LMFDB - Embedded newform 546.2.bm.b.277.2

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			277.2
Root			$-1.77962i$ of defining polynomial
Character	$\chi$	$=$	546.277
Dual form			546.2.bm.b.205.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.51386 - 0.824914i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.51386 - 0.824914i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.889808 + 1.54119i) q^{10} +(-0.0253148 + 0.0146155i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.100748 + 3.60414i) q^{13} +(-0.824914 + 2.51386i) q^{14} +(1.54119 + 0.889808i) q^{15} +1.00000 q^{16} +6.11260 q^{17} +(0.866025 + 0.500000i) q^{18} +(5.76702 + 3.32959i) q^{19} +(1.54119 - 0.889808i) q^{20} +(0.542536 + 2.58953i) q^{21} +(0.0146155 + 0.0253148i) q^{22} -4.80277 q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.916484 + 1.58740i) q^{25} +(3.60414 - 0.100748i) q^{26} +1.00000 q^{27} +(2.51386 + 0.824914i) q^{28} +(-2.29119 + 3.96846i) q^{29} +(0.889808 - 1.54119i) q^{30} +(-3.81631 - 2.20335i) q^{31} -1.00000i q^{32} +(0.0253148 + 0.0146155i) q^{33} -6.11260i q^{34} +(4.60836 - 0.965505i) q^{35} +(0.500000 - 0.866025i) q^{36} +10.9631i q^{37} +(3.32959 - 5.76702i) q^{38} +(3.07091 - 1.88932i) q^{39} +(-0.889808 - 1.54119i) q^{40} +(-6.40202 - 3.69621i) q^{41} +(2.58953 - 0.542536i) q^{42} +(4.27767 + 7.40915i) q^{43} +(0.0253148 - 0.0146155i) q^{44} -1.77962i q^{45} +4.80277i q^{46} +(-4.84344 + 2.79636i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(5.63903 + 4.14745i) q^{49} +(1.58740 + 0.916484i) q^{50} +(-3.05630 - 5.29367i) q^{51} +(-0.100748 - 3.60414i) q^{52} +(0.0633613 - 0.109745i) q^{53} -1.00000i q^{54} +(0.0260100 - 0.0450507i) q^{55} +(0.824914 - 2.51386i) q^{56} -6.65918i q^{57} +(3.96846 + 2.29119i) q^{58} -12.7534i q^{59} +(-1.54119 - 0.889808i) q^{60} +(3.21492 - 5.56841i) q^{61} +(-2.20335 + 3.81631i) q^{62} +(1.97133 - 1.76461i) q^{63} -1.00000 q^{64} +(-3.36227 - 5.46503i) q^{65} +(0.0146155 - 0.0253148i) q^{66} +(-4.93323 + 2.84820i) q^{67} -6.11260 q^{68} +(2.40138 + 4.15932i) q^{69} +(-0.965505 - 4.60836i) q^{70} +(-7.24189 + 4.18111i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.21521 + 3.01100i) q^{73} +10.9631 q^{74} +1.83297 q^{75} +(-5.76702 - 3.32959i) q^{76} +(0.0756946 - 0.0158589i) q^{77} +(-1.88932 - 3.07091i) q^{78} +(0.798515 + 1.38307i) q^{79} +(-1.54119 + 0.889808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.69621 + 6.40202i) q^{82} -8.39736i q^{83} +(-0.542536 - 2.58953i) q^{84} +(-9.42070 + 5.43904i) q^{85} +(7.40915 - 4.27767i) q^{86} +4.58238 q^{87} +(-0.0146155 - 0.0253148i) q^{88} +13.5008i q^{89} -1.77962 q^{90} +(2.71984 - 9.14344i) q^{91} +4.80277 q^{92} +4.40670i q^{93} +(2.79636 + 4.84344i) q^{94} -11.8508 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-9.75571 + 5.63246i) q^{97} +(4.14745 - 5.63903i) q^{98} -0.0292310i 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
$5$	−1.54119	+	0.889808i	−0.689242	+	0.397934i	−0.803328	−	0.595537i	$-0.796939\pi$
$5$	−1.54119	+	0.889808i	−0.689242	+	0.397934i	0.114086	+	0.993471i	$0.463606\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−2.51386	−	0.824914i	−0.950152	−	0.311788i
$7$	−2.51386	−	0.824914i	−0.950152	−	0.311788i
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.889808	+	1.54119i	0.281382	+	0.487368i
$11$	−0.0253148	+	0.0146155i	−0.00763271	+	0.00440675i	−0.503811	−	0.863814i	$-0.668069\pi$
$11$	−0.0253148	+	0.0146155i	−0.00763271	+	0.00440675i	0.496179	+	0.868220i	$0.334736\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.100748	+	3.60414i	0.0279425	+	0.999610i
$13$	0.100748	+	3.60414i	0.0279425	+	0.999610i
$14$	−0.824914	+	2.51386i	−0.220468	+	0.671859i
$15$	1.54119	+	0.889808i	0.397934	+	0.229747i
$16$	1.00000			0.250000
$17$	6.11260			1.48252			0.741262	−	0.671216i	$-0.234228\pi$
$17$	6.11260			1.48252			0.741262	+	0.671216i	$0.234228\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	5.76702	+	3.32959i	1.32304	+	0.763860i	0.984213	−	0.176987i	$-0.0566351\pi$
$19$	5.76702	+	3.32959i	1.32304	+	0.763860i	0.338831	+	0.940847i	$0.389968\pi$
$20$	1.54119	−	0.889808i	0.344621	−	0.198967i
$21$	0.542536	+	2.58953i	0.118391	+	0.565081i
$22$	0.0146155	+	0.0253148i	0.00311604	+	0.00539714i
$23$	−4.80277			−1.00145			−0.500723	−	0.865608i	$-0.666932\pi$
$23$	−4.80277			−1.00145			−0.500723	+	0.865608i	$0.666932\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−0.916484	+	1.58740i	−0.183297	+	0.317479i
$26$	3.60414	−	0.100748i	0.706831	−	0.0197583i
$27$	1.00000			0.192450
$28$	2.51386	+	0.824914i	0.475076	+	0.155894i
$29$	−2.29119	+	3.96846i	−0.425463	+	0.736924i	−0.996464	−	0.0840257i	$-0.973222\pi$
$29$	−2.29119	+	3.96846i	−0.425463	+	0.736924i	0.571000	+	0.820950i	$0.306556\pi$
$30$	0.889808	−	1.54119i	0.162456	−	0.281382i
$31$	−3.81631	−	2.20335i	−0.685430	−	0.395733i	0.116468	−	0.993194i	$-0.462843\pi$
$31$	−3.81631	−	2.20335i	−0.685430	−	0.395733i	−0.801898	+	0.597461i	$0.796176\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.0253148	+	0.0146155i	0.00440675	+	0.00254424i
$34$		−	6.11260i		−	1.04830i
$35$	4.60836	−	0.965505i	0.778956	−	0.163200i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$			10.9631i			1.80233i	0.433479	+	0.901164i	$0.357286\pi$
$37$			10.9631i			1.80233i	−0.433479	+	0.901164i	$0.642714\pi$
$38$	3.32959	−	5.76702i	0.540131	−	0.935534i
$39$	3.07091	−	1.88932i	0.491738	−	0.302534i
$40$	−0.889808	−	1.54119i	−0.140691	−	0.243684i
$41$	−6.40202	−	3.69621i	−0.999827	−	0.577251i	−0.0916301	−	0.995793i	$-0.529208\pi$
$41$	−6.40202	−	3.69621i	−0.999827	−	0.577251i	−0.908197	+	0.418543i	$0.862541\pi$
$42$	2.58953	−	0.542536i	0.399573	−	0.0837151i
$43$	4.27767	+	7.40915i	0.652339	+	1.12988i	0.982554	+	0.185979i	$0.0595455\pi$
$43$	4.27767	+	7.40915i	0.652339	+	1.12988i	−0.330215	+	0.943906i	$0.607121\pi$
$44$	0.0253148	−	0.0146155i	0.00381635	−	0.00220337i
$45$		−	1.77962i		−	0.265289i
$46$			4.80277i			0.708129i
$47$	−4.84344	+	2.79636i	−0.706488	+	0.407891i	−0.809759	−	0.586762i	$-0.800402\pi$
$47$	−4.84344	+	2.79636i	−0.706488	+	0.407891i	0.103271	+	0.994653i	$0.467069\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	5.63903	+	4.14745i	0.805576	+	0.592492i
$50$	1.58740	+	0.916484i	0.224492	+	0.129610i
$51$	−3.05630	−	5.29367i	−0.427968	−	0.741262i
$52$	−0.100748	−	3.60414i	−0.0139712	−	0.499805i
$53$	0.0633613	−	0.109745i	0.00870334	−	0.0150746i	−0.861641	−	0.507518i	$-0.830563\pi$
$53$	0.0633613	−	0.109745i	0.00870334	−	0.0150746i	0.870344	+	0.492444i	$0.163896\pi$
$54$		−	1.00000i		−	0.136083i
$55$	0.0260100	−	0.0450507i	0.00350719	−	0.00607463i
$56$	0.824914	−	2.51386i	0.110234	−	0.335929i
$57$		−	6.65918i		−	0.882030i
$58$	3.96846	+	2.29119i	0.521084	+	0.300848i
$59$		−	12.7534i		−	1.66035i	−0.557500	−	0.830177i	$-0.688239\pi$
$59$		−	12.7534i		−	1.66035i	0.557500	−	0.830177i	$-0.311761\pi$
$60$	−1.54119	−	0.889808i	−0.198967	−	0.114874i
$61$	3.21492	−	5.56841i	0.411629	−	0.712962i	−0.583439	−	0.812157i	$-0.698293\pi$
$61$	3.21492	−	5.56841i	0.411629	−	0.712962i	0.995068	+	0.0991949i	$0.0316267\pi$
$62$	−2.20335	+	3.81631i	−0.279825	+	0.484672i
$63$	1.97133	−	1.76461i	0.248364	−	0.222320i
$64$	−1.00000			−0.125000
$65$	−3.36227	−	5.46503i	−0.417038	−	0.677854i
$66$	0.0146155	−	0.0253148i	0.00179905	−	0.00311604i
$67$	−4.93323	+	2.84820i	−0.602690	+	0.347963i	−0.770099	−	0.637924i	$-0.779793\pi$
$67$	−4.93323	+	2.84820i	−0.602690	+	0.347963i	0.167409	+	0.985887i	$0.446460\pi$
$68$	−6.11260			−0.741262
$69$	2.40138	+	4.15932i	0.289093	+	0.500723i
$70$	−0.965505	−	4.60836i	−0.115400	−	0.550805i
$71$	−7.24189	+	4.18111i	−0.859455	+	0.496206i	−0.863830	−	0.503784i	$-0.831941\pi$
$71$	−7.24189	+	4.18111i	−0.859455	+	0.496206i	0.00437501	+	0.999990i	$0.498607\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	5.21521	+	3.01100i	0.610394	+	0.352411i	0.773120	−	0.634260i	$-0.218695\pi$
$73$	5.21521	+	3.01100i	0.610394	+	0.352411i	−0.162726	+	0.986671i	$0.552029\pi$
$74$	10.9631			1.27444
$75$	1.83297			0.211653
$76$	−5.76702	−	3.32959i	−0.661522	−	0.381930i
$77$	0.0756946	−	0.0158589i	0.00862620	−	0.00180729i
$78$	−1.88932	−	3.07091i	−0.213924	−	0.347712i
$79$	0.798515	+	1.38307i	0.0898400	+	0.155607i	0.907443	−	0.420174i	$-0.138031\pi$
$79$	0.798515	+	1.38307i	0.0898400	+	0.155607i	−0.817603	+	0.575782i	$0.804698\pi$
$80$	−1.54119	+	0.889808i	−0.172311	+	0.0994835i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.69621	+	6.40202i	−0.408178	+	0.706985i
$83$		−	8.39736i		−	0.921730i	−0.887470	−	0.460865i	$-0.847539\pi$
