LMFDB - Embedded newform 546.2.k.b.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.4
Root			$1.19003 + 0.764088i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.b.445.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.65876 - 2.06119i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.65876 - 2.06119i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.11561 q^{10} +4.04474 q^{11} +(0.500000 - 0.866025i) q^{12} +(1.81454 + 3.11568i) q^{13} +(-2.61442 - 0.405935i) q^{14} +(-2.05781 + 3.56422i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.357690 + 0.619538i) q^{17} +(-0.500000 - 0.866025i) q^{18} -3.84879 q^{19} +(2.05781 + 3.56422i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-2.02237 - 3.50284i) q^{22} +(2.04891 + 3.54881i) q^{23} -1.00000 q^{24} +(-5.96913 - 10.3388i) q^{25} +(1.79099 - 3.12928i) q^{26} -1.00000 q^{27} +(0.955663 + 2.46713i) q^{28} +(4.50457 - 7.80214i) q^{29} +4.11561 q^{30} +(1.82642 + 3.16346i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.04474 q^{33} +0.715381 q^{34} +(-3.93314 - 10.1537i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.59797 - 6.23187i) q^{37} +(1.92440 + 3.33315i) q^{38} +(-1.81454 - 3.11568i) q^{39} +(2.05781 - 3.56422i) q^{40} +(-2.88423 + 4.99563i) q^{41} +(2.61442 + 0.405935i) q^{42} +(1.28209 + 2.22064i) q^{43} +(-2.02237 + 3.50284i) q^{44} +(2.05781 - 3.56422i) q^{45} +(2.04891 - 3.54881i) q^{46} +(1.28800 - 2.23088i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.49702 - 6.83805i) q^{49} +(-5.96913 + 10.3388i) q^{50} +(0.357690 - 0.619538i) q^{51} +(-3.60553 + 0.0135995i) q^{52} +(-1.35888 - 2.35365i) q^{53} +(0.500000 + 0.866025i) q^{54} +(8.32328 - 14.4163i) q^{55} +(1.65876 - 2.06119i) q^{56} +3.84879 q^{57} -9.00914 q^{58} +(-6.45133 + 11.1740i) q^{59} +(-2.05781 - 3.56422i) q^{60} -9.43076 q^{61} +(1.82642 - 3.16346i) q^{62} +(1.65876 - 2.06119i) q^{63} +1.00000 q^{64} +(14.8389 - 0.0559702i) q^{65} +(2.02237 + 3.50284i) q^{66} -1.16632 q^{67} +(-0.357690 - 0.619538i) q^{68} +(-2.04891 - 3.54881i) q^{69} +(-6.82682 + 8.48306i) q^{70} +(5.10254 + 8.83786i) q^{71} +1.00000 q^{72} +(-1.25673 - 2.17673i) q^{73} +(-3.59797 + 6.23187i) q^{74} +(5.96913 + 10.3388i) q^{75} +(1.92440 - 3.33315i) q^{76} +(6.70925 - 8.33697i) q^{77} +(-1.79099 + 3.12928i) q^{78} +(-6.70468 + 11.6129i) q^{79} -4.11561 q^{80} +1.00000 q^{81} +5.76846 q^{82} -15.5024 q^{83} +(-0.955663 - 2.46713i) q^{84} +(1.47212 + 2.54978i) q^{85} +(1.28209 - 2.22064i) q^{86} +(-4.50457 + 7.80214i) q^{87} +4.04474 q^{88} +(5.45685 + 9.45154i) q^{89} -4.11561 q^{90} +(9.43190 + 1.42805i) q^{91} -4.09781 q^{92} +(-1.82642 - 3.16346i) q^{93} -2.57600 q^{94} +(-7.92007 + 13.7180i) q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.10135 - 5.37170i) q^{97} +(-5.17342 + 4.71548i) q^{98} +4.04474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.05781	−	3.56422i	0.920279	−	1.59397i	0.121296	−	0.992616i	$-0.461295\pi$
$5$	2.05781	−	3.56422i	0.920279	−	1.59397i	0.798983	−	0.601353i	$-0.205372\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.65876	−	2.06119i	0.626953	−	0.779057i
$7$	1.65876	−	2.06119i	0.626953	−	0.779057i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	−4.11561			−1.30147
$11$	4.04474			1.21953			0.609767	−	0.792581i	$-0.291263\pi$
$11$	4.04474			1.21953			0.609767	+	0.792581i	$0.291263\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.81454	+	3.11568i	0.503263	+	0.864133i
$13$	1.81454	+	3.11568i	0.503263	+	0.864133i
$14$	−2.61442	−	0.405935i	−0.698734	−	0.108491i
$15$	−2.05781	+	3.56422i	−0.531323	+	0.920279i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.357690	+	0.619538i	−0.0867527	+	0.150260i	−0.906137	−	0.422985i	$-0.860982\pi$
$17$	−0.357690	+	0.619538i	−0.0867527	+	0.150260i	0.819384	+	0.573245i	$0.194316\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−3.84879			−0.882973			−0.441487	−	0.897268i	$-0.645549\pi$
$19$	−3.84879			−0.882973			−0.441487	+	0.897268i	$0.645549\pi$
$20$	2.05781	+	3.56422i	0.460139	+	0.796985i
$21$	−1.65876	+	2.06119i	−0.361972	+	0.449789i
$22$	−2.02237	−	3.50284i	−0.431170	−	0.746809i
$23$	2.04891	+	3.54881i	0.427227	+	0.739978i	0.996625	−	0.0820832i	$-0.0261573\pi$
$23$	2.04891	+	3.54881i	0.427227	+	0.739978i	−0.569399	+	0.822061i	$0.692824\pi$
$24$	−1.00000			−0.204124
$25$	−5.96913	−	10.3388i	−1.19383	−	2.06777i
$26$	1.79099	−	3.12928i	0.351241	−	0.613702i
$27$	−1.00000			−0.192450
$28$	0.955663	+	2.46713i	0.180603	+	0.466243i
$29$	4.50457	−	7.80214i	0.836478	−	1.44882i	−0.0563442	−	0.998411i	$-0.517944\pi$
$29$	4.50457	−	7.80214i	0.836478	−	1.44882i	0.892822	−	0.450410i	$-0.148722\pi$
$30$	4.11561			0.751405
$31$	1.82642	+	3.16346i	0.328035	+	0.568174i	0.982122	−	0.188246i	$-0.0602802\pi$
$31$	1.82642	+	3.16346i	0.328035	+	0.568174i	−0.654087	+	0.756420i	$0.726947\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.04474			−0.704098
$34$	0.715381			0.122687
$35$	−3.93314	−	10.1537i	−0.664821	−	1.71629i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.59797	−	6.23187i	−0.591503	−	1.02451i	−0.994030	−	0.109105i	$-0.965201\pi$
$37$	−3.59797	−	6.23187i	−0.591503	−	1.02451i	0.402527	−	0.915408i	$-0.368132\pi$
$38$	1.92440	+	3.33315i	0.312178	+	0.540709i
$39$	−1.81454	−	3.11568i	−0.290559	−	0.498908i
$40$	2.05781	−	3.56422i	0.325368	−	0.563553i
$41$	−2.88423	+	4.99563i	−0.450441	+	0.780187i	−0.998413	−	0.0563098i	$-0.982067\pi$
$41$	−2.88423	+	4.99563i	−0.450441	+	0.780187i	0.547972	+	0.836496i	$0.315400\pi$
$42$	2.61442	+	0.405935i	0.403415	+	0.0626371i
$43$	1.28209	+	2.22064i	0.195516	+	0.338644i	0.947070	−	0.321028i	$-0.104028\pi$
$43$	1.28209	+	2.22064i	0.195516	+	0.338644i	−0.751553	+	0.659672i	$0.770695\pi$
$44$	−2.02237	+	3.50284i	−0.304883	+	0.528074i
$45$	2.05781	−	3.56422i	0.306760	−	0.531323i
$46$	2.04891	−	3.54881i	0.302095	−	0.523244i
$47$	1.28800	−	2.23088i	0.187874	−	0.325408i	−0.756667	−	0.653800i	$-0.773174\pi$
$47$	1.28800	−	2.23088i	0.187874	−	0.325408i	0.944541	+	0.328393i	$0.106507\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.49702	−	6.83805i	−0.213859	−	0.976864i
$50$	−5.96913	+	10.3388i	−0.844163	+	1.46213i
$51$	0.357690	−	0.619538i	0.0500867	−	0.0867527i
$52$	−3.60553	+	0.0135995i	−0.499996	+	0.00188591i
$53$	−1.35888	−	2.35365i	−0.186656	−	0.323298i	0.757477	−	0.652862i	$-0.226432\pi$
$53$	−1.35888	−	2.35365i	−0.186656	−	0.323298i	−0.944133	+	0.329564i	$0.893098\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	8.32328	−	14.4163i	1.12231	−	1.94390i
$56$	1.65876	−	2.06119i	0.221661	−	0.275438i
$57$	3.84879			0.509785
$58$	−9.00914			−1.18296
$59$	−6.45133	+	11.1740i	−0.839892	+	1.45474i	0.0500924	+	0.998745i	$0.484048\pi$
$59$	−6.45133	+	11.1740i	−0.839892	+	1.45474i	−0.889984	+	0.455991i	$0.849285\pi$
$60$	−2.05781	−	3.56422i	−0.265662	−	0.460139i
$61$	−9.43076			−1.20749			−0.603743	−	0.797179i	$-0.706325\pi$
$61$	−9.43076			−1.20749			−0.603743	+	0.797179i	$0.706325\pi$
$62$	1.82642	−	3.16346i	0.231956	−	0.401760i
$63$	1.65876	−	2.06119i	0.208984	−	0.259686i
$64$	1.00000			0.125000
$65$	14.8389	−	0.0559702i	1.84054	−	0.00694225i
$66$	2.02237	+	3.50284i	0.248936	+	0.431170i
$67$	−1.16632			−0.142488			−0.0712441	−	0.997459i	$-0.522697\pi$
$67$	−1.16632			−0.142488			−0.0712441	+	0.997459i	$0.522697\pi$
$68$	−0.357690	−	0.619538i	−0.0433763	−	0.0751300i
$69$	−2.04891	−	3.54881i	−0.246659	−	0.427227i
$70$	−6.82682	+	8.48306i	−0.815961	+	1.01392i
$71$	5.10254	+	8.83786i	0.605560	+	1.04886i	0.991963	+	0.126531i	$0.0403843\pi$
$71$	5.10254	+	8.83786i	0.605560	+	1.04886i	−0.386402	+	0.922330i	$0.626282\pi$
$72$	1.00000			0.117851
$73$	−1.25673	−	2.17673i	−0.147090	−	0.254767i	0.783061	−	0.621945i	$-0.213657\pi$
$73$	−1.25673	−	2.17673i	−0.147090	−	0.254767i	−0.930151	+	0.367178i	$0.880324\pi$
$74$	−3.59797	+	6.23187i	−0.418256	+	0.724440i
$75$	5.96913	+	10.3388i	0.689256	+	1.19383i
$76$	1.92440	−	3.33315i	0.220743	−	0.382339i
$77$	6.70925	−	8.33697i	0.764590	−	0.950086i
$78$	−1.79099	+	3.12928i	−0.202789	+	0.354321i
$79$	−6.70468	+	11.6129i	−0.754336	+	1.30655i	0.191368	+	0.981518i	$0.438708\pi$
$79$	−6.70468	+	11.6129i	−0.754336	+	1.30655i	−0.945704	+	0.325030i	$0.894626\pi$
$80$	−4.11561			−0.460139
$81$	1.00000			0.111111
$82$	5.76846			0.637020
$83$	−15.5024			−1.70161			−0.850807	−	0.525479i	$-0.823886\pi$
$83$	−15.5024			−1.70161			−0.850807	+	0.525479i	$0.823886\pi$
