Properties

Label 275.3.q.f.24.3
Level 275275
Weight 33
Character 275.24
Analytic conductor 7.4937.493
Analytic rank 00
Dimension 2424
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] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 275=5211 275 = 5^{2} \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 275.q (of order 1010, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,-26,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.493207269917.49320726991
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 24.3
Character χ\chi == 275.24
Dual form 275.3.q.f.149.3

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+(0.0941972+0.289909i)q2+(3.03467+4.17687i)q3+(3.16089+2.29652i)q4+(1.49677+0.486330i)q6+(8.179745.94293i)q7+(1.94998+1.41674i)q8+(5.45583+16.7913i)q9+(1.50807+10.8961i)q11+20.1718iq12+(1.498914.61316i)q13+(2.493421.81157i)q14+(4.60237+14.1646i)q16+(0.8835562.71930i)q17+(4.354033.16339i)q18+(12.5616+17.2895i)q1952.2005iq21+(3.016831.46359i)q22+12.1155iq23+(11.83513.84545i)q24+(1.19620+0.869094i)q26+(42.4999+13.8091i)q27+(12.207237.5699i)q28+(28.061038.6227i)q29+(9.6373729.6608i)q3114.1812q32+(50.0882+26.7672i)q33+0.871580q34+(55.8070+40.5461i)q36+(11.677316.0724i)q37+(6.19566+2.01309i)q38+(23.81727.73869i)q39+(23.5474+32.4102i)q41+(15.1334+4.91714i)q42+28.7133q43+(29.7901+30.9782i)q44+(3.512401.14125i)q46+(2.31141+3.18139i)q47+(45.1971+62.2085i)q48+(16.4479+50.6214i)q49+(8.6768711.9427i)q51+(15.332111.1394i)q52+(59.9100+19.4659i)q5313.6219iq54+24.3699q56+(34.0958+104.936i)q57+(8.55381+11.7733i)q58+(41.475830.1339i)q59+(31.600110.2675i)q61+(7.69112+5.58793i)q62+(144.417104.925i)q63+(17.0737+52.5473i)q64+(3.0418917.0424i)q6690.1298iq67+(3.4521210.6245i)q68+(50.6049+36.7666i)q69+(1.85591+5.71191i)q71+(13.150240.4722i)q72+(105.90276.9424i)q73+(3.55957+4.89933i)q74+83.4983iq76+(77.090580.1652i)q77+7.63380iq78+(85.460427.7678i)q79+(58.100042.2121i)q81+(11.6141+3.77365i)q82+(27.3155+84.0686i)q83+(119.880165.000i)q84+(2.70472+8.32426i)q86+246.478q87+(12.496323.3837i)q88+118.531q89+(39.6764+28.8266i)q91+(27.8236+38.2959i)q92+(153.13549.7567i)q93+(1.14004+0.370422i)q94+(43.035359.2330i)q96+(63.554420.6501i)q9716.2250q98+(174.73384.7699i)q99+O(q100)q+(-0.0941972 + 0.289909i) q^{2} +(3.03467 + 4.17687i) q^{3} +(3.16089 + 2.29652i) q^{4} +(-1.49677 + 0.486330i) q^{6} +(-8.17974 - 5.94293i) q^{7} +(-1.94998 + 1.41674i) q^{8} +(-5.45583 + 16.7913i) q^{9} +(-1.50807 + 10.8961i) q^{11} +20.1718i q^{12} +(1.49891 - 4.61316i) q^{13} +(2.49342 - 1.81157i) q^{14} +(4.60237 + 14.1646i) q^{16} +(-0.883556 - 2.71930i) q^{17} +(-4.35403 - 3.16339i) q^{18} +(12.5616 + 17.2895i) q^{19} -52.2005i q^{21} +(-3.01683 - 1.46359i) q^{22} +12.1155i q^{23} +(-11.8351 - 3.84545i) q^{24} +(1.19620 + 0.869094i) q^{26} +(-42.4999 + 13.8091i) q^{27} +(-12.2072 - 37.5699i) q^{28} +(28.0610 - 38.6227i) q^{29} +(9.63737 - 29.6608i) q^{31} -14.1812 q^{32} +(-50.0882 + 26.7672i) q^{33} +0.871580 q^{34} +(-55.8070 + 40.5461i) q^{36} +(11.6773 - 16.0724i) q^{37} +(-6.19566 + 2.01309i) q^{38} +(23.8172 - 7.73869i) q^{39} +(23.5474 + 32.4102i) q^{41} +(15.1334 + 4.91714i) q^{42} +28.7133 q^{43} +(-29.7901 + 30.9782i) q^{44} +(-3.51240 - 1.14125i) q^{46} +(2.31141 + 3.18139i) q^{47} +(-45.1971 + 62.2085i) q^{48} +(16.4479 + 50.6214i) q^{49} +(8.67687 - 11.9427i) q^{51} +(15.3321 - 11.1394i) q^{52} +(59.9100 + 19.4659i) q^{53} -13.6219i q^{54} +24.3699 q^{56} +(-34.0958 + 104.936i) q^{57} +(8.55381 + 11.7733i) q^{58} +(-41.4758 - 30.1339i) q^{59} +(31.6001 - 10.2675i) q^{61} +(7.69112 + 5.58793i) q^{62} +(144.417 - 104.925i) q^{63} +(-17.0737 + 52.5473i) q^{64} +(-3.04189 - 17.0424i) q^{66} -90.1298i q^{67} +(3.45212 - 10.6245i) q^{68} +(-50.6049 + 36.7666i) q^{69} +(1.85591 + 5.71191i) q^{71} +(-13.1502 - 40.4722i) q^{72} +(-105.902 - 76.9424i) q^{73} +(3.55957 + 4.89933i) q^{74} +83.4983i q^{76} +(77.0905 - 80.1652i) q^{77} +7.63380i q^{78} +(-85.4604 - 27.7678i) q^{79} +(-58.1000 - 42.2121i) q^{81} +(-11.6141 + 3.77365i) q^{82} +(27.3155 + 84.0686i) q^{83} +(119.880 - 165.000i) q^{84} +(-2.70472 + 8.32426i) q^{86} +246.478 q^{87} +(-12.4963 - 23.3837i) q^{88} +118.531 q^{89} +(-39.6764 + 28.8266i) q^{91} +(-27.8236 + 38.2959i) q^{92} +(153.135 - 49.7567i) q^{93} +(-1.14004 + 0.370422i) q^{94} +(-43.0353 - 59.2330i) q^{96} +(-63.5544 - 20.6501i) q^{97} -16.2250 q^{98} +(-174.733 - 84.7699i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q26q4+40q68q9+24q11+120q1486q16+160q19420q24240q2610q2992q3120q3478q36+570q39+460q41976q44+410q46+1338q99+O(q100) 24 q - 26 q^{4} + 40 q^{6} - 8 q^{9} + 24 q^{11} + 120 q^{14} - 86 q^{16} + 160 q^{19} - 420 q^{24} - 240 q^{26} - 10 q^{29} - 92 q^{31} - 20 q^{34} - 78 q^{36} + 570 q^{39} + 460 q^{41} - 976 q^{44} + 410 q^{46}+ \cdots - 1338 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/275Z)×\left(\mathbb{Z}/275\mathbb{Z}\right)^\times.

