Properties

Label 42.5.b.a.29.7
Level 4242
Weight 55
Character 42.29
Analytic conductor 4.3424.342
Analytic rank 00
Dimension 88
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42,5,Mod(29,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.29");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 42=237 42 = 2 \cdot 3 \cdot 7
Weight: k k == 5 5
Character orbit: [χ][\chi] == 42.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: 4.341538449524.34153844952
Analytic rank: 00
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x844x6+646x43060x2+6561 x^{8} - 44x^{6} + 646x^{4} - 3060x^{2} + 6561 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 273372 2^{7}\cdot 3^{3}\cdot 7^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 29.7
Root 1.88752+0.707107i-1.88752 + 0.707107i of defining polynomial
Character χ\chi == 42.29
Dual form 42.5.b.a.29.3

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+2.82843iq2+(6.597926.12106i)q38.00000q447.9925iq5+(17.3130+18.6617i)q618.5203q722.6274iq8+(6.0651880.7726i)q9+135.743q10+123.237iq11+(52.7834+48.9685i)q12+241.627q1352.3832iq14+(293.765316.651i)q15+64.0000q16+64.4425iq17+(228.459+17.1549i)q18+125.357q19+383.940iq20+(122.195+113.364i)q21348.566q22+287.613iq23+(138.504149.294i)q241678.28q25+683.426iq26+(454.397570.057i)q27+148.162q28+94.2775iq29+(895.624830.893i)q30+429.829q31+181.019iq32+(754.339+813.106i)q33182.271q34+888.834iq35+(48.5215+646.181i)q36+2118.52q37+354.563iq38+(1594.241479.02i)q391085.95q401220.23iq41+(320.641345.620i)q42+976.206q43985.893iq44+(3876.48291.083i)q45813.493q46+526.553iq47+(422.267391.748i)q48+343.000q494746.90iq50+(394.457+425.187i)q511933.02q52+1567.07iq53+(1612.361285.23i)q54+5914.43q55+419.066iq56+(827.096767.318i)q57266.657q58+5826.08iq59+(2350.12+2533.21i)q604955.04q61+1215.74iq62+(112.329+1495.93i)q63512.000q6411596.3iq65+(2299.81+2133.59i)q661321.11q67515.540iq68+(1760.50+1897.65i)q692514.00q70+3717.89iq71+(1827.68137.239i)q72+2023.01q73+5992.07iq74+(11073.2+10272.9i)q751002.86q762282.37iq77+(4183.29+4509.19i)q78+4711.86q793071.52iq80+(6487.43979.801i)q81+3451.32q824420.87iq83+(977.562906.909i)q84+3092.76q85+2761.13iq86+(577.078+622.036i)q87+2788.53q888482.72iq89+(823.30810964.3i)q904475.00q912300.91iq92+(2835.982631.01i)q931489.32q946016.20iq95+(1108.03+1194.35i)q9616341.1q97+970.151iq98+(9954.14+747.452i)q99+O(q100)q+2.82843i q^{2} +(6.59792 - 6.12106i) q^{3} -8.00000 q^{4} -47.9925i q^{5} +(17.3130 + 18.6617i) q^{6} -18.5203 q^{7} -22.6274i q^{8} +(6.06518 - 80.7726i) q^{9} +135.743 q^{10} +123.237i q^{11} +(-52.7834 + 48.9685i) q^{12} +241.627 q^{13} -52.3832i q^{14} +(-293.765 - 316.651i) q^{15} +64.0000 q^{16} +64.4425i q^{17} +(228.459 + 17.1549i) q^{18} +125.357 q^{19} +383.940i q^{20} +(-122.195 + 113.364i) q^{21} -348.566 q^{22} +287.613i q^{23} +(-138.504 - 149.294i) q^{24} -1678.28 q^{25} +683.426i q^{26} +(-454.397 - 570.057i) q^{27} +148.162 q^{28} +94.2775i q^{29} +(895.624 - 830.893i) q^{30} +429.829 q^{31} +181.019i q^{32} +(754.339 + 813.106i) q^{33} -182.271 q^{34} +888.834i q^{35} +(-48.5215 + 646.181i) q^{36} +2118.52 q^{37} +354.563i q^{38} +(1594.24 - 1479.02i) q^{39} -1085.95 q^{40} -1220.23i q^{41} +(-320.641 - 345.620i) q^{42} +976.206 q^{43} -985.893i q^{44} +(-3876.48 - 291.083i) q^{45} -813.493 q^{46} +526.553i q^{47} +(422.267 - 391.748i) q^{48} +343.000 q^{49} -4746.90i q^{50} +(394.457 + 425.187i) q^{51} -1933.02 q^{52} +1567.07i q^{53} +(1612.36 - 1285.23i) q^{54} +5914.43 q^{55} +419.066i q^{56} +(827.096 - 767.318i) q^{57} -266.657 q^{58} +5826.08i q^{59} +(2350.12 + 2533.21i) q^{60} -4955.04 q^{61} +1215.74i q^{62} +(-112.329 + 1495.93i) q^{63} -512.000 q^{64} -11596.3i q^{65} +(-2299.81 + 2133.59i) q^{66} -1321.11 q^{67} -515.540i q^{68} +(1760.50 + 1897.65i) q^{69} -2514.00 q^{70} +3717.89i q^{71} +(-1827.68 - 137.239i) q^{72} +2023.01 q^{73} +5992.07i q^{74} +(-11073.2 + 10272.9i) q^{75} -1002.86 q^{76} -2282.37i q^{77} +(4183.29 + 4509.19i) q^{78} +4711.86 q^{79} -3071.52i q^{80} +(-6487.43 - 979.801i) q^{81} +3451.32 q^{82} -4420.87i q^{83} +(977.562 - 906.909i) q^{84} +3092.76 q^{85} +2761.13i q^{86} +(577.078 + 622.036i) q^{87} +2788.53 q^{88} -8482.72i q^{89} +(823.308 - 10964.3i) q^{90} -4475.00 q^{91} -2300.91i q^{92} +(2835.98 - 2631.01i) q^{93} -1489.32 q^{94} -6016.20i q^{95} +(1108.03 + 1194.35i) q^{96} -16341.1 q^{97} +970.151i q^{98} +(9954.14 + 747.452i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+12q364q432q6+152q9+256q1096q12520q13616q15+512q16+768q18+1336q19196q211024q22+256q243672q25+36q27++10976q99+O(q100) 8 q + 12 q^{3} - 64 q^{4} - 32 q^{6} + 152 q^{9} + 256 q^{10} - 96 q^{12} - 520 q^{13} - 616 q^{15} + 512 q^{16} + 768 q^{18} + 1336 q^{19} - 196 q^{21} - 1024 q^{22} + 256 q^{24} - 3672 q^{25} + 36 q^{27}+ \cdots + 10976 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/42Z)×\left(\mathbb{Z}/42\mathbb{Z}\right)^\times.

