Properties

Label 152.4.b.b.75.52
Level 152152
Weight 44
Character 152.75
Analytic conductor 8.9688.968
Analytic rank 00
Dimension 5656
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [152,4,Mod(75,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.75");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 152=2319 152 = 2^{3} \cdot 19
Weight: k k == 4 4
Character orbit: [χ][\chi] == 152.b (of order 22, degree 11, 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: 8.968290320878.96829032087
Analytic rank: 00
Dimension: 5656
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 75.52
Character χ\chi == 152.75
Dual form 152.4.b.b.75.51

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+(2.66988+0.933662i)q2+0.255308iq3+(6.25655+4.98554i)q411.8859iq5+(0.238371+0.681642i)q6+31.1204iq7+(12.0494+19.1523i)q8+26.9348q9+(11.097431.7339i)q1021.9564q11+(1.27285+1.59735i)q12+38.7293q13+(29.0559+83.0878i)q14+3.03456q15+(14.2888+62.3845i)q16+101.750q17+(71.9128+25.1480i)q18+(20.222480.3122i)q19+(59.257474.3645i)q207.94528q21+(58.620920.4998i)q22+57.3504iq23+(4.88973+3.07632i)q2416.2739q25+(103.403+36.1601i)q26+13.7700iq27+(155.152+194.706i)q28206.088q29+(8.10191+2.83325i)q30312.889q31+(20.0965+179.900i)q325.60563iq33+(271.660+94.9998i)q34+369.893q35+(168.519+134.285i)q36156.076q37+(20.9931233.305i)q38+9.88790iq39+(227.642143.218i)q40399.236iq41+(21.21307.41821i)q42+96.2576q43+(137.371109.464i)q44320.144iq45+(53.5459+153.119i)q46209.396iq47+(15.9273+3.64805i)q48625.479q49+(43.449315.1943i)q50+25.9775iq51+(242.312+193.086i)q52+455.858q53+(12.8565+36.7642i)q54+260.970iq55+(596.027+374.984i)q56+(20.50435.16293i)q57+(550.230192.416i)q58451.215iq59+(18.9858+15.1289i)q60385.501iq61+(835.377292.132i)q62+838.222iq63+(221.622+461.549i)q64460.332iq65+(5.2337714.9664i)q66261.804iq67+(636.602+507.277i)q6814.6420q69+(987.571+345.355i)q70+546.989q71+(324.550+515.864i)q72443.977q73+(416.706145.723i)q744.15485iq75+(273.877603.297i)q76683.291iq77+(9.23196+26.3995i)q78950.449q79+(741.494169.835i)q80+723.724q81+(372.7511065.91i)q82537.548q83+(49.710139.6115i)q841209.38iq85+(256.997+89.8721i)q8652.6158iq87+(264.562420.515i)q88+1404.85iq89+(298.906854.746i)q90+1205.27iq91+(285.922+358.815i)q9279.8830iq93+(195.505559.063i)q94+(954.581+240.361i)q95+(45.93005.13081i)q96398.059iq97+(1669.96583.987i)q98591.391q99+O(q100)q+(2.66988 + 0.933662i) q^{2} +0.255308i q^{3} +(6.25655 + 4.98554i) q^{4} -11.8859i q^{5} +(-0.238371 + 0.681642i) q^{6} +31.1204i q^{7} +(12.0494 + 19.1523i) q^{8} +26.9348 q^{9} +(11.0974 - 31.7339i) q^{10} -21.9564 q^{11} +(-1.27285 + 1.59735i) q^{12} +38.7293 q^{13} +(-29.0559 + 83.0878i) q^{14} +3.03456 q^{15} +(14.2888 + 62.3845i) q^{16} +101.750 q^{17} +(71.9128 + 25.1480i) q^{18} +(-20.2224 - 80.3122i) q^{19} +(59.2574 - 74.3645i) q^{20} -7.94528 q^{21} +(-58.6209 - 20.4998i) q^{22} +57.3504i q^{23} +(-4.88973 + 3.07632i) q^{24} -16.2739 q^{25} +(103.403 + 36.1601i) q^{26} +13.7700i q^{27} +(-155.152 + 194.706i) q^{28} -206.088 q^{29} +(8.10191 + 2.83325i) q^{30} -312.889 q^{31} +(-20.0965 + 179.900i) q^{32} -5.60563i q^{33} +(271.660 + 94.9998i) q^{34} +369.893 q^{35} +(168.519 + 134.285i) q^{36} -156.076 q^{37} +(20.9931 - 233.305i) q^{38} +9.88790i q^{39} +(227.642 - 143.218i) q^{40} -399.236i q^{41} +(-21.2130 - 7.41821i) q^{42} +96.2576 q^{43} +(-137.371 - 109.464i) q^{44} -320.144i q^{45} +(-53.5459 + 153.119i) q^{46} -209.396i q^{47} +(-15.9273 + 3.64805i) q^{48} -625.479 q^{49} +(-43.4493 - 15.1943i) q^{50} +25.9775i q^{51} +(242.312 + 193.086i) q^{52} +455.858 q^{53} +(-12.8565 + 36.7642i) q^{54} +260.970i q^{55} +(-596.027 + 374.984i) q^{56} +(20.5043 - 5.16293i) q^{57} +(-550.230 - 192.416i) q^{58} -451.215i q^{59} +(18.9858 + 15.1289i) q^{60} -385.501i q^{61} +(-835.377 - 292.132i) q^{62} +838.222i q^{63} +(-221.622 + 461.549i) q^{64} -460.332i q^{65} +(5.23377 - 14.9664i) q^{66} -261.804i q^{67} +(636.602 + 507.277i) q^{68} -14.6420 q^{69} +(987.571 + 345.355i) q^{70} +546.989 q^{71} +(324.550 + 515.864i) q^{72} -443.977 q^{73} +(-416.706 - 145.723i) q^{74} -4.15485i q^{75} +(273.877 - 603.297i) q^{76} -683.291i q^{77} +(-9.23196 + 26.3995i) q^{78} -950.449 q^{79} +(741.494 - 169.835i) q^{80} +723.724 q^{81} +(372.751 - 1065.91i) q^{82} -537.548 q^{83} +(-49.7101 - 39.6115i) q^{84} -1209.38i q^{85} +(256.997 + 89.8721i) q^{86} -52.6158i q^{87} +(-264.562 - 420.515i) q^{88} +1404.85i q^{89} +(298.906 - 854.746i) q^{90} +1205.27i q^{91} +(-285.922 + 358.815i) q^{92} -79.8830i q^{93} +(195.505 - 559.063i) q^{94} +(-954.581 + 240.361i) q^{95} +(-45.9300 - 5.13081i) q^{96} -398.059i q^{97} +(-1669.96 - 583.987i) q^{98} -591.391 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 56q+2q414q6528q940q11262q16184q1784q1912q20+238q241504q25+378q26382q28+512q30+40q35+1464q36+958q38+6152q99+O(q100) 56 q + 2 q^{4} - 14 q^{6} - 528 q^{9} - 40 q^{11} - 262 q^{16} - 184 q^{17} - 84 q^{19} - 12 q^{20} + 238 q^{24} - 1504 q^{25} + 378 q^{26} - 382 q^{28} + 512 q^{30} + 40 q^{35} + 1464 q^{36} + 958 q^{38}+ \cdots - 6152 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/152Z)×\left(\mathbb{Z}/152\mathbb{Z}\right)^\times.

