LMFDB - Embedded newform 546.2.bd.b.121.1

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			121.1
Root			$-3.31964i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.57090 - 0.624890i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.57090 - 0.624890i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.31964 q^{10} +4.84030i q^{11} +(0.500000 - 0.866025i) q^{12} +(2.96948 - 2.04504i) q^{13} +(2.53891 - 0.744278i) q^{14} +(-2.87489 - 1.65982i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.71061 + 4.69492i) q^{17} +(-0.866025 + 0.500000i) q^{18} +6.97343i q^{19} +(-2.87489 + 1.65982i) q^{20} +(-2.57090 - 0.624890i) q^{21} +(-2.42015 - 4.19183i) q^{22} +(3.11910 + 5.40244i) q^{23} +1.00000i q^{24} +(3.01000 + 5.21347i) q^{25} +(-1.54912 + 3.25580i) q^{26} +1.00000 q^{27} +(-1.82662 + 1.91402i) q^{28} +(-0.459279 + 0.795495i) q^{29} +3.31964 q^{30} +(-4.25364 + 2.45584i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.84030i q^{33} -5.42123i q^{34} +(6.35384 + 6.06371i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.76960 - 3.90843i) q^{37} +(-3.48672 - 6.03917i) q^{38} +(2.96948 - 2.04504i) q^{39} +(1.65982 - 2.87489i) q^{40} +(-6.91006 - 3.98953i) q^{41} +(2.53891 - 0.744278i) q^{42} +(-2.86888 - 4.96904i) q^{43} +(4.19183 + 2.42015i) q^{44} +(-2.87489 - 1.65982i) q^{45} +(-5.40244 - 3.11910i) q^{46} +(-1.99396 - 1.15121i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(6.21903 + 3.21305i) q^{49} +(-5.21347 - 3.01000i) q^{50} +(-2.71061 + 4.69492i) q^{51} +(-0.286318 - 3.59416i) q^{52} +(2.54507 + 4.40819i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(8.03403 - 13.9153i) q^{55} +(0.624890 - 2.57090i) q^{56} +6.97343i q^{57} -0.918558i q^{58} +(-7.30349 - 4.21667i) q^{59} +(-2.87489 + 1.65982i) q^{60} -3.64615 q^{61} +(2.45584 - 4.25364i) q^{62} +(-2.57090 - 0.624890i) q^{63} -1.00000 q^{64} +(-11.9313 + 0.950473i) q^{65} +(-2.42015 - 4.19183i) q^{66} +8.80414i q^{67} +(2.71061 + 4.69492i) q^{68} +(3.11910 + 5.40244i) q^{69} +(-8.53445 - 2.07441i) q^{70} +(-6.84209 + 3.95028i) q^{71} +1.00000i q^{72} +(-1.61061 + 0.929885i) q^{73} +(-3.90843 + 6.76960i) q^{74} +(3.01000 + 5.21347i) q^{75} +(6.03917 + 3.48672i) q^{76} +(3.02466 - 12.4439i) q^{77} +(-1.54912 + 3.25580i) q^{78} +(-1.39270 + 2.41222i) q^{79} +3.31964i q^{80} +1.00000 q^{81} +7.97905 q^{82} +5.97886i q^{83} +(-1.82662 + 1.91402i) q^{84} +(15.5854 - 8.99826i) q^{85} +(4.96904 + 2.86888i) q^{86} +(-0.459279 + 0.795495i) q^{87} -4.84030 q^{88} +(5.38939 - 3.11156i) q^{89} +3.31964 q^{90} +(-8.91215 + 3.40200i) q^{91} +6.23820 q^{92} +(-4.25364 + 2.45584i) q^{93} +2.30242 q^{94} +(11.5746 - 20.0479i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-0.466544 + 0.269360i) q^{97} +(-6.99236 + 0.326927i) q^{98} +4.84030i 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$	−2.87489	−	1.65982i	−1.28569	−	0.742293i	−0.307808	−	0.951449i	$-0.599595\pi$
$5$	−2.87489	−	1.65982i	−1.28569	−	0.742293i	−0.977882	+	0.209155i	$0.932929\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−2.57090	−	0.624890i	−0.971708	−	0.236186i
$7$	−2.57090	−	0.624890i	−0.971708	−	0.236186i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	3.31964			1.04976
$11$			4.84030i			1.45941i	0.683764	+	0.729703i	$0.260342\pi$
$11$			4.84030i			1.45941i	−0.683764	+	0.729703i	$0.739658\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.96948	−	2.04504i	0.823585	−	0.567192i
$13$	2.96948	−	2.04504i	0.823585	−	0.567192i
$14$	2.53891	−	0.744278i	0.678551	−	0.198917i
$15$	−2.87489	−	1.65982i	−0.742293	−	0.428563i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.71061	+	4.69492i	−0.657421	+	1.13869i	0.323860	+	0.946105i	$0.395019\pi$
$17$	−2.71061	+	4.69492i	−0.657421	+	1.13869i	−0.981281	+	0.192581i	$0.938314\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$			6.97343i			1.59982i	0.600123	+	0.799908i	$0.295118\pi$
$19$			6.97343i			1.59982i	−0.600123	+	0.799908i	$0.704882\pi$
$20$	−2.87489	+	1.65982i	−0.642845	+	0.371147i
$21$	−2.57090	−	0.624890i	−0.561016	−	0.136362i
$22$	−2.42015	−	4.19183i	−0.515978	−	0.893700i
$23$	3.11910	+	5.40244i	0.650377	+	1.12649i	0.983031	+	0.183437i	$0.0587223\pi$
$23$	3.11910	+	5.40244i	0.650377	+	1.12649i	−0.332655	+	0.943049i	$0.607944\pi$
$24$			1.00000i			0.204124i
$25$	3.01000	+	5.21347i	0.601999	+	1.04269i
$26$	−1.54912	+	3.25580i	−0.303808	+	0.638514i
$27$	1.00000			0.192450
$28$	−1.82662	+	1.91402i	−0.345199	+	0.361715i
$29$	−0.459279	+	0.795495i	−0.0852860	+	0.147720i	−0.905513	−	0.424318i	$-0.860514\pi$
$29$	−0.459279	+	0.795495i	−0.0852860	+	0.147720i	0.820227	+	0.572038i	$0.193847\pi$
$30$	3.31964			0.606080
$31$	−4.25364	+	2.45584i	−0.763976	+	0.441082i	−0.830722	−	0.556688i	$-0.812072\pi$
$31$	−4.25364	+	2.45584i	−0.763976	+	0.441082i	0.0667452	+	0.997770i	$0.478739\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$			4.84030i			0.842589i
$34$		−	5.42123i		−	0.929733i
$35$	6.35384	+	6.06371i	1.07400	+	1.02495i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.76960	−	3.90843i	1.11292	−	0.642542i	0.173332	−	0.984863i	$-0.444547\pi$
$37$	6.76960	−	3.90843i	1.11292	−	0.642542i	0.939583	+	0.342322i	$0.111213\pi$
$38$	−3.48672	−	6.03917i	−0.565620	−	0.979683i
$39$	2.96948	−	2.04504i	0.475497	−	0.327469i
$40$	1.65982	−	2.87489i	0.262440	−	0.454560i
$41$	−6.91006	−	3.98953i	−1.07917	−	0.623059i	−0.148498	−	0.988913i	$-0.547444\pi$
$41$	−6.91006	−	3.98953i	−1.07917	−	0.623059i	−0.930673	+	0.365853i	$0.880777\pi$
$42$	2.53891	−	0.744278i	0.391762	−	0.114845i
$43$	−2.86888	−	4.96904i	−0.437500	−	0.757772i	0.559996	−	0.828495i	$-0.310803\pi$
$43$	−2.86888	−	4.96904i	−0.437500	−	0.757772i	−0.997496	+	0.0707235i	$0.977469\pi$
$44$	4.19183	+	2.42015i	0.631942	+	0.364852i
$45$	−2.87489	−	1.65982i	−0.428563	−	0.247431i
$46$	−5.40244	−	3.11910i	−0.796546	−	0.459886i
$47$	−1.99396	−	1.15121i	−0.290849	−	0.167922i	0.347476	−	0.937689i	$-0.387039\pi$
$47$	−1.99396	−	1.15121i	−0.290849	−	0.167922i	−0.638325	+	0.769767i	$0.720372\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	6.21903	+	3.21305i	0.888432	+	0.459008i
$50$	−5.21347	−	3.01000i	−0.737295	−	0.425678i
$51$	−2.71061	+	4.69492i	−0.379562	+	0.657421i
$52$	−0.286318	−	3.59416i	−0.0397052	−	0.498421i
$53$	2.54507	+	4.40819i	0.349592	+	0.605512i	0.986177	−	0.165695i	$-0.0529868\pi$
$53$	2.54507	+	4.40819i	0.349592	+	0.605512i	−0.636585	+	0.771207i	$0.719653\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	8.03403	−	13.9153i	1.08331	−	1.87634i
$56$	0.624890	−	2.57090i	0.0835044	−	0.343551i
$57$			6.97343i			0.923654i
$58$		−	0.918558i		−	0.120613i
$59$	−7.30349	−	4.21667i	−0.950833	−	0.548964i	−0.0574934	−	0.998346i	$-0.518311\pi$
$59$	−7.30349	−	4.21667i	−0.950833	−	0.548964i	−0.893340	+	0.449382i	$0.851644\pi$
$60$	−2.87489	+	1.65982i	−0.371147	+	0.214282i
$61$	−3.64615			−0.466842			−0.233421	−	0.972376i	$-0.574992\pi$
$61$	−3.64615			−0.466842			−0.233421	+	0.972376i	$0.574992\pi$
$62$	2.45584	−	4.25364i	0.311892	−	0.540213i
$63$	−2.57090	−	0.624890i	−0.323903	−	0.0787287i
$64$	−1.00000			−0.125000
$65$	−11.9313	+	0.950473i	−1.47990	+	0.117892i
$66$	−2.42015	−	4.19183i	−0.297900	−	0.515978i
$67$			8.80414i			1.07560i	0.843073	+	0.537798i	$0.180744\pi$
$67$			8.80414i			1.07560i	−0.843073	+	0.537798i	$0.819256\pi$
$68$	2.71061	+	4.69492i	0.328710	+	0.569343i
$69$	3.11910	+	5.40244i	0.375495	+	0.650377i
$70$	−8.53445	−	2.07441i	−1.02006	−	0.247939i
$71$	−6.84209	+	3.95028i	−0.812007	+	0.468812i	−0.847652	−	0.530552i	$-0.821985\pi$
$71$	−6.84209	+	3.95028i	−0.812007	+	0.468812i	0.0356457	+	0.999364i	$0.488651\pi$
$72$			1.00000i			0.117851i
$73$	−1.61061	+	0.929885i	−0.188507	+	0.108835i	−0.591284	−	0.806464i	$-0.701379\pi$
$73$	−1.61061	+	0.929885i	−0.188507	+	0.108835i	0.402776	+	0.915298i	$0.368045\pi$
$74$	−3.90843	+	6.76960i	−0.454346	+	0.786950i
$75$	3.01000	+	5.21347i	0.347564	+	0.601999i
$76$	6.03917	+	3.48672i	0.692740	+	0.399954i
$77$	3.02466	−	12.4439i	0.344691	−	1.41812i
$78$	−1.54912	+	3.25580i	−0.175404	+	0.368646i
$79$	−1.39270	+	2.41222i	−0.156691	+	0.271396i	−0.933673	−	0.358126i	$-0.883416\pi$
$79$	−1.39270	+	2.41222i	−0.156691	+	0.271396i	0.776983	+	0.629522i	$0.216749\pi$
$80$			3.31964i			0.371147i
$81$	1.00000			0.111111
$82$	7.97905			0.881139
$83$			5.97886i			0.656265i	0.944632	+	0.328132i	$0.106419\pi$
$83$			5.97886i			0.656265i	−0.944632	+	0.328132i	$0.893581\pi$
