Properties

Label 220.3.s.a.31.15
Level 220220
Weight 33
Character 220.31
Analytic conductor 5.9955.995
Analytic rank 00
Dimension 9696
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [220,3,Mod(31,220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(220, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("220.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 220=22511 220 = 2^{2} \cdot 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 220.s (of order 1010, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.994565815935.99456581593
Analytic rank: 00
Dimension: 9696
Relative dimension: 2424 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 31.15
Character χ\chi == 220.31
Dual form 220.3.s.a.71.15

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.445649+1.94972i)q2+(2.29101+3.15331i)q3+(3.60279+1.73778i)q4+(0.690983+2.12663i)q5+(5.12707+5.87209i)q6+(5.93140+8.16388i)q7+(4.993766.24999i)q8+(1.91346+5.88902i)q9+(3.83838+2.29495i)q10+(4.2722910.1364i)q11+(13.73387.37944i)q12+(4.4301013.6344i)q13+(18.56067.92633i)q14+(5.12286+7.05101i)q15+(9.9602412.5217i)q16+(4.83979+14.8953i)q17+(12.33471.10627i)q18+(15.4818+21.3089i)q19+(6.185086.46102i)q2039.3321q21+(21.6671+3.81245i)q22+31.4161iq23+(8.2673630.0657i)q24+(4.04508+2.93893i)q25+(28.5576+2.56126i)q26+(10.40883.38201i)q27+(7.1826039.7202i)q28+(43.334131.4841i)q29+(16.03056.84585i)q30+(3.325521.08053i)q31+(28.8526+13.8393i)q32+(41.75129.75089i)q33+(26.8849+16.0743i)q34+(21.46006.97278i)q35+(3.3400324.5421i)q36+(18.1817+13.2098i)q37+(34.6469+39.6815i)q38+(53.143017.2672i)q39+(9.8407914.9385i)q40+(26.5611+19.2978i)q41+(17.528376.6865i)q4214.5302iq43+(2.22275+43.9438i)q4413.8459q45+(61.2525+14.0006i)q46+(29.1619+40.1379i)q47+(62.3039+2.72027i)q48+(16.325550.2447i)q49+(7.532766.57704i)q50+(35.8816+49.3868i)q51+(7.73293+56.8206i)q52+(11.938536.7430i)q53+(11.2326+18.7870i)q54+(24.5085+2.08145i)q55+(80.64413.69727i)q56+(31.7245+97.6379i)q57+(42.073298.5201i)q58+(22.571131.0665i)q59+(6.2034934.3057i)q60+(16.8808+51.9537i)q61+(0.6247066.96536i)q62+(36.727750.5514i)q63+(14.1247+62.4219i)q64+32.0565q65+(37.6179+77.0575i)q66+57.3989iq67+(43.321645.2544i)q68+(99.0646+71.9747i)q69+(4.0313144.9484i)q70+(22.46557.29949i)q71+(46.361717.4493i)q72+(34.485225.0550i)q73+(17.6526+41.3360i)q74+(18.53476.02228i)q75+(92.808049.8676i)q76+(57.4120+95.0018i)q77+(57.3493+95.9187i)q78+(66.861421.7246i)q79+(33.5114+12.5294i)q80+(79.5966+57.8303i)q81+(49.462143.1866i)q82+(118.31138.4415i)q83+(141.70668.3506i)q84+(28.3326+20.5849i)q85+(28.32976.47537i)q86208.776iq87+(84.6874+23.9173i)q88+153.780q89+(6.1704326.9956i)q90+(85.0332+117.038i)q91+(54.5943113.186i)q92+(4.2115712.9619i)q93+(65.2615+74.7448i)q94+(34.6184+47.6482i)q95+(22.4619+122.687i)q96+(35.4826109.204i)q97+(90.687554.2216i)q98+(51.5189+44.5553i)q99+O(q100)q+(0.445649 + 1.94972i) q^{2} +(2.29101 + 3.15331i) q^{3} +(-3.60279 + 1.73778i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-5.12707 + 5.87209i) q^{6} +(-5.93140 + 8.16388i) q^{7} +(-4.99376 - 6.24999i) q^{8} +(-1.91346 + 5.88902i) q^{9} +(-3.83838 + 2.29495i) q^{10} +(4.27229 - 10.1364i) q^{11} +(-13.7338 - 7.37944i) q^{12} +(4.43010 - 13.6344i) q^{13} +(-18.5606 - 7.92633i) q^{14} +(-5.12286 + 7.05101i) q^{15} +(9.96024 - 12.5217i) q^{16} +(4.83979 + 14.8953i) q^{17} +(-12.3347 - 1.10627i) q^{18} +(15.4818 + 21.3089i) q^{19} +(-6.18508 - 6.46102i) q^{20} -39.3321 q^{21} +(21.6671 + 3.81245i) q^{22} +31.4161i q^{23} +(8.26736 - 30.0657i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(28.5576 + 2.56126i) q^{26} +(10.4088 - 3.38201i) q^{27} +(7.18260 - 39.7202i) q^{28} +(-43.3341 - 31.4841i) q^{29} +(-16.0305 - 6.84585i) q^{30} +(-3.32552 - 1.08053i) q^{31} +(28.8526 + 13.8393i) q^{32} +(41.7512 - 9.75089i) q^{33} +(-26.8849 + 16.0743i) q^{34} +(-21.4600 - 6.97278i) q^{35} +(-3.34003 - 24.5421i) q^{36} +(18.1817 + 13.2098i) q^{37} +(-34.6469 + 39.6815i) q^{38} +(53.1430 - 17.2672i) q^{39} +(9.84079 - 14.9385i) q^{40} +(-26.5611 + 19.2978i) q^{41} +(-17.5283 - 76.6865i) q^{42} -14.5302i q^{43} +(2.22275 + 43.9438i) q^{44} -13.8459 q^{45} +(-61.2525 + 14.0006i) q^{46} +(29.1619 + 40.1379i) q^{47} +(62.3039 + 2.72027i) q^{48} +(-16.3255 - 50.2447i) q^{49} +(-7.53276 - 6.57704i) q^{50} +(-35.8816 + 49.3868i) q^{51} +(7.73293 + 56.8206i) q^{52} +(11.9385 - 36.7430i) q^{53} +(11.2326 + 18.7870i) q^{54} +(24.5085 + 2.08145i) q^{55} +(80.6441 - 3.69727i) q^{56} +(-31.7245 + 97.6379i) q^{57} +(42.0732 - 98.5201i) q^{58} +(22.5711 - 31.0665i) q^{59} +(6.20349 - 34.3057i) q^{60} +(16.8808 + 51.9537i) q^{61} +(0.624706 - 6.96536i) q^{62} +(-36.7277 - 50.5514i) q^{63} +(-14.1247 + 62.4219i) q^{64} +32.0565 q^{65} +(37.6179 + 77.0575i) q^{66} +57.3989i q^{67} +(-43.3216 - 45.2544i) q^{68} +(-99.0646 + 71.9747i) q^{69} +(4.03131 - 44.9484i) q^{70} +(22.4655 - 7.29949i) q^{71} +(46.3617 - 17.4493i) q^{72} +(-34.4852 - 25.0550i) q^{73} +(-17.6526 + 41.3360i) q^{74} +(-18.5347 - 6.02228i) q^{75} +(-92.8080 - 49.8676i) q^{76} +(57.4120 + 95.0018i) q^{77} +(57.3493 + 95.9187i) q^{78} +(-66.8614 - 21.7246i) q^{79} +(33.5114 + 12.5294i) q^{80} +(79.5966 + 57.8303i) q^{81} +(-49.4621 - 43.1866i) q^{82} +(118.311 - 38.4415i) q^{83} +(141.706 - 68.3506i) q^{84} +(-28.3326 + 20.5849i) q^{85} +(28.3297 - 6.47537i) q^{86} -208.776i q^{87} +(-84.6874 + 23.9173i) q^{88} +153.780 q^{89} +(-6.17043 - 26.9956i) q^{90} +(85.0332 + 117.038i) q^{91} +(-54.5943 - 113.186i) q^{92} +(-4.21157 - 12.9619i) q^{93} +(-65.2615 + 74.7448i) q^{94} +(-34.6184 + 47.6482i) q^{95} +(22.4619 + 122.687i) q^{96} +(35.4826 - 109.204i) q^{97} +(90.6875 - 54.2216i) q^{98} +(51.5189 + 44.5553i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q+2q24q4+120q5+20q610q8+64q9+10q10+70q1220q1337q144q16+24q17+45q18+5q2015q2262q24120q25+12q26++158q98+O(q100) 96 q + 2 q^{2} - 4 q^{4} + 120 q^{5} + 20 q^{6} - 10 q^{8} + 64 q^{9} + 10 q^{10} + 70 q^{12} - 20 q^{13} - 37 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} + 5 q^{20} - 15 q^{22} - 62 q^{24} - 120 q^{25} + 12 q^{26}+ \cdots + 158 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/220Z)×\left(\mathbb{Z}/220\mathbb{Z}\right)^\times.