nn 2929 3131
χ(n)\chi(n) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.82843i 0.707107i
33 6.59792 6.12106i 0.733103 0.680118i
44 −8.00000 −0.500000
55 47.9925i 1.91970i −0.280513 0.959850i 0.590505π-0.590505\pi
0.280513 0.959850i 0.409495π-0.409495\pi
66 17.3130 + 18.6617i 0.480916 + 0.518382i
77 −18.5203 −0.377964
88 22.6274i 0.353553i
99 6.06518 80.7726i 0.0748788 0.997193i
1010 135.743 1.35743
1111 123.237i 1.01848i 0.860623 + 0.509242i 0.170074π0.170074\pi
−0.860623 + 0.509242i 0.829926π0.829926\pi
1212 −52.7834 + 48.9685i −0.366551 + 0.340059i
1313 241.627 1.42975 0.714874 0.699253i 0.246484π-0.246484\pi
0.714874 + 0.699253i 0.246484π0.246484\pi
1414 52.3832i 0.267261i
1515 −293.765 316.651i −1.30562 1.40734i
1616 64.0000 0.250000
1717 64.4425i 0.222984i 0.993765 + 0.111492i 0.0355630π0.0355630\pi
−0.993765 + 0.111492i 0.964437π0.964437\pi
1818 228.459 + 17.1549i 0.705122 + 0.0529473i
1919 125.357 0.347249 0.173625 0.984812i 0.444452π-0.444452\pi
0.173625 + 0.984812i 0.444452π0.444452\pi
2020 383.940i 0.959850i
2121 −122.195 + 113.364i −0.277087 + 0.257060i
2222 −348.566 −0.720177
2323 287.613i 0.543693i 0.962341 + 0.271846i 0.0876342π0.0876342\pi
−0.962341 + 0.271846i 0.912366π0.912366\pi
2424 −138.504 149.294i −0.240458 0.259191i
2525 −1678.28 −2.68525
2626 683.426i 1.01098i
2727 −454.397 570.057i −0.623315 0.781971i
2828 148.162 0.188982
2929 94.2775i 0.112102i 0.998428 + 0.0560508i 0.0178509π0.0178509\pi
−0.998428 + 0.0560508i 0.982149π0.982149\pi
3030 895.624 830.893i 0.995138 0.923215i
3131 429.829 0.447273 0.223637 0.974673i 0.428207π-0.428207\pi
0.223637 + 0.974673i 0.428207π0.428207\pi
3232 181.019i 0.176777i
3333 754.339 + 813.106i 0.692690 + 0.746653i
3434 −182.271 −0.157674
3535 888.834i 0.725579i
3636 −48.5215 + 646.181i −0.0374394 + 0.498596i
3737 2118.52 1.54749 0.773746 0.633496i 0.218381π-0.218381\pi
0.773746 + 0.633496i 0.218381π0.218381\pi
3838 354.563i 0.245542i
3939 1594.24 1479.02i 1.04815 0.972398i
4040 −1085.95 −0.678717
4141 1220.23i 0.725893i −0.931810 0.362946i 0.881771π-0.881771\pi
0.931810 0.362946i 0.118229π-0.118229\pi
4242 −320.641 345.620i −0.181769 0.195930i
4343 976.206 0.527964 0.263982 0.964528i 0.414964π-0.414964\pi
0.263982 + 0.964528i 0.414964π0.414964\pi
4444 985.893i 0.509242i
4545 −3876.48 291.083i −1.91431 0.143745i
4646 −813.493 −0.384449
4747 526.553i 0.238367i 0.992872 + 0.119183i 0.0380277π0.0380277\pi
−0.992872 + 0.119183i 0.961972π0.961972\pi
4848 422.267 391.748i 0.183276 0.170030i
4949 343.000 0.142857
5050 4746.90i 1.89876i
5151 394.457 + 425.187i 0.151656 + 0.163470i
5252 −1933.02 −0.714874
5353 1567.07i 0.557875i 0.960309 + 0.278937i 0.0899822π0.0899822\pi
−0.960309 + 0.278937i 0.910018π0.910018\pi
5454 1612.36 1285.23i 0.552937 0.440750i
5555 5914.43 1.95518
5656 419.066i 0.133631i
5757 827.096 767.318i 0.254569 0.236171i
5858 −266.657 −0.0792678
5959 5826.08i 1.67368i 0.547448 + 0.836840i 0.315599π0.315599\pi
−0.547448 + 0.836840i 0.684401π0.684401\pi
6060 2350.12 + 2533.21i 0.652811 + 0.703669i
6161 −4955.04 −1.33164 −0.665821 0.746112i 0.731918π-0.731918\pi
−0.665821 + 0.746112i 0.731918π0.731918\pi
6262 1215.74i 0.316270i
6363 −112.329 + 1495.93i −0.0283015 + 0.376903i
6464 −512.000 −0.125000
6565 11596.3i 2.74469i
6666 −2299.81 + 2133.59i −0.527964 + 0.489806i
6767 −1321.11 −0.294300 −0.147150 0.989114i 0.547010π-0.547010\pi
−0.147150 + 0.989114i 0.547010π0.547010\pi
6868 515.540i 0.111492i
6969 1760.50 + 1897.65i 0.369775 + 0.398582i
7070 −2514.00 −0.513062
7171 3717.89i 0.737531i 0.929522 + 0.368765i 0.120219π0.120219\pi
−0.929522 + 0.368765i 0.879781π0.879781\pi
7272 −1827.68 137.239i −0.352561 0.0264737i
7373 2023.01 0.379622 0.189811 0.981821i 0.439212π-0.439212\pi
0.189811 + 0.981821i 0.439212π0.439212\pi
7474 5992.07i 1.09424i
7575 −11073.2 + 10272.9i −1.96856 + 1.82629i
7676 −1002.86 −0.173625
7777 2282.37i 0.384951i
7878 4183.29 + 4509.19i 0.687589 + 0.741156i
7979 4711.86 0.754985 0.377493 0.926013i 0.376786π-0.376786\pi
0.377493 + 0.926013i 0.376786π0.376786\pi
8080 3071.52i 0.479925i
8181 −6487.43 979.801i −0.988786 0.149337i
8282 3451.32 0.513284
8383 4420.87i 0.641729i −0.947125 0.320865i 0.896027π-0.896027\pi
0.947125 0.320865i 0.103973π-0.103973\pi
8484 977.562 906.909i 0.138543 0.128530i
8585 3092.76 0.428063
8686 2761.13i 0.373327i
8787 577.078 + 622.036i 0.0762424 + 0.0821820i
8888 2788.53 0.360089
8989 8482.72i 1.07091i −0.844562 0.535457i 0.820139π-0.820139\pi
0.844562 0.535457i 0.179861π-0.179861\pi
9090 823.308 10964.3i 0.101643 1.35362i
9191 −4475.00 −0.540394
9292 2300.91i 0.271846i
9393 2835.98 2631.01i 0.327897 0.304199i
9494 −1489.32 −0.168551
9595 6016.20i 0.666615i
9696 1108.03 + 1194.35i 0.120229 + 0.129595i
9797 −16341.1 −1.73675 −0.868375 0.495908i 0.834835π-0.834835\pi
−0.868375 + 0.495908i 0.834835π0.834835\pi
9898 970.151i 0.101015i
9999 9954.14 + 747.452i 1.01563 + 0.0762629i
100100 13426.2 1.34262
101101 5191.39i 0.508910i 0.967085 + 0.254455i 0.0818960π0.0818960\pi
−0.967085 + 0.254455i 0.918104π0.918104\pi
102102 −1202.61 + 1115.69i −0.115591 + 0.107237i
103103 9498.09 0.895286 0.447643 0.894212i 0.352264π-0.352264\pi
0.447643 + 0.894212i 0.352264π0.352264\pi
104104 5467.41i 0.505492i
105105 5440.61 + 5864.46i 0.493479 + 0.531924i
106106 −4432.35 −0.394477
107107 3676.19i 0.321093i −0.987028 0.160546i 0.948674π-0.948674\pi
0.987028 0.160546i 0.0513256π-0.0513256\pi
108108 3635.17 + 4560.45i 0.311657 + 0.390985i
109109 −11597.2 −0.976113 −0.488056 0.872812i 0.662294π-0.662294\pi
−0.488056 + 0.872812i 0.662294π0.662294\pi
110110 16728.5i 1.38252i
111111 13977.8 12967.6i 1.13447 1.05248i
112112 −1185.30 −0.0944911
113113 1074.40i 0.0841413i −0.999115 0.0420706i 0.986605π-0.986605\pi
0.999115 0.0420706i 0.0133955π-0.0133955\pi
114114 2170.30 + 2339.38i 0.166998 + 0.180008i
115115 13803.3 1.04373
116116 754.220i 0.0560508i
117117 1465.51 19516.9i 0.107058 1.42573i
118118 −16478.6 −1.18347
119119 1193.49i 0.0842802i
120120 −7164.99 + 6647.15i −0.497569 + 0.461607i
121121 −546.261 −0.0373103
122122 14015.0i 0.941613i
123123 −7469.08 8050.96i −0.493693 0.532154i
124124 −3438.64 −0.223637
125125 50549.6i 3.23517i
126126 −4231.13 317.714i −0.266511 0.0200122i
127127 −19449.2 −1.20585 −0.602927 0.797797i 0.705999π-0.705999\pi
−0.602927 + 0.797797i 0.705999π0.705999\pi
128128 1448.15i 0.0883883i
129129 6440.93 5975.42i 0.387052 0.359078i
130130 32799.3 1.94079
131131 14919.5i 0.869382i −0.900580 0.434691i 0.856858π-0.856858\pi
0.900580 0.434691i 0.143142π-0.143142\pi
132132 −6034.71 6504.85i −0.346345 0.373327i
133133 −2321.64 −0.131248
134134 3736.67i 0.208102i
135135 −27358.5 + 21807.6i −1.50115 + 1.19658i
136136 1458.17 0.0788369
