Properties

Label 115.5.f.a.47.11
Level 115115
Weight 55
Character 115.47
Analytic conductor 11.88811.888
Analytic rank 00
Dimension 8888
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [115,5,Mod(47,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.47"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Level: N N == 115=523 115 = 5 \cdot 23
Weight: k k == 5 5
Character orbit: [χ][\chi] == 115.f (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.887545754611.8875457546
Analytic rank: 00
Dimension: 8888
Relative dimension: 4444 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 47.11
Character χ\chi == 115.47
Dual form 115.5.f.a.93.11

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(3.552533.55253i)q2+(5.80472+5.80472i)q3+9.24088iq4+(21.450412.8406i)q5+41.2428q6+(2.81474+2.81474i)q7+(24.0119+24.0119i)q8+13.6105iq9+(30.5864+121.820i)q10184.488q11+(53.640753.6407i)q12+(37.0012+37.0012i)q1319.9989iq14+(199.05049.9772i)q15+318.460q16+(250.449+250.449i)q17+(48.351648.3516i)q18597.288iq19+(118.659198.220i)q2032.6775q21+(655.399+655.399i)q22+(77.996877.9968i)q23278.765iq24+(295.237+550.872i)q25+262.895q26+(549.187549.187i)q27+(26.0107+26.0107i)q28947.586iq29+(884.674529.584i)q30+1231.51q31+(747.147747.147i)q32+(1070.901070.90i)q331779.46iq34+(24.234296.5202i)q35125.773q36+(636.569+636.569i)q37+(2121.88+2121.88i)q38429.563iq39+(823.393206.737i)q401338.23q41+(116.088+116.088i)q42+(1237.701237.70i)q431704.83iq44+(174.767291.950i)q45554.171q46+(2390.39+2390.39i)q47+(1848.57+1848.57i)q482385.15iq49+(908.1513005.82i)q502907.58q51+(341.924341.924i)q52+(1149.05+1149.05i)q53+3902.00iq54+(3957.34+2368.94i)q55135.175q56+(3467.09+3467.09i)q57+(3366.32+3366.32i)q58+6455.33iq59+(461.833+1839.39i)q602543.50q61+(4374.964374.96i)q62+(38.3099+38.3099i)q63+213.155iq64+(1268.81318.571i)q657608.81q66+(4108.36+4108.36i)q67+(2314.37+2314.37i)q68+905.499iq69+(256.798+428.983i)q70+7900.01q71+(326.814326.814i)q72+(2910.79+2910.79i)q734522.86iq74+(4911.431483.89i)q75+5519.46q76+(519.286519.286i)q77+(1526.03+1526.03i)q785119.73iq79+(6831.094089.23i)q80+5273.31q81+(4754.09+4754.09i)q82+(1562.28+1562.28i)q83301.969iq84+(2156.318588.16i)q858793.93q86+(5500.47+5500.47i)q87+(4429.924429.92i)q888134.38iq89+(1658.02+416.295i)q90208.297q91+(720.759+720.759i)q92+(7148.55+7148.55i)q9316983.8iq94+(7669.55+12812.0i)q95+8673.96q96+(4131.07+4131.07i)q97+(8473.32+8473.32i)q982510.97iq99+O(q100)q+(-3.55253 - 3.55253i) q^{2} +(-5.80472 + 5.80472i) q^{3} +9.24088i q^{4} +(-21.4504 - 12.8406i) q^{5} +41.2428 q^{6} +(2.81474 + 2.81474i) q^{7} +(-24.0119 + 24.0119i) q^{8} +13.6105i q^{9} +(30.5864 + 121.820i) q^{10} -184.488 q^{11} +(-53.6407 - 53.6407i) q^{12} +(-37.0012 + 37.0012i) q^{13} -19.9989i q^{14} +(199.050 - 49.9772i) q^{15} +318.460 q^{16} +(250.449 + 250.449i) q^{17} +(48.3516 - 48.3516i) q^{18} -597.288i q^{19} +(118.659 - 198.220i) q^{20} -32.6775 q^{21} +(655.399 + 655.399i) q^{22} +(77.9968 - 77.9968i) q^{23} -278.765i q^{24} +(295.237 + 550.872i) q^{25} +262.895 q^{26} +(-549.187 - 549.187i) q^{27} +(-26.0107 + 26.0107i) q^{28} -947.586i q^{29} +(-884.674 - 529.584i) q^{30} +1231.51 q^{31} +(-747.147 - 747.147i) q^{32} +(1070.90 - 1070.90i) q^{33} -1779.46i q^{34} +(-24.2342 - 96.5202i) q^{35} -125.773 q^{36} +(636.569 + 636.569i) q^{37} +(-2121.88 + 2121.88i) q^{38} -429.563i q^{39} +(823.393 - 206.737i) q^{40} -1338.23 q^{41} +(116.088 + 116.088i) q^{42} +(1237.70 - 1237.70i) q^{43} -1704.83i q^{44} +(174.767 - 291.950i) q^{45} -554.171 q^{46} +(2390.39 + 2390.39i) q^{47} +(-1848.57 + 1848.57i) q^{48} -2385.15i q^{49} +(908.151 - 3005.82i) q^{50} -2907.58 q^{51} +(-341.924 - 341.924i) q^{52} +(-1149.05 + 1149.05i) q^{53} +3902.00i q^{54} +(3957.34 + 2368.94i) q^{55} -135.175 q^{56} +(3467.09 + 3467.09i) q^{57} +(-3366.32 + 3366.32i) q^{58} +6455.33i q^{59} +(461.833 + 1839.39i) q^{60} -2543.50 q^{61} +(-4374.96 - 4374.96i) q^{62} +(-38.3099 + 38.3099i) q^{63} +213.155i q^{64} +(1268.81 - 318.571i) q^{65} -7608.81 q^{66} +(4108.36 + 4108.36i) q^{67} +(-2314.37 + 2314.37i) q^{68} +905.499i q^{69} +(-256.798 + 428.983i) q^{70} +7900.01 q^{71} +(-326.814 - 326.814i) q^{72} +(-2910.79 + 2910.79i) q^{73} -4522.86i q^{74} +(-4911.43 - 1483.89i) q^{75} +5519.46 q^{76} +(-519.286 - 519.286i) q^{77} +(-1526.03 + 1526.03i) q^{78} -5119.73i q^{79} +(-6831.09 - 4089.23i) q^{80} +5273.31 q^{81} +(4754.09 + 4754.09i) q^{82} +(-1562.28 + 1562.28i) q^{83} -301.969i q^{84} +(-2156.31 - 8588.16i) q^{85} -8793.93 q^{86} +(5500.47 + 5500.47i) q^{87} +(4429.92 - 4429.92i) q^{88} -8134.38i q^{89} +(-1658.02 + 416.295i) q^{90} -208.297 q^{91} +(720.759 + 720.759i) q^{92} +(-7148.55 + 7148.55i) q^{93} -16983.8i q^{94} +(-7669.55 + 12812.0i) q^{95} +8673.96 q^{96} +(4131.07 + 4131.07i) q^{97} +(-8473.32 + 8473.32i) q^{98} -2510.97i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 88q48q5+160q7+180q8+16q10+312q11720q12760q1360q154528q16+420q17+980q18+1344q20+1976q21+720q221176q25+1872q26+22320q98+O(q100) 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/115Z)×\left(\mathbb{Z}/115\mathbb{Z}\right)^\times.

