LMFDB - Embedded newform 175.2.x.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.776182 - 0.0406780i) q^{2} +(-0.706831 + 0.872864i) q^{3} +(-1.38824 + 0.145910i) q^{4} +(2.15686 + 0.589873i) q^{5} +(-0.513123 + 0.706254i) q^{6} +(2.33503 + 1.24404i) q^{7} +(-2.60695 + 0.412900i) q^{8} +(0.361454 + 1.70051i) q^{9} +(1.69811 + 0.370112i) q^{10} +(1.29854 + 0.276014i) q^{11} +(0.853891 - 1.31488i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(1.86302 + 0.870614i) q^{14} +(-2.03941 + 1.46571i) q^{15} +(0.724094 - 0.153911i) q^{16} +(0.333224 - 0.868077i) q^{17} +(0.349728 + 1.30520i) q^{18} +(0.550884 - 5.24131i) q^{19} +(-3.08031 - 0.504177i) q^{20} +(-2.73635 + 1.15884i) q^{21} +(1.01913 + 0.161415i) q^{22} +(-0.0599482 - 1.14388i) q^{23} +(1.48227 - 2.56736i) q^{24} +(4.30410 + 2.54455i) q^{25} +(-1.35285 + 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.42310 - 1.38631i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-1.52334 + 1.22061i) q^{30} +(-3.98545 - 8.95147i) q^{31} +(5.65478 - 1.51519i) q^{32} +(-1.15877 + 0.938356i) q^{33} +(0.223331 - 0.687341i) q^{34} +(4.30252 + 4.06058i) q^{35} +(-0.749906 - 2.30797i) q^{36} +(6.42719 + 4.17386i) q^{37} +(0.214381 - 4.09062i) q^{38} +(0.469333 - 2.20804i) q^{39} +(-5.86638 - 0.647200i) q^{40} +(-0.0622653 - 0.0202312i) q^{41} +(-2.07676 + 1.01078i) q^{42} +(-3.34331 + 3.34331i) q^{43} +(-1.84296 - 0.193703i) q^{44} +(-0.223477 + 3.88097i) q^{45} +(-0.0930614 - 0.885420i) q^{46} +(-0.174263 + 0.0668935i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(3.90475 + 5.80972i) q^{49} +(3.44427 + 1.79995i) q^{50} +(0.522180 + 0.904443i) q^{51} +(2.35288 - 1.52798i) q^{52} +(8.68044 + 7.02928i) q^{53} +(-3.77898 - 1.68251i) q^{54} +(2.63796 + 1.36130i) q^{55} +(-6.60097 - 2.27900i) q^{56} +(4.18557 + 4.18557i) q^{57} +(-3.36247 - 4.15230i) q^{58} +(-3.22860 - 3.58572i) q^{59} +(2.61734 - 2.33232i) q^{60} +(-3.39928 - 3.06073i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-1.27148 + 4.42040i) q^{63} +(2.91943 - 0.948580i) q^{64} +(-4.40066 + 0.911685i) q^{65} +(-0.861248 + 0.775472i) q^{66} +(-7.93020 - 3.04412i) q^{67} +(-0.335933 + 1.25372i) q^{68} +(1.04082 + 0.756203i) q^{69} +(3.50472 + 2.97673i) q^{70} +(8.72491 - 6.33902i) q^{71} +(-1.64443 - 4.28389i) q^{72} +(0.896926 + 1.38114i) q^{73} +(5.15845 + 2.97823i) q^{74} +(-5.26331 + 1.95833i) q^{75} +7.35658i q^{76} +(2.68877 + 2.25993i) q^{77} +(0.274469 - 1.73293i) q^{78} +(-4.24463 + 9.53360i) q^{79} +(1.65256 + 0.0951587i) q^{80} +(0.696236 - 0.309984i) q^{81} +(-0.0491522 - 0.0131703i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(3.62962 - 2.00801i) q^{84} +(1.23077 - 1.67576i) q^{85} +(-2.45902 + 2.73102i) q^{86} +(7.71037 + 0.404083i) q^{87} +(-3.49920 - 0.183385i) q^{88} +(10.5019 - 11.6635i) q^{89} +(-0.0155886 + 3.02143i) q^{90} +(-5.31661 - 0.0971966i) q^{91} +(0.250126 + 1.57923i) q^{92} +(10.6304 + 2.84842i) q^{93} +(-0.132539 + 0.0590102i) q^{94} +(4.27989 - 10.9798i) q^{95} +(-2.67442 + 6.00684i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(3.26713 + 4.35057i) q^{98} +2.30795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.776182	−	0.0406780i	0.548844	−	0.0287637i	0.224101	−	0.974566i	$-0.428056\pi$
$2$	0.776182	−	0.0406780i	0.548844	−	0.0287637i	0.324743	+	0.945802i	$0.394722\pi$
$3$	−0.706831	+	0.872864i	−0.408089	+	0.503948i	−0.939208	−	0.343349i	$-0.888439\pi$
$3$	−0.706831	+	0.872864i	−0.408089	+	0.503948i	0.531119	+	0.847297i	$0.321772\pi$
$4$	−1.38824	+	0.145910i	−0.694120	+	0.0729549i
$5$	2.15686	+	0.589873i	0.964578	+	0.263799i
$5$	2.15686	+	0.589873i	0.964578	+	0.263799i
$6$	−0.513123	+	0.706254i	−0.209482	+	0.288327i
$7$	2.33503	+	1.24404i	0.882559	+	0.470201i
$7$	2.33503	+	1.24404i	0.882559	+	0.470201i
$8$	−2.60695	+	0.412900i	−0.921695	+	0.145982i
$9$	0.361454	+	1.70051i	0.120485	+	0.566836i
$10$	1.69811	+	0.370112i	0.536990	+	0.117040i
$11$	1.29854	+	0.276014i	0.391525	+	0.0832213i	0.399468	−	0.916747i	$-0.369195\pi$
$11$	1.29854	+	0.276014i	0.391525	+	0.0832213i	−0.00794259	+	0.999968i	$0.502528\pi$
$12$	0.853891	−	1.31488i	0.246497	−	0.379572i
$13$	−1.79077	+	0.912442i	−0.496670	+	0.253066i	−0.684336	−	0.729167i	$-0.739908\pi$
$13$	−1.79077	+	0.912442i	−0.496670	+	0.253066i	0.187666	+	0.982233i	$0.439908\pi$
$14$	1.86302	+	0.870614i	0.497912	+	0.232681i
$15$	−2.03941	+	1.46571i	−0.526575	+	0.378444i
$16$	0.724094	−	0.153911i	0.181023	−	0.0384777i
$17$	0.333224	−	0.868077i	0.0808186	−	0.210540i	−0.887217	−	0.461352i	$-0.847364\pi$
$17$	0.333224	−	0.868077i	0.0808186	−	0.210540i	0.968036	+	0.250813i	$0.0806978\pi$
$18$	0.349728	+	1.30520i	0.0824316	+	0.307639i
$19$	0.550884	−	5.24131i	0.126382	−	1.20244i	−0.729027	−	0.684485i	$-0.760027\pi$
$19$	0.550884	−	5.24131i	0.126382	−	1.20244i	0.855408	−	0.517954i	$-0.173306\pi$
$20$	−3.08031	−	0.504177i	−0.688778	−	0.112737i
$21$	−2.73635	+	1.15884i	−0.597120	+	0.252880i
$22$	1.01913	+	0.161415i	0.217280	+	0.0344138i
$23$	−0.0599482	−	1.14388i	−0.0125001	−	0.238515i	−0.997733	−	0.0672962i	$-0.978563\pi$
$23$	−0.0599482	−	1.14388i	−0.0125001	−	0.238515i	0.985233	−	0.171219i	$-0.0547706\pi$
$24$	1.48227	−	2.56736i	0.302566	−	0.524060i
$25$	4.30410	+	2.54455i	0.860820	+	0.508909i
$26$	−1.35285	+	0.781066i	−0.265315	+	0.153180i
$27$	−4.74204	−	2.41619i	−0.912607	−	0.464996i
$28$	−3.42310	−	1.38631i	−0.646905	−	0.261989i
$29$	−4.04060	−	5.56140i	−0.750320	−	1.03273i	−0.997958	−	0.0638742i	$-0.979654\pi$
$29$	−4.04060	−	5.56140i	−0.750320	−	1.03273i	0.247638	−	0.968853i	$-0.420346\pi$
$30$	−1.52334	+	1.22061i	−0.278122	+	0.222853i
$31$	−3.98545	−	8.95147i	−0.715808	−	1.60773i	−0.791915	−	0.610631i	$-0.790916\pi$
$31$	−3.98545	−	8.95147i	−0.715808	−	1.60773i	0.0761073	−	0.997100i	$-0.475751\pi$
$32$	5.65478	−	1.51519i	0.999634	−	0.267851i
$33$	−1.15877	+	0.938356i	−0.201716	+	0.163347i
$34$	0.223331	−	0.687341i	0.0383009	−	0.117878i
$35$	4.30252	+	4.06058i	0.727258	+	0.686364i
$36$	−0.749906	−	2.30797i	−0.124984	−	0.384662i
$37$	6.42719	+	4.17386i	1.05662	+	0.686179i	0.951302	−	0.308259i	$-0.0997464\pi$
$37$	6.42719	+	4.17386i	1.05662	+	0.686179i	0.105321	+	0.994438i	$0.466413\pi$
$38$	0.214381	−	4.09062i	0.0347771	−	0.663587i
$39$	0.469333	−	2.20804i	0.0751534	−	0.353569i
$40$	−5.86638	−	0.647200i	−0.927557	−	0.102331i
$41$	−0.0622653	−	0.0202312i	−0.00972421	−	0.00315959i	0.304151	−	0.952624i	$-0.401627\pi$
$41$	−0.0622653	−	0.0202312i	−0.00972421	−	0.00315959i	−0.313875	+	0.949464i	$0.601627\pi$
$42$	−2.07676	+	1.01078i	−0.320452	+	0.155967i
$43$	−3.34331	+	3.34331i	−0.509850	+	0.509850i	−0.914480	−	0.404630i	$-0.867400\pi$
$43$	−3.34331	+	3.34331i	−0.509850	+	0.509850i	0.404630	+	0.914480i	$0.367400\pi$
$44$	−1.84296	−	0.193703i	−0.277837	−	0.0292018i
$45$	−0.223477	+	3.88097i	−0.0333140	+	0.578541i
$46$	−0.0930614	−	0.885420i	−0.0137212	−	0.130548i
$47$	−0.174263	+	0.0668935i	−0.0254189	+	0.00975741i	−0.371044	−	0.928615i	$-0.621000\pi$
$47$	−0.174263	+	0.0668935i	−0.0254189	+	0.00975741i	0.345625	+	0.938373i	$0.387667\pi$
$48$	−0.377469	+	0.740824i	−0.0544829	+	0.106929i
$49$	3.90475	+	5.80972i	0.557822	+	0.829961i
$50$	3.44427	+	1.79995i	0.487094	+	0.254551i
$51$	0.522180	+	0.904443i	0.0731199	+	0.126647i
$52$	2.35288	−	1.52798i	0.326286	−	0.211892i
$53$	8.68044	+	7.02928i	1.19235	+	0.965546i	0.999876	−	0.0157564i	$-0.00501564\pi$
$53$	8.68044	+	7.02928i	1.19235	+	0.965546i	0.192474	+	0.981302i	$0.438349\pi$
$54$	−3.77898	−	1.68251i	−0.514254	−	0.228960i
$55$	2.63796	+	1.36130i	0.355703	+	0.183557i
$56$	−6.60097	−	2.27900i	−0.882092	−	0.304544i
$57$	4.18557	+	4.18557i	0.554392	+	0.554392i
$58$	−3.36247	−	4.15230i	−0.441514	−	0.545224i
$59$	−3.22860	−	3.58572i	−0.420327	−	0.466821i	0.495374	−	0.868680i	$-0.335031\pi$
$59$	−3.22860	−	3.58572i	−0.420327	−	0.466821i	−0.915702	+	0.401859i	$0.868364\pi$
$60$	2.61734	−	2.33232i	0.337897	−	0.301101i
$61$	−3.39928	−	3.06073i	−0.435233	−	0.391886i	0.422182	−	0.906511i	$-0.361264\pi$
$61$	−3.39928	−	3.06073i	−0.435233	−	0.391886i	−0.857415	+	0.514625i	$0.827931\pi$
$62$	−3.45756	−	6.78585i	−0.439111	−	0.861804i
$63$	−1.27148	+	4.42040i	−0.160192	+	0.556919i
$64$	2.91943	−	0.948580i	0.364929	−	0.118573i
$65$	−4.40066	+	0.911685i	−0.545835	+	0.113081i
$66$	−0.861248	+	0.775472i	−0.106012	+	0.0954540i
$67$	−7.93020	−	3.04412i	−0.968829	−	0.371899i	−0.178064	−	0.984019i	$-0.556983\pi$
$67$	−7.93020	−	3.04412i	−0.968829	−	0.371899i	−0.790765	+	0.612120i	$0.790317\pi$
$68$	−0.335933	+	1.25372i	−0.0407379	+	0.152036i
$69$	1.04082	+	0.756203i	0.125300	+	0.0910361i
$70$	3.50472	+	2.97673i	0.418894	+	0.355788i
$71$	8.72491	−	6.33902i	1.03546	−	0.752303i	0.0660625	−	0.997815i	$-0.478956\pi$
$71$	8.72491	−	6.33902i	1.03546	−	0.752303i	0.969393	+	0.245513i	$0.0789563\pi$
$72$	−1.64443	−	4.28389i	−0.193798	−	0.504862i
$73$	0.896926	+	1.38114i	0.104977	+	0.161651i	0.887255	−	0.461279i	$-0.152609\pi$
$73$	0.896926	+	1.38114i	0.104977	+	0.161651i	−0.782278	+	0.622929i	$0.785942\pi$
$74$	5.15845	+	2.97823i	0.599658	+	0.346213i
$75$	−5.26331	+	1.95833i	−0.607755	+	0.226128i
$76$			7.35658i			0.843857i
$77$	2.68877	+	2.25993i	0.306414	+	0.257543i
$78$	0.274469	−	1.73293i	0.0310775	−	0.196216i
$79$	−4.24463	+	9.53360i	−0.477558	+	1.07261i	0.500775	+	0.865577i	$0.333048\pi$
$79$	−4.24463	+	9.53360i	−0.477558	+	1.07261i	−0.978333	+	0.207036i	$0.933618\pi$
$80$	1.65256	+	0.0951587i	0.184762	+	0.0106391i
$81$	0.696236	−	0.309984i	0.0773596	−	0.0344427i
