LMFDB - Embedded newform 1122.2.b.a.1055.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(1055,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1122.1055");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.b (of order $2$, degree $1$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 18x^{14} + 124x^{12} + 420x^{10} + 746x^{8} + 681x^{6} + 288x^{4} + 42x^{2} + 1 $ x^16 + 18x^14 + 124x^12 + 420x^10 + 746x^8 + 681x^6 + 288x^4 + 42*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1055.5
Root			$0.886946i$ of defining polynomial
Character	$\chi$	$=$	1122.1055
Dual form			1122.2.b.a.1055.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.423385 - 1.67951i) q^{3} +1.00000 q^{4} +4.07146i q^{5} +(0.423385 + 1.67951i) q^{6} +4.79476i q^{7} -1.00000 q^{8} +(-2.64149 + 1.42216i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.423385 - 1.67951i) q^{3} +1.00000 q^{4} +4.07146i q^{5} +(0.423385 + 1.67951i) q^{6} +4.79476i q^{7} -1.00000 q^{8} +(-2.64149 + 1.42216i) q^{9} -4.07146i q^{10} +(2.78151 - 1.80643i) q^{11} +(-0.423385 - 1.67951i) q^{12} +2.57431i q^{13} -4.79476i q^{14} +(6.83805 - 1.72380i) q^{15} +1.00000 q^{16} +1.00000 q^{17} +(2.64149 - 1.42216i) q^{18} +4.54838i q^{19} +4.07146i q^{20} +(8.05283 - 2.03003i) q^{21} +(-2.78151 + 1.80643i) q^{22} -5.62472i q^{23} +(0.423385 + 1.67951i) q^{24} -11.5768 q^{25} -2.57431i q^{26} +(3.50689 + 3.83428i) q^{27} +4.79476i q^{28} -7.91832 q^{29} +(-6.83805 + 1.72380i) q^{30} -0.355300 q^{31} -1.00000 q^{32} +(-4.21157 - 3.90675i) q^{33} -1.00000 q^{34} -19.5217 q^{35} +(-2.64149 + 1.42216i) q^{36} +5.35573 q^{37} -4.54838i q^{38} +(4.32358 - 1.08993i) q^{39} -4.07146i q^{40} -1.52886 q^{41} +(-8.05283 + 2.03003i) q^{42} +4.45168i q^{43} +(2.78151 - 1.80643i) q^{44} +(-5.79026 - 10.7547i) q^{45} +5.62472i q^{46} -9.23503i q^{47} +(-0.423385 - 1.67951i) q^{48} -15.9897 q^{49} +11.5768 q^{50} +(-0.423385 - 1.67951i) q^{51} +2.57431i q^{52} -9.72335i q^{53} +(-3.50689 - 3.83428i) q^{54} +(7.35482 + 11.3248i) q^{55} -4.79476i q^{56} +(7.63903 - 1.92571i) q^{57} +7.91832 q^{58} +11.6299i q^{59} +(6.83805 - 1.72380i) q^{60} -4.09863i q^{61} +0.355300 q^{62} +(-6.81889 - 12.6653i) q^{63} +1.00000 q^{64} -10.4812 q^{65} +(4.21157 + 3.90675i) q^{66} -5.11830 q^{67} +1.00000 q^{68} +(-9.44676 + 2.38142i) q^{69} +19.5217 q^{70} +7.91292i q^{71} +(2.64149 - 1.42216i) q^{72} +4.26429i q^{73} -5.35573 q^{74} +(4.90144 + 19.4433i) q^{75} +4.54838i q^{76} +(8.66141 + 13.3367i) q^{77} +(-4.32358 + 1.08993i) q^{78} -9.05706i q^{79} +4.07146i q^{80} +(4.95494 - 7.51323i) q^{81} +1.52886 q^{82} +7.26631 q^{83} +(8.05283 - 2.03003i) q^{84} +4.07146i q^{85} -4.45168i q^{86} +(3.35250 + 13.2989i) q^{87} +(-2.78151 + 1.80643i) q^{88} +12.2301i q^{89} +(5.79026 + 10.7547i) q^{90} -12.3432 q^{91} -5.62472i q^{92} +(0.150429 + 0.596728i) q^{93} +9.23503i q^{94} -18.5185 q^{95} +(0.423385 + 1.67951i) q^{96} +0.0605836 q^{97} +15.9897 q^{98} +(-4.77830 + 8.72742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9	$ 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9} + 6 q^{11} + q^{12} + 16 q^{16} + 16 q^{17} + 3 q^{18} + 24 q^{21} - 6 q^{22} - q^{24} - 22 q^{25} + 13 q^{27} - 20 q^{29} + 24 q^{31} - 16 q^{32} - 3 q^{33} - 16 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - q^{39} + 22 q^{41} - 24 q^{42} + 6 q^{44} - 15 q^{45} + q^{48} - 54 q^{49} + 22 q^{50} + q^{51} - 13 q^{54} - 10 q^{55} + 8 q^{57} + 20 q^{58} - 24 q^{62} - 36 q^{63} + 16 q^{64} - 68 q^{65} + 3 q^{66} + 12 q^{67} + 16 q^{68} - 40 q^{69} - 12 q^{70} + 3 q^{72} - 6 q^{74} + q^{75} + 10 q^{77} + q^{78} + 17 q^{81} - 22 q^{82} - 10 q^{83} + 24 q^{84} + 12 q^{87} - 6 q^{88} + 15 q^{90} + 4 q^{91} + 6 q^{93} - 48 q^{95} - q^{96} + 54 q^{98} + 31 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9 + 6 * q^11 + q^12 + 16 * q^16 + 16 * q^17 + 3 * q^18 + 24 * q^21 - 6 * q^22 - q^24 - 22 * q^25 + 13 * q^27 - 20 * q^29 + 24 * q^31 - 16 * q^32 - 3 * q^33 - 16 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - q^39 + 22 * q^41 - 24 * q^42 + 6 * q^44 - 15 * q^45 + q^48 - 54 * q^49 + 22 * q^50 + q^51 - 13 * q^54 - 10 * q^55 + 8 * q^57 + 20 * q^58 - 24 * q^62 - 36 * q^63 + 16 * q^64 - 68 * q^65 + 3 * q^66 + 12 * q^67 + 16 * q^68 - 40 * q^69 - 12 * q^70 + 3 * q^72 - 6 * q^74 + q^75 + 10 * q^77 + q^78 + 17 * q^81 - 22 * q^82 - 10 * q^83 + 24 * q^84 + 12 * q^87 - 6 * q^88 + 15 * q^90 + 4 * q^91 + 6 * q^93 - 48 * q^95 - q^96 + 54 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.423385	−	1.67951i	−0.244441	−	0.969664i
$3$	−0.423385	−	1.67951i	−0.244441	−	0.969664i
$4$	1.00000			0.500000
$5$			4.07146i			1.82081i	0.413715	+	0.910407i	$0.364231\pi$
$5$			4.07146i			1.82081i	−0.413715	+	0.910407i	$0.635769\pi$
$6$	0.423385	+	1.67951i	0.172846	+	0.685656i
$7$			4.79476i			1.81225i	0.423013	+	0.906124i	$0.360973\pi$
$7$			4.79476i			1.81225i	−0.423013	+	0.906124i	$0.639027\pi$
$8$	−1.00000			−0.353553
$9$	−2.64149	+	1.42216i	−0.880497	+	0.474052i
$10$		−	4.07146i		−	1.28751i
$11$	2.78151	−	1.80643i	0.838657	−	0.544660i
$11$	2.78151	−	1.80643i	0.838657	−	0.544660i
$12$	−0.423385	−	1.67951i	−0.122221	−	0.484832i
$13$			2.57431i			0.713986i	0.934107	+	0.356993i	$0.116198\pi$
$13$			2.57431i			0.713986i	−0.934107	+	0.356993i	$0.883802\pi$
$14$		−	4.79476i		−	1.28145i
$15$	6.83805	−	1.72380i	1.76558	−	0.445082i
$16$	1.00000			0.250000
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	2.64149	−	1.42216i	0.622605	−	0.335206i
$19$			4.54838i			1.04347i	0.853108	+	0.521735i	$0.174715\pi$
$19$			4.54838i			1.04347i	−0.853108	+	0.521735i	$0.825285\pi$
$20$			4.07146i			0.910407i
$21$	8.05283	−	2.03003i	1.75727	−	0.442988i
$22$	−2.78151	+	1.80643i	−0.593020	+	0.385133i
$23$		−	5.62472i		−	1.17283i	−0.810009	−	0.586417i	$-0.800538\pi$
$23$		−	5.62472i		−	1.17283i	0.810009	−	0.586417i	$-0.199462\pi$
$24$	0.423385	+	1.67951i	0.0864231	+	0.342828i
$25$	−11.5768			−2.31536
$26$		−	2.57431i		−	0.504864i
$27$	3.50689	+	3.83428i	0.674901	+	0.737908i
$28$			4.79476i			0.906124i
$29$	−7.91832			−1.47040			−0.735198	−	0.677853i	$-0.762911\pi$
$29$	−7.91832			−1.47040			−0.735198	+	0.677853i	$0.762911\pi$
$30$	−6.83805	+	1.72380i	−1.24845	+	0.314721i
$31$	−0.355300			−0.0638137			−0.0319069	−	0.999491i	$-0.510158\pi$
$31$	−0.355300			−0.0638137			−0.0319069	+	0.999491i	$0.510158\pi$
$32$	−1.00000			−0.176777
$33$	−4.21157	−	3.90675i	−0.733140	−	0.680078i
$34$	−1.00000			−0.171499
$35$	−19.5217			−3.29976
$36$	−2.64149	+	1.42216i	−0.440248	+	0.237026i
$37$	5.35573			0.880477			0.440239	−	0.897881i	$-0.354894\pi$
$37$	5.35573			0.880477			0.440239	+	0.897881i	$0.354894\pi$
$38$		−	4.54838i		−	0.737844i
$39$	4.32358	−	1.08993i	0.692326	−	0.174528i
$40$		−	4.07146i		−	0.643755i
$41$	−1.52886			−0.238767			−0.119384	−	0.992848i	$-0.538092\pi$
$41$	−1.52886			−0.238767			−0.119384	+	0.992848i	$0.538092\pi$
$42$	−8.05283	+	2.03003i	−1.24258	+	0.313240i
$43$			4.45168i			0.678874i	0.940629	+	0.339437i	$0.110237\pi$
$43$			4.45168i			0.678874i	−0.940629	+	0.339437i	$0.889763\pi$
$44$	2.78151	−	1.80643i	0.419328	−	0.272330i
$45$	−5.79026	−	10.7547i	−0.863160	−	1.60322i
$46$			5.62472i			0.829319i
$47$		−	9.23503i		−	1.34707i	−0.739157	−	0.673534i	$-0.764776\pi$
$47$		−	9.23503i		−	1.34707i	0.739157	−	0.673534i	$-0.235224\pi$
$48$	−0.423385	−	1.67951i	−0.0611104	−	0.242416i
$49$	−15.9897			−2.28424
$50$	11.5768			1.63721
$51$	−0.423385	−	1.67951i	−0.0592858	−	0.235178i
$52$			2.57431i			0.356993i
$53$		−	9.72335i		−	1.33560i	−0.744339	−	0.667802i	$-0.767235\pi$
$53$		−	9.72335i		−	1.33560i	0.744339	−	0.667802i	$-0.232765\pi$
$54$	−3.50689	−	3.83428i	−0.477227	−	0.521780i