nn 4747 5151
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −3.55253 3.55253i −0.888131 0.888131i 0.106212 0.994344i 0.466128π-0.466128\pi
−0.994344 + 0.106212i 0.966128π0.966128\pi
33 −5.80472 + 5.80472i −0.644969 + 0.644969i −0.951773 0.306804i 0.900740π-0.900740\pi
0.306804 + 0.951773i 0.400740π0.400740\pi
44 9.24088i 0.577555i
55 −21.4504 12.8406i −0.858015 0.513625i
66 41.2428 1.14563
77 2.81474 + 2.81474i 0.0574436 + 0.0574436i 0.735245 0.677801i 0.237067π-0.237067\pi
−0.677801 + 0.735245i 0.737067π0.737067\pi
88 −24.0119 + 24.0119i −0.375187 + 0.375187i
99 13.6105i 0.168031i
1010 30.5864 + 121.820i 0.305864 + 1.21820i
1111 −184.488 −1.52470 −0.762348 0.647168i 0.775953π-0.775953\pi
−0.762348 + 0.647168i 0.775953π0.775953\pi
1212 −53.6407 53.6407i −0.372505 0.372505i
1313 −37.0012 + 37.0012i −0.218942 + 0.218942i −0.808053 0.589110i 0.799478π-0.799478\pi
0.589110 + 0.808053i 0.299478π0.299478\pi
1414 19.9989i 0.102035i
1515 199.050 49.9772i 0.884665 0.222121i
1616 318.460 1.24399
1717 250.449 + 250.449i 0.866607 + 0.866607i 0.992095 0.125488i 0.0400496π-0.0400496\pi
−0.125488 + 0.992095i 0.540050π0.540050\pi
1818 48.3516 48.3516i 0.149233 0.149233i
1919 597.288i 1.65454i −0.561807 0.827268i 0.689894π-0.689894\pi
0.561807 0.827268i 0.310106π-0.310106\pi
2020 118.659 198.220i 0.296647 0.495551i
2121 −32.6775 −0.0740987
2222 655.399 + 655.399i 1.35413 + 1.35413i
2323 77.9968 77.9968i 0.147442 0.147442i
2424 278.765i 0.483967i
2525 295.237 + 550.872i 0.472379 + 0.881395i
2626 262.895 0.388899
2727 −549.187 549.187i −0.753343 0.753343i
2828 −26.0107 + 26.0107i −0.0331769 + 0.0331769i
2929 947.586i 1.12674i −0.826206 0.563368i 0.809505π-0.809505\pi
0.826206 0.563368i 0.190495π-0.190495\pi
3030 −884.674 529.584i −0.982971 0.588426i
3131 1231.51 1.28148 0.640742 0.767756i 0.278627π-0.278627\pi
0.640742 + 0.767756i 0.278627π0.278627\pi
3232 −747.147 747.147i −0.729636 0.729636i
3333 1070.90 1070.90i 0.983381 0.983381i
3434 1779.46i 1.53932i
3535 −24.2342 96.5202i −0.0197830 0.0787920i
3636 −125.773 −0.0970469
3737 636.569 + 636.569i 0.464988 + 0.464988i 0.900286 0.435298i 0.143357π-0.143357\pi
−0.435298 + 0.900286i 0.643357π0.643357\pi
3838 −2121.88 + 2121.88i −1.46945 + 1.46945i
3939 429.563i 0.282422i
4040 823.393 206.737i 0.514621 0.129211i
4141 −1338.23 −0.796090 −0.398045 0.917366i 0.630311π-0.630311\pi
−0.398045 + 0.917366i 0.630311π0.630311\pi
4242 116.088 + 116.088i 0.0658094 + 0.0658094i
4343 1237.70 1237.70i 0.669390 0.669390i −0.288185 0.957575i 0.593052π-0.593052\pi
0.957575 + 0.288185i 0.0930518π0.0930518\pi
4444 1704.83i 0.880596i
4545 174.767 291.950i 0.0863047 0.144173i
4646 −554.171 −0.261896
4747 2390.39 + 2390.39i 1.08211 + 1.08211i 0.996312 + 0.0858006i 0.0273448π0.0273448\pi
0.0858006 + 0.996312i 0.472655π0.472655\pi
4848 −1848.57 + 1848.57i −0.802332 + 0.802332i
4949 2385.15i 0.993400i
5050 908.151 3005.82i 0.363260 1.20233i
5151 −2907.58 −1.11787
5252 −341.924 341.924i −0.126451 0.126451i
5353 −1149.05 + 1149.05i −0.409060 + 0.409060i −0.881411 0.472351i 0.843406π-0.843406\pi
0.472351 + 0.881411i 0.343406π0.343406\pi
5454 3902.00i 1.33814i
5555 3957.34 + 2368.94i 1.30821 + 0.783121i
5656 −135.175 −0.0431042
5757 3467.09 + 3467.09i 1.06712 + 1.06712i
5858 −3366.32 + 3366.32i −1.00069 + 1.00069i
5959 6455.33i 1.85445i 0.374509 + 0.927223i 0.377811π0.377811\pi
−0.374509 + 0.927223i 0.622189π0.622189\pi
6060 461.833 + 1839.39i 0.128287 + 0.510943i
6161 −2543.50 −0.683553 −0.341777 0.939781i 0.611029π-0.611029\pi
−0.341777 + 0.939781i 0.611029π0.611029\pi
6262 −4374.96 4374.96i −1.13813 1.13813i
6363 −38.3099 + 38.3099i −0.00965229 + 0.00965229i
6464 213.155i 0.0520398i
6565 1268.81 318.571i 0.300310 0.0754015i
6666 −7608.81 −1.74674
6767 4108.36 + 4108.36i 0.915207 + 0.915207i 0.996676 0.0814689i 0.0259611π-0.0259611\pi
−0.0814689 + 0.996676i 0.525961π0.525961\pi
6868 −2314.37 + 2314.37i −0.500513 + 0.500513i
6969 905.499i 0.190191i
7070 −256.798 + 428.983i −0.0524077 + 0.0875475i
7171 7900.01 1.56715 0.783576 0.621296i 0.213393π-0.213393\pi
0.783576 + 0.621296i 0.213393π0.213393\pi
7272 −326.814 326.814i −0.0630428 0.0630428i
7373 −2910.79 + 2910.79i −0.546218 + 0.546218i −0.925345 0.379127i 0.876224π-0.876224\pi
0.379127 + 0.925345i 0.376224π0.376224\pi
7474 4522.86i 0.825942i
7575 −4911.43 1483.89i −0.873142 0.263803i
7676 5519.46 0.955586
7777 −519.286 519.286i −0.0875840 0.0875840i
7878 −1526.03 + 1526.03i −0.250827 + 0.250827i
7979 5119.73i 0.820338i −0.912010 0.410169i 0.865470π-0.865470\pi
0.912010 0.410169i 0.134530π-0.134530\pi
8080 −6831.09 4089.23i −1.06736 0.638942i
8181 5273.31 0.803735
8282 4754.09 + 4754.09i 0.707033 + 0.707033i
8383 −1562.28 + 1562.28i −0.226779 + 0.226779i −0.811346 0.584566i 0.801265π-0.801265\pi
0.584566 + 0.811346i 0.301265π0.301265\pi
8484 301.969i 0.0427961i
8585 −2156.31 8588.16i −0.298451 1.18867i
8686 −8793.93 −1.18901
8787 5500.47 + 5500.47i 0.726710 + 0.726710i
8888 4429.92 4429.92i 0.572045 0.572045i
8989 8134.38i 1.02694i −0.858108 0.513469i 0.828360π-0.828360\pi
0.858108 0.513469i 0.171640π-0.171640\pi
9090 −1658.02 + 416.295i −0.204694 + 0.0513944i
9191 −208.297 −0.0251536
9292 720.759 + 720.759i 0.0851558 + 0.0851558i
9393 −7148.55 + 7148.55i −0.826517 + 0.826517i
9494 16983.8i 1.92212i
9595 −7669.55 + 12812.0i −0.849811 + 1.41962i
9696 8673.96 0.941185
9797 4131.07 + 4131.07i 0.439055 + 0.439055i 0.891694 0.452639i 0.149517π-0.149517\pi
−0.452639 + 0.891694i 0.649517π0.649517\pi
9898 −8473.32 + 8473.32i −0.882270 + 0.882270i
9999 2510.97i 0.256195i
100100 −5090.54 + 2728.25i −0.509054 + 0.272825i
101101 −4631.78 −0.454052 −0.227026 0.973889i 0.572900π-0.572900\pi
−0.227026 + 0.973889i 0.572900π0.572900\pi
102102 10329.2 + 10329.2i 0.992815 + 0.992815i
103103 3386.02 3386.02i 0.319165 0.319165i −0.529281 0.848446i 0.677538π-0.677538\pi
0.848446 + 0.529281i 0.177538π0.177538\pi
104104 1776.94i 0.164288i
105105 700.945 + 419.600i 0.0635778 + 0.0380589i
106106 8164.06 0.726598
107107 −14295.8 14295.8i −1.24865 1.24865i −0.956317 0.292332i 0.905569π-0.905569\pi
−0.292332 0.956317i 0.594431π-0.594431\pi
108108 5074.97 5074.97i 0.435097 0.435097i
109109 11279.1i 0.949335i 0.880165 + 0.474668i 0.157432π0.157432\pi
−0.880165 + 0.474668i 0.842568π0.842568\pi
110110 −5642.82 22474.3i −0.466349 1.85738i
111111 −7390.21 −0.599806
112112 896.382 + 896.382i 0.0714590 + 0.0714590i
113113 4876.21 4876.21i 0.381878 0.381878i −0.489900 0.871779i 0.662967π-0.662967\pi
0.871779 + 0.489900i 0.162967π0.162967\pi
114114 24633.8i 1.89549i
115115 −2674.59 + 671.533i −0.202237 + 0.0507775i
116116 8756.53 0.650753
117117 −503.604 503.604i −0.0367890 0.0367890i
118118 22932.7 22932.7i 1.64699 1.64699i
119119 1409.90i 0.0995621i
120120 −3579.52 + 5979.62i −0.248578 + 0.415251i
121121 19394.9 1.32470
122122 9035.86 + 9035.86i 0.607085 + 0.607085i
123123 7768.04 7768.04i 0.513453 0.513453i
124124 11380.2i 0.740128i
125125 740.599 15607.4i 0.0473983 0.998876i
126126 272.194 0.0171450
127127 17482.6 + 17482.6i 1.08392 + 1.08392i 0.996140 + 0.0877818i 0.0279778π0.0279778\pi
0.0877818 + 0.996140i 0.472022π0.472022\pi
128128 −11197.1 + 11197.1i −0.683418 + 0.683418i
129129 14369.0i 0.863471i
130130 −5639.21 3375.74i −0.333681 0.199748i
131131 21656.5 1.26196 0.630981 0.775798i 0.282653π-0.282653\pi
0.630981 + 0.775798i 0.282653π0.282653\pi
132132 9896.08 + 9896.08i 0.567957 + 0.567957i
133133 1681.21 1681.21i 0.0950426 0.0950426i
