Properties

Label 160.4.u.a.43.10
Level 160160
Weight 44
Character 160.43
Analytic conductor 9.4409.440
Analytic rank 00
Dimension 280280
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [160,4,Mod(43,160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(160, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 5, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("160.43");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 160=255 160 = 2^{5} \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 160.u (of order 88, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 9.440305600929.44030560092
Analytic rank: 00
Dimension: 280280
Relative dimension: 7070 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 43.10
Character χ\chi == 160.43
Dual form 160.4.u.a.67.10

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+(2.56149+1.19949i)q2+(0.5328731.28647i)q3+(5.122476.14494i)q4+(11.0603+1.63392i)q5+(0.178152+3.93445i)q6+4.38872iq7+(5.75039+21.8845i)q8+(17.7208+17.7208i)q9+(26.371017.4519i)q10+(6.9832116.8590i)q11+(5.175659.86438i)q12+(10.411025.1344i)q13+(5.2642111.2417i)q14+(3.79175+15.0994i)q15+(11.520662.9546i)q16+(87.087087.0870i)q17+(66.647624.1359i)q18+(37.5516+90.6575i)q19+(46.6157+76.3346i)q20+(5.64596+2.33863i)q21+(2.33465+51.5604i)q22194.901iq23+(25.0896+19.0594i)q24+(119.66136.1433i)q25+(3.48065+76.8695i)q26+(66.974927.7419i)q27+(26.9684+22.4811i)q28+(53.8252129.945i)q29+(8.3990043.2252i)q30299.439iq31+(105.023+147.439i)q32+(17.967417.9674i)q33+(327.532+118.613i)q34+(7.1708248.5406i)q35+(199.66818.1191i)q36+(51.1973+123.601i)q37+(204.930187.176i)q38+(26.786926.7869i)q39+(27.8435251.445i)q40+(276.236276.236i)q41+(17.2672+0.781859i)q42+(18.7517+7.76720i)q43+(67.8261129.271i)q44+(224.952167.043i)q45+(233.781+499.237i)q46+(138.163+138.163i)q47+(87.128118.7259i)q48+323.739q49+(263.156+236.112i)q50+(158.441+65.6284i)q51+(101.119192.725i)q52+(136.689329.995i)q53+(138.280+151.396i)q54+(49.6902+197.875i)q55+(96.045225.2369i)q56+136.638q57+(293.740+268.291i)q58+(324.305+782.941i)q59+(73.3619+100.646i)q60+(573.445237.529i)q61+(359.172+767.009i)q62+(77.7718+77.7718i)q63+(445.866251.689i)q64+(74.0814+295.005i)q65+(67.5749+24.4717i)q66+(753.754312.215i)q67+(981.245+89.0440i)q68+(250.734103.858i)q69+(76.5917+115.735i)q70+(282.902+282.902i)q71+(489.714+285.911i)q72488.899q73+(279.399255.193i)q74+(17.2667173.200i)q75+(749.442+233.638i)q76+(73.9893+30.6474i)q77+(100.745+36.4839i)q78358.166iq79+(230.284+677.473i)q80+575.704iq81+(376.235+1038.92i)q82+(58.6897+24.3101i)q83+(43.292022.7145i)q84+(1105.50+820.915i)q85+(38.715642.3880i)q86195.853q87+(328.795+249.770i)q88+(627.946627.946i)q89+(776.579+158.053i)q90+(110.308+45.6911i)q91+(1197.66998.375i)q92+(385.219159.563i)q93+(188.178519.626i)q94+(563.459941.343i)q95+(245.63956.5428i)q96+(747.095747.095i)q97+(829.255+388.320i)q98+(422.503175.007i)q99+O(q100)q+(-2.56149 + 1.19949i) q^{2} +(0.532873 - 1.28647i) q^{3} +(5.12247 - 6.14494i) q^{4} +(-11.0603 + 1.63392i) q^{5} +(0.178152 + 3.93445i) q^{6} +4.38872i q^{7} +(-5.75039 + 21.8845i) q^{8} +(17.7208 + 17.7208i) q^{9} +(26.3710 - 17.4519i) q^{10} +(6.98321 - 16.8590i) q^{11} +(-5.17565 - 9.86438i) q^{12} +(10.4110 - 25.1344i) q^{13} +(-5.26421 - 11.2417i) q^{14} +(-3.79175 + 15.0994i) q^{15} +(-11.5206 - 62.9546i) q^{16} +(-87.0870 - 87.0870i) q^{17} +(-66.6476 - 24.1359i) q^{18} +(37.5516 + 90.6575i) q^{19} +(-46.6157 + 76.3346i) q^{20} +(5.64596 + 2.33863i) q^{21} +(2.33465 + 51.5604i) q^{22} -194.901i q^{23} +(25.0896 + 19.0594i) q^{24} +(119.661 - 36.1433i) q^{25} +(3.48065 + 76.8695i) q^{26} +(66.9749 - 27.7419i) q^{27} +(26.9684 + 22.4811i) q^{28} +(-53.8252 - 129.945i) q^{29} +(-8.39900 - 43.2252i) q^{30} -299.439i q^{31} +(105.023 + 147.439i) q^{32} +(-17.9674 - 17.9674i) q^{33} +(327.532 + 118.613i) q^{34} +(-7.17082 - 48.5406i) q^{35} +(199.668 - 18.1191i) q^{36} +(51.1973 + 123.601i) q^{37} +(-204.930 - 187.176i) q^{38} +(-26.7869 - 26.7869i) q^{39} +(27.8435 - 251.445i) q^{40} +(276.236 - 276.236i) q^{41} +(-17.2672 + 0.781859i) q^{42} +(-18.7517 + 7.76720i) q^{43} +(-67.8261 - 129.271i) q^{44} +(-224.952 - 167.043i) q^{45} +(233.781 + 499.237i) q^{46} +(-138.163 + 138.163i) q^{47} +(-87.1281 - 18.7259i) q^{48} +323.739 q^{49} +(-263.156 + 236.112i) q^{50} +(-158.441 + 65.6284i) q^{51} +(-101.119 - 192.725i) q^{52} +(-136.689 - 329.995i) q^{53} +(-138.280 + 151.396i) q^{54} +(-49.6902 + 197.875i) q^{55} +(-96.0452 - 25.2369i) q^{56} +136.638 q^{57} +(293.740 + 268.291i) q^{58} +(-324.305 + 782.941i) q^{59} +(73.3619 + 100.646i) q^{60} +(573.445 - 237.529i) q^{61} +(359.172 + 767.009i) q^{62} +(-77.7718 + 77.7718i) q^{63} +(-445.866 - 251.689i) q^{64} +(-74.0814 + 295.005i) q^{65} +(67.5749 + 24.4717i) q^{66} +(-753.754 - 312.215i) q^{67} +(-981.245 + 89.0440i) q^{68} +(-250.734 - 103.858i) q^{69} +(76.5917 + 115.735i) q^{70} +(-282.902 + 282.902i) q^{71} +(-489.714 + 285.911i) q^{72} -488.899 q^{73} +(-279.399 - 255.193i) q^{74} +(17.2667 - 173.200i) q^{75} +(749.442 + 233.638i) q^{76} +(73.9893 + 30.6474i) q^{77} +(100.745 + 36.4839i) q^{78} -358.166i q^{79} +(230.284 + 677.473i) q^{80} +575.704i q^{81} +(-376.235 + 1038.92i) q^{82} +(58.6897 + 24.3101i) q^{83} +(43.2920 - 22.7145i) q^{84} +(1105.50 + 820.915i) q^{85} +(38.7156 - 42.3880i) q^{86} -195.853 q^{87} +(328.795 + 249.770i) q^{88} +(627.946 - 627.946i) q^{89} +(776.579 + 158.053i) q^{90} +(110.308 + 45.6911i) q^{91} +(-1197.66 - 998.375i) q^{92} +(-385.219 - 159.563i) q^{93} +(188.178 - 519.626i) q^{94} +(-563.459 - 941.343i) q^{95} +(245.639 - 56.5428i) q^{96} +(747.095 - 747.095i) q^{97} +(-829.255 + 388.320i) q^{98} +(422.503 - 175.007i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 280q4q24q34q58q6+80q8+8q108q11+44q124q13+64q148q158q16+28q1848q19312q208q21436q22+736q24++3480q98+O(q100) 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/160Z)×\left(\mathbb{Z}/160\mathbb{Z}\right)^\times.

