LMFDB - Embedded newform 231.2.y.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	231.16
Dual form			231.2.y.b.130.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15881 + 0.246312i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.544926 - 0.242617i) q^{4} +(2.21930 + 2.46479i) q^{5} +(-0.366091 + 1.12671i) q^{6} +(-1.26723 + 2.32253i) q^{7} +(-2.48858 - 1.80806i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(1.15881 + 0.246312i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.544926 - 0.242617i) q^{4} +(2.21930 + 2.46479i) q^{5} +(-0.366091 + 1.12671i) q^{6} +(-1.26723 + 2.32253i) q^{7} +(-2.48858 - 1.80806i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.96464 + 3.40285i) q^{10} +(3.04998 - 1.30293i) q^{11} +(0.298248 - 0.516580i) q^{12} +(0.329683 + 1.01466i) q^{13} +(-2.04054 + 2.37923i) q^{14} +(-2.68326 + 1.94951i) q^{15} +(-1.64017 - 1.82160i) q^{16} +(-0.427026 + 0.0907671i) q^{17} +(-1.08227 - 0.481859i) q^{18} +(3.38323 - 1.50631i) q^{19} +(-0.611357 - 1.88156i) q^{20} +(-2.17734 - 1.50306i) q^{21} +(3.85527 - 0.758601i) q^{22} +(2.92176 - 5.06064i) q^{23} +(2.05828 - 2.28596i) q^{24} +(-0.627221 + 5.96761i) q^{25} +(0.132116 + 1.25700i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.25403 - 0.958155i) q^{28} +(-5.83740 + 4.24112i) q^{29} +(-3.58957 + 1.59818i) q^{30} +(5.05258 - 5.61146i) q^{31} +(1.62409 + 2.81301i) q^{32} +(0.976985 + 3.16946i) q^{33} -0.517198 q^{34} +(-8.53689 + 2.03095i) q^{35} +(0.482575 + 0.350611i) q^{36} +(-0.670760 - 6.38186i) q^{37} +(4.29153 - 0.912193i) q^{38} +(-1.04356 + 0.221816i) q^{39} +(-1.06644 - 10.1465i) q^{40} +(-6.60776 - 4.80082i) q^{41} +(-2.15290 - 2.27806i) q^{42} -0.285700 q^{43} +(-1.97812 - 0.0299739i) q^{44} +(-1.65835 - 2.87234i) q^{45} +(4.63226 - 5.14464i) q^{46} +(7.38021 - 3.28588i) q^{47} +(1.98306 - 1.44078i) q^{48} +(-3.78827 - 5.88634i) q^{49} +(-2.19672 + 6.76081i) q^{50} +(-0.0456335 - 0.434174i) q^{51} +(0.0665204 - 0.632900i) q^{52} +(-6.27355 + 6.96748i) q^{53} +(0.592348 - 1.02598i) q^{54} +(9.98028 + 4.62594i) q^{55} +(7.35287 - 3.48858i) q^{56} +(1.14441 + 3.52214i) q^{57} +(-7.80906 + 3.47682i) q^{58} +(-11.4376 - 5.09235i) q^{59} +(1.93516 - 0.411331i) q^{60} +(7.91192 + 8.78708i) q^{61} +(7.23714 - 5.25809i) q^{62} +(1.72242 - 2.00830i) q^{63} +(2.70406 + 8.32224i) q^{64} +(-1.76925 + 3.06443i) q^{65} +(0.351460 + 3.91344i) q^{66} +(2.91531 + 5.04946i) q^{67} +(0.254719 + 0.0541421i) q^{68} +(4.72751 + 3.43474i) q^{69} +(-10.3929 + 0.250740i) q^{70} +(2.17902 - 6.70633i) q^{71} +(2.05828 + 2.28596i) q^{72} +(6.72945 + 2.99614i) q^{73} +(0.794647 - 7.56056i) q^{74} +(-5.86935 - 1.24757i) q^{75} -2.20906 q^{76} +(-0.838918 + 8.73477i) q^{77} -1.26392 q^{78} +(-5.16188 - 1.09719i) q^{79} +(0.849805 - 8.08536i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-6.47462 - 7.19080i) q^{82} +(-0.529504 + 1.62965i) q^{83} +(0.821824 + 1.34731i) q^{84} +(-1.17142 - 0.851087i) q^{85} +(-0.331072 - 0.0703715i) q^{86} +(-3.60771 - 6.24874i) q^{87} +(-9.94591 - 2.27209i) q^{88} +(-1.84124 + 3.18912i) q^{89} +(-1.21421 - 3.73696i) q^{90} +(-2.77436 - 0.520106i) q^{91} +(-2.81994 + 2.04880i) q^{92} +(5.05258 + 5.61146i) q^{93} +(9.36160 - 1.98987i) q^{94} +(11.2211 + 4.99597i) q^{95} +(-2.96737 + 1.32116i) q^{96} +(-1.23481 - 3.80036i) q^{97} +(-2.94000 - 7.75423i) q^{98} +(-3.25422 + 0.640334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	1.15881	+	0.246312i	0.819401	+	0.174169i	0.598495	−	0.801126i	$-0.295765\pi$
$2$	1.15881	+	0.246312i	0.819401	+	0.174169i	0.220905	+	0.975295i	$0.429099\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	−0.544926	−	0.242617i	−0.272463	−	0.121308i
$5$	2.21930	+	2.46479i	0.992503	+	1.10229i	0.994755	+	0.102288i	$0.0326164\pi$
$5$	2.21930	+	2.46479i	0.992503	+	1.10229i	−0.00225222	+	0.999997i	$0.500717\pi$
$6$	−0.366091	+	1.12671i	−0.149456	+	0.459979i
$7$	−1.26723	+	2.32253i	−0.478967	+	0.877833i
$7$	−1.26723	+	2.32253i	−0.478967	+	0.877833i
$8$	−2.48858	−	1.80806i	−0.879847	−	0.639246i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.96464	+	3.40285i	0.621273	+	1.07608i
$11$	3.04998	−	1.30293i	0.919603	−	0.392849i
$11$	3.04998	−	1.30293i	0.919603	−	0.392849i
$12$	0.298248	−	0.516580i	0.0860967	−	0.149124i
$13$	0.329683	+	1.01466i	0.0914375	+	0.281416i	0.986309	−	0.164908i	$-0.0527329\pi$
$13$	0.329683	+	1.01466i	0.0914375	+	0.281416i	−0.894871	+	0.446324i	$0.852733\pi$
$14$	−2.04054	+	2.37923i	−0.545357	+	0.635876i
$15$	−2.68326	+	1.94951i	−0.692816	+	0.503360i
$16$	−1.64017	−	1.82160i	−0.410044	−	0.455400i
$17$	−0.427026	+	0.0907671i	−0.103569	+	0.0220143i	−0.259405	−	0.965769i	$-0.583526\pi$
$17$	−0.427026	+	0.0907671i	−0.103569	+	0.0220143i	0.155836	+	0.987783i	$0.450193\pi$
$18$	−1.08227	−	0.481859i	−0.255094	−	0.113575i
$19$	3.38323	−	1.50631i	0.776165	−	0.345571i	0.0198708	−	0.999803i	$-0.493675\pi$
$19$	3.38323	−	1.50631i	0.776165	−	0.345571i	0.756294	+	0.654232i	$0.227008\pi$
$20$	−0.611357	−	1.88156i	−0.136704	−	0.420731i
$21$	−2.17734	−	1.50306i	−0.475135	−	0.327994i
$22$	3.85527	−	0.758601i	0.821945	−	0.161734i
$23$	2.92176	−	5.06064i	0.609229	−	1.05522i	−0.382138	−	0.924105i	$-0.624812\pi$
$23$	2.92176	−	5.06064i	0.609229	−	1.05522i	0.991368	−	0.131111i	$-0.0418545\pi$
$24$	2.05828	−	2.28596i	0.420146	−	0.466619i
$25$	−0.627221	+	5.96761i	−0.125444	+	1.19352i
$26$	0.132116	+	1.25700i	0.0259101	+	0.246518i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	1.25403	−	0.958155i	0.236989	−	0.181074i
$29$	−5.83740	+	4.24112i	−1.08398	+	0.787556i	−0.978372	−	0.206852i	$-0.933678\pi$
$29$	−5.83740	+	4.24112i	−1.08398	+	0.787556i	−0.105606	+	0.994408i	$0.533678\pi$
$30$	−3.58957	+	1.59818i	−0.655363	+	0.291787i
$31$	5.05258	−	5.61146i	0.907471	−	1.00785i	−0.0924558	−	0.995717i	$-0.529472\pi$
$31$	5.05258	−	5.61146i	0.907471	−	1.00785i	0.999926	−	0.0121315i	$-0.00386166\pi$
$32$	1.62409	+	2.81301i	0.287102	+	0.497275i
$33$	0.976985	+	3.16946i	0.170071	+	0.551733i
$34$	−0.517198			−0.0886986
$35$	−8.53689	+	2.03095i	−1.44300	+	0.343293i
$36$	0.482575	+	0.350611i	0.0804291	+	0.0584352i
$37$	−0.670760	−	6.38186i	−0.110272	−	1.04917i	−0.900053	−	0.435781i	$-0.856472\pi$
$37$	−0.670760	−	6.38186i	−0.110272	−	1.04917i	0.789780	−	0.613390i	$-0.210194\pi$
$38$	4.29153	−	0.912193i	0.696178	−	0.147977i
$39$	−1.04356	+	0.221816i	−0.167104	+	0.0355190i
$40$	−1.06644	−	10.1465i	−0.168618	−	1.60430i
$41$	−6.60776	−	4.80082i	−1.03196	−	0.749762i	−0.0632590	−	0.997997i	$-0.520149\pi$
$41$	−6.60776	−	4.80082i	−1.03196	−	0.749762i	−0.968700	+	0.248235i	$0.920149\pi$
$42$	−2.15290	−	2.27806i	−0.332200	−	0.351512i
$43$	−0.285700			−0.0435689			−0.0217845	−	0.999763i	$-0.506935\pi$
$43$	−0.285700			−0.0435689			−0.0217845	+	0.999763i	$0.506935\pi$
$44$	−1.97812	−	0.0299739i	−0.298213	−	0.00451874i
$45$	−1.65835	−	2.87234i	−0.247212	−	0.428184i
$46$	4.63226	−	5.14464i	0.682989	−	0.758536i
$47$	7.38021	−	3.28588i	1.07651	−	0.479295i	0.209618	−	0.977783i	$-0.432778\pi$
$47$	7.38021	−	3.28588i	1.07651	−	0.479295i	0.866896	+	0.498488i	$0.166111\pi$
$48$	1.98306	−	1.44078i	0.286231	−	0.207959i
$49$	−3.78827	−	5.88634i	−0.541182	−	0.840906i
$50$	−2.19672	+	6.76081i	−0.310663	+	0.956123i
$51$	−0.0456335	−	0.434174i	−0.00638997	−	0.0607965i
$52$	0.0665204	−	0.632900i	0.00922473	−	0.0877674i
$53$	−6.27355	+	6.96748i	−0.861738	+	0.957057i	−0.999442	−	0.0334161i	$-0.989361\pi$
$53$	−6.27355	+	6.96748i	−0.861738	+	0.957057i	0.137703	+	0.990474i	$0.456028\pi$
$54$	0.592348	−	1.02598i	0.0806084	−	0.139618i
$55$	9.98028	+	4.62594i	1.34574	+	0.623762i
$56$	7.35287	−	3.48858i	0.982569	−	0.466181i
$57$	1.14441	+	3.52214i	0.151581	+	0.466519i
$58$	−7.80906	+	3.47682i	−1.02538	+	0.456529i
$59$	−11.4376	−	5.09235i	−1.48905	−	0.662968i	−0.508828	−	0.860868i	$-0.669921\pi$
$59$	−11.4376	−	5.09235i	−1.48905	−	0.662968i	−0.980222	+	0.197900i	$0.936588\pi$
$60$	1.93516	−	0.411331i	0.249828	−	0.0531026i
$61$	7.91192	+	8.78708i	1.01302	+	1.12507i	0.992120	+	0.125289i	$0.0399857\pi$
$61$	7.91192	+	8.78708i	1.01302	+	1.12507i	0.0208975	+	0.999782i	$0.493348\pi$
$62$	7.23714	−	5.25809i	0.919118	−	0.667778i
$63$	1.72242	−	2.00830i	0.217004	−	0.253023i
$64$	2.70406	+	8.32224i	0.338007	+	1.04028i
$65$	−1.76925	+	3.06443i	−0.219448	+	0.380096i
$66$	0.351460	+	3.91344i	0.0432618	+	0.481711i
$67$	2.91531	+	5.04946i	0.356162	+	0.616890i	0.987316	−	0.158767i	$-0.0507520\pi$
$67$	2.91531	+	5.04946i	0.356162	+	0.616890i	−0.631155	+	0.775657i	$0.717419\pi$
$68$	0.254719	+	0.0541421i	0.0308892	+	0.00656570i
$69$	4.72751	+	3.43474i	0.569125	+	0.413494i
$70$	−10.3929	+	0.250740i	−1.24219	+	0.0299692i
$71$	2.17902	−	6.70633i	0.258602	−	0.795895i	−0.734497	−	0.678612i	$-0.762582\pi$
$71$	2.17902	−	6.70633i	0.258602	−	0.795895i	0.993099	−	0.117283i	$-0.0374183\pi$
$72$	2.05828	+	2.28596i	0.242571	+	0.269403i
$73$	6.72945	+	2.99614i	0.787622	+	0.350672i	0.760815	−	0.648969i	$-0.224799\pi$
$73$	6.72945	+	2.99614i	0.787622	+	0.350672i	0.0268070	+	0.999641i	$0.491466\pi$
$74$	0.794647	−	7.56056i	0.0923758	−	0.878897i
$75$	−5.86935	−	1.24757i	−0.677734	−	0.144057i
$76$	−2.20906			−0.253397
$77$	−0.838918	+	8.73477i	−0.0956035	+	0.995419i
$78$	−1.26392			−0.143111
$79$	−5.16188	−	1.09719i	−0.580756	−	0.123444i	−0.0918393	−	0.995774i	$-0.529275\pi$