134134 29190.1i 1.62565i
135135 4728.37 + 18832.2i 0.259444 + 1.03332i
136136 −12027.6 −0.650279
137137 −11090.1 11090.1i −0.590872 0.590872i 0.346995 0.937867i 0.387202π-0.387202\pi
−0.937867 + 0.346995i 0.887202π0.887202\pi
138138 3216.81 3216.81i 0.168915 0.168915i
139139 9088.05i 0.470371i 0.971950 + 0.235186i 0.0755698π0.0755698\pi
−0.971950 + 0.235186i 0.924430π0.924430\pi
140140 891.931 223.945i 0.0455067 0.0114258i
141141 −27751.1 −1.39586
142142 −28065.0 28065.0i −1.39184 1.39184i
143143 6826.28 6826.28i 0.333820 0.333820i
144144 4334.40i 0.209028i
145145 −12167.6 + 20326.1i −0.578720 + 0.966757i
146146 20681.3 0.970226
147147 13845.2 + 13845.2i 0.640712 + 0.640712i
148148 −5882.46 + 5882.46i −0.268556 + 0.268556i
149149 15283.6i 0.688420i 0.938893 + 0.344210i 0.111853π0.111853\pi
−0.938893 + 0.344210i 0.888147π0.888147\pi
150150 12176.4 + 22719.5i 0.541174 + 1.00976i
151151 17214.9 0.755006 0.377503 0.926008i 0.376783π-0.376783\pi
0.377503 + 0.926008i 0.376783π0.376783\pi
152152 14342.0 + 14342.0i 0.620760 + 0.620760i
153153 −3408.74 + 3408.74i −0.145617 + 0.145617i
154154 3689.55i 0.155572i
155155 −26416.3 15813.3i −1.09953 0.658202i
156156 3969.54 0.163114
157157 2011.48 + 2011.48i 0.0816051 + 0.0816051i 0.746731 0.665126i 0.231622π-0.231622\pi
−0.665126 + 0.746731i 0.731622π0.731622\pi
158158 −18188.0 + 18188.0i −0.728568 + 0.728568i
159159 13339.8i 0.527662i
160160 6432.75 + 25620.4i 0.251279 + 1.00080i
161161 439.081 0.0169392
162162 −18733.6 18733.6i −0.713822 0.713822i
163163 11789.4 11789.4i 0.443727 0.443727i −0.449535 0.893263i 0.648410π-0.648410\pi
0.893263 + 0.449535i 0.148410π0.148410\pi
164164 12366.4i 0.459786i
165165 −36722.3 + 9220.20i −1.34884 + 0.338667i
166166 11100.1 0.402820
167167 5270.11 + 5270.11i 0.188967 + 0.188967i 0.795250 0.606282i 0.207340π-0.207340\pi
−0.606282 + 0.795250i 0.707340π0.707340\pi
168168 784.651 784.651i 0.0278008 0.0278008i
169169 25822.8i 0.904129i
170170 −22849.3 + 38170.0i −0.790634 + 1.32076i
171171 8129.37 0.278013
172172 11437.5 + 11437.5i 0.386609 + 0.386609i
173173 36577.3 36577.3i 1.22214 1.22214i 0.255264 0.966871i 0.417838π-0.417838\pi
0.966871 0.255264i 0.0821624π-0.0821624\pi
174174 39081.1i 1.29083i
175175 −719.546 + 2381.58i −0.0234954 + 0.0777657i
176176 −58752.1 −1.89670
177177 −37471.4 37471.4i −1.19606 1.19606i
178178 −28897.6 + 28897.6i −0.912056 + 0.912056i
179179 20451.5i 0.638292i −0.947706 0.319146i 0.896604π-0.896604\pi
0.947706 0.319146i 0.103396π-0.103396\pi
180180 2697.87 + 1615.00i 0.0832677 + 0.0498457i
181181 1374.32 0.0419497 0.0209749 0.999780i 0.493323π-0.493323\pi
0.0209749 + 0.999780i 0.493323π0.493323\pi
182182 739.982 + 739.982i 0.0223397 + 0.0223397i
183183 14764.3 14764.3i 0.440871 0.440871i
184184 3745.71i 0.110637i
185185 −5480.70 21828.6i −0.160137 0.637797i
186186 50790.8 1.46811
187187 −46205.0 46205.0i −1.32131 1.32131i
188188 −22089.3 + 22089.3i −0.624980 + 0.624980i
189189 3091.64i 0.0865495i
190190 72761.4 18268.9i 2.01555 0.506063i
191191 24341.8 0.667247 0.333624 0.942706i 0.391729π-0.391729\pi
0.333624 + 0.942706i 0.391729π0.391729\pi
192192 −1237.30 1237.30i −0.0335640 0.0335640i
193193 −26283.8 + 26283.8i −0.705624 + 0.705624i −0.965612 0.259988i 0.916282π-0.916282\pi
0.259988 + 0.965612i 0.416282π0.416282\pi
194194 29351.5i 0.779877i
195195 −5515.86 + 9214.29i −0.145059 + 0.242322i
196196 22040.9 0.573743
197197 −19169.8 19169.8i −0.493952 0.493952i 0.415597 0.909549i 0.363573π-0.363573\pi
−0.909549 + 0.415597i 0.863573π0.863573\pi
198198 −8920.29 + 8920.29i −0.227535 + 0.227535i
199199 54177.6i 1.36809i −0.729441 0.684043i 0.760220π-0.760220\pi
0.729441 0.684043i 0.239780π-0.239780\pi
200200 −20316.7 6138.30i −0.507918 0.153457i
201201 −47695.8 −1.18056
202202 16454.5 + 16454.5i 0.403258 + 0.403258i
203203 2667.21 2667.21i 0.0647239 0.0647239i
204204 26868.6i 0.645631i
205205 28705.5 + 17183.7i 0.683057 + 0.408892i
206206 −24057.9 −0.566921
207207 1061.57 + 1061.57i 0.0247748 + 0.0247748i
208208 −11783.4 + 11783.4i −0.272361 + 0.272361i
209209 110193.i 2.52266i
210210 −999.487 3980.76i −0.0226641 0.0902668i
211211 73142.2 1.64287 0.821435 0.570302i 0.193174π-0.193174\pi
0.821435 + 0.570302i 0.193174π0.193174\pi
212212 −10618.2 10618.2i −0.236255 0.236255i
213213 −45857.4 + 45857.4i −1.01076 + 1.01076i
214214 101572.i 2.21793i
215215 −42442.0 + 10656.3i −0.918162 + 0.230531i
216216 26374.1 0.565289
217217 3466.37 + 3466.37i 0.0736131 + 0.0736131i
218218 40069.1 40069.1i 0.843135 0.843135i
219219 33792.7i 0.704586i
220220 −21891.1 + 36569.3i −0.452296 + 0.755564i
221221 −18533.9 −0.379473
222222 26253.9 + 26253.9i 0.532707 + 0.532707i
223223 −3617.58 + 3617.58i −0.0727458 + 0.0727458i −0.742544 0.669798i 0.766381π-0.766381\pi
0.669798 + 0.742544i 0.266381π0.266381\pi
224224 4206.05i 0.0838259i
225225 −7497.63 + 4018.32i −0.148101 + 0.0793741i
226226 −34645.7 −0.678316
227227 20111.1 + 20111.1i 0.390287 + 0.390287i 0.874790 0.484502i 0.160999π-0.160999\pi
−0.484502 + 0.874790i 0.660999π0.660999\pi
228228 −32038.9 + 32038.9i −0.616323 + 0.616323i
229229 22418.6i 0.427501i 0.976888 + 0.213751i 0.0685680π0.0685680\pi
−0.976888 + 0.213751i 0.931432π0.931432\pi
230230 11887.2 + 7115.90i 0.224710 + 0.134516i
231231 6028.62 0.112978
232232 22753.4 + 22753.4i 0.422737 + 0.422737i
233233 31110.1 31110.1i 0.573046 0.573046i −0.359933 0.932978i 0.617200π-0.617200\pi
0.932978 + 0.359933i 0.117200π0.117200\pi
234234 3578.13i 0.0653469i
235235 −20580.6 81968.8i −0.372669 1.48427i
236236 −59652.9 −1.07104
237237 29718.6 + 29718.6i 0.529092 + 0.529092i
238238 5008.70 5008.70i 0.0884243 0.0884243i
239239 18817.0i 0.329423i 0.986342 + 0.164711i 0.0526693π0.0526693\pi
−0.986342 + 0.164711i 0.947331π0.947331\pi
240240 63389.4 15915.7i 1.10051 0.276315i
241241 73856.4 1.27161 0.635805 0.771849i 0.280668π-0.280668\pi
0.635805 + 0.771849i 0.280668π0.280668\pi
242242 −68900.8 68900.8i −1.17650 1.17650i
243243 13874.1 13874.1i 0.234959 0.234959i
244244 23504.2i 0.394790i
245245 −30626.9 + 51162.5i −0.510235 + 0.852352i
246246 −55192.3 −0.912028
247247 22100.4 + 22100.4i 0.362248 + 0.362248i
248248 −29570.9 + 29570.9i −0.480796 + 0.480796i
249249 18137.2i 0.292531i
250250 −58076.8 + 52814.8i −0.929229 + 0.845037i
251251 77295.7 1.22690 0.613448 0.789735i 0.289782π-0.289782\pi
0.613448 + 0.789735i 0.289782π0.289782\pi
252252 −354.017 354.017i −0.00557473 0.00557473i
253253 −14389.5 + 14389.5i −0.224804 + 0.224804i
254254 124215.i 1.92533i
255255 62368.6 + 37335.1i 0.959148 + 0.574165i
256256 82966.6 1.26597
257257 −46347.9 46347.9i −0.701720 0.701720i 0.263060 0.964780i 0.415268π-0.415268\pi
−0.964780 + 0.263060i 0.915268π0.915268\pi
258258 51046.3 51046.3i 0.766876 0.766876i
259259 3583.55i 0.0534213i
260260 2943.88 + 11724.9i 0.0435485 + 0.173445i
261261 12897.1 0.189326
262262 −76935.4 76935.4i −1.12079 1.12079i
263263 −25093.0 + 25093.0i −0.362777 + 0.362777i −0.864835 0.502057i 0.832577π-0.832577\pi
0.502057 + 0.864835i 0.332577π0.332577\pi
264264 51428.9i 0.737903i
265265 39402.1 9893.03i 0.561083 0.140876i
266266 −11945.1 −0.168821
267267 47217.8 + 47217.8i 0.662343 + 0.662343i
268268 −37964.9 + 37964.9i −0.528582 + 0.528582i
269269 35536.6i 0.491102i −0.969384 0.245551i 0.921031π-0.921031\pi
0.969384 0.245551i 0.0789689π-0.0789689\pi
270270 50104.1 83699.4i 0.687300 1.14814i
271271 −134131. −1.82638 −0.913189 0.407536i 0.866388π-0.866388\pi
−0.913189 + 0.407536i 0.866388π0.866388\pi
