Properties

Label 273.2.j.c.172.2
Level 273273
Weight 22
Character 273.172
Analytic conductor 2.1802.180
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [273,2,Mod(100,273)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("273.100"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 273=3713 273 = 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 273.j (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.179915975182.17991597518
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20+18x184x17+211x1659x15+1458x14526x13+7324x12++1369 x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 172.2
Root 1.14017+1.97483i1.14017 + 1.97483i of defining polynomial
Character χ\chi == 273.172
Dual form 273.2.j.c.100.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.14017+1.97483i)q2+1.00000q3+(1.599972.77124i)q4+(1.468622.54373i)q5+(1.14017+1.97483i)q6+(2.34076+1.23322i)q7+2.73629q8+1.00000q9+6.69792q105.16954q11+(1.599972.77124i)q12+(0.3647573.58705i)q13+(0.2334576.02869i)q14+(1.468622.54373i)q15+(0.08011720.138767i)q16+(2.526464.37595i)q17+(1.14017+1.97483i)q18+2.25859q19+(4.69952+8.13980i)q20+(2.34076+1.23322i)q21+(5.8941610.2090i)q22+(2.61602+4.53108i)q23+2.73629q24+(1.81371+3.14143i)q25+(7.49971+3.36952i)q26+1.00000q27+(7.16271+4.51367i)q28+(0.216901+0.375683i)q29+6.69792q30+(1.34122+2.32306i)q31+(2.91898+5.05582i)q325.16954q33+11.5224q34+(6.57468+4.14312i)q35+(1.599972.77124i)q36+(2.123863.67863i)q37+(2.57517+4.46033i)q38+(0.3647573.58705i)q39+(4.018576.96037i)q40+(0.269622+0.466999i)q41+(0.2334576.02869i)q42+(4.66348+8.07739i)q43+(8.27113+14.3260i)q44+(1.468622.54373i)q45+(5.9654110.3324i)q46+(4.870548.43603i)q47+(0.08011720.138767i)q48+(3.958325.77336i)q49+(4.135877.16354i)q50+(2.526464.37595i)q51+(9.35697+6.75002i)q52+(0.3775710.653972i)q53+(1.14017+1.97483i)q54+(7.59211+13.1499i)q55+(6.40499+3.37445i)q56+2.25859q570.989214q58+(1.82385+3.15901i)q59+(4.69952+8.13980i)q60+6.95468q61+(3.058435.29736i)q62+(2.34076+1.23322i)q6312.9921q64+(8.58881+6.19587i)q65+(5.8941610.2090i)q6613.3602q67+(8.08453+14.0028i)q68+(2.61602+4.53108i)q69+(15.6782+8.26003i)q70+(3.904876.76343i)q71+2.73629q72+(7.94401+13.7594i)q73+(4.84312+8.38853i)q74+(1.81371+3.14143i)q75+(3.613686.25908i)q76+(12.10076.37520i)q77+(7.49971+3.36952i)q78+(7.7923513.4967i)q790.470648q80+1.00000q811.22966q82+13.2349q83+(7.16271+4.51367i)q84+(7.42083+12.8532i)q85+(10.634318.4192i)q86+(0.216901+0.375683i)q8714.1453q88+(2.001433.46658i)q89+6.69792q90+(5.27744+7.94661i)q91+16.7423q92+(1.34122+2.32306i)q93+22.2130q94+(3.317015.74523i)q95+(2.91898+5.05582i)q96+(2.696534.67053i)q97+(6.88826+14.3996i)q985.16954q99+O(q100)q+(-1.14017 + 1.97483i) q^{2} +1.00000 q^{3} +(-1.59997 - 2.77124i) q^{4} +(-1.46862 - 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(-2.34076 + 1.23322i) q^{7} +2.73629 q^{8} +1.00000 q^{9} +6.69792 q^{10} -5.16954 q^{11} +(-1.59997 - 2.77124i) q^{12} +(-0.364757 - 3.58705i) q^{13} +(0.233457 - 6.02869i) q^{14} +(-1.46862 - 2.54373i) q^{15} +(0.0801172 - 0.138767i) q^{16} +(-2.52646 - 4.37595i) q^{17} +(-1.14017 + 1.97483i) q^{18} +2.25859 q^{19} +(-4.69952 + 8.13980i) q^{20} +(-2.34076 + 1.23322i) q^{21} +(5.89416 - 10.2090i) q^{22} +(-2.61602 + 4.53108i) q^{23} +2.73629 q^{24} +(-1.81371 + 3.14143i) q^{25} +(7.49971 + 3.36952i) q^{26} +1.00000 q^{27} +(7.16271 + 4.51367i) q^{28} +(0.216901 + 0.375683i) q^{29} +6.69792 q^{30} +(-1.34122 + 2.32306i) q^{31} +(2.91898 + 5.05582i) q^{32} -5.16954 q^{33} +11.5224 q^{34} +(6.57468 + 4.14312i) q^{35} +(-1.59997 - 2.77124i) q^{36} +(2.12386 - 3.67863i) q^{37} +(-2.57517 + 4.46033i) q^{38} +(-0.364757 - 3.58705i) q^{39} +(-4.01857 - 6.96037i) q^{40} +(0.269622 + 0.466999i) q^{41} +(0.233457 - 6.02869i) q^{42} +(-4.66348 + 8.07739i) q^{43} +(8.27113 + 14.3260i) q^{44} +(-1.46862 - 2.54373i) q^{45} +(-5.96541 - 10.3324i) q^{46} +(-4.87054 - 8.43603i) q^{47} +(0.0801172 - 0.138767i) q^{48} +(3.95832 - 5.77336i) q^{49} +(-4.13587 - 7.16354i) q^{50} +(-2.52646 - 4.37595i) q^{51} +(-9.35697 + 6.75002i) q^{52} +(0.377571 - 0.653972i) q^{53} +(-1.14017 + 1.97483i) q^{54} +(7.59211 + 13.1499i) q^{55} +(-6.40499 + 3.37445i) q^{56} +2.25859 q^{57} -0.989214 q^{58} +(1.82385 + 3.15901i) q^{59} +(-4.69952 + 8.13980i) q^{60} +6.95468 q^{61} +(-3.05843 - 5.29736i) q^{62} +(-2.34076 + 1.23322i) q^{63} -12.9921 q^{64} +(-8.58881 + 6.19587i) q^{65} +(5.89416 - 10.2090i) q^{66} -13.3602 q^{67} +(-8.08453 + 14.0028i) q^{68} +(-2.61602 + 4.53108i) q^{69} +(-15.6782 + 8.26003i) q^{70} +(3.90487 - 6.76343i) q^{71} +2.73629 q^{72} +(-7.94401 + 13.7594i) q^{73} +(4.84312 + 8.38853i) q^{74} +(-1.81371 + 3.14143i) q^{75} +(-3.61368 - 6.25908i) q^{76} +(12.1007 - 6.37520i) q^{77} +(7.49971 + 3.36952i) q^{78} +(-7.79235 - 13.4967i) q^{79} -0.470648 q^{80} +1.00000 q^{81} -1.22966 q^{82} +13.2349 q^{83} +(7.16271 + 4.51367i) q^{84} +(-7.42083 + 12.8532i) q^{85} +(-10.6343 - 18.4192i) q^{86} +(0.216901 + 0.375683i) q^{87} -14.1453 q^{88} +(2.00143 - 3.46658i) q^{89} +6.69792 q^{90} +(5.27744 + 7.94661i) q^{91} +16.7423 q^{92} +(-1.34122 + 2.32306i) q^{93} +22.2130 q^{94} +(-3.31701 - 5.74523i) q^{95} +(2.91898 + 5.05582i) q^{96} +(2.69653 - 4.67053i) q^{97} +(6.88826 + 14.3996i) q^{98} -5.16954 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+20q316q49q712q8+20q9+8q10+16q1116q125q139q1420q1614q19+12q209q219q2214q2312q2432q25++16q99+O(q100) 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/273Z)×\left(\mathbb{Z}/273\mathbb{Z}\right)^\times.

