LMFDB - Embedded newform 546.2.bm.b.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (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			277.6
Root			$-2.55339i$ of defining polynomial
Character	$\chi$	$=$	546.277
Dual form			546.2.bm.b.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.21130 + 1.27669i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.74192 + 1.99141i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.21130 + 1.27669i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.74192 + 1.99141i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.27669 - 2.21130i) q^{10} +(-0.449678 + 0.259622i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.57238 - 3.24463i) q^{13} +(-1.99141 + 1.74192i) q^{14} +(2.21130 + 1.27669i) q^{15} +1.00000 q^{16} -0.868301 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.00705 - 2.31347i) q^{19} +(2.21130 - 1.27669i) q^{20} +(0.853651 - 2.50425i) q^{21} +(-0.259622 - 0.449678i) q^{22} -8.52091 q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.759893 - 1.31617i) q^{25} +(3.24463 - 1.57238i) q^{26} +1.00000 q^{27} +(-1.74192 - 1.99141i) q^{28} +(-1.98376 + 3.43598i) q^{29} +(-1.27669 + 2.21130i) q^{30} +(-3.49539 - 2.01806i) q^{31} +1.00000i q^{32} +(0.449678 + 0.259622i) q^{33} -0.868301i q^{34} +(-6.39433 - 2.17970i) q^{35} +(0.500000 - 0.866025i) q^{36} -5.92304i q^{37} +(2.31347 - 4.00705i) q^{38} +(-2.02374 + 2.98403i) q^{39} +(1.27669 + 2.21130i) q^{40} +(-5.87598 - 3.39250i) q^{41} +(2.50425 + 0.853651i) q^{42} +(2.24805 + 3.89373i) q^{43} +(0.449678 - 0.259622i) q^{44} -2.55339i q^{45} -8.52091i q^{46} +(-2.81446 + 1.62493i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.931425 + 6.93776i) q^{49} +(1.31617 + 0.759893i) q^{50} +(0.434150 + 0.751971i) q^{51} +(1.57238 + 3.24463i) q^{52} +(-4.12845 + 7.15068i) q^{53} +1.00000i q^{54} +(0.662914 - 1.14820i) q^{55} +(1.99141 - 1.74192i) q^{56} +4.62695i q^{57} +(-3.43598 - 1.98376i) q^{58} +1.40079i q^{59} +(-2.21130 - 1.27669i) q^{60} +(3.01909 - 5.22921i) q^{61} +(2.01806 - 3.49539i) q^{62} +(-2.59557 + 0.512843i) q^{63} -1.00000 q^{64} +(7.61939 + 5.16740i) q^{65} +(-0.259622 + 0.449678i) q^{66} +(9.54619 - 5.51150i) q^{67} +0.868301 q^{68} +(4.26046 + 7.37933i) q^{69} +(2.17970 - 6.39433i) q^{70} +(4.47375 - 2.58292i) q^{71} +(0.866025 + 0.500000i) q^{72} +(10.3558 + 5.97895i) q^{73} +5.92304 q^{74} -1.51979 q^{75} +(4.00705 + 2.31347i) q^{76} +(-1.30032 - 0.443252i) q^{77} +(-2.98403 - 2.02374i) q^{78} +(5.47473 + 9.48251i) q^{79} +(-2.21130 + 1.27669i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.39250 - 5.87598i) q^{82} -12.9984i q^{83} +(-0.853651 + 2.50425i) q^{84} +(1.92007 - 1.10855i) q^{85} +(-3.89373 + 2.24805i) q^{86} +3.96752 q^{87} +(0.259622 + 0.449678i) q^{88} +8.02946i q^{89} +2.55339 q^{90} +(3.72243 - 8.78314i) q^{91} +8.52091 q^{92} +4.03613i q^{93} +(-1.62493 - 2.81446i) q^{94} +11.8144 q^{95} +(0.866025 - 0.500000i) q^{96} +(-13.0095 + 7.51106i) q^{97} +(-6.93776 - 0.931425i) q^{98} -0.519243i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	−2.21130	+	1.27669i	−0.988923	+	0.570955i	−0.904952	−	0.425513i	$-0.860093\pi$
$5$	−2.21130	+	1.27669i	−0.988923	+	0.570955i	−0.0839705	+	0.996468i	$0.526760\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.74192	+	1.99141i	0.658384	+	0.752682i
$7$	1.74192	+	1.99141i	0.658384	+	0.752682i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.27669	−	2.21130i	−0.403726	−	0.699274i
$11$	−0.449678	+	0.259622i	−0.135583	+	0.0782788i	−0.566257	−	0.824229i	$-0.691609\pi$
$11$	−0.449678	+	0.259622i	−0.135583	+	0.0782788i	0.430674	+	0.902507i	$0.358276\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.57238	−	3.24463i	−0.436099	−	0.899899i
$13$	−1.57238	−	3.24463i	−0.436099	−	0.899899i
$14$	−1.99141	+	1.74192i	−0.532227	+	0.465548i
$15$	2.21130	+	1.27669i	0.570955	+	0.329641i
$16$	1.00000			0.250000
$17$	−0.868301			−0.210594			−0.105297	−	0.994441i	$-0.533579\pi$
$17$	−0.868301			−0.210594			−0.105297	+	0.994441i	$0.533579\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−4.00705	−	2.31347i	−0.919281	−	0.530747i	−0.0358753	−	0.999356i	$-0.511422\pi$
$19$	−4.00705	−	2.31347i	−0.919281	−	0.530747i	−0.883406	+	0.468609i	$0.844755\pi$
$20$	2.21130	−	1.27669i	0.494461	−	0.285477i
$21$	0.853651	−	2.50425i	0.186282	−	0.546473i
$22$	−0.259622	−	0.449678i	−0.0553515	−	0.0958716i
$23$	−8.52091			−1.77673			−0.888367	−	0.459135i	$-0.848159\pi$
$23$	−8.52091			−1.77673			−0.888367	+	0.459135i	$0.848159\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.759893	−	1.31617i	0.151979	−	0.263235i
$26$	3.24463	−	1.57238i	0.636324	−	0.308369i
$27$	1.00000			0.192450
$28$	−1.74192	−	1.99141i	−0.329192	−	0.376341i
$29$	−1.98376	+	3.43598i	−0.368375	+	0.638045i	−0.989312	−	0.145816i	$-0.953419\pi$
$29$	−1.98376	+	3.43598i	−0.368375	+	0.638045i	0.620936	+	0.783861i	$0.286753\pi$
$30$	−1.27669	+	2.21130i	−0.233091	+	0.403726i
$31$	−3.49539	−	2.01806i	−0.627791	−	0.362455i	0.152105	−	0.988364i	$-0.451395\pi$
$31$	−3.49539	−	2.01806i	−0.627791	−	0.362455i	−0.779896	+	0.625909i	$0.784728\pi$
$32$			1.00000i			0.176777i
$33$	0.449678	+	0.259622i	0.0782788	+	0.0451943i
$34$		−	0.868301i		−	0.148912i
$35$	−6.39433	−	2.17970i	−1.08084	−	0.368437i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$		−	5.92304i		−	0.973741i	−0.873474	−	0.486871i	$-0.838138\pi$
$37$		−	5.92304i		−	0.973741i	0.873474	−	0.486871i	$-0.161862\pi$
$38$	2.31347	−	4.00705i	0.375295	−	0.650030i
$39$	−2.02374	+	2.98403i	−0.324058	+	0.477828i
$40$	1.27669	+	2.21130i	0.201863	+	0.349637i
$41$	−5.87598	−	3.39250i	−0.917674	−	0.529819i	−0.0347817	−	0.999395i	$-0.511074\pi$
$41$	−5.87598	−	3.39250i	−0.917674	−	0.529819i	−0.882892	+	0.469576i	$0.844407\pi$
$42$	2.50425	+	0.853651i	0.386415	+	0.131721i
$43$	2.24805	+	3.89373i	0.342824	+	0.593789i	0.984956	−	0.172805i	$-0.0552831\pi$
$43$	2.24805	+	3.89373i	0.342824	+	0.593789i	−0.642132	+	0.766594i	$0.721950\pi$
$44$	0.449678	−	0.259622i	0.0677915	−	0.0391394i
$45$		−	2.55339i		−	0.380636i
$46$		−	8.52091i		−	1.25634i
$47$	−2.81446	+	1.62493i	−0.410531	+	0.237020i	−0.691018	−	0.722838i	$-0.742837\pi$
$47$	−2.81446	+	1.62493i	−0.410531	+	0.237020i	0.280487	+	0.959858i	$0.409504\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.931425	+	6.93776i	−0.133061	+	0.991108i
$50$	1.31617	+	0.759893i	0.186135	+	0.107465i
$51$	0.434150	+	0.751971i	0.0607932	+	0.105297i
$52$	1.57238	+	3.24463i	0.218050	+	0.449949i
$53$	−4.12845	+	7.15068i	−0.567086	+	0.982222i	0.429766	+	0.902940i	$0.358596\pi$
$53$	−4.12845	+	7.15068i	−0.567086	+	0.982222i	−0.996852	+	0.0792817i	$0.974737\pi$
$54$			1.00000i			0.136083i
$55$	0.662914	−	1.14820i	0.0893873	−	0.154823i
$56$	1.99141	−	1.74192i	0.266113	−	0.232774i
$57$			4.62695i			0.612854i
$58$	−3.43598	−	1.98376i	−0.451166	−	0.260481i
$59$			1.40079i			0.182368i	0.995834	+	0.0911839i	$0.0290651\pi$
$59$			1.40079i			0.182368i	−0.995834	+	0.0911839i	$0.970935\pi$
$60$	−2.21130	−	1.27669i	−0.285477	−	0.164820i
$61$	3.01909	−	5.22921i	0.386554	−	0.669532i	−0.605429	−	0.795899i	$-0.706999\pi$
$61$	3.01909	−	5.22921i	0.386554	−	0.669532i	0.991983	+	0.126368i	$0.0403319\pi$
$62$	2.01806	−	3.49539i	0.256294	−	0.443915i
$63$	−2.59557	+	0.512843i	−0.327011	+	0.0646121i
$64$	−1.00000			−0.125000
$65$	7.61939	+	5.16740i	0.945070	+	0.640937i
$66$	−0.259622	+	0.449678i	−0.0319572	+	0.0553515i
$67$	9.54619	−	5.51150i	1.16625	−	0.673337i	0.213458	−	0.976952i	$-0.431527\pi$
$67$	9.54619	−	5.51150i	1.16625	−	0.673337i	0.952795	+	0.303616i	$0.0981939\pi$
$68$	0.868301			0.105297
$69$	4.26046	+	7.37933i	0.512899	+	0.888367i
$70$	2.17970	−	6.39433i	0.260524	−	0.764268i
$71$	4.47375	−	2.58292i	0.530937	−	0.306536i	−0.210461	−	0.977602i	$-0.567497\pi$
$71$	4.47375	−	2.58292i	0.530937	−	0.306536i	0.741398	+	0.671066i	$0.234163\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	10.3558	+	5.97895i	1.21206	+	0.699783i	0.963208	−	0.268759i	$-0.0866134\pi$
$73$	10.3558	+	5.97895i	1.21206	+	0.699783i	0.248852	+	0.968542i	$0.419947\pi$
$74$	5.92304			0.688539
$75$	−1.51979			−0.175490
$76$	4.00705	+	2.31347i	0.459640	+	0.265374i
$77$	−1.30032	−	0.443252i	−0.148185	−	0.0505133i
$78$	−2.98403	−	2.02374i	−0.337875	−	0.229144i
$79$	5.47473	+	9.48251i	0.615955	+	1.06687i	0.990216	+	0.139542i	$0.0445630\pi$
$79$	5.47473	+	9.48251i	0.615955	+	1.06687i	−0.374261	+	0.927323i	$0.622104\pi$
$80$	−2.21130	+	1.27669i	−0.247231	+	0.142739i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.39250	−	5.87598i	0.374639	−	0.648894i