nn 101101 177177
χ(n)\chi(n) e(110)e\left(\frac{1}{10}\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 −0.0941972 + 0.289909i −0.0470986 + 0.144955i −0.971840 0.235641i 0.924281π-0.924281\pi
0.924742 + 0.380596i 0.124281π0.124281\pi
33 3.03467 + 4.17687i 1.01156 + 1.39229i 0.917957 + 0.396679i 0.129837π0.129837\pi
0.0935994 + 0.995610i 0.470163π0.470163\pi
44 3.16089 + 2.29652i 0.790223 + 0.574131i
55 0 0
66 −1.49677 + 0.486330i −0.249462 + 0.0810550i
77 −8.17974 5.94293i −1.16853 0.848990i −0.177701 0.984084i 0.556866π-0.556866\pi
−0.990833 + 0.135095i 0.956866π0.956866\pi
88 −1.94998 + 1.41674i −0.243747 + 0.177093i
99 −5.45583 + 16.7913i −0.606203 + 1.86570i
1010 0 0
1111 −1.50807 + 10.8961i −0.137097 + 0.990558i
1212 20.1718i 1.68099i
1313 1.49891 4.61316i 0.115301 0.354859i −0.876709 0.481021i 0.840266π-0.840266\pi
0.992010 + 0.126162i 0.0402661π0.0402661\pi
1414 2.49342 1.81157i 0.178101 0.129398i
1515 0 0
1616 4.60237 + 14.1646i 0.287648 + 0.885290i
1717 −0.883556 2.71930i −0.0519739 0.159959i 0.921701 0.387902i 0.126800π-0.126800\pi
−0.973675 + 0.227943i 0.926800π0.926800\pi
1818 −4.35403 3.16339i −0.241891 0.175744i
1919 12.5616 + 17.2895i 0.661136 + 0.909975i 0.999518 0.0310333i 0.00987978π-0.00987978\pi
−0.338383 + 0.941009i 0.609880π0.609880\pi
2020 0 0
2121 52.2005i 2.48574i
2222 −3.01683 1.46359i −0.137129 0.0665267i
2323 12.1155i 0.526762i 0.964692 + 0.263381i 0.0848376π0.0848376\pi
−0.964692 + 0.263381i 0.915162π0.915162\pi
2424 −11.8351 3.84545i −0.493128 0.160227i
2525 0 0
2626 1.19620 + 0.869094i 0.0460079 + 0.0334267i
2727 −42.4999 + 13.8091i −1.57407 + 0.511447i
2828 −12.2072 37.5699i −0.435972 1.34178i
2929 28.0610 38.6227i 0.967622 1.33182i 0.0243833 0.999703i 0.492238π-0.492238\pi
0.943239 0.332115i 0.107762π-0.107762\pi
3030 0 0
3131 9.63737 29.6608i 0.310883 0.956800i −0.666533 0.745476i 0.732222π-0.732222\pi
0.977416 0.211324i 0.0677776π-0.0677776\pi
3232 −14.1812 −0.443163
3333 −50.0882 + 26.7672i −1.51782 + 0.811127i
3434 0.871580 0.0256347
3535 0 0
3636 −55.8070 + 40.5461i −1.55019 + 1.12628i
3737 11.6773 16.0724i 0.315602 0.434389i −0.621516 0.783402i 0.713483π-0.713483\pi
0.937118 + 0.349012i 0.113483π0.113483\pi
3838 −6.19566 + 2.01309i −0.163044 + 0.0529761i
3939 23.8172 7.73869i 0.610699 0.198428i
4040 0 0
4141 23.5474 + 32.4102i 0.574326 + 0.790493i 0.993059 0.117617i 0.0375255π-0.0375255\pi
−0.418733 + 0.908110i 0.637526π0.637526\pi
4242 15.1334 + 4.91714i 0.360319 + 0.117075i
4343 28.7133 0.667752 0.333876 0.942617i 0.391643π-0.391643\pi
0.333876 + 0.942617i 0.391643π0.391643\pi
4444 −29.7901 + 30.9782i −0.677047 + 0.704050i
4545 0 0
4646 −3.51240 1.14125i −0.0763566 0.0248098i
4747 2.31141 + 3.18139i 0.0491790 + 0.0676891i 0.832898 0.553426i 0.186680π-0.186680\pi
−0.783719 + 0.621115i 0.786680π0.786680\pi
4848 −45.1971 + 62.2085i −0.941607 + 1.29601i
4949 16.4479 + 50.6214i 0.335671 + 1.03309i
5050 0 0
5151 8.67687 11.9427i 0.170135 0.234170i
5252 15.3321 11.1394i 0.294848 0.214220i
5353 59.9100 + 19.4659i 1.13038 + 0.367282i 0.813719 0.581258i 0.197439π-0.197439\pi
0.316658 + 0.948540i 0.397439π0.397439\pi
5454 13.6219i 0.252257i
5555 0 0
5656 24.3699 0.435177
5757 −34.0958 + 104.936i −0.598172 + 1.84098i
5858 8.55381 + 11.7733i 0.147479 + 0.202988i
5959 −41.4758 30.1339i −0.702979 0.510744i 0.177922 0.984045i 0.443063π-0.443063\pi
−0.880901 + 0.473300i 0.843063π0.843063\pi
6060 0 0
6161 31.6001 10.2675i 0.518035 0.168320i −0.0383184 0.999266i 0.512200π-0.512200\pi
0.556353 + 0.830946i 0.312200π0.312200\pi
6262 7.69112 + 5.58793i 0.124050 + 0.0901279i
6363 144.417 104.925i 2.29233 1.66548i
6464 −17.0737 + 52.5473i −0.266776 + 0.821052i
6565 0 0
6666 −3.04189 17.0424i −0.0460892 0.258218i
6767 90.1298i 1.34522i −0.739997 0.672611i 0.765173π-0.765173\pi
0.739997 0.672611i 0.234827π-0.234827\pi
6868 3.45212 10.6245i 0.0507665 0.156243i
6969 −50.6049 + 36.7666i −0.733405 + 0.532850i
7070 0 0
7171 1.85591 + 5.71191i 0.0261396 + 0.0804494i 0.963275 0.268516i 0.0865331π-0.0865331\pi
−0.937136 + 0.348965i 0.886533π0.886533\pi
7272 −13.1502 40.4722i −0.182642 0.562114i
7373 −105.902 76.9424i −1.45071 1.05401i −0.985664 0.168722i 0.946036π-0.946036\pi
−0.465051 0.885284i 0.653964π-0.653964\pi
7474 3.55957 + 4.89933i 0.0481023 + 0.0662072i
7575 0 0
7676 83.4983i 1.09866i
7777 77.0905 80.1652i 1.00118 1.04111i
7878 7.63380i 0.0978693i
7979 −85.4604 27.7678i −1.08178 0.351491i −0.286714 0.958016i 0.592563π-0.592563\pi
−0.795064 + 0.606525i 0.792563π0.792563\pi
8080 0 0
8181 −58.1000 42.2121i −0.717284 0.521137i
8282 −11.6141 + 3.77365i −0.141636 + 0.0460202i
8383 27.3155 + 84.0686i 0.329103 + 1.01287i 0.969554 + 0.244876i 0.0787473π0.0787473\pi
−0.640451 + 0.767999i 0.721253π0.721253\pi
8484 119.880 165.000i 1.42714 1.96429i
8585 0 0
8686 −2.70472 + 8.32426i −0.0314502 + 0.0967937i
8787 246.478 2.83308
8888 −12.4963 23.3837i −0.142003 0.265724i
8989 118.531 1.33180 0.665902 0.746039i 0.268047π-0.268047\pi
0.665902 + 0.746039i 0.268047π0.268047\pi
9090 0 0
9191 −39.6764 + 28.8266i −0.436004 + 0.316775i
9292 −27.8236 + 38.2959i −0.302430 + 0.416260i
9393 153.135 49.7567i 1.64662 0.535018i
9494 −1.14004 + 0.370422i −0.0121281 + 0.00394066i
9595 0 0
9696 −43.0353 59.2330i −0.448284 0.617010i
9797 −63.5544 20.6501i −0.655200 0.212887i −0.0374942 0.999297i 0.511938π-0.511938\pi
−0.617705 + 0.786410i 0.711938π0.711938\pi
9898 −16.2250 −0.165561
9999 −174.733 84.7699i −1.76498 0.856262i
100100 0 0
101101 12.3073 + 3.99890i 0.121855 + 0.0395931i 0.369310 0.929306i 0.379594π-0.379594\pi
−0.247455 + 0.968899i 0.579594π0.579594\pi
102102 2.64496 + 3.64047i 0.0259310 + 0.0356909i
103103 −66.4251 + 91.4263i −0.644904 + 0.887634i −0.998865 0.0476260i 0.984834π-0.984834\pi
0.353961 + 0.935260i 0.384834π0.384834\pi
104104 3.61282 + 11.1191i 0.0347387 + 0.106915i
105105 0 0
106106 −11.2867 + 15.5348i −0.106478 + 0.146555i
107107 12.9688 9.42241i 0.121204 0.0880599i −0.525532 0.850774i 0.676134π-0.676134\pi
0.646736 + 0.762714i 0.276134π0.276134\pi
108108 −166.051 53.9531i −1.53751 0.499566i
109109 156.813i 1.43865i −0.694671 0.719327i 0.744450π-0.744450\pi
0.694671 0.719327i 0.255550π-0.255550\pi
110110 0 0
111111 102.569 0.924045
112112 46.5333 143.215i 0.415476 1.27870i
113113 18.8099 + 25.8896i 0.166459 + 0.229112i 0.884095 0.467307i 0.154776π-0.154776\pi
−0.717636 + 0.696419i 0.754776π0.754776\pi
114114 −27.2102 19.7694i −0.238686 0.173416i
115115 0 0
116116 177.396 57.6394i 1.52928 0.496892i
117117 69.2833 + 50.3372i 0.592165 + 0.430233i
118118 12.6430 9.18568i 0.107144 0.0778447i
119119 −8.93338 + 27.4941i −0.0750704 + 0.231043i
120120 0 0
121121 −116.451 32.8642i −0.962409 0.271605i
122122 10.1283i 0.0830192i
123123 −63.9145 + 196.709i −0.519630 + 1.59926i
124124 98.5794 71.6221i 0.794995 0.577598i
125125 0 0
126126 16.8151 + 51.7514i 0.133453 + 0.410726i
127127 33.3284 + 102.574i 0.262428 + 0.807671i 0.992275 + 0.124060i 0.0395915π0.0395915\pi
−0.729846 + 0.683611i 0.760408π0.760408\pi
128128 −59.5170 43.2416i −0.464977 0.337825i
129129 87.1355 + 119.932i 0.675469 + 0.929703i
130130 0 0
131131 48.6741i 0.371558i 0.982592 + 0.185779i 0.0594808π0.0594808\pi
−0.982592 + 0.185779i 0.940519π0.940519\pi
132132 −219.795 30.4205i −1.66511 0.230458i
133133 216.076i 1.62463i
134134 26.1295 + 8.48998i 0.194996 + 0.0633580i
