LMFDB - Embedded newform 546.2.bd.b.361.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.7
Root			$2.62249i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.34750 + 1.22035i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.34750 + 1.22035i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -2.62249 q^{10} +5.01074i q^{11} +(0.500000 + 0.866025i) q^{12} +(3.59427 - 0.285022i) q^{13} +(-2.64317 - 0.116897i) q^{14} +(-2.27114 + 1.31124i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.44859 - 5.97313i) q^{17} +(0.866025 + 0.500000i) q^{18} +3.03338i q^{19} +(-2.27114 - 1.31124i) q^{20} +(-2.34750 + 1.22035i) q^{21} +(-2.50537 + 4.33943i) q^{22} +(-2.49983 + 4.32984i) q^{23} +1.00000i q^{24} +(0.938722 - 1.62591i) q^{25} +(3.25524 + 1.55030i) q^{26} +1.00000 q^{27} +(-2.23060 - 1.42282i) q^{28} +(2.18859 + 3.79075i) q^{29} -2.62249 q^{30} +(4.93016 + 2.84643i) q^{31} +(-0.866025 + 0.500000i) q^{32} +5.01074i q^{33} -6.89718i q^{34} +(3.73133 - 5.84973i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.70976 - 2.14183i) q^{37} +(-1.51669 + 2.62699i) q^{38} +(3.59427 - 0.285022i) q^{39} +(-1.31124 - 2.27114i) q^{40} +(4.95053 - 2.85819i) q^{41} +(-2.64317 - 0.116897i) q^{42} +(6.44053 - 11.1553i) q^{43} +(-4.33943 + 2.50537i) q^{44} +(-2.27114 + 1.31124i) q^{45} +(-4.32984 + 2.49983i) q^{46} +(0.499608 - 0.288449i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.02150 - 5.72953i) q^{49} +(1.62591 - 0.938722i) q^{50} +(-3.44859 - 5.97313i) q^{51} +(2.04397 + 2.97022i) q^{52} +(-3.49408 + 6.05193i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-6.57031 - 11.3801i) q^{55} +(-1.22035 - 2.34750i) q^{56} +3.03338i q^{57} +4.37718i q^{58} +(9.08332 - 5.24426i) q^{59} +(-2.27114 - 1.31124i) q^{60} +14.3150 q^{61} +(2.84643 + 4.93016i) q^{62} +(-2.34750 + 1.22035i) q^{63} -1.00000 q^{64} +(-7.78936 + 5.36029i) q^{65} +(-2.50537 + 4.33943i) q^{66} +2.47913i q^{67} +(3.44859 - 5.97313i) q^{68} +(-2.49983 + 4.32984i) q^{69} +(6.15629 - 3.20035i) q^{70} +(2.82667 + 1.63198i) q^{71} +1.00000i q^{72} +(4.20527 + 2.42791i) q^{73} +(-2.14183 - 3.70976i) q^{74} +(0.938722 - 1.62591i) q^{75} +(-2.62699 + 1.51669i) q^{76} +(-6.11485 - 11.7627i) q^{77} +(3.25524 + 1.55030i) q^{78} +(-3.69502 - 6.39996i) q^{79} -2.62249i q^{80} +1.00000 q^{81} +5.71638 q^{82} +9.16995i q^{83} +(-2.23060 - 1.42282i) q^{84} +(15.6645 + 9.04389i) q^{85} +(11.1553 - 6.44053i) q^{86} +(2.18859 + 3.79075i) q^{87} -5.01074 q^{88} +(-13.3582 - 7.71235i) q^{89} -2.62249 q^{90} +(-8.08971 + 5.05535i) q^{91} -4.99967 q^{92} +(4.93016 + 2.84643i) q^{93} +0.576897 q^{94} +(-3.97750 - 6.88924i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-12.1886 - 7.03709i) q^{97} +(6.34749 - 2.95117i) q^{98} +5.01074i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.27114	+	1.31124i	−1.01569	+	0.586406i	−0.912851	−	0.408292i	$-0.866124\pi$
$5$	−2.27114	+	1.31124i	−1.01569	+	0.586406i	−0.102834	+	0.994699i	$0.532791\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−2.34750	+	1.22035i	−0.887271	+	0.461248i
$7$	−2.34750	+	1.22035i	−0.887271	+	0.461248i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−2.62249			−0.829304
$11$			5.01074i			1.51080i	0.655267	+	0.755398i	$0.272556\pi$
$11$			5.01074i			1.51080i	−0.655267	+	0.755398i	$0.727444\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.59427	−	0.285022i	0.996871	−	0.0790510i
$13$	3.59427	−	0.285022i	0.996871	−	0.0790510i
$14$	−2.64317	−	0.116897i	−0.706416	−	0.0312420i
$15$	−2.27114	+	1.31124i	−0.586406	+	0.338562i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.44859	−	5.97313i	−0.836406	−	1.44870i	−0.892880	−	0.450294i	$-0.851319\pi$
$17$	−3.44859	−	5.97313i	−0.836406	−	1.44870i	0.0564743	−	0.998404i	$-0.482014\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$			3.03338i			0.695906i	0.937512	+	0.347953i	$0.113123\pi$
$19$			3.03338i			0.695906i	−0.937512	+	0.347953i	$0.886877\pi$
$20$	−2.27114	−	1.31124i	−0.507843	−	0.293203i
$21$	−2.34750	+	1.22035i	−0.512266	+	0.266302i
$22$	−2.50537	+	4.33943i	−0.534147	+	0.925169i
$23$	−2.49983	+	4.32984i	−0.521251	+	0.902834i	0.478443	+	0.878119i	$0.341201\pi$
$23$	−2.49983	+	4.32984i	−0.521251	+	0.902834i	−0.999695	+	0.0247154i	$0.992132\pi$
$24$			1.00000i			0.204124i
$25$	0.938722	−	1.62591i	0.187744	−	0.325183i
$26$	3.25524	+	1.55030i	0.638405	+	0.304038i
$27$	1.00000			0.192450
$28$	−2.23060	−	1.42282i	−0.421544	−	0.268888i
$29$	2.18859	+	3.79075i	0.406411	+	0.703924i	0.994485	−	0.104883i	$-0.0334468\pi$
$29$	2.18859	+	3.79075i	0.406411	+	0.703924i	−0.588074	+	0.808807i	$0.700113\pi$
$30$	−2.62249			−0.478799
$31$	4.93016	+	2.84643i	0.885484	+	0.511234i	0.872463	−	0.488681i	$-0.162522\pi$
$31$	4.93016	+	2.84643i	0.885484	+	0.511234i	0.0130211	+	0.999915i	$0.495855\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$			5.01074i			0.872258i
$34$		−	6.89718i		−	1.18286i
$35$	3.73133	−	5.84973i	0.630709	−	0.988784i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.70976	−	2.14183i	−0.609881	−	0.352115i	0.163038	−	0.986620i	$-0.447871\pi$
$37$	−3.70976	−	2.14183i	−0.609881	−	0.352115i	−0.772919	+	0.634505i	$0.781204\pi$
$38$	−1.51669	+	2.62699i	−0.246040	+	0.426153i
$39$	3.59427	−	0.285022i	0.575543	−	0.0456401i
$40$	−1.31124	−	2.27114i	−0.207326	−	0.359099i
$41$	4.95053	−	2.85819i	0.773143	−	0.446374i	−0.0608516	−	0.998147i	$-0.519382\pi$
$41$	4.95053	−	2.85819i	0.773143	−	0.446374i	0.833995	+	0.551772i	$0.186048\pi$
$42$	−2.64317	−	0.116897i	−0.407850	−	0.0180376i
$43$	6.44053	−	11.1553i	0.982172	−	1.70117i	0.328285	−	0.944579i	$-0.393529\pi$
$43$	6.44053	−	11.1553i	0.982172	−	1.70117i	0.653886	−	0.756593i	$-0.273137\pi$
$44$	−4.33943	+	2.50537i	−0.654194	+	0.377699i
$45$	−2.27114	+	1.31124i	−0.338562	+	0.195469i
$46$	−4.32984	+	2.49983i	−0.638400	+	0.368580i
$47$	0.499608	−	0.288449i	0.0728753	−	0.0420746i	−0.463120	−	0.886296i	$-0.653270\pi$
$47$	0.499608	−	0.288449i	0.0728753	−	0.0420746i	0.535995	+	0.844221i	$0.319937\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	4.02150	−	5.72953i	0.574500	−	0.818505i
$50$	1.62591	−	0.938722i	0.229939	−	0.132755i
$51$	−3.44859	−	5.97313i	−0.482899	−	0.836406i
$52$	2.04397	+	2.97022i	0.283448	+	0.411895i
$53$	−3.49408	+	6.05193i	−0.479949	+	0.831296i	−0.999735	−	0.0229999i	$-0.992678\pi$
$53$	−3.49408	+	6.05193i	−0.479949	+	0.831296i	0.519786	+	0.854296i	$0.326012\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−6.57031	−	11.3801i	−0.885940	−	1.53449i
$56$	−1.22035	−	2.34750i	−0.163076	−	0.313698i
$57$			3.03338i			0.401781i
$58$			4.37718i			0.574752i
$59$	9.08332	−	5.24426i	1.18255	−	0.682744i	0.225945	−	0.974140i	$-0.427453\pi$
$59$	9.08332	−	5.24426i	1.18255	−	0.682744i	0.956603	+	0.291396i	$0.0941197\pi$
$60$	−2.27114	−	1.31124i	−0.293203	−	0.169281i
$61$	14.3150			1.83285			0.916425	−	0.400206i	$-0.131061\pi$
$61$	14.3150			1.83285			0.916425	+	0.400206i	$0.131061\pi$
$62$	2.84643	+	4.93016i	0.361497	+	0.626132i
$63$	−2.34750	+	1.22035i	−0.295757	+	0.153749i
$64$	−1.00000			−0.125000
$65$	−7.78936	+	5.36029i	−0.966151	+	0.664862i
$66$	−2.50537	+	4.33943i	−0.308390	+	0.534147i
$67$			2.47913i			0.302873i	0.988467	+	0.151437i	$0.0483900\pi$
$67$			2.47913i			0.302873i	−0.988467	+	0.151437i	$0.951610\pi$
$68$	3.44859	−	5.97313i	0.418203	−	0.724349i
$69$	−2.49983	+	4.32984i	−0.300945	+	0.521251i
$70$	6.15629	−	3.20035i	0.735817	−	0.382515i
$71$	2.82667	+	1.63198i	0.335463	+	0.193680i	0.658264	−	0.752787i	$-0.271291\pi$
$71$	2.82667	+	1.63198i	0.335463	+	0.193680i	−0.322801	+	0.946467i	$0.604624\pi$
$72$			1.00000i			0.117851i
$73$	4.20527	+	2.42791i	0.492189	+	0.284166i	0.725482	−	0.688241i	$-0.241617\pi$
$73$	4.20527	+	2.42791i	0.492189	+	0.284166i	−0.233293	+	0.972406i	$0.574950\pi$
$74$	−2.14183	−	3.70976i	−0.248983	−	0.431251i
$75$	0.938722	−	1.62591i	0.108394	−	0.187744i
$76$	−2.62699	+	1.51669i	−0.301336	+	0.173976i
$77$	−6.11485	−	11.7627i	−0.696852	−	1.34049i
$78$	3.25524	+	1.55030i	0.368583	+	0.175537i
$79$	−3.69502	−	6.39996i	−0.415722	−	0.720052i	0.579782	−	0.814772i	$-0.303138\pi$
$79$	−3.69502	−	6.39996i	−0.415722	−	0.720052i	−0.995504	+	0.0947200i	$0.969804\pi$
$80$		−	2.62249i		−	0.293203i
$81$	1.00000			0.111111
$82$	5.71638			0.631269
$83$			9.16995i			1.00653i	0.864131	+	0.503266i	$0.167869\pi$
$83$			9.16995i			1.00653i	−0.864131	+	0.503266i	$0.832131\pi$
$84$	−2.23060	−	1.42282i	−0.243379	−	0.155242i
