LMFDB - Embedded newform 150.2.l.a.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	150.53
Dual form			150.2.l.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(-1.37558 - 1.05251i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.04600 - 1.97633i) q^{5} +(-1.70348 - 0.313291i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.784450 + 2.89562i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(-1.37558 - 1.05251i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.04600 - 1.97633i) q^{5} +(-1.70348 - 0.313291i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.784450 + 2.89562i) q^{9} +(-1.82923 - 1.28605i) q^{10} +(-2.73512 - 0.888693i) q^{11} +(-1.66004 + 0.494220i) q^{12} +(1.97121 - 3.86872i) q^{13} +(0.202010 - 0.621723i) q^{14} +(-0.641245 + 3.81953i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(5.75574 + 0.911620i) q^{17} +(2.01354 + 2.22389i) q^{18} +(4.28299 + 5.89503i) q^{19} +(-2.21371 - 0.315425i) q^{20} +(-1.12238 + 0.149340i) q^{21} +(-2.84047 + 0.449885i) q^{22} +(0.316926 + 0.622003i) q^{23} +(-1.25474 + 1.19400i) q^{24} +(-2.81176 + 4.13449i) q^{25} -4.34197i q^{26} +(1.96860 - 4.80881i) q^{27} +(-0.102264 - 0.645670i) q^{28} +(2.60237 + 1.89073i) q^{29} +(1.16268 + 3.69434i) q^{30} +(-4.82678 + 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.82702 + 4.10120i) q^{33} +(5.54227 - 1.80079i) q^{34} +(-1.39707 - 0.430043i) q^{35} +(2.80370 + 1.06737i) q^{36} +(-1.93977 - 0.988365i) q^{37} +(6.49246 + 3.30807i) q^{38} +(-6.78343 + 3.24703i) q^{39} +(-2.11563 + 0.723957i) q^{40} +(6.34331 - 2.06107i) q^{41} +(-0.932251 + 0.642614i) q^{42} +(-5.08751 - 5.08751i) q^{43} +(-2.32663 + 1.69040i) q^{44} +(4.90217 - 4.57916i) q^{45} +(0.564767 + 0.410327i) q^{46} +(-0.474965 - 2.99881i) q^{47} +(-0.575917 + 1.63350i) q^{48} +6.57265i q^{49} +(-0.628281 + 4.96037i) q^{50} +(-6.95800 - 7.31198i) q^{51} +(-1.97121 - 3.86872i) q^{52} +(2.23241 - 0.353579i) q^{53} +(-0.429121 - 5.17840i) q^{54} +(1.10458 + 6.33507i) q^{55} +(-0.384246 - 0.528869i) q^{56} +(0.312969 - 12.6170i) q^{57} +(3.17710 + 0.503203i) q^{58} +(-2.66341 - 8.19714i) q^{59} +(2.71315 + 2.76384i) q^{60} +(2.77903 - 8.55298i) q^{61} +(-2.70861 + 5.31594i) q^{62} +(1.70111 + 0.975888i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-9.70777 + 0.150921i) q^{65} +(4.38080 + 2.37076i) q^{66} +(-2.22497 + 14.0479i) q^{67} +(4.12066 - 4.12066i) q^{68} +(0.218706 - 1.18918i) q^{69} +(-1.44003 + 0.251084i) q^{70} +(-7.15246 + 9.84451i) q^{71} +(2.98269 - 0.321816i) q^{72} +(0.498794 - 0.254148i) q^{73} -2.17706 q^{74} +(8.21940 - 2.72792i) q^{75} +7.28665 q^{76} +(-1.67510 + 0.853507i) q^{77} +(-4.56996 + 5.97273i) q^{78} +(6.00067 - 8.25922i) q^{79} +(-1.55637 + 1.60553i) q^{80} +(-7.76928 + 4.54294i) q^{81} +(4.71623 - 4.71623i) q^{82} +(-0.742236 + 4.68629i) q^{83} +(-0.538901 + 0.995806i) q^{84} +(-4.21885 - 12.3288i) q^{85} +(-6.84269 - 2.22332i) q^{86} +(-1.58976 - 5.33987i) q^{87} +(-1.30562 + 2.56242i) q^{88} +(-1.78693 + 5.49959i) q^{89} +(2.28898 - 6.30560i) q^{90} +(-0.877122 - 2.69950i) q^{91} +(0.689496 + 0.109205i) q^{92} +(10.3306 + 0.256256i) q^{93} +(-1.78463 - 2.45633i) q^{94} +(7.17051 - 14.6308i) q^{95} +(0.228447 + 1.71692i) q^{96} +(5.26300 - 0.833578i) q^{97} +(2.98392 + 5.85628i) q^{98} +(0.427760 - 8.61700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	−1.37558	−	1.05251i	−0.794192	−	0.607666i
$3$	−1.37558	−	1.05251i	−0.794192	−	0.607666i
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	−1.04600	−	1.97633i	−0.467786	−	0.883842i
$5$	−1.04600	−	1.97633i	−0.467786	−	0.883842i
$6$	−1.70348	−	0.313291i	−0.695443	−	0.127901i
$7$	0.462249	−	0.462249i	0.174714	−	0.174714i	−0.614333	−	0.789047i	$-0.710575\pi$
$7$	0.462249	−	0.462249i	0.174714	−	0.174714i	0.789047	+	0.614333i	$0.210575\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	0.784450	+	2.89562i	0.261483	+	0.965208i
$10$	−1.82923	−	1.28605i	−0.578453	−	0.406684i
$11$	−2.73512	−	0.888693i	−0.824669	−	0.267951i	−0.133871	−	0.990999i	$-0.542741\pi$
$11$	−2.73512	−	0.888693i	−0.824669	−	0.267951i	−0.690798	+	0.723048i	$0.742741\pi$
$12$	−1.66004	+	0.494220i	−0.479213	+	0.142669i
$13$	1.97121	−	3.86872i	0.546716	−	1.07299i	−0.438025	−	0.898963i	$-0.644322\pi$
$13$	1.97121	−	3.86872i	0.546716	−	1.07299i	0.984741	−	0.174028i	$-0.0556783\pi$
$14$	0.202010	−	0.621723i	0.0539895	−	0.166163i
$15$	−0.641245	+	3.81953i	−0.165569	+	0.986198i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	5.75574	+	0.911620i	1.39597	+	0.221100i	0.808668	−	0.588266i	$-0.200189\pi$
$17$	5.75574	+	0.911620i	1.39597	+	0.221100i	0.587305	+	0.809366i	$0.300189\pi$
$18$	2.01354	+	2.22389i	0.474595	+	0.524175i
$19$	4.28299	+	5.89503i	0.982585	+	1.35241i	0.935425	+	0.353525i	$0.115017\pi$
$19$	4.28299	+	5.89503i	0.982585	+	1.35241i	0.0471595	+	0.998887i	$0.484983\pi$
$20$	−2.21371	−	0.315425i	−0.495000	−	0.0705312i
$21$	−1.12238	+	0.149340i	−0.244924	+	0.0325886i
$22$	−2.84047	+	0.449885i	−0.605589	+	0.0959159i
$23$	0.316926	+	0.622003i	0.0660837	+	0.129697i	0.921685	−	0.387938i	$-0.126813\pi$
$23$	0.316926	+	0.622003i	0.0660837	+	0.129697i	−0.855602	+	0.517635i	$0.826813\pi$
$24$	−1.25474	+	1.19400i	−0.256123	+	0.243724i
$25$	−2.81176	+	4.13449i	−0.562353	+	0.826898i
$26$		−	4.34197i		−	0.851530i
$27$	1.96860	−	4.80881i	0.378856	−	0.925455i
$28$	−0.102264	−	0.645670i	−0.0193261	−	0.122020i
$29$	2.60237	+	1.89073i	0.483247	+	0.351100i	0.802582	−	0.596542i	$-0.203459\pi$
$29$	2.60237	+	1.89073i	0.483247	+	0.351100i	−0.319334	+	0.947642i	$0.603459\pi$
$30$	1.16268	+	3.69434i	0.212275	+	0.674492i
$31$	−4.82678	+	3.50686i	−0.866915	+	0.629850i	−0.929757	−	0.368173i	$-0.879983\pi$
$31$	−4.82678	+	3.50686i	−0.866915	+	0.629850i	0.0628427	+	0.998023i	$0.479983\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.82702	+	4.10120i	0.492121	+	0.713928i
$34$	5.54227	−	1.80079i	0.950491	−	0.308833i
$35$	−1.39707	−	0.430043i	−0.236148	−	0.0726906i
$36$	2.80370	+	1.06737i	0.467283	+	0.177895i
$37$	−1.93977	−	0.988365i	−0.318897	−	0.162486i	0.287213	−	0.957867i	$-0.407271\pi$
$37$	−1.93977	−	0.988365i	−0.318897	−	0.162486i	−0.606110	+	0.795380i	$0.707271\pi$
$38$	6.49246	+	3.30807i	1.05322	+	0.536640i
$39$	−6.78343	+	3.24703i	−1.08622	+	0.519940i
$40$	−2.11563	+	0.723957i	−0.334510	+	0.114468i
$41$	6.34331	−	2.06107i	0.990659	−	0.321884i	0.231532	−	0.972827i	$-0.425626\pi$
$41$	6.34331	−	2.06107i	0.990659	−	0.321884i	0.759127	+	0.650943i	$0.225626\pi$
$42$	−0.932251	+	0.642614i	−0.143849	+	0.0991574i
$43$	−5.08751	−	5.08751i	−0.775838	−	0.775838i	0.203282	−	0.979120i	$-0.434839\pi$
$43$	−5.08751	−	5.08751i	−0.775838	−	0.775838i	−0.979120	+	0.203282i	$0.934839\pi$
$44$	−2.32663	+	1.69040i	−0.350753	+	0.254837i
$45$	4.90217	−	4.57916i	0.730773	−	0.682621i
$46$	0.564767	+	0.410327i	0.0832703	+	0.0604994i
$47$	−0.474965	−	2.99881i	−0.0692808	−	0.437422i	−0.997809	−	0.0661599i	$-0.978925\pi$
$47$	−0.474965	−	2.99881i	−0.0692808	−	0.437422i	0.928528	−	0.371262i	$-0.121075\pi$
$48$	−0.575917	+	1.63350i	−0.0831265	+	0.235775i
$49$			6.57265i			0.938950i
$50$	−0.628281	+	4.96037i	−0.0888524	+	0.701502i
$51$	−6.95800	−	7.31198i	−0.974315	−	1.02388i
$52$	−1.97121	−	3.86872i	−0.273358	−	0.536495i
$53$	2.23241	−	0.353579i	0.306645	−	0.0485679i	−0.00121543	−	0.999999i	$-0.500387\pi$
$53$	2.23241	−	0.353579i	0.306645	−	0.0485679i	0.307861	+	0.951431i	$0.400387\pi$
$54$	−0.429121	−	5.17840i	−0.0583960	−	0.704691i
$55$	1.10458	+	6.33507i	0.148942	+	0.854220i
$56$	−0.384246	−	0.528869i	−0.0513470	−	0.0706731i
$57$	0.312969	−	12.6170i	0.0414538	−	1.67116i
$58$	3.17710	+	0.503203i	0.417174	+	0.0660738i
$59$	−2.66341	−	8.19714i	−0.346747	−	1.06718i	−0.960642	−	0.277790i	$-0.910398\pi$
$59$	−2.66341	−	8.19714i	−0.346747	−	1.06718i	0.613895	−	0.789388i	$-0.289602\pi$
$60$	2.71315	+	2.76384i	0.350266	+	0.356810i
$61$	2.77903	−	8.55298i	0.355818	−	1.09510i	−0.599715	−	0.800214i	$-0.704719\pi$
$61$	2.77903	−	8.55298i	0.355818	−	1.09510i	0.955533	−	0.294883i	$-0.0952806\pi$
$62$	−2.70861	+	5.31594i	−0.343994	+	0.675126i
$63$	1.70111	+	0.975888i	0.214320	+	0.122950i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	−9.70777	+	0.150921i	−1.20410	+	0.0187195i
$66$	4.38080	+	2.37076i	0.539239	+	0.291820i
$67$	−2.22497	+	14.0479i	−0.271823	+	1.71622i	0.353141	+	0.935570i	$0.385114\pi$
$67$	−2.22497	+	14.0479i	−0.271823	+	1.71622i	−0.624964	+	0.780654i	$0.714886\pi$
$68$	4.12066	−	4.12066i	0.499703	−	0.499703i
$69$	0.218706	−	1.18918i	0.0263291	−	0.143161i
$70$	−1.44003	+	0.251084i	−0.172117	+	0.0300103i
$71$	−7.15246	+	9.84451i	−0.848840	+	1.16833i	0.135277	+	0.990808i	$0.456808\pi$
$71$	−7.15246	+	9.84451i	−0.848840	+	1.16833i	−0.984117	+	0.177521i	$0.943192\pi$
$72$	2.98269	−	0.321816i	0.351513	−	0.0379264i
$73$	0.498794	−	0.254148i	0.0583794	−	0.0297458i	−0.424557	−	0.905401i	$-0.639570\pi$
$73$	0.498794	−	0.254148i	0.0583794	−	0.0297458i	0.482937	+	0.875655i	$0.339570\pi$
$74$	−2.17706			−0.253078
$75$	8.21940	−	2.72792i	0.949094	−	0.314993i
$76$	7.28665			0.835837
$77$	−1.67510	+	0.853507i	−0.190896	+	0.0972661i
$78$	−4.56996	+	5.97273i	−0.517446	+	0.676279i
$79$	6.00067	−	8.25922i	0.675128	−	0.929234i	−0.324734	−	0.945805i	$-0.605275\pi$
$79$	6.00067	−	8.25922i	0.675128	−	0.929234i	0.999863	+	0.0165708i	$0.00527490\pi$
