Properties

Label 115.4.e.a.22.8
Level 115115
Weight 44
Character 115.22
Analytic conductor 6.7856.785
Analytic rank 00
Dimension 6868
Inner twists 44

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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] = [115,4,Mod(22,115)] 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, 2])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.22"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 115=523 115 = 5 \cdot 23
Weight: k k == 4 4
Character orbit: [χ][\chi] == 115.e (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: 6.785219650666.78521965066
Analytic rank: 00
Dimension: 6868
Relative dimension: 3434 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 22.8
Character χ\chi == 115.22
Dual form 115.4.e.a.68.8

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+(2.665092.66509i)q2+(2.23283+2.23283i)q3+6.20541iq4+(7.411378.37088i)q5+11.9014q6+(10.9048+10.9048i)q7+(4.78275+4.78275i)q8+17.0290iq9+(42.0611+2.55718i)q10+18.9440iq11+(13.855613.8556i)q12+(43.964043.9640i)q13+58.1244q14+(2.14242+35.2390i)q15+75.1362q16+(38.7029+38.7029i)q17+(45.383745.3837i)q18+123.640q19+(51.9447+45.9906i)q2048.6969iq21+(50.487450.4874i)q22+(109.778+10.7567i)q2321.3581iq24+(15.1432124.079i)q25234.336q26+(98.309198.3091i)q27+(67.668667.6686i)q28+59.0042iq29+(88.205499.6249i)q30+342.953q31+(161.983161.983i)q32+(42.298642.2986i)q33+206.293q34+(10.4632+172.102i)q35105.672q36+(302.912+302.912i)q37+(329.512329.512i)q38+196.328iq39+(4.58909+75.4826i)q40+137.839q41+(129.782+129.782i)q42+(155.399+155.399i)q43117.555q44+(142.547+126.208i)q45+(263.902321.237i)q46+(234.217+234.217i)q47+(167.766+167.766i)q48+105.172iq49+(290.325+371.041i)q50172.834iq51+(272.815+272.815i)q52+(342.095342.095i)q53+524.005iq54+(158.578+140.401i)q55104.310iq56+(276.067+276.067i)q57+(157.251157.251i)q5887.0009iq59+(218.672+13.2946i)q60+565.294iq61+(914.002914.002i)q62+(185.697185.697i)q63+262.307iq64+(42.1838693.851i)q65+225.459iq66+(4.05177+4.05177i)q67+(240.167240.167i)q68+(269.134+221.098i)q69+(430.782486.552i)q70556.502q71+(81.445381.4453i)q72+(305.536305.536i)q73+1614.57q74+(310.860+243.236i)q75+767.238iq76+(206.580206.580i)q77+(523.232523.232i)q78328.493q79+(556.862628.956i)q8020.7681q81+(367.354367.354i)q82+(810.460+810.460i)q83+302.184q84+(37.1357+610.818i)q85828.302iq86+(131.746131.746i)q87+(90.604390.6043i)q88+194.282q89+(43.5461716.257i)q90+958.835iq91+(66.7494+681.220i)q92+(765.755+765.755i)q931248.42iq94+(916.3431034.98i)q95+723.358q96+(1067.111067.11i)q97+(280.292280.292i)q98322.596q99+O(q100)q+(-2.66509 - 2.66509i) q^{2} +(-2.23283 + 2.23283i) q^{3} +6.20541i q^{4} +(7.41137 - 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 + 10.9048i) q^{7} +(-4.78275 + 4.78275i) q^{8} +17.0290i q^{9} +(-42.0611 + 2.55718i) q^{10} +18.9440i q^{11} +(-13.8556 - 13.8556i) q^{12} +(43.9640 - 43.9640i) q^{13} +58.1244 q^{14} +(2.14242 + 35.2390i) q^{15} +75.1362 q^{16} +(-38.7029 + 38.7029i) q^{17} +(45.3837 - 45.3837i) q^{18} +123.640 q^{19} +(51.9447 + 45.9906i) q^{20} -48.6969i q^{21} +(50.4874 - 50.4874i) q^{22} +(109.778 + 10.7567i) q^{23} -21.3581i q^{24} +(-15.1432 - 124.079i) q^{25} -234.336 q^{26} +(-98.3091 - 98.3091i) q^{27} +(-67.6686 - 67.6686i) q^{28} +59.0042i q^{29} +(88.2054 - 99.6249i) q^{30} +342.953 q^{31} +(-161.983 - 161.983i) q^{32} +(-42.2986 - 42.2986i) q^{33} +206.293 q^{34} +(10.4632 + 172.102i) q^{35} -105.672 q^{36} +(-302.912 + 302.912i) q^{37} +(-329.512 - 329.512i) q^{38} +196.328i q^{39} +(4.58909 + 75.4826i) q^{40} +137.839 q^{41} +(-129.782 + 129.782i) q^{42} +(155.399 + 155.399i) q^{43} -117.555 q^{44} +(142.547 + 126.208i) q^{45} +(-263.902 - 321.237i) q^{46} +(234.217 + 234.217i) q^{47} +(-167.766 + 167.766i) q^{48} +105.172i q^{49} +(-290.325 + 371.041i) q^{50} -172.834i q^{51} +(272.815 + 272.815i) q^{52} +(-342.095 - 342.095i) q^{53} +524.005i q^{54} +(158.578 + 140.401i) q^{55} -104.310i q^{56} +(-276.067 + 276.067i) q^{57} +(157.251 - 157.251i) q^{58} -87.0009i q^{59} +(-218.672 + 13.2946i) q^{60} +565.294i q^{61} +(-914.002 - 914.002i) q^{62} +(-185.697 - 185.697i) q^{63} +262.307i q^{64} +(-42.1838 - 693.851i) q^{65} +225.459i q^{66} +(-4.05177 + 4.05177i) q^{67} +(-240.167 - 240.167i) q^{68} +(-269.134 + 221.098i) q^{69} +(430.782 - 486.552i) q^{70} -556.502 q^{71} +(-81.4453 - 81.4453i) q^{72} +(305.536 - 305.536i) q^{73} +1614.57 q^{74} +(310.860 + 243.236i) q^{75} +767.238i q^{76} +(-206.580 - 206.580i) q^{77} +(523.232 - 523.232i) q^{78} -328.493 q^{79} +(556.862 - 628.956i) q^{80} -20.7681 q^{81} +(-367.354 - 367.354i) q^{82} +(810.460 + 810.460i) q^{83} +302.184 q^{84} +(37.1357 + 610.818i) q^{85} -828.302i q^{86} +(-131.746 - 131.746i) q^{87} +(-90.6043 - 90.6043i) q^{88} +194.282 q^{89} +(-43.5461 - 716.257i) q^{90} +958.835i q^{91} +(-66.7494 + 681.220i) q^{92} +(-765.755 + 765.755i) q^{93} -1248.42i q^{94} +(916.343 - 1034.98i) q^{95} +723.358 q^{96} +(1067.11 - 1067.11i) q^{97} +(280.292 - 280.292i) q^{98} -322.596 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 68q4q2+4q3+32q6+28q8+200q12100q13832q16112q1846q23372q25312q26704q271056q31+560q32348q35+2424q36+3612q98+O(q100) 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36}+ \cdots - 3612 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) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −2.66509 2.66509i −0.942252 0.942252i 0.0561697 0.998421i 0.482111π-0.482111\pi
−0.998421 + 0.0561697i 0.982111π0.982111\pi
33 −2.23283 + 2.23283i −0.429708 + 0.429708i −0.888529 0.458821i 0.848272π-0.848272\pi
0.458821 + 0.888529i 0.348272π0.348272\pi
44 6.20541i 0.775676i
55 7.41137 8.37088i 0.662893 0.748714i
66 11.9014 0.809785
77 −10.9048 + 10.9048i −0.588803 + 0.588803i −0.937307 0.348505i 0.886690π-0.886690\pi
0.348505 + 0.937307i 0.386690π0.386690\pi
88 −4.78275 + 4.78275i −0.211370 + 0.211370i
99 17.0290i 0.630703i
1010 −42.0611 + 2.55718i −1.33009 + 0.0808650i
1111 18.9440i 0.519257i 0.965709 + 0.259628i 0.0836001π0.0836001\pi
−0.965709 + 0.259628i 0.916400π0.916400\pi
1212 −13.8556 13.8556i −0.333314 0.333314i
1313 43.9640 43.9640i 0.937955 0.937955i −0.0602292 0.998185i 0.519183π-0.519183\pi
0.998185 + 0.0602292i 0.0191832π0.0191832\pi
1414 58.1244 1.10960
1515 2.14242 + 35.2390i 0.0368780 + 0.606578i
1616 75.1362 1.17400
1717 −38.7029 + 38.7029i −0.552166 + 0.552166i −0.927066 0.374899i 0.877677π-0.877677\pi
0.374899 + 0.927066i 0.377677π0.377677\pi
1818 45.3837 45.3837i 0.594281 0.594281i
1919 123.640 1.49290 0.746448 0.665444i 0.231758π-0.231758\pi
0.746448 + 0.665444i 0.231758π0.231758\pi
2020 51.9447 + 45.9906i 0.580759 + 0.514190i
2121 48.6969i 0.506026i
2222 50.4874 50.4874i 0.489271 0.489271i
2323 109.778 + 10.7567i 0.995234 + 0.0975182i
2424 21.3581i 0.181654i
2525 −15.1432 124.079i −0.121146 0.992635i
2626 −234.336 −1.76758
2727 −98.3091 98.3091i −0.700725 0.700725i
2828 −67.6686 67.6686i −0.456720 0.456720i
2929 59.0042i 0.377821i 0.981994 + 0.188910i 0.0604955π0.0604955\pi
−0.981994 + 0.188910i 0.939504π0.939504\pi
3030 88.2054 99.6249i 0.536801 0.606298i
3131 342.953 1.98698 0.993488 0.113938i 0.0363464π-0.0363464\pi
0.993488 + 0.113938i 0.0363464π0.0363464\pi
3232 −161.983 161.983i −0.894836 0.894836i
3333 −42.2986 42.2986i −0.223129 0.223129i