$83$		−	12.9984i		−	1.42676i	−0.700778	−	0.713379i	$-0.747164\pi$
$83$		−	12.9984i		−	1.42676i	0.700778	−	0.713379i	$-0.252836\pi$
$84$	−0.853651	+	2.50425i	−0.0931410	+	0.273236i
$85$	1.92007	−	1.10855i	0.208261	−	0.120240i
$86$	−3.89373	+	2.24805i	−0.419872	+	0.242413i
$87$	3.96752			0.425363
$88$	0.259622	+	0.449678i	0.0276757	+	0.0479358i
$89$			8.02946i			0.851121i	0.904930	+	0.425560i	$0.139923\pi$
$89$			8.02946i			0.851121i	−0.904930	+	0.425560i	$0.860077\pi$
$90$	2.55339			0.269151
$91$	3.72243	−	8.78314i	0.390217	−	0.920723i
$92$	8.52091			0.888367
$93$			4.03613i			0.418527i
$94$	−1.62493	−	2.81446i	−0.167599	−	0.290290i
$95$	11.8144			1.21213
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−13.0095	+	7.51106i	−1.32092	+	0.762632i	−0.983875	−	0.178857i	$-0.942760\pi$
$97$	−13.0095	+	7.51106i	−1.32092	+	0.762632i	−0.337043	+	0.941489i	$0.609427\pi$
$98$	−6.93776	−	0.931425i	−0.700819	−	0.0940881i
$99$		−	0.519243i		−	0.0521859i
$100$	−0.759893	+	1.31617i	−0.0759893	+	0.131617i
$101$	4.25033	+	7.36178i	0.422923	+	0.732525i	0.996224	−	0.0868203i	$-0.0276706\pi$
$101$	4.25033	+	7.36178i	0.422923	+	0.732525i	−0.573301	+	0.819345i	$0.694337\pi$
$102$	−0.751971	+	0.434150i	−0.0744562	+	0.0429873i
$103$	−7.78135	−	13.4777i	−0.766719	−	1.32800i	−0.939333	−	0.343007i	$-0.888554\pi$
$103$	−7.78135	−	13.4777i	−0.766719	−	1.32800i	0.172613	−	0.984990i	$-0.444779\pi$
$104$	−3.24463	+	1.57238i	−0.318162	+	0.154184i
$105$	1.30949	+	6.62750i	0.127793	+	0.646778i
$106$	−7.15068	−	4.12845i	−0.694536	−	0.400990i
$107$	−2.74056			−0.264940			−0.132470	−	0.991187i	$-0.542291\pi$
$107$	−2.74056			−0.264940			−0.132470	+	0.991187i	$0.542291\pi$
$108$	−1.00000			−0.0962250
$109$	−12.3004	−	7.10162i	−1.17816	−	0.680212i	−0.222573	−	0.974916i	$-0.571445\pi$
$109$	−12.3004	−	7.10162i	−1.17816	−	0.680212i	−0.955588	+	0.294704i	$0.904779\pi$
$110$	1.14820	+	0.662914i	0.109477	+	0.0632064i
$111$	−5.12950	+	2.96152i	−0.486871	+	0.281095i
$112$	1.74192	+	1.99141i	0.164596	+	0.188171i
$113$	9.29913	+	16.1066i	0.874788	+	1.51518i	0.856988	+	0.515336i	$0.172333\pi$
$113$	9.29913	+	16.1066i	0.874788	+	1.51518i	0.0178004	+	0.999842i	$0.494334\pi$
$114$	−4.62695			−0.433353
$115$	18.8423	−	10.8786i	1.75705	−	1.01443i
$116$	1.98376	−	3.43598i	0.184188	−	0.319022i
$117$	3.59612	+	0.260597i	0.332462	+	0.0240922i
$118$	−1.40079			−0.128954
$119$	−1.51251	−	1.72914i	−0.138652	−	0.158510i
$120$	1.27669	−	2.21130i	0.116546	−	0.201863i
$121$	−5.36519	+	9.29279i	−0.487745	+	0.844799i
$122$	5.22921	+	3.01909i	0.473430	+	0.273335i
$123$			6.78500i			0.611783i
$124$	3.49539	+	2.01806i	0.313895	+	0.181228i
$125$		−	8.88633i		−	0.794818i
$126$	−0.512843	−	2.59557i	−0.0456877	−	0.231232i
$127$	−5.67318	+	9.82624i	−0.503413	+	0.871938i	0.496579	+	0.867992i	$0.334589\pi$
$127$	−5.67318	+	9.82624i	−0.503413	+	0.871938i	−0.999992	+	0.00394597i	$0.998744\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.24805	−	3.89373i	0.197930	−	0.342824i
$130$	−5.16740	+	7.61939i	−0.453211	+	0.668265i
$131$	−1.43219	−	2.48062i	−0.125131	−	0.216733i	0.796653	−	0.604437i	$-0.206602\pi$
$131$	−1.43219	−	2.48062i	−0.125131	−	0.216733i	−0.921784	+	0.387704i	$0.873268\pi$
$132$	−0.449678	−	0.259622i	−0.0391394	−	0.0225972i
$133$	−2.37290	−	12.0096i	−0.205756	−	1.04136i
$134$	5.51150	+	9.54619i	0.476121	+	0.824665i
$135$	−2.21130	+	1.27669i	−0.190318	+	0.109880i
$136$			0.868301i			0.0744562i
$137$			9.80651i			0.837827i	0.908026	+	0.418913i	$0.137589\pi$
$137$			9.80651i			0.837827i	−0.908026	+	0.418913i	$0.862411\pi$
$138$	−7.37933	+	4.26046i	−0.628170	+	0.362674i
$139$	−3.49317	−	6.05035i	−0.296287	−	0.513184i	0.678996	−	0.734142i	$-0.262415\pi$
$139$	−3.49317	−	6.05035i	−0.296287	−	0.513184i	−0.975283	+	0.220957i	$0.929082\pi$
$140$	6.39433	+	2.17970i	0.540419	+	0.184218i
$141$	2.81446	+	1.62493i	0.237020	+	0.136844i
$142$	2.58292	+	4.47375i	0.216754	+	0.375429i
$143$	1.54944	+	1.05082i	0.129571	+	0.0878736i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		−	10.1306i		−	0.841303i
$146$	−5.97895	+	10.3558i	−0.494821	+	0.857055i
$147$	6.47398	−	2.66224i	0.533965	−	0.219578i
$148$			5.92304i			0.486871i
$149$	0.548493	+	0.316672i	0.0449343	+	0.0259428i	0.522299	−	0.852763i	$-0.325075\pi$
$149$	0.548493	+	0.316672i	0.0449343	+	0.0259428i	−0.477365	+	0.878705i	$0.658408\pi$
$150$		−	1.51979i		−	0.124090i
$151$	−3.43434	−	1.98282i	−0.279483	−	0.161360i	0.353706	−	0.935357i	$-0.384921\pi$
$151$	−3.43434	−	1.98282i	−0.279483	−	0.161360i	−0.633189	+	0.773997i	$0.718255\pi$
$152$	−2.31347	+	4.00705i	−0.187647	+	0.325015i
$153$	0.434150	−	0.751971i	0.0350990	−	0.0607932i
$154$	0.443252	−	1.30032i	0.0357183	−	0.104782i
$155$	10.3058			0.827782
$156$	2.02374	−	2.98403i	0.162029	−	0.238914i
$157$	−4.83448	+	8.37356i	−0.385833	+	0.668283i	−0.991884	−	0.127143i	$-0.959419\pi$
$157$	−4.83448	+	8.37356i	−0.385833	+	0.668283i	0.606051	+	0.795426i	$0.292753\pi$
$158$	−9.48251	+	5.47473i	−0.754388	+	0.435546i
$159$	8.25690			0.654815
$160$	−1.27669	−	2.21130i	−0.100931	−	0.174818i
$161$	−14.8428	−	16.9686i	−1.16977	−	1.33732i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	20.5444	+	11.8613i	1.60917	+	0.929052i	0.989557	+	0.144140i	$0.0460417\pi$
$163$	20.5444	+	11.8613i	1.60917	+	0.929052i	0.619608	+	0.784912i	$0.287292\pi$
$164$	5.87598	+	3.39250i	0.458837	+	0.264910i
$165$	−1.32583			−0.103216
$166$	12.9984			1.00887
$167$	3.53346	+	2.04005i	0.273428	+	0.157864i	0.630444	−	0.776234i	$-0.282873\pi$
$167$	3.53346	+	2.04005i	0.273428	+	0.157864i	−0.357017	+	0.934098i	$0.616206\pi$
$168$	−2.50425	−	0.853651i	−0.193207	−	0.0658606i
$169$	−8.05526	+	10.2036i	−0.619635	+	0.784890i
$170$	1.10855	+	1.92007i	0.0850222	+	0.147263i
$171$	4.00705	−	2.31347i	0.306427	−	0.176916i
$172$	−2.24805	−	3.89373i	−0.171412	−	0.296894i
$173$	−6.89043	+	11.9346i	−0.523869	+	0.907368i	0.475745	+	0.879583i	$0.342179\pi$
$173$	−6.89043	+	11.9346i	−0.523869	+	0.907368i	−0.999614	+	0.0277848i	$0.991155\pi$
$174$			3.96752i			0.300777i
$175$	3.94471	−	0.779411i	0.298192	−	0.0589180i
$176$	−0.449678	+	0.259622i	−0.0338957	+	0.0195697i
$177$	1.21312	−	0.700397i	0.0911839	−	0.0526451i
$178$	−8.02946			−0.601833
$179$	−1.92793	−	3.33928i	−0.144100	−	0.249589i	0.784937	−	0.619576i	$-0.212696\pi$
$179$	−1.92793	−	3.33928i	−0.144100	−	0.249589i	−0.929037	+	0.369987i	$0.879362\pi$
$180$			2.55339i			0.190318i
$181$	−3.18446			−0.236699			−0.118349	−	0.992972i	$-0.537760\pi$
$181$	−3.18446			−0.236699			−0.118349	+	0.992972i	$0.537760\pi$
$182$	8.78314	+	3.72243i	0.651049	+	0.275925i
$183$	−6.03817			−0.446354
$184$			8.52091i			0.628170i
$185$	7.56190	+	13.0976i	0.555962	+	0.962955i
$186$	−4.03613			−0.295943
$187$	0.390455	−	0.225430i	0.0285529	−	0.0164850i
$188$	2.81446	−	1.62493i	0.205266	−	0.118510i
$189$	1.74192	+	1.99141i	0.126706	+	0.144854i
$190$			11.8144i			0.857105i
$191$	−6.70696	+	11.6168i	−0.485299	+	0.840562i	−0.999857	−	0.0168934i	$-0.994622\pi$
$191$	−6.70696	+	11.6168i	−0.485299	+	0.840562i	0.514559	+	0.857455i	$0.327956\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	5.18745	−	2.99498i	0.373401	−	0.215583i	−0.301542	−	0.953453i	$-0.597501\pi$
$193$	5.18745	−	2.99498i	0.373401	−	0.215583i	0.674943	+	0.737870i	$0.264168\pi$
$194$	−7.51106	−	13.0095i	−0.539262	−	0.934030i
$195$	0.665404	−	9.18229i	0.0476506	−	0.657557i
$196$	0.931425	−	6.93776i	0.0665303	−	0.495554i
$197$	−3.78655	−	2.18617i	−0.269781	−	0.155758i	0.359007	−	0.933335i	$-0.383115\pi$
$197$	−3.78655	−	2.18617i	−0.269781	−	0.155758i	−0.628788	+	0.777577i	$0.716449\pi$
$198$	0.519243			0.0369010
$199$	9.69511			0.687268			0.343634	−	0.939104i	$-0.388342\pi$
$199$	9.69511			0.687268			0.343634	+	0.939104i	$0.388342\pi$
$200$	−1.31617	−	0.759893i	−0.0930675	−	0.0537326i
$201$	−9.54619	−	5.51150i	−0.673337	−	0.388751i
$202$	−7.36178	+	4.25033i	−0.517973	+	0.299052i
$203$	−10.2980	+	2.03472i	−0.722778	+	0.142809i
$204$	−0.434150	−	0.751971i	−0.0303966	−	0.0526485i
$205$	17.3247			1.21001
$206$	13.4777	−	7.78135i	0.939036	−	0.542153i
$207$	4.26046	−	7.37933i	0.296122	−	0.512899i
$208$	−1.57238	−	3.24463i	−0.109025	−	0.224975i
$209$	2.40251			0.166185
$210$	−6.62750	+	1.30949i	−0.457341	+	0.0903631i
$211$	3.54943	−	6.14780i	0.244353	−	0.423232i	−0.717596	−	0.696459i	$-0.754758\pi$
$211$	3.54943	−	6.14780i	0.244353	−	0.423232i	0.961950	+	0.273227i	$0.0880911\pi$
$212$	4.12845	−	7.15068i	0.283543	−	0.491111i
$213$	−4.47375	−	2.58292i	−0.306536	−	0.176979i