$80$	−1.55637	+	1.60553i	−0.174007	+	0.179503i
$81$	−7.76928	+	4.54294i	−0.863253	+	0.504771i
$82$	4.71623	−	4.71623i	0.520820	−	0.520820i
$83$	−0.742236	+	4.68629i	−0.0814709	+	0.514387i	0.912879	+	0.408231i	$0.133854\pi$
$83$	−0.742236	+	4.68629i	−0.0814709	+	0.514387i	−0.994349	+	0.106156i	$0.966146\pi$
$84$	−0.538901	+	0.995806i	−0.0587989	+	0.108651i
$85$	−4.21885	−	12.3288i	−0.457599	−	1.33725i
$86$	−6.84269	−	2.22332i	−0.737866	−	0.239747i
$87$	−1.58976	−	5.33987i	−0.170440	−	0.572494i
$88$	−1.30562	+	2.56242i	−0.139179	+	0.273155i
$89$	−1.78693	+	5.49959i	−0.189414	+	0.582956i	−0.999996	−	0.00266864i	$-0.999151\pi$
$89$	−1.78693	+	5.49959i	−0.189414	+	0.582956i	0.810583	+	0.585624i	$0.199151\pi$
$90$	2.28898	−	6.30560i	0.241279	−	0.664669i
$91$	−0.877122	−	2.69950i	−0.0919473	−	0.282985i
$92$	0.689496	+	0.109205i	0.0718849	+	0.0113854i
$93$	10.3306	+	0.256256i	1.07124	+	0.0265725i
$94$	−1.78463	−	2.45633i	−0.184070	−	0.253351i
$95$	7.17051	−	14.6308i	0.735679	−	1.50109i
$96$	0.228447	+	1.71692i	0.0233158	+	0.175232i
$97$	5.26300	−	0.833578i	0.534377	−	0.0846370i	0.116587	−	0.993181i	$-0.462805\pi$
$97$	5.26300	−	0.833578i	0.534377	−	0.0846370i	0.417790	+	0.908544i	$0.362805\pi$
$98$	2.98392	+	5.85628i	0.301422	+	0.591573i
$99$	0.427760	−	8.61700i	0.0429915	−	0.866042i
$100$	1.69216	+	4.70495i	0.169216	+	0.470495i
$101$			12.5590i			1.24967i	0.780758	+	0.624833i	$0.214833\pi$
$101$			12.5590i			1.24967i	−0.780758	+	0.624833i	$0.785167\pi$
$102$	−9.51920	−	3.35615i	−0.942541	−	0.332309i
$103$	−0.958193	−	6.04979i	−0.0944135	−	0.596104i	−0.988851	−	0.148910i	$-0.952424\pi$
$103$	−0.958193	−	6.04979i	−0.0944135	−	0.596104i	0.894437	−	0.447194i	$-0.147576\pi$
$104$	−3.51273	−	2.55215i	−0.344451	−	0.250258i
$105$	1.46916	+	2.06199i	0.143375	+	0.201229i
$106$	1.82857	−	1.32854i	0.177607	−	0.129039i
$107$	0.411529	+	0.411529i	0.0397840	+	0.0397840i	0.726719	−	0.686935i	$-0.241044\pi$
$107$	0.411529	+	0.411529i	0.0397840	+	0.0397840i	−0.686935	+	0.726719i	$0.741044\pi$
$108$	−2.73330	−	4.41917i	−0.263011	−	0.425235i
$109$	−11.0499	+	3.59033i	−1.05839	+	0.343891i	−0.785955	−	0.618284i	$-0.787828\pi$
$109$	−11.0499	+	3.59033i	−1.05839	+	0.343891i	−0.272433	+	0.962175i	$0.587828\pi$
$110$	3.86025	+	5.14312i	0.368061	+	0.490377i
$111$	1.62806	+	3.40121i	0.154528	+	0.322828i
$112$	−0.582467	−	0.296782i	−0.0550380	−	0.0280433i
$113$	−12.6233	−	6.43189i	−1.18750	−	0.605061i	−0.255249	−	0.966875i	$-0.582158\pi$
$113$	−12.6233	−	6.43189i	−1.18750	−	0.605061i	−0.932250	+	0.361814i	$0.882158\pi$
$114$	−5.44913	−	11.3839i	−0.510358	−	1.06620i
$115$	0.897778	−	1.27697i	0.0837182	−	0.119078i
$116$	3.05927	−	0.994016i	0.284046	−	0.0922921i
$117$	12.7487	+	2.67307i	1.17862	+	0.247126i
$118$	−6.09455	−	6.09455i	−0.561048	−	0.561048i
$119$	3.08198	−	2.23919i	0.282525	−	0.205266i
$120$	3.67219	+	1.23086i	0.335224	+	0.112361i
$121$	−2.20810	−	1.60428i	−0.200736	−	0.145844i
$122$	−1.40684	−	8.88241i	−0.127369	−	0.804176i
$123$	−10.8950	−	3.84123i	−0.982372	−	0.346352i
$124$			5.96622i			0.535783i
$125$	11.1122	+	1.23229i	0.993907	+	0.110220i
$126$	1.95874	+	0.0972348i	0.174499	+	0.00866236i
$127$	6.58036	+	12.9147i	0.583912	+	1.14599i	0.974282	+	0.225334i	$0.0723474\pi$
$127$	6.58036	+	12.9147i	0.583912	+	1.14599i	−0.390369	+	0.920658i	$0.627653\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	1.64364	+	12.3529i	0.144714	+	1.08762i
$130$	−8.58117	+	4.54171i	−0.752618	+	0.398334i
$131$	3.23088	+	4.44693i	0.282283	+	0.388530i	0.926489	−	0.376323i	$-0.122812\pi$
$131$	3.23088	+	4.44693i	0.282283	+	0.388530i	−0.644205	+	0.764853i	$0.722812\pi$
$132$	4.97962	+	0.123522i	0.433421	+	0.0107512i
$133$	4.70477	+	0.745163i	0.407956	+	0.0646138i
$134$	4.39515	+	13.5269i	0.379683	+	1.16854i
$135$	−11.5629	+	1.13942i	−0.995180	+	0.0980659i
$136$	1.80079	−	5.54227i	0.154417	−	0.475246i
$137$	−9.55034	+	18.7436i	−0.815941	+	1.60137i	−0.0170834	+	0.999854i	$0.505438\pi$
$137$	−9.55034	+	18.7436i	−0.815941	+	1.60137i	−0.798858	+	0.601520i	$0.794562\pi$
$138$	−0.345010	−	1.15886i	−0.0293692	−	0.0986488i
$139$	11.0917	+	3.60392i	0.940788	+	0.305681i	0.738967	−	0.673742i	$-0.235314\pi$
$139$	11.0917	+	3.60392i	0.940788	+	0.305681i	0.201821	+	0.979422i	$0.435314\pi$
$140$	−1.16909	+	0.877479i	−0.0988061	+	0.0741605i
$141$	−2.50292	+	4.62502i	−0.210784	+	0.389497i
$142$	−1.90357	+	12.0187i	−0.159744	+	1.00858i
$143$	−8.82961	+	8.82961i	−0.738369	+	0.738369i
$144$	2.51149	−	1.64085i	0.209291	−	0.136738i
$145$	1.01463	−	7.12084i	0.0842603	−	0.591354i
$146$	0.329048	−	0.452896i	0.0272322	−	0.0374819i
$147$	6.91778	−	9.04122i	0.570569	−	0.745707i
$148$	−1.93977	+	0.988365i	−0.159449	+	0.0812431i
$149$	10.0289			0.821602			0.410801	−	0.911725i	$-0.365249\pi$
$149$	10.0289			0.821602			0.410801	+	0.911725i	$0.365249\pi$
$150$	6.08508	−	6.16212i	0.496845	−	0.503135i
$151$	17.9175			1.45811			0.729054	−	0.684456i	$-0.239960\pi$
$151$	17.9175			1.45811			0.729054	+	0.684456i	$0.239960\pi$
$152$	6.49246	−	3.30807i	0.526608	−	0.268320i
$153$	1.87538	+	17.3816i	0.151616	+	1.40522i
$154$	−1.10504	+	1.52096i	−0.0890469	+	0.122562i
$155$	11.9795	+	5.87113i	0.962218	+	0.471580i
$156$	−1.36030	+	7.39646i	−0.108911	+	0.592191i
$157$	−6.42991	+	6.42991i	−0.513163	+	0.513163i	−0.915494	−	0.402331i	$-0.868200\pi$
$157$	−6.42991	+	6.42991i	−0.513163	+	0.513163i	0.402331	+	0.915494i	$0.368200\pi$
$158$	1.59703	−	10.0833i	0.127053	−	0.802181i
$159$	−3.44301	−	1.86326i	−0.273049	−	0.147766i
$160$	−0.657842	+	2.13711i	−0.0520070	+	0.168953i
$161$	0.434019	+	0.141021i	0.0342055	+	0.0111140i
$162$	−4.86002	+	7.57497i	−0.381840	+	0.595146i
$163$	−4.21139	+	8.26532i	−0.329862	+	0.647390i	−0.995060	−	0.0992767i	$-0.968347\pi$
$163$	−4.21139	+	8.26532i	−0.329862	+	0.647390i	0.665198	+	0.746667i	$0.268347\pi$
$164$	2.06107	−	6.34331i	0.160942	−	0.495329i
$165$	5.14827	−	9.87699i	0.400792	−	0.768922i
$166$	1.46619	+	4.51248i	0.113799	+	0.350237i
$167$	5.01819	+	0.794803i	0.388319	+	0.0615037i	0.347542	−	0.937665i	$-0.387017\pi$
$167$	5.01819	+	0.794803i	0.388319	+	0.0615037i	0.0407774	+	0.999168i	$0.487017\pi$
$168$	−0.0280779	+	1.13193i	−0.00216626	+	0.0873299i
$169$	−3.44013	−	4.73493i	−0.264625	−	0.364226i
$170$	−9.35618	−	9.06972i	−0.717586	−	0.695616i
$171$	−13.7100	+	17.0263i	−1.04843	+	1.30203i
$172$	−7.10625	+	1.12552i	−0.541846	+	0.0858200i
$173$	−8.65954	−	16.9953i	−0.658373	−	1.29213i	−0.942777	−	0.333425i	$-0.891796\pi$
$173$	−8.65954	−	16.9953i	−0.658373	−	1.29213i	0.284404	−	0.958705i	$-0.408204\pi$
$174$	−3.84073	−	4.03612i	−0.291165	−	0.305978i
$175$	0.611428	+	3.21090i	0.0462196	+	0.242721i
$176$			2.87587i			0.216777i
$177$	−4.96383	+	14.0791i	−0.373104	+	1.05825i
$178$	0.904600	+	5.71142i	0.0678026	+	0.428089i
$179$	−3.24712	−	2.35917i	−0.242701	−	0.176332i	0.459785	−	0.888030i	$-0.347927\pi$
$179$	−3.24712	−	2.35917i	−0.242701	−	0.176332i	−0.702486	+	0.711698i	$0.747927\pi$
$180$	−0.823191	−	6.65750i	−0.0613570	−	0.496221i
$181$	3.30770	−	2.40319i	0.245860	−	0.178628i	−0.458030	−	0.888937i	$-0.651445\pi$
$181$	3.30770	−	2.40319i	0.245860	−	0.178628i	0.703890	+	0.710309i	$0.251445\pi$
$182$	−2.00707	−	2.00707i	−0.148774	−	0.148774i
$183$	−12.8249	+	8.84036i	−0.948042	+	0.653498i
$184$	0.663923	−	0.215722i	0.0489451	−	0.0159032i
$185$	0.0756718	+	4.86747i	0.00556350	+	0.357863i
$186$	9.32099	−	4.46168i	0.683448	−	0.327146i
$187$	−14.9325	−	7.60848i	−1.09197	−	0.556387i
$188$	−2.70527	−	1.37840i	−0.197302	−	0.100530i
$189$	−1.31288	−	3.13285i	−0.0954983	−	0.227881i
$190$	−0.253275	−	16.2915i	−0.0183745	−	1.18191i
$191$	11.5725	−	3.76012i	0.837354	−	0.272073i	0.141214	−	0.989979i	$-0.454899\pi$
$191$	11.5725	−	3.76012i	0.837354	−	0.272073i	0.696140	+	0.717906i	$0.254899\pi$
$192$	0.983013	+	1.42607i	0.0709428	+	0.102918i
$193$	−9.01719	−	9.01719i	−0.649071	−	0.649071i	0.303697	−	0.952769i	$-0.401779\pi$
$193$	−9.01719	−	9.01719i	−0.649071	−	0.649071i	−0.952769	+	0.303697i	$0.901779\pi$
$194$	4.31093	−	3.13208i	0.309507	−	0.224870i
$195$	13.5127	+	10.0099i	0.967662	+	0.716824i
$196$	5.31739	+	3.86331i	0.379813	+	0.275951i
$197$	−0.0641446	−	0.404993i	−0.00457012	−	0.0288546i	0.985298	−	0.170845i	$-0.0546498\pi$
$197$	−0.0641446	−	0.404993i	−0.00457012	−	0.0288546i	−0.989868	+	0.141990i	$0.954650\pi$
$198$	−3.53090	−	7.87201i	−0.250930	−	0.559439i
$199$		−	10.9949i		−	0.779406i	−0.920941	−	0.389703i	$-0.872578\pi$
$199$		−	10.9949i		−	0.779406i	0.920941	−	0.389703i	$-0.127422\pi$
$200$	3.64373	+	3.42392i	0.257651	+	0.242108i
$201$	17.8462	−	16.9822i	1.25877	−	1.19783i
$202$	5.70166	+	11.1901i	0.401168	+	0.787336i
$203$	2.07693	−	0.328953i	0.145772	−	0.0230880i
$204$	−10.0053	+	1.33127i	−0.700513	+	0.0932076i
$205$	−10.7085	−	10.3806i	−0.747911	−	0.725012i
$206$	−3.60030	−	4.95539i	−0.250845	−	0.345259i
$207$	−1.55247	+	1.40563i	−0.107904	+	0.0976980i
$208$	−4.28851	−	0.679234i	−0.297355	−	0.0470964i
$209$	−6.47560	−	19.9298i	−0.447927	−	1.37858i
$210$	2.24515	+	1.17026i	0.154930	+	0.0807557i
$211$	6.64735	−	20.4585i	0.457623	−	1.40842i	−0.410406	−	0.911903i	$-0.634613\pi$
$211$	6.64735	−	20.4585i	0.457623	−	1.40842i	0.868028	−	0.496515i	$-0.165387\pi$
$212$	1.02613	−	2.01389i	0.0704747	−	0.138314i
$213$	20.2002	−	6.01391i	1.38410	−	0.412066i
$214$	0.553505	+	0.179845i	0.0378368	+	0.0122939i
