.21305 - 10.2922i) q^{62} +(-6.09849 + 5.17769i) q^{64} +(-3.31333 + 1.91295i) q^{65} +(2.22499 + 1.86699i) q^{67} +(3.05443 + 7.04358i) q^{68} +(1.00215 + 3.33571i) q^{70} +(1.17754 + 6.67818i) q^{71} +(11.1504 + 4.05843i) q^{73} +(2.12725 + 2.85164i) q^{74} +(-3.65701 + 7.91368i) q^{76} +15.5853 q^{77} +(4.29071 + 1.56169i) q^{79} +(-1.47302 + 3.45141i) q^{80} +(1.87629 + 6.24532i) q^{82} +(0.641515 + 0.370379i) q^{83} +(2.75872 + 2.31484i) q^{85} +(-11.1332 + 11.8233i) q^{86} +(12.8943 + 10.7562i) q^{88} +(-5.87516 - 16.1419i) q^{89} +(1.85908 - 10.5434i) q^{91} +(-0.364387 + 0.729058i) q^{92} +(-0.308673 + 5.38926i) q^{94} +(0.125156 + 4.08739i) q^{95} +(2.43876 + 2.90640i) q^{97} +(0.140585 + 0.0604816i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 60q+3q23q43q86q106q13+9q1427q1618q1930q20+12q2218q28+12q31+63q3239q34+48q38+33q40+12q41+18q43+117q98+O(q100) 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/684Z)×\left(\mathbb{Z}/684\mathbb{Z}\right)^\times.

nn 325325 343343 533533
χ(n)\chi(n) e(518)e\left(\frac{5}{18}\right) 1-1 11

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 −1.13356 + 0.845604i −0.801547 + 0.597932i
33 0 0
44 0.569909 1.91708i 0.284954 0.958541i
55 −0.162908 0.923898i −0.0728547 0.413180i −0.999322 0.0368055i 0.988282π-0.988282\pi
0.926468 0.376374i 0.122829π-0.122829\pi
66 0 0
77 2.27351 + 1.31261i 0.859305 + 0.496120i 0.863780 0.503870i 0.168091π-0.168091\pi
−0.00447442 + 0.999990i 0.501424π0.501424\pi
88 0.975067 + 2.65504i 0.344738 + 0.938699i
99 0 0
1010 0.965918 + 0.909537i 0.305450 + 0.287621i
1111 5.14137 2.96837i 1.55018 0.894998i 0.552057 0.833807i 0.313843π-0.313843\pi
0.998126 0.0611917i 0.0194901π-0.0194901\pi
1212 0 0
1313 −1.39481 3.83220i −0.386850 1.06286i −0.968411 0.249358i 0.919780π-0.919780\pi
0.581562 0.813502i 0.302442π-0.302442\pi
1414 −3.68710 + 0.434566i −0.985419 + 0.116143i
1515 0 0
1616 −3.35041 2.18512i −0.837602 0.546281i
1717 −2.94059 + 2.46745i −0.713198 + 0.598444i −0.925495 0.378761i 0.876350π-0.876350\pi
0.212296 + 0.977205i 0.431906π0.431906\pi
1818 0 0
1919 −4.31383 0.625180i −0.989661 0.143426i
2020 −1.86403 0.214229i −0.416810 0.0479031i
2121 0 0
2222 −3.31798 + 7.71239i −0.707396 + 1.64429i
2323 −0.401333 0.0707658i −0.0836836 0.0147557i 0.131650 0.991296i 0.457973π-0.457973\pi
−0.215333 + 0.976541i 0.569084π0.569084\pi
2424 0 0
2525 3.87141 1.40908i 0.774283 0.281816i
2626 4.82161 + 3.16457i 0.945596 + 0.620623i
2727 0 0
2828 3.81207 3.61043i 0.720414 0.682308i
2929 4.15634 4.95333i 0.771813 0.919811i −0.226720 0.973960i 0.572800π-0.572800\pi
0.998533 + 0.0541493i 0.0172447π0.0172447\pi
3030 0 0
3131 −3.66403 + 6.34629i −0.658080 + 1.13983i 0.323032 + 0.946388i 0.395298π0.395298\pi
−0.981112 + 0.193440i 0.938036π0.938036\pi
3232 5.64563 0.356152i 0.998016 0.0629594i
3333 0 0
3434 1.24685 5.28357i 0.213833 0.906125i
3535 0.842345 2.31432i 0.142382 0.391192i
3636 0 0
3737 2.51566i 0.413571i −0.978386 0.206786i 0.933700π-0.933700\pi
0.978386 0.206786i 0.0663003π-0.0663003\pi
3838 5.41864 2.93911i 0.879019 0.476787i
3939 0 0
4040 2.29414 1.33339i 0.362736 0.210828i
4141 1.57709 4.33302i 0.246300 0.676703i −0.753514 0.657431i 0.771643π-0.771643\pi
0.999814 0.0192719i 0.00613482π-0.00613482\pi
4242 0 0
4343 11.3090 1.99407i 1.72460 0.304093i 0.778422 0.627741i 0.216020π-0.216020\pi
0.946178 + 0.323648i 0.104909π0.104909\pi
4444 −2.76050 11.5481i −0.416161 1.74095i
4545 0 0
4646 0.514774 0.259151i 0.0758992 0.0382098i
4747 2.45354 2.92401i 0.357886 0.426511i −0.556819 0.830634i 0.687978π-0.687978\pi
0.914705 + 0.404122i 0.132423π0.132423\pi
4848 0 0
4949 −0.0541088 0.0937192i −0.00772983 0.0133885i
5050 −3.19695 + 4.87096i −0.452117 + 0.688857i
5151 0 0
5252 −8.14155 + 0.489954i −1.12903 + 0.0679444i
5353 4.84195 + 0.853766i 0.665092 + 0.117274i 0.495995 0.868326i 0.334804π-0.334804\pi
0.169098 + 0.985599i 0.445915π0.445915\pi
5454 0 0
5555 −3.58005 4.26653i −0.482733 0.575299i
5656 −1.26821 + 7.31614i −0.169472 + 0.977660i
5757 0 0
5858 −0.522897 + 9.12951i −0.0686597 + 1.19876i
5959 −1.21047 + 1.01570i −0.157589 + 0.132233i −0.718173 0.695865i 0.755021π-0.755021\pi
0.560584 + 0.828098i 0.310577π0.310577\pi
6060 0 0
6161 1.11276 6.31077i 0.142474 0.808012i −0.826886 0.562369i 0.809890π-0.809890\pi
0.969360 0.245643i 0.0789989π-0.0789989\pi
6262 −1.21305 10.2922i −0.154058 1.30711i
6363 0 0
6464 −6.09849 + 5.17769i −0.762311 + 0.647211i
6565 −3.31333 + 1.91295i −0.410969 + 0.237273i
6666 0 0
6767 2.22499 + 1.86699i 0.271826 + 0.228089i 0.768503 0.639846i 0.221002π-0.221002\pi
−0.496677 + 0.867936i 0.665446π0.665446\pi
6868 3.05443 + 7.04358i 0.370405 + 0.854159i
6969 0 0
7070 1.00215 + 3.33571i 0.119780 + 0.398694i
7171 1.17754 + 6.67818i 0.139749 + 0.792555i 0.971434 + 0.237308i 0.0762651π0.0762651\pi
−0.831686 + 0.555247i 0.812624π0.812624\pi
7272 0 0
7373 11.1504 + 4.05843i 1.30506 + 0.475003i 0.898642 0.438684i 0.144555π-0.144555\pi
0.406419 + 0.913687i 0.366777π0.366777\pi
7474 2.12725 + 2.85164i 0.247288 + 0.331497i
7575 0 0
7676 −3.65701 + 7.91368i −0.419488 + 0.907761i
7777 15.5853 1.77611
7878 0 0
7979 4.29071 + 1.56169i 0.482742 + 0.175704i 0.571916 0.820312i 0.306200π-0.306200\pi
−0.0891737 + 0.996016i 0.528423π0.528423\pi
8080 −1.47302 + 3.45141i −0.164689 + 0.385879i
8181 0 0
8282 1.87629 + 6.24532i 0.207202 + 0.689680i
8383 0.641515 + 0.370379i 0.0704154 + 0.0406543i 0.534794 0.844982i 0.320389π-0.320389\pi
−0.464379 + 0.885637i 0.653722π0.653722\pi
8484 0 0
8585 2.75872 + 2.31484i 0.299225 + 0.251080i
8686 −11.1332 + 11.8233i −1.20052 + 1.27494i
8787 0 0
8888 12.8943 + 10.7562i 1.37454 + 1.14661i
8989 −5.87516 16.1419i −0.622766 1.71103i −0.700114 0.714031i 0.746868π-0.746868\pi
0.0773486 0.997004i 0.475355π-0.475355\pi
9090 0 0
9191 1.85908 10.5434i 0.194885 1.10525i
9292 −0.364387 + 0.729058i −0.0379899 + 0.0760095i
9393 0 0
9494 −0.308673 + 5.38926i −0.0318371 + 0.555860i
9595 0.125156 + 4.08739i 0.0128407 + 0.419357i
9696 0 0
9797 2.43876 + 2.90640i 0.247618 + 0.295100i 0.875509 0.483201i 0.160526π-0.160526\pi
−0.627891 + 0.778301i 0.716082π0.716082\pi
9898 0.140585 + 0.0604816i 0.0142012 + 0.00610956i
9999 0 0
100100 −0.494968 8.22487i −0.0494968 0.822487i
