LMFDB - Embedded newform 175.2.t.a.109.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(4,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([3, 20])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.t (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	175.109
Dual form			175.2.t.a.114.5

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50837 - 0.158536i) q^{2} +(0.602430 - 2.83421i) q^{3} +(0.293755 + 0.0624396i) q^{4} +(2.11119 - 0.736792i) q^{5} +(-1.35801 + 4.17954i) q^{6} +(2.50069 - 0.864026i) q^{7} +(2.45170 + 0.796607i) q^{8} +(-4.92920 - 2.19462i) q^{9} +(-3.30127 + 0.776656i) q^{10} +(-0.272386 + 0.121274i) q^{11} +(0.353934 - 0.794949i) q^{12} +(-0.705999 - 0.971725i) q^{13} +(-3.90895 + 0.906822i) q^{14} +(-0.816379 - 6.42744i) q^{15} +(-4.12050 - 1.83456i) q^{16} +(-4.91093 + 4.42182i) q^{17} +(7.08713 + 4.09176i) q^{18} +(-3.02972 + 0.643988i) q^{19} +(0.666179 - 0.0846145i) q^{20} +(-0.942341 - 7.60801i) q^{21} +(0.430086 - 0.139743i) q^{22} +(6.59043 + 0.692682i) q^{23} +(3.73473 - 6.46875i) q^{24} +(3.91427 - 3.11102i) q^{25} +(0.910856 + 1.57765i) q^{26} +(-4.08014 + 5.61583i) q^{27} +(0.788540 - 0.0976700i) q^{28} +(1.97373 + 6.07451i) q^{29} +(0.212421 + 9.82438i) q^{30} +(-0.766311 - 0.851074i) q^{31} +(1.45939 + 0.842577i) q^{32} +(0.179623 + 0.845059i) q^{33} +(8.10853 - 5.89119i) q^{34} +(4.64284 - 3.66662i) q^{35} +(-1.31095 - 0.952458i) q^{36} +(1.12361 - 2.52366i) q^{37} +(4.67204 - 0.491052i) q^{38} +(-3.17939 + 1.41556i) q^{39} +(5.76295 - 0.124606i) q^{40} +(-7.69071 + 5.58763i) q^{41} +(0.215255 + 11.6251i) q^{42} +2.00893i q^{43} +(-0.0875871 + 0.0186172i) q^{44} +(-12.0235 - 1.00147i) q^{45} +(-9.83100 - 2.08964i) q^{46} +(5.57728 + 5.02181i) q^{47} +(-7.68185 + 10.5732i) q^{48} +(5.50692 - 4.32133i) q^{49} +(-6.39739 + 4.07202i) q^{50} +(9.57389 + 16.5825i) q^{51} +(-0.146717 - 0.329531i) q^{52} +(1.52605 - 7.17950i) q^{53} +(7.04468 - 7.82391i) q^{54} +(-0.485706 + 0.456725i) q^{55} +(6.81924 - 0.126268i) q^{56} +8.97484i q^{57} +(-2.01408 - 9.47552i) q^{58} +(1.28678 + 12.2429i) q^{59} +(0.161511 - 1.93907i) q^{60} +(0.978410 - 9.30895i) q^{61} +(1.02096 + 1.40522i) q^{62} +(-14.2226 - 1.22911i) q^{63} +(5.23034 + 3.80006i) q^{64} +(-2.20646 - 1.53132i) q^{65} +(-0.136966 - 1.30314i) q^{66} +(6.12477 - 5.51477i) q^{67} +(-1.71871 + 0.992297i) q^{68} +(5.93348 - 18.2614i) q^{69} +(-7.58441 + 4.79456i) q^{70} +(-1.15037 - 3.54049i) q^{71} +(-10.3367 - 9.30719i) q^{72} +(-3.39653 - 7.62873i) q^{73} +(-2.09491 + 3.62849i) q^{74} +(-6.45922 - 12.9681i) q^{75} -0.930207 q^{76} +(-0.576370 + 0.538618i) q^{77} +(5.02012 - 1.63113i) q^{78} +(-5.18279 + 5.75607i) q^{79} +(-10.0509 - 0.837167i) q^{80} +(2.62722 + 2.91782i) q^{81} +(12.4863 - 7.20896i) q^{82} +(1.86230 + 0.605097i) q^{83} +(0.198223 - 2.29373i) q^{84} +(-7.10996 + 12.9537i) q^{85} +(0.318489 - 3.03022i) q^{86} +(18.4055 - 1.93449i) q^{87} +(-0.764418 + 0.0803436i) q^{88} +(0.434658 - 4.13550i) q^{89} +(17.9771 + 3.41675i) q^{90} +(-2.60508 - 1.81998i) q^{91} +(1.89272 + 0.614983i) q^{92} +(-2.87377 + 1.65917i) q^{93} +(-7.61647 - 8.45895i) q^{94} +(-5.92185 + 3.59186i) q^{95} +(3.26722 - 3.62861i) q^{96} +(-3.80086 + 1.23497i) q^{97} +(-8.99156 + 5.64512i) q^{98} +1.60880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22}+ \cdots - 44 q^{99}+O(q^{100}) $ 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.50837	−	0.158536i	−1.06658	−	0.112102i	−0.445060	−	0.895501i	$-0.646818\pi$
$2$	−1.50837	−	0.158536i	−1.06658	−	0.112102i	−0.621520	+	0.783399i	$0.713484\pi$
$3$	0.602430	−	2.83421i	0.347813	−	1.63633i	−0.362168	−	0.932113i	$-0.617963\pi$
$3$	0.602430	−	2.83421i	0.347813	−	1.63633i	0.709982	−	0.704220i	$-0.248703\pi$
$4$	0.293755	+	0.0624396i	0.146878	+	0.0312198i
$5$	2.11119	−	0.736792i	0.944154	−	0.329504i
$5$	2.11119	−	0.736792i	0.944154	−	0.329504i
$6$	−1.35801	+	4.17954i	−0.554407	+	1.70629i
$7$	2.50069	−	0.864026i	0.945173	−	0.326571i
$7$	2.50069	−	0.864026i	0.945173	−	0.326571i
$8$	2.45170	+	0.796607i	0.866808	+	0.281643i
$9$	−4.92920	−	2.19462i	−1.64307	−	0.731540i
$10$	−3.30127	+	0.776656i	−1.04395	+	0.245600i
$11$	−0.272386	+	0.121274i	−0.0821275	+	0.0365655i	−0.447389	−	0.894339i	$-0.647646\pi$
$11$	−0.272386	+	0.121274i	−0.0821275	+	0.0365655i	0.365262	+	0.930905i	$0.380979\pi$
$12$	0.353934	−	0.794949i	0.102172	−	0.229482i
$13$	−0.705999	−	0.971725i	−0.195809	−	0.269508i	0.699811	−	0.714328i	$-0.253268\pi$
$13$	−0.705999	−	0.971725i	−0.195809	−	0.269508i	−0.895620	+	0.444820i	$0.853268\pi$
$14$	−3.90895	+	0.906822i	−1.04471	+	0.242358i
$15$	−0.816379	−	6.42744i	−0.210788	−	1.65956i
$16$	−4.12050	−	1.83456i	−1.03012	−	0.458641i
$17$	−4.91093	+	4.42182i	−1.19108	+	1.07245i	−0.195290	+	0.980745i	$0.562565\pi$
$17$	−4.91093	+	4.42182i	−1.19108	+	1.07245i	−0.995786	+	0.0917046i	$0.970768\pi$
$18$	7.08713	+	4.09176i	1.67045	+	0.964437i
$19$	−3.02972	+	0.643988i	−0.695066	+	0.147741i	−0.541879	−	0.840456i	$-0.682287\pi$
$19$	−3.02972	+	0.643988i	−0.695066	+	0.147741i	−0.153187	+	0.988197i	$0.548954\pi$
$20$	0.666179	−	0.0846145i	0.148962	−	0.0189204i
$21$	−0.942341	−	7.60801i	−0.205636	−	1.66020i
$22$	0.430086	−	0.139743i	0.0916946	−	0.0297934i
$23$	6.59043	+	0.692682i	1.37420	+	0.144434i	0.762670	−	0.646788i	$-0.223888\pi$
$23$	6.59043	+	0.692682i	1.37420	+	0.144434i	0.611529	+	0.791222i	$0.290555\pi$
$24$	3.73473	−	6.46875i	0.762349	−	1.32043i
$25$	3.91427	−	3.11102i	0.782855	−	0.622204i
$26$	0.910856	+	1.57765i	0.178634	+	0.309402i
$27$	−4.08014	+	5.61583i	−0.785224	+	1.08077i
$28$	0.788540	−	0.0976700i	0.149020	−	0.0184579i
$29$	1.97373	+	6.07451i	0.366512	+	1.12801i	0.949029	+	0.315189i	$0.102068\pi$
$29$	1.97373	+	6.07451i	0.366512	+	1.12801i	−0.582517	+	0.812818i	$0.697932\pi$
$30$	0.212421	+	9.82438i	0.0387826	+	1.79368i
$31$	−0.766311	−	0.851074i	−0.137634	−	0.152857i	0.670387	−	0.742011i	$-0.266128\pi$
$31$	−0.766311	−	0.851074i	−0.137634	−	0.152857i	−0.808021	+	0.589154i	$0.799461\pi$
$32$	1.45939	+	0.842577i	0.257985	+	0.148948i
$33$	0.179623	+	0.845059i	0.0312683	+	0.147106i
$34$	8.10853	−	5.89119i	1.39060	−	1.01033i
$35$	4.64284	−	3.66662i	0.784782	−	0.619771i
$36$	−1.31095	−	0.952458i	−0.218491	−	0.158743i
$37$	1.12361	−	2.52366i	0.184720	−	0.414888i	−0.797321	−	0.603555i	$-0.793750\pi$
$37$	1.12361	−	2.52366i	0.184720	−	0.414888i	0.982041	+	0.188668i	$0.0604169\pi$
$38$	4.67204	−	0.491052i	0.757906	−	0.0796591i
$39$	−3.17939	+	1.41556i	−0.509110	+	0.226670i
$40$	5.76295	−	0.124606i	0.911203	−	0.0197019i
$41$	−7.69071	+	5.58763i	−1.20109	+	0.872641i	−0.994391	−	0.105765i	$-0.966271\pi$
$41$	−7.69071	+	5.58763i	−1.20109	+	0.872641i	−0.206695	+	0.978405i	$0.566271\pi$
$42$	0.215255	+	11.6251i	0.0332146	+	1.79379i
$43$			2.00893i			0.306359i	0.988198	+	0.153180i	$0.0489513\pi$
$43$			2.00893i			0.306359i	−0.988198	+	0.153180i	$0.951049\pi$
$44$	−0.0875871	+	0.0186172i	−0.0132043	+	0.00280665i
$45$	−12.0235	−	1.00147i	−1.79235	−	0.149291i
$46$	−9.83100	−	2.08964i	−1.44950	−	0.308101i
$47$	5.57728	+	5.02181i	0.813530	+	0.732506i	0.966760	−	0.255685i	$-0.0823009\pi$
$47$	5.57728	+	5.02181i	0.813530	+	0.732506i	−0.153230	+	0.988191i	$0.548968\pi$
$48$	−7.68185	+	10.5732i	−1.10878	+	1.52610i
$49$	5.50692	−	4.32133i	0.786702	−	0.617332i
$50$	−6.39739	+	4.07202i	−0.904727	+	0.575871i
$51$	9.57389	+	16.5825i	1.34061	+	2.32201i
$52$	−0.146717	−	0.329531i	−0.0203460	−	0.0456978i
$53$	1.52605	−	7.17950i	0.209619	−	0.986181i	−0.739959	−	0.672651i	$-0.765155\pi$
$53$	1.52605	−	7.17950i	0.209619	−	0.986181i	0.949579	−	0.313529i	$-0.101511\pi$
$54$	7.04468	−	7.82391i	0.958660	−	1.06470i
$55$	−0.485706	+	0.456725i	−0.0654926	+	0.0615848i
$56$	6.81924	−	0.126268i	0.911260	−	0.0168733i
$57$			8.97484i			1.18875i
$58$	−2.01408	−	9.47552i	−0.264462	−	1.24420i
$59$	1.28678	+	12.2429i	0.167525	+	1.59389i	0.678701	+	0.734415i	$0.262543\pi$
$59$	1.28678	+	12.2429i	0.167525	+	1.59389i	−0.511176	+	0.859476i	$0.670790\pi$
$60$	0.161511	−	1.93907i	0.0208510	−	0.250332i
$61$	0.978410	−	9.30895i	0.125273	−	1.19189i	−0.733557	−	0.679628i	$-0.762141\pi$
$61$	0.978410	−	9.30895i	0.125273	−	1.19189i	0.858830	−	0.512261i	$-0.171192\pi$
$62$	1.02096	+	1.40522i	0.129661	+	0.178464i
$63$	−14.2226	−	1.22911i	−1.79188	−	0.154854i
$64$	5.23034	+	3.80006i	0.653792	+	0.475008i
$65$	−2.20646	−	1.53132i	−0.273678	−	0.189937i
$66$	−0.136966	−	1.30314i	−0.0168593	−	0.160405i
$67$	6.12477	−	5.51477i	0.748260	−	0.673737i	−0.204018	−	0.978967i	$-0.565400\pi$
$67$	6.12477	−	5.51477i	0.748260	−	0.673737i	0.952279	+	0.305230i	$0.0987335\pi$
$68$	−1.71871	+	0.992297i	−0.208424	+	0.120334i
$69$	5.93348	−	18.2614i	0.714307	−	2.19841i
$70$	−7.58441	+	4.79456i	−0.906511	+	0.573060i
$71$	−1.15037	−	3.54049i	−0.136524	−	0.420179i	0.859300	−	0.511472i	$-0.170900\pi$
$71$	−1.15037	−	3.54049i	−0.136524	−	0.420179i	−0.995824	+	0.0912938i	$0.970900\pi$
$72$	−10.3367	−	9.30719i	−1.21819	−	1.09686i
$73$	−3.39653	−	7.62873i	−0.397534	−	0.892875i	−0.995798	−	0.0915763i	$-0.970809\pi$
$73$	−3.39653	−	7.62873i	−0.397534	−	0.892875i	0.598265	−	0.801299i	$-0.295857\pi$
$74$	−2.09491	+	3.62849i	−0.243528	+	0.421803i
$75$	−6.45922	−	12.9681i	−0.745846	−	1.49742i
$76$	−0.930207			−0.106702
$77$	−0.576370	+	0.538618i	−0.0656834	+	0.0613812i
$78$	5.02012	−	1.63113i	0.568416	−	0.184690i