nn 3939 7777 9797
χ(n)\chi(n) 1-1 1-1 1-1

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 2.66988 + 0.933662i 0.943946 + 0.330099i
33 0.255308i 0.0491340i 0.999698 + 0.0245670i 0.00782071π0.00782071\pi
−0.999698 + 0.0245670i 0.992179π0.992179\pi
44 6.25655 + 4.98554i 0.782069 + 0.623192i
55 11.8859i 1.06310i −0.847026 0.531552i 0.821609π-0.821609\pi
0.847026 0.531552i 0.178391π-0.178391\pi
66 −0.238371 + 0.681642i −0.0162191 + 0.0463799i
77 31.1204i 1.68034i 0.542320 + 0.840172i 0.317546π0.317546\pi
−0.542320 + 0.840172i 0.682454π0.682454\pi
88 12.0494 + 19.1523i 0.532515 + 0.846420i
99 26.9348 0.997586
1010 11.0974 31.7339i 0.350930 1.00351i
1111 −21.9564 −0.601827 −0.300913 0.953652i 0.597291π-0.597291\pi
−0.300913 + 0.953652i 0.597291π0.597291\pi
1212 −1.27285 + 1.59735i −0.0306199 + 0.0384262i
1313 38.7293 0.826276 0.413138 0.910669i 0.364433π-0.364433\pi
0.413138 + 0.910669i 0.364433π0.364433\pi
1414 −29.0559 + 83.0878i −0.554681 + 1.58615i
1515 3.03456 0.0522346
1616 14.2888 + 62.3845i 0.223263 + 0.974758i
1717 101.750 1.45164 0.725821 0.687883i 0.241460π-0.241460\pi
0.725821 + 0.687883i 0.241460π0.241460\pi
1818 71.9128 + 25.1480i 0.941667 + 0.329303i
1919 −20.2224 80.3122i −0.244175 0.969731i
2020 59.2574 74.3645i 0.662518 0.831421i
2121 −7.94528 −0.0825620
2222 −58.6209 20.4998i −0.568092 0.198663i
2323 57.3504i 0.519929i 0.965618 + 0.259965i 0.0837109π0.0837109\pi
−0.965618 + 0.259965i 0.916289π0.916289\pi
2424 −4.88973 + 3.07632i −0.0415880 + 0.0261646i
2525 −16.2739 −0.130191
2626 103.403 + 36.1601i 0.779960 + 0.272753i
2727 13.7700i 0.0981494i
2828 −155.152 + 194.706i −1.04718 + 1.31414i
2929 −206.088 −1.31964 −0.659819 0.751424i 0.729367π-0.729367\pi
−0.659819 + 0.751424i 0.729367π0.729367\pi
3030 8.10191 + 2.83325i 0.0493066 + 0.0172426i
3131 −312.889 −1.81279 −0.906395 0.422431i 0.861177π-0.861177\pi
−0.906395 + 0.422431i 0.861177π0.861177\pi
3232 −20.0965 + 179.900i −0.111019 + 0.993818i
3333 5.60563i 0.0295702i
3434 271.660 + 94.9998i 1.37027 + 0.479186i
3535 369.893 1.78638
3636 168.519 + 134.285i 0.780181 + 0.621688i
3737 −156.076 −0.693481 −0.346741 0.937961i 0.612712π-0.612712\pi
−0.346741 + 0.937961i 0.612712π0.612712\pi
3838 20.9931 233.305i 0.0896192 0.995976i
3939 9.88790i 0.0405982i
4040 227.642 143.218i 0.899833 0.566120i
4141 399.236i 1.52074i −0.649493 0.760368i 0.725019π-0.725019\pi
0.649493 0.760368i 0.274981π-0.274981\pi
4242 −21.2130 7.41821i −0.0779341 0.0272537i
4343 96.2576 0.341375 0.170688 0.985325i 0.445401π-0.445401\pi
0.170688 + 0.985325i 0.445401π0.445401\pi
4444 −137.371 109.464i −0.470670 0.375054i
4545 320.144i 1.06054i
4646 −53.5459 + 153.119i −0.171628 + 0.490785i
4747 209.396i 0.649863i −0.945737 0.324932i 0.894659π-0.894659\pi
0.945737 0.324932i 0.105341π-0.105341\pi
4848 −15.9273 + 3.64805i −0.0478938 + 0.0109698i
4949 −625.479 −1.82356
5050 −43.4493 15.1943i −0.122893 0.0429759i
5151 25.9775i 0.0713250i
5252 242.312 + 193.086i 0.646204 + 0.514928i
5353 455.858 1.18145 0.590725 0.806873i 0.298842π-0.298842\pi
0.590725 + 0.806873i 0.298842π0.298842\pi
5454 −12.8565 + 36.7642i −0.0323991 + 0.0926478i
5555 260.970i 0.639804i
5656 −596.027 + 374.984i −1.42228 + 0.894809i
5757 20.5043 5.16293i 0.0476468 0.0119973i
5858 −550.230 192.416i −1.24567 0.435612i
5959 451.215i 0.995647i −0.867279 0.497823i 0.834133π-0.834133\pi
0.867279 0.497823i 0.165867π-0.165867\pi
6060 18.9858 + 15.1289i 0.0408510 + 0.0325522i
6161 385.501i 0.809154i −0.914504 0.404577i 0.867419π-0.867419\pi
0.914504 0.404577i 0.132581π-0.132581\pi
6262 −835.377 292.132i −1.71118 0.598401i
6363 838.222i 1.67629i
6464 −221.622 + 461.549i −0.432855 + 0.901464i
6565 460.332i 0.878417i
6666 5.23377 14.9664i 0.00976109 0.0279126i
6767 261.804i 0.477380i −0.971096 0.238690i 0.923282π-0.923282\pi
0.971096 0.238690i 0.0767179π-0.0767179\pi
6868 636.602 + 507.277i 1.13528 + 0.904652i
6969 −14.6420 −0.0255462
7070 987.571 + 345.355i 1.68625 + 0.589683i
7171 546.989 0.914306 0.457153 0.889388i 0.348869π-0.348869\pi
0.457153 + 0.889388i 0.348869π0.348869\pi
7272 324.550 + 515.864i 0.531230 + 0.844377i
7373 −443.977 −0.711830 −0.355915 0.934518i 0.615831π-0.615831\pi
−0.355915 + 0.934518i 0.615831π0.615831\pi
7474 −416.706 145.723i −0.654609 0.228918i
7575 4.15485i 0.00639680i
7676 273.877 603.297i 0.413367 0.910565i
7777 683.291i 1.01128i
7878 −9.23196 + 26.3995i −0.0134015 + 0.0383226i
7979 −950.449 −1.35359 −0.676797 0.736170i 0.736632π-0.736632\pi
−0.676797 + 0.736170i 0.736632π0.736632\pi
8080 741.494 169.835i 1.03627 0.237352i
8181 723.724 0.992763
8282 372.751 1065.91i 0.501994 1.43549i
8383 −537.548 −0.710886 −0.355443 0.934698i 0.615670π-0.615670\pi
−0.355443 + 0.934698i 0.615670π0.615670\pi
8484 −49.7101 39.6115i −0.0645692 0.0514520i
8585 1209.38i 1.54325i
8686 256.997 + 89.8721i 0.322240 + 0.112688i
8787 52.6158i 0.0648391i
8888 −264.562 420.515i −0.320482 0.509398i
8989 1404.85i 1.67319i 0.547822 + 0.836595i 0.315457π0.315457\pi
−0.547822 + 0.836595i 0.684543π0.684543\pi
9090 298.906 854.746i 0.350083 1.00109i
9191 1205.27i 1.38843i
9292 −285.922 + 358.815i −0.324016 + 0.406621i
9393 79.8830i 0.0890697i
9494 195.505 559.063i 0.214520 0.613436i
9595 −954.581 + 240.361i −1.03093 + 0.259584i
9696 −45.9300 5.13081i −0.0488303 0.00545480i
9797 398.059i 0.416668i −0.978058 0.208334i 0.933196π-0.933196\pi
0.978058 0.208334i 0.0668041π-0.0668041\pi
9898 −1669.96 583.987i −1.72134 0.601955i
9999 −591.391 −0.600374
100100 −101.818 81.1340i −0.101818 0.0811340i
101101 1111.11i 1.09464i 0.836922 + 0.547322i 0.184353π0.184353\pi
−0.836922 + 0.547322i 0.815647π0.815647\pi
102102 −24.2542 + 69.3569i −0.0235444 + 0.0673270i
103103 998.893 0.955571 0.477786 0.878477i 0.341440π-0.341440\pi
0.477786 + 0.878477i 0.341440π0.341440\pi
104104 466.667 + 741.756i 0.440004 + 0.699376i
105105 94.4366i 0.0877721i
106106 1217.09 + 425.617i 1.11523 + 0.389996i
107107 82.6255i 0.0746515i −0.999303 0.0373257i 0.988116π-0.988116\pi
0.999303 0.0373257i 0.0118839π-0.0118839\pi
108108 −68.6508 + 86.1526i −0.0611659 + 0.0767596i
109109 −836.605 −0.735158 −0.367579 0.929992i 0.619813π-0.619813\pi
−0.367579 + 0.929992i 0.619813π0.619813\pi
110110 −243.658 + 696.761i −0.211199 + 0.603941i
111111 39.8475i 0.0340735i
112112 −1941.43 + 444.674i −1.63793 + 0.375159i
113113 580.927i 0.483620i −0.970324 0.241810i 0.922259π-0.922259\pi
0.970324 0.241810i 0.0777411π-0.0777411\pi
114114 59.5646 + 5.35970i 0.0489363 + 0.00440335i
115115 681.659 0.552739
116116 −1289.40 1027.46i −1.03205 0.822388i
117117 1043.17 0.824281
118118 421.282 1204.69i 0.328662 0.939837i
119119 3166.49i 2.43926i
120120 36.5647 + 58.1187i 0.0278157 + 0.0442124i
121121 −848.918 −0.637805
122122 359.928 1029.24i 0.267101 0.763798i
123123 101.928 0.0747199
124124 −1957.60 1559.92i −1.41773 1.12972i
125125 1292.30i 0.924698i
126126 −782.617 + 2237.96i −0.553341 + 1.58232i
127127 1015.44 0.709496 0.354748 0.934962i 0.384567π-0.384567\pi
0.354748 + 0.934962i 0.384567π0.384567\pi
128128 −1022.63 + 1025.36i −0.706164 + 0.708048i
129129 24.5753i 0.0167732i
130130 429.794 1229.03i 0.289965 0.829178i
131131 1970.99 1.31455 0.657276 0.753650i 0.271708π-0.271708\pi
0.657276 + 0.753650i 0.271708π0.271708\pi
132132 27.9471 35.0719i 0.0184279 0.0231259i
133133 2499.35 629.329i 1.62948 0.410299i