137137 19699.7i 1.04959i 0.851229 + 0.524795i 0.175858π0.175858\pi
−0.851229 + 0.524795i 0.824142π0.824142\pi
138138 −5367.37 + 4979.44i −0.281840 + 0.261471i
139139 22226.3 1.15037 0.575184 0.818024i 0.304930π-0.304930\pi
0.575184 + 0.818024i 0.304930π0.304930\pi
140140 7110.67i 0.362789i
141141 3223.06 + 3474.15i 0.162118 + 0.174747i
142142 −10515.8 −0.521513
143143 29777.4i 1.45618i
144144 388.172 5169.45i 0.0187197 0.249298i
145145 4524.61 0.215202
146146 5721.92i 0.268433i
147147 2263.09 2099.52i 0.104729 0.0971597i
148148 −16948.1 −0.773746
149149 6791.29i 0.305900i −0.988234 0.152950i 0.951123π-0.951123\pi
0.988234 0.152950i 0.0488774π-0.0488774\pi
150150 −29056.0 31319.7i −1.29138 1.39198i
151151 −8470.50 −0.371497 −0.185748 0.982597i 0.559471π-0.559471\pi
−0.185748 + 0.982597i 0.559471π0.559471\pi
152152 2836.51i 0.122771i
153153 5205.19 + 390.856i 0.222358 + 0.0166968i
154154 6455.53 0.272201
155155 20628.6i 0.858630i
156156 −12753.9 + 11832.1i −0.524076 + 0.486199i
157157 −13638.2 −0.553297 −0.276649 0.960971i 0.589224π-0.589224\pi
−0.276649 + 0.960971i 0.589224π0.589224\pi
158158 13327.2i 0.533855i
159159 9592.14 + 10339.4i 0.379421 + 0.408980i
160160 8687.57 0.339358
161161 5326.67i 0.205496i
162162 2771.30 18349.2i 0.105597 0.699178i
163163 −38643.6 −1.45446 −0.727232 0.686392i 0.759193π-0.759193\pi
−0.727232 + 0.686392i 0.759193π0.759193\pi
164164 9761.81i 0.362946i
165165 39023.0 36202.6i 1.43335 1.32976i
166166 12504.1 0.453771
167167 33982.6i 1.21850i 0.792980 + 0.609248i 0.208529π0.208529\pi
−0.792980 + 0.609248i 0.791471π0.791471\pi
168168 2565.13 + 2764.96i 0.0908846 + 0.0979650i
169169 29822.8 1.04418
170170 8747.64i 0.302686i
171171 760.313 10125.4i 0.0260016 0.346275i
172172 −7809.65 −0.263982
173173 12224.7i 0.408457i 0.978923 + 0.204229i 0.0654686π0.0654686\pi
−0.978923 + 0.204229i 0.934531π0.934531\pi
174174 −1759.38 + 1632.22i −0.0581115 + 0.0539115i
175175 31082.2 1.01493
176176 7887.14i 0.254621i
177177 35661.8 + 38440.0i 1.13830 + 1.22698i
178178 23992.7 0.757251
179179 53278.8i 1.66283i −0.555651 0.831416i 0.687531π-0.687531\pi
0.555651 0.831416i 0.312469π-0.312469\pi
180180 31011.8 + 2328.67i 0.957156 + 0.0718724i
181181 19789.7 0.604064 0.302032 0.953298i 0.402335π-0.402335\pi
0.302032 + 0.953298i 0.402335π0.402335\pi
182182 12657.2i 0.382116i
183183 −32693.0 + 30330.1i −0.976230 + 0.905673i
184184 6507.95 0.192224
185185 101673.i 2.97072i
186186 7441.63 + 8021.37i 0.215101 + 0.231858i
187187 −7941.68 −0.227106
188188 4212.42i 0.119183i
189189 8415.54 + 10557.6i 0.235591 + 0.295557i
190190 17016.4 0.471368
191191 22349.2i 0.612626i 0.951931 + 0.306313i 0.0990954π0.0990954\pi
−0.951931 + 0.306313i 0.900905π0.900905\pi
192192 −3378.14 + 3133.98i −0.0916378 + 0.0850148i
193193 −55747.5 −1.49662 −0.748308 0.663351i 0.769134π-0.769134\pi
−0.748308 + 0.663351i 0.769134π0.769134\pi
194194 46219.5i 1.22807i
195195 −70981.7 76511.6i −1.86671 2.01214i
196196 −2744.00 −0.0714286
197197 3307.33i 0.0852208i −0.999092 0.0426104i 0.986433π-0.986433\pi
0.999092 0.0426104i 0.0135674π-0.0135674\pi
198198 −2114.11 + 28154.6i −0.0539260 + 0.718155i
199199 31962.3 0.807107 0.403554 0.914956i 0.367775π-0.367775\pi
0.403554 + 0.914956i 0.367775π0.367775\pi
200200 37975.2i 0.949379i
201201 −8716.61 + 8086.62i −0.215752 + 0.200159i
202202 −14683.5 −0.359854
203203 1746.04i 0.0423704i
204204 −3155.65 3401.49i −0.0758279 0.0817352i
205205 −58561.7 −1.39350
206206 26864.7i 0.633063i
207207 23231.3 + 1744.43i 0.542166 + 0.0407110i
208208 15464.2 0.357437
209209 15448.6i 0.353668i
210210 −16587.2 + 15388.4i −0.376127 + 0.348942i
211211 8820.58 0.198122 0.0990609 0.995081i 0.468416π-0.468416\pi
0.0990609 + 0.995081i 0.468416π0.468416\pi
212212 12536.6i 0.278937i
213213 22757.5 + 24530.4i 0.501608 + 0.540686i
214214 10397.8 0.227047
215215 46850.6i 1.01353i
216216 −12898.9 + 10281.8i −0.276468 + 0.220375i
217217 −7960.55 −0.169053
218218 32801.8i 0.690216i
219219 13347.6 12382.9i 0.278302 0.258188i
220220 −47315.5 −0.977592
221221 15571.1i 0.318812i
222222 36677.8 + 39535.2i 0.744214 + 0.802191i
223223 −52110.8 −1.04790 −0.523948 0.851750i 0.675541π-0.675541\pi
−0.523948 + 0.851750i 0.675541π0.675541\pi
224224 3352.53i 0.0668153i
225225 −10179.1 + 135559.i −0.201068 + 2.67771i
226226 3038.86 0.0594969
227227 60377.1i 1.17171i 0.810415 + 0.585856i 0.199241π0.199241\pi
−0.810415 + 0.585856i 0.800759π0.800759\pi
228228 −6616.77 + 6138.55i −0.127285 + 0.118085i
229229 3035.47 0.0578835 0.0289418 0.999581i 0.490786π-0.490786\pi
0.0289418 + 0.999581i 0.490786π0.490786\pi
230230 39041.6i 0.738026i
231231 −13970.6 15058.9i −0.261812 0.282208i
232232 2133.26 0.0396339
233233 34594.5i 0.637228i 0.947885 + 0.318614i 0.103217π0.103217\pi
−0.947885 + 0.318614i 0.896783π0.896783\pi
234234 55202.1 + 4145.10i 1.00815 + 0.0757013i
235235 25270.6 0.457593
236236 46608.6i 0.836840i
237237 31088.5 28841.6i 0.553482 0.513479i
238238 3375.70 0.0595951
239239 78309.8i 1.37095i −0.728098 0.685473i 0.759595π-0.759595\pi
0.728098 0.685473i 0.240405π-0.240405\pi
240240 −18801.0 20265.7i −0.326406 0.351834i
241241 28362.2 0.488322 0.244161 0.969735i 0.421487π-0.421487\pi
0.244161 + 0.969735i 0.421487π0.421487\pi
242242 1545.06i 0.0263824i
243243 −48801.0 + 33245.3i −0.826449 + 0.563012i
244244 39640.3 0.665821
245245 16461.4i 0.274243i
246246 22771.5 21125.7i 0.376290 0.349094i
247247 30289.7 0.496479
248248 9725.93i 0.158135i
249249 −27060.4 29168.6i −0.436452 0.470453i
250250 −142976. −2.28761
251251 89655.5i 1.42308i 0.702646 + 0.711540i 0.252002π0.252002\pi
−0.702646 + 0.711540i 0.747998π0.747998\pi
252252 898.630 11967.4i 0.0141508 0.188452i
253253 −35444.5 −0.553742
254254 55010.7i 0.852667i
255255 20405.8 18931.0i 0.313814 0.291134i
256256 4096.00 0.0625000
257257 12337.1i 0.186787i −0.995629 0.0933933i 0.970229π-0.970229\pi
0.995629 0.0933933i 0.0297714π-0.0297714\pi
258258 16901.0 + 18217.7i 0.253906 + 0.273687i
259259 −39235.5 −0.584897
260260 92770.5i 1.37234i
261261 7615.04 + 571.810i 0.111787 + 0.00839404i
262262 42198.6 0.614746
263263 39803.9i 0.575458i 0.957712 + 0.287729i 0.0929003π0.0929003\pi
−0.957712 + 0.287729i 0.907100π0.907100\pi
264264 18398.5 17068.7i 0.263982 0.244903i
265265 75207.7 1.07095
266266 6566.60i 0.0928063i
267267 −51923.2 55968.3i −0.728349 0.785091i
268268 10568.9 0.147150
269269 38209.6i 0.528042i 0.964517 + 0.264021i 0.0850488π0.0850488\pi
−0.964517 + 0.264021i 0.914951π0.914951\pi
270270 −61681.3 77381.4i −0.846108 1.06147i
271271 134877. 1.83653 0.918267 0.395961i 0.129588π-0.129588\pi
0.918267 + 0.395961i 0.129588π0.129588\pi
272272 4124.32i 0.0557461i
273273 −29525.7 + 27391.8i −0.396164 + 0.367532i
274274 −55719.3 −0.742172