$79$	−5.18279	+	5.75607i	−0.583110	+	0.647609i	−0.960446	−	0.278468i	$-0.910173\pi$
$79$	−5.18279	+	5.75607i	−0.583110	+	0.647609i	0.377336	+	0.926076i	$0.376840\pi$
$80$	−10.0509	−	0.837167i	−1.12372	−	0.0935982i
$81$	2.62722	+	2.91782i	0.291913	+	0.324203i
$82$	12.4863	−	7.20896i	1.37888	−	0.796096i
$83$	1.86230	+	0.605097i	0.204414	+	0.0664180i	0.409434	−	0.912340i	$-0.365726\pi$
$83$	1.86230	+	0.605097i	0.204414	+	0.0664180i	−0.205021	+	0.978758i	$0.565726\pi$
$84$	0.198223	−	2.29373i	0.0216279	−	0.250266i
$85$	−7.10996	+	12.9537i	−0.771184	+	1.40502i
$86$	0.318489	−	3.03022i	0.0343435	−	0.326757i
$87$	18.4055	−	1.93449i	1.97327	−	0.207399i
$88$	−0.764418	+	0.0803436i	−0.0814872	+	0.00856465i
$89$	0.434658	−	4.13550i	0.0460737	−	0.438362i	−0.947032	−	0.321139i	$-0.895934\pi$
$89$	0.434658	−	4.13550i	0.0460737	−	0.438362i	0.993106	−	0.117223i	$-0.0373991\pi$
$90$	17.9771	+	3.41675i	1.89495	+	0.360157i
$91$	−2.60508	−	1.81998i	−0.273087	−	0.190786i
$92$	1.89272	+	0.614983i	0.197330	+	0.0641164i
$93$	−2.87377	+	1.65917i	−0.297997	+	0.172048i
$94$	−7.61647	−	8.45895i	−0.785579	−	0.872474i
$95$	−5.92185	+	3.59186i	−0.607569	+	0.368517i
$96$	3.26722	−	3.62861i	0.333459	−	0.370344i
$97$	−3.80086	+	1.23497i	−0.385919	+	0.125393i	−0.495549	−	0.868580i	$-0.665033\pi$
$97$	−3.80086	+	1.23497i	−0.385919	+	0.125393i	0.109630	+	0.993972i	$0.465033\pi$
$98$	−8.99156	+	5.64512i	−0.908285	+	0.570243i
$99$	1.60880			0.161690
$100$	1.34409	−	0.669473i	0.134409	−	0.0669473i
$101$	1.53118	−	2.65208i	0.152358	−	0.263892i	−0.779736	−	0.626108i	$-0.784647\pi$
$101$	1.53118	−	2.65208i	0.152358	−	0.263892i	0.932094	+	0.362217i	$0.117980\pi$
$102$	−11.8121	−	26.5303i	−1.16957	−	2.62689i
$103$	6.38836	+	5.75210i	0.629463	+	0.566771i	0.920890	−	0.389822i	$-0.127463\pi$
$103$	6.38836	+	5.75210i	0.629463	+	0.566771i	−0.291427	+	0.956593i	$0.594130\pi$
$104$	−0.956819	−	2.94479i	−0.0938238	−	0.288760i
$105$	−7.59498	−	15.3677i	−0.741195	−	1.49973i
$106$	−3.44006	+	10.5874i	−0.334128	+	1.02834i
$107$	13.5997	−	7.85178i	1.31473	−	0.759060i	0.331856	−	0.943330i	$-0.392325\pi$
$107$	13.5997	−	7.85178i	1.31473	−	0.759060i	0.982876	+	0.184270i	$0.0589920\pi$
$108$	−1.54921	+	1.39492i	−0.149073	+	0.134226i
$109$	1.46598	+	13.9479i	0.140416	+	1.33596i	0.807007	+	0.590541i	$0.201086\pi$
$109$	1.46598	+	13.9479i	0.140416	+	1.33596i	−0.666592	+	0.745423i	$0.732248\pi$
$110$	0.805033	−	0.611909i	0.0767568	−	0.0583433i
$111$	−6.47570	−	4.70487i	−0.614646	−	0.446567i
$112$	−11.8892	−	1.02746i	−1.12342	−	0.0970858i
$113$	3.13291	+	4.31207i	0.294719	+	0.405646i	0.930540	−	0.366191i	$-0.119338\pi$
$113$	3.13291	+	4.31207i	0.294719	+	0.405646i	−0.635821	+	0.771837i	$0.719338\pi$
$114$	1.42284	−	13.5374i	0.133261	−	1.26789i
$115$	14.4240	−	3.39339i	1.34505	−	0.316435i
$116$	0.200503	+	1.90766i	0.0186162	+	0.177121i
$117$	1.34744	+	6.33923i	0.124571	+	0.586062i
$118$		−	18.6709i		−	1.71879i
$119$	−8.46016	+	15.3008i	−0.775542	+	1.40262i
$120$	3.11862	−	16.4085i	0.284690	−	1.49788i
$121$	−7.30095	+	8.10853i	−0.663723	+	0.737139i
$122$	−2.95161	+	13.8862i	−0.267226	+	1.25720i
$123$	11.2034	+	25.1632i	1.01018	+	2.26889i
$124$	−0.171967	−	0.297856i	−0.0154431	−	0.0267482i
$125$	5.97161	−	9.45198i	0.534117	−	0.845410i
$126$	21.2581	+	4.10876i	1.89382	+	0.366037i
$127$	−5.51739	+	7.59404i	−0.489590	+	0.673862i	−0.980312	−	0.197454i	$-0.936733\pi$
$127$	−5.51739	+	7.59404i	−0.489590	+	0.673862i	0.490723	+	0.871316i	$0.336733\pi$
$128$	−9.79147	−	8.81628i	−0.865452	−	0.779256i
$129$	5.69374	+	1.21024i	0.501306	+	0.106556i
$130$	3.08539	+	2.65961i	0.270607	+	0.233263i
$131$	−6.97393	+	1.48236i	−0.609315	+	0.129514i	−0.502227	−	0.864736i	$-0.667486\pi$
$131$	−6.97393	+	1.48236i	−0.609315	+	0.129514i	−0.107088	+	0.994250i	$0.534153\pi$
$132$			0.259456i			0.0225828i
$133$	−7.01998	+	4.22818i	−0.608710	+	0.366629i
$134$	−10.1127	+	7.34733i	−0.873606	+	0.634712i
$135$	−4.47627	+	14.8623i	−0.385256	+	1.27915i
$136$	−15.5626	+	6.92892i	−1.33448	+	0.594150i
$137$	−15.5667	+	1.63612i	−1.32995	+	0.139783i	−0.742701	−	0.669623i	$-0.766455\pi$
$137$	−15.5667	+	1.63612i	−1.32995	+	0.139783i	−0.587248	+	0.809407i	$0.699789\pi$
$138$	−11.8450	+	26.6043i	−1.00831	+	2.26471i
$139$	5.33788	+	3.87820i	0.452753	+	0.328944i	0.790682	−	0.612227i	$-0.209726\pi$
$139$	5.33788	+	3.87820i	0.452753	+	0.328944i	−0.337929	+	0.941172i	$0.609726\pi$
$140$	1.59280	−	0.787191i	0.134616	−	0.0665298i
$141$	17.5928	−	12.7819i	1.48158	−	1.07643i
$142$	1.17390	+	5.52275i	0.0985112	+	0.463459i
$143$	0.310150	+	0.179065i	0.0259360	+	0.0149742i
$144$	16.2846	+	18.0859i	1.35705	+	1.50715i
$145$	8.64257	+	11.3702i	0.717726	+	0.944246i
$146$	3.91380	+	12.0454i	0.323908	+	0.996887i
$147$	−8.93002	−	18.2111i	−0.736536	−	1.50202i
$148$	0.487642	−	0.671181i	0.0400839	−	0.0551708i
$149$	5.90514	+	10.2280i	0.483768	+	0.837911i	0.999826	−	0.0186424i	$-0.00593442\pi$
$149$	5.90514	+	10.2280i	0.483768	+	0.837911i	−0.516058	+	0.856554i	$0.672601\pi$
$150$	7.68699	+	20.5847i	0.627640	+	1.68073i
$151$	0.789055	−	1.36668i	0.0642124	−	0.111219i	−0.832132	−	0.554578i	$-0.812880\pi$
$151$	0.789055	−	1.36668i	0.0642124	−	0.111219i	0.896344	+	0.443359i	$0.146213\pi$
$152$	−7.94099	−	0.834632i	−0.644099	−	0.0676976i
$153$	33.9112	−	11.0184i	2.74156	−	0.890786i
$154$	0.954770	−	0.721061i	0.0769376	−	0.0581047i
$155$	−2.24490	−	1.23217i	−0.180314	−	0.0989703i
$156$	−1.02235	+	0.217307i	−0.0818534	+	0.0173985i
$157$	−10.8421	−	6.25969i	−0.865294	−	0.499578i	0.000487578	−	1.00000i	$-0.499845\pi$
$157$	−10.8421	−	6.25969i	−0.865294	−	0.499578i	−0.865782	+	0.500422i	$0.833178\pi$
$158$	8.73012	−	7.86063i	0.694531	−	0.625359i
$159$	−19.4289	−	8.65030i	−1.54081	−	0.686013i
$160$	3.70185	+	0.703578i	0.292657	+	0.0556227i
$161$	17.0791	−	3.96212i	1.34602	−	0.312259i
$162$	−3.50024	−	4.81767i	−0.275005	−	0.378512i
$163$	−0.228117	+	0.512360i	−0.0178675	+	0.0401311i	−0.922259	−	0.386573i	$-0.873659\pi$
$163$	−0.228117	+	0.512360i	−0.0178675	+	0.0401311i	0.904391	+	0.426704i	$0.140325\pi$
$164$	−2.60807	+	1.16119i	−0.203656	+	0.0906736i
$165$	1.00185	+	1.65174i	0.0779941	+	0.128588i
$166$	−2.71311	−	1.20795i	−0.210578	−	0.0937553i
$167$	−16.7998	−	5.45858i	−1.30001	−	0.422397i	−0.424422	−	0.905465i	$-0.639523\pi$
$167$	−16.7998	−	5.45858i	−1.30001	−	0.422397i	−0.875583	+	0.483067i	$0.839523\pi$
$168$	3.75025	−	19.4033i	0.289338	−	1.49699i
$169$	3.57141	−	10.9917i	0.274724	−	0.845512i
$170$	12.7781	−	18.4118i	0.980035	−	1.41212i
$171$	16.3474	+	3.47475i	1.25012	+	0.265721i
$172$	−0.125437	+	0.590134i	−0.00956447	+	0.0449973i
$173$	−12.6831	−	1.33304i	−0.964275	−	0.101349i	−0.390714	−	0.920512i	$-0.627772\pi$
$173$	−12.6831	−	1.33304i	−0.964275	−	0.101349i	−0.573561	+	0.819163i	$0.694438\pi$
$174$	−28.0690			−2.12790
$175$	7.10039	−	11.1617i	0.536739	−	0.843748i
$176$	1.34485			0.101372
$177$	35.4742	+	3.72849i	2.66640	+	0.280250i
$178$	−1.31125	+	6.16896i	−0.0982825	+	0.462383i
$179$	−6.91116	−	1.46901i	−0.516564	−	0.109799i	−0.0577496	−	0.998331i	$-0.518392\pi$
$179$	−6.91116	−	1.46901i	−0.516564	−	0.109799i	−0.458815	+	0.888532i	$0.651726\pi$
$180$	−3.46942	−	1.04493i	−0.258596	−	0.0778843i
$181$	−3.42377	+	10.5373i	−0.254487	+	0.783231i	0.739443	+	0.673219i	$0.235089\pi$
$181$	−3.42377	+	10.5373i	−0.254487	+	0.783231i	−0.993930	+	0.110012i	$0.964911\pi$
$182$	3.64090	+	3.15821i	0.269881	+	0.234102i
$183$	−25.7941	−	8.38101i	−1.90675	−	0.619542i
$184$	15.6060	+	6.94823i	1.15049	+	0.512231i
$185$	0.512736	−	6.15581i	0.0376971	−	0.452584i
$186$	4.59776	−	2.04705i	0.337124	−	0.150097i
$187$	0.801418	−	1.80001i	0.0586055	−	0.131630i
$188$	1.32480	+	1.82342i	0.0966206	+	0.132987i
$189$	−5.35095	+	17.5688i	−0.389224	+	1.27794i
$190$	9.50178	−	4.47903i	0.689332	−	0.324943i
$191$	1.18175	+	0.526147i	0.0855082	+	0.0380707i	0.449045	−	0.893509i	$-0.351764\pi$
$191$	1.18175	+	0.526147i	0.0855082	+	0.0380707i	−0.363537	+	0.931580i	$0.618431\pi$
$192$	13.9211	−	12.5346i	1.00467	−	0.904608i
$193$	0.709630	+	0.409705i	0.0510803	+	0.0294912i	0.525323	−	0.850903i	$-0.323945\pi$
$193$	0.709630	+	0.409705i	0.0510803	+	0.0294912i	−0.474242	+	0.880394i	$0.657278\pi$
$194$	5.92890	−	1.26023i	0.425670	−	0.0904789i
$195$	−5.66934	+	5.33106i	−0.405990	+	0.381765i
$196$	1.88751	−	0.925562i	0.134822	−	0.0661116i
$197$	21.3985	−	6.95278i	1.52458	−	0.495365i	0.577506	−	0.816387i	$-0.304026\pi$
$197$	21.3985	−	6.95278i	1.52458	−	0.495365i	0.947072	+	0.321021i	$0.104026\pi$
$198$	−2.42666	−	0.255052i	−0.172455	−	0.0181258i
$199$	−0.379861	+	0.657939i	−0.0269276	+	0.0466400i	−0.879175	−	0.476499i	$-0.841906\pi$
$199$	−0.379861	+	0.657939i	−0.0269276	+	0.0466400i	0.852248	+	0.523139i	$0.175239\pi$
$200$	12.0749	−	4.50917i	0.853824	−	0.318846i
$201$	−11.9403	−	20.6812i	−0.842203	−	1.45874i
$202$	−2.73004	+	3.75757i	−0.192085	+	0.264382i
$203$	10.1842	+	13.4851i	0.714792	+	0.946470i
$204$	1.77698	+	5.46897i	0.124413	+	0.382905i
$205$	−12.1196	+	17.4630i	−0.846473	+	1.21967i
$206$	−8.72410	−	9.68909i	−0.607837	−	0.675071i
$207$	−30.9654	−	17.8779i	−2.15224	−	1.24260i
$208$	1.12638	+	5.29919i	0.0781002	+	0.367433i
$209$	0.747156	−	0.542841i	0.0516819	−	0.0375491i
$210$	9.01972	+	24.3842i	0.622420	+	1.68267i
$211$	8.51968	+	6.18991i	0.586519	+	0.426131i	0.841068	−	0.540929i	$-0.181927\pi$