$84$	−0.955663	−	2.46713i	−0.104271	−	0.269185i
$85$	1.47212	+	2.54978i	0.159673	+	0.276562i
$86$	1.28209	−	2.22064i	0.138251	−	0.239458i
$87$	−4.50457	+	7.80214i	−0.482941	+	0.836478i
$88$	4.04474			0.431170
$89$	5.45685	+	9.45154i	0.578425	+	1.00186i	0.995660	+	0.0930629i	$0.0296658\pi$
$89$	5.45685	+	9.45154i	0.578425	+	1.00186i	−0.417235	+	0.908798i	$0.637001\pi$
$90$	−4.11561			−0.433824
$91$	9.43190	+	1.42805i	0.988731	+	0.149701i
$92$	−4.09781			−0.427227
$93$	−1.82642	−	3.16346i	−0.189391	−	0.328035i
$94$	−2.57600			−0.265694
$95$	−7.92007	+	13.7180i	−0.812582	+	1.40743i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−3.10135	−	5.37170i	−0.314895	−	0.545414i	0.664520	−	0.747270i	$-0.268636\pi$
$97$	−3.10135	−	5.37170i	−0.314895	−	0.545414i	−0.979415	+	0.201856i	$0.935303\pi$
$98$	−5.17342	+	4.71548i	−0.522594	+	0.476335i
$99$	4.04474			0.406511
$100$	11.9383			1.19383
$101$	16.3065			1.62256			0.811278	−	0.584660i	$-0.198772\pi$
$101$	16.3065			1.62256			0.811278	+	0.584660i	$0.198772\pi$
$102$	−0.715381			−0.0708333
$103$	1.46023	−	2.52920i	0.143881	−	0.249209i	−0.785074	−	0.619402i	$-0.787375\pi$
$103$	1.46023	−	2.52920i	0.143881	−	0.249209i	0.928955	+	0.370193i	$0.120708\pi$
$104$	1.81454	+	3.11568i	0.177930	+	0.305517i
$105$	3.93314	+	10.1537i	0.383835	+	0.990903i
$106$	−1.35888	+	2.35365i	−0.131986	+	0.228606i
$107$	2.01938	+	3.49768i	0.195221	+	0.338133i	0.946973	−	0.321313i	$-0.104124\pi$
$107$	2.01938	+	3.49768i	0.195221	+	0.338133i	−0.751752	+	0.659446i	$0.770791\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	6.93314	+	12.0085i	0.664074	+	1.15021i	0.979535	+	0.201272i	$0.0645074\pi$
$109$	6.93314	+	12.0085i	0.664074	+	1.15021i	−0.315461	+	0.948938i	$0.602159\pi$
$110$	−16.6466			−1.58719
$111$	3.59797	+	6.23187i	0.341504	+	0.591503i
$112$	−2.61442	−	0.405935i	−0.247040	−	0.0383572i
$113$	−7.30902	−	12.6596i	−0.687575	−	1.19091i	−0.972620	−	0.232401i	$-0.925342\pi$
$113$	−7.30902	−	12.6596i	−0.687575	−	1.19091i	0.285045	−	0.958514i	$-0.407991\pi$
$114$	−1.92440	−	3.33315i	−0.180236	−	0.312178i
$115$	16.8650			1.57267
$116$	4.50457	+	7.80214i	0.418239	+	0.724411i
$117$	1.81454	+	3.11568i	0.167754	+	0.288044i
$118$	12.9027			1.18779
$119$	0.683663	+	1.76493i	0.0626713	+	0.161791i
$120$	−2.05781	+	3.56422i	−0.187851	+	0.325368i
$121$	5.35989			0.487262
$122$	4.71538	+	8.16728i	0.426911	+	0.739431i
$123$	2.88423	−	4.99563i	0.260062	−	0.450441i
$124$	−3.65285			−0.328035
$125$	−28.5552			−2.55405
$126$	−2.61442	−	0.405935i	−0.232911	−	0.0361635i
$127$	−1.26603	+	2.19283i	−0.112342	+	0.194582i	−0.916714	−	0.399544i	$-0.869169\pi$
$127$	−1.26603	+	2.19283i	−0.112342	+	0.194582i	0.804372	+	0.594126i	$0.202502\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.28209	−	2.22064i	−0.112881	−	0.195516i
$130$	−7.46794	−	12.8229i	−0.654982	−	1.12464i
$131$	6.21657	−	10.7674i	0.543144	−	0.940753i	−0.455577	−	0.890196i	$-0.650567\pi$
$131$	6.21657	−	10.7674i	0.543144	−	0.940753i	0.998721	−	0.0505568i	$-0.0160996\pi$
$132$	2.02237	−	3.50284i	0.176025	−	0.304883i
$133$	−6.38423	+	7.93309i	−0.553583	+	0.687886i
$134$	0.583158	+	1.01006i	0.0503772	+	0.0872558i
$135$	−2.05781	+	3.56422i	−0.177108	+	0.306760i
$136$	−0.357690	+	0.619538i	−0.0306717	+	0.0531250i
$137$	5.19240	−	8.99351i	0.443617	−	0.768367i	−0.554338	−	0.832292i	$-0.687028\pi$
$137$	5.19240	−	8.99351i	0.443617	−	0.768367i	0.997955	+	0.0639247i	$0.0203617\pi$
$138$	−2.04891	+	3.54881i	−0.174415	+	0.302095i
$139$	−0.636394	−	1.10227i	−0.0539783	−	0.0934931i	0.837774	−	0.546018i	$-0.183857\pi$
$139$	−0.636394	−	1.10227i	−0.0539783	−	0.0934931i	−0.891752	+	0.452525i	$0.850524\pi$
$140$	10.7600	+	1.67067i	0.909382	+	0.141197i
$141$	−1.28800	+	2.23088i	−0.108469	+	0.187874i
$142$	5.10254	−	8.83786i	0.428196	−	0.741657i
$143$	7.33934	+	12.6021i	0.613746	+	1.05384i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−18.5391	−	32.1106i	−1.53959	−	2.66664i
$146$	−1.25673	+	2.17673i	−0.104008	+	0.180147i
$147$	1.49702	+	6.83805i	0.123472	+	0.563993i
$148$	7.19594			0.591503
$149$	23.3619			1.91388			0.956942	−	0.290278i	$-0.0937477\pi$
$149$	23.3619			1.91388			0.956942	+	0.290278i	$0.0937477\pi$
$150$	5.96913	−	10.3388i	0.487378	−	0.844163i
$151$	1.19832	+	2.07555i	0.0975178	+	0.168906i	0.910657	−	0.413164i	$-0.135576\pi$
$151$	1.19832	+	2.07555i	0.0975178	+	0.168906i	−0.813139	+	0.582070i	$0.802243\pi$
$152$	−3.84879			−0.312178
$153$	−0.357690	+	0.619538i	−0.0289176	+	0.0500867i
$154$	−10.5747	−	1.64190i	−0.852130	−	0.132308i
$155$	15.0337			1.20754
$156$	3.60553	−	0.0135995i	0.288673	−	0.00108883i
$157$	5.79083	+	10.0300i	0.462158	+	0.800482i	0.999068	−	0.0431579i	$-0.0137419\pi$
$157$	5.79083	+	10.0300i	0.462158	+	0.800482i	−0.536910	+	0.843640i	$0.680409\pi$
$158$	13.4094			1.06679
$159$	1.35888	+	2.35365i	0.107766	+	0.186656i
$160$	2.05781	+	3.56422i	0.162684	+	0.281777i
$161$	10.7134	+	1.66344i	0.844336	+	0.131098i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	17.9086			1.40271			0.701356	−	0.712811i	$-0.252578\pi$
$163$	17.9086			1.40271			0.701356	+	0.712811i	$0.252578\pi$
$164$	−2.88423	−	4.99563i	−0.225220	−	0.390093i
$165$	−8.32328	+	14.4163i	−0.647967	+	1.12231i
$166$	7.75122	+	13.4255i	0.601611	+	1.04202i
$167$	3.15398	−	5.46286i	0.244062	−	0.422728i	−0.717805	−	0.696244i	$-0.754853\pi$
$167$	3.15398	−	5.46286i	0.244062	−	0.422728i	0.961868	+	0.273516i	$0.0881865\pi$
$168$	−1.65876	+	2.06119i	−0.127976	+	0.159024i
$169$	−6.41489	+	11.3070i	−0.493453	+	0.869773i
$170$	1.47212	−	2.54978i	0.112906	−	0.195559i
$171$	−3.84879			−0.294324
$172$	−2.56417			−0.195516
$173$	−3.65127			−0.277601			−0.138800	−	0.990320i	$-0.544325\pi$
$173$	−3.65127			−0.277601			−0.138800	+	0.990320i	$0.544325\pi$
$174$	9.00914			0.682981
$175$	−31.2117	−	4.84616i	−2.35938	−	0.366335i
$176$	−2.02237	−	3.50284i	−0.152442	−	0.264037i
$177$	6.45133	−	11.1740i	0.484912	−	0.839892i
$178$	5.45685	−	9.45154i	0.409008	−	0.708423i
$179$	12.5191			0.935723			0.467861	−	0.883802i	$-0.345025\pi$
$179$	12.5191			0.935723			0.467861	+	0.883802i	$0.345025\pi$
$180$	2.05781	+	3.56422i	0.153380	+	0.265662i
$181$	−18.1728			−1.35077			−0.675385	−	0.737465i	$-0.736023\pi$
$181$	−18.1728			−1.35077			−0.675385	+	0.737465i	$0.736023\pi$
$182$	−3.47922	−	8.88229i	−0.257897	−	0.658399i
$183$	9.43076			0.697142
$184$	2.04891	+	3.54881i	0.151047	+	0.261622i
$185$	−29.6157			−2.17739
$186$	−1.82642	+	3.16346i	−0.133920	+	0.231956i
$187$	−1.44676	+	2.50587i	−0.105798	+	0.183247i
$188$	1.28800	+	2.23088i	0.0939371	+	0.162704i
$189$	−1.65876	+	2.06119i	−0.120657	+	0.149930i
$190$	15.8401			1.14916
$191$	4.46007			0.322720			0.161360	−	0.986896i	$-0.448412\pi$
$191$	4.46007			0.322720			0.161360	+	0.986896i	$0.448412\pi$
$192$	−1.00000			−0.0721688
$193$	−8.68485			−0.625149			−0.312575	−	0.949893i	$-0.601191\pi$
$193$	−8.68485			−0.625149			−0.312575	+	0.949893i	$0.601191\pi$
$194$	−3.10135	+	5.37170i	−0.222664	+	0.385666i
$195$	−14.8389	+	0.0559702i	−1.06264	+	0.00400811i
$196$	6.67043	+	2.12257i	0.476460	+	0.151612i
$197$	−1.23397	+	2.13730i	−0.0879166	+	0.152276i	−0.906630	−	0.421926i	$-0.861354\pi$
$197$	−1.23397	+	2.13730i	−0.0879166	+	0.152276i	0.818714	+	0.574202i	$0.194688\pi$
$198$	−2.02237	−	3.50284i	−0.143723	−	0.248936i
$199$	−10.2841	+	17.8125i	−0.729018	+	1.26270i	0.228280	+	0.973595i	$0.426690\pi$
$199$	−10.2841	+	17.8125i	−0.729018	+	1.26270i	−0.957298	+	0.289101i	$0.906644\pi$
$200$	−5.96913	−	10.3388i	−0.422081	−	0.731066i
$201$	1.16632			0.0822656
$202$	−8.15325	−	14.1218i	−0.573660	−	0.993609i
$203$	−8.60970	−	22.2267i	−0.604282	−	1.56001i
$204$	0.357690	+	0.619538i	0.0250433	+	0.0433763i
$205$	11.8704	+	20.5601i	0.829063	+	1.43598i
$206$	−2.92046			−0.203478
$207$	2.04891	+	3.54881i	0.142409	+	0.246659i
$208$	1.79099	−	3.12928i	0.124182	−	0.216976i
$209$	−15.5673			−1.07682
$210$	6.82682	−	8.48306i	0.471095	−	0.585387i
$211$	2.22726	−	3.85773i	0.153331	−	0.265577i	−0.779119	−	0.626876i	$-0.784333\pi$
$211$	2.22726	−	3.85773i	0.153331	−	0.265577i	0.932450	+	0.361299i	$0.117667\pi$
$212$	2.71776			0.186656
$213$	−5.10254	−	8.83786i	−0.349620	−	0.605560i
$214$	2.01938	−	3.49768i	0.138042	−	0.239096i
$215$	10.5531			0.719718
$216$	−1.00000			−0.0680414
$217$	9.55009	+	1.48282i	0.648303	+	0.100660i
$218$	6.93314	−	12.0085i	0.469571	−	0.813321i