nn 9292 106106 157157
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\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 −1.14017 + 1.97483i −0.806222 + 1.39642i 0.109242 + 0.994015i 0.465158π0.465158\pi
−0.915463 + 0.402402i 0.868176π0.868176\pi
33 1.00000 0.577350
44 −1.59997 2.77124i −0.799987 1.38562i
55 −1.46862 2.54373i −0.656788 1.13759i −0.981442 0.191758i 0.938581π-0.938581\pi
0.324654 0.945833i 0.394752π-0.394752\pi
66 −1.14017 + 1.97483i −0.465472 + 0.806222i
77 −2.34076 + 1.23322i −0.884724 + 0.466114i
88 2.73629 0.967423
99 1.00000 0.333333
1010 6.69792 2.11807
1111 −5.16954 −1.55868 −0.779338 0.626604i 0.784444π-0.784444\pi
−0.779338 + 0.626604i 0.784444π0.784444\pi
1212 −1.59997 2.77124i −0.461873 0.799987i
1313 −0.364757 3.58705i −0.101165 0.994870i
1414 0.233457 6.02869i 0.0623939 1.61124i
1515 −1.46862 2.54373i −0.379197 0.656788i
1616 0.0801172 0.138767i 0.0200293 0.0346918i
1717 −2.52646 4.37595i −0.612756 1.06132i −0.990774 0.135526i 0.956728π-0.956728\pi
0.378018 0.925798i 0.376606π-0.376606\pi
1818 −1.14017 + 1.97483i −0.268741 + 0.465472i
1919 2.25859 0.518155 0.259078 0.965856i 0.416581π-0.416581\pi
0.259078 + 0.965856i 0.416581π0.416581\pi
2020 −4.69952 + 8.13980i −1.05084 + 1.82011i
2121 −2.34076 + 1.23322i −0.510796 + 0.269111i
2222 5.89416 10.2090i 1.25664 2.17656i
2323 −2.61602 + 4.53108i −0.545478 + 0.944796i 0.453099 + 0.891460i 0.350319π0.350319\pi
−0.998577 + 0.0533353i 0.983015π0.983015\pi
2424 2.73629 0.558542
2525 −1.81371 + 3.14143i −0.362742 + 0.628287i
2626 7.49971 + 3.36952i 1.47081 + 0.660817i
2727 1.00000 0.192450
2828 7.16271 + 4.51367i 1.35362 + 0.853004i
2929 0.216901 + 0.375683i 0.0402775 + 0.0697626i 0.885461 0.464713i 0.153842π-0.153842\pi
−0.845184 + 0.534476i 0.820509π0.820509\pi
3030 6.69792 1.22287
3131 −1.34122 + 2.32306i −0.240890 + 0.417234i −0.960968 0.276659i 0.910773π-0.910773\pi
0.720078 + 0.693893i 0.244106π0.244106\pi
3232 2.91898 + 5.05582i 0.516008 + 0.893751i
3333 −5.16954 −0.899902
3434 11.5224 1.97607
3535 6.57468 + 4.14312i 1.11132 + 0.700316i
3636 −1.59997 2.77124i −0.266662 0.461873i
3737 2.12386 3.67863i 0.349160 0.604764i −0.636940 0.770913i 0.719800π-0.719800\pi
0.986101 + 0.166150i 0.0531335π0.0531335\pi
3838 −2.57517 + 4.46033i −0.417748 + 0.723561i
3939 −0.364757 3.58705i −0.0584078 0.574388i
4040 −4.01857 6.96037i −0.635392 1.10053i
4141 0.269622 + 0.466999i 0.0421079 + 0.0729330i 0.886311 0.463090i 0.153259π-0.153259\pi
−0.844203 + 0.536023i 0.819926π0.819926\pi
4242 0.233457 6.02869i 0.0360231 0.930247i
4343 −4.66348 + 8.07739i −0.711175 + 1.23179i 0.253242 + 0.967403i 0.418503π0.418503\pi
−0.964416 + 0.264388i 0.914830π0.914830\pi
4444 8.27113 + 14.3260i 1.24692 + 2.15973i
4545 −1.46862 2.54373i −0.218929 0.379197i
4646 −5.96541 10.3324i −0.879552 1.52343i
4747 −4.87054 8.43603i −0.710442 1.23052i −0.964691 0.263383i 0.915162π-0.915162\pi
0.254250 0.967139i 0.418172π-0.418172\pi
4848 0.0801172 0.138767i 0.0115639 0.0200293i
4949 3.95832 5.77336i 0.565475 0.824766i
5050 −4.13587 7.16354i −0.584900 1.01308i
5151 −2.52646 4.37595i −0.353775 0.612756i
5252 −9.35697 + 6.75002i −1.29758 + 0.936059i
5353 0.377571 0.653972i 0.0518634 0.0898300i −0.838928 0.544242i 0.816817π-0.816817\pi
0.890792 + 0.454412i 0.150151π0.150151\pi
5454 −1.14017 + 1.97483i −0.155157 + 0.268741i
5555 7.59211 + 13.1499i 1.02372 + 1.77313i
5656 −6.40499 + 3.37445i −0.855903 + 0.450930i
5757 2.25859 0.299157
5858 −0.989214 −0.129890
5959 1.82385 + 3.15901i 0.237445 + 0.411267i 0.959981 0.280067i 0.0903566π-0.0903566\pi
−0.722535 + 0.691334i 0.757023π0.757023\pi
6060 −4.69952 + 8.13980i −0.606705 + 1.05084i
6161 6.95468 0.890455 0.445228 0.895417i 0.353123π-0.353123\pi
0.445228 + 0.895417i 0.353123π0.353123\pi
6262 −3.05843 5.29736i −0.388422 0.672766i
6363 −2.34076 + 1.23322i −0.294908 + 0.155371i
6464 −12.9921 −1.62401
6565 −8.58881 + 6.19587i −1.06531 + 0.768503i
6666 5.89416 10.2090i 0.725520 1.25664i
6767 −13.3602 −1.63221 −0.816107 0.577901i 0.803872π-0.803872\pi
−0.816107 + 0.577901i 0.803872π0.803872\pi
6868 −8.08453 + 14.0028i −0.980393 + 1.69809i
6969 −2.61602 + 4.53108i −0.314932 + 0.545478i
7070 −15.6782 + 8.26003i −1.87391 + 0.987262i
7171 3.90487 6.76343i 0.463423 0.802672i −0.535706 0.844404i 0.679955π-0.679955\pi
0.999129 + 0.0417329i 0.0132879π0.0132879\pi
7272 2.73629 0.322474
7373 −7.94401 + 13.7594i −0.929776 + 1.61042i −0.146083 + 0.989272i 0.546667π0.546667\pi
−0.783694 + 0.621147i 0.786667π0.786667\pi
7474 4.84312 + 8.38853i 0.563001 + 0.975147i
7575 −1.81371 + 3.14143i −0.209429 + 0.362742i
7676 −3.61368 6.25908i −0.414517 0.717965i
7777 12.1007 6.37520i 1.37900 0.726521i
7878 7.49971 + 3.36952i 0.849175 + 0.381523i
7979 −7.79235 13.4967i −0.876708 1.51850i −0.854932 0.518740i 0.826401π-0.826401\pi
−0.0217756 0.999763i 0.506932π-0.506932\pi
8080 −0.470648 −0.0526200
8181 1.00000 0.111111
8282 −1.22966 −0.135793
8383 13.2349 1.45272 0.726360 0.687315i 0.241211π-0.241211\pi
0.726360 + 0.687315i 0.241211π0.241211\pi
8484 7.16271 + 4.51367i 0.781515 + 0.492482i
8585 −7.42083 + 12.8532i −0.804902 + 1.39413i
8686 −10.6343 18.4192i −1.14673 1.98619i
8787 0.216901 + 0.375683i 0.0232542 + 0.0402775i
8888 −14.1453 −1.50790
8989 2.00143 3.46658i 0.212151 0.367457i −0.740236 0.672347i 0.765286π-0.765286\pi
0.952388 + 0.304890i 0.0986197π0.0986197\pi
9090 6.69792 0.706023
9191 5.27744 + 7.94661i 0.553227 + 0.833031i
9292 16.7423 1.74550
9393 −1.34122 + 2.32306i −0.139078 + 0.240890i
9494 22.2130 2.29109
9595 −3.31701 5.74523i −0.340318 0.589449i
9696 2.91898 + 5.05582i 0.297917 + 0.516008i
9797 2.69653 4.67053i 0.273791 0.474220i −0.696038 0.718005i 0.745056π-0.745056\pi
0.969829 + 0.243784i 0.0783889π0.0783889\pi
9898 6.88826 + 14.3996i 0.695819 + 1.45458i
9999 −5.16954 −0.519559
100100 11.6075 1.16075
101101 −3.15240 −0.313676 −0.156838 0.987624i 0.550130π-0.550130\pi
−0.156838 + 0.987624i 0.550130π0.550130\pi
102102 11.5224 1.14088
103103 −6.59727 11.4268i −0.650048 1.12592i −0.983111 0.183012i 0.941415π-0.941415\pi
0.333062 0.942905i 0.391918π-0.391918\pi
104104 −0.998078 9.81520i −0.0978696 0.962460i
105105 6.57468 + 4.14312i 0.641623 + 0.404327i
106106 0.860990 + 1.49128i 0.0836267 + 0.144846i
107107 −2.93351 + 5.08098i −0.283593 + 0.491197i −0.972267 0.233874i 0.924860π-0.924860\pi
0.688674 + 0.725071i 0.258193π0.258193\pi
108108 −1.59997 2.77124i −0.153958 0.266662i
109109 2.74399 4.75273i 0.262826 0.455229i −0.704166 0.710036i 0.748679π-0.748679\pi
0.966992 + 0.254807i 0.0820120π0.0820120\pi
110110 −34.6252 −3.30138
111111 2.12386 3.67863i 0.201588 0.349160i
112112 −0.0164045 + 0.423623i −0.00155008 + 0.0400286i
113113 0.794808 1.37665i 0.0747692 0.129504i −0.826217 0.563352i 0.809511π-0.809511\pi
0.900986 + 0.433848i 0.142845π0.142845\pi
114114 −2.57517 + 4.46033i −0.241187 + 0.417748i
115115 15.3678 1.43305
116116 0.694071 1.20217i 0.0644428 0.111618i
117117 −0.364757 3.58705i −0.0337218 0.331623i
118118 −8.31800 −0.765734
119119 11.3104 + 7.12737i 1.03682 + 0.653365i
120120 −4.01857 6.96037i −0.366844 0.635392i
121121 15.7242 1.42947
122122 −7.92951 + 13.7343i −0.717904 + 1.24345i
123123 0.269622 + 0.466999i 0.0243110 + 0.0421079i
124124 8.58366 0.770835
125125 −4.03162 −0.360599
126126 0.233457 6.02869i 0.0207980 0.537079i
127127 0.348278 + 0.603236i 0.0309047 + 0.0535285i 0.881064 0.472997i 0.156828π-0.156828\pi
−0.850159 + 0.526525i 0.823494π0.823494\pi
128128 8.97519 15.5455i 0.793302 1.37404i
129129 −4.66348 + 8.07739i −0.410597 + 0.711175i
130130 −2.44311 24.0258i −0.214275 2.10720i
131131 3.35469 + 5.81049i 0.293101 + 0.507665i 0.974541 0.224208i 0.0719796π-0.0719796\pi
−0.681441 + 0.731873i 0.738646π0.738646\pi
132132 8.27113 + 14.3260i 0.719910 + 1.24692i
133133 −5.28681 + 2.78534i −0.458425 + 0.241520i
134134 15.2329 26.3842i 1.31593 2.27925i
135135 −1.46862 2.54373i −0.126399 0.218929i
136136 −6.91311 11.9739i −0.592794 1.02675i