134134 244.436 698.986i 0.157583 0.450621i
135135 163.668 0.104343
136136 1226.03 + 1948.74i 0.773022 + 1.22870i
137137 −755.460 −0.471119 −0.235559 0.971860i 0.575692π-0.575692\pi
−0.235559 + 0.971860i 0.575692π0.575692\pi
138138 −39.0924 13.6707i −0.0241143 0.00843279i
139139 2128.52 1.29884 0.649419 0.760431i 0.275012π-0.275012\pi
0.649419 + 0.760431i 0.275012π0.275012\pi
140140 2314.25 + 1844.12i 1.39707 + 1.11326i
141141 53.4605 0.0319304
142142 1460.40 + 510.703i 0.863055 + 0.301812i
143143 −850.355 −0.497275
144144 384.867 + 1680.32i 0.222724 + 0.972405i
145145 2449.53i 1.40291i
146146 −1185.37 414.525i −0.671929 0.234975i
147147 159.690i 0.0895986i
148148 −976.500 778.125i −0.542350 0.432172i
149149 1029.90i 0.566258i −0.959082 0.283129i 0.908628π-0.908628\pi
0.959082 0.283129i 0.0913724π-0.0913724\pi
150150 3.87922 11.0930i 0.00211158 0.00603824i
151151 1189.40 0.641005 0.320502 0.947248i 0.396148π-0.396148\pi
0.320502 + 0.947248i 0.396148π0.396148\pi
152152 1294.50 1355.02i 0.690773 0.723072i
153153 2740.61 1.44814
154154 637.963 1824.31i 0.333821 0.954590i
155155 3718.96i 1.92719i
156156 −49.2965 + 61.8641i −0.0253005 + 0.0317506i
157157 3448.86i 1.75318i 0.481241 + 0.876588i 0.340186π0.340186\pi
−0.481241 + 0.876588i 0.659814π0.659814\pi
158158 −2537.59 887.398i −1.27772 0.446820i
159159 116.384i 0.0580494i
160160 2138.27 + 238.865i 1.05653 + 0.118025i
161161 −1784.77 −0.873660
162162 1932.26 + 675.714i 0.937115 + 0.327711i
163163 −2774.87 −1.33340 −0.666701 0.745325i 0.732294π-0.732294\pi
−0.666701 + 0.745325i 0.732294π0.732294\pi
164164 1990.41 2497.84i 0.947711 1.18932i
165165 −66.6278 −0.0314362
166166 −1435.19 501.888i −0.671039 0.234663i
167167 150.985 0.0699615 0.0349807 0.999388i 0.488863π-0.488863\pi
0.0349807 + 0.999388i 0.488863π0.488863\pi
168168 −95.7363 152.170i −0.0439656 0.0698822i
169169 −697.039 −0.317269
170170 1129.16 3228.91i 0.509425 1.45674i
171171 −544.686 2163.20i −0.243586 0.967390i
172172 602.240 + 479.896i 0.266979 + 0.212743i
173173 −1161.80 −0.510579 −0.255289 0.966865i 0.582171π-0.582171\pi
−0.255289 + 0.966865i 0.582171π0.582171\pi
174174 49.1254 140.478i 0.0214034 0.0612047i
175175 506.449i 0.218766i
176176 −313.731 1369.74i −0.134366 0.586635i
177177 115.199 0.0489201
178178 −1311.66 + 3750.79i −0.552319 + 1.57940i
179179 4506.82i 1.88188i 0.338580 + 0.940938i 0.390053π0.390053\pi
−0.338580 + 0.940938i 0.609947π0.609947\pi
180180 1596.09 2003.00i 0.660919 0.829414i
181181 1300.89 0.534222 0.267111 0.963666i 0.413931π-0.413931\pi
0.267111 + 0.963666i 0.413931π0.413931\pi
182182 −1125.32 + 3217.94i −0.458319 + 1.31060i
183183 98.4215 0.0397570
184184 −1098.39 + 691.040i −0.440079 + 0.276870i
185185 1855.10i 0.737243i
186186 74.5837 213.278i 0.0294018 0.0840770i
187187 −2234.05 −0.873637
188188 1043.95 1310.10i 0.404990 0.508238i
189189 −428.527 −0.164925
190190 −2773.03 249.521i −1.05883 0.0952746i
191191 1713.84i 0.649263i −0.945841 0.324631i 0.894760π-0.894760\pi
0.945841 0.324631i 0.105240π-0.105240\pi
192192 −117.837 56.5817i −0.0442925 0.0212679i
193193 836.962i 0.312154i −0.987745 0.156077i 0.950115π-0.950115\pi
0.987745 0.156077i 0.0498849π-0.0498849\pi
194194 371.653 1062.77i 0.137542 0.393312i
195195 117.526 0.0431602
196196 −3913.34 3118.35i −1.42615 1.13643i
197197 567.220i 0.205141i 0.994726 + 0.102570i 0.0327067π0.0327067\pi
−0.994726 + 0.102570i 0.967293π0.967293\pi
198198 −1578.94 552.159i −0.566720 0.198183i
199199 3533.62i 1.25875i −0.777101 0.629376i 0.783310π-0.783310\pi
0.777101 0.629376i 0.216690π-0.216690\pi
200200 −196.091 311.682i −0.0693287 0.110196i
201201 66.8406 0.0234556
202202 −1037.40 + 2966.52i −0.361342 + 1.03329i
203203 6413.53i 2.21745i
204204 −129.512 + 162.530i −0.0444492 + 0.0557811i
205205 −4745.27 −1.61670
206206 2666.93 + 932.628i 0.902008 + 0.315433i
207207 1544.72i 0.518674i
208208 553.397 + 2416.11i 0.184477 + 0.805419i
209209 444.010 + 1763.36i 0.146951 + 0.583610i
210210 −88.1719 + 252.135i −0.0289735 + 0.0828521i
211211 3990.60i 1.30201i −0.759073 0.651006i 0.774347π-0.774347\pi
0.759073 0.651006i 0.225653π-0.225653\pi
212212 2852.10 + 2272.69i 0.923975 + 0.736270i
213213 139.651i 0.0449235i
214214 77.1443 220.600i 0.0246424 0.0704670i
215215 1144.11i 0.362918i
216216 −263.727 + 165.921i −0.0830757 + 0.0522661i
217217 9737.23i 3.04611i
218218 −2233.64 781.106i −0.693949 0.242675i
219219 113.351i 0.0349751i
220220 −1301.08 + 1632.77i −0.398721 + 0.500371i
221221 3940.70 1.19946
222222 37.2041 106.388i 0.0112476 0.0321636i
223223 −1073.95 −0.322498 −0.161249 0.986914i 0.551552π-0.551552\pi
−0.161249 + 0.986914i 0.551552π0.551552\pi
224224 −5598.57 625.413i −1.66996 0.186550i
225225 −438.334 −0.129877
226226 542.390 1551.01i 0.159643 0.456511i
227227 3165.76i 0.925633i 0.886454 + 0.462816i 0.153161π0.153161\pi
−0.886454 + 0.462816i 0.846839π0.846839\pi
228228 154.026 + 69.9230i 0.0447397 + 0.0203104i
229229 2500.47i 0.721553i −0.932652 0.360776i 0.882512π-0.882512\pi
0.932652 0.360776i 0.117488π-0.117488\pi
230230 1819.95 + 636.439i 0.521756 + 0.182459i
231231 174.450 0.0496880
232232 −2483.24 3947.05i −0.702728 1.11697i
233233 1034.30 0.290812 0.145406 0.989372i 0.453551π-0.453551\pi
0.145406 + 0.989372i 0.453551π0.453551\pi
234234 2785.13 + 973.966i 0.778077 + 0.272095i
235235 −2488.86 −0.690873
236236 2249.55 2823.05i 0.620479 0.778664i
237237 242.657i 0.0665075i
238238 −2956.43 + 8454.16i −0.805198 + 2.30253i
239239 1446.06i 0.391370i −0.980667 0.195685i 0.937307π-0.937307\pi
0.980667 0.195685i 0.0626931π-0.0626931\pi
240240 43.3603 + 189.309i 0.0116621 + 0.0509161i
241241 3098.89i 0.828288i 0.910211 + 0.414144i 0.135919π0.135919\pi
−0.910211 + 0.414144i 0.864081π0.864081\pi
242242 −2266.51 792.603i −0.602053 0.210539i
243243 556.562i 0.146928i
244244 1921.93 2411.91i 0.504258 0.632814i
245245 7434.37i 1.93863i
246246 272.136 + 95.1664i 0.0705315 + 0.0246650i
247247 −783.199 3110.44i −0.201756 0.801265i
248248 −3770.14 5992.54i −0.965339 1.53438i
249249 137.240i 0.0349287i
250250 1206.58 3450.30i 0.305242 0.872865i
251251 3586.47 0.901897 0.450948 0.892550i 0.351086π-0.351086\pi
0.450948 + 0.892550i 0.351086π0.351086\pi
252252 −4178.99 + 5244.38i −1.04465 + 1.31097i
253253 1259.21i 0.312907i
254254 2711.11 + 948.081i 0.669726 + 0.234204i
255255 308.765 0.0758260
256256 −3687.66 + 1782.80i −0.900307 + 0.435255i
257257 6739.57i 1.63581i 0.575355 + 0.817904i 0.304864π0.304864\pi
−0.575355 + 0.817904i 0.695136π0.695136\pi
258258 −22.9450 + 65.6132i −0.00553681 + 0.0158330i
259259 4857.16i 1.16529i
260260 2295.00 2880.09i 0.547423 0.686983i
261261 −5550.93 −1.31645
262262 5262.32 + 1840.24i 1.24087 + 0.433933i
263263 2998.75i 0.703083i −0.936172 0.351541i 0.885658π-0.885658\pi
0.936172 0.351541i 0.114342π-0.114342\pi
264264 107.361 67.5448i 0.0250288 0.0157466i
265265 5418.26i 1.25600i
266266 7260.55 + 653.314i 1.67358 + 0.150591i
267267 −358.669 −0.0822105
268268 1305.23 1637.99i 0.297499 0.373344i
269269 −3587.92 −0.813231 −0.406615 0.913599i 0.633291π-0.633291\pi
−0.406615 + 0.913599i 0.633291π0.633291\pi
270270 436.975 + 152.811i 0.0984943 + 0.0344436i
271271 2610.23i 0.585092i −0.956251 0.292546i 0.905498π-0.905498\pi
0.956251 0.292546i 0.0945025π-0.0945025\pi
272272 1453.88 + 6347.61i 0.324098 + 1.41500i
273273 −307.715 −0.0682190
274274 −2016.99 705.344i −0.444711 0.155516i
