Properties

Label 850.2.v.a.607.3
Level 850850
Weight 22
Character 850.607
Analytic conductor 6.7876.787
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [850,2,Mod(107,850)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(850, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("850.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 850=25217 850 = 2 \cdot 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 850.v (of order 1616, 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: 6.787284171816.78728417181
Analytic rank: 00
Dimension: 2424
Relative dimension: 33 over Q(ζ16)\Q(\zeta_{16})
Twist minimal: yes
Sato-Tate group: SU(2)[C16]\mathrm{SU}(2)[C_{16}]

Embedding invariants

Embedding label 607.3
Character χ\chi == 850.607
Dual form 850.2.v.a.843.3

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+(0.382683+0.923880i)q2+(0.4373192.19855i)q3+(0.7071070.707107i)q4+(1.86384+1.24538i)q6+(1.94597+1.30026i)q7+(0.9238800.382683i)q8+(1.870750.774889i)q9+(2.082423.11656i)q11+(1.86384+1.24538i)q12+1.83794q13+(1.94597+1.30026i)q14+1.00000iq16+(2.84065+2.98843i)q17+(1.431811.43181i)q18+(6.193462.56542i)q19+(3.709703.70970i)q21+(2.08242+3.11656i)q22+(5.00678+0.995910i)q23+(0.4373192.19855i)q24+(0.703348+1.69803i)q26+(1.214391.81746i)q27+(0.4565902.29543i)q28+(0.598780+0.119105i)q29+(2.46039+3.68223i)q31+(0.9238800.382683i)q32+(5.941245.94124i)q33+(1.673883.76804i)q34+(0.774889+1.87075i)q36+(1.649150.328036i)q37+6.70375iq38+(0.8037654.04080i)q39+(3.389710.674255i)q41+(2.00768+4.84696i)q42+(0.926479+2.23672i)q43+(3.67624+0.731249i)q44+(0.9959105.00678i)q4610.6121iq47+(2.19855+0.437319i)q48+(0.5826391.40662i)q49+(5.32794+7.55222i)q51+(1.299621.29962i)q52+(1.76897+0.732730i)q53+(1.21439+1.81746i)q54+(2.29543+0.456590i)q56+(2.9316814.7386i)q57+(0.339182+0.507621i)q58+(4.8616911.7372i)q59+(1.293146.50106i)q61+(4.34349+0.863974i)q62+(2.632873.94037i)q63+(0.7071070.707107i)q64+(7.762613.21538i)q66+(0.9831640.983164i)q67+(4.121780.104492i)q68+11.4432iq69+(7.078984.73002i)q712.02488q72+(3.82200+2.55378i)q73+(0.9341691.39808i)q74+(6.193462.56542i)q76+(8.104673.35707i)q77+(3.42563+2.28893i)q78+(4.286632.86424i)q79+(7.760147.76014i)q81+(0.674255+3.38971i)q82+(5.34887+12.9133i)q835.24631q842.42101q86+(0.5237161.26436i)q87+(0.7312493.67624i)q88+(11.096311.0963i)q89+(3.57658+2.38979i)q91+(4.24454+2.83611i)q92+(9.171563.79898i)q93+(9.80427+4.06106i)q94+(1.24538+1.86384i)q96+(9.355646.25124i)q97+1.52251q98+(6.31067+4.21666i)q99+O(q100)q+(-0.382683 + 0.923880i) q^{2} +(0.437319 - 2.19855i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.86384 + 1.24538i) q^{6} +(1.94597 + 1.30026i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-1.87075 - 0.774889i) q^{9} +(2.08242 - 3.11656i) q^{11} +(-1.86384 + 1.24538i) q^{12} +1.83794 q^{13} +(-1.94597 + 1.30026i) q^{14} +1.00000i q^{16} +(-2.84065 + 2.98843i) q^{17} +(1.43181 - 1.43181i) q^{18} +(6.19346 - 2.56542i) q^{19} +(3.70970 - 3.70970i) q^{21} +(2.08242 + 3.11656i) q^{22} +(-5.00678 + 0.995910i) q^{23} +(-0.437319 - 2.19855i) q^{24} +(-0.703348 + 1.69803i) q^{26} +(1.21439 - 1.81746i) q^{27} +(-0.456590 - 2.29543i) q^{28} +(0.598780 + 0.119105i) q^{29} +(2.46039 + 3.68223i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-5.94124 - 5.94124i) q^{33} +(-1.67388 - 3.76804i) q^{34} +(0.774889 + 1.87075i) q^{36} +(-1.64915 - 0.328036i) q^{37} +6.70375i q^{38} +(0.803765 - 4.04080i) q^{39} +(3.38971 - 0.674255i) q^{41} +(2.00768 + 4.84696i) q^{42} +(0.926479 + 2.23672i) q^{43} +(-3.67624 + 0.731249i) q^{44} +(0.995910 - 5.00678i) q^{46} -10.6121i q^{47} +(2.19855 + 0.437319i) q^{48} +(-0.582639 - 1.40662i) q^{49} +(5.32794 + 7.55222i) q^{51} +(-1.29962 - 1.29962i) q^{52} +(1.76897 + 0.732730i) q^{53} +(1.21439 + 1.81746i) q^{54} +(2.29543 + 0.456590i) q^{56} +(-2.93168 - 14.7386i) q^{57} +(-0.339182 + 0.507621i) q^{58} +(4.86169 - 11.7372i) q^{59} +(-1.29314 - 6.50106i) q^{61} +(-4.34349 + 0.863974i) q^{62} +(-2.63287 - 3.94037i) q^{63} +(0.707107 - 0.707107i) q^{64} +(7.76261 - 3.21538i) q^{66} +(0.983164 - 0.983164i) q^{67} +(4.12178 - 0.104492i) q^{68} +11.4432i q^{69} +(7.07898 - 4.73002i) q^{71} -2.02488 q^{72} +(-3.82200 + 2.55378i) q^{73} +(0.934169 - 1.39808i) q^{74} +(-6.19346 - 2.56542i) q^{76} +(8.10467 - 3.35707i) q^{77} +(3.42563 + 2.28893i) q^{78} +(-4.28663 - 2.86424i) q^{79} +(-7.76014 - 7.76014i) q^{81} +(-0.674255 + 3.38971i) q^{82} +(-5.34887 + 12.9133i) q^{83} -5.24631 q^{84} -2.42101 q^{86} +(0.523716 - 1.26436i) q^{87} +(0.731249 - 3.67624i) q^{88} +(-11.0963 - 11.0963i) q^{89} +(3.57658 + 2.38979i) q^{91} +(4.24454 + 2.83611i) q^{92} +(9.17156 - 3.79898i) q^{93} +(9.80427 + 4.06106i) q^{94} +(-1.24538 + 1.86384i) q^{96} +(9.35564 - 6.25124i) q^{97} +1.52251 q^{98} +(-6.31067 + 4.21666i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+8q932q1316q18+48q27+16q29+16q318q3316q34+16q37+32q39+48q4148q42+16q4316q44+32q46+8q48+16q49+24q99+O(q100) 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/850Z)×\left(\mathbb{Z}/850\mathbb{Z}\right)^\times.

nn 477477 751751
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) e(1316)e\left(\frac{13}{16}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.382683 + 0.923880i −0.270598 + 0.653281i
33 0.437319 2.19855i 0.252486 1.26934i −0.621511 0.783405i 0.713481π-0.713481\pi
0.873998 0.485930i 0.161519π-0.161519\pi
44 −0.707107 0.707107i −0.353553 0.353553i
55 0 0
66 1.86384 + 1.24538i 0.760911 + 0.508424i
77 1.94597 + 1.30026i 0.735509 + 0.491452i 0.866029 0.499994i 0.166665π-0.166665\pi
−0.130519 + 0.991446i 0.541665π0.541665\pi
88 0.923880 0.382683i 0.326641 0.135299i
99 −1.87075 0.774889i −0.623583 0.258296i
1010 0 0
1111 2.08242 3.11656i 0.627873 0.939679i −0.372061 0.928208i 0.621349π-0.621349\pi
0.999934 0.0114704i 0.00365123π-0.00365123\pi
1212 −1.86384 + 1.24538i −0.538045 + 0.359510i
1313 1.83794 0.509752 0.254876 0.966974i 0.417965π-0.417965\pi
0.254876 + 0.966974i 0.417965π0.417965\pi
1414 −1.94597 + 1.30026i −0.520084 + 0.347509i
1515 0 0
1616 1.00000i 0.250000i
1717 −2.84065 + 2.98843i −0.688960 + 0.724800i
1818 1.43181 1.43181i 0.337481 0.337481i
1919 6.19346 2.56542i 1.42088 0.588547i 0.465797 0.884892i 0.345768π-0.345768\pi
0.955081 + 0.296345i 0.0957678π0.0957678\pi
2020 0 0
2121 3.70970 3.70970i 0.809523 0.809523i
2222 2.08242 + 3.11656i 0.443973 + 0.664453i
2323 −5.00678 + 0.995910i −1.04398 + 0.207661i −0.687157 0.726509i 0.741142π-0.741142\pi
−0.356828 + 0.934170i 0.616142π0.616142\pi
2424 −0.437319 2.19855i −0.0892674 0.448778i
2525 0 0
2626 −0.703348 + 1.69803i −0.137938 + 0.333011i
2727 1.21439 1.81746i 0.233710 0.349771i
2828 −0.456590 2.29543i −0.0862874 0.433796i
2929 0.598780 + 0.119105i 0.111191 + 0.0221172i 0.250372 0.968150i 0.419447π-0.419447\pi
−0.139181 + 0.990267i 0.544447π0.544447\pi
3030 0 0
3131 2.46039 + 3.68223i 0.441899 + 0.661349i 0.983836 0.179070i 0.0573090π-0.0573090\pi
−0.541937 + 0.840419i 0.682309π0.682309\pi
3232 −0.923880 0.382683i −0.163320 0.0676495i
3333 −5.94124 5.94124i −1.03424 1.03424i
3434 −1.67388 3.76804i −0.287067 0.646214i
3535 0 0
3636 0.774889 + 1.87075i 0.129148 + 0.311791i
