LMFDB - Embedded newform 798.2.bp.f.739.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (of order $9$, degree $6$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			739.6
Character	$\chi$	$=$	798.739
Dual form			798.2.bp.f.541.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.57278 + 1.31972i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.90041 + 1.84077i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.57278 + 1.31972i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.90041 + 1.84077i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.92930 - 0.702209i) q^{10} +(-0.806567 - 1.39701i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.11584 - 2.61450i) q^{13} +(1.15623 - 2.37974i) q^{14} +(1.92930 + 0.702209i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.34468 + 2.80652i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.28501 + 3.71197i) q^{19} +2.05312 q^{20} +(-1.15623 + 2.37974i) q^{21} +(1.23573 + 1.03690i) q^{22} +(0.537746 + 3.04971i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-0.136260 - 0.772767i) q^{25} +(-2.03372 + 3.52251i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.272579 + 2.63167i) q^{28} +(0.946775 + 5.36943i) q^{29} -2.05312 q^{30} -1.22367 q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.23573 - 1.03690i) q^{33} +(-4.10286 - 1.49332i) q^{34} +(-5.41824 + 0.387110i) q^{35} +(0.173648 - 0.984808i) q^{36} +(-0.205823 - 0.356495i) q^{37} +(-3.41678 - 2.70659i) q^{38} +(2.03372 - 3.52251i) q^{39} +(-1.92930 + 0.702209i) q^{40} +(8.57734 + 7.19724i) q^{41} +(0.272579 - 2.63167i) q^{42} +(-7.03084 + 2.55902i) q^{43} +(-1.51585 - 0.551724i) q^{44} +2.05312 q^{45} +(-1.54838 - 2.68187i) q^{46} +(2.49682 - 2.09508i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(0.223150 - 6.99644i) q^{49} +(0.392344 + 0.679560i) q^{50} +(4.10286 + 1.49332i) q^{51} +(0.706304 - 4.00565i) q^{52} +(3.10568 - 2.60597i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(0.575116 - 3.26164i) q^{55} +(-0.643944 - 2.56619i) q^{56} +(3.41678 + 2.70659i) q^{57} +(-2.72613 - 4.72180i) q^{58} +(5.64145 + 4.73374i) q^{59} +(1.92930 - 0.702209i) q^{60} +(-0.997693 - 5.65820i) q^{61} +(1.14988 - 0.418520i) q^{62} +(-0.272579 + 2.63167i) q^{63} +(-0.500000 - 0.866025i) q^{64} +8.35096 q^{65} +(1.51585 + 0.551724i) q^{66} +(4.58954 + 1.67046i) q^{67} +4.36617 q^{68} +(1.54838 + 2.68187i) q^{69} +(4.95908 - 2.21691i) q^{70} +(-9.51829 + 3.46438i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-9.68013 + 3.52328i) q^{73} +(0.315339 + 0.264600i) q^{74} +(-0.392344 - 0.679560i) q^{75} +(4.13643 + 1.37476i) q^{76} +(4.10439 + 1.17020i) q^{77} +(-0.706304 + 4.00565i) q^{78} +(0.0321419 - 0.182286i) q^{79} +(1.57278 - 1.31972i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-10.5217 - 3.82957i) q^{82} +(1.08414 + 1.87779i) q^{83} +(0.643944 + 2.56619i) q^{84} +(1.55663 + 8.82809i) q^{85} +(5.73159 - 4.80938i) q^{86} +(2.72613 + 4.72180i) q^{87} +1.61313 q^{88} +(6.99290 + 2.54521i) q^{89} +(-1.92930 + 0.702209i) q^{90} +(-1.10870 + 10.7042i) q^{91} +(2.37225 + 1.99056i) q^{92} +(-1.14988 + 0.418520i) q^{93} +(-1.62969 + 2.82270i) q^{94} +(-1.30494 + 8.85370i) q^{95} +(0.500000 + 0.866025i) q^{96} +(1.87770 - 10.6490i) q^{97} +(2.18323 + 6.65083i) q^{98} +(-1.51585 - 0.551724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 6 q^{5} - 21 q^{8}+O(q^{10}) $ 42 * q + 6 * q^5 - 21 * q^8	$ 42 q + 6 q^{5} - 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} - 24 q^{13} - 3 q^{14} + 3 q^{15} - 21 q^{18} + 18 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{22} + 15 q^{23} - 18 q^{25} + 9 q^{26} + 21 q^{27} - 12 q^{28} + 9 q^{29} + 6 q^{30} - 6 q^{31} + 3 q^{33} + 9 q^{34} + 12 q^{35} - 15 q^{37} + 9 q^{38} - 9 q^{39} - 3 q^{40} + 3 q^{41} + 12 q^{42} + 6 q^{44} - 6 q^{45} - 18 q^{46} + 15 q^{47} - 30 q^{50} - 9 q^{51} + 21 q^{52} + 12 q^{53} - 15 q^{55} - 9 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} - 3 q^{61} + 6 q^{62} - 12 q^{63} - 21 q^{64} + 72 q^{65} - 6 q^{66} + 3 q^{67} - 36 q^{68} + 18 q^{69} - 6 q^{70} + 12 q^{71} + 9 q^{73} + 12 q^{74} + 30 q^{75} + 51 q^{77} - 21 q^{78} - 51 q^{79} + 6 q^{80} + 12 q^{82} + 24 q^{83} - 6 q^{85} + 9 q^{86} + 18 q^{87} + 18 q^{88} + 12 q^{89} - 3 q^{90} + 6 q^{92} - 6 q^{93} + 30 q^{94} - 21 q^{95} + 21 q^{96} - 27 q^{97} + 36 q^{98} + 6 q^{99}+O(q^{100}) $ 42 * q + 6 * q^5 - 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 - 24 * q^13 - 3 * q^14 + 3 * q^15 - 21 * q^18 + 18 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^22 + 15 * q^23 - 18 * q^25 + 9 * q^26 + 21 * q^27 - 12 * q^28 + 9 * q^29 + 6 * q^30 - 6 * q^31 + 3 * q^33 + 9 * q^34 + 12 * q^35 - 15 * q^37 + 9 * q^38 - 9 * q^39 - 3 * q^40 + 3 * q^41 + 12 * q^42 + 6 * q^44 - 6 * q^45 - 18 * q^46 + 15 * q^47 - 30 * q^50 - 9 * q^51 + 21 * q^52 + 12 * q^53 - 15 * q^55 - 9 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 - 3 * q^61 + 6 * q^62 - 12 * q^63 - 21 * q^64 + 72 * q^65 - 6 * q^66 + 3 * q^67 - 36 * q^68 + 18 * q^69 - 6 * q^70 + 12 * q^71 + 9 * q^73 + 12 * q^74 + 30 * q^75 + 51 * q^77 - 21 * q^78 - 51 * q^79 + 6 * q^80 + 12 * q^82 + 24 * q^83 - 6 * q^85 + 9 * q^86 + 18 * q^87 + 18 * q^88 + 12 * q^89 - 3 * q^90 + 6 * q^92 - 6 * q^93 + 30 * q^94 - 21 * q^95 + 21 * q^96 - 27 * q^97 + 36 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.57278	+	1.31972i	0.703370	+	0.590197i	0.922730	−	0.385446i	$-0.125953\pi$
$5$	1.57278	+	1.31972i	0.703370	+	0.590197i	−0.219360	+	0.975644i	$0.570397\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−1.90041	+	1.84077i	−0.718289	+	0.695745i
$7$	−1.90041	+	1.84077i	−0.718289	+	0.695745i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−1.92930	−	0.702209i	−0.610099	−	0.222058i
$11$	−0.806567	−	1.39701i	−0.243189	−	0.421216i	0.718432	−	0.695597i	$-0.244860\pi$
$11$	−0.806567	−	1.39701i	−0.243189	−	0.421216i	−0.961621	+	0.274382i	$0.911527\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.11584	−	2.61450i	0.864179	−	0.725132i	−0.0986851	−	0.995119i	$-0.531464\pi$
$13$	3.11584	−	2.61450i	0.864179	−	0.725132i	0.962864	+	0.269986i	$0.0870192\pi$
$14$	1.15623	−	2.37974i	0.309014	−	0.636011i
$15$	1.92930	+	0.702209i	0.498144	+	0.181310i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	3.34468	+	2.80652i	0.811204	+	0.680681i	0.950895	−	0.309514i	$-0.100166\pi$
$17$	3.34468	+	2.80652i	0.811204	+	0.680681i	−0.139691	+	0.990195i	$0.544611\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.28501	+	3.71197i	0.524217	+	0.851585i
$19$	2.28501	+	3.71197i	0.524217	+	0.851585i
$20$	2.05312			0.459092
$21$	−1.15623	+	2.37974i	−0.252309	+	0.519301i
$22$	1.23573	+	1.03690i	0.263459	+	0.221068i
$23$	0.537746	+	3.04971i	0.112128	+	0.635908i	0.988132	+	0.153605i	$0.0490884\pi$
$23$	0.537746	+	3.04971i	0.112128	+	0.635908i	−0.876005	+	0.482303i	$0.839800\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	−0.136260	−	0.772767i	−0.0272519	−	0.154553i
$26$	−2.03372	+	3.52251i	−0.398846	+	0.690821i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.272579	+	2.63167i	−0.0515127	+	0.497339i
$29$	0.946775	+	5.36943i	0.175812	+	0.997078i	0.937203	+	0.348785i	$0.113406\pi$
$29$	0.946775	+	5.36943i	0.175812	+	0.997078i	−0.761391	+	0.648293i	$0.775483\pi$
$30$	−2.05312			−0.374847
$31$	−1.22367			−0.219778			−0.109889	−	0.993944i	$-0.535050\pi$
$31$	−1.22367			−0.219778			−0.109889	+	0.993944i	$0.535050\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−1.23573	−	1.03690i	−0.215113	−	0.180502i
$34$	−4.10286	−	1.49332i	−0.703634	−	0.256102i
$35$	−5.41824	+	0.387110i	−0.915850	+	0.0654335i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	−0.205823	−	0.356495i	−0.0338370	−	0.0586075i	0.848611	−	0.529017i	$-0.177439\pi$
$37$	−0.205823	−	0.356495i	−0.0338370	−	0.0586075i	−0.882448	+	0.470410i	$0.844106\pi$
$38$	−3.41678	−	2.70659i	−0.554274	−	0.439067i
$39$	2.03372	−	3.52251i	0.325656	−	0.564053i
$40$	−1.92930	+	0.702209i	−0.305050	+	0.111029i
$41$	8.57734	+	7.19724i	1.33956	+	1.12402i	0.981740	+	0.190228i	$0.0609229\pi$
$41$	8.57734	+	7.19724i	1.33956	+	1.12402i	0.357816	+	0.933792i	$0.383522\pi$
$42$	0.272579	−	2.63167i	0.0420599	−	0.406076i
$43$	−7.03084	+	2.55902i	−1.07219	+	0.390246i	−0.816996	−	0.576643i	$-0.804362\pi$
$43$	−7.03084	+	2.55902i	−1.07219	+	0.390246i	−0.255197	+	0.966889i	$0.582140\pi$
$44$	−1.51585	−	0.551724i	−0.228523	−	0.0831755i
$45$	2.05312			0.306061
$46$	−1.54838	−	2.68187i	−0.228296	−	0.395420i
$47$	2.49682	−	2.09508i	0.364199	−	0.305599i	−0.442263	−	0.896886i	$-0.645824\pi$
$47$	2.49682	−	2.09508i	0.364199	−	0.305599i	0.806462	+	0.591286i	$0.201380\pi$
$48$	−0.173648	−	0.984808i	−0.0250640	−	0.142145i
$49$	0.223150	−	6.99644i	0.0318786	−	0.999492i
$50$	0.392344	+	0.679560i	0.0554858	+	0.0961043i
$51$	4.10286	+	1.49332i	0.574515	+	0.209106i
$52$	0.706304	−	4.00565i	0.0979467	−	0.555484i
$53$	3.10568	−	2.60597i	0.426598	−	0.357958i	−0.404069	−	0.914729i	$-0.632404\pi$
$53$	3.10568	−	2.60597i	0.426598	−	0.357958i	0.830666	+	0.556771i	$0.187960\pi$
$54$	−0.173648	+	0.984808i	−0.0236305	+	0.134015i
$55$	0.575116	−	3.26164i	0.0775486	−	0.439800i
$56$	−0.643944	−	2.56619i	−0.0860507	−	0.342922i
$57$	3.41678	+	2.70659i	0.452563	+	0.358497i
$58$	−2.72613	−	4.72180i	−0.357958	−	0.620002i
$59$	5.64145	+	4.73374i	0.734455	+	0.616281i	0.931342	−	0.364145i	$-0.118639\pi$
$59$	5.64145	+	4.73374i	0.734455	+	0.616281i	−0.196887	+	0.980426i	$0.563083\pi$
$60$	1.92930	−	0.702209i	0.249072	−	0.0906548i
$61$	−0.997693	−	5.65820i	−0.127741	−	0.724458i	−0.979642	−	0.200754i	$-0.935661\pi$
