LMFDB - Embedded newform 798.2.bp.a.613.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 14x^{9} + 69x^{8} - 72x^{7} + 151x^{6} - 78x^{5} + 180x^{4} - 66x^{3} + 117x^{2} + 27x + 9 $ x^12 + 9x^10 - 14x^9 + 69x^8 - 72x^7 + 151x^6 - 78x^5 + 180x^4 - 66x^3 + 117x^2 + 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.1
Root			$-1.56099 + 2.70372i$ of defining polynomial
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.483291 + 2.74088i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(2.62797 + 0.306212i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.483291 + 2.74088i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(2.62797 + 0.306212i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(2.13203 - 1.78898i) q^{10} +(2.61334 + 4.52644i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.0246691 - 0.139905i) q^{13} +(-1.81631 - 1.92380i) q^{14} +(-2.13203 + 1.78898i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0407195 - 0.230932i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.73006 - 2.25535i) q^{19} -2.78316 q^{20} +(1.81631 + 1.92380i) q^{21} +(0.907604 - 5.14728i) q^{22} +(-5.78102 - 2.10412i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-2.58038 - 0.939182i) q^{25} +(-0.0710318 + 0.123031i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.154782 + 2.64122i) q^{28} +(2.13485 + 0.777023i) q^{29} +2.78316 q^{30} +5.50214 q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.907604 + 5.14728i) q^{33} +(-0.179633 + 0.150730i) q^{34} +(-2.10937 + 7.05496i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-1.76109 - 3.05029i) q^{37} +(1.40768 + 4.12534i) q^{38} +(0.0710318 - 0.123031i) q^{39} +(2.13203 + 1.78898i) q^{40} +(-1.00141 + 5.67927i) q^{41} +(-0.154782 - 2.64122i) q^{42} +(-5.15749 - 4.32764i) q^{43} +(-4.00387 + 3.35965i) q^{44} -2.78316 q^{45} +(3.07602 + 5.32782i) q^{46} +(0.521631 + 2.95831i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(6.81247 + 1.60943i) q^{49} +(1.37299 + 2.37809i) q^{50} +(0.179633 - 0.150730i) q^{51} +(0.133496 - 0.0485886i) q^{52} +(1.66969 + 9.46929i) q^{53} +(0.939693 - 0.342020i) q^{54} +(-13.6694 + 4.97526i) q^{55} +(1.57917 - 2.12278i) q^{56} +(-1.40768 - 4.12534i) q^{57} +(-1.13593 - 1.96749i) q^{58} +(0.763592 - 4.33054i) q^{59} +(-2.13203 - 1.78898i) q^{60} +(-6.54808 - 2.38330i) q^{61} +(-4.21489 - 3.53671i) q^{62} +(0.154782 + 2.64122i) q^{63} +(-0.500000 - 0.866025i) q^{64} +0.395386 q^{65} +(4.00387 - 3.35965i) q^{66} +(-1.75385 + 1.47165i) q^{67} +0.234494 q^{68} +(-3.07602 - 5.32782i) q^{69} +(6.15071 - 4.04854i) q^{70} +(10.8362 + 9.09261i) q^{71} +(0.939693 + 0.342020i) q^{72} +(5.08355 + 4.26560i) q^{73} +(-0.611619 + 3.46866i) q^{74} +(-1.37299 - 2.37809i) q^{75} +(1.57337 - 4.06503i) q^{76} +(5.48173 + 12.6956i) q^{77} +(-0.133496 + 0.0485886i) q^{78} +(7.14199 - 2.59947i) q^{79} +(-0.483291 - 2.74088i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(4.41768 - 3.70688i) q^{82} +(-5.34978 - 9.26609i) q^{83} +(-1.57917 + 2.12278i) q^{84} +(0.613276 + 0.223214i) q^{85} +(1.16911 + 6.63034i) q^{86} +(1.13593 + 1.96749i) q^{87} +5.22668 q^{88} +(5.79518 - 4.86273i) q^{89} +(2.13203 + 1.78898i) q^{90} +(-0.0219889 - 0.375221i) q^{91} +(1.06829 - 6.05857i) q^{92} +(4.21489 + 3.53671i) q^{93} +(1.50198 - 2.60150i) q^{94} +(7.98436 - 9.13366i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-8.36336 + 3.04401i) q^{97} +(-4.18413 - 5.61187i) q^{98} +(-4.00387 + 3.35965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 12 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^5 + 12 * q^7 + 6 * q^8	$ 12 q - 3 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{10} + 18 q^{11} - 6 q^{12} - 9 q^{13} - 9 q^{14} - 3 q^{15} + 6 q^{18} - 3 q^{19} + 18 q^{20} + 9 q^{21} + 18 q^{22} + 6 q^{23} - 21 q^{25} + 3 q^{26} - 6 q^{27} + 15 q^{28} - 3 q^{29} - 18 q^{30} - 18 q^{33} - 18 q^{34} + 12 q^{35} + 6 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} - 9 q^{41} - 15 q^{42} + 51 q^{43} + 18 q^{45} + 9 q^{46} - 30 q^{47} + 24 q^{49} + 21 q^{50} + 18 q^{51} - 9 q^{52} - 6 q^{53} + 9 q^{55} + 15 q^{56} + 3 q^{57} - 6 q^{59} - 3 q^{60} - 36 q^{61} + 18 q^{62} + 15 q^{63} - 6 q^{64} + 6 q^{65} - 15 q^{67} - 6 q^{68} - 9 q^{69} + 42 q^{70} - 3 q^{71} - 15 q^{73} + 27 q^{74} - 21 q^{75} - 9 q^{76} + 27 q^{77} + 9 q^{78} + 63 q^{79} - 3 q^{80} - 9 q^{82} - 24 q^{83} - 15 q^{84} - 60 q^{85} + 48 q^{86} + 36 q^{88} + 21 q^{89} + 3 q^{90} - 3 q^{91} - 12 q^{92} - 18 q^{93} + 6 q^{94} + 9 q^{95} + 6 q^{96} - 45 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 3 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^10 + 18 * q^11 - 6 * q^12 - 9 * q^13 - 9 * q^14 - 3 * q^15 + 6 * q^18 - 3 * q^19 + 18 * q^20 + 9 * q^21 + 18 * q^22 + 6 * q^23 - 21 * q^25 + 3 * q^26 - 6 * q^27 + 15 * q^28 - 3 * q^29 - 18 * q^30 - 18 * q^33 - 18 * q^34 + 12 * q^35 + 6 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 + 18 * q^45 + 9 * q^46 - 30 * q^47 + 24 * q^49 + 21 * q^50 + 18 * q^51 - 9 * q^52 - 6 * q^53 + 9 * q^55 + 15 * q^56 + 3 * q^57 - 6 * q^59 - 3 * q^60 - 36 * q^61 + 18 * q^62 + 15 * q^63 - 6 * q^64 + 6 * q^65 - 15 * q^67 - 6 * q^68 - 9 * q^69 + 42 * q^70 - 3 * q^71 - 15 * q^73 + 27 * q^74 - 21 * q^75 - 9 * q^76 + 27 * q^77 + 9 * q^78 + 63 * q^79 - 3 * q^80 - 9 * q^82 - 24 * q^83 - 15 * q^84 - 60 * q^85 + 48 * q^86 + 36 * q^88 + 21 * q^89 + 3 * q^90 - 3 * q^91 - 12 * q^92 - 18 * q^93 + 6 * q^94 + 9 * q^95 + 6 * q^96 - 45 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.483291	+	2.74088i	−0.216134	+	1.22576i	0.662793	+	0.748803i	$0.269371\pi$
$5$	−0.483291	+	2.74088i	−0.216134	+	1.22576i	−0.878927	+	0.476956i	$0.841740\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	2.62797	+	0.306212i	0.993280	+	0.115737i
$7$	2.62797	+	0.306212i	0.993280	+	0.115737i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	2.13203	−	1.78898i	0.674206	−	0.565726i
$11$	2.61334	+	4.52644i	0.787952	+	1.36477i	0.927220	+	0.374518i	$0.122192\pi$
$11$	2.61334	+	4.52644i	0.787952	+	1.36477i	−0.139268	+	0.990255i	$0.544475\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.0246691	−	0.139905i	−0.00684197	−	0.0388027i	0.981196	−	0.193016i	$-0.0618269\pi$
$13$	−0.0246691	−	0.139905i	−0.00684197	−	0.0388027i	−0.988038	+	0.154213i	$0.950716\pi$
$14$	−1.81631	−	1.92380i	−0.485430	−	0.514157i
$15$	−2.13203	+	1.78898i	−0.550487	+	0.461913i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.0407195	−	0.230932i	0.00987592	−	0.0560092i	−0.979472	−	0.201583i	$-0.935392\pi$
$17$	0.0407195	−	0.230932i	0.00987592	−	0.0560092i	0.989347	+	0.145573i	$0.0465027\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−3.73006	−	2.25535i	−0.855736	−	0.517414i
$19$	−3.73006	−	2.25535i	−0.855736	−	0.517414i
$20$	−2.78316			−0.622334
$21$	1.81631	+	1.92380i	0.396352	+	0.419808i
$22$	0.907604	−	5.14728i	0.193502	−	1.09740i
$23$	−5.78102	−	2.10412i	−1.20543	−	0.438739i	−0.340311	−	0.940313i	$-0.610532\pi$
$23$	−5.78102	−	2.10412i	−1.20543	−	0.438739i	−0.865115	+	0.501574i	$0.832755\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−2.58038	−	0.939182i	−0.516077	−	0.187836i
$26$	−0.0710318	+	0.123031i	−0.0139305	+	0.0241283i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	0.154782	+	2.64122i	0.0292511	+	0.499144i
$29$	2.13485	+	0.777023i	0.396432	+	0.144290i	0.532541	−	0.846404i	$-0.321237\pi$
$29$	2.13485	+	0.777023i	0.396432	+	0.144290i	−0.136108	+	0.990694i	$0.543460\pi$
$30$	2.78316			0.508133
$31$	5.50214			0.988214			0.494107	−	0.869401i	$-0.335495\pi$
$31$	5.50214			0.988214			0.494107	+	0.869401i	$0.335495\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.907604	+	5.14728i	−0.157994	+	0.896026i
$34$	−0.179633	+	0.150730i	−0.0308068	+	0.0258500i
$35$	−2.10937	+	7.05496i	−0.356548	+	1.19251i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−1.76109	−	3.05029i	−0.289521	−	0.501465i	0.684175	−	0.729318i	$-0.260163\pi$
$37$	−1.76109	−	3.05029i	−0.289521	−	0.501465i	−0.973695	+	0.227853i	$0.926829\pi$
$38$	1.40768	+	4.12534i	0.228356	+	0.669219i
$39$	0.0710318	−	0.123031i	0.0113742	−	0.0197007i
$40$	2.13203	+	1.78898i	0.337103	+	0.282863i
$41$	−1.00141	+	5.67927i	−0.156394	+	0.886952i	0.801107	+	0.598521i	$0.204245\pi$
$41$	−1.00141	+	5.67927i	−0.156394	+	0.886952i	−0.957501	+	0.288431i	$0.906866\pi$
$42$	−0.154782	−	2.64122i	−0.0238834	−	0.407549i
$43$	−5.15749	−	4.32764i	−0.786509	−	0.659960i	0.158370	−	0.987380i	$-0.449376\pi$
$43$	−5.15749	−	4.32764i	−0.786509	−	0.659960i	−0.944879	+	0.327420i	$0.893821\pi$
$44$	−4.00387	+	3.35965i	−0.603606	+	0.506486i
$45$	−2.78316			−0.414889
$46$	3.07602	+	5.32782i	0.453534	+	0.785544i
$47$	0.521631	+	2.95831i	0.0760876	+	0.431514i	0.998926	+	0.0463277i	$0.0147518\pi$
$47$	0.521631	+	2.95831i	0.0760876	+	0.431514i	−0.922839	+	0.385187i	$0.874137\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	6.81247	+	1.60943i	0.973210	+	0.229919i
$50$	1.37299	+	2.37809i	0.194171	+	0.336313i
$51$	0.179633	−	0.150730i	0.0251536	−	0.0211064i
$52$	0.133496	−	0.0485886i	0.0185126	−	0.00673803i
$53$	1.66969	+	9.46929i	0.229350	+	1.30071i	0.854193	+	0.519956i	$0.174052\pi$
$53$	1.66969	+	9.46929i	0.229350	+	1.30071i	−0.624843	+	0.780750i	$0.714837\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	−13.6694	+	4.97526i	−1.84318	+	0.670864i
$56$	1.57917	−	2.12278i	0.211026	−	0.283669i
$57$	−1.40768	−	4.12534i	−0.186452	−	0.546415i
$58$	−1.13593	−	1.96749i	−0.149155	−	0.258344i
$59$	0.763592	−	4.33054i	0.0994111	−	0.563789i	−0.893895	−	0.448277i	$-0.852038\pi$
$59$	0.763592	−	4.33054i	0.0994111	−	0.563789i	0.993306	−	0.115512i	$-0.0368509\pi$
