Properties

Label 845.2.o.i.357.5
Level 845845
Weight 22
Character 845.357
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 144144
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(258,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.258");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.o (of order 1212, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 144144
Relative dimension: 3636 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 357.5
Character χ\chi == 845.357
Dual form 845.2.o.i.258.5

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+(1.18621+2.05458i)q2+(0.604804+2.25716i)q3+(1.814193.14226i)q4+(2.15457+0.598181i)q5+(5.354921.43485i)q6+(3.23750+1.86917i)q7+3.86318q8+(2.13090+1.23027i)q9+(1.326775.13630i)q10+(1.744770.467511i)q11+(5.995365.99536i)q128.86890iq14+(2.653284.50143i)q15+(0.954169+1.65267i)q16+(0.3721530.0997182i)q175.83745iq18+(1.417545.29032i)q19+(5.78843+5.68502i)q20+(6.177066.17706i)q21+(1.10913+4.13933i)q22+(8.92587+2.39168i)q23+(2.33647+8.71981i)q24+(4.284362.57765i)q25+(0.891365+0.891365i)q27+(11.7468+6.78204i)q28+(0.6621400.382287i)q29+(12.39590.111731i)q30+(3.27268+3.27268i)q31+(1.59949+2.77040i)q32+(2.11049+3.65548i)q33+(0.6463300.646330i)q34+(5.857325.96387i)q35+(7.73169+4.46389i)q36+(1.001310.578108i)q37+(9.18786+9.18786i)q38+(8.32350+2.31088i)q40+(0.789472+2.94635i)q41+(20.01855.36394i)q42+(0.4899981.82870i)q43+(4.634384.63438i)q44+(3.855253.92538i)q45+(5.6740621.1759i)q46+1.94248iq47+(4.307421.15417i)q48+(3.487586.04067i)q49+(0.213823+11.8602i)q500.900318iq51+(1.18715+1.18715i)q53+(2.88872+0.774031i)q54+(3.47958+2.05098i)q55+(12.5070+7.22094i)q56+12.7984q57+(1.570870.906945i)q58+(6.155481.64935i)q59+(9.33112+16.5037i)q60+(1.85832+3.21870i)q61+(2.8418910.6061i)q62+(4.599187.96601i)q6311.4060q6410.0139q66+(5.528079.57490i)q67+(0.361815+1.35031i)q68+(10.796818.7006i)q69+(5.30521+19.1087i)q70+(10.7163+2.87143i)q71+(8.23204+4.75277i)q724.49691q73+(2.375531.37151i)q74+(8.40935+8.11150i)q75+(19.1952+5.14335i)q76+(4.77484+4.77484i)q777.15052iq79+(1.067234.13156i)q80+(5.16367+8.94374i)q81+(6.989971.87296i)q8211.4388iq83+(8.20360+30.6163i)q84+(0.8614800.00776503i)q85+(3.17596+3.17596i)q86+(0.4624171.72576i)q87+(6.740371.80608i)q88+(0.599649+2.23792i)q89+(3.49185+12.5772i)q90+(23.7085+23.7085i)q92+(9.366305.40763i)q93+(3.990982.30419i)q94+(0.110383+12.2463i)q95+(5.28585+5.28585i)q96+(0.4414850.764675i)q97+(8.27401+14.3310i)q98+(3.14277+3.14277i)q99+O(q100)q+(-1.18621 + 2.05458i) q^{2} +(0.604804 + 2.25716i) q^{3} +(-1.81419 - 3.14226i) q^{4} +(-2.15457 + 0.598181i) q^{5} +(-5.35492 - 1.43485i) q^{6} +(-3.23750 + 1.86917i) q^{7} +3.86318 q^{8} +(-2.13090 + 1.23027i) q^{9} +(1.32677 - 5.13630i) q^{10} +(1.74477 - 0.467511i) q^{11} +(5.99536 - 5.99536i) q^{12} -8.86890i q^{14} +(-2.65328 - 4.50143i) q^{15} +(-0.954169 + 1.65267i) q^{16} +(-0.372153 - 0.0997182i) q^{17} -5.83745i q^{18} +(1.41754 - 5.29032i) q^{19} +(5.78843 + 5.68502i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-1.10913 + 4.13933i) q^{22} +(-8.92587 + 2.39168i) q^{23} +(2.33647 + 8.71981i) q^{24} +(4.28436 - 2.57765i) q^{25} +(0.891365 + 0.891365i) q^{27} +(11.7468 + 6.78204i) q^{28} +(-0.662140 - 0.382287i) q^{29} +(12.3959 - 0.111731i) q^{30} +(-3.27268 + 3.27268i) q^{31} +(1.59949 + 2.77040i) q^{32} +(2.11049 + 3.65548i) q^{33} +(0.646330 - 0.646330i) q^{34} +(5.85732 - 5.96387i) q^{35} +(7.73169 + 4.46389i) q^{36} +(-1.00131 - 0.578108i) q^{37} +(9.18786 + 9.18786i) q^{38} +(-8.32350 + 2.31088i) q^{40} +(0.789472 + 2.94635i) q^{41} +(20.0185 - 5.36394i) q^{42} +(0.489998 - 1.82870i) q^{43} +(-4.63438 - 4.63438i) q^{44} +(3.85525 - 3.92538i) q^{45} +(5.67406 - 21.1759i) q^{46} +1.94248i q^{47} +(-4.30742 - 1.15417i) q^{48} +(3.48758 - 6.04067i) q^{49} +(0.213823 + 11.8602i) q^{50} -0.900318i q^{51} +(-1.18715 + 1.18715i) q^{53} +(-2.88872 + 0.774031i) q^{54} +(-3.47958 + 2.05098i) q^{55} +(-12.5070 + 7.22094i) q^{56} +12.7984 q^{57} +(1.57087 - 0.906945i) q^{58} +(-6.15548 - 1.64935i) q^{59} +(-9.33112 + 16.5037i) q^{60} +(1.85832 + 3.21870i) q^{61} +(-2.84189 - 10.6061i) q^{62} +(4.59918 - 7.96601i) q^{63} -11.4060 q^{64} -10.0139 q^{66} +(5.52807 - 9.57490i) q^{67} +(0.361815 + 1.35031i) q^{68} +(-10.7968 - 18.7006i) q^{69} +(5.30521 + 19.1087i) q^{70} +(10.7163 + 2.87143i) q^{71} +(-8.23204 + 4.75277i) q^{72} -4.49691 q^{73} +(2.37553 - 1.37151i) q^{74} +(8.40935 + 8.11150i) q^{75} +(-19.1952 + 5.14335i) q^{76} +(-4.77484 + 4.77484i) q^{77} -7.15052i q^{79} +(1.06723 - 4.13156i) q^{80} +(-5.16367 + 8.94374i) q^{81} +(-6.98997 - 1.87296i) q^{82} -11.4388i q^{83} +(-8.20360 + 30.6163i) q^{84} +(0.861480 - 0.00776503i) q^{85} +(3.17596 + 3.17596i) q^{86} +(0.462417 - 1.72576i) q^{87} +(6.74037 - 1.80608i) q^{88} +(0.599649 + 2.23792i) q^{89} +(3.49185 + 12.5772i) q^{90} +(23.7085 + 23.7085i) q^{92} +(-9.36630 - 5.40763i) q^{93} +(-3.99098 - 2.30419i) q^{94} +(0.110383 + 12.2463i) q^{95} +(-5.28585 + 5.28585i) q^{96} +(-0.441485 - 0.764675i) q^{97} +(8.27401 + 14.3310i) q^{98} +(-3.14277 + 3.14277i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q+4q380q412q10128q1280q16+8q1724q22+36q23+96q25128q274q3080q3556q3848q40+56q42+76q43+76q48+92q95+O(q100) 144 q + 4 q^{3} - 80 q^{4} - 12 q^{10} - 128 q^{12} - 80 q^{16} + 8 q^{17} - 24 q^{22} + 36 q^{23} + 96 q^{25} - 128 q^{27} - 4 q^{30} - 80 q^{35} - 56 q^{38} - 48 q^{40} + 56 q^{42} + 76 q^{43} + 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 171171 677677
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\right) e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.18621 + 2.05458i −0.838777 + 1.45280i 0.0521412 + 0.998640i 0.483395π0.483395\pi
−0.890918 + 0.454164i 0.849938π0.849938\pi
33 0.604804 + 2.25716i 0.349184 + 1.30317i 0.887648 + 0.460522i 0.152338π0.152338\pi
−0.538465 + 0.842648i 0.680995π0.680995\pi
44 −1.81419 3.14226i −0.907093 1.57113i
55 −2.15457 + 0.598181i −0.963554 + 0.267515i
66 −5.35492 1.43485i −2.18614 0.585774i
77 −3.23750 + 1.86917i −1.22366 + 0.706479i −0.965696 0.259676i 0.916384π-0.916384\pi
−0.257962 + 0.966155i 0.583051π0.583051\pi
88 3.86318 1.36584
99 −2.13090 + 1.23027i −0.710299 + 0.410091i
1010 1.32677 5.13630i 0.419560 1.62424i
1111 1.74477 0.467511i 0.526069 0.140960i 0.0139966 0.999902i 0.495545π-0.495545\pi
0.512072 + 0.858942i 0.328878π0.328878\pi
1212 5.99536 5.99536i 1.73071 1.73071i
1313 0 0
1414 8.86890i 2.37031i
1515 −2.65328 4.50143i −0.685074 1.16226i
1616 −0.954169 + 1.65267i −0.238542 + 0.413167i
1717 −0.372153 0.0997182i −0.0902604 0.0241852i 0.213406 0.976964i 0.431544π-0.431544\pi
−0.303667 + 0.952778i 0.598211π0.598211\pi
1818 5.83745i 1.37590i
1919 1.41754 5.29032i 0.325205 1.21368i −0.588901 0.808205i 0.700439π-0.700439\pi
0.914106 0.405476i 0.132894π-0.132894\pi
2020 5.78843 + 5.68502i 1.29433 + 1.27121i
2121 −6.17706 6.17706i −1.34794 1.34794i
2222 −1.10913 + 4.13933i −0.236468 + 0.882509i
2323 −8.92587 + 2.39168i −1.86117 + 0.498699i −0.999955 0.00953735i 0.996964π-0.996964\pi
−0.861217 + 0.508237i 0.830297π0.830297\pi
2424 2.33647 + 8.71981i 0.476929 + 1.77992i
2525 4.28436 2.57765i 0.856872 0.515529i
2626 0 0
2727 0.891365 + 0.891365i 0.171543 + 0.171543i
2828 11.7468 + 6.78204i 2.21994 + 1.28169i
2929 −0.662140 0.382287i −0.122956 0.0709889i 0.437260 0.899335i 0.355949π-0.355949\pi
−0.560217 + 0.828346i 0.689282π0.689282\pi
3030 12.3959 0.111731i 2.26317 0.0203992i
3131 −3.27268 + 3.27268i −0.587792 + 0.587792i −0.937033 0.349241i 0.886439π-0.886439\pi
0.349241 + 0.937033i 0.386439π0.386439\pi
3232 1.59949 + 2.77040i 0.282753 + 0.489742i
3333 2.11049 + 3.65548i 0.367389 + 0.636337i
3434 0.646330 0.646330i 0.110845 0.110845i
3535 5.85732 5.96387i 0.990067 1.00808i
3636 7.73169 + 4.46389i 1.28861 + 0.743982i