$61$	−0.997693	−	5.65820i	−0.127741	−	0.724458i	0.851900	−	0.523704i	$-0.175450\pi$
$62$	1.14988	−	0.418520i	0.146034	−	0.0531521i
$63$	−0.272579	+	2.63167i	−0.0343418	+	0.331560i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	8.35096			1.03581
$66$	1.51585	+	0.551724i	0.186588	+	0.0679125i
$67$	4.58954	+	1.67046i	0.560702	+	0.204079i	0.606795	−	0.794858i	$-0.292455\pi$
$67$	4.58954	+	1.67046i	0.560702	+	0.204079i	−0.0460933	+	0.998937i	$0.514677\pi$
$68$	4.36617			0.529476
$69$	1.54838	+	2.68187i	0.186403	+	0.322859i
$70$	4.95908	−	2.21691i	0.592724	−	0.264972i
$71$	−9.51829	+	3.46438i	−1.12961	+	0.411146i	−0.838152	−	0.545437i	$-0.816364\pi$
$71$	−9.51829	+	3.46438i	−1.12961	+	0.411146i	−0.291462	+	0.956583i	$0.594142\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	−9.68013	+	3.52328i	−1.13297	+	0.412369i	−0.839371	−	0.543559i	$-0.817076\pi$
$73$	−9.68013	+	3.52328i	−1.13297	+	0.412369i	−0.293602	+	0.955928i	$0.594854\pi$
$74$	0.315339	+	0.264600i	0.0366574	+	0.0307592i
$75$	−0.392344	−	0.679560i	−0.0453040	−	0.0784688i
$76$	4.13643	+	1.37476i	0.474481	+	0.157696i
$77$	4.10439	+	1.17020i	0.467739	+	0.133357i
$78$	−0.706304	+	4.00565i	−0.0799732	+	0.453550i
$79$	0.0321419	−	0.182286i	0.00361624	−	0.0205087i	−0.982946	−	0.183893i	$-0.941130\pi$
$79$	0.0321419	−	0.182286i	0.00361624	−	0.0205087i	0.986562	+	0.163384i	$0.0522411\pi$
$80$	1.57278	−	1.31972i	0.175842	−	0.147549i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−10.5217	−	3.82957i	−1.16192	−	0.422906i
$83$	1.08414	+	1.87779i	0.119000	+	0.206114i	0.919372	−	0.393390i	$-0.128698\pi$
$83$	1.08414	+	1.87779i	0.119000	+	0.206114i	−0.800372	+	0.599504i	$0.795364\pi$
$84$	0.643944	+	2.56619i	0.0702601	+	0.279994i
$85$	1.55663	+	8.82809i	0.168840	+	0.957541i
$86$	5.73159	−	4.80938i	0.618054	−	0.518608i
$87$	2.72613	+	4.72180i	0.292272	+	0.506230i
$88$	1.61313			0.171961
$89$	6.99290	+	2.54521i	0.741246	+	0.269791i	0.684917	−	0.728621i	$-0.259838\pi$
$89$	6.99290	+	2.54521i	0.741246	+	0.269791i	0.0563287	+	0.998412i	$0.482061\pi$
$90$	−1.92930	+	0.702209i	−0.203366	+	0.0740194i
$91$	−1.10870	+	10.7042i	−0.116223	+	1.12210i
$92$	2.37225	+	1.99056i	0.247324	+	0.207530i
$93$	−1.14988	+	0.418520i	−0.119237	+	0.0433985i
$94$	−1.62969	+	2.82270i	−0.168089	+	0.291139i
$95$	−1.30494	+	8.85370i	−0.133884	+	0.908371i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	1.87770	−	10.6490i	0.190652	−	1.08124i	−0.727824	−	0.685764i	$-0.759468\pi$
$97$	1.87770	−	10.6490i	0.190652	−	1.08124i	0.918476	−	0.395477i	$-0.129421\pi$
$98$	2.18323	+	6.65083i	0.220540	+	0.671835i
$99$	−1.51585	−	0.551724i	−0.152349	−	0.0554504i
$100$	−0.601106	−	0.504388i	−0.0601106	−	0.0504388i
$101$	0.109942	+	0.623514i	0.0109397	+	0.0620420i	0.989789	−	0.142541i	$-0.0455273\pi$
$101$	0.109942	+	0.623514i	0.0109397	+	0.0620420i	−0.978849	+	0.204583i	$0.934416\pi$
$102$	−4.36617			−0.432315
$103$	−15.4229			−1.51966			−0.759832	−	0.650120i	$-0.774719\pi$
$103$	−15.4229			−1.51966			−0.759832	+	0.650120i	$0.774719\pi$
$104$	0.706304	+	4.00565i	0.0692588	+	0.392786i
$105$	−4.95908	+	2.21691i	−0.483957	+	0.216348i
$106$	−2.02709	+	3.51102i	−0.196888	+	0.341020i
$107$	3.29124	−	5.70060i	0.318176	−	0.551097i	−0.661931	−	0.749564i	$-0.730263\pi$
$107$	3.29124	−	5.70060i	0.318176	−	0.551097i	0.980108	+	0.198467i	$0.0635963\pi$
$108$	−0.173648	−	0.984808i	−0.0167093	−	0.0947632i
$109$	0.345962	−	1.96205i	0.0331372	−	0.187930i	−0.963746	−	0.266821i	$-0.914027\pi$
$109$	0.345962	−	1.96205i	0.0331372	−	0.187930i	0.996883	+	0.0788908i	$0.0251378\pi$
$110$	0.575116	+	3.26164i	0.0548352	+	0.310986i
$111$	−0.315339	−	0.264600i	−0.0299306	−	0.0251148i
$112$	1.48280	+	2.19119i	0.140111	+	0.207048i
$113$	−6.81863			−0.641443			−0.320721	−	0.947174i	$-0.603925\pi$
$113$	−6.81863			−0.641443			−0.320721	+	0.947174i	$0.603925\pi$
$114$	−4.13643	−	1.37476i	−0.387412	−	0.128758i
$115$	−3.17901	+	5.50620i	−0.296444	+	0.513456i
$116$	4.17667	+	3.50465i	0.387794	+	0.325398i
$117$	0.706304	−	4.00565i	0.0652978	−	0.370322i
$118$	−6.92027	−	2.51877i	−0.637062	−	0.231872i
$119$	−11.5224	+	0.823227i	−1.05626	+	0.0754651i
$120$	−1.57278	+	1.31972i	−0.143575	+	0.120474i
$121$	4.19890	−	7.27271i	0.381718	−	0.661155i
$122$	2.87274	+	4.97573i	0.260086	+	0.450482i
$123$	10.5217	+	3.82957i	0.948707	+	0.345301i
$124$	−0.937387	+	0.786561i	−0.0841798	+	0.0706353i
$125$	5.93834	−	10.2855i	0.531141	−	0.919963i
$126$	−0.643944	−	2.56619i	−0.0573671	−	0.228614i
$127$	9.55069	−	8.01398i	0.847487	−	0.711126i	−0.111748	−	0.993737i	$-0.535645\pi$
$127$	9.55069	−	8.01398i	0.847487	−	0.711126i	0.959235	+	0.282611i	$0.0912005\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−5.73159	+	4.80938i	−0.504639	+	0.423442i
$130$	−7.84733	+	2.85620i	−0.688257	+	0.250505i
$131$	12.8478	−	4.67621i	1.12252	−	0.408563i	0.286947	−	0.957947i	$-0.407360\pi$
$131$	12.8478	−	4.67621i	1.12252	−	0.408563i	0.835570	+	0.549384i	$0.185138\pi$
$132$	−1.61313			−0.140405
$133$	−11.1753	−	2.84811i	−0.969025	−	0.246963i
$134$	−4.88409			−0.421921
$135$	1.92930	−	0.702209i	0.166048	−	0.0604365i
$136$	−4.10286	+	1.49332i	−0.351817	+	0.128051i
$137$	−5.50330	+	4.61782i	−0.470179	+	0.394527i	−0.846860	−	0.531816i	$-0.821510\pi$
$137$	−5.50330	+	4.61782i	−0.470179	+	0.394527i	0.376681	+	0.926343i	$0.377065\pi$
$138$	−2.37225	−	1.99056i	−0.201939	−	0.169447i
$139$	15.3515	−	12.8815i	1.30210	−	1.09259i	0.312321	−	0.949977i	$-0.398894\pi$
$139$	15.3515	−	12.8815i	1.30210	−	1.09259i	0.989778	−	0.142614i	$-0.0455508\pi$
$140$	−3.90178	+	3.77932i	−0.329761	+	0.319411i
$141$	1.62969	−	2.82270i	0.137244	−	0.237714i
$142$	7.75938	−	6.51090i	0.651153	−	0.546382i
$143$	−6.16563	−	2.24411i	−0.515596	−	0.187662i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−5.59708	+	9.69442i	−0.464812	+	0.805078i
$146$	7.89131	−	6.62160i	0.653090	−	0.548007i
$147$	−2.18323	−	6.65083i	−0.180070	−	0.548551i
$148$	−0.386820	−	0.140791i	−0.0317964	−	0.0115729i
$149$	2.56818	−	14.5649i	0.210394	−	1.19320i	−0.678329	−	0.734758i	$-0.737296\pi$
$149$	2.56818	−	14.5649i	0.210394	−	1.19320i	0.888723	−	0.458445i	$-0.151593\pi$
$150$	0.601106	+	0.504388i	0.0490801	+	0.0411831i
$151$	−4.83455	+	8.37368i	−0.393430	+	0.681441i	−0.992899	−	0.118957i	$-0.962045\pi$
$151$	−4.83455	+	8.37368i	−0.393430	+	0.681441i	0.599469	+	0.800398i	$0.295378\pi$
$152$	−4.35717	+	0.122891i	−0.353413	+	0.00996781i
$153$	4.36617			0.352984
$154$	−4.25710	+	0.304151i	−0.343047	+	0.0245092i
$155$	−1.92457	−	1.61491i	−0.154585	−	0.129712i
$156$	−0.706304	−	4.00565i	−0.0565496	−	0.320709i
$157$	−0.366082	+	2.07615i	−0.0292165	+	0.165695i	−0.995925	−	0.0901851i	$-0.971254\pi$
$157$	−0.366082	+	2.07615i	−0.0292165	+	0.165695i	0.966709	+	0.255880i	$0.0823653\pi$
$158$	0.0321419	+	0.182286i	0.00255707	+	0.0145019i
$159$	2.02709	−	3.51102i	0.160758	−	0.278442i
$160$	−1.02656	+	1.77806i	−0.0811568	+	0.140568i
$161$	−6.63574	−	4.80584i	−0.522970	−	0.378754i
$162$	0.173648	+	0.984808i	0.0136431	+	0.0773738i
$163$	−10.3000			−0.806754			−0.403377	−	0.915034i	$-0.632164\pi$
$163$	−10.3000			−0.806754			−0.403377	+	0.915034i	$0.632164\pi$
$164$	11.1969			0.874333
$165$	−0.575116	−	3.26164i	−0.0447727	−	0.253919i
$166$	−1.66100	−	1.39375i	−0.128919	−	0.108176i
$167$	−7.38429	−	2.68766i	−0.571414	−	0.207978i	0.0401215	−	0.999195i	$-0.487225\pi$
$167$	−7.38429	−	2.68766i	−0.571414	−	0.207978i	−0.611535	+	0.791217i	$0.709448\pi$
$168$	−1.48280	−	2.19119i	−0.114400	−	0.169054i
$169$	0.615425	−	3.49025i	0.0473404	−	0.268481i
$170$	−4.48214	−	7.76329i	−0.343764	−	0.595417i
$171$	4.13643	+	1.37476i	0.316321	+	0.105130i
$172$	−3.74103	+	6.47966i	−0.285251	+	0.494069i
$173$	−18.2428	+	6.63984i	−1.38698	+	0.504818i	−0.924285	−	0.381703i	$-0.875338\pi$
$173$	−18.2428	+	6.63984i	−1.38698	+	0.504818i	−0.462690	+	0.886520i	$0.653116\pi$
$174$	−4.17667	−	3.50465i	−0.316633	−	0.265686i
$175$	1.68143	+	1.21776i	0.127104	+	0.0920537i
$176$	−1.51585	+	0.551724i	−0.114261	+	0.0415878i
$177$	6.92027	+	2.51877i	0.520159	+	0.189322i
$178$	−7.44169			−0.557778
$179$	−0.0458502	−	0.0794149i	−0.00342701	−	0.00593575i	0.864307	−	0.502965i	$-0.167758\pi$
$179$	−0.0458502	−	0.0794149i	−0.00342701	−	0.00593575i	−0.867734	+	0.497029i	$0.834424\pi$
$180$	1.57278	−	1.31972i	0.117228	−	0.0983662i
$181$	−1.02469	−	5.81129i	−0.0761644	−	0.431949i	−0.998916	−	0.0465539i	$-0.985176\pi$
$181$	−1.02469	−	5.81129i	−0.0761644	−	0.431949i	0.922751	−	0.385396i	$-0.125935\pi$
$182$	−2.61921	−	10.4378i	−0.194148	−	0.773704i
$183$	−2.87274	−	4.97573i	−0.212359	−	0.367817i
$184$	−2.91000	−	1.05915i	−0.214528	−	0.0780817i
$185$	0.146760	−	0.832318i	0.0107900	−	0.0611933i
$186$	0.937387	−	0.786561i	0.0687326	−	0.0576735i
$187$	1.22304	−	6.93621i	0.0894376	−	0.507226i
$188$	0.565984	−	3.20985i	0.0412786	−	0.234103i
$189$	0.643944	+	2.56619i	0.0468400	+	0.186663i
$190$	−1.80190	−	8.76608i	−0.130723	−	0.635958i
$191$	−10.1027	−	17.4983i	−0.731003	−	1.26613i	−0.956455	−	0.291880i	$-0.905719\pi$
$191$	−10.1027	−	17.4983i	−0.731003	−	1.26613i	0.225452	−	0.974254i	$-0.427614\pi$
$192$	−0.766044	−	0.642788i	−0.0552845	−	0.0463892i
$193$	12.9157	−	4.70093i	0.929692	−	0.338380i	0.167604	−	0.985854i	$-0.446397\pi$
$193$	12.9157	−	4.70093i	0.929692	−	0.338380i	0.762087	+	0.647474i	$0.224175\pi$
$194$	1.87770	+	10.6490i	0.134811	+	0.764553i
$195$	7.84733	−	2.85620i	0.561959	−	0.204536i
$196$	−4.32628	−	5.50302i	−0.309020	−	0.393073i
$197$	−6.23447	−	10.7984i	−0.444188	−	0.769356i	0.553807	−	0.832645i	$-0.313174\pi$