137137 −6.24965 10.8247i −0.533944 0.924818i −0.999214 0.0396491i 0.987376π-0.987376\pi
0.465270 0.885169i 0.345957π-0.345957\pi
138138 −5.96541 10.3324i −0.507810 0.879552i
139139 −0.657614 + 1.13902i −0.0557781 + 0.0966105i −0.892566 0.450916i 0.851097π-0.851097\pi
0.836788 + 0.547527i 0.184431π0.184431\pi
140140 0.962254 24.8489i 0.0813253 2.10011i
141141 −4.87054 8.43603i −0.410174 0.710442i
142142 8.90442 + 15.4229i 0.747243 + 1.29426i
143143 1.88563 + 18.5434i 0.157684 + 1.55068i
144144 0.0801172 0.138767i 0.00667643 0.0115639i
145145 0.637091 1.10347i 0.0529075 0.0916385i
146146 −18.1150 31.3762i −1.49921 2.59671i
147147 3.95832 5.77336i 0.326477 0.476179i
148148 −13.5925 −1.11729
149149 21.1927 1.73618 0.868088 0.496411i 0.165349π-0.165349\pi
0.868088 + 0.496411i 0.165349π0.165349\pi
150150 −4.13587 7.16354i −0.337692 0.584900i
151151 7.90358 13.6894i 0.643185 1.11403i −0.341533 0.939870i 0.610946π-0.610946\pi
0.984718 0.174159i 0.0557205π-0.0557205\pi
152152 6.18014 0.501275
153153 −2.52646 4.37595i −0.204252 0.353775i
154154 −1.20686 + 31.1656i −0.0972518 + 2.51139i
155155 7.87898 0.632855
156156 −9.35697 + 6.75002i −0.749157 + 0.540434i
157157 −2.76205 + 4.78402i −0.220436 + 0.381806i −0.954940 0.296798i 0.904081π-0.904081\pi
0.734505 + 0.678604i 0.237415π0.237415\pi
158158 35.5384 2.82728
159159 0.377571 0.653972i 0.0299433 0.0518634i
160160 8.57376 14.8502i 0.677815 1.17401i
161161 0.535646 13.8323i 0.0422148 1.09014i
162162 −1.14017 + 1.97483i −0.0895802 + 0.155157i
163163 −3.14870 −0.246625 −0.123313 0.992368i 0.539352π-0.539352\pi
−0.123313 + 0.992368i 0.539352π0.539352\pi
164164 0.862777 1.49437i 0.0673715 0.116691i
165165 7.59211 + 13.1499i 0.591045 + 1.02372i
166166 −15.0900 + 26.1367i −1.17121 + 2.02860i
167167 6.71152 + 11.6247i 0.519353 + 0.899546i 0.999747 + 0.0224932i 0.00716043π0.00716043\pi
−0.480394 + 0.877053i 0.659506π0.659506\pi
168168 −6.40499 + 3.37445i −0.494156 + 0.260344i
169169 −12.7339 + 2.61680i −0.979531 + 0.201293i
170170 −16.9220 29.3098i −1.29786 2.24796i
171171 2.25859 0.172718
172172 29.8458 2.27572
173173 −12.8488 −0.976879 −0.488439 0.872598i 0.662434π-0.662434\pi
−0.488439 + 0.872598i 0.662434π0.662434\pi
174174 −0.989214 −0.0749921
175175 0.371368 9.59005i 0.0280728 0.724940i
176176 −0.414169 + 0.717362i −0.0312192 + 0.0540732i
177177 1.82385 + 3.15901i 0.137089 + 0.237445i
178178 4.56394 + 7.90498i 0.342082 + 0.592503i
179179 18.6663 1.39518 0.697591 0.716496i 0.254255π-0.254255\pi
0.697591 + 0.716496i 0.254255π0.254255\pi
180180 −4.69952 + 8.13980i −0.350281 + 0.606705i
181181 0.878433 0.0652934 0.0326467 0.999467i 0.489606π-0.489606\pi
0.0326467 + 0.999467i 0.489606π0.489606\pi
182182 −21.7104 + 1.36158i −1.60928 + 0.100927i
183183 6.95468 0.514104
184184 −7.15818 + 12.3983i −0.527708 + 0.914017i
185185 −12.4766 −0.917298
186186 −3.05843 5.29736i −0.224255 0.388422i
187187 13.0606 + 22.6217i 0.955088 + 1.65426i
188188 −15.5855 + 26.9948i −1.13669 + 1.96880i
189189 −2.34076 + 1.23322i −0.170265 + 0.0897038i
190190 15.1278 1.09749
191191 −15.9513 −1.15419 −0.577097 0.816675i 0.695815π-0.695815\pi
−0.577097 + 0.816675i 0.695815π0.695815\pi
192192 −12.9921 −0.937621
193193 3.95066 0.284375 0.142187 0.989840i 0.454586π-0.454586\pi
0.142187 + 0.989840i 0.454586π0.454586\pi
194194 6.14900 + 10.6504i 0.441473 + 0.764653i
195195 −8.58881 + 6.19587i −0.615057 + 0.443696i
196196 −22.3325 1.73222i −1.59518 0.123730i
197197 −6.72353 11.6455i −0.479032 0.829708i 0.520679 0.853753i 0.325679π-0.325679\pi
−0.999711 + 0.0240448i 0.992346π0.992346\pi
198198 5.89416 10.2090i 0.418879 0.725520i
199199 −10.4145 18.0385i −0.738268 1.27872i −0.953275 0.302105i 0.902311π-0.902311\pi
0.215007 0.976612i 0.431023π-0.431023\pi
200200 −4.96282 + 8.59586i −0.350925 + 0.607819i
201201 −13.3602 −0.942359
202202 3.59427 6.22546i 0.252892 0.438022i
203203 −0.971014 0.611897i −0.0681518 0.0429468i
204204 −8.08453 + 14.0028i −0.566030 + 0.980393i
205205 0.791947 1.37169i 0.0553120 0.0958031i
206206 30.0880 2.09633
207207 −2.61602 + 4.53108i −0.181826 + 0.314932i
208208 −0.526988 0.236769i −0.0365401 0.0164169i
209209 −11.6759 −0.807636
210210 −15.6782 + 8.26003i −1.08190 + 0.569996i
211211 7.17814 + 12.4329i 0.494164 + 0.855917i 0.999977 0.00672604i 0.00214098π-0.00214098\pi
−0.505814 + 0.862643i 0.668808π0.668808\pi
212212 −2.41641 −0.165960
213213 3.90487 6.76343i 0.267557 0.463423i
214214 −6.68939 11.5864i −0.457277 0.792027i
215215 27.3956 1.86836
216216 2.73629 0.186181
217217 0.274623 7.09175i 0.0186426 0.481419i
218218 6.25722 + 10.8378i 0.423793 + 0.734030i
219219 −7.94401 + 13.7594i −0.536807 + 0.929776i
220220 24.2943 42.0790i 1.63792 2.83697i
221221 −14.7752 + 10.6587i −0.993890 + 0.716981i
222222 4.84312 + 8.38853i 0.325049 + 0.563001i
223223 0.596931 + 1.03392i 0.0399735 + 0.0692361i 0.885320 0.464982i 0.153939π-0.153939\pi
−0.845346 + 0.534218i 0.820606π0.820606\pi
224224 −13.0676 8.23472i −0.873115 0.550205i
225225 −1.81371 + 3.14143i −0.120914 + 0.209429i
226226 1.81243 + 3.13922i 0.120561 + 0.208818i
227227 7.94437 + 13.7600i 0.527286 + 0.913286i 0.999494 + 0.0317993i 0.0101237π0.0101237\pi
−0.472208 + 0.881487i 0.656543π0.656543\pi
228228 −3.61368 6.25908i −0.239322 0.414517i
229229 −4.39323 7.60931i −0.290313 0.502837i 0.683571 0.729884i 0.260426π-0.260426\pi
−0.973884 + 0.227047i 0.927093π0.927093\pi
230230 −17.5219 + 30.3488i −1.15536 + 2.00114i
231231 12.1007 6.37520i 0.796165 0.419457i
232232 0.593502 + 1.02798i 0.0389653 + 0.0674899i
233233 2.86714 + 4.96604i 0.187833 + 0.325336i 0.944527 0.328432i 0.106520π-0.106520\pi
−0.756695 + 0.653769i 0.773187π0.773187\pi
234234 7.49971 + 3.36952i 0.490271 + 0.220272i
235235 −14.3060 + 24.7787i −0.933220 + 1.61638i
236236 5.83623 10.1086i 0.379906 0.658017i
237237 −7.79235 13.4967i −0.506168 0.876708i
238238 −26.9711 + 14.2096i −1.74828 + 0.921074i
239239 −11.5411 −0.746532 −0.373266 0.927724i 0.621762π-0.621762\pi
−0.373266 + 0.927724i 0.621762π0.621762\pi
240240 −0.470648 −0.0303802
241241 2.83030 + 4.90223i 0.182316 + 0.315780i 0.942669 0.333730i 0.108307π-0.108307\pi
−0.760353 + 0.649510i 0.774974π0.774974\pi
242242 −17.9282 + 31.0526i −1.15247 + 1.99614i
243243 1.00000 0.0641500
244244 −11.1273 19.2730i −0.712352 1.23383i
245245 −20.4992 1.59001i −1.30964 0.101582i
246246 −1.22966 −0.0784003
247247 −0.823835 8.10167i −0.0524193 0.515497i
248248 −3.66996 + 6.35655i −0.233043 + 0.403642i
249249 13.2349 0.838728
250250 4.59673 7.96177i 0.290723 0.503546i
251251 12.1872 21.1088i 0.769249 1.33238i −0.168721 0.985664i 0.553964π-0.553964\pi
0.937971 0.346715i 0.112703π-0.112703\pi
252252 7.16271 + 4.51367i 0.451208 + 0.284335i
253253 13.5236 23.4236i 0.850223 1.47263i
254254 −1.58839 −0.0996641
255255 −7.42083 + 12.8532i −0.464710 + 0.804902i
256256 7.47442 + 12.9461i 0.467151 + 0.809130i
257257 −2.30268 + 3.98836i −0.143637 + 0.248787i −0.928864 0.370422i 0.879213π-0.879213\pi
0.785226 + 0.619209i 0.212547π0.212547\pi
258258 −10.6343 18.4192i −0.662064 1.14673i
259259 −0.434873 + 11.2300i −0.0270217 + 0.697798i
260260 30.9121 + 13.8884i 1.91709 + 0.861320i
261261 0.216901 + 0.375683i 0.0134258 + 0.0232542i
262262 −15.2997 −0.945216
263263 22.9824 1.41715 0.708576 0.705634i 0.249338π-0.249338\pi
0.708576 + 0.705634i 0.249338π0.249338\pi
264264 −14.1453 −0.870586
265265 −2.21804 −0.136253
266266 0.527282 13.6163i 0.0323297 0.834870i
267267 2.00143 3.46658i 0.122486 0.212151i
268268 21.3760 + 37.0244i 1.30575 + 2.26162i
269269 −7.00246 12.1286i −0.426948 0.739495i 0.569652 0.821886i 0.307078π-0.307078\pi
−0.996600 + 0.0823905i 0.973745π0.973745\pi
270270 6.69792 0.407622
271271 9.55299 16.5463i 0.580303 1.00511i −0.415141 0.909757i 0.636268π-0.636268\pi
0.995443 0.0953563i 0.0303990π-0.0303990\pi
272272 −0.809651 −0.0490923
273273 5.27744 + 7.94661i 0.319405 + 0.480951i
274274 28.5027 1.72191
275275 9.37604 16.2398i 0.565397 0.979296i