$84$	−1.82662	+	1.91402i	−0.199300	+	0.208836i
$85$	15.5854	−	8.99826i	1.69048	−	0.975998i
$86$	4.96904	+	2.86888i	0.535825	+	0.309359i
$87$	−0.459279	+	0.795495i	−0.0492399	+	0.0852860i
$88$	−4.84030			−0.515978
$89$	5.38939	−	3.11156i	0.571274	−	0.329825i	−0.186384	−	0.982477i	$-0.559677\pi$
$89$	5.38939	−	3.11156i	0.571274	−	0.329825i	0.757658	+	0.652652i	$0.226344\pi$
$90$	3.31964			0.349921
$91$	−8.91215	+	3.40200i	−0.934247	+	0.356626i
$92$	6.23820			0.650377
$93$	−4.25364	+	2.45584i	−0.441082	+	0.254659i
$94$	2.30242			0.237477
$95$	11.5746	−	20.0479i	1.18753	−	2.05687i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−0.466544	+	0.269360i	−0.0473704	+	0.0273493i	−0.523498	−	0.852027i	$-0.675373\pi$
$97$	−0.466544	+	0.269360i	−0.0473704	+	0.0273493i	0.476128	+	0.879376i	$0.342040\pi$
$98$	−6.99236	+	0.326927i	−0.706335	+	0.0330246i
$99$			4.84030i			0.486469i
$100$	6.01999			0.601999
$101$	−15.9708			−1.58916			−0.794578	−	0.607163i	$-0.792308\pi$
$101$	−15.9708			−1.58916			−0.794578	+	0.607163i	$0.792308\pi$
$102$		−	5.42123i		−	0.536782i
$103$	1.31241	−	2.27316i	0.129316	−	0.223981i	−0.794096	−	0.607792i	$-0.792055\pi$
$103$	1.31241	−	2.27316i	0.129316	−	0.223981i	0.923412	+	0.383811i	$0.125389\pi$
$104$	2.04504	+	2.96948i	0.200533	+	0.291181i
$105$	6.35384	+	6.06371i	0.620072	+	0.591758i
$106$	−4.40819	−	2.54507i	−0.428161	−	0.247199i
$107$	−3.49091	−	6.04644i	−0.337479	−	0.584532i	0.646478	−	0.762932i	$-0.276241\pi$
$107$	−3.49091	−	6.04644i	−0.337479	−	0.584532i	−0.983958	+	0.178401i	$0.942908\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−7.17312	+	4.14140i	−0.687060	+	0.396674i	−0.802510	−	0.596639i	$-0.796502\pi$
$109$	−7.17312	+	4.14140i	−0.687060	+	0.396674i	0.115450	+	0.993313i	$0.463169\pi$
$110$			16.0681i			1.53203i
$111$	6.76960	−	3.90843i	0.642542	−	0.370972i
$112$	0.744278	+	2.53891i	0.0703277	+	0.239904i
$113$	2.78680	+	4.82688i	0.262160	+	0.454075i	0.966816	−	0.255475i	$-0.0822318\pi$
$113$	2.78680	+	4.82688i	0.262160	+	0.454075i	−0.704655	+	0.709550i	$0.748898\pi$
$114$	−3.48672	−	6.03917i	−0.326561	−	0.565620i
$115$		−	20.7085i		−	1.93108i
$116$	0.459279	+	0.795495i	0.0426430	+	0.0738598i
$117$	2.96948	−	2.04504i	0.274528	−	0.189064i
$118$	8.43334			0.776352
$119$	9.90252	−	10.3763i	0.907763	−	0.951197i
$120$	1.65982	−	2.87489i	0.151520	−	0.262440i
$121$	−12.4285			−1.12987
$122$	3.15766	−	1.82308i	0.285881	−	0.165054i
$123$	−6.91006	−	3.98953i	−0.623059	−	0.359724i
$124$			4.91168i			0.441082i
$125$		−	3.38601i		−	0.302854i
$126$	2.53891	−	0.744278i	0.226184	−	0.0663056i
$127$	−5.35058	+	9.26748i	−0.474787	+	0.822356i	−0.999583	−	0.0288723i	$-0.990808\pi$
$127$	−5.35058	+	9.26748i	−0.474787	+	0.822356i	0.524796	+	0.851228i	$0.324142\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.86888	−	4.96904i	−0.252591	−	0.437500i
$130$	9.85759	−	6.78880i	0.864568	−	0.595417i
$131$	8.39711	−	14.5442i	0.733659	−	1.27073i	−0.221650	−	0.975126i	$-0.571144\pi$
$131$	8.39711	−	14.5442i	0.733659	−	1.27073i	0.955309	−	0.295608i	$-0.0955224\pi$
$132$	4.19183	+	2.42015i	0.364852	+	0.210647i
$133$	4.35763	−	17.9280i	0.377854	−	1.55455i
$134$	−4.40207	−	7.62461i	−0.380281	−	0.658666i
$135$	−2.87489	−	1.65982i	−0.247431	−	0.142854i
$136$	−4.69492	−	2.71061i	−0.402586	−	0.232433i
$137$	13.9497	+	8.05384i	1.19180	+	0.688086i	0.958714	−	0.284371i	$-0.0917846\pi$
$137$	13.9497	+	8.05384i	1.19180	+	0.688086i	0.233085	+	0.972456i	$0.425118\pi$
$138$	−5.40244	−	3.11910i	−0.459886	−	0.265515i
$139$	5.04105	+	8.73136i	0.427577	+	0.740584i	0.996657	−	0.0816975i	$-0.0260341\pi$
$139$	5.04105	+	8.73136i	0.427577	+	0.740584i	−0.569081	+	0.822282i	$0.692701\pi$
$140$	8.42825	−	2.47073i	0.712317	−	0.208815i
$141$	−1.99396	−	1.15121i	−0.167922	−	0.0969496i
$142$	3.95028	−	6.84209i	0.331500	−	0.574175i
$143$	9.89862	+	14.3732i	0.827764	+	1.20195i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.64075	−	1.52464i	0.219303	−	0.126614i
$146$	0.929885	−	1.61061i	0.0769578	−	0.133295i
$147$	6.21903	+	3.21305i	0.512937	+	0.265008i
$148$		−	7.81686i		−	0.642542i
$149$		−	7.78228i		−	0.637549i	−0.947831	−	0.318775i	$-0.896729\pi$
$149$		−	7.78228i		−	0.637549i	0.947831	−	0.318775i	$-0.103271\pi$
$150$	−5.21347	−	3.01000i	−0.425678	−	0.245765i
$151$	12.2591	−	7.07781i	0.997634	−	0.575984i	0.0900867	−	0.995934i	$-0.471286\pi$
$151$	12.2591	−	7.07781i	0.997634	−	0.575984i	0.907547	+	0.419950i	$0.137952\pi$
$152$	−6.97343			−0.565620
$153$	−2.71061	+	4.69492i	−0.219140	+	0.379562i
$154$	3.60253	+	12.2891i	0.290300	+	0.990282i
$155$	16.3050			1.30965
$156$	−0.286318	−	3.59416i	−0.0229238	−	0.287764i
$157$	0.648559	+	1.12334i	0.0517606	+	0.0896520i	0.890745	−	0.454504i	$-0.150183\pi$
$157$	0.648559	+	1.12334i	0.0517606	+	0.0896520i	−0.838984	+	0.544156i	$0.816850\pi$
$158$		−	2.78540i		−	0.221594i
$159$	2.54507	+	4.40819i	0.201837	+	0.349592i
$160$	−1.65982	−	2.87489i	−0.131220	−	0.227280i
$161$	−4.64295	−	15.8382i	−0.365916	−	1.24823i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			21.6263i			1.69391i	0.531669	+	0.846953i	$0.321565\pi$
$163$			21.6263i			1.69391i	−0.531669	+	0.846953i	$0.678435\pi$
$164$	−6.91006	+	3.98953i	−0.539585	+	0.311530i
$165$	8.03403	−	13.9153i	0.625448	−	1.08331i
$166$	−2.98943	−	5.17784i	−0.232025	−	0.401879i
$167$	11.2333	+	6.48557i	0.869261	+	0.501868i	0.867103	−	0.498130i	$-0.165980\pi$
$167$	11.2333	+	6.48557i	0.869261	+	0.501868i	0.00215851	+	0.999998i	$0.499313\pi$
$168$	0.624890	−	2.57090i	0.0482113	−	0.198349i
$169$	4.63561	−	12.1454i	0.356585	−	0.934263i
$170$	−8.99826	+	15.5854i	−0.690135	+	1.19535i
$171$			6.97343i			0.533272i
$172$	−5.73775			−0.437500
$173$	13.4521			1.02275			0.511374	−	0.859358i	$-0.329137\pi$
$173$	13.4521			1.02275			0.511374	+	0.859358i	$0.329137\pi$
$174$		−	0.918558i		−	0.0696357i
$175$	−4.48055	−	15.2842i	−0.338698	−	1.15538i
$176$	4.19183	−	2.42015i	0.315971	−	0.182426i
$177$	−7.30349	−	4.21667i	−0.548964	−	0.316944i
$178$	−3.11156	+	5.38939i	−0.233222	+	0.403952i
$179$	4.73997			0.354282			0.177141	−	0.984185i	$-0.443315\pi$
$179$	4.73997			0.354282			0.177141	+	0.984185i	$0.443315\pi$
$180$	−2.87489	+	1.65982i	−0.214282	+	0.123716i
$181$	−16.7842			−1.24756			−0.623780	−	0.781600i	$-0.714404\pi$
$181$	−16.7842			−1.24756			−0.623780	+	0.781600i	$0.714404\pi$
$182$	6.01715	−	7.40229i	0.446021	−	0.548694i
$183$	−3.64615			−0.269531
$184$	−5.40244	+	3.11910i	−0.398273	+	0.229943i
$185$	−25.9491			−1.90782
$186$	2.45584	−	4.25364i	0.180071	−	0.311892i
$187$	−22.7249	−	13.1202i	−1.66181	−	0.959444i
$188$	−1.99396	+	1.15121i	−0.145424	+	0.0839608i
$189$	−2.57090	−	0.624890i	−0.187005	−	0.0454540i
$190$			23.1493i			1.67942i
$191$	13.9870			1.01206			0.506032	−	0.862515i	$-0.331112\pi$
$191$	13.9870			1.01206			0.506032	+	0.862515i	$0.331112\pi$
$192$	−1.00000			−0.0721688
$193$		−	11.6032i		−	0.835215i	−0.908627	−	0.417608i	$-0.862869\pi$
$193$		−	11.6032i		−	0.835215i	0.908627	−	0.417608i	$-0.137131\pi$
$194$	0.269360	−	0.466544i	0.0193389	−	0.0334959i
$195$	−11.9313	+	0.950473i	−0.854420	+	0.0680648i
$196$	5.89210	−	3.77931i	0.420864	−	0.269951i
$197$	−16.7733	−	9.68409i	−1.19505	−	0.689963i	−0.235603	−	0.971849i	$-0.575706\pi$
$197$	−16.7733	−	9.68409i	−1.19505	−	0.689963i	−0.959448	+	0.281887i	$0.909040\pi$
$198$	−2.42015	−	4.19183i	−0.171993	−	0.297900i
$199$	7.97985	−	13.8215i	0.565677	−	0.979781i	−0.431310	−	0.902204i	$-0.641948\pi$
$199$	7.97985	−	13.8215i	0.565677	−	0.979781i	0.996986	−	0.0775767i	$-0.0247183\pi$
$200$	−5.21347	+	3.01000i	−0.368648	+	0.212839i
$201$			8.80414i			0.620996i
$202$	13.8311	−	7.98541i	0.973155	−	0.561851i
$203$	1.67786	−	1.75814i	0.117762	−	0.123397i
$204$	2.71061	+	4.69492i	0.189781	+	0.328710i
$205$	13.2438	+	22.9389i	0.924986	+	1.60212i
$206$			2.62482i			0.182880i
$207$	3.11910	+	5.40244i	0.216792	+	0.375495i
$208$	−3.25580	−	1.54912i	−0.225749	−	0.107412i
$209$	−33.7535			−2.33478
$210$	−8.53445	−	2.07441i	−0.588933	−	0.143148i
$211$	−7.94467	+	13.7606i	−0.546934	+	0.947317i	0.451549	+	0.892247i	$0.350872\pi$
$211$	−7.94467	+	13.7606i	−0.546934	+	0.947317i	−0.998482	+	0.0550706i	$0.982462\pi$
$212$	5.09014			0.349592
$213$	−6.84209	+	3.95028i	−0.468812	+	0.270669i
$214$	6.04644	+	3.49091i	0.413326	+	0.238634i
$215$			19.0473i			1.29901i
$216$			1.00000i			0.0680414i
$217$	12.4703	−	3.65566i	0.846539	−	0.248162i
$218$	4.14140	−	7.17312i	0.280491	−	0.485825i
$219$	−1.61061	+	0.929885i	−0.108835	+	0.0628358i
