Properties

Label 702.2.w.d.157.6
Level 702702
Weight 22
Character 702.157
Analytic conductor 5.6055.605
Analytic rank 00
Dimension 6666
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] = [702,2,Mod(79,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([10, 0])) 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("702.79"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 702=23313 702 = 2 \cdot 3^{3} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 702.w (of order 99, degree 66, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [66] 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: 5.605498221895.60549822189
Analytic rank: 00
Dimension: 6666
Relative dimension: 1111 over Q(ζ9)\Q(\zeta_{9})
Twist minimal: yes
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 157.6
Character χ\chi == 702.157
Dual form 702.2.w.d.313.6

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+(0.766044+0.642788i)q2+(0.1476531.72575i)q3+(0.1736480.984808i)q4+(0.9927990.361349i)q5+(1.22240+1.22709i)q6+(0.163744+0.928638i)q7+(0.500000+0.866025i)q8+(2.95640+0.509623i)q9+(0.528257+0.914969i)q10+(5.675162.06559i)q11+(1.725170.154263i)q12+(0.766044+0.642788i)q13+(0.7223530.606126i)q14+(0.7701871.65996i)q15+(0.9396930.342020i)q16+(2.246983.89189i)q17+(1.937152.29073i)q18+(2.236733.87413i)q19+(0.1834621.04046i)q20+(1.578420.419697i)q21+(5.675162.06559i)q22+(0.7066384.00754i)q23+(1.420710.990744i)q24+(2.97515+2.49644i)q251.00000q26+(1.31600+5.02674i)q27+0.942964q28+(3.81360+3.19999i)q29+(1.65700+0.776540i)q30+(0.895825+5.08048i)q31+(0.9396930.342020i)q32+(2.72673+10.0989i)q33+(0.780369+4.42569i)q34+(0.498128+0.862783i)q35+(0.0114923+2.99998i)q36+(0.109691+0.189991i)q37+(4.20368+1.53001i)q38+(0.9961791.41691i)q39+(0.809337+0.679115i)q40+(7.797116.54255i)q41+(0.939361+1.33609i)q42+(7.111372.58833i)q43+(3.01969+5.23026i)q44+(2.75096+1.57425i)q45+(2.03468+3.52417i)q46+(1.8782810.6523i)q47+(0.451491+1.67217i)q48+(5.742292.09002i)q49+(0.6744113.82477i)q50+(7.048183.30307i)q51+(0.7660440.642788i)q52+4.28078q53+(4.239243.00480i)q546.38070q55+(0.722353+0.606126i)q56+(6.35551+4.43206i)q57+(0.8644734.90267i)q58+(6.68285+2.43236i)q59+(1.76849+0.470236i)q60+(0.672600+3.81450i)q61+(2.579434.46770i)q62+(0.9573482.66198i)q63+(0.500000+0.866025i)q64+(0.992799+0.361349i)q65+(4.402649.48890i)q66+(0.975443+0.818494i)q67+(3.442582.88866i)q68+(7.020340.627752i)q69+(0.9361740.340739i)q70+(2.60038+4.50399i)q71+(1.919552.30550i)q72+(5.52605+9.57140i)q73+(0.03809540.216050i)q74+(4.74752+4.76574i)q75+(4.20368+1.53001i)q76+(0.9889135.60840i)q77+(0.147653+1.72575i)q78+(11.76639.87308i)q791.05651q80+(8.480573.01330i)q81+10.1784q82+(8.14121+6.83129i)q83+(0.1392311.62732i)q84+(0.8244714.67581i)q85+(7.111372.58833i)q86+(6.08546+6.10882i)q87+(1.048735.94763i)q88+(7.8369113.5739i)q89+(1.095452.97422i)q90+(0.471482+0.816631i)q91+(3.823951.39180i)q92+(8.89988+0.795819i)q93+(8.28598+6.95276i)q94+(3.620543.03799i)q95+(0.7289881.57117i)q96+(16.15665.88052i)q97+(3.05541+5.29212i)q98+(17.8307+3.21451i)q99+O(q100)q+(-0.766044 + 0.642788i) q^{2} +(-0.147653 - 1.72575i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.992799 - 0.361349i) q^{5} +(1.22240 + 1.22709i) q^{6} +(0.163744 + 0.928638i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.95640 + 0.509623i) q^{9} +(-0.528257 + 0.914969i) q^{10} +(-5.67516 - 2.06559i) q^{11} +(-1.72517 - 0.154263i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-0.722353 - 0.606126i) q^{14} +(-0.770187 - 1.65996i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.24698 - 3.89189i) q^{17} +(1.93715 - 2.29073i) q^{18} +(-2.23673 - 3.87413i) q^{19} +(-0.183462 - 1.04046i) q^{20} +(1.57842 - 0.419697i) q^{21} +(5.67516 - 2.06559i) q^{22} +(0.706638 - 4.00754i) q^{23} +(1.42071 - 0.990744i) q^{24} +(-2.97515 + 2.49644i) q^{25} -1.00000 q^{26} +(1.31600 + 5.02674i) q^{27} +0.942964 q^{28} +(-3.81360 + 3.19999i) q^{29} +(1.65700 + 0.776540i) q^{30} +(-0.895825 + 5.08048i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-2.72673 + 10.0989i) q^{33} +(0.780369 + 4.42569i) q^{34} +(0.498128 + 0.862783i) q^{35} +(-0.0114923 + 2.99998i) q^{36} +(-0.109691 + 0.189991i) q^{37} +(4.20368 + 1.53001i) q^{38} +(0.996179 - 1.41691i) q^{39} +(0.809337 + 0.679115i) q^{40} +(-7.79711 - 6.54255i) q^{41} +(-0.939361 + 1.33609i) q^{42} +(-7.11137 - 2.58833i) q^{43} +(-3.01969 + 5.23026i) q^{44} +(-2.75096 + 1.57425i) q^{45} +(2.03468 + 3.52417i) q^{46} +(-1.87828 - 10.6523i) q^{47} +(-0.451491 + 1.67217i) q^{48} +(5.74229 - 2.09002i) q^{49} +(0.674411 - 3.82477i) q^{50} +(-7.04818 - 3.30307i) q^{51} +(0.766044 - 0.642788i) q^{52} +4.28078 q^{53} +(-4.23924 - 3.00480i) q^{54} -6.38070 q^{55} +(-0.722353 + 0.606126i) q^{56} +(-6.35551 + 4.43206i) q^{57} +(0.864473 - 4.90267i) q^{58} +(-6.68285 + 2.43236i) q^{59} +(-1.76849 + 0.470236i) q^{60} +(0.672600 + 3.81450i) q^{61} +(-2.57943 - 4.46770i) q^{62} +(-0.957348 - 2.66198i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.992799 + 0.361349i) q^{65} +(-4.40264 - 9.48890i) q^{66} +(0.975443 + 0.818494i) q^{67} +(-3.44258 - 2.88866i) q^{68} +(-7.02034 - 0.627752i) q^{69} +(-0.936174 - 0.340739i) q^{70} +(-2.60038 + 4.50399i) q^{71} +(-1.91955 - 2.30550i) q^{72} +(5.52605 + 9.57140i) q^{73} +(-0.0380954 - 0.216050i) q^{74} +(4.74752 + 4.76574i) q^{75} +(-4.20368 + 1.53001i) q^{76} +(0.988913 - 5.60840i) q^{77} +(0.147653 + 1.72575i) q^{78} +(11.7663 - 9.87308i) q^{79} -1.05651 q^{80} +(8.48057 - 3.01330i) q^{81} +10.1784 q^{82} +(-8.14121 + 6.83129i) q^{83} +(-0.139231 - 1.62732i) q^{84} +(0.824471 - 4.67581i) q^{85} +(7.11137 - 2.58833i) q^{86} +(6.08546 + 6.10882i) q^{87} +(-1.04873 - 5.94763i) q^{88} +(-7.83691 - 13.5739i) q^{89} +(1.09545 - 2.97422i) q^{90} +(-0.471482 + 0.816631i) q^{91} +(-3.82395 - 1.39180i) q^{92} +(8.89988 + 0.795819i) q^{93} +(8.28598 + 6.95276i) q^{94} +(-3.62054 - 3.03799i) q^{95} +(-0.728988 - 1.57117i) q^{96} +(-16.1566 - 5.88052i) q^{97} +(-3.05541 + 5.29212i) q^{98} +(17.8307 + 3.21451i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 66q+3q5+9q63q7+33q86q99q103q11+3q1427q15+12q1712q1821q196q2018q21+3q223q2566q26+9q27+15q99+O(q100) 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/702Z)×\left(\mathbb{Z}/702\mathbb{Z}\right)^\times.