$82$	−0.0491522	−	0.0131703i	−0.00542796	−	0.00145442i
$83$	−0.978599	−	6.17863i	−0.107415	−	0.678193i	−0.981362	−	0.192170i	$-0.938447\pi$
$83$	−0.978599	−	6.17863i	−0.107415	−	0.678193i	0.873946	−	0.486022i	$-0.161553\pi$
$84$	3.62962	−	2.00801i	0.396024	−	0.219092i
$85$	1.23077	−	1.67576i	0.133496	−	0.181762i
$86$	−2.45902	+	2.73102i	−0.265163	+	0.294493i
$87$	7.71037	+	0.404083i	0.826638	+	0.0433223i
$88$	−3.49920	−	0.183385i	−0.373016	−	0.0195489i
$89$	10.5019	−	11.6635i	1.11320	−	1.23633i	0.144125	−	0.989559i	$-0.453963\pi$
$89$	10.5019	−	11.6635i	1.11320	−	1.23633i	0.969073	−	0.246773i	$-0.0793701\pi$
$90$	−0.0155886	+	3.02143i	−0.00164319	+	0.318487i
$91$	−5.31661	−	0.0971966i	−0.557332	−	0.0101890i
$92$	0.250126	+	1.57923i	0.0260774	+	0.164646i
$93$	10.6304	+	2.84842i	1.10233	+	0.295367i
$94$	−0.132539	+	0.0590102i	−0.0136704	+	0.00608644i
$95$	4.27989	−	10.9798i	0.439107	−	1.12651i
$96$	−2.67442	+	6.00684i	−0.272957	+	0.613071i
$97$	−2.72136	+	17.1820i	−0.276312	+	1.74457i	0.325149	+	0.945663i	$0.394586\pi$
$97$	−2.72136	+	17.1820i	−0.276312	+	1.74457i	−0.601461	+	0.798902i	$0.705414\pi$
$98$	3.26713	+	4.35057i	0.330030	+	0.439474i
$99$			2.30795i			0.231958i
$100$	−6.34640	−	2.90443i	−0.634640	−	0.290443i
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	0.339418	−	0.940636i	$-0.389770\pi$
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	−0.644905	+	0.764262i	$0.723103\pi$
$102$	0.442098	+	0.680771i	0.0437742	+	0.0674064i
$103$	2.28092	+	5.94199i	0.224745	+	0.585482i	0.998869	−	0.0475531i	$-0.0151423\pi$
$103$	2.28092	+	5.94199i	0.224745	+	0.585482i	−0.774123	+	0.633035i	$0.781809\pi$
$104$	4.29169	−	3.11810i	0.420835	−	0.305755i
$105$	−6.58549	+	0.885366i	−0.642678	+	0.0864029i
$106$	7.02354	+	5.10290i	0.682186	+	0.495637i
$107$	2.55108	−	9.52075i	0.246622	−	0.920406i	−0.725939	−	0.687759i	$-0.758595\pi$
$107$	2.55108	−	9.52075i	0.246622	−	0.920406i	0.972561	−	0.232647i	$-0.0747386\pi$
$108$	6.93564	+	2.66234i	0.667382	+	0.256184i
$109$	−8.04882	+	7.24719i	−0.770937	+	0.694155i	−0.957546	−	0.288279i	$-0.906917\pi$
$109$	−8.04882	+	7.24719i	−0.770937	+	0.694155i	0.186609	+	0.982434i	$0.440250\pi$
$110$	2.10292	+	0.949309i	0.200505	+	0.0905130i
$111$	−8.18615	+	2.65984i	−0.776995	+	0.252461i
$112$	1.88225	+	0.541411i	0.177856	+	0.0511586i
$113$	−3.00115	−	5.89008i	−0.282324	−	0.554092i	0.705678	−	0.708533i	$-0.250643\pi$
$113$	−3.00115	−	5.89008i	−0.282324	−	0.554092i	−0.988002	+	0.154440i	$0.950643\pi$
$114$	3.41903	+	3.07851i	0.320221	+	0.288328i
$115$	0.545443	−	2.50255i	0.0508628	−	0.233364i
$116$	6.42078	+	7.13100i	0.596154	+	0.662096i
$117$	−2.19890	−	2.71541i	−0.203288	−	0.251040i
$118$	−2.65184	−	2.65184i	−0.244122	−	0.244122i
$119$	1.85801	−	1.61245i	0.170323	−	0.147813i
$120$	4.71146	−	4.66309i	0.430095	−	0.425680i
$121$	−8.43897	−	3.75727i	−0.767179	−	0.341570i
$122$	−2.76297	−	2.23741i	−0.250147	−	0.202565i
$123$	0.0616702	−	0.0400491i	0.00556061	−	0.00361110i
$124$	6.83886	+	11.8453i	0.614148	+	1.06374i
$125$	7.78239	+	8.02711i	0.696078	+	0.717966i
$126$	−0.807091	+	3.48276i	−0.0719014	+	0.310269i
$127$	−8.39463	+	16.4754i	−0.744903	+	1.46195i	0.137023	+	0.990568i	$0.456246\pi$
$127$	−8.39463	+	16.4754i	−0.744903	+	1.46195i	−0.881927	+	0.471387i	$0.843754\pi$
$128$	−8.70343	+	3.34093i	−0.769281	+	0.295299i
$129$	−0.555099	−	5.28141i	−0.0488737	−	0.465003i
$130$	−3.37863	+	0.886644i	−0.296325	+	0.0777638i
$131$	16.6657	+	1.75164i	1.45609	+	0.153041i	0.799255	−	0.600992i	$-0.205228\pi$
$131$	16.6657	+	1.75164i	1.45609	+	0.153041i	0.656836	+	0.754033i	$0.271894\pi$
$132$	1.47174	−	1.47174i	0.128098	−	0.128098i
$133$	7.80671	−	11.5533i	0.676928	−	1.00180i
$134$	−6.27911	−	2.04021i	−0.542433	−	0.176247i
$135$	−8.80268	−	8.00859i	−0.757614	−	0.689270i
$136$	−0.510268	+	2.40062i	−0.0437551	+	0.205852i
$137$	−0.172842	+	3.29801i	−0.0147669	+	0.281768i	0.981258	+	0.192697i	$0.0617234\pi$
$137$	−0.172842	+	3.29801i	−0.0147669	+	0.281768i	−0.996025	+	0.0890717i	$0.971610\pi$
$138$	0.838630	+	0.544613i	0.0713889	+	0.0463605i
$139$	−2.66592	−	8.20486i	−0.226120	−	0.695927i	−0.998176	−	0.0603721i	$-0.980771\pi$
$139$	−2.66592	−	8.20486i	−0.226120	−	0.695927i	0.772055	−	0.635555i	$-0.219229\pi$
$140$	−6.56540	−	5.00928i	−0.554878	−	0.423362i
$141$	0.0647859	−	0.199391i	0.00545596	−	0.0167917i
$142$	6.51426	−	5.27514i	0.546665	−	0.442680i
$143$	−2.57723	+	0.690568i	−0.215519	+	0.0577482i
$144$	0.523454	+	1.17570i	0.0436211	+	0.0979747i
$145$	−5.43449	−	14.3786i	−0.451309	−	1.19408i
$146$	0.752360	+	1.03553i	0.0622658	+	0.0857015i
$147$	−7.83110	−	0.698176i	−0.645898	−	0.0575846i
$148$	−9.53148	−	4.85653i	−0.783483	−	0.399205i
$149$	−0.0342344	+	0.0197652i	−0.00280459	+	0.00161923i	−0.501402	−	0.865215i	$-0.667182\pi$
$149$	−0.0342344	+	0.0197652i	−0.00280459	+	0.00161923i	0.498597	+	0.866834i	$0.333849\pi$
$150$	−4.00563	+	1.73412i	−0.327058	+	0.141590i
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	−0.595037	−	0.803698i	$-0.702863\pi$
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	0.993542	+	0.113468i	$0.0361960\pi$
$152$	0.728012	+	13.8913i	0.0590496	+	1.12673i
$153$	1.59662	+	0.252879i	0.129079	+	0.0204441i
$154$	2.17890	+	1.64475i	0.175581	+	0.132537i
$155$	−3.31584	−	21.6580i	−0.266334	−	1.73961i
$156$	−0.329372	+	3.13377i	−0.0263709	+	0.250902i
$157$	−3.40702	−	12.7152i	−0.271910	−	1.01478i	−0.957884	−	0.287156i	$-0.907290\pi$
$157$	−3.40702	−	12.7152i	−0.271910	−	1.01478i	0.685974	−	0.727626i	$-0.259376\pi$
$158$	−2.90680	+	7.57247i	−0.231253	+	0.602434i
$159$	−12.2712	+	2.60832i	−0.973170	+	0.206854i
$160$	13.0904	+	0.0675377i	1.03488	+	0.00533933i
$161$	1.28304	−	2.74557i	0.101118	−	0.216381i
$162$	0.527797	−	0.268926i	0.0414676	−	0.0211288i
$163$	1.90187	−	2.92862i	0.148966	−	0.229387i	−0.756308	−	0.654216i	$-0.772999\pi$
$163$	1.90187	−	2.92862i	0.148966	−	0.229387i	0.905274	+	0.424828i	$0.139666\pi$
$164$	0.0893911	+	0.0190007i	0.00698027	+	0.00148370i
$165$	−3.05282	+	1.34037i	−0.237662	+	0.104348i
$166$	−1.01091	−	4.75594i	−0.0784615	−	0.369132i
$167$	−18.9176	+	2.99626i	−1.46389	+	0.231857i	−0.836979	−	0.547235i	$-0.815681\pi$
$167$	−18.9176	+	2.99626i	−1.46389	+	0.231857i	−0.626910	+	0.779092i	$0.715681\pi$
$168$	6.65503	−	4.15088i	0.513447	−	0.320247i
$169$	−5.26691	+	7.24928i	−0.405147	+	0.557637i
$170$	0.887137	−	1.35076i	0.0680403	−	0.103599i
$171$	9.11202	−	0.957712i	0.696813	−	0.0732380i
$172$	4.15350	−	5.12914i	0.316701	−	0.391093i
$173$	−4.95159	+	0.259502i	−0.376462	+	0.0197296i	−0.239629	−	0.970865i	$-0.577026\pi$
$173$	−4.95159	+	0.259502i	−0.376462	+	0.0197296i	−0.136833	+	0.990594i	$0.543692\pi$
$174$	6.00109			0.454941
$175$	6.88471	+	11.2961i	0.520435	+	0.853901i
$176$	0.982748			0.0740774
$177$	5.41192	−	0.283626i	0.406785	−	0.0213187i
$178$	7.67694	−	9.48023i	0.575411	−	0.710573i
$179$	−20.1419	+	2.11700i	−1.50548	+	0.158232i	−0.821052	−	0.570853i	$-0.806613\pi$
$179$	−20.1419	+	2.11700i	−1.50548	+	0.158232i	−0.684424	+	0.729085i	$0.739946\pi$
$180$	−0.256033	−	5.42033i	−0.0190835	−	0.404007i
$181$	2.67679	−	3.68429i	0.198965	−	0.273851i	−0.697863	−	0.716231i	$-0.745866\pi$
$181$	2.67679	−	3.68429i	0.198965	−	0.273851i	0.896828	+	0.442380i	$0.145866\pi$
$182$	−4.13061	+	0.140827i	−0.306181	+	0.0104388i
$183$	5.07431	−	0.803693i	0.375104	−	0.0594107i
$184$	0.628589	+	2.95728i	0.0463402	+	0.218014i
$185$	11.4005	+	12.7937i	0.838182	+	0.940609i
$186$	8.36704	+	1.77847i	0.613501	+	0.130404i
$187$	0.672306	−	1.03526i	0.0491639	−	0.0757058i
$188$	0.232159	−	0.118291i	0.0169319	−	0.00862725i
$189$	−8.06700	−	11.5412i	−0.586788	−	0.839495i
$190$	2.87534	−	8.69645i	0.208599	−	0.630907i
$191$	15.1405	−	3.21821i	1.09553	−	0.232861i	0.375510	−	0.926818i	$-0.377468\pi$
$191$	15.1405	−	3.21821i	1.09553	−	0.232861i	0.720016	+	0.693957i	$0.244134\pi$
$192$	−1.23556	+	3.21875i	−0.0891690	+	0.232293i
$193$	−2.02940	−	7.57383i	−0.146080	−	0.545176i	−0.999705	−	0.0242890i	$-0.992268\pi$
$193$	−2.02940	−	7.57383i	−0.146080	−	0.545176i	0.853625	−	0.520887i	$-0.174399\pi$
$194$	−1.41334	+	13.4470i	−0.101472	+	0.965442i
$195$	2.31475	−	4.48558i	0.165763	−	0.321219i
$196$	−6.26843	−	7.49555i	−0.447745	−	0.535396i
$197$	−16.1577	−	2.55912i	−1.15119	−	0.182330i	−0.448469	−	0.893799i	$-0.648030\pi$
$197$	−16.1577	−	2.55912i	−1.15119	−	0.182330i	−0.702718	+	0.711469i	$0.748030\pi$
$198$	0.0938827	+	1.79139i	0.00667196	+	0.127308i
$199$	−13.6561	+	23.6530i	−0.968053	+	1.67672i	−0.266874	+	0.963731i	$0.585991\pi$
$199$	−13.6561	+	23.6530i	−0.968053	+	1.67672i	−0.701179	+	0.712985i	$0.747343\pi$
$200$	−12.2712	−	4.85634i	−0.867706	−	0.343395i
$201$	8.26242	−	4.77031i	0.582786	−	0.336472i
$202$	−2.45507	−	1.25092i	−0.172738	−	0.0880144i
$203$	−2.51634	−	18.0127i	−0.176613	−	1.26424i
$204$	−0.856878	−	1.17939i	−0.0599935	−	0.0825739i
$205$	−0.122364	−	0.0803646i	−0.00854626	−	0.00561291i
$206$	2.01212	+	4.51928i	0.140191	+	0.314873i
$207$	1.92351	−	0.515402i	0.133693	−	0.0358229i
$208$	−1.15625	+	0.936312i	−0.0801715	+	0.0649216i
$209$	2.16202	−	6.65402i	0.149550	−	0.460268i
$210$	−5.07553	+	0.955090i	−0.350245	+	0.0659075i
$211$	4.53761	+	13.9653i	0.312382	+	0.961413i	0.976819	+	0.214068i	$0.0686715\pi$
$211$	4.53761	+	13.9653i	0.312382	+	0.961413i	−0.664437	+	0.747345i	$0.731328\pi$
$212$	−13.0762	−	8.49176i	−0.898075	−	0.583216i
$213$	−0.633938	+	12.0963i	−0.0434367	+	0.828823i
$214$	1.59282	−	7.49361i	0.108883	−	0.512253i