$215$	−4.73306	+	15.3761i	−0.322792	+	1.04864i
$216$	−4.44165	−	2.69662i	−0.302216	−	0.183482i
$217$	−0.610130	+	3.85221i	−0.0414184	+	0.261505i
$218$	−8.21555	+	8.21555i	−0.556427	+	0.556427i
$219$	−0.953626	−	0.175384i	−0.0644400	−	0.0118513i
$220$	5.77444	+	2.83003i	0.389312	+	0.190801i
$221$	14.8726	−	20.4704i	1.00044	−	1.37699i
$222$	2.99472	+	2.29138i	0.200993	+	0.153787i
$223$	5.65554	−	2.88164i	0.378723	−	0.192969i	−0.254258	−	0.967137i	$-0.581831\pi$
$223$	5.65554	−	2.88164i	0.378723	−	0.192969i	0.632981	+	0.774167i	$0.281831\pi$
$224$	−0.653718			−0.0436784
$225$	−14.1776	−	4.89851i	−0.945174	−	0.326567i
$226$	−14.1675			−0.942405
$227$	−12.5844	+	6.41208i	−0.835257	+	0.425584i	−0.818660	−	0.574278i	$-0.805283\pi$
$227$	−12.5844	+	6.41208i	−0.835257	+	0.425584i	−0.0165960	+	0.999862i	$0.505283\pi$
$228$	−10.0234	−	7.66927i	−0.663815	−	0.507910i
$229$	−8.94288	+	12.3088i	−0.590962	+	0.813389i	−0.994844	−	0.101422i	$-0.967661\pi$
$229$	−8.94288	+	12.3088i	−0.590962	+	0.813389i	0.403882	+	0.914811i	$0.367661\pi$
$230$	0.220195	−	1.54537i	0.0145192	−	0.101899i
$231$	3.20256	+	0.588991i	0.210713	+	0.0387528i
$232$	2.27455	−	2.27455i	0.149332	−	0.149332i
$233$	1.18798	−	7.50060i	0.0778271	−	0.491381i	−0.917729	−	0.397208i	$-0.869979\pi$
$233$	1.18798	−	7.50060i	0.0778271	−	0.491381i	0.995556	−	0.0941731i	$-0.0300207\pi$
$234$	12.5727	−	3.40606i	0.821904	−	0.222661i
$235$	−5.42983	+	4.07545i	−0.354203	+	0.265853i
$236$	−8.19714	−	2.66341i	−0.533589	−	0.173373i
$237$	−16.9473	+	5.04547i	−1.10085	+	0.327738i
$238$	1.72949	−	3.39432i	0.112106	−	0.220021i
$239$	3.85885	−	11.8763i	0.249608	−	0.768215i	−0.745236	−	0.666801i	$-0.767663\pi$
$239$	3.85885	−	11.8763i	0.249608	−	0.768215i	0.994844	−	0.101414i	$-0.0323367\pi$
$240$	3.83074	−	0.570439i	0.247273	−	0.0368217i
$241$	7.01360	+	21.5856i	0.451786	+	1.39045i	0.874868	+	0.484362i	$0.160948\pi$
$241$	7.01360	+	21.5856i	0.451786	+	1.39045i	−0.423082	+	0.906092i	$0.639052\pi$
$242$	−2.69576	−	0.426966i	−0.173290	−	0.0274464i
$243$	15.4688	+	1.92805i	0.992322	+	0.123684i
$244$	−5.28603	−	7.27560i	−0.338403	−	0.465772i
$245$	12.9897	−	6.87500i	0.829884	−	0.439228i
$246$	−11.4514	+	1.52368i	−0.730116	+	0.0971465i
$247$	31.2489	−	4.94934i	1.98832	−	0.314919i
$248$	2.70861	+	5.31594i	0.171997	+	0.337563i
$249$	5.95337	−	5.66517i	0.377279	−	0.359015i
$250$	10.4605	−	3.94686i	0.661581	−	0.249621i
$251$		−	8.40399i		−	0.530455i	−0.964186	−	0.265228i	$-0.914553\pi$
$251$		−	8.40399i		−	0.530455i	0.964186	−	0.265228i	$-0.0854471\pi$
$252$	1.78940	−	0.802614i	0.112721	−	0.0505599i
$253$	−0.314061	−	1.98290i	−0.0197448	−	0.124664i
$254$	11.7263	+	8.51964i	0.735773	+	0.534570i
$255$	−7.17280	+	21.3997i	−0.449178	+	1.34010i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.2293	−	21.2293i	−1.32425	−	1.32425i	−0.910303	−	0.413942i	$-0.864152\pi$
$257$	−21.2293	−	21.2293i	−1.32425	−	1.32425i	−0.413942	−	0.910303i	$-0.635848\pi$
$258$	7.07261	+	10.2604i	0.440321	+	0.638782i
$259$	−1.35353	+	0.439788i	−0.0841042	+	0.0273271i
$260$	−5.58398	+	7.94246i	−0.346304	+	0.492570i
$261$	−3.43342	+	9.01866i	−0.212523	+	0.558241i
$262$	4.89760	+	2.49545i	0.302575	+	0.154169i
$263$	−3.75527	−	1.91341i	−0.231560	−	0.117986i	0.334361	−	0.942445i	$-0.391479\pi$
$263$	−3.75527	−	1.91341i	−0.231560	−	0.117986i	−0.565921	+	0.824459i	$0.691479\pi$
$264$	4.49296	−	2.15064i	0.276522	−	0.132363i
$265$	−3.03390	−	4.04214i	−0.186371	−	0.248307i
$266$	4.53028	−	1.47198i	0.277769	−	0.0902527i
$267$	8.24643	−	5.68438i	0.504673	−	0.347879i
$268$	10.0572	+	10.0572i	0.614340	+	0.614340i
$269$	−16.4085	+	11.9215i	−1.00044	+	0.726865i	−0.962183	−	0.272402i	$-0.912182\pi$
$269$	−16.4085	+	11.9215i	−1.00044	+	0.726865i	−0.0382610	+	0.999268i	$0.512182\pi$
$270$	−9.78537	+	6.26470i	−0.595519	+	0.381258i
$271$	−5.48031	−	3.98168i	−0.332905	−	0.241870i	0.408757	−	0.912643i	$-0.365962\pi$
$271$	−5.48031	−	3.98168i	−0.332905	−	0.241870i	−0.741662	+	0.670773i	$0.765962\pi$
$272$	−0.911620	−	5.75574i	−0.0552751	−	0.348993i
$273$	−1.63470	+	4.63657i	−0.0989365	+	0.280618i
$274$			21.0364i			1.27086i
$275$	11.3648	−	8.80951i	0.685323	−	0.531234i
$276$	−0.833518	−	0.875921i	−0.0501719	−	0.0527243i
$277$	−11.1150	−	21.8145i	−0.667837	−	1.31070i	−0.937579	−	0.347772i	$-0.886938\pi$
$277$	−11.1150	−	21.8145i	−0.667837	−	1.31070i	0.269742	−	0.962933i	$-0.413062\pi$
$278$	11.5189	−	1.82442i	0.690861	−	0.109422i
$279$	−13.9409	−	11.2256i	−0.834620	−	0.672058i
$280$	−0.643299	+	1.31260i	−0.0384444	+	0.0784426i
$281$	11.8968	+	16.3745i	0.709702	+	0.976820i	0.999803	+	0.0198246i	$0.00631077\pi$
$281$	11.8968	+	16.3745i	0.709702	+	0.976820i	−0.290102	+	0.956996i	$0.593689\pi$
$282$	−0.130408	+	5.25722i	−0.00776566	+	0.313063i
$283$	−8.20158	−	1.29900i	−0.487533	−	0.0772177i	−0.0921715	−	0.995743i	$-0.529381\pi$
$283$	−8.20158	−	1.29900i	−0.487533	−	0.0772177i	−0.395362	+	0.918525i	$0.629381\pi$
$284$	3.76027	+	11.5729i	0.223131	+	0.686726i
$285$	−25.2627	+	12.5788i	−1.49643	+	0.745106i
$286$	−3.85868	+	11.8758i	−0.228168	+	0.702230i
$287$	1.97946	−	3.88491i	0.116844	−	0.229319i
$288$	1.49283	−	2.60221i	0.0879656	−	0.153336i
$289$	16.1295	+	5.24081i	0.948797	+	0.308283i
$290$	−2.32875	−	6.80535i	−0.136749	−	0.399624i
$291$	−8.11704	−	4.39270i	−0.475829	−	0.257505i
$292$	0.0875735	−	0.552918i	0.00512485	−	0.0323571i
$293$	1.20804	−	1.20804i	0.0705747	−	0.0705747i	−0.670938	−	0.741513i	$-0.734109\pi$
$293$	1.20804	−	1.20804i	0.0705747	−	0.0705747i	0.741513	+	0.670938i	$0.234109\pi$
$294$	2.05916	−	11.1964i	0.120092	−	0.652987i
$295$	−13.4143	+	13.8380i	−0.781013	+	0.805680i
$296$	−1.27964	+	1.76128i	−0.0743778	+	0.102372i
$297$	−9.65789	+	11.4032i	−0.560408	+	0.661679i
$298$	8.93584	−	4.55304i	0.517639	−	0.263750i
$299$	3.03109			0.175292
$300$	2.62431	−	8.25306i	0.151514	−	0.476491i
$301$	−4.70339			−0.271099
$302$	15.9646	−	8.13439i	0.918661	−	0.468081i
$303$	13.2185	−	17.2759i	0.759380	−	0.992475i
$304$	4.28299	−	5.89503i	0.245646	−	0.338103i
$305$	−19.8104	+	3.45414i	−1.13434	+	0.197784i
$306$	9.56205	+	14.6357i	0.546626	+	0.836667i
$307$	4.52656	−	4.52656i	0.258344	−	0.258344i	−0.566036	−	0.824380i	$-0.691524\pi$
$307$	4.52656	−	4.52656i	0.258344	−	0.258344i	0.824380	+	0.566036i	$0.191524\pi$
$308$	−0.294098	+	1.85686i	−0.0167578	+	0.105805i
$309$	−5.04939	+	9.33049i	−0.287250	+	0.530793i
$310$	13.3393	−	0.207378i	0.757620	−	0.0117783i
$311$	−32.9364	−	10.7017i	−1.86765	−	0.606838i	−0.992381	−	0.123210i	$-0.960681\pi$
$311$	−32.9364	−	10.7017i	−1.86765	−	0.606838i	−0.875274	−	0.483628i	$-0.839319\pi$
$312$	2.14589	+	7.20786i	0.121487	+	0.408065i
$313$	−11.8701	+	23.2965i	−0.670940	+	1.31679i	0.264869	+	0.964285i	$0.414671\pi$
$313$	−11.8701	+	23.2965i	−0.670940	+	1.31679i	−0.935808	+	0.352509i	$0.885329\pi$
$314$	−2.80998	+	8.64821i	−0.158576	+	0.488047i
$315$	0.149314	−	4.38273i	0.00841288	−	0.246939i
$316$	−3.15474	−	9.70929i	−0.177468	−	0.546190i
$317$	13.4990	+	2.13804i	0.758181	+	0.120084i	0.523544	−	0.851999i	$-0.324610\pi$
$317$	13.4990	+	2.13804i	0.758181	+	0.120084i	0.234638	+	0.972083i	$0.424610\pi$
$318$	−3.91365	−	0.0970796i	−0.219466	−	0.00544396i
$319$	−5.43750	−	7.48407i	−0.304441	−	0.419028i
$320$	0.384087	+	2.20283i	0.0214711	+	0.123142i
$321$	−0.132954	−	0.999229i	−0.00742075	−	0.0557715i
$322$	0.450736	−	0.0713896i	0.0251185	−	0.00397838i
$323$	19.2777	+	37.8347i	1.07264	+	2.10518i
$324$	−0.891349	+	8.95575i	−0.0495194	+	0.497542i
$325$	10.4526	+	19.0279i	0.579806	+	1.05548i
$326$			9.27639i			0.513772i
$327$	18.9789	+	6.69132i	1.04953	+	0.370031i
$328$	−1.04338	−	6.58764i	−0.0576110	−	0.363741i
$329$	−1.60575	−	1.16664i	−0.0885278	−	0.0643192i
$330$	0.103084	−	11.1377i	0.00567460	−	0.613112i
$331$	−8.55071	+	6.21245i	−0.469989	+	0.341467i	−0.797437	−	0.603402i	$-0.793811\pi$
$331$	−8.55071	+	6.21245i	−0.469989	+	0.341467i	0.327448	+	0.944869i	$0.393811\pi$
$332$	3.35501	+	3.35501i	0.184130	+	0.184130i
$333$	1.34028	−	6.39218i	0.0734467	−	0.350289i
$334$	4.83207	−	1.57004i	0.264399	−	0.0859085i
$335$	30.0906	−	10.2968i	1.64403	−	0.562577i
$336$	0.488866	+	1.02130i	0.0266698	+	0.0557165i
$337$	−28.0951	−	14.3152i	−1.53044	−	0.779796i	−0.532652	−	0.846334i	$-0.678805\pi$
$337$	−28.0951	−	14.3152i	−1.53044	−	0.779796i	−0.997784	+	0.0665380i	$0.978805\pi$
$338$	−5.21479	−	2.65707i	−0.283647	−	0.144526i
$339$	10.5947	+	22.1337i	0.575428	+	1.20214i
$340$	−12.4540	−	3.83357i	−0.675412	−	0.207904i
$341$	16.3183	−	5.30214i	0.883686	−	0.287127i
$342$	−4.48593	+	21.3947i	−0.242571	+	1.15689i
$343$	6.27394	+	6.27394i	0.338761	+	0.338761i
$344$	−5.82074	+	4.22901i	−0.313833	+	0.228013i
$345$	−2.57899	+	0.811653i	−0.138848	+	0.0436979i
$346$	−15.4314	−	11.2116i	−0.829598	−	0.602738i
$347$	2.04407	+	12.9057i	0.109731	+	0.692816i	0.979814	+	0.199911i	$0.0640652\pi$
$347$	2.04407	+	12.9057i	0.109731	+	0.692816i	−0.870083	+	0.492905i	$0.835935\pi$
$348$	−5.25448	−	1.85256i	−0.281670	−	0.0993074i
$349$		−	30.4326i		−	1.62902i	−0.580151	−	0.814509i	$-0.697007\pi$
$349$		−	30.4326i		−	1.62902i	0.580151	−	0.814509i	$-0.302993\pi$
$350$	2.00250	+	2.58335i	0.107038	+	0.138086i
$351$	−14.7234	−	17.0951i	−0.785878	−	0.912471i
$352$	1.30562	+	2.56242i	0.0695897	+	0.136577i
$353$	2.87776	−	0.455793i	0.153168	−	0.0242594i	−0.0793796	−	0.996844i	$-0.525294\pi$