$220$	−8.03403	−	13.9153i	−0.541654	−	0.938172i
$221$	1.55220	+	19.4848i	0.104412	+	1.31069i
$222$	−3.90843	+	6.76960i	−0.262317	+	0.454346i
$223$	21.3888	+	12.3488i	1.43230	+	0.826940i	0.997296	−	0.0734882i	$-0.0234131\pi$
$223$	21.3888	+	12.3488i	1.43230	+	0.826940i	0.435005	+	0.900428i	$0.356746\pi$
$224$	−1.91402	−	1.82662i	−0.127886	−	0.122046i
$225$	3.01000	+	5.21347i	0.200666	+	0.347564i
$226$	−4.82688	−	2.78680i	−0.321079	−	0.185375i
$227$	13.8269	+	7.98297i	0.917724	+	0.529848i	0.882908	−	0.469546i	$-0.155582\pi$
$227$	13.8269	+	7.98297i	0.917724	+	0.529848i	0.0348156	+	0.999394i	$0.488916\pi$
$228$	6.03917	+	3.48672i	0.399954	+	0.230913i
$229$	5.05038	+	2.91584i	0.333738	+	0.192684i	0.657500	−	0.753455i	$-0.271614\pi$
$229$	5.05038	+	2.91584i	0.333738	+	0.192684i	−0.323761	+	0.946139i	$0.604947\pi$
$230$	10.3543	+	17.9341i	0.682741	+	1.18254i
$231$	3.02466	−	12.4439i	0.199008	−	0.818750i
$232$	−0.795495	−	0.459279i	−0.0522268	−	0.0301532i
$233$	−5.79484	+	10.0370i	−0.379632	+	0.657543i	−0.991009	−	0.133797i	$-0.957283\pi$
$233$	−5.79484	+	10.0370i	−0.379632	+	0.657543i	0.611376	+	0.791340i	$0.290616\pi$
$234$	−1.54912	+	3.25580i	−0.101269	+	0.212838i
$235$	3.82161	+	6.61922i	0.249294	+	0.431790i
$236$	−7.30349	+	4.21667i	−0.475416	+	0.274482i
$237$	−1.39270	+	2.41222i	−0.0904654	+	0.156691i
$238$	−3.38767	+	13.9374i	−0.219590	+	0.903429i
$239$		−	21.8120i		−	1.41090i	−0.708760	−	0.705450i	$-0.750745\pi$
$239$		−	21.8120i		−	1.41090i	0.708760	−	0.705450i	$-0.249255\pi$
$240$			3.31964i			0.214282i
$241$	−17.5918	−	10.1566i	−1.13319	−	0.654246i	−0.188452	−	0.982082i	$-0.560347\pi$
$241$	−17.5918	−	10.1566i	−1.13319	−	0.654246i	−0.944734	+	0.327837i	$0.893680\pi$
$242$	10.7634	−	6.21427i	0.691900	−	0.399468i
$243$	1.00000			0.0641500
$244$	−1.82308	+	3.15766i	−0.116710	+	0.202148i
$245$	−12.5459	−	19.5596i	−0.801530	−	1.24962i
$246$	7.97905			0.508726
$247$	14.2610	+	20.7075i	0.907403	+	1.31758i
$248$	−2.45584	−	4.25364i	−0.155946	−	0.270106i
$249$			5.97886i			0.378895i
$250$	1.69300	+	2.93237i	0.107075	+	0.185459i
$251$	9.39667	+	16.2755i	0.593112	+	1.02730i	0.993810	+	0.111091i	$0.0354344\pi$
$251$	9.39667	+	16.2755i	0.593112	+	1.02730i	−0.400698	+	0.916210i	$0.631232\pi$
$252$	−1.82662	+	1.91402i	−0.115066	+	0.120572i
$253$	−26.1494	+	15.0974i	−1.64400	+	0.949164i
$254$		−	10.7012i		−	0.671451i
$255$	15.5854	−	8.99826i	0.975998	−	0.563493i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.50923	−	16.4705i	−0.593170	−	1.02740i	−0.993802	−	0.111161i	$-0.964543\pi$
$257$	−9.50923	−	16.4705i	−0.593170	−	1.02740i	0.400633	−	0.916239i	$-0.368790\pi$
$258$	4.96904	+	2.86888i	0.309359	+	0.178608i
$259$	−19.8463	+	5.81792i	−1.23319	+	0.361508i
$260$	−5.14253	+	10.8081i	−0.318926	+	0.670288i
$261$	−0.459279	+	0.795495i	−0.0284287	+	0.0492399i
$262$			16.7942i			1.03755i
$263$	−20.3146			−1.25265			−0.626327	−	0.779560i	$-0.715443\pi$
$263$	−20.3146			−1.25265			−0.626327	+	0.779560i	$0.715443\pi$
$264$	−4.84030			−0.297900
$265$		−	16.8974i		−	1.03800i
$266$	5.19018	+	17.7049i	0.318230	+	1.08556i
$267$	5.38939	−	3.11156i	0.329825	−	0.190425i
$268$	7.62461	+	4.40207i	0.465747	+	0.268899i
$269$	6.16010	−	10.6696i	0.375588	−	0.650537i	−0.614827	−	0.788662i	$-0.710774\pi$
$269$	6.16010	−	10.6696i	0.375588	−	0.650537i	0.990415	+	0.138125i	$0.0441076\pi$
$270$	3.31964			0.202027
$271$	10.2332	−	5.90816i	0.621624	−	0.358895i	−0.155877	−	0.987776i	$-0.549820\pi$
$271$	10.2332	−	5.90816i	0.621624	−	0.358895i	0.777501	+	0.628882i	$0.216487\pi$
$272$	5.42123			0.328710
$273$	−8.91215	+	3.40200i	−0.539388	+	0.205898i
$274$	−16.1077			−0.973100
$275$	−25.2348	+	14.5693i	−1.52171	+	0.878562i
$276$	6.23820			0.375495
$277$	−16.1656	+	27.9997i	−0.971299	+	1.68234i	−0.279654	+	0.960101i	$0.590220\pi$
$277$	−16.1656	+	27.9997i	−0.971299	+	1.68234i	−0.691645	+	0.722238i	$0.743114\pi$
$278$	−8.73136	−	5.04105i	−0.523672	−	0.302342i
$279$	−4.25364	+	2.45584i	−0.254659	+	0.147027i
$280$	−6.06371	+	6.35384i	−0.362376	+	0.379715i
$281$			0.624762i			0.0372702i	0.999826	+	0.0186351i	$0.00593208\pi$
$281$			0.624762i			0.0372702i	−0.999826	+	0.0186351i	$0.994068\pi$
$282$	2.30242			0.137107
$283$	−12.5738			−0.747432			−0.373716	−	0.927543i	$-0.621917\pi$
$283$	−12.5738			−0.747432			−0.373716	+	0.927543i	$0.621917\pi$
$284$			7.90056i			0.468812i
$285$	11.5746	−	20.0479i	0.685622	−	1.18753i
$286$	−15.7590	−	7.49823i	−0.931852	−	0.443380i
$287$	15.2720	+	14.5747i	0.901481	+	0.860317i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−6.19487	−	10.7298i	−0.364404	−	0.631166i
$290$	−1.52464	+	2.64075i	−0.0895300	+	0.155070i
$291$	−0.466544	+	0.269360i	−0.0273493	+	0.0157901i
$292$			1.85977i			0.108835i
$293$	17.5615	−	10.1391i	1.02595	−	0.592334i	0.110129	−	0.993917i	$-0.464873\pi$
$293$	17.5615	−	10.1391i	1.02595	−	0.592334i	0.915822	+	0.401584i	$0.131540\pi$
$294$	−6.99236	+	0.326927i	−0.407803	+	0.0190668i
$295$	13.9978	+	24.2449i	0.814984	+	1.41159i
$296$	3.90843	+	6.76960i	0.227173	+	0.393475i
$297$			4.84030i			0.280863i
$298$	3.89114	+	6.73965i	0.225408	+	0.390417i
$299$	20.3103	+	9.66374i	1.17458	+	0.558868i
$300$	6.01999			0.347564
$301$	4.27049	+	14.5676i	0.246147	+	0.839664i
$302$	−7.07781	+	12.2591i	−0.407282	+	0.705434i
$303$	−15.9708			−0.917499
$304$	6.03917	−	3.48672i	0.346370	−	0.199977i
$305$	10.4823	+	6.05195i	0.600214	+	0.346534i
$306$		−	5.42123i		−	0.309911i
$307$		−	23.8860i		−	1.36325i	−0.731703	−	0.681624i	$-0.761274\pi$
$307$		−	23.8860i		−	1.36325i	0.731703	−	0.681624i	$-0.238726\pi$
$308$	−9.26443	−	8.84139i	−0.527890	−	0.503785i
$309$	1.31241	−	2.27316i	0.0746605	−	0.129316i
$310$	−14.1205	+	8.15250i	−0.801993	+	0.463031i
$311$	−14.1582	−	24.5227i	−0.802837	−	1.39055i	−0.917742	−	0.397177i	$-0.869990\pi$
$311$	−14.1582	−	24.5227i	−0.802837	−	1.39055i	0.114905	−	0.993376i	$-0.463344\pi$
$312$	2.04504	+	2.96948i	0.115778	+	0.168114i
$313$	−15.7533	+	27.2855i	−0.890427	+	1.54226i	−0.0510628	+	0.998695i	$0.516261\pi$
$313$	−15.7533	+	27.2855i	−0.890427	+	1.54226i	−0.839364	+	0.543569i	$0.817072\pi$
$314$	−1.12334	−	0.648559i	−0.0633935	−	0.0366003i
$315$	6.35384	+	6.06371i	0.357999	+	0.341651i
$316$	1.39270	+	2.41222i	0.0783454	+	0.135698i
$317$	2.06314	+	1.19116i	0.115878	+	0.0669020i	0.556819	−	0.830634i	$-0.312022\pi$
$317$	2.06314	+	1.19116i	0.115878	+	0.0669020i	−0.440941	+	0.897536i	$0.645355\pi$
$318$	−4.40819	−	2.54507i	−0.247199	−	0.142720i
$319$	−3.85044	−	2.22305i	−0.215583	−	0.124467i
$320$	2.87489	+	1.65982i	0.160711	+	0.0927867i
$321$	−3.49091	−	6.04644i	−0.194844	−	0.337479i
$322$	11.9400	+	11.3948i	0.665391	+	0.635008i
$323$	−32.7397	−	18.9023i	−1.82169	−	1.05175i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	19.5999	+	9.32571i	1.08721	+	0.517297i
$326$	−10.8132	−	18.7290i	−0.598886	−	1.03730i
$327$	−7.17312	+	4.14140i	−0.396674	+	0.229020i
$328$	3.98953	−	6.91006i	0.220285	−	0.381544i
$329$	4.40688	+	4.20565i	0.242959	+	0.231865i
$330$			16.0681i			0.884517i
$331$			30.3382i			1.66754i	0.552113	+	0.833769i	$0.313822\pi$
$331$			30.3382i			1.66754i	−0.552113	+	0.833769i	$0.686178\pi$
$332$	5.17784	+	2.98943i	0.284171	+	0.164066i
$333$	6.76960	−	3.90843i	0.370972	−	0.214181i
$334$	−12.9711			−0.709749
$335$	14.6133	−	25.3109i	0.798408	−	1.38288i
$336$	0.744278	+	2.53891i	0.0406037	+	0.138509i
$337$	16.6355			0.906194			0.453097	−	0.891461i	$-0.350319\pi$
$337$	16.6355			0.906194			0.453097	+	0.891461i	$0.350319\pi$
$338$	2.05815	+	12.8360i	0.111949	+	0.698189i
$339$	2.78680	+	4.82688i	0.151358	+	0.262160i
$340$		−	17.9965i		−	0.975998i
$341$	−11.8870	−	20.5889i	−0.643718	−	1.11495i
$342$	−3.48672	−	6.03917i	−0.188540	−	0.326561i
$343$	−13.9807	−	12.1466i	−0.754885	−	0.655857i
$344$	4.96904	−	2.86888i	0.267913	−	0.154679i
$345$		−	20.7085i		−	1.11491i
$346$	−11.6499	+	6.72607i	−0.626302	+	0.361596i
$347$	3.00469	−	5.20427i	0.161300	−	0.279380i	−0.774035	−	0.633143i	$-0.781765\pi$
$347$	3.00469	−	5.20427i	0.161300	−	0.279380i	0.935335	+	0.353763i	$0.115098\pi$
$348$	0.459279	+	0.795495i	0.0246199	+	0.0426430i
$349$	−8.66674	−	5.00374i	−0.463920	−	0.267844i	0.249771	−	0.968305i	$-0.419645\pi$
$349$	−8.66674	−	5.00374i	−0.463920	−	0.267844i	−0.713691	+	0.700461i	$0.752978\pi$
$350$	11.5224	+	10.9962i	0.615897	+	0.587773i
$351$	2.96948	−	2.04504i	0.158499	−	0.109156i
$352$	−2.42015	+	4.19183i	−0.128995	+	0.223425i
