LMFDB - Embedded newform 175.2.x.a.103.12

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			103.12
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.776182 + 0.0406780i) q^{2} +(-0.706831 - 0.872864i) q^{3} +(-1.38824 - 0.145910i) q^{4} +(2.15686 - 0.589873i) q^{5} +(-0.513123 - 0.706254i) q^{6} +(2.33503 - 1.24404i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(0.361454 - 1.70051i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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	0.324743	−	0.945802i	$-0.394722\pi$
$2$	0.776182	+	0.0406780i	0.548844	+	0.0287637i	0.224101	+	0.974566i	$0.428056\pi$
$3$	−0.706831	−	0.872864i	−0.408089	−	0.503948i	0.531119	−	0.847297i	$-0.321772\pi$
$3$	−0.706831	−	0.872864i	−0.408089	−	0.503948i	−0.939208	+	0.343349i	$0.888439\pi$
$4$	−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	−0.00794259	−	0.999968i	$-0.502528\pi$
$11$	1.29854	−	0.276014i	0.391525	−	0.0832213i	0.399468	+	0.916747i	$0.369195\pi$
$12$	0.853891	+	1.31488i	0.246497	+	0.379572i
$13$	−1.79077	−	0.912442i	−0.496670	−	0.253066i	0.187666	−	0.982233i	$-0.439908\pi$
$13$	−1.79077	−	0.912442i	−0.496670	−	0.253066i	−0.684336	+	0.729167i	$0.739908\pi$
$14$	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	0.968036	−	0.250813i	$-0.0806978\pi$
$17$	0.333224	+	0.868077i	0.0808186	+	0.210540i	−0.887217	+	0.461352i	$0.847364\pi$
$18$	0.349728	−	1.30520i	0.0824316	−	0.307639i
$19$	0.550884	+	5.24131i	0.126382	+	1.20244i	0.855408	+	0.517954i	$0.173306\pi$
$19$	0.550884	+	5.24131i	0.126382	+	1.20244i	−0.729027	+	0.684485i	$0.760027\pi$
$20$	−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	0.985233	+	0.171219i	$0.0547706\pi$
$23$	−0.0599482	+	1.14388i	−0.0125001	+	0.238515i	−0.997733	+	0.0672962i	$0.978563\pi$
$24$	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	0.247638	+	0.968853i	$0.420346\pi$
$29$	−4.04060	+	5.56140i	−0.750320	+	1.03273i	−0.997958	+	0.0638742i	$0.979654\pi$
$30$	−1.52334	−	1.22061i	−0.278122	−	0.222853i
$31$	−3.98545	+	8.95147i	−0.715808	+	1.60773i	0.0761073	+	0.997100i	$0.475751\pi$
$31$	−3.98545	+	8.95147i	−0.715808	+	1.60773i	−0.791915	+	0.610631i	$0.790916\pi$
$32$	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	0.105321	−	0.994438i	$-0.466413\pi$
$37$	6.42719	−	4.17386i	1.05662	−	0.686179i	0.951302	+	0.308259i	$0.0997464\pi$
$38$	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	−0.313875	−	0.949464i	$-0.601627\pi$
$41$	−0.0622653	+	0.0202312i	−0.00972421	+	0.00315959i	0.304151	+	0.952624i	$0.401627\pi$
$42$	−2.07676	−	1.01078i	−0.320452	−	0.155967i
$43$	−3.34331	−	3.34331i	−0.509850	−	0.509850i	0.404630	−	0.914480i	$-0.367400\pi$
$43$	−3.34331	−	3.34331i	−0.509850	−	0.509850i	−0.914480	+	0.404630i	$0.867400\pi$
$44$	−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	0.345625	−	0.938373i	$-0.387667\pi$
$47$	−0.174263	−	0.0668935i	−0.0254189	−	0.00975741i	−0.371044	+	0.928615i	$0.621000\pi$
$48$	−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	0.192474	−	0.981302i	$-0.438349\pi$
$53$	8.68044	−	7.02928i	1.19235	−	0.965546i	0.999876	+	0.0157564i	$0.00501564\pi$
$54$	−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	−0.915702	−	0.401859i	$-0.868364\pi$