$85$	15.6645	+	9.04389i	1.69905	+	0.980947i
$86$	11.1553	−	6.44053i	1.20291	−	0.694500i
$87$	2.18859	+	3.79075i	0.234641	+	0.406411i
$88$	−5.01074			−0.534147
$89$	−13.3582	−	7.71235i	−1.41596	−	0.817507i	−0.420023	−	0.907514i	$-0.637978\pi$
$89$	−13.3582	−	7.71235i	−1.41596	−	0.817507i	−0.995941	+	0.0900063i	$0.971311\pi$
$90$	−2.62249			−0.276435
$91$	−8.08971	+	5.05535i	−0.848032	+	0.529945i
$92$	−4.99967			−0.521251
$93$	4.93016	+	2.84643i	0.511234	+	0.295161i
$94$	0.576897			0.0595024
$95$	−3.97750	−	6.88924i	−0.408083	−	0.706821i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−12.1886	−	7.03709i	−1.23756	−	0.714508i	−0.268969	−	0.963149i	$-0.586683\pi$
$97$	−12.1886	−	7.03709i	−1.23756	−	0.714508i	−0.968596	+	0.248641i	$0.920016\pi$
$98$	6.34749	−	2.95117i	0.641193	−	0.298113i
$99$			5.01074i			0.503598i
$100$	1.87744			0.187744
$101$	−9.23409			−0.918826			−0.459413	−	0.888223i	$-0.651940\pi$
$101$	−9.23409			−0.918826			−0.459413	+	0.888223i	$0.651940\pi$
$102$		−	6.89718i		−	0.682923i
$103$	−2.43903	−	4.22453i	−0.240325	−	0.416255i	0.720482	−	0.693474i	$-0.243921\pi$
$103$	−2.43903	−	4.22453i	−0.240325	−	0.416255i	−0.960807	+	0.277219i	$0.910587\pi$
$104$	0.285022	+	3.59427i	0.0279487	+	0.352447i
$105$	3.73133	−	5.84973i	0.364140	−	0.570875i
$106$	−6.05193	+	3.49408i	−0.587815	+	0.339375i
$107$	0.0863737	−	0.149604i	0.00835006	−	0.0144627i	−0.861820	−	0.507214i	$-0.830675\pi$
$107$	0.0863737	−	0.149604i	0.00835006	−	0.0144627i	0.870170	+	0.492751i	$0.164009\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	10.9212	+	6.30538i	1.04606	+	0.603946i	0.921545	−	0.388271i	$-0.126928\pi$
$109$	10.9212	+	6.30538i	1.04606	+	0.603946i	0.124520	+	0.992217i	$0.460261\pi$
$110$		−	13.1406i		−	1.25291i
$111$	−3.70976	−	2.14183i	−0.352115	−	0.203294i
$112$	0.116897	−	2.64317i	0.0110457	−	0.249756i
$113$	−6.33262	+	10.9684i	−0.595722	+	1.03182i	0.397722	+	0.917506i	$0.369801\pi$
$113$	−6.33262	+	10.9684i	−0.595722	+	1.03182i	−0.993444	+	0.114316i	$0.963533\pi$
$114$	−1.51669	+	2.62699i	−0.142051	+	0.246040i
$115$		−	13.1116i		−	1.22266i
$116$	−2.18859	+	3.79075i	−0.203205	+	0.351962i
$117$	3.59427	−	0.285022i	0.332290	−	0.0263503i
$118$	10.4885			0.965546
$119$	15.3849	+	9.81344i	1.41033	+	0.899597i
$120$	−1.31124	−	2.27114i	−0.119700	−	0.207326i
$121$	−14.1075			−1.28250
$122$	12.3972	+	7.15751i	1.12239	+	0.648011i
$123$	4.95053	−	2.85819i	0.446374	−	0.257714i
$124$			5.69286i			0.511234i
$125$		−	8.18887i		−	0.732434i
$126$	−2.64317	−	0.116897i	−0.235472	−	0.0104140i
$127$	3.67120	+	6.35871i	0.325767	+	0.564244i	0.981667	−	0.190603i	$-0.0610443\pi$
$127$	3.67120	+	6.35871i	0.325767	+	0.564244i	−0.655901	+	0.754847i	$0.727711\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	6.44053	−	11.1553i	0.567057	−	0.982172i
$130$	−9.42593	+	0.747468i	−0.826708	+	0.0655573i
$131$	5.41067	+	9.37156i	0.472733	+	0.818797i	0.999513	−	0.0312046i	$-0.00993434\pi$
$131$	5.41067	+	9.37156i	0.472733	+	0.818797i	−0.526780	+	0.850001i	$0.676601\pi$
$132$	−4.33943	+	2.50537i	−0.377699	+	0.218065i
$133$	−3.70178	−	7.12086i	−0.320985	−	0.617457i
$134$	−1.23956	+	2.14699i	−0.107082	+	0.185471i
$135$	−2.27114	+	1.31124i	−0.195469	+	0.112854i
$136$	5.97313	−	3.44859i	0.512192	−	0.295714i
$137$	11.9618	−	6.90614i	1.02196	−	0.590031i	0.107292	−	0.994228i	$-0.465782\pi$
$137$	11.9618	−	6.90614i	1.02196	−	0.590031i	0.914672	+	0.404196i	$0.132449\pi$
$138$	−4.32984	+	2.49983i	−0.368580	+	0.212800i
$139$	5.75709	−	9.97158i	0.488310	−	0.845778i	−0.511599	−	0.859224i	$-0.670947\pi$
$139$	5.75709	−	9.97158i	0.488310	−	0.845778i	0.999910	+	0.0134459i	$0.00428009\pi$
$140$	6.93168	+	0.306560i	0.585834	+	0.0259091i
$141$	0.499608	−	0.288449i	0.0420746	−	0.0242918i
$142$	1.63198	+	2.82667i	0.136952	+	0.237209i
$143$	1.42817	+	18.0099i	0.119430	+	1.50607i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−9.94119	−	5.73955i	−0.825571	−	0.476644i
$146$	2.42791	+	4.20527i	0.200935	+	0.348030i
$147$	4.02150	−	5.72953i	0.331688	−	0.472564i
$148$		−	4.28366i		−	0.352115i
$149$			16.5087i			1.35245i	0.736697	+	0.676223i	$0.236385\pi$
$149$			16.5087i			1.35245i	−0.736697	+	0.676223i	$0.763615\pi$
$150$	1.62591	−	0.938722i	0.132755	−	0.0766463i
$151$	5.69210	+	3.28634i	0.463217	+	0.267438i	0.713396	−	0.700761i	$-0.247156\pi$
$151$	5.69210	+	3.28634i	0.463217	+	0.267438i	−0.250179	+	0.968200i	$0.580490\pi$
$152$	−3.03338			−0.246040
$153$	−3.44859	−	5.97313i	−0.278802	−	0.482899i
$154$	0.585739	−	13.2442i	0.0472002	−	1.06725i
$155$	−14.9295			−1.19916
$156$	2.04397	+	2.97022i	0.163649	+	0.237808i
$157$	4.40621	−	7.63178i	0.351654	−	0.609083i	−0.634885	−	0.772606i	$-0.718953\pi$
$157$	4.40621	−	7.63178i	0.351654	−	0.609083i	0.986539	+	0.163524i	$0.0522860\pi$
$158$		−	7.39004i		−	0.587920i
$159$	−3.49408	+	6.05193i	−0.277099	+	0.479949i
$160$	1.31124	−	2.27114i	0.103663	−	0.179549i
$161$	0.584445	−	13.2150i	0.0460607	−	1.04148i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	9.36526i		−	0.733544i	−0.930311	−	0.366772i	$-0.880463\pi$
$163$		−	9.36526i		−	0.733544i	0.930311	−	0.366772i	$-0.119537\pi$
$164$	4.95053	+	2.85819i	0.386572	+	0.223187i
$165$	−6.57031	−	11.3801i	−0.511498	−	0.885940i
$166$	−4.58497	+	7.94141i	−0.355863	+	0.616373i
$167$	−2.26138	+	1.30561i	−0.174991	+	0.101031i	−0.584937	−	0.811079i	$-0.698881\pi$
$167$	−2.26138	+	1.30561i	−0.174991	+	0.101031i	0.409946	+	0.912110i	$0.365547\pi$
$168$	−1.22035	−	2.34750i	−0.0941519	−	0.181113i
$169$	12.8375	−	2.04889i	0.987502	−	0.157607i
$170$	9.04389	+	15.6645i	0.693635	+	1.20141i
$171$			3.03338i			0.231969i
$172$	12.8811			0.982172
$173$	−4.99495			−0.379759			−0.189880	−	0.981807i	$-0.560810\pi$
$173$	−4.99495			−0.379759			−0.189880	+	0.981807i	$0.560810\pi$
$174$			4.37718i			0.331833i
$175$	−0.219467	+	4.96240i	−0.0165901	+	0.375122i
$176$	−4.33943	−	2.50537i	−0.327097	−	0.188849i
$177$	9.08332	−	5.24426i	0.682744	−	0.394183i
$178$	−7.71235	−	13.3582i	−0.578065	−	1.00124i
$179$	−7.52240			−0.562251			−0.281125	−	0.959671i	$-0.590708\pi$
$179$	−7.52240			−0.562251			−0.281125	+	0.959671i	$0.590708\pi$
$180$	−2.27114	−	1.31124i	−0.169281	−	0.0977344i
$181$	−7.14351			−0.530973			−0.265487	−	0.964115i	$-0.585533\pi$
$181$	−7.14351			−0.530973			−0.265487	+	0.964115i	$0.585533\pi$
$182$	−9.53357	+	0.333204i	−0.706675	+	0.0246987i
$183$	14.3150			1.05820
$184$	−4.32984	−	2.49983i	−0.319200	−	0.184290i
$185$	11.2339			0.825929
$186$	2.84643	+	4.93016i	0.208711	+	0.361497i
$187$	29.9298	−	17.2800i	2.18869	−	1.26364i
$188$	0.499608	+	0.288449i	0.0364376	+	0.0210373i
$189$	−2.34750	+	1.22035i	−0.170755	+	0.0887673i
$190$		−	7.95501i		−	0.577117i
$191$	7.92903			0.573724			0.286862	−	0.957972i	$-0.407388\pi$
$191$	7.92903			0.573724			0.286862	+	0.957972i	$0.407388\pi$
$192$	−1.00000			−0.0721688
$193$			10.7806i			0.776005i	0.921658	+	0.388002i	$0.126835\pi$
$193$			10.7806i			0.776005i	−0.921658	+	0.388002i	$0.873165\pi$
$194$	−7.03709	−	12.1886i	−0.505234	−	0.875090i
$195$	−7.78936	+	5.36029i	−0.557807	+	0.383858i
$196$	6.97267	+	0.617955i	0.498048	+	0.0441396i
$197$	−16.5289	+	9.54296i	−1.17763	+	0.679908i	−0.955466	−	0.295100i	$-0.904647\pi$
$197$	−16.5289	+	9.54296i	−1.17763	+	0.679908i	−0.222169	+	0.975008i	$0.571314\pi$
$198$	−2.50537	+	4.33943i	−0.178049	+	0.308390i
$199$	11.7571	+	20.3638i	0.833436	+	1.44355i	0.895297	+	0.445469i	$0.146963\pi$
$199$	11.7571	+	20.3638i	0.833436	+	1.44355i	−0.0618609	+	0.998085i	$0.519704\pi$
$200$	1.62591	+	0.938722i	0.114970	+	0.0663777i
$201$			2.47913i			0.174864i
$202$	−7.99696	−	4.61704i	−0.562664	−	0.324854i
$203$	−9.76375	−	6.22794i	−0.685281	−	0.437115i
$204$	3.44859	−	5.97313i	0.241450	−	0.418203i
$205$	−7.49557	+	12.9827i	−0.523513	+	0.906752i
$206$		−	4.87807i		−	0.339871i
$207$	−2.49983	+	4.32984i	−0.173750	+	0.300945i
$208$	−1.55030	+	3.25524i	−0.107494	+	0.225710i
$209$	−15.1995			−1.05137
$210$	6.15629	−	3.20035i	0.424824	−	0.220845i
$211$	2.44732	+	4.23888i	0.168480	+	0.291816i	0.937886	−	0.346944i	$-0.112781\pi$
$211$	2.44732	+	4.23888i	0.168480	+	0.291816i	−0.769406	+	0.638761i	$0.779447\pi$
$212$	−6.98817			−0.479949
$213$	2.82667	+	1.63198i	0.193680	+	0.111821i
$214$	0.149604	−	0.0863737i	0.0102267	−	0.00590439i
$215$			33.7804i			2.30381i
$216$			1.00000i			0.0680414i
$217$	−15.0472	−	0.665477i	−1.02147	−	0.0451755i
$218$	6.30538	+	10.9212i	0.427054	+	0.739680i
$219$	4.20527	+	2.42791i	0.284166	+	0.164063i