$353$	2.87776	−	0.455793i	0.153168	−	0.0242594i	0.232547	+	0.972585i	$0.425294\pi$
$354$	1.96898	+	14.7981i	0.104650	+	0.786511i
$355$	26.9375	+	3.83825i	1.42969	+	0.203713i
$356$	3.39893	+	4.67823i	0.180143	+	0.247946i
$357$	−6.59628	−	0.163624i	−0.349112	−	0.00865988i
$358$	−3.96424	−	0.627874i	−0.209517	−	0.0331842i
$359$	2.44510	+	7.52523i	0.129047	+	0.397167i	0.994617	−	0.103622i	$-0.0330433\pi$
$359$	2.44510	+	7.52523i	0.129047	+	0.397167i	−0.865569	+	0.500789i	$0.833043\pi$
$360$	−3.75591	−	5.55816i	−0.197954	−	0.292941i
$361$	−10.5360	+	32.4266i	−0.554528	+	1.70666i
$362$	1.85616	−	3.64292i	0.0975577	−	0.191468i
$363$	1.34890	+	4.53086i	0.0707991	+	0.237809i
$364$	−2.69950	−	0.877122i	−0.141492	−	0.0459737i
$365$	−1.02402	−	0.719943i	−0.0535997	−	0.0376835i
$366$	−7.41360	+	13.6992i	−0.387515	+	0.716068i
$367$	3.44380	−	21.7433i	0.179765	−	1.13499i	−0.718497	−	0.695530i	$-0.755170\pi$
$367$	3.44380	−	21.7433i	0.179765	−	1.13499i	0.898262	−	0.439460i	$-0.144830\pi$
$368$	0.493624	−	0.493624i	0.0257319	−	0.0257319i
$369$	10.9441	+	16.7510i	0.569726	+	0.872024i
$370$	2.27721	+	4.30259i	0.118386	+	0.223681i
$371$	0.868488	−	1.19537i	0.0450897	−	0.0620606i
$372$	6.27950	−	8.20703i	0.325577	−	0.425515i
$373$	19.0344	−	9.69853i	0.985566	−	0.502171i	0.114545	−	0.993418i	$-0.463459\pi$
$373$	19.0344	−	9.69853i	0.985566	−	0.502171i	0.871020	+	0.491247i	$0.163459\pi$
$374$	−16.7591			−0.866593
$375$	−13.9888	−	13.3908i	−0.722377	−	0.691500i
$376$	−3.03619			−0.156580
$377$	12.4445	−	6.34081i	0.640926	−	0.326568i
$378$	−2.59207	−	2.19535i	−0.133322	−	0.112917i
$379$	−0.581554	+	0.800441i	−0.0298724	+	0.0411159i	−0.823692	−	0.567038i	$-0.808089\pi$
$379$	−0.581554	+	0.800441i	−0.0298724	+	0.0411159i	0.793820	+	0.608153i	$0.208089\pi$
$380$	−7.62185	−	14.4008i	−0.390993	−	0.738747i
$381$	4.54100	−	24.6911i	0.232642	−	1.26496i
$382$	8.60408	−	8.60408i	0.440223	−	0.440223i
$383$	1.97847	−	12.4916i	0.101095	−	0.638289i	−0.884158	−	0.467187i	$-0.845267\pi$
$383$	1.97847	−	12.4916i	0.101095	−	0.638289i	0.985253	−	0.171102i	$-0.0547326\pi$
$384$	1.52329	+	0.824362i	0.0777353	+	0.0420681i
$385$	3.43897	+	2.41778i	0.175266	+	0.123222i
$386$	−12.1281	−	3.94066i	−0.617304	−	0.200574i
$387$	10.7406	−	18.7224i	0.545976	−	0.951714i
$388$	2.41914	−	4.74782i	0.122813	−	0.241034i
$389$	−8.45598	+	26.0248i	−0.428735	+	1.31951i	0.470636	+	0.882327i	$0.344024\pi$
$389$	−8.45598	+	26.0248i	−0.428735	+	1.31951i	−0.899372	+	0.437185i	$0.855976\pi$
$390$	16.5843	+	2.78427i	0.839778	+	0.140987i
$391$	1.25712	+	3.86900i	0.0635751	+	0.195664i
$392$	6.49173	+	1.02819i	0.327882	+	0.0519314i
$393$	0.236089	−	9.51764i	0.0119091	−	0.480102i
$394$	−0.241016	−	0.331731i	−0.0121422	−	0.0167123i
$395$	−22.5996	−	3.22016i	−1.13711	−	0.162024i
$396$	−6.71987	−	5.41101i	−0.337686	−	0.271914i
$397$	3.51235	−	0.556301i	0.176280	−	0.0279199i	−0.0676706	−	0.997708i	$-0.521557\pi$
$397$	3.51235	−	0.556301i	0.176280	−	0.0279199i	0.243950	+	0.969788i	$0.421557\pi$
$398$	−4.99157	−	9.79650i	−0.250205	−	0.491054i
$399$	−5.68751	−	5.97685i	−0.284732	−	0.299217i
$400$	4.80101	+	1.39652i	0.240051	+	0.0698259i
$401$			16.6499i			0.831458i	0.909489	+	0.415729i	$0.136473\pi$
$401$			16.6499i			0.831458i	−0.909489	+	0.415729i	$0.863527\pi$
$402$	8.19128	−	23.2333i	0.408544	−	1.15877i
$403$	4.05246	+	25.5862i	0.201867	+	1.27454i
$404$	10.1604	+	7.38199i	0.505501	+	0.367268i
$405$	17.1050	+	10.6027i	0.849956	+	0.526854i
$406$	1.70122	−	1.23601i	0.0844299	−	0.0613419i
$407$	4.42716	+	4.42716i	0.219446	+	0.219446i
$408$	−8.31043	+	5.72849i	−0.411427	+	0.283603i
$409$	−4.09420	+	1.33029i	−0.202445	+	0.0657784i	−0.408484	−	0.912765i	$-0.633943\pi$
$409$	−4.09420	+	1.33029i	−0.202445	+	0.0657784i	0.206039	+	0.978544i	$0.433943\pi$
$410$	−14.2540	−	4.38764i	−0.703955	−	0.216690i
$411$	32.8651	−	15.7315i	1.62112	−	0.775979i
$412$	−5.45760	−	2.78078i	−0.268876	−	0.136999i
$413$	−5.02028	−	2.55796i	−0.247032	−	0.125869i
$414$	−0.745122	+	1.95723i	−0.0366207	+	0.0961928i
$415$	10.0380	−	3.43496i	0.492748	−	0.168616i
$416$	−4.12946	+	1.34174i	−0.202463	+	0.0657843i
$417$	−11.4644	−	16.6316i	−0.561415	−	0.814454i
$418$	−14.8178	−	14.8178i	−0.724761	−	0.724761i
$419$	−5.84455	+	4.24631i	−0.285525	+	0.207446i	−0.721324	−	0.692598i	$-0.756466\pi$
$419$	−5.84455	+	4.24631i	−0.285525	+	0.207446i	0.435799	+	0.900044i	$0.356466\pi$
$420$	2.53173	+	0.0234322i	0.123536	+	0.00114338i
$421$	−11.7630	−	8.54631i	−0.573293	−	0.416521i	0.263007	−	0.964794i	$-0.415286\pi$
$421$	−11.7630	−	8.54631i	−0.573293	−	0.416521i	−0.836300	+	0.548272i	$0.815286\pi$
$422$	−3.36511	−	21.2464i	−0.163811	−	1.03426i
$423$	8.31084	−	3.72774i	0.404087	−	0.181249i
$424$		−	2.26024i		−	0.109767i
$425$	−19.9529	+	21.2338i	−0.967856	+	1.02999i
$426$	15.2683	−	14.5291i	0.739750	−	0.703939i
$427$	−2.66900	−	5.23821i	−0.129162	−	0.253495i
$428$	0.574824	−	0.0910432i	0.0277852	−	0.00440074i
$429$	21.4391	−	2.85260i	1.03509	−	0.137725i
$430$	2.76344	+	15.8490i	0.133265	+	0.764307i
$431$	−2.43967	−	3.35792i	−0.117515	−	0.161745i	0.746207	−	0.665714i	$-0.231873\pi$
$431$	−2.43967	−	3.35792i	−0.117515	−	0.161745i	−0.863722	+	0.503968i	$0.831873\pi$
$432$	−5.18178	−	0.386242i	−0.249308	−	0.0185831i
$433$	28.8682	+	4.57227i	1.38732	+	0.219729i	0.805020	−	0.593248i	$-0.202154\pi$
$433$	28.8682	+	4.57227i	1.38732	+	0.219729i	0.582296	+	0.812977i	$0.302154\pi$
$434$	1.20524	+	3.70934i	0.0578532	+	0.178054i
$435$	−8.89046	+	8.72740i	−0.426265	+	0.418447i
$436$	−3.59033	+	11.0499i	−0.171945	+	0.529194i
$437$	−2.30933	+	4.53232i	−0.110470	+	0.216810i
$438$	−0.929309	+	0.276669i	−0.0444041	+	0.0132198i
$439$	10.7432	+	3.49067i	0.512744	+	0.166601i	0.553950	−	0.832550i	$-0.313120\pi$
$439$	10.7432	+	3.49067i	0.512744	+	0.166601i	−0.0412056	+	0.999151i	$0.513120\pi$
$440$	6.42987	−	0.0999616i	0.306532	−	0.00476548i
$441$	−19.0319	+	5.15592i	−0.906282	+	0.245520i
$442$	3.95823	−	24.9913i	0.188274	−	1.18871i
$443$	−12.3286	+	12.3286i	−0.585749	+	0.585749i	−0.936477	−	0.350728i	$-0.885934\pi$
$443$	−12.3286	+	12.3286i	−0.585749	+	0.585749i	0.350728	+	0.936477i	$0.385934\pi$
$444$	3.70858	+	0.682054i	0.176001	+	0.0323689i
$445$	12.7381	−	2.22102i	0.603846	−	0.105287i
$446$	3.73089	−	5.13513i	0.176663	−	0.243155i
$447$	−13.7956	−	10.5555i	−0.652510	−	0.499260i
$448$	−0.582467	+	0.296782i	−0.0275190	+	0.0140216i
$449$	−11.4060			−0.538284			−0.269142	−	0.963101i	$-0.586740\pi$
$449$	−11.4060			−0.538284			−0.269142	+	0.963101i	$0.586740\pi$
$450$	−14.8562	+	2.07189i	−0.700329	+	0.0976700i
$451$	−19.1813			−0.903214
$452$	−12.6233	+	6.43189i	−0.593750	+	0.302531i
$453$	−24.6470	−	18.8584i	−1.15802	−	0.886043i
$454$	−8.30177	+	11.4264i	−0.389621	+	0.536268i
$455$	−4.41764	+	4.55717i	−0.207102	+	0.213643i
$456$	−12.4127	−	2.28285i	−0.581277	−	0.106904i
$457$	−4.54539	+	4.54539i	−0.212624	+	0.212624i	−0.805381	−	0.592757i	$-0.798039\pi$
$457$	−4.54539	+	4.54539i	−0.212624	+	0.212624i	0.592757	+	0.805381i	$0.298039\pi$
$458$	−2.38008	+	15.0272i	−0.111214	+	0.702176i
$459$	15.7145	−	25.8836i	0.733492	−	1.20814i
$460$	−0.505387	−	1.47690i	−0.0235638	−	0.0688608i
$461$	−18.3653	−	5.96726i	−0.855359	−	0.277923i	−0.151670	−	0.988431i	$-0.548465\pi$
$461$	−18.3653	−	5.96726i	−0.855359	−	0.277923i	−0.703689	+	0.710508i	$0.748465\pi$
$462$	3.12090	−	0.929138i	0.145197	−	0.0432274i
$463$	2.03171	−	3.98746i	0.0944216	−	0.185313i	−0.838965	−	0.544186i	$-0.816839\pi$
$463$	2.03171	−	3.98746i	0.0944216	−	0.185313i	0.933387	+	0.358873i	$0.116839\pi$
$464$	0.994016	−	3.05927i	0.0461460	−	0.142023i
$465$	−10.2994	−	20.6848i	−0.477623	−	0.959233i
$466$	−2.34671	−	7.22242i	−0.108709	−	0.334572i
$467$	−1.74215	−	0.275929i	−0.0806170	−	0.0127685i	0.115996	−	0.993250i	$-0.462994\pi$
$467$	−1.74215	−	0.275929i	−0.0806170	−	0.0127685i	−0.196613	+	0.980481i	$0.562994\pi$
$468$	9.65605	−	8.74271i	0.446351	−	0.404132i
$469$	5.46513	+	7.52211i	0.252356	+	0.347339i
$470$	−2.98780	+	6.09634i	−0.137817	+	0.281203i
$471$	15.6124	−	2.07733i	0.719382	−	0.0957183i
$472$	−8.51287	+	1.34831i	−0.391837	+	0.0620609i
$473$	9.39370	+	18.4362i	0.431923	+	0.847696i
$474$	−12.8096	+	12.1895i	−0.588363	+	0.559881i
$475$	−36.4157	+	1.13254i	−1.67087	+	0.0519646i
$476$		−	3.80954i		−	0.174610i
$477$	2.77505	+	6.18686i	0.127061	+	0.283277i
$478$	−1.95347	−	12.3338i	−0.0893498	−	0.564133i
$479$	−13.7743	−	10.0076i	−0.629363	−	0.457259i	0.226817	−	0.973937i	$-0.427168\pi$
$479$	−13.7743	−	10.0076i	−0.629363	−	0.457259i	−0.856179	+	0.516679i	$0.827168\pi$
$480$	3.15424	−	2.24739i	0.143971	−	0.102579i
$481$	−7.64742	+	5.55617i	−0.348692	+	0.253340i
$482$	16.0488	+	16.0488i	0.731005	+	0.731005i
$483$	−0.448602	−	0.650795i	−0.0204121	−	0.0296122i
$484$	−2.59578	+	0.843419i	−0.117990	+	0.0383372i
$485$	−7.15253	−	9.52951i	−0.324780	−	0.432713i
$486$	14.6581	−	5.30477i	0.664904	−	0.240629i
$487$	25.0891	+	12.7835i	1.13690	+	0.579277i	0.918043	−	0.396481i	$-0.129769\pi$
$487$	25.0891	+	12.7835i	1.13690	+	0.579277i	0.218852	+	0.975758i	$0.429769\pi$
$488$	−8.01294	−	4.08280i	−0.362729	−	0.184820i
$489$	14.4924	−	6.93710i	0.655371	−	0.313706i
$490$	8.45275	−	12.0229i	0.381856	−	0.543139i
$491$	−8.69557	+	2.82536i	−0.392426	+	0.127507i	−0.498582	−	0.866843i	$-0.666146\pi$
$491$	−8.69557	+	2.82536i	−0.392426	+	0.127507i	0.106156	+	0.994349i	$0.466146\pi$