$215$	−9.18319	+	5.23893i	−0.626288	+	0.357292i
$216$	13.3599	+	4.34090i	0.909027	+	0.295361i
$217$	1.82978	−	25.8600i	0.124214	−	1.75549i
$218$	−5.95255	+	5.95255i	−0.403158	+	0.403158i
$219$	−1.83953	−	0.193342i	−0.124304	−	0.0130648i
$220$	−3.86075	−	1.50490i	−0.260292	−	0.101461i
$221$	0.195344	+	1.85857i	0.0131402	+	0.125021i
$222$	−6.24575	+	2.39752i	−0.419187	+	0.160911i
$223$	9.81559	−	19.2642i	0.657301	−	1.29003i	−0.286046	−	0.958216i	$-0.592341\pi$
$223$	9.81559	−	19.2642i	0.657301	−	1.29003i	0.943346	−	0.331809i	$-0.107659\pi$
$224$	15.0891	+	3.49672i	1.00818	+	0.233634i
$225$	−2.77129	+	8.23890i	−0.184753	+	0.549260i
$226$	−2.56903	−	4.44970i	−0.170890	−	0.295989i
$227$	−7.88440	+	5.12019i	−0.523306	+	0.339839i	−0.779107	−	0.626891i	$-0.784327\pi$
$227$	−7.88440	+	5.12019i	−0.523306	+	0.339839i	0.255801	+	0.966729i	$0.417661\pi$
$228$	−6.42129	−	5.19986i	−0.425260	−	0.344369i
$229$	−2.84380	−	1.26614i	−0.187923	−	0.0836689i	0.310618	−	0.950535i	$-0.399464\pi$
$229$	−2.84380	−	1.26614i	−0.187923	−	0.0836689i	−0.498541	+	0.866866i	$0.666131\pi$
$230$	0.321565	−	1.96462i	0.0212033	−	0.129543i
$231$	−3.87312	+	0.749537i	−0.254833	+	0.0493159i
$232$	12.8299	+	12.8299i	0.842326	+	0.842326i
$233$	18.3487	+	22.6587i	1.20206	+	1.48442i	0.831420	+	0.555644i	$0.187528\pi$
$233$	18.3487	+	22.6587i	1.20206	+	1.48442i	0.370640	+	0.928777i	$0.379138\pi$
$234$	−1.81720	−	2.01821i	−0.118794	−	0.131934i
$235$	−0.415321	+	0.0414867i	−0.0270925	+	0.00270629i
$236$	5.00526	+	4.50675i	0.325814	+	0.293365i
$237$	−5.32129	−	10.4436i	−0.345655	−	0.678386i
$238$	1.37656	−	1.32713i	0.0892292	−	0.0860252i
$239$	3.05660	−	0.993150i	0.197715	−	0.0642416i	−0.208485	−	0.978025i	$-0.566853\pi$
$239$	3.05660	−	0.993150i	0.197715	−	0.0642416i	0.406201	+	0.913784i	$0.366853\pi$
$240$	−1.25114	+	1.37520i	−0.0807607	+	0.0887686i
$241$	−19.9300	+	17.9451i	−1.28381	+	1.15594i	−0.304733	+	0.952438i	$0.598567\pi$
$241$	−19.9300	+	17.9451i	−1.28381	+	1.15594i	−0.979074	+	0.203506i	$0.934766\pi$
$242$	−6.70302	−	2.57305i	−0.430886	−	0.165402i
$243$	3.91085	−	14.5955i	0.250881	−	0.936301i
$244$	5.16561	+	3.75303i	0.330694	+	0.240263i
$245$	4.99501	+	14.8341i	0.319120	+	0.947714i
$246$	0.0462382	−	0.0335940i	0.00294804	−	0.00214188i
$247$	3.79589	+	9.88862i	0.241527	+	0.629198i
$248$	14.0859	+	21.6904i	0.894457	+	1.37734i
$249$	6.08480	+	3.51306i	0.385609	+	0.222631i
$250$	6.36708	+	5.91393i	0.402689	+	0.374030i
$251$			13.7541i			0.868150i	0.900877	+	0.434075i	$0.142925\pi$
$251$			13.7541i			0.868150i	−0.900877	+	0.434075i	$0.857075\pi$
$252$	1.12014	−	6.32210i	0.0705625	−	0.398255i
$253$	0.237881	−	1.50192i	0.0149555	−	0.0944250i
$254$	−5.84558	+	13.1294i	−0.366784	+	0.823811i
$255$	0.592764	+	2.25878i	0.0371203	+	0.141450i
$256$	−12.2281	+	5.44431i	−0.764257	+	0.340269i
$257$	8.92621	+	2.39177i	0.556802	+	0.149195i	0.526237	−	0.850338i	$-0.323603\pi$
$257$	8.92621	+	2.39177i	0.556802	+	0.149195i	0.0305651	+	0.999533i	$0.490269\pi$
$258$	−0.645695	−	4.07676i	−0.0401992	−	0.253808i
$259$	9.81526	+	17.7418i	0.609890	+	1.10242i
$260$	5.97615	−	1.90774i	0.370625	−	0.118313i
$261$	7.99672	−	8.88126i	0.494985	−	0.549736i
$262$	13.0069	+	0.681663i	0.803569	+	0.0421133i
$263$	8.38032	+	0.439194i	0.516752	+	0.0270819i	0.308930	−	0.951085i	$-0.400029\pi$
$263$	8.38032	+	0.439194i	0.516752	+	0.0270819i	0.207822	+	0.978167i	$0.433362\pi$
$264$	2.63341	−	2.92470i	0.162075	−	0.180003i
$265$	14.5761	+	20.2815i	0.895404	+	1.24588i
$266$	5.58947	−	9.28504i	0.342712	−	0.569303i
$267$	2.75761	+	17.4109i	0.168763	+	1.06553i
$268$	11.4532	+	3.06887i	0.699615	+	0.187461i
$269$	4.02317	−	1.79123i	0.245297	−	0.109213i	−0.280406	−	0.959882i	$-0.590469\pi$
$269$	4.02317	−	1.79123i	0.245297	−	0.109213i	0.525703	+	0.850668i	$0.323802\pi$
$270$	−7.15826	−	5.85805i	−0.435638	−	0.356510i
$271$	−1.39604	+	3.13556i	−0.0848035	+	0.190472i	−0.950970	−	0.309285i	$-0.899910\pi$
$271$	−1.39604	+	3.13556i	−0.0848035	+	0.190472i	0.866166	+	0.499756i	$0.166577\pi$
$272$	0.107679	−	0.679856i	0.00652898	−	0.0412223i
$273$	3.84278	−	4.57197i	0.232576	−	0.276708i
$274$			2.56689i			0.155072i
$275$	4.88673	+	4.49219i	0.294681	+	0.270889i
$276$	−1.55525	−	0.897924i	−0.0936150	−	0.0540487i
$277$	4.19321	+	6.45697i	0.251945	+	0.387962i	0.941901	−	0.335889i	$-0.109037\pi$
$277$	4.19321	+	6.45697i	0.251945	+	0.387962i	−0.689956	+	0.723851i	$0.742370\pi$
$278$	−2.40300	−	6.26003i	−0.144122	−	0.375451i
$279$	13.7815	−	10.0128i	0.825076	−	0.599453i
$280$	−12.8931	−	8.80922i	−0.770508	−	0.526452i
$281$	19.6291	+	14.2614i	1.17097	+	0.850761i	0.991125	−	0.132934i	$-0.0424398\pi$
$281$	19.6291	+	14.2614i	1.17097	+	0.850761i	0.179847	+	0.983695i	$0.442440\pi$
$282$	0.0421749	−	0.157399i	0.00251148	−	0.00937296i
$283$	−6.76781	−	2.59792i	−0.402304	−	0.154430i	0.148798	−	0.988868i	$-0.452459\pi$
$283$	−6.76781	−	2.59792i	−0.402304	−	0.154430i	−0.551103	+	0.834437i	$0.685793\pi$
$284$	−11.1873	+	10.0731i	−0.663846	+	0.597730i
$285$	6.55874	+	11.4966i	0.388506	+	0.681003i
$286$	−1.97231	+	0.640843i	−0.116625	+	0.0378939i
$287$	−0.120223	−	0.124701i	−0.00709655	−	0.00736086i
$288$	4.62055	+	9.06833i	0.272268	+	0.534357i
$289$	11.9909	+	10.7967i	0.705350	+	0.635100i
$290$	−4.80305	−	10.9394i	−0.282045	−	0.642382i
$291$	−13.0740	−	14.5201i	−0.766410	−	0.851185i
$292$	−1.44667	−	1.78649i	−0.0846599	−	0.104546i
$293$	−22.0206	−	22.0206i	−1.28645	−	1.28645i	−0.936925	−	0.349529i	$-0.886342\pi$
$293$	−22.0206	−	22.0206i	−1.28645	−	1.28645i	−0.349529	−	0.936925i	$-0.613658\pi$
$294$	−6.10676	−	0.223359i	−0.356154	−	0.0130265i
$295$	−4.84852	−	9.63836i	−0.282291	−	0.561167i
$296$	−18.4787	−	8.22726i	−1.07405	−	0.478200i
$297$	−5.49084	−	4.44640i	−0.318611	−	0.258006i
$298$	−0.0257681	+	0.0167340i	−0.00149271	+	0.000969375i
$299$	1.15108	+	1.99372i	0.0665684	+	0.115300i
$300$	7.02100	−	3.48660i	0.405358	−	0.201299i
$301$	−11.9659	+	3.64755i	−0.689705	+	0.210241i
$302$	3.45587	−	6.78253i	0.198863	−	0.390291i
$303$	3.71722	−	1.42691i	0.213549	−	0.0819738i
$304$	−0.407803	−	3.87999i	−0.0233891	−	0.222533i
$305$	−5.52634	−	8.60671i	−0.316437	−	0.492819i
$306$	1.24955	+	0.131333i	0.0714322	+	0.00750783i
$307$	−2.33566	+	2.33566i	−0.133303	+	0.133303i	−0.770610	−	0.637307i	$-0.780048\pi$
$307$	−2.33566	+	2.33566i	−0.133303	+	0.133303i	0.637307	+	0.770610i	$0.280048\pi$
$308$	−4.06240	−	2.74501i	−0.231477	−	0.156412i
$309$	−6.79877	−	2.20905i	−0.386768	−	0.125669i
$310$	−3.45470	−	16.6757i	−0.196214	−	0.947114i
$311$	1.28441	−	6.04267i	0.0728321	−	0.342648i	−0.926611	−	0.376022i	$-0.877292\pi$
$311$	1.28441	−	6.04267i	0.0728321	−	0.342648i	0.999443	+	0.0333736i	$0.0106251\pi$
$312$	−0.311828	+	5.95003i	−0.0176538	+	0.336854i
$313$	9.39345	+	6.10018i	0.530949	+	0.344802i	0.782107	−	0.623144i	$-0.214145\pi$
$313$	9.39345	+	6.10018i	0.530949	+	0.344802i	−0.251158	+	0.967946i	$0.580811\pi$
$314$	−3.16170	−	9.73071i	−0.178425	−	0.549136i
$315$	−5.34989	+	8.78418i	−0.301432	+	0.494933i
$316$	4.50152	−	13.8542i	0.253230	−	0.779362i
$317$	6.98886	−	5.65947i	0.392534	−	0.317867i	−0.412654	−	0.910888i	$-0.635398\pi$
$317$	6.98886	−	5.65947i	0.392534	−	0.317867i	0.805187	+	0.593021i	$0.202065\pi$
$318$	−9.41859	+	2.52370i	−0.528168	+	0.141522i
$319$	−3.71186	−	8.33698i	−0.207824	−	0.466781i
$320$	6.85635	−	0.323864i	0.383281	−	0.0181045i
$321$	6.50714	+	8.95630i	0.363193	+	0.499892i
$322$	0.884192	−	2.18326i	0.0492741	−	0.121668i
$323$	−4.36630	−	2.22474i	−0.242947	−	0.123788i
$324$	−0.921313	+	0.531920i	−0.0511840	+	0.0295511i
$325$	−10.0294	−	0.629452i	−0.556331	−	0.0349157i
$326$	1.35707	−	2.35051i	0.0751610	−	0.130183i
$327$	−0.636653	−	12.1481i	−0.0352070	−	0.671790i
$328$	0.170676	+	0.0270324i	0.00942401	+	0.00149262i
$329$	−0.490129	−	0.0605914i	−0.0270217	−	0.00334051i
$330$	−2.31502	+	1.16456i	−0.127438	+	0.0641068i
$331$	0.755353	−	7.18671i	0.0415180	−	0.395017i	−0.953953	−	0.299955i	$-0.903028\pi$
$331$	0.755353	−	7.18671i	0.0415180	−	0.395017i	0.995471	−	0.0950622i	$-0.0303050\pi$
$332$	2.26005	+	8.43463i	0.124036	+	0.462910i
$333$	−4.77456	+	12.4381i	−0.261644	+	0.681606i
$334$	−14.5616	+	3.09517i	−0.796777	+	0.169360i
$335$	−15.3087	−	11.2436i	−0.836404	−	0.614301i
$336$	−1.80301	+	1.26026i	−0.0983624	+	0.0687531i
$337$	9.03950	−	4.60585i	0.492413	−	0.250897i	−0.190108	−	0.981763i	$-0.560884\pi$
$337$	9.03950	−	4.60585i	0.492413	−	0.250897i	0.682521	+	0.730866i	$0.260884\pi$
$338$	−3.79320	+	5.84101i	−0.206323	+	0.317709i
$339$	7.26254	+	1.54370i	0.394447	+	0.0838423i
$340$	−1.46410	+	2.50594i	−0.0794018	+	0.135904i
$341$	−2.70455	−	12.7239i	−0.146459	−	0.689038i
$342$	7.03363	−	1.11402i	0.380335	−	0.0602392i
$343$	1.89023	+	18.4235i	0.102063	+	0.994778i
$344$	7.33539	−	10.0963i	0.395498	−	0.544356i
$345$	1.79885	+	2.24498i	0.0968468	+	0.120866i
$346$	−3.83278	+	0.402841i	−0.206051	+	0.0216569i
$347$	−5.04462	+	6.22958i	−0.270809	+	0.334422i	−0.894349	−	0.447370i	$-0.852361\pi$
$347$	−5.04462	+	6.22958i	−0.270809	+	0.334422i	0.623540	+	0.781792i	$0.285694\pi$
$348$	−10.7628	+	0.564054i	−0.576946	+	0.0302365i
$349$	8.82065			0.472158			0.236079	−	0.971734i	$-0.424138\pi$
$349$	8.82065			0.472158			0.236079	+	0.971734i	$0.424138\pi$
$350$	5.80329	+	8.48774i	0.310199	+	0.453689i
$351$	10.6965			0.570939
$352$	7.76119	−	0.406747i	0.413673	−	0.0216797i
$353$	−10.5951	+	13.0839i	−0.563923	+	0.696387i	−0.976740	−	0.214427i	$-0.931211\pi$