nn 101101 111111 177177
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\right) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.445649 + 1.94972i 0.222825 + 0.974859i
33 2.29101 + 3.15331i 0.763671 + 1.05110i 0.996900 + 0.0786807i 0.0250708π0.0250708\pi
−0.233229 + 0.972422i 0.574929π0.574929\pi
44 −3.60279 + 1.73778i −0.900698 + 0.434445i
55 0.690983 + 2.12663i 0.138197 + 0.425325i
66 −5.12707 + 5.87209i −0.854512 + 0.978682i
77 −5.93140 + 8.16388i −0.847343 + 1.16627i 0.137099 + 0.990557i 0.456222π0.456222\pi
−0.984442 + 0.175711i 0.943778π0.943778\pi
88 −4.99376 6.24999i −0.624220 0.781248i
99 −1.91346 + 5.88902i −0.212607 + 0.654336i
1010 −3.83838 + 2.29495i −0.383838 + 0.229495i
1111 4.27229 10.1364i 0.388390 0.921495i
1212 −13.7338 7.37944i −1.14448 0.614953i
1313 4.43010 13.6344i 0.340777 1.04880i −0.623029 0.782199i 0.714098π-0.714098\pi
0.963806 0.266604i 0.0859017π-0.0859017\pi
1414 −18.5606 7.92633i −1.32576 0.566167i
1515 −5.12286 + 7.05101i −0.341524 + 0.470067i
1616 9.96024 12.5217i 0.622515 0.782608i
1717 4.83979 + 14.8953i 0.284694 + 0.876197i 0.986490 + 0.163820i 0.0523815π0.0523815\pi
−0.701797 + 0.712377i 0.747619π0.747619\pi
1818 −12.3347 1.10627i −0.685259 0.0614592i
1919 15.4818 + 21.3089i 0.814833 + 1.12152i 0.990560 + 0.137082i 0.0437725π0.0437725\pi
−0.175727 + 0.984439i 0.556228π0.556228\pi
2020 −6.18508 6.46102i −0.309254 0.323051i
2121 −39.3321 −1.87296
2222 21.6671 + 3.81245i 0.984870 + 0.173293i
2323 31.4161i 1.36592i 0.730457 + 0.682959i 0.239307π0.239307\pi
−0.730457 + 0.682959i 0.760693π0.760693\pi
2424 8.26736 30.0657i 0.344473 1.25274i
2525 −4.04508 + 2.93893i −0.161803 + 0.117557i
2626 28.5576 + 2.56126i 1.09837 + 0.0985099i
2727 10.4088 3.38201i 0.385510 0.125260i
2828 7.18260 39.7202i 0.256521 1.41858i
2929 −43.3341 31.4841i −1.49428 1.08566i −0.972591 0.232522i 0.925302π-0.925302\pi
−0.521689 0.853136i 0.674698π-0.674698\pi
3030 −16.0305 6.84585i −0.534349 0.228195i
3131 −3.32552 1.08053i −0.107275 0.0348557i 0.254888 0.966971i 0.417961π-0.417961\pi
−0.362163 + 0.932115i 0.617961π0.617961\pi
3232 28.8526 + 13.8393i 0.901644 + 0.432480i
3333 41.7512 9.75089i 1.26519 0.295481i
3434 −26.8849 + 16.0743i −0.790731 + 0.472774i
3535 −21.4600 6.97278i −0.613143 0.199222i
3636 −3.34003 24.5421i −0.0927786 0.681725i
3737 18.1817 + 13.2098i 0.491397 + 0.357021i 0.805721 0.592295i 0.201778π-0.201778\pi
−0.314325 + 0.949316i 0.601778π0.601778\pi
3838 −34.6469 + 39.6815i −0.911760 + 1.04425i
3939 53.1430 17.2672i 1.36264 0.442749i
4040 9.84079 14.9385i 0.246020 0.373463i
4141 −26.5611 + 19.2978i −0.647831 + 0.470677i −0.862532 0.506003i 0.831122π-0.831122\pi
0.214701 + 0.976680i 0.431122π0.431122\pi
4242 −17.5283 76.6865i −0.417341 1.82587i
4343 14.5302i 0.337911i −0.985624 0.168956i 0.945961π-0.945961\pi
0.985624 0.168956i 0.0540394π-0.0540394\pi
4444 2.22275 + 43.9438i 0.0505171 + 0.998723i
4545 −13.8459 −0.307687
4646 −61.2525 + 14.0006i −1.33158 + 0.304360i
4747 29.1619 + 40.1379i 0.620465 + 0.853997i 0.997387 0.0722482i 0.0230174π-0.0230174\pi
−0.376922 + 0.926245i 0.623017π0.623017\pi
4848 62.3039 + 2.72027i 1.29800 + 0.0566723i
4949 −16.3255 50.2447i −0.333173 1.02540i
5050 −7.53276 6.57704i −0.150655 0.131541i
5151 −35.8816 + 49.3868i −0.703561 + 0.968368i
5252 7.73293 + 56.8206i 0.148710 + 1.09270i
5353 11.9385 36.7430i 0.225255 0.693264i −0.773010 0.634393i 0.781250π-0.781250\pi
0.998266 0.0588709i 0.0187500π-0.0187500\pi
5454 11.2326 + 18.7870i 0.208012 + 0.347907i
5555 24.5085 + 2.08145i 0.445609 + 0.0378445i
5656 80.6441 3.69727i 1.44007 0.0660226i
5757 −31.7245 + 97.6379i −0.556570 + 1.71295i
5858 42.0732 98.5201i 0.725400 1.69862i
5959 22.5711 31.0665i 0.382562 0.526551i −0.573699 0.819066i 0.694492π-0.694492\pi
0.956261 + 0.292515i 0.0944922π0.0944922\pi
6060 6.20349 34.3057i 0.103392 0.571762i
6161 16.8808 + 51.9537i 0.276734 + 0.851699i 0.988755 + 0.149542i 0.0477798π0.0477798\pi
−0.712022 + 0.702158i 0.752220π0.752220\pi
6262 0.624706 6.96536i 0.0100759 0.112345i
6363 −36.7277 50.5514i −0.582980 0.802403i
6464 −14.1247 + 62.4219i −0.220698 + 0.975342i
6565 32.0565 0.493177
6666 37.6179 + 77.0575i 0.569968 + 1.16754i
6767 57.3989i 0.856700i 0.903613 + 0.428350i 0.140905π0.140905\pi
−0.903613 + 0.428350i 0.859095π0.859095\pi
6868 −43.3216 45.2544i −0.637083 0.665505i
6969 −99.0646 + 71.9747i −1.43572 + 1.04311i
7070 4.03131 44.9484i 0.0575901 0.642120i
7171 22.4655 7.29949i 0.316416 0.102810i −0.146504 0.989210i 0.546802π-0.546802\pi
0.462919 + 0.886400i 0.346802π0.346802\pi
7272 46.3617 17.4493i 0.643912 0.242351i
7373 −34.4852 25.0550i −0.472400 0.343219i 0.325976 0.945378i 0.394307π-0.394307\pi
−0.798376 + 0.602159i 0.794307π0.794307\pi
7474 −17.6526 + 41.3360i −0.238549 + 0.558595i
7575 −18.5347 6.02228i −0.247129 0.0802971i
7676 −92.8080 49.8676i −1.22116 0.656152i
7777 57.4120 + 95.0018i 0.745611 + 1.23379i
7878 57.3493 + 95.9187i 0.735247 + 1.22973i
7979 −66.8614 21.7246i −0.846347 0.274995i −0.146432 0.989221i 0.546779π-0.546779\pi
−0.699915 + 0.714226i 0.746779π0.746779\pi
8080 33.5114 + 12.5294i 0.418892 + 0.156618i
8181 79.5966 + 57.8303i 0.982675 + 0.713955i
8282 −49.4621 43.1866i −0.603196 0.526665i
8383 118.311 38.4415i 1.42543 0.463151i 0.508108 0.861293i 0.330345π-0.330345\pi
0.917324 + 0.398143i 0.130345π0.130345\pi
8484 141.706 68.3506i 1.68697 0.813698i
8585 −28.3326 + 20.5849i −0.333325 + 0.242175i
8686 28.3297 6.47537i 0.329416 0.0752950i
8787 208.776i 2.39973i
8888 −84.6874 + 23.9173i −0.962357 + 0.271787i
8989 153.780 1.72787 0.863934 0.503605i 0.167993π-0.167993\pi
0.863934 + 0.503605i 0.167993π0.167993\pi
9090 −6.17043 26.9956i −0.0685603 0.299951i
9191 85.0332 + 117.038i 0.934431 + 1.28613i
9292 −54.5943 113.186i −0.593416 1.23028i
9393 −4.21157 12.9619i −0.0452857 0.139375i
9494 −65.2615 + 74.7448i −0.694271 + 0.795157i
9595 −34.6184 + 47.6482i −0.364404 + 0.501560i
9696 22.4619 + 122.687i 0.233978 + 1.27799i
9797 35.4826 109.204i 0.365800 1.12582i −0.583679 0.811985i 0.698387π-0.698387\pi
0.949479 0.313831i 0.101613π-0.101613\pi
9898 90.6875 54.2216i 0.925383 0.553282i
9999 51.5189 + 44.5553i 0.520393 + 0.450053i
100100 9.46640 17.6178i 0.0946640 0.176178i
101101 39.3577 121.130i 0.389680 1.19931i −0.543348 0.839507i 0.682844π-0.682844\pi
0.933028 0.359804i 0.117156π-0.117156\pi
102102 −112.281 47.9498i −1.10079 0.470096i
103103 −35.3665 + 48.6778i −0.343364 + 0.472600i −0.945420 0.325853i 0.894348π-0.894348\pi
0.602056 + 0.798454i 0.294348π0.294348\pi
104104 −107.338 + 40.3991i −1.03210 + 0.388453i
105105 −27.1778 83.6448i −0.258836 0.796617i
106106 76.9589 + 6.90225i 0.726027 + 0.0651156i
107107 −34.2590 47.1535i −0.320178 0.440687i 0.618344 0.785908i 0.287804π-0.287804\pi
−0.938522 + 0.345221i 0.887804π0.887804\pi
108108 −31.6234 + 30.2728i −0.292810 + 0.280304i
109109 42.1557 0.386750 0.193375 0.981125i 0.438057π-0.438057\pi
0.193375 + 0.981125i 0.438057π0.438057\pi
110110 6.86397 + 48.7123i 0.0623998 + 0.442839i
111111 87.5961i 0.789154i
112112 43.1476 + 155.586i 0.385247 + 1.38916i
113113 164.771 119.713i 1.45815 1.05941i 0.474315 0.880355i 0.342696π-0.342696\pi
0.983839 0.179056i 0.0573044π-0.0573044\pi
114114 −204.504 18.3415i −1.79390 0.160890i
115115 −66.8103 + 21.7080i −0.580959 + 0.188765i
116116 210.836 + 38.1255i 1.81755 + 0.328668i
117117 71.8167 + 52.1779i 0.613818 + 0.445965i
118118 70.6297 + 30.1626i 0.598557 + 0.255615i
119119 −150.311 48.8389i −1.26311 0.410411i
120120 69.6511 3.19327i 0.580425 0.0266106i
121121 −84.4951 86.6116i −0.698307 0.715799i
122122 −93.7720 + 56.0658i −0.768623 + 0.459556i
123123 −121.703 39.5439i −0.989459 0.321495i
124124 13.8589 1.88611i 0.111765 0.0152106i
125125 −9.04508 6.57164i −0.0723607 0.0525731i
126126 82.1932 94.1369i 0.652327 0.747118i
127127 −46.6425 + 15.1551i −0.367264 + 0.119331i −0.486834 0.873494i 0.661848π-0.661848\pi
0.119570 + 0.992826i 0.461848π0.461848\pi
128128 −128.000 + 0.279173i −0.999998 + 0.00218104i
129129 45.8181 33.2888i 0.355179 0.258053i
130130 14.2860 + 62.5011i 0.109892 + 0.480778i
131131 182.347i 1.39196i 0.718060 + 0.695981i 0.245030π0.245030\pi
−0.718060 + 0.695981i 0.754970π0.754970\pi
132132 −133.476 + 107.685i −1.01118 + 0.815794i
133133 −265.792 −1.99844
134134 −111.912 + 25.5798i −0.835161 + 0.190894i
135135 14.3846 + 19.7986i 0.106552 + 0.146657i
136136 68.9270 104.632i 0.506816 0.769356i