$60$	−2.13203	−	1.78898i	−0.275243	−	0.230957i
$61$	−6.54808	−	2.38330i	−0.838395	−	0.305151i	−0.113096	−	0.993584i	$-0.536077\pi$
$61$	−6.54808	−	2.38330i	−0.838395	−	0.305151i	−0.725300	+	0.688433i	$0.758299\pi$
$62$	−4.21489	−	3.53671i	−0.535291	−	0.449163i
$63$	0.154782	+	2.64122i	0.0195007	+	0.332762i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.395386			0.0490416
$66$	4.00387	−	3.35965i	0.492842	−	0.413544i
$67$	−1.75385	+	1.47165i	−0.214267	+	0.179791i	−0.743604	−	0.668620i	$-0.766885\pi$
$67$	−1.75385	+	1.47165i	−0.214267	+	0.179791i	0.529337	+	0.848412i	$0.322441\pi$
$68$	0.234494			0.0284366
$69$	−3.07602	−	5.32782i	−0.370309	−	0.641394i
$70$	6.15071	−	4.04854i	0.735150	−	0.483893i
$71$	10.8362	+	9.09261i	1.28601	+	1.07909i	0.992385	+	0.123175i	$0.0393077\pi$
$71$	10.8362	+	9.09261i	1.28601	+	1.07909i	0.293630	+	0.955919i	$0.405137\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	5.08355	+	4.26560i	0.594984	+	0.499251i	0.889829	−	0.456294i	$-0.150823\pi$
$73$	5.08355	+	4.26560i	0.594984	+	0.499251i	−0.294845	+	0.955545i	$0.595268\pi$
$74$	−0.611619	+	3.46866i	−0.0710993	+	0.403224i
$75$	−1.37299	−	2.37809i	−0.158540	−	0.274599i
$76$	1.57337	−	4.06503i	0.180478	−	0.466291i
$77$	5.48173	+	12.6956i	0.624701	+	1.44680i
$78$	−0.133496	+	0.0485886i	−0.0151155	+	0.00550157i
$79$	7.14199	−	2.59947i	0.803537	−	0.292464i	0.0925857	−	0.995705i	$-0.470487\pi$
$79$	7.14199	−	2.59947i	0.803537	−	0.292464i	0.710951	+	0.703241i	$0.248265\pi$
$80$	−0.483291	−	2.74088i	−0.0540336	−	0.306440i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	4.41768	−	3.70688i	0.487852	−	0.409356i
$83$	−5.34978	−	9.26609i	−0.587215	−	1.01709i	−0.994595	−	0.103827i	$-0.966891\pi$
$83$	−5.34978	−	9.26609i	−0.587215	−	1.01709i	0.407380	−	0.913259i	$-0.366442\pi$
$84$	−1.57917	+	2.12278i	−0.172302	+	0.231615i
$85$	0.613276	+	0.223214i	0.0665192	+	0.0242110i
$86$	1.16911	+	6.63034i	0.126068	+	0.714968i
$87$	1.13593	+	1.96749i	0.121785	+	0.210937i
$88$	5.22668			0.557166
$89$	5.79518	−	4.86273i	0.614288	−	0.515449i	−0.281714	−	0.959498i	$-0.590903\pi$
$89$	5.79518	−	4.86273i	0.614288	−	0.515449i	0.896002	+	0.444050i	$0.146459\pi$
$90$	2.13203	+	1.78898i	0.224735	+	0.188575i
$91$	−0.0219889	−	0.375221i	−0.00230506	−	0.0393339i
$92$	1.06829	−	6.05857i	0.111377	−	0.631650i
$93$	4.21489	+	3.53671i	0.437063	+	0.366740i
$94$	1.50198	−	2.60150i	0.154917	−	0.268324i
$95$	7.98436	−	9.13366i	0.819178	−	0.937094i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.36336	+	3.04401i	−0.849171	+	0.309073i	−0.729702	−	0.683765i	$-0.760341\pi$
$97$	−8.36336	+	3.04401i	−0.849171	+	0.309073i	−0.119469	+	0.992838i	$0.538119\pi$
$98$	−4.18413	−	5.61187i	−0.422661	−	0.566884i
$99$	−4.00387	+	3.35965i	−0.402404	+	0.337657i
$100$	0.476835	−	2.70427i	0.0476835	−	0.270427i
$101$	−17.3952	−	6.33134i	−1.73089	−	0.629992i	−0.732196	−	0.681094i	$-0.761504\pi$
$101$	−17.3952	−	6.33134i	−1.73089	−	0.629992i	−0.998693	+	0.0511021i	$0.983727\pi$
$102$	−0.234494			−0.0232184
$103$	6.28413			0.619193			0.309597	−	0.950868i	$-0.399806\pi$
$103$	6.28413			0.619193			0.309597	+	0.950868i	$0.399806\pi$
$104$	−0.133496	−	0.0485886i	−0.0130904	−	0.00476450i
$105$	−6.15071	+	4.04854i	−0.600248	+	0.395097i
$106$	4.80768	−	8.32715i	0.466963	−	0.808804i
$107$	−4.42385	+	7.66234i	−0.427670	+	0.740746i	−0.996666	−	0.0815946i	$-0.973999\pi$
$107$	−4.42385	+	7.66234i	−0.427670	+	0.740746i	0.568996	+	0.822340i	$0.307332\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	16.6340	−	6.05430i	1.59325	−	0.579896i	0.615221	−	0.788355i	$-0.289067\pi$
$109$	16.6340	−	6.05430i	1.59325	−	0.579896i	0.978031	+	0.208458i	$0.0668445\pi$
$110$	13.6694	+	4.97526i	1.30333	+	0.474373i
$111$	0.611619	−	3.46866i	0.0580523	−	0.329231i
$112$	−2.57422	+	0.611074i	−0.243241	+	0.0577410i
$113$	17.7452			1.66932			0.834662	−	0.550763i	$-0.185663\pi$
$113$	17.7452			1.66932			0.834662	+	0.550763i	$0.185663\pi$
$114$	−1.57337	+	4.06503i	−0.147360	+	0.380725i
$115$	8.56105	−	14.8282i	0.798322	−	1.38273i
$116$	−0.394505	+	2.23735i	−0.0366289	+	0.207733i
$117$	0.133496	−	0.0485886i	0.0123417	−	0.00449202i
$118$	−3.36856	+	2.82656i	−0.310101	+	0.260206i
$119$	0.177724	−	0.594413i	0.0162919	−	0.0544897i
$120$	0.483291	+	2.74088i	0.0441182	+	0.250207i
$121$	−8.15910	+	14.1320i	−0.741736	+	1.28473i
$122$	3.48416	+	6.03474i	0.315441	+	0.546360i
$123$	−4.41768	+	3.70688i	−0.398329	+	0.334238i
$124$	0.955437	+	5.41855i	0.0858008	+	0.486601i
$125$	−3.13664	+	5.43282i	−0.280550	+	0.485927i
$126$	1.57917	−	2.12278i	0.140684	−	0.189113i
$127$	1.44848	+	8.21476i	0.128532	+	0.728942i	0.979147	+	0.203153i	$0.0651189\pi$
$127$	1.44848	+	8.21476i	0.128532	+	0.728942i	−0.850615	+	0.525789i	$0.823770\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−1.16911	−	6.63034i	−0.102934	−	0.583769i
$130$	−0.302883	−	0.254149i	−0.0265646	−	0.0222903i
$131$	7.00456	+	5.87752i	0.611991	+	0.513521i	0.895275	−	0.445515i	$-0.146979\pi$
$131$	7.00456	+	5.87752i	0.611991	+	0.513521i	−0.283284	+	0.959036i	$0.591424\pi$
$132$	−5.22668			−0.454924
$133$	−9.11189	−	7.06920i	−0.790101	−	0.612977i
$134$	2.28949			0.197782
$135$	−2.13203	−	1.78898i	−0.183496	−	0.153971i
$136$	−0.179633	−	0.150730i	−0.0154034	−	0.0129250i
$137$	−3.32136	−	18.8364i	−0.283763	−	1.60930i	−0.709671	−	0.704533i	$-0.751157\pi$
$137$	−3.32136	−	18.8364i	−0.283763	−	1.60930i	0.425908	−	0.904766i	$-0.359955\pi$
$138$	−1.06829	+	6.05857i	−0.0909388	+	0.515740i
$139$	−1.58587	−	8.99392i	−0.134512	−	0.762855i	−0.975198	−	0.221333i	$-0.928959\pi$
$139$	−1.58587	−	8.99392i	−0.134512	−	0.762855i	0.840687	−	0.541522i	$-0.182152\pi$
$140$	−7.31407	−	0.852238i	−0.618152	−	0.0720273i
$141$	−1.50198	+	2.60150i	−0.126489	+	0.219086i
$142$	−2.45636	−	13.9307i	−0.206133	−	1.16904i
$143$	0.568804	−	0.477283i	0.0475658	−	0.0399124i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.16148	+	5.47584i	−0.262547	+	0.454744i
$146$	−1.15235	−	6.53528i	−0.0953689	−	0.540864i
$147$	4.18413	+	5.61187i	0.345101	+	0.462859i
$148$	2.69814	−	2.26401i	0.221786	−	0.186100i
$149$	−10.7363	+	3.90771i	−0.879556	+	0.320132i	−0.742031	−	0.670366i	$-0.766137\pi$
$149$	−10.7363	+	3.90771i	−0.879556	+	0.320132i	−0.137525	+	0.990498i	$0.543915\pi$
$150$	−0.476835	+	2.70427i	−0.0389335	+	0.220803i
$151$	7.27180	−	12.5951i	0.591771	−	1.02498i	−0.402223	−	0.915542i	$-0.631762\pi$
$151$	7.27180	−	12.5951i	0.591771	−	1.02498i	0.993994	−	0.109435i	$-0.0349042\pi$
$152$	−3.81823	+	2.10265i	−0.309699	+	0.170548i
$153$	0.234494			0.0189577
$154$	3.96132	−	13.2490i	0.319212	−	1.06763i
$155$	−2.65914	+	15.0807i	−0.213587	+	1.21131i
$156$	0.133496	+	0.0485886i	0.0106882	+	0.00389020i
$157$	−2.93755	+	1.06918i	−0.234442	+	0.0853299i	−0.456570	−	0.889688i	$-0.650922\pi$
$157$	−2.93755	+	1.06918i	−0.234442	+	0.0853299i	0.222128	+	0.975018i	$0.428700\pi$
$158$	−7.14199	−	2.59947i	−0.568187	−	0.206803i
$159$	−4.80768	+	8.32715i	−0.381274	+	0.660386i
$160$	−1.39158	+	2.41029i	−0.110014	+	0.190550i
$161$	−14.5480	−	7.29978i	−1.14655	−	0.575304i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	18.9358			1.48316			0.741581	−	0.670863i	$-0.234076\pi$
$163$	18.9358			1.48316			0.741581	+	0.670863i	$0.234076\pi$
$164$	−5.76688			−0.450318
$165$	−13.6694	−	4.97526i	−1.06416	−	0.387324i
$166$	−1.85796	+	10.5370i	−0.144206	+	0.817831i
$167$	2.89867	−	2.43227i	0.224306	−	0.188215i	−0.523708	−	0.851898i	$-0.675452\pi$
$167$	2.89867	−	2.43227i	0.224306	−	0.188215i	0.748014	+	0.663683i	$0.231007\pi$
$168$	2.57422	−	0.611074i	0.198605	−	0.0471454i
$169$	12.1970	−	4.43936i	0.938234	−	0.341489i
$170$	−0.326317	−	0.565198i	−0.0250274	−	0.0433487i
$171$	1.57337	−	4.06503i	0.120319	−	0.310861i
$172$	3.36631	−	5.83062i	0.256679	−	0.444581i
$173$	−18.6496	−	15.6489i	−1.41790	−	1.18976i	−0.952452	−	0.304690i	$-0.901447\pi$
$173$	−18.6496	−	15.6489i	−1.41790	−	1.18976i	−0.465453	−	0.885073i	$-0.654108\pi$
$174$	0.394505	−	2.23735i	0.0299073	−	0.169613i
$175$	−6.49358	−	3.25829i	−0.490869	−	0.246304i
$176$	−4.00387	−	3.35965i	−0.301803	−	0.253243i
$177$	3.36856	−	2.82656i	0.253197	−	0.212457i
$178$	−7.56507			−0.567026
$179$	−2.53658	−	4.39349i	−0.189593	−	0.328385i	0.755522	−	0.655124i	$-0.227384\pi$
$179$	−2.53658	−	4.39349i	−0.189593	−	0.328385i	−0.945115	+	0.326739i	$0.894050\pi$
$180$	−0.483291	−	2.74088i	−0.0360224	−	0.204293i
$181$	−11.2941	−	4.11070i	−0.839481	−	0.305546i	−0.113737	−	0.993511i	$-0.536282\pi$
$181$	−11.2941	−	4.11070i	−0.839481	−	0.305546i	−0.725744	+	0.687965i	$0.758504\pi$
$182$	−0.224343	+	0.301570i	−0.0166294	+	0.0223539i
$183$	−3.48416	−	6.03474i	−0.257556	−	0.446101i
$184$	−4.71273	+	3.95445i	−0.347427	+	0.291526i
$185$	9.21160	−	3.35275i	0.677250	−	0.246499i
$186$	−0.955437	−	5.41855i	−0.0700561	−	0.397308i
$187$	1.15171	−	0.419189i	0.0842215	−	0.0306541i
$188$	−2.82279	+	1.02741i	−0.205873	+	0.0749317i
$189$	−1.57917	+	2.12278i	−0.114868	+	0.154410i
$190$	−11.9874	+	1.86455i	−0.869656	+	0.135268i
$191$	9.73518	+	16.8618i	0.704413	+	1.22008i	0.966903	+	0.255144i	$0.0821228\pi$
$191$	9.73518	+	16.8618i	0.704413	+	1.22008i	−0.262490	+	0.964935i	$0.584544\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	−14.6693	−	12.3090i	−1.05592	−	0.886021i	−0.0622149	−	0.998063i	$-0.519816\pi$
$193$	−14.6693	−	12.3090i	−1.05592	−	0.886021i	−0.993703	+	0.112042i	$0.964261\pi$
$194$	8.36336	+	3.04401i	0.600454	+	0.218548i
$195$	0.302883	+	0.254149i	0.0216899	+	0.0182000i
$196$	−0.402011	+	6.98845i	−0.0287151	+	0.499175i
$197$	1.87074	+	3.24021i	0.133285	+	0.230856i	0.924941	−	0.380111i	$-0.124114\pi$
