LMFDB - Embedded newform 342.2.x.c.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	342.41
Dual form			342.2.x.c.317.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-1.71328 - 0.254334i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.343019 + 0.408794i) q^{5} +(-0.547977 + 1.64308i) q^{6} +(-1.00033 + 1.73262i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.87063 + 0.871489i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-1.71328 - 0.254334i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.343019 + 0.408794i) q^{5} +(-0.547977 + 1.64308i) q^{6} +(-1.00033 + 1.73262i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.87063 + 0.871489i) q^{9} +(0.343019 + 0.408794i) q^{10} +2.45964i q^{11} +(1.52297 + 0.824971i) q^{12} +(1.28006 + 1.52552i) q^{13} +(1.53259 + 1.28600i) q^{14} +(0.691657 - 0.613136i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.87798 - 2.23809i) q^{17} +(1.35673 - 2.67568i) q^{18} +(1.97124 + 3.88770i) q^{19} +(0.462148 - 0.266822i) q^{20} +(2.15450 - 2.71403i) q^{21} +(2.42227 + 0.427112i) q^{22} +(0.114448 - 0.314444i) q^{23} +(1.07690 - 1.35657i) q^{24} +(0.818790 + 4.64359i) q^{25} +(1.72463 - 0.995713i) q^{26} +(-4.69653 - 2.22320i) q^{27} +(1.53259 - 1.28600i) q^{28} +(1.12239 + 0.408515i) q^{29} +(-0.483716 - 0.787619i) q^{30} +5.49459i q^{31} +(0.766044 - 0.642788i) q^{32} +(0.625570 - 4.21404i) q^{33} +(-1.87798 - 2.23809i) q^{34} +(-0.365153 - 1.00325i) q^{35} +(-2.39944 - 1.80074i) q^{36} +0.913995i q^{37} +(4.17094 - 1.26621i) q^{38} +(-1.80511 - 2.93920i) q^{39} +(-0.182517 - 0.501460i) q^{40} +(0.292432 - 1.65846i) q^{41} +(-2.29868 - 2.59305i) q^{42} +(-3.78464 + 1.37750i) q^{43} +(0.841246 - 2.31130i) q^{44} +(-1.34094 + 0.874559i) q^{45} +(-0.289793 - 0.167312i) q^{46} +(-3.21923 + 8.84477i) q^{47} +(-1.14896 - 1.29610i) q^{48} +(1.49869 + 2.59581i) q^{49} +4.71523 q^{50} +(-3.78672 + 3.35683i) q^{51} +(-0.681108 - 1.87133i) q^{52} +(-1.97722 - 11.2134i) q^{53} +(-3.00497 + 4.23912i) q^{54} +(-1.00549 - 0.843703i) q^{55} +(-1.00033 - 1.73262i) q^{56} +(-2.38851 - 7.16205i) q^{57} +(0.597209 - 1.03440i) q^{58} +(0.0205717 - 0.00748749i) q^{59} +(-0.859650 + 0.339599i) q^{60} +(-10.5246 + 8.83119i) q^{61} +(5.41111 + 0.954125i) q^{62} +(-4.38152 + 4.10193i) q^{63} +(-0.500000 - 0.866025i) q^{64} -1.06271 q^{65} +(-4.04139 - 1.34783i) q^{66} +(-4.50583 + 0.794499i) q^{67} +(-2.53019 + 1.46081i) q^{68} +(-0.276055 + 0.509621i) q^{69} +(-1.05142 + 0.185393i) q^{70} +(1.63492 - 9.27209i) q^{71} +(-2.19005 + 2.05029i) q^{72} +(8.22297 - 2.99292i) q^{73} +(0.900109 + 0.158714i) q^{74} +(-0.221791 - 8.16400i) q^{75} +(-0.522693 - 4.32745i) q^{76} +(-4.26161 - 2.46044i) q^{77} +(-3.20800 + 1.26730i) q^{78} +(-0.293366 + 0.349620i) q^{79} +(-0.525536 + 0.0926662i) q^{80} +(7.48102 + 5.00344i) q^{81} +(-1.58249 - 0.575979i) q^{82} +(-3.14484 - 1.81567i) q^{83} +(-2.95282 + 1.81348i) q^{84} +(0.270735 + 1.53541i) q^{85} +(0.699373 + 3.96634i) q^{86} +(-1.81906 - 0.985360i) q^{87} +(-2.13011 - 1.22982i) q^{88} +(2.47214 + 0.899785i) q^{89} +(0.628421 + 1.47243i) q^{90} +(-3.92363 + 0.691841i) q^{91} +(-0.215092 + 0.256337i) q^{92} +(1.39746 - 9.41375i) q^{93} +(8.15139 + 4.70620i) q^{94} +(-2.26544 - 0.527721i) q^{95} +(-1.47593 + 0.906441i) q^{96} +(-0.211218 - 0.0372434i) q^{97} +(2.81662 - 1.02517i) q^{98} +(-2.14355 + 7.06071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−1.71328	−	0.254334i	−0.989160	−	0.146840i
$3$	−1.71328	−	0.254334i	−0.989160	−	0.146840i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.343019	+	0.408794i	−0.153403	+	0.182818i	−0.837273	−	0.546786i	$-0.815851\pi$
$5$	−0.343019	+	0.408794i	−0.153403	+	0.182818i	0.683870	+	0.729604i	$0.260296\pi$
$6$	−0.547977	+	1.64308i	−0.223711	+	0.670786i
$7$	−1.00033	+	1.73262i	−0.378088	+	0.654868i	−0.990784	−	0.135451i	$-0.956752\pi$
$7$	−1.00033	+	1.73262i	−0.378088	+	0.654868i	0.612696	+	0.790319i	$0.290085\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.87063	+	0.871489i	0.956876	+	0.290496i
$10$	0.343019	+	0.408794i	0.108472	+	0.129272i
$11$			2.45964i			0.741609i	0.928711	+	0.370804i	$0.120918\pi$
$11$			2.45964i			0.741609i	−0.928711	+	0.370804i	$0.879082\pi$
$12$	1.52297	+	0.824971i	0.439642	+	0.238149i
$13$	1.28006	+	1.52552i	0.355026	+	0.423103i	0.913767	−	0.406239i	$-0.133160\pi$
$13$	1.28006	+	1.52552i	0.355026	+	0.423103i	−0.558741	+	0.829342i	$0.688715\pi$
$14$	1.53259	+	1.28600i	0.409602	+	0.343697i
$15$	0.691657	−	0.613136i	0.178585	−	0.158311i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.87798	−	2.23809i	0.455476	−	0.542816i	−0.488615	−	0.872500i	$-0.662498\pi$
$17$	1.87798	−	2.23809i	0.455476	−	0.542816i	0.944091	+	0.329684i	$0.106942\pi$
$18$	1.35673	−	2.67568i	0.319784	−	0.630665i
$19$	1.97124	+	3.88770i	0.452234	+	0.891899i
$19$	1.97124	+	3.88770i	0.452234	+	0.891899i
$20$	0.462148	−	0.266822i	0.103340	−	0.0596631i
$21$	2.15450	−	2.71403i	0.470150	−	0.592251i
$22$	2.42227	+	0.427112i	0.516430	+	0.0910605i
$23$	0.114448	−	0.314444i	0.0238641	−	0.0655661i	−0.927189	−	0.374595i	$-0.877782\pi$
$23$	0.114448	−	0.314444i	0.0238641	−	0.0655661i	0.951053	+	0.309029i	$0.100004\pi$
$24$	1.07690	−	1.35657i	0.219821	−	0.276909i
$25$	0.818790	+	4.64359i	0.163758	+	0.928718i
$26$	1.72463	−	0.995713i	0.338227	−	0.195275i
$27$	−4.69653	−	2.22320i	−0.903847	−	0.427855i
$28$	1.53259	−	1.28600i	0.289632	−	0.243030i
$29$	1.12239	+	0.408515i	0.208422	+	0.0758593i	0.444121	−	0.895967i	$-0.353516\pi$
$29$	1.12239	+	0.408515i	0.208422	+	0.0758593i	−0.235700	+	0.971826i	$0.575738\pi$
$30$	−0.483716	−	0.787619i	−0.0883141	−	0.143799i
$31$			5.49459i			0.986857i	0.869786	+	0.493429i	$0.164257\pi$
$31$			5.49459i			0.986857i	−0.869786	+	0.493429i	$0.835743\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	0.625570	−	4.21404i	0.108898	−	0.733570i
$34$	−1.87798	−	2.23809i	−0.322070	−	0.383829i
$35$	−0.365153	−	1.00325i	−0.0617221	−	0.169580i
$36$	−2.39944	−	1.80074i	−0.399907	−	0.300124i
$37$			0.913995i			0.150260i	0.997174	+	0.0751299i	$0.0239372\pi$
$37$			0.913995i			0.150260i	−0.997174	+	0.0751299i	$0.976063\pi$
$38$	4.17094	−	1.26621i	0.676616	−	0.205406i
$39$	−1.80511	−	2.93920i	−0.289049	−	0.470649i
$40$	−0.182517	−	0.501460i	−0.0288584	−	0.0792879i
$41$	0.292432	−	1.65846i	0.0456702	−	0.259009i	−0.953420	−	0.301645i	$-0.902464\pi$
$41$	0.292432	−	1.65846i	0.0456702	−	0.259009i	0.999091	+	0.0426359i	$0.0135755\pi$
$42$	−2.29868	−	2.59305i	−0.354693	−	0.400117i
$43$	−3.78464	+	1.37750i	−0.577152	+	0.210066i	−0.614069	−	0.789252i	$-0.710469\pi$
$43$	−3.78464	+	1.37750i	−0.577152	+	0.210066i	0.0369170	+	0.999318i	$0.488246\pi$
$44$	0.841246	−	2.31130i	0.126823	−	0.348442i
$45$	−1.34094	+	0.874559i	−0.199896	+	0.130372i
$46$	−0.289793	−	0.167312i	−0.0427276	−	0.0246688i
$47$	−3.21923	+	8.84477i	−0.469573	+	1.29014i	0.448518	+	0.893774i	$0.351952\pi$
$47$	−3.21923	+	8.84477i	−0.469573	+	1.29014i	−0.918091	+	0.396369i	$0.870270\pi$
$48$	−1.14896	−	1.29610i	−0.165838	−	0.187076i
$49$	1.49869	+	2.59581i	0.214099	+	0.370830i
$50$	4.71523			0.666834
$51$	−3.78672	+	3.35683i	−0.530246	+	0.470050i
$52$	−0.681108	−	1.87133i	−0.0944527	−	0.259507i
$53$	−1.97722	−	11.2134i	−0.271593	−	1.54028i	−0.749581	−	0.661912i	$-0.769745\pi$
$53$	−1.97722	−	11.2134i	−0.271593	−	1.54028i	0.477989	−	0.878366i	$-0.341366\pi$
$54$	−3.00497	+	4.23912i	−0.408924	+	0.576872i
$55$	−1.00549	−	0.843703i	−0.135580	−	0.113765i
$56$	−1.00033	−	1.73262i	−0.133674	−	0.231531i
$57$	−2.38851	−	7.16205i	−0.316366	−	0.948637i
$58$	0.597209	−	1.03440i	0.0784174	−	0.135823i
$59$	0.0205717	−	0.00748749i	0.00267821	−	0.000974789i	−0.340681	−	0.940179i	$-0.610658\pi$
$59$	0.0205717	−	0.00748749i	0.00267821	−	0.000974789i	0.343359	+	0.939204i	$0.388435\pi$
$60$	−0.859650	+	0.339599i	−0.110980	+	0.0438420i
$61$	−10.5246	+	8.83119i	−1.34754	+	1.13072i	−0.367918	+	0.929858i	$0.619929\pi$
$61$	−10.5246	+	8.83119i	−1.34754	+	1.13072i	−0.979620	+	0.200860i	$0.935626\pi$
$62$	5.41111	+	0.954125i	0.687212	+	0.121174i
$63$	−4.38152	+	4.10193i	−0.552020	+	0.516794i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.06271			−0.131813
$66$	−4.04139	−	1.34783i	−0.497461	−	0.165906i
$67$	−4.50583	+	0.794499i	−0.550474	+	0.0970634i	−0.441965	−	0.897032i	$-0.645719\pi$
$67$	−4.50583	+	0.794499i	−0.550474	+	0.0970634i	−0.108509	+	0.994096i	$0.534608\pi$
$68$	−2.53019	+	1.46081i	−0.306831	+	0.177149i
$69$	−0.276055	+	0.509621i	−0.0332331	+	0.0613511i
$70$	−1.05142	+	0.185393i	−0.125668	+	0.0221587i
$71$	1.63492	−	9.27209i	0.194029	−	1.10039i	−0.719765	−	0.694218i	$-0.755750\pi$
$71$	1.63492	−	9.27209i	0.194029	−	1.10039i	0.913794	−	0.406177i	$-0.133138\pi$
$72$	−2.19005	+	2.05029i	−0.258099	+	0.241629i
$73$	8.22297	−	2.99292i	0.962426	−	0.350295i	0.187443	−	0.982276i	$-0.439980\pi$
$73$	8.22297	−	2.99292i	0.962426	−	0.350295i	0.774984	+	0.631981i	$0.217758\pi$
$74$	0.900109	+	0.158714i	0.104636	+	0.0184501i
$75$	−0.221791	−	8.16400i	−0.0256102	−	0.942697i
$76$	−0.522693	−	4.32745i	−0.0599570	−	0.496392i
$77$	−4.26161	−	2.46044i	−0.485656	−	0.280393i
$78$	−3.20800	+	1.26730i	−0.363235	+	0.143494i
$79$	−0.293366	+	0.349620i	−0.0330062	+	0.0393353i	−0.782295	−	0.622908i	$-0.785951\pi$