$353$		−	21.8802i		−	1.16457i	−0.812986	−	0.582283i	$-0.802159\pi$
$353$		−	21.8802i		−	1.16457i	0.812986	−	0.582283i	$-0.197841\pi$
$354$	8.43334			0.448227
$355$	26.2270			1.39198
$356$		−	6.22313i		−	0.329825i
$357$	9.90252	−	10.3763i	0.524097	−	0.549174i
$358$	−4.10493	+	2.36998i	−0.216952	+	0.125258i
$359$	−3.97403	−	2.29441i	−0.209741	−	0.121094i	0.391450	−	0.920199i	$-0.371974\pi$
$359$	−3.97403	−	2.29441i	−0.209741	−	0.121094i	−0.601191	+	0.799105i	$0.705307\pi$
$360$	1.65982	−	2.87489i	0.0874801	−	0.151520i
$361$	−29.6288			−1.55941
$362$	14.5355	−	8.39210i	0.763971	−	0.441079i
$363$	−12.4285			−0.652329
$364$	−1.50986	+	9.41915i	−0.0791382	+	0.493697i
$365$	6.17376			0.323149
$366$	3.15766	−	1.82308i	0.165054	−	0.0952937i
$367$	37.4060			1.95258			0.976289	−	0.216473i	$-0.0694553\pi$
$367$	37.4060			1.95258			0.976289	+	0.216473i	$0.0694553\pi$
$368$	3.11910	−	5.40244i	0.162594	−	0.281621i
$369$	−6.91006	−	3.98953i	−0.359724	−	0.207686i
$370$	22.4726	−	12.9746i	1.16830	−	0.674516i
$371$	−3.78848	−	12.9234i	−0.196688	−	0.670949i
$372$			4.91168i			0.254659i
$373$	15.8114			0.818683			0.409341	−	0.912381i	$-0.365758\pi$
$373$	15.8114			0.818683			0.409341	+	0.912381i	$0.365758\pi$
$374$	26.2404			1.35686
$375$		−	3.38601i		−	0.174853i
$376$	1.15121	−	1.99396i	0.0593692	−	0.102831i
$377$	0.263000	+	3.30145i	0.0135452	+	0.170033i
$378$	2.53891	−	0.744278i	0.130587	−	0.0382816i
$379$	−4.44021	−	2.56356i	−0.228078	−	0.131681i	0.381607	−	0.924325i	$-0.375371\pi$
$379$	−4.44021	−	2.56356i	−0.228078	−	0.131681i	−0.609685	+	0.792644i	$0.708704\pi$
$380$	−11.5746	−	20.0479i	−0.593766	−	1.02843i
$381$	−5.35058	+	9.26748i	−0.274119	+	0.474787i
$382$	−12.1131	+	6.99350i	−0.619760	+	0.357819i
$383$		−	20.2282i		−	1.03361i	−0.856102	−	0.516807i	$-0.827120\pi$
$383$		−	20.2282i		−	1.03361i	0.856102	−	0.516807i	$-0.172880\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−29.3502	+	30.7545i	−1.49583	+	1.56740i
$386$	5.80159	+	10.0487i	0.295293	+	0.511463i
$387$	−2.86888	−	4.96904i	−0.145833	−	0.252591i
$388$			0.538719i			0.0273493i
$389$	−3.08894	−	5.35019i	−0.156615	−	0.271266i	0.777031	−	0.629463i	$-0.216725\pi$
$389$	−3.08894	−	5.35019i	−0.156615	−	0.271266i	−0.933646	+	0.358197i	$0.883392\pi$
$390$	9.85759	−	6.78880i	0.499159	−	0.343764i
$391$	−33.8187			−1.71028
$392$	−3.21305	+	6.21903i	−0.162284	+	0.314108i
$393$	8.39711	−	14.5442i	0.423578	−	0.733659i
$394$	19.3682			0.975755
$395$	8.00771	−	4.62325i	0.402911	−	0.232621i
$396$	4.19183	+	2.42015i	0.210647	+	0.121617i
$397$			33.7680i			1.69477i	0.530981	+	0.847384i	$0.321823\pi$
$397$			33.7680i			1.69477i	−0.530981	+	0.847384i	$0.678177\pi$
$398$			15.9597i			0.799988i
$399$	4.35763	−	17.9280i	0.218154	−	0.897522i
$400$	3.01000	−	5.21347i	0.150500	−	0.260673i
$401$	20.7571	−	11.9841i	1.03656	−	0.598460i	0.117705	−	0.993049i	$-0.462446\pi$
$401$	20.7571	−	11.9841i	1.03656	−	0.598460i	0.918858	+	0.394589i	$0.129113\pi$
$402$	−4.40207	−	7.62461i	−0.219555	−	0.380281i
$403$	−7.60880	+	15.9914i	−0.379021	+	0.796590i
$404$	−7.98541	+	13.8311i	−0.397289	+	0.688124i
$405$	−2.87489	−	1.65982i	−0.142854	−	0.0824771i
$406$	−0.573998	+	2.36152i	−0.0284870	+	0.117200i
$407$	18.9180	+	32.7669i	0.937730	+	1.62420i
$408$	−4.69492	−	2.71061i	−0.232433	−	0.134195i
$409$	−1.19686	−	0.691006i	−0.0591808	−	0.0341680i	0.470118	−	0.882604i	$-0.344211\pi$
$409$	−1.19686	−	0.691006i	−0.0591808	−	0.0341680i	−0.529298	+	0.848436i	$0.677545\pi$
$410$	−22.9389	−	13.2438i	−1.13287	−	0.654064i
$411$	13.9497	+	8.05384i	0.688086	+	0.397267i
$412$	−1.31241	−	2.27316i	−0.0646579	−	0.111991i
$413$	16.1416	+	15.4045i	0.794274	+	0.758006i
$414$	−5.40244	−	3.11910i	−0.265515	−	0.153295i
$415$	9.92382	−	17.1886i	0.487141	−	0.843753i
$416$	3.59416	−	0.286318i	0.176218	−	0.0140379i
$417$	5.04105	+	8.73136i	0.246861	+	0.427577i
$418$	29.2314	−	16.8768i	1.42976	−	0.825470i
$419$	−10.2059	+	17.6771i	−0.498590	+	0.863584i	−0.999999	−	0.00162717i	$-0.999482\pi$
$419$	−10.2059	+	17.6771i	−0.498590	+	0.863584i	0.501409	+	0.865211i	$0.332815\pi$
$420$	8.42825	−	2.47073i	0.411257	−	0.120560i
$421$			8.53522i			0.415981i	0.978131	+	0.207991i	$0.0666923\pi$
$421$			8.53522i			0.415981i	−0.978131	+	0.207991i	$0.933308\pi$
$422$		−	15.8893i		−	0.773481i
$423$	−1.99396	−	1.15121i	−0.0969496	−	0.0559739i
$424$	−4.40819	+	2.54507i	−0.214081	+	0.123600i
$425$	−32.6358			−1.58307
$426$	3.95028	−	6.84209i	0.191392	−	0.331500i
$427$	9.37388	+	2.27844i	0.453634	+	0.110262i
$428$	−6.98183			−0.337479
$429$	9.89862	+	14.3732i	0.477910	+	0.693944i
$430$	−9.52363	−	16.4954i	−0.459270	−	0.795479i
$431$			29.2920i			1.41095i	0.708737	+	0.705473i	$0.249265\pi$
$431$			29.2920i			1.41095i	−0.708737	+	0.705473i	$0.750735\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−7.92957	−	13.7344i	−0.381071	−	0.660034i	0.610145	−	0.792290i	$-0.291111\pi$
$433$	−7.92957	−	13.7344i	−0.381071	−	0.660034i	−0.991216	+	0.132256i	$0.957778\pi$
$434$	−8.97177	+	9.40105i	−0.430659	+	0.451265i
$435$	2.64075	−	1.52464i	0.126614	−	0.0731009i
$436$			8.28280i			0.396674i
$437$	−37.6735	+	21.7508i	−1.80217	+	1.04048i
$438$	0.929885	−	1.61061i	0.0444316	−	0.0769578i
$439$	−5.56714	−	9.64257i	−0.265705	−	0.460215i	0.702043	−	0.712134i	$-0.252271\pi$
$439$	−5.56714	−	9.64257i	−0.265705	−	0.460215i	−0.967748	+	0.251920i	$0.918938\pi$
$440$	13.9153	+	8.03403i	0.663388	+	0.383007i
$441$	6.21903	+	3.21305i	0.296144	+	0.153003i
$442$	−11.0866	−	16.0982i	−0.527338	−	0.765715i
$443$	−1.87317	+	3.24442i	−0.0889970	+	0.154147i	−0.907087	−	0.420942i	$-0.861699\pi$
$443$	−1.87317	+	3.24442i	−0.0889970	+	0.154147i	0.818090	+	0.575090i	$0.195033\pi$
$444$		−	7.81686i		−	0.370972i
$445$	−20.6585			−0.979308
$446$	−24.6977			−1.16947
$447$		−	7.78228i		−	0.368089i
$448$	2.57090	+	0.624890i	0.121463	+	0.0295233i
$449$	10.4838	−	6.05280i	0.494759	−	0.285649i	−0.231788	−	0.972766i	$-0.574457\pi$
$449$	10.4838	−	6.05280i	0.494759	−	0.285649i	0.726547	+	0.687117i	$0.241124\pi$
$450$	−5.21347	−	3.01000i	−0.245765	−	0.141893i
$451$	19.3105	−	33.4468i	0.909297	−	1.57495i
$452$	5.57360			0.262160
$453$	12.2591	−	7.07781i	0.575984	−	0.332545i
$454$	−15.9659			−0.749318
$455$	31.2682	+	5.01219i	1.46587	+	0.234975i
$456$	−6.97343			−0.326561
$457$	31.7689	−	18.3418i	1.48609	−	0.857994i	0.486214	−	0.873840i	$-0.338377\pi$
$457$	31.7689	−	18.3418i	1.48609	−	0.857994i	0.999874	+	0.0158460i	$0.00504414\pi$
$458$	−5.83167			−0.272496
$459$	−2.71061	+	4.69492i	−0.126521	+	0.219140i
$460$	−17.9341	−	10.3543i	−0.836183	−	0.482771i
$461$	−1.86597	+	1.07732i	−0.0869071	+	0.0501758i	−0.542824	−	0.839847i	$-0.682645\pi$
$461$	−1.86597	+	1.07732i	−0.0869071	+	0.0501758i	0.455917	+	0.890022i	$0.349312\pi$
$462$	3.60253	+	12.2891i	0.167605	+	0.571740i
$463$		−	38.0453i		−	1.76811i	−0.467379	−	0.884057i	$-0.654802\pi$
$463$		−	38.0453i		−	1.76811i	0.467379	−	0.884057i	$-0.345198\pi$
$464$	0.918558			0.0426430
$465$	16.3050			0.756126
$466$		−	11.5897i		−	0.536881i
$467$	−2.78062	+	4.81618i	−0.128672	+	0.222866i	−0.923162	−	0.384410i	$-0.874405\pi$
$467$	−2.78062	+	4.81618i	−0.128672	+	0.222866i	0.794490	+	0.607277i	$0.207738\pi$
$468$	−0.286318	−	3.59416i	−0.0132351	−	0.166140i
$469$	5.50161	−	22.6345i	0.254041	−	1.04517i
$470$	−6.61922	−	3.82161i	−0.305322	−	0.176278i
$471$	0.648559	+	1.12334i	0.0298840	+	0.0517606i
$472$	4.21667	−	7.30349i	0.194088	−	0.336170i
$473$	24.0517	−	13.8862i	1.10590	−	0.638490i
$474$		−	2.78540i		−	0.127937i
$475$	−36.3558	+	20.9900i	−1.66812	+	0.963088i
$476$	−4.03490	−	13.7640i	−0.184940	−	0.630872i
$477$	2.54507	+	4.40819i	0.116531	+	0.201837i
$478$	10.9060	+	18.8897i	0.498829	+	0.863997i
$479$			35.5451i			1.62410i	0.583590	+	0.812048i	$0.301647\pi$
$479$			35.5451i			1.62410i	−0.583590	+	0.812048i	$0.698353\pi$
$480$	−1.65982	−	2.87489i	−0.0757600	−	0.131220i
$481$	12.1093	−	25.4501i	0.552136	−	1.16043i
$482$	20.3132			0.925243
$483$	−4.64295	−	15.8382i	−0.211262	−	0.720663i
$484$	−6.21427	+	10.7634i	−0.282467	+	0.489247i
$485$	1.78835			0.0812049
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	19.1508	+	11.0567i	0.867805	+	0.501028i	0.866618	−	0.498972i	$-0.166289\pi$
$487$	19.1508	+	11.0567i	0.867805	+	0.501028i	0.00118711	+	0.999999i	$0.499622\pi$
$488$		−	3.64615i		−	0.165054i
$489$			21.6263i			0.977977i
$490$	20.6449	+	10.6662i	0.932642	+	0.481849i
$491$	−0.690710	+	1.19635i	−0.0311713	+	0.0539903i	−0.881190	−	0.472762i	$-0.843257\pi$