nn 3131 9797 101101
χ(n)\chi(n) 1-1 e(34)e\left(\frac{3}{4}\right) e(58)e\left(\frac{5}{8}\right)

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 −2.56149 + 1.19949i −0.905624 + 0.424082i
33 0.532873 1.28647i 0.102551 0.247581i −0.864273 0.503023i 0.832221π-0.832221\pi
0.966824 + 0.255442i 0.0822210π0.0822210\pi
44 5.12247 6.14494i 0.640309 0.768118i
55 −11.0603 + 1.63392i −0.989264 + 0.146142i
66 0.178152 + 3.93445i 0.0121217 + 0.267706i
77 4.38872i 0.236969i 0.992956 + 0.118484i 0.0378035π0.0378035\pi
−0.992956 + 0.118484i 0.962196π0.962196\pi
88 −5.75039 + 21.8845i −0.254134 + 0.967169i
99 17.7208 + 17.7208i 0.656327 + 0.656327i
1010 26.3710 17.4519i 0.833924 0.551879i
1111 6.98321 16.8590i 0.191411 0.462106i −0.798816 0.601576i 0.794540π-0.794540\pi
0.990226 + 0.139470i 0.0445397π0.0445397\pi
1212 −5.17565 9.86438i −0.124507 0.237300i
1313 10.4110 25.1344i 0.222115 0.536234i −0.773062 0.634331i 0.781276π-0.781276\pi
0.995177 + 0.0980973i 0.0312756π0.0312756\pi
1414 −5.26421 11.2417i −0.100494 0.214605i
1515 −3.79175 + 15.0994i −0.0652684 + 0.259910i
1616 −11.5206 62.9546i −0.180010 0.983665i
1717 −87.0870 87.0870i −1.24245 1.24245i −0.958980 0.283472i 0.908514π-0.908514\pi
−0.283472 0.958980i 0.591486π-0.591486\pi
1818 −66.6476 24.1359i −0.872722 0.316049i
1919 37.5516 + 90.6575i 0.453417 + 1.09464i 0.971014 + 0.239021i 0.0768264π0.0768264\pi
−0.517598 + 0.855624i 0.673174π0.673174\pi
2020 −46.6157 + 76.3346i −0.521180 + 0.853447i
2121 5.64596 + 2.33863i 0.0586690 + 0.0243015i
2222 2.33465 + 51.5604i 0.0226250 + 0.499668i
2323 194.901i 1.76694i −0.468485 0.883471i 0.655200π-0.655200\pi
0.468485 0.883471i 0.344800π-0.344800\pi
2424 25.0896 + 19.0594i 0.213391 + 0.162103i
2525 119.661 36.1433i 0.957285 0.289146i
2626 3.48065 + 76.8695i 0.0262543 + 0.579821i
2727 66.9749 27.7419i 0.477383 0.197738i
2828 26.9684 + 22.4811i 0.182020 + 0.151733i
2929 −53.8252 129.945i −0.344658 0.832078i −0.997232 0.0743529i 0.976311π-0.976311\pi
0.652574 0.757725i 0.273689π-0.273689\pi
3030 −8.39900 43.2252i −0.0511147 0.263060i
3131 299.439i 1.73486i −0.497556 0.867432i 0.665769π-0.665769\pi
0.497556 0.867432i 0.334231π-0.334231\pi
3232 105.023 + 147.439i 0.580176 + 0.814491i
3333 −17.9674 17.9674i −0.0947794 0.0947794i
3434 327.532 + 118.613i 1.65210 + 0.598293i
3535 −7.17082 48.5406i −0.0346311 0.234425i
3636 199.668 18.1191i 0.924388 0.0838845i
3737 51.1973 + 123.601i 0.227480 + 0.549186i 0.995869 0.0907967i 0.0289413π-0.0289413\pi
−0.768389 + 0.639983i 0.778941π0.778941\pi
3838 −204.930 187.176i −0.874844 0.799050i
3939 −26.7869 26.7869i −0.109983 0.109983i
4040 27.8435 251.445i 0.110061 0.993925i
4141 276.236 276.236i 1.05222 1.05222i 0.0536571 0.998559i 0.482912π-0.482912\pi
0.998559 0.0536571i 0.0170878π-0.0170878\pi
4242 −17.2672 + 0.781859i −0.0634379 + 0.00287246i
4343 −18.7517 + 7.76720i −0.0665025 + 0.0275462i −0.415687 0.909508i 0.636459π-0.636459\pi
0.349184 + 0.937054i 0.386459π0.386459\pi
4444 −67.8261 129.271i −0.232390 0.442917i
4545 −224.952 167.043i −0.745198 0.553363i
4646 233.781 + 499.237i 0.749329 + 1.60019i
4747 −138.163 + 138.163i −0.428789 + 0.428789i −0.888216 0.459427i 0.848055π-0.848055\pi
0.459427 + 0.888216i 0.348055π0.348055\pi
4848 −87.1281 18.7259i −0.261997 0.0563093i
4949 323.739 0.943846
5050 −263.156 + 236.112i −0.744318 + 0.667825i
5151 −158.441 + 65.6284i −0.435023 + 0.180193i
5252 −101.119 192.725i −0.269668 0.513966i
5353 −136.689 329.995i −0.354257 0.855252i −0.996085 0.0884030i 0.971824π-0.971824\pi
0.641828 0.766849i 0.278176π-0.278176\pi
5454 −138.280 + 151.396i −0.348472 + 0.381526i
5555 −49.6902 + 197.875i −0.121822 + 0.485118i
5656 −96.0452 25.2369i −0.229189 0.0602218i
5757 136.638 0.317512
5858 293.740 + 268.291i 0.665000 + 0.607386i
5959 −324.305 + 782.941i −0.715609 + 1.72763i −0.0301226 + 0.999546i 0.509590π0.509590\pi
−0.685486 + 0.728086i 0.740410π0.740410\pi
6060 73.3619 + 100.646i 0.157850 + 0.216557i
6161 573.445 237.529i 1.20364 0.498564i 0.311467 0.950257i 0.399180π-0.399180\pi
0.892174 + 0.451693i 0.149180π0.149180\pi
6262 359.172 + 767.009i 0.735725 + 1.57113i
6363 −77.7718 + 77.7718i −0.155529 + 0.155529i
6464 −445.866 251.689i −0.870832 0.491581i
6565 −74.0814 + 295.005i −0.141364 + 0.562937i
6666 67.5749 + 24.4717i 0.126029 + 0.0456402i
6767 −753.754 312.215i −1.37441 0.569301i −0.431432 0.902146i 0.641991π-0.641991\pi
−0.942982 + 0.332845i 0.891991π0.891991\pi
6868 −981.245 + 89.0440i −1.74990 + 0.158797i
6969 −250.734 103.858i −0.437462 0.181203i
7070 76.5917 + 115.735i 0.130778 + 0.197614i
7171 −282.902 + 282.902i −0.472877 + 0.472877i −0.902844 0.429968i 0.858525π-0.858525\pi
0.429968 + 0.902844i 0.358525π0.358525\pi
7272 −489.714 + 285.911i −0.801574 + 0.467984i
7373 −488.899 −0.783853 −0.391927 0.919996i 0.628191π-0.628191\pi
−0.391927 + 0.919996i 0.628191π0.628191\pi
7474 −279.399 255.193i −0.438912 0.400886i
7575 17.2667 173.200i 0.0265838 0.266658i
7676 749.442 + 233.638i 1.13114 + 0.352633i
7777 73.9893 + 30.6474i 0.109505 + 0.0453584i
7878 100.745 + 36.4839i 0.146245 + 0.0529614i
7979 358.166i 0.510086i −0.966930 0.255043i 0.917910π-0.917910\pi
0.966930 0.255043i 0.0820897π-0.0820897\pi
8080 230.284 + 677.473i 0.321832 + 0.946797i
8181 575.704i 0.789717i
8282 −376.235 + 1038.92i −0.506686 + 1.39914i
8383 58.6897 + 24.3101i 0.0776148 + 0.0321491i 0.421153 0.906990i 0.361626π-0.361626\pi
−0.343538 + 0.939139i 0.611626π0.611626\pi
8484 43.2920 22.7145i 0.0562327 0.0295042i
8585 1105.50 + 820.915i 1.41069 + 1.04754i
8686 38.7156 42.3880i 0.0485443 0.0531490i
8787 −195.853 −0.241352
8888 328.795 + 249.770i 0.398291 + 0.302563i
8989 627.946 627.946i 0.747889 0.747889i −0.226193 0.974082i 0.572628π-0.572628\pi
0.974082 + 0.226193i 0.0726281π0.0726281\pi
9090 776.579 + 158.053i 0.909540 + 0.185114i
9191 110.308 + 45.6911i 0.127071 + 0.0526344i
9292 −1197.66 998.375i −1.35722 1.13139i
9393 −385.219 159.563i −0.429520 0.177913i
9494 188.178 519.626i 0.206480 0.570163i
9595 −563.459 941.343i −0.608523 1.01663i
9696 245.639 56.5428i 0.261151 0.0601133i
9797 747.095 747.095i 0.782021 0.782021i −0.198150 0.980172i 0.563493π-0.563493\pi
0.980172 + 0.198150i 0.0634935π0.0634935\pi
9898 −829.255 + 388.320i −0.854769 + 0.400268i
9999 422.503 175.007i 0.428921 0.177665i
100100 390.859 920.450i 0.390859 0.920450i
101101 93.2268 225.069i 0.0918457 0.221735i −0.871280 0.490786i 0.836710π-0.836710\pi
0.963126 + 0.269051i 0.0867099π0.0867099\pi
102102 327.125 358.154i 0.317551 0.347672i
103103 −859.746 −0.822459 −0.411230 0.911532i 0.634901π-0.634901\pi
−0.411230 + 0.911532i 0.634901π0.634901\pi
104104 490.188 + 372.373i 0.462182 + 0.351098i
105105 −66.2671 16.6409i −0.0615906 0.0154666i
106106 745.951 + 681.324i 0.683520 + 0.624302i
107107 536.672 + 1295.64i 0.484879 + 1.17060i 0.957266 + 0.289209i 0.0933923π0.0933923\pi
−0.472387 + 0.881391i 0.656608π0.656608\pi
108108 172.605 553.664i 0.153786 0.493300i
109109 −700.242 + 290.050i −0.615330 + 0.254878i −0.668506 0.743707i 0.733066π-0.733066\pi
0.0531754 + 0.998585i 0.483066π0.483066\pi
110110 −110.067 566.459i −0.0954047 0.490997i
111111 186.291 0.159297
112112 276.290 50.5608i 0.233098 0.0426566i
113113 658.201 658.201i 0.547950 0.547950i −0.377897 0.925848i 0.623353π-0.623353\pi
0.925848 + 0.377897i 0.123353π0.123353\pi
114114 −349.998 + 163.896i −0.287546 + 0.134651i
115115 318.453 + 2155.67i 0.258225 + 1.74797i
116116 −1074.22 334.889i −0.859821 0.268049i
117117 629.895 260.911i 0.497725 0.206164i
118118 −108.423 2394.50i −0.0845857 1.86806i
119119 382.201 382.201i 0.294422 0.294422i
120120 −308.640 169.808i −0.234790 0.129177i
121121 705.700 + 705.700i 0.530203 + 0.530203i
122122 −1183.96 + 1296.27i −0.878613 + 0.961954i
123123 −208.171 502.569i −0.152603 0.368415i
124124 −1840.03 1533.87i −1.33258 1.11085i
125125 −1264.43 + 595.272i −0.904751 + 0.425942i
126126 105.926 292.498i 0.0748937 0.206808i
127127 959.974 + 959.974i 0.670739 + 0.670739i 0.957886 0.287147i 0.0927069π-0.0927069\pi
−0.287147 + 0.957886i 0.592707π0.592707\pi
128128 1443.98 + 109.890i 0.997117 + 0.0758828i
129129 28.2624i 0.0192897i
130130 −164.096 844.513i −0.110709 0.569759i
131131 −685.015 1653.77i −0.456870 1.10298i −0.969658 0.244467i 0.921387π-0.921387\pi
0.512787 0.858516i 0.328613π-0.328613\pi
132132 −202.446 + 18.3711i −0.133490 + 0.0121137i
133133 −397.870 + 164.803i −0.259397 + 0.107446i
134134 2305.23 104.381i 1.48613 0.0672920i