$214$		−	2.74056i		−	0.187341i
$215$	−9.94221	−	5.74014i	−0.678053	−	0.391474i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.06990	−	10.4761i	−0.140514	−	0.711161i
$218$	7.10162	−	12.3004i	0.480982	−	0.833086i
$219$		−	11.9579i		−	0.808040i
$220$	−0.662914	+	1.14820i	−0.0446937	+	0.0774117i
$221$	1.36530	+	2.81732i	0.0918398	+	0.189513i
$222$	−2.96152	−	5.12950i	−0.198764	−	0.344269i
$223$	−5.20714	−	3.00634i	−0.348696	−	0.201320i	0.315415	−	0.948954i	$-0.397856\pi$
$223$	−5.20714	−	3.00634i	−0.348696	−	0.201320i	−0.664111	+	0.747634i	$0.731190\pi$
$224$	−1.99141	+	1.74192i	−0.133057	+	0.116387i
$225$	0.759893	+	1.31617i	0.0506595	+	0.0877449i
$226$	−16.1066	+	9.29913i	−1.07139	+	0.618569i
$227$		−	3.60284i		−	0.239129i	−0.992826	−	0.119564i	$-0.961850\pi$
$227$		−	3.60284i		−	0.239129i	0.992826	−	0.119564i	$-0.0381498\pi$
$228$		−	4.62695i		−	0.306427i
$229$	−23.8424	+	13.7654i	−1.57555	+	0.909644i	−0.580081	+	0.814559i	$0.696979\pi$
$229$	−23.8424	+	13.7654i	−1.57555	+	0.909644i	−0.995469	+	0.0950854i	$0.969688\pi$
$230$	10.8786	+	18.8423i	0.717313	+	1.24242i
$231$	0.266290	+	1.34773i	0.0175206	+	0.0886743i
$232$	3.43598	+	1.98376i	0.225583	+	0.130240i
$233$	−5.84917	−	10.1311i	−0.383192	−	0.663708i	0.608325	−	0.793688i	$-0.291842\pi$
$233$	−5.84917	−	10.1311i	−0.383192	−	0.663708i	−0.991517	+	0.129981i	$0.958509\pi$
$234$	−0.260597	+	3.59612i	−0.0170357	+	0.235086i
$235$	4.14908	−	7.18641i	0.270656	−	0.468790i
$236$		−	1.40079i		−	0.0911839i
$237$	5.47473	−	9.48251i	0.355622	−	0.615955i
$238$	1.72914	−	1.51251i	0.112084	−	0.0980415i
$239$		−	16.4292i		−	1.06272i	−0.847147	−	0.531359i	$-0.821682\pi$
$239$		−	16.4292i		−	1.06272i	0.847147	−	0.531359i	$-0.178318\pi$
$240$	2.21130	+	1.27669i	0.142739	+	0.0824102i
$241$			14.3659i			0.925392i	0.886517	+	0.462696i	$0.153118\pi$
$241$			14.3659i			0.925392i	−0.886517	+	0.462696i	$0.846882\pi$
$242$	−9.29279	−	5.36519i	−0.597363	−	0.344888i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.01909	+	5.22921i	−0.193277	+	0.334766i
$245$	−6.79773	−	16.5306i	−0.434291	−	1.05610i
$246$	−6.78500			−0.432596
$247$	−1.20577	+	16.6391i	−0.0767211	+	1.05872i
$248$	−2.01806	+	3.49539i	−0.128147	+	0.221958i
$249$	−11.2569	+	6.49919i	−0.713379	+	0.411870i
$250$	8.88633			0.562021
$251$	−9.52013	−	16.4893i	−0.600905	−	1.04080i	−0.992684	−	0.120739i	$-0.961474\pi$
$251$	−9.52013	−	16.4893i	−0.600905	−	1.04080i	0.391779	−	0.920059i	$-0.371860\pi$
$252$	2.59557	−	0.512843i	0.163506	−	0.0323061i
$253$	3.83166	−	2.21221i	0.240895	−	0.139081i
$254$	−9.82624	−	5.67318i	−0.616553	−	0.355967i
$255$	−1.92007	−	1.10855i	−0.120240	−	0.0694203i
$256$	1.00000			0.0625000
$257$	23.3332			1.45548			0.727742	−	0.685851i	$-0.240570\pi$
$257$	23.3332			1.45548			0.727742	+	0.685851i	$0.240570\pi$
$258$	3.89373	+	2.24805i	0.242413	+	0.139957i
$259$	11.7952	−	10.3175i	0.732918	−	0.641096i
$260$	−7.61939	−	5.16740i	−0.472535	−	0.320469i
$261$	−1.98376	−	3.43598i	−0.122792	−	0.212682i
$262$	2.48062	−	1.43219i	0.153253	−	0.0884809i
$263$	−10.3167	−	17.8690i	−0.636152	−	1.10185i	−0.986270	−	0.165142i	$-0.947192\pi$
$263$	−10.3167	−	17.8690i	−0.636152	−	1.10185i	0.350118	−	0.936706i	$-0.386142\pi$
$264$	0.259622	−	0.449678i	0.0159786	−	0.0276757i
$265$		−	21.0831i		−	1.29512i
$266$	12.0096	−	2.37290i	0.736354	−	0.145492i
$267$	6.95371	−	4.01473i	0.425560	−	0.245697i
$268$	−9.54619	+	5.51150i	−0.583127	+	0.336668i
$269$	−8.74233			−0.533029			−0.266515	−	0.963831i	$-0.585872\pi$
$269$	−8.74233			−0.533029			−0.266515	+	0.963831i	$0.585872\pi$
$270$	−1.27669	−	2.21130i	−0.0776971	−	0.134575i
$271$			10.1211i			0.614811i	0.951579	+	0.307406i	$0.0994608\pi$
$271$			10.1211i			0.614811i	−0.951579	+	0.307406i	$0.900539\pi$
$272$	−0.868301			−0.0526485
$273$	−9.46764	+	1.16785i	−0.573007	+	0.0706813i
$274$	−9.80651			−0.592433
$275$			0.789139i			0.0475868i
$276$	−4.26046	−	7.37933i	−0.256449	−	0.444183i
$277$	−4.97733			−0.299059			−0.149529	−	0.988757i	$-0.547776\pi$
$277$	−4.97733			−0.299059			−0.149529	+	0.988757i	$0.547776\pi$
$278$	6.05035	−	3.49317i	0.362876	−	0.209507i
$279$	3.49539	−	2.01806i	0.209264	−	0.120818i
$280$	−2.17970	+	6.39433i	−0.130262	+	0.382134i
$281$		−	27.2729i		−	1.62696i	−0.581591	−	0.813481i	$-0.697570\pi$
$281$		−	27.2729i		−	1.62696i	0.581591	−	0.813481i	$-0.302430\pi$
$282$	−1.62493	+	2.81446i	−0.0967632	+	0.167599i
$283$	4.90256	+	8.49149i	0.291427	+	0.504767i	0.974147	−	0.225913i	$-0.0725366\pi$
$283$	4.90256	+	8.49149i	0.291427	+	0.504767i	−0.682720	+	0.730680i	$0.739203\pi$
$284$	−4.47375	+	2.58292i	−0.265468	+	0.153268i
$285$	−5.90719	−	10.2316i	−0.349912	−	0.606065i
$286$	−1.05082	+	1.54944i	−0.0621360	+	0.0916202i
$287$	−3.47964	−	17.6109i	−0.205396	−	1.03954i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−16.2461			−0.955650
$290$	10.1306			0.594891
$291$	13.0095	+	7.51106i	0.762632	+	0.440306i
$292$	−10.3558	−	5.97895i	−0.606030	−	0.349891i
$293$	24.3101	−	14.0354i	1.42021	−	0.819959i	0.423895	−	0.905711i	$-0.360663\pi$
$293$	24.3101	−	14.0354i	1.42021	−	0.819959i	0.996317	+	0.0857521i	$0.0273293\pi$
$294$	2.66224	+	6.47398i	0.155265	+	0.377570i
$295$	−1.78838	−	3.09757i	−0.104124	−	0.180348i
$296$	−5.92304			−0.344269
$297$	−0.449678	+	0.259622i	−0.0260929	+	0.0150648i
$298$	−0.316672	+	0.548493i	−0.0183443	+	0.0317733i
$299$	13.3981	+	27.6472i	0.774832	+	1.59888i
$300$	1.51979			0.0877449
$301$	−3.83810	+	11.2594i	−0.221224	+	0.648979i
$302$	1.98282	−	3.43434i	0.114098	−	0.197624i
$303$	4.25033	−	7.36178i	0.244175	−	0.422923i
$304$	−4.00705	−	2.31347i	−0.229820	−	0.132687i
$305$			15.4178i			0.882820i
$306$	0.751971	+	0.434150i	0.0429873	+	0.0248187i
$307$		−	27.0072i		−	1.54139i	−0.637207	−	0.770693i	$-0.719910\pi$
$307$		−	27.0072i		−	1.54139i	0.637207	−	0.770693i	$-0.280090\pi$
$308$	1.30032	+	0.443252i	0.0740924	+	0.0252566i
$309$	−7.78135	+	13.4777i	−0.442666	+	0.766719i
$310$			10.3058i			0.585330i
$311$	12.0954	−	20.9499i	0.685869	−	1.18796i	−0.287294	−	0.957843i	$-0.592756\pi$
$311$	12.0954	−	20.9499i	0.685869	−	1.18796i	0.973163	−	0.230118i	$-0.0739111\pi$
$312$	2.98403	+	2.02374i	0.168938	+	0.114572i
$313$	11.8941	+	20.6011i	0.672293	+	1.16444i	0.977252	+	0.212080i	$0.0680236\pi$
$313$	11.8941	+	20.6011i	0.672293	+	1.16444i	−0.304960	+	0.952365i	$0.598643\pi$
$314$	−8.37356	−	4.83448i	−0.472548	−	0.272825i
$315$	5.08484	−	4.44780i	0.286498	−	0.250605i
$316$	−5.47473	−	9.48251i	−0.307977	−	0.533433i
$317$	7.55286	−	4.36064i	0.424211	−	0.244918i	−0.272667	−	0.962109i	$-0.587906\pi$
$317$	7.55286	−	4.36064i	0.424211	−	0.244918i	0.696877	+	0.717190i	$0.254572\pi$
$318$			8.25690i			0.463024i
$319$		−	2.06011i		−	0.115344i
$320$	2.21130	−	1.27669i	0.123615	−	0.0713693i
$321$	1.37028	+	2.37339i	0.0764814	+	0.132470i
$322$	16.9686	−	14.8428i	0.945625	−	0.827154i
$323$	3.47933	+	2.00879i	0.193595	+	0.111772i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−5.46534	−	0.396051i	−0.303162	−	0.0219690i
$326$	−11.8613	+	20.5444i	−0.656939	+	1.13785i
$327$			14.2032i			0.785441i
$328$	−3.39250	+	5.87598i	−0.187319	+	0.324447i
$329$	−8.13847	−	2.77425i	−0.448688	−	0.152949i
$330$		−	1.32583i		−	0.0729845i
$331$	10.3972	+	6.00281i	0.571480	+	0.329944i	0.757740	−	0.652556i	$-0.226303\pi$
$331$	10.3972	+	6.00281i	0.571480	+	0.329944i	−0.186260	+	0.982500i	$0.559637\pi$
$332$			12.9984i			0.713379i
$333$	5.12950	+	2.96152i	0.281095	+	0.162290i
$334$	−2.04005	+	3.53346i	−0.111626	+	0.193343i
$335$	−14.0730	+	24.3751i	−0.768889	+	1.33176i
$336$	0.853651	−	2.50425i	0.0465705	−	0.136618i
$337$	22.4347			1.22210			0.611049	−	0.791593i	$-0.290748\pi$
$337$	22.4347			1.22210			0.611049	+	0.791593i	$0.290748\pi$
$338$	−10.2036	−	8.05526i	−0.555001	−	0.438148i
$339$	9.29913	−	16.1066i	0.505059	−	0.874788i
$340$	−1.92007	+	1.10855i	−0.104131	+	0.0601198i
$341$	2.09573			0.113490
$342$	2.31347	+	4.00705i	0.125098	+	0.216677i
$343$	−15.4384	+	10.2302i	−0.833594	+	0.552377i
$344$	3.89373	−	2.24805i	0.209936	−	0.121207i
$345$	−18.8423	−	10.8786i	−1.01443	−	0.585684i
$346$	−11.9346	−	6.89043i	−0.641606	−	0.370432i
$347$	29.2720			1.57140			0.785701	−	0.618606i	$-0.212302\pi$
$347$	29.2720			1.57140			0.785701	+	0.618606i	$0.212302\pi$
$348$	−3.96752			−0.212682
$349$	−22.1028	−	12.7610i	−1.18313	−	0.683083i	−0.226397	−	0.974035i	$-0.572695\pi$
$349$	−22.1028	−	12.7610i	−1.18313	−	0.683083i	−0.956738	+	0.290952i	$0.906028\pi$
$350$	0.779411	+	3.94471i	0.0416613	+	0.210854i
$351$	−1.57238	−	3.24463i	−0.0839273	−	0.173186i