3737 −1.64915 0.328036i −0.271119 0.0539289i 0.0576586 0.998336i 0.481637π-0.481637\pi
−0.328777 + 0.944408i 0.606637π0.606637\pi
3838 6.70375i 1.08749i
3939 0.803765 4.04080i 0.128705 0.647046i
4040 0 0
4141 3.38971 0.674255i 0.529384 0.105301i 0.0768405 0.997043i 0.475517π-0.475517\pi
0.452543 + 0.891742i 0.350517π0.350517\pi
4242 2.00768 + 4.84696i 0.309791 + 0.747902i
4343 0.926479 + 2.23672i 0.141287 + 0.341096i 0.978645 0.205558i 0.0659010π-0.0659010\pi
−0.837358 + 0.546655i 0.815901π0.815901\pi
4444 −3.67624 + 0.731249i −0.554213 + 0.110240i
4545 0 0
4646 0.995910 5.00678i 0.146839 0.738209i
4747 10.6121i 1.54793i −0.633229 0.773965i 0.718271π-0.718271\pi
0.633229 0.773965i 0.281729π-0.281729\pi
4848 2.19855 + 0.437319i 0.317334 + 0.0631216i
4949 −0.582639 1.40662i −0.0832342 0.200945i
5050 0 0
5151 5.32794 + 7.55222i 0.746061 + 1.05752i
5252 −1.29962 1.29962i −0.180224 0.180224i
5353 1.76897 + 0.732730i 0.242986 + 0.100648i 0.500853 0.865532i 0.333020π-0.333020\pi
−0.257867 + 0.966180i 0.583020π0.583020\pi
5454 1.21439 + 1.81746i 0.165258 + 0.247326i
5555 0 0
5656 2.29543 + 0.456590i 0.306740 + 0.0610144i
5757 −2.93168 14.7386i −0.388311 1.95217i
5858 −0.339182 + 0.507621i −0.0445367 + 0.0666539i
5959 4.86169 11.7372i 0.632938 1.52805i −0.202973 0.979184i 0.565061π-0.565061\pi
0.835912 0.548864i 0.184939π-0.184939\pi
6060 0 0
6161 −1.29314 6.50106i −0.165570 0.832375i −0.970888 0.239533i 0.923006π-0.923006\pi
0.805318 0.592842i 0.201994π-0.201994\pi
6262 −4.34349 + 0.863974i −0.551624 + 0.109725i
6363 −2.63287 3.94037i −0.331711 0.496440i
6464 0.707107 0.707107i 0.0883883 0.0883883i
6565 0 0
6666 7.76261 3.21538i 0.955511 0.395786i
6767 0.983164 0.983164i 0.120113 0.120113i −0.644495 0.764608i 0.722933π-0.722933\pi
0.764608 + 0.644495i 0.222933π0.222933\pi
6868 4.12178 0.104492i 0.499839 0.0126715i
6969 11.4432i 1.37760i
7070 0 0
7171 7.07898 4.73002i 0.840120 0.561350i −0.0593975 0.998234i 0.518918π-0.518918\pi
0.899518 + 0.436884i 0.143918π0.143918\pi
7272 −2.02488 −0.238635
7373 −3.82200 + 2.55378i −0.447331 + 0.298897i −0.758758 0.651373i 0.774193π-0.774193\pi
0.311426 + 0.950270i 0.399193π0.399193\pi
7474 0.934169 1.39808i 0.108595 0.162524i
7575 0 0
7676 −6.19346 2.56542i −0.710439 0.294273i
7777 8.10467 3.35707i 0.923613 0.382573i
7878 3.42563 + 2.28893i 0.387876 + 0.259170i
7979 −4.28663 2.86424i −0.482284 0.322252i 0.290551 0.956860i 0.406162π-0.406162\pi
−0.772834 + 0.634608i 0.781162π0.781162\pi
8080 0 0
8181 −7.76014 7.76014i −0.862238 0.862238i
8282 −0.674255 + 3.38971i −0.0744590 + 0.374331i
8383 −5.34887 + 12.9133i −0.587114 + 1.41742i 0.299135 + 0.954211i 0.403302π0.403302\pi
−0.886249 + 0.463208i 0.846698π0.846698\pi
8484 −5.24631 −0.572419
8585 0 0
8686 −2.42101 −0.261064
8787 0.523716 1.26436i 0.0561483 0.135554i
8888 0.731249 3.67624i 0.0779514 0.391888i
8989 −11.0963 11.0963i −1.17620 1.17620i −0.980704 0.195500i 0.937367π-0.937367\pi
−0.195500 0.980704i 0.562633π-0.562633\pi
9090 0 0
9191 3.57658 + 2.38979i 0.374927 + 0.250518i
9292 4.24454 + 2.83611i 0.442524 + 0.295685i
9393 9.17156 3.79898i 0.951046 0.393936i
9494 9.80427 + 4.06106i 1.01123 + 0.418867i
9595 0 0
9696 −1.24538 + 1.86384i −0.127106 + 0.190228i
9797 9.35564 6.25124i 0.949921 0.634717i 0.0189540 0.999820i 0.493966π-0.493966\pi
0.930967 + 0.365103i 0.118966π0.118966\pi
9898 1.52251 0.153797
9999 −6.31067 + 4.21666i −0.634247 + 0.423790i
100100 0 0
101101 16.4108i 1.63294i 0.577389 + 0.816469i 0.304072π0.304072\pi
−0.577389 + 0.816469i 0.695928π0.695928\pi
102102 −9.01626 + 2.03227i −0.892743 + 0.201224i
103103 −11.2381 + 11.2381i −1.10733 + 1.10733i −0.113825 + 0.993501i 0.536310π0.536310\pi
−0.993501 + 0.113825i 0.963690π0.963690\pi
104104 1.69803 0.703348i 0.166506 0.0689689i
105105 0 0
106106 −1.35391 + 1.35391i −0.131503 + 0.131503i
107107 −0.445180 0.666259i −0.0430372 0.0644097i 0.809327 0.587358i 0.199832π-0.199832\pi
−0.852364 + 0.522948i 0.824832π0.824832\pi
108108 −2.14385 + 0.426437i −0.206292 + 0.0410340i
109109 2.71439 + 13.6462i 0.259991 + 1.30707i 0.861320 + 0.508063i 0.169638π0.169638\pi
−0.601328 + 0.799002i 0.705362π0.705362\pi
110110 0 0
111111 −1.44241 + 3.48229i −0.136908 + 0.330524i
112112 −1.30026 + 1.94597i −0.122863 + 0.183877i
113113 0.0285995 + 0.143780i 0.00269042 + 0.0135256i 0.982107 0.188323i 0.0603051π-0.0603051\pi
−0.979417 + 0.201849i 0.935305π0.935305\pi
114114 14.7386 + 2.93168i 1.38039 + 0.274577i
115115 0 0
116116 −0.339182 0.507621i −0.0314922 0.0471314i
117117 −3.43832 1.42420i −0.317872 0.131667i
118118 8.98323 + 8.98323i 0.826974 + 0.826974i
119119 −9.41357 + 2.12182i −0.862940 + 0.194507i
120120 0 0
121121 −1.16697 2.81731i −0.106088 0.256119i
122122 6.50106 + 1.29314i 0.588578 + 0.117075i
123123 7.74732i 0.698552i
124124 0.863974 4.34349i 0.0775871 0.390057i
125125 0 0
126126 4.64799 0.924542i 0.414075 0.0823647i
127127 8.16676 + 19.7163i 0.724683 + 1.74954i 0.659547 + 0.751664i 0.270748π0.270748\pi
0.0651365 + 0.997876i 0.479252π0.479252\pi
128128 0.382683 + 0.923880i 0.0338248 + 0.0816602i
129129 5.32271 1.05875i 0.468639 0.0932180i
130130 0 0
131131 −2.51893 + 12.6635i −0.220080 + 1.10642i 0.699837 + 0.714302i 0.253256π0.253256\pi
−0.919917 + 0.392113i 0.871744π0.871744\pi
132132 8.40219i 0.731317i
133133 15.3880 + 3.06087i 1.33431 + 0.265411i
134134 0.532085 + 1.28457i 0.0459651 + 0.110970i
135135 0 0
136136 −1.48080 + 3.84802i −0.126978 + 0.329965i
137137 1.52157 + 1.52157i 0.129997 + 0.129997i 0.769111 0.639115i 0.220699π-0.220699\pi
−0.639115 + 0.769111i 0.720699π0.720699\pi
138138 −10.5721 4.37912i −0.899959 0.372775i
139139 10.8206 + 16.1941i 0.917788 + 1.37357i 0.927584 + 0.373614i 0.121882π0.121882\pi
−0.00979673 + 0.999952i 0.503118π0.503118\pi
140140 0 0
141141 −23.3312 4.64086i −1.96484 0.390831i
142142 1.66096 + 8.35023i 0.139385 + 0.700735i
143143 3.82736 5.72804i 0.320060 0.479003i
144144 0.774889 1.87075i 0.0645741 0.155896i
145145 0 0
146146 −0.896768 4.50836i −0.0742170 0.373114i
147147 −3.34732 + 0.665823i −0.276082 + 0.0549161i
148148 0.934169 + 1.39808i 0.0767882 + 0.114922i
149149 −13.4649 + 13.4649i −1.10308 + 1.10308i −0.109047 + 0.994037i 0.534780π0.534780\pi
−0.994037 + 0.109047i 0.965220π0.965220\pi
150150 0 0
151151 −5.17302 + 2.14274i −0.420975 + 0.174373i −0.583107 0.812396i 0.698163π-0.698163\pi
0.162132 + 0.986769i 0.448163π0.448163\pi
152152 4.74027 4.74027i 0.384487 0.384487i
153153 7.62985 3.38940i 0.616836 0.274017i
154154 8.77244i 0.706903i
155155 0 0
156156 −3.42563 + 2.28893i −0.274270 + 0.183261i
157157 2.43885 0.194642 0.0973209 0.995253i 0.468973π-0.468973\pi
0.0973209 + 0.995253i 0.468973π0.468973\pi
158158 4.28663 2.86424i 0.341026 0.227866i
159159 2.38455 3.56873i 0.189107 0.283019i
160160 0 0
161161 −11.0380 4.57209i −0.869916 0.360331i
162162 10.1391 4.19976i 0.796604 0.329964i
163163 −5.99898 4.00839i −0.469876 0.313961i 0.297993 0.954568i 0.403683π-0.403683\pi
−0.767869 + 0.640607i 0.778683π0.778683\pi
164164 −2.87366 1.92012i −0.224395 0.149936i
165165 0 0
166166 −9.88341 9.88341i −0.767102 0.767102i
167167 −3.00246 + 15.0944i −0.232337 + 1.16804i 0.671779 + 0.740752i 0.265531π0.265531\pi
−0.904116 + 0.427287i 0.859469π0.859469\pi