137137 14.0829 + 43.3427i 0.102795 + 0.316370i 0.989207 0.146528i 0.0468097π-0.0468097\pi
−0.886412 + 0.462898i 0.846810π0.846810\pi
138138 −184.478 161.073i −1.33680 1.16719i
139139 107.375 147.790i 0.772485 1.06323i −0.223587 0.974684i 0.571777π-0.571777\pi
0.996072 0.0885501i 0.0282233π-0.0282233\pi
140140 89.4332 12.1713i 0.638808 0.0869379i
141141 −59.7568 + 183.913i −0.423807 + 1.30434i
142142 24.2437 + 40.5484i 0.170730 + 0.285552i
143143 −119.278 103.156i −0.834113 0.721368i
144144 54.6822 + 82.6159i 0.379738 + 0.573721i
145145 37.0118 113.910i 0.255253 0.785589i
146146 33.4818 78.4021i 0.229327 0.537001i
147147 121.035 166.591i 0.823368 1.13327i
148148 −88.4605 15.9963i −0.597706 0.108083i
149149 5.08288 + 15.6435i 0.0341133 + 0.104990i 0.966663 0.256051i 0.0824215π-0.0824215\pi
−0.932550 + 0.361041i 0.882421π0.882421\pi
150150 3.48178 38.8212i 0.0232119 0.258808i
151151 −138.149 190.145i −0.914891 1.25924i −0.965469 0.260520i 0.916106π-0.916106\pi
0.0505772 0.998720i 0.483894π-0.483894\pi
152152 55.8678 203.173i 0.367551 1.33666i
153153 −96.9798 −0.633855
154154 −159.641 + 154.275i −1.03663 + 1.00178i
155155 7.81877i 0.0504437i
156156 −161.457 + 154.561i −1.03498 + 0.990776i
157157 −30.8588 + 22.4202i −0.196553 + 0.142804i −0.681709 0.731624i 0.738763π-0.738763\pi
0.485156 + 0.874428i 0.338763π0.338763\pi
158158 12.5601 140.042i 0.0794941 0.886344i
159159 143.213 46.5328i 0.900713 0.292659i
160160 −9.49447 + 70.9215i −0.0593405 + 0.443259i
161161 −256.477 186.342i −1.59303 1.15740i
162162 −77.2806 + 180.963i −0.477041 + 1.11706i
163163 −142.320 46.2426i −0.873129 0.283697i −0.162028 0.986786i 0.551803π-0.551803\pi
−0.711102 + 0.703089i 0.751803π0.751803\pi
164164 62.1588 115.683i 0.379017 0.705385i
165165 49.5859 + 82.0515i 0.300520 + 0.497282i
166166 127.675 + 213.541i 0.769128 + 1.28639i
167167 −15.8118 5.13756i −0.0946814 0.0307638i 0.261293 0.965259i 0.415851π-0.415851\pi
−0.355975 + 0.934496i 0.615851π0.615851\pi
168168 196.415 + 245.825i 1.16914 + 1.46325i
169169 −29.5483 21.4681i −0.174842 0.127030i
170170 −52.7611 46.0670i −0.310359 0.270982i
171171 −155.112 + 50.3991i −0.907090 + 0.294731i
172172 25.2503 + 52.3492i 0.146804 + 0.304356i
173173 178.159 129.440i 1.02982 0.748208i 0.0615472 0.998104i 0.480397π-0.480397\pi
0.968273 + 0.249896i 0.0803965π0.0803965\pi
174174 407.055 93.0410i 2.33939 0.534718i
175175 50.4555i 0.288317i
176176 −84.3728 154.458i −0.479391 0.877601i
177177 149.673 0.845610
178178 68.5321 + 299.828i 0.385012 + 1.68443i
179179 −26.8738 36.9886i −0.150133 0.206640i 0.727326 0.686292i 0.240763π-0.240763\pi
−0.877459 + 0.479652i 0.840763π0.840763\pi
180180 49.8840 24.0612i 0.277133 0.133673i
181181 −9.53021 29.3310i −0.0526531 0.162050i 0.921272 0.388918i 0.127151π-0.127151\pi
−0.973925 + 0.226869i 0.927151π0.927151\pi
182182 −190.296 + 217.949i −1.04558 + 1.19752i
183183 −125.152 + 172.257i −0.683890 + 0.941293i
184184 196.350 156.885i 1.06712 0.852633i
185185 −15.5290 + 47.7934i −0.0839406 + 0.258342i
186186 23.3951 13.9878i 0.125780 0.0752034i
187187 171.663 + 14.5789i 0.917983 + 0.0779620i
188188 −174.815 93.9315i −0.929867 0.499636i
189189 −34.1282 + 105.036i −0.180573 + 0.555746i
190190 −108.328 46.2617i −0.570148 0.243483i
191191 40.1389 55.2465i 0.210152 0.289249i −0.690909 0.722941i 0.742790π-0.742790\pi
0.901061 + 0.433693i 0.142790π0.142790\pi
192192 −229.195 + 98.4699i −1.19373 + 0.512864i
193193 −1.87513 5.77106i −0.00971570 0.0299019i 0.946081 0.323930i 0.105004π-0.105004\pi
−0.955797 + 0.294028i 0.905004π0.905004\pi
194194 228.730 + 20.5142i 1.17902 + 0.105743i
195195 73.4418 + 101.084i 0.376625 + 0.518379i
196196 146.132 + 152.651i 0.745570 + 0.778833i
197197 −299.121 −1.51838 −0.759191 0.650868i 0.774405π-0.774405\pi
−0.759191 + 0.650868i 0.774405π0.774405\pi
198198 −63.9108 + 120.303i −0.322782 + 0.607593i
199199 284.631i 1.43031i 0.698968 + 0.715153i 0.253643π0.253643\pi
−0.698968 + 0.715153i 0.746357π0.746357\pi
200200 38.5684 + 10.6054i 0.192842 + 0.0530271i
201201 −180.996 + 131.502i −0.900479 + 0.654237i
202202 253.710 + 22.7546i 1.25599 + 0.112647i
203203 514.064 167.030i 2.53234 0.822806i
204204 43.4506 240.285i 0.212993 1.17787i
205205 −59.3924 43.1511i −0.289719 0.210493i
206206 −110.669 47.2615i −0.537229 0.229425i
207207 −185.010 60.1134i −0.893769 0.290403i
208208 −126.602 191.275i −0.608663 0.919590i
209209 282.139 65.8930i 1.34995 0.315277i
210210 150.972 90.2653i 0.718914 0.429835i
211211 −120.100 39.0227i −0.569192 0.184942i 0.0102608 0.999947i 0.496734π-0.496734\pi
−0.579453 + 0.815006i 0.696734π0.696734\pi
212212 20.8392 + 153.124i 0.0982983 + 0.722283i
213213 74.4863 + 54.1175i 0.349701 + 0.254073i
214214 76.6685 87.8094i 0.358264 0.410324i
215215 30.9003 10.0401i 0.143722 0.0466982i
216216 −73.1164 48.1657i −0.338502 0.222989i
217217 28.5463 20.7401i 0.131550 0.0955765i
218218 18.7867 + 82.1917i 0.0861774 + 0.377026i
219219 166.144i 0.758647i
220220 −91.9162 + 35.0914i −0.417801 + 0.159506i
221221 224.530 1.01597
222222 −170.788 + 39.0372i −0.769314 + 0.175843i
223223 −86.9465 119.672i −0.389894 0.536644i 0.568277 0.822837i 0.307610π-0.307610\pi
−0.958172 + 0.286193i 0.907610π0.907610\pi
224224 −284.119 + 153.462i −1.26839 + 0.685100i
225225 −9.56730 29.4451i −0.0425213 0.130867i
226226 306.838 + 267.907i 1.35769 + 1.18543i
227227 160.251 220.566i 0.705950 0.971657i −0.293925 0.955829i 0.594961π-0.594961\pi
0.999875 0.0158285i 0.00503857π-0.00503857\pi
228228 −55.3765 406.899i −0.242879 1.78465i
229229 −17.6079 + 54.1915i −0.0768903 + 0.236644i −0.982113 0.188294i 0.939704π-0.939704\pi
0.905222 + 0.424938i 0.139704π0.139704\pi
230230 −72.0984 120.587i −0.313471 0.524292i
231231 −168.038 + 398.688i −0.727438 + 1.72592i
232232 19.6252 + 428.062i 0.0845915 + 1.84509i
233233 −57.1928 + 176.021i −0.245463 + 0.755457i 0.750097 + 0.661328i 0.230007π0.230007\pi
−0.995560 + 0.0941291i 0.969993π0.969993\pi
234234 −69.7270 + 163.275i −0.297979 + 0.697758i
235235 −65.2079 + 89.7510i −0.277480 + 0.381919i
236236 −27.3324 + 151.150i −0.115815 + 0.640465i
237237 −84.6760 260.606i −0.357283 1.09960i
238238 28.2361 314.828i 0.118639 1.32281i
239239 −132.395 182.225i −0.553952 0.762449i 0.436590 0.899661i 0.356186π-0.356186\pi
−0.990542 + 0.137211i 0.956186π0.956186\pi
240240 37.2659 + 134.377i 0.155275 + 0.559903i
241241 −454.253 −1.88487 −0.942433 0.334394i 0.891468π-0.891468\pi
−0.942433 + 0.334394i 0.891468π0.891468\pi
242242 131.213 203.340i 0.542202 0.840248i
243243 284.983i 1.17277i
244244 −151.102 157.843i −0.619270 0.646898i
245245 95.5711 69.4365i 0.390086 0.283414i
246246 22.8623 254.910i 0.0929360 1.03622i
247247 359.121 116.685i 1.45393 0.472411i
248248 9.85358 + 26.1804i 0.0397322 + 0.105566i
249249 392.269 + 285.000i 1.57538 + 1.14458i
250250 8.78190 20.5640i 0.0351276 0.0822560i
251251 −106.411 34.5752i −0.423950 0.137750i 0.0892687 0.996008i 0.471547π-0.471547\pi
−0.513219 + 0.858258i 0.671547π0.671547\pi
252252 220.170 + 118.302i 0.873689 + 0.469450i
253253 318.448 + 134.219i 1.25869 + 0.530508i
254254 −50.3343 84.1859i −0.198167 0.331441i
255255 −129.821 42.1813i −0.509101 0.165417i
256256 −57.5873 249.439i −0.224950 0.974370i
257257 229.966 + 167.080i 0.894811 + 0.650118i 0.937128 0.348986i 0.113474π-0.113474\pi
−0.0423168 + 0.999104i 0.513474π0.513474\pi
258258 85.3226 + 74.4972i 0.330708 + 0.288749i
259259 −215.686 + 70.0805i −0.832763 + 0.270581i
260260 −115.493 + 55.7071i −0.444203 + 0.214258i
261261 268.328 194.952i 1.02808 0.746943i
262262 −355.525 + 81.2629i −1.35697 + 0.310164i
263263 140.080i 0.532624i 0.963887 + 0.266312i 0.0858052π0.0858052\pi
−0.963887 + 0.266312i 0.914195π0.914195\pi
264264 −269.438 212.251i −1.02060 0.803980i
265265 86.3880 0.325992
266266 −118.450 518.220i −0.445301 1.94819i
267267 352.312 + 484.917i 1.31952 + 1.81617i
268268 −99.7467 206.796i −0.372189 0.771628i
269269 57.8515 + 178.049i 0.215061 + 0.661891i 0.999149 + 0.0412410i 0.0131311π0.0131311\pi
−0.784088 + 0.620650i 0.786869π0.786869\pi
270270 −32.1913 + 36.8691i −0.119227 + 0.136552i
271271 −224.294 + 308.714i −0.827651 + 1.13916i 0.160704 + 0.987003i 0.448623π0.448623\pi
−0.988356 + 0.152162i 0.951377π0.951377\pi
272272 234.721 + 87.7587i 0.862945 + 0.322642i
273273 −174.245 + 536.271i −0.638261 + 1.96436i
274274 −78.2300 + 46.7733i −0.285511 + 0.170706i
275275 12.5085 + 53.5587i 0.0454855 + 0.194759i