$197$	−6.23447	−	10.7984i	−0.444188	−	0.769356i	−0.997995	+	0.0632890i	$0.979841\pi$
$198$	1.61313			0.114640
$199$	6.81252	+	2.47955i	0.482926	+	0.175771i	0.571999	−	0.820254i	$-0.306168\pi$
$199$	6.81252	+	2.47955i	0.482926	+	0.175771i	−0.0890726	+	0.996025i	$0.528390\pi$
$200$	0.737366	+	0.268379i	0.0521396	+	0.0189773i
$201$	4.88409			0.344497
$202$	−0.316567	−	0.548309i	−0.0222735	−	0.0385789i
$203$	−11.6831	−	8.46135i	−0.819995	−	0.593870i
$204$	4.10286	−	1.49332i	0.287257	−	0.104553i
$205$	3.99194	+	22.6394i	0.278809	+	1.58120i
$206$	14.4928	−	5.27494i	1.00976	−	0.367523i
$207$	2.37225	+	1.99056i	0.164883	+	0.138353i
$208$	−2.03372	−	3.52251i	−0.141013	−	0.244242i
$209$	3.34266	−	6.18614i	0.231217	−	0.427905i
$210$	3.90178	−	3.77932i	0.269249	−	0.260798i
$211$	2.54479	−	14.4322i	0.175190	−	0.993554i	−0.762733	−	0.646713i	$-0.776143\pi$
$211$	2.54479	−	14.4322i	0.175190	−	0.993554i	0.937924	−	0.346841i	$-0.112746\pi$
$212$	0.704000	−	3.99258i	0.0483509	−	0.274212i
$213$	−7.75938	+	6.51090i	−0.531664	+	0.446119i
$214$	−1.14304	+	6.48248i	−0.0781363	+	0.443133i
$215$	−14.4352	−	5.25397i	−0.984471	−	0.358318i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	2.32548	−	2.25250i	0.157864	−	0.152909i
$218$	0.345962	+	1.96205i	0.0234315	+	0.132887i
$219$	−7.89131	+	6.62160i	−0.533245	+	0.447446i
$220$	−1.65598	−	2.86824i	−0.111646	−	0.193377i
$221$	17.7591			1.19461
$222$	0.386820	+	0.140791i	0.0259617	+	0.00944927i
$223$	−17.2159	+	6.26609i	−1.15286	+	0.419608i	−0.846543	−	0.532320i	$-0.821320\pi$
$223$	−17.2159	+	6.26609i	−1.15286	+	0.419608i	−0.306321	+	0.951928i	$0.599098\pi$
$224$	−2.14281	−	1.55190i	−0.143172	−	0.103690i
$225$	−0.601106	−	0.504388i	−0.0400737	−	0.0336259i
$226$	6.40742	−	2.33211i	0.426215	−	0.155130i
$227$	−7.94119	+	13.7545i	−0.527075	+	0.912921i	0.472427	+	0.881370i	$0.343378\pi$
$227$	−7.94119	+	13.7545i	−0.527075	+	0.912921i	−0.999502	+	0.0315514i	$0.989955\pi$
$228$	4.35717	−	0.122891i	0.288560	−	0.00813868i
$229$	−9.81606	−	17.0019i	−0.648664	−	1.12352i	−0.983442	−	0.181222i	$-0.941995\pi$
$229$	−9.81606	−	17.0019i	−0.648664	−	1.12352i	0.334779	−	0.942297i	$-0.391338\pi$
$230$	1.10406	−	6.26142i	0.0727994	−	0.412866i
$231$	4.25710	−	0.304151i	0.280097	−	0.0200117i
$232$	−5.12345	−	1.86478i	−0.336371	−	0.122429i
$233$	−20.0527	−	16.8262i	−1.31370	−	1.10232i	−0.987601	−	0.156985i	$-0.949822\pi$
$233$	−20.0527	−	16.8262i	−1.31370	−	1.10232i	−0.326095	−	0.945337i	$-0.605733\pi$
$234$	0.706304	+	4.00565i	0.0461725	+	0.261857i
$235$	6.69189			0.436531
$236$	7.36440			0.479381
$237$	−0.0321419	−	0.182286i	−0.00208784	−	0.0118407i
$238$	10.5460	−	4.71448i	0.683594	−	0.305594i
$239$	−8.20763	+	14.2160i	−0.530908	+	0.919559i	0.468442	+	0.883494i	$0.344816\pi$
$239$	−8.20763	+	14.2160i	−0.530908	+	0.919559i	−0.999349	+	0.0360648i	$0.988518\pi$
$240$	1.02656	−	1.77806i	0.0662642	−	0.114773i
$241$	−3.88733	−	22.0462i	−0.250405	−	1.42012i	−0.807597	−	0.589735i	$-0.799232\pi$
$241$	−3.88733	−	22.0462i	−0.250405	−	1.42012i	0.557192	−	0.830384i	$-0.311879\pi$
$242$	−1.45826	+	8.27022i	−0.0937407	+	0.531630i
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$	−4.40130	−	3.69313i	−0.281764	−	0.236428i
$245$	9.58432	−	10.7094i	0.612320	−	0.684198i
$246$	−11.1969			−0.713890
$247$	16.8247	+	5.59175i	1.07053	+	0.355795i
$248$	0.611836	−	1.05973i	0.0388516	−	0.0672930i
$249$	1.66100	+	1.39375i	0.105262	+	0.0883251i
$250$	−2.06236	+	11.6962i	−0.130435	+	0.739735i
$251$	−22.6344	−	8.23825i	−1.42867	−	0.519994i	−0.492121	−	0.870527i	$-0.663778\pi$
$251$	−22.6344	−	8.23825i	−1.42867	−	0.519994i	−0.936550	+	0.350533i	$0.886001\pi$
$252$	1.48280	+	2.19119i	0.0934075	+	0.138032i
$253$	3.82676	−	3.21103i	0.240586	−	0.201876i
$254$	−6.23377	+	10.7972i	−0.391142	+	0.677477i
$255$	4.48214	+	7.76329i	0.280682	+	0.486156i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−12.2112	+	10.2464i	−0.761716	+	0.639155i	−0.938573	−	0.345081i	$-0.887851\pi$
$257$	−12.2112	+	10.2464i	−0.761716	+	0.639155i	0.176857	+	0.984237i	$0.443407\pi$
$258$	3.74103	−	6.47966i	0.232906	−	0.403406i
$259$	1.04737	+	0.298617i	0.0650806	+	0.0185552i
$260$	6.39721	−	5.36789i	0.396738	−	0.332903i
$261$	4.17667	+	3.50465i	0.258530	+	0.216932i
$262$	−10.4736	+	8.78841i	−0.647062	+	0.542950i
$263$	11.1126	−	4.04465i	0.685231	−	0.249404i	0.0241389	−	0.999709i	$-0.492316\pi$
$263$	11.1126	−	4.04465i	0.685231	−	0.249404i	0.661092	+	0.750305i	$0.270093\pi$
$264$	1.51585	−	0.551724i	0.0932941	−	0.0339563i
$265$	8.32372			0.511322
$266$	11.4755	−	1.14584i	0.703608	−	0.0702562i
$267$	7.44169			0.455424
$268$	4.58954	−	1.67046i	0.280351	−	0.102039i
$269$	−1.72943	+	0.629463i	−0.105446	+	0.0383790i	−0.394204	−	0.919023i	$-0.628980\pi$
$269$	−1.72943	+	0.629463i	−0.105446	+	0.0383790i	0.288759	+	0.957402i	$0.406757\pi$
$270$	−1.57278	+	1.31972i	−0.0957165	+	0.0803157i
$271$	−19.7437	−	16.5669i	−1.19934	−	1.00637i	−0.999649	−	0.0265091i	$-0.991561\pi$
$271$	−19.7437	−	16.5669i	−1.19934	−	1.00637i	−0.199694	−	0.979858i	$-0.563995\pi$
$272$	3.34468	−	2.80652i	0.202801	−	0.170170i
$273$	2.61921	+	10.4378i	0.158522	+	0.631727i
$274$	3.59203	−	6.22157i	0.217002	−	0.375859i
$275$	−0.969664	+	0.813645i	−0.0584730	+	0.0490646i
$276$	2.91000	+	1.05915i	0.175161	+	0.0637535i
$277$	13.8362	+	23.9650i	0.831335	+	1.43991i	0.896980	+	0.442072i	$0.145756\pi$
$277$	13.8362	+	23.9650i	0.831335	+	1.43991i	−0.0656445	+	0.997843i	$0.520910\pi$
$278$	−10.0200	+	17.3551i	−0.600959	+	1.04089i
$279$	−0.937387	+	0.786561i	−0.0561199	+	0.0470902i
$280$	2.37387	−	4.88589i	0.141866	−	0.291988i
$281$	26.1648	+	9.52320i	1.56086	+	0.568107i	0.970933	−	0.239350i	$-0.0769344\pi$
$281$	26.1648	+	9.52320i	1.56086	+	0.568107i	0.589927	+	0.807457i	$0.299157\pi$
$282$	−0.565984	+	3.20985i	−0.0337039	+	0.191144i
$283$	11.1420	+	9.34922i	0.662321	+	0.555753i	0.910782	−	0.412889i	$-0.135480\pi$
$283$	11.1420	+	9.34922i	0.662321	+	0.555753i	−0.248460	+	0.968642i	$0.579925\pi$
$284$	−5.06458	+	8.77211i	−0.300527	+	0.520529i
$285$	1.80190	+	8.76608i	0.106735	+	0.519258i
$286$	6.56133			0.387979
$287$	−29.5490	+	2.11114i	−1.74422	+	0.124617i
$288$	0.766044	+	0.642788i	0.0451396	+	0.0378766i
$289$	0.358309	+	2.03207i	0.0210770	+	0.119534i
$290$	1.94385	−	11.0241i	0.114147	−	0.647357i
$291$	−1.87770	−	10.6490i	−0.110073	−	0.624255i
$292$	−5.15069	+	8.92125i	−0.301421	+	0.522077i
$293$	−1.29401	+	2.24130i	−0.0755970	+	0.130938i	−0.901346	−	0.433100i	$-0.857420\pi$
$293$	−1.29401	+	2.24130i	−0.0755970	+	0.130938i	0.825749	+	0.564038i	$0.190753\pi$
$294$	4.32628	+	5.50302i	0.252314	+	0.320943i
$295$	2.62556	+	14.8903i	0.152866	+	0.866947i
$296$	0.411645			0.0239264
$297$	−1.61313			−0.0936035
$298$	2.56818	+	14.5649i	0.148771	+	0.843722i
$299$	9.64900	+	8.09647i	0.558016	+	0.468231i
$300$	−0.737366	−	0.268379i	−0.0425718	−	0.0154949i
$301$	8.65095	−	17.8053i	0.498633	−	1.02628i
$302$	1.67902	−	9.52220i	0.0966168	−	0.547941i
$303$	0.316567	+	0.548309i	0.0181863	+	0.0314995i
$304$	4.05237	−	1.60572i	0.232419	−	0.0920943i
$305$	5.89809	−	10.2158i	0.337724	−	0.584955i
$306$	−4.10286	+	1.49332i	−0.234545	+	0.0853673i
$307$	−20.4982	−	17.2000i	−1.16989	−	0.981657i	−0.169900	−	0.985461i	$-0.554345\pi$
$307$	−20.4982	−	17.2000i	−1.16989	−	0.981657i	−0.999993	+	0.00380462i	$0.998789\pi$
$308$	3.89634	−	1.74182i	0.222014	−	0.0992495i
$309$	−14.4928	+	5.27494i	−0.824466	+	0.300081i
$310$	2.36084	+	0.859274i	0.134086	+	0.0488035i
$311$	−16.1655			−0.916663			−0.458332	−	0.888781i	$-0.651553\pi$
$311$	−16.1655			−0.916663			−0.458332	+	0.888781i	$0.651553\pi$
$312$	2.03372	+	3.52251i	0.115137	+	0.199423i
$313$	−9.08806	+	7.62579i	−0.513687	+	0.431035i	−0.862425	−	0.506186i	$-0.831055\pi$
$313$	−9.08806	+	7.62579i	−0.513687	+	0.431035i	0.348737	+	0.937221i	$0.386611\pi$
$314$	−0.366082	−	2.07615i	−0.0206592	−	0.117164i
$315$	−3.90178	+	3.77932i	−0.219841	+	0.212941i
$316$	−0.0925489	−	0.160299i	−0.00520628	−	0.00901754i
$317$	11.8080	+	4.29776i	0.663203	+	0.241386i	0.651618	−	0.758547i	$-0.274090\pi$
$317$	11.8080	+	4.29776i	0.663203	+	0.241386i	0.0115842	+	0.999933i	$0.496313\pi$
$318$	−0.704000	+	3.99258i	−0.0394784	+	0.223893i
$319$	6.73753	−	5.65346i	0.377229	−	0.316533i
$320$	0.356521	−	2.02193i	0.0199301	−	0.113029i
$321$	1.14304	−	6.48248i	0.0637980	−	0.361817i
$322$	7.87925	+	2.24646i	0.439094	+	0.125190i
$323$	−2.77509	+	18.8283i	−0.154410	+	1.04763i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.44496	−	2.05157i	−0.135622	−	0.113801i
$326$	9.67879	−	3.52279i	0.536059	−	0.195109i
$327$	−0.345962	−	1.96205i	−0.0191318	−	0.108502i
$328$	−10.5217	+	3.82957i	−0.580962	+	0.211453i
$329$	−0.888438	+	8.57760i	−0.0489812	+	0.472898i
$330$	1.65598	+	2.86824i	0.0911587	+	0.157892i
$331$	−1.91099			−0.105038			−0.0525188	−	0.998620i	$-0.516725\pi$
$331$	−1.91099			−0.105038			−0.0525188	+	0.998620i	$0.516725\pi$
$332$	2.03752	+	0.741597i	0.111824	+	0.0407004i
$333$	−0.386820	−	0.140791i	−0.0211976	−	0.00771530i
$334$	7.85820			0.429982
$335$	5.01381	+	8.68418i	0.273934	+	0.474467i
$336$	2.14281	+	1.55190i	0.116900	+	0.0846629i
$337$	7.83719	−	2.85250i	0.426919	−	0.155386i	−0.119619	−	0.992820i	$-0.538167\pi$
$337$	7.83719	−	2.85250i	0.426919	−	0.155386i	0.546538	+	0.837434i	$0.315945\pi$
$338$	0.615425	+	3.49025i	0.0334747	+	0.189844i
$339$	−6.40742	+	2.33211i	−0.348003	+	0.126663i
$340$	6.86703	+	5.76213i	0.372417	+	0.312495i
$341$	0.986973	+	1.70949i	0.0534476	+	0.0925739i
$342$	−4.35717	+	0.122891i	−0.235609	+	0.00664521i
$343$	12.4547	+	13.7069i	0.672493	+	0.740103i
$344$	1.29925	−	7.36839i	0.0700507	−	0.397277i