275275 206826.i 2.73488i
276276 −14084.0 15181.2i −0.184888 0.199291i
277277 134803. 1.75688 0.878438 0.477856i 0.158586π-0.158586\pi
0.878438 + 0.477856i 0.158586π0.158586\pi
278278 62865.4i 0.813434i
279279 2606.99 34718.4i 0.0334913 0.446017i
280280 20112.0 0.256531
281281 3288.42i 0.0416462i −0.999783 0.0208231i 0.993371π-0.993371\pi
0.999783 0.0208231i 0.00662868π-0.00662868\pi
282282 −9826.39 + 9116.20i −0.123565 + 0.114635i
283283 −129266. −1.61403 −0.807016 0.590529i 0.798919π-0.798919\pi
−0.807016 + 0.590529i 0.798919π0.798919\pi
284284 29743.1i 0.368765i
285285 −36825.5 39694.4i −0.453377 0.488697i
286286 −84223.1 −1.02967
287287 22598.9i 0.274362i
288288 14621.4 + 1097.92i 0.176280 + 0.0132368i
289289 79368.2 0.950278
290290 12797.5i 0.152171i
291291 −107817. + 100025.i −1.27322 + 1.18119i
292292 −16184.0 −0.189811
293293 168398.i 1.96157i −0.195104 0.980783i 0.562504π-0.562504\pi
0.195104 0.980783i 0.437496π-0.437496\pi
294294 5938.35 + 6400.98i 0.0687023 + 0.0740545i
295295 279608. 3.21296
296296 47936.5i 0.547121i
297297 70251.9 55998.3i 0.796425 0.634836i
298298 19208.7 0.216304
299299 69495.3i 0.777344i
300300 88585.4 82182.9i 0.984282 0.913143i
301301 −18079.6 −0.199552
302302 23958.2i 0.262688i
303303 31776.8 + 34252.4i 0.346119 + 0.373083i
304304 8022.85 0.0868123
305305 237805.i 2.55635i
306306 −1105.51 + 14722.5i −0.0118064 + 0.157231i
307307 −44393.8 −0.471027 −0.235514 0.971871i 0.575677π-0.575677\pi
−0.235514 + 0.971871i 0.575677π0.575677\pi
308308 18259.0i 0.192475i
309309 62667.7 58138.4i 0.656336 0.608900i
310310 58346.5 0.607143
311311 146724.i 1.51699i 0.651681 + 0.758493i 0.274064π0.274064\pi
−0.651681 + 0.758493i 0.725936π0.725936\pi
312312 −33466.3 36073.5i −0.343795 0.370578i
313313 −54255.1 −0.553799 −0.276899 0.960899i 0.589307π-0.589307\pi
−0.276899 + 0.960899i 0.589307π0.589307\pi
314314 38574.7i 0.391240i
315315 71793.4 + 5390.94i 0.723542 + 0.0543304i
316316 −37694.9 −0.377493
317317 130350.i 1.29715i 0.761149 + 0.648577i 0.224636π0.224636\pi
−0.761149 + 0.648577i 0.775364π0.775364\pi
318318 −29244.3 + 27130.7i −0.289192 + 0.268291i
319319 −11618.4 −0.114174
320320 24572.2i 0.239963i
321321 −22502.2 24255.2i −0.218381 0.235394i
322322 15066.1 0.145308
323323 8078.32i 0.0774312i
324324 51899.4 + 7838.41i 0.494393 + 0.0746686i
325325 −405519. −3.83923
326326 109301.i 1.02846i
327327 −76517.4 + 70987.2i −0.715591 + 0.663872i
328328 −27610.6 −0.256642
329329 9751.89i 0.0900943i
330330 102396. + 110374.i 0.940280 + 1.01353i
331331 −35032.0 −0.319749 −0.159875 0.987137i 0.551109π-0.551109\pi
−0.159875 + 0.987137i 0.551109π0.551109\pi
332332 35367.0i 0.320865i
333333 12849.2 171118.i 0.115874 1.54315i
334334 −96117.4 −0.861607
335335 63403.6i 0.564968i
336336 −7820.50 + 7255.27i −0.0692717 + 0.0642651i
337337 −184305. −1.62285 −0.811423 0.584459i 0.801307π-0.801307\pi
−0.811423 + 0.584459i 0.801307π0.801307\pi
338338 84351.7i 0.738347i
339339 −6576.47 7088.81i −0.0572260 0.0616842i
340340 −24742.1 −0.214032
341341 52970.7i 0.455541i
342342 28639.0 + 2150.49i 0.244853 + 0.0183859i
343343 −6352.45 −0.0539949
344344 22089.0i 0.186664i
345345 91073.0 84490.8i 0.765159 0.709858i
346346 −34576.7 −0.288823
347347 15320.3i 0.127235i −0.997974 0.0636176i 0.979736π-0.979736\pi
0.997974 0.0636176i 0.0202638π-0.0202638\pi
348348 −4616.63 4976.29i −0.0381212 0.0410910i
349349 85296.5 0.700294 0.350147 0.936695i 0.386132π-0.386132\pi
0.350147 + 0.936695i 0.386132π0.386132\pi
350350 87913.7i 0.717663i
351351 −109795. 137741.i −0.891184 1.11802i
352352 −22308.2 −0.180044
353353 120060.i 0.963493i −0.876311 0.481746i 0.840003π-0.840003\pi
0.876311 0.481746i 0.159997π-0.159997\pi
354354 −108725. + 100867.i −0.867605 + 0.804899i
355355 178431. 1.41584
356356 67861.7i 0.535457i
357357 −7305.44 7874.57i −0.0573205 0.0617860i
358358 150695. 1.17580
359359 164672.i 1.27771i −0.769328 0.638854i 0.779409π-0.779409\pi
0.769328 0.638854i 0.220591π-0.220591\pi
360360 −6586.46 + 87714.7i −0.0508215 + 0.676811i
361361 −114607. −0.879418
362362 55973.8i 0.427138i
363363 −3604.19 + 3343.70i −0.0273523 + 0.0253754i
364364 35800.0 0.270197
365365 97089.1i 0.728760i
366366 −85786.5 92469.7i −0.640408 0.690299i
367367 179523. 1.33287 0.666435 0.745563i 0.267819π-0.267819\pi
0.666435 + 0.745563i 0.267819π0.267819\pi
368368 18407.3i 0.135923i
369369 −98560.8 7400.89i −0.723855 0.0543540i
370370 287574. 2.10062
371371 29022.6i 0.210857i
372372 −22687.9 + 21048.1i −0.163949 + 0.152099i
373373 154860. 1.11307 0.556534 0.830825i 0.312131π-0.312131\pi
0.556534 + 0.830825i 0.312131π0.312131\pi
374374 22462.4i 0.160588i
375375 309417. + 333522.i 2.20030 + 2.37171i
376376 11914.5 0.0842755
377377 22780.0i 0.160277i
378378 −29861.4 + 23802.7i −0.208991 + 0.166588i
379379 −241643. −1.68227 −0.841135 0.540826i 0.818112π-0.818112\pi
−0.841135 + 0.540826i 0.818112π0.818112\pi
380380 48129.6i 0.333307i
381381 −128324. + 119050.i −0.884014 + 0.820123i
382382 −63213.1 −0.433192
383383 95222.8i 0.649147i 0.945860 + 0.324574i 0.105221π0.105221\pi
−0.945860 + 0.324574i 0.894779π0.894779\pi
384384 −8864.25 9554.81i −0.0601145 0.0647977i
385385 −109537. −0.738990
386386 157678.i 1.05827i
387387 5920.87 78850.7i 0.0395333 0.526482i
388388 130729. 0.868375
389389 224301.i 1.48228i −0.671349 0.741142i 0.734285π-0.734285\pi
0.671349 0.741142i 0.265715π-0.265715\pi
390390 216407. 200767.i 1.42280 1.31997i
391391 −18534.5 −0.121235
392392 7761.20i 0.0505076i
393393 −91323.0 98437.5i −0.591283 0.637347i
394394 9354.55 0.0602602
395395 226134.i 1.44935i
396396 −79633.1 5979.62i −0.507813 0.0381314i
397397 −79675.1 −0.505524 −0.252762 0.967528i 0.581339π-0.581339\pi
−0.252762 + 0.967528i 0.581339π0.581339\pi
398398 90402.9i 0.570711i
399399 −15318.0 + 14210.9i −0.0962182 + 0.0892641i
400400 −107410. −0.671312
401401 87504.0i 0.544176i −0.962272 0.272088i 0.912286π-0.912286\pi
0.962272 0.272088i 0.0877142π-0.0877142\pi
402402 −22872.4 24654.3i −0.141534 0.152560i
403403 103859. 0.639488
404404 41531.1i 0.254455i
405405 −47023.1 + 311348.i −0.286683 + 1.89817i
406406 4938.56 0.0299604
407407 261079.i 1.57610i
408408 9620.88 8925.53i 0.0577955 0.0536184i
409409 260159. 1.55522 0.777612 0.628745i 0.216431π-0.216431\pi
0.777612 + 0.628745i 0.216431π0.216431\pi
410410 165637.i 0.985351i
411411 120583. + 129977.i 0.713845 + 0.769457i
412412 −75984.7 −0.447643
413413 107900.i 0.632591i
414414 −4933.99 + 65708.0i −0.0287871 + 0.383369i
415415 −212169. −1.23193
416416 43739.2i 0.252746i
417417 146647. 136048.i 0.843338 0.782387i
418418 −43695.2 −0.250081
419419 222361.i 1.26658i −0.773916 0.633288i 0.781705π-0.781705\pi
0.773916 0.633288i 0.218295π-0.218295\pi