$197$	1.87074	+	3.24021i	0.133285	+	0.230856i	−0.791656	+	0.610967i	$0.790781\pi$
$198$	5.22668			0.371444
$199$	6.17336	−	5.18006i	0.437618	−	0.367205i	−0.397199	−	0.917732i	$-0.630018\pi$
$199$	6.17336	−	5.18006i	0.437618	−	0.367205i	0.834817	+	0.550528i	$0.185573\pi$
$200$	−2.10355	+	1.76509i	−0.148743	+	0.124810i
$201$	−2.28949			−0.161488
$202$	9.25580	+	16.0315i	0.651236	+	1.12797i
$203$	5.37240	+	2.69571i	0.377068	+	0.189202i
$204$	0.179633	+	0.150730i	0.0125768	+	0.0105532i
$205$	−15.0822	−	5.48947i	−1.05339	−	0.383402i
$206$	−4.81392	−	4.03936i	−0.335402	−	0.281435i
$207$	1.06829	−	6.05857i	0.0742512	−	0.421100i
$208$	0.0710318	+	0.123031i	0.00492517	+	0.00853064i
$209$	0.460789	−	22.7779i	0.0318734	−	1.57558i
$210$	7.31407	+	0.852238i	0.504719	+	0.0588100i
$211$	12.0757	−	4.39519i	0.831324	−	0.302577i	0.108922	−	0.994050i	$-0.465260\pi$
$211$	12.0757	−	4.39519i	0.831324	−	0.302577i	0.722402	+	0.691473i	$0.243038\pi$
$212$	−9.03549	+	3.28865i	−0.620560	+	0.225865i
$213$	2.45636	+	13.9307i	0.168307	+	0.954515i
$214$	8.31412	−	3.02609i	0.568342	−	0.206859i
$215$	14.3541	−	12.0445i	0.978942	−	0.821430i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	14.4595	+	1.68482i	0.981573	+	0.114373i
$218$	−16.6340	−	6.05430i	−1.12660	−	0.410049i
$219$	1.15235	+	6.53528i	0.0778684	+	0.441614i
$220$	−7.27335	−	12.5978i	−0.490369	−	0.849344i
$221$	−0.0333131			−0.00224088
$222$	−2.69814	+	2.26401i	−0.181087	+	0.151950i
$223$	2.51641	+	2.11152i	0.168511	+	0.141398i	0.723143	−	0.690698i	$-0.242697\pi$
$223$	2.51641	+	2.11152i	0.168511	+	0.141398i	−0.554632	+	0.832096i	$0.687141\pi$
$224$	2.36475	+	1.18656i	0.158002	+	0.0792807i
$225$	0.476835	−	2.70427i	0.0317890	−	0.180285i
$226$	−13.5936	−	11.4064i	−0.904231	−	0.758740i
$227$	6.99839	−	12.1216i	0.464499	−	0.804537i	−0.534679	−	0.845055i	$-0.679568\pi$
$227$	6.99839	−	12.1216i	0.464499	−	0.804537i	0.999179	+	0.0405184i	$0.0129009\pi$
$228$	3.81823	−	2.10265i	0.252868	−	0.139252i
$229$	4.78478	+	8.28748i	0.316187	+	0.547652i	0.979689	−	0.200522i	$-0.0642639\pi$
$229$	4.78478	+	8.28748i	0.316187	+	0.547652i	−0.663502	+	0.748175i	$0.730931\pi$
$230$	−16.0895	+	5.85610i	−1.06091	+	0.386140i
$231$	−3.96132	+	13.2490i	−0.260635	+	0.871719i
$232$	1.74035	−	1.46033i	0.114259	−	0.0958750i
$233$	5.20411	−	29.5139i	0.340932	−	1.93352i	−0.0172001	−	0.999852i	$-0.505475\pi$
$233$	5.20411	−	29.5139i	0.340932	−	1.93352i	0.358132	−	0.933671i	$-0.383414\pi$
$234$	−0.133496	−	0.0485886i	−0.00872691	−	0.00317634i
$235$	−8.36048			−0.545377
$236$	4.39735			0.286243
$237$	7.14199	+	2.59947i	0.463922	+	0.168854i
$238$	−0.518226	+	0.341108i	−0.0335916	+	0.0221108i
$239$	−8.10283	+	14.0345i	−0.524129	+	0.907818i	0.475477	+	0.879728i	$0.342276\pi$
$239$	−8.10283	+	14.0345i	−0.524129	+	0.907818i	−0.999605	+	0.0280893i	$0.991058\pi$
$240$	1.39158	−	2.41029i	0.0898261	−	0.155583i
$241$	4.11819	+	1.49890i	0.265276	+	0.0965525i	0.471234	−	0.882008i	$-0.343809\pi$
$241$	4.11819	+	1.49890i	0.265276	+	0.0965525i	−0.205958	+	0.978561i	$0.566031\pi$
$242$	15.3341	−	5.58115i	0.985713	−	0.358770i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	1.21004	−	6.86245i	0.0774646	−	0.439324i
$245$	−7.70367	+	17.8943i	−0.492169	+	1.14323i
$246$	5.76688			0.367683
$247$	−0.223519	+	0.577493i	−0.0142221	+	0.0367450i
$248$	2.75107	−	4.76500i	0.174693	−	0.302578i
$249$	1.85796	−	10.5370i	0.117743	−	0.667756i
$250$	5.89496	−	2.14559i	0.372830	−	0.135699i
$251$	1.41089	−	1.18388i	0.0890546	−	0.0747257i	−0.597174	−	0.802112i	$-0.703710\pi$
$251$	1.41089	−	1.18388i	0.0890546	−	0.0747257i	0.686228	+	0.727386i	$0.259265\pi$
$252$	−2.57422	+	0.611074i	−0.162160	+	0.0384940i
$253$	−5.58361	−	31.6662i	−0.351038	−	1.99084i
$254$	4.17074	−	7.22394i	0.261696	−	0.453270i
$255$	0.326317	+	0.565198i	0.0204348	+	0.0353941i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−1.91649	−	10.8690i	−0.119547	−	0.677987i	−0.984398	−	0.175957i	$-0.943698\pi$
$257$	−1.91649	−	10.8690i	−0.119547	−	0.677987i	0.864850	−	0.502030i	$-0.167413\pi$
$258$	−3.36631	+	5.83062i	−0.209577	+	0.362999i
$259$	−3.69405	−	8.55535i	−0.229537	−	0.531603i
$260$	0.0686580	+	0.389379i	0.00425799	+	0.0241483i
$261$	−0.394505	+	2.23735i	−0.0244192	+	0.138488i
$262$	−1.58780	−	9.00488i	−0.0980949	−	0.556324i
$263$	−12.0507	−	10.1117i	−0.743077	−	0.623515i	0.190585	−	0.981671i	$-0.438961\pi$
$263$	−12.0507	−	10.1117i	−0.743077	−	0.623515i	−0.933662	+	0.358155i	$0.883406\pi$
$264$	4.00387	+	3.35965i	0.246421	+	0.206772i
$265$	−26.7611			−1.64392
$266$	2.43612	+	11.2723i	0.149368	+	0.691151i
$267$	7.56507			0.462975
$268$	−1.75385	−	1.47165i	−0.107133	−	0.0898956i
$269$	−1.75035	−	1.46872i	−0.106721	−	0.0895496i	0.587866	−	0.808958i	$-0.299968\pi$
$269$	−1.75035	−	1.46872i	−0.106721	−	0.0895496i	−0.694587	+	0.719409i	$0.744413\pi$
$270$	0.483291	+	2.74088i	0.0294121	+	0.166805i
$271$	−1.76209	+	9.99329i	−0.107039	+	0.607049i	0.883347	+	0.468719i	$0.155284\pi$
$271$	−1.76209	+	9.99329i	−0.107039	+	0.607049i	−0.990386	+	0.138330i	$0.955827\pi$
$272$	0.0407195	+	0.230932i	0.00246898	+	0.0140023i
$273$	0.224343	−	0.301570i	0.0135779	−	0.0182519i
$274$	−9.56347	+	16.5644i	−0.577751	+	1.00069i
$275$	−2.49227	−	14.1343i	−0.150289	−	0.852333i
$276$	4.71273	−	3.95445i	0.283673	−	0.238030i
$277$	5.25814	+	9.10736i	0.315931	+	0.547208i	0.979635	−	0.200787i	$-0.0643499\pi$
$277$	5.25814	+	9.10736i	0.315931	+	0.547208i	−0.663704	+	0.747995i	$0.731017\pi$
$278$	−4.56633	+	7.90912i	−0.273871	+	0.474358i
$279$	0.955437	+	5.41855i	0.0572005	+	0.324400i
$280$	5.05509	+	5.35424i	0.302100	+	0.319977i
$281$	13.3836	−	11.2302i	0.798401	−	0.669938i	−0.149409	−	0.988776i	$-0.547737\pi$
$281$	13.3836	−	11.2302i	0.798401	−	0.669938i	0.947809	+	0.318838i	$0.103293\pi$
$282$	2.82279	−	1.02741i	0.168095	−	0.0611815i
$283$	−5.50719	+	31.2328i	−0.327369	+	1.85660i	0.165111	+	0.986275i	$0.447202\pi$
$283$	−5.50719	+	31.2328i	−0.327369	+	1.85660i	−0.492479	+	0.870324i	$0.663909\pi$
$284$	−7.07280	+	12.2504i	−0.419693	+	0.726930i
$285$	11.9874	−	1.86455i	0.710071	−	0.110446i
$286$	−0.742521			−0.0439062
$287$	−4.37073	+	14.6183i	−0.257996	+	0.862891i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	15.9231	+	5.79554i	0.936653	+	0.340914i
$290$	5.94164	−	2.16258i	0.348905	−	0.126991i
$291$	−8.36336	−	3.04401i	−0.490269	−	0.178443i
$292$	−3.31805	+	5.74703i	−0.194174	+	0.336320i
$293$	11.2809	−	19.5391i	0.659039	−	1.14149i	−0.321826	−	0.946799i	$-0.604297\pi$
$293$	11.2809	−	19.5391i	0.659039	−	1.14149i	0.980865	−	0.194690i	$-0.0623699\pi$
$294$	0.402011	−	6.98845i	0.0234458	−	0.407574i
$295$	11.5005	+	4.18582i	0.669582	+	0.243708i
$296$	−3.52217			−0.204722
$297$	−5.22668			−0.303283
$298$	10.7363	+	3.90771i	0.621940	+	0.226368i
$299$	−0.151765	+	0.860702i	−0.00877679	+	0.0497757i
$300$	2.10355	−	1.76509i	0.121448	−	0.101907i
$301$	−12.2285	−	12.9522i	−0.704842	−	0.746553i
$302$	−13.6665	+	4.97420i	−0.786419	+	0.286233i
$303$	−9.25580	−	16.0315i	−0.531732	−	0.920987i
$304$	4.27649	+	0.843582i	0.245274	+	0.0483827i
$305$	9.69697	−	16.7957i	0.555247	−	0.961716i
$306$	−0.179633	−	0.150730i	−0.0102689	−	0.00861666i
$307$	−0.837388	+	4.74906i	−0.0477922	+	0.271043i	−0.999335	−	0.0364745i	$-0.988387\pi$
$307$	−0.837388	+	4.74906i	−0.0477922	+	0.271043i	0.951542	+	0.307518i	$0.0994983\pi$
$308$	−11.5508	+	7.60302i	−0.658169	+	0.433222i
$309$	4.81392	+	4.03936i	0.273854	+	0.229791i
$310$	11.7307	−	9.84323i	0.666260	−	0.559058i
$311$	−17.0741			−0.968181			−0.484090	−	0.875018i	$-0.660849\pi$
$311$	−17.0741			−0.968181			−0.484090	+	0.875018i	$0.660849\pi$
$312$	−0.0710318	−	0.123031i	−0.00402138	−	0.00696524i
$313$	1.74237	+	9.88146i	0.0984844	+	0.558533i	0.993624	+	0.112747i	$0.0359648\pi$
$313$	1.74237	+	9.88146i	0.0984844	+	0.558533i	−0.895139	+	0.445786i	$0.852924\pi$
$314$	2.93755	+	1.06918i	0.165776	+	0.0603374i
$315$	−7.31407	−	0.852238i	−0.412101	−	0.0480182i
$316$	3.80018	+	6.58210i	0.213777	+	0.370272i
$317$	−1.09049	+	0.915027i	−0.0612479	+	0.0513931i	−0.672898	−	0.739736i	$-0.734951\pi$
$317$	−1.09049	+	0.915027i	−0.0612479	+	0.0513931i	0.611650	+	0.791129i	$0.290506\pi$
$318$	9.03549	−	3.28865i	0.506685	−	0.184418i
$319$	2.06195	+	11.6939i	0.115447	+	0.654733i
$320$	2.61532	−	0.951897i	0.146201	−	0.0532127i
$321$	−8.31412	+	3.02609i	−0.464049	+	0.168900i
$322$	6.45224	+	14.9433i	0.359569	+	0.832756i
$323$	−0.672719	+	0.769553i	−0.0374311	+	0.0428191i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.0677409	+	0.384178i	−0.00375759	+	0.0213104i
$326$	−14.5056	−	12.1717i	−0.803392	−	0.674126i
$327$	16.6340	+	6.05430i	0.919865	+	0.334803i
$328$	4.41768	+	3.70688i	0.243926	+	0.204678i
$329$	0.464958	+	7.93409i	0.0256340	+	0.437421i
$330$	7.27335	+	12.5978i	0.400385	+	0.693487i
$331$	−9.27640			−0.509877			−0.254939	−	0.966957i	$-0.582055\pi$
$331$	−9.27640			−0.509877			−0.254939	+	0.966957i	$0.582055\pi$
$332$	8.19634	−	6.87755i	0.449833	−	0.377454i
$333$	2.69814	−	2.26401i	0.147857	−	0.124067i
$334$	−3.78395			−0.207048
$335$	−3.18601	−	5.51832i	−0.174070	−	0.301498i
$336$	−2.36475	−	1.18656i	−0.129008	−	0.0647324i
$337$	−1.87620	−	1.57432i	−0.102203	−	0.0857588i	0.590254	−	0.807217i	$-0.299028\pi$
$337$	−1.87620	−	1.57432i	−0.102203	−	0.0857588i	−0.692457	+	0.721459i	$0.743472\pi$
$338$	−12.1970	−	4.43936i	−0.663431	−	0.241469i
$339$	13.5936	+	11.4064i	0.738302	+	0.619509i
$340$	−0.113329	+	0.642720i	−0.00614612	+	0.0348564i
$341$	14.3790	+	24.9051i	0.778665	+	1.34869i
$342$	−3.81823	+	2.10265i	−0.206466	+	0.113699i