$55$	7.35482	+	11.3248i	0.991724	+	1.52704i
$56$		−	4.79476i		−	0.640726i
$57$	7.63903	−	1.92571i	1.01181	−	0.255067i
$58$	7.91832			1.03973
$59$			11.6299i			1.51408i	0.653366	+	0.757042i	$0.273356\pi$
$59$			11.6299i			1.51408i	−0.653366	+	0.757042i	$0.726644\pi$
$60$	6.83805	−	1.72380i	0.882788	−	0.222541i
$61$		−	4.09863i		−	0.524776i	−0.964962	−	0.262388i	$-0.915490\pi$
$61$		−	4.09863i		−	0.524776i	0.964962	−	0.262388i	$-0.0845100\pi$
$62$	0.355300			0.0451231
$63$	−6.81889	−	12.6653i	−0.859100	−	1.59568i
$64$	1.00000			0.125000
$65$	−10.4812			−1.30003
$66$	4.21157	+	3.90675i	0.518408	+	0.480888i
$67$	−5.11830			−0.625299			−0.312650	−	0.949868i	$-0.601217\pi$
$67$	−5.11830			−0.625299			−0.312650	+	0.949868i	$0.601217\pi$
$68$	1.00000			0.121268
$69$	−9.44676	+	2.38142i	−1.13726	+	0.286689i
$70$	19.5217			2.33329
$71$			7.91292i			0.939091i	0.882908	+	0.469546i	$0.155582\pi$
$71$			7.91292i			0.939091i	−0.882908	+	0.469546i	$0.844418\pi$
$72$	2.64149	−	1.42216i	0.311303	−	0.167603i
$73$			4.26429i			0.499097i	0.968362	+	0.249549i	$0.0802823\pi$
$73$			4.26429i			0.499097i	−0.968362	+	0.249549i	$0.919718\pi$
$74$	−5.35573			−0.622591
$75$	4.90144	+	19.4433i	0.565970	+	2.24512i
$76$			4.54838i			0.521735i
$77$	8.66141	+	13.3367i	0.987059	+	1.51985i
$78$	−4.32358	+	1.08993i	−0.489549	+	0.123410i
$79$		−	9.05706i		−	1.01900i	−0.860471	−	0.509500i	$-0.829831\pi$
$79$		−	9.05706i		−	1.01900i	0.860471	−	0.509500i	$-0.170169\pi$
$80$			4.07146i			0.455203i
$81$	4.95494	−	7.51323i	0.550549	−	0.834803i
$82$	1.52886			0.168834
$83$	7.26631			0.797581			0.398791	−	0.917042i	$-0.369430\pi$
$83$	7.26631			0.797581			0.398791	+	0.917042i	$0.369430\pi$
$84$	8.05283	−	2.03003i	0.878636	−	0.221494i
$85$			4.07146i			0.441612i
$86$		−	4.45168i		−	0.480037i
$87$	3.35250	+	13.2989i	0.359426	+	1.42579i
$88$	−2.78151	+	1.80643i	−0.296510	+	0.192566i
$89$			12.2301i			1.29639i	0.761473	+	0.648197i	$0.224477\pi$
$89$			12.2301i			1.29639i	−0.761473	+	0.648197i	$0.775523\pi$
$90$	5.79026	+	10.7547i	0.610347	+	1.13365i
$91$	−12.3432			−1.29392
$92$		−	5.62472i		−	0.586417i
$93$	0.150429	+	0.596728i	0.0155987	+	0.0618779i
$94$			9.23503i			0.952520i
$95$	−18.5185			−1.89996
$96$	0.423385	+	1.67951i	0.0432116	+	0.171414i
$97$	0.0605836			0.00615133			0.00307567	−	0.999995i	$-0.499021\pi$
$97$	0.0605836			0.00615133			0.00307567	+	0.999995i	$0.499021\pi$
$98$	15.9897			1.61520
$99$	−4.77830	+	8.72742i	−0.480237	+	0.877139i
$100$	−11.5768			−1.15768
$101$	10.6605			1.06076			0.530380	−	0.847760i	$-0.322049\pi$
$101$	10.6605			1.06076			0.530380	+	0.847760i	$0.322049\pi$
$102$	0.423385	+	1.67951i	0.0419214	+	0.166296i
$103$	1.38499			0.136467			0.0682334	−	0.997669i	$-0.478264\pi$
$103$	1.38499			0.136467			0.0682334	+	0.997669i	$0.478264\pi$
$104$		−	2.57431i		−	0.252432i
$105$	8.26518	+	32.7868i	0.806599	+	3.19966i
$106$			9.72335i			0.944415i
$107$	4.25253			0.411108			0.205554	−	0.978646i	$-0.434100\pi$
$107$	4.25253			0.411108			0.205554	+	0.978646i	$0.434100\pi$
$108$	3.50689	+	3.83428i	0.337451	+	0.368954i
$109$		−	5.49088i		−	0.525931i	−0.964805	−	0.262966i	$-0.915299\pi$
$109$		−	5.49088i		−	0.525931i	0.964805	−	0.262966i	$-0.0847005\pi$
$110$	−7.35482	−	11.3248i	−0.701255	−	1.07978i
$111$	−2.26754	−	8.99499i	−0.215225	−	0.853767i
$112$			4.79476i			0.453062i
$113$			17.3599i			1.63308i	0.577286	+	0.816542i	$0.304112\pi$
$113$			17.3599i			1.63308i	−0.577286	+	0.816542i	$0.695888\pi$
$114$	−7.63903	+	1.92571i	−0.715461	+	0.180360i
$115$	22.9008			2.13551
$116$	−7.91832			−0.735198
$117$	−3.66108	−	6.80002i	−0.338467	−	0.628662i
$118$		−	11.6299i		−	1.07062i
$119$			4.79476i			0.439535i
$120$	−6.83805	+	1.72380i	−0.624226	+	0.157360i
$121$	4.47360	−	10.0492i	0.406691	−	0.913566i
$122$			4.09863i			0.371073i
$123$	0.647295	+	2.56773i	0.0583646	+	0.231524i
$124$	−0.355300			−0.0319069
$125$		−	26.7772i		−	2.39502i
$126$	6.81889	+	12.6653i	0.607475	+	1.12831i
$127$			3.35314i			0.297543i	0.988872	+	0.148772i	$0.0475319\pi$
$127$			3.35314i			0.297543i	−0.988872	+	0.148772i	$0.952468\pi$
$128$	−1.00000			−0.0883883
$129$	7.47662	−	1.88477i	0.658280	−	0.165945i
$130$	10.4812			0.919263
$131$	−14.6947			−1.28388			−0.641939	−	0.766755i	$-0.721870\pi$
$131$	−14.6947			−1.28388			−0.641939	+	0.766755i	$0.721870\pi$
$132$	−4.21157	−	3.90675i	−0.366570	−	0.340039i
$133$	−21.8084			−1.89102
$134$	5.11830			0.442153
$135$	−15.6111	+	14.2782i	−1.34359	+	1.22887i
$136$	−1.00000			−0.0857493
$137$		−	21.6014i		−	1.84553i	−0.385361	−	0.922766i	$-0.625923\pi$
$137$		−	21.6014i		−	1.84553i	0.385361	−	0.922766i	$-0.374077\pi$
$138$	9.44676	−	2.38142i	0.804161	−	0.202720i
$139$			8.89537i			0.754496i	0.926112	+	0.377248i	$0.123130\pi$
$139$			8.89537i			0.754496i	−0.926112	+	0.377248i	$0.876870\pi$
$140$	−19.5217			−1.64988
$141$	−15.5103	+	3.90997i	−1.30620	+	0.329279i
$142$		−	7.91292i		−	0.664038i
$143$	4.65032	+	7.16048i	0.388880	+	0.598789i
$144$	−2.64149	+	1.42216i	−0.220124	+	0.118513i
$145$		−	32.2391i		−	2.67731i
$146$		−	4.26429i		−	0.352915i
$147$	6.76979	+	26.8548i	0.558363	+	2.21495i
$148$	5.35573			0.440239
$149$	−18.8204			−1.54183			−0.770914	−	0.636940i	$-0.780200\pi$
$149$	−18.8204			−1.54183			−0.770914	+	0.636940i	$0.780200\pi$
$150$	−4.90144	−	19.4433i	−0.400201	−	1.58754i
$151$			16.6132i			1.35196i	0.736920	+	0.675980i	$0.236279\pi$
$151$			16.6132i			1.35196i	−0.736920	+	0.675980i	$0.763721\pi$
$152$		−	4.54838i		−	0.368922i
$153$	−2.64149	+	1.42216i	−0.213552	+	0.114975i
$154$	−8.66141	−	13.3367i	−0.697956	−	1.07470i
$155$		−	1.44659i		−	0.116193i
$156$	4.32358	−	1.08993i	0.346163	−	0.0872639i
$157$	13.0711			1.04318			0.521592	−	0.853195i	$-0.325338\pi$
$157$	13.0711			1.04318			0.521592	+	0.853195i	$0.325338\pi$
$158$			9.05706i			0.720541i
$159$	−16.3304	+	4.11672i	−1.29509	+	0.326477i
$160$		−	4.07146i		−	0.321877i
$161$	26.9692			2.12547
$162$	−4.95494	+	7.51323i	−0.389297	+	0.590295i
$163$	1.55929			0.122133			0.0610665	−	0.998134i	$-0.480550\pi$
$163$	1.55929			0.122133			0.0610665	+	0.998134i	$0.480550\pi$
$164$	−1.52886			−0.119384
$165$	15.9062	−	17.1472i	1.23829	−	1.33491i
$166$	−7.26631			−0.563975
$167$	−2.47630			−0.191622			−0.0958111	−	0.995400i	$-0.530544\pi$
$167$	−2.47630			−0.191622			−0.0958111	+	0.995400i	$0.530544\pi$
$168$	−8.05283	+	2.03003i	−0.621289	+	0.156620i
$169$	6.37292			0.490224
$170$		−	4.07146i		−	0.312267i
$171$	−6.46851	−	12.0145i	−0.494659	−	0.918771i
$172$			4.45168i			0.339437i
$173$	−5.92606			−0.450550			−0.225275	−	0.974295i	$-0.572328\pi$
$173$	−5.92606			−0.450550			−0.225275	+	0.974295i	$0.572328\pi$
$174$	−3.35250	−	13.2989i	−0.254152	−	1.00819i
$175$		−	55.5079i		−	4.19601i
$176$	2.78151	−	1.80643i	0.209664	−	0.136165i
$177$	19.5325	−	4.92393i	1.46815	−	0.370105i
$178$		−	12.2301i		−	0.916688i
$179$		−	7.57467i		−	0.566158i	−0.959097	−	0.283079i	$-0.908644\pi$
$179$		−	7.57467i		−	0.566158i	0.959097	−	0.283079i	$-0.0913558\pi$
$180$	−5.79026	−	10.7547i	−0.431580	−	0.801610i
$181$	2.71865			0.202076			0.101038	−	0.994883i	$-0.467784\pi$
$181$	2.71865			0.202076			0.101038	+	0.994883i	$0.467784\pi$
$182$	12.3432			0.914939
$183$	−6.88368	+	1.73530i	−0.508856	+	0.128277i
$184$			5.62472i			0.414660i
$185$			21.8057i			1.60318i
$186$	−0.150429	−	0.596728i	−0.0110300	−	0.0437542i
$187$	2.78151	−	1.80643i	0.203404	−	0.132099i
$188$		−	9.23503i		−	0.673534i
$189$	−18.3844	+	16.8147i	−1.33727	+	1.22309i
$190$	18.5185			1.34348
$191$			20.5365i			1.48597i	0.669310	+	0.742983i	$0.266590\pi$
$191$			20.5365i			1.48597i	−0.669310	+	0.742983i	$0.733410\pi$
$192$	−0.423385	−	1.67951i	−0.0305552	−	0.121208i
$193$		−	3.45941i		−	0.249014i	−0.992219	−	0.124507i	$-0.960265\pi$