$83$		−	8.39736i		−	0.921730i	0.887470	−	0.460865i	$-0.152461\pi$
$84$	−0.542536	−	2.58953i	−0.0591955	−	0.282541i
$85$	−9.42070	+	5.43904i	−1.02182	+	0.589947i
$86$	7.40915	−	4.27767i	0.798949	−	0.461273i
$87$	4.58238			0.491283
$88$	−0.0146155	−	0.0253148i	−0.00155802	−	0.00269857i
$89$			13.5008i			1.43108i	0.698573	+	0.715539i	$0.253819\pi$
$89$			13.5008i			1.43108i	−0.698573	+	0.715539i	$0.746181\pi$
$90$	−1.77962			−0.187588
$91$	2.71984	−	9.14344i	0.285117	−	0.958493i
$92$	4.80277			0.500723
$93$			4.40670i			0.456953i
$94$	2.79636	+	4.84344i	0.288423	+	0.499563i
$95$	−11.8508			−1.21586
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−9.75571	+	5.63246i	−0.990543	+	0.571890i	−0.905436	−	0.424482i	$-0.860456\pi$
$97$	−9.75571	+	5.63246i	−0.990543	+	0.571890i	−0.0851062	+	0.996372i	$0.527123\pi$
$98$	4.14745	−	5.63903i	0.418955	−	0.569628i
$99$		−	0.0292310i		−	0.00293783i
$100$	0.916484	−	1.58740i	0.0916484	−	0.158740i
$101$	−0.321007	−	0.556000i	−0.0319414	−	0.0553241i	0.849613	−	0.527407i	$-0.176836\pi$
$101$	−0.321007	−	0.556000i	−0.0319414	−	0.0553241i	−0.881554	+	0.472083i	$0.843502\pi$
$102$	−5.29367	+	3.05630i	−0.524151	+	0.302619i
$103$	9.07044	+	15.7105i	0.893737	+	1.54800i	0.835361	+	0.549702i	$0.185259\pi$
$103$	9.07044	+	15.7105i	0.893737	+	1.54800i	0.0583760	+	0.998295i	$0.481408\pi$
$104$	−3.60414	+	0.100748i	−0.353415	+	0.00987915i
$105$	−3.14033	−	3.50821i	−0.306465	−	0.342366i
$106$	−0.109745	−	0.0633613i	−0.0106594	−	0.00615419i
$107$	0.552995			0.0534600			0.0267300	−	0.999643i	$-0.491491\pi$
$107$	0.552995			0.0534600			0.0267300	+	0.999643i	$0.491491\pi$
$108$	−1.00000			−0.0962250
$109$	−17.1187	−	9.88349i	−1.63968	−	0.946667i	−0.980945	−	0.194288i	$-0.937760\pi$
$109$	−17.1187	−	9.88349i	−1.63968	−	0.946667i	−0.658731	−	0.752379i	$-0.728906\pi$
$110$	−0.0450507	−	0.0260100i	−0.00429541	−	0.00247996i
$111$	9.49435	−	5.48157i	0.901164	−	0.520287i
$112$	−2.51386	−	0.824914i	−0.237538	−	0.0779471i
$113$	−1.00335	−	1.73785i	−0.0943873	−	0.163484i	0.814965	−	0.579510i	$-0.196756\pi$
$113$	−1.00335	−	1.73785i	−0.0943873	−	0.163484i	−0.909353	+	0.416026i	$0.863423\pi$
$114$	−6.65918			−0.623689
$115$	7.40199	−	4.27354i	0.690239	−	0.398510i
$116$	2.29119	−	3.96846i	0.212732	−	0.368462i
$117$	−3.17165	−	1.71482i	−0.293219	−	0.158535i
$118$	−12.7534			−1.17405
$119$	−15.3663	−	5.04237i	−1.40862	−	0.462233i
$120$	−0.889808	+	1.54119i	−0.0812280	+	0.140691i
$121$	−5.49957	+	9.52554i	−0.499961	+	0.865958i
$122$	−5.56841	−	3.21492i	−0.504140	−	0.291065i
$123$			7.39241i			0.666552i
$124$	3.81631	+	2.20335i	0.342715	+	0.197866i
$125$		−	12.1601i		−	1.08763i
$126$	−1.76461	−	1.97133i	−0.157204	−	0.175620i
$127$	5.01216	−	8.68131i	0.444757	−	0.770342i	−0.553278	−	0.832997i	$-0.686623\pi$
$127$	5.01216	−	8.68131i	0.444757	−	0.770342i	0.998035	+	0.0626548i	$0.0199567\pi$
$128$			1.00000i			0.0883883i
$129$	4.27767	−	7.40915i	0.376628	−	0.652339i
$130$	−5.46503	+	3.36227i	−0.479315	+	0.294890i
$131$	0.434167	+	0.751999i	0.0379333	+	0.0657025i	0.884369	−	0.466789i	$-0.154589\pi$
$131$	0.434167	+	0.751999i	0.0379333	+	0.0657025i	−0.846435	+	0.532491i	$0.821256\pi$
$132$	−0.0253148	−	0.0146155i	−0.00220337	−	0.00127212i
$133$	−11.7509	−	13.1274i	−1.01893	−	1.13829i
$134$	2.84820	+	4.93323i	0.246047	+	0.426166i
$135$	−1.54119	+	0.889808i	−0.132645	+	0.0765825i
$136$			6.11260i			0.524151i
$137$			19.6304i			1.67714i	0.544795	+	0.838569i	$0.316607\pi$
$137$			19.6304i			1.67714i	−0.544795	+	0.838569i	$0.683393\pi$
$138$	4.15932	−	2.40138i	0.354065	−	0.204419i
$139$	−1.50591	−	2.60832i	−0.127730	−	0.221235i	0.795067	−	0.606522i	$-0.207436\pi$
$139$	−1.50591	−	2.60832i	−0.127730	−	0.221235i	−0.922797	+	0.385287i	$0.874102\pi$
$140$	−4.60836	+	0.965505i	−0.389478	+	0.0816001i
$141$	4.84344	+	2.79636i	0.407891	+	0.235496i
$142$	4.18111	+	7.24189i	0.350871	+	0.607726i
$143$	−0.0552268	−	0.0897658i	−0.00461830	−	0.00750659i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		−	8.15488i		−	0.677226i
$146$	3.01100	−	5.21521i	0.249192	−	0.431614i
$147$	0.772276	−	6.95727i	0.0636963	−	0.573826i
$148$		−	10.9631i		−	0.901164i
$149$	12.8141	+	7.39820i	1.04977	+	0.606084i	0.922585	−	0.385795i	$-0.126073\pi$
$149$	12.8141	+	7.39820i	1.04977	+	0.606084i	0.127184	+	0.991879i	$0.459406\pi$
$150$		−	1.83297i		−	0.149661i
$151$	−0.606515	−	0.350172i	−0.0493575	−	0.0284966i	0.475118	−	0.879922i	$-0.342405\pi$
$151$	−0.606515	−	0.350172i	−0.0493575	−	0.0284966i	−0.524476	+	0.851425i	$0.675739\pi$
$152$	−3.32959	+	5.76702i	−0.270065	+	0.467767i
$153$	−3.05630	+	5.29367i	−0.247087	+	0.427968i
$154$	−0.0158589	−	0.0756946i	−0.00127795	−	0.00609964i
$155$	7.84222			0.629903
$156$	−3.07091	+	1.88932i	−0.245869	+	0.151267i
$157$	−4.48136	+	7.76194i	−0.357651	+	0.619470i	−0.987568	−	0.157193i	$-0.949756\pi$
$157$	−4.48136	+	7.76194i	−0.357651	+	0.619470i	0.629917	+	0.776663i	$0.283089\pi$
$158$	1.38307	−	0.798515i	0.110031	−	0.0635264i
$159$	−0.126723			−0.0100498
$160$	0.889808	+	1.54119i	0.0703455	+	0.121842i
$161$	12.0735	+	3.96187i	0.951525	+	0.312239i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	5.80295	+	3.35033i	0.454522	+	0.262418i	0.709738	−	0.704466i	$-0.248813\pi$
$163$	5.80295	+	3.35033i	0.454522	+	0.262418i	−0.255216	+	0.966884i	$0.582147\pi$
$164$	6.40202	+	3.69621i	0.499914	+	0.288625i
$165$	−0.0520200			−0.00404975
$166$	−8.39736			−0.651761
$167$	4.07956	+	2.35534i	0.315686	+	0.182261i	0.649468	−	0.760389i	$-0.274992\pi$
$167$	4.07956	+	2.35534i	0.315686	+	0.182261i	−0.333782	+	0.942650i	$0.608325\pi$
$168$	−2.58953	+	0.542536i	−0.199786	+	0.0418576i
$169$	−12.9797	+	0.726220i	−0.998438	+	0.0558631i
$170$	5.43904	+	9.42070i	0.417155	+	0.722534i
$171$	−5.76702	+	3.32959i	−0.441015	+	0.254620i
$172$	−4.27767	−	7.40915i	−0.326170	−	0.564942i
$173$	11.2521	−	19.4892i	0.855482	−	1.48174i	−0.0207149	−	0.999785i	$-0.506594\pi$
$173$	11.2521	−	19.4892i	0.855482	−	1.48174i	0.876197	−	0.481953i	$-0.160072\pi$
$174$		−	4.58238i		−	0.347389i
$175$	3.61338	−	3.23448i	0.273146	−	0.244504i
$176$	−0.0253148	+	0.0146155i	−0.00190818	+	0.00110169i
$177$	−11.0448	+	6.37671i	−0.830177	+	0.479303i
$178$	13.5008			1.01192
$179$	−8.08343	−	14.0009i	−0.604184	−	1.04648i	−0.992180	−	0.124816i	$-0.960166\pi$
$179$	−8.08343	−	14.0009i	−0.604184	−	1.04648i	0.387996	−	0.921661i	$-0.373167\pi$
$180$			1.77962i			0.132645i
$181$	−13.5438			−1.00671			−0.503353	−	0.864081i	$-0.667900\pi$
$181$	−13.5438			−1.00671			−0.503353	+	0.864081i	$0.667900\pi$
$182$	−9.14344	−	2.71984i	−0.677757	−	0.201608i
$183$	−6.42985			−0.475308
$184$		−	4.80277i		−	0.354065i
$185$	−9.75508	−	16.8963i	−0.717208	−	1.24224i
$186$	4.40670			0.323115
$187$	−0.154739	+	0.0893389i	−0.0113157	+	0.00653311i
$188$	4.84344	−	2.79636i	0.353244	−	0.203946i
$189$	−2.51386	−	0.824914i	−0.182857	−	0.0600037i
$190$			11.8508i			0.859746i
$191$	−0.868384	+	1.50408i	−0.0628340	+	0.108832i	−0.895731	−	0.444596i	$-0.853347\pi$
$191$	−0.868384	+	1.50408i	−0.0628340	+	0.108832i	0.832897	+	0.553428i	$0.186681\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.9761	−	6.91443i	0.862062	−	0.497711i	−0.00264058	−	0.999997i	$-0.500841\pi$
$193$	11.9761	−	6.91443i	0.862062	−	0.497711i	0.864702	+	0.502285i	$0.167507\pi$
$194$	5.63246	+	9.75571i	0.404387	+	0.700419i
$195$	−3.05172	+	5.64432i	−0.218538	+	0.404198i
$196$	−5.63903	−	4.14745i	−0.402788	−	0.296246i
$197$	−3.25356	−	1.87845i	−0.231807	−	0.133834i	0.379598	−	0.925151i	$-0.376062\pi$
$197$	−3.25356	−	1.87845i	−0.231807	−	0.133834i	−0.611405	+	0.791318i	$0.709395\pi$
$198$	−0.0292310			−0.00207736
$199$	16.9615			1.20237			0.601185	−	0.799110i	$-0.294695\pi$
$199$	16.9615			1.20237			0.601185	+	0.799110i	$0.294695\pi$
$200$	−1.58740	−	0.916484i	−0.112246	−	0.0648052i
$201$	4.93323	+	2.84820i	0.347963	+	0.200897i
$202$	−0.556000	+	0.321007i	−0.0391201	+	0.0225860i
$203$	9.03338	−	8.08613i	0.634019	−	0.567535i
$204$	3.05630	+	5.29367i	0.213984	+	0.370631i
$205$	13.1557			0.918831
$206$	15.7105	−	9.07044i	1.09460	−	0.631967i
$207$	2.40138	−	4.15932i	0.166908	−	0.289093i
$208$	0.100748	+	3.60414i	0.00698561	+	0.249902i
$209$	−0.194655			−0.0134645
$210$	−3.50821	+	3.14033i	−0.242089	+	0.216704i
$211$	8.09895	−	14.0278i	0.557555	−	0.965713i	−0.440145	−	0.897927i	$-0.645073\pi$
$211$	8.09895	−	14.0278i	0.557555	−	0.965713i	0.997700	−	0.0677867i	$-0.0215937\pi$
$212$	−0.0633613	+	0.109745i	−0.00435167	+	0.00753732i
$213$	7.24189	+	4.18111i	0.496206	+	0.286485i
$214$		−	0.552995i		−	0.0378020i