nn 379379 677677
χ(n)\chi(n) 11 e(79)e\left(\frac{7}{9}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.766044 + 0.642788i −0.541675 + 0.454519i
33 −0.147653 1.72575i −0.0852475 0.996360i
44 0.173648 0.984808i 0.0868241 0.492404i
55 0.992799 0.361349i 0.443993 0.161600i −0.110342 0.993894i 0.535195π-0.535195\pi
0.554335 + 0.832293i 0.312972π0.312972\pi
66 1.22240 + 1.22709i 0.499041 + 0.500957i
77 0.163744 + 0.928638i 0.0618894 + 0.350992i 0.999989 + 0.00462747i 0.00147298π0.00147298\pi
−0.938100 + 0.346365i 0.887416π0.887416\pi
88 0.500000 + 0.866025i 0.176777 + 0.306186i
99 −2.95640 + 0.509623i −0.985466 + 0.169874i
1010 −0.528257 + 0.914969i −0.167050 + 0.289338i
1111 −5.67516 2.06559i −1.71113 0.622799i −0.714113 0.700030i 0.753170π-0.753170\pi
−0.997013 + 0.0772314i 0.975392π0.975392\pi
1212 −1.72517 0.154263i −0.498013 0.0445318i
1313 0.766044 + 0.642788i 0.212463 + 0.178277i
1414 −0.722353 0.606126i −0.193057 0.161994i
1515 −0.770187 1.65996i −0.198861 0.428601i
1616 −0.939693 0.342020i −0.234923 0.0855050i
1717 2.24698 3.89189i 0.544973 0.943921i −0.453635 0.891187i 0.649873π-0.649873\pi
0.998609 0.0527339i 0.0167935π-0.0167935\pi
1818 1.93715 2.29073i 0.456591 0.539930i
1919 −2.23673 3.87413i −0.513141 0.888787i −0.999884 0.0152415i 0.995148π-0.995148\pi
0.486742 0.873546i 0.338185π-0.338185\pi
2020 −0.183462 1.04046i −0.0410233 0.232655i
2121 1.57842 0.419697i 0.344439 0.0915854i
2222 5.67516 2.06559i 1.20995 0.440385i
2323 0.706638 4.00754i 0.147344 0.835630i −0.818111 0.575061i 0.804978π-0.804978\pi
0.965455 0.260570i 0.0839104π-0.0839104\pi
2424 1.42071 0.990744i 0.290002 0.202235i
2525 −2.97515 + 2.49644i −0.595029 + 0.499289i
2626 −1.00000 −0.196116
2727 1.31600 + 5.02674i 0.253264 + 0.967397i
2828 0.942964 0.178203
2929 −3.81360 + 3.19999i −0.708168 + 0.594224i −0.924084 0.382188i 0.875171π-0.875171\pi
0.215916 + 0.976412i 0.430726π0.430726\pi
3030 1.65700 + 0.776540i 0.302526 + 0.141776i
3131 −0.895825 + 5.08048i −0.160895 + 0.912481i 0.792302 + 0.610130i 0.208883π0.208883\pi
−0.953197 + 0.302351i 0.902228π0.902228\pi
3232 0.939693 0.342020i 0.166116 0.0604612i
3333 −2.72673 + 10.0989i −0.474663 + 1.75799i
3434 0.780369 + 4.42569i 0.133832 + 0.759000i
3535 0.498128 + 0.862783i 0.0841990 + 0.145837i
3636 −0.0114923 + 2.99998i −0.00191538 + 0.499996i
3737 −0.109691 + 0.189991i −0.0180332 + 0.0312344i −0.874901 0.484302i 0.839074π-0.839074\pi
0.856868 + 0.515536i 0.172407π0.172407\pi
3838 4.20368 + 1.53001i 0.681927 + 0.248201i
3939 0.996179 1.41691i 0.159516 0.226887i
4040 0.809337 + 0.679115i 0.127967 + 0.107377i
4141 −7.79711 6.54255i −1.21770 1.02177i −0.998942 0.0459968i 0.985354π-0.985354\pi
−0.218762 0.975778i 0.570202π-0.570202\pi
4242 −0.939361 + 1.33609i −0.144947 + 0.206164i
4343 −7.11137 2.58833i −1.08447 0.394716i −0.262903 0.964822i 0.584680π-0.584680\pi
−0.821571 + 0.570106i 0.806902π0.806902\pi
4444 −3.01969 + 5.23026i −0.455236 + 0.788491i
4545 −2.75096 + 1.57425i −0.410088 + 0.234675i
4646 2.03468 + 3.52417i 0.299998 + 0.519611i
4747 −1.87828 10.6523i −0.273975 1.55379i −0.742198 0.670180i 0.766217π-0.766217\pi
0.468223 0.883610i 0.344894π-0.344894\pi
4848 −0.451491 + 1.67217i −0.0651672 + 0.241357i
4949 5.74229 2.09002i 0.820327 0.298575i
5050 0.674411 3.82477i 0.0953761 0.540905i
5151 −7.04818 3.30307i −0.986943 0.462522i
5252 0.766044 0.642788i 0.106231 0.0891386i
5353 4.28078 0.588010 0.294005 0.955804i 0.405012π-0.405012\pi
0.294005 + 0.955804i 0.405012π0.405012\pi
5454 −4.23924 3.00480i −0.576888 0.408901i
5555 −6.38070 −0.860373
5656 −0.722353 + 0.606126i −0.0965284 + 0.0809970i
5757 −6.35551 + 4.43206i −0.841808 + 0.587040i
5858 0.864473 4.90267i 0.113511 0.643752i
5959 −6.68285 + 2.43236i −0.870033 + 0.316666i −0.738180 0.674603i 0.764315π-0.764315\pi
−0.131852 + 0.991269i 0.542092π0.542092\pi
6060 −1.76849 + 0.470236i −0.228311 + 0.0607072i
6161 0.672600 + 3.81450i 0.0861175 + 0.488397i 0.997110 + 0.0759735i 0.0242064π0.0242064\pi
−0.910992 + 0.412423i 0.864682π0.864682\pi
6262 −2.57943 4.46770i −0.327587 0.567398i
6363 −0.957348 2.66198i −0.120615 0.335378i
6464 −0.500000 + 0.866025i −0.0625000 + 0.108253i
6565 0.992799 + 0.361349i 0.123142 + 0.0448199i
6666 −4.40264 9.48890i −0.541927 1.16800i
6767 0.975443 + 0.818494i 0.119169 + 0.0999949i 0.700425 0.713726i 0.252994π-0.252994\pi
−0.581256 + 0.813721i 0.697438π0.697438\pi
6868 −3.44258 2.88866i −0.417474 0.350302i
6969 −7.02034 0.627752i −0.845149 0.0755724i
7070 −0.936174 0.340739i −0.111894 0.0407262i
7171 −2.60038 + 4.50399i −0.308608 + 0.534525i −0.978058 0.208332i 0.933197π-0.933197\pi
0.669450 + 0.742857i 0.266530π0.266530\pi
7272 −1.91955 2.30550i −0.226221 0.271706i
7373 5.52605 + 9.57140i 0.646776 + 1.12025i 0.983888 + 0.178784i 0.0572163π0.0572163\pi
−0.337113 + 0.941464i 0.609450π0.609450\pi
7474 −0.0380954 0.216050i −0.00442850 0.0251153i
7575 4.74752 + 4.76574i 0.548196 + 0.550300i
7676 −4.20368 + 1.53001i −0.482195 + 0.175505i
7777 0.988913 5.60840i 0.112697 0.639137i
7878 0.147653 + 1.72575i 0.0167184 + 0.195402i
7979 11.7663 9.87308i 1.32381 1.11081i 0.338327 0.941028i 0.390139π-0.390139\pi
0.985482 0.169780i 0.0543056π-0.0543056\pi
8080 −1.05651 −0.118122
8181 8.48057 3.01330i 0.942285 0.334811i
8282 10.1784 1.12402
8383 −8.14121 + 6.83129i −0.893614 + 0.749831i −0.968932 0.247328i 0.920447π-0.920447\pi
0.0753178 + 0.997160i 0.476003π0.476003\pi
8484 −0.139231 1.62732i −0.0151914 0.177555i
8585 0.824471 4.67581i 0.0894264 0.507163i
8686 7.11137 2.58833i 0.766839 0.279106i
8787 6.08546 + 6.10882i 0.652430 + 0.654934i
8888 −1.04873 5.94763i −0.111795 0.634020i
8989 −7.83691 13.5739i −0.830710 1.43883i −0.897476 0.441064i 0.854601π-0.854601\pi
0.0667654 0.997769i 0.478732π-0.478732\pi
9090 1.09545 2.97422i 0.115471 0.313511i
9191 −0.471482 + 0.816631i −0.0494248 + 0.0856062i
9292 −3.82395 1.39180i −0.398675 0.145106i
9393 8.89988 + 0.795819i 0.922875 + 0.0825226i
9494 8.28598 + 6.95276i 0.854634 + 0.717123i
9595 −3.62054 3.03799i −0.371460 0.311692i
9696 −0.728988 1.57117i −0.0744021 0.160357i
9797 −16.1566 5.88052i −1.64045 0.597077i −0.653336 0.757068i 0.726631π-0.726631\pi
−0.987118 + 0.159991i 0.948853π0.948853\pi
9898 −3.05541 + 5.29212i −0.308643 + 0.534585i
9999 17.8307 + 3.21451i 1.79205 + 0.323071i
100100 1.94189 + 3.36345i 0.194189 + 0.336345i
101101 0.195410 + 1.10823i 0.0194440 + 0.110273i 0.992985 0.118240i 0.0377251π-0.0377251\pi
−0.973541 + 0.228512i 0.926614π0.926614\pi
102102 7.52239 2.00018i 0.744828 0.198048i
103103 6.92927 2.52205i 0.682761 0.248505i 0.0227287 0.999742i 0.492765π-0.492765\pi
0.660033 + 0.751237i 0.270542π0.270542\pi
104104 −0.173648 + 0.984808i −0.0170276 + 0.0965683i
105105 1.41539 0.987034i 0.138128 0.0963247i
106106 −3.27927 + 2.75163i −0.318510 + 0.267262i
107107 −7.73587 −0.747855 −0.373928 0.927458i 0.621989π-0.621989\pi
−0.373928 + 0.927458i 0.621989π0.621989\pi
108108 5.17890 0.423123i 0.498340 0.0407150i
109109 13.7473 1.31675 0.658377 0.752688i 0.271243π-0.271243\pi
0.658377 + 0.752688i 0.271243π0.271243\pi
110110 4.88790 4.10143i 0.466043 0.391056i
111111 0.344073 + 0.161247i 0.0326579 + 0.0153049i
112112 0.163744 0.928638i 0.0154724 0.0877481i
113113 4.68906 1.70668i 0.441110 0.160551i −0.111911 0.993718i 0.535697π-0.535697\pi
0.553021 + 0.833167i 0.313475π0.313475\pi
114114 2.01973 7.48039i 0.189165 0.700603i
115115 −0.746573 4.23403i −0.0696183 0.394825i
116116 2.48915 + 4.31134i 0.231112 + 0.400298i
117117 −2.59231 1.50994i −0.239659 0.139594i
118118 3.55587 6.15895i 0.327344 0.566977i
119119 3.98209 + 1.44936i 0.365037 + 0.132863i
120120 1.05248 1.49698i 0.0960777 0.136655i
121121 19.5143 + 16.3745i 1.77403 + 1.48859i
122122 −2.96716 2.48974i −0.268634 0.225410i
123123 −10.1395 + 14.4219i −0.914249 + 1.30038i
124124 4.84774 + 1.76443i 0.435339 + 0.158451i
125125 −4.69292 + 8.12838i −0.419748 + 0.727024i
126126 2.44446 + 1.42382i 0.217770 + 0.126844i
127127 −3.62693 6.28203i −0.321838 0.557440i 0.659029 0.752117i 0.270967π-0.270967\pi
−0.980867 + 0.194677i 0.937634π0.937634\pi
128128 −0.173648 0.984808i −0.0153485 0.0870455i
129129 −3.41678 + 12.6546i −0.300831 + 1.11417i
130130 −0.992799 + 0.361349i −0.0870742 + 0.0316924i
131131 1.40969 7.99478i 0.123166 0.698507i −0.859215 0.511615i 0.829047π-0.829047\pi
0.982380 0.186892i 0.0598414π-0.0598414\pi
132132 9.47196 + 4.43896i 0.824429 + 0.386362i
133133 3.23142 2.71148i 0.280199 0.235115i
134134 −1.27335 −0.110001
135135 3.12293 + 4.51501i 0.268779 + 0.388590i
136136 4.49396 0.385354