$193$		−	3.45941i		−	0.249014i	0.992219	−	0.124507i	$-0.0397349\pi$
$194$	−0.0605836			−0.00434965
$195$	4.43759	+	17.6033i	0.317782	+	1.26060i
$196$	−15.9897			−1.14212
$197$	−6.31827			−0.450158			−0.225079	−	0.974340i	$-0.572264\pi$
$197$	−6.31827			−0.450158			−0.225079	+	0.974340i	$0.572264\pi$
$198$	4.77830	−	8.72742i	0.339579	−	0.620231i
$199$	0.756526			0.0536287			0.0268143	−	0.999640i	$-0.491464\pi$
$199$	0.756526			0.0536287			0.0268143	+	0.999640i	$0.491464\pi$
$200$	11.5768			0.818603
$201$	2.16701	+	8.59622i	0.152849	+	0.606330i
$202$	−10.6605			−0.750070
$203$		−	37.9664i		−	2.66472i
$204$	−0.423385	−	1.67951i	−0.0296429	−	0.117589i
$205$		−	6.22468i		−	0.434751i
$206$	−1.38499			−0.0964967
$207$	7.99923	+	14.8576i	0.555985	+	1.03268i
$208$			2.57431i			0.178496i
$209$	8.21634	+	12.6514i	0.568336	+	0.875113i
$210$	−8.26518	−	32.7868i	−0.570352	−	2.26250i
$211$			11.6543i			0.802313i	0.916010	+	0.401156i	$0.131392\pi$
$211$			11.6543i			0.802313i	−0.916010	+	0.401156i	$0.868608\pi$
$212$		−	9.72335i		−	0.667802i
$213$	13.2898	−	3.35021i	0.910603	−	0.229553i
$214$	−4.25253			−0.290697
$215$	−18.1248			−1.23610
$216$	−3.50689	−	3.83428i	−0.238614	−	0.260890i
$217$		−	1.70358i		−	0.115646i
$218$			5.49088i			0.371889i
$219$	7.16191	−	1.80544i	0.483957	−	0.122000i
$220$	7.35482	+	11.3248i	0.495862	+	0.763519i
$221$			2.57431i			0.173167i
$222$	2.26754	+	8.99499i	0.152187	+	0.603705i
$223$	−0.142411			−0.00953654			−0.00476827	−	0.999989i	$-0.501518\pi$
$223$	−0.142411			−0.00953654			−0.00476827	+	0.999989i	$0.501518\pi$
$224$		−	4.79476i		−	0.320363i
$225$	30.5800	−	16.4640i	2.03867	−	1.09760i
$226$		−	17.3599i		−	1.15476i
$227$	−6.24693			−0.414623			−0.207312	−	0.978275i	$-0.566471\pi$
$227$	−6.24693			−0.414623			−0.207312	+	0.978275i	$0.566471\pi$
$228$	7.63903	−	1.92571i	0.505907	−	0.127534i
$229$	10.0198			0.662128			0.331064	−	0.943608i	$-0.392592\pi$
$229$	10.0198			0.662128			0.331064	+	0.943608i	$0.392592\pi$
$230$	−22.9008			−1.51004
$231$	18.7319	−	20.1934i	1.23247	−	1.32863i
$232$	7.91832			0.519863
$233$	−27.9235			−1.82933			−0.914666	−	0.404211i	$-0.867546\pi$
$233$	−27.9235			−1.82933			−0.914666	+	0.404211i	$0.867546\pi$
$234$	3.66108	+	6.80002i	0.239332	+	0.444531i
$235$	37.6001			2.45276
$236$			11.6299i			0.757042i
$237$	−15.2114	+	3.83462i	−0.988087	+	0.249086i
$238$		−	4.79476i		−	0.310798i
$239$	16.6886			1.07949			0.539747	−	0.841828i	$-0.318520\pi$
$239$	16.6886			1.07949			0.539747	+	0.841828i	$0.318520\pi$
$240$	6.83805	−	1.72380i	0.441394	−	0.111271i
$241$		−	14.9599i		−	0.963652i	−0.876267	−	0.481826i	$-0.839974\pi$
$241$		−	14.9599i		−	0.963652i	0.876267	−	0.481826i	$-0.160026\pi$
$242$	−4.47360	+	10.0492i	−0.287574	+	0.645989i
$243$	−14.7164	−	5.14087i	−0.944055	−	0.329787i
$244$		−	4.09863i		−	0.262388i
$245$		−	65.1014i		−	4.15918i
$246$	−0.647295	−	2.56773i	−0.0412700	−	0.163712i
$247$	−11.7089			−0.745022
$248$	0.355300			0.0225616
$249$	−3.07645	−	12.2038i	−0.194962	−	0.773386i
$250$			26.7772i			1.69354i
$251$			11.2495i			0.710063i	0.934854	+	0.355032i	$0.115530\pi$
$251$			11.2495i			0.710063i	−0.934854	+	0.355032i	$0.884470\pi$
$252$	−6.81889	−	12.6653i	−0.429550	−	0.797839i
$253$	−10.1607	−	15.6452i	−0.638796	−	0.983606i
$254$		−	3.35314i		−	0.210395i
$255$	6.83805	−	1.72380i	0.428215	−	0.107948i
$256$	1.00000			0.0625000
$257$			18.3690i			1.14583i	0.819616	+	0.572913i	$0.194187\pi$
$257$			18.3690i			1.14583i	−0.819616	+	0.572913i	$0.805813\pi$
$258$	−7.47662	+	1.88477i	−0.465474	+	0.117341i
$259$			25.6794i			1.59564i
$260$	−10.4812			−0.650017
$261$	20.9162	−	11.2611i	1.29468	−	0.697044i
$262$	14.6947			0.907839
$263$	7.76831			0.479015			0.239507	−	0.970895i	$-0.423014\pi$
$263$	7.76831			0.479015			0.239507	+	0.970895i	$0.423014\pi$
$264$	4.21157	+	3.90675i	0.259204	+	0.240444i
$265$	39.5882			2.43189
$266$	21.8084			1.33716
$267$	20.5406	−	5.17806i	1.25707	−	0.316892i
$268$	−5.11830			−0.312650
$269$			6.64285i			0.405022i	0.979280	+	0.202511i	$0.0649102\pi$
$269$			6.64285i			0.405022i	−0.979280	+	0.202511i	$0.935090\pi$
$270$	15.6111	−	14.2782i	0.950063	−	0.868942i
$271$			11.5920i			0.704162i	0.935969	+	0.352081i	$0.114526\pi$
$271$			11.5920i			0.704162i	−0.935969	+	0.352081i	$0.885474\pi$
$272$	1.00000			0.0606339
$273$	5.22593	+	20.7305i	0.316287	+	1.25467i
$274$			21.6014i			1.30499i
$275$	−32.2010	+	20.9127i	−1.94179	+	1.26108i
$276$	−9.44676	+	2.38142i	−0.568628	+	0.143345i
$277$			14.4698i			0.869406i	0.900574	+	0.434703i	$0.143147\pi$
$277$			14.4698i			0.869406i	−0.900574	+	0.434703i	$0.856853\pi$
$278$		−	8.89537i		−	0.533509i
$279$	0.938521	−	0.505292i	0.0561878	−	0.0302510i
$280$	19.5217			1.16664
$281$	−12.0617			−0.719541			−0.359770	−	0.933041i	$-0.617145\pi$
$281$	−12.0617			−0.719541			−0.359770	+	0.933041i	$0.617145\pi$
$282$	15.5103	−	3.90997i	0.923625	−	0.232836i
$283$			3.34479i			0.198827i	0.995046	+	0.0994135i	$0.0316967\pi$
$283$			3.34479i			0.198827i	−0.995046	+	0.0994135i	$0.968303\pi$
$284$			7.91292i			0.469546i
$285$	7.84047	+	31.1020i	0.464430	+	1.84233i
$286$	−4.65032	−	7.16048i	−0.274979	−	0.423408i
$287$		−	7.33049i		−	0.432705i
$288$	2.64149	−	1.42216i	0.155651	−	0.0838014i
$289$	1.00000			0.0588235
$290$			32.2391i			1.89315i
$291$	−0.0256502	−	0.101751i	−0.00150364	−	0.00596473i
$292$			4.26429i			0.249549i
$293$	1.72105			0.100545			0.0502724	−	0.998736i	$-0.483991\pi$
$293$	1.72105			0.100545			0.0502724	+	0.998736i	$0.483991\pi$
$294$	−6.76979	−	26.8548i	−0.394822	−	1.56620i
$295$	−47.3507			−2.75686
$296$	−5.35573			−0.311296
$297$	16.6808	+	4.33013i	0.967920	+	0.251260i
$298$	18.8204			1.09024
$299$	14.4798			0.837387
$300$	4.90144	+	19.4433i	0.282985	+	1.12256i
$301$	−21.3447			−1.23029
$302$		−	16.6132i		−	0.955980i
$303$	−4.51350	−	17.9044i	−0.259294	−	1.02858i
$304$			4.54838i			0.260867i
$305$	16.6874			0.955519
$306$	2.64149	−	1.42216i	0.151004	−	0.0812993i
$307$		−	15.5925i		−	0.889913i	−0.895552	−	0.444957i	$-0.853219\pi$
$307$		−	15.5925i		−	0.889913i	0.895552	−	0.444957i	$-0.146781\pi$
$308$	8.66141	+	13.3367i	0.493530	+	0.759927i
$309$	−0.586383	−	2.32610i	−0.0333582	−	0.132327i
$310$			1.44659i			0.0821607i
$311$			28.3662i			1.60850i	0.594291	+	0.804250i	$0.297433\pi$
$311$			28.3662i			1.60850i	−0.594291	+	0.804250i	$0.702567\pi$
$312$	−4.32358	+	1.08993i	−0.244774	+	0.0617049i
$313$	6.39671			0.361564			0.180782	−	0.983523i	$-0.442137\pi$
$313$	6.39671			0.361564			0.180782	+	0.983523i	$0.442137\pi$
$314$	−13.0711			−0.737643
$315$	51.5663	−	27.7629i	2.90543	−	1.56426i
$316$		−	9.05706i		−	0.509500i
$317$		−	29.7857i		−	1.67293i	−0.548019	−	0.836466i	$-0.684618\pi$
$317$		−	29.7857i		−	1.67293i	0.548019	−	0.836466i	$-0.315382\pi$
$318$	16.3304	−	4.11672i	0.915765	−	0.230854i
$319$	−22.0249	+	14.3039i	−1.23316	+	0.800866i
$320$			4.07146i			0.227602i
$321$	−1.80046	−	7.14215i	−0.100492	−	0.398636i
$322$	−26.9692			−1.50293
$323$			4.54838i			0.253078i
$324$	4.95494	−	7.51323i	0.275274	−	0.417401i
$325$		−	29.8023i		−	1.65313i
$326$	−1.55929			−0.0863610
$327$	−9.22198	+	2.32476i	−0.509976	+	0.128559i
$328$	1.52886			0.0844170
$329$	44.2797			2.44122
$330$	−15.9062	+	17.1472i	−0.875606	+	0.943924i
$331$	−12.4742			−0.685644			−0.342822	−	0.939400i	$-0.611383\pi$
$331$	−12.4742			−0.685644			−0.342822	+	0.939400i	$0.611383\pi$
$332$	7.26631			0.398791
$333$	−14.1471	+	7.61669i	−0.775257	+	0.417392i
$334$	2.47630			0.135497
$335$		−	20.8389i		−	1.13855i
$336$	8.05283	−	2.03003i	0.439318	−	0.110747i
$337$			14.7125i			0.801440i	0.916201	+	0.400720i	$0.131240\pi$
$337$			14.7125i			0.801440i	−0.916201	+	0.400720i	$0.868760\pi$