135135 0 0
136136 5.57546 + 4.05081i 0.0409961 + 0.0297854i
137137 71.4507 23.2157i 0.521538 0.169458i −0.0364052 0.999337i 0.511591π-0.511591\pi
0.557943 + 0.829879i 0.311591π0.311591\pi
138138 −5.89214 18.1341i −0.0426967 0.131407i
139139 28.3745 39.0542i 0.204133 0.280965i −0.694660 0.719338i 0.744445π-0.744445\pi
0.898793 + 0.438373i 0.144445π0.144445\pi
140140 0 0
141141 −6.27385 + 19.3089i −0.0444954 + 0.136943i
142142 −1.83076 −0.0128926
143143 48.0052 + 23.2892i 0.335700 + 0.162862i
144144 −262.953 −1.82606
145145 0 0
146146 32.2820 23.4542i 0.221110 0.160646i
147147 −161.525 + 222.320i −1.09881 + 1.51238i
148148 73.8213 23.9860i 0.498793 0.162068i
149149 −114.600 + 37.2357i −0.769126 + 0.249904i −0.667191 0.744887i 0.732503π-0.732503\pi
−0.101935 + 0.994791i 0.532503π0.532503\pi
150150 0 0
151151 −45.4102 62.5018i −0.300730 0.413919i 0.631733 0.775186i 0.282344π-0.282344\pi
−0.932462 + 0.361268i 0.882344π0.882344\pi
152152 −48.9896 15.9177i −0.322300 0.104722i
153153 50.4812 0.329943
154154 15.9789 + 29.9006i 0.103759 + 0.194160i
155155 0 0
156156 93.0559 + 30.2357i 0.596512 + 0.193819i
157157 −31.8599 43.8515i −0.202930 0.279309i 0.695407 0.718616i 0.255224π-0.255224\pi
−0.898337 + 0.439307i 0.855224π0.855224\pi
158158 16.1003 22.1601i 0.101900 0.140254i
159159 100.501 + 309.309i 0.632079 + 1.94534i
160160 0 0
161161 72.0017 99.1018i 0.447215 0.615539i
162162 17.7105 12.8675i 0.109324 0.0794287i
163163 193.205 + 62.7761i 1.18531 + 0.385129i 0.834336 0.551257i 0.185852π-0.185852\pi
0.350971 + 0.936386i 0.385852π0.385852\pi
164164 156.522i 0.954404i
165165 0 0
166166 −26.9453 −0.162321
167167 −41.0093 + 126.214i −0.245565 + 0.755771i 0.749978 + 0.661462i 0.230064π0.230064\pi
−0.995543 + 0.0943081i 0.969936π0.969936\pi
168168 73.9546 + 101.790i 0.440206 + 0.605891i
169169 117.689 + 85.5063i 0.696387 + 0.505954i
170170 0 0
171171 −358.848 + 116.597i −2.09853 + 0.681852i
172172 90.7598 + 65.9408i 0.527673 + 0.383377i
173173 −90.4855 + 65.7416i −0.523037 + 0.380009i −0.817747 0.575578i 0.804777π-0.804777\pi
0.294709 + 0.955587i 0.404777π0.404777\pi
174174 −23.2175 + 71.4562i −0.133434 + 0.410668i
175175 0 0
176176 −161.281 + 28.7868i −0.916367 + 0.163562i
177177 264.685i 1.49540i
178178 −11.1652 + 34.3631i −0.0627261 + 0.193051i
179179 −38.7619 + 28.1621i −0.216547 + 0.157330i −0.690771 0.723074i 0.742729π-0.742729\pi
0.474224 + 0.880404i 0.342729π0.342729\pi
180180 0 0
181181 2.09873 + 6.45923i 0.0115952 + 0.0356864i 0.956687 0.291119i 0.0940277π-0.0940277\pi
−0.945092 + 0.326806i 0.894028π0.894028\pi
182182 −4.61968 14.2179i −0.0253829 0.0781204i
183183 138.782 + 100.831i 0.758371 + 0.550989i
184184 −17.1646 23.6250i −0.0932857 0.128397i
185185 0 0
186186 49.0823i 0.263883i
187187 30.9624 5.52645i 0.165574 0.0295532i
188188 15.3642i 0.0817246i
189189 429.705 + 139.619i 2.27357 + 0.738728i
190190 0 0
191191 60.7195 + 44.1153i 0.317903 + 0.230970i 0.735280 0.677763i 0.237051π-0.237051\pi
−0.417377 + 0.908733i 0.637051π0.637051\pi
192192 −271.296 + 88.1494i −1.41300 + 0.459112i
193193 −117.250 360.857i −0.607511 1.86973i −0.478513 0.878081i 0.658824π-0.658824\pi
−0.128998 0.991645i 0.541176π-0.541176\pi
194194 11.9733 16.4798i 0.0617180 0.0849475i
195195 0 0
196196 −64.2633 + 197.782i −0.327874 + 1.00909i
197197 −91.4898 −0.464415 −0.232208 0.972666i 0.574595π-0.574595\pi
−0.232208 + 0.972666i 0.574595π0.574595\pi
198198 41.0349 42.6715i 0.207247 0.215513i
199199 −24.0213 −0.120710 −0.0603551 0.998177i 0.519223π-0.519223\pi
−0.0603551 + 0.998177i 0.519223π0.519223\pi
200200 0 0
201201 376.460 273.514i 1.87294 1.36077i
202202 −2.31864 + 3.19133i −0.0114784 + 0.0157987i
203203 −459.064 + 149.159i −2.26140 + 0.734773i
204204 54.8533 17.8229i 0.268889 0.0873673i
205205 0 0
206206 −20.2483 27.8693i −0.0982926 0.135288i
207207 −203.436 66.1002i −0.982781 0.319325i
208208 72.2423 0.347319
209209 −207.333 + 110.799i −0.992023 + 0.530138i
210210 0 0
211211 −349.688 113.620i −1.65729 0.538486i −0.676987 0.735995i 0.736715π-0.736715\pi
−0.980301 + 0.197509i 0.936715π0.936715\pi
212212 144.665 + 199.115i 0.682383 + 0.939219i
213213 −18.2258 + 25.0856i −0.0855671 + 0.117773i
214214 1.51002 + 4.64735i 0.00705615 + 0.0217166i
215215 0 0
216216 63.3100 87.1387i 0.293102 0.403420i
217217 −255.103 + 185.343i −1.17559 + 0.854117i
218218 45.4616 + 14.7714i 0.208540 + 0.0677586i
219219 675.834i 3.08600i
220220 0 0
221221 −13.8690 −0.0627555
222222 −9.66172 + 29.7357i −0.0435212 + 0.133945i
223223 −104.183 143.396i −0.467190 0.643032i 0.508790 0.860891i 0.330093π-0.330093\pi
−0.975980 + 0.217858i 0.930093π0.930093\pi
224224 115.999 + 84.2779i 0.517851 + 0.376241i
225225 0 0
226226 −9.27747 + 3.01443i −0.0410508 + 0.0133382i
227227 14.9656 + 10.8732i 0.0659279 + 0.0478994i 0.620261 0.784395i 0.287027π-0.287027\pi
−0.554333 + 0.832295i 0.687027π0.687027\pi
228228 −348.761 + 253.390i −1.52966 + 1.11136i
229229 41.3284 127.196i 0.180473 0.555440i −0.819368 0.573268i 0.805675π-0.805675\pi
0.999841 + 0.0178283i 0.00567522π0.00567522\pi
230230 0 0
231231 568.784 + 78.7219i 2.46227 + 0.340787i
232232 115.069i 0.495985i
233233 −13.6070 + 41.8780i −0.0583991 + 0.179734i −0.976001 0.217767i 0.930123π-0.930123\pi
0.917602 + 0.397501i 0.130123π0.130123\pi
234234 −21.1195 + 15.3442i −0.0902544 + 0.0655736i
235235 0 0
236236 −61.8973 190.500i −0.262277 0.807204i
237237 −143.362 441.223i −0.604903 1.86170i
238238 −7.12930 5.17974i −0.0299550 0.0217636i
239239 −97.2433 133.844i −0.406876 0.560017i 0.555577 0.831465i 0.312497π-0.312497\pi
−0.962453 + 0.271448i 0.912497π0.912497\pi
240240 0 0
241241 68.3979i 0.283809i −0.989880 0.141904i 0.954677π-0.954677\pi
0.989880 0.141904i 0.0453225π-0.0453225\pi
242242 20.4970 30.6646i 0.0846985 0.126713i
243243 31.4080i 0.129251i
244244 123.464 + 40.1160i 0.506001 + 0.164410i
245245 0 0
246246 −51.0071 37.0588i −0.207346 0.150645i
247247 98.5880 32.0332i 0.399142 0.129689i
248248 23.2290 + 71.4915i 0.0936653 + 0.288272i
249249 −268.250 + 369.214i −1.07731 + 1.48279i
250250 0 0
251251 104.767 322.440i 0.417399 1.28462i −0.492688 0.870206i 0.663986π-0.663986\pi
0.910087 0.414417i 0.136014π-0.136014\pi
252252 697.449 2.76766
253253 −132.012 18.2710i −0.521788 0.0722175i
254254 −32.8767 −0.129436
255255 0 0
256256 −160.655 + 116.723i −0.627559 + 0.455949i
257257 −148.075 + 203.807i −0.576167 + 0.793025i −0.993269 0.115835i 0.963046π-0.963046\pi
0.417102 + 0.908860i 0.363046π0.363046\pi
258258 −42.9772 + 13.9641i −0.166578 + 0.0541246i
259259 −191.034 + 62.0708i −0.737584 + 0.239656i
260260 0 0
261261 495.430 + 681.901i 1.89820 + 2.61265i
262262 −14.1111 4.58496i −0.0538590 0.0174999i
263263 424.803 1.61522 0.807610 0.589717i 0.200761π-0.200761\pi
0.807610 + 0.589717i 0.200761π0.200761\pi
264264 59.7486 123.157i 0.226320 0.466505i
265265 0 0
266266 62.6425 + 20.3538i 0.235498 + 0.0765180i
267267 359.701 + 495.086i 1.34720 + 1.85426i
268268 206.985 284.891i 0.772333 1.06303i
269269 −154.300 474.888i −0.573608 1.76538i −0.640872 0.767648i 0.721427π-0.721427\pi
0.0672640 0.997735i 0.478573π-0.478573\pi
270270 0 0
271271 −138.031 + 189.983i −0.509339 + 0.701045i −0.983808 0.179227i 0.942640π-0.942640\pi
0.474468 + 0.880273i 0.342640π0.342640\pi
272272 34.4515 25.0305i 0.126660 0.0920239i
273273 −240.809 78.2437i −0.882086 0.286607i