$79$	−5.16188	−	1.09719i	−0.580756	−	0.123444i	−0.488917	+	0.872330i	$0.662608\pi$
$80$	0.849805	−	8.08536i	0.0950111	−	0.903971i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−6.47462	−	7.19080i	−0.715002	−	0.794091i
$83$	−0.529504	+	1.62965i	−0.0581206	+	0.178877i	−0.975902	−	0.218209i	$-0.929979\pi$
$83$	−0.529504	+	1.62965i	−0.0581206	+	0.178877i	0.917781	+	0.397086i	$0.129979\pi$
$84$	0.821824	+	1.34731i	0.0896684	+	0.147004i
$85$	−1.17142	−	0.851087i	−0.127058	−	0.0923133i
$86$	−0.331072	−	0.0703715i	−0.0357004	−	0.00758835i
$87$	−3.60771	−	6.24874i	−0.386787	−	0.669935i
$88$	−9.94591	−	2.27209i	−1.06024	−	0.242206i
$89$	−1.84124	+	3.18912i	−0.195171	+	0.338046i	−0.946957	−	0.321362i	$-0.895860\pi$
$89$	−1.84124	+	3.18912i	−0.195171	+	0.338046i	0.751786	+	0.659408i	$0.229193\pi$
$90$	−1.21421	−	3.73696i	−0.127989	−	0.393911i
$91$	−2.77436	−	0.520106i	−0.290831	−	0.0545219i
$92$	−2.81994	+	2.04880i	−0.293999	+	0.213603i
$93$	5.05258	+	5.61146i	0.523928	+	0.581881i
$94$	9.36160	−	1.98987i	0.965575	−	0.205239i
$95$	11.2211	+	4.99597i	1.15126	+	0.512576i
$96$	−2.96737	+	1.32116i	−0.302855	+	0.134840i
$97$	−1.23481	−	3.80036i	−0.125376	−	0.385868i	0.868593	−	0.495526i	$-0.165025\pi$
$97$	−1.23481	−	3.80036i	−0.125376	−	0.385868i	−0.993969	+	0.109658i	$0.965025\pi$
$98$	−2.94000	−	7.75423i	−0.296985	−	0.783296i
$99$	−3.25422	+	0.640334i	−0.327062	+	0.0643560i
$100$	1.78963	−	3.09973i	0.178963	−	0.309973i
$101$	−4.63470	+	5.14735i	−0.461169	+	0.512181i	−0.928211	−	0.372055i	$-0.878653\pi$
$101$	−4.63470	+	5.14735i	−0.461169	+	0.512181i	0.467041	+	0.884236i	$0.345320\pi$
$102$	0.0540619	−	0.514364i	0.00535292	−	0.0509296i
$103$	1.80757	+	17.1979i	0.178105	+	1.69456i	0.609813	+	0.792546i	$0.291245\pi$
$103$	1.80757	+	17.1979i	0.178105	+	1.69456i	−0.431707	+	0.902014i	$0.642089\pi$
$104$	1.01412	−	3.12115i	0.0994429	−	0.306054i
$105$	−1.12748	−	8.70242i	−0.110030	−	0.849269i
$106$	−8.98601	+	6.52872i	−0.872799	+	0.634125i
$107$	−7.65145	+	3.40665i	−0.739694	+	0.329333i	−0.741760	−	0.670665i	$-0.766009\pi$
$107$	−7.65145	+	3.40665i	−0.739694	+	0.329333i	0.00206661	+	0.999998i	$0.499342\pi$
$108$	−0.399133	+	0.443282i	−0.0384066	+	0.0426549i
$109$	−0.594633	−	1.02994i	−0.0569555	−	0.0986499i	0.836142	−	0.548513i	$-0.184806\pi$
$109$	−0.594633	−	1.02994i	−0.0569555	−	0.0986499i	−0.893097	+	0.449863i	$0.851473\pi$
$110$	10.4258	+	7.81884i	0.994060	+	0.745497i
$111$	6.41701			0.609076
$112$	6.30919	−	1.50097i	0.596162	−	0.141829i
$113$	−4.48283	−	3.25697i	−0.421709	−	0.306390i	0.356616	−	0.934251i	$-0.383930\pi$
$113$	−4.48283	−	3.25697i	−0.421709	−	0.306390i	−0.778325	+	0.627861i	$0.783930\pi$
$114$	0.458609	+	4.36337i	0.0429526	+	0.408667i
$115$	18.9577	−	4.02958i	1.76781	−	0.375760i
$116$	4.20991	−	0.894845i	0.390881	−	0.0830843i
$117$	−0.111519	−	1.06103i	−0.0103099	−	0.0980923i
$118$	−11.9997	−	8.71828i	−1.10466	−	0.802583i
$119$	0.330329	−	1.10680i	0.0302812	−	0.101460i
$120$	10.2024			0.931343
$121$	7.60473	−	7.94783i	0.691340	−	0.722530i
$122$	7.00403	+	12.1313i	0.634115	+	1.09832i
$123$	5.46522	−	6.06974i	0.492782	−	0.547290i
$124$	−4.11472	+	1.83199i	−0.369512	+	0.164517i
$125$	−2.68454	+	1.95043i	−0.240113	+	0.174452i
$126$	2.49062	−	1.90299i	0.221882	−	0.169531i
$127$	−2.78658	+	8.57621i	−0.247269	+	0.761016i	0.747986	+	0.663715i	$0.231021\pi$
$127$	−2.78658	+	8.57621i	−0.247269	+	0.761016i	−0.995255	+	0.0973012i	$0.968979\pi$
$128$	0.404560	+	3.84913i	0.0357584	+	0.340218i
$129$	0.0298638	−	0.284135i	0.00262936	−	0.0250167i
$130$	−2.80503	+	3.11530i	−0.246017	+	0.273230i
$131$	−0.753759	+	1.30555i	−0.0658562	+	0.114066i	−0.897073	−	0.441881i	$-0.854311\pi$
$131$	−0.753759	+	1.30555i	−0.0658562	+	0.114066i	0.831217	+	0.555948i	$0.187645\pi$
$132$	0.236580	−	1.96415i	0.0205916	−	0.170958i
$133$	−0.788869	+	9.76647i	−0.0684036	+	0.846860i
$134$	2.13454	+	6.56943i	0.184396	+	0.567512i
$135$	3.02995	−	1.34902i	0.260777	−	0.116105i
$136$	1.22680	+	0.546207i	0.105197	+	0.0468369i
$137$	−9.20995	+	1.95764i	−0.786859	+	0.167252i	−0.583782	−	0.811911i	$-0.698428\pi$
$137$	−9.20995	+	1.95764i	−0.786859	+	0.167252i	−0.203078	+	0.979163i	$0.565094\pi$
$138$	4.63226	+	5.14464i	0.394324	+	0.437941i
$139$	−16.0361	+	11.6509i	−1.36017	+	0.988219i	−0.361733	+	0.932282i	$0.617815\pi$
$139$	−16.0361	+	11.6509i	−1.36017	+	0.988219i	−0.998434	+	0.0559378i	$0.982185\pi$
$140$	5.14471	+	0.964474i	0.434808	+	0.0815130i
$141$	2.49644	+	7.68325i	0.210238	+	0.647046i
$142$	4.17691	−	7.23463i	0.350519	−	0.607116i
$143$	2.32756	+	2.66513i	0.194640	+	0.222870i
$144$	1.22560	+	2.12280i	0.102133	+	0.176900i
$145$	−23.4084	−	4.97561i	−1.94396	−	0.413202i
$146$	7.06015	+	5.12950i	0.584302	+	0.424520i
$147$	6.25008	−	3.15223i	0.515498	−	0.259992i
$148$	−1.18283	+	3.64037i	−0.0972280	+	0.299237i
$149$	−7.11787	−	7.90519i	−0.583118	−	0.647619i	0.377329	−	0.926079i	$-0.376843\pi$
$149$	−7.11787	−	7.90519i	−0.583118	−	0.647619i	−0.960448	+	0.278461i	$0.910176\pi$
$150$	−6.49416	−	2.89139i	−0.530246	−	0.236081i
$151$	2.16687	−	20.6164i	0.176338	−	1.67774i	−0.446032	−	0.895017i	$-0.647163\pi$
$151$	2.16687	−	20.6164i	0.176338	−	1.67774i	0.622370	−	0.782723i	$-0.286170\pi$
$152$	−11.1429	−	2.36850i	−0.903811	−	0.192111i
$153$	0.436566			0.0352942
$154$	−3.12362	+	9.91528i	−0.251709	+	0.798996i
$155$	25.0443			2.01160
$156$	0.622479	+	0.132312i	0.0498382	+	0.0105934i
$157$	−0.573443	+	5.45594i	−0.0457657	+	0.435432i	0.947516	+	0.319709i	$0.103585\pi$
$157$	−0.573443	+	5.45594i	−0.0457657	+	0.435432i	−0.993282	+	0.115723i	$0.963082\pi$
$158$	−5.71137	−	2.54287i	−0.454372	−	0.202300i
$159$	−6.27355	−	6.96748i	−0.497525	−	0.552557i
$160$	−3.32912	+	10.2460i	−0.263190	+	0.810015i
$161$	8.05094	+	13.1989i	0.634503	+	1.04022i
$162$	0.958439	+	0.696347i	0.0753021	+	0.0547102i
$163$	12.3334	+	2.62154i	0.966025	+	0.205335i	0.663807	−	0.747904i	$-0.268940\pi$
$163$	12.3334	+	2.62154i	0.966025	+	0.205335i	0.302218	+	0.953239i	$0.402273\pi$
$164$	2.43598	+	4.21924i	0.190218	+	0.329467i
$165$	−5.64382	+	9.44206i	−0.439371	+	0.735063i
$166$	−1.01499	+	1.75802i	−0.0787789	+	0.136449i
$167$	0.214019	+	0.658683i	0.0165613	+	0.0509704i	0.958996	−	0.283421i	$-0.0914693\pi$
$167$	0.214019	+	0.658683i	0.0165613	+	0.0509704i	−0.942434	+	0.334391i	$0.891469\pi$
$168$	2.70088	+	7.67725i	0.208378	+	0.592313i
$169$	9.59638	−	6.97218i	0.738183	−	0.536321i
$170$	−1.14782	−	1.27478i	−0.0880336	−	0.0977713i
$171$	−3.62247	+	0.769980i	−0.277017	+	0.0588819i
$172$	0.155686	+	0.0693157i	0.0118709	+	0.00528527i
$173$	18.0835	−	8.05130i	1.37486	−	0.612129i	0.419553	−	0.907731i	$-0.362187\pi$
$173$	18.0835	−	8.05130i	1.37486	−	0.612129i	0.955311	+	0.295602i	$0.0955202\pi$
$174$	−2.64150	−	8.12971i	−0.200252	−	0.616312i
$175$	−13.0651	−	9.01905i	−0.987629	−	0.681776i
$176$	−7.37592	−	3.41880i	−0.555981	−	0.257702i
$177$	6.26001	−	10.8427i	0.470531	−	0.814984i
$178$	−2.91916	+	3.24206i	−0.218800	+	0.243003i
$179$	2.36577	−	22.5088i	0.176826	−	1.68239i	−0.442121	−	0.896955i	$-0.645774\pi$
$179$	2.36577	−	22.5088i	0.176826	−	1.68239i	0.618947	−	0.785433i	$-0.287559\pi$
$180$	0.206798	+	1.96756i	0.0154138	+	0.146653i
$181$	0.784340	−	2.41395i	0.0582996	−	0.179428i	−0.917666	−	0.397353i	$-0.869929\pi$
$181$	0.784340	−	2.41395i	0.0582996	−	0.179428i	0.975965	+	0.217925i	$0.0699289\pi$
$182$	−3.08684	−	1.28606i	−0.228811	−	0.0953291i
$183$	−9.56596	+	6.95008i	−0.707136	+	0.513765i
$184$	−16.4210	+	7.31110i	−1.21057	+	0.538981i
$185$	14.2413	−	15.8166i	1.04704	−	1.16286i
$186$	4.47280	+	7.74712i	0.327962	+	0.568046i
$187$	−1.18416	+	0.833223i	−0.0865940	+	0.0609313i
$188$	−4.81887			−0.351453
$189$	1.81726	+	1.92290i	0.132186	+	0.139871i
$190$	11.7726	+	8.55327i	0.854072	+	0.620519i
$191$	1.17601	+	11.1890i	0.0850930	+	0.809606i	0.950956	+	0.309325i	$0.100103\pi$
$191$	1.17601	+	11.1890i	0.0850930	+	0.809606i	−0.865863	+	0.500281i	$0.833230\pi$
$192$	−8.55930	+	1.81933i	−0.617714	+	0.131299i
$193$	−23.6689	+	5.03097i	−1.70372	+	0.362137i	−0.954044	−	0.299665i	$-0.903125\pi$
$193$	−23.6689	+	5.03097i	−1.70372	+	0.362137i	−0.749678	+	0.661803i	$0.769792\pi$
$194$	−0.494834	−	4.70803i	−0.0355270	−	0.338017i
$195$	−2.86271	−	2.07988i	−0.205003	−	0.148943i
$196$	0.636204	+	4.12671i	0.0454431	+	0.294765i
$197$	2.89368			0.206166			0.103083	−	0.994673i	$-0.467129\pi$
$197$	2.89368			0.206166			0.103083	+	0.994673i	$0.467129\pi$
$198$	−3.92874	−	0.0595310i	−0.279203	−	0.00423069i
$199$	−3.20853	−	5.55734i	−0.227447	−	0.393949i	0.729604	−	0.683870i	$-0.239704\pi$
$199$	−3.20853	−	5.55734i	−0.227447	−	0.393949i	−0.957051	+	0.289921i	$0.906371\pi$
$200$	12.3507	−	13.7168i	0.873325	−	0.969926i
$201$	−5.32653	+	2.37152i	−0.375705	+	0.167274i
$202$	−6.63858	+	4.82321i	−0.467089	+	0.339360i
$203$	−2.45281	−	18.9320i	−0.172153	−	1.32876i
$204$	−0.0804709	+	0.247664i	−0.00563409	+	0.0173399i
$205$	−2.83163	−	26.9412i	−0.197770	−	1.88165i
$206$	−2.14142	+	20.3743i	−0.149200	+	1.41954i
$207$	−3.91008	+	4.34258i	−0.271769	+	0.301830i
$208$	1.30756	−	2.26477i	0.0906632	−	0.157033i
$209$	8.35614	−	9.00232i	0.578007	−	0.622704i
$210$	0.836983	−	10.3621i	0.0577573	−	0.715056i
$211$	−5.27295	−	16.2285i	−0.363005	−	1.11721i	−0.951221	−	0.308510i	$-0.900170\pi$