$492$	−9.51156	+	6.55645i	−0.428814	+	0.295588i
$493$	13.2549	+	13.2549i	0.596972	+	0.596972i
$494$	25.5960	−	18.5966i	1.15162	−	0.836701i
$495$	−17.4775	+	8.16800i	−0.785555	+	0.367124i
$496$	4.82678	+	3.50686i	0.216729	+	0.157463i
$497$	1.24440	+	7.85683i	0.0558189	+	0.352427i
$498$	2.73256	−	7.75047i	0.122449	−	0.347307i
$499$			12.9235i			0.578536i	0.957248	+	0.289268i	$0.0934119\pi$
$499$			12.9235i			0.578536i	−0.957248	+	0.289268i	$0.906588\pi$
$500$	7.52855	−	8.26565i	0.336687	−	0.369651i
$501$	−6.06639	−	6.37500i	−0.271026	−	0.284814i
$502$	−3.81533	−	7.48801i	−0.170287	−	0.334206i
$503$	22.2567	−	3.52512i	0.992379	−	0.157177i	0.360928	−	0.932594i	$-0.382460\pi$
$503$	22.2567	−	3.52512i	0.992379	−	0.157177i	0.631450	+	0.775416i	$0.282460\pi$
$504$	1.22999	−	1.52750i	0.0547879	−	0.0680404i
$505$	24.8207	−	13.1367i	1.10451	−	0.584576i
$506$	−1.18005	−	1.62420i	−0.0524595	−	0.0722044i
$507$	−0.251380	+	10.1341i	−0.0111642	+	0.450069i
$508$	14.3160	+	2.26744i	0.635171	+	0.100601i
$509$	1.15005	+	3.53949i	0.0509750	+	0.156885i	0.973304	−	0.229522i	$-0.0737162\pi$
$509$	1.15005	+	3.53949i	0.0509750	+	0.156885i	−0.922329	+	0.386407i	$0.873716\pi$
$510$	3.32423	+	22.3236i	0.147199	+	0.988506i
$511$	0.113087	−	0.348047i	0.00500268	−	0.0153967i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	36.7795	−	8.99114i	1.62386	−	0.396969i
$514$	−28.5533	−	9.27753i	−1.25943	−	0.409214i
$515$	−10.9541	+	8.22179i	−0.482696	+	0.362296i
$516$	10.9598	+	5.93114i	0.482480	+	0.261104i
$517$	−1.36594	+	8.62420i	−0.0600739	+	0.379292i
$518$	−1.00634	+	1.00634i	−0.0442162	+	0.0442162i
$519$	−5.97581	+	32.4927i	−0.262309	+	1.42627i
$520$	−1.36957	+	9.61186i	−0.0600594	+	0.421508i
$521$	25.0327	−	34.4546i	1.09670	−	1.50948i	0.257021	−	0.966406i	$-0.417259\pi$
$521$	25.0327	−	34.4546i	1.09670	−	1.50948i	0.839683	−	0.543077i	$-0.182741\pi$
$522$	1.03519	+	9.59442i	0.0453089	+	0.419937i
$523$	−19.8847	+	10.1317i	−0.869495	+	0.443030i	−0.831028	−	0.556230i	$-0.812247\pi$
$523$	−19.8847	+	10.1317i	−0.869495	+	0.443030i	−0.0384667	+	0.999260i	$0.512247\pi$
$524$	5.49670			0.240125
$525$	2.53843	−	5.06038i	0.110786	−	0.220853i
$526$	−4.21464			−0.183767
$527$	−30.9786	+	15.7844i	−1.34945	+	0.687579i
$528$	3.02688	−	3.95600i	0.131728	−	0.172163i
$529$	13.2326	−	18.2131i	0.575331	−	0.791875i
$530$	−4.53831	−	2.22421i	−0.197132	−	0.0966136i
$531$	21.6465	−	14.1425i	0.939380	−	0.613732i
$532$	3.36825	−	3.36825i	0.146032	−	0.146032i
$533$	4.53032	−	28.6033i	0.196230	−	1.23895i
$534$	4.76697	−	8.80862i	0.206287	−	0.381186i
$535$	0.382857	−	1.24378i	0.0165524	−	0.0537731i
$536$	13.5269	+	4.39515i	0.584272	+	0.189842i
$537$	1.98363	+	6.66285i	0.0855999	+	0.287523i
$538$	−9.20785	+	18.0714i	−0.396979	+	0.779114i
$539$	5.84107	−	17.9770i	0.251593	−	0.774323i
$540$	−5.87472	+	10.0244i	−0.252808	+	0.431380i
$541$	0.576378	+	1.77391i	0.0247804	+	0.0762663i	0.962682	−	0.270635i	$-0.0872338\pi$
$541$	0.576378	+	1.77391i	0.0247804	+	0.0762663i	−0.937902	+	0.346902i	$0.887234\pi$
$542$	−6.69064	−	1.05969i	−0.287387	−	0.0455177i
$543$	−7.07940	−	0.175607i	−0.303806	−	0.00753604i
$544$	−3.42531	−	4.71454i	−0.146859	−	0.202134i
$545$	18.6539	+	18.0827i	0.799044	+	0.774580i
$546$	0.648429	+	4.87335i	0.0277502	+	0.208560i
$547$	−24.0199	+	3.80438i	−1.02702	+	0.162663i	−0.647138	−	0.762373i	$-0.724034\pi$
$547$	−24.0199	+	3.80438i	−1.02702	+	0.162663i	−0.379878	+	0.925036i	$0.624034\pi$
$548$	9.55034	+	18.7436i	0.407970	+	0.800687i
$549$	26.9462	+	1.33765i	1.15004	+	0.0570894i
$550$	6.12667	−	13.0088i	0.261242	−	0.554699i
$551$			23.4390i			0.998535i
$552$	−1.14033	−	0.402042i	−0.0485357	−	0.0171121i
$553$	−1.04401	−	6.59162i	−0.0443958	−	0.280304i
$554$	−19.8071	−	14.3907i	−0.841524	−	0.611403i
$555$	5.01896	−	6.77524i	0.213043	−	0.287593i
$556$	9.43519	−	6.85506i	0.400141	−	0.290720i
$557$	18.2820	+	18.2820i	0.774632	+	0.774632i	0.978912	−	0.204281i	$-0.0654855\pi$
$557$	18.2820	+	18.2820i	0.774632	+	0.774632i	−0.204281	+	0.978912i	$0.565485\pi$
$558$	−17.5177	−	3.67302i	−0.741585	−	0.155491i
$559$	−29.7107	+	9.65360i	−1.25663	+	0.408304i
$560$	0.0227224	+	1.46158i	0.000960197	+	0.0617631i
$561$	12.5328	+	26.1826i	0.529137	+	1.10543i
$562$	18.0340	+	9.18876i	0.760717	+	0.387604i
$563$	−0.869364	−	0.442963i	−0.0366393	−	0.0186687i	0.435575	−	0.900153i	$-0.356545\pi$
$563$	−0.869364	−	0.442963i	−0.0366393	−	0.0186687i	−0.472214	+	0.881484i	$0.656545\pi$
$564$	2.27053	+	4.74342i	0.0956068	+	0.199734i
$565$	0.492442	+	31.6756i	0.0207172	+	1.33260i
$566$	−7.89740	+	2.56602i	−0.331952	+	0.107858i
$567$	−1.49137	+	5.69131i	−0.0626316	+	0.239012i
$568$	8.60442	+	8.60442i	0.361033	+	0.361033i
$569$	22.6112	−	16.4280i	0.947909	−	0.688696i	−0.00240243	−	0.999997i	$-0.500765\pi$
$569$	22.6112	−	16.4280i	0.947909	−	0.688696i	0.950311	+	0.311301i	$0.100765\pi$
$570$	−16.7985	+	22.6768i	−0.703613	+	0.949828i
$571$	−4.29121	−	3.11775i	−0.179582	−	0.130474i	0.494363	−	0.869256i	$-0.335401\pi$
$571$	−4.29121	−	3.11775i	−0.179582	−	0.130474i	−0.673945	+	0.738782i	$0.735401\pi$
$572$	1.95339	+	12.3332i	0.0816753	+	0.515678i
$573$	−19.8764	−	7.00776i	−0.830349	−	0.292754i
$574$		−	4.36014i		−	0.181989i
$575$	−3.46278	−	0.438597i	−0.144408	−	0.0182908i
$576$	0.148741	−	2.99631i	0.00619754	−	0.124846i
$577$	−3.71857	−	7.29810i	−0.154806	−	0.303824i	0.800558	−	0.599255i	$-0.204537\pi$
$577$	−3.71857	−	7.29810i	−0.154806	−	0.303824i	−0.955364	+	0.295432i	$0.904537\pi$
$578$	16.7508	−	2.65307i	0.696742	−	0.110353i
$579$	2.91321	+	21.8946i	0.121069	+	0.909907i
$580$	−5.16450	−	5.00638i	−0.214444	−	0.207879i
$581$	1.82313	+	2.50933i	0.0756364	+	0.104105i
$582$	−9.22658	−	0.228869i	−0.382454	−	0.00948694i
$583$	−6.42013	−	1.01685i	−0.265895	−	0.0421136i
$584$	−0.172991	−	0.532411i	−0.00715841	−	0.0220313i
$585$	−8.05227	−	27.9917i	−0.332920	−	1.15731i
$586$	0.527935	−	1.62482i	0.0218088	−	0.0671205i
$587$	15.9900	−	31.3821i	0.659978	−	1.29528i	−0.281939	−	0.959432i	$-0.590977\pi$
$587$	15.9900	−	31.3821i	0.659978	−	1.29528i	0.941917	−	0.335847i	$-0.109023\pi$
$588$	−3.24833	−	10.9109i	−0.133959	−	0.449958i
$589$	−41.3460	−	13.4341i	−1.70363	−	0.553544i
$590$	−5.66993	+	18.4197i	−0.233427	+	0.758329i
$591$	−0.338023	+	0.624614i	−0.0139044	+	0.0256932i
$592$	−0.340567	+	2.15026i	−0.0139972	+	0.0883750i
$593$	2.52481	−	2.52481i	0.103681	−	0.103681i	−0.653363	−	0.757045i	$-0.726643\pi$
$593$	2.52481	−	2.52481i	0.103681	−	0.103681i	0.757045	+	0.653363i	$0.226643\pi$
$594$	−3.42831	+	14.5449i	−0.140665	+	0.596784i
$595$	−7.64913	−	3.74881i	−0.313584	−	0.153686i
$596$	5.89486	−	8.11358i	0.241463	−	0.332345i
$597$	−11.5722	+	15.1243i	−0.473619	+	0.618998i
$598$	2.70072	−	1.37608i	0.110441	−	0.0562723i
$599$	39.4333			1.61120			0.805600	−	0.592460i	$-0.201843\pi$
$599$	39.4333			1.61120			0.805600	+	0.592460i	$0.201843\pi$
$600$	−1.40854	−	8.54494i	−0.0575033	−	0.348846i
$601$	28.0191			1.14292			0.571462	−	0.820629i	$-0.306376\pi$
$601$	28.0191			1.14292			0.571462	+	0.820629i	$0.306376\pi$
$602$	−4.19075	+	2.13529i	−0.170802	+	0.0870281i
$603$	−42.4228	+	4.57720i	−1.72759	+	0.186398i
$604$	10.5317	−	14.4956i	0.428527	−	0.589817i
$605$	−0.860909	+	6.04201i	−0.0350009	+	0.245643i
$606$	3.93462	−	21.3940i	0.159833	−	0.869072i
$607$	−3.59236	+	3.59236i	−0.145809	+	0.145809i	−0.776243	−	0.630434i	$-0.782877\pi$
$607$	−3.59236	+	3.59236i	−0.145809	+	0.145809i	0.630434	+	0.776243i	$0.282877\pi$
$608$	1.13988	−	7.19694i	0.0462284	−	0.291875i
$609$	−3.20321	−	1.73348i	−0.129801	−	0.0702443i
$610$	−16.0830	+	12.0714i	−0.651183	+	0.488756i
$611$	−12.5378	−	4.07379i	−0.507226	−	0.164808i
$612$	15.1643	+	8.69942i	0.612981	+	0.351653i
$613$	6.96688	−	13.6733i	0.281390	−	0.552258i	−0.706445	−	0.707768i	$-0.749702\pi$
$613$	6.96688	−	13.6733i	0.281390	−	0.552258i	0.987834	+	0.155510i	$0.0497021\pi$
$614$	1.97818	−	6.08821i	0.0798328	−	0.245700i
$615$	3.80469	+	25.5501i	0.153420	+	1.03028i
$616$	0.580955	+	1.78800i	0.0234074	+	0.0720404i
$617$	−7.10625	−	1.12552i	−0.286087	−	0.0453117i	0.0117417	−	0.999931i	$-0.496262\pi$
$617$	−7.10625	−	1.12552i	−0.286087	−	0.0453117i	−0.297829	+	0.954619i	$0.596262\pi$
$618$	−0.263084	+	10.6059i	−0.0105828	+	0.426632i
$619$	−7.42133	−	10.2146i	−0.298288	−	0.410559i	0.633396	−	0.773828i	$-0.281661\pi$
$619$	−7.42133	−	10.2146i	−0.298288	−	0.410559i	−0.931684	+	0.363269i	$0.881661\pi$
$620$	11.7912	−	6.24068i	0.473547	−	0.250632i
$621$	3.61499	−	0.299565i	0.145065	−	0.0120211i
$622$	−34.2051	+	5.41755i	−1.37150	+	0.217224i
$623$	1.71618	+	3.36818i	0.0687571	+	0.134943i
$624$	5.18430	+	5.44804i	0.207538	+	0.218096i
$625$	−9.18798	−	23.2504i	−0.367519	−	0.930016i
$626$			26.1462i			1.04501i
$627$	−12.0686	+	34.2308i	−0.481975	+	1.36704i
$628$	1.42250	+	8.98132i	0.0567640	+	0.358394i
$629$	−10.2638	−	7.45711i	−0.409246	−	0.297334i
$630$	−1.85668	−	3.97283i	−0.0739719	−	0.158281i
$631$	−2.09574	+	1.52265i	−0.0834301	+	0.0606155i	−0.628718	−	0.777633i	$-0.716420\pi$
$631$	−2.09574	+	1.52265i	−0.0834301	+	0.0606155i	0.545288	+	0.838249i	$0.316420\pi$
$632$	−7.21882	−	7.21882i	−0.287149	−	0.287149i
$633$	−30.6767	+	21.1459i	−1.21929	+	0.840473i
$634$	12.9984	−	4.22343i	0.516231	−	0.167734i
$635$	18.6406	−	26.5137i	0.739730	−	1.05217i
$636$	−3.53116	+	1.69026i	−0.140019	+	0.0670231i