135135 −695.435 + 416.266i −0.443359 + 0.265381i
136136 2406.64 1405.07i 1.51741 0.885913i
137137 698.957i 0.435883i 0.975962 + 0.217941i 0.0699341π0.0699341\pi
−0.975962 + 0.217941i 0.930066π0.930066\pi
138138 766.829 34.7220i 0.473021 0.0214183i
139139 −690.919 286.188i −0.421604 0.174634i 0.161787 0.986826i 0.448274π-0.448274\pi
−0.583391 + 0.812192i 0.698274π0.698274\pi
140140 −335.011 204.583i −0.202240 0.123503i
141141 104.119 + 251.365i 0.0621871 + 0.150133i
142142 385.313 1063.99i 0.227710 0.628787i
143143 −351.038 351.038i −0.205282 0.205282i
144144 911.452 1319.76i 0.527461 0.763751i
145145 807.643 + 1349.29i 0.462559 + 0.772775i
146146 1252.31 586.427i 0.709876 0.332418i
147147 172.512 416.481i 0.0967928 0.233678i
148148 1021.78 + 318.539i 0.567498 + 0.176917i
149149 −197.771 + 477.461i −0.108738 + 0.262518i −0.968877 0.247543i 0.920377π-0.920377\pi
0.860139 + 0.510060i 0.170377π0.170377\pi
150150 163.522 + 464.360i 0.0890101 + 0.252766i
151151 177.952 + 177.952i 0.0959039 + 0.0959039i 0.753431 0.657527i 0.228397π-0.228397\pi
−0.657527 + 0.753431i 0.728397π0.728397\pi
152152 −2199.93 + 300.483i −1.17394 + 0.160344i
153153 3086.51i 1.63091i
154154 −226.284 + 10.2461i −0.118406 + 0.00536141i
155155 489.259 + 3311.88i 0.253537 + 1.71624i
156156 −301.819 + 27.3889i −0.154903 + 0.0140568i
157157 1042.15 2515.97i 0.529762 1.27896i −0.401917 0.915676i 0.631656π-0.631656\pi
0.931679 0.363283i 0.118344π-0.118344\pi
158158 429.615 + 917.439i 0.216319 + 0.461946i
159159 −497.367 −0.248074
160160 −1402.49 1459.12i −0.692978 0.720959i
161161 855.367 0.418710
162162 −690.549 1474.66i −0.334905 0.715187i
163163 −53.3116 + 128.706i −0.0256177 + 0.0618466i −0.936171 0.351546i 0.885656π-0.885656\pi
0.910553 + 0.413392i 0.135656π0.135656\pi
164164 −282.444 3112.47i −0.134483 1.48197i
165165 228.082 + 169.367i 0.107613 + 0.0799105i
166166 −179.493 + 8.12742i −0.0839237 + 0.00380006i
167167 203.594i 0.0943389i −0.998887 0.0471695i 0.984980π-0.984980\pi
0.998887 0.0471695i 0.0150201π-0.0150201\pi
168168 −83.6463 + 110.111i −0.0384134 + 0.0505670i
169169 1030.16 + 1030.16i 0.468895 + 0.468895i
170170 −3816.41 776.734i −1.72180 0.350428i
171171 −941.081 + 2271.97i −0.420855 + 1.01603i
172172 −48.3259 + 155.015i −0.0214234 + 0.0687198i
173173 −944.292 + 2279.72i −0.414990 + 1.00187i 0.568788 + 0.822484i 0.307412π0.307412\pi
−0.983778 + 0.179390i 0.942588π0.942588\pi
174174 501.675 234.923i 0.218574 0.102353i
175175 158.623 + 525.157i 0.0685187 + 0.226847i
176176 −1141.80 245.399i −0.489014 0.105100i
177177 834.417 + 834.417i 0.354342 + 0.354342i
178178 −855.266 + 2361.69i −0.360140 + 0.994473i
179179 134.345 + 324.337i 0.0560973 + 0.135431i 0.949443 0.313939i 0.101649π-0.101649\pi
−0.893346 + 0.449370i 0.851649π0.851649\pi
180180 −2178.78 + 526.644i −0.902205 + 0.218076i
181181 −1693.34 701.403i −0.695386 0.288038i 0.00685640 0.999976i 0.497818π-0.497818\pi
−0.702242 + 0.711938i 0.747818π0.747818\pi
182182 −337.359 + 15.2756i −0.137399 + 0.00622144i
183183 864.292i 0.349127i
184184 4265.32 + 1120.76i 1.70893 + 0.449040i
185185 −768.212 1283.41i −0.305298 0.510046i
186186 1178.13 53.3456i 0.464433 0.0210295i
187187 −2076.34 + 860.050i −0.811964 + 0.336327i
188188 141.267 + 1556.73i 0.0548031 + 0.603918i
189189 121.752 + 293.934i 0.0468578 + 0.113125i
190190 2572.42 + 1735.38i 0.982227 + 0.662620i
191191 689.819i 0.261327i 0.991427 + 0.130664i 0.0417108π0.0417108\pi
−0.991427 + 0.130664i 0.958289π0.958289\pi
192192 −561.381 + 439.475i −0.211011 + 0.165189i
193193 1080.44 + 1080.44i 0.402963 + 0.402963i 0.879276 0.476313i 0.158027π-0.158027\pi
−0.476313 + 0.879276i 0.658027π0.658027\pi
194194 −1017.55 + 2809.81i −0.376576 + 1.03986i
195195 340.039 + 252.504i 0.124875 + 0.0927291i
196196 1658.34 1989.36i 0.604353 0.724985i
197197 −870.009 2100.39i −0.314647 0.759626i −0.999521 0.0309637i 0.990142π-0.990142\pi
0.684873 0.728662i 0.259858π-0.259858\pi
198198 −872.320 + 955.064i −0.313097 + 0.342795i
199199 −3536.09 3536.09i −1.25963 1.25963i −0.951269 0.308363i 0.900219π-0.900219\pi
−0.308363 0.951269i 0.599781π-0.599781\pi
200200 102.884 + 2826.56i 0.0363751 + 0.999338i
201201 −803.310 + 803.310i −0.281896 + 0.281896i
202202 31.1679 + 688.337i 0.0108563 + 0.239759i
203203 570.294 236.224i 0.197176 0.0816732i
204204 −408.327 + 1309.79i −0.140140 + 0.449528i
205205 −2603.91 + 3506.61i −0.887146 + 1.19469i
206206 2202.23 1031.25i 0.744838 0.348790i
207207 3453.81 3453.81i 1.15969 1.15969i
208208 −1702.27 365.857i −0.567457 0.121960i
209209 1790.62 0.592631
210210 189.703 36.8609i 0.0623370 0.0121126i
211211 −107.274 + 44.4344i −0.0350003 + 0.0144976i −0.400115 0.916465i 0.631030π-0.631030\pi
0.365115 + 0.930963i 0.381030π0.381030\pi
212212 −2727.98 850.448i −0.883768 0.275514i
213213 213.194 + 514.695i 0.0685811 + 0.165570i
214214 −2928.78 2675.04i −0.935548 0.854495i
215215 194.708 116.546i 0.0617628 0.0369693i
216216 221.987 + 1625.24i 0.0699274 + 0.511962i
217217 1314.15 0.411108
218218 1445.75 1582.89i 0.449168 0.491774i
219219 −260.521 + 628.954i −0.0803853 + 0.194067i
220220 961.395 + 1318.95i 0.294624 + 0.404199i
221221 −3095.55 + 1282.22i −0.942213 + 0.390277i
222222 −477.182 + 223.453i −0.144263 + 0.0675549i
223223 2187.91 2187.91i 0.657010 0.657010i −0.297661 0.954672i 0.596207π-0.596207\pi
0.954672 + 0.297661i 0.0962066π0.0962066\pi
224224 −647.067 + 460.917i −0.193009 + 0.137483i
225225 2760.98 + 1480.00i 0.818067 + 0.438517i
226226 −896.474 + 2475.48i −0.263861 + 0.728613i
227227 4010.25 + 1661.10i 1.17255 + 0.485688i 0.882036 0.471182i 0.156172π-0.156172\pi
0.290518 + 0.956870i 0.406172π0.406172\pi
228228 699.926 839.634i 0.203306 0.243887i
229229 −84.3136 34.9238i −0.0243301 0.0100779i 0.370485 0.928838i 0.379191π-0.379191\pi
−0.394815 + 0.918761i 0.629191π0.629191\pi
230230 −3401.40 5139.74i −0.975139 1.47350i
231231 78.8539 78.8539i 0.0224598 0.0224598i
232232 3153.31 430.702i 0.892349 0.121883i
233233 −2349.23 −0.660528 −0.330264 0.943889i 0.607138π-0.607138\pi
−0.330264 + 0.943889i 0.607138π0.607138\pi
234234 −1300.51 + 1423.87i −0.363321 + 0.397784i
235235 1302.37 1753.87i 0.361521 0.486849i
236236 3149.89 + 6003.43i 0.868814 + 1.65589i
237237 −460.770 190.857i −0.126288 0.0523101i
238238 −520.559 + 1437.45i −0.141777 + 0.391495i
239239 2812.35i 0.761154i 0.924749 + 0.380577i 0.124275π0.124275\pi
−0.924749 + 0.380577i 0.875725π0.875725\pi
240240 994.260 + 64.7534i 0.267413 + 0.0174159i
241241 5243.52i 1.40151i −0.713400 0.700757i 0.752846π-0.752846\pi
0.713400 0.700757i 0.247154π-0.247154\pi
242242 −2654.12 961.167i −0.705013 0.255315i
243243 2548.95 + 1055.81i 0.672902 + 0.278725i
244244 1477.85 4740.52i 0.387745 1.24377i
245245 −3580.65 + 528.964i −0.933712 + 0.137936i
246246 1136.05 + 1037.63i 0.294439 + 0.268930i
247247 2669.57 0.687696
248248 6553.08 + 1721.89i 1.67791 + 0.440887i
249249 62.5483 62.5483i 0.0159190 0.0159190i
250250 2524.80 3041.45i 0.638729 0.769432i
251251 519.263 + 215.086i 0.130580 + 0.0540880i 0.447017 0.894526i 0.352486π-0.352486\pi
−0.316437 + 0.948614i 0.602486π0.602486\pi
252252 79.5195 + 876.287i 0.0198780 + 0.219051i
253253 −3285.83 1361.04i −0.816516 0.338212i
254254 −3610.44 1307.49i −0.891886 0.322989i
255255 1645.17 984.751i 0.404019 0.241833i
256256 −3830.55 + 1450.55i −0.935193 + 0.354138i
257257 811.327 811.327i 0.196923 0.196923i −0.601757 0.798679i 0.705532π-0.705532\pi
0.798679 + 0.601757i 0.205532π0.205532\pi
258258 −33.9003 72.3939i −0.00818040 0.0174692i
259259 −542.451 + 224.691i −0.130140 + 0.0539058i
260260 1433.31 + 1966.38i 0.341885 + 0.469038i
261261 1348.91 3256.57i 0.319907 0.772324i
262262 3738.33 + 3414.46i 0.881508 + 0.805137i
263263 −4405.00 −1.03279 −0.516396 0.856350i 0.672727π-0.672727\pi
−0.516396 + 0.856350i 0.672727π0.672727\pi
264264 496.527 289.888i 0.115754 0.0675811i
265265 2051.00 + 3426.51i 0.475442 + 0.794297i
266266 821.462 899.382i 0.189350 0.207311i
267267 −473.218 1142.45i −0.108466 0.261860i
268268 −5779.63 + 3032.46i −1.31734 + 0.691183i
269269 −4183.57 + 1732.89i −0.948241 + 0.392774i −0.802569 0.596559i 0.796534π-0.796534\pi
−0.145671 + 0.989333i 0.546534π0.546534\pi
270270 1282.05 1900.43i 0.288973 0.428356i
271271 −2858.16 −0.640667 −0.320333 0.947305i 0.603795π-0.603795\pi
−0.320333 + 0.947305i 0.603795π0.603795\pi
272272 −4479.23 + 6485.82i −0.998504 + 1.44581i
273273 117.560 117.560i 0.0260626 0.0260626i