3434 206.293 1.04056
3535 10.4632 + 172.102i 0.0505317 + 0.831158i
3636 −105.672 −0.489221
3737 −302.912 + 302.912i −1.34590 + 1.34590i −0.455839 + 0.890062i 0.650661π0.650661\pi
−0.890062 + 0.455839i 0.849339π0.849339\pi
3838 −329.512 329.512i −1.40668 1.40668i
3939 196.328i 0.806093i
4040 4.58909 + 75.4826i 0.0181400 + 0.298371i
4141 137.839 0.525045 0.262523 0.964926i 0.415446π-0.415446\pi
0.262523 + 0.964926i 0.415446π0.415446\pi
4242 −129.782 + 129.782i −0.476804 + 0.476804i
4343 155.399 + 155.399i 0.551118 + 0.551118i 0.926763 0.375646i 0.122579π-0.122579\pi
−0.375646 + 0.926763i 0.622579π0.622579\pi
4444 −117.555 −0.402775
4545 142.547 + 126.208i 0.472216 + 0.418088i
4646 −263.902 321.237i −0.845874 1.02965i
4747 234.217 + 234.217i 0.726894 + 0.726894i 0.970000 0.243106i 0.0781662π-0.0781662\pi
−0.243106 + 0.970000i 0.578166π0.578166\pi
4848 −167.766 + 167.766i −0.504478 + 0.504478i
4949 105.172i 0.306623i
5050 −290.325 + 371.041i −0.821162 + 1.04946i
5151 172.834i 0.474540i
5252 272.815 + 272.815i 0.727549 + 0.727549i
5353 −342.095 342.095i −0.886610 0.886610i 0.107586 0.994196i 0.465688π-0.465688\pi
−0.994196 + 0.107586i 0.965688π0.965688\pi
5454 524.005i 1.32052i
5555 158.578 + 140.401i 0.388775 + 0.344212i
5656 104.310i 0.248910i
5757 −276.067 + 276.067i −0.641509 + 0.641509i
5858 157.251 157.251i 0.356002 0.356002i
5959 87.0009i 0.191975i −0.995383 0.0959877i 0.969399π-0.969399\pi
0.995383 0.0959877i 0.0306009π-0.0306009\pi
6060 −218.672 + 13.2946i −0.470508 + 0.0286053i
6161 565.294i 1.18653i 0.805006 + 0.593267i 0.202162π0.202162\pi
−0.805006 + 0.593267i 0.797838π0.797838\pi
6262 −914.002 914.002i −1.87223 1.87223i
6363 −185.697 185.697i −0.371359 0.371359i
6464 262.307i 0.512319i
6565 −42.1838 693.851i −0.0804963 1.32402i
6666 225.459i 0.420487i
6767 −4.05177 + 4.05177i −0.00738809 + 0.00738809i −0.710791 0.703403i 0.751663π-0.751663\pi
0.703403 + 0.710791i 0.251663π0.251663\pi
6868 −240.167 240.167i −0.428302 0.428302i
6969 −269.134 + 221.098i −0.469564 + 0.385755i
7070 430.782 486.552i 0.735546 0.830773i
7171 −556.502 −0.930206 −0.465103 0.885257i 0.653983π-0.653983\pi
−0.465103 + 0.885257i 0.653983π0.653983\pi
7272 −81.4453 81.4453i −0.133311 0.133311i
7373 305.536 305.536i 0.489866 0.489866i −0.418398 0.908264i 0.637408π-0.637408\pi
0.908264 + 0.418398i 0.137408π0.137408\pi
7474 1614.57 2.53636
7575 310.860 + 243.236i 0.478600 + 0.374486i
7676 767.238i 1.15800i
7777 −206.580 206.580i −0.305740 0.305740i
7878 523.232 523.232i 0.759543 0.759543i
7979 −328.493 −0.467828 −0.233914 0.972257i 0.575153π-0.575153\pi
−0.233914 + 0.972257i 0.575153π0.575153\pi
8080 556.862 628.956i 0.778238 0.878992i
8181 −20.7681 −0.0284885
8282 −367.354 367.354i −0.494725 0.494725i
8383 810.460 + 810.460i 1.07180 + 1.07180i 0.997214 + 0.0745876i 0.0237641π0.0237641\pi
0.0745876 + 0.997214i 0.476236π0.476236\pi
8484 302.184 0.392512
8585 37.1357 + 610.818i 0.0473875 + 0.779442i
8686 828.302i 1.03858i
8787 −131.746 131.746i −0.162352 0.162352i
8888 −90.6043 90.6043i −0.109755 0.109755i
8989 194.282 0.231391 0.115696 0.993285i 0.463090π-0.463090\pi
0.115696 + 0.993285i 0.463090π0.463090\pi
9090 −43.5461 716.257i −0.0510018 0.838891i
9191 958.835i 1.10454i
9292 −66.7494 + 681.220i −0.0756425 + 0.771979i
9393 −765.755 + 765.755i −0.853819 + 0.853819i
9494 1248.42i 1.36983i
9595 916.343 1034.98i 0.989630 1.11775i
9696 723.358 0.769036
9797 1067.11 1067.11i 1.11700 1.11700i 0.124820 0.992179i 0.460165π-0.460165\pi
0.992179 0.124820i 0.0398353π-0.0398353\pi
9898 280.292 280.292i 0.288916 0.288916i
9999 −322.596 −0.327497
100100 769.963 93.9697i 0.769963 0.0939697i
101101 −1196.74 −1.17901 −0.589504 0.807766i 0.700677π-0.700677\pi
−0.589504 + 0.807766i 0.700677π0.700677\pi
102102 −460.617 + 460.617i −0.447136 + 0.447136i
103103 647.268 + 647.268i 0.619196 + 0.619196i 0.945325 0.326129i 0.105745π-0.105745\pi
−0.326129 + 0.945325i 0.605745π0.605745\pi
104104 420.538i 0.396511i
105105 −407.636 360.911i −0.378869 0.335441i
106106 1823.43i 1.67082i
107107 −1091.38 + 1091.38i −0.986049 + 0.986049i −0.999904 0.0138547i 0.995590π-0.995590\pi
0.0138547 + 0.999904i 0.495590π0.495590\pi
108108 610.048 610.048i 0.543536 0.543536i
109109 26.4427 0.0232362 0.0116181 0.999933i 0.496302π-0.496302\pi
0.0116181 + 0.999933i 0.496302π0.496302\pi
110110 −48.4431 796.805i −0.0419897 0.690658i
111111 1352.70i 1.15669i
112112 −819.343 + 819.343i −0.691256 + 0.691256i
113113 −70.7193 70.7193i −0.0588736 0.0588736i 0.677057 0.735931i 0.263255π-0.263255\pi
−0.735931 + 0.677057i 0.763255π0.763255\pi
114114 1471.49 1.20892
115115 903.651 839.220i 0.732747 0.680501i
116116 −366.145 −0.293066
117117 748.662 + 748.662i 0.591571 + 0.591571i
118118 −231.865 + 231.865i −0.180889 + 0.180889i
119119 844.093i 0.650234i
120120 −178.786 158.293i −0.136007 0.120417i
121121 972.126 0.730372
122122 1506.56 1506.56i 1.11801 1.11801i
123123 −307.771 + 307.771i −0.225616 + 0.225616i
124124 2128.17i 1.54125i
125125 −1150.88 792.836i −0.823506 0.567307i
126126 989.799i 0.699828i
127127 556.054 + 556.054i 0.388518 + 0.388518i 0.874159 0.485640i 0.161414π-0.161414\pi
−0.485640 + 0.874159i 0.661414π0.661414\pi
128128 −596.789 + 596.789i −0.412103 + 0.412103i
129129 −693.956 −0.473639
130130 −1736.75 + 1961.60i −1.17172 + 1.32341i
131131 423.960 0.282760 0.141380 0.989955i 0.454846π-0.454846\pi
0.141380 + 0.989955i 0.454846π0.454846\pi
132132 262.480 262.480i 0.173075 0.173075i
133133 −1348.27 + 1348.27i −0.879021 + 0.879021i
134134 21.5966 0.0139229
135135 −1551.54 + 94.3284i −0.989149 + 0.0601370i
136136 370.212i 0.233422i
137137 651.809 651.809i 0.406480 0.406480i −0.474029 0.880509i 0.657201π-0.657201\pi
0.880509 + 0.474029i 0.157201π0.157201\pi
138138 1306.51 + 128.019i 0.805926 + 0.0789688i
139139 959.361i 0.585409i −0.956203 0.292705i 0.905445π-0.905445\pi
0.956203 0.292705i 0.0945553π-0.0945553\pi
140140 −1067.96 + 64.9286i −0.644709 + 0.0391962i
141141 −1045.93 −0.624704
142142 1483.13 + 1483.13i 0.876488 + 0.876488i
143143 832.853 + 832.853i 0.487040 + 0.487040i
144144 1279.49i 0.740447i
145145 493.917 + 437.302i 0.282880 + 0.250455i
146146 −1628.56 −0.923155
147147 −234.830 234.830i −0.131758 0.131758i
148148 −1879.69 1879.69i −1.04398 1.04398i
149149 −2261.05 −1.24317 −0.621584 0.783347i 0.713511π-0.713511\pi
−0.621584 + 0.783347i 0.713511π0.713511\pi
150150 −180.225 1476.71i −0.0981019 0.803821i
151151 676.556 0.364618 0.182309 0.983241i 0.441643π-0.441643\pi
0.182309 + 0.983241i 0.441643π0.441643\pi
152152 −591.340 + 591.340i −0.315553 + 0.315553i
153153 −659.070 659.070i −0.348253 0.348253i
154154 1101.11i 0.576167i
155155 2541.75 2870.82i 1.31715 1.48768i
156156 −1218.29 −0.625267
157157 2211.51 2211.51i 1.12419 1.12419i 0.133086 0.991105i 0.457511π-0.457511\pi
0.991105 0.133086i 0.0424886π-0.0424886\pi
158158 875.464 + 875.464i 0.440811 + 0.440811i
159159 1527.68 0.761966
160160 −2556.45 + 155.424i −1.26316 + 0.0767958i
161161 −1314.41 + 1079.81i −0.643415 + 0.528577i
162162 55.3490 + 55.3490i 0.0268434 + 0.0268434i
163163 −11.1549 + 11.1549i −0.00536025 + 0.00536025i −0.709782 0.704422i 0.751206π-0.751206\pi
0.704422 + 0.709782i 0.251206π0.251206\pi
164164 855.348i 0.407265i
165165 −667.567 + 40.5859i −0.314970 + 0.0191491i