168168 2.00768 4.84696i 0.154896 0.373951i
169169 −9.62199 −0.740153
170170 0 0
171171 −13.5743 −1.03805
172172 0.926479 2.23672i 0.0706434 0.170548i
173173 0.592427 2.97833i 0.0450414 0.226438i −0.951708 0.307005i 0.900673π-0.900673\pi
0.996749 + 0.0805670i 0.0256731π0.0256731\pi
174174 0.967701 + 0.967701i 0.0733612 + 0.0733612i
175175 0 0
176176 3.11656 + 2.08242i 0.234920 + 0.156968i
177177 −23.6787 15.8216i −1.77980 1.18922i
178178 14.4980 6.00527i 1.08667 0.450114i
179179 −12.6642 5.24569i −0.946568 0.392081i −0.144628 0.989486i 0.546199π-0.546199\pi
−0.801940 + 0.597405i 0.796199π0.796199\pi
180180 0 0
181181 5.41668 8.10663i 0.402618 0.602561i −0.573656 0.819096i 0.694476π-0.694476\pi
0.976275 + 0.216535i 0.0694755π0.0694755\pi
182182 −3.57658 + 2.38979i −0.265114 + 0.177143i
183183 −14.8584 −1.09837
184184 −4.24454 + 2.83611i −0.312912 + 0.209081i
185185 0 0
186186 9.92722i 0.727899i
187187 3.39818 + 15.0762i 0.248500 + 1.10248i
188188 −7.50387 + 7.50387i −0.547276 + 0.547276i
189189 4.72635 1.95772i 0.343791 0.142403i
190190 0 0
191191 −13.0447 + 13.0447i −0.943881 + 0.943881i −0.998507 0.0546255i 0.982603π-0.982603\pi
0.0546255 + 0.998507i 0.482603π0.482603\pi
192192 −1.24538 1.86384i −0.0898776 0.134511i
193193 20.4235 4.06249i 1.47012 0.292424i 0.605899 0.795542i 0.292814π-0.292814\pi
0.864218 + 0.503117i 0.167814π0.167814\pi
194194 2.19514 + 11.0357i 0.157602 + 0.792319i
195195 0 0
196196 −0.582639 + 1.40662i −0.0416171 + 0.100473i
197197 2.35217 3.52027i 0.167585 0.250809i −0.738166 0.674619i 0.764308π-0.764308\pi
0.905751 + 0.423811i 0.139308π0.139308\pi
198198 −1.48069 7.44395i −0.105228 0.529018i
199199 25.8402 + 5.13993i 1.83176 + 0.364360i 0.985671 0.168681i 0.0539508π-0.0539508\pi
0.846089 + 0.533041i 0.178951π0.178951\pi
200200 0 0
201201 −1.73158 2.59150i −0.122136 0.182790i
202202 −15.1616 6.28015i −1.06677 0.441870i
203203 1.01034 + 1.01034i 0.0709122 + 0.0709122i
204204 1.57280 9.10765i 0.110118 0.637663i
205205 0 0
206206 −6.08203 14.6833i −0.423755 1.02304i
207207 10.1381 + 2.01660i 0.704649 + 0.140163i
208208 1.83794i 0.127438i
209209 4.90211 24.6446i 0.339086 1.70470i
210210 0 0
211211 21.7949 4.33527i 1.50042 0.298452i 0.624545 0.780989i 0.285284π-0.285284\pi
0.875876 + 0.482536i 0.160284π0.160284\pi
212212 −0.732730 1.76897i −0.0503241 0.121493i
213213 −7.30343 17.6320i −0.500423 1.20813i
214214 0.785906 0.156326i 0.0537234 0.0106863i
215215 0 0
216216 0.426437 2.14385i 0.0290154 0.145870i
217217 10.3647i 0.703600i
218218 −13.6462 2.71439i −0.924235 0.183842i
219219 3.94318 + 9.51969i 0.266456 + 0.643281i
220220 0 0
221221 −5.22094 + 5.49254i −0.351198 + 0.369468i
222222 −2.66523 2.66523i −0.178878 0.178878i
223223 −11.8905 4.92520i −0.796246 0.329816i −0.0527941 0.998605i 0.516813π-0.516813\pi
−0.743452 + 0.668790i 0.766813π0.766813\pi
224224 −1.30026 1.94597i −0.0868772 0.130021i
225225 0 0
226226 −0.143780 0.0285995i −0.00956408 0.00190241i
227227 −4.99137 25.0933i −0.331289 1.66550i −0.683780 0.729688i 0.739665π-0.739665\pi
0.352491 0.935815i 0.385335π-0.385335\pi
228228 −8.34872 + 12.4947i −0.552908 + 0.827485i
229229 4.78226 11.5454i 0.316021 0.762942i −0.683437 0.730010i 0.739515π-0.739515\pi
0.999458 0.0329322i 0.0104845π-0.0104845\pi
230230 0 0
231231 −3.83636 19.2867i −0.252414 1.26897i
232232 0.598780 0.119105i 0.0393118 0.00781961i
233233 −3.93433 5.88814i −0.257747 0.385745i 0.679917 0.733289i 0.262016π-0.262016\pi
−0.937664 + 0.347544i 0.887016π0.887016\pi
234234 2.63157 2.63157i 0.172031 0.172031i
235235 0 0
236236 −11.7372 + 4.86169i −0.764024 + 0.316469i
237237 −8.17180 + 8.17180i −0.530815 + 0.530815i
238238 1.64211 9.50899i 0.106442 0.616376i
239239 19.6102i 1.26848i 0.773137 + 0.634239i 0.218687π0.218687\pi
−0.773137 + 0.634239i 0.781313π0.781313\pi
240240 0 0
241241 −3.93961 + 2.63236i −0.253772 + 0.169565i −0.675949 0.736948i 0.736266π-0.736266\pi
0.422177 + 0.906513i 0.361266π0.361266\pi
242242 3.04943 0.196025
243243 −15.0023 + 10.0242i −0.962401 + 0.643056i
244244 −3.68255 + 5.51133i −0.235751 + 0.352827i
245245 0 0
246246 7.15759 + 2.96477i 0.456351 + 0.189027i
247247 11.3832 4.71507i 0.724295 0.300013i
248248 3.68223 + 2.46039i 0.233822 + 0.156235i
249249 26.0514 + 17.4070i 1.65094 + 1.10312i
250250 0 0
251251 1.58594 + 1.58594i 0.100104 + 0.100104i 0.755385 0.655281i 0.227450π-0.227450\pi
−0.655281 + 0.755385i 0.727450π0.727450\pi
252252 −0.924542 + 4.64799i −0.0582407 + 0.292796i
253253 −7.32240 + 17.6778i −0.460355 + 1.11140i
254254 −21.3408 −1.33904
255255 0 0
256256 −1.00000 −0.0625000
257257 2.51235 6.06534i 0.156716 0.378345i −0.825947 0.563748i 0.809359π-0.809359\pi
0.982663 + 0.185403i 0.0593589π0.0593589\pi
258258 −1.05875 + 5.32271i −0.0659151 + 0.331378i
259259 −2.78267 2.78267i −0.172907 0.172907i
260260 0 0
261261 −1.02787 0.686803i −0.0636238 0.0425120i
262262 −10.7356 7.17330i −0.663248 0.443168i
263263 −4.74347 + 1.96481i −0.292495 + 0.121155i −0.524106 0.851653i 0.675600π-0.675600\pi
0.231611 + 0.972808i 0.425600π0.425600\pi
264264 −7.76261 3.21538i −0.477756 0.197893i
265265 0 0
266266 −8.71662 + 13.0453i −0.534450 + 0.799861i
267267 −29.2484 + 19.5432i −1.78997 + 1.19602i
268268 −1.39040 −0.0849325
269269 −22.7608 + 15.2083i −1.38775 + 0.927266i −0.387767 + 0.921757i 0.626754π0.626754\pi
−0.999985 + 0.00550888i 0.998246π0.998246\pi
270270 0 0
271271 17.4427i 1.05957i 0.848132 + 0.529785i 0.177727π0.177727\pi
−0.848132 + 0.529785i 0.822273π0.822273\pi
272272 −2.98843 2.84065i −0.181200 0.172240i
273273 6.81819 6.81819i 0.412656 0.412656i
274274 −1.98803 + 0.823469i −0.120101 + 0.0497476i
275275 0 0
276276 8.09156 8.09156i 0.487055 0.487055i
277277 −12.6377 18.9137i −0.759327 1.13641i −0.986692 0.162603i 0.948011π-0.948011\pi
0.227365 0.973810i 0.426989π-0.426989\pi
278278 −19.1022 + 3.79967i −1.14568 + 0.227889i
279279 −1.74945 8.79506i −0.104737 0.526546i
280280 0 0
281281 −3.35617 + 8.10250i −0.200212 + 0.483355i −0.991815 0.127681i 0.959247π-0.959247\pi
0.791603 + 0.611035i 0.209247π0.209247\pi
282282 13.2161 19.7792i 0.787005 1.17784i
283283 4.18603 + 21.0446i 0.248834 + 1.25097i 0.879869 + 0.475216i 0.157630π0.157630\pi
−0.631035 + 0.775754i 0.717370π0.717370\pi
284284 −8.35023 1.66096i −0.495495 0.0985600i
285285 0 0
286286 3.82736 + 5.72804i 0.226316 + 0.338706i
287287 7.47300 + 3.09542i 0.441117 + 0.182717i
288288 1.43181 + 1.43181i 0.0843701 + 0.0843701i
289289 −0.861383 16.9782i −0.0506696 0.998715i
290290 0 0
291291 −9.65227 23.3026i −0.565826 1.36603i
292292 4.50836 + 0.896768i 0.263832 + 0.0524794i
293293 30.1287i 1.76014i −0.474847 0.880068i 0.657497π-0.657497\pi
0.474847 0.880068i 0.342503π-0.342503\pi
294294 0.665823 3.34732i 0.0388316 0.195219i
295295 0 0
296296 −1.64915 + 0.328036i −0.0958549 + 0.0190667i
297297 −3.13537 7.56945i −0.181933 0.439224i
298298 −7.28713 17.5927i −0.422132 1.01912i
299299 −9.20213 + 1.83042i −0.532173 + 0.105856i
300300 0 0
301301 −1.10541 + 5.55726i −0.0637146 + 0.320315i
302302 5.59924i 0.322200i
303303 36.0801 + 7.17677i 2.07275 + 0.412295i
304304 2.56542 + 6.19346i 0.147137 + 0.355219i
305305 0 0
306306 0.211583 + 8.34613i 0.0120954 + 0.477116i