$79$	−0.293366	+	0.349620i	−0.0330062	+	0.0393353i	0.749289	+	0.662243i	$0.230396\pi$
$80$	−0.525536	+	0.0926662i	−0.0587567	+	0.0103604i
$81$	7.48102	+	5.00344i	0.831224	+	0.555938i
$82$	−1.58249	−	0.575979i	−0.174757	−	0.0636062i
$83$	−3.14484	−	1.81567i	−0.345191	−	0.199296i	0.317374	−	0.948300i	$-0.397199\pi$
$83$	−3.14484	−	1.81567i	−0.345191	−	0.199296i	−0.662565	+	0.749004i	$0.730532\pi$
$84$	−2.95282	+	1.81348i	−0.322179	+	0.197866i
$85$	0.270735	+	1.53541i	0.0293653	+	0.166539i
$86$	0.699373	+	3.96634i	0.0754154	+	0.427702i
$87$	−1.81906	−	0.985360i	−0.195023	−	0.105642i
$88$	−2.13011	−	1.22982i	−0.227070	−	0.131099i
$89$	2.47214	+	0.899785i	0.262046	+	0.0953770i	0.469702	−	0.882825i	$-0.344361\pi$
$89$	2.47214	+	0.899785i	0.262046	+	0.0953770i	−0.207656	+	0.978202i	$0.566583\pi$
$90$	0.628421	+	1.47243i	0.0662414	+	0.155208i
$91$	−3.92363	+	0.691841i	−0.411308	+	0.0725247i
$92$	−0.215092	+	0.256337i	−0.0224249	+	0.0267250i
$93$	1.39746	−	9.41375i	0.144910	−	0.976160i
$94$	8.15139	+	4.70620i	0.840751	+	0.485408i
$95$	−2.26544	−	0.527721i	−0.232430	−	0.0541431i
$96$	−1.47593	+	0.906441i	−0.150636	+	0.0925133i
$97$	−0.211218	−	0.0372434i	−0.0214459	−	0.00378150i	0.162915	−	0.986640i	$-0.447910\pi$
$97$	−0.211218	−	0.0372434i	−0.0214459	−	0.00378150i	−0.184361	+	0.982859i	$0.559022\pi$
$98$	2.81662	−	1.02517i	0.284522	−	0.103557i
$99$	−2.14355	+	7.06071i	−0.215435	+	0.709628i
$100$	0.818790	−	4.64359i	0.0818790	−	0.464359i
$101$	−0.517453	+	0.0912410i	−0.0514885	+	0.00907882i	−0.199333	−	0.979932i	$-0.563878\pi$
$101$	−0.517453	+	0.0912410i	−0.0514885	+	0.00907882i	0.147845	+	0.989011i	$0.452766\pi$
$102$	2.64827	+	4.31209i	0.262218	+	0.426961i
$103$	1.35195	−	0.780549i	0.133212	−	0.0769098i	−0.431913	−	0.901915i	$-0.642161\pi$
$103$	1.35195	−	0.780549i	0.133212	−	0.0769098i	0.565125	+	0.825005i	$0.308828\pi$
$104$	−1.96117	+	0.345808i	−0.192309	+	0.0339092i
$105$	0.370447	+	1.81171i	0.0361519	+	0.176805i
$106$	−11.3864			−1.10594
$107$	9.40358	+	16.2875i	0.909078	+	1.57457i	0.815347	+	0.578972i	$0.196546\pi$
$107$	9.40358	+	16.2875i	0.909078	+	1.57457i	0.0937310	+	0.995598i	$0.470121\pi$
$108$	3.65291	+	3.69543i	0.351502	+	0.355593i
$109$	1.84880	+	0.325993i	0.177083	+	0.0312245i	0.261486	−	0.965207i	$-0.415787\pi$
$109$	1.84880	+	0.325993i	0.177083	+	0.0312245i	−0.0844035	+	0.996432i	$0.526898\pi$
$110$	−1.00549	+	0.843703i	−0.0958694	+	0.0804439i
$111$	0.232460	−	1.56593i	0.0220641	−	0.148631i
$112$	−1.88000	+	0.684264i	−0.177643	+	0.0646569i
$113$	5.94010	−	10.2885i	0.558797	−	0.967865i	−0.438800	−	0.898585i	$-0.644596\pi$
$113$	5.94010	−	10.2885i	0.558797	−	0.967865i	0.997597	−	0.0692805i	$-0.0220703\pi$
$114$	−7.46801	+	1.10855i	−0.699443	+	0.103825i
$115$	0.0892849	+	0.154646i	0.00832586	+	0.0144208i
$116$	−0.914977	−	0.767757i	−0.0849535	−	0.0712844i
$117$	2.34511	+	5.49477i	0.216806	+	0.507991i
$118$	−0.00380150	−	0.0215594i	−0.000349956	−	0.00198470i
$119$	1.99916	+	5.49263i	0.183262	+	0.503509i
$120$	0.185163	+	0.905560i	0.0169030	+	0.0826660i
$121$	4.95018			0.450016
$122$	6.86945	+	11.8982i	0.621931	+	1.07722i
$123$	−0.922821	+	2.76703i	−0.0832079	+	0.249495i
$124$	1.87926	−	5.16322i	0.168763	−	0.463671i
$125$	−4.48988	−	2.59223i	−0.401587	−	0.231856i
$126$	3.27876	+	5.02725i	0.292096	+	0.447863i
$127$	7.55928	−	20.7689i	0.670778	−	1.84295i	0.151243	−	0.988497i	$-0.451672\pi$
$127$	7.55928	−	20.7689i	0.670778	−	1.84295i	0.519535	−	0.854449i	$-0.326105\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	6.83448	−	1.39747i	0.601742	−	0.123040i
$130$	−0.184538	+	1.04657i	−0.0161850	+	0.0917899i
$131$	−3.32590	−	9.13783i	−0.290585	−	0.798376i	−0.995981	−	0.0895625i	$-0.971453\pi$
$131$	−3.32590	−	9.13783i	−0.290585	−	0.798376i	0.705396	−	0.708813i	$-0.250769\pi$
$132$	−2.02913	+	3.74594i	−0.176613	+	0.326043i
$133$	−8.70778	−	0.473557i	−0.755060	−	0.0410626i
$134$			4.57533i			0.395249i
$135$	2.51983	−	1.15731i	0.216873	−	0.0996058i
$136$	0.999251	+	2.74542i	0.0856851	+	0.235418i
$137$	1.22275	+	1.45721i	0.104466	+	0.124498i	0.815744	−	0.578413i	$-0.196328\pi$
$137$	1.22275	+	1.45721i	0.104466	+	0.124498i	−0.711278	+	0.702911i	$0.751883\pi$
$138$	0.453942	+	0.360356i	0.0386421	+	0.0306755i
$139$	−10.8768	+	9.12671i	−0.922557	+	0.774118i	−0.974466	−	0.224534i	$-0.927914\pi$
$139$	−10.8768	+	9.12671i	−0.922557	+	0.774118i	0.0519088	+	0.998652i	$0.483469\pi$
$140$			1.06764i			0.0902316i
$141$	7.76496	−	14.3348i	0.653928	−	1.20721i
$142$	−8.84733	−	3.22016i	−0.742451	−	0.270230i
$143$	−3.75223	+	3.14850i	−0.313777	+	0.263290i
$144$	1.63885	+	2.51280i	0.136571	+	0.209400i
$145$	−0.551998	+	0.318696i	−0.0458410	+	0.0264663i
$146$	−1.51954	−	8.61776i	−0.125758	−	0.713211i
$147$	−1.90747	−	4.82851i	−0.157326	−	0.398249i
$148$	0.312605	−	0.858874i	0.0256959	−	0.0705990i
$149$	17.0236	+	3.00171i	1.39462	+	0.245910i	0.819932	−	0.572460i	$-0.194011\pi$
$149$	17.0236	+	3.00171i	1.39462	+	0.245910i	0.574691	+	0.818370i	$0.305122\pi$
$150$	−8.07848	−	1.19924i	−0.659605	−	0.0979177i
$151$	13.9240	−	8.03903i	1.13312	−	0.654207i	0.188402	−	0.982092i	$-0.439669\pi$
$151$	13.9240	−	8.03903i	1.13312	−	0.654207i	0.944718	+	0.327885i	$0.106336\pi$
$152$	−4.35247	−	0.236701i	−0.353032	−	0.0191990i
$153$	7.34144	−	4.78808i	0.593520	−	0.387093i
$154$	−3.16308	+	3.76962i	−0.254889	+	0.303764i
$155$	−2.24616	−	1.88475i	−0.180416	−	0.151387i
$156$	0.690983	+	3.37933i	0.0553229	+	0.270563i
$157$	−2.47857	−	2.07976i	−0.197811	−	0.165983i	0.538502	−	0.842624i	$-0.318990\pi$
$157$	−2.47857	−	2.07976i	−0.197811	−	0.165983i	−0.736313	+	0.676641i	$0.763435\pi$
$158$	0.293366	+	0.349620i	0.0233389	+	0.0278143i
$159$	0.535582	+	19.7145i	0.0424744	+	1.56346i
$160$			0.533643i			0.0421882i
$161$	0.430325	+	0.512841i	0.0339144	+	0.0404176i
$162$	6.22649	−	6.49852i	0.489199	−	0.510572i
$163$	11.5699	−	20.0396i	0.906221	−	1.56962i	0.0869516	−	0.996213i	$-0.472287\pi$
$163$	11.5699	−	20.0396i	0.906221	−	1.56962i	0.819270	−	0.573409i	$-0.194379\pi$
$164$	−0.842024	+	1.45843i	−0.0657511	+	0.113884i
$165$	1.50809	+	1.70123i	0.117405	+	0.132440i
$166$	−2.33419	+	2.78177i	−0.181168	+	0.215908i
$167$	−13.6856	−	4.98117i	−1.05903	−	0.385454i	−0.246964	−	0.969025i	$-0.579433\pi$
$167$	−13.6856	−	4.98117i	−1.05903	−	0.385454i	−0.812063	+	0.583570i	$0.801655\pi$
$168$	1.27317	+	3.22287i	0.0982274	+	0.248650i
$169$	1.56878	−	8.89697i	0.120675	−	0.684382i
$170$	1.55910			0.119577
$171$	2.27063	+	12.8781i	0.173639	+	0.984809i
$172$	4.02753			0.307096
$173$	0.689253	−	3.90895i	0.0524029	−	0.297192i	−0.947331	−	0.320256i	$-0.896231\pi$
$173$	0.689253	−	3.90895i	0.0524029	−	0.297192i	0.999734	+	0.0230642i	$0.00734221\pi$
$174$	−1.28627	+	1.62032i	−0.0975115	+	0.122836i
$175$	−8.86462	−	3.22646i	−0.670102	−	0.243897i
$176$	−1.58103	+	1.88419i	−0.119174	+	0.142026i
$177$	−0.0371494	+	0.00759605i	−0.00279232	+	0.000570954i
$178$	1.31540	−	2.27833i	0.0985932	−	0.170768i
$179$	−9.82552	+	17.0183i	−0.734394	+	1.27201i	0.220594	+	0.975366i	$0.429200\pi$
$179$	−9.82552	+	17.0183i	−0.734394	+	1.27201i	−0.954989	+	0.296642i	$0.904133\pi$
$180$	1.55919	−	0.363188i	0.116215	−	0.0270705i
$181$	7.09287	+	8.45295i	0.527209	+	0.628303i	0.962270	−	0.272098i	$-0.0877175\pi$
$181$	7.09287	+	8.45295i	0.527209	+	0.628303i	−0.435061	+	0.900401i	$0.643273\pi$
$182$			3.98415i			0.295325i
$183$	20.2776	−	12.4535i	1.49897	−	0.920590i
$184$	0.215092	+	0.256337i	0.0158568	+	0.0188974i
$185$	−0.373636	−	0.313518i	−0.0274703	−	0.0230503i
$186$	−9.02806	−	3.01091i	−0.661970	−	0.220771i
$187$	5.50488	+	4.61915i	0.402557	+	0.337785i
$188$	6.05018	−	7.21032i	0.441255	−	0.525867i
$189$	8.55002	−	5.91336i	0.621922	−	0.430134i
$190$	−0.913094	+	2.13939i	−0.0662428	+	0.155208i
$191$	10.7713	−	6.21884i	0.779387	−	0.449979i	−0.0568259	−	0.998384i	$-0.518098\pi$
$191$	10.7713	−	6.21884i	0.779387	−	0.449979i	0.836213	+	0.548405i	$0.184765\pi$
$192$	0.636378	+	1.61091i	0.0459266	+	0.116257i
$193$	24.4917	+	4.31854i	1.76295	+	0.310856i	0.958908	−	0.283718i	$-0.0915678\pi$
$193$	24.4917	+	4.31854i	1.76295	+	0.310856i	0.804042	+	0.594573i	$0.202679\pi$
$194$	−0.0733552	+	0.201542i	−0.00526660	+	0.0144699i
$195$	1.82072	+	0.270284i	0.130384	+	0.0193554i
$196$	−0.520490	−	2.95185i	−0.0371779	−	0.210846i
$197$	−19.5104	+	11.2644i	−1.39006	+	0.802552i	−0.993322	−	0.115379i	$-0.963192\pi$
$197$	−19.5104	+	11.2644i	−1.39006	+	0.802552i	−0.396739	+	0.917931i	$0.629858\pi$
$198$	6.58122	+	3.33706i	0.467707	+	0.237155i
$199$	−3.57737	+	3.00177i	−0.253593	+	0.212790i	−0.760718	−	0.649083i	$-0.775153\pi$
$199$	−3.57737	+	3.00177i	−0.253593	+	0.212790i	0.507125	+	0.861873i	$0.330708\pi$
$200$	−4.43086	−	1.61270i	−0.313309	−	0.114035i
$201$	7.92179	−	0.215211i	0.558760	−	0.0151798i
$202$			0.525436i			0.0369695i
$203$	−1.83055	+	1.53602i	−0.128480	+	0.107807i
$204$	4.70645	−	1.85925i	0.329517	−	0.130174i
$205$	0.577661	+	0.688430i	0.0403456	+	0.0480820i
$206$	−0.533927	−	1.46695i	−0.0372005	−	0.102207i
$207$	0.602572	−	0.802911i	0.0418817	−	0.0558062i
$208$			1.99143i			0.138081i
$209$	−9.56233	+	4.84855i	−0.661440	+	0.335381i
$210$	1.84852	−	0.0502185i	0.127560	−	0.00346540i
$211$	2.47804	+	6.80835i	0.170595	+	0.468706i	0.995298	−	0.0968599i	$-0.0308799\pi$