272272 79758.2 + 79758.2i 1.07805 + 1.07805i
273273 1209.11 1209.11i 0.0162233 0.0162233i
274274 78795.5i 1.04954i
275275 −54467.7 101629.i −0.720234 1.34386i
276276 −8367.61 −0.109846
277277 −21251.3 21251.3i −0.276966 0.276966i 0.554931 0.831896i 0.312745π-0.312745\pi
−0.831896 + 0.554931i 0.812745π0.812745\pi
278278 32285.5 32285.5i 0.417752 0.417752i
279279 16761.4i 0.215329i
280280 2899.55 + 1735.73i 0.0369840 + 0.0221394i
281281 −28206.2 −0.357216 −0.178608 0.983920i 0.557159π-0.557159\pi
−0.178608 + 0.983920i 0.557159π0.557159\pi
282282 98586.3 + 98586.3i 1.23971 + 1.23971i
283283 7699.00 7699.00i 0.0961305 0.0961305i −0.657406 0.753537i 0.728346π-0.728346\pi
0.753537 + 0.657406i 0.228346π0.228346\pi
284284 73003.1i 0.905117i
285285 −29850.8 118890.i −0.367507 1.46371i
286286 −48501.1 −0.592952
287287 −3766.76 3766.76i −0.0457303 0.0457303i
288288 10169.0 10169.0i 0.122601 0.122601i
289289 41928.9i 0.502016i
290290 115435. 28983.2i 1.37259 0.344628i
291291 −47959.4 −0.566354
292292 −26898.3 26898.3i −0.315471 0.315471i
293293 −14289.1 + 14289.1i −0.166445 + 0.166445i −0.785415 0.618970i 0.787550π-0.787550\pi
0.618970 + 0.785415i 0.287550π0.287550\pi
294294 98370.5i 1.13807i
295295 82890.4 138469.i 0.952490 1.59114i
296296 −30570.5 −0.348915
297297 101319. + 101319.i 1.14862 + 1.14862i
298298 54295.4 54295.4i 0.611408 0.611408i
299299 5771.95i 0.0645625i
300300 13712.5 45385.9i 0.152361 0.504288i
301301 6967.61 0.0769044
302302 −61156.3 61156.3i −0.670544 0.670544i
303303 26886.2 26886.2i 0.292849 0.292849i
304304 190212.i 2.05822i
305305 54559.1 + 32660.1i 0.586499 + 0.351090i
306306 24219.3 0.258653
307307 −48387.2 48387.2i −0.513397 0.513397i 0.402169 0.915566i 0.368257π-0.368257\pi
−0.915566 + 0.402169i 0.868257π0.868257\pi
308308 4798.66 4798.66i 0.0505846 0.0505846i
309309 39309.8i 0.411703i
310310 37667.3 + 150022.i 0.391960 + 1.56110i
311311 −39390.4 −0.407258 −0.203629 0.979048i 0.565274π-0.565274\pi
−0.203629 + 0.979048i 0.565274π0.565274\pi
312312 10314.6 + 10314.6i 0.105961 + 0.105961i
313313 40352.4 40352.4i 0.411889 0.411889i −0.470507 0.882396i 0.655929π-0.655929\pi
0.882396 + 0.470507i 0.155929π0.155929\pi
314314 14291.7i 0.144952i
315315 1313.69 329.839i 0.0132395 0.00332415i
316316 47310.8 0.473790
317317 −20437.7 20437.7i −0.203383 0.203383i 0.598065 0.801448i 0.295936π-0.295936\pi
−0.801448 + 0.598065i 0.795936π0.795936\pi
318318 −47390.1 + 47390.1i −0.468633 + 0.468633i
319319 174818.i 1.71793i
320320 2737.04 4572.25i 0.0267289 0.0446509i
321321 165966. 1.61068
322322 −1559.85 1559.85i −0.0150442 0.0150442i
323323 149590. 149590.i 1.43383 1.43383i
324324 48730.0i 0.464201i
325325 −31307.1 9458.81i −0.296398 0.0895509i
326326 −83764.2 −0.788176
327327 −65471.7 65471.7i −0.612292 0.612292i
328328 32133.5 32133.5i 0.298682 0.298682i
329329 13456.6i 0.124321i
330330 163212. + 97701.9i 1.49873 + 0.897171i
331331 −106355. −0.970740 −0.485370 0.874309i 0.661315π-0.661315\pi
−0.485370 + 0.874309i 0.661315π0.661315\pi
332332 −14436.9 14436.9i −0.130978 0.130978i
333333 −8664.01 + 8664.01i −0.0781323 + 0.0781323i
334334 37444.4i 0.335655i
335335 −35372.0 140880.i −0.315188 1.25533i
336336 −10406.5 −0.0921777
337337 −92531.5 92531.5i −0.814760 0.814760i 0.170583 0.985343i 0.445435π-0.445435\pi
−0.985343 + 0.170583i 0.945435π0.945435\pi
338338 91736.2 91736.2i 0.802985 0.802985i
339339 56610.0i 0.492599i
340340 79362.2 19926.2i 0.686524 0.172372i
341341 −227198. −1.95387
342342 −28879.8 28879.8i −0.246912 0.246912i
343343 13471.8 13471.8i 0.114508 0.114508i
344344 59439.2i 0.502292i
345345 11627.2 19423.3i 0.0976868 0.163187i
346346 −259884. −2.17083
347347 151780. + 151780.i 1.26053 + 1.26053i 0.950835 + 0.309698i 0.100228π0.100228\pi
0.309698 + 0.950835i 0.399772π0.399772\pi
348348 −50829.2 + 50829.2i −0.419715 + 0.419715i
349349 100880.i 0.828239i −0.910223 0.414119i 0.864090π-0.864090\pi
0.910223 0.414119i 0.135910π-0.135910\pi
350350 11016.8 5904.40i 0.0899332 0.0481992i
351351 40641.2 0.329877
352352 137840. + 137840.i 1.11247 + 1.11247i
353353 44859.7 44859.7i 0.360004 0.360004i −0.503810 0.863814i 0.668069π-0.668069\pi
0.863814 + 0.503810i 0.168069π0.168069\pi
354354 266236.i 2.12452i
355355 −169458. 101441.i −1.34464 0.804928i
356356 75168.8 0.593113
357357 −8184.07 8184.07i −0.0642145 0.0642145i
358358 −72654.5 + 72654.5i −0.566887 + 0.566887i
359359 72835.5i 0.565138i 0.959247 + 0.282569i 0.0911866π0.0911866\pi
−0.959247 + 0.282569i 0.908813π0.908813\pi
360360 2813.79 + 11206.8i 0.0217113 + 0.0864720i
361361 −226432. −1.73749
362362 −4882.29 4882.29i −0.0372569 0.0372569i
363363 −112582. + 112582.i −0.854388 + 0.854388i
364364 1924.85i 0.0145276i
365365 99814.0 25061.2i 0.749214 0.188112i
366366 −104901. −0.783102
367367 −64183.5 64183.5i −0.476531 0.476531i 0.427489 0.904020i 0.359398π-0.359398\pi
−0.904020 + 0.427489i 0.859398π0.859398\pi
368368 24838.9 24838.9i 0.183416 0.183416i
369369 18213.9i 0.133768i
370370 −58076.3 + 97017.0i −0.424224 + 0.708670i
371371 −6468.55 −0.0469958
372372 −66058.9 66058.9i −0.477359 0.477359i
373373 −167651. + 167651.i −1.20501 + 1.20501i −0.232383 + 0.972624i 0.574652π0.574652\pi
−0.972624 + 0.232383i 0.925348π0.925348\pi
374374 328289.i 2.34700i
375375 86297.8 + 94895.8i 0.613673 + 0.674814i
376376 −114796. −0.811989
377377 35061.8 + 35061.8i 0.246690 + 0.246690i
378378 −10983.1 + 10983.1i −0.0768674 + 0.0768674i
379379 52795.3i 0.367550i 0.982968 + 0.183775i 0.0588318π0.0588318\pi
−0.982968 + 0.183775i 0.941168π0.941168\pi
380380 −118395. 70873.4i −0.819907 0.490813i
381381 −202963. −1.39819
382382 −86475.1 86475.1i −0.592603 0.592603i
383383 81271.5 81271.5i 0.554040 0.554040i −0.373565 0.927604i 0.621865π-0.621865\pi
0.927604 + 0.373565i 0.121865π0.121865\pi
384384 129992.i 0.881566i
385385 4470.92 + 17806.8i 0.0301631 + 0.120134i
386386 186748. 1.25337
387387 16845.7 + 16845.7i 0.112478 + 0.112478i
388388 −38174.7 + 38174.7i −0.253578 + 0.253578i
389389 63912.5i 0.422364i −0.977447 0.211182i 0.932269π-0.932269\pi
0.977447 0.211182i 0.0677312π-0.0677312\pi
390390 52329.2 13138.8i 0.344045 0.0863825i
391391 39068.5 0.255549
392392 57272.2 + 57272.2i 0.372711 + 0.372711i
393393 −125710. + 125710.i −0.813926 + 0.813926i
394394 136202.i 0.877388i
395395 −65740.5 + 109820.i −0.421346 + 0.703862i
396396 23203.6 0.147967
397397 185435. + 185435.i 1.17655 + 1.17655i 0.980617 + 0.195936i 0.0627745π0.0627745\pi
0.195936 + 0.980617i 0.437225π0.437225\pi
398398 −192467. + 192467.i −1.21504 + 1.21504i
399399 19517.9i 0.122599i
400400 94021.2 + 175431.i 0.587633 + 1.09644i
401401 159570. 0.992345 0.496172 0.868224i 0.334738π-0.334738\pi
0.496172 + 0.868224i 0.334738π0.334738\pi
402402 169441. + 169441.i 1.04849 + 1.04849i
403403 −45567.2 + 45567.2i −0.280571 + 0.280571i
404404 42801.7i 0.262240i
405405 −113114. 67712.5i −0.689617 0.412818i
406406 −18950.6 −0.114967
407407 −117439. 117439.i −0.708966 0.708966i
408408 69816.6 69816.6i 0.419410 0.419410i
409409 15836.9i 0.0946727i −0.998879 0.0473363i 0.984927π-0.984927\pi
0.998879 0.0473363i 0.0150733π-0.0150733\pi
410410 −40931.5 163022.i −0.243495 0.969794i
411411 128749. 0.762188
412412 31289.8 + 31289.8i 0.184335 + 0.184335i
413413 −18170.1 + 18170.1i −0.106526 + 0.106526i
414414 7542.53i 0.0440065i
415415 53572.3 13450.9i 0.311060 0.0781006i
416416 55290.7 0.319496
417417 −52753.6 52753.6i −0.303375 0.303375i
418418 391462. 391462.i 2.24046 2.24046i