$491$	−0.690710	+	1.19635i	−0.0311713	+	0.0539903i	0.850019	+	0.526752i	$0.176590\pi$
$492$	−6.91006	+	3.98953i	−0.311530	+	0.179862i
$493$	−2.48986	−	4.31256i	−0.112138	−	0.194228i
$494$	−22.7041	−	10.8027i	−1.02151	−	0.486037i
$495$	8.03403	−	13.9153i	0.361103	−	0.625448i
$496$	4.25364	+	2.45584i	0.190994	+	0.110271i
$497$	20.0588	−	5.88022i	0.899760	−	0.263764i
$498$	−2.98943	−	5.17784i	−0.133960	−	0.232025i
$499$	5.74809	+	3.31866i	0.257320	+	0.148564i	0.623111	−	0.782133i	$-0.285868\pi$
$499$	5.74809	+	3.31866i	0.257320	+	0.148564i	−0.365792	+	0.930697i	$0.619202\pi$
$500$	−2.93237	−	1.69300i	−0.131139	−	0.0757134i
$501$	11.2333	+	6.48557i	0.501868	+	0.289754i
$502$	−16.2755	−	9.39667i	−0.726411	−	0.419394i
$503$	−3.41926	−	5.92234i	−0.152457	−	0.264064i	0.779673	−	0.626187i	$-0.215385\pi$
$503$	−3.41926	−	5.92234i	−0.152457	−	0.264064i	−0.932130	+	0.362123i	$0.882052\pi$
$504$	0.624890	−	2.57090i	0.0278348	−	0.114517i
$505$	45.9143	+	26.5087i	2.04316	+	1.17962i
$506$	15.0974	−	26.1494i	0.671160	−	1.16248i
$507$	4.63561	−	12.1454i	0.205875	−	0.539397i
$508$	5.35058	+	9.26748i	0.237394	+	0.411178i
$509$	−23.1147	+	13.3453i	−1.02454	+	0.591519i	−0.915416	−	0.402509i	$-0.868138\pi$
$509$	−23.1147	+	13.3453i	−1.02454	+	0.591519i	−0.109125	+	0.994028i	$0.534805\pi$
$510$	−8.99826	+	15.5854i	−0.398450	+	0.690135i
$511$	4.72178	−	1.38419i	0.208879	−	0.0612328i
$512$		−	1.00000i		−	0.0441942i
$513$			6.97343i			0.307885i
$514$	16.4705	+	9.50923i	0.726482	+	0.419434i
$515$	−7.54608	+	4.35673i	−0.332520	+	0.191980i
$516$	−5.73775			−0.252591
$517$	5.57222	−	9.65136i	0.245066	−	0.424466i
$518$	14.2784	−	14.9616i	0.627358	−	0.657375i
$519$	13.4521			0.590484
$520$	−0.950473	−	11.9313i	−0.0416810	−	0.523223i
$521$	5.45450	+	9.44747i	0.238966	+	0.413901i	0.960418	−	0.278563i	$-0.0898582\pi$
$521$	5.45450	+	9.44747i	0.238966	+	0.413901i	−0.721452	+	0.692465i	$0.756525\pi$
$522$		−	0.918558i		−	0.0402042i
$523$	−9.39598	−	16.2743i	−0.410857	−	0.711626i	0.584126	−	0.811663i	$-0.301437\pi$
$523$	−9.39598	−	16.2743i	−0.410857	−	0.711626i	−0.994984	+	0.100037i	$0.968104\pi$
$524$	−8.39711	−	14.5442i	−0.366830	−	0.635367i
$525$	−4.48055	−	15.2842i	−0.195547	−	0.667057i
$526$	17.5930	−	10.1573i	0.767091	−	0.442880i
$527$		−	26.6274i		−	1.15991i
$528$	4.19183	−	2.42015i	0.182426	−	0.105324i
$529$	−7.95754	+	13.7829i	−0.345980	+	0.599255i
$530$	8.44871	+	14.6336i	0.366989	+	0.635643i
$531$	−7.30349	−	4.21667i	−0.316944	−	0.182988i
$532$	−13.3473	−	12.7378i	−0.578678	−	0.552254i
$533$	−28.6780	+	2.28455i	−1.24218	+	0.0989548i
$534$	−3.11156	+	5.38939i	−0.134651	+	0.233222i
$535$			23.1771i			1.00204i
$536$	−8.80414			−0.380281
$537$	4.73997			0.204545
$538$			12.3202i			0.531161i
$539$	−15.5522	+	30.1020i	−0.669879	+	1.29658i
$540$	−2.87489	+	1.65982i	−0.123716	+	0.0714272i
$541$	2.95325	+	1.70506i	0.126970	+	0.0733061i	0.562140	−	0.827042i	$-0.309978\pi$
$541$	2.95325	+	1.70506i	0.126970	+	0.0733061i	−0.435170	+	0.900348i	$0.643312\pi$
$542$	−5.90816	+	10.2332i	−0.253777	+	0.439555i
$543$	−16.7842			−0.720279
$544$	−4.69492	+	2.71061i	−0.201293	+	0.116217i
$545$	27.4959			1.17780
$546$	6.01715	−	7.40229i	0.257510	−	0.316789i
$547$	13.6809			0.584953			0.292476	−	0.956273i	$-0.405521\pi$
$547$	13.6809			0.584953			0.292476	+	0.956273i	$0.405521\pi$
$548$	13.9497	−	8.05384i	0.595900	−	0.344043i
$549$	−3.64615			−0.155614
$550$	14.5693	−	25.2348i	0.621237	−	1.07601i
$551$	−5.54733	−	3.20275i	−0.236324	−	0.136442i
$552$	−5.40244	+	3.11910i	−0.229943	+	0.132758i
$553$	5.08786	−	5.33130i	0.216358	−	0.226710i
$554$		−	32.3313i		−	1.37362i
$555$	−25.9491			−1.10148
$556$	10.0821			0.427577
$557$		−	22.5382i		−	0.954973i	−0.878639	−	0.477487i	$-0.841548\pi$
$557$		−	22.5382i		−	0.954973i	0.878639	−	0.477487i	$-0.158452\pi$
$558$	2.45584	−	4.25364i	0.103964	−	0.180071i
$559$	−18.6810	−	8.88849i	−0.790121	−	0.375943i
$560$	2.07441	−	8.53445i	0.0876597	−	0.360646i
$561$	−22.7249	−	13.1202i	−0.959444	−	0.553935i
$562$	−0.312381	−	0.541060i	−0.0131770	−	0.0228232i
$563$	−11.6258	+	20.1366i	−0.489971	+	0.848655i	−0.999933	−	0.0115419i	$-0.996326\pi$
$563$	−11.6258	+	20.1366i	−0.489971	+	0.848655i	0.509962	+	0.860197i	$0.329659\pi$
$564$	−1.99396	+	1.15121i	−0.0839608	+	0.0484748i
$565$		−	18.5023i		−	0.778399i
$566$	10.8892	−	6.28688i	0.457707	−	0.264257i
$567$	−2.57090	−	0.624890i	−0.107968	−	0.0262429i
$568$	−3.95028	−	6.84209i	−0.165750	−	0.287088i
$569$	17.7797	+	30.7954i	0.745364	+	1.29101i	0.950024	+	0.312175i	$0.101058\pi$
$569$	17.7797	+	30.7954i	0.745364	+	1.29101i	−0.204660	+	0.978833i	$0.565609\pi$
$570$			23.1493i			0.969616i
$571$	−0.735579	−	1.27406i	−0.0307830	−	0.0533178i	0.850223	−	0.526422i	$-0.176467\pi$
$571$	−0.735579	−	1.27406i	−0.0307830	−	0.0533178i	−0.881006	+	0.473104i	$0.843133\pi$
$572$	17.3969	−	1.38587i	0.727399	−	0.0579460i
$573$	13.9870			0.584315
$574$	−20.5133	−	4.98603i	−0.856210	−	0.208113i
$575$	−18.7769	+	32.5226i	−0.783053	+	1.35629i
$576$	−1.00000			−0.0416667
$577$	14.0755	−	8.12650i	0.585971	−	0.338311i	−0.177532	−	0.984115i	$-0.556811\pi$
$577$	14.0755	−	8.12650i	0.585971	−	0.338311i	0.763503	+	0.645804i	$0.223478\pi$
$578$	10.7298	+	6.19487i	0.446302	+	0.257672i
$579$		−	11.6032i		−	0.482212i
$580$		−	3.04928i		−	0.126614i
$581$	3.73613	−	15.3710i	0.155001	−	0.637698i
$582$	0.269360	−	0.466544i	0.0111653	−	0.0193389i
$583$	−21.3370	+	12.3189i	−0.883688	+	0.510197i
$584$	−0.929885	−	1.61061i	−0.0384789	−	0.0666474i
$585$	−11.9313	+	0.950473i	−0.493300	+	0.0392972i
$586$	−10.1391	+	17.5615i	−0.418843	+	0.725457i
$587$	16.9203	+	9.76894i	0.698376	+	0.403207i	0.806742	−	0.590904i	$-0.201229\pi$
$587$	16.9203	+	9.76894i	0.698376	+	0.403207i	−0.108366	+	0.994111i	$0.534562\pi$
$588$	5.89210	−	3.77931i	0.242986	−	0.155856i
$589$	−17.1256	−	29.6625i	−0.705650	−	1.22222i
$590$	−24.2449	−	13.9978i	−0.998148	−	0.576281i
$591$	−16.7733	−	9.68409i	−0.689963	−	0.398350i
$592$	−6.76960	−	3.90843i	−0.278229	−	0.160635i
$593$	5.59347	+	3.22939i	0.229696	+	0.132615i	0.610432	−	0.792069i	$-0.290996\pi$
$593$	5.59347	+	3.22939i	0.229696	+	0.132615i	−0.380736	+	0.924684i	$0.624329\pi$
$594$	−2.42015	−	4.19183i	−0.0993000	−	0.171993i
$595$	−45.6915	+	13.3944i	−1.87317	+	0.549118i
$596$	−6.73965	−	3.89114i	−0.276067	−	0.159387i
$597$	7.97985	−	13.8215i	0.326594	−	0.565677i
$598$	−22.4211	+	1.78611i	−0.916867	+	0.0730395i
$599$	−1.33645	−	2.31480i	−0.0546058	−	0.0945800i	0.837430	−	0.546544i	$-0.184057\pi$
$599$	−1.33645	−	2.31480i	−0.0546058	−	0.0945800i	−0.892036	+	0.451964i	$0.850724\pi$
$600$	−5.21347	+	3.01000i	−0.212839	+	0.122883i
$601$	−11.2155	+	19.4258i	−0.457489	+	0.792394i	−0.998828	−	0.0484108i	$-0.984584\pi$
$601$	−11.2155	+	19.4258i	−0.457489	+	0.792394i	0.541339	+	0.840805i	$0.317918\pi$
$602$	−10.9822	−	10.4807i	−0.447600	−	0.427161i
$603$			8.80414i			0.358532i
$604$		−	14.1556i		−	0.575984i
$605$	35.7307	+	20.6291i	1.45266	+	0.838693i
$606$	13.8311	−	7.98541i	0.561851	−	0.324385i
$607$	−8.93203			−0.362540			−0.181270	−	0.983433i	$-0.558021\pi$
$607$	−8.93203			−0.362540			−0.181270	+	0.983433i	$0.558021\pi$
$608$	−3.48672	+	6.03917i	−0.141405	+	0.244921i
$609$	1.67786	−	1.75814i	0.0679902	−	0.0712433i
$610$	−12.1039			−0.490073
$611$	−8.27529	+	0.659226i	−0.334783	+	0.0266694i
$612$	2.71061	+	4.69492i	0.109570	+	0.189781i
$613$			8.22103i			0.332044i	0.986122	+	0.166022i	$0.0530923\pi$
$613$			8.22103i			0.332044i	−0.986122	+	0.166022i	$0.946908\pi$
$614$	11.9430	+	20.6859i	0.481981	+	0.834815i
$615$	13.2438	+	22.9389i	0.534041	+	0.924986i
$616$	12.4439	+	3.02466i	0.501380	+	0.121867i
$617$	−12.8168	+	7.39980i	−0.515986	+	0.297905i	−0.735291	−	0.677752i	$-0.762955\pi$
$617$	−12.8168	+	7.39980i	−0.515986	+	0.297905i	0.219305	+	0.975656i	$0.429621\pi$
$618$			2.62482i			0.105586i
$619$	25.6395	−	14.8030i	1.03054	−	0.594981i	0.113399	−	0.993550i	$-0.463826\pi$
$619$	25.6395	−	14.8030i	1.03054	−	0.594981i	0.917139	+	0.398568i	$0.130493\pi$
$620$	8.15250	−	14.1205i	0.327412	−	0.567095i
$621$	3.11910	+	5.40244i	0.125165	+	0.216792i
$622$	24.5227	+	14.1582i	0.983270	+	0.567691i
$623$	−15.7999	+	4.63174i	−0.633012	+	0.185567i
$624$	−3.25580	−	1.54912i	−0.130336	−	0.0620146i
$625$	9.42983	−	16.3329i	0.377193	−	0.653318i
$626$		−	31.5065i		−	1.25925i
$627$	−33.7535			−1.34799
$628$	1.29712			0.0517606
$629$			42.3770i			1.68968i
$630$	−8.53445	−	2.07441i	−0.340021	−	0.0826463i