275275 357.315 0.0783524
276276 −91.6084 72.9982i −0.0199789 0.0159202i
277277 5163.37i 1.11999i 0.828497 + 0.559994i 0.189197π0.189197\pi
−0.828497 + 0.559994i 0.810803π0.810803\pi
278278 5682.89 + 1987.32i 1.22603 + 0.428745i
279279 −8427.60 −1.80841
280280 4457.01 + 7084.30i 0.951275 + 1.51203i
281281 5390.26i 1.14433i −0.820140 0.572163i 0.806104π-0.806104\pi
0.820140 0.572163i 0.193896π-0.193896\pi
282282 142.733 + 49.9140i 0.0301406 + 0.0105402i
283283 −7541.59 −1.58410 −0.792051 0.610455i 0.790987π-0.790987\pi
−0.792051 + 0.610455i 0.790987π0.790987\pi
284284 3422.27 + 2727.04i 0.715050 + 0.569788i
285285 −61.3659 243.712i −0.0127544 0.0506535i
286286 −2270.35 793.944i −0.469400 0.164150i
287287 12424.4 2.55536
288288 −541.297 + 4845.58i −0.110751 + 0.991419i
289289 5440.00 1.10727
290290 −2287.03 + 6539.96i −0.463101 + 1.32427i
291291 101.628 0.0204726
292292 −2777.77 2213.46i −0.556700 0.443607i
293293 −2730.96 −0.544520 −0.272260 0.962224i 0.587771π-0.587771\pi
−0.272260 + 0.962224i 0.587771π0.587771\pi
294294 149.096 426.353i 0.0295764 0.0845763i
295295 −5363.08 −1.05848
296296 −1880.63 2989.22i −0.369289 0.586976i
297297 302.339i 0.0590689i
298298 961.575 2749.70i 0.186921 0.534517i
299299 2221.14i 0.429605i
300300 20.7141 25.9950i 0.00398644 0.00500274i
301301 2995.58i 0.573628i
302302 3175.55 + 1110.49i 0.605074 + 0.211595i
303303 −283.674 −0.0537843
304304 4721.29 2409.13i 0.890738 0.454517i
305305 −4582.02 −0.860215
306306 7317.11 + 2558.80i 1.36696 + 0.478030i
307307 1024.35i 0.190433i 0.995457 + 0.0952163i 0.0303543π0.0303543\pi
−0.995457 + 0.0952163i 0.969646π0.969646\pi
308308 3406.57 4275.04i 0.630219 0.790887i
309309 255.025i 0.0469510i
310310 −3472.25 + 9929.18i −0.636163 + 1.81916i
311311 2526.27i 0.460617i 0.973118 + 0.230308i 0.0739735π0.0739735\pi
−0.973118 + 0.230308i 0.926027π0.926027\pi
312312 −189.376 + 119.144i −0.0343632 + 0.0216192i
313313 10532.3 1.90199 0.950994 0.309209i 0.100064π-0.100064\pi
0.950994 + 0.309209i 0.100064π0.100064\pi
314314 −3220.07 + 9208.04i −0.578723 + 1.65490i
315315 9963.00 1.78207
316316 −5946.53 4738.50i −1.05860 0.843549i
317317 6189.48 1.09664 0.548322 0.836267i 0.315267π-0.315267\pi
0.548322 + 0.836267i 0.315267π0.315267\pi
318318 −108.663 + 310.732i −0.0191621 + 0.0547955i
319319 4524.94 0.794194
320320 5485.92 + 2634.16i 0.958350 + 0.460170i
321321 21.0949 0.00366793
322322 −4765.12 1666.37i −0.824688 0.288395i
323323 −2057.62 8171.75i −0.354455 1.40770i
324324 4528.02 + 3608.16i 0.776409 + 0.618682i
325325 −630.276 −0.107574
326326 −7408.58 2590.79i −1.25866 0.440156i
327327 213.592i 0.0361213i
328328 7646.29 4810.57i 1.28718 0.809815i
329329 6516.50 1.09199
330330 −177.888 62.2079i −0.0296740 0.0103771i
331331 4035.04i 0.670048i 0.942210 + 0.335024i 0.108745π0.108745\pi
−0.942210 + 0.335024i 0.891255π0.891255\pi
332332 −3363.20 2679.97i −0.555962 0.443019i
333333 −4203.89 −0.691807
334334 403.112 + 140.969i 0.0660399 + 0.0230942i
335335 −3111.77 −0.507504
336336 −113.529 495.663i −0.0184331 0.0804780i
337337 9651.06i 1.56002i 0.625767 + 0.780010i 0.284786π0.284786\pi
−0.625767 + 0.780010i 0.715214π0.715214\pi
338338 −1861.01 650.799i −0.299485 0.104730i
339339 148.315 0.0237622
340340 6029.43 7566.57i 0.961740 1.20693i
341341 6869.90 1.09099
342342 565.445 6284.03i 0.0894029 0.993572i
343343 8790.88i 1.38386i
344344 1159.85 + 1843.55i 0.181788 + 0.288947i
345345 174.033i 0.0271583i
346346 −3101.87 1084.73i −0.481959 0.168542i
347347 −1311.88 −0.202955 −0.101478 0.994838i 0.532357π-0.532357\pi
−0.101478 + 0.994838i 0.532357π0.532357\pi
348348 262.318 329.193i 0.0404072 0.0507087i
349349 7143.37i 1.09563i 0.836599 + 0.547816i 0.184541π0.184541\pi
−0.836599 + 0.547816i 0.815459π0.815459\pi
350350 472.853 1352.16i 0.0722144 0.206503i
351351 533.302i 0.0810985i
352352 441.247 3949.96i 0.0668141 0.598106i
353353 3355.30 0.505905 0.252952 0.967479i 0.418598π-0.418598\pi
0.252952 + 0.967479i 0.418598π0.418598\pi
354354 307.567 + 107.557i 0.0461780 + 0.0161485i
355355 6501.44i 0.972002i
356356 −7003.93 + 8789.52i −1.04272 + 1.30855i
357357 −808.430 −0.119851
358358 −4207.85 + 12032.7i −0.621206 + 1.77639i
359359 5647.41i 0.830247i 0.909765 + 0.415124i 0.136262π0.136262\pi
−0.909765 + 0.415124i 0.863738π0.863738\pi
360360 6131.49 3857.56i 0.897661 0.564753i
361361 −6041.11 + 3248.21i −0.880757 + 0.473569i
362362 3473.22 + 1214.59i 0.504277 + 0.176346i
363363 216.735i 0.0313379i
364364 −6008.93 + 7540.85i −0.865257 + 1.08585i
365365 5277.05i 0.756750i
366366 262.774 + 91.8925i 0.0375285 + 0.0131238i
367367 6607.22i 0.939766i −0.882729 0.469883i 0.844296π-0.844296\pi
0.882729 0.469883i 0.155704π-0.155704\pi
368368 −3577.78 + 819.470i −0.506806 + 0.116081i
369369 10753.3i 1.51706i
370370 −1732.04 + 4952.91i −0.243363 + 0.695917i
371371 14186.5i 1.98524i
372372 398.260 499.792i 0.0555075 0.0696586i
373373 −9677.75 −1.34342 −0.671709 0.740815i 0.734439π-0.734439\pi
−0.671709 + 0.740815i 0.734439π0.734439\pi
374374 −5964.66 2085.85i −0.824667 0.288387i
375375 329.935 0.0454341
376376 4010.42 2523.11i 0.550058 0.346062i
377377 −7981.64 −1.09039
378378 −1144.12 400.100i −0.155680 0.0544416i
379379 7594.94i 1.02936i −0.857384 0.514678i 0.827911π-0.827911\pi
0.857384 0.514678i 0.172089π-0.172089\pi
380380 −7170.71 3255.27i −0.968025 0.439452i
381381 259.251i 0.0348604i
382382 1600.15 4575.75i 0.214321 0.612869i
383383 689.095 0.0919350 0.0459675 0.998943i 0.485363π-0.485363\pi
0.0459675 + 0.998943i 0.485363π0.485363\pi
384384 −261.783 261.087i −0.0347893 0.0346967i
385385 −8121.51 −1.07509
386386 781.439 2234.59i 0.103042 0.294657i
387387 2592.68 0.340551
388388 1984.54 2490.48i 0.259664 0.325863i
389389 918.749i 0.119749i −0.998206 0.0598746i 0.980930π-0.980930\pi
0.998206 0.0598746i 0.0190701π-0.0190701\pi
390390 313.781 + 109.730i 0.0407409 + 0.0142471i
391391 5835.38i 0.754752i
392392 −7536.68 11979.4i −0.971071 1.54349i
393393 503.210i 0.0645893i
394394 −529.591 + 1514.41i −0.0677168 + 0.193642i
395395 11296.9i 1.43901i
396396 −3700.07 2948.40i −0.469534 0.374148i
397397 6718.99i 0.849411i −0.905332 0.424706i 0.860378π-0.860378\pi
0.905332 0.424706i 0.139622π-0.139622\pi
398398 3299.21 9434.36i 0.415514 1.18819i
399399 160.673 + 638.103i 0.0201596 + 0.0800630i
400400 −232.535 1015.24i −0.0290668 0.126905i
401401 2657.88i 0.330993i 0.986210 + 0.165496i 0.0529226π0.0529226\pi
−0.986210 + 0.165496i 0.947077π0.947077\pi
402402 178.457 + 62.4065i 0.0221408 + 0.00774267i
403403 −12118.0 −1.49786
404404 −5539.46 + 6951.69i −0.682174 + 0.856088i
405405 8602.09i 1.05541i
406406 5988.07 17123.4i 0.731978 2.09315i
407407 3426.87 0.417355
408408 −497.529 + 313.015i −0.0603710 + 0.0379817i
409409 865.521i 0.104639i 0.998630 + 0.0523194i 0.0166614π0.0166614\pi
−0.998630 + 0.0523194i 0.983339π0.983339\pi
410410 −12669.3 4430.47i −1.52608 0.533672i
411411 192.875i 0.0231480i
412412 6249.62 + 4980.02i 0.747322 + 0.595504i
413413 14042.0 1.67303
414414 −1442.25 + 4124.23i −0.171214 + 0.489601i
415415 6389.23i 0.755747i
416416 −778.326 + 6967.42i −0.0917321 + 0.821168i
417417 543.427i 0.0638171i
418418 −460.932 + 5122.53i −0.0539352 + 0.599405i
419419 10425.9 1.21561 0.607804 0.794087i 0.292051π-0.292051\pi
0.607804 + 0.794087i 0.292051π0.292051\pi
420420 −470.817 + 590.847i −0.0546989 + 0.0686438i