$343$	17.4101	+	6.31561i	0.940059	+	0.341011i
$344$	−6.32659	+	2.30269i	−0.341107	+	0.124153i
$345$	16.0895	−	5.85610i	0.866230	−	0.315282i
$346$	4.22752	+	23.9755i	0.227273	+	1.28893i
$347$	19.8543	−	7.22638i	1.06584	−	0.387932i	0.251218	−	0.967931i	$-0.419169\pi$
$347$	19.8543	−	7.22638i	1.06584	−	0.387932i	0.814618	+	0.579998i	$0.196947\pi$
$348$	−1.74035	+	1.46033i	−0.0932924	+	0.0782817i
$349$	3.36349	+	5.82573i	0.180043	+	0.311844i	0.941895	−	0.335907i	$-0.109043\pi$
$349$	3.36349	+	5.82573i	0.180043	+	0.311844i	−0.761852	+	0.647751i	$0.775710\pi$
$350$	2.87998	+	6.66999i	0.153942	+	0.356526i
$351$	0.133496	+	0.0485886i	0.00712549	+	0.00259347i
$352$	0.907604	+	5.14728i	0.0483754	+	0.274351i
$353$	−7.23087	−	12.5242i	−0.384860	−	0.666598i	0.606889	−	0.794786i	$-0.292417\pi$
$353$	−7.23087	−	12.5242i	−0.384860	−	0.666598i	−0.991750	+	0.128189i	$0.959084\pi$
$354$	−4.39735			−0.233716
$355$	−30.1588	+	25.3062i	−1.60066	+	1.34311i
$356$	5.79518	+	4.86273i	0.307144	+	0.257724i
$357$	0.518226	−	0.341108i	0.0274274	−	0.0180534i
$358$	−0.880945	+	4.99609i	−0.0465594	+	0.264052i
$359$	−0.354859	−	0.297762i	−0.0187287	−	0.0157153i	0.633375	−	0.773845i	$-0.281669\pi$
$359$	−0.354859	−	0.297762i	−0.0187287	−	0.0157153i	−0.652104	+	0.758130i	$0.726113\pi$
$360$	−1.39158	+	2.41029i	−0.0733427	+	0.127033i
$361$	8.82676	+	16.8252i	0.464567	+	0.885538i
$362$	6.00944	+	10.4087i	0.315849	+	0.547067i
$363$	−15.3341	+	5.58115i	−0.804831	+	0.292935i
$364$	0.365702	−	0.0868113i	0.0191680	−	0.00455015i
$365$	−14.1483	+	11.8719i	−0.740558	+	0.621402i
$366$	−1.21004	+	6.86245i	−0.0632496	+	0.358706i
$367$	28.6550	+	10.4296i	1.49578	+	0.544420i	0.954964	−	0.296720i	$-0.0958930\pi$
$367$	28.6550	+	10.4296i	1.49578	+	0.544420i	0.540817	+	0.841140i	$0.318115\pi$
$368$	6.15203			0.320697
$369$	−5.76688			−0.300212
$370$	−9.21160	−	3.35275i	−0.478888	−	0.174301i
$371$	1.48829	+	25.3963i	0.0772680	+	1.31851i
$372$	−2.75107	+	4.76500i	−0.142636	+	0.247054i
$373$	−13.8528	+	23.9937i	−0.717269	+	1.24235i	0.244808	+	0.969571i	$0.421275\pi$
$373$	−13.8528	+	23.9937i	−0.717269	+	1.24235i	−0.962078	+	0.272775i	$0.912058\pi$
$374$	−1.15171	−	0.419189i	−0.0595536	−	0.0216757i
$375$	−5.89496	+	2.14559i	−0.304414	+	0.110798i
$376$	2.82279	+	1.02741i	0.145574	+	0.0529847i
$377$	0.0560448	−	0.317846i	0.00288645	−	0.0163699i
$378$	2.57422	−	0.611074i	0.132403	−	0.0314302i
$379$	26.5746			1.36505			0.682523	−	0.730864i	$-0.260883\pi$
$379$	26.5746			1.36505			0.682523	+	0.730864i	$0.260883\pi$
$380$	10.3814	+	6.27701i	0.532553	+	0.322004i
$381$	−4.17074	+	7.22394i	−0.213674	+	0.370094i
$382$	3.38099	−	19.1746i	0.172987	−	0.981056i
$383$	26.3146	−	9.57773i	1.34461	−	0.489399i	0.433350	−	0.901226i	$-0.357331\pi$
$383$	26.3146	−	9.57773i	1.34461	−	0.489399i	0.911262	+	0.411827i	$0.135109\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	−37.4463	+	8.88910i	−1.90844	+	0.453031i
$386$	3.32526	+	18.8585i	0.169251	+	0.959871i
$387$	3.36631	−	5.83062i	0.171119	−	0.296387i
$388$	−4.45005	−	7.70772i	−0.225917	−	0.391300i
$389$	−1.81001	+	1.51878i	−0.0917714	+	0.0770053i	−0.687519	−	0.726166i	$-0.741300\pi$
$389$	−1.81001	+	1.51878i	−0.0917714	+	0.0770053i	0.595748	+	0.803172i	$0.296856\pi$
$390$	−0.0686580	−	0.389379i	−0.00347663	−	0.0197170i
$391$	−0.721308	+	1.24934i	−0.0364781	+	0.0631819i
$392$	4.80005	−	5.09505i	0.242439	−	0.257339i
$393$	1.58780	+	9.00488i	0.0800941	+	0.454236i
$394$	0.649700	−	3.68463i	0.0327314	−	0.185629i
$395$	3.67318	+	20.8316i	0.184818	+	1.04815i
$396$	−4.00387	−	3.35965i	−0.201202	−	0.168829i
$397$	−7.59537	−	6.37327i	−0.381201	−	0.319865i	0.431973	−	0.901887i	$-0.357818\pi$
$397$	−7.59537	−	6.37327i	−0.381201	−	0.319865i	−0.813174	+	0.582021i	$0.802262\pi$
$398$	−8.05875			−0.403948
$399$	−2.43612	−	11.2723i	−0.121958	−	0.564322i
$400$	2.74599			0.137299
$401$	6.77980	+	5.68893i	0.338567	+	0.284091i	0.796180	−	0.605060i	$-0.206851\pi$
$401$	6.77980	+	5.68893i	0.338567	+	0.284091i	−0.457613	+	0.889152i	$0.651295\pi$
$402$	1.75385	+	1.47165i	0.0874740	+	0.0733994i
$403$	−0.135733	−	0.769779i	−0.00676133	−	0.0383454i
$404$	3.21451	−	18.2304i	0.159928	−	0.906995i
$405$	−0.483291	−	2.74088i	−0.0240149	−	0.136195i
$406$	−2.38273	−	5.51835i	−0.118253	−	0.273871i
$407$	9.20464	−	15.9429i	0.456257	−	0.790261i
$408$	−0.0407195	−	0.230932i	−0.00201591	−	0.0114328i
$409$	−2.28513	+	1.91745i	−0.112992	+	0.0948119i	−0.697533	−	0.716552i	$-0.745719\pi$
$409$	−2.28513	+	1.91745i	−0.112992	+	0.0948119i	0.584541	+	0.811364i	$0.301275\pi$
$410$	8.02508	+	13.8998i	0.396330	+	0.686464i
$411$	9.56347	−	16.5644i	0.471731	−	0.817063i
$412$	1.09123	+	6.18866i	0.0537609	+	0.304893i
$413$	3.33276	−	11.1467i	0.163995	−	0.548494i
$414$	−4.71273	+	3.95445i	−0.231618	+	0.194351i
$415$	27.9827	−	10.1849i	1.37362	−	0.499956i
$416$	0.0246691	−	0.139905i	0.00120950	−	0.00685942i
$417$	4.56633	−	7.90912i	0.223614	−	0.387311i
$418$	−14.9943	+	17.1527i	−0.733397	+	0.838966i
$419$	12.1667			0.594382			0.297191	−	0.954818i	$-0.403950\pi$
$419$	12.1667			0.594382			0.297191	+	0.954818i	$0.403950\pi$
$420$	−5.05509	−	5.35424i	−0.246663	−	0.261260i
$421$	0.252612	−	1.43263i	0.0123115	−	0.0698223i	−0.978033	−	0.208450i	$-0.933158\pi$
$421$	0.252612	−	1.43263i	0.0123115	−	0.0698223i	0.990345	+	0.138628i	$0.0442692\pi$
$422$	−12.0757	−	4.39519i	−0.587835	−	0.213954i
$423$	−2.82279	+	1.02741i	−0.137249	+	0.0499545i
$424$	9.03549	+	3.28865i	0.438802	+	0.159711i
$425$	−0.321959	+	0.557649i	−0.0156173	+	0.0270499i
$426$	7.07280	−	12.2504i	0.342678	−	0.593536i
$427$	−16.4784	−	8.26836i	−0.797444	−	0.400134i
$428$	−8.31412	−	3.02609i	−0.401878	−	0.146272i
$429$	0.742521			0.0358492
$430$	−18.7380			−0.903625
$431$	25.4957	+	9.27968i	1.22808	+	0.446986i	0.872941	−	0.487825i	$-0.162210\pi$
$431$	25.4957	+	9.27968i	1.22808	+	0.446986i	0.355144	+	0.934812i	$0.384432\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	−20.1904	+	16.9418i	−0.970288	+	0.814169i	−0.982596	−	0.185756i	$-0.940527\pi$
$433$	−20.1904	+	16.9418i	−0.970288	+	0.814169i	0.0123077	+	0.999924i	$0.496082\pi$
$434$	−9.99362	−	10.5850i	−0.479709	−	0.508097i
$435$	−5.94164	+	2.16258i	−0.284880	+	0.103688i
$436$	8.85079	+	15.3300i	0.423876	+	0.734175i
$437$	16.8180	+	20.8867i	0.804516	+	0.999148i
$438$	3.31805	−	5.74703i	0.158543	−	0.274604i
$439$	−31.8808	−	26.7511i	−1.52159	−	1.27676i	−0.835931	−	0.548835i	$-0.815071\pi$
$439$	−31.8808	−	26.7511i	−1.52159	−	1.27676i	−0.685655	−	0.727927i	$-0.740484\pi$
$440$	−2.52601	+	14.3257i	−0.120423	+	0.682951i
$441$	−0.402011	+	6.98845i	−0.0191434	+	0.332783i
$442$	0.0255193	+	0.0214132i	0.00121383	+	0.00101852i
$443$	9.59690	−	8.05276i	0.455962	−	0.382598i	−0.385680	−	0.922632i	$-0.626033\pi$
$443$	9.59690	−	8.05276i	0.455962	−	0.382598i	0.841643	+	0.540034i	$0.181589\pi$
$444$	3.52217			0.167155
$445$	10.5274	+	18.2340i	0.499047	+	0.864375i
$446$	−0.570423	−	3.23503i	−0.0270103	−	0.153183i
$447$	−10.7363	−	3.90771i	−0.507812	−	0.184828i
$448$	−1.04880	−	2.42900i	−0.0495510	−	0.114759i
$449$	3.93834	+	6.82141i	0.185862	+	0.321922i	0.943867	−	0.330327i	$-0.107159\pi$
$449$	3.93834	+	6.82141i	0.185862	+	0.321922i	−0.758005	+	0.652249i	$0.773826\pi$
$450$	−2.10355	+	1.76509i	−0.0991622	+	0.0832069i
$451$	−28.3239	+	10.3090i	−1.33372	+	0.485434i
$452$	3.08141	+	17.4756i	0.144937	+	0.821981i
$453$	13.6665	−	4.97420i	0.642109	−	0.233708i
$454$	−13.1527	+	4.78718i	−0.617285	+	0.224674i
$455$	1.03906	+	0.121072i	0.0487120	+	0.00567594i
$456$	−4.27649	−	0.843582i	−0.200265	−	0.0395043i
$457$	−11.6279	−	20.1401i	−0.543930	−	0.942114i	−0.998673	−	0.0514918i	$-0.983602\pi$
$457$	−11.6279	−	20.1401i	−0.543930	−	0.942114i	0.454743	−	0.890622i	$-0.349731\pi$
$458$	1.66174	−	9.42418i	0.0776479	−	0.440363i
$459$	0.179633	+	0.150730i	0.00838455	+	0.00703547i
$460$	16.0895	+	5.85610i	0.750177	+	0.273042i
$461$	−2.13472	−	1.79124i	−0.0994237	−	0.0834264i	0.591721	−	0.806143i	$-0.298449\pi$
$461$	−2.13472	−	1.79124i	−0.0994237	−	0.0834264i	−0.691145	+	0.722717i	$0.742893\pi$
$462$	11.5508	−	7.60302i	0.537393	−	0.353724i
$463$	4.92890	+	8.53710i	0.229065	+	0.396753i	0.957531	−	0.288329i	$-0.0930997\pi$
$463$	4.92890	+	8.53710i	0.229065	+	0.396753i	−0.728466	+	0.685082i	$0.759766\pi$
$464$	−2.27186			−0.105469
$465$	−11.7307	+	9.84323i	−0.543999	+	0.456469i
$466$	−22.9578	+	19.2639i	−1.06350	+	0.892381i
$467$	29.4185			1.36132			0.680662	−	0.732597i	$-0.261692\pi$
$467$	29.4185			1.36132			0.680662	+	0.732597i	$0.261692\pi$
$468$	0.0710318	+	0.123031i	0.00328344	+	0.00568709i
$469$	−5.05970	+	3.33041i	−0.233635	+	0.153784i
$470$	6.40450	+	5.37401i	0.295417	+	0.247885i
$471$	−2.93755	−	1.06918i	−0.135355	−	0.0492653i
$472$	−3.36856	−	2.82656i	−0.155051	−	0.130103i
$473$	6.11055	−	34.6547i	0.280963	−	1.59342i
$474$	−3.80018	−	6.58210i	−0.174548	−	0.302326i
$475$	7.50681	+	9.32289i	0.344436	+	0.427763i
$476$	0.616244	+	0.0718050i	0.0282455	+	0.00329118i
$477$	−9.03549	+	3.28865i	−0.413707	+	0.150577i
$478$	15.2283	−	5.54266i	0.696528	−	0.253516i
$479$	3.63690	+	20.6259i	0.166174	+	0.942422i	0.947845	+	0.318731i	$0.103257\pi$
$479$	3.63690	+	20.6259i	0.166174	+	0.942422i	−0.781671	+	0.623691i	$0.785632\pi$
$480$	−2.61532	+	0.951897i	−0.119372	+	0.0434480i
$481$	−0.383308	+	0.321633i	−0.0174773	+	0.0146652i
$482$	−2.19124	−	3.79534i	−0.0998084	−	0.172873i
$483$	−6.45224	−	14.9433i	−0.293587	−	0.679942i
$484$	−15.3341	−	5.58115i	−0.697004	−	0.253689i
$485$	−4.30134	−	24.3941i	−0.195314	−	1.10768i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	35.1207			1.59147			0.795735	−	0.605644i	$-0.207085\pi$