$215$	−13.1854	−	7.61261i	−0.899239	−	0.519176i
$216$			1.00000i			0.0680414i
$217$	7.77612	+	8.68705i	0.527877	+	0.589715i
$218$	−9.88349	+	17.1187i	−0.669395	+	1.15943i
$219$		−	6.02201i		−	0.406929i
$220$	−0.0260100	+	0.0450507i	−0.00175359	+	0.00303731i
$221$	0.615832	+	22.0307i	0.0414254	+	1.48194i
$222$	−5.48157	−	9.49435i	−0.367899	−	0.637219i
$223$	8.12362	+	4.69017i	0.543998	+	0.314077i	0.746698	−	0.665164i	$-0.231638\pi$
$223$	8.12362	+	4.69017i	0.543998	+	0.314077i	−0.202700	+	0.979241i	$0.564972\pi$
$224$	−0.824914	+	2.51386i	−0.0551169	+	0.167965i
$225$	−0.916484	−	1.58740i	−0.0610989	−	0.105826i
$226$	−1.73785	+	1.00335i	−0.115600	+	0.0667419i
$227$			3.04812i			0.202311i	0.994871	+	0.101155i	$0.0322539\pi$
$227$			3.04812i			0.202311i	−0.994871	+	0.101155i	$0.967746\pi$
$228$			6.65918i			0.441015i
$229$	−6.40547	+	3.69820i	−0.423285	+	0.244384i	−0.696482	−	0.717574i	$-0.745252\pi$
$229$	−6.40547	+	3.69820i	−0.423285	+	0.244384i	0.273197	+	0.961958i	$0.411919\pi$
$230$	−4.27354	−	7.40199i	−0.281789	−	0.488072i
$231$	−0.0515815	−	0.0576240i	−0.00339381	−	0.00379138i
$232$	−3.96846	−	2.29119i	−0.260542	−	0.150424i
$233$	6.38845	+	11.0651i	0.418522	+	0.724901i	0.995791	−	0.0916531i	$-0.0292151\pi$
$233$	6.38845	+	11.0651i	0.418522	+	0.724901i	−0.577269	+	0.816554i	$0.695882\pi$
$234$	−1.71482	+	3.17165i	−0.112101	+	0.207337i
$235$	4.97645	−	8.61946i	0.324628	−	0.562272i
$236$			12.7534i			0.830177i
$237$	0.798515	−	1.38307i	0.0518691	−	0.0898400i
$238$	−5.04237	+	15.3663i	−0.326848	+	0.996046i
$239$		−	23.2357i		−	1.50299i	−0.659739	−	0.751495i	$-0.729333\pi$
$239$		−	23.2357i		−	1.50299i	0.659739	−	0.751495i	$-0.270667\pi$
$240$	1.54119	+	0.889808i	0.0994835	+	0.0574368i
$241$		−	8.55083i		−	0.550807i	−0.961329	−	0.275404i	$-0.911188\pi$
$241$		−	8.55083i		−	0.550807i	0.961329	−	0.275404i	$-0.0888115\pi$
$242$	9.52554	+	5.49957i	0.612325	+	0.353526i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.21492	+	5.56841i	−0.205814	+	0.356481i
$245$	−12.3813	−	1.37435i	−0.791010	−	0.0878043i
$246$	7.39241			0.471323
$247$	−11.4193	+	21.1206i	−0.726593	+	1.34387i
$248$	2.20335	−	3.81631i	0.139913	−	0.242336i
$249$	−7.27232	+	4.19868i	−0.460865	+	0.266080i
$250$	−12.1601			−0.769070
$251$	10.8191	+	18.7393i	0.682898	+	1.18281i	0.974092	+	0.226150i	$0.0726141\pi$
$251$	10.8191	+	18.7393i	0.682898	+	1.18281i	−0.291194	+	0.956664i	$0.594053\pi$
$252$	−1.97133	+	1.76461i	−0.124182	+	0.111160i
$253$	0.121581	−	0.0701949i	0.00764374	−	0.00441312i
$254$	−8.68131	−	5.01216i	−0.544714	−	0.314491i
$255$	9.42070	+	5.43904i	0.589947	+	0.340606i
$256$	1.00000			0.0625000
$257$	1.38446			0.0863605			0.0431802	−	0.999067i	$-0.486251\pi$
$257$	1.38446			0.0863605			0.0431802	+	0.999067i	$0.486251\pi$
$258$	−7.40915	−	4.27767i	−0.461273	−	0.266316i
$259$	9.04364	−	27.5598i	0.561945	−	1.71248i
$260$	3.36227	+	5.46503i	0.208519	+	0.338927i
$261$	−2.29119	−	3.96846i	−0.141821	−	0.245641i
$262$	0.751999	−	0.434167i	0.0464587	−	0.0268229i
$263$	1.09543	+	1.89735i	0.0675474	+	0.116995i	0.897821	−	0.440360i	$-0.145149\pi$
$263$	1.09543	+	1.89735i	0.0675474	+	0.116995i	−0.830274	+	0.557356i	$0.811816\pi$
$264$	−0.0146155	+	0.0253148i	−0.000899523	+	0.00155802i
$265$			0.225518i			0.0138534i
$266$	−13.1274	+	11.7509i	−0.804894	+	0.720492i
$267$	11.6920	−	6.75038i	0.715539	−	0.413116i
$268$	4.93323	−	2.84820i	0.301345	−	0.173981i
$269$	31.1246			1.89770			0.948850	−	0.315726i	$-0.102248\pi$
$269$	31.1246			1.89770			0.948850	+	0.315726i	$0.102248\pi$
$270$	0.889808	+	1.54119i	0.0541520	+	0.0937940i
$271$		−	24.9082i		−	1.51307i	−0.653955	−	0.756533i	$-0.726891\pi$
$271$		−	24.9082i		−	1.51307i	0.653955	−	0.756533i	$-0.273109\pi$
$272$	6.11260			0.370631
$273$	−9.27837	+	2.21627i	−0.561553	+	0.134135i
$274$	19.6304			1.18592
$275$		−	0.0535796i		−	0.00323097i
$276$	−2.40138	−	4.15932i	−0.144546	−	0.250361i
$277$	−6.03351			−0.362518			−0.181259	−	0.983435i	$-0.558017\pi$
$277$	−6.03351			−0.362518			−0.181259	+	0.983435i	$0.558017\pi$
$278$	−2.60832	+	1.50591i	−0.156437	+	0.0903187i
$279$	3.81631	−	2.20335i	0.228477	−	0.131911i
$280$	0.965505	+	4.60836i	0.0577000	+	0.275402i
$281$			8.67723i			0.517640i	0.965926	+	0.258820i	$0.0833336\pi$
$281$			8.67723i			0.517640i	−0.965926	+	0.258820i	$0.916666\pi$
$282$	2.79636	−	4.84344i	0.166521	−	0.288423i
$283$	11.3754	+	19.7028i	0.676199	+	1.17121i	0.976117	+	0.217247i	$0.0697076\pi$
$283$	11.3754	+	19.7028i	0.676199	+	1.17121i	−0.299917	+	0.953965i	$0.596959\pi$
$284$	7.24189	−	4.18111i	0.429727	−	0.248103i
$285$	5.92539	+	10.2631i	0.350990	+	0.607932i
$286$	−0.0897658	+	0.0552268i	−0.00530796	+	0.00326563i
$287$	13.0448	+	14.5729i	0.770008	+	0.860210i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	20.3639			1.19788
$290$	−8.15488			−0.478871
$291$	9.75571	+	5.63246i	0.571890	+	0.330181i
$292$	−5.21521	−	3.01100i	−0.305197	−	0.176206i
$293$	−17.0486	+	9.84301i	−0.995989	+	0.575035i	−0.907059	−	0.421003i	$-0.861678\pi$
$293$	−17.0486	+	9.84301i	−0.995989	+	0.575035i	−0.0889301	+	0.996038i	$0.528345\pi$
$294$	−6.95727	−	0.772276i	−0.405756	−	0.0450401i
$295$	11.3481	+	19.6555i	0.660712	+	1.14439i
$296$	−10.9631			−0.637219
$297$	−0.0253148	+	0.0146155i	−0.00146892	+	0.000848079i
$298$	7.39820	−	12.8141i	0.428566	−	0.742298i
$299$	−0.483869	−	17.3099i	−0.0279829	−	1.00105i
$300$	−1.83297			−0.105826
$301$	−4.64158	−	22.1543i	−0.267536	−	1.27695i
$302$	−0.350172	+	0.606515i	−0.0201501	+	0.0349010i
$303$	−0.321007	+	0.556000i	−0.0184414	+	0.0319414i
$304$	5.76702	+	3.32959i	0.330761	+	0.190965i
$305$			11.4427i			0.655204i
$306$	5.29367	+	3.05630i	0.302619	+	0.174717i
$307$			5.38807i			0.307514i	0.988109	+	0.153757i	$0.0491372\pi$
$307$			5.38807i			0.307514i	−0.988109	+	0.153757i	$0.950863\pi$
$308$	−0.0756946	+	0.0158589i	−0.00431310	+	0.000903644i
$309$	9.07044	−	15.7105i	0.515999	−	0.893737i
$310$		−	7.84222i		−	0.445408i
$311$	1.17445	−	2.03422i	0.0665972	−	0.115350i	−0.830804	−	0.556565i	$-0.812119\pi$
$311$	1.17445	−	2.03422i	0.0665972	−	0.115350i	0.897401	+	0.441215i	$0.145452\pi$
$312$	1.88932	+	3.07091i	0.106962	+	0.173856i
$313$	−12.6664	−	21.9389i	−0.715948	−	1.24006i	−0.962593	−	0.270953i	$-0.912661\pi$
$313$	−12.6664	−	21.9389i	−0.715948	−	1.24006i	0.246645	−	0.969106i	$-0.420672\pi$
$314$	7.76194	+	4.48136i	0.438031	+	0.252898i
$315$	−1.46803	+	4.47371i	−0.0827141	+	0.252065i
$316$	−0.798515	−	1.38307i	−0.0449200	−	0.0778037i
$317$	−24.2674	+	14.0108i	−1.36299	+	0.786923i	−0.990021	−	0.140921i	$-0.954994\pi$
$317$	−24.2674	+	14.0108i	−1.36299	+	0.786923i	−0.372970	+	0.927844i	$0.621660\pi$
$318$			0.126723i			0.00710625i
$319$		−	0.133948i		−	0.00749964i
$320$	1.54119	−	0.889808i	0.0861553	−	0.0497418i
$321$	−0.276497	−	0.478908i	−0.0154326	−	0.0267300i
$322$	3.96187	−	12.0735i	0.220786	−	0.672830i
$323$	35.2515	+	20.3525i	1.96144	+	1.13244i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−5.81354	−	3.14321i	−0.322477	−	0.174354i
$326$	3.35033	−	5.80295i	0.185558	−	0.321395i
$327$			19.7670i			1.09312i
$328$	3.69621	−	6.40202i	0.204089	−	0.353492i
$329$	14.4825	−	3.03425i	0.798447	−	0.167284i
$330$			0.0520200i			0.00286361i
$331$	−9.38821	−	5.42029i	−0.516023	−	0.297926i	0.219283	−	0.975661i	$-0.429628\pi$
$331$	−9.38821	−	5.42029i	−0.516023	−	0.297926i	−0.735306	+	0.677735i	$0.762962\pi$
$332$			8.39736i			0.460865i
$333$	−9.49435	−	5.48157i	−0.520287	−	0.300388i
$334$	2.35534	−	4.07956i	0.128878	−	0.223224i
$335$	5.06870	−	8.77925i	0.276933	−	0.479661i
$336$	0.542536	+	2.58953i	0.0295978	+	0.141270i
$337$	12.1641			0.662620			0.331310	−	0.943522i	$-0.392509\pi$
$337$	12.1641			0.662620			0.331310	+	0.943522i	$0.392509\pi$
$338$	0.726220	+	12.9797i	0.0395012	+	0.706003i
$339$	−1.00335	+	1.73785i	−0.0544945	+	0.0943873i
$340$	9.42070	−	5.43904i	0.510909	−	0.294973i
$341$	0.128812			0.00697558
$342$	3.32959	+	5.76702i	0.180044	+	0.311845i
$343$	−10.7545	−	15.0778i	−0.580687	−	0.814127i
$344$	−7.40915	+	4.27767i	−0.399474	+	0.230637i
$345$	−7.40199	−	4.27354i	−0.398510	−	0.230080i
$346$	−19.4892	−	11.2521i	−1.04775	−	0.604917i
$347$	−20.4608			−1.09839			−0.549196	−	0.835693i	$-0.685066\pi$
$347$	−20.4608			−1.09839			−0.549196	+	0.835693i	$0.685066\pi$
$348$	−4.58238			−0.245641
$349$	29.4511	+	17.0036i	1.57648	+	0.910181i	0.995345	+	0.0963745i	$0.0307246\pi$
$349$	29.4511	+	17.0036i	1.57648	+	0.910181i	0.581135	+	0.813807i	$0.302609\pi$
$350$	−3.23448	−	3.61338i	−0.172890	−	0.193143i
$351$	0.100748	+	3.60414i	0.00537753	+	0.192375i