419419 15156.5i 0.0863318i −0.999068 0.0431659i 0.986256π-0.986256\pi
0.999068 0.0431659i 0.0137444π-0.0137444\pi
420420 −3877.47 + 6477.35i −0.0219811 + 0.0367197i
421421 140633. 0.793456 0.396728 0.917936i 0.370146π-0.370146\pi
0.396728 + 0.917936i 0.370146π0.370146\pi
422422 −259840. 259840.i −1.45908 1.45908i
423423 −32534.3 + 32534.3i −0.181828 + 0.181828i
424424 55181.9i 0.306948i
425425 −64023.7 + 211908.i −0.354457 + 1.17319i
426426 325819. 1.79538
427427 −7159.29 7159.29i −0.0392658 0.0392658i
428428 132106. 132106.i 0.721163 0.721163i
429429 79249.3i 0.430607i
430430 188633. + 112920.i 1.02019 + 0.610706i
431431 −83775.8 −0.450987 −0.225493 0.974245i 0.572399π-0.572399\pi
−0.225493 + 0.974245i 0.572399π0.572399\pi
432432 −174894. 174894.i −0.937148 0.937148i
433433 93346.8 93346.8i 0.497879 0.497879i −0.412898 0.910777i 0.635484π-0.635484\pi
0.910777 + 0.412898i 0.135484π0.135484\pi
434434 24628.7i 0.130756i
435435 −47357.7 188617.i −0.250272 0.996784i
436436 −104228. −0.548293
437437 −46586.5 46586.5i −0.243948 0.243948i
438438 −120049. + 120049.i −0.625765 + 0.625765i
439439 131771.i 0.683737i −0.939748 0.341869i 0.888940π-0.888940\pi
0.939748 0.341869i 0.111060π-0.111060\pi
440440 −151906. + 38140.5i −0.784640 + 0.197007i
441441 32463.1 0.166922
442442 65842.0 + 65842.0i 0.337022 + 0.337022i
443443 −1523.66 + 1523.66i −0.00776389 + 0.00776389i −0.710978 0.703214i 0.751747π-0.751747\pi
0.703214 + 0.710978i 0.251747π0.251747\pi
444444 68292.1i 0.346421i
445445 −104450. + 174485.i −0.527461 + 0.881128i
446446 25703.1 0.129216
447447 −88717.1 88717.1i −0.444010 0.444010i
448448 −599.975 + 599.975i −0.00298935 + 0.00298935i
449449 171320.i 0.849795i 0.905241 + 0.424898i 0.139690π0.139690\pi
−0.905241 + 0.424898i 0.860310π0.860310\pi
450450 40910.7 + 12360.4i 0.202028 + 0.0610388i
451451 246887. 1.21380
452452 45060.4 + 45060.4i 0.220556 + 0.220556i
453453 −99927.6 + 99927.6i −0.486955 + 0.486955i
454454 142891.i 0.693253i
455455 4468.06 + 2674.67i 0.0215822 + 0.0129195i
456456 −166503. −0.800742
457457 −73654.8 73654.8i −0.352670 0.352670i 0.508432 0.861102i 0.330225π-0.330225\pi
−0.861102 + 0.508432i 0.830225π0.830225\pi
458458 79642.7 79642.7i 0.379677 0.379677i
459459 275087.i 1.30571i
460460 −6205.56 24715.5i −0.0293268 0.116803i
461461 274304. 1.29072 0.645358 0.763881i 0.276708π-0.276708\pi
0.645358 + 0.763881i 0.276708π0.276708\pi
462462 −21416.8 21416.8i −0.100339 0.100339i
463463 −1734.02 + 1734.02i −0.00808894 + 0.00808894i −0.711140 0.703051i 0.751821π-0.751821\pi
0.703051 + 0.711140i 0.251821π0.251821\pi
464464 301768.i 1.40164i
465465 245131. 61547.2i 1.13368 0.284644i
466466 −221039. −1.01788
467467 222292. + 222292.i 1.01927 + 1.01927i 0.999811 + 0.0194620i 0.00619532π0.00619532\pi
0.0194620 + 0.999811i 0.493805π0.493805\pi
468468 4653.74 4653.74i 0.0212476 0.0212476i
469469 23127.9i 0.105146i
470470 −218083. + 364309.i −0.987247 + 1.64921i
471471 −23352.2 −0.105265
472472 −155005. 155005.i −0.695764 0.695764i
473473 −228341. + 228341.i −1.02062 + 1.02062i
474474 211152.i 0.939807i
475475 329029. 176341.i 1.45830 0.781569i
476476 −13028.7 −0.0575026
477477 −15639.1 15639.1i −0.0687346 0.0687346i
478478 66847.8 66847.8i 0.292571 0.292571i
479479 69849.2i 0.304432i −0.988347 0.152216i 0.951359π-0.951359\pi
0.988347 0.152216i 0.0486410π-0.0486410\pi
480480 −186060. 111379.i −0.807550 0.483416i
481481 −47107.7 −0.203611
482482 −262377. 262377.i −1.12936 1.12936i
483483 −2548.74 + 2548.74i −0.0109253 + 0.0109253i
484484 179226.i 0.765085i
485485 −35567.5 141658.i −0.151206 0.602225i
486486 −98576.2 −0.417349
487487 −3885.73 3885.73i −0.0163838 0.0163838i 0.698867 0.715251i 0.253688π-0.253688\pi
−0.715251 + 0.698867i 0.753688π0.753688\pi
488488 61074.4 61074.4i 0.256460 0.256460i
489489 136868.i 0.572380i
490490 290559. 72953.2i 1.21016 0.303845i
491491 323891. 1.34349 0.671747 0.740781i 0.265544π-0.265544\pi
0.671747 + 0.740781i 0.265544π0.265544\pi
492492 71783.5 + 71783.5i 0.296548 + 0.296548i
493493 237322. 237322.i 0.976438 0.976438i
494494 157024.i 0.643447i
495495 −32242.4 + 53861.3i −0.131588 + 0.219820i
496496 392186. 1.59415
497497 22236.5 + 22236.5i 0.0900229 + 0.0900229i
498498 −64433.0 + 64433.0i −0.259806 + 0.259806i
499499 216973.i 0.871373i −0.900099 0.435686i 0.856506π-0.856506\pi
0.900099 0.435686i 0.143494π-0.143494\pi
500500 144226. + 6843.78i 0.576906 + 0.0273751i
501501 −61183.0 −0.243756
502502 −274595. 274595.i −1.08964 1.08964i
503503 308050. 308050.i 1.21755 1.21755i 0.249056 0.968489i 0.419880π-0.419880\pi
0.968489 0.249056i 0.0801204π-0.0801204\pi
504504 1839.79i 0.00724282i
505505 99353.4 + 59474.9i 0.389583 + 0.233212i
506506 102238. 0.399311
507507 −149894. 149894.i −0.583135 0.583135i
508508 −161554. + 161554.i −0.626024 + 0.626024i
509509 480107.i 1.85311i 0.376154 + 0.926557i 0.377246π0.377246\pi
−0.376154 + 0.926557i 0.622754π0.622754\pi
510510 −88932.2 354200.i −0.341916 1.36178i
511511 −16386.2 −0.0627534
512512 −115587. 115587.i −0.440929 0.440929i
513513 −328023. + 328023.i −1.24643 + 1.24643i
514514 329304.i 1.24644i
515515 −116110. + 29152.8i −0.437779 + 0.109917i
516516 −132782. −0.498702
517517 −440998. 440998.i −1.64989 1.64989i
518518 12730.7 12730.7i 0.0474451 0.0474451i
519519 424642.i 1.57648i
520520 −22817.0 + 38116.1i −0.0843825 + 0.140962i
521521 409811. 1.50976 0.754880 0.655863i 0.227695π-0.227695\pi
0.754880 + 0.655863i 0.227695π0.227695\pi
522522 −45817.3 45817.3i −0.168147 0.168147i
523523 −24703.1 + 24703.1i −0.0903125 + 0.0903125i −0.750820 0.660507i 0.770341π-0.770341\pi
0.660507 + 0.750820i 0.270341π0.270341\pi
524524 200125.i 0.728852i
525525 −9647.61 18001.1i −0.0350027 0.0653103i
526526 178287. 0.644388
527527 308430. + 308430.i 1.11054 + 1.11054i
528528 341040. 341040.i 1.22331 1.22331i
529529 12167.0i 0.0434783i
530530 −175122. 104832.i −0.623432 0.373199i
531531 −87860.1 −0.311604
532532 15535.8 + 15535.8i 0.0548923 + 0.0548923i
533533 49516.0 49516.0i 0.174298 0.174298i
534534 335485.i 1.17650i
535535 123083. + 490216.i 0.430022 + 1.71270i
536536 −197300. −0.686747
537537 118715. + 118715.i 0.411678 + 0.411678i
538538 −126245. + 126245.i −0.436163 + 0.436163i
539539 440033.i 1.51463i
540540 −174026. + 43694.3i −0.596797 + 0.149843i
541541 300988. 1.02838 0.514191 0.857675i 0.328092π-0.328092\pi
0.514191 + 0.857675i 0.328092π0.328092\pi
542542 476504. + 476504.i 1.62206 + 1.62206i
543543 −7977.51 + 7977.51i −0.0270563 + 0.0270563i
544544 374245.i 1.26462i
545545 144830. 241940.i 0.487602 0.814544i
546546 −8590.77 −0.0288169
547547 26389.6 + 26389.6i 0.0881978 + 0.0881978i 0.749829 0.661631i 0.230136π-0.230136\pi
−0.661631 + 0.749829i 0.730136π0.730136\pi
548548 102482. 102482.i 0.341261 0.341261i
549549 34618.3i 0.114858i
550550 −167543. + 554539.i −0.553861 + 1.83319i
551551 −565981. −1.86423
552552 −21742.8 21742.8i −0.0713571 0.0713571i
553553 14410.7 14410.7i 0.0471232 0.0471232i
554554 150992.i 0.491964i
555555 158523. + 94894.9i 0.514643 + 0.308075i
556556 −83981.6 −0.271665
557557 −142081. 142081.i −0.457959 0.457959i 0.440026 0.897985i 0.354969π-0.354969\pi
−0.897985 + 0.440026i 0.854969π0.854969\pi
558558 59545.3 59545.3i 0.191240 0.191240i
559559 91592.9i 0.293115i
560560 −7717.63 30737.8i −0.0246098 0.0980160i
561561 536414. 1.70441
562562 100203. + 100203.i 0.317255 + 0.317255i
563563 115383. 115383.i 0.364021 0.364021i −0.501270 0.865291i 0.667134π-0.667134\pi
0.865291 + 0.501270i 0.167134π0.167134\pi
564564 256444.i 0.806185i