137137 6.55060 5.49661i 0.559656 0.469607i −0.318539 0.947910i 0.603192π-0.603192\pi
0.878195 + 0.478303i 0.158748π0.158748\pi
138138 5.78140 4.03170i 0.492145 0.343201i
139139 −0.147405 + 0.835973i −0.0125027 + 0.0709063i −0.990421 0.138082i 0.955906π-0.955906\pi
0.977918 + 0.208989i 0.0670172π0.0670172\pi
140140 0.936174 0.340739i 0.0791211 0.0287977i
141141 −18.1057 + 4.81427i −1.52478 + 0.405435i
142142 −0.903103 5.12175i −0.0757867 0.429808i
143143 −3.01969 5.23026i −0.252519 0.437376i
144144 2.95241 + 0.532258i 0.246034 + 0.0443549i
145145 −2.62983 + 4.55499i −0.218395 + 0.378271i
146146 −10.3856 3.78004i −0.859517 0.312839i
147147 −4.45471 9.60114i −0.367419 0.791888i
148148 0.168057 + 0.141017i 0.0138142 + 0.0115915i
149149 16.2858 + 13.6654i 1.33419 + 1.11952i 0.983079 + 0.183180i 0.0586391π0.0586391\pi
0.351107 + 0.936335i 0.385805π0.385805\pi
150150 −6.70017 0.599122i −0.547066 0.0489181i
151151 −11.2469 4.09354i −0.915261 0.333128i −0.158910 0.987293i 0.550798π-0.550798\pi
−0.756352 + 0.654165i 0.773020π0.773020\pi
152152 2.23673 3.87413i 0.181423 0.314234i
153153 −4.65958 + 12.6511i −0.376704 + 1.02278i
154154 2.84746 + 4.93195i 0.229455 + 0.397428i
155155 0.946453 + 5.36760i 0.0760209 + 0.431136i
156156 −1.22240 1.22709i −0.0978701 0.0982457i
157157 −0.593026 + 0.215844i −0.0473286 + 0.0172262i −0.365576 0.930781i 0.619128π-0.619128\pi
0.318247 + 0.948008i 0.396906π0.396906\pi
158158 −2.66720 + 15.1264i −0.212191 + 1.20339i
159159 −0.632069 7.38753i −0.0501264 0.585869i
160160 0.809337 0.679115i 0.0639837 0.0536887i
161161 3.83727 0.302419
162162 −4.55958 + 7.75952i −0.358235 + 0.609646i
163163 −4.24591 −0.332565 −0.166283 0.986078i 0.553176π-0.553176\pi
−0.166283 + 0.986078i 0.553176π0.553176\pi
164164 −7.79711 + 6.54255i −0.608852 + 0.510887i
165165 0.942129 + 11.0115i 0.0733446 + 0.857241i
166166 1.84546 10.4661i 0.143236 0.812330i
167167 12.7050 4.62424i 0.983143 0.357835i 0.200082 0.979779i 0.435879π-0.435879\pi
0.783061 + 0.621944i 0.213657π0.213657\pi
168168 1.15268 + 1.15710i 0.0889309 + 0.0892722i
169169 0.173648 + 0.984808i 0.0133576 + 0.0757544i
170170 2.37397 + 4.11184i 0.182075 + 0.315363i
171171 8.58701 + 10.3136i 0.656665 + 0.788700i
172172 −3.78388 + 6.55387i −0.288518 + 0.499728i
173173 14.3388 + 5.21891i 1.09016 + 0.396786i 0.823680 0.567054i 0.191917π-0.191917\pi
0.266480 + 0.963840i 0.414139π0.414139\pi
174174 −8.58841 0.767967i −0.651085 0.0582194i
175175 −2.80546 2.35406i −0.212073 0.177950i
176176 4.62644 + 3.88204i 0.348731 + 0.292620i
177177 5.18437 + 11.1738i 0.389681 + 0.839871i
178178 14.7286 + 5.36076i 1.10395 + 0.401806i
179179 8.06946 13.9767i 0.603139 1.04467i −0.389203 0.921152i 0.627250π-0.627250\pi
0.992343 0.123516i 0.0394171π-0.0394171\pi
180180 1.07263 + 2.98253i 0.0799492 + 0.222305i
181181 −1.26590 2.19260i −0.0940935 0.162975i 0.815136 0.579269i 0.196662π-0.196662\pi
−0.909230 + 0.416294i 0.863329π0.863329\pi
182182 −0.163744 0.928638i −0.0121375 0.0688353i
183183 6.48355 1.72396i 0.479278 0.127439i
184184 3.82395 1.39180i 0.281905 0.102605i
185185 −0.0402484 + 0.228260i −0.00295912 + 0.0167820i
186186 −7.32925 + 5.11110i −0.537407 + 0.374764i
187187 −20.7910 + 17.4458i −1.52039 + 1.27576i
188188 −10.8166 −0.788880
189189 −4.45254 + 2.04519i −0.323875 + 0.148766i
190190 4.72628 0.342880
191191 18.2839 15.3420i 1.32298 1.11011i 0.337312 0.941393i 0.390482π-0.390482\pi
0.985665 0.168717i 0.0539622π-0.0539622\pi
192192 1.56837 + 0.735002i 0.113187 + 0.0530442i
193193 3.07617 17.4459i 0.221428 1.25578i −0.647970 0.761666i 0.724382π-0.724382\pi
0.869397 0.494114i 0.164507π-0.164507\pi
194194 16.1566 5.88052i 1.15998 0.422197i
195195 0.477007 1.76667i 0.0341592 0.126514i
196196 −1.06113 6.01798i −0.0757952 0.429856i
197197 6.00516 + 10.4012i 0.427850 + 0.741058i 0.996682 0.0813957i 0.0259378π-0.0259378\pi
−0.568832 + 0.822454i 0.692604π0.692604\pi
198198 −15.7254 + 8.99890i −1.11755 + 0.639524i
199199 6.05953 10.4954i 0.429549 0.744000i −0.567285 0.823522i 0.692006π-0.692006\pi
0.996833 + 0.0795220i 0.0253394π0.0253394\pi
200200 −3.64956 1.32833i −0.258063 0.0939271i
201201 1.26848 1.80422i 0.0894720 0.127260i
202202 −0.862046 0.723343i −0.0606534 0.0508942i
203203 −3.59609 3.01748i −0.252396 0.211785i
204204 −4.47679 + 6.36753i −0.313438 + 0.445816i
205205 −10.1051 3.67796i −0.705772 0.256880i
206206 −3.68699 + 6.38605i −0.256885 + 0.444937i
207207 −0.0467663 + 12.2080i −0.00325048 + 0.848515i
208208 −0.500000 0.866025i −0.0346688 0.0600481i
209209 4.69145 + 26.6065i 0.324514 + 1.84041i
210210 −0.449801 + 1.66591i −0.0310392 + 0.114959i
211211 5.99532 2.18212i 0.412735 0.150223i −0.127303 0.991864i 0.540632π-0.540632\pi
0.540038 + 0.841641i 0.318410π0.318410\pi
212212 0.743349 4.21574i 0.0510534 0.289538i
213213 8.15670 + 3.82257i 0.558888 + 0.261918i
214214 5.92602 4.97252i 0.405095 0.339915i
215215 −7.99545 −0.545285
216216 −3.69529 + 3.65306i −0.251432 + 0.248559i
217217 −4.86461 −0.330231
218218 −10.5311 + 8.83661i −0.713253 + 0.598491i
219219 15.7019 10.9498i 1.06103 0.739920i
220220 −1.10800 + 6.28376i −0.0747011 + 0.423651i
221221 4.22295 1.53703i 0.284066 0.103392i
222222 −0.367222 + 0.0976435i −0.0246464 + 0.00655340i
223223 3.81831 + 21.6547i 0.255693 + 1.45011i 0.794288 + 0.607541i 0.207844π0.207844\pi
−0.538595 + 0.842565i 0.681045π0.681045\pi
224224 0.471482 + 0.816631i 0.0315022 + 0.0545635i
225225 7.52347 8.89668i 0.501564 0.593112i
226226 −2.49500 + 4.32146i −0.165965 + 0.287459i
227227 6.71029 + 2.44235i 0.445378 + 0.162104i 0.554966 0.831873i 0.312731π-0.312731\pi
−0.109589 + 0.993977i 0.534953π0.534953\pi
228228 3.26110 + 7.02857i 0.215972 + 0.465479i
229229 5.33821 + 4.47929i 0.352759 + 0.296000i 0.801897 0.597463i 0.203824π-0.203824\pi
−0.449138 + 0.893462i 0.648269π0.648269\pi
230230 3.29349 + 2.76357i 0.217166 + 0.182224i
231231 −9.82470 0.878515i −0.646417 0.0578020i
232232 −4.67807 1.70268i −0.307131 0.111786i
233233 −5.73131 + 9.92692i −0.375471 + 0.650334i −0.990397 0.138250i 0.955852π-0.955852\pi
0.614927 + 0.788584i 0.289186π0.289186\pi
234234 2.95640 0.509623i 0.193266 0.0333151i
235235 −5.71394 9.89683i −0.372736 0.645598i
236236 1.23494 + 7.00370i 0.0803878 + 0.455902i
237237 −18.7757 18.8478i −1.21962 1.22430i
238238 −3.98209 + 1.44936i −0.258120 + 0.0939481i
239239 4.17722 23.6902i 0.270202 1.53239i −0.483600 0.875289i 0.660671π-0.660671\pi
0.753802 0.657102i 0.228218π-0.228218\pi
240240 0.155998 + 1.82328i 0.0100696 + 0.117692i
241241 17.3282 14.5401i 1.11621 0.936610i 0.117802 0.993037i 0.462415π-0.462415\pi
0.998407 + 0.0564267i 0.0179707π0.0179707\pi
242242 −25.4741 −1.63754
243243 −6.45236 14.1904i −0.413919 0.910314i
244244 3.87335 0.247966
245245 4.94571 4.14995i 0.315970 0.265130i
246246 −1.50287 17.5653i −0.0958196 1.11993i
247247 0.776809 4.40550i 0.0494272 0.280315i
248248 −4.84774 + 1.76443i −0.307831 + 0.112042i
249249 12.9911 + 13.0410i 0.823280 + 0.826440i
250250 −1.62983 9.24325i −0.103080 0.584594i
251251 10.0545 + 17.4149i 0.634634 + 1.09922i 0.986593 + 0.163203i 0.0521824π0.0521824\pi
−0.351959 + 0.936016i 0.614484π0.614484\pi
252252 −2.78778 + 0.480556i −0.175613 + 0.0302722i
253253 −12.2882 + 21.2838i −0.772554 + 1.33810i
254254 6.81640 + 2.48097i 0.427699 + 0.155670i
255255 −8.19099 0.732431i −0.512940 0.0458666i
256256 0.766044 + 0.642788i 0.0478778 + 0.0401742i
257257 −16.3206 13.6946i −1.01805 0.854247i −0.0286701 0.999589i 0.509127π-0.509127\pi
−0.989381 + 0.145342i 0.953572π0.953572\pi
258258 −5.51681 11.8902i −0.343461 0.740254i
259259 −0.194394 0.0707538i −0.0120791 0.00439643i
260260 0.528257 0.914969i 0.0327611 0.0567439i
261261 9.64373 11.4039i 0.596932 0.705886i
262262 4.05905 + 7.03049i 0.250769 + 0.434345i
263263 −0.281406 1.59593i −0.0173522 0.0984095i 0.974902 0.222636i 0.0714661π-0.0714661\pi
−0.992254 + 0.124227i 0.960355π0.960355\pi
264264 −10.1093 + 2.68802i −0.622181 + 0.165436i
265265 4.24995 1.54686i 0.261072 0.0950226i
266266 −0.732503 + 4.15423i −0.0449126 + 0.254712i
267267 −22.2680 + 15.5287i −1.36278 + 0.950343i
268268 0.975443 0.818494i 0.0595846 0.0499975i
269269 −14.0341 −0.855674 −0.427837 0.903856i 0.640724π-0.640724\pi
−0.427837 + 0.903856i 0.640724π0.640724\pi
270270 −5.29450 1.45131i −0.322213 0.0883242i
271271 −7.49080 −0.455034 −0.227517 0.973774i 0.573061π-0.573061\pi
−0.227517 + 0.973774i 0.573061π0.573061\pi
272272 −3.44258 + 2.88866i −0.208737 + 0.175151i
273273 1.47891 + 0.693080i 0.0895079 + 0.0419471i
274274 −1.48490 + 8.42129i −0.0897061 + 0.508749i