166166 4319.90i 2.01981i
167167 −2023.17 2023.17i −0.937470 0.937470i 0.0606869 0.998157i 0.480671π-0.480671\pi
−0.998157 + 0.0606869i 0.980671π0.980671\pi
168168 232.905 + 232.905i 0.106959 + 0.106959i
169169 1668.67i 0.759521i
170170 1528.92 1726.86i 0.689779 0.779081i
171171 2105.47i 0.941573i
172172 −964.312 + 964.312i −0.427489 + 0.427489i
173173 305.721 305.721i 0.134356 0.134356i −0.636731 0.771086i 0.719714π-0.719714\pi
0.771086 + 0.636731i 0.219714π0.219714\pi
174174 702.230i 0.305954i
175175 1518.19 + 1187.92i 0.655797 + 0.513135i
176176 1423.38i 0.609609i
177177 194.258 + 194.258i 0.0824933 + 0.0824933i
178178 −517.778 517.778i −0.218029 0.218029i
179179 3865.17i 1.61395i −0.590587 0.806974i 0.701104π-0.701104\pi
0.590587 0.806974i 0.298896π-0.298896\pi
180180 −783.172 + 884.565i −0.324301 + 0.366287i
181181 667.154i 0.273973i 0.990573 + 0.136987i 0.0437417π0.0437417\pi
−0.990573 + 0.136987i 0.956258π0.956258\pi
182182 2555.38 2555.38i 1.04076 1.04076i
183183 −1262.20 1262.20i −0.509863 0.509863i
184184 −576.489 + 473.596i −0.230975 + 0.189750i
185185 290.646 + 4780.62i 0.115507 + 1.89988i
186186 4081.61 1.60902
187187 −733.187 733.187i −0.286716 0.286716i
188188 −1453.41 + 1453.41i −0.563834 + 0.563834i
189189 2144.08 0.825178
190190 −5200.45 + 316.170i −1.98568 + 0.120723i
191191 1067.82i 0.404527i 0.979331 + 0.202263i 0.0648297π0.0648297\pi
−0.979331 + 0.202263i 0.935170π0.935170\pi
192192 −585.686 585.686i −0.220147 0.220147i
193193 417.876 417.876i 0.155852 0.155852i −0.624874 0.780726i 0.714850π-0.714850\pi
0.780726 + 0.624874i 0.214850π0.214850\pi
194194 −5687.91 −2.10499
195195 1643.44 + 1455.06i 0.603533 + 0.534354i
196196 −652.633 −0.237840
197197 572.015 + 572.015i 0.206875 + 0.206875i 0.802938 0.596063i 0.203269π-0.203269\pi
−0.596063 + 0.802938i 0.703269π0.703269\pi
198198 859.749 + 859.749i 0.308584 + 0.308584i
199199 −3406.06 −1.21331 −0.606657 0.794964i 0.707490π-0.707490\pi
−0.606657 + 0.794964i 0.707490π0.707490\pi
200200 665.867 + 521.014i 0.235419 + 0.184206i
201201 18.0938i 0.00634944i
202202 3189.41 + 3189.41i 1.11092 + 1.11092i
203203 −643.427 643.427i −0.222462 0.222462i
204204 1072.50 0.368089
205205 1021.58 1153.83i 0.348049 0.393109i
206206 3450.05i 1.16688i
207207 −183.175 + 1869.41i −0.0615050 + 0.627697i
208208 3303.29 3303.29i 1.10116 1.10116i
209209 2342.24i 0.775196i
210210 124.527 + 2048.25i 0.0409198 + 0.673060i
211211 −2577.48 −0.840954 −0.420477 0.907303i 0.638137π-0.638137\pi
−0.420477 + 0.907303i 0.638137π0.638137\pi
212212 2122.84 2122.84i 0.687722 0.687722i
213213 1242.57 1242.57i 0.399717 0.399717i
214214 5817.23 1.85821
215215 2452.54 149.106i 0.777962 0.0472975i
216216 940.375 0.296224
217217 −3739.83 + 3739.83i −1.16994 + 1.16994i
218218 −70.4721 70.4721i −0.0218944 0.0218944i
219219 1364.42i 0.420999i
220220 −871.244 + 984.039i −0.266997 + 0.301563i
221221 3403.07i 1.03581i
222222 −3605.06 + 3605.06i −1.08989 + 1.08989i
223223 −1070.51 + 1070.51i −0.321465 + 0.321465i −0.849329 0.527864i 0.822993π-0.822993\pi
0.527864 + 0.849329i 0.322993π0.322993\pi
224224 3532.77 1.05376
225225 2112.94 257.873i 0.626057 0.0764069i
226226 376.947i 0.110947i
227227 −1638.67 + 1638.67i −0.479129 + 0.479129i −0.904853 0.425724i 0.860019π-0.860019\pi
0.425724 + 0.904853i 0.360019π0.360019\pi
228228 −1713.11 1713.11i −0.497603 0.497603i
229229 −2319.00 −0.669188 −0.334594 0.942362i 0.608599π-0.608599\pi
−0.334594 + 0.942362i 0.608599π0.608599\pi
230230 −4644.91 171.714i −1.33164 0.0492283i
231231 922.514 0.262757
232232 −282.202 282.202i −0.0798598 0.0798598i
233233 597.533 597.533i 0.168007 0.168007i −0.618096 0.786103i 0.712096π-0.712096\pi
0.786103 + 0.618096i 0.212096π0.212096\pi
234234 3990.50i 1.11482i
235235 3696.47 224.733i 1.02609 0.0623828i
236236 539.876 0.148911
237237 733.468 733.468i 0.201029 0.201029i
238238 −2249.58 + 2249.58i −0.612684 + 0.612684i
239239 226.067i 0.0611845i 0.999532 + 0.0305922i 0.00973933π0.00973933\pi
−0.999532 + 0.0305922i 0.990261π0.990261\pi
240240 160.973 + 2647.73i 0.0432948 + 0.712125i
241241 5848.33i 1.56317i −0.623799 0.781585i 0.714412π-0.714412\pi
0.623799 0.781585i 0.285588π-0.285588\pi
242242 −2590.80 2590.80i −0.688195 0.688195i
243243 2700.72 2700.72i 0.712967 0.712967i
244244 −3507.88 −0.920365
245245 880.379 + 779.466i 0.229573 + 0.203258i
246246 1640.47 0.425174
247247 5435.72 5435.72i 1.40027 1.40027i
248248 −1640.26 + 1640.26i −0.419987 + 0.419987i
249249 −3619.23 −0.921123
250250 954.232 + 5180.19i 0.241404 + 1.31050i
251251 6646.18i 1.67133i −0.549241 0.835664i 0.685083π-0.685083\pi
0.549241 0.835664i 0.314917π-0.314917\pi
252252 1152.33 1152.33i 0.288055 0.288055i
253253 −203.774 + 2079.64i −0.0506370 + 0.516782i
254254 2963.87i 0.732164i
255255 −1446.77 1280.93i −0.355295 0.314569i
256256 5279.45 1.28893
257257 1313.92 + 1313.92i 0.318910 + 0.318910i 0.848348 0.529438i 0.177597π-0.177597\pi
−0.529438 + 0.848348i 0.677597π0.677597\pi
258258 1849.46 + 1849.46i 0.446287 + 0.446287i
259259 6606.37i 1.58494i
260260 4305.63 261.768i 1.02701 0.0624390i
261261 −1004.78 −0.238292
262262 −1129.89 1129.89i −0.266431 0.266431i
263263 4634.72 + 4634.72i 1.08665 + 1.08665i 0.995871 + 0.0907786i 0.0289356π0.0289356\pi
0.0907786 + 0.995871i 0.471064π0.471064\pi
264264 404.608 0.0943253
265265 −5399.02 + 328.243i −1.25154 + 0.0760898i
266266 7186.52 1.65652
267267 −433.797 + 433.797i −0.0994305 + 0.0994305i
268268 −25.1429 25.1429i −0.00573076 0.00573076i
269269 4119.24i 0.933661i −0.884347 0.466830i 0.845396π-0.845396\pi
0.884347 0.466830i 0.154604π-0.154604\pi
270270 4386.38 + 3883.59i 0.988691 + 0.875363i
271271 5232.41 1.17287 0.586433 0.809998i 0.300532π-0.300532\pi
0.586433 + 0.809998i 0.300532π0.300532\pi
272272 −2907.99 + 2907.99i −0.648245 + 0.648245i
273273 −2140.91 2140.91i −0.474630 0.474630i
274274 −3474.26 −0.766014
275275 2350.56 286.872i 0.515432 0.0629057i
276276 −1372.01 1670.09i −0.299221 0.364229i
277277 −6408.30 6408.30i −1.39003 1.39003i −0.825229 0.564798i 0.808954π-0.808954\pi
−0.564798 0.825229i 0.691046π-0.691046\pi
278278 −2556.78 + 2556.78i −0.551603 + 0.551603i
279279 5840.14i 1.25319i
280280 −873.163 773.077i −0.186362 0.165001i
281281 2894.08i 0.614400i −0.951645 0.307200i 0.900608π-0.900608\pi
0.951645 0.307200i 0.0993921π-0.0993921\pi
282282 2787.50 + 2787.50i 0.588628 + 0.588628i
283283 1464.96 + 1464.96i 0.307714 + 0.307714i 0.844022 0.536308i 0.180181π-0.180181\pi
−0.536308 + 0.844022i 0.680181π0.680181\pi
284284 3453.32i 0.721538i
285285 264.889 + 4356.96i 0.0550549 + 0.905558i
286286 4439.26i 0.917828i
287287 −1503.11 + 1503.11i −0.309148 + 0.309148i
288288 2758.40 2758.40i 0.564376 0.564376i
289289 1917.17i 0.390225i
290290 −150.884 2481.78i −0.0305525 0.502535i
291291 4765.36i 0.959966i
292292 1895.97 + 1895.97i 0.379977 + 0.379977i
293293 1164.58 + 1164.58i 0.232202 + 0.232202i 0.813611 0.581409i 0.197498π-0.197498\pi
−0.581409 + 0.813611i 0.697498π0.697498\pi
294294 1251.69i 0.248299i
295295 −728.274 644.796i −0.143735 0.127259i
296296 2897.50i 0.568966i
297297 1862.36 1862.36i 0.363856 0.363856i
298298 6025.89 + 6025.89i 1.17138 + 1.17138i
299299 5299.20 4353.39i 1.02495 0.842017i
300300 −1509.38 + 1929.01i −0.290479 + 0.371238i