274274 −838.389 1790.37i −0.184850 0.394746i
275275 226.277 2269.75i 0.0496182 0.497713i
276276 −1922.58 + 1008.74i −0.419296 + 0.219997i
277277 −2133.15 + 883.582i −0.462703 + 0.191658i −0.601842 0.798615i 0.705566π-0.705566\pi
0.139139 + 0.990273i 0.455566π0.455566\pi
278278 2113.06 95.6792i 0.455874 0.0206419i
279279 5306.30 5306.30i 1.13864 1.13864i
280280 1103.52 + 122.197i 0.235529 + 0.0260810i
281281 −3977.03 3977.03i −0.844305 0.844305i 0.145110 0.989416i 0.453646π-0.453646\pi
−0.989416 + 0.145110i 0.953646π0.953646\pi
282282 −568.208 518.980i −0.119987 0.109592i
283283 2664.72 + 6433.20i 0.559721 + 1.35129i 0.909987 + 0.414636i 0.136091π0.136091\pi
−0.350266 + 0.936650i 0.613909π0.613909\pi
284284 289.259 + 3187.57i 0.0604379 + 0.666012i
285285 −1511.26 + 223.256i −0.314103 + 0.0464019i
286286 1320.25 + 478.116i 0.272964 + 0.0988517i
287287 1212.32 + 1212.32i 0.249342 + 0.249342i
288288 −751.641 + 4473.83i −0.153788 + 0.915358i
289289 10255.3i 2.08738i
290290 −3687.22 2487.44i −0.746625 0.503680i
291291 −563.008 1359.22i −0.113416 0.273811i
292292 −2504.37 + 3004.26i −0.501908 + 0.602092i
293293 5022.19 2080.26i 1.00136 0.414778i 0.179066 0.983837i 0.442692π-0.442692\pi
0.822297 + 0.569059i 0.192692π0.192692\pi
294294 57.6747 + 1273.74i 0.0114410 + 0.252673i
295295 2307.65 9189.46i 0.455445 1.81366i
296296 −2999.36 + 409.674i −0.588967 + 0.0804453i
297297 1322.86i 0.258451i
298298 −66.1194 1460.24i −0.0128530 0.283856i
299299 −4898.73 2029.12i −0.947494 0.392465i
300300 −975.853 993.312i −0.187803 0.191163i
301301 −34.0881 82.2960i −0.00652759 0.0157590i
302302 −669.271 242.371i −0.127524 0.0461817i
303303 −239.867 239.867i −0.0454785 0.0454785i
304304 5274.68 3408.47i 0.995144 0.643057i
305305 −5954.37 + 3564.10i −1.11786 + 0.669114i
306306 3702.22 + 7906.06i 0.691640 + 1.47699i
307307 −657.943 + 1588.41i −0.122315 + 0.295295i −0.973163 0.230117i 0.926089π-0.926089\pi
0.850848 + 0.525412i 0.176089π0.176089\pi
308308 567.334 297.670i 0.104957 0.0550692i
309309 −458.136 + 1106.04i −0.0843444 + 0.203625i
310310 −5225.79 7896.50i −0.957435 1.44674i
311311 −4402.87 4402.87i −0.802778 0.802778i 0.180751 0.983529i 0.442147π-0.442147\pi
−0.983529 + 0.180751i 0.942147π0.942147\pi
312312 740.255 432.184i 0.134323 0.0784218i
313313 10630.6i 1.91974i −0.280448 0.959869i 0.590483π-0.590483\pi
0.280448 0.959869i 0.409517π-0.409517\pi
314314 348.415 + 7694.69i 0.0626185 + 1.38292i
315315 733.107 987.253i 0.131130 0.176589i
316316 −2200.91 1834.69i −0.391806 0.326613i
317317 270.066 651.998i 0.0478500 0.115520i −0.898147 0.439695i 0.855087π-0.855087\pi
0.945997 + 0.324175i 0.105087π0.105087\pi
318318 1274.00 596.584i 0.224662 0.105204i
319319 −2566.62 −0.450480
320320 5342.65 + 2055.25i 0.933323 + 0.359037i
321321 1952.78 0.339544
322322 −2191.01 + 1026.00i −0.379194 + 0.177568i
323323 4624.83 11165.3i 0.796696 1.92339i
324324 3537.67 + 2949.03i 0.606596 + 0.505663i
325325 337.348 3383.89i 0.0575775 0.577552i
326326 −17.8233 393.625i −0.00302804 0.0668738i
327327 1055.40i 0.178482i
328328 4456.84 + 7633.77i 0.750268 + 1.28508i
329329 −606.357 606.357i −0.101610 0.101610i
330330 −787.384 160.252i −0.131346 0.0267321i
331331 −1170.83 + 2826.63i −0.194424 + 0.469382i −0.990786 0.135439i 0.956755π-0.956755\pi
0.796361 + 0.604821i 0.206755π0.206755\pi
332332 450.020 236.117i 0.0743917 0.0390320i
333333 −1283.06 + 3097.57i −0.211144 + 0.509748i
334334 244.208 + 521.505i 0.0400075 + 0.0854356i
335335 8846.88 + 2221.62i 1.44286 + 0.362329i
336336 82.1827 382.381i 0.0133435 0.0620851i
337337 −2095.81 2095.81i −0.338771 0.338771i 0.517133 0.855905i 0.326999π-0.326999\pi
−0.855905 + 0.517133i 0.826999π0.826999\pi
338338 −3874.42 1403.09i −0.623493 0.225793i
339339 −496.018 1197.49i −0.0794691 0.191855i
340340 10707.4 2588.13i 1.70791 0.412827i
341341 −5048.23 2091.04i −0.801692 0.332072i
342342 −314.625 6948.45i −0.0497456 1.09862i
343343 2926.13i 0.460631i
344344 −62.1521 455.036i −0.00974133 0.0713195i
345345 2942.89 + 739.016i 0.459246 + 0.115325i
346346 −315.699 6972.15i −0.0490522 1.08331i
347347 5881.56 2436.22i 0.909909 0.376897i 0.121887 0.992544i 0.461105π-0.461105\pi
0.788022 + 0.615647i 0.211105π0.211105\pi
348348 −1003.25 + 1203.50i −0.154540 + 0.185387i
349349 1022.77 + 2469.20i 0.156871 + 0.378719i 0.982701 0.185199i 0.0592931π-0.0592931\pi
−0.825830 + 0.563919i 0.809293π0.809293\pi
350350 −1036.23 1154.92i −0.158254 0.176380i
351351 1972.20i 0.299909i
352352 3219.06 740.984i 0.487434 0.112200i
353353 −2600.94 2600.94i −0.392164 0.392164i 0.483294 0.875458i 0.339440π-0.339440\pi
−0.875458 + 0.483294i 0.839440π0.839440\pi
354354 −3138.22 1136.48i −0.471171 0.170631i
355355 2666.74 3591.22i 0.398692 0.536907i
356356 −642.057 7075.33i −0.0955870 1.05335i
357357 −288.025 695.354i −0.0427000 0.103087i
358358 −733.161 669.642i −0.108237 0.0988595i
359359 380.108 + 380.108i 0.0558812 + 0.0558812i 0.734495 0.678614i 0.237419π-0.237419\pi
−0.678614 + 0.734495i 0.737419π0.737419\pi
360360 4949.23 3962.41i 0.724576 0.580104i
361361 −1958.61 + 1958.61i −0.285554 + 0.285554i
362362 5178.79 234.495i 0.751909 0.0340464i
363363 1283.91 531.813i 0.185641 0.0768951i
364364 845.819 443.785i 0.121794 0.0639029i
365365 5407.37 798.822i 0.775438 0.114554i
366366 1036.71 + 2213.88i 0.148059 + 0.316178i
367367 1761.24 1761.24i 0.250507 0.250507i −0.570672 0.821178i 0.693317π-0.693317\pi
0.821178 + 0.570672i 0.193317π0.193317\pi
368368 −12269.9 + 2245.38i −1.73808 + 0.318067i
369369 9790.28 1.38120
370370 3507.20 + 2365.99i 0.492786 + 0.332438i
371371 1448.26 599.888i 0.202668 0.0839478i
372372 −2953.78 + 1549.79i −0.411683 + 0.216002i
373373 3327.94 + 8034.36i 0.461969 + 1.11529i 0.967588 + 0.252534i 0.0812641π0.0812641\pi
−0.505619 + 0.862757i 0.668736π0.668736\pi
374374 4286.92 4693.55i 0.592704 0.648925i
375375 92.0197 + 1943.85i 0.0126717 + 0.267680i
376376 −2229.13 3818.11i −0.305742 0.523681i
377377 −3826.48 −0.522742
378378 −664.436 606.871i −0.0904098 0.0825769i
379379 −1500.77 + 3623.17i −0.203402 + 0.491055i −0.992358 0.123395i 0.960622π-0.960622\pi
0.788956 + 0.614450i 0.210622π0.210622\pi
380380 −8670.80 1359.58i −1.17053 0.183539i
381381 1746.52 723.433i 0.234848 0.0972771i
382382 −827.427 1766.96i −0.110824 0.236664i
383383 2216.63 2216.63i 0.295730 0.295730i −0.543609 0.839339i 0.682942π-0.682942\pi
0.839339 + 0.543609i 0.182942π0.182942\pi
384384 910.828 1799.08i 0.121043 0.239085i
385385 −868.420 218.077i −0.114958 0.0288681i
386386 −4063.51 1471.57i −0.535822 0.194043i
387387 −469.937 194.654i −0.0617267 0.0255680i
388388 −763.884 8417.83i −0.0999493 1.10142i
389389 14139.1 + 5856.61i 1.84288 + 0.763347i 0.949226 + 0.314596i 0.101869π0.101869\pi
0.893657 + 0.448751i 0.148131π0.148131\pi
390390 −1173.88 238.914i −0.152415 0.0310202i
391391 −16973.3 + 16973.3i −2.19534 + 2.19534i
392392 −1861.63 + 7084.88i −0.239863 + 0.912858i
393393 −2492.55 −0.319931
394394 4747.90 + 4336.56i 0.607096 + 0.554499i
395395 585.215 + 3961.43i 0.0745452 + 0.504610i
396396 1088.86 3492.72i 0.138174 0.443222i
397397 −2906.41 1203.87i −0.367427 0.152193i 0.191328 0.981526i 0.438721π-0.438721\pi
−0.558755 + 0.829333i 0.688721π0.688721\pi
398398 13299.1 + 4816.17i 1.67494 + 0.606565i
399399 599.668i 0.0752404i
400400 −3653.95 7116.79i −0.456744 0.889598i
401401 3501.36i 0.436034i 0.975945 + 0.218017i 0.0699588π0.0699588\pi
−0.975945 + 0.218017i 0.930041π0.930041\pi
402402 1094.11 3021.23i 0.135745 0.374839i
403403 −7526.22 3117.46i −0.930292 0.385340i
404404 −905.487 1725.78i −0.111509 0.212527i
405405 −940.654 6367.46i −0.115411 0.781239i
406406 −1177.46 + 1289.14i −0.143932 + 0.157584i
407407 2441.31 0.297325
408408 −525.150 3844.80i −0.0637226 0.466534i
409409 −2554.77 + 2554.77i −0.308864 + 0.308864i −0.844469 0.535605i 0.820084π-0.820084\pi
0.535605 + 0.844469i 0.320084π0.320084\pi
410410 2463.77 12105.5i 0.296773 1.45816i
411411 899.187 + 372.455i 0.107916 + 0.0447004i
412412 −4404.02 + 5283.09i −0.526628 + 0.631745i
413413 −3436.11 1423.28i −0.409395 0.169577i
414414 −4704.11 + 12989.7i −0.558440 + 1.54205i
415415 −688.846 172.982i −0.0814798 0.0204611i
416416 4799.18 1104.71i 0.565624 0.130199i
417417 −736.344 + 736.344i −0.0864722 + 0.0864722i
418418 −4586.66 + 2147.83i −0.536701 + 0.251324i
419419 −3963.99 + 1641.94i −0.462181 + 0.191442i −0.601609 0.798791i 0.705474π-0.705474\pi
0.139428 + 0.990232i 0.455474π0.455474\pi