$219$	1.25673	+	2.17673i	0.0849222	+	0.147090i
$220$	8.32328	+	14.4163i	0.561155	+	0.971950i
$221$	−2.57932	+	0.00972881i	−0.173504	+	0.000654431i
$222$	3.59797	−	6.23187i	0.241480	−	0.418256i
$223$	−2.49662	+	4.32427i	−0.167186	+	0.289574i	−0.937429	−	0.348175i	$-0.886801\pi$
$223$	−2.49662	+	4.32427i	−0.167186	+	0.289574i	0.770243	+	0.637750i	$0.220135\pi$
$224$	0.955663	+	2.46713i	0.0638529	+	0.164842i
$225$	−5.96913	−	10.3388i	−0.397942	−	0.689256i
$226$	−7.30902	+	12.6596i	−0.486189	+	0.842104i
$227$	0.786363	−	1.36202i	0.0521927	−	0.0904005i	−0.838749	−	0.544519i	$-0.816712\pi$
$227$	0.786363	−	1.36202i	0.0521927	−	0.0904005i	0.890941	+	0.454118i	$0.150046\pi$
$228$	−1.92440	+	3.33315i	−0.127446	+	0.220743i
$229$	0.828619	−	1.43521i	0.0547567	−	0.0948413i	−0.837348	−	0.546671i	$-0.815895\pi$
$229$	0.828619	−	1.43521i	0.0547567	−	0.0948413i	0.892104	+	0.451829i	$0.149228\pi$
$230$	−8.43251	−	14.6055i	−0.556023	−	0.963060i
$231$	−6.70925	+	8.33697i	−0.441437	+	0.548532i
$232$	4.50457	−	7.80214i	0.295739	−	0.512236i
$233$	−3.86181	+	6.68885i	−0.252996	+	0.438201i	−0.964349	−	0.264633i	$-0.914749\pi$
$233$	−3.86181	+	6.68885i	−0.252996	+	0.438201i	0.711354	+	0.702834i	$0.248082\pi$
$234$	1.79099	−	3.12928i	0.117080	−	0.204567i
$235$	−5.30091	−	9.18145i	−0.345793	−	0.598932i
$236$	−6.45133	−	11.1740i	−0.419946	−	0.727368i
$237$	6.70468	−	11.6129i	0.435516	−	0.754336i
$238$	1.18665	−	1.47454i	0.0769189	−	0.0955800i
$239$	−28.7630			−1.86052			−0.930261	−	0.366899i	$-0.880420\pi$
$239$	−28.7630			−1.86052			−0.930261	+	0.366899i	$0.880420\pi$
$240$	4.11561			0.265662
$241$	−12.8102	+	22.1879i	−0.825178	+	1.42925i	0.0766048	+	0.997062i	$0.475592\pi$
$241$	−12.8102	+	22.1879i	−0.825178	+	1.42925i	−0.901783	+	0.432189i	$0.857741\pi$
$242$	−2.67994	−	4.64180i	−0.172273	−	0.298386i
$243$	−1.00000			−0.0641500
$244$	4.71538	−	8.16728i	0.301871	−	0.522856i
$245$	−27.4529	−	8.73568i	−1.75390	−	0.558102i
$246$	−5.76846			−0.367784
$247$	−6.98379	−	11.9916i	−0.444368	−	0.763007i
$248$	1.82642	+	3.16346i	0.115978	+	0.200880i
$249$	15.5024			0.982427
$250$	14.2776	+	24.7295i	0.902995	+	1.56403i
$251$	0.339652	+	0.588295i	0.0214387	+	0.0371329i	0.876546	−	0.481319i	$-0.159842\pi$
$251$	0.339652	+	0.588295i	0.0214387	+	0.0371329i	−0.855107	+	0.518452i	$0.826509\pi$
$252$	0.955663	+	2.46713i	0.0602011	+	0.155414i
$253$	8.28729	+	14.3540i	0.521017	+	0.902428i
$254$	2.53206			0.158876
$255$	−1.47212	−	2.54978i	−0.0921874	−	0.159673i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.22293	+	2.11818i	0.0762846	+	0.132129i	0.901644	−	0.432479i	$-0.142361\pi$
$257$	1.22293	+	2.11818i	0.0762846	+	0.132129i	−0.825360	+	0.564607i	$0.809028\pi$
$258$	−1.28209	+	2.22064i	−0.0798192	+	0.138251i
$259$	−18.8133	−	2.92108i	−1.16900	−	0.181507i
$260$	−7.37100	+	12.8789i	−0.457130	+	0.798715i
$261$	4.50457	−	7.80214i	0.278826	−	0.482941i
$262$	−12.4331			−0.768122
$263$	25.3192			1.56125			0.780625	−	0.625000i	$-0.214901\pi$
$263$	25.3192			1.56125			0.780625	+	0.625000i	$0.214901\pi$
$264$	−4.04474			−0.248936
$265$	−11.1852			−0.687103
$266$	10.0624	+	1.56236i	0.616964	+	0.0957943i
$267$	−5.45685	−	9.45154i	−0.333954	−	0.578425i
$268$	0.583158	−	1.01006i	0.0356220	−	0.0616992i
$269$	6.78327	−	11.7490i	0.413583	−	0.716348i	−0.581695	−	0.813407i	$-0.697610\pi$
$269$	6.78327	−	11.7490i	0.413583	−	0.716348i	0.995279	+	0.0970593i	$0.0309437\pi$
$270$	4.11561			0.250468
$271$	2.42970	+	4.20837i	0.147594	+	0.255640i	0.930338	−	0.366704i	$-0.119514\pi$
$271$	2.42970	+	4.20837i	0.147594	+	0.255640i	−0.782744	+	0.622344i	$0.786180\pi$
$272$	0.715381			0.0433763
$273$	−9.43190	−	1.42805i	−0.570844	−	0.0864297i
$274$	−10.3848			−0.627369
$275$	−24.1436	−	41.8179i	−1.45591	−	2.52171i
$276$	4.09781			0.246659
$277$	−6.03127	+	10.4465i	−0.362384	+	0.627667i	−0.988353	−	0.152181i	$-0.951370\pi$
$277$	−6.03127	+	10.4465i	−0.362384	+	0.627667i	0.625969	+	0.779848i	$0.284704\pi$
$278$	−0.636394	+	1.10227i	−0.0381684	+	0.0661096i
$279$	1.82642	+	3.16346i	0.109345	+	0.189391i
$280$	−3.93314	−	10.1537i	−0.235050	−	0.606802i
$281$	18.3963			1.09743			0.548716	−	0.836009i	$-0.315117\pi$
$281$	18.3963			1.09743			0.548716	+	0.836009i	$0.315117\pi$
$282$	2.57600			0.153399
$283$	−0.694306			−0.0412722			−0.0206361	−	0.999787i	$-0.506569\pi$
$283$	−0.694306			−0.0412722			−0.0206361	+	0.999787i	$0.506569\pi$
$284$	−10.2051			−0.605560
$285$	7.92007	−	13.7180i	0.469144	−	0.812582i
$286$	7.24406	−	12.6571i	0.428350	−	0.748430i
$287$	5.51270	+	14.2315i	0.325404	+	0.840060i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.24412	+	14.2792i	0.484948	+	0.839954i
$290$	−18.5391	+	32.1106i	−1.08865	+	1.88560i
$291$	3.10135	+	5.37170i	0.181805	+	0.314895i
$292$	2.51347			0.147090
$293$	5.44518	+	9.43133i	0.318111	+	0.550984i	0.980094	−	0.198535i	$-0.0636183\pi$
$293$	5.44518	+	9.43133i	0.318111	+	0.550984i	−0.661983	+	0.749519i	$0.730285\pi$
$294$	5.17342	−	4.71548i	0.301720	−	0.275012i
$295$	26.5512	+	45.9880i	1.54587	+	2.67752i
$296$	−3.59797	−	6.23187i	−0.209128	−	0.362220i
$297$	−4.04474			−0.234699
$298$	−11.6810	−	20.2320i	−0.676661	−	1.17201i
$299$	−7.33912	+	12.8232i	−0.424433	+	0.741584i
$300$	−11.9383			−0.689256
$301$	6.70384	+	1.04089i	0.386403	+	0.0599957i
$302$	1.19832	−	2.07555i	0.0689555	−	0.119434i
$303$	−16.3065			−0.936783
$304$	1.92440	+	3.33315i	0.110372	+	0.191169i
$305$	−19.4067	+	33.6134i	−1.11122	+	1.92470i
$306$	0.715381			0.0408956
$307$	23.7724			1.35676			0.678382	−	0.734709i	$-0.262681\pi$
$307$	23.7724			1.35676			0.678382	+	0.734709i	$0.262681\pi$
$308$	3.86540	+	9.97887i	0.220252	+	0.568599i
$309$	−1.46023	+	2.52920i	−0.0830697	+	0.143881i
$310$	−7.51685	−	13.0196i	−0.426928	−	0.739462i
$311$	−10.9242	−	18.9212i	−0.619454	−	1.07293i	−0.989586	−	0.143946i	$-0.954021\pi$
$311$	−10.9242	−	18.9212i	−0.619454	−	1.07293i	0.370132	−	0.928979i	$-0.379312\pi$
$312$	−1.81454	−	3.11568i	−0.102728	−	0.176390i
$313$	16.0323	−	27.7688i	0.906199	−	1.56958i	0.0868992	−	0.996217i	$-0.472304\pi$
$313$	16.0323	−	27.7688i	0.906199	−	1.56958i	0.819300	−	0.573365i	$-0.194362\pi$
$314$	5.79083	−	10.0300i	0.326795	−	0.566026i
$315$	−3.93314	−	10.1537i	−0.221607	−	0.572098i
$316$	−6.70468	−	11.6129i	−0.377168	−	0.653274i
$317$	10.3068	−	17.8520i	0.578889	−	1.00267i	−0.416718	−	0.909036i	$-0.636820\pi$
$317$	10.3068	−	17.8520i	0.578889	−	1.00267i	0.995607	−	0.0936296i	$-0.0298469\pi$
$318$	1.35888	−	2.35365i	0.0762021	−	0.131986i
$319$	18.2198	−	31.5576i	1.02011	−	1.76689i
$320$	2.05781	−	3.56422i	0.115035	−	0.199246i
$321$	−2.01938	−	3.49768i	−0.112711	−	0.195221i
$322$	−3.91613	−	10.1098i	−0.218237	−	0.563398i
$323$	1.37668	−	2.38447i	0.0766003	−	0.132676i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	21.3813	−	37.3581i	1.18602	−	2.07226i
$326$	−8.95432	−	15.5093i	−0.495934	−	0.858982i
$327$	−6.93314	−	12.0085i	−0.383403	−	0.664074i
$328$	−2.88423	+	4.99563i	−0.159255	+	0.275838i
$329$	−2.46179	−	6.35532i	−0.135723	−	0.350380i
$330$	16.6466			0.916363
$331$	11.9956			0.659338			0.329669	−	0.944097i	$-0.393063\pi$
$331$	11.9956			0.659338			0.329669	+	0.944097i	$0.393063\pi$
$332$	7.75122	−	13.4255i	0.425403	−	0.736820i
$333$	−3.59797	−	6.23187i	−0.197168	−	0.341504i
$334$	−6.30796			−0.345156
$335$	−2.40005	+	4.15701i	−0.131129	+	0.227122i
$336$	2.61442	+	0.405935i	0.142629	+	0.0221456i
$337$	−17.6146			−0.959526			−0.479763	−	0.877398i	$-0.659277\pi$
$337$	−17.6146			−0.959526			−0.479763	+	0.877398i	$0.659277\pi$
$338$	12.9996	−	0.0980666i	0.707087	−	0.00533412i
$339$	7.30902	+	12.6596i	0.396972	+	0.687575i
$340$	−2.94423			−0.159673
$341$	7.38740	+	12.7954i	0.400050	+	0.692907i
$342$	1.92440	+	3.33315i	0.104059	+	0.180236i
$343$	−16.5777	−	8.25707i	−0.895113	−	0.445840i
$344$	1.28209	+	2.22064i	0.0691255	+	0.119729i
$345$	−16.8650			−0.907982
$346$	1.82563	+	3.16209i	0.0981467	+	0.169995i
$347$	7.92519	−	13.7268i	0.425447	−	0.736895i	−0.571015	−	0.820939i	$-0.693450\pi$
$347$	7.92519	−	13.7268i	0.425447	−	0.736895i	0.996462	+	0.0840442i	$0.0267837\pi$
$348$	−4.50457	−	7.80214i	−0.241470	−	0.418239i
$349$	5.15206	−	8.92363i	0.275783	−	0.477671i	−0.694549	−	0.719445i	$-0.744396\pi$
$349$	5.15206	−	8.92363i	0.275783	−	0.477671i	0.970332	+	0.241775i	$0.0777294\pi$
$350$	11.4090	+	29.4532i	0.609834	+	1.57434i
$351$	−1.81454	−	3.11568i	−0.0968530	−	0.166303i
