Properties

Label 99.4.f.e.82.4
Level 9999
Weight 44
Character 99.82
Analytic conductor 5.8415.841
Analytic rank 00
Dimension 2424
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,4,Mod(37,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 99=3211 99 = 3^{2} \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 99.f (of order 55, 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: 5.841189090575.84118909057
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 82.4
Character χ\chi == 99.82
Dual form 99.4.f.e.64.4

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+(0.0654439+0.201416i)q2+(6.435854.67592i)q4+(5.73265+17.6433i)q5+(17.3440+12.6012i)q7+(2.73367+1.98613i)q83.92880q10+(29.4005+21.6012i)q11+(1.29584+3.98820i)q13+(3.673132.66869i)q14+(19.445159.8458i)q16+(26.8314+82.5787i)q17+(85.7906+62.3305i)q19+(45.6041+140.355i)q20+(2.42673+7.33539i)q22148.322q23+(177.295128.813i)q25+(0.718481+0.522007i)q26+(52.7014+162.198i)q28+(211.201153.447i)q29+(14.4456+44.4590i)q31+40.3584q3218.3886q34+(122.899378.243i)q35+(245.717178.524i)q37+(6.93988+21.3587i)q38+(50.7129+36.8451i)q40+(116.32384.5140i)q41+174.897q43+(290.223+1.54754i)q44+(9.7067629.8743i)q46+(300.564218.373i)q47+(36.0324110.896i)q49+(14.342044.1401i)q50+(26.9884+19.6082i)q52+(44.9117138.224i)q53+(549.659+394.890i)q5572.4402q56+(44.7284+32.4971i)q58+(164.834119.759i)q59+(56.4889+173.855i)q61+(8.00936+5.81914i)q62+(152.919470.637i)q6477.7936q65153.054q67+(213.448+656.925i)q68+(68.141249.5075i)q70+(48.7916150.165i)q71+(525.951382.126i)q73+(52.0381+37.8079i)q74+843.588q76+(782.1224.17047i)q77+(313.345+964.378i)q79+(944.405+686.150i)q80+(9.4097728.9603i)q82+(94.2610+290.105i)q83+(1303.14946.789i)q85+(11.4459+35.2270i)q86+(37.4685+117.443i)q88+1345.51q89+(72.731052.8422i)q91+(954.577+693.541i)q92+(24.313674.8296i)q94+(1591.52+1156.31i)q95+(320.534+986.501i)q97+24.6944q98+O(q100)q+(0.0654439 + 0.201416i) q^{2} +(6.43585 - 4.67592i) q^{4} +(-5.73265 + 17.6433i) q^{5} +(-17.3440 + 12.6012i) q^{7} +(2.73367 + 1.98613i) q^{8} -3.92880 q^{10} +(29.4005 + 21.6012i) q^{11} +(1.29584 + 3.98820i) q^{13} +(-3.67313 - 2.66869i) q^{14} +(19.4451 - 59.8458i) q^{16} +(-26.8314 + 82.5787i) q^{17} +(85.7906 + 62.3305i) q^{19} +(45.6041 + 140.355i) q^{20} +(-2.42673 + 7.33539i) q^{22} -148.322 q^{23} +(-177.295 - 128.813i) q^{25} +(-0.718481 + 0.522007i) q^{26} +(-52.7014 + 162.198i) q^{28} +(211.201 - 153.447i) q^{29} +(14.4456 + 44.4590i) q^{31} +40.3584 q^{32} -18.3886 q^{34} +(-122.899 - 378.243i) q^{35} +(245.717 - 178.524i) q^{37} +(-6.93988 + 21.3587i) q^{38} +(-50.7129 + 36.8451i) q^{40} +(-116.323 - 84.5140i) q^{41} +174.897 q^{43} +(290.223 + 1.54754i) q^{44} +(-9.70676 - 29.8743i) q^{46} +(-300.564 - 218.373i) q^{47} +(36.0324 - 110.896i) q^{49} +(14.3420 - 44.1401i) q^{50} +(26.9884 + 19.6082i) q^{52} +(-44.9117 - 138.224i) q^{53} +(-549.659 + 394.890i) q^{55} -72.4402 q^{56} +(44.7284 + 32.4971i) q^{58} +(164.834 - 119.759i) q^{59} +(-56.4889 + 173.855i) q^{61} +(-8.00936 + 5.81914i) q^{62} +(-152.919 - 470.637i) q^{64} -77.7936 q^{65} -153.054 q^{67} +(213.448 + 656.925i) q^{68} +(68.1412 - 49.5075i) q^{70} +(48.7916 - 150.165i) q^{71} +(525.951 - 382.126i) q^{73} +(52.0381 + 37.8079i) q^{74} +843.588 q^{76} +(-782.122 - 4.17047i) q^{77} +(313.345 + 964.378i) q^{79} +(944.405 + 686.150i) q^{80} +(9.40977 - 28.9603i) q^{82} +(-94.2610 + 290.105i) q^{83} +(-1303.14 - 946.789i) q^{85} +(11.4459 + 35.2270i) q^{86} +(37.4685 + 117.443i) q^{88} +1345.51 q^{89} +(-72.7310 - 52.8422i) q^{91} +(-954.577 + 693.541i) q^{92} +(24.3136 - 74.8296i) q^{94} +(-1591.52 + 1156.31i) q^{95} +(320.534 + 986.501i) q^{97} +24.6944 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q4q428q7+208q10+20q13224q1640q19586q22+362q25150q28+670q312520q34516q37+2002q40+4008q43+2174q46+342q49+1224q97+O(q100) 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49}+ \cdots - 1224 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/99Z)×\left(\mathbb{Z}/99\mathbb{Z}\right)^\times.

nn 4646 5656
χ(n)\chi(n) e(25)e\left(\frac{2}{5}\right) 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 0.0654439 + 0.201416i 0.0231379 + 0.0712112i 0.961959 0.273195i 0.0880803π-0.0880803\pi
−0.938821 + 0.344406i 0.888080π0.888080\pi
33 0 0
44 6.43585 4.67592i 0.804481 0.584490i
55 −5.73265 + 17.6433i −0.512744 + 1.57806i 0.274605 + 0.961557i 0.411453π0.411453\pi
−0.787350 + 0.616507i 0.788547π0.788547\pi
66 0 0
77 −17.3440 + 12.6012i −0.936488 + 0.680398i −0.947573 0.319540i 0.896472π-0.896472\pi
0.0110848 + 0.999939i 0.496472π0.496472\pi
88 2.73367 + 1.98613i 0.120812 + 0.0877752i
99 0 0
1010 −3.92880 −0.124240
1111 29.4005 + 21.6012i 0.805871 + 0.592091i
1212 0 0
1313 1.29584 + 3.98820i 0.0276464 + 0.0850867i 0.963928 0.266164i 0.0857564π-0.0857564\pi
−0.936281 + 0.351251i 0.885756π0.885756\pi
1414 −3.67313 2.66869i −0.0701204 0.0509454i
1515 0 0
1616 19.4451 59.8458i 0.303829 0.935090i
1717 −26.8314 + 82.5787i −0.382799 + 1.17813i 0.555266 + 0.831673i 0.312616π0.312616\pi
−0.938065 + 0.346460i 0.887384π0.887384\pi
1818 0 0
1919 85.7906 + 62.3305i 1.03588 + 0.752611i 0.969477 0.245182i 0.0788477π-0.0788477\pi
0.0664031 + 0.997793i 0.478848π0.478848\pi
2020 45.6041 + 140.355i 0.509869 + 1.56922i
2121 0 0
2222 −2.42673 + 7.33539i −0.0235173 + 0.0710868i
2323 −148.322 −1.34466 −0.672331 0.740251i 0.734707π-0.734707\pi
−0.672331 + 0.740251i 0.734707π0.734707\pi
2424 0 0
2525 −177.295 128.813i −1.41836 1.03050i
2626 −0.718481 + 0.522007i −0.00541945 + 0.00393746i
2727 0 0
2828 −52.7014 + 162.198i −0.355701 + 1.09474i
2929 211.201 153.447i 1.35238 0.982562i 0.353492 0.935438i 0.384994π-0.384994\pi
0.998889 0.0471249i 0.0150059π-0.0150059\pi
3030 0 0
3131 14.4456 + 44.4590i 0.0836937 + 0.257583i 0.984143 0.177379i 0.0567619π-0.0567619\pi
−0.900449 + 0.434962i 0.856762π0.856762\pi
3232 40.3584 0.222951
3333 0 0
3434 −18.3886 −0.0927535
3535 −122.899 378.243i −0.593533 1.82671i
3636 0 0
3737 245.717 178.524i 1.09177 0.793219i 0.112074 0.993700i 0.464251π-0.464251\pi
0.979698 + 0.200481i 0.0642505π0.0642505\pi
3838 −6.93988 + 21.3587i −0.0296262 + 0.0911801i
3939 0 0
4040 −50.7129 + 36.8451i −0.200461 + 0.145643i
4141 −116.323 84.5140i −0.443090 0.321923i 0.343772 0.939053i 0.388295π-0.388295\pi
−0.786861 + 0.617130i 0.788295π0.788295\pi
4242 0 0
4343 174.897 0.620268 0.310134 0.950693i 0.399626π-0.399626\pi