$352$	0.0146155	+	0.0253148i	0.000779010	+	0.00134928i
$353$	−6.89231	+	3.97928i	−0.366841	+	0.211796i	−0.672077	−	0.740481i	$-0.734598\pi$
$353$	−6.89231	+	3.97928i	−0.366841	+	0.211796i	0.305237	+	0.952277i	$0.401264\pi$
$354$	6.37671	+	11.0448i	0.338918	+	0.587024i
$355$	7.44077	−	12.8878i	0.394915	−	0.684013i
$356$		−	13.5008i		−	0.715539i
$357$	3.31631	+	15.8288i	0.175518	+	0.837747i
$358$	−14.0009	+	8.08343i	−0.739971	+	0.427222i
$359$	−10.5261	+	6.07723i	−0.555545	+	0.320744i	−0.751355	−	0.659898i	$-0.770600\pi$
$359$	−10.5261	+	6.07723i	−0.555545	+	0.320744i	0.195811	+	0.980642i	$0.437266\pi$
$360$	1.77962			0.0937940
$361$	12.6723	+	21.9491i	0.666964	+	1.15522i
$362$			13.5438i			0.711848i
$363$	10.9991			0.577305
$364$	−2.71984	+	9.14344i	−0.142558	+	0.479246i
$365$	−10.7169			−0.560946
$366$			6.42985i			0.336093i
$367$	0.468911	+	0.812177i	0.0244769	+	0.0423953i	0.878004	−	0.478653i	$-0.158875\pi$
$367$	0.468911	+	0.812177i	0.0244769	+	0.0423953i	−0.853527	+	0.521048i	$0.825541\pi$
$368$	−4.80277			−0.250361
$369$	6.40202	−	3.69621i	0.333276	−	0.192417i
$370$	−16.8963	+	9.75508i	−0.878397	+	0.507142i
$371$	−0.249812	+	0.223616i	−0.0129696	+	0.0116096i
$372$		−	4.40670i		−	0.228477i
$373$	5.53182	−	9.58139i	0.286427	−	0.496105i	−0.686528	−	0.727104i	$-0.740866\pi$
$373$	5.53182	−	9.58139i	0.286427	−	0.496105i	0.972954	+	0.230998i	$0.0741992\pi$
$374$	0.0893389	+	0.154739i	0.00461960	+	0.00800139i
$375$	−10.5309	+	6.08003i	−0.543814	+	0.313971i
$376$	−2.79636	−	4.84344i	−0.144211	−	0.249781i
$377$	−14.5337	−	7.85797i	−0.748525	−	0.404706i
$378$	−0.824914	+	2.51386i	−0.0424290	+	0.129299i
$379$	−9.27986	−	5.35773i	−0.476675	−	0.275208i	0.242355	−	0.970188i	$-0.422080\pi$
$379$	−9.27986	−	5.35773i	−0.476675	−	0.275208i	−0.719030	+	0.694979i	$0.755413\pi$
$380$	11.8508			0.607932
$381$	−10.0243			−0.513561
$382$	1.50408	+	0.868384i	0.0769557	+	0.0444304i
$383$	11.7672	+	6.79380i	0.601276	+	0.347147i	0.769544	−	0.638594i	$-0.220484\pi$
$383$	11.7672	+	6.79380i	0.601276	+	0.347147i	−0.168267	+	0.985741i	$0.553817\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−0.102549	+	0.0917952i	−0.00522636	+	0.00467832i
$386$	−6.91443	−	11.9761i	−0.351935	−	0.609570i
$387$	−8.55535			−0.434893
$388$	9.75571	−	5.63246i	0.495271	−	0.285945i
$389$	6.60006	−	11.4316i	0.334637	−	0.579608i	−0.648778	−	0.760977i	$-0.724720\pi$
$389$	6.60006	−	11.4316i	0.334637	−	0.579608i	0.983415	+	0.181370i	$0.0580531\pi$
$390$	5.64432	+	3.05172i	0.285811	+	0.154530i
$391$	−29.3574			−1.48467
$392$	−4.14745	+	5.63903i	−0.209478	+	0.284814i
$393$	0.434167	−	0.751999i	0.0219008	−	0.0379333i
$394$	−1.87845	+	3.25356i	−0.0946348	+	0.163912i
$395$	−2.46133	−	1.42105i	−0.123843	−	0.0715008i
$396$			0.0292310i			0.00146892i
$397$	17.5261	+	10.1187i	0.879609	+	0.507843i	0.870530	−	0.492116i	$-0.163776\pi$
$397$	17.5261	+	10.1187i	0.879609	+	0.507843i	0.00907981	+	0.999959i	$0.497110\pi$
$398$		−	16.9615i		−	0.850204i
$399$	−5.49325	+	16.7403i	−0.275006	+	0.838062i
$400$	−0.916484	+	1.58740i	−0.0458242	+	0.0793699i
$401$		−	2.30791i		−	0.115251i	−0.998338	−	0.0576257i	$-0.981647\pi$
$401$		−	2.30791i		−	0.115251i	0.998338	−	0.0576257i	$-0.0183530\pi$
$402$	2.84820	−	4.93323i	0.142055	−	0.246047i
$403$	7.55670	−	13.9765i	0.376426	−	0.696220i
$404$	0.321007	+	0.556000i	0.0159707	+	0.0276621i
$405$	1.54119	+	0.889808i	0.0765825	+	0.0442149i
$406$	−8.08613	−	9.03338i	−0.401308	−	0.448319i
$407$	−0.160232	−	0.277530i	−0.00794240	−	0.0137566i
$408$	5.29367	−	3.05630i	0.262076	−	0.151309i
$409$			0.145951i			0.00721680i	0.999993	+	0.00360840i	$0.00114859\pi$
$409$			0.145951i			0.00721680i	−0.999993	+	0.00360840i	$0.998851\pi$
$410$		−	13.1557i		−	0.649711i
$411$	17.0004	−	9.81520i	0.838569	−	0.484148i
$412$	−9.07044	−	15.7105i	−0.446868	−	0.773999i
$413$	−10.5205	+	32.0604i	−0.517679	+	1.57759i
$414$	−4.15932	−	2.40138i	−0.204419	−	0.118022i
$415$	7.47203	+	12.9419i	0.366788	+	0.635295i
$416$	3.60414	−	0.100748i	0.176708	−	0.00493957i
$417$	−1.50591	+	2.60832i	−0.0737449	+	0.127730i
$418$			0.194655i			0.00952087i
$419$	12.7971	−	22.1652i	0.625178	−	1.08284i	−0.363328	−	0.931661i	$-0.618360\pi$
$419$	12.7971	−	22.1652i	0.625178	−	1.08284i	0.988506	−	0.151179i	$-0.0483071\pi$
$420$	3.14033	+	3.50821i	0.153233	+	0.171183i
$421$		−	15.2002i		−	0.740810i	−0.928870	−	0.370405i	$-0.879219\pi$
$421$		−	15.2002i		−	0.740810i	0.928870	−	0.370405i	$-0.120781\pi$
$422$	−14.0278	−	8.09895i	−0.682862	−	0.394251i
$423$		−	5.59272i		−	0.271928i
$424$	0.109745	+	0.0633613i	0.00532969	+	0.00307710i
$425$	−5.60210	+	9.70313i	−0.271742	+	0.470671i
$426$	4.18111	−	7.24189i	0.202575	−	0.350871i
$427$	−12.6753	+	11.3462i	−0.613403	+	0.549081i
$428$	−0.552995			−0.0267300
$429$	−0.0501260	+	0.0927107i	−0.00242011	+	0.00447612i
$430$	−7.61261	+	13.1854i	−0.367113	+	0.635858i
$431$	−32.1677	+	18.5721i	−1.54947	+	0.894584i	−0.551283	+	0.834318i	$0.685862\pi$
$431$	−32.1677	+	18.5721i	−1.54947	+	0.894584i	−0.998182	+	0.0602659i	$0.980805\pi$
$432$	1.00000			0.0481125
$433$	3.09784	+	5.36562i	0.148873	+	0.257855i	0.930811	−	0.365501i	$-0.119102\pi$
$433$	3.09784	+	5.36562i	0.148873	+	0.257855i	−0.781938	+	0.623356i	$0.785769\pi$
$434$	8.68705	−	7.77612i	0.416992	−	0.373266i
$435$	−7.06233	+	4.07744i	−0.338613	+	0.195498i
$436$	17.1187	+	9.88349i	0.819838	+	0.473333i
$437$	−27.6976	−	15.9912i	−1.32496	−	0.764964i
$438$	−6.02201			−0.287743
$439$	21.9471			1.04748			0.523740	−	0.851878i	$-0.324536\pi$
$439$	21.9471			1.04748			0.523740	+	0.851878i	$0.324536\pi$
$440$	0.0450507	+	0.0260100i	0.00214771	+	0.00123998i
$441$	−6.41131	+	2.80982i	−0.305300	+	0.133801i
$442$	22.0307	−	0.615832i	1.04789	−	0.0292921i
$443$	−3.54473	−	6.13966i	−0.168415	−	0.291704i	0.769447	−	0.638710i	$-0.220532\pi$
$443$	−3.54473	−	6.13966i	−0.168415	−	0.291704i	−0.937863	+	0.347006i	$0.887198\pi$
$444$	−9.49435	+	5.48157i	−0.450582	+	0.260144i
$445$	−12.0131	−	20.8073i	−0.569474	−	0.986359i
$446$	4.69017	−	8.12362i	0.222086	−	0.384664i
$447$		−	14.7964i		−	0.699846i
$448$	2.51386	+	0.824914i	0.118769	+	0.0389735i
$449$	−7.50529	+	4.33318i	−0.354196	+	0.204495i	−0.666532	−	0.745476i	$-0.732222\pi$
$449$	−7.50529	+	4.33318i	−0.354196	+	0.204495i	0.312336	+	0.949972i	$0.398889\pi$
$450$	−1.58740	+	0.916484i	−0.0748306	+	0.0432035i
$451$	0.216088			0.0101752
$452$	1.00335	+	1.73785i	0.0471936	+	0.0817418i
$453$			0.700344i			0.0329050i
$454$	3.04812			0.143055
$455$	3.94410	+	16.5119i	0.184902	+	0.774091i
$456$	6.65918			0.311845
$457$			11.6757i			0.546167i	0.961990	+	0.273084i	$0.0880436\pi$
$457$			11.6757i			0.546167i	−0.961990	+	0.273084i	$0.911956\pi$
$458$	3.69820	+	6.40547i	0.172805	+	0.299308i
$459$	6.11260			0.285312
$460$	−7.40199	+	4.27354i	−0.345119	+	0.199255i
$461$	−8.18825	+	4.72749i	−0.381365	+	0.220181i	−0.678412	−	0.734682i	$-0.737332\pi$
$461$	−8.18825	+	4.72749i	−0.381365	+	0.220181i	0.297047	+	0.954863i	$0.403998\pi$
$462$	−0.0576240	+	0.0515815i	−0.00268091	+	0.00239979i
$463$			9.04408i			0.420314i	0.977668	+	0.210157i	$0.0673975\pi$
$463$			9.04408i			0.420314i	−0.977668	+	0.210157i	$0.932602\pi$
$464$	−2.29119	+	3.96846i	−0.106366	+	0.184231i
$465$	−3.92111	−	6.79157i	−0.181837	−	0.314951i
$466$	11.0651	−	6.38845i	0.512582	−	0.295939i
$467$	−9.79237	−	16.9609i	−0.453137	−	0.784856i	0.545442	−	0.838149i	$-0.316362\pi$
$467$	−9.79237	−	16.9609i	−0.453137	−	0.784856i	−0.998579	+	0.0532924i	$0.983028\pi$
$468$	3.17165	+	1.71482i	0.146610	+	0.0792676i
$469$	14.7510	−	3.09050i	0.681137	−	0.142706i
$470$	−8.61946	−	4.97645i	−0.397586	−	0.229546i
$471$	8.96271			0.412980
$472$	12.7534			0.587024
$473$	−0.216577	−	0.125041i	−0.00995822	−	0.00574938i
$474$	−1.38307	−	0.798515i	−0.0635264	−	0.0366770i
$475$	−10.5708	+	6.10303i	−0.485020	+	0.280026i
$476$	15.3663	+	5.04237i	0.704311	+	0.231117i
$477$	0.0633613	+	0.109745i	0.00290111	+	0.00502488i
$478$	−23.2357			−1.06277
$479$	−30.5975	+	17.6655i	−1.39804	+	0.807156i	−0.994187	−	0.107669i	$-0.965661\pi$
$479$	−30.5975	+	17.6655i	−1.39804	+	0.807156i	−0.403849	+	0.914826i	$0.632328\pi$
$480$	0.889808	−	1.54119i	0.0406140	−	0.0703455i
$481$	−39.5127	+	1.10451i	−1.80162	+	0.0503615i
$482$	−8.55083			−0.389480
$483$	−2.60567	−	12.4369i	−0.118562	−	0.565898i
$484$	5.49957	−	9.52554i	0.249981	−	0.432979i
$485$	10.0236	−	17.3614i	0.455149	−	0.788342i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$		−	35.2234i		−	1.59612i	−0.602575	−	0.798062i	$-0.705859\pi$
$487$		−	35.2234i		−	1.59612i	0.602575	−	0.798062i	$-0.294141\pi$
$488$	5.56841	+	3.21492i	0.252070	+	0.145533i