$352$	−2.02237	+	3.50284i	−0.107793	+	0.186702i
$353$	−16.0195			−0.852632			−0.426316	−	0.904574i	$-0.640189\pi$
$353$	−16.0195			−0.852632			−0.426316	+	0.904574i	$0.640189\pi$
$354$	−12.9027			−0.685769
$355$	42.0002			2.22914
$356$	−10.9137			−0.578425
$357$	−0.683663	−	1.76493i	−0.0361833	−	0.0934103i
$358$	−6.25956	−	10.8419i	−0.330828	−	0.573011i
$359$	4.55623	−	7.89162i	0.240469	−	0.416504i	−0.720379	−	0.693580i	$-0.756032\pi$
$359$	4.55623	−	7.89162i	0.240469	−	0.416504i	0.960848	+	0.277077i	$0.0893656\pi$
$360$	2.05781	−	3.56422i	0.108456	−	0.187851i
$361$	−4.18681			−0.220358
$362$	9.08638	+	15.7381i	0.477570	+	0.827175i
$363$	−5.35989			−0.281321
$364$	−5.95268	+	7.45423i	−0.312005	+	0.390708i
$365$	−10.3445			−0.541454
$366$	−4.71538	−	8.16728i	−0.246477	−	0.426911i
$367$	10.2238			0.533677			0.266839	−	0.963741i	$-0.414021\pi$
$367$	10.2238			0.533677			0.266839	+	0.963741i	$0.414021\pi$
$368$	2.04891	−	3.54881i	0.106807	−	0.184995i
$369$	−2.88423	+	4.99563i	−0.150147	+	0.260062i
$370$	14.8079	+	25.6480i	0.769824	+	1.33337i
$371$	−7.10537	−	1.10323i	−0.368892	−	0.0572769i
$372$	3.65285			0.189391
$373$	−28.1592			−1.45803			−0.729015	−	0.684497i	$-0.760022\pi$
$373$	−28.1592			−1.45803			−0.729015	+	0.684497i	$0.760022\pi$
$374$	2.89353			0.149621
$375$	28.5552			1.47458
$376$	1.28800	−	2.23088i	0.0664236	−	0.115049i
$377$	32.4827	−	0.122520i	1.67294	−	0.00631008i
$378$	2.61442	+	0.405935i	0.134472	+	0.0208790i
$379$	−3.08112	+	5.33666i	−0.158267	+	0.274126i	−0.934244	−	0.356635i	$-0.883924\pi$
$379$	−3.08112	+	5.33666i	−0.158267	+	0.274126i	0.775977	+	0.630761i	$0.217257\pi$
$380$	−7.92007	−	13.7180i	−0.406291	−	0.703716i
$381$	1.26603	−	2.19283i	0.0648608	−	0.112342i
$382$	−2.23004	−	3.86254i	−0.114099	−	0.197625i
$383$	−18.9632			−0.968973			−0.484487	−	0.874799i	$-0.660994\pi$
$383$	−18.9632			−0.968973			−0.484487	+	0.874799i	$0.660994\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−15.9085	−	41.0692i	−0.810772	−	2.09308i
$386$	4.34243	+	7.52130i	0.221024	+	0.382824i
$387$	1.28209	+	2.22064i	0.0651721	+	0.112881i
$388$	6.20271			0.314895
$389$	1.08192	+	1.87394i	0.0548554	+	0.0950123i	0.892149	−	0.451741i	$-0.149197\pi$
$389$	1.08192	+	1.87394i	0.0548554	+	0.0950123i	−0.837294	+	0.546753i	$0.815864\pi$
$390$	7.46794	+	12.8229i	0.378154	+	0.649314i
$391$	−2.93150			−0.148252
$392$	−1.49702	−	6.83805i	−0.0756107	−	0.345374i
$393$	−6.21657	+	10.7674i	−0.313584	+	0.543144i
$394$	2.46794			0.124333
$395$	27.5939	+	47.7940i	1.38840	+	2.40478i
$396$	−2.02237	+	3.50284i	−0.101628	+	0.176025i
$397$	20.7716			1.04250			0.521249	−	0.853405i	$-0.325466\pi$
$397$	20.7716			1.04250			0.521249	+	0.853405i	$0.325466\pi$
$398$	20.5681			1.03099
$399$	6.38423	−	7.93309i	0.319611	−	0.397151i
$400$	−5.96913	+	10.3388i	−0.298457	+	0.516942i
$401$	−1.15403	−	1.99885i	−0.0576297	−	0.0998176i	0.835771	−	0.549078i	$-0.185021\pi$
$401$	−1.15403	−	1.99885i	−0.0576297	−	0.0998176i	−0.893401	+	0.449260i	$0.851688\pi$
$402$	−0.583158	−	1.01006i	−0.0290853	−	0.0503772i
$403$	−6.54220	+	11.4308i	−0.325890	+	0.569407i
$404$	−8.15325	+	14.1218i	−0.405639	+	0.702588i
$405$	2.05781	−	3.56422i	0.102253	−	0.177108i
$406$	−14.9440	+	18.5696i	−0.741659	+	0.921592i
$407$	−14.5528	−	25.2063i	−0.721358	−	1.24943i
$408$	0.357690	−	0.619538i	0.0177083	−	0.0306717i
$409$	−8.01566	+	13.8835i	−0.396349	+	0.686497i	−0.993272	−	0.115802i	$-0.963056\pi$
$409$	−8.01566	+	13.8835i	−0.396349	+	0.686497i	0.596923	+	0.802298i	$0.296390\pi$
$410$	11.8704	−	20.5601i	0.586236	−	1.01539i
$411$	−5.19240	+	8.99351i	−0.256122	+	0.443617i
$412$	1.46023	+	2.52920i	0.0719405	+	0.124605i
$413$	12.3306	+	31.8325i	0.606749	+	1.56637i
$414$	2.04891	−	3.54881i	0.100698	−	0.174415i
$415$	−31.9010	+	55.2542i	−1.56596	+	2.71232i
$416$	−3.60553	+	0.0135995i	−0.176775	+	0.000666770i
$417$	0.636394	+	1.10227i	0.0311644	+	0.0539783i
$418$	7.78367	+	13.4817i	0.380712	+	0.659412i
$419$	1.48519	−	2.57242i	0.0725561	−	0.125671i	−0.827465	−	0.561518i	$-0.810218\pi$
$419$	1.48519	−	2.57242i	0.0725561	−	0.125671i	0.900021	+	0.435847i	$0.143551\pi$
$420$	−10.7600	−	1.67067i	−0.525032	−	0.0815203i
$421$	34.3026			1.67181			0.835903	−	0.548878i	$-0.184945\pi$
$421$	34.3026			1.67181			0.835903	+	0.548878i	$0.184945\pi$
$422$	−4.45453			−0.216843
$423$	1.28800	−	2.23088i	0.0626248	−	0.108469i
$424$	−1.35888	−	2.35365i	−0.0659929	−	0.114303i
$425$	8.54041			0.414271
$426$	−5.10254	+	8.83786i	−0.247219	+	0.428196i
$427$	−15.6434	+	19.4386i	−0.757037	+	0.940700i
$428$	−4.03877			−0.195221
$429$	−7.33934	−	12.6021i	−0.354346	−	0.608435i
$430$	−5.27657	−	9.13929i	−0.254459	−	0.440736i
$431$	−23.4495			−1.12952			−0.564762	−	0.825254i	$-0.691032\pi$
$431$	−23.4495			−1.12952			−0.564762	+	0.825254i	$0.691032\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	0.402426	+	0.697022i	0.0193394	+	0.0334968i	0.875533	−	0.483158i	$-0.160510\pi$
$433$	0.402426	+	0.697022i	0.0193394	+	0.0334968i	−0.856194	+	0.516655i	$0.827177\pi$
$434$	−3.49089	−	9.01203i	−0.167568	−	0.432591i
$435$	18.5391	+	32.1106i	0.888880	+	1.53959i
$436$	−13.8663			−0.664074
$437$	−7.88581	−	13.6586i	−0.377230	−	0.653381i
$438$	1.25673	−	2.17673i	0.0600491	−	0.104008i
$439$	0.798877	+	1.38370i	0.0381283	+	0.0660402i	0.884460	−	0.466616i	$-0.154527\pi$
$439$	0.798877	+	1.38370i	0.0381283	+	0.0660402i	−0.846332	+	0.532657i	$0.821194\pi$
$440$	8.32328	−	14.4163i	0.396797	−	0.687272i
$441$	−1.49702	−	6.83805i	−0.0712865	−	0.325621i
$442$	1.29809	+	2.22890i	0.0617437	+	0.106018i
$443$	−3.27335	+	5.66960i	−0.155521	+	0.269371i	−0.933249	−	0.359231i	$-0.883039\pi$
$443$	−3.27335	+	5.66960i	−0.155521	+	0.269371i	0.777727	+	0.628602i	$0.216372\pi$
$444$	−7.19594			−0.341504
$445$	44.9166			2.12925
$446$	4.99324			0.236437
$447$	−23.3619			−1.10498
$448$	1.65876	−	2.06119i	0.0783691	−	0.0973821i
$449$	−6.34113	−	10.9832i	−0.299257	−	0.518328i	0.676710	−	0.736250i	$-0.263405\pi$
$449$	−6.34113	−	10.9832i	−0.299257	−	0.518328i	−0.975966	+	0.217923i	$0.930072\pi$
$450$	−5.96913	+	10.3388i	−0.281388	+	0.487378i
$451$	−11.6659	+	20.2060i	−0.549328	+	0.951464i
$452$	14.6180			0.687575
$453$	−1.19832	−	2.07555i	−0.0563019	−	0.0975178i
$454$	−1.57273			−0.0738117
$455$	24.4989	−	30.6787i	1.14853	−	1.43824i
$456$	3.84879			0.180236
$457$	5.37753	+	9.31415i	0.251550	+	0.435697i	0.963953	−	0.266073i	$-0.0857264\pi$
$457$	5.37753	+	9.31415i	0.251550	+	0.435697i	−0.712403	+	0.701771i	$0.752393\pi$
$458$	−1.65724			−0.0774376
$459$	0.357690	−	0.619538i	0.0166956	−	0.0289176i
$460$	−8.43251	+	14.6055i	−0.393168	+	0.680986i
$461$	9.19640	+	15.9286i	0.428319	+	0.741870i	0.996724	−	0.0808788i	$-0.0257727\pi$
$461$	9.19640	+	15.9286i	0.428319	+	0.741870i	−0.568405	+	0.822749i	$0.692439\pi$
$462$	10.5747	+	1.64190i	0.491978	+	0.0763880i
$463$	−34.6818			−1.61180			−0.805901	−	0.592050i	$-0.798319\pi$
$463$	−34.6818			−1.61180			−0.805901	+	0.592050i	$0.798319\pi$
$464$	−9.00914			−0.418239
$465$	−15.0337			−0.697171
$466$	7.72362			0.357790
$467$	14.1236	−	24.4627i	0.653561	−	1.13200i	−0.328692	−	0.944437i	$-0.606608\pi$
$467$	14.1236	−	24.4627i	0.653561	−	1.13200i	0.982253	−	0.187563i	$-0.0600589\pi$
$468$	−3.60553	+	0.0135995i	−0.166665	+	0.000628636i
$469$	−1.93464	+	2.40400i	−0.0893334	+	0.111006i
$470$	−5.30091	+	9.18145i	−0.244513	+	0.423509i
$471$	−5.79083	−	10.0300i	−0.266827	−	0.462158i
$472$	−6.45133	+	11.1740i	−0.296947	+	0.514327i
$473$	5.18570	+	8.98189i	0.238439	+	0.412988i
$474$	−13.4094			−0.615913
$475$	22.9739	+	39.7920i	1.05412	+	1.82578i
$476$	−1.87031	−	0.290398i	−0.0857255	−	0.0133104i
$477$	−1.35888	−	2.35365i	−0.0622187	−	0.107766i
$478$	14.3815	+	24.9095i	0.657794	+	1.13933i
$479$	−12.4585			−0.569243			−0.284622	−	0.958640i	$-0.591868\pi$
$479$	−12.4585			−0.569243			−0.284622	+	0.958640i	$0.591868\pi$
$480$	−2.05781	−	3.56422i	−0.0939256	−	0.162684i
$481$	12.8878	−	22.5181i	0.587634	−	1.02674i
$482$	25.6204			1.16698
$483$	−10.7134	−	1.66344i	−0.487478	−	0.0756894i
$484$	−2.67994	+	4.64180i	−0.121816	+	0.210991i
$485$	−25.5279			−1.15916
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−4.17049	+	7.22350i	−0.188983	+	0.327328i	−0.944911	−	0.327326i	$-0.893852\pi$
$487$	−4.17049	+	7.22350i	−0.188983	+	0.327328i	0.755929	+	0.654654i	$0.227186\pi$
$488$	−9.43076			−0.426911
$489$	−17.9086			−0.809856
$490$	6.16114	+	28.1428i	0.278332	+	1.27136i