307307 3.26677 + 3.26677i 0.186445 + 0.186445i 0.794157 0.607713i 0.207913π-0.207913\pi
−0.607713 + 0.794157i 0.707913π0.707913\pi
308308 −8.10467 3.35707i −0.461807 0.191287i
309309 19.7930 + 29.6223i 1.12598 + 1.68515i
310310 0 0
311311 21.3083 + 4.23849i 1.20828 + 0.240343i 0.757827 0.652455i 0.226261π-0.226261\pi
0.450457 + 0.892798i 0.351261π0.351261\pi
312312 −0.803765 4.04080i −0.0455042 0.228765i
313313 −11.6411 + 17.4221i −0.657993 + 0.984757i 0.341007 + 0.940061i 0.389232π0.389232\pi
−0.999001 + 0.0446961i 0.985768π0.985768\pi
314314 −0.933309 + 2.25321i −0.0526697 + 0.127156i
315315 0 0
316316 1.00579 + 5.05643i 0.0565799 + 0.284446i
317317 5.61256 1.11641i 0.315233 0.0627037i −0.0349384 0.999389i 0.511123π-0.511123\pi
0.350171 + 0.936686i 0.386123π0.386123\pi
318318 2.38455 + 3.56873i 0.133719 + 0.200124i
319319 1.61811 1.61811i 0.0905967 0.0905967i
320320 0 0
321321 −1.65949 + 0.687384i −0.0926238 + 0.0383660i
322322 8.44812 8.44812i 0.470795 0.470795i
323323 −9.92692 + 25.7962i −0.552349 + 1.43534i
324324 10.9745i 0.609694i
325325 0 0
326326 5.99898 4.00839i 0.332253 0.222004i
327327 31.1889 1.72475
328328 2.87366 1.92012i 0.158671 0.106021i
329329 13.7984 20.6508i 0.760732 1.13852i
330330 0 0
331331 −27.3797 11.3411i −1.50493 0.623361i −0.530423 0.847733i 0.677967π-0.677967\pi
−0.974503 + 0.224372i 0.927967π0.927967\pi
332332 12.9133 5.34887i 0.708710 0.293557i
333333 2.83095 + 1.89158i 0.155135 + 0.103658i
334334 −12.7964 8.55028i −0.700188 0.467851i
335335 0 0
336336 3.70970 + 3.70970i 0.202381 + 0.202381i
337337 −6.41803 + 32.2656i −0.349612 + 1.75762i 0.260662 + 0.965430i 0.416059π0.416059\pi
−0.610275 + 0.792190i 0.708941π0.708941\pi
338338 3.68218 8.88956i 0.200284 0.483528i
339339 0.328614 0.0178479
340340 0 0
341341 16.5995 0.898912
342342 5.19467 12.5410i 0.280895 0.678142i
343343 3.89129 19.5629i 0.210110 1.05629i
344344 1.71191 + 1.71191i 0.0923000 + 0.0923000i
345345 0 0
346346 2.52491 + 1.68709i 0.135740 + 0.0906985i
347347 −16.3048 10.8945i −0.875290 0.584850i 0.0347382 0.999396i 0.488940π-0.488940\pi
−0.910028 + 0.414546i 0.863940π0.863940\pi
348348 −1.26436 + 0.523716i −0.0677770 + 0.0280741i
349349 8.38547 + 3.47337i 0.448864 + 0.185925i 0.595652 0.803242i 0.296894π-0.296894\pi
−0.146788 + 0.989168i 0.546894π0.546894\pi
350350 0 0
351351 2.23197 3.34038i 0.119134 0.178297i
352352 −3.11656 + 2.08242i −0.166113 + 0.110993i
353353 30.7498 1.63665 0.818323 0.574759i 0.194904π-0.194904\pi
0.818323 + 0.574759i 0.194904π0.194904\pi
354354 23.6787 15.8216i 1.25851 0.840907i
355355 0 0
356356 15.6925i 0.831702i
357357 0.548195 + 21.6241i 0.0290136 + 1.14447i
358358 9.69278 9.69278i 0.512279 0.512279i
359359 −14.0992 + 5.84010i −0.744129 + 0.308228i −0.722344 0.691534i 0.756935π-0.756935\pi
−0.0217856 + 0.999763i 0.506935π0.506935\pi
360360 0 0
361361 18.3426 18.3426i 0.965399 0.965399i
362362 5.41668 + 8.10663i 0.284694 + 0.426075i
363363 −6.70433 + 1.33357i −0.351886 + 0.0699945i
364364 −0.839184 4.21886i −0.0439852 0.221128i
365365 0 0
366366 5.68608 13.7274i 0.297216 0.717543i
367367 −18.3527 + 27.4667i −0.958003 + 1.43375i −0.0577767 + 0.998330i 0.518401π0.518401\pi
−0.900226 + 0.435423i 0.856599π0.856599\pi
368368 −0.995910 5.00678i −0.0519154 0.260996i
369369 −6.86377 1.36529i −0.357313 0.0710741i
370370 0 0
371371 2.48963 + 3.72599i 0.129255 + 0.193444i
372372 −9.17156 3.79898i −0.475523 0.196968i
373373 −2.61742 2.61742i −0.135525 0.135525i 0.636090 0.771615i 0.280551π-0.280551\pi
−0.771615 + 0.636090i 0.780551π0.780551\pi
374374 −15.2290 2.62991i −0.787475 0.135989i
375375 0 0
376376 −4.06106 9.80427i −0.209433 0.505617i
377377 1.10052 + 0.218907i 0.0566796 + 0.0112743i
378378 5.11576i 0.263126i
379379 1.01649 5.11024i 0.0522136 0.262495i −0.945857 0.324583i 0.894776π-0.894776\pi
0.998071 + 0.0620880i 0.0197759π0.0197759\pi
380380 0 0
381381 46.9188 9.33274i 2.40373 0.478131i
382382 −7.05974 17.0437i −0.361208 0.872033i
383383 −0.781961 1.88782i −0.0399564 0.0964632i 0.902642 0.430393i 0.141625π-0.141625\pi
−0.942598 + 0.333930i 0.891625π0.891625\pi
384384 2.19855 0.437319i 0.112194 0.0223169i
385385 0 0
386386 −4.06249 + 20.4235i −0.206775 + 1.03953i
387387 4.90226i 0.249196i
388388 −11.0357 2.19514i −0.560254 0.111441i
389389 −1.19281 2.87969i −0.0604777 0.146006i 0.890752 0.454490i 0.150178π-0.150178\pi
−0.951230 + 0.308484i 0.900178π0.900178\pi
390390 0 0
391391 11.2463 17.7914i 0.568750 0.899750i
392392 −1.07658 1.07658i −0.0543753 0.0543753i
393393 26.7398 + 11.0760i 1.34885 + 0.558710i
394394 2.35217 + 3.52027i 0.118500 + 0.177348i
395395 0 0
396396 7.44395 + 1.48069i 0.374072 + 0.0744076i
397397 1.62321 + 8.16045i 0.0814668 + 0.409561i 0.999902 + 0.0139900i 0.00445331π0.00445331\pi
−0.918435 + 0.395571i 0.870547π0.870547\pi
398398 −14.6373 + 21.9062i −0.733700 + 1.09806i
399399 13.4590 32.4928i 0.673791 1.62668i
400400 0 0
401401 3.90028 + 19.6080i 0.194771 + 0.979178i 0.947234 + 0.320544i 0.103866π0.103866\pi
−0.752463 + 0.658635i 0.771134π0.771134\pi
402402 3.05688 0.608051i 0.152463 0.0303268i
403403 4.52204 + 6.76771i 0.225259 + 0.337124i
404404 11.6042 11.6042i 0.577331 0.577331i
405405 0 0
406406 −1.32008 + 0.546794i −0.0655144 + 0.0271369i
407407 −4.45657 + 4.45657i −0.220904 + 0.220904i
408408 7.81249 + 4.93843i 0.386776 + 0.244489i
409409 30.7813i 1.52203i −0.648731 0.761017i 0.724700π-0.724700\pi
0.648731 0.761017i 0.275300π-0.275300\pi
410410 0 0
411411 4.01067 2.67985i 0.197832 0.132187i
412412 15.8931 0.782997
413413 24.7221 16.5188i 1.21649 0.812835i
414414 −5.74279 + 8.59470i −0.282243 + 0.422406i
415415 0 0
416416 −1.69803 0.703348i −0.0832529 0.0344845i
417417 40.3356 16.7076i 1.97524 0.818173i
418418 20.8927 + 13.9600i 1.02189 + 0.682808i
419419 −12.4734 8.33444i −0.609364 0.407164i 0.212244 0.977217i 0.431923π-0.431923\pi
−0.821608 + 0.570053i 0.806923π0.806923\pi
420420 0 0
421421 9.43644 + 9.43644i 0.459904 + 0.459904i 0.898624 0.438720i 0.144568π-0.144568\pi
−0.438720 + 0.898624i 0.644568π0.644568\pi
422422 −4.33527 + 21.7949i −0.211038 + 1.06096i
423423 −8.22318 + 19.8525i −0.399825 + 0.965262i
424424 1.91472 0.0929868
425425 0 0
426426 19.0848 0.924661
427427 5.93664 14.3323i 0.287294 0.693589i
428428 −0.156326 + 0.785906i −0.00755632 + 0.0379882i
429429 −10.9196 10.9196i −0.527205 0.527205i
430430 0 0
431431 −0.709006 0.473743i −0.0341516 0.0228194i 0.538377 0.842704i 0.319038π-0.319038\pi
−0.572529 + 0.819885i 0.694038π0.694038\pi
432432 1.81746 + 1.21439i 0.0874428 + 0.0584274i
433433 8.69207 3.60038i 0.417714 0.173023i −0.163919 0.986474i 0.552414π-0.552414\pi
0.581634 + 0.813451i 0.302414π0.302414\pi
434434 −9.57571 3.96639i −0.459649 0.190393i
435435 0 0
436436 7.72993 11.5687i 0.370197 0.554038i
437437 −28.4544 + 19.0126i −1.36116 + 0.909496i
438438 −10.3040 −0.492346
439439 −21.0410 + 14.0592i −1.00423 + 0.671007i −0.944944 0.327233i 0.893884π-0.893884\pi
−0.0592901 + 0.998241i 0.518884π0.518884\pi
440440 0 0
441441 3.08290i 0.146805i
442442 −3.07648 6.92542i −0.146333 0.329409i
443443 15.8653 15.8653i 0.753785 0.753785i −0.221398 0.975184i 0.571062π-0.571062\pi
0.975184 + 0.221398i 0.0710620π0.0710620\pi