$211$	2.47804	+	6.80835i	0.170595	+	0.468706i	−0.824703	+	0.565566i	$0.808658\pi$
$212$	−1.97722	+	11.2134i	−0.135796	+	0.770139i
$213$	−5.15928	+	15.4698i	−0.353508	+	1.05998i
$214$	17.6729	−	6.43243i	1.20810	−	0.439712i
$215$	0.735092	−	2.01965i	0.0501328	−	0.137739i
$216$	4.27361	−	2.95571i	0.290782	−	0.201111i
$217$	−9.52002	−	5.49638i	−0.646261	−	0.373119i
$218$	0.642081	−	1.76410i	0.0434872	−	0.119480i
$219$	−14.8494	+	3.03631i	−1.00343	+	0.205175i
$220$	0.656285	+	1.13672i	0.0442467	+	0.0766375i
$221$	5.81818			0.391373
$222$	−1.50177	−	0.500849i	−0.100792	−	0.0336148i
$223$	−3.31112	−	9.09723i	−0.221729	−	0.609196i	0.778091	−	0.628151i	$-0.216188\pi$
$223$	−3.31112	−	9.09723i	−0.221729	−	0.609196i	−0.999820	+	0.0189556i	$0.993966\pi$
$224$	0.347410	+	1.97026i	0.0232123	+	0.131643i
$225$	−1.69639	+	14.0436i	−0.113093	+	0.936239i
$226$	−9.10076	−	7.63644i	−0.605373	−	0.507968i
$227$	1.41008	+	2.44233i	0.0935902	+	0.162103i	0.909019	−	0.416754i	$-0.136832\pi$
$227$	1.41008	+	2.44233i	0.0935902	+	0.162103i	−0.815429	+	0.578857i	$0.803499\pi$
$228$	−0.205100	+	7.54705i	−0.0135831	+	0.499815i
$229$	−6.47630	+	11.2173i	−0.427966	+	0.741259i	−0.996692	−	0.0812678i	$-0.974103\pi$
$229$	−6.47630	+	11.2173i	−0.427966	+	0.741259i	0.568726	+	0.822527i	$0.307436\pi$
$230$	0.167801	−	0.0610745i	0.0110645	−	0.00402713i
$231$	6.67554	+	5.29929i	0.439218	+	0.348668i
$232$	−0.914977	+	0.767757i	−0.0600712	+	0.0504057i
$233$	−27.4801	−	4.84549i	−1.80028	−	0.317439i	−0.829702	−	0.558207i	$-0.811489\pi$
$233$	−27.4801	−	4.84549i	−1.80028	−	0.317439i	−0.970583	+	0.240768i	$0.922601\pi$
$234$	5.81851	−	1.35533i	0.380368	−	0.0886007i
$235$	−2.51143	−	4.34993i	−0.163828	−	0.283758i
$236$	−0.0218920			−0.00142505
$237$	0.591537	−	0.524382i	0.0384244	−	0.0340623i
$238$	5.75634	−	1.01500i	0.373128	−	0.0657925i
$239$	12.2664	−	7.08201i	0.793447	−	0.458097i	−0.0477276	−	0.998860i	$-0.515198\pi$
$239$	12.2664	−	7.08201i	0.793447	−	0.458097i	0.841175	+	0.540763i	$0.181865\pi$
$240$	0.923956	−	0.0251010i	0.0596411	−	0.00162026i
$241$	15.9636	−	2.81482i	1.02831	−	0.181318i	0.366051	−	0.930595i	$-0.380710\pi$
$241$	15.9636	−	2.81482i	1.02831	−	0.181318i	0.662257	+	0.749276i	$0.269599\pi$
$242$	0.859589	−	4.87497i	0.0552565	−	0.313375i
$243$	−11.5445	−	10.4750i	−0.740580	−	0.671968i
$244$	12.9103	−	4.69898i	0.826500	−	0.300821i
$245$	−1.57523	−	0.277756i	−0.100638	−	0.0177452i
$246$	2.56475	+	1.38929i	0.163522	+	0.0885780i
$247$	−3.40745	+	7.98368i	−0.216811	+	0.507989i
$248$	−4.75845	−	2.74729i	−0.302162	−	0.174453i
$249$	4.92619	+	3.91059i	0.312185	+	0.247824i
$250$	−3.33251	+	3.97153i	−0.210766	+	0.251182i
$251$	4.75379	−	0.838222i	0.300057	−	0.0529081i	−0.0215929	−	0.999767i	$-0.506874\pi$
$251$	4.75379	−	0.838222i	0.300057	−	0.0529081i	0.321650	+	0.946859i	$0.395763\pi$
$252$	5.52023	−	2.35598i	0.347742	−	0.148413i
$253$	0.773418	+	0.281501i	0.0486244	+	0.0176978i
$254$	−19.1408	−	11.0509i	−1.20100	−	0.693397i
$255$	−0.0733355	−	2.69944i	−0.00459245	−	0.169046i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	3.00106	+	17.0198i	0.187201	+	1.06167i	0.923095	+	0.384572i	$0.125651\pi$
$257$	3.00106	+	17.0198i	0.187201	+	1.06167i	−0.735894	+	0.677096i	$0.763238\pi$
$258$	−0.189443	−	6.97332i	−0.0117942	−	0.434140i
$259$	−1.58360	−	0.914294i	−0.0984003	−	0.0568114i
$260$	0.998622	+	0.363469i	0.0619319	+	0.0225414i
$261$	2.86594	+	2.15084i	0.177397	+	0.133134i
$262$	−9.57654	+	1.68860i	−0.591641	+	0.104322i
$263$	5.13228	−	6.11641i	0.316470	−	0.377154i	−0.584236	−	0.811584i	$-0.698606\pi$
$263$	5.13228	−	6.11641i	0.316470	−	0.377154i	0.900706	+	0.434430i	$0.143050\pi$
$264$	3.33668	+	2.64878i	0.205358	+	0.163021i
$265$	5.26220	+	3.03813i	0.323254	+	0.186631i
$266$	−1.97845	+	8.49326i	−0.121307	+	0.520755i
$267$	−4.00661	−	2.17033i	−0.245200	−	0.132822i
$268$	4.50583	+	0.794499i	0.275237	+	0.0485317i
$269$	−15.6170	+	5.68413i	−0.952187	+	0.346568i	−0.770967	−	0.636875i	$-0.780227\pi$
$269$	−15.6170	+	5.68413i	−0.952187	+	0.346568i	−0.181220	+	0.983443i	$0.558004\pi$
$270$	−0.702168	−	2.68251i	−0.0427326	−	0.163253i
$271$	−2.29134	+	12.9948i	−0.139189	+	0.789379i	0.832662	+	0.553781i	$0.186816\pi$
$271$	−2.29134	+	12.9948i	−0.139189	+	0.789379i	−0.971851	+	0.235597i	$0.924295\pi$
$272$	2.87723	−	0.507333i	0.174458	−	0.0307616i
$273$	6.89821	−	0.187403i	0.417499	−	0.0113422i
$274$	1.64740	−	0.951129i	0.0995233	−	0.0574598i
$275$	−11.4216	+	2.01393i	−0.688746	+	0.121444i
$276$	0.433707	−	0.384471i	0.0261061	−	0.0231424i
$277$	−20.9485			−1.25868			−0.629338	−	0.777132i	$-0.716674\pi$
$277$	−20.9485			−1.25868			−0.629338	+	0.777132i	$0.716674\pi$
$278$	7.09932	+	12.2964i	0.425789	+	0.737488i
$279$	−4.78847	+	15.7729i	−0.286678	+	0.944300i
$280$	1.05142	+	0.185393i	0.0628341	+	0.0110793i
$281$	1.31679	−	1.10492i	0.0785531	−	0.0659138i	−0.602666	−	0.797994i	$-0.705895\pi$
$281$	1.31679	−	1.10492i	0.0785531	−	0.0659138i	0.681219	+	0.732080i	$0.261450\pi$
$282$	−12.7686	−	10.1362i	−0.760361	−	0.603602i
$283$	16.5957	−	6.04033i	0.986510	−	0.359060i	0.202142	−	0.979356i	$-0.435210\pi$
$283$	16.5957	−	6.04033i	0.986510	−	0.359060i	0.784368	+	0.620296i	$0.212987\pi$
$284$	−4.70756	+	8.15374i	−0.279343	+	0.483836i
$285$	3.74711	+	1.48031i	0.221960	+	0.0876861i
$286$	2.44909	+	4.24196i	0.144818	+	0.250832i
$287$	2.58096	+	2.16568i	0.152349	+	0.127836i
$288$	2.75921	−	1.17761i	0.162588	−	0.0693911i
$289$	1.46979	+	8.33558i	0.0864581	+	0.490328i
$290$	0.218001	+	0.598953i	0.0128015	+	0.0351717i
$291$	0.352402	+	0.117528i	0.0206582	+	0.00688962i
$292$	−8.75071			−0.512096
$293$	−10.0872	−	17.4716i	−0.589303	−	1.02070i	−0.994324	−	0.106395i	$-0.966069\pi$
$293$	−10.0872	−	17.4716i	−0.589303	−	1.02070i	0.405021	−	0.914307i	$-0.367264\pi$
$294$	−5.08638	+	1.04003i	−0.296644	+	0.0606558i
$295$	−0.00399565	+	0.0109780i	−0.000232636	+	0.000639161i
$296$	−0.791543	−	0.456997i	−0.0460075	−	0.0265624i
$297$	5.46827	−	11.5518i	0.317301	−	0.670301i
$298$	5.91222	−	16.2437i	0.342486	−	0.940971i
$299$	0.626192	−	0.227915i	0.0362136	−	0.0131807i
$300$	−2.58384	+	7.74750i	−0.149178	+	0.447302i
$301$	1.39920	−	7.93528i	0.0806488	−	0.457382i
$302$	−5.49902	−	15.1084i	−0.316433	−	0.869393i
$303$	0.909746	−	0.0247150i	0.0522635	−	0.00141984i
$304$	−0.988903	+	4.24524i	−0.0567175	+	0.243481i
$305$		−	7.33167i		−	0.419810i
$306$	−3.44051	−	8.06135i	−0.196681	−	0.460837i
$307$	−4.89206	−	13.4408i	−0.279204	−	0.767108i	−0.997453	−	0.0713217i	$-0.977278\pi$
$307$	−4.89206	−	13.4408i	−0.279204	−	0.767108i	0.718249	−	0.695786i	$-0.244944\pi$
$308$	3.16308	+	3.76962i	0.180233	+	0.214794i
$309$	−2.51479	+	0.993449i	−0.143061	+	0.0565154i
$310$	−2.24616	+	1.88475i	−0.127573	+	0.107047i
$311$			26.1817i			1.48463i	0.670052	+	0.742314i	$0.266272\pi$
$311$			26.1817i			1.48463i	−0.670052	+	0.742314i	$0.733728\pi$
$312$	3.44798	−	0.0936710i	0.195203	−	0.00530307i
$313$	−24.0438	−	8.75124i	−1.35904	−	0.494649i	−0.443281	−	0.896383i	$-0.646186\pi$
$313$	−24.0438	−	8.75124i	−1.35904	−	0.494649i	−0.915757	+	0.401734i	$0.868408\pi$
$314$	−2.47857	+	2.07976i	−0.139874	+	0.117368i
$315$	−0.173898	−	3.19818i	−0.00979803	−	0.180197i
$316$	0.395251	−	0.228198i	0.0222346	−	0.0128371i
$317$	−0.737265	−	4.18124i	−0.0414089	−	0.234842i	0.957078	−	0.289830i	$-0.0935989\pi$
$317$	−0.737265	−	4.18124i	−0.0414089	−	0.234842i	−0.998487	+	0.0549885i	$0.982488\pi$
$318$	19.5080	+	2.89594i	1.09395	+	0.162396i
$319$	−1.00480	+	2.76066i	−0.0562579	+	0.154567i
$320$	0.525536	+	0.0926662i	0.0293783	+	0.00518020i
$321$	−11.9685	−	30.2966i	−0.668015	−	1.69099i
$322$	0.579775	−	0.334733i	0.0323096	−	0.0186540i
$323$	12.4030	+	2.88919i	0.690119	+	0.160759i
$324$	−5.31858	−	7.26035i	−0.295477	−	0.403353i
$325$	−6.03579	+	7.19318i	−0.334805	+	0.399006i
$326$	−17.7260	−	14.8739i	−0.981755	−	0.823790i
$327$	−3.08459	−	1.02873i	−0.170578	−	0.0568889i
$328$	1.29006	+	1.08249i	0.0712314	+	0.0597703i
$329$	−12.1043	−	14.4254i	−0.667332	−	0.795296i
$330$	1.93726	−	1.18977i	0.106643	−	0.0654945i
$331$		−	30.0728i		−	1.65295i	−0.562971	−	0.826477i	$-0.690342\pi$
$331$		−	30.0728i		−	1.65295i	0.562971	−	0.826477i	$-0.309658\pi$
$332$	2.33419	+	2.78177i	0.128105	+	0.152670i
$333$	−0.796536	+	2.62374i	−0.0436499	+	0.143780i
$334$	−7.28198	+	12.6128i	−0.398452	+	0.690139i
$335$	1.22080	−	2.11448i	0.0666993	−	0.115527i
$336$	3.39499	−	0.694185i	0.185212	−	0.0378709i
$337$	−7.65609	+	9.12417i	−0.417054	+	0.497025i	−0.933141	−	0.359511i	$-0.882944\pi$
$337$	−7.65609	+	9.12417i	−0.417054	+	0.497025i	0.516087	+	0.856536i	$0.327388\pi$
$338$	−8.48939	−	3.08989i	−0.461762	−	0.168068i
$339$	−12.7938	+	16.1164i	−0.694861	+	0.875320i
$340$	0.270735	−	1.53541i	0.0146827	−	0.0832695i
$341$	−13.5147			−0.731862
$342$	13.0767		0.000120997i	0.707107		6.54275e-6i
$343$	−20.0013			−1.07997
$344$	0.699373	−	3.96634i	0.0377077	−	0.213851i
$345$	−0.113638	−	0.287659i	−0.00611806	−	0.0154871i
$346$	−3.72987	−	1.35756i	−0.200519	−	0.0729830i
$347$	−6.04137	+	7.19982i	−0.324318	+	0.386507i	−0.903426	−	0.428744i	$-0.858956\pi$
$347$	−6.04137	+	7.19982i	−0.324318	+	0.386507i	0.579109	+	0.815250i	$0.303401\pi$
$348$	1.37234	+	1.54809i	0.0735652	+	0.0829863i
$349$	7.07468	−	12.2537i	0.378699	−	0.655926i	−0.612174	−	0.790723i	$-0.709705\pi$