101101 −9.11983 + 3.31935i −0.907457 + 0.330287i −0.753237 0.657749i 0.771509π-0.771509\pi
−0.154220 + 0.988037i 0.549286π0.549286\pi
102102 0 0
103103 −7.76969 13.4575i −0.765570 1.32601i −0.939945 0.341327i 0.889124π-0.889124\pi
0.174374 0.984679i 0.444210π-0.444210\pi
104104 8.81461 7.43992i 0.864344 0.729544i
105105 0 0
106106 −6.21058 + 3.12657i −0.603224 + 0.303680i
107107 −8.60129 + 14.8979i −0.831518 + 1.44023i 0.0653163 + 0.997865i 0.479194π0.479194\pi
−0.896834 + 0.442367i 0.854139π0.854139\pi
108108 0 0
109109 −3.11205 + 0.548739i −0.298081 + 0.0525597i −0.320688 0.947185i 0.603914π-0.603914\pi
0.0226078 + 0.999744i 0.492803π0.492803\pi
110110 7.66599 + 1.80906i 0.730923 + 0.172487i
111111 0 0
112112 −4.74896 9.36568i −0.448735 0.884973i
113113 19.3153i 1.81703i 0.417850 + 0.908516i 0.362784π0.362784\pi
−0.417850 + 0.908516i 0.637216π0.637216\pi
114114 0 0
115115 0.382319i 0.0356514i
116116 −7.12721 10.7910i −0.661745 1.00192i
117117 0 0
118118 0.513253 2.17493i 0.0472487 0.200219i
119119 −9.92426 + 1.74991i −0.909755 + 0.160414i
120120 0 0
121121 12.1225 20.9968i 1.10204 1.90880i
122122 4.07504 + 8.09458i 0.368936 + 0.732849i
123123 0 0
124124 10.0782 + 10.6411i 0.905049 + 0.955595i
125125 −4.27791 7.40955i −0.382628 0.662731i
126126 0 0
127127 −13.9783 + 5.08769i −1.24037 + 0.451459i −0.877138 0.480238i 0.840550π-0.840550\pi
−0.363236 + 0.931697i 0.618328π0.618328\pi
128128 2.53472 11.0261i 0.224040 0.974580i
129129 0 0
130130 2.13826 4.97021i 0.187537 0.435917i
131131 −2.07131 2.46849i −0.180971 0.215673i 0.667931 0.744223i 0.267180π-0.267180\pi
−0.848902 + 0.528551i 0.822736π0.822736\pi
132132 0 0
133133 −8.98691 7.08373i −0.779264 0.614237i
134134 −4.10089 0.234881i −0.354263 0.0202906i
135135 0 0
136136 −9.41845 5.40146i −0.807626 0.463172i
137137 −1.36502 + 7.74139i −0.116621 + 0.661391i 0.869314 + 0.494261i 0.164561π0.164561\pi
−0.985935 + 0.167130i 0.946550π0.946550\pi
138138 0 0
139139 0.00238476 + 0.00655208i 0.000202273 + 0.000555740i 0.939794 0.341742i 0.111017π-0.111017\pi
−0.939591 + 0.342298i 0.888795π0.888795\pi
140140 −3.95669 2.93380i −0.334401 0.247951i
141141 0 0
142142 −6.98191 6.57438i −0.585909 0.551709i
143143 −18.5466 15.5625i −1.55095 1.30140i
144144 0 0
145145 −5.25348 3.03310i −0.436277 0.251885i
146146 −16.0715 + 4.82839i −1.33009 + 0.399600i
147147 0 0
148148 −4.82272 1.43369i −0.396425 0.117849i
149149 10.8510 + 3.94945i 0.888950 + 0.323552i 0.745816 0.666152i 0.232060π-0.232060\pi
0.143134 + 0.989703i 0.454282π0.454282\pi
150150 0 0
151151 3.85210 0.313480 0.156740 0.987640i 0.449902π-0.449902\pi
0.156740 + 0.987640i 0.449902π0.449902\pi
152152 −2.54640 12.0630i −0.206540 0.978438i
153153 0 0
154154 −17.6668 + 13.1790i −1.42363 + 1.06199i
155155 6.46023 + 2.35133i 0.518898 + 0.188863i
156156 0 0
157157 3.30340 + 18.7345i 0.263640 + 1.49518i 0.772880 + 0.634553i 0.218816π0.218816\pi
−0.509240 + 0.860625i 0.670073π0.670073\pi
158158 −6.18433 + 1.85797i −0.491999 + 0.147812i
159159 0 0
160160 −1.24877 5.15797i −0.0987237 0.407773i
161161 −0.819545 0.687680i −0.0645892 0.0541968i
162162 0 0
163163 5.72920 3.30775i 0.448745 0.259083i −0.258555 0.965997i 0.583246π-0.583246\pi
0.707300 + 0.706913i 0.249913π0.249913\pi
164164 −7.40795 5.49283i −0.578464 0.428918i
165165 0 0
166166 −1.04039 + 0.122621i −0.0807497 + 0.00951726i
167167 0.143711 0.815026i 0.0111207 0.0630686i −0.978742 0.205093i 0.934250π-0.934250\pi
0.989863 + 0.142025i 0.0453613π0.0453613\pi
168168 0 0
169169 −2.78168 + 2.33410i −0.213975 + 0.179546i
170170 −5.08460 0.291223i −0.389971 0.0223358i
171171 0 0
172172 2.62227 22.8166i 0.199946 1.73975i
173173 −3.66715 4.37034i −0.278808 0.332271i 0.608408 0.793624i 0.291808π-0.291808\pi
−0.887216 + 0.461354i 0.847364π0.847364\pi
174174 0 0
175175 10.6513 + 1.87810i 0.805160 + 0.141971i
176176 −23.7120 1.28928i −1.78736 0.0971829i
177177 0 0
178178 20.3095 + 13.3297i 1.52226 + 0.999103i
179179 2.18671 + 3.78750i 0.163442 + 0.283091i 0.936101 0.351731i 0.114407π-0.114407\pi
−0.772659 + 0.634822i 0.781074π0.781074\pi
180180 0 0
181181 −5.17743 + 6.17022i −0.384835 + 0.458628i −0.923334 0.383998i 0.874547π-0.874547\pi
0.538499 + 0.842626i 0.318992π0.318992\pi
182182 6.80813 + 13.5236i 0.504652 + 1.00243i
183183 0 0
184184 −0.203440 1.13456i −0.0149978 0.0836406i
185185 −2.32421 + 0.409821i −0.170879 + 0.0301306i
186186 0 0
187187 −7.79437 + 21.4149i −0.569981 + 1.56601i
188188 −4.20728 6.37006i −0.306848 0.464584i
189189 0 0
190190 −3.59818 4.52746i −0.261040 0.328457i
191191 3.21322i 0.232501i −0.993220 0.116250i 0.962913π-0.962913\pi
0.993220 0.116250i 0.0370875π-0.0370875\pi
192192 0 0
193193 −2.03628 + 5.59463i −0.146575 + 0.402711i −0.991153 0.132721i 0.957629π-0.957629\pi
0.844579 + 0.535431i 0.179851π0.179851\pi
194194 −5.22213 1.23235i −0.374927 0.0884775i
195195 0 0
196196 −0.210505 + 0.0503197i −0.0150360 + 0.00359426i
197197 6.98997 12.1070i 0.498015 0.862587i −0.501982 0.864878i 0.667396π-0.667396\pi
0.999997 + 0.00229054i 0.000729101π0.000729101\pi
198198 0 0
199199 −6.33587 + 7.55079i −0.449138 + 0.535261i −0.942342 0.334652i 0.891381π-0.891381\pi
0.493204 + 0.869914i 0.335826π0.335826\pi
200200 7.51605 + 8.90482i 0.531465 + 0.629666i
201201 0 0
202202 7.53101 11.4744i 0.529880 0.807339i
203203 15.9513 5.80578i 1.11956 0.407486i
204204 0 0
205205 −4.26018 0.751186i −0.297544 0.0524651i
206206 20.1871 + 8.68478i 1.40650 + 0.605097i
207207 0 0
208208 −3.70066 + 15.8872i −0.256594 + 1.10158i
209209 −24.0348 + 9.59078i −1.66252 + 0.663408i
210210 0 0
211211 −11.1612 + 9.36536i −0.768369 + 0.644738i −0.940291 0.340373i 0.889447π-0.889447\pi
0.171922 + 0.985111i 0.445002π0.445002\pi
212212 4.39621 8.79584i 0.301933 0.604101i
213213 0 0
214214 −2.84763 24.1609i −0.194660 1.65160i
215215 −3.68464 10.1235i −0.251291 0.690415i
216216 0 0
217217 −16.6604 + 9.61889i −1.13098 + 0.652973i
218218 3.06368 3.25359i 0.207498 0.220361i
219219 0 0
220220 −10.2196 + 4.43171i −0.689005 + 0.298786i
221221 13.5573 + 7.82731i 0.911963 + 0.526522i
222222 0 0
223223 −0.947405 5.37300i −0.0634429 0.359803i −0.999958 0.00917516i 0.997079π-0.997079\pi
0.936515 0.350628i 0.114032π-0.114032\pi
224224 13.3029 + 6.60080i 0.888836 + 0.441034i