444444 3.48229 1.44241i 0.165262 0.0684538i
445445 0 0
446446 9.10058 9.10058i 0.430925 0.430925i
447447 23.7147 + 35.4916i 1.12167 + 1.67870i
448448 2.29543 0.456590i 0.108449 0.0215719i
449449 −4.30949 21.6653i −0.203378 1.02245i −0.938701 0.344732i 0.887970π-0.887970\pi
0.735324 0.677716i 0.237030π-0.237030\pi
450450 0 0
451451 4.95744 11.9683i 0.233437 0.563566i
452452 0.0814446 0.121890i 0.00383083 0.00573325i
453453 2.44866 + 12.3102i 0.115048 + 0.578385i
454454 25.0933 + 4.99137i 1.17769 + 0.234257i
455455 0 0
456456 −8.34872 12.4947i −0.390965 0.585120i
457457 −12.0290 4.98260i −0.562695 0.233076i 0.0831596 0.996536i 0.473499π-0.473499\pi
−0.645855 + 0.763460i 0.723499π0.723499\pi
458458 8.83647 + 8.83647i 0.412901 + 0.412901i
459459 1.98170 + 8.79191i 0.0924976 + 0.410371i
460460 0 0
461461 −1.87457 4.52561i −0.0873073 0.210779i 0.874195 0.485575i 0.161390π-0.161390\pi
−0.961503 + 0.274796i 0.911390π0.911390\pi
462462 19.2867 + 3.83636i 0.897297 + 0.178483i
463463 5.65812i 0.262955i −0.991319 0.131478i 0.958028π-0.958028\pi
0.991319 0.131478i 0.0419722π-0.0419722\pi
464464 −0.119105 + 0.598780i −0.00552930 + 0.0277977i
465465 0 0
466466 6.94554 1.38155i 0.321746 0.0639992i
467467 10.5662 + 25.5090i 0.488944 + 1.18042i 0.955252 + 0.295793i 0.0955839π0.0955839\pi
−0.466308 + 0.884622i 0.654416π0.654416\pi
468468 1.42420 + 3.43832i 0.0658335 + 0.158936i
469469 3.19158 0.634845i 0.147373 0.0293144i
470470 0 0
471471 1.06656 5.36195i 0.0491444 0.247066i
472472 12.7042i 0.584759i
473473 8.90019 + 1.77036i 0.409231 + 0.0814011i
474474 −4.42255 10.6770i −0.203134 0.490409i
475475 0 0
476476 8.15675 + 5.15604i 0.373864 + 0.236327i
477477 −2.74151 2.74151i −0.125525 0.125525i
478478 −18.1175 7.50450i −0.828673 0.343248i
479479 1.20322 + 1.80075i 0.0549767 + 0.0822784i 0.857940 0.513751i 0.171744π-0.171744\pi
−0.802963 + 0.596029i 0.796744π0.796744\pi
480480 0 0
481481 −3.03103 0.602910i −0.138203 0.0274903i
482482 −0.924362 4.64708i −0.0421035 0.211669i
483483 −14.8791 + 22.2682i −0.677023 + 1.01324i
484484 −1.16697 + 2.81731i −0.0530439 + 0.128059i
485485 0 0
486486 −3.52005 17.6965i −0.159673 0.802728i
487487 34.1092 6.78474i 1.54564 0.307446i 0.652695 0.757620i 0.273638π-0.273638\pi
0.892941 + 0.450174i 0.148638π0.148638\pi
488488 −3.68255 5.51133i −0.166701 0.249486i
489489 −11.4361 + 11.4361i −0.517159 + 0.517159i
490490 0 0
491491 1.19271 0.494037i 0.0538263 0.0222956i −0.355608 0.934635i 0.615726π-0.615726\pi
0.409434 + 0.912340i 0.365726π0.365726\pi
492492 −5.47818 + 5.47818i −0.246976 + 0.246976i
493493 −2.05686 + 1.45107i −0.0926364 + 0.0653531i
494494 12.3211i 0.554351i
495495 0 0
496496 −3.68223 + 2.46039i −0.165337 + 0.110475i
497497 19.9258 0.893793
498498 −26.0514 + 17.4070i −1.16739 + 0.780026i
499499 6.25854 9.36656i 0.280171 0.419305i −0.664519 0.747272i 0.731363π-0.731363\pi
0.944689 + 0.327967i 0.106363π0.106363\pi
500500 0 0
501501 31.8728 + 13.2021i 1.42397 + 0.589828i
502502 −2.07213 + 0.858306i −0.0924839 + 0.0383081i
503503 −2.04917 1.36921i −0.0913680 0.0610501i 0.509047 0.860739i 0.329998π-0.329998\pi
−0.600415 + 0.799689i 0.704998π0.704998\pi
504504 −3.94037 2.63287i −0.175518 0.117277i
505505 0 0
506506 −13.5300 13.5300i −0.601483 0.601483i
507507 −4.20788 + 21.1545i −0.186879 + 0.939502i
508508 8.16676 19.7163i 0.362342 0.874770i
509509 0.909764 0.0403246 0.0201623 0.999797i 0.493582π-0.493582\pi
0.0201623 + 0.999797i 0.493582π0.493582\pi
510510 0 0
511511 −10.7581 −0.475910
512512 0.382683 0.923880i 0.0169124 0.0408301i
513513 2.85873 14.3718i 0.126216 0.634531i
514514 4.64221 + 4.64221i 0.204759 + 0.204759i
515515 0 0
516516 −4.51238 3.01507i −0.198646 0.132731i
517517 −33.0732 22.0988i −1.45456 0.971904i
518518 3.63574 1.50597i 0.159745 0.0661686i
519519 −6.28894 2.60496i −0.276054 0.114345i
520520 0 0
521521 −11.4721 + 17.1692i −0.502603 + 0.752198i −0.992848 0.119386i 0.961907π-0.961907\pi
0.490245 + 0.871585i 0.336907π0.336907\pi
522522 1.02787 0.686803i 0.0449888 0.0300606i
523523 −36.0415 −1.57599 −0.787993 0.615684i 0.788880π-0.788880\pi
−0.787993 + 0.615684i 0.788880π0.788880\pi
524524 10.7356 7.17330i 0.468987 0.313367i
525525 0 0
526526 5.13429i 0.223866i
527527 −17.9932 3.10725i −0.783796 0.135354i
528528 5.94124 5.94124i 0.258559 0.258559i
529529 2.82674 1.17087i 0.122902 0.0509075i
530530 0 0
531531 −18.1900 + 18.1900i −0.789379 + 0.789379i
532532 −8.71662 13.0453i −0.377913 0.565587i
533533 6.23007 1.23924i 0.269854 0.0536774i
534534 −6.86264 34.5008i −0.296976 1.49300i
535535 0 0
536536 0.532085 1.28457i 0.0229826 0.0554848i
537537 −17.0712 + 25.5489i −0.736678 + 1.10252i
538538 −5.34044 26.8482i −0.230243 1.15751i
539539 −5.59710 1.11333i −0.241084 0.0479546i
540540 0 0
541541 23.7268 + 35.5096i 1.02009 + 1.52668i 0.839677 + 0.543086i 0.182744π0.182744\pi
0.180416 + 0.983590i 0.442256π0.442256\pi
542542 −16.1150 6.67504i −0.692197 0.286717i
543543 −15.4540 15.4540i −0.663196 0.663196i
544544 3.76804 1.67388i 0.161553 0.0717668i
545545 0 0
546546 3.68998 + 8.90840i 0.157917 + 0.381244i
547547 16.4468 + 3.27148i 0.703216 + 0.139878i 0.533731 0.845655i 0.320790π-0.320790\pi
0.169485 + 0.985533i 0.445790π0.445790\pi
548548 2.15183i 0.0919216i
549549 −2.61846 + 13.1639i −0.111753 + 0.561821i
550550 0 0
551551 4.01407 0.798449i 0.171005 0.0340151i
552552 4.37912 + 10.5721i 0.186388 + 0.449980i
553553 −4.61743 11.1475i −0.196353 0.474038i
554554 22.3102 4.43778i 0.947870 0.188543i
555555 0 0
556556 3.79967 19.1022i 0.161142 0.810116i
557557 27.0952i 1.14806i −0.818835 0.574029i 0.805379π-0.805379\pi
0.818835 0.574029i 0.194621π-0.194621\pi
558558 8.79506 + 1.74945i 0.372325 + 0.0740600i
559559 1.70281 + 4.11095i 0.0720212 + 0.173874i
560560 0 0
561561 34.6320 0.877958i 1.46216 0.0370674i
562562 −6.20139 6.20139i −0.261590 0.261590i
563563 −14.8543 6.15287i −0.626036 0.259313i 0.0470317 0.998893i 0.485024π-0.485024\pi
−0.673068 + 0.739581i 0.735024π0.735024\pi
564564 13.2161 + 19.7792i 0.556497 + 0.832856i
565565 0 0
566566 −21.0446 4.18603i −0.884570 0.175952i
567567 −5.01085 25.1912i −0.210436 1.05793i
568568 4.73002 7.07898i 0.198467 0.297027i
569569 −8.22349 + 19.8533i −0.344747 + 0.832292i 0.652476 + 0.757810i 0.273730π0.273730\pi
−0.997222 + 0.0744822i 0.976270π0.976270\pi
570570 0 0
571571 0.517900 + 2.60366i 0.0216735 + 0.108960i 0.990108 0.140309i 0.0448097π-0.0448097\pi
−0.968434 + 0.249269i 0.919810π0.919810\pi
572572 −6.75669 + 1.34399i −0.282511 + 0.0561950i
573573 22.9748 + 34.3842i 0.959785 + 1.43642i
574574 −5.71958 + 5.71958i −0.238731 + 0.238731i
575575 0 0
576576 −1.87075 + 0.774889i −0.0779478 + 0.0322871i
577577 −13.7472 + 13.7472i −0.572302 + 0.572302i −0.932771 0.360469i 0.882617π-0.882617\pi
0.360469 + 0.932771i 0.382617π0.382617\pi
578578 16.0154 + 5.70145i 0.666153 + 0.237149i
579579 46.6788i 1.93990i
580580 0 0
581581 −27.1994 + 18.1741i −1.12842 + 0.753987i
582582 25.2226 1.04551
583583 5.96733 3.98724i 0.247141 0.165135i
584584 −2.55378 + 3.82200i −0.105676 + 0.158155i
585585 0 0
586586 27.8353 + 11.5297i 1.14986 + 0.476289i
587587 −34.6515 + 14.3531i −1.43022 + 0.592416i −0.957406 0.288746i 0.906762π-0.906762\pi