$220$	6.57031	−	11.3801i	0.442970	−	0.767246i
$221$	−14.0976	−	20.4861i	−0.948310	−	1.37805i
$222$	−2.14183	−	3.70976i	−0.143750	−	0.248983i
$223$	−8.72547	+	5.03765i	−0.584301	+	0.337346i	−0.762841	−	0.646587i	$-0.776196\pi$
$223$	−8.72547	+	5.03765i	−0.584301	+	0.337346i	0.178540	+	0.983933i	$0.442863\pi$
$224$	1.42282	−	2.23060i	0.0950661	−	0.149038i
$225$	0.938722	−	1.62591i	0.0625815	−	0.108394i
$226$	−10.9684	+	6.33262i	−0.729608	+	0.421239i
$227$	12.3996	−	7.15891i	0.822990	−	0.475154i	−0.0284563	−	0.999595i	$-0.509059\pi$
$227$	12.3996	−	7.15891i	0.822990	−	0.475154i	0.851447	+	0.524441i	$0.175726\pi$
$228$	−2.62699	+	1.51669i	−0.173976	+	0.100445i
$229$	−13.3945	+	7.73332i	−0.885134	+	0.511032i	−0.872348	−	0.488886i	$-0.837403\pi$
$229$	−13.3945	+	7.73332i	−0.885134	+	0.511032i	−0.0127863	+	0.999918i	$0.504070\pi$
$230$	6.55579	−	11.3550i	0.432276	−	0.748723i
$231$	−6.11485	−	11.7627i	−0.402328	−	0.773929i
$232$	−3.79075	+	2.18859i	−0.248875	+	0.143688i
$233$	2.31317	+	4.00653i	0.151541	+	0.262477i	0.931794	−	0.362987i	$-0.118243\pi$
$233$	2.31317	+	4.00653i	0.151541	+	0.262477i	−0.780253	+	0.625464i	$0.784910\pi$
$234$	3.25524	+	1.55030i	0.212802	+	0.101346i
$235$	−0.756453	+	1.31022i	−0.0493456	+	0.0854690i
$236$	9.08332	+	5.24426i	0.591274	+	0.341372i
$237$	−3.69502	−	6.39996i	−0.240017	−	0.415722i
$238$	8.41696	+	16.1911i	0.545591	+	1.04951i
$239$			8.48540i			0.548875i	0.961605	+	0.274437i	$0.0884916\pi$
$239$			8.48540i			0.548875i	−0.961605	+	0.274437i	$0.911508\pi$
$240$		−	2.62249i		−	0.169281i
$241$	−3.68833	+	2.12946i	−0.237586	+	0.137170i	−0.614067	−	0.789254i	$-0.710467\pi$
$241$	−3.68833	+	2.12946i	−0.237586	+	0.137170i	0.376481	+	0.926425i	$0.377134\pi$
$242$	−12.2175	−	7.05376i	−0.785369	−	0.453433i
$243$	1.00000			0.0641500
$244$	7.15751	+	12.3972i	0.458213	+	0.793648i
$245$	−1.62058	+	18.2857i	−0.103535	+	1.16823i
$246$	5.71638			0.364463
$247$	0.864582	+	10.9028i	0.0550120	+	0.693728i
$248$	−2.84643	+	4.93016i	−0.180749	+	0.313066i
$249$			9.16995i			0.581122i
$250$	4.09443	−	7.09177i	0.258955	−	0.448523i
$251$	−1.00766	+	1.74531i	−0.0636027	+	0.110163i	−0.896073	−	0.443906i	$-0.853592\pi$
$251$	−1.00766	+	1.74531i	−0.0636027	+	0.110163i	0.832471	+	0.554069i	$0.186926\pi$
$252$	−2.23060	−	1.42282i	−0.140515	−	0.0896292i
$253$	−21.6957	−	12.5260i	−1.36400	−	0.787504i
$254$			7.34240i			0.460703i
$255$	15.6645	+	9.04389i	0.980947	+	0.566350i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.4978	−	19.9147i	0.717211	−	1.24225i	−0.244889	−	0.969551i	$-0.578752\pi$
$257$	11.4978	−	19.9147i	0.717211	−	1.24225i	0.962100	−	0.272695i	$-0.0879151\pi$
$258$	11.1553	−	6.44053i	0.694500	−	0.400970i
$259$	11.3224	+	0.500746i	0.703542	+	0.0311148i
$260$	−8.53682	−	4.06564i	−0.529431	−	0.252140i
$261$	2.18859	+	3.79075i	0.135470	+	0.234641i
$262$			10.8213i			0.668545i
$263$	22.0383			1.35894			0.679470	−	0.733703i	$-0.262210\pi$
$263$	22.0383			1.35894			0.679470	+	0.733703i	$0.262210\pi$
$264$	−5.01074			−0.308390
$265$		−	18.3264i		−	1.12578i
$266$	0.354592	−	8.01774i	0.0217415	−	0.491599i
$267$	−13.3582	−	7.71235i	−0.817507	−	0.471988i
$268$	−2.14699	+	1.23956i	−0.131148	+	0.0757184i
$269$	−2.18641	−	3.78698i	−0.133308	−	0.230896i	0.791642	−	0.610985i	$-0.209227\pi$
$269$	−2.18641	−	3.78698i	−0.133308	−	0.230896i	−0.924950	+	0.380089i	$0.875893\pi$
$270$	−2.62249			−0.159600
$271$	−13.4302	−	7.75390i	−0.815824	−	0.471016i	0.0331504	−	0.999450i	$-0.489446\pi$
$271$	−13.4302	−	7.75390i	−0.815824	−	0.471016i	−0.848974	+	0.528434i	$0.822779\pi$
$272$	6.89718			0.418203
$273$	−8.08971	+	5.05535i	−0.489612	+	0.305964i
$274$	13.8123			0.834430
$275$	8.14704	+	4.70369i	0.491285	+	0.283643i
$276$	−4.99967			−0.300945
$277$	−14.3794	−	24.9058i	−0.863972	−	1.49644i	−0.868064	−	0.496452i	$-0.834636\pi$
$277$	−14.3794	−	24.9058i	−0.863972	−	1.49644i	0.00409153	−	0.999992i	$-0.498698\pi$
$278$	9.97158	−	5.75709i	0.598056	−	0.345288i
$279$	4.93016	+	2.84643i	0.295161	+	0.170411i
$280$	5.84973	+	3.73133i	0.349588	+	0.222989i
$281$		−	13.5100i		−	0.805941i	−0.915213	−	0.402970i	$-0.867978\pi$
$281$		−	13.5100i		−	0.805941i	0.915213	−	0.402970i	$-0.132022\pi$
$282$	0.576897			0.0343537
$283$	−19.0071			−1.12986			−0.564928	−	0.825140i	$-0.691096\pi$
$283$	−19.0071			−1.12986			−0.564928	+	0.825140i	$0.691096\pi$
$284$			3.26395i			0.193680i
$285$	−3.97750	−	6.88924i	−0.235607	−	0.408083i
$286$	−7.76814	+	16.3112i	−0.459340	+	0.964499i
$287$	−8.13338	+	12.7510i	−0.480098	+	0.752666i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−15.2856	+	26.4754i	−0.899150	+	1.55737i
$290$	−5.73955	−	9.94119i	−0.337038	−	0.583767i
$291$	−12.1886	−	7.03709i	−0.714508	−	0.412522i
$292$			4.85582i			0.284166i
$293$	−7.14308	−	4.12406i	−0.417303	−	0.240930i	0.276620	−	0.960979i	$-0.410786\pi$
$293$	−7.14308	−	4.12406i	−0.417303	−	0.240930i	−0.693923	+	0.720049i	$0.744119\pi$
$294$	6.34749	−	2.95117i	0.370193	−	0.172116i
$295$	−13.7530	+	23.8209i	−0.800731	+	1.38691i
$296$	2.14183	−	3.70976i	0.124491	−	0.215625i
$297$			5.01074i			0.290753i
$298$	−8.25436	+	14.2970i	−0.478162	+	0.828201i
$299$	−7.75097	+	16.2751i	−0.448250	+	0.941214i
$300$	1.87744			0.108394
$301$	−1.50575	+	34.0468i	−0.0867902	+	1.96243i
$302$	3.28634	+	5.69210i	0.189107	+	0.327544i
$303$	−9.23409			−0.530485
$304$	−2.62699	−	1.51669i	−0.150668	−	0.0869882i
$305$	−32.5114	+	18.7705i	−1.86160	+	1.07479i
$306$		−	6.89718i		−	0.394286i
$307$		−	2.94195i		−	0.167906i	−0.996470	−	0.0839531i	$-0.973245\pi$
$307$		−	2.94195i		−	0.167906i	0.996470	−	0.0839531i	$-0.0267546\pi$
$308$	7.12938	−	11.1770i	0.406234	−	0.636867i
$309$	−2.43903	−	4.22453i	−0.138752	−	0.240325i
$310$	−12.9293	−	7.46473i	−0.734335	−	0.423968i
$311$	7.47126	−	12.9406i	0.423656	−	0.733794i	−0.572638	−	0.819809i	$-0.694080\pi$
$311$	7.47126	−	12.9406i	0.423656	−	0.733794i	0.996294	+	0.0860145i	$0.0274131\pi$
$312$	0.285022	+	3.59427i	0.0161362	+	0.203485i
$313$	12.1929	+	21.1187i	0.689182	+	1.19370i	0.972103	+	0.234555i	$0.0753632\pi$
$313$	12.1929	+	21.1187i	0.689182	+	1.19370i	−0.282921	+	0.959143i	$0.591303\pi$
$314$	7.63178	−	4.40621i	0.430686	−	0.248657i
$315$	3.73133	−	5.84973i	0.210236	−	0.329595i
$316$	3.69502	−	6.39996i	0.207861	−	0.360026i
$317$	24.6493	−	14.2313i	1.38444	−	0.799309i	0.391762	−	0.920067i	$-0.371866\pi$
$317$	24.6493	−	14.2313i	1.38444	−	0.799309i	0.992682	+	0.120758i	$0.0385324\pi$
$318$	−6.05193	+	3.49408i	−0.339375	+	0.195938i
$319$	−18.9945	+	10.9665i	−1.06349	+	0.614004i
$320$	2.27114	−	1.31124i	0.126961	−	0.0733008i
$321$	0.0863737	−	0.149604i	0.00482091	−	0.00835006i
$322$	7.11362	−	11.1523i	0.396427	−	0.621492i
$323$	18.1188	−	10.4609i	1.00816	−	0.582060i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	2.91060	−	6.11153i	0.161451	−	0.339007i
$326$	4.68263	−	8.11055i	0.259347	−	0.449202i
$327$	10.9212	+	6.30538i	0.603946	+	0.348688i
$328$	2.85819	+	4.95053i	0.157817	+	0.273347i
$329$	−0.820821	+	1.28683i	−0.0452533	+	0.0709451i
$330$		−	13.1406i		−	0.723367i
$331$		−	6.27684i		−	0.345006i	−0.985009	−	0.172503i	$-0.944815\pi$
$331$		−	6.27684i		−	0.345006i	0.985009	−	0.172503i	$-0.0551855\pi$
$332$	−7.94141	+	4.58497i	−0.435841	+	0.251633i
$333$	−3.70976	−	2.14183i	−0.203294	−	0.117372i
$334$	−2.61122			−0.142879
$335$	−3.25074	−	5.63045i	−0.177607	−	0.307624i
$336$	0.116897	−	2.64317i	0.00637724	−	0.144197i
$337$	9.99063			0.544224			0.272112	−	0.962266i	$-0.412278\pi$
$337$	9.99063			0.544224			0.272112	+	0.962266i	$0.412278\pi$
$338$	12.1421	+	4.64437i	0.660441	+	0.252620i
$339$	−6.33262	+	10.9684i	−0.343941	+	0.595722i
$340$			18.0878i			0.980947i
$341$	−14.2627	+	24.7038i	−0.772370	+	1.33778i
$342$	−1.51669	+	2.62699i	−0.0820133	+	0.142051i
$343$	−2.44844	+	18.3577i	−0.132203	+	0.991223i
$344$	11.1553	+	6.44053i	0.601455	+	0.347250i
$345$		−	13.1116i		−	0.705903i
$346$	−4.32576	−	2.49748i	−0.232554	−	0.134265i
$347$	1.95465	+	3.38555i	0.104931	+	0.181746i	0.913710	−	0.406367i	$-0.133204\pi$
$347$	1.95465	+	3.38555i	0.104931	+	0.181746i	−0.808779	+	0.588113i	$0.799871\pi$
$348$	−2.18859	+	3.79075i	−0.117321	+	0.203205i
$349$	13.3325	−	7.69750i	0.713671	−	0.412038i	−0.0987480	−	0.995112i	$-0.531484\pi$
$349$	13.3325	−	7.69750i	0.713671	−	0.412038i	0.812419	+	0.583074i	$0.198150\pi$
$350$	−2.67126	+	4.18783i	−0.142785	+	0.223849i
$351$	3.59427	−	0.285022i	0.191848	−	0.0152134i
$352$	−2.50537	−	4.33943i	−0.133537	−	0.231292i