420420 −441.709 + 321.965i −0.0513171 + 0.0374054i
421421 2849.62 6879.60i 0.329886 0.796416i −0.668714 0.743520i 0.733155π-0.733155\pi
0.998600 0.0528961i 0.0168452π-0.0168452\pi
422422 221.483 242.492i 0.0255489 0.0279723i
423423 −4896.71 −0.562852
424424 8007.81 1093.76i 0.917202 0.125278i
425425 −13568.5 7273.27i −1.54863 0.830130i
426426 −1163.46 1062.66i −0.132324 0.120860i
427427 1042.45 + 2516.69i 0.118144 + 0.285225i
428428 10710.7 + 3339.06i 1.20963 + 0.377102i
429429 −638.659 + 264.541i −0.0718759 + 0.0297720i
430430 −358.948 + 532.082i −0.0402558 + 0.0596728i
431431 16102.3 1.79958 0.899789 0.436325i 0.143720π-0.143720\pi
0.899789 + 0.436325i 0.143720π0.143720\pi
432432 −2518.07 3896.77i −0.280442 0.433990i
433433 −10666.3 + 10666.3i −1.18381 + 1.18381i −0.205062 + 0.978749i 0.565740π0.565740\pi
−0.978749 + 0.205062i 0.934260π0.934260\pi
434434 −3366.19 + 1576.31i −0.372310 + 0.174344i
435435 2166.19 320.008i 0.238761 0.0352717i
436436 −1804.63 + 5788.72i −0.198225 + 0.635847i
437437 17669.2 7318.84i 1.93417 0.801161i
438438 −87.0983 1923.55i −0.00950163 0.209842i
439439 −7409.97 + 7409.97i −0.805601 + 0.805601i −0.983965 0.178364i 0.942920π-0.942920\pi
0.178364 + 0.983965i 0.442920π0.442920\pi
440440 −4044.67 2225.31i −0.438232 0.241108i
441441 5736.93 + 5736.93i 0.619472 + 0.619472i
442442 6391.21 6997.45i 0.687781 0.753020i
443443 1271.21 + 3068.97i 0.136336 + 0.329144i 0.977272 0.211991i 0.0679947π-0.0679947\pi
−0.840936 + 0.541135i 0.817995π0.817995\pi
444444 954.269 1144.75i 0.101999 0.122359i
445445 −5919.26 + 7971.29i −0.630561 + 0.849158i
446446 −2979.95 + 8228.68i −0.316378 + 0.873630i
447447 508.853 + 508.853i 0.0538432 + 0.0538432i
448448 1104.59 1956.78i 0.116489 0.206360i
449449 9677.29i 1.01715i 0.861018 + 0.508574i 0.169827π0.169827\pi
−0.861018 + 0.508574i 0.830173π0.830173\pi
450450 −8847.45 479.247i −0.926828 0.0502043i
451451 −2728.04 6586.08i −0.284830 0.687642i
452452 −672.993 7416.23i −0.0700330 0.771748i
453453 323.755 134.104i 0.0335791 0.0139089i
454454 −12264.7 + 555.344i −1.26786 + 0.0574088i
455455 −1294.70 325.123i −0.133398 0.0334989i
456456 −785.724 + 2990.27i −0.0806905 + 0.307088i
457457 3725.75i 0.381364i −0.981652 0.190682i 0.938930π-0.938930\pi
0.981652 0.190682i 0.0610699π-0.0610699\pi
458458 257.859 11.6758i 0.0263078 0.00119121i
459459 −8248.61 3416.69i −0.838806 0.347445i
460460 14877.7 + 9085.46i 1.50799 + 0.920895i
461461 1245.99 + 3008.08i 0.125881 + 0.303905i 0.974239 0.225520i 0.0724080π-0.0724080\pi
−0.848357 + 0.529424i 0.822408π0.822408\pi
462462 −107.399 + 296.567i −0.0108153 + 0.0298649i
463463 9723.04 + 9723.04i 0.975957 + 0.975957i 0.999718 0.0237606i 0.00756395π-0.00756395\pi
−0.0237606 + 0.999718i 0.507564π0.507564\pi
464464 −7560.56 + 4885.59i −0.756444 + 0.488810i
465465 4521.35 + 1135.40i 0.450909 + 0.113232i
466466 6017.53 2817.87i 0.598190 0.280118i
467467 −2481.47 + 5990.80i −0.245886 + 0.593621i −0.997847 0.0655865i 0.979108π-0.979108\pi
0.751961 + 0.659208i 0.229108π0.229108\pi
468468 1623.34 5207.18i 0.160339 0.514320i
469469 1370.23 3308.02i 0.134906 0.325693i
470470 −1232.28 + 6054.69i −0.120938 + 0.594217i
471471 −2681.39 2681.39i −0.262318 0.262318i
472472 −15269.4 11599.5i −1.48905 1.13116i
473473 370.374i 0.0360039i
474474 1409.19 63.8080i 0.136553 0.00618311i
475475 7770.10 + 9490.89i 0.750562 + 0.916783i
476476 −390.789 4306.41i −0.0376298 0.414672i
477477 3425.56 8270.03i 0.328817 0.793833i
478478 −3373.37 7203.81i −0.322792 0.689319i
479479 11217.1 1.06999 0.534993 0.844856i 0.320314π-0.320314\pi
0.534993 + 0.844856i 0.320314π0.320314\pi
480480 −2624.46 + 1026.74i −0.249562 + 0.0976330i
481481 3639.66 0.345019
482482 6289.52 + 13431.2i 0.594357 + 1.26924i
483483 455.802 1100.40i 0.0429394 0.103665i
484484 7951.41 721.558i 0.746751 0.0677647i
485485 −7042.41 + 9483.80i −0.659339 + 0.887911i
486486 −7795.54 + 352.982i −0.727598 + 0.0329456i
487487 8810.28i 0.819778i 0.912135 + 0.409889i 0.134433π0.134433\pi
−0.912135 + 0.409889i 0.865567π0.865567\pi
488488 1900.67 + 13915.5i 0.176310 + 1.29083i
489489 137.167 + 137.167i 0.0126849 + 0.0126849i
490490 8537.32 5649.88i 0.787096 0.520889i
491491 −5828.62 + 14071.5i −0.535727 + 1.29336i 0.391954 + 0.919985i 0.371799π0.371799\pi
−0.927681 + 0.373375i 0.878201π0.878201\pi
492492 −4154.60 1295.20i −0.380699 0.118683i
493493 −6629.08 + 16004.0i −0.605596 + 1.46204i
494494 −6838.09 + 3202.12i −0.622794 + 0.291640i
495495 −4387.07 + 2625.96i −0.398352 + 0.238441i
496496 −18851.0 + 3449.72i −1.70652 + 0.312292i
497497 −1241.58 1241.58i −0.112057 0.112057i
498498 −85.1911 + 235.243i −0.00766567 + 0.0211676i
499499 −7242.18 17484.2i −0.649709 1.56854i −0.813196 0.581990i 0.802274π-0.802274\pi
0.163487 0.986545i 0.447726π-0.447726\pi
500500 −2819.08 + 10819.1i −0.252146 + 0.967689i
501501 −261.918 108.490i −0.0233565 0.00967460i
502502 −1588.08 + 71.9082i −0.141194 + 0.00639326i
503503 2667.87i 0.236490i 0.992984 + 0.118245i 0.0377268π0.0377268\pi
−0.992984 + 0.118245i 0.962273π0.962273\pi
504504 −1254.78 2149.22i −0.110898 0.189948i
505505 −663.371 + 2641.66i −0.0584547 + 0.232777i
506506 10049.2 455.026i 0.882886 0.0399770i
507507 1874.22 776.327i 0.164176 0.0680038i
508508 10816.4 981.546i 0.944687 0.0857265i
509509 −2186.69 5279.15i −0.190419 0.459713i 0.799619 0.600507i 0.205035π-0.205035\pi
−0.990039 + 0.140794i 0.955035π0.955035\pi
510510 −3032.91 + 4495.79i −0.263332 + 0.390347i
511511 2145.64i 0.185749i
512512 8072.01 8310.26i 0.696749 0.717315i
513513 5030.03 + 5030.03i 0.432907 + 0.432907i
514514 −1105.03 + 3051.38i −0.0948265 + 0.261849i
515515 9509.05 1404.76i 0.813629 0.120196i
516516 173.671 + 144.773i 0.0148167 + 0.0123513i
517517 1364.46 + 3294.10i 0.116071 + 0.280221i
518518 1119.97 1226.20i 0.0949974 0.104008i
519519 2429.61 + 2429.61i 0.205487 + 0.205487i
520520 −6030.06 3317.63i −0.508530 0.279784i
521521 10176.2 10176.2i 0.855713 0.855713i −0.135117 0.990830i 0.543141π-0.543141\pi
0.990830 + 0.135117i 0.0431409π0.0431409\pi
522522 450.973 + 9959.67i 0.0378133 + 0.835101i
523523 1426.49 590.871i 0.119266 0.0494015i −0.322253 0.946654i 0.604440π-0.604440\pi
0.441518 + 0.897252i 0.354440π0.354440\pi
524524 −13671.3 4262.02i −1.13976 0.355319i
525525 760.125 + 75.7786i 0.0631896 + 0.00629952i
526526 11283.4 5283.74i 0.935320 0.437988i
527527 −26077.2 + 26077.2i −2.15549 + 2.15549i
528528 −924.133 + 1338.12i −0.0761700 + 0.110292i
529529 −25819.4 −2.12209
530530 −9363.67 6316.83i −0.767419 0.517708i
531531 −19621.3 + 8127.42i −1.60357 + 0.664218i
532532 −1025.37 + 3289.09i −0.0835630 + 0.268045i
533533 −4067.14 9818.95i −0.330521 0.797947i
534534 2582.49 + 2358.75i 0.209280 + 0.191148i
535535 −8052.72 13453.3i −0.650747 1.08717i
536536 11167.1 14700.2i 0.899895 1.18461i
537537 488.839 0.0392830
538538 8637.60 9456.92i 0.692181 0.757837i
539539 2260.74 5457.91i 0.180662 0.436157i
540540 −1004.42 + 6405.72i −0.0800429 + 0.510478i
541541 −4024.70 + 1667.09i −0.319844 + 0.132484i −0.536829 0.843691i 0.680378π-0.680378\pi
0.216985 + 0.976175i 0.430378π0.430378\pi
542542 7321.14 3428.32i 0.580203 0.271695i
543543 −1804.67 + 1804.67i −0.142626 + 0.142626i
544544 3693.85 21986.1i 0.291126 1.73281i
545545 7270.97 4352.18i 0.571475 0.342067i
546546 −160.118 + 442.142i −0.0125502 + 0.0346555i
547547 −7683.09 3182.44i −0.600558 0.248759i 0.0616277 0.998099i 0.480371π-0.480371\pi
−0.662185 + 0.749340i 0.730371π0.730371\pi
548548 4295.05 + 3580.39i 0.334809 + 0.279099i
549549 14371.1 + 5952.71i 1.11720 + 0.462761i
550550 2142.93 + 6085.36i 0.166136 + 0.471783i
551551 9759.30 9759.30i 0.754556 0.754556i
552552 3714.70 4889.98i 0.286427 0.377050i
553553 1571.89 0.120875
554554 4404.21 4821.97i 0.337756 0.369794i
555555 −2060.43 + 304.384i −0.157586 + 0.0232800i
556556 −5297.82 + 2779.67i −0.404096 + 0.212022i
557557 10501.9 + 4350.01i 0.798883 + 0.330908i 0.744509 0.667612i 0.232684π-0.232684\pi
0.0543741 + 0.998521i 0.482684π0.482684\pi
558558 −7227.21 + 19956.9i −0.548302 + 1.51405i
559559 552.178i 0.0417793i
560560 −2973.24 + 1010.65i −0.224361 + 0.0762641i
561561 3129.45i 0.235518i
562562 14957.5 + 5416.74i 1.12268 + 0.406568i
563563 23610.3 + 9779.70i 1.76742 + 0.732087i 0.995326 + 0.0965736i 0.0307883π0.0307883\pi
0.772089 + 0.635514i 0.219212π0.219212\pi
564564 2077.97 + 647.806i 0.155139 + 0.0483644i
565565 −6204.46 + 8355.36i −0.461989 + 0.622146i