$211$	8.51968	+	6.18991i	0.586519	+	0.426131i	−0.254550	+	0.967060i	$0.581927\pi$
$212$	0.896570	−	2.01373i	0.0615767	−	0.138304i
$213$	−10.7275	+	1.12751i	−0.735037	+	0.0772555i
$214$	−21.7582	+	9.68736i	−1.48736	+	0.662214i
$215$	1.48017	+	4.24125i	0.100946	+	0.289251i
$216$	−14.4769	+	10.5181i	−0.985029	+	0.715665i
$217$	−2.65166	−	1.46616i	−0.180006	−	0.0995296i
$218$		−	21.2710i		−	1.44065i
$219$	−23.6676	+	5.03070i	−1.59931	+	0.339943i
$220$	−0.171196	+	0.103838i	−0.0115421	+	0.00700076i
$221$	7.76391	+	1.65027i	0.522257	+	0.111009i
$222$	9.02187	+	8.12333i	0.605508	+	0.545202i
$223$	−4.68314	+	6.44579i	−0.313606	+	0.431642i	−0.936502	−	0.350663i	$-0.885956\pi$
$223$	−4.68314	+	6.44579i	−0.313606	+	0.431642i	0.622895	+	0.782305i	$0.285956\pi$
$224$	4.37748	+	0.846077i	0.292483	+	0.0565309i
$225$	−26.1217	+	6.74450i	−1.74145	+	0.449633i
$226$	−4.04196	−	7.00089i	−0.268867	−	0.465692i
$227$	−0.659828	−	1.48200i	−0.0437943	−	0.0983637i	0.890323	−	0.455329i	$-0.150478\pi$
$227$	−0.659828	−	1.48200i	−0.0437943	−	0.0983637i	−0.934118	+	0.356965i	$0.883812\pi$
$228$	−0.560385	+	2.63640i	−0.0371124	+	0.174600i
$229$	−5.69224	+	6.32187i	−0.376154	+	0.417761i	−0.901262	−	0.433274i	$-0.857358\pi$
$229$	−5.69224	+	6.32187i	−0.376154	+	0.417761i	0.525108	+	0.851035i	$0.324025\pi$
$230$	−22.2948	+	2.83176i	−1.47007	+	0.186721i
$231$	1.17934	+	1.95803i	0.0775946	+	0.128829i
$232$			16.4652i			1.08099i
$233$	−3.41340	−	16.0588i	−0.223619	−	1.05205i	−0.936475	−	0.350736i	$-0.885932\pi$
$233$	−3.41340	−	16.0588i	−0.223619	−	1.05205i	0.712855	−	0.701311i	$-0.247402\pi$
$234$	−1.02745	−	9.77552i	−0.0671664	−	0.639046i
$235$	15.4747	+	6.49271i	1.00946	+	0.423538i
$236$	−0.386443	+	3.67676i	−0.0251553	+	0.239337i
$237$	13.1917	+	18.1568i	0.856890	+	1.17941i
$238$	15.1868	−	21.7380i	0.984414	−	1.40907i
$239$	−14.8595	−	10.7960i	−0.961178	−	0.698337i	−0.00775395	−	0.999970i	$-0.502468\pi$
$239$	−14.8595	−	10.7960i	−0.961178	−	0.698337i	−0.953424	+	0.301633i	$0.902468\pi$
$240$	−8.42765	+	27.9819i	−0.544002	+	1.80623i
$241$	−0.884478	−	8.41525i	−0.0569742	−	0.542074i	−0.985364	−	0.170465i	$-0.945473\pi$
$241$	−0.884478	−	8.41525i	−0.0569742	−	0.542074i	0.928389	−	0.371609i	$-0.121194\pi$
$242$	12.2980	−	11.0732i	0.790548	−	0.711812i
$243$	−8.18224	+	4.72402i	−0.524891	+	0.303046i
$244$	0.868659	−	2.67346i	0.0556102	−	0.171151i
$245$	8.44225	−	13.1806i	0.539355	−	0.842078i
$246$	−12.9096	−	39.7317i	−0.823086	−	2.53320i
$247$	2.76476	+	2.48940i	0.175918	+	0.158397i
$248$	−1.20080	−	2.69703i	−0.0762506	−	0.171262i
$249$	2.83688	−	4.91362i	0.179780	−	0.311388i
$250$	−10.5059	+	13.3104i	−0.664451	+	0.841822i
$251$	28.8626			1.82179			0.910895	−	0.412638i	$-0.135392\pi$
$251$	28.8626			1.82179			0.910895	+	0.412638i	$0.135392\pi$
$252$	−4.10122	−	1.24911i	−0.258353	−	0.0786867i
$253$	−1.87915	+	0.610572i	−0.118141	+	0.0383863i
$254$	9.52621	−	10.5799i	0.597727	−	0.663844i
$255$	32.4302	+	27.9548i	2.03086	+	1.75060i
$256$	4.71954	+	5.24158i	0.294971	+	0.327599i
$257$	−24.1450	+	13.9401i	−1.50612	+	0.869560i	−0.506148	+	0.862447i	$0.668931\pi$
$257$	−24.1450	+	13.9401i	−1.50612	+	0.869560i	−0.999975	+	0.00711374i	$0.997736\pi$
$258$	−8.39641	−	2.72816i	−0.522738	−	0.169848i
$259$	0.629284	−	7.28173i	0.0391018	−	0.452465i
$260$	−0.552544	−	0.587605i	−0.0342673	−	0.0364417i
$261$	3.60235	−	34.2740i	0.222980	−	2.12151i
$262$	10.7543	−	1.13032i	0.664402	−	0.0698315i
$263$	6.86450	−	0.721488i	0.423283	−	0.0444889i	0.109507	−	0.993986i	$-0.465073\pi$
$263$	6.86450	−	0.721488i	0.423283	−	0.0444889i	0.313776	+	0.949497i	$0.398406\pi$
$264$	−0.232798	+	2.21492i	−0.0143277	+	0.136319i
$265$	−2.06802	−	16.2817i	−0.127037	−	1.00018i
$266$	11.2591	−	5.26474i	0.690337	−	0.322802i
$267$	−11.4590	−	3.72326i	−0.701281	−	0.227860i
$268$	2.14352	−	1.23756i	0.130937	−	0.0755963i
$269$	−11.7091	−	13.0043i	−0.713917	−	0.792886i	0.271609	−	0.962408i	$-0.412444\pi$
$269$	−11.7091	−	13.0043i	−0.713917	−	0.792886i	−0.985526	+	0.169522i	$0.945778\pi$
$270$	9.10809	−	21.7083i	0.554301	−	1.32112i
$271$	7.92973	−	8.80685i	0.481697	−	0.534978i	−0.452487	−	0.891771i	$-0.649463\pi$
$271$	7.92973	−	8.80685i	0.481697	−	0.534978i	0.934184	+	0.356793i	$0.116130\pi$
$272$	28.3476	−	9.21069i	1.71883	−	0.558480i
$273$	−6.72760	+	6.28694i	−0.407173	+	0.380503i
$274$	23.7397			1.43417
$275$	−0.688908	+	1.32210i	−0.0415427	+	0.0797256i
$276$	2.88322	−	4.99389i	0.173550	−	0.300597i
$277$	5.60381	+	12.5864i	0.336700	+	0.756241i	0.999969	+	0.00785985i	$0.00250189\pi$
$277$	5.60381	+	12.5864i	0.336700	+	0.756241i	−0.663269	+	0.748381i	$0.730831\pi$
$278$	−7.43667	−	6.69601i	−0.446022	−	0.401600i
$279$	1.90951	+	5.87688i	0.114320	+	0.351839i
$280$	14.3037	−	5.29094i	0.854810	−	0.316194i
$281$	−2.06261	+	6.34806i	−0.123045	+	0.378694i	−0.993540	−	0.113484i	$-0.963799\pi$
$281$	−2.06261	+	6.34806i	−0.123045	+	0.378694i	0.870495	+	0.492178i	$0.163799\pi$
$282$	−28.5629	+	16.4908i	−1.70089	+	0.982011i
$283$	−2.71933	+	2.44849i	−0.161647	+	0.145548i	−0.745985	−	0.665963i	$-0.768021\pi$
$283$	−2.71933	+	2.44849i	−0.161647	+	0.145548i	0.584338	+	0.811511i	$0.301354\pi$
$284$	−0.116862	−	1.11187i	−0.00693447	−	0.0659771i
$285$	6.61259	+	18.9476i	0.391696	+	1.12236i
$286$	−0.439433	−	0.319266i	−0.0259842	−	0.0188786i
$287$	−14.4042	+	20.6179i	−0.850255	+	1.21704i
$288$	−5.34446	−	7.35602i	−0.314926	−	0.433458i
$289$	2.78775	−	26.5237i	0.163986	−	1.56022i
$290$	−11.2336	−	18.5207i	−0.659660	−	1.08757i
$291$	1.21043	+	11.5164i	0.0709564	+	0.675105i
$292$	−0.521413	−	2.45306i	−0.0305134	−	0.143554i
$293$			29.0587i			1.69763i	0.528693	+	0.848813i	$0.322682\pi$
$293$			29.0587i			1.69763i	−0.528693	+	0.848813i	$0.677318\pi$
$294$	10.5827	+	28.8848i	0.617194	+	1.68459i
$295$	11.7371	+	24.8991i	0.683362	+	1.44968i
$296$	4.76512	−	5.29220i	0.276967	−	0.307603i
$297$	0.430319	−	2.02449i	0.0249696	−	0.117473i
$298$	−7.28564	−	16.3638i	−0.422046	−	0.947930i
$299$	−3.97974	−	6.89312i	−0.230155	−	0.398639i
$300$	−1.08771	−	4.21274i	−0.0627989	−	0.243223i
$301$	1.73577	+	5.02372i	0.100048	+	0.289562i
$302$	−1.40686	+	1.93637i	−0.0809555	+	0.111426i
$303$	−6.59412	−	5.93737i	−0.378822	−	0.341093i
$304$	13.6654	+	2.90467i	0.783765	+	0.166594i
$305$	−4.79315	−	20.3739i	−0.274455	−	1.16660i
$306$	−52.8975	+	11.2437i	−3.02395	+	0.642760i
$307$		−	27.1407i		−	1.54900i	−0.632571	−	0.774502i	$-0.718000\pi$
$307$		−	27.1407i		−	1.54900i	0.632571	−	0.774502i	$-0.282000\pi$
$308$	−0.202943	+	0.122234i	−0.0115637	+	0.00696490i
$309$	20.1512	−	14.6407i	1.14636	−	0.832881i
$310$	3.19079	+	2.21447i	0.181225	+	0.125773i
$311$	−19.9462	+	8.88061i	−1.13104	+	0.503573i	−0.884956	−	0.465675i	$-0.845812\pi$
$311$	−19.9462	+	8.88061i	−1.13104	+	0.503573i	−0.246088	+	0.969248i	$0.579145\pi$
$312$	−8.92256	+	0.937799i	−0.505141	+	0.0530924i
$313$	4.58011	−	10.2871i	0.258883	−	0.581460i	−0.736608	−	0.676320i	$-0.763574\pi$
$313$	4.58011	−	10.2871i	0.258883	−	0.581460i	0.995491	+	0.0948597i	$0.0302402\pi$
$314$	15.3615	+	11.1608i	0.866901	+	0.629841i
$315$	−30.9323	+	7.88422i	−1.74284	+	0.444225i
$316$	−1.88188	+	1.36726i	−0.105864	+	0.0769146i
$317$	0.528910	+	2.48833i	0.0297065	+	0.139758i	0.990502	−	0.137501i	$-0.0439071\pi$
$317$	0.528910	+	2.48833i	0.0297065	+	0.139758i	−0.960795	+	0.277260i	$0.910574\pi$
$318$	27.9346	+	16.1280i	1.56649	+	0.904416i
$319$	−1.27430	−	1.41525i	−0.0713469	−	0.0792388i
$320$	13.8421	+	4.16899i	0.773797	+	0.233054i
$321$	−14.0608	−	43.2745i	−0.784795	−	2.41535i
$322$	−26.3898	+	3.26869i	−1.47065	+	0.182157i
$323$	12.0312	−	16.5595i	0.669432	−	0.921395i
$324$	0.589571	+	1.02117i	0.0327540	+	0.0567315i
$325$	−5.78653	−	1.60722i	−0.320979	−	0.0891524i
$326$	0.425313	−	0.736665i	0.0235559	−	0.0408001i
$327$	40.4144	+	4.24772i	2.23492	+	0.234900i
$328$	−23.3065	+	7.57273i	−1.28688	+	0.418134i
$329$	18.2860	+	7.73907i	1.00814	+	0.426669i
$330$	−1.24930	−	2.65027i	−0.0687719	−	0.145892i
$331$	−3.45566	+	0.734523i	−0.189940	+	0.0403730i	−0.301899	−	0.953340i	$-0.597621\pi$
$331$	−3.45566	+	0.734523i	−0.189940	+	0.0403730i	0.111959	+	0.993713i	$0.464287\pi$
$332$	0.509277	+	0.294031i	0.0279502	+	0.0161371i
$333$	−11.0770	+	9.97375i	−0.607014	+	0.546558i
$334$	24.4749	+	10.8969i	1.33921	+	0.596254i
$335$	8.86734	−	16.1554i	0.484475	−	0.882666i
$336$	−10.0745	+	33.0775i	−0.549607	+	1.80453i
$337$	−6.84062	−	9.41531i	−0.372633	−	0.512885i	0.580981	−	0.813917i	$-0.302669\pi$
$337$	−6.84062	−	9.41531i	−0.372633	−	0.512885i	−0.953614	+	0.301032i	$0.902669\pi$
$338$	−7.12958	+	16.0133i	−0.387798	+	0.871009i
$339$	14.1087	−	6.28159i	0.766279	−	0.341169i
$340$	−2.89741	+	3.36126i	−0.157134	+	0.182290i
$341$	0.311946	+	0.138887i	0.0168928	+	0.00752117i
$342$	−24.1071	−	7.83287i	−1.30356	−	0.423553i
$343$	10.0374	−	15.5644i	0.541967	−	0.840400i
$344$	−1.60033	+	4.92531i	−0.0862840	+	0.265555i
$345$	−0.928117	−	42.9251i	−0.0499682	−	2.31101i
$346$	18.9194	+	4.02145i	1.01711	+	0.216194i
$347$	−6.10279	+	28.7114i	−0.327615	+	1.54131i	0.438575	+	0.898694i	$0.355483\pi$
$347$	−6.10279	+	28.7114i	−0.327615	+	1.54131i	−0.766190	+	0.642614i	$0.777850\pi$
$348$	5.52749	+	0.580963i	0.296305	+	0.0311429i
$349$	−10.2072			−0.546381			−0.273190	−	0.961960i	$-0.588079\pi$
$349$	−10.2072			−0.546381			−0.273190	+	0.961960i	$0.588079\pi$
$350$	−12.4796	+	15.7104i	−0.667061	+	0.839755i
$351$	8.33762			0.445029