275275 22.0411 8.02229i 1.32913 0.483762i
276276 −1.83728 + 6.80467i −0.110591 + 0.409593i
277277 −0.642030 3.64113i −0.0385758 0.218774i 0.959426 0.281961i 0.0909848π-0.0909848\pi
−0.998002 + 0.0631865i 0.979874π0.979874\pi
278278 −0.424435 0.735143i −0.0254559 0.0440909i
279279 0.0592869 15.4764i 0.00354942 0.926550i
280280 −0.498128 + 0.862783i −0.0297688 + 0.0515611i
281281 6.40992 + 2.33302i 0.382384 + 0.139176i 0.526058 0.850449i 0.323670π-0.323670\pi
−0.143674 + 0.989625i 0.545892π0.545892\pi
282282 10.7753 15.3261i 0.641657 0.912655i
283283 8.78620 + 7.37250i 0.522285 + 0.438250i 0.865428 0.501034i 0.167047π-0.167047\pi
−0.343142 + 0.939283i 0.611491π0.611491\pi
284284 3.98401 + 3.34299i 0.236408 + 0.198370i
285285 −4.70822 + 6.69670i −0.278891 + 0.396678i
286286 5.67516 + 2.06559i 0.335579 + 0.122141i
287287 4.79894 8.31200i 0.283272 0.490642i
288288 −2.60380 + 1.49004i −0.153431 + 0.0878012i
289289 −1.59786 2.76757i −0.0939916 0.162798i
290290 −0.913329 5.17974i −0.0536325 0.304165i
291291 −7.76272 + 28.7505i −0.455059 + 1.68538i
292292 10.3856 3.78004i 0.607770 0.221210i
293293 −0.742844 + 4.21288i −0.0433974 + 0.246119i −0.998788 0.0492277i 0.984324π-0.984324\pi
0.955390 + 0.295347i 0.0954351π0.0954351\pi
294294 9.58400 + 4.49146i 0.558950 + 0.261947i
295295 −5.75579 + 4.82969i −0.335115 + 0.281195i
296296 −0.219383 −0.0127514
297297 2.91467 31.2459i 0.169127 1.81307i
298298 −21.2596 −1.23154
299299 3.11731 2.61574i 0.180279 0.151272i
300300 5.51773 3.84783i 0.318566 0.222155i
301301 1.23918 7.02771i 0.0714249 0.405071i
302302 11.2469 4.09354i 0.647187 0.235557i
303303 1.88366 0.500861i 0.108214 0.0287737i
304304 0.776809 + 4.40550i 0.0445530 + 0.252673i
305305 2.04612 + 3.54399i 0.117161 + 0.202928i
306306 −4.56251 12.6864i −0.260822 0.725234i
307307 12.1554 21.0537i 0.693744 1.20160i −0.276858 0.960911i 0.589293π-0.589293\pi
0.970602 0.240689i 0.0773734π-0.0773734\pi
308308 −5.35148 1.94778i −0.304929 0.110985i
309309 −5.37554 11.5858i −0.305804 0.659092i
310310 −4.17525 3.50345i −0.237138 0.198983i
311311 −19.2224 16.1295i −1.09000 0.914619i −0.0932884 0.995639i 0.529738π-0.529738\pi
−0.996712 + 0.0810198i 0.974182π0.974182\pi
312312 1.72517 + 0.154263i 0.0976684 + 0.00873341i
313313 −28.6829 10.4397i −1.62125 0.590088i −0.637632 0.770341i 0.720086π-0.720086\pi
−0.983620 + 0.180253i 0.942308π0.942308\pi
314314 0.315542 0.546536i 0.0178071 0.0308428i
315315 −1.91236 2.29687i −0.107749 0.129414i
316316 −7.67989 13.3020i −0.432028 0.748294i
317317 4.41663 + 25.0480i 0.248063 + 1.40683i 0.813271 + 0.581886i 0.197685π0.197685\pi
−0.565208 + 0.824949i 0.691204π0.691204\pi
318318 5.23281 + 5.25289i 0.293441 + 0.294568i
319319 28.2527 10.2831i 1.58185 0.575745i
320320 −0.183462 + 1.04046i −0.0102558 + 0.0581637i
321321 1.14222 + 13.3502i 0.0637528 + 0.745133i
322322 −2.93952 + 2.46655i −0.163813 + 0.137455i
323323 −20.1036 −1.11859
324324 −1.49488 8.87498i −0.0830490 0.493055i
325325 −3.88378 −0.215433
326326 3.25256 2.72922i 0.180142 0.151157i
327327 −2.02983 23.7244i −0.112250 1.31196i
328328 1.76746 10.0238i 0.0975917 0.553470i
329329 9.58453 3.48848i 0.528412 0.192326i
330330 −7.79974 7.82968i −0.429362 0.431010i
331331 1.58117 + 8.96727i 0.0869090 + 0.492885i 0.996928 + 0.0783196i 0.0249555π0.0249555\pi
−0.910019 + 0.414566i 0.863933π0.863933\pi
332332 5.31380 + 9.20377i 0.291633 + 0.505122i
333333 0.227468 0.617591i 0.0124651 0.0338438i
334334 −6.76019 + 11.7090i −0.369901 + 0.640688i
335335 1.26418 + 0.460124i 0.0690696 + 0.0251393i
336336 −1.62677 0.145464i −0.0887476 0.00793573i
337337 −5.63851 4.73127i −0.307149 0.257729i 0.476163 0.879357i 0.342027π-0.342027\pi
−0.783313 + 0.621628i 0.786472π0.786472\pi
338338 −0.766044 0.642788i −0.0416673 0.0349630i
339339 −3.63765 7.84013i −0.197570 0.425818i
340340 −4.46160 1.62389i −0.241964 0.0880679i
341341 15.5781 26.9821i 0.843604 1.46116i
342342 −13.2075 2.38104i −0.714179 0.128752i
343343 6.18152 + 10.7067i 0.333771 + 0.578107i
344344 −1.31413 7.45279i −0.0708530 0.401827i
345345 −7.19662 + 1.91356i −0.387453 + 0.103023i
346346 −14.3388 + 5.21891i −0.770860 + 0.280570i
347347 1.10453 6.26410i 0.0592942 0.336274i −0.940701 0.339236i 0.889832π-0.889832\pi
0.999996 + 0.00296144i 0.000942658π0.000942658\pi
348348 7.07274 4.93222i 0.379139 0.264395i
349349 −1.10743 + 0.929245i −0.0592794 + 0.0497413i −0.671946 0.740600i 0.734541π-0.734541\pi
0.612667 + 0.790341i 0.290097π0.290097\pi
350350 3.66226 0.195756
351351 −2.22301 + 4.69662i −0.118656 + 0.250687i
352352 −6.03938 −0.321900
353353 −17.9550 + 15.0661i −0.955650 + 0.801886i −0.980240 0.197812i 0.936616π-0.936616\pi
0.0245898 + 0.999698i 0.492172π0.492172\pi
354354 −11.1538 5.22714i −0.592818 0.277819i
355355 −0.954141 + 5.41120i −0.0506406 + 0.287197i
356356 −14.7286 + 5.36076i −0.780612 + 0.284120i
357357 1.91326 7.08607i 0.101261 0.375035i
358358 2.80249 + 15.8937i 0.148116 + 0.840010i
359359 9.49801 + 16.4510i 0.501286 + 0.868253i 0.999999 + 0.00148539i 0.000472815π0.000472815\pi
−0.498713 + 0.866767i 0.666194π0.666194\pi
360360 −2.73881 1.59528i −0.144348 0.0840784i
361361 −0.505936 + 0.876308i −0.0266282 + 0.0461214i
362362 2.37911 + 0.865926i 0.125043 + 0.0455121i
363363 25.3768 36.0945i 1.33194 1.89447i
364364 0.722353 + 0.606126i 0.0378616 + 0.0317696i
365365 8.94488 + 7.50565i 0.468196 + 0.392863i
366366 −3.85855 + 5.48817i −0.201689 + 0.286871i
367367 −20.5833 7.49170i −1.07444 0.391063i −0.256603 0.966517i 0.582603π-0.582603\pi
−0.817835 + 0.575453i 0.804826π0.804826\pi
368368 −2.03468 + 3.52417i −0.106065 + 0.183710i
369369 26.3856 + 15.3688i 1.37358 + 0.800068i
370370 −0.115891 0.200728i −0.00602487 0.0104354i
371371 0.700952 + 3.97529i 0.0363916 + 0.206387i
372372 2.32918 8.62648i 0.120762 0.447262i
373373 −22.2096 + 8.08362i −1.14997 + 0.418554i −0.845503 0.533970i 0.820700π-0.820700\pi
−0.304464 + 0.952524i 0.598477π0.598477\pi
374374 4.71295 26.7284i 0.243701 1.38209i
375375 14.7204 + 6.89861i 0.760160 + 0.356243i
376376 8.28598 6.95276i 0.427317 0.358561i
377377 −4.97830 −0.256396
378378 2.09622 4.42874i 0.107818 0.227790i
379379 −20.2681 −1.04110 −0.520551 0.853831i 0.674273π-0.674273\pi
−0.520551 + 0.853831i 0.674273π0.674273\pi
380380 −3.62054 + 3.03799i −0.185730 + 0.155846i
381381 −10.3057 + 7.18672i −0.527975 + 0.368187i
382382 −4.14462 + 23.5053i −0.212057 + 1.20264i
383383 −23.1248 + 8.41674i −1.18162 + 0.430076i −0.856775 0.515691i 0.827535π-0.827535\pi
−0.324848 + 0.945766i 0.605313π0.605313\pi
384384 −1.67389 + 0.445082i −0.0854202 + 0.0227130i
385385 −1.04480 5.92536i −0.0532480 0.301984i
386386 8.85749 + 15.3416i 0.450834 + 0.780868i
387387 22.3431 + 4.02800i 1.13576 + 0.204755i
388388 −8.59675 + 14.8900i −0.436434 + 0.755926i
389389 −0.149819 0.0545297i −0.00759613 0.00276477i 0.338219 0.941067i 0.390175π-0.390175\pi
−0.345815 + 0.938303i 0.612398π0.612398\pi
390390 0.770187 + 1.65996i 0.0389999 + 0.0840556i
391391 −14.0091 11.7550i −0.708471 0.594477i
392392 4.68116 + 3.92796i 0.236434 + 0.198392i
393393 −14.0051 1.25232i −0.706464 0.0631713i
394394 −11.2860 4.10777i −0.568581 0.206947i
395395 8.11392 14.0537i 0.408256 0.707119i
396396 6.26195 17.0016i 0.314675 0.854364i
397397 −8.17891 14.1663i −0.410488 0.710986i 0.584455 0.811426i 0.301308π-0.301308\pi
−0.994943 + 0.100440i 0.967975π0.967975\pi
398398 2.10445 + 11.9349i 0.105487 + 0.598244i
399399 −5.15646 5.17625i −0.258146 0.259136i
400400 3.64956 1.32833i 0.182478 0.0664165i
401401 5.35715 30.3819i 0.267524 1.51720i −0.494228 0.869332i 0.664549π-0.664549\pi
0.761752 0.647869i 0.224340π-0.224340\pi
402402 0.188014 + 2.19748i 0.00937728 + 0.109600i
403403 −3.95191 + 3.31605i −0.196859 + 0.165184i
404404 1.12532 0.0559868
405405 7.33065 6.05605i 0.364263 0.300927i
406406 4.69436 0.232977
407407 1.01496 0.851653i 0.0503097 0.0422149i
408408 −0.663547 7.75544i −0.0328505 0.383951i
409409 5.10149 28.9320i 0.252252 1.43059i −0.550776 0.834653i 0.685668π-0.685668\pi
0.803029 0.595940i 0.203221π-0.203221\pi
410410 10.1051 3.67796i 0.499056 0.181641i
411411 −10.4530 10.4931i −0.515607 0.517586i
412412 −1.28048 7.26195i −0.0630846 0.357771i
413413 −3.35306 5.80767i −0.164993 0.285777i
414414 −7.81133 9.38194i −0.383906 0.461097i
415415 −5.61411 + 9.72392i −0.275586 + 0.477328i
416416 0.939693 + 0.342020i 0.0460722 + 0.0167689i
417417 1.46444 + 0.130949i 0.0717141 + 0.00641260i
418418 −20.6962 17.3662i −1.01228 0.849407i
419419 8.94566 + 7.50630i 0.437024 + 0.366707i 0.834594 0.550865i 0.185702π-0.185702\pi