$59$	−3.22860	+	3.58572i	−0.420327	+	0.466821i	0.495374	+	0.868680i	$0.335031\pi$
$60$	2.61734	+	2.33232i	0.337897	+	0.301101i
$61$	−3.39928	+	3.06073i	−0.435233	+	0.391886i	−0.857415	−	0.514625i	$-0.827931\pi$
$61$	−3.39928	+	3.06073i	−0.435233	+	0.391886i	0.422182	+	0.906511i	$0.361264\pi$
$62$	−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	−0.790765	−	0.612120i	$-0.790317\pi$
$67$	−7.93020	+	3.04412i	−0.968829	+	0.371899i	−0.178064	+	0.984019i	$0.556983\pi$
$68$	−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	0.969393	−	0.245513i	$-0.0789563\pi$
$71$	8.72491	+	6.33902i	1.03546	+	0.752303i	0.0660625	+	0.997815i	$0.478956\pi$
$72$	−1.64443	+	4.28389i	−0.193798	+	0.504862i
$73$	0.896926	−	1.38114i	0.104977	−	0.161651i	−0.782278	−	0.622929i	$-0.785942\pi$
$73$	0.896926	−	1.38114i	0.104977	−	0.161651i	0.887255	+	0.461279i	$0.152609\pi$
$74$	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	−0.978333	−	0.207036i	$-0.933618\pi$
$79$	−4.24463	−	9.53360i	−0.477558	−	1.07261i	0.500775	−	0.865577i	$-0.333048\pi$
$80$	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	0.873946	+	0.486022i	$0.161553\pi$
$83$	−0.978599	+	6.17863i	−0.107415	+	0.678193i	−0.981362	+	0.192170i	$0.938447\pi$
$84$	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	0.969073	+	0.246773i	$0.0793701\pi$
$89$	10.5019	+	11.6635i	1.11320	+	1.23633i	0.144125	+	0.989559i	$0.453963\pi$
$90$	−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	−0.601461	−	0.798902i	$-0.705414\pi$
$97$	−2.72136	−	17.1820i	−0.276312	−	1.74457i	0.325149	−	0.945663i	$-0.394586\pi$
$98$	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	−0.644905	−	0.764262i	$-0.723103\pi$
$101$	−3.07011	+	1.77253i	−0.305487	+	0.176373i	0.339418	+	0.940636i	$0.389770\pi$
$102$	0.442098	−	0.680771i	0.0437742	−	0.0674064i
$103$	2.28092	−	5.94199i	0.224745	−	0.585482i	−0.774123	−	0.633035i	$-0.781809\pi$
$103$	2.28092	−	5.94199i	0.224745	−	0.585482i	0.998869	+	0.0475531i	$0.0151423\pi$
$104$	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	0.972561	+	0.232647i	$0.0747386\pi$
$107$	2.55108	+	9.52075i	0.246622	+	0.920406i	−0.725939	+	0.687759i	$0.758595\pi$
$108$	6.93564	−	2.66234i	0.667382	−	0.256184i
$109$	−8.04882	−	7.24719i	−0.770937	−	0.694155i	0.186609	−	0.982434i	$-0.440250\pi$
$109$	−8.04882	−	7.24719i	−0.770937	−	0.694155i	−0.957546	+	0.288279i	$0.906917\pi$
$110$	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	−0.988002	−	0.154440i	$-0.950643\pi$
$113$	−3.00115	+	5.89008i	−0.282324	+	0.554092i	0.705678	+	0.708533i	$0.250643\pi$
$114$	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	−0.881927	−	0.471387i	$-0.843754\pi$
$127$	−8.39463	−	16.4754i	−0.744903	−	1.46195i	0.137023	−	0.990568i	$-0.456246\pi$
$128$	−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	0.656836	−	0.754033i	$-0.271894\pi$
$131$	16.6657	−	1.75164i	1.45609	−	0.153041i	0.799255	+	0.600992i	$0.205228\pi$
$132$	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	−0.996025	−	0.0890717i	$-0.971610\pi$
$137$	−0.172842	−	3.29801i	−0.0147669	−	0.281768i	0.981258	−	0.192697i	$-0.0617234\pi$
$138$	0.838630	−	0.544613i	0.0713889	−	0.0463605i