$352$	−0.499699	−	0.0525205i	−0.0266341	−	0.00279935i
$353$	−5.02610	+	23.6459i	−0.267512	+	1.25855i	0.615102	+	0.788448i	$0.289115\pi$
$353$	−5.02610	+	23.6459i	−0.267512	+	1.25855i	−0.882614	+	0.470098i	$0.844218\pi$
$354$	−52.9172	−	11.2479i	−2.81252	−	0.597819i
$355$	−5.03727	−	6.62707i	−0.267350	−	0.351728i
$356$	0.385902	−	1.18768i	0.0204528	−	0.0629471i
$357$	38.2690	+	33.1955i	2.02541	+	1.75689i
$358$	10.1917	+	3.31148i	0.538648	+	0.175017i
$359$	−9.64610	−	4.29472i	−0.509102	−	0.226667i	0.136077	−	0.990698i	$-0.456551\pi$
$359$	−9.64610	−	4.29472i	−0.509102	−	0.226667i	−0.645179	+	0.764032i	$0.723217\pi$
$360$	−28.6802	−	12.0333i	−1.51158	−	0.634210i
$361$	−8.59286	+	3.82579i	−0.452256	+	0.201357i
$362$	6.83486	−	15.3514i	0.359233	−	0.806849i
$363$	18.5830	+	25.5773i	0.975353	+	1.34246i
$364$	−0.651617	−	0.697289i	−0.0341540	−	0.0365479i
$365$	−12.7915	−	13.6032i	−0.669538	−	0.712023i
$366$	37.5784	+	16.7310i	1.96425	+	0.874542i
$367$	11.0698	−	9.96730i	0.577839	−	0.520289i	−0.327571	−	0.944827i	$-0.606230\pi$
$367$	11.0698	−	9.96730i	0.577839	−	0.520289i	0.905410	+	0.424538i	$0.139563\pi$
$368$	−25.8851	−	14.9448i	−1.34935	−	0.779049i
$369$	50.1717	−	10.6643i	2.61184	−	0.555163i
$370$	−1.74932	+	9.20395i	−0.0909426	+	0.478491i
$371$	−2.38710	−	19.2723i	−0.123932	−	1.00057i
$372$	−0.947784	+	0.307954i	−0.0491403	+	0.0159667i
$373$	9.03214	+	0.949316i	0.467666	+	0.0491537i	0.335431	−	0.942065i	$-0.391118\pi$
$373$	9.03214	+	0.949316i	0.467666	+	0.0491537i	0.132235	+	0.991218i	$0.457785\pi$
$374$	−1.49420	+	2.58804i	−0.0772634	+	0.133824i
$375$	−23.1914	−	22.6190i	−1.19760	−	1.16804i
$376$	9.67344	+	16.7549i	0.498869	+	0.864067i
$377$	4.50930	−	6.20652i	0.232241	−	0.319652i
$378$	10.8565	−	25.6520i	0.558399	−	1.31940i
$379$	−4.37202	−	13.4557i	−0.224576	−	0.691173i	−0.998334	−	0.0576924i	$-0.981626\pi$
$379$	−4.37202	−	13.4557i	−0.224576	−	0.691173i	0.773759	−	0.633480i	$-0.218374\pi$
$380$	−1.96385	+	0.685370i	−0.100743	+	0.0351587i
$381$	18.1993	+	20.2123i	0.932377	+	1.03551i
$382$	−1.69910	−	0.980975i	−0.0869335	−	0.0501911i
$383$	1.33476	+	6.27954i	0.0682029	+	0.320869i	0.999002	−	0.0446613i	$-0.0142209\pi$
$383$	1.33476	+	6.27954i	0.0682029	+	0.320869i	−0.930799	+	0.365531i	$0.880888\pi$
$384$	−30.8859	+	22.4399i	−1.57614	+	1.14513i
$385$	−0.819979	+	1.56179i	−0.0417900	+	0.0795963i
$386$	−1.00543	−	0.730489i	−0.0511751	−	0.0371809i
$387$	4.40884	−	9.90243i	0.224114	−	0.503369i
$388$	−1.19363	+	0.125456i	−0.0605976	+	0.00636906i
$389$	−14.1250	+	6.28884i	−0.716165	+	0.318857i	−0.732271	−	0.681013i	$-0.761540\pi$
$389$	−14.1250	+	6.28884i	−0.716165	+	0.318857i	0.0161064	+	0.999870i	$0.494873\pi$
$390$	9.39663	−	7.14242i	0.475817	−	0.361671i
$391$	−35.4281	+	25.7400i	−1.79168	+	1.30173i
$392$	16.9437	−	6.20776i	0.855787	−	0.313539i
$393$			20.6586i			1.04209i
$394$	−33.3791	+	7.09495i	−1.68161	+	0.357438i
$395$	−6.70084	+	15.9708i	−0.337156	+	0.803579i
$396$	0.472592	+	0.100453i	0.0237486	+	0.00504793i
$397$	−17.2289	−	15.5130i	−0.864695	−	0.778575i	0.111887	−	0.993721i	$-0.464311\pi$
$397$	−17.2289	−	15.5130i	−0.864695	−	0.778575i	−0.976582	+	0.215146i	$0.930977\pi$
$398$	0.677278	−	0.932194i	0.0339489	−	0.0467267i
$399$	7.75449	+	22.4433i	0.388210	+	1.12357i
$400$	−21.8361	+	5.63797i	−1.09181	+	0.281899i
$401$	−0.524412	−	0.908308i	−0.0261879	−	0.0453588i	0.852634	−	0.522508i	$-0.175003\pi$
$401$	−0.524412	−	0.908308i	−0.0261879	−	0.0453588i	−0.878822	+	0.477149i	$0.841670\pi$
$402$	14.7317	+	33.0879i	0.734749	+	1.65027i
$403$	−0.285995	+	1.34550i	−0.0142464	+	0.0670242i
$404$	0.615386	−	0.683455i	0.0306166	−	0.0340032i
$405$	7.69640	+	4.22437i	0.382437	+	0.209911i
$406$	−13.2237	−	21.9551i	−0.656281	−	1.08961i
$407$			0.823676i			0.0408281i
$408$	10.2626	+	48.2819i	0.508076	+	2.39031i
$409$	0.595411	+	5.66496i	0.0294412	+	0.280114i	0.999331	+	0.0365704i	$0.0116433\pi$
$409$	0.595411	+	5.66496i	0.0294412	+	0.280114i	−0.969890	+	0.243544i	$0.921690\pi$
$410$	21.0495	−	24.4193i	1.03956	−	1.20598i
$411$	−4.74071	+	45.1049i	−0.233842	+	2.22486i
$412$	1.51745	+	2.08860i	0.0747596	+	0.102898i
$413$	13.7960	+	29.5039i	0.678859	+	1.45179i
$414$	43.8730	+	31.8756i	2.15624	+	1.56660i
$415$	4.37750	−	0.0946495i	0.214883	−	0.00464616i
$416$	−0.211573	−	2.01298i	−0.0103732	−	0.0986944i
$417$	14.2073	−	12.7923i	0.695736	−	0.626443i
$418$	−1.21305	+	0.700354i	−0.0593321	+	0.0342554i
$419$	6.28785	−	19.3520i	0.307182	−	0.945407i	−0.671673	−	0.740848i	$-0.734424\pi$
$419$	6.28785	−	19.3520i	0.307182	−	0.945407i	0.978854	−	0.204559i	$-0.0655762\pi$
$420$	−1.27152	−	4.98856i	−0.0620436	−	0.243417i
$421$	9.00232	+	27.7063i	0.438746	+	1.35032i	0.889198	+	0.457522i	$0.151263\pi$
$421$	9.00232	+	27.7063i	0.438746	+	1.35032i	−0.450452	+	0.892801i	$0.648737\pi$
$422$	−11.8695	−	10.6874i	−0.577799	−	0.520252i
$423$	−16.4706	−	36.9935i	−0.800826	−	1.79869i
$424$	9.46066	−	16.3864i	0.459450	−	0.795792i
$425$	−5.46635	+	32.5863i	−0.265157	+	1.58067i
$426$	16.3598			0.792636
$427$	−5.59647	−	24.1242i	−0.270832	−	1.16745i
$428$	4.48524	−	1.45734i	0.216802	−	0.0704433i
$429$	0.694352	−	0.771156i	0.0335236	−	0.0372317i
$430$	−1.56025	−	6.63203i	−0.0752419	−	0.319825i
$431$	12.2972	+	13.6574i	0.592336	+	0.657856i	0.962554	−	0.271089i	$-0.0873837\pi$
$431$	12.2972	+	13.6574i	0.592336	+	0.657856i	−0.370218	+	0.928945i	$0.620717\pi$
$432$	27.1148	−	15.6547i	1.30456	−	0.753189i
$433$	12.4459	+	4.04392i	0.598112	+	0.194338i	0.592398	−	0.805645i	$-0.298181\pi$
$433$	12.4459	+	4.04392i	0.598112	+	0.194338i	0.00571375	+	0.999984i	$0.498181\pi$
$434$	3.76724	+	2.63190i	0.180834	+	0.126335i
$435$	37.4322	−	17.6451i	1.79474	−	0.846018i
$436$	−0.440260	+	4.18880i	−0.0210846	+	0.200607i
$437$	−20.4133	+	2.14552i	−0.976499	+	0.102634i
$438$	36.4971	−	3.83600i	1.74390	−	0.183291i
$439$	1.28349	−	12.2116i	0.0612578	−	0.582829i	−0.920240	−	0.391355i	$-0.872006\pi$
$439$	1.28349	−	12.2116i	0.0612578	−	0.582829i	0.981498	−	0.191474i	$-0.0613269\pi$
$440$	−1.55464	+	0.732838i	−0.0741145	+	0.0349367i
$441$	−36.6284	+	9.21508i	−1.74421	+	0.438813i
$442$	−11.4492	−	3.72008i	−0.544585	−	0.176946i
$443$	−0.710842	+	0.410405i	−0.0337731	+	0.0194989i	−0.516792	−	0.856111i	$-0.672874\pi$
$443$	−0.710842	+	0.410405i	−0.0337731	+	0.0194989i	0.483018	+	0.875610i	$0.339540\pi$
$444$	−1.60850	−	1.78642i	−0.0763360	−	0.0847798i
$445$	−2.12936	−	9.05109i	−0.100941	−	0.429063i
$446$	8.08580	−	8.98019i	0.382874	−	0.425224i
$447$	32.5458	−	10.5748i	1.53936	−	0.500169i
$448$	16.3628	+	4.98364i	0.773070	+	0.235455i
$449$	−31.7045			−1.49623			−0.748114	−	0.663570i	$-0.769040\pi$
$449$	−31.7045			−1.49623			−0.748114	+	0.663570i	$0.769040\pi$
$450$	40.4705	−	6.03197i	1.90780	−	0.284350i
$451$	1.41721	−	2.45468i	0.0667337	−	0.115586i
$452$	0.651063	+	1.46231i	0.0306234	+	0.0687813i
$453$	−3.39812	−	3.05968i	−0.159658	−	0.143756i
$454$	0.760315	+	2.34001i	0.0356834	+	0.109822i
$455$	−6.84078	−	1.92293i	−0.320701	−	0.0901483i
$456$	−7.14942	+	22.0036i	−0.334802	+	1.03041i
$457$	1.22234	−	0.705719i	0.0571787	−	0.0330121i	−0.471138	−	0.882059i	$-0.656157\pi$
$457$	1.22234	−	0.705719i	0.0571787	−	0.0330121i	0.528317	+	0.849047i	$0.322823\pi$
$458$	9.58826	−	8.63331i	0.448030	−	0.403408i
$459$	−4.79493	−	45.6207i	−0.223808	−	2.12939i
$460$	4.44902	−	0.0961958i	0.207436	−	0.00448515i
$461$	−8.04550	−	5.84539i	−0.374716	−	0.272247i	0.384448	−	0.923147i	$-0.374392\pi$
$461$	−8.04550	−	5.84539i	−0.374716	−	0.272247i	−0.759164	+	0.650900i	$0.774392\pi$
$462$	−1.46846	−	3.14041i	−0.0683188	−	0.146105i
$463$	−7.20026	−	9.91031i	−0.334624	−	0.460571i	0.608237	−	0.793755i	$-0.291877\pi$
$463$	−7.20026	−	9.91031i	−0.334624	−	0.460571i	−0.942862	+	0.333184i	$0.891877\pi$
$464$	3.01133	−	28.6509i	0.139798	−	1.33008i
$465$	−4.84463	+	5.62021i	−0.224664	+	0.260631i
$466$	2.60278	+	24.7638i	0.120571	+	1.14716i
$467$	−7.35286	−	34.5925i	−0.340250	−	1.60075i	−0.732417	−	0.680856i	$-0.761608\pi$
$467$	−7.35286	−	34.5925i	−0.340250	−	1.60075i	0.392167	−	0.919894i	$-0.371726\pi$
$468$			1.94631i			0.0899684i
$469$	10.5513	−	19.0827i	0.487212	−	0.881158i
$470$	−22.3123	−	12.2467i	−1.02919	−	0.564899i
$471$	−24.2729	+	26.9578i	−1.11844	+	1.24215i
$472$	−6.59798	+	31.0410i	−0.303697	+	1.42878i
$473$	−0.243632	−	0.547206i	−0.0112022	−	0.0251605i
$474$	−17.0194	−	29.4785i	−0.781728	−	1.35399i
$475$	−9.85571	+	11.9463i	−0.452211	+	0.548133i
$476$	−3.44059	+	3.96644i	−0.157699	+	0.181801i
$477$	−23.2785	+	32.0401i	−1.06585	+	1.46702i
$478$	20.7020	+	18.6402i	0.946888	+	0.852582i
$479$	21.8267	+	4.63940i	0.997285	+	0.211980i	0.677510	−	0.735514i	$-0.263059\pi$
$479$	21.8267	+	4.63940i	0.997285	+	0.211980i	0.319776	+	0.947493i	$0.396392\pi$
$480$	4.22419	−	10.0680i	0.192807	−	0.459538i
$481$	−3.24557	+	0.689868i	−0.147985	+	0.0314553i
$482$			12.8335i			0.584552i
$483$	−0.940502	−	50.7928i	−0.0427943	−	2.31115i
$484$	−2.65098	+	1.92605i	−0.120499	+	0.0875479i
$485$	−7.11443	+	5.40771i	−0.323050	+	0.245552i
$486$	13.0908	−	5.82839i	0.593810	−	0.264381i
$487$	11.1993	−	1.17709i	0.507487	−	0.0533390i	0.152674	−	0.988277i	$-0.451211\pi$
$487$	11.1993	−	1.17709i	0.507487	−	0.0533390i	0.354812	+	0.934938i	$0.384545\pi$
$488$	9.81434	−	22.0434i	0.444274	−	0.997856i
$489$	1.31471	+	0.955195i	0.0594534	+	0.0431954i
$490$	−14.8236	+	18.5429i	−0.669664	+	0.837681i