301301 −3389.17 −0.648999
302302 −1803.08 1803.08i −0.343562 0.343562i
303303 2672.10 2672.10i 0.506628 0.506628i
304304 9289.85 1.75266
305305 4732.01 + 4189.61i 0.888374 + 0.786545i
306306 3512.96i 0.656283i
307307 1757.91 + 1757.91i 0.326806 + 0.326806i 0.851371 0.524565i 0.175772π-0.175772\pi
−0.524565 + 0.851371i 0.675772π0.675772\pi
308308 1281.91 1281.91i 0.237155 0.237155i
309309 −2890.47 −0.532146
310310 −14425.0 + 876.992i −2.64285 + 0.160677i
311311 2236.39 0.407762 0.203881 0.978996i 0.434644π-0.434644\pi
0.203881 + 0.978996i 0.434644π0.434644\pi
312312 −938.988 938.988i −0.170384 0.170384i
313313 −2726.31 2726.31i −0.492333 0.492333i 0.416708 0.909041i 0.363184π-0.363184\pi
−0.909041 + 0.416708i 0.863184π0.863184\pi
314314 −11787.8 −2.11854
315315 −2930.72 + 178.178i −0.524214 + 0.0318704i
316316 2038.43i 0.362883i
317317 −2582.03 2582.03i −0.457480 0.457480i 0.440348 0.897827i 0.354855π-0.354855\pi
−0.897827 + 0.440348i 0.854855π0.854855\pi
318318 −4071.39 4071.39i −0.717964 0.717964i
319319 −1117.77 −0.196186
320320 2195.74 + 1944.06i 0.383580 + 0.339613i
321321 4873.71i 0.847426i
322322 6380.80 + 625.224i 1.10431 + 0.108206i
323323 −4785.23 + 4785.23i −0.824327 + 0.824327i
324324 128.875i 0.0220979i
325325 −6120.78 4789.27i −1.04468 0.817418i
326326 59.4577 0.0101014
327327 −59.0419 + 59.0419i −0.00998478 + 0.00998478i
328328 −659.250 + 659.250i −0.110979 + 0.110979i
329329 −5108.16 −0.855994
330330 1887.29 + 1670.96i 0.314824 + 0.278738i
331331 −6499.87 −1.07935 −0.539676 0.841873i 0.681453π-0.681453\pi
−0.539676 + 0.841873i 0.681453π0.681453\pi
332332 −5029.24 + 5029.24i −0.831371 + 0.831371i
333333 −5158.27 5158.27i −0.848864 0.848864i
334334 10783.9i 1.76666i
335335 3.88770 + 63.9460i 0.000634053 + 0.0104291i
336336 3658.90i 0.594076i
337337 −2735.52 + 2735.52i −0.442176 + 0.442176i −0.892743 0.450567i 0.851222π-0.851222\pi
0.450567 + 0.892743i 0.351222π0.351222\pi
338338 −4447.15 + 4447.15i −0.715659 + 0.715659i
339339 315.808 0.0505968
340340 −3790.38 + 230.442i −0.604594 + 0.0367573i
341341 6496.90i 1.03175i
342342 5611.26 5611.26i 0.887199 0.887199i
343343 −4887.21 4887.21i −0.769343 0.769343i
344344 −1486.47 −0.232979
345345 −143.863 + 3891.53i −0.0224502 + 0.607284i
346346 −1629.55 −0.253194
347347 6733.74 + 6733.74i 1.04175 + 1.04175i 0.999090 + 0.0426573i 0.0135824π0.0135824\pi
0.0426573 + 0.999090i 0.486418π0.486418\pi
348348 817.538 817.538i 0.125933 0.125933i
349349 6515.26i 0.999295i 0.866229 + 0.499648i 0.166537π0.166537\pi
−0.866229 + 0.499648i 0.833463π0.833463\pi
350350 −880.190 7212.04i −0.134423 1.10143i
351351 −8644.12 −1.31450
352352 3068.60 3068.60i 0.464650 0.464650i
353353 −639.089 + 639.089i −0.0963605 + 0.0963605i −0.753644 0.657283i 0.771706π-0.771706\pi
0.657283 + 0.753644i 0.271706π0.271706\pi
354354 1035.43i 0.155459i
355355 −4124.44 + 4658.41i −0.616627 + 0.696458i
356356 1205.60i 0.179484i
357357 1884.71 + 1884.71i 0.279410 + 0.279410i
358358 −10301.0 + 10301.0i −1.52075 + 1.52075i
359359 827.280 0.121622 0.0608108 0.998149i 0.480631π-0.480631\pi
0.0608108 + 0.998149i 0.480631π0.480631\pi
360360 −1285.39 + 78.1475i −0.188183 + 0.0114409i
361361 8427.91 1.22874
362362 1778.02 1778.02i 0.258152 0.258152i
363363 −2170.59 + 2170.59i −0.313847 + 0.313847i
364364 −5949.96 −0.856766
365365 −293.164 4822.04i −0.0420408 0.691499i
366366 6727.78i 0.960837i
367367 23.1366 23.1366i 0.00329079 0.00329079i −0.705459 0.708750i 0.749259π-0.749259\pi
0.708750 + 0.705459i 0.249259π0.249259\pi
368368 8248.33 + 808.214i 1.16841 + 0.114487i
369369 2347.26i 0.331148i
370370 11966.2 13515.4i 1.68133 1.89900i
371371 7460.93 1.04408
372372 −4751.82 4751.82i −0.662287 0.662287i
373373 5882.41 + 5882.41i 0.816567 + 0.816567i 0.985609 0.169042i 0.0540672π-0.0540672\pi
−0.169042 + 0.985609i 0.554067π0.554067\pi
374374 3908.02i 0.540317i
375375 4339.99 799.461i 0.597643 0.110091i
376376 −2240.40 −0.307287
377377 2594.06 + 2594.06i 0.354379 + 0.354379i
378378 −5714.16 5714.16i −0.777525 0.777525i
379379 7914.92 1.07272 0.536362 0.843988i 0.319798π-0.319798\pi
0.536362 + 0.843988i 0.319798π0.319798\pi
380380 6422.46 + 5686.28i 0.867013 + 0.767632i
381381 −2483.14 −0.333899
382382 2845.83 2845.83i 0.381166 0.381166i
383383 −5318.45 5318.45i −0.709556 0.709556i 0.256886 0.966442i 0.417304π-0.417304\pi
−0.966442 + 0.256886i 0.917304π0.917304\pi
384384 2665.05i 0.354168i
385385 −3260.29 + 198.215i −0.431584 + 0.0262389i
386386 −2227.35 −0.293703
387387 −2646.28 + 2646.28i −0.347591 + 0.347591i
388388 6621.87 + 6621.87i 0.866429 + 0.866429i
389389 −2642.55 −0.344428 −0.172214 0.985060i 0.555092π-0.555092\pi
−0.172214 + 0.985060i 0.555092π0.555092\pi
390390 −502.045 8257.77i −0.0651847 1.07218i
391391 −4665.05 + 3832.43i −0.603381 + 0.495688i
392392 −503.010 503.010i −0.0648108 0.0648108i
393393 −946.630 + 946.630i −0.121504 + 0.121504i
394394 3048.94i 0.389857i
395395 −2434.58 + 2749.78i −0.310120 + 0.350269i
396396 2001.84i 0.254031i
397397 7988.94 + 7988.94i 1.00996 + 1.00996i 0.999950 + 0.0100085i 0.00318586π0.00318586\pi
0.0100085 + 0.999950i 0.496814π0.496814\pi
398398 9077.46 + 9077.46i 1.14325 + 1.14325i
399399 6020.90i 0.755444i
400400 −1137.80 9322.85i −0.142225 1.16536i
401401 10087.1i 1.25618i 0.778141 + 0.628090i 0.216163π0.216163\pi
−0.778141 + 0.628090i 0.783837π0.783837\pi
402402 −48.2215 + 48.2215i −0.00598277 + 0.00598277i
403403 15077.6 15077.6i 1.86369 1.86369i
404404 7426.24i 0.914527i
405405 −153.920 + 173.848i −0.0188849 + 0.0213298i
406406 3429.58i 0.419230i
407407 −5738.35 5738.35i −0.698868 0.698868i
408408 826.620 + 826.620i 0.100303 + 0.100303i
409409 378.591i 0.0457705i −0.999738 0.0228853i 0.992715π-0.992715\pi
0.999738 0.0228853i 0.00728524π-0.00728524\pi
410410 −5797.67 + 352.479i −0.698357 + 0.0424578i
411411 2910.75i 0.349335i
412412 −4016.56 + 4016.56i −0.480295 + 0.480295i
413413 948.725 + 948.725i 0.113036 + 0.113036i
414414 5470.33 4493.98i 0.649401 0.533495i
415415 12790.9 777.643i 1.51296 0.0919832i
416416 −14242.8 −1.67863
417417 2142.09 + 2142.09i 0.251555 + 0.251555i
418418 6242.27 6242.27i 0.730430 0.730430i
419419 −2865.04 −0.334049 −0.167025 0.985953i 0.553416π-0.553416\pi
−0.167025 + 0.985953i 0.553416π0.553416\pi
420420 2239.60 2529.55i 0.260194 0.293879i
421421 8714.92i 1.00888i −0.863446 0.504441i 0.831699π-0.831699\pi
0.863446 0.504441i 0.168301π-0.168301\pi
422422 6869.23 + 6869.23i 0.792390 + 0.792390i
423423 −3988.47 + 3988.47i −0.458454 + 0.458454i
424424 3272.31 0.374805
425425 5388.31 + 4216.14i 0.614992 + 0.481207i
426426 −6623.13 −0.753267
427427 −6164.41 6164.41i −0.698634 0.698634i
428428 −6772.43 6772.43i −0.764855 0.764855i
429429 −3719.23 −0.418569
430430 −6933.62 6138.86i −0.777602 0.688470i
431431 10921.2i 1.22054i 0.792192 + 0.610272i 0.208940π0.208940\pi
−0.792192 + 0.610272i 0.791060π0.791060\pi
432432 −7386.57 7386.57i −0.822654 0.822654i
433433 −4506.50 4506.50i −0.500158 0.500158i 0.411329 0.911487i 0.365065π-0.365065\pi
−0.911487 + 0.411329i 0.865065π0.865065\pi
434434 19934.0 2.20475
435435 −2079.25 + 126.411i −0.229178 + 0.0139333i
436436 164.088i 0.0180238i
437437 13573.0 + 1329.96i 1.48578 + 0.145584i
438438 3636.29 3636.29i 0.396687 0.396687i
439439 3381.56i 0.367638i 0.982960 + 0.183819i 0.0588461π0.0588461\pi