$353$	−10.5951	+	13.0839i	−0.563923	+	0.696387i	0.412817	+	0.910814i	$0.364545\pi$
$354$	4.18910	−	0.440292i	0.222648	−	0.0234012i
$355$	22.5576	−	8.52579i	1.19723	−	0.452502i
$356$	−12.8773	+	17.7241i	−0.682497	+	0.939376i
$357$	0.0941494	+	2.76151i	0.00498292	+	0.146155i
$358$	−15.5477	+	2.46251i	−0.821720	+	0.130148i
$359$	−2.87394	−	13.5208i	−0.151681	−	0.713602i	−0.986590	−	0.163215i	$-0.947813\pi$
$359$	−2.87394	−	13.5208i	−0.151681	−	0.713602i	0.834910	−	0.550387i	$-0.185520\pi$
$360$	−1.01986	−	10.2098i	−0.0537514	−	0.538102i
$361$	−8.58309	−	1.82439i	−0.451742	−	0.0960206i
$362$	1.92781	−	2.96857i	0.101323	−	0.156024i
$363$	9.24451	−	4.71031i	0.485211	−	0.247227i
$364$	7.39491	−	0.640814i	0.387599	−	0.0335878i
$365$	1.11984	+	3.50801i	0.0586153	+	0.183618i
$366$	3.90590	−	0.830225i	0.204165	−	0.0433966i
$367$	−0.372403	+	0.970143i	−0.0194393	+	0.0506410i	−0.942957	−	0.332916i	$-0.891968\pi$
$367$	−0.372403	+	0.970143i	−0.0194393	+	0.0506410i	0.923517	+	0.383557i	$0.125301\pi$
$368$	−0.219464	−	0.819049i	−0.0114403	−	0.0426959i
$369$	0.0118973	−	0.113195i	0.000619350	−	0.00589272i
$370$	9.36929	+	9.46647i	0.487086	+	0.492138i
$371$	11.5244	+	27.2124i	0.598319	+	1.41280i
$372$	−15.1732	−	2.40320i	−0.786695	−	0.124600i
$373$	−1.15167	−	21.9752i	−0.0596314	−	1.13783i	−0.850544	−	0.525904i	$-0.823727\pi$
$373$	−1.15167	−	21.9752i	−0.0596314	−	1.13783i	0.790912	−	0.611930i	$-0.209606\pi$
$374$	0.479720	−	0.830899i	0.0248057	−	0.0429648i
$375$	−12.5074	+	1.11916i	−0.645880	+	0.0577930i
$376$	0.426675	−	0.246341i	0.0220041	−	0.0127041i
$377$	12.3102	+	6.27237i	0.634009	+	0.323044i
$378$	−6.73093	−	8.62989i	−0.346202	−	0.443874i
$379$	−17.8299	−	24.5408i	−0.915862	−	1.26058i	−0.965125	−	0.261790i	$-0.915687\pi$
$379$	−17.8299	−	24.5408i	−0.915862	−	1.26058i	0.0492625	−	0.998786i	$-0.484313\pi$
$380$	−4.33944	+	15.8671i	−0.222609	+	0.813966i
$381$	−8.44719	−	18.9727i	−0.432762	−	0.972000i
$382$	11.6209	−	3.11380i	0.594575	−	0.159316i
$383$	−16.6188	+	13.4576i	−0.849179	+	0.687652i	−0.951683	−	0.307081i	$-0.900648\pi$
$383$	−16.6188	+	13.4576i	−0.849179	+	0.687652i	0.102504	+	0.994733i	$0.467315\pi$
$384$	3.23567	−	9.95838i	0.165120	−	0.508186i
$385$	4.46623	+	6.46039i	0.227620	+	0.329252i
$386$	−1.88327	−	5.79612i	−0.0958562	−	0.295015i
$387$	−6.89379	−	4.47688i	−0.350431	−	0.227572i
$388$	1.27088	−	24.2498i	0.0645190	−	1.23110i
$389$	4.37542	−	20.5847i	0.221842	−	1.04369i	−0.716395	−	0.697695i	$-0.754209\pi$
$389$	4.37542	−	20.5847i	0.221842	−	1.04369i	0.938238	−	0.345992i	$-0.112457\pi$
$390$	1.61420	−	3.57579i	0.0817383	−	0.181067i
$391$	−1.01295	−	0.329128i	−0.0512271	−	0.0166447i
$392$	−12.5783	−	13.5334i	−0.635301	−	0.683539i
$393$	−13.3088	+	13.3088i	−0.671340	+	0.671340i
$394$	−12.6454	−	1.32909i	−0.637066	−	0.0669583i
$395$	−14.7787	+	18.0589i	−0.743596	+	0.908639i
$396$	−0.336752	−	3.20399i	−0.0169224	−	0.161006i
$397$	4.78454	−	1.83661i	0.240129	−	0.0921770i	−0.235327	−	0.971916i	$-0.575616\pi$
$397$	4.78454	−	1.83661i	0.240129	−	0.0921770i	0.475457	+	0.879739i	$0.342283\pi$
$398$	−9.63744	+	18.9145i	−0.483081	+	0.948100i
$399$	4.56645	+	14.9804i	0.228608	+	0.749960i
$400$	3.50821	+	1.18004i	0.175410	+	0.0590022i
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	−0.874556	−	0.484924i	$-0.838847\pi$
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	0.0173216	−	0.999850i	$-0.494486\pi$
$402$	6.21910	−	4.03873i	0.310180	−	0.201433i
$403$	15.3047	+	12.3935i	0.762382	+	0.617364i
$404$	4.52068	+	2.01273i	0.224912	+	0.100137i
$405$	1.68454	−	0.257902i	0.0837053	−	0.0128153i
$406$	−2.68586	−	13.8788i	−0.133297	−	0.688792i
$407$	7.19393	+	7.19393i	0.356590	+	0.356590i
$408$	−1.73474	−	2.14223i	−0.0858825	−	0.106056i
$409$	17.5576	+	19.4997i	0.868168	+	0.964198i	0.999632	−	0.0271225i	$-0.00863443\pi$
$409$	17.5576	+	19.4997i	0.868168	+	0.964198i	−0.131464	+	0.991321i	$0.541968\pi$
$410$	−0.0982457	−	0.0574001i	−0.00485201	−	0.00283479i
$411$	−2.75655	−	2.48201i	−0.135970	−	0.122428i
$412$	−4.03345	−	7.91610i	−0.198714	−	0.389998i
$413$	−3.07812	−	12.3893i	−0.151464	−	0.609635i
$414$	1.47203	−	0.478291i	0.0723462	−	0.0235067i
$415$	1.53390	−	13.9037i	0.0752963	−	0.682505i
$416$	−8.74388	+	7.87302i	−0.428704	+	0.386007i
$417$	9.04608	+	3.47247i	0.442989	+	0.170047i
$418$	1.40745	−	5.25268i	0.0688407	−	0.256917i
$419$	20.8379	+	15.1396i	1.01800	+	0.739617i	0.965871	−	0.259023i	$-0.0834006\pi$
$419$	20.8379	+	15.1396i	1.01800	+	0.739617i	0.0521248	+	0.998641i	$0.483401\pi$
$420$	9.01305	−	2.18999i	0.439792	−	0.106860i
$421$	−9.53283	+	6.92601i	−0.464602	+	0.337553i	−0.795334	−	0.606172i	$-0.792704\pi$
$421$	−9.53283	+	6.92601i	−0.464602	+	0.337553i	0.330732	+	0.943725i	$0.392704\pi$
$422$	4.09009	+	10.6551i	0.199103	+	0.518680i
$423$	−0.176741	−	0.272158i	−0.00859345	−	0.0132328i
$424$	−25.5318	−	14.7408i	−1.23994	−	0.715877i
$425$	3.64309	−	2.88839i	0.176716	−	0.140107i
$426$			9.41470i			0.456144i
$427$	−4.12978	−	11.3757i	−0.199854	−	0.550510i
$428$	−2.15233	+	13.5893i	−0.104037	+	0.656864i
$429$	1.21890	−	2.73769i	0.0588489	−	0.132177i
$430$	−6.91472	+	4.43992i	−0.333457	+	0.214112i
$431$	−14.2385	+	6.33937i	−0.685842	+	0.305357i	−0.719914	−	0.694063i	$-0.755819\pi$
$431$	−14.2385	+	6.33937i	−0.685842	+	0.305357i	0.0340723	+	0.999419i	$0.489152\pi$
$432$	−3.80556	−	1.01970i	−0.183095	−	0.0490602i
$433$	0.121416	+	0.766591i	0.00583489	+	0.0368400i	0.990434	−	0.137987i	$-0.0440633\pi$
$433$	0.121416	+	0.766591i	0.00583489	+	0.0368400i	−0.984599	+	0.174827i	$0.944063\pi$
$434$	0.368312	−	20.1465i	0.0176796	−	0.967063i
$435$	16.3918	+	5.41969i	0.785928	+	0.259854i
$436$	10.1163	−	11.2352i	0.484481	−	0.538070i
$437$	−6.02845	−	0.315938i	−0.288380	−	0.0151134i
$438$	−1.43567	−	0.0752404i	−0.0685991	−	0.00359512i
$439$	7.06803	−	7.84984i	0.337339	−	0.374653i	−0.550478	−	0.834850i	$-0.685555\pi$
$439$	7.06803	−	7.84984i	0.337339	−	0.374653i	0.887817	+	0.460197i	$0.152221\pi$
$440$	−7.43911	−	2.45962i	−0.354646	−	0.117258i
$441$	−8.46810	+	8.74002i	−0.403243	+	0.416191i
$442$	0.227225	+	1.43464i	0.0108080	+	0.0682391i
$443$	26.2546	+	7.03490i	1.24739	+	0.334238i	0.821329	−	0.570455i	$-0.193233\pi$
$443$	26.2546	+	7.03490i	1.24739	+	0.334238i	0.426064	+	0.904693i	$0.359900\pi$
$444$	10.9762	−	4.88694i	0.520909	−	0.231924i
$445$	29.5311	−	18.9618i	1.39991	−	0.898878i
$446$	6.83506	−	15.3518i	0.323650	−	0.726929i
$447$	0.00694557	−	0.0438526i	0.000328514	−	0.00207416i
$448$	7.99703	+	1.41691i	0.377824	+	0.0669426i
$449$		−	39.0168i		−	1.84131i	−0.390372	−	0.920657i	$-0.627654\pi$
$449$		−	39.0168i		−	1.84131i	0.390372	−	0.920657i	$-0.372346\pi$
$450$	−1.81588	+	6.50762i	−0.0856016	+	0.306772i
$451$	−0.0752701	−	0.0434572i	−0.00354433	−	0.00204632i
$452$	5.02573	+	7.73894i	0.236390	+	0.364009i
$453$	3.94207	+	10.2694i	0.185215	+	0.482501i
$454$	−5.91145	+	4.29492i	−0.277438	+	0.201571i
$455$	−11.4099	−	3.34576i	−0.534902	−	0.156852i
$456$	−12.6398	−	9.18334i	−0.591912	−	0.430049i
$457$	−5.95677	+	22.2310i	−0.278646	+	1.03992i	0.674713	+	0.738080i	$0.264268\pi$
$457$	−5.95677	+	22.2310i	−0.278646	+	1.03992i	−0.953359	+	0.301840i	$0.902399\pi$
$458$	−2.25881	−	0.867075i	−0.105547	−	0.0405158i
$459$	−3.67760	+	3.31133i	−0.171656	+	0.154560i
$460$	−0.392059	+	3.55372i	−0.0182798	+	0.165693i
$461$	−23.0880	+	7.50175i	−1.07532	+	0.349391i	−0.792556	−	0.609799i	$-0.791250\pi$
$461$	−23.0880	+	7.50175i	−1.07532	+	0.349391i	−0.282760	+	0.959191i	$0.591250\pi$
$462$	−2.97576	+	0.739328i	−0.138445	+	0.0343967i
$463$	2.79874	+	5.49284i	0.130069	+	0.255274i	0.946851	−	0.321671i	$-0.104245\pi$
$463$	2.79874	+	5.49284i	0.130069	+	0.255274i	−0.816783	+	0.576945i	$0.804245\pi$
$464$	−3.78173	−	3.40509i	−0.175563	−	0.158077i
$465$	21.2482	+	12.4143i	0.985362	+	0.575697i
$466$	15.1636	+	16.8409i	0.702441	+	0.780140i
$467$	18.4601	+	22.7963i	0.854231	+	1.05489i	0.997868	+	0.0652571i	$0.0207868\pi$
$467$	18.4601	+	22.7963i	0.854231	+	1.05489i	−0.143637	+	0.989630i	$0.545880\pi$
$468$	3.44880	+	3.44880i	0.159421	+	0.159421i
$469$	−14.7303	−	16.9736i	−0.680182	−	0.783767i
$470$	−0.320677	+	0.0490956i	−0.0147917	+	0.00226461i
$471$	13.5068	+	6.01362i	0.622361	+	0.277093i
$472$	9.89733	+	8.01470i	0.455561	+	0.368906i
$473$	−5.26423	+	3.41863i	−0.242050	+	0.157189i
$474$	−4.55512	−	7.88970i	−0.209224	−	0.362386i
$475$	15.7078	−	21.1574i	0.720725	−	0.970768i
$476$	−2.34409	+	2.50956i	−0.107441	+	0.115026i
$477$	−8.81577	+	17.3019i	−0.403646	+	0.792200i
$478$	2.33208	−	0.895202i	0.106667	−	0.0409456i
$479$	0.950688	+	9.04519i	0.0434380	+	0.413285i	0.994536	+	0.104395i	$0.0332908\pi$
$479$	0.950688	+	9.04519i	0.0434380	+	0.413285i	−0.951098	+	0.308890i	$0.900043\pi$
$480$	−9.31162	+	11.3784i	−0.425015	+	0.519349i
$481$	−15.3180	−	1.60999i	−0.698441	−	0.0734091i
$482$	−14.7394	+	14.7394i	−0.671360	+	0.671360i
$483$	1.48961	+	3.06058i	0.0677798	+	0.139261i
$484$	12.2635	+	3.98466i	0.557433	+	0.181121i
$485$	−16.0048	+	35.4539i	−0.726739	+	1.60988i
$486$	2.44182	−	11.4878i	0.110763	−	0.521099i
$487$	−0.0277991	+	0.530438i	−0.00125970	+	0.0240364i	−0.999187	−	0.0403139i	$-0.987164\pi$
$487$	−0.0277991	+	0.530438i	−0.00125970	+	0.0240364i	0.997927	+	0.0643504i	$0.0204975\pi$
$488$	10.1255	+	6.57559i	0.458361	+	0.297663i
$489$	1.21199	+	3.73011i	0.0548080	+	0.168682i
$490$	4.48046	+	11.3108i	0.202407	+	0.510968i
$491$	1.98288	−	6.10267i	0.0894861	−	0.275410i	−0.896291	−	0.443466i	$-0.853749\pi$