225225 0 0
226226 −16.3331 21.8950i −1.08646 1.45644i
227227 −4.73837 −0.314497 −0.157248 0.987559i 0.550262π-0.550262\pi
−0.157248 + 0.987559i 0.550262π0.550262\pi
228228 0 0
229229 −25.7074 −1.69879 −0.849397 0.527755i 0.823034π-0.823034\pi
−0.849397 + 0.527755i 0.823034π0.823034\pi
230230 −0.323290 0.433381i −0.0213171 0.0285763i
231231 0 0
232232 17.2040 + 6.20542i 1.12950 + 0.407406i
233233 −2.50999 14.2349i −0.164435 0.932556i −0.949645 0.313327i 0.898556π-0.898556\pi
0.785210 0.619229i 0.212555π-0.212555\pi
234234 0 0
235235 −3.10119 1.79047i −0.202300 0.116798i
236236 1.25733 + 2.89942i 0.0818451 + 0.188736i
237237 0 0
238238 9.76999 10.3756i 0.633294 0.672551i
239239 −13.1429 + 7.58808i −0.850146 + 0.490832i −0.860700 0.509112i 0.829974π-0.829974\pi
0.0105542 + 0.999944i 0.496640π0.496640\pi
240240 0 0
241241 −1.91914 5.27279i −0.123623 0.339650i 0.862408 0.506214i 0.168955π-0.168955\pi
−0.986031 + 0.166563i 0.946733π0.946733\pi
242242 4.01339 + 34.0519i 0.257991 + 2.18894i
243243 0 0
244244 −11.4641 5.72982i −0.733914 0.366814i
245245 −0.0777723 + 0.0652587i −0.00496869 + 0.00416922i
246246 0 0
247247 3.62114 + 17.4035i 0.230408 + 1.10736i
248248 −20.4223 3.54010i −1.29682 0.224797i
249249 0 0
250250 11.1148 + 4.78175i 0.702962 + 0.302424i
251251 20.4595 + 3.60756i 1.29139 + 0.227707i 0.776810 0.629735i 0.216837π-0.216837\pi
0.514580 + 0.857442i 0.327948π0.327948\pi
252252 0 0
253253 −2.27346 + 0.827472i −0.142931 + 0.0520227i
254254 11.5431 17.5873i 0.724276 1.10353i
255255 0 0
256256 6.45047 + 14.6421i 0.403154 + 0.915132i
257257 10.5434 12.5652i 0.657681 0.783793i −0.329370 0.944201i 0.606836π-0.606836\pi
0.987051 + 0.160408i 0.0512809π0.0512809\pi
258258 0 0
259259 3.30208 5.71936i 0.205181 0.355384i
260260 1.77899 + 7.44214i 0.110328 + 0.461542i
261261 0 0
262262 4.43531 + 1.04667i 0.274014 + 0.0646635i
263263 −4.15539 + 11.4168i −0.256232 + 0.703992i 0.743159 + 0.669114i 0.233326π0.233326\pi
−0.999392 + 0.0348776i 0.988896π0.988896\pi
264264 0 0
265265 4.61255i 0.283347i
266266 16.1772 + 0.430457i 0.991889 + 0.0263930i
267267 0 0
268268 4.84722 3.20148i 0.296091 0.195562i
269269 −5.91660 + 16.2557i −0.360741 + 0.991129i 0.618027 + 0.786157i 0.287932π0.287932\pi
−0.978768 + 0.204972i 0.934290π0.934290\pi
270270 0 0
271271 −6.08103 + 1.07225i −0.369396 + 0.0651345i −0.355265 0.934766i 0.615609π-0.615609\pi
−0.0141312 + 0.999900i 0.504498π0.504498\pi
272272 15.2439 1.84140i 0.924295 0.111652i
273273 0 0
274274 −4.99882 9.92957i −0.301990 0.599867i
275275 15.7217 18.7364i 0.948055 1.12985i
276276 0 0
277277 13.7725 + 23.8547i 0.827511 + 1.43329i 0.899985 + 0.435920i 0.143577π0.143577\pi
−0.0724748 + 0.997370i 0.523090π0.523090\pi
278278 −0.00824373 0.00541060i −0.000494426 0.000324506i
279279 0 0
280280 6.96597 0.0201599i 0.416296 0.00120478i
281281 −7.27059 1.28200i −0.433727 0.0764778i −0.0474780 0.998872i 0.515118π-0.515118\pi
−0.386249 + 0.922394i 0.626230π0.626230\pi
282282 0 0
283283 −5.57965 6.64957i −0.331676 0.395276i 0.574272 0.818664i 0.305285π-0.305285\pi
−0.905948 + 0.423388i 0.860841π0.860841\pi
284284 13.4737 + 1.54851i 0.799518 + 0.0918870i
285285 0 0
286286 34.1833 + 1.95787i 2.02130 + 0.115771i
287287 9.27308 7.78104i 0.547373 0.459300i
288288 0 0
289289 −0.393247 + 2.23021i −0.0231321 + 0.131189i
290290 8.51992 1.00417i 0.500307 0.0589668i
291291 0 0
292292 14.1351 19.0634i 0.827193 1.11560i
293293 −8.59522 + 4.96245i −0.502138 + 0.289910i −0.729596 0.683878i 0.760292π-0.760292\pi
0.227458 + 0.973788i 0.426959π0.426959\pi
294294 0 0
295295 1.13560 + 0.952881i 0.0661171 + 0.0554789i
296296 6.67917 2.45293i 0.388219 0.142574i
297297 0 0
298298 −15.6399 + 4.69873i −0.905997 + 0.272190i
299299 0.288593 + 1.63669i 0.0166897 + 0.0946522i
300300 0 0
301301 28.3284 + 10.3107i 1.63282 + 0.594299i
302302 −4.36658 + 3.25735i −0.251269 + 0.187440i
303303 0 0
304304 13.0870 + 11.5209i 0.750591 + 0.660767i
305305 −6.01179 −0.344234
306306 0 0
307307 23.6159 + 8.59549i 1.34783 + 0.490571i 0.912271 0.409588i 0.134328π-0.134328\pi
0.435562 + 0.900159i 0.356550π0.356550\pi
308308 8.88218 29.8782i 0.506109 1.70247i
309309 0 0
310310 −9.31134 + 2.79742i −0.528848 + 0.158883i
311311 −17.9579 10.3680i −1.01830 0.587916i −0.104689 0.994505i 0.533385π-0.533385\pi
−0.913611 + 0.406589i 0.866718π0.866718\pi
312312 0 0
313313 13.2291 + 11.1005i 0.747752 + 0.627439i 0.934907 0.354892i 0.115482π-0.115482\pi
−0.187155 + 0.982330i 0.559927π0.559927\pi
314314 −19.5866 18.4433i −1.10533 1.04082i
315315 0 0
316316 5.43920 7.33561i 0.305979 0.412661i
317317 1.69445 + 4.65547i 0.0951699 + 0.261477i 0.978138 0.207955i 0.0666808π-0.0666808\pi
−0.882968 + 0.469432i 0.844459π0.844459\pi
318318 0 0
319319 6.66595 37.8045i 0.373222 2.11665i
320320 5.77715 + 4.79089i 0.322952 + 0.267819i
321321 0 0
322322 1.51051 + 0.0865150i 0.0841772 + 0.00482129i
323323 14.2278 8.80576i 0.791657 0.489966i
324324 0 0
325325 −10.7997 12.8706i −0.599062 0.713934i
326326 −3.69733 + 8.59416i −0.204776 + 0.475987i
327327 0 0
328328 13.0421 0.0377445i 0.720130 0.00208409i
329329 9.41623 3.42723i 0.519134 0.188949i
330330 0 0
331331 6.79791 + 11.7743i 0.373647 + 0.647175i 0.990123 0.140198i 0.0447739π-0.0447739\pi
−0.616477 + 0.787373i 0.711441π0.711441\pi
332332 1.07565 1.01875i 0.0590340 0.0559114i
333333 0 0
334334 0.526284 + 1.04540i 0.0287970 + 0.0572019i
335335 1.36244 2.35981i 0.0744380 0.128930i
336336 0 0
337337 −7.24750 + 1.27793i −0.394797 + 0.0696133i −0.367522 0.930015i 0.619794π-0.619794\pi
−0.0272743 + 0.999628i 0.508683π0.508683\pi
338338 1.17947 4.99804i 0.0641545 0.271857i
339339 0 0
340340 6.00995 3.96944i 0.325936 0.215273i
341341 43.5049i 2.35592i
342342 0 0
343343 18.6606i 1.00758i
344344 16.3213 + 28.0814i 0.879988 + 1.51405i
345345 0 0
346346 7.85250 + 1.85308i 0.422153 + 0.0996221i
347347 −7.29437 + 1.28619i −0.391582 + 0.0690465i −0.365973 0.930625i 0.619264π-0.619264\pi
−0.0256094 + 0.999672i 0.508153π0.508153\pi
348348 0 0
349349 −10.0951 + 17.4851i −0.540376 + 0.935958i 0.458507 + 0.888691i 0.348385π0.348385\pi
−0.998882 + 0.0472671i 0.984949π0.984949\pi
350350 −13.6620 + 6.87781i −0.730262 + 0.367634i
351351 0 0
352352 27.9691 18.5895i 1.49076 0.990821i