$349$	7.07468	−	12.2537i	0.378699	−	0.655926i	0.990873	+	0.134797i	$0.0430383\pi$
$350$	−4.71677	+	8.16968i	−0.252122	+	0.436688i
$351$	−2.62032	−	10.0105i	−0.139862	−	0.534321i
$352$	1.58103	+	1.88419i	0.0842689	+	0.100428i
$353$			4.82744i			0.256939i	0.991713	+	0.128469i	$0.0410064\pi$
$353$			4.82744i			0.256939i	−0.991713	+	0.128469i	$0.958994\pi$
$354$	0.00102974	+	0.0379040i	5.47298e−5	+	0.00201458i
$355$	3.22957	+	3.84885i	0.171408	+	0.204276i
$356$	−2.01531	−	1.69104i	−0.106811	−	0.0896251i
$357$	−2.02814	−	9.91885i	−0.107341	−	0.524961i
$358$	15.0536	+	12.6315i	0.795606	+	0.667593i
$359$	10.3137	−	12.2914i	0.544338	−	0.648717i	−0.421816	−	0.906681i	$-0.638607\pi$
$359$	10.3137	−	12.2914i	0.544338	−	0.648717i	0.966154	+	0.257964i	$0.0830517\pi$
$360$	−0.0869205	−	1.59857i	−0.00458111	−	0.0842519i
$361$	−11.2284	+	15.3272i	−0.590968	+	0.806695i
$362$	9.55620	−	5.51727i	0.502263	−	0.289981i
$363$	−8.48102	−	1.25900i	−0.445138	−	0.0660803i
$364$	3.92363	+	0.691841i	0.205654	+	0.0362623i
$365$	−1.59715	+	4.38813i	−0.0835987	+	0.229685i
$366$	−8.74314	−	22.1321i	−0.457011	−	1.15686i
$367$	−0.219263	−	1.24350i	−0.0114454	−	0.0649103i	0.978550	−	0.206009i	$-0.0660476\pi$
$367$	−0.219263	−	1.24350i	−0.0114454	−	0.0649103i	−0.989996	+	0.141099i	$0.954937\pi$
$368$	0.289793	−	0.167312i	0.0151065	−	0.00872174i
$369$	2.28480	−	4.50598i	0.118942	−	0.234572i
$370$	−0.373636	+	0.313518i	−0.0194244	+	0.0162990i
$371$	21.4064	+	7.79129i	1.11136	+	0.404503i
$372$	−4.53287	+	8.36807i	−0.235019	+	0.433864i
$373$		−	32.4230i		−	1.67880i	−0.543516	−	0.839399i	$-0.682907\pi$
$373$		−	32.4230i		−	1.67880i	0.543516	−	0.839399i	$-0.317093\pi$
$374$	5.50488	−	4.61915i	0.284651	−	0.238850i
$375$	7.03310	+	5.58314i	0.363188	+	0.288312i
$376$	−6.05018	−	7.21032i	−0.312014	−	0.371844i
$377$	0.813527	+	2.23515i	0.0418988	+	0.115116i
$378$	−4.33883	−	9.44697i	−0.223165	−	0.485900i
$379$		−	19.7492i		−	1.01445i	−0.861814	−	0.507224i	$-0.830672\pi$
$379$		−	19.7492i		−	1.01445i	0.861814	−	0.507224i	$-0.169328\pi$
$380$	1.94833	+	1.27072i	0.0999472	+	0.0651867i
$381$	−18.2334	+	33.6604i	−0.934124	+	1.72447i
$382$	−4.25394	−	11.6876i	−0.217650	−	0.597989i
$383$	0.155280	−	0.880638i	0.00793445	−	0.0449985i	−0.980583	−	0.196102i	$-0.937172\pi$
$383$	0.155280	−	0.880638i	0.00793445	−	0.0449985i	0.988518	+	0.151104i	$0.0482827\pi$
$384$	1.69694	−	0.346979i	0.0865966	−	0.0177067i
$385$	2.46763	−	0.898144i	0.125762	−	0.0457736i
$386$	8.50587	−	23.3697i	0.432937	−	1.18949i
$387$	−12.0648	+	0.656009i	−0.613287	+	0.0333468i
$388$	0.185742	+	0.107238i	0.00942962	+	0.00544419i
$389$	−4.57209	+	12.5617i	−0.231814	+	0.636905i	−0.999994	−	0.00332901i	$-0.998940\pi$
$389$	−4.57209	+	12.5617i	−0.231814	+	0.636905i	0.768180	+	0.640234i	$0.221163\pi$
$390$	0.582342	−	1.74612i	0.0294880	−	0.0884183i
$391$	−0.488821	−	0.846663i	−0.0247208	−	0.0428176i
$392$	−2.99738			−0.151391
$393$	3.37412	+	16.5015i	0.170202	+	0.832391i
$394$	7.70527	+	21.1701i	0.388186	+	1.06653i
$395$	−0.0422925	−	0.239853i	−0.00212797	−	0.0120683i
$396$	4.42918	−	5.90176i	0.222575	−	0.296575i
$397$	11.4148	+	9.57818i	0.572894	+	0.480715i	0.882605	−	0.470116i	$-0.155788\pi$
$397$	11.4148	+	9.57818i	0.572894	+	0.480715i	−0.309711	+	0.950831i	$0.600232\pi$
$398$	2.33496	+	4.04427i	0.117041	+	0.202721i
$399$	14.7984	+	3.02602i	0.740846	+	0.151490i
$400$	−2.35761	+	4.08350i	−0.117881	+	0.204175i
$401$	21.2051	−	7.71804i	1.05893	−	0.385420i	0.246906	−	0.969039i	$-0.420586\pi$
$401$	21.2051	−	7.71804i	1.05893	−	0.385420i	0.812028	+	0.583619i	$0.198364\pi$
$402$	1.16366	−	7.83881i	0.0580382	−	0.390964i
$403$	−8.38211	+	7.03343i	−0.417543	+	0.350360i
$404$	0.517453	+	0.0912410i	0.0257443	+	0.00453941i
$405$	−4.61151	+	1.34192i	−0.229148	+	0.0666806i
$406$	1.19481	+	2.06947i	0.0592973	+	0.102706i
$407$	−2.24810			−0.111434
$408$	−1.01374	−	4.95780i	−0.0501876	−	0.245448i
$409$	11.0895	−	1.95538i	0.548342	−	0.0966874i	0.107388	−	0.994217i	$-0.465751\pi$
$409$	11.0895	−	1.95538i	0.548342	−	0.0966874i	0.440954	+	0.897530i	$0.354640\pi$
$410$	0.778281	−	0.449341i	0.0384365	−	0.0221913i
$411$	−1.72429	−	2.80760i	−0.0850528	−	0.138489i
$412$	−1.53738	+	0.271082i	−0.0757414	+	0.0133552i
$413$	−0.00760549	+	0.0431329i	−0.000374241	+	0.00212243i
$414$	−0.686077	−	0.732842i	−0.0337189	−	0.0360172i
$415$	1.82098	−	0.662782i	0.0893883	−	0.0325347i
$416$	1.96117	+	0.345808i	0.0961544	+	0.0169546i
$417$	20.9562	−	12.8702i	1.02623	−	0.630258i
$418$	3.11441	+	10.2590i	0.152331	+	0.501784i
$419$	−24.1574	−	13.9473i	−1.18017	−	0.681369i	−0.224113	−	0.974563i	$-0.571949\pi$
$419$	−24.1574	−	13.9473i	−1.18017	−	0.681369i	−0.956053	+	0.293194i	$0.905282\pi$
$420$	0.271536	−	1.82915i	0.0132496	−	0.0892535i
$421$	−14.1574	+	16.8721i	−0.689989	+	0.822297i	−0.991354	−	0.131212i	$-0.958113\pi$
$421$	−14.1574	+	16.8721i	−0.689989	+	0.822297i	0.301365	+	0.953509i	$0.402558\pi$
$422$	7.13523	−	1.25813i	0.347337	−	0.0612450i
$423$	−16.9493	+	22.5845i	−0.824105	+	1.09810i
$424$	10.6997	+	3.89437i	0.519623	+	0.189127i
$425$	11.9304	+	6.88803i	0.578711	+	0.334119i
$426$	14.3389	+	7.76721i	0.694723	+	0.376322i
$427$	−4.77303	−	27.0692i	−0.230983	−	1.30997i
$428$	−3.26583	−	18.5214i	−0.157860	−	0.895267i
$429$	7.22938	−	4.43992i	0.349038	−	0.214361i
$430$	−1.86132	−	1.07463i	−0.0897607	−	0.0518234i
$431$	2.48825	+	0.905650i	0.119855	+	0.0436236i	0.401251	−	0.915968i	$-0.368575\pi$
$431$	2.48825	+	0.905650i	0.119855	+	0.0436236i	−0.281396	+	0.959592i	$0.590798\pi$
$432$	−2.16871	−	4.72194i	−0.104342	−	0.227184i
$433$	10.0737	−	1.77627i	0.484113	−	0.0853622i	0.0737352	−	0.997278i	$-0.476508\pi$
$433$	10.0737	−	1.77627i	0.484113	−	0.0853622i	0.410378	+	0.911916i	$0.365397\pi$
$434$	−7.06602	+	8.42095i	−0.339180	+	0.404218i
$435$	1.02678	−	0.405623i	0.0492304	−	0.0194481i
$436$	−1.62581	−	0.938660i	−0.0778620	−	0.0449537i
$437$	1.44807	−	0.174906i	0.0692705	−	0.00836687i
$438$	0.411608	+	15.1511i	0.0196674	+	0.723947i
$439$	9.97020	+	1.75802i	0.475852	+	0.0839055i	0.406430	−	0.913682i	$-0.366773\pi$
$439$	9.97020	+	1.75802i	0.475852	+	0.0839055i	0.0694217	+	0.997587i	$0.477885\pi$
$440$	1.23341	−	0.448925i	0.0588006	−	0.0214017i
$441$	2.03997	+	8.75770i	0.0971414	+	0.417033i
$442$	1.01032	−	5.72979i	0.0480558	−	0.272538i
$443$	24.6350	−	4.34381i	1.17044	−	0.206381i	0.445560	−	0.895252i	$-0.353005\pi$
$443$	24.6350	−	4.34381i	1.17044	−	0.206381i	0.724883	+	0.688872i	$0.241894\pi$
$444$	−0.754019	+	1.39198i	−0.0357842	+	0.0660606i
$445$	−1.21582	+	0.701953i	−0.0576353	+	0.0332757i
$446$	−9.53399	+	1.68110i	−0.451448	+	0.0796024i
$447$	−28.4026	−	9.47243i	−1.34340	−	0.448031i
$448$	2.00065			0.0945220
$449$	12.3712	+	21.4275i	0.583833	+	1.01123i	0.995020	+	0.0996768i	$0.0317809\pi$
$449$	12.3712	+	21.4275i	0.583833	+	1.01123i	−0.411187	+	0.911551i	$0.634886\pi$
$450$	13.5357	+	4.10927i	0.638077	+	0.193713i
$451$	4.07922	+	0.719277i	0.192083	+	0.0338694i
$452$	−9.10076	+	7.63644i	−0.428064	+	0.359188i
$453$	−25.9003	+	10.2317i	−1.21690	+	0.480728i
$454$	2.65008	−	0.964550i	0.124374	−	0.0452686i
$455$	1.06306	−	1.84127i	0.0498369	−	0.0863201i
$456$	7.39678	+	1.51252i	0.346386	+	0.0708300i
$457$	18.3705	+	31.8186i	0.859334	+	1.48841i	0.872565	+	0.488497i	$0.162455\pi$
$457$	18.3705	+	31.8186i	0.859334	+	1.48841i	−0.0132314	+	0.999912i	$0.504212\pi$
$458$	9.92227	+	8.32578i	0.463637	+	0.389038i
$459$	−13.7957	+	6.33612i	−0.643928	+	0.295745i
$460$	−0.0310083	−	0.175857i	−0.00144577	−	0.00819937i
$461$	−9.48436	−	26.0581i	−0.441731	−	1.21365i	−0.938353	−	0.345679i	$-0.887649\pi$
$461$	−9.48436	−	26.0581i	−0.441731	−	1.21365i	0.496622	−	0.867967i	$-0.334573\pi$
$462$	6.37798	−	5.65391i	0.296730	−	0.263044i
$463$	15.7970			0.734147			0.367073	−	0.930192i	$-0.380360\pi$
$463$	15.7970			0.734147			0.367073	+	0.930192i	$0.380360\pi$
$464$	0.597209	+	1.03440i	0.0277247	+	0.0480206i
$465$	3.36893	+	3.80037i	0.156230	+	0.176238i
$466$	−9.54376	+	26.2213i	−0.442106	+	1.21468i
$467$	34.9101	+	20.1554i	1.61545	+	0.932679i	0.988078	+	0.153957i	$0.0492017\pi$
$467$	34.9101	+	20.1554i	1.61545	+	0.932679i	0.627369	+	0.778722i	$0.284132\pi$
$468$	−0.324366	−	5.96547i	−0.0149938	−	0.275754i
$469$	3.13074	−	8.60163i	0.144564	−	0.397186i
$470$	−4.71995	+	1.71792i	−0.217715	+	0.0792418i
$471$	3.71751	+	4.19359i	0.171294	+	0.193231i
$472$	−0.00380150	+	0.0215594i	−0.000174978	+	0.000992351i
$473$	−3.38814	−	9.30885i	−0.155787	−	0.428021i
$474$	−0.413696	−	0.673608i	−0.0190017	−	0.0309398i
$475$	−16.4388	+	12.3369i	−0.754266	+	0.566054i
$476$		−	5.84514i		−	0.267911i
$477$	4.09647	−	33.9126i	0.187564	−	1.55275i
$478$	−4.84438	−	13.3098i	−0.221577	−	0.608777i
$479$	20.3738	+	24.2806i	0.930903	+	1.10941i	0.993777	+	0.111386i	$0.0355290\pi$
$479$	20.3738	+	24.2806i	0.930903	+	1.10941i	−0.0628738	+	0.998021i	$0.520027\pi$
$480$	0.135724	−	0.914278i	0.00619491	−	0.0417309i
$481$	−1.39432	+	1.16997i	−0.0635755	+	0.0533461i
$482$		−	16.2099i		−	0.738341i
$483$	−0.606832	−	0.988085i	−0.0276118	−	0.0449594i
$484$	−4.65165	−	1.69306i	−0.211438	−	0.0769573i
$485$	0.0876767	−	0.0735695i	0.00398119	−	0.00334062i
$486$	−12.3205	+	9.55015i	−0.558869	+	0.433204i
$487$	−4.44690	+	2.56742i	−0.201508	+	0.116341i	−0.597359	−	0.801974i	$-0.703783\pi$