$487$	35.1207			1.59147			0.795735	+	0.605644i	$0.207085\pi$
$488$	−5.33804	+	4.47915i	−0.241642	+	0.202761i
$489$	14.5056	+	12.1717i	0.655967	+	0.550422i
$490$	17.4036	−	8.75602i	0.786215	−	0.395557i
$491$	0.0973166	−	0.551910i	0.00439184	−	0.0249074i	−0.982533	−	0.186088i	$-0.940419\pi$
$491$	0.0973166	−	0.551910i	0.00439184	−	0.0249074i	0.986925	+	0.161181i	$0.0515302\pi$
$492$	−4.41768	−	3.70688i	−0.199165	−	0.167119i
$493$	0.266369	−	0.461365i	0.0119967	−	0.0207788i
$494$	0.542431	−	0.298710i	0.0244051	−	0.0134396i
$495$	−7.27335	−	12.5978i	−0.326913	−	0.566229i
$496$	−5.17032	+	1.88184i	−0.232154	+	0.0844973i
$497$	25.6928	+	27.2133i	1.15248	+	1.22068i
$498$	−8.19634	+	6.87755i	−0.367287	+	0.308190i
$499$	3.18852	−	18.0830i	0.142738	−	0.809506i	−0.826418	−	0.563057i	$-0.809625\pi$
$499$	3.18852	−	18.0830i	0.142738	−	0.809506i	0.969156	−	0.246449i	$-0.0792638\pi$
$500$	−5.89496	−	2.14559i	−0.263631	−	0.0959537i
$501$	3.78395			0.169054
$502$	−1.84179			−0.0822029
$503$	12.5222	+	4.55770i	0.558336	+	0.203218i	0.605746	−	0.795658i	$-0.292875\pi$
$503$	12.5222	+	4.55770i	0.558336	+	0.203218i	−0.0474104	+	0.998875i	$0.515097\pi$
$504$	2.36475	+	1.18656i	0.105335	+	0.0528538i
$505$	25.7604	−	44.6183i	1.14632	−	1.98549i
$506$	−16.0774	+	27.8468i	−0.714726	+	1.23794i
$507$	12.1970	+	4.43936i	0.541690	+	0.197159i
$508$	−7.83844	+	2.85296i	−0.347774	+	0.126580i
$509$	−9.61025	−	3.49785i	−0.425967	−	0.155039i	0.120136	−	0.992757i	$-0.461667\pi$
$509$	−9.61025	−	3.49785i	−0.425967	−	0.155039i	−0.546103	+	0.837718i	$0.683889\pi$
$510$	0.113329	−	0.642720i	0.00501829	−	0.0284601i
$511$	12.0532	+	12.7665i	0.533204	+	0.564758i
$512$	−1.00000			−0.0441942
$513$	3.81823	−	2.10265i	0.168579	−	0.0928344i
$514$	−5.51831	+	9.55800i	−0.243402	+	0.421585i
$515$	−3.03706	+	17.2240i	−0.133829	+	0.758981i
$516$	6.32659	−	2.30269i	0.278513	−	0.101370i
$517$	−12.0274	+	10.0922i	−0.528966	+	0.443855i
$518$	−2.66947	+	8.92827i	−0.117290	+	0.392286i
$519$	−4.22752	−	23.9755i	−0.185568	−	1.05241i
$520$	0.197693	−	0.342414i	0.00866941	−	0.0150159i
$521$	−0.161589	−	0.279880i	−0.00707933	−	0.0122618i	0.862464	−	0.506118i	$-0.168920\pi$
$521$	−0.161589	−	0.279880i	−0.00707933	−	0.0122618i	−0.869543	+	0.493857i	$0.835587\pi$
$522$	1.74035	−	1.46033i	0.0761730	−	0.0639167i
$523$	−6.67935	−	37.8805i	−0.292068	−	1.65640i	−0.678887	−	0.734243i	$-0.737537\pi$
$523$	−6.67935	−	37.8805i	−0.292068	−	1.65640i	0.386819	−	0.922156i	$-0.373574\pi$
$524$	−4.57190	+	7.91876i	−0.199724	+	0.345933i
$525$	−2.87998	−	6.66999i	−0.125693	−	0.291102i
$526$	2.73167	+	15.4921i	0.119106	+	0.675486i
$527$	0.224044	−	1.27062i	0.00975953	−	0.0553490i
$528$	−0.907604	−	5.14728i	−0.0394984	−	0.224006i
$529$	11.3738	+	9.54379i	0.494515	+	0.414947i
$530$	20.5002	+	17.2017i	0.890472	+	0.747195i
$531$	4.39735			0.190829
$532$	5.37954	−	10.2010i	0.233232	−	0.442270i
$533$	0.819263			0.0354862
$534$	−5.79518	−	4.86273i	−0.250782	−	0.210431i
$535$	−18.8635	−	15.8284i	−0.815541	−	0.684320i
$536$	0.397565	+	2.25470i	0.0171722	+	0.0973884i
$537$	0.880945	−	4.99609i	0.0380156	−	0.215597i
$538$	0.396773	+	2.25021i	0.0171061	+	0.0970136i
$539$	10.5183	+	35.0422i	0.453055	+	1.50938i
$540$	1.39158	−	2.41029i	0.0598841	−	0.103722i
$541$	3.09521	+	17.5538i	0.133073	+	0.754696i	0.976182	+	0.216953i	$0.0696118\pi$
$541$	3.09521	+	17.5538i	0.133073	+	0.754696i	−0.843109	+	0.537743i	$0.819277\pi$
$542$	7.77340	−	6.52266i	0.333896	−	0.280172i
$543$	−6.00944	−	10.4087i	−0.257890	−	0.446678i
$544$	0.117247	−	0.203078i	0.00502693	−	0.00870689i
$545$	8.55501	+	48.5179i	0.366456	+	2.07828i
$546$	−0.365702	+	0.0868113i	−0.0156506	+	0.00371518i
$547$	14.6347	−	12.2799i	0.625733	−	0.525052i	−0.273867	−	0.961768i	$-0.588303\pi$
$547$	14.6347	−	12.2799i	0.625733	−	0.525052i	0.899600	+	0.436716i	$0.143858\pi$
$548$	17.9734	−	6.54180i	0.767788	−	0.279452i
$549$	1.21004	−	6.86245i	0.0516431	−	0.292882i
$550$	−7.17620	+	12.4295i	−0.305994	+	0.529997i
$551$	−6.21068	−	7.71319i	−0.264584	−	0.328593i
$552$	−6.15203			−0.261848
$553$	19.5649	−	4.64437i	0.831986	−	0.197499i
$554$	1.82613	−	10.3565i	0.0775849	−	0.440006i
$555$	9.21160	+	3.35275i	0.391011	+	0.142316i
$556$	8.58190	−	3.12356i	0.363954	−	0.132468i
$557$	−42.9067	−	15.6167i	−1.81801	−	0.661703i	−0.995697	−	0.0926736i	$-0.970459\pi$
$557$	−42.9067	−	15.6167i	−1.81801	−	0.661703i	−0.822317	−	0.569029i	$-0.807319\pi$
$558$	2.75107	−	4.76500i	0.116462	−	0.201718i
$559$	−0.478230	+	0.828318i	−0.0202270	+	0.0350341i
$560$	−0.430784	−	7.35094i	−0.0182039	−	0.310634i
$561$	1.15171	+	0.419189i	0.0486253	+	0.0176982i
$562$	−17.4711			−0.736974
$563$	16.5743			0.698521			0.349261	−	0.937026i	$-0.386433\pi$
$563$	16.5743			0.698521			0.349261	+	0.937026i	$0.386433\pi$
$564$	−2.82279	−	1.02741i	−0.118861	−	0.0432618i
$565$	−8.57607	+	48.6373i	−0.360798	+	2.04619i
$566$	24.2948	−	20.3858i	1.02119	−	0.856878i
$567$	−2.57422	+	0.611074i	−0.108107	+	0.0256627i
$568$	13.2925	−	4.83808i	0.557741	−	0.203001i
$569$	−10.4509	−	18.1014i	−0.438123	−	0.758851i	0.559422	−	0.828883i	$-0.311023\pi$
$569$	−10.4509	−	18.1014i	−0.438123	−	0.758851i	−0.997545	+	0.0700319i	$0.977690\pi$
$570$	−10.3814	−	6.27701i	−0.434828	−	0.262915i
$571$	17.1613	−	29.7243i	0.718179	−	1.24392i	−0.243542	−	0.969890i	$-0.578309\pi$
$571$	17.1613	−	29.7243i	0.718179	−	1.24392i	0.961721	−	0.274032i	$-0.0883573\pi$
$572$	0.568804	+	0.477283i	0.0237829	+	0.0199562i
$573$	−3.38099	+	19.1746i	−0.141243	+	0.801029i
$574$	12.7446	−	8.38882i	0.531951	−	0.350143i
$575$	12.9411	+	10.8589i	0.539681	+	0.452846i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−25.1601			−1.04743			−0.523715	−	0.851894i	$-0.675454\pi$
$577$	−25.1601			−1.04743			−0.523715	+	0.851894i	$0.675454\pi$
$578$	−8.47251	−	14.6748i	−0.352410	−	0.610392i
$579$	−3.32526	−	18.8585i	−0.138193	−	0.783731i
$580$	−5.94164	−	2.16258i	−0.246713	−	0.0897962i
$581$	−11.2217	−	25.9892i	−0.465554	−	1.07821i
$582$	4.45005	+	7.70772i	0.184461	+	0.319495i
$583$	−38.4987	+	32.3042i	−1.59445	+	1.33790i
$584$	6.23589	−	2.26968i	0.258043	−	0.0939200i
$585$	0.0686580	+	0.389379i	0.00283866	+	0.0160988i
$586$	−21.2012	+	7.71661i	−0.875813	+	0.318770i
$587$	−21.2563	+	7.73666i	−0.877341	+	0.319326i	−0.741136	−	0.671354i	$-0.765713\pi$
$587$	−21.2563	+	7.73666i	−0.877341	+	0.319326i	−0.136205	+	0.990681i	$0.543491\pi$
$588$	−4.80005	+	5.09505i	−0.197951	+	0.210116i
$589$	−20.5234	−	12.4093i	−0.845650	−	0.511315i
$590$	−6.11926	−	10.5989i	−0.251926	−	0.436349i
$591$	−0.649700	+	3.68463i	−0.0267251	+	0.151566i
$592$	2.69814	+	2.26401i	0.110893	+	0.0930502i
$593$	−45.4775	−	16.5525i	−1.86754	−	0.679728i	−0.972113	−	0.234513i	$-0.924650\pi$
$593$	−45.4775	−	16.5525i	−1.86754	−	0.679728i	−0.895424	−	0.445215i	$-0.853127\pi$
$594$	4.00387	+	3.35965i	0.164281	+	0.137848i
$595$	1.54332	+	0.774394i	0.0632700	+	0.0317470i
$596$	−5.71269	−	9.89467i	−0.234001	−	0.405302i
$597$	8.05875			0.329823
$598$	0.669507	−	0.561783i	0.0273782	−	0.0229730i
$599$	−3.99238	+	3.35000i	−0.163124	+	0.136877i	−0.720696	−	0.693251i	$-0.756178\pi$
$599$	−3.99238	+	3.35000i	−0.163124	+	0.136877i	0.557572	+	0.830129i	$0.311733\pi$
$600$	−2.74599			−0.112104
$601$	21.8270	+	37.8055i	0.890343	+	1.54212i	0.839465	+	0.543414i	$0.182869\pi$
$601$	21.8270	+	37.8055i	0.890343	+	1.54212i	0.0508777	+	0.998705i	$0.483798\pi$
$602$	1.04209	+	17.7823i	0.0424724	+	0.724754i
$603$	−1.75385	−	1.47165i	−0.0714223	−	0.0599304i
$604$	13.6665	+	4.97420i	0.556082	+	0.202397i
$605$	−34.7908	−	29.1930i	−1.41445	−	1.18686i
$606$	−3.21451	+	18.2304i	−0.130580	+	0.740558i
$607$	−12.3975	−	21.4731i	−0.503199	−	0.871566i	−0.999993	−	0.00369756i	$-0.998823\pi$
$607$	−12.3975	−	21.4731i	−0.503199	−	0.871566i	0.496794	−	0.867868i	$-0.334510\pi$
$608$	−2.73374	−	3.39510i	−0.110868	−	0.137689i
$609$	2.38273	+	5.51835i	0.0965529	+	0.223615i
$610$	−18.2244	+	6.63312i	−0.737882	+	0.268567i
$611$	0.401016	−	0.145958i	0.0162234	−	0.00590482i
$612$	0.0407195	+	0.230932i	0.00164599	+	0.00933486i
$613$	−17.7169	+	6.44844i	−0.715580	+	0.260450i	−0.674048	−	0.738687i	$-0.735446\pi$
$613$	−17.7169	+	6.44844i	−0.715580	+	0.260450i	−0.0415321	+	0.999137i	$0.513224\pi$
$614$	3.69411	−	3.09973i	0.149082	−	0.125095i
$615$	−8.02508	−	13.8998i	−0.323602	−	0.560496i
$616$	13.7356	+	1.60047i	0.553422	+	0.0644850i
$617$	−39.6087	−	14.4164i	−1.59459	−	0.580382i	−0.616276	−	0.787530i	$-0.711359\pi$
$617$	−39.6087	−	14.4164i	−1.59459	−	0.580382i	−0.978310	+	0.207149i	$0.933582\pi$
$618$	−1.09123	−	6.18866i	−0.0438956	−	0.248944i
$619$	−7.42371	−	12.8582i	−0.298384	−	0.516816i	0.677382	−	0.735631i	$-0.263114\pi$
$619$	−7.42371	−	12.8582i	−0.298384	−	0.516816i	−0.975766	+	0.218815i	$0.929781\pi$
$620$	−15.3134			−0.614999
$621$	4.71273	−	3.95445i	0.189115	−	0.158687i
$622$	13.0795	+	10.9750i	0.524439	+	0.440057i
$623$	16.7186	−	11.0046i	0.669817	−	0.440889i
$624$	−0.0246691	+	0.139905i	−0.000987553	+	0.00560069i
$625$	−23.8925	−	20.0482i	−0.955701	−	0.801929i
$626$	5.01695	−	8.68961i	0.200518	−	0.347307i
$627$	14.9943	−	17.1527i	0.598817	−	0.685013i
$628$	−1.56304	−	2.70726i	−0.0623720	−	0.108032i
$629$	−0.776120	+	0.282484i	−0.0309459	+	0.0112634i
$630$	5.05509	+	5.35424i	0.201400	+	0.213318i
$631$	−27.8154	+	23.3399i	−1.10731	+	0.929147i	−0.997895	−	0.0648488i	$-0.979343\pi$
$631$	−27.8154	+	23.3399i	−1.10731	+	0.929147i	−0.109419	+	0.993996i	$0.534899\pi$
$632$	1.31979	−	7.48489i	0.0524983	−	0.297733i
$633$	12.0757	+	4.39519i	0.479965	+	0.174693i
$634$	1.42353			0.0565356
$635$	−23.2157			−0.921287