−0.982960 + 0.183819i 0.941154π0.941154\pi
440440 −1429.94 + 86.9356i −0.154931 + 0.00941930i
441441 −1790.97 −0.193388
442442 9069.48 9069.48i 0.975998 0.975998i
443443 6813.81 6813.81i 0.730776 0.730776i −0.239997 0.970774i 0.577147π-0.577147\pi
0.970774 + 0.239997i 0.0771466π0.0771466\pi
444444 8394.04 0.897215
445445 1439.89 1626.31i 0.153387 0.173246i
446446 5706.01 0.605802
447447 5048.52 5048.52i 0.534199 0.534199i
448448 −2860.40 2860.40i −0.301655 0.301655i
449449 7966.78i 0.837363i −0.908133 0.418681i 0.862492π-0.862492\pi
0.908133 0.418681i 0.137508π-0.137508\pi
450450 −6318.44 4943.93i −0.661898 0.517909i
451451 2611.22i 0.272633i
452452 438.842 438.842i 0.0456668 0.0456668i
453453 −1510.63 + 1510.63i −0.156679 + 0.156679i
454454 8734.39 0.902919
455455 8026.29 + 7106.28i 0.826986 + 0.732193i
456456 2640.72i 0.271191i
457457 2700.58 2700.58i 0.276429 0.276429i −0.555253 0.831682i 0.687378π-0.687378\pi
0.831682 + 0.555253i 0.187378π0.187378\pi
458458 6180.35 + 6180.35i 0.630543 + 0.630543i
459459 7609.69 0.773834
460460 5207.70 + 5607.52i 0.527849 + 0.568374i
461461 −5487.65 −0.554415 −0.277207 0.960810i 0.589409π-0.589409\pi
−0.277207 + 0.960810i 0.589409π0.589409\pi
462462 −2458.58 2458.58i −0.247584 0.247584i
463463 3096.37 3096.37i 0.310801 0.310801i −0.534419 0.845220i 0.679470π-0.679470\pi
0.845220 + 0.534419i 0.179470π0.179470\pi
464464 4433.35i 0.443562i
465465 734.749 + 12085.3i 0.0732756 + 1.20526i
466466 −3184.96 −0.316610
467467 1288.36 1288.36i 0.127662 0.127662i −0.640389 0.768051i 0.721227π-0.721227\pi
0.768051 + 0.640389i 0.221227π0.221227\pi
468468 −4645.75 + 4645.75i −0.458867 + 0.458867i
469469 88.3672i 0.00870025i
470470 −10450.3 9252.48i −1.02561 0.908053i
471471 9875.85i 0.966146i
472472 416.103 + 416.103i 0.0405778 + 0.0405778i
473473 −2943.87 + 2943.87i −0.286172 + 0.286172i
474474 −3909.52 −0.378840
475475 −1872.31 15341.2i −0.180858 1.48190i
476476 5237.94 0.504371
477477 5825.52 5825.52i 0.559187 0.559187i
478478 602.490 602.490i 0.0576511 0.0576511i
479479 −12639.3 −1.20564 −0.602822 0.797876i 0.705957π-0.705957\pi
−0.602822 + 0.797876i 0.705957π0.705957\pi
480480 5361.08 6055.14i 0.509789 0.575788i
481481 26634.4i 2.52479i
482482 −15586.3 + 15586.3i −1.47290 + 1.47290i
483483 523.816 5345.87i 0.0493467 0.503614i
484484 6032.44i 0.566532i
485485 −1023.90 16841.4i −0.0958620 1.57676i
486486 −14395.3 −1.34359
487487 4365.88 + 4365.88i 0.406236 + 0.406236i 0.880424 0.474188i 0.157258π-0.157258\pi
−0.474188 + 0.880424i 0.657258π0.657258\pi
488488 −2703.66 2703.66i −0.250797 0.250797i
489489 49.8140i 0.00460668i
490490 −268.943 4423.64i −0.0247951 0.407836i
491491 −3537.80 −0.325170 −0.162585 0.986695i 0.551983π-0.551983\pi
−0.162585 + 0.986695i 0.551983π0.551983\pi
492492 −1909.84 1909.84i −0.175005 0.175005i
493493 −2283.63 2283.63i −0.208620 0.208620i
494494 −28973.4 −2.63881
495495 −2390.88 + 2700.42i −0.217095 + 0.245201i
496496 25768.2 2.33272
497497 6068.53 6068.53i 0.547708 0.547708i
498498 9645.58 + 9645.58i 0.867930 + 0.867930i
499499 10053.3i 0.901902i 0.892549 + 0.450951i 0.148915π0.148915\pi
−0.892549 + 0.450951i 0.851085π0.851085\pi
500500 4919.87 7141.71i 0.440047 0.638774i
501501 9034.77 0.805676
502502 −17712.7 + 17712.7i −1.57481 + 1.57481i
503503 4941.64 + 4941.64i 0.438046 + 0.438046i 0.891354 0.453308i 0.149756π-0.149756\pi
−0.453308 + 0.891354i 0.649756π0.649756\pi
504504 1776.29 0.156988
505505 −8869.45 + 10017.7i −0.781556 + 0.882739i
506506 6085.50 4999.35i 0.534651 0.439226i
507507 3725.84 + 3725.84i 0.326372 + 0.326372i
508508 −3450.54 + 3450.54i −0.301364 + 0.301364i
509509 15010.7i 1.30715i 0.756864 + 0.653573i 0.226731π0.226731\pi
−0.756864 + 0.653573i 0.773269π0.773269\pi
510510 441.966 + 7269.57i 0.0383737 + 0.631181i
511511 6663.60i 0.576869i
512512 −9295.90 9295.90i −0.802392 0.802392i
513513 −12155.0 12155.0i −1.04611 1.04611i
514514 7003.41i 0.600987i
515515 10215.3 621.059i 0.874061 0.0531400i
516516 4306.28i 0.367390i
517517 −4437.00 + 4437.00i −0.377445 + 0.377445i
518518 −17606.6 + 17606.6i −1.49341 + 1.49341i
519519 1365.25i 0.115467i
520520 3520.27 + 3116.76i 0.296873 + 0.262844i
521521 23063.8i 1.93943i −0.244236 0.969716i 0.578537π-0.578537\pi
0.244236 0.969716i 0.421463π-0.421463\pi
522522 2677.83 + 2677.83i 0.224531 + 0.224531i
523523 4272.34 + 4272.34i 0.357202 + 0.357202i 0.862781 0.505579i 0.168721π-0.168721\pi
−0.505579 + 0.862781i 0.668721π0.668721\pi
524524 2630.85i 0.219330i
525525 −6042.29 + 737.428i −0.502299 + 0.0613028i
526526 24703.9i 2.04779i
527527 −13273.3 + 13273.3i −1.09714 + 1.09714i
528528 −3178.16 3178.16i −0.261954 0.261954i
529529 11935.6 + 2361.70i 0.980980 + 0.194107i
530530 15263.7 + 13514.1i 1.25097 + 1.10757i
531531 1481.54 0.121079
532532 −8366.56 8366.56i −0.681835 0.681835i
533533 6059.96 6059.96i 0.492469 0.492469i
534534 2312.22 0.187377
535535 1047.18 + 17224.4i 0.0846238 + 1.39191i
536536 38.7572i 0.00312324i
537537 8630.26 + 8630.26i 0.693526 + 0.693526i
538538 −10978.2 + 10978.2i −0.879743 + 0.879743i
539539 −1992.37 −0.159216
540540 −585.346 9627.92i −0.0466468 0.767259i
541541 −19660.0 −1.56238 −0.781192 0.624290i 0.785388π-0.785388\pi
−0.781192 + 0.624290i 0.785388π0.785388\pi
542542 −13944.9 13944.9i −1.10513 1.10513i
543543 −1489.64 1489.64i −0.117728 0.117728i
544544 12538.4 0.988197
545545 195.976 221.348i 0.0154031 0.0173973i
546546 11411.4i 0.894441i
547547 −9956.97 9956.97i −0.778299 0.778299i 0.201243 0.979541i 0.435502π-0.435502\pi
−0.979541 + 0.201243i 0.935502π0.935502\pi
548548 4044.74 + 4044.74i 0.315297 + 0.315297i
549549 −9626.38 −0.748350
550550 −7028.99 5499.90i −0.544940 0.426394i
551551 7295.29i 0.564047i
552552 229.742 2344.66i 0.0177146 0.180789i
553553 3582.15 3582.15i 0.275458 0.275458i
554554 34157.4i 2.61951i
555555 −11323.3 10025.3i −0.866029 0.766761i
556556 5953.22 0.454088
557557 −9154.53 + 9154.53i −0.696391 + 0.696391i −0.963630 0.267239i 0.913889π-0.913889\pi
0.267239 + 0.963630i 0.413889π0.413889\pi
558558 15564.5 15564.5i 1.18082 1.18082i
559559 13663.9 1.03385
560560 786.167 + 12931.1i 0.0593243 + 0.975782i
561561 3274.16 0.246408
562562 −7712.99 + 7712.99i −0.578919 + 0.578919i
563563 2226.16 + 2226.16i 0.166645 + 0.166645i 0.785503 0.618858i 0.212404π-0.212404\pi
−0.618858 + 0.785503i 0.712404π0.712404\pi
564564 6490.42i 0.484568i
565565 −1116.11 + 67.8558i −0.0831063 + 0.00505259i
566566 7808.52i 0.579888i
567567 226.472 226.472i 0.0167741 0.0167741i
568568 2661.61 2661.61i 0.196617 0.196617i
569569 7597.95 0.559794 0.279897 0.960030i 0.409700π-0.409700\pi
0.279897 + 0.960030i 0.409700π0.409700\pi
570570 10905.7 12317.6i 0.801388 0.905139i
571571 11583.9i 0.848988i −0.905431 0.424494i 0.860452π-0.860452\pi
0.905431 0.424494i 0.139548π-0.139548\pi
572572 −5168.19 + 5168.19i −0.377785 + 0.377785i
573573 −2384.25 2384.25i −0.173828 0.173828i
574574 8011.82 0.582591
575575 −327.717 13784.1i −0.0237683 0.999717i
576576 −4466.82 −0.323121
577577 −17653.1 17653.1i −1.27367 1.27367i −0.944146 0.329527i 0.893111π-0.893111\pi
−0.329527 0.944146i 0.606889π-0.606889\pi
578578 5109.44 5109.44i 0.367690 0.367690i
579579 1866.09i 0.133941i
580580 −2713.63 + 3064.95i −0.194272 + 0.219423i
581581 −17675.8 −1.26216