353353 10.6908 + 18.5171i 0.569016 + 0.985564i 0.996664 + 0.0816189i 0.0260090π0.0260090\pi
−0.427648 + 0.903945i 0.640658π0.640658\pi
354354 0 0
355355 5.97813 2.17586i 0.317286 0.115483i
356356 −34.2936 + 2.06377i −1.81756 + 0.109380i
357357 0 0
358358 −5.68148 2.44426i −0.300276 0.129183i
359359 13.3436 + 15.9023i 0.704248 + 0.839290i 0.993000 0.118114i 0.0376848π-0.0376848\pi
−0.288752 + 0.957404i 0.593240π0.593240\pi
360360 0 0
361361 18.2183 + 5.39384i 0.958858 + 0.283887i
362362 0.651357 11.3723i 0.0342345 0.597717i
363363 0 0
364364 −19.1530 9.57277i −1.00389 0.501749i
365365 1.93308 10.9630i 0.101182 0.573831i
366366 0 0
367367 3.99066 + 10.9643i 0.208311 + 0.572330i 0.999215 0.0396103i 0.0126116π-0.0126116\pi
−0.790904 + 0.611940i 0.790389π0.790389\pi
368368 1.19000 + 1.11406i 0.0620328 + 0.0580742i
369369 0 0
370370 2.28808 2.42992i 0.118952 0.126325i
371371 9.88754 + 8.29663i 0.513336 + 0.430740i
372372 0 0
373373 −22.7922 13.1591i −1.18013 0.681351i −0.224089 0.974569i 0.571941π-0.571941\pi
−0.956046 + 0.293218i 0.905274π0.905274\pi
374374 −9.27311 30.8659i −0.479501 1.59604i
375375 0 0
376376 10.1557 + 3.66314i 0.523743 + 0.188912i
377377 −24.7794 9.01898i −1.27621 0.464501i
378378 0 0
379379 −15.1616 −0.778798 −0.389399 0.921069i 0.627317π-0.627317\pi
−0.389399 + 0.921069i 0.627317π0.627317\pi
380380 7.90719 + 2.08950i 0.405630 + 0.107189i
381381 0 0
382382 2.71711 + 3.64238i 0.139020 + 0.186360i
383383 29.2153 + 10.6335i 1.49283 + 0.543346i 0.954193 0.299193i 0.0967173π-0.0967173\pi
0.538637 + 0.842538i 0.318940π0.318940\pi
384384 0 0
385385 −2.53897 14.3992i −0.129398 0.733851i
386386 −2.42260 8.06373i −0.123307 0.410433i
387387 0 0
388388 6.96167 3.01892i 0.353425 0.153262i
389389 −26.2800 22.0515i −1.33245 1.11806i −0.983499 0.180913i 0.942095π-0.942095\pi
−0.348947 0.937142i 0.613461π-0.613461\pi
390390 0 0
391391 1.35477 0.782175i 0.0685135 0.0395563i
392392 0.196069 0.235044i 0.00990297 0.0118715i
393393 0 0
394394 2.31417 + 19.6347i 0.116586 + 0.989183i
395395 0.743851 4.21859i 0.0374272 0.212260i
396396 0 0
397397 −6.93811 + 5.82177i −0.348214 + 0.292186i −0.800072 0.599904i 0.795206π-0.795206\pi
0.451859 + 0.892090i 0.350761π0.350761\pi
398398 0.797097 13.9169i 0.0399548 0.697591i
399399 0 0
400400 −16.0498 3.73853i −0.802492 0.186926i
401401 5.10512 + 6.08405i 0.254938 + 0.303823i 0.878300 0.478110i 0.158678π-0.158678\pi
−0.623362 + 0.781933i 0.714234π0.714234\pi
402402 0 0
403403 29.4309 + 5.18945i 1.46606 + 0.258505i
404404 1.16599 + 19.3752i 0.0580101 + 0.963952i
405405 0 0
406406 −13.1723 + 20.0696i −0.653730 + 0.996040i
407407 −7.46741 12.9339i −0.370146 0.641111i
408408 0 0
409409 −17.5748 + 20.9449i −0.869020 + 1.03566i 0.130005 + 0.991513i 0.458501π0.458501\pi
−0.999025 + 0.0441446i 0.985944π0.985944\pi
410410 5.46437 2.75092i 0.269866 0.135858i
411411 0 0
412412 −30.2271 + 7.22559i −1.48918 + 0.355979i
413413 −4.08522 + 0.720335i −0.201021 + 0.0354454i
414414 0 0
415415 0.237684 0.653032i 0.0116675 0.0320561i
416416 −9.23940 21.1384i −0.452999 1.03640i
417417 0 0
418418 19.1348 31.1956i 0.935916 1.52583i
419419 13.4784i 0.658462i 0.944249 + 0.329231i 0.106789π0.106789\pi
−0.944249 + 0.329231i 0.893211π0.893211\pi
420420 0 0
421421 13.2512 36.4074i 0.645825 1.77439i 0.0132242 0.999913i 0.495790π-0.495790\pi
0.632601 0.774478i 0.281987π-0.281987\pi
422422 4.73249 20.0541i 0.230374 0.976220i
423423 0 0
424424 2.45444 + 13.6880i 0.119198 + 0.664750i
425425 −7.90742 + 13.6960i −0.383566 + 0.664356i
426426 0 0
427427 10.8135 12.8870i 0.523300 0.623644i
428428 23.6585 + 24.9798i 1.14358 + 1.20744i
429429 0 0
430430 12.7372 + 8.35980i 0.614243 + 0.403145i
431431 −37.1856 + 13.5345i −1.79117 + 0.651932i −0.792029 + 0.610484i 0.790975π0.790975\pi
−0.999141 + 0.0414488i 0.986803π0.986803\pi
432432 0 0
433433 35.8179 + 6.31566i 1.72130 + 0.303511i 0.945052 0.326919i 0.106011π-0.106011\pi
0.776246 + 0.630431i 0.217122π0.217122\pi
434434 10.7518 24.9917i 0.516102 1.19964i
435435 0 0
436436 −0.721609 + 6.27879i −0.0345588 + 0.300700i
437437 1.68704 + 0.556177i 0.0807021 + 0.0266055i
438438 0 0
439439 −8.70974 + 7.30834i −0.415693 + 0.348808i −0.826522 0.562905i 0.809684π-0.809684\pi
0.410829 + 0.911713i 0.365239π0.365239\pi
440440 7.83704 13.6653i 0.373616 0.651469i
441441 0 0
442442 −21.9868 + 2.59139i −1.04581 + 0.123260i
443443 7.73933 + 21.2636i 0.367707 + 1.01027i 0.976231 + 0.216731i 0.0695395π0.0695395\pi
−0.608525 + 0.793535i 0.708238π0.708238\pi
444444 0 0
445445 −13.9563 + 8.05769i −0.661594 + 0.381971i
446446 5.61737 + 5.28948i 0.265990 + 0.250464i
447447 0 0
448448 −20.6612 + 3.76657i −0.976152 + 0.177954i
449449 26.6431 + 15.3824i 1.25737 + 0.725941i 0.972562 0.232644i 0.0747378π-0.0747378\pi
0.284805 + 0.958585i 0.408071π0.408071\pi
450450 0 0
451451 −4.75361 26.9590i −0.223839 1.26945i
452452 37.0291 + 11.0080i 1.74170 + 0.517771i
453453 0 0
454454 5.37122 4.00679i 0.252084 0.188048i
455455 −10.0439 −0.470863
456456 0 0
457457 −24.2691 −1.13526 −0.567631 0.823283i 0.692140π-0.692140\pi
−0.567631 + 0.823283i 0.692140π0.692140\pi
458458 29.1409 21.7383i 1.36166 1.01576i
459459 0 0
460460 0.732936 + 0.217887i 0.0341733 + 0.0101590i
461461 −6.43606 36.5007i −0.299757 1.70001i −0.647212 0.762310i 0.724065π-0.724065\pi
0.347455 0.937697i 0.387046π-0.387046\pi
462462 0 0
463463 −18.1684 10.4895i −0.844355 0.487489i 0.0143872 0.999896i 0.495420π-0.495420\pi
−0.858742 + 0.512408i 0.828754π0.828754\pi
464464 −24.7491 + 7.51357i −1.14895 + 0.348809i
465465 0 0
466466 14.8823 + 14.0136i 0.689408 + 0.649167i
467467 34.2174 19.7554i 1.58339 0.914172i 0.589032 0.808110i 0.299509π-0.299509\pi
0.994360 0.106062i 0.0338242π-0.0338242\pi
468468 0 0
469469 2.60791 + 7.16517i 0.120422 + 0.330857i
470470 5.02942 0.592773i 0.231990 0.0273426i
471471 0 0
472472 −3.87701 2.22346i −0.178454 0.102343i
473473 52.2244 43.8215i 2.40128 2.01491i
474474 0 0
475475 −17.5816 + 3.65820i −0.806697 + 0.167850i
476476 −2.30119 + 20.0229i −0.105475 + 0.917748i
477477 0 0
478478 8.48178 19.7152i 0.387947 0.901754i
479479 −12.6442 2.22951i −0.577728 0.101869i −0.122854 0.992425i 0.539205π-0.539205\pi
−0.454874 + 0.890556i 0.650316π0.650316\pi
480480 0 0