3737 −1.00131 0.578108i −0.164615 0.0950403i 0.415429 0.909625i 0.363631π-0.363631\pi
−0.580044 + 0.814585i 0.696965π0.696965\pi
3838 9.18786 + 9.18786i 1.49047 + 1.49047i
3939 0 0
4040 −8.32350 + 2.31088i −1.31606 + 0.365382i
4141 0.789472 + 2.94635i 0.123295 + 0.460142i 0.999773 0.0212988i 0.00678014π-0.00678014\pi
−0.876478 + 0.481441i 0.840113π0.840113\pi
4242 20.0185 5.36394i 3.08892 0.827675i
4343 0.489998 1.82870i 0.0747240 0.278874i −0.918447 0.395545i 0.870556π-0.870556\pi
0.993171 + 0.116671i 0.0372224π0.0372224\pi
4444 −4.63438 4.63438i −0.698660 0.698660i
4545 3.85525 3.92538i 0.574706 0.585161i
4646 5.67406 21.1759i 0.836595 3.12222i
4747 1.94248i 0.283340i 0.989914 + 0.141670i 0.0452472π0.0452472\pi
−0.989914 + 0.141670i 0.954753π0.954753\pi
4848 −4.30742 1.15417i −0.621723 0.166590i
4949 3.48758 6.04067i 0.498226 0.862953i
5050 0.213823 + 11.8602i 0.0302391 + 1.67728i
5151 0.900318i 0.126070i
5252 0 0
5353 −1.18715 + 1.18715i −0.163068 + 0.163068i −0.783924 0.620856i 0.786785π-0.786785\pi
0.620856 + 0.783924i 0.286785π0.286785\pi
5454 −2.88872 + 0.774031i −0.393105 + 0.105332i
5555 −3.47958 + 2.05098i −0.469187 + 0.276553i
5656 −12.5070 + 7.22094i −1.67132 + 0.964938i
5757 12.7984 1.69519
5858 1.57087 0.906945i 0.206266 0.119088i
5959 −6.15548 1.64935i −0.801375 0.214728i −0.165187 0.986262i 0.552823π-0.552823\pi
−0.636187 + 0.771535i 0.719490π0.719490\pi
6060 −9.33112 + 16.5037i −1.20464 + 2.13062i
6161 1.85832 + 3.21870i 0.237933 + 0.412113i 0.960121 0.279584i 0.0901966π-0.0901966\pi
−0.722188 + 0.691697i 0.756863π0.756863\pi
6262 −2.84189 10.6061i −0.360920 1.34697i
6363 4.59918 7.96601i 0.579442 1.00362i
6464 −11.4060 −1.42575
6565 0 0
6666 −10.0139 −1.23263
6767 5.52807 9.57490i 0.675361 1.16976i −0.301002 0.953623i 0.597321π-0.597321\pi
0.976363 0.216136i 0.0693455π-0.0693455\pi
6868 0.361815 + 1.35031i 0.0438765 + 0.163749i
6969 −10.7968 18.7006i −1.29978 2.25129i
7070 5.30521 + 19.1087i 0.634094 + 2.28393i
7171 10.7163 + 2.87143i 1.27179 + 0.340776i 0.830717 0.556695i 0.187931π-0.187931\pi
0.441075 + 0.897470i 0.354597π0.354597\pi
7272 −8.23204 + 4.75277i −0.970155 + 0.560119i
7373 −4.49691 −0.526323 −0.263161 0.964752i 0.584765π-0.584765\pi
−0.263161 + 0.964752i 0.584765π0.584765\pi
7474 2.37553 1.37151i 0.276150 0.159435i
7575 8.40935 + 8.11150i 0.971028 + 0.936636i
7676 −19.1952 + 5.14335i −2.20184 + 0.589982i
7777 −4.77484 + 4.77484i −0.544144 + 0.544144i
7878 0 0
7979 7.15052i 0.804496i −0.915531 0.402248i 0.868229π-0.868229\pi
0.915531 0.402248i 0.131771π-0.131771\pi
8080 1.06723 4.13156i 0.119320 0.461923i
8181 −5.16367 + 8.94374i −0.573741 + 0.993749i
8282 −6.98997 1.87296i −0.771914 0.206834i
8383 11.4388i 1.25557i −0.778388 0.627783i 0.783962π-0.783962\pi
0.778388 0.627783i 0.216038π-0.216038\pi
8484 −8.20360 + 30.6163i −0.895087 + 3.34051i
8585 0.861480 0.00776503i 0.0934407 0.000842235i
8686 3.17596 + 3.17596i 0.342472 + 0.342472i
8787 0.462417 1.72576i 0.0495763 0.185021i
8888 6.74037 1.80608i 0.718526 0.192529i
8989 0.599649 + 2.23792i 0.0635626 + 0.237219i 0.990397 0.138251i 0.0441480π-0.0441480\pi
−0.926835 + 0.375470i 0.877481π0.877481\pi
9090 3.49185 + 12.5772i 0.368074 + 1.32575i
9191 0 0
9292 23.7085 + 23.7085i 2.47178 + 2.47178i
9393 −9.36630 5.40763i −0.971240 0.560746i
9494 −3.99098 2.30419i −0.411638 0.237659i
9595 0.110383 + 12.2463i 0.0113251 + 1.25644i
9696 −5.28585 + 5.28585i −0.539485 + 0.539485i
9797 −0.441485 0.764675i −0.0448260 0.0776409i 0.842742 0.538318i 0.180940π-0.180940\pi
−0.887568 + 0.460677i 0.847607π0.847607\pi
9898 8.27401 + 14.3310i 0.835801 + 1.44765i
9999 −3.14277 + 3.14277i −0.315860 + 0.315860i
100100 −15.8723 8.78625i −1.58723 0.878625i
101101 6.87788 + 3.97094i 0.684374 + 0.395124i 0.801501 0.597993i 0.204035π-0.204035\pi
−0.117127 + 0.993117i 0.537368π0.537368\pi
102102 1.84977 + 1.06797i 0.183155 + 0.105744i
103103 −10.7428 10.7428i −1.05852 1.05852i −0.998178 0.0603388i 0.980782π-0.980782\pi
−0.0603388 0.998178i 0.519218π-0.519218\pi
104104 0 0
105105 17.0039 + 9.61392i 1.65941 + 0.938222i
106106 −1.03088 3.84731i −0.100128 0.373684i
107107 −10.0926 + 2.70430i −0.975686 + 0.261434i −0.711227 0.702963i 0.751860π-0.751860\pi
−0.264459 + 0.964397i 0.585193π0.585193\pi
108108 1.18380 4.41800i 0.113911 0.425123i
109109 −4.13475 4.13475i −0.396037 0.396037i 0.480796 0.876833i 0.340348π-0.340348\pi
−0.876833 + 0.480796i 0.840348π0.840348\pi
110110 −0.0863677 9.58195i −0.00823484 0.913603i
111111 0.699283 2.60976i 0.0663730 0.247707i
112112 7.13401i 0.674101i
113113 14.1646 + 3.79539i 1.33249 + 0.357040i 0.853644 0.520857i 0.174388π-0.174388\pi
0.478849 + 0.877897i 0.341054π0.341054\pi
114114 −15.1816 + 26.2953i −1.42189 + 2.46278i
115115 17.8008 10.4923i 1.65993 0.978414i
116116 2.77416i 0.257574i
117117 0 0
118118 10.6904 10.6904i 0.984132 0.984132i
119119 1.39123 0.372780i 0.127534 0.0341727i
120120 −10.2501 17.3898i −0.935702 1.58747i
121121 −6.70061 + 3.86860i −0.609146 + 0.351691i
122122 −8.81743 −0.798292
123123 −6.17290 + 3.56393i −0.556592 + 0.321348i
124124 16.2209 + 4.34637i 1.45668 + 0.390316i
125125 −7.68906 + 8.11655i −0.687730 + 0.725966i
126126 10.9112 + 18.8987i 0.972046 + 1.68363i
127127 −1.82032 6.79351i −0.161527 0.602827i −0.998458 0.0555178i 0.982319π-0.982319\pi
0.836931 0.547309i 0.184348π-0.184348\pi
128128 10.3309 17.8937i 0.913134 1.58159i
129129 4.42401 0.389513
130130 0 0
131131 −9.34748 −0.816693 −0.408347 0.912827i 0.633895π-0.633895\pi
−0.408347 + 0.912827i 0.633895π0.633895\pi
132132 7.65764 13.2634i 0.666512 1.15443i
133133 5.29923 + 19.7770i 0.459501 + 1.71488i
134134 13.1149 + 22.7157i 1.13295 + 1.96233i
135135 −2.45371 1.38731i −0.211181 0.119401i
136136 −1.43770 0.385229i −0.123281 0.0330331i
137137 11.8630 6.84910i 1.01352 0.585158i 0.101303 0.994856i 0.467699π-0.467699\pi
0.912222 + 0.409697i 0.134366π0.134366\pi
138138 51.2290 4.36090
139139 −7.78210 + 4.49300i −0.660069 + 0.381091i −0.792303 0.610127i 0.791118π-0.791118\pi
0.132234 + 0.991219i 0.457785π0.457785\pi
140140 −29.3663 7.58566i −2.48190 0.641105i
141141 −4.38449 + 1.17482i −0.369241 + 0.0989377i
142142 −18.6113 + 18.6113i −1.56183 + 1.56183i
143143 0 0
144144 4.69556i 0.391297i
145145 1.65531 + 0.427585i 0.137466 + 0.0355090i
146146 5.33427 9.23923i 0.441467 0.764644i
147147 15.7441 + 4.21861i 1.29855 + 0.347945i
148148 4.19518i 0.344842i
149149 3.28972 12.2774i 0.269505 1.00581i −0.689930 0.723876i 0.742359π-0.742359\pi
0.959435 0.281930i 0.0909745π-0.0909745\pi
150150 −26.6409 + 7.65570i −2.17522 + 0.625086i
151151 −2.96123 2.96123i −0.240981 0.240981i 0.576275 0.817256i 0.304506π-0.304506\pi
−0.817256 + 0.576275i 0.804506π0.804506\pi
152152 5.47620 20.4374i 0.444178 1.65770i
153153 0.915701 0.245361i 0.0740300 0.0198363i
154154 −4.14631 15.4742i −0.334119 1.24695i
155155 5.09358 9.00889i 0.409126 0.723612i
156156 0 0
157157 −13.0366 13.0366i −1.04044 1.04044i −0.999147 0.0412907i 0.986853π-0.986853\pi
−0.0412907 0.999147i 0.513147π-0.513147\pi
158158 14.6913 + 8.48201i 1.16878 + 0.674793i
159159 −3.39759 1.96160i −0.269446 0.155565i
160160 −5.10342 5.01224i −0.403461 0.396252i
161161 24.4270 24.4270i 1.92512 1.92512i
162162 −12.2504 21.2183i −0.962482 1.66707i
163163 −7.92191 13.7211i −0.620492 1.07472i −0.989394 0.145255i 0.953600π-0.953600\pi
0.368903 0.929468i 0.379734π-0.379734\pi
164164 7.82595 7.82595i 0.611104 0.611104i
165165 −6.73384 6.61353i −0.524229 0.514863i
166166 23.5018 + 13.5688i 1.82409 + 1.05314i
167167 −10.8109 6.24168i −0.836573 0.482996i 0.0195249 0.999809i 0.493785π-0.493785\pi
−0.856098 + 0.516814i 0.827118π0.827118\pi
168168 −23.8631 23.8631i −1.84108 1.84108i
169169 0 0
170170 −1.00594 + 1.77919i −0.0771523 + 0.136457i
171171 3.48792 + 13.0171i 0.266728 + 0.995441i
172172 −6.63520 + 1.77790i −0.505929 + 0.135563i