$139$	−2.66592	+	8.20486i	−0.226120	+	0.695927i	0.772055	+	0.635555i	$0.219229\pi$
$139$	−2.66592	+	8.20486i	−0.226120	+	0.695927i	−0.998176	+	0.0603721i	$0.980771\pi$
$140$	−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	0.498597	−	0.866834i	$-0.333849\pi$
$149$	−0.0342344	−	0.0197652i	−0.00280459	−	0.00161923i	−0.501402	+	0.865215i	$0.667182\pi$
$150$	−4.00563	−	1.73412i	−0.327058	−	0.141590i
$151$	4.89690	+	8.48169i	0.398504	+	0.690230i	0.993542	−	0.113468i	$-0.0361960\pi$
$151$	4.89690	+	8.48169i	0.398504	+	0.690230i	−0.595037	+	0.803698i	$0.702863\pi$
$152$	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	0.685974	+	0.727626i	$0.259376\pi$
$157$	−3.40702	+	12.7152i	−0.271910	+	1.01478i	−0.957884	+	0.287156i	$0.907290\pi$
$158$	−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	0.905274	−	0.424828i	$-0.139666\pi$
$163$	1.90187	+	2.92862i	0.148966	+	0.229387i	−0.756308	+	0.654216i	$0.772999\pi$
$164$	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	−0.626910	−	0.779092i	$-0.715681\pi$
$167$	−18.9176	−	2.99626i	−1.46389	−	0.231857i	−0.836979	+	0.547235i	$0.815681\pi$
$168$	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	−0.136833	−	0.990594i	$-0.543692\pi$
$173$	−4.95159	−	0.259502i	−0.376462	−	0.0197296i	−0.239629	+	0.970865i	$0.577026\pi$
$174$	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	−0.684424	−	0.729085i	$-0.739946\pi$
$179$	−20.1419	−	2.11700i	−1.50548	−	0.158232i	−0.821052	+	0.570853i	$0.806613\pi$
$180$	−0.256033	+	5.42033i	−0.0190835	+	0.404007i
$181$	2.67679	+	3.68429i	0.198965	+	0.273851i	0.896828	−	0.442380i	$-0.145866\pi$
$181$	2.67679	+	3.68429i	0.198965	+	0.273851i	−0.697863	+	0.716231i	$0.745866\pi$
$182$	−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	0.720016	−	0.693957i	$-0.244134\pi$
$191$	15.1405	+	3.21821i	1.09553	+	0.232861i	0.375510	+	0.926818i	$0.377468\pi$
$192$	−1.23556	−	3.21875i	−0.0891690	−	0.232293i
$193$	−2.02940	+	7.57383i	−0.146080	+	0.545176i	0.853625	+	0.520887i	$0.174399\pi$
$193$	−2.02940	+	7.57383i	−0.146080	+	0.545176i	−0.999705	+	0.0242890i	$0.992268\pi$
$194$	−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	−0.702718	−	0.711469i	$-0.748030\pi$
$197$	−16.1577	+	2.55912i	−1.15119	+	0.182330i	−0.448469	+	0.893799i	$0.648030\pi$
$198$	0.0938827	−	1.79139i	0.00667196	−	0.127308i
$199$	−13.6561	−	23.6530i	−0.968053	−	1.67672i	−0.701179	−	0.712985i	$-0.747343\pi$
$199$	−13.6561	−	23.6530i	−0.968053	−	1.67672i	−0.266874	−	0.963731i	$-0.585991\pi$
$200$	−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	−0.664437	−	0.747345i	$-0.731328\pi$
$211$	4.53761	−	13.9653i	0.312382	−	0.961413i	0.976819	−	0.214068i	$-0.0686715\pi$
$212$	−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	0.943346	+	0.331809i	$0.107659\pi$
$223$	9.81559	+	19.2642i	0.657301	+	1.29003i	−0.286046	+	0.958216i	$0.592341\pi$
$224$	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	0.255801	−	0.966729i	$-0.417661\pi$
$227$	−7.88440	−	5.12019i	−0.523306	−	0.339839i	−0.779107	+	0.626891i	$0.784327\pi$
$228$	−6.42129	+	5.19986i	−0.425260	+	0.344369i
$229$	−2.84380	+	1.26614i	−0.187923	+	0.0836689i	−0.498541	−	0.866866i	$-0.666131\pi$
$229$	−2.84380	+	1.26614i	−0.187923	+	0.0836689i	0.310618	+	0.950535i	$0.399464\pi$