$636$	−9.03549	−	3.28865i	−0.358280	−	0.130403i
$637$	0.0571111	−	0.992803i	0.00226283	−	0.0393363i
$638$	5.93715	−	10.2834i	0.235054	−	0.407126i
$639$	−7.07280	+	12.2504i	−0.279795	+	0.484620i
$640$	−2.61532	−	0.951897i	−0.103379	−	0.0376270i
$641$	−22.3273	+	8.12647i	−0.881875	+	0.320976i	−0.742966	−	0.669329i	$-0.766582\pi$
$641$	−22.3273	+	8.12647i	−0.881875	+	0.320976i	−0.138909	+	0.990305i	$0.544359\pi$
$642$	8.31412	+	3.02609i	0.328132	+	0.119430i
$643$	7.51701	−	42.6311i	0.296442	−	1.68121i	−0.364841	−	0.931070i	$-0.618877\pi$
$643$	7.51701	−	42.6311i	0.296442	−	1.68121i	0.661283	−	0.750136i	$-0.270012\pi$
$644$	4.66264	−	15.5946i	0.183734	−	0.614514i
$645$	18.7380			0.737807
$646$	1.00999	−	0.157097i	0.0397376	−	0.00618089i
$647$	−7.42265	+	12.8564i	−0.291815	+	0.505438i	−0.974239	−	0.225519i	$-0.927592\pi$
$647$	−7.42265	+	12.8564i	−0.291815	+	0.505438i	0.682424	+	0.730956i	$0.260926\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	21.5975	−	7.86083i	0.847775	−	0.308565i
$650$	0.298837	−	0.250754i	0.0117214	−	0.00983539i
$651$	9.99362	+	10.5850i	0.391681	+	0.414860i
$652$	3.28816	+	18.6481i	0.128774	+	0.730315i
$653$	−11.4405	+	19.8155i	−0.447700	+	0.775440i	−0.998236	−	0.0593718i	$-0.981090\pi$
$653$	−11.4405	+	19.8155i	−0.447700	+	0.775440i	0.550535	+	0.834812i	$0.314424\pi$
$654$	−8.85079	−	15.3300i	−0.346093	−	0.599451i
$655$	−19.4948	+	16.3581i	−0.761725	+	0.639163i
$656$	−1.00141	−	5.67927i	−0.0390984	−	0.221738i
$657$	−3.31805	+	5.74703i	−0.129449	+	0.224213i
$658$	4.74376	−	6.37674i	0.184931	−	0.248591i
$659$	−3.27085	−	18.5499i	−0.127414	−	0.722602i	−0.979845	−	0.199761i	$-0.935983\pi$
$659$	−3.27085	−	18.5499i	−0.127414	−	0.722602i	0.852430	−	0.522841i	$-0.175128\pi$
$660$	2.52601	−	14.3257i	0.0983247	−	0.557627i
$661$	5.37939	+	30.5080i	0.209234	+	1.18662i	0.890637	+	0.454716i	$0.150259\pi$
$661$	5.37939	+	30.5080i	0.209234	+	1.18662i	−0.681403	+	0.731909i	$0.738630\pi$
$662$	7.10614	+	5.96276i	0.276188	+	0.231749i
$663$	−0.0255193	−	0.0214132i	−0.000991087	−	0.000831621i
$664$	−10.6996			−0.415224
$665$	23.7795	−	21.5581i	0.922129	−	0.835987i
$666$	−3.52217			−0.136481
$667$	−10.7067	−	8.98397i	−0.414564	−	0.347861i
$668$	2.89867	+	2.43227i	0.112153	+	0.0941075i
$669$	0.570423	+	3.23503i	0.0220538	+	0.125074i
$670$	−1.10649	+	6.27521i	−0.0427474	+	0.242432i
$671$	−6.32447	−	35.8679i	−0.244153	−	1.38466i
$672$	1.04880	+	2.42900i	0.0404583	+	0.0937006i
$673$	14.8165	−	25.6629i	0.571134	−	0.989233i	−0.425316	−	0.905045i	$-0.639837\pi$
$673$	14.8165	−	25.6629i	0.571134	−	0.989233i	0.996450	−	0.0841883i	$-0.0268297\pi$
$674$	0.425301	+	2.41200i	0.0163820	+	0.0929068i
$675$	2.10355	−	1.76509i	0.0809656	−	0.0679382i
$676$	6.48991	+	11.2409i	0.249612	+	0.432340i
$677$	−3.82872	+	6.63154i	−0.147150	+	0.254871i	−0.930173	−	0.367122i	$-0.880343\pi$
$677$	−3.82872	+	6.63154i	−0.147150	+	0.254871i	0.783023	+	0.621992i	$0.213677\pi$
$678$	−3.08141	−	17.4756i	−0.118341	−	0.671145i
$679$	−22.9108	+	5.43862i	−0.879235	+	0.208715i
$680$	0.499947	−	0.419506i	0.0191721	−	0.0160873i
$681$	13.1527	−	4.78718i	0.504011	−	0.183445i
$682$	4.99377	−	28.3211i	0.191221	−	1.08447i
$683$	−8.96704	+	15.5314i	−0.343114	+	0.594292i	−0.985009	−	0.172501i	$-0.944815\pi$
$683$	−8.96704	+	15.5314i	−0.343114	+	0.594292i	0.641895	+	0.766793i	$0.278149\pi$
$684$	4.27649	+	0.843582i	0.163516	+	0.0322551i
$685$	53.2334			2.03394
$686$	−9.27735	−	16.0291i	−0.354211	−	0.611992i
$687$	−1.66174	+	9.42418i	−0.0633992	+	0.359555i
$688$	6.32659	+	2.30269i	0.241199	+	0.0877893i
$689$	1.28361	−	0.467197i	0.0489018	−	0.0177988i
$690$	−16.0895	−	5.85610i	−0.612517	−	0.222938i
$691$	−13.1779	+	22.8248i	−0.501311	+	0.868296i	0.498688	+	0.866782i	$0.333815\pi$
$691$	−13.1779	+	22.8248i	−0.501311	+	0.868296i	−0.999999	+	0.00151470i	$0.999518\pi$
$692$	12.1727	−	21.0837i	0.462736	−	0.801482i
$693$	−11.5508	+	7.60302i	−0.438779	+	0.288815i
$694$	−19.8543	−	7.22638i	−0.753660	−	0.274310i
$695$	25.4177			0.964148
$696$	2.27186			0.0861147
$697$	1.27075	+	0.462514i	0.0481329	+	0.0175189i
$698$	1.16813	−	6.62477i	0.0442142	−	0.250751i
$699$	22.9578	−	19.2639i	0.868343	−	0.728626i
$700$	2.08119	−	6.96073i	0.0786616	−	0.263091i
$701$	23.2880	−	8.47614i	0.879576	−	0.320139i	0.137537	−	0.990497i	$-0.456081\pi$
$701$	23.2880	−	8.47614i	0.879576	−	0.320139i	0.742039	+	0.670357i	$0.233859\pi$
$702$	−0.0710318	−	0.123031i	−0.00268092	−	0.00464349i
$703$	−0.310518	+	15.3497i	−0.0117114	+	0.578923i
$704$	2.61334	−	4.52644i	0.0984940	−	0.170597i
$705$	−6.40450	−	5.37401i	−0.241207	−	0.202397i
$706$	−2.51125	+	14.2420i	−0.0945123	+	0.536006i
$707$	−43.7754	−	21.9652i	−1.64634	−	0.826087i
$708$	3.36856	+	2.82656i	0.126598	+	0.106229i
$709$	3.98980	−	3.34784i	0.149840	−	0.125731i	−0.564786	−	0.825237i	$-0.691041\pi$
$709$	3.98980	−	3.34784i	0.149840	−	0.125731i	0.714626	+	0.699507i	$0.246597\pi$
$710$	39.3695			1.47751
$711$	3.80018	+	6.58210i	0.142518	+	0.246848i
$712$	−1.31366	−	7.45014i	−0.0492315	−	0.279206i
$713$	−31.8080	−	11.5772i	−1.19122	−	0.433568i
$714$	−0.616244	−	0.0718050i	−0.0230623	−	0.00268723i
$715$	1.03328	+	1.78969i	0.0386424	+	0.0669306i
$716$	3.88627	−	3.26097i	0.145237	−	0.121868i
$717$	−15.2283	+	5.54266i	−0.568713	+	0.206995i
$718$	0.0804400	+	0.456198i	0.00300199	+	0.0170251i
$719$	−48.5805	+	17.6819i	−1.81175	+	0.659422i	−0.814943	+	0.579542i	$0.803232\pi$
$719$	−48.5805	+	17.6819i	−1.81175	+	0.659422i	−0.996804	+	0.0798804i	$0.974546\pi$
$720$	2.61532	−	0.951897i	0.0974671	−	0.0354751i
$721$	16.5145	+	1.92428i	0.615032	+	0.0716638i
$722$	4.05335	−	18.5626i	0.150850	−	0.690829i
$723$	2.19124	+	3.79534i	0.0814932	+	0.141150i
$724$	2.08706	−	11.8363i	0.0775649	−	0.439892i
$725$	−4.77897	−	4.01003i	−0.177487	−	0.148929i
$726$	15.3341	+	5.58115i	0.569102	+	0.207136i
$727$	−15.7742	−	13.2361i	−0.585031	−	0.490900i	0.301564	−	0.953446i	$-0.402491\pi$
$727$	−15.7742	−	13.2361i	−0.585031	−	0.490900i	−0.886595	+	0.462546i	$0.846936\pi$
$728$	−0.335945	−	0.168568i	−0.0124510	−	0.00624753i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	18.4693			0.683581
$731$	−1.20940	+	1.01481i	−0.0447313	+	0.0375340i
$732$	5.33804	−	4.47915i	0.197300	−	0.165554i
$733$	8.25597			0.304941			0.152471	−	0.988308i	$-0.451277\pi$
$733$	8.25597			0.304941			0.152471	+	0.988308i	$0.451277\pi$
$734$	−15.2470	−	26.4086i	−0.562778	−	0.974760i
$735$	−17.4036	+	8.75602i	−0.641942	+	0.322971i
$736$	−4.71273	−	3.95445i	−0.173714	−	0.145763i
$737$	−11.2448	−	4.09276i	−0.414206	−	0.150759i
$738$	4.41768	+	3.70688i	0.162617	+	0.136452i
$739$	3.20796	−	18.1932i	0.118007	−	0.669249i	−0.867211	−	0.497941i	$-0.834090\pi$
$739$	3.20796	−	18.1932i	0.118007	−	0.669249i	0.985218	−	0.171308i	$-0.0547994\pi$
$740$	4.90139	+	8.48946i	0.180179	+	0.312079i
$741$	−0.542431	+	0.298710i	−0.0199267	+	0.0109734i
$742$	15.1843	−	20.4113i	0.557434	−	0.749324i
$743$	18.3175	−	6.66703i	0.672005	−	0.244590i	0.0165939	−	0.999862i	$-0.494718\pi$
$743$	18.3175	−	6.66703i	0.672005	−	0.244590i	0.655411	+	0.755273i	$0.272496\pi$
$744$	5.17032	−	1.88184i	0.189553	−	0.0689918i
$745$	−5.52178	−	31.3156i	−0.202302	−	1.14731i
$746$	26.0347	−	9.47585i	0.953198	−	0.346936i
$747$	8.19634	−	6.87755i	0.299888	−	0.251636i
$748$	0.612813	+	1.06142i	0.0224067	+	0.0388095i
$749$	−13.9721	+	18.7818i	−0.510528	+	0.686271i
$750$	5.89496	+	2.14559i	0.215253	+	0.0783459i
$751$	7.50758	+	42.5776i	0.273956	+	1.55368i	0.742260	+	0.670112i	$0.233754\pi$
$751$	7.50758	+	42.5776i	0.273956	+	1.55368i	−0.468305	+	0.883567i	$0.655135\pi$
$752$	−1.50198	−	2.60150i	−0.0547714	−	0.0948668i
$753$	1.84179			0.0671184
$754$	−0.247240	+	0.207459i	−0.00900395	+	0.00755521i
$755$	31.0073	+	26.0182i	1.12847	+	0.946900i
$756$	−2.36475	−	1.18656i	−0.0860053	−	0.0431549i
$757$	1.38813	−	7.87245i	0.0504523	−	0.286129i	−0.949135	−	0.314871i	$-0.898039\pi$
$757$	1.38813	−	7.87245i	0.0504523	−	0.286129i	0.999587	+	0.0287416i	$0.00914999\pi$
$758$	−20.3573	−	17.0818i	−0.739412	−	0.620440i
$759$	16.0774	−	27.8468i	0.583571	−	1.01077i
$760$	−3.91781	−	11.4815i	−0.142114	−	0.416477i
$761$	14.0579	+	24.3490i	0.509599	+	0.882651i	0.999938	+	0.0111194i	$0.00353949\pi$
$761$	14.0579	+	24.3490i	0.509599	+	0.882651i	−0.490339	+	0.871532i	$0.663127\pi$
$762$	7.83844	−	2.85296i	0.283957	−	0.103352i
$763$	45.5677	−	10.8170i	1.64966	−	0.391601i
$764$	−14.9152	+	12.5153i	−0.539611	+	0.452788i
$765$	−0.113329	+	0.642720i	−0.00409741	+	0.0232376i
$766$	−26.3146	−	9.57773i	−0.950785	−	0.346057i
$767$	−0.624703			−0.0225567
$768$	1.00000			0.0360844
$769$	12.5468	+	4.56665i	0.452448	+	0.164678i	0.558185	−	0.829716i	$-0.311498\pi$
$769$	12.5468	+	4.56665i	0.452448	+	0.164678i	−0.105737	+	0.994394i	$0.533720\pi$
$770$	34.3994	+	17.2606i	1.23967	+	0.622029i
$771$	5.51831	−	9.55800i	0.198737	−	0.344223i
$772$	9.57470	−	16.5839i	0.344601	−	0.596866i
$773$	9.55352	+	3.47720i	0.343616	+	0.125066i	0.508063	−	0.861320i	$-0.330362\pi$
$773$	9.55352	+	3.47720i	0.343616	+	0.125066i	−0.164447	+	0.986386i	$0.552584\pi$
$774$	−6.32659	+	2.30269i	−0.227405	+	0.0827685i
$775$	−14.1976	−	5.16752i	−0.509994	−	0.185623i
$776$	−1.54549	+	8.76489i	−0.0554797	+	0.314641i
$777$	2.66947	−	8.92827i	0.0957666	−	0.320300i
$778$	2.36281			0.0847107
$779$	16.5441	−	18.9255i	0.592753	−	0.678076i
$780$	−0.197693	+	0.342414i	−0.00707854	+	0.0122604i
$781$	−12.8386	+	72.8113i	−0.459401	+	2.60539i
$782$	1.35562	−	0.493404i	0.0484767	−	0.0176441i
$783$	−1.74035	+	1.46033i	−0.0621950	+	0.0521878i
$784$	−6.95208	+	0.817627i	−0.248289	+	0.0292010i
$785$	−1.51080	−	8.56820i	−0.0539229	−	0.305812i