$491$	1.98288	−	6.10267i	0.0894861	−	0.275410i	0.985777	+	0.168056i	$0.0537489\pi$
$492$	−0.0797694	+	0.0645960i	−0.00359628	+	0.00291221i
$493$	−6.17415	+	1.65436i	−0.278070	+	0.0745086i
$494$	3.34855	+	7.52097i	0.150658	+	0.338384i
$495$	−1.36140	+	4.97793i	−0.0611902	+	0.223741i
$496$	−4.26357	−	5.86830i	−0.191440	−	0.263494i
$497$	28.2589	−	3.94772i	1.26758	−	0.177079i
$498$	4.86582	+	2.47926i	0.218043	+	0.111098i
$499$	5.43364	−	3.13711i	0.243243	−	0.140437i	−0.373423	−	0.927661i	$-0.621816\pi$
$499$	5.43364	−	3.13711i	0.243243	−	0.140437i	0.616666	+	0.787225i	$0.288483\pi$
$500$	−11.9751	−	10.0080i	−0.535541	−	0.447572i
$501$	10.7562	−	18.6303i	0.480553	−	0.832343i
$502$	0.559489	+	10.6757i	0.0249712	+	0.476479i
$503$	−4.92568	−	0.780151i	−0.219625	−	0.0347852i	0.0456521	−	0.998957i	$-0.485463\pi$
$503$	−4.92568	−	0.780151i	−0.219625	−	0.0347852i	−0.265277	+	0.964172i	$0.585463\pi$
$504$	1.48951	−	12.0488i	0.0663480	−	0.536695i
$505$	−5.57623	−	5.63407i	−0.248139	−	0.250713i
$506$	0.123544	−	1.17544i	0.00549220	−	0.0522548i
$507$	−2.60482	−	9.72131i	−0.115684	−	0.431739i
$508$	9.24984	−	24.0966i	0.410395	−	1.06912i
$509$	−22.1320	+	4.70429i	−0.980982	+	0.208514i	−0.670374	−	0.742024i	$-0.733866\pi$
$509$	−22.1320	+	4.70429i	−0.980982	+	0.208514i	−0.310609	+	0.950538i	$0.600533\pi$
$510$	0.551976	+	1.72911i	0.0244419	+	0.0765663i
$511$	0.376159	+	4.34082i	0.0166403	+	0.192027i
$512$	7.34327	−	3.74158i	0.324530	−	0.165356i
$513$	−15.2763	+	23.5235i	−0.674467	+	1.03859i
$514$	7.02566	+	1.49335i	0.309889	+	0.0658688i
$515$	1.41460	+	14.1615i	0.0623348	+	0.624030i
$516$	1.54122	+	7.25087i	0.0678484	+	0.319202i
$517$	−0.244752	+	0.0387649i	−0.0107642	+	0.00170488i
$518$	8.34013	+	13.3716i	0.366444	+	0.587513i
$519$	3.27343	−	4.50548i	0.143687	−	0.197769i
$520$	11.0959	−	4.19375i	0.486586	−	0.183908i
$521$	30.6917	−	3.22582i	1.34463	−	0.141326i	0.595287	−	0.803513i	$-0.297038\pi$
$521$	30.6917	−	3.22582i	1.34463	−	0.141326i	0.749339	+	0.662187i	$0.230372\pi$
$522$	5.84564	−	7.21877i	0.255857	−	0.315957i
$523$	−30.5923	+	1.60327i	−1.33771	+	0.0701062i	−0.707716	−	0.706497i	$-0.750274\pi$
$523$	−30.5923	+	1.60327i	−1.33771	+	0.0701062i	−0.629990	+	0.776603i	$0.716941\pi$
$524$	−23.3916			−1.02187
$525$	−14.7262	−	1.97499i	−0.642706	−	0.0861955i
$526$	6.52252			0.284395
$527$	−9.09861	+	0.476838i	−0.396342	+	0.0207714i
$528$	−0.694637	+	0.857805i	−0.0302302	+	0.0373312i
$529$	21.5691	−	2.26701i	0.937789	−	0.0985656i
$530$	12.1387	+	15.1492i	0.527273	+	0.658041i
$531$	4.93056	−	6.78633i	0.213968	−	0.294502i
$532$	−9.15184	+	17.1778i	−0.396783	+	0.744754i
$533$	0.129963	−	0.0205840i	0.00562930	−	0.000891594i
$534$	2.84865	+	13.4018i	0.123273	+	0.579954i
$535$	11.1183	−	19.0301i	0.480688	−	0.822744i
$536$	21.9306	+	4.66148i	0.947256	+	0.201345i
$537$	12.3891	−	19.0775i	0.534628	−	0.823254i
$538$	3.04985	−	1.55398i	0.131488	−	0.0669966i
$539$	3.46693	+	8.62194i	0.149331	+	0.371373i
$540$	13.3888	+	9.83344i	0.576161	+	0.423164i
$541$	−38.7310	+	8.23253i	−1.66518	+	0.353944i	−0.941712	−	0.336419i	$-0.890784\pi$
$541$	−38.7310	+	8.23253i	−1.66518	+	0.353944i	−0.723463	+	0.690363i	$0.757451\pi$
$542$	−0.956035	+	2.49056i	−0.0410652	+	0.106979i
$543$	1.32384	+	4.94065i	0.0568115	+	0.212023i
$544$	0.569001	−	5.41369i	0.0243957	−	0.232110i
$545$	−21.6351	+	10.8834i	−0.926747	+	0.466194i
$546$	2.79672	−	3.70500i	0.119689	−	0.158559i
$547$	37.0235	+	5.86395i	1.58301	+	0.250724i	0.885079	−	0.465440i	$-0.154104\pi$
$547$	37.0235	+	5.86395i	1.58301	+	0.250724i	0.697932	+	0.716164i	$0.254104\pi$
$548$	−0.241267	−	4.60365i	−0.0103064	−	0.196658i
$549$	3.97611	−	6.88682i	0.169696	−	0.293922i
$550$	3.97573	+	3.28798i	0.169525	+	0.140200i
$551$	−31.3750	+	18.1143i	−1.33662	+	0.771697i
$552$	−3.02561	−	1.54162i	−0.128778	−	0.0656159i
$553$	−21.7715	+	16.9808i	−0.925817	+	0.722097i
$554$	3.51735	+	4.84122i	0.149438	+	0.205684i
$555$	−19.2254	+	0.908122i	−0.816071	+	0.0385476i
$556$	4.89811	+	11.0013i	0.207726	+	0.466560i
$557$	5.81572	−	1.55832i	0.246420	−	0.0660280i	−0.133495	−	0.991050i	$-0.542620\pi$
$557$	5.81572	−	1.55832i	0.246420	−	0.0660280i	0.379915	+	0.925021i	$0.375953\pi$
$558$	10.2896	−	8.33239i	0.435595	−	0.352738i
$559$	2.93652	−	9.03767i	0.124201	−	0.382253i
$560$	3.74040	+	2.27804i	0.158061	+	0.0962647i
$561$	0.428435	+	1.31859i	0.0180885	+	0.0556708i
$562$	15.8159	+	10.2709i	0.667152	+	0.433253i
$563$	1.58169	−	30.1805i	0.0666604	−	1.27196i	−0.736600	−	0.676329i	$-0.763570\pi$
$563$	1.58169	−	30.1805i	0.0666604	−	1.27196i	0.803260	−	0.595628i	$-0.203097\pi$
$564$	−0.0608453	+	0.286255i	−0.00256205	+	0.0120535i
$565$	−2.99866	−	14.4744i	−0.126154	−	0.608942i
$566$	−5.35873	−	1.74116i	−0.225244	−	0.0731863i
$567$	2.01137	+	0.142319i	0.0844694	+	0.00597682i
$568$	−20.1280	+	20.1280i	−0.844552	+	0.844552i
$569$	−4.95634	−	0.520932i	−0.207781	−	0.0218386i	6.62580e−5	−	1.00000i	$-0.499979\pi$
$569$	−4.95634	−	0.520932i	−0.207781	−	0.0218386i	−0.207847	+	0.978161i	$0.566646\pi$
$570$	5.55844	+	8.65670i	0.232817	+	0.362589i
$571$	0.255295	+	2.42897i	0.0106837	+	0.101649i	0.998564	−	0.0535674i	$-0.0170592\pi$
$571$	0.255295	+	2.42897i	0.0106837	+	0.101649i	−0.987880	+	0.155216i	$0.950393\pi$
$572$	3.47706	−	1.33472i	0.145383	−	0.0558073i
$573$	−7.89270	+	15.4903i	−0.329722	+	0.647117i
$574$	−0.0983877	−	0.0919002i	−0.00410662	−	0.00383584i
$575$	2.65263	−	5.07591i	0.110622	−	0.211680i
$576$	2.66831	+	4.62165i	0.111180	+	0.192569i
$577$	20.3829	−	13.2368i	0.848553	−	0.551057i	−0.0455274	−	0.998963i	$-0.514497\pi$
$577$	20.3829	−	13.2368i	0.848553	−	0.551057i	0.894081	+	0.447906i	$0.147830\pi$
$578$	9.74635	+	7.89244i	0.405395	+	0.328282i
$579$	8.04537	+	3.58203i	0.334354	+	0.148864i
$580$	9.64235	+	19.1680i	0.400377	+	0.795908i
$581$	5.40137	−	15.6447i	0.224087	−	0.649052i
$582$	−10.7384	−	10.7384i	−0.445123	−	0.445123i
$583$	9.33174	+	11.5237i	0.386481	+	0.477264i
$584$	−2.90851	−	3.23023i	−0.120355	−	0.133668i
$585$	−3.14097	−	7.15383i	−0.129863	−	0.295774i
$586$	−17.9877	−	16.1962i	−0.743066	−	0.669060i
$587$	−4.09368	−	8.03430i	−0.168964	−	0.331611i	0.790961	−	0.611866i	$-0.209581\pi$
$587$	−4.09368	−	8.03430i	−0.168964	−	0.331611i	−0.959926	+	0.280255i	$0.909581\pi$
$588$	10.9733	−	0.173399i	0.452532	−	0.00715085i
$589$	−49.1130	+	15.9578i	−2.02366	+	0.657528i
$590$	−4.15540	−	7.28390i	−0.171075	−	0.299873i
$591$	13.6545	−	12.2946i	0.561671	−	0.505731i
$592$	5.29629	+	2.03306i	0.217676	+	0.0835581i
$593$	6.63849	−	24.7752i	0.272610	−	1.01740i	−0.684816	−	0.728716i	$-0.740117\pi$
$593$	6.63849	−	24.7752i	0.272610	−	1.01740i	0.957426	−	0.288679i	$-0.0932160\pi$
$594$	−4.44277	−	3.22786i	−0.182289	−	0.132441i
$595$	4.95860	−	2.38184i	0.203283	−	0.0976458i
$596$	0.0446416	−	0.0324340i	0.00182859	−	0.00132855i
$597$	−10.9933	−	28.6386i	−0.449926	−	1.17210i
$598$	0.974545	+	1.50067i	0.0398521	+	0.0613669i
$599$	23.1803	+	13.3832i	0.947123	+	0.546822i	0.892186	−	0.451668i	$-0.149171\pi$
$599$	23.1803	+	13.3832i	0.947123	+	0.546822i	0.0549370	+	0.998490i	$0.482504\pi$
$600$	12.9126	−	7.27848i	0.527155	−	0.297143i
$601$		−	3.83116i		−	0.156276i	−0.996943	−	0.0781382i	$-0.975102\pi$
$601$		−	3.83116i		−	0.156276i	0.996943	−	0.0781382i	$-0.0248975\pi$
$602$	−9.13938	+	3.31791i	−0.372493	+	0.135228i
$603$	2.31015	−	14.5857i	0.0940764	−	0.593975i
$604$	−5.56051	+	12.4891i	−0.226254	+	0.508175i
$605$	−15.9854	−	13.0818i	−0.649898	−	0.531852i
$606$	2.82720	−	1.25875i	0.114847	−	0.0511332i
$607$	−32.5210	−	8.71399i	−1.31999	−	0.353690i	−0.471015	−	0.882125i	$-0.656112\pi$
$607$	−32.5210	−	8.71399i	−1.31999	−	0.353690i	−0.848974	+	0.528435i	$0.822779\pi$
$608$	−4.82648	−	30.4732i	−0.195740	−	1.23585i
$609$	17.5013	+	10.5355i	0.709187	+	0.426921i
$610$	−4.63955	−	6.45557i	−0.187850	−	0.261379i
$611$	0.251029	−	0.278796i	0.0101555	−	0.0112789i
$612$	−2.25339	−	0.118095i	−0.0910877	−	0.00477370i
$613$	−44.3520	−	2.32439i	−1.79136	−	0.0938813i	−0.872537	−	0.488547i	$-0.837527\pi$
$613$	−44.3520	−	2.32439i	−1.79136	−	0.0938813i	−0.918825	+	0.394666i	$0.870860\pi$
$614$	−1.71789	+	1.90791i	−0.0693284	+	0.0769970i
$615$	0.156638	−	0.0500028i	0.00631625	−	0.00201631i
$616$	−7.94261	−	4.78134i	−0.320017	−	0.192646i
$617$	−5.46815	−	34.5246i	−0.220140	−	1.38991i	−0.811902	−	0.583794i	$-0.801568\pi$
$617$	−5.46815	−	34.5246i	−0.220140	−	1.38991i	0.591762	−	0.806112i	$-0.298432\pi$
$618$	−5.36695	−	1.43807i	−0.215890	−	0.0578476i
$619$	12.2138	−	5.43792i	0.490913	−	0.218568i	−0.146324	−	0.989237i	$-0.546744\pi$
$619$	12.2138	−	5.43792i	0.490913	−	0.218568i	0.637237	+	0.770668i	$0.280077\pi$
$620$	7.76329	+	29.5826i	0.311781	+	1.18807i
$621$	−2.47955	+	5.56917i	−0.0995011	+	0.223483i
$622$	0.751132	−	4.74246i	0.0301176	−	0.190155i
$623$	39.0321	−	14.1700i	1.56379	−	0.567709i
$624$		−	1.67106i		−	0.0668960i
$625$	12.0506	+	21.9040i	0.482022	+	0.876159i
$626$	7.53917	+	4.35274i	0.301326	+	0.173971i
$627$	4.27987	+	6.59042i	0.170921	+	0.263196i
$628$	6.58503	+	17.1546i	0.262771	+	0.684543i
$629$	5.76493	−	4.18846i	0.229863	−	0.167005i
$630$	−3.79517	+	7.03575i	−0.151203	+	0.280311i
$631$	11.1996	+	8.13699i	0.445849	+	0.323928i	0.787955	−	0.615733i	$-0.211140\pi$
$631$	11.1996	+	8.13699i	0.445849	+	0.323928i	−0.342106	+	0.939662i	$0.611140\pi$
$632$	7.12911	−	26.6062i	0.283581	−	1.05834i
$633$	−15.3972	−	5.91041i	−0.611982	−	0.234918i
$634$	5.19442	−	4.67707i	0.206297	−	0.185750i
$635$	−27.8244	+	30.5834i	−1.10418	+	1.21366i