$352$	−0.259622	−	0.449678i	−0.0138379	−	0.0239679i
$353$	3.16688	−	1.82840i	0.168556	−	0.0973158i	−0.413349	−	0.910573i	$-0.635641\pi$
$353$	3.16688	−	1.82840i	0.168556	−	0.0973158i	0.581905	+	0.813257i	$0.302308\pi$
$354$	0.700397	+	1.21312i	0.0372257	+	0.0644768i
$355$	−6.59520	+	11.4232i	−0.350037	+	0.606282i
$356$		−	8.02946i		−	0.425560i
$357$	−0.741226	+	2.17444i	−0.0392298	+	0.115084i
$358$	3.33928	−	1.92793i	0.176486	−	0.101894i
$359$	−29.7911	+	17.1999i	−1.57231	+	0.907775i	−0.576428	+	0.817148i	$0.695554\pi$
$359$	−29.7911	+	17.1999i	−1.57231	+	0.907775i	−0.995885	+	0.0906276i	$0.971113\pi$
$360$	−2.55339			−0.134575
$361$	1.20431	+	2.08593i	0.0633849	+	0.109786i
$362$		−	3.18446i		−	0.167371i
$363$	10.7304			0.563199
$364$	−3.72243	+	8.78314i	−0.195108	+	0.460361i
$365$	−30.5331			−1.59818
$366$		−	6.03817i		−	0.315620i
$367$	−3.19602	−	5.53566i	−0.166831	−	0.288959i	0.770473	−	0.637472i	$-0.220020\pi$
$367$	−3.19602	−	5.53566i	−0.166831	−	0.288959i	−0.937304	+	0.348513i	$0.886687\pi$
$368$	−8.52091			−0.444183
$369$	5.87598	−	3.39250i	0.305891	−	0.176606i
$370$	−13.0976	+	7.56190i	−0.680912	+	0.393125i
$371$	−21.4314	+	4.23449i	−1.11266	+	0.219844i
$372$		−	4.03613i		−	0.209264i
$373$	−9.11185	+	15.7822i	−0.471794	+	0.817171i	−0.999479	−	0.0322690i	$-0.989727\pi$
$373$	−9.11185	+	15.7822i	−0.471794	+	0.817171i	0.527685	+	0.849440i	$0.323060\pi$
$374$	0.225430	+	0.390455i	0.0116567	+	0.0201900i
$375$	−7.69579	+	4.44317i	−0.397409	+	0.229444i
$376$	1.62493	+	2.81446i	0.0837994	+	0.145145i
$377$	14.2677	+	1.03392i	0.734824	+	0.0532498i
$378$	−1.99141	+	1.74192i	−0.102427	+	0.0895947i
$379$	−6.69334	−	3.86440i	−0.343814	−	0.198501i	0.318143	−	0.948043i	$-0.396941\pi$
$379$	−6.69334	−	3.86440i	−0.343814	−	0.198501i	−0.661957	+	0.749542i	$0.730274\pi$
$380$	−11.8144			−0.606065
$381$	11.3464			0.581292
$382$	−11.6168	−	6.70696i	−0.594367	−	0.343158i
$383$	8.50425	+	4.90993i	0.434547	+	0.250886i	0.701282	−	0.712884i	$-0.252612\pi$
$383$	8.50425	+	4.90993i	0.434547	+	0.250886i	−0.266735	+	0.963770i	$0.585945\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	3.44128	−	0.679942i	0.175384	−	0.0346530i
$386$	2.99498	+	5.18745i	0.152440	+	0.264034i
$387$	−4.49610			−0.228549
$388$	13.0095	−	7.51106i	0.660459	−	0.381316i
$389$	4.70287	−	8.14562i	0.238445	−	0.412999i	−0.721823	−	0.692078i	$-0.756696\pi$
$389$	4.70287	−	8.14562i	0.238445	−	0.412999i	0.960268	+	0.279078i	$0.0900289\pi$
$390$	9.18229	+	0.665404i	0.464963	+	0.0336941i
$391$	7.39871			0.374169
$392$	6.93776	+	0.931425i	0.350410	+	0.0470440i
$393$	−1.43219	+	2.48062i	−0.0722444	+	0.125131i
$394$	2.18617	−	3.78655i	0.110138	−	0.190764i
$395$	−24.2125	−	13.9791i	−1.21826	−	0.703365i
$396$			0.519243i			0.0260929i
$397$	9.99586	+	5.77112i	0.501678	+	0.289644i	0.729406	−	0.684081i	$-0.239796\pi$
$397$	9.99586	+	5.77112i	0.501678	+	0.289644i	−0.227728	+	0.973725i	$0.573130\pi$
$398$			9.69511i			0.485972i
$399$	−9.21414	+	8.05977i	−0.461284	+	0.403493i
$400$	0.759893	−	1.31617i	0.0379947	−	0.0658087i
$401$		−	33.5631i		−	1.67606i	−0.545623	−	0.838030i	$-0.683707\pi$
$401$		−	33.5631i		−	1.67606i	0.545623	−	0.838030i	$-0.316293\pi$
$402$	5.51150	−	9.54619i	0.274888	−	0.476121i
$403$	−1.05180	+	14.5144i	−0.0523940	+	0.723014i
$404$	−4.25033	−	7.36178i	−0.211462	−	0.366262i
$405$	2.21130	+	1.27669i	0.109880	+	0.0634394i
$406$	−2.03472	−	10.2980i	−0.100981	−	0.511081i
$407$	1.53775	+	2.66346i	0.0762233	+	0.132023i
$408$	0.751971	−	0.434150i	0.0372281	−	0.0214936i
$409$			18.3070i			0.905221i	0.891708	+	0.452611i	$0.149507\pi$
$409$			18.3070i			0.905221i	−0.891708	+	0.452611i	$0.850493\pi$
$410$			17.3247i			0.855607i
$411$	8.49269	−	4.90326i	0.418913	−	0.241860i
$412$	7.78135	+	13.4777i	0.383360	+	0.663999i
$413$	−2.78955	+	2.44007i	−0.137265	+	0.120068i
$414$	7.37933	+	4.26046i	0.362674	+	0.209390i
$415$	16.5950	+	28.7433i	0.814614	+	1.41095i
$416$	3.24463	−	1.57238i	0.159081	−	0.0770921i
$417$	−3.49317	+	6.05035i	−0.171061	+	0.296287i
$418$			2.40251i			0.117511i
$419$	−8.13046	+	14.0824i	−0.397199	+	0.687969i	−0.993379	−	0.114882i	$-0.963351\pi$
$419$	−8.13046	+	14.0824i	−0.397199	+	0.687969i	0.596180	+	0.802851i	$0.296684\pi$
$420$	−1.30949	−	6.62750i	−0.0638964	−	0.323389i
$421$			20.7347i			1.01055i	0.862959	+	0.505274i	$0.168608\pi$
$421$			20.7347i			1.01055i	−0.862959	+	0.505274i	$0.831392\pi$
$422$	6.14780	+	3.54943i	0.299270	+	0.172784i
$423$		−	3.24986i		−	0.158014i
$424$	7.15068	+	4.12845i	0.347268	+	0.200495i
$425$	−0.659816	+	1.14283i	−0.0320058	+	0.0554356i
$426$	2.58292	−	4.47375i	0.125143	−	0.216754i
$427$	15.6725	−	3.09663i	0.758446	−	0.149857i
$428$	2.74056			0.132470
$429$	0.135313	−	1.86726i	0.00653297	−	0.0901522i
$430$	5.74014	−	9.94221i	0.276814	−	0.479456i
$431$	−23.4819	+	13.5573i	−1.13108	+	0.653030i	−0.944207	−	0.329353i	$-0.893169\pi$
$431$	−23.4819	+	13.5573i	−1.13108	+	0.653030i	−0.186875	+	0.982384i	$0.559836\pi$
$432$	1.00000			0.0481125
$433$	9.82893	+	17.0242i	0.472348	+	0.818131i	0.999499	−	0.0316404i	$-0.0100731\pi$
$433$	9.82893	+	17.0242i	0.472348	+	0.818131i	−0.527151	+	0.849772i	$0.676740\pi$
$434$	10.4761	−	2.06990i	0.502867	−	0.0993584i
$435$	−8.77338	+	5.06531i	−0.420651	+	0.242863i
$436$	12.3004	+	7.10162i	0.589081	+	0.340106i
$437$	34.1437	+	19.7129i	1.63332	+	0.942996i
$438$	11.9579			0.571370
$439$	−17.5185			−0.836111			−0.418055	−	0.908422i	$-0.637288\pi$
$439$	−17.5185			−0.836111			−0.418055	+	0.908422i	$0.637288\pi$
$440$	−1.14820	−	0.662914i	−0.0547383	−	0.0316032i
$441$	−5.54256	−	4.27552i	−0.263931	−	0.203596i
$442$	−2.81732	+	1.36530i	−0.134006	+	0.0649405i
$443$	−17.0463	−	29.5250i	−0.809894	−	1.40278i	−0.912937	−	0.408100i	$-0.866191\pi$
$443$	−17.0463	−	29.5250i	−0.809894	−	1.40278i	0.103044	−	0.994677i	$-0.467142\pi$
$444$	5.12950	−	2.96152i	0.243435	−	0.140547i
$445$	−10.2512	−	17.7555i	−0.485951	−	0.841692i
$446$	3.00634	−	5.20714i	0.142355	−	0.246565i
$447$		−	0.633345i		−	0.0299562i
$448$	−1.74192	−	1.99141i	−0.0822980	−	0.0940853i
$449$	24.4229	−	14.1006i	1.15259	−	0.665447i	0.203072	−	0.979164i	$-0.434907\pi$
$449$	24.4229	−	14.1006i	1.15259	−	0.665447i	0.949517	+	0.313716i	$0.101574\pi$
$450$	−1.31617	+	0.759893i	−0.0620450	+	0.0358217i
$451$	3.52306			0.165895
$452$	−9.29913	−	16.1066i	−0.437394	−	0.757589i
$453$			3.96564i			0.186322i
$454$	3.60284			0.169090
$455$	2.98197	+	24.1745i	0.139797	+	1.13332i
$456$	4.62695			0.216677
$457$		−	22.8685i		−	1.06974i	−0.844934	−	0.534871i	$-0.820360\pi$
$457$		−	22.8685i		−	1.06974i	0.844934	−	0.534871i	$-0.179640\pi$
$458$	−13.7654	−	23.8424i	−0.643216	−	1.11408i
$459$	−0.868301			−0.0405288
$460$	−18.8423	+	10.8786i	−0.878526	+	0.507217i
$461$	−20.8622	+	12.0448i	−0.971648	+	0.560981i	−0.899738	−	0.436430i	$-0.856243\pi$
$461$	−20.8622	+	12.0448i	−0.971648	+	0.560981i	−0.0719098	+	0.997411i	$0.522909\pi$
$462$	−1.34773	+	0.266290i	−0.0627022	+	0.0123889i
$463$		−	12.2189i		−	0.567860i	−0.958845	−	0.283930i	$-0.908362\pi$
$463$		−	12.2189i		−	0.567860i	0.958845	−	0.283930i	$-0.0916384\pi$
$464$	−1.98376	+	3.43598i	−0.0920939	+	0.159511i
$465$	−5.15290	−	8.92509i	−0.238960	−	0.413891i
$466$	10.1311	−	5.84917i	0.469312	−	0.270958i
$467$	−7.51520	−	13.0167i	−0.347762	−	0.602341i	0.638090	−	0.769962i	$-0.279725\pi$
$467$	−7.51520	−	13.0167i	−0.347762	−	0.602341i	−0.985852	+	0.167621i	$0.946392\pi$
$468$	−3.59612	−	0.260597i	−0.166231	−	0.0120461i
$469$	27.6044	+	9.40979i	1.27465	+	0.434504i
$470$	7.18641	+	4.14908i	0.331484	+	0.191383i
$471$	9.66896			0.445522
$472$	1.40079			0.0644768
$473$	−2.02179	−	1.16728i	−0.0929622	−	0.0536718i
$474$	9.48251	+	5.47473i	0.435546	+	0.251463i
$475$	−6.08986	+	3.51598i	−0.279422	+	0.161324i
$476$	1.51251	+	1.72914i	0.0693258	+	0.0792551i
$477$	−4.12845	−	7.15068i	−0.189029	−	0.327407i
$478$	16.4292			0.751455
$479$	−0.784884	+	0.453153i	−0.0358623	+	0.0207051i	−0.517824	−	0.855487i	$-0.673258\pi$
$479$	−0.784884	+	0.453153i	−0.0358623	+	0.0207051i	0.481962	+	0.876192i	$0.339924\pi$
$480$	−1.27669	+	2.21130i	−0.0582728	+	0.100931i
$481$	−19.2181	+	9.31325i	−0.876268	+	0.424648i
$482$	−14.3659			−0.654351
$483$	−7.27389	+	21.3385i	−0.330973	+	0.970936i
$484$	5.36519	−	9.29279i	0.243872	−	0.422399i
$485$	19.1786	−	33.2184i	0.870857	−	1.50837i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$			28.7559i			1.30305i	0.758625	+	0.651527i	$0.225871\pi$
$487$			28.7559i			1.30305i	−0.758625	+	0.651527i	$0.774129\pi$
$488$	−5.22921	−	3.01909i	−0.236715	−	0.136668i