173173 4.18301 15.6112i 0.318029 1.18690i −0.603108 0.797660i 0.706071π-0.706071\pi
0.921137 0.389239i 0.127262π-0.127262\pi
174174 2.99719 + 2.99719i 0.227216 + 0.227216i
175175 −9.05254 + 16.3533i −0.684307 + 1.23619i
176176 −0.892168 + 3.32962i −0.0672497 + 0.250979i
177177 14.8914i 1.11931i
178178 −5.30928 1.42262i −0.397947 0.106630i
179179 −9.22405 + 15.9765i −0.689438 + 1.19414i 0.282582 + 0.959243i 0.408809π0.408809\pi
−0.972020 + 0.234898i 0.924524π0.924524\pi
180180 −19.3287 4.99283i −1.44068 0.372143i
181181 2.18983i 0.162769i −0.996683 0.0813844i 0.974066π-0.974066\pi
0.996683 0.0813844i 0.0259342π-0.0259342\pi
182182 0 0
183183 −6.14120 + 6.14120i −0.453971 + 0.453971i
184184 −34.4822 + 9.23949i −2.54206 + 0.681144i
185185 2.50321 + 0.646609i 0.184040 + 0.0475396i
186186 22.2208 12.8292i 1.62931 0.940681i
187187 −0.695942 −0.0508923
188188 6.10379 3.52402i 0.445164 0.257016i
189189 −4.55190 1.21968i −0.331102 0.0887185i
190190 −25.2919 14.2999i −1.83487 1.03742i
191191 −4.07316 7.05492i −0.294724 0.510476i 0.680197 0.733029i 0.261894π-0.261894\pi
−0.974921 + 0.222553i 0.928561π0.928561\pi
192192 −6.89839 25.7451i −0.497849 1.85800i
193193 −11.6235 + 20.1326i −0.836681 + 1.44917i 0.0559740 + 0.998432i 0.482174π0.482174\pi
−0.892655 + 0.450741i 0.851160π0.851160\pi
194194 2.09477 0.150396
195195 0 0
196196 −25.3085 −1.80775
197197 −11.0344 + 19.1122i −0.786172 + 1.36169i 0.142125 + 0.989849i 0.454606π0.454606\pi
−0.928297 + 0.371840i 0.878727π0.878727\pi
198198 −2.72907 10.1850i −0.193947 0.723819i
199199 4.06851 + 7.04686i 0.288409 + 0.499538i 0.973430 0.228984i 0.0735405π-0.0735405\pi
−0.685021 + 0.728523i 0.740207π0.740207\pi
200200 16.5513 9.95792i 1.17035 0.704131i
201201 24.9554 + 6.68679i 1.76022 + 0.471650i
202202 −16.3172 + 9.42075i −1.14807 + 0.662841i
203203 2.85823 0.200609
204204 −2.82904 + 1.63335i −0.198072 + 0.114357i
205205 −3.46342 5.87587i −0.241896 0.410389i
206206 34.8150 9.32865i 2.42568 0.649958i
207207 16.0777 16.0777i 1.11748 1.11748i
208208 0 0
209209 9.89312i 0.684321i
210210 −39.9227 + 23.5317i −2.75493 + 1.62384i
211211 12.3867 21.4544i 0.852737 1.47698i −0.0259913 0.999662i 0.508274π-0.508274\pi
0.878729 0.477322i 0.158392π-0.158392\pi
212212 5.88407 + 1.57663i 0.404120 + 0.108284i
213213 25.9250i 1.77635i
214214 6.41572 23.9438i 0.438570 1.63676i
215215 0.0381560 + 4.23317i 0.00260222 + 0.288700i
216216 3.44350 + 3.44350i 0.234301 + 0.234301i
217217 4.47810 16.7125i 0.303993 1.13452i
218218 13.3998 3.59047i 0.907551 0.243177i
219219 −2.71974 10.1502i −0.183783 0.685889i
220220 12.7573 + 7.21291i 0.860098 + 0.486295i
221221 0 0
222222 4.53245 + 4.53245i 0.304198 + 0.304198i
223223 −25.5668 14.7610i −1.71208 0.988469i −0.931752 0.363096i 0.881720π-0.881720\pi
−0.780326 0.625373i 0.784947π-0.784947\pi
224224 −10.3567 5.97944i −0.691986 0.399518i
225225 −5.95832 + 10.7636i −0.397221 + 0.717576i
226226 −24.6001 + 24.6001i −1.63637 + 1.63637i
227227 3.93339 + 6.81284i 0.261068 + 0.452184i 0.966526 0.256568i 0.0825918π-0.0825918\pi
−0.705458 + 0.708752i 0.749259π0.749259\pi
228228 −23.2187 40.2160i −1.53770 2.66337i
229229 12.4410 12.4410i 0.822125 0.822125i −0.164288 0.986412i 0.552533π-0.552533\pi
0.986412 + 0.164288i 0.0525326π0.0525326\pi
230230 0.441838 + 49.0191i 0.0291339 + 3.23222i
231231 −13.6654 7.88973i −0.899118 0.519106i
232232 −2.55797 1.47684i −0.167939 0.0969595i
233233 1.52992 + 1.52992i 0.100228 + 0.100228i 0.755443 0.655214i 0.227422π-0.227422\pi
−0.655214 + 0.755443i 0.727422π0.727422\pi
234234 0 0
235235 −1.16196 4.18522i −0.0757976 0.273013i
236236 5.98447 + 22.3344i 0.389556 + 1.45384i
237237 16.1398 4.32466i 1.04840 0.280917i
238238 −0.884391 + 3.30059i −0.0573265 + 0.213946i
239239 7.05936 + 7.05936i 0.456632 + 0.456632i 0.897548 0.440916i 0.145346π-0.145346\pi
−0.440916 + 0.897548i 0.645346π0.645346\pi
240240 9.97105 0.0898749i 0.643628 0.00580140i
241241 −3.75087 + 13.9984i −0.241615 + 0.901719i 0.733440 + 0.679755i 0.237914π0.237914\pi
−0.975055 + 0.221965i 0.928753π0.928753\pi
242242 18.3559i 1.17996i
243243 −19.6576 5.26723i −1.26103 0.337893i
244244 6.74268 11.6787i 0.431656 0.747649i
245245 −3.90084 + 15.1013i −0.249215 + 0.964785i
246246 16.9102i 1.07816i
247247 0 0
248248 −12.6430 + 12.6430i −0.802829 + 0.802829i
249249 25.8191 6.91820i 1.63622 0.438423i
250250 −7.55522 25.4257i −0.477834 1.60806i
251251 −15.3843 + 8.88214i −0.971050 + 0.560636i −0.899556 0.436805i 0.856110π-0.856110\pi
−0.0714936 + 0.997441i 0.522777π0.522777\pi
252252 −33.3751 −2.10243
253253 −14.4555 + 8.34588i −0.908808 + 0.524701i
254254 16.1171 + 4.31855i 1.01127 + 0.270970i
255255 0.538553 + 1.93980i 0.0337255 + 0.121475i
256256 13.1033 + 22.6956i 0.818955 + 1.41847i
257257 −2.33322 8.70771i −0.145543 0.543172i −0.999731 0.0232081i 0.992612π-0.992612\pi
0.854188 0.519964i 0.174055π-0.174055\pi
258258 −5.24781 + 9.08947i −0.326714 + 0.565885i
259259 4.32232 0.268576
260260 0 0
261261 1.88127 0.116448
262262 11.0881 19.2051i 0.685023 1.18650i
263263 −1.10325 4.11740i −0.0680295 0.253890i 0.923533 0.383519i 0.125288π-0.125288\pi
−0.991563 + 0.129629i 0.958621π0.958621\pi
264264 8.15321 + 14.1218i 0.501795 + 0.869135i
265265 1.84768 3.26794i 0.113502 0.200748i
266266 −46.9193 12.5720i −2.87681 0.770838i
267267 −4.68867 + 2.70700i −0.286942 + 0.165666i
268268 −40.1158 −2.45046
269269 −1.55678 + 0.898805i −0.0949183 + 0.0548011i −0.546708 0.837323i 0.684119π-0.684119\pi
0.451790 + 0.892125i 0.350786π0.350786\pi
270270 5.76095 3.39568i 0.350600 0.206655i
271271 −2.84859 + 0.763276i −0.173039 + 0.0463657i −0.344298 0.938860i 0.611883π-0.611883\pi
0.171259 + 0.985226i 0.445216π0.445216\pi
272272 0.519898 0.519898i 0.0315235 0.0315235i
273273 0 0
274274 32.4979i 1.96327i
275275 6.27016 6.50039i 0.378105 0.391989i
276276 −39.1748 + 67.8527i −2.35804 + 4.08425i
277277 27.5242 + 7.37510i 1.65377 + 0.443127i 0.960665 0.277709i 0.0895752π-0.0895752\pi
0.693106 + 0.720836i 0.256242π0.256242\pi
278278 21.3186i 1.27860i
279279 2.94746 11.0001i 0.176460 0.658556i
280280 22.6279 23.0395i 1.35227 1.37687i
281281 2.57874 + 2.57874i 0.153835 + 0.153835i 0.779828 0.625993i 0.215306π-0.215306\pi
−0.625993 + 0.779828i 0.715306π0.715306\pi
282282 2.78717 10.4018i 0.165973 0.619421i
283283 7.54151 2.02074i 0.448296 0.120121i −0.0276057 0.999619i 0.508788π-0.508788\pi
0.475902 + 0.879498i 0.342122π0.342122\pi
284284 −10.4186 38.8827i −0.618230 2.30727i
285285 −27.5751 + 7.65576i −1.63341 + 0.453488i
286286 0 0
287287 −8.06314 8.06314i −0.475952 0.475952i
288288 −6.81670 3.93563i −0.401678 0.231909i
289289 −14.5939 8.42578i −0.858463 0.495634i
290290 −2.84204 + 2.89374i −0.166891 + 0.169927i
291291 1.45898 1.45898i 0.0855269 0.0855269i
292292 8.15822 + 14.1305i 0.477424 + 0.826922i
293293 11.2799 + 19.5374i 0.658979 + 1.14139i 0.980880 + 0.194612i 0.0623449π0.0623449\pi
−0.321901 + 0.946773i 0.604322π0.604322\pi
294294 −27.3432 + 27.3432i −1.59469 + 1.59469i
295295 14.2490 0.128435i 0.829610 0.00747776i
296296 −3.86825 2.23333i −0.224837 0.129810i
297297 1.97195 + 1.13851i 0.114424 + 0.0660629i
298298 21.3226 + 21.3226i 1.23518 + 1.23518i
299299 0 0
300300 10.2323 41.1402i 0.590765 2.37523i
301301 1.83178 + 6.83629i 0.105582 + 0.394037i
302302 9.59671 2.57143i 0.552229 0.147969i
303303 −4.80328 + 17.9261i −0.275941 + 1.02983i
304304 7.39057 + 7.39057i 0.423878 + 0.423878i
305305 −5.92925 5.82332i −0.339508 0.333442i
306306 −0.582100 + 2.17243i −0.0332764 + 0.124189i
307307 20.4085i 1.16477i −0.812912 0.582387i 0.802119π-0.802119\pi
0.812912 0.582387i 0.197881π-0.197881\pi
308308 23.6662 + 6.34135i 1.34851 + 0.361332i
309309 17.7509 30.7454i 1.00981 1.74904i
310310 12.4674 + 21.1516i 0.708100 + 1.20133i
311311 21.3762i 1.21213i 0.795413 + 0.606067i 0.207254π0.207254\pi