$631$	−5.80637	+	3.35231i	−0.231148	+	0.133453i	−0.611101	−	0.791552i	$-0.709273\pi$
$631$	−5.80637	+	3.35231i	−0.231148	+	0.133453i	0.379954	+	0.925006i	$0.375940\pi$
$632$	−2.41222	−	1.39270i	−0.0959531	−	0.0553985i
$633$	−7.94467	+	13.7606i	−0.315772	+	0.546934i
$634$	−2.38231			−0.0946137
$635$	30.7647	−	17.7620i	1.22086	−	0.704863i
$636$	5.09014			0.201837
$637$	25.0381	−	3.17707i	0.992045	−	0.125880i
$638$	4.44610			0.176023
$639$	−6.84209	+	3.95028i	−0.270669	+	0.156271i
$640$	−3.31964			−0.131220
$641$	23.5692	−	40.8230i	0.930927	−	1.61241i	0.149185	−	0.988809i	$-0.452335\pi$
$641$	23.5692	−	40.8230i	0.930927	−	1.61241i	0.781741	−	0.623603i	$-0.214332\pi$
$642$	6.04644	+	3.49091i	0.238634	+	0.137775i
$643$	22.7365	−	13.1269i	0.896641	−	0.517676i	0.0205324	−	0.999789i	$-0.493464\pi$
$643$	22.7365	−	13.1269i	0.896641	−	0.517676i	0.876109	+	0.482113i	$0.160131\pi$
$644$	−16.0378	−	3.89818i	−0.631976	−	0.153610i
$645$			19.0473i			0.749985i
$646$	37.8046			1.48740
$647$	−38.1427			−1.49954			−0.749772	−	0.661697i	$-0.769837\pi$
$647$	−38.1427			−1.49954			−0.749772	+	0.661697i	$0.769837\pi$
$648$			1.00000i			0.0392837i
$649$	20.4100	−	35.3511i	0.801161	−	1.38765i
$650$	−21.6368	+	1.72363i	−0.848667	+	0.0676065i
$651$	12.4703	−	3.65566i	0.488750	−	0.143277i
$652$	18.7290	+	10.8132i	0.733482	+	0.423476i
$653$	−7.21077	−	12.4894i	−0.282179	−	0.488749i	0.689742	−	0.724055i	$-0.257724\pi$
$653$	−7.21077	−	12.4894i	−0.282179	−	0.488749i	−0.971921	+	0.235307i	$0.924391\pi$
$654$	4.14140	−	7.17312i	0.161942	−	0.280491i
$655$	−48.2815	+	27.8754i	−1.88652	+	1.08918i
$656$			7.97905i			0.311530i
$657$	−1.61061	+	0.929885i	−0.0628358	+	0.0362783i
$658$	−5.91930	−	1.43876i	−0.230758	−	0.0560887i
$659$	2.67525	+	4.63366i	0.104213	+	0.180502i	0.913416	−	0.407027i	$-0.133434\pi$
$659$	2.67525	+	4.63366i	0.104213	+	0.180502i	−0.809204	+	0.587528i	$0.800101\pi$
$660$	−8.03403	−	13.9153i	−0.312724	−	0.541654i
$661$			45.5254i			1.77073i	0.464894	+	0.885366i	$0.346092\pi$
$661$			45.5254i			1.77073i	−0.464894	+	0.885366i	$0.653908\pi$
$662$	−15.1691	−	26.2737i	−0.589564	−	1.02115i
$663$	1.55220	+	19.4848i	0.0602823	+	0.756727i
$664$	−5.97886			−0.232025
$665$	−42.2849	+	44.3081i	−1.63974	+	1.71819i
$666$	−3.90843	+	6.76960i	−0.151449	+	0.262317i
$667$	−5.73015			−0.221872
$668$	11.2333	−	6.48557i	0.434631	−	0.250934i
$669$	21.3888	+	12.3488i	0.826940	+	0.477434i
$670$			29.2265i			1.12912i
$671$		−	17.6485i		−	0.681312i
$672$	−1.91402	−	1.82662i	−0.0738348	−	0.0704634i
$673$	−21.3333	+	36.9503i	−0.822337	+	1.42433i	0.0815998	+	0.996665i	$0.473997\pi$
$673$	−21.3333	+	36.9503i	−0.822337	+	1.42433i	−0.903937	+	0.427665i	$0.859336\pi$
$674$	−14.4068	+	8.31775i	−0.554928	+	0.320388i
$675$	3.01000	+	5.21347i	0.115855	+	0.200666i
$676$	−8.20043	−	10.0873i	−0.315401	−	0.387972i
$677$	16.4015	−	28.4082i	0.630361	−	1.09182i	−0.357117	−	0.934060i	$-0.616240\pi$
$677$	16.4015	−	28.4082i	0.630361	−	1.09182i	0.987478	−	0.157758i	$-0.0504264\pi$
$678$	−4.82688	−	2.78680i	−0.185375	−	0.107026i
$679$	1.36776	−	0.400957i	0.0524897	−	0.0153873i
$680$	8.99826	+	15.5854i	0.345067	+	0.597674i
$681$	13.8269	+	7.98297i	0.529848	+	0.305908i
$682$	20.5889	+	11.8870i	0.788390	+	0.455177i
$683$	13.9992	+	8.08243i	0.535664	+	0.309266i	0.743320	−	0.668936i	$-0.233250\pi$
$683$	13.9992	+	8.08243i	0.535664	+	0.309266i	−0.207656	+	0.978202i	$0.566583\pi$
$684$	6.03917	+	3.48672i	0.230913	+	0.133318i
$685$	−26.7358	−	46.3078i	−1.02152	−	1.76933i
$686$	18.1809	+	3.52896i	0.694151	+	0.134736i
$687$	5.05038	+	2.91584i	0.192684	+	0.111246i
$688$	−2.86888	+	4.96904i	−0.109375	+	0.189443i
$689$	16.5725	+	7.88526i	0.631361	+	0.300404i
$690$	10.3543	+	17.9341i	0.394180	+	0.682741i
$691$	−19.2327	+	11.1040i	−0.731648	+	0.422417i	−0.819025	−	0.573758i	$-0.805485\pi$
$691$	−19.2327	+	11.1040i	−0.731648	+	0.422417i	0.0873769	+	0.996175i	$0.472152\pi$
$692$	6.72607	−	11.6499i	0.255687	−	0.442863i
$693$	3.02466	−	12.4439i	0.114897	−	0.472706i
$694$			6.00937i			0.228113i
$695$		−	33.4689i		−	1.26955i
$696$	−0.795495	−	0.459279i	−0.0301532	−	0.0174089i
$697$	37.4610	−	21.6281i	1.41894	−	0.819224i
$698$	10.0075			0.378789
$699$	−5.79484	+	10.0370i	−0.219181	+	0.379632i
$700$	−15.4768	−	3.76183i	−0.584967	−	0.142184i
$701$	−0.442053			−0.0166961			−0.00834805	−	0.999965i	$-0.502657\pi$
$701$	−0.442053			−0.0166961			−0.00834805	+	0.999965i	$0.502657\pi$
$702$	−1.54912	+	3.25580i	−0.0584679	+	0.122882i
$703$	27.2552	+	47.2073i	1.02795	+	1.78046i
$704$		−	4.84030i		−	0.182426i
$705$	3.82161	+	6.61922i	0.143930	+	0.249294i
$706$	10.9401	+	18.9488i	0.411736	+	0.713149i
$707$	41.0593	+	9.97999i	1.54419	+	0.375336i
$708$	−7.30349	+	4.21667i	−0.274482	+	0.158472i
$709$			23.7944i			0.893617i	0.894630	+	0.446809i	$0.147439\pi$
$709$			23.7944i			0.893617i	−0.894630	+	0.446809i	$0.852561\pi$
$710$	−22.7133	+	13.1135i	−0.852413	+	0.492141i
$711$	−1.39270	+	2.41222i	−0.0522302	+	0.0904654i
$712$	3.11156	+	5.38939i	0.116611	+	0.201976i
$713$	−26.5350	−	15.3200i	−0.993745	−	0.573739i
$714$	−3.38767	+	13.9374i	−0.126780	+	0.521595i
$715$	−4.60058	−	57.7512i	−0.172052	−	2.15977i
$716$	2.36998	−	4.10493i	0.0885705	−	0.153409i
$717$		−	21.8120i		−	0.814584i
$718$	4.58881			0.171253
$719$	−29.3096			−1.09306			−0.546532	−	0.837438i	$-0.684052\pi$
$719$	−29.3096			−1.09306			−0.546532	+	0.837438i	$0.684052\pi$
$720$			3.31964i			0.123716i
$721$	−4.79455	+	5.02396i	−0.178558	+	0.187102i
$722$	25.6593	−	14.8144i	0.954939	−	0.551334i
$723$	−17.5918	−	10.1566i	−0.654246	−	0.377729i
$724$	−8.39210	+	14.5355i	−0.311890	+	0.540209i
$725$	−5.52971			−0.205368
$726$	10.7634	−	6.21427i	0.399468	−	0.230633i
$727$	41.1850			1.52747			0.763734	−	0.645531i	$-0.223364\pi$
$727$	41.1850			1.52747			0.763734	+	0.645531i	$0.223364\pi$
$728$	−3.40200	−	8.91215i	−0.126086	−	0.330306i
$729$	1.00000			0.0370370
$730$	−5.34663	+	3.08688i	−0.197888	+	0.114251i
$731$	31.1057			1.15049
$732$	−1.82308	+	3.15766i	−0.0673828	+	0.116710i
$733$	−0.0649817	−	0.0375172i	−0.00240015	−	0.00138573i	0.498799	−	0.866717i	$-0.333774\pi$
$733$	−0.0649817	−	0.0375172i	−0.00240015	−	0.00138573i	−0.501200	+	0.865332i	$0.667108\pi$
$734$	−32.3945	+	18.7030i	−1.19570	+	0.690340i
$735$	−12.5459	−	19.5596i	−0.462764	−	0.721468i
$736$			6.23820i			0.229943i
$737$	−42.6147			−1.56973
$738$	7.97905			0.293713
$739$		−	22.3495i		−	0.822140i	−0.911604	−	0.411070i	$-0.865155\pi$
$739$		−	22.3495i		−	0.822140i	0.911604	−	0.411070i	$-0.134845\pi$
$740$	−12.9746	+	22.4726i	−0.476955	+	0.826110i
$741$	14.2610	+	20.7075i	0.523889	+	0.760708i
$742$	9.74262	+	9.29775i	0.357663	+	0.341331i
$743$	28.6927	+	16.5658i	1.05263	+	0.607738i	0.923386	−	0.383874i	$-0.125410\pi$
$743$	28.6927	+	16.5658i	1.05263	+	0.607738i	0.129248	+	0.991612i	$0.458744\pi$
$744$	−2.45584	−	4.25364i	−0.0900355	−	0.155946i
$745$	−12.9172	+	22.3732i	−0.473248	+	0.819690i
$746$	−13.6931	+	7.90570i	−0.501339	+	0.289448i
$747$			5.97886i			0.218755i
$748$	−22.7249	+	13.1202i	−0.830903	+	0.479722i
$749$	5.19643	+	17.7262i	0.189873	+	0.647702i
$750$	1.69300	+	2.93237i	0.0618197	+	0.107075i
$751$	−4.84349	−	8.38916i	−0.176741	−	0.306125i	0.764021	−	0.645191i	$-0.223222\pi$
$751$	−4.84349	−	8.38916i	−0.176741	−	0.306125i	−0.940763	+	0.339066i	$0.889889\pi$
$752$			2.30242i			0.0839608i
$753$	9.39667	+	16.2755i	0.342434	+	0.593112i
$754$	−1.87849	−	2.72764i	−0.0684106	−	0.0993348i
$755$	−46.9916			−1.71020
$756$	−1.82662	+	1.91402i	−0.0664335	+	0.0696121i
$757$	19.4924	−	33.7618i	0.708462	−	1.22709i	−0.256966	−	0.966421i	$-0.582723\pi$
$757$	19.4924	−	33.7618i	0.708462	−	1.22709i	0.965428	−	0.260672i	$-0.0839440\pi$
$758$	5.12712			0.186225
$759$	−26.1494	+	15.0974i	−0.949164	+	0.548000i
$760$	20.0479	+	11.5746i	0.727212	+	0.419856i
$761$			43.6360i			1.58180i	0.611943	+	0.790902i	$0.290388\pi$
$761$			43.6360i			1.58180i	−0.611943	+	0.790902i	$0.709612\pi$
$762$		−	10.7012i		−	0.387662i
$763$	21.0293	−	6.16471i	0.761311	−	0.223178i
$764$	6.99350	−	12.1131i	0.253016	−	0.438237i
$765$	15.5854	−	8.99826i	0.563493	−	0.325333i
$766$	10.1141	+	17.5182i	0.365438	+	0.632957i
$767$	−30.3108	+	2.41462i	−1.09446	+	0.0871869i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−0.826746	−	0.477322i	−0.0298132	−	0.0172127i	0.485019	−	0.874503i	$-0.338813\pi$
$769$	−0.826746	−	0.477322i	−0.0298132	−	0.0172127i	−0.514833	+	0.857291i	$0.672146\pi$