−0.397570 + 0.917572i 0.630147π0.630147\pi
420420 −0.726259 1.56529i −0.0354378 0.0763782i
421421 −23.4373 8.53048i −1.14226 0.415750i −0.299534 0.954086i 0.596831π-0.596831\pi
−0.842731 + 0.538335i 0.819053π0.819053\pi
422422 −3.19005 + 5.52532i −0.155289 + 0.268968i
423423 10.9816 + 30.5351i 0.533942 + 1.48467i
424424 2.14039 + 3.70726i 0.103946 + 0.180041i
425425 3.03078 + 17.1884i 0.147014 + 0.833760i
426426 −8.70549 + 2.31477i −0.421783 + 0.112151i
427427 −3.43216 + 1.24920i −0.166094 + 0.0604532i
428428 −1.34332 + 7.61835i −0.0649318 + 0.368247i
429429 −8.58023 + 5.98348i −0.414257 + 0.288885i
430430 6.12487 5.13938i 0.295367 0.247843i
431431 −6.19927 −0.298608 −0.149304 0.988791i 0.547703π-0.547703\pi
−0.149304 + 0.988791i 0.547703π0.547703\pi
432432 0.482611 5.17369i 0.0232196 0.248919i
433433 11.1272 0.534740 0.267370 0.963594i 0.413845π-0.413845\pi
0.267370 + 0.963594i 0.413845π0.413845\pi
434434 3.72651 3.12691i 0.178878 0.150097i
435435 8.24906 + 3.86585i 0.395512 + 0.185353i
436436 2.38720 13.5385i 0.114326 0.648375i
437437 −17.1063 + 6.22619i −0.818306 + 0.297839i
438438 −4.98993 + 18.4810i −0.238428 + 0.883057i
439439 −1.50998 8.56355i −0.0720676 0.408716i −0.999405 0.0344896i 0.989019π-0.989019\pi
0.927337 0.374226i 0.122092π-0.122092\pi
440440 −3.19035 5.52585i −0.152094 0.263434i
441441 −15.9114 + 9.10534i −0.757684 + 0.433588i
442442 −2.24698 + 3.89189i −0.106878 + 0.185118i
443443 8.45904 + 3.07884i 0.401901 + 0.146280i 0.535059 0.844815i 0.320289π-0.320289\pi
−0.133158 + 0.991095i 0.542512π0.542512\pi
444444 0.218545 0.310845i 0.0103717 0.0147521i
445445 −12.6854 10.6443i −0.601346 0.504589i
446446 −16.8444 14.1341i −0.797604 0.669269i
447447 21.1784 30.1229i 1.00170 1.42477i
448448 −0.886097 0.322513i −0.0418641 0.0152373i
449449 1.48396 2.57029i 0.0700324 0.121300i −0.828883 0.559422i 0.811023π-0.811023\pi
0.898915 + 0.438123i 0.144356π0.144356\pi
450450 −0.0446334 + 11.6512i −0.00210404 + 0.549245i
451451 30.7356 + 53.2357i 1.44728 + 2.50677i
452452 −0.866504 4.91419i −0.0407569 0.231144i
453453 −5.40377 + 20.0137i −0.253891 + 0.940328i
454454 −6.71029 + 2.44235i −0.314930 + 0.114625i
455455 −0.172998 + 0.981120i −0.00811027 + 0.0459956i
456456 −7.01603 3.28800i −0.328556 0.153975i
457457 9.94731 8.34678i 0.465315 0.390446i −0.379767 0.925082i 0.623996π-0.623996\pi
0.845082 + 0.534636i 0.179551π0.179551\pi
458458 −6.96854 −0.325618
459459 22.5205 + 6.17327i 1.05117 + 0.288144i
460460 −4.29934 −0.200458
461461 −7.84898 + 6.58608i −0.365563 + 0.306744i −0.807004 0.590547i 0.798912π-0.798912\pi
0.441440 + 0.897291i 0.354468π0.354468\pi
462462 8.09085 5.64221i 0.376420 0.262499i
463463 0.0948232 0.537769i 0.00440681 0.0249923i −0.982525 0.186130i 0.940405π-0.940405\pi
0.986932 + 0.161138i 0.0515164π0.0515164\pi
464464 4.67807 1.70268i 0.217174 0.0790449i
465465 9.12337 2.42588i 0.423086 0.112497i
466466 −1.99046 11.2885i −0.0922065 0.522929i
467467 −18.2591 31.6258i −0.844932 1.46347i −0.885680 0.464296i 0.846307π-0.846307\pi
0.0407478 0.999169i 0.487026π-0.487026\pi
468468 −1.93715 + 2.29073i −0.0895449 + 0.105889i
469469 −0.600362 + 1.03986i −0.0277221 + 0.0480161i
470470 10.7387 + 3.90856i 0.495339 + 0.180289i
471471 0.460054 + 0.991542i 0.0211981 + 0.0456878i
472472 −5.44791 4.57134i −0.250760 0.210413i
473473 35.0118 + 29.3784i 1.60984 + 1.35082i
474474 26.4982 + 2.36944i 1.21710 + 0.108832i
475475 16.3262 + 5.94223i 0.749095 + 0.272648i
476476 2.11882 3.66991i 0.0971161 0.168210i
477477 −12.6557 + 2.18158i −0.579464 + 0.0998878i
478478 12.0278 + 20.8328i 0.550140 + 0.952870i
479479 0.0727771 + 0.412739i 0.00332527 + 0.0188585i 0.986425 0.164211i 0.0525078π-0.0525078\pi
−0.983100 + 0.183069i 0.941397π0.941397\pi
480480 −1.29148 1.29644i −0.0589477 0.0591740i
481481 −0.206152 + 0.0750334i −0.00939974 + 0.00342123i
482482 −3.92799 + 22.2767i −0.178915 + 1.01468i
483483 −0.566584 6.62215i −0.0257805 0.301318i
484484 19.5143 16.3745i 0.887015 0.744294i
485485 −18.1652 −0.824839
486486 14.0642 + 6.72296i 0.637965 + 0.304960i
487487 −42.0986 −1.90767 −0.953834 0.300334i 0.902902π-0.902902\pi
−0.953834 + 0.300334i 0.902902π0.902902\pi
488488 −2.96716 + 2.48974i −0.134317 + 0.112705i
489489 0.626921 + 7.32736i 0.0283504 + 0.331355i
490490 −1.12110 + 6.35809i −0.0506462 + 0.287229i
491491 −24.4011 + 8.88127i −1.10121 + 0.400806i −0.827761 0.561081i 0.810385π-0.810385\pi
−0.273445 + 0.961888i 0.588163π0.588163\pi
492492 12.4420 + 12.4898i 0.560931 + 0.563084i
493493 3.88491 + 22.0324i 0.174968 + 0.992291i
494494 2.23673 + 3.87413i 0.100635 + 0.174305i
495495 18.8639 3.25175i 0.847868 0.146155i
496496 2.57943 4.46770i 0.115820 0.200606i
497497 −4.60838 1.67731i −0.206714 0.0752377i
498498 −18.3344 1.63944i −0.821583 0.0734652i
499499 23.5418 + 19.7539i 1.05388 + 0.884306i 0.993496 0.113869i 0.0363245π-0.0363245\pi
0.0603793 + 0.998176i 0.480769π0.480769\pi
500500 7.18997 + 6.03310i 0.321545 + 0.269809i
501501 −9.85620 21.2428i −0.440343 0.949060i
502502 −18.8963 6.87768i −0.843382 0.306966i
503503 −0.553021 + 0.957860i −0.0246580 + 0.0427089i −0.878091 0.478494i 0.841183π-0.841183\pi
0.853433 + 0.521202i 0.174516π0.174516\pi
504504 1.82667 2.16008i 0.0813661 0.0962174i
505505 0.594460 + 1.02963i 0.0264531 + 0.0458181i
506506 −4.26766 24.2031i −0.189720 1.07596i
507507 1.67389 0.445082i 0.0743400 0.0197668i
508508 −6.81640 + 2.48097i −0.302429 + 0.110075i
509509 −7.56918 + 42.9270i −0.335498 + 1.90270i 0.0867623 + 0.996229i 0.472348π0.472348\pi
−0.422260 + 0.906475i 0.638763π0.638763\pi
510510 6.74546 4.70399i 0.298694 0.208296i
511511 −7.98352 + 6.69897i −0.353170 + 0.296345i
512512 −1.00000 −0.0441942
513513 16.5307 16.3418i 0.729849 0.721510i
514514 21.3050 0.939725
515515 5.96803 5.00778i 0.262983 0.220669i
516516 11.8690 + 5.56232i 0.522504 + 0.244867i
517517 −11.3436 + 64.3330i −0.498893 + 2.82936i
518518 0.194394 0.0707538i 0.00854120 0.00310874i
519519 6.88933 25.5158i 0.302408 1.12002i
520520 0.183462 + 1.04046i 0.00804533 + 0.0456274i
521521 13.0657 + 22.6304i 0.572419 + 0.991458i 0.996317 + 0.0857482i 0.0273281π0.0273281\pi
−0.423898 + 0.905710i 0.639339π0.639339\pi
522522 −0.0572120 + 14.9348i −0.00250410 + 0.653678i
523523 8.72776 15.1169i 0.381638 0.661017i −0.609658 0.792664i 0.708693π-0.708693\pi
0.991297 + 0.131647i 0.0420266π0.0420266\pi
524524 −7.62853 2.77656i −0.333254 0.121294i
525525 −3.64827 + 5.18909i −0.159224 + 0.226470i
526526 1.24142 + 1.04167i 0.0541283 + 0.0454190i
527527 17.7597 + 14.9022i 0.773627 + 0.649150i
528528 6.01631 8.55725i 0.261826 0.372406i
529529 6.05187 + 2.20270i 0.263125 + 0.0957696i
530530 −2.26135 + 3.91678i −0.0982268 + 0.170134i
531531 18.5176 10.5967i 0.803594 0.459860i
532532 −2.10916 3.65317i −0.0914436 0.158385i
533533 −1.76746 10.0238i −0.0765572 0.434178i
534534 7.07659 26.2093i 0.306234 1.13419i
535535 −7.68017 + 2.79535i −0.332043 + 0.120854i
536536 −0.221115 + 1.25401i −0.00955071 + 0.0541648i
537537 −25.3117 11.8621i −1.09228 0.511889i
538538 10.7507 9.02094i 0.463497 0.388920i
539539 −36.9056 −1.58964
540540 4.98871 2.29147i 0.214680 0.0986090i
541541 −30.3642 −1.30546 −0.652729 0.757591i 0.726376π-0.726376\pi
−0.652729 + 0.757591i 0.726376π0.726376\pi
542542 5.73829 4.81500i 0.246481 0.206822i
543543 −3.59696 + 2.50836i −0.154360 + 0.107644i
544544 0.780369 4.42569i 0.0334580 0.189750i
545545 13.6483 4.96758i 0.584630 0.212788i
546546 −1.57842 + 0.419697i −0.0675500 + 0.0179614i
547547 2.91602 + 16.5376i 0.124680 + 0.707095i 0.981497 + 0.191475i 0.0613272π0.0613272\pi
−0.856817 + 0.515620i 0.827562π0.827562\pi
548548 −4.27560 7.40556i −0.182645 0.316350i
549549 −3.93243 10.9344i −0.167832 0.466669i
550550 −11.7278 + 20.3132i −0.500075 + 0.866156i
551551 20.9272 + 7.61688i 0.891528 + 0.324490i
552552 −2.96652 6.39367i −0.126263 0.272132i
553553 11.0952 + 9.30996i 0.471815 + 0.395900i
554554 2.83230 + 2.37658i 0.120333 + 0.100971i
555555 0.399861 + 0.0357552i 0.0169732 + 0.00151772i
556556 0.797677 + 0.290331i 0.0338290 + 0.0123128i
557557 5.48725 9.50420i 0.232502 0.402706i −0.726042 0.687651i 0.758642π-0.758642\pi
0.958544 + 0.284945i 0.0919753π0.0919753\pi
558558 9.90265 + 11.8938i 0.419213 + 0.503503i
559559 −3.78388 6.55387i −0.160041 0.277199i
560560 −0.172998 0.981120i −0.00731050 0.0414599i
561561 33.1768 + 33.3041i 1.40073 + 1.40610i
562562 −6.40992 + 2.33302i −0.270386 + 0.0984125i
563563 0.484875 2.74986i 0.0204351 0.115893i −0.972884 0.231294i 0.925704π-0.925704\pi