$230$	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	0.370640	−	0.928777i	$-0.379138\pi$
$233$	18.3487	−	22.6587i	1.20206	−	1.48442i	0.831420	−	0.555644i	$-0.187528\pi$
$234$	−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	0.406201	−	0.913784i	$-0.366853\pi$
$239$	3.05660	+	0.993150i	0.197715	+	0.0642416i	−0.208485	+	0.978025i	$0.566853\pi$
$240$	−1.25114	−	1.37520i	−0.0807607	−	0.0887686i
$241$	−19.9300	−	17.9451i	−1.28381	−	1.15594i	−0.979074	−	0.203506i	$-0.934766\pi$
$241$	−19.9300	−	17.9451i	−1.28381	−	1.15594i	−0.304733	−	0.952438i	$-0.598567\pi$
$242$	−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	$-0.857075\pi$
$251$		−	13.7541i		−	0.868150i	0.900877	−	0.434075i	$-0.142925\pi$
$252$	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	0.0305651	−	0.999533i	$-0.490269\pi$
$257$	8.92621	−	2.39177i	0.556802	−	0.149195i	0.526237	+	0.850338i	$0.323603\pi$
$258$	−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	0.207822	−	0.978167i	$-0.433362\pi$
$263$	8.38032	−	0.439194i	0.516752	−	0.0270819i	0.308930	+	0.951085i	$0.400029\pi$
$264$	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	0.525703	−	0.850668i	$-0.323802\pi$
$269$	4.02317	+	1.79123i	0.245297	+	0.109213i	−0.280406	+	0.959882i	$0.590469\pi$
$270$	−7.15826	+	5.85805i	−0.435638	+	0.356510i
$271$	−1.39604	−	3.13556i	−0.0848035	−	0.190472i	0.866166	−	0.499756i	$-0.166577\pi$
$271$	−1.39604	−	3.13556i	−0.0848035	−	0.190472i	−0.950970	+	0.309285i	$0.899910\pi$
$272$	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	−0.689956	−	0.723851i	$-0.742370\pi$
$277$	4.19321	−	6.45697i	0.251945	−	0.387962i	0.941901	+	0.335889i	$0.109037\pi$
$278$	−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	0.179847	−	0.983695i	$-0.442440\pi$
$281$	19.6291	−	14.2614i	1.17097	−	0.850761i	0.991125	+	0.132934i	$0.0424398\pi$
$282$	0.0421749	+	0.157399i	0.00251148	+	0.00937296i
$283$	−6.76781	+	2.59792i	−0.402304	+	0.154430i	−0.551103	−	0.834437i	$-0.685793\pi$
$283$	−6.76781	+	2.59792i	−0.402304	+	0.154430i	0.148798	+	0.988868i	$0.452459\pi$
$284$	−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	−0.349529	+	0.936925i	$0.613658\pi$
$293$	−22.0206	+	22.0206i	−1.28645	+	1.28645i	−0.936925	+	0.349529i	$0.886342\pi$
$294$	−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	0.637307	−	0.770610i	$-0.280048\pi$
$307$	−2.33566	−	2.33566i	−0.133303	−	0.133303i	−0.770610	+	0.637307i	$0.780048\pi$
$308$	−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	0.999443	−	0.0333736i	$-0.0106251\pi$
$311$	1.28441	+	6.04267i	0.0728321	+	0.342648i	−0.926611	+	0.376022i	$0.877292\pi$
$312$	−0.311828	−	5.95003i	−0.0176538	−	0.336854i
$313$	9.39345	−	6.10018i	0.530949	−	0.344802i	−0.251158	−	0.967946i	$-0.580811\pi$
$313$	9.39345	−	6.10018i	0.530949	−	0.344802i	0.782107	+	0.623144i	$0.214145\pi$
$314$	−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	0.805187	−	0.593021i	$-0.202065\pi$
$317$	6.98886	+	5.65947i	0.392534	+	0.317867i	−0.412654	+	0.910888i	$0.635398\pi$
$318$	−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	0.995471	+	0.0950622i	$0.0303050\pi$
$331$	0.755353	+	7.18671i	0.0415180	+	0.395017i	−0.953953	+	0.299955i	$0.903028\pi$