421421 −8091.59 −0.936722 −0.468361 0.883537i 0.655155π-0.655155\pi
−0.468361 + 0.883537i 0.655155π0.655155\pi
422422 3725.87 10654.4i 0.429793 1.22903i
423423 5640.05i 0.648295i
424424 5492.83 + 8730.72i 0.629140 + 1.00000i
425425 −1655.86 −0.188991
426426 −130.387 + 372.851i −0.0148292 + 0.0424054i
427427 11997.0 1.35966
428428 411.932 516.950i 0.0465222 0.0583826i
429429 217.102i 0.0244331i
430430 1068.21 3054.63i 0.119799 0.342575i
431431 4972.36 0.555708 0.277854 0.960623i 0.410377π-0.410377\pi
0.277854 + 0.960623i 0.410377π0.410377\pi
432432 −859.034 + 196.757i −0.0956720 + 0.0219131i
433433 4916.49i 0.545661i 0.962062 + 0.272831i 0.0879599π0.0879599\pi
−0.962062 + 0.272831i 0.912040π0.912040\pi
434434 9091.28 25997.3i 1.00552 2.87536i
435435 −625.384 −0.0689308
436436 −5234.26 4170.92i −0.574944 0.458145i
437437 4605.94 1159.76i 0.504192 0.126954i
438438 105.831 302.634i 0.0115453 0.0330146i
439439 −9969.73 −1.08389 −0.541947 0.840413i 0.682313π-0.682313\pi
−0.541947 + 0.840413i 0.682313π0.682313\pi
440440 −4998.19 + 3144.55i −0.541543 + 0.340706i
441441 −16847.2 −1.81915
442442 10521.2 + 3679.28i 1.13222 + 0.395940i
443443 −12954.5 −1.38936 −0.694678 0.719321i 0.744453π-0.744453\pi
−0.694678 + 0.719321i 0.744453π0.744453\pi
444444 198.661 249.308i 0.0212343 0.0266478i
445445 16697.9 1.77878
446446 −2867.32 1002.71i −0.304421 0.106456i
447447 262.941 0.0278225
448448 −14363.6 6896.95i −1.51477 0.727345i
449449 1992.49i 0.209424i 0.994503 + 0.104712i 0.0333922π0.0333922\pi
−0.994503 + 0.104712i 0.966608π0.966608\pi
450450 −1170.30 409.256i −0.122597 0.0428722i
451451 8765.77i 0.915219i
452452 2896.24 3634.60i 0.301388 0.378224i
453453 303.662i 0.0314951i
454454 −2955.75 + 8452.20i −0.305551 + 0.873748i
455455 14325.7 1.47604
456456 345.948 + 330.495i 0.0355274 + 0.0339404i
457457 12912.0 1.32166 0.660831 0.750535i 0.270204π-0.270204\pi
0.660831 + 0.750535i 0.270204π0.270204\pi
458458 2334.59 6675.96i 0.238184 0.681107i
459459 1401.09i 0.142478i
460460 4264.83 + 3398.44i 0.432280 + 0.344463i
461461 14539.6i 1.46893i −0.678646 0.734466i 0.737433π-0.737433\pi
0.678646 0.734466i 0.262567π-0.262567\pi
462462 465.760 + 162.877i 0.0469028 + 0.0164020i
463463 5767.23i 0.578889i 0.957195 + 0.289445i 0.0934706π0.0934706\pi
−0.957195 + 0.289445i 0.906529π0.906529\pi
464464 −2944.75 12856.7i −0.294627 1.28633i
465465 −949.479 −0.0946904
466466 2761.45 + 965.685i 0.274510 + 0.0959967i
467467 −3777.72 −0.374330 −0.187165 0.982329i 0.559930π-0.559930\pi
−0.187165 + 0.982329i 0.559930π0.559930\pi
468468 6526.63 + 5200.75i 0.644644 + 0.513685i
469469 8147.44 0.802162
470470 −6644.95 2323.75i −0.652147 0.228057i
471471 −880.520 −0.0861406
472472 8641.80 5436.89i 0.842735 0.530197i
473473 −2113.47 −0.205449
474474 226.560 647.866i 0.0219541 0.0627795i
475475 329.096 + 1306.99i 0.0317894 + 0.126250i
476476 −15786.7 + 19811.3i −1.52013 + 1.90767i
477477 12278.4 1.17860
478478 1350.13 3860.80i 0.129191 0.369433i
479479 16308.7i 1.55566i 0.628474 + 0.777830i 0.283680π0.283680\pi
−0.628474 + 0.777830i 0.716320π0.716320\pi
480480 −60.9841 + 545.918i −0.00579902 + 0.0519117i
481481 −6044.73 −0.573006
482482 −2893.32 + 8273.69i −0.273417 + 0.781859i
483483 455.665i 0.0429264i
484484 −5311.30 4232.31i −0.498807 0.397475i
485485 −4731.28 −0.442962
486486 −519.641 + 1485.96i −0.0485008 + 0.138692i
487487 7770.87 0.723063 0.361532 0.932360i 0.382254π-0.382254\pi
0.361532 + 0.932360i 0.382254π0.382254\pi
488488 7383.24 4645.08i 0.684884 0.430887i
489489 708.446i 0.0655154i
490490 −6941.19 + 19848.9i −0.639941 + 1.82996i
491491 −16888.6 −1.55228 −0.776141 0.630559i 0.782826π-0.782826\pi
−0.776141 + 0.630559i 0.782826π0.782826\pi
492492 637.718 + 508.166i 0.0584361 + 0.0465648i
493493 −20969.4 −1.91564
494494 813.048 9035.75i 0.0740502 0.822951i
495495 7029.19i 0.638260i
496496 −4470.82 19519.4i −0.404729 1.76703i
497497 17022.5i 1.53635i
498498 128.136 366.415i 0.0115299 0.0329708i
499499 961.553 0.0862626 0.0431313 0.999069i 0.486267π-0.486267\pi
0.0431313 + 0.999069i 0.486267π0.486267\pi
500500 6442.83 8085.37i 0.576264 0.723177i
501501 38.5477i 0.00343749i
502502 9575.46 + 3348.55i 0.851342 + 0.297716i
503503 5526.02i 0.489847i 0.969542 + 0.244924i 0.0787629π0.0787629\pi
−0.969542 + 0.244924i 0.921237π0.921237\pi
504504 −16053.9 + 10100.1i −1.41884 + 0.892649i
505505 13206.5 1.16372
506506 1175.67 3361.93i 0.103291 0.295368i
507507 177.960i 0.0155887i
508508 6353.17 + 5062.53i 0.554875 + 0.442152i
509509 2723.71 0.237184 0.118592 0.992943i 0.462162π-0.462162\pi
0.118592 + 0.992943i 0.462162π0.462162\pi
510510 824.367 + 288.282i 0.0715756 + 0.0250301i
511511 13816.7i 1.19612i
512512 −11510.2 + 1316.85i −0.993519 + 0.113666i
513513 1105.90 278.462i 0.0951785 0.0239657i
514514 −6292.48 + 17993.9i −0.539979 + 1.54411i
515515 11872.7i 1.01587i
516516 −122.521 + 153.757i −0.0104529 + 0.0131178i
517517 4597.58i 0.391105i
518518 4534.95 12968.0i 0.384660 1.09997i
519519 296.617i 0.0250868i
520520 8816.41 5546.74i 0.743510 0.467771i
521521 5935.63i 0.499126i −0.968359 0.249563i 0.919713π-0.919713\pi
0.968359 0.249563i 0.0802869π-0.0802869\pi
522522 −14820.3 5182.70i −1.24266 0.434560i
523523 1446.58i 0.120945i 0.998170 + 0.0604726i 0.0192608π0.0192608\pi
−0.998170 + 0.0604726i 0.980739π0.980739\pi
524524 12331.6 + 9826.46i 1.02807 + 0.819219i
525525 129.300 0.0107488
526526 2799.82 8006.31i 0.232087 0.663672i
527527 −31836.3 −2.63152
528528 349.705 80.0980i 0.0288238 0.00660192i
529529 8877.94 0.729673
530530 5058.83 14466.1i 0.414606 1.18560i
531531 12153.4i 0.993243i
532532 18774.8 + 8523.17i 1.53006 + 0.694598i
533533 15462.1i 1.25655i
534534 −957.605 334.876i −0.0776023 0.0271376i
535535 −982.075 −0.0793623
536536 5014.15 3154.59i 0.404064 0.254212i
537537 −1150.63 −0.0924641
538538 −9579.32 3349.90i −0.767646 0.268447i
539539 13733.3 1.09746
540540 1024.00 + 815.974i 0.0816035 + 0.0650258i
541541 2569.96i 0.204235i −0.994772 0.102118i 0.967438π-0.967438\pi
0.994772 0.102118i 0.0325618π-0.0325618\pi
542542 2437.07 6969.00i 0.193139 0.552296i
543543 332.127i 0.0262485i
544544 −2044.82 + 18304.8i −0.161160 + 1.44267i
545545 9943.78i 0.781550i
546546 −821.564 287.302i −0.0643951 0.0225191i
547547 7507.83i 0.586858i 0.955981 + 0.293429i 0.0947965π0.0947965\pi
−0.955981 + 0.293429i 0.905204π0.905204\pi
548548 −4726.57 3766.37i −0.368447 0.293597i
549549 10383.4i 0.807201i
550550 953.989 + 333.611i 0.0739604 + 0.0258641i
551551 4167.58 + 16551.4i 0.322223 + 1.27969i
552552 −176.428 280.428i −0.0136038 0.0216228i
553553 29578.4i 2.27450i
554554 −4820.84 + 13785.6i −0.369707 + 1.05721i
555555 −473.622 −0.0362237
556556 13317.2 + 10611.8i 1.01578 + 0.809425i
557557 12498.0i 0.950728i −0.879789 0.475364i 0.842316π-0.842316\pi
0.879789 0.475364i 0.157684π-0.157684\pi
558558 −22500.7 7868.53i −1.70705 0.596956i
559559 3727.99 0.282070
560560 5285.34 + 23075.6i 0.398833 + 1.74129i
561561 570.371i 0.0429253i
562562 5032.68 14391.4i 0.377741 1.08018i
563563 14437.3i 1.08075i 0.841425 + 0.540374i 0.181717π0.181717\pi
−0.841425 + 0.540374i 0.818283π0.818283\pi
564564 334.478 + 266.529i 0.0249718 + 0.0198988i
565565 −6904.83 −0.514138
566566 −20135.2 7041.29i −1.49531 0.522911i
567567 22522.6i 1.66818i
568568 6590.92 + 10476.1i 0.486882 + 0.773887i