274274 22.9011i 0.0835806i
275275 0 0
276276 −244.392 −0.885479
277277 −42.0248 + 129.339i −0.151714 + 0.466928i −0.997813 0.0660976i 0.978945π-0.978945\pi
0.846099 + 0.533026i 0.178945π0.178945\pi
278278 8.64937 + 11.9048i 0.0311128 + 0.0428232i
279279 445.464 + 323.648i 1.59664 + 1.16003i
280280 0 0
281281 −287.964 + 93.5652i −1.02478 + 0.332972i −0.772726 0.634740i 0.781107π-0.781107\pi
−0.252057 + 0.967712i 0.581107π0.581107\pi
282282 −5.00685 3.63769i −0.0177548 0.0128996i
283283 −8.61523 + 6.25933i −0.0304425 + 0.0221178i −0.602902 0.797815i 0.705989π-0.705989\pi
0.572460 + 0.819933i 0.305989π0.305989\pi
284284 −7.25119 + 22.3169i −0.0255324 + 0.0785805i
285285 0 0
286286 −11.2737 + 11.7234i −0.0394186 + 0.0409908i
287287 405.047i 1.41131i
288288 77.3703 238.121i 0.268647 0.826810i
289289 227.192 165.065i 0.786131 0.571158i
290290 0 0
291291 −106.614 328.124i −0.366371 1.12757i
292292 −158.045 486.414i −0.541251 1.66580i
293293 267.010 + 193.994i 0.911296 + 0.662095i 0.941342 0.337453i 0.109565π-0.109565\pi
−0.0300463 + 0.999549i 0.509565π0.509565\pi
294294 −49.2374 67.7695i −0.167474 0.230509i
295295 0 0
296296 47.8845i 0.161772i
297297 −86.3727 483.910i −0.290817 1.62933i
298298 36.7310i 0.123259i
299299 55.8909 + 18.1600i 0.186926 + 0.0607359i
300300 0 0
301301 −234.868 170.641i −0.780291 0.566914i
302302 22.3973 7.27734i 0.0741634 0.0240971i
303303 20.6459 + 63.5415i 0.0681382 + 0.209708i
304304 −187.087 + 257.503i −0.615418 + 0.847050i
305305 0 0
306306 −4.75519 + 14.6350i −0.0155398 + 0.0478267i
307307 111.473 0.363104 0.181552 0.983381i 0.441888π-0.441888\pi
0.181552 + 0.983381i 0.441888π0.441888\pi
308308 427.776 76.3534i 1.38888 0.247901i
309309 −583.454 −1.88820
310310 0 0
311311 −327.747 + 238.122i −1.05385 + 0.765665i −0.972940 0.231057i 0.925782π-0.925782\pi
−0.0809071 + 0.996722i 0.525782π0.525782\pi
312312 −35.4794 + 48.8331i −0.113716 + 0.156516i
313313 161.450 52.4582i 0.515814 0.167598i −0.0395307 0.999218i 0.512586π-0.512586\pi
0.555345 + 0.831620i 0.312586π0.312586\pi
314314 15.7141 5.10581i 0.0500448 0.0162605i
315315 0 0
316316 −206.362 284.033i −0.653044 0.898838i
317317 −367.389 119.372i −1.15895 0.376567i −0.334445 0.942415i 0.608549π-0.608549\pi
−0.824510 + 0.565848i 0.808549π0.808549\pi
318318 −99.1383 −0.311756
319319 378.520 + 364.003i 1.18658 + 1.14107i
320320 0 0
321321 78.7123 + 25.5752i 0.245210 + 0.0796735i
322322 21.9482 + 30.2091i 0.0681620 + 0.0938170i
323323 35.9167 49.4350i 0.111197 0.153050i
324324 −86.7068 266.856i −0.267613 0.823630i
325325 0 0
326326 −36.3987 + 50.0986i −0.111653 + 0.153677i
327327 654.988 475.877i 2.00302 1.45528i
328328 −91.8337 29.8386i −0.279981 0.0909713i
329329 39.7595i 0.120849i
330330 0 0
331331 118.966 0.359413 0.179706 0.983720i 0.442485π-0.442485\pi
0.179706 + 0.983720i 0.442485π0.442485\pi
332332 −106.724 + 328.463i −0.321458 + 0.989346i
333333 206.168 + 283.765i 0.619122 + 0.852148i
334334 −32.7275 23.7780i −0.0979867 0.0711915i
335335 0 0
336336 739.402 240.246i 2.20060 0.715018i
337337 358.847 + 260.717i 1.06483 + 0.773642i 0.974975 0.222313i 0.0713607π-0.0713607\pi
0.0898516 + 0.995955i 0.471361π0.471361\pi
338338 −35.8751 + 26.0648i −0.106139 + 0.0771147i
339339 −51.0556 + 157.133i −0.150606 + 0.463519i
340340 0 0
341341 308.654 + 149.741i 0.905144 + 0.439122i
342342 115.016i 0.336305i
343343 13.2053 40.6417i 0.0384993 0.118489i
344344 −55.9903 + 40.6793i −0.162763 + 0.118254i
345345 0 0
346346 −10.5356 32.4252i −0.0304497 0.0937146i
347347 163.076 + 501.898i 0.469961 + 1.44639i 0.852635 + 0.522507i 0.175003π0.175003\pi
−0.382674 + 0.923883i 0.624997π0.624997\pi
348348 779.091 + 566.042i 2.23877 + 1.62656i
349349 −318.255 438.040i −0.911905 1.25513i −0.966512 0.256622i 0.917390π-0.917390\pi
0.0546065 0.998508i 0.482610π-0.482610\pi
350350 0 0
351351 216.758i 0.617543i
352352 21.3862 154.520i 0.0607563 0.438978i
353353 216.813i 0.614201i −0.951677 0.307101i 0.900641π-0.900641\pi
0.951677 0.307101i 0.0993588π-0.0993588\pi
354354 76.7347 + 24.9326i 0.216765 + 0.0704311i
355355 0 0
356356 374.662 + 272.208i 1.05242 + 0.764630i
357357 −141.949 + 46.1221i −0.397616 + 0.129193i
358358 −4.51321 13.8902i −0.0126067 0.0387995i
359359 329.315 453.263i 0.917311 1.26257i −0.0472967 0.998881i 0.515061π-0.515061\pi
0.964608 0.263689i 0.0849394π-0.0849394\pi
360360 0 0
361361 −29.5795 + 91.0363i −0.0819376 + 0.252178i
362362 −2.07029 −0.00571902
363363 −216.123 586.134i −0.595379 1.61469i
364364 −191.614 −0.526411
365365 0 0
366366 −42.3047 + 30.7362i −0.115587 + 0.0839786i
367367 18.1911 25.0380i 0.0495671 0.0682233i −0.783514 0.621374i 0.786575π-0.786575\pi
0.833081 + 0.553151i 0.186575π0.186575\pi
368368 −171.612 + 55.7602i −0.466337 + 0.151522i
369369 −672.680 + 218.567i −1.82298 + 0.592323i
370370 0 0
371371 −374.364 515.267i −1.00907 1.38886i
372372 598.312 + 194.403i 1.60837 + 0.522590i
373373 −483.806 −1.29707 −0.648534 0.761186i 0.724617π-0.724617\pi
−0.648534 + 0.761186i 0.724617π0.724617\pi
374374 −1.31440 + 9.49685i −0.00351444 + 0.0253927i
375375 0 0
376376 −9.01440 2.92896i −0.0239745 0.00778977i
377377 −136.112 187.342i −0.361040 0.496928i
378378 −80.9540 + 111.424i −0.214164 + 0.294771i
379379 −25.3368 77.9786i −0.0668517 0.205748i 0.912050 0.410078i 0.134499π-0.134499\pi
−0.978902 + 0.204330i 0.934499π0.934499\pi
380380 0 0
381381 −327.298 + 450.487i −0.859050 + 1.18238i
382382 −18.5090 + 13.4476i −0.0484530 + 0.0352031i
383383 −693.283 225.261i −1.81014 0.588150i −0.999998 0.00191562i 0.999390π-0.999390\pi
−0.810141 0.586234i 0.800610π-0.800610\pi
384384 379.819i 0.989111i
385385 0 0
386386 115.660 0.299638
387387 −156.655 + 482.135i −0.404793 + 1.24583i
388388 −153.465 211.227i −0.395529 0.544399i
389389 193.321 + 140.456i 0.496969 + 0.361069i 0.807858 0.589377i 0.200627π-0.200627\pi
−0.310889 + 0.950446i 0.600627π0.600627\pi
390390 0 0
391391 32.9458 10.7047i 0.0842604 0.0273779i
392392 −103.790 75.4082i −0.264772 0.192368i
393393 −203.305 + 147.710i −0.517316 + 0.375852i
394394 8.61808 26.5237i 0.0218733 0.0673191i
395395 0 0
396396 −357.635 669.226i −0.903120 1.68997i
397397 354.733i 0.893535i −0.894650 0.446768i 0.852575π-0.852575\pi
0.894650 0.446768i 0.147425π-0.147425\pi
398398 2.26274 6.96401i 0.00568528 0.0174975i
399399 902.522 655.721i 2.26196 1.64341i
400400 0 0
401401 79.1417 + 243.573i 0.197361 + 0.607414i 0.999941 + 0.0108700i 0.00346008π0.00346008\pi
−0.802580 + 0.596545i 0.796540π0.796540\pi
402402 43.8328 + 134.904i 0.109037 + 0.335581i
403403 −122.384 88.9175i −0.303684 0.220639i
404404 29.7187 + 40.9042i 0.0735610 + 0.101248i
405405 0 0
406406 147.137i 0.362407i
407407 157.517 + 151.476i 0.387020 + 0.372176i
408408 35.5808i 0.0872079i
409409 −261.500 84.9666i −0.639365 0.207742i −0.0286458 0.999590i 0.509119π-0.509119\pi
−0.610719 + 0.791847i 0.709119π0.709119\pi
410410 0 0
411411 313.798 + 227.988i 0.763500 + 0.554715i
412412 −419.925 + 136.442i −1.01924 + 0.331170i
413413 160.177 + 492.975i 0.387839 + 1.19364i
414414 38.3261 52.7514i 0.0925752 0.127419i
415415 0 0
416416 −21.2563 + 65.4202i −0.0510969 + 0.157260i
417417 249.232 0.597678
418418 −12.5914 70.5446i −0.0301231 0.168767i
419419 −44.0757 −0.105193 −0.0525963 0.998616i 0.516750π-0.516750\pi
−0.0525963 + 0.998616i 0.516750π0.516750\pi
420420 0 0