$489$		−	23.7227i		−	1.07278i
$490$	16.5306	−	6.79773i	0.746776	−	0.307090i
$491$	−13.8621	+	24.0099i	−0.625589	+	1.08355i	0.362838	+	0.931852i	$0.381808\pi$
$491$	−13.8621	+	24.0099i	−0.625589	+	1.08355i	−0.988427	+	0.151700i	$0.951525\pi$
$492$		−	6.78500i		−	0.305891i
$493$	1.72250	−	2.98346i	0.0775776	−	0.134368i
$494$	−16.6391	−	1.20577i	−0.748627	−	0.0542500i
$495$	0.662914	+	1.14820i	0.0297958	+	0.0516078i
$496$	−3.49539	−	2.01806i	−0.156948	−	0.0906138i
$497$	12.9366	+	4.40983i	0.580285	+	0.197808i
$498$	−6.49919	−	11.2569i	−0.291236	−	0.504435i
$499$	3.50306	−	2.02249i	0.156818	−	0.0905392i	−0.419537	−	0.907738i	$-0.637808\pi$
$499$	3.50306	−	2.02249i	0.156818	−	0.0905392i	0.576356	+	0.817199i	$0.304474\pi$
$500$			8.88633i			0.397409i
$501$		−	4.08009i		−	0.182285i
$502$	16.4893	−	9.52013i	0.735955	−	0.424904i
$503$	−0.861181	−	1.49161i	−0.0383982	−	0.0665076i	0.846188	−	0.532885i	$-0.178892\pi$
$503$	−0.861181	−	1.49161i	−0.0383982	−	0.0665076i	−0.884586	+	0.466377i	$0.845559\pi$
$504$	0.512843	+	2.59557i	0.0228438	+	0.115616i
$505$	−18.7975	−	10.8527i	−0.836477	−	0.482940i
$506$	2.21221	+	3.83166i	0.0983448	+	0.170338i
$507$	12.8642	+	1.87427i	0.571318	+	0.0832395i
$508$	5.67318	−	9.82624i	0.251707	−	0.435969i
$509$			41.8260i			1.85391i	0.375178	+	0.926953i	$0.377582\pi$
$509$			41.8260i			1.85391i	−0.375178	+	0.926953i	$0.622418\pi$
$510$	1.10855	−	1.92007i	0.0490876	−	0.0850222i
$511$	6.13252	+	31.0376i	0.271287	+	1.37302i
$512$			1.00000i			0.0441942i
$513$	−4.00705	−	2.31347i	−0.176916	−	0.102142i
$514$			23.3332i			1.02918i
$515$	34.4138	+	19.8688i	1.51645	+	0.875524i
$516$	−2.24805	+	3.89373i	−0.0989648	+	0.171412i
$517$	0.843734	−	1.46139i	0.0371074	−	0.0642718i
$518$	10.3175	+	11.7952i	0.453323	+	0.518251i
$519$	13.7809			0.604912
$520$	5.16740	−	7.61939i	0.226606	−	0.334133i
$521$	−14.7751	+	25.5912i	−0.647308	+	1.12117i	0.336455	+	0.941700i	$0.390772\pi$
$521$	−14.7751	+	25.5912i	−0.647308	+	1.12117i	−0.983763	+	0.179471i	$0.942561\pi$
$522$	3.43598	−	1.98376i	0.150389	−	0.0868269i
$523$	10.8626			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$523$	10.8626			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$524$	1.43219	+	2.48062i	0.0625655	+	0.108367i
$525$	−2.64735	−	3.02652i	−0.115540	−	0.132088i
$526$	17.8690	−	10.3167i	0.779124	−	0.449828i
$527$	3.03505	+	1.75229i	0.132209	+	0.0763308i
$528$	0.449678	+	0.259622i	0.0195697	+	0.0112986i
$529$	49.6059			2.15678
$530$	21.0831			0.915790
$531$	−1.21312	−	0.700397i	−0.0526451	−	0.0303946i
$532$	2.37290	+	12.0096i	0.102878	+	0.520681i
$533$	−1.76815	+	24.3997i	−0.0765870	+	1.05687i
$534$	4.01473	+	6.95371i	0.173734	+	0.300917i
$535$	6.06019	−	3.49885i	0.262005	−	0.151268i
$536$	−5.51150	−	9.54619i	−0.238060	−	0.412333i
$537$	−1.92793	+	3.33928i	−0.0831965	+	0.144100i
$538$		−	8.74233i		−	0.376909i
$539$	−1.38235	−	3.36157i	−0.0595420	−	0.144793i
$540$	2.21130	−	1.27669i	0.0951591	−	0.0549401i
$541$	9.53428	−	5.50462i	0.409911	−	0.236662i	−0.280841	−	0.959754i	$-0.590613\pi$
$541$	9.53428	−	5.50462i	0.409911	−	0.236662i	0.690751	+	0.723092i	$0.257280\pi$
$542$	−10.1211			−0.434737
$543$	1.59223	+	2.75782i	0.0683291	+	0.118349i
$544$		−	0.868301i		−	0.0372281i
$545$	36.2664			1.55348
$546$	−1.16785	−	9.46764i	−0.0499793	−	0.405177i
$547$	−36.2418			−1.54959			−0.774793	−	0.632215i	$-0.782146\pi$
$547$	−36.2418			−1.54959			−0.774793	+	0.632215i	$0.782146\pi$
$548$		−	9.80651i		−	0.418913i
$549$	3.01909	+	5.22921i	0.128851	+	0.223177i
$550$	−0.789139			−0.0336490
$551$	15.8981	−	9.17876i	0.677281	−	0.391028i
$552$	7.37933	−	4.26046i	0.314085	−	0.181337i
$553$	−9.34701	+	27.4202i	−0.397475	+	1.16603i
$554$		−	4.97733i		−	0.211466i
$555$	7.56190	−	13.0976i	0.320985	−	0.555962i
$556$	3.49317	+	6.05035i	0.148144	+	0.256592i
$557$	−9.61691	+	5.55232i	−0.407481	+	0.235260i	−0.689707	−	0.724089i	$-0.742261\pi$
$557$	−9.61691	+	5.55232i	−0.407481	+	0.235260i	0.282226	+	0.959348i	$0.408927\pi$
$558$	2.01806	+	3.49539i	0.0854315	+	0.147972i
$559$	9.09895	−	13.4165i	0.384845	−	0.567458i
$560$	−6.39433	−	2.17970i	−0.270210	−	0.0921092i
$561$	−0.390455	−	0.225430i	−0.0164850	−	0.00951764i
$562$	27.2729			1.15044
$563$	10.3121			0.434604			0.217302	−	0.976104i	$-0.430274\pi$
$563$	10.3121			0.434604			0.217302	+	0.976104i	$0.430274\pi$
$564$	−2.81446	−	1.62493i	−0.118510	−	0.0684219i
$565$	−41.1263	−	23.7443i	−1.73020	−	0.998929i
$566$	−8.49149	+	4.90256i	−0.356924	+	0.206070i
$567$	0.853651	−	2.50425i	0.0358500	−	0.105169i
$568$	−2.58292	−	4.47375i	−0.108377	−	0.187714i
$569$	−33.8195			−1.41779			−0.708894	−	0.705315i	$-0.750806\pi$
$569$	−33.8195			−1.41779			−0.708894	+	0.705315i	$0.750806\pi$
$570$	10.2316	−	5.90719i	0.428553	−	0.247425i
$571$	6.09944	−	10.5645i	0.255254	−	0.442112i	−0.709711	−	0.704493i	$-0.751174\pi$
$571$	6.09944	−	10.5645i	0.255254	−	0.442112i	0.964964	+	0.262381i	$0.0845077\pi$
$572$	−1.54944	−	1.05082i	−0.0647853	−	0.0439368i
$573$	13.4139			0.560374
$574$	17.6109	−	3.47964i	0.735067	−	0.145237i
$575$	−6.47498	+	11.2150i	−0.270025	+	0.467698i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−22.1116	−	12.7661i	−0.920517	−	0.531460i	−0.0367167	−	0.999326i	$-0.511690\pi$
$577$	−22.1116	−	12.7661i	−0.920517	−	0.531460i	−0.883800	+	0.467865i	$0.845023\pi$
$578$		−	16.2461i		−	0.675747i
$579$	−5.18745	−	2.99498i	−0.215583	−	0.124467i
$580$			10.1306i			0.420651i
$581$	25.8851	−	22.6422i	1.07390	−	0.939355i
$582$	−7.51106	+	13.0095i	−0.311343	+	0.539262i
$583$		−	4.28734i		−	0.177563i
$584$	5.97895	−	10.3558i	0.247411	−	0.428528i
$585$	−8.28480	+	4.01489i	−0.342534	+	0.165995i
$586$	14.0354	+	24.3101i	0.579799	+	1.00424i
$587$	17.3456	+	10.0145i	0.715928	+	0.413341i	0.813252	−	0.581912i	$-0.197695\pi$
$587$	17.3456	+	10.0145i	0.715928	+	0.413341i	−0.0973243	+	0.995253i	$0.531028\pi$
$588$	−6.47398	+	2.66224i	−0.266983	+	0.109789i
$589$	9.33747	+	16.1730i	0.384744	+	0.666396i
$590$	3.09757	−	1.78838i	0.127525	−	0.0736266i
$591$			4.37233i			0.179854i
$592$		−	5.92304i		−	0.243435i
$593$	3.62655	−	2.09379i	0.148924	−	0.0859816i	−0.423686	−	0.905809i	$-0.639264\pi$
$593$	3.62655	−	2.09379i	0.148924	−	0.0859816i	0.572611	+	0.819827i	$0.305931\pi$
$594$	−0.259622	−	0.449678i	−0.0106524	−	0.0184505i
$595$	5.55220	+	1.89264i	0.227618	+	0.0775905i
$596$	−0.548493	−	0.316672i	−0.0224671	−	0.0129714i
$597$	−4.84755	−	8.39621i	−0.198397	−	0.343634i
$598$	−27.6472	+	13.3981i	−1.13058	+	0.547889i
$599$	13.7033	−	23.7348i	0.559900	−	0.969776i	−0.437604	−	0.899168i	$-0.644173\pi$
$599$	13.7033	−	23.7348i	0.559900	−	0.969776i	0.997504	−	0.0706079i	$-0.0224939\pi$
$600$			1.51979i			0.0620450i
$601$	−12.7864	+	22.1467i	−0.521569	+	0.903383i	0.478117	+	0.878296i	$0.341320\pi$
$601$	−12.7864	+	22.1467i	−0.521569	+	0.903383i	−0.999685	+	0.0250869i	$0.992014\pi$
$602$	−11.2594	−	3.83810i	−0.458897	−	0.156429i
$603$			11.0230i			0.448891i
$604$	3.43434	+	1.98282i	0.139741	+	0.0806798i
$605$		−	27.3988i		−	1.11392i
$606$	7.36178	+	4.25033i	0.299052	+	0.172658i
$607$	18.1780	−	31.4852i	0.737822	−	1.27795i	−0.215652	−	0.976470i	$-0.569188\pi$
$607$	18.1780	−	31.4852i	0.737822	−	1.27795i	0.953474	−	0.301475i	$-0.0974791\pi$
$608$	2.31347	−	4.00705i	0.0938237	−	0.162507i
$609$	6.91111	+	7.90097i	0.280052	+	0.320163i
$610$	−15.4178			−0.624248
$611$	9.69769	+	6.57688i	0.392327	+	0.266072i
$612$	−0.434150	+	0.751971i	−0.0175495	+	0.0303966i
$613$	19.4132	−	11.2082i	0.784092	−	0.452696i	−0.0537867	−	0.998552i	$-0.517129\pi$
$613$	19.4132	−	11.2082i	0.784092	−	0.452696i	0.837878	+	0.545857i	$0.183796\pi$
$614$	27.0072			1.08992
$615$	−8.66236	−	15.0037i	−0.349300	−	0.605006i
$616$	−0.443252	+	1.30032i	−0.0178591	+	0.0523912i
$617$	−9.38150	+	5.41641i	−0.377685	+	0.218056i	−0.676810	−	0.736157i	$-0.736638\pi$
$617$	−9.38150	+	5.41641i	−0.377685	+	0.218056i	0.299126	+	0.954214i	$0.403305\pi$
$618$	−13.4777	−	7.78135i	−0.542153	−	0.313012i
$619$	−35.7658	−	20.6494i	−1.43755	−	0.829969i	−0.439869	−	0.898062i	$-0.644975\pi$
$619$	−35.7658	−	20.6494i	−1.43755	−	0.829969i	−0.997679	+	0.0680933i	$0.978308\pi$
$620$	−10.3058			−0.413891
$621$	−8.52091			−0.341932
$622$	20.9499	+	12.0954i	0.840015	+	0.484983i
$623$	−15.9899	+	13.9867i	−0.640623	+	0.560364i
$624$	−2.02374	+	2.98403i	−0.0810146	+	0.119457i
$625$	15.1446	+	26.2312i	0.605784	+	1.04925i
$626$	−20.6011	+	11.8941i	−0.823387	+	0.475383i
$627$	−1.20125	−	2.08063i	−0.0479735	−	0.0830925i
$628$	4.83448	−	8.37356i	0.192917	−	0.334142i
$629$			5.14298i			0.205064i