−0.795413 + 0.606067i 0.792746π0.792746\pi
312312 0 0
313313 −5.22723 + 5.22723i −0.295461 + 0.295461i −0.839233 0.543772i 0.816996π-0.816996\pi
0.543772 + 0.839233i 0.316996π0.316996\pi
314314 42.2490 11.3206i 2.38425 0.638857i
315315 −5.14415 + 19.9145i −0.289840 + 1.12205i
316316 −22.4688 + 12.9724i −1.26397 + 0.729753i
317317 −25.8830 −1.45373 −0.726867 0.686779i 0.759024π-0.759024\pi
−0.726867 + 0.686779i 0.759024π0.759024\pi
318318 8.06051 4.65374i 0.452011 0.260969i
319319 −1.33401 0.357446i −0.0746901 0.0200132i
320320 24.5751 6.82285i 1.37379 0.381409i
321321 −12.2080 21.1450i −0.681387 1.18020i
322322 21.2116 + 79.1627i 1.18207 + 4.41156i
323323 −1.05508 + 1.82745i −0.0587063 + 0.101682i
324324 37.4715 2.08175
325325 0 0
326326 37.5882 2.08182
327327 6.83207 11.8335i 0.377814 0.654393i
328328 3.04987 + 11.3823i 0.168401 + 0.628481i
329329 −3.63083 6.28878i −0.200174 0.346711i
330330 21.5757 5.99015i 1.18771 0.329747i
331331 10.1654 + 2.72380i 0.558738 + 0.149714i 0.527127 0.849787i 0.323269π-0.323269\pi
0.0316117 + 0.999500i 0.489936π0.489936\pi
332332 −35.9436 + 20.7520i −1.97266 + 1.13892i
333333 2.84492 0.155901
334334 25.6480 14.8079i 1.40340 0.810251i
335335 −6.18310 + 23.9366i −0.337819 + 1.30780i
336336 16.1026 4.31468i 0.878468 0.235385i
337337 6.67935 6.67935i 0.363847 0.363847i −0.501380 0.865227i 0.667174π-0.667174\pi
0.865227 + 0.501380i 0.167174π0.167174\pi
338338 0 0
339339 34.2672i 1.86114i
340340 −1.58729 2.69291i −0.0860826 0.146044i
341341 −4.18008 + 7.24011i −0.226364 + 0.392074i
342342 −30.8820 8.27480i −1.66991 0.447450i
343343 0.0928245i 0.00501205i
344344 1.89295 7.06459i 0.102061 0.380897i
345345 34.4488 + 33.8333i 1.85466 + 1.82153i
346346 27.1125 + 27.1125i 1.45758 + 1.45758i
347347 −1.84430 + 6.88301i −0.0990071 + 0.369500i −0.997596 0.0692910i 0.977926π-0.977926\pi
0.898589 + 0.438791i 0.144593π0.144593\pi
348348 −6.26171 + 1.67782i −0.335663 + 0.0899406i
349349 8.44064 + 31.5009i 0.451817 + 1.68620i 0.697281 + 0.716798i 0.254393π0.254393\pi
−0.245464 + 0.969406i 0.578940π0.578940\pi
350350 −22.8609 37.9976i −1.22197 2.03106i
351351 0 0
352352 4.08594 + 4.08594i 0.217781 + 0.217781i
353353 11.1895 + 6.46025i 0.595556 + 0.343844i 0.767291 0.641299i 0.221604π-0.221604\pi
−0.171736 + 0.985143i 0.554937π0.554937\pi
354354 30.5955 + 17.6643i 1.62613 + 0.938849i
355355 −24.8067 + 0.223597i −1.31660 + 0.0118673i
356356 5.94425 5.94425i 0.315045 0.315045i
357357 1.68285 + 2.91478i 0.0890657 + 0.154266i
358358 −21.8833 37.9030i −1.15657 2.00324i
359359 −12.5304 + 12.5304i −0.661330 + 0.661330i −0.955693 0.294364i 0.904892π-0.904892\pi
0.294364 + 0.955693i 0.404892π0.404892\pi
360360 14.8935 15.1644i 0.784957 0.799236i
361361 −9.52355 5.49842i −0.501239 0.289391i
362362 4.49917 + 2.59760i 0.236471 + 0.136527i
363363 −12.7846 12.7846i −0.671017 0.671017i
364364 0 0
365365 9.68891 2.68996i 0.507140 0.140799i
366366 −5.33281 19.9023i −0.278751 1.04031i
367367 33.6660 9.02077i 1.75735 0.470880i 0.771179 0.636618i 0.219667π-0.219667\pi
0.986170 + 0.165738i 0.0530006π0.0530006\pi
368368 4.56413 17.0336i 0.237922 0.887936i
369369 −5.30710 5.30710i −0.276277 0.276277i
370370 −4.29784 + 4.37602i −0.223434 + 0.227499i
371371 1.62442 6.06240i 0.0843354 0.314744i
372372 39.2418i 2.03459i
373373 −14.4253 3.86524i −0.746912 0.200135i −0.134764 0.990878i 0.543028π-0.543028\pi
−0.612148 + 0.790743i 0.709694π0.709694\pi
374374 0.825533 1.42987i 0.0426873 0.0739366i
375375 −22.9707 12.4465i −1.18620 0.642735i
376376 7.50416i 0.386997i
377377 0 0
378378 7.90543 7.90543i 0.406611 0.406611i
379379 −31.2859 + 8.38303i −1.60705 + 0.430607i −0.947161 0.320758i 0.896062π-0.896062\pi
−0.659887 + 0.751365i 0.729396π0.729396\pi
380380 38.2809 22.5639i 1.96377 1.15751i
381381 14.2331 8.21748i 0.729183 0.420994i
382382 19.3265 0.988829
383383 −27.9113 + 16.1146i −1.42620 + 0.823418i −0.996819 0.0797046i 0.974602π-0.974602\pi
−0.429383 + 0.903122i 0.641269π0.641269\pi
384384 46.6371 + 12.4964i 2.37994 + 0.637702i
385385 7.43152 13.1440i 0.378745 0.669878i
386386 −27.5759 47.7629i −1.40358 2.43107i
387387 1.20566 + 4.49960i 0.0612874 + 0.228728i
388388 −1.60187 + 2.77452i −0.0813227 + 0.140855i
389389 −11.7818 −0.597359 −0.298679 0.954354i 0.596546π-0.596546\pi
−0.298679 + 0.954354i 0.596546π0.596546\pi
390390 0 0
391391 3.56028 0.180051
392392 13.4732 23.3362i 0.680498 1.17866i
393393 −5.65339 21.0987i −0.285176 1.06429i
394394 −26.1783 45.3422i −1.31884 2.28431i
395395 4.27730 + 15.4063i 0.215214 + 0.775175i
396396 15.5770 + 4.17383i 0.782772 + 0.209743i
397397 7.05618 4.07389i 0.354139 0.204462i −0.312367 0.949961i 0.601122π-0.601122\pi
0.666507 + 0.745499i 0.267789π0.267789\pi
398398 −19.3044 −0.967642
399399 −41.4348 + 23.9224i −2.07433 + 1.19762i
400400 0.171996 + 9.54014i 0.00859978 + 0.477007i
401401 15.9505 4.27393i 0.796531 0.213430i 0.162471 0.986713i 0.448054π-0.448054\pi
0.634060 + 0.773284i 0.281387π0.281387\pi
402402 −43.3409 + 43.3409i −2.16165 + 2.16165i
403403 0 0
404404 28.8161i 1.43366i
405405 5.77553 22.3588i 0.286988 1.11102i
406406 −3.39047 + 5.87246i −0.168266 + 0.291445i
407407 −2.01733 0.540543i −0.0999955 0.0267937i
408408 3.47809i 0.172191i
409409 −1.09321 + 4.07993i −0.0540560 + 0.201740i −0.987673 0.156534i 0.949968π-0.949968\pi
0.933617 + 0.358274i 0.116635π0.116635\pi
410410 16.1808 0.145847i 0.799111 0.00720286i
411411 22.6343 + 22.6343i 1.11647 + 1.11647i
412412 −14.2672 + 53.2460i −0.702895 + 2.62324i
413413 23.0112 6.16584i 1.13231 0.303401i
414414 13.9613 + 52.1043i 0.686161 + 2.56079i
415415 6.84245 + 24.6456i 0.335882 + 1.20981i
416416 0 0
417417 −14.8481 14.8481i −0.727112 0.727112i
418418 20.3261 + 11.7353i 0.994184 + 0.573993i
419419 −14.7910 8.53958i −0.722587 0.417186i 0.0931173 0.995655i 0.470317π-0.470317\pi
−0.815704 + 0.578470i 0.803650π0.803650\pi
420420 −0.638812 70.8722i −0.0311709 3.45821i
421421 9.26544 9.26544i 0.451570 0.451570i −0.444305 0.895875i 0.646549π-0.646549\pi
0.895875 + 0.444305i 0.146549π0.146549\pi
422422 29.3865 + 50.8989i 1.43051 + 2.47772i
423423 −2.38979 4.13923i −0.116195 0.201256i
424424 −4.58619 + 4.58619i −0.222725 + 0.222725i
425425 −1.85148 + 0.532051i −0.0898098 + 0.0258083i
426426 −53.2649 30.7525i −2.58070 1.48997i
427427 −12.0326 6.94703i −0.582299 0.336190i
428428 26.8074 + 26.8074i 1.29578 + 1.29578i
429429 0 0
430430 −8.74262 4.94303i −0.421607 0.238374i
431431 −2.77316 10.3496i −0.133578 0.498521i 0.866421 0.499314i 0.166414π-0.166414\pi
−1.00000 0.000792423i 0.999748π0.999748\pi
432432 −2.32364 + 0.622619i −0.111796 + 0.0299558i
433433 1.32163 4.93240i 0.0635136 0.237036i −0.926870 0.375381i 0.877512π-0.877512\pi
0.990384 + 0.138345i 0.0441784π0.0441784\pi
434434 29.0251 + 29.0251i 1.39325 + 1.39325i
435435 0.0360083 + 3.99489i 0.00172646 + 0.191540i
436436 −5.49126 + 20.4937i −0.262984 + 0.981468i
437437 50.6109i 2.42105i
438438 24.0806 + 6.45237i 1.15061 + 0.308306i
439439 −10.1196 + 17.5277i −0.482985 + 0.836554i −0.999809 0.0195376i 0.993781π-0.993781\pi
0.516825 + 0.856091i 0.327114π0.327114\pi
440440 −13.4423 + 7.92329i −0.640835 + 0.377728i
441441 17.1627i 0.817273i
442442 0 0
443443 2.66083 2.66083i 0.126420 0.126420i −0.641066 0.767486i 0.721508π-0.721508\pi
0.767486 + 0.641066i 0.221508π0.221508\pi
444444 −9.46918 + 2.53726i −0.449387 + 0.120413i
445445 −2.63067 4.46306i −0.124706 0.211569i
446446 60.6551 35.0192i 2.87210 1.65821i
447447 29.7017 1.40484
448448 36.9269 21.3197i 1.74463 1.00726i
449449 −29.7674 7.97615i −1.40481 0.376418i −0.524741 0.851262i 0.675838π-0.675838\pi
−0.880070 + 0.474844i 0.842505π0.842505\pi
450450 −15.0469 25.0097i −0.709317 1.17897i
451451 2.75490 + 4.77163i 0.129723 + 0.224687i
452452 −13.7711 51.3944i −0.647737 2.41739i