0.310134 + 0.950693i 0.399626π0.399626\pi
4444 290.223 + 1.54754i 0.994379 + 0.00530228i
4545 0 0
4646 −9.70676 29.8743i −0.0311127 0.0957550i
4747 −300.564 218.373i −0.932805 0.677722i 0.0138731 0.999904i 0.495584π-0.495584\pi
−0.946678 + 0.322181i 0.895584π0.895584\pi
4848 0 0
4949 36.0324 110.896i 0.105051 0.323313i
5050 14.3420 44.1401i 0.0405652 0.124847i
5151 0 0
5252 26.9884 + 19.6082i 0.0719733 + 0.0522917i
5353 −44.9117 138.224i −0.116398 0.358237i 0.875838 0.482605i 0.160309π-0.160309\pi
−0.992236 + 0.124369i 0.960309π0.960309\pi
5454 0 0
5555 −549.659 + 394.890i −1.34756 + 0.968125i
5656 −72.4402 −0.172861
5757 0 0
5858 44.7284 + 32.4971i 0.101261 + 0.0735702i
5959 164.834 119.759i 0.363722 0.264259i −0.390881 0.920441i 0.627830π-0.627830\pi
0.754603 + 0.656182i 0.227830π0.227830\pi
6060 0 0
6161 −56.4889 + 173.855i −0.118568 + 0.364915i −0.992675 0.120819i 0.961448π-0.961448\pi
0.874106 + 0.485735i 0.161448π0.161448\pi
6262 −8.00936 + 5.81914i −0.0164063 + 0.0119199i
6363 0 0
6464 −152.919 470.637i −0.298671 0.919214i
6565 −77.7936 −0.148448
6666 0 0
6767 −153.054 −0.279083 −0.139542 0.990216i 0.544563π-0.544563\pi
−0.139542 + 0.990216i 0.544563π0.544563\pi
6868 213.448 + 656.925i 0.380653 + 1.17153i
6969 0 0
7070 68.1412 49.5075i 0.116349 0.0845325i
7171 48.7916 150.165i 0.0815564 0.251005i −0.901961 0.431817i 0.857873π-0.857873\pi
0.983518 + 0.180812i 0.0578726π0.0578726\pi
7272 0 0
7373 525.951 382.126i 0.843260 0.612664i −0.0800196 0.996793i 0.525498π-0.525498\pi
0.923279 + 0.384129i 0.125498π0.125498\pi
7474 52.0381 + 37.8079i 0.0817474 + 0.0593930i
7575 0 0
7676 843.588 1.27324
7777 −782.122 4.17047i −1.15755 0.00617233i
7878 0 0
7979 313.345 + 964.378i 0.446255 + 1.37343i 0.881102 + 0.472926i 0.156802π0.156802\pi
−0.434847 + 0.900504i 0.643198π0.643198\pi
8080 944.405 + 686.150i 1.31985 + 0.958924i
8181 0 0
8282 9.40977 28.9603i 0.0126724 0.0390016i
8383 −94.2610 + 290.105i −0.124656 + 0.383653i −0.993838 0.110839i 0.964646π-0.964646\pi
0.869182 + 0.494493i 0.164646π0.164646\pi
8484 0 0
8585 −1303.14 946.789i −1.66289 1.20816i
8686 11.4459 + 35.2270i 0.0143517 + 0.0441701i
8787 0 0
8888 37.4685 + 117.443i 0.0453882 + 0.142267i
8989 1345.51 1.60252 0.801259 0.598318i 0.204164π-0.204164\pi
0.801259 + 0.598318i 0.204164π0.204164\pi
9090 0 0
9191 −72.7310 52.8422i −0.0837833 0.0608722i
9292 −954.577 + 693.541i −1.08176 + 0.785941i
9393 0 0
9494 24.3136 74.8296i 0.0266783 0.0821073i
9595 −1591.52 + 1156.31i −1.71881 + 1.24879i
9696 0 0
9797 320.534 + 986.501i 0.335518 + 1.03262i 0.966466 + 0.256794i 0.0826661π0.0826661\pi
−0.630948 + 0.775825i 0.717334π0.717334\pi
9898 24.6944 0.0254542
9999 0 0
100100 −1743.36 −1.74336
101101 225.488 + 693.982i 0.222148 + 0.683701i 0.998569 + 0.0534860i 0.0170333π0.0170333\pi
−0.776421 + 0.630215i 0.782967π0.782967\pi
102102 0 0
103103 137.058 99.5783i 0.131114 0.0952596i −0.520296 0.853986i 0.674178π-0.674178\pi
0.651409 + 0.758727i 0.274178π0.274178\pi
104104 −4.37866 + 13.4761i −0.00412849 + 0.0127062i
105105 0 0
106106 24.9013 18.0919i 0.0228173 0.0165777i
107107 938.826 + 682.097i 0.848222 + 0.616269i 0.924655 0.380805i 0.124353π-0.124353\pi
−0.0764332 + 0.997075i 0.524353π0.524353\pi
108108 0 0
109109 963.937 0.847050 0.423525 0.905884i 0.360793π-0.360793\pi
0.423525 + 0.905884i 0.360793π0.360793\pi
110110 −115.509 84.8668i −0.100121 0.0735612i
111111 0 0
112112 416.871 + 1283.00i 0.351701 + 1.08243i
113113 −485.899 353.026i −0.404509 0.293893i 0.366866 0.930274i 0.380431π-0.380431\pi
−0.771375 + 0.636381i 0.780431π0.780431\pi
114114 0 0
115115 850.277 2616.88i 0.689467 2.12196i
116116 641.755 1975.12i 0.513668 1.58091i
117117 0 0
118118 34.9087 + 25.3627i 0.0272340 + 0.0197866i
119119 −575.222 1770.35i −0.443114 1.36376i
120120 0 0
121121 397.779 + 1270.17i 0.298857 + 0.954298i
122122 −38.7139 −0.0287295
123123 0 0
124124 300.856 + 218.585i 0.217885 + 0.158302i
125125 1413.01 1026.62i 1.01107 0.734586i
126126 0 0
127127 596.515 1835.88i 0.416789 1.28274i −0.493853 0.869546i 0.664412π-0.664412\pi
0.910641 0.413198i 0.135588π-0.135588\pi
128128 345.991 251.377i 0.238919 0.173585i
129129 0 0
130130 −5.09112 15.6689i −0.00343477 0.0105711i
131131 50.4283 0.0336331 0.0168166 0.999859i 0.494647π-0.494647\pi
0.0168166 + 0.999859i 0.494647π0.494647\pi
132132 0 0
133133 −2273.39 −1.48216
134134 −10.0165 30.8276i −0.00645741 0.0198739i
135135 0 0
136136 −237.360 + 172.452i −0.149658 + 0.108733i
137137 265.998 818.658i 0.165881 0.510531i −0.833219 0.552944i 0.813505π-0.813505\pi
0.999100 + 0.0424130i 0.0135045π0.0135045\pi
138138 0 0
139139 −991.138 + 720.104i −0.604800 + 0.439413i −0.847579 0.530669i 0.821941π-0.821941\pi
0.242779 + 0.970082i 0.421941π0.421941\pi
140140 −2559.59 1859.65i −1.54518 1.12264i
141141 0 0
142142 33.4388 0.0197614
143143 −48.0513 + 145.247i −0.0280997 + 0.0849381i
144144 0 0
145145 1496.56 + 4605.94i 0.857121 + 2.63795i
146146 111.387 + 80.9271i 0.0631398 + 0.0458738i
147147 0 0
148148 746.634 2297.90i 0.414682 1.27626i
149149 −667.923 + 2055.66i −0.367237 + 1.13024i 0.581331 + 0.813667i 0.302532π0.302532\pi
−0.948568 + 0.316573i 0.897468π0.897468\pi
150150 0 0
151151 −2079.02 1510.50i −1.12045 0.814057i −0.136176 0.990685i 0.543481π-0.543481\pi
−0.984278 + 0.176627i 0.943481π0.943481\pi
152152 110.727 + 340.782i 0.0590863 + 0.181849i
153153 0 0
154154 −50.3451 157.805i −0.0263437 0.0825731i
155155 −867.214 −0.449396
156156 0 0
157157 −1889.81 1373.03i −0.960658 0.697959i −0.00735419 0.999973i 0.502341π-0.502341\pi
−0.953303 + 0.302014i 0.902341π0.902341\pi
158158 −173.734 + 126.225i −0.0874782 + 0.0635567i
159159 0 0
160160 −231.361 + 712.055i −0.114317 + 0.351831i
161161 2572.49 1869.03i 1.25926 0.914906i
162162 0 0
163163 477.263 + 1468.87i 0.229338 + 0.705831i 0.997822 + 0.0659615i 0.0210115π0.0210115\pi
−0.768484 + 0.639869i 0.778989π0.778989\pi
164164 −1143.82 −0.544618
165165 0 0
166166 −64.6006 −0.0302047
167167 −969.584 2984.07i −0.449274 1.38272i −0.877728 0.479159i 0.840942π-0.840942\pi
0.428455 0.903563i 0.359058π-0.359058\pi
168168 0 0
169169 1763.18 1281.03i 0.802542 0.583081i
170170 105.415 324.435i 0.0475588 0.146371i
171171 0 0
172172 1125.61 817.804i 0.498994 0.362541i
173173 2411.39 + 1751.98i 1.05974 + 0.769944i 0.974040 0.226377i 0.0726883π-0.0726883\pi
0.0856971 + 0.996321i 0.472688π0.472688\pi
174174 0 0