$491$	28.1497	−	20.4520i	1.27038	−	0.922985i	0.271162	−	0.962534i	$-0.412592\pi$
$491$	28.1497	−	20.4520i	1.27038	−	0.922985i	0.999218	+	0.0395486i	$0.0125920\pi$
$492$	1.71987	+	8.09137i	0.0775379	+	0.364787i
$493$	−36.5532	−	21.1040i	−1.64628	−	0.950478i
$494$	−3.77563	−	4.19326i	−0.169874	−	0.188664i
$495$	3.39648	−	1.18535i	0.152660	−	0.0532775i
$496$	1.59623	+	4.91270i	0.0716729	+	0.220587i
$497$	−5.93581	−	7.85972i	−0.266257	−	0.352556i
$498$	−5.05805	+	6.96181i	−0.226657	+	0.311966i
$499$	18.7370	+	32.4534i	0.838784	+	1.45282i	0.890912	+	0.454176i	$0.150066\pi$
$499$	18.7370	+	32.4534i	0.838784	+	1.45282i	−0.0521285	+	0.998640i	$0.516601\pi$
$500$	2.34437	−	2.40370i	0.104843	−	0.107497i
$501$	−25.5915	+	44.3257i	−1.14334	+	1.98033i
$502$	−43.5355	−	4.57577i	−1.94308	−	0.204226i
$503$	−7.49603	+	2.43561i	−0.334231	+	0.108598i	−0.471325	−	0.881960i	$-0.656224\pi$
$503$	−7.49603	+	2.43561i	−0.334231	+	0.108598i	0.137093	+	0.990558i	$0.456224\pi$
$504$	−33.8905	−	14.3433i	−1.50960	−	0.638899i
$505$	1.27858	−	6.72721i	0.0568961	−	0.299357i
$506$	2.93125	−	0.623056i	0.130310	−	0.0276982i
$507$	−29.0012	−	16.7438i	−1.28799	−	0.743620i
$508$	−2.09493	+	1.88628i	−0.0929475	+	0.0836903i
$509$	−24.6623	−	10.9804i	−1.09314	−	0.486697i	−0.220661	−	0.975351i	$-0.570821\pi$
$509$	−24.6623	−	10.9804i	−1.09314	−	0.486697i	−0.872478	+	0.488654i	$0.837488\pi$
$510$	−44.4849	−	47.3076i	−1.96982	−	2.09482i
$511$	−15.0851	−	16.1424i	−0.667325	−	0.714098i
$512$	9.20115	+	12.6643i	0.406637	+	0.559688i
$513$	8.74518	−	19.6420i	0.386109	−	0.867215i
$514$	38.6296	−	17.1990i	1.70388	−	0.758616i
$515$	17.7252	+	7.43691i	0.781064	+	0.327709i
$516$	1.59700	+	0.711030i	0.0703039	+	0.0313013i
$517$	−2.12819	−	0.691491i	−0.0935977	−	0.0304117i
$518$	−2.10361	+	10.8838i	−0.0924274	+	0.478206i
$519$	−11.4188	+	35.1434i	−0.501229	+	1.54262i
$520$	−4.18972	−	5.51203i	−0.183732	−	0.241719i
$521$	−24.7092	−	5.25210i	−1.08253	−	0.230099i	−0.368086	−	0.929792i	$-0.619987\pi$
$521$	−24.7092	−	5.25210i	−1.08253	−	0.230099i	−0.714444	+	0.699693i	$0.753320\pi$
$522$	−10.8673	+	51.1269i	−0.475651	+	2.23776i
$523$	−10.4099	−	1.09413i	−0.455194	−	0.0478428i	−0.125842	−	0.992050i	$-0.540163\pi$
$523$	−10.4099	−	1.09413i	−0.455194	−	0.0478428i	−0.329351	+	0.944207i	$0.606830\pi$
$524$	−2.14119			−0.0935381
$525$	−27.3573	−	26.8482i	−1.19397	−	1.17175i
$526$	−10.4686			−0.456452
$527$	7.52660	+	0.791078i	0.327864	+	0.0344599i
$528$	0.810179	−	3.81159i	0.0352585	−	0.165878i
$529$	20.4566	+	4.34818i	0.889416	+	0.189051i
$530$	0.538096	+	24.8867i	0.0233734	+	1.08101i
$531$	20.5257	−	63.1717i	0.890741	−	2.74142i
$532$	−2.32616	+	0.803723i	−0.100852	+	0.0348458i
$533$	10.8593	+	3.52839i	0.470367	+	0.152832i
$534$	16.6942	+	7.43273i	0.722428	+	0.321646i
$535$	22.9264	−	26.5968i	0.991196	−	1.14988i
$536$	19.4092	−	8.64155i	0.838351	−	0.373258i
$537$	−8.32698	+	18.7027i	−0.359336	+	0.807082i
$538$	15.6000	+	21.4716i	0.672566	+	0.925707i
$539$	−0.975943	+	1.84492i	−0.0420369	+	0.0794662i
$540$	−2.24292	+	4.08639i	−0.0965200	+	0.175850i
$541$	−21.3906	−	9.52370i	−0.919653	−	0.409456i	−0.108370	−	0.994111i	$-0.534563\pi$
$541$	−21.3906	−	9.52370i	−0.919653	−	0.409456i	−0.811282	+	0.584655i	$0.801230\pi$
$542$	−13.3572	+	12.0269i	−0.573740	+	0.516598i
$543$	27.8023	+	16.0517i	1.19311	+	0.688844i
$544$	−10.8927	+	2.31531i	−0.467019	+	0.0992680i
$545$	13.3717	+	28.3665i	0.572779	+	1.21509i
$546$	11.1444	−	8.41648i	0.476937	−	0.360192i
$547$	−33.2127	+	10.7915i	−1.42007	+	0.461409i	−0.915625	−	0.402034i	$-0.868303\pi$
$547$	−33.2127	+	10.7915i	−1.42007	+	0.461409i	−0.504447	+	0.863443i	$0.668303\pi$
$548$	−4.67494	−	0.491356i	−0.199704	−	0.0209897i
$549$	−25.2524	+	43.7384i	−1.07775	+	1.86671i
$550$	1.24873	−	1.88500i	0.0532460	−	0.0803767i
$551$	−9.89175	−	17.1330i	−0.421403	−	0.729891i
$552$	29.0943	−	40.0448i	1.23833	−	1.70442i
$553$	−7.98716	+	18.8722i	−0.339649	+	0.802529i
$554$	−6.45723	−	19.8733i	−0.274341	−	0.844336i
$555$	−17.1380	−	5.16165i	−0.727466	−	0.219100i
$556$	1.32588	+	1.47253i	0.0562297	+	0.0624494i
$557$	20.3983	+	11.7770i	0.864304	+	0.499006i	0.865451	−	0.500993i	$-0.167032\pi$
$557$	20.3983	+	11.7770i	0.864304	+	0.499006i	−0.00114721	+	0.999999i	$0.500365\pi$
$558$	−1.94856	−	9.16724i	−0.0824890	−	0.388080i
$559$	1.95213	−	1.41831i	0.0825663	−	0.0599879i
$560$	−25.8574	+	6.59071i	−1.09268	+	0.278508i
$561$	−4.61882	−	3.35577i	−0.195007	−	0.141681i
$562$	4.11758	−	9.24824i	0.173690	−	0.390113i
$563$	1.74096	−	0.182982i	0.0733728	−	0.00771179i	−0.0677709	−	0.997701i	$-0.521589\pi$
$563$	1.74096	−	0.182982i	0.0733728	−	0.00771179i	0.141144	+	0.989989i	$0.454922\pi$
$564$	5.96607	−	2.65627i	0.251217	−	0.111849i
$565$	9.79127	+	6.79532i	0.411922	+	0.285881i
$566$	4.48993	−	3.26213i	0.188726	−	0.137117i
$567$	9.09094	+	5.02659i	0.381784	+	0.211097i
$568$		−	9.59662i		−	0.402665i
$569$	−8.60793	+	1.82967i	−0.360863	+	0.0767038i	−0.384775	−	0.923010i	$-0.625721\pi$
$569$	−8.60793	+	1.82967i	−0.360863	+	0.0767038i	0.0239122	+	0.999714i	$0.492388\pi$
$570$	−6.97036	−	29.6284i	−0.291956	−	1.24100i
$571$	−1.52957	−	0.325119i	−0.0640103	−	0.0136058i	0.175795	−	0.984427i	$-0.443750\pi$
$571$	−1.52957	−	0.325119i	−0.0640103	−	0.0136058i	−0.239806	+	0.970821i	$0.577084\pi$
$572$	0.0799273	+	0.0719669i	0.00334193	+	0.00300909i
$573$	2.20313	−	3.03235i	0.0920372	−	0.126678i
$574$	24.9956	−	28.8159i	1.04330	−	1.20275i
$575$	27.9517	−	17.7916i	1.16567	−	0.741962i
$576$	−17.4417	−	30.2099i	−0.726736	−	1.25874i
$577$	5.97507	+	13.4202i	0.248746	+	0.558692i	0.994161	−	0.107909i	$-0.0344154\pi$
$577$	5.97507	+	13.4202i	0.248746	+	0.558692i	−0.745415	+	0.666600i	$0.767749\pi$
$578$	−8.40994	+	39.5656i	−0.349807	+	1.64571i
$579$	1.58869	−	1.76442i	0.0660238	−	0.0733269i
$580$	1.82885	+	3.87970i	0.0759387	+	0.161096i
$581$	5.17985	−	0.0959125i	0.214896	−	0.00397912i
$582$		−	17.5629i		−	0.728008i
$583$	0.455013	+	2.14067i	0.0188447	+	0.0886574i
$584$	−2.25018	−	21.4091i	−0.0931133	−	0.885914i
$585$	7.51541	+	12.3905i	0.310724	+	0.512286i
$586$	4.60685	−	43.8313i	0.190307	−	1.81065i
$587$	4.57144	+	6.29204i	0.188683	+	0.259700i	0.892870	−	0.450315i	$-0.148688\pi$
$587$	4.57144	+	6.29204i	0.188683	+	0.259700i	−0.704187	+	0.710015i	$0.748688\pi$
$588$	−1.48615	−	5.90718i	−0.0612877	−	0.243608i
$589$	2.86979	+	2.08503i	0.118248	+	0.0859120i
$590$	−13.7565	−	39.4178i	−0.566348	−	1.62280i
$591$	−6.81458	−	64.8364i	−0.280314	−	2.66701i
$592$	−9.25964	+	8.33742i	−0.380569	+	0.342666i
$593$	9.65143	−	5.57226i	0.396337	−	0.228825i	−0.288565	−	0.957460i	$-0.593178\pi$
$593$	9.65143	−	5.57226i	0.396337	−	0.228825i	0.684902	+	0.728635i	$0.259845\pi$
$594$	−0.970036	+	2.98546i	−0.0398011	+	0.122495i
$595$	−6.58752	+	38.5363i	−0.270062	+	1.57984i
$596$	1.09603	+	3.37324i	0.0448953	+	0.138173i
$597$	1.63590	+	1.47297i	0.0669528	+	0.0602846i
$598$	4.91012	+	11.0283i	0.200790	+	0.450981i
$599$	8.65074	−	14.9835i	0.353460	−	0.612210i	−0.633393	−	0.773830i	$-0.718338\pi$
$599$	8.65074	−	14.9835i	0.353460	−	0.612210i	0.986853	+	0.161620i	$0.0516718\pi$
$600$	−5.50565	−	36.9393i	−0.224767	−	1.50804i
$601$	5.91240			0.241172			0.120586	−	0.992703i	$-0.461523\pi$
$601$	5.91240			0.241172			0.120586	+	0.992703i	$0.461523\pi$
$602$	−1.82174	−	7.85282i	−0.0742488	−	0.320057i
$603$	−42.2931	+	13.7418i	−1.72231	+	0.559611i
$604$	0.317124	−	0.352202i	0.0129036	−	0.0143309i
$605$	−9.43942	+	22.4979i	−0.383767	+	0.914672i
$606$	9.00510	+	10.0012i	0.365807	+	0.406270i
$607$	33.6092	−	19.4043i	1.36415	−	0.787595i	0.373980	−	0.927437i	$-0.377993\pi$
$607$	33.6092	−	19.4043i	1.36415	−	0.787595i	0.990174	+	0.139842i	$0.0446594\pi$
$608$	−4.96414	−	1.61295i	−0.201323	−	0.0654137i
$609$	44.3550	−	20.7404i	1.79735	−	0.840443i
$610$	3.99985	+	31.4912i	0.161949	+	1.27504i
$611$	0.942257	−	8.96498i	0.0381196	−	0.362684i
$612$	10.6496	−	1.11932i	0.430483	−	0.0452456i
$613$	11.8635	−	1.24691i	0.479163	−	0.0503620i	0.138131	−	0.990414i	$-0.455890\pi$
$613$	11.8635	−	1.24691i	0.479163	−	0.0503620i	0.341031	+	0.940052i	$0.389224\pi$
$614$	−4.30279	+	40.9383i	−0.173647	+	1.65214i
$615$	42.1926	+	44.8699i	1.70137	+	1.80933i
$616$	−1.84216	+	0.861392i	−0.0742225	+	0.0347065i
$617$	24.8966	+	8.08939i	1.00230	+	0.325667i	0.763784	−	0.645472i	$-0.223339\pi$
$617$	24.8966	+	8.08939i	1.00230	+	0.325667i	0.238515	+	0.971139i	$0.423339\pi$
$618$	−32.7166	+	18.8889i	−1.31605	+	0.759824i
$619$	16.3012	+	18.1044i	0.655202	+	0.727676i	0.975587	−	0.219611i	$-0.0704789\pi$
$619$	16.3012	+	18.1044i	0.655202	+	0.727676i	−0.320385	+	0.947287i	$0.603812\pi$
$620$	−0.582513	−	0.502127i	−0.0233943	−	0.0201659i
$621$	−30.7799	+	34.1845i	−1.23515	+	1.37178i
$622$	31.4941	−	10.2331i	1.26280	−	0.410308i
$623$	−2.48623	−	10.7172i	−0.0996088	−	0.429374i
$624$	15.6976			0.628407
$625$	5.64308	−	24.3548i	0.225723	−	0.974191i
$626$	−8.53938	+	14.7906i	−0.341302	+	0.591153i
$627$	−1.08842	−	2.44462i	−0.0434671	−	0.0976288i
$628$	−2.79407	−	2.51579i	−0.111496	−	0.100391i
$629$	5.64124	+	17.3619i	0.224931	+	0.692266i
$630$	47.9073	−	6.98844i	1.90867	−	0.278426i
$631$	4.79933	−	14.7708i	0.191058	−	0.588017i	−0.808942	−	0.587889i	$-0.799959\pi$
$631$	4.79933	−	14.7708i	0.191058	−	0.588017i	1.00000		0.000127907i	$-4.07141e-5\pi$
$632$	−17.2920	+	9.98354i	−0.687839	+	0.397124i