$491$	8.82502	−	15.2854i	0.398268	−	0.689820i	−0.595245	−	0.803545i	$-0.702945\pi$
$491$	8.82502	−	15.2854i	0.398268	−	0.689820i	0.993512	+	0.113725i	$0.0362781\pi$
$492$	2.88423	+	4.99563i	0.130031	+	0.225220i
$493$	3.22248	+	5.58150i	0.145133	+	0.251378i
$494$	−6.89313	+	12.0439i	−0.310137	+	0.541882i
$495$	8.32328	−	14.4163i	0.374104	−	0.647967i
$496$	1.82642	−	3.16346i	0.0820088	−	0.142043i
$497$	26.6804	+	4.14260i	1.19678	+	0.185821i
$498$	−7.75122	−	13.4255i	−0.347340	−	0.601611i
$499$	−18.9853	+	32.8834i	−0.849897	+	1.47207i	0.0314021	+	0.999507i	$0.490003\pi$
$499$	−18.9853	+	32.8834i	−0.849897	+	1.47207i	−0.881299	+	0.472558i	$0.843331\pi$
$500$	14.2776	−	24.7295i	0.638514	−	1.10594i
$501$	−3.15398	+	5.46286i	−0.140909	+	0.244062i
$502$	0.339652	−	0.588295i	0.0151594	−	0.0262569i
$503$	−10.4517	−	18.1029i	−0.466019	−	0.807169i	0.533228	−	0.845972i	$-0.320979\pi$
$503$	−10.4517	−	18.1029i	−0.466019	−	0.807169i	−0.999247	+	0.0388027i	$0.987646\pi$
$504$	1.65876	−	2.06119i	0.0738871	−	0.0918127i
$505$	33.5556	−	58.1200i	1.49320	−	2.58631i
$506$	8.28729	−	14.3540i	0.368415	−	0.638113i
$507$	6.41489	−	11.3070i	0.284895	−	0.502163i
$508$	−1.26603	−	2.19283i	−0.0561711	−	0.0972911i
$509$	7.51054	+	13.0086i	0.332899	+	0.576598i	0.983079	−	0.183183i	$-0.0586399\pi$
$509$	7.51054	+	13.0086i	0.332899	+	0.576598i	−0.650180	+	0.759780i	$0.725307\pi$
$510$	−1.47212	+	2.54978i	−0.0651864	+	0.112906i
$511$	−6.57127	−	1.02030i	−0.290696	−	0.0451356i
$512$	1.00000			0.0441942
$513$	3.84879			0.169928
$514$	1.22293	−	2.11818i	0.0539413	−	0.0934291i
$515$	−6.00975	−	10.4092i	−0.264821	−	0.458684i
$516$	2.56417			0.112881
$517$	5.20962	−	9.02333i	0.229119	−	0.396846i
$518$	6.87689	+	17.7533i	0.302153	+	0.780035i
$519$	3.65127			0.160273
$520$	14.8389	−	0.0559702i	0.650731	−	0.00245446i
$521$	10.4549	+	18.1084i	0.458037	+	0.793344i	0.998857	−	0.0477946i	$-0.0152193\pi$
$521$	10.4549	+	18.1084i	0.458037	+	0.793344i	−0.540820	+	0.841138i	$0.681886\pi$
$522$	−9.00914			−0.394319
$523$	6.18390	+	10.7108i	0.270403	+	0.468352i	0.968965	−	0.247198i	$-0.0795097\pi$
$523$	6.18390	+	10.7108i	0.270403	+	0.468352i	−0.698562	+	0.715550i	$0.746176\pi$
$524$	6.21657	+	10.7674i	0.271572	+	0.470377i
$525$	31.2117	+	4.84616i	1.36219	+	0.211504i
$526$	−12.6596	−	21.9271i	−0.551985	−	0.956067i
$527$	−2.61318			−0.113832
$528$	2.02237	+	3.50284i	0.0880123	+	0.152442i
$529$	3.10396	−	5.37622i	0.134955	−	0.233749i
$530$	5.59261	+	9.68669i	0.242928	+	0.420763i
$531$	−6.45133	+	11.1740i	−0.279964	+	0.484912i
$532$	−3.67815	−	9.49545i	−0.159468	−	0.411680i
$533$	−20.7983	+	0.0784481i	−0.900876	+	0.00339796i
$534$	−5.45685	+	9.45154i	−0.236141	+	0.409008i
$535$	16.6220			0.718632
$536$	−1.16632			−0.0503772
$537$	−12.5191			−0.540240
$538$	−13.5665			−0.584895
$539$	−6.05503	−	27.6581i	−0.260809	−	1.19132i
$540$	−2.05781	−	3.56422i	−0.0885539	−	0.153380i
$541$	2.37409	−	4.11204i	0.102070	−	0.176791i	−0.810467	−	0.585784i	$-0.800787\pi$
$541$	2.37409	−	4.11204i	0.102070	−	0.176791i	0.912537	+	0.408993i	$0.134120\pi$
$542$	2.42970	−	4.20837i	0.104365	−	0.180765i
$543$	18.1728			0.779868
$544$	−0.357690	−	0.619538i	−0.0153359	−	0.0265625i
$545$	57.0682			2.44453
$546$	3.47922	+	8.88229i	0.148897	+	0.380127i
$547$	2.85148			0.121921			0.0609603	−	0.998140i	$-0.480584\pi$
$547$	2.85148			0.121921			0.0609603	+	0.998140i	$0.480584\pi$
$548$	5.19240	+	8.99351i	0.221808	+	0.384184i
$549$	−9.43076			−0.402495
$550$	−24.1436	+	41.8179i	−1.02948	+	1.78312i
$551$	−17.3371	+	30.0288i	−0.738587	+	1.27927i
$552$	−2.04891	−	3.54881i	−0.0872073	−	0.151047i
$553$	12.8148	+	33.0826i	0.544942	+	1.40682i
$554$	12.0625			0.512488
$555$	29.6157			1.25712
$556$	1.27279			0.0539783
$557$	14.0997			0.597424			0.298712	−	0.954343i	$-0.403443\pi$
$557$	14.0997			0.597424			0.298712	+	0.954343i	$0.403443\pi$
$558$	1.82642	−	3.16346i	0.0773187	−	0.133920i
$559$	−4.59239	+	8.02400i	−0.194238	+	0.339379i
$560$	−6.82682	+	8.48306i	−0.288486	+	0.358475i
$561$	1.44676	−	2.50587i	0.0610824	−	0.105798i
$562$	−9.19816	−	15.9317i	−0.388001	−	0.672037i
$563$	0.457406	−	0.792251i	0.0192774	−	0.0333894i	−0.856226	−	0.516602i	$-0.827197\pi$
$563$	0.457406	−	0.792251i	0.0192774	−	0.0333894i	0.875503	+	0.483212i	$0.160530\pi$
$564$	−1.28800	−	2.23088i	−0.0542346	−	0.0939371i
$565$	−60.1622			−2.53104
$566$	0.347153	+	0.601286i	0.0145919	+	0.0252740i
$567$	1.65876	−	2.06119i	0.0696615	−	0.0865619i
$568$	5.10254	+	8.83786i	0.214098	+	0.370828i
$569$	11.0384	+	19.1191i	0.462755	+	0.801515i	0.999097	−	0.0424858i	$-0.0135277\pi$
$569$	11.0384	+	19.1191i	0.462755	+	0.801515i	−0.536342	+	0.844001i	$0.680194\pi$
$570$	−15.8401			−0.663470
$571$	−1.38518	−	2.39921i	−0.0579682	−	0.100404i	0.835585	−	0.549361i	$-0.185129\pi$
$571$	−1.38518	−	2.39921i	−0.0579682	−	0.100404i	−0.893553	+	0.448957i	$0.851796\pi$
$572$	−14.5834	+	0.0550063i	−0.609762	+	0.00229993i
$573$	−4.46007			−0.186322
$574$	9.56850	−	11.8899i	0.399382	−	0.496275i
$575$	24.4604	−	42.3666i	1.02007	−	1.76681i
$576$	1.00000			0.0416667
$577$	−13.6418	−	23.6282i	−0.567914	−	0.983656i	−0.996772	−	0.0802839i	$-0.974417\pi$
$577$	−13.6418	−	23.6282i	−0.567914	−	0.983656i	0.428858	−	0.903372i	$-0.358916\pi$
$578$	8.24412	−	14.2792i	0.342910	−	0.593938i
$579$	8.68485			0.360930
$580$	37.0781			1.53959
$581$	−25.7149	+	31.9535i	−1.06683	+	1.32565i
$582$	3.10135	−	5.37170i	0.128555	−	0.222664i
$583$	−5.49630	−	9.51987i	−0.227634	−	0.394273i
$584$	−1.25673	−	2.17673i	−0.0520040	−	0.0900736i
$585$	14.8389	−	0.0559702i	0.613515	−	0.00231408i
$586$	5.44518	−	9.43133i	0.224938	−	0.389604i
$587$	−15.1737	+	26.2816i	−0.626286	+	1.08476i	0.362005	+	0.932176i	$0.382092\pi$
$587$	−15.1737	+	26.2816i	−0.626286	+	1.08476i	−0.988291	+	0.152583i	$0.951241\pi$
$588$	−6.67043	−	2.12257i	−0.275084	−	0.0875334i
$589$	−7.02952	−	12.1755i	−0.289646	−	0.501682i
$590$	26.5512	−	45.9880i	1.09309	−	1.89330i
$591$	1.23397	−	2.13730i	0.0507587	−	0.0879166i
$592$	−3.59797	+	6.23187i	−0.147876	+	0.256128i
$593$	−21.2192	+	36.7527i	−0.871367	+	1.50925i	−0.0107847	+	0.999942i	$0.503433\pi$
$593$	−21.2192	+	36.7527i	−0.871367	+	1.50925i	−0.860583	+	0.509311i	$0.829900\pi$
$594$	2.02237	+	3.50284i	0.0829788	+	0.143723i
$595$	7.69747	+	1.19517i	0.315565	+	0.0489970i
$596$	−11.6810	+	20.2320i	−0.478471	+	0.828736i
$597$	10.2841	−	17.8125i	0.420899	−	0.729018i
$598$	14.7748	−	0.0557282i	0.604185	−	0.00227889i
$599$	15.1759	+	26.2854i	0.620071	+	1.07399i	0.989472	+	0.144724i	$0.0462294\pi$
$599$	15.1759	+	26.2854i	0.620071	+	1.07399i	−0.369401	+	0.929270i	$0.620437\pi$
$600$	5.96913	+	10.3388i	0.243689	+	0.422081i
$601$	−2.44125	+	4.22836i	−0.0995805	+	0.172479i	−0.911511	−	0.411275i	$-0.865083\pi$
$601$	−2.44125	+	4.22836i	−0.0995805	+	0.172479i	0.811931	+	0.583754i	$0.198417\pi$
$602$	−2.45048	−	6.32614i	−0.0998743	−	0.257834i
$603$	−1.16632			−0.0474960
$604$	−2.39664			−0.0975178
$605$	11.0296	−	19.1038i	0.448417	−	0.776681i
$606$	8.15325	+	14.1218i	0.331203	+	0.573660i
$607$	−12.7969			−0.519409			−0.259704	−	0.965688i	$-0.583625\pi$
$607$	−12.7969			−0.519409			−0.259704	+	0.965688i	$0.583625\pi$
$608$	1.92440	−	3.33315i	0.0780445	−	0.135177i
$609$	8.60970	+	22.2267i	0.348883	+	0.900670i
$610$	38.8134			1.57151
$611$	9.28784	−	0.0350323i	0.375746	−	0.00141726i
$612$	−0.357690	−	0.619538i	−0.0144588	−	0.0250433i
$613$	4.04991			0.163574			0.0817871	−	0.996650i	$-0.473937\pi$
$613$	4.04991			0.163574			0.0817871	+	0.996650i	$0.473937\pi$
$614$	−11.8862	−	20.5875i	−0.479689	−	0.830845i
$615$	−11.8704	−	20.5601i	−0.478660	−	0.829063i
$616$	6.70925	−	8.33697i	0.270324	−	0.335906i
$617$	−7.16474	−	12.4097i	−0.288441	−	0.499595i	0.684996	−	0.728546i	$-0.259804\pi$
$617$	−7.16474	−	12.4097i	−0.288441	−	0.499595i	−0.973438	+	0.228951i	$0.926470\pi$
$618$	2.92046			0.117478
$619$	−18.3950	−	31.8611i	−0.739358	−	1.28061i	−0.952785	−	0.303646i	$-0.901796\pi$
$619$	−18.3950	−	31.8611i	−0.739358	−	1.28061i	0.213427	−	0.976959i	$-0.431537\pi$
$620$	−7.51685	+	13.0196i	−0.301884	+	0.522878i
$621$	−2.04891	−	3.54881i	−0.0822198	−	0.142409i
$622$	−10.9242	+	18.9212i	−0.438020	+	0.758673i
$623$	28.5330	+	4.43025i	1.14315	+	0.177494i
$624$	−1.79099	+	3.12928i	−0.0716968	+	0.125271i
$625$	−28.9154	+	50.0829i	−1.15662	+	2.00332i
$626$	−32.0646			−1.28156
$627$	15.5673			0.621700
$628$	−11.5817			−0.462158