175175 4698.20 2.02943
176176 1864.43 1339.46i 0.798506 0.573668i
177177 0 0
178178 88.0557 + 271.007i 0.0370789 + 0.114117i
179179 −1045.40 759.528i −0.436519 0.317150i 0.347731 0.937594i 0.386952π-0.386952\pi
−0.784250 + 0.620445i 0.786952π0.786952\pi
180180 0 0
181181 357.508 1100.30i 0.146814 0.451847i −0.850426 0.526095i 0.823656π-0.823656\pi
0.997240 + 0.0742478i 0.0236556π0.0236556\pi
182182 5.88344 18.1074i 0.00239621 0.00737477i
183183 0 0
184184 −405.462 294.586i −0.162451 0.118028i
185185 1741.13 + 5358.66i 0.691950 + 2.12960i
186186 0 0
187187 −2572.65 + 1848.26i −1.00605 + 0.722772i
188188 −2955.48 −1.14655
189189 0 0
190190 −337.055 244.884i −0.128697 0.0935041i
191191 −1185.92 + 861.618i −0.449266 + 0.326411i −0.789306 0.614000i 0.789559π-0.789559\pi
0.340040 + 0.940411i 0.389559π0.389559\pi
192192 0 0
193193 −800.582 + 2463.94i −0.298586 + 0.918955i 0.683407 + 0.730038i 0.260498π0.260498\pi
−0.981993 + 0.188917i 0.939502π0.939502\pi
194194 −177.720 + 129.121i −0.0657709 + 0.0477853i
195195 0 0
196196 −286.643 882.197i −0.104462 0.321500i
197197 2831.08 1.02389 0.511944 0.859019i 0.328926π-0.328926\pi
0.511944 + 0.859019i 0.328926π0.328926\pi
198198 0 0
199199 −4220.54 −1.50345 −0.751724 0.659478i 0.770777π-0.770777\pi
−0.751724 + 0.659478i 0.770777π0.770777\pi
200200 −228.828 704.261i −0.0809030 0.248994i
201201 0 0
202202 −125.022 + 90.8338i −0.0435471 + 0.0316388i
203203 −1729.47 + 5322.75i −0.597955 + 1.84032i
204204 0 0
205205 2157.95 1567.84i 0.735207 0.534159i
206206 29.0262 + 21.0888i 0.00981725 + 0.00713265i
207207 0 0
208208 263.875 0.0879635
209209 1175.88 + 3685.73i 0.389172 + 1.21984i
210210 0 0
211211 −151.201 465.350i −0.0493324 0.151829i 0.923356 0.383946i 0.125435π-0.125435\pi
−0.972688 + 0.232116i 0.925435π0.925435\pi
212212 −935.370 679.586i −0.303026 0.220161i
213213 0 0
214214 −75.9446 + 233.734i −0.0242592 + 0.0746621i
215215 −1002.62 + 3085.76i −0.318039 + 0.978823i
216216 0 0
217217 −810.779 589.065i −0.253637 0.184278i
218218 63.0838 + 194.152i 0.0195990 + 0.0603194i
219219 0 0
220220 −1691.05 + 5111.61i −0.518229 + 1.56648i
221221 −364.109 −0.110826
222222 0 0
223223 1142.63 + 830.169i 0.343122 + 0.249292i 0.745978 0.665971i 0.231982π-0.231982\pi
−0.402856 + 0.915263i 0.631982π0.631982\pi
224224 −699.977 + 508.563i −0.208791 + 0.151695i
225225 0 0
226226 39.3059 120.971i 0.0115690 0.0356057i
227227 1833.50 1332.11i 0.536095 0.389496i −0.286538 0.958069i 0.592504π-0.592504\pi
0.822633 + 0.568573i 0.192504π0.192504\pi
228228 0 0
229229 −1068.63 3288.89i −0.308370 0.949066i −0.978398 0.206730i 0.933718π-0.933718\pi
0.670028 0.742336i 0.266282π-0.266282\pi
230230 582.727 0.167060
231231 0 0
232232 882.117 0.249629
233233 1012.89 + 3117.36i 0.284793 + 0.876503i 0.986461 + 0.163998i 0.0524392π0.0524392\pi
−0.701668 + 0.712504i 0.747561π0.747561\pi
234234 0 0
235235 5575.85 4051.09i 1.54778 1.12453i
236236 500.864 1541.50i 0.138150 0.425183i
237237 0 0
238238 318.932 231.717i 0.0868625 0.0631093i
239239 −2911.30 2115.19i −0.787935 0.572469i 0.119415 0.992844i 0.461898π-0.461898\pi
−0.907350 + 0.420376i 0.861898π0.861898\pi
240240 0 0
241241 3946.71 1.05490 0.527448 0.849587i 0.323149π-0.323149\pi
0.527448 + 0.849587i 0.323149π0.323149\pi
242242 −229.800 + 163.244i −0.0610418 + 0.0433625i
243243 0 0
244244 449.377 + 1383.04i 0.117903 + 0.362869i
245245 1750.02 + 1271.46i 0.456344 + 0.331554i
246246 0 0
247247 −137.415 + 422.921i −0.0353989 + 0.108947i
248248 −48.8116 + 150.227i −0.0124982 + 0.0384654i
249249 0 0
250250 299.250 + 217.418i 0.0757049 + 0.0550028i
251251 −1212.75 3732.47i −0.304973 0.938611i −0.979687 0.200532i 0.935733π-0.935733\pi
0.674714 0.738079i 0.264267π-0.264267\pi
252252 0 0
253253 −4360.73 3203.92i −1.08362 0.796162i
254254 408.814 0.100989
255255 0 0
256256 −3129.51 2273.72i −0.764041 0.555108i
257257 4477.03 3252.75i 1.08665 0.789498i 0.107820 0.994170i 0.465613π-0.465613\pi
0.978831 + 0.204672i 0.0656129π0.0656129\pi
258258 0 0
259259 −2012.11 + 6192.62i −0.482726 + 1.48568i
260260 −500.668 + 363.756i −0.119423 + 0.0867662i
261261 0 0
262262 3.30022 + 10.1570i 0.000778200 + 0.00239505i
263263 −6186.25 −1.45042 −0.725210 0.688528i 0.758257π-0.758257\pi
−0.725210 + 0.688528i 0.758257π0.758257\pi
264264 0 0
265265 2696.19 0.625003
266266 −148.780 457.896i −0.0342942 0.105547i
267267 0 0
268268 −985.035 + 715.670i −0.224517 + 0.163121i
269269 1464.92 4508.55i 0.332036 1.02190i −0.636128 0.771583i 0.719465π-0.719465\pi
0.968164 0.250317i 0.0805349π-0.0805349\pi
270270 0 0
271271 −4143.89 + 3010.71i −0.928868 + 0.674862i −0.945715 0.324996i 0.894637π-0.894637\pi
0.0168471 + 0.999858i 0.494637π0.494637\pi
272272 4420.25 + 3211.50i 0.985356 + 0.715903i
273273 0 0
274274 182.299 0.0401936
275275 −2430.07 7616.94i −0.532868 1.67025i
276276 0 0
277277 341.958 + 1052.44i 0.0741742 + 0.228285i 0.981269 0.192641i 0.0617053π-0.0617053\pi
−0.907095 + 0.420926i 0.861705π0.861705\pi
278278 −209.904 152.504i −0.0452850 0.0329014i
279279 0 0
280280 415.274 1278.08i 0.0886335 0.272786i
281281 2718.17 8365.66i 0.577054 1.77599i −0.0520205 0.998646i 0.516566π-0.516566\pi
0.629075 0.777345i 0.283434π-0.283434\pi
282282 0 0
283283 −166.756 121.155i −0.0350269 0.0254485i 0.570134 0.821552i 0.306891π-0.306891\pi
−0.605161 + 0.796103i 0.706891π0.706891\pi
284284 −388.145 1194.59i −0.0810991 0.249597i
285285 0 0
286286 −32.3997 0.172763i −0.00669871 3.57192e-5i
287287 3082.49 0.633984
288288 0 0
289289 −2124.61 1543.62i −0.432446 0.314191i
290290 −829.767 + 602.861i −0.168019 + 0.122073i
291291 0 0
292292 1598.15 4918.61i 0.320291 0.985754i
293293 −6843.27 + 4971.93i −1.36447 + 0.991342i −0.366318 + 0.930490i 0.619382π0.619382\pi
−0.998147 + 0.0608524i 0.980618π0.980618\pi
294294 0 0
295295 1168.01 + 3594.75i 0.230522 + 0.709473i
296296 1026.28 0.201524
297297 0 0
298298 −457.753 −0.0889829
299299 −192.202 591.537i −0.0371750 0.114413i
300300 0 0
301301 −3033.41 + 2203.90i −0.580874 + 0.422030i
302302 168.179 517.601i 0.0320450 0.0986245i
303303 0 0
304304 5398.43 3922.19i 1.01849 0.739976i
305305 −2743.54 1993.30i −0.515064 0.374216i
306306 0 0
307307 −847.003 −0.157463 −0.0787313 0.996896i 0.525087π-0.525087\pi
−0.0787313 + 0.996896i 0.525087π0.525087\pi
308308 −5053.12 + 3630.30i −0.934832 + 0.671609i
309309 0 0
310310 −56.7539 174.671i −0.0103981 0.0320020i