$487$	−4.44690	+	2.56742i	−0.201508	+	0.116341i	0.395851	+	0.918315i	$0.370450\pi$
$488$	−2.38573	−	13.5302i	−0.107997	−	0.612482i
$489$	−24.9191	+	31.3907i	−1.12688	+	1.41954i
$490$	−0.547073	+	1.50307i	−0.0247142	+	0.0679018i
$491$	43.2530	+	7.62668i	1.95198	+	0.344187i	0.999175	+	0.0406111i	$0.0129305\pi$
$491$	43.2530	+	7.62668i	1.95198	+	0.344187i	0.952807	+	0.303576i	$0.0981806\pi$
$492$	1.81355	−	2.28454i	0.0817611	−	0.102995i
$493$	3.02211	−	1.74481i	0.136109	−	0.0785825i
$494$	7.27069	+	4.74203i	0.327124	+	0.213354i
$495$	−2.15110	−	3.29823i	−0.0966847	−	0.148244i
$496$	−3.53185	+	4.20910i	−0.158585	+	0.188994i
$497$	14.4295	+	12.1078i	0.647253	+	0.543110i
$498$	4.70660	−	4.17228i	0.210908	−	0.186964i
$499$	−6.89119	−	5.78240i	−0.308492	−	0.258856i	0.475376	−	0.879783i	$-0.342312\pi$
$499$	−6.89119	−	5.78240i	−0.308492	−	0.258856i	−0.783868	+	0.620927i	$0.786756\pi$
$500$	3.33251	+	3.97153i	0.149034	+	0.177612i
$501$	22.1804	+	12.0148i	0.990947	+	0.536783i
$502$		−	4.82713i		−	0.215445i
$503$	−6.88608	−	8.20651i	−0.307035	−	0.365910i	0.590358	−	0.807141i	$-0.298986\pi$
$503$	−6.88608	−	8.20651i	−0.307035	−	0.365910i	−0.897394	+	0.441231i	$0.854542\pi$
$504$	−1.36161	−	5.84547i	−0.0606510	−	0.260378i
$505$	0.140198	−	0.242829i	0.00623871	−	0.0108058i
$506$	0.411527	−	0.712786i	0.0182946	−	0.0316872i
$507$	−4.95055	+	14.8440i	−0.219862	+	0.659244i
$508$	−14.2068	+	16.9310i	−0.630325	+	0.751192i
$509$	20.5324	+	7.47318i	0.910083	+	0.331243i	0.754286	−	0.656546i	$-0.227983\pi$
$509$	20.5324	+	7.47318i	0.910083	+	0.331243i	0.155797	+	0.987789i	$0.450206\pi$
$510$	−2.67117	−	0.396532i	−0.118281	−	0.0175587i
$511$	−3.04008	+	17.2412i	−0.134485	+	0.762704i
$512$	1.00000			0.0441942
$513$	−0.614881	−	22.6412i	−0.0271476	−	0.999631i
$514$	17.2824			0.762294
$515$	−0.144661	+	0.820413i	−0.00637453	+	0.0361517i
$516$	−6.90027	−	1.02434i	−0.303768	−	0.0450940i
$517$	−21.7549	−	7.91815i	−0.956781	−	0.348240i
$518$	−1.17539	+	1.40078i	−0.0516438	+	0.0615467i
$519$	−2.17506	+	6.52180i	−0.0954745	+	0.286275i
$520$	0.531355	−	0.920335i	0.0233015	−	0.0403593i
$521$	−2.54506	+	4.40817i	−0.111501	+	0.193126i	−0.916376	−	0.400319i	$-0.868899\pi$
$521$	−2.54506	+	4.40817i	−0.111501	+	0.193126i	0.804875	+	0.593445i	$0.202233\pi$
$522$	2.61583	−	2.44891i	0.114492	−	0.107186i
$523$	18.7043	+	22.2909i	0.817881	+	0.974713i	0.999963	−	0.00857023i	$-0.00272802\pi$
$523$	18.7043	+	22.2909i	0.817881	+	0.974713i	−0.182082	+	0.983283i	$0.558284\pi$
$524$			9.72427i			0.424807i
$525$	14.3669	+	7.78239i	0.627025	+	0.339651i
$526$	−5.13228	−	6.11641i	−0.223778	−	0.266688i
$527$	12.2974	+	10.3187i	0.535682	+	0.449490i
$528$	3.18795	−	2.82603i	0.138738	−	0.122987i
$529$	17.5332	+	14.7121i	0.762315	+	0.639658i
$530$	3.90575	−	4.65469i	0.169655	−	0.202187i
$531$	0.0655790	−	0.00356579i	0.00284589	−	0.000154742i
$532$	8.02067	+	3.42323i	0.347740	+	0.148416i
$533$	2.90435	−	1.67683i	0.125802	−	0.0726316i
$534$	−2.83310	+	3.56887i	−0.122600	+	0.154440i
$535$	−9.88384	−	1.74279i	−0.427315	−	0.0753473i
$536$	1.56486	−	4.29941i	0.0675915	−	0.185706i
$537$	21.1622	−	26.6581i	0.913215	−	1.15038i
$538$	2.88591	+	16.3668i	0.124420	+	0.705623i
$539$	−6.38476	+	3.68624i	−0.275011	+	0.158778i
$540$	−2.76369	+	0.225687i	−0.118930	+	0.00971203i
$541$	−22.9508	+	19.2580i	−0.986733	+	0.827967i	−0.985091	−	0.172031i	$-0.944967\pi$
$541$	−22.9508	+	19.2580i	−0.986733	+	0.827967i	−0.00164165	+	0.999999i	$0.500523\pi$
$542$	12.3995	+	4.51305i	0.532604	+	0.193852i
$543$	−10.0022	−	16.2862i	−0.429234	−	0.698908i
$544$		−	2.92161i		−	0.125263i
$545$	−0.767438	+	0.643957i	−0.0328734	+	0.0275841i
$546$	1.01331	−	6.82596i	0.0433655	−	0.292124i
$547$	6.94810	+	8.28042i	0.297079	+	0.354045i	0.893850	−	0.448367i	$-0.147994\pi$
$547$	6.94810	+	8.28042i	0.297079	+	0.354045i	−0.596770	+	0.802412i	$0.703550\pi$
$548$	−0.650611	−	1.78754i	−0.0277927	−	0.0763599i
$549$	−37.9085	+	16.1790i	−1.61790	+	0.690503i
$550$			11.5977i			0.494530i
$551$	0.624314	+	5.16878i	0.0265966	+	0.220197i
$552$	−0.303317	−	0.493881i	−0.0129100	−	0.0210210i
$553$	−0.312295	−	0.858025i	−0.0132802	−	0.0364869i
$554$	−3.63768	+	20.6303i	−0.154550	+	0.876497i
$555$	0.560403	+	0.632171i	0.0237878	+	0.0268342i
$556$	13.3424	−	4.85622i	0.565842	−	0.205950i
$557$	11.3884	−	31.2894i	0.482543	−	1.32578i	−0.424764	−	0.905304i	$-0.639643\pi$
$557$	11.3884	−	31.2894i	0.482543	−	1.32578i	0.907306	−	0.420471i	$-0.138135\pi$
$558$	14.7018	+	7.45466i	0.622376	+	0.315581i
$559$	−6.94598	−	4.01027i	−0.293784	−	0.169616i
$560$	0.365153	−	1.00325i	0.0154305	−	0.0423950i
$561$	−8.25658	−	9.31395i	−0.348593	−	0.393235i
$562$	−0.859473	−	1.48865i	−0.0362547	−	0.0627950i
$563$	0.876128			0.0369244			0.0184622	−	0.999830i	$-0.494123\pi$
$563$	0.876128			0.0369244			0.0184622	+	0.999830i	$0.494123\pi$
$564$	−12.1995	+	10.8145i	−0.513690	+	0.455373i
$565$	2.16833	+	5.95745i	0.0912225	+	0.250632i
$566$	−3.06676	−	17.3924i	−0.128905	−	0.731059i
$567$	−16.1525	+	7.95666i	−0.678341	+	0.334148i
$568$	7.21241	+	6.05193i	0.302626	+	0.253933i
$569$	−22.6094	−	39.1607i	−0.947836	−	1.64170i	−0.749971	−	0.661471i	$-0.769933\pi$
$569$	−22.6094	−	39.1607i	−0.947836	−	1.64170i	−0.197865	−	0.980229i	$-0.563401\pi$
$570$	2.10850	−	3.43313i	0.0883154	−	0.143798i
$571$	13.6079	−	23.5695i	0.569471	−	0.986353i	−0.427147	−	0.904182i	$-0.640481\pi$
$571$	13.6079	−	23.5695i	0.569471	−	0.986353i	0.996618	−	0.0821706i	$-0.0261852\pi$
$572$	4.60279	−	1.67528i	0.192452	−	0.0700469i
$573$	−20.0359	+	7.91507i	−0.837014	+	0.330657i
$574$	2.58096	−	2.16568i	0.107727	−	0.0903937i
$575$	1.55386	+	0.273987i	0.0648003	+	0.0114260i
$576$	−0.680583	−	2.92178i	−0.0283576	−	0.121741i
$577$	−3.28094	−	5.68275i	−0.136587	−	0.236576i	0.789615	−	0.613602i	$-0.210280\pi$
$577$	−3.28094	−	5.68275i	−0.136587	−	0.236576i	−0.926203	+	0.377026i	$0.876947\pi$
$578$	8.46417			0.352063
$579$	−40.8626	−	13.6279i	−1.69819	−	0.566357i
$580$	0.627709	−	0.110682i	0.0260642	−	0.00459582i
$581$	6.29173	−	3.63253i	0.261025	−	0.150703i
$582$	0.176937	−	0.326640i	0.00733426	−	0.0135397i
$583$	27.5809	−	4.86326i	1.14228	−	0.201415i
$584$	−1.51954	+	8.61776i	−0.0628792	+	0.356606i
$585$	−3.05065	−	0.926141i	−0.126129	−	0.0382912i
$586$	−18.9578	+	6.90008i	−0.783140	+	0.285040i
$587$	41.5311	+	7.32305i	1.71417	+	0.302255i	0.942609	−	0.333899i	$-0.108364\pi$
$587$	41.5311	+	7.32305i	1.71417	+	0.302255i	0.771562	+	0.636154i	$0.219476\pi$
$588$	0.140988	+	5.18971i	0.00581426	+	0.214020i
$589$	−21.3613	+	10.8312i	−0.880177	+	0.446291i
$590$	0.0101173	+	0.00584125i	0.000416524	+	0.000240480i
$591$	36.2917	−	14.3368i	1.49284	−	0.589736i
$592$	−0.587505	+	0.700161i	−0.0241463	+	0.0287764i
$593$	20.8539	−	3.67711i	0.856368	−	0.151001i	0.271808	−	0.962351i	$-0.412378\pi$
$593$	20.8539	−	3.67711i	0.856368	−	0.151001i	0.584560	+	0.811351i	$0.301267\pi$
$594$	−10.4267	−	7.39113i	−0.427813	−	0.303262i
$595$	−2.93111	−	1.06684i	−0.120164	−	0.0437360i
$596$	−14.9703	−	8.64308i	−0.613206	−	0.354035i
$597$	6.89247	−	4.23301i	0.282090	−	0.173246i
$598$	−0.115716	−	0.656255i	−0.00473196	−	0.0268363i
$599$	−5.70119	−	32.3331i	−0.232944	−	1.32109i	−0.846900	−	0.531753i	$-0.821534\pi$
$599$	−5.70119	−	32.3331i	−0.232944	−	1.32109i	0.613955	−	0.789341i	$-0.289577\pi$
$600$	7.18112	+	3.88992i	0.293168	+	0.158805i
$601$	−9.18882	−	5.30517i	−0.374820	−	0.216402i	0.300742	−	0.953705i	$-0.402766\pi$
$601$	−9.18882	−	5.30517i	−0.374820	−	0.216402i	−0.675562	+	0.737303i	$0.736099\pi$
$602$	−7.57176	−	2.75589i	−0.308602	−	0.112322i
$603$	−13.6269	−	1.64607i	−0.554932	−	0.0670330i
$604$	−15.8338	+	2.79193i	−0.644268	+	0.113602i
$605$	−1.69801	+	2.02360i	−0.0690338	+	0.0822712i
$606$	0.133636	−	0.900216i	0.00542860	−	0.0365688i
$607$	−8.50623	−	4.91107i	−0.345257	−	0.199334i	0.317337	−	0.948313i	$-0.397211\pi$
$607$	−8.50623	−	4.91107i	−0.345257	−	0.199334i	−0.662594	+	0.748978i	$0.730545\pi$
$608$	4.00902	+	1.71106i	0.162587	+	0.0693926i
$609$	3.52690	−	2.16605i	0.142917	−	0.0877727i
$610$	−7.22028	−	1.27313i	−0.292341	−	0.0515476i
$611$	−17.6137	+	6.41087i	−0.712574	+	0.259356i
$612$	−8.53632	+	1.98840i	−0.345060	+	0.0803763i
$613$	−6.46003	+	36.6367i	−0.260918	+	1.47974i	0.519493	+	0.854474i	$0.326121\pi$
$613$	−6.46003	+	36.6367i	−0.260918	+	1.47974i	−0.780412	+	0.625266i	$0.784990\pi$
$614$	−14.0861	+	2.48376i	−0.568469	+	0.100237i
$615$	−0.814602	−	1.32639i	−0.0328479	−	0.0534852i
$616$	4.26161	−	2.46044i	0.171705	−	0.0991341i
$617$	27.5781	−	4.86276i	1.11025	−	0.195767i	0.411694	−	0.911322i	$-0.364937\pi$
$617$	27.5781	−	4.86276i	1.11025	−	0.195767i	0.698557	+	0.715555i	$0.253826\pi$
$618$	0.541669	+	2.64909i	0.0217891	+	0.106562i
$619$	−0.416499			−0.0167405			−0.00837026	−	0.999965i	$-0.502664\pi$
$619$	−0.416499			−0.0167405			−0.00837026	+	0.999965i	$0.502664\pi$
$620$	1.46607	+	2.53932i	0.0588790	+	0.101981i
$621$	−1.23658	+	1.22235i	−0.0496222	+	0.0490513i
$622$	25.7839	+	4.54641i	1.03384	+	0.182294i
$623$	−4.03193	+	3.38319i	−0.161536	+	0.135545i
$624$	0.506487	−	3.41186i	0.0202757	−	0.136584i
$625$	−19.5545	+	7.11726i	−0.782180	+	0.284690i
$626$	−12.7935	+	22.1589i	−0.511329	+	0.885648i
$627$	17.6161	−	5.87488i	0.703518	−	0.234620i
$628$	1.61777	+	2.80206i	0.0645560	+	0.111814i