582582 12700.1 12700.1i 0.904530 0.904530i
583583 6480.64 6480.64i 0.460378 0.460378i
584584 2922.60i 0.207086i
585585 11815.6 718.347i 0.835066 0.0507692i
586586 6207.40i 0.437586i
587587 316.403 + 316.403i 0.0222476 + 0.0222476i 0.718143 0.695895i 0.244992π-0.244992\pi
−0.695895 + 0.718143i 0.744992π0.744992\pi
588588 1457.22 1457.22i 0.102202 0.102202i
589589 42402.8 2.96635
590590 222.477 + 3659.35i 0.0155241 + 0.255344i
591591 −2554.42 −0.177792
592592 −22759.6 + 22759.6i −1.58009 + 1.58009i
593593 −15783.6 + 15783.6i −1.09301 + 1.09301i −0.0978059 + 0.995206i 0.531182π0.531182\pi
−0.995206 + 0.0978059i 0.968818π0.968818\pi
594594 −9926.74 −0.685689
595595 −7065.80 6255.88i −0.486839 0.431036i
596596 14030.7i 0.964296i
597597 7605.14 7605.14i 0.521370 0.521370i
598598 −25725.0 2520.67i −1.75916 0.172371i
599599 3848.82i 0.262535i −0.991347 0.131268i 0.958095π-0.958095\pi
0.991347 0.131268i 0.0419047π-0.0419047\pi
600600 −2650.10 + 323.430i −0.180316 + 0.0220066i
601601 11585.6 0.786335 0.393168 0.919467i 0.371379π-0.371379\pi
0.393168 + 0.919467i 0.371379π0.371379\pi
602602 9032.45 + 9032.45i 0.611520 + 0.611520i
603603 −68.9974 68.9974i −0.00465969 0.00465969i
604604 4198.30i 0.282825i
605605 7204.78 8137.55i 0.484159 0.546840i
606606 −14242.8 −0.954743
607607 −3419.34 3419.34i −0.228644 0.228644i 0.583482 0.812126i 0.301690π-0.301690\pi
−0.812126 + 0.583482i 0.801690π0.801690\pi
608608 −20027.6 20027.6i −1.33590 1.33590i
609609 2873.32 0.191187
610610 −1445.56 23776.9i −0.0959490 1.57820i
611611 20594.2 1.36359
612612 4089.80 4089.80i 0.270131 0.270131i
613613 −15696.2 15696.2i −1.03420 1.03420i −0.999394 0.0348041i 0.988919π-0.988919\pi
−0.0348041 0.999394i 0.511081π-0.511081\pi
614614 9370.00i 0.615867i
615615 295.309 + 4857.32i 0.0193626 + 0.318481i
616616 1976.04 0.129248
617617 −7730.86 + 7730.86i −0.504429 + 0.504429i −0.912811 0.408382i 0.866093π-0.866093\pi
0.408382 + 0.912811i 0.366093π0.366093\pi
618618 7703.37 + 7703.37i 0.501416 + 0.501416i
619619 −18911.8 −1.22799 −0.613997 0.789308i 0.710439π-0.710439\pi
−0.613997 + 0.789308i 0.710439π0.710439\pi
620620 17814.6 + 15772.6i 1.15396 + 1.02168i
621621 −9734.73 11849.7i −0.629052 0.765719i
622622 −5960.18 5960.18i −0.384214 0.384214i
623623 −2118.60 + 2118.60i −0.136244 + 0.136244i
624624 14751.3i 0.946356i
625625 −15166.4 + 3757.92i −0.970647 + 0.240507i
626626 14531.7i 0.927803i
627627 −5229.81 5229.81i −0.333108 0.333108i
628628 13723.3 + 13723.3i 0.872007 + 0.872007i
629629 23447.1i 1.48632i
630630 8285.49 + 7335.77i 0.523971 + 0.463911i
631631 5284.78i 0.333414i 0.986007 + 0.166707i 0.0533133π0.0533133\pi
−0.986007 + 0.166707i 0.946687π0.946687\pi
632632 1571.10 1571.10i 0.0988846 0.0988846i
633633 5755.08 5755.08i 0.361364 0.361364i
634634 13762.7i 0.862122i
635635 8775.78 533.539i 0.548435 0.0333430i
636636 9479.85i 0.591039i
637637 4623.77 + 4623.77i 0.287599 + 0.287599i
638638 2978.97 + 2978.97i 0.184856 + 0.184856i
639639 9476.66i 0.586683i
640640 572.624 + 9418.67i 0.0353671 + 0.581728i
641641 15200.5i 0.936633i 0.883561 + 0.468316i 0.155139π0.155139\pi
−0.883561 + 0.468316i 0.844861π0.844861\pi
642642 −12988.9 + 12988.9i −0.798488 + 0.798488i
643643 −7121.12 7121.12i −0.436749 0.436749i 0.454168 0.890916i 0.349937π-0.349937\pi
−0.890916 + 0.454168i 0.849937π0.849937\pi
644644 −6700.66 8156.44i −0.410005 0.499082i
645645 −5143.17 + 5809.02i −0.313972 + 0.354620i
646646 25506.2 1.55345
647647 −8196.32 8196.32i −0.498038 0.498038i 0.412789 0.910827i 0.364555π-0.364555\pi
−0.910827 + 0.412789i 0.864555π0.864555\pi
648648 99.3288 99.3288i 0.00602161 0.00602161i
649649 1648.14 0.0996845
650650 3548.60 + 29076.3i 0.214135 + 1.75456i
651651 16700.8i 1.00546i
652652 −69.2208 69.2208i −0.00415782 0.00415782i
653653 18159.3 18159.3i 1.08825 1.08825i 0.0925400 0.995709i 0.470501π-0.470501\pi
0.995709 0.0925400i 0.0294986π-0.0294986\pi
654654 314.704 0.0188164
655655 3142.13 3548.92i 0.187440 0.211707i
656656 10356.7 0.616405
657657 5202.96 + 5202.96i 0.308960 + 0.308960i
658658 13613.7 + 13613.7i 0.806562 + 0.806562i
659659 1528.01 0.0903230 0.0451615 0.998980i 0.485620π-0.485620\pi
0.0451615 + 0.998980i 0.485620π0.485620\pi
660660 −251.852 4142.53i −0.0148535 0.244315i
661661 29321.0i 1.72535i −0.505759 0.862675i 0.668788π-0.668788\pi
0.505759 0.862675i 0.331212π-0.331212\pi
662662 17322.7 + 17322.7i 1.01702 + 1.01702i
663663 −7598.46 7598.46i −0.445098 0.445098i
664664 −7752.46 −0.453093
665665 1293.68 + 21278.7i 0.0754385 + 1.24083i
666666 27494.5i 1.59969i
667667 −634.688 + 6477.38i −0.0368444 + 0.376020i
668668 12554.6 12554.6i 0.727173 0.727173i
669669 4780.53i 0.276272i
670670 160.061 180.783i 0.00922938 0.0104243i
671671 −10708.9 −0.616116
672672 −7888.06 + 7888.06i −0.452810 + 0.452810i
673673 9123.62 9123.62i 0.522570 0.522570i −0.395777 0.918347i 0.629525π-0.629525\pi
0.918347 + 0.395777i 0.129525π0.129525\pi
674674 14580.8 0.833282
675675 −10709.4 + 13686.8i −0.610675 + 0.780454i
676676 10354.8 0.589142
677677 19862.8 19862.8i 1.12760 1.12760i 0.137038 0.990566i 0.456242π-0.456242\pi
0.990566 0.137038i 0.0437581π-0.0437581\pi
678678 −841.656 841.656i −0.0476749 0.0476749i
679679 23273.3i 1.31538i
680680 −3099.00 2743.78i −0.174767 0.154734i
681681 7317.72i 0.411771i
682682 17314.8 17314.8i 0.972169 0.972169i
683683 −9499.06 + 9499.06i −0.532169 + 0.532169i −0.921217 0.389048i 0.872804π-0.872804\pi
0.389048 + 0.921217i 0.372804π0.372804\pi
684684 −13065.3 −0.730356
685685 −625.416 10287.0i −0.0348846 0.573791i
686686 26049.7i 1.44983i
687687 5177.93 5177.93i 0.287555 0.287555i
688688 11676.1 + 11676.1i 0.647014 + 0.647014i
689689 −30079.7 −1.66320
690690 10754.7 9987.86i 0.593368 0.551060i
691691 −13891.8 −0.764791 −0.382395 0.923999i 0.624901π-0.624901\pi
−0.382395 + 0.923999i 0.624901π0.624901\pi
692692 1897.13 + 1897.13i 0.104217 + 0.104217i
693693 3517.84 3517.84i 0.192831 0.192831i
694694 35892.1i 1.96318i
695695 −8030.69 7110.18i −0.438304 0.388064i
696696 1260.22 0.0686328
697697 −5334.77 + 5334.77i −0.289912 + 0.289912i
698698 17363.8 17363.8i 0.941588 0.941588i
699699 2668.38i 0.144388i
700700 −7371.55 + 9420.99i −0.398027 + 0.508686i
701701 18088.4i 0.974591i 0.873237 + 0.487295i 0.162016π0.162016\pi
−0.873237 + 0.487295i 0.837984π0.837984\pi
702702 23037.4 + 23037.4i 1.23859 + 1.23859i
703703 −37452.1 + 37452.1i −2.00929 + 2.00929i
704704 −4969.14 −0.266025
705705 −7751.78 + 8755.36i −0.414112 + 0.467725i
706706 3406.46 0.181592
707707 13050.1 13050.1i 0.694202 0.694202i
708708 −1205.45 + 1205.45i −0.0639881 + 0.0639881i
709709 11448.7 0.606441 0.303221 0.952920i 0.401938π-0.401938\pi
0.303221 + 0.952920i 0.401938π0.401938\pi
710710 23407.1 1423.07i 1.23726 0.0752211i
711711 5593.90i 0.295060i
712712 −929.200 + 929.200i −0.0489091 + 0.0489091i
713713 37648.9 + 3689.03i 1.97751 + 0.193766i
714714 10045.9i 0.526550i
715715 13144.3 799.130i 0.687509 0.0417983i
716716 23985.0 1.25190
717717 −504.769 504.769i −0.0262914 0.0262914i
718718 −2204.78 2204.78i −0.114598 0.114598i
719719 14259.4i 0.739619i −0.929108 0.369810i 0.879423π-0.879423\pi
0.929108 0.369810i 0.120577π-0.120577\pi
720720 10710.5 + 9482.79i 0.554383 + 0.490837i
721721 −14116.6 −0.729168
722722 −22461.1 22461.1i −1.15778 1.15778i