$629$	5.14784			0.205258
$630$	−6.82682	+	8.48306i	−0.271987	+	0.337973i
$631$	−18.8504	−	32.6498i	−0.750422	−	1.29977i	−0.947618	−	0.319405i	$-0.896517\pi$
$631$	−18.8504	−	32.6498i	−0.750422	−	1.29977i	0.197197	−	0.980364i	$-0.436816\pi$
$632$	−6.70468	+	11.6129i	−0.266698	+	0.461935i
$633$	−2.22726	+	3.85773i	−0.0885258	+	0.153331i
$634$	−20.6137			−0.818673
$635$	5.21049	+	9.02484i	0.206772	+	0.358140i
$636$	−2.71776			−0.107766
$637$	18.5888	−	17.0721i	0.736514	−	0.676423i
$638$	−36.4396			−1.44266
$639$	5.10254	+	8.83786i	0.201853	+	0.349620i
$640$	−4.11561			−0.162684
$641$	0.594040	−	1.02891i	0.0234632	−	0.0406394i	−0.854055	−	0.520182i	$-0.825864\pi$
$641$	0.594040	−	1.02891i	0.0234632	−	0.0406394i	0.877519	+	0.479543i	$0.159197\pi$
$642$	−2.01938	+	3.49768i	−0.0796987	+	0.138042i
$643$	−14.9781	−	25.9429i	−0.590679	−	1.02309i	−0.994141	−	0.108090i	$-0.965527\pi$
$643$	−14.9781	−	25.9429i	−0.590679	−	1.02309i	0.403462	−	0.914996i	$-0.367807\pi$
$644$	−6.79730	+	8.44638i	−0.267851	+	0.332834i
$645$	−10.5531			−0.415529
$646$	−2.75335			−0.108329
$647$	−30.4218			−1.19600			−0.598002	−	0.801495i	$-0.704038\pi$
$647$	−30.4218			−1.19600			−0.598002	+	0.801495i	$0.704038\pi$
$648$	1.00000			0.0392837
$649$	−26.0939	+	45.1960i	−1.02428	+	1.77410i
$650$	−43.0437	+	0.162354i	−1.68831	+	0.00636806i
$651$	−9.55009	−	1.48282i	−0.374298	−	0.0581162i
$652$	−8.95432	+	15.5093i	−0.350678	+	0.607392i
$653$	6.14648	+	10.6460i	0.240530	+	0.416611i	0.960865	−	0.277015i	$-0.0893453\pi$
$653$	6.14648	+	10.6460i	0.240530	+	0.416611i	−0.720335	+	0.693626i	$0.756012\pi$
$654$	−6.93314	+	12.0085i	−0.271107	+	0.469571i
$655$	−25.5850	−	44.3145i	−0.999688	−	1.73151i
$656$	5.76846			0.225220
$657$	−1.25673	−	2.17673i	−0.0490299	−	0.0849222i
$658$	−4.27298	+	5.30963i	−0.166578	+	0.206991i
$659$	17.0038	+	29.4514i	0.662374	+	1.14727i	0.979990	+	0.199046i	$0.0637844\pi$
$659$	17.0038	+	29.4514i	0.662374	+	1.14727i	−0.317616	+	0.948219i	$0.602882\pi$
$660$	−8.32328	−	14.4163i	−0.323983	−	0.561155i
$661$	13.8167			0.537407			0.268703	−	0.963223i	$-0.413405\pi$
$661$	13.8167			0.537407			0.268703	+	0.963223i	$0.413405\pi$
$662$	−5.99781	−	10.3885i	−0.233111	−	0.403761i
$663$	2.57932	−	0.00972881i	0.100173	−	0.000377836i
$664$	−15.5024			−0.601611
$665$	15.1378	+	39.0796i	0.587020	+	1.51544i
$666$	−3.59797	+	6.23187i	−0.139419	+	0.241480i
$667$	36.9178			1.42946
$668$	3.15398	+	5.46286i	0.122031	+	0.211364i
$669$	2.49662	−	4.32427i	0.0965248	−	0.167186i
$670$	4.80010			0.185444
$671$	−38.1449			−1.47257
$672$	−0.955663	−	2.46713i	−0.0368655	−	0.0951714i
$673$	19.8004	−	34.2952i	0.763248	−	1.32198i	−0.177920	−	0.984045i	$-0.556937\pi$
$673$	19.8004	−	34.2952i	0.763248	−	1.32198i	0.941168	−	0.337939i	$-0.109730\pi$
$674$	8.80728	+	15.2547i	0.339244	+	0.587587i
$675$	5.96913	+	10.3388i	0.229752	+	0.397942i
$676$	−6.58474	−	11.2090i	−0.253259	−	0.431114i
$677$	16.8735	−	29.2258i	0.648503	−	1.12324i	−0.334978	−	0.942226i	$-0.608729\pi$
$677$	16.8735	−	29.2258i	0.648503	−	1.12324i	0.983481	−	0.181013i	$-0.0579378\pi$
$678$	7.30902	−	12.6596i	0.280701	−	0.486189i
$679$	−16.2165	−	2.51789i	−0.622333	−	0.0966279i
$680$	1.47212	+	2.54978i	0.0564530	+	0.0977795i
$681$	−0.786363	+	1.36202i	−0.0301335	+	0.0521927i
$682$	7.38740	−	12.7954i	0.282878	−	0.489959i
$683$	−8.39495	+	14.5405i	−0.321224	+	0.556376i	−0.980741	−	0.195313i	$-0.937428\pi$
$683$	−8.39495	+	14.5405i	−0.321224	+	0.556376i	0.659517	+	0.751690i	$0.270761\pi$
$684$	1.92440	−	3.33315i	0.0735811	−	0.127446i
$685$	−21.3699	−	37.0138i	−0.816503	−	1.41422i
$686$	1.13803	+	18.4853i	0.0434503	+	0.705771i
$687$	−0.828619	+	1.43521i	−0.0316138	+	0.0547567i
$688$	1.28209	−	2.22064i	0.0488791	−	0.0846610i
$689$	4.86746	−	8.50461i	0.185435	−	0.324000i
$690$	8.43251	+	14.6055i	0.321020	+	0.556023i
$691$	1.67963	+	2.90920i	0.0638960	+	0.110671i	0.896204	−	0.443643i	$-0.146314\pi$
$691$	1.67963	+	2.90920i	0.0638960	+	0.110671i	−0.832308	+	0.554314i	$0.812981\pi$
$692$	1.82563	−	3.16209i	0.0694002	−	0.120205i
$693$	6.70925	−	8.33697i	0.254863	−	0.316695i
$694$	−15.8504			−0.601672
$695$	−5.23831			−0.198700
$696$	−4.50457	+	7.80214i	−0.170745	+	0.295739i
$697$	−2.06332	−	3.57378i	−0.0781539	−	0.135367i
$698$	−10.3041			−0.390017
$699$	3.86181	−	6.68885i	0.146067	−	0.252996i
$700$	19.8027	−	24.6070i	0.748473	−	0.930059i
$701$	−51.6652			−1.95137			−0.975683	−	0.219186i	$-0.929660\pi$
$701$	−51.6652			−1.95137			−0.975683	+	0.219186i	$0.929660\pi$
$702$	−1.79099	+	3.12928i	−0.0675964	+	0.118107i
$703$	13.8478	+	23.9852i	0.522281	+	0.904618i
$704$	4.04474			0.152442
$705$	5.30091	+	9.18145i	0.199644	+	0.345793i
$706$	8.00975	+	13.8733i	0.301451	+	0.522128i
$707$	27.0486	−	33.6108i	1.01727	−	1.26406i
$708$	6.45133	+	11.1740i	0.242456	+	0.419946i
$709$	−19.3061			−0.725055			−0.362527	−	0.931973i	$-0.618086\pi$
$709$	−19.3061			−0.725055			−0.362527	+	0.931973i	$0.618086\pi$
$710$	−21.0001	−	36.3732i	−0.788119	−	1.36506i
$711$	−6.70468	+	11.6129i	−0.251445	+	0.435516i
$712$	5.45685	+	9.45154i	0.204504	+	0.354211i
$713$	−7.48434	+	12.9633i	−0.280291	+	0.485478i
$714$	−1.18665	+	1.47454i	−0.0444091	+	0.0551832i
$715$	60.0196	−	0.226385i	2.24461	−	0.00846631i
$716$	−6.25956	+	10.8419i	−0.233931	+	0.405180i
$717$	28.7630			1.07417
$718$	−9.11246			−0.340074
$719$	−8.55314			−0.318978			−0.159489	−	0.987200i	$-0.550985\pi$
$719$	−8.55314			−0.318978			−0.159489	+	0.987200i	$0.550985\pi$
$720$	−4.11561			−0.153380
$721$	−2.79098	−	7.20515i	−0.103941	−	0.268334i
$722$	2.09340	+	3.62588i	0.0779084	+	0.134941i
$723$	12.8102	−	22.1879i	0.476417	−	0.825178i
$724$	9.08638	−	15.7381i	0.337693	−	0.584901i
$725$	−107.553			−3.99444
$726$	2.67994	+	4.64180i	0.0994620	+	0.172273i
$727$	37.0524			1.37420			0.687100	−	0.726563i	$-0.258884\pi$
$727$	37.0524			1.37420			0.687100	+	0.726563i	$0.258884\pi$
$728$	9.43190	+	1.42805i	0.349569	+	0.0529272i
$729$	1.00000			0.0370370
$730$	5.17223	+	8.95857i	0.191433	+	0.331571i
$731$	−1.83436			−0.0678463
$732$	−4.71538	+	8.16728i	−0.174285	+	0.301871i
$733$	7.89197	−	13.6693i	0.291497	−	0.504887i	−0.682667	−	0.730729i	$-0.739180\pi$
$733$	7.89197	−	13.6693i	0.291497	−	0.504887i	0.974164	+	0.225843i	$0.0725135\pi$
$734$	−5.11189	−	8.85406i	−0.188683	−	0.326809i
$735$	27.4529	+	8.73568i	1.01262	+	0.322220i
$736$	−4.09781			−0.151047
$737$	−4.71744			−0.173769
$738$	5.76846			0.212340
$739$	−36.3450			−1.33697			−0.668487	−	0.743724i	$-0.733058\pi$
$739$	−36.3450			−1.33697			−0.668487	+	0.743724i	$0.733058\pi$
$740$	14.8079	−	25.6480i	0.544348	−	0.942838i
$741$	6.98379	+	11.9916i	0.256556	+	0.440522i
$742$	2.59726	+	6.70504i	0.0953483	+	0.246150i
$743$	−15.1149	+	26.1797i	−0.554511	+	0.960441i	0.443430	+	0.896309i	$0.353761\pi$
$743$	−15.1149	+	26.1797i	−0.554511	+	0.960441i	−0.997941	+	0.0641324i	$0.979572\pi$
$744$	−1.82642	−	3.16346i	−0.0669599	−	0.115978i
$745$	48.0743	−	83.2672i	1.76131	−	3.05067i
$746$	14.0796	+	24.3866i	0.515492	+	0.892858i
$747$	−15.5024			−0.567204
$748$	−1.44676	−	2.50587i	−0.0528989	−	0.0916236i
$749$	10.5591	+	1.63948i	0.385819	+	0.0599052i
$750$	−14.2776	−	24.7295i	−0.521344	−	0.902995i
$751$	−15.3619	−	26.6076i	−0.560563	−	0.970924i	−0.997447	−	0.0714063i	$-0.977251\pi$
$751$	−15.3619	−	26.6076i	−0.560563	−	0.970924i	0.436884	−	0.899518i	$-0.356082\pi$
$752$	−2.57600			−0.0939371
$753$	−0.339652	−	0.588295i	−0.0123776	−	0.0214387i
$754$	−16.3474	−	28.0696i	−0.595339	−	1.02223i
$755$	9.86363			0.358974
$756$	−0.955663	−	2.46713i	−0.0347571	−	0.0897285i
$757$	−7.78491	+	13.4839i	−0.282947	+	0.490079i	−0.972109	−	0.234528i	$-0.924646\pi$
$757$	−7.78491	+	13.4839i	−0.282947	+	0.490079i	0.689162	+	0.724607i	$0.257979\pi$
$758$	6.16224			0.223823
$759$	−8.28729	−	14.3540i	−0.300809	−	0.521017i
$760$	−7.92007	+	13.7180i	−0.287291	+	0.497603i
$761$	23.8556			0.864765			0.432382	−	0.901690i	$-0.357673\pi$
$761$	23.8556			0.864765			0.432382	+	0.901690i	$0.357673\pi$
$762$	−2.53206			−0.0917270
$763$	36.2523	+	5.62880i	1.31242	+	0.203776i
$764$	−2.23004	+	3.86254i	−0.0806799	+	0.139742i
$765$	1.47212	+	2.54978i	0.0532244	+	0.0921874i
$766$	9.48159	+	16.4226i	0.342584	+	0.593373i
$767$	−46.5209	+	0.175470i	−1.67977	+	0.00633584i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−23.2870	+	40.3342i	−0.839750	+	1.45449i	0.0503539	+	0.998731i	$0.483965\pi$