481481 −9.64049 + 3.50885i −0.439569 + 0.159990i
482482 6.63415 + 4.35419i 0.302177 + 0.198328i
483483 0 0
484484 −33.3438 35.2060i −1.51563 1.60027i
485485 2.28792 2.72664i 0.103889 0.123810i
486486 0 0
487487 −16.9204 + 29.3070i −0.766736 + 1.32803i 0.172587 + 0.984994i 0.444787π0.444787\pi
−0.939324 + 0.343032i 0.888546π0.888546\pi
488488 17.8404 3.19900i 0.807596 0.144812i
489489 0 0
490490 0.0329764 0.139739i 0.00148972 0.00631277i
491491 −11.0221 + 30.2830i −0.497420 + 1.36665i 0.396339 + 0.918104i 0.370280π0.370280\pi
−0.893759 + 0.448547i 0.851942π0.851942\pi
492492 0 0
493493 24.8213i 1.11789i
494494 −18.8212 16.6658i −0.846806 0.749829i
495495 0 0
496496 26.1434 13.2563i 1.17387 0.595225i
497497 −6.08870 + 16.7286i −0.273115 + 0.750378i
498498 0 0
499499 13.9952 2.46774i 0.626513 0.110471i 0.148627 0.988893i 0.452515π-0.452515\pi
0.477885 + 0.878422i 0.341403π0.341403\pi
500500 −16.6427 + 3.97833i −0.744286 + 0.177916i
501501 0 0
502502 −26.2426 + 13.2112i −1.17126 + 0.589646i
503503 −9.64008 + 11.4886i −0.429830 + 0.512251i −0.936873 0.349669i 0.886294π-0.886294\pi
0.507043 + 0.861921i 0.330738π0.330738\pi
504504 0 0
505505 4.55243 + 7.88505i 0.202581 + 0.350880i
506506 1.87739 2.86043i 0.0834600 0.127162i
507507 0 0
508508 1.78716 + 29.6971i 0.0792922 + 1.31760i
509509 17.9890 + 3.17194i 0.797348 + 0.140594i 0.557457 0.830206i 0.311777π-0.311777\pi
0.239891 + 0.970800i 0.422888π0.422888\pi
510510 0 0
511511 20.0235 + 23.8631i 0.885786 + 1.05564i
512512 −19.6934 11.1432i −0.870334 0.492462i
513513 0 0
514514 −1.32644 + 23.1589i −0.0585066 + 1.02150i
515515 −11.1676 + 9.37074i −0.492104 + 0.412924i
516516 0 0
517517 3.93500 22.3165i 0.173061 0.981478i
518518 1.09322 + 9.27548i 0.0480333 + 0.407541i
519519 0 0
520520 −8.30970 6.93178i −0.364404 0.303979i
521521 5.73358 3.31029i 0.251193 0.145026i −0.369117 0.929383i 0.620340π-0.620340\pi
0.620310 + 0.784356i 0.287007π0.287007\pi
522522 0 0
523523 −4.96107 4.16283i −0.216932 0.182028i 0.527845 0.849341i 0.323000π-0.323000\pi
−0.744778 + 0.667313i 0.767445π0.767445\pi
524524 −5.91275 + 2.56405i −0.258300 + 0.112011i
525525 0 0
526526 −4.94374 16.4555i −0.215557 0.717492i
527527 −4.88473 27.7027i −0.212782 1.20675i
528528 0 0
529529 −21.4569 7.80966i −0.932907 0.339551i
530530 3.90039 + 5.22859i 0.169422 + 0.227116i
531531 0 0
532532 −18.7018 + 13.1916i −0.810827 + 0.571927i
533533 −18.8047 −0.814522
534534 0 0
535535 15.1653 + 5.51973i 0.655654 + 0.238639i
536536 −2.78742 + 7.72789i −0.120398 + 0.333794i
537537 0 0
538538 −7.03909 23.4299i −0.303477 1.01013i
539539 −0.556387 0.321230i −0.0239653 0.0138364i
540540 0 0
541541 −28.8161 24.1796i −1.23890 1.03956i −0.997609 0.0691090i 0.977984π-0.977984\pi
−0.241292 0.970453i 0.577571π-0.577571\pi
542542 5.98650 6.35760i 0.257142 0.273082i
543543 0 0
544544 −15.7227 + 14.9776i −0.674106 + 0.642160i
545545 1.01396 + 2.78583i 0.0434332 + 0.119332i
546546 0 0
547547 1.80391 10.2305i 0.0771298 0.437425i −0.921649 0.388024i 0.873158π-0.873158\pi
0.998779 0.0494007i 0.0157311π-0.0157311\pi
548548 14.0629 + 7.02873i 0.600739 + 0.300252i
549549 0 0
550550 −1.97790 + 34.5332i −0.0843380 + 1.47250i
551551 −21.0265 + 18.7694i −0.895758 + 0.799603i
552552 0 0
553553 7.70506 + 9.18254i 0.327653 + 0.390481i
554554 −35.7836 15.3946i −1.52030 0.654054i
555555 0 0
556556 0.0139200 0.000837696i 0.000590338 3.55262e-5i
557557 −32.8112 + 11.9423i −1.39026 + 0.506012i −0.925271 0.379306i 0.876163π-0.876163\pi
−0.464985 + 0.885318i 0.653940π0.653940\pi
558558 0 0
559559 −23.4155 40.5568i −0.990370 1.71537i
560560 −7.87928 + 5.91330i −0.332961 + 0.249883i
561561 0 0
562562 9.32571 4.69482i 0.393381 0.198039i
563563 10.3868 17.9905i 0.437753 0.758210i −0.559763 0.828653i 0.689108π-0.689108\pi
0.997516 + 0.0704427i 0.0224412π0.0224412\pi
564564 0 0
565565 17.8454 3.14662i 0.750761 0.132379i
566566 11.9478 + 2.81950i 0.502202 + 0.118513i
567567 0 0
568568 −16.5827 + 9.63811i −0.695793 + 0.404406i
569569 0.315660i 0.0132332i 0.999978 + 0.00661658i 0.00210614π0.00210614\pi
−0.999978 + 0.00661658i 0.997894π0.997894\pi
570570 0 0
571571 21.2742i 0.890299i 0.895456 + 0.445150i 0.146850π0.146850\pi
−0.895456 + 0.445150i 0.853150π0.853150\pi
572572 −40.4044 + 26.6862i −1.68939 + 1.11581i
573573 0 0
574574 −3.93190 + 16.6616i −0.164114 + 0.695442i
575575 −1.65344 + 0.291546i −0.0689532 + 0.0121583i
576576 0 0
577577 11.4507 19.8332i 0.476699 0.825667i −0.522944 0.852367i 0.675166π-0.675166\pi
0.999643 + 0.0266997i 0.00849980π0.00849980\pi
578578 −1.44011 2.86061i −0.0599006 0.118986i
579579 0 0
580580 −8.80869 + 8.34276i −0.365761 + 0.346414i
581581 0.972325 + 1.68412i 0.0403389 + 0.0698689i
582582 0 0
583583 27.4286 9.98318i 1.13597 0.413461i
584584 0.0971304 + 33.5621i 0.00401929 + 1.38881i
585585 0 0
586586 5.54692 12.8934i 0.229141 0.532621i
587587 −9.56479 11.3989i −0.394781 0.470482i 0.531640 0.846970i 0.321576π-0.321576\pi
−0.926421 + 0.376488i 0.877131π0.877131\pi
588588 0 0
589589 19.7736 25.0862i 0.814757 1.03366i
590590 −2.09303 0.119879i −0.0861686 0.00493535i
591591 0 0
592592 −5.49702 + 8.42847i −0.225926 + 0.346408i
593593 0.999120 5.66629i 0.0410289 0.232687i −0.957397 0.288776i 0.906752π-0.906752\pi
0.998426 + 0.0560888i 0.0178630π0.0178630\pi
594594 0 0
595595 3.23348 + 8.88393i 0.132560 + 0.364205i
596596 13.7555 18.5515i 0.563448 0.759898i
597597 0 0
598598 −1.71113 1.61125i −0.0699732 0.0658889i
599599 12.8004 + 10.7408i 0.523008 + 0.438856i 0.865679 0.500599i 0.166887π-0.166887\pi
−0.342671 + 0.939456i 0.611331π0.611331\pi
600600 0 0
601601 −2.32187 1.34053i −0.0947110 0.0546814i 0.451896 0.892070i 0.350748π-0.350748\pi
−0.546607 + 0.837389i 0.684081π0.684081\pi
602602 −40.8307 + 12.2668i −1.66414 + 0.499959i
603603 0 0
604604 2.19535 7.38480i 0.0893274 0.300483i
605605 −21.3737 7.77940i −0.868965 0.316277i
606606 0 0
607607 −35.3587 −1.43517 −0.717583 0.696473i 0.754752π-0.754752\pi
−0.717583 + 0.696473i 0.754752π0.754752\pi
608608 −24.5770 1.99316i −0.996728 0.0808332i
609609 0 0
610610 6.81471 5.08359i 0.275920 0.205829i
611611 −14.6276 5.32402i −0.591770 0.215387i
612612 0 0
613613 −4.31337 24.4623i −0.174215 0.988024i −0.939046 0.343792i 0.888288π-0.888288\pi