723723 13058.3 + 13058.3i 0.671706 + 0.671706i
724724 −4139.96 −0.212514
725725 7321.20 893.512i 0.375038 0.0457713i
726726 11569.6 0.591445
727727 5679.43 5679.43i 0.289737 0.289737i −0.547240 0.836976i 0.684321π-0.684321\pi
0.836976 + 0.547240i 0.184321π0.184321\pi
728728 −4585.87 4585.87i −0.233467 0.233467i
729729 11499.7i 0.584246i
730730 −12069.9 + 13632.5i −0.611953 + 0.691179i
731731 −12028.7 −0.608617
732732 7832.49 7832.49i 0.395488 0.395488i
733733 −15227.1 15227.1i −0.767291 0.767291i 0.210338 0.977629i 0.432544π-0.432544\pi
−0.977629 + 0.210338i 0.932544π0.932544\pi
734734 −123.322 −0.00620150
735735 −3706.15 + 225.321i −0.185991 + 0.0113076i
736736 −16039.8 19524.6i −0.803308 0.977834i
737737 −76.7566 76.7566i −0.00383632 0.00383632i
738738 6255.66 6255.66i 0.312024 0.312024i
739739 35436.4i 1.76393i 0.471311 + 0.881967i 0.343781π0.343781\pi
−0.471311 + 0.881967i 0.656219π0.656219\pi
740740 −29665.7 + 1803.58i −1.47369 + 0.0895957i
741741 24274.0i 1.20341i
742742 −19884.1 19884.1i −0.983783 0.983783i
743743 −15295.3 15295.3i −0.755222 0.755222i 0.220226 0.975449i 0.429320π-0.429320\pi
−0.975449 + 0.220226i 0.929320π0.929320\pi
744744 7324.84i 0.360943i
745745 −16757.5 + 18926.9i −0.824088 + 0.930778i
746746 31354.3i 1.53882i
747747 −13801.3 + 13801.3i −0.675988 + 0.675988i
748748 4549.72 4549.72i 0.222399 0.222399i
749749 23802.4i 1.16118i
750750 −13697.1 9435.83i −0.666863 0.459397i
751751 25279.5i 1.22831i −0.789185 0.614155i 0.789497π-0.789497\pi
0.789185 0.614155i 0.210503π-0.210503\pi
752752 17598.1 + 17598.1i 0.853376 + 0.853376i
753753 14839.8 + 14839.8i 0.718183 + 0.718183i
754754 13826.8i 0.667828i
755755 5014.20 5663.36i 0.241703 0.272995i
756756 13304.9i 0.640071i
757757 10121.6 10121.6i 0.485965 0.485965i −0.421065 0.907030i 0.638344π-0.638344\pi
0.907030 + 0.421065i 0.138344π0.138344\pi
758758 −21094.0 21094.0i −1.01078 1.01078i
759759 −4188.48 5098.47i −0.200306 0.243824i
760760 567.396 + 9332.68i 0.0270811 + 0.445437i
761761 33559.8 1.59861 0.799305 0.600926i 0.205201π-0.205201\pi
0.799305 + 0.600926i 0.205201π0.205201\pi
762762 6617.80 + 6617.80i 0.314616 + 0.314616i
763763 −288.351 + 288.351i −0.0136815 + 0.0136815i
764764 −6626.25 −0.313782
765765 −10401.6 + 632.383i −0.491596 + 0.0298874i
766766 28348.3i 1.33716i
767767 −3824.91 3824.91i −0.180064 0.180064i
768768 −11788.1 + 11788.1i −0.553862 + 0.553862i
769769 −21057.2 −0.987440 −0.493720 0.869621i 0.664363π-0.664363\pi
−0.493720 + 0.869621i 0.664363π0.664363\pi
770770 9217.24 + 8160.72i 0.431385 + 0.381937i
771771 −5867.50 −0.274076
772772 2593.09 + 2593.09i 0.120890 + 0.120890i
773773 11098.1 + 11098.1i 0.516394 + 0.516394i 0.916478 0.400084i 0.131019π-0.131019\pi
−0.400084 + 0.916478i 0.631019π0.631019\pi
774774 14105.1 0.655037
775775 −5193.41 42553.4i −0.240713 1.97234i
776776 10207.5i 0.472200i
777777 14750.9 + 14750.9i 0.681061 + 0.681061i
778778 7042.64 + 7042.64i 0.324538 + 0.324538i
779779 17042.5 0.783838
780780 −9029.23 + 10198.2i −0.414485 + 0.468146i
781781 10542.4i 0.483016i
782782 22646.5 + 2219.03i 1.03560 + 0.101473i
783783 5800.64 5800.64i 0.264749 0.264749i
784784 7902.20i 0.359976i
785785 −2121.96 34902.6i −0.0964792 1.58692i
786786 5045.71 0.228975
787787 1443.79 1443.79i 0.0653944 0.0653944i −0.673653 0.739048i 0.735276π-0.735276\pi
0.739048 + 0.673653i 0.235276π0.235276\pi
788788 −3549.59 + 3549.59i −0.160468 + 0.160468i
789789 −20697.0 −0.933883
790790 13816.8 840.015i 0.622252 0.0378309i
791791 1542.36 0.0693298
792792 1542.90 1542.90i 0.0692229 0.0692229i
793793 24852.6 + 24852.6i 1.11292 + 1.11292i
794794 42582.5i 1.90327i
795795 11322.2 12788.0i 0.505102 0.570495i
796796 21136.0i 0.941138i
797797 18915.6 18915.6i 0.840685 0.840685i −0.148263 0.988948i 0.547368π-0.547368\pi
0.988948 + 0.148263i 0.0473681π0.0473681\pi
798798 −16046.2 + 16046.2i −0.711818 + 0.711818i
799799 −18129.7 −0.802733
800800 −17645.8 + 22551.6i −0.779840 + 0.996651i
801801 3308.41i 0.145939i
802802 26883.1 26883.1i 1.18364 1.18364i
803803 5788.06 + 5788.06i 0.254366 + 0.254366i
804804 112.279 0.00492510
805805 −702.605 + 19005.6i −0.0307622 + 0.832124i
806806 −80366.3 −3.51214
807807 9197.56 + 9197.56i 0.401201 + 0.401201i
808808 5723.69 5723.69i 0.249206 0.249206i
809809 10249.3i 0.445424i −0.974884 0.222712i 0.928509π-0.928509\pi
0.974884 0.222712i 0.0714909π-0.0714909\pi
810810 873.531 53.1078i 0.0378923 0.00230373i
811811 −3859.70 −0.167117 −0.0835587 0.996503i 0.526629π-0.526629\pi
−0.0835587 + 0.996503i 0.526629π0.526629\pi
812812 3992.73 3992.73i 0.172558 0.172558i
813813 −11683.1 + 11683.1i −0.503989 + 0.503989i
814814 30586.4i 1.31702i
815815 10.7032 + 176.050i 0.000460022 + 0.00756657i
816816 12986.1i 0.557112i
817817 19213.5 + 19213.5i 0.822761 + 0.822761i
818818 −1008.98 + 1008.98i −0.0431273 + 0.0431273i
819819 −16328.0 −0.696637
820820 7160.02 + 6339.30i 0.304925 + 0.269973i
821821 29254.9 1.24361 0.621804 0.783173i 0.286400π-0.286400\pi
0.621804 + 0.783173i 0.286400π0.286400\pi
822822 7757.42 7757.42i 0.329162 0.329162i
823823 −12146.6 + 12146.6i −0.514463 + 0.514463i −0.915891 0.401428i 0.868514π-0.868514\pi
0.401428 + 0.915891i 0.368514π0.368514\pi
824824 −6191.44 −0.261758
825825 −4607.85 + 5888.92i −0.194454 + 0.248516i
826826 5056.87i 0.213016i
827827 5754.51 5754.51i 0.241963 0.241963i −0.575699 0.817662i 0.695270π-0.695270\pi
0.817662 + 0.575699i 0.195270π0.195270\pi
828828 −11600.5 1136.67i −0.486889 0.0477079i
829829 31276.9i 1.31036i −0.755471 0.655182i 0.772592π-0.772592\pi
0.755471 0.655182i 0.227408π-0.227408\pi
830830 −36161.3 32016.4i −1.51226 1.33892i
831831 28617.3 1.19461
832832 11532.1 + 11532.1i 0.480532 + 0.480532i
833833 −4070.45 4070.45i −0.169307 0.169307i
834834 11417.7i 0.474056i
835835 −31930.1 + 1941.25i −1.32334 + 0.0804546i
836836 −14534.5 −0.601301
837837 −33715.4 33715.4i −1.39232 1.39232i
838838 7635.60 + 7635.60i 0.314758 + 0.314758i
839839 42594.8 1.75273 0.876363 0.481652i 0.159963π-0.159963\pi
0.876363 + 0.481652i 0.159963π0.159963\pi
840840 3675.77 223.475i 0.150983 0.00917930i
841841 20907.5 0.857252
842842 −23226.1 + 23226.1i −0.950621 + 0.950621i
843843 6461.98 + 6461.98i 0.264012 + 0.264012i
844844 15994.3i 0.652308i
845845 −13968.2 12367.1i −0.568664 0.503481i
846846 21259.3 0.863958
847847 −10600.8 + 10600.8i −0.430045 + 0.430045i
848848 −25703.7 25703.7i −1.04088 1.04088i
849849 −6542.02 −0.264454
850850 −3123.94 25596.7i −0.126059 1.03290i
851851 −36511.5 + 29994.8i −1.47074 + 1.20824i
852852 7710.67 + 7710.67i 0.310051 + 0.310051i
853853 −34306.5 + 34306.5i −1.37706 + 1.37706i −0.527513 + 0.849547i 0.676876π0.676876\pi
−0.849547 + 0.527513i 0.823124π0.823124\pi
854854 32857.4i 1.31658i
855855 17624.6 + 15604.4i 0.704969 + 0.624162i
856856 10439.6i 0.416842i
857857 30152.9 + 30152.9i 1.20187 + 1.20187i 0.973597 + 0.228272i 0.0733075π0.0733075\pi
0.228272 + 0.973597i 0.426692π0.426692\pi
858858 9912.09 + 9912.09i 0.394398 + 0.394398i
859859 39680.0i 1.57609i 0.615615 + 0.788047i 0.288908π0.288908\pi
−0.615615 + 0.788047i 0.711092π0.711092\pi
860860 925.265 + 15219.0i 0.0366875 + 0.603446i
861861 6712.35i 0.265687i
862862 29105.9 29105.9i 1.15006 1.15006i
863863 −19509.0 + 19509.0i −0.769517 + 0.769517i −0.978021 0.208504i 0.933140π-0.933140\pi