$332$	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	0.682521	−	0.730866i	$-0.260884\pi$
$337$	9.03950	+	4.60585i	0.492413	+	0.250897i	−0.190108	+	0.981763i	$0.560884\pi$
$338$	−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	0.623540	−	0.781792i	$-0.285694\pi$
$347$	−5.04462	−	6.22958i	−0.270809	−	0.334422i	−0.894349	+	0.447370i	$0.852361\pi$
$348$	−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	0.412817	−	0.910814i	$-0.364545\pi$
$353$	−10.5951	−	13.0839i	−0.563923	−	0.696387i	−0.976740	+	0.214427i	$0.931211\pi$
$354$	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	0.834910	+	0.550387i	$0.185520\pi$
$359$	−2.87394	+	13.5208i	−0.151681	+	0.713602i	−0.986590	+	0.163215i	$0.947813\pi$
$360$	−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	0.923517	−	0.383557i	$-0.125301\pi$
$367$	−0.372403	−	0.970143i	−0.0194393	−	0.0506410i	−0.942957	+	0.332916i	$0.891968\pi$
$368$	−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	0.790912	+	0.611930i	$0.209606\pi$
$373$	−1.15167	+	21.9752i	−0.0596314	+	1.13783i	−0.850544	+	0.525904i	$0.823727\pi$
$374$	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	0.0492625	+	0.998786i	$0.484313\pi$
$379$	−17.8299	+	24.5408i	−0.915862	+	1.26058i	−0.965125	+	0.261790i	$0.915687\pi$
$380$	−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	0.102504	−	0.994733i	$-0.467315\pi$
$383$	−16.6188	−	13.4576i	−0.849179	−	0.687652i	−0.951683	+	0.307081i	$0.900648\pi$
$384$	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	0.938238	+	0.345992i	$0.112457\pi$
$389$	4.37542	+	20.5847i	0.221842	+	1.04369i	−0.716395	+	0.697695i	$0.754209\pi$
$390$	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	0.475457	−	0.879739i	$-0.342283\pi$
$397$	4.78454	+	1.83661i	0.240129	+	0.0921770i	−0.235327	+	0.971916i	$0.575616\pi$
$398$	−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	0.0173216	+	0.999850i	$0.494486\pi$
$401$	−17.1661	+	29.7326i	−0.857235	+	1.48477i	−0.874556	+	0.484924i	$0.838847\pi$
$402$	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	−0.131464	−	0.991321i	$-0.541968\pi$
$409$	17.5576	−	19.4997i	0.868168	−	0.964198i	0.999632	+	0.0271225i	$0.00863443\pi$
$410$	−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	0.0521248	−	0.998641i	$-0.483401\pi$
$419$	20.8379	−	15.1396i	1.01800	−	0.739617i	0.965871	+	0.259023i	$0.0834006\pi$
$420$	9.01305	+	2.18999i	0.439792	+	0.106860i
$421$	−9.53283	−	6.92601i	−0.464602	−	0.337553i	0.330732	−	0.943725i	$-0.392704\pi$
$421$	−9.53283	−	6.92601i	−0.464602	−	0.337553i	−0.795334	+	0.606172i	$0.792704\pi$
$422$	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	0.0340723	−	0.999419i	$-0.489152\pi$
$431$	−14.2385	−	6.33937i	−0.685842	−	0.305357i	−0.719914	+	0.694063i	$0.755819\pi$
$432$	−3.80556	+	1.01970i	−0.183095	+	0.0490602i
$433$	0.121416	−	0.766591i	0.00583489	−	0.0368400i	−0.984599	−	0.174827i	$-0.944063\pi$
$433$	0.121416	−	0.766591i	0.00583489	−	0.0368400i	0.990434	+	0.137987i	$0.0440633\pi$
$434$	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	0.887817	−	0.460197i	$-0.152221\pi$
$439$	7.06803	+	7.84984i	0.337339	+	0.374653i	−0.550478	+	0.834850i	$0.685555\pi$