0.764831 0.644232i 0.222823π-0.222823\pi
614614 −34.0384 + 10.2262i −1.37368 + 0.412697i
615615 0 0
616616 15.1967 + 41.3795i 0.612292 + 1.66723i
617617 2.84603 + 2.38810i 0.114577 + 0.0961415i 0.698276 0.715829i 0.253951π-0.253951\pi
−0.583699 + 0.811970i 0.698395π0.698395\pi
618618 0 0
619619 30.3051 17.4967i 1.21807 0.703250i 0.253562 0.967319i 0.418398π-0.418398\pi
0.964504 + 0.264069i 0.0850646π0.0850646\pi
620620 8.18943 11.0447i 0.328896 0.443568i
621621 0 0
622622 29.1236 3.43254i 1.16775 0.137632i
623623 7.83076 44.4105i 0.313733 1.77927i
624624 0 0
625625 9.63126 8.08159i 0.385251 0.323264i
626626 −24.3826 1.39652i −0.974524 0.0558163i
627627 0 0
628628 37.7983 + 4.34408i 1.50831 + 0.173347i
629629 6.20725 + 7.39752i 0.247499 + 0.294958i
630630 0 0
631631 −32.6231 5.75233i −1.29871 0.228997i −0.518801 0.854895i 0.673621π-0.673621\pi
−0.779904 + 0.625899i 0.784732π0.784732\pi
632632 0.0373759 + 12.9148i 0.00148673 + 0.513721i
633633 0 0
634634 −5.85744 3.84441i −0.232629 0.152681i
635635 6.97769 + 12.0857i 0.276901 + 0.479607i
636636 0 0
637637 −0.283679 + 0.338076i −0.0112398 + 0.0133951i
638638 24.4114 + 48.4904i 0.966456 + 1.91975i
639639 0 0
640640 −10.5999 0.545581i −0.418999 0.0215660i
641641 −11.5354 + 2.03399i −0.455619 + 0.0803379i −0.396748 0.917928i 0.629861π-0.629861\pi
−0.0588712 + 0.998266i 0.518750π0.518750\pi
642642 0 0
643643 −14.1267 + 38.8127i −0.557101 + 1.53062i 0.266720 + 0.963774i 0.414060π0.414060\pi
−0.823822 + 0.566849i 0.808162π0.808162\pi
644644 −1.78540 + 1.17922i −0.0703548 + 0.0464678i
645645 0 0
646646 −8.68188 + 22.0129i −0.341584 + 0.866088i
647647 15.5407i 0.610967i −0.952197 0.305484i 0.901182π-0.901182\pi
0.952197 0.305484i 0.0988181π-0.0988181\pi
648648 0 0
649649 −3.20848 + 8.81521i −0.125944 + 0.346027i
650650 23.1256 + 5.45731i 0.907060 + 0.214053i
651651 0 0
652652 −3.07612 12.8685i −0.120470 0.503968i
653653 9.90157 17.1500i 0.387478 0.671132i −0.604631 0.796506i 0.706679π-0.706679\pi
0.992110 + 0.125373i 0.0400128π0.0400128\pi
654654 0 0
655655 −1.94320 + 2.31581i −0.0759270 + 0.0904863i
656656 −14.7521 + 11.0712i −0.575971 + 0.432259i
657657 0 0
658658 −7.77577 + 11.8474i −0.303131 + 0.461858i
659659 20.5503 7.47970i 0.800526 0.291368i 0.0908217 0.995867i 0.471051π-0.471051\pi
0.709705 + 0.704499i 0.248828π0.248828\pi
660660 0 0
661661 39.3132 + 6.93199i 1.52911 + 0.269623i 0.874005 0.485917i 0.161514π-0.161514\pi
0.655103 + 0.755540i 0.272625π0.272625\pi
662662 −17.6622 7.59854i −0.686462 0.295326i
663663 0 0
664664 −0.357851 + 2.06439i −0.0138873 + 0.0801139i
665665 −5.08061 + 9.45699i −0.197017 + 0.366726i
666666 0 0
667667 −2.01860 + 1.69381i −0.0781605 + 0.0655845i
668668 −1.48057 0.739997i −0.0572850 0.0286313i
669669 0 0
670670 0.451063 + 3.82707i 0.0174261 + 0.147853i
671671 −13.0116 35.7491i −0.502308 1.38008i
672672 0 0
673673 22.9216 13.2338i 0.883561 0.510124i 0.0117304 0.999931i 0.496266π-0.496266\pi
0.871831 + 0.489807i 0.162933π0.162933\pi
674674 7.13485 7.57712i 0.274824 0.291860i
675675 0 0
676676 2.88937 + 6.66293i 0.111129 + 0.256266i
677677 20.4055 + 11.7811i 0.784248 + 0.452786i 0.837934 0.545772i 0.183764π-0.183764\pi
−0.0536855 + 0.998558i 0.517097π0.517097\pi
678678 0 0
679679 1.72957 + 9.80886i 0.0663747 + 0.376429i
680680 −3.45606 + 9.58163i −0.132534 + 0.367439i
681681 0 0
682682 −36.7879 49.3153i −1.40868 1.88838i
683683 12.5259 0.479292 0.239646 0.970860i 0.422969π-0.422969\pi
0.239646 + 0.970860i 0.422969π0.422969\pi
684684 0 0
685685 7.37462 0.281770
686686 15.7795 + 21.1529i 0.602464 + 0.807622i
687687 0 0
688688 −42.2469 18.0305i −1.61065 0.687407i
689689 −3.48178 19.7461i −0.132645 0.752268i
690690 0 0
691691 −17.6035 10.1634i −0.669667 0.386633i 0.126283 0.991994i 0.459695π-0.459695\pi
−0.795951 + 0.605362i 0.793029π0.793029\pi
692692 −10.4682 + 4.53953i −0.397943 + 0.172567i
693693 0 0
694694 7.18098 7.62612i 0.272586 0.289484i
695695 0.00566495 0.00327066i 0.000214884 0.000124063i
696696 0 0
697697 6.05392 + 16.6330i 0.229309 + 0.630020i
698698 −3.34217 28.3568i −0.126503 1.07332i
699699 0 0
700700 9.67073 19.3490i 0.365519 0.731323i
701701 18.7774 15.7561i 0.709211 0.595099i −0.215167 0.976577i 0.569029π-0.569029\pi
0.924378 + 0.381479i 0.124585π0.124585\pi
702702 0 0
703703 −1.57274 + 10.8521i −0.0593169 + 0.409295i
704704 −15.9853 + 44.7230i −0.602469 + 1.68556i
705705 0 0
706706 −27.7768 11.9500i −1.04539 0.449743i
707707 −25.0910 4.42422i −0.943645 0.166390i
708708 0 0
709709 24.6478 8.97106i 0.925667 0.336915i 0.165176 0.986264i 0.447181π-0.447181\pi
0.760491 + 0.649349i 0.224958π0.224958\pi
710710 −4.93664 + 7.52159i −0.185269 + 0.282280i
711711 0 0
712712 37.1287 31.3382i 1.39146 1.17445i
713713 1.91960 2.28769i 0.0718894 0.0856745i
714714 0 0
715715 −11.3567 + 19.6704i −0.424718 + 0.735632i
716716 8.50717 2.03358i 0.317928 0.0759984i
717717 0 0
718718 −28.5728 6.74276i −1.06633 0.251638i
719719 4.64524 12.7627i 0.173238 0.475968i −0.822438 0.568854i 0.807387π-0.807387\pi
0.995677 + 0.0928858i 0.0296091π0.0296091\pi
720720 0 0
721721 40.7943i 1.51926i
722722 −25.2126 + 9.29122i −0.938314 + 0.345784i
723723 0 0
724724 8.87815 + 13.4420i 0.329954 + 0.499568i
725725 9.11127 25.0330i 0.338384 0.929703i
726726 0 0
727727 −18.5330 + 3.26787i −0.687352 + 0.121199i −0.506407 0.862295i 0.669027π-0.669027\pi
−0.180945 + 0.983493i 0.557916π0.557916\pi
728728 29.8058 5.34455i 1.10468 0.198082i
729729 0 0
730730 7.07912 + 14.0618i 0.262010 + 0.520452i
731731 −28.3347 + 33.7680i −1.04800 + 1.24896i
732732 0 0
733733 11.3569 + 19.6706i 0.419475 + 0.726552i 0.995887 0.0906076i 0.0288809π-0.0288809\pi
−0.576412 + 0.817159i 0.695548π0.695548\pi
734734 −13.7951 9.05411i −0.509185 0.334193i
735735 0 0
736736 −2.29098 0.256582i −0.0844466 0.00945774i
737737 16.9814 + 2.99429i 0.625520 + 0.110296i
738738 0 0
739739 22.4003 + 26.6956i 0.824008 + 0.982015i 0.999997 0.00237743i 0.000756759π-0.000756759\pi
−0.175989 + 0.984392i 0.556312π0.556312\pi
740740 −0.538927 + 4.68926i −0.0198114 + 0.172381i
741741 0 0
742742 −18.2238 1.04377i −0.669015 0.0383182i
743743 −18.5624 + 15.5757i −0.680987 + 0.571416i −0.916295 0.400505i 0.868835π-0.868835\pi
0.235307 + 0.971921i 0.424390π0.424390\pi