276276 16.7423 1.00777
277277 −6.45998 11.1890i −0.388142 0.672282i 0.604057 0.796941i 0.293550π-0.293550\pi
−0.992200 + 0.124658i 0.960216π0.960216\pi
278278 −1.49958 2.59735i −0.0899390 0.155779i
279279 −1.34122 + 2.32306i −0.0802967 + 0.139078i
280280 17.9902 + 11.3368i 1.07512 + 0.677502i
281281 −19.6264 −1.17082 −0.585408 0.810739i 0.699066π-0.699066\pi
−0.585408 + 0.810739i 0.699066π0.699066\pi
282282 22.2130 1.32276
283283 3.26727 0.194219 0.0971095 0.995274i 0.469040π-0.469040\pi
0.0971095 + 0.995274i 0.469040π0.469040\pi
284284 −24.9907 −1.48293
285285 −3.31701 5.74523i −0.196483 0.340318i
286286 −38.7701 17.4189i −2.29252 1.03000i
287287 −1.20704 0.760629i −0.0712490 0.0448985i
288288 2.91898 + 5.05582i 0.172003 + 0.297917i
289289 −4.26597 + 7.38888i −0.250939 + 0.434640i
290290 1.45278 + 2.51629i 0.0853104 + 0.147762i
291291 2.69653 4.67053i 0.158073 0.273791i
292292 50.8408 2.97523
293293 9.50947 16.4709i 0.555549 0.962239i −0.442311 0.896862i 0.645841π-0.645841\pi
0.997861 0.0653778i 0.0208252π-0.0208252\pi
294294 6.88826 + 14.3996i 0.401731 + 0.839803i
295295 5.35710 9.27878i 0.311903 0.540231i
296296 5.81149 10.0658i 0.337786 0.585062i
297297 −5.16954 −0.299967
298298 −24.1633 + 41.8521i −1.39974 + 2.42442i
299299 17.2074 + 7.73106i 0.995132 + 0.447099i
300300 11.6075 0.670162
301301 0.954876 24.6584i 0.0550382 1.42128i
302302 18.0229 + 31.2165i 1.03710 + 1.79631i
303303 −3.15240 −0.181101
304304 0.180952 0.313418i 0.0103783 0.0179757i
305305 −10.2138 17.6908i −0.584840 1.01297i
306306 11.5224 0.658689
307307 −8.30660 −0.474083 −0.237041 0.971500i 0.576178π-0.576178\pi
−0.237041 + 0.971500i 0.576178π0.576178\pi
308308 −37.0279 23.3336i −2.10986 1.32956i
309309 −6.59727 11.4268i −0.375306 0.650048i
310310 −8.98338 + 15.5597i −0.510221 + 0.883729i
311311 5.42853 9.40250i 0.307824 0.533167i −0.670062 0.742305i 0.733733π-0.733733\pi
0.977886 + 0.209138i 0.0670659π0.0670659\pi
312312 −0.998078 9.81520i −0.0565051 0.555676i
313313 0.566928 + 0.981949i 0.0320447 + 0.0555030i 0.881603 0.471992i 0.156465π-0.156465\pi
−0.849558 + 0.527495i 0.823131π0.823131\pi
314314 −6.29842 10.9092i −0.355440 0.615641i
315315 6.57468 + 4.14312i 0.370441 + 0.233439i
316316 −24.9351 + 43.1889i −1.40271 + 2.42956i
317317 −4.98712 8.63795i −0.280105 0.485155i 0.691306 0.722562i 0.257036π-0.257036\pi
−0.971410 + 0.237407i 0.923702π0.923702\pi
318318 0.860990 + 1.49128i 0.0482819 + 0.0836267i
319319 −1.12128 1.94211i −0.0627795 0.108737i
320320 19.0804 + 33.0483i 1.06663 + 1.84746i
321321 −2.93351 + 5.08098i −0.163732 + 0.283593i
322322 26.7058 + 16.8290i 1.48825 + 0.937843i
323323 −5.70622 9.88347i −0.317503 0.549931i
324324 −1.59997 2.77124i −0.0888874 0.153958i
325325 11.9301 + 5.36001i 0.661760 + 0.297320i
326326 3.59005 6.21815i 0.198835 0.344392i
327327 2.74399 4.75273i 0.151743 0.262826i
328328 0.737763 + 1.27784i 0.0407362 + 0.0705571i
329329 21.8043 + 13.7403i 1.20211 + 0.757525i
330330 −34.6252 −1.90605
331331 −1.65514 −0.0909746 −0.0454873 0.998965i 0.514484π-0.514484\pi
−0.0454873 + 0.998965i 0.514484π0.514484\pi
332332 −21.1755 36.6770i −1.16216 2.01291i
333333 2.12386 3.67863i 0.116387 0.201588i
334334 −30.6091 −1.67486
335335 19.6212 + 33.9849i 1.07202 + 1.85679i
336336 −0.0164045 + 0.423623i −0.000894938 + 0.0231105i
337337 −12.4081 −0.675913 −0.337956 0.941162i 0.609736π-0.609736\pi
−0.337956 + 0.941162i 0.609736π0.609736\pi
338338 9.35107 28.1309i 0.508631 1.53012i
339339 0.794808 1.37665i 0.0431680 0.0747692i
340340 47.4925 2.57564
341341 6.93349 12.0092i 0.375469 0.650332i
342342 −2.57517 + 4.46033i −0.139249 + 0.241187i
343343 −2.14565 + 18.3955i −0.115854 + 0.993266i
344344 −12.7606 + 22.1021i −0.688007 + 1.19166i
345345 15.3678 0.827374
346346 14.6498 25.3743i 0.787581 1.36413i
347347 −6.62262 11.4707i −0.355521 0.615780i 0.631686 0.775224i 0.282363π-0.282363\pi
−0.987207 + 0.159444i 0.949030π0.949030\pi
348348 0.694071 1.20217i 0.0372061 0.0644428i
349349 17.5068 + 30.3227i 0.937119 + 1.62314i 0.770812 + 0.637063i 0.219851π0.219851\pi
0.166307 + 0.986074i 0.446816π0.446816\pi
350350 18.5153 + 11.6677i 0.989685 + 0.623663i
351351 −0.364757 3.58705i −0.0194693 0.191463i
352352 −15.0898 26.1363i −0.804289 1.39307i
353353 23.1083 1.22993 0.614964 0.788555i 0.289171π-0.289171\pi
0.614964 + 0.788555i 0.289171π0.289171\pi
354354 −8.31800 −0.442097
355355 −22.9391 −1.21748
356356 −12.8089 −0.678873
357357 11.3104 + 7.12737i 0.598608 + 0.377221i
358358 −21.2827 + 36.8628i −1.12483 + 1.94826i
359359 −6.44458 11.1623i −0.340132 0.589126i 0.644325 0.764752i 0.277138π-0.277138\pi
−0.984457 + 0.175626i 0.943805π0.943805\pi
360360 −4.01857 6.96037i −0.211797 0.366844i
361361 −13.8988 −0.731515
362362 −1.00156 + 1.73476i −0.0526409 + 0.0911768i
363363 15.7242 0.825305
364364 13.5781 27.3394i 0.711688 1.43297i
365365 46.6670 2.44266
366366 −7.92951 + 13.7343i −0.414482 + 0.717904i
367367 −26.4929 −1.38292 −0.691460 0.722415i 0.743032π-0.743032\pi
−0.691460 + 0.722415i 0.743032π0.743032\pi
368368 0.419177 + 0.726035i 0.0218511 + 0.0378472i
369369 0.269622 + 0.466999i 0.0140360 + 0.0243110i
370370 14.2254 24.6392i 0.739545 1.28093i
371371 −0.0773099 + 1.99642i −0.00401373 + 0.103649i
372372 8.58366 0.445042
373373 −12.3710 −0.640545 −0.320273 0.947325i 0.603775π-0.603775\pi
−0.320273 + 0.947325i 0.603775π0.603775\pi
374374 −59.5653 −3.08005
375375 −4.03162 −0.208192
376376 −13.3272 23.0834i −0.687298 1.19043i
377377 1.26848 0.915067i 0.0653300 0.0471284i
378378 0.233457 6.02869i 0.0120077 0.310082i
379379 −14.0179 24.2797i −0.720050 1.24716i −0.960979 0.276621i 0.910785π-0.910785\pi
0.240929 0.970543i 0.422548π-0.422548\pi
380380 −10.6143 + 18.3844i −0.544500 + 0.943102i
381381 0.348278 + 0.603236i 0.0178428 + 0.0309047i
382382 18.1872 31.5011i 0.930537 1.61174i
383383 −26.2903 −1.34337 −0.671687 0.740835i 0.734430π-0.734430\pi
−0.671687 + 0.740835i 0.734430π0.734430\pi
384384 8.97519 15.5455i 0.458013 0.793302i
385385 −33.9881 21.4181i −1.73219 1.09157i
386386 −4.50442 + 7.80188i −0.229269 + 0.397105i
387387 −4.66348 + 8.07739i −0.237058 + 0.410597i
388388 −17.2575 −0.876117
389389 −13.4205 + 23.2449i −0.680445 + 1.17856i 0.294400 + 0.955682i 0.404880π0.404880\pi
−0.974845 + 0.222883i 0.928453π0.928453\pi
390390 −2.44311 24.0258i −0.123712 1.21659i
391391 26.4371 1.33698
392392 10.8311 15.7976i 0.547053 0.797897i
393393 3.35469 + 5.81049i 0.169222 + 0.293101i
394394 30.6639 1.54482
395395 −22.8881 + 39.6433i −1.15162 + 1.99467i
396396 8.27113 + 14.3260i 0.415640 + 0.719910i
397397 24.5243 1.23084 0.615419 0.788200i 0.288987π-0.288987\pi
0.615419 + 0.788200i 0.288987π0.288987\pi
398398 47.4974 2.38083
399399 −5.28681 + 2.78534i −0.264672 + 0.139441i
400400 0.290618 + 0.503366i 0.0145309 + 0.0251683i
401401 −1.58285 + 2.74158i −0.0790438 + 0.136908i −0.902838 0.429982i 0.858520π-0.858520\pi
0.823794 + 0.566889i 0.191853π0.191853\pi
402402 15.2329 26.3842i 0.759750 1.31593i
403403 8.82216 + 3.96367i 0.439463 + 0.197445i
404404 5.04376 + 8.73605i 0.250936 + 0.434635i
405405 −1.46862 2.54373i −0.0729765 0.126399i
406406 2.31551 1.21992i 0.114917 0.0605437i
407407 −10.9794 + 19.0169i −0.544228 + 0.942630i
408408 −6.91311 11.9739i −0.342250 0.592794i
409409 −9.53424 16.5138i −0.471438 0.816555i 0.528028 0.849227i 0.322932π-0.322932\pi
−0.999466 + 0.0326723i 0.989598π0.989598\pi
410410 1.80591 + 3.12792i 0.0891874 + 0.154477i
411411 −6.24965 10.8247i −0.308273 0.533944i
412412 −21.1109 + 36.5652i −1.04006 + 1.80144i
413413 −8.16496 5.14526i −0.401771 0.253182i
414414 −5.96541 10.3324i −0.293184 0.507810i
415415 −19.4371 33.6660i −0.954129 1.65260i
416416 17.0708 12.3147i 0.836964 0.603777i
417417 −0.657614 + 1.13902i −0.0322035 + 0.0557781i
418418 13.3125 23.0579i 0.651134 1.12780i
419419 7.80534 + 13.5192i 0.381316 + 0.660458i 0.991251 0.131993i 0.0421377π-0.0421377\pi
−0.609935 + 0.792452i 0.708804π0.708804\pi