$630$	4.44780	+	5.08484i	0.177205	+	0.202585i
$631$	4.11495	−	2.37577i	0.163814	−	0.0945779i	−0.415852	−	0.909432i	$-0.636517\pi$
$631$	4.11495	−	2.37577i	0.163814	−	0.0945779i	0.579666	+	0.814854i	$0.303183\pi$
$632$	9.48251	−	5.47473i	0.377194	−	0.217773i
$633$	−7.09887			−0.282155
$634$	4.36064	+	7.55286i	0.173183	+	0.299962i
$635$		−	28.9717i		−	1.14971i
$636$	−8.25690			−0.327407
$637$	23.9750	−	7.88664i	0.949924	−	0.312480i
$638$	2.06011			0.0815605
$639$			5.16584i			0.204358i
$640$	1.27669	+	2.21130i	0.0504657	+	0.0874092i
$641$	8.01307			0.316497			0.158249	−	0.987399i	$-0.449415\pi$
$641$	8.01307			0.316497			0.158249	+	0.987399i	$0.449415\pi$
$642$	−2.37339	+	1.37028i	−0.0936703	+	0.0540806i
$643$	−41.7271	+	24.0911i	−1.64556	+	0.950062i	−0.666747	+	0.745284i	$0.732314\pi$
$643$	−41.7271	+	24.0911i	−1.64556	+	0.950062i	−0.978809	+	0.204777i	$0.934353\pi$
$644$	14.8428	+	16.9686i	0.584886	+	0.668658i
$645$			11.4803i			0.452035i
$646$	−2.00879	+	3.47933i	−0.0790348	+	0.136892i
$647$	−13.1082	−	22.7041i	−0.515337	−	0.892590i	−0.999842	−	0.0178012i	$-0.994333\pi$
$647$	−13.1082	−	22.7041i	−0.515337	−	0.892590i	0.484504	−	0.874789i	$-0.339000\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−0.363676	−	0.629906i	−0.0142755	−	0.0247260i
$650$	0.396051	−	5.46534i	0.0155344	−	0.214368i
$651$	−8.03759	+	7.03062i	−0.315018	+	0.275552i
$652$	−20.5444	−	11.8613i	−0.804583	−	0.464526i
$653$	27.1318			1.06175			0.530874	−	0.847451i	$-0.321864\pi$
$653$	27.1318			1.06175			0.530874	+	0.847451i	$0.321864\pi$
$654$	−14.2032			−0.555391
$655$	6.33399	+	3.65693i	0.247490	+	0.142888i
$656$	−5.87598	−	3.39250i	−0.229419	−	0.132455i
$657$	−10.3558	+	5.97895i	−0.404020	+	0.233261i
$658$	2.77425	−	8.13847i	0.108151	−	0.317271i
$659$	−18.6795	−	32.3538i	−0.727649	−	1.26033i	−0.957874	−	0.287188i	$-0.907279\pi$
$659$	−18.6795	−	32.3538i	−0.727649	−	1.26033i	0.230225	−	0.973137i	$-0.426054\pi$
$660$	1.32583			0.0516078
$661$	−10.8466	+	6.26227i	−0.421882	+	0.243574i	−0.695882	−	0.718156i	$-0.744987\pi$
$661$	−10.8466	+	6.26227i	−0.421882	+	0.243574i	0.274000	+	0.961730i	$0.411653\pi$
$662$	−6.00281	+	10.3972i	−0.233306	+	0.404097i
$663$	1.75722	−	2.59104i	0.0682447	−	0.100628i
$664$	−12.9984			−0.504435
$665$	20.5797	+	23.5273i	0.798047	+	0.912349i
$666$	−2.96152	+	5.12950i	−0.114756	+	0.198764i
$667$	16.9035	−	29.2777i	0.654505	−	1.13364i
$668$	−3.53346	−	2.04005i	−0.136714	−	0.0789318i
$669$			6.01269i			0.232464i
$670$	−24.3751	−	14.0730i	−0.941693	−	0.543687i
$671$			3.13528i			0.121036i
$672$	2.50425	+	0.853651i	0.0966036	+	0.0329303i
$673$	−0.488082	+	0.845383i	−0.0188142	+	0.0325871i	−0.875279	−	0.483618i	$-0.839322\pi$
$673$	−0.488082	+	0.845383i	−0.0188142	+	0.0325871i	0.856465	+	0.516205i	$0.172656\pi$
$674$			22.4347i			0.864154i
$675$	0.759893	−	1.31617i	0.0292483	−	0.0506595i
$676$	8.05526	−	10.2036i	0.309818	−	0.392445i
$677$	11.9057	+	20.6213i	0.457574	+	0.792541i	0.998832	−	0.0483154i	$-0.0153853\pi$
$677$	11.9057	+	20.6213i	0.457574	+	0.792541i	−0.541258	+	0.840856i	$0.682052\pi$
$678$	16.1066	+	9.29913i	0.618569	+	0.357131i
$679$	−37.6192	−	12.8236i	−1.44369	−	0.492126i
$680$	−1.10855	−	1.92007i	−0.0425111	−	0.0736314i
$681$	−3.12015	+	1.80142i	−0.119564	+	0.0690306i
$682$			2.09573i			0.0802497i
$683$		−	42.6064i		−	1.63029i	−0.579258	−	0.815144i	$-0.696658\pi$
$683$		−	42.6064i		−	1.63029i	0.579258	−	0.815144i	$-0.303342\pi$
$684$	−4.00705	+	2.31347i	−0.153213	+	0.0884578i
$685$	−12.5199	−	21.6851i	−0.478361	−	0.828546i
$686$	−10.2302	−	15.4384i	−0.390590	−	0.589440i
$687$	23.8424	+	13.7654i	0.909644	+	0.525183i
$688$	2.24805	+	3.89373i	0.0857061	+	0.148447i
$689$	29.6928	+	2.15172i	1.13121	+	0.0819740i
$690$	10.8786	−	18.8423i	0.414141	−	0.717313i
$691$		−	38.6569i		−	1.47058i	−0.677753	−	0.735289i	$-0.737046\pi$
$691$		−	38.6569i		−	1.47058i	0.677753	−	0.735289i	$-0.262954\pi$
$692$	6.89043	−	11.9346i	0.261935	−	0.453684i
$693$	1.03403	−	0.904480i	0.0392794	−	0.0343584i
$694$			29.2720i			1.11115i
$695$	15.4489	+	8.91942i	0.586010	+	0.338333i
$696$		−	3.96752i		−	0.150389i
$697$	5.10212	+	2.94571i	0.193257	+	0.111577i
$698$	12.7610	−	22.1028i	0.483013	−	0.836603i
$699$	−5.84917	+	10.1311i	−0.221236	+	0.383192i
$700$	−3.94471	+	0.779411i	−0.149096	+	0.0294590i
$701$	−12.0226			−0.454087			−0.227044	−	0.973885i	$-0.572906\pi$
$701$	−12.0226			−0.454087			−0.227044	+	0.973885i	$0.572906\pi$
$702$	3.24463	−	1.57238i	0.122461	−	0.0593456i
$703$	−13.7028	+	23.7339i	−0.516810	+	0.895142i
$704$	0.449678	−	0.259622i	0.0169479	−	0.00978485i
$705$	−8.29815			−0.312526
$706$	1.82840	+	3.16688i	0.0688127	+	0.119187i
$707$	−7.25659	+	21.2878i	−0.272912	+	0.800610i
$708$	−1.21312	+	0.700397i	−0.0455920	+	0.0263225i
$709$	−27.2218	−	15.7165i	−1.02233	−	0.590245i	−0.107555	−	0.994199i	$-0.534302\pi$
$709$	−27.2218	−	15.7165i	−1.02233	−	0.590245i	−0.914779	+	0.403954i	$0.867636\pi$
$710$	−11.4232	−	6.59520i	−0.428706	−	0.247513i
$711$	−10.9495			−0.410637
$712$	8.02946			0.300917
$713$	29.7839	+	17.1958i	1.11542	+	0.643986i
$714$	−2.17444	−	0.741226i	−0.0813765	−	0.0277397i
$715$	−4.76784	−	0.345507i	−0.178307	−	0.0129212i
$716$	1.92793	+	3.33928i	0.0720502	+	0.124795i
$717$	−14.2281	+	8.21461i	−0.531359	+	0.306780i
$718$	−17.1999	−	29.7911i	−0.641894	−	1.11179i
$719$	−25.6676	+	44.4577i	−0.957241	+	1.65799i	−0.228088	+	0.973641i	$0.573247\pi$
$719$	−25.6676	+	44.4577i	−0.957241	+	1.65799i	−0.729154	+	0.684350i	$0.760086\pi$
$720$		−	2.55339i		−	0.0951591i
$721$	13.2851	−	38.9729i	0.494764	−	1.45143i
$722$	−2.08593	+	1.20431i	−0.0776303	+	0.0448199i
$723$	12.4413	−	7.18297i	0.462696	−	0.267138i
$724$	3.18446			0.118349
$725$	3.01490	+	5.22195i	0.111970	+	0.193938i
$726$			10.7304i			0.398242i
$727$	−10.6652			−0.395549			−0.197774	−	0.980248i	$-0.563371\pi$
$727$	−10.6652			−0.395549			−0.197774	+	0.980248i	$0.563371\pi$
$728$	−8.78314	−	3.72243i	−0.325525	−	0.137963i
$729$	1.00000			0.0370370
$730$		−	30.5331i		−	1.13008i
$731$	−1.95198	−	3.38093i	−0.0721967	−	0.125048i
$732$	6.03817			0.223177
$733$	−1.58513	+	0.915174i	−0.0585481	+	0.0338027i	−0.528988	−	0.848629i	$-0.677428\pi$
$733$	−1.58513	+	0.915174i	−0.0585481	+	0.0338027i	0.470440	+	0.882432i	$0.344095\pi$
$734$	5.53566	−	3.19602i	0.204325	−	0.117967i
$735$	−10.9170	+	14.1523i	−0.402681	+	0.522016i
$736$		−	8.52091i		−	0.314085i
$737$	−2.86181	+	4.95679i	−0.105416	+	0.182586i
$738$	3.39250	+	5.87598i	0.124880	+	0.216298i
$739$	−38.8381	+	22.4232i	−1.42868	+	0.824849i	−0.997017	−	0.0771851i	$-0.975407\pi$
$739$	−38.8381	+	22.4232i	−1.42868	+	0.824849i	−0.431664	+	0.902034i	$0.642073\pi$
$740$	−7.56190	−	13.0976i	−0.277981	−	0.481477i
$741$	15.0127	−	7.27530i	0.551506	−	0.267265i
$742$	−4.23449	−	21.4314i	−0.155453	−	0.786770i
$743$	31.7298	+	18.3192i	1.16405	+	0.672066i	0.952272	−	0.305251i	$-0.0987405\pi$
$743$	31.7298	+	18.3192i	1.16405	+	0.672066i	0.211781	+	0.977317i	$0.432074\pi$
$744$	4.03613			0.147972
$745$	−1.61717			−0.0592487
$746$	−15.7822	−	9.11185i	−0.577827	−	0.333609i
$747$	11.2569	+	6.49919i	0.411870	+	0.237793i
$748$	−0.390455	+	0.225430i	−0.0142765	+	0.00824252i
$749$	−4.77383	−	5.45757i	−0.174432	−	0.199415i
$750$	−4.44317	−	7.69579i	−0.162242	−	0.281011i
$751$	37.6469			1.37375			0.686877	−	0.726774i	$-0.258981\pi$
$751$	37.6469			1.37375			0.686877	+	0.726774i	$0.258981\pi$
$752$	−2.81446	+	1.62493i	−0.102633	+	0.0592551i
$753$	−9.52013	+	16.4893i	−0.346933	+	0.600905i
$754$	−1.03392	+	14.2677i	−0.0376533	+	0.519599i
$755$	10.1258			0.368516
$756$	−1.74192	−	1.99141i	−0.0633530	−	0.0724269i
$757$	−0.733508	+	1.27047i	−0.0266598	+	0.0461761i	−0.879047	−	0.476734i	$-0.841820\pi$
$757$	−0.733508	+	1.27047i	−0.0266598	+	0.0461761i	0.852388	+	0.522910i	$0.175154\pi$
$758$	3.86440	−	6.69334i	0.140361	−	0.243113i
$759$	−3.83166	−	2.21221i	−0.139081	−	0.0802982i
$760$		−	11.8144i		−	0.428553i
$761$	−12.5091	−	7.22215i	−0.453455	−	0.261803i	0.255833	−	0.966721i	$-0.417650\pi$
$761$	−12.5091	−	7.22215i	−0.453455	−	0.261803i	−0.709288	+	0.704918i	$0.750984\pi$
$762$			11.3464i			0.411035i
$763$	−7.28403	−	36.8655i	−0.263699	−	1.33462i
$764$	6.70696	−	11.6168i	0.242649	−	0.420281i
$765$			2.21711i			0.0801597i
$766$	−4.90993	+	8.50425i	−0.177403	+	0.307271i
$767$	4.54506	−	2.20258i	0.164113	−	0.0795304i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−36.5814	−	21.1203i	−1.31916	−	0.761617i	−0.335566	−	0.942017i	$-0.608928\pi$
$769$	−36.5814	−	21.1203i	−1.31916	−	0.761617i	−0.983593	+	0.180400i	$0.942261\pi$