$637$	25.4278	+	12.9561i	1.00748	+	0.513339i
$638$	−8.24255	−	4.19979i	−0.326326	−	0.166271i
$639$	−34.1167	−	12.9883i	−1.34964	−	0.513809i
$640$	1.34229	+	1.78837i	0.0530586	+	0.0706914i
$641$	3.49095	−	1.13428i	0.137884	−	0.0448012i	−0.239262	−	0.970955i	$-0.576905\pi$
$641$	3.49095	−	1.13428i	0.137884	−	0.0448012i	0.377146	+	0.926154i	$0.376905\pi$
$642$	−0.572103	−	0.829960i	−0.0225791	−	0.0327559i
$643$	9.94703	+	9.94703i	0.392273	+	0.392273i	0.875497	−	0.483224i	$-0.160534\pi$
$643$	9.94703	+	9.94703i	0.392273	+	0.392273i	−0.483224	+	0.875497i	$0.660534\pi$
$644$	0.369198	−	0.268238i	0.0145485	−	0.0105701i
$645$	22.6942	−	16.1696i	0.893585	−	0.636675i
$646$	34.3532	+	24.9591i	1.35161	+	0.982001i
$647$	0.617590	+	3.89931i	0.0242800	+	0.153298i	0.996850	−	0.0793138i	$-0.0252729\pi$
$647$	0.617590	+	3.89931i	0.0242800	+	0.153298i	−0.972570	+	0.232612i	$0.925273\pi$
$648$	3.27163	+	8.38430i	0.128522	+	0.329366i
$649$			24.7871i			0.972979i
$650$	17.9518	+	12.2086i	0.704128	+	0.478860i
$651$	4.89377	−	4.65686i	0.191802	−	0.182517i
$652$	4.21139	+	8.26532i	0.164931	+	0.323695i
$653$	−14.3859	+	2.27850i	−0.562962	+	0.0891644i	−0.431428	−	0.902147i	$-0.641990\pi$
$653$	−14.3859	+	2.27850i	−0.562962	+	0.0891644i	−0.131534	+	0.991312i	$0.541990\pi$
$654$	19.9481	−	2.65422i	0.780033	−	0.103788i
$655$	5.40909	−	11.0368i	0.211351	−	0.431243i
$656$	−3.92038	−	5.39594i	−0.153065	−	0.210676i
$657$	1.12720	+	1.24495i	0.0439761	+	0.0485703i
$658$	−1.96038	−	0.310493i	−0.0764235	−	0.0121043i
$659$	−4.21526	−	12.9732i	−0.164203	−	0.505365i	0.834774	−	0.550593i	$-0.185598\pi$
$659$	−4.21526	−	12.9732i	−0.164203	−	0.505365i	−0.998977	+	0.0452283i	$0.985598\pi$
$660$	−4.96457	−	9.97059i	−0.193246	−	0.388105i
$661$	−2.48143	+	7.63705i	−0.0965164	+	0.297047i	−0.987646	−	0.156702i	$-0.949914\pi$
$661$	−2.48143	+	7.63705i	−0.0965164	+	0.297047i	0.891130	+	0.453749i	$0.149914\pi$
$662$	−4.79834	+	9.41728i	−0.186493	+	0.366013i
$663$	−42.0037	+	12.5051i	−1.63129	+	0.485659i
$664$	4.51248	+	1.46619i	0.175118	+	0.0568994i
$665$	−3.44851	−	10.0776i	−0.133728	−	0.390794i
$666$	−1.70779	−	6.30395i	−0.0661757	−	0.244273i
$667$	−0.351281	+	2.21790i	−0.0136017	+	0.0858775i
$668$	3.59263	−	3.59263i	0.139003	−	0.139003i
$669$	−10.8126	−	1.98857i	−0.418040	−	0.0768828i
$670$	22.1363	−	22.8354i	0.855198	−	0.882209i
$671$	−15.2019	+	20.9237i	−0.586865	+	0.807750i
$672$	0.899243	+	0.688045i	0.0346891	+	0.0265419i
$673$	−24.0809	+	12.2698i	−0.928251	+	0.472967i	−0.851660	−	0.524095i	$-0.824404\pi$
$673$	−24.0809	+	12.2698i	−0.928251	+	0.472967i	−0.0765912	+	0.997063i	$0.524404\pi$
$674$	−31.5318			−1.21456
$675$	14.3467	+	21.6604i	0.552206	+	0.833708i
$676$	−5.85270			−0.225104
$677$	16.4613	−	8.38747i	0.632660	−	0.322357i	−0.108086	−	0.994142i	$-0.534472\pi$
$677$	16.4613	−	8.38747i	0.632660	−	0.322357i	0.740746	+	0.671785i	$0.234472\pi$
$678$	19.4885	+	14.9114i	0.748451	+	0.572668i
$679$	2.04750	−	2.81814i	0.0785757	−	0.108150i
$680$	−12.8370	+	2.23826i	−0.492276	+	0.0858333i
$681$	24.0596	+	4.42487i	0.921968	+	0.169561i
$682$	12.1326	−	12.1326i	0.464581	−	0.464581i
$683$	5.94046	−	37.5066i	0.227305	−	1.43515i	−0.565033	−	0.825068i	$-0.691137\pi$
$683$	5.94046	−	37.5066i	0.227305	−	1.43515i	0.792338	−	0.610082i	$-0.208863\pi$
$684$	5.71601	+	21.0994i	0.218557	+	0.806756i
$685$	47.0332	−	0.731199i	1.79705	−	0.0279377i
$686$	8.43843	+	2.74181i	0.322181	+	0.104683i
$687$	25.2568	−	7.51932i	0.963607	−	0.286880i
$688$	−3.26638	+	6.41064i	−0.124530	+	0.244403i
$689$	3.03266	−	9.33356i	0.115535	−	0.355580i
$690$	−1.92941	+	1.89402i	−0.0734514	+	0.0721042i
$691$	−2.65184	−	8.16151i	−0.100881	−	0.310479i	0.887861	−	0.460112i	$-0.152191\pi$
$691$	−2.65184	−	8.16151i	−0.100881	−	0.310479i	−0.988742	+	0.149633i	$0.952191\pi$
$692$	−18.8394	−	2.98388i	−0.716168	−	0.113430i
$693$	−3.78547	−	4.18093i	−0.143798	−	0.158820i
$694$	7.68036	+	10.5711i	0.291542	+	0.401274i
$695$	−4.47942	−	25.6906i	−0.169914	−	0.974501i
$696$	−5.52282	+	0.734846i	−0.209342	+	0.0278543i
$697$	38.3894	−	6.08028i	1.45410	−	0.230307i
$698$	−13.8161	−	27.1156i	−0.522947	−	1.02634i
$699$	−9.52861	+	9.06733i	−0.360405	+	0.342958i
$700$	2.95706	+	1.39266i	0.111766	+	0.0526377i
$701$			52.4507i			1.98104i	0.137384	+	0.990518i	$0.456131\pi$
$701$			52.4507i			1.98104i	−0.137384	+	0.990518i	$0.543869\pi$
$702$	−20.8797	−	8.54758i	−0.788053	−	0.322608i
$703$	−2.48160	−	15.6682i	−0.0935951	−	0.590937i
$704$	2.32663	+	1.69040i	0.0876881	+	0.0637092i
$705$	11.7586	+	0.108831i	0.442855	+	0.00409881i
$706$	2.35718	−	1.71259i	0.0887136	−	0.0644542i
$707$	5.80538	+	5.80538i	0.218334	+	0.218334i
$708$	8.47258	+	12.2913i	0.318419	+	0.461936i
$709$	5.89184	−	1.91438i	0.221273	−	0.0718959i	−0.196283	−	0.980547i	$-0.562887\pi$
$709$	5.89184	−	1.91438i	0.221273	−	0.0718959i	0.417555	+	0.908652i	$0.362887\pi$
$710$	25.7440	−	8.80946i	0.966155	−	0.330613i
$711$	28.6228	+	10.8967i	1.07344	+	0.408660i
$712$	5.15235	+	2.62525i	0.193092	+	0.0983855i
$713$	−3.71101	−	1.89085i	−0.138978	−	0.0708130i
$714$	−5.95161	+	2.84886i	−0.222734	+	0.106616i
$715$	26.6860	+	8.21444i	0.998000	+	0.307203i
$716$	−3.81721	+	1.24029i	−0.142656	+	0.0463517i
$717$	−17.8081	+	12.2754i	−0.665055	+	0.458432i
$718$	5.59498	+	5.59498i	0.208803	+	0.208803i
$719$	3.26095	−	2.36922i	0.121613	−	0.0883570i	−0.525316	−	0.850907i	$-0.676053\pi$
$719$	3.26095	−	2.36922i	0.121613	−	0.0883570i	0.646929	+	0.762550i	$0.276053\pi$
$720$	−5.86989	−	3.24721i	−0.218758	−	0.121016i
$721$	−3.23943	−	2.35359i	−0.120643	−	0.0876521i
$722$	5.33368	+	33.6756i	0.198499	+	1.25327i
$723$	13.0713	−	37.0747i	0.486127	−	1.37882i
$724$		−	4.08855i		−	0.151950i
$725$	−15.1344	+	5.44317i	−0.562079	+	0.202154i
$726$	3.25885	+	3.42464i	0.120947	+	0.127100i
$727$	−13.8279	−	27.1388i	−0.512850	−	1.00652i	−0.991693	−	0.128624i	$-0.958944\pi$
$727$	−13.8279	−	27.1388i	−0.512850	−	1.00652i	0.478844	−	0.877900i	$-0.341056\pi$
$728$	−2.80348	+	0.444028i	−0.103904	+	0.0164568i
$729$	−19.2493	−	18.9332i	−0.712936	−	0.701229i
$730$	−1.23926	−	0.176578i	−0.0458669	−	0.00653545i
$731$	−24.6445	−	33.9203i	−0.911510	−	1.25459i
$732$	−0.386264	+	15.5718i	−0.0142767	+	0.575549i
$733$	−13.6402	−	2.16039i	−0.503812	−	0.0797960i	−0.100645	−	0.994922i	$-0.532091\pi$
$733$	−13.6402	−	2.16039i	−0.503812	−	0.0797960i	−0.403167	+	0.915126i	$0.632091\pi$
$734$	−6.80279	−	20.9368i	−0.251096	−	0.772793i
$735$	−25.1044	−	4.21468i	−0.925991	−	0.155461i
$736$	0.215722	−	0.663923i	0.00795161	−	0.0244725i
$737$	18.5698	−	36.4453i	0.684028	−	1.34248i
$738$	17.3561	+	9.95678i	0.638885	+	0.366514i
$739$	−25.2888	−	8.21683i	−0.930264	−	0.302261i	−0.195593	−	0.980685i	$-0.562663\pi$
$739$	−25.2888	−	8.21683i	−0.930264	−	0.302261i	−0.734671	+	0.678424i	$0.762663\pi$
$740$	3.98234	+	2.79981i	0.146394	+	0.102923i
$741$	−48.1946	−	26.0815i	−1.77047	−	0.958129i
$742$	0.231141	−	1.45937i	0.00848547	−	0.0535751i
$743$	−19.0708	+	19.0708i	−0.699641	+	0.699641i	−0.964333	−	0.264692i	$-0.914730\pi$
$743$	−19.0708	+	19.0708i	−0.699641	+	0.699641i	0.264692	+	0.964333i	$0.414730\pi$
$744$	1.86917	−	10.1633i	0.0685270	−	0.372606i
$745$	−10.4903	−	19.8205i	−0.384334	−	0.726166i
$746$	12.5568	−	17.2829i	0.459736	−	0.632772i
$747$	−14.1520	+	1.52692i	−0.517794	+	0.0558672i
$748$	−14.9325	+	7.60848i	−0.545985	+	0.278193i
$749$	0.380457			0.0139016
$750$	−18.5434	−	5.58055i	−0.677109	−	0.203773i
$751$	−27.8529			−1.01637			−0.508183	−	0.861249i	$-0.669683\pi$
$751$	−27.8529			−1.01637			−0.508183	+	0.861249i	$0.669683\pi$
$752$	−2.70527	+	1.37840i	−0.0986509	+	0.0502652i
$753$	−8.84528	+	11.5604i	−0.322340	+	0.421283i
$754$	8.20949	−	11.2994i	0.298972	−	0.411500i
$755$	−18.7418	−	35.4109i	−0.682082	−	1.28874i
$756$	−3.30622	−	0.779295i	−0.120246	−	0.0283427i
$757$	−14.2550	+	14.2550i	−0.518108	+	0.518108i	−0.916998	−	0.398891i	$-0.869395\pi$
$757$	−14.2550	+	14.2550i	−0.518108	+	0.518108i	0.398891	+	0.916998i	$0.369395\pi$
$758$	−0.154776	+	0.977218i	−0.00562172	+	0.0354942i
$759$	−1.65500	+	3.05819i	−0.0600729	+	0.111005i
$760$	−13.3290	−	9.37099i	−0.483492	−	0.339922i
$761$	20.4602	+	6.64792i	0.741681	+	0.240987i	0.655398	−	0.755284i	$-0.272501\pi$
$761$	20.4602	+	6.64792i	0.741681	+	0.240987i	0.0862835	+	0.996271i	$0.472501\pi$
$762$	−7.16346	−	24.0615i	−0.259505	−	0.871656i
$763$	−3.44817	+	6.76742i	−0.124832	+	0.244997i
$764$	3.76012	−	11.5725i	0.136036	−	0.418677i
$765$	32.3901	−	21.8875i	1.17107	−	0.791345i
$766$	−3.90822	−	12.0283i	−0.141210	−	0.434599i
$767$	−36.9626	−	5.85431i	−1.33464	−	0.211387i
$768$	1.73152	+	0.0429510i	0.0624808	+	0.00154986i
$769$	5.35630	+	7.37231i	0.193153	+	0.265852i	0.894599	−	0.446871i	$-0.147462\pi$
$769$	5.35630	+	7.37231i	0.193153	+	0.265852i	−0.701446	+	0.712723i	$0.747462\pi$
$770$	4.16180	+	0.593002i	0.149981	+	0.0213703i
$771$	6.85860	+	51.5466i	0.247006	+	1.85641i
$772$	−12.5952	+	1.99489i	−0.453312	+	0.0717976i
$773$	−20.4388	−	40.1134i	−0.735132	−	1.44278i	−0.890529	−	0.454926i	$-0.849666\pi$
$773$	−20.4388	−	40.1134i	−0.735132	−	1.44278i	0.155397	−	0.987852i	$-0.450334\pi$
$774$	1.07017	−	21.5579i	0.0384663	−	0.774884i
$775$	−0.927311	−	29.8167i	−0.0333100	−	1.07105i
$776$		−	5.32861i		−	0.191286i
$777$	2.32477	+	0.819637i	0.0834007	+	0.0294043i
$778$	4.28069	+	27.0272i	0.153470	+	0.968973i