$489$		−	6.70067i		−	0.303015i
$490$	−1.37435	+	12.3813i	−0.0620870	+	0.559329i
$491$	−1.60083	+	2.77271i	−0.0722442	+	0.125131i	−0.899885	−	0.436128i	$-0.856349\pi$
$491$	−1.60083	+	2.77271i	−0.0722442	+	0.125131i	0.827640	+	0.561259i	$0.189683\pi$
$492$		−	7.39241i		−	0.333276i
$493$	−14.0051	+	24.2576i	−0.630760	+	1.09251i
$494$	21.1206	+	11.4193i	0.950261	+	0.513779i
$495$	0.0260100	+	0.0450507i	0.00116906	+	0.00202488i
$496$	−3.81631	−	2.20335i	−0.171357	−	0.0989332i
$497$	21.6542	−	4.53680i	0.971323	−	0.203503i
$498$	4.19868	+	7.27232i	0.188147	+	0.325881i
$499$	9.15044	−	5.28301i	0.409630	−	0.236500i	−0.281001	−	0.959708i	$-0.590666\pi$
$499$	9.15044	−	5.28301i	0.409630	−	0.236500i	0.690631	+	0.723207i	$0.257333\pi$
$500$			12.1601i			0.543814i
$501$		−	4.71067i		−	0.210457i
$502$	18.7393	−	10.8191i	0.836376	−	0.482882i
$503$	16.8302	+	29.1508i	0.750422	+	1.29977i	0.947618	+	0.319406i	$0.103483\pi$
$503$	16.8302	+	29.1508i	0.750422	+	1.29977i	−0.197196	+	0.980364i	$0.563183\pi$
$504$	1.76461	+	1.97133i	0.0786021	+	0.0878100i
$505$	0.989467	+	0.571269i	0.0440307	+	0.0254211i
$506$	−0.0701949	−	0.121581i	−0.00312054	−	0.00540494i
$507$	7.11877	+	10.8776i	0.316156	+	0.483093i
$508$	−5.01216	+	8.68131i	−0.222379	+	0.385171i
$509$		−	40.4188i		−	1.79153i	−0.444525	−	0.895766i	$-0.646628\pi$
$509$		−	40.4188i		−	1.79153i	0.444525	−	0.895766i	$-0.353372\pi$
$510$	5.43904	−	9.42070i	0.240845	−	0.417155i
$511$	−10.6265	−	11.8714i	−0.470089	−	0.525158i
$512$		−	1.00000i		−	0.0441942i
$513$	5.76702	+	3.32959i	0.254620	+	0.147005i
$514$		−	1.38446i		−	0.0610661i
$515$	−27.9586	−	16.1419i	−1.23200	−	0.711297i
$516$	−4.27767	+	7.40915i	−0.188314	+	0.326170i
$517$	0.0817406	−	0.141579i	0.00359495	−	0.00622663i
$518$	−27.5598	−	9.04364i	−1.21091	−	0.397355i
$519$	−22.5042			−0.987826
$520$	5.46503	−	3.36227i	0.239658	−	0.147445i
$521$	6.99447	−	12.1148i	0.306433	−	0.530758i	−0.671146	−	0.741325i	$-0.734198\pi$
$521$	6.99447	−	12.1148i	0.306433	−	0.530758i	0.977579	+	0.210567i	$0.0675310\pi$
$522$	−3.96846	+	2.29119i	−0.173695	+	0.100283i
$523$	−36.7015			−1.60484			−0.802422	−	0.596756i	$-0.796456\pi$
$523$	−36.7015			−1.60484			−0.802422	+	0.596756i	$0.796456\pi$
$524$	−0.434167	−	0.751999i	−0.0189667	−	0.0328512i
$525$	−4.60783	−	1.51204i	−0.201102	−	0.0659909i
$526$	1.89735	−	1.09543i	0.0827283	−	0.0477632i
$527$	−23.3276	−	13.4682i	−1.01617	−	0.586684i
$528$	0.0253148	+	0.0146155i	0.00110169	+	0.000636059i
$529$	0.0665581			0.00289383
$530$	0.225518			0.00979585
$531$	11.0448	+	6.37671i	0.479303	+	0.276726i
$532$	11.7509	+	13.1274i	0.509465	+	0.569146i
$533$	12.6767	−	23.4462i	0.549088	−	1.01557i
$534$	−6.75038	−	11.6920i	−0.292117	−	0.505962i
$535$	−0.852272	+	0.492059i	−0.0368469	+	0.0212736i
$536$	−2.84820	−	4.93323i	−0.123023	−	0.213083i
$537$	−8.08343	+	14.0009i	−0.348826	+	0.604184i
$538$		−	31.1246i		−	1.34188i
$539$	−0.203368	−	0.0225744i	−0.00875969	−	0.000972350i
$540$	1.54119	−	0.889808i	0.0663224	−	0.0382912i
$541$	−8.41504	+	4.85843i	−0.361791	+	0.208880i	−0.669866	−	0.742482i	$-0.733648\pi$
$541$	−8.41504	+	4.85843i	−0.361791	+	0.208880i	0.308075	+	0.951362i	$0.400315\pi$
$542$	−24.9082			−1.06990
$543$	6.77192	+	11.7293i	0.290611	+	0.503353i
$544$		−	6.11260i		−	0.262076i
$545$	35.1776			1.50684
$546$	2.21627	+	9.27837i	0.0948475	+	0.397078i
$547$	−8.41788			−0.359922			−0.179961	−	0.983674i	$-0.557597\pi$
$547$	−8.41788			−0.359922			−0.179961	+	0.983674i	$0.557597\pi$
$548$		−	19.6304i		−	0.838569i
$549$	3.21492	+	5.56841i	0.137210	+	0.237654i
$550$	−0.0535796			−0.00228464
$551$	−26.4267	+	15.2574i	−1.12581	+	0.649989i
$552$	−4.15932	+	2.40138i	−0.177032	+	0.102210i
$553$	−0.866446	−	4.13555i	−0.0368450	−	0.175862i
$554$			6.03351i			0.256339i
$555$	−9.75508	+	16.8963i	−0.414080	+	0.717208i
$556$	1.50591	+	2.60832i	0.0638649	+	0.110617i
$557$	17.3344	−	10.0080i	0.734481	−	0.424053i	−0.0855783	−	0.996331i	$-0.527274\pi$
$557$	17.3344	−	10.0080i	0.734481	−	0.424053i	0.820059	+	0.572279i	$0.193940\pi$
$558$	−2.20335	−	3.81631i	−0.0932752	−	0.161557i
$559$	−26.2727	+	16.1638i	−1.11122	+	0.683656i
$560$	4.60836	−	0.965505i	0.194739	−	0.0408000i
$561$	0.154739	+	0.0893389i	0.00653311	+	0.00377189i
$562$	8.67723			0.366027
$563$	11.3464			0.478193			0.239097	−	0.970996i	$-0.423149\pi$
$563$	11.3464			0.478193			0.239097	+	0.970996i	$0.423149\pi$
$564$	−4.84344	−	2.79636i	−0.203946	−	0.117748i
$565$	3.09271	+	1.78558i	0.130111	+	0.0751198i
$566$	19.7028	−	11.3754i	0.828172	−	0.478145i
$567$	0.542536	+	2.58953i	0.0227844	+	0.108750i
$568$	−4.18111	−	7.24189i	−0.175435	−	0.303863i
$569$	11.2803			0.472893			0.236446	−	0.971645i	$-0.424017\pi$
$569$	11.2803			0.472893			0.236446	+	0.971645i	$0.424017\pi$
$570$	10.2631	−	5.92539i	0.429873	−	0.248187i
$571$	6.97786	−	12.0860i	0.292014	−	0.505784i	−0.682272	−	0.731099i	$-0.739008\pi$
$571$	6.97786	−	12.0860i	0.292014	−	0.505784i	0.974286	+	0.225315i	$0.0723412\pi$
$572$	0.0552268	+	0.0897658i	0.00230915	+	0.00375330i
$573$	1.73677			0.0725545
$574$	14.5729	−	13.0448i	0.608260	−	0.544478i
$575$	4.40166	−	7.62390i	0.183562	−	0.317938i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−35.8798	−	20.7152i	−1.49370	−	0.862385i	−0.493722	−	0.869620i	$-0.664364\pi$
$577$	−35.8798	−	20.7152i	−1.49370	−	0.862385i	−0.999974	+	0.00723460i	$0.997697\pi$
$578$		−	20.3639i		−	0.847027i
$579$	−11.9761	−	6.91443i	−0.497711	−	0.287354i
$580$			8.15488i			0.338613i
$581$	−6.92710	+	21.1098i	−0.287384	+	0.875783i
$582$	5.63246	−	9.75571i	0.233473	−	0.404387i
$583$			0.00370423i			0.000153414i
$584$	−3.01100	+	5.21521i	−0.124596	+	0.215807i
$585$	6.41399	−	0.179293i	0.265186	−	0.00741284i
$586$	9.84301	+	17.0486i	0.406611	+	0.704271i
$587$	7.56169	+	4.36574i	0.312104	+	0.180194i	0.647868	−	0.761753i	$-0.275661\pi$
$587$	7.56169	+	4.36574i	0.312104	+	0.180194i	−0.335763	+	0.941946i	$0.608994\pi$
$588$	−0.772276	+	6.95727i	−0.0318481	+	0.286913i
$589$	−14.6725	−	25.4135i	−0.604569	−	1.04714i
$590$	19.6555	−	11.3481i	0.809203	−	0.467194i
$591$			3.75689i			0.154538i
$592$			10.9631i			0.450582i
$593$	34.7875	−	20.0846i	1.42855	−	0.824774i	0.431544	−	0.902092i	$-0.357969\pi$
$593$	34.7875	−	20.0846i	1.42855	−	0.824774i	0.997006	+	0.0773179i	$0.0246357\pi$
$594$	0.0146155	+	0.0253148i	0.000599682	+	0.00103868i
$595$	28.1691	−	5.90175i	1.15482	−	0.241948i
$596$	−12.8141	−	7.39820i	−0.524884	−	0.303042i
$597$	−8.48076	−	14.6891i	−0.347094	−	0.601185i
$598$	−17.3099	+	0.483869i	−0.707853	+	0.0197869i
$599$	−16.9134	+	29.2948i	−0.691062	+	1.19695i	0.280428	+	0.959875i	$0.409524\pi$
$599$	−16.9134	+	29.2948i	−0.691062	+	1.19695i	−0.971490	+	0.237080i	$0.923810\pi$
$600$			1.83297i			0.0748306i
$601$	−14.8249	+	25.6775i	−0.604720	+	1.04741i	0.387376	+	0.921922i	$0.373382\pi$
$601$	−14.8249	+	25.6775i	−0.604720	+	1.04741i	−0.992096	+	0.125484i	$0.959952\pi$
$602$	−22.1543	+	4.64158i	−0.902942	+	0.189177i
$603$		−	5.69640i		−	0.231975i
$604$	0.606515	+	0.350172i	0.0246788	+	0.0142483i
$605$		−	19.5743i		−	0.795806i
$606$	0.556000	+	0.321007i	0.0225860	+	0.0130400i
$607$	−14.0507	+	24.3366i	−0.570302	+	0.987791i	0.426233	+	0.904613i	$0.359840\pi$
$607$	−14.0507	+	24.3366i	−0.570302	+	0.987791i	−0.996535	+	0.0831779i	$0.973493\pi$
$608$	3.32959	−	5.76702i	0.135033	−	0.233883i
$609$	−11.5195	−	3.78007i	−0.466793	−	0.153176i
$610$	11.4427			0.463300
$611$	−10.5665	−	17.1747i	−0.427473	−	0.694815i
$612$	3.05630	−	5.29367i	0.123544	−	0.213984i
$613$	40.2040	−	23.2118i	1.62382	−	0.937515i	0.637940	−	0.770086i	$-0.279787\pi$
$613$	40.2040	−	23.2118i	1.62382	−	0.937515i	0.985884	−	0.167430i	$-0.0535467\pi$
$614$	5.38807			0.217445
$615$	−6.57783	−	11.3931i	−0.265244	−	0.459415i
$616$	0.0158589	+	0.0756946i	0.000638973	+	0.00304982i
$617$	−22.1378	+	12.7812i	−0.891233	+	0.514553i	−0.874346	−	0.485304i	$-0.838709\pi$
$617$	−22.1378	+	12.7812i	−0.891233	+	0.514553i	−0.0168872	+	0.999857i	$0.505376\pi$
$618$	−15.7105	−	9.07044i	−0.631967	−	0.364866i
$619$	9.23893	+	5.33410i	0.371344	+	0.214395i	0.674045	−	0.738690i	$-0.264555\pi$
$619$	9.23893	+	5.33410i	0.371344	+	0.214395i	−0.302702	+	0.953085i	$0.597889\pi$
$620$	−7.84222			−0.314951
$621$	−4.80277			−0.192728
$622$	−2.03422	−	1.17445i	−0.0815646	−	0.0470914i
$623$	11.1370	−	33.9391i	0.446193	−	1.35974i
$624$	3.07091	−	1.88932i	0.122935	−	0.0756334i
$625$	6.23769	+	10.8040i	0.249508	+	0.432160i
$626$	−21.9389	+	12.6664i	−0.876854	+	0.506252i
$627$	0.0973273	+	0.168576i	0.00388688	+	0.00673227i