$770$	0.679942	+	3.44128i	0.0245034	+	0.124015i
$771$	−11.6666	−	20.2071i	−0.420162	−	0.727742i
$772$	−5.18745	+	2.99498i	−0.186700	+	0.107792i
$773$			6.87947i			0.247437i	0.992317	+	0.123719i	$0.0394821\pi$
$773$			6.87947i			0.247437i	−0.992317	+	0.123719i	$0.960518\pi$
$774$		−	4.49610i		−	0.161609i
$775$	−5.31225	+	3.06703i	−0.190822	+	0.110171i
$776$	7.51106	+	13.0095i	0.269631	+	0.467015i
$777$	−14.8328	−	5.05621i	−0.532123	−	0.181390i
$778$	8.14562	+	4.70287i	0.292035	+	0.168606i
$779$	15.6969	+	27.1878i	0.562400	+	0.974106i
$780$	−0.665404	+	9.18229i	−0.0238253	+	0.328779i
$781$	−1.34116	+	2.32296i	−0.0479906	+	0.0831222i
$782$			7.39871i			0.264577i
$783$	−1.98376	+	3.43598i	−0.0708939	+	0.122792i
$784$	−0.931425	+	6.93776i	−0.0332652	+	0.247777i
$785$		−	24.6886i		−	0.881174i
$786$	−2.48062	−	1.43219i	−0.0884809	−	0.0510845i
$787$			30.4132i			1.08411i	0.840342	+	0.542057i	$0.182354\pi$
$787$			30.4132i			1.08411i	−0.840342	+	0.542057i	$0.817646\pi$
$788$	3.78655	+	2.18617i	0.134890	+	0.0778790i
$789$	−10.3167	+	17.8690i	−0.367283	+	0.636152i
$790$	13.9791	−	24.2125i	0.497354	−	0.861442i
$791$	−15.8764	+	46.5747i	−0.564501	+	1.65601i
$792$	−0.519243			−0.0184505
$793$	−21.7140	−	1.57353i	−0.771087	−	0.0558776i
$794$	−5.77112	+	9.99586i	−0.204809	+	0.354740i
$795$	−18.2585	+	10.5415i	−0.647561	+	0.373870i
$796$	−9.69511			−0.343634
$797$	8.31093	+	14.3949i	0.294388	+	0.509895i	0.974842	−	0.222895i	$-0.0715508\pi$
$797$	8.31093	+	14.3949i	0.294388	+	0.509895i	−0.680454	+	0.732791i	$0.738218\pi$
$798$	−8.05977	−	9.21414i	−0.285313	−	0.326177i
$799$	2.44380	−	1.41093i	0.0864554	−	0.0499150i
$800$	1.31617	+	0.759893i	0.0465338	+	0.0268663i
$801$	−6.95371	−	4.01473i	−0.245697	−	0.141853i
$802$	33.5631			1.18515
$803$	−6.20905			−0.219113
$804$	9.54619	+	5.51150i	0.336668	+	0.194376i
$805$	54.4855	+	18.5730i	1.92036	+	0.654614i
$806$	−14.5144	−	1.05180i	−0.511248	−	0.0370481i
$807$	4.37116	+	7.57108i	0.153872	+	0.266515i
$808$	7.36178	−	4.25033i	0.258987	−	0.149526i
$809$	−16.9058	−	29.2817i	−0.594376	−	1.02949i	−0.993635	−	0.112652i	$-0.964066\pi$
$809$	−16.9058	−	29.2817i	−0.594376	−	1.02949i	0.399258	−	0.916839i	$-0.369268\pi$
$810$	−1.27669	+	2.21130i	−0.0448584	+	0.0776971i
$811$			34.4041i			1.20809i	0.796950	+	0.604045i	$0.206445\pi$
$811$			34.4041i			1.20809i	−0.796950	+	0.604045i	$0.793555\pi$
$812$	10.2980	−	2.03472i	0.361389	−	0.0714045i
$813$	8.76510	−	5.06054i	0.307406	−	0.177481i
$814$	−2.66346	+	1.53775i	−0.0933541	+	0.0538980i
$815$	−60.5732			−2.12179
$816$	0.434150	+	0.751971i	0.0151983	+	0.0263242i
$817$		−	20.8032i		−	0.727812i
$818$	−18.3070			−0.640088
$819$	5.74520	+	7.61529i	0.200754	+	0.266100i
$820$	−17.3247			−0.605006
$821$			15.2913i			0.533671i	0.963742	+	0.266836i	$0.0859781\pi$
$821$			15.2913i			0.533671i	−0.963742	+	0.266836i	$0.914022\pi$
$822$	4.90326	+	8.49269i	0.171021	+	0.296216i
$823$	−14.2969			−0.498360			−0.249180	−	0.968457i	$-0.580161\pi$
$823$	−14.2969			−0.498360			−0.249180	+	0.968457i	$0.580161\pi$
$824$	−13.4777	+	7.78135i	−0.469518	+	0.271076i
$825$	0.683414	−	0.394569i	0.0237934	−	0.0137371i
$826$	−2.44007	−	2.78955i	−0.0849010	−	0.0970610i
$827$		−	40.6945i		−	1.41509i	−0.706670	−	0.707543i	$-0.749804\pi$
$827$		−	40.6945i		−	1.41509i	0.706670	−	0.707543i	$-0.250196\pi$
$828$	−4.26046	+	7.37933i	−0.148061	+	0.256449i
$829$	−15.9598	−	27.6432i	−0.554306	−	0.960087i	−0.997957	−	0.0638871i	$-0.979650\pi$
$829$	−15.9598	−	27.6432i	−0.554306	−	0.960087i	0.443651	−	0.896200i	$-0.353683\pi$
$830$	−28.7433	+	16.5950i	−0.997695	+	0.576019i
$831$	2.48866	+	4.31049i	0.0863308	+	0.149529i
$832$	1.57238	+	3.24463i	0.0545124	+	0.112487i
$833$	0.808757	−	6.02406i	0.0280218	−	0.208721i
$834$	−6.05035	−	3.49317i	−0.209507	−	0.120959i
$835$	−10.4181			−0.360532
$836$	−2.40251			−0.0830925
$837$	−3.49539	−	2.01806i	−0.120818	−	0.0697545i
$838$	−14.0824	−	8.13046i	−0.486468	−	0.280862i
$839$	13.8203	−	7.97917i	0.477131	−	0.275471i	−0.242089	−	0.970254i	$-0.577833\pi$
$839$	13.8203	−	7.97917i	0.477131	−	0.275471i	0.719220	+	0.694782i	$0.244499\pi$
$840$	6.62750	−	1.30949i	0.228670	−	0.0451816i
$841$	6.62937	+	11.4824i	0.228599	+	0.395945i
$842$	−20.7347			−0.714565
$843$	−23.6190	+	13.6364i	−0.813481	+	0.469664i
$844$	−3.54943	+	6.14780i	−0.122177	+	0.211616i
$845$	4.78575	−	32.8472i	0.164635	−	1.12998i
$846$	3.24986			0.111732
$847$	−27.8515	+	5.50300i	−0.956988	+	0.189085i
$848$	−4.12845	+	7.15068i	−0.141772	+	0.245555i
$849$	4.90256	−	8.49149i	0.168256	−	0.291427i
$850$	−1.14283	−	0.659816i	−0.0391989	−	0.0226315i
$851$			50.4697i			1.73008i
$852$	4.47375	+	2.58292i	0.153268	+	0.0884894i
$853$			21.8333i			0.747559i	0.927518	+	0.373779i	$0.121938\pi$
$853$			21.8333i			0.747559i	−0.927518	+	0.373779i	$0.878062\pi$
$854$	3.09663	+	15.6725i	0.105965	+	0.536302i
$855$	−5.90719	+	10.2316i	−0.202022	+	0.349912i
$856$			2.74056i			0.0936703i
$857$	−27.3267	+	47.3312i	−0.933461	+	1.61680i	−0.156106	+	0.987740i	$0.549894\pi$
$857$	−27.3267	+	47.3312i	−0.933461	+	1.61680i	−0.777355	+	0.629062i	$0.783439\pi$
$858$	1.86726	+	0.135313i	0.0637472	+	0.00461951i
$859$	−19.0946	−	33.0728i	−0.651500	−	1.12843i	−0.982759	−	0.184891i	$-0.940807\pi$
$859$	−19.0946	−	33.0728i	−0.651500	−	1.12843i	0.331259	−	0.943540i	$-0.392527\pi$
$860$	9.94221	+	5.74014i	0.339027	+	0.195737i
$861$	−13.5117	+	11.8189i	−0.460478	+	0.402788i
$862$	−13.5573	−	23.4819i	−0.461762	−	0.799796i
$863$	−5.85315	+	3.37932i	−0.199244	+	0.115033i	−0.596303	−	0.802760i	$-0.703364\pi$
$863$	−5.85315	+	3.37932i	−0.199244	+	0.115033i	0.397059	+	0.917793i	$0.370031\pi$
$864$			1.00000i			0.0340207i
$865$		−	35.1878i		−	1.19642i
$866$	−17.0242	+	9.82893i	−0.578506	+	0.334001i
$867$	8.12303	+	14.0695i	0.275872	+	0.477825i
$868$	2.06990	+	10.4761i	0.0702570	+	0.355581i
$869$	−4.92372	−	2.84271i	−0.167026	−	0.0964325i
$870$	−5.06531	−	8.77338i	−0.171730	−	0.297445i
$871$	−32.8930	−	22.3077i	−1.11454	−	0.755868i
$872$	−7.10162	+	12.3004i	−0.240491	+	0.416543i
$873$		−	15.0221i		−	0.508421i
$874$	−19.7129	+	34.1437i	−0.666799	+	1.15493i
$875$	17.6963	−	15.4793i	0.598245	−	0.523295i
$876$			11.9579i			0.404020i
$877$	16.7929	+	9.69540i	0.567057	+	0.327390i	0.755973	−	0.654603i	$-0.227164\pi$
$877$	16.7929	+	9.69540i	0.567057	+	0.327390i	−0.188916	+	0.981993i	$0.560497\pi$
$878$		−	17.5185i		−	0.591220i
$879$	−24.3101	−	14.0354i	−0.819959	−	0.473404i
$880$	0.662914	−	1.14820i	0.0223468	−	0.0387059i
$881$	28.6313	−	49.5909i	0.964615	−	1.67076i	0.253968	−	0.967213i	$-0.418264\pi$
$881$	28.6313	−	49.5909i	0.964615	−	1.67076i	0.710647	−	0.703549i	$-0.248402\pi$
$882$	4.27552	−	5.54256i	0.143964	−	0.186628i
$883$	27.5353			0.926637			0.463318	−	0.886192i	$-0.346659\pi$
$883$	27.5353			0.926637			0.463318	+	0.886192i	$0.346659\pi$
$884$	−1.36530	−	2.81732i	−0.0459199	−	0.0947566i
$885$	−1.78838	+	3.09757i	−0.0601159	+	0.104124i
$886$	29.5250	−	17.0463i	0.991913	−	0.572681i
$887$	6.32268			0.212295			0.106147	−	0.994350i	$-0.466148\pi$
$887$	6.32268			0.212295			0.106147	+	0.994350i	$0.466148\pi$
$888$	2.96152	+	5.12950i	0.0993820	+	0.172135i
$889$	−29.4503	+	5.81890i	−0.987731	+	0.195160i
$890$	17.7555	−	10.2512i	0.595166	−	0.343620i
$891$	0.449678	+	0.259622i	0.0150648	+	0.00869765i
$892$	5.20714	+	3.00634i	0.174348	+	0.100660i
$893$	15.0369			0.503192
$894$	0.633345			0.0211822
$895$	8.52647	+	4.92276i	0.285008	+	0.164550i
$896$	1.99141	−	1.74192i	0.0665283	−	0.0581935i
$897$	17.2441	−	25.4267i	0.575765	−	0.848973i
$898$	14.1006	+	24.4229i	0.470542	+	0.815003i
$899$	13.8680	−	8.00672i	0.462525	−	0.267039i
$900$	−0.759893	−	1.31617i	−0.0253298	−	0.0438725i
$901$	3.58474	−	6.20894i	0.119425	−	0.206850i
$902$			3.52306i			0.117305i
$903$	11.6699	−	2.30579i	0.388351	−	0.0767319i
$904$	16.1066	−	9.29913i	0.535696	−	0.309284i
$905$	7.04179	−	4.06558i	0.234077	−	0.135144i
$906$	−3.96564			−0.131750
$907$	21.5270	+	37.2859i	0.714793	+	1.23806i	0.963039	+	0.269360i	$0.0868122\pi$
$907$	21.5270	+	37.2859i	0.714793	+	1.23806i	−0.248247	+	0.968697i	$0.579854\pi$
$908$			3.60284i			0.119564i
$909$	−8.50066			−0.281949
$910$	−24.1745	+	2.98197i	−0.801378	+	0.0988512i
$911$	21.4332			0.710114			0.355057	−	0.934845i	$-0.384461\pi$
$911$	21.4332			0.710114			0.355057	+	0.934845i	$0.384461\pi$
$912$			4.62695i			0.153213i
$913$	3.37466	+	5.84508i	0.111685	+	0.193444i
$914$	22.8685			0.756422
$915$	13.3522	−	7.70889i	0.441410	−	0.254848i
$916$	23.8424	−	13.7654i	0.787775	−	0.454822i