569569 3732.90i 0.275029i 0.990500 + 0.137514i 0.0439113π0.0439113\pi
−0.990500 + 0.137514i 0.956089π0.956089\pi
570570 63.7047 707.977i 0.00468122 0.0520244i
571571 7948.75 0.582566 0.291283 0.956637i 0.405918π-0.405918\pi
0.291283 + 0.956637i 0.405918π0.405918\pi
572572 −5320.29 4239.48i −0.388903 0.309898i
573573 437.557 0.0319009
574574 33171.6 + 11600.2i 2.41212 + 0.843523i
575575 933.312i 0.0676901i
576576 −5969.34 + 12431.8i −0.431810 + 0.899287i
577577 −1091.83 −0.0787758 −0.0393879 0.999224i 0.512541π-0.512541\pi
−0.0393879 + 0.999224i 0.512541π0.512541\pi
578578 14524.2 + 5079.12i 1.04520 + 0.365508i
579579 213.683 0.0153374
580580 −12212.2 + 15325.6i −0.874285 + 1.09717i
581581 16728.7i 1.19453i
582582 271.334 + 94.8859i 0.0193250 + 0.00675799i
583583 −10009.0 −0.711028
584584 −5349.68 8503.19i −0.379061 0.602507i
585585 12398.9i 0.876296i
586586 −7291.35 2549.79i −0.513998 0.179746i
587587 3678.42 0.258645 0.129322 0.991603i 0.458720π-0.458720\pi
0.129322 + 0.991603i 0.458720π0.458720\pi
588588 796.140 999.107i 0.0558371 0.0700723i
589589 6327.36 + 25128.8i 0.442639 + 1.75792i
590590 −14318.8 5007.30i −0.999145 0.349402i
591591 −144.816 −0.0100794
592592 −2230.15 9736.75i −0.154829 0.675976i
593593 −17520.6 −1.21330 −0.606648 0.794970i 0.707486π-0.707486\pi
−0.606648 + 0.794970i 0.707486π0.707486\pi
594594 282.282 807.209i 0.0194986 0.0557579i
595595 37636.5 2.59319
596596 5134.59 6443.60i 0.352887 0.442852i
597597 902.161 0.0618476
598598 −2073.80 + 5930.19i −0.141812 + 0.405524i
599599 14805.7 1.00992 0.504960 0.863143i 0.331507π-0.331507\pi
0.504960 + 0.863143i 0.331507π0.331507\pi
600600 79.5749 50.0636i 0.00541438 0.00340640i
601601 9476.86i 0.643210i −0.946874 0.321605i 0.895778π-0.895778\pi
0.946874 0.321605i 0.104222π-0.104222\pi
602602 −2796.86 + 7997.84i −0.189354 + 0.541474i
603603 7051.64i 0.476227i
604604 7441.52 + 5929.78i 0.501310 + 0.399469i
605605 10090.1i 0.678053i
606606 −757.376 264.856i −0.0507695 0.0177542i
607607 1962.54 0.131231 0.0656155 0.997845i 0.479099π-0.479099\pi
0.0656155 + 0.997845i 0.479099π0.479099\pi
608608 14854.6 2024.01i 0.990845 0.135008i
609609 1637.42 0.108952
610610 −12233.5 4278.06i −0.811997 0.283957i
611611 8109.77i 0.536966i
612612 17146.8 + 13663.4i 1.13254 + 0.902468i
613613 9072.88i 0.597798i 0.954285 + 0.298899i 0.0966194π0.0966194\pi
−0.954285 + 0.298899i 0.903381π0.903381\pi
614614 −956.398 + 2734.90i −0.0628617 + 0.179758i
615615 1211.50i 0.0794350i
616616 13086.6 8233.28i 0.855964 0.538520i
617617 9669.18 0.630902 0.315451 0.948942i 0.397844π-0.397844\pi
0.315451 + 0.948942i 0.397844π0.397844\pi
618618 −238.107 + 680.887i −0.0154985 + 0.0443193i
619619 4803.50 0.311905 0.155952 0.987765i 0.450155π-0.450155\pi
0.155952 + 0.987765i 0.450155π0.450155\pi
620620 −18541.0 + 23267.8i −1.20101 + 1.50719i
621621 −789.714 −0.0510308
622622 −2358.69 + 6744.85i −0.152049 + 0.434797i
623623 −43719.5 −2.81153
624624 −616.852 + 141.287i −0.0395735 + 0.00906409i
625625 −17394.4 −1.11324
626626 28120.1 + 9833.63i 1.79537 + 0.627845i
627627 −450.201 + 113.359i −0.0286751 + 0.00722031i
628628 −17194.4 + 21577.9i −1.09257 + 1.37110i
629629 −15880.7 −1.00669
630630 26600.0 + 9302.08i 1.68218 + 0.588260i
631631 1994.73i 0.125846i 0.998018 + 0.0629232i 0.0200423π0.0200423\pi
−0.998018 + 0.0629232i 0.979958π0.979958\pi
632632 −11452.4 18203.3i −0.720809 1.14571i
633633 1018.83 0.0639731
634634 16525.2 + 5778.89i 1.03517 + 0.362001i
635635 12069.4i 0.754268i
636636 −580.237 + 728.162i −0.0361759 + 0.0453986i
637637 −24224.4 −1.50676
638638 12081.0 + 4224.76i 0.749676 + 0.262163i
639639 14733.1 0.912098
640640 12187.3 + 12154.9i 0.752729 + 0.750726i
641641 12599.6i 0.776374i 0.921581 + 0.388187i 0.126899π0.126899\pi
−0.921581 + 0.388187i 0.873101π0.873101\pi
642642 56.3210 + 19.6955i 0.00346232 + 0.00121078i
643643 13231.7 0.811517 0.405759 0.913980i 0.367007π-0.367007\pi
0.405759 + 0.913980i 0.367007π0.367007\pi
644644 −11166.5 8898.02i −0.683262 0.544458i
645645 292.099 0.0178316
646646 2136.04 23738.7i 0.130095 1.44580i
647647 345.667i 0.0210040i 0.999945 + 0.0105020i 0.00334295π0.00334295\pi
−0.999945 + 0.0105020i 0.996657π0.996657\pi
648648 8720.48 + 13861.0i 0.528662 + 0.840295i
649649 9907.03i 0.599207i
650650 −1682.76 588.465i −0.101544 0.0355100i
651651 2485.99 0.149668
652652 −17361.1 13834.2i −1.04281 0.830966i
653653 28907.1i 1.73234i −0.499745 0.866172i 0.666573π-0.666573\pi
0.499745 0.866172i 0.333427π-0.333427\pi
654654 199.423 570.265i 0.0119236 0.0340965i
655655 23427.0i 1.39751i
656656 24906.1 5704.62i 1.48235 0.339524i
657657 −11958.4 −0.710112
658658 17398.3 + 6084.20i 1.03078 + 0.360467i
659659 17748.5i 1.04914i 0.851368 + 0.524569i 0.175773π0.175773\pi
−0.851368 + 0.524569i 0.824227π0.824227\pi
660660 −416.860 332.175i −0.0245852 0.0195908i
661661 29973.2 1.76373 0.881864 0.471504i 0.156289π-0.156289\pi
0.881864 + 0.471504i 0.156289π0.156289\pi
662662 −3767.37 + 10773.1i −0.221183 + 0.632490i
663663 1006.09i 0.0589341i
664664 −6477.16 10295.3i −0.378558 0.601709i
665665 −7480.12 29706.9i −0.436190 1.73231i
666666 −11223.9 3925.01i −0.653028 0.228365i
667667 11819.2i 0.686119i
668668 944.645 + 752.741i 0.0547147 + 0.0435995i
669669 274.188i 0.0158456i
670670 −8308.05 2905.34i −0.479057 0.167527i
671671 8464.21i 0.486970i
672672 159.673 1429.36i 0.00916594 0.0820517i
673673 26244.4i 1.50319i 0.659624 + 0.751595i 0.270715π0.270715\pi
−0.659624 + 0.751595i 0.729285π0.729285\pi
674674 −9010.83 + 25767.2i −0.514961 + 1.47257i
675675 224.091i 0.0127782i
676676 −4361.06 3475.12i −0.248126 0.197719i
677677 −12259.6 −0.695972 −0.347986 0.937500i 0.613134π-0.613134\pi
−0.347986 + 0.937500i 0.613134π0.613134\pi
678678 395.985 + 138.476i 0.0224302 + 0.00784389i
679679 12387.8 0.700146
680680 23162.5 14572.4i 1.30624 0.821803i
681681 −808.243 −0.0454801
682682 18341.8 + 6414.17i 1.02983 + 0.360134i
683683 9968.98i 0.558495i −0.960219 0.279248i 0.909915π-0.909915\pi
0.960219 0.279248i 0.0900850π-0.0900850\pi
684684 7376.83 16249.7i 0.412369 0.908366i
685685 8979.29i 0.500848i
686686 8207.71 23470.6i 0.456810 1.30629i
687687 638.389 0.0354528
688688 1375.41 + 6004.98i 0.0762165 + 0.332759i
689689 17655.1 0.976203
690690 −162.488 + 464.647i −0.00896494 + 0.0256360i
691691 −24599.5 −1.35428 −0.677142 0.735852i 0.736782π-0.736782\pi
−0.677142 + 0.735852i 0.736782π0.736782\pi
692692 −7268.87 5792.20i −0.399308 0.318189i
693693 18404.3i 1.00883i
694694 −3502.57 1224.85i −0.191579 0.0669954i
695695 25299.3i 1.38080i
696696 1007.71 633.991i 0.0548812 0.0345278i
697697 40622.1i 2.20757i
698698 −6669.49 + 19072.0i −0.361668 + 1.03422i
699699 264.064i 0.0142887i
700700 2524.92 3168.63i 0.136333 0.171090i
701701 14471.8i 0.779734i 0.920871 + 0.389867i 0.127479π0.127479\pi
−0.920871 + 0.389867i 0.872521π0.872521\pi
702702 −497.924 + 1423.85i −0.0267706 + 0.0765526i
703703 3156.24 + 12534.8i 0.169331 + 0.672490i
704704 4866.00 10133.9i 0.260503 0.542525i
705705 635.424i 0.0339453i
706706 8958.25 + 3132.71i 0.477547 + 0.166999i
707707 −34578.1 −1.83938
708708 720.746 + 574.327i 0.0382589 + 0.0304866i
709709 18759.1i 0.993671i 0.867845 + 0.496836i 0.165505π0.165505\pi
−0.867845 + 0.496836i 0.834495π0.834495\pi
710710 6070.15 17358.1i 0.320857 0.917518i
711711 −25600.2 −1.35033
712712 −26906.1 + 16927.7i −1.41622 + 0.890999i