0.208504 + 0.978021i 0.433140π0.433140\pi
864864 31848.7i 1.25407i
865865 −293.342 4824.97i −0.0115306 0.189658i
866866 24020.5i 0.942550i
867867 −4280.72 4280.72i −0.167683 0.167683i
868868 −23207.2 23207.2i −0.907492 0.907492i
869869 6222.97i 0.242923i
870870 5878.28 + 5204.49i 0.229072 + 0.202815i
871871 356.264i 0.0138594i
872872 −126.469 + 126.469i −0.00491143 + 0.00491143i
873873 18171.8 + 18171.8i 0.704494 + 0.704494i
874874 −32628.9 39717.8i −1.26280 1.53716i
875875 21195.8 3904.44i 0.818915 0.150851i
876876 −8466.76 −0.326558
877877 −10899.2 10899.2i −0.419658 0.419658i 0.465428 0.885086i 0.345901π-0.345901\pi
−0.885086 + 0.465428i 0.845901π0.845901\pi
878878 9012.17 9012.17i 0.346408 0.346408i
879879 −5200.59 −0.199558
880880 11914.9 + 10549.2i 0.456423 + 0.404106i
881881 10123.2i 0.387128i −0.981088 0.193564i 0.937995π-0.937995\pi
0.981088 0.193564i 0.0620046π-0.0620046\pi
882882 4773.08 + 4773.08i 0.182220 + 0.182220i
883883 22947.2 22947.2i 0.874559 0.874559i −0.118406 0.992965i 0.537778π-0.537778\pi
0.992965 + 0.118406i 0.0377784π0.0377784\pi
884884 −21117.4 −0.803457
885885 3065.82 186.392i 0.116448 0.00707966i
886886 −36318.8 −1.37715
887887 10590.2 + 10590.2i 0.400883 + 0.400883i 0.878544 0.477661i 0.158515π-0.158515\pi
−0.477661 + 0.878544i 0.658515π0.658515\pi
888888 6469.62 + 6469.62i 0.244489 + 0.244489i
889889 −12127.3 −0.457521
890890 −8171.70 + 496.812i −0.307771 + 0.0187114i
891891 393.431i 0.0147929i
892892 −6642.96 6642.96i −0.249353 0.249353i
893893 28958.6 + 28958.6i 1.08518 + 1.08518i
894894 −26909.5 −1.00670
895895 −32354.9 28646.2i −1.20839 1.06988i
896896 13015.7i 0.485295i
897897 −2111.83 + 21552.6i −0.0786087 + 0.802251i
898898 −21232.2 + 21232.2i −0.789006 + 0.789006i
899899 20235.7i 0.750720i
900900 1600.21 + 13111.7i 0.0592670 + 0.485618i
901901 26480.1 0.979112
902902 6959.14 6959.14i 0.256889 0.256889i
903903 7567.44 7567.44i 0.278880 0.278880i
904904 676.466 0.0248882
905905 5584.66 + 4944.52i 0.205128 + 0.181615i
906906 8051.94 0.295262
907907 −25408.5 + 25408.5i −0.930182 + 0.930182i −0.997717 0.0675352i 0.978486π-0.978486\pi
0.0675352 + 0.997717i 0.478486π0.478486\pi
908908 −10168.6 10168.6i −0.371649 0.371649i
909909 20379.2i 0.743603i
910910 −2451.91 40329.7i −0.0893187 1.46914i
911911 20676.1i 0.751953i −0.926629 0.375977i 0.877307π-0.877307\pi
0.926629 0.375977i 0.122693π-0.122693\pi
912912 −20742.6 + 20742.6i −0.753133 + 0.753133i
913913 −15353.3 + 15353.3i −0.556541 + 0.556541i
914914 −14394.6 −0.520931
915915 −19920.4 + 1211.10i −0.719726 + 0.0437569i
916916 14390.4i 0.519073i
917917 −4623.19 + 4623.19i −0.166490 + 0.166490i
918918 −20280.5 20280.5i −0.729146 0.729146i
919919 −7362.30 −0.264265 −0.132133 0.991232i 0.542183π-0.542183\pi
−0.132133 + 0.991232i 0.542183π0.542183\pi
920920 −308.157 + 8335.72i −0.0110431 + 0.298718i
921921 −7850.23 −0.280862
922922 14625.1 + 14625.1i 0.522398 + 0.522398i
923923 −24466.1 + 24466.1i −0.872492 + 0.872492i
924924 5724.57i 0.203815i
925925 42172.1 + 32998.0i 1.49904 + 1.17294i
926926 −16504.2 −0.585705
927927 −11022.3 + 11022.3i −0.390528 + 0.390528i
928928 9557.65 9557.65i 0.338088 0.338088i
929929 2698.64i 0.0953061i −0.998864 0.0476531i 0.984826π-0.984826\pi
0.998864 0.0476531i 0.0151742π-0.0151742\pi
930930 30250.3 34166.7i 1.06661 1.20470i
931931 13003.5i 0.457756i
932932 3707.94 + 3707.94i 0.130319 + 0.130319i
933933 −4993.47 + 4993.47i −0.175218 + 0.175218i
934934 −6867.21 −0.240580
935935 −11571.3 + 703.499i −0.404731 + 0.0246063i
936936 −7161.33 −0.250080
937937 −21145.4 + 21145.4i −0.737236 + 0.737236i −0.972042 0.234806i 0.924554π-0.924554\pi
0.234806 + 0.972042i 0.424554π0.424554\pi
938938 −235.507 + 235.507i −0.00819783 + 0.00819783i
939939 12174.8 0.423118
940940 1394.56 + 22938.1i 0.0483888 + 0.795912i
941941 29419.1i 1.01917i −0.860421 0.509584i 0.829799π-0.829799\pi
0.860421 0.509584i 0.170201π-0.170201\pi
942942 26320.0 26320.0i 0.910353 0.910353i
943943 15131.8 + 1482.69i 0.522543 + 0.0512015i
944944 6536.91i 0.225380i
945945 15890.5 17947.8i 0.547005 0.617822i
946946 15691.3 0.539291
947947 −26514.1 26514.1i −0.909813 0.909813i 0.0864433 0.996257i 0.472450π-0.472450\pi
−0.996257 + 0.0864433i 0.972450π0.972450\pi
948948 4551.47 + 4551.47i 0.155933 + 0.155933i
949949 26865.1i 0.918945i
950950 −35895.8 + 45875.5i −1.22591 + 1.56674i
951951 11530.4 0.393165
952952 4037.08 + 4037.08i 0.137440 + 0.137440i
953953 22263.0 + 22263.0i 0.756737 + 0.756737i 0.975727 0.218990i 0.0702763π-0.0702763\pi
−0.218990 + 0.975727i 0.570276π0.570276\pi
954954 −31051.1 −1.05379
955955 8938.58 + 7914.00i 0.302875 + 0.268158i
956956 −1402.84 −0.0474593
957957 2495.79 2495.79i 0.0843026 0.0843026i
958958 33684.8 + 33684.8i 1.13602 + 1.13602i
959959 14215.7i 0.478673i
960960 −9243.45 + 561.971i −0.310762 + 0.0188933i
961961 87826.0 2.94807
962962 70983.1 70983.1i 2.37899 2.37899i
963963 −18585.0 18585.0i −0.621904 0.621904i
964964 36291.2 1.21251
965965 −400.956 6595.02i −0.0133754 0.220001i
966966 −15643.2 + 12851.2i −0.521028 + 0.428034i
967967 29502.6 + 29502.6i 0.981115 + 0.981115i 0.999825 0.0187100i 0.00595592π-0.00595592\pi
−0.0187100 + 0.999825i 0.505956π0.505956\pi
968968 −4649.43 + 4649.43i −0.154379 + 0.154379i
969969 21369.2i 0.708439i
970970 −42155.2 + 47612.8i −1.39538 + 1.57603i
971971 23515.6i 0.777189i −0.921409 0.388595i 0.872961π-0.872961\pi
0.921409 0.388595i 0.127039π-0.127039\pi
972972 16759.0 + 16759.0i 0.553031 + 0.553031i
973973 10461.6 + 10461.6i 0.344691 + 0.344691i
974974 23270.9i 0.765552i
975975 24360.2 2973.03i 0.800156 0.0976546i
976976 42474.1i 1.39299i
977977 −273.011 + 273.011i −0.00894001 + 0.00894001i −0.711563 0.702623i 0.752012π-0.752012\pi
0.702623 + 0.711563i 0.252012π0.252012\pi
978978 −132.759 + 132.759i −0.00434065 + 0.00434065i
979979 3680.47i 0.120151i
980980 −4836.91 + 5463.11i −0.157663 + 0.178074i
981981 450.292i 0.0146551i
982982 9428.55 + 9428.55i 0.306392 + 0.306392i
983983 −19120.1 19120.1i −0.620384 0.620384i 0.325246 0.945630i 0.394553π-0.394553\pi
−0.945630 + 0.325246i 0.894553π0.894553\pi
984984 2943.98i 0.0953768i
985985 9027.68 548.853i 0.292026 0.0177542i
986986 12172.2i 0.393145i
987987 11405.6 11405.6i 0.367827 0.367827i
988988 33730.9 + 33730.9i 1.08616 + 1.08616i
989989 15387.8 + 18731.0i 0.494747 + 0.602235i
990990 13568.8 824.936i 0.435600 0.0264830i
991991 13161.6 0.421890 0.210945 0.977498i 0.432346π-0.432346\pi
0.210945 + 0.977498i 0.432346π0.432346\pi
992992 −55552.5 55552.5i −1.77802 1.77802i
993993 14513.1 14513.1i 0.463806 0.463806i
994994 −32346.4 −1.03216
995995 −25243.6 + 28511.7i −0.804297 + 0.908425i
996996 22458.8i 0.714493i
997997 −441.130 441.130i −0.0140128 0.0140128i 0.700066 0.714078i 0.253154π-0.253154\pi
−0.714078 + 0.700066i 0.753154π0.753154\pi
998998 26793.1 26793.1i 0.849819 0.849819i
999999 59557.9 1.88621
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 115.4.e.a.22.8 yes 68
5.3 odd 4 inner 115.4.e.a.68.7 yes 68
23.22 odd 2 inner 115.4.e.a.22.7 68
115.68 even 4 inner 115.4.e.a.68.8 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.e.a.22.7 68 23.22 odd 2 inner
115.4.e.a.22.8 yes 68 1.1 even 1 trivial
115.4.e.a.68.7 yes 68 5.3 odd 4 inner
115.4.e.a.68.8 yes 68 115.68 even 4 inner