276276 231.833 431.462i 0.839975 1.56327i
277277 109.054 335.633i 0.393696 1.21167i −0.536277 0.844042i 0.680170π-0.680170\pi
0.929973 0.367629i 0.119830π-0.119830\pi
278278 336.000 + 143.489i 1.20863 + 0.516149i
279279 12.7265 17.5165i 0.0456147 0.0627832i
280280 63.5864 + 168.945i 0.227094 + 0.603376i
281281 −26.0818 80.2716i −0.0928178 0.285664i 0.893861 0.448344i 0.147986π-0.147986\pi
−0.986679 + 0.162680i 0.947986π0.947986\pi
282282 −385.208 34.5484i −1.36599 0.122512i
283283 92.0563 + 126.705i 0.325287 + 0.447719i 0.940072 0.340975i 0.110757π-0.110757\pi
−0.614785 + 0.788695i 0.710757π0.710757\pi
284284 −68.2537 + 65.3387i −0.240330 + 0.230066i
285285 −229.560 −0.805475
286286 147.968 278.530i 0.517371 0.973881i
287287 331.304i 1.15437i
288288 −136.708 + 143.433i −0.474682 + 0.498030i
289289 35.3581 25.6892i 0.122346 0.0888899i
290290 238.587 + 21.3983i 0.822715 + 0.0737873i
291291 425.645 138.301i 1.46270 0.475260i
292292 167.783 + 30.3402i 0.574600 + 0.103905i
293293 80.9237 + 58.7945i 0.276190 + 0.200664i 0.717254 0.696812i 0.245399π-0.245399\pi
−0.441064 + 0.897476i 0.645399π0.645399\pi
294294 378.744 + 161.743i 1.28824 + 0.550147i
295295 81.6631 + 26.5340i 0.276824 + 0.0899456i
296296 −8.23414 179.602i −0.0278181 0.606762i
297297 10.1876 119.957i 0.0343018 0.403895i
298298 −28.2352 + 16.8817i −0.0947490 + 0.0566500i
299299 428.341 + 139.176i 1.43258 + 0.465473i
300300 77.2420 10.5122i 0.257473 0.0350405i
301301 118.623 + 86.1844i 0.394095 + 0.286327i
302302 309.164 354.089i 1.02372 1.17248i
303303 472.130 153.404i 1.55819 0.506285i
304304 421.027 + 18.3826i 1.38496 + 0.0604690i
305305 −98.8217 + 71.7982i −0.324006 + 0.235404i
306306 −43.2190 189.083i −0.141238 0.617919i
307307 242.867i 0.791098i −0.918445 0.395549i 0.870554π-0.870554\pi
0.918445 0.395549i 0.129446π-0.129446\pi
308308 −371.936 242.502i −1.20758 0.787345i
309309 −234.521 −0.758969
310310 15.2444 3.48443i 0.0491754 0.0112401i
311311 −131.087 180.426i −0.421501 0.580147i 0.544475 0.838777i 0.316729π-0.316729\pi
−0.965976 + 0.258630i 0.916729π0.916729\pi
312312 −373.303 245.915i −1.19648 0.788188i
313313 −59.1509 182.048i −0.188981 0.581623i 0.811014 0.585027i 0.198916π-0.198916\pi
−0.999994 + 0.00340475i 0.998916π0.998916\pi
314314 −57.4652 50.1743i −0.183010 0.159791i
315315 82.1257 113.036i 0.260717 0.358846i
316316 278.640 37.9213i 0.881774 0.120004i
317317 38.2517 117.727i 0.120668 0.371378i −0.872419 0.488759i 0.837450π-0.837450\pi
0.993087 + 0.117381i 0.0374499π0.0374499\pi
318318 154.549 + 258.488i 0.486002 + 0.812856i
319319 −504.273 + 304.745i −1.58079 + 0.955313i
320320 −142.508 + 13.0946i −0.445338 + 0.0409205i
321321 70.2017 216.059i 0.218697 0.673080i
322322 249.014 583.101i 0.773337 1.81087i
323323 −242.475 + 333.738i −0.750696 + 1.03324i
324324 −387.267 70.0293i −1.19527 0.216140i
325325 22.1505 + 68.1722i 0.0681553 + 0.209761i
326326 26.7351 298.092i 0.0820096 0.914392i
327327 96.5792 + 132.930i 0.295349 + 0.406514i
328328 253.250 + 69.6380i 0.772105 + 0.212311i
329329 −500.651 −1.52174
330330 −137.879 + 133.245i −0.417816 + 0.403772i
331331 40.8096i 0.123292i −0.998098 0.0616459i 0.980365π-0.980365\pi
0.998098 0.0616459i 0.0196350π-0.0196350\pi
332332 −359.446 + 344.095i −1.08267 + 1.03643i
333333 −112.582 + 81.7959i −0.338085 + 0.245633i
334334 2.97028 33.1181i 0.00889305 0.0991559i
335335 −122.066 + 39.6617i −0.364376 + 0.118393i
336336 −391.757 + 492.506i −1.16594 + 1.46579i
337337 370.611 + 269.265i 1.09974 + 0.799005i 0.981017 0.193923i 0.0621212π-0.0621212\pi
0.118719 + 0.992928i 0.462121π0.462121\pi
338338 28.6885 67.1780i 0.0848773 0.198752i
339339 754.987 + 245.310i 2.22710 + 0.723628i
340340 66.3047 123.399i 0.195014 0.362938i
341341 −25.1603 + 29.0926i −0.0737838 + 0.0853157i
342342 −167.390 279.965i −0.489444 0.818611i
343343 36.7614 + 11.9445i 0.107176 + 0.0348236i
344344 −90.8134 + 72.5603i −0.263993 + 0.210931i
345345 −221.515 160.940i −0.642073 0.466493i
346346 331.768 + 289.674i 0.958866 + 0.837209i
347347 −280.498 + 91.1393i −0.808351 + 0.262649i −0.683899 0.729576i 0.739717π-0.739717\pi
−0.124452 + 0.992226i 0.539717π0.539717\pi
348348 362.807 + 752.178i 1.04255 + 2.16143i
349349 −265.125 + 192.625i −0.759671 + 0.551933i −0.898809 0.438340i 0.855567π-0.855567\pi
0.139138 + 0.990273i 0.455567π0.455567\pi
350350 98.3740 22.4855i 0.281069 0.0642442i
351351 156.900i 0.447009i
352352 263.548 233.337i 0.748717 0.662890i
353353 45.2529 0.128195 0.0640975 0.997944i 0.479583π-0.479583\pi
0.0640975 + 0.997944i 0.479583π0.479583\pi
354354 66.7017 + 291.820i 0.188423 + 0.824350i
355355 31.0466 + 42.7320i 0.0874552 + 0.120372i
356356 −554.039 + 267.236i −1.55629 + 0.750664i
357357 −190.359 585.866i −0.533219 1.64108i
358358 60.1410 68.8803i 0.167992 0.192403i
359359 87.1505 119.952i 0.242759 0.334129i −0.670200 0.742181i 0.733792π-0.733792\pi
0.912959 + 0.408052i 0.133792π0.133792\pi
360360 69.1432 + 86.5368i 0.192065 + 0.240380i
361361 −102.827 + 316.470i −0.284840 + 0.876648i
362362 52.9399 31.6525i 0.146243 0.0874379i
363363 79.5337 464.867i 0.219101 1.28063i
364364 −509.744 273.895i −1.40039 0.752459i
365365 29.4539 90.6497i 0.0806956 0.248355i
366366 −391.626 167.245i −1.07002 0.456952i
367367 −226.710 + 312.039i −0.617737 + 0.850243i −0.997186 0.0749703i 0.976114π-0.976114\pi
0.379448 + 0.925213i 0.376114π0.376114\pi
368368 393.384 + 312.912i 1.06898 + 0.850304i
369369 −62.8213 193.344i −0.170248 0.523968i
370370 −100.104 8.97808i −0.270551 0.0242651i
371371 229.153 + 315.402i 0.617663 + 0.850141i
372372 37.6983 + 39.3802i 0.101340 + 0.105861i
373373 −303.778 −0.814418 −0.407209 0.913335i 0.633498π-0.633498\pi
−0.407209 + 0.913335i 0.633498π0.633498\pi
374374 48.0767 + 341.191i 0.128547 + 0.912276i
375375 43.5776i 0.116207i
376376 105.234 382.700i 0.279877 1.01782i
377377 −621.242 + 451.359i −1.64786 + 1.19724i
378378 −220.000 19.7312i −0.582010 0.0521990i
379379 −288.379 + 93.7002i −0.760896 + 0.247230i −0.663663 0.748032i 0.730999π-0.730999\pi
−0.0972327 + 0.995262i 0.530999π0.530999\pi
380380 41.9210 231.826i 0.110318 0.610068i
381381 −154.647 112.358i −0.405898 0.294902i
382382 125.603 + 53.6390i 0.328804 + 0.140416i
383383 −61.1702 19.8754i −0.159713 0.0518940i 0.228069 0.973645i 0.426759π-0.426759\pi
−0.387782 + 0.921751i 0.626759π0.626759\pi
384384 −294.129 402.983i −0.765961 1.04943i
385385 −162.363 + 187.739i −0.421721 + 0.487633i
386386 10.4163 6.22784i 0.0269852 0.0161343i
387387 85.5685 + 27.8029i 0.221107 + 0.0718421i
388388 61.9364 + 455.101i 0.159630 + 1.17294i
389389 101.467 + 73.7198i 0.260840 + 0.189511i 0.710517 0.703680i 0.248461π-0.248461\pi
−0.449678 + 0.893191i 0.648461π0.648461\pi
390390 −164.356 + 188.239i −0.421425 + 0.482663i
391391 −467.954 + 152.047i −1.19681 + 0.388868i
392392 −232.503 + 352.944i −0.593120 + 0.900368i
393393 −574.996 + 417.759i −1.46309 + 1.06300i
394394 −133.303 583.202i −0.338333 1.48021i
395395 157.201i 0.397976i
396396 −263.039 70.9949i −0.664241 0.179280i
397397 77.6330 0.195549 0.0977746 0.995209i 0.468828π-0.468828\pi
0.0977746 + 0.995209i 0.468828π0.468828\pi
398398 −554.949 + 126.845i −1.39435 + 0.318707i
399399 −608.933 838.125i −1.52615 2.10056i
400400 −3.48958 + 79.9239i −0.00872395 + 0.199810i
401401 −225.616 694.376i −0.562634 1.73161i −0.674878 0.737930i 0.735804π-0.735804\pi
0.112243 0.993681i 0.464196π-0.464196\pi
402402 −337.052 294.288i −0.838437 0.732060i
403403 −29.4648 + 40.5548i −0.0731136 + 0.100632i
404404 68.7006 + 504.803i 0.170051 + 1.24951i
405405 −67.9836 + 209.232i −0.167861 + 0.516623i
406406 554.753 + 927.843i 1.36639 + 2.28533i
407407 211.577 127.862i 0.519846 0.314157i
408408 487.851 22.3664i 1.19571 0.0548195i
409409 23.9146 73.6017i 0.0584710 0.179955i −0.917555 0.397609i 0.869840π-0.869840\pi
0.976026 + 0.217653i 0.0698402π0.0698402\pi
410410 57.6642 135.029i 0.140644 0.329338i
411411 −104.409 + 143.706i −0.254036 + 0.349651i
412412 42.8269 236.835i 0.103949 0.574843i
413413 119.745 + 368.536i 0.289938 + 0.892339i
414414 34.7545 387.507i 0.0839482 0.936007i
415415 163.502 + 225.041i 0.393980 + 0.542266i
416416 316.512 332.079i 0.760845 0.798268i
417417 712.024 1.70749
418418 254.208 + 520.727i 0.608153 + 1.24576i
419419 40.6843i 0.0970985i 0.998821 + 0.0485493i 0.0154598π0.0154598\pi
−0.998821 + 0.0485493i 0.984540π0.984540\pi
420420 243.272 + 254.126i 0.579220 + 0.605061i