$636$	16.6548	−	5.41147i	0.660405	−	0.214579i
$637$	−12.2935	−	6.84101i	−0.487088	−	0.271051i
$638$	−3.22021	−	6.32003i	−0.127489	−	0.250212i
$639$	13.9332	+	12.5455i	0.551189	+	0.496293i
$640$	−20.7428	+	2.07201i	−0.819931	+	0.0819035i
$641$	−1.56927	−	1.74285i	−0.0619824	−	0.0688384i	0.711356	−	0.702832i	$-0.248081\pi$
$641$	−1.56927	−	1.74285i	−0.0619824	−	0.0688384i	−0.773339	+	0.633993i	$0.781415\pi$
$642$	5.41505	+	6.68703i	0.213715	+	0.263916i
$643$	−16.5284	−	16.5284i	−0.651816	−	0.651816i	0.301614	−	0.953430i	$-0.402475\pi$
$643$	−16.5284	−	16.5284i	−0.651816	−	0.651816i	−0.953430	+	0.301614i	$0.902475\pi$
$644$	−1.38057	+	3.99872i	−0.0544020	+	0.157572i
$645$	1.91809	−	11.7187i	0.0755247	−	0.461424i
$646$	−3.47954	−	1.54919i	−0.136901	−	0.0609521i
$647$	−9.11290	−	7.37948i	−0.358265	−	0.290117i	0.433242	−	0.901278i	$-0.357370\pi$
$647$	−9.11290	−	7.37948i	−0.358265	−	0.290117i	−0.791507	+	0.611161i	$0.790703\pi$
$648$	−1.68706	+	1.09559i	−0.0662739	+	0.0430388i
$649$	−3.20276	−	5.54735i	−0.125719	−	0.217752i
$650$	−7.81024	−	0.0805937i	−0.306343	−	0.00316115i
$651$	21.2789	+	19.8758i	0.833986	+	0.778994i
$652$	−2.21293	+	4.34313i	−0.0866652	+	0.170090i
$653$	−19.4319	+	7.45920i	−0.760429	+	0.291901i	−0.707515	−	0.706698i	$-0.750184\pi$
$653$	−19.4319	+	7.45920i	−0.760429	+	0.291901i	−0.0529133	+	0.998599i	$0.516851\pi$
$654$	−0.988318	−	9.40322i	−0.0386463	−	0.367695i
$655$	34.9124	+	13.6087i	1.36414	+	0.531736i
$656$	−0.0481998	−	0.00506600i	−0.00188188	−	0.000197794i
$657$	−2.02445	+	2.02445i	−0.0789813	+	0.0789813i
$658$	−0.382894	−	0.0270925i	−0.0149268	−	0.00105618i
$659$	30.5370	+	9.92209i	1.18955	+	0.386510i	0.835908	−	0.548870i	$-0.184942\pi$
$659$	30.5370	+	9.92209i	1.18955	+	0.386510i	0.353646	+	0.935379i	$0.384942\pi$
$660$	4.04247	−	2.30620i	0.157353	−	0.0897686i
$661$	2.10304	−	9.89402i	0.0817988	−	0.384833i	−0.918136	−	0.396266i	$-0.870306\pi$
$661$	2.10304	−	9.89402i	0.0817988	−	0.384833i	0.999935	+	0.0114328i	$0.00363925\pi$
$662$	0.293951	−	5.60892i	0.0114247	−	0.217997i
$663$	−1.76035	−	1.14319i	−0.0683665	−	0.0443977i
$664$	5.10231	+	15.7033i	0.198008	+	0.609406i
$665$	23.6530	−	20.3139i	0.917223	−	0.787741i
$666$	−3.19997	+	9.84849i	−0.123996	+	0.381621i
$667$	−6.11935	+	4.95535i	−0.236942	+	0.191872i
$668$	25.8250	−	6.91979i	0.999199	−	0.267735i
$669$	9.87704	+	22.1842i	0.381868	+	0.857691i
$670$	−12.3397	−	8.10432i	−0.476725	−	0.313097i
$671$	−3.56931	−	4.91273i	−0.137792	−	0.189654i
$672$	−13.7176	+	10.6991i	−0.529167	+	0.412727i
$673$	10.0639	+	5.12781i	0.387935	+	0.197663i	0.637070	−	0.770806i	$-0.280146\pi$
$673$	10.0639	+	5.12781i	0.387935	+	0.197663i	−0.249135	+	0.968469i	$0.580146\pi$
$674$	6.82894	−	3.94269i	0.263041	−	0.151867i
$675$	−14.2621	−	22.4659i	−0.548949	−	0.864712i
$676$	6.25399	−	10.8322i	0.240538	−	0.416624i
$677$	−1.27981	−	24.4201i	−0.0491869	−	0.938542i	−0.906095	−	0.423074i	$-0.860951\pi$
$677$	−1.27981	−	24.4201i	−0.0491869	−	0.938542i	0.856908	−	0.515469i	$-0.172382\pi$
$678$	5.69985	+	0.902768i	0.218901	+	0.0346706i
$679$	−27.7294	+	36.7350i	−1.06416	+	1.40976i
$680$	−2.51664	+	4.87681i	−0.0965086	+	0.187017i
$681$	1.10371	−	10.5011i	0.0422943	−	0.402404i
$682$	−2.61681	−	9.76605i	−0.100203	−	0.373961i
$683$	−5.90842	+	15.3920i	−0.226079	+	0.588957i	−0.998960	−	0.0455944i	$-0.985482\pi$
$683$	−5.90842	+	15.3920i	−0.226079	+	0.588957i	0.772881	+	0.634552i	$0.218815\pi$
$684$	−12.5099	+	2.65907i	−0.478329	+	0.101672i
$685$	−2.31820	+	7.01141i	−0.0885740	+	0.267892i
$686$	2.21659	+	14.2231i	0.0846299	+	0.543042i
$687$	3.11525	−	1.58730i	0.118854	−	0.0605593i
$688$	−1.90630	+	2.93544i	−0.0726770	+	0.111913i
$689$	−21.9585	−	4.66741i	−0.836550	−	0.177814i
$690$	1.48756	+	1.66934i	0.0566303	+	0.0635506i
$691$	5.84621	+	27.5043i	0.222400	+	1.04631i	0.937687	+	0.347480i	$0.112963\pi$
$691$	5.84621	+	27.5043i	0.222400	+	1.04631i	−0.715287	+	0.698831i	$0.753704\pi$
$692$	6.83613	−	1.08274i	0.259870	−	0.0411594i
$693$	−2.87117	+	5.38914i	−0.109067	+	0.204716i
$694$	−3.66214	+	5.04050i	−0.139013	+	0.191335i
$695$	−0.910198	−	19.2693i	−0.0345258	−	0.730926i
$696$	−20.2674	+	2.13019i	−0.768233	+	0.0807445i
$697$	−0.0383106	+	0.0473096i	−0.00145112	+	0.00179198i
$698$	6.84643	−	0.358806i	0.259141	−	0.0135810i
$699$	−32.7474			−1.23862
$700$	−11.2058	−	14.6771i	−0.423541	−	0.554741i
$701$	−35.1051			−1.32590			−0.662951	−	0.748663i	$-0.730696\pi$
$701$	−35.1051			−1.32590			−0.662951	+	0.748663i	$0.730696\pi$
$702$	8.30246	−	0.435113i	0.313356	−	0.0164223i
$703$	25.4172	−	31.3876i	0.958627	−	1.18381i
$704$	4.05282	−	0.425969i	0.152747	−	0.0160543i
$705$	0.257349	−	0.391842i	0.00969234	−	0.0147576i
$706$	−7.69154	+	10.5865i	−0.289475	+	0.398428i
$707$	−4.96372	−	7.95823i	−0.186680	−	0.299300i
$708$	−7.47165	+	1.18339i	−0.280802	+	0.0444746i
$709$	−10.9224	−	51.3859i	−0.410200	−	1.92984i	−0.365421	−	0.930842i	$-0.619075\pi$
$709$	−10.9224	−	51.3859i	−0.410200	−	1.92984i	−0.0447789	−	0.998997i	$-0.514258\pi$
$710$	17.1620	−	7.53517i	0.644079	−	0.282790i
$711$	−17.7462	−	3.77207i	−0.665534	−	0.141464i
$712$	−22.5620	+	34.7425i	−0.845548	+	1.30203i
$713$	−10.0005	+	5.09550i	−0.374521	+	0.190828i
$714$	0.185410	+	2.13961i	0.00693879	+	0.0800728i
$715$	−5.96608	−	0.0307811i	−0.223119	−	0.00115115i
$716$	27.6529	−	5.87780i	1.03344	−	0.219664i
$717$	−1.29362	+	3.36999i	−0.0483110	+	0.125854i
$718$	−2.78070	−	10.3777i	−0.103775	−	0.387293i
$719$	−0.289532	+	2.75471i	−0.0107977	+	0.102733i	−0.998593	−	0.0530223i	$-0.983115\pi$
$719$	−0.289532	+	2.75471i	−0.0107977	+	0.102733i	0.987796	+	0.155756i	$0.0497812\pi$
$720$	0.435506	+	2.84458i	0.0162303	+	0.106011i
$721$	−2.06603	+	16.7123i	−0.0769430	+	0.622398i
$722$	−6.73625	−	1.06692i	−0.250697	−	0.0397066i
$723$	−1.57644	−	30.0803i	−0.0586286	−	1.11870i
$724$	−3.17846	+	5.50525i	−0.118126	+	0.204601i
$725$	−3.23988	−	34.2183i	−0.120326	−	1.27084i
$726$	6.98382	−	4.03211i	0.259194	−	0.149646i
$727$	5.31536	+	2.70831i	0.197136	+	0.100446i	0.549772	−	0.835315i	$-0.314715\pi$
$727$	5.31536	+	2.70831i	0.197136	+	0.100446i	−0.352636	+	0.935761i	$0.614715\pi$
$728$	13.9003	−	1.94184i	0.515178	−	0.0719695i
$729$	11.3195	+	15.5799i	0.419239	+	0.577033i
$730$	1.01190	+	2.67730i	0.0374522	+	0.0990914i
$731$	1.78818	+	4.01632i	0.0661383	+	0.148549i
$732$	−6.92710	+	1.85611i	−0.256033	+	0.0686038i
$733$	23.4127	−	18.9592i	0.864768	−	0.700275i	−0.0905384	−	0.995893i	$-0.528859\pi$
$733$	23.4127	−	18.9592i	0.864768	−	0.700275i	0.955306	+	0.295618i	$0.0955255\pi$
$734$	−0.249589	+	0.768156i	−0.00921250	+	0.0283532i
$735$	−16.4788	−	6.12522i	−0.607828	−	0.225932i
$736$	−2.07219	−	6.37755i	−0.0763820	−	0.235080i
$737$	−9.45749	−	6.14177i	−0.348371	−	0.226235i
$738$	0.00462993	−	0.0883442i	0.000170430	−	0.00325200i
$739$	−9.39272	+	44.1893i	−0.345517	+	1.62553i	0.371472	+	0.928444i	$0.378853\pi$
$739$	−9.39272	+	44.1893i	−0.345517	+	1.62553i	−0.716989	+	0.697084i	$0.754480\pi$
$740$	−17.6933	−	16.0972i	−0.650420	−	0.591746i
$741$	−11.3145	−	3.67629i	−0.415648	−	0.135052i
$742$	10.0520	+	20.6530i	0.369021	+	0.758194i
$743$	23.4363	−	23.4363i	0.859793	−	0.859793i	−0.131520	−	0.991313i	$-0.541986\pi$
$743$	23.4363	−	23.4363i	0.859793	−	0.859793i	0.991313	+	0.131520i	$0.0419858\pi$
$744$	−28.8891	−	3.03637i	−1.05913	−	0.111319i
$745$	−0.0854978	+	0.0224369i	−0.00313240	+	0.000822026i
$746$	−1.78782	−	17.0099i	−0.0654566	−	0.622778i
$747$	10.1531	−	3.89741i	0.371482	−	0.142599i
$748$	−0.782267	+	1.53529i	−0.0286025	+	0.0561356i
$749$	17.8010	−	19.0576i	0.650434	−	0.696351i
$750$	−9.66250	+	1.37745i	−0.352825	+	0.0502972i
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	0.965637	+	0.259895i	$0.0836881\pi$
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	−0.257742	+	0.966214i	$0.582979\pi$
$752$	−0.115887	+	0.0752582i	−0.00422598	+	0.00274438i
$753$	−12.0054	−	9.72182i	−0.437503	−	0.354283i
$754$	9.81013	+	4.36775i	0.357264	+	0.159064i
$755$	15.5651	−	15.4053i	0.566470	−	0.560655i
$756$	12.8829	+	14.8448i	0.468546	+	0.539901i
$757$	2.63808	+	2.63808i	0.0958825	+	0.0958825i	0.753421	−	0.657538i	$-0.228402\pi$
$757$	2.63808	+	2.63808i	0.0958825	+	0.0958825i	−0.657538	+	0.753421i	$0.728402\pi$
$758$	−14.8376	−	18.3229i	−0.538924	−	0.665516i
$759$	1.14283	+	1.26924i	0.0414821	+	0.0460706i
$760$	−6.62387	+	30.3910i	−0.240273	+	1.10240i
$761$	29.5054	+	26.5668i	1.06957	+	0.963044i	0.999405	−	0.0344912i	$-0.0109811\pi$
$761$	29.5054	+	26.5668i	1.06957	+	0.963044i	0.0701640	+	0.997535i	$0.477648\pi$
$762$	−7.32833	−	14.3827i	−0.265477	−	0.521029i
$763$	−27.8100	+	6.90941i	−1.00679	+	0.250138i
$764$	−20.5490	+	6.67679i	−0.743438	+	0.241558i
$765$	3.29452	+	1.48723i	0.119113	+	0.0537708i
$766$	−12.3518	+	11.1216i	−0.446287	+	0.401839i
$767$	9.05342	+	3.47528i	0.326900	+	0.125485i
$768$	3.89107	−	14.5217i	0.140407	−	0.524006i
$769$	−0.563611	−	0.409487i	−0.0203243	−	0.0147665i	0.577577	−	0.816336i	$-0.303998\pi$
$769$	−0.563611	−	0.409487i	−0.0203243	−	0.0147665i	−0.597901	+	0.801570i	$0.703998\pi$
$770$	3.72940	+	4.83277i	0.134398	+	0.174161i
$771$	−8.39701	+	6.10079i	−0.302411	+	0.219714i
$772$	3.92239	+	10.2182i	0.141170	+	0.367760i
$773$	17.8463	+	27.4809i	0.641888	+	0.988421i	0.998531	+	0.0541802i	$0.0172546\pi$
$773$	17.8463	+	27.4809i	0.641888	+	0.988421i	−0.356643	+	0.934241i	$0.616079\pi$
$774$	−5.53295	−	3.19445i	−0.198878	−	0.114822i
$775$	5.62365	−	48.6692i	0.202008	−	1.74825i
$776$		−	45.9162i		−	1.64829i