$770$	10.0408	−	41.3093i	0.361844	−	1.48868i
$771$	−9.50923	−	16.4705i	−0.342467	−	0.593170i
$772$	−10.0487	−	5.80159i	−0.361659	−	0.208804i
$773$	19.2103	+	11.0911i	0.690948	+	0.398919i	0.803967	−	0.594674i	$-0.202719\pi$
$773$	19.2103	+	11.0911i	0.690948	+	0.398919i	−0.113019	+	0.993593i	$0.536052\pi$
$774$	4.96904	+	2.86888i	0.178608	+	0.103120i
$775$	−25.6069	−	14.7841i	−0.919827	−	0.531062i
$776$	−0.269360	−	0.466544i	−0.00966945	−	0.0167480i
$777$	−19.8463	+	5.81792i	−0.711981	+	0.208717i
$778$	5.35019	+	3.08894i	0.191814	+	0.110744i
$779$	27.8207	−	48.1869i	0.996780	−	1.72647i
$780$	−5.14253	+	10.8081i	−0.184132	+	0.386991i
$781$	−19.1206	−	33.1178i	−0.684188	−	1.18505i
$782$	29.2878	−	16.9093i	1.04733	−	0.604677i
$783$	−0.459279	+	0.795495i	−0.0164133	+	0.0284287i
$784$	−0.326927	−	6.99236i	−0.0116760	−	0.249727i
$785$		−	4.30596i		−	0.153686i
$786$			16.7942i			0.599030i
$787$	8.12934	+	4.69348i	0.289780	+	0.167304i	0.637843	−	0.770167i	$-0.279827\pi$
$787$	8.12934	+	4.69348i	0.289780	+	0.167304i	−0.348063	+	0.937471i	$0.613160\pi$
$788$	−16.7733	+	9.68409i	−0.597525	+	0.344981i
$789$	−20.3146			−0.723220
$790$	−4.62325	+	8.00771i	−0.164488	+	0.284901i
$791$	−4.14831	−	14.1509i	−0.147497	−	0.503147i
$792$	−4.84030			−0.171993
$793$	−10.8272	+	7.45653i	−0.384484	+	0.264789i
$794$	−16.8840	−	29.2439i	−0.599191	−	1.03783i
$795$		−	16.8974i		−	0.599290i
$796$	−7.97985	−	13.8215i	−0.282838	−	0.489890i
$797$	4.13426	+	7.16075i	0.146443	+	0.253647i	0.929910	−	0.367786i	$-0.119884\pi$
$797$	4.13426	+	7.16075i	0.146443	+	0.253647i	−0.783467	+	0.621433i	$0.786551\pi$
$798$	5.19018	+	17.7049i	0.183730	+	0.626747i
$799$	10.8097	−	6.24099i	0.382420	−	0.220790i
$800$			6.01999i			0.212839i
$801$	5.38939	−	3.11156i	0.190425	−	0.109942i
$802$	−11.9841	+	20.7571i	−0.423175	+	0.732960i
$803$	−4.50092	−	7.79583i	−0.158834	−	0.275109i
$804$	7.62461	+	4.40207i	0.268899	+	0.155249i
$805$	−12.9406	+	53.2396i	−0.456095	+	1.87645i
$806$	−1.40630	−	17.6534i	−0.0495350	−	0.621814i
$807$	6.16010	−	10.6696i	0.216846	−	0.375588i
$808$		−	15.9708i		−	0.561851i
$809$	52.4633			1.84451			0.922256	−	0.386579i	$-0.126343\pi$
$809$	52.4633			1.84451			0.922256	+	0.386579i	$0.126343\pi$
$810$	3.31964			0.116640
$811$		−	11.2172i		−	0.393890i	−0.980415	−	0.196945i	$-0.936898\pi$
$811$		−	11.2172i		−	0.393890i	0.980415	−	0.196945i	$-0.0631020\pi$
$812$	−0.683663	−	2.33213i	−0.0239919	−	0.0818419i
$813$	10.2332	−	5.90816i	0.358895	−	0.207208i
$814$	−32.7669	−	18.9180i	−1.14848	−	0.663075i
$815$	35.8958	−	62.1733i	1.25737	−	2.17784i
$816$	5.42123			0.189781
$817$	34.6513	−	20.0059i	1.21229	−	0.699919i
$818$	1.38201			0.0483209
$819$	−8.91215	+	3.40200i	−0.311416	+	0.118875i
$820$	26.4876			0.924986
$821$	−37.9947	+	21.9362i	−1.32602	+	0.765580i	−0.984682	−	0.174359i	$-0.944215\pi$
$821$	−37.9947	+	21.9362i	−1.32602	+	0.765580i	−0.341342	+	0.939939i	$0.610881\pi$
$822$	−16.1077			−0.561820
$823$	14.4230	−	24.9814i	0.502755	−	0.870797i	−0.497240	−	0.867613i	$-0.665653\pi$
$823$	14.4230	−	24.9814i	0.502755	−	0.870797i	0.999995	−	0.00318403i	$-0.00101351\pi$
$824$	2.27316	+	1.31241i	0.0791894	+	0.0457200i
$825$	−25.2348	+	14.5693i	−0.878562	+	0.507238i
$826$	−21.6813	−	5.26991i	−0.754387	−	0.183363i
$827$		−	14.3678i		−	0.499618i	−0.968295	−	0.249809i	$-0.919632\pi$
$827$		−	14.3678i		−	0.499618i	0.968295	−	0.249809i	$-0.0803678\pi$
$828$	6.23820			0.216792
$829$	3.27974			0.113910			0.0569550	−	0.998377i	$-0.481861\pi$
$829$	3.27974			0.113910			0.0569550	+	0.998377i	$0.481861\pi$
$830$			19.8476i			0.688922i
$831$	−16.1656	+	27.9997i	−0.560780	+	0.971299i
$832$	−2.96948	+	2.04504i	−0.102948	+	0.0708991i
$833$	−31.9424	+	20.4885i	−1.10674	+	0.709884i
$834$	−8.73136	−	5.04105i	−0.302342	−	0.174557i
$835$	−21.5297	−	37.2906i	−0.745067	−	1.29049i
$836$	−16.8768	+	29.2314i	−0.583695	+	1.01099i
$837$	−4.25364	+	2.45584i	−0.147027	+	0.0848863i
$838$		−	20.4118i		−	0.705113i
$839$	24.9564	−	14.4086i	0.861590	−	0.497439i	−0.00295444	−	0.999996i	$-0.500940\pi$
$839$	24.9564	−	14.4086i	0.861590	−	0.497439i	0.864544	+	0.502556i	$0.167607\pi$
$840$	−6.06371	+	6.35384i	−0.209218	+	0.219228i
$841$	14.0781	+	24.3840i	0.485453	+	0.840829i
$842$	−4.26761	−	7.39171i	−0.147072	−	0.254735i
$843$			0.624762i			0.0215179i
$844$	7.94467	+	13.7606i	0.273467	+	0.473659i
$845$	−33.4861	+	27.2225i	−1.15196	+	0.936481i
$846$	2.30242			0.0791590
$847$	31.9525	+	7.76646i	1.09790	+	0.266859i
$848$	2.54507	−	4.40819i	0.0873981	−	0.151378i
$849$	−12.5738			−0.431530
$850$	28.2634	−	16.3179i	0.969427	−	0.559699i
$851$	42.2301	+	24.3815i	1.44763	+	0.835789i
$852$			7.90056i			0.270669i
$853$		−	12.2038i		−	0.417851i	−0.977932	−	0.208926i	$-0.933003\pi$
$853$		−	12.2038i		−	0.417851i	0.977932	−	0.208926i	$-0.0669966\pi$
$854$	−9.25724	+	2.71375i	−0.316776	+	0.0928627i
$855$	11.5746	−	20.0479i	0.395844	−	0.685622i
$856$	6.04644	−	3.49091i	0.206663	−	0.119317i
$857$	7.44836	+	12.9009i	0.254431	+	0.440688i	0.964741	−	0.263202i	$-0.0847784\pi$
$857$	7.44836	+	12.9009i	0.254431	+	0.440688i	−0.710310	+	0.703889i	$0.751445\pi$
$858$	−15.7590	−	7.49823i	−0.538005	−	0.255985i
$859$	−24.2792	+	42.0527i	−0.828394	+	1.43482i	0.0709036	+	0.997483i	$0.477412\pi$
$859$	−24.2792	+	42.0527i	−0.828394	+	1.43482i	−0.899298	+	0.437337i	$0.855922\pi$
$860$	16.4954	+	9.52363i	0.562489	+	0.324753i
$861$	15.2720	+	14.5747i	0.520470	+	0.496704i
$862$	−14.6460	−	25.3676i	−0.498845	−	0.864025i
$863$	8.26166	+	4.76987i	0.281230	+	0.162368i	0.633980	−	0.773349i	$-0.281420\pi$
$863$	8.26166	+	4.76987i	0.281230	+	0.162368i	−0.352750	+	0.935718i	$0.614753\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−38.6734	−	22.3281i	−1.31494	−	0.759179i
$866$	13.7344	+	7.92957i	0.466714	+	0.269458i
$867$	−6.19487	−	10.7298i	−0.210389	−	0.364404i
$868$	3.06926	−	12.6274i	0.104177	−	0.428603i
$869$	−11.6759	−	6.74108i	−0.396078	−	0.228675i
$870$	−1.52464	+	2.64075i	−0.0516902	+	0.0895300i
$871$	18.0048	+	26.1437i	0.610070	+	0.885846i
$872$	−4.14140	−	7.17312i	−0.140246	−	0.242912i
$873$	−0.466544	+	0.269360i	−0.0157901	+	0.00911644i
$874$	21.7508	−	37.6735i	0.735733	−	1.27433i
$875$	−2.11588	+	8.70507i	−0.0715298	+	0.294285i
$876$			1.85977i			0.0628358i
$877$		−	42.6590i		−	1.44049i	−0.693719	−	0.720246i	$-0.744029\pi$
$877$		−	42.6590i		−	1.44049i	0.693719	−	0.720246i	$-0.255971\pi$
$878$	9.64257	+	5.56714i	0.325421	+	0.187882i
$879$	17.5615	−	10.1391i	0.592334	−	0.341984i
$880$	−16.0681			−0.541654
$881$	−8.12329	+	14.0700i	−0.273681	+	0.474029i	−0.969801	−	0.243896i	$-0.921574\pi$
$881$	−8.12329	+	14.0700i	−0.273681	+	0.474029i	0.696121	+	0.717925i	$0.254908\pi$
$882$	−6.99236	+	0.326927i	−0.235445	+	0.0110082i
$883$	−4.99907			−0.168232			−0.0841160	−	0.996456i	$-0.526807\pi$
$883$	−4.99907			−0.168232			−0.0841160	+	0.996456i	$0.526807\pi$
$884$	17.6504	+	8.39815i	0.593648	+	0.282461i
$885$	13.9978	+	24.2449i	0.470531	+	0.814984i
$886$		−	3.74634i		−	0.125861i
$887$	27.0751	+	46.8955i	0.909093	+	1.57460i	0.815327	+	0.579001i	$0.196557\pi$
$887$	27.0751	+	46.8955i	0.909093	+	1.57460i	0.0937662	+	0.995594i	$0.470109\pi$
$888$	3.90843	+	6.76960i	0.131158	+	0.227173i
$889$	19.5469	−	20.4822i	0.655584	−	0.686951i
$890$	17.8908	−	10.3293i	0.599701	−	0.346238i
$891$			4.84030i			0.162156i
$892$	21.3888	−	12.3488i	0.716151	−	0.413470i
$893$	8.02790	−	13.9047i	0.268644	−	0.465304i
$894$	3.89114	+	6.73965i	0.130139	+	0.225408i
$895$	−13.6269	−	7.86749i	−0.455497	−	0.262981i
$896$	−2.53891	+	0.744278i	−0.0848189	+	0.0248646i
$897$	20.3103	+	9.66374i	0.678141	+	0.322663i
$898$	−6.05280	+	10.4838i	−0.201984	+	0.349847i
$899$		−	4.51167i		−	0.150472i
$900$	6.01999			0.200666
$901$	−27.5948			−0.919317
$902$			38.6210i			1.28594i
$903$	4.27049	+	14.5676i	0.142113	+	0.484780i
$904$	−4.82688	+	2.78680i	−0.160540	+	0.0926877i
$905$	48.2528	+	27.8587i	1.60398	+	0.926056i
$906$	−7.07781	+	12.2591i	−0.235145	+	0.407282i
$907$	−9.34221			−0.310203			−0.155102	−	0.987899i	$-0.549570\pi$
$907$	−9.34221			−0.310203			−0.155102	+	0.987899i	$0.549570\pi$
$908$	13.8269	−	7.98297i	0.458862	−	0.264924i
$909$	−15.9708			−0.529718
$910$	−29.5851	+	11.2934i	−0.980737	+	0.374372i
$911$	28.5910			0.947262			0.473631	−	0.880723i	$-0.342943\pi$
$911$	28.5910			0.947262			0.473631	+	0.880723i	$0.342943\pi$
$912$	6.03917	−	3.48672i	0.199977	−	0.115457i
$913$	−28.9395			−0.957757
$914$	−18.3418	+	31.7689i	−0.606693	+	1.05082i