0.993319 + 0.115401i 0.0368152π0.0368152\pi
564564 1.59710 + 18.6667i 0.0672500 + 0.786008i
565565 4.03859 3.38878i 0.169905 0.142567i
566566 −11.4696 −0.482102
567567 4.18691 + 7.38197i 0.175833 + 0.310014i
568568 −5.20076 −0.218219
569569 −9.30978 + 7.81183i −0.390286 + 0.327489i −0.816725 0.577028i 0.804213π-0.804213\pi
0.426438 + 0.904517i 0.359768π0.359768\pi
570570 −0.697849 8.15636i −0.0292297 0.341632i
571571 −0.913391 + 5.18010i −0.0382242 + 0.216780i −0.997937 0.0642030i 0.979549π-0.979549\pi
0.959713 + 0.280983i 0.0906606π0.0906606\pi
572572 −5.67516 + 2.06559i −0.237291 + 0.0863667i
573573 −29.1761 29.2881i −1.21885 1.22353i
574574 1.66665 + 9.45206i 0.0695647 + 0.394521i
575575 7.90225 + 13.6871i 0.329547 + 0.570792i
576576 1.03685 2.81513i 0.0432022 0.117297i
577577 −3.27442 + 5.67147i −0.136316 + 0.236106i −0.926099 0.377280i 0.876860π-0.876860\pi
0.789783 + 0.613386i 0.210193π0.210193\pi
578578 3.00299 + 1.09300i 0.124908 + 0.0454628i
579579 −30.5613 2.73276i −1.27008 0.113570i
580580 4.02913 + 3.38084i 0.167300 + 0.140382i
581581 −7.67687 6.44166i −0.318490 0.267245i
582582 −12.5339 27.0139i −0.519545 1.11976i
583583 −24.2941 8.84233i −1.00616 0.366212i
584584 −5.52605 + 9.57140i −0.228670 + 0.396068i
585585 −3.11926 0.562339i −0.128966 0.0232498i
586586 −2.13893 3.70474i −0.0883585 0.153041i
587587 3.83698 + 21.7606i 0.158369 + 0.898157i 0.955640 + 0.294536i 0.0951650π0.0951650\pi
−0.797271 + 0.603621i 0.793724π0.793724\pi
588588 −10.2288 + 2.71982i −0.421830 + 0.112163i
589589 21.6862 7.89312i 0.893563 0.325230i
590590 1.30473 7.39951i 0.0537150 0.304633i
591591 17.0632 11.8992i 0.701887 0.489466i
592592 0.168057 0.141017i 0.00690710 0.00579575i
593593 11.6498 0.478399 0.239200 0.970970i 0.423115π-0.423115\pi
0.239200 + 0.970970i 0.423115π0.423115\pi
594594 17.8517 + 25.8093i 0.732465 + 1.05897i
595595 4.47714 0.183545
596596 16.2858 13.6654i 0.667093 0.559758i
597597 −19.0071 8.90753i −0.777909 0.364561i
598598 −0.706638 + 4.00754i −0.0288966 + 0.163881i
599599 −40.7962 + 14.8486i −1.66689 + 0.606697i −0.991422 0.130697i 0.958278π-0.958278\pi
−0.675463 + 0.737394i 0.736056π0.736056\pi
600600 −1.75349 + 6.49434i −0.0715860 + 0.265130i
601601 0.843575 + 4.78415i 0.0344101 + 0.195150i 0.997167 0.0752189i 0.0239656π-0.0239656\pi
−0.962757 + 0.270369i 0.912854π0.912854\pi
602602 3.56806 + 6.18007i 0.145423 + 0.251881i
603603 −3.30092 1.92268i −0.134424 0.0782978i
604604 −5.98436 + 10.3652i −0.243500 + 0.421755i
605605 25.2907 + 9.20507i 1.02821 + 0.374239i
606606 −1.12102 + 1.59448i −0.0455384 + 0.0647712i
607607 29.9042 + 25.0926i 1.21377 + 1.01848i 0.999127 + 0.0417863i 0.0133049π0.0133049\pi
0.214648 + 0.976691i 0.431140π0.431140\pi
608608 −3.42687 2.87549i −0.138978 0.116616i
609609 −4.67643 + 6.65148i −0.189498 + 0.269531i
610610 −3.84545 1.39963i −0.155698 0.0566694i
611611 5.40829 9.36743i 0.218796 0.378966i
612612 11.6498 + 6.78562i 0.470913 + 0.274293i
613613 −18.1246 31.3927i −0.732045 1.26794i −0.956008 0.293341i 0.905233π-0.905233\pi
0.223963 0.974598i 0.428101π-0.428101\pi
614614 4.22152 + 23.9414i 0.170367 + 0.966197i
615615 −4.85517 + 17.9819i −0.195779 + 0.725101i
616616 5.35148 1.94778i 0.215617 0.0784782i
617617 −4.68550 + 26.5728i −0.188631 + 1.06978i 0.732569 + 0.680693i 0.238321π0.238321\pi
−0.921200 + 0.389088i 0.872790π0.872790\pi
618618 11.5651 + 5.41989i 0.465216 + 0.218020i
619619 8.61308 7.22723i 0.346189 0.290487i −0.453069 0.891476i 0.649671π-0.649671\pi
0.799257 + 0.600989i 0.205226π0.205226\pi
620620 5.45040 0.218893
621621 21.0748 1.72184i 0.845703 0.0690951i
622622 25.0930 1.00614
623623 11.3220 9.50030i 0.453607 0.380621i
624624 −1.42071 + 0.990744i −0.0568740 + 0.0396615i
625625 1.65011 9.35824i 0.0660044 0.374329i
626626 28.6829 10.4397i 1.14640 0.417255i
627627 45.2234 12.0248i 1.80605 0.480223i
628628 0.109587 + 0.621497i 0.00437299 + 0.0248004i
629629 0.492949 + 0.853813i 0.0196552 + 0.0340438i
630630 2.94135 + 0.530265i 0.117186 + 0.0211263i
631631 −9.21442 + 15.9598i −0.366820 + 0.635352i −0.989067 0.147470i 0.952887π-0.952887\pi
0.622246 + 0.782822i 0.286220π0.286220\pi
632632 14.4335 + 5.25336i 0.574133 + 0.208967i
633633 −4.65101 10.0242i −0.184861 0.398427i
634634 −19.4839 16.3489i −0.773803 0.649298i
635635 −5.87082 4.92620i −0.232976 0.195490i
636636 −7.38506 0.660365i −0.292837 0.0261852i
637637 5.74229 + 2.09002i 0.227518 + 0.0828097i
638638 −15.0329 + 26.0378i −0.595160 + 1.03085i
639639 5.39242 14.6408i 0.213321 0.579181i
640640 −0.528257 0.914969i −0.0208812 0.0361673i
641641 6.65029 + 37.7157i 0.262671 + 1.48968i 0.775587 + 0.631241i 0.217454π0.217454\pi
−0.512916 + 0.858439i 0.671435π0.671435\pi
642642 −9.45631 9.49260i −0.373211 0.374643i
643643 12.7143 4.62764i 0.501404 0.182496i −0.0789211 0.996881i 0.525148π-0.525148\pi
0.580326 + 0.814385i 0.302925π0.302925\pi
644644 0.666334 3.77897i 0.0262572 0.148912i
645645 1.18055 + 13.7981i 0.0464842 + 0.543300i
646646 15.4002 12.9223i 0.605914 0.508422i
647647 22.4717 0.883455 0.441727 0.897149i 0.354366π-0.354366\pi
0.441727 + 0.897149i 0.354366π0.354366\pi
648648 6.84988 + 5.83774i 0.269089 + 0.229328i
649649 42.9505 1.68596
650650 2.97515 2.49644i 0.116695 0.0979186i
651651 0.718275 + 8.39509i 0.0281514 + 0.329029i
652652 −0.737294 + 4.18140i −0.0288747 + 0.163756i
653653 21.8773 7.96270i 0.856126 0.311604i 0.123591 0.992333i 0.460559π-0.460559\pi
0.732535 + 0.680729i 0.238337π0.238337\pi
654654 16.8047 + 16.8692i 0.657115 + 0.659637i
655655 −1.48936 8.44660i −0.0581942 0.330036i
656656 5.08920 + 8.81476i 0.198700 + 0.344158i
657657 −21.2150 25.4807i −0.827677 0.994096i
658658 −5.09982 + 8.83315i −0.198812 + 0.344352i
659659 −14.0119 5.09993i −0.545828 0.198665i 0.0543641 0.998521i 0.482687π-0.482687\pi
−0.600192 + 0.799856i 0.704909π0.704909\pi
660660 11.0078 + 0.984304i 0.428477 + 0.0383140i
661661 −31.8036 26.6864i −1.23702 1.03798i −0.997751 0.0670251i 0.978649π-0.978649\pi
−0.239265 0.970954i 0.576906π-0.576906\pi
662662 −6.97529 5.85297i −0.271103 0.227482i
663663 −3.27605 7.06078i −0.127231 0.274218i
664664 −9.98667 3.63485i −0.387558 0.141060i
665665 2.22836 3.85963i 0.0864120 0.149670i
666666 0.222729 + 0.619315i 0.00863058 + 0.0239980i
667667 10.1293 + 17.5444i 0.392207 + 0.679322i
668668 −2.34779 13.3150i −0.0908387 0.515172i
669669 36.8067 9.78681i 1.42303 0.378380i
670670 −1.26418 + 0.460124i −0.0488396 + 0.0177761i
671671 4.06209 23.0372i 0.156815 0.889343i
672672 1.33968 0.934236i 0.0516793 0.0360389i
673673 8.97139 7.52789i 0.345822 0.290179i −0.453288 0.891364i 0.649749π-0.649749\pi
0.799110 + 0.601185i 0.205305π0.205305\pi
674674 7.36056 0.283518
675675 −16.4643 11.6700i −0.633710 0.449177i
676676 1.00000 0.0384615
677677 5.43432 4.55994i 0.208858 0.175253i −0.532358 0.846519i 0.678694π-0.678694\pi
0.741216 + 0.671267i 0.234249π0.234249\pi
678678 7.82614 + 3.66766i 0.300561 + 0.140855i
679679 2.81533 15.9665i 0.108043 0.612740i
680680 4.46160 1.62389i 0.171095 0.0622734i
681681 3.22407 11.9409i 0.123547 0.457575i
682682 5.41023 + 30.6830i 0.207168 + 1.17491i
683683 −17.5761 30.4427i −0.672531 1.16486i −0.977184 0.212394i 0.931874π-0.931874\pi
0.304654 0.952463i 0.401459π-0.401459\pi
684684 11.6480 6.66562i 0.445373 0.254866i
685685 4.51724 7.82408i 0.172595 0.298943i
686686 −11.6175 4.22841i −0.443556 0.161441i
687687 6.94191 9.87377i 0.264850 0.376708i
688688 5.79724 + 4.86446i 0.221018 + 0.185456i
689689 3.27927 + 2.75163i 0.124930 + 0.104829i
690690 4.28292 6.09177i 0.163048 0.231910i
691691 −1.83561 0.668107i −0.0698299 0.0254160i 0.306869 0.951752i 0.400719π-0.400719\pi
−0.376699 + 0.926336i 0.622941π0.622941\pi
692692 7.62953 13.2147i 0.290031 0.502349i
693693 −0.0654476 + 17.0846i −0.00248615 + 0.648992i
694694 3.18037 + 5.50855i 0.120725 + 0.209102i
695695 0.155735 + 0.883218i 0.00590737 + 0.0335024i
696696 −2.24766 + 8.32457i −0.0851974 + 0.315542i
697697 −42.9828 + 15.6445i −1.62809 + 0.592577i
698698 0.251034 1.42369i 0.00950178 0.0538873i
699699 17.9776 + 8.42505i 0.679975 + 0.318665i
700700 −2.80546 + 2.35406i −0.106036 + 0.0889750i
701701 11.2600 0.425284 0.212642 0.977130i 0.431793π-0.431793\pi
0.212642 + 0.977130i 0.431793π0.431793\pi
702702 −1.31600 5.02674i −0.0496692 0.189722i
703703 0.981401 0.0370142
704704 4.62644 3.88204i 0.174365 0.146310i
705705 −16.2357 + 11.3221i −0.611473 + 0.426415i
706706 4.07008 23.0826i 0.153179 0.868723i
707707 −0.997144 + 0.362931i −0.0375014 + 0.0136494i
708708 11.9043 3.16531i 0.447389 0.118960i