$779$	39.3184	+	28.5665i	1.40873	+	1.02350i
$780$	16.0407	−	5.04830i	0.574350	−	0.180758i
$781$	28.3116	−	20.5695i	1.01307	−	0.736036i
$782$	2.87659	+	2.87659i	0.102867	+	0.102867i
$783$	14.2152	−	8.79220i	0.508009	−	0.314208i
$784$	6.25096	−	2.03106i	0.223249	−	0.0725379i
$785$	19.4333	+	5.98194i	0.693605	+	0.213504i
$786$	−4.11056	−	8.58746i	−0.146619	−	0.306305i
$787$	22.6577	+	11.5447i	0.807659	+	0.411523i	0.808514	−	0.588477i	$-0.200272\pi$
$787$	22.6577	+	11.5447i	0.807659	+	0.411523i	−0.000855029		1.00000i	$0.500272\pi$
$788$	−0.365350	−	0.186155i	−0.0130150	−	0.00663150i
$789$	3.15181	+	6.58451i	0.112207	+	0.234415i
$790$	−21.5984	+	7.39084i	−0.768435	+	0.262954i
$791$	−8.80823	+	2.86197i	−0.313185	+	0.101760i
$792$	−8.44400	−	1.77049i	−0.300044	−	0.0629116i
$793$	−27.6110	−	27.6110i	−0.980497	−	0.980497i
$794$	2.87697	−	2.09024i	0.102100	−	0.0741798i
$795$	−0.0810172	+	8.75349i	−0.00287338	+	0.310454i
$796$	−8.89504	−	6.46262i	−0.315276	−	0.229062i
$797$	1.71644	+	10.8372i	0.0607996	+	0.383874i	0.999259	+	0.0384845i	$0.0122530\pi$
$797$	1.71644	+	10.8372i	0.0607996	+	0.383874i	−0.938460	+	0.345389i	$0.887747\pi$
$798$	−7.78104	−	2.74334i	−0.275446	−	0.0971131i
$799$		−	17.6934i		−	0.625946i
$800$	4.91174	−	0.935308i	0.173656	−	0.0330681i
$801$	−17.3265	−	0.860112i	−0.612202	−	0.0303906i
$802$	7.55891	+	14.8352i	0.266914	+	0.523849i
$803$	−1.59012	+	0.251850i	−0.0561141	+	0.00888760i
$804$	−3.24920	−	24.4198i	−0.114591	−	0.861218i
$805$	−0.175280	−	1.00527i	−0.00617779	−	0.0354312i
$806$	15.2267	+	20.9577i	0.536337	+	0.738204i
$807$	35.1187	+	0.871135i	1.23624	+	0.0306654i
$808$	12.4044	+	1.96466i	0.436384	+	0.0691165i
$809$	13.0207	+	40.0735i	0.457782	+	1.40891i	0.867838	+	0.496848i	$0.165509\pi$
$809$	13.0207	+	40.0735i	0.457782	+	1.40891i	−0.410056	+	0.912060i	$0.634491\pi$
$810$	20.0542	+	1.68158i	0.704634	+	0.0590849i
$811$	4.38556	−	13.4974i	0.153998	−	0.473957i	−0.844060	−	0.536249i	$-0.819841\pi$
$811$	4.38556	−	13.4974i	0.153998	−	0.473957i	0.998058	+	0.0622916i	$0.0198409\pi$
$812$	0.954659	−	1.87362i	0.0335020	−	0.0657513i
$813$	3.34786	+	11.2452i	0.117415	+	0.394386i
$814$	5.95451	+	1.93474i	0.208706	+	0.0678126i
$815$	20.7401	−	0.322435i	0.726495	−	0.0112944i
$816$	−4.80396	+	8.87698i	−0.168172	+	0.310756i
$817$	8.20127	−	51.7808i	0.286926	−	1.81158i
$818$	−3.04402	+	3.04402i	−0.106432	+	0.106432i
$819$	7.12869	−	4.65744i	0.249097	−	0.162744i
$820$	−14.6924	+	2.56176i	−0.513079	+	0.0894606i
$821$	−9.28341	+	12.7775i	−0.323993	+	0.445939i	−0.939681	−	0.342052i	$-0.888878\pi$
$821$	−9.28341	+	12.7775i	−0.323993	+	0.445939i	0.615688	+	0.787990i	$0.288878\pi$
$822$	22.1410	−	28.9373i	0.772258	−	1.00931i
$823$	21.3898	−	10.8987i	0.745603	−	0.379904i	−0.0395404	−	0.999218i	$-0.512589\pi$
$823$	21.3898	−	10.8987i	0.745603	−	0.379904i	0.785143	+	0.619314i	$0.212589\pi$
$824$	−6.12520			−0.213382
$825$	−24.9053	+	0.156657i	−0.867091	+	0.00545411i
$826$	−5.63439			−0.196046
$827$	23.7234	−	12.0877i	0.824944	−	0.420330i	0.0100569	−	0.999949i	$-0.496799\pi$
$827$	23.7234	−	12.0877i	0.824944	−	0.420330i	0.814887	+	0.579619i	$0.196799\pi$
$828$	0.224657	+	2.08219i	0.00780737	+	0.0723610i
$829$	−9.16301	+	12.6118i	−0.318245	+	0.438026i	−0.937930	−	0.346824i	$-0.887260\pi$
$829$	−9.16301	+	12.6118i	−0.318245	+	0.438026i	0.619686	+	0.784850i	$0.287260\pi$
$830$	7.38452	−	7.61775i	0.256320	−	0.264416i
$831$	−7.67030	+	41.7062i	−0.266080	+	1.44677i
$832$	−3.07024	+	3.07024i	−0.106441	+	0.106441i
$833$	−5.99176	+	37.8305i	−0.207602	+	1.31075i
$834$	−17.7655	−	9.61415i	−0.615168	−	0.332911i
$835$	−3.67824	−	10.7490i	−0.127291	−	0.371983i
$836$	−19.9298	−	6.47560i	−0.689288	−	0.223963i
$837$	7.36184	+	30.1146i	0.254462	+	1.04091i
$838$	−3.27974	+	6.43686i	−0.113297	+	0.222358i
$839$	−4.03893	+	12.4305i	−0.139439	+	0.429150i	−0.996254	−	0.0864743i	$-0.972440\pi$
$839$	−4.03893	+	12.4305i	−0.139439	+	0.429150i	0.856815	+	0.515624i	$0.172440\pi$
$840$	2.26643	−	1.12850i	0.0781992	−	0.0389371i
$841$	−5.76404	−	17.7399i	−0.198760	−	0.611720i
$842$	−14.3608	−	2.27453i	−0.494907	−	0.0783856i
$843$	0.869329	−	35.0459i	0.0299413	−	1.20705i
$844$	−12.6440	−	17.4030i	−0.435225	−	0.599036i
$845$	−5.75941	+	11.7516i	−0.198130	+	0.404267i
$846$	5.71266	−	7.09448i	0.196405	−	0.243913i
$847$	−1.76227	+	0.279116i	−0.0605522	+	0.00959053i
$848$	−1.02613	−	2.01389i	−0.0352374	−	0.0691572i
$849$	9.91473	+	10.4191i	0.340273	+	0.357583i
$850$	−8.13819	+	27.9778i	−0.279138	+	0.959632i
$851$		−	1.51978i		−	0.0520975i
$852$	7.00804	−	19.8772i	0.240092	−	0.680982i
$853$	6.36392	+	40.1802i	0.217897	+	1.37574i	0.817722	+	0.575614i	$0.195237\pi$
$853$	6.36392	+	40.1802i	0.217897	+	1.37574i	−0.599825	+	0.800131i	$0.704763\pi$
$854$	−4.75619	−	3.45558i	−0.162754	−	0.118247i
$855$	47.9902	+	9.28597i	1.64123	+	0.317574i
$856$	0.470839	−	0.342085i	0.0160930	−	0.0116922i
$857$	−24.0957	−	24.0957i	−0.823093	−	0.823093i	0.163457	−	0.986550i	$-0.447735\pi$
$857$	−24.0957	−	24.0957i	−0.823093	−	0.823093i	−0.986550	+	0.163457i	$0.947735\pi$
$858$	17.8073	−	12.2748i	0.607931	−	0.419056i
$859$	−17.4179	+	5.65942i	−0.594291	+	0.193097i	−0.590693	−	0.806897i	$-0.701145\pi$
$859$	−17.4179	+	5.65942i	−0.594291	+	0.193097i	−0.00359858	+	0.999994i	$0.501145\pi$
$860$	9.65754	+	12.8670i	0.329319	+	0.438761i
$861$	−6.81182	+	3.26061i	−0.232146	+	0.111121i
$862$	−3.69822	−	1.88434i	−0.125962	−	0.0641808i
$863$	7.06405	+	3.59931i	0.240463	+	0.122522i	0.570070	−	0.821596i	$-0.306916\pi$
$863$	7.06405	+	3.59931i	0.240463	+	0.122522i	−0.329607	+	0.944118i	$0.606916\pi$
$864$	−4.79235	+	2.00833i	−0.163039	+	0.0683249i
$865$	−24.5305	+	34.8912i	−0.834061	+	1.18634i
$866$	27.7975	−	9.03196i	0.944598	−	0.306918i
$867$	−16.6715	−	24.1857i	−0.566194	−	0.821388i
$868$	2.75788	+	2.75788i	0.0936085	+	0.0936085i
$869$	−23.7524	+	17.2572i	−0.805747	+	0.585409i
$870$	−3.95930	+	11.8124i	−0.134233	+	0.400476i
$871$	49.9615	+	36.2992i	1.69288	+	1.22995i
$872$	1.81754	+	11.4755i	0.0615497	+	0.388609i
$873$	6.54229	+	14.5858i	0.221423	+	0.493654i
$874$			5.08674i			0.172062i
$875$	5.70624	−	4.56698i	0.192906	−	0.154392i
$876$	−0.702415	+	0.668411i	−0.0237324	+	0.0225835i
$877$	23.3612	+	45.8490i	0.788853	+	1.54821i	0.835621	+	0.549306i	$0.185108\pi$
$877$	23.3612	+	45.8490i	0.788853	+	1.54821i	−0.0467683	+	0.998906i	$0.514892\pi$
$878$	11.1570	−	1.76709i	0.376530	−	0.0596365i
$879$	−2.93324	+	0.390286i	−0.0989358	+	0.0131640i
$880$	5.68367	−	3.00817i	0.191597	−	0.101405i
$881$	−1.69050	−	2.32677i	−0.0569544	−	0.0783909i	0.779590	−	0.626290i	$-0.215428\pi$
$881$	−1.69050	−	2.32677i	−0.0569544	−	0.0783909i	−0.836544	+	0.547900i	$0.815428\pi$
$882$	−14.6168	+	13.2343i	−0.492175	+	0.445621i
$883$	−36.4793	−	5.77775i	−1.22763	−	0.194437i	−0.491255	−	0.871016i	$-0.663462\pi$
$883$	−36.4793	−	5.77775i	−1.22763	−	0.194437i	−0.736370	+	0.676579i	$0.763462\pi$
$884$	−7.81899	−	24.0644i	−0.262981	−	0.809372i
$885$	33.0171	−	4.91661i	1.10986	−	0.165270i
$886$	−5.38779	+	16.5819i	−0.181006	+	0.557081i
$887$	−2.57475	+	5.05323i	−0.0864515	+	0.169671i	−0.930184	−	0.367093i	$-0.880353\pi$
$887$	−2.57475	+	5.05323i	−0.0864515	+	0.169671i	0.843733	+	0.536763i	$0.180353\pi$
$888$	3.61402	−	1.07595i	0.121278	−	0.0361064i
$889$	9.01156	+	2.92803i	0.302238	+	0.0982031i
$890$	10.3414	−	7.76194i	0.346646	−	0.260181i
$891$	25.2872	−	5.52097i	0.847152	−	0.184960i
$892$	0.992947	−	6.26922i	0.0332463	−	0.209909i
$893$	15.6438	−	15.6438i	0.523500	−	0.523500i
$894$	−17.0841	−	3.14198i	−0.571378	−	0.105083i
$895$	−1.26601	+	8.88507i	−0.0423180	+	0.296995i
$896$	−0.384246	+	0.528869i	−0.0128368	+	0.0176683i
$897$	−4.16951	−	3.19025i	−0.139216	−	0.106519i
$898$	−10.1628	+	5.17823i	−0.339138	+	0.172800i
$899$	−19.1916			−0.640075
$900$	−12.2964	+	8.59065i	−0.409879	+	0.286355i
$901$	13.1715			0.438807
$902$	−17.0907	+	8.70815i	−0.569058	+	0.289950i
$903$	6.46990	+	4.95036i	0.215305	+	0.164738i
$904$	−8.32742	+	11.4617i	−0.276966	+	0.381211i
$905$	−8.20936	−	4.02338i	−0.272888	−	0.133742i
$906$	−30.5222	−	5.61341i	−1.01403	−	0.186493i
$907$	−23.6056	+	23.6056i	−0.783811	+	0.783811i	−0.980472	−	0.196661i	$-0.936990\pi$
$907$	−23.6056	+	23.6056i	−0.783811	+	0.783811i	0.196661	+	0.980472i	$0.436990\pi$
$908$	−2.20945	+	13.9499i	−0.0733232	+	0.462944i
$909$	−36.3661	+	9.85190i	−1.20619	+	0.326767i
$910$	−1.86724	+	6.06603i	−0.0618983	+	0.201087i
$911$	40.8162	+	13.2620i	1.35230	+	0.439390i	0.893466	−	0.449131i	$-0.148266\pi$
$911$	40.8162	+	13.2620i	1.35230	+	0.439390i	0.458837	+	0.888521i	$0.348266\pi$
$912$	−12.0962	+	3.60121i	−0.400544	+	0.119248i
$913$	6.19478	−	12.1579i	0.205017	−	0.402369i
$914$	−1.98641	+	6.11354i	−0.0657046	+	0.202218i
$915$	30.8863	+	16.0991i	1.02107	+	0.532221i
$916$	4.70155	+	14.4699i	0.155344	+	0.478098i
$917$	3.54906	+	0.562115i	0.117200	+	0.0185627i
$918$	2.25082	−	30.1967i	0.0742882	−	0.996641i
$919$	7.08527	+	9.75204i	0.233722	+	0.321690i	0.909727	−	0.415206i	$-0.136291\pi$
$919$	7.08527	+	9.75204i	0.233722	+	0.321690i	−0.676006	+	0.736896i	$0.736291\pi$
$920$	−1.12080	−	1.08649i	−0.0369517	−	0.0358204i
$921$	−10.9909	+	1.46241i	−0.362162	+	0.0481880i
$922$	−19.0727	+	3.02082i	−0.628126	+	0.0994854i
$923$	23.9867	+	47.0765i	0.789531	+	1.54954i
$924$	2.35892	−	2.24473i	0.0776029	−	0.0738461i