$915$	10.4823	+	6.05195i	0.346534	+	0.200071i
$916$	5.05038	−	2.91584i	0.166869	−	0.0963420i
$917$	−30.6766	+	32.1444i	−1.01303	+	1.06150i
$918$		−	5.42123i		−	0.178927i
$919$	−25.0128			−0.825096			−0.412548	−	0.910936i	$-0.635361\pi$
$919$	−25.0128			−0.825096			−0.412548	+	0.910936i	$0.635361\pi$
$920$	20.7085			0.682741
$921$		−	23.8860i		−	0.787071i
$922$	1.07732	−	1.86597i	0.0354797	−	0.0614526i
$923$	−12.2389	+	25.7226i	−0.402850	+	0.846671i
$924$	−9.26443	−	8.84139i	−0.304777	−	0.290860i
$925$	40.7529	+	23.5287i	1.33995	+	0.773619i
$926$	19.0226	+	32.9482i	0.625123	+	1.08274i
$927$	1.31241	−	2.27316i	0.0431052	−	0.0746605i
$928$	−0.795495	+	0.459279i	−0.0261134	+	0.0150766i
$929$		−	11.1158i		−	0.364697i	−0.983234	−	0.182349i	$-0.941630\pi$
$929$		−	11.1158i		−	0.364697i	0.983234	−	0.182349i	$-0.0583700\pi$
$930$	−14.1205	+	8.15250i	−0.463031	+	0.267331i
$931$	−22.4060	+	43.3680i	−0.734328	+	1.42133i
$932$	5.79484	+	10.0370i	0.189816	+	0.328771i
$933$	−14.1582	−	24.5227i	−0.463518	−	0.802837i
$934$		−	5.56125i		−	0.181970i
$935$	43.5543	+	75.4383i	1.42438	+	2.46710i
$936$	2.04504	+	2.96948i	0.0668443	+	0.0970605i
$937$	33.2870			1.08744			0.543719	−	0.839267i	$-0.317016\pi$
$937$	33.2870			1.08744			0.543719	+	0.839267i	$0.317016\pi$
$938$	6.55273	+	22.3529i	0.213954	+	0.729848i
$939$	−15.7533	+	27.2855i	−0.514088	+	0.890427i
$940$	7.64322			0.249294
$941$	−39.3672	+	22.7287i	−1.28333	+	0.740934i	−0.977457	−	0.211137i	$-0.932283\pi$
$941$	−39.3672	+	22.7287i	−1.28333	+	0.740934i	−0.305878	+	0.952071i	$0.598950\pi$
$942$	−1.12334	−	0.648559i	−0.0366003	−	0.0211312i
$943$		−	49.7749i		−	1.62089i
$944$			8.43334i			0.274482i
$945$	6.35384	+	6.06371i	0.206691	+	0.197253i
$946$	−13.8862	+	24.0517i	−0.451480	+	0.781987i
$947$	−28.0937	+	16.2199i	−0.912924	+	0.527077i	−0.881371	−	0.472425i	$-0.843379\pi$
$947$	−28.0937	+	16.2199i	−0.912924	+	0.527077i	−0.0315530	+	0.999502i	$0.510045\pi$
$948$	1.39270	+	2.41222i	0.0452327	+	0.0783454i
$949$	−2.88101	+	6.05503i	−0.0935216	+	0.196555i
$950$	20.9900	−	36.3558i	0.681006	−	1.17954i
$951$	2.06314	+	1.19116i	0.0669020	+	0.0386259i
$952$	10.3763	+	9.90252i	0.336299	+	0.320943i
$953$	11.1179	+	19.2568i	0.360144	+	0.623788i	0.987984	−	0.154554i	$-0.0493941\pi$
$953$	11.1179	+	19.2568i	0.360144	+	0.623788i	−0.627840	+	0.778342i	$0.716061\pi$
$954$	−4.40819	−	2.54507i	−0.142720	−	0.0823997i
$955$	−40.2111	−	23.2159i	−1.30120	−	0.751248i
$956$	−18.8897	−	10.9060i	−0.610938	−	0.352725i
$957$	−3.85044	−	2.22305i	−0.124467	−	0.0718610i
$958$	−17.7725	−	30.7829i	−0.574205	−	0.994552i
$959$	−30.8304	−	29.4226i	−0.995565	−	0.950105i
$960$	2.87489	+	1.65982i	0.0927867	+	0.0535704i
$961$	−3.43769	+	5.95426i	−0.110893	+	0.192073i
$962$	2.23811	+	28.0951i	0.0721596	+	0.905822i
$963$	−3.49091	−	6.04644i	−0.112493	−	0.194844i
$964$	−17.5918	+	10.1566i	−0.566593	+	0.327123i
$965$	−19.2592	+	33.3579i	−0.619975	+	1.07383i
$966$	11.9400	+	11.3948i	0.384164	+	0.366622i
$967$		−	48.5963i		−	1.56275i	−0.624061	−	0.781376i	$-0.714518\pi$
$967$		−	48.5963i		−	1.56275i	0.624061	−	0.781376i	$-0.285482\pi$
$968$		−	12.4285i		−	0.399468i
$969$	−32.7397	−	18.9023i	−1.05175	−	0.607229i
$970$	−1.54876	+	0.894176i	−0.0497276	+	0.0287103i
$971$	−26.3510			−0.845645			−0.422823	−	0.906212i	$-0.638961\pi$
$971$	−26.3510			−0.845645			−0.422823	+	0.906212i	$0.638961\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−7.50389	−	25.5975i	−0.240564	−	0.820619i
$974$	−22.1134			−0.708560
$975$	19.5999	+	9.32571i	0.627698	+	0.298662i
$976$	1.82308	+	3.15766i	0.0583552	+	0.101074i
$977$		−	35.0542i		−	1.12148i	−0.827991	−	0.560742i	$-0.810516\pi$
$977$		−	35.0542i		−	1.12148i	0.827991	−	0.560742i	$-0.189484\pi$
$978$	−10.8132	−	18.7290i	−0.345767	−	0.598886i
$979$	15.0609	+	26.0863i	0.481349	+	0.833721i
$980$	−23.2121	+	1.08528i	−0.741483	+	0.0346680i
$981$	−7.17312	+	4.14140i	−0.229020	+	0.132225i
$982$		−	1.38142i		−	0.0440829i
$983$	5.98021	−	3.45268i	0.190739	−	0.110123i	−0.401589	−	0.915820i	$-0.631542\pi$
$983$	5.98021	−	3.45268i	0.190739	−	0.110123i	0.592329	+	0.805697i	$0.298209\pi$
$984$	3.98953	−	6.91006i	0.127181	−	0.220285i
$985$	32.1477	+	55.6814i	1.02431	+	1.77416i
$986$	4.31256	+	2.48986i	0.137340	+	0.0792932i
$987$	4.40688	+	4.20565i	0.140273	+	0.133867i
$988$	25.0637	−	1.99662i	0.797382	−	0.0635210i
$989$	17.8966	−	30.9978i	0.569079	−	0.985674i
$990$			16.0681i			0.510676i
$991$	4.74673			0.150785			0.0753924	−	0.997154i	$-0.475979\pi$
$991$	4.74673			0.150785			0.0753924	+	0.997154i	$0.475979\pi$
$992$	−4.91168			−0.155946
$993$			30.3382i			0.962754i
$994$	−14.4313	+	15.1218i	−0.457734	+	0.479635i
$995$	−45.8824	+	26.4902i	−1.45457	+	0.839796i
$996$	5.17784	+	2.98943i	0.164066	+	0.0947237i
$997$	−19.8351	+	34.3554i	−0.628184	+	1.08805i	0.359732	+	0.933056i	$0.382868\pi$
$997$	−19.8351	+	34.3554i	−0.628184	+	1.08805i	−0.987916	+	0.154991i	$0.950465\pi$
$998$	−6.63732			−0.210101
$999$	6.76960	−	3.90843i	0.214181	−	0.123657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.121.1	✓	20
3.2	odd	2		1638.2.cr.b.667.10		20
7.4	even	3		546.2.bm.b.277.5	yes	20
13.10	even	6		546.2.bm.b.205.10	yes	20
21.11	odd	6		1638.2.dt.b.1369.6		20
39.23	odd	6		1638.2.dt.b.1297.1		20
91.88	even	6	inner	546.2.bd.b.361.1	yes	20
273.179	odd	6		1638.2.cr.b.361.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.1	✓	20	1.1	even	1	trivial
546.2.bd.b.361.1	yes	20	91.88	even	6	inner
546.2.bm.b.205.10	yes	20	13.10	even	6
546.2.bm.b.277.5	yes	20	7.4	even	3
1638.2.cr.b.361.10		20	273.179	odd	6
1638.2.cr.b.667.10		20	3.2	odd	2
1638.2.dt.b.1297.1		20	39.23	odd	6
1638.2.dt.b.1369.6		20	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.57090 - 0.624890i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.57090 - 0.624890i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.31964 q^{10} +4.84030i q^{11} +(0.500000 - 0.866025i) q^{12} +(2.96948 - 2.04504i) q^{13} +(2.53891 - 0.744278i) q^{14} +(-2.87489 - 1.65982i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.71061 + 4.69492i) q^{17} +(-0.866025 + 0.500000i) q^{18} +6.97343i q^{19} +(-2.87489 + 1.65982i) q^{20} +(-2.57090 - 0.624890i) q^{21} +(-2.42015 - 4.19183i) q^{22} +(3.11910 + 5.40244i) q^{23} +1.00000i q^{24} +(3.01000 + 5.21347i) q^{25} +(-1.54912 + 3.25580i) q^{26} +1.00000 q^{27} +(-1.82662 + 1.91402i) q^{28} +(-0.459279 + 0.795495i) q^{29} +3.31964 q^{30} +(-4.25364 + 2.45584i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.84030i q^{33} -5.42123i q^{34} +(6.35384 + 6.06371i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.76960 - 3.90843i) q^{37} +(-3.48672 - 6.03917i) q^{38} +(2.96948 - 2.04504i) q^{39} +(1.65982 - 2.87489i) q^{40} +(-6.91006 - 3.98953i) q^{41} +(2.53891 - 0.744278i) q^{42} +(-2.86888 - 4.96904i) q^{43} +(4.19183 + 2.42015i) q^{44} +(-2.87489 - 1.65982i) q^{45} +(-5.40244 - 3.11910i) q^{46} +(-1.99396 - 1.15121i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(6.21903 + 3.21305i) q^{49} +(-5.21347 - 3.01000i) q^{50} +(-2.71061 + 4.69492i) q^{51} +(-0.286318 - 3.59416i) q^{52} +(2.54507 + 4.40819i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(8.03403 - 13.9153i) q^{55} +(0.624890 - 2.57090i) q^{56} +6.97343i q^{57} -0.918558i q^{58} +(-7.30349 - 4.21667i) q^{59} +(-2.87489 + 1.65982i) q^{60} -3.64615 q^{61} +(2.45584 - 4.25364i) q^{62} +(-2.57090 - 0.624890i) q^{63} -1.00000 q^{64} +(-11.9313 + 0.950473i) q^{65} +(-2.42015 - 4.19183i) q^{66} +8.80414i q^{67} +(2.71061 + 4.69492i) q^{68} +(3.11910 + 5.40244i) q^{69} +(-8.53445 - 2.07441i) q^{70} +(-6.84209 + 3.95028i) q^{71} +1.00000i q^{72} +(-1.61061 + 0.929885i) q^{73} +(-3.90843 + 6.76960i) q^{74} +(3.01000 + 5.21347i) q^{75} +(6.03917 + 3.48672i) q^{76} +(3.02466 - 12.4439i) q^{77} +(-1.54912 + 3.25580i) q^{78} +(-1.39270 + 2.41222i) q^{79} +3.31964i q^{80} +1.00000 q^{81} +7.97905 q^{82} +5.97886i q^{83} +(-1.82662 + 1.91402i) q^{84} +(15.5854 - 8.99826i) q^{85} +(4.96904 + 2.86888i) q^{86} +(-0.459279 + 0.795495i) q^{87} -4.84030 q^{88} +(5.38939 - 3.11156i) q^{89} +3.31964 q^{90} +(-8.91215 + 3.40200i) q^{91} +6.23820 q^{92} +(-4.25364 + 2.45584i) q^{93} +2.30242 q^{94} +(11.5746 - 20.0479i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-0.466544 + 0.269360i) q^{97} +(-6.99236 + 0.326927i) q^{98} +4.84030i 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

Introduction

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