$345$	−1.10406	+	6.26142i	−0.0594405	+	0.337104i
$346$	14.8717	−	12.4788i	0.799506	−	0.670865i
$347$	1.71738	−	9.73973i	0.0921936	−	0.522856i	−0.903378	−	0.428846i	$-0.858920\pi$
$347$	1.71738	−	9.73973i	0.0921936	−	0.522856i	0.995571	−	0.0940100i	$-0.0299686\pi$
$348$	5.12345	+	1.86478i	0.274646	+	0.0999628i
$349$	−2.92182	−	5.06074i	−0.156402	−	0.270895i	0.777167	−	0.629294i	$-0.216656\pi$
$349$	−2.92182	−	5.06074i	−0.156402	−	0.270895i	−0.933568	+	0.358399i	$0.883323\pi$
$350$	−1.99653	−	0.569231i	−0.106719	−	0.0304267i
$351$	−0.706304	−	4.00565i	−0.0376997	−	0.213806i
$352$	1.23573	−	1.03690i	0.0658647	−	0.0552671i
$353$	−0.787843	−	1.36458i	−0.0419327	−	0.0726295i	0.844297	−	0.535875i	$-0.180018\pi$
$353$	−0.787843	−	1.36458i	−0.0419327	−	0.0726295i	−0.886230	+	0.463245i	$0.846685\pi$
$354$	−7.36440			−0.391413
$355$	−19.5422	−	7.11279i	−1.03719	−	0.377508i
$356$	6.99290	−	2.54521i	0.370623	−	0.134896i
$357$	−10.5460	+	4.71448i	−0.558152	+	0.249517i
$358$	0.0702466	+	0.0589439i	0.00371265	+	0.00311528i
$359$	16.3302	−	5.94371i	0.861876	−	0.313697i	0.127003	−	0.991902i	$-0.459464\pi$
$359$	16.3302	−	5.94371i	0.861876	−	0.313697i	0.734873	+	0.678205i	$0.237242\pi$
$360$	−1.02656	+	1.77806i	−0.0541045	+	0.0937118i
$361$	−8.55746	+	16.9638i	−0.450392	+	0.892831i
$362$	2.95047	+	5.11036i	0.155073	+	0.268595i
$363$	1.45826	−	8.27022i	0.0765389	−	0.434074i
$364$	6.03120	+	8.91254i	0.316121	+	0.467144i
$365$	−19.8745	−	7.23372i	−1.04028	−	0.378630i
$366$	4.40130	+	3.69313i	0.230059	+	0.193043i
$367$	−3.02180	−	17.1375i	−0.157737	−	0.894569i	−0.956241	−	0.292580i	$-0.905486\pi$
$367$	−3.02180	−	17.1375i	−0.157737	−	0.894569i	0.798505	−	0.601989i	$-0.205625\pi$
$368$	3.09675			0.161429
$369$	11.1969			0.582889
$370$	0.146760	+	0.832318i	0.00762970	+	0.0432702i
$371$	−1.10508	+	10.6693i	−0.0573731	+	0.553920i
$372$	−0.611836	+	1.05973i	−0.0317222	+	0.0549445i
$373$	−18.8028	+	32.5674i	−0.973571	+	1.68628i	−0.289000	+	0.957329i	$0.593323\pi$
$373$	−18.8028	+	32.5674i	−0.973571	+	1.68628i	−0.684571	+	0.728946i	$0.740010\pi$
$374$	1.22304	+	6.93621i	0.0632419	+	0.358663i
$375$	2.06236	−	11.6962i	0.106500	−	0.603991i
$376$	0.565984	+	3.20985i	0.0291884	+	0.165536i
$377$	16.9884	+	14.2549i	0.874946	+	0.734167i
$378$	−1.48280	−	2.19119i	−0.0762669	−	0.112703i
$379$	4.80351			0.246740			0.123370	−	0.992361i	$-0.460630\pi$
$379$	4.80351			0.246740			0.123370	+	0.992361i	$0.460630\pi$
$380$	4.69141	+	7.62113i	0.240664	+	0.390956i
$381$	6.23377	−	10.7972i	0.319366	−	0.553158i
$382$	15.4782	+	12.9877i	0.791932	+	0.664510i
$383$	2.85351	−	16.1831i	0.145808	−	0.826917i	−0.820907	−	0.571061i	$-0.806532\pi$
$383$	2.85351	−	16.1831i	0.145808	−	0.826917i	0.966715	−	0.255855i	$-0.0823570\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	4.91097	+	7.25713i	0.250286	+	0.369858i
$386$	−10.5290	+	8.83485i	−0.535910	+	0.449682i
$387$	−3.74103	+	6.47966i	−0.190167	+	0.329379i
$388$	−5.40663	−	9.36456i	−0.274480	−	0.475414i
$389$	−26.4126	−	9.61341i	−1.33917	−	0.487419i	−0.429622	−	0.903009i	$-0.641353\pi$
$389$	−26.4126	−	9.61341i	−1.33917	−	0.487419i	−0.909552	+	0.415590i	$0.863575\pi$
$390$	−6.39721	+	5.36789i	−0.323935	+	0.271814i
$391$	−6.76047	+	11.7095i	−0.341892	+	0.592174i
$392$	5.94752	+	3.69148i	0.300395	+	0.186448i
$393$	10.4736	−	8.78841i	0.528324	−	0.443316i
$394$	9.55177	+	8.01488i	0.481211	+	0.403784i
$395$	0.291119	−	0.244277i	0.0146478	−	0.0122909i
$396$	−1.51585	+	0.551724i	−0.0761743	+	0.0277252i
$397$	32.4931	−	11.8265i	1.63078	−	0.593555i	0.645387	−	0.763855i	$-0.276696\pi$
$397$	32.4931	−	11.8265i	1.63078	−	0.593555i	0.985392	+	0.170300i	$0.0544737\pi$
$398$	−7.24973			−0.363396
$399$	−11.4755	+	1.14584i	−0.574493	+	0.0573639i
$400$	−0.784688			−0.0392344
$401$	1.10532	−	0.402303i	0.0551969	−	0.0200900i	−0.314274	−	0.949332i	$-0.601761\pi$
$401$	1.10532	−	0.402303i	0.0551969	−	0.0200900i	0.369471	+	0.929242i	$0.379539\pi$
$402$	−4.58954	+	1.67046i	−0.228905	+	0.0833148i
$403$	−3.81277	+	3.19929i	−0.189928	+	0.159368i
$404$	0.485008	+	0.406970i	0.0241301	+	0.0202475i
$405$	1.57278	−	1.31972i	0.0781522	−	0.0655775i
$406$	13.8725	+	3.95520i	0.688481	+	0.196293i
$407$	−0.332019	+	0.575074i	−0.0164576	+	0.0285054i
$408$	−3.34468	+	2.80652i	−0.165586	+	0.138943i
$409$	33.5318	+	12.2046i	1.65804	+	0.603478i	0.990053	−	0.140694i	$-0.0449333\pi$
$409$	33.5318	+	12.2046i	1.65804	+	0.603478i	0.667989	+	0.744172i	$0.267155\pi$
$410$	−11.4943	−	19.9088i	−0.567664	−	0.983224i
$411$	−3.59203	+	6.22157i	−0.177182	+	0.306888i
$412$	−11.8146	+	9.91365i	−0.582065	+	0.488410i
$413$	−19.4348	+	1.38853i	−0.956325	+	0.0683252i
$414$	−2.91000	−	1.05915i	−0.143019	−	0.0520545i
$415$	−0.773039	+	4.38412i	−0.0379470	+	0.215208i
$416$	3.11584	+	2.61450i	0.152767	+	0.128186i
$417$	10.0200	−	17.3551i	0.490681	−	0.849885i
$418$	−1.02529	+	6.95633i	−0.0501486	+	0.340245i
$419$	−4.62143			−0.225772			−0.112886	−	0.993608i	$-0.536009\pi$
$419$	−4.62143			−0.225772			−0.112886	+	0.993608i	$0.536009\pi$
$420$	−2.37387	+	4.88589i	−0.115833	+	0.238407i
$421$	10.2901	+	8.63443i	0.501509	+	0.420816i	0.858130	−	0.513433i	$-0.171627\pi$
$421$	10.2901	+	8.63443i	0.501509	+	0.420816i	−0.356620	+	0.934249i	$0.616071\pi$
$422$	2.54479	+	14.4322i	0.123878	+	0.702549i
$423$	0.565984	−	3.20985i	0.0275191	−	0.156068i
$424$	0.704000	+	3.99258i	0.0341893	+	0.193897i
$425$	1.71304	−	2.96707i	0.0830947	−	0.143924i
$426$	5.06458	−	8.77211i	0.245380	−	0.425010i
$427$	12.3115	+	8.91640i	0.595793	+	0.431495i
$428$	−1.14304	−	6.48248i	−0.0552507	−	0.313342i
$429$	−6.56133			−0.316784
$430$	15.3616			0.740802
$431$	5.39306	+	30.5856i	0.259775	+	1.47326i	0.783512	+	0.621376i	$0.213426\pi$
$431$	5.39306	+	30.5856i	0.259775	+	1.47326i	−0.523738	+	0.851880i	$0.675463\pi$
$432$	−0.766044	−	0.642788i	−0.0368563	−	0.0309261i
$433$	32.6131	+	11.8702i	1.56728	+	0.570445i	0.972390	−	0.233360i	$-0.0749720\pi$
$433$	32.6131	+	11.8702i	1.56728	+	0.570445i	0.594894	+	0.803804i	$0.297194\pi$
$434$	−1.41484	+	2.91202i	−0.0679146	+	0.139781i
$435$	−1.94385	+	11.0241i	−0.0932002	+	0.528565i
$436$	−0.996159	−	1.72540i	−0.0477074	−	0.0826316i
$437$	−10.0917	+	8.96471i	−0.482750	+	0.428840i
$438$	5.15069	−	8.92125i	0.246109	−	0.426274i
$439$	−33.2085	+	12.0869i	−1.58495	+	0.576876i	−0.976274	−	0.216539i	$-0.930523\pi$
$439$	−33.2085	+	12.0869i	−1.58495	+	0.576876i	−0.608680	+	0.793415i	$0.708301\pi$
$440$	2.53711	+	2.12889i	0.120952	+	0.101491i
$441$	−4.32628	−	5.50302i	−0.206013	−	0.262049i
$442$	−16.6881	+	6.07398i	−0.793773	+	0.288910i
$443$	20.1427	+	7.33135i	0.957009	+	0.348323i	0.772861	−	0.634576i	$-0.218825\pi$
$443$	20.1427	+	7.33135i	0.957009	+	0.348323i	0.184148	+	0.982898i	$0.441047\pi$
$444$	−0.411645			−0.0195358
$445$	7.63935	+	13.2317i	0.362140	+	0.627245i
$446$	14.0346	−	11.7764i	0.664555	−	0.557628i
$447$	−2.56818	−	14.5649i	−0.121471	−	0.688896i
$448$	2.54436	+	0.725423i	0.120210	+	0.0342730i
$449$	14.6623	+	25.3959i	0.691957	+	1.19850i	0.971196	+	0.238283i	$0.0765846\pi$
$449$	14.6623	+	25.3959i	0.691957	+	1.19850i	−0.279239	+	0.960222i	$0.590082\pi$
$450$	0.737366	+	0.268379i	0.0347598	+	0.0126515i
$451$	3.13646	−	17.7877i	0.147690	−	0.837591i
$452$	−5.22338	+	4.38293i	−0.245687	+	0.206156i
$453$	−1.67902	+	9.52220i	−0.0788873	+	0.447392i
$454$	2.75795	−	15.6411i	0.129437	−	0.734073i
$455$	−15.8703	+	15.3722i	−0.744010	+	0.720659i
$456$	−4.05237	+	1.60572i	−0.189769	+	0.0751947i
$457$	−2.93494	−	5.08347i	−0.137291	−	0.237795i	0.789179	−	0.614163i	$-0.210506\pi$
$457$	−2.93494	−	5.08347i	−0.137291	−	0.237795i	−0.926470	+	0.376368i	$0.877173\pi$
$458$	15.0391	+	12.6193i	0.702730	+	0.589661i
$459$	4.10286	−	1.49332i	0.191505	−	0.0697021i
$460$	1.10406	+	6.26142i	0.0514770	+	0.291940i
$461$	33.3535	−	12.1397i	1.55343	−	0.565402i	0.584209	−	0.811603i	$-0.301405\pi$
$461$	33.3535	−	12.1397i	1.55343	−	0.565402i	0.969219	+	0.246201i	$0.0791824\pi$
$462$	−3.89634	+	1.74182i	−0.181274	+	0.0810369i
$463$	16.0040	+	27.7198i	0.743770	+	1.28825i	0.950767	+	0.309906i	$0.100298\pi$
$463$	16.0040	+	27.7198i	0.743770	+	1.28825i	−0.206997	+	0.978342i	$0.566369\pi$
$464$	5.45226			0.253115
$465$	−2.36084	−	0.859274i	−0.109481	−	0.0398479i
$466$	24.5983	+	8.95304i	1.13949	+	0.414742i
$467$	−14.3596			−0.664484			−0.332242	−	0.943194i	$-0.607805\pi$
$467$	−14.3596			−0.664484			−0.332242	+	0.943194i	$0.607805\pi$
$468$	−2.03372	−	3.52251i	−0.0940088	−	0.162828i
$469$	−11.7969	+	5.27372i	−0.544732	+	0.243518i
$470$	−6.28832	+	2.28876i	−0.290059	+	0.105573i
$471$	0.366082	+	2.07615i	0.0168682	+	0.0956641i
$472$	−6.92027	+	2.51877i	−0.318531	+	0.115936i
$473$	9.24582	+	7.75817i	0.425123	+	0.356721i
$474$	0.0925489	+	0.160299i	0.00425091	+	0.00736279i
$475$	2.55713	−	2.27157i	0.117329	−	0.104227i
$476$	−8.29753	+	8.03710i	−0.380317	+	0.368380i
$477$	0.704000	−	3.99258i	0.0322339	−	0.182808i
$478$	2.85048	−	16.1659i	0.130378	−	0.739410i
$479$	14.8468	−	12.4579i	0.678366	−	0.569217i	−0.237162	−	0.971470i	$-0.576217\pi$
$479$	14.8468	−	12.4579i	0.678366	−	0.569217i	0.915528	+	0.402253i	$0.131773\pi$
$480$	−0.356521	+	2.02193i	−0.0162729	+	0.0922881i
$481$	−1.57337	−	0.572659i	−0.0717394	−	0.0261110i
$482$	11.1931	+	19.3871i	0.509833	+	0.883057i
$483$	−7.87925	−	2.24646i	−0.358518	−	0.102217i
$484$	−1.45826	−	8.27022i	−0.0662847	−	0.375919i
$485$	17.0069	−	14.2705i	0.772245	−	0.647990i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	1.27124			0.0576055			0.0288028	−	0.999585i	$-0.490831\pi$
$487$	1.27124			0.0576055			0.0288028	+	0.999585i	$0.490831\pi$