$353$		−	30.0836i		−	1.60119i	−0.599208	−	0.800594i	$-0.704518\pi$
$353$		−	30.0836i		−	1.60119i	0.599208	−	0.800594i	$-0.295482\pi$
$354$	10.4885			0.557458
$355$	−8.55968			−0.454300
$356$		−	15.4247i		−	0.817507i
$357$	15.3849	+	9.81344i	0.814254	+	0.519383i
$358$	−6.51459	−	3.76120i	−0.344307	−	0.198786i
$359$	−7.23357	+	4.17631i	−0.381773	+	0.220417i	−0.678590	−	0.734518i	$-0.737408\pi$
$359$	−7.23357	+	4.17631i	−0.381773	+	0.220417i	0.296816	+	0.954935i	$0.404075\pi$
$360$	−1.31124	−	2.27114i	−0.0691086	−	0.119700i
$361$	9.79859			0.515715
$362$	−6.18646	−	3.57176i	−0.325153	−	0.187727i
$363$	−14.1075			−0.740453
$364$	−8.42292	−	4.47822i	−0.441481	−	0.234723i
$365$	−12.7343			−0.666546
$366$	12.3972	+	7.15751i	0.648011	+	0.374129i
$367$	12.3640			0.645394			0.322697	−	0.946502i	$-0.395410\pi$
$367$	12.3640			0.645394			0.322697	+	0.946502i	$0.395410\pi$
$368$	−2.49983	−	4.32984i	−0.130313	−	0.225708i
$369$	4.95053	−	2.85819i	0.257714	−	0.148791i
$370$	9.72880	+	5.61693i	0.505776	+	0.292010i
$371$	0.816894	−	18.4709i	0.0424110	−	0.958961i
$372$			5.69286i			0.295161i
$373$	−22.6398			−1.17224			−0.586122	−	0.810223i	$-0.699346\pi$
$373$	−22.6398			−1.17224			−0.586122	+	0.810223i	$0.699346\pi$
$374$	34.5600			1.78705
$375$		−	8.18887i		−	0.422871i
$376$	0.288449	+	0.499608i	0.0148756	+	0.0257653i
$377$	8.94683	+	13.0012i	0.460785	+	0.669594i
$378$	−2.64317	−	0.116897i	−0.135950	−	0.00601252i
$379$	9.43601	−	5.44788i	0.484695	−	0.279839i	−0.237676	−	0.971344i	$-0.576386\pi$
$379$	9.43601	−	5.44788i	0.484695	−	0.279839i	0.722371	+	0.691506i	$0.243052\pi$
$380$	3.97750	−	6.88924i	0.204042	−	0.353411i
$381$	3.67120	+	6.35871i	0.188081	+	0.325767i
$382$	6.86674	+	3.96451i	0.351333	+	0.202842i
$383$		−	1.26963i		−	0.0648751i	−0.999474	−	0.0324375i	$-0.989673\pi$
$383$		−	1.26963i		−	0.0648751i	0.999474	−	0.0324375i	$-0.0103270\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	29.3115	+	18.6967i	1.49385	+	0.952873i
$386$	−5.39030	+	9.33627i	−0.274359	+	0.475204i
$387$	6.44053	−	11.1553i	0.327391	−	0.567057i
$388$		−	14.0742i		−	0.714508i
$389$	15.3303	−	26.5529i	0.777279	−	1.34629i	−0.156226	−	0.987721i	$-0.549933\pi$
$389$	15.3303	−	26.5529i	0.777279	−	1.34629i	0.933505	−	0.358565i	$-0.116734\pi$
$390$	−9.42593	+	0.747468i	−0.477300	+	0.0378495i
$391$	34.4836			1.74391
$392$	5.72953	+	4.02150i	0.289385	+	0.203116i
$393$	5.41067	+	9.37156i	0.272932	+	0.472733i
$394$	−19.0859			−0.961535
$395$	16.7838	+	9.69014i	0.844486	+	0.487564i
$396$	−4.33943	+	2.50537i	−0.218065	+	0.125900i
$397$			26.4480i			1.32738i	0.748006	+	0.663692i	$0.231012\pi$
$397$			26.4480i			1.32738i	−0.748006	+	0.663692i	$0.768988\pi$
$398$			23.5141i			1.17866i
$399$	−3.70178	−	7.12086i	−0.185321	−	0.356489i
$400$	0.938722	+	1.62591i	0.0469361	+	0.0812957i
$401$	−18.9775	−	10.9567i	−0.947693	−	0.547151i	−0.0553295	−	0.998468i	$-0.517621\pi$
$401$	−18.9775	−	10.9567i	−0.947693	−	0.547151i	−0.892364	+	0.451317i	$0.850954\pi$
$402$	−1.23956	+	2.14699i	−0.0618238	+	0.107082i
$403$	18.5316	+	8.82563i	0.923126	+	0.439636i
$404$	−4.61704	−	7.99696i	−0.229707	−	0.397863i
$405$	−2.27114	+	1.31124i	−0.112854	+	0.0651562i
$406$	−5.34168	−	10.2754i	−0.265103	−	0.509961i
$407$	10.7322	−	18.5886i	0.531973	−	0.921405i
$408$	5.97313	−	3.44859i	0.295714	−	0.170731i
$409$	−8.96270	+	5.17462i	−0.443177	+	0.255868i	−0.704944	−	0.709263i	$-0.749028\pi$
$409$	−8.96270	+	5.17462i	−0.443177	+	0.255868i	0.261767	+	0.965131i	$0.415695\pi$
$410$	−12.9827	+	7.49557i	−0.641170	+	0.370180i
$411$	11.9618	−	6.90614i	0.590031	−	0.340655i
$412$	2.43903	−	4.22453i	0.120163	−	0.208128i
$413$	−14.9233	+	23.3957i	−0.734326	+	1.15123i
$414$	−4.32984	+	2.49983i	−0.212800	+	0.122860i
$415$	−12.0240	−	20.8262i	−0.590237	−	1.02232i
$416$	−2.97022	+	2.04397i	−0.145627	+	0.100214i
$417$	5.75709	−	9.97158i	0.281926	−	0.488310i
$418$	−13.1631	−	7.59975i	−0.643831	−	0.371716i
$419$	−8.98405	−	15.5608i	−0.438900	−	0.760197i	0.558705	−	0.829366i	$-0.311298\pi$
$419$	−8.98405	−	15.5608i	−0.438900	−	0.760197i	−0.997605	+	0.0691697i	$0.977965\pi$
$420$	6.93168	+	0.306560i	0.338231	+	0.0149586i
$421$		−	7.16224i		−	0.349066i	−0.984651	−	0.174533i	$-0.944158\pi$
$421$		−	7.16224i		−	0.349066i	0.984651	−	0.174533i	$-0.0558416\pi$
$422$			4.89463i			0.238267i
$423$	0.499608	−	0.288449i	0.0242918	−	0.0140249i
$424$	−6.05193	−	3.49408i	−0.293908	−	0.169688i
$425$	−12.9491			−0.628122
$426$	1.63198	+	2.82667i	0.0790695	+	0.136952i
$427$	−33.6045	+	17.4693i	−1.62624	+	0.845399i
$428$	0.172747			0.00835006
$429$	1.42817	+	18.0099i	0.0689529	+	0.869528i
$430$	−16.8902	+	29.2547i	−0.814519	+	1.41079i
$431$		−	31.7765i		−	1.53062i	−0.643661	−	0.765311i	$-0.722585\pi$
$431$		−	31.7765i		−	1.53062i	0.643661	−	0.765311i	$-0.277415\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	2.56335	−	4.43985i	0.123187	−	0.213365i	−0.797836	−	0.602874i	$-0.794022\pi$
$433$	2.56335	−	4.43985i	0.123187	−	0.213365i	0.921023	+	0.389509i	$0.127355\pi$
$434$	−12.6985	−	8.09992i	−0.609548	−	0.388808i
$435$	−9.94119	−	5.73955i	−0.476644	−	0.275190i
$436$			12.6108i			0.603946i
$437$	−13.1341	−	7.58295i	−0.628287	−	0.362742i
$438$	2.42791	+	4.20527i	0.116010	+	0.200935i
$439$	−18.1599	+	31.4539i	−0.866725	+	1.50121i	−0.00140016	+	0.999999i	$0.500446\pi$
$439$	−18.1599	+	31.4539i	−0.866725	+	1.50121i	−0.865324	+	0.501212i	$0.832888\pi$
$440$	11.3801	−	6.57031i	0.542525	−	0.313227i
$441$	4.02150	−	5.72953i	0.191500	−	0.272835i
$442$	−1.96585	−	24.7903i	−0.0935060	−	1.17916i
$443$	7.15190	+	12.3874i	0.339797	+	0.588545i	0.984394	−	0.175977i	$-0.0563084\pi$
$443$	7.15190	+	12.3874i	0.339797	+	0.588545i	−0.644598	+	0.764522i	$0.722975\pi$
$444$		−	4.28366i		−	0.203294i
$445$	40.4511			1.91757
$446$	−10.0753			−0.477079
$447$			16.5087i			0.780835i
$448$	2.34750	−	1.22035i	0.110909	−	0.0576560i
$449$	−5.30462	−	3.06262i	−0.250340	−	0.144534i	0.369580	−	0.929199i	$-0.379502\pi$
$449$	−5.30462	−	3.06262i	−0.250340	−	0.144534i	−0.619920	+	0.784665i	$0.712835\pi$
$450$	1.62591	−	0.938722i	0.0766463	−	0.0442518i
$451$	14.3217	+	24.8058i	0.674380	+	1.16806i
$452$	−12.6652			−0.595722
$453$	5.69210	+	3.28634i	0.267438	+	0.154406i
$454$	14.3178			0.671969
$455$	11.7441	−	22.0890i	0.550571	−	1.03555i
$456$	−3.03338			−0.142051
$457$	−18.5805	−	10.7274i	−0.869157	−	0.501808i	−0.00208888	−	0.999998i	$-0.500665\pi$
$457$	−18.5805	−	10.7274i	−0.869157	−	0.501808i	−0.867068	+	0.498190i	$0.833998\pi$
$458$	−15.4666			−0.722709
$459$	−3.44859	−	5.97313i	−0.160966	−	0.278802i
$460$	11.3550	−	6.55579i	0.529427	−	0.305665i
$461$	−23.6097	−	13.6311i	−1.09961	−	0.634862i	−0.163494	−	0.986544i	$-0.552277\pi$
$461$	−23.6097	−	13.6311i	−1.09961	−	0.634862i	−0.936120	+	0.351682i	$0.885610\pi$
$462$	0.585739	−	13.2442i	0.0272510	−	0.616177i
$463$			26.5768i			1.23513i	0.786521	+	0.617564i	$0.211880\pi$
$463$			26.5768i			1.23513i	−0.786521	+	0.617564i	$0.788120\pi$
$464$	−4.37718			−0.203205
$465$	−14.9295			−0.692337
$466$			4.62635i			0.214311i
$467$	−9.69582	−	16.7937i	−0.448669	−	0.777118i	0.549631	−	0.835408i	$-0.314768\pi$
$467$	−9.69582	−	16.7937i	−0.448669	−	0.777118i	−0.998300	+	0.0582902i	$0.981435\pi$
$468$	2.04397	+	2.97022i	0.0944826	+	0.137298i
$469$	−3.02540	−	5.81975i	−0.139700	−	0.268731i
$470$	−1.31022	+	0.756453i	−0.0604357	+	0.0348926i
$471$	4.40621	−	7.63178i	0.203028	−	0.351654i
$472$	5.24426	+	9.08332i	0.241387	+	0.418094i
$473$	55.8965	+	32.2718i	2.57012	+	1.48386i
$474$		−	7.39004i		−	0.339436i
$475$	4.93202	+	2.84750i	0.226297	+	0.130652i
$476$	−0.806258	+	18.2304i	−0.0369548	+	0.835589i
$477$	−3.49408	+	6.05193i	−0.159983	+	0.277099i
$478$	−4.24270	+	7.34857i	−0.194057	+	0.336116i
$479$			24.6896i			1.12810i	0.825742	+	0.564048i	$0.190757\pi$
$479$			24.6896i			1.12810i	−0.825742	+	0.564048i	$0.809243\pi$
$480$	1.31124	−	2.27114i	0.0598498	−	0.103663i
$481$	−13.9443	−	6.64095i	−0.635807	−	0.302801i
$482$	−4.25892			−0.193988
$483$	0.584445	−	13.2150i	0.0265932	−	0.601302i
$484$	−7.05376	−	12.2175i	−0.320626	−	0.555340i
$485$	36.9094			1.67597
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−22.7389	+	13.1283i	−1.03040	+	0.594901i	−0.917099	−	0.398660i	$-0.869475\pi$
$487$	−22.7389	+	13.1283i	−1.03040	+	0.594901i	−0.113300	+	0.993561i	$0.536142\pi$
$488$			14.3150i			0.648011i
$489$		−	9.36526i		−	0.423512i
$490$	−10.5463	+	15.0256i	−0.476435	+	0.678789i