$440$	−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	0.426064	−	0.904693i	$-0.359900\pi$
$443$	26.2546	−	7.03490i	1.24739	−	0.334238i	0.821329	+	0.570455i	$0.193233\pi$
$444$	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	$0.372346\pi$
$449$			39.0168i			1.84131i	−0.390372	+	0.920657i	$0.627654\pi$
$450$	−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	−0.953359	−	0.301840i	$-0.902399\pi$
$457$	−5.95677	−	22.2310i	−0.278646	−	1.03992i	0.674713	−	0.738080i	$-0.264268\pi$
$458$	−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	−0.282760	−	0.959191i	$-0.591250\pi$
$461$	−23.0880	−	7.50175i	−1.07532	−	0.349391i	−0.792556	+	0.609799i	$0.791250\pi$
$462$	−2.97576	−	0.739328i	−0.138445	−	0.0343967i
$463$	2.79874	−	5.49284i	0.130069	−	0.255274i	−0.816783	−	0.576945i	$-0.804245\pi$
$463$	2.79874	−	5.49284i	0.130069	−	0.255274i	0.946851	+	0.321671i	$0.104245\pi$
$464$	−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	−0.143637	−	0.989630i	$-0.545880\pi$
$467$	18.4601	−	22.7963i	0.854231	−	1.05489i	0.997868	−	0.0652571i	$-0.0207868\pi$
$468$	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	−0.951098	−	0.308890i	$-0.900043\pi$
$479$	0.950688	−	9.04519i	0.0434380	−	0.413285i	0.994536	−	0.104395i	$-0.0332908\pi$
$480$	−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	0.997927	−	0.0643504i	$-0.0204975\pi$
$487$	−0.0277991	−	0.530438i	−0.00125970	−	0.0240364i	−0.999187	+	0.0403139i	$0.987164\pi$
$488$	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	0.985777	−	0.168056i	$-0.0537489\pi$
$491$	1.98288	+	6.10267i	0.0894861	+	0.275410i	−0.896291	+	0.443466i	$0.853749\pi$
$492$	−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	0.616666	−	0.787225i	$-0.288483\pi$
$499$	5.43364	+	3.13711i	0.243243	+	0.140437i	−0.373423	+	0.927661i	$0.621816\pi$
$500$	−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	−0.265277	−	0.964172i	$-0.585463\pi$
$503$	−4.92568	+	0.780151i	−0.219625	+	0.0347852i	0.0456521	+	0.998957i	$0.485463\pi$
$504$	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	−0.310609	−	0.950538i	$-0.600533\pi$
$509$	−22.1320	−	4.70429i	−0.980982	−	0.208514i	−0.670374	+	0.742024i	$0.733866\pi$
$510$	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	0.749339	−	0.662187i	$-0.230372\pi$
$521$	30.6917	+	3.22582i	1.34463	+	0.141326i	0.595287	+	0.803513i	$0.297038\pi$
$522$	5.84564	+	7.21877i	0.255857	+	0.315957i
$523$	−30.5923	−	1.60327i	−1.33771	−	0.0701062i	−0.629990	−	0.776603i	$-0.716941\pi$
$523$	−30.5923	−	1.60327i	−1.33771	−	0.0701062i	−0.707716	+	0.706497i	$0.750274\pi$
$524$	−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	−0.723463	−	0.690363i	$-0.757451\pi$
$541$	−38.7310	−	8.23253i	−1.66518	−	0.353944i	−0.941712	+	0.336419i	$0.890784\pi$
$542$	−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	0.697932	−	0.716164i	$-0.254104\pi$
$547$	37.0235	−	5.86395i	1.58301	−	0.250724i	0.885079	+	0.465440i	$0.154104\pi$
$548$	−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	0.379915	−	0.925021i	$-0.375953\pi$
$557$	5.81572	+	1.55832i	0.246420	+	0.0660280i	−0.133495	+	0.991050i	$0.542620\pi$
$558$	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	0.803260	+	0.595628i	$0.203097\pi$