$488$	5.39899	+	1.96507i	0.244401	+	0.0889546i
$489$	−9.67879	+	3.52279i	−0.437690	+	0.159306i
$490$	−5.34349	+	13.3416i	−0.241394	+	0.602711i
$491$	21.5140	+	18.0524i	0.970914	+	0.814693i	0.982694	−	0.185237i	$-0.0593054\pi$
$491$	21.5140	+	18.0524i	0.970914	+	0.814693i	−0.0117801	+	0.999931i	$0.503750\pi$
$492$	10.5217	−	3.82957i	0.474353	−	0.172651i
$493$	−11.9027	+	20.6162i	−0.536072	+	0.928505i
$494$	−17.7225	+	0.499854i	−0.797374	+	0.0224895i
$495$	−1.65598	−	2.86824i	−0.0744308	−	0.128918i
$496$	−0.212488	+	1.20508i	−0.00954101	+	0.0541098i
$497$	11.7116	−	24.1047i	0.525337	−	1.08124i
$498$	−2.03752	−	0.741597i	−0.0913036	−	0.0332318i
$499$	−2.37229	−	1.99059i	−0.106198	−	0.0891109i	0.588142	−	0.808757i	$-0.299859\pi$
$499$	−2.37229	−	1.99059i	−0.106198	−	0.0891109i	−0.694341	+	0.719646i	$0.744304\pi$
$500$	−2.06236	−	11.6962i	−0.0922317	−	0.523072i
$501$	−7.85820			−0.351078
$502$	24.0870			1.07506
$503$	−6.98804	−	39.6312i	−0.311581	−	1.76707i	−0.590780	−	0.806833i	$-0.701180\pi$
$503$	−6.98804	−	39.6312i	−0.311581	−	1.76707i	0.279198	−	0.960233i	$-0.409931\pi$
$504$	−2.14281	−	1.55190i	−0.0954481	−	0.0691270i
$505$	−0.649950	+	1.12575i	−0.0289224	+	0.0500950i
$506$	−2.49774	+	4.32621i	−0.111038	+	0.192324i
$507$	−0.615425	−	3.49025i	−0.0273320	−	0.155007i
$508$	2.16497	−	12.2781i	0.0960548	−	0.544754i
$509$	−1.25675	−	7.12741i	−0.0557046	−	0.315917i	0.944205	−	0.329358i	$-0.106832\pi$
$509$	−1.25675	−	7.12741i	−0.0557046	−	0.315917i	−0.999910	+	0.0134416i	$0.995721\pi$
$510$	−6.86703	−	5.76213i	−0.304077	−	0.255151i
$511$	11.9107	−	24.5146i	0.526899	−	1.08446i
$512$	1.00000			0.0441942
$513$	4.35717	−	0.122891i	0.192374	−	0.00542579i
$514$	7.97032	−	13.8050i	0.351556	−	0.608912i
$515$	−24.2569	−	20.3539i	−1.06889	−	0.896901i
$516$	−1.29925	+	7.36839i	−0.0571961	+	0.324375i
$517$	−4.94072	−	1.79827i	−0.217293	−	0.0790880i
$518$	−1.08634	+	0.0776144i	−0.0477311	+	0.00341018i
$519$	−14.8717	+	12.4788i	−0.652794	+	0.547759i
$520$	−4.17548	+	7.23214i	−0.183107	+	0.317150i
$521$	−2.05543	−	3.56011i	−0.0900499	−	0.155971i	0.817482	−	0.575954i	$-0.195369\pi$
$521$	−2.05543	−	3.56011i	−0.0900499	−	0.155971i	−0.907532	+	0.419983i	$0.862036\pi$
$522$	−5.12345	−	1.86478i	−0.224247	−	0.0816193i
$523$	1.08192	−	0.907838i	0.0473090	−	0.0396970i	−0.618827	−	0.785528i	$-0.712392\pi$
$523$	1.08192	−	0.907838i	0.0473090	−	0.0396970i	0.666136	+	0.745831i	$0.267947\pi$
$524$	6.83617	−	11.8406i	0.298639	−	0.517259i
$525$	1.99653	+	0.569231i	0.0871356	+	0.0248433i
$526$	−9.05905	+	7.60145i	−0.394994	+	0.331439i
$527$	−4.09279	−	3.43426i	−0.178285	−	0.149599i
$528$	−1.23573	+	1.03690i	−0.0537783	+	0.0451254i
$529$	12.6014	−	4.58653i	0.547886	−	0.199414i
$530$	−7.82174	+	2.84688i	−0.339754	+	0.123661i
$531$	7.36440			0.319588
$532$	−10.3915	+	5.00159i	−0.450530	+	0.216846i
$533$	45.5428			1.97268
$534$	−6.99290	+	2.54521i	−0.302612	+	0.110142i
$535$	12.6996	−	4.62228i	0.549052	−	0.199839i
$536$	−3.74143	+	3.13943i	−0.161605	+	0.135603i
$537$	−0.0702466	−	0.0589439i	−0.00303137	−	0.00254362i
$538$	1.40985	−	1.18300i	0.0607829	−	0.0510029i
$539$	−9.95412	+	5.33135i	−0.428754	+	0.229638i
$540$	1.02656	−	1.77806i	0.0441762	−	0.0765154i
$541$	−4.12759	+	3.46346i	−0.177459	+	0.148906i	−0.727191	−	0.686436i	$-0.759174\pi$
$541$	−4.12759	+	3.46346i	−0.177459	+	0.148906i	0.549732	+	0.835341i	$0.314730\pi$
$542$	24.2192	+	8.81506i	1.04030	+	0.378639i
$543$	−2.95047	−	5.11036i	−0.126617	−	0.219307i
$544$	−2.18308	+	3.78121i	−0.0935989	+	0.162118i
$545$	3.13348	−	2.62930i	0.134224	−	0.112627i
$546$	−6.03120	−	8.91254i	−0.258111	−	0.381421i
$547$	17.0466	+	6.20446i	0.728860	+	0.265283i	0.679682	−	0.733507i	$-0.262118\pi$
$547$	17.0466	+	6.20446i	0.728860	+	0.265283i	0.0491780	+	0.998790i	$0.484340\pi$
$548$	−1.24750	+	7.07491i	−0.0532905	+	0.302225i
$549$	−4.40130	−	3.69313i	−0.187843	−	0.157619i
$550$	0.632903	−	1.09622i	0.0269871	−	0.0467430i
$551$	−17.7678	+	15.7836i	−0.756932	+	0.672404i
$552$	−3.09675			−0.131807
$553$	0.274463	+	0.405584i	0.0116713	+	0.0172472i
$554$	−21.1983	−	17.7874i	−0.900627	−	0.755716i
$555$	−0.146760	−	0.832318i	−0.00622962	−	0.0353299i
$556$	3.47991	−	19.7355i	0.147581	−	0.836973i
$557$	0.464391	+	2.63369i	0.0196769	+	0.111593i	0.993064	−	0.117573i	$-0.0375113\pi$
$557$	0.464391	+	2.63369i	0.0196769	+	0.111593i	−0.973387	+	0.229166i	$0.926400\pi$
$558$	0.611836	−	1.05973i	0.0259011	−	0.0448620i
$559$	−15.2164	+	26.3556i	−0.643586	+	1.11472i
$560$	−0.559639	+	5.40315i	−0.0236491	+	0.228325i
$561$	−1.22304	−	6.93621i	−0.0516368	−	0.292847i
$562$	−27.8440			−1.17453
$563$	−20.3046			−0.855737			−0.427869	−	0.903841i	$-0.640735\pi$
$563$	−20.3046			−0.855737			−0.427869	+	0.903841i	$0.640735\pi$
$564$	−0.565984	−	3.20985i	−0.0238322	−	0.135159i
$565$	−10.7242	−	8.99870i	−0.451172	−	0.378578i
$566$	−13.6676	−	4.97462i	−0.574494	−	0.209099i
$567$	1.48280	+	2.19119i	0.0622717	+	0.0920213i
$568$	1.75891	−	9.97527i	0.0738022	−	0.418553i
$569$	−1.95776	−	3.39094i	−0.0820736	−	0.142156i	0.822067	−	0.569391i	$-0.192821\pi$
$569$	−1.95776	−	3.39094i	−0.0820736	−	0.142156i	−0.904140	+	0.427235i	$0.859488\pi$
$570$	−4.69141	−	7.62113i	−0.196501	−	0.319214i
$571$	11.0862	−	19.2018i	0.463943	−	0.803572i	−0.535210	−	0.844719i	$-0.679768\pi$
$571$	11.0862	−	19.2018i	0.463943	−	0.803572i	0.999153	+	0.0411465i	$0.0131010\pi$
$572$	−6.16563	+	2.24411i	−0.257798	+	0.0938308i
$573$	−15.4782	−	12.9877i	−0.646610	−	0.542570i
$574$	27.0449	−	12.0902i	1.12883	−	0.504634i
$575$	2.28344	−	0.831104i	0.0952261	−	0.0346595i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	−41.8968			−1.74418			−0.872092	−	0.489341i	$-0.837237\pi$
$577$	−41.8968			−1.74418			−0.872092	+	0.489341i	$0.837237\pi$
$578$	−1.03171	−	1.78697i	−0.0429135	−	0.0743283i
$579$	10.5290	−	8.83485i	0.437569	−	0.367164i
$580$	1.94385	+	11.0241i	0.0807138	+	0.457751i
$581$	−5.51690	−	1.57293i	−0.228879	−	0.0652559i
$582$	5.40663	+	9.36456i	0.224112	+	0.388174i
$583$	−6.14552	−	2.23679i	−0.254521	−	0.0926382i
$584$	1.78882	−	10.1449i	0.0740217	−	0.419798i
$585$	6.39721	−	5.36789i	0.264492	−	0.221935i
$586$	0.449406	−	2.54871i	0.0185648	−	0.105286i
$587$	4.47146	−	25.3589i	0.184557	−	1.04667i	−0.741967	−	0.670437i	$-0.766107\pi$
$587$	4.47146	−	25.3589i	0.184557	−	1.04667i	0.926523	−	0.376237i	$-0.122782\pi$
$588$	−5.94752	−	3.69148i	−0.245272	−	0.152234i
$589$	−2.79610	−	4.54223i	−0.115211	−	0.187160i
$590$	−7.56000	−	13.0943i	−0.311240	−	0.539084i
$591$	−9.55177	−	8.01488i	−0.392907	−	0.329688i
$592$	−0.386820	+	0.140791i	−0.0158982	+	0.00578647i
$593$	−1.56924	−	8.89960i	−0.0644409	−	0.365463i	−0.999927	−	0.0120986i	$-0.996149\pi$
$593$	−1.56924	−	8.89960i	−0.0644409	−	0.365463i	0.935486	−	0.353364i	$-0.114962\pi$
$594$	1.51585	−	0.551724i	0.0621961	−	0.0226375i
$595$	−19.2087	−	13.9116i	−0.787480	−	0.570321i
$596$	−7.39479	−	12.8082i	−0.302903	−	0.524643i
$597$	7.24973			0.296712
$598$	−11.8362	−	4.30804i	−0.484020	−	0.176169i
$599$	−39.9729	−	14.5490i	−1.63325	−	0.594454i	−0.647410	−	0.762142i	$-0.724148\pi$
$599$	−39.9729	−	14.5490i	−1.63325	−	0.594454i	−0.985840	+	0.167688i	$0.946370\pi$
$600$	0.784688			0.0320348
$601$	13.5791	+	23.5197i	0.553904	+	0.959390i	0.997988	+	0.0634045i	$0.0201958\pi$
$601$	13.5791	+	23.5197i	0.553904	+	0.959390i	−0.444084	+	0.895985i	$0.646471\pi$
$602$	−2.03946	+	19.6903i	−0.0831220	+	0.802518i
$603$	4.58954	−	1.67046i	0.186901	−	0.0680262i
$604$	1.67902	+	9.52220i	0.0683184	+	0.387453i
$605$	16.2019	−	5.89701i	0.658701	−	0.239748i
$606$	−0.485008	−	0.406970i	−0.0197021	−	0.0165320i
$607$	1.97530	+	3.42133i	0.0801751	+	0.138867i	0.903325	−	0.428957i	$-0.141119\pi$
$607$	1.97530	+	3.42133i	0.0801751	+	0.138867i	−0.823150	+	0.567824i	$0.807785\pi$
$608$	−3.25879	+	2.89487i	−0.132161	+	0.117403i
$609$	−13.8725	−	3.95520i	−0.562142	−	0.160273i
$610$	−2.04839	+	11.6170i	−0.0829367	+	0.470357i
$611$	2.30211	−	13.0559i	0.0931333	−	0.528185i
$612$	3.34468	−	2.80652i	0.135201	−	0.113447i
$613$	−4.22511	+	23.9618i	−0.170651	+	0.967808i	0.772394	+	0.635143i	$0.219059\pi$
$613$	−4.22511	+	23.9618i	−0.170651	+	0.967808i	−0.943045	+	0.332665i	$0.892052\pi$
$614$	25.1447	+	9.15194i	1.01476	+	0.369342i
$615$	11.4943	+	19.9088i	0.463496	+	0.802799i
$616$	−3.06562	+	2.96940i	−0.123517	+	0.119641i
$617$	−3.58216	−	20.3154i	−0.144212	−	0.817868i	−0.967996	−	0.250964i	$-0.919252\pi$
$617$	−3.58216	−	20.3154i	−0.144212	−	0.817868i	0.823784	−	0.566903i	$-0.191859\pi$
$618$	11.8146	−	9.91365i	0.475254	−	0.398785i
$619$	19.3869	+	33.5790i	0.779223	+	1.34965i	0.932390	+	0.361454i	$0.117720\pi$
$619$	19.3869	+	33.5790i	0.779223	+	1.34965i	−0.153166	+	0.988200i	$0.548947\pi$
$620$	−2.51235			−0.100898
$621$	2.91000	+	1.05915i	0.116774	+	0.0425023i
$622$	15.1906	−	5.52894i	0.609089	−	0.221690i
$623$	−17.9745	+	8.03535i	−0.720135	+	0.321930i
$624$	−3.11584	−	2.61450i	−0.124734	−	0.104664i
$625$	19.2269	−	6.99801i	0.769075	−	0.279921i
$626$	5.93181	−	10.2742i	0.237083	−	0.410639i
$627$	1.02529	−	6.95633i	0.0409462	−	0.277809i
$628$	1.05409	+	1.82574i	0.0420628	+	0.0728549i
$629$	0.312100	−	1.77001i	0.0124442	−	0.0705748i
$630$	2.37387	−	4.88589i	0.0945774	−	0.194658i
$631$	−4.05991	−	1.47769i	−0.161623	−	0.0588258i	0.259942	−	0.965624i	$-0.416297\pi$
$631$	−4.05991	−	1.47769i	−0.161623	−	0.0588258i	−0.421564	+	0.906798i	$0.638519\pi$
$632$	0.141793	+	0.118979i	0.00564023	+	0.00473271i
$633$	−2.54479	−	14.4322i	−0.101146	−	0.573629i
$634$	−12.5658			−0.499052
$635$	25.5974			1.01580
$636$	−0.704000	−	3.99258i	−0.0279154	−	0.158316i