$491$	−11.0510	−	19.1408i	−0.498723	−	0.863813i	0.501276	−	0.865287i	$-0.332864\pi$
$491$	−11.0510	−	19.1408i	−0.498723	−	0.863813i	−0.999999	+	0.00147433i	$0.999531\pi$
$492$	4.95053	+	2.85819i	0.223187	+	0.128857i
$493$	15.0951	−	26.1455i	0.679849	−	1.17753i
$494$	−4.70264	+	9.87438i	−0.211582	+	0.444270i
$495$	−6.57031	−	11.3801i	−0.295313	−	0.511498i
$496$	−4.93016	+	2.84643i	−0.221371	+	0.127809i
$497$	−8.62717	−	0.381545i	−0.386982	−	0.0171146i
$498$	−4.58497	+	7.94141i	−0.205458	+	0.355863i
$499$	28.1585	−	16.2573i	1.26055	−	0.727778i	0.287368	−	0.957820i	$-0.407220\pi$
$499$	28.1585	−	16.2573i	1.26055	−	0.727778i	0.973181	+	0.230042i	$0.0738864\pi$
$500$	7.09177	−	4.09443i	0.317153	−	0.183109i
$501$	−2.26138	+	1.30561i	−0.101031	+	0.0583303i
$502$	−1.74531	+	1.00766i	−0.0778971	+	0.0449739i
$503$	9.95552	−	17.2435i	0.443895	−	0.768848i	−0.554080	−	0.832464i	$-0.686930\pi$
$503$	9.95552	−	17.2435i	0.443895	−	0.768848i	0.997974	+	0.0636154i	$0.0202631\pi$
$504$	−1.22035	−	2.34750i	−0.0543586	−	0.104566i
$505$	20.9719	−	12.1081i	0.933238	−	0.538805i
$506$	−12.5260	−	21.6957i	−0.556850	−	0.964492i
$507$	12.8375	−	2.04889i	0.570134	−	0.0909946i
$508$	−3.67120	+	6.35871i	−0.162883	+	0.282122i
$509$	−2.34934	−	1.35639i	−0.104133	−	0.0601209i	0.447029	−	0.894519i	$-0.352482\pi$
$509$	−2.34934	−	1.35639i	−0.104133	−	0.0601209i	−0.551162	+	0.834398i	$0.685815\pi$
$510$	9.04389	+	15.6645i	0.400470	+	0.693635i
$511$	−12.8348	−	0.567630i	−0.567776	−	0.0251105i
$512$		−	1.00000i		−	0.0441942i
$513$			3.03338i			0.133927i
$514$	19.9147	−	11.4978i	0.878401	−	0.507145i
$515$	11.0788	+	6.39634i	0.488189	+	0.281856i
$516$	12.8811			0.567057
$517$	1.44534	+	2.50341i	0.0635660	+	0.110100i
$518$	9.55514	+	6.09488i	0.419829	+	0.267793i
$519$	−4.99495			−0.219254
$520$	−5.36029	−	7.78936i	−0.235064	−	0.341586i
$521$	−2.90626	+	5.03379i	−0.127326	+	0.220534i	−0.922640	−	0.385663i	$-0.873973\pi$
$521$	−2.90626	+	5.03379i	−0.127326	+	0.220534i	0.795314	+	0.606198i	$0.207306\pi$
$522$			4.37718i			0.191584i
$523$	19.6486	−	34.0323i	0.859172	−	1.48813i	−0.0135471	−	0.999908i	$-0.504312\pi$
$523$	19.6486	−	34.0323i	0.859172	−	1.48813i	0.872719	−	0.488222i	$-0.162354\pi$
$524$	−5.41067	+	9.37156i	−0.236366	+	0.409398i
$525$	−0.219467	+	4.96240i	−0.00957833	+	0.216577i
$526$	19.0857	+	11.0191i	0.832177	+	0.480458i
$527$		−	39.2647i		−	1.71040i
$528$	−4.33943	−	2.50537i	−0.188849	−	0.109032i
$529$	−0.998341	−	1.72918i	−0.0434062	−	0.0751817i
$530$	9.16319	−	15.8711i	0.398024	−	0.689397i
$531$	9.08332	−	5.24426i	0.394183	−	0.227581i
$532$	4.31596	−	6.76627i	0.187120	−	0.293355i
$533$	16.9789	−	11.6841i	0.735437	−	0.506095i
$534$	−7.71235	−	13.3582i	−0.333746	−	0.578065i
$535$			0.453028i			0.0195861i
$536$	−2.47913			−0.107082
$537$	−7.52240			−0.324616
$538$		−	4.37283i		−	0.188526i
$539$	28.7092	+	20.1507i	1.23659	+	0.867952i
$540$	−2.27114	−	1.31124i	−0.0977344	−	0.0564270i
$541$	20.1625	−	11.6408i	0.866854	−	0.500478i	0.000552417	−	1.00000i	$-0.499824\pi$
$541$	20.1625	−	11.6408i	0.866854	−	0.500478i	0.866301	+	0.499522i	$0.166491\pi$
$542$	−7.75390	−	13.4302i	−0.333059	−	0.576875i
$543$	−7.14351			−0.306557
$544$	5.97313	+	3.44859i	0.256096	+	0.147857i
$545$	−33.0716			−1.41663
$546$	−9.53357	+	0.333204i	−0.407999	+	0.0142598i
$547$	−9.23824			−0.394999			−0.197499	−	0.980303i	$-0.563282\pi$
$547$	−9.23824			−0.394999			−0.197499	+	0.980303i	$0.563282\pi$
$548$	11.9618	+	6.90614i	0.510982	+	0.295016i
$549$	14.3150			0.610950
$550$	4.70369	+	8.14704i	0.200566	+	0.347391i
$551$	−11.4988	+	6.63883i	−0.489865	+	0.282824i
$552$	−4.32984	−	2.49983i	−0.184290	−	0.106400i
$553$	16.4842	+	10.5147i	0.700981	+	0.447130i
$554$		−	28.7587i		−	1.22184i
$555$	11.2339			0.476850
$556$	11.5142			0.488310
$557$			23.8434i			1.01028i	0.863038	+	0.505139i	$0.168559\pi$
$557$			23.8434i			1.01028i	−0.863038	+	0.505139i	$0.831441\pi$
$558$	2.84643	+	4.93016i	0.120499	+	0.208711i
$559$	19.9695	−	41.9309i	0.844619	−	1.77349i
$560$	3.20035	+	6.15629i	0.135239	+	0.260151i
$561$	29.9298	−	17.2800i	1.26364	−	0.729562i
$562$	6.75501	−	11.7000i	0.284943	−	0.493536i
$563$	1.04048	+	1.80217i	0.0438511	+	0.0759523i	0.887118	−	0.461543i	$-0.152704\pi$
$563$	1.04048	+	1.80217i	0.0438511	+	0.0759523i	−0.843267	+	0.537495i	$0.819371\pi$
$564$	0.499608	+	0.288449i	0.0210373	+	0.0121459i
$565$		−	33.2144i		−	1.39734i
$566$	−16.4607	−	9.50356i	−0.691893	−	0.399465i
$567$	−2.34750	+	1.22035i	−0.0985857	+	0.0512498i
$568$	−1.63198	+	2.82667i	−0.0684762	+	0.118604i
$569$	17.6844	−	30.6303i	0.741370	−	1.28409i	−0.210502	−	0.977593i	$-0.567510\pi$
$569$	17.6844	−	30.6303i	0.741370	−	1.28409i	0.951872	−	0.306497i	$-0.0991568\pi$
$570$		−	7.95501i		−	0.333199i
$571$	18.0174	−	31.2071i	0.754006	−	1.30598i	−0.191861	−	0.981422i	$-0.561452\pi$
$571$	18.0174	−	31.2071i	0.754006	−	1.30598i	0.945867	−	0.324555i	$-0.105214\pi$
$572$	−14.8830	+	10.2418i	−0.622289	+	0.428232i
$573$	7.92903			0.331240
$574$	−13.4192	+	6.97598i	−0.560107	+	0.291172i
$575$	4.69330	+	8.12903i	0.195724	+	0.339004i
$576$	−1.00000			−0.0416667
$577$	−34.4738	−	19.9034i	−1.43516	−	0.828591i	−0.437654	−	0.899143i	$-0.644191\pi$
$577$	−34.4738	−	19.9034i	−1.43516	−	0.828591i	−0.997508	+	0.0705519i	$0.977524\pi$
$578$	−26.4754	+	15.2856i	−1.10123	+	0.635795i
$579$			10.7806i			0.448026i
$580$		−	11.4791i		−	0.476644i
$581$	−11.1905	−	21.5264i	−0.464261	−	0.893067i
$582$	−7.03709	−	12.1886i	−0.291697	−	0.505234i
$583$	−30.3247	−	17.5079i	−1.25592	−	0.725105i
$584$	−2.42791	+	4.20527i	−0.100468	+	0.174015i
$585$	−7.78936	+	5.36029i	−0.322050	+	0.221621i
$586$	−4.12406	−	7.14308i	−0.170363	−	0.295078i
$587$	12.1473	−	7.01325i	0.501373	−	0.289468i	−0.227907	−	0.973683i	$-0.573188\pi$
$587$	12.1473	−	7.01325i	0.501373	−	0.289468i	0.729280	+	0.684215i	$0.239855\pi$
$588$	6.97267	+	0.617955i	0.287548	+	0.0254840i
$589$	−8.63432	+	14.9551i	−0.355771	+	0.616213i
$590$	−23.8209	+	13.7530i	−0.980691	+	0.566202i
$591$	−16.5289	+	9.54296i	−0.679908	+	0.392545i
$592$	3.70976	−	2.14183i	0.152470	−	0.0880287i
$593$	15.5416	−	8.97292i	0.638215	−	0.368474i	−0.145711	−	0.989327i	$-0.546547\pi$
$593$	15.5416	−	8.97292i	0.638215	−	0.368474i	0.783927	+	0.620853i	$0.213214\pi$
$594$	−2.50537	+	4.33943i	−0.102797	+	0.178049i
$595$	−47.8090	−	2.11440i	−1.95998	−	0.0866820i
$596$	−14.2970	+	8.25436i	−0.585627	+	0.338112i
$597$	11.7571	+	20.3638i	0.481185	+	0.833436i
$598$	−14.8501	+	10.2192i	−0.607266	+	0.417893i
$599$	15.2420	−	26.4000i	0.622772	−	1.07867i	−0.366195	−	0.930538i	$-0.619340\pi$
$599$	15.2420	−	26.4000i	0.622772	−	1.07867i	0.988967	−	0.148135i	$-0.0473270\pi$
$600$	1.62591	+	0.938722i	0.0663777	+	0.0383232i
$601$	−7.94423	−	13.7598i	−0.324052	−	0.561274i	0.657268	−	0.753657i	$-0.271712\pi$
$601$	−7.94423	−	13.7598i	−0.324052	−	0.561274i	−0.981320	+	0.192383i	$0.938379\pi$
$602$	−18.3274	+	28.7325i	−0.746970	+	1.17105i
$603$			2.47913i			0.100958i
$604$			6.57267i			0.267438i
$605$	32.0402	−	18.4984i	1.30262	−	0.752067i
$606$	−7.99696	−	4.61704i	−0.324854	−	0.187555i
$607$	4.29143			0.174184			0.0870919	−	0.996200i	$-0.472243\pi$
$607$	4.29143			0.174184			0.0870919	+	0.996200i	$0.472243\pi$
$608$	−1.51669	−	2.62699i	−0.0615100	−	0.106538i
$609$	−9.76375	−	6.22794i	−0.395647	−	0.252369i
$610$	−37.5410			−1.51999
$611$	1.71351	−	1.17916i	0.0693212	−	0.0477038i
$612$	3.44859	−	5.97313i	0.139401	−	0.241450i
$613$		−	8.36726i		−	0.337950i	−0.985620	−	0.168975i	$-0.945954\pi$
$613$		−	8.36726i		−	0.337950i	0.985620	−	0.168975i	$-0.0540458\pi$
$614$	1.47098	−	2.54781i	0.0593638	−	0.102821i
$615$	−7.49557	+	12.9827i	−0.302251	+	0.523513i
$616$	11.7627	−	6.11485i	0.473933	−	0.246374i
$617$	22.4455	+	12.9589i	0.903621	+	0.521706i	0.878373	−	0.477976i	$-0.158629\pi$
$617$	22.4455	+	12.9589i	0.903621	+	0.521706i	0.0252476	+	0.999681i	$0.491963\pi$
$618$		−	4.87807i		−	0.196225i
$619$	−4.60270	−	2.65737i	−0.184998	−	0.106809i	0.404641	−	0.914476i	$-0.367397\pi$
$619$	−4.60270	−	2.65737i	−0.184998	−	0.106809i	−0.589639	+	0.807667i	$0.700730\pi$
$620$	−7.46473	−	12.9293i	−0.299791	−	0.519253i
$621$	−2.49983	+	4.32984i	−0.100315	+	0.173750i
$622$	12.9406	−	7.47126i	0.518871	−	0.299570i
$623$	40.7701	+	1.80310i	1.63342	+	0.0722395i
$624$	−1.55030	+	3.25524i	−0.0620616	+	0.130314i
$625$	15.4312	+	26.7276i	0.617248	+	1.06911i
$626$			24.3857i			0.974650i
$627$	−15.1995			−0.607009
$628$	8.81242			0.351654
$629$			29.5452i			1.17804i