$338$	−6.37292			−0.346641
$339$	29.1561	−	7.34993i	1.58354	−	0.399193i
$340$			4.07146i			0.220806i
$341$	−0.988270	+	0.641825i	−0.0535178	+	0.0347568i
$342$	6.46851	+	12.0145i	0.349777	+	0.649669i
$343$		−	43.1034i		−	2.32736i
$344$		−	4.45168i		−	0.240018i
$345$	−9.69587	−	38.4621i	−0.522008	−	2.07073i
$346$	5.92606			0.318587
$347$	25.1368			1.34941			0.674707	−	0.738086i	$-0.264270\pi$
$347$	25.1368			1.34941			0.674707	+	0.738086i	$0.264270\pi$
$348$	3.35250	+	13.2989i	0.179713	+	0.712895i
$349$			7.45414i			0.399011i	0.979897	+	0.199505i	$0.0639336\pi$
$349$			7.45414i			0.399011i	−0.979897	+	0.199505i	$0.936066\pi$
$350$			55.5079i			2.96702i
$351$	−9.87064	+	9.02783i	−0.526856	+	0.481870i
$352$	−2.78151	+	1.80643i	−0.148255	+	0.0962832i
$353$		−	2.60469i		−	0.138634i	−0.997595	−	0.0693168i	$-0.977918\pi$
$353$		−	2.60469i		−	0.138634i	0.997595	−	0.0693168i	$-0.0220819\pi$
$354$	−19.5325	+	4.92393i	−1.03814	+	0.261704i
$355$	−32.2172			−1.70991
$356$			12.2301i			0.648197i
$357$	8.05283	−	2.03003i	0.426201	−	0.107440i
$358$			7.57467i			0.400334i
$359$	7.37005			0.388977			0.194488	−	0.980905i	$-0.437695\pi$
$359$	7.37005			0.388977			0.194488	+	0.980905i	$0.437695\pi$
$360$	5.79026	+	10.7547i	0.305173	+	0.566824i
$361$	−1.68773			−0.0888281
$362$	−2.71865			−0.142889
$363$	−18.7718	−	3.25875i	−0.985264	−	0.171040i
$364$	−12.3432			−0.646959
$365$	−17.3619			−0.908763
$366$	6.88368	−	1.73530i	0.359816	−	0.0907055i
$367$	3.43567			0.179340			0.0896702	−	0.995972i	$-0.471419\pi$
$367$	3.43567			0.179340			0.0896702	+	0.995972i	$0.471419\pi$
$368$		−	5.62472i		−	0.293209i
$369$	4.03846	−	2.17427i	0.210234	−	0.113188i
$370$		−	21.8057i		−	1.13362i
$371$	46.6211			2.42045
$372$	0.150429	+	0.596728i	0.00779936	+	0.0309389i
$373$		−	30.6755i		−	1.58832i	−0.607711	−	0.794158i	$-0.707912\pi$
$373$		−	30.6755i		−	1.58832i	0.607711	−	0.794158i	$-0.292088\pi$
$374$	−2.78151	+	1.80643i	−0.143828	+	0.0934085i
$375$	−44.9725	+	11.3371i	−2.32237	+	0.585443i
$376$			9.23503i			0.476260i
$377$		−	20.3842i		−	1.04984i
$378$	18.3844	−	16.8147i	0.945594	−	0.864854i
$379$	−6.90631			−0.354753			−0.177377	−	0.984143i	$-0.556761\pi$
$379$	−6.90631			−0.354753			−0.177377	+	0.984143i	$0.556761\pi$
$380$	−18.5185			−0.949981
$381$	5.63163	−	1.41967i	0.288517	−	0.0727319i
$382$		−	20.5365i		−	1.05074i
$383$			8.94380i			0.457007i	0.973543	+	0.228503i	$0.0733832\pi$
$383$			8.94380i			0.457007i	−0.973543	+	0.228503i	$0.926617\pi$
$384$	0.423385	+	1.67951i	0.0216058	+	0.0857070i
$385$	−54.2997	+	35.2646i	−2.76737	+	1.79725i
$386$			3.45941i			0.176079i
$387$	−6.33098	−	11.7591i	−0.321822	−	0.597747i
$388$	0.0605836			0.00307567
$389$		−	37.7077i		−	1.91186i	−0.293598	−	0.955929i	$-0.594853\pi$
$389$		−	37.7077i		−	1.91186i	0.293598	−	0.955929i	$-0.405147\pi$
$390$	−4.43759	−	17.6033i	−0.224706	−	0.891377i
$391$		−	5.62472i		−	0.284454i
$392$	15.9897			0.807601
$393$	6.22150	+	24.6798i	0.313833	+	1.24493i
$394$	6.31827			0.318310
$395$	36.8755			1.85541
$396$	−4.77830	+	8.72742i	−0.240119	+	0.438569i
$397$	30.7172			1.54165			0.770826	−	0.637045i	$-0.219844\pi$
$397$	30.7172			1.54165			0.770826	+	0.637045i	$0.219844\pi$
$398$	−0.756526			−0.0379212
$399$	9.23333	+	36.6273i	0.462245	+	1.83366i
$400$	−11.5768			−0.578840
$401$		−	1.35005i		−	0.0674184i	−0.999432	−	0.0337092i	$-0.989268\pi$
$401$		−	1.35005i		−	0.0674184i	0.999432	−	0.0337092i	$-0.0107320\pi$
$402$	−2.16701	−	8.59622i	−0.108081	−	0.428740i
$403$		−	0.914652i		−	0.0455621i
$404$	10.6605			0.530380
$405$	30.5898	+	20.1739i	1.52002	+	1.00245i
$406$			37.9664i			1.88424i
$407$	14.8970	−	9.67478i	0.738418	−	0.479561i
$408$	0.423385	+	1.67951i	0.0209607	+	0.0831480i
$409$			31.8859i			1.57666i	0.615254	+	0.788329i	$0.289054\pi$
$409$			31.8859i			1.57666i	−0.615254	+	0.788329i	$0.710946\pi$
$410$			6.22468i			0.307415i
$411$	−36.2797	+	9.14571i	−1.78955	+	0.451125i
$412$	1.38499			0.0682334
$413$	−55.7625			−2.74390
$414$	−7.99923	−	14.8576i	−0.393141	−	0.730213i
$415$			29.5845i			1.45225i
$416$		−	2.57431i		−	0.126216i
$417$	14.9398	−	3.76617i	0.731607	−	0.184430i
$418$	−8.21634	−	12.6514i	−0.401874	−	0.618798i
$419$			6.43054i			0.314152i	0.987587	+	0.157076i	$0.0502068\pi$
$419$			6.43054i			0.314152i	−0.987587	+	0.157076i	$0.949793\pi$
$420$	8.26518	+	32.7868i	0.403300	+	1.59983i
$421$	−0.960351			−0.0468046			−0.0234023	−	0.999726i	$-0.507450\pi$
$421$	−0.960351			−0.0468046			−0.0234023	+	0.999726i	$0.507450\pi$
$422$		−	11.6543i		−	0.567321i
$423$	13.1337	+	24.3942i	0.638580	+	1.18609i
$424$			9.72335i			0.472208i
$425$	−11.5768			−0.561557
$426$	−13.2898	+	3.35021i	−0.643894	+	0.162318i
$427$	19.6519			0.951024
$428$	4.25253			0.205554
$429$	10.0572	−	10.8419i	0.485566	−	0.523451i
$430$	18.1248			0.874057
$431$	1.91773			0.0923738			0.0461869	−	0.998933i	$-0.485293\pi$
$431$	1.91773			0.0923738			0.0461869	+	0.998933i	$0.485293\pi$
$432$	3.50689	+	3.83428i	0.168725	+	0.184477i
$433$	10.0096			0.481031			0.240516	−	0.970645i	$-0.422683\pi$
$433$	10.0096			0.481031			0.240516	+	0.970645i	$0.422683\pi$
$434$			1.70358i			0.0817742i
$435$	−54.1459	+	13.6496i	−2.59610	+	0.654447i
$436$		−	5.49088i		−	0.262966i
$437$	25.5833			1.22382
$438$	−7.16191	+	1.80544i	−0.342209	+	0.0862671i
$439$		−	23.1549i		−	1.10512i	−0.833472	−	0.552562i	$-0.813650\pi$
$439$		−	23.1549i		−	1.10512i	0.833472	−	0.552562i	$-0.186350\pi$
$440$	−7.35482	−	11.3248i	−0.350628	−	0.539889i
$441$	42.2366	−	22.7398i	2.01127	−	1.08285i
$442$		−	2.57431i		−	0.122448i
$443$		−	10.9209i		−	0.518869i	−0.965761	−	0.259435i	$-0.916464\pi$
$443$		−	10.9209i		−	0.518869i	0.965761	−	0.259435i	$-0.0835362\pi$
$444$	−2.26754	−	8.99499i	−0.107613	−	0.426884i
$445$	−49.7946			−2.36049
$446$	0.142411			0.00674335
$447$	7.96828	+	31.6090i	0.376887	+	1.49505i
$448$			4.79476i			0.226531i
$449$			13.2072i			0.623286i	0.950199	+	0.311643i	$0.100879\pi$
$449$			13.2072i			0.623286i	−0.950199	+	0.311643i	$0.899121\pi$
$450$	−30.5800	+	16.4640i	−1.44156	+	0.776122i
$451$	−4.25253	+	2.76178i	−0.200244	+	0.130047i
$452$			17.3599i			0.816542i
$453$	27.9019	−	7.03376i	1.31095	−	0.330475i
$454$	6.24693			0.293183
$455$		−	50.2549i		−	2.35598i
$456$	−7.63903	+	1.92571i	−0.357730	+	0.0901799i
$457$			21.3501i			0.998717i	0.866395	+	0.499359i	$0.166431\pi$
$457$			21.3501i			0.998717i	−0.866395	+	0.499359i	$0.833569\pi$
$458$	−10.0198			−0.468195
$459$	3.50689	+	3.83428i	0.163688	+	0.178969i
$460$	22.9008			1.06776
$461$	4.75396			0.221414			0.110707	−	0.993853i	$-0.464688\pi$
$461$	4.75396			0.221414			0.110707	+	0.993853i	$0.464688\pi$
$462$	−18.7319	+	20.1934i	−0.871487	+	0.939484i
$463$	34.9504			1.62428			0.812142	−	0.583460i	$-0.198301\pi$
$463$	34.9504			1.62428			0.812142	+	0.583460i	$0.198301\pi$
$464$	−7.91832			−0.367599
$465$	−2.42956	+	0.612464i	−0.112668	+	0.0284023i
$466$	27.9235			1.29353
$467$		−	17.6209i		−	0.815400i	−0.913116	−	0.407700i	$-0.866331\pi$
$467$		−	17.6209i		−	0.815400i	0.913116	−	0.407700i	$-0.133669\pi$
$468$	−3.66108	−	6.80002i	−0.169233	−	0.314331i
$469$		−	24.5410i		−	1.13320i
$470$	−37.6001			−1.73436
$471$	−5.53409	−	21.9529i	−0.254997	−	1.01154i
$472$		−	11.6299i		−	0.535310i
$473$	8.04166	+	12.3824i	0.369756	+	0.569343i
$474$	15.2114	−	3.83462i	0.698683	−	0.176130i
$475$		−	52.6557i		−	2.41601i
$476$			4.79476i			0.219767i
$477$	13.8281	+	25.6841i	0.633146	+	1.17600i
$478$	−16.6886			−0.763317
$479$	−21.9110			−1.00114			−0.500569	−	0.865696i	$-0.666876\pi$
$479$	−21.9110			−1.00114			−0.500569	+	0.865696i	$0.666876\pi$
$480$	−6.83805	+	1.72380i	−0.312113	+	0.0786802i
$481$			13.7873i			0.628648i
$482$			14.9599i			0.681405i