421421 475.690 345.609i 1.12991 0.820924i 0.144224 0.989545i 0.453931π-0.453931\pi
0.985681 + 0.168621i 0.0539313π0.0539313\pi
422422 22.5610 251.551i 0.0534620 0.596092i
423423 −292.173 + 94.9327i −0.690716 + 0.224427i
424424 −289.261 + 108.870i −0.682220 + 0.256769i
425425 −63.3537 46.0292i −0.149068 0.108304i
426426 −72.3190 + 169.345i −0.169763 + 0.397523i
427427 −524.270 170.346i −1.22780 0.398936i
428428 205.371 + 110.350i 0.479838 + 0.257826i
429429 52.0140 612.452i 0.121245 1.42763i
430430 33.3461 + 55.7724i 0.0775490 + 0.129703i
431431 93.6683 + 30.4347i 0.217328 + 0.0706141i 0.415657 0.909521i 0.363552π-0.363552\pi
−0.198329 + 0.980135i 0.563552π0.563552\pi
432432 61.3251 164.021i 0.141956 0.379679i
433433 256.526 + 186.377i 0.592440 + 0.430433i 0.843187 0.537620i 0.180676π-0.180676\pi
−0.250748 + 0.968052i 0.580676π0.580676\pi
434434 53.1590 + 46.4144i 0.122486 + 0.106946i
435435 443.989 144.261i 1.02066 0.331634i
436436 −151.878 + 73.2574i −0.348345 + 0.168021i
437437 −669.443 + 486.379i −1.53191 + 1.11299i
438438 323.933 74.0418i 0.739573 0.169045i
439439 142.749i 0.325168i −0.986695 0.162584i 0.948017π-0.948017\pi
0.986695 0.162584i 0.0519828π-0.0519828\pi
440440 −109.381 163.572i −0.248593 0.371755i
441441 327.130 0.741792
442442 100.062 + 437.771i 0.226384 + 0.990432i
443443 167.484 + 230.522i 0.378068 + 0.520365i 0.955071 0.296376i 0.0957782π-0.0957782\pi
−0.577004 + 0.816742i 0.695778π0.695778\pi
444444 −152.223 315.591i −0.342844 0.710790i
445445 106.260 + 327.033i 0.238786 + 0.734906i
446446 194.578 222.853i 0.436274 0.499669i
447447 −37.6838 + 51.8673i −0.0843038 + 0.116034i
448448 −425.826 485.562i −0.950504 1.08384i
449449 −128.570 + 395.697i −0.286347 + 0.881285i 0.699645 + 0.714491i 0.253342π0.253342\pi
−0.985992 + 0.166794i 0.946658π0.946658\pi
450450 53.1460 31.7757i 0.118102 0.0706127i
451451 82.1341 + 351.680i 0.182116 + 0.779779i
452452 −385.602 + 717.639i −0.853101 + 1.58770i
453453 283.086 871.250i 0.624914 1.92329i
454454 501.457 + 214.148i 1.10453 + 0.471692i
455455 −190.140 + 261.705i −0.417890 + 0.575176i
456456 768.660 289.303i 1.68566 0.634436i
457457 62.0743 + 191.045i 0.135830 + 0.418042i 0.995718 0.0924406i 0.0294668π-0.0294668\pi
−0.859888 + 0.510482i 0.829467π0.829467\pi
458458 −113.505 10.1800i −0.247827 0.0222270i
459459 100.753 + 138.674i 0.219504 + 0.302122i
460460 202.980 194.311i 0.441261 0.422415i
461461 853.193 1.85074 0.925372 0.379060i 0.123753π-0.123753\pi
0.925372 + 0.379060i 0.123753π0.123753\pi
462462 −852.215 149.952i −1.84462 0.324571i
463463 190.986i 0.412496i 0.978500 + 0.206248i 0.0661254π0.0661254\pi
−0.978500 + 0.206248i 0.933875π0.933875\pi
464464 −825.853 + 229.029i −1.77986 + 0.493597i
465465 24.6550 17.9129i 0.0530215 0.0385223i
466466 −368.680 33.0660i −0.791159 0.0709571i
467467 −598.229 + 194.376i −1.28100 + 0.416223i −0.868933 0.494929i 0.835194π-0.835194\pi
−0.412070 + 0.911152i 0.635194π0.635194\pi
468468 −349.414 63.1845i −0.746612 0.135010i
469469 −468.597 340.456i −0.999142 0.725919i
470470 −204.049 87.1395i −0.434147 0.185403i
471471 −141.396 45.9422i −0.300203 0.0975418i
472472 −306.880 + 14.0694i −0.650170 + 0.0298081i
473473 −147.284 62.0771i −0.311384 0.131241i
474474 470.372 281.233i 0.992346 0.593319i
475475 −125.251 40.6964i −0.263685 0.0856766i
476476 626.409 85.2504i 1.31599 0.179097i
477477 193.536 + 140.612i 0.405737 + 0.294785i
478478 296.286 339.340i 0.619846 0.709917i
479479 679.143 220.667i 1.41784 0.460683i 0.502922 0.864332i 0.332258π-0.332258\pi
0.914914 + 0.403649i 0.132258π0.132258\pi
480480 −245.389 + 132.543i −0.511227 + 0.276131i
481481 260.654 189.376i 0.541901 0.393714i
482482 −202.438 885.665i −0.419995 1.83748i
483483 1235.66i 2.55831i
484484 454.930 + 165.210i 0.939939 + 0.341343i
485485 256.754 0.529390
486486 −555.636 + 127.002i −1.14328 + 0.261322i
487487 −396.275 545.426i −0.813706 1.11997i −0.990741 0.135766i 0.956650π-0.956650\pi
0.177035 0.984205i 0.443350π-0.443350\pi
488488 240.411 364.949i 0.492646 0.747846i
489489 −180.240 554.721i −0.368589 1.13440i
490490 177.973 + 155.392i 0.363210 + 0.317127i
491491 158.938 218.759i 0.323703 0.445539i −0.615890 0.787832i 0.711204π-0.711204\pi
0.939593 + 0.342293i 0.111204π0.111204\pi
492492 507.191 69.0256i 1.03088 0.140296i
493493 259.238 797.853i 0.525838 1.61836i
494494 387.546 + 648.183i 0.784505 + 1.31211i
495495 −59.1537 + 140.348i −0.119503 + 0.283532i
496496 −46.6530 + 30.8790i −0.0940586 + 0.0622560i
497497 −73.6599 + 226.702i −0.148209 + 0.456141i
498498 −380.856 + 891.825i −0.764770 + 1.79081i
499499 −87.4694 + 120.391i −0.175289 + 0.241265i −0.887617 0.460582i 0.847641π-0.847641\pi
0.712328 + 0.701847i 0.247641π0.247641\pi
500500 44.0076 + 7.95789i 0.0880153 + 0.0159158i
501501 −20.0247 61.6296i −0.0399694 0.123013i
502502 19.9896 222.881i 0.0398200 0.443985i
503503 159.226 + 219.155i 0.316552 + 0.435697i 0.937411 0.348226i 0.113216π-0.113216\pi
−0.620858 + 0.783923i 0.713216π0.713216\pi
504504 −132.536 + 481.990i −0.262968 + 0.956329i
505505 284.795 0.563950
506506 −119.772 + 680.697i −0.236704 + 1.34525i
507507 142.358i 0.280786i
508508 141.707 135.655i 0.278951 0.267038i
509509 752.384 546.639i 1.47816 1.07395i 0.500018 0.866015i 0.333327π-0.333327\pi
0.978143 0.207932i 0.0666733π-0.0666733\pi
510510 24.3871 271.912i 0.0478179 0.533161i
511511 409.091 132.922i 0.800570 0.260121i
512512 460.671 223.441i 0.899749 0.436409i
513513 233.214 + 169.440i 0.454607 + 0.330292i
514514 −223.275 + 522.829i −0.434387 + 1.01718i
515515 −127.957 41.5758i −0.248461 0.0807298i
516516 −107.225 + 199.555i −0.207800 + 0.386734i
517517 531.443 124.117i 1.02794 0.240072i
518518 −232.757 389.295i −0.449339 0.751534i
519519 816.328 + 265.241i 1.57289 + 0.511062i
520520 −160.082 200.353i −0.307851 0.385294i
521521 −385.014 279.729i −0.738990 0.536908i 0.153405 0.988163i 0.450976π-0.450976\pi
−0.892395 + 0.451256i 0.850976π0.850976\pi
522522 499.682 + 436.284i 0.957245 + 0.835794i
523523 121.680 39.5362i 0.232658 0.0755951i −0.190368 0.981713i 0.560968π-0.560968\pi
0.423026 + 0.906118i 0.360968π0.360968\pi
524524 −316.879 656.959i −0.604731 1.25374i
525525 159.102 115.594i 0.303051 0.220179i
526526 −273.117 + 62.4266i −0.519233 + 0.118682i
527527 54.7643i 0.103917i
528528 293.754 619.918i 0.556352 1.17409i
529529 −457.972 −0.865731
530530 38.4988 + 168.432i 0.0726392 + 0.317796i
531531 139.762 + 192.366i 0.263206 + 0.362272i
532532 957.594 461.888i 1.79999 0.868211i
533533 145.446 + 447.636i 0.272882 + 0.839843i
534534 −788.442 + 903.012i −1.47648 + 1.69103i
535535 76.6056 105.439i 0.143188 0.197081i
536536 358.742 286.636i 0.669295 0.534770i
537537 55.0683 169.483i 0.102548 0.315610i
538538 −321.363 + 192.141i −0.597329 + 0.357140i
539539 −579.050 49.1773i −1.07430 0.0912380i
540540 −86.2303 46.3332i −0.159686 0.0858023i
541541 −127.830 + 393.421i −0.236285 + 0.727211i 0.760663 + 0.649147i 0.224874π0.224874\pi
−0.996948 + 0.0780645i 0.975126π0.975126\pi
542542 −701.860 299.731i −1.29495 0.553009i
543543 70.6557 97.2493i 0.130121 0.179096i
544544 −66.5013 + 496.749i −0.122245 + 0.913142i
545545 29.1289 + 89.6495i 0.0534475 + 0.164494i
546546 −1123.23 100.740i −2.05720 0.184505i
547547 227.278 + 312.821i 0.415499 + 0.571885i 0.964549 0.263904i 0.0850103π-0.0850103\pi
−0.549050 + 0.835790i 0.685010π0.685010\pi
548548 −126.058 131.682i −0.230033 0.240295i
549549 −338.257 −0.616133
550550 −98.8500 + 48.2565i −0.179727 + 0.0877390i
551551 1410.83i 2.56050i
552552 944.546 + 259.728i 1.71113 + 0.470522i
553553 573.939 416.991i 1.03786 0.754053i
554554 702.989 + 63.0493i 1.26893 + 0.113807i
555555 −186.284 + 60.5274i −0.335647 + 0.109058i
556556 −130.026 + 719.050i −0.233859 + 1.29326i
557557 579.184 + 420.802i 1.03983 + 0.755479i 0.970252 0.242097i 0.0778353π-0.0778353\pi
0.0695761 + 0.997577i 0.477835π0.477835\pi
558558 39.8238 + 17.0068i 0.0713688 + 0.0304782i
559559 −198.111 64.3701i −0.354402 0.115152i
560560 −301.058 + 199.266i −0.537604 + 0.355832i
561561 347.310 + 574.706i 0.619091 + 1.02443i
562562 144.884 86.6251i 0.257800 0.154137i
563563 909.437 + 295.494i 1.61534 + 0.524856i 0.970836 0.239744i 0.0770636π-0.0770636\pi
0.644505 + 0.764600i 0.277064π0.277064\pi
564564 −104.308 766.443i −0.184944 1.35894i
565565 368.440 + 267.687i 0.652106 + 0.473783i
566566 −206.013 + 235.950i −0.363981 + 0.416872i