453453 4.89300 8.47493i 0.229893 0.398187i
454454 −18.6633 −0.875913
455455 0 0
456456 49.4426 2.31536
457457 −5.08990 + 8.81597i −0.238096 + 0.412394i −0.960168 0.279424i 0.909857π-0.909857\pi
0.722072 + 0.691818i 0.243190π0.243190\pi
458458 10.8033 + 40.3186i 0.504807 + 1.88396i
459459 −0.242839 0.420610i −0.0113348 0.0196324i
460460 −65.2635 36.8996i −3.04293 1.72045i
461461 −18.6200 4.98920i −0.867218 0.232370i −0.202334 0.979317i 0.564853π-0.564853\pi
−0.664884 + 0.746946i 0.731519π0.731519\pi
462462 32.4201 18.7177i 1.50832 0.870828i
463463 −16.7929 −0.780432 −0.390216 0.920723i 0.627600π-0.627600\pi
−0.390216 + 0.920723i 0.627600π0.627600\pi
464464 1.26359 0.729533i 0.0586606 0.0338677i
465465 23.4151 + 6.04840i 1.08585 + 0.280488i
466466 −4.95814 + 1.32853i −0.229681 + 0.0615430i
467467 9.75781 9.75781i 0.451538 0.451538i −0.444327 0.895865i 0.646557π-0.646557\pi
0.895865 + 0.444327i 0.146557π0.146557\pi
468468 0 0
469469 41.3316i 1.90851i
470470 9.97717 + 2.57722i 0.460212 + 0.118878i
471471 21.5412 37.3104i 0.992564 1.71917i
472472 −23.7797 6.37175i −1.09455 0.293284i
473473 3.41974i 0.157240i
474474 −10.2599 + 38.2905i −0.471253 + 1.75874i
475475 −7.56334 26.3195i −0.347030 1.20762i
476476 −3.69533 3.69533i −0.169375 0.169375i
477477 1.06918 3.99023i 0.0489543 0.182700i
478478 −22.8779 + 6.13011i −1.04641 + 0.280384i
479479 3.57686 + 13.3490i 0.163431 + 0.609933i 0.998235 + 0.0593859i 0.0189142π0.0189142\pi
−0.834804 + 0.550547i 0.814419π0.814419\pi
480480 8.22685 14.5506i 0.375503 0.664143i
481481 0 0
482482 −24.3115 24.3115i −1.10736 1.10736i
483483 69.9091 + 40.3621i 3.18098 + 1.83654i
484484 24.3123 + 14.0367i 1.10510 + 0.638033i
485485 1.40862 + 1.38346i 0.0639624 + 0.0628196i
486486 34.1399 34.1399i 1.54862 1.54862i
487487 10.2296 + 17.7182i 0.463547 + 0.802887i 0.999135 0.0415923i 0.0132431π-0.0132431\pi
−0.535587 + 0.844480i 0.679910π0.679910\pi
488488 7.17902 + 12.4344i 0.324979 + 0.562880i
489489 26.1796 26.1796i 1.18388 1.18388i
490490 −26.3995 25.9278i −1.19261 1.17130i
491491 8.82381 + 5.09443i 0.398213 + 0.229908i 0.685713 0.727872i 0.259491π-0.259491\pi
−0.287500 + 0.957781i 0.592824π0.592824\pi
492492 22.3976 + 12.9312i 1.00976 + 0.582986i
493493 0.208297 + 0.208297i 0.00938121 + 0.00938121i
494494 0 0
495495 4.89137 8.65126i 0.219851 0.388845i
496496 −2.28597 8.53136i −0.102643 0.383069i
497497 −40.0612 + 10.7344i −1.79699 + 0.481502i
498498 −16.4129 + 61.2537i −0.735478 + 2.74484i
499499 −7.90149 7.90149i −0.353719 0.353719i 0.507772 0.861491i 0.330469π-0.330469\pi
−0.861491 + 0.507772i 0.830469π0.830469\pi
500500 39.4537 + 9.43612i 1.76442 + 0.421996i
501501 7.54998 28.1769i 0.337308 1.25885i
502502 42.1443i 1.88099i
503503 −13.6747 3.66412i −0.609723 0.163375i −0.0592717 0.998242i 0.518878π-0.518878\pi
−0.550452 + 0.834867i 0.685545π0.685545\pi
504504 17.7675 30.7741i 0.791426 1.37079i
505505 −17.1942 4.44147i −0.765133 0.197643i
506506 39.5998i 1.76043i
507507 0 0
508508 −18.0446 + 18.0446i −0.800600 + 0.800600i
509509 −22.3950 + 6.00073i −0.992643 + 0.265978i −0.718360 0.695671i 0.755107π-0.755107\pi
−0.274283 + 0.961649i 0.588440π0.588440\pi
510510 −4.62430 1.19451i −0.204768 0.0528939i
511511 14.5587 8.40548i 0.644039 0.371836i
512512 −20.8492 −0.921415
513513 5.97914 3.45206i 0.263986 0.152412i
514514 20.6583 + 5.53539i 0.911200 + 0.244155i
515515 29.5722 + 16.7200i 1.30311 + 0.736769i
516516 −8.02598 13.9014i −0.353324 0.611975i
517517 0.908131 + 3.38919i 0.0399396 + 0.149056i
518518 −5.12718 + 8.88054i −0.225275 + 0.390188i
519519 37.7669 1.65778
520520 0 0
521521 −35.0306 −1.53472 −0.767359 0.641218i 0.778429π-0.778429\pi
−0.767359 + 0.641218i 0.778429π0.778429\pi
522522 −2.23158 + 3.86521i −0.0976737 + 0.169176i
523523 10.4519 + 39.0069i 0.457029 + 1.70565i 0.682055 + 0.731301i 0.261087π0.261087\pi
−0.225026 + 0.974353i 0.572247π0.572247\pi
524524 16.9581 + 29.3722i 0.740817 + 1.28313i
525525 −42.3870 10.5425i −1.84992 0.460111i
526526 9.76819 + 2.61738i 0.425913 + 0.114123i
527527 1.54429 0.891594i 0.0672702 0.0388384i
528528 −8.05506 −0.350551
529529 54.0324 31.1956i 2.34923 1.35633i
530530 4.52250 + 7.67266i 0.196445 + 0.333279i
531531 15.1458 4.05832i 0.657274 0.176116i
532532 52.5307 52.5307i 2.27749 2.27749i
533533 0 0
534534 12.8443i 0.555827i
535535 20.1275 11.8638i 0.870188 0.512916i
536536 21.3559 36.9895i 0.922435 1.59771i
537537 −41.6403 11.1575i −1.79691 0.481481i
538538 4.26468i 0.183864i
539539 3.26097 12.1701i 0.140460 0.524203i
540540 0.0921822 + 10.2270i 0.00396689 + 0.440101i
541541 16.7846 + 16.7846i 0.721626 + 0.721626i 0.968936 0.247310i 0.0795467π-0.0795467\pi
−0.247310 + 0.968936i 0.579547π0.579547\pi
542542 1.81081 6.75804i 0.0777810 0.290283i
543543 4.94279 1.32442i 0.212116 0.0568362i
544544 −0.318997 1.19051i −0.0136769 0.0510428i
545545 11.3819 + 6.43528i 0.487549 + 0.275657i
546546 0 0
547547 10.0151 + 10.0151i 0.428216 + 0.428216i 0.888020 0.459804i 0.152080π-0.152080\pi
−0.459804 + 0.888020i 0.652080π0.652080\pi
548548 −43.0434 24.8511i −1.83872 1.06159i
549549 −7.91978 4.57249i −0.338008 0.195149i
550550 5.91783 + 20.5933i 0.252337 + 0.878103i
551551 −2.96103 + 2.96103i −0.126144 + 0.126144i
552552 −41.7100 72.2438i −1.77529 3.07490i
553553 13.3655 + 23.1498i 0.568360 + 0.984428i
554554 −47.8022 + 47.8022i −2.03092 + 2.03092i
555555 0.0544530 + 6.04121i 0.00231140 + 0.256435i
556556 28.2364 + 16.3023i 1.19749 + 0.691370i
557557 15.5555 + 8.98097i 0.659108 + 0.380536i 0.791937 0.610603i 0.209073π-0.209073\pi
−0.132829 + 0.991139i 0.542406π0.542406\pi
558558 19.1041 + 19.1041i 0.808743 + 0.808743i
559559 0 0
560560 4.26743 + 15.3707i 0.180332 + 0.649532i
561561 −0.420908 1.57085i −0.0177708 0.0663214i
562562 −8.35714 + 2.23929i −0.352525 + 0.0944587i
563563 −3.89312 + 14.5293i −0.164075 + 0.612338i 0.834081 + 0.551642i 0.185999π0.185999\pi
−0.998156 + 0.0606957i 0.980668π0.980668\pi
564564 11.6459 + 11.6459i 0.490380 + 0.490380i
565565 −32.7890 + 0.295546i −1.37944 + 0.0124337i
566566 −4.79405 + 17.8916i −0.201509 + 0.752041i
567567 38.6071i 1.62135i
568568 41.3990 + 11.0928i 1.73706 + 0.465445i
569569 −10.9760 + 19.0110i −0.460138 + 0.796983i −0.998967 0.0454320i 0.985534π-0.985534\pi
0.538829 + 0.842415i 0.318867π0.318867\pi
570570 16.9805 65.7364i 0.711234 2.75340i
571571 12.0101i 0.502606i −0.967908 0.251303i 0.919141π-0.919141\pi
0.967908 0.251303i 0.0808590π-0.0808590\pi
572572 0 0
573573 13.4606 13.4606i 0.562325 0.562325i
574574 26.1309 7.00175i 1.09068 0.292247i
575575 −32.0767 + 33.2545i −1.33769 + 1.38681i
576576 24.3050 14.0325i 1.01271 0.584688i
577577 −21.1801 −0.881741 −0.440870 0.897571i 0.645330π-0.645330\pi
−0.440870 + 0.897571i 0.645330π0.645330\pi
578578 34.6228 19.9895i 1.44012 0.831453i
579579 −52.4723 14.0599i −2.18068 0.584310i
580580 −1.65945 5.97712i −0.0689048 0.248186i
581581 21.3810 + 37.0329i 0.887032 + 1.53638i
582582 1.26693 + 4.72824i 0.0525158 + 0.195992i
583583 −1.51631 + 2.62632i −0.0627991 + 0.108771i
584584 −17.3724 −0.718873
585585 0 0
586586 −53.5214 −2.21095
587587 −17.2507 + 29.8791i −0.712013 + 1.23324i 0.252087 + 0.967705i 0.418883π0.418883\pi
−0.964100 + 0.265539i 0.914450π0.914450\pi
588588 −15.3067 57.1253i −0.631237 2.35581i
589589 12.6744 + 21.9527i 0.522239 + 0.904544i
590590 −16.6385 + 29.4280i −0.684994 + 1.21153i
591591 −49.8130 13.3473i −2.04903 0.549036i
592592 1.91084 1.10322i 0.0785351 0.0453423i
593593 −28.3656 −1.16483 −0.582417 0.812890i 0.697893π-0.697893\pi
−0.582417 + 0.812890i 0.697893π0.697893\pi
594594 −4.67830 + 2.70102i −0.191953 + 0.110824i
595595 −2.77452 + 1.63539i −0.113744 + 0.0670445i
596596 −44.5470 + 11.9363i −1.82472 + 0.488932i
597597 −13.4452 + 13.4452i −0.550276 + 0.550276i
598598 0 0
599599 3.01612i 0.123235i −0.998100 0.0616176i 0.980374π-0.980374\pi