$483$	−11.4183	−	45.2949i	−0.519552	−	2.06099i
$484$	4.47360	−	10.0492i	0.203345	−	0.456783i
$485$			0.246664i			0.0112004i
$486$	14.7164	+	5.14087i	0.667548	+	0.233195i
$487$	−18.5751			−0.841716			−0.420858	−	0.907127i	$-0.638271\pi$
$487$	−18.5751			−0.841716			−0.420858	+	0.907127i	$0.638271\pi$
$488$			4.09863i			0.185536i
$489$	−0.660180	−	2.61884i	−0.0298544	−	0.118428i
$490$			65.1014i			2.94098i
$491$	−8.75916			−0.395295			−0.197648	−	0.980273i	$-0.563330\pi$
$491$	−8.75916			−0.395295			−0.197648	+	0.980273i	$0.563330\pi$
$492$	0.647295	+	2.56773i	0.0291823	+	0.115762i
$493$	−7.91832			−0.356623
$494$	11.7089			0.526810
$495$	−35.5334	−	19.4547i	−1.59711	−	0.874422i
$496$	−0.355300			−0.0159534
$497$	−37.9405			−1.70187
$498$	3.07645	+	12.2038i	0.137859	+	0.546866i
$499$	1.95828			0.0876645			0.0438323	−	0.999039i	$-0.486043\pi$
$499$	1.95828			0.0876645			0.0438323	+	0.999039i	$0.486043\pi$
$500$		−	26.7772i		−	1.19751i
$501$	1.04843	+	4.15897i	0.0468404	+	0.185809i
$502$		−	11.2495i		−	0.502090i
$503$	3.41142			0.152108			0.0760538	−	0.997104i	$-0.475768\pi$
$503$	3.41142			0.152108			0.0760538	+	0.997104i	$0.475768\pi$
$504$	6.81889	+	12.6653i	0.303738	+	0.564157i
$505$			43.4038i			1.93144i
$506$	10.1607	+	15.6452i	0.451697	+	0.695514i
$507$	−2.69820	−	10.7034i	−0.119831	−	0.475353i
$508$			3.35314i			0.148772i
$509$			4.69659i			0.208173i	0.994568	+	0.104086i	$0.0331918\pi$
$509$			4.69659i			0.208173i	−0.994568	+	0.104086i	$0.966808\pi$
$510$	−6.83805	+	1.72380i	−0.302794	+	0.0763310i
$511$	−20.4462			−0.904488
$512$	−1.00000			−0.0441942
$513$	−17.4398	+	15.9507i	−0.769984	+	0.704239i
$514$		−	18.3690i		−	0.810222i
$515$			5.63892i			0.248481i
$516$	7.47662	−	1.88477i	0.329140	−	0.0829725i
$517$	−16.6825	−	25.6873i	−0.733694	−	1.12973i
$518$		−	25.6794i		−	1.12829i
$519$	2.50901	+	9.95287i	0.110133	+	0.436882i
$520$	10.4812			0.459632
$521$			3.32317i			0.145591i	0.997347	+	0.0727953i	$0.0231920\pi$
$521$			3.32317i			0.145591i	−0.997347	+	0.0727953i	$0.976808\pi$
$522$	−20.9162	+	11.2611i	−0.915476	+	0.492885i
$523$			8.02106i			0.350737i	0.984503	+	0.175368i	$0.0561116\pi$
$523$			8.02106i			0.350737i	−0.984503	+	0.175368i	$0.943888\pi$
$524$	−14.6947			−0.641939
$525$	−93.2260	+	23.5012i	−4.06872	+	1.02568i
$526$	−7.76831			−0.338715
$527$	−0.355300			−0.0154771
$528$	−4.21157	−	3.90675i	−0.183285	−	0.170019i
$529$	−8.63745			−0.375541
$530$	−39.5882			−1.71960
$531$	−16.5395	−	30.7203i	−0.717755	−	1.33315i
$532$	−21.8084			−0.945512
$533$		−	3.93575i		−	0.170476i
$534$	−20.5406	+	5.17806i	−0.888880	+	0.224077i
$535$			17.3140i			0.748550i
$536$	5.11830			0.221077
$537$	−12.7217	+	3.20700i	−0.548983	+	0.138392i
$538$		−	6.64285i		−	0.286394i
$539$	−44.4755	+	28.8843i	−1.91569	+	1.24414i
$540$	−15.6111	+	14.2782i	−0.671796	+	0.614435i
$541$			41.8224i			1.79809i	0.437860	+	0.899043i	$0.355737\pi$
$541$			41.8224i			1.79809i	−0.437860	+	0.899043i	$0.644263\pi$
$542$		−	11.5920i		−	0.497918i
$543$	−1.15104	−	4.56599i	−0.0493957	−	0.195946i
$544$	−1.00000			−0.0428746
$545$	22.3559			0.957622
$546$	−5.22593	−	20.7305i	−0.223649	−	0.887183i
$547$			33.5931i			1.43634i	0.695869	+	0.718169i	$0.255019\pi$
$547$			33.5931i			1.43634i	−0.695869	+	0.718169i	$0.744981\pi$
$548$		−	21.6014i		−	0.922766i
$549$	5.82890	+	10.8265i	0.248771	+	0.462063i
$550$	32.2010	−	20.9127i	1.37305	−	0.891721i
$551$		−	36.0155i		−	1.53431i
$552$	9.44676	−	2.38142i	0.402081	−	0.101360i
$553$	43.4264			1.84668
$554$		−	14.4698i		−	0.614763i
$555$	36.6228	−	9.23219i	1.55455	−	0.391885i
$556$			8.89537i			0.377248i
$557$	44.9677			1.90534			0.952671	−	0.304002i	$-0.0983230\pi$
$557$	44.9677			1.90534			0.952671	+	0.304002i	$0.0983230\pi$
$558$	−0.938521	+	0.505292i	−0.0397307	+	0.0213907i
$559$	−11.4600			−0.484707
$560$	−19.5217			−0.824941
$561$	−4.21157	−	3.90675i	−0.177813	−	0.164943i
$562$	12.0617			0.508792
$563$	3.48936			0.147059			0.0735296	−	0.997293i	$-0.476574\pi$
$563$	3.48936			0.147059			0.0735296	+	0.997293i	$0.476574\pi$
$564$	−15.5103	+	3.90997i	−0.653101	+	0.164640i
$565$	−70.6802			−2.97354
$566$		−	3.34479i		−	0.140592i
$567$	36.0241	+	23.7577i	1.51287	+	0.997731i
$568$		−	7.91292i		−	0.332019i
$569$	−12.7550			−0.534717			−0.267359	−	0.963597i	$-0.586151\pi$
$569$	−12.7550			−0.534717			−0.267359	+	0.963597i	$0.586151\pi$
$570$	−7.84047	−	31.1020i	−0.328401	−	1.30272i
$571$			23.8987i			1.00013i	0.865988	+	0.500065i	$0.166691\pi$
$571$			23.8987i			1.00013i	−0.865988	+	0.500065i	$0.833309\pi$
$572$	4.65032	+	7.16048i	0.194440	+	0.299395i
$573$	34.4911	−	8.69483i	1.44089	−	0.363232i
$574$			7.33049i			0.305969i
$575$			65.1162i			2.71553i
$576$	−2.64149	+	1.42216i	−0.110062	+	0.0592565i
$577$	−10.8405			−0.451296			−0.225648	−	0.974209i	$-0.572450\pi$
$577$	−10.8405			−0.451296			−0.225648	+	0.974209i	$0.572450\pi$
$578$	−1.00000			−0.0415945
$579$	−5.81011	+	1.46466i	−0.241460	+	0.0608693i
$580$		−	32.2391i		−	1.33866i
$581$			34.8402i			1.44541i
$582$	0.0256502	+	0.101751i	0.00106323	+	0.00421770i
$583$	−17.5646	−	27.0456i	−0.727451	−	1.12011i
$584$		−	4.26429i		−	0.176458i
$585$	27.6860	−	14.9059i	1.14468	−	0.616284i
$586$	−1.72105			−0.0710959
$587$		−	14.2826i		−	0.589506i	−0.955573	−	0.294753i	$-0.904763\pi$
$587$		−	14.2826i		−	0.589506i	0.955573	−	0.294753i	$-0.0952374\pi$
$588$	6.76979	+	26.8548i	0.279182	+	1.10747i
$589$		−	1.61604i		−	0.0665876i
$590$	47.3507			1.94940
$591$	2.67506	+	10.6116i	0.110037	+	0.436502i
$592$	5.35573			0.220119
$593$	−9.31428			−0.382491			−0.191246	−	0.981542i	$-0.561253\pi$
$593$	−9.31428			−0.382491			−0.191246	+	0.981542i	$0.561253\pi$
$594$	−16.6808	−	4.33013i	−0.684423	−	0.177667i
$595$	−19.5217			−0.800310
$596$	−18.8204			−0.770914
$597$	−0.320302	−	1.27059i	−0.0131091	−	0.0520018i
$598$	−14.4798			−0.592122
$599$		−	12.4153i		−	0.507275i	−0.967299	−	0.253638i	$-0.918373\pi$
$599$		−	12.4153i		−	0.507275i	0.967299	−	0.253638i	$-0.0816270\pi$
$600$	−4.90144	−	19.4433i	−0.200101	−	0.793770i
$601$			16.2793i			0.664047i	0.943271	+	0.332024i	$0.107731\pi$
$601$			16.2793i			0.664047i	−0.943271	+	0.332024i	$0.892269\pi$
$602$	21.3447			0.869945
$603$	13.5199	−	7.27902i	0.550574	−	0.296425i
$604$			16.6132i			0.675980i
$605$	40.9150	+	18.2141i	1.66343	+	0.740507i
$606$	4.51350	+	17.9044i	0.183348	+	0.727316i
$607$		−	20.2972i		−	0.823840i	−0.911220	−	0.411920i	$-0.864858\pi$
$607$		−	20.2972i		−	0.823840i	0.911220	−	0.411920i	$-0.135142\pi$
$608$		−	4.54838i		−	0.184461i
$609$	−63.7649	+	16.0744i	−2.58388	+	0.651368i
$610$	−16.6874			−0.675654
$611$	23.7738			0.961787
$612$	−2.64149	+	1.42216i	−0.106776	+	0.0574873i
$613$		−	42.1895i		−	1.70402i	−0.523527	−	0.852009i	$-0.675384\pi$
$613$		−	42.1895i		−	1.70402i	0.523527	−	0.852009i	$-0.324616\pi$
$614$			15.5925i			0.629264i
$615$	−10.4544	+	2.63544i	−0.421562	+	0.106271i
$616$	−8.66141	−	13.3367i	−0.348978	−	0.537349i
$617$		−	16.9281i		−	0.681499i	−0.940154	−	0.340749i	$-0.889319\pi$
$617$		−	16.9281i		−	0.681499i	0.940154	−	0.340749i	$-0.110681\pi$
$618$	0.586383	+	2.32610i	0.0235878	+	0.0935693i
$619$	18.3615			0.738009			0.369005	−	0.929428i	$-0.379699\pi$
$619$	18.3615			0.738009			0.369005	+	0.929428i	$0.379699\pi$
$620$		−	1.44659i		−	0.0580964i
$621$	21.5668	−	19.7253i	0.865444	−	0.791548i
$622$		−	28.3662i		−	1.13738i
$623$	−58.6406			−2.34939
$624$	4.32358	−	1.08993i	0.173082	−	0.0436319i
$625$	51.1383			2.04553
$626$	−6.39671			−0.255664
$627$	17.7694	−	19.1558i	0.709640	−	0.765009i
$628$	13.0711			0.521592
$629$	5.35573			0.213547
$630$	−51.5663	+	27.7629i	−2.05445	+	1.10610i
$631$	11.3092			0.450214			0.225107	−	0.974334i	$-0.427727\pi$