567567 −944.240 + 306.802i −1.66533 + 0.541097i
568568 −157.809 103.957i −0.277833 0.183023i
569569 247.679 179.950i 0.435289 0.316256i −0.348471 0.937319i 0.613299π-0.613299\pi
0.783760 + 0.621064i 0.213299π0.213299\pi
570570 −102.303 447.578i −0.179480 0.785225i
571571 17.5331i 0.0307059i −0.999882 0.0153529i 0.995113π-0.995113\pi
0.999882 0.0153529i 0.00488718π-0.00488718\pi
572572 608.996 + 164.369i 1.06468 + 0.287359i
573573 266.168 0.464517
574574 645.949 147.645i 1.12535 0.257222i
575575 −92.3296 127.081i −0.160573 0.221010i
576576 −340.577 202.622i −0.591279 0.351775i
577577 −135.283 416.359i −0.234460 0.721593i −0.997193 0.0748790i 0.976143π-0.976143\pi
0.762733 0.646714i 0.223857π-0.223857\pi
578578 65.8440 + 57.4900i 0.113917 + 0.0994636i
579579 13.9020 19.1344i 0.0240103 0.0330474i
580580 64.6057 + 474.714i 0.111389 + 0.818473i
581581 −387.917 + 1193.89i −0.667672 + 2.05488i
582582 459.335 + 768.254i 0.789236 + 1.32002i
583583 −321.439 277.991i −0.551353 0.476828i
584584 15.6177 + 340.651i 0.0267427 + 0.583306i
585585 −61.3388 + 188.781i −0.104853 + 0.322703i
586586 −78.5691 + 183.980i −0.134077 + 0.313959i
587587 −572.907 + 788.538i −0.975991 + 1.34334i −0.0370295 + 0.999314i 0.511790π0.511790\pi
−0.938962 + 0.344022i 0.888210π0.888210\pi
588588 −146.567 + 810.524i −0.249263 + 1.37844i
589589 −28.4603 87.5917i −0.0483197 0.148713i
590590 −15.3406 + 171.045i −0.0260010 + 0.289907i
591591 −685.290 943.221i −1.15954 1.59598i
592592 346.503 96.0936i 0.585309 0.162320i
593593 −698.683 −1.17822 −0.589109 0.808054i 0.700521π-0.700521\pi
−0.589109 + 0.808054i 0.700521π0.700521\pi
594594 238.422 33.5957i 0.401384 0.0565584i
595595 353.401i 0.593952i
596596 −45.4975 47.5274i −0.0763381 0.0797439i
597597 −897.528 + 652.092i −1.50340 + 1.09228i
598598 −80.4647 + 897.167i −0.134556 + 1.50028i
599599 −591.792 + 192.285i −0.987967 + 0.321010i −0.758047 0.652199i 0.773846π-0.773846\pi
−0.229920 + 0.973210i 0.573846π0.573846\pi
600600 54.9186 + 145.915i 0.0915310 + 0.243192i
601601 −591.649 429.858i −0.984441 0.715238i −0.0257443 0.999669i 0.508196π-0.508196\pi
−0.958697 + 0.284430i 0.908196π0.908196\pi
602602 −115.171 + 269.689i −0.191314 + 0.447988i
603603 −338.023 109.830i −0.560569 0.182140i
604604 828.151 + 444.982i 1.37111 + 0.736725i
605605 125.806 239.537i 0.207944 0.395929i
606606 509.500 + 852.156i 0.840759 + 1.40620i
607607 −722.955 234.902i −1.19103 0.386989i −0.354576 0.935027i 0.615375π-0.615375\pi
−0.836453 + 0.548038i 0.815375π0.815375\pi
608608 151.790 + 829.076i 0.249654 + 1.36361i
609609 1704.42 + 1238.34i 2.79872 + 2.03339i
610610 −184.026 160.678i −0.301682 0.263406i
611611 676.447 219.791i 1.10711 0.359723i
612612 349.398 168.530i 0.570912 0.275375i
613613 −505.486 + 367.257i −0.824611 + 0.599115i −0.918029 0.396512i 0.870220π-0.870220\pi
0.0934189 + 0.995627i 0.470220π0.470220\pi
614614 473.522 108.234i 0.771209 0.176276i
615615 286.142i 0.465272i
616616 307.058 833.241i 0.498470 1.35266i
617617 −11.7045 −0.0189700 −0.00948501 0.999955i 0.503019π-0.503019\pi
−0.00948501 + 0.999955i 0.503019π0.503019\pi
618618 −104.514 457.250i −0.169117 0.739887i
619619 −427.221 588.019i −0.690179 0.949950i 0.309820 0.950795i 0.399731π-0.399731\pi
−1.00000 0.000844784i 0.999731π0.999731\pi
620620 13.5873 + 28.1694i 0.0219150 + 0.0454345i
621621 106.250 + 327.003i 0.171094 + 0.526575i
622622 293.360 335.989i 0.471640 0.540175i
623623 −912.133 + 1255.44i −1.46410 + 2.01516i
624624 313.102 837.427i 0.501765 1.34203i
625625 7.72542 23.7764i 0.0123607 0.0380423i
626626 328.581 196.457i 0.524890 0.313829i
627627 854.165 + 738.711i 1.36231 + 1.17817i
628628 72.2163 134.401i 0.114994 0.214014i
629629 −108.768 + 334.755i −0.172923 + 0.532202i
630630 256.988 + 109.747i 0.407918 + 0.174202i
631631 621.792 855.823i 0.985407 1.35630i 0.0515422 0.998671i 0.483586π-0.483586\pi
0.933865 0.357626i 0.116414π-0.116414\pi
632632 198.112 + 526.371i 0.313468 + 0.832865i
633633 −152.099 468.112i −0.240283 0.739514i
634634 246.581 + 22.1152i 0.388928 + 0.0348820i
635635 −64.4584 88.7194i −0.101509 0.139716i
636636 −435.104 + 416.521i −0.684126 + 0.654908i
637637 −757.382 −1.18898
638638 −818.895 847.379i −1.28353 1.32818i
639639 146.267i 0.228900i
640640 −89.0393 272.015i −0.139124 0.425023i
641641 −352.881 + 256.383i −0.550516 + 0.399973i −0.827976 0.560764i 0.810507π-0.810507\pi
0.277460 + 0.960737i 0.410507π0.410507\pi
642642 452.539 + 40.5871i 0.704889 + 0.0632197i
643643 −541.940 + 176.087i −0.842831 + 0.273852i −0.698440 0.715668i 0.746122π-0.746122\pi
−0.144391 + 0.989521i 0.546122π0.546122\pi
644644 1247.85 + 225.649i 1.93766 + 0.350387i
645645 102.452 + 74.4361i 0.158841 + 0.115405i
646646 −758.753 324.027i −1.17454 0.501590i
647647 1052.80 + 342.075i 1.62720 + 0.528710i 0.973626 0.228151i 0.0732679π-0.0732679\pi
0.653576 + 0.756861i 0.273268π0.273268\pi
648648 −36.0478 786.269i −0.0556294 1.21338i
649649 −218.474 361.516i −0.336631 0.557036i
650650 −123.045 + 73.5681i −0.189300 + 0.113182i
651651 130.800 + 42.4994i 0.200921 + 0.0652833i
652652 593.109 80.7185i 0.909677 0.123801i
653653 −33.5591 24.3821i −0.0513922 0.0373386i 0.561793 0.827278i 0.310112π-0.310112\pi
−0.613185 + 0.789940i 0.710112π0.710112\pi
654654 −216.135 + 247.542i −0.330482 + 0.378505i
655655 −387.784 + 125.999i −0.592037 + 0.192364i
656656 −22.9135 + 524.801i −0.0349291 + 0.800001i
657657 213.535 155.142i 0.325016 0.236138i
658658 −223.115 976.128i −0.339080 1.48348i
659659 125.542i 0.190504i 0.995453 + 0.0952518i 0.0303656π0.0303656\pi
−0.995453 + 0.0952518i 0.969634π0.969634\pi
660660 −321.235 209.445i −0.486720 0.317341i
661661 −770.578 −1.16578 −0.582888 0.812553i 0.698077π-0.698077\pi
−0.582888 + 0.812553i 0.698077π0.698077\pi
662662 79.5672 18.1868i 0.120192 0.0274725i
663663 514.402 + 708.014i 0.775870 + 1.06789i
664664 −831.075 547.473i −1.25162 0.824508i
665665 −183.658 565.241i −0.276177 0.849986i
666666 −209.651 183.052i −0.314792 0.274852i
667667 989.107 1361.39i 1.48292 2.04106i
668668 65.8946 8.96784i 0.0986445 0.0134249i
669669 178.166 548.338i 0.266317 0.819638i
670670 −131.728 220.319i −0.196608 0.328834i
671671 598.745 + 50.8499i 0.892317 + 0.0757823i
672672 −1134.83 544.331i −1.68874 0.810016i
673673 150.772 464.028i 0.224029 0.689492i −0.774359 0.632746i 0.781928π-0.781928\pi
0.998389 0.0567455i 0.0180724π-0.0180724\pi
674674 −359.827 + 842.584i −0.533868 + 1.25012i
675675 −32.1649 + 44.2711i −0.0476516 + 0.0655868i
676676 143.763 + 25.9966i 0.212667 + 0.0384566i
677677 −328.420 1010.77i −0.485111 1.49302i −0.831820 0.555045i 0.812701π-0.812701\pi
0.346709 0.937973i 0.387299π-0.387299\pi
678678 −141.826 + 1581.33i −0.209183 + 2.33235i
679679 681.068 + 937.409i 1.00305 + 1.38057i
680680 270.142 + 74.2827i 0.397267 + 0.109239i
681681 1062.65 1.56042
682682 −67.9351 36.0903i −0.0996116 0.0529184i
683683 632.151i 0.925551i −0.886476 0.462775i 0.846854π-0.846854\pi
0.886476 0.462775i 0.153146π-0.153146\pi
684684 471.255 451.129i 0.688970 0.659545i
685685 −82.4428 + 59.8982i −0.120354 + 0.0874426i
686686 −6.90570 + 76.9974i −0.0100666 + 0.112241i
687687 −211.222 + 68.6303i −0.307456 + 0.0998985i
688688 −181.943 144.724i −0.264452 0.210355i
689689 −448.081 325.550i −0.650336 0.472497i
690690 215.070 503.615i 0.311695 0.729877i
691691 −595.551 193.506i −0.861868 0.280038i −0.155459 0.987842i 0.549686π-0.549686\pi
−0.706408 + 0.707804i 0.749686π0.749686\pi
692692 −416.931 + 775.946i −0.602502 + 1.12131i
693693 −669.323 + 156.319i −0.965834 + 0.225568i
694694 −302.700 506.275i −0.436166 0.729503i
695695 388.488 + 126.227i 0.558975 + 0.181622i
696696 −1304.85 + 1042.58i −1.87478 + 1.49796i
697697 −415.997 302.239i −0.596839 0.433629i
698698 −493.717 431.076i −0.707330 0.617588i
699699 −686.079 + 222.921i −0.981515 + 0.318914i
700700 87.6806 + 181.781i 0.125258 + 0.259687i
701701 −1132.88 + 823.084i −1.61609 + 1.17416i −0.779230 + 0.626738i 0.784390π0.784390\pi
−0.836859 + 0.547419i 0.815610π0.815610\pi
702702 305.911 69.9225i 0.435771 0.0996047i
703703 591.943i 0.842024i
704704 572.392 + 409.858i 0.813056 + 0.582185i
705705 −432.405 −0.613340
706706 20.1669 + 88.2303i 0.0285650 + 0.124972i
707707 755.448 + 1039.78i 1.06853 + 1.47070i
708708 −539.241 + 260.099i −0.761639 + 0.367371i
709709 0.00587285 + 0.0180748i 8.28329e−6 + 2.54934e-5i 0.951061 0.309004i 0.0999957π-0.0999957\pi