$630$	6.15629	−	3.20035i	0.245272	−	0.127505i
$631$	4.21716	+	2.43478i	0.167883	+	0.0969271i	0.581587	−	0.813484i	$-0.302432\pi$
$631$	4.21716	+	2.43478i	0.167883	+	0.0969271i	−0.413704	+	0.910411i	$0.635765\pi$
$632$	6.39996	−	3.69502i	0.254577	−	0.146980i
$633$	2.44732	+	4.23888i	0.0972721	+	0.168480i
$634$	28.4626			1.13039
$635$	−16.6756	−	9.62768i	−0.661753	−	0.382063i
$636$	−6.98817			−0.277099
$637$	12.8213	−	21.7397i	0.507999	−	0.861358i
$638$	−21.9329			−0.868333
$639$	2.82667	+	1.63198i	0.111821	+	0.0645600i
$640$	2.62249			0.103663
$641$	9.60785	+	16.6413i	0.379487	+	0.657291i	0.990988	−	0.133953i	$-0.0427671\pi$
$641$	9.60785	+	16.6413i	0.379487	+	0.657291i	−0.611500	+	0.791244i	$0.709434\pi$
$642$	0.149604	−	0.0863737i	0.00590439	−	0.00340890i
$643$	−12.2082	−	7.04841i	−0.481444	−	0.277962i	0.239574	−	0.970878i	$-0.422992\pi$
$643$	−12.2082	−	7.04841i	−0.481444	−	0.277962i	−0.721018	+	0.692916i	$0.756326\pi$
$644$	11.7367	−	6.10134i	0.462491	−	0.240426i
$645$			33.7804i			1.33010i
$646$	20.9218			0.823157
$647$	−28.1839			−1.10802			−0.554012	−	0.832509i	$-0.686904\pi$
$647$	−28.1839			−1.10802			−0.554012	+	0.832509i	$0.686904\pi$
$648$			1.00000i			0.0392837i
$649$	26.2776	+	45.5142i	1.03149	+	1.78659i
$650$	5.57642	−	3.83744i	0.218725	−	0.150517i
$651$	−15.0472	−	0.665477i	−0.589746	−	0.0260821i
$652$	8.11055	−	4.68263i	0.317634	−	0.183386i
$653$	22.2048	−	38.4599i	0.868941	−	1.50505i	0.00586180	−	0.999983i	$-0.498134\pi$
$653$	22.2048	−	38.4599i	0.868941	−	1.50505i	0.863080	−	0.505068i	$-0.168533\pi$
$654$	6.30538	+	10.9212i	0.246560	+	0.427054i
$655$	−24.5768	−	14.1894i	−0.960295	−	0.554427i
$656$			5.71638i			0.223187i
$657$	4.20527	+	2.42791i	0.164063	+	0.0947218i
$658$	−1.35427	+	0.704016i	−0.0527948	+	0.0274454i
$659$	−8.69801	+	15.0654i	−0.338826	+	0.586864i	−0.984212	−	0.176992i	$-0.943363\pi$
$659$	−8.69801	+	15.0654i	−0.338826	+	0.586864i	0.645386	+	0.763857i	$0.276697\pi$
$660$	6.57031	−	11.3801i	0.255749	−	0.442970i
$661$		−	0.791848i		−	0.0307993i	−0.999881	−	0.0153997i	$-0.995098\pi$
$661$		−	0.791848i		−	0.0307993i	0.999881	−	0.0153997i	$-0.00490206\pi$
$662$	3.13842	−	5.43590i	0.121978	−	0.211272i
$663$	−14.0976	−	20.4861i	−0.547507	−	0.795615i
$664$	−9.16995			−0.355863
$665$	17.7445	+	11.3185i	0.688101	+	0.438914i
$666$	−2.14183	−	3.70976i	−0.0829943	−	0.143750i
$667$	−21.8844			−0.847369
$668$	−2.26138	−	1.30561i	−0.0874954	−	0.0505155i
$669$	−8.72547	+	5.03765i	−0.337346	+	0.194767i
$670$		−	6.50148i		−	0.251174i
$671$			71.7289i			2.76906i
$672$	1.42282	−	2.23060i	0.0548864	−	0.0860473i
$673$	10.4137	+	18.0371i	0.401420	+	0.695280i	0.993898	−	0.110307i	$-0.0351834\pi$
$673$	10.4137	+	18.0371i	0.401420	+	0.695280i	−0.592477	+	0.805587i	$0.701850\pi$
$674$	8.65214	+	4.99532i	0.333268	+	0.192412i
$675$	0.938722	−	1.62591i	0.0361314	−	0.0625815i
$676$	8.19316	+	10.0932i	0.315121	+	0.388199i
$677$	−14.2416	−	24.6671i	−0.547347	−	0.948034i	−0.998455	−	0.0555641i	$-0.982304\pi$
$677$	−14.2416	−	24.6671i	−0.547347	−	0.948034i	0.451108	−	0.892470i	$-0.351029\pi$
$678$	−10.9684	+	6.33262i	−0.421239	+	0.243203i
$679$	37.2004	+	1.64523i	1.42762	+	0.0631379i
$680$	−9.04389	+	15.6645i	−0.346817	+	0.600705i
$681$	12.3996	−	7.15891i	0.475154	−	0.274330i
$682$	−24.7038	+	14.2627i	−0.945957	+	0.546148i
$683$	7.08612	−	4.09118i	0.271143	−	0.156544i	−0.358264	−	0.933620i	$-0.616631\pi$
$683$	7.08612	−	4.09118i	0.271143	−	0.156544i	0.629407	+	0.777076i	$0.283298\pi$
$684$	−2.62699	+	1.51669i	−0.100445	+	0.0579921i
$685$	−18.1113	+	31.3696i	−0.691996	+	1.19857i
$686$	−11.2993	+	14.6740i	−0.431408	+	0.560256i
$687$	−13.3945	+	7.73332i	−0.511032	+	0.295045i
$688$	6.44053	+	11.1553i	0.245543	+	0.425293i
$689$	−10.8337	+	22.7481i	−0.412732	+	0.866635i
$690$	6.55579	−	11.3550i	0.249574	−	0.432276i
$691$	1.10054	+	0.635398i	0.0418666	+	0.0241717i	0.520787	−	0.853687i	$-0.325638\pi$
$691$	1.10054	+	0.635398i	0.0418666	+	0.0241717i	−0.478921	+	0.877858i	$0.658972\pi$
$692$	−2.49748	−	4.32576i	−0.0949398	−	0.164441i
$693$	−6.11485	−	11.7627i	−0.232284	−	0.446828i
$694$			3.90930i			0.148395i
$695$			30.1958i			1.14539i
$696$	−3.79075	+	2.18859i	−0.143688	+	0.0829583i
$697$	−34.1447	−	19.7135i	−1.29332	−	0.746701i
$698$	15.3950			0.582710
$699$	2.31317	+	4.00653i	0.0874922	+	0.151541i
$700$	−4.40730	+	2.29114i	−0.166580	+	0.0865968i
$701$	13.9585			0.527207			0.263604	−	0.964631i	$-0.415089\pi$
$701$	13.9585			0.527207			0.263604	+	0.964631i	$0.415089\pi$
$702$	3.25524	+	1.55030i	0.122861	+	0.0585122i
$703$	6.49699	−	11.2531i	0.245039	−	0.424419i
$704$		−	5.01074i		−	0.188849i
$705$	−0.756453	+	1.31022i	−0.0284897	+	0.0493456i
$706$	15.0418	−	26.0531i	0.566105	−	0.980523i
$707$	21.6770	−	11.2688i	0.815248	−	0.423807i
$708$	9.08332	+	5.24426i	0.341372	+	0.197091i
$709$			2.21567i			0.0832113i	0.999134	+	0.0416057i	$0.0132473\pi$
$709$			2.21567i			0.0832113i	−0.999134	+	0.0416057i	$0.986753\pi$
$710$	−7.41290	−	4.27984i	−0.278201	−	0.160619i
$711$	−3.69502	−	6.39996i	−0.138574	−	0.240017i
$712$	7.71235	−	13.3582i	0.289032	−	0.500619i
$713$	−24.6492	+	14.2312i	−0.923119	+	0.532963i
$714$	8.41696	+	16.1911i	0.314997	+	0.605938i
$715$	−26.8590	−	39.0305i	−1.00447	−	1.45966i
$716$	−3.76120	−	6.51459i	−0.140563	−	0.243462i
$717$			8.48540i			0.316893i
$718$	−8.35261			−0.311717
$719$	6.10672			0.227742			0.113871	−	0.993496i	$-0.463675\pi$
$719$	6.10672			0.227742			0.113871	+	0.993496i	$0.463675\pi$
$720$		−	2.62249i		−	0.0977344i
$721$	10.8810	+	6.94061i	0.405231	+	0.258482i
$722$	8.48583	+	4.89930i	0.315810	+	0.182333i
$723$	−3.68833	+	2.12946i	−0.137170	+	0.0791954i
$724$	−3.57176	−	6.18646i	−0.132743	−	0.229918i
$725$	8.21791			0.305206
$726$	−12.2175	−	7.05376i	−0.453433	−	0.261790i
$727$	6.95455			0.257930			0.128965	−	0.991649i	$-0.458835\pi$
$727$	6.95455			0.257930			0.128965	+	0.991649i	$0.458835\pi$
$728$	−5.05535	−	8.08971i	−0.187364	−	0.299825i
$729$	1.00000			0.0370370
$730$	−11.0283	−	6.36717i	−0.408174	−	0.235660i
$731$	−88.8430			−3.28598
$732$	7.15751	+	12.3972i	0.264549	+	0.458213i
$733$	13.1539	−	7.59443i	0.485852	−	0.280506i	−0.237000	−	0.971510i	$-0.576164\pi$
$733$	13.1539	−	7.59443i	0.485852	−	0.280506i	0.722852	+	0.691003i	$0.242831\pi$
$734$	10.7075	+	6.18199i	0.395222	+	0.228181i
$735$	−1.62058	+	18.2857i	−0.0597760	+	0.674480i
$736$		−	4.99967i		−	0.184290i
$737$	−12.4223			−0.457580
$738$	5.71638			0.210423
$739$			48.1214i			1.77018i	0.465424	+	0.885088i	$0.345902\pi$
$739$			48.1214i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$740$	5.61693	+	9.72880i	0.206482	+	0.357638i
$741$	0.864582	+	10.9028i	0.0317612	+	0.400524i
$742$	9.94290	−	15.5878i	0.365015	−	0.572247i
$743$	35.6831	−	20.6017i	1.30909	−	0.755802i	0.327143	−	0.944975i	$-0.393914\pi$
$743$	35.6831	−	20.6017i	1.30909	−	0.755802i	0.981944	+	0.189173i	$0.0605807\pi$
$744$	−2.84643	+	4.93016i	−0.104355	+	0.180749i
$745$	−21.6470	−	37.4936i	−0.793083	−	1.37366i
$746$	−19.6066	−	11.3199i	−0.717849	−	0.414451i
$747$			9.16995i			0.335511i
$748$	29.9298	+	17.2800i	1.09434	+	0.631819i
$749$	−0.0201936	+	0.456600i	−0.000737858	+	0.0166838i
$750$	4.09443	−	7.09177i	0.149508	−	0.258955i
$751$	−21.3607	+	36.9979i	−0.779465	+	1.35007i	0.152786	+	0.988259i	$0.451176\pi$
$751$	−21.3607	+	36.9979i	−0.779465	+	1.35007i	−0.932251	+	0.361813i	$0.882158\pi$
$752$			0.576897i			0.0210373i
$753$	−1.00766	+	1.74531i	−0.0367210	+	0.0636027i
$754$	1.24759	+	15.7328i	0.0454347	+	0.572953i
$755$	−17.2368			−0.627310
$756$	−2.23060	−	1.42282i	−0.0811262	−	0.0517474i
$757$	−21.7752	−	37.7157i	−0.791432	−	1.37080i	−0.925080	−	0.379772i	$-0.876003\pi$
$757$	−21.7752	−	37.7157i	−0.791432	−	1.37080i	0.133648	−	0.991029i	$-0.457331\pi$
$758$	10.8958			0.395752
$759$	−21.6957	−	12.5260i	−0.787504	−	0.454666i
$760$	6.88924	−	3.97750i	0.249899	−	0.144279i
$761$		−	9.54931i		−	0.346162i	−0.984908	−	0.173081i	$-0.944628\pi$
$761$		−	9.54931i		−	0.346162i	0.984908	−	0.173081i	$-0.0553723\pi$
$762$			7.34240i			0.265987i
$763$	−33.3324	−	1.47416i	−1.20671	−	0.0533680i
$764$	3.96451	+	6.86674i	0.143431	+	0.248430i
$765$	15.6645	+	9.04389i	0.566350	+	0.326982i
$766$	0.634815	−	1.09953i	0.0229368	−	0.0397277i
$767$	31.1532	−	21.4382i	1.12488	−	0.774089i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−22.0605	+	12.7366i	−0.795521	+	0.459294i	−0.841903	−	0.539630i	$-0.818564\pi$
$769$	−22.0605	+	12.7366i	−0.795521	+	0.459294i	0.0463817	+	0.998924i	$0.485231\pi$