$777$	−22.4239	−	3.97304i	−0.804452	−	0.142532i
$778$	2.55878	−	16.1555i	0.0917365	−	0.579202i
$779$	−0.140339	+	0.315207i	−0.00502817	+	0.0112935i
$780$	−2.55893	+	6.56481i	−0.0916245	+	0.235058i
$781$	13.0793	−	5.82329i	0.468015	−	0.208374i
$782$	−0.799623	−	0.214258i	−0.0285945	−	0.00766186i
$783$	5.72327	+	36.1353i	0.204533	+	1.29137i
$784$	3.72159	+	3.60580i	0.132914	+	0.128779i
$785$	0.151863	−	29.4346i	0.00542024	−	1.05057i
$786$	−9.78868	+	10.8714i	−0.349151	+	0.387771i
$787$	−26.6351	−	1.39588i	−0.949438	−	0.0497579i	−0.428674	−	0.903459i	$-0.641019\pi$
$787$	−26.6351	−	1.39588i	−0.949438	−	0.0497579i	−0.520763	+	0.853701i	$0.674353\pi$
$788$	22.8041	+	1.19511i	0.812363	+	0.0425741i
$789$	−6.30682	+	7.00444i	−0.224529	+	0.249365i
$790$	−10.7364	+	14.6181i	−0.381982	+	0.520090i
$791$	0.319693	−	17.4871i	0.0113670	−	0.621768i
$792$	−0.952952	−	6.01670i	−0.0338617	−	0.213794i
$793$	8.88006	+	2.37940i	0.315340	+	0.0844951i
$794$	3.63897	−	1.62017i	0.129142	−	0.0574978i
$795$	−28.0059	−	1.61265i	−0.993266	−	0.0571949i
$796$	15.5067	−	34.8286i	0.549620	−	1.23447i
$797$	−2.59453	+	16.3812i	−0.0919030	+	0.580252i	0.898165	+	0.439660i	$0.144901\pi$
$797$	−2.59453	+	16.3812i	−0.0919030	+	0.580252i	−0.990067	+	0.140593i	$0.955099\pi$
$798$	4.15377	+	11.4418i	0.147042	+	0.405035i
$799$			0.173565i			0.00614027i
$800$	28.1942	+	7.86731i	0.996817	+	0.278151i
$801$	23.6299	+	13.6427i	0.834921	+	0.482042i
$802$	−14.5335	−	22.3796i	−0.513196	−	0.790252i
$803$	0.783481	+	2.04104i	0.0276484	+	0.0720267i
$804$	−10.7742	+	7.82790i	−0.379976	+	0.276069i
$805$	4.38689	−	5.16498i	0.154617	−	0.182042i
$806$	12.3834	+	8.99706i	0.436186	+	0.316908i
$807$	−1.28020	+	4.77777i	−0.0450652	+	0.168186i
$808$	8.73549	+	3.35324i	0.307314	+	0.117967i
$809$	32.1490	−	28.9471i	1.13030	−	1.01773i	0.130645	−	0.991429i	$-0.458295\pi$
$809$	32.1490	−	28.9471i	1.13030	−	1.01773i	0.999654	−	0.0262968i	$-0.00837151\pi$
$810$	1.29702	−	0.268703i	0.0455725	−	0.00944126i
$811$	24.7816	−	8.05202i	0.870198	−	0.282745i	0.160317	−	0.987066i	$-0.448748\pi$
$811$	24.7816	−	8.05202i	0.870198	−	0.282745i	0.709881	+	0.704321i	$0.248748\pi$
$812$	6.12152	+	24.6388i	0.214823	+	0.864652i
$813$	−1.75015	−	3.43487i	−0.0613805	−	0.120466i
$814$	5.87644	+	5.29117i	0.205969	+	0.185455i
$815$	5.82958	−	5.19477i	0.204201	−	0.181965i
$816$	0.517311	+	0.574532i	0.0181095	+	0.0201127i
$817$	15.6816	+	19.3651i	0.548629	+	0.677500i
$818$	14.4211	+	14.4211i	0.504223	+	0.504223i
$819$	−1.75643	−	9.07607i	−0.0613745	−	0.317144i
$820$	0.181596	+	0.0937112i	0.00634162	+	0.00327254i
$821$	24.2885	+	10.8140i	0.847676	+	0.377410i	0.784151	−	0.620571i	$-0.213099\pi$
$821$	24.2885	+	10.8140i	0.847676	+	0.377410i	0.0635253	+	0.997980i	$0.479766\pi$
$822$	−2.24055	−	1.81436i	−0.0781480	−	0.0632830i
$823$	2.03336	−	1.32048i	0.0708785	−	0.0460290i	−0.508713	−	0.860936i	$-0.669879\pi$
$823$	2.03336	−	1.32048i	0.0708785	−	0.0460290i	0.579592	+	0.814907i	$0.303212\pi$
$824$	−8.39968	−	14.5487i	−0.292617	−	0.506827i
$825$	−7.37516	+	1.09023i	−0.256770	+	0.0379568i
$826$	−2.89315	−	9.49111i	−0.100666	−	0.330238i
$827$	2.88877	−	5.66953i	0.100452	−	0.197149i	−0.835311	−	0.549778i	$-0.814712\pi$
$827$	2.88877	−	5.66953i	0.100452	−	0.197149i	0.935763	+	0.352629i	$0.114712\pi$
$828$	−2.59509	+	0.996160i	−0.0901855	+	0.0346190i
$829$	−1.85268	−	17.6271i	−0.0643462	−	0.612213i	−0.978414	−	0.206653i	$-0.933743\pi$
$829$	−1.85268	−	17.6271i	−0.0643462	−	0.612213i	0.914068	−	0.405561i	$-0.132924\pi$
$830$	0.625014	−	10.8542i	0.0216946	−	0.376755i
$831$	−8.59994	−	0.903890i	−0.298329	−	0.0313556i
$832$	−4.36250	+	4.36250i	−0.151242	+	0.151242i
$833$	6.34445	−	1.45369i	0.219822	−	0.0503674i
$834$	7.16266	+	2.32729i	0.248023	+	0.0805875i
$835$	−42.5701	−	4.69648i	−1.47320	−	0.162528i
$836$	−2.03052	+	9.55283i	−0.0702269	+	0.330391i
$837$	−2.72928	+	52.0778i	−0.0943379	+	1.80007i
$838$	16.7898	+	10.9034i	0.579995	+	0.376653i
$839$	7.84911	+	24.1571i	0.270981	+	0.833995i	0.990255	+	0.139268i	$0.0444749\pi$
$839$	7.84911	+	24.1571i	0.270981	+	0.833995i	−0.719273	+	0.694727i	$0.755525\pi$
$840$	16.8025	−	5.02725i	0.579740	−	0.173457i
$841$	−5.64130	+	17.3621i	−0.194528	+	0.598695i
$842$	−7.11748	+	5.76362i	−0.245284	+	0.198627i
$843$	−26.3226	+	7.05313i	−0.906600	+	0.242923i
$844$	−8.33697	−	18.7251i	−0.286970	−	0.644546i
$845$	−15.6361	+	12.5289i	−0.537900	+	0.431007i
$846$	−0.148254	−	0.204054i	−0.00509708	−	0.00701553i
$847$	−15.0311	−	19.2717i	−0.516474	−	0.662184i
$848$	7.36733	+	3.75384i	0.252995	+	0.128908i
$849$	7.05132	−	4.07108i	0.242001	−	0.139719i
$850$	2.71021	−	2.39011i	0.0929594	−	0.0819801i
$851$	4.38910	−	7.60214i	0.150456	−	0.260598i
$852$	−0.884906	−	16.8850i	−0.0303164	−	0.578471i
$853$	19.9447	+	3.15894i	0.682895	+	0.108160i	0.488237	−	0.872711i	$-0.337640\pi$
$853$	19.9447	+	3.15894i	0.682895	+	0.108160i	0.194658	+	0.980871i	$0.437640\pi$
$854$	−3.66821	−	8.66164i	−0.125523	−	0.296395i
$855$	20.2183	+	3.30928i	0.691451	+	0.113175i
$856$	−2.71941	+	25.8734i	−0.0929475	+	0.884336i
$857$	0.962594	+	3.59245i	0.0328816	+	0.122716i	0.980416	−	0.196938i	$-0.0630999\pi$
$857$	0.962594	+	3.59245i	0.0328816	+	0.122716i	−0.947534	+	0.319654i	$0.896433\pi$
$858$	0.834723	−	2.17453i	0.0284970	−	0.0742372i
$859$	21.6111	−	4.59358i	0.737361	−	0.156731i	0.176103	−	0.984372i	$-0.443651\pi$
$859$	21.6111	−	4.59358i	0.737361	−	0.156731i	0.561258	+	0.827641i	$0.310318\pi$
$860$	11.9841	−	8.61281i	0.408653	−	0.293694i
$861$	0.193824	−	0.0167960i	0.00660552	−	0.000572408i
$862$	−10.7938	+	5.49970i	−0.367637	+	0.187320i
$863$	−21.4531	+	33.0348i	−0.730270	+	1.12452i	0.257146	+	0.966373i	$0.417218\pi$
$863$	−21.4531	+	33.0348i	−0.730270	+	1.12452i	−0.987416	+	0.158145i	$0.949449\pi$
$864$	−30.4762	−	6.47792i	−1.03682	−	0.220383i
$865$	−10.8330	−	2.36110i	−0.368332	−	0.0802797i
$866$	0.125424	+	0.590076i	0.00426210	+	0.0200516i
$867$	−17.8996	+	2.83502i	−0.607903	+	0.0962823i
$868$	1.23305	+	36.1669i	0.0418525	+	1.22758i
$869$	−8.14324	+	11.2082i	−0.276240	+	0.380212i
$870$	12.9435	+	3.53988i	0.438826	+	0.120013i
$871$	16.9787	−	1.78454i	0.575303	−	0.0604667i
$872$	17.9905	−	22.2164i	0.609235	−	0.752343i
$873$	−30.2017	+	1.58281i	−1.02217	+	0.0535699i
$874$	−4.69203			−0.158710
$875$	8.18613	+	28.4251i	0.276742	+	0.960944i
$876$	2.58191			0.0872347
$877$	22.4814	−	1.17820i	0.759145	−	0.0397851i	0.331164	−	0.943573i	$-0.392559\pi$
$877$	22.4814	−	1.17820i	0.759145	−	0.0397851i	0.427980	+	0.903788i	$0.359225\pi$
$878$	5.16677	−	6.38042i	0.174370	−	0.215329i
$879$	34.7858	−	3.65613i	1.17329	−	0.123318i
$880$	2.11965	+	0.579696i	0.0714534	+	0.0195416i
$881$	1.48864	−	2.04893i	0.0501535	−	0.0690304i	−0.783204	−	0.621765i	$-0.786416\pi$
$881$	1.48864	−	2.04893i	0.0501535	−	0.0690304i	0.833357	+	0.552735i	$0.186416\pi$
$882$	−6.21726	+	7.12831i	−0.209346	+	0.240023i
$883$	41.9699	−	6.64738i	1.41240	−	0.223702i	0.596833	−	0.802366i	$-0.296426\pi$
$883$	41.9699	−	6.64738i	1.41240	−	0.223702i	0.815566	+	0.578664i	$0.196426\pi$
$884$	−0.542368	−	2.55164i	−0.0182418	−	0.0858209i
$885$	11.8401	+	2.58060i	0.397999	+	0.0867459i
$886$	20.6645	+	4.39238i	0.694238	+	0.147565i
$887$	−17.3204	+	26.6711i	−0.581563	+	0.895528i	−0.999919	−	0.0127551i	$-0.995940\pi$
$887$	−17.3204	+	26.6711i	−0.581563	+	0.895528i	0.418356	+	0.908283i	$0.362606\pi$
$888$	20.2426	−	10.3141i	0.679298	−	0.346120i
$889$	−40.0977	+	28.0274i	−1.34483	+	0.940008i
$890$	22.1502	−	15.9191i	0.742477	−	0.533610i
$891$	0.989652	−	0.210357i	0.0331546	−	0.00704723i
$892$	−10.8156	+	28.1755i	−0.362132	+	0.943385i
$893$	0.254611	+	0.950220i	0.00852022	+	0.0317979i
$894$	0.00360720	−	0.0343202i	0.000120643	−	0.00114784i
$895$	−44.6920	−	7.31508i	−1.49389	−	0.244516i
$896$	−24.4790	−	3.02618i	−0.817787	−	0.101098i
$897$	−2.55386	−	0.404492i	−0.0852710	−	0.0135056i
$898$	−1.58712	−	30.2841i	−0.0529630	−	1.01059i
$899$	−33.6791	+	58.3340i	−1.12326	+	1.94555i
$900$	2.64508	−	11.8419i	0.0881692	−	0.394731i
$901$	8.99448	−	5.19297i	0.299650	−	0.173003i
$902$	−0.0601911	−	0.0306689i	−0.00200414	−	0.00102116i
$903$	5.27409	−	13.0228i	0.175511	−	0.433373i
$904$	10.2558	+	14.1160i	0.341104	+	0.469490i
$905$	7.94674	−	6.36754i	0.264158	−	0.211664i
$906$	3.47751	+	7.81061i	0.115532	+	0.259490i
$907$	−21.0096	+	5.62950i	−0.697611	+	0.186924i	−0.590160	−	0.807286i	$-0.700936\pi$
$907$	−21.0096	+	5.62950i	−0.697611	+	0.186924i	−0.107451	+	0.994210i	$0.534269\pi$
$908$	10.1983	−	8.25846i	0.338444	−	0.274067i
$909$	1.90450	−	5.86143i	0.0631681	−	0.194411i
$910$	−8.99223	−	2.13279i	−0.298089	−	0.0707014i
$911$	1.19819	+	3.68765i	0.0396978	+	0.122177i	0.968941	−	0.247290i	$-0.0795401\pi$
$911$	1.19819	+	3.68765i	0.0396978	+	0.122177i	−0.929244	+	0.369468i	$0.879540\pi$
$912$	3.67495	+	2.38654i	0.121690	+	0.0790263i
$913$	0.434634	−	8.29332i	0.0143843	−	0.274469i
$914$	−3.71923	+	17.4976i	−0.123021	+	0.578769i
$915$	11.4187	+	1.25975i	0.377490	+	0.0416459i
$916$	4.13261	+	1.34277i	0.136545	+	0.0443663i
$917$	36.7359	+	24.8229i	1.21313	+	0.819724i
$918$	−2.71979	+	2.71979i	−0.0897665	+	0.0897665i
$919$	−7.89240	−	0.829525i	−0.260346	−	0.0273635i	−0.0265440	−	0.999648i	$-0.508450\pi$
$919$	−7.89240	−	0.829525i	−0.260346	−	0.0273635i	−0.233802	+	0.972284i	$0.575117\pi$
$920$	−0.388639	+	6.74923i	−0.0128130	+	0.222516i
$921$	−0.387796	−	3.68963i	−0.0127783	−	0.121578i
$922$	−17.6154	+	6.76190i	−0.580131	+	0.222691i