$211$	−5.27295	−	16.2285i	−0.363005	−	1.11721i	0.588217	−	0.808703i	$-0.299830\pi$
$212$	5.10904	−	2.27469i	0.350891	−	0.156227i
$213$	6.44182	+	2.86808i	0.441386	+	0.196518i
$214$	−9.70566	+	2.06300i	−0.663465	+	0.141024i
$215$	−0.634056	−	0.704191i	−0.0432423	−	0.0480254i
$216$	−2.48858	+	1.80806i	−0.169327	+	0.123023i
$217$	6.63001	+	18.8458i	0.450074	+	1.27933i
$218$	−0.435380	−	1.33996i	−0.0294877	−	0.0907537i
$219$	−3.68315	+	6.37940i	−0.248884	+	0.431080i
$220$	−4.31618	−	4.94217i	−0.290997	−	0.333201i
$221$	−0.232880	−	0.403361i	−0.0156652	−	0.0271330i
$222$	7.43608	+	1.58059i	0.499077	+	0.106082i
$223$	0.796968	+	0.579031i	0.0533689	+	0.0387748i	0.614150	−	0.789189i	$-0.289499\pi$
$223$	0.796968	+	0.579031i	0.0533689	+	0.0387748i	−0.560781	+	0.827964i	$0.689499\pi$
$224$	−8.59139	+	0.207278i	−0.574036	+	0.0138493i
$225$	1.85425	−	5.70679i	0.123617	−	0.380453i
$226$	−4.39251	−	4.87837i	−0.292185	−	0.324504i
$227$	−0.685355	−	0.305140i	−0.0454886	−	0.0202528i	0.383866	−	0.923389i	$-0.374592\pi$
$227$	−0.685355	−	0.305140i	−0.0454886	−	0.0202528i	−0.429355	+	0.903136i	$0.641259\pi$
$228$	0.230910	−	2.19696i	0.0152924	−	0.145497i
$229$	10.4868	+	2.22903i	0.692986	+	0.147299i	0.540923	−	0.841072i	$-0.318075\pi$
$229$	10.4868	+	2.22903i	0.692986	+	0.147299i	0.152063	+	0.988371i	$0.451408\pi$
$230$	22.9608			1.51399
$231$	−8.59923	−	1.74735i	−0.565788	−	0.114967i
$232$	22.1951			1.45718
$233$	−13.3214	−	2.83154i	−0.872711	−	0.185501i	−0.250279	−	0.968174i	$-0.580522\pi$
$233$	−13.3214	−	2.83154i	−0.872711	−	0.185501i	−0.622433	+	0.782673i	$0.713856\pi$
$234$	0.132116	−	1.25700i	0.00863669	−	0.0821726i
$235$	24.4779	+	10.8983i	1.59676	+	0.710925i
$236$	4.99716	+	5.54991i	0.325287	+	0.361268i
$237$	1.63074	−	5.01891i	0.105928	−	0.326013i
$238$	0.655407	−	1.20121i	0.0424837	−	0.0778626i
$239$	−18.5468	−	13.4750i	−1.19969	−	0.871628i	−0.205439	−	0.978670i	$-0.565862\pi$
$239$	−18.5468	−	13.4750i	−1.19969	−	0.871628i	−0.994255	+	0.107041i	$0.965862\pi$
$240$	7.95224	+	1.69030i	0.513315	+	0.109108i
$241$	5.88338	+	10.1903i	0.378982	+	0.656416i	0.990914	−	0.134494i	$-0.0429410\pi$
$241$	5.88338	+	10.1903i	0.378982	+	0.656416i	−0.611933	+	0.790910i	$0.709608\pi$
$242$	10.7701	−	7.33687i	0.692326	−	0.471632i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.17952	−	6.70787i	−0.139529	−	0.429427i
$245$	6.10124	−	22.4009i	0.389794	−	1.43114i
$246$	7.82819	−	5.68751i	0.499107	−	0.362622i
$247$	2.64378	+	2.93621i	0.168220	+	0.186827i
$248$	−22.7196	+	4.82921i	−1.44270	+	0.306655i
$249$	−1.56537	−	0.696948i	−0.0992013	−	0.0441673i
$250$	−3.59128	+	1.59894i	−0.227133	+	0.101126i
$251$	−0.296412	−	0.912262i	−0.0187094	−	0.0575815i	0.941266	−	0.337666i	$-0.109637\pi$
$251$	−0.296412	−	0.912262i	−0.0187094	−	0.0575815i	−0.959975	+	0.280085i	$0.909637\pi$
$252$	−1.42584	+	0.676490i	−0.0898192	+	0.0426149i
$253$	2.31764	−	19.2417i	0.145709	−	1.20972i
$254$	−5.34154	+	9.25181i	−0.335158	+	0.580510i
$255$	0.968871	−	1.07604i	0.0606731	−	0.0673843i
$256$	1.35008	−	12.8451i	0.0843797	−	0.802820i
$257$	−0.836952	−	7.96306i	−0.0522076	−	0.496722i	−0.989115	−	0.147145i	$-0.952992\pi$
$257$	−0.836952	−	7.96306i	−0.0522076	−	0.496722i	0.936907	−	0.349578i	$-0.113675\pi$
$258$	0.104592	−	0.321902i	0.00651164	−	0.0200408i
$259$	15.6720	+	6.52940i	0.973813	+	0.405717i
$260$	1.70759	−	1.24064i	0.105900	−	0.0769411i
$261$	6.59162	−	2.93478i	0.408011	−	0.181658i
$262$	−1.19503	+	1.32722i	−0.0738295	+	0.0819959i
$263$	−4.52755	−	7.84194i	−0.279181	−	0.483555i	0.692001	−	0.721897i	$-0.256729\pi$
$263$	−4.52755	−	7.84194i	−0.279181	−	0.483555i	−0.971181	+	0.238342i	$0.923396\pi$
$264$	3.29928	−	9.65392i	0.203056	−	0.594158i
$265$	−31.0963			−1.91023
$266$	−3.31975	+	11.1232i	−0.203547	+	0.682004i
$267$	−2.97919	−	2.16451i	−0.182323	−	0.132466i
$268$	−0.363543	−	3.45888i	−0.0222069	−	0.211285i
$269$	−30.4644	+	6.47541i	−1.85745	+	0.394812i	−0.993977	−	0.109589i	$-0.965047\pi$
$269$	−30.4644	+	6.47541i	−1.85745	+	0.394812i	−0.863469	+	0.504401i	$0.831713\pi$
$270$	3.84341	−	0.816943i	0.233903	−	0.0497175i
$271$	−2.87870	−	27.3890i	−0.174868	−	1.66376i	−0.632455	−	0.774597i	$-0.717953\pi$
$271$	−2.87870	−	27.3890i	−0.174868	−	1.66376i	0.457586	−	0.889165i	$-0.348714\pi$
$272$	0.865738	+	0.628995i	0.0524931	+	0.0381384i
$273$	0.807255	−	2.70479i	0.0488573	−	0.163701i
$274$	−11.1548			−0.673883
$275$	5.86238	+	19.0183i	0.353515	+	1.14685i
$276$	−1.74282	−	3.01865i	−0.104905	−	0.181701i
$277$	−0.0750616	+	0.0833644i	−0.00451002	+	0.00500888i	−0.745396	−	0.666622i	$-0.767739\pi$
$277$	−0.0750616	+	0.0833644i	−0.00451002	+	0.00500888i	0.740886	+	0.671631i	$0.234406\pi$
$278$	−21.4526	+	9.55130i	−1.28664	+	0.572849i
$279$	−6.10886	+	4.43835i	−0.365728	+	0.265717i
$280$	24.9169	+	10.3810i	1.48907	+	0.620386i
$281$	−6.01275	+	18.5053i	−0.358691	+	1.10394i	0.595148	+	0.803616i	$0.297093\pi$
$281$	−6.01275	+	18.5053i	−0.358691	+	1.10394i	−0.953838	+	0.300320i	$0.902907\pi$
$282$	1.00041	+	9.51831i	0.0595738	+	0.566807i
$283$	−1.15518	+	10.9908i	−0.0686683	+	0.653335i	0.905007	+	0.425396i	$0.139865\pi$
$283$	−1.15518	+	10.9908i	−0.0686683	+	0.653335i	−0.973675	+	0.227939i	$0.926801\pi$
$284$	−2.81447	+	3.12579i	−0.167008	+	0.185481i
$285$	−6.14153	+	10.6374i	−0.363793	+	0.630108i
$286$	2.04073	+	3.66168i	0.120671	+	0.216520i
$287$	19.5236	−	9.26298i	1.15244	−	0.546777i
$288$	−1.00374	−	3.08921i	−0.0591462	−	0.182033i
$289$	−15.3562	+	6.83700i	−0.903304	+	0.402177i
$290$	−25.9003	−	11.5316i	−1.52092	−	0.677156i
$291$	3.90861	−	0.830801i	0.229127	−	0.0487024i
$292$	−2.94013	−	3.26535i	−0.172058	−	0.191090i
$293$	−3.10125	+	2.25319i	−0.181177	+	0.131633i	−0.674677	−	0.738113i	$-0.735717\pi$
$293$	−3.10125	+	2.25319i	−0.181177	+	0.131633i	0.493500	+	0.869746i	$0.335717\pi$
$294$	8.01907	−	2.11336i	0.467682	−	0.123254i
$295$	−12.8320	−	39.4928i	−0.747106	−	2.29936i
$296$	−9.86955	+	17.0946i	−0.573656	+	0.993601i
$297$	−0.296667	−	3.30333i	−0.0172144	−	0.191679i
$298$	−6.30109	−	10.9138i	−0.365013	−	0.632220i
$299$	6.09807	+	1.29619i	0.352661	+	0.0749603i
$300$	2.89568	+	2.10383i	0.167182	+	0.121465i
$301$	0.362047	−	0.663547i	0.0208681	−	0.0382462i
$302$	7.58906	−	23.3567i	0.436702	−	1.34403i
$303$	−4.63470	−	5.14735i	−0.266256	−	0.295708i
$304$	−8.29297	−	3.69227i	−0.475634	−	0.211766i
$305$	−4.09932	+	39.0024i	−0.234726	+	2.23327i
$306$	0.505896	+	0.107531i	0.0289201	+	0.00614716i
$307$	21.8518			1.24715			0.623573	−	0.781765i	$-0.285681\pi$
$307$	21.8518			1.24715			0.623573	+	0.781765i	$0.285681\pi$
$308$	2.57635	−	4.55627i	0.146801	−	0.259617i
$309$	−17.2926			−0.983743
$310$	29.0215	+	6.16871i	1.64831	+	0.350359i
$311$	0.156932	−	1.49311i	0.00889882	−	0.0846666i	−0.989171	−	0.146767i	$-0.953113\pi$
$311$	0.156932	−	1.49311i	0.00889882	−	0.0846666i	0.998070	+	0.0621004i	$0.0197799\pi$
$312$	2.99805	+	1.33482i	0.169731	+	0.0755691i
$313$	12.2416	+	13.5957i	0.691937	+	0.768474i	0.982071	−	0.188512i	$-0.0603664\pi$
$313$	12.2416	+	13.5957i	0.691937	+	0.768474i	−0.290134	+	0.956986i	$0.593700\pi$
$314$	−2.00838	+	6.18114i	−0.113339	+	0.348822i
$315$	8.77260	−	0.211650i	0.494280	−	0.0119251i
$316$	2.54664	+	1.85024i	0.143260	+	0.104084i
$317$	33.5082	+	7.12239i	1.88201	+	0.400033i	0.997755	−	0.0669756i	$-0.0213350\pi$
$317$	33.5082	+	7.12239i	1.88201	+	0.400033i	0.884253	+	0.467009i	$0.154668\pi$
$318$	−5.55366	−	9.61922i	−0.311434	−	0.539419i
$319$	−12.2781	+	20.5411i	−0.687439	+	1.15008i
$320$	−14.5114	+	25.1345i	−0.811212	+	1.40506i
$321$	−2.58819	−	7.96563i	−0.144459	−	0.444598i
$322$	6.07846	+	17.2780i	0.338739	+	0.962864i
$323$	−1.30800	+	0.950318i	−0.0727791	+	0.0528771i
$324$	−0.399133	−	0.443282i	−0.0221741	−	0.0246268i
$325$	−6.26186	+	1.33100i	−0.347346	+	0.0738306i
$326$	13.6463	+	6.07572i	0.755798	+	0.336503i
$327$	1.08645	−	0.483718i	0.0600808	−	0.0267497i
$328$	7.76379	+	23.8945i	0.428683	+	1.31935i
$329$	−1.72085	+	21.3047i	−0.0948735	+	1.17457i
$330$	−8.86580	+	9.55139i	−0.488046	+	0.525787i
$331$	3.55061	−	6.14983i	0.195159	−	0.338025i	−0.751794	−	0.659399i	$-0.770811\pi$
$331$	3.55061	−	6.14983i	0.195159	−	0.338025i	0.946953	+	0.321373i	$0.104144\pi$
$332$	0.683919	−	0.759569i	0.0375349	−	0.0416868i
$333$	−0.670760	+	6.38186i	−0.0367574	+	0.349724i
$334$	0.0857653	+	0.816003i	0.00469287	+	0.0446497i
$335$	−5.97589	+	18.3919i	−0.326498	+	1.00486i
$336$	0.833261	+	6.43152i	0.0454581	+	0.350868i
$337$	7.92867	−	5.76051i	0.431902	−	0.313795i	−0.350507	−	0.936560i	$-0.613991\pi$
$337$	7.92867	−	5.76051i	0.431902	−	0.313795i	0.782409	+	0.622765i	$0.213991\pi$
$338$	12.8377	−	5.71571i	0.698278	−	0.310894i
$339$	3.70771	−	4.11783i	0.201375	−	0.223650i
$340$	0.431849	+	0.747985i	0.0234203	+	0.0405652i
$341$	8.09891	−	23.6980i	0.438581	−	1.28332i
$342$	−4.38740			−0.237244
$343$	18.4718	−	1.33904i	0.997383	−	0.0723014i
$344$	0.710989	+	0.516564i	0.0383340	+	0.0278513i
$345$	2.02589	+	19.2750i	0.109070	+	1.03773i
$346$	22.9384	−	4.87572i	1.23318	−	0.262120i
$347$	−22.0589	+	4.68876i	−1.18418	+	0.251706i	−0.757585	−	0.652736i	$-0.773621\pi$
$347$	−22.0589	+	4.68876i	−1.18418	+	0.251706i	−0.426597	+	0.904442i	$0.640288\pi$
$348$	0.449887	+	4.28039i	0.0241165	+	0.229453i
$349$	20.5132	+	14.9037i	1.09805	+	0.797777i	0.980740	−	0.195318i	$-0.0625740\pi$