421421 65.8608 47.8507i 0.156439 0.113660i −0.506812 0.862057i 0.669176π-0.669176\pi
0.663251 + 0.748397i 0.269176π0.269176\pi
422422 65.8792 90.6750i 0.156112 0.214870i
423423 −66.0303 + 21.4546i −0.156100 + 0.0507200i
424424 −144.401 + 46.9188i −0.340569 + 0.110658i
425425 0 0
426426 −5.55574 7.64682i −0.0130416 0.0179503i
427427 −319.500 103.812i −0.748243 0.243119i
428428 62.6319 0.146336
429429 48.4038 + 271.186i 0.112829 + 0.632136i
430430 0 0
431431 690.547 + 224.372i 1.60220 + 0.520585i 0.967649 0.252299i 0.0811866π-0.0811866\pi
0.634547 + 0.772884i 0.281187π0.281187\pi
432432 −391.201 538.442i −0.905558 1.24639i
433433 −204.033 + 280.828i −0.471208 + 0.648563i −0.976786 0.214218i 0.931280π-0.931280\pi
0.505577 + 0.862781i 0.331280π0.331280\pi
434434 −29.7027 91.4156i −0.0684394 0.210635i
435435 0 0
436436 360.126 495.670i 0.825976 1.13686i
437437 −209.472 + 152.190i −0.479340 + 0.348261i
438438 195.930 + 63.6617i 0.447330 + 0.145346i
439439 72.1914i 0.164445i 0.996614 + 0.0822226i 0.0262018π0.0262018\pi
−0.996614 + 0.0822226i 0.973798π0.973798\pi
440440 0 0
441441 −939.738 −2.13092
442442 1.30642 4.02074i 0.00295569 0.00909669i
443443 −220.886 304.024i −0.498614 0.686284i 0.483333 0.875436i 0.339426π-0.339426\pi
−0.981948 + 0.189153i 0.939426π0.939426\pi
444444 324.210 + 235.552i 0.730202 + 0.530523i
445445 0 0
446446 51.3857 16.6962i 0.115214 0.0374355i
447447 −503.301 365.670i −1.12595 0.818053i
448448 451.943 328.356i 1.00880 0.732937i
449449 −34.6764 + 106.723i −0.0772302 + 0.237690i −0.982217 0.187750i 0.939881π-0.939881\pi
0.904987 + 0.425440i 0.139881π0.139881\pi
450450 0 0
451451 −388.657 + 207.699i −0.861767 + 0.460529i
452452 125.032i 0.276619i
453453 123.256 379.344i 0.272089 0.837405i
454454 −4.56195 + 3.31445i −0.0100483 + 0.00730055i
455455 0 0
456456 −82.1812 252.928i −0.180222 0.554666i
457457 −57.6949 177.567i −0.126247 0.388549i 0.867879 0.496775i 0.165483π-0.165483\pi
−0.994126 + 0.108227i 0.965483π0.965483\pi
458458 32.9822 + 23.9630i 0.0720136 + 0.0523209i
459459 75.1021 + 103.369i 0.163621 + 0.225205i
460460 0 0
461461 559.922i 1.21458i −0.794479 0.607291i 0.792256π-0.792256\pi
0.794479 0.607291i 0.207744π-0.207744\pi
462462 −76.4000 + 157.480i −0.165368 + 0.340866i
463463 648.611i 1.40089i 0.713708 + 0.700444i 0.247014π0.247014\pi
−0.713708 + 0.700444i 0.752986π0.752986\pi
464464 676.224 + 219.719i 1.45738 + 0.473532i
465465 0 0
466466 −10.8591 7.88958i −0.0233028 0.0169304i
467467 856.339 278.242i 1.83370 0.595806i 0.834722 0.550671i 0.185628π-0.185628\pi
0.998981 0.0451348i 0.0143717π-0.0143717\pi
468468 103.396 + 318.221i 0.220932 + 0.679960i
469469 −535.635 + 737.238i −1.14208 + 1.57194i
470470 0 0
471471 86.4772 266.149i 0.183603 0.565073i
472472 123.569 0.261798
473473 −43.3016 + 312.864i −0.0915468 + 0.661447i
474474 141.419 0.298352
475475 0 0
476476 −91.3783 + 66.3902i −0.191971 + 0.139475i
477477 −653.718 + 899.765i −1.37048 + 1.88630i
478478 47.9626 15.5840i 0.100340 0.0326025i
479479 441.790 143.546i 0.922317 0.299679i 0.190900 0.981609i 0.438859π-0.438859\pi
0.731417 + 0.681930i 0.238859π0.238859\pi
480480 0 0
481481 −56.6415 77.9603i −0.117758 0.162080i
482482 19.8292 + 6.44289i 0.0411394 + 0.0133670i
483483 632.437 1.30939
484484 −292.617 371.314i −0.604581 0.767177i
485485 0 0
486486 −9.10546 2.95854i −0.0187355 0.00608753i
487487 −19.3672 26.6567i −0.0397685 0.0547366i 0.788670 0.614817i 0.210770π-0.210770\pi
−0.828438 + 0.560081i 0.810770π0.810770\pi
488488 −47.0731 + 64.7906i −0.0964613 + 0.132768i
489489 324.106 + 997.496i 0.662794 + 2.03987i
490490 0 0
491491 −469.003 + 645.528i −0.955200 + 1.31472i −0.00602158 + 0.999982i 0.501917π0.501917\pi
−0.949179 + 0.314738i 0.898083π0.898083\pi
492492 −653.773 + 474.994i −1.32881 + 0.965434i
493493 −129.820 42.1812i −0.263327 0.0855603i
494494 31.5990i 0.0639656i
495495 0 0
496496 464.489 0.936470
497497 18.7646 57.7514i 0.0377557 0.116200i
498498 −81.7701 112.547i −0.164197 0.225998i
499499 479.816 + 348.607i 0.961555 + 0.698611i 0.953511 0.301357i 0.0974396π-0.0974396\pi
0.00804363 + 0.999968i 0.497440π0.497440\pi
500500 0 0
501501 −651.627 + 211.727i −1.30065 + 0.422608i
502502 83.6096 + 60.7459i 0.166553 + 0.121008i
503503 634.532 461.015i 1.26150 0.916530i 0.262665 0.964887i 0.415398π-0.415398\pi
0.998830 + 0.0483569i 0.0153985π0.0153985\pi
504504 −132.958 + 409.203i −0.263806 + 0.811910i
505505 0 0
506506 17.7321 36.5505i 0.0350437 0.0722342i
507507 751.056i 1.48137i
508508 −130.217 + 400.766i −0.256332 + 0.788909i
509509 −639.768 + 464.819i −1.25691 + 0.913200i −0.998602 0.0528625i 0.983165π-0.983165\pi
−0.258310 + 0.966062i 0.583165π0.583165\pi
510510 0 0
511511 408.989 + 1258.74i 0.800369 + 2.46328i
512512 −109.640 337.436i −0.214140 0.659055i
513513 −772.619 561.340i −1.50608 1.09423i
514514 −45.1374 62.1263i −0.0878160 0.120868i
515515 0 0
516516 579.200i 1.12248i
517517 −38.1506 + 20.3877i −0.0737922 + 0.0394346i
518518 61.2295i 0.118204i
519519 −549.187 178.442i −1.05816 0.343818i
520520 0 0
521521 −514.280 373.646i −0.987101 0.717171i −0.0278170 0.999613i 0.508856π-0.508856\pi
−0.959284 + 0.282442i 0.908856π0.908856\pi
522522 −244.357 + 79.3966i −0.468118 + 0.152101i
523523 −58.7556 180.831i −0.112343 0.345757i 0.879040 0.476747i 0.158184π-0.158184\pi
−0.991384 + 0.130990i 0.958184π0.958184\pi
524524 −111.781 + 153.854i −0.213323 + 0.293614i
525525 0 0
526526 −40.0152 + 123.154i −0.0760746 + 0.234134i
527527 −89.1719 −0.169207
528528 −609.672 586.289i −1.15468 1.11040i
529529 382.214 0.722522
530530 0 0
531531 732.273 532.027i 1.37905 1.00193i
532532 496.225 682.995i 0.932753 1.28382i
533533 184.809 60.0480i 0.346733 0.112660i
534534 −177.413 + 57.6449i −0.332234 + 0.107949i
535535 0 0
536536 127.691 + 175.751i 0.238229 + 0.327894i
537537 −235.259 76.4403i −0.438099 0.142347i
538538 152.209 0.282917
539539 −576.382 + 102.878i −1.06936 + 0.190868i
540540 0 0
541541 37.6026 + 12.2178i 0.0695058 + 0.0225838i 0.343563 0.939129i 0.388366π-0.388366\pi
−0.274058 + 0.961713i 0.588366π0.588366\pi
542542 −42.0758 57.9123i −0.0776306 0.106849i
543543 −20.6104 + 28.3678i −0.0379565 + 0.0522427i
544544 12.5299 + 38.5630i 0.0230329 + 0.0708879i
545545 0 0
546546 45.3671 62.4425i 0.0830900 0.114364i
547547 −478.368 + 347.554i −0.874529 + 0.635383i −0.931799 0.362976i 0.881761π-0.881761\pi
0.0572690 + 0.998359i 0.481761π0.481761\pi
548548 279.164 + 90.7057i 0.509423 + 0.165521i
549549 586.626i 1.06853i
550550 0 0
551551 1020.26 1.85165
552552 46.5896 143.388i 0.0844015 0.259761i
553553 534.022 + 735.018i 0.965682 + 1.32915i
554554 −33.5380 24.3668i −0.0605379 0.0439833i
555555 0 0
556556 179.378 58.2834i 0.322622 0.104826i
557557 176.596 + 128.305i 0.317049 + 0.230350i 0.734915 0.678159i 0.237222π-0.237222\pi
−0.417866 + 0.908509i 0.637222π0.637222\pi
558558 −135.790 + 98.6573i −0.243351 + 0.176805i
559559 43.0386 132.459i 0.0769921 0.236957i
560560 0 0
561561 117.044 + 112.555i 0.208634 + 0.200632i
562562 92.2970i 0.164229i
563563 −115.865 + 356.595i −0.205799 + 0.633383i 0.793881 + 0.608073i 0.208057π0.208057\pi
−0.999680 + 0.0253101i 0.991943π0.991943\pi
564564 −64.1743 + 46.6254i −0.113784 + 0.0826691i
565565 0 0
566566 −1.00311 3.08725i −0.00177227 0.00545450i
567567 224.379 + 690.568i 0.395730 + 1.21793i
568568 −11.7113 8.50874i −0.0206184 0.0149802i