$633$	22.6760	−	20.4176i	0.901291	−	0.811526i
$634$	−0.403303	−	3.83717i	−0.0160172	−	0.152393i
$635$	−6.05305	+	20.0977i	−0.240208	+	0.797551i
$636$	−5.16722	−	3.75420i	−0.204893	−	0.148864i
$637$	−8.08702	−	2.30035i	−0.320419	−	0.0911434i
$638$	1.69774	+	2.33674i	0.0672143	+	0.0925126i
$639$	−2.09960	+	19.9764i	−0.0830591	+	0.790254i
$640$	−27.1674	−	11.3986i	−1.07389	−	0.450569i
$641$	3.08280	+	29.3309i	0.121763	+	1.15850i	0.869302	+	0.494282i	$0.164569\pi$
$641$	3.08280	+	29.3309i	0.121763	+	1.15850i	−0.747538	+	0.664219i	$0.768764\pi$
$642$	14.3483	+	67.5032i	0.566280	+	2.66414i
$643$		−	36.3038i		−	1.43168i	−0.698264	−	0.715840i	$-0.746044\pi$
$643$		−	36.3038i		−	1.43168i	0.698264	−	0.715840i	$-0.253956\pi$
$644$	5.26447	−	0.0974794i	0.207449	−	0.00384123i
$645$	12.9123	−	1.64005i	0.508421	−	0.0645769i
$646$	−20.7728	+	23.0705i	−0.817293	+	0.907696i
$647$	3.33336	−	15.6822i	0.131048	−	0.616532i	−0.862778	−	0.505583i	$-0.831278\pi$
$647$	3.33336	−	15.6822i	0.131048	−	0.616532i	0.993826	−	0.110949i	$-0.0353891\pi$
$648$	4.11681	+	9.24650i	0.161723	+	0.363237i
$649$	−1.83525	−	3.17875i	−0.0720399	−	0.124777i
$650$	8.47344	+	3.34166i	0.332356	+	0.131071i
$651$	−5.75285	+	6.63210i	−0.225472	+	0.259932i
$652$	−0.0990022	+	0.136265i	−0.00387723	+	0.00533654i
$653$	13.5716	+	12.2199i	0.531096	+	0.478201i	0.890502	−	0.454980i	$-0.150354\pi$
$653$	13.5716	+	12.2199i	0.531096	+	0.478201i	−0.359405	+	0.933182i	$0.617020\pi$
$654$	−60.2865	−	12.8143i	−2.35739	−	0.501078i
$655$	−13.6311	+	8.26788i	−0.532612	+	0.323053i
$656$	41.9404	−	8.91470i	1.63750	−	0.348061i
$657$			45.0576i			1.75786i
$658$	−26.3552	−	14.5724i	−1.02743	−	0.568091i
$659$	−3.05262	+	2.21786i	−0.118913	+	0.0863955i	−0.645652	−	0.763632i	$-0.723414\pi$
$659$	−3.05262	+	2.21786i	−0.118913	+	0.0863955i	0.526739	+	0.850027i	$0.323414\pi$
$660$	0.191165	+	0.547762i	0.00744110	+	0.0213216i
$661$	1.63193	−	0.726582i	0.0634747	−	0.0282608i	−0.374754	−	0.927124i	$-0.622273\pi$
$661$	1.63193	−	0.726582i	0.0634747	−	0.0282608i	0.438228	+	0.898864i	$0.355606\pi$
$662$	5.32886	−	0.560086i	0.207112	−	0.0217684i
$663$	9.35443	−	21.0104i	0.363296	−	0.815976i
$664$	4.08378	+	2.96704i	0.158481	+	0.115143i
$665$	−11.7053	+	14.0988i	−0.453910	+	0.546727i
$666$	18.2894	−	13.2880i	0.708699	−	0.514900i
$667$	8.80001	+	41.4008i	0.340738	+	1.60304i
$668$	−4.59419	−	2.65245i	−0.177754	−	0.102627i
$669$	15.4475	+	17.1561i	0.597233	+	0.663295i
$670$	−15.9365	+	22.9626i	−0.615679	+	0.887123i
$671$	0.862429	+	2.65428i	0.0332937	+	0.102468i
$672$	5.03509	−	11.8970i	0.194233	−	0.458937i
$673$	16.1740	−	22.2615i	0.623460	−	0.858119i	−0.374139	−	0.927373i	$-0.622062\pi$
$673$	16.1740	−	22.2615i	0.623460	−	0.858119i	0.997599	+	0.0692535i	$0.0220617\pi$
$674$	8.82553	+	15.2863i	0.339947	+	0.588805i
$675$	1.50019	+	34.6753i	0.0577423	+	1.33465i
$676$	1.73543	−	3.00586i	0.0667474	−	0.115610i
$677$	−29.2116	−	3.07026i	−1.12269	−	0.118000i	−0.475061	−	0.879953i	$-0.657574\pi$
$677$	−29.2116	−	3.07026i	−1.12269	−	0.118000i	−0.647632	+	0.761953i	$0.724241\pi$
$678$	−22.2770	+	7.23824i	−0.855543	+	0.277983i
$679$	−8.43773	+	6.37233i	−0.323810	+	0.244548i
$680$	−27.7505	+	26.0947i	−1.06418	+	1.00069i
$681$	−4.59780	+	0.977292i	−0.176188	+	0.0374499i
$682$	−0.448512	−	0.258948i	−0.0171744	−	0.00991564i
$683$	−14.6880	+	13.2251i	−0.562020	+	0.506045i	−0.900457	−	0.434944i	$-0.856768\pi$
$683$	−14.6880	+	13.2251i	−0.562020	+	0.506045i	0.338438	+	0.940989i	$0.390101\pi$
$684$	4.58518	+	2.04145i	0.175319	+	0.0780569i
$685$	−31.6587	+	14.9236i	−1.20962	+	0.570200i
$686$	−17.6076	+	21.8856i	−0.672261	+	0.835598i
$687$	14.4883	+	19.9415i	0.552765	+	0.760816i
$688$	3.68551	−	8.27780i	0.140509	−	0.315588i
$689$	−8.05389	+	3.58582i	−0.306829	+	0.136609i
$690$	−5.40523	+	64.8941i	−0.205774	+	2.47047i
$691$	30.8780	+	13.7478i	1.17465	+	0.522989i	0.898863	−	0.438229i	$-0.144394\pi$
$691$	30.8780	+	13.7478i	1.17465	+	0.522989i	0.275789	+	0.961218i	$0.411061\pi$
$692$	−3.64248	−	1.18351i	−0.138466	−	0.0449904i
$693$	4.02310	−	1.39004i	0.152825	−	0.0528033i
$694$	13.7571	−	42.3399i	0.522211	−	1.60720i
$695$	14.1267	+	4.25471i	0.535857	+	0.161390i
$696$	46.6658	+	9.91912i	1.76886	+	0.375983i
$697$	13.0611	−	61.4474i	0.494723	−	2.32749i
$698$	15.3963	+	1.61822i	0.582759	+	0.0612504i
$699$	−47.5704			−1.79928
$700$	2.78271	−	2.83547i	0.105177	−	0.107171i
$701$	−39.9977			−1.51069			−0.755347	−	0.655325i	$-0.772532\pi$
$701$	−39.9977			−1.51069			−0.755347	+	0.655325i	$0.772532\pi$
$702$	−12.5762	−	1.32182i	−0.474659	−	0.0498887i
$703$	−1.77901	+	8.36959i	−0.0670967	+	0.315665i
$704$	−1.88552	−	0.400780i	−0.0710632	−	0.0151050i
$705$	27.7242	−	39.9473i	1.04415	−	1.50450i
$706$	11.3300	−	34.8700i	0.426409	−	1.31235i
$707$	1.53754	−	7.95501i	0.0578251	−	0.299179i
$708$	10.1879	+	3.31026i	0.382885	+	0.124407i
$709$	14.4487	+	6.43298i	0.542633	+	0.241596i	0.659701	−	0.751528i	$-0.270683\pi$
$709$	14.4487	+	6.43298i	0.542633	+	0.241596i	−0.117068	+	0.993124i	$0.537350\pi$
$710$	6.54744	+	10.7947i	0.245721	+	0.405117i
$711$	38.1794	−	16.9986i	1.43184	−	0.637496i
$712$	4.36002	−	9.79276i	0.163399	−	0.366999i
$713$	−4.46079	−	6.13976i	−0.167058	−	0.229936i
$714$	−52.4612	−	56.1382i	−1.96331	−	2.10092i
$715$	0.786720	+	0.149525i	0.0294216	+	0.00559191i
$716$	−1.93846	−	0.863060i	−0.0724438	−	0.0322541i
$717$	−39.5500	+	35.6110i	−1.47702	+	1.32992i
$718$	13.8690	+	8.00729i	0.517588	+	0.298829i
$719$	−1.03010	+	0.218955i	−0.0384163	+	0.00816563i	−0.227080	−	0.973876i	$-0.572918\pi$
$719$	−1.03010	+	0.218955i	−0.0384163	+	0.00816563i	0.188663	+	0.982042i	$0.439584\pi$
$720$	47.7054	+	26.1844i	1.77788	+	0.975834i
$721$	20.9453	+	8.86452i	0.780043	+	0.330132i
$722$	13.5677	−	4.40843i	0.504939	−	0.164065i
$723$	−24.3834	−	2.56280i	−0.906829	−	0.0953116i
$724$	−1.66370	+	2.88160i	−0.0618307	+	0.107094i
$725$	26.6236	+	17.6370i	0.988777	+	0.655021i
$726$	−23.9751	−	41.5261i	−0.889799	−	1.54118i
$727$	−14.7472	+	20.2978i	−0.546944	+	0.752804i	−0.989594	−	0.143891i	$-0.954039\pi$
$727$	−14.7472	+	20.2978i	−0.546944	+	0.752804i	0.442650	+	0.896695i	$0.354039\pi$
$728$	−4.93708	−	6.53728i	−0.182980	−	0.242288i
$729$	12.0995	+	37.2385i	0.448131	+	1.37921i
$730$	17.1378	+	22.5466i	0.634297	+	0.834486i
$731$	−8.88315	−	9.86574i	−0.328555	−	0.364897i
$732$	−7.05384	−	4.07254i	−0.260718	−	0.150525i
$733$	2.69534	+	12.6806i	0.0995545	+	0.468367i	0.999478	+	0.0323185i	$0.0102891\pi$
$733$	2.69534	+	12.6806i	0.0995545	+	0.468367i	−0.899923	+	0.436049i	$0.856378\pi$
$734$	−18.2776	+	13.2794i	−0.674637	+	0.490152i
$735$	−32.2708	−	31.8675i	−1.19033	−	1.17545i
$736$	9.03434	+	6.56383i	0.333010	+	0.241946i
$737$	−0.999505	+	2.24492i	−0.0368172	+	0.0826929i
$738$	−77.3683	+	8.13174i	−2.84797	+	0.299333i
$739$	−34.4420	+	15.3346i	−1.26697	+	0.564091i	−0.926546	−	0.376182i	$-0.877237\pi$
$739$	−34.4420	+	15.3346i	−1.26697	+	0.564091i	−0.340423	+	0.940272i	$0.610570\pi$
$740$	0.534985	−	1.77628i	0.0196664	−	0.0652975i
$741$	8.72107	−	6.33623i	0.320377	−	0.232767i
$742$	0.545276	+	29.4482i	0.0200177	+	1.08108i
$743$		−	15.1585i		−	0.556113i	−0.960565	−	0.278057i	$-0.910310\pi$
$743$		−	15.1585i		−	0.556113i	0.960565	−	0.278057i	$-0.0896903\pi$
$744$	−8.36735	+	1.77854i	−0.306762	+	0.0652043i
$745$	20.0028	+	17.2424i	0.732847	+	0.631714i
$746$	−13.4733	−	2.86384i	−0.493293	−	0.104853i
$747$	−7.85167	−	7.06968i	−0.287278	−	0.258666i
$748$	0.347813	−	0.478723i	0.0127173	−	0.0175038i
$749$	27.2245	−	31.3854i	0.994761	−	1.14680i
$750$	31.3954	+	37.7945i	1.14640	+	1.38006i
$751$	1.14689	+	1.98648i	0.0418508	+	0.0724877i	0.886192	−	0.463318i	$-0.153341\pi$
$751$	1.14689	+	1.98648i	0.0418508	+	0.0724877i	−0.844341	+	0.535806i	$0.820008\pi$
$752$	−13.7683	−	30.9242i	−0.502080	−	1.12769i
$753$	17.3877	−	81.8027i	0.633643	−	2.98106i
$754$	−7.78565	+	8.64685i	−0.283537	+	0.314900i
$755$	0.658886	−	3.46670i	0.0239793	−	0.126166i
$756$	−2.66886	+	4.82682i	−0.0970654	+	0.175550i
$757$		−	46.5833i		−	1.69310i	−0.532311	−	0.846549i	$-0.678676\pi$
$757$		−	46.5833i		−	1.69310i	0.532311	−	0.846549i	$-0.321324\pi$
$758$	4.46142	+	20.9893i	0.162046	+	0.762366i
$759$	0.598435	+	5.69373i	0.0217218	+	0.206669i
$760$	−17.3799	+	4.08879i	−0.630436	+	0.148316i
$761$	−0.0975398	+	0.928029i	−0.00353581	+	0.0336410i	−0.996148	−	0.0876930i	$-0.972051\pi$
$761$	−0.0975398	+	0.928029i	−0.00353581	+	0.0336410i	0.992612	+	0.121334i	$0.0387172\pi$
$762$	−24.2469	−	33.3730i	−0.878372	−	1.20897i
$763$	15.7173	+	33.6127i	0.569004	+	1.21686i
$764$	0.314292	+	0.228346i	0.0113707	+	0.00826128i
$765$	63.4748	−	48.2475i	2.29494	−	1.74439i
$766$	−1.01777	−	9.68348i	−0.0367737	−	0.349878i
$767$	10.9883	−	9.89388i	0.396764	−	0.357247i
$768$	17.6990	−	10.2185i	0.638656	−	0.368728i
$769$	−9.05322	+	27.8629i	−0.326467	+	1.00476i	0.644307	+	0.764767i	$0.277146\pi$
$769$	−9.05322	+	27.8629i	−0.326467	+	1.00476i	−0.970774	+	0.239996i	$0.922854\pi$
$770$	1.48443	−	2.22577i	0.0534952	−	0.0802110i
$771$	24.9636	+	76.8299i	0.899041	+	2.76696i
$772$	0.182876	+	0.164662i	0.00658184	+	0.00592631i
$773$	18.7788	+	42.1779i	0.675428	+	1.51704i	0.846847	+	0.531837i	$0.178498\pi$
$773$	18.7788	+	42.1779i	0.675428	+	1.51704i	−0.171419	+	0.985198i	$0.554835\pi$
$774$	−8.22007	+	14.2376i	−0.295464	+	0.511759i
$775$	−5.64726	−	0.947329i	−0.202856	−	0.0340291i