$349$	20.5132	+	14.9037i	1.09805	+	0.797777i	0.117306	+	0.993096i	$0.462574\pi$
$350$	−12.9184	−	13.6694i	−0.690519	−	0.730662i
$351$	1.06687			0.0569456
$352$	8.61861	+	6.46354i	0.459373	+	0.344508i
$353$	1.74985	+	3.03083i	0.0931351	+	0.161315i	0.908829	−	0.417169i	$-0.136978\pi$
$353$	1.74985	+	3.03083i	0.0931351	+	0.161315i	−0.815694	+	0.578484i	$0.803644\pi$
$354$	9.92483	−	11.0226i	0.527499	−	0.585847i
$355$	21.3656	−	9.51257i	1.13397	−	0.504875i
$356$	1.77707	−	1.29112i	0.0941847	−	0.0684292i
$357$	1.06621	+	0.444212i	0.0564298	+	0.0235102i
$358$	8.28567	−	25.5007i	0.437911	−	1.34775i
$359$	1.48979	+	14.1744i	0.0786282	+	0.748097i	0.960814	+	0.277195i	$0.0894048\pi$
$359$	1.48979	+	14.1744i	0.0786282	+	0.748097i	−0.882185	+	0.470902i	$0.843928\pi$
$360$	−1.06644	+	10.1465i	−0.0562061	+	0.534765i
$361$	−3.53624	+	3.92739i	−0.186118	+	0.206705i
$362$	1.50349	−	2.60411i	0.0790214	−	0.136869i
$363$	7.10938	+	8.39385i	0.373146	+	0.440563i
$364$	1.38563	+	0.956523i	0.0726268	+	0.0501354i
$365$	7.54983	+	23.2360i	0.395176	+	1.21623i
$366$	−12.7970	+	5.69759i	−0.668910	+	0.297818i
$367$	22.0425	+	9.81397i	1.15061	+	0.512285i	0.891258	−	0.453498i	$-0.149824\pi$
$367$	22.0425	+	9.81397i	1.15061	+	0.512285i	0.259353	+	0.965783i	$0.416491\pi$
$368$	−14.0107	+	2.97806i	−0.730356	+	0.155242i
$369$	5.46522	+	6.06974i	0.284508	+	0.315978i
$370$	20.3987	−	14.8205i	1.06048	−	0.770483i
$371$	−8.23216	−	23.3999i	−0.427393	−	1.21486i
$372$	−1.39185	−	4.28367i	−0.0721640	−	0.222098i
$373$	1.30755	−	2.26475i	0.0677025	−	0.117264i	−0.830187	−	0.557485i	$-0.811766\pi$
$373$	1.30755	−	2.26475i	0.0677025	−	0.117264i	0.897890	+	0.440221i	$0.145100\pi$
$374$	−1.57744	+	0.673873i	−0.0815675	+	0.0348452i
$375$	−1.65914	−	2.87371i	−0.0856775	−	0.148398i
$376$	−24.3073	−	5.16668i	−1.25356	−	0.266451i
$377$	−6.22778	−	4.52474i	−0.320747	−	0.233036i
$378$	1.63222	+	2.67589i	0.0839524	+	0.137633i
$379$	−9.84838	+	30.3102i	−0.505877	+	1.55693i	0.293414	+	0.955985i	$0.405209\pi$
$379$	−9.84838	+	30.3102i	−0.505877	+	1.55693i	−0.799291	+	0.600944i	$0.794791\pi$
$380$	−4.90258	−	5.44486i	−0.251497	−	0.279316i
$381$	−8.23795	−	3.66777i	−0.422043	−	0.187906i
$382$	−1.39321	+	13.2555i	−0.0712830	+	0.678212i
$383$	−3.71916	−	0.790532i	−0.190040	−	0.0403943i	0.111908	−	0.993719i	$-0.464304\pi$
$383$	−3.71916	−	0.790532i	−0.190040	−	0.0403943i	−0.301949	+	0.953324i	$0.597637\pi$
$384$	−3.87033			−0.197507
$385$	−23.3912	+	17.3174i	−1.19212	+	0.882574i
$386$	−28.6669			−1.45910
$387$	0.279457	+	0.0594005i	0.0142056	+	0.00301950i
$388$	−0.249149	+	2.37050i	−0.0126486	+	0.120344i
$389$	27.2505	+	12.1327i	1.38166	+	0.615153i	0.956970	−	0.290188i	$-0.0937178\pi$
$389$	27.2505	+	12.1327i	1.38166	+	0.615153i	0.424686	+	0.905341i	$0.360384\pi$
$390$	−2.80503	−	3.11530i	−0.142038	−	0.157749i
$391$	−0.788327	+	2.42622i	−0.0398674	+	0.122699i
$392$	−1.21543	+	21.4981i	−0.0613886	+	1.08582i
$393$	−1.21961	−	0.886097i	−0.0615211	−	0.0446977i
$394$	3.35322	+	0.712749i	0.168933	+	0.0359078i
$395$	−8.75143	−	15.1579i	−0.440332	−	0.762678i
$396$	1.92867	+	0.440594i	0.0969191	+	0.0221407i
$397$	−4.08559	+	7.07644i	−0.205050	+	0.355157i	−0.950149	−	0.311798i	$-0.899069\pi$
$397$	−4.08559	+	7.07644i	−0.205050	+	0.355157i	0.745099	+	0.666954i	$0.232402\pi$
$398$	−2.34923	−	7.23019i	−0.117756	−	0.362417i
$399$	−9.63051	−	1.80542i	−0.482128	−	0.0903841i
$400$	11.8993	−	8.64537i	0.594967	−	0.432269i
$401$	9.62479	+	10.6894i	0.480639	+	0.533804i	0.933881	−	0.357584i	$-0.116399\pi$
$401$	9.62479	+	10.6894i	0.480639	+	0.533804i	−0.453242	+	0.891388i	$0.649733\pi$
$402$	−6.75656	+	1.43615i	−0.336987	+	0.0716287i
$403$	7.35946	+	3.27664i	0.366601	+	0.163221i
$404$	3.77440	−	1.68047i	0.187783	−	0.0836065i
$405$	1.02492	+	3.15437i	0.0509285	+	0.156742i
$406$	1.82084	−	22.5427i	0.0903670	−	1.11877i
$407$	−10.3609	−	18.5906i	−0.513572	−	0.921500i
$408$	−0.671450	+	1.16299i	−0.0332418	+	0.0575764i
$409$	−1.50634	+	1.67296i	−0.0744836	+	0.0827224i	−0.779235	−	0.626732i	$-0.784392\pi$
$409$	−1.50634	+	1.67296i	−0.0744836	+	0.0827224i	0.704751	+	0.709455i	$0.251059\pi$
$410$	3.35462	−	31.9171i	0.165673	−	1.57627i
$411$	−0.984210	−	9.36413i	−0.0485475	−	0.461898i
$412$	3.18750	−	9.81012i	0.157037	−	0.483310i
$413$	26.3212	−	20.1110i	1.29518	−	0.989598i
$414$	−5.60066	+	4.06912i	−0.275257	+	0.199986i
$415$	−5.19186	+	2.31156i	−0.254858	+	0.113470i
$416$	−2.31881	+	2.57530i	−0.113689	+	0.126264i
$417$	−9.91088	−	17.1661i	−0.485338	−	0.840630i
$418$	11.9005	−	8.37374i	0.582075	−	0.409573i
$419$	−8.25053			−0.403065			−0.201532	−	0.979482i	$-0.564592\pi$
$419$	−8.25053			−0.403065			−0.201532	+	0.979482i	$0.564592\pi$
$420$	−1.49696	+	5.01572i	−0.0730442	+	0.244742i
$421$	−2.59071	−	1.88226i	−0.126263	−	0.0917356i	0.522861	−	0.852418i	$-0.324865\pi$
$421$	−2.59071	−	1.88226i	−0.126263	−	0.0917356i	−0.649125	+	0.760682i	$0.724865\pi$
$422$	−2.11306	−	20.1045i	−0.102862	−	0.978669i
$423$	−7.90211	+	1.67964i	−0.384214	+	0.0816671i
$424$	28.2099	−	5.99620i	1.36999	−	0.291201i
$425$	−0.273823	−	2.60525i	−0.0132824	−	0.126373i
$426$	6.75839	+	4.91026i	0.327445	+	0.237903i
$427$	−30.4344	+	7.24044i	−1.47283	+	0.350389i
$428$	4.99598			0.241490
$429$	−2.89383	+	2.03622i	−0.139715	+	0.0983098i
$430$	−0.561298	−	0.972197i	−0.0270682	−	0.0468835i
$431$	−25.0417	+	27.8116i	−1.20622	+	1.33964i	−0.281229	+	0.959641i	$0.590742\pi$
$431$	−25.0417	+	27.8116i	−1.20622	+	1.33964i	−0.924987	+	0.379998i	$0.875925\pi$
$432$	−2.23928	+	0.996994i	−0.107738	+	0.0479679i
$433$	−1.73771	+	1.26252i	−0.0835091	+	0.0606729i	−0.628756	−	0.777602i	$-0.716436\pi$
$433$	−1.73771	+	1.26252i	−0.0835091	+	0.0606729i	0.545247	+	0.838275i	$0.316436\pi$
$434$	3.04096	+	23.4717i	0.145971	+	1.12668i
$435$	7.39520	−	22.7601i	0.354573	−	1.09126i
$436$	0.0741517	+	0.705506i	0.00355122	+	0.0337876i
$437$	2.26209	−	21.5224i	0.108210	−	1.02955i
$438$	−5.83938	+	6.48529i	−0.279017	+	0.309879i
$439$	6.72587	−	11.6496i	0.321008	−	0.556003i	−0.659688	−	0.751540i	$-0.729312\pi$
$439$	6.72587	−	11.6496i	0.321008	−	0.556003i	0.980696	+	0.195537i	$0.0626449\pi$
$440$	−16.4728	−	29.5570i	−0.785308	−	1.40907i
$441$	2.48165	+	6.54533i	0.118174	+	0.311683i
$442$	−0.170511	−	0.524779i	−0.00811038	−	0.0249612i
$443$	2.00242	−	0.891536i	0.0951380	−	0.0423582i	−0.358616	−	0.933485i	$-0.616751\pi$
$443$	2.00242	−	0.891536i	0.0951380	−	0.0423582i	0.453754	+	0.891127i	$0.350085\pi$
$444$	−3.49679	−	1.55687i	−0.165950	−	0.0738859i
$445$	−11.9468	+	2.53936i	−0.566331	+	0.120377i
$446$	0.780910	+	0.867289i	0.0369772	+	0.0410673i
$447$	8.60591	−	6.25256i	0.407045	−	0.295736i
$448$	−22.7553	−	4.26591i	−1.07509	−	0.201545i
$449$	−2.39573	−	7.37329i	−0.113061	−	0.347967i	0.878476	−	0.477786i	$-0.158560\pi$
$449$	−2.39573	−	7.37329i	−0.113061	−	0.347967i	−0.991538	+	0.129819i	$0.958560\pi$
$450$	3.55437	−	6.15635i	0.167555	−	0.290213i
$451$	−26.4087	−	6.03293i	−1.24354	−	0.284080i
$452$	1.65261	+	2.86241i	0.0777325	+	0.134637i
$453$	20.2770	+	4.31001i	0.952696	+	0.202502i
$454$	−0.719035	−	0.522409i	−0.0337460	−	0.0245179i
$455$	−4.87519	−	7.99246i	−0.228552	−	0.374692i
$456$	3.52028	−	10.8343i	0.164852	−	0.507363i
$457$	−9.19908	−	10.2166i	−0.430315	−	0.477913i	0.488521	−	0.872552i	$-0.337536\pi$
$457$	−9.19908	−	10.2166i	−0.430315	−	0.477913i	−0.918836	+	0.394639i	$0.870870\pi$
$458$	11.6031	+	5.16604i	0.542178	+	0.241393i
$459$	−0.0456335	+	0.434174i	−0.00212999	+	0.0202655i
$460$	−11.3082	−	2.40362i	−0.527246	−	0.112070i
$461$	−5.24645			−0.244352			−0.122176	−	0.992508i	$-0.538987\pi$
$461$	−5.24645			−0.244352			−0.122176	+	0.992508i	$0.538987\pi$
$462$	−9.53446	−	4.14294i	−0.443583	−	0.192747i
$463$	23.7813			1.10521			0.552606	−	0.833443i	$-0.313634\pi$
$463$	23.7813			1.10521			0.552606	+	0.833443i	$0.313634\pi$
$464$	17.3000	+	3.67722i	0.803131	+	0.170711i
$465$	−2.61784	+	24.9071i	−0.121399	+	1.15504i
$466$	−14.7395	−	6.56243i	−0.682792	−	0.303999i
$467$	−1.98068	−	2.19977i	−0.0916549	−	0.101793i	0.695572	−	0.718456i	$-0.255151\pi$
$467$	−1.98068	−	2.19977i	−0.0916549	−	0.101793i	−0.787227	+	0.616663i	$0.788484\pi$
$468$	−0.196654	+	0.605239i	−0.00909034	+	0.0279772i
$469$	−15.4219	+	0.372071i	−0.712116	+	0.0171807i
$470$	25.6808	+	18.6582i	1.18457	+	0.860639i
$471$	−5.36612	−	1.14060i	−0.247258	−	0.0525562i
$472$	19.2562	+	33.3527i	0.886337	+	1.53518i
$473$	−0.871380	+	0.372248i	−0.0400661	+	0.0171160i
$474$	3.12594	−	5.41428i	0.143579	−	0.248686i
$475$	6.86703	+	21.1345i	0.315081	+	0.969719i
$476$	−0.448533	+	0.522981i	−0.0205585	+	0.0239708i
$477$	7.58508	−	5.51088i	0.347297	−	0.252326i
$478$	−18.1731	−	20.1833i	−0.831219	−	0.923162i
$479$	18.2698	−	3.88337i	0.834768	−	0.177435i	0.229351	−	0.973344i	$-0.426340\pi$
$479$	18.2698	−	3.88337i	0.834768	−	0.177435i	0.605417	+	0.795908i	$0.293006\pi$
$480$	−9.84185	−	4.38187i	−0.449217	−	0.200004i
$481$	6.25427	−	2.78458i	0.285170	−	0.126966i
$482$	4.30771	+	13.2578i	0.196211	+	0.603874i
$483$	−13.9681	+	6.62718i	−0.635570	+	0.301547i
$484$	−6.07229	+	2.48594i	−0.276013	+	0.112997i
$485$	6.62665	−	11.4777i	0.300901	−	0.521175i
$486$	−0.792716	+	0.880401i	−0.0359583	+	0.0399358i
$487$	1.85263	−	17.6266i	0.0839507	−	0.798738i	−0.868836	−	0.495099i	$-0.835132\pi$
$487$	1.85263	−	17.6266i	0.0839507	−	0.798738i	0.952787	−	0.303639i	$-0.0982016\pi$