569569 131.674 + 181.234i 0.231413 + 0.318513i 0.908894 0.417028i 0.136928π-0.136928\pi
−0.677480 + 0.735541i 0.736928π0.736928\pi
570570 0 0
571571 176.017i 0.308262i −0.988050 0.154131i 0.950742π-0.950742\pi
0.988050 0.154131i 0.0492577π-0.0492577\pi
572572 98.2549 + 183.860i 0.171774 + 0.321433i
573573 387.492i 0.676252i
574574 117.427 + 38.1543i 0.204577 + 0.0664710i
575575 0 0
576576 −789.188 573.378i −1.37012 0.995449i
577577 −635.162 + 206.377i −1.10080 + 0.357672i −0.802411 0.596772i 0.796450π-0.796450\pi
−0.298391 + 0.954444i 0.596450π0.596450\pi
578578 26.4529 + 81.4137i 0.0457663 + 0.140854i
579579 1151.44 1584.82i 1.98867 2.73716i
580580 0 0
581581 276.180 849.994i 0.475352 1.46298i
582582 105.169 0.180703
583583 −302.452 + 623.432i −0.518785 + 1.06935i
584584 315.514 0.540264
585585 0 0
586586 −81.3922 + 59.1349i −0.138895 + 0.100913i
587587 −57.4195 + 79.0311i −0.0978185 + 0.134636i −0.855121 0.518429i 0.826517π-0.826517\pi
0.757302 + 0.653065i 0.226517π0.226517\pi
588588 −1021.13 + 331.784i −1.73661 + 0.564259i
589589 633.882 205.961i 1.07620 0.349679i
590590 0 0
591591 −277.641 382.141i −0.469782 0.646600i
592592 281.403 + 91.4335i 0.475343 + 0.154448i
593593 −479.081 −0.807893 −0.403947 0.914783i 0.632362π-0.632362\pi
−0.403947 + 0.914783i 0.632362π0.632362\pi
594594 148.426 + 20.5427i 0.249875 + 0.0345837i
595595 0 0
596596 −447.751 145.483i −0.751259 0.244099i
597597 −72.8968 100.334i −0.122105 0.168063i
598598 −10.5295 + 14.4927i −0.0176079 + 0.0242352i
599599 −146.829 451.894i −0.245124 0.754414i −0.995616 0.0935345i 0.970183π-0.970183\pi
0.750492 0.660879i 0.229817π-0.229817\pi
600600 0 0
601601 316.409 435.499i 0.526470 0.724624i −0.460117 0.887858i 0.652193π-0.652193\pi
0.986587 + 0.163234i 0.0521926π0.0521926\pi
602602 71.5943 52.0163i 0.118927 0.0864059i
603603 1513.40 + 491.733i 2.50978 + 0.815477i
604604 301.847i 0.499747i
605605 0 0
606606 −20.3660 −0.0336073
607607 127.052 391.027i 0.209312 0.644196i −0.790197 0.612853i 0.790022π-0.790022\pi
0.999509 0.0313426i 0.00997830π-0.00997830\pi
608608 −178.138 245.186i −0.292991 0.403267i
609609 −2016.13 1464.80i −3.31055 2.40526i
610610 0 0
611611 18.1408 5.89431i 0.0296904 0.00964700i
612612 159.566 + 115.931i 0.260728 + 0.189430i
613613 201.079 146.092i 0.328025 0.238324i −0.411567 0.911379i 0.635019π-0.635019\pi
0.739592 + 0.673056i 0.235019π0.235019\pi
614614 −10.5004 + 32.3170i −0.0171017 + 0.0526336i
615615 0 0
616616 −36.7514 + 265.538i −0.0596614 + 0.431067i
617617 1141.96i 1.85082i −0.378964 0.925411i 0.623720π-0.623720\pi
0.378964 0.925411i 0.376280π-0.376280\pi
618618 54.9597 169.149i 0.0889316 0.273703i
619619 4.57281 3.32234i 0.00738742 0.00536727i −0.584085 0.811692i 0.698547π-0.698547\pi
0.591473 + 0.806325i 0.298547π0.298547\pi
620620 0 0
621621 −167.304 514.909i −0.269411 0.829161i
622622 −38.1609 117.447i −0.0613519 0.188822i
623623 −969.549 704.418i −1.55626 1.13069i
624624 219.232 + 301.746i 0.351333 + 0.483568i
625625 0 0
626626 51.7472i 0.0826633i
627627 −1091.98 529.763i −1.74159 0.844917i
628628 211.777i 0.337224i
629629 −54.0233 17.5532i −0.0858876 0.0279066i
630630 0 0
631631 601.402 + 436.944i 0.953094 + 0.692463i 0.951537 0.307536i 0.0995043π-0.0995043\pi
0.00155713 + 0.999999i 0.499504π0.499504\pi
632632 205.986 66.9288i 0.325927 0.105900i
633633 −586.610 1805.40i −0.926714 2.85213i
634634 69.2140 95.2649i 0.109170 0.150260i
635635 0 0
636636 −392.664 + 1208.49i −0.617396 + 1.90015i
637637 258.179 0.405304
638638 −141.183 + 75.4485i −0.221290 + 0.118258i
639639 −106.036 −0.165940
640640 0 0
641641 −292.789 + 212.724i −0.456769 + 0.331862i −0.792263 0.610180i 0.791097π-0.791097\pi
0.335493 + 0.942043i 0.391097π0.391097\pi
642642 −14.8290 + 20.4103i −0.0230981 + 0.0317918i
643643 615.565 200.009i 0.957333 0.311056i 0.211641 0.977347i 0.432119π-0.432119\pi
0.745692 + 0.666291i 0.232119π0.232119\pi
644644 455.179 147.897i 0.706800 0.229653i
645645 0 0
646646 10.9484 + 15.0692i 0.0169480 + 0.0233269i
647647 694.892 + 225.784i 1.07402 + 0.348971i 0.792053 0.610453i 0.209012π-0.209012\pi
0.281969 + 0.959423i 0.409012π0.409012\pi
648648 173.097 0.267125
649649 390.891 406.482i 0.602298 0.626320i
650650 0 0
651651 −1548.31 503.076i −2.37835 0.772774i
652652 466.534 + 642.128i 0.715542 + 0.984859i
653653 −176.964 + 243.570i −0.271001 + 0.373001i −0.922727 0.385453i 0.874045π-0.874045\pi
0.651726 + 0.758454i 0.274045π0.274045\pi
654654 76.2630 + 234.713i 0.116610 + 0.358889i
655655 0 0
656656 −350.705 + 482.704i −0.534611 + 0.735829i
657657 1869.75 1358.45i 2.84589 2.06766i
658658 11.5266 + 3.74523i 0.0175177 + 0.00569184i
659659 596.433i 0.905057i 0.891750 + 0.452529i 0.149478π0.149478\pi
−0.891750 + 0.452529i 0.850522π0.850522\pi
660660 0 0
661661 882.175 1.33461 0.667303 0.744786i 0.267449π-0.267449\pi
0.667303 + 0.744786i 0.267449π0.267449\pi
662662 −11.2062 + 34.4892i −0.0169278 + 0.0520985i
663663 −42.0877 57.9288i −0.0634807 0.0873737i
664664 −172.368 125.233i −0.259591 0.188604i
665665 0 0
666666 −101.687 + 33.0400i −0.152683 + 0.0496096i
667667 467.934 + 339.974i 0.701551 + 0.509707i
668668 −419.479 + 304.769i −0.627962 + 0.456241i
669669 282.784 870.320i 0.422697 1.30093i
670670 0 0
671671 64.2210 + 359.803i 0.0957094 + 0.536220i
672672 740.266i 1.10159i
673673 124.617 383.533i 0.185167 0.569886i −0.814784 0.579764i 0.803145π-0.803145\pi
0.999951 + 0.00987877i 0.00314456π0.00314456\pi
674674 −109.387 + 79.4741i −0.162295 + 0.117914i
675675 0 0
676676 175.636 + 540.553i 0.259817 + 0.799634i
677677 −193.523 595.604i −0.285854 0.879769i −0.986141 0.165908i 0.946945π-0.946945\pi
0.700287 0.713861i 0.253055π-0.253055\pi
678678 −40.7450 29.6029i −0.0600958 0.0436622i
679679 397.136 + 546.611i 0.584884 + 0.805024i
680680 0 0
681681 95.5059i 0.140244i
682682 −72.4855 + 75.3765i −0.106284 + 0.110523i
683683 935.585i 1.36982i −0.728629 0.684909i 0.759842π-0.759842\pi
0.728629 0.684909i 0.240158π-0.240158\pi
684684 −1402.05 455.553i −2.04978 0.666013i
685685 0 0
686686 10.5385 + 7.65666i 0.0153622 + 0.0111613i
687687 656.698 213.374i 0.955892 0.310588i
688688 132.149 + 406.714i 0.192078 + 0.591154i
689689 179.599 247.197i 0.260666 0.358776i
690690 0 0
691691 255.366 785.937i 0.369561 1.13739i −0.577515 0.816380i 0.695977π-0.695977\pi
0.947076 0.321011i 0.104023π-0.104023\pi
692692 −436.992 −0.631491
693693 925.486 + 1731.82i 1.33548 + 2.49902i
694694 −160.866 −0.231795
695695 0 0
696696 −480.626 + 349.195i −0.690555 + 0.501718i
697697 67.3278 92.6687i 0.0965965 0.132954i
698698 156.971 51.0029i 0.224886 0.0730700i
699699 −216.212 + 70.2514i −0.309316 + 0.100503i
700700 0 0
701701 −139.111 191.469i −0.198446 0.273138i 0.698184 0.715919i 0.253992π-0.253992\pi
−0.896630 + 0.442781i 0.853992π0.853992\pi
702702 −62.8400 20.4180i −0.0895157 0.0290854i
703703 424.570 0.603940
704704 −546.814 265.282i −0.776725 0.376821i
705705 0 0
706706 62.8561 + 20.4232i 0.0890313 + 0.0289280i
707707 −76.9057 105.852i −0.108778 0.149719i
708708 607.856 836.642i 0.858554 1.18170i
709709 278.848 + 858.205i 0.393297 + 1.21044i 0.930280 + 0.366851i 0.119564π0.119564\pi
−0.536982 + 0.843593i 0.680436π0.680436\pi
710710 0 0
711711 932.515 1283.50i 1.31155 1.80520i
712712 −231.132 + 167.927i −0.324623 + 0.235853i
713713 359.356 + 116.762i 0.504006 + 0.163761i
714714 45.4969i 0.0637212i
715715 0 0