$631$	11.3092			0.450214			0.225107	+	0.974334i	$0.427727\pi$
$632$			9.05706i			0.360271i
$633$	19.5734	−	4.93424i	0.777974	−	0.196118i
$634$			29.7857i			1.18294i
$635$	−13.6522			−0.541771
$636$	−16.3304	+	4.11672i	−0.647544	+	0.163239i
$637$		−	41.1624i		−	1.63092i
$638$	22.0249	−	14.3039i	0.871974	−	0.566298i
$639$	−11.2534	−	20.9019i	−0.445178	−	0.826867i
$640$		−	4.07146i		−	0.160939i
$641$			37.8476i			1.49489i	0.664323	+	0.747446i	$0.268720\pi$
$641$			37.8476i			1.49489i	−0.664323	+	0.747446i	$0.731280\pi$
$642$	1.80046	+	7.14215i	0.0710584	+	0.281878i
$643$	29.5912			1.16696			0.583481	−	0.812127i	$-0.301690\pi$
$643$	29.5912			1.16696			0.583481	+	0.812127i	$0.301690\pi$
$644$	26.9692			1.06273
$645$	7.67378	+	30.4408i	0.302155	+	1.19861i
$646$		−	4.54838i		−	0.178954i
$647$			19.4975i			0.766525i	0.923640	+	0.383262i	$0.125199\pi$
$647$			19.4975i			0.766525i	−0.923640	+	0.383262i	$0.874801\pi$
$648$	−4.95494	+	7.51323i	−0.194648	+	0.295147i
$649$	21.0086	+	32.3487i	0.824661	+	1.26980i
$650$			29.8023i			1.16894i
$651$	−2.86117	+	0.721268i	−0.112138	+	0.0282687i
$652$	1.55929			0.0610665
$653$			48.5131i			1.89846i	0.314578	+	0.949232i	$0.398137\pi$
$653$			48.5131i			1.89846i	−0.314578	+	0.949232i	$0.601863\pi$
$654$	9.22198	−	2.32476i	0.360608	−	0.0909052i
$655$		−	59.8288i		−	2.33770i
$656$	−1.52886			−0.0596918
$657$	−6.06449	−	11.2641i	−0.236598	−	0.439454i
$658$	−44.2797			−1.72620
$659$	22.5480			0.878346			0.439173	−	0.898402i	$-0.355272\pi$
$659$	22.5480			0.878346			0.439173	+	0.898402i	$0.355272\pi$
$660$	15.9062	−	17.1472i	0.619147	−	0.667455i
$661$	40.1237			1.56063			0.780316	−	0.625386i	$-0.215058\pi$
$661$	40.1237			1.56063			0.780316	+	0.625386i	$0.215058\pi$
$662$	12.4742			0.484824
$663$	4.32358	−	1.08993i	0.167914	−	0.0423292i
$664$	−7.26631			−0.281988
$665$		−	88.7919i		−	3.44320i
$666$	14.1471	−	7.61669i	0.548190	−	0.295141i
$667$			44.5383i			1.72453i
$668$	−2.47630			−0.0958111
$669$	0.0602946	+	0.239180i	0.00233113	+	0.00924724i
$670$			20.8389i			0.805079i
$671$	−7.40390	−	11.4004i	−0.285825	−	0.440107i
$672$	−8.05283	+	2.03003i	−0.310645	+	0.0783100i
$673$			16.1708i			0.623338i	0.950191	+	0.311669i	$0.100888\pi$
$673$			16.1708i			0.623338i	−0.950191	+	0.311669i	$0.899112\pi$
$674$		−	14.7125i		−	0.566704i
$675$	−40.5986	−	44.3887i	−1.56264	−	1.70852i
$676$	6.37292			0.245112
$677$	9.65140			0.370933			0.185467	−	0.982651i	$-0.440620\pi$
$677$	9.65140			0.370933			0.185467	+	0.982651i	$0.440620\pi$
$678$	−29.1561	+	7.34993i	−1.11973	+	0.282272i
$679$			0.290484i			0.0111477i
$680$		−	4.07146i		−	0.156133i
$681$	2.64486	+	10.4918i	0.101351	+	0.402045i
$682$	0.988270	−	0.641825i	0.0378428	−	0.0245768i
$683$			26.8700i			1.02815i	0.857745	+	0.514075i	$0.171865\pi$
$683$			26.8700i			1.02815i	−0.857745	+	0.514075i	$0.828135\pi$
$684$	−6.46851	−	12.0145i	−0.247329	−	0.459386i
$685$	87.9493			3.36037
$686$			43.1034i			1.64569i
$687$	−4.24224	−	16.8284i	−0.161852	−	0.642042i
$688$			4.45168i			0.169719i
$689$	25.0309			0.953603
$690$	9.69587	+	38.4621i	0.369115	+	1.46423i
$691$	24.7811			0.942719			0.471360	−	0.881941i	$-0.343763\pi$
$691$	24.7811			0.942719			0.471360	+	0.881941i	$0.343763\pi$
$692$	−5.92606			−0.225275
$693$	−41.8458	−	22.9108i	−1.58959	−	0.870309i
$694$	−25.1368			−0.954180
$695$	−36.2172			−1.37380
$696$	−3.35250	−	13.2989i	−0.127076	−	0.504093i
$697$	−1.52886			−0.0579096
$698$		−	7.45414i		−	0.282143i
$699$	11.8224	+	46.8978i	0.447165	+	1.77384i
$700$		−	55.5079i		−	2.09800i
$701$	29.9252			1.13026			0.565130	−	0.825002i	$-0.308826\pi$
$701$	29.9252			1.13026			0.565130	+	0.825002i	$0.308826\pi$
$702$	9.87064	−	9.02783i	0.372543	−	0.340734i
$703$			24.3599i			0.918751i
$704$	2.78151	−	1.80643i	0.104832	−	0.0680825i
$705$	−15.9193	−	63.1496i	−0.599556	−	2.37835i
$706$			2.60469i			0.0980287i
$707$			51.1145i			1.92236i
$708$	19.5325	−	4.92393i	0.734077	−	0.185053i
$709$	−6.10968			−0.229454			−0.114727	−	0.993397i	$-0.536599\pi$
$709$	−6.10968			−0.229454			−0.114727	+	0.993397i	$0.536599\pi$
$710$	32.2172			1.20909
$711$	12.8806	+	23.9241i	0.483059	+	0.897225i
$712$		−	12.2301i		−	0.458344i
$713$			1.99846i			0.0748429i
$714$	−8.05283	+	2.03003i	−0.301370	+	0.0759719i
$715$	−29.1536	+	18.9336i	−1.09028	+	0.708077i
$716$		−	7.57467i		−	0.283079i
$717$	−7.06569	−	28.0286i	−0.263873	−	1.04675i
$718$	−7.37005			−0.275048
$719$			17.3107i			0.645579i	0.946471	+	0.322790i	$0.104621\pi$
$719$			17.3107i			0.645579i	−0.946471	+	0.322790i	$0.895379\pi$
$720$	−5.79026	−	10.7547i	−0.215790	−	0.400805i
$721$			6.64068i			0.247312i
$722$	1.68773			0.0628110
$723$	−25.1253	+	6.33380i	−0.934419	+	0.235557i
$724$	2.71865			0.101038
$725$	91.6688			3.40449
$726$	18.7718	+	3.25875i	0.696687	+	0.120943i
$727$	−4.20516			−0.155961			−0.0779803	−	0.996955i	$-0.524847\pi$
$727$	−4.20516			−0.155961			−0.0779803	+	0.996955i	$0.524847\pi$
$728$	12.3432			0.457469
$729$	−2.40344	+	26.8928i	−0.0890164	+	0.996030i
$730$	17.3619			0.642593
$731$			4.45168i			0.164651i
$732$	−6.88368	+	1.73530i	−0.254428	+	0.0641385i
$733$			27.8143i			1.02734i	0.857987	+	0.513672i	$0.171715\pi$
$733$			27.8143i			1.02734i	−0.857987	+	0.513672i	$0.828285\pi$
$734$	−3.43567			−0.126813
$735$	−109.338	+	27.5630i	−4.03300	+	1.01668i
$736$			5.62472i			0.207330i
$737$	−14.2366	+	9.24586i	−0.524412	+	0.340576i
$738$	−4.03846	+	2.17427i	−0.148658	+	0.0800361i
$739$			35.6113i			1.30998i	0.755636	+	0.654991i	$0.227328\pi$
$739$			35.6113i			1.30998i	−0.755636	+	0.654991i	$0.772672\pi$
$740$			21.8057i			0.801592i
$741$	4.95739	+	19.6653i	0.182114	+	0.722421i
$742$	−46.6211			−1.71151
$743$	35.6074			1.30631			0.653154	−	0.757225i	$-0.273446\pi$
$743$	35.6074			1.30631			0.653154	+	0.757225i	$0.273446\pi$
$744$	−0.150429	−	0.596728i	−0.00551498	−	0.0218771i
$745$		−	76.6265i		−	2.80738i
$746$			30.6755i			1.12311i
$747$	−19.1939	+	10.3338i	−0.702268	+	0.378095i
$748$	2.78151	−	1.80643i	0.101702	−	0.0660497i
$749$			20.3898i			0.745029i
$750$	44.9725	−	11.3371i	1.64216	−	0.413971i
$751$	1.60225			0.0584669			0.0292334	−	0.999573i	$-0.490693\pi$
$751$	1.60225			0.0584669			0.0292334	+	0.999573i	$0.490693\pi$
$752$		−	9.23503i		−	0.336767i
$753$	18.8936	−	4.76288i	0.688523	−	0.173569i
$754$			20.3842i			0.742350i
$755$	−67.6399			−2.46167
$756$	−18.3844	+	16.8147i	−0.668636	+	0.611544i
$757$	−30.4905			−1.10820			−0.554098	−	0.832452i	$-0.686937\pi$
$757$	−30.4905			−1.10820			−0.554098	+	0.832452i	$0.686937\pi$
$758$	6.90631			0.250848
$759$	−21.9744	+	23.6889i	−0.797619	+	0.859852i
$760$	18.5185			0.671738
$761$	33.3992			1.21072			0.605360	−	0.795952i	$-0.293029\pi$
$761$	33.3992			1.21072			0.605360	+	0.795952i	$0.293029\pi$
$762$	−5.63163	+	1.41967i	−0.204012	+	0.0514292i
$763$	26.3274			0.953117
$764$			20.5365i			0.742983i
$765$	−5.79026	−	10.7547i	−0.209347	−	0.388838i
$766$		−	8.94380i		−	0.323153i
$767$	−29.9390			−1.08103
$768$	−0.423385	−	1.67951i	−0.0152776	−	0.0606040i
$769$			1.31668i			0.0474806i	0.999718	+	0.0237403i	$0.00755749\pi$
$769$			1.31668i			0.0474806i	−0.999718	+	0.0237403i	$0.992443\pi$
$770$	54.2997	−	35.2646i	1.95683	−	1.27085i
$771$	30.8509	−	7.77716i	1.11107	−	0.280088i
$772$		−	3.45941i		−	0.124507i
$773$			16.6818i			0.600003i	0.953939	+	0.300001i	$0.0969871\pi$
$773$			16.6818i			0.600003i	−0.953939	+	0.300001i	$0.903013\pi$
$774$	6.33098	+	11.7591i	0.227562	+	0.422671i
$775$	4.11323			0.147752
$776$	−0.0605836			−0.00217483
$777$	43.1288	−	10.8723i	1.54724	−	0.390041i
$778$			37.7077i			1.35189i
$779$		−	6.95382i		−	0.249146i
$780$	4.43759	+	17.6033i	0.158891	+	0.630298i
$781$	14.2942	+	22.0099i	0.511486	+	0.787575i
$782$			5.62472i			0.201139i