$637$	−17.5969	−	22.3832i	−0.697215	−	0.886856i
$638$	−4.39761	+	7.61689i	−0.174103	+	0.301555i
$639$	−5.06458	+	8.77211i	−0.200352	+	0.347019i
$640$	0.356521	+	2.02193i	0.0140927	+	0.0799238i
$641$	6.67002	−	37.8276i	0.263450	−	1.49410i	−0.509962	−	0.860197i	$-0.670341\pi$
$641$	6.67002	−	37.8276i	0.263450	−	1.49410i	0.773412	−	0.633903i	$-0.218548\pi$
$642$	1.14304	+	6.48248i	0.0451120	+	0.255843i
$643$	−34.6770	−	29.0974i	−1.36753	−	1.14749i	−0.973577	−	0.228359i	$-0.926664\pi$
$643$	−34.6770	−	29.0974i	−1.36753	−	1.14749i	−0.393949	−	0.919132i	$-0.628891\pi$
$644$	−8.17241	+	0.583883i	−0.322038	+	0.0230082i
$645$	−15.3616			−0.604862
$646$	−3.83192	−	18.6419i	−0.150765	−	0.733457i
$647$	−21.0102	+	36.3908i	−0.825998	+	1.43067i	0.0751567	+	0.997172i	$0.476054\pi$
$647$	−21.0102	+	36.3908i	−0.825998	+	1.43067i	−0.901154	+	0.433498i	$0.857279\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	2.06290	−	11.6993i	0.0809758	−	0.459237i
$650$	2.99919	+	1.09162i	0.117638	+	0.0428167i
$651$	1.41484	−	2.91202i	0.0554520	−	0.114131i
$652$	−7.89022	+	6.62068i	−0.309005	+	0.259286i
$653$	−24.3139	+	42.1129i	−0.951477	+	1.64801i	−0.209246	+	0.977863i	$0.567101\pi$
$653$	−24.3139	+	42.1129i	−0.951477	+	1.64801i	−0.742231	+	0.670144i	$0.766232\pi$
$654$	0.996159	+	1.72540i	0.0389529	+	0.0674684i
$655$	26.3781	+	9.60084i	1.03068	+	0.375136i
$656$	8.57734	−	7.19724i	0.334889	−	0.281005i
$657$	−5.15069	+	8.92125i	−0.200947	+	0.348051i
$658$	−2.09885	−	8.36417i	−0.0818218	−	0.326069i
$659$	4.99461	−	4.19098i	0.194563	−	0.163257i	−0.540302	−	0.841471i	$-0.681690\pi$
$659$	4.99461	−	4.19098i	0.194563	−	0.163257i	0.734865	+	0.678214i	$0.237246\pi$
$660$	−2.53711	−	2.12889i	−0.0987568	−	0.0828668i
$661$	7.46049	−	6.26010i	0.290180	−	0.243490i	−0.486063	−	0.873924i	$-0.661568\pi$
$661$	7.46049	−	6.26010i	0.290180	−	0.243490i	0.776243	+	0.630434i	$0.217123\pi$
$662$	1.79575	−	0.653598i	0.0697936	−	0.0254028i
$663$	16.6881	−	6.07398i	0.648113	−	0.235894i
$664$	−2.16829			−0.0841458
$665$	−13.8177	−	19.2278i	−0.535826	−	0.745622i
$666$	0.411645			0.0159509
$667$	−15.8661	+	5.77477i	−0.614336	+	0.223600i
$668$	−7.38429	+	2.68766i	−0.285707	+	0.103989i
$669$	−14.0346	+	11.7764i	−0.542607	+	0.455302i
$670$	−7.68161	−	6.44563i	−0.296766	−	0.249017i
$671$	−7.09988	+	5.95750i	−0.274088	+	0.229987i
$672$	−2.54436	−	0.725423i	−0.0981508	−	0.0279838i
$673$	24.3296	−	42.1402i	0.937839	−	1.62438i	0.168347	−	0.985728i	$-0.446157\pi$
$673$	24.3296	−	42.1402i	0.937839	−	1.62438i	0.769492	−	0.638656i	$-0.220509\pi$
$674$	−6.38894	+	5.36095i	−0.246093	+	0.206496i
$675$	−0.737366	−	0.268379i	−0.0283812	−	0.0103299i
$676$	−1.77205	−	3.06927i	−0.0681556	−	0.118049i
$677$	−4.95928	+	8.58972i	−0.190600	+	0.330130i	−0.945449	−	0.325769i	$-0.894377\pi$
$677$	−4.95928	+	8.58972i	−0.190600	+	0.330130i	0.754849	+	0.655899i	$0.227710\pi$
$678$	5.22338	−	4.38293i	0.200603	−	0.168325i
$679$	16.0339	+	23.6939i	0.615324	+	0.909289i
$680$	−8.42366	−	3.06596i	−0.323033	−	0.117574i
$681$	−2.75795	+	15.6411i	−0.105685	+	0.599368i
$682$	−1.51213	−	1.26883i	−0.0579025	−	0.0485859i
$683$	−21.3388	+	36.9598i	−0.816505	+	1.41423i	0.0917364	+	0.995783i	$0.470758\pi$
$683$	−21.3388	+	36.9598i	−0.816505	+	1.41423i	−0.908242	+	0.418446i	$0.862575\pi$
$684$	4.05237	−	1.60572i	0.154946	−	0.0613962i
$685$	−14.7497			−0.563559
$686$	−16.3917	−	8.62051i	−0.625837	−	0.329132i
$687$	−15.0391	−	12.6193i	−0.573777	−	0.481456i
$688$	1.29925	+	7.36839i	0.0495333	+	0.280917i
$689$	2.86348	−	16.2396i	0.109090	−	0.618680i
$690$	−1.10406	−	6.26142i	−0.0420308	−	0.238368i
$691$	22.2127	−	38.4736i	0.845012	−	1.46360i	−0.0405981	−	0.999176i	$-0.512926\pi$
$691$	22.2127	−	38.4736i	0.845012	−	1.46360i	0.885610	−	0.464429i	$-0.153740\pi$
$692$	−9.70680	+	16.8127i	−0.368997	+	0.639122i
$693$	3.89634	−	1.74182i	0.148010	−	0.0661664i
$694$	1.71738	+	9.73973i	0.0651907	+	0.369715i
$695$	41.1446			1.56070
$696$	−5.45226			−0.206667
$697$	8.48925	+	48.1449i	0.321553	+	1.82362i
$698$	4.47649	+	3.75622i	0.169438	+	0.142175i
$699$	−24.5983	−	8.95304i	−0.930393	−	0.338635i
$700$	2.07081	−	0.147950i	0.0782693	−	0.00559200i
$701$	−3.65966	+	20.7549i	−0.138223	+	0.783903i	0.834337	+	0.551254i	$0.185851\pi$
$701$	−3.65966	+	20.7549i	−0.138223	+	0.783903i	−0.972561	+	0.232649i	$0.925261\pi$
$702$	2.03372	+	3.52251i	0.0767579	+	0.132949i
$703$	0.852993	−	1.57860i	0.0321712	−	0.0595381i
$704$	−0.806567	+	1.39701i	−0.0303986	+	0.0526520i
$705$	6.28832	−	2.28876i	0.236832	−	0.0861997i
$706$	1.20705	+	1.01283i	0.0454278	+	0.0381184i
$707$	−1.35668	−	0.982557i	−0.0510232	−	0.0369529i
$708$	6.92027	−	2.51877i	0.260080	−	0.0946612i
$709$	−9.07988	−	3.30481i	−0.341002	−	0.124115i	0.165842	−	0.986152i	$-0.446966\pi$
$709$	−9.07988	−	3.30481i	−0.341002	−	0.124115i	−0.506844	+	0.862038i	$0.669188\pi$
$710$	20.7964			0.780475
$711$	−0.0925489	−	0.160299i	−0.00347085	−	0.00601169i
$712$	−5.70066	+	4.78343i	−0.213641	+	0.179266i
$713$	−0.658024	−	3.73184i	−0.0246432	−	0.139759i
$714$	8.29753	−	8.03710i	0.310527	−	0.300781i
$715$	−6.73561	−	11.6664i	−0.251897	−	0.436299i
$716$	−0.0861703	−	0.0313634i	−0.00322033	−	0.00117211i
$717$	−2.85048	+	16.1659i	−0.106453	+	0.603726i
$718$	−13.3125	+	11.1705i	−0.496819	+	0.416880i
$719$	2.32582	−	13.1904i	0.0867384	−	0.491918i	−0.910230	−	0.414104i	$-0.864095\pi$
$719$	2.32582	−	13.1904i	0.0867384	−	0.491918i	0.996968	−	0.0778137i	$-0.0247939\pi$
$720$	0.356521	−	2.02193i	0.0132868	−	0.0753529i
$721$	29.3099	−	28.3900i	1.09156	−	1.05730i
$722$	2.23942	−	18.8676i	0.0833427	−	0.702178i
$723$	−11.1931	−	19.3871i	−0.416277	−	0.721013i
$724$	−4.52038	−	3.79305i	−0.167999	−	0.140968i
$725$	4.02031	−	1.46327i	0.149311	−	0.0543446i
$726$	1.45826	+	8.27022i	0.0541212	+	0.306937i
$727$	−34.1451	+	12.4278i	−1.26637	+	0.460921i	−0.885902	−	0.463873i	$-0.846459\pi$
$727$	−34.1451	+	12.4278i	−1.26637	+	0.460921i	−0.380468	+	0.924794i	$0.624237\pi$
$728$	−8.71574	−	6.31225i	−0.323027	−	0.233948i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	21.1500			0.782796
$731$	−30.6978	−	11.1731i	−1.13540	−	0.413252i
$732$	−5.39899	−	1.96507i	−0.199552	−	0.0726311i
$733$	27.3217			1.00915			0.504575	−	0.863368i	$-0.331649\pi$
$733$	27.3217			1.00915			0.504575	+	0.863368i	$0.331649\pi$
$734$	8.70092	+	15.0704i	0.321157	+	0.556260i
$735$	5.34349	−	13.3416i	0.197098	−	0.492111i
$736$	−2.91000	+	1.05915i	−0.107264	+	0.0390409i
$737$	−1.36812	−	7.75899i	−0.0503953	−	0.285806i
$738$	−10.5217	+	3.82957i	−0.387308	+	0.140969i
$739$	9.29065	+	7.79578i	0.341762	+	0.286772i	0.797472	−	0.603356i	$-0.206170\pi$
$739$	9.29065	+	7.79578i	0.341762	+	0.286772i	−0.455710	+	0.890128i	$0.650615\pi$
$740$	−0.422579	−	0.731928i	−0.0155343	−	0.0269062i
$741$	17.7225	−	0.499854i	0.651053	−	0.0183626i
$742$	−2.61066	−	10.4038i	−0.0958404	−	0.381935i
$743$	−0.854332	+	4.84516i	−0.0313424	+	0.177752i	−0.996460	−	0.0840638i	$-0.973210\pi$
$743$	−0.854332	+	4.84516i	−0.0313424	+	0.177752i	0.965118	+	0.261815i	$0.0843211\pi$
$744$	0.212488	−	1.20508i	0.00779020	−	0.0441804i
$745$	23.2608	−	19.5181i	0.852210	−	0.715089i
$746$	6.53014	−	37.0343i	0.239085	−	1.35592i
$747$	2.03752	+	0.741597i	0.0745490	+	0.0271336i
$748$	−3.52161	−	6.09960i	−0.128763	−	0.223023i
$749$	4.23875	+	16.8919i	0.154881	+	0.617217i
$750$	2.06236	+	11.6962i	0.0753068	+	0.427086i
$751$	30.0236	−	25.1928i	1.09558	−	0.919299i	0.0984579	−	0.995141i	$-0.468609\pi$
$751$	30.0236	−	25.1928i	1.09558	−	0.919299i	0.997120	+	0.0758424i	$0.0241646\pi$
$752$	−1.62969	−	2.82270i	−0.0594285	−	0.102933i
$753$	−24.0870			−0.877781
$754$	−20.8393	−	7.58490i	−0.758924	−	0.276226i
$755$	−18.6546	+	6.78973i	−0.678911	+	0.247104i
$756$	2.14281	+	1.55190i	0.0779331	+	0.0564419i
$757$	−20.0000	−	16.7820i	−0.726912	−	0.609952i	0.202376	−	0.979308i	$-0.435134\pi$
$757$	−20.0000	−	16.7820i	−0.726912	−	0.609952i	−0.929288	+	0.369356i	$0.879578\pi$
$758$	−4.51383	+	1.64290i	−0.163950	+	0.0596728i
$759$	2.49774	−	4.32621i	0.0906622	−	0.157032i
$760$	−7.01506	−	5.55697i	−0.254463	−	0.201572i
$761$	−2.88473	−	4.99650i	−0.104571	−	0.181123i	0.808992	−	0.587820i	$-0.200014\pi$
$761$	−2.88473	−	4.99650i	−0.104571	−	0.181123i	−0.913563	+	0.406697i	$0.866680\pi$
$762$	−2.16497	+	12.2781i	−0.0784284	+	0.444790i
$763$	2.95421	+	4.36554i	0.106949	+	0.158043i
$764$	−18.9868	−	6.91063i	−0.686918	−	0.250018i
$765$	6.86703	+	5.76213i	0.248278	+	0.208330i
$766$	2.85351	+	16.1831i	0.103102	+	0.584718i
$767$	29.9543			1.08159
$768$	−1.00000			−0.0360844
$769$	1.78224	+	10.1076i	0.0642692	+	0.364489i	0.999933	+	0.0115954i	$0.00369100\pi$
$769$	1.78224	+	10.1076i	0.0642692	+	0.364489i	−0.935664	+	0.352893i	$0.885198\pi$
$770$	−7.09689	−	5.13982i	−0.255754	−	0.185226i
$771$	−7.97032	+	13.8050i	−0.287044	+	0.497175i
$772$	6.87230	−	11.9032i	0.247339	−	0.428404i
$773$	2.01129	+	11.4066i	0.0723411	+	0.410267i	0.999377	+	0.0352941i	$0.0112368\pi$
$773$	2.01129	+	11.4066i	0.0723411	+	0.410267i	−0.927036	+	0.374973i	$0.877652\pi$
$774$	1.29925	−	7.36839i	0.0467005	−	0.264851i
$775$	0.166737	+	0.945613i	0.00598938	+	0.0339674i
$776$	8.28344	+	6.95063i	0.297358	+	0.249513i
$777$	1.08634	−	0.0776144i	0.0389723	−	0.00278440i
$778$	28.1077			1.00771
$779$	−7.11665	+	48.2846i	−0.254980	+	1.72998i
$780$	4.17548	−	7.23214i	0.149506	−	0.258952i
$781$	12.5169	+	10.5029i	0.447891	+	0.375825i
$782$	2.34789	−	13.3155i	0.0839603	−	0.476163i
$783$	5.12345	+	1.86478i	0.183097	+	0.0666419i
$784$	−6.85140	−	1.43468i	−0.244693	−	0.0512386i
$785$	−3.31571	+	2.78221i	−0.118343	+	0.0993015i
$786$	−6.83617	+	11.8406i	−0.243838	+	0.422340i