713713 17944.3i 0.942523i
714714 −2158.41 754.801i −0.113133 0.0395626i
715715 10107.2i 0.528655i
716716 −22468.9 + 28197.2i −1.17277 + 1.47176i
717717 369.189 0.0192296
718718 −5272.77 + 15077.9i −0.274064 + 0.783709i
719719 4210.87i 0.218413i 0.994019 + 0.109206i 0.0348310π0.0348310\pi
−0.994019 + 0.109206i 0.965169π0.965169\pi
720720 19972.0 4574.48i 1.03377 0.236779i
721721 31085.9i 1.60569i
722722 −19161.8 + 3031.98i −0.987712 + 0.156286i
723723 −791.172 −0.0406971
724724 8139.06 + 6485.62i 0.417798 + 0.332923i
725725 3353.84 0.171805
726726 202.358 578.658i 0.0103446 0.0295813i
727727 8248.16i 0.420780i −0.977618 0.210390i 0.932527π-0.932527\pi
0.977618 0.210390i 0.0674734π-0.0674734\pi
728728 −23083.7 + 14522.9i −1.17519 + 0.739359i
729729 19398.5 0.985544
730730 −4926.99 + 14089.1i −0.249803 + 0.714331i
731731 9794.18 0.495555
732732 615.779 + 490.684i 0.0310927 + 0.0247762i
733733 6704.17i 0.337823i −0.985631 0.168911i 0.945975π-0.945975\pi
0.985631 0.168911i 0.0540252π-0.0540252\pi
734734 6168.91 17640.5i 0.310216 0.887089i
735735 −1898.05 −0.0952527
736736 −10317.3 1152.54i −0.516715 0.0577219i
737737 5748.26i 0.287300i
738738 10040.0 28710.2i 0.500782 1.43203i
739739 −21399.5 −1.06521 −0.532606 0.846363i 0.678787π-0.678787\pi
−0.532606 + 0.846363i 0.678787π0.678787\pi
740740 −9248.69 + 11606.5i −0.459444 + 0.576574i
741741 794.119 199.957i 0.0393694 0.00991309i
742742 −13245.4 + 37876.2i −0.655327 + 1.87396i
743743 27163.2 1.34121 0.670606 0.741814i 0.266034π-0.266034\pi
0.670606 + 0.741814i 0.266034π0.266034\pi
744744 1529.94 962.546i 0.0753904 0.0474310i
745745 −12241.2 −0.601991
746746 −25838.5 9035.75i −1.26811 0.443462i
747747 −14478.8 −0.709170
748748 −13977.5 11138.0i −0.683244 0.544444i
749749 2571.34 0.125440
750750 880.889 + 308.048i 0.0428874 + 0.0149978i
751751 −2808.18 −0.136448 −0.0682238 0.997670i 0.521733π-0.521733\pi
−0.0682238 + 0.997670i 0.521733π0.521733\pi
752752 13063.1 2992.03i 0.633460 0.145091i
753753 915.654i 0.0443138i
754754 −21310.0 7452.15i −1.02926 0.359935i
755755 14137.0i 0.681455i
756756 −2681.10 2136.44i −0.128983 0.102780i
757757 26808.1i 1.28713i 0.765392 + 0.643565i 0.222545π0.222545\pi
−0.765392 + 0.643565i 0.777455π0.777455\pi
758758 7091.11 20277.6i 0.339790 0.971657i
759759 321.485 0.0153744
760760 −16105.6 15386.2i −0.768701 0.734364i
761761 28180.4 1.34236 0.671182 0.741293i 0.265787π-0.265787\pi
0.671182 + 0.741293i 0.265787π0.265787\pi
762762 −242.052 + 692.169i −0.0115074 + 0.0329063i
763763 26035.5i 1.23532i
764764 8544.42 10722.7i 0.404615 0.507768i
765765 32574.5i 1.53952i
766766 1839.80 + 643.382i 0.0867817 + 0.0303477i
767767 17475.2i 0.822678i
768768 −455.164 941.488i −0.0213858 0.0442357i
769769 9132.92 0.428272 0.214136 0.976804i 0.431306π-0.431306\pi
0.214136 + 0.976804i 0.431306π0.431306\pi
770770 −21683.5 7582.74i −1.01483 0.354887i
771771 −1720.66 −0.0803738
772772 4172.70 5236.49i 0.194532 0.244126i
773773 12663.5 0.589231 0.294616 0.955616i 0.404808π-0.404808\pi
0.294616 + 0.955616i 0.404808π0.404808\pi
774774 6922.15 + 2420.69i 0.321462 + 0.112416i
775775 5091.91 0.236009
776776 7623.75 4796.40i 0.352676 0.221882i
777777 1240.07 0.0572552
778778 857.801 2452.95i 0.0395291 0.113037i
779779 −32063.5 + 8073.50i −1.47470 + 0.371326i
780780 735.309 + 585.932i 0.0337542 + 0.0268971i
781781 −12009.9 −0.550253
782782 −5448.28 + 15579.8i −0.249143 + 0.712445i
783783 2837.82i 0.129522i
784784 −8937.37 39020.2i −0.407133 1.77753i
785785 40992.7 1.86381
786786 −469.828 + 1343.51i −0.0213209 + 0.0609688i
787787 37712.8i 1.70815i −0.520148 0.854076i 0.674123π-0.674123\pi
0.520148 0.854076i 0.325877π-0.325877\pi
788788 −2827.89 + 3548.84i −0.127842 + 0.160434i
789789 765.604 0.0345453
790790 −10547.5 + 30161.4i −0.475017 + 1.35835i
791791 18078.7 0.812648
792792 −7125.93 11326.5i −0.319708 0.508168i
793793 14930.2i 0.668584i
794794 6273.26 17938.9i 0.280390 0.801798i
795795 1383.33 0.0617126
796796 17617.0 22108.3i 0.784445 0.984431i
797797 4970.27 0.220898 0.110449 0.993882i 0.464771π-0.464771\pi
0.110449 + 0.993882i 0.464771π0.464771\pi
798798 −166.796 + 1853.68i −0.00739915 + 0.0822298i
799799 21306.0i 0.943369i
800800 327.049 2927.67i 0.0144536 0.129386i
801801 37839.4i 1.66915i
802802 −2481.56 + 7096.22i −0.109260 + 0.312439i
803803 9748.12 0.428398
804804 418.191 + 333.236i 0.0183439 + 0.0146173i
805805 21213.5i 0.928792i
806806 −32353.6 11314.1i −1.41390 0.494444i
807807 916.023i 0.0399573i
808808 −21280.2 + 13388.2i −0.926530 + 0.582915i
809809 −20762.7 −0.902321 −0.451160 0.892443i 0.648990π-0.648990\pi
−0.451160 + 0.892443i 0.648990π0.648990\pi
810810 8031.45 22966.6i 0.348391 0.996251i
811811 36963.0i 1.60043i 0.599715 + 0.800214i 0.295281π0.295281\pi
−0.599715 + 0.800214i 0.704719π0.704719\pi
812812 31974.9 40126.6i 1.38190 1.73420i
813813 666.411 0.0287479
814814 9149.34 + 3199.54i 0.393961 + 0.137769i
815815 32981.8i 1.41755i
816816 −1620.59 + 371.188i −0.0695247 + 0.0159242i
817817 −1946.56 7730.66i −0.0833555 0.331042i
818818 −808.105 + 2310.84i −0.0345412 + 0.0987734i
819819 32463.8i 1.38508i
820820 −29689.0 23657.7i −1.26437 1.00752i
821821 10288.3i 0.437351i 0.975798 + 0.218675i 0.0701736π0.0701736\pi
−0.975798 + 0.218675i 0.929826π0.929826\pi
822822 180.080 514.953i 0.00764113 0.0218504i
823823 28596.2i 1.21118i −0.795777 0.605590i 0.792937π-0.792937\pi
0.795777 0.605590i 0.207063π-0.207063\pi
824824 12036.1 + 19131.1i 0.508856 + 0.808815i
825825 91.2253i 0.00384977i
826826 37490.4 + 13110.5i 1.57925 + 0.552266i
827827 24872.9i 1.04585i 0.852379 + 0.522924i 0.175159π0.175159\pi
−0.852379 + 0.522924i 0.824841π0.824841\pi
828828 −7701.27 + 9664.63i −0.323234 + 0.405639i
829829 −25851.3 −1.08306 −0.541528 0.840683i 0.682154π-0.682154\pi
−0.541528 + 0.840683i 0.682154π0.682154\pi
830830 −5965.38 + 17058.5i −0.249471 + 0.713384i
831831 −1318.25 −0.0550295
832832 −8583.25 + 17875.5i −0.357657 + 0.744857i
833833 −63642.3 −2.64715
834834 −507.377 + 1450.89i −0.0210660 + 0.0602399i
835835 1794.59i 0.0743764i
836836 −6013.35 + 13246.2i −0.248775 + 0.548002i
837837 4308.47i 0.177924i
838838 27836.0 + 9734.28i 1.14747 + 0.401271i
839839 182.166 0.00749590 0.00374795 0.999993i 0.498807π-0.498807\pi
0.00374795 + 0.999993i 0.498807π0.498807\pi
840840 −1808.68 + 1137.91i −0.0742921 + 0.0467400i
841841 18083.1 0.741446
842842 −21603.6 7554.81i −0.884215 0.309211i
843843 1376.17 0.0562254
844844 19895.3 24967.4i 0.811403 1.01826i
845845 8284.92i 0.337290i
846846 5265.90 15058.3i 0.214002 0.611955i
847847 26418.7i 1.07173i
848848 6513.67 + 28438.5i 0.263774 + 1.15163i
849849 1925.43i 0.0778333i
850850 −4420.96 1546.01i −0.178397 0.0623857i
851851 8951.04i 0.360561i
852852 −696.234 + 873.731i −0.0279960 + 0.0351333i
853853 27467.2i 1.10253i 0.834330 + 0.551266i 0.185855π0.185855\pi
−0.834330 + 0.551266i 0.814145π0.814145\pi
854854 32030.5 + 11201.1i 1.28344 + 0.448822i
855855 −25711.5 + 6474.07i −1.02844 + 0.258957i
856856 1582.47 995.591i 0.0631865 0.0397531i
857857 37989.6i 1.51424i 0.653278 + 0.757118i 0.273393π0.273393\pi
−0.653278 + 0.757118i 0.726607π0.726607\pi
858858 202.700 579.638i 0.00806535 0.0230635i
859859 −15744.7 −0.625382 −0.312691 0.949855i 0.601230π-0.601230\pi
−0.312691 + 0.949855i 0.601230π0.601230\pi
860860 5703.98 7158.15i 0.226168 0.283827i
861861 3172.04i 0.125555i