$776$	−10.3024			−0.369834
$777$	−20.2589	−	6.17026i	−0.726783	−	0.221357i
$778$	22.3027	−	7.24659i	0.799591	−	0.259803i
$779$	19.7024	−	21.8817i	0.705910	−	0.783993i
$780$	−1.99827	+	1.21204i	−0.0715494	+	0.0433978i
$781$	0.742716	+	0.824869i	0.0265765	+	0.0295161i
$782$	57.5194	−	33.2089i	2.05689	−	1.18755i
$783$	−42.1665	−	13.7007i	−1.50691	−	0.489624i
$784$	−30.6190	+	7.70322i	−1.09353	+	0.275115i
$785$	−27.5019	−	5.22704i	−0.981584	−	0.186561i
$786$	3.27514	−	31.1609i	0.116820	−	1.11147i
$787$	15.2667	−	1.60459i	0.544199	−	0.0571976i	0.171559	−	0.985174i	$-0.445119\pi$
$787$	15.2667	−	1.60459i	0.544199	−	0.0571976i	0.372639	+	0.927976i	$0.378453\pi$
$788$	6.72004	−	0.706304i	0.239391	−	0.0251611i
$789$	2.09053	−	19.8901i	0.0744249	−	0.708106i
$790$	12.6393	−	23.0276i	0.449687	−	0.819285i
$791$	11.5602	+	8.07626i	0.411033	+	0.287159i
$792$	3.94429	+	1.28158i	0.140154	+	0.0455389i
$793$	−9.73649	+	5.62137i	−0.345753	+	0.199621i
$794$	23.5283	+	26.1308i	0.834986	+	0.927346i
$795$	−47.3916	−	3.94740i	−1.68081	−	0.140000i
$796$	−0.152668	+	0.169554i	−0.00541116	+	0.00600970i
$797$	−4.26542	+	1.38592i	−0.151089	+	0.0490918i	−0.383585	−	0.923506i	$-0.625311\pi$
$797$	−4.26542	+	1.38592i	−0.151089	+	0.0490918i	0.232496	+	0.972597i	$0.425311\pi$
$798$	−8.13858	−	35.0822i	−0.288103	−	1.24190i
$799$	−49.5952			−1.75455
$800$	8.33371	−	1.24210i	0.294641	−	0.0439150i
$801$	−11.2184	+	19.4308i	−0.396381	+	0.686553i
$802$	0.647008	+	1.45320i	0.0228467	+	0.0513144i
$803$	1.85033	+	1.66605i	0.0652969	+	0.0587936i
$804$	−2.21619	−	6.82075i	−0.0781592	−	0.240549i
$805$	33.1381	−	20.9486i	1.16796	−	0.738340i
$806$	0.644698	−	1.98418i	0.0227085	−	0.0698896i
$807$	−43.9108	+	25.3519i	−1.54573	+	0.892430i
$808$	5.86666	−	5.28236i	0.206388	−	0.185833i
$809$	−3.26234	−	31.0391i	−0.114698	−	1.09128i	−0.888825	−	0.458246i	$-0.848478\pi$
$809$	−3.26234	−	31.0391i	−0.114698	−	1.09128i	0.774127	−	0.633030i	$-0.218189\pi$
$810$	−10.9393	−	7.59208i	−0.384368	−	0.266759i
$811$	21.7660	+	15.8139i	0.764308	+	0.555302i	0.900229	−	0.435418i	$-0.143399\pi$
$811$	21.7660	+	15.8139i	0.764308	+	0.555302i	−0.135921	+	0.990720i	$0.543399\pi$
$812$	2.14966	+	4.59722i	0.0754383	+	0.161331i
$813$	−20.1834	−	27.7800i	−0.707862	−	0.974289i
$814$	0.130582	−	1.24241i	0.00457691	−	0.0435464i
$815$	−0.104097	+	1.24977i	−0.00364636	+	0.0437774i
$816$	−9.02760	−	85.8919i	−0.316029	−	3.00682i
$817$	−1.29373	−	6.08651i	−0.0452618	−	0.212940i
$818$		−	8.63926i		−	0.302065i
$819$	8.84680	+	14.6882i	0.309132	+	0.513248i
$820$	−4.65059	+	4.37310i	−0.162406	+	0.152715i
$821$	−9.48684	+	10.5362i	−0.331093	+	0.367716i	−0.885589	−	0.464471i	$-0.846245\pi$
$821$	−9.48684	+	10.5362i	−0.331093	+	0.367716i	0.554495	+	0.832187i	$0.312911\pi$
$822$	14.3015	−	67.2833i	0.498822	−	2.34677i
$823$	−14.2424	−	31.9889i	−0.496458	−	1.11506i	−0.971917	−	0.235325i	$-0.924384\pi$
$823$	−14.2424	−	31.9889i	−0.496458	−	1.11506i	0.475458	−	0.879738i	$-0.342282\pi$
$824$	11.0802	+	19.1915i	0.385997	+	0.668566i
$825$	3.33209	+	2.74898i	0.116009	+	0.0957073i
$826$	−16.1321	−	46.6900i	−0.561308	−	1.62455i
$827$	8.81071	−	12.1269i	0.306378	−	0.421694i	−0.627869	−	0.778319i	$-0.716073\pi$
$827$	8.81071	−	12.1269i	0.306378	−	0.421694i	0.934248	+	0.356625i	$0.116073\pi$
$828$	−7.97995	−	7.18518i	−0.277322	−	0.249702i
$829$	−16.6836	−	3.54621i	−0.579446	−	0.123165i	−0.0911406	−	0.995838i	$-0.529051\pi$
$829$	−16.6836	−	3.54621i	−0.579446	−	0.123165i	−0.488305	+	0.872673i	$0.662385\pi$
$830$	−6.61790	−	0.551226i	−0.229711	−	0.0191333i
$831$	39.0483	−	8.29997i	1.35457	−	0.287923i
$832$		−	7.76529i		−	0.269213i
$833$	−7.93596	+	45.5724i	−0.274965	+	1.57899i
$834$	−23.4580	+	17.0432i	−0.812283	+	0.590158i
$835$	−39.4894	+	0.853832i	−1.36659	+	0.0295481i
$836$	0.253376	−	0.112810i	0.00876318	−	0.00390162i
$837$	7.90615	−	0.830970i	0.273277	−	0.0287225i
$838$	−12.5524	+	28.1932i	−0.433616	+	0.973917i
$839$	5.30538	+	3.85458i	0.183162	+	0.133075i	0.675588	−	0.737279i	$-0.263890\pi$
$839$	5.30538	+	3.85458i	0.183162	+	0.133075i	−0.492426	+	0.870354i	$0.663890\pi$
$840$	−6.37867	−	43.7272i	−0.220085	−	1.50873i
$841$	−9.54254	+	6.93306i	−0.329053	+	0.239071i
$842$	−9.18639	−	43.2186i	−0.316584	−	1.48941i
$843$	16.7492	+	9.67014i	0.576872	+	0.333057i
$844$	2.11620	+	2.35028i	0.0728427	+	0.0809000i
$845$	−0.558641	−	25.8369i	−0.0192178	−	0.888817i
$846$	18.9789	+	58.4111i	0.652509	+	2.00822i
$847$	−11.2514	+	26.5851i	−0.386604	+	0.913476i
$848$	−19.4593	+	26.7835i	−0.668236	+	0.919748i
$849$	5.30135	+	9.18220i	0.181942	+	0.315132i
$850$	13.4114	−	48.2856i	0.460007	−	1.65618i
$851$	9.15315	−	15.8537i	0.313766	−	0.543459i
$852$	−3.22166	−	0.338610i	−0.110372	−	0.0116006i
$853$	32.0356	−	10.4090i	1.09688	−	0.356398i	0.295979	−	0.955195i	$-0.404354\pi$
$853$	32.0356	−	10.4090i	1.09688	−	0.356398i	0.800901	+	0.598797i	$0.204354\pi$
$854$	4.61700	+	37.2755i	0.157991	+	1.27554i
$855$	37.0727	−	4.70878i	1.26786	−	0.161037i
$856$	39.5972	−	8.41664i	1.35340	−	0.287675i
$857$	12.4752	+	7.20257i	0.426145	+	0.246035i	0.697703	−	0.716387i	$-0.254205\pi$
$857$	12.4752	+	7.20257i	0.426145	+	0.246035i	−0.271558	+	0.962422i	$0.587539\pi$
$858$	−1.16960	+	1.05311i	−0.0399294	+	0.0359526i
$859$	11.5983	+	5.16390i	0.395729	+	0.176190i	0.594946	−	0.803765i	$-0.297173\pi$
$859$	11.5983	+	5.16390i	0.395729	+	0.176190i	−0.199217	+	0.979955i	$0.563840\pi$
$860$	0.169985	+	1.33831i	0.00579643	+	0.0456359i
$861$	49.7580	+	53.2455i	1.69575	+	1.81460i
$862$	−16.3836	−	22.5501i	−0.558027	−	0.768058i
$863$	13.7498	−	30.8826i	0.468049	−	1.05126i	−0.513157	−	0.858295i	$-0.671524\pi$
$863$	13.7498	−	30.8826i	0.468049	−	1.05126i	0.981206	−	0.192962i	$-0.0618093\pi$
$864$	−10.6863	+	4.75783i	−0.363554	+	0.161865i
$865$	−27.7586	+	6.53047i	−0.943819	+	0.222042i
$866$	−18.1319	−	8.07286i	−0.616148	−	0.274327i
$867$	−73.4944	−	23.8798i	−2.49600	−	0.811000i
$868$	−0.687392	−	0.596261i	−0.0233316	−	0.0202384i
$869$	0.713658	−	2.19641i	0.0242092	−	0.0745082i
$870$	−59.2590	+	20.6810i	−2.00907	+	0.701152i
$871$	−9.68293	−	2.05817i	−0.328094	−	0.0697384i
$872$	−7.51682	+	35.3639i	−0.254552	+	1.19757i
$873$	21.4455	+	2.25401i	0.725820	+	0.0762868i
$874$	31.1309			1.05302
$875$	6.76641	−	28.7961i	0.228746	−	0.973486i
$876$	−7.26659			−0.245515
$877$	−6.76819	−	0.711366i	−0.228546	−	0.0240211i	−0.0104367	−	0.999946i	$-0.503322\pi$
$877$	−6.76819	−	0.711366i	−0.228546	−	0.0240211i	−0.218109	+	0.975924i	$0.569989\pi$
$878$	−3.87197	+	18.2162i	−0.130673	+	0.614767i
$879$	82.3584	+	17.5058i	2.77788	+	0.590457i
$880$	2.83924	−	0.990876i	0.0957108	−	0.0334024i
$881$	−9.86492	+	30.3611i	−0.332358	+	1.02289i	0.635651	+	0.771976i	$0.280732\pi$
$881$	−9.86492	+	30.3611i	−0.332358	+	1.02289i	−0.968009	+	0.250915i	$0.919268\pi$
$882$	56.7101	−	8.09284i	1.90953	−	0.272500i
$883$	28.3455	+	9.21002i	0.953903	+	0.309942i	0.744301	−	0.667845i	$-0.232783\pi$
$883$	28.3455	+	9.21002i	0.953903	+	0.309942i	0.209603	+	0.977787i	$0.432783\pi$
$884$	2.17765	+	0.969551i	0.0732422	+	0.0326095i
$885$	77.6400	−	18.2656i	2.60984	−	0.613990i
$886$	1.13728	−	0.506349i	0.0382076	−	0.0170111i
$887$	−5.42143	+	12.1767i	−0.182034	+	0.408854i	−0.981396	−	0.191995i	$-0.938504\pi$
$887$	−5.42143	+	12.1767i	−0.182034	+	0.408854i	0.799362	+	0.600849i	$0.205171\pi$
$888$	−12.1286	−	16.6935i	−0.407008	−	0.560199i
$889$	−7.23585	+	23.7575i	−0.242683	+	0.796802i
$890$	1.77693	+	13.9900i	0.0595629	+	0.468945i
$891$	−1.06947	−	0.476161i	−0.0358288	−	0.0159520i
$892$	−1.77817	+	1.60107i	−0.0595375	+	0.0536078i
$893$	−20.1316	−	11.6230i	−0.673679	−	0.388948i
$894$	−50.7676	+	10.7910i	−1.69792	+	0.360905i
$895$	−15.6731	+	1.99072i	−0.523896	+	0.0665424i
$896$	−32.1029	−	13.5867i	−1.07248	−	0.453900i
$897$	−21.9341	+	7.12681i	−0.732357	+	0.237957i
$898$	47.8222	+	5.02631i	1.59585	+	0.167730i
$899$	3.65737	−	6.33475i	0.121980	−	0.211276i
$900$	−8.09452	+	0.350200i	−0.269817	+	0.0116733i
$901$	24.2522	+	42.0060i	0.807957	+	1.39942i
$902$	−2.52683	+	3.47788i	−0.0841343	+	0.115801i
$903$	15.2840	−	1.89310i	0.508619	−	0.0629984i
$904$	4.24593	+	13.0676i	0.141217	+	0.434623i
$905$	0.535548	+	24.7689i	0.0178022	+	0.823345i
$906$	4.64055	+	5.15386i	0.154172	+	0.171225i
$907$	−28.4092	−	16.4021i	−0.943312	−	0.544622i	−0.0523151	−	0.998631i	$-0.516660\pi$
$907$	−28.4092	−	16.4021i	−0.943312	−	0.544622i	−0.890997	+	0.454009i	$0.849993\pi$
$908$	−0.101293	−	0.476544i	−0.00336151	−	0.0158147i
$909$	−13.3678	+	9.71226i	−0.443381	+	0.322135i
$910$	10.0136	+	3.98500i	0.331947	+	0.132102i
$911$	−14.0742	−	10.2255i	−0.466300	−	0.338787i	0.329698	−	0.944087i	$-0.393053\pi$
$911$	−14.0742	−	10.2255i	−0.466300	−	0.338787i	−0.795997	+	0.605300i	$0.793053\pi$
$912$	16.4649	−	36.9808i	0.545208	−	1.22456i
$913$	−0.580647	+	0.0610284i	−0.0192166	+	0.00201975i
$914$	−1.95563	+	0.870701i	−0.0646864	+	0.0288002i
$915$	−60.6314	+	1.31096i	−2.00441	+	0.0433390i
$916$	−2.06686	+	1.50166i	−0.0682910	+	0.0496163i
$917$	−16.1589	+	9.73257i	−0.533613	+	0.321398i
$918$			69.5731i			2.29625i
$919$	−0.160887	+	0.0341976i	−0.00530717	+	0.00112807i	−0.210565	−	0.977580i	$-0.567530\pi$
$919$	−0.160887	+	0.0341976i	−0.00530717	+	0.00112807i	0.205257	+	0.978708i	$0.434197\pi$
$920$	38.0667	+	3.17069i	1.25502	+	0.104535i
$921$	−76.9226	−	16.3504i	−2.53469	−	0.538764i