$769$	−23.2870	+	40.3342i	−0.839750	+	1.45449i	−0.890104	+	0.455758i	$0.849368\pi$
$770$	−27.6127	+	34.3117i	−0.995092	+	1.23651i
$771$	−1.22293	−	2.11818i	−0.0440429	−	0.0762846i
$772$	4.34243	−	7.52130i	0.156287	−	0.270698i
$773$	−3.75330	+	6.50090i	−0.134997	+	0.233821i	−0.925596	−	0.378512i	$-0.876436\pi$
$773$	−3.75330	+	6.50090i	−0.134997	+	0.233821i	0.790599	+	0.612334i	$0.209769\pi$
$774$	1.28209	−	2.22064i	0.0460836	−	0.0798192i
$775$	21.8043	−	37.7662i	0.783234	−	1.35660i
$776$	−3.10135	−	5.37170i	−0.111332	−	0.192833i
$777$	18.8133	+	2.92108i	0.674922	+	0.104793i
$778$	1.08192	−	1.87394i	0.0387886	−	0.0671839i
$779$	11.1008	−	19.2271i	0.397727	−	0.688884i
$780$	7.37100	−	12.8789i	0.263924	−	0.461138i
$781$	20.6384	+	35.7468i	0.738501	+	1.27912i
$782$	1.46575	+	2.53875i	0.0524151	+	0.0907856i
$783$	−4.50457	+	7.80214i	−0.160980	+	0.278826i
$784$	−5.17342	+	4.71548i	−0.184765	+	0.168410i
$785$	47.6656			1.70126
$786$	12.4331			0.443475
$787$	−21.2447	+	36.7970i	−0.757293	+	1.31167i	0.186933	+	0.982373i	$0.440145\pi$
$787$	−21.2447	+	36.7970i	−0.757293	+	1.31167i	−0.944226	+	0.329298i	$0.893188\pi$
$788$	−1.23397	−	2.13730i	−0.0439583	−	0.0761380i
$789$	−25.3192			−0.901388
$790$	27.5939	−	47.7940i	0.981746	−	1.70043i
$791$	−38.2178	−	5.93397i	−1.35887	−	0.210988i
$792$	4.04474			0.143723
$793$	−17.1125	−	29.3832i	−0.607683	−	1.04343i
$794$	−10.3858	−	17.9888i	−0.368579	−	0.638397i
$795$	11.1852			0.396699
$796$	−10.2841	−	17.8125i	−0.364509	−	0.631348i
$797$	−9.27713	−	16.0685i	−0.328613	−	0.569174i	0.653624	−	0.756819i	$-0.273248\pi$
$797$	−9.27713	−	16.0685i	−0.328613	−	0.569174i	−0.982237	+	0.187645i	$0.939914\pi$
$798$	−10.0624	−	1.56236i	−0.356204	−	0.0553069i
$799$	0.921412	+	1.59593i	0.0325972	+	0.0564600i
$800$	11.9383			0.422081
$801$	5.45685	+	9.45154i	0.192808	+	0.333954i
$802$	−1.15403	+	1.99885i	−0.0407504	+	0.0705817i
$803$	−5.08316	−	8.80429i	−0.179381	−	0.310697i
$804$	−0.583158	+	1.01006i	−0.0205664	+	0.0356220i
$805$	27.9750	−	34.7620i	0.985991	−	1.22520i
$806$	13.1704	−	0.0496768i	0.463909	−	0.00174979i
$807$	−6.78327	+	11.7490i	−0.238783	+	0.413583i
$808$	16.3065			0.573660
$809$	37.3361			1.31267			0.656334	−	0.754470i	$-0.272106\pi$
$809$	37.3361			1.31267			0.656334	+	0.754470i	$0.272106\pi$
$810$	−4.11561			−0.144608
$811$	19.9446			0.700350			0.350175	−	0.936684i	$-0.386122\pi$
$811$	19.9446			0.700350			0.350175	+	0.936684i	$0.386122\pi$
$812$	23.5537	+	3.65712i	0.826573	+	0.128340i
$813$	−2.42970	−	4.20837i	−0.0852133	−	0.147594i
$814$	−14.5528	+	25.2063i	−0.510077	+	0.883479i
$815$	36.8525	−	63.8304i	1.29089	−	2.23588i
$816$	−0.715381			−0.0250433
$817$	−4.93448	−	8.54677i	−0.172636	−	0.299014i
$818$	16.0313			0.560522
$819$	9.43190	+	1.42805i	0.329577	+	0.0499002i
$820$	−23.7407			−0.829063
$821$	−12.0631	−	20.8939i	−0.421005	−	0.729203i	0.575033	−	0.818130i	$-0.304989\pi$
$821$	−12.0631	−	20.8939i	−0.421005	−	0.729203i	−0.996038	+	0.0889276i	$0.971656\pi$
$822$	10.3848			0.362212
$823$	−1.63853	+	2.83802i	−0.0571155	+	0.0989270i	−0.893169	−	0.449720i	$-0.851524\pi$
$823$	−1.63853	+	2.83802i	−0.0571155	+	0.0989270i	0.836054	+	0.548647i	$0.184857\pi$
$824$	1.46023	−	2.52920i	0.0508696	−	0.0881087i
$825$	24.1436	+	41.8179i	0.840571	+	1.45591i
$826$	21.4025	−	26.5949i	0.744687	−	0.925353i
$827$	49.4538			1.71968			0.859838	−	0.510566i	$-0.170564\pi$
$827$	49.4538			1.71968			0.859838	+	0.510566i	$0.170564\pi$
$828$	−4.09781			−0.142409
$829$	36.5908			1.27085			0.635426	−	0.772161i	$-0.280824\pi$
$829$	36.5908			1.27085			0.635426	+	0.772161i	$0.280824\pi$
$830$	63.8020			2.21460
$831$	6.03127	−	10.4465i	0.209222	−	0.362384i
$832$	1.81454	+	3.11568i	0.0629079	+	0.108017i
$833$	4.77190	+	1.51845i	0.165337	+	0.0526111i
$834$	0.636394	−	1.10227i	0.0220365	−	0.0381684i
$835$	−12.9806	−	22.4830i	−0.449211	−	0.778056i
$836$	7.78367	−	13.4817i	0.269204	−	0.466275i
$837$	−1.82642	−	3.16346i	−0.0631304	−	0.109345i
$838$	−2.97037			−0.102610
$839$	−21.2148	−	36.7451i	−0.732416	−	1.26858i	−0.955848	−	0.293862i	$-0.905059\pi$
$839$	−21.2148	−	36.7451i	−0.732416	−	1.26858i	0.223431	−	0.974720i	$-0.428274\pi$
$840$	3.93314	+	10.1537i	0.135706	+	0.350337i
$841$	−26.0823	−	45.1759i	−0.899389	−	1.55779i
$842$	−17.1513	−	29.7069i	−0.591072	−	1.02377i
$843$	−18.3963			−0.633603
$844$	2.22726	+	3.85773i	0.0766656	+	0.132789i
$845$	27.1002	+	46.1318i	0.932277	+	1.58698i
$846$	−2.57600			−0.0885648
$847$	8.89078	−	11.0477i	0.305491	−	0.379605i
$848$	−1.35888	+	2.35365i	−0.0466641	+	0.0808245i
$849$	0.694306			0.0238285
$850$	−4.27020	−	7.39621i	−0.146467	−	0.253688i
$851$	14.7438	−	25.5370i	0.505412	−	0.875399i
$852$	10.2051			0.349620
$853$	31.5639			1.08073			0.540363	−	0.841432i	$-0.318287\pi$
$853$	31.5639			1.08073			0.540363	+	0.841432i	$0.318287\pi$
$854$	24.6560	+	3.82827i	0.843712	+	0.131001i
$855$	−7.92007	+	13.7180i	−0.270861	+	0.469144i
$856$	2.01938	+	3.49768i	0.0690211	+	0.119548i
$857$	−13.0273	−	22.5639i	−0.445004	−	0.770769i	0.553049	−	0.833149i	$-0.313464\pi$
$857$	−13.0273	−	22.5639i	−0.445004	−	0.770769i	−0.998052	+	0.0623801i	$0.980131\pi$
$858$	−7.24406	+	12.6571i	−0.247308	+	0.432106i
$859$	19.9113	−	34.4875i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$859$	19.9113	−	34.4875i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710786\pi$
$860$	−5.27657	+	9.13929i	−0.179930	+	0.311647i
$861$	−5.51270	−	14.2315i	−0.187872	−	0.485009i
$862$	11.7248	+	20.3079i	0.399347	+	0.691689i
$863$	10.4795	−	18.1510i	0.356725	−	0.617866i	−0.630687	−	0.776038i	$-0.717227\pi$
$863$	10.4795	−	18.1510i	0.356725	−	0.617866i	0.987412	+	0.158172i	$0.0505600\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−7.51360	+	13.0139i	−0.255470	+	0.442487i
$866$	0.402426	−	0.697022i	0.0136750	−	0.0236858i
$867$	−8.24412	−	14.2792i	−0.279985	−	0.484948i
$868$	−6.05920	+	7.52922i	−0.205663	+	0.255558i
$869$	−27.1187	+	46.9709i	−0.919938	+	1.59338i
$870$	18.5391	−	32.1106i	0.628533	−	1.08865i
$871$	−2.11633	−	3.63386i	−0.0717090	−	0.123129i
$872$	6.93314	+	12.0085i	0.234786	+	0.406661i
$873$	−3.10135	−	5.37170i	−0.104965	−	0.181805i
$874$	−7.88581	+	13.6586i	−0.266742	+	0.462010i
$875$	−47.3663	+	58.8577i	−1.60127	+	1.98975i
$876$	−2.51347			−0.0849222
$877$	−14.4891			−0.489263			−0.244632	−	0.969616i	$-0.578667\pi$
$877$	−14.4891			−0.489263			−0.244632	+	0.969616i	$0.578667\pi$
$878$	0.798877	−	1.38370i	0.0269608	−	0.0466974i
$879$	−5.44518	−	9.43133i	−0.183661	−	0.318111i
$880$	−16.6466			−0.561155
$881$	−22.1191	+	38.3114i	−0.745211	+	1.29074i	0.204886	+	0.978786i	$0.434318\pi$
$881$	−22.1191	+	38.3114i	−0.745211	+	1.29074i	−0.950096	+	0.311957i	$0.899016\pi$
$882$	−5.17342	+	4.71548i	−0.174198	+	0.158778i
$883$	−51.8997			−1.74656			−0.873282	−	0.487216i	$-0.838012\pi$
$883$	−51.8997			−1.74656			−0.873282	+	0.487216i	$0.838012\pi$
$884$	1.28124	−	2.23862i	0.0430927	−	0.0752931i
$885$	−26.5512	−	45.9880i	−0.892508	−	1.54587i
$886$	6.54669			0.219940
$887$	−14.3951	−	24.9331i	−0.483340	−	0.837170i	0.516477	−	0.856301i	$-0.327243\pi$
$887$	−14.3951	−	24.9331i	−0.483340	−	0.837170i	−0.999817	+	0.0191313i	$0.993910\pi$
$888$	3.59797	+	6.23187i	0.120740	+	0.209128i
$889$	2.41980	+	6.24692i	0.0811574	+	0.209515i
$890$	−22.4583	−	38.8989i	−0.752803	−	1.30389i
$891$	4.04474			0.135504
$892$	−2.49662	−	4.32427i	−0.0835929	−	0.144787i
$893$	−4.95725	+	8.58621i	−0.165888	+	0.287326i
$894$	11.6810	+	20.2320i	0.390670	+	0.676661i
$895$	25.7619	−	44.6210i	0.861126	−	1.49151i
$896$	−2.61442	−	0.405935i	−0.0873418	−	0.0135613i
$897$	7.33912	−	12.8232i	0.245046	−	0.428154i
$898$	−6.34113	+	10.9832i	−0.211606	+	0.366513i
$899$	32.9090			1.09758
$900$	11.9383			0.397942
$901$	1.94423			0.0647717
$902$	23.3319			0.776867
$903$	−6.70384	−	1.04089i	−0.223090	−	0.0346385i
$904$	−7.30902	−	12.6596i	−0.243095	−	0.421052i
$905$	−37.3960	+	64.7718i	−1.24309	+	2.15309i
$906$	−1.19832	+	2.07555i	−0.0398115	+	0.0689555i
$907$	−33.1216			−1.09978			−0.549892	−	0.835236i	$-0.685331\pi$
$907$	−33.1216			−1.09978			−0.549892	+	0.835236i	$0.685331\pi$
$908$	0.786363	+	1.36202i	0.0260964	+	0.0452002i
$909$	16.3065			0.540852
$910$	−38.8180	−	5.87731i	−1.28680	−	0.194831i
$911$	−20.6630			−0.684597			−0.342298	−	0.939591i	$-0.611205\pi$
$911$	−20.6630			−0.684597			−0.342298	+	0.939591i	$0.611205\pi$
$912$	−1.92440	−	3.33315i	−0.0637231	−	0.110372i