$628$	4.48136	−	7.76194i	0.178826	−	0.309735i
$629$			67.0133i			2.67199i
$630$	4.47371	+	1.46803i	0.178237	+	0.0584877i
$631$	−2.30419	+	1.33033i	−0.0917284	+	0.0529594i	−0.545163	−	0.838330i	$-0.683532\pi$
$631$	−2.30419	+	1.33033i	−0.0917284	+	0.0529594i	0.453434	+	0.891290i	$0.350199\pi$
$632$	−1.38307	+	0.798515i	−0.0550155	+	0.0317632i
$633$	−16.1979			−0.643809
$634$	14.0108	+	24.2674i	0.556439	+	0.963780i
$635$			17.8394i			0.707936i
$636$	0.126723			0.00502488
$637$	−14.3799	+	20.7417i	−0.569751	+	0.821817i
$638$	−0.133948			−0.00530304
$639$		−	8.36222i		−	0.330804i
$640$	−0.889808	−	1.54119i	−0.0351727	−	0.0609210i
$641$	20.9906			0.829079			0.414539	−	0.910031i	$-0.363943\pi$
$641$	20.9906			0.829079			0.414539	+	0.910031i	$0.363943\pi$
$642$	−0.478908	+	0.276497i	−0.0189010	+	0.0109125i
$643$	−2.73391	+	1.57843i	−0.107815	+	0.0622471i	−0.552938	−	0.833222i	$-0.686493\pi$
$643$	−2.73391	+	1.57843i	−0.107815	+	0.0622471i	0.445123	+	0.895470i	$0.353160\pi$
$644$	−12.0735	−	3.96187i	−0.475763	−	0.156120i
$645$			15.2252i			0.599493i
$646$	20.3525	−	35.2515i	0.800756	−	1.38695i
$647$	−8.67231	−	15.0209i	−0.340944	−	0.590532i	0.643665	−	0.765308i	$-0.277413\pi$
$647$	−8.67231	−	15.0209i	−0.340944	−	0.590532i	−0.984608	+	0.174776i	$0.944080\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	0.186398	+	0.322851i	0.00731676	+	0.0126730i
$650$	−3.14321	+	5.81354i	−0.123287	+	0.228026i
$651$	3.63515	−	11.0778i	0.142473	−	0.434175i
$652$	−5.80295	−	3.35033i	−0.227261	−	0.131209i
$653$	34.4341			1.34751			0.673755	−	0.738955i	$-0.264680\pi$
$653$	34.4341			1.34751			0.673755	+	0.738955i	$0.264680\pi$
$654$	19.7670			0.772950
$655$	−1.33827	−	0.772650i	−0.0522905	−	0.0301899i
$656$	−6.40202	−	3.69621i	−0.249957	−	0.144313i
$657$	−5.21521	+	3.01100i	−0.203465	+	0.117470i
$658$	−3.03425	−	14.4825i	−0.118288	−	0.564587i
$659$	4.87150	+	8.43769i	0.189767	+	0.328686i	0.945172	−	0.326572i	$-0.105893\pi$
$659$	4.87150	+	8.43769i	0.189767	+	0.328686i	−0.755406	+	0.655257i	$0.772560\pi$
$660$	0.0520200			0.00202488
$661$	10.5437	−	6.08743i	0.410104	−	0.236774i	−0.280731	−	0.959787i	$-0.590577\pi$
$661$	10.5437	−	6.08743i	0.410104	−	0.236774i	0.690834	+	0.723013i	$0.257243\pi$
$662$	−5.42029	+	9.38821i	−0.210665	+	0.364883i
$663$	18.7712	−	11.5487i	0.729014	−	0.448513i
$664$	8.39736			0.325881
$665$	29.7912	+	9.77587i	1.15526	+	0.379092i
$666$	−5.48157	+	9.49435i	−0.212406	+	0.367899i
$667$	11.0041	−	19.0596i	0.426079	−	0.737990i
$668$	−4.07956	−	2.35534i	−0.157843	−	0.0911307i
$669$		−	9.38035i		−	0.362665i
$670$	−8.77925	−	5.06870i	−0.339172	−	0.195821i
$671$			0.187951i			0.00725577i
$672$	2.58953	−	0.542536i	0.0998932	−	0.0209288i
$673$	−10.4665	+	18.1284i	−0.403452	+	0.698800i	−0.994140	−	0.108100i	$-0.965523\pi$
$673$	−10.4665	+	18.1284i	−0.403452	+	0.698800i	0.590688	+	0.806900i	$0.298857\pi$
$674$		−	12.1641i		−	0.468543i
$675$	−0.916484	+	1.58740i	−0.0352755	+	0.0610989i
$676$	12.9797	−	0.726220i	0.499219	−	0.0279315i
$677$	−1.32267	−	2.29094i	−0.0508345	−	0.0880480i	0.839488	−	0.543378i	$-0.182855\pi$
$677$	−1.32267	−	2.29094i	−0.0508345	−	0.0880480i	−0.890323	+	0.455330i	$0.849521\pi$
$678$	1.73785	+	1.00335i	0.0667419	+	0.0385334i
$679$	29.1708	−	6.11163i	1.11947	−	0.234543i
$680$	−5.43904	−	9.42070i	−0.208578	−	0.361267i
$681$	2.63975	−	1.52406i	0.101155	−	0.0584020i
$682$		−	0.128812i		−	0.00493248i
$683$			30.5767i			1.16999i	0.811038	+	0.584993i	$0.198903\pi$
$683$			30.5767i			1.16999i	−0.811038	+	0.584993i	$0.801097\pi$
$684$	5.76702	−	3.32959i	0.220507	−	0.127310i
$685$	−17.4673	−	30.2542i	−0.667391	−	1.15595i
$686$	−15.0778	+	10.7545i	−0.575674	+	0.410608i
$687$	6.40547	+	3.69820i	0.244384	+	0.141095i
$688$	4.27767	+	7.40915i	0.163085	+	0.282471i
$689$	0.401920	+	0.217307i	0.0153119	+	0.00827872i
$690$	−4.27354	+	7.40199i	−0.162691	+	0.281789i
$691$		−	12.3153i		−	0.468496i	−0.972177	−	0.234248i	$-0.924737\pi$
$691$		−	12.3153i		−	0.468496i	0.972177	−	0.234248i	$-0.0752628\pi$
$692$	−11.2521	+	19.4892i	−0.427741	+	0.740869i
$693$	−0.0241131	+	0.0734829i	−0.000915981	+	0.00279138i
$694$			20.4608i			0.776681i
$695$	4.64180	+	2.67995i	0.176074	+	0.101656i
$696$			4.58238i			0.173695i
$697$	−39.1330	−	22.5934i	−1.48227	−	0.855788i
$698$	17.0036	−	29.4511i	0.643595	−	1.11474i
$699$	6.38845	−	11.0651i	0.241634	−	0.418522i
$700$	−3.61338	+	3.23448i	−0.136573	+	0.122252i
$701$	41.1257			1.55330			0.776648	−	0.629935i	$-0.216918\pi$
$701$	41.1257			1.55330			0.776648	+	0.629935i	$0.216918\pi$
$702$	3.60414	−	0.100748i	0.136030	−	0.00380249i
$703$	−36.5027	+	63.2246i	−1.37673	+	2.38456i
$704$	0.0253148	−	0.0146155i	0.000954088	−	0.000550843i
$705$	−9.95290			−0.374848
$706$	3.97928	+	6.89231i	0.149762	+	0.259395i
$707$	0.348316	+	1.66251i	0.0130998	+	0.0625253i
$708$	11.0448	−	6.37671i	0.415089	−	0.239652i
$709$	26.9141	+	15.5389i	1.01078	+	0.583574i	0.911420	−	0.411478i	$-0.134987\pi$
$709$	26.9141	+	15.5389i	1.01078	+	0.583574i	0.0993599	+	0.995052i	$0.468320\pi$
$710$	−12.8878	−	7.44077i	−0.483670	−	0.279247i
$711$	−1.59703			−0.0598933
$712$	−13.5008			−0.505962
$713$	18.3288	+	10.5822i	0.686421	+	0.396305i
$714$	15.8288	−	3.31631i	0.592376	−	0.124110i
$715$	0.164989	+	0.0892050i	0.00617026	+	0.00333608i
$716$	8.08343	+	14.0009i	0.302092	+	0.523238i
$717$	−20.1227	+	11.6178i	−0.751495	+	0.433876i
$718$	6.07723	+	10.5261i	0.226800	+	0.392829i
$719$	−9.11892	+	15.7944i	−0.340078	+	0.589033i	−0.984447	−	0.175682i	$-0.943787\pi$
$719$	−9.11892	+	15.7944i	−0.340078	+	0.589033i	0.644369	+	0.764715i	$0.277120\pi$
$720$		−	1.77962i		−	0.0663224i
$721$	−9.84207	−	46.9763i	−0.366538	−	1.74949i
$722$	21.9491	−	12.6723i	0.816861	−	0.471615i
$723$	−7.40524	+	4.27542i	−0.275404	+	0.159004i
$724$	13.5438			0.503353
$725$	−4.19968	−	7.27406i	−0.155972	−	0.270152i
$726$		−	10.9991i		−	0.408217i
$727$	−8.65849			−0.321126			−0.160563	−	0.987026i	$-0.551331\pi$
$727$	−8.65849			−0.321126			−0.160563	+	0.987026i	$0.551331\pi$
$728$	9.14344	+	2.71984i	0.338878	+	0.100804i
$729$	1.00000			0.0370370
$730$			10.7169i			0.396649i
$731$	26.1477	+	45.2892i	0.967108	+	1.67508i
$732$	6.42985			0.237654
$733$	10.5215	−	6.07458i	0.388620	−	0.224370i	−0.292942	−	0.956130i	$-0.594634\pi$
$733$	10.5215	−	6.07458i	0.388620	−	0.224370i	0.681562	+	0.731760i	$0.261301\pi$
$734$	0.812177	−	0.468911i	0.0299780	−	0.0173078i
$735$	5.00041	+	11.4097i	0.184443	+	0.420852i
$736$			4.80277i			0.177032i
$737$	0.0832558	−	0.144203i	0.00306677	−	0.00531180i
$738$	−3.69621	−	6.40202i	−0.136059	−	0.235662i
$739$	8.93308	−	5.15752i	0.328609	−	0.189722i	−0.326615	−	0.945158i	$-0.605908\pi$
$739$	8.93308	−	5.15752i	0.328609	−	0.189722i	0.655223	+	0.755435i	$0.272575\pi$
$740$	9.75508	+	16.8963i	0.358604	+	0.621120i
$741$	24.0006	−	0.670898i	0.881685	−	0.0246461i
$742$	0.223616	+	0.249812i	0.00820922	+	0.00917088i
$743$	−13.3027	−	7.68032i	−0.488029	−	0.281764i	0.235727	−	0.971819i	$-0.424253\pi$
$743$	−13.3027	−	7.68032i	−0.488029	−	0.281764i	−0.723756	+	0.690055i	$0.757586\pi$
$744$	−4.40670			−0.161557
$745$	−26.3319			−0.964726
$746$	−9.58139	−	5.53182i	−0.350800	−	0.202534i
$747$	7.27232	+	4.19868i	0.266080	+	0.153622i
$748$	0.154739	−	0.0893389i	0.00565783	−	0.00326655i
$749$	−1.39015	−	0.456173i	−0.0507951	−	0.0166682i
$750$	6.08003	+	10.5309i	0.222011	+	0.384535i
$751$	20.2783			0.739966			0.369983	−	0.929039i	$-0.379364\pi$
$751$	20.2783			0.739966			0.369983	+	0.929039i	$0.379364\pi$
$752$	−4.84344	+	2.79636i	−0.176622	+	0.101973i
$753$	10.8191	−	18.7393i	0.394271	−	0.682898i
$754$	−7.85797	+	14.5337i	−0.286170	+	0.529287i
$755$	1.24634			0.0453591
$756$	2.51386	+	0.824914i	0.0914284	+	0.0300018i
$757$	−2.14762	+	3.71978i	−0.0780564	+	0.135198i	−0.902411	−	0.430876i	$-0.858205\pi$
$757$	−2.14762	+	3.71978i	−0.0780564	+	0.135198i	0.824355	+	0.566073i	$0.191538\pi$
$758$	−5.35773	+	9.27986i	−0.194602	+	0.337060i
$759$	−0.121581	−	0.0701949i	−0.00441312	−	0.00254791i
$760$		−	11.8508i		−	0.429873i
$761$	−8.67876	−	5.01068i	−0.314605	−	0.181637i	0.334380	−	0.942438i	$-0.391473\pi$
$761$	−8.67876	−	5.01068i	−0.314605	−	0.181637i	−0.648985	+	0.760801i	$0.724806\pi$
$762$			10.0243i			0.363143i
$763$	34.8811	+	38.9672i	1.26278	+	1.41071i
$764$	0.868384	−	1.50408i	0.0314170	−	0.0544159i
$765$		−	10.8781i		−	0.393298i
$766$	6.79380	−	11.7672i	0.245470	−	0.425167i
$767$	45.9652	−	1.28488i	1.65971	−	0.0463944i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	29.2300	+	16.8760i	1.05406	+	0.608563i	0.923784	−	0.382914i	$-0.125080\pi$