−0.951052 + 0.309030i 0.899996π0.899996\pi
710710 −69.4793 + 79.5755i −0.0978582 + 0.112078i
711711 255.873 352.179i 0.359878 0.495330i
712712 −767.942 961.125i −1.07857 1.34989i
713713 33.9460 104.475i 0.0476100 0.146529i
714714 1057.44 632.237i 1.48101 0.885487i
715715 136.955 324.939i 0.191545 0.454460i
716716 161.099 + 86.5616i 0.224998 + 0.120896i
717717 271.295 834.961i 0.378376 1.16452i
718718 272.712 + 116.462i 0.379821 + 0.162203i
719719 483.507 665.490i 0.672471 0.925577i −0.327342 0.944906i 0.606153π-0.606153\pi
0.999813 + 0.0193288i 0.00615294π0.00615294\pi
720720 −137.909 + 173.375i −0.191540 + 0.240798i
721721 −187.627 577.456i −0.260231 0.800910i
722722 −662.852 59.4496i −0.918077 0.0823401i
723723 −1040.70 1432.40i −1.43942 1.98119i
724724 85.3061 + 89.1120i 0.117826 + 0.123083i
725725 267.820 0.369406
726726 941.804 52.0996i 1.29725 0.0717626i
727727 839.149i 1.15426i 0.816651 + 0.577132i 0.195828π0.195828\pi
−0.816651 + 0.577132i 0.804172π0.804172\pi
728728 306.851 1115.92i 0.421499 1.53285i
729729 −182.269 + 132.426i −0.250026 + 0.181654i
730730 189.867 + 17.0287i 0.260092 + 0.0233270i
731731 216.432 70.3230i 0.296077 0.0962012i
732732 151.552 838.092i 0.207038 1.14493i
733733 −50.1402 36.4290i −0.0684041 0.0496985i 0.553058 0.833143i 0.313461π-0.313461\pi
−0.621462 + 0.783444i 0.713461π0.713461\pi
734734 −709.421 302.960i −0.966513 0.412752i
735735 437.909 + 142.285i 0.595795 + 0.193585i
736736 −434.778 + 906.436i −0.590731 + 1.23157i
737737 581.821 + 245.225i 0.789445 + 0.332733i
738738 348.970 208.648i 0.472859 0.282720i
739739 1148.56 + 373.191i 1.55421 + 0.504995i 0.955254 0.295785i 0.0955813π-0.0955813\pi
0.598959 + 0.800780i 0.295581π0.295581\pi
740740 −27.1066 199.176i −0.0366305 0.269156i
741741 1190.70 + 865.091i 1.60688 + 1.16746i
742742 −512.823 + 587.343i −0.691136 + 0.791567i
743743 899.643 292.312i 1.21082 0.393421i 0.367092 0.930185i 0.380353π-0.380353\pi
0.843732 + 0.536764i 0.180353π0.180353\pi
744744 −59.9800 + 91.0509i −0.0806183 + 0.122380i
745745 −29.7557 + 21.6188i −0.0399405 + 0.0290185i
746746 −135.379 592.281i −0.181473 0.793943i
747747 770.291i 1.03118i
748748 −643.801 + 245.788i −0.860696 + 0.328593i
749749 588.160 0.785260
750750 84.9641 19.4203i 0.113285 0.0258938i
751751 −362.830 499.393i −0.483130 0.664971i 0.495973 0.868338i 0.334812π-0.334812\pi
−0.979103 + 0.203367i 0.934812π0.934812\pi
752752 793.054 + 34.6258i 1.05459 + 0.0460449i
753753 −134.764 414.760i −0.178969 0.550810i
754754 −1156.88 1010.10i −1.53432 1.33965i
755755 308.910 425.178i 0.409152 0.563149i
756756 −59.5724 437.730i −0.0787995 0.579008i
757757 −428.022 + 1317.32i −0.565419 + 1.74018i 0.101286 + 0.994857i 0.467704π0.467704\pi
−0.666705 + 0.745322i 0.732296π0.732296\pi
758758 −311.205 520.501i −0.410561 0.686677i
759759 306.335 + 1311.66i 0.403603 + 1.72814i
760760 470.676 21.5790i 0.619311 0.0283934i
761761 333.154 1025.34i 0.437784 1.34736i −0.452423 0.891804i 0.649440π-0.649440\pi
0.890207 0.455557i 0.150560π-0.150560\pi
762762 150.147 351.591i 0.197044 0.461405i
763763 −250.043 + 344.154i −0.327710 + 0.451054i
764764 −48.6060 + 268.794i −0.0636204 + 0.351825i
765765 −67.0114 206.240i −0.0875966 0.269594i
766766 11.4910 128.122i 0.0150012 0.167261i
767767 −323.582 445.372i −0.421880 0.580668i
768768 654.624 753.058i 0.852375 0.980544i
769769 −259.985 −0.338081 −0.169041 0.985609i 0.554067π-0.554067\pi
−0.169041 + 0.985609i 0.554067π0.554067\pi
770770 −438.394 232.896i −0.569343 0.302462i
771771 1107.94i 1.43701i
772772 16.7845 + 17.5334i 0.0217416 + 0.0227116i
773773 −230.519 + 167.482i −0.298213 + 0.216665i −0.726823 0.686825i 0.759004π-0.759004\pi
0.428609 + 0.903490i 0.359004π0.359004\pi
774774 −16.0742 + 179.225i −0.0207677 + 0.231557i
775775 16.6276 5.40264i 0.0214550 0.00697114i
776776 −859.716 + 323.574i −1.10788 + 0.416977i
777777 −715.124 519.568i −0.920365 0.668685i
778778 −98.5142 + 230.684i −0.126625 + 0.296509i
779779 −822.428 267.223i −1.05575 0.343033i
780780 −440.257 236.559i −0.564432 0.303281i
781781 21.9882 258.906i 0.0281540 0.331506i
782782 −504.993 844.618i −0.645771 1.08007i
783783 −557.534 181.154i −0.712049 0.231359i
784784 −791.757 296.026i −1.00989 0.377584i
785785 −69.0023 50.1331i −0.0879010 0.0638638i
786786 −1070.76 934.906i −1.36229 1.18945i
787787 −1171.33 + 380.588i −1.48835 + 0.483594i −0.936595 0.350413i 0.886041π-0.886041\pi
−0.551754 + 0.834007i 0.686041π0.686041\pi
788788 1077.67 519.807i 1.36760 0.659654i
789789 −441.716 + 320.925i −0.559843 + 0.406749i
790790 306.497 70.0564i 0.387971 0.0886790i
791791 2055.24i 2.59828i
792792 21.1966 544.491i 0.0267634 0.687489i
793793 783.142 0.987569
794794 34.5971 + 151.362i 0.0435732 + 0.190633i
795795 197.916 + 272.408i 0.248951 + 0.342651i
796796 −494.626 1025.47i −0.621389 1.28827i
797797 −209.605 645.099i −0.262993 0.809409i −0.992149 0.125062i 0.960087π-0.960087\pi
0.729156 0.684348i 0.239913π-0.239913\pi
798798 1362.74 1560.76i 1.70769 1.95584i
799799 −456.730 + 628.635i −0.571627 + 0.786777i
800800 −157.384 + 28.8143i −0.196730 + 0.0360179i
801801 −294.252 + 905.615i −0.367356 + 1.13061i
802802 1253.29 749.336i 1.56271 0.934334i
803803 −401.299 + 242.515i −0.499750 + 0.302012i
804804 423.572 788.305i 0.526830 0.980479i
805805 219.058 674.190i 0.272121 0.837503i
806806 −92.2013 39.3747i −0.114394 0.0488520i
807807 −428.904 + 590.335i −0.531479 + 0.731518i
808808 −953.606 + 358.912i −1.18021 + 0.444198i
809809 444.042 + 1366.62i 0.548878 + 1.68927i 0.711588 + 0.702597i 0.247976π0.247976\pi
−0.162710 + 0.986674i 0.552024π0.552024\pi
810810 −438.240 39.3047i −0.541037 0.0485243i
811811 112.426 + 154.741i 0.138627 + 0.190803i 0.872686 0.488283i 0.162376π-0.162376\pi
−0.734059 + 0.679086i 0.762376π0.762376\pi
812812 −1561.81 + 1495.10i −1.92341 + 1.84126i
813813 −1487.33 −1.82943
814814 343.583 + 355.534i 0.422093 + 0.436775i
815815 334.615i 0.410570i
816816 261.018 + 941.203i 0.319876 + 1.15344i
817817 309.622 224.954i 0.378975 0.275341i
818818 154.160 + 13.8262i 0.188460 + 0.0169025i
819819 −851.948 + 276.815i −1.04023 + 0.337991i
820820 288.966 + 52.2535i 0.352397 + 0.0637238i
821821 998.232 + 725.258i 1.21587 + 0.883384i 0.995751 0.0920884i 0.0293543π-0.0293543\pi
0.220123 + 0.975472i 0.429354π0.429354\pi
822822 −326.717 139.525i −0.397466 0.169738i
823823 660.377 + 214.570i 0.802403 + 0.260716i 0.681377 0.731933i 0.261382π-0.261382\pi
0.121026 + 0.992649i 0.461382π0.461382\pi
824824 480.848 22.0453i 0.583553 0.0267540i
825825 −140.230 + 162.147i −0.169976 + 0.196542i
826826 −665.177 + 397.706i −0.805299 + 0.481484i
827827 −183.354 59.5753i −0.221710 0.0720379i 0.196056 0.980593i 0.437187π-0.437187\pi
−0.417766 + 0.908555i 0.637187π0.637187\pi
828828 771.017 104.931i 0.931180 0.126728i
829829 −661.852 480.864i −0.798374 0.580053i 0.112062 0.993701i 0.464254π-0.464254\pi
−0.910437 + 0.413648i 0.864254π0.864254\pi
830830 −365.901 + 419.071i −0.440845 + 0.504905i
831831 1308.20 425.059i 1.57424 0.511503i
832832 788.514 + 469.117i 0.947733 + 0.563843i
833833 669.401 486.348i 0.803602 0.583851i
834834 317.313 + 1388.25i 0.380471 + 1.66456i
835835 37.1757i 0.0445218i
836836 −901.982 + 727.695i −1.07893 + 0.870449i
837837 −38.2689 −0.0457215
838838 −79.3229 + 18.1309i −0.0946573 + 0.0216360i
839839 −853.898 1175.29i −1.01776 1.40082i −0.913765 0.406243i 0.866839π-0.866839\pi
−0.103991 0.994578i 0.533161π-0.533161\pi
840840 −387.059 + 587.563i −0.460785 + 0.699480i
841841 626.715 + 1928.83i 0.745202 + 2.29350i
842842 885.831 + 773.441i 1.05206 + 0.918576i
843843 193.367 266.147i 0.229380 0.315714i
844844 500.507 68.1159i 0.593018 0.0807060i
845845 25.2372 77.6723i 0.0298666 0.0919198i
846846 −315.298 527.347i −0.372693 0.623342i
847847 1208.26 176.079i 1.42652 0.207886i
848848 −341.175 515.460i −0.402329 0.607854i
849849 −188.637 + 580.564i −0.222187 + 0.683820i
850850 61.5103 144.035i 0.0723651 0.169453i
851851 −414.999 + 571.197i −0.487661 + 0.671207i
852852 −362.403 65.5332i −0.425356 0.0769169i
853853 −268.775 827.205i −0.315094 0.969760i −0.975716 0.219041i 0.929707π-0.929707\pi
0.660622 0.750719i 0.270293π-0.270293\pi
854854 98.4852 1098.09i 0.115322 1.28582i
855855 −214.360 295.041i −0.250714 0.345078i
856856 −123.627 + 449.592i −0.144425 + 0.525224i
857857 −515.903 −0.601987 −0.300993 0.953626i 0.597318π-0.597318\pi
−0.300993 + 0.953626i 0.597318π0.597318\pi