$787$	10.9077	+	18.8927i	0.388818	+	0.673453i	0.992291	−	0.123931i	$-0.0395501\pi$
$787$	10.9077	+	18.8927i	0.388818	+	0.673453i	−0.603473	+	0.797384i	$0.706217\pi$
$788$	−11.7170	−	4.26463i	−0.417400	−	0.151921i
$789$	9.05905	−	7.60145i	0.322511	−	0.270619i
$790$	−0.190014	+	0.329114i	−0.00676040	+	0.0117094i
$791$	12.9582	−	12.5515i	0.460742	−	0.446281i
$792$	1.23573	−	1.03690i	0.0439098	−	0.0368447i
$793$	−17.9020	−	15.0216i	−0.635719	−	0.533432i
$794$	−26.4886	+	22.2266i	−0.940045	+	0.788791i
$795$	7.82174	−	2.84688i	0.277408	−	0.100968i
$796$	6.81252	−	2.47955i	0.241463	−	0.0878854i
$797$	29.8203			1.05629			0.528145	−	0.849154i	$-0.322888\pi$
$797$	29.8203			1.05629			0.528145	+	0.849154i	$0.322888\pi$
$798$	10.3915	−	5.00159i	0.367856	−	0.177054i
$799$	14.2310			0.503455
$800$	0.737366	−	0.268379i	0.0260698	−	0.00948864i
$801$	6.99290	−	2.54521i	0.247082	−	0.0899305i
$802$	−0.901063	+	0.756081i	−0.0318176	+	0.0266982i
$803$	12.7297	+	10.6815i	0.449223	+	0.376943i
$804$	3.74143	−	3.13943i	0.131950	−	0.110719i
$805$	−4.09421	−	16.3159i	−0.144302	−	0.575059i
$806$	2.48861	−	4.31040i	0.0876575	−	0.151827i
$807$	−1.40985	+	1.18300i	−0.0496290	+	0.0416437i
$808$	−0.594951	−	0.216544i	−0.0209303	−	0.00761800i
$809$	−3.15708	−	5.46822i	−0.110997	−	0.192252i	0.805176	−	0.593037i	$-0.202071\pi$
$809$	−3.15708	−	5.46822i	−0.110997	−	0.192252i	−0.916173	+	0.400784i	$0.868738\pi$
$810$	−1.02656	+	1.77806i	−0.0360697	+	0.0624745i
$811$	−4.03620	+	3.38677i	−0.141730	+	0.118926i	−0.710896	−	0.703297i	$-0.751710\pi$
$811$	−4.03620	+	3.38677i	−0.141730	+	0.118926i	0.569166	+	0.822222i	$0.307266\pi$
$812$	−14.3886	+	1.02801i	−0.504943	+	0.0360759i
$813$	−24.2192	−	8.81506i	−0.849404	−	0.309158i
$814$	0.115309	−	0.653951i	0.00404158	−	0.0229210i
$815$	−16.1996	−	13.5931i	−0.567447	−	0.476144i
$816$	2.18308	−	3.78121i	0.0764232	−	0.132369i
$817$	−25.5645	−	20.2509i	−0.894390	−	0.708489i
$818$	−35.6838			−1.24766
$819$	6.03120	+	8.91254i	0.210747	+	0.311429i
$820$	17.6103	+	14.7768i	0.614979	+	0.516029i
$821$	2.36867	+	13.4334i	0.0826673	+	0.468830i	0.997836	+	0.0657576i	$0.0209464\pi$
$821$	2.36867	+	13.4334i	0.0826673	+	0.468830i	−0.915168	+	0.403072i	$0.867942\pi$
$822$	1.24750	−	7.07491i	0.0435115	−	0.246766i
$823$	−0.865989	−	4.91127i	−0.0301865	−	0.171196i	0.965987	−	0.258589i	$-0.0832575\pi$
$823$	−0.865989	−	4.91127i	−0.0301865	−	0.171196i	−0.996174	+	0.0873930i	$0.972146\pi$
$824$	7.71145	−	13.3566i	0.268641	−	0.465300i
$825$	−0.632903	+	1.09622i	−0.0220349	+	0.0381655i
$826$	17.7879	−	7.95189i	0.618918	−	0.276682i
$827$	5.14622	+	29.1857i	0.178952	+	1.01488i	0.933483	+	0.358621i	$0.116753\pi$
$827$	5.14622	+	29.1857i	0.178952	+	1.01488i	−0.754532	+	0.656264i	$0.772136\pi$
$828$	3.09675			0.107620
$829$	−51.5550			−1.79058			−0.895290	−	0.445484i	$-0.853032\pi$
$829$	−51.5550			−1.79058			−0.895290	+	0.445484i	$0.853032\pi$
$830$	−0.773039	−	4.38412i	−0.0268326	−	0.152175i
$831$	21.1983	+	17.7874i	0.735359	+	0.617040i
$832$	−3.82215	−	1.39115i	−0.132509	−	0.0482294i
$833$	20.3820	−	22.7746i	0.706195	−	0.789092i
$834$	−3.47991	+	19.7355i	−0.120499	+	0.683386i
$835$	−8.06692	−	13.9723i	−0.279167	−	0.483532i
$836$	−1.41575	−	6.88749i	−0.0489647	−	0.238209i
$837$	−0.611836	+	1.05973i	−0.0211481	+	0.0366297i
$838$	4.34272	−	1.58062i	0.150017	−	0.0546017i
$839$	−14.7378	−	12.3665i	−0.508805	−	0.426938i	0.351903	−	0.936036i	$-0.385535\pi$
$839$	−14.7378	−	12.3665i	−0.508805	−	0.426938i	−0.860708	+	0.509098i	$0.829979\pi$
$840$	0.559639	−	5.40315i	0.0193094	−	0.186426i
$841$	−0.683287	+	0.248696i	−0.0235616	+	0.00857573i
$842$	−12.6227	−	4.59428i	−0.435007	−	0.158329i
$843$	27.8440			0.958998
$844$	−7.32743	−	12.6915i	−0.252220	−	0.436859i
$845$	5.57409	−	4.67721i	0.191754	−	0.160901i
$846$	0.565984	+	3.20985i	0.0194589	+	0.110357i
$847$	5.40771	+	21.5504i	0.185811	+	0.740479i
$848$	−2.02709	−	3.51102i	−0.0696105	−	0.120569i
$849$	13.6676	+	4.97462i	0.469072	+	0.170728i
$850$	−0.594933	+	3.37403i	−0.0204060	+	0.115728i
$851$	0.976526	−	0.819403i	0.0334749	−	0.0280888i
$852$	−1.75891	+	9.97527i	−0.0602592	+	0.341747i
$853$	−6.83927	+	38.7874i	−0.234172	+	1.32806i	0.610178	+	0.792264i	$0.291098\pi$
$853$	−6.83927	+	38.7874i	−0.234172	+	1.32806i	−0.844350	+	0.535792i	$0.820013\pi$
$854$	−14.6186	−	4.16791i	−0.500237	−	0.142623i
$855$	4.69141	+	7.62113i	0.160443	+	0.260637i
$856$	3.29124	+	5.70060i	0.112492	+	0.194842i
$857$	−1.88616	−	1.58268i	−0.0644301	−	0.0540633i	0.610004	−	0.792398i	$-0.291168\pi$
$857$	−1.88616	−	1.58268i	−0.0644301	−	0.0540633i	−0.674434	+	0.738335i	$0.735612\pi$
$858$	6.16563	−	2.24411i	0.210491	−	0.0766125i
$859$	−0.420675	−	2.38577i	−0.0143532	−	0.0814013i	0.976790	−	0.214200i	$-0.0687146\pi$
$859$	−0.420675	−	2.38577i	−0.0143532	−	0.0814013i	−0.991143	+	0.132799i	$0.957603\pi$
$860$	−14.4352	+	5.25397i	−0.492235	+	0.179159i
$861$	−27.0449	+	12.0902i	−0.921687	+	0.412032i
$862$	−15.5287	−	26.8965i	−0.528910	−	0.916099i
$863$	48.3006			1.64417			0.822085	−	0.569364i	$-0.192811\pi$
$863$	48.3006			1.64417			0.822085	+	0.569364i	$0.192811\pi$
$864$	0.939693	+	0.342020i	0.0319690	+	0.0116358i
$865$	−37.4547	−	13.6324i	−1.27350	−	0.463516i
$866$	−34.7061			−1.17936
$867$	1.03171	+	1.78697i	0.0350387	+	0.0606888i
$868$	0.333548	−	3.22030i	0.0113214	−	0.109304i
$869$	−0.280580	+	0.102123i	−0.00951804	+	0.00346428i
$870$	−1.94385	−	11.0241i	−0.0659025	−	0.373752i
$871$	18.6677	−	6.79448i	0.632531	−	0.230222i
$872$	1.52620	+	1.28064i	0.0516838	+	0.0433678i
$873$	−5.40663	−	9.36456i	−0.182987	−	0.316942i
$874$	6.41696	−	11.8756i	0.217057	−	0.401699i
$875$	7.64791	+	30.4778i	0.258547	+	1.03034i
$876$	−1.78882	+	10.1449i	−0.0604385	+	0.342764i
$877$	−2.88567	+	16.3655i	−0.0974423	+	0.552623i	0.896529	+	0.442984i	$0.146080\pi$
$877$	−2.88567	+	16.3655i	−0.0974423	+	0.552623i	−0.993972	+	0.109638i	$0.965031\pi$
$878$	27.0718	−	22.7159i	0.913629	−	0.766626i
$879$	−0.449406	+	2.54871i	−0.0151581	+	0.0859658i
$880$	−3.11222	−	1.13276i	−0.104913	−	0.0381852i
$881$	16.8773	+	29.2323i	0.568610	+	0.984862i	0.996704	+	0.0811276i	$0.0258521\pi$
$881$	16.8773	+	29.2323i	0.568610	+	0.984862i	−0.428093	+	0.903735i	$0.640815\pi$
$882$	5.94752	+	3.69148i	0.200263	+	0.124298i
$883$	−1.75476	−	9.95173i	−0.0590524	−	0.334903i	0.940941	−	0.338571i	$-0.109943\pi$
$883$	−1.75476	−	9.95173i	−0.0590524	−	0.334903i	−0.999993	+	0.00366827i	$0.998832\pi$
$884$	13.6043	−	11.4154i	0.457562	−	0.383940i
$885$	7.56000	+	13.0943i	0.254127	+	0.440160i
$886$	−21.4354			−0.720137
$887$	37.0408	+	13.4818i	1.24371	+	0.452673i	0.878271	−	0.478163i	$-0.158697\pi$
$887$	37.0408	+	13.4818i	1.24371	+	0.452673i	0.365437	+	0.930836i	$0.380919\pi$
$888$	0.386820	−	0.140791i	0.0129808	−	0.00472464i
$889$	−3.39840	+	32.8105i	−0.113979	+	1.10043i
$890$	−11.7042	−	9.82096i	−0.392324	−	0.329199i
$891$	−1.51585	+	0.551724i	−0.0507829	+	0.0184835i
$892$	−9.16041	+	15.8663i	−0.306713	+	0.531243i
$893$	13.4822	+	4.48085i	0.451163	+	0.149946i
$894$	7.39479	+	12.8082i	0.247319	+	0.428369i
$895$	0.0326931	−	0.185412i	0.00109281	−	0.00619764i
$896$	−2.63902	+	0.188547i	−0.0881636	+	0.00629891i
$897$	11.8362	+	4.30804i	0.395201	+	0.143841i
$898$	−22.4640	−	18.8495i	−0.749632	−	0.629016i
$899$	−1.15854	−	6.57042i	−0.0386395	−	0.219136i
$900$	−0.784688			−0.0261563
$901$	17.7012			0.589713
$902$	3.13646	+	17.7877i	0.104433	+	0.592267i
$903$	2.03946	−	19.6903i	0.0678689	−	0.655253i
$904$	3.40932	−	5.90511i	0.113392	−	0.196401i
$905$	6.05767	−	10.4922i	0.201364	−	0.348772i
$906$	−1.67902	−	9.52220i	−0.0557817	−	0.316354i
$907$	0.588353	−	3.33672i	0.0195359	−	0.110794i	−0.973480	−	0.228770i	$-0.926530\pi$
$907$	0.588353	−	3.33672i	0.0195359	−	0.110794i	0.993016	+	0.117976i	$0.0376407\pi$
$908$	2.75795	+	15.6411i	0.0915257	+	0.519068i
$909$	0.485008	+	0.406970i	0.0160867	+	0.0134983i
$910$	9.65559	−	19.8731i	0.320080	−	0.658786i
$911$	39.5189			1.30932			0.654660	−	0.755924i	$-0.272812\pi$
$911$	39.5189			1.30932			0.654660	+	0.755924i	$0.272812\pi$
$912$	3.25879	−	2.89487i	0.107909	−	0.0958588i
$913$	1.74887	−	3.02913i	0.0578791	−	0.100249i
$914$	4.49659	+	3.77309i	0.148734	+	0.124803i
$915$	2.04839	−	11.6170i	0.0677175	−	0.384045i
$916$	−18.4482	−	6.71458i	−0.609545	−	0.221856i
$917$	−15.8083	+	32.5365i	−0.522036	+	1.07445i
$918$	−3.34468	+	2.80652i	−0.110391	+	0.0926289i
$919$	−6.57111	+	11.3815i	−0.216761	+	0.375441i	−0.953816	−	0.300392i	$-0.902883\pi$
$919$	−6.57111	+	11.3815i	−0.216761	+	0.375441i	0.737055	+	0.675833i	$0.236216\pi$
$920$	−3.17901	−	5.50620i	−0.104809	−	0.181534i
$921$	−25.1447	−	9.15194i	−0.828547	−	0.301567i
$922$	−27.1900	+	22.8151i	−0.895456	+	0.751377i
$923$	−20.5999	+	35.6800i	−0.678053	+	1.17442i
$924$	3.06562	−	2.96940i	0.100852	−	0.0976862i
$925$	−0.247442	+	0.207629i	−0.00813586	+	0.00682680i
$926$	−24.5196	−	20.5744i	−0.805764	−	0.676116i
$927$	−11.8146	+	9.91365i	−0.388043	+	0.325607i
$928$	−5.12345	+	1.86478i	−0.168185	+	0.0612145i
$929$	30.7149	−	11.1793i	1.00772	−	0.366782i	0.215166	−	0.976578i	$-0.430971\pi$
$929$	30.7149	−	11.1793i	1.00772	−	0.366782i	0.792558	+	0.609796i	$0.208749\pi$
$930$	2.51235			0.0823831
$931$	26.4805	−	15.1586i	0.867863	−	0.496804i
$932$	−26.1769			−0.857454
$933$	−15.1906	+	5.52894i	−0.497319	+	0.181009i
$934$	13.4936	−	4.91128i	0.441525	−	0.160702i
$935$	11.0774	−	9.29508i	0.362271	−	0.303982i
$936$	3.11584	+	2.61450i	0.101844	+	0.0854577i
$937$	1.19962	−	1.00660i	0.0391900	−	0.0328843i	−0.622982	−	0.782236i	$-0.714079\pi$
$937$	1.19962	−	1.00660i	0.0391900	−	0.0328843i	0.662172	+	0.749352i	$0.269635\pi$