420420 −43524.9 46915.7i −0.246740 0.265962i
421421 274759. 1.55020 0.775100 0.631838i 0.217699π-0.217699\pi
0.775100 + 0.631838i 0.217699π0.217699\pi
422422 24948.4i 0.140093i
423423 42531.0 + 3193.64i 0.237698 + 0.0178486i
424424 35458.8 0.197239
425425 108153.i 0.598769i
426426 −69382.4 + 64367.8i −0.382323 + 0.354690i
427427 91768.6 0.503313
428428 29409.5i 0.160546i
429429 182269. + 196469.i 0.990372 + 1.06753i
430430 132513. 0.716676
431431 79239.0i 0.426564i 0.976991 + 0.213282i 0.0684154π0.0684154\pi
−0.976991 + 0.213282i 0.931585π0.931585\pi
432432 −29081.4 36483.6i −0.155829 0.195493i
433433 −56355.8 −0.300582 −0.150291 0.988642i 0.548021π-0.548021\pi
−0.150291 + 0.988642i 0.548021π0.548021\pi
434434 22515.8i 0.119539i
435435 29853.1 27695.4i 0.157765 0.146363i
436436 92777.6 0.488056
437437 36054.4i 0.188797i
438438 35024.3 + 37752.8i 0.182566 + 0.196789i
439439 −83094.4 −0.431164 −0.215582 0.976486i 0.569165π-0.569165\pi
−0.215582 + 0.976486i 0.569165π0.569165\pi
440440 133828.i 0.691262i
441441 2080.36 27705.0i 0.0106970 0.142456i
442442 −44041.7 −0.225434
443443 139917.i 0.712955i 0.934304 + 0.356477i 0.116022π0.116022\pi
−0.934304 + 0.356477i 0.883978π0.883978\pi
444444 −111822. + 103741.i −0.567235 + 0.526238i
445445 −407107. −2.05584
446446 147392.i 0.740974i
447447 −41569.9 44808.4i −0.208048 0.224256i
448448 9482.37 0.0472456
449449 100269.i 0.497361i 0.968586 + 0.248681i 0.0799970π0.0799970\pi
−0.968586 + 0.248681i 0.920003π0.920003\pi
450450 −383419. 28790.8i −1.89343 0.142177i
451451 150376. 0.739310
452452 8595.20i 0.0420706i
453453 −55887.7 + 51848.4i −0.272345 + 0.252662i
454454 −170772. −0.828525
455455 214767.i 1.03739i
456456 −17362.4 18715.0i −0.0834989 0.0900039i
457457 −82991.3 −0.397375 −0.198687 0.980063i 0.563668π-0.563668\pi
−0.198687 + 0.980063i 0.563668π0.563668\pi
458458 8585.60i 0.0409298i
459459 36735.9 29282.5i 0.174367 0.138990i
460460 −110426. −0.521863
461461 321734.i 1.51389i −0.653478 0.756946i 0.726691π-0.726691\pi
0.653478 0.756946i 0.273309π-0.273309\pi
462462 42593.1 39514.7i 0.199552 0.185129i
463463 −102874. −0.479894 −0.239947 0.970786i 0.577130π-0.577130\pi
−0.239947 + 0.970786i 0.577130π0.577130\pi
464464 6033.76i 0.0280254i
465465 −126269. 136106.i −0.583970 0.629464i
466466 −97847.9 −0.450588
467467 87221.5i 0.399935i −0.979803 0.199968i 0.935916π-0.935916\pi
0.979803 0.199968i 0.0640837π-0.0640837\pi
468468 −11724.1 + 156135.i −0.0535289 + 0.712867i
469469 24467.4 0.111235
470470 71476.0i 0.323567i
471471 −89984.0 + 83480.4i −0.405624 + 0.376308i
472472 131829. 0.591735
473473 120304.i 0.537723i
474474 81576.4 + 87931.6i 0.363085 + 0.391371i
475475 −210384. −0.932451
476476 9547.93i 0.0421401i
477477 126576. + 9504.57i 0.556309 + 0.0417730i
478478 221494. 0.969406
479479 131399.i 0.572691i 0.958126 + 0.286345i 0.0924405π0.0924405\pi
−0.958126 + 0.286345i 0.907559π0.907559\pi
480480 57319.9 53177.2i 0.248784 0.230804i
481481 511892. 2.21252
482482 80220.5i 0.345296i
483483 −32604.9 35145.0i −0.139762 0.150650i
484484 4370.09 0.0186552
485485 784249.i 3.33404i
486486 −94031.9 138030.i −0.398110 0.584387i
487487 −115823. −0.488355 −0.244178 0.969731i 0.578518π-0.578518\pi
−0.244178 + 0.969731i 0.578518π0.578518\pi
488488 112120.i 0.470806i
489489 −254968. + 236540.i −1.06627 + 0.989207i
490490 46560.0 0.193919
491491 455525.i 1.88951i 0.327775 + 0.944756i 0.393701π0.393701\pi
−0.327775 + 0.944756i 0.606299π0.606299\pi
492492 59752.6 + 64407.6i 0.246846 + 0.266077i
493493 −6075.48 −0.0249969
494494 85672.2i 0.351064i
495495 35872.1 477724.i 0.146402 1.94970i
496496 27509.1 0.111818
497497 68856.3i 0.278760i
498498 82501.2 76538.5i 0.332661 0.308618i
499499 −353733. −1.42061 −0.710305 0.703894i 0.751443π-0.751443\pi
−0.710305 + 0.703894i 0.751443π0.751443\pi
500500 404397.i 1.61759i
501501 208010. + 224215.i 0.828721 + 0.893282i
502502 −253584. −1.00627
503503 424746.i 1.67878i −0.543530 0.839390i 0.682912π-0.682912\pi
0.543530 0.839390i 0.317088π-0.317088\pi
504504 33849.0 + 2541.71i 0.133255 + 0.0100061i
505505 249148. 0.976954
506506 100252.i 0.391555i
507507 196769. 182548.i 0.765492 0.710166i
508508 155594. 0.602927
509509 49005.7i 0.189152i 0.995518 + 0.0945760i 0.0301495π0.0301495\pi
−0.995518 + 0.0945760i 0.969850π0.969850\pi
510510 53544.8 + 57716.3i 0.205863 + 0.221900i
511511 −37466.6 −0.143484
512512 11585.2i 0.0441942i
513513 −56961.8 71460.6i −0.216446 0.271539i
514514 34894.5 0.132078
515515 455837.i 1.71868i
516516 −51527.4 + 47803.3i −0.193526 + 0.179539i
517517 −64890.6 −0.242773
518518 110975.i 0.413584i
519519 74828.2 + 80657.7i 0.277799 + 0.299441i
520520 −262395. −0.970394
521521 158536.i 0.584054i −0.956410 0.292027i 0.905670π-0.905670\pi
0.956410 0.292027i 0.0943298π-0.0943298\pi
522522 −1617.32 + 21538.6i −0.00593548 + 0.0790453i
523523 137079. 0.501151 0.250575 0.968097i 0.419380π-0.419380\pi
0.250575 + 0.968097i 0.419380π0.419380\pi
524524 119356.i 0.434691i
525525 205078. 190256.i 0.744047 0.690272i
526526 −112582. −0.406910
527527 27699.3i 0.0997349i
528528 48277.7 + 52038.8i 0.173172 + 0.186663i
529529 197120. 0.704398
530530 212719.i 0.757278i
531531 470588. + 35336.2i 1.66898 + 0.125323i
532532 18573.2 0.0656240
533533 294840.i 1.03784i
534534 158302. 146861.i 0.555143 0.515020i
535535 −176430. −0.616402
536536 29893.4i 0.104051i
537537 −326123. 351529.i −1.13092 1.21903i
538538 −108073. −0.373382
539539 42270.2i 0.145498i
540540 218868. 174461.i 0.750575 0.598289i
541541 −171295. −0.585263 −0.292632 0.956225i 0.594531π-0.594531\pi
−0.292632 + 0.956225i 0.594531π0.594531\pi
542542 381490.i 1.29863i
543543 130571. 121134.i 0.442841 0.410835i
544544 −11665.3 −0.0394185
545545 556578.i 1.87384i
546546 −77475.7 83511.4i −0.259884 0.280130i
547547 −131375. −0.439075 −0.219537 0.975604i 0.570455π-0.570455\pi
−0.219537 + 0.975604i 0.570455π0.570455\pi
548548 157598.i 0.524795i
549549 −30053.2 + 400231.i −0.0997117 + 1.32790i
550550 584991. 1.93386
551551 11818.3i 0.0389272i
552552 42938.9 39835.6i 0.140920 0.130735i
553553 −87264.9 −0.285358
554554 381281.i 1.24230i
555555 −622346. 670830.i −2.02044 2.17784i
556556 −177810. −0.575184
557557 256492.i 0.826729i −0.910566 0.413365i 0.864353π-0.864353\pi
0.910566 0.413365i 0.135647π-0.135647\pi
558558 98198.6 + 7373.69i 0.315382 + 0.0236819i
559559 235878. 0.754856
560560 56885.4i 0.181395i
561561 −52398.6 + 48611.5i −0.166492 + 0.154459i
562562 9301.07 0.0294483
563563 167229.i 0.527587i −0.964579 0.263794i 0.915026π-0.915026\pi
0.964579 0.263794i 0.0849738π-0.0849738\pi
564564 −25784.5 27793.2i −0.0810589 0.0873737i
565565 −51563.2 −0.161526
566566 365620.i 1.14129i
567567 120149. + 18146.2i 0.373726 + 0.0564441i