$923$	−9.84030	+	19.3127i	−0.323897	+	0.635684i
$924$	5.26745	−	1.60566i	0.173286	−	0.0528224i
$925$	17.0427	+	34.3190i	0.560359	+	1.12840i
$926$	2.39577	+	4.14960i	0.0787299	+	0.136364i
$927$	−9.27996	+	6.02647i	−0.304794	+	0.197935i
$928$	−31.2753	−	25.3262i	−1.02666	−	0.831375i
$929$	44.5122	+	19.8181i	1.46040	+	0.650211i	0.974619	−	0.223870i	$-0.0718693\pi$
$929$	44.5122	+	19.8181i	1.46040	+	0.650211i	0.485779	+	0.874082i	$0.338536\pi$
$930$	16.9975	+	8.77140i	0.557369	+	0.287625i
$931$	32.6017	−	17.2656i	1.06848	−	0.565856i
$932$	−28.7785	−	28.7785i	−0.942670	−	0.942670i
$933$	4.36656	+	5.39226i	0.142955	+	0.176535i
$934$	15.2557	+	16.9432i	0.499182	+	0.554398i
$935$	2.06074	−	1.83634i	0.0673935	−	0.0600547i
$936$	6.85360	+	6.17101i	0.224017	+	0.201706i
$937$	18.7668	+	36.8319i	0.613085	+	1.20325i	0.963765	+	0.266752i	$0.0859503\pi$
$937$	18.7668	+	36.8319i	0.613085	+	1.20325i	−0.350680	+	0.936495i	$0.614050\pi$
$938$	−12.1238	−	12.5754i	−0.395858	−	0.410601i
$939$	−11.9642	+	3.88740i	−0.390437	+	0.126861i
$940$	0.570511	−	0.118193i	0.0186080	−	0.00385502i
$941$	33.6343	−	30.2845i	1.09645	−	0.987246i	0.0964808	−	0.995335i	$-0.469241\pi$
$941$	33.6343	−	30.2845i	1.09645	−	0.987246i	0.999967	+	0.00808856i	$0.00257470\pi$
$942$	10.7284	+	4.11824i	0.349549	+	0.134179i
$943$	−0.0194094	+	0.0724368i	−0.000632057	+	0.00235887i
$944$	−2.88969	−	2.09948i	−0.0940513	−	0.0683323i
$945$	−10.5916	−	29.6512i	−0.344544	−	0.964553i
$946$	−3.94694	+	2.86762i	−0.128326	+	0.0932344i
$947$	2.86529	+	7.46435i	0.0931095	+	0.242559i	0.972224	−	0.234052i	$-0.0751985\pi$
$947$	2.86529	+	7.46435i	0.0931095	+	0.242559i	−0.879115	+	0.476611i	$0.841865\pi$
$948$	8.91106	+	13.7218i	0.289418	+	0.445664i
$949$	−2.86640	−	1.65492i	−0.0930472	−	0.0537208i
$950$	11.3315	−	17.0610i	0.367642	−	0.553530i
$951$			10.1006i			0.327535i
$952$	−4.17795	+	4.97074i	−0.135408	+	0.161102i
$953$	0.239793	−	1.51399i	0.00776765	−	0.0490430i	−0.983500	−	0.180908i	$-0.942096\pi$
$953$	0.239793	−	1.51399i	0.00776765	−	0.0490430i	0.991268	+	0.131865i	$0.0420965\pi$
$954$	−6.13884	+	13.7881i	−0.198752	+	0.446405i
$955$	34.5542	+	1.98973i	1.11815	+	0.0643860i
$956$	−4.09839	+	1.82472i	−0.132551	+	0.0590156i
$957$	9.90071	+	2.65289i	0.320044	+	0.0857556i
$958$	1.10585	+	6.98204i	0.0357283	+	0.225580i
$959$	−4.50644	+	7.48595i	−0.145520	+	0.241734i
$960$	−4.56359	+	6.21357i	−0.147289	+	0.200542i
$961$	−43.5019	+	48.3137i	−1.40329	+	1.55851i
$962$	−11.9551	−	0.626538i	−0.385447	−	0.0202004i
$963$	17.1122	+	0.896813i	0.551433	+	0.0288994i
$964$	25.0493	−	27.8201i	0.806783	−	0.896024i
$965$	0.0904578	−	17.5328i	0.00291194	−	0.564401i
$966$	1.28071	+	2.31497i	0.0412062	+	0.0744830i
$967$	−3.11543	−	19.6701i	−0.100186	−	0.632547i	−0.985774	−	0.168076i	$-0.946245\pi$
$967$	−3.11543	−	19.6701i	−0.100186	−	0.632547i	0.885588	−	0.464471i	$-0.153755\pi$
$968$	23.5513	+	6.31056i	0.756969	+	0.202829i
$969$	5.02813	−	2.23867i	0.161527	−	0.0719163i
$970$	−10.9804	+	28.1697i	−0.352560	+	0.904475i
$971$	−12.0980	+	27.1725i	−0.388242	+	0.872007i	0.608665	+	0.793427i	$0.291705\pi$
$971$	−12.0980	+	27.1725i	−0.388242	+	0.872007i	−0.996908	+	0.0785798i	$0.974961\pi$
$972$	−3.29957	+	20.8327i	−0.105834	+	0.668208i
$973$	3.98212	−	22.4751i	0.127661	−	0.720519i
$974$			0.412847i			0.0132285i
$975$	7.63851	−	8.30938i	0.244628	−	0.266113i
$976$	−2.93248	−	1.69307i	−0.0938663	−	0.0541938i
$977$	−17.4584	−	26.8835i	−0.558542	−	0.860080i	0.440752	−	0.897629i	$-0.354712\pi$
$977$	−17.4584	−	26.8835i	−0.558542	−	0.860080i	−0.999295	+	0.0375488i	$0.988045\pi$
$978$	1.09246	+	2.84595i	0.0349329	+	0.0910033i
$979$	16.8565	−	12.2469i	0.538735	−	0.391414i
$980$	−9.09871	−	19.8644i	−0.290648	−	0.634546i
$981$	−15.2332	−	11.0676i	−0.486358	−	0.353360i
$982$	1.29083	−	4.81745i	0.0411921	−	0.153731i
$983$	−36.0017	−	13.8198i	−1.14828	−	0.440782i	−0.291550	−	0.956555i	$-0.594171\pi$
$983$	−36.0017	−	13.8198i	−1.14828	−	0.440782i	−0.856725	+	0.515774i	$0.827504\pi$
$984$	−0.144235	+	0.129870i	−0.00459803	+	0.00414009i
$985$	−33.3403	−	15.0506i	−1.06231	−	0.479553i
$986$	−4.72497	+	1.53524i	−0.150474	+	0.0488919i
$987$	0.399326	−	0.384988i	0.0127107	−	0.0122543i
$988$	−6.71245	−	13.1739i	−0.213551	−	0.419118i
$989$	4.02477	+	3.62392i	0.127980	+	0.115234i
$990$	−0.854200	+	3.91916i	−0.0271482	+	0.124559i
$991$	3.12017	+	3.46530i	0.0991154	+	0.110079i	0.790662	−	0.612253i	$-0.209737\pi$
$991$	3.12017	+	3.46530i	0.0991154	+	0.110079i	−0.691546	+	0.722332i	$0.743070\pi$
$992$	−36.1001	−	44.5799i	−1.14618	−	1.41541i
$993$	5.73911	+	5.73911i	0.182125	+	0.182125i
$994$	21.7735	−	4.21366i	0.690613	−	0.133649i
$995$	−43.4065	+	42.9609i	−1.37608	+	1.36195i
$996$	−8.95976	−	3.98914i	−0.283901	−	0.126401i
$997$	−12.6622	−	10.2537i	−0.401017	−	0.324737i	0.407505	−	0.913203i	$-0.366399\pi$
$997$	−12.6622	−	10.2537i	−0.401017	−	0.324737i	−0.808522	+	0.588466i	$0.799732\pi$
$998$	4.08988	−	2.65600i	0.129463	−	0.0840743i
$999$	−20.3931	−	35.3220i	−0.645210	−	1.11754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.17.12	yes	288
5.2	odd	4		875.2.bb.a.143.12		288
5.3	odd	4		875.2.bb.b.143.7		288
5.4	even	2		875.2.bb.c.857.7		288
7.5	odd	6	inner	175.2.x.a.117.7	yes	288
25.3	odd	20	inner	175.2.x.a.3.7	✓	288
25.4	even	10		875.2.bb.a.507.12		288
25.21	even	5		875.2.bb.b.507.7		288
25.22	odd	20		875.2.bb.c.493.12		288
35.12	even	12		875.2.bb.a.768.12		288
35.19	odd	6		875.2.bb.c.607.12		288
35.33	even	12		875.2.bb.b.768.7		288
175.47	even	60		875.2.bb.c.243.7		288
175.54	odd	30		875.2.bb.a.257.12		288
175.96	odd	30		875.2.bb.b.257.7		288
175.103	even	60	inner	175.2.x.a.103.12	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.7	✓	288	25.3	odd	20	inner
175.2.x.a.17.12	yes	288	1.1	even	1	trivial
175.2.x.a.103.12	yes	288	175.103	even	60	inner
175.2.x.a.117.7	yes	288	7.5	odd	6	inner
875.2.bb.a.143.12		288	5.2	odd	4
875.2.bb.a.257.12		288	175.54	odd	30
875.2.bb.a.507.12		288	25.4	even	10
875.2.bb.a.768.12		288	35.12	even	12
875.2.bb.b.143.7		288	5.3	odd	4
875.2.bb.b.257.7		288	175.96	odd	30
875.2.bb.b.507.7		288	25.21	even	5
875.2.bb.b.768.7		288	35.33	even	12
875.2.bb.c.243.7		288	175.47	even	60
875.2.bb.c.493.12		288	25.22	odd	20
875.2.bb.c.607.12		288	35.19	odd	6
875.2.bb.c.857.7		288	5.4	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.776182 - 0.0406780i) q^{2} +(-0.706831 + 0.872864i) q^{3} +(-1.38824 + 0.145910i) q^{4} +(2.15686 + 0.589873i) q^{5} +(-0.513123 + 0.706254i) q^{6} +(2.33503 + 1.24404i) q^{7} +(-2.60695 + 0.412900i) q^{8} +(0.361454 + 1.70051i) q^{9} +(1.69811 + 0.370112i) q^{10} +(1.29854 + 0.276014i) q^{11} +(0.853891 - 1.31488i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(1.86302 + 0.870614i) q^{14} +(-2.03941 + 1.46571i) q^{15} +(0.724094 - 0.153911i) q^{16} +(0.333224 - 0.868077i) q^{17} +(0.349728 + 1.30520i) q^{18} +(0.550884 - 5.24131i) q^{19} +(-3.08031 - 0.504177i) q^{20} +(-2.73635 + 1.15884i) q^{21} +(1.01913 + 0.161415i) q^{22} +(-0.0599482 - 1.14388i) q^{23} +(1.48227 - 2.56736i) q^{24} +(4.30410 + 2.54455i) q^{25} +(-1.35285 + 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.42310 - 1.38631i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-1.52334 + 1.22061i) q^{30} +(-3.98545 - 8.95147i) q^{31} +(5.65478 - 1.51519i) q^{32} +(-1.15877 + 0.938356i) q^{33} +(0.223331 - 0.687341i) q^{34} +(4.30252 + 4.06058i) q^{35} +(-0.749906 - 2.30797i) q^{36} +(6.42719 + 4.17386i) q^{37} +(0.214381 - 4.09062i) q^{38} +(0.469333 - 2.20804i) q^{39} +(-5.86638 - 0.647200i) q^{40} +(-0.0622653 - 0.0202312i) q^{41} +(-2.07676 + 1.01078i) q^{42} +(-3.34331 + 3.34331i) q^{43} +(-1.84296 - 0.193703i) q^{44} +(-0.223477 + 3.88097i) q^{45} +(-0.0930614 - 0.885420i) q^{46} +(-0.174263 + 0.0668935i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(3.90475 + 5.80972i) q^{49} +(3.44427 + 1.79995i) q^{50} +(0.522180 + 0.904443i) q^{51} +(2.35288 - 1.52798i) q^{52} +(8.68044 + 7.02928i) q^{53} +(-3.77898 - 1.68251i) q^{54} +(2.63796 + 1.36130i) q^{55} +(-6.60097 - 2.27900i) q^{56} +(4.18557 + 4.18557i) q^{57} +(-3.36247 - 4.15230i) q^{58} +(-3.22860 - 3.58572i) q^{59} +(2.61734 - 2.33232i) q^{60} +(-3.39928 - 3.06073i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-1.27148 + 4.42040i) q^{63} +(2.91943 - 0.948580i) q^{64} +(-4.40066 + 0.911685i) q^{65} +(-0.861248 + 0.775472i) q^{66} +(-7.93020 - 3.04412i) q^{67} +(-0.335933 + 1.25372i) q^{68} +(1.04082 + 0.756203i) q^{69} +(3.50472 + 2.97673i) q^{70} +(8.72491 - 6.33902i) q^{71} +(-1.64443 - 4.28389i) q^{72} +(0.896926 + 1.38114i) q^{73} +(5.15845 + 2.97823i) q^{74} +(-5.26331 + 1.95833i) q^{75} +7.35658i q^{76} +(2.68877 + 2.25993i) q^{77} +(0.274469 - 1.73293i) q^{78} +(-4.24463 + 9.53360i) q^{79} +(1.65256 + 0.0951587i) q^{80} +(0.696236 - 0.309984i) q^{81} +(-0.0491522 - 0.0131703i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(3.62962 - 2.00801i) q^{84} +(1.23077 - 1.67576i) q^{85} +(-2.45902 + 2.73102i) q^{86} +(7.71037 + 0.404083i) q^{87} +(-3.49920 - 0.183385i) q^{88} +(10.5019 - 11.6635i) q^{89} +(-0.0155886 + 3.02143i) q^{90} +(-5.31661 - 0.0971966i) q^{91} +(0.250126 + 1.57923i) q^{92} +(10.6304 + 2.84842i) q^{93} +(-0.132539 + 0.0590102i) q^{94} +(4.27989 - 10.9798i) q^{95} +(-2.67442 + 6.00684i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(3.26713 + 4.35057i) q^{98} +2.30795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

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