709709 −1.85073 10.4960i −0.0695057 0.394186i −0.999637 0.0269581i 0.991418π-0.991418\pi
0.930131 0.367228i 0.119693π-0.119693\pi
710710 −2.74734 4.75853i −0.103106 0.178585i
711711 −29.7542 + 35.1851i −1.11587 + 1.31954i
712712 7.83691 13.5739i 0.293700 0.508704i
713713 19.7272 + 7.18012i 0.738790 + 0.268897i
714714 3.08920 + 6.65807i 0.115610 + 0.249172i
715715 −4.88790 4.10143i −0.182797 0.153385i
716716 −12.3631 10.3739i −0.462032 0.387691i
717717 −41.5000 3.71089i −1.54985 0.138586i
718718 −17.8504 6.49702i −0.666172 0.242467i
719719 13.8580 24.0028i 0.516817 0.895154i −0.482992 0.875625i 0.660450π-0.660450\pi
0.999809 0.0195290i 0.00621666π-0.00621666\pi
720720 3.12348 0.538424i 0.116405 0.0200659i
721721 3.47670 + 6.02182i 0.129479 + 0.224264i
722722 −0.175710 0.996500i −0.00653924 0.0370859i
723723 −27.6511 27.7572i −1.02835 1.03230i
724724 −2.37911 + 0.865926i −0.0884190 + 0.0321819i
725725 3.35742 19.0409i 0.124691 0.707161i
726726 3.76133 + 43.9619i 0.139596 + 1.63158i
727727 −19.1756 + 16.0902i −0.711183 + 0.596753i −0.924931 0.380136i 0.875877π-0.875877\pi
0.213748 + 0.976889i 0.431433π0.431433\pi
728728 −0.942964 −0.0349486
729729 −23.5363 + 13.2304i −0.871714 + 0.490015i
730730 −11.6767 −0.432175
731731 −26.0526 + 21.8607i −0.963590 + 0.808548i
732732 −0.571911 6.68441i −0.0211384 0.247063i
733733 4.53128 25.6982i 0.167367 0.949183i −0.779224 0.626745i 0.784387π-0.784387\pi
0.946591 0.322438i 0.104502π-0.104502\pi
734734 20.5833 7.49170i 0.759742 0.276524i
735735 −7.89200 7.92229i −0.291101 0.292218i
736736 −0.706638 4.00754i −0.0260470 0.147720i
737737 −3.84512 6.65995i −0.141637 0.245322i
738738 −30.0914 + 5.18715i −1.10768 + 0.190942i
739739 −2.07244 + 3.58958i −0.0762361 + 0.132045i −0.901623 0.432523i 0.857624π-0.857624\pi
0.825387 + 0.564567i 0.190957π0.190957\pi
740740 0.217803 + 0.0792739i 0.00800660 + 0.00291416i
741741 −7.71747 0.690089i −0.283508 0.0253511i
742742 −3.09223 2.59469i −0.113519 0.0952540i
743743 −3.42001 2.86973i −0.125468 0.105280i 0.577895 0.816111i 0.303874π-0.303874\pi
−0.703363 + 0.710831i 0.748319π0.748319\pi
744744 3.76074 + 8.10544i 0.137876 + 0.297160i
745745 21.1065 + 7.68215i 0.773284 + 0.281452i
746746 11.8175 20.4684i 0.432668 0.749403i
747747 20.5873 24.3449i 0.753249 0.890735i
748748 13.5704 + 23.5046i 0.496182 + 0.859413i
749749 −1.26670 7.18383i −0.0462843 0.262491i
750750 −15.7108 + 4.17747i −0.573679 + 0.152540i
751751 8.02534 2.92099i 0.292849 0.106588i −0.191418 0.981509i 0.561309π-0.561309\pi
0.484267 + 0.874920i 0.339086π0.339086\pi
752752 −1.87828 + 10.6523i −0.0684938 + 0.388448i
753753 28.5691 19.9229i 1.04112 0.726029i
754754 3.81360 3.19999i 0.138883 0.116537i
755755 −12.6451 −0.460203
756756 1.24094 + 4.74004i 0.0451326 + 0.172394i
757757 36.3144 1.31987 0.659935 0.751323i 0.270584π-0.270584\pi
0.659935 + 0.751323i 0.270584π0.270584\pi
758758 15.5263 13.0281i 0.563939 0.473201i
759759 38.5449 + 18.0637i 1.39909 + 0.655672i
760760 0.820710 4.65448i 0.0297703 0.168836i
761761 −17.8889 + 6.51102i −0.648471 + 0.236024i −0.645251 0.763971i 0.723247π-0.723247\pi
−0.00322002 + 0.999995i 0.501025π0.501025\pi
762762 3.27506 12.1297i 0.118643 0.439413i
763763 2.25104 + 12.7663i 0.0814932 + 0.462171i
764764 −11.9340 20.6702i −0.431756 0.747823i
765765 −0.0545646 + 14.2437i −0.00197279 + 0.514983i
766766 12.3045 21.3119i 0.444578 0.770032i
767767 −6.68285 2.43236i −0.241304 0.0878274i
768768 0.996179 1.41691i 0.0359465 0.0511282i
769769 35.4657 + 29.7593i 1.27893 + 1.07315i 0.993391 + 0.114779i 0.0366160π0.0366160\pi
0.285536 + 0.958368i 0.407828π0.407828\pi
770770 4.60911 + 3.86750i 0.166101 + 0.139375i
771771 −21.2236 + 30.1873i −0.764351 + 1.08717i
772772 −16.6466 6.05888i −0.599126 0.218064i
773773 4.03431 6.98763i 0.145104 0.251328i −0.784308 0.620372i 0.786982π-0.786982\pi
0.929412 + 0.369044i 0.120315π0.120315\pi
774774 −19.7050 + 11.2762i −0.708280 + 0.405316i
775775 −10.0179 17.3515i −0.359854 0.623286i
776776 −2.98562 16.9323i −0.107178 0.607834i
777777 −0.0934001 + 0.345922i −0.00335071 + 0.0124099i
778778 0.149819 0.0545297i 0.00537128 0.00195498i
779779 −7.90667 + 44.8410i −0.283286 + 1.60659i
780780 −1.65700 0.776540i −0.0593302 0.0278046i
781781 24.0610 20.1896i 0.860970 0.722440i
782782 18.2876 0.653963
783783 −21.1042 14.9588i −0.754204 0.534584i
784784 −6.11082 −0.218244
785785 −0.510761 + 0.428579i −0.0182298 + 0.0152966i
786786 11.5335 8.04297i 0.411386 0.286883i
787787 −1.98260 + 11.2439i −0.0706719 + 0.400800i 0.928866 + 0.370415i 0.120785π0.120785\pi
−0.999538 + 0.0303852i 0.990327π0.990327\pi
788788 11.2860 4.10777i 0.402048 0.146333i
789789 −2.71262 + 0.721280i −0.0965720 + 0.0256782i
790790 2.81793 + 15.9813i 0.100258 + 0.568589i
791791 2.35269 + 4.07499i 0.0836522 + 0.144890i
792792 6.13151 + 17.0491i 0.217874 + 0.605814i
793793 −1.93667 + 3.35442i −0.0687733 + 0.119119i
794794 15.3713 + 5.59471i 0.545508 + 0.198549i
795795 −3.29700 7.10594i −0.116932 0.252022i
796796 −9.28373 7.78998i −0.329053 0.276108i
797797 −40.0526 33.6081i −1.41874 1.19046i −0.952013 0.306056i 0.900990π-0.900990\pi
−0.466722 0.884404i 0.654565π-0.654565\pi
798798 7.27730 + 0.650729i 0.257614 + 0.0230356i
799799 −45.6778 16.6254i −1.61597 0.588163i
800800 −1.94189 + 3.36345i −0.0686561 + 0.118916i
801801 30.0866 + 36.1360i 1.06306 + 1.27680i
802802 15.4253 + 26.7174i 0.544687 + 0.943425i
803803 −11.5907 65.7338i −0.409025 2.31970i
804804 −1.55654 1.56251i −0.0548949 0.0551056i
805805 3.80963 1.38659i 0.134272 0.0488710i
806806 0.895825 5.08048i 0.0315541 0.178952i
807807 2.07218 + 24.2193i 0.0729440 + 0.852559i
808808 −0.862046 + 0.723343i −0.0303267 + 0.0254471i
809809 33.0759 1.16289 0.581443 0.813587i 0.302488π-0.302488\pi
0.581443 + 0.813587i 0.302488π0.302488\pi
810810 −1.72285 + 9.35125i −0.0605348 + 0.328569i
811811 −5.23894 −0.183964 −0.0919820 0.995761i 0.529320π-0.529320\pi
−0.0919820 + 0.995761i 0.529320π0.529320\pi
812812 −3.59609 + 3.01748i −0.126198 + 0.105893i
813813 1.10604 + 12.9272i 0.0387905 + 0.453377i
814814 −0.230073 + 1.30481i −0.00806405 + 0.0457335i
815815 −4.21534 + 1.53426i −0.147657 + 0.0537427i
816816 5.49341 + 5.51449i 0.192308 + 0.193046i
817817 5.87870 + 33.3398i 0.205670 + 1.16641i
818818 14.6891 + 25.4423i 0.513594 + 0.889570i
819819 0.977714 2.65456i 0.0341641 0.0927580i
820820 −5.37682 + 9.31292i −0.187767 + 0.325221i
821821 −4.24352 1.54451i −0.148100 0.0539039i 0.266907 0.963722i 0.413998π-0.413998\pi
−0.415006 + 0.909818i 0.636221π0.636221\pi
822822 14.7523 + 1.31913i 0.514544 + 0.0460100i
823823 −8.58241 7.20150i −0.299164 0.251028i 0.480832 0.876813i 0.340335π-0.340335\pi
−0.779996 + 0.625784i 0.784779π0.784779\pi
824824 5.64879 + 4.73990i 0.196785 + 0.165122i
825825 −17.0989 36.8528i −0.595306 1.28305i
826826 6.30169 + 2.29363i 0.219264 + 0.0798055i
827827 −20.7061 + 35.8641i −0.720023 + 1.24712i 0.240967 + 0.970533i 0.422535π0.422535\pi
−0.960990 + 0.276583i 0.910798π0.910798\pi
828828 12.0144 + 2.16595i 0.417530 + 0.0752721i
829829 −0.130998 0.226896i −0.00454976 0.00788042i 0.863742 0.503935i 0.168115π-0.168115\pi
−0.868291 + 0.496055i 0.834782π0.834782\pi
830830 −1.94976 11.0576i −0.0676771 0.383816i
831831 −6.18887 + 1.64560i −0.214689 + 0.0570854i
832832 −0.939693 + 0.342020i −0.0325780 + 0.0118574i
833833 4.76869 27.0446i 0.165225 0.937040i
834834 −1.20600 + 0.841013i −0.0417604 + 0.0291219i
835835 10.9426 9.18189i 0.378683 0.317752i
836836 27.0170 0.934401
837837 −26.7172 + 2.18283i −0.923480 + 0.0754496i
838838 −11.6777 −0.403400
839839 23.9977 20.1364i 0.828492 0.695187i −0.126452 0.991973i 0.540359π-0.540359\pi
0.954944 + 0.296785i 0.0959146π0.0959146\pi
840840 1.56249 + 0.732250i 0.0539112 + 0.0252650i
841841 −0.732187 + 4.15244i −0.0252478 + 0.143188i
842842 23.4373 8.53048i 0.807703 0.293980i
843843 3.07976 11.4064i 0.106072 0.392856i
844844 −1.10789 6.28316i −0.0381352 0.216275i
845845 0.528257 + 0.914969i 0.0181726 + 0.0314759i
846846 −28.0399 16.3324i −0.964033 0.561520i
847847 −12.0106 + 20.8030i −0.412689 + 0.714799i
848848 −4.02261 1.46411i −0.138137 0.0502778i
849849 11.4257 16.2513i 0.392131 0.557744i
850850 −13.3702 11.2189i −0.458594 0.384806i
851851 0.683885 + 0.573848i 0.0234433 + 0.0196713i
852852 5.18089 7.36900i 0.177494 0.252458i
853853 26.2998 + 9.57234i 0.900488 + 0.327751i 0.750448 0.660929i 0.229838π-0.229838\pi
0.150039 + 0.988680i 0.452060π0.452060\pi
854854 1.82621 3.16309i 0.0624917 0.108239i
855855 12.2520 + 7.13641i 0.419009 + 0.244060i
856856 −3.86794 6.69946i −0.132203 0.228983i