744744 0 0
745745 1.88117 10.6686i 0.0689207 0.390869i
746746 36.9636 4.35658i 1.35333 0.159506i
747747 0 0
748748 36.6120 + 27.1470i 1.33867 + 0.992591i
749749 −39.1102 + 22.5803i −1.42906 + 0.825065i
750750 0 0
751751 −25.2781 21.2109i −0.922412 0.773995i 0.0520279 0.998646i 0.483432π-0.483432\pi
−0.974439 + 0.224650i 0.927876π0.927876\pi
752752 −14.6097 + 4.43535i −0.532761 + 0.161741i
753753 0 0
754754 35.7154 10.7300i 1.30068 0.390765i
755755 −0.627539 3.55895i −0.0228385 0.129523i
756756 0 0
757757 18.3827 + 6.69076i 0.668131 + 0.243180i 0.653743 0.756717i 0.273198π-0.273198\pi
0.0143881 + 0.999896i 0.495420π0.495420\pi
758758 17.1865 12.8207i 0.624243 0.465668i
759759 0 0
760760 −10.7301 + 4.31777i −0.389223 + 0.156622i
761761 7.99819 0.289934 0.144967 0.989436i 0.453692π-0.453692\pi
0.144967 + 0.989436i 0.453692π0.453692\pi
762762 0 0
763763 −7.79556 2.83735i −0.282218 0.102719i
764764 −6.16001 1.83124i −0.222861 0.0662521i
765765 0 0
766766 −42.1089 + 12.6509i −1.52146 + 0.457094i
767767 5.58073 + 3.22204i 0.201509 + 0.116341i
768768 0 0
769769 9.49371 + 7.96617i 0.342352 + 0.287267i 0.797710 0.603041i 0.206044π-0.206044\pi
−0.455358 + 0.890308i 0.650489π0.650489\pi
770770 15.0541 + 14.1754i 0.542512 + 0.510845i
771771 0 0
772772 9.56488 + 7.09215i 0.344248 + 0.255252i
773773 11.5697 + 31.7874i 0.416132 + 1.14331i 0.953875 + 0.300204i 0.0970547π0.0970547\pi
−0.537743 + 0.843109i 0.680723π0.680723\pi
774774 0 0
775775 −5.24256 + 29.7320i −0.188318 + 1.06801i
776776 −5.33866 + 9.30893i −0.191647 + 0.334171i
777777 0 0
778778 48.4367 + 2.77423i 1.73654 + 0.0994611i
779779 −9.51221 + 17.7059i −0.340810 + 0.634381i
780780 0 0
781781 25.8775 + 30.8397i 0.925971 + 1.10353i
782782 −0.874297 + 2.03224i −0.0312648 + 0.0726726i
783783 0 0
784784 −0.0235015 + 0.432232i −0.000839339 + 0.0154369i
785785 16.7706 6.10401i 0.598570 0.217862i
786786 0 0
787787 7.27170 + 12.5950i 0.259208 + 0.448962i 0.966030 0.258430i 0.0832051π-0.0832051\pi
−0.706822 + 0.707392i 0.749872π0.749872\pi
788788 −19.2264 20.3002i −0.684914 0.723166i
789789 0 0
790790 2.72405 + 5.41102i 0.0969175 + 0.192515i
791791 −25.3535 + 43.9135i −0.901466 + 1.56139i
792792 0 0
793793 −25.7362 + 4.53799i −0.913920 + 0.161149i
794794 2.94185 12.4662i 0.104402 0.442409i
795795 0 0
796796 10.8646 + 16.4496i 0.385086 + 0.583042i
797797 3.14479i 0.111394i 0.998448 + 0.0556971i 0.0177381π0.0177381\pi
−0.998448 + 0.0556971i 0.982262π0.982262\pi
798798 0 0
799799 14.6523i 0.518362i
800800 21.3547 9.33396i 0.755004 0.330005i
801801 0 0
802802 −10.9316 2.57971i −0.386010 0.0910928i
803803 69.3755 12.2328i 2.44821 0.431685i
804804 0 0
805805 −0.501835 + 0.869205i −0.0176874 + 0.0306354i
806806 −37.7498 + 19.0043i −1.32968 + 0.669398i
807807 0 0
808808 −17.7055 20.9769i −0.622876 0.737966i
809809 7.09419 + 12.2875i 0.249419 + 0.432006i 0.963365 0.268195i 0.0864272π-0.0864272\pi
−0.713946 + 0.700201i 0.753094π0.753094\pi
810810 0 0
811811 5.23170 1.90418i 0.183710 0.0668649i −0.248527 0.968625i 0.579947π-0.579947\pi
0.432237 + 0.901760i 0.357724π0.357724\pi
812812 −2.03940 33.8886i −0.0715690 1.18926i
813813 0 0
814814 19.4017 + 8.34689i 0.680030 + 0.292558i
815815 −3.98936 4.75434i −0.139741 0.166537i
816816 0 0
817817 −50.0316 + 1.53197i −1.75038 + 0.0535967i
818818 2.21104 38.6036i 0.0773072 1.34974i
819819 0 0
820820 −3.86800 + 7.73902i −0.135076 + 0.270258i
821821 4.88607 27.7103i 0.170525 0.967096i −0.772658 0.634823i 0.781073π-0.781073\pi
0.943183 0.332274i 0.107816π-0.107816\pi
822822 0 0
823823 −13.8813 38.1386i −0.483872 1.32943i −0.906148 0.422961i 0.860991π-0.860991\pi
0.422276 0.906467i 0.361231π-0.361231\pi
824824 28.1542 33.7508i 0.980800 1.17577i
825825 0 0
826826 4.02172 4.27102i 0.139934 0.148608i
827827 −28.7314 24.1085i −0.999088 0.838334i −0.0122298 0.999925i 0.503893π-0.503893\pi
−0.986858 + 0.161591i 0.948337π0.948337\pi
828828 0 0
829829 29.0901 + 16.7952i 1.01034 + 0.583320i 0.911291 0.411762i 0.135087π-0.135087\pi
0.0990493 + 0.995083i 0.468420π0.468420\pi
830830 0.282777 + 0.941236i 0.00981534 + 0.0326708i
831831 0 0
832832 28.3481 + 16.1487i 0.982794 + 0.559857i
833833 0.390359 + 0.142079i 0.0135252 + 0.00492275i
834834 0 0
835835 −0.776413 −0.0268689
836836 4.68868 + 51.5425i 0.162161 + 1.78264i
837837 0 0
838838 −11.3974 15.2785i −0.393715 0.527788i
839839 −2.98358 1.08593i −0.103005 0.0374906i 0.290004 0.957026i 0.406343π-0.406343\pi
−0.393008 + 0.919535i 0.628566π0.628566\pi
840840 0 0
841841 −2.22455 12.6160i −0.0767085 0.435035i
842842 15.7652 + 52.4752i 0.543306 + 1.80842i
843843 0 0
844844 11.5933 + 26.7343i 0.399058 + 0.920234i
845845 2.60963 + 2.18974i 0.0897741 + 0.0753294i
846846 0 0
847847 55.1211 31.8242i 1.89398 1.09349i
848848 −14.3569 13.4407i −0.493018 0.461556i
849849 0 0
850850 −2.61791 22.2118i −0.0897936 0.761859i
851851 −0.178022 + 1.00961i −0.00610253 + 0.0346091i
852852 0 0
853853 31.0068 26.0178i 1.06165 0.890833i 0.0673834 0.997727i 0.478535π-0.478535\pi
0.994270 + 0.106894i 0.0340905π0.0340905\pi
854854 −1.36041 + 23.7520i −0.0465522 + 0.812778i
855855 0 0
856856 −47.9413 8.31036i −1.63860 0.284042i
857857 −4.59201 5.47255i −0.156860 0.186939i 0.681891 0.731454i 0.261158π-0.261158\pi
−0.838751 + 0.544515i 0.816714π0.816714\pi
858858 0 0
859859 33.5177 + 5.91007i 1.14361 + 0.201649i 0.713184 0.700977i 0.247253π-0.247253\pi
0.430425 + 0.902626i 0.358364π0.358364\pi
860860 −21.5074 + 1.29431i −0.733398 + 0.0441355i
861861 0 0
862862 30.7073 46.7864i 1.04589 1.59355i
863863 −3.20642 5.55368i −0.109148 0.189049i 0.806277 0.591538i 0.201479π-0.201479\pi
−0.915425 + 0.402488i 0.868146π0.868146\pi
864864 0 0
865865 −3.44034 + 4.10003i −0.116975 + 0.139405i
866866 −45.9422 + 23.1286i −1.56118 + 0.785941i
867867 0 0
868868 8.94529 + 37.4213i 0.303623 + 1.27016i
869869 26.6958 4.70719i 0.905593 0.159680i
870870 0 0
871871 4.05124 11.1307i 0.137271 0.377149i
872872 −4.49138 7.72757i −0.152097 0.261689i
873873 0 0
874874 −2.38266 + 0.796109i −0.0805948 + 0.0269288i
875875 22.4609i 0.759317i
876876 0 0
877877 2.85384 7.84086i 0.0963673 0.264767i −0.882137 0.470993i 0.843896π-0.843896\pi
0.978504 + 0.206226i 0.0661181π0.0661181\pi
878878 3.69304 15.6494i 0.124634 0.528142i