565565 −167210. + 41982.9i −0.523800 + 0.131515i
566566 −54701.8 −0.170753
567567 14843.0 + 14843.0i 0.0461695 + 0.0461695i
568568 −189695. + 189695.i −0.587975 + 0.587975i
569569 25415.5i 0.0785008i −0.999229 0.0392504i 0.987503π-0.987503\pi
0.999229 0.0392504i 0.0124970π-0.0124970\pi
570570 −316314. + 528405.i −0.973573 + 1.62636i
571571 196811. 0.603639 0.301820 0.953365i 0.402406π-0.402406\pi
0.301820 + 0.953365i 0.402406π0.402406\pi
572572 63080.9 + 63080.9i 0.192799 + 0.192799i
573573 −141298. + 141298.i −0.430354 + 0.430354i
574574 26763.0i 0.0812291i
575575 65993.8 + 19938.7i 0.199603 + 0.0603062i
576576 −2901.14 −0.00874427
577577 167061. + 167061.i 0.501793 + 0.501793i 0.911995 0.410202i 0.134542π-0.134542\pi
−0.410202 + 0.911995i 0.634542π0.634542\pi
578578 148953. 148953.i 0.445856 0.445856i
579579 305140.i 0.910211i
580580 −187831. 112439.i −0.558355 0.334243i
581581 −8794.84 −0.0260541
582582 170377. + 170377.i 0.502996 + 0.502996i
583583 211986. 211986.i 0.623692 0.623692i
584584 139788.i 0.409867i
585585 4335.91 + 17269.1i 0.0126697 + 0.0504612i
586586 101525. 0.295650
587587 −115256. 115256.i −0.334494 0.334494i 0.519796 0.854290i 0.326008π-0.326008\pi
−0.854290 + 0.519796i 0.826008π0.826008\pi
588588 −127941. + 127941.i −0.370047 + 0.370047i
589589 735564.i 2.12026i
590590 −786386. + 197445.i −2.25908 + 0.567208i
591591 222550. 0.637167
592592 202722. + 202722.i 0.578439 + 0.578439i
593593 −100599. + 100599.i −0.286077 + 0.286077i −0.835527 0.549449i 0.814837π-0.814837\pi
0.549449 + 0.835527i 0.314837π0.314837\pi
594594 719873.i 2.04025i
595595 18104.0 30242.9i 0.0511376 0.0854258i
596596 −141234. −0.397601
597597 314486. + 314486.i 0.882373 + 0.882373i
598598 20505.0 20505.0i 0.0573400 0.0573400i
599599 505775.i 1.40962i 0.709394 + 0.704812i 0.248969π0.248969\pi
−0.709394 + 0.704812i 0.751031π0.751031\pi
600600 153564. 82301.8i 0.426567 0.228616i
601601 −420577. −1.16439 −0.582193 0.813051i 0.697805π-0.697805\pi
−0.582193 + 0.813051i 0.697805π0.697805\pi
602602 −24752.6 24752.6i −0.0683012 0.0683012i
603603 −55916.8 + 55916.8i −0.153783 + 0.153783i
604604 159081.i 0.436057i
605605 −416027. 249042.i −1.13661 0.680397i
606606 −191028. −0.520177
607607 466115. + 466115.i 1.26507 + 1.26507i 0.948602 + 0.316470i 0.102498π0.102498\pi
0.316470 + 0.948602i 0.397502π0.397502\pi
608608 −446262. + 446262.i −1.20721 + 1.20721i
609609 30964.8i 0.0834897i
610610 −77796.5 309849.i −0.209074 0.832702i
611611 −176894. −0.473840
612612 −31499.7 31499.7i −0.0841015 0.0841015i
613613 −425779. + 425779.i −1.13309 + 1.13309i −0.143426 + 0.989661i 0.545812π0.545812\pi
−0.989661 + 0.143426i 0.954188π0.954188\pi
614614 343793.i 0.911928i
615615 −266374. + 66880.9i −0.704273 + 0.176828i
616616 24938.1 0.0657207
617617 371023. + 371023.i 0.974609 + 0.974609i 0.999686 0.0250764i 0.00798290π-0.00798290\pi
−0.0250764 + 0.999686i 0.507983π0.507983\pi
618618 139649. 139649.i 0.365646 0.365646i
619619 735915.i 1.92064i −0.278895 0.960322i 0.589968π-0.589968\pi
0.278895 0.960322i 0.410032π-0.410032\pi
620620 146129. 244110.i 0.380148 0.635041i
621621 −85669.7 −0.222149
622622 139935. + 139935.i 0.361699 + 0.361699i
623623 22896.1 22896.1i 0.0589911 0.0589911i
624624 136799.i 0.351328i
625625 −216295. + 325276.i −0.553716 + 0.832706i
626626 −286706. −0.731624
627627 −639637. 639637.i −1.62704 1.62704i
628628 −18587.9 + 18587.9i −0.0471314 + 0.0471314i
629629 318857.i 0.805925i
630630 −5838.66 3495.14i −0.0147107 0.00880610i
631631 610188. 1.53252 0.766258 0.642533i 0.222117π-0.222117\pi
0.766258 + 0.642533i 0.222117π0.222117\pi
632632 122935. + 122935.i 0.307780 + 0.307780i
633633 −424570. + 424570.i −1.05960 + 1.05960i
634634 145211.i 0.361261i
635635 −150521. 599495.i −0.373292 1.48675i
636636 123272. 0.304754
637637 88253.6 + 88253.6i 0.217497 + 0.217497i
638638 621047. 621047.i 1.52575 1.52575i
639639 107523.i 0.263329i
640640 383960. 96404.4i 0.937403 0.235362i
641641 −251941. −0.613172 −0.306586 0.951843i 0.599187π-0.599187\pi
−0.306586 + 0.951843i 0.599187π0.599187\pi
642642 −589598. 589598.i −1.43049 1.43049i
643643 43628.3 43628.3i 0.105523 0.105523i −0.652374 0.757897i 0.726227π-0.726227\pi
0.757897 + 0.652374i 0.226227π0.226227\pi
644644 4057.50i 0.00978332i
645645 184507. 308221.i 0.443500 0.740871i
646646 −1.06285e6 −2.54687
647647 440782. + 440782.i 1.05297 + 1.05297i 0.998516 + 0.0544523i 0.0173413π0.0173413\pi
0.0544523 + 0.998516i 0.482659π0.482659\pi
648648 −126622. + 126622.i −0.301551 + 0.301551i
649649 1.19093e6i 2.82747i
650650 77616.4 + 144822.i 0.183708 + 0.342773i
651651 −40242.6 −0.0949563
652652 108944. + 108944.i 0.256277 + 0.256277i
653653 −265254. + 265254.i −0.622064 + 0.622064i −0.946059 0.323995i 0.894974π-0.894974\pi
0.323995 + 0.946059i 0.394974π0.394974\pi
654654 465180.i 1.08759i
655655 −464540. 278083.i −1.08278 0.648175i
656656 −426172. −0.990325
657657 −39617.3 39617.3i −0.0917812 0.0917812i
658658 47805.0 47805.0i 0.110413 0.110413i
659659 456316.i 1.05074i −0.850874 0.525369i 0.823927π-0.823927\pi
0.850874 0.525369i 0.176073π-0.176073\pi
660660 −85202.8 339346.i −0.195599 0.779032i
661661 350242. 0.801614 0.400807 0.916162i 0.368730π-0.368730\pi
0.400807 + 0.916162i 0.368730π0.368730\pi
662662 377830. + 377830.i 0.862145 + 0.862145i
663663 107584. 107584.i 0.244749 0.244749i
664664 75026.9i 0.170169i
665665 −57650.3 + 14474.8i −0.130364 + 0.0327317i
666666 61558.2 0.138783
667667 −73908.6 73908.6i −0.166128 0.166128i
668668 −48700.4 + 48700.4i −0.109139 + 0.109139i
669669 41998.0i 0.0938375i
670670 −374820. + 626139.i −0.834973 + 1.39483i
671671 469246. 1.04221
672672 24414.9 + 24414.9i 0.0540651 + 0.0540651i
673673 −522535. + 522535.i −1.15368 + 1.15368i −0.167871 + 0.985809i 0.553689π0.553689\pi
−0.985809 + 0.167871i 0.946311π0.946311\pi
674674 657441.i 1.44723i
675675 140392. 464672.i 0.308130 1.01986i
676676 −238626. −0.522184
677677 −220817. 220817.i −0.481788 0.481788i 0.423914 0.905702i 0.360656π-0.360656\pi
−0.905702 + 0.423914i 0.860656π0.860656\pi
678678 201109. 201109.i 0.437493 0.437493i
679679 23255.7i 0.0504418i
680680 257996. + 154441.i 0.557949 + 0.333999i
681681 −233479. −0.503446
682682 807128. + 807128.i 1.73530 + 1.73530i
683683 17459.2 17459.2i 0.0374268 0.0374268i −0.688146 0.725572i 0.741575π-0.741575\pi
0.725572 + 0.688146i 0.241575π0.241575\pi
684684 75122.5i 0.160568i
685685 95482.7 + 380290.i 0.203490 + 0.810463i
686686 −95717.6 −0.203397
687687 −130134. 130134.i −0.275725 0.275725i
688688 394159. 394159.i 0.832711 0.832711i
689689 85032.5i 0.179121i
690690 −110308. + 27695.9i −0.231690 + 0.0581725i
691691 637693. 1.33553 0.667767 0.744370i 0.267250π-0.267250\pi
0.667767 + 0.744370i 0.267250π0.267250\pi
692692 338006. + 338006.i 0.705851 + 0.705851i
693693 7067.73 7067.73i 0.0147168 0.0147168i
694694 1.07840e6i 2.23904i
695695 116696. 194942.i 0.241594 0.403586i
696696 −264154. −0.545304
697697 −335158. 335158.i −0.689898 0.689898i
698698 −358380. + 358380.i −0.735585 + 0.735585i
699699 361171.i 0.739193i
700700 −22007.9 6649.24i −0.0449140 0.0135699i
701701 −125311. −0.255008 −0.127504 0.991838i 0.540697π-0.540697\pi
−0.127504 + 0.991838i 0.540697π0.540697\pi
702702 −144379. 144379.i −0.292974 0.292974i
703703 380215. 380215.i 0.769340 0.769340i
704704 39324.6i 0.0793448i
705705 595270. + 356341.i 1.19767 + 0.716947i
706706 −318731. −0.639462
707707 −13037.2 13037.2i −0.0260824 0.0260824i