716716 −187.197 −0.261449
717717 263.947 812.345i 0.368127 1.13298i
718718 100.385 + 138.167i 0.139811 + 0.192434i
719719 −318.157 231.154i −0.442499 0.321494i 0.344128 0.938923i 0.388174π-0.388174\pi
−0.786627 + 0.617428i 0.788174π0.788174\pi
720720 0 0
721721 1086.68 353.084i 1.50718 0.489714i
722722 −23.6060 17.1507i −0.0326952 0.0237545i
723723 285.689 207.565i 0.395144 0.287089i
724724 −8.19991 + 25.2367i −0.0113258 + 0.0348574i
725725 0 0
726726 190.284 7.44370i 0.262099 0.0102530i
727727 1284.55i 1.76691i 0.468514 + 0.883456i 0.344790π0.344790\pi
−0.468514 + 0.883456i 0.655210π0.655210\pi
728728 36.5282 112.422i 0.0501761 0.154426i
729729 −654.087 + 475.222i −0.897238 + 0.651882i
730730 0 0
731731 −25.3698 78.0803i −0.0347056 0.106813i
732732 207.114 + 637.432i 0.282943 + 0.870809i
733733 339.175 + 246.425i 0.462722 + 0.336187i 0.794598 0.607136i 0.207682π-0.207682\pi
−0.331876 + 0.943323i 0.607682π0.607682\pi
734734 5.54518 + 7.63228i 0.00755474 + 0.0103982i
735735 0 0
736736 171.813i 0.233441i
737737 982.066 + 135.922i 1.33252 + 0.184426i
738738 215.605i 0.292147i
739739 269.243 + 87.4823i 0.364334 + 0.118379i 0.485462 0.874258i 0.338651π-0.338651\pi
−0.121128 + 0.992637i 0.538651π0.538651\pi
740740 0 0
741741 432.981 + 314.579i 0.584319 + 0.424533i
742742 184.645 59.9947i 0.248847 0.0808554i
743743 3.47057 + 10.6813i 0.00467102 + 0.0143759i 0.953365 0.301820i 0.0975942π-0.0975942\pi
−0.948694 + 0.316196i 0.897594π0.897594\pi
744744 −228.118 + 313.978i −0.306610 + 0.422013i
745745 0 0
746746 45.5732 140.260i 0.0610901 0.188016i
747747 −1560.65 −2.08923
748748 110.560 + 53.6373i 0.147808 + 0.0717076i
749749 −162.078 −0.216393
750750 0 0
751751 −700.813 + 509.171i −0.933174 + 0.677990i −0.946768 0.321917i 0.895673π-0.895673\pi
0.0135942 + 0.999908i 0.495673π0.495673\pi
752752 −34.4252 + 47.3822i −0.0457782 + 0.0630083i
753753 1664.72 540.902i 2.21079 0.718329i
754754 67.1335 21.8130i 0.0890365 0.0289297i
755755 0 0
756756 1037.61 + 1428.15i 1.37250 + 1.88909i
757757 117.605 + 38.2121i 0.155356 + 0.0504783i 0.385663 0.922640i 0.373973π-0.373973\pi
−0.230306 + 0.973118i 0.573973π0.573973\pi
758758 24.9934 0.0329728
759759 −324.299 606.845i −0.427271 0.799532i
760760 0 0
761761 627.999 + 204.049i 0.825228 + 0.268133i 0.691034 0.722822i 0.257155π-0.257155\pi
0.134194 + 0.990955i 0.457155π0.457155\pi
762762 −99.7698 137.321i −0.130932 0.180212i
763763 −931.931 + 1282.69i −1.22140 + 1.68112i
764764 90.6160 + 278.887i 0.118607 + 0.365036i
765765 0 0
766766 130.611 179.770i 0.170510 0.234687i
767767 −201.181 + 146.167i −0.262296 + 0.190569i
768768 −975.071 316.820i −1.26962 0.412526i
769769 753.219i 0.979479i −0.871869 0.489739i 0.837092π-0.837092\pi
0.871869 0.489739i 0.162908π-0.162908\pi
770770 0 0
771771 −1300.63 −1.68695
772772 458.103 1409.90i 0.593398 1.82629i
773773 −97.8922 134.737i −0.126639 0.174304i 0.740989 0.671517i 0.234357π-0.234357\pi
−0.867629 + 0.497213i 0.834357π0.834357\pi
774774 −125.019 90.8315i −0.161523 0.117353i
775775 0 0
776776 153.185 49.7729i 0.197404 0.0641404i
777777 −838.988 609.560i −1.07978 0.784505i
778778 −58.9297 + 42.8149i −0.0757451 + 0.0550320i
779779 −264.565 + 814.247i −0.339621 + 1.04525i
780780 0 0
781781 −65.0365 + 11.6083i −0.0832734 + 0.0148634i
782782 10.5596i 0.0135034i
783783 −659.249 + 2028.96i −0.841953 + 2.59126i
784784 −641.335 + 465.957i −0.818030 + 0.594333i
785785 0 0
786786 −23.6717 72.8539i −0.0301166 0.0926894i
787787 107.043 + 329.445i 0.136014 + 0.418609i 0.995746 0.0921365i 0.0293696π-0.0293696\pi
−0.859732 + 0.510745i 0.829370π0.829370\pi
788788 −289.190 210.108i −0.366992 0.266635i
789789 1289.14 + 1774.34i 1.63389 + 2.24885i
790790 0 0
791791 323.556i 0.409047i
792792 460.822 82.2517i 0.581846 0.103853i
793793 161.167i 0.203236i
794794 102.840 + 33.4149i 0.129522 + 0.0420843i
795795 0 0
796796 −75.9289 55.1656i −0.0953880 0.0693035i
797797 −42.8487 + 13.9224i −0.0537625 + 0.0174685i −0.335775 0.941942i 0.608998π-0.608998\pi
0.282012 + 0.959411i 0.408998π0.408998\pi
798798 105.084 + 323.417i 0.131685 + 0.405284i
799799 6.60890 9.09636i 0.00827146 0.0113847i
800800 0 0
801801 −646.683 + 1990.28i −0.807344 + 2.48475i
802802 −78.0690 −0.0973429
803803 998.082 1037.89i 1.24294 1.29252i
804804 1818.08 2.26130
805805 0 0
806806 37.3063 27.1046i 0.0462857 0.0336285i
807807 1515.29 2085.62i 1.87769 2.58441i
808808 −29.6644 + 9.63856i −0.0367134 + 0.0119289i
809809 1187.16 385.731i 1.46744 0.476800i 0.537106 0.843515i 0.319518π-0.319518\pi
0.930333 + 0.366715i 0.119518π0.119518\pi
810810 0 0
811811 −62.7425 86.3577i −0.0773644 0.106483i 0.768581 0.639753i 0.220963π-0.220963\pi
−0.845945 + 0.533270i 0.820963π0.820963\pi
812812 −1793.60 582.776i −2.20887 0.717704i
813813 −1212.41 −1.49128
814814 −58.7518 + 31.3971i −0.0721767 + 0.0385713i
815815 0 0
816816 209.098 + 67.9401i 0.256248 + 0.0832599i
817817 360.685 + 496.440i 0.441475 + 0.607638i
818818 49.2652 67.8077i 0.0602264 0.0828945i
819819 −267.568 823.491i −0.326701 1.00548i
820820 0 0
821821 −361.534 + 497.608i −0.440358 + 0.606100i −0.970292 0.241939i 0.922217π-0.922217\pi
0.529934 + 0.848039i 0.322217π0.322217\pi
822822 −95.6547 + 69.4972i −0.116368 + 0.0845465i
823823 363.528 + 118.117i 0.441711 + 0.143521i 0.521425 0.853297i 0.325401π-0.325401\pi
−0.0797139 + 0.996818i 0.525401π0.525401\pi
824824 272.386i 0.330566i
825825 0 0
826826 −158.006 −0.191291
827827 −295.494 + 909.438i −0.357309 + 1.09968i 0.597350 + 0.801981i 0.296220π0.296220\pi
−0.954659 + 0.297703i 0.903780π0.903780\pi
828828 −491.238 676.131i −0.593282 0.816583i
829829 −591.020 429.401i −0.712931 0.517975i 0.171187 0.985239i 0.445240π-0.445240\pi
−0.884118 + 0.467264i 0.845240π0.845240\pi
830830 0 0
831831 −667.764 + 216.970i −0.803566 + 0.261095i
832832 216.817 + 157.527i 0.260598 + 0.189335i
833833 123.122 89.4537i 0.147806 0.107387i
834834 −23.4769 + 72.2545i −0.0281498 + 0.0866361i
835835 0 0
836836 −909.809 125.921i −1.08829 0.150623i
837837 1393.66i 1.66507i
838838 4.15181 12.7780i 0.00495443 0.0152482i
839839 −739.591 + 537.345i −0.881515 + 0.640458i −0.933652 0.358182i 0.883397π-0.883397\pi
0.0521367 + 0.998640i 0.483397π0.483397\pi
840840 0 0
841841 −444.409 1367.75i −0.528429 1.62634i
842842 7.66845 + 23.6010i 0.00910742 + 0.0280297i
843843 −1264.68 918.847i −1.50022 1.08997i
844844 −844.394 1162.21i −1.00047 1.37702i
845845 0 0
846846 21.1638i 0.0250163i
847847 757.233 + 960.883i 0.894018 + 1.13445i
848848 938.193i 1.10636i
849849 −52.2888 16.9896i −0.0615887 0.0200114i
850850 0 0
851851 194.726 + 141.476i 0.228820 + 0.166247i
852852 −115.220 + 37.4371i −0.135234 + 0.0439403i
853853 338.270 + 1041.09i 0.396565 + 1.22050i 0.927736 + 0.373237i 0.121752π0.121752\pi
−0.531171 + 0.847265i 0.678248π0.678248\pi
854854 60.1920 82.8472i 0.0704824 0.0970107i
855855 0 0
856856 −11.9398 + 36.7470i −0.0139484 + 0.0429287i
857857 −1161.22 −1.35499 −0.677494 0.735528i 0.736934π-0.736934\pi
−0.677494 + 0.735528i 0.736934π0.736934\pi
858858 −83.1789 11.5123i −0.0969451 0.0134176i
859859 465.631 0.542061 0.271031 0.962571i 0.412636π-0.412636\pi
0.271031 + 0.962571i 0.412636π0.412636\pi
860860 0 0
861861 1691.83 1229.19i 1.96496 1.42763i
862862 −130.095 + 179.061i −0.150922 + 0.207727i
863863 738.720 240.025i 0.855990 0.278128i 0.152037 0.988375i 0.451417π-0.451417\pi