−0.472814 + 0.881162i 0.656762π0.656762\pi
588588 2.83772 + 1.89610i 0.117026 + 0.0781940i
589589 24.6848 + 16.4938i 1.01712 + 0.679617i
590590 0 0
591591 −6.71084 6.71084i −0.276047 0.276047i
592592 0.328036 1.64915i 0.0134822 0.0677797i
593593 −12.9310 + 31.2183i −0.531014 + 1.28198i 0.399838 + 0.916586i 0.369066π0.369066\pi
−0.930852 + 0.365396i 0.880934π0.880934\pi
594594 8.19311 0.336168
595595 0 0
596596 19.0422 0.779998
597597 22.6008 54.5632i 0.924989 2.23312i
598598 1.83042 9.20213i 0.0748514 0.376303i
599599 −9.94392 9.94392i −0.406297 0.406297i 0.474148 0.880445i 0.342756π-0.342756\pi
−0.880445 + 0.474148i 0.842756π0.842756\pi
600600 0 0
601601 −11.0793 7.40292i −0.451932 0.301972i 0.308694 0.951161i 0.400108π-0.400108\pi
−0.760626 + 0.649190i 0.775108π0.775108\pi
602602 −4.71122 3.14793i −0.192015 0.128300i
603603 −2.60110 + 1.07741i −0.105925 + 0.0438755i
604604 5.17302 + 2.14274i 0.210487 + 0.0871867i
605605 0 0
606606 −20.4377 + 30.5872i −0.830226 + 1.24252i
607607 30.4622 20.3542i 1.23642 0.826152i 0.246693 0.969094i 0.420656π-0.420656\pi
0.989731 + 0.142942i 0.0456561π0.0456561\pi
608608 −6.70375 −0.271873
609609 2.66314 1.77945i 0.107916 0.0721070i
610610 0 0
611611 19.5043i 0.789060i
612612 −7.79178 2.99845i −0.314964 0.121205i
613613 −14.5991 + 14.5991i −0.589652 + 0.589652i −0.937537 0.347885i 0.886900π-0.886900\pi
0.347885 + 0.937537i 0.386900π0.386900\pi
614614 −4.26824 + 1.76796i −0.172252 + 0.0713493i
615615 0 0
616616 6.20305 6.20305i 0.249928 0.249928i
617617 −12.4489 18.6311i −0.501174 0.750060i 0.491501 0.870877i 0.336449π-0.336449\pi
−0.992675 + 0.120817i 0.961449π0.961449\pi
618618 −34.9418 + 6.95036i −1.40557 + 0.279585i
619619 6.26244 + 31.4834i 0.251709 + 1.26543i 0.875264 + 0.483646i 0.160688π0.160688\pi
−0.623555 + 0.781780i 0.714312π0.714312\pi
620620 0 0
621621 −4.27015 + 10.3091i −0.171355 + 0.413688i
622622 −12.0702 + 18.0643i −0.483971 + 0.724314i
623623 −7.16505 36.0211i −0.287062 1.44316i
624624 4.04080 + 0.803765i 0.161761 + 0.0321764i
625625 0 0
626626 −11.6411 17.4221i −0.465272 0.696328i
627627 −52.0386 21.5551i −2.07822 0.860828i
628628 −1.72453 1.72453i −0.0688163 0.0688163i
629629 5.66498 3.99653i 0.225877 0.159352i
630630 0 0
631631 −10.6606 25.7369i −0.424390 1.02457i −0.981037 0.193819i 0.937912π-0.937912\pi
0.556647 0.830749i 0.312088π-0.312088\pi
632632 −5.05643 1.00579i −0.201134 0.0400080i
633633 49.8131i 1.97989i
634634 −1.11641 + 5.61256i −0.0443382 + 0.222903i
635635 0 0
636636 −4.20960 + 0.837342i −0.166922 + 0.0332028i
637637 −1.07085 2.58527i −0.0424288 0.102432i
638638 0.875714 + 2.11416i 0.0346699 + 0.0837004i
639639 −16.9082 + 3.36326i −0.668879 + 0.133048i
640640 0 0
641641 −3.83093 + 19.2594i −0.151313 + 0.760700i 0.828376 + 0.560173i 0.189265π0.189265\pi
−0.979688 + 0.200527i 0.935735π0.935735\pi
642642 1.79622i 0.0708912i
643643 9.58258 + 1.90609i 0.377900 + 0.0751690i 0.380386 0.924828i 0.375791π-0.375791\pi
−0.00248571 + 0.999997i 0.500791π0.500791\pi
644644 4.57209 + 11.0380i 0.180166 + 0.434958i
645645 0 0
646646 −20.0337 19.0430i −0.788214 0.749238i
647647 3.93429 + 3.93429i 0.154673 + 0.154673i 0.780201 0.625528i 0.215117π-0.215117\pi
−0.625528 + 0.780201i 0.715117π0.715117\pi
648648 −10.1391 4.19976i −0.398302 0.164982i
649649 −26.4555 39.5935i −1.03847 1.55418i
650650 0 0
651651 22.7873 + 4.53267i 0.893104 + 0.177649i
652652 1.40756 + 7.07627i 0.0551242 + 0.277128i
653653 1.42563 2.13360i 0.0557891 0.0834942i −0.802526 0.596617i 0.796511π-0.796511\pi
0.858315 + 0.513122i 0.171511π0.171511\pi
654654 −11.9355 + 28.8148i −0.466714 + 1.12675i
655655 0 0
656656 0.674255 + 3.38971i 0.0263252 + 0.132346i
657657 9.12889 1.81585i 0.356152 0.0708431i
658658 13.7984 + 20.6508i 0.537919 + 0.805053i
659659 −20.6837 + 20.6837i −0.805724 + 0.805724i −0.983984 0.178259i 0.942953π-0.942953\pi
0.178259 + 0.983984i 0.442953π0.442953\pi
660660 0 0
661661 20.8000 8.61565i 0.809027 0.335110i 0.0604611 0.998171i 0.480743π-0.480743\pi
0.748566 + 0.663061i 0.230743π0.230743\pi
662662 20.9555 20.9555i 0.814460 0.814460i
663663 9.79242 + 13.8805i 0.380306 + 0.539074i
664664 13.9773i 0.542423i
665665 0 0
666666 −2.83095 + 1.89158i −0.109697 + 0.0732973i
667667 −3.11657 −0.120674
668668 12.7964 8.55028i 0.495108 0.330820i
669669 −16.0283 + 23.9880i −0.619688 + 0.927429i
670670 0 0
671671 −22.9538 9.50778i −0.886122 0.367044i
672672 −4.84696 + 2.00768i −0.186975 + 0.0774478i
673673 −24.0812 16.0905i −0.928260 0.620244i −0.00317165 0.999995i 0.501010π-0.501010\pi
−0.925089 + 0.379751i 0.876010π0.876010\pi
674674 −27.3535 18.2770i −1.05362 0.704004i
675675 0 0
676676 6.80377 + 6.80377i 0.261684 + 0.261684i
677677 −2.97809 + 14.9719i −0.114457 + 0.575416i 0.880409 + 0.474216i 0.157268π0.157268\pi
−0.994866 + 0.101200i 0.967732π0.967732\pi
678678 −0.125755 + 0.303600i −0.00482960 + 0.0116597i
679679 26.3341 1.01061
680680 0 0
681681 −57.3518 −2.19773
682682 −6.35234 + 15.3359i −0.243244 + 0.587242i
683683 2.38725 12.0015i 0.0913457 0.459226i −0.907856 0.419282i 0.862282π-0.862282\pi
0.999202 0.0399442i 0.0127180π-0.0127180\pi
684684 9.59849 + 9.59849i 0.367008 + 0.367008i
685685 0 0
686686 16.5846 + 11.0815i 0.633203 + 0.423092i
687687 −23.2918 15.5631i −0.888638 0.593769i
688688 −2.23672 + 0.926479i −0.0852741 + 0.0353217i
689689 3.25125 + 1.34671i 0.123863 + 0.0513056i
690690 0 0
691691 2.95856 4.42779i 0.112549 0.168441i −0.770919 0.636933i 0.780203π-0.780203\pi
0.883468 + 0.468492i 0.155203π0.155203\pi
692692 −2.52491 + 1.68709i −0.0959826 + 0.0641335i
693693 −17.7632 −0.674767
694694 16.3048 10.8945i 0.618923 0.413551i
695695 0 0
696696 1.36854i 0.0518742i
697697 −7.61403 + 12.0452i −0.288402 + 0.456245i
698698 −6.41796 + 6.41796i −0.242923 + 0.242923i
699699 −14.6659 + 6.07483i −0.554717 + 0.229771i
700700 0 0
701701 20.0755 20.0755i 0.758242 0.758242i −0.217760 0.976002i 0.569875π-0.569875\pi
0.976002 + 0.217760i 0.0698750π0.0698750\pi
702702 2.23197 + 3.34038i 0.0842404 + 0.126075i
703703 −11.0555 + 2.19908i −0.416966 + 0.0829397i
704704 −0.731249 3.67624i −0.0275600 0.138553i
705705 0 0
706706 −11.7674 + 28.4091i −0.442873 + 1.06919i
707707 −21.3383 + 31.9351i −0.802510 + 1.20104i
708708 5.55580 + 27.9309i 0.208800 + 1.04971i
709709 4.13454 + 0.822411i 0.155276 + 0.0308863i 0.272116 0.962264i 0.412277π-0.412277\pi
−0.116840 + 0.993151i 0.537277π0.537277\pi
710710 0 0
711711 5.79974 + 8.67993i 0.217507 + 0.325523i
712712 −14.4980 6.00527i −0.543335 0.225057i
713713 −15.9858 15.9858i −0.598672 0.598672i
714714 −20.1879 7.76873i −0.755512 0.290738i
715715 0 0
716716 5.24569 + 12.6642i 0.196041 + 0.473284i
717717 43.1141 + 8.57592i 1.61012 + 0.320274i
718718 15.2609i 0.569532i
719719 −4.31495 + 21.6927i −0.160921 + 0.809003i 0.813026 + 0.582227i 0.197818π0.197818\pi
−0.973947 + 0.226776i 0.927182π0.927182\pi
720720 0 0
721721 −36.4816 + 7.25664i −1.35865 + 0.270251i
722722 9.92693 + 23.9657i 0.369442 + 0.891913i
723723 4.06452 + 9.81262i 0.151161 + 0.364935i
724724 −9.56242 + 1.90208i −0.355385 + 0.0706904i
725725 0 0
726726 1.33357 6.70433i 0.0494936 0.248821i
727727 13.9898i 0.518853i −0.965763 0.259427i 0.916466π-0.916466\pi