311311 1728.52 + 1255.85i 0.315163 + 0.228979i 0.734109 0.679032i 0.237600π-0.237600\pi
−0.418946 + 0.908011i 0.637600π0.637600\pi
312312 0 0
313313 1210.83 3726.56i 0.218659 0.672964i −0.780214 0.625512i 0.784890π-0.784890\pi
0.998874 0.0474516i 0.0151100π-0.0151100\pi
314314 152.873 470.494i 0.0274749 0.0845589i
315315 0 0
316316 6526.00 + 4741.41i 1.16176 + 0.844068i
317317 −2669.87 8217.02i −0.473044 1.45588i −0.848578 0.529071i 0.822540π-0.822540\pi
0.375533 0.926809i 0.377460π-0.377460\pi
318318 0 0
319319 9524.04 + 50.7846i 1.67161 + 0.00891345i
320320 9180.23 1.60372
321321 0 0
322322 544.805 + 395.824i 0.0942882 + 0.0685044i
323323 −7449.06 + 5412.06i −1.28321 + 0.932306i
324324 0 0
325325 283.983 874.010i 0.0484694 0.149173i
326326 −264.619 + 192.257i −0.0449566 + 0.0326629i
327327 0 0
328328 −150.134 462.066i −0.0252737 0.0777845i
329329 7964.74 1.33468
330330 0 0
331331 −3048.65 −0.506250 −0.253125 0.967434i 0.581458π-0.581458\pi
−0.253125 + 0.967434i 0.581458π0.581458\pi
332332 749.860 + 2307.83i 0.123958 + 0.381502i
333333 0 0
334334 537.586 390.579i 0.0880701 0.0639866i
335335 877.408 2700.38i 0.143098 0.440411i
336336 0 0
337337 −6783.37 + 4928.41i −1.09648 + 0.796639i −0.980482 0.196610i 0.937007π-0.937007\pi
−0.115998 + 0.993249i 0.537007π0.537007\pi
338338 373.409 + 271.297i 0.0600910 + 0.0436587i
339339 0 0
340340 −12814.0 −2.04392
341341 −535.658 + 1619.16i −0.0850660 + 0.257133i
342342 0 0
343343 −1499.84 4616.02i −0.236104 0.726652i
344344 478.110 + 347.367i 0.0749360 + 0.0544442i
345345 0 0
346346 −195.065 + 600.348i −0.0303085 + 0.0932800i
347347 1998.22 6149.90i 0.309136 0.951423i −0.668965 0.743294i 0.733263π-0.733263\pi
0.978101 0.208129i 0.0667374π-0.0667374\pi
348348 0 0
349349 −3397.32 2468.30i −0.521072 0.378581i 0.295935 0.955208i 0.404369π-0.404369\pi
−0.817008 + 0.576627i 0.804369π0.804369\pi
350350 307.468 + 946.291i 0.0469568 + 0.144518i
351351 0 0
352352 1186.56 + 871.789i 0.179670 + 0.132007i
353353 −6402.27 −0.965322 −0.482661 0.875807i 0.660330π-0.660330\pi
−0.482661 + 0.875807i 0.660330π0.660330\pi
354354 0 0
355355 2369.70 + 1721.69i 0.354284 + 0.257402i
356356 8659.52 6291.51i 1.28920 0.936656i
357357 0 0
358358 84.5657 260.267i 0.0124845 0.0384232i
359359 −3771.89 + 2740.44i −0.554520 + 0.402882i −0.829449 0.558582i 0.811346π-0.811346\pi
0.274929 + 0.961464i 0.411346π0.411346\pi
360360 0 0
361361 1355.39 + 4171.46i 0.197607 + 0.608173i
362362 245.014 0.0355736
363363 0 0
364364 −715.172 −0.102981
365365 3726.86 + 11470.1i 0.534447 + 1.64486i
366366 0 0
367367 −444.555 + 322.988i −0.0632305 + 0.0459397i −0.618952 0.785429i 0.712442π-0.712442\pi
0.555721 + 0.831369i 0.312442π0.312442\pi
368368 −2884.13 + 8876.43i −0.408548 + 1.25738i
369369 0 0
370370 −965.372 + 701.384i −0.135641 + 0.0985492i
371371 2520.73 + 1831.42i 0.352749 + 0.256287i
372372 0 0
373373 2727.49 0.378616 0.189308 0.981918i 0.439375π-0.439375\pi
0.189308 + 0.981918i 0.439375π0.439375\pi
374374 −540.634 397.215i −0.0747474 0.0549185i
375375 0 0
376376 −387.927 1193.92i −0.0532070 0.163754i
377377 885.659 + 643.469i 0.120991 + 0.0879054i
378378 0 0
379379 −3040.92 + 9358.98i −0.412141 + 1.26844i 0.502643 + 0.864494i 0.332361π0.332361\pi
−0.914783 + 0.403945i 0.867639π0.867639\pi
380380 −4836.00 + 14883.7i −0.652846 + 2.00925i
381381 0 0
382382 −251.154 182.474i −0.0336392 0.0244403i
383383 3173.50 + 9767.01i 0.423389 + 1.30306i 0.904528 + 0.426413i 0.140223π0.140223\pi
−0.481139 + 0.876644i 0.659777π0.659777\pi
384384 0 0
385385 4557.21 13775.3i 0.603265 1.82352i
386386 −548.669 −0.0723485
387387 0 0
388388 6675.71 + 4850.19i 0.873474 + 0.634616i
389389 −5019.79 + 3647.09i −0.654276 + 0.475360i −0.864725 0.502245i 0.832507π-0.832507\pi
0.210449 + 0.977605i 0.432507π0.432507\pi
390390 0 0
391391 3979.69 12248.2i 0.514735 1.58419i
392392 318.755 231.589i 0.0410703 0.0298393i
393393 0 0
394394 185.277 + 570.223i 0.0236906 + 0.0729123i
395395 −18811.1 −2.39618
396396 0 0
397397 14388.1 1.81894 0.909471 0.415767i 0.136487π-0.136487\pi
0.909471 + 0.415767i 0.136487π0.136487\pi
398398 −276.209 850.083i −0.0347867 0.107062i
399399 0 0
400400 −11156.4 + 8105.61i −1.39455 + 1.01320i
401401 803.328 2472.39i 0.100041 0.307893i −0.888494 0.458888i 0.848248π-0.848248\pi
0.988535 + 0.150995i 0.0482478π0.0482478\pi
402402 0 0
403403 −158.592 + 115.224i −0.0196030 + 0.0142424i
404404 4696.21 + 3412.00i 0.578330 + 0.420181i
405405 0 0
406406 −1185.27 −0.144887
407407 11080.5 + 59.0840i 1.34948 + 0.00719579i
408408 0 0
409409 −1046.25 3220.02i −0.126488 0.389290i 0.867681 0.497121i 0.165609π-0.165609\pi
−0.994169 + 0.107831i 0.965609π0.965609\pi
410410 457.012 + 332.039i 0.0550493 + 0.0399957i
411411 0 0
412412 416.463 1281.74i 0.0498002 0.153269i
413413 −1349.78 + 4154.20i −0.160819 + 0.494951i
414414 0 0
415415 −4578.05 3326.15i −0.541512 0.393432i
416416 52.2982 + 160.957i 0.00616378 + 0.0189702i
417417 0 0
418418 −665.410 + 478.048i −0.0778618 + 0.0559380i
419419 627.249 0.0731339 0.0365670 0.999331i 0.488358π-0.488358\pi
0.0365670 + 0.999331i 0.488358π0.488358\pi
420420 0 0
421421 6662.59 + 4840.66i 0.771294 + 0.560378i 0.902354 0.430997i 0.141838π-0.141838\pi
−0.131059 + 0.991375i 0.541838π0.541838\pi
422422 83.8336 60.9087i 0.00967051 0.00702604i
423423 0 0
424424 151.757 467.059i 0.0173820 0.0534962i
425425 15394.3 11184.6i 1.75701 1.27655i
426426 0 0
427427 −1211.03 3727.16i −0.137250 0.422412i
428428 9231.58 1.04258
429429 0 0
430430 −687.136 −0.0770619
431431 −5310.74 16344.8i −0.593525 1.82668i −0.561933 0.827183i 0.689942π-0.689942\pi
−0.0315922 0.999501i 0.510058π-0.510058\pi
432432 0 0
433433 −8105.23 + 5888.80i −0.899568 + 0.653574i −0.938355 0.345673i 0.887651π-0.887651\pi
0.0387874 + 0.999247i 0.487651π0.487651\pi
434434 65.5864 201.854i 0.00725403 0.0223256i
435435 0 0
436436 6203.75 4507.29i 0.681436 0.495092i
437437 −12724.6 9244.98i −1.39291 1.01201i
438438 0 0
439439 −13539.5 −1.47199 −0.735995 0.676987i 0.763285π-0.763285\pi
−0.735995 + 0.676987i 0.763285π0.763285\pi
440440 −2286.88 12.1942i −0.247779 0.00132122i
441441 0 0
442442 −23.8288 73.3374i −0.00256429 0.00789209i
443443 −2196.39 1595.77i −0.235561 0.171145i 0.463742 0.885970i 0.346506π-0.346506\pi
−0.699304 + 0.714825i 0.746506π0.746506\pi
444444 0 0
445445 −7713.36 + 23739.3i −0.821682 + 2.52888i
446446 −92.4309 + 284.473i −0.00981330 + 0.0302022i