708708 346268. 346268.i 0.690791 0.690791i
709709 719014.i 1.43036i 0.698942 + 0.715179i 0.253655π0.253655\pi
−0.698942 + 0.715179i 0.746345π0.746345\pi
710710 241633. + 962377.i 0.479335 + 1.90910i
711711 69682.0 0.137842
712712 195322. + 195322.i 0.385294 + 0.385294i
713713 96053.6 96053.6i 0.188945 0.188945i
714714 58148.2i 0.114062i
715715 −234080. + 58772.6i −0.457881 + 0.114964i
716716 188990. 0.368649
717717 −109227. 109227.i −0.212467 0.212467i
718718 258750. 258750.i 0.501917 0.501917i
719719 784081.i 1.51671i −0.651841 0.758356i 0.726003π-0.726003\pi
0.651841 0.758356i 0.273997π-0.273997\pi
720720 55656.3 92974.4i 0.107362 0.179349i
721721 19061.5 0.0366680
722722 804404. + 804404.i 1.54312 + 1.54312i
723723 −428716. + 428716.i −0.820149 + 0.820149i
724724 12699.9i 0.0242283i
725725 521999. 279762.i 0.993101 0.532247i
726726 799900. 1.51762
727727 −288195. 288195.i −0.545277 0.545277i 0.379794 0.925071i 0.375995π-0.375995\pi
−0.925071 + 0.379794i 0.875995π0.875995\pi
728728 5001.63 5001.63i 0.00943731 0.00943731i
729729 588208.i 1.10682i
730730 −443622. 265561.i −0.832468 0.498332i
731731 619963. 1.16020
732732 136435. + 136435.i 0.254627 + 0.254627i
733733 −369280. + 369280.i −0.687302 + 0.687302i −0.961635 0.274333i 0.911543π-0.911543\pi
0.274333 + 0.961635i 0.411543π0.411543\pi
734734 456027.i 0.846444i
735735 −119203. 474764.i −0.220655 0.878826i
736736 −116550. −0.215158
737737 −757945. 757945.i −1.39541 1.39541i
738738 −64705.4 + 64705.4i −0.118803 + 0.118803i
739739 123689.i 0.226486i −0.993567 0.113243i 0.963876π-0.963876\pi
0.993567 0.113243i 0.0361239π-0.0361239\pi
740740 201715. 50646.5i 0.368363 0.0924882i
741741 −256573. −0.467277
742742 22979.7 + 22979.7i 0.0417384 + 0.0417384i
743743 −702418. + 702418.i −1.27238 + 1.27238i −0.327549 + 0.944834i 0.606223π0.606223\pi
−0.944834 + 0.327549i 0.893777π0.893777\pi
744744 343301.i 0.620197i
745745 196251. 327839.i 0.353590 0.590675i
746746 1.19117e6 2.14041
747747 −21263.4 21263.4i −0.0381059 0.0381059i
748748 426975. 426975.i 0.763130 0.763130i
749749 80477.7i 0.143454i
750750 30544.4 643695.i 0.0543011 1.14435i
751751 −453211. −0.803565 −0.401783 0.915735i 0.631609π-0.631609\pi
−0.401783 + 0.915735i 0.631609π0.631609\pi
752752 761243. + 761243.i 1.34613 + 1.34613i
753753 −448680. + 448680.i −0.791309 + 0.791309i
754754 249116.i 0.438186i
755755 −369266. 221050.i −0.647806 0.387790i
756756 28569.4 0.0499871
757757 −169459. 169459.i −0.295715 0.295715i 0.543618 0.839333i 0.317054π-0.317054\pi
−0.839333 + 0.543618i 0.817054π0.817054\pi
758758 187557. 187557.i 0.326433 0.326433i
759759 167054.i 0.289983i
760760 −123481. 491803.i −0.213784 0.851459i
761761 −163848. −0.282925 −0.141462 0.989944i 0.545180π-0.545180\pi
−0.141462 + 0.989944i 0.545180π0.545180\pi
762762 721031. + 721031.i 1.24178 + 1.24178i
763763 −31747.6 + 31747.6i −0.0545333 + 0.0545333i
764764 224940.i 0.385372i
765765 116889. 29348.4i 0.199733 0.0501489i
766766 −577438. −0.984120
767767 −238855. 238855.i −0.406016 0.406016i
768768 −481598. + 481598.i −0.816511 + 0.816511i
769769 574664.i 0.971765i −0.874024 0.485883i 0.838498π-0.838498\pi
0.874024 0.485883i 0.161502π-0.161502\pi
770770 47376.1 79142.3i 0.0799058 0.133483i
771771 538073. 0.905175
772772 −242885. 242885.i −0.407537 0.407537i
773773 250860. 250860.i 0.419828 0.419828i −0.465316 0.885144i 0.654059π-0.654059\pi
0.885144 + 0.465316i 0.154059π0.154059\pi
774774 119690.i 0.199790i
775775 363586. + 678403.i 0.605346 + 1.12949i
776776 −198390. −0.329455
777777 −20801.5 20801.5i −0.0344550 0.0344550i
778778 −227051. + 227051.i −0.375115 + 0.375115i
779779 799307.i 1.31716i
780780 −85148.2 50971.4i −0.139954 0.0837794i
781781 −1.45746e6 −2.38943
782782 −138792. 138792.i −0.226961 0.226961i
783783 −520402. + 520402.i −0.848820 + 0.848820i
784784 759577.i 1.23578i
785785 −17318.4 68975.8i −0.0281040 0.111933i
786786 893176. 1.44575
787787 565274. + 565274.i 0.912661 + 0.912661i 0.996481 0.0838197i 0.0267120π-0.0267120\pi
−0.0838197 + 0.996481i 0.526712π0.526712\pi
788788 177146. 177146.i 0.285284 0.285284i
789789 291315.i 0.467960i
790790 623684. 156594.i 0.999333 0.250912i
791791 27450.5 0.0438730
792792 60293.3 + 60293.3i 0.0961211 + 0.0961211i
793793 94112.6 94112.6i 0.149659 0.149659i
794794 1.31753e6i 2.08987i
795795 −171292. + 286144.i −0.271020 + 0.452742i
796796 500649. 0.790146
797797 242456. + 242456.i 0.381695 + 0.381695i 0.871713 0.490017i 0.163010π-0.163010\pi
−0.490017 + 0.871713i 0.663010π0.663010\pi
798798 69337.8 69337.8i 0.108884 0.108884i
799799 1.19734e6i 1.87553i
800800 190997. 632168.i 0.298433 0.987762i
801801 110713. 0.172557
802802 −566877. 566877.i −0.881333 0.881333i
803803 537007. 537007.i 0.832815 0.832815i
804804 440751.i 0.681838i
805805 −9418.45 5638.07i −0.0145341 0.00870039i
806806 323757. 0.498368
807807 206280. + 206280.i 0.316745 + 0.316745i
808808 111218. 111218.i 0.170354 0.170354i
809809 293367.i 0.448243i 0.974561 + 0.224122i 0.0719513π0.0719513\pi
−0.974561 + 0.224122i 0.928049π0.928049\pi
810810 161291. + 642392.i 0.245833 + 0.979107i
811811 −484540. −0.736696 −0.368348 0.929688i 0.620076π-0.620076\pi
−0.368348 + 0.929688i 0.620076π0.620076\pi
812812 24647.3 + 24647.3i 0.0373816 + 0.0373816i
813813 778593. 778593.i 1.17796 1.17796i
814814 834414.i 1.25931i
815815 −404270. + 101504.i −0.608634 + 0.152815i
816816 −925948. −1.39061
817817 −739264. 739264.i −1.10753 1.10753i
818818 −56261.1 + 56261.1i −0.0840818 + 0.0840818i
819819 2835.03i 0.00422658i
820820 −158792. + 265264.i −0.236158 + 0.394503i
821821 972880. 1.44335 0.721677 0.692229i 0.243371π-0.243371\pi
0.721677 + 0.692229i 0.243371π0.243371\pi
822822 −457386. 457386.i −0.676923 0.676923i
823823 −244515. + 244515.i −0.361000 + 0.361000i −0.864181 0.503181i 0.832163π-0.832163\pi
0.503181 + 0.864181i 0.332163π0.332163\pi
824824 162610.i 0.239493i
825825 906100. + 273760.i 1.33128 + 0.402219i
826826 129099. 0.189218
827827 −301109. 301109.i −0.440263 0.440263i 0.451837 0.892100i 0.350769π-0.350769\pi
−0.892100 + 0.451837i 0.850769π0.850769\pi
828828 −9809.87 + 9809.87i −0.0143088 + 0.0143088i
829829 954722.i 1.38921i −0.719391 0.694605i 0.755579π-0.755579\pi
0.719391 0.694605i 0.244421π-0.244421\pi
830830 −238101. 142532.i −0.345625 0.206898i
831831 246716. 0.357268
832832 −7886.99 7886.99i −0.0113937 0.0113937i
833833 597361. 597361.i 0.860888 0.860888i
834834 374817.i 0.538874i
835835 −45374.3 180717.i −0.0650784 0.259195i
836836 −1.01828e6 −1.45698
837837 −676328. 676328.i −0.965398 0.965398i
838838 −53843.8 + 53843.8i −0.0766740 + 0.0766740i
839839 1.09935e6i 1.56175i −0.624685 0.780877i 0.714773π-0.714773\pi
0.624685 0.780877i 0.285227π-0.285227\pi
840840 −26906.5 + 6755.65i −0.0381327 + 0.00957433i
841841 −190638. −0.269536
842842 −499602. 499602.i −0.704693 0.704693i
843843 163729. 163729.i 0.230393 0.230393i
844844 675898.i 0.948848i
845845 331581. 553909.i 0.464383 0.775756i
846846 231158. 0.322974
847847 54591.5 + 54591.5i 0.0760954 + 0.0760954i
848848 −365927. + 365927.i −0.508865 + 0.508865i
849849 89381.0i 0.124002i
850850 980253. 525361.i 1.35675 0.727144i
851851 99300.7 0.137118
852852 −423762. 423762.i −0.583772 0.583772i
853853 207155. 207155.i 0.284706 0.284706i −0.550277 0.834982i 0.685478π-0.685478\pi
0.834982 + 0.550277i 0.185478π0.185478\pi
854854 50867.1i 0.0697464i
855855 −174378. 104386.i −0.238539 0.142794i
856856 686539. 0.936953
857857 285095. + 285095.i 0.388176 + 0.388176i 0.874036 0.485860i 0.161494π-0.161494\pi