$917$	2.44518	−	7.17313i	0.0807469	−	0.236877i
$918$		−	0.868301i		−	0.0286582i
$919$	22.9191	−	39.6970i	0.756030	−	1.30948i	−0.188831	−	0.982010i	$-0.560470\pi$
$919$	22.9191	−	39.6970i	0.756030	−	1.30948i	0.944861	−	0.327473i	$-0.106197\pi$
$920$	−10.8786	−	18.8423i	−0.358657	−	0.621212i
$921$	−23.3890	+	13.5036i	−0.770693	+	0.444960i
$922$	−12.0448	−	20.8622i	−0.396674	−	0.687059i
$923$	−15.4151	−	10.4543i	−0.507393	−	0.344109i
$924$	−0.266290	−	1.34773i	−0.00876030	−	0.0443371i
$925$	−7.79574	−	4.50088i	−0.256322	−	0.147988i
$926$	12.2189			0.401538
$927$	15.5627			0.511146
$928$	−3.43598	−	1.98376i	−0.112791	−	0.0651202i
$929$	−16.4490	−	9.49685i	−0.539675	−	0.311581i	0.205272	−	0.978705i	$-0.434192\pi$
$929$	−16.4490	−	9.49685i	−0.539675	−	0.311581i	−0.744947	+	0.667123i	$0.767525\pi$
$930$	8.92509	−	5.15290i	0.292665	−	0.168970i
$931$	19.7826	−	25.6451i	0.648348	−	0.840485i
$932$	5.84917	+	10.1311i	0.191596	+	0.331854i
$933$	−24.1909			−0.791973
$934$	13.0167	−	7.51520i	0.425920	−	0.245905i
$935$	−0.575609	+	0.996984i	−0.0188244	+	0.0326049i
$936$	0.260597	−	3.59612i	0.00851787	−	0.117543i
$937$	30.7500			1.00456			0.502280	−	0.864705i	$-0.332495\pi$
$937$	30.7500			1.00456			0.502280	+	0.864705i	$0.332495\pi$
$938$	−9.40979	+	27.6044i	−0.307241	+	0.901314i
$939$	11.8941	−	20.6011i	0.388148	−	0.672293i
$940$	−4.14908	+	7.18641i	−0.135328	+	0.234395i
$941$	−19.1978	−	11.0838i	−0.625830	−	0.361323i	0.153305	−	0.988179i	$-0.451008\pi$
$941$	−19.1978	−	11.0838i	−0.625830	−	0.361323i	−0.779135	+	0.626856i	$0.784341\pi$
$942$			9.66896i			0.315032i
$943$	50.0687	+	28.9072i	1.63046	+	0.941348i
$944$			1.40079i			0.0455920i
$945$	−6.39433	−	2.17970i	−0.208007	−	0.0709057i
$946$	1.16728	−	2.02179i	0.0379517	−	0.0657342i
$947$		−	42.2814i		−	1.37396i	−0.726676	−	0.686981i	$-0.758936\pi$
$947$		−	42.2814i		−	1.37396i	0.726676	−	0.686981i	$-0.241064\pi$
$948$	−5.47473	+	9.48251i	−0.177811	+	0.307977i
$949$	3.11619	−	43.0020i	0.101156	−	1.39591i
$950$	−3.51598	−	6.08986i	−0.114074	−	0.197581i
$951$	−7.55286	−	4.36064i	−0.244918	−	0.141404i
$952$	−1.72914	+	1.51251i	−0.0560418	+	0.0490208i
$953$	11.3076	+	19.5853i	0.366289	+	0.634431i	0.988982	−	0.148035i	$-0.0472948\pi$
$953$	11.3076	+	19.5853i	0.366289	+	0.634431i	−0.622693	+	0.782466i	$0.713961\pi$
$954$	7.15068	−	4.12845i	0.231512	−	0.133663i
$955$		−	34.2509i		−	1.10833i
$956$			16.4292i			0.531359i
$957$	−1.78411	+	1.03005i	−0.0576720	+	0.0332969i
$958$	−0.453153	−	0.784884i	−0.0146407	−	0.0253585i
$959$	−19.5288	+	17.0822i	−0.630617	+	0.551612i
$960$	−2.21130	−	1.27669i	−0.0713693	−	0.0412051i
$961$	−7.35483	−	12.7389i	−0.237253	−	0.410934i
$962$	−9.31325	−	19.2181i	−0.300271	−	0.619615i
$963$	1.37028	−	2.37339i	0.0441566	−	0.0764814i
$964$		−	14.3659i		−	0.462696i
$965$	−7.64733	+	13.2456i	−0.246176	+	0.426390i
$966$	−21.3385	−	7.27389i	−0.686555	−	0.234033i
$967$		−	24.8036i		−	0.797629i	−0.917032	−	0.398815i	$-0.869422\pi$
$967$		−	24.8036i		−	0.797629i	0.917032	−	0.398815i	$-0.130578\pi$
$968$	9.29279	+	5.36519i	0.298682	+	0.172444i
$969$		−	4.01758i		−	0.129063i
$970$	33.2184	+	19.1786i	1.06658	+	0.615789i
$971$	−20.7015	+	35.8560i	−0.664342	+	1.15067i	0.315121	+	0.949051i	$0.397955\pi$
$971$	−20.7015	+	35.8560i	−0.664342	+	1.15067i	−0.979463	+	0.201623i	$0.935379\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	5.96390	−	17.4956i	0.191194	−	0.560882i
$974$	−28.7559			−0.921398
$975$	2.38968	+	4.93115i	0.0765309	+	0.157923i
$976$	3.01909	−	5.22921i	0.0966386	−	0.167383i
$977$	16.7244	−	9.65585i	0.535062	−	0.308918i	−0.208013	−	0.978126i	$-0.566700\pi$
$977$	16.7244	−	9.65585i	0.535062	−	0.308918i	0.743075	+	0.669208i	$0.233366\pi$
$978$	23.7227			0.758568
$979$	−2.08462	−	3.61067i	−0.0666247	−	0.115397i
$980$	6.79773	+	16.5306i	0.217146	+	0.528050i
$981$	12.3004	−	7.10162i	0.392720	−	0.226737i
$982$	−24.0099	−	13.8621i	−0.766187	−	0.442358i
$983$	9.97803	+	5.76082i	0.318250	+	0.183742i	0.650612	−	0.759410i	$-0.274512\pi$
$983$	9.97803	+	5.76082i	0.318250	+	0.183742i	−0.332362	+	0.943152i	$0.607846\pi$
$984$	6.78500			0.216298
$985$	11.1643			0.355723
$986$	2.98346	+	1.72250i	0.0950128	+	0.0548557i
$987$	1.66667	+	8.43524i	0.0530506	+	0.268497i
$988$	1.20577	−	16.6391i	0.0383605	−	0.529359i
$989$	−19.1554	−	33.1782i	−0.609107	−	1.05500i
$990$	−1.14820	+	0.662914i	−0.0364922	+	0.0210688i
$991$	5.63816	+	9.76558i	0.179102	+	0.310214i	0.941573	−	0.336808i	$-0.109347\pi$
$991$	5.63816	+	9.76558i	0.179102	+	0.310214i	−0.762471	+	0.647022i	$0.776014\pi$
$992$	2.01806	−	3.49539i	0.0640736	−	0.110979i
$993$		−	12.0056i		−	0.380987i
$994$	−4.40983	+	12.9366i	−0.139871	+	0.410323i
$995$	−21.4388	+	12.3777i	−0.679655	+	0.392399i
$996$	11.2569	−	6.49919i	0.356689	−	0.205935i
$997$	−21.3658			−0.676663			−0.338332	−	0.941027i	$-0.609863\pi$
$997$	−21.3658			−0.676663			−0.338332	+	0.941027i	$0.609863\pi$
$998$	2.02249	+	3.50306i	0.0640209	+	0.110887i
$999$		−	5.92304i		−	0.187397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.277.6	yes	20
3.2	odd	2		1638.2.dt.b.1369.5		20
7.2	even	3		546.2.bd.b.121.10	✓	20
13.10	even	6		546.2.bd.b.361.10	yes	20
21.2	odd	6		1638.2.cr.b.667.1		20
39.23	odd	6		1638.2.cr.b.361.1		20
91.23	even	6	inner	546.2.bm.b.205.1	yes	20
273.23	odd	6		1638.2.dt.b.1297.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.10	✓	20	7.2	even	3
546.2.bd.b.361.10	yes	20	13.10	even	6
546.2.bm.b.205.1	yes	20	91.23	even	6	inner
546.2.bm.b.277.6	yes	20	1.1	even	1	trivial
1638.2.cr.b.361.1		20	39.23	odd	6
1638.2.cr.b.667.1		20	21.2	odd	6
1638.2.dt.b.1297.10		20	273.23	odd	6
1638.2.dt.b.1369.5		20	3.2	odd	2

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.21130 + 1.27669i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.74192 + 1.99141i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.21130 + 1.27669i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.74192 + 1.99141i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.27669 - 2.21130i) q^{10} +(-0.449678 + 0.259622i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.57238 - 3.24463i) q^{13} +(-1.99141 + 1.74192i) q^{14} +(2.21130 + 1.27669i) q^{15} +1.00000 q^{16} -0.868301 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.00705 - 2.31347i) q^{19} +(2.21130 - 1.27669i) q^{20} +(0.853651 - 2.50425i) q^{21} +(-0.259622 - 0.449678i) q^{22} -8.52091 q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.759893 - 1.31617i) q^{25} +(3.24463 - 1.57238i) q^{26} +1.00000 q^{27} +(-1.74192 - 1.99141i) q^{28} +(-1.98376 + 3.43598i) q^{29} +(-1.27669 + 2.21130i) q^{30} +(-3.49539 - 2.01806i) q^{31} +1.00000i q^{32} +(0.449678 + 0.259622i) q^{33} -0.868301i q^{34} +(-6.39433 - 2.17970i) q^{35} +(0.500000 - 0.866025i) q^{36} -5.92304i q^{37} +(2.31347 - 4.00705i) q^{38} +(-2.02374 + 2.98403i) q^{39} +(1.27669 + 2.21130i) q^{40} +(-5.87598 - 3.39250i) q^{41} +(2.50425 + 0.853651i) q^{42} +(2.24805 + 3.89373i) q^{43} +(0.449678 - 0.259622i) q^{44} -2.55339i q^{45} -8.52091i q^{46} +(-2.81446 + 1.62493i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.931425 + 6.93776i) q^{49} +(1.31617 + 0.759893i) q^{50} +(0.434150 + 0.751971i) q^{51} +(1.57238 + 3.24463i) q^{52} +(-4.12845 + 7.15068i) q^{53} +1.00000i q^{54} +(0.662914 - 1.14820i) q^{55} +(1.99141 - 1.74192i) q^{56} +4.62695i q^{57} +(-3.43598 - 1.98376i) q^{58} +1.40079i q^{59} +(-2.21130 - 1.27669i) q^{60} +(3.01909 - 5.22921i) q^{61} +(2.01806 - 3.49539i) q^{62} +(-2.59557 + 0.512843i) q^{63} -1.00000 q^{64} +(7.61939 + 5.16740i) q^{65} +(-0.259622 + 0.449678i) q^{66} +(9.54619 - 5.51150i) q^{67} +0.868301 q^{68} +(4.26046 + 7.37933i) q^{69} +(2.17970 - 6.39433i) q^{70} +(4.47375 - 2.58292i) q^{71} +(0.866025 + 0.500000i) q^{72} +(10.3558 + 5.97895i) q^{73} +5.92304 q^{74} -1.51979 q^{75} +(4.00705 + 2.31347i) q^{76} +(-1.30032 - 0.443252i) q^{77} +(-2.98403 - 2.02374i) q^{78} +(5.47473 + 9.48251i) q^{79} +(-2.21130 + 1.27669i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.39250 - 5.87598i) q^{82} -12.9984i q^{83} +(-0.853651 + 2.50425i) q^{84} +(1.92007 - 1.10855i) q^{85} +(-3.89373 + 2.24805i) q^{86} +3.96752 q^{87} +(0.259622 + 0.449678i) q^{88} +8.02946i q^{89} +2.55339 q^{90} +(3.72243 - 8.78314i) q^{91} +8.52091 q^{92} +4.03613i q^{93} +(-1.62493 - 2.81446i) q^{94} +11.8144 q^{95} +(0.866025 - 0.500000i) q^{96} +(-13.0095 + 7.51106i) q^{97} +(-6.93776 - 0.931425i) q^{98} -0.519243i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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