$938$	9.28179	−	8.99047i	0.303061	−	0.293549i
$939$	−5.93181	+	10.2742i	−0.193577	+	0.335286i
$940$	5.12628	−	4.30146i	0.167201	−	0.140298i
$941$	45.1147	+	16.4204i	1.47070	+	0.535290i	0.948290	−	0.317406i	$-0.102812\pi$
$941$	45.1147	+	16.4204i	1.47070	+	0.535290i	0.522408	+	0.852696i	$0.325034\pi$
$942$	−1.05409	−	1.82574i	−0.0343441	−	0.0594858i
$943$	−17.3371	+	30.0287i	−0.564572	+	0.977868i
$944$	5.64145	−	4.73374i	0.183614	−	0.154070i
$945$	−2.37387	+	4.88589i	−0.0772221	+	0.158938i
$946$	−11.3417	−	4.12803i	−0.368750	−	0.134214i
$947$	−1.17713	+	6.67583i	−0.0382516	+	0.216935i	−0.997942	−	0.0641240i	$-0.979575\pi$
$947$	−1.17713	+	6.67583i	−0.0382516	+	0.216935i	0.959690	+	0.281059i	$0.0906858\pi$
$948$	−0.141793	−	0.118979i	−0.00460523	−	0.00386424i
$949$	−20.9501	+	36.2867i	−0.680070	+	1.17792i
$950$	−1.62600	+	3.00917i	−0.0527543	+	0.0976304i
$951$	12.5658			0.407474
$952$	5.04828	−	10.3903i	0.163616	−	0.336752i
$953$	−18.7176	−	15.7060i	−0.606324	−	0.508766i	0.287148	−	0.957886i	$-0.407293\pi$
$953$	−18.7176	−	15.7060i	−0.606324	−	0.508766i	−0.893471	+	0.449120i	$0.851737\pi$
$954$	0.704000	+	3.99258i	0.0227928	+	0.129265i
$955$	7.20362	−	40.8538i	0.233104	−	1.32200i
$956$	2.85048	+	16.1659i	0.0921912	+	0.522842i
$957$	4.39761	−	7.61689i	0.142155	−	0.246219i
$958$	−9.69054	+	16.7845i	−0.313087	+	0.542283i
$959$	1.95823	−	18.9061i	0.0632344	−	0.610509i
$960$	−0.356521	−	2.02193i	−0.0115067	−	0.0652575i
$961$	−29.5026			−0.951698
$962$	1.67434			0.0539830
$963$	−1.14304	−	6.48248i	−0.0368338	−	0.208895i
$964$	−17.1489	−	14.3896i	−0.552328	−	0.463458i
$965$	26.5175	+	9.65158i	0.853628	+	0.310695i
$966$	8.17241	−	0.583883i	0.262943	−	0.0187861i
$967$	5.94566	−	33.7195i	0.191199	−	1.08435i	−0.726529	−	0.687136i	$-0.758868\pi$
$967$	5.94566	−	33.7195i	0.191199	−	1.08435i	0.917728	−	0.397209i	$-0.130021\pi$
$968$	4.19890	+	7.27271i	0.134958	+	0.233754i
$969$	3.83192	+	18.6419i	0.123099	+	0.598865i
$970$	−11.1005	+	19.2266i	−0.356415	+	0.617329i
$971$	−8.47275	+	3.08383i	−0.271903	+	0.0989647i	−0.474373	−	0.880324i	$-0.657325\pi$
$971$	−8.47275	+	3.08383i	−0.271903	+	0.0989647i	0.202470	+	0.979288i	$0.435103\pi$
$972$	−0.766044	−	0.642788i	−0.0245709	−	0.0206174i
$973$	−5.46249	+	52.7387i	−0.175119	+	1.69072i
$974$	−1.19458	+	0.434791i	−0.0382767	+	0.0139316i
$975$	−2.99919	−	1.09162i	−0.0960511	−	0.0349597i
$976$	−5.74548			−0.183908
$977$	−8.99099	−	15.5728i	−0.287647	−	0.498219i	0.685601	−	0.727978i	$-0.259540\pi$
$977$	−8.99099	−	15.5728i	−0.287647	−	0.498219i	−0.973248	+	0.229759i	$0.926206\pi$
$978$	7.89022	−	6.62068i	0.252301	−	0.211706i
$979$	−2.08455	−	11.8221i	−0.0666225	−	0.377835i
$980$	0.458155	−	14.3646i	0.0146352	−	0.458859i
$981$	−0.996159	−	1.72540i	−0.0318049	−	0.0550877i
$982$	−26.3908	−	9.60548i	−0.842166	−	0.306523i
$983$	−0.804410	+	4.56204i	−0.0256567	+	0.145506i	−0.994945	−	0.100420i	$-0.967981\pi$
$983$	−0.804410	+	4.56204i	−0.0256567	+	0.145506i	0.969288	+	0.245927i	$0.0790923\pi$
$984$	−8.57734	+	7.19724i	−0.273436	+	0.229440i
$985$	4.44544	−	25.2113i	0.141643	−	0.803300i
$986$	4.13378	−	23.4438i	0.131646	−	0.746603i
$987$	2.09885	+	8.36417i	0.0668072	+	0.266234i
$988$	16.4828	−	6.53117i	0.524387	−	0.207784i
$989$	−11.5851	−	20.0659i	−0.368383	−	0.638059i
$990$	2.53711	+	2.12889i	0.0806346	+	0.0676605i
$991$	24.8295	−	9.03721i	0.788736	−	0.287077i	0.0839257	−	0.996472i	$-0.473254\pi$
$991$	24.8295	−	9.03721i	0.788736	−	0.287077i	0.704811	+	0.709395i	$0.251032\pi$
$992$	−0.212488	−	1.20508i	−0.00674651	−	0.0382614i
$993$	−1.79575	+	0.653598i	−0.0569863	+	0.0207413i
$994$	−2.76100	+	26.6566i	−0.0875736	+	0.845497i
$995$	7.44229	+	12.8904i	0.235936	+	0.408654i
$996$	2.16829			0.0687048
$997$	−5.72210	−	2.08267i	−0.181221	−	0.0659590i	0.249816	−	0.968293i	$-0.419630\pi$
$997$	−5.72210	−	2.08267i	−0.181221	−	0.0659590i	−0.431037	+	0.902334i	$0.641852\pi$
$998$	2.91004	+	1.05917i	0.0921158	+	0.0335274i
$999$	−0.411645			−0.0130239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.f.739.6	yes	42
7.2	even	3		798.2.bq.e.625.6	yes	42
19.9	even	9		798.2.bq.e.655.6	yes	42
133.9	even	9	inner	798.2.bp.f.541.6	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.f.541.6	✓	42	133.9	even	9	inner
798.2.bp.f.739.6	yes	42	1.1	even	1	trivial
798.2.bq.e.625.6	yes	42	7.2	even	3
798.2.bq.e.655.6	yes	42	19.9	even	9

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.57278 + 1.31972i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.90041 + 1.84077i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.57278 + 1.31972i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.90041 + 1.84077i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.92930 - 0.702209i) q^{10} +(-0.806567 - 1.39701i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.11584 - 2.61450i) q^{13} +(1.15623 - 2.37974i) q^{14} +(1.92930 + 0.702209i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.34468 + 2.80652i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.28501 + 3.71197i) q^{19} +2.05312 q^{20} +(-1.15623 + 2.37974i) q^{21} +(1.23573 + 1.03690i) q^{22} +(0.537746 + 3.04971i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-0.136260 - 0.772767i) q^{25} +(-2.03372 + 3.52251i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.272579 + 2.63167i) q^{28} +(0.946775 + 5.36943i) q^{29} -2.05312 q^{30} -1.22367 q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.23573 - 1.03690i) q^{33} +(-4.10286 - 1.49332i) q^{34} +(-5.41824 + 0.387110i) q^{35} +(0.173648 - 0.984808i) q^{36} +(-0.205823 - 0.356495i) q^{37} +(-3.41678 - 2.70659i) q^{38} +(2.03372 - 3.52251i) q^{39} +(-1.92930 + 0.702209i) q^{40} +(8.57734 + 7.19724i) q^{41} +(0.272579 - 2.63167i) q^{42} +(-7.03084 + 2.55902i) q^{43} +(-1.51585 - 0.551724i) q^{44} +2.05312 q^{45} +(-1.54838 - 2.68187i) q^{46} +(2.49682 - 2.09508i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(0.223150 - 6.99644i) q^{49} +(0.392344 + 0.679560i) q^{50} +(4.10286 + 1.49332i) q^{51} +(0.706304 - 4.00565i) q^{52} +(3.10568 - 2.60597i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(0.575116 - 3.26164i) q^{55} +(-0.643944 - 2.56619i) q^{56} +(3.41678 + 2.70659i) q^{57} +(-2.72613 - 4.72180i) q^{58} +(5.64145 + 4.73374i) q^{59} +(1.92930 - 0.702209i) q^{60} +(-0.997693 - 5.65820i) q^{61} +(1.14988 - 0.418520i) q^{62} +(-0.272579 + 2.63167i) q^{63} +(-0.500000 - 0.866025i) q^{64} +8.35096 q^{65} +(1.51585 + 0.551724i) q^{66} +(4.58954 + 1.67046i) q^{67} +4.36617 q^{68} +(1.54838 + 2.68187i) q^{69} +(4.95908 - 2.21691i) q^{70} +(-9.51829 + 3.46438i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-9.68013 + 3.52328i) q^{73} +(0.315339 + 0.264600i) q^{74} +(-0.392344 - 0.679560i) q^{75} +(4.13643 + 1.37476i) q^{76} +(4.10439 + 1.17020i) q^{77} +(-0.706304 + 4.00565i) q^{78} +(0.0321419 - 0.182286i) q^{79} +(1.57278 - 1.31972i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-10.5217 - 3.82957i) q^{82} +(1.08414 + 1.87779i) q^{83} +(0.643944 + 2.56619i) q^{84} +(1.55663 + 8.82809i) q^{85} +(5.73159 - 4.80938i) q^{86} +(2.72613 + 4.72180i) q^{87} +1.61313 q^{88} +(6.99290 + 2.54521i) q^{89} +(-1.92930 + 0.702209i) q^{90} +(-1.10870 + 10.7042i) q^{91} +(2.37225 + 1.99056i) q^{92} +(-1.14988 + 0.418520i) q^{93} +(-1.62969 + 2.82270i) q^{94} +(-1.30494 + 8.85370i) q^{95} +(0.500000 + 0.866025i) q^{96} +(1.87770 - 10.6490i) q^{97} +(2.18323 + 6.65083i) q^{98} +(-1.51585 - 0.551724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 6 q^{5} - 21 q^{8}+O(q^{10}) \) 42 * q + 6 * q^5 - 21 * q^8	\( 42 q + 6 q^{5} - 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} - 24 q^{13} - 3 q^{14} + 3 q^{15} - 21 q^{18} + 18 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{22} + 15 q^{23} - 18 q^{25} + 9 q^{26} + 21 q^{27} - 12 q^{28} + 9 q^{29} + 6 q^{30} - 6 q^{31} + 3 q^{33} + 9 q^{34} + 12 q^{35} - 15 q^{37} + 9 q^{38} - 9 q^{39} - 3 q^{40} + 3 q^{41} + 12 q^{42} + 6 q^{44} - 6 q^{45} - 18 q^{46} + 15 q^{47} - 30 q^{50} - 9 q^{51} + 21 q^{52} + 12 q^{53} - 15 q^{55} - 9 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} - 3 q^{61} + 6 q^{62} - 12 q^{63} - 21 q^{64} + 72 q^{65} - 6 q^{66} + 3 q^{67} - 36 q^{68} + 18 q^{69} - 6 q^{70} + 12 q^{71} + 9 q^{73} + 12 q^{74} + 30 q^{75} + 51 q^{77} - 21 q^{78} - 51 q^{79} + 6 q^{80} + 12 q^{82} + 24 q^{83} - 6 q^{85} + 9 q^{86} + 18 q^{87} + 18 q^{88} + 12 q^{89} - 3 q^{90} + 6 q^{92} - 6 q^{93} + 30 q^{94} - 21 q^{95} + 21 q^{96} - 27 q^{97} + 36 q^{98} + 6 q^{99}+O(q^{100}) \) 42 * q + 6 * q^5 - 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 - 24 * q^13 - 3 * q^14 + 3 * q^15 - 21 * q^18 + 18 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^22 + 15 * q^23 - 18 * q^25 + 9 * q^26 + 21 * q^27 - 12 * q^28 + 9 * q^29 + 6 * q^30 - 6 * q^31 + 3 * q^33 + 9 * q^34 + 12 * q^35 - 15 * q^37 + 9 * q^38 - 9 * q^39 - 3 * q^40 + 3 * q^41 + 12 * q^42 + 6 * q^44 - 6 * q^45 - 18 * q^46 + 15 * q^47 - 30 * q^50 - 9 * q^51 + 21 * q^52 + 12 * q^53 - 15 * q^55 - 9 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 - 3 * q^61 + 6 * q^62 - 12 * q^63 - 21 * q^64 + 72 * q^65 - 6 * q^66 + 3 * q^67 - 36 * q^68 + 18 * q^69 - 6 * q^70 + 12 * q^71 + 9 * q^73 + 12 * q^74 + 30 * q^75 + 51 * q^77 - 21 * q^78 - 51 * q^79 + 6 * q^80 + 12 * q^82 + 24 * q^83 - 6 * q^85 + 9 * q^86 + 18 * q^87 + 18 * q^88 + 12 * q^89 - 3 * q^90 + 6 * q^92 - 6 * q^93 + 30 * q^94 - 21 * q^95 + 21 * q^96 - 27 * q^97 + 36 * q^98 + 6 * q^99

Introduction

L-functions

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