$629$	2.04560	+	1.71646i	0.0815634	+	0.0684398i
$630$	−3.17979	−	0.384102i	−0.126686	−	0.0153030i
$631$	3.45294	+	19.5826i	0.137459	+	0.779570i	0.973116	+	0.230317i	$0.0739764\pi$
$631$	3.45294	+	19.5826i	0.137459	+	0.779570i	−0.835656	+	0.549253i	$0.814913\pi$
$632$	−0.156097	−	0.428872i	−0.00620919	−	0.0170596i
$633$	−2.51397	−	12.2948i	−0.0999212	−	0.488676i
$634$	−4.24574			−0.168620
$635$	5.89725	+	10.2143i	0.234025	+	0.405344i
$636$	6.23948	−	18.7088i	0.247411	−	0.741851i
$637$	−2.04154	+	5.60909i	−0.0808889	+	0.222240i
$638$	2.54424	+	1.46892i	0.100727	+	0.0581550i
$639$	12.7738	−	25.1919i	0.505323	−	0.996577i
$640$	0.182517	−	0.501460i	0.00721461	−	0.0198220i
$641$	−6.59278	+	2.39957i	−0.260399	+	0.0947775i	−0.468921	−	0.883240i	$-0.655357\pi$
$641$	−6.59278	+	2.39957i	−0.260399	+	0.0947775i	0.208522	+	0.978018i	$0.433135\pi$
$642$	−31.9146	+	6.52569i	−1.25957	+	0.257548i
$643$	7.55575	−	42.8508i	0.297970	−	1.68987i	−0.356911	−	0.934138i	$-0.616170\pi$
$643$	7.55575	−	42.8508i	0.297970	−	1.68987i	0.654881	−	0.755732i	$-0.272719\pi$
$644$	−0.228971	−	0.629093i	−0.00902273	−	0.0247897i
$645$	−1.77308	+	3.27325i	−0.0698150	+	0.128884i
$646$	4.99905	−	11.7128i	0.196685	−	0.460835i
$647$		−	32.3844i		−	1.27316i	−0.771210	−	0.636581i	$-0.780348\pi$
$647$		−	32.3844i		−	1.27316i	0.771210	−	0.636581i	$-0.219652\pi$
$648$	−8.07361	+	3.97703i	−0.317162	+	0.156232i
$649$	0.0184165	+	0.0505990i	0.000722912	+	0.00198618i
$650$	6.03579	+	7.19318i	0.236743	+	0.282140i
$651$	14.9125	+	11.8381i	0.584467	+	0.463971i
$652$	−17.7260	+	14.8739i	−0.694206	+	0.582508i
$653$			25.7764i			1.00871i	0.863496	+	0.504355i	$0.168270\pi$
$653$			25.7764i			1.00871i	−0.863496	+	0.504355i	$0.831730\pi$
$654$	−1.54873	+	2.85909i	−0.0605603	+	0.111799i
$655$	4.87634	+	1.77484i	0.190534	+	0.0693488i
$656$	1.29006	−	1.08249i	0.0503682	−	0.0422640i
$657$	26.2134	−	1.42533i	1.02268	−	0.0556073i
$658$	−16.3081	+	9.41549i	−0.635756	+	0.367054i
$659$	−2.99852	−	17.0055i	−0.116806	−	0.662439i	−0.985840	−	0.167687i	$-0.946370\pi$
$659$	−2.99852	−	17.0055i	−0.116806	−	0.662439i	0.869034	−	0.494752i	$-0.164741\pi$
$660$	−0.835290	−	2.11443i	−0.0325136	−	0.0823040i
$661$	0.263071	−	0.722783i	0.0102323	−	0.0281130i	−0.934471	−	0.356038i	$-0.884127\pi$
$661$	0.263071	−	0.722783i	0.0102323	−	0.0281130i	0.944704	+	0.327925i	$0.106349\pi$
$662$	−29.6160	−	5.22209i	−1.15106	−	0.202962i
$663$	−9.96815	−	1.47976i	−0.387131	−	0.0574692i
$664$	3.14484	−	1.81567i	0.122043	−	0.0704618i
$665$	3.18052	−	3.39725i	0.123335	−	0.131740i
$666$	2.44556	+	1.24004i	0.0947636	+	0.0480507i
$667$	0.256910	−	0.306173i	0.00994759	−	0.0118551i
$668$	11.1566	+	9.36153i	0.431663	+	0.362208i
$669$	3.35913	+	16.4282i	0.129871	+	0.635151i
$670$	−1.87037	−	1.56943i	−0.0722587	−	0.0606323i
$671$	−21.7215	−	25.8867i	−0.838551	−	0.999346i
$672$	−0.0941050	−	3.46396i	−0.00363018	−	0.133625i
$673$		−	36.4842i		−	1.40636i	−0.711011	−	0.703181i	$-0.751763\pi$
$673$		−	36.4842i		−	1.40636i	0.711011	−	0.703181i	$-0.248237\pi$
$674$	7.65609	+	9.12417i	0.294902	+	0.351450i
$675$	6.47815	−	23.6291i	0.249344	−	0.909484i
$676$	−4.51711	+	7.82387i	−0.173735	+	0.300918i
$677$	−14.0454	+	24.3274i	−0.539810	+	0.934978i	0.459104	+	0.888383i	$0.348171\pi$
$677$	−14.0454	+	24.3274i	−0.539810	+	0.934978i	−0.998914	+	0.0465956i	$0.985163\pi$
$678$	13.6499	+	15.3980i	0.524221	+	0.591355i
$679$	0.275816	−	0.328704i	0.0105848	−	0.0126145i
$680$	−1.46507	−	0.533243i	−0.0561830	−	0.0204490i
$681$	−1.79469	−	4.54301i	−0.0687725	−	0.174089i
$682$	−2.34680	+	13.3094i	−0.0898637	+	0.509643i
$683$	13.4763			0.515655			0.257828	−	0.966191i	$-0.416993\pi$
$683$	13.4763			0.515655			0.257828	+	0.966191i	$0.416993\pi$
$684$	2.27086	−	12.8780i	0.0868286	−	0.492403i
$685$	−1.01513			−0.0387860
$686$	−3.47319	+	19.6974i	−0.132607	+	0.752052i
$687$	13.9486	−	17.5712i	0.532173	−	0.670382i
$688$	−3.78464	−	1.37750i	−0.144288	−	0.0525166i
$689$	14.5753	−	17.3702i	0.555274	−	0.661750i
$690$	−0.303022	+	0.0619600i	−0.0115359	+	0.00235878i
$691$	24.7545	−	42.8760i	0.941705	−	1.63108i	0.179487	−	0.983760i	$-0.442556\pi$
$691$	24.7545	−	42.8760i	0.941705	−	1.63108i	0.762218	−	0.647320i	$-0.224110\pi$
$692$	−1.98462	+	3.43747i	−0.0754441	+	0.130673i
$693$	−10.0893	−	10.7770i	−0.383259	−	0.409383i
$694$	6.04137	+	7.19982i	0.229327	+	0.273301i
$695$		−	7.57701i		−	0.287412i
$696$	1.76287	−	1.08267i	0.0668216	−	0.0410385i
$697$	−3.16261	−	3.76905i	−0.119792	−	0.142763i
$698$	−10.8390	−	9.09503i	−0.410264	−	0.344252i
$699$	45.8487	+	15.2908i	1.73416	+	0.578351i
$700$	7.22651	+	6.06376i	0.273136	+	0.229189i
$701$	11.9457	−	14.2363i	0.451182	−	0.537698i	−0.491726	−	0.870750i	$-0.663634\pi$
$701$	11.9457	−	14.2363i	0.451182	−	0.537698i	0.942908	+	0.333052i	$0.108078\pi$
$702$	−10.3134	+	0.842210i	−0.389255	+	0.0317872i
$703$	−3.55334	+	1.80171i	−0.134017	+	0.0679527i
$704$	2.13011	−	1.22982i	0.0802815	−	0.0463506i
$705$	3.19644	+	8.09137i	0.120385	+	0.304739i
$706$	4.75410	+	0.838276i	0.178923	+	0.0315489i
$707$	0.359537	−	0.987819i	0.0135218	−	0.0371508i
$708$	0.0375070	+	0.00556787i	0.00140960	+	0.000209253i
$709$	−5.15842	−	29.2549i	−0.193729	−	1.09869i	−0.914218	−	0.405223i	$-0.867194\pi$
$709$	−5.15842	−	29.2549i	−0.193729	−	1.09869i	0.720489	−	0.693466i	$-0.243917\pi$
$710$	4.35119	−	2.51216i	0.163297	−	0.0942797i
$711$	−1.14683	+	0.747963i	−0.0430096	+	0.0280508i
$712$	−2.01531	+	1.69104i	−0.0755268	+	0.0633745i
$713$	1.72774	+	0.628845i	0.0647043	+	0.0235504i
$714$	−10.1203	+	0.274938i	−0.378744	+	0.0102893i
$715$		−	2.61388i		−	0.0977537i
$716$	15.0536	−	12.6315i	0.562579	−	0.472059i
$717$	−22.8169	+	9.01367i	−0.852113	+	0.336622i
$718$	−10.3137	−	12.2914i	−0.384905	−	0.458712i
$719$	−8.48343	−	23.3080i	−0.316379	−	0.869243i	−0.991332	−	0.131383i	$-0.958058\pi$
$719$	−8.48343	−	23.3080i	−0.316379	−	0.869243i	0.674953	−	0.737861i	$-0.264164\pi$
$720$	−1.58938	−	0.191988i	−0.0592325	−	0.00715499i
$721$			3.12322i			0.116315i
$722$	13.1446	+	13.7193i	0.489190	+	0.510581i
$723$	−28.0660	+	0.762467i	−1.04379	+	0.0283565i
$724$	−3.77404	−	10.3691i	−0.140261	−	0.385364i
$725$	−0.977978	+	5.54639i	−0.0363212	+	0.205988i
$726$	−2.71259	+	8.13355i	−0.100673	+	0.301864i
$727$	15.8328	−	5.76268i	0.587207	−	0.213726i	−0.0312935	−	0.999510i	$-0.509963\pi$
$727$	15.8328	−	5.76268i	0.587207	−	0.213726i	0.618501	+	0.785784i	$0.287740\pi$
$728$	1.36266	−	3.74388i	0.0505036	−	0.138757i
$729$	17.1148	+	20.8826i	0.633880	+	0.773431i
$730$	4.04413	+	2.33488i	0.149680	+	0.0864177i
$731$	−4.02451	+	11.0573i	−0.148852	+	0.408968i
$732$	−23.3141	+	4.76711i	−0.861713	+	0.176197i
$733$	15.0144	+	26.0056i	0.554568	+	0.960540i	0.997937	+	0.0642008i	$0.0204498\pi$
$733$	15.0144	+	26.0056i	0.554568	+	0.960540i	−0.443369	+	0.896339i	$0.646217\pi$
$734$	−1.26269			−0.0466066
$735$	2.62817	+	0.876508i	0.0969414	+	0.0323305i
$736$	−0.114448	−	0.314444i	−0.00421862	−	0.0115905i
$737$	−1.95418	−	11.0827i	−0.0719831	−	0.408237i
$738$	−4.04078	−	3.03254i	−0.148743	−	0.111629i
$739$	33.3427	+	27.9778i	1.22653	+	1.02918i	0.998457	+	0.0555379i	$0.0176874\pi$
$739$	33.3427	+	27.9778i	1.22653	+	1.02918i	0.228074	+	0.973644i	$0.426757\pi$
$740$	0.243874	+	0.422401i	0.00896497	+	0.0155278i
$741$	7.86842	−	12.8116i	0.289053	−	0.470646i
$742$	11.3901	−	19.7282i	0.418144	−	0.724246i
$743$	−47.1230	+	17.1514i	−1.72877	+	0.629223i	−0.998542	−	0.0539758i	$-0.982811\pi$
$743$	−47.1230	+	17.1514i	−1.72877	+	0.629223i	−0.730233	+	0.683198i	$0.760588\pi$
$744$	7.45381	+	5.91711i	0.273270	+	0.216932i
$745$	−7.06649	+	5.92949i	−0.258896	+	0.217240i
$746$	−31.9304	−	5.63019i	−1.16905	−	0.206136i
$747$	−7.44533	−	7.95282i	−0.272410	−	0.290978i
$748$	−3.59306	−	6.22336i	−0.131375	−	0.227549i
$749$	−37.6266			−1.37485
$750$	6.71960	−	5.95675i	0.245365	−	0.217510i
$751$	0.838987	−	0.147936i	0.0306151	−	0.00539826i	−0.158320	−	0.987388i	$-0.550608\pi$
$751$	0.838987	−	0.147936i	0.0306151	−	0.00539826i	0.188935	+	0.981990i	$0.439497\pi$
$752$	−8.15139	+	4.70620i	−0.297250	+	0.171618i
$753$	−8.35775	+	0.227054i	−0.304573	+	0.00827432i
$754$	2.34246	−	0.413039i	0.0853073	−	0.0150420i
$755$	−1.48989	+	8.44960i	−0.0542227	+	0.307512i
$756$	−10.0569	+	2.63246i	−0.365765	+	0.0957418i
$757$	4.96691	−	1.80781i	0.180525	−	0.0657059i	−0.250176	−	0.968200i	$-0.580488\pi$
$757$	4.96691	−	1.80781i	0.180525	−	0.0657059i	0.430701	+	0.902495i	$0.358266\pi$
$758$	−19.4492	−	3.42941i	−0.706425	−	0.124562i
$759$	−1.25348	−	0.678996i	−0.0454985	−	0.0246460i
$760$	1.58974	−	1.69807i	0.0576660	−	0.0615955i
$761$	−16.9847	−	9.80610i	−0.615694	−	0.355471i	0.159497	−	0.987198i	$-0.449013\pi$
$761$	−16.9847	−	9.80610i	−0.615694	−	0.355471i	−0.775191	+	0.631727i	$0.782346\pi$
$762$	29.9828	+	23.8014i	1.08616	+	0.862235i
$763$	−2.41423	+	2.87716i	−0.0874008	+	0.104160i
$764$	−12.2487	+	2.15978i	−0.443143	+	0.0781381i
$765$	−0.560916	+	4.64354i	−0.0202800	+	0.167888i
$766$	−0.840295	−	0.305843i	−0.0303611	−	0.0110505i
$767$	0.0377555	+	0.0217981i	0.00136327	+	0.000787085i
$768$	−0.0470371	−	1.73141i	−0.00169731	−	0.0624769i
$769$	1.93387	+	10.9675i	0.0697371	+	0.395499i	0.999618	+	0.0276379i	$0.00879855\pi$
$769$	1.93387	+	10.9675i	0.0697371	+	0.395499i	−0.929881	+	0.367861i	$0.880090\pi$