420420 0.962254 24.8489i 0.0469532 1.21250i
421421 −18.0525 −0.879827 −0.439913 0.898040i 0.644991π-0.644991\pi
−0.439913 + 0.898040i 0.644991π0.644991\pi
422422 −32.7372 −1.59362
423423 −4.87054 8.43603i −0.236814 0.410174i
424424 1.03314 1.78945i 0.0501738 0.0869036i
425425 18.3290 0.889088
426426 8.90442 + 15.4229i 0.431421 + 0.747243i
427427 −16.2792 + 8.57667i −0.787807 + 0.415054i
428428 18.7741 0.907481
429429 1.88563 + 18.5434i 0.0910388 + 0.895285i
430430 −31.2356 + 54.1017i −1.50632 + 2.60902i
431431 −17.5165 −0.843741 −0.421871 0.906656i 0.638626π-0.638626\pi
−0.421871 + 0.906656i 0.638626π0.638626\pi
432432 0.0801172 0.138767i 0.00385464 0.00667643i
433433 −3.02961 + 5.24744i −0.145594 + 0.252176i −0.929594 0.368584i 0.879843π-0.879843\pi
0.784001 + 0.620760i 0.213176π0.213176\pi
434434 13.6919 + 8.62813i 0.657232 + 0.414163i
435435 0.637091 1.10347i 0.0305462 0.0529075i
436436 −17.5612 −0.841030
437437 −5.90851 + 10.2338i −0.282642 + 0.489551i
438438 −18.1150 31.3762i −0.865570 1.49921i
439439 −11.6912 + 20.2497i −0.557990 + 0.966467i 0.439674 + 0.898157i 0.355094π0.355094\pi
−0.997664 + 0.0683098i 0.978239π0.978239\pi
440440 20.7742 + 35.9819i 0.990370 + 1.71537i
441441 3.95832 5.77336i 0.188492 0.274922i
442442 −4.20286 41.3313i −0.199910 1.96593i
443443 4.44712 + 7.70264i 0.211289 + 0.365963i 0.952118 0.305730i 0.0989005π-0.0989005\pi
−0.740829 + 0.671693i 0.765567π0.765567\pi
444444 −13.5925 −0.645070
445445 −11.7574 −0.557354
446446 −2.72241 −0.128910
447447 21.1927 1.00238
448448 30.4113 16.0221i 1.43680 0.756973i
449449 −19.3671 + 33.5448i −0.913989 + 1.58308i −0.105614 + 0.994407i 0.533681π0.533681\pi
−0.808375 + 0.588668i 0.799652π0.799652\pi
450450 −4.13587 7.16354i −0.194967 0.337692i
451451 −1.39382 2.41417i −0.0656326 0.113679i
452452 −5.08668 −0.239258
453453 7.90358 13.6894i 0.371343 0.643185i
454454 −36.2317 −1.70044
455455 12.4634 25.0950i 0.584295 1.17647i
456456 6.18014 0.289411
457457 −11.2001 + 19.3992i −0.523920 + 0.907457i 0.475692 + 0.879612i 0.342198π0.342198\pi
−0.999612 + 0.0278448i 0.991136π0.991136\pi
458458 20.0361 0.936227
459459 −2.52646 4.37595i −0.117925 0.204252i
460460 −24.5881 42.5878i −1.14642 1.98567i
461461 −1.40367 + 2.43123i −0.0653755 + 0.113234i −0.896860 0.442314i 0.854158π-0.854158\pi
0.831485 + 0.555547i 0.187491π0.187491\pi
462462 −1.20686 + 31.1656i −0.0561484 + 1.44995i
463463 37.7530 1.75453 0.877266 0.480004i 0.159365π-0.159365\pi
0.877266 + 0.480004i 0.159365π0.159365\pi
464464 0.0695099 0.00322692
465465 7.87898 0.365379
466466 −13.0761 −0.605740
467467 −8.04389 13.9324i −0.372227 0.644716i 0.617681 0.786429i 0.288072π-0.288072\pi
−0.989908 + 0.141713i 0.954739π0.954739\pi
468468 −9.35697 + 6.75002i −0.432526 + 0.312020i
469469 31.2731 16.4762i 1.44406 0.760798i
470470 −32.6225 56.5038i −1.50476 2.60633i
471471 −2.76205 + 4.78402i −0.127269 + 0.220436i
472472 4.99058 + 8.64394i 0.229710 + 0.397870i
473473 24.1081 41.7564i 1.10849 1.91996i
474474 35.5384 1.63233
475475 −4.09642 + 7.09520i −0.187956 + 0.325550i
476476 1.65536 42.7473i 0.0758731 1.95932i
477477 0.377571 0.653972i 0.0172878 0.0299433i
478478 13.1588 22.7917i 0.601870 1.04247i
479479 8.54850 0.390591 0.195295 0.980744i 0.437433π-0.437433\pi
0.195295 + 0.980744i 0.437433π0.437433\pi
480480 8.57376 14.8502i 0.391337 0.677815i
481481 −13.9701 6.27659i −0.636984 0.286188i
482482 −12.9081 −0.587948
483483 0.535646 13.8323i 0.0243727 0.629392i
484484 −25.1583 43.5754i −1.14356 1.98070i
485485 −15.8407 −0.719291
486486 −1.14017 + 1.97483i −0.0517191 + 0.0895802i
487487 17.7881 + 30.8098i 0.806054 + 1.39613i 0.915577 + 0.402142i 0.131734π0.131734\pi
−0.109524 + 0.993984i 0.534932π0.534932\pi
488488 19.0300 0.861447
489489 −3.14870 −0.142389
490490 26.5125 38.6695i 1.19771 1.74691i
491491 15.6990 + 27.1914i 0.708485 + 1.22713i 0.965419 + 0.260703i 0.0839544π0.0839544\pi
−0.256934 + 0.966429i 0.582712π0.582712\pi
492492 0.862777 1.49437i 0.0388970 0.0673715i
493493 1.09598 1.89829i 0.0493605 0.0854949i
494494 16.9387 + 7.61034i 0.762110 + 0.342406i
495495 7.59211 + 13.1499i 0.341240 + 0.591045i
496496 0.214909 + 0.372234i 0.00964972 + 0.0167138i
497497 −0.799545 + 20.6471i −0.0358645 + 0.926151i
498498 −15.0900 + 26.1367i −0.676200 + 1.17121i
499499 2.14606 + 3.71708i 0.0960708 + 0.166399i 0.910055 0.414488i 0.136039π-0.136039\pi
−0.813984 + 0.580887i 0.802706π0.802706\pi
500500 6.45048 + 11.1726i 0.288474 + 0.499652i
501501 6.71152 + 11.6247i 0.299849 + 0.519353i
502502 27.7909 + 48.1353i 1.24037 + 2.14839i
503503 7.83439 13.5696i 0.349318 0.605037i −0.636810 0.771021i 0.719747π-0.719747\pi
0.986129 + 0.165984i 0.0530799π0.0530799\pi
504504 −6.40499 + 3.37445i −0.285301 + 0.150310i
505505 4.62969 + 8.01886i 0.206019 + 0.356835i
506506 30.8385 + 53.4138i 1.37094 + 2.37453i
507507 −12.7339 + 2.61680i −0.565533 + 0.116216i
508508 1.11447 1.93032i 0.0494467 0.0856442i
509509 −0.851865 + 1.47547i −0.0377583 + 0.0653992i −0.884287 0.466944i 0.845355π-0.845355\pi
0.846529 + 0.532343i 0.178688π0.178688\pi
510510 −16.9220 29.3098i −0.749319 1.29786i
511511 1.62658 42.0043i 0.0719558 1.85816i
512512 1.81234 0.0800947
513513 2.25859 0.0997190
514514 −5.25089 9.09481i −0.231607 0.401155i
515515 −19.3778 + 33.5633i −0.853888 + 1.47898i
516516 29.8458 1.31389
517517 25.1785 + 43.6104i 1.10735 + 1.91798i
518518 −21.6815 13.6629i −0.952631 0.600313i
519519 −12.8488 −0.564001
520520 −23.5014 + 16.9537i −1.03061 + 0.743468i
521521 8.39696 14.5440i 0.367878 0.637183i −0.621356 0.783528i 0.713418π-0.713418\pi
0.989234 + 0.146346i 0.0467512π0.0467512\pi
522522 −0.989214 −0.0432967
523523 3.74526 6.48697i 0.163769 0.283656i −0.772449 0.635077i 0.780968π-0.780968\pi
0.936217 + 0.351422i 0.114302π0.114302\pi
524524 10.7348 18.5933i 0.468953 0.812251i
525525 0.371368 9.59005i 0.0162078 0.418544i
526526 −26.2038 + 45.3863i −1.14254 + 1.97894i
527527 13.5541 0.590427
528528 −0.414169 + 0.717362i −0.0180244 + 0.0312192i
529529 −2.18713 3.78822i −0.0950926 0.164705i
530530 2.52894 4.38025i 0.109850 0.190266i
531531 1.82385 + 3.15901i 0.0791485 + 0.137089i
532532 16.1776 + 10.1945i 0.701388 + 0.441989i
533533 1.57681 1.13749i 0.0682990 0.0492702i
534534 4.56394 + 7.90498i 0.197501 + 0.342082i
535535 17.2329 0.745041
536536 −36.5574 −1.57904
537537 18.6663 0.805509
538538 31.9360 1.37686
539539 −20.4627 + 29.8456i −0.881392 + 1.28554i
540540 −4.69952 + 8.13980i −0.202235 + 0.350281i
541541 4.78963 + 8.29588i 0.205922 + 0.356668i 0.950426 0.310950i 0.100647π-0.100647\pi
−0.744504 + 0.667618i 0.767314π0.767314\pi
542542 21.7840 + 37.7311i 0.935705 + 1.62069i
543543 0.878433 0.0376972
544544 14.7494 25.5466i 0.632373 1.09530i
545545 −16.1195 −0.690485
546546 −21.7104 + 1.36158i −0.929119 + 0.0582704i
547547 −30.1843 −1.29059 −0.645293 0.763935i 0.723265π-0.723265\pi
−0.645293 + 0.763935i 0.723265π0.723265\pi
548548 −19.9986 + 34.6385i −0.854296 + 1.47968i
549549 6.95468 0.296818
550550 21.3806 + 37.0322i 0.911670 + 1.57906i
551551 0.489889 + 0.848513i 0.0208700 + 0.0361479i
552552 −7.15818 + 12.3983i −0.304672 + 0.527708i
553553 34.8845 + 21.9829i 1.48344 + 0.934810i
554554 29.4619 1.25172
555555 −12.4766 −0.529602
556556 4.20866 0.178487
557557 −4.67142 −0.197935 −0.0989673 0.995091i 0.531554π-0.531554\pi
−0.0989673 + 0.995091i 0.531554π0.531554\pi
558558 −3.05843 5.29736i −0.129474 0.224255i
559559 30.6751 + 13.7819i 1.29742 + 0.582912i
560560 1.10167 0.580414i 0.0465542 0.0245270i
561561 13.0606 + 22.6217i 0.551420 + 0.955088i
562562 22.3775 38.7589i 0.943937 1.63495i
563563 7.19090 + 12.4550i 0.303060 + 0.524915i 0.976828 0.214028i 0.0686584π-0.0686584\pi
−0.673767 + 0.738943i 0.735325π0.735325\pi
564564 −15.5855 + 26.9948i −0.656267 + 1.13669i
565565 −4.66909 −0.196430
566566 −3.72524 + 6.45231i −0.156584 + 0.271211i
567567 −2.34076 + 1.23322i −0.0983027 + 0.0517905i
568568 10.6848 18.5067i 0.448326 0.776523i