566566 −14542.2 13282.3i −1.07995 0.986389i
567567 −2526.60 −0.187138
568568 −4564.38 7817.96i −0.337178 0.577525i
569569 14640.3 14640.3i 1.07865 1.07865i 0.0820220 0.996631i 0.473862π-0.473862\pi
0.996631 0.0820220i 0.0261378π-0.0261378\pi
570570 3603.29 2384.60i 0.264781 0.175228i
571571 9537.59 + 3950.60i 0.699012 + 0.289540i 0.703749 0.710449i 0.251508π-0.251508\pi
−0.00473738 + 0.999989i 0.501508π0.501508\pi
572572 −3955.29 + 358.927i −0.289124 + 0.0262369i
573573 887.431 + 367.586i 0.0646997 + 0.0267995i
574574 −4559.52 1651.19i −0.331552 0.120069i
575575 −7044.37 23322.0i −0.510905 1.69147i
576576 −3440.97 12361.3i −0.248913 0.894188i
577577 5329.12 5329.12i 0.384496 0.384496i −0.488223 0.872719i 0.662355π-0.662355\pi
0.872719 + 0.488223i 0.162355π0.162355\pi
578578 −12301.1 26268.8i −0.885220 1.89038i
579579 1965.69 814.216i 0.141090 0.0584416i
580580 12428.4 + 1948.78i 0.889763 + 0.139515i
581581 −106.690 + 257.573i −0.00761833 + 0.0183923i
582582 3072.51 + 2806.32i 0.218831 + 0.199872i
583583 −6517.91 −0.463026
584584 2811.36 10699.3i 0.199204 0.758119i
585585 −6540.52 + 3914.95i −0.462252 + 0.276690i
586586 −10369.0 + 11352.6i −0.730958 + 0.800293i
587587 −7340.17 17720.7i −0.516118 1.24602i −0.940271 0.340428i 0.889428π-0.889428\pi
0.424153 0.905591i 0.360572π-0.360572\pi
588588 −1675.56 3193.48i −0.117515 0.223975i
589589 27146.4 11244.4i 1.89906 0.786616i
590590 5111.60 + 26306.7i 0.356680 + 1.83564i
591591 −3165.69 −0.220337
592592 7191.43 4647.06i 0.499267 0.322623i
593593 6821.87 6821.87i 0.472413 0.472413i −0.430282 0.902695i 0.641586π-0.641586\pi
0.902695 + 0.430282i 0.141586π0.141586\pi
594594 1586.75 + 3388.48i 0.109604 + 0.234059i
595595 −3602.77 + 4851.74i −0.248234 + 0.334289i
596596 1920.90 + 3661.07i 0.132018 + 0.251616i
597597 −6433.36 + 2664.78i −0.441038 + 0.182684i
598598 14981.9 678.382i 1.02451 0.0463898i
599599 −4493.46 + 4493.46i −0.306507 + 0.306507i −0.843553 0.537046i 0.819540π-0.819540\pi
0.537046 + 0.843553i 0.319540π0.319540\pi
600600 3691.10 + 1373.84i 0.251148 + 0.0934778i
601601 −2816.44 2816.44i −0.191157 0.191157i 0.605039 0.796196i 0.293157π-0.293157\pi
−0.796196 + 0.605039i 0.793157π0.793157\pi
602602 186.029 + 169.912i 0.0125947 + 0.0115035i
603603 −7824.44 18889.9i −0.528417 1.27571i
604604 2005.05 181.950i 0.135074 0.0122574i
605605 −8958.31 6652.19i −0.601995 0.447025i
606606 902.133 + 326.700i 0.0604730 + 0.0218998i
607607 9851.85 + 9851.85i 0.658772 + 0.658772i 0.955089 0.296318i 0.0957587π-0.0957587\pi
−0.296318 + 0.955089i 0.595759π0.595759\pi
608608 −9422.64 + 15057.7i −0.628517 + 1.00439i
609609 859.544i 0.0571929i
610610 10977.0 16271.6i 0.728598 1.08003i
611611 2034.22 + 4911.05i 0.134690 + 0.325172i
612612 −18966.4 15810.5i −1.25273 1.04429i
613613 26460.6 10960.3i 1.74345 0.722159i 0.744963 0.667106i 0.232467π-0.232467\pi
0.998483 0.0550534i 0.0175329π-0.0175329\pi
614614 −219.966 4857.90i −0.0144578 0.319298i
615615 3123.59 + 5218.43i 0.204805 + 0.342158i
616616 −1096.17 + 1442.99i −0.0716981 + 0.0943825i
617617 3562.11i 0.232423i −0.993224 0.116211i 0.962925π-0.962925\pi
0.993224 0.116211i 0.0370750π-0.0370750\pi
618618 −153.165 3382.63i −0.00996960 0.220177i
619619 −18858.4 7811.41i −1.22453 0.507217i −0.325682 0.945479i 0.605594π-0.605594\pi
−0.898847 + 0.438263i 0.855594π0.855594\pi
620620 22857.5 + 13958.6i 1.48061 + 0.904176i
621621 −5406.93 13053.5i −0.349392 0.843508i
622622 16559.1 + 5996.73i 1.06746 + 0.386571i
623623 2755.88 + 2755.88i 0.177226 + 0.177226i
624624 −1377.76 + 1994.96i −0.0883885 + 0.127985i
625625 13012.3 8649.86i 0.832789 0.553591i
626626 12751.3 + 27230.2i 0.814127 + 1.73856i
627627 954.174 2303.58i 0.0607752 0.146724i
628628 −10122.1 19292.0i −0.643180 1.22585i
629629 6305.43 15222.7i 0.399704 0.964972i
630630 −693.651 + 3408.19i −0.0438662 + 0.215533i
631631 7732.51 + 7732.51i 0.487839 + 0.487839i 0.907624 0.419785i 0.137894π-0.137894\pi
−0.419785 + 0.907624i 0.637894π0.637894\pi
632632 7838.30 + 2059.59i 0.493340 + 0.129630i
633633 161.683i 0.0101522i
634634 90.2895 + 1994.03i 0.00565592 + 0.124910i
635635 −12186.1 9049.08i −0.761561 0.565515i
636636 −2547.75 + 3056.29i −0.158844 + 0.190550i
637637 3370.46 8137.00i 0.209643 0.506122i
638638 6574.37 3078.62i 0.407965 0.191040i
639639 −10026.5 −0.620723
640640 −16150.4 + 1143.93i −0.997501 + 0.0706528i
641641 10687.2 0.658534 0.329267 0.944237i 0.393198π-0.393198\pi
0.329267 + 0.944237i 0.393198π0.393198\pi
642642 −5002.03 + 2342.33i −0.307499 + 0.143994i
643643 5562.66 13429.4i 0.341166 0.823648i −0.656432 0.754385i 0.727935π-0.727935\pi
0.997598 0.0692630i 0.0220648π-0.0220648\pi
644644 4381.59 5256.18i 0.268104 0.321619i
645645 −46.1785 312.591i −0.00281904 0.0190826i
646646 1546.19 + 34147.3i 0.0941703 + 2.07973i
647647 6534.02i 0.397031i 0.980098 + 0.198515i 0.0636120π0.0636120\pi
−0.980098 + 0.198515i 0.936388π0.936388\pi
648648 −12599.0 3310.52i −0.763790 0.200694i
649649 10934.9 + 10934.9i 0.661375 + 0.661375i
650650 3194.81 + 9072.45i 0.192786 + 0.547463i
651651 700.277 1690.62i 0.0421598 0.101783i
652652 517.801 + 986.887i 0.0311022 + 0.0592783i
653653 −1572.19 + 3795.61i −0.0942186 + 0.227464i −0.963962 0.266041i 0.914284π-0.914284\pi
0.869743 + 0.493505i 0.164284π0.164284\pi
654654 −1265.94 2703.40i −0.0756912 0.161638i
655655 10278.6 + 17172.0i 0.613158 + 1.02437i
656656 −20572.8 14207.9i −1.22444 0.845619i
657657 −8663.70 8663.70i −0.514464 0.514464i
658658 2280.49 + 825.861i 0.135111 + 0.0489292i
659659 −9693.56 23402.3i −0.573000 1.38335i −0.898989 0.437972i 0.855697π-0.855697\pi
0.325988 0.945374i 0.394303π-0.394303\pi
660660 2209.10 533.971i 0.130286 0.0314921i
661661 21979.2 + 9104.09i 1.29333 + 0.535716i 0.919977 0.391973i 0.128207π-0.128207\pi
0.373355 + 0.927688i 0.378207π0.378207\pi
662662 −391.434 8644.76i −0.0229812 0.507535i
663663 4665.59i 0.273298i
664664 −869.503 + 1144.60i −0.0508182 + 0.0668965i
665665 4131.29 2472.86i 0.240909 0.144201i
666666 −428.956 9473.41i −0.0249575 0.551182i
667667 −25326.5 + 10490.6i −1.47023 + 0.608991i
668668 −1251.08 1042.91i −0.0724634 0.0604060i
669669 −1648.80 3980.56i −0.0952860 0.230041i
670670 −25326.0 + 4921.05i −1.46034 + 0.283756i
671671 11326.4i 0.651641i
672672 248.151 + 1078.04i 0.0142450 + 0.0618845i
673673 1163.20 + 1163.20i 0.0666242 + 0.0666242i 0.739634 0.673010i 0.234999π-0.234999\pi
−0.673010 + 0.739634i 0.734999π0.734999\pi
674674 7882.28 + 2854.50i 0.450466 + 0.163132i
675675 7011.58 5740.31i 0.399816 0.327326i
676676 11607.3 1053.31i 0.660405 0.0599291i
677677 −1872.95 4521.71i −0.106327 0.256696i 0.861757 0.507321i 0.169364π-0.169364\pi
−0.968084 + 0.250625i 0.919364π0.919364\pi
678678 2706.92 + 2472.40i 0.153331 + 0.140047i
679679 3278.79 + 3278.79i 0.185315 + 0.185315i
680680 −24322.4 + 19472.8i −1.37165 + 1.09816i
681681 4273.91 4273.91i 0.240494 0.240494i
682682 15439.2 699.085i 0.866857 0.0392512i
683683 11049.7 4576.96i 0.619044 0.256416i −0.0510461 0.998696i 0.516256π-0.516256\pi
0.670090 + 0.742280i 0.266256π0.266256\pi
684684 9140.47 + 17421.0i 0.510957 + 0.973842i
685685 −1142.04 7730.68i −0.0637009 0.431203i
686686 −3509.85 7495.26i −0.195345 0.417158i
687687 −89.8569 + 89.8569i −0.00499018 + 0.00499018i
688688 705.012 + 1091.02i 0.0390673 + 0.0604575i
689689 −9717.31 −0.537301
690690 −8424.63 + 1636.97i −0.464812 + 0.0903167i
691691 10285.8 4260.53i 0.566269 0.234556i −0.0811353 0.996703i 0.525855π-0.525855\pi
0.647404 + 0.762147i 0.275855π0.275855\pi
692692 9171.66 + 17480.4i 0.503835 + 0.960269i
693693 768.055 + 1854.25i 0.0421010 + 0.101641i
694694 −12143.3 + 13295.2i −0.664200 + 0.727203i
695695 8109.38 + 2036.42i 0.442599 + 0.111145i
696696 1126.23 4286.15i 0.0613357 0.233428i
697697 −48113.2 −2.61466
698698 −5581.59 5098.02i −0.302674 0.276451i
699699 −1251.84 + 3022.21i −0.0677382 + 0.163534i
700700 4039.60 + 1715.37i 0.218118 + 0.0926214i
701701 15593.9 6459.21i 0.840191 0.348018i 0.0792621 0.996854i 0.474744π-0.474744\pi
0.760929 + 0.648835i 0.224744π0.224744\pi
702702 2365.62 + 5051.77i 0.127186 + 0.271605i
703703 −9282.83 + 9282.83i −0.498021 + 0.498021i
704704 −7356.80 + 5759.24i −0.393849 + 0.308323i
705705 −1562.30 2610.05i −0.0834602 0.139433i
706706 9782.07 + 3542.49i 0.521463 + 0.188843i
707707 987.767 + 409.146i 0.0525443 + 0.0217645i
708708 9401.72 853.168i 0.499065 0.0452882i
709709 −5467.01 2264.51i −0.289588 0.119951i 0.233160 0.972438i 0.425093π-0.425093\pi