568568 84126.3 0.260757
569569 227471.i 0.702591i 0.936265 + 0.351295i 0.114259π0.114259\pi
−0.936265 + 0.351295i 0.885741π0.885741\pi
570570 112273. 104158.i 0.345561 0.320586i
571571 162502. 0.498409 0.249205 0.968451i 0.419831π-0.419831\pi
0.249205 + 0.968451i 0.419831π0.419831\pi
572572 238219.i 0.728088i
573573 136801. + 147458.i 0.416658 + 0.449118i
574574 −63919.3 −0.194003
575575 482696.i 1.45995i
576576 −3105.37 + 41355.6i −0.00935985 + 0.124649i
577577 159511. 0.479113 0.239557 0.970882i 0.422998π-0.422998\pi
0.239557 + 0.970882i 0.422998π0.422998\pi
578578 224487.i 0.671948i
579579 −367817. + 341234.i −1.09717 + 1.01788i
580580 −36196.9 −0.107601
581581 81875.7i 0.242551i
582582 −282913. 304953.i −0.835231 0.900299i
583583 −193120. −0.568187
584584 45775.4i 0.134217i
585585 −936664. 70333.7i −2.73698 0.205519i
586586 476303. 1.38704
587587 207293.i 0.601601i 0.953687 + 0.300801i 0.0972539π0.0972539\pi
−0.953687 + 0.300801i 0.902746π0.902746\pi
588588 −18104.7 + 16796.2i −0.0523645 + 0.0485799i
589589 53882.1 0.155315
590590 790851.i 2.27191i
591591 −20244.4 21821.5i −0.0579602 0.0624756i
592592 135585. 0.386873
593593 373791.i 1.06297i −0.847069 0.531483i 0.821635π-0.821635\pi
0.847069 0.531483i 0.178365π-0.178365\pi
594594 158387. + 198702.i 0.448897 + 0.563158i
595595 −57278.7 −0.161793
596596 54330.3i 0.152950i
597597 210884. 195643.i 0.591692 0.548928i
598598 −196562. −0.549665
599599 153142.i 0.426815i 0.976963 + 0.213408i 0.0684563π0.0684563\pi
−0.976963 + 0.213408i 0.931544π0.931544\pi
600600 232448. + 250557.i 0.645690 + 0.695992i
601601 352527. 0.975987 0.487993 0.872847i 0.337729π-0.337729\pi
0.487993 + 0.872847i 0.337729π0.337729\pi
602602 51136.8i 0.141104i
603603 −8012.79 + 106710.i −0.0220368 + 0.293474i
604604 67764.0 0.185748
605605 26216.4i 0.0716247i
606606 −96880.4 + 89878.4i −0.263810 + 0.244743i
607607 179592. 0.487427 0.243714 0.969847i 0.421634π-0.421634\pi
0.243714 + 0.969847i 0.421634π0.421634\pi
608608 22692.0i 0.0613856i
609609 −10687.6 11520.3i −0.0288169 0.0310619i
610610 −672613. −1.80761
611611 127230.i 0.340805i
612612 −41641.5 3126.84i −0.111179 0.00834840i
613613 235777. 0.627452 0.313726 0.949513i 0.398423π-0.398423\pi
0.313726 + 0.949513i 0.398423π0.398423\pi
614614 125565.i 0.333067i
615615 −386386. + 358460.i −1.02158 + 0.947742i
616616 −51644.2 −0.136101
617617 477167.i 1.25343i 0.779248 + 0.626716i 0.215601π0.215601\pi
−0.779248 + 0.626716i 0.784399π0.784399\pi
618618 164440. + 177251.i 0.430557 + 0.464100i
619619 51174.4 0.133559 0.0667793 0.997768i 0.478728π-0.478728\pi
0.0667793 + 0.997768i 0.478728π0.478728\pi
620620 165029.i 0.429315i
621621 163956. 130691.i 0.425152 0.338892i
622622 −414999. −1.07267
623623 157102.i 0.404768i
624624 102031. 94657.1i 0.262038 0.243099i
625625 1.37708e6 3.52532
626626 153457.i 0.391595i
627627 94561.7 + 101929.i 0.240536 + 0.259275i
628628 109106. 0.276649
629629 136522.i 0.345067i
630630 −15247.9 + 203062.i −0.0384174 + 0.511621i
631631 −570880. −1.43379 −0.716896 0.697180i 0.754438π-0.754438\pi
−0.716896 + 0.697180i 0.754438π0.754438\pi
632632 106617.i 0.266928i
633633 58197.5 53991.3i 0.145244 0.134746i
634634 −368685. −0.917226
635635 933416.i 2.31488i
636636 −76737.1 82715.3i −0.189710 0.204490i
637637 82878.2 0.204250
638638 32861.9i 0.0807331i
639639 300304. + 22549.7i 0.735460 + 0.0552254i
640640 −69500.6 −0.169679
641641 570798.i 1.38921i −0.719394 0.694603i 0.755580π-0.755580\pi
0.719394 0.694603i 0.244420π-0.244420\pi
642642 68604.1 63645.8i 0.166449 0.154419i
643643 −708381. −1.71335 −0.856673 0.515860i 0.827473π-0.827473\pi
−0.856673 + 0.515860i 0.827473π0.827473\pi
644644 42613.4i 0.102748i
645645 −286775. 309116.i −0.689322 0.743024i
646646 −22848.9 −0.0547521
647647 61606.2i 0.147169i −0.997289 0.0735844i 0.976556π-0.976556\pi
0.997289 0.0735844i 0.0234438π-0.0234438\pi
648648 −22170.4 + 146794.i −0.0527987 + 0.349589i
649649 −717986. −1.70462
650650 1.14698e6i 2.71475i
651651 −52523.1 + 48727.0i −0.123933 + 0.114976i
652652 309149. 0.727232
653653 524113.i 1.22913i −0.788865 0.614567i 0.789331π-0.789331\pi
0.788865 0.614567i 0.210669π-0.210669\pi
654654 −200782. 216424.i −0.469428 0.505999i
655655 −716023. −1.66895
656656 78094.4i 0.181473i
657657 12269.9 163403.i 0.0284256 0.378556i
658658 27582.5 0.0637063
659659 234214.i 0.539313i −0.962957 0.269657i 0.913090π-0.913090\pi
0.962957 0.269657i 0.0869102π-0.0869102\pi
660660 −312184. + 289621.i −0.716676 + 0.664878i
661661 −227410. −0.520484 −0.260242 0.965543i 0.583802π-0.583802\pi
−0.260242 + 0.965543i 0.583802π0.583802\pi
662662 99085.6i 0.226097i
663663 95311.6 + 102737.i 0.216830 + 0.233722i
664664 −100033. −0.226885
665665 111422.i 0.251957i
666666 483995. + 36343.0i 1.09117 + 0.0819355i
667667 −27115.5 −0.0609488
668668 271861.i 0.609248i
669669 −343823. + 318973.i −0.768215 + 0.712693i
670670 −179332. −0.399493
671671 610642.i 1.35626i
672672 −20521.0 22119.7i −0.0454423 0.0489825i
673673 203616. 0.449553 0.224776 0.974410i 0.427835π-0.427835\pi
0.224776 + 0.974410i 0.427835π0.427835\pi
674674 521293.i 1.14753i
675675 762605. + 956716.i 1.67376 + 2.09979i
676676 −238583. −0.522090
677677 494274.i 1.07843i 0.842169 + 0.539213i 0.181278π0.181278\pi
−0.842169 + 0.539213i 0.818722π0.818722\pi
678678 20050.2 18601.1i 0.0436173 0.0404649i
679679 302641. 0.656430
680680 69981.1i 0.151343i
681681 369572. + 398364.i 0.796902 + 0.858985i
682682 −149824. −0.322116
683683 43360.8i 0.0929514i 0.998919 + 0.0464757i 0.0147990π0.0147990\pi
−0.998919 + 0.0464757i 0.985201π0.985201\pi
684684 −6082.51 + 81003.3i −0.0130008 + 0.173137i
685685 945440. 2.01490
686686 17967.4i 0.0381802i
687687 20027.8 18580.3i 0.0424345 0.0393676i
688688 62477.2 0.131991
689689 378647.i 0.797621i
690690 238976. + 257593.i 0.501945 + 0.541049i
691691 429593. 0.899708 0.449854 0.893102i 0.351476π-0.351476\pi
0.449854 + 0.893102i 0.351476π0.351476\pi
692692 97797.7i 0.204229i
693693 −184353. 13843.0i −0.383870 0.0288247i
694694 43332.2 0.0899689
695695 1.06669e6i 2.20836i
696696 14075.1 13057.8i 0.0290557 0.0269557i
697697 78634.4 0.161863
698698 241255.i 0.495182i
699699 211755. + 228252.i 0.433390 + 0.467153i
700700 −248658. −0.507464
701701 281406.i 0.572660i 0.958131 + 0.286330i 0.0924354π0.0924354\pi
−0.958131 + 0.286330i 0.907565π0.907565\pi
702702 389591. 310546.i 0.790561 0.630162i
703703 265571. 0.537365
704704 63097.1i 0.127311i
705705 166733. 154683.i 0.335463 0.311217i
706706 339581. 0.681292
707707 96145.9i 0.192350i
708708 −285294. 307520.i −0.569150 0.613489i
709709 −273533. −0.544148 −0.272074 0.962276i 0.587709π-0.587709\pi
−0.272074 + 0.962276i 0.587709π0.587709\pi
710710 504679.i 1.00115i