0.703953 + 0.710247i 0.251417π0.251417\pi
864864 602.700 195.829i 0.697570 0.226654i
865865 0 0
866866 −62.1952 85.6043i −0.0718189 0.0988502i
867867 1378.91 + 448.034i 1.59043 + 0.516763i
868868 −1232.00 −1.41935
869869 431.442 889.313i 0.496480 1.02337i
870870 0 0
871871 −415.783 135.096i −0.477363 0.155105i
872872 222.164 + 305.782i 0.254775 + 0.350668i
873873 693.484 954.498i 0.794368 1.09335i
874874 −24.3897 75.0637i −0.0279058 0.0858852i
875875 0 0
876876 1552.07 2136.24i 1.77177 2.43863i
877877 −1120.57 + 814.144i −1.27773 + 0.928329i −0.999482 0.0321793i 0.989755π-0.989755\pi
−0.278253 + 0.960508i 0.589755π0.589755\pi
878878 −20.9290 6.80023i −0.0238371 0.00774514i
879879 1703.97i 1.93853i
880880 0 0
881881 −1570.42 −1.78255 −0.891273 0.453467i 0.850187π-0.850187\pi
−0.891273 + 0.453467i 0.850187π0.850187\pi
882882 88.5206 272.439i 0.100364 0.308887i
883883 643.690 + 885.963i 0.728981 + 1.00336i 0.999177 + 0.0405507i 0.0129112π0.0129112\pi
−0.270197 + 0.962805i 0.587089π0.587089\pi
884884 −43.8383 31.8504i −0.0495908 0.0360299i
885885 0 0
886886 108.946 35.3987i 0.122964 0.0399534i
887887 −716.448 520.530i −0.807720 0.586843i 0.105449 0.994425i 0.466372π-0.466372\pi
−0.913169 + 0.407582i 0.866372π0.866372\pi
888888 −200.007 + 145.314i −0.225233 + 0.163642i
889889 336.974 1037.10i 0.379048 1.16659i
890890 0 0
891891 547.567 569.407i 0.614554 0.639065i
892892 692.520i 0.776368i
893893 −25.9697 + 79.9265i −0.0290814 + 0.0895033i
894894 153.421 111.467i 0.171611 0.124683i
895895 0 0
896896 229.852 + 707.411i 0.256531 + 0.789521i
897897 93.7583 + 288.558i 0.104524 + 0.321693i
898898 −27.6735 20.1060i −0.0308168 0.0223897i
899899 −875.145 1204.53i −0.973465 1.33986i
900900 0 0
901901 180.113i 0.199903i
902902 −23.6034 132.240i −0.0261678 0.146607i
903903 1498.85i 1.65986i
904904 −73.3577 23.8354i −0.0811479 0.0263666i
905905 0 0
906906 98.3650 + 71.4664i 0.108571 + 0.0788812i
907907 297.496 96.6622i 0.327999 0.106573i −0.140388 0.990097i 0.544835π-0.544835\pi
0.468388 + 0.883523i 0.344835π0.344835\pi
908908 22.3343 + 68.7378i 0.0245972 + 0.0757025i
909909 −134.294 + 184.839i −0.147738 + 0.203344i
910910 0 0
911911 −140.671 + 432.942i −0.154414 + 0.475238i −0.998101 0.0615976i 0.980380π-0.980380\pi
0.843687 + 0.536836i 0.180380π0.180380\pi
912912 −1643.30 −1.80187
913913 −957.216 + 170.853i −1.04843 + 0.187133i
914914 56.9129 0.0622680
915915 0 0
916916 422.743 307.141i 0.461510 0.335306i
917917 289.267 398.141i 0.315449 0.434178i
918918 −37.0421 + 12.0357i −0.0403509 + 0.0131108i
919919 −981.783 + 319.001i −1.06832 + 0.347117i −0.789832 0.613324i 0.789832π-0.789832\pi
−0.278485 + 0.960441i 0.589832π0.589832\pi
920920 0 0
921921 338.284 + 465.607i 0.367300 + 0.505545i
922922 162.327 + 52.7431i 0.176059 + 0.0572051i
923923 29.1318 0.0315621
924924 1617.08 + 1555.06i 1.75008 + 1.68296i
925925 0 0
926926 −188.038 61.0973i −0.203065 0.0659798i
927927 −1172.76 1614.17i −1.26512 1.74129i
928928 −397.939 + 547.717i −0.428814 + 0.590212i
929929 431.640 + 1328.45i 0.464629 + 1.42998i 0.859449 + 0.511222i 0.170807π0.170807\pi
−0.394820 + 0.918758i 0.629193π0.629193\pi
930930 0 0
931931 −668.609 + 920.262i −0.718162 + 0.988466i
932932 −139.184 + 101.123i −0.149339 + 0.108501i
933933 −1989.21 646.332i −2.13205 0.692746i
934934 274.470i 0.293865i
935935 0 0
936936 −206.416 −0.220530
937937 −370.868 + 1141.42i −0.395804 + 1.21816i 0.532530 + 0.846411i 0.321241π0.321241\pi
−0.928334 + 0.371748i 0.878759π0.878759\pi
938938 −163.277 224.731i −0.174069 0.239586i
939939 709.058 + 515.161i 0.755120 + 0.548627i
940940 0 0
941941 29.9217 9.72215i 0.0317978 0.0103317i −0.293075 0.956089i 0.594679π-0.594679\pi
0.324873 + 0.945758i 0.394679π0.394679\pi
942942 69.0133 + 50.1411i 0.0732625 + 0.0532283i
943943 −392.667 + 285.289i −0.416401 + 0.302533i
944944 235.949 726.177i 0.249946 0.769255i
945945 0 0
946946 −86.6233 42.0245i −0.0915680 0.0444233i
947947 540.682i 0.570942i −0.958387 0.285471i 0.907850π-0.907850\pi
0.958387 0.285471i 0.0921501π-0.0921501\pi
948948 560.127 1723.89i 0.590851 1.81845i
949949 −513.685 + 373.214i −0.541291 + 0.393271i
950950 0 0
951951 −616.304 1896.79i −0.648059 1.99452i
952952 −21.5322 66.2692i −0.0226178 0.0696105i
953953 462.279 + 335.865i 0.485077 + 0.352429i 0.803288 0.595591i 0.203082π-0.203082\pi
−0.318211 + 0.948020i 0.603082π0.603082\pi
954954 −199.272 274.274i −0.208880 0.287499i
955955 0 0
956956 646.388i 0.676138i
957957 −371.705 + 2685.66i −0.388407 + 2.80633i
958958 141.601i 0.147809i
959959 −722.418 234.728i −0.753303 0.244763i
960960 0 0
961961 −9.41808 6.84263i −0.00980029 0.00712033i
962962 27.9369 9.07724i 0.0290404 0.00943580i
963963 87.4590 + 269.171i 0.0908193 + 0.279513i
964964 157.077 216.198i 0.162943 0.224272i
965965 0 0
966966 −59.5738 + 183.349i −0.0616705 + 0.189802i
967967 −1228.33 −1.27025 −0.635125 0.772410i 0.719051π-0.719051\pi
−0.635125 + 0.772410i 0.719051π0.719051\pi
968968 273.638 100.897i 0.282684 0.104233i
969969 315.479 0.325571
970970 0 0
971971 −1282.98 + 932.137i −1.32129 + 0.959976i −0.321379 + 0.946951i 0.604146π0.604146\pi
−0.999915 + 0.0130253i 0.995854π0.995854\pi
972972 −72.1291 + 99.2772i −0.0742069 + 0.102137i
973973 −464.193 + 150.825i −0.477074 + 0.155011i
974974 9.55237 3.10375i 0.00980736 0.00318660i
975975 0 0
976976 290.871 + 400.350i 0.298024 + 0.410194i
977977 895.345 + 290.915i 0.916422 + 0.297764i 0.728998 0.684515i 0.239986π-0.239986\pi
0.187424 + 0.982279i 0.439986π0.439986\pi
978978 −319.713 −0.326905
979979 −178.752 + 1291.52i −0.182586 + 1.31923i
980980 0 0
981981 2633.10 + 855.547i 2.68410 + 0.872117i
982982 −142.966 196.775i −0.145586 0.200382i
983983 410.154 564.528i 0.417247 0.574291i −0.547720 0.836662i 0.684504π-0.684504\pi
0.964967 + 0.262370i 0.0845042π0.0845042\pi
984984 −154.053 474.127i −0.156558 0.481837i
985985 0 0
986986 24.4574 33.6628i 0.0248047 0.0341408i
987987 166.070 120.657i 0.168257 0.122246i
988988 385.191 + 125.156i 0.389870 + 0.126676i
989989 347.877i 0.351746i
990990 0 0
991991 1202.24 1.21315 0.606577 0.795025i 0.292542π-0.292542\pi
0.606577 + 0.795025i 0.292542π0.292542\pi
992992 −136.670 + 420.626i −0.137772 + 0.424018i
993993 361.021 + 496.903i 0.363566 + 0.500406i
994994 14.9751 + 10.8800i 0.0150655 + 0.0109457i
995995 0 0
996996 −1695.82 + 551.004i −1.70263 + 0.553217i
997997 −655.602 476.323i −0.657575 0.477756i 0.208268 0.978072i 0.433217π-0.433217\pi
−0.865843 + 0.500316i 0.833217π0.833217\pi
998998 −146.262 + 106.265i −0.146555 + 0.106478i
999999 −274.339 + 844.329i −0.274614 + 0.845174i
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 275.3.q.f.24.3 24
5.2 odd 4 275.3.x.f.101.2 12
5.3 odd 4 55.3.i.d.46.2 yes 12
5.4 even 2 inner 275.3.q.f.24.4 24
11.6 odd 10 inner 275.3.q.f.149.4 24
55.17 even 20 275.3.x.f.226.2 12
55.18 even 20 605.3.c.d.241.5 12
55.28 even 20 55.3.i.d.6.2 12
55.39 odd 10 inner 275.3.q.f.149.3 24
55.48 odd 20 605.3.c.d.241.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.3.i.d.6.2 12 55.28 even 20
55.3.i.d.46.2 yes 12 5.3 odd 4
275.3.q.f.24.3 24 1.1 even 1 trivial
275.3.q.f.24.4 24 5.4 even 2 inner
275.3.q.f.149.3 24 55.39 odd 10 inner
275.3.q.f.149.4 24 11.6 odd 10 inner
275.3.x.f.101.2 12 5.2 odd 4
275.3.x.f.226.2 12 55.17 even 20
605.3.c.d.241.5 12 55.18 even 20
605.3.c.d.241.8 12 55.48 odd 20