−0.522748 + 0.852487i 0.675093π0.675093\pi
710710 −2523.21 + 12397.6i −0.133373 + 0.655314i
711711 6347.00 6347.00i 0.334784 0.334784i
712712 10131.4 + 17353.2i 0.533271 + 0.913399i
713713 −58360.9 −3.06541
714714 1571.84 + 1435.66i 0.0823875 + 0.0752497i
715715 4456.16 + 3309.02i 0.233078 + 0.173077i
716716 2681.21 + 835.867i 0.139946 + 0.0436282i
717717 3618.00 + 1498.63i 0.188447 + 0.0780574i
718718 −1429.58 517.710i −0.0743056 0.0269091i
719719 15105.7i 0.783514i −0.920069 0.391757i 0.871867π-0.871867\pi
0.920069 0.391757i 0.128133π-0.128133\pi
720720 −7924.55 + 16086.2i −0.410181 + 0.832635i
721721 3773.19i 0.194897i
722722 2667.64 7366.30i 0.137506 0.379702i
723723 −6745.63 2794.13i −0.346988 0.143727i
724724 −12984.2 + 6812.54i −0.666509 + 0.349705i
725725 −11137.4 13603.9i −0.570528 0.696879i
726726 −2650.82 + 2902.26i −0.135511 + 0.148365i
727727 −25073.0 −1.27910 −0.639550 0.768749i 0.720879π-0.720879\pi
−0.639550 + 0.768749i 0.720879π0.720879\pi
728728 −1634.24 + 2151.30i −0.0831993 + 0.109523i
729729 −8274.74 + 8274.74i −0.420400 + 0.420400i
730730 −12892.8 + 8532.24i −0.653674 + 0.432592i
731731 2309.45 + 956.606i 0.116851 + 0.0484013i
732732 −5311.02 4427.31i −0.268171 0.223549i
733733 20663.8 + 8559.23i 1.04125 + 0.431299i 0.836760 0.547570i 0.184447π-0.184447\pi
0.204488 + 0.978869i 0.434447π0.434447\pi
734734 −2398.82 + 6623.98i −0.120629 + 0.333100i
735735 −1227.54 + 4888.27i −0.0616033 + 0.245315i
736736 28736.0 20469.1i 1.43916 1.02514i
737737 −10527.2 + 10527.2i −0.526155 + 0.526155i
738738 −25077.7 + 11743.3i −1.25084 + 0.585741i
739739 −6694.29 + 2772.86i −0.333225 + 0.138026i −0.543022 0.839719i 0.682720π-0.682720\pi
0.209797 + 0.977745i 0.432720π0.432720\pi
740740 −11821.6 1853.63i −0.587260 0.0920822i
741741 1422.54 3434.33i 0.0705243 0.170261i
742742 −2990.14 + 3273.77i −0.147940 + 0.161973i
743743 25936.0 1.28062 0.640309 0.768117i 0.278806π-0.278806\pi
0.640309 + 0.768117i 0.278806π0.278806\pi
744744 5707.12 7512.79i 0.281227 0.370204i
745745 1407.27 5604.01i 0.0692060 0.275591i
746746 −18161.6 16588.1i −0.891345 0.814122i
747747 609.235 + 1470.82i 0.0298404 + 0.0720410i
748748 −5351.05 + 17164.6i −0.261569 + 0.839037i
749749 −5686.20 + 2355.30i −0.277396 + 0.114901i
750750 −2567.33 4868.78i −0.124994 0.237044i
751751 −8285.64 −0.402593 −0.201296 0.979530i 0.564515π-0.564515\pi
−0.201296 + 0.979530i 0.564515π0.564515\pi
752752 10289.7 + 7106.24i 0.498971 + 0.344598i
753753 553.403 553.403i 0.0267824 0.0267824i
754754 9801.49 4589.81i 0.473408 0.221686i
755755 −2258.96 1677.44i −0.108890 0.0808586i
756756 2429.88 + 757.514i 0.116897 + 0.0364425i
757757 −1015.10 + 420.467i −0.0487375 + 0.0201877i −0.406919 0.913464i 0.633397π-0.633397\pi
0.358182 + 0.933652i 0.383397π0.383397\pi
758758 −501.741 11080.9i −0.0240423 0.530970i
759759 −3501.86 + 3501.86i −0.167470 + 0.167470i
760760 23841.0 6917.94i 1.13790 0.330184i
761761 27010.0 + 27010.0i 1.28661 + 1.28661i 0.936831 + 0.349781i 0.113744π0.113744\pi
0.349781 + 0.936831i 0.386256π0.386256\pi
762762 −3605.95 + 3947.99i −0.171430 + 0.187691i
763763 −1272.95 3073.17i −0.0603982 0.145814i
764764 4238.90 + 3533.57i 0.200730 + 0.167330i
765765 5043.11 + 34137.7i 0.238345 + 1.61340i
766766 −3019.07 + 8336.70i −0.142406 + 0.393234i
767767 16302.4 + 16302.4i 0.767467 + 0.767467i
768768 −175.110 + 5700.85i −0.00822750 + 0.267854i
769769 8525.03i 0.399766i 0.979820 + 0.199883i 0.0640563π0.0640563\pi
−0.979820 + 0.199883i 0.935944π0.935944\pi
770770 2486.03 483.055i 0.116351 0.0226079i
771771 −611.413 1476.08i −0.0285597 0.0689491i
772772 12173.8 1104.72i 0.567543 0.0515023i
773773 −9347.35 + 3871.80i −0.434930 + 0.180154i −0.589396 0.807844i 0.700634π-0.700634\pi
0.154466 + 0.987998i 0.450634π0.450634\pi
774774 1437.22 65.0774i 0.0667441 0.00302217i
775775 −10822.7 35831.0i −0.501630 1.66076i
776776 12053.7 + 20645.9i 0.557609 + 0.955085i
777777 817.578i 0.0377483i
778778 −43242.1 + 1958.00i −1.99268 + 0.0902284i
779779 35416.0 + 14669.8i 1.62890 + 0.674711i
780780 3293.46 796.078i 0.151186 0.0365438i
781781 2793.87 + 6744.99i 0.128006 + 0.309033i
782782 23117.8 63836.4i 1.05715 2.91916i
783783 −7209.87 7209.87i −0.329068 0.329068i
784784 −3729.67 20380.9i −0.169901 0.928428i
785785 −7415.60 + 29530.2i −0.337164 + 1.34265i
786786 6384.65 2989.78i 0.289737 0.135677i
787787 5650.30 13641.0i 0.255923 0.617853i −0.742738 0.669582i 0.766473π-0.766473\pi
0.998661 + 0.0517291i 0.0164732π0.0164732\pi
788788 −17363.3 5413.01i −0.784954 0.244709i
789789 −2347.31 + 5666.90i −0.105914 + 0.255700i
790790 −6250.69 9445.20i −0.281506 0.425373i
791791 2888.66 + 2888.66i 0.129847 + 0.129847i
792792 1400.38 + 10252.6i 0.0628287 + 0.459990i
793793 16886.1i 0.756171i
794794 8888.76 402.483i 0.397293 0.0179894i
795795 5501.02 812.657i 0.245410 0.0362541i
796796 −39842.6 + 3615.55i −1.77410 + 0.160992i
797797 −13193.1 + 31851.0i −0.586354 + 1.41558i 0.300610 + 0.953747i 0.402810π0.402810\pi
−0.886964 + 0.461838i 0.847190π0.847190\pi
798798 −719.292 1536.04i −0.0319081 0.0681395i
799799 24064.3 1.06550
800800 17896.0 + 13846.7i 0.790901 + 0.611945i
801801 22255.5 0.981720
802802 −4199.83 8968.70i −0.184914 0.394883i
803803 −3414.09 + 8242.33i −0.150038 + 0.362224i
804804 821.362 + 9051.23i 0.0360289 + 0.397030i
805805 −9460.62 + 1397.60i −0.414215 + 0.0611913i
806806 23017.7 1042.24i 1.00591 0.0455476i
807807 6305.45i 0.275046i
808808 4389.45 + 3334.46i 0.191114 + 0.145181i
809809 10514.0 + 10514.0i 0.456924 + 0.456924i 0.897645 0.440720i 0.145277π-0.145277\pi
−0.440720 + 0.897645i 0.645277π0.645277\pi
810810 10047.2 + 15181.9i 0.435828 + 0.658564i
811811 −8209.30 + 19819.0i −0.355447 + 0.858125i 0.640481 + 0.767974i 0.278735π0.278735\pi
−0.995928 + 0.0901508i 0.971265π0.971265\pi
812812 1469.73 4714.47i 0.0635192 0.203751i
813813 −1523.04 + 3676.93i −0.0657013 + 0.158617i
814814 −6253.39 + 2928.31i −0.269264 + 0.126090i
815815 379.348 1510.63i 0.0163043 0.0649264i
816816 5956.95 + 9218.51i 0.255557 + 0.395481i
817817 −1408.31 1408.31i −0.0603067 0.0603067i
818818 3479.61 9608.43i 0.148731 0.410698i
819819 1145.07 + 2764.43i 0.0488545 + 0.117945i
820820 8209.44 + 33963.4i 0.349617 + 1.44640i
821821 −21991.9 9109.36i −0.934865 0.387234i −0.137343 0.990524i 0.543856π-0.543856\pi
−0.797522 + 0.603290i 0.793856π0.793856\pi
822822 −2750.01 + 124.520i −0.116688 + 0.00528364i
823823 26861.4i 1.13770i 0.822441 + 0.568850i 0.192612π0.192612\pi
−0.822441 + 0.568850i 0.807388π0.807388\pi
824824 4943.87 18815.1i 0.209015 0.795457i
825825 −2799.39 1500.59i −0.118136 0.0633258i
826826 10508.8 475.837i 0.442672 0.0200442i
827827 10125.7 4194.21i 0.425763 0.176357i −0.159504 0.987197i 0.550990π-0.550990\pi
0.585267 + 0.810840i 0.300990π0.300990\pi
828828 −3531.42 38915.5i −0.148219 1.63334i
829829 −11895.1 28717.2i −0.498350 1.20312i −0.950372 0.311117i 0.899297π-0.899297\pi
0.452022 0.892007i 0.350703π-0.350703\pi
830830 1971.96 383.168i 0.0824673 0.0160241i
831831 3215.08i 0.134211i
832832 −10968.0 + 8586.25i −0.457027 + 0.357782i
833833 −28193.5 28193.5i −1.17268 1.17268i
834834 1002.90 2769.37i 0.0416400 0.114983i
835835 332.657 + 2251.81i 0.0137869 + 0.0933261i
836836 9172.41 11003.3i 0.379467 0.455210i
837837 −8307.01 20054.9i −0.343049 0.828194i
838838 8184.25 8960.57i 0.337375 0.369377i
839839 3865.38 + 3865.38i 0.159056 + 0.159056i 0.782148 0.623093i 0.214124π-0.214124\pi
−0.623093 + 0.782148i 0.714124π0.714124\pi
840840 745.241 1354.53i 0.0306110 0.0556379i
841841 3256.96 3256.96i 0.133542 0.133542i
842842 952.695 + 21040.1i 0.0389929 + 0.861152i
843843 −7235.58 + 2997.08i −0.295619 + 0.122449i
844844 −276.462 + 886.807i −0.0112751 + 0.0361673i
845845 −13077.1 9710.71i −0.532387 0.395336i
846846 12542.9 5873.53i 0.509732 0.238695i
847847 −3097.12 + 3097.12i −0.125641 + 0.125641i
848848 −19200.0 + 12406.9i −0.777511 + 0.502423i
849849 9696.08 0.391953
850850 43479.8 + 2355.20i 1.75452 + 0.0950386i
851851 24090.0 9978.40i 0.970381 0.401945i
852852 4254.85 + 1326.45i 0.171090 + 0.0533372i
853853 15711.3 + 37930.5i 0.630651 + 1.52253i 0.838807 + 0.544429i 0.183254π0.183254\pi
−0.208156 + 0.978096i 0.566746π0.566746\pi
854854 −5688.95 5196.08i −0.227953 0.208204i
855855 6696.42 26666.3i 0.267851 1.06663i
856856 −31440.6 + 4294.37i −1.25539 + 0.171470i
857857 −15626.7 −0.622870 −0.311435 0.950267i 0.600810π-0.600810\pi
−0.311435 + 0.950267i 0.600810π0.600810\pi