$786$	4.57190	−	7.91876i	0.163074	−	0.282453i
$787$	−21.9549	−	38.0270i	−0.782608	−	1.35552i	−0.930418	−	0.366501i	$-0.880556\pi$
$787$	−21.9549	−	38.0270i	−0.782608	−	1.35552i	0.147809	−	0.989016i	$-0.452778\pi$
$788$	−2.86614	+	2.40497i	−0.102102	+	0.0856737i
$789$	−2.73167	−	15.4921i	−0.0972499	−	0.551532i
$790$	10.5765	−	18.3190i	0.376295	−	0.651762i
$791$	46.6337	+	5.43378i	1.65811	+	0.193203i
$792$	0.907604	+	5.14728i	0.0322503	+	0.182901i
$793$	−0.171902	+	0.974904i	−0.00610442	+	0.0346199i
$794$	1.72173	+	9.76442i	0.0611019	+	0.346526i
$795$	−20.5002	−	17.2017i	−0.727067	−	0.610082i
$796$	6.17336	+	5.18006i	0.218809	+	0.183602i
$797$	−16.1797			−0.573116			−0.286558	−	0.958063i	$-0.592511\pi$
$797$	−16.1797			−0.573116			−0.286558	+	0.958063i	$0.592511\pi$
$798$	−5.37954	+	10.2010i	−0.190434	+	0.361112i
$799$	0.704409			0.0249202
$800$	−2.10355	−	1.76509i	−0.0743716	−	0.0624052i
$801$	5.79518	+	4.86273i	0.204763	+	0.171816i
$802$	−1.53686	−	8.71594i	−0.0542682	−	0.307771i
$803$	−6.02295	+	34.1578i	−0.212545	+	1.20540i
$804$	−0.397565	−	2.25470i	−0.0140210	−	0.0795173i
$805$	27.0388	−	36.3465i	0.952991	−	1.28105i
$806$	−0.390827	+	0.676932i	−0.0137663	+	0.0238439i
$807$	−0.396773	−	2.25021i	−0.0139671	−	0.0792112i
$808$	−14.1807	+	11.8990i	−0.498876	+	0.418606i
$809$	6.12832	+	10.6146i	0.215460	+	0.373188i	0.953415	−	0.301662i	$-0.0975415\pi$
$809$	6.12832	+	10.6146i	0.215460	+	0.373188i	−0.737955	+	0.674850i	$0.764208\pi$
$810$	−1.39158	+	2.41029i	−0.0488952	+	0.0846889i
$811$	6.59872	+	37.4232i	0.231713	+	1.31411i	0.849428	+	0.527705i	$0.176947\pi$
$811$	6.59872	+	37.4232i	0.231713	+	1.31411i	−0.617715	+	0.786402i	$0.711941\pi$
$812$	−1.72185	+	5.75888i	−0.0604251	+	0.202097i
$813$	−7.77340	+	6.52266i	−0.272625	+	0.228760i
$814$	−17.2991	+	6.29635i	−0.606332	+	0.220687i
$815$	−9.15148	+	51.9006i	−0.320562	+	1.81800i
$816$	−0.117247	+	0.203078i	−0.00410447	+	0.00710915i
$817$	9.47739	+	27.7743i	0.331572	+	0.971701i
$818$	2.98302			0.104299
$819$	0.365702	−	0.0868113i	0.0127787	−	0.00303343i
$820$	2.78708	−	15.8063i	0.0973290	−	0.551980i
$821$	−29.9323	−	10.8945i	−1.04464	−	0.380219i	−0.238005	−	0.971264i	$-0.576493\pi$
$821$	−29.9323	−	10.8945i	−1.04464	−	0.380219i	−0.806639	+	0.591045i	$0.798716\pi$
$822$	−17.9734	+	6.54180i	−0.626896	+	0.228171i
$823$	22.7971	+	8.29748i	0.794658	+	0.289232i	0.707271	−	0.706943i	$-0.249926\pi$
$823$	22.7971	+	8.29748i	0.794658	+	0.289232i	0.0873870	+	0.996174i	$0.472148\pi$
$824$	3.14206	−	5.44221i	0.109459	−	0.189588i
$825$	7.17620	−	12.4295i	0.249843	−	0.432741i
$826$	−9.71802	+	6.39663i	−0.338133	+	0.222567i
$827$	−2.75955	−	1.00439i	−0.0959588	−	0.0349261i	0.293595	−	0.955930i	$-0.405148\pi$
$827$	−2.75955	−	1.00439i	−0.0959588	−	0.0349261i	−0.389553	+	0.921004i	$0.627371\pi$
$828$	6.15203			0.213798
$829$	8.97716			0.311790			0.155895	−	0.987774i	$-0.450174\pi$
$829$	8.97716			0.311790			0.155895	+	0.987774i	$0.450174\pi$
$830$	−27.9827	−	10.1849i	−0.971295	−	0.353523i
$831$	−1.82613	+	10.3565i	−0.0633478	+	0.359263i
$832$	−0.108827	+	0.0913167i	−0.00377290	+	0.00316584i
$833$	0.649070	−	1.50768i	0.0224889	−	0.0522380i
$834$	−8.58190	+	3.12356i	−0.297167	+	0.108160i
$835$	5.26567	+	9.12040i	0.182226	+	0.315625i
$836$	22.5119	−	3.50156i	0.778590	−	0.121104i
$837$	−2.75107	+	4.76500i	−0.0950910	+	0.164702i
$838$	−9.32023	−	7.82060i	−0.321962	−	0.270158i
$839$	7.58484	−	43.0157i	0.261858	−	1.48507i	−0.515979	−	0.856602i	$-0.672572\pi$
$839$	7.58484	−	43.0157i	0.261858	−	1.48507i	0.777836	−	0.628467i	$-0.216317\pi$
$840$	0.430784	+	7.35094i	0.0148634	+	0.253632i
$841$	−18.2615	−	15.3232i	−0.629705	−	0.528386i
$842$	−1.11439	+	0.935085i	−0.0384044	+	0.0322251i
$843$	17.4711			0.601737
$844$	6.42534	+	11.1290i	0.221169	+	0.383076i
$845$	6.27303	+	35.5761i	0.215799	+	1.22386i
$846$	2.82279	+	1.02741i	0.0970495	+	0.0353231i
$847$	−25.7693	+	34.6400i	−0.885443	+	1.19024i
$848$	−4.80768	−	8.32715i	−0.165097	−	0.285956i
$849$	−24.2948	+	20.3858i	−0.833796	+	0.699638i
$850$	0.605085	−	0.220233i	0.0207542	−	0.00755392i
$851$	3.76270	+	21.3393i	0.128984	+	0.731503i
$852$	−13.2925	+	4.83808i	−0.455394	+	0.165750i
$853$	34.8425	−	12.6816i	1.19298	−	0.434211i	0.332214	−	0.943204i	$-0.392204\pi$
$853$	34.8425	−	12.6816i	1.19298	−	0.434211i	0.860771	+	0.508993i	$0.169982\pi$
$854$	7.30836	+	16.9260i	0.250087	+	0.579196i
$855$	10.3814	+	6.27701i	0.355035	+	0.214669i
$856$	4.42385	+	7.66234i	0.151204	+	0.261893i
$857$	−0.654047	+	3.70929i	−0.0223418	+	0.126707i	−0.993939	−	0.109935i	$-0.964936\pi$
$857$	−0.654047	+	3.70929i	−0.0223418	+	0.126707i	0.971597	+	0.236642i	$0.0760468\pi$
$858$	−0.568804	−	0.477283i	−0.0194186	−	0.0162942i
$859$	−35.3474	−	12.8654i	−1.20604	−	0.438962i	−0.340710	−	0.940169i	$-0.610667\pi$
$859$	−35.3474	−	12.8654i	−1.20604	−	0.438962i	−0.865328	+	0.501207i	$0.832890\pi$
$860$	14.3541	+	12.0445i	0.489471	+	0.410715i
$861$	−12.7446	+	8.38882i	−0.434336	+	0.285890i
$862$	−13.5660	−	23.4970i	−0.462059	−	0.800310i
$863$	−20.7968			−0.707930			−0.353965	−	0.935259i	$-0.615167\pi$
$863$	−20.7968			−0.707930			−0.353965	+	0.935259i	$0.615167\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	51.9049	−	43.5534i	1.76482	−	1.48086i
$866$	26.3567			0.895637
$867$	8.47251	+	14.6748i	0.287741	+	0.498383i
$868$	0.851634	+	14.5324i	0.0289063	+	0.493261i
$869$	30.4308	+	25.5345i	1.03229	+	0.866198i
$870$	5.94164	+	2.16258i	0.201440	+	0.0733183i
$871$	0.249158	+	0.209068i	0.00844240	+	0.00708401i
$872$	3.07385	−	17.4327i	0.104094	−	0.590344i
$873$	−4.45005	−	7.70772i	−0.150611	−	0.260867i
$874$	0.542369	−	26.8106i	0.0183459	−	0.906882i
$875$	−9.90660	+	13.3168i	−0.334904	+	0.450191i
$876$	−6.23589	+	2.26968i	−0.210691	+	0.0766854i
$877$	1.12432	−	0.409219i	0.0379656	−	0.0138184i	−0.322968	−	0.946410i	$-0.604680\pi$
$877$	1.12432	−	0.409219i	0.0379656	−	0.0138184i	0.360933	+	0.932592i	$0.382458\pi$
$878$	7.22678	+	40.9851i	0.243892	+	1.38318i
$879$	21.2012	−	7.71661i	0.715099	−	0.260275i
$880$	11.1434	−	9.35044i	0.375644	−	0.315203i
$881$	−5.23658	−	9.07002i	−0.176425	−	0.305577i	0.764229	−	0.644945i	$-0.223120\pi$
$881$	−5.23658	−	9.07002i	−0.176425	−	0.305577i	−0.940653	+	0.339369i	$0.889787\pi$
$882$	4.80005	−	5.09505i	0.161626	−	0.171559i
$883$	−33.6942	−	12.2637i	−1.13390	−	0.412706i	−0.294194	−	0.955746i	$-0.595051\pi$
$883$	−33.6942	−	12.2637i	−1.13390	−	0.412706i	−0.839707	+	0.543040i	$0.817273\pi$
$884$	−0.00578475	−	0.0328070i	−0.000194562	−	0.00110342i
$885$	6.11926	+	10.5989i	0.205697	+	0.356277i
$886$	−12.5279			−0.420882
$887$	12.6049	−	10.5768i	0.423231	−	0.355133i	−0.406159	−	0.913802i	$-0.633132\pi$
$887$	12.6049	−	10.5768i	0.423231	−	0.355133i	0.829391	+	0.558669i	$0.188688\pi$
$888$	−2.69814	−	2.26401i	−0.0905437	−	0.0759752i
$889$	1.29111	+	22.0317i	0.0433026	+	0.738920i
$890$	3.65613	−	20.7349i	0.122554	−	0.695037i
$891$	−4.00387	−	3.35965i	−0.134135	−	0.112552i
$892$	−1.64247	+	2.84484i	−0.0549939	+	0.0952522i
$893$	4.72633	−	12.2112i	0.158160	−	0.408631i
$894$	5.71269	+	9.89467i	0.191061	+	0.330927i
$895$	13.2679	−	4.82913i	0.443498	−	0.161420i
$896$	−0.757903	+	2.53487i	−0.0253198	+	0.0846842i
$897$	−0.669507	+	0.561783i	−0.0223542	+	0.0187574i
$898$	1.36777	−	7.75702i	0.0456432	−	0.258855i
$899$	11.7463	+	4.27529i	0.391760	+	0.142589i
$900$	2.74599			0.0915329
$901$	2.25475			0.0751165
$902$	28.3239	+	10.3090i	0.943082	+	0.343254i
$903$	−1.04209	−	17.7823i	−0.0346786	−	0.591759i
$904$	8.87258	−	15.3678i	0.295097	−	0.511124i
$905$	16.7253	−	28.9690i	0.555966	−	0.962962i
$906$	−13.6665	−	4.97420i	−0.454039	−	0.165257i
$907$	−13.5817	+	4.94333i	−0.450973	+	0.164141i	−0.557514	−	0.830168i	$-0.688245\pi$
$907$	−13.5817	+	4.94333i	−0.450973	+	0.164141i	0.106541	+	0.994308i	$0.466022\pi$
$908$	13.1527	+	4.78718i	0.436487	+	0.158868i
$909$	3.21451	−	18.2304i	0.106618	−	0.604663i
$910$	−0.718144	−	0.760643i	−0.0238063	−	0.0252151i
$911$	−30.1710			−0.999611			−0.499806	−	0.866138i	$-0.666595\pi$
$911$	−30.1710			−0.999611			−0.499806	+	0.866138i	$0.666595\pi$
$912$	2.73374	+	3.39510i	0.0905231	+	0.112423i
$913$	27.9616	−	48.4309i	0.925394	−	1.60283i
$914$	−4.03833	+	22.9025i	−0.133576	+	0.757547i
$915$	18.2244	−	6.63312i	0.602478	−	0.219284i
$916$	−7.33071	+	6.15120i	−0.242213	+	0.203241i
$917$	16.6080	+	17.5908i	0.548445	+	0.580901i
$918$	−0.0407195	−	0.230932i	−0.00134394	−	0.00762188i
$919$	−11.7861	+	20.4141i	−0.388787	+	0.673398i	−0.992287	−	0.123965i	$-0.960439\pi$
$919$	−11.7861	+	20.4141i	−0.388787	+	0.673398i	0.603500	+	0.797363i	$0.293772\pi$
$920$	−8.56105	−	14.8282i	−0.282249	−	0.488870i
$921$	−3.69411	+	3.09973i	−0.121725	+	0.102140i
$922$	0.483901	+	2.74434i	0.0159364	+	0.0903800i
$923$	1.00479	−	1.74034i	0.0330729	−	0.0572840i
$924$	−13.7356	−	1.60047i	−0.451867	−	0.0526517i
$925$	1.67950	+	9.52490i	0.0552215	+	0.313177i
$926$	1.71179	−	9.70804i	0.0562529	−	0.319026i
$927$	1.09123	+	6.18866i	0.0358406	+	0.203262i
$928$	1.74035	+	1.46033i	0.0571297	+	0.0479375i
$929$	−42.4391	−	35.6107i	−1.39238	−	1.16835i	−0.964364	−	0.264578i	$-0.914767\pi$
$929$	−42.4391	−	35.6107i	−1.39238	−	1.16835i	−0.428019	−	0.903770i	$-0.640788\pi$
$930$	15.3134			0.502145
$931$	−21.7811	−	21.3678i	−0.713847	−	0.700302i
$932$	29.9692			0.981675
$933$	−13.0795	−	10.9750i	−0.428203	−	0.359305i
$934$	−22.5359	−	18.9098i	−0.737396	−	0.618749i
$935$	0.592334	+	3.35929i	0.0193714	+	0.109861i
$936$	0.0246691	−	0.139905i	0.000806334	−	0.00457295i
$937$	9.09770	+	51.5956i	0.297209	+	1.68556i	0.658087	+	0.752942i	$0.271366\pi$