$770$	−0.455999	−	2.58610i	−0.0164331	−	0.0931966i
$771$	−0.812914	−	29.9229i	−0.0292764	−	1.07765i
$772$	−21.5376	−	12.4347i	−0.775156	−	0.447536i
$773$	−48.6792	−	17.7178i	−1.75087	−	0.637264i	−0.751132	−	0.660153i	$-0.770492\pi$
$773$	−48.6792	−	17.7178i	−1.75087	−	0.637264i	−0.999738	+	0.0228881i	$0.992714\pi$
$774$	−1.44898	+	11.9954i	−0.0520826	+	0.431166i
$775$	−25.5146	+	4.49892i	−0.916512	+	0.161606i
$776$	0.137863	−	0.164298i	0.00494898	−	0.00589797i
$777$	2.48061	+	1.96920i	0.0889915	+	0.0706447i
$778$	11.5770	+	6.68396i	0.415054	+	0.239631i
$779$	7.02406	−	2.13235i	0.251663	−	0.0763994i
$780$	−1.61847	−	0.876705i	−0.0579506	−	0.0313911i
$781$	22.8060	+	4.02131i	0.816063	+	0.143894i
$782$	−0.918683	+	0.334373i	−0.0328520	+	0.0119572i
$783$	−4.36311	−	4.41389i	−0.155925	−	0.157740i
$784$	−0.520490	+	2.95185i	−0.0185889	+	0.105423i
$785$	1.70039	−	0.299825i	0.0606896	−	0.0107012i
$786$	16.8367	−	0.457402i	0.600546	−	0.0163150i
$787$	19.4574	−	11.2337i	0.693582	−	0.400440i	−0.111371	−	0.993779i	$-0.535524\pi$
$787$	19.4574	−	11.2337i	0.693582	−	0.400440i	0.804952	+	0.593339i	$0.202191\pi$
$788$	22.1864	−	3.91207i	0.790359	−	0.139362i
$789$	−10.3486	+	9.17379i	−0.368421	+	0.326595i
$790$	−0.243553			−0.00866522
$791$	11.8841	+	20.5838i	0.422549	+	0.731876i
$792$	−5.04298	−	5.38672i	−0.179194	−	0.191409i
$793$	−26.9443	−	4.75102i	−0.956822	−	0.168713i
$794$	11.4148	−	9.57818i	0.405097	−	0.339917i
$795$	−8.24290	−	6.54351i	−0.292345	−	0.232074i
$796$	4.38829	−	1.59721i	0.155539	−	0.0566115i
$797$	−27.8989	+	48.3224i	−0.988231	+	1.71167i	−0.361642	+	0.932317i	$0.617784\pi$
$797$	−27.8989	+	48.3224i	−0.988231	+	1.71167i	−0.626589	+	0.779350i	$0.715550\pi$
$798$	5.54976	−	14.0481i	0.196459	−	0.497298i
$799$	13.7497	+	23.8152i	0.486430	+	0.842521i
$800$	3.61207	+	3.03089i	0.127706	+	0.107158i
$801$	6.31244	+	4.73739i	0.223039	+	0.167387i
$802$	−3.91855	−	22.2232i	−0.138369	−	0.784729i
$803$	7.36150	+	20.2255i	0.259782	+	0.713744i
$804$	−7.51765	−	2.50718i	−0.265127	−	0.0884214i
$805$	−0.357256			−0.0125916
$806$	5.47103	+	9.47611i	0.192709	+	0.333782i
$807$	28.2019	−	5.76654i	0.992755	−	0.202992i
$808$	0.179710	−	0.493748i	0.00632216	−	0.0173700i
$809$	−15.2804	−	8.82216i	−0.537231	−	0.310171i	0.206725	−	0.978399i	$-0.433720\pi$
$809$	−15.2804	−	8.82216i	−0.537231	−	0.310171i	−0.743956	+	0.668228i	$0.767053\pi$
$810$	0.520754	+	4.77447i	0.0182974	+	0.167758i
$811$	12.0826	−	33.1967i	0.424278	−	1.16569i	−0.524958	−	0.851128i	$-0.675919\pi$
$811$	12.0826	−	33.1967i	0.424278	−	1.16569i	0.949236	−	0.314565i	$-0.101859\pi$
$812$	2.24550	−	0.817297i	0.0788018	−	0.0286815i
$813$	7.23071	−	21.6809i	0.253592	−	0.760383i
$814$	−0.390378	+	2.21394i	−0.0136827	+	0.0775987i
$815$	4.22338	+	11.6037i	0.147939	+	0.406458i
$816$	−5.05852	+	0.137424i	−0.177084	+	0.00481081i
$817$	−12.8157	−	11.9982i	−0.448366	−	0.419762i
$818$		−	11.2606i		−	0.393718i
$819$	−11.8662	−	1.43338i	−0.414639	−	0.0500862i
$820$	−0.307367	−	0.844484i	−0.0107337	−	0.0294907i
$821$	−22.7724	−	27.1391i	−0.794763	−	0.947162i	0.204736	−	0.978817i	$-0.434367\pi$
$821$	−22.7724	−	27.1391i	−0.794763	−	0.947162i	−0.999499	+	0.0316553i	$0.989922\pi$
$822$	−3.06436	+	1.21056i	−0.106882	+	0.0422230i
$823$	−26.5143	+	22.2481i	−0.924230	+	0.775521i	−0.974772	−	0.223201i	$-0.928349\pi$
$823$	−26.5143	+	22.2481i	−0.924230	+	0.775521i	0.0505427	+	0.998722i	$0.483905\pi$
$824$			1.56110i			0.0543835i
$825$	20.0805	−	0.545525i	0.699113	−	0.0189927i
$826$	0.0411569	+	0.0149799i	0.00143203	+	0.000521217i
$827$	−6.02188	+	5.05295i	−0.209401	+	0.175708i	−0.741456	−	0.671001i	$-0.765864\pi$
$827$	−6.02188	+	5.05295i	−0.209401	+	0.175708i	0.532055	+	0.846710i	$0.321420\pi$
$828$	−0.840844	+	0.548398i	−0.0292214	+	0.0190581i
$829$	−10.3872	+	5.99703i	−0.360761	+	0.208285i	−0.669414	−	0.742889i	$-0.733455\pi$
$829$	−10.3872	+	5.99703i	−0.360761	+	0.208285i	0.308654	+	0.951175i	$0.400122\pi$
$830$	−0.336503	−	1.90840i	−0.0116802	−	0.0662416i
$831$	35.8906	+	5.32793i	1.24503	+	0.184824i
$832$	0.681108	−	1.87133i	0.0236132	−	0.0648766i
$833$	8.62416	+	1.52067i	0.298809	+	0.0526882i
$834$	−9.03571	−	22.8727i	−0.312881	−	0.792017i
$835$	6.73071	−	3.88598i	0.232926	−	0.134480i
$836$	10.6440	−	1.28564i	0.368129	−	0.0444646i
$837$	12.2156	−	25.8055i	0.422232	−	0.891968i
$838$	−17.9303	+	21.3685i	−0.619391	+	0.738162i
$839$	−35.8811	−	30.1078i	−1.23875	−	1.03944i	−0.997620	−	0.0689445i	$-0.978037\pi$
$839$	−35.8811	−	30.1078i	−1.23875	−	1.03944i	−0.241132	−	0.970492i	$-0.577519\pi$
$840$	−1.75421	−	0.585040i	−0.0605261	−	0.0201858i
$841$	−21.1224	−	17.7238i	−0.728359	−	0.611166i
$842$	14.1574	+	16.8721i	0.487896	+	0.581452i
$843$	−2.53704	+	1.55812i	−0.0873804	+	0.0536646i
$844$		−	7.24530i		−	0.249393i
$845$	3.09891	+	3.69314i	0.106606	+	0.127048i
$846$	19.2982	+	20.6136i	0.663486	+	0.708710i
$847$	−4.95180	+	8.57676i	−0.170146	+	0.294701i
$848$	5.69319	−	9.86089i	0.195505	−	0.338624i
$849$	−29.9692	+	6.12791i	−1.02854	+	0.210309i
$850$	8.85509	−	10.5531i	0.303727	−	0.361968i
$851$	0.287400	+	0.104605i	0.00985194	+	0.00358581i
$852$	10.1391	−	12.7723i	0.347361	−	0.437572i
$853$	−6.02809	+	34.1870i	−0.206398	+	1.17054i	0.688827	+	0.724926i	$0.258126\pi$
$853$	−6.02809	+	34.1870i	−0.206398	+	1.17054i	−0.895225	+	0.445615i	$0.852985\pi$
$854$	−27.4868			−0.940578
$855$	−6.04334	−	3.48920i	−0.206678	−	0.119328i
$856$	−18.8072			−0.642815
$857$	−7.67987	+	43.5547i	−0.262339	+	1.48780i	0.514166	+	0.857690i	$0.328101\pi$
$857$	−7.67987	+	43.5547i	−0.262339	+	1.48780i	−0.776506	+	0.630110i	$0.783010\pi$
$858$	−3.11710	−	7.89053i	−0.106416	−	0.269378i
$859$	17.0992	+	6.22360i	0.583417	+	0.212346i	0.616832	−	0.787095i	$-0.288416\pi$
$859$	17.0992	+	6.22360i	0.583417	+	0.212346i	−0.0334145	+	0.999442i	$0.510638\pi$
$860$	−1.38152	+	1.64643i	−0.0471095	+	0.0561429i
$861$	−3.87108	−	4.36683i	−0.131926	−	0.148821i
$862$	1.32397	−	2.29319i	0.0450947	−	0.0781063i
$863$	−24.0408	+	41.6399i	−0.818358	+	1.41744i	0.0885327	+	0.996073i	$0.471782\pi$
$863$	−24.0408	+	41.6399i	−0.818358	+	1.41744i	−0.906891	+	0.421365i	$0.861551\pi$
$864$	−5.02679	+	1.31580i	−0.171015	+	0.0447645i
$865$	1.36153	+	1.62261i	0.0462934	+	0.0551703i
$866$		−	10.2291i		−	0.347600i
$867$	−0.398130	−	14.6550i	−0.0135212	−	0.497709i
$868$	7.06602	+	8.42095i	0.239836	+	0.285826i
$869$	−0.859938	−	0.721574i	−0.0291714	−	0.0244777i
$870$	−0.221162	−	1.08162i	−0.00749809	−	0.0366703i
$871$	−6.97977	−	5.85672i	−0.236500	−	0.198447i
$872$	−1.20672	+	1.43811i	−0.0408646	+	0.0487006i
$873$	−0.573871	−	0.290986i	−0.0194226	−	0.00984838i
$874$	0.0792059	−	1.45644i	0.00267918	−	0.0492648i
$875$	8.98269	−	5.18616i	0.303670	−	0.175324i
$876$	14.9924	+	2.22560i	0.506545	+	0.0751961i
$877$	6.51606	+	1.14896i	0.220032	+	0.0387975i	0.282577	−	0.959245i	$-0.408811\pi$
$877$	6.51606	+	1.14896i	0.220032	+	0.0387975i	−0.0625454	+	0.998042i	$0.519922\pi$
$878$	3.46261	−	9.51345i	0.116858	−	0.321064i
$879$	12.8386	+	32.4992i	0.433035	+	1.09617i
$880$	−0.227925	−	1.29263i	−0.00768336	−	0.0435745i
$881$	−33.3800	+	19.2720i	−1.12460	+	0.649289i	−0.942572	−	0.334004i	$-0.891600\pi$
$881$	−33.3800	+	19.2720i	−1.12460	+	0.649289i	−0.182030	+	0.983293i	$0.558267\pi$
$882$	8.97889	−	0.488218i	0.302335	−	0.0164391i
$883$	3.10907	−	2.60882i	0.104628	−	0.0877937i	−0.588973	−	0.808153i	$-0.700467\pi$
$883$	3.10907	−	2.60882i	0.104628	−	0.0877937i	0.693601	+	0.720359i	$0.256023\pi$
$884$	−5.46730	−	1.98993i	−0.183885	−	0.0669287i
$885$	0.00963772	−	0.0177920i	0.000323968	−	0.000598073i
$886$		−	25.0150i		−	0.840396i
$887$	−17.0326	+	14.2921i	−0.571899	+	0.479881i	−0.882276	−	0.470733i	$-0.843989\pi$
$887$	−17.0326	+	14.2921i	−0.571899	+	0.479881i	0.310376	+	0.950614i	$0.399545\pi$
$888$	1.23990	+	0.984279i	0.0416084	+	0.0330302i
$889$	28.4229	+	33.8731i	0.953273	+	1.13607i
$890$	0.480164	+	1.31924i	0.0160951	+	0.0442210i
$891$	−12.3067	+	18.4006i	−0.412288	+	0.616443i
$892$			9.68107i			0.324146i
$893$	−40.7317	+	4.91980i	−1.36303	+	0.164635i
$894$	−14.2606	+	26.3262i	−0.476945	+	0.880481i
$895$	−3.58664	−	9.85422i	−0.119888	−	0.329390i
$896$	0.347410	−	1.97026i	0.0116061	−	0.0658217i
$897$	−1.13081	+	0.231220i	−0.0377565	+	0.00772020i
$898$	23.2502	−	8.46239i	0.775870	−	0.282394i
$899$	−2.24462	+	6.16705i	−0.0748623	+	0.205682i
$900$	6.39728	−	12.6165i	0.213243	−	0.420549i
$901$	−28.8097	−	16.6333i	−0.959791	−	0.554136i
$902$	1.41670	−	3.89235i	0.0471709	−	0.129601i
$903$	−4.41543	+	13.2395i	−0.146936	+	0.440582i
$904$	5.94010	+	10.2885i	0.197565	+	0.342192i
$905$	−5.88851			−0.195741
$906$	5.57875	+	27.2835i	0.185342	+	0.906434i
$907$	−3.86968	−	10.6319i	−0.128491	−	0.353025i	0.858720	−	0.512445i	$-0.171260\pi$
$907$	−3.86968	−	10.6319i	−0.128491	−	0.353025i	−0.987211	+	0.159419i	$0.949038\pi$
$908$	−0.489715	−	2.77731i	−0.0162518	−	0.0921683i
$909$	−1.56493	−	0.189036i	−0.0519055	−	0.00626992i
$910$	−1.62870	−	1.36664i	−0.0539909	−	0.0453037i
$911$	−14.6497	−	25.3740i	−0.485366	−	0.840679i	0.514492	−	0.857495i	$-0.327980\pi$
$911$	−14.6497	−	25.3740i	−0.485366	−	0.840679i	−0.999859	+	0.0168160i	$0.994647\pi$
$912$	2.77397	−	7.02176i	0.0918554	−	0.232514i
$913$	4.46590	−	7.73517i	0.147800	−	0.255997i