862862 13275.6 + 4642.50i 0.524558 + 0.183439i
863863 −18939.0 −0.747033 −0.373517 0.927624i 0.621848π-0.621848\pi
−0.373517 + 0.927624i 0.621848π0.621848\pi
864864 −2477.22 276.729i −0.0975427 0.0108964i
865865 13809.0i 0.542799i
866866 −4590.34 + 13126.5i −0.180123 + 0.515075i
867867 1388.88i 0.0544045i
868868 48545.3 60921.4i 1.89831 2.38227i
869869 20868.4 0.814629
870870 −1669.70 583.898i −0.0650669 0.0227540i
871871 10139.5i 0.394447i
872872 −10080.6 16022.9i −0.391483 0.622253i
873873 10721.7i 0.415662i
874874 13380.1 + 1203.96i 0.517837 + 0.0465957i
875875 40217.0 1.55381
876876 565.115 709.185i 0.0217962 0.0273529i
877877 −21287.1 −0.819630 −0.409815 0.912169i 0.634407π-0.634407\pi
−0.409815 + 0.912169i 0.634407π0.634407\pi
878878 −26618.0 9308.36i −1.02314 0.357793i
879879 697.236i 0.0267545i
880880 −16280.5 + 3728.96i −0.623655 + 0.142845i
881881 −32856.5 −1.25649 −0.628243 0.778017i 0.716226π-0.716226\pi
−0.628243 + 0.778017i 0.716226π0.716226\pi
882882 −44980.0 15729.6i −1.71718 0.600501i
883883 7030.80 0.267956 0.133978 0.990984i 0.457225π-0.457225\pi
0.133978 + 0.990984i 0.457225π0.457225\pi
884884 24655.2 + 19646.5i 0.938058 + 0.747492i
885885 1369.24i 0.0520072i
886886 −34586.9 12095.1i −1.31148 0.458626i
887887 −13987.6 −0.529492 −0.264746 0.964318i 0.585288π-0.585288\pi
−0.264746 + 0.964318i 0.585288π0.585288\pi
888888 763.172 480.141i 0.0288405 0.0181447i
889889 31601.0i 1.19220i
890890 44581.4 + 15590.2i 1.67907 + 0.587173i
891891 −15890.4 −0.597471
892892 −6719.22 5354.22i −0.252216 0.200978i
893893 −16817.1 + 4234.49i −0.630193 + 0.158681i
894894 702.021 + 245.498i 0.0262630 + 0.00918420i
895895 53567.5 2.00063
896896 −31909.7 31824.8i −1.18976 1.18660i
897897 −567.075 −0.0211082
898898 −1860.32 + 5319.72i −0.0691309 + 0.197685i
899899 64482.5 2.39223
900900 −2742.46 2185.33i −0.101572 0.0809381i
901901 46383.4 1.71504
902902 −8184.27 + 23403.6i −0.302113 + 0.863918i
903903 −764.794 −0.0281847
904904 11126.1 6999.86i 0.409346 0.257535i
905905 15462.2i 0.567934i
906906 −283.518 + 810.743i −0.0103965 + 0.0297297i
907907 32555.9i 1.19184i 0.803043 + 0.595922i 0.203213π0.203213\pi
−0.803043 + 0.595922i 0.796787π0.796787\pi
908908 −15783.0 + 19806.7i −0.576847 + 0.723909i
909909 29927.4i 1.09200i
910910 38248.0 + 13375.4i 1.39330 + 0.487241i
911911 42685.1 1.55238 0.776191 0.630498i 0.217149π-0.217149\pi
0.776191 + 0.630498i 0.217149π0.217149\pi
912912 615.070 + 1205.38i 0.0223323 + 0.0437655i
913913 11802.6 0.427830
914914 34473.6 + 12055.5i 1.24758 + 0.436280i
915915 1169.83i 0.0422658i
916916 12466.2 15644.3i 0.449666 0.564304i
917917 61338.1i 2.20890i
918918 −1308.15 + 3740.75i −0.0470319 + 0.134491i
919919 26396.2i 0.947477i −0.880666 0.473739i 0.842904π-0.842904\pi
0.880666 0.473739i 0.157096π-0.157096\pi
920920 8213.61 + 13055.3i 0.294342 + 0.467850i
921921 −261.525 −0.00935672
922922 13575.1 38819.1i 0.484893 1.38659i
923923 21184.5 0.755468
924924 1091.45 + 869.725i 0.0388595 + 0.0309652i
925925 2539.97 0.0902849
926926 −5384.64 + 15397.8i −0.191091 + 0.546440i
927927 26905.0 0.953264
928928 4141.65 37075.2i 0.146505 1.31148i
929929 −15313.5 −0.540818 −0.270409 0.962746i 0.587159π-0.587159\pi
−0.270409 + 0.962746i 0.587159π0.587159\pi
930930 −2535.00 886.492i −0.0893826 0.0312572i
931931 12648.7 + 50233.7i 0.445267 + 1.76836i
932932 6471.14 + 5156.53i 0.227435 + 0.181232i
933933 −644.977 −0.0226320
934934 −10086.1 3527.11i −0.353347 0.123566i
935935 26553.7i 0.928768i
936936 12569.6 + 19979.1i 0.438942 + 0.697688i
937937 13341.6 0.465156 0.232578 0.972578i 0.425284π-0.425284\pi
0.232578 + 0.972578i 0.425284π0.425284\pi
938938 21752.7 + 7606.96i 0.757198 + 0.264793i
939939 2688.99i 0.0934523i
940940 −15571.7 12408.3i −0.540310 0.430546i
941941 50527.3 1.75042 0.875209 0.483745i 0.160724π-0.160724\pi
0.875209 + 0.483745i 0.160724π0.160724\pi
942942 −2350.89 822.108i −0.0813121 0.0284350i
943943 22896.3 0.790675
944944 28148.8 6447.33i 0.970515 0.222291i
945945 5093.42i 0.175332i
946946 −5642.71 1973.26i −0.193933 0.0678185i
947947 −24534.8 −0.841895 −0.420947 0.907085i 0.638302π-0.638302\pi
−0.420947 + 0.907085i 0.638302π0.638302\pi
948948 1209.78 1518.20i 0.0414469 0.0520134i
949949 −17194.9 −0.588168
950950 −341.639 + 3796.78i −0.0116676 + 0.129667i
951951 1580.22i 0.0538825i
952952 −60645.6 + 38154.5i −2.06464 + 1.29894i
953953 42716.0i 1.45195i −0.687723 0.725974i 0.741389π-0.741389\pi
0.687723 0.725974i 0.258611π-0.258611\pi
954954 32782.0 + 11463.9i 1.11253 + 0.389054i
955955 −20370.5 −0.690234
956956 7209.36 9047.32i 0.243899 0.306079i
957957 1155.25i 0.0390219i
958958 −15226.8 + 43542.2i −0.513523 + 1.46846i
959959 23510.2i 0.791641i
960960 −672.523 + 1400.60i −0.0226100 + 0.0470876i
961961 68108.4 2.28621
962962 −16138.7 5643.74i −0.540887 0.189149i
963963 2225.50i 0.0744712i
964964 −15449.7 + 19388.4i −0.516182 + 0.647778i
965965 −9948.01 −0.331853
966966 425.437 1216.57i 0.0141700 0.0405202i
967967 15724.2i 0.522912i −0.965215 0.261456i 0.915797π-0.915797\pi
0.965215 0.261456i 0.0842027π-0.0842027\pi
968968 −10229.0 16258.7i −0.339641 0.539851i
969969 2086.31 525.327i 0.0691661 0.0174158i
970970 −12632.0 4417.42i −0.418132 0.146221i
971971 11018.1i 0.364148i −0.983285 0.182074i 0.941719π-0.941719\pi
0.983285 0.182074i 0.0582810π-0.0582810\pi
972972 −2774.76 + 3482.16i −0.0915643 + 0.114908i
973973 66240.3i 2.18249i
974974 20747.3 + 7255.37i 0.682533 + 0.238683i
975975 160.914i 0.00528552i
976976 24049.3 5508.37i 0.788730 0.180654i
977977 20874.0i 0.683540i 0.939784 + 0.341770i 0.111026π0.111026\pi
−0.939784 + 0.341770i 0.888974π0.888974\pi
978978 661.450 1891.47i 0.0216266 0.0618431i
979979 30845.4i 1.00697i
980980 −37064.3 + 46513.5i −1.20814 + 1.51614i
981981 −22533.8 −0.733383
982982 −45090.5 15768.2i −1.46527 0.512407i
983983 19012.5 0.616891 0.308445 0.951242i 0.400191π-0.400191\pi
0.308445 + 0.951242i 0.400191π0.400191\pi
984984 1228.18 + 1952.16i 0.0397895 + 0.0632444i
985985 6741.90 0.218086
986986 −55985.7 19578.3i −1.80826 0.632353i
987987 1663.71i 0.0536541i
988988 10607.1 23365.3i 0.341555 0.752377i
989989 5520.41i 0.177491i
990990 −6562.89 + 18767.1i −0.210689 + 0.602483i
991991 35028.4 1.12282 0.561410 0.827538i 0.310259π-0.310259\pi
0.561410 + 0.827538i 0.310259π0.310259\pi
992992 6287.99 56288.8i 0.201254 1.80158i
993993 −1030.18 −0.0329222
994994 −15893.3 + 45448.2i −0.507147 + 1.45023i
995995 −42000.2 −1.33819
996996 684.216 858.651i 0.0217673 0.0273167i
997997 17746.0i 0.563711i −0.959457 0.281856i 0.909050π-0.909050\pi
0.959457 0.281856i 0.0909499π-0.0909499\pi
998998 2567.23 + 897.766i 0.0814273 + 0.0284752i
999999 2149.17i 0.0680648i
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 152.4.b.b.75.52 yes 56
4.3 odd 2 608.4.b.b.303.27 56
8.3 odd 2 inner 152.4.b.b.75.6 yes 56
8.5 even 2 608.4.b.b.303.28 56
19.18 odd 2 inner 152.4.b.b.75.5 56
76.75 even 2 608.4.b.b.303.29 56
152.37 odd 2 608.4.b.b.303.30 56
152.75 even 2 inner 152.4.b.b.75.51 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.4.b.b.75.5 56 19.18 odd 2 inner
152.4.b.b.75.6 yes 56 8.3 odd 2 inner
152.4.b.b.75.51 yes 56 152.75 even 2 inner
152.4.b.b.75.52 yes 56 1.1 even 1 trivial
608.4.b.b.303.27 56 4.3 odd 2
608.4.b.b.303.28 56 8.5 even 2
608.4.b.b.303.29 56 76.75 even 2
608.4.b.b.303.30 56 152.37 odd 2