858858 1318.61 1443.68i 0.0524667 0.0574435i
859859 13908.1 33577.2i 0.552433 1.33369i −0.363213 0.931706i 0.618320π-0.618320\pi
0.915646 0.401985i 0.131680π-0.131680\pi
860860 281.217 1793.48i 0.0111505 0.0711129i
861861 2205.63 913.604i 0.0873029 0.0361621i
862862 −41245.8 + 19314.4i −1.62974 + 0.763169i
863863 −28444.4 + 28444.4i −1.12197 + 1.12197i −0.130522 + 0.991445i 0.541665π0.541665\pi
−0.991445 + 0.130522i 0.958335π0.958335\pi
864864 11124.1 + 6961.16i 0.438022 + 0.274101i
865865 6719.27 26757.3i 0.264118 1.05176i
866866 14527.6 40115.7i 0.570054 1.57412i
867867 13193.1 + 5464.77i 0.516795 + 0.214064i
868868 6731.71 8075.39i 0.263236 0.315780i
869869 −6038.31 2501.15i −0.235714 0.0976360i
870870 −5164.83 + 3418.01i −0.201269 + 0.133197i
871871 −15694.7 + 15694.7i −0.610556 + 0.610556i
872872 −2320.94 16992.4i −0.0901341 0.659902i
873873 26478.3 1.02652
874874 −36480.8 + 39941.1i −1.41188 + 1.54580i
875875 −2612.48 5549.22i −0.100935 0.214398i
876876 2530.37 + 4822.68i 0.0975951 + 0.186008i
877877 17259.8 + 7149.22i 0.664562 + 0.275270i 0.689357 0.724422i 0.257893π-0.257893\pi
−0.0247951 + 0.999693i 0.507893π0.507893\pi
878878 10092.4 27868.7i 0.387930 1.07121i
879879 7569.40i 0.290455i
880880 13029.6 + 848.583i 0.499123 + 0.0325065i
881881 18203.4i 0.696126i −0.937471 0.348063i 0.886839π-0.886839\pi
0.937471 0.348063i 0.113161π-0.113161\pi
882882 −21576.4 7813.72i −0.823715 0.298301i
883883 18005.4 + 7458.09i 0.686218 + 0.284241i 0.698424 0.715685i 0.253885π-0.253885\pi
−0.0122053 + 0.999926i 0.503885π0.503885\pi
884884 −7977.69 + 25590.1i −0.303528 + 0.973628i
885885 −10592.3 7865.53i −0.402323 0.298754i
886886 −6937.37 6336.33i −0.263054 0.240263i
887887 35176.9 1.33159 0.665797 0.746133i 0.268092π-0.268092\pi
0.665797 + 0.746133i 0.268092π0.268092\pi
888888 −1071.24 + 4076.89i −0.0404827 + 0.154067i
889889 −4213.06 + 4213.06i −0.158944 + 0.158944i
890890 5600.69 27518.4i 0.210939 1.03643i
891891 9705.78 + 4020.26i 0.364933 + 0.151160i
892892 −2237.08 24652.1i −0.0839718 0.925351i
893893 −17713.7 7337.25i −0.663792 0.274951i
894894 −1913.78 693.060i −0.0715956 0.0259277i
895895 −2015.84 3367.76i −0.0752872 0.125779i
896896 −482.277 + 6337.22i −0.0179818 + 0.236285i
897897 −5220.80 + 5220.80i −0.194334 + 0.194334i
898898 −11607.8 24788.3i −0.431354 0.921153i
899899 −38910.7 + 16117.3i −1.44354 + 0.597935i
900900 23237.5 9384.80i 0.860648 0.347585i
901901 −16834.5 + 40642.1i −0.622462 + 1.50276i
902902 14887.8 + 13597.9i 0.549566 + 0.501953i
903903 −124.036 −0.00457105
904904 10619.5 + 18189.4i 0.390708 + 0.669213i
905905 19874.9 + 4990.96i 0.730014 + 0.183320i
906906 −668.440 + 731.844i −0.0245115 + 0.0268365i
907907 −8009.21 19335.9i −0.293210 0.707872i −1.00000 0.000448085i 0.999857π-0.999857\pi
0.706790 0.707424i 0.250143π-0.250143\pi
908908 30749.8 16133.8i 1.12386 0.589669i
909909 5640.47 2336.36i 0.205812 0.0852499i
910910 3706.33 720.170i 0.135015 0.0262345i
911911 36146.4 1.31458 0.657291 0.753637i 0.271702π-0.271702\pi
0.657291 + 0.753637i 0.271702π0.271702\pi
912912 −1574.16 8602.00i −0.0571552 0.312325i
913913 819.685 819.685i 0.0297126 0.0297126i
914914 4468.99 + 9543.48i 0.161730 + 0.345372i
915915 1412.18 + 9559.33i 0.0510223 + 0.345379i
916916 −646.499 + 339.206i −0.0233198 + 0.0122355i
917917 7257.95 3006.34i 0.261372 0.108264i
918918 25227.0 1142.28i 0.906988 0.0410684i
919919 25024.4 25024.4i 0.898236 0.898236i −0.0970439 0.995280i 0.530939π-0.530939\pi
0.995280 + 0.0970439i 0.0309387π0.0309387\pi
920920 −49007.0 5426.72i −1.75621 0.194471i
921921 1692.85 + 1692.85i 0.0605659 + 0.0605659i
922922 −6799.73 6210.62i −0.242882 0.221839i
923923 4165.28 + 10055.9i 0.148539 + 0.358605i
924924 −80.6259 888.479i −0.00287056 0.0316329i
925925 10593.6 + 12939.7i 0.376559 + 0.459953i
926926 −36568.1 13242.8i −1.29774 0.469964i
927927 −15235.4 15235.4i −0.539802 0.539802i
928928 13506.1 21583.2i 0.477758 0.763472i
929929 34790.8i 1.22869i 0.789039 + 0.614344i 0.210579π0.210579\pi
−0.789039 + 0.614344i 0.789421π0.789421\pi
930930 −12943.3 + 2514.98i −0.456373 + 0.0886770i
931931 12156.9 + 29349.4i 0.427955 + 1.03318i
932932 −12033.9 + 14435.9i −0.422942 + 0.507363i
933933 −8010.33 + 3317.99i −0.281079 + 0.116427i
934934 −829.613 18321.9i −0.0290640 0.641873i
935935 21559.7 12905.0i 0.754095 0.451378i
936936 2087.78 + 15285.3i 0.0729071 + 0.533778i
937937 44073.0i 1.53661i 0.640085 + 0.768304i 0.278899π0.278899\pi
−0.640085 + 0.768304i 0.721101π0.721101\pi
938938 458.098 + 10117.0i 0.0159461 + 0.352167i
939939 −13676.0 5664.77i −0.475291 0.196872i
940940 −4106.04 16987.1i −0.142473 0.589425i
941941 −9968.74 24066.7i −0.345347 0.833742i −0.997156 0.0753588i 0.975990π-0.975990\pi
0.651809 0.758383i 0.274010π-0.274010\pi
942942 10084.6 + 3652.07i 0.348806 + 0.126317i
943943 −53838.8 53838.8i −1.85921 1.85921i
944944 53025.9 + 11396.5i 1.82823 + 0.392929i
945945 −1826.88 3052.07i −0.0628870 0.105062i
946946 −444.258 948.710i −0.0152686 0.0326059i
947947 −16724.6 + 40376.9i −0.573894 + 1.38550i 0.324321 + 0.945947i 0.394864π0.394864\pi
−0.898215 + 0.439556i 0.855136π0.855136\pi
948948 −3533.08 + 1853.74i −0.121044 + 0.0635093i
949949 −5089.94 + 12288.2i −0.174106 + 0.420329i
950950 −31287.2 14990.7i −1.06852 0.511961i
951951 −694.865 694.865i −0.0236935 0.0236935i
952952 6166.48 + 10562.1i 0.209934 + 0.359579i
953953 3266.63i 0.111035i −0.998458 0.0555176i 0.982319π-0.982319\pi
0.998458 0.0555176i 0.0176809π-0.0176809\pi
954954 1145.24 + 25292.5i 0.0388665 + 0.858359i
955955 −1127.11 7629.60i −0.0381910 0.258522i
956956 17281.7 + 14406.2i 0.584656 + 0.487373i
957957 −1367.68 + 3301.88i −0.0461974 + 0.111530i
958958 −28732.6 + 13454.8i −0.969005 + 0.453762i
959959 −3067.53 −0.103291
960960 5490.97 5777.97i 0.184605 0.194253i
961961 −59872.5 −2.00975
962962 −9322.96 + 4365.72i −0.312458 + 0.146316i
963963 −13449.5 + 32470.1i −0.450058 + 1.08654i
964964 −32221.1 26859.8i −1.07653 0.897401i
965965 −13715.4 10184.6i −0.457526 0.339746i
966966 152.385 + 3365.40i 0.00507548 + 0.112091i
967967 19957.7i 0.663698i 0.943333 + 0.331849i 0.107672π0.107672\pi
−0.943333 + 0.331849i 0.892328π0.892328\pi
968968 −19502.0 + 11385.9i −0.647538 + 0.378053i
969969 −11899.4 11899.4i −0.394494 0.394494i
970970 6663.39 32739.9i 0.220565 1.08373i
971971 −6543.01 + 15796.2i −0.216246 + 0.522065i −0.994360 0.106059i 0.966177π-0.966177\pi
0.778113 + 0.628124i 0.216177π0.216177\pi
972972 19544.8 10254.8i 0.644959 0.338398i
973973 1256.00 3032.25i 0.0413828 0.0999069i
974974 −10567.8 22567.4i −0.347653 0.742410i
975975 −4173.51 2237.17i −0.137086 0.0734839i
976976 −21559.9 33364.5i −0.707087 1.09423i
977977 26603.6 + 26603.6i 0.871161 + 0.871161i 0.992599 0.121438i 0.0387505π-0.0387505\pi
−0.121438 + 0.992599i 0.538751π0.538751\pi
978978 −515.884 186.823i −0.0168672 0.00610832i
979979 −6201.44 14971.6i −0.202450 0.488758i
980980 −15091.3 + 24712.5i −0.491913 + 0.805522i
981981 −17548.8 7268.95i −0.571141 0.236575i
982982 −1948.64 43035.5i −0.0633235 1.39849i
983983 1333.07i 0.0432536i −0.999766 0.0216268i 0.993115π-0.993115\pi
0.999766 0.0216268i 0.00688457π-0.00688457\pi
984984 12195.5 1665.75i 0.395101 0.0539658i
985985 13054.4 + 21809.4i 0.422283 + 0.705487i
986986 −2216.26 48945.7i −0.0715821 1.58088i
987987 −1103.17 + 456.948i −0.0355768 + 0.0147364i
988988 13674.8 16404.4i 0.440338 0.528232i
989989 1513.84 + 3654.72i 0.0486726 + 0.117506i
990990 8087.63 11988.6i 0.259638 0.384872i
991991 19096.0i 0.612114i −0.952013 0.306057i 0.900990π-0.900990\pi
0.952013 0.306057i 0.0990099π-0.0990099\pi
992992 44148.9 31448.0i 1.41303 1.00653i
993993 3012.47 + 3012.47i 0.0962716 + 0.0962716i
994994 4669.54 + 1691.03i 0.149003 + 0.0539601i
995995 44887.9 + 33332.5i 1.43019 + 1.06202i
996996 −63.9539 704.757i −0.00203459 0.0224208i
997997 4611.95 + 11134.2i 0.146501 + 0.353685i 0.980047 0.198765i 0.0636930π-0.0636930\pi
−0.833546 + 0.552450i 0.813693π0.813693\pi
998998 39522.8 + 36098.7i 1.25358 + 1.14497i
999999 6857.87 + 6857.87i 0.217191 + 0.217191i
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 160.4.u.a.43.10 280
5.2 odd 4 160.4.ba.a.107.25 yes 280
32.3 odd 8 160.4.ba.a.3.25 yes 280
160.67 even 8 inner 160.4.u.a.67.10 yes 280
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.u.a.43.10 280 1.1 even 1 trivial
160.4.u.a.67.10 yes 280 160.67 even 8 inner
160.4.ba.a.3.25 yes 280 32.3 odd 8
160.4.ba.a.107.25 yes 280 5.2 odd 4