711711 28578.3 380589.i 0.0565324 0.752866i
712712 −191942. −0.378626
713713 123625.i 0.243179i
714714 22272.6 20662.9i 0.0436893 0.0405317i
715715 1.42909e6 2.79542
716716 426230.i 0.831416i
717717 −479339. 516682.i −0.932405 1.00504i
718718 465763. 0.903475
719719 886466.i 1.71476i −0.514681 0.857381i 0.672090π-0.672090\pi
0.514681 0.857381i 0.327910π-0.327910\pi
720720 −248095. 18629.3i −0.478578 0.0359362i
721721 −175907. −0.338386
722722 324156.i 0.621842i
723723 187132. 173607.i 0.357990 0.332117i
724724 −158318. −0.302032
725725 158224.i 0.301021i
726726 −9457.40 10194.2i −0.0179431 0.0193410i
727727 541251. 1.02407 0.512036 0.858964i 0.328892π-0.328892\pi
0.512036 + 0.858964i 0.328892π0.328892\pi
728728 101258.i 0.191058i
729729 −118489. + 518064.i −0.222957 + 0.974828i
730730 274609. 0.515311
731731 62909.1i 0.117728i
732732 261544. 242641.i 0.488115 0.452837i
733733 −698311. −1.29969 −0.649846 0.760066i 0.725167π-0.725167\pi
−0.649846 + 0.760066i 0.725167π0.725167\pi
734734 507768.i 0.942482i
735735 −100761. 108611.i −0.186518 0.201048i
736736 −52063.6 −0.0961122
737737 162810.i 0.299740i
738738 20932.9 278772.i 0.0384341 0.511843i
739739 −584503. −1.07028 −0.535140 0.844763i 0.679741π-0.679741\pi
−0.535140 + 0.844763i 0.679741π0.679741\pi
740740 813383.i 1.48536i
741741 199849. 185405.i 0.363970 0.337665i
742742 82088.2 0.149098
743743 1.06823e6i 1.93503i −0.252822 0.967513i 0.581359π-0.581359\pi
0.252822 0.967513i 0.418641π-0.418641\pi
744744 −59533.0 64170.9i −0.107550 0.115929i
745745 −325931. −0.587237
746746 438011.i 0.787059i
747747 −357085. 26813.4i −0.639928 0.0480519i
748748 63533.4 0.113553
749749 68084.0i 0.121362i
750750 −943344. + 875164.i −1.67706 + 1.55585i
751751 −526620. −0.933722 −0.466861 0.884331i 0.654615π-0.654615\pi
−0.466861 + 0.884331i 0.654615π0.654615\pi
752752 33699.4i 0.0595917i
753753 548787. + 591540.i 0.967862 + 1.04326i
754754 −64431.7 −0.113333
755755 406520.i 0.713162i
756756 −67324.3 84460.8i −0.117795 0.147779i
757757 −412218. −0.719342 −0.359671 0.933079i 0.617111π-0.617111\pi
−0.359671 + 0.933079i 0.617111π0.617111\pi
758758 683469.i 1.18954i
759759 −233860. + 216958.i −0.405950 + 0.376610i
760760 −136131. −0.235684
761761 51994.6i 0.0897819i 0.998992 + 0.0448909i 0.0142940π0.0142940\pi
−0.998992 + 0.0448909i 0.985706π0.985706\pi
762762 −336724. 362956.i −0.579914 0.625092i
763763 214783. 0.368936
764764 178794.i 0.306313i
765765 18758.1 249810.i 0.0320529 0.426862i
766766 −269331. −0.459017
767767 1.40774e6i 2.39294i
768768 27025.1 25071.9i 0.0458189 0.0425074i
769769 260902. 0.441189 0.220595 0.975366i 0.429200π-0.429200\pi
0.220595 + 0.975366i 0.429200π0.429200\pi
770770 309817.i 0.522545i
771771 −75516.0 81399.0i −0.127037 0.136934i
772772 445980. 0.748308
773773 323742.i 0.541801i −0.962607 0.270900i 0.912679π-0.912679\pi
0.962607 0.270900i 0.0873214π-0.0873214\pi
774774 223023. + 16746.7i 0.372279 + 0.0279543i
775775 −721375. −1.20104
776776 369756.i 0.614034i
777777 −258873. + 240163.i −0.428789 + 0.397799i
778778 634418. 1.04813
779779 152964.i 0.252066i
780780 567854. + 612093.i 0.933356 + 1.00607i
781781 −458181. −0.751164
782782 52423.6i 0.0857261i
783783 53743.5 42839.4i 0.0876602 0.0698746i
784784 21952.0 0.0357143
785785 654533.i 1.06217i
786786 278423. 258301.i 0.450672 0.418100i
787787 −642009. −1.03655 −0.518277 0.855213i 0.673426π-0.673426\pi
−0.518277 + 0.855213i 0.673426π0.673426\pi
788788 26458.7i 0.0426104i
789789 243642. + 262623.i 0.391380 + 0.421870i
790790 639604. 1.02484
791791 19898.2i 0.0318024i
792792 16912.9 225237.i 0.0269630 0.359078i
793793 −1.19727e6 −1.90391
794794 225355.i 0.357459i
795795 496214. 460351.i 0.785118 0.728374i
796796 −255698. −0.403554
797797 26635.0i 0.0419311i −0.999780 0.0209656i 0.993326π-0.993326\pi
0.999780 0.0209656i 0.00667404π-0.00667404\pi
798798 −40194.6 43325.9i −0.0631192 0.0680365i
799799 −33932.4 −0.0531521
800800 303801.i 0.474690i
801801 −685171. 51449.2i −1.06791 0.0801888i
802802 247499. 0.384790
803803 249308.i 0.386639i
804804 69732.8 64693.0i 0.107876 0.100079i
805805 −255640. −0.394492
806806 293757.i 0.452186i
807807 233883. + 252104.i 0.359131 + 0.387109i
808808 117468. 0.179927
809809 904872.i 1.38258i −0.722578 0.691290i 0.757043π-0.757043\pi
0.722578 0.691290i 0.242957π-0.242957\pi
810810 −880625. 133001.i −1.34221 0.202715i
811811 −528283. −0.803203 −0.401601 0.915815i 0.631546π-0.631546\pi
−0.401601 + 0.915815i 0.631546π0.631546\pi
812812 13968.3i 0.0211852i
813813 889908. 825590.i 1.34637 1.24906i
814814 −738442. −1.11447
815815 1.85460e6i 2.79213i
816816 25245.2 + 27211.9i 0.0379139 + 0.0408676i
817817 122374. 0.183335
818818 735842.i 1.09971i
819819 −27141.7 + 361458.i −0.0404641 + 0.538877i
820820 468494. 0.696748
821821 277365.i 0.411495i 0.978605 + 0.205748i 0.0659626π0.0659626\pi
−0.978605 + 0.205748i 0.934037π0.934037\pi
822822 −367632. + 341061.i −0.544088 + 0.504764i
823823 554443. 0.818572 0.409286 0.912406i 0.365778π-0.365778\pi
0.409286 + 0.912406i 0.365778π0.365778\pi
824824 214917.i 0.316531i
825825 −1.26599e6 1.36462e6i −1.86004 2.00495i
826826 305189. 0.447310
827827 844426.i 1.23467i 0.786701 + 0.617335i 0.211787π0.211787\pi
−0.786701 + 0.617335i 0.788213π0.788213\pi
828828 −185850. 13955.4i −0.271083 0.0203555i
829829 74784.2 0.108818 0.0544090 0.998519i 0.482673π-0.482673\pi
0.0544090 + 0.998519i 0.482673π0.482673\pi
830830 600104.i 0.871104i
831831 889422. 825140.i 1.28797 1.19488i
832832 −123713. −0.178719
833833 22103.8i 0.0318549i
834834 384803. + 414781.i 0.553231 + 0.596330i
835835 1.63091e6 2.33915
836836 123589.i 0.176834i
837837 −195313. 245027.i −0.278792 0.349755i
838838 628933. 0.895605
839839 463620.i 0.658625i −0.944221 0.329313i 0.893183π-0.893183\pi
0.944221 0.329313i 0.106817π-0.106817\pi
840840 132698. 123107.i 0.188063 0.174471i
841841 698393. 0.987433
842842 777136.i 1.09616i
843843 −20128.7 21696.8i −0.0283243 0.0305309i
844844 −70564.6 −0.0990609
845845 1.43127e6i 2.00451i
846846 −9032.97 + 120296.i −0.0126209 + 0.168078i
847847 10116.9 0.0141020
848848 100293.i 0.139469i
849849 −852889. + 791247.i −1.18325 + 1.09773i
850850 305902. 0.423394
851851 609314.i 0.841360i
852852 −182060. 196243.i −0.250804 0.270343i
853853 301646. 0.414572 0.207286 0.978280i 0.433537π-0.433537\pi
0.207286 + 0.978280i 0.433537π0.433537\pi
854854 259561.i 0.355896i
855855 −485944. 36489.3i −0.664743 0.0499153i
856856 −83182.7 −0.113523
857857 656980.i 0.894520i −0.894404 0.447260i 0.852400π-0.852400\pi
0.894404 0.447260i 0.147600π-0.147600\pi
858858 −555697. + 515535.i −0.754855 + 0.700299i
859859 −104640. −0.141812 −0.0709060 0.997483i 0.522589π-0.522589\pi
−0.0709060 + 0.997483i 0.522589π0.522589\pi