$563$	1.58169	+	30.1805i	0.0666604	+	1.27196i	−0.736600	+	0.676329i	$0.763570\pi$
$564$	−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	−0.207847	−	0.978161i	$-0.566646\pi$
$569$	−4.95634	+	0.520932i	−0.207781	+	0.0218386i	6.62580e−5		1.00000i	$0.499979\pi$
$570$	5.55844	−	8.65670i	0.232817	−	0.362589i
$571$	0.255295	−	2.42897i	0.0106837	−	0.101649i	−0.987880	−	0.155216i	$-0.950393\pi$
$571$	0.255295	−	2.42897i	0.0106837	−	0.101649i	0.998564	+	0.0535674i	$0.0170592\pi$
$572$	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	0.894081	−	0.447906i	$-0.147830\pi$
$577$	20.3829	+	13.2368i	0.848553	+	0.551057i	−0.0455274	+	0.998963i	$0.514497\pi$
$578$	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	−0.959926	−	0.280255i	$-0.909581\pi$
$587$	−4.09368	+	8.03430i	−0.168964	+	0.331611i	0.790961	+	0.611866i	$0.209581\pi$
$588$	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	0.957426	+	0.288679i	$0.0932160\pi$
$593$	6.63849	+	24.7752i	0.272610	+	1.01740i	−0.684816	+	0.728716i	$0.740117\pi$
$594$	−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	0.0549370	−	0.998490i	$-0.482504\pi$
$599$	23.1803	−	13.3832i	0.947123	−	0.546822i	0.892186	+	0.451668i	$0.149171\pi$
$600$	12.9126	+	7.27848i	0.527155	+	0.297143i
$601$			3.83116i			0.156276i	0.996943	+	0.0781382i	$0.0248975\pi$
$601$			3.83116i			0.156276i	−0.996943	+	0.0781382i	$0.975102\pi$
$602$	−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	−0.848974	−	0.528435i	$-0.822779\pi$
$607$	−32.5210	+	8.71399i	−1.31999	+	0.353690i	−0.471015	+	0.882125i	$0.656112\pi$
$608$	−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	−0.918825	−	0.394666i	$-0.870860\pi$
$613$	−44.3520	+	2.32439i	−1.79136	+	0.0938813i	−0.872537	+	0.488547i	$0.837527\pi$
$614$	−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	0.591762	+	0.806112i	$0.298432\pi$
$617$	−5.46815	+	34.5246i	−0.220140	+	1.38991i	−0.811902	+	0.583794i	$0.801568\pi$
$618$	−5.36695	+	1.43807i	−0.215890	+	0.0578476i
$619$	12.2138	+	5.43792i	0.490913	+	0.218568i	0.637237	−	0.770668i	$-0.280077\pi$
$619$	12.2138	+	5.43792i	0.490913	+	0.218568i	−0.146324	+	0.989237i	$0.546744\pi$
$620$	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	−0.342106	−	0.939662i	$-0.611140\pi$
$631$	11.1996	−	8.13699i	0.445849	−	0.323928i	0.787955	+	0.615733i	$0.211140\pi$
$632$	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	−0.773339	−	0.633993i	$-0.781415\pi$
$641$	−1.56927	+	1.74285i	−0.0619824	+	0.0688384i	0.711356	+	0.702832i	$0.248081\pi$
$642$	5.41505	−	6.68703i	0.213715	−	0.263916i
$643$	−16.5284	+	16.5284i	−0.651816	+	0.651816i	−0.953430	−	0.301614i	$-0.902475\pi$
$643$	−16.5284	+	16.5284i	−0.651816	+	0.651816i	0.301614	+	0.953430i	$0.402475\pi$
$644$	−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	−0.791507	−	0.611161i	$-0.790703\pi$
$647$	−9.11290	+	7.37948i	−0.358265	+	0.290117i	0.433242	+	0.901278i	$0.357370\pi$
$648$	−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	−0.0529133	−	0.998599i	$-0.516851\pi$
$653$	−19.4319	−	7.45920i	−0.760429	−	0.291901i	−0.707515	+	0.706698i	$0.750184\pi$
$654$	−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	0.353646	−	0.935379i	$-0.384942\pi$