447447 0 0
448448 8582.81 + 6235.78i 0.905133 + 0.657618i
449449 1659.48 + 5107.34i 0.174422 + 0.536816i 0.999607 0.0280473i 0.00892891π-0.00892891\pi
−0.825185 + 0.564863i 0.808929π0.808929\pi
450450 0 0
451451 −1594.37 4997.48i −0.166465 0.521778i
452452 −4777.90 −0.497198
453453 0 0
454454 388.300 + 282.117i 0.0401406 + 0.0291639i
455455 1349.25 980.289i 0.139020 0.101004i
456456 0 0
457457 −1616.02 + 4973.61i −0.165415 + 0.509094i −0.999067 0.0431964i 0.986246π-0.986246\pi
0.833652 + 0.552290i 0.186246π0.186246\pi
458458 592.500 430.476i 0.0604491 0.0439188i
459459 0 0
460460 −6764.08 20817.7i −0.685602 2.11007i
461461 14846.7 1.49995 0.749976 0.661465i 0.230065π-0.230065\pi
0.749976 + 0.661465i 0.230065π0.230065\pi
462462 0 0
463463 10918.5 1.09595 0.547977 0.836494i 0.315398π-0.315398\pi
0.547977 + 0.836494i 0.315398π0.315398\pi
464464 −5076.31 15623.3i −0.507892 1.56313i
465465 0 0
466466 −561.598 + 408.025i −0.0558273 + 0.0405609i
467467 −2226.36 + 6852.03i −0.220607 + 0.678960i 0.778100 + 0.628140i 0.216183π0.216183\pi
−0.998708 + 0.0508198i 0.983817π0.983817\pi
468468 0 0
469469 2654.58 1928.66i 0.261358 0.189888i
470470 1180.86 + 857.944i 0.115891 + 0.0842000i
471471 0 0
472472 688.458 0.0671374
473473 5142.06 + 3777.98i 0.499857 + 0.367255i
474474 0 0
475475 −7181.32 22101.8i −0.693687 2.13495i
476476 −11980.1 8704.02i −1.15358 0.838127i
477477 0 0
478478 235.505 724.808i 0.0225350 0.0693556i
479479 2880.68 8865.82i 0.274784 0.845699i −0.714492 0.699643i 0.753342π-0.753342\pi
0.989276 0.146055i 0.0466578π-0.0466578\pi
480480 0 0
481481 1030.40 + 748.628i 0.0976759 + 0.0709657i
482482 258.288 + 794.930i 0.0244081 + 0.0751205i
483483 0 0
484484 8499.26 + 6314.65i 0.798202 + 0.593036i
485485 −19242.6 −1.80157
486486 0 0
487487 7916.06 + 5751.36i 0.736573 + 0.535152i 0.891636 0.452753i 0.149558π-0.149558\pi
−0.155063 + 0.987905i 0.549558π0.549558\pi
488488 −499.719 + 363.067i −0.0463550 + 0.0336789i
489489 0 0
490490 −141.564 + 435.690i −0.0130515 + 0.0401683i
491491 5451.28 3960.59i 0.501045 0.364030i −0.308371 0.951266i 0.599784π-0.599784\pi
0.809416 + 0.587236i 0.199784π0.199784\pi
492492 0 0
493493 7004.58 + 21557.9i 0.639900 + 1.96941i
494494 −94.1759 −0.00857728
495495 0 0
496496 2941.58 0.266292
497497 1046.01 + 3219.30i 0.0944066 + 0.290554i
498498 0 0
499499 14846.8 10786.9i 1.33194 0.967708i 0.332237 0.943196i 0.392197π-0.392197\pi
0.999700 0.0245123i 0.00780328π-0.00780328\pi
500500 4293.58 13214.3i 0.384030 1.18192i
501501 0 0
502502 672.410 488.535i 0.0597832 0.0434350i
503503 995.261 + 723.099i 0.0882236 + 0.0640982i 0.631023 0.775764i 0.282635π-0.282635\pi
−0.542799 + 0.839863i 0.682635π0.682635\pi
504504 0 0
505505 −13536.8 −1.19283
506506 359.937 1088.00i 0.0316228 0.0955877i
507507 0 0
508508 −4745.37 14604.7i −0.414452 1.27555i
509509 −895.023 650.272i −0.0779395 0.0566263i 0.548133 0.836391i 0.315339π-0.315339\pi
−0.626073 + 0.779765i 0.715339π0.715339\pi
510510 0 0
511511 −4306.87 + 13255.2i −0.372847 + 1.14750i
512512 1310.41 4033.03i 0.113110 0.348118i
513513 0 0
514514 948.149 + 688.871i 0.0813640 + 0.0591144i
515515 971.184 + 2989.00i 0.0830980 + 0.255749i
516516 0 0
517517 −4119.64 12912.8i −0.350448 1.09846i
518518 −1378.97 −0.116966
519519 0 0
520520 −212.662 154.508i −0.0179343 0.0130300i
521521 4770.34 3465.85i 0.401137 0.291443i −0.368867 0.929482i 0.620254π-0.620254\pi
0.770004 + 0.638039i 0.220254π0.220254\pi
522522 0 0
523523 −231.034 + 711.048i −0.0193162 + 0.0594493i −0.960250 0.279141i 0.909950π-0.909950\pi
0.940934 + 0.338591i 0.109950π0.109950\pi
524524 324.549 235.798i 0.0270572 0.0196582i
525525 0 0
526526 −404.853 1246.01i −0.0335597 0.103286i
527527 −4058.96 −0.335505
528528 0 0
529529 9832.34 0.808116
530530 176.449 + 543.055i 0.0144613 + 0.0445072i
531531 0 0
532532 −14631.2 + 10630.2i −1.19237 + 0.866310i
533533 186.321 573.438i 0.0151416 0.0466011i
534534 0 0
535535 −17416.4 + 12653.8i −1.40743 + 1.02256i
536536 −418.400 303.985i −0.0337166 0.0244966i
537537 0 0
538538 1003.96 0.0804534
539539 3454.86 2482.07i 0.276088 0.198349i
540540 0 0
541541 −3280.34 10095.9i −0.260690 0.802320i −0.992655 0.120978i 0.961397π-0.961397\pi
0.731966 0.681342i 0.238603π-0.238603\pi
542542 −877.597 637.612i −0.0695499 0.0505309i
543543 0 0
544544 −1082.87 + 3332.74i −0.0853453 + 0.262666i
545545 −5525.92 + 17007.0i −0.434320 + 1.33670i
546546 0 0
547547 8538.55 + 6203.62i 0.667426 + 0.484913i 0.869162 0.494527i 0.164659π-0.164659\pi
−0.201737 + 0.979440i 0.564659π0.564659\pi
548548 −2116.05 6512.55i −0.164951 0.507668i
549549 0 0
550550 1375.14 987.936i 0.106611 0.0765923i
551551 27683.5 2.14039
552552 0 0
553553 −17586.9 12777.7i −1.35239 0.982570i
554554 −189.598 + 137.751i −0.0145402 + 0.0105641i
555555 0 0
556556 −3011.67 + 9268.96i −0.229718 + 0.706999i
557557 −9481.81 + 6888.94i −0.721287 + 0.524046i −0.886795 0.462162i 0.847074π-0.847074\pi
0.165508 + 0.986208i 0.447074π0.447074\pi
558558 0 0
559559 226.639 + 697.524i 0.0171482 + 0.0527766i
560560 −25026.0 −1.88847
561561 0 0
562562 1862.86 0.139822
563563 2079.55 + 6400.21i 0.155671 + 0.479106i 0.998228 0.0595008i 0.0189509π-0.0189509\pi
−0.842557 + 0.538607i 0.818951π0.818951\pi
564564 0 0
565565 9014.04 6549.08i 0.671192 0.487650i
566566 13.4894 41.5162i 0.00100177 0.00308314i
567567 0 0
568568 431.627 313.595i 0.0318850 0.0231658i
569569 −1059.77 769.965i −0.0780804 0.0567287i 0.548060 0.836439i 0.315366π-0.315366\pi
−0.626141 + 0.779710i 0.715366π0.715366\pi
570570 0 0
571571 −3206.49 −0.235005 −0.117502 0.993073i 0.537489π-0.537489\pi
−0.117502 + 0.993073i 0.537489π0.537489\pi
572572 369.911 + 1159.47i 0.0270398 + 0.0847551i
573573 0 0
574574 201.730 + 620.861i 0.0146691 + 0.0451468i
575575 26296.7 + 19105.7i 1.90722 + 1.38567i
576576 0 0
577577 3560.42 10957.9i 0.256884 0.790609i −0.736568 0.676363i 0.763555π-0.763555\pi
0.993453 0.114246i 0.0364451π-0.0364451\pi
578578 171.866 528.950i 0.0123680 0.0380647i
579579 0 0
580580 31168.6 + 22645.3i 2.23139 + 1.62120i
581581 −2020.80 6219.39i −0.144298 0.444103i
582582 0 0
583583 1665.38 5034.01i 0.118307 0.357611i
584584 2196.73 0.155653
585585 0 0
586586 −1449.28 1052.96i −0.102166 0.0742276i
587587 −1818.93 + 1321.53i −0.127897 + 0.0929224i −0.649894 0.760024i 0.725187π-0.725187\pi
0.521998 + 0.852947i 0.325187π0.325187\pi
588588 0 0