$783$	−27.7687	−	30.3611i	−0.992372	−	1.08502i
$784$	−15.9897			−0.571060
$785$			53.2183i			1.89944i
$786$	−6.22150	−	24.6798i	−0.221914	−	0.880299i
$787$			14.2557i			0.508159i	0.967183	+	0.254080i	$0.0817726\pi$
$787$			14.2557i			0.508159i	−0.967183	+	0.254080i	$0.918227\pi$
$788$	−6.31827			−0.225079
$789$	−3.28899	−	13.0469i	−0.117091	−	0.464483i
$790$	−36.8755			−1.31197
$791$	−83.2366			−2.95955
$792$	4.77830	−	8.72742i	0.169789	−	0.310115i
$793$	10.5512			0.374683
$794$	−30.7172			−1.09011
$795$	−16.7611	−	66.4887i	−0.594454	−	2.35811i
$796$	0.756526			0.0268143
$797$		−	35.1548i		−	1.24525i	−0.782521	−	0.622624i	$-0.786067\pi$
$797$		−	35.1548i		−	1.24525i	0.782521	−	0.622624i	$-0.213933\pi$
$798$	−9.23333	−	36.6273i	−0.326856	−	1.29659i
$799$		−	9.23503i		−	0.326712i
$800$	11.5768			0.409302
$801$	−17.3932	−	32.3058i	−0.614558	−	1.14147i
$802$			1.35005i			0.0476720i
$803$	7.70316	+	11.8612i	0.271839	+	0.418572i
$804$	2.16701	+	8.59622i	0.0764246	+	0.303165i
$805$			109.804i			3.87008i
$806$			0.914652i			0.0322173i
$807$	11.1567	−	2.81249i	0.392735	−	0.0990042i
$808$	−10.6605			−0.375035
$809$	−47.1237			−1.65678			−0.828391	−	0.560151i	$-0.810743\pi$
$809$	−47.1237			−1.65678			−0.828391	+	0.560151i	$0.810743\pi$
$810$	−30.5898	−	20.1739i	−1.07482	−	0.708837i
$811$		−	14.2763i		−	0.501310i	−0.968077	−	0.250655i	$-0.919354\pi$
$811$		−	14.2763i		−	0.501310i	0.968077	−	0.250655i	$-0.0806459\pi$
$812$		−	37.9664i		−	1.33236i
$813$	19.4688	−	4.90787i	0.682801	−	0.172127i
$814$	−14.8970	+	9.67478i	−0.522141	+	0.339101i
$815$			6.34858i			0.222381i
$816$	−0.423385	−	1.67951i	−0.0148214	−	0.0587945i
$817$	−20.2479			−0.708385
$818$		−	31.8859i		−	1.11487i
$819$	32.6044	−	17.5540i	1.13929	−	0.613385i
$820$		−	6.22468i		−	0.217375i
$821$	−16.8744			−0.588922			−0.294461	−	0.955664i	$-0.595140\pi$
$821$	−16.8744			−0.588922			−0.294461	+	0.955664i	$0.595140\pi$
$822$	36.2797	−	9.14571i	1.26540	−	0.318993i
$823$	6.12550			0.213522			0.106761	−	0.994285i	$-0.465952\pi$
$823$	6.12550			0.213522			0.106761	+	0.994285i	$0.465952\pi$
$824$	−1.38499			−0.0482483
$825$	48.7565	+	45.2277i	1.69748	+	1.57463i
$826$	55.7625			1.94023
$827$	11.1077			0.386252			0.193126	−	0.981174i	$-0.438137\pi$
$827$	11.1077			0.386252			0.193126	+	0.981174i	$0.438137\pi$
$828$	7.99923	+	14.8576i	0.277992	+	0.516339i
$829$	−46.9752			−1.63152			−0.815758	−	0.578393i	$-0.803680\pi$
$829$	−46.9752			−1.63152			−0.815758	+	0.578393i	$0.803680\pi$
$830$		−	29.5845i		−	1.02689i
$831$	24.3021	−	6.12630i	0.843032	−	0.212519i
$832$			2.57431i			0.0892482i
$833$	−15.9897			−0.554010
$834$	−14.9398	+	3.76617i	−0.517324	+	0.130412i
$835$		−	10.0822i		−	0.348908i
$836$	8.21634	+	12.6514i	0.284168	+	0.437556i
$837$	−1.24600	−	1.36232i	−0.0430680	−	0.0470886i
$838$		−	6.43054i		−	0.222139i
$839$			25.1642i			0.868765i	0.900728	+	0.434383i	$0.143033\pi$
$839$			25.1642i			0.868765i	−0.900728	+	0.434383i	$0.856967\pi$
$840$	−8.26518	−	32.7868i	−0.285176	−	1.13125i
$841$	33.6998			1.16206
$842$	0.960351			0.0330959
$843$	5.10675	+	20.2577i	0.175886	+	0.697713i
$844$			11.6543i			0.401156i
$845$			25.9471i			0.892607i
$846$	−13.1337	−	24.3942i	−0.451544	−	0.838691i
$847$	48.1836	+	21.4498i	1.65561	+	0.737024i
$848$		−	9.72335i		−	0.333901i
$849$	5.61760	−	1.41613i	0.192795	−	0.0486016i
$850$	11.5768			0.397081
$851$		−	30.1245i		−	1.03265i
$852$	13.2898	−	3.35021i	0.455302	−	0.114776i
$853$		−	25.5957i		−	0.876379i	−0.898883	−	0.438189i	$-0.855620\pi$
$853$		−	25.5957i		−	0.876379i	0.898883	−	0.438189i	$-0.144380\pi$
$854$	−19.6519			−0.672475
$855$	48.9165	−	26.3363i	1.67291	−	0.900681i
$856$	−4.25253			−0.145348
$857$	−36.7932			−1.25683			−0.628415	−	0.777878i	$-0.716296\pi$
$857$	−36.7932			−1.25683			−0.628415	+	0.777878i	$0.716296\pi$
$858$	−10.0572	+	10.8419i	−0.343347	+	0.370136i
$859$	30.2778			1.03306			0.516532	−	0.856268i	$-0.327223\pi$
$859$	30.2778			1.03306			0.516532	+	0.856268i	$0.327223\pi$
$860$	−18.1248			−0.618052
$861$	−12.3116	+	3.10362i	−0.419579	+	0.105771i
$862$	−1.91773			−0.0653182
$863$		−	5.71212i		−	0.194443i	−0.995263	−	0.0972214i	$-0.969005\pi$
$863$		−	5.71212i		−	0.194443i	0.995263	−	0.0972214i	$-0.0309955\pi$
$864$	−3.50689	−	3.83428i	−0.119307	−	0.130445i
$865$		−	24.1277i		−	0.820368i
$866$	−10.0096			−0.340141
$867$	−0.423385	−	1.67951i	−0.0143789	−	0.0570391i
$868$		−	1.70358i		−	0.0578231i
$869$	−16.3610	−	25.1923i	−0.555008	−	0.854591i
$870$	54.1459	−	13.6496i	1.83572	−	0.462764i
$871$		−	13.1761i		−	0.446455i
$872$			5.49088i			0.185945i
$873$	−0.160031	+	0.0861594i	−0.00541623	+	0.00291605i
$874$	−25.5833			−0.865369
$875$	128.390			4.34038
$876$	7.16191	−	1.80544i	0.241978	−	0.0610001i
$877$		−	41.9623i		−	1.41697i	−0.705727	−	0.708484i	$-0.749379\pi$
$877$		−	41.9623i		−	1.41697i	0.705727	−	0.708484i	$-0.250621\pi$
$878$			23.1549i			0.781441i
$879$	−0.728667	−	2.89052i	−0.0245773	−	0.0974947i
$880$	7.35482	+	11.3248i	0.247931	+	0.381759i
$881$		−	7.05198i		−	0.237587i	−0.992919	−	0.118794i	$-0.962097\pi$
$881$		−	7.05198i		−	0.237587i	0.992919	−	0.118794i	$-0.0379027\pi$
$882$	−42.2366	+	22.7398i	−1.42218	+	0.765690i
$883$	−8.47204			−0.285107			−0.142553	−	0.989787i	$-0.545531\pi$
$883$	−8.47204			−0.285107			−0.142553	+	0.989787i	$0.545531\pi$
$884$			2.57431i			0.0865835i
$885$	20.0476	+	79.5259i	0.673892	+	2.67323i
$886$			10.9209i			0.366896i
$887$	47.8035			1.60509			0.802543	−	0.596595i	$-0.203480\pi$
$887$	47.8035			1.60509			0.802543	+	0.596595i	$0.203480\pi$
$888$	2.26754	+	8.99499i	0.0760936	+	0.301852i
$889$	−16.0775			−0.539222
$890$	49.7946			1.66912
$891$	0.210074	−	29.8489i	0.00703774	−	0.999975i
$892$	−0.142411			−0.00476827
$893$	42.0044			1.40562
$894$	−7.96828	−	31.6090i	−0.266499	−	1.05716i
$895$	30.8400			1.03087
$896$		−	4.79476i		−	0.160182i
$897$	−6.13052	−	24.3189i	−0.204692	−	0.811984i
$898$		−	13.2072i		−	0.440730i
$899$	2.81338			0.0938314
$900$	30.5800	−	16.4640i	1.01933	−	0.548801i
$901$		−	9.72335i		−	0.323932i
$902$	4.25253	−	2.76178i	0.141594	−	0.0919571i
$903$	9.03703	+	35.8486i	0.300734	+	1.19297i
$904$		−	17.3599i		−	0.577382i
$905$			11.0689i			0.367942i
$906$	−27.9019	+	7.03376i	−0.926979	+	0.233681i
$907$	−8.75556			−0.290724			−0.145362	−	0.989379i	$-0.546435\pi$
$907$	−8.75556			−0.290724			−0.145362	+	0.989379i	$0.546435\pi$
$908$	−6.24693			−0.207312
$909$	−28.1596	+	15.1609i	−0.933995	+	0.502855i
$910$			50.2549i			1.66593i
$911$		−	22.7770i		−	0.754634i	−0.926084	−	0.377317i	$-0.876847\pi$
$911$		−	22.7770i		−	0.754634i	0.926084	−	0.377317i	$-0.123153\pi$
$912$	7.63903	−	1.92571i	0.252954	−	0.0637668i
$913$	20.2113	−	13.1261i	0.668897	−	0.434411i
$914$		−	21.3501i		−	0.706200i
$915$	−7.06520	−	28.0266i	−0.233568	−	0.926532i
$916$	10.0198			0.331064
$917$		−	70.4573i		−	2.32671i
$918$	−3.50689	−	3.83428i	−0.115745	−	0.126550i
$919$			35.0107i			1.15490i	0.816427	+	0.577449i	$0.195952\pi$
$919$			35.0107i			1.15490i	−0.816427	+	0.577449i	$0.804048\pi$
$920$	−22.9008			−0.755018
$921$	−26.1878	+	6.60165i	−0.862917	+	0.217532i
$922$	−4.75396			−0.156563
$923$	−20.3703			−0.670498
$924$	18.7319	−	20.1934i	0.616235	−	0.664315i
$925$	−62.0023			−2.03862
$926$	−34.9504			−1.14854
$927$	−3.65843	+	1.96967i	−0.120159	+	0.0646924i
$928$	7.91832			0.259932
$929$			18.4339i			0.604796i	0.953182	+	0.302398i	$0.0977872\pi$
$929$			18.4339i			0.604796i	−0.953182	+	0.302398i	$0.902213\pi$
$930$	2.42956	−	0.612464i	0.0796683	−	0.0200835i
$931$		−	72.7271i		−	2.38354i
$932$	−27.9235			−0.914666
$933$	47.6413	−	12.0098i	1.55971	−	0.393184i
$934$			17.6209i			0.576575i
$935$	7.35482	+	11.3248i	0.240528	+	0.370361i