$925$	9.54057	−	5.24093i	0.313692	−	0.172321i
$926$		−	4.47523i		−	0.147065i
$927$	16.7663	−	7.52032i	0.550676	−	0.247000i
$928$	−0.503203	−	3.17710i	−0.0165185	−	0.104293i
$929$	−15.3269	−	11.1356i	−0.502859	−	0.365349i	0.307249	−	0.951629i	$-0.400592\pi$
$929$	−15.3269	−	11.1356i	−0.502859	−	0.365349i	−0.810108	+	0.586280i	$0.800592\pi$
$930$	−18.5675	−	13.7544i	−0.608853	−	0.451026i
$931$	−38.7460	+	28.1506i	−1.26985	+	0.922598i
$932$	−5.36984	−	5.36984i	−0.175895	−	0.175895i
$933$	34.0431	+	49.3870i	1.11452	+	1.61686i
$934$	−1.67753	+	0.545064i	−0.0548906	+	0.0178350i
$935$	0.582525	+	37.4700i	0.0190506	+	1.22540i
$936$	4.63450	−	12.1736i	0.151483	−	0.397905i
$937$	34.7728	+	17.7176i	1.13598	+	0.578809i	0.917778	−	0.397095i	$-0.129982\pi$
$937$	34.7728	+	17.7176i	1.13598	+	0.578809i	0.218199	+	0.975904i	$0.429982\pi$
$938$	8.28444	+	4.22113i	0.270497	+	0.137825i
$939$	40.8481	−	19.5528i	1.33303	−	0.638080i
$940$	0.105534	+	6.78831i	0.00344214	+	0.221410i
$941$	−26.0266	+	8.45656i	−0.848443	+	0.275676i	−0.700794	−	0.713364i	$-0.747171\pi$
$941$	−26.0266	+	8.45656i	−0.848443	+	0.275676i	−0.147649	+	0.989040i	$0.547171\pi$
$942$	12.9677	−	8.93880i	0.422510	−	0.291242i
$943$	3.29235	+	3.29235i	0.107214	+	0.107214i
$944$	−6.97291	+	5.06611i	−0.226949	+	0.164888i
$945$	−4.81826	+	5.87165i	−0.156738	+	0.191005i
$946$	16.7397	+	12.1621i	0.544254	+	0.395424i
$947$	4.63200	+	29.2453i	0.150520	+	0.950344i	0.941135	+	0.338031i	$0.109761\pi$
$947$	4.63200	+	29.2453i	0.150520	+	0.950344i	−0.790615	+	0.612313i	$0.790239\pi$
$948$	−5.87951	+	16.6763i	−0.190958	+	0.541622i
$949$		−	2.43068i		−	0.0789031i
$950$	−31.9324	+	17.5415i	−1.03602	+	0.569120i
$951$	−16.3187	−	17.1489i	−0.529171	−	0.556091i
$952$	−1.72949	−	3.39432i	−0.0560532	−	0.110011i
$953$	8.50033	−	1.34632i	0.275353	−	0.0436116i	−0.0172309	−	0.999852i	$-0.505485\pi$
$953$	8.50033	−	1.34632i	0.275353	−	0.0436116i	0.292584	+	0.956240i	$0.405485\pi$
$954$	5.28136	+	4.25269i	0.170990	+	0.137686i
$955$	−19.5360	−	18.9379i	−0.632171	−	0.612816i
$956$	−7.33996	−	10.1026i	−0.237391	−	0.326741i
$957$	−0.397333	+	16.0180i	−0.0128439	+	0.517788i
$958$	−16.8163	−	2.66344i	−0.543311	−	0.0860519i
$959$	4.24957	+	13.0788i	0.137226	+	0.422338i
$960$	1.79016	−	3.43443i	0.0577772	−	0.110846i
$961$	1.42019	−	4.37089i	0.0458125	−	0.140996i
$962$	−4.29145	+	8.42244i	−0.138362	+	0.271550i
$963$	−0.868809	+	1.51446i	−0.0279970	+	0.0488027i
$964$	21.5856	+	7.01360i	0.695227	+	0.225893i
$965$	−8.38895	+	27.2529i	−0.270050	+	0.877303i
$966$	−0.695162	−	0.376201i	−0.0223665	−	0.0121041i
$967$	−4.89692	+	30.9179i	−0.157474	+	0.994254i	0.774722	+	0.632302i	$0.217890\pi$
$967$	−4.89692	+	30.9179i	−0.157474	+	0.994254i	−0.932197	+	0.361952i	$0.882110\pi$
$968$	−1.92995	+	1.92995i	−0.0620309	+	0.0620309i
$969$	13.3033	−	72.3347i	0.427362	−	2.32373i
$970$	−10.6993	−	5.24367i	−0.343533	−	0.168364i
$971$	16.9971	−	23.3945i	0.545463	−	0.750765i	−0.443925	−	0.896064i	$-0.646414\pi$
$971$	16.9971	−	23.3945i	0.545463	−	0.750765i	0.989388	+	0.145299i	$0.0464143\pi$
$972$	10.6521	−	11.3812i	0.341667	−	0.365053i
$973$	6.79305	−	3.46123i	0.217775	−	0.110962i
$974$	28.1581			0.902245
$975$	5.64861	−	37.1759i	0.180900	−	1.19058i
$976$	−8.99313			−0.287863
$977$	1.82021	−	0.927445i	0.0582338	−	0.0296716i	−0.424631	−	0.905366i	$-0.639596\pi$
$977$	1.82021	−	0.927445i	0.0582338	−	0.0296716i	0.482865	+	0.875695i	$0.339596\pi$
$978$	9.76348	−	12.7604i	0.312202	−	0.408034i
$979$	9.77490	−	13.4540i	0.312407	−	0.429992i
$980$	2.07318	−	14.5499i	0.0662253	−	0.464781i
$981$	−19.0643	−	29.1799i	−0.608677	−	0.931643i
$982$	−6.46512	+	6.46512i	−0.206310	+	0.206310i
$983$	−4.54655	+	28.7058i	−0.145012	+	0.915572i	0.802685	+	0.596403i	$0.203404\pi$
$983$	−4.54655	+	28.7058i	−0.145012	+	0.915572i	−0.947698	+	0.319169i	$0.896596\pi$
$984$	−5.49829	+	10.1600i	−0.175279	+	0.323889i
$985$	−0.733305	+	0.550395i	−0.0233650	+	0.0175370i
$986$	17.8278	+	5.79262i	0.567754	+	0.184474i
$987$	0.980934	+	3.29488i	0.0312235	+	0.104877i
$988$	14.3635	−	28.1900i	0.456965	−	0.896845i
$989$	1.55208	−	4.77681i	0.0493533	−	0.151894i
$990$	−11.8644	+	15.2124i	−0.377074	+	0.483480i
$991$	−4.33291	−	13.3353i	−0.137640	−	0.423611i	0.858352	−	0.513062i	$-0.171489\pi$
$991$	−4.33291	−	13.3353i	−0.137640	−	0.423611i	−0.995991	+	0.0894508i	$0.971489\pi$
$992$	5.89277	+	0.933323i	0.187096	+	0.0296330i
$993$	18.3009	+	0.453961i	0.580760	+	0.0144060i
$994$	4.67569	+	6.43554i	0.148304	+	0.204123i
$995$	−21.7295	+	11.5006i	−0.688871	+	0.364595i
$996$	−1.08391	−	8.14628i	−0.0343451	−	0.258125i
$997$	−35.5407	+	5.62909i	−1.12558	+	0.178275i	−0.691347	−	0.722523i	$-0.742982\pi$
$997$	−35.5407	+	5.62909i	−1.12558	+	0.178275i	−0.434238	+	0.900798i	$0.642982\pi$
$998$	5.86715	+	11.5149i	0.185722	+	0.364499i
$999$	−8.57149	+	7.38231i	−0.271190	+	0.233566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.53.7	yes	80
3.2	odd	2	inner	150.2.l.a.53.4	yes	80
5.2	odd	4		750.2.l.c.257.7		80
5.3	odd	4		750.2.l.a.257.4		80
5.4	even	2		750.2.l.b.743.4		80
15.2	even	4		750.2.l.c.257.2		80
15.8	even	4		750.2.l.a.257.9		80
15.14	odd	2		750.2.l.b.743.7		80
25.6	even	5		750.2.l.c.143.2		80
25.8	odd	20		750.2.l.b.107.7		80
25.17	odd	20	inner	150.2.l.a.17.4	✓	80
25.19	even	10		750.2.l.a.143.9		80
75.8	even	20		750.2.l.b.107.4		80
75.17	even	20	inner	150.2.l.a.17.7	yes	80
75.44	odd	10		750.2.l.a.143.4		80
75.56	odd	10		750.2.l.c.143.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.4	✓	80	25.17	odd	20	inner
150.2.l.a.17.7	yes	80	75.17	even	20	inner
150.2.l.a.53.4	yes	80	3.2	odd	2	inner
150.2.l.a.53.7	yes	80	1.1	even	1	trivial
750.2.l.a.143.4		80	75.44	odd	10
750.2.l.a.143.9		80	25.19	even	10
750.2.l.a.257.4		80	5.3	odd	4
750.2.l.a.257.9		80	15.8	even	4
750.2.l.b.107.4		80	75.8	even	20
750.2.l.b.107.7		80	25.8	odd	20
750.2.l.b.743.4		80	5.4	even	2
750.2.l.b.743.7		80	15.14	odd	2
750.2.l.c.143.2		80	25.6	even	5
750.2.l.c.143.7		80	75.56	odd	10
750.2.l.c.257.2		80	15.2	even	4
750.2.l.c.257.7		80	5.2	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(-1.37558 - 1.05251i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.04600 - 1.97633i) q^{5} +(-1.70348 - 0.313291i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.784450 + 2.89562i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(-1.37558 - 1.05251i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.04600 - 1.97633i) q^{5} +(-1.70348 - 0.313291i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.784450 + 2.89562i) q^{9} +(-1.82923 - 1.28605i) q^{10} +(-2.73512 - 0.888693i) q^{11} +(-1.66004 + 0.494220i) q^{12} +(1.97121 - 3.86872i) q^{13} +(0.202010 - 0.621723i) q^{14} +(-0.641245 + 3.81953i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(5.75574 + 0.911620i) q^{17} +(2.01354 + 2.22389i) q^{18} +(4.28299 + 5.89503i) q^{19} +(-2.21371 - 0.315425i) q^{20} +(-1.12238 + 0.149340i) q^{21} +(-2.84047 + 0.449885i) q^{22} +(0.316926 + 0.622003i) q^{23} +(-1.25474 + 1.19400i) q^{24} +(-2.81176 + 4.13449i) q^{25} -4.34197i q^{26} +(1.96860 - 4.80881i) q^{27} +(-0.102264 - 0.645670i) q^{28} +(2.60237 + 1.89073i) q^{29} +(1.16268 + 3.69434i) q^{30} +(-4.82678 + 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.82702 + 4.10120i) q^{33} +(5.54227 - 1.80079i) q^{34} +(-1.39707 - 0.430043i) q^{35} +(2.80370 + 1.06737i) q^{36} +(-1.93977 - 0.988365i) q^{37} +(6.49246 + 3.30807i) q^{38} +(-6.78343 + 3.24703i) q^{39} +(-2.11563 + 0.723957i) q^{40} +(6.34331 - 2.06107i) q^{41} +(-0.932251 + 0.642614i) q^{42} +(-5.08751 - 5.08751i) q^{43} +(-2.32663 + 1.69040i) q^{44} +(4.90217 - 4.57916i) q^{45} +(0.564767 + 0.410327i) q^{46} +(-0.474965 - 2.99881i) q^{47} +(-0.575917 + 1.63350i) q^{48} +6.57265i q^{49} +(-0.628281 + 4.96037i) q^{50} +(-6.95800 - 7.31198i) q^{51} +(-1.97121 - 3.86872i) q^{52} +(2.23241 - 0.353579i) q^{53} +(-0.429121 - 5.17840i) q^{54} +(1.10458 + 6.33507i) q^{55} +(-0.384246 - 0.528869i) q^{56} +(0.312969 - 12.6170i) q^{57} +(3.17710 + 0.503203i) q^{58} +(-2.66341 - 8.19714i) q^{59} +(2.71315 + 2.76384i) q^{60} +(2.77903 - 8.55298i) q^{61} +(-2.70861 + 5.31594i) q^{62} +(1.70111 + 0.975888i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-9.70777 + 0.150921i) q^{65} +(4.38080 + 2.37076i) q^{66} +(-2.22497 + 14.0479i) q^{67} +(4.12066 - 4.12066i) q^{68} +(0.218706 - 1.18918i) q^{69} +(-1.44003 + 0.251084i) q^{70} +(-7.15246 + 9.84451i) q^{71} +(2.98269 - 0.321816i) q^{72} +(0.498794 - 0.254148i) q^{73} -2.17706 q^{74} +(8.21940 - 2.72792i) q^{75} +7.28665 q^{76} +(-1.67510 + 0.853507i) q^{77} +(-4.56996 + 5.97273i) q^{78} +(6.00067 - 8.25922i) q^{79} +(-1.55637 + 1.60553i) q^{80} +(-7.76928 + 4.54294i) q^{81} +(4.71623 - 4.71623i) q^{82} +(-0.742236 + 4.68629i) q^{83} +(-0.538901 + 0.995806i) q^{84} +(-4.21885 - 12.3288i) q^{85} +(-6.84269 - 2.22332i) q^{86} +(-1.58976 - 5.33987i) q^{87} +(-1.30562 + 2.56242i) q^{88} +(-1.78693 + 5.49959i) q^{89} +(2.28898 - 6.30560i) q^{90} +(-0.877122 - 2.69950i) q^{91} +(0.689496 + 0.109205i) q^{92} +(10.3306 + 0.256256i) q^{93} +(-1.78463 - 2.45633i) q^{94} +(7.17051 - 14.6308i) q^{95} +(0.228447 + 1.71692i) q^{96} +(5.26300 - 0.833578i) q^{97} +(2.98392 + 5.85628i) q^{98} +(0.427760 - 8.61700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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