$488$	−3.80190	−	36.1726i	−0.172104	−	1.63746i
$489$	−3.89637	+	11.9918i	−0.176200	+	0.542287i
$490$	12.5878	−	24.4555i	0.568657	−	1.10479i
$491$	10.1172	−	7.35059i	0.456584	−	0.331727i	−0.335606	−	0.942002i	$-0.608941\pi$
$491$	10.1172	−	7.35059i	0.456584	−	0.331727i	0.792190	+	0.610275i	$0.208941\pi$
$492$	−4.45076	+	1.98160i	−0.200656	+	0.0893376i
$493$	2.10777	−	2.34091i	0.0949290	−	0.105429i
$494$	2.34041	+	4.05370i	0.105300	+	0.182385i
$495$	−8.80040	−	6.59987i	−0.395548	−	0.296642i
$496$	−18.5089			−0.831076
$497$	12.8143	+	13.5593i	0.574801	+	0.608217i
$498$	−1.64230	−	1.19320i	−0.0735930	−	0.0534685i
$499$	−1.97761	−	18.8157i	−0.0885298	−	0.842305i	−0.945211	−	0.326459i	$-0.894144\pi$
$499$	−1.97761	−	18.8157i	−0.0885298	−	0.842305i	0.856682	−	0.515846i	$-0.172522\pi$
$500$	1.93608	−	0.411527i	0.0865843	−	0.0184041i
$501$	−0.677446	+	0.143996i	−0.0302661	+	0.00643325i
$502$	−0.118783	−	1.13015i	−0.00530155	−	0.0504409i
$503$	5.87890	+	4.27127i	0.262127	+	0.190447i	0.711084	−	0.703107i	$-0.248204\pi$
$503$	5.87890	+	4.27127i	0.262127	+	0.190447i	−0.448957	+	0.893553i	$0.648204\pi$
$504$	−7.91751	+	1.88360i	−0.352674	+	0.0839021i
$505$	−22.9729			−1.02228
$506$	7.42516	−	21.7266i	0.330089	−	0.965863i
$507$	5.93089	+	10.2726i	0.263400	+	0.456222i
$508$	3.59921	−	3.99733i	0.159689	−	0.177353i
$509$	−24.6439	+	10.9722i	−1.09232	+	0.486333i	−0.872205	−	0.489140i	$-0.837311\pi$
$509$	−24.6439	+	10.9722i	−1.09232	+	0.486333i	−0.220117	+	0.975473i	$0.570644\pi$
$510$	1.38778	−	1.00828i	0.0614518	−	0.0446474i
$511$	−15.4864	+	11.8325i	−0.685076	+	0.523441i
$512$	7.12038	−	21.9143i	0.314679	−	0.968484i
$513$	−0.387111	−	3.68311i	−0.0170914	−	0.162613i
$514$	0.991533	−	9.43381i	0.0437347	−	0.416107i
$515$	−38.3776	+	42.6226i	−1.69112	+	1.87818i
$516$	−0.0852095	+	0.147587i	−0.00375114	+	0.00649716i
$517$	18.2282	−	19.6378i	0.801675	−	0.863669i
$518$	16.5526	+	11.4265i	0.727280	+	0.502053i
$519$	6.11695	+	18.8260i	0.268504	+	0.826372i
$520$	9.94361	−	4.42718i	0.436056	−	0.194145i
$521$	15.5343	+	6.91634i	0.680572	+	0.303010i	0.717753	−	0.696298i	$-0.245171\pi$
$521$	15.5343	+	6.91634i	0.680572	+	0.303010i	−0.0371803	+	0.999309i	$0.511838\pi$
$522$	8.36129	−	1.77725i	0.365964	−	0.0777880i
$523$	25.0691	+	27.8420i	1.09619	+	1.21745i	0.974383	+	0.224894i	$0.0722037\pi$
$523$	25.0691	+	27.8420i	1.09619	+	1.21745i	0.121812	+	0.992553i	$0.461130\pi$
$524$	0.727490	−	0.528553i	0.0317806	−	0.0230899i
$525$	10.3353	−	12.0508i	0.451070	−	0.525939i
$526$	−3.31499	−	10.2025i	−0.144541	−	0.444850i
$527$	−1.64825	+	2.85485i	−0.0717987	+	0.124359i
$528$	4.17106	−	6.97815i	0.181522	−	0.303685i
$529$	−5.57338	−	9.65338i	−0.242321	−	0.419712i
$530$	−36.0346	−	7.65939i	−1.56524	−	0.332703i
$531$	10.1289	+	7.35909i	0.439558	+	0.319357i
$532$	2.79938	−	5.13061i	0.121369	−	0.222440i
$533$	2.69273	−	8.28737i	0.116635	−	0.358966i
$534$	−2.91916	−	3.24206i	−0.126325	−	0.140298i
$535$	−25.3775	−	11.2988i	−1.09717	−	0.488490i
$536$	1.87475	−	17.8371i	0.0809769	−	0.770444i
$537$	22.1382	+	4.70562i	0.955335	+	0.203063i
$538$	−36.8973			−1.59076
$539$	−19.2237	−	13.0173i	−0.828021	−	0.560697i
$540$	−1.97839			−0.0851365
$541$	3.36718	+	0.715716i	0.144766	+	0.0307710i	0.279725	−	0.960080i	$-0.409757\pi$
$541$	3.36718	+	0.715716i	0.144766	+	0.0307710i	−0.134958	+	0.990851i	$0.543090\pi$
$542$	3.41038	−	32.4476i	0.146488	−	1.39374i
$543$	2.31874	+	1.03237i	0.0995067	+	0.0443033i
$544$	−0.948858	−	1.05381i	−0.0406819	−	0.0451819i
$545$	1.21890	−	3.75138i	0.0522119	−	0.160692i
$546$	1.60168	−	2.93550i	0.0685454	−	0.125628i
$547$	12.3927	+	9.00383i	0.529874	+	0.384976i	0.820311	−	0.571918i	$-0.193801\pi$
$547$	12.3927	+	9.00383i	0.529874	+	0.384976i	−0.290437	+	0.956894i	$0.593801\pi$
$548$	5.49369	+	1.16772i	0.234679	+	0.0498826i
$549$	−5.91209	−	10.2400i	−0.252322	−	0.437034i
$550$	2.10893	+	23.4825i	0.0899251	+	1.00130i
$551$	−13.3608	+	23.1416i	−0.569189	+	0.985865i
$552$	−5.55458	−	17.0953i	−0.236419	−	0.727622i
$553$	9.08952	−	10.5982i	0.386526	−	0.450682i
$554$	−0.107516	+	0.0781147i	−0.00456790	+	0.00331878i
$555$	14.2413	+	15.8166i	0.604509	+	0.671375i
$556$	11.5652	−	2.45826i	0.490474	−	0.104254i
$557$	37.1525	+	16.5414i	1.57420	+	0.700880i	0.993563	−	0.113282i	$-0.0361363\pi$
$557$	37.1525	+	16.5414i	1.57420	+	0.700880i	0.580639	+	0.814161i	$0.302803\pi$
$558$	−8.17221	+	3.63850i	−0.345957	+	0.154030i
$559$	−0.0941904	−	0.289888i	−0.00398383	−	0.0122610i
$560$	17.7016	+	12.2197i	0.748028	+	0.516376i
$561$	−0.704881	−	1.26476i	−0.0297601	−	0.0533984i
$562$	−11.5257	+	19.9631i	−0.486183	+	0.842093i
$563$	−10.4016	+	11.5522i	−0.438376	+	0.486866i	−0.921331	−	0.388779i	$-0.872897\pi$
$563$	−10.4016	+	11.5522i	−0.438376	+	0.486866i	0.482955	+	0.875645i	$0.339564\pi$
$564$	0.503710	−	4.79248i	0.0212100	−	0.201800i
$565$	−1.92103	−	18.2774i	−0.0808185	−	0.768936i
$566$	−4.04580	+	12.4517i	−0.170058	+	0.523383i
$567$	−2.10233	+	1.60631i	−0.0882894	+	0.0674586i
$568$	−17.5481	+	12.7495i	−0.736303	+	0.534955i
$569$	16.0703	−	7.15496i	0.673702	−	0.299951i	−0.0412257	−	0.999150i	$-0.513126\pi$
$569$	16.0703	−	7.15496i	0.673702	−	0.299951i	0.714928	+	0.699198i	$0.246460\pi$
$570$	−9.73698	+	10.8140i	−0.407837	+	0.452949i
$571$	−3.71068	−	6.42709i	−0.155287	−	0.268965i	0.777876	−	0.628417i	$-0.216297\pi$
$571$	−3.71068	−	6.42709i	−0.155287	−	0.268965i	−0.933164	+	0.359452i	$0.882964\pi$
$572$	−0.621740	−	2.01700i	−0.0259962	−	0.0843351i
$573$	−11.2506			−0.470001
$574$	24.9056	−	5.92512i	1.03954	−	0.247310i
$575$	28.3673	+	20.6101i	1.18300	+	0.859499i
$576$	−0.914678	−	8.70258i	−0.0381116	−	0.362608i
$577$	−33.3795	+	7.09504i	−1.38961	+	0.295370i	−0.841148	−	0.540806i	$-0.818119\pi$
$577$	−33.3795	+	7.09504i	−1.38961	+	0.295370i	−0.548461	+	0.836176i	$0.684786\pi$
$578$	−19.4789	+	4.14036i	−0.810214	+	0.172216i
$579$	−2.52934	−	24.0651i	−0.105116	−	1.00011i
$580$	11.5487	+	8.39061i	0.479533	+	0.348401i
$581$	−3.11390	−	3.29492i	−0.129186	−	0.136696i
$582$	4.73397			0.196229
$583$	−10.0560	+	29.4247i	−0.416478	+	1.21865i
$584$	−11.3296	−	19.6234i	−0.468821	−	0.812022i
$585$	2.36772	−	2.62962i	0.0978931	−	0.108721i
$586$	−4.14874	+	1.84714i	−0.171383	+	0.0763046i
$587$	−20.8120	+	15.1208i	−0.859003	+	0.624102i	−0.927614	−	0.373541i	$-0.878143\pi$
$587$	−20.8120	+	15.1208i	−0.859003	+	0.624102i	0.0686105	+	0.997644i	$0.478143\pi$
$588$	−4.17061	+	0.201359i	−0.171993	+	0.00830391i
$589$	8.64143	−	26.5956i	0.356064	−	1.09585i
$590$	−5.14224	−	48.9252i	−0.211703	−	2.01422i
$591$	−0.302472	+	2.87783i	−0.0124420	+	0.118378i
$592$	−10.5250	+	11.6892i	−0.432575	+	0.480424i
$593$	5.54177	−	9.59863i	0.227573	−	0.394168i	−0.729515	−	0.683965i	$-0.760254\pi$
$593$	5.54177	−	9.59863i	0.227573	−	0.394168i	0.957088	+	0.289796i	$0.0935875\pi$
$594$	0.469870	−	3.90100i	0.0192790	−	0.160060i
$595$	3.46113	−	1.64214i	0.141892	−	0.0673211i
$596$	1.96078	+	6.03465i	0.0803166	+	0.247189i
$597$	5.86228	−	2.61005i	0.239927	−	0.106822i
$598$	6.74723	+	3.00406i	0.275915	+	0.122845i
$599$	40.6285	−	8.63584i	1.66003	−	0.352851i	0.720011	−	0.693963i	$-0.244137\pi$
$599$	40.6285	−	8.63584i	1.66003	−	0.352851i	0.940023	+	0.341112i	$0.110803\pi$
$600$	12.3507	+	13.7168i	0.504215	+	0.559987i
$601$	−19.6136	+	14.2501i	−0.800054	+	0.581273i	−0.910930	−	0.412561i	$-0.864634\pi$
$601$	−19.6136	+	14.2501i	−0.800054	+	0.581273i	0.110876	+	0.993834i	$0.464634\pi$
$602$	0.582983	−	0.679747i	0.0237606	−	0.0277044i
$603$	−1.80176	−	5.54524i	−0.0733733	−	0.225820i
$604$	−6.18267	+	10.7087i	−0.251569	+	0.435731i
$605$	36.4669	+	1.10540i	1.48259	+	0.0449408i
$606$	−4.10287	−	7.10637i	−0.166668	−	0.288677i
$607$	5.26219	+	1.11851i	0.213586	+	0.0453991i	0.313462	−	0.949601i	$-0.398511\pi$
$607$	5.26219	+	1.11851i	0.213586	+	0.0453991i	−0.0998759	+	0.995000i	$0.531845\pi$
$608$	9.73193	+	7.07066i	0.394682	+	0.286753i
$609$	19.0847	−	0.460441i	0.773350	−	0.0186580i
$610$	−14.3571	+	44.1866i	−0.581301	+	1.78906i
$611$	5.76717	+	6.40509i	0.233315	+	0.259122i
$612$	−0.237896	−	0.105918i	−0.00961637	−	0.00428148i
$613$	3.04526	−	28.9738i	0.122997	−	1.17024i	−0.742684	−	0.669642i	$-0.766447\pi$
$613$	3.04526	−	28.9738i	0.122997	−	1.17024i	0.865681	−	0.500597i	$-0.166886\pi$
$614$	25.3220	+	5.38235i	1.02191	+	0.217214i
$615$	27.0896			1.09236
$616$	17.8807	−	20.2204i	0.720435	−	0.814703i
$617$	−16.8276			−0.677455			−0.338727	−	0.940885i	$-0.609996\pi$
$617$	−16.8276			−0.677455			−0.338727	+	0.940885i	$0.609996\pi$
$618$	−20.0388	−	4.25938i	−0.806080	−	0.171338i
$619$	−5.00259	+	47.5964i	−0.201071	+	1.91306i	0.171718	+	0.985146i	$0.445068\pi$
$619$	−5.00259	+	47.5964i	−0.201071	+	1.91306i	−0.372789	+	0.927916i	$0.621599\pi$
$620$	−13.6473	−	6.07615i	−0.548087	−	0.244024i
$621$	−3.91008	−	4.34258i	−0.156906	−	0.174262i
$622$	0.549626	−	1.69158i	0.0220380	−	0.0678260i
$623$	−5.07355	−	8.31767i	−0.203268	−	0.333240i
$624$	2.11568	+	1.53713i	0.0846951	+	0.0615346i
$625$	18.5815	+	3.94963i	0.743262	+	0.157985i
$626$	10.8369	+	18.7701i	0.433130	+	0.750202i
$627$	8.07955	+	9.25137i	0.322666	+	0.369464i
$628$	1.63619	−	2.83396i	0.0652909	−	0.113087i
$629$	0.865694	+	2.66433i	0.0345175	+	0.106234i
$630$	10.2179	+	1.91554i	0.407090	+	0.0763168i
$631$	−19.2278	+	13.9698i	−0.765448	+	0.556131i	−0.900577	−	0.434697i	$-0.856855\pi$