$769$	29.2300	+	16.8760i	1.05406	+	0.608563i	0.130278	+	0.991477i	$0.458413\pi$
$770$	0.0917952	+	0.102549i	0.00330807	+	0.00369559i
$771$	−0.692232	−	1.19898i	−0.0249301	−	0.0431802i
$772$	−11.9761	+	6.91443i	−0.431031	+	0.248856i
$773$		−	32.1067i		−	1.15480i	−0.816462	−	0.577399i	$-0.804068\pi$
$773$		−	32.1067i		−	1.15480i	0.816462	−	0.577399i	$-0.195932\pi$
$774$			8.55535i			0.307516i
$775$	6.99518	−	4.03867i	0.251274	−	0.145073i
$776$	−5.63246	−	9.75571i	−0.202194	−	0.350210i
$777$	−28.3893	+	5.94789i	−1.01846	+	0.213379i
$778$	−11.4316	−	6.60006i	−0.409844	−	0.236624i
$779$	−24.6137	−	42.6322i	−0.881877	−	1.52746i
$780$	3.05172	−	5.64432i	0.109269	−	0.202099i
$781$	0.122218	−	0.211688i	0.00437331	−	0.00757479i
$782$			29.3574i			1.04982i
$783$	−2.29119	+	3.96846i	−0.0818805	+	0.141821i
$784$	5.63903	+	4.14745i	0.201394	+	0.148123i
$785$		−	15.9502i		−	0.569286i
$786$	−0.751999	−	0.434167i	−0.0268229	−	0.0154862i
$787$			29.3995i			1.04798i	0.851724	+	0.523990i	$0.175557\pi$
$787$			29.3995i			1.04798i	−0.851724	+	0.523990i	$0.824443\pi$
$788$	3.25356	+	1.87845i	0.115903	+	0.0669169i
$789$	1.09543	−	1.89735i	0.0389985	−	0.0675474i
$790$	−1.42105	+	2.46133i	−0.0505587	+	0.0875702i
$791$	1.08871	+	5.19641i	0.0387100	+	0.184763i
$792$	0.0292310			0.00103868
$793$	20.3932	+	11.0260i	0.724185	+	0.391546i
$794$	10.1187	−	17.5261i	0.359099	−	0.621978i
$795$	0.195304	−	0.112759i	0.00692672	−	0.00399914i
$796$	−16.9615			−0.601185
$797$	−1.39371	−	2.41398i	−0.0493678	−	0.0855075i	0.840286	−	0.542144i	$-0.182387\pi$
$797$	−1.39371	−	2.41398i	−0.0493678	−	0.0855075i	−0.889653	+	0.456637i	$0.849054\pi$
$798$	16.7403	+	5.49325i	0.592599	+	0.194459i
$799$	−29.6060	+	17.0930i	−1.04739	+	0.604709i
$800$	1.58740	+	0.916484i	0.0561230	+	0.0324026i
$801$	−11.6920	−	6.75038i	−0.413116	−	0.238513i
$802$	−2.30791			−0.0814951
$803$	−0.176029			−0.00621195
$804$	−4.93323	−	2.84820i	−0.173981	−	0.100448i
$805$	−22.1329	+	4.63710i	−0.780082	+	0.163436i
$806$	−13.9765	−	7.55670i	−0.492302	−	0.266173i
$807$	−15.5623	−	26.9547i	−0.547819	−	0.948850i
$808$	0.556000	−	0.321007i	0.0195600	−	0.0112930i
$809$	6.32800	+	10.9604i	0.222481	+	0.385348i	0.955561	−	0.294795i	$-0.0952512\pi$
$809$	6.32800	+	10.9604i	0.222481	+	0.385348i	−0.733080	+	0.680142i	$0.761918\pi$
$810$	0.889808	−	1.54119i	0.0312647	−	0.0541520i
$811$			7.23316i			0.253990i	0.991903	+	0.126995i	$0.0405333\pi$
$811$			7.23316i			0.253990i	−0.991903	+	0.126995i	$0.959467\pi$
$812$	−9.03338	+	8.08613i	−0.317010	+	0.283768i
$813$	−21.5712	+	12.4541i	−0.756533	+	0.436785i
$814$	−0.277530	+	0.160232i	−0.00972741	+	0.00561612i
$815$	−11.9246			−0.417701
$816$	−3.05630	−	5.29367i	−0.106992	−	0.185315i
$817$			56.9716i			1.99318i
$818$	0.145951			0.00510305
$819$	6.55853	+	6.92717i	0.229174	+	0.242055i
$820$	−13.1557			−0.459415
$821$			23.1538i			0.808072i	0.914743	+	0.404036i	$0.132393\pi$
$821$			23.1538i			0.808072i	−0.914743	+	0.404036i	$0.867607\pi$
$822$	−9.81520	−	17.0004i	−0.342344	−	0.592958i
$823$	−39.4898			−1.37653			−0.688264	−	0.725460i	$-0.741627\pi$
$823$	−39.4898			−1.37653			−0.688264	+	0.725460i	$0.741627\pi$
$824$	−15.7105	+	9.07044i	−0.547300	+	0.315984i
$825$	−0.0464013	+	0.0267898i	−0.00161548	+	0.000932701i
$826$	32.0604	+	10.5205i	1.11552	+	0.366054i
$827$			42.9388i			1.49313i	0.665314	+	0.746564i	$0.268298\pi$
$827$			42.9388i			1.49313i	−0.665314	+	0.746564i	$0.731702\pi$
$828$	−2.40138	+	4.15932i	−0.0834538	+	0.144546i
$829$	10.1338	+	17.5522i	0.351960	+	0.609613i	0.986593	−	0.163201i	$-0.0521819\pi$
$829$	10.1338	+	17.5522i	0.351960	+	0.609613i	−0.634633	+	0.772814i	$0.718849\pi$
$830$	12.9419	−	7.47203i	0.449221	−	0.259358i
$831$	3.01675	+	5.22517i	0.104650	+	0.181259i
$832$	−0.100748	−	3.60414i	−0.00349281	−	0.124951i
$833$	34.4692	+	25.3517i	1.19429	+	0.878384i
$834$	2.60832	+	1.50591i	0.0903187	+	0.0521455i
$835$	−8.38319			−0.290112
$836$	0.194655			0.00673227
$837$	−3.81631	−	2.20335i	−0.131911	−	0.0761588i
$838$	−22.1652	−	12.7971i	−0.765684	−	0.442068i
$839$	38.1707	−	22.0379i	1.31780	−	0.760832i	0.334426	−	0.942422i	$-0.391458\pi$
$839$	38.1707	−	22.0379i	1.31780	−	0.760832i	0.983374	+	0.181590i	$0.0581243\pi$
$840$	3.50821	−	3.14033i	0.121045	−	0.108352i
$841$	4.00089	+	6.92975i	0.137962	+	0.238957i
$842$	−15.2002			−0.523832
$843$	7.51470	−	4.33861i	0.258820	−	0.149430i
$844$	−8.09895	+	14.0278i	−0.278777	+	0.482857i
$845$	19.3580	−	12.6687i	0.665936	−	0.435816i
$846$	−5.59272			−0.192282
$847$	21.6829	−	19.4092i	0.745034	−	0.666910i
$848$	0.0633613	−	0.109745i	0.00217584	−	0.00376866i
$849$	11.3754	−	19.7028i	0.390404	−	0.676199i
$850$	9.70313	+	5.60210i	0.332815	+	0.192151i
$851$		−	52.6534i		−	1.80493i
$852$	−7.24189	−	4.18111i	−0.248103	−	0.143242i
$853$			21.7050i			0.743165i	0.928400	+	0.371583i	$0.121185\pi$
$853$			21.7050i			0.743165i	−0.928400	+	0.371583i	$0.878815\pi$
$854$	11.3462	+	12.6753i	0.388259	+	0.433741i
$855$	5.92539	−	10.2631i	0.202644	−	0.350990i
$856$			0.552995i			0.0189010i
$857$	−14.1784	+	24.5577i	−0.484325	+	0.838876i	−0.999838	−	0.0180062i	$-0.994268\pi$
$857$	−14.1784	+	24.5577i	−0.484325	+	0.838876i	0.515513	+	0.856882i	$0.327601\pi$
$858$	0.0927107	+	0.0501260i	0.00316509	+	0.00171127i
$859$	−1.23295	−	2.13552i	−0.0420675	−	0.0728631i	0.844225	−	0.535989i	$-0.180061\pi$
$859$	−1.23295	−	2.13552i	−0.0420675	−	0.0728631i	−0.886293	+	0.463126i	$0.846728\pi$
$860$	13.1854	+	7.61261i	0.449620	+	0.259588i
$861$	6.09811	−	18.5835i	0.207823	−	0.633325i
$862$	18.5721	+	32.1677i	0.632567	+	1.09564i
$863$	−12.6037	+	7.27673i	−0.429034	+	0.247703i	−0.698935	−	0.715185i	$-0.746342\pi$
$863$	−12.6037	+	7.27673i	−0.429034	+	0.247703i	0.269901	+	0.962888i	$0.413009\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			40.0489i			1.36170i
$866$	5.36562	−	3.09784i	0.182331	−	0.105269i
$867$	−10.1820	−	17.6357i	−0.345797	−	0.598939i
$868$	−7.77612	−	8.68705i	−0.263939	−	0.294858i
$869$	−0.0404285	−	0.0233414i	−0.00137144	−	0.000791804i
$870$	4.07744	+	7.06233i	0.138238	+	0.239435i
$871$	−10.7623	−	17.4931i	−0.364668	−	0.592731i
$872$	9.88349	−	17.1187i	0.334697	−	0.579713i
$873$		−	11.2649i		−	0.381260i
$874$	−15.9912	+	27.6976i	−0.540912	+	0.936886i
$875$	−10.0310	+	30.5687i	−0.339110	+	1.03341i
$876$			6.02201i			0.203465i
$877$	32.2283	+	18.6070i	1.08827	+	0.628314i	0.933116	−	0.359576i	$-0.117079\pi$
$877$	32.2283	+	18.6070i	1.08827	+	0.628314i	0.155155	+	0.987890i	$0.450412\pi$
$878$		−	21.9471i		−	0.740680i
$879$	17.0486	+	9.84301i	0.575035	+	0.331996i
$880$	0.0260100	−	0.0450507i	0.000876797	−	0.00151866i
$881$	16.2543	−	28.1532i	0.547620	−	0.948506i	−0.450817	−	0.892617i	$-0.648867\pi$
$881$	16.2543	−	28.1532i	0.547620	−	0.948506i	0.998437	−	0.0558898i	$-0.0177995\pi$
$882$	2.80982	+	6.41131i	0.0946117	+	0.215880i
$883$	−47.0222			−1.58242			−0.791211	−	0.611543i	$-0.790549\pi$
$883$	−47.0222			−1.58242			−0.791211	+	0.611543i	$0.790549\pi$
$884$	−0.615832	−	22.0307i	−0.0207127	−	0.740972i
$885$	11.3481	−	19.6555i	0.381462	−	0.660712i
$886$	−6.13966	+	3.54473i	−0.206266	+	0.119088i
$887$	−17.4704			−0.586600			−0.293300	−	0.956020i	$-0.594754\pi$
$887$	−17.4704			−0.586600			−0.293300	+	0.956020i	$0.594754\pi$
$888$	5.48157	+	9.49435i	0.183949	+	0.318610i
$889$	−19.7612	+	17.6890i	−0.662770	+	0.593271i
$890$	−20.8073	+	12.0131i	−0.697461	+	0.402679i
$891$	0.0253148	+	0.0146155i	0.000848079	+	0.000489638i
$892$	−8.12362	−	4.69017i	−0.271999	−	0.157039i
$893$	−37.2429			−1.24629
$894$	−14.7964			−0.494866
$895$	24.9162	+	14.3854i	0.832858	+	0.480851i
$896$	0.824914	−	2.51386i	0.0275584	−	0.0839823i
$897$	−14.7488	+	9.07397i	−0.492449	+	0.302971i
$898$	4.33318	+	7.50529i	0.144600	+	0.250455i
$899$	17.4878	−	10.0966i	0.583250	−	0.336740i
$900$	0.916484	+	1.58740i	0.0305495	+	0.0529132i
$901$	0.387302	−	0.670828i	0.0129029	−	0.0223485i
$902$		−	0.216088i		−	0.00719494i
$903$	−16.8654	+	15.0969i	−0.561245	+	0.502393i
$904$	1.73785	−	1.00335i	0.0578002	−	0.0333709i
$905$	20.8736	−	12.0514i	0.693864	−	0.400602i
$906$	0.700344			0.0232674
$907$	7.78461	+	13.4833i	0.258484	+	0.447707i	0.965836	−	0.259154i	$-0.0834438\pi$
$907$	7.78461	+	13.4833i	0.258484	+	0.447707i	−0.707352	+	0.706861i	$0.750110\pi$
$908$		−	3.04812i		−	0.101155i
$909$	0.642014			0.0212943
$910$	16.5119	−	3.94410i	0.547365	−	0.130746i
$911$	−11.8389			−0.392241			−0.196120	−	0.980580i	$-0.562834\pi$
$911$	−11.8389			−0.392241			−0.196120	+	0.980580i	$0.562834\pi$
$912$		−	6.65918i		−	0.220507i
$913$	0.122732	+	0.212578i	0.00406183	+	0.00703529i
$914$	11.6757			0.386199