$913$	−62.7032			−2.07517
$914$	5.37753	−	9.31415i	0.177873	−	0.308085i
$915$	19.4067	−	33.6134i	0.641565	−	1.11122i
$916$	0.828619	+	1.43521i	0.0273783	+	0.0474207i
$917$	−11.8819	−	30.6741i	−0.392374	−	1.01295i
$918$	−0.715381			−0.0236111
$919$	51.6174			1.70270			0.851350	−	0.524598i	$-0.175784\pi$
$919$	51.6174			1.70270			0.851350	+	0.524598i	$0.175784\pi$
$920$	16.8650			0.556023
$921$	−23.7724			−0.783328
$922$	9.19640	−	15.9286i	0.302867	−	0.524581i
$923$	−18.2772	+	31.9345i	−0.601600	+	1.05114i
$924$	−3.86540	−	9.97887i	−0.127162	−	0.328281i
$925$	−42.9535	+	74.3977i	−1.41230	+	2.44618i
$926$	17.3409	+	30.0354i	0.569858	+	0.987023i
$927$	1.46023	−	2.52920i	0.0479603	−	0.0830697i
$928$	4.50457	+	7.80214i	0.147870	+	0.256118i
$929$	−34.5180			−1.13250			−0.566250	−	0.824234i	$-0.691606\pi$
$929$	−34.5180			−1.13250			−0.566250	+	0.824234i	$0.691606\pi$
$930$	7.51685	+	13.0196i	0.246487	+	0.426928i
$931$	5.76170	+	26.3182i	0.188832	+	0.862545i
$932$	−3.86181	−	6.68885i	−0.126498	−	0.219101i
$933$	10.9242	+	18.9212i	0.357642	+	0.619454i
$934$	−28.2471			−0.924274
$935$	5.95432	+	10.3132i	0.194727	+	0.337277i
$936$	1.81454	+	3.11568i	0.0593101	+	0.101839i
$937$	14.3652			0.469291			0.234646	−	0.972081i	$-0.424607\pi$
$937$	14.3652			0.469291			0.234646	+	0.972081i	$0.424607\pi$
$938$	3.04924	+	0.473448i	0.0995614	+	0.0154586i
$939$	−16.0323	+	27.7688i	−0.523194	+	0.906199i
$940$	10.6018			0.345793
$941$	4.16447	+	7.21307i	0.135758	+	0.235139i	0.925887	−	0.377801i	$-0.123320\pi$
$941$	4.16447	+	7.21307i	0.135758	+	0.235139i	−0.790129	+	0.612941i	$0.789986\pi$
$942$	−5.79083	+	10.0300i	−0.188675	+	0.326795i
$943$	−23.6381			−0.769762
$944$	12.9027			0.419946
$945$	3.93314	+	10.1537i	0.127945	+	0.330301i
$946$	5.18570	−	8.98189i	0.168602	−	0.292027i
$947$	0.160717	+	0.278371i	0.00522262	+	0.00904583i	0.868625	−	0.495470i	$-0.165004\pi$
$947$	0.160717	+	0.278371i	0.00522262	+	0.00904583i	−0.863402	+	0.504516i	$0.831671\pi$
$948$	6.70468	+	11.6129i	0.217758	+	0.377168i
$949$	4.50159	−	7.86534i	0.146128	−	0.255320i
$950$	22.9739	−	39.7920i	0.745373	−	1.29102i
$951$	−10.3068	+	17.8520i	−0.334222	+	0.578889i
$952$	0.683663	+	1.76493i	0.0221576	+	0.0572019i
$953$	−9.79426	−	16.9642i	−0.317267	−	0.549523i	0.662650	−	0.748930i	$-0.269432\pi$
$953$	−9.79426	−	16.9642i	−0.317267	−	0.549523i	−0.979917	+	0.199407i	$0.936099\pi$
$954$	−1.35888	+	2.35365i	−0.0439953	+	0.0762021i
$955$	9.17797	−	15.8967i	0.296992	−	0.514405i
$956$	14.3815	−	24.9095i	0.465130	−	0.805630i
$957$	−18.2198	+	31.5576i	−0.588962	+	1.02011i
$958$	6.22925	+	10.7894i	0.201258	+	0.348589i
$959$	−9.92437	−	25.6206i	−0.320475	−	0.827333i
$960$	−2.05781	+	3.56422i	−0.0664154	+	0.115035i
$961$	8.82835	−	15.2912i	0.284786	−	0.493263i
$962$	−25.9452	+	0.0978611i	−0.836506	+	0.00315517i
$963$	2.01938	+	3.49768i	0.0650737	+	0.112711i
$964$	−12.8102	−	22.1879i	−0.412589	−	0.714625i
$965$	−17.8717	+	30.9548i	−0.575312	+	0.996469i
$966$	3.91613	+	10.1098i	0.125999	+	0.325278i
$967$	−21.5461			−0.692875			−0.346437	−	0.938073i	$-0.612609\pi$
$967$	−21.5461			−0.692875			−0.346437	+	0.938073i	$0.612609\pi$
$968$	5.35989			0.172273
$969$	−1.37668	+	2.38447i	−0.0442252	+	0.0766003i
$970$	12.7640	+	22.1078i	0.409826	+	0.709840i
$971$	−17.0756			−0.547983			−0.273991	−	0.961732i	$-0.588344\pi$
$971$	−17.0756			−0.547983			−0.273991	+	0.961732i	$0.588344\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−3.32761	−	0.516669i	−0.106678	−	0.0165637i
$974$	8.34097			0.267262
$975$	−21.3813	+	37.3581i	−0.684748	+	1.19642i
$976$	4.71538	+	8.16728i	0.150936	+	0.261428i
$977$	8.72087			0.279005			0.139503	−	0.990222i	$-0.455450\pi$
$977$	8.72087			0.279005			0.139503	+	0.990222i	$0.455450\pi$
$978$	8.95432	+	15.5093i	0.286327	+	0.495934i
$979$	22.0715	+	38.2290i	0.705409	+	1.22180i
$980$	21.2918	−	19.4071i	0.680141	−	0.619937i
$981$	6.93314	+	12.0085i	0.221358	+	0.383403i
$982$	−17.6500			−0.563236
$983$	11.0826	+	19.1956i	0.353480	+	0.612245i	0.986857	−	0.161598i	$-0.0516649\pi$
$983$	11.0826	+	19.1956i	0.353480	+	0.612245i	−0.633377	+	0.773844i	$0.718332\pi$
$984$	2.88423	−	4.99563i	0.0919459	−	0.159255i
$985$	5.07854	+	8.79628i	0.161816	+	0.280273i
$986$	3.22248	−	5.58150i	0.102625	−	0.177751i
$987$	2.46179	+	6.35532i	0.0783596	+	0.202292i
$988$	13.8769	−	0.0523416i	0.441484	−	0.00166521i
$989$	−5.25375	+	9.09976i	−0.167060	+	0.289356i
$990$	−16.6466			−0.529062
$991$	17.9521			0.570267			0.285134	−	0.958488i	$-0.407962\pi$
$991$	17.9521			0.570267			0.285134	+	0.958488i	$0.407962\pi$
$992$	−3.65285			−0.115978
$993$	−11.9956			−0.380669
$994$	−9.75262	−	25.1772i	−0.309334	−	0.798573i
$995$	42.3252	+	73.3095i	1.34180	+	2.32407i
$996$	−7.75122	+	13.4255i	−0.245607	+	0.425403i
$997$	−29.4747	+	51.0516i	−0.933472	+	1.61682i	−0.156137	+	0.987735i	$0.549904\pi$
$997$	−29.4747	+	51.0516i	−0.933472	+	1.61682i	−0.777336	+	0.629086i	$0.783429\pi$
$998$	37.9705			1.20194
$999$	3.59797	+	6.23187i	0.113835	+	0.197168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.b.373.4	yes	8
3.2	odd	2		1638.2.p.i.919.1		8
7.4	even	3		546.2.j.d.529.4	yes	8
13.3	even	3		546.2.j.d.289.4	✓	8
21.11	odd	6		1638.2.m.g.1621.1		8
39.29	odd	6		1638.2.m.g.289.1		8
91.81	even	3	inner	546.2.k.b.445.4	yes	8
273.263	odd	6		1638.2.p.i.991.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.4	✓	8	13.3	even	3
546.2.j.d.529.4	yes	8	7.4	even	3
546.2.k.b.373.4	yes	8	1.1	even	1	trivial
546.2.k.b.445.4	yes	8	91.81	even	3	inner
1638.2.m.g.289.1		8	39.29	odd	6
1638.2.m.g.1621.1		8	21.11	odd	6
1638.2.p.i.919.1		8	3.2	odd	2
1638.2.p.i.991.1		8	273.263	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.65876 - 2.06119i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.65876 - 2.06119i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.11561 q^{10} +4.04474 q^{11} +(0.500000 - 0.866025i) q^{12} +(1.81454 + 3.11568i) q^{13} +(-2.61442 - 0.405935i) q^{14} +(-2.05781 + 3.56422i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.357690 + 0.619538i) q^{17} +(-0.500000 - 0.866025i) q^{18} -3.84879 q^{19} +(2.05781 + 3.56422i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-2.02237 - 3.50284i) q^{22} +(2.04891 + 3.54881i) q^{23} -1.00000 q^{24} +(-5.96913 - 10.3388i) q^{25} +(1.79099 - 3.12928i) q^{26} -1.00000 q^{27} +(0.955663 + 2.46713i) q^{28} +(4.50457 - 7.80214i) q^{29} +4.11561 q^{30} +(1.82642 + 3.16346i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.04474 q^{33} +0.715381 q^{34} +(-3.93314 - 10.1537i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.59797 - 6.23187i) q^{37} +(1.92440 + 3.33315i) q^{38} +(-1.81454 - 3.11568i) q^{39} +(2.05781 - 3.56422i) q^{40} +(-2.88423 + 4.99563i) q^{41} +(2.61442 + 0.405935i) q^{42} +(1.28209 + 2.22064i) q^{43} +(-2.02237 + 3.50284i) q^{44} +(2.05781 - 3.56422i) q^{45} +(2.04891 - 3.54881i) q^{46} +(1.28800 - 2.23088i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.49702 - 6.83805i) q^{49} +(-5.96913 + 10.3388i) q^{50} +(0.357690 - 0.619538i) q^{51} +(-3.60553 + 0.0135995i) q^{52} +(-1.35888 - 2.35365i) q^{53} +(0.500000 + 0.866025i) q^{54} +(8.32328 - 14.4163i) q^{55} +(1.65876 - 2.06119i) q^{56} +3.84879 q^{57} -9.00914 q^{58} +(-6.45133 + 11.1740i) q^{59} +(-2.05781 - 3.56422i) q^{60} -9.43076 q^{61} +(1.82642 - 3.16346i) q^{62} +(1.65876 - 2.06119i) q^{63} +1.00000 q^{64} +(14.8389 - 0.0559702i) q^{65} +(2.02237 + 3.50284i) q^{66} -1.16632 q^{67} +(-0.357690 - 0.619538i) q^{68} +(-2.04891 - 3.54881i) q^{69} +(-6.82682 + 8.48306i) q^{70} +(5.10254 + 8.83786i) q^{71} +1.00000 q^{72} +(-1.25673 - 2.17673i) q^{73} +(-3.59797 + 6.23187i) q^{74} +(5.96913 + 10.3388i) q^{75} +(1.92440 - 3.33315i) q^{76} +(6.70925 - 8.33697i) q^{77} +(-1.79099 + 3.12928i) q^{78} +(-6.70468 + 11.6129i) q^{79} -4.11561 q^{80} +1.00000 q^{81} +5.76846 q^{82} -15.5024 q^{83} +(-0.955663 - 2.46713i) q^{84} +(1.47212 + 2.54978i) q^{85} +(1.28209 - 2.22064i) q^{86} +(-4.50457 + 7.80214i) q^{87} +4.04474 q^{88} +(5.45685 + 9.45154i) q^{89} -4.11561 q^{90} +(9.43190 + 1.42805i) q^{91} -4.09781 q^{92} +(-1.82642 - 3.16346i) q^{93} -2.57600 q^{94} +(-7.92007 + 13.7180i) q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.10135 - 5.37170i) q^{97} +(-5.17342 + 4.71548i) q^{98} +4.04474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

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