569569 7.28779 12.6228i 0.305520 0.529176i −0.671857 0.740681i 0.734503π-0.734503\pi
0.977377 + 0.211505i 0.0678364π0.0678364\pi
570570 15.1278 0.633635
571571 −12.9575 + 22.4430i −0.542254 + 0.939211i 0.456520 + 0.889713i 0.349096π0.349096\pi
−0.998774 + 0.0494981i 0.984238π0.984238\pi
572572 48.3712 34.8945i 2.02250 1.45901i
573573 −15.9513 −0.666375
574574 2.87834 1.51645i 0.120140 0.0632952i
575575 −9.48940 16.4361i −0.395735 0.685433i
576576 −12.9921 −0.541336
577577 11.7875 20.4165i 0.490719 0.849950i −0.509224 0.860634i 0.670068π-0.670068\pi
0.999943 + 0.0106839i 0.00340085π0.00340085\pi
578578 −9.72786 16.8491i −0.404626 0.700832i
579579 3.95066 0.164184
580580 −4.07731 −0.169301
581581 −30.9797 + 16.3216i −1.28526 + 0.677133i
582582 6.14900 + 10.6504i 0.254884 + 0.441473i
583583 −1.95187 + 3.38074i −0.0808382 + 0.140016i
584584 −21.7371 + 37.6497i −0.899487 + 1.55796i
585585 −8.58881 + 6.19587i −0.355103 + 0.256168i
586586 21.6848 + 37.5592i 0.895791 + 1.55156i
587587 −23.7561 41.1468i −0.980521 1.69831i −0.660361 0.750948i 0.729597π-0.729597\pi
−0.320160 0.947364i 0.603737π-0.603737\pi
588588 −22.3325 1.73222i −0.920979 0.0714355i
589589 −3.02926 + 5.24683i −0.124818 + 0.216192i
590590 12.2160 + 21.1588i 0.502925 + 0.871092i
591591 −6.72353 11.6455i −0.276569 0.479032i
592592 −0.340316 0.589444i −0.0139869 0.0242260i
593593 −2.36887 4.10300i −0.0972779 0.168490i 0.813279 0.581874i 0.197680π-0.197680\pi
−0.910557 + 0.413384i 0.864347π0.864347\pi
594594 5.89416 10.2090i 0.241840 0.418879i
595595 1.51946 39.2379i 0.0622917 1.60860i
596596 −33.9078 58.7300i −1.38892 2.40568i
597597 −10.4145 18.0385i −0.426239 0.738268i
598598 −34.8870 + 25.1671i −1.42663 + 1.02916i
599599 1.07453 1.86114i 0.0439041 0.0760441i −0.843238 0.537540i 0.819354π-0.819354\pi
0.887142 + 0.461496i 0.152687π0.152687\pi
600600 −4.96282 + 8.59586i −0.202606 + 0.350925i
601601 0.736182 + 1.27511i 0.0300295 + 0.0520126i 0.880650 0.473768i 0.157107π-0.157107\pi
−0.850620 + 0.525781i 0.823773π0.823773\pi
602602 47.6074 + 30.0004i 1.94033 + 1.22273i
603603 −13.3602 −0.544071
604604 −50.5821 −2.05816
605605 −23.0929 39.9980i −0.938859 1.62615i
606606 3.59427 6.22546i 0.146007 0.252892i
607607 −12.9859 −0.527082 −0.263541 0.964648i 0.584890π-0.584890\pi
−0.263541 + 0.964648i 0.584890π0.584890\pi
608608 6.59277 + 11.4190i 0.267372 + 0.463102i
609609 −0.971014 0.611897i −0.0393475 0.0247953i
610610 46.5818 1.88604
611611 −28.4839 + 20.5480i −1.15234 + 0.831283i
612612 −8.08453 + 14.0028i −0.326798 + 0.566030i
613613 −40.1092 −1.61999 −0.809997 0.586433i 0.800532π-0.800532\pi
−0.809997 + 0.586433i 0.800532π0.800532\pi
614614 9.47093 16.4041i 0.382216 0.662017i
615615 0.791947 1.37169i 0.0319344 0.0553120i
616616 33.1109 17.4444i 1.33407 0.702853i
617617 8.82052 15.2776i 0.355101 0.615052i −0.632035 0.774940i 0.717780π-0.717780\pi
0.987135 + 0.159888i 0.0511133π0.0511133\pi
618618 30.0880 1.21032
619619 13.3825 23.1792i 0.537890 0.931652i −0.461128 0.887334i 0.652555π-0.652555\pi
0.999017 0.0443184i 0.0141116π-0.0141116\pi
620620 −12.6062 21.8345i −0.506276 0.876895i
621621 −2.61602 + 4.53108i −0.104977 + 0.181826i
622622 12.3789 + 21.4409i 0.496349 + 0.859701i
623623 −0.409805 + 10.5826i −0.0164185 + 0.423985i
624624 −0.526988 0.236769i −0.0210964 0.00947833i
625625 14.9895 + 25.9625i 0.599579 + 1.03850i
626626 −2.58558 −0.103340
627627 −11.6759 −0.466289
628628 17.6768 0.705383
629629 −21.4634 −0.855800
630630 −15.6782 + 8.26003i −0.624635 + 0.329087i
631631 10.1224 17.5324i 0.402964 0.697955i −0.591118 0.806585i 0.701313π-0.701313\pi
0.994082 + 0.108630i 0.0346465π0.0346465\pi
632632 −21.3221 36.9309i −0.848147 1.46903i
633633 7.17814 + 12.4329i 0.285306 + 0.494164i
634634 22.7447 0.903306
635635 1.02298 1.77185i 0.0405957 0.0703138i
636636 −2.41641 −0.0958170
637637 −22.1532 12.0928i −0.877741 0.479136i
638638 5.11379 0.202457
639639 3.90487 6.76343i 0.154474 0.267557i
640640 −52.7247 −2.08413
641641 7.38825 + 12.7968i 0.291819 + 0.505445i 0.974240 0.225515i 0.0724063π-0.0724063\pi
−0.682421 + 0.730959i 0.739073π0.739073\pi
642642 −6.68939 11.5864i −0.264009 0.457277i
643643 4.74073 8.21118i 0.186956 0.323817i −0.757278 0.653093i 0.773471π-0.773471\pi
0.944234 + 0.329276i 0.106804π0.106804\pi
644644 −39.1896 + 20.6469i −1.54429 + 0.813603i
645645 27.3956 1.07870
646646 26.0242 1.02391
647647 −49.9026 −1.96187 −0.980937 0.194327i 0.937748π-0.937748\pi
−0.980937 + 0.194327i 0.937748π0.937748\pi
648648 2.73629 0.107491
649649 −9.42848 16.3306i −0.370100 0.641033i
650650 −24.1874 + 17.4485i −0.948708 + 0.684388i
651651 0.274623 7.09175i 0.0107633 0.277948i
652652 5.03784 + 8.72579i 0.197297 + 0.341728i
653653 −20.7019 + 35.8568i −0.810128 + 1.40318i 0.102645 + 0.994718i 0.467269π0.467269\pi
−0.912774 + 0.408466i 0.866064π0.866064\pi
654654 6.25722 + 10.8378i 0.244677 + 0.423793i
655655 9.85355 17.0668i 0.385010 0.666857i
656656 0.0864055 0.00337357
657657 −7.94401 + 13.7594i −0.309925 + 0.536807i
658658 −51.9953 + 27.3936i −2.02699 + 1.06791i
659659 1.08993 1.88781i 0.0424576 0.0735387i −0.844016 0.536318i 0.819815π-0.819815\pi
0.886473 + 0.462780i 0.153148π0.153148\pi
660660 24.2943 42.0790i 0.945656 1.63792i
661661 32.8566 1.27797 0.638986 0.769218i 0.279354π-0.279354\pi
0.638986 + 0.769218i 0.279354π0.279354\pi
662662 1.88714 3.26862i 0.0733457 0.127038i
663663 −14.7752 + 10.6587i −0.573822 + 0.413949i
664664 36.2145 1.40539
665665 14.8495 + 9.35760i 0.575838 + 0.362872i
666666 4.84312 + 8.38853i 0.187667 + 0.325049i
667667 −2.26967 −0.0878819
668668 21.4765 37.1984i 0.830951 1.43925i
669669 0.596931 + 1.03392i 0.0230787 + 0.0399735i
670670 −89.4858 −3.45714
671671 −35.9525 −1.38793
672672 −13.0676 8.23472i −0.504093 0.317661i
673673 −5.61199 9.72024i −0.216326 0.374688i 0.737356 0.675505i 0.236074π-0.236074\pi
−0.953682 + 0.300817i 0.902741π0.902741\pi
674674 14.1473 24.5039i 0.544936 0.943856i
675675 −1.81371 + 3.14143i −0.0698097 + 0.120914i
676676 27.6257 + 31.1018i 1.06253 + 1.19622i
677677 10.0207 + 17.3564i 0.385127 + 0.667059i 0.991787 0.127902i 0.0408244π-0.0408244\pi
−0.606660 + 0.794961i 0.707491π0.707491\pi
678678 1.81243 + 3.13922i 0.0696060 + 0.120561i
679679 −0.552131 + 14.2580i −0.0211888 + 0.547172i
680680 −20.3055 + 35.1702i −0.778680 + 1.34871i
681681 7.94437 + 13.7600i 0.304429 + 0.527286i
682682 15.8107 + 27.3849i 0.605423 + 1.04862i
683683 −7.33004 12.6960i −0.280476 0.485799i 0.691026 0.722830i 0.257159π-0.257159\pi
−0.971502 + 0.237031i 0.923826π0.923826\pi
684684 −3.61368 6.25908i −0.138172 0.239322i
685685 −18.3568 + 31.7949i −0.701376 + 1.21482i
686686 −33.8817 25.2113i −1.29361 0.962573i
687687 −4.39323 7.60931i −0.167612 0.290313i
688688 0.747251 + 1.29428i 0.0284887 + 0.0493438i
689689 −2.48355 1.11583i −0.0946159 0.0425096i
690690 −17.5219 + 30.3488i −0.667047 + 1.15536i
691691 −14.4726 + 25.0673i −0.550565 + 0.953606i 0.447669 + 0.894199i 0.352254π0.352254\pi
−0.998234 + 0.0594069i 0.981079π0.981079\pi
692692 20.5578 + 35.6071i 0.781490 + 1.35358i
693693 12.1007 6.37520i 0.459666 0.242174i
694694 30.2036 1.14651
695695 3.86315 0.146538
696696 0.593502 + 1.02798i 0.0224966 + 0.0389653i
697697 1.36238 2.35971i 0.0516037 0.0893803i
698698 −79.8430 −3.02210
699699 2.86714 + 4.96604i 0.108445 + 0.187833i
700700 −27.1705 + 14.3147i −1.02695 + 0.541044i
701701 −37.6521 −1.42210 −0.711051 0.703141i 0.751780π-0.751780\pi
−0.711051 + 0.703141i 0.751780π0.751780\pi
702702 7.49971 + 3.36952i 0.283058 + 0.127174i
703703 4.79692 8.30851i 0.180919 0.313362i
704704 67.1630 2.53130
705705 −14.3060 + 24.7787i −0.538795 + 0.933220i
706706 −26.3473 + 45.6349i −0.991595 + 1.71749i
707707 7.37902 3.88761i 0.277517 0.146209i
708708 5.83623 10.1086i 0.219339 0.379906i
709709 22.4214 0.842053 0.421026 0.907048i 0.361670π-0.361670\pi
0.421026 + 0.907048i 0.361670π0.361670\pi
710710 26.1545 45.3009i 0.981560 1.70011i