$631$	−19.2278	+	13.9698i	−0.765448	+	0.556131i	0.135128	+	0.990828i	$0.456855\pi$
$632$	10.8620	+	12.0634i	0.432066	+	0.479858i
$633$	16.6907	−	3.54772i	0.663397	−	0.141009i
$634$	37.0752	+	16.5069i	1.47244	+	0.655575i
$635$	−27.3228	+	12.1649i	−1.08427	+	0.482749i
$636$	1.72819	+	5.31883i	0.0685273	+	0.210905i
$637$	4.72370	−	5.78443i	0.187160	−	0.229187i
$638$	−19.2874	+	20.7789i	−0.763596	+	0.822645i
$639$	−3.52573	+	6.10674i	−0.139476	+	0.241579i
$640$	−8.58944	+	9.53954i	−0.339527	+	0.377083i
$641$	−1.21762	+	11.5849i	−0.0480931	+	0.457575i	0.943802	+	0.330513i	$0.107222\pi$
$641$	−1.21762	+	11.5849i	−0.0480931	+	0.457575i	−0.991895	+	0.127063i	$0.959445\pi$
$642$	−1.03718	−	9.86813i	−0.0409343	−	0.389464i
$643$	8.60776	−	26.4920i	0.339457	−	1.04474i	−0.625028	−	0.780602i	$-0.714912\pi$
$643$	8.60776	−	26.4920i	0.339457	−	1.04474i	0.964485	−	0.264138i	$-0.0850876\pi$
$644$	−1.18491	−	9.14568i	−0.0466918	−	0.360390i
$645$	0.766610	−	0.556975i	0.0301852	−	0.0219309i
$646$	−1.74980	+	0.779059i	−0.0688448	+	0.0306517i
$647$	21.2369	−	23.5860i	0.834908	−	0.927260i	−0.163331	−	0.986571i	$-0.552224\pi$
$647$	21.2369	−	23.5860i	0.834908	−	0.927260i	0.998240	+	0.0593116i	$0.0188906\pi$
$648$	−1.53803	−	2.66394i	−0.0604195	−	0.104650i
$649$	−41.5195	−	0.629132i	−1.62978	−	0.0246956i
$650$	−7.58414			−0.297474
$651$	−19.4355	+	4.62377i	−0.761739	+	0.181220i
$652$	−6.08474	−	4.42083i	−0.238297	−	0.173133i
$653$	0.146717	+	1.39592i	0.00574149	+	0.0546266i	0.997018	−	0.0771757i	$-0.0245902\pi$
$653$	0.146717	+	1.39592i	0.00574149	+	0.0546266i	−0.991276	+	0.131802i	$0.957924\pi$
$654$	1.37813	−	0.292931i	0.0538892	−	0.0114545i
$655$	−4.89072	+	1.03955i	−0.191096	+	0.0406187i
$656$	2.09272	+	19.9109i	0.0817069	+	0.777389i
$657$	−5.95946	−	4.32980i	−0.232501	−	0.168922i
$658$	−7.24174	+	24.2642i	−0.282312	+	0.945916i
$659$	−5.02576			−0.195776			−0.0978880	−	0.995197i	$-0.531209\pi$
$659$	−5.02576			−0.195776			−0.0978880	+	0.995197i	$0.531209\pi$
$660$	5.36626	−	3.77594i	0.208882	−	0.146978i
$661$	−17.2653	−	29.9044i	−0.671543	−	1.16315i	−0.977466	−	0.211091i	$-0.932298\pi$
$661$	−17.2653	−	29.9044i	−0.671543	−	1.16315i	0.305923	−	0.952056i	$-0.401035\pi$
$662$	5.62925	−	6.25192i	0.218787	−	0.242988i
$663$	0.425494	−	0.189442i	0.0165248	−	0.00735732i
$664$	4.26421	−	3.09813i	0.165484	−	0.120231i
$665$	−25.8230	+	19.7304i	−1.00137	+	0.765111i
$666$	−2.34921	+	7.23013i	−0.0910301	+	0.280162i
$667$	4.40728	+	41.9325i	0.170651	+	1.62363i
$668$	0.0431829	−	0.410858i	0.00167080	−	0.0158966i
$669$	−0.659165	+	0.732077i	−0.0254848	+	0.0283037i
$670$	−11.4551	+	19.8407i	−0.442547	+	0.766514i
$671$	35.5802	+	16.4917i	1.37356	+	0.636655i
$672$	0.691903	−	8.56599i	0.0266907	−	0.330440i
$673$	0.591021	+	1.81898i	0.0227822	+	0.0701164i	0.961801	−	0.273749i	$-0.0882637\pi$
$673$	0.591021	+	1.81898i	0.0227822	+	0.0701164i	−0.939019	+	0.343865i	$0.888264\pi$
$674$	10.6067	−	4.72240i	0.408554	−	0.181900i
$675$	5.48171	+	2.44061i	0.210991	+	0.0939393i
$676$	−6.92088	+	1.47108i	−0.266188	+	0.0565799i
$677$	−8.56965	−	9.51756i	−0.329358	−	0.365790i	0.555608	−	0.831444i	$-0.312486\pi$
$677$	−8.56965	−	9.51756i	−0.329358	−	0.365790i	−0.884966	+	0.465655i	$0.845819\pi$
$678$	5.31079	−	3.85851i	0.203960	−	0.148185i
$679$	10.3912	+	1.94803i	0.398779	+	0.0747586i
$680$	1.37636	+	4.23600i	0.0527810	+	0.162443i
$681$	0.375107	−	0.649705i	0.0143741	−	0.0248967i
$682$	15.2222	−	25.4666i	0.582888	−	0.975165i
$683$	−17.2569	−	29.8899i	−0.660319	−	1.14371i	−0.980532	−	0.196360i	$-0.937088\pi$
$683$	−17.2569	−	29.8899i	−0.660319	−	1.14371i	0.320213	−	0.947346i	$-0.396245\pi$
$684$	2.16079	+	0.459290i	0.0826198	+	0.0175614i
$685$	−25.2648	−	18.3560i	−0.965320	−	0.701346i
$686$	21.7351	+	2.99813i	0.829849	+	0.114469i
$687$	−3.31299	+	10.1963i	−0.126398	+	0.389015i
$688$	0.468599	+	0.520432i	0.0178652	+	0.0198413i
$689$	−9.13790	−	4.06845i	−0.348126	−	0.154996i
$690$	−2.40006	+	22.8350i	−0.0913687	+	0.869315i
$691$	46.2297	+	9.82643i	1.75866	+	0.373815i	0.970396	−	0.241521i	$-0.0776463\pi$
$691$	46.2297	+	9.82643i	1.75866	+	0.373815i	0.788265	+	0.615336i	$0.210980\pi$
$692$	−11.8075			−0.448856
$693$	2.63665	−	8.36947i	0.100158	−	0.317930i
$694$	−26.7169			−1.01416
$695$	−64.3061	−	13.6687i	−2.43927	−	0.518483i
$696$	−2.32002	+	22.0735i	−0.0879400	+	0.836693i
$697$	3.25744	+	1.45031i	0.123384	+	0.0549342i
$698$	20.0999	+	22.3232i	0.760792	+	0.844945i
$699$	4.20849	−	12.9524i	0.159180	−	0.489905i
$700$	4.93134	+	8.08452i	0.186387	+	0.305566i
$701$	22.3885	+	16.2662i	0.845600	+	0.614365i	0.923929	−	0.382563i	$-0.124958\pi$
$701$	22.3885	+	16.2662i	0.845600	+	0.614365i	−0.0783290	+	0.996928i	$0.524958\pi$
$702$	1.23630	+	0.262784i	0.0466612	+	0.00991815i
$703$	−11.8824	−	20.5809i	−0.448152	−	0.776223i
$704$	19.0906	+	21.8594i	0.719505	+	0.823858i
$705$	−13.3972	+	23.2046i	−0.504568	+	0.873937i
$706$	1.28121	+	3.94316i	0.0482189	+	0.148403i
$707$	−6.08166	−	17.2871i	−0.228724	−	0.650147i
$708$	−6.04185	+	4.38966i	−0.227067	+	0.164974i
$709$	−9.45730	−	10.5034i	−0.355176	−	0.394463i	0.538906	−	0.842366i	$-0.318838\pi$
$709$	−9.45730	−	10.5034i	−0.355176	−	0.394463i	−0.894082	+	0.447903i	$0.852171\pi$
$710$	27.1016	−	5.76063i	1.01711	−	0.216193i
$711$	4.82096	+	2.14643i	0.180800	+	0.0804974i
$712$	10.3482	−	4.60732i	0.387815	−	0.172667i
$713$	−13.6351	−	41.9647i	−0.510640	−	1.57159i
$714$	1.12612	+	0.777376i	0.0421439	+	0.0290926i
$715$	−1.40343	+	11.6517i	−0.0524852	+	0.435747i
$716$	−6.75018	+	11.6917i	−0.252266	+	0.436938i
$717$	15.3399	−	17.0367i	0.572879	−	0.636247i
$718$	−1.76495	+	16.7924i	−0.0658674	+	0.626686i
$719$	1.17018	+	11.1335i	0.0436404	+	0.415210i	0.994432	+	0.105379i	$0.0336057\pi$
$719$	1.17018	+	11.1335i	0.0436404	+	0.415210i	−0.950792	+	0.309831i	$0.899728\pi$
$720$	−2.51228	+	7.73199i	−0.0936270	+	0.288154i
$721$	−42.2332	−	17.5955i	−1.57285	−	0.655291i
$722$	−5.06518	+	3.68007i	−0.188507	+	0.136958i
$723$	−10.7495	+	4.78597i	−0.399777	+	0.177992i
$724$	−1.01307	+	1.12513i	−0.0376505	+	0.0418151i
$725$	−21.6480	−	37.4954i	−0.803986	−	1.39254i
$726$	6.17090	+	11.4780i	0.229023	+	0.425988i
$727$	−27.7076			−1.02762			−0.513810	−	0.857904i	$-0.671766\pi$
$727$	−27.7076			−1.02762			−0.513810	+	0.857904i	$0.671766\pi$
$728$	5.96383	+	6.31053i	0.221034	+	0.233884i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	3.02549	+	28.7857i	0.111979	+	1.06541i
$731$	0.122001	−	0.0259322i	0.00451239	−	0.000959137i
$732$	6.89894	−	1.46642i	0.254992	−	0.0542003i
$733$	2.43924	+	23.2078i	0.0900953	+	0.857200i	0.942475	+	0.334276i	$0.108492\pi$
$733$	2.43924	+	23.2078i	0.0900953	+	0.857200i	−0.852380	+	0.522923i	$0.824841\pi$
$734$	23.1258	+	16.8018i	0.853587	+	0.620167i
$735$	21.6404	+	8.40934i	0.798218	+	0.310183i
$736$	18.9808			0.699643
$737$	15.4707	+	11.6023i	0.569872	+	0.427376i
$738$	4.83809	+	8.37981i	0.178092	+	0.308465i
$739$	35.8809	−	39.8498i	1.31990	−	1.46590i	0.537273	−	0.843408i	$-0.319454\pi$
$739$	35.8809	−	39.8498i	1.31990	−	1.46590i	0.782628	−	0.622490i	$-0.213879\pi$
$740$	−11.5978	+	5.16367i	−0.426344	+	0.189820i
$741$	−3.19648	+	2.32238i	−0.117426	+	0.0853147i
$742$	−3.77582	−	29.1436i	−0.138615	−	1.06990i
$743$	−3.88710	+	11.9633i	−0.142604	+	0.438889i	−0.996695	−	0.0812338i	$-0.974114\pi$
$743$	−3.88710	+	11.9633i	−0.142604	+	0.438889i	0.854091	+	0.520123i	$0.174114\pi$
$744$	−2.42790	−	23.1000i	−0.0890113	−	0.846886i
$745$	3.68790	−	35.0880i	0.135114	−	1.28553i
$746$	2.07304	−	2.30234i	0.0758993	−	0.0842947i
$747$	0.856755	−	1.48394i	0.0313470	−	0.0542947i
$748$	0.847430	−	0.166749i	0.0309851	−	0.00609695i
$749$	1.78409	−	22.0877i	0.0651894	−	0.807067i
$750$	−1.21479	−	3.73875i	−0.0443579	−	0.136520i
$751$	−45.9144	+	20.4424i	−1.67544	+	0.745954i	−0.675476	+	0.737382i	$0.736062\pi$
$751$	−45.9144	+	20.4424i	−1.67544	+	0.745954i	−0.999963	+	0.00857220i	$0.997271\pi$
$752$	−18.0904	−	8.05436i	−0.659689	−	0.293712i
$753$	0.938248	−	0.199431i	0.0341917	−	0.00726766i
$754$	−6.10229	−	6.77728i	−0.222232	−	0.246814i
$755$	55.6240	−	40.4132i	2.02437	−	1.47079i
$756$	−0.523743	−	1.48874i	−0.0190484	−	0.0541449i
$757$	−10.2285	−	31.4801i	−0.371761	−	1.14416i	−0.945638	−	0.325221i	$-0.894561\pi$
$757$	−10.2285	−	31.4801i	−0.371761	−	1.14416i	0.573877	−	0.818941i	$-0.305439\pi$
$758$	−18.8781	+	32.6979i	−0.685685	+	1.18764i
$759$	18.8940	+	4.31625i	0.685810	+	0.156670i
$760$	−18.8917	−	32.7214i	−0.685274	−	1.18693i
$761$	−23.7412	−	5.04635i	−0.860618	−	0.182930i	−0.243597	−	0.969877i	$-0.578327\pi$
$761$	−23.7412	−	5.04635i	−0.860618	−	0.182930i	−0.617021	+	0.786947i	$0.711661\pi$
$762$	−8.64279	−	6.27935i	−0.313095	−	0.227477i
$763$	3.14559	−	0.0758911i	0.113878	−	0.00274744i
$764$	2.07379	−	6.38248i	0.0750272	−	0.230910i
$765$	0.968871	+	1.07604i	0.0350296	+	0.0389043i
$766$	−4.11508	−	1.83215i	−0.148684	−	0.0661983i
$767$	1.39622	−	13.2841i	0.0504145	−	0.479662i
$768$	12.6336	+	2.68536i	0.455877	+	0.0968996i
$769$	18.6609			0.672928			0.336464	−	0.941696i	$-0.390769\pi$
$769$	18.6609			0.672928			0.336464	+	0.941696i	$0.390769\pi$
$770$	−31.3713	+	14.3060i	−1.13054	+	0.515551i
$771$	8.00693			0.288362
$772$	14.1184	+	3.00095i	0.508131	+	0.108007i
$773$	−1.77123	+	16.8521i	−0.0637067	+	0.606129i	0.915367	+	0.402621i	$0.131901\pi$