$936$	3.66108	+	6.80002i	0.119666	+	0.222266i
$937$		−	17.0084i		−	0.555640i	−0.960633	−	0.277820i	$-0.910388\pi$
$937$		−	17.0084i		−	0.555640i	0.960633	−	0.277820i	$-0.0896119\pi$
$938$			24.5410i			0.801292i
$939$	−2.70827	−	10.7433i	−0.0883812	−	0.350595i
$940$	37.6001			1.22638
$941$	−7.06014			−0.230154			−0.115077	−	0.993357i	$-0.536711\pi$
$941$	−7.06014			−0.230154			−0.115077	+	0.993357i	$0.536711\pi$
$942$	5.53409	+	21.9529i	0.180310	+	0.715265i
$943$			8.59939i			0.280035i
$944$			11.6299i			0.378521i
$945$	−68.4603	−	74.8516i	−2.22702	−	2.43492i
$946$	−8.04166	−	12.3824i	−0.261457	−	0.402586i
$947$		−	14.7310i		−	0.478692i	−0.970934	−	0.239346i	$-0.923067\pi$
$947$		−	14.7310i		−	0.478692i	0.970934	−	0.239346i	$-0.0769331\pi$
$948$	−15.2114	+	3.83462i	−0.494043	+	0.124543i
$949$	−10.9776			−0.356348
$950$			52.6557i			1.70838i
$951$	−50.0253	+	12.6108i	−1.62218	+	0.408934i
$952$		−	4.79476i		−	0.155399i
$953$	−1.29427			−0.0419255			−0.0209628	−	0.999780i	$-0.506673\pi$
$953$	−1.29427			−0.0419255			−0.0209628	+	0.999780i	$0.506673\pi$
$954$	−13.8281	−	25.6841i	−0.447702	−	0.831554i
$955$	−83.6134			−2.70567
$956$	16.6886			0.539747
$957$	33.3485	+	30.9349i	1.07801	+	0.999983i
$958$	21.9110			0.707912
$959$	103.573			3.34456
$960$	6.83805	−	1.72380i	0.220697	−	0.0556353i
$961$	−30.8738			−0.995928
$962$		−	13.7873i		−	0.444521i
$963$	−11.2330	+	6.04776i	−0.361979	+	0.194886i
$964$		−	14.9599i		−	0.481826i
$965$	14.0849			0.453408
$966$	11.4183	+	45.2949i	0.367379	+	1.45734i
$967$		−	22.1308i		−	0.711680i	−0.934547	−	0.355840i	$-0.884195\pi$
$967$		−	22.1308i		−	0.711680i	0.934547	−	0.355840i	$-0.115805\pi$
$968$	−4.47360	+	10.0492i	−0.143787	+	0.322994i
$969$	7.63903	−	1.92571i	0.245401	−	0.0618629i
$970$		−	0.246664i		−	0.00791990i
$971$		−	3.01415i		−	0.0967288i	−0.998830	−	0.0483644i	$-0.984599\pi$
$971$		−	3.01415i		−	0.0967288i	0.998830	−	0.0483644i	$-0.0154009\pi$
$972$	−14.7164	−	5.14087i	−0.472028	−	0.164894i
$973$	−42.6511			−1.36733
$974$	18.5751			0.595183
$975$	−50.0532	+	12.6178i	−1.60298	+	0.404095i
$976$		−	4.09863i		−	0.131194i
$977$		−	12.0668i		−	0.386050i	−0.981194	−	0.193025i	$-0.938170\pi$
$977$		−	12.0668i		−	0.386050i	0.981194	−	0.193025i	$-0.0618298\pi$
$978$	0.660180	+	2.61884i	0.0211102	+	0.0837412i
$979$	22.0930	+	34.0183i	0.706094	+	1.08723i
$980$		−	65.1014i		−	2.07959i
$981$	7.80889	+	14.5041i	0.249319	+	0.463081i
$982$	8.75916			0.279516
$983$			59.4225i			1.89528i	0.319334	+	0.947642i	$0.396541\pi$
$983$			59.4225i			1.89528i	−0.319334	+	0.947642i	$0.603459\pi$
$984$	−0.647295	−	2.56773i	−0.0206350	−	0.0818561i
$985$		−	25.7246i		−	0.819654i
$986$	7.91832			0.252171
$987$	−18.7474	−	74.3681i	−0.596735	−	2.36716i
$988$	−11.7089			−0.372511
$989$	25.0394			0.796208
$990$	35.5334	+	19.4547i	1.12932	+	0.618310i
$991$	16.1986			0.514566			0.257283	−	0.966336i	$-0.417173\pi$
$991$	16.1986			0.514566			0.257283	+	0.966336i	$0.417173\pi$
$992$	0.355300			0.0112808
$993$	5.28139	+	20.9505i	0.167600	+	0.664845i
$994$	37.9405			1.20340
$995$			3.08017i			0.0976478i
$996$	−3.07645	−	12.2038i	−0.0974810	−	0.386693i
$997$			18.8652i			0.597468i	0.954336	+	0.298734i	$0.0965644\pi$
$997$			18.8652i			0.597468i	−0.954336	+	0.298734i	$0.903436\pi$
$998$	−1.95828			−0.0619882
$999$	18.7820	+	20.5354i	0.594235	+	0.649711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.b.a.1055.5	✓	16
3.2	odd	2		1122.2.b.c.1055.6	yes	16
11.10	odd	2		1122.2.b.c.1055.5	yes	16
33.32	even	2	inner	1122.2.b.a.1055.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.b.a.1055.5	✓	16	1.1	even	1	trivial
1122.2.b.a.1055.6	yes	16	33.32	even	2	inner
1122.2.b.c.1055.5	yes	16	11.10	odd	2
1122.2.b.c.1055.6	yes	16	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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.423385 - 1.67951i) q^{3} +1.00000 q^{4} +4.07146i q^{5} +(0.423385 + 1.67951i) q^{6} +4.79476i q^{7} -1.00000 q^{8} +(-2.64149 + 1.42216i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.423385 - 1.67951i) q^{3} +1.00000 q^{4} +4.07146i q^{5} +(0.423385 + 1.67951i) q^{6} +4.79476i q^{7} -1.00000 q^{8} +(-2.64149 + 1.42216i) q^{9} -4.07146i q^{10} +(2.78151 - 1.80643i) q^{11} +(-0.423385 - 1.67951i) q^{12} +2.57431i q^{13} -4.79476i q^{14} +(6.83805 - 1.72380i) q^{15} +1.00000 q^{16} +1.00000 q^{17} +(2.64149 - 1.42216i) q^{18} +4.54838i q^{19} +4.07146i q^{20} +(8.05283 - 2.03003i) q^{21} +(-2.78151 + 1.80643i) q^{22} -5.62472i q^{23} +(0.423385 + 1.67951i) q^{24} -11.5768 q^{25} -2.57431i q^{26} +(3.50689 + 3.83428i) q^{27} +4.79476i q^{28} -7.91832 q^{29} +(-6.83805 + 1.72380i) q^{30} -0.355300 q^{31} -1.00000 q^{32} +(-4.21157 - 3.90675i) q^{33} -1.00000 q^{34} -19.5217 q^{35} +(-2.64149 + 1.42216i) q^{36} +5.35573 q^{37} -4.54838i q^{38} +(4.32358 - 1.08993i) q^{39} -4.07146i q^{40} -1.52886 q^{41} +(-8.05283 + 2.03003i) q^{42} +4.45168i q^{43} +(2.78151 - 1.80643i) q^{44} +(-5.79026 - 10.7547i) q^{45} +5.62472i q^{46} -9.23503i q^{47} +(-0.423385 - 1.67951i) q^{48} -15.9897 q^{49} +11.5768 q^{50} +(-0.423385 - 1.67951i) q^{51} +2.57431i q^{52} -9.72335i q^{53} +(-3.50689 - 3.83428i) q^{54} +(7.35482 + 11.3248i) q^{55} -4.79476i q^{56} +(7.63903 - 1.92571i) q^{57} +7.91832 q^{58} +11.6299i q^{59} +(6.83805 - 1.72380i) q^{60} -4.09863i q^{61} +0.355300 q^{62} +(-6.81889 - 12.6653i) q^{63} +1.00000 q^{64} -10.4812 q^{65} +(4.21157 + 3.90675i) q^{66} -5.11830 q^{67} +1.00000 q^{68} +(-9.44676 + 2.38142i) q^{69} +19.5217 q^{70} +7.91292i q^{71} +(2.64149 - 1.42216i) q^{72} +4.26429i q^{73} -5.35573 q^{74} +(4.90144 + 19.4433i) q^{75} +4.54838i q^{76} +(8.66141 + 13.3367i) q^{77} +(-4.32358 + 1.08993i) q^{78} -9.05706i q^{79} +4.07146i q^{80} +(4.95494 - 7.51323i) q^{81} +1.52886 q^{82} +7.26631 q^{83} +(8.05283 - 2.03003i) q^{84} +4.07146i q^{85} -4.45168i q^{86} +(3.35250 + 13.2989i) q^{87} +(-2.78151 + 1.80643i) q^{88} +12.2301i q^{89} +(5.79026 + 10.7547i) q^{90} -12.3432 q^{91} -5.62472i q^{92} +(0.150429 + 0.596728i) q^{93} +9.23503i q^{94} -18.5185 q^{95} +(0.423385 + 1.67951i) q^{96} +0.0605836 q^{97} +15.9897 q^{98} +(-4.77830 + 8.72742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9	\( 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9} + 6 q^{11} + q^{12} + 16 q^{16} + 16 q^{17} + 3 q^{18} + 24 q^{21} - 6 q^{22} - q^{24} - 22 q^{25} + 13 q^{27} - 20 q^{29} + 24 q^{31} - 16 q^{32} - 3 q^{33} - 16 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - q^{39} + 22 q^{41} - 24 q^{42} + 6 q^{44} - 15 q^{45} + q^{48} - 54 q^{49} + 22 q^{50} + q^{51} - 13 q^{54} - 10 q^{55} + 8 q^{57} + 20 q^{58} - 24 q^{62} - 36 q^{63} + 16 q^{64} - 68 q^{65} + 3 q^{66} + 12 q^{67} + 16 q^{68} - 40 q^{69} - 12 q^{70} + 3 q^{72} - 6 q^{74} + q^{75} + 10 q^{77} + q^{78} + 17 q^{81} - 22 q^{82} - 10 q^{83} + 24 q^{84} + 12 q^{87} - 6 q^{88} + 15 q^{90} + 4 q^{91} + 6 q^{93} - 48 q^{95} - q^{96} + 54 q^{98} + 31 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9 + 6 * q^11 + q^12 + 16 * q^16 + 16 * q^17 + 3 * q^18 + 24 * q^21 - 6 * q^22 - q^24 - 22 * q^25 + 13 * q^27 - 20 * q^29 + 24 * q^31 - 16 * q^32 - 3 * q^33 - 16 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - q^39 + 22 * q^41 - 24 * q^42 + 6 * q^44 - 15 * q^45 + q^48 - 54 * q^49 + 22 * q^50 + q^51 - 13 * q^54 - 10 * q^55 + 8 * q^57 + 20 * q^58 - 24 * q^62 - 36 * q^63 + 16 * q^64 - 68 * q^65 + 3 * q^66 + 12 * q^67 + 16 * q^68 - 40 * q^69 - 12 * q^70 + 3 * q^72 - 6 * q^74 + q^75 + 10 * q^77 + q^78 + 17 * q^81 - 22 * q^82 - 10 * q^83 + 24 * q^84 + 12 * q^87 - 6 * q^88 + 15 * q^90 + 4 * q^91 + 6 * q^93 - 48 * q^95 - q^96 + 54 * q^98 + 31 * q^99

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