$659$	30.5370	−	9.92209i	1.18955	−	0.386510i	0.835908	+	0.548870i	$0.184942\pi$
$660$	4.04247	+	2.30620i	0.157353	+	0.0897686i
$661$	2.10304	+	9.89402i	0.0817988	+	0.384833i	0.999935	−	0.0114328i	$-0.00363925\pi$
$661$	2.10304	+	9.89402i	0.0817988	+	0.384833i	−0.918136	+	0.396266i	$0.870306\pi$
$662$	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	−0.249135	−	0.968469i	$-0.580146\pi$
$673$	10.0639	−	5.12781i	0.387935	−	0.197663i	0.637070	+	0.770806i	$0.280146\pi$
$674$	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	0.856908	+	0.515469i	$0.172382\pi$
$677$	−1.27981	+	24.4201i	−0.0491869	+	0.938542i	−0.906095	+	0.423074i	$0.860951\pi$
$678$	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	0.772881	−	0.634552i	$-0.218815\pi$
$683$	−5.90842	−	15.3920i	−0.226079	−	0.588957i	−0.998960	+	0.0455944i	$0.985482\pi$
$684$	−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	−0.715287	−	0.698831i	$-0.753704\pi$
$691$	5.84621	−	27.5043i	0.222400	−	1.04631i	0.937687	−	0.347480i	$-0.112963\pi$
$692$	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	−0.0447789	+	0.998997i	$0.514258\pi$
$709$	−10.9224	+	51.3859i	−0.410200	+	1.92984i	−0.365421	+	0.930842i	$0.619075\pi$
$710$	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	0.987796	−	0.155756i	$-0.0497812\pi$
$719$	−0.289532	−	2.75471i	−0.0107977	−	0.102733i	−0.998593	+	0.0530223i	$0.983115\pi$
$720$	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	−0.352636	−	0.935761i	$-0.614715\pi$
$727$	5.31536	−	2.70831i	0.197136	−	0.100446i	0.549772	+	0.835315i	$0.314715\pi$
$728$	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	0.955306	−	0.295618i	$-0.0955255\pi$
$733$	23.4127	+	18.9592i	0.864768	+	0.700275i	−0.0905384	+	0.995893i	$0.528859\pi$
$734$	−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	−0.716989	−	0.697084i	$-0.754480\pi$
$739$	−9.39272	−	44.1893i	−0.345517	−	1.62553i	0.371472	−	0.928444i	$-0.378853\pi$
$740$	−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	0.991313	−	0.131520i	$-0.0419858\pi$
$743$	23.4363	+	23.4363i	0.859793	+	0.859793i	−0.131520	+	0.991313i	$0.541986\pi$
$744$	−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	−0.257742	−	0.966214i	$-0.582979\pi$
$751$	19.3994	−	33.6008i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836881\pi$
$752$	−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	−0.657538	−	0.753421i	$-0.728402\pi$
$757$	2.63808	−	2.63808i	0.0958825	−	0.0958825i	0.753421	+	0.657538i	$0.228402\pi$
$758$	−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	0.0701640	−	0.997535i	$-0.477648\pi$
$761$	29.5054	−	26.5668i	1.06957	−	0.963044i	0.999405	+	0.0344912i	$0.0109811\pi$
$762$	−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

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)

\(f(q)\)	\(=\)	\(q+(0.776182 + 0.0406780i) q^{2} +(-0.706831 - 0.872864i) q^{3} +(-1.38824 - 0.145910i) q^{4} +(2.15686 - 0.589873i) q^{5} +(-0.513123 - 0.706254i) q^{6} +(2.33503 - 1.24404i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(0.361454 - 1.70051i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 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

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