−0.485860 + 0.874036i 0.661494π0.661494\pi
858858 281535. 281535.i 0.382435 0.382435i
859859 868658.i 1.17723i 0.808412 + 0.588617i 0.200327π0.200327\pi
−0.808412 + 0.588617i 0.799673π0.799673\pi
860860 −98473.6 392202.i −0.133144 0.530289i
861861 43730.0 0.0589893
862862 297616. + 297616.i 0.400536 + 0.400536i
863863 −572841. + 572841.i −0.769152 + 0.769152i −0.977957 0.208805i 0.933043π-0.933043\pi
0.208805 + 0.977957i 0.433043π0.433043\pi
864864 820647.i 1.09933i
865865 −1.25427e6 + 314921.i −1.67633 + 0.420891i
866866 −663234. −0.884363
867867 −243385. 243385.i −0.323785 0.323785i
868868 −32032.3 + 32032.3i −0.0425156 + 0.0425156i
869869 944529.i 1.25077i
870870 −501826. + 838304.i −0.663001 + 1.10755i
871871 −304029. −0.400755
872872 −270832. 270832.i −0.356178 0.356178i
873873 −56225.8 + 56225.8i −0.0737747 + 0.0737747i
874874 331000.i 0.433316i
875875 46015.4 41846.3i 0.0601018 0.0546563i
876876 312274. 0.406937
877877 −253892. 253892.i −0.330104 0.330104i 0.522522 0.852626i 0.324991π-0.324991\pi
−0.852626 + 0.522522i 0.824991π0.824991\pi
878878 −468118. + 468118.i −0.607249 + 0.607249i
879879 165889.i 0.214704i
880880 1.26026e6 + 754414.i 1.62740 + 0.974191i
881881 826450. 1.06479 0.532396 0.846496i 0.321292π-0.321292\pi
0.532396 + 0.846496i 0.321292π0.321292\pi
882882 −115326. 115326.i −0.148248 0.148248i
883883 −575862. + 575862.i −0.738578 + 0.738578i −0.972303 0.233724i 0.924909π-0.924909\pi
0.233724 + 0.972303i 0.424909π0.424909\pi
884884 171269.i 0.219167i
885885 322619. + 1.28493e6i 0.411911 + 1.64056i
886886 10825.6 0.0137907
887887 −461037. 461037.i −0.585988 0.585988i 0.350555 0.936542i 0.385993π-0.385993\pi
−0.936542 + 0.350555i 0.885993π0.885993\pi
888888 177453. 177453.i 0.225039 0.225039i
889889 98417.7i 0.124529i
890890 990927. 248801.i 1.25101 0.314103i
891891 −972863. −1.22545
892892 −33429.6 33429.6i −0.0420147 0.0420147i
893893 1.42775e6 1.42775e6i 1.79040 1.79040i
894894 630340.i 0.788678i
895895 −262610. + 438692.i −0.327842 + 0.547664i
896896 −63033.9 −0.0785160
897897 −33504.5 33504.5i −0.0416408 0.0416408i
898898 608617. 608617.i 0.754730 0.754730i
899899 1.16696e6i 1.44390i
900900 −37132.8 69284.7i −0.0458429 0.0855367i
901901 −575558. −0.708989
902902 −877073. 877073.i −1.07801 1.07801i
903903 −40445.0 + 40445.0i −0.0496009 + 0.0496009i
904904 234174.i 0.286551i
905905 −29479.6 17647.1i −0.0359935 0.0215464i
906906 709991. 0.864960
907907 663568. + 663568.i 0.806624 + 0.806624i 0.984121 0.177498i 0.0568002π-0.0568002\pi
−0.177498 + 0.984121i 0.556800π0.556800\pi
908908 −185844. + 185844.i −0.225412 + 0.225412i
909909 63040.7i 0.0762946i
910910 −6371.06 25374.7i −0.00769359 0.0306421i
911911 −746557. −0.899552 −0.449776 0.893141i 0.648496π-0.648496\pi
−0.449776 + 0.893141i 0.648496π0.648496\pi
912912 1.10413e6 + 1.10413e6i 1.32749 + 1.32749i
913913 288223. 288223.i 0.345770 0.345770i
914914 523321.i 0.626435i
915915 −506283. + 127117.i −0.604716 + 0.151831i
916916 −207168. −0.246906
917917 60957.4 + 60957.4i 0.0724917 + 0.0724917i
918918 −977255. + 977255.i −1.15964 + 1.15964i
919919 431660.i 0.511106i −0.966795 0.255553i 0.917743π-0.917743\pi
0.966795 0.255553i 0.0822575π-0.0822575\pi
920920 48097.2 80346.9i 0.0568257 0.0949278i
921921 561748. 0.662250
922922 −974473. 974473.i −1.14633 1.14633i
923923 −292310. + 292310.i −0.343115 + 0.343115i
924924 55709.7i 0.0652510i
925925 −162730. + 538607.i −0.190188 + 0.629490i
926926 12320.3 0.0143681
927927 46085.4 + 46085.4i 0.0536295 + 0.0536295i
928928 −707986. + 707986.i −0.822107 + 0.822107i
929929 338533.i 0.392256i −0.980578 0.196128i 0.937163π-0.937163\pi
0.980578 0.196128i 0.0628369π-0.0628369\pi
930930 −1.08948e6 652186.i −1.25966 0.754059i
931931 −1.42462e6 −1.64362
932932 287485. + 287485.i 0.330965 + 0.330965i
933933 228650. 228650.i 0.262669 0.262669i
934934 1.57940e6i 1.81050i
935935 397813. + 1.58441e6i 0.455047 + 1.81236i
936936 24185.0 0.0276054
937937 374415. + 374415.i 0.426456 + 0.426456i 0.887419 0.460963i 0.152496π-0.152496\pi
−0.460963 + 0.887419i 0.652496π0.652496\pi
938938 82162.6 82162.6i 0.0933831 0.0933831i
939939 468468.i 0.531311i
940940 757464. 190183.i 0.857247 0.215237i
941941 419785. 0.474075 0.237038 0.971500i 0.423824π-0.423824\pi
0.237038 + 0.971500i 0.423824π0.423824\pi
942942 82959.3 + 82959.3i 0.0934896 + 0.0934896i
943943 −104377. + 104377.i −0.117377 + 0.117377i
944944 2.05577e6i 2.30690i
945945 −39698.5 + 66316.7i −0.0444540 + 0.0742608i
946946 1.62238e6 1.81288
947947 −114973. 114973.i −0.128202 0.128202i 0.640094 0.768296i 0.278895π-0.278895\pi
−0.768296 + 0.640094i 0.778895π0.778895\pi
948948 −274626. + 274626.i −0.305580 + 0.305580i
949949 215406.i 0.239180i
950950 −1.79534e6 542427.i −1.98930 0.601028i
951951 237270. 0.262351
952952 −33854.4 33854.4i −0.0373544 0.0373544i
953953 447662. 447662.i 0.492906 0.492906i −0.416315 0.909221i 0.636679π-0.636679\pi
0.909221 + 0.416315i 0.136679π0.136679\pi
954954 111117.i 0.122091i
955955 −522142. 312564.i −0.572508 0.342715i
956956 −173885. −0.190260
957957 −1.01477e6 1.01477e6i −1.10801 1.10801i
958958 −248141. + 248141.i −0.270376 + 0.270376i
959959 62431.3i 0.0678836i
960960 10652.9 + 42428.4i 0.0115591 + 0.0460378i
961961 593087. 0.642202
962962 167351. + 167351.i 0.180833 + 0.180833i
963963 194572. 194572.i 0.209811 0.209811i
964964 682499.i 0.734425i
965965 901298. 226297.i 0.967862 0.243010i
966966 18108.9 0.0194061
967967 372268. + 372268.i 0.398110 + 0.398110i 0.877566 0.479456i 0.159166π-0.159166\pi
−0.479456 + 0.877566i 0.659166π0.659166\pi
968968 −465709. + 465709.i −0.497008 + 0.497008i
969969 1.73666e6i 1.84956i
970970 −376891. + 629600.i −0.400564 + 0.669146i
971971 563807. 0.597987 0.298993 0.954255i 0.403349π-0.403349\pi
0.298993 + 0.954255i 0.403349π0.403349\pi
972972 128209. + 128209.i 0.135702 + 0.135702i
973973 −25580.5 + 25580.5i −0.0270198 + 0.0270198i
974974 27608.3i 0.0291020i
975975 236634. 126823.i 0.248925 0.133410i
976976 −810004. −0.850330
977977 455228. + 455228.i 0.476914 + 0.476914i 0.904143 0.427230i 0.140510π-0.140510\pi
−0.427230 + 0.904143i 0.640510π0.640510\pi
978978 486228. 486228.i 0.508349 0.508349i
979979 1.50070e6i 1.56577i
980980 −472786. 283019.i −0.492280 0.294689i
981981 −153513. −0.159517
982982 −1.15063e6 1.15063e6i −1.19320 1.19320i
983983 608097. 608097.i 0.629312 0.629312i −0.318583 0.947895i 0.603207π-0.603207\pi
0.947895 + 0.318583i 0.103207π0.103207\pi
984984 373051.i 0.385282i
985985 165047. + 657350.i 0.170112 + 0.677524i
986986 −1.68619e6 −1.73441
987987 −78111.9 78111.9i −0.0801832 0.0801832i
988988 −204227. + 204227.i −0.209218 + 0.209218i
989989 193074.i 0.197392i
990990 305886. 76801.5i 0.312096 0.0783609i
991991 1.03618e6 1.05508 0.527541 0.849529i 0.323114π-0.323114\pi
0.527541 + 0.849529i 0.323114π0.323114\pi
992992 −920116. 920116.i −0.935017 0.935017i
993993 617362. 617362.i 0.626097 0.626097i
994994 157991.i 0.159904i
995995 −695674. + 1.16213e6i −0.702683 + 1.17384i
996996 167604. 0.168953
997997 524380. + 524380.i 0.527541 + 0.527541i 0.919838 0.392298i 0.128320π-0.128320\pi
−0.392298 + 0.919838i 0.628320π0.628320\pi
998998 −770801. + 770801.i −0.773894 + 0.773894i
999999 699191.i 0.700592i
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 115.5.f.a.47.11 88
5.3 odd 4 inner 115.5.f.a.93.11 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.5.f.a.47.11 88 1.1 even 1 trivial
115.5.f.a.93.11 yes 88 5.3 odd 4 inner