$770$	16.0361	+	30.8476i	0.577902	+	1.11167i
$771$	11.4978	−	19.9147i	0.414082	−	0.717211i
$772$	−9.33627	+	5.39030i	−0.336020	+	0.194001i
$773$	14.7720	−	8.52865i	0.531314	−	0.306754i	−0.210238	−	0.977650i	$-0.567424\pi$
$773$	14.7720	−	8.52865i	0.531314	−	0.306754i	0.741551	+	0.670896i	$0.234090\pi$
$774$	11.1553	−	6.44053i	0.400970	−	0.231500i
$775$	9.25611	−	5.34402i	0.332489	−	0.191963i
$776$	7.03709	−	12.1886i	0.252617	−	0.437545i
$777$	11.3224	+	0.500746i	0.406190	+	0.0179642i
$778$	26.5529	−	15.3303i	0.951968	−	0.549619i
$779$	8.66999	+	15.0169i	0.310634	+	0.538035i
$780$	−8.53682	−	4.06564i	−0.305667	−	0.145573i
$781$	−8.17741	+	14.1637i	−0.292611	+	0.506817i
$782$	29.8637	+	17.2418i	1.06792	+	0.616566i
$783$	2.18859	+	3.79075i	0.0782138	+	0.135470i
$784$	2.95117	+	6.34749i	0.105399	+	0.226696i
$785$			23.1105i			0.824848i
$786$			10.8213i			0.385984i
$787$	−34.2123	+	19.7525i	−1.21954	+	0.704099i	−0.964818	−	0.262917i	$-0.915316\pi$
$787$	−34.2123	+	19.7525i	−1.21954	+	0.704099i	−0.254717	+	0.967016i	$0.581982\pi$
$788$	−16.5289	−	9.54296i	−0.588817	−	0.339954i
$789$	22.0383			0.784584
$790$	9.69014	+	16.7838i	0.344760	+	0.597141i
$791$	1.48052	−	33.4763i	0.0526414	−	1.19028i
$792$	−5.01074			−0.178049
$793$	51.4520	−	4.08010i	1.82711	−	0.144889i
$794$	−13.2240	+	22.9046i	−0.469301	+	0.812854i
$795$		−	18.3264i		−	0.649970i
$796$	−11.7571	+	20.3638i	−0.416718	+	0.721777i
$797$	−8.76369	+	15.1792i	−0.310426	+	0.537673i	−0.978455	−	0.206462i	$-0.933805\pi$
$797$	−8.76369	+	15.1792i	−0.310426	+	0.537673i	0.668029	+	0.744135i	$0.267138\pi$
$798$	0.354592	−	8.01774i	0.0125524	−	0.283825i
$799$	−3.44589	−	1.98948i	−0.121907	−	0.0703828i
$800$			1.87744i			0.0663777i
$801$	−13.3582	−	7.71235i	−0.471988	−	0.272502i
$802$	−10.9567	−	18.9775i	−0.386894	−	0.670120i
$803$	−12.1656	+	21.0715i	−0.429316	+	0.743597i
$804$	−2.14699	+	1.23956i	−0.0757184	+	0.0437160i
$805$	16.0007	+	30.7794i	0.563950	+	1.08483i
$806$	11.6360	+	16.9090i	0.409862	+	0.595595i
$807$	−2.18641	−	3.78698i	−0.0769654	−	0.133308i
$808$		−	9.23409i		−	0.324854i
$809$	7.21823			0.253779			0.126890	−	0.991917i	$-0.459501\pi$
$809$	7.21823			0.253779			0.126890	+	0.991917i	$0.459501\pi$
$810$	−2.62249			−0.0921448
$811$			33.6889i			1.18298i	0.806314	+	0.591488i	$0.201459\pi$
$811$			33.6889i			1.18298i	−0.806314	+	0.591488i	$0.798541\pi$
$812$	0.511678	−	11.5696i	0.0179564	−	0.406014i
$813$	−13.4302	−	7.75390i	−0.471016	−	0.271941i
$814$	18.5886	−	10.7322i	0.651532	−	0.376162i
$815$	12.2801	+	21.2698i	0.430155	+	0.745050i
$816$	6.89718			0.241450
$817$	33.8384	+	19.5366i	1.18385	+	0.683499i
$818$	−10.3492			−0.361852
$819$	−8.08971	+	5.05535i	−0.282677	+	0.176648i
$820$	−14.9911			−0.523513
$821$	−5.50808	−	3.18009i	−0.192233	−	0.110986i	0.400794	−	0.916168i	$-0.368734\pi$
$821$	−5.50808	−	3.18009i	−0.192233	−	0.110986i	−0.593028	+	0.805182i	$0.702068\pi$
$822$	13.8123			0.481759
$823$	4.94605	+	8.56680i	0.172408	+	0.298620i	0.939261	−	0.343203i	$-0.111512\pi$
$823$	4.94605	+	8.56680i	0.172408	+	0.298620i	−0.766853	+	0.641823i	$0.778178\pi$
$824$	4.22453	−	2.43903i	0.147168	−	0.0849678i
$825$	8.14704	+	4.70369i	0.283643	+	0.163762i
$826$	−24.6218	+	12.7996i	−0.856701	+	0.445357i
$827$		−	0.161968i		−	0.00563219i	−0.999996	−	0.00281610i	$-0.999104\pi$
$827$		−	0.161968i		−	0.00563219i	0.999996	−	0.00281610i	$-0.000896393\pi$
$828$	−4.99967			−0.173750
$829$	2.49876			0.0867857			0.0433928	−	0.999058i	$-0.486183\pi$
$829$	2.49876			0.0867857			0.0433928	+	0.999058i	$0.486183\pi$
$830$		−	24.0481i		−	0.834721i
$831$	−14.3794	−	24.9058i	−0.498815	−	0.863972i
$832$	−3.59427	+	0.285022i	−0.124609	+	0.00988137i
$833$	−48.0918	−	4.26215i	−1.66628	−	0.147675i
$834$	9.97158	−	5.75709i	0.345288	−	0.199352i
$835$	3.42394	−	5.93044i	0.118490	−	0.205231i
$836$	−7.59975	−	13.1631i	−0.262843	−	0.455257i
$837$	4.93016	+	2.84643i	0.170411	+	0.0983871i
$838$		−	17.9681i		−	0.620698i
$839$	33.8670	+	19.5531i	1.16922	+	0.675048i	0.953496	−	0.301407i	$-0.0974563\pi$
$839$	33.8670	+	19.5531i	1.16922	+	0.675048i	0.215722	+	0.976455i	$0.430790\pi$
$840$	5.84973	+	3.73133i	0.201835	+	0.128743i
$841$	4.92015	−	8.52195i	0.169660	−	0.293860i
$842$	3.58112	−	6.20268i	0.123413	−	0.213758i
$843$		−	13.5100i		−	0.465310i
$844$	−2.44732	+	4.23888i	−0.0842401	+	0.145908i
$845$	−26.4692	+	21.4865i	−0.910569	+	0.739157i
$846$	0.576897			0.0198341
$847$	33.1174	−	17.2161i	1.13793	−	0.591552i
$848$	−3.49408	−	6.05193i	−0.119987	−	0.207824i
$849$	−19.0071			−0.652323
$850$	−11.2142	−	6.47454i	−0.384645	−	0.222075i
$851$	18.5476	−	10.7084i	0.635802	−	0.367081i
$852$			3.26395i			0.111821i
$853$		−	3.18625i		−	0.109095i	−0.998511	−	0.0545476i	$-0.982628\pi$
$853$		−	3.18625i		−	0.109095i	0.998511	−	0.0545476i	$-0.0173717\pi$
$854$	−37.8370	−	1.67338i	−1.29476	−	0.0572618i
$855$	−3.97750	−	6.88924i	−0.136028	−	0.235607i
$856$	0.149604	+	0.0863737i	0.00511335	+	0.00295219i
$857$	−21.1932	+	36.7078i	−0.723947	+	1.25391i	0.235459	+	0.971884i	$0.424341\pi$
$857$	−21.1932	+	36.7078i	−0.723947	+	1.25391i	−0.959406	+	0.282029i	$0.908993\pi$
$858$	−7.76814	+	16.3112i	−0.265200	+	0.556854i
$859$	6.71141	+	11.6245i	0.228990	+	0.396623i	0.957509	−	0.288403i	$-0.0931242\pi$
$859$	6.71141	+	11.6245i	0.228990	+	0.396623i	−0.728519	+	0.685026i	$0.759791\pi$
$860$	−29.2547	+	16.8902i	−0.997577	+	0.575952i
$861$	−8.13338	+	12.7510i	−0.277185	+	0.434552i
$862$	15.8883	−	27.5193i	0.541157	−	0.937311i
$863$	−34.2623	+	19.7813i	−1.16630	+	0.673365i	−0.952806	−	0.303579i	$-0.901818\pi$
$863$	−34.2623	+	19.7813i	−1.16630	+	0.673365i	−0.213496	+	0.976944i	$0.568485\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	11.3442	−	6.54960i	0.385716	−	0.222693i
$866$	4.43985	−	2.56335i	0.150872	−	0.0871061i
$867$	−15.2856	+	26.4754i	−0.519125	+	0.899150i
$868$	−6.94728	−	13.3640i	−0.235806	−	0.453603i
$869$	32.0685	−	18.5148i	1.08785	−	0.628071i
$870$	−5.73955	−	9.94119i	−0.194589	−	0.337038i
$871$	0.706606	+	8.91064i	0.0239424	+	0.301926i
$872$	−6.30538	+	10.9212i	−0.213527	+	0.369840i
$873$	−12.1886	−	7.03709i	−0.412522	−	0.238169i
$874$	−7.58295	−	13.1341i	−0.256497	−	0.444266i
$875$	9.99327	+	19.2234i	0.337834	+	0.649868i
$876$			4.85582i			0.164063i
$877$		−	27.7042i		−	0.935503i	−0.883860	−	0.467752i	$-0.845064\pi$
$877$		−	27.7042i		−	0.935503i	0.883860	−	0.467752i	$-0.154936\pi$
$878$	−31.4539	+	18.1599i	−1.06152	+	0.612867i
$879$	−7.14308	−	4.12406i	−0.240930	−	0.139101i
$880$	13.1406			0.442970
$881$	18.7398	+	32.4583i	0.631360	+	1.09355i	0.987274	+	0.159029i	$0.0508364\pi$
$881$	18.7398	+	32.4583i	0.631360	+	1.09355i	−0.355914	+	0.934519i	$0.615830\pi$
$882$	6.34749	−	2.95117i	0.213731	−	0.0993711i
$883$	25.4665			0.857015			0.428508	−	0.903538i	$-0.359040\pi$
$883$	25.4665			0.857015			0.428508	+	0.903538i	$0.359040\pi$
$884$	10.6927	−	22.4520i	0.359634	−	0.755142i
$885$	−13.7530	+	23.8209i	−0.462302	+	0.800731i
$886$			14.3038i			0.480545i
$887$	14.8882	−	25.7871i	0.499896	−	0.865846i	−0.500104	−	0.865966i	$-0.666705\pi$
$887$	14.8882	−	25.7871i	0.499896	−	0.865846i	1.00000		0.000119786i	$3.81289e-5\pi$
$888$	2.14183	−	3.70976i	0.0718751	−	0.124491i
$889$	−16.3780	−	10.4469i	−0.549300	−	0.350378i
$890$	35.0317	+	20.2255i	1.17426	+	0.677962i
$891$			5.01074i			0.167866i
$892$	−8.72547	−	5.03765i	−0.292150	−	0.168673i
$893$	0.874975	+	1.51550i	0.0292799	+	0.0507143i
$894$	−8.25436	+	14.2970i	−0.276067	+	0.478162i
$895$	17.0844	−	9.86371i	0.571070	−	0.329707i
$896$	2.64317	+	0.116897i	0.0883020	+	0.00390524i
$897$	−7.75097	+	16.2751i	−0.258797	+	0.543410i
$898$	−3.06262	−	5.30462i	−0.102201	−	0.177017i
$899$			24.9187i			0.831085i
$900$	1.87744			0.0625815
$901$	48.1987			1.60573
$902$			28.6433i			0.953718i
$903$	−1.50575	+	34.0468i	−0.0501083	+	1.13301i
$904$	−10.9684	−	6.33262i	−0.364804	−	0.210620i
$905$	16.2239	−	9.36689i	0.539302	−	0.311366i
$906$	3.28634	+	5.69210i	0.109181	+	0.189107i
$907$	45.3138			1.50462			0.752311	−	0.658808i	$-0.228939\pi$
$907$	45.3138			1.50462			0.752311	+	0.658808i	$0.228939\pi$
$908$	12.3996	+	7.15891i	0.411495	+	0.237577i
$909$	−9.23409			−0.306275
$910$	21.2152	−	13.2576i	0.703276	−	0.439485i
$911$	−44.3887			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$911$	−44.3887			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$912$	−2.62699	−	1.51669i	−0.0869882	−	0.0502227i
$913$	−45.9482			−1.52066