857857 2.00764 + 11.3859i 0.0685796 + 0.388934i 0.999706 + 0.0242381i 0.00771599π0.00771599\pi
−0.931127 + 0.364696i 0.881173π0.881173\pi
858858 2.72673 10.0989i 0.0930890 0.344770i
859859 −36.0388 + 13.1170i −1.22963 + 0.447548i −0.873470 0.486878i 0.838136π-0.838136\pi
−0.356158 + 0.934426i 0.615913π0.615913\pi
860860 −1.38840 + 7.87398i −0.0473439 + 0.268501i
861861 −15.0530 7.05445i −0.513004 0.240415i
862862 4.74892 3.98482i 0.161749 0.135723i
863863 27.7266 0.943826 0.471913 0.881645i 0.343564π-0.343564\pi
0.471913 + 0.881645i 0.343564π0.343564\pi
864864 2.95588 + 4.27349i 0.100561 + 0.145387i
865865 16.1214 0.548145
866866 −8.52394 + 7.15244i −0.289655 + 0.243050i
867867 −4.54019 + 3.16614i −0.154193 + 0.107528i
868868 −0.844731 + 4.79071i −0.0286720 + 0.162607i
869869 −87.1693 + 31.7270i −2.95702 + 1.07627i
870870 −8.80407 + 2.34098i −0.298486 + 0.0793666i
871871 0.221115 + 1.25401i 0.00749219 + 0.0424903i
872872 6.87366 + 11.9055i 0.232772 + 0.403172i
873873 50.7622 + 9.15138i 1.71804 + 0.309727i
874874 9.10208 15.7653i 0.307882 0.533268i
875875 −8.31676 3.02705i −0.281158 0.102333i
876876 −8.05686 17.3647i −0.272216 0.586700i
877877 −13.9776 11.7286i −0.471991 0.396047i 0.375529 0.926810i 0.377461π-0.377461\pi
−0.847520 + 0.530763i 0.821905π0.821905\pi
878878 6.66126 + 5.58946i 0.224807 + 0.188635i
879879 7.38003 + 0.659916i 0.248922 + 0.0222584i
880880 5.99589 + 2.18233i 0.202122 + 0.0735662i
881881 11.8334 20.4961i 0.398679 0.690532i −0.594884 0.803811i 0.702802π-0.702802\pi
0.993563 + 0.113279i 0.0361355π0.0361355\pi
882882 6.33601 17.2027i 0.213345 0.579246i
883883 −16.7180 28.9564i −0.562604 0.974459i −0.997268 0.0738663i 0.976466π-0.976466\pi
0.434664 0.900593i 0.356867π-0.356867\pi
884884 −0.780369 4.42569i −0.0262466 0.148852i
885885 9.18467 + 9.21992i 0.308739 + 0.309924i
886886 −8.45904 + 3.07884i −0.284187 + 0.103436i
887887 −1.58993 + 9.01693i −0.0533846 + 0.302759i −0.999796 0.0202050i 0.993568π-0.993568\pi
0.946411 + 0.322964i 0.104679π0.104679\pi
888888 0.0323925 + 0.378599i 0.00108702 + 0.0127050i
889889 5.23984 4.39675i 0.175739 0.147462i
890890 16.5596 0.555079
891891 −54.3529 0.416434i −1.82089 0.0139511i
892892 21.9888 0.736238
893893 −37.0670 + 31.1029i −1.24040 + 1.04082i
894894 3.13905 + 36.6887i 0.104985 + 1.22705i
895895 2.96087 16.7920i 0.0989711 0.561293i
896896 0.886097 0.322513i 0.0296024 0.0107744i
897897 −4.97438 4.99347i −0.166090 0.166727i
898898 0.515374 + 2.92283i 0.0171982 + 0.0975360i
899899 −12.8412 22.2416i −0.428277 0.741797i
900900 −7.45508 8.95406i −0.248503 0.298469i
901901 9.61883 16.6603i 0.320450 0.555035i
902902 −57.7641 21.0244i −1.92333 0.700036i
903903 −12.3110 1.10084i −0.409685 0.0366336i
904904 3.82256 + 3.20751i 0.127136 + 0.106680i
905905 −2.04908 1.71938i −0.0681137 0.0571542i
906906 −8.72506 18.8049i −0.289871 0.624751i
907907 27.3310 + 9.94767i 0.907511 + 0.330307i 0.753259 0.657725i 0.228481π-0.228481\pi
0.154252 + 0.988031i 0.450703π0.450703\pi
908908 3.57047 6.18424i 0.118490 0.205231i
909909 −1.14249 3.17677i −0.0378939 0.105367i
910910 −0.498128 0.862783i −0.0165128 0.0286010i
911911 9.85747 + 55.9045i 0.326593 + 1.85220i 0.498239 + 0.867040i 0.333980π0.333980\pi
−0.171646 + 0.985159i 0.554909π0.554909\pi
912912 7.48808 1.99106i 0.247955 0.0659306i
913913 60.3133 21.9523i 1.99608 0.726514i
914914 −2.25487 + 12.7880i −0.0745845 + 0.422990i
915915 5.81391 4.05437i 0.192202 0.134033i
916916 5.33821 4.47929i 0.176379 0.148000i
917917 7.65509 0.252793
918918 −21.2198 + 9.74692i −0.700359 + 0.321696i
919919 20.3277 0.670550 0.335275 0.942120i 0.391171π-0.391171\pi
0.335275 + 0.942120i 0.391171π0.391171\pi
920920 3.29349 2.76357i 0.108583 0.0911120i
921921 −38.1282 17.8684i −1.25637 0.588785i
922922 1.77922 10.0905i 0.0585955 0.332311i
923923 −4.88712 + 1.77877i −0.160861 + 0.0585488i
924924 −2.57121 + 9.52288i −0.0845866 + 0.313280i
925925 −0.147954 0.839090i −0.00486470 0.0275891i
926926 0.273033 + 0.472906i 0.00897241 + 0.0155407i
927927 −19.2004 + 10.9875i −0.630623 + 0.360877i
928928 −2.48915 + 4.31134i −0.0817104 + 0.141527i
929929 6.19874 + 2.25616i 0.203374 + 0.0740221i 0.441699 0.897163i 0.354376π-0.354376\pi
−0.238325 + 0.971186i 0.576598π0.576598\pi
930930 −5.42958 + 7.72272i −0.178043 + 0.253238i
931931 −20.9410 17.5716i −0.686313 0.575885i
932932 8.78088 + 7.36803i 0.287627 + 0.241348i
933933 −24.9972 + 35.5545i −0.818370 + 1.16400i
934934 34.3160 + 12.4900i 1.12285 + 0.408685i
935935 −14.3373 + 24.8330i −0.468880 + 0.812124i
936936 0.0114923 2.99998i 0.000375637 0.0980573i
937937 −18.3372 31.7609i −0.599049 1.03758i −0.992962 0.118435i 0.962212π-0.962212\pi
0.393913 0.919148i 0.371121π-0.371121\pi
938938 −0.208503 1.18248i −0.00680788 0.0386094i
939939 −13.7812 + 51.0408i −0.449732 + 1.66565i
940940 −10.7387 + 3.90856i −0.350257 + 0.127483i
941941 0.596058 3.38041i 0.0194309 0.110198i −0.973550 0.228475i 0.926626π-0.926626\pi
0.992981 + 0.118277i 0.0377371π0.0377371\pi
942942 −0.989772 0.463849i −0.0322485 0.0151130i
943943 −31.7293 + 26.6240i −1.03325 + 0.866998i
944944 7.11174 0.231467
945945 −3.68145 + 3.63938i −0.119758 + 0.118389i
946946 −45.7046 −1.48598
947947 −29.9115 + 25.0988i −0.971994 + 0.815600i −0.982862 0.184341i 0.940985π-0.940985\pi
0.0108682 + 0.999941i 0.496540π0.496540\pi
948948 −21.8218 + 15.2176i −0.708741 + 0.494245i
949949 −1.91918 + 10.8842i −0.0622992 + 0.353316i
950950 −16.3262 + 5.94223i −0.529690 + 0.192792i
951951 42.5743 11.3204i 1.38057 0.367089i
952952 0.735860 + 4.17327i 0.0238494 + 0.135256i
953953 −12.6295 21.8750i −0.409111 0.708600i 0.585680 0.810543i 0.300828π-0.300828\pi
−0.994790 + 0.101942i 0.967494π0.967494\pi
954954 8.29252 9.80610i 0.268480 0.317484i
955955 12.6084 21.8384i 0.407999 0.706675i
956956 −22.6049 8.22752i −0.731095 0.266097i
957957 −21.9177 47.2386i −0.708498 1.52701i
958958 −0.321054 0.269396i −0.0103728 0.00870380i
959959 6.17698 + 5.18310i 0.199465 + 0.167371i
960960 1.82266 + 0.162981i 0.0588263 + 0.00526019i
961961 4.12172 + 1.50018i 0.132959 + 0.0483930i
962962 0.109691 0.189991i 0.00353659 0.00612556i
963963 22.8703 3.94238i 0.736986 0.127041i
964964 −11.3102 19.5898i −0.364277 0.630946i
965965 −3.25002 18.4318i −0.104622 0.593341i
966966 4.69066 + 4.70866i 0.150920 + 0.151499i
967967 22.6528 8.24493i 0.728464 0.265139i 0.0489492 0.998801i 0.484413π-0.484413\pi
0.679514 + 0.733662i 0.262191π0.262191\pi
968968 −4.42354 + 25.0871i −0.142178 + 0.806331i
969969 2.96835 + 34.6937i 0.0953573 + 1.11452i
970970 13.9153 11.6764i 0.446795 0.374905i
971971 15.9939 0.513269 0.256635 0.966509i 0.417386π-0.417386\pi
0.256635 + 0.966509i 0.417386π0.417386\pi
972972 −15.0952 + 3.89020i −0.484180 + 0.124778i
973973 −0.800454 −0.0256614
974974 32.2494 27.0604i 1.03334 0.867072i
975975 0.573451 + 6.70241i 0.0183651 + 0.214649i
976976 0.672600 3.81450i 0.0215294 0.122099i
977977 −53.7336 + 19.5574i −1.71909 + 0.625698i −0.997760 0.0668931i 0.978691π-0.978691\pi
−0.721331 + 0.692591i 0.756469π0.756469\pi
978978 −5.19019 5.21011i −0.165964 0.166601i
979979 16.4376 + 93.2220i 0.525347 + 2.97939i
980980 −3.22808 5.59121i −0.103117 0.178605i
981981 −40.6425 + 7.00595i −1.29762 + 0.223683i
982982 12.9836 22.4882i 0.414322 0.717626i
983983 −10.4941 3.81954i −0.334710 0.121824i 0.169198 0.985582i 0.445882π-0.445882\pi
−0.503907 + 0.863758i 0.668105π0.668105\pi
984984 −17.5595 1.57015i −0.559775 0.0500545i
985985 9.72041 + 8.15639i 0.309718 + 0.259884i
986986 −17.1382 14.3806i −0.545791 0.457973i
987987 −7.43542 16.0254i −0.236672 0.510094i
988988 −4.20368 1.53001i −0.133737 0.0486762i
989989 −15.3980 + 26.6701i −0.489628 + 0.848060i
990990 −12.3604 + 14.6165i −0.392839 + 0.464541i
991991 23.7202 + 41.0847i 0.753498 + 1.30510i 0.946118 + 0.323824i 0.104968π0.104968\pi
−0.192619 + 0.981274i 0.561698π0.561698\pi
992992 0.895825 + 5.08048i 0.0284425 + 0.161305i
993993 15.2418 4.05274i 0.483683 0.128610i
994994 4.60838 1.67731i 0.146169 0.0532011i
995995 2.22338 12.6094i 0.0704860 0.399746i
996996 15.0988 10.5292i 0.478423 0.333631i
997997 45.4239 38.1151i 1.43859 1.20712i 0.498178 0.867075i 0.334003π-0.334003\pi
0.940410 0.340044i 0.110442π-0.110442\pi
998998 −30.7316 −0.972792
999999 −1.09939 0.301362i −0.0347832 0.00953468i
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 702.2.w.d.157.6 66
27.16 even 9 inner 702.2.w.d.313.6 yes 66
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
702.2.w.d.157.6 66 1.1 even 1 trivial
702.2.w.d.313.6 yes 66 27.16 even 9 inner