0.965763 0.259427i 0.0835335π-0.0835335\pi
728728 4.21886 + 0.839184i 0.156361 + 0.0311022i
729729 2.87875 + 6.94991i 0.106620 + 0.257404i
730730 0 0
731731 −9.31607 3.58503i −0.344567 0.132597i
732732 10.5065 + 10.5065i 0.388332 + 0.388332i
733733 −33.9907 14.0794i −1.25548 0.520035i −0.346958 0.937881i 0.612785π-0.612785\pi
−0.908518 + 0.417845i 0.862785π0.862785\pi
734734 −18.3527 27.4667i −0.677410 1.01382i
735735 0 0
736736 5.00678 + 0.995910i 0.184552 + 0.0367097i
737737 −1.01673 5.11145i −0.0374518 0.188283i
738738 3.88801 5.81882i 0.143120 0.214194i
739739 −9.20457 + 22.2218i −0.338596 + 0.817442i 0.659255 + 0.751919i 0.270872π0.270872\pi
−0.997851 + 0.0655233i 0.979128π0.979128\pi
740740 0 0
741741 −5.38824 27.0885i −0.197942 0.995122i
742742 −4.39510 + 0.874240i −0.161349 + 0.0320944i
743743 3.30617 + 4.94803i 0.121292 + 0.181526i 0.887147 0.461487i 0.152684π-0.152684\pi
−0.765855 + 0.643013i 0.777684π0.777684\pi
744744 7.01961 7.01961i 0.257351 0.257351i
745745 0 0
746746 3.41982 1.41654i 0.125209 0.0518631i
747747 20.0128 20.0128i 0.732229 0.732229i
748748 8.25763 13.0634i 0.301929 0.477645i
749749 1.87537i 0.0685246i
750750 0 0
751751 −11.7286 + 7.83680i −0.427983 + 0.285969i −0.750847 0.660476i 0.770354π-0.770354\pi
0.322864 + 0.946445i 0.395354π0.395354\pi
752752 10.6121 0.386982
753753 4.18034 2.79322i 0.152340 0.101790i
754754 −0.623394 + 0.932975i −0.0227027 + 0.0339770i
755755 0 0
756756 −4.72635 1.95772i −0.171896 0.0712015i
757757 29.1438 12.0718i 1.05925 0.438755i 0.216064 0.976379i 0.430678π-0.430678\pi
0.843185 + 0.537624i 0.180678π0.180678\pi
758758 4.33225 + 2.89472i 0.157354 + 0.105141i
759759 35.6634 + 23.8295i 1.29450 + 0.864957i
760760 0 0
761761 −8.41792 8.41792i −0.305149 0.305149i 0.537875 0.843024i 0.319227π-0.319227\pi
−0.843024 + 0.537875i 0.819227π0.819227\pi
762762 −9.33274 + 46.9188i −0.338089 + 1.69969i
763763 −12.4614 + 30.0845i −0.451133 + 1.08913i
764764 18.4480 0.667425
765765 0 0
766766 2.04336 0.0738297
767767 8.93548 21.5722i 0.322641 0.778925i
768768 −0.437319 + 2.19855i −0.0157804 + 0.0793334i
769769 −7.10275 7.10275i −0.256132 0.256132i 0.567347 0.823479i 0.307970π-0.307970\pi
−0.823479 + 0.567347i 0.807970π0.807970\pi
770770 0 0
771771 −12.2363 8.17601i −0.440678 0.294452i
772772 −17.3142 11.5690i −0.623152 0.416377i
773773 −1.12415 + 0.465637i −0.0404328 + 0.0167478i −0.402808 0.915284i 0.631966π-0.631966\pi
0.362375 + 0.932032i 0.381966π0.381966\pi
774774 4.52909 + 1.87601i 0.162795 + 0.0674319i
775775 0 0
776776 6.25124 9.35564i 0.224406 0.335848i
777777 −7.33477 + 4.90094i −0.263133 + 0.175820i
778778 3.11695 0.111748
779779 19.2643 12.8720i 0.690215 0.461187i
780780 0 0
781781 31.9120i 1.14190i
782782 12.1333 + 17.1987i 0.433888 + 0.615025i
783783 0.943622 0.943622i 0.0337223 0.0337223i
784784 1.40662 0.582639i 0.0502363 0.0208085i
785785 0 0
786786 −20.4658 + 20.4658i −0.729990 + 0.729990i
787787 3.54648 + 5.30768i 0.126418 + 0.189198i 0.889280 0.457364i 0.151206π-0.151206\pi
−0.762862 + 0.646562i 0.776206π0.776206\pi
788788 −4.15244 + 0.825971i −0.147924 + 0.0294240i
789789 2.24532 + 11.2880i 0.0799357 + 0.401864i
790790 0 0
791791 −0.131297 + 0.316978i −0.00466837 + 0.0112705i
792792 −4.21666 + 6.31067i −0.149832 + 0.224240i
793793 −2.37671 11.9485i −0.0843995 0.424305i
794794 −8.16045 1.62321i −0.289603 0.0576057i
795795 0 0
796796 −14.6373 21.9062i −0.518804 0.776446i
797797 3.16463 + 1.31083i 0.112097 + 0.0464320i 0.438027 0.898962i 0.355677π-0.355677\pi
−0.325930 + 0.945394i 0.605677π0.605677\pi
798798 24.8689 + 24.8689i 0.880350 + 0.880350i
799799 31.7134 + 30.1452i 1.12194 + 1.06646i
800800 0 0
801801 12.1600 + 29.3568i 0.429651 + 1.03727i
802802 −19.6080 3.90028i −0.692384 0.137724i
803803 17.2295i 0.608017i
804804 −0.608051 + 3.05688i −0.0214443 + 0.107808i
805805 0 0
806806 −7.98306 + 1.58793i −0.281191 + 0.0559324i
807807 23.4825 + 56.6918i 0.826623 + 1.99564i
808808 6.28015 + 15.1616i 0.220935 + 0.533384i
809809 27.1193 5.39436i 0.953464 0.189656i 0.306239 0.951955i 0.400929π-0.400929\pi
0.647225 + 0.762299i 0.275929π0.275929\pi
810810 0 0
811811 −7.20886 + 36.2414i −0.253137 + 1.27261i 0.619794 + 0.784764i 0.287216π0.287216\pi
−0.872932 + 0.487843i 0.837784π0.837784\pi
812812 1.42884i 0.0501425i
813813 38.3487 + 7.62804i 1.34495 + 0.267527i
814814 −2.41188 5.82279i −0.0845363 0.204089i
815815 0 0
816816 −7.55222 + 5.32794i −0.264381 + 0.186515i
817817 11.4762 + 11.4762i 0.401502 + 0.401502i
818818 28.4382 + 11.7795i 0.994317 + 0.411860i
819819 −4.83905 7.24215i −0.169090 0.253061i
820820 0 0
821821 −14.0812 2.80092i −0.491436 0.0977528i −0.0568496 0.998383i 0.518106π-0.518106\pi
−0.434587 + 0.900630i 0.643106π0.643106\pi
822822 0.941037 + 4.73091i 0.0328224 + 0.165009i
823823 26.8104 40.1247i 0.934553 1.39866i 0.0175205 0.999847i 0.494423π-0.494423\pi
0.917033 0.398812i 0.130577π-0.130577\pi
824824 −6.08203 + 14.6833i −0.211878 + 0.511518i
825825 0 0
826826 5.80062 + 29.1617i 0.201829 + 1.01466i
827827 23.6452 4.70333i 0.822225 0.163551i 0.233988 0.972239i 0.424822π-0.424822\pi
0.588237 + 0.808689i 0.299822π0.299822\pi
828828 −5.74279 8.59470i −0.199576 0.298686i
829829 16.0770 16.0770i 0.558377 0.558377i −0.370468 0.928845i 0.620803π-0.620803\pi
0.928845 + 0.370468i 0.120803π0.120803\pi
830830 0 0
831831 −47.1094 + 19.5134i −1.63421 + 0.676911i
832832 1.29962 1.29962i 0.0450561 0.0450561i
833833 5.85864 + 2.25453i 0.202990 + 0.0781149i
834834 43.6590i 1.51179i
835835 0 0
836836 −20.8927 + 13.9600i −0.722588 + 0.482818i
837837 9.68020 0.334597
838838 12.4734 8.33444i 0.430885 0.287908i
839839 12.5864 18.8368i 0.434530 0.650320i −0.547988 0.836486i 0.684606π-0.684606\pi
0.982518 + 0.186166i 0.0596062π0.0596062\pi
840840 0 0
841841 −26.4482 10.9552i −0.912005 0.377765i
842842 −12.3293 + 5.10697i −0.424896 + 0.175998i
843843 16.3461 + 10.9221i 0.562988 + 0.376177i
844844 −18.4768 12.3458i −0.635998 0.424960i
845845 0 0
846846 −15.1945 15.1945i −0.522396 0.522396i
847847 1.39234 6.99977i 0.0478414 0.240515i
848848 −0.732730 + 1.76897i −0.0251620 + 0.0607465i
849849 48.0983 1.65073
850850 0 0
851851 8.58362 0.294243
852852 −7.30343 + 17.6320i −0.250211 + 0.604064i
853853 −7.76738 + 39.0492i −0.265950 + 1.33702i 0.584684 + 0.811261i 0.301219π0.301219\pi
−0.850634 + 0.525759i 0.823781π0.823781\pi
854854 10.9695 + 10.9695i 0.375368 + 0.375368i
855855 0 0
856856 −0.666259 0.445180i −0.0227723 0.0152159i
857857 −10.1407 6.77577i −0.346398 0.231456i 0.370184 0.928958i 0.379295π-0.379295\pi
−0.716582 + 0.697502i 0.754295π0.754295\pi
858858 14.2672 5.90966i 0.487074 0.201752i
859859 28.2759 + 11.7123i 0.964762 + 0.399617i 0.808760 0.588139i 0.200139π-0.200139\pi
0.156002 + 0.987757i 0.450139π0.450139\pi
860860 0 0
861861 10.0735 15.0761i 0.343305 0.513792i
862862 0.709006 0.473743i 0.0241488 0.0161357i
863863 32.7720 1.11557 0.557785 0.829985i 0.311651π-0.311651\pi
0.557785 + 0.829985i 0.311651π0.311651\pi
864864 −1.81746 + 1.21439i −0.0618314 + 0.0413144i
865865 0 0
866866 9.40823i 0.319705i
867867 −37.7041 5.53108i −1.28050 0.187845i
868868 7.32893 7.32893i 0.248760 0.248760i
869869 −17.8531 + 7.39501i −0.605626 + 0.250859i