0.998100 0.0616176i 0.0196259π-0.0196259\pi
600600 32.4868 + 31.3362i 1.32627 + 1.27930i
601601 −6.79040 + 11.7613i −0.276986 + 0.479754i −0.970634 0.240560i 0.922669π-0.922669\pi
0.693648 + 0.720314i 0.256002π0.256002\pi
602602 −16.2185 4.34575i −0.661019 0.177119i
603603 27.2042i 1.10784i
604604 −3.93274 + 14.6772i −0.160021 + 0.597206i
605605 12.1228 12.3434i 0.492863 0.501829i
606606 −31.1328 31.1328i −1.26468 1.26468i
607607 −9.28061 + 34.6357i −0.376689 + 1.40582i 0.474173 + 0.880431i 0.342747π0.342747\pi
−0.850862 + 0.525389i 0.823920π0.823920\pi
608608 16.9236 4.53467i 0.686344 0.183905i
609609 1.72867 + 6.45149i 0.0700493 + 0.261427i
610610 18.9978 5.27442i 0.769198 0.213555i
611611 0 0
612612 −2.43224 2.43224i −0.0983175 0.0983175i
613613 3.89843 + 2.25076i 0.157456 + 0.0909074i 0.576658 0.816986i 0.304357π-0.304357\pi
−0.419202 + 0.907893i 0.637690π0.637690\pi
614614 41.9308 + 24.2087i 1.69219 + 0.976986i
615615 11.1681 11.3712i 0.450341 0.458533i
616616 −18.4461 + 18.4461i −0.743213 + 0.743213i
617617 −19.2350 33.3160i −0.774372 1.34125i −0.935147 0.354260i 0.884733π-0.884733\pi
0.160776 0.986991i 0.448600π-0.448600\pi
618618 42.1125 + 72.9410i 1.69401 + 2.93412i
619619 −5.85514 + 5.85514i −0.235338 + 0.235338i −0.814916 0.579578i 0.803217π-0.803217\pi
0.579578 + 0.814916i 0.303217π0.303217\pi
620620 −37.5490 + 0.338451i −1.50800 + 0.0135925i
621621 −10.0881 5.82435i −0.404820 0.233723i
622622 −43.9191 25.3567i −1.76099 1.01671i
623623 −6.12441 6.12441i −0.245369 0.245369i
624624 0 0
625625 11.7115 22.0871i 0.468459 0.883485i
626626 −4.53915 16.9403i −0.181421 0.677072i
627627 22.3303 5.98339i 0.891787 0.238954i
628628 −17.3137 + 64.6155i −0.690890 + 2.57844i
629629 0.314994 + 0.314994i 0.0125596 + 0.0125596i
630630 −34.8138 34.1918i −1.38701 1.36223i
631631 −9.66827 + 36.0825i −0.384888 + 1.43642i 0.453456 + 0.891279i 0.350191π0.350191\pi
−0.838344 + 0.545142i 0.816476π0.816476\pi
632632 27.6237i 1.09881i
633633 55.9176 + 14.9831i 2.22252 + 0.595524i
634634 30.7026 53.1785i 1.21936 2.11199i
635635 7.98575 + 13.5482i 0.316905 + 0.537645i
636636 14.2348i 0.564448i
637637 0 0
638638 2.31681 2.31681i 0.0917235 0.0917235i
639639 −26.3680 + 7.06528i −1.04310 + 0.279498i
640640 −11.5551 + 44.7330i −0.456754 + 1.76823i
641641 −2.97232 + 1.71607i −0.117399 + 0.0677806i −0.557550 0.830143i 0.688258π-0.688258\pi
0.440150 + 0.897924i 0.354925π0.354925\pi
642642 57.9252 2.28613
643643 −14.2572 + 8.23137i −0.562247 + 0.324614i −0.754047 0.656820i 0.771901π-0.771901\pi
0.191800 + 0.981434i 0.438568π0.438568\pi
644644 −121.071 32.4409i −4.77087 1.27835i
645645 −9.53185 + 2.64636i −0.375316 + 0.104200i
646646 −2.50309 4.33549i −0.0984829 0.170577i
647647 −4.93784 18.4283i −0.194127 0.724490i −0.992491 0.122316i 0.960968π-0.960968\pi
0.798365 0.602174i 0.205699π-0.205699\pi
648648 −19.9482 + 34.5513i −0.783639 + 1.35730i
649649 −11.5110 −0.451846
650650 0 0
651651 40.4311 1.58462
652652 −28.7436 + 49.7854i −1.12569 + 1.94975i
653653 −9.90911 36.9813i −0.387773 1.44719i −0.833748 0.552145i 0.813810π-0.813810\pi
0.445975 0.895046i 0.352857π-0.352857\pi
654654 16.2085 + 28.0740i 0.633803 + 1.09778i
655655 20.1398 5.59149i 0.786928 0.218477i
656656 −5.62263 1.50658i −0.219527 0.0588220i
657657 9.58244 5.53243i 0.373847 0.215841i
658658 17.2277 0.671605
659659 −34.0246 + 19.6441i −1.32541 + 0.765225i −0.984586 0.174903i 0.944039π-0.944039\pi
−0.340823 + 0.940128i 0.610706π0.610706\pi
660660 −8.56501 + 33.1577i −0.333393 + 1.29066i
661661 −26.1828 + 7.01565i −1.01839 + 0.272877i −0.729132 0.684373i 0.760076π-0.760076\pi
−0.289260 + 0.957251i 0.593409π0.593409\pi
662662 −17.6545 + 17.6545i −0.686161 + 0.686161i
663663 0 0
664664 44.1900i 1.71490i
665665 −23.2478 39.4410i −0.901510 1.52946i
666666 −3.37468 + 5.84511i −0.130766 + 0.226493i
667667 6.82448 + 1.82861i 0.264245 + 0.0708042i
668668 45.2943i 1.75249i
669669 17.8550 66.6357i 0.690314 2.57629i
670670 −41.8451 41.0974i −1.61662 1.58773i
671671 4.74713 + 4.74713i 0.183261 + 0.183261i
672672 7.23277 26.9931i 0.279010 1.04128i
673673 −6.86071 + 1.83832i −0.264461 + 0.0708621i −0.388613 0.921401i 0.627046π-0.627046\pi
0.124152 + 0.992263i 0.460379π0.460379\pi
674674 5.80011 + 21.6463i 0.223412 + 0.833785i
675675 6.11655 + 1.52130i 0.235426 + 0.0585550i
676676 0 0
677677 19.2265 + 19.2265i 0.738933 + 0.738933i 0.972372 0.233439i 0.0749978π-0.0749978\pi
−0.233439 + 0.972372i 0.574998π0.574998\pi
678678 −70.4045 40.6481i −2.70387 1.56108i
679679 2.85861 + 1.65042i 0.109703 + 0.0633373i
680680 3.32805 0.0299977i 0.127625 0.00115036i
681681 −12.9987 + 12.9987i −0.498112 + 0.498112i
682682 −9.91690 17.1766i −0.379738 0.657725i
683683 2.30838 + 3.99823i 0.0883277 + 0.152988i 0.906804 0.421552i 0.138514π-0.138514\pi
−0.818477 + 0.574540i 0.805181π0.805181\pi
684684 34.5753 34.5753i 1.32202 1.32202i
685685 −21.4627 + 21.8531i −0.820047 + 0.834964i
686686 0.190715 + 0.110109i 0.00728153 + 0.00420399i
687687 35.6057 + 20.5569i 1.35844 + 0.784296i
688688 2.55469 + 2.55469i 0.0973967 + 0.0973967i
689689 0 0
690690 −110.377 + 30.6442i −4.20197 + 1.16661i
691691 2.74019 + 10.2265i 0.104242 + 0.389036i 0.998258 0.0589986i 0.0187907π-0.0187907\pi
−0.894016 + 0.448035i 0.852124π0.852124\pi
692692 −56.6433 + 15.1775i −2.15326 + 0.576963i
693693 4.30033 16.0491i 0.163356 0.609653i
694694 −11.9539 11.9539i −0.453766 0.453766i
695695 14.0795 14.3356i 0.534065 0.543780i
696696 1.78640 6.66694i 0.0677133 0.252710i
697697 1.17522i 0.0445146i
698698 −74.7333 20.0247i −2.82870 0.757947i
699699 −2.52797 + 4.37857i −0.0956166 + 0.165613i
700700 67.8094 1.22251i 2.56295 0.0462065i
701701 48.9646i 1.84937i −0.380735 0.924684i 0.624329π-0.624329\pi
0.380735 0.924684i 0.375671π-0.375671\pi
702702 0 0
703703 −4.47777 + 4.47777i −0.168882 + 0.168882i
704704 −19.9009 + 5.33243i −0.750043 + 0.200973i
705705 8.74394 5.15395i 0.329316 0.194109i
706706 −26.5461 + 15.3264i −0.999076 + 0.576817i
707707 −29.6895 −1.11659
708708 −46.7927 + 27.0158i −1.75858 + 1.01532i
709709 23.7942 + 6.37565i 0.893611 + 0.239442i 0.676271 0.736653i 0.263595π-0.263595\pi
0.217341 + 0.976096i 0.430262π0.430262\pi
710710 28.9665 51.2324i 1.08709 1.92272i
711711 8.79710 + 15.2370i 0.329917 + 0.571433i
712712 2.31655 + 8.64548i 0.0868164 + 0.324003i
713713 21.3843 37.0388i 0.800850 1.38711i
714714 −7.98484 −0.298825
715715 0 0
716716 66.9366 2.50154
717717 −11.6646 + 20.2036i −0.435621 + 0.754518i
718718 −10.8810 40.6084i −0.406074 1.51549i
719719 −23.3017 40.3597i −0.869007 1.50516i −0.863012 0.505183i 0.831425π-0.831425\pi
−0.00599476 0.999982i 0.501908π-0.501908\pi
720720 2.80879 + 10.1169i 0.104678 + 0.377035i
721721 54.8597 + 14.6996i 2.04308 + 0.547442i
722722 22.5938 13.0446i 0.840856 0.485468i
723723 −33.8652 −1.25946
724724 −6.88102 + 3.97276i −0.255731 + 0.147646i
725725 −3.82225 + 0.0689099i −0.141955 + 0.00255925i
726726 41.4321 11.1017i 1.53769 0.412023i
727727 −16.4412 + 16.4412i −0.609770 + 0.609770i −0.942886 0.333116i 0.891900π-0.891900\pi
0.333116 + 0.942886i 0.391900π0.391900\pi
728728 0 0
729729 16.5738i 0.613846i
730730 −5.96634 + 23.0974i −0.220824 + 0.854875i
731731 −0.364709 + 0.631694i −0.0134892 + 0.0233641i
732732 30.4386 + 8.15599i 1.12504 + 0.301454i
733733 30.6968i 1.13381i 0.823782 + 0.566907i 0.191860π0.191860\pi
−0.823782 + 0.566907i 0.808140π0.808140\pi
734734 −21.4010 + 79.8698i −0.789927 + 2.94805i
735735 −36.4452 + 0.328502i −1.34430 + 0.0121170i
736736 −20.9028 20.9028i −0.770486 0.770486i
737737 5.16886 19.2905i 0.190397 0.710573i
738738 17.1992 4.60850i 0.633110 0.169641i
739739 −8.93434 33.3434i −0.328655 1.22656i −0.910586 0.413319i 0.864369π-0.864369\pi
0.581931 0.813238i 0.302297π-0.302297\pi
740740 −2.50948 9.03881i −0.0922502 0.332273i