$914$	−10.7274	−	18.5805i	−0.354832	−	0.614587i
$915$	−32.5114	+	18.7705i	−1.07479	+	0.620533i
$916$	−13.3945	−	7.73332i	−0.442567	−	0.255516i
$917$	−24.1381	−	15.3968i	−0.797111	−	0.508448i
$918$		−	6.89718i		−	0.227641i
$919$	−29.3318			−0.967568			−0.483784	−	0.875188i	$-0.660738\pi$
$919$	−29.3318			−0.967568			−0.483784	+	0.875188i	$0.660738\pi$
$920$	13.1116			0.432276
$921$		−	2.94195i		−	0.0969407i
$922$	−13.6311	−	23.6097i	−0.448915	−	0.777544i
$923$	10.6249	+	5.06010i	0.349724	+	0.166555i
$924$	7.12938	−	11.1770i	0.234539	−	0.367695i
$925$	−6.96487	+	4.02117i	−0.229003	+	0.132215i
$926$	−13.2884	+	23.0162i	−0.436684	+	0.756358i
$927$	−2.43903	−	4.22453i	−0.0801084	−	0.138752i
$928$	−3.79075	−	2.18859i	−0.124437	−	0.0718440i
$929$			27.9191i			0.915995i	0.888954	+	0.457997i	$0.151433\pi$
$929$			27.9191i			0.915995i	−0.888954	+	0.457997i	$0.848567\pi$
$930$	−12.9293	−	7.46473i	−0.423968	−	0.244778i
$931$	17.3799	+	12.1987i	0.569602	+	0.399798i
$932$	−2.31317	+	4.00653i	−0.0757705	+	0.131238i
$933$	7.47126	−	12.9406i	0.244598	−	0.423656i
$934$		−	19.3916i		−	0.634514i
$935$	−45.3166	+	78.4906i	−1.48201	+	2.56692i
$936$	0.285022	+	3.59427i	0.00931625	+	0.117482i
$937$	−38.6927			−1.26404			−0.632018	−	0.774953i	$-0.717773\pi$
$937$	−38.6927			−1.26404			−0.632018	+	0.774953i	$0.717773\pi$
$938$	0.289802	−	6.55275i	0.00946236	−	0.213955i
$939$	12.1929	+	21.1187i	0.397899	+	0.689182i
$940$	−1.51291			−0.0493456
$941$	2.94391	+	1.69967i	0.0959688	+	0.0554076i	0.547216	−	0.836991i	$-0.315688\pi$
$941$	2.94391	+	1.69967i	0.0959688	+	0.0554076i	−0.451247	+	0.892399i	$0.649021\pi$
$942$	7.63178	−	4.40621i	0.248657	−	0.143562i
$943$			28.5800i			0.930693i
$944$			10.4885i			0.341372i
$945$	3.73133	−	5.84973i	0.121380	−	0.190292i
$946$	32.2718	+	55.8965i	1.04925	+	1.81735i
$947$	−18.0395	−	10.4151i	−0.586206	−	0.338446i	0.177390	−	0.984141i	$-0.443235\pi$
$947$	−18.0395	−	10.4151i	−0.586206	−	0.338446i	−0.763596	+	0.645694i	$0.776568\pi$
$948$	3.69502	−	6.39996i	0.120009	−	0.207861i
$949$	15.8069	+	7.52797i	0.513112	+	0.244368i
$950$	2.84750	+	4.93202i	0.0923852	+	0.160016i
$951$	24.6493	−	14.2313i	0.799309	−	0.461481i
$952$	−9.81344	+	15.3849i	−0.318056	+	0.498626i
$953$	−12.1372	+	21.0222i	−0.393162	+	0.680977i	−0.992865	−	0.119246i	$-0.961952\pi$
$953$	−12.1372	+	21.0222i	−0.393162	+	0.680977i	0.599703	+	0.800223i	$0.295286\pi$
$954$	−6.05193	+	3.49408i	−0.195938	+	0.113125i
$955$	−18.0079	+	10.3969i	−0.582723	+	0.336435i
$956$	−7.34857	+	4.24270i	−0.237670	+	0.137219i
$957$	−18.9945	+	10.9665i	−0.614004	+	0.354495i
$958$	−12.3448	+	21.3818i	−0.398842	+	0.690815i
$959$	−19.6524	+	30.8097i	−0.634609	+	0.994897i
$960$	2.27114	−	1.31124i	0.0733008	−	0.0423202i
$961$	0.704348	+	1.21997i	0.0227209	+	0.0393537i
$962$	−8.75568	−	12.7234i	−0.282294	−	0.410219i
$963$	0.0863737	−	0.149604i	0.00278335	−	0.00482091i
$964$	−3.68833	−	2.12946i	−0.118793	−	0.0685852i
$965$	−14.1360	−	24.4843i	−0.455054	−	0.788176i
$966$	7.11362	−	11.1523i	0.228877	−	0.358818i
$967$		−	47.4200i		−	1.52492i	−0.647033	−	0.762462i	$-0.723990\pi$
$967$		−	47.4200i		−	1.52492i	0.647033	−	0.762462i	$-0.276010\pi$
$968$		−	14.1075i		−	0.453433i
$969$	18.1188	−	10.4609i	0.582060	−	0.336052i
$970$	31.9645	+	18.4547i	1.02632	+	0.592544i
$971$	32.9127			1.05622			0.528110	−	0.849176i	$-0.322901\pi$
$971$	32.9127			1.05622			0.528110	+	0.849176i	$0.322901\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−1.34597	+	30.4339i	−0.0431498	+	0.975667i
$974$	−26.2566			−0.841317
$975$	2.91060	−	6.11153i	0.0932137	−	0.195726i
$976$	−7.15751	+	12.3972i	−0.229106	+	0.396824i
$977$			47.6840i			1.52555i	0.646667	+	0.762773i	$0.276163\pi$
$977$			47.6840i			1.52555i	−0.646667	+	0.762773i	$0.723837\pi$
$978$	4.68263	−	8.11055i	0.149734	−	0.259347i
$979$	38.6446	−	66.9344i	1.23509	−	2.13923i
$980$	−16.6462	+	7.73941i	−0.531744	+	0.247226i
$981$	10.9212	+	6.30538i	0.348688	+	0.201315i
$982$		−	22.1019i		−	0.705300i
$983$	24.8943	+	14.3727i	0.794003	+	0.458418i	0.841370	−	0.540459i	$-0.181750\pi$
$983$	24.8943	+	14.3727i	0.794003	+	0.458418i	−0.0473666	+	0.998878i	$0.515083\pi$
$984$	2.85819	+	4.95053i	0.0911158	+	0.157817i
$985$	25.0263	−	43.3468i	0.797404	−	1.38114i
$986$	26.1455	−	15.0951i	0.832642	−	0.480726i
$987$	−0.820821	+	1.28683i	−0.0261270	+	0.0409602i
$988$	−9.00980	+	6.20014i	−0.286640	+	0.197253i
$989$	32.2005	+	55.7729i	1.02392	+	1.77348i
$990$		−	13.1406i		−	0.417636i
$991$	8.72038			0.277012			0.138506	−	0.990362i	$-0.455770\pi$
$991$	8.72038			0.277012			0.138506	+	0.990362i	$0.455770\pi$
$992$	−5.69286			−0.180749
$993$		−	6.27684i		−	0.199189i
$994$	−7.28058	−	4.64401i	−0.230926	−	0.147299i
$995$	−53.4039	−	30.8328i	−1.69302	−	0.977464i
$996$	−7.94141	+	4.58497i	−0.251633	+	0.145280i
$997$	0.441010	+	0.763851i	0.0139669	+	0.0241914i	0.872924	−	0.487856i	$-0.162221\pi$
$997$	0.441010	+	0.763851i	0.0139669	+	0.0241914i	−0.858957	+	0.512047i	$0.828887\pi$
$998$	32.5147			1.02923
$999$	−3.70976	−	2.14183i	−0.117372	−	0.0677645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.361.7	yes	20
3.2	odd	2		1638.2.cr.b.361.4		20
7.2	even	3		546.2.bm.b.205.4	yes	20
13.4	even	6		546.2.bm.b.277.9	yes	20
21.2	odd	6		1638.2.dt.b.1297.7		20
39.17	odd	6		1638.2.dt.b.1369.2		20
91.30	even	6	inner	546.2.bd.b.121.7	✓	20
273.212	odd	6		1638.2.cr.b.667.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.7	✓	20	91.30	even	6	inner
546.2.bd.b.361.7	yes	20	1.1	even	1	trivial
546.2.bm.b.205.4	yes	20	7.2	even	3
546.2.bm.b.277.9	yes	20	13.4	even	6
1638.2.cr.b.361.4		20	3.2	odd	2
1638.2.cr.b.667.4		20	273.212	odd	6
1638.2.dt.b.1297.7		20	21.2	odd	6
1638.2.dt.b.1369.2		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.34750 + 1.22035i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.34750 + 1.22035i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -2.62249 q^{10} +5.01074i q^{11} +(0.500000 + 0.866025i) q^{12} +(3.59427 - 0.285022i) q^{13} +(-2.64317 - 0.116897i) q^{14} +(-2.27114 + 1.31124i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.44859 - 5.97313i) q^{17} +(0.866025 + 0.500000i) q^{18} +3.03338i q^{19} +(-2.27114 - 1.31124i) q^{20} +(-2.34750 + 1.22035i) q^{21} +(-2.50537 + 4.33943i) q^{22} +(-2.49983 + 4.32984i) q^{23} +1.00000i q^{24} +(0.938722 - 1.62591i) q^{25} +(3.25524 + 1.55030i) q^{26} +1.00000 q^{27} +(-2.23060 - 1.42282i) q^{28} +(2.18859 + 3.79075i) q^{29} -2.62249 q^{30} +(4.93016 + 2.84643i) q^{31} +(-0.866025 + 0.500000i) q^{32} +5.01074i q^{33} -6.89718i q^{34} +(3.73133 - 5.84973i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.70976 - 2.14183i) q^{37} +(-1.51669 + 2.62699i) q^{38} +(3.59427 - 0.285022i) q^{39} +(-1.31124 - 2.27114i) q^{40} +(4.95053 - 2.85819i) q^{41} +(-2.64317 - 0.116897i) q^{42} +(6.44053 - 11.1553i) q^{43} +(-4.33943 + 2.50537i) q^{44} +(-2.27114 + 1.31124i) q^{45} +(-4.32984 + 2.49983i) q^{46} +(0.499608 - 0.288449i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.02150 - 5.72953i) q^{49} +(1.62591 - 0.938722i) q^{50} +(-3.44859 - 5.97313i) q^{51} +(2.04397 + 2.97022i) q^{52} +(-3.49408 + 6.05193i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-6.57031 - 11.3801i) q^{55} +(-1.22035 - 2.34750i) q^{56} +3.03338i q^{57} +4.37718i q^{58} +(9.08332 - 5.24426i) q^{59} +(-2.27114 - 1.31124i) q^{60} +14.3150 q^{61} +(2.84643 + 4.93016i) q^{62} +(-2.34750 + 1.22035i) q^{63} -1.00000 q^{64} +(-7.78936 + 5.36029i) q^{65} +(-2.50537 + 4.33943i) q^{66} +2.47913i q^{67} +(3.44859 - 5.97313i) q^{68} +(-2.49983 + 4.32984i) q^{69} +(6.15629 - 3.20035i) q^{70} +(2.82667 + 1.63198i) q^{71} +1.00000i q^{72} +(4.20527 + 2.42791i) q^{73} +(-2.14183 - 3.70976i) q^{74} +(0.938722 - 1.62591i) q^{75} +(-2.62699 + 1.51669i) q^{76} +(-6.11485 - 11.7627i) q^{77} +(3.25524 + 1.55030i) q^{78} +(-3.69502 - 6.39996i) q^{79} -2.62249i q^{80} +1.00000 q^{81} +5.71638 q^{82} +9.16995i q^{83} +(-2.23060 - 1.42282i) q^{84} +(15.6645 + 9.04389i) q^{85} +(11.1553 - 6.44053i) q^{86} +(2.18859 + 3.79075i) q^{87} -5.01074 q^{88} +(-13.3582 - 7.71235i) q^{89} -2.62249 q^{90} +(-8.08971 + 5.05535i) q^{91} -4.99967 q^{92} +(4.93016 + 2.84643i) q^{93} +0.576897 q^{94} +(-3.97750 - 6.88924i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-12.1886 - 7.03709i) q^{97} +(6.34749 - 2.95117i) q^{98} +5.01074i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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