589589 −1531.85 + 4714.56i −0.107163 + 0.329814i
590590 −647.601 + 470.510i −0.0451886 + 0.0328315i
591591 0 0
592592 −5905.90 18176.5i −0.410019 1.26191i
593593 11998.0 0.830861 0.415431 0.909625i 0.363631π-0.363631\pi
0.415431 + 0.909625i 0.363631π0.363631\pi
594594 0 0
595595 34532.4 2.37931
596596 5313.43 + 16353.0i 0.365179 + 1.12390i
597597 0 0
598598 106.566 77.4250i 0.00728733 0.00529455i
599599 −6683.63 + 20570.1i −0.455903 + 1.40312i 0.414169 + 0.910200i 0.364072π0.364072\pi
−0.870072 + 0.492924i 0.835928π0.835928\pi
600600 0 0
601601 2703.52 1964.22i 0.183492 0.133315i −0.492247 0.870455i 0.663824π-0.663824\pi
0.675739 + 0.737141i 0.263824π0.263824\pi
602602 −642.419 466.745i −0.0434935 0.0315998i
603603 0 0
604604 −20443.3 −1.37719
605605 −24690.3 263.317i −1.65918 0.0176948i
606606 0 0
607607 1078.41 + 3318.99i 0.0721106 + 0.221934i 0.980616 0.195940i 0.0627756π-0.0627756\pi
−0.908505 + 0.417873i 0.862776π0.862776\pi
608608 3462.38 + 2515.56i 0.230950 + 0.167795i
609609 0 0
610610 221.934 683.041i 0.0147309 0.0453370i
611611 481.430 1481.69i 0.0318765 0.0981059i
612612 0 0
613613 2552.59 + 1854.56i 0.168186 + 0.122194i 0.668694 0.743537i 0.266854π-0.266854\pi
−0.500508 + 0.865732i 0.666854π0.666854\pi
614614 −55.4312 170.600i −0.00364336 0.0112131i
615615 0 0
616616 −2129.78 1564.79i −0.139304 0.102349i
617617 204.683 0.0133553 0.00667767 0.999978i 0.497874π-0.497874\pi
0.00667767 + 0.999978i 0.497874π0.497874\pi
618618 0 0
619619 −13999.8 10171.4i −0.909044 0.660459i 0.0317289 0.999497i 0.489899π-0.489899\pi
−0.940773 + 0.339037i 0.889899π0.889899\pi
620620 −5581.26 + 4055.02i −0.361530 + 0.262667i
621621 0 0
622622 −139.826 + 430.339i −0.00901367 + 0.0277412i
623623 −23336.6 + 16955.0i −1.50074 + 1.09035i
624624 0 0
625625 1547.45 + 4762.57i 0.0990370 + 0.304805i
626626 829.830 0.0529819
627627 0 0
628628 −18582.7 −1.18078
629629 8149.31 + 25081.0i 0.516588 + 1.58990i
630630 0 0
631631 −2010.05 + 1460.38i −0.126813 + 0.0921347i −0.649383 0.760461i 0.724973π-0.724973\pi
0.522571 + 0.852596i 0.324973π0.324973\pi
632632 −1058.79 + 3258.63i −0.0666401 + 0.205097i
633633 0 0
634634 1480.31 1075.51i 0.0927297 0.0673721i
635635 28971.4 + 21049.0i 1.81055 + 1.31544i
636636 0 0
637637 488.969 0.0304139
638638 613.062 + 1921.62i 0.0380429 + 0.119244i
639639 0 0
640640 2451.68 + 7545.49i 0.151424 + 0.466034i
641641 −13255.1 9630.41i −0.816764 0.593414i 0.0990195 0.995085i 0.468429π-0.468429\pi
−0.915784 + 0.401671i 0.868429π0.868429\pi
642642 0 0
643643 −3764.00 + 11584.4i −0.230852 + 0.710489i 0.766793 + 0.641895i 0.221851π0.221851\pi
−0.997645 + 0.0685945i 0.978149π0.978149\pi
644644 7816.77 24057.5i 0.478298 1.47205i
645645 0 0
646646 −1577.57 1146.17i −0.0960815 0.0698073i
647647 −2292.65 7056.06i −0.139310 0.428751i 0.856926 0.515440i 0.172371π-0.172371\pi
−0.996235 + 0.0866885i 0.972371π0.972371\pi
648648 0 0
649649 7433.14 + 39.6354i 0.449578 + 0.00239726i
650650 194.624 0.0117443
651651 0 0
652652 9939.89 + 7221.75i 0.597049 + 0.433782i
653653 −9933.63 + 7217.21i −0.595303 + 0.432513i −0.844209 0.536015i 0.819929π-0.819929\pi
0.248905 + 0.968528i 0.419929π0.419929\pi
654654 0 0
655655 −289.088 + 889.720i −0.0172452 + 0.0530752i
656656 −7319.72 + 5318.09i −0.435651 + 0.316519i
657657 0 0
658658 521.244 + 1604.22i 0.0308818 + 0.0950443i
659659 17155.7 1.01410 0.507049 0.861917i 0.330736π-0.330736\pi
0.507049 + 0.861917i 0.330736π0.330736\pi
660660 0 0
661661 −6971.48 −0.410226 −0.205113 0.978738i 0.565756π-0.565756\pi
−0.205113 + 0.978738i 0.565756π0.565756\pi
662662 −199.515 614.045i −0.0117136 0.0360507i
663663 0 0
664664 −833.864 + 605.837i −0.0487352 + 0.0354082i
665665 13032.6 40110.1i 0.759971 2.33895i
666666 0 0
667667 −31325.7 + 22759.5i −1.81850 + 1.32121i
668668 −20193.4 14671.4i −1.16962 0.849778i
669669 0 0
670670 601.321 0.0346732
671671 −5416.27 + 3891.19i −0.311614 + 0.223872i
672672 0 0
673673 −8621.49 26534.2i −0.493810 1.51979i −0.818804 0.574074i 0.805362π-0.805362\pi
0.324994 0.945716i 0.394638π-0.394638\pi
674674 −1436.59 1043.74i −0.0820999 0.0596491i
675675 0 0
676676 5357.60 16489.0i 0.304825 0.938155i
677677 2336.86 7192.12i 0.132663 0.408295i −0.862556 0.505961i 0.831138π-0.831138\pi
0.995219 + 0.0976664i 0.0311378π0.0311378\pi
678678 0 0
679679 −17990.4 13070.8i −1.01680 0.738749i
680680 −1681.92 5176.41i −0.0948509 0.291921i
681681 0 0
682682 −361.179 1.92590i −0.0202790 0.000108133i
683683 28882.3 1.61809 0.809043 0.587750i 0.199986π-0.199986\pi
0.809043 + 0.587750i 0.199986π0.199986\pi
684684 0 0
685685 12918.9 + 9386.16i 0.720595 + 0.523543i
686686 831.584 604.181i 0.0462829 0.0336265i
687687 0 0
688688 3400.89 10466.8i 0.188456 0.580007i
689689 493.067 358.234i 0.0272632 0.0198079i
690690 0 0
691691 7893.89 + 24294.9i 0.434584 + 1.33751i 0.893512 + 0.449039i 0.148234π0.148234\pi
−0.458928 + 0.888474i 0.651766π0.651766\pi
692692 23711.4 1.30256
693693 0 0
694694 1369.46 0.0749047
695695 −7023.15 21615.0i −0.383314 1.17972i
696696 0 0
697697 10100.2 7338.21i 0.548883 0.398787i
698698 274.820 845.808i 0.0149027 0.0458658i
699699 0 0
700700 30236.9 21968.4i 1.63264 1.18618i
701701 −5340.41 3880.03i −0.287738 0.209054i 0.434547 0.900649i 0.356908π-0.356908\pi
−0.722285 + 0.691595i 0.756908π0.756908\pi
702702 0 0
703703 32207.7 1.72793
704704 5670.41 17140.2i 0.303568 0.917608i
705705 0 0
706706 −418.990 1289.52i −0.0223355 0.0687417i
707707 −12655.8 9195.01i −0.673228 0.489129i
708708 0 0
709709 −5952.67 + 18320.4i −0.315314 + 0.970436i 0.660311 + 0.750992i 0.270424π0.270424\pi
−0.975625 + 0.219444i 0.929576π0.929576\pi
710710 −191.693 + 589.970i −0.0101325 + 0.0311847i
711711 0 0
712712 3678.18 + 2672.36i 0.193604 + 0.140661i
713713 −2142.60 6594.23i −0.112540 0.346362i
714714 0 0
715715 −2287.17 1680.43i −0.119630 0.0878946i
716716 −10279.5 −0.536542
717717 0 0
718718 −798.814 580.372i −0.0415202 0.0301662i
719719 21731.1 15788.5i 1.12717 0.818933i 0.141885 0.989883i 0.454684π-0.454684\pi
0.985280 + 0.170950i 0.0546835π0.0546835\pi
720720 0 0
721721 −1122.33 + 3454.17i −0.0579718 + 0.178419i
722722 −751.495 + 545.993i −0.0387365 + 0.0281437i
723723 0 0
724724 −2844.03 8753.02i −0.145991 0.449314i
725725 −57210.8 −2.93070
726726 0 0
727727 −17670.1 −0.901442 −0.450721 0.892665i 0.648833π-0.648833\pi
−0.450721 + 0.892665i 0.648833π0.648833\pi
728728 −93.8712 288.906i −0.00477898 0.0147082i