$915$	9.90963	−	5.72133i	0.327602	−	0.189141i
$916$	6.40547	−	3.69820i	0.211643	−	0.122192i
$917$	−0.471102	−	2.24857i	−0.0155572	−	0.0742545i
$918$		−	6.11260i		−	0.201746i
$919$	−0.893493	+	1.54757i	−0.0294736	+	0.0510498i	−0.880386	−	0.474258i	$-0.842716\pi$
$919$	−0.893493	+	1.54757i	−0.0294736	+	0.0510498i	0.850912	+	0.525308i	$0.176050\pi$
$920$	4.27354	+	7.40199i	0.140894	+	0.244036i
$921$	4.66621	−	2.69404i	0.153757	−	0.0887715i
$922$	4.72749	+	8.18825i	0.155692	+	0.269666i
$923$	−15.7989	−	25.6796i	−0.520028	−	0.845254i
$924$	0.0515815	+	0.0576240i	0.00169691	+	0.00189569i
$925$	−17.4028	−	10.0475i	−0.572202	−	0.330361i
$926$	9.04408			0.297207
$927$	−18.1409			−0.595824
$928$	3.96846	+	2.29119i	0.130271	+	0.0752120i
$929$	28.2697	+	16.3215i	0.927500	+	0.535492i	0.886020	−	0.463647i	$-0.153459\pi$
$929$	28.2697	+	16.3215i	0.927500	+	0.535492i	0.0414800	+	0.999139i	$0.486793\pi$
$930$	−6.79157	+	3.92111i	−0.222704	+	0.128578i
$931$	18.7111	+	42.6940i	0.613232	+	1.39924i
$932$	−6.38845	−	11.0651i	−0.209261	−	0.362450i
$933$	−2.34891			−0.0768999
$934$	−16.9609	+	9.79237i	−0.554977	+	0.320416i
$935$	0.158989	−	0.275377i	0.00519949	−	0.00900578i
$936$	1.71482	−	3.17165i	0.0560507	−	0.103669i
$937$	16.5322			0.540083			0.270041	−	0.962849i	$-0.412963\pi$
$937$	16.5322			0.540083			0.270041	+	0.962849i	$0.412963\pi$
$938$	−3.09050	−	14.7510i	−0.100908	−	0.481637i
$939$	−12.6664	+	21.9389i	−0.413353	+	0.715948i
$940$	−4.97645	+	8.61946i	−0.162314	+	0.281136i
$941$	20.6335	+	11.9128i	0.672634	+	0.388345i	0.797074	−	0.603882i	$-0.206380\pi$
$941$	20.6335	+	11.9128i	0.672634	+	0.388345i	−0.124440	+	0.992227i	$0.539713\pi$
$942$		−	8.96271i		−	0.292021i
$943$	30.7474	+	17.7520i	1.00127	+	0.578085i
$944$		−	12.7534i		−	0.415089i
$945$	4.60836	−	0.965505i	0.149910	−	0.0314079i
$946$	−0.125041	+	0.216577i	−0.00406543	+	0.00704153i
$947$		−	38.2397i		−	1.24262i	−0.783564	−	0.621311i	$-0.786600\pi$
$947$		−	38.2397i		−	1.24262i	0.783564	−	0.621311i	$-0.213400\pi$
$948$	−0.798515	+	1.38307i	−0.0259346	+	0.0449200i
$949$	−10.3267	+	19.0997i	−0.335218	+	0.620003i
$950$	6.10303	+	10.5708i	0.198008	+	0.342961i
$951$	24.2674	+	14.0108i	0.786923	+	0.454330i
$952$	5.04237	−	15.3663i	0.163424	−	0.498023i
$953$	16.8722	+	29.2234i	0.546543	+	0.946640i	0.998508	+	0.0546042i	$0.0173897\pi$
$953$	16.8722	+	29.2234i	0.546543	+	0.946640i	−0.451965	+	0.892035i	$0.649277\pi$
$954$	0.109745	−	0.0633613i	0.00355313	−	0.00205140i
$955$		−	3.09078i		−	0.100015i
$956$			23.2357i			0.751495i
$957$	−0.116002	+	0.0669739i	−0.00374982	+	0.00216496i
$958$	17.6655	+	30.5975i	0.570746	+	0.988561i
$959$	16.1934	−	49.3482i	0.522912	−	1.59354i
$960$	−1.54119	−	0.889808i	−0.0497418	−	0.0287184i
$961$	−5.79052	−	10.0295i	−0.186791	−	0.323531i
$962$	1.10451	+	39.5127i	0.0356109	+	1.27394i
$963$	−0.276497	+	0.478908i	−0.00891001	+	0.0154326i
$964$			8.55083i			0.275404i
$965$	−12.3050	+	21.3129i	−0.396113	+	0.686087i
$966$	−12.4369	+	2.60567i	−0.400151	+	0.0838361i
$967$		−	19.3580i		−	0.622511i	−0.950326	−	0.311256i	$-0.899250\pi$
$967$		−	19.3580i		−	0.622511i	0.950326	−	0.311256i	$-0.100750\pi$
$968$	−9.52554	−	5.49957i	−0.306162	−	0.176763i
$969$		−	40.7049i		−	1.30763i
$970$	−17.3614	−	10.0236i	−0.557442	−	0.321839i
$971$	26.4945	−	45.8898i	0.850249	−	1.47267i	−0.0307347	−	0.999528i	$-0.509785\pi$
$971$	26.4945	−	45.8898i	0.850249	−	1.47267i	0.880984	−	0.473147i	$-0.156882\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	1.63402	+	7.79921i	0.0523844	+	0.250031i
$974$	−35.2234			−1.12863
$975$	0.184668	+	6.60628i	0.00591410	+	0.211570i
$976$	3.21492	−	5.56841i	0.102907	−	0.178240i
$977$	−4.89511	+	2.82619i	−0.156608	+	0.0904180i	−0.576256	−	0.817269i	$-0.695487\pi$
$977$	−4.89511	+	2.82619i	−0.156608	+	0.0904180i	0.419648	+	0.907687i	$0.362154\pi$
$978$	−6.70067			−0.214264
$979$	−0.197321	−	0.341769i	−0.00630639	−	0.0109230i
$980$	12.3813	+	1.37435i	0.395505	+	0.0439021i
$981$	17.1187	−	9.88349i	0.546558	−	0.315556i
$982$	2.77271	+	1.60083i	0.0884808	+	0.0510844i
$983$	17.5700	+	10.1441i	0.560397	+	0.323546i	0.753305	−	0.657671i	$-0.228458\pi$
$983$	17.5700	+	10.1441i	0.560397	+	0.323546i	−0.192908	+	0.981217i	$0.561792\pi$
$984$	−7.39241			−0.235662
$985$	6.68583			0.213028
$986$	24.2576	+	14.0051i	0.772520	+	0.446014i
$987$	−9.86900	−	11.0251i	−0.314134	−	0.350933i
$988$	11.4193	−	21.1206i	0.363296	−	0.671936i
$989$	−20.5447	−	35.5844i	−0.653282	−	1.13152i
$990$	0.0450507	−	0.0260100i	0.00143180	−	0.000826652i
$991$	19.6047	+	33.9564i	0.622764	+	1.07866i	0.988969	+	0.148125i	$0.0473237\pi$
$991$	19.6047	+	33.9564i	0.622764	+	1.07866i	−0.366205	+	0.930534i	$0.619343\pi$
$992$	−2.20335	+	3.81631i	−0.0699564	+	0.121168i
$993$			10.8406i			0.344015i
$994$	−4.53680	−	21.6542i	−0.143899	−	0.686829i
$995$	−26.1410	+	15.0925i	−0.828724	+	0.478464i
$996$	7.27232	−	4.19868i	0.230432	−	0.133040i
$997$	0.641727			0.0203237			0.0101619	−	0.999948i	$-0.496765\pi$
$997$	0.641727			0.0203237			0.0101619	+	0.999948i	$0.496765\pi$
$998$	−5.28301	−	9.15044i	−0.167231	−	0.289652i
$999$			10.9631i			0.346858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.277.2	yes	20
3.2	odd	2		1638.2.dt.b.1369.9		20
7.2	even	3		546.2.bd.b.121.4	✓	20
13.10	even	6		546.2.bd.b.361.4	yes	20
21.2	odd	6		1638.2.cr.b.667.7		20
39.23	odd	6		1638.2.cr.b.361.7		20
91.23	even	6	inner	546.2.bm.b.205.7	yes	20
273.23	odd	6		1638.2.dt.b.1297.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.4	✓	20	7.2	even	3
546.2.bd.b.361.4	yes	20	13.10	even	6
546.2.bm.b.205.7	yes	20	91.23	even	6	inner
546.2.bm.b.277.2	yes	20	1.1	even	1	trivial
1638.2.cr.b.361.7		20	39.23	odd	6
1638.2.cr.b.667.7		20	21.2	odd	6
1638.2.dt.b.1297.4		20	273.23	odd	6
1638.2.dt.b.1369.9		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.51386 - 0.824914i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.51386 - 0.824914i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.889808 + 1.54119i) q^{10} +(-0.0253148 + 0.0146155i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.100748 + 3.60414i) q^{13} +(-0.824914 + 2.51386i) q^{14} +(1.54119 + 0.889808i) q^{15} +1.00000 q^{16} +6.11260 q^{17} +(0.866025 + 0.500000i) q^{18} +(5.76702 + 3.32959i) q^{19} +(1.54119 - 0.889808i) q^{20} +(0.542536 + 2.58953i) q^{21} +(0.0146155 + 0.0253148i) q^{22} -4.80277 q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.916484 + 1.58740i) q^{25} +(3.60414 - 0.100748i) q^{26} +1.00000 q^{27} +(2.51386 + 0.824914i) q^{28} +(-2.29119 + 3.96846i) q^{29} +(0.889808 - 1.54119i) q^{30} +(-3.81631 - 2.20335i) q^{31} -1.00000i q^{32} +(0.0253148 + 0.0146155i) q^{33} -6.11260i q^{34} +(4.60836 - 0.965505i) q^{35} +(0.500000 - 0.866025i) q^{36} +10.9631i q^{37} +(3.32959 - 5.76702i) q^{38} +(3.07091 - 1.88932i) q^{39} +(-0.889808 - 1.54119i) q^{40} +(-6.40202 - 3.69621i) q^{41} +(2.58953 - 0.542536i) q^{42} +(4.27767 + 7.40915i) q^{43} +(0.0253148 - 0.0146155i) q^{44} -1.77962i q^{45} +4.80277i q^{46} +(-4.84344 + 2.79636i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(5.63903 + 4.14745i) q^{49} +(1.58740 + 0.916484i) q^{50} +(-3.05630 - 5.29367i) q^{51} +(-0.100748 - 3.60414i) q^{52} +(0.0633613 - 0.109745i) q^{53} -1.00000i q^{54} +(0.0260100 - 0.0450507i) q^{55} +(0.824914 - 2.51386i) q^{56} -6.65918i q^{57} +(3.96846 + 2.29119i) q^{58} -12.7534i q^{59} +(-1.54119 - 0.889808i) q^{60} +(3.21492 - 5.56841i) q^{61} +(-2.20335 + 3.81631i) q^{62} +(1.97133 - 1.76461i) q^{63} -1.00000 q^{64} +(-3.36227 - 5.46503i) q^{65} +(0.0146155 - 0.0253148i) q^{66} +(-4.93323 + 2.84820i) q^{67} -6.11260 q^{68} +(2.40138 + 4.15932i) q^{69} +(-0.965505 - 4.60836i) q^{70} +(-7.24189 + 4.18111i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.21521 + 3.01100i) q^{73} +10.9631 q^{74} +1.83297 q^{75} +(-5.76702 - 3.32959i) q^{76} +(0.0756946 - 0.0158589i) q^{77} +(-1.88932 - 3.07091i) q^{78} +(0.798515 + 1.38307i) q^{79} +(-1.54119 + 0.889808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.69621 + 6.40202i) q^{82} -8.39736i q^{83} +(-0.542536 - 2.58953i) q^{84} +(-9.42070 + 5.43904i) q^{85} +(7.40915 - 4.27767i) q^{86} +4.58238 q^{87} +(-0.0146155 - 0.0253148i) q^{88} +13.5008i q^{89} -1.77962 q^{90} +(2.71984 - 9.14344i) q^{91} +4.80277 q^{92} +4.40670i q^{93} +(2.79636 + 4.84344i) q^{94} -11.8508 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-9.75571 + 5.63246i) q^{97} +(4.14745 - 5.63903i) q^{98} -0.0292310i 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

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