$922$	11.2089	+	10.0925i	0.369145	+	0.332380i
$923$	−2.62822	+	3.61743i	−0.0865088	+	0.119069i
$924$	0.224177	+	0.648820i	0.00737488	+	0.0213446i
$925$	−3.45307	−	13.3739i	−0.113536	−	0.439730i
$926$	9.28952	+	16.0899i	0.305273	+	0.528748i
$927$	−18.8658	−	42.3733i	−0.619634	−	1.39172i
$928$	−2.23781	+	10.5281i	−0.0734597	+	0.345601i
$929$	34.7569	−	38.6015i	1.14034	−	1.26647i	0.181227	−	0.983441i	$-0.441993\pi$
$929$	34.7569	−	38.6015i	1.14034	−	1.26647i	0.959110	−	0.283032i	$-0.0913403\pi$
$930$	8.19850	−	7.70932i	0.268839	−	0.252799i
$931$	−13.9016	+	16.6388i	−0.455605	+	0.545315i
$932$		−	4.93049i		−	0.161503i
$933$	13.1533	+	61.8816i	0.430621	+	2.02591i
$934$	5.60669	+	53.3440i	0.183456	+	1.74547i
$935$	0.365711	−	4.39065i	0.0119600	−	0.143590i
$936$	−1.74634	+	16.6153i	−0.0570808	+	0.543088i
$937$	−34.6594	−	47.7045i	−1.13227	−	1.55844i	−0.783681	−	0.621164i	$-0.786660\pi$
$937$	−34.6594	−	47.7045i	−1.13227	−	1.55844i	−0.348592	−	0.937275i	$-0.613340\pi$
$938$	−18.9405	+	27.1111i	−0.618430	+	0.885207i
$939$	−26.3966	−	19.1782i	−0.861420	−	0.625858i
$940$	4.14038	+	2.87350i	0.135044	+	0.0937233i
$941$	−4.40289	−	41.8907i	−0.143530	−	1.36560i	−0.794855	−	0.606800i	$-0.792453\pi$
$941$	−4.40289	−	41.8907i	−0.143530	−	1.36560i	0.651325	−	0.758799i	$-0.274214\pi$
$942$	40.8863	−	36.8142i	1.33215	−	1.19947i
$943$	−54.5555	+	31.4976i	−1.77657	+	1.02570i
$944$	17.1582	−	52.8075i	0.558452	−	1.71874i
$945$	1.64768	+	41.0337i	0.0535991	+	1.33483i
$946$	0.280735	+	0.864014i	0.00912748	+	0.0280915i
$947$	18.4931	+	16.6513i	0.600945	+	0.541093i	0.912469	−	0.409145i	$-0.134173\pi$
$947$	18.4931	+	16.6513i	0.600945	+	0.541093i	−0.311525	+	0.950238i	$0.600840\pi$
$948$	2.74142	+	6.15732i	0.0890371	+	0.199981i
$949$	−5.01508	+	8.68637i	−0.162796	+	0.281971i
$950$	16.7600	−	16.4569i	0.543766	−	0.533934i
$951$	7.37107			0.239023
$952$	−32.9305	+	30.7736i	−1.06728	+	0.997378i
$953$	−44.6274	+	14.5003i	−1.44562	+	0.469712i	−0.923646	−	0.383247i	$-0.874806\pi$
$953$	−44.6274	+	14.5003i	−1.44562	+	0.469712i	−0.521978	+	0.852959i	$0.674806\pi$
$954$	40.1921	−	44.6379i	1.30127	−	1.44520i
$955$	2.88256	+	0.240097i	0.0932773	+	0.00776936i
$956$	−3.69094	−	4.09920i	−0.119374	−	0.132578i
$957$	−4.77879	+	2.75904i	−0.154476	+	0.0891870i
$958$	−32.1872	−	10.4583i	−1.03992	−	0.337891i
$959$	−37.5138	+	17.5414i	−1.21138	+	0.566442i
$960$	20.1547	−	36.7199i	0.650491	−	1.18513i
$961$	3.10329	−	29.5258i	0.100106	−	0.952445i
$962$	5.00490	−	0.526036i	0.161364	−	0.0169601i
$963$	−84.2672	+	8.85684i	−2.71547	+	0.285408i
$964$	0.265624	−	2.52725i	0.00855519	−	0.0813972i
$965$	1.80003	+	0.342117i	0.0579451	+	0.0110131i
$966$	−6.63387	+	76.7635i	−0.213441	+	2.46982i
$967$	57.5816	+	18.7094i	1.85170	+	0.601654i	0.996523	+	0.0833195i	$0.0265522\pi$
$967$	57.5816	+	18.7094i	1.85170	+	0.601654i	0.855178	+	0.518335i	$0.173448\pi$
$968$	−24.3591	+	14.0637i	−0.782930	+	0.452025i
$969$	−39.6852	−	44.0748i	−1.27487	−	1.41589i
$970$	11.5885	−	7.02895i	0.372085	−	0.225686i
$971$	17.5779	−	19.5222i	0.564100	−	0.626497i	−0.391849	−	0.920030i	$-0.628164\pi$
$971$	17.5779	−	19.5222i	0.564100	−	0.626497i	0.955949	+	0.293533i	$0.0948310\pi$
$972$	−2.69854	+	0.876809i	−0.0865557	+	0.0281237i
$973$	16.6993	+	5.08611i	0.535353	+	0.163053i
$974$	−17.0792			−0.547254
$975$	−8.04118	+	15.4320i	−0.257524	+	0.494220i
$976$	−21.1094	+	36.5625i	−0.675695	+	1.17034i
$977$	−1.72461	−	3.87354i	−0.0551752	−	0.123925i	0.883854	−	0.467763i	$-0.154940\pi$
$977$	−1.72461	−	3.87354i	−0.0551752	−	0.123925i	−0.939029	+	0.343837i	$0.888273\pi$
$978$	−1.83164	−	1.64922i	−0.0585694	−	0.0527362i
$979$	0.383134	+	1.17917i	0.0122450	+	0.0376863i
$980$	3.30294	−	3.34474i	0.105509	−	0.106844i
$981$	23.3842	−	71.9691i	0.746600	−	2.29780i
$982$	−45.7026	+	26.3864i	−1.45843	+	0.842025i
$983$	25.3658	−	22.8395i	0.809045	−	0.728467i	−0.156788	−	0.987632i	$-0.550114\pi$
$983$	25.3658	−	22.8395i	0.809045	−	0.728467i	0.965833	+	0.259165i	$0.0834473\pi$
$984$	7.42220	+	70.6175i	0.236611	+	2.25120i
$985$	40.0535	−	30.4449i	1.27621	−	0.970055i
$986$	51.7901	+	37.6277i	1.64933	+	1.19831i
$987$	32.9502	−	47.1642i	1.04882	−	1.50125i
$988$	0.656726	+	0.903905i	0.0208932	+	0.0287571i
$989$	−1.39155	+	13.2397i	−0.0442488	+	0.420999i
$990$	−5.31107	+	1.24948i	−0.168797	+	0.0397111i
$991$	−0.813413	−	7.73910i	−0.0258389	−	0.245841i	−0.999816	−	0.0191934i	$-0.993890\pi$
$991$	−0.813413	−	7.73910i	−0.0258389	−	0.245841i	0.973977	−	0.226647i	$-0.0727765\pi$
$992$	−0.401248	−	1.88772i	−0.0127396	−	0.0599352i
$993$			10.2366i			0.324848i
$994$	7.70735	+	12.7964i	0.244462	+	0.405877i
$995$	−0.317196	+	1.66891i	−0.0100558	+	0.0529081i
$996$	1.14015	−	1.26627i	0.0361271	−	0.0401232i
$997$	10.2366	−	48.1592i	0.324195	−	1.52522i	−0.450439	−	0.892807i	$-0.648733\pi$
$997$	10.2366	−	48.1592i	0.324195	−	1.52522i	0.774634	−	0.632410i	$-0.217934\pi$
$998$	−23.1173	−	51.9223i	−0.731766	−	1.64357i
$999$	9.58800	+	16.6069i	0.303351	+	0.525419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.t.a.109.5	yes	144
5.2	odd	4		875.2.q.b.326.27		288
5.3	odd	4		875.2.q.b.326.10		288
5.4	even	2		875.2.u.a.424.14		144
7.2	even	3	inner	175.2.t.a.9.14	✓	144
25.2	odd	20		875.2.q.b.676.10		288
25.11	even	5		875.2.u.a.74.5		144
25.14	even	10	inner	175.2.t.a.39.14	yes	144
25.23	odd	20		875.2.q.b.676.27		288
35.2	odd	12		875.2.q.b.576.10		288
35.9	even	6		875.2.u.a.674.5		144
35.23	odd	12		875.2.q.b.576.27		288
175.2	odd	60		875.2.q.b.51.27		288
175.23	odd	60		875.2.q.b.51.10		288
175.86	even	15		875.2.u.a.324.14		144
175.114	even	30	inner	175.2.t.a.114.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.9.14	✓	144	7.2	even	3	inner
175.2.t.a.39.14	yes	144	25.14	even	10	inner
175.2.t.a.109.5	yes	144	1.1	even	1	trivial
175.2.t.a.114.5	yes	144	175.114	even	30	inner
875.2.q.b.51.10		288	175.23	odd	60
875.2.q.b.51.27		288	175.2	odd	60
875.2.q.b.326.10		288	5.3	odd	4
875.2.q.b.326.27		288	5.2	odd	4
875.2.q.b.576.10		288	35.2	odd	12
875.2.q.b.576.27		288	35.23	odd	12
875.2.q.b.676.10		288	25.2	odd	20
875.2.q.b.676.27		288	25.23	odd	20
875.2.u.a.74.5		144	25.11	even	5
875.2.u.a.324.14		144	175.86	even	15
875.2.u.a.424.14		144	5.4	even	2
875.2.u.a.674.5		144	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50837 - 0.158536i) q^{2} +(0.602430 - 2.83421i) q^{3} +(0.293755 + 0.0624396i) q^{4} +(2.11119 - 0.736792i) q^{5} +(-1.35801 + 4.17954i) q^{6} +(2.50069 - 0.864026i) q^{7} +(2.45170 + 0.796607i) q^{8} +(-4.92920 - 2.19462i) q^{9} +(-3.30127 + 0.776656i) q^{10} +(-0.272386 + 0.121274i) q^{11} +(0.353934 - 0.794949i) q^{12} +(-0.705999 - 0.971725i) q^{13} +(-3.90895 + 0.906822i) q^{14} +(-0.816379 - 6.42744i) q^{15} +(-4.12050 - 1.83456i) q^{16} +(-4.91093 + 4.42182i) q^{17} +(7.08713 + 4.09176i) q^{18} +(-3.02972 + 0.643988i) q^{19} +(0.666179 - 0.0846145i) q^{20} +(-0.942341 - 7.60801i) q^{21} +(0.430086 - 0.139743i) q^{22} +(6.59043 + 0.692682i) q^{23} +(3.73473 - 6.46875i) q^{24} +(3.91427 - 3.11102i) q^{25} +(0.910856 + 1.57765i) q^{26} +(-4.08014 + 5.61583i) q^{27} +(0.788540 - 0.0976700i) q^{28} +(1.97373 + 6.07451i) q^{29} +(0.212421 + 9.82438i) q^{30} +(-0.766311 - 0.851074i) q^{31} +(1.45939 + 0.842577i) q^{32} +(0.179623 + 0.845059i) q^{33} +(8.10853 - 5.89119i) q^{34} +(4.64284 - 3.66662i) q^{35} +(-1.31095 - 0.952458i) q^{36} +(1.12361 - 2.52366i) q^{37} +(4.67204 - 0.491052i) q^{38} +(-3.17939 + 1.41556i) q^{39} +(5.76295 - 0.124606i) q^{40} +(-7.69071 + 5.58763i) q^{41} +(0.215255 + 11.6251i) q^{42} +2.00893i q^{43} +(-0.0875871 + 0.0186172i) q^{44} +(-12.0235 - 1.00147i) q^{45} +(-9.83100 - 2.08964i) q^{46} +(5.57728 + 5.02181i) q^{47} +(-7.68185 + 10.5732i) q^{48} +(5.50692 - 4.32133i) q^{49} +(-6.39739 + 4.07202i) q^{50} +(9.57389 + 16.5825i) q^{51} +(-0.146717 - 0.329531i) q^{52} +(1.52605 - 7.17950i) q^{53} +(7.04468 - 7.82391i) q^{54} +(-0.485706 + 0.456725i) q^{55} +(6.81924 - 0.126268i) q^{56} +8.97484i q^{57} +(-2.01408 - 9.47552i) q^{58} +(1.28678 + 12.2429i) q^{59} +(0.161511 - 1.93907i) q^{60} +(0.978410 - 9.30895i) q^{61} +(1.02096 + 1.40522i) q^{62} +(-14.2226 - 1.22911i) q^{63} +(5.23034 + 3.80006i) q^{64} +(-2.20646 - 1.53132i) q^{65} +(-0.136966 - 1.30314i) q^{66} +(6.12477 - 5.51477i) q^{67} +(-1.71871 + 0.992297i) q^{68} +(5.93348 - 18.2614i) q^{69} +(-7.58441 + 4.79456i) q^{70} +(-1.15037 - 3.54049i) q^{71} +(-10.3367 - 9.30719i) q^{72} +(-3.39653 - 7.62873i) q^{73} +(-2.09491 + 3.62849i) q^{74} +(-6.45922 - 12.9681i) q^{75} -0.930207 q^{76} +(-0.576370 + 0.538618i) q^{77} +(5.02012 - 1.63113i) q^{78} +(-5.18279 + 5.75607i) q^{79} +(-10.0509 - 0.837167i) q^{80} +(2.62722 + 2.91782i) q^{81} +(12.4863 - 7.20896i) q^{82} +(1.86230 + 0.605097i) q^{83} +(0.198223 - 2.29373i) q^{84} +(-7.10996 + 12.9537i) q^{85} +(0.318489 - 3.03022i) q^{86} +(18.4055 - 1.93449i) q^{87} +(-0.764418 + 0.0803436i) q^{88} +(0.434658 - 4.13550i) q^{89} +(17.9771 + 3.41675i) q^{90} +(-2.60508 - 1.81998i) q^{91} +(1.89272 + 0.614983i) q^{92} +(-2.87377 + 1.65917i) q^{93} +(-7.61647 - 8.45895i) q^{94} +(-5.92185 + 3.59186i) q^{95} +(3.26722 - 3.62861i) q^{96} +(-3.80086 + 1.23497i) q^{97} +(-8.99156 + 5.64512i) q^{98} +1.60880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22}+ \cdots - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

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