741741 0 0
742742 10.5288 + 10.5288i 0.386523 + 0.386523i
743743 −0.266725 0.153994i −0.00978520 0.00564949i 0.495099 0.868836i 0.335132π-0.335132\pi
−0.504885 + 0.863187i 0.668465π0.668465\pi
744744 −36.1837 20.8907i −1.32656 0.765889i
745745 0.256170 + 28.4204i 0.00938534 + 1.04124i
746746 25.0528 25.0528i 0.917249 0.917249i
747747 14.0728 + 24.3748i 0.514897 + 0.891828i
748748 1.26257 + 2.18683i 0.0461641 + 0.0799586i
749749 27.6199 27.6199i 1.00921 1.00921i
750750 52.8203 32.4309i 1.92873 1.18421i
751751 −18.1008 10.4505i −0.660509 0.381345i 0.131962 0.991255i 0.457872π-0.457872\pi
−0.792471 + 0.609910i 0.791206π0.791206\pi
752752 −3.21028 1.85346i −0.117067 0.0675886i
753753 −29.3529 29.3529i −1.06968 1.06968i
754754 0 0
755755 8.15153 + 4.60883i 0.296665 + 0.167733i
756756 4.42545 + 16.5160i 0.160952 + 0.600681i
757757 32.4416 8.69270i 1.17911 0.315942i 0.384537 0.923110i 0.374361π-0.374361\pi
0.794573 + 0.607168i 0.207695π0.207695\pi
758758 19.8881 74.2232i 0.722367 2.69591i
759759 −27.5807 27.5807i −1.00112 1.00112i
760760 0.426430 + 47.3097i 0.0154682 + 1.71610i
761761 12.4256 46.3730i 0.450428 1.68102i −0.250764 0.968048i 0.580682π-0.580682\pi
0.701192 0.712973i 0.252652π-0.252652\pi
762762 38.9906i 1.41248i
763763 21.1148 + 5.65768i 0.764406 + 0.204822i
764764 −14.7789 + 25.5979i −0.534684 + 0.926099i
765765 −1.82617 + 1.07640i −0.0660254 + 0.0389175i
766766 76.4612i 2.76266i
767767 0 0
768768 −43.3025 + 43.3025i −1.56255 + 1.56255i
769769 22.6156 6.05983i 0.815539 0.218523i 0.173144 0.984897i 0.444608π-0.444608\pi
0.642395 + 0.766374i 0.277941π0.277941\pi
770770 18.1899 + 30.8601i 0.655519 + 1.11212i
771771 18.2435 10.5329i 0.657025 0.379334i
772772 84.3490 3.03579
773773 23.2908 13.4470i 0.837712 0.483653i −0.0187736 0.999824i 0.505976π-0.505976\pi
0.856486 + 0.516170i 0.172643π0.172643\pi
774774 −10.6749 2.86034i −0.383703 0.102813i
775775 −5.58553 + 22.4572i −0.200638 + 0.806686i
776776 −1.70554 2.95408i −0.0612252 0.106045i
777777 2.61416 + 9.75617i 0.0937823 + 0.350000i
778778 13.9756 24.2065i 0.501051 0.867845i
779779 16.7062 0.598563
780780 0 0
781781 20.0399 0.717086
782782 −4.22324 + 7.31487i −0.151023 + 0.261579i
783783 −0.249452 0.930966i −0.00891467 0.0332700i
784784 6.65549 + 11.5276i 0.237696 + 0.411702i
785785 35.8867 + 20.2901i 1.28085 + 0.724186i
786786 50.0551 + 13.4122i 1.78540 + 0.478398i
787787 1.25975 0.727317i 0.0449053 0.0259261i −0.477379 0.878697i 0.658413π-0.658413\pi
0.522285 + 0.852771i 0.325080π0.325080\pi
788788 80.0741 2.85252
789789 8.62637 4.98043i 0.307107 0.177308i
790790 −36.7272 9.48706i −1.30669 0.337535i
791791 −52.9520 + 14.1885i −1.88276 + 0.504483i
792792 −12.1411 + 12.1411i −0.431414 + 0.431414i
793793 0 0
794794 19.3299i 0.685994i
795795 8.49375 + 2.19403i 0.301242 + 0.0778144i
796796 14.7620 25.5686i 0.523227 0.906256i
797797 12.0194 + 3.22058i 0.425748 + 0.114079i 0.465330 0.885138i 0.345936π-0.345936\pi
−0.0395816 + 0.999216i 0.512603π0.512603\pi
798798 113.508i 4.01813i
799799 0.193701 0.722901i 0.00685264 0.0255744i
800800 13.9939 + 7.74646i 0.494759 + 0.273879i
801801 −4.03104 4.03104i −0.142430 0.142430i
802802 −10.1396 + 37.8413i −0.358040 + 1.33622i
803803 −7.84608 + 2.10235i −0.276882 + 0.0741904i
804804 −24.2622 90.5476i −0.855661 3.19337i
805805 −38.0180 + 67.2415i −1.33996 + 2.36995i
806806 0 0
807807 −2.97029 2.97029i −0.104559 0.104559i
808808 26.5705 + 15.3405i 0.934746 + 0.539676i
809809 6.25034 + 3.60863i 0.219750 + 0.126873i 0.605835 0.795591i 0.292839π-0.292839\pi
−0.386084 + 0.922463i 0.626173π0.626173\pi
810810 39.0867 + 38.3884i 1.37337 + 1.34883i
811811 −15.0515 + 15.0515i −0.528530 + 0.528530i −0.920134 0.391604i 0.871920π-0.871920\pi
0.391604 + 0.920134i 0.371920π0.371920\pi
812812 −5.18537 8.98132i −0.181971 0.315183i
813813 −3.44567 5.96807i −0.120845 0.209309i
814814 3.50357 3.50357i 0.122800 0.122800i
815815 25.2760 + 24.8245i 0.885381 + 0.869563i
816816 1.48793 + 0.859056i 0.0520879 + 0.0300730i
817817 −8.97980 5.18449i −0.314163 0.181382i
818818 −7.08575 7.08575i −0.247747 0.247747i
819819 0 0
820820 −12.1802 + 21.5429i −0.425352 + 0.752311i
821821 −4.53915 16.9404i −0.158418 0.591222i −0.998788 0.0492105i 0.984329π-0.984329\pi
0.840371 0.542012i 0.182337π-0.182337\pi
822822 −73.3529 + 19.6548i −2.55847 + 0.685541i
823823 2.83413 10.5771i 0.0987916 0.368695i −0.898775 0.438409i 0.855542π-0.855542\pi
0.997567 + 0.0697141i 0.0222087π0.0222087\pi
824824 −41.5013 41.5013i −1.44576 1.44576i
825825 18.4646 + 10.2213i 0.642856 + 0.355859i
826826 −14.6280 + 54.5923i −0.508972 + 1.89951i
827827 1.86613i 0.0648917i 0.999473 + 0.0324458i 0.0103296π0.0103296\pi
−0.999473 + 0.0324458i 0.989670π0.989670\pi
828828 −79.6882 21.3524i −2.76936 0.742047i
829829 17.3922 30.1241i 0.604055 1.04625i −0.388145 0.921598i 0.626884π-0.626884\pi
0.992200 0.124656i 0.0397826π-0.0397826\pi
830830 −58.7529 15.1766i −2.03934 0.526786i
831831 66.5870i 2.30988i
832832 0 0
833833 −1.90028 + 1.90028i −0.0658408 + 0.0658408i
834834 48.1193 12.8935i 1.66624 0.446467i
835835 27.0265 + 6.98127i 0.935291 + 0.241597i
836836 −31.0868 + 17.9480i −1.07516 + 0.620743i
837837 −5.83431 −0.201663
838838 35.0904 20.2595i 1.21218 0.699851i
839839 18.7439 + 5.02241i 0.647111 + 0.173393i 0.567422 0.823427i 0.307941π-0.307941\pi
0.0796889 + 0.996820i 0.474607π0.474607\pi
840840 65.6892 + 37.1403i 2.26649 + 1.28146i
841841 −14.2077 24.6085i −0.489921 0.848568i
842842 8.04579 + 30.0273i 0.277276 + 1.03481i
843843 −4.26099 + 7.38026i −0.146756 + 0.254190i
844844 −89.8873 −3.09405
845845 0 0
846846 11.3391 0.389848
847847 14.4621 25.0491i 0.496925 0.860699i
848848 −0.829228 3.09472i −0.0284758 0.106273i
849849 9.12227 + 15.8002i 0.313075 + 0.542263i
850850 1.10310 4.43512i 0.0378360 0.152123i
851851 10.3202 + 2.76530i 0.353773 + 0.0947931i
852852 81.4633 47.0328i 2.79089 1.61132i
853853 2.67051 0.0914364 0.0457182 0.998954i 0.485442π-0.485442\pi
0.0457182 + 0.998954i 0.485442π0.485442\pi
854854 28.5464 16.4813i 0.976837 0.563977i
855855 −15.3015 25.9598i −0.523301 0.887807i
856856 −38.9894 + 10.4472i −1.33263 + 0.357077i
857857 17.5773 17.5773i 0.600430 0.600430i −0.339996 0.940427i 0.610426π-0.610426\pi
0.940427 + 0.339996i 0.110426π0.110426\pi
858858 0 0
859859 52.8699i 1.80390i −0.431844 0.901949i 0.642137π-0.642137\pi
0.431844 0.901949i 0.357863π-0.357863\pi
860860 13.2325 7.79965i 0.451225 0.265966i
861861 13.3232 23.0764i 0.454052 0.786441i
862862 24.5535 + 6.57909i 0.836296 + 0.224085i
863863 3.40127i 0.115780i 0.998323 + 0.0578902i 0.0184373π0.0184373\pi
−0.998323 + 0.0578902i 0.981563π0.981563\pi
864864 −1.04371 + 3.89517i −0.0355076 + 0.132516i
865865 0.325730 + 36.1377i 0.0110752 + 1.22872i
866866 8.56625 + 8.56625i 0.291093 + 0.291093i
867867 10.1919 38.0366i 0.346134 1.29179i
868868 −60.6392 + 16.2482i −2.05823 + 0.551500i
869869 −3.34294 12.4760i −0.113402 0.423220i
870870 −8.25052 4.66479i −0.279719 0.158151i
871871 0 0
872872 −15.9733 15.9733i −0.540923 0.540923i
873873 1.88152 + 1.08630i 0.0636798 + 0.0367655i
874874 −103.984 60.0352i −3.51731 2.03072i
875875 9.72210 40.6494i 0.328667 1.37420i
876876 −26.9605 + 26.9605i −0.910912 + 0.910912i
877877 −9.83752 17.0391i −0.332189 0.575369i 0.650751 0.759291i 0.274454π-0.274454\pi
−0.982941 + 0.183922i 0.941121π0.941121\pi
878878 −24.0080 41.5832i −0.810232 1.40336i
879879 −37.2768 + 37.2768i −1.25732 + 1.25732i
880880 −0.0694729 7.70758i −0.00234193 0.259822i
881881 2.06350 + 1.19137i 0.0695212 + 0.0401381i 0.534358 0.845258i 0.320554π-0.320554\pi
−0.464836 + 0.885397i 0.653887π0.653887\pi
882882 −35.2621 20.3586i −1.18734 0.685510i
883883 30.4180 + 30.4180i 1.02365 + 1.02365i 0.999714 + 0.0239343i 0.00761926π0.00761926\pi
0.0239343 + 0.999714i 0.492381π0.492381\pi
884884 0 0