729729 0 0
730730 −2066.36 + 1501.30i −0.104766 + 0.0761172i
731731 −4692.74 + 14442.8i −0.237438 + 0.730759i
732732 0 0
733733 12711.4 9235.38i 0.640528 0.465371i −0.219504 0.975612i 0.570444π-0.570444\pi
0.860031 + 0.510241i 0.170444π0.170444\pi
734734 −94.1484 68.4028i −0.00473444 0.00343977i
735735 0 0
736736 −5986.03 −0.299794
737737 −4499.88 3306.15i −0.224905 0.165243i
738738 0 0
739739 5653.11 + 17398.5i 0.281398 + 0.866053i 0.987455 + 0.157899i 0.0504720π0.0504720\pi
−0.706058 + 0.708154i 0.749528π0.749528\pi
740740 36262.4 + 26346.1i 1.80139 + 1.30879i
741741 0 0
742742 −203.910 + 627.571i −0.0100886 + 0.0310496i
743743 −2963.38 + 9120.35i −0.146320 + 0.450327i −0.997178 0.0750681i 0.976083π-0.976083\pi
0.850858 + 0.525395i 0.176083π0.176083\pi
744744 0 0
745745 −32439.6 23568.7i −1.59529 1.15905i
746746 178.497 + 549.359i 0.00876040 + 0.0269617i
747747 0 0
748748 −7914.88 + 23924.7i −0.386894 + 1.16948i
749749 −24878.2 −1.21366
750750 0 0
751751 15875.4 + 11534.2i 0.771375 + 0.560437i 0.902378 0.430945i 0.141820π-0.141820\pi
−0.131003 + 0.991382i 0.541820π0.541820\pi
752752 −18913.2 + 13741.2i −0.917145 + 0.666345i
753753 0 0
754754 −71.6438 + 220.497i −0.00346036 + 0.0106499i
755755 38568.5 28021.6i 1.85914 1.35074i
756756 0 0
757757 −6612.31 20350.6i −0.317475 0.977088i −0.974724 0.223414i 0.928280π-0.928280\pi
0.657249 0.753674i 0.271720π-0.271720\pi
758758 −2084.05 −0.0998632
759759 0 0
760760 −6647.27 −0.317266
761761 −5366.23 16515.6i −0.255618 0.786713i −0.993707 0.112009i 0.964271π-0.964271\pi
0.738089 0.674704i 0.235729π-0.235729\pi
762762 0 0
763763 −16718.5 + 12146.7i −0.793252 + 0.576331i
764764 −3603.52 + 11090.5i −0.170642 + 0.525183i
765765 0 0
766766 −1759.54 + 1278.38i −0.0829960 + 0.0603001i
767767 691.222 + 502.202i 0.0325405 + 0.0236421i
768768 0 0
769769 −7235.62 −0.339302 −0.169651 0.985504i 0.554264π-0.554264\pi
−0.169651 + 0.985504i 0.554264π0.554264\pi
770770 3072.80 + 16.3850i 0.143813 + 0.000766848i
771771 0 0
772772 6368.75 + 19601.0i 0.296912 + 0.913803i
773773 −29115.2 21153.4i −1.35472 0.984263i −0.998761 0.0497615i 0.984154π-0.984154\pi
−0.355960 0.934501i 0.615846π-0.615846\pi
774774 0 0
775775 3165.74 9743.14i 0.146731 0.451592i
776776 −1083.08 + 3333.39i −0.0501036 + 0.154203i
777777 0 0
778778 −1063.10 772.385i −0.0489895 0.0355930i
779779 −4711.66 14501.0i −0.216705 0.666948i
780780 0 0
781781 4678.24 3360.98i 0.214342 0.153989i
782782 2727.43 0.124722
783783 0 0
784784 −5936.03 4312.78i −0.270409 0.196464i
785785 35058.3 25471.4i 1.59399 1.15810i
786786 0 0
787787 6781.01 20869.8i 0.307137 0.945271i −0.671734 0.740792i 0.734450π-0.734450\pi
0.978871 0.204478i 0.0655498π-0.0655498\pi
788788 18220.4 13237.9i 0.823698 0.598452i
789789 0 0
790790 −1231.07 3788.85i −0.0554425 0.170635i
791791 12876.0 0.578783
792792 0 0
793793 −766.568 −0.0343274
794794 941.617 + 2898.00i 0.0420865 + 0.129529i
795795 0 0
796796 −27162.8 + 19734.9i −1.20950 + 0.878750i
797797 435.879 1341.50i 0.0193722 0.0596214i −0.940903 0.338676i 0.890021π-0.890021\pi
0.960275 + 0.279054i 0.0900210π0.0900210\pi
798798 0 0
799799 26097.5 18961.0i 1.15552 0.839537i
800800 −7155.36 5198.67i −0.316225 0.229751i
801801 0 0
802802 550.551 0.0242402
803803 23717.6 + 126.468i 1.04231 + 0.00555787i
804804 0 0
805805 18228.5 + 56101.7i 0.798102 + 2.45630i
806806 −33.5868 24.4022i −0.00146780 0.00106642i
807807 0 0
808808 −761.925 + 2344.96i −0.0331738 + 0.102098i
809809 −4078.19 + 12551.4i −0.177233 + 0.545467i −0.999728 0.0233046i 0.992581π-0.992581\pi
0.822495 + 0.568772i 0.192581π0.192581\pi
810810 0 0
811811 −24529.0 17821.4i −1.06206 0.771631i −0.0875906 0.996157i 0.527917π-0.527917\pi
−0.974468 + 0.224526i 0.927917π0.927917\pi
812812 13758.2 + 42343.3i 0.594602 + 1.83000i
813813 0 0
814814 713.252 + 2235.66i 0.0307119 + 0.0962650i
815815 −28651.6 −1.23144
816816 0 0
817817 15004.5 + 10901.4i 0.642524 + 0.466821i
818818 580.092 421.461i 0.0247951 0.0180147i
819819 0 0
820820 6557.13 20180.8i 0.279250 0.859443i
821821 −18468.6 + 13418.3i −0.785092 + 0.570403i −0.906503 0.422200i 0.861258π-0.861258\pi
0.121411 + 0.992602i 0.461258π0.461258\pi
822822 0 0
823823 2612.94 + 8041.79i 0.110670 + 0.340607i 0.991019 0.133719i 0.0426919π-0.0426919\pi
−0.880349 + 0.474326i 0.842692π0.842692\pi
824824 572.445 0.0242015
825825 0 0
826826 −925.056 −0.0389671
827827 −6279.59 19326.6i −0.264042 0.812637i −0.991913 0.126923i 0.959490π-0.959490\pi
0.727871 0.685714i 0.240510π-0.240510\pi
828828 0 0
829829 28127.5 20435.8i 1.17842 0.856171i 0.186426 0.982469i 0.440310π-0.440310\pi
0.991992 + 0.126298i 0.0403096π0.0403096\pi
830830 370.333 1139.77i 0.0154873 0.0476649i
831831 0 0
832832 1678.84 1219.75i 0.0699557 0.0508258i
833833 8190.87 + 5951.02i 0.340693 + 0.247528i
834834 0 0
835835 58207.2 2.41239
836836 24801.9 + 18222.5i 1.02607 + 0.753873i
837837 0 0
838838 41.0496 + 126.338i 0.00169217 + 0.00520795i
839839 −20046.1 14564.3i −0.824872 0.599305i 0.0932319 0.995644i 0.470280π-0.470280\pi
−0.918104 + 0.396340i 0.870280π0.870280\pi
840840 0 0
841841 13523.4 41620.8i 0.554489 1.70654i
842842 −538.958 + 1658.74i −0.0220590 + 0.0678908i
843843 0 0
844844 −3149.05 2287.92i −0.128430 0.0933097i
845845 12493.8 + 38452.1i 0.508640 + 1.56543i
846846 0 0
847847 −22904.7 17017.4i −0.929179 0.690346i
848848 −9145.44 −0.370349
849849 0 0
850850 3260.21 + 2368.68i 0.131558 + 0.0955825i
851851 −36445.1 + 26478.9i −1.46806 + 1.06661i
852852 0 0
853853 −4036.24 + 12422.3i −0.162014 + 0.498628i −0.998804 0.0488960i 0.984430π-0.984430\pi
0.836790 + 0.547524i 0.184430π0.184430\pi
854854 671.455 487.840i 0.0269048 0.0195475i
855855 0 0
856856 1211.71 + 3729.25i 0.0483824 + 0.148906i
857857 40272.1 1.60521 0.802607 0.596508i 0.203446π-0.203446\pi
0.802607 + 0.596508i 0.203446π0.203446\pi
858858 0 0
859859 −44537.4 −1.76903 −0.884515 0.466512i 0.845510π-0.845510\pi
−0.884515 + 0.466512i 0.845510π0.845510\pi
860860 7976.02 + 24547.7i 0.316256 + 0.973335i
861861 0 0
862862 2944.54 2139.33i 0.116347 0.0845313i
863863 −4560.22 + 14034.9i −0.179874 + 0.553597i −0.999822 0.0188413i 0.994002π-0.994002\pi
0.819948 + 0.572438i 0.194002π0.194002\pi
864864 0 0
865865 −44734.3 + 32501.4i −1.75839 + 1.27755i
866866 −1716.53 1247.14i −0.0673559 0.0489369i
867867 0 0
868868 −7972.47 −0.311755
869869 −11619.2 + 35121.8i −0.453572 + 1.37103i