870870 0 0
871871 1.80699 1.80699i 0.0612276 0.0612276i
872872 7.72993 + 11.5687i 0.261768 + 0.391764i
873873 −22.3461 + 4.44491i −0.756299 + 0.150437i
874874 −6.67633 33.5642i −0.225830 1.13533i
875875 0 0
876876 3.94318 9.51969i 0.133228 0.321640i
877877 24.0243 35.9550i 0.811244 1.21411i −0.162554 0.986700i 0.551973π-0.551973\pi
0.973798 0.227413i 0.0730267π-0.0730267\pi
878878 −4.93692 24.8196i −0.166613 0.837621i
879879 −66.2395 13.1759i −2.23420 0.444411i
880880 0 0
881881 −15.1740 22.7095i −0.511225 0.765103i 0.482626 0.875827i 0.339683π-0.339683\pi
−0.993851 + 0.110724i 0.964683π0.964683\pi
882882 −2.84823 1.17978i −0.0959049 0.0397251i
883883 −4.46322 4.46322i −0.150199 0.150199i 0.628008 0.778207i 0.283871π-0.283871\pi
−0.778207 + 0.628008i 0.783871π0.783871\pi
884884 7.57557 0.192049i 0.254794 0.00645930i
885885 0 0
886886 8.58626 + 20.7291i 0.288461 + 0.696407i
887887 32.0754 + 6.38020i 1.07699 + 0.214226i 0.701549 0.712621i 0.252492π-0.252492\pi
0.375439 + 0.926847i 0.377492π0.377492\pi
888888 3.76920i 0.126486i
889889 −9.74399 + 48.9864i −0.326803 + 1.64295i
890890 0 0
891891 −40.3448 + 8.02509i −1.35160 + 0.268851i
892892 4.92520 + 11.8905i 0.164908 + 0.398123i
893893 −27.2244 65.7255i −0.911029 2.19942i
894894 −41.8652 + 8.32751i −1.40018 + 0.278514i
895895 0 0
896896 −0.456590 + 2.29543i −0.0152536 + 0.0766851i
897897 21.0319i 0.702233i
898898 21.6653 + 4.30949i 0.722980 + 0.143810i
899899 1.03466 + 2.49789i 0.0345079 + 0.0833093i
900900 0 0
901901 −7.21473 + 3.20499i −0.240357 + 0.106774i
902902 9.16016 + 9.16016i 0.305000 + 0.305000i
903903 11.7345 + 4.86059i 0.390500 + 0.161750i
904904 0.0814446 + 0.121890i 0.00270881 + 0.00405402i
905905 0 0
906906 −12.3102 2.44866i −0.408980 0.0813511i
907907 −9.55754 48.0490i −0.317353 1.59544i −0.729274 0.684221i 0.760142π-0.760142\pi
0.411922 0.911219i 0.364858π-0.364858\pi
908908 −14.2142 + 21.2731i −0.471716 + 0.705973i
909909 12.7166 30.7005i 0.421782 1.01827i
910910 0 0
911911 3.36353 + 16.9096i 0.111439 + 0.560241i 0.995651 + 0.0931564i 0.0296957π0.0296957\pi
−0.884213 + 0.467085i 0.845304π0.845304\pi
912912 14.7386 2.93168i 0.488042 0.0970777i
913913 29.1065 + 43.5610i 0.963285 + 1.44166i
914914 9.20664 9.20664i 0.304528 0.304528i
915915 0 0
916916 −11.5454 + 4.78226i −0.381471 + 0.158010i
917917 −21.3676 + 21.3676i −0.705620 + 0.705620i
918918 −8.88102 1.53367i −0.293117 0.0506186i
919919 34.3332i 1.13255i −0.824217 0.566274i 0.808385π-0.808385\pi
0.824217 0.566274i 0.191615π-0.191615\pi
920920 0 0
921921 8.61080 5.75355i 0.283735 0.189586i
922922 4.89848 0.161323
923923 13.0107 8.69348i 0.428253 0.286149i
924924 −10.9250 + 16.3504i −0.359407 + 0.537890i
925925 0 0
926926 5.22742 + 2.16527i 0.171784 + 0.0711552i
927927 29.7320 12.3154i 0.976527 0.404491i
928928 −0.507621 0.339182i −0.0166635 0.0111342i
929929 9.78051 + 6.53513i 0.320888 + 0.214411i 0.705573 0.708637i 0.250690π-0.250690\pi
−0.384685 + 0.923048i 0.625690π0.625690\pi
930930 0 0
931931 −7.21711 7.21711i −0.236531 0.236531i
932932 −1.38155 + 6.94554i −0.0452543 + 0.227509i
933933 18.6371 44.9939i 0.610151 1.47303i
934934 −27.6107 −0.903451
935935 0 0
936936 −3.72161 −0.121645
937937 8.46339 20.4324i 0.276487 0.667498i −0.723246 0.690590i 0.757351π-0.757351\pi
0.999733 + 0.0230916i 0.00735093π0.00735093\pi
938938 −0.634845 + 3.19158i −0.0207284 + 0.104209i
939939 33.2126 + 33.2126i 1.08385 + 1.08385i
940940 0 0
941941 −6.14772 4.10778i −0.200410 0.133910i 0.451316 0.892364i 0.350955π-0.350955\pi
−0.651726 + 0.758455i 0.725955π0.725955\pi
942942 4.54564 + 3.03730i 0.148105 + 0.0989606i
943943 −16.3000 + 6.75169i −0.530802 + 0.219865i
944944 11.7372 + 4.86169i 0.382012 + 0.158235i
945945 0 0
946946 −5.04155 + 7.54522i −0.163915 + 0.245316i
947947 −6.90636 + 4.61468i −0.224427 + 0.149957i −0.662701 0.748884i 0.730590π-0.730590\pi
0.438274 + 0.898841i 0.355590π0.355590\pi
948948 11.5567 0.375343
949949 −7.02459 + 4.69368i −0.228028 + 0.152363i
950950 0 0
951951 12.8277i 0.415968i
952952 −7.88502 + 5.56272i −0.255555 + 0.180289i
953953 −18.9533 + 18.9533i −0.613958 + 0.613958i −0.943975 0.330017i 0.892946π-0.892946\pi
0.330017 + 0.943975i 0.392946π0.392946\pi
954954 3.58195 1.48369i 0.115970 0.0480363i
955955 0 0
956956 13.8665 13.8665i 0.448475 0.448475i
957957 −2.84987 4.26513i −0.0921231 0.137872i
958958 −2.12413 + 0.422516i −0.0686275 + 0.0136509i
959959 0.982504 + 4.93938i 0.0317267 + 0.159501i
960960 0 0
961961 4.35786 10.5208i 0.140576 0.339381i
962962 1.71694 2.56959i 0.0553564 0.0828468i
963963 0.316543 + 1.59137i 0.0102004 + 0.0512811i
964964 4.64708 + 0.924362i 0.149672 + 0.0297717i
965965 0 0
966966 −14.8791 22.2682i −0.478728 0.716466i
967967 −2.71453 1.12440i −0.0872936 0.0361582i 0.338609 0.940927i 0.390043π-0.390043\pi
−0.425903 + 0.904769i 0.640043π0.640043\pi
968968 −2.15627 2.15627i −0.0693052 0.0693052i
969969 52.3730 + 33.1060i 1.68246 + 1.06352i
970970 0 0
971971 21.5927 + 52.1293i 0.692941 + 1.67291i 0.738769 + 0.673959i 0.235408π0.235408\pi
−0.0458273 + 0.998949i 0.514592π0.514592\pi
972972 17.6965 + 3.52005i 0.567615 + 0.112906i
973973 45.5828i 1.46132i
974974 −6.78474 + 34.1092i −0.217397 + 1.09293i
975975 0 0
976976 6.50106 1.29314i 0.208094 0.0413924i
977977 −0.198220 0.478546i −0.00634163 0.0153100i 0.920677 0.390325i 0.127637π-0.127637\pi
−0.927019 + 0.375015i 0.877637π0.877637\pi
978978 −6.18918 14.9420i −0.197908 0.477793i
979979 −57.6894 + 11.4751i −1.84376 + 0.366747i
980980 0 0
981981 5.49632 27.6319i 0.175484 0.882218i
982982 1.29098i 0.0411969i
983983 18.9985 + 3.77904i 0.605958 + 0.120533i 0.488527 0.872549i 0.337534π-0.337534\pi
0.117431 + 0.993081i 0.462534π0.462534\pi
984984 −2.96477 7.15759i −0.0945135 0.228176i
985985 0 0
986986 −0.553491 2.45559i −0.0176268 0.0782021i
987987 −39.3676 39.3676i −1.25308 1.25308i
988988 −11.3832 4.71507i −0.362147 0.150006i
989989 −6.86624 10.2761i −0.218334 0.326760i
990990 0 0
991991 17.3723 + 3.45556i 0.551848 + 0.109769i 0.463135 0.886288i 0.346725π-0.346725\pi
0.0887133 + 0.996057i 0.471725π0.471725\pi
992992 −0.863974 4.34349i −0.0274312 0.137906i
993993 −36.9076 + 55.2361i −1.17123 + 1.75287i
994994 −7.62526 + 18.4090i −0.241859 + 0.583898i
995995 0 0
996996 −6.11253 30.7297i −0.193683 0.973709i
997997 −39.3912 + 7.83540i −1.24753 + 0.248150i −0.774317 0.632798i 0.781907π-0.781907\pi
−0.473215 + 0.880947i 0.656907π0.656907\pi
998998 6.25854 + 9.36656i 0.198110 + 0.296493i
999999 −2.59891 + 2.59891i −0.0822258 + 0.0822258i
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 850.2.v.a.607.3 yes 24
5.2 odd 4 850.2.s.a.743.1 yes 24
5.3 odd 4 850.2.s.b.743.3 yes 24
5.4 even 2 850.2.v.b.607.1 yes 24
17.10 odd 16 850.2.s.b.707.3 yes 24
85.27 even 16 850.2.v.b.843.1 yes 24
85.44 odd 16 850.2.s.a.707.1 24
85.78 even 16 inner 850.2.v.a.843.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
850.2.s.a.707.1 24 85.44 odd 16
850.2.s.a.743.1 yes 24 5.2 odd 4
850.2.s.b.707.3 yes 24 17.10 odd 16
850.2.s.b.743.3 yes 24 5.3 odd 4
850.2.v.a.607.3 yes 24 1.1 even 1 trivial
850.2.v.a.843.3 yes 24 85.78 even 16 inner
850.2.v.b.607.1 yes 24 5.4 even 2
850.2.v.b.843.1 yes 24 85.27 even 16