885885 8.90776 + 32.0846i 0.299431 + 1.07851i
886886 2.31057 + 8.62317i 0.0776252 + 0.289701i
887887 21.9337 5.87711i 0.736461 0.197334i 0.128956 0.991650i 0.458837π-0.458837\pi
0.607504 + 0.794316i 0.292171π0.292171\pi
888888 2.70146 10.0820i 0.0906550 0.338329i
889889 18.5915 + 18.5915i 0.623538 + 0.623538i
890890 12.2902 0.110779i 0.411969 0.00371332i
891891 −4.82814 + 18.0189i −0.161749 + 0.603655i
892892 107.117i 3.58653i
893893 10.2763 + 2.75354i 0.343885 + 0.0921436i
894894 −35.2325 + 61.0244i −1.17835 + 2.04096i
895895 10.3170 39.9402i 0.344860 1.33505i
896896 77.2410i 2.58044i
897897 0 0
898898 51.6980 51.6980i 1.72518 1.72518i
899899 3.41808 0.915872i 0.113999 0.0305460i
900900 44.6317 0.804648i 1.48772 0.0268216i
901901 0.560184 0.323423i 0.0186624 0.0107748i
902902 −13.0716 −0.435235
903903 −14.3227 + 8.26923i −0.476630 + 0.275183i
904904 54.7204 + 14.6623i 1.81997 + 0.487660i
905905 1.30992 + 4.71815i 0.0435431 + 0.156837i
906906 11.6082 + 20.1061i 0.385658 + 0.667980i
907907 5.99131 + 22.3599i 0.198938 + 0.742448i 0.991212 + 0.132282i 0.0422305π0.0422305\pi
−0.792274 + 0.610166i 0.791103π0.791103\pi
908908 14.2718 24.7195i 0.473627 0.820345i
909909 −19.5414 −0.648147
910910 0 0
911911 −23.7450 −0.786707 −0.393354 0.919387i 0.628685π-0.628685\pi
−0.393354 + 0.919387i 0.628685π0.628685\pi
912912 −12.2118 + 21.1515i −0.404375 + 0.700397i
913913 −5.34774 19.9580i −0.176984 0.660515i
914914 −12.0754 20.9152i −0.399418 0.691813i
915915 9.55812 16.9052i 0.315982 0.558869i
916916 −61.6632 16.5226i −2.03741 0.545922i
917917 30.2624 17.4720i 0.999354 0.576977i
918918 1.15223 0.0380293
919919 49.3350 28.4836i 1.62741 0.939586i 0.642549 0.766245i 0.277877π-0.277877\pi
0.984862 0.173342i 0.0554565π-0.0554565\pi
920920 68.7676 40.5337i 2.26720 1.33636i
921921 46.0652 12.3431i 1.51790 0.406720i
922922 32.3379 32.3379i 1.06499 1.06499i
923923 0 0
924924 57.2537i 1.88351i
925925 −5.78014 + 0.104208i −0.190050 + 0.00342634i
926926 19.9199 34.5023i 0.654608 1.13381i
927927 36.1083 + 9.67519i 1.18595 + 0.317775i
928928 2.44586i 0.0802892i
929929 −7.56304 + 28.2256i −0.248135 + 0.926053i 0.723647 + 0.690171i 0.242465π0.242465\pi
−0.971782 + 0.235882i 0.924202π0.924202\pi
930930 −40.2021 + 40.9334i −1.31828 + 1.34226i
931931 −27.0133 27.0133i −0.885325 0.885325i
932932 2.03185 7.58297i 0.0665555 0.248388i
933933 −48.2495 + 12.9284i −1.57962 + 0.423257i
934934 8.47335 + 31.6230i 0.277256 + 1.03473i
935935 1.49946 0.416299i 0.0490375 0.0136144i
936936 0 0
937937 −1.77191 1.77191i −0.0578859 0.0578859i 0.677571 0.735457i 0.263033π-0.263033\pi
−0.735457 + 0.677571i 0.763033π0.763033\pi
938938 −84.9188 49.0279i −2.77270 1.60082i
939939 −14.9601 8.63724i −0.488205 0.281866i
940940 −11.0430 + 11.2439i −0.360184 + 0.366737i
941941 −15.5682 + 15.5682i −0.507507 + 0.507507i −0.913761 0.406253i 0.866835π-0.866835\pi
0.406253 + 0.913761i 0.366835π0.366835\pi
942942 51.1047 + 88.5159i 1.66508 + 2.88400i
943943 −14.0934 24.4106i −0.458946 0.794917i
944944 8.59920 8.59920i 0.279880 0.279880i
945945 10.5370 0.0949760i 0.342768 0.00308957i
946946 7.02612 + 4.05653i 0.228439 + 0.131889i
947947 −0.313387 0.180934i −0.0101837 0.00587957i 0.494899 0.868950i 0.335205π-0.335205\pi
−0.505083 + 0.863071i 0.668538π0.668538\pi
948948 −42.8699 42.8699i −1.39235 1.39235i
949949 0 0
950950 63.0471 + 15.6810i 2.04552 + 0.508760i
951951 −15.6541 58.4220i −0.507620 1.89446i
952952 5.37459 1.44012i 0.174191 0.0466745i
953953 10.4907 39.1517i 0.339826 1.26825i −0.558715 0.829360i 0.688705π-0.688705\pi
0.898541 0.438889i 0.144628π-0.144628\pi
954954 6.92996 + 6.92996i 0.224366 + 0.224366i
955955 12.9960 + 12.7639i 0.420542 + 0.413029i
956956 9.37537 34.9894i 0.303221 1.13164i
957957 3.22725i 0.104322i
958958 −31.6695 8.48582i −1.02320 0.274164i
959959 −25.6043 + 44.3479i −0.826805 + 1.43207i
960960 30.2633 + 51.3433i 0.976745 + 1.65710i
961961 9.57907i 0.309002i
962962 0 0
963963 18.1792 18.1792i 0.585817 0.585817i
964964 50.7916 13.6096i 1.63589 0.438334i
965965 13.0008 50.3300i 0.418512 1.62018i
966966 −165.854 + 95.7557i −5.33626 + 3.08089i
967967 −12.2654 −0.394430 −0.197215 0.980360i 0.563190π-0.563190\pi
−0.197215 + 0.980360i 0.563190π0.563190\pi
968968 −25.8857 + 14.9451i −0.831997 + 0.480354i
969969 −4.76297 1.27623i −0.153009 0.0409985i
970970 −4.51334 + 1.25305i −0.144915 + 0.0402332i
971971 −11.3099 19.5894i −0.362953 0.628654i 0.625492 0.780231i 0.284898π-0.284898\pi
−0.988445 + 0.151577i 0.951565π0.951565\pi
972972 19.1115 + 71.3250i 0.613001 + 2.28775i
973973 16.7963 29.0921i 0.538466 0.932651i
974974 −48.5378 −1.55525
975975 0 0
976976 −7.09261 −0.227029
977977 −17.5846 + 30.4574i −0.562581 + 0.974419i 0.434689 + 0.900581i 0.356858π0.356858\pi
−0.997270 + 0.0738385i 0.976475π0.976475\pi
978978 22.7335 + 84.8424i 0.726936 + 2.71296i
979979 2.09250 + 3.62432i 0.0668767 + 0.115834i
980980 54.5290 15.1391i 1.74186 0.483600i
981981 13.8976 + 3.72385i 0.443716 + 0.118893i
982982 −20.9338 + 12.0861i −0.668024 + 0.385684i
983983 12.2764 0.391555 0.195778 0.980648i 0.437277π-0.437277\pi
0.195778 + 0.980648i 0.437277π0.437277\pi
984984 −23.8470 + 13.7681i −0.760215 + 0.438911i
985985 12.3419 47.7792i 0.393247 1.52237i
986986 −0.675045 + 0.180878i −0.0214978 + 0.00576032i
987987 11.9988 11.9988i 0.381927 0.381927i
988988 0 0
989989 17.4946i 0.556297i
990990 11.9725 + 20.3119i 0.380510 + 0.645555i
991991 −16.5995 + 28.7512i −0.527301 + 0.913312i 0.472193 + 0.881495i 0.343463π0.343463\pi
−0.999494 + 0.0318165i 0.989871π0.989871\pi
992992 −14.3013 3.83202i −0.454066 0.121667i
993993 24.5922i 0.780409i
994994 25.4664 95.0419i 0.807745 3.01455i
995995 −12.9812 12.7493i −0.411531 0.404179i
996996 −68.5794 68.5794i −2.17302 2.17302i
997997 −9.72750 + 36.3035i −0.308073 + 1.14974i 0.622194 + 0.782863i 0.286241π0.286241\pi
−0.930268 + 0.366882i 0.880425π0.880425\pi
998998 25.6070 6.86138i 0.810576 0.217193i
999999 −0.377229 1.40784i −0.0119350 0.0445421i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 845.2.o.i.357.5 144
5.3 odd 4 845.2.t.i.188.32 144
13.2 odd 12 845.2.t.i.427.5 144
13.3 even 3 inner 845.2.o.i.587.5 144
13.4 even 6 845.2.k.f.577.5 yes 72
13.5 odd 4 845.2.t.i.657.32 144
13.6 odd 12 845.2.f.f.437.5 yes 72
13.7 odd 12 845.2.f.f.437.32 yes 72
13.8 odd 4 845.2.t.i.657.5 144
13.9 even 3 845.2.k.f.577.32 yes 72
13.10 even 6 inner 845.2.o.i.587.32 144
13.11 odd 12 845.2.t.i.427.32 144
13.12 even 2 inner 845.2.o.i.357.32 144
65.3 odd 12 845.2.t.i.418.5 144
65.8 even 4 inner 845.2.o.i.488.5 144
65.18 even 4 inner 845.2.o.i.488.32 144
65.23 odd 12 845.2.t.i.418.32 144
65.28 even 12 inner 845.2.o.i.258.32 144
65.33 even 12 845.2.k.f.268.32 yes 72
65.38 odd 4 845.2.t.i.188.5 144
65.43 odd 12 845.2.f.f.408.32 yes 72
65.48 odd 12 845.2.f.f.408.5 72
65.58 even 12 845.2.k.f.268.5 yes 72
65.63 even 12 inner 845.2.o.i.258.5 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.f.f.408.5 72 65.48 odd 12
845.2.f.f.408.32 yes 72 65.43 odd 12
845.2.f.f.437.5 yes 72 13.6 odd 12
845.2.f.f.437.32 yes 72 13.7 odd 12
845.2.k.f.268.5 yes 72 65.58 even 12
845.2.k.f.268.32 yes 72 65.33 even 12
845.2.k.f.577.5 yes 72 13.4 even 6
845.2.k.f.577.32 yes 72 13.9 even 3
845.2.o.i.258.5 144 65.63 even 12 inner
845.2.o.i.258.32 144 65.28 even 12 inner
845.2.o.i.357.5 144 1.1 even 1 trivial
845.2.o.i.357.32 144 13.12 even 2 inner
845.2.o.i.488.5 144 65.8 even 4 inner
845.2.o.i.488.32 144 65.18 even 4 inner
845.2.o.i.587.5 144 13.3 even 3 inner
845.2.o.i.587.32 144 13.10 even 6 inner
845.2.t.i.188.5 144 65.38 odd 4
845.2.t.i.188.32 144 5.3 odd 4
845.2.t.i.418.5 144 65.3 odd 12
845.2.t.i.418.32 144 65.23 odd 12
845.2.t.i.427.5 144 13.2 odd 12
845.2.t.i.427.32 144 13.11 odd 12
845.2.t.i.657.5 144 13.8 odd 4
845.2.t.i.657.32 144 13.5 odd 4