$937$	9.09770	+	51.5956i	0.297209	+	1.68556i	−0.360878	+	0.932613i	$0.617523\pi$
$938$	6.01671	+	0.701069i	0.196452	+	0.0228907i
$939$	−5.01695	+	8.68961i	−0.163722	+	0.283575i
$940$	−1.45178	−	8.23346i	−0.0473519	−	0.268546i
$941$	−25.1035	+	21.0643i	−0.818349	+	0.686677i	−0.952585	−	0.304273i	$-0.901587\pi$
$941$	−25.1035	+	21.0643i	−0.818349	+	0.686677i	0.134236	+	0.990949i	$0.457142\pi$
$942$	1.56304	+	2.70726i	0.0509265	+	0.0882074i
$943$	17.7390	−	30.7249i	0.577662	−	1.00054i
$944$	0.763592	+	4.33054i	0.0248528	+	0.140947i
$945$	−5.05509	−	5.35424i	−0.164442	−	0.174174i
$946$	−26.9565	+	22.6192i	−0.876433	+	0.735414i
$947$	37.3091	−	13.5794i	1.21238	−	0.441271i	0.344854	−	0.938656i	$-0.387929\pi$
$947$	37.3091	−	13.5794i	1.21238	−	0.441271i	0.867530	+	0.497385i	$0.165706\pi$
$948$	−1.31979	+	7.48489i	−0.0428647	+	0.243098i
$949$	0.471374	−	0.816444i	0.0153014	−	0.0265029i
$950$	0.242089	−	11.9670i	0.00785439	−	0.388262i
$951$	−1.42353			−0.0461611
$952$	−0.425915	−	0.451120i	−0.0138040	−	0.0146209i
$953$	−4.55647	+	25.8410i	−0.147598	+	0.837072i	0.817646	+	0.575722i	$0.195279\pi$
$953$	−4.55647	+	25.8410i	−0.147598	+	0.837072i	−0.965244	+	0.261350i	$0.915832\pi$
$954$	9.03549	+	3.28865i	0.292535	+	0.106474i
$955$	−50.9211	+	18.5338i	−1.64777	+	0.599739i
$956$	−15.2283	−	5.54266i	−0.492520	−	0.179263i
$957$	−5.93715	+	10.2834i	−0.191921	+	0.332417i
$958$	10.4720	−	18.1381i	0.338336	−	0.586016i
$959$	−2.96051	−	50.5185i	−0.0955998	−	1.63133i
$960$	2.61532	+	0.951897i	0.0844090	+	0.0307223i
$961$	−0.726406			−0.0234325
$962$	0.500373			0.0161327
$963$	−8.31412	−	3.02609i	−0.267919	−	0.0975145i
$964$	−0.761011	+	4.31591i	−0.0245105	+	0.139006i
$965$	40.8270	−	34.2579i	1.31427	−	1.10280i
$966$	−4.66264	+	15.5946i	−0.150018	+	0.501749i
$967$	6.00221	−	2.18463i	0.193018	−	0.0702529i	−0.243702	−	0.969850i	$-0.578362\pi$
$967$	6.00221	−	2.18463i	0.193018	−	0.0702529i	0.436721	+	0.899597i	$0.356140\pi$
$968$	8.15910	+	14.1320i	0.262243	+	0.454219i
$969$	−1.00999	+	0.157097i	−0.0324456	+	0.00504667i
$970$	−12.3852	+	21.4518i	−0.397665	+	0.688776i
$971$	17.7959	+	14.9325i	0.571097	+	0.479208i	0.882010	−	0.471231i	$-0.156190\pi$
$971$	17.7959	+	14.9325i	0.571097	+	0.479208i	−0.310912	+	0.950439i	$0.600635\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	−1.41357	−	24.1214i	−0.0453171	−	0.773296i
$974$	−26.9040	−	22.5752i	−0.862060	−	0.723355i
$975$	−0.298837	+	0.250754i	−0.00957045	+	0.00803057i
$976$	6.96832			0.223050
$977$	−13.7436	−	23.8045i	−0.439695	−	0.761574i	0.557971	−	0.829861i	$-0.311580\pi$
$977$	−13.7436	−	23.8045i	−0.439695	−	0.761574i	−0.997666	+	0.0682864i	$0.978247\pi$
$978$	−3.28816	−	18.6481i	−0.105144	−	0.596300i
$979$	37.1557	+	13.5236i	1.18750	+	0.432215i
$980$	−18.9602	−	4.47932i	−0.605661	−	0.143087i
$981$	8.85079	+	15.3300i	0.282584	+	0.489450i
$982$	−0.429310	+	0.360234i	−0.0136998	+	0.0114955i
$983$	−34.0919	+	12.4084i	−1.08736	+	0.395767i	−0.822643	−	0.568559i	$-0.807501\pi$
$983$	−34.0919	+	12.4084i	−1.08736	+	0.395767i	−0.264718	+	0.964326i	$0.585279\pi$
$984$	1.00141	+	5.67927i	0.0319237	+	0.181048i
$985$	−9.78514	+	3.56150i	−0.311781	+	0.113479i
$986$	−0.500610	+	0.182207i	−0.0159427	+	0.00580266i
$987$	−4.74376	+	6.37674i	−0.150995	+	0.202974i
$988$	−0.607533	−	0.119842i	−0.0193282	−	0.00381269i
$989$	20.7096	+	35.8702i	0.658528	+	1.14060i
$990$	−2.52601	+	14.3257i	−0.0802818	+	0.455301i
$991$	−20.2083	−	16.9568i	−0.641938	−	0.538650i	0.262675	−	0.964884i	$-0.415395\pi$
$991$	−20.2083	−	16.9568i	−0.641938	−	0.538650i	−0.904613	+	0.426235i	$0.859840\pi$
$992$	5.17032	+	1.88184i	0.164158	+	0.0597486i
$993$	−7.10614	−	5.96276i	−0.225506	−	0.189222i
$994$	−2.18948	−	37.3616i	−0.0694462	−	1.18504i
$995$	11.2144	+	19.4239i	0.355520	+	0.615779i
$996$	10.6996			0.339029
$997$	−39.3986	+	33.0594i	−1.24777	+	1.04700i	−0.250891	+	0.968015i	$0.580724\pi$
$997$	−39.3986	+	33.0594i	−1.24777	+	1.04700i	−0.996876	+	0.0789858i	$0.974832\pi$
$998$	−14.0661	+	11.8028i	−0.445254	+	0.373612i
$999$	3.52217			0.111437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.a.613.1	yes	12
7.2	even	3		798.2.bq.c.499.2	yes	12
19.4	even	9		798.2.bq.c.403.2	yes	12
133.23	even	9	inner	798.2.bp.a.289.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.a.289.1	✓	12	133.23	even	9	inner
798.2.bp.a.613.1	yes	12	1.1	even	1	trivial
798.2.bq.c.403.2	yes	12	19.4	even	9
798.2.bq.c.499.2	yes	12	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.483291 + 2.74088i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(2.62797 + 0.306212i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.483291 + 2.74088i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(2.62797 + 0.306212i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(2.13203 - 1.78898i) q^{10} +(2.61334 + 4.52644i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.0246691 - 0.139905i) q^{13} +(-1.81631 - 1.92380i) q^{14} +(-2.13203 + 1.78898i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0407195 - 0.230932i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.73006 - 2.25535i) q^{19} -2.78316 q^{20} +(1.81631 + 1.92380i) q^{21} +(0.907604 - 5.14728i) q^{22} +(-5.78102 - 2.10412i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-2.58038 - 0.939182i) q^{25} +(-0.0710318 + 0.123031i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.154782 + 2.64122i) q^{28} +(2.13485 + 0.777023i) q^{29} +2.78316 q^{30} +5.50214 q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.907604 + 5.14728i) q^{33} +(-0.179633 + 0.150730i) q^{34} +(-2.10937 + 7.05496i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-1.76109 - 3.05029i) q^{37} +(1.40768 + 4.12534i) q^{38} +(0.0710318 - 0.123031i) q^{39} +(2.13203 + 1.78898i) q^{40} +(-1.00141 + 5.67927i) q^{41} +(-0.154782 - 2.64122i) q^{42} +(-5.15749 - 4.32764i) q^{43} +(-4.00387 + 3.35965i) q^{44} -2.78316 q^{45} +(3.07602 + 5.32782i) q^{46} +(0.521631 + 2.95831i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(6.81247 + 1.60943i) q^{49} +(1.37299 + 2.37809i) q^{50} +(0.179633 - 0.150730i) q^{51} +(0.133496 - 0.0485886i) q^{52} +(1.66969 + 9.46929i) q^{53} +(0.939693 - 0.342020i) q^{54} +(-13.6694 + 4.97526i) q^{55} +(1.57917 - 2.12278i) q^{56} +(-1.40768 - 4.12534i) q^{57} +(-1.13593 - 1.96749i) q^{58} +(0.763592 - 4.33054i) q^{59} +(-2.13203 - 1.78898i) q^{60} +(-6.54808 - 2.38330i) q^{61} +(-4.21489 - 3.53671i) q^{62} +(0.154782 + 2.64122i) q^{63} +(-0.500000 - 0.866025i) q^{64} +0.395386 q^{65} +(4.00387 - 3.35965i) q^{66} +(-1.75385 + 1.47165i) q^{67} +0.234494 q^{68} +(-3.07602 - 5.32782i) q^{69} +(6.15071 - 4.04854i) q^{70} +(10.8362 + 9.09261i) q^{71} +(0.939693 + 0.342020i) q^{72} +(5.08355 + 4.26560i) q^{73} +(-0.611619 + 3.46866i) q^{74} +(-1.37299 - 2.37809i) q^{75} +(1.57337 - 4.06503i) q^{76} +(5.48173 + 12.6956i) q^{77} +(-0.133496 + 0.0485886i) q^{78} +(7.14199 - 2.59947i) q^{79} +(-0.483291 - 2.74088i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(4.41768 - 3.70688i) q^{82} +(-5.34978 - 9.26609i) q^{83} +(-1.57917 + 2.12278i) q^{84} +(0.613276 + 0.223214i) q^{85} +(1.16911 + 6.63034i) q^{86} +(1.13593 + 1.96749i) q^{87} +5.22668 q^{88} +(5.79518 - 4.86273i) q^{89} +(2.13203 + 1.78898i) q^{90} +(-0.0219889 - 0.375221i) q^{91} +(1.06829 - 6.05857i) q^{92} +(4.21489 + 3.53671i) q^{93} +(1.50198 - 2.60150i) q^{94} +(7.98436 - 9.13366i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-8.36336 + 3.04401i) q^{97} +(-4.18413 - 5.61187i) q^{98} +(-4.00387 + 3.35965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 12 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^5 + 12 * q^7 + 6 * q^8	\( 12 q - 3 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{10} + 18 q^{11} - 6 q^{12} - 9 q^{13} - 9 q^{14} - 3 q^{15} + 6 q^{18} - 3 q^{19} + 18 q^{20} + 9 q^{21} + 18 q^{22} + 6 q^{23} - 21 q^{25} + 3 q^{26} - 6 q^{27} + 15 q^{28} - 3 q^{29} - 18 q^{30} - 18 q^{33} - 18 q^{34} + 12 q^{35} + 6 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} - 9 q^{41} - 15 q^{42} + 51 q^{43} + 18 q^{45} + 9 q^{46} - 30 q^{47} + 24 q^{49} + 21 q^{50} + 18 q^{51} - 9 q^{52} - 6 q^{53} + 9 q^{55} + 15 q^{56} + 3 q^{57} - 6 q^{59} - 3 q^{60} - 36 q^{61} + 18 q^{62} + 15 q^{63} - 6 q^{64} + 6 q^{65} - 15 q^{67} - 6 q^{68} - 9 q^{69} + 42 q^{70} - 3 q^{71} - 15 q^{73} + 27 q^{74} - 21 q^{75} - 9 q^{76} + 27 q^{77} + 9 q^{78} + 63 q^{79} - 3 q^{80} - 9 q^{82} - 24 q^{83} - 15 q^{84} - 60 q^{85} + 48 q^{86} + 36 q^{88} + 21 q^{89} + 3 q^{90} - 3 q^{91} - 12 q^{92} - 18 q^{93} + 6 q^{94} + 9 q^{95} + 6 q^{96} - 45 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 3 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^10 + 18 * q^11 - 6 * q^12 - 9 * q^13 - 9 * q^14 - 3 * q^15 + 6 * q^18 - 3 * q^19 + 18 * q^20 + 9 * q^21 + 18 * q^22 + 6 * q^23 - 21 * q^25 + 3 * q^26 - 6 * q^27 + 15 * q^28 - 3 * q^29 - 18 * q^30 - 18 * q^33 - 18 * q^34 + 12 * q^35 + 6 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 + 18 * q^45 + 9 * q^46 - 30 * q^47 + 24 * q^49 + 21 * q^50 + 18 * q^51 - 9 * q^52 - 6 * q^53 + 9 * q^55 + 15 * q^56 + 3 * q^57 - 6 * q^59 - 3 * q^60 - 36 * q^61 + 18 * q^62 + 15 * q^63 - 6 * q^64 + 6 * q^65 - 15 * q^67 - 6 * q^68 - 9 * q^69 + 42 * q^70 - 3 * q^71 - 15 * q^73 + 27 * q^74 - 21 * q^75 - 9 * q^76 + 27 * q^77 + 9 * q^78 + 63 * q^79 - 3 * q^80 - 9 * q^82 - 24 * q^83 - 15 * q^84 - 60 * q^85 + 48 * q^86 + 36 * q^88 + 21 * q^89 + 3 * q^90 - 3 * q^91 - 12 * q^92 - 18 * q^93 + 6 * q^94 + 9 * q^95 + 6 * q^96 - 45 * q^97 - 24 * q^98

Introduction

L-functions

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