$914$	34.5252	−	12.5661i	1.14199	−	0.415651i
$915$	−1.86469	+	12.5612i	−0.0616448	+	0.415260i
$916$	9.92227	−	8.32578i	0.327841	−	0.275091i
$917$	19.1593	+	3.37831i	0.632697	+	0.111562i
$918$	3.84426	+	14.6864i	0.126880	+	0.484722i
$919$	−19.5551	−	33.8705i	−0.645064	−	1.11728i	−0.984287	−	0.176578i	$-0.943497\pi$
$919$	−19.5551	−	33.8705i	−0.645064	−	1.11728i	0.339223	−	0.940706i	$-0.389836\pi$
$920$	−0.178570			−0.00588727
$921$	4.96299	+	24.2720i	0.163536	+	0.799791i
$922$	−27.3091	+	4.81534i	−0.899378	+	0.158585i
$923$	16.2376	−	9.37477i	0.534466	−	0.308574i
$924$	−4.46049	−	7.26287i	−0.146739	−	0.238931i
$925$	−4.24422	+	0.748370i	−0.139549	+	0.0246063i
$926$	2.74311	−	15.5570i	0.0901443	−	0.511234i
$927$	4.56119	−	1.06246i	0.149809	−	0.0348957i
$928$	1.12239	−	0.408515i	0.0368441	−	0.0134102i
$929$	28.4727	+	5.02050i	0.934158	+	0.164717i	0.619954	−	0.784638i	$-0.287151\pi$
$929$	28.4727	+	5.02050i	0.934158	+	0.164717i	0.314204	+	0.949356i	$0.398262\pi$
$930$	4.32764	−	2.65782i	0.141909	−	0.0871534i
$931$	−7.13744	+	10.9434i	−0.233920	+	0.358657i
$932$	24.1656	+	13.9520i	0.791572	+	0.457014i
$933$	6.65890	−	44.8565i	0.218003	−	1.46854i
$934$	25.9112	−	30.8798i	0.847841	−	1.01042i
$935$	−3.77656	+	0.665910i	−0.123507	+	0.0217776i
$936$	−5.93116	−	0.716454i	−0.193866	−	0.0234180i
$937$	35.7520	+	13.0126i	1.16797	+	0.425105i	0.851937	−	0.523645i	$-0.175428\pi$
$937$	35.7520	+	13.0126i	1.16797	+	0.425105i	0.316029	+	0.948750i	$0.397650\pi$
$938$	−7.92730	−	4.57683i	−0.258836	−	0.149439i
$939$	38.9680	+	21.1084i	1.27167	+	0.688848i
$940$	0.872212	+	4.94656i	0.0284484	+	0.161339i
$941$	1.22939	+	6.97224i	0.0400771	+	0.227289i	0.998267	−	0.0588438i	$-0.0187414\pi$
$941$	1.22939	+	6.97224i	0.0400771	+	0.227289i	−0.958190	+	0.286132i	$0.907630\pi$
$942$	4.77542	−	2.93283i	0.155592	−	0.0955566i
$943$	−0.488025	−	0.281762i	−0.0158923	−	0.00917542i
$944$	0.0205717	+	0.00748749i	0.000669552	+	0.000243697i
$945$	−0.515471	+	5.52359i	−0.0167683	+	0.179683i
$946$	−9.75577	+	1.72021i	−0.317188	+	0.0559287i
$947$	13.2966	−	15.8463i	0.432083	−	0.514936i	−0.505439	−	0.862862i	$-0.668669\pi$
$947$	13.2966	−	15.8463i	0.432083	−	0.514936i	0.937522	+	0.347926i	$0.113114\pi$
$948$	−0.735212	+	0.290441i	−0.0238786	+	0.00943307i
$949$	15.0917	+	8.71319i	0.489897	+	0.282842i
$950$	9.29486	+	18.3314i	0.301565	+	0.594748i
$951$	0.199707	+	7.35113i	0.00647596	+	0.238377i
$952$	−5.75634	−	1.01500i	−0.186564	−	0.0328963i
$953$	18.5914	−	6.76670i	0.602233	−	0.219195i	−0.0228683	−	0.999738i	$-0.507280\pi$
$953$	18.5914	−	6.76670i	0.602233	−	0.219195i	0.625101	+	0.780544i	$0.285058\pi$
$954$	−32.6861	−	9.92310i	−1.05825	−	0.321272i
$955$	−1.15255	+	6.53645i	−0.0372957	+	0.211514i
$956$	−13.9488	+	2.45955i	−0.451137	+	0.0795477i
$957$	2.42363	−	4.47422i	0.0783448	−	0.144631i
$958$	27.4496	−	15.8480i	0.886855	−	0.512026i
$959$	−3.74794	+	0.660863i	−0.121027	+	0.0213404i
$960$	−0.876820	−	0.292424i	−0.0282992	−	0.00943795i
$961$	0.809502			0.0261130
$962$	0.910077	+	1.57630i	0.0293421	+	0.0508219i
$963$	12.7998	+	54.9504i	0.412469	+	1.77075i
$964$	−15.9636	−	2.81482i	−0.514154	−	0.0906592i
$965$	−10.1665	+	8.53072i	−0.327272	+	0.274613i
$966$	−1.07845	+	0.426034i	−0.0346985	+	0.0137074i
$967$	−46.9151	+	17.0757i	−1.50869	+	0.549118i	−0.958294	−	0.285786i	$-0.907745\pi$
$967$	−46.9151	+	17.0757i	−1.50869	+	0.549118i	−0.550396	+	0.834904i	$0.685523\pi$
$968$	−2.47509	+	4.28698i	−0.0795524	+	0.137789i
$969$	−20.5149	−	8.10448i	−0.659032	−	0.260353i
$970$	−0.0572269	−	0.0991199i	−0.00183744	−	0.00318255i
$971$	22.4089	+	18.8033i	0.719136	+	0.603427i	0.927146	−	0.374700i	$-0.122254\pi$
$971$	22.4089	+	18.8033i	0.719136	+	0.603427i	−0.208010	+	0.978127i	$0.566699\pi$
$972$	7.26564	+	13.7917i	0.233045	+	0.442368i
$973$	−4.93275	−	27.9750i	−0.158137	−	0.896838i
$974$	1.75622	+	4.82516i	0.0562728	+	0.154608i
$975$	12.1704	−	10.7888i	0.389766	−	0.345518i
$976$	−13.7389			−0.439771
$977$	8.60383	+	14.9023i	0.275261	+	0.476766i	0.970201	−	0.242302i	$-0.0779024\pi$
$977$	8.60383	+	14.9023i	0.275261	+	0.476766i	−0.694940	+	0.719068i	$0.744569\pi$
$978$	26.5867	+	29.9915i	0.850148	+	0.959021i
$979$	−2.21315	+	6.08057i	−0.0707324	+	0.194336i
$980$	1.38524	+	0.799767i	0.0442498	+	0.0255476i
$981$	5.02312	+	2.54701i	0.160376	+	0.0813199i
$982$	15.0216	−	41.2716i	0.479359	−	1.31703i
$983$	23.5969	−	8.58857i	0.752624	−	0.273933i	0.0629147	−	0.998019i	$-0.479960\pi$
$983$	23.5969	−	8.58857i	0.752624	−	0.273933i	0.689710	+	0.724086i	$0.257738\pi$
$984$	−1.93491	−	2.18270i	−0.0616827	−	0.0695820i
$985$	2.08765	−	11.8396i	0.0665180	−	0.377242i
$986$	−1.19352	−	3.27918i	−0.0380095	−	0.104430i
$987$	17.0692	+	27.7932i	0.543318	+	0.884666i
$988$	5.93253	−	6.33679i	0.188739	−	0.201600i
$989$			1.34771i			0.0428546i
$990$	−3.62166	+	1.54569i	−0.115104	+	0.0491252i
$991$	−0.0679374	−	0.186656i	−0.00215810	−	0.00592934i	0.938609	−	0.344983i	$-0.112115\pi$
$991$	−0.0679374	−	0.186656i	−0.00215810	−	0.00592934i	−0.940767	+	0.339054i	$0.889893\pi$
$992$	3.53185	+	4.20910i	0.112136	+	0.133639i
$993$	−7.64855	+	51.5231i	−0.242719	+	1.63504i
$994$	14.4295	−	12.1078i	0.457677	−	0.384037i
$995$		−	2.49207i		−	0.0790040i
$996$	−3.29160	−	5.35961i	−0.104298	−	0.169826i
$997$	3.78920	+	1.37916i	0.120005	+	0.0436783i	0.401325	−	0.915936i	$-0.368550\pi$
$997$	3.78920	+	1.37916i	0.120005	+	0.0436783i	−0.281320	+	0.959614i	$0.590772\pi$
$998$	−6.89119	+	5.78240i	−0.218137	+	0.183039i
$999$	2.03199	−	4.29260i	0.0642894	−	0.135812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.41.1	✓	60
9.2	odd	6		342.2.bf.c.155.7	yes	60
19.13	odd	18		342.2.bf.c.203.7	yes	60
171.146	even	18	inner	342.2.x.c.317.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.41.1	✓	60	1.1	even	1	trivial
342.2.x.c.317.1	yes	60	171.146	even	18	inner
342.2.bf.c.155.7	yes	60	9.2	odd	6
342.2.bf.c.203.7	yes	60	19.13	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.71328 - 0.254334i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.343019 + 0.408794i) q^{5} +(-0.547977 + 1.64308i) q^{6} +(-1.00033 + 1.73262i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.87063 + 0.871489i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.71328 - 0.254334i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.343019 + 0.408794i) q^{5} +(-0.547977 + 1.64308i) q^{6} +(-1.00033 + 1.73262i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.87063 + 0.871489i) q^{9} +(0.343019 + 0.408794i) q^{10} +2.45964i q^{11} +(1.52297 + 0.824971i) q^{12} +(1.28006 + 1.52552i) q^{13} +(1.53259 + 1.28600i) q^{14} +(0.691657 - 0.613136i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.87798 - 2.23809i) q^{17} +(1.35673 - 2.67568i) q^{18} +(1.97124 + 3.88770i) q^{19} +(0.462148 - 0.266822i) q^{20} +(2.15450 - 2.71403i) q^{21} +(2.42227 + 0.427112i) q^{22} +(0.114448 - 0.314444i) q^{23} +(1.07690 - 1.35657i) q^{24} +(0.818790 + 4.64359i) q^{25} +(1.72463 - 0.995713i) q^{26} +(-4.69653 - 2.22320i) q^{27} +(1.53259 - 1.28600i) q^{28} +(1.12239 + 0.408515i) q^{29} +(-0.483716 - 0.787619i) q^{30} +5.49459i q^{31} +(0.766044 - 0.642788i) q^{32} +(0.625570 - 4.21404i) q^{33} +(-1.87798 - 2.23809i) q^{34} +(-0.365153 - 1.00325i) q^{35} +(-2.39944 - 1.80074i) q^{36} +0.913995i q^{37} +(4.17094 - 1.26621i) q^{38} +(-1.80511 - 2.93920i) q^{39} +(-0.182517 - 0.501460i) q^{40} +(0.292432 - 1.65846i) q^{41} +(-2.29868 - 2.59305i) q^{42} +(-3.78464 + 1.37750i) q^{43} +(0.841246 - 2.31130i) q^{44} +(-1.34094 + 0.874559i) q^{45} +(-0.289793 - 0.167312i) q^{46} +(-3.21923 + 8.84477i) q^{47} +(-1.14896 - 1.29610i) q^{48} +(1.49869 + 2.59581i) q^{49} +4.71523 q^{50} +(-3.78672 + 3.35683i) q^{51} +(-0.681108 - 1.87133i) q^{52} +(-1.97722 - 11.2134i) q^{53} +(-3.00497 + 4.23912i) q^{54} +(-1.00549 - 0.843703i) q^{55} +(-1.00033 - 1.73262i) q^{56} +(-2.38851 - 7.16205i) q^{57} +(0.597209 - 1.03440i) q^{58} +(0.0205717 - 0.00748749i) q^{59} +(-0.859650 + 0.339599i) q^{60} +(-10.5246 + 8.83119i) q^{61} +(5.41111 + 0.954125i) q^{62} +(-4.38152 + 4.10193i) q^{63} +(-0.500000 - 0.866025i) q^{64} -1.06271 q^{65} +(-4.04139 - 1.34783i) q^{66} +(-4.50583 + 0.794499i) q^{67} +(-2.53019 + 1.46081i) q^{68} +(-0.276055 + 0.509621i) q^{69} +(-1.05142 + 0.185393i) q^{70} +(1.63492 - 9.27209i) q^{71} +(-2.19005 + 2.05029i) q^{72} +(8.22297 - 2.99292i) q^{73} +(0.900109 + 0.158714i) q^{74} +(-0.221791 - 8.16400i) q^{75} +(-0.522693 - 4.32745i) q^{76} +(-4.26161 - 2.46044i) q^{77} +(-3.20800 + 1.26730i) q^{78} +(-0.293366 + 0.349620i) q^{79} +(-0.525536 + 0.0926662i) q^{80} +(7.48102 + 5.00344i) q^{81} +(-1.58249 - 0.575979i) q^{82} +(-3.14484 - 1.81567i) q^{83} +(-2.95282 + 1.81348i) q^{84} +(0.270735 + 1.53541i) q^{85} +(0.699373 + 3.96634i) q^{86} +(-1.81906 - 0.985360i) q^{87} +(-2.13011 - 1.22982i) q^{88} +(2.47214 + 0.899785i) q^{89} +(0.628421 + 1.47243i) q^{90} +(-3.92363 + 0.691841i) q^{91} +(-0.215092 + 0.256337i) q^{92} +(1.39746 - 9.41375i) q^{93} +(8.15139 + 4.70620i) q^{94} +(-2.26544 - 0.527721i) q^{95} +(-1.47593 + 0.906441i) q^{96} +(-0.211218 - 0.0372434i) q^{97} +(2.81662 - 1.02517i) q^{98} +(-2.14355 + 7.06071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

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