858858 1217.29 171.526i 1.41875 0.199914i
859859 1004.50i 1.16938i 0.811256 + 0.584691i 0.198784π0.198784\pi
−0.811256 + 0.584691i 0.801216π0.801216\pi
860860 −93.8798 + 89.8703i −0.109163 + 0.104500i
861861 1044.70 759.022i 1.21336 0.881558i
862862 −17.5958 + 196.190i −0.0204127 + 0.227598i
863863 −189.314 + 61.5119i −0.219367 + 0.0712768i −0.416639 0.909072i 0.636792π-0.636792\pi
0.197271 + 0.980349i 0.436792π0.436792\pi
864864 347.125 + 46.4707i 0.401765 + 0.0537855i
865865 398.375 + 289.437i 0.460549 + 0.334609i
866866 −249.062 + 583.213i −0.287601 + 0.673456i
867867 162.012 + 52.6408i 0.186865 + 0.0607160i
868868 −66.8047 + 124.329i −0.0769639 + 0.143237i
869869 −505.861 + 584.924i −0.582119 + 0.673100i
870870 479.131 + 801.363i 0.550726 + 0.921107i
871871 782.602 + 254.283i 0.898509 + 0.291943i
872872 −210.516 263.473i −0.241417 0.302148i
873873 575.211 + 417.915i 0.658890 + 0.478712i
874874 −1246.64 1088.47i −1.42636 1.24539i
875875 107.300 34.8639i 0.122629 0.0398445i
876876 288.721 + 598.581i 0.329590 + 0.683312i
877877 264.570 192.222i 0.301677 0.219181i −0.426640 0.904421i 0.640303π-0.640303\pi
0.728317 + 0.685240i 0.240303π0.240303\pi
878878 278.319 63.6158i 0.316992 0.0724554i
879879 389.876i 0.443545i
880880 270.174 286.157i 0.307016 0.325179i
881881 −1330.90 −1.51066 −0.755332 0.655342i 0.772524π-0.772524\pi
−0.755332 + 0.655342i 0.772524π0.772524\pi
882882 145.785 + 637.812i 0.165290 + 0.723143i
883883 43.4139 + 59.7541i 0.0491663 + 0.0676716i 0.832892 0.553435i 0.186683π-0.186683\pi
−0.783726 + 0.621107i 0.786683π0.786683\pi
884884 −808.937 + 390.185i −0.915087 + 0.441385i
885885 103.421 + 318.299i 0.116860 + 0.359659i
886886 −374.813 + 429.278i −0.423040 + 0.484513i
887887 −302.036 + 415.718i −0.340515 + 0.468678i −0.944592 0.328248i 0.893542π-0.893542\pi
0.604077 + 0.796926i 0.293542π0.293542\pi
888888 547.475 437.434i 0.616525 0.492606i
889889 152.932 470.675i 0.172026 0.529443i
890890 −590.268 + 352.918i −0.663222 + 0.396537i
891891 926.254 559.759i 1.03957 0.628237i
892892 521.213 + 280.058i 0.584319 + 0.313966i
893893 −403.815 + 1242.81i −0.452200 + 1.39173i
894894 −117.920 50.3581i −0.131902 0.0563290i
895895 60.0917 82.7091i 0.0671415 0.0924124i
896896 756.939 1046.63i 0.844798 1.16811i
897897 542.468 + 1669.55i 0.604758 + 1.86125i
898898 −828.794 74.3325i −0.922933 0.0827756i
899899 110.089 + 151.525i 0.122457 + 0.168548i
900900 85.6381 + 89.4588i 0.0951535 + 0.0993986i
901901 605.080 0.671565
902902 −649.074 + 316.864i −0.719595 + 0.351291i
903903 571.503i 0.632894i
904904 −1571.04 431.999i −1.73787 0.477875i
905905 55.7908 40.5344i 0.0616473 0.0447894i
906906 1824.85 + 163.666i 2.01418 + 0.180647i
907907 874.489 284.139i 0.964156 0.313273i 0.215701 0.976459i 0.430796π-0.430796\pi
0.748454 + 0.663186i 0.230796π0.230796\pi
908908 −194.055 + 1073.13i −0.213716 + 1.18187i
909909 638.030 + 463.556i 0.701904 + 0.509963i
910910 −594.987 254.090i −0.653832 0.279220i
911911 −288.635 93.7832i −0.316833 0.102945i 0.146283 0.989243i 0.453269π-0.453269\pi
−0.463117 + 0.886297i 0.653269π0.653269\pi
912912 906.612 + 1369.74i 0.994092 + 1.50191i
913913 115.797 1363.48i 0.126832 1.49341i
914914 −344.821 + 206.167i −0.377265 + 0.225565i
915915 −452.804 147.125i −0.494867 0.160792i
916916 −30.7353 225.839i −0.0335539 0.246549i
917917 −1488.66 1081.57i −1.62340 1.17947i
918918 −225.475 + 258.239i −0.245615 + 0.281306i
919919 412.101 133.900i 0.448423 0.145701i −0.0760956 0.997101i 0.524245π-0.524245\pi
0.524518 + 0.851399i 0.324245π0.324245\pi
920920 469.310 + 309.159i 0.510119 + 0.336043i
921921 765.835 556.412i 0.831525 0.604138i
922922 380.225 + 1663.48i 0.412391 + 1.80421i
923923 338.642i 0.366893i
924924 −87.4256 1728.40i −0.0946165 1.87057i
925925 −112.369 −0.121480
926926 −372.368 + 85.1127i −0.402125 + 0.0919143i
927927 −218.992 301.417i −0.236238 0.325154i
928928 −814.583 1508.11i −0.877783 1.62512i
929929 102.465 + 315.354i 0.110296 + 0.339455i 0.990937 0.134329i 0.0428877π-0.0428877\pi
−0.880641 + 0.473784i 0.842888π0.842888\pi
930930 45.9125 + 40.0874i 0.0493683 + 0.0431047i
931931 817.911 1125.76i 0.878530 1.20919i
932932 −99.8326 733.557i −0.107117 0.787079i
933933 268.616 826.715i 0.287906 0.886082i
934934 −645.579 1079.75i −0.691198 1.15605i
935935 87.6122 + 375.137i 0.0937029 + 0.401216i
936936 −32.5244 709.417i −0.0347483 0.757924i
937937 92.0134 283.188i 0.0982000 0.302229i −0.889874 0.456206i 0.849208π-0.849208\pi
0.988074 + 0.153977i 0.0492082π0.0492082\pi
938938 454.963 1065.36i 0.485035 1.13577i
939939 438.537 603.595i 0.467026 0.642806i
940940 78.9631 436.671i 0.0840033 0.464544i
941941 120.205 + 369.952i 0.127741 + 0.393148i 0.994391 0.105770i 0.0337308π-0.0337308\pi
−0.866649 + 0.498918i 0.833731π0.833731\pi
942942 26.5615 296.155i 0.0281969 0.314390i
943943 −606.260 834.446i −0.642906 0.884884i
944944 −164.192 592.059i −0.173933 0.627181i
945945 −246.954 −0.261327
946946 55.3956 314.828i 0.0585577 0.332799i
947947 455.871i 0.481384i −0.970602 0.240692i 0.922626π-0.922626\pi
0.970602 0.240692i 0.0773744π-0.0773744\pi
948948 757.946 + 791.761i 0.799521 + 0.835191i
949949 −494.383 + 359.190i −0.520952 + 0.378494i
950950 23.5286 262.340i 0.0247669 0.276147i
951951 458.864 149.094i 0.482506 0.156776i
952952 445.373 + 1183.33i 0.467829 + 1.24299i
953953 1198.70 + 870.908i 1.25782 + 0.913859i 0.998649 0.0519722i 0.0165507π-0.0165507\pi
0.259171 + 0.965831i 0.416551π0.416551\pi
954954 −187.905 + 440.005i −0.196966 + 0.461221i
955955 145.224 + 47.1862i 0.152067 + 0.0494096i
956956 793.658 + 426.448i 0.830186 + 0.446075i
957957 −2116.25 891.952i −2.21134 0.932029i
958958 732.898 + 1225.80i 0.765029 + 1.27954i
959959 −437.376 142.112i −0.456075 0.148188i
960960 −367.779 419.372i −0.383103 0.436846i
961961 −767.574 557.675i −0.798724 0.580307i
962962 485.391 + 423.807i 0.504564 + 0.440547i
963963 343.241 111.526i 0.356429 0.115811i
964964 1636.58 789.392i 1.69770 0.818871i
965965 10.9772 7.97541i 0.0113753 0.00826467i
966966 2409.19 550.672i 2.49399 0.570054i
967967 455.350i 0.470889i −0.971888 0.235445i 0.924345π-0.924345\pi
0.971888 0.235445i 0.0756546π-0.0756546\pi
968968 −119.373 + 960.611i −0.123319 + 0.992367i
969969 −1607.89 −1.65933
970970 114.422 + 500.598i 0.117961 + 0.516081i
971971 −954.786 1314.15i −0.983301 1.35340i −0.935032 0.354564i 0.884629π-0.884629\pi
−0.0482698 0.998834i 0.515371π-0.515371\pi
972972 −495.238 1026.73i −0.509504 1.05631i
973973 569.649 + 1753.20i 0.585456 + 1.80185i
974974 886.826 1015.69i 0.910499 1.04281i
975975 −164.221 + 226.031i −0.168432 + 0.231826i
976976 818.686 + 306.094i 0.838818 + 0.313621i
977977 437.833 1347.51i 0.448140 1.37923i −0.430862 0.902418i 0.641791π-0.641791\pi
0.879003 0.476817i 0.158209π-0.158209\pi
978978 1001.23 598.628i 1.02375 0.612094i
979979 656.993 1558.79i 0.671086 1.59222i
980980 −223.658 + 416.247i −0.228222 + 0.424742i
981981 −80.6632 + 248.256i −0.0822255 + 0.253064i
982982 497.350 + 212.394i 0.506466 + 0.216287i
983983 241.022 331.739i 0.245191 0.337476i −0.668629 0.743596i 0.733119π-0.733119\pi
0.913820 + 0.406120i 0.133119π0.133119\pi
984984 360.610 + 958.118i 0.366473 + 0.973697i
985985 −206.688 636.119i −0.209835 0.645806i
986986 1671.12 + 149.878i 1.69485 + 0.152006i
987987 −1147.00 1578.71i −1.16211 1.59950i
988988 −1091.06 + 1044.47i −1.10432 + 1.05715i
989989 456.482 0.461559
990990 −300.002 52.7869i −0.303032 0.0533201i
991991 1155.69i 1.16618i −0.812407 0.583090i 0.801843π-0.801843\pi
0.812407 0.583090i 0.198157π-0.198157\pi
992992 −80.9961 77.1991i −0.0816493 0.0778216i
993993 128.685 93.4953i 0.129592 0.0941544i
994994 −474.831 42.5864i −0.477697 0.0428435i
995995 −605.303 + 196.675i −0.608345 + 0.197663i
996996 −1908.53 345.119i −1.91620 0.346505i
997997 890.773 + 647.184i 0.893453 + 0.649132i 0.936776 0.349929i 0.113794π-0.113794\pi
−0.0433229 + 0.999061i 0.513794π0.513794\pi
998998 −273.710 116.888i −0.274258 0.117123i
999999 233.924 + 76.0066i 0.234158 + 0.0760827i
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 220.3.s.a.31.15 yes 96
4.3 odd 2 inner 220.3.s.a.31.5 96
11.5 even 5 inner 220.3.s.a.71.5 yes 96
44.27 odd 10 inner 220.3.s.a.71.15 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
220.3.s.a.31.5 96 4.3 odd 2 inner
220.3.s.a.31.15 yes 96 1.1 even 1 trivial
220.3.s.a.71.5 yes 96 11.5 even 5 inner
220.3.s.a.71.15 yes 96 44.27 odd 10 inner