860860 374805.i 0.506767i
861861 138329. + 149106.i 0.186598 + 0.201135i
862862 −224122. −0.301627
863863 1.12056e6i 1.50457i 0.658839 + 0.752284i 0.271048π0.271048\pi
−0.658839 + 0.752284i 0.728952π0.728952\pi
864864 103191. 82254.6i 0.138234 0.110188i
865865 586695. 0.784115
866866 159398.i 0.212543i
867867 523665. 485818.i 0.696651 0.646301i
868868 63684.4 0.0845267
869869 580674.i 0.768941i
870870 78334.5 + 84437.2i 0.103494 + 0.111557i
871871 −319217. −0.420775
872872 262415.i 0.345108i
873873 −99111.6 + 1.31991e6i −0.130046 + 1.73187i
874874 −101977. −0.133500
875875 936192.i 1.22278i
876876 −106781. + 99063.6i −0.139151 + 0.129094i
877877 −20694.4 −0.0269062 −0.0134531 0.999910i 0.504282π-0.504282\pi
−0.0134531 + 0.999910i 0.504282π0.504282\pi
878878 235027.i 0.304879i
879879 −1.03078e6 1.11108e6i −1.33410 1.43803i
880880 378524. 0.488796
881881 711224.i 0.916336i −0.888866 0.458168i 0.848506π-0.848506\pi
0.888866 0.458168i 0.151494π-0.151494\pi
882882 78361.6 + 5884.14i 0.100732 + 0.00756390i
883883 260420. 0.334004 0.167002 0.985957i 0.446591π-0.446591\pi
0.167002 + 0.985957i 0.446591π0.446591\pi
884884 124569.i 0.159406i
885885 1.84483e6 1.71150e6i 2.35543 2.18519i
886886 −395744. −0.504135
887887 649369.i 0.825362i 0.910876 + 0.412681i 0.135408π0.135408\pi
−0.910876 + 0.412681i 0.864592π0.864592\pi
888888 −293423. 316282.i −0.372107 0.401096i
889889 360204. 0.455770
890890 1.15147e6i 1.45370i
891891 120747. 799488.i 0.152098 1.00706i
892892 416886. 0.523948
893893 66007.1i 0.0827728i
894894 126737. 117577.i 0.158573 0.147112i
895895 −2.55698e6 −3.19214
896896 26820.2i 0.0334077i
897897 425385. + 458525.i 0.528685 + 0.569873i
898898 −283602. −0.351688
899899 40523.2i 0.0501401i
900900 81432.6 1.08447e6i 0.100534 1.33886i
901901 −100986. −0.124397
902902 425329.i 0.522771i
903903 −119288. + 110666.i −0.146292 + 0.135719i
904904 −24310.9 −0.0297484
905905 949759.i 1.15962i
906906 −146650. 158074.i −0.178659 0.192577i
907907 1.11128e6 1.35086 0.675429 0.737425i 0.263958π-0.263958\pi
0.675429 + 0.737425i 0.263958π0.263958\pi
908908 483017.i 0.585856i
909909 419322. + 31486.7i 0.507481 + 0.0381066i
910910 −607452. −0.733549
911911 125363.i 0.151054i 0.997144 + 0.0755272i 0.0240640π0.0240640\pi
−0.997144 + 0.0755272i 0.975936π0.975936\pi
912912 52934.1 49108.4i 0.0636424 0.0590426i
913913 544813. 0.653591
914914 234735.i 0.280986i
915915 1.45562e6 + 1.56902e6i 1.73862 + 1.87407i
916916 −24283.8 −0.0289418
917917 276313.i 0.328596i
918918 82823.3 + 103905.i 0.0982804 + 0.123296i
919919 748471. 0.886225 0.443113 0.896466i 0.353874π-0.353874\pi
0.443113 + 0.896466i 0.353874π0.353874\pi
920920 312333.i 0.369013i
921921 −292907. + 271738.i −0.345311 + 0.320354i
922922 910000. 1.07048
923923 898345.i 1.05448i
924924 111764. + 120471.i 0.130906 + 0.141104i
925925 −3.55547e6 −4.15540
926926 290973.i 0.339336i
927927 57607.6 767185.i 0.0670379 0.892773i
928928 −17066.0 −0.0198170
929929 132284.i 0.153276i −0.997059 0.0766381i 0.975581π-0.975581\pi
0.997059 0.0766381i 0.0244186π-0.0244186\pi
930930 384966. 357142.i 0.445098 0.412929i
931931 42997.5 0.0496071
932932 276756.i 0.318614i
933933 898109. + 968076.i 1.03173 + 1.11211i
934934 246700. 0.282797
935935 381141.i 0.435976i
936936 −441617. 33160.8i −0.504073 0.0378507i
937937 318721. 0.363020 0.181510 0.983389i 0.441901π-0.441901\pi
0.181510 + 0.983389i 0.441901π0.441901\pi
938938 69204.2i 0.0786550i
939939 −357971. + 332099.i −0.405991 + 0.376649i
940940 −202165. −0.228797
941941 897526.i 1.01360i −0.862063 0.506802i 0.830828π-0.830828\pi
0.862063 0.506802i 0.169172π-0.169172\pi
942942 −236118. 254513.i −0.266090 0.286819i
943943 350953. 0.394663
944944 372869.i 0.418420i
945945 506686. 403883.i 0.567381 0.452264i
946946 −340272. −0.380228
947947 416790.i 0.464748i 0.972626 + 0.232374i 0.0746494π0.0746494\pi
−0.972626 + 0.232374i 0.925351π0.925351\pi
948948 −248708. + 230733.i −0.276741 + 0.256740i
949949 488814. 0.542764
950950 595057.i 0.659343i
951951 797879. + 860037.i 0.882218 + 0.950947i
952952 −27005.6 −0.0297975
953953 1.57654e6i 1.73587i −0.496676 0.867936i 0.665446π-0.665446\pi
0.496676 0.867936i 0.334554π-0.334554\pi
954954 −26883.0 + 358012.i −0.0295380 + 0.393370i
955955 1.07259e6 1.17606
956956 626479.i 0.685473i
957957 −76657.6 + 71117.2i −0.0837011 + 0.0776517i
958958 −371652. −0.404954
959959 364844.i 0.396707i
960960 150408. + 162125.i 0.163203 + 0.175917i
961961 −738768. −0.799947
962962 1.44785e6i 1.56449i
963963 −296935. 22296.8i −0.320191 0.0240430i
964964 −226898. −0.244161
965965 2.67546e6i 2.87305i
966966 99405.0 92220.6i 0.106526 0.0988266i
967967 −449565. −0.480772 −0.240386 0.970677i 0.577274π-0.577274\pi
−0.240386 + 0.970677i 0.577274π0.577274\pi
968968 12360.5i 0.0131912i
969969 49447.9 + 53300.1i 0.0526624 + 0.0567650i
970970 −2.21819e6 −2.35752
971971 397697.i 0.421807i −0.977507 0.210904i 0.932359π-0.932359\pi
0.977507 0.210904i 0.0676407π-0.0676407\pi
972972 390408. 265962.i 0.413224 0.281506i
973973 −411636. −0.434799
974974 327596.i 0.345319i
975975 −2.67558e6 + 2.48221e6i −2.81455 + 2.61113i
976976 −317122. −0.332910
977977 1.19821e6i 1.25529i 0.778499 + 0.627646i 0.215982π0.215982\pi
−0.778499 + 0.627646i 0.784018π0.784018\pi
978978 −669036. 721158.i −0.699475 0.753967i
979979 1.04538e6 1.09071
980980 131691.i 0.137121i
981981 −70339.1 + 936736.i −0.0730901 + 0.973372i
982982 −1.28842e6 −1.33609
983983 1.59614e6i 1.65183i −0.563798 0.825913i 0.690660π-0.690660\pi
0.563798 0.825913i 0.309340π-0.309340\pi
984984 −182172. + 169006.i −0.188145 + 0.174547i
985985 −158727. −0.163598
986986 17184.0i 0.0176755i
987987 −59691.9 64342.2i −0.0612747 0.0660483i
988988 −242318. −0.248240
989989 280770.i 0.287050i
990990 1.35121e6 + 101462.i 1.37864 + 0.103522i
991991 1.43265e6 1.45879 0.729396 0.684092i 0.239801π-0.239801\pi
0.729396 + 0.684092i 0.239801π0.239801\pi
992992 77807.4i 0.0790675i
993993 −231139. + 214433.i −0.234409 + 0.217467i
994994 194755. 0.197113
995995 1.53395e6i 1.54940i
996996 216483. + 233349.i 0.218226 + 0.235227i
997997 −397969. −0.400368 −0.200184 0.979758i 0.564154π-0.564154\pi
−0.200184 + 0.979758i 0.564154π0.564154\pi
998998 1.00051e6i 1.00452i
999999 −962646. 1.20767e6i −0.964575 1.21009i
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 42.5.b.a.29.7 yes 8
3.2 odd 2 inner 42.5.b.a.29.3 8
4.3 odd 2 336.5.d.a.113.4 8
7.6 odd 2 294.5.b.d.197.6 8
12.11 even 2 336.5.d.a.113.3 8
21.20 even 2 294.5.b.d.197.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.5.b.a.29.3 8 3.2 odd 2 inner
42.5.b.a.29.7 yes 8 1.1 even 1 trivial
294.5.b.d.197.2 8 21.20 even 2
294.5.b.d.197.6 8 7.6 odd 2
336.5.d.a.113.3 8 12.11 even 2
336.5.d.a.113.4 8 4.3 odd 2