$773$	−1.77123	+	16.8521i	−0.0637067	+	0.606129i	−0.979073	+	0.203508i	$0.934766\pi$
$774$	0.309206	+	0.137667i	0.0111142	+	0.00494835i
$775$	30.3179	+	33.6714i	1.08905	+	1.20951i
$776$	−3.79835	+	11.6901i	−0.136353	+	0.419651i
$777$	−8.13181	+	14.9037i	−0.291727	+	0.534667i
$778$	28.5897	+	20.7716i	1.02499	+	0.744698i
$779$	−29.5871	−	6.28892i	−1.06007	−	0.225324i
$780$	1.05535	+	1.82792i	0.0377876	+	0.0654500i
$781$	−2.09193	−	23.2933i	−0.0748553	−	0.833499i
$782$	−1.51113	+	2.61735i	−0.0540378	+	0.0935962i
$783$	2.22969	+	6.86228i	0.0796826	+	0.245238i
$784$	−4.50912	+	16.5553i	−0.161040	+	0.591262i
$785$	−14.7204	+	10.6950i	−0.525393	+	0.381720i
$786$	−1.19503	−	1.32722i	−0.0426255	−	0.0473404i
$787$	−12.8147	+	2.72385i	−0.456795	+	0.0970947i	−0.430562	−	0.902561i	$-0.641685\pi$
$787$	−12.8147	+	2.72385i	−0.456795	+	0.0970947i	−0.0262330	+	0.999656i	$0.508351\pi$
$788$	−1.57684	−	0.702055i	−0.0561727	−	0.0250097i
$789$	8.27224	−	3.68304i	0.294500	−	0.131120i
$790$	−6.40764	−	19.7207i	−0.227974	−	0.701631i
$791$	13.2452	−	6.28418i	0.470944	−	0.223440i
$792$	9.25617	+	4.29031i	0.328904	+	0.152450i
$793$	−6.30746	+	10.9248i	−0.223985	+	0.387953i
$794$	−6.47742	+	7.19391i	−0.229875	+	0.255302i
$795$	3.25044	−	30.9259i	0.115281	−	1.09683i
$796$	0.400109	+	3.80678i	0.0141815	+	0.134928i
$797$	−3.52535	+	10.8499i	−0.124874	+	0.384324i	−0.993878	−	0.110482i	$-0.964761\pi$
$797$	−3.52535	+	10.8499i	−0.124874	+	0.384324i	0.869004	+	0.494805i	$0.164761\pi$
$798$	−10.7152	−	4.46425i	−0.379314	−	0.158033i
$799$	−2.85329	+	2.07304i	−0.100942	+	0.0733387i
$800$	−17.8056	+	7.92757i	−0.629523	+	0.280282i
$801$	2.46406	−	2.73662i	0.0870633	−	0.0966936i
$802$	8.52035	+	14.7577i	0.300864	+	0.521112i
$803$	24.4284	+	0.370157i	0.862061	+	0.0130625i
$804$	3.47793			0.122657
$805$	−14.6649	+	49.1361i	−0.516868	+	1.73182i
$806$	7.72113	+	5.60973i	0.271965	+	0.197594i
$807$	−3.25554	−	30.9744i	−0.114600	−	1.09035i
$808$	20.8406	−	4.42980i	0.733168	−	0.155840i
$809$	9.17166	−	1.94950i	0.322458	−	0.0685407i	−0.0438386	−	0.999039i	$-0.513959\pi$
$809$	9.17166	−	1.94950i	0.322458	−	0.0685407i	0.366297	+	0.930498i	$0.380625\pi$
$810$	0.410721	+	3.90775i	0.0144313	+	0.137304i
$811$	0.112190	+	0.0815107i	0.00393952	+	0.00286223i	0.589753	−	0.807583i	$-0.299225\pi$
$811$	0.112190	+	0.0815107i	0.00393952	+	0.00286223i	−0.585814	+	0.810446i	$0.699225\pi$
$812$	−3.25661	+	10.9116i	−0.114285	+	0.382923i
$813$	27.5399			0.965865
$814$	−7.42724	−	24.0949i	−0.260325	−	0.844526i
$815$	20.9100	+	36.2171i	0.732444	+	1.26863i
$816$	−0.716044	+	0.795247i	−0.0250665	+	0.0278392i
$817$	−0.966589	+	0.430353i	−0.0338167	+	0.0150562i
$818$	−2.15762	+	1.56761i	−0.0754396	+	0.0548101i
$819$	2.60559	+	1.08556i	0.0910468	+	0.0379326i
$820$	−4.99335	+	15.3679i	−0.174375	+	0.536672i
$821$	−4.45561	−	42.3923i	−0.155502	−	1.47950i	−0.742463	−	0.669887i	$-0.766343\pi$
$821$	−4.45561	−	42.3923i	−0.155502	−	1.47950i	0.586961	−	0.809615i	$-0.300324\pi$
$822$	1.16599	−	11.0936i	0.0406685	−	0.386935i
$823$	−4.37180	+	4.85537i	−0.152391	+	0.169248i	−0.814507	−	0.580154i	$-0.802992\pi$
$823$	−4.37180	+	4.85537i	−0.152391	+	0.169248i	0.662115	+	0.749402i	$0.269659\pi$
$824$	26.5966	−	46.0666i	0.926535	−	1.60481i
$825$	−19.5269	+	3.84231i	−0.679839	+	0.133772i
$826$	35.4548	−	16.8216i	1.23363	−	0.585297i
$827$	11.7598	+	36.1929i	0.408928	+	1.25855i	0.917570	+	0.397573i	$0.130148\pi$
$827$	11.7598	+	36.1929i	0.408928	+	1.25855i	−0.508642	+	0.860978i	$0.669852\pi$
$828$	3.18429	−	1.41774i	0.110662	−	0.0492697i
$829$	−9.32464	−	4.15160i	−0.323858	−	0.144191i	0.238367	−	0.971175i	$-0.423388\pi$
$829$	−9.32464	−	4.15160i	−0.323858	−	0.144191i	−0.562225	+	0.826984i	$0.690055\pi$
$830$	−6.58573	+	1.39984i	−0.228594	+	0.0485892i
$831$	−0.0750616	−	0.0833644i	−0.00260386	−	0.00289188i
$832$	−7.55275	+	5.48739i	−0.261844	+	0.190241i
$833$	2.15198	+	2.16977i	0.0745615	+	0.0751780i
$834$	−7.25657	−	22.3334i	−0.251274	−	0.773343i
$835$	−1.14854	+	1.98933i	−0.0397469	+	0.0688436i
$836$	−6.73759	+	2.87826i	−0.233024	+	0.0995466i
$837$	−3.77548	−	6.53933i	−0.130500	−	0.226032i
$838$	−9.56078	−	2.03221i	−0.330272	−	0.0702014i
$839$	10.6470	+	7.73552i	0.367576	+	0.267060i	0.756205	−	0.654335i	$-0.227051\pi$
$839$	10.6470	+	7.73552i	0.367576	+	0.267060i	−0.388629	+	0.921394i	$0.627051\pi$
$840$	−12.9287	+	23.6952i	−0.446082	+	0.817564i
$841$	7.12665	−	21.9336i	0.245747	−	0.756330i
$842$	−2.53851	−	2.81930i	−0.0874827	−	0.0971594i
$843$	−17.7755	−	7.91415i	−0.612220	−	0.272578i
$844$	−1.06393	+	10.1226i	−0.0366219	+	0.348435i
$845$	38.4822	+	8.17964i	1.32383	+	0.281388i
$846$	−9.57074			−0.329049
$847$	8.82213	+	27.7339i	0.303132	+	0.952949i
$848$	22.9817			0.789194
$849$	−10.8098	−	2.29770i	−0.370993	−	0.0788570i
$850$	0.324397	−	3.08643i	0.0111267	−	0.105864i
$851$	−34.2561	−	15.2518i	−1.17428	−	0.522824i
$852$	−2.81447	−	3.12579i	−0.0964221	−	0.107088i
$853$	2.24799	−	6.91860i	0.0769697	−	0.236888i	−0.905167	−	0.425055i	$-0.860255\pi$
$853$	2.24799	−	6.91860i	0.0769697	−	0.236888i	0.982137	+	0.188167i	$0.0602546\pi$
$854$	−37.0511	+	0.893902i	−1.26786	+	0.0305887i
$855$	−9.93720	−	7.21980i	−0.339845	−	0.246912i
$856$	25.2007	+	5.35657i	0.861342	+	0.183084i
$857$	11.7752	+	20.3952i	0.402232	+	0.696687i	0.993995	−	0.109425i	$-0.0349011\pi$
$857$	11.7752	+	20.3952i	0.402232	+	0.696687i	−0.591763	+	0.806112i	$0.701568\pi$
$858$	−3.85494	+	1.64681i	−0.131605	+	0.0562210i
$859$	1.30060	−	2.25270i	0.0443759	−	0.0768613i	−0.842984	−	0.537938i	$-0.819203\pi$
$859$	1.30060	−	2.25270i	0.0443759	−	0.0768613i	0.887360	+	0.461077i	$0.152537\pi$
$860$	0.174665	+	0.537564i	0.00595603	+	0.0183308i
$861$	7.17147	+	20.3849i	0.244403	+	0.694714i
$862$	−35.8689	+	26.0602i	−1.22170	+	0.887616i
$863$	−19.6073	−	21.7761i	−0.667440	−	0.741267i	0.310404	−	0.950605i	$-0.399536\pi$
$863$	−19.6073	−	21.7761i	−0.667440	−	0.741267i	−0.977843	+	0.209338i	$0.932869\pi$
$864$	3.17720	−	0.675336i	0.108091	−	0.0229754i
$865$	59.9775	+	26.7037i	2.03930	+	0.907954i
$866$	−2.32465	+	1.03500i	−0.0789947	+	0.0351707i
$867$	−5.19439	−	15.9867i	−0.176411	−	0.542937i
$868$	0.959431	−	11.8781i	0.0325652	−	0.403169i
$869$	−17.1732	+	3.37917i	−0.582560	+	0.114630i
$870$	14.1757	−	24.5530i	0.480601	−	0.832426i
$871$	−4.16235	+	4.62276i	−0.141036	+	0.156636i
$872$	−0.382392	+	3.63821i	−0.0129494	+	0.123205i
$873$	0.417689	+	3.97404i	0.0141366	+	0.134501i
$874$	7.92255	−	24.3831i	0.267984	−	0.824770i
$875$	−1.12801	−	8.70657i	−0.0381338	−	0.294336i
$876$	3.55479	−	2.58271i	0.120105	−	0.0872615i
$877$	46.9602	−	20.9080i	1.58573	−	0.706013i	0.590824	−	0.806801i	$-0.298803\pi$
$877$	46.9602	−	20.9080i	1.58573	−	0.706013i	0.994908	+	0.100787i	$0.0321362\pi$
$878$	10.6634	−	11.8429i	0.359873	−	0.399680i
$879$	−1.91668	−	3.31978i	−0.0646479	−	0.111973i
$880$	−7.94279	−	25.7674i	−0.267751	−	0.868619i
$881$	−28.2212			−0.950795			−0.475397	−	0.879771i	$-0.657696\pi$
$881$	−28.2212			−0.950795			−0.475397	+	0.879771i	$0.657696\pi$
$882$	1.26356	+	8.19604i	0.0425463	+	0.275975i
$883$	35.1259	+	25.5205i	1.18208	+	0.858832i	0.992405	−	0.123015i	$-0.0392564\pi$
$883$	35.1259	+	25.5205i	1.18208	+	0.858832i	0.189676	+	0.981847i	$0.439256\pi$
$884$	0.0290405	+	0.276302i	0.000976739	+	0.00929305i
$885$	40.6177	−	8.63356i	1.36535	−	0.290214i
$886$	2.54002	−	0.539898i	0.0853336	−	0.0181382i
$887$	1.18283	+	11.2539i	0.0397155	+	0.377868i	0.996268	+	0.0863089i	$0.0275072\pi$
$887$	1.18283	+	11.2539i	0.0397155	+	0.377868i	−0.956553	+	0.291559i	$0.905826\pi$
$888$	−15.9693	−	11.6023i	−0.535893	−	0.389349i
$889$	−16.3873	−	17.3399i	−0.549611	−	0.581562i
$890$	−14.4695			−0.485018
$891$	3.31624	+	0.0502501i	0.111098	+	0.00168344i
$892$	−0.293806	−	0.508887i	−0.00983735	−	0.0170388i
$893$	20.0194	−	22.2338i	0.669922	−	0.744024i
$894$	11.5127	−	5.12577i	0.385041	−	0.171431i
$895$	60.7298	−	44.1228i	2.02997	−	1.47486i
$896$	−9.45238	−	3.93812i	−0.315782	−	0.131563i
$897$	−1.92651	+	5.92918i	−0.0643242	+	0.197970i
$898$	−0.960055	−	9.13432i	−0.0320375	−	0.304816i
$899$	−5.69507	+	54.1850i	−0.189941	+	1.80717i
$900$	−2.39499	+	2.65991i	−0.0798330	+	0.0886635i
$901$	2.04655	−	3.54473i	0.0681804	−	0.118092i
$902$	−29.1166	−	13.4958i	−0.969476	−	0.449360i
$903$	0.622068	+	0.429424i	0.0207011	+	0.0142903i
$904$	5.26710	+	16.2105i	0.175181	+	0.539152i
$905$	7.69056	−	3.42406i	0.255643	−	0.113820i
$906$	22.4355	+	9.98893i	0.745370	+	0.331860i
$907$	−50.9718	+	10.8344i	−1.69249	+	0.359750i	−0.950515	−	0.310679i	$-0.899444\pi$
$907$	−50.9718	+	10.8344i	−1.69249	+	0.359750i	−0.741974	+	0.670428i	$0.766110\pi$
$908$	0.299436	+	0.332557i	0.00993712	+	0.0110363i
$909$	5.60361	−	4.07126i	0.185860	−	0.135035i
$910$	−3.68076	−	10.4625i	−0.122016	−	0.346830i
$911$	2.43440	+	7.49231i	0.0806552	+	0.248231i	0.983251	−	0.182259i	$-0.0583408\pi$
$911$	2.43440	+	7.49231i	0.0806552	+	0.248231i	−0.902595	+	0.430490i	$0.858341\pi$
$912$	4.53889	−	7.86159i	0.150298	−	0.260323i
$913$	0.508342	+	5.66029i	0.0168237	+	0.187328i
$914$	−8.14349	−	14.1049i	−0.269363	−	0.466550i
$915$	−38.3602	−	8.15372i	−1.26815	−	0.269554i
$916$	−5.17372	−	3.75892i	−0.170944	−	0.124198i
$917$	−2.07699	−	3.40505i	−0.0685883	−	0.112445i
$918$	−0.159823	+	0.491884i	−0.00527494	+	0.0162346i