870870 0 0
871871 −198.335 610.412i −0.00771563 0.0237463i
872872 2635.08 + 1914.50i 0.102334 + 0.0743499i
873873 0 0
874874 1029.33 3167.97i 0.0398373 0.122606i
875875 −11570.8 + 35611.2i −0.447045 + 1.37586i
876876 0 0
877877 −11771.8 8552.74i −0.453258 0.329311i 0.337623 0.941281i 0.390377π-0.390377\pi
−0.790881 + 0.611971i 0.790377π0.790377\pi
878878 −886.076 2727.06i −0.0340588 0.104822i
879879 0 0
880880 12944.3 + 40573.4i 0.495856 + 1.55424i
881881 −13139.5 −0.502476 −0.251238 0.967925i 0.580838π-0.580838\pi
−0.251238 + 0.967925i 0.580838π0.580838\pi
882882 0 0
883883 −25815.2 18755.8i −0.983861 0.714817i −0.0252930 0.999680i 0.508052π-0.508052\pi
−0.958568 + 0.284863i 0.908052π0.908052\pi
884884 −2343.35 + 1702.55i −0.0891578 + 0.0647770i
885885 0 0
886886 177.673 546.821i 0.00673707 0.0207346i
887887 6871.20 4992.22i 0.260104 0.188977i −0.450089 0.892984i 0.648608π-0.648608\pi
0.710193 + 0.704007i 0.248608π0.248608\pi
888888 0 0
889889 12788.3 + 39358.4i 0.482459 + 1.48486i
890890 −5286.26 −0.199096
891891 0 0
892892 11235.6 0.421744
893893 −12174.3 37468.7i −0.456213 1.40408i
894894 0 0
895895 19393.5 14090.2i 0.724305 0.526238i
896896 −2833.23 + 8719.78i −0.105638 + 0.325120i
897897 0 0
898898 −920.096 + 668.489i −0.0341916 + 0.0248416i
899899 9873.00 + 7173.15i 0.366277 + 0.266116i
900900 0 0
901901 12619.4 0.466608
902902 902.228 648.185i 0.0333048 0.0239271i
903903 0 0
904904 −627.132 1930.11i −0.0230731 0.0710117i
905905 17363.4 + 12615.2i 0.637766 + 0.463364i
906906 0 0
907907 4266.48 13130.9i 0.156192 0.480710i −0.842088 0.539341i 0.818674π-0.818674\pi
0.998280 + 0.0586309i 0.0186735π0.0186735\pi
908908 5571.26 17146.6i 0.203622 0.626684i
909909 0 0
910910 285.746 + 207.607i 0.0104092 + 0.00756274i
911911 6457.15 + 19873.1i 0.234835 + 0.722748i 0.997143 + 0.0755340i 0.0240661π0.0240661\pi
−0.762308 + 0.647214i 0.775934π0.775934\pi
912912 0 0
913913 −9037.94 + 6493.10i −0.327615 + 0.235367i
914914 −1107.52 −0.0400805
915915 0 0
916916 −22256.1 16170.0i −0.802798 0.583267i
917917 −874.628 + 635.454i −0.0314970 + 0.0228839i
918918 0 0
919919 −3616.18 + 11129.4i −0.129800 + 0.399485i −0.994745 0.102383i 0.967353π-0.967353\pi
0.864945 + 0.501867i 0.167353π0.167353\pi
920920 7521.83 5464.93i 0.269552 0.195841i
921921 0 0
922922 971.624 + 2990.35i 0.0347058 + 0.106813i
923923 662.115 0.0236119
924924 0 0
925925 −66560.5 −2.36594
926926 714.550 + 2199.16i 0.0253581 + 0.0780441i
927927 0 0
928928 8523.74 6192.86i 0.301515 0.219063i
929929 −9323.94 + 28696.1i −0.329288 + 1.01344i 0.640180 + 0.768225i 0.278860π0.278860\pi
−0.969468 + 0.245219i 0.921140π0.921140\pi
930930 0 0
931931 10003.5 7267.95i 0.352149 0.255851i
932932 21095.4 + 15326.7i 0.741418 + 0.538671i
933933 0 0
934934 −1525.81 −0.0534539
935935 −17861.3 55985.5i −0.624736 1.95821i
936936 0 0
937937 16674.1 + 51317.7i 0.581345 + 1.78919i 0.613479 + 0.789711i 0.289770π0.289770\pi
−0.0321342 + 0.999484i 0.510230π0.510230\pi
938938 562.189 + 408.454i 0.0195694 + 0.0142180i
939939 0 0
940940 16942.8 52144.4i 0.587885 1.80932i
941941 2538.21 7811.81i 0.0879313 0.270625i −0.897416 0.441186i 0.854558π-0.854558\pi
0.985347 + 0.170561i 0.0545580π0.0545580\pi
942942 0 0
943943 17253.3 + 12535.3i 0.595806 + 0.432878i
944944 −3961.86 12193.3i −0.136597 0.420402i
945945 0 0
946946 −424.428 + 1282.94i −0.0145870 + 0.0440929i
947947 16429.1 0.563752 0.281876 0.959451i 0.409043π-0.409043\pi
0.281876 + 0.959451i 0.409043π0.409043\pi
948948 0 0
949949 2205.55 + 1602.42i 0.0754426 + 0.0548123i
950950 3981.68 2892.86i 0.135982 0.0987966i
951951 0 0
952952 1943.67 5982.01i 0.0661710 0.203654i
953953 9432.80 6853.33i 0.320628 0.232950i −0.415816 0.909449i 0.636504π-0.636504\pi
0.736443 + 0.676499i 0.236504π0.236504\pi
954954 0 0
955955 −8403.34 25862.8i −0.284739 0.876336i
956956 −28627.2 −0.968482
957957 0 0
958958 1974.24 0.0665812
959959 5702.56 + 17550.7i 0.192018 + 0.590971i
960960 0 0
961961 22333.5 16226.2i 0.749673 0.544669i
962962 −83.3521 + 256.531i −0.00279353 + 0.00859762i
963963 0 0
964964 25400.4 18454.5i 0.848644 0.616576i
965965 −38882.5 28249.8i −1.29707 0.942377i
966966 0 0
967967 15270.1 0.507809 0.253905 0.967229i 0.418285π-0.418285\pi
0.253905 + 0.967229i 0.418285π0.418285\pi
968968 −1435.32 + 4262.26i −0.0476581 + 0.141523i
969969 0 0
970970 −1259.31 3875.77i −0.0416847 0.128292i
971971 24556.6 + 17841.4i 0.811594 + 0.589658i 0.914292 0.405055i 0.132748π-0.132748\pi
−0.102698 + 0.994713i 0.532748π0.532748\pi
972972 0 0
973973 8116.16 24979.0i 0.267412 0.823010i
974974 −640.355 + 1970.81i −0.0210660 + 0.0648346i
975975 0 0
976976 9306.05 + 6761.24i 0.305204 + 0.221744i
977977 −16241.9 49987.4i −0.531857 1.63689i −0.750344 0.661047i 0.770112π-0.770112\pi
0.218488 0.975840i 0.429888π-0.429888\pi
978978 0 0
979979 39558.8 + 29064.7i 1.29142 + 0.948836i
980980 17208.1 0.560910
981981 0 0
982982 1154.48 + 838.778i 0.0375162 + 0.0272571i
983983 27337.5 19861.9i 0.887012 0.644452i −0.0480855 0.998843i 0.515312π-0.515312\pi
0.935097 + 0.354392i 0.115312π0.115312\pi
984984 0 0
985985 −16229.6 + 49949.5i −0.524992 + 1.61576i
986986 −3883.69 + 2821.67i −0.125438 + 0.0911361i
987987 0 0
988988 1093.16 + 3364.40i 0.0352004 + 0.108336i
989989 −25941.0 −0.834051
990990 0 0
991991 5221.81 0.167383 0.0836914 0.996492i 0.473329π-0.473329\pi
0.0836914 + 0.996492i 0.473329π0.473329\pi
992992 583.001 + 1794.29i 0.0186596 + 0.0574283i
993993 0 0
994994 −579.962 + 421.367i −0.0185063 + 0.0134456i
995995 24194.9 74464.2i 0.770884 2.37254i
996996 0 0
997997 −11623.6 + 8445.03i −0.369230 + 0.268262i −0.756892 0.653540i 0.773283π-0.773283\pi
0.387661 + 0.921802i 0.373283π0.373283\pi
998998 3144.28 + 2284.45i 0.0997299 + 0.0724580i
999999 0 0
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 99.4.f.e.82.4 yes 24
3.2 odd 2 inner 99.4.f.e.82.3 yes 24
11.3 even 5 1089.4.a.bm.1.7 12
11.8 odd 10 1089.4.a.bl.1.6 12
11.9 even 5 inner 99.4.f.e.64.4 yes 24
33.8 even 10 1089.4.a.bl.1.7 12
33.14 odd 10 1089.4.a.bm.1.6 12
33.20 odd 10 inner 99.4.f.e.64.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.4.f.e.64.3 24 33.20 odd 10 inner
99.4.f.e.64.4 yes 24 11.9 even 5 inner
99.4.f.e.82.3 yes 24 3.2 odd 2 inner
99.4.f.e.82.4 yes 24 1.1 even 1 trivial
1089.4.a.bl.1.6 12 11.8 odd 10
1089.4.a.bl.1.7 12 33.8 even 10
1089.4.a.bm.1.6 12 33.14 odd 10
1089.4.a.bm.1.7 12 11.3 even 5