711711 −7.79235 13.4967i −0.292236 0.506168i
712712 5.47649 9.48555i 0.205240 0.355486i
713713 −7.01731 12.1543i −0.262800 0.455184i
714714 −26.9711 + 14.2096i −1.00937 + 0.531782i
715715 44.4002 32.0298i 1.66047 1.19785i
716716 −29.8655 51.7286i −1.11613 1.93319i
717717 −11.5411 −0.431010
718718 29.3917 1.09689
719719 8.37217 0.312229 0.156115 0.987739i 0.450103π-0.450103\pi
0.156115 + 0.987739i 0.450103π0.450103\pi
720720 −0.470648 −0.0175400
721721 29.5344 + 18.6115i 1.09992 + 0.693129i
722722 15.8470 27.4478i 0.589763 1.02150i
723723 2.83030 + 4.90223i 0.105260 + 0.182316i
724724 −1.40547 2.43434i −0.0522338 0.0904717i
725725 −1.57358 −0.0584412
726726 −17.9282 + 31.0526i −0.665379 + 1.15247i
727727 20.0990 0.745432 0.372716 0.927945i 0.378427π-0.378427\pi
0.372716 + 0.927945i 0.378427π0.378427\pi
728728 14.4406 + 21.7442i 0.535204 + 0.805893i
729729 1.00000 0.0370370
730730 −53.2083 + 92.1596i −1.96933 + 3.41098i
731731 47.1284 1.74311
732732 −11.1273 19.2730i −0.411277 0.712352i
733733 5.77804 + 10.0079i 0.213417 + 0.369649i 0.952782 0.303656i 0.0982074π-0.0982074\pi
−0.739365 + 0.673305i 0.764874π0.764874\pi
734734 30.2064 52.3191i 1.11494 1.93113i
735735 −20.4992 1.59001i −0.756123 0.0586485i
736736 −30.5444 −1.12588
737737 69.0664 2.54409
738738 −1.22966 −0.0452644
739739 24.2650 0.892601 0.446300 0.894883i 0.352741π-0.352741\pi
0.446300 + 0.894883i 0.352741π0.352741\pi
740740 19.9622 + 34.5756i 0.733826 + 1.27102i
741741 −0.823835 8.10167i −0.0302643 0.297622i
742742 −3.85445 2.42893i −0.141501 0.0891689i
743743 0.777681 + 1.34698i 0.0285303 + 0.0494160i 0.879938 0.475088i 0.157584π-0.157584\pi
−0.851408 + 0.524504i 0.824251π0.824251\pi
744744 −3.66996 + 6.35655i −0.134547 + 0.233043i
745745 −31.1241 53.9086i −1.14030 1.97506i
746746 14.1050 24.4306i 0.516422 0.894468i
747747 13.2349 0.484240
748748 41.7933 72.3881i 1.52811 2.64677i
749749 0.600653 15.5110i 0.0219474 0.566761i
750750 4.59673 7.96177i 0.167849 0.290723i
751751 17.6793 30.6214i 0.645125 1.11739i −0.339148 0.940733i 0.610139π-0.610139\pi
0.984273 0.176656i 0.0565281π-0.0565281\pi
752752 −1.56086 −0.0569186
753753 12.1872 21.1088i 0.444126 0.769249i
754754 0.360823 + 3.54836i 0.0131404 + 0.129224i
755755 −46.4295 −1.68974
756756 7.16271 + 4.51367i 0.260505 + 0.164161i
757757 9.73684 + 16.8647i 0.353891 + 0.612958i 0.986928 0.161164i 0.0515249π-0.0515249\pi
−0.633036 + 0.774122i 0.718192π0.718192\pi
758758 63.9310 2.32208
759759 13.5236 23.4236i 0.490877 0.850223i
760760 −9.07629 15.7206i −0.329232 0.570246i
761761 17.6396 0.639434 0.319717 0.947513i 0.396412π-0.396412\pi
0.319717 + 0.947513i 0.396412π0.396412\pi
762762 −1.58839 −0.0575411
763763 −0.561848 + 14.5089i −0.0203403 + 0.525259i
764764 25.5216 + 44.2048i 0.923341 + 1.59927i
765765 −7.42083 + 12.8532i −0.268301 + 0.464710i
766766 29.9754 51.9190i 1.08306 1.87591i
767767 10.6663 7.69452i 0.385136 0.277833i
768768 7.47442 + 12.9461i 0.269710 + 0.467151i
769769 −2.32077 4.01969i −0.0836890 0.144954i 0.821143 0.570723i 0.193337π-0.193337\pi
−0.904832 + 0.425769i 0.860004π0.860004\pi
770770 81.0492 42.7006i 2.92081 1.53882i
771771 −2.30268 + 3.98836i −0.0829290 + 0.143637i
772772 −6.32095 10.9482i −0.227496 0.394034i
773773 −10.0222 17.3590i −0.360475 0.624360i 0.627564 0.778565i 0.284052π-0.284052\pi
−0.988039 + 0.154204i 0.950719π0.950719\pi
774774 −10.6343 18.4192i −0.382243 0.662064i
775775 −4.86516 8.42670i −0.174762 0.302696i
776776 7.37848 12.7799i 0.264872 0.458772i
777777 −0.434873 + 11.2300i −0.0156010 + 0.402874i
778778 −30.6032 53.0063i −1.09718 1.90037i
779779 0.608965 + 1.05476i 0.0218184 + 0.0377906i
780780 30.9121 + 13.8884i 1.10683 + 0.497283i
781781 −20.1864 + 34.9638i −0.722326 + 1.25110i
782782 −30.1427 + 52.2087i −1.07790 + 1.86698i
783783 0.216901 + 0.375683i 0.00775140 + 0.0134258i
784784 −0.484023 1.01183i −0.0172865 0.0361368i
785785 16.2257 0.579119
786786 −15.2997 −0.545721
787787 5.05832 + 8.76128i 0.180310 + 0.312306i 0.941986 0.335652i 0.108957π-0.108957\pi
−0.761676 + 0.647958i 0.775623π0.775623\pi
788788 −21.5150 + 37.2650i −0.766438 + 1.32751i
789789 22.9824 0.818193
790790 −52.1925 90.4001i −1.85693 3.21629i
791791 −0.162742 + 4.20258i −0.00578643 + 0.149426i
792792 −14.1453 −0.502633
793793 −2.53676 24.9468i −0.0900831 0.885887i
794794 −27.9618 + 48.4313i −0.992328 + 1.71876i
795795 −2.21804 −0.0786657
796796 −33.3260 + 57.7223i −1.18121 + 2.04591i
797797 −4.44188 + 7.69357i −0.157340 + 0.272520i −0.933908 0.357512i 0.883625π-0.883625\pi
0.776569 + 0.630032i 0.216958π0.216958\pi
798798 0.527282 13.6163i 0.0186656 0.482013i
799799 −24.6104 + 42.6265i −0.870655 + 1.50802i
800800 −21.1767 −0.748710
801801 2.00143 3.46658i 0.0707171 0.122486i
802802 −3.60944 6.25172i −0.127454 0.220756i
803803 41.0669 71.1300i 1.44922 2.51012i
804804 21.3760 + 37.0244i 0.753875 + 1.30575i
805805 −35.9723 + 18.9519i −1.26786 + 0.667967i
806806 −17.8863 + 12.9030i −0.630020 + 0.454489i
807807 −7.00246 12.1286i −0.246498 0.426948i
808808 −8.62587 −0.303457
809809 −41.7569 −1.46809 −0.734047 0.679099i 0.762371π-0.762371\pi
−0.734047 + 0.679099i 0.762371π0.762371\pi
810810 6.69792 0.235341
811811 −31.3690 −1.10151 −0.550757 0.834666i 0.685661π-0.685661\pi
−0.550757 + 0.834666i 0.685661π0.685661\pi
812812 −0.142115 + 3.66993i −0.00498726 + 0.128789i
813813 9.55299 16.5463i 0.335038 0.580303i
814814 −25.0367 43.3649i −0.877537 1.51994i
815815 4.62425 + 8.00944i 0.161981 + 0.280559i
816816 −0.809651 −0.0283434
817817 −10.5329 + 18.2435i −0.368499 + 0.638259i
818818 43.4826 1.52033
819819 5.27744 + 7.94661i 0.184409 + 0.277677i
820820 −5.06838 −0.176995
821821 −15.2754 + 26.4577i −0.533114 + 0.923381i 0.466138 + 0.884712i 0.345645π0.345645\pi
−0.999252 + 0.0386690i 0.987688π0.987688\pi
822822 28.5027 0.994144
823823 −1.67437 2.90010i −0.0583650 0.101091i 0.835367 0.549693i 0.185255π-0.185255\pi
−0.893732 + 0.448602i 0.851922π0.851922\pi
824824 −18.0520 31.2670i −0.628872 1.08924i
825825 9.37604 16.2398i 0.326432 0.565397i
826826 19.4705 10.2580i 0.677464 0.356920i
827827 −48.2646 −1.67833 −0.839163 0.543880i 0.816955π-0.816955\pi
−0.839163 + 0.543880i 0.816955π0.816955\pi
828828 16.7423 0.581834
829829 49.8292 1.73064 0.865320 0.501219i 0.167115π-0.167115\pi
0.865320 + 0.501219i 0.167115π0.167115\pi
830830 88.6463 3.07696
831831 −6.45998 11.1890i −0.224094 0.388142i
832832 4.73894 + 46.6032i 0.164293 + 1.61568i
833833 −35.2645 2.73528i −1.22184 0.0947719i
834834 −1.49958 2.59735i −0.0519263 0.0899390i
835835 19.7134 34.1446i 0.682210 1.18162i
836836 18.6811 + 32.3566i 0.646098 + 1.11907i
837837 −1.34122 + 2.32306i −0.0463593 + 0.0802967i
838838 −35.5976 −1.22970
839839 16.4441 28.4819i 0.567712 0.983305i −0.429080 0.903266i 0.641162π-0.641162\pi
0.996792 0.0800390i 0.0255045π-0.0255045\pi
840840 17.9902 + 11.3368i 0.620721 + 0.391156i
841841 14.4059 24.9518i 0.496755 0.860406i
842842 20.5830 35.6507i 0.709335 1.22860i
843843 −19.6264 −0.675971
844844 22.9697 39.7846i 0.790649 1.36944i
845845 25.3577 + 28.5485i 0.872333 + 0.982099i
846846 22.2130 0.763698
847847 −36.8065 + 19.3914i −1.26469 + 0.666297i
848848 −0.0604999 0.104789i −0.00207757 0.00359846i
849849 3.26727 0.112132
850850 −20.8982 + 36.1967i −0.716802 + 1.24154i
851851 11.1121 + 19.2468i 0.380919 + 0.659771i
852852 −24.9907 −0.856169
853853 −17.9823 −0.615701 −0.307850 0.951435i 0.599610π-0.599610\pi
−0.307850 + 0.951435i 0.599610π0.599610\pi
854854 1.62361 41.9276i 0.0555590 1.43473i
855855 −3.31701 5.74523i −0.113439 0.196483i
856856 −8.02691 + 13.9030i −0.274354 + 0.475195i
857857 23.5502 40.7901i 0.804459 1.39336i −0.112196 0.993686i 0.535789π-0.535789\pi
0.916656 0.399678i 0.130878π-0.130878\pi
858858 −38.7701 17.4189i −1.32359 0.594670i
859859 −13.8486 23.9866i −0.472510 0.818411i 0.526995 0.849868i 0.323319π-0.323319\pi
−0.999505 + 0.0314573i 0.989985π0.989985\pi
860860 −43.8322 75.9197i −1.49467 2.58884i