$919$	−21.7604	−	24.1674i	−0.717810	−	0.797209i	0.268294	−	0.963337i	$-0.413540\pi$
$919$	−21.7604	−	24.1674i	−0.717810	−	0.797209i	−0.986104	+	0.166128i	$0.946874\pi$
$920$	−54.4634	−	24.2487i	−1.79561	−	0.799456i
$921$	−2.28413	+	21.7320i	−0.0752647	+	0.716095i
$922$	−6.07963	−	1.29226i	−0.200222	−	0.0425585i
$923$	7.52302			0.247623
$924$	4.26200	+	3.03849i	0.140210	+	0.0999591i
$925$	38.5051			1.26604
$926$	27.5580	+	5.85763i	0.905611	+	0.192494i
$927$	1.80757	−	17.1979i	0.0593685	−	0.564853i
$928$	−21.4108	−	9.53270i	−0.702844	−	0.312926i
$929$	−25.2582	−	28.0521i	−0.828695	−	0.920359i	0.169175	−	0.985586i	$-0.445890\pi$
$929$	−25.2582	−	28.0521i	−0.828695	−	0.920359i	−0.997870	+	0.0652265i	$0.979223\pi$
$930$	−9.16849	+	28.2177i	−0.300646	+	0.925295i
$931$	−21.6832	−	14.2085i	−0.710639	−	0.465665i
$932$	6.57217	+	4.77496i	0.215279	+	0.156409i
$933$	1.46853	+	0.312145i	0.0480775	+	0.0102192i
$934$	−1.75340	−	3.03697i	−0.0573729	−	0.0993728i
$935$	−4.68172	−	1.06951i	−0.153108	−	0.0349769i
$936$	−1.64088	+	2.84210i	−0.0536340	+	0.0928968i
$937$	−0.105074	−	0.323384i	−0.00343261	−	0.0105645i	0.949326	−	0.314294i	$-0.101768\pi$
$937$	−0.105074	−	0.323384i	−0.00343261	−	0.0105645i	−0.952758	+	0.303730i	$0.901768\pi$
$938$	−17.9626	−	3.36743i	−0.586500	−	0.109951i
$939$	−14.8008	+	10.7534i	−0.483006	+	0.350925i
$940$	−10.6945	−	11.8775i	−0.348818	−	0.387401i
$941$	25.0220	−	5.31860i	0.815695	−	0.173381i	0.218871	−	0.975754i	$-0.429762\pi$
$941$	25.0220	−	5.31860i	0.815695	−	0.173381i	0.596824	+	0.802372i	$0.296429\pi$
$942$	−5.93735	−	2.64348i	−0.193449	−	0.0861292i
$943$	−43.6015	+	19.4126i	−1.41986	+	0.632163i
$944$	9.48346	+	29.1871i	0.308660	+	0.949959i
$945$	−0.706496	+	8.74667i	−0.0229823	+	0.284529i
$946$	−1.10145	+	0.216733i	−0.0358113	+	0.00704659i
$947$	−0.533206	+	0.923540i	−0.0173269	+	0.0300110i	−0.874559	−	0.484919i	$-0.838849\pi$
$947$	−0.533206	+	0.923540i	−0.0173269	+	0.0300110i	0.857232	+	0.514930i	$0.172182\pi$
$948$	−2.10630	+	2.33929i	−0.0684096	+	0.0759765i
$949$	−0.821481	+	7.81587i	−0.0266664	+	0.253714i
$950$	2.75187	+	26.1823i	0.0892825	+	0.849466i
$951$	−10.5859	+	32.5801i	−0.343272	+	1.05648i
$952$	−2.82322	+	2.15711i	−0.0915010	+	0.0699124i
$953$	2.66800	−	1.93842i	0.0864251	−	0.0627915i	−0.543734	−	0.839258i	$-0.682990\pi$
$953$	2.66800	−	1.93842i	0.0864251	−	0.0627915i	0.630159	+	0.776466i	$0.282990\pi$
$954$	10.1470	−	4.51776i	0.328523	−	0.146268i
$955$	−24.9685	+	27.7303i	−0.807962	+	0.897333i
$956$	6.83736	+	11.8427i	0.221136	+	0.383019i
$957$	−19.1451	−	14.3579i	−0.618874	−	0.464126i
$958$	22.1277			0.714913
$959$	7.12444	−	23.8711i	0.230060	−	0.770839i
$960$	−23.4799	−	17.0592i	−0.757812	−	0.550583i
$961$	−2.71953	−	25.8746i	−0.0877267	−	0.834664i
$962$	7.93337	−	1.68629i	0.255782	−	0.0543681i
$963$	8.19253	−	1.74138i	0.264001	−	0.0561151i
$964$	−0.733666	−	6.98037i	−0.0236298	−	0.224822i
$965$	−64.9287	−	47.1734i	−2.09013	−	1.51857i
$966$	−17.8187	+	4.23912i	−0.573307	+	0.136391i
$967$	−35.8499			−1.15285			−0.576427	−	0.817149i	$-0.695553\pi$
$967$	−35.8499			−1.15285			−0.576427	+	0.817149i	$0.695553\pi$
$968$	−33.2952	+	6.02901i	−1.07015	+	0.193780i
$969$	−0.808389	−	1.40017i	−0.0259692	−	0.0449799i
$970$	10.5061	−	11.6682i	0.337331	−	0.374644i
$971$	0.917982	−	0.408712i	0.0294594	−	0.0131162i	−0.391954	−	0.919985i	$-0.628201\pi$
$971$	0.917982	−	0.408712i	0.0294594	−	0.0131162i	0.421413	+	0.906869i	$0.361534\pi$
$972$	0.482575	−	0.350611i	0.0154786	−	0.0112459i
$973$	−6.73820	−	52.0088i	−0.216017	−	1.66732i
$974$	6.48849	−	19.9695i	0.207905	−	0.639865i
$975$	−0.669166	−	6.36669i	−0.0214305	−	0.203897i
$976$	3.02960	−	28.8247i	0.0969750	−	0.922656i
$977$	10.8070	−	12.0024i	0.345746	−	0.383990i	−0.545042	−	0.838409i	$-0.683486\pi$
$977$	10.8070	−	12.0024i	0.345746	−	0.383990i	0.890788	+	0.454419i	$0.150153\pi$
$978$	−7.46886	+	12.9365i	−0.238828	+	0.413662i
$979$	−1.46053	+	12.1258i	−0.0466788	+	0.387541i
$980$	−8.75954	+	10.7265i	−0.279813	+	0.342647i
$981$	0.367504	+	1.13106i	0.0117335	+	0.0361120i
$982$	13.5344	−	6.02592i	0.431902	−	0.192295i
$983$	54.1882	+	24.1261i	1.72834	+	0.769505i	0.996078	+	0.0884763i	$0.0281997\pi$
$983$	54.1882	+	24.1261i	1.72834	+	0.769505i	0.732257	+	0.681028i	$0.238467\pi$
$984$	−24.5751	+	5.22360i	−0.783426	+	0.166522i
$985$	6.42196	+	7.13231i	0.204621	+	0.227254i
$986$	3.01909	−	2.19350i	0.0961474	−	0.0698552i
$987$	−21.0081	−	3.93837i	−0.668696	−	0.125360i
$988$	−0.728289	−	2.24144i	−0.0231700	−	0.0713098i
$989$	−0.834749	+	1.44583i	−0.0265435	+	0.0459746i
$990$	−8.57234	−	9.81562i	−0.272447	−	0.311961i
$991$	−0.503342	−	0.871814i	−0.0159892	−	0.0276941i	0.857920	−	0.513783i	$-0.171756\pi$
$991$	−0.503342	−	0.871814i	−0.0159892	−	0.0276941i	−0.873909	+	0.486089i	$0.838423\pi$
$992$	23.9910	+	5.09944i	0.761714	+	0.161907i
$993$	5.74501	+	4.17399i	0.182312	+	0.132458i
$994$	11.5095	+	18.8689i	0.365060	+	0.598486i
$995$	6.57695	−	20.2418i	0.208503	−	0.641707i
$996$	0.683919	+	0.759569i	0.0216708	+	0.0240679i
$997$	45.4512	+	20.2362i	1.43946	+	0.640887i	0.970229	−	0.242191i	$-0.0778660\pi$
$997$	45.4512	+	20.2362i	1.43946	+	0.640887i	0.469227	+	0.883078i	$0.344533\pi$
$998$	2.34286	−	22.2908i	0.0741620	−	0.705604i
$999$	−6.27678	−	1.33417i	−0.198589	−	0.0422113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.16.6	✓	64
3.2	odd	2		693.2.by.c.478.3		64
7.4	even	3	inner	231.2.y.b.214.3	yes	64
11.9	even	5	inner	231.2.y.b.163.3	yes	64
21.11	odd	6		693.2.by.c.676.6		64
33.20	odd	10		693.2.by.c.163.6		64
77.53	even	15	inner	231.2.y.b.130.6	yes	64
231.53	odd	30		693.2.by.c.361.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.6	✓	64	1.1	even	1	trivial
231.2.y.b.130.6	yes	64	77.53	even	15	inner
231.2.y.b.163.3	yes	64	11.9	even	5	inner
231.2.y.b.214.3	yes	64	7.4	even	3	inner
693.2.by.c.163.6		64	33.20	odd	10
693.2.by.c.361.3		64	231.53	odd	30
693.2.by.c.478.3		64	3.2	odd	2
693.2.by.c.676.6		64	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15881 + 0.246312i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.544926 - 0.242617i) q^{4} +(2.21930 + 2.46479i) q^{5} +(-0.366091 + 1.12671i) q^{6} +(-1.26723 + 2.32253i) q^{7} +(-2.48858 - 1.80806i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(1.15881 + 0.246312i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.544926 - 0.242617i) q^{4} +(2.21930 + 2.46479i) q^{5} +(-0.366091 + 1.12671i) q^{6} +(-1.26723 + 2.32253i) q^{7} +(-2.48858 - 1.80806i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.96464 + 3.40285i) q^{10} +(3.04998 - 1.30293i) q^{11} +(0.298248 - 0.516580i) q^{12} +(0.329683 + 1.01466i) q^{13} +(-2.04054 + 2.37923i) q^{14} +(-2.68326 + 1.94951i) q^{15} +(-1.64017 - 1.82160i) q^{16} +(-0.427026 + 0.0907671i) q^{17} +(-1.08227 - 0.481859i) q^{18} +(3.38323 - 1.50631i) q^{19} +(-0.611357 - 1.88156i) q^{20} +(-2.17734 - 1.50306i) q^{21} +(3.85527 - 0.758601i) q^{22} +(2.92176 - 5.06064i) q^{23} +(2.05828 - 2.28596i) q^{24} +(-0.627221 + 5.96761i) q^{25} +(0.132116 + 1.25700i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.25403 - 0.958155i) q^{28} +(-5.83740 + 4.24112i) q^{29} +(-3.58957 + 1.59818i) q^{30} +(5.05258 - 5.61146i) q^{31} +(1.62409 + 2.81301i) q^{32} +(0.976985 + 3.16946i) q^{33} -0.517198 q^{34} +(-8.53689 + 2.03095i) q^{35} +(0.482575 + 0.350611i) q^{36} +(-0.670760 - 6.38186i) q^{37} +(4.29153 - 0.912193i) q^{38} +(-1.04356 + 0.221816i) q^{39} +(-1.06644 - 10.1465i) q^{40} +(-6.60776 - 4.80082i) q^{41} +(-2.15290 - 2.27806i) q^{42} -0.285700 q^{43} +(-1.97812 - 0.0299739i) q^{44} +(-1.65835 - 2.87234i) q^{45} +(4.63226 - 5.14464i) q^{46} +(7.38021 - 3.28588i) q^{47} +(1.98306 - 1.44078i) q^{48} +(-3.78827 - 5.88634i) q^{49} +(-2.19672 + 6.76081i) q^{50} +(-0.0456335 - 0.434174i) q^{51} +(0.0665204 - 0.632900i) q^{52} +(-6.27355 + 6.96748i) q^{53} +(0.592348 - 1.02598i) q^{54} +(9.98028 + 4.62594i) q^{55} +(7.35287 - 3.48858i) q^{56} +(1.14441 + 3.52214i) q^{57} +(-7.80906 + 3.47682i) q^{58} +(-11.4376 - 5.09235i) q^{59} +(1.93516 - 0.411331i) q^{60} +(7.91192 + 8.78708i) q^{61} +(7.23714 - 5.25809i) q^{62} +(1.72242 - 2.00830i) q^{63} +(2.70406 + 8.32224i) q^{64} +(-1.76925 + 3.06443i) q^{65} +(0.351460 + 3.91344i) q^{66} +(2.91531 + 5.04946i) q^{67} +(0.254719 + 0.0541421i) q^{68} +(4.72751 + 3.43474i) q^{69} +(-10.3929 + 0.250740i) q^{70} +(2.17902 - 6.70633i) q^{71} +(2.05828 + 2.28596i) q^{72} +(6.72945 + 2.99614i) q^{73} +(0.794647 - 7.56056i) q^{74} +(-5.86935 - 1.24757i) q^{75} -2.20906 q^{76} +(-0.838918 + 8.73477i) q^{77} -1.26392 q^{78} +(-5.16188 - 1.09719i) q^{79} +(0.849805 - 8.08536i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-6.47462 - 7.19080i) q^{82} +(-0.529504 + 1.62965i) q^{83} +(0.821824 + 1.34731i) q^{84} +(-1.17142 - 0.851087i) q^{85} +(-0.331072 - 0.0703715i) q^{86} +(-3.60771 - 6.24874i) q^{87} +(-9.94591 - 2.27209i) q^{88} +(-1.84124 + 3.18912i) q^{89} +(-1.21421 - 3.73696i) q^{90} +(-2.77436 - 0.520106i) q^{91} +(-2.81994 + 2.04880i) q^{92} +(5.05258 + 5.61146i) q^{93} +(9.36160 - 1.98987i) q^{94} +(11.2211 + 4.99597i) q^{95} +(-2.96737 + 1.32116i) q^{96} +(-1.23481 - 3.80036i) q^{97} +(-2.94000 - 7.75423i) q^{98} +(-3.25422 + 0.640334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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