879879 0 0
880880 2.67171 + 22.1175i 0.0900634 + 0.745580i
881881 9.44775 16.3640i 0.318303 0.551316i −0.661831 0.749653i 0.730220π-0.730220\pi
0.980134 + 0.198336i 0.0635538π0.0635538\pi
882882 0 0
883883 7.40855 8.82916i 0.249317 0.297125i −0.626842 0.779146i 0.715653π-0.715653\pi
0.876159 + 0.482021i 0.160097π0.160097\pi
884884 22.7320 21.5296i 0.764561 0.724119i
885885 0 0
886886 −26.7536 17.5592i −0.898805 0.589912i
887887 15.5662 5.66563i 0.522661 0.190233i −0.0671973 0.997740i 0.521406π-0.521406\pi
0.589859 + 0.807507i 0.299183π0.299183\pi
888888 0 0
889889 −38.4579 6.78117i −1.28984 0.227433i
890890 9.00670 20.9354i 0.301905 0.701756i
891891 0 0
892892 −10.8404 1.24587i −0.362964 0.0417147i
893893 −12.4122 + 11.0798i −0.415358 + 0.370772i
894894 0 0
895895 3.14303 2.63731i 0.105060 0.0881556i
896896 20.2357 21.7409i 0.676027 0.726311i
897897 0 0
898898 −43.2090 + 5.09266i −1.44190 + 0.169944i
899899 16.2063 + 44.5265i 0.540511 + 1.48504i
900900 0 0
901901 −16.3448 + 9.43668i −0.544525 + 0.314381i
902902 28.1852 + 26.5400i 0.938463 + 0.883685i
903903 0 0
904904 −51.2830 + 18.8337i −1.70565 + 0.626401i
905905 6.54409 + 3.77823i 0.217533 + 0.125593i
906906 0 0
907907 −3.05694 17.3368i −0.101504 0.575658i −0.992559 0.121763i 0.961145π-0.961145\pi
0.891055 0.453895i 0.149966π-0.149966\pi
908908 −2.70044 + 9.08385i −0.0896173 + 0.301458i
909909 0 0
910910 11.3853 8.49312i 0.377419 0.281544i
911911 30.1503 0.998923 0.499462 0.866336i 0.333531π-0.333531\pi
0.499462 + 0.866336i 0.333531π0.333531\pi
912912 0 0
913913 4.39769 0.145542
914914 27.5105 20.5220i 0.909965 0.678809i
915915 0 0
916916 −14.6509 + 49.2832i −0.484079 + 1.62836i
917917 −1.46897 8.33094i −0.0485097 0.275112i
918918 0 0
919919 11.6050 + 6.70014i 0.382813 + 0.221017i 0.679041 0.734100i 0.262396π-0.262396\pi
−0.296228 + 0.955117i 0.595729π0.595729\pi
920920 −1.01507 + 0.372786i −0.0334659 + 0.0122904i
921921 0 0
922922 38.1608 + 35.9333i 1.25676 + 1.18340i
923923 23.9497 13.8274i 0.788313 0.455133i
924924 0 0
925925 −3.54476 9.73915i −0.116551 0.320221i
926926 29.4648 3.47276i 0.968275 0.114122i
927927 0 0
928928 21.7010 29.4450i 0.712371 0.966579i
929929 −23.6357 + 19.8327i −0.775461 + 0.650689i −0.942101 0.335329i 0.891153π-0.891153\pi
0.166640 + 0.986018i 0.446708π0.446708\pi
930930 0 0
931931 0.174825 + 0.438117i 0.00572966 + 0.0143587i
932932 −28.7199 3.30071i −0.940750 0.108118i
933933 0 0
934934 −22.0821 + 51.3283i −0.722550 + 1.67951i
935935 21.0549 + 3.71255i 0.688569 + 0.121413i
936936 0 0
937937 −24.9043 + 9.06443i −0.813588 + 0.296122i −0.715105 0.699017i 0.753621π-0.753621\pi
−0.0984830 + 0.995139i 0.531399π0.531399\pi
938938 −9.01511 5.91688i −0.294354 0.193193i
939939 0 0
940940 −5.19988 + 4.92484i −0.169602 + 0.160630i
941941 19.3496 23.0600i 0.630780 0.751734i −0.352104 0.935961i 0.614534π-0.614534\pi
0.982884 + 0.184227i 0.0589781π0.0589781\pi
942942 0 0
943943 −0.939566 + 1.62738i −0.0305965 + 0.0529947i
944944 6.27499 0.757996i 0.204233 0.0246707i
945945 0 0
946946 −22.1438 + 93.8354i −0.719957 + 3.05085i
947947 −8.91757 + 24.5008i −0.289782 + 0.796170i 0.706314 + 0.707898i 0.250357π0.250357\pi
−0.996096 + 0.0882717i 0.971866π0.971866\pi
948948 0 0
949949 48.3914i 1.57085i
950950 16.8363 19.0138i 0.546243 0.616890i
951951 0 0
952952 −14.3229 24.6430i −0.464208 0.798685i
953953 0.413730 1.13671i 0.0134020 0.0368217i −0.932811 0.360365i 0.882652π-0.882652\pi
0.946213 + 0.323544i 0.104874π0.104874\pi
954954 0 0
955955 −2.96869 + 0.523460i −0.0960646 + 0.0169388i
956956 7.05669 + 29.5206i 0.228230 + 0.954764i
957957 0 0
958958 16.2182 8.16470i 0.523987 0.263790i
959959 −13.2648 + 15.8084i −0.428343 + 0.510479i
960960 0 0
961961 −11.3503 19.6592i −0.366138 0.634169i
962962 7.96096 12.1295i 0.256672 0.391071i
963963 0 0
964964 −11.2021 + 0.674137i −0.360796 + 0.0217125i
965965 5.50060 + 0.969904i 0.177071 + 0.0312223i
966966 0 0
967967 22.9011 + 27.2925i 0.736451 + 0.877668i 0.996118 0.0880305i 0.0280573π-0.0280573\pi
−0.259667 + 0.965698i 0.583613π0.583613\pi
968968 67.5675 + 11.7125i 2.17170 + 0.376452i
969969 0 0
970970 −0.287837 + 5.02548i −0.00924188 + 0.161358i
971971 10.6081 8.90129i 0.340432 0.285656i −0.456503 0.889722i 0.650898π-0.650898\pi
0.796934 + 0.604066i 0.206454π0.206454\pi
972972 0 0
973973 −0.00317855 + 0.0180265i −0.000101900 + 0.000577902i
974974 −5.60184 47.5291i −0.179495 1.52293i
975975 0 0
976976 −17.5180 + 18.7122i −0.560738 + 0.598961i
977977 −6.07278 + 3.50612i −0.194285 + 0.112171i −0.593987 0.804475i 0.702447π-0.702447\pi
0.399702 + 0.916645i 0.369114π0.369114\pi
978978 0 0
979979 −78.1215 65.5517i −2.49677 2.09504i
980980 0.0807831 + 0.186287i 0.00258052 + 0.00595073i
981981 0 0
982982 −13.1132 43.6478i −0.418459 1.39286i
983983 −1.42112 8.05956i −0.0453266 0.257060i 0.953721 0.300693i 0.0972179π-0.0972179\pi
−0.999048 + 0.0436329i 0.986107π0.986107\pi
984984 0 0
985985 −12.3243 4.48570i −0.392686 0.142926i
986986 −20.9890 28.1364i −0.668425 0.896045i
987987 0 0
988988 35.4276 + 2.97635i 1.12710 + 0.0946904i
989989 −4.67977 −0.148808
990990 0 0
991991 50.4787 + 18.3727i 1.60351 + 0.583629i 0.980141 0.198300i 0.0635420π-0.0635420\pi
0.623367 + 0.781929i 0.285764π0.285764\pi
992992 −18.4255 + 37.1338i −0.585011 + 1.17900i
993993 0 0
994994 −7.24384 24.1114i −0.229761 0.764768i
995995 8.00833 + 4.62361i 0.253881 + 0.146578i
996996 0 0
997997 8.97721 + 7.53277i 0.284311 + 0.238565i 0.773778 0.633456i 0.218364π-0.218364\pi
−0.489467 + 0.872022i 0.662809π0.662809\pi
998998 −13.7777 + 14.6317i −0.436125 + 0.463160i
999999 0 0
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 684.2.cf.c.127.3 60
3.2 odd 2 228.2.w.a.127.8 yes 60
4.3 odd 2 684.2.cf.b.127.8 60
12.11 even 2 228.2.w.b.127.3 yes 60
19.3 odd 18 684.2.cf.b.307.8 60
57.41 even 18 228.2.w.b.79.3 yes 60
76.3 even 18 inner 684.2.cf.c.307.3 60
228.155 odd 18 228.2.w.a.79.8 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
228.2.w.a.79.8 60 228.155 odd 18
228.2.w.a.127.8 yes 60 3.2 odd 2
228.2.w.b.79.3 yes 60 57.41 even 18
228.2.w.b.127.3 yes 60 12.11 even 2
684.2.cf.b.127.8 60 4.3 odd 2
684.2.cf.b.307.8 60 19.3 odd 18
684.2.cf.c.127.3 60 1.1 even 1 trivial
684.2.cf.c.307.3 60 76.3 even 18 inner