861861 −1.20704 0.760629i −0.0411357 0.0259222i
862862 19.9718 34.5922i 0.680242 1.17821i
863863 18.5569 + 32.1414i 0.631683 + 1.09411i 0.987208 + 0.159440i 0.0509689π0.0509689\pi
−0.355525 + 0.934667i 0.615698π0.615698\pi
864864 2.91898 + 5.05582i 0.0993057 + 0.172003i
865865 18.8701 + 32.6840i 0.641602 + 1.11129i
866866 −6.90854 11.9659i −0.234762 0.406619i
867867 −4.26597 + 7.38888i −0.144880 + 0.250939i
868868 −20.0923 + 10.5856i −0.681977 + 0.359298i
869869 40.2829 + 69.7720i 1.36650 + 2.36685i
870870 1.45278 + 2.51629i 0.0492540 + 0.0853104i
871871 4.87324 + 47.9239i 0.165123 + 1.62384i
872872 7.50833 13.0048i 0.254264 0.440399i
873873 2.69653 4.67053i 0.0912637 0.158073i
874874 −13.4734 23.3366i −0.455745 0.789373i
875875 9.43705 4.97188i 0.319031 0.168080i
876876 50.8408 1.71775
877877 28.2981 0.955559 0.477780 0.878480i 0.341442π-0.341442\pi
0.477780 + 0.878480i 0.341442π0.341442\pi
878878 −26.6599 46.1763i −0.899727 1.55837i
879879 9.50947 16.4709i 0.320746 0.555549i
880880 2.43303 0.0820176
881881 −9.74919 16.8861i −0.328458 0.568907i 0.653748 0.756713i 0.273196π-0.273196\pi
−0.982206 + 0.187806i 0.939862π0.939862\pi
882882 6.88826 + 14.3996i 0.231940 + 0.484861i
883883 36.8164 1.23897 0.619485 0.785009i 0.287342π-0.287342\pi
0.619485 + 0.785009i 0.287342π0.287342\pi
884884 53.1777 + 23.8920i 1.78856 + 0.803575i
885885 5.35710 9.27878i 0.180077 0.311903i
886886 −20.2819 −0.681383
887887 11.0920 19.2118i 0.372432 0.645070i −0.617507 0.786565i 0.711857π-0.711857\pi
0.989939 + 0.141495i 0.0451908π0.0451908\pi
888888 5.81149 10.0658i 0.195021 0.337786i
889889 −1.55916 0.982526i −0.0522926 0.0329529i
890890 13.4054 23.2189i 0.449351 0.778298i
891891 −5.16954 −0.173186
892892 1.91015 3.30847i 0.0639565 0.110776i
893893 −11.0005 19.0535i −0.368119 0.637601i
894894 −24.1633 + 41.8521i −0.808142 + 1.39974i
895895 −27.4137 47.4820i −0.916340 1.58715i
896896 −1.83772 + 47.4567i −0.0613941 + 1.58542i
897897 17.2074 + 7.73106i 0.574540 + 0.258133i
898898 −44.1635 76.4935i −1.47376 2.55262i
899899 −1.16365 −0.0388098
900900 11.6075 0.386918
901901 −3.81567 −0.127118
902902 6.35678 0.211658
903903 0.954876 24.6584i 0.0317763 0.820579i
904904 2.17482 3.76690i 0.0723335 0.125285i
905905 −1.29009 2.23450i −0.0428839 0.0742771i
906906 18.0229 + 31.2165i 0.598769 + 1.03710i
907907 −46.6084 −1.54761 −0.773803 0.633427i 0.781648π-0.781648\pi
−0.773803 + 0.633427i 0.781648π0.781648\pi
908908 25.4215 44.0314i 0.843644 1.46123i
909909 −3.15240 −0.104559
910910 35.3479 + 53.2257i 1.17177 + 1.76442i
911911 0.542513 0.0179743 0.00898714 0.999960i 0.497139π-0.497139\pi
0.00898714 + 0.999960i 0.497139π0.497139\pi
912912 0.180952 0.313418i 0.00599191 0.0103783i
913913 −68.4184 −2.26432
914914 −25.5401 44.2368i −0.844792 1.46322i
915915 −10.2138 17.6908i −0.337658 0.584840i
916916 −14.0581 + 24.3494i −0.464493 + 0.804526i
917917 −15.0182 9.46389i −0.495943 0.312525i
918918 11.5224 0.380294
919919 33.6621 1.11041 0.555205 0.831713i 0.312640π-0.312640\pi
0.555205 + 0.831713i 0.312640π0.312640\pi
920920 42.0507 1.38637
921921 −8.30660 −0.273712
922922 −3.20085 5.54403i −0.105414 0.182583i
923923 −25.6851 11.5400i −0.845436 0.379843i
924924 −37.0279 23.3336i −1.21813 0.767620i
925925 7.70412 + 13.3439i 0.253310 + 0.438746i
926926 −43.0449 + 74.5559i −1.41454 + 2.45006i
927927 −6.59727 11.4268i −0.216683 0.375306i
928928 −1.26626 + 2.19322i −0.0415669 + 0.0719961i
929929 −42.6784 −1.40023 −0.700116 0.714029i 0.746869π-0.746869\pi
−0.700116 + 0.714029i 0.746869π0.746869\pi
930930 −8.98338 + 15.5597i −0.294576 + 0.510221i
931931 8.94021 13.0396i 0.293004 0.427357i
932932 9.17471 15.8911i 0.300528 0.520529i
933933 5.42853 9.40250i 0.177722 0.307824i
934934 36.6856 1.20039
935935 38.3623 66.4454i 1.25458 2.17300i
936936 −0.998078 9.81520i −0.0326232 0.320820i
937937 −10.2859 −0.336026 −0.168013 0.985785i 0.553735π-0.553735\pi
−0.168013 + 0.985785i 0.553735π0.553735\pi
938938 −3.11904 + 80.5448i −0.101840 + 2.62988i
939939 0.566928 + 0.981949i 0.0185010 + 0.0320447i
940940 91.5568 2.98625
941941 5.84119 10.1172i 0.190417 0.329813i −0.754971 0.655758i 0.772349π-0.772349\pi
0.945389 + 0.325945i 0.105683π0.105683\pi
942942 −6.29842 10.9092i −0.205214 0.355440i
943943 −2.82135 −0.0918758
944944 0.584488 0.0190235
945945 6.57468 + 4.14312i 0.213874 + 0.134776i
946946 54.9746 + 95.2188i 1.78738 + 3.09583i
947947 −15.9404 + 27.6096i −0.517993 + 0.897190i 0.481789 + 0.876287i 0.339987π0.339987\pi
−0.999782 + 0.0209026i 0.993346π0.993346\pi
948948 −24.9351 + 43.1889i −0.809855 + 1.40271i
949949 52.2535 + 23.4768i 1.69622 + 0.762088i
950950 −9.34122 16.1795i −0.303069 0.524931i
951951 −4.98712 8.63795i −0.161718 0.280105i
952952 30.9484 + 19.5025i 1.00304 + 0.632080i
953953 3.72492 6.45175i 0.120662 0.208993i −0.799367 0.600843i 0.794832π-0.794832\pi
0.920029 + 0.391850i 0.128165π0.128165\pi
954954 0.860990 + 1.49128i 0.0278756 + 0.0482819i
955955 23.4264 + 40.5758i 0.758062 + 1.31300i
956956 18.4655 + 31.9831i 0.597215 + 1.03441i
957957 −1.12128 1.94211i −0.0362458 0.0627795i
958958 −9.74674 + 16.8818i −0.314903 + 0.545428i
959959 27.9782 + 17.6309i 0.903464 + 0.569330i
960960 19.0804 + 33.0483i 0.615819 + 1.06663i
961961 11.9023 + 20.6153i 0.383944 + 0.665010i
962962 28.3236 20.4323i 0.913188 0.658764i
963963 −2.93351 + 5.08098i −0.0945309 + 0.163732i
964964 9.05681 15.6869i 0.291700 0.505240i
965965 −5.80203 10.0494i −0.186774 0.323502i
966966 26.7058 + 16.8290i 0.859244 + 0.541464i
967967 −51.0981 −1.64320 −0.821602 0.570061i 0.806920π-0.806920\pi
−0.821602 + 0.570061i 0.806920π0.806920\pi
968968 43.0258 1.38290
969969 −5.70622 9.88347i −0.183310 0.317503i
970970 18.0611 31.2828i 0.579908 1.00443i
971971 5.01835 0.161046 0.0805232 0.996753i 0.474341π-0.474341\pi
0.0805232 + 0.996753i 0.474341π0.474341\pi
972972 −1.59997 2.77124i −0.0513192 0.0888874i
973973 0.134650 3.47716i 0.00431669 0.111473i
974974 −81.1256 −2.59943
975975 11.9301 + 5.36001i 0.382068 + 0.171658i
976976 0.557189 0.965080i 0.0178352 0.0308915i
977977 −27.6611 −0.884958 −0.442479 0.896779i 0.645901π-0.645901\pi
−0.442479 + 0.896779i 0.645901π0.645901\pi
978978 3.59005 6.21815i 0.114797 0.198835i
979979 −10.3465 + 17.9206i −0.330675 + 0.572746i
980980 28.3918 + 59.3519i 0.906943 + 1.89593i
981981 2.74399 4.75273i 0.0876088 0.151743i
982982 −71.5980 −2.28478
983983 2.23464 3.87050i 0.0712738 0.123450i −0.828186 0.560453i 0.810627π-0.810627\pi
0.899460 + 0.437003i 0.143960π0.143960\pi
984984 0.737763 + 1.27784i 0.0235190 + 0.0407362i
985985 −19.7487 + 34.2057i −0.629245 + 1.08988i
986986 2.49921 + 4.32875i 0.0795910 + 0.137856i
987987 21.8043 + 13.7403i 0.694038 + 0.437357i
988988 −21.1335 + 15.2455i −0.672347 + 0.485024i
989989 −24.3995 42.2613i −0.775860 1.34383i
990990 −34.6252 −1.10046
991991 10.4243 0.331139 0.165570 0.986198i 0.447054π-0.447054\pi
0.165570 + 0.986198i 0.447054π0.447054\pi
992992 −15.6600 −0.497204
993993 −1.65514 −0.0525242
994994 −39.8630 25.1202i −1.26438 0.796765i
995995 −30.5901 + 52.9836i −0.969771 + 1.67969i
996996 −21.1755 36.6770i −0.670971 1.16216i
997997 7.25600 + 12.5678i 0.229800 + 0.398025i 0.957749 0.287607i 0.0928596π-0.0928596\pi
−0.727949 + 0.685631i 0.759526π0.759526\pi
998998 −9.78748 −0.309817
999999 2.12386 3.67863i 0.0671960 0.116387i
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 273.2.j.c.172.2 yes 20
3.2 odd 2 819.2.n.f.172.9 20
7.2 even 3 273.2.l.c.16.9 yes 20
13.9 even 3 273.2.l.c.256.9 yes 20
21.2 odd 6 819.2.s.f.289.2 20
39.35 odd 6 819.2.s.f.802.2 20
91.9 even 3 inner 273.2.j.c.100.2 20
273.191 odd 6 819.2.n.f.100.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.j.c.100.2 20 91.9 even 3 inner
273.2.j.c.172.2 yes 20 1.1 even 1 trivial
273.2.l.c.16.9 yes 20 7.2 even 3
273.2.l.c.256.9 yes 20 13.9 even 3
819.2.n.f.100.9 20 273.191 odd 6
819.2.n.f.172.9 20 3.2 odd 2
819.2.s.f.289.2 20 21.2 odd 6
819.2.s.f.802.2 20 39.35 odd 6