LMFDB - Embedded newform 546.2.k.c.445.3

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.3
Root			$1.26359 - 0.635098i$ of defining polynomial
Character	$\chi$	$=$	546.445
Dual form			546.2.k.c.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.611519 + 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.48662 - 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.611519 + 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.48662 - 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.22304 q^{10} +0.140571 q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.39335 - 2.69665i) q^{13} +(1.15207 + 2.38175i) q^{14} +(0.611519 + 1.05918i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0932782 - 0.161563i) q^{17} +(-0.500000 + 0.866025i) q^{18} +0.895909 q^{19} +(0.611519 - 1.05918i) q^{20} +(1.48662 - 2.18860i) q^{21} +(-0.0702857 + 0.121738i) q^{22} +(-0.0182404 + 0.0315933i) q^{23} +1.00000 q^{24} +(1.75209 - 3.03471i) q^{25} +(1.13869 + 3.42102i) q^{26} +1.00000 q^{27} +(-2.63869 - 0.193156i) q^{28} +(2.99337 + 5.18466i) q^{29} -1.22304 q^{30} +(-1.82050 + 3.15319i) q^{31} +(-0.500000 - 0.866025i) q^{32} +0.140571 q^{33} +0.186556 q^{34} +(3.22722 + 0.236237i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.181804 - 0.314894i) q^{37} +(-0.447955 + 0.775880i) q^{38} +(2.39335 - 2.69665i) q^{39} +(0.611519 + 1.05918i) q^{40} +(1.70480 + 2.95279i) q^{41} +(1.15207 + 2.38175i) q^{42} +(-2.06841 + 3.58258i) q^{43} +(-0.0702857 - 0.121738i) q^{44} +(0.611519 + 1.05918i) q^{45} +(-0.0182404 - 0.0315933i) q^{46} +(0.358745 + 0.621364i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.57990 - 6.50724i) q^{49} +(1.75209 + 3.03471i) q^{50} +(-0.0932782 - 0.161563i) q^{51} +(-3.53204 - 0.724375i) q^{52} +(3.49556 - 6.05448i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.0859621 + 0.148891i) q^{55} +(1.48662 - 2.18860i) q^{56} +0.895909 q^{57} -5.98674 q^{58} +(3.49812 + 6.05892i) q^{59} +(0.611519 - 1.05918i) q^{60} +0.373113 q^{61} +(-1.82050 - 3.15319i) q^{62} +(1.48662 - 2.18860i) q^{63} +1.00000 q^{64} +(4.31981 + 0.885937i) q^{65} +(-0.0702857 + 0.121738i) q^{66} -4.85806 q^{67} +(-0.0932782 + 0.161563i) q^{68} +(-0.0182404 + 0.0315933i) q^{69} +(-1.81820 + 2.67673i) q^{70} +(-5.31198 + 9.20062i) q^{71} +1.00000 q^{72} +(-4.80900 + 8.32943i) q^{73} +(0.181804 + 0.314894i) q^{74} +(1.75209 - 3.03471i) q^{75} +(-0.447955 - 0.775880i) q^{76} +(0.208977 - 0.307654i) q^{77} +(1.13869 + 3.42102i) q^{78} +(-2.94837 - 5.10673i) q^{79} -1.22304 q^{80} +1.00000 q^{81} -3.40959 q^{82} -9.14057 q^{83} +(-2.63869 - 0.193156i) q^{84} +(0.114083 - 0.197597i) q^{85} +(-2.06841 - 3.58258i) q^{86} +(2.99337 + 5.18466i) q^{87} +0.140571 q^{88} +(3.17736 - 5.50335i) q^{89} -1.22304 q^{90} +(-2.34386 - 9.24696i) q^{91} +0.0364808 q^{92} +(-1.82050 + 3.15319i) q^{93} -0.717490 q^{94} +(0.547865 + 0.948930i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(3.24059 - 5.61287i) q^{97} +(6.92538 + 1.01936i) q^{98} +0.140571 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	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 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 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.611519	+	1.05918i	0.273479	+	0.473680i	0.969750	−	0.244099i	$-0.0784921\pi$
$5$	0.611519	+	1.05918i	0.273479	+	0.473680i	−0.696271	+	0.717779i	$0.745159\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.48662	−	2.18860i	0.561891	−	0.827211i
$7$	1.48662	−	2.18860i	0.561891	−	0.827211i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	−1.22304			−0.386758
$11$	0.140571			0.0423839			0.0211919	−	0.999775i	$-0.493254\pi$
$11$	0.140571			0.0423839			0.0211919	+	0.999775i	$0.493254\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.39335	−	2.69665i	0.663795	−	0.747915i
$13$	2.39335	−	2.69665i	0.663795	−	0.747915i
$14$	1.15207	+	2.38175i	0.307903	+	0.636550i
$15$	0.611519	+	1.05918i	0.157893	+	0.273479i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0932782	−	0.161563i	−0.0226233	−	0.0391847i	0.854492	−	0.519464i	$-0.173868\pi$
$17$	−0.0932782	−	0.161563i	−0.0226233	−	0.0391847i	−0.877115	+	0.480280i	$0.840535\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.895909			0.205536			0.102768	−	0.994705i	$-0.467230\pi$
$19$	0.895909			0.205536			0.102768	+	0.994705i	$0.467230\pi$
$20$	0.611519	−	1.05918i	0.136740	−	0.236840i
$21$	1.48662	−	2.18860i	0.324408	−	0.477591i
$22$	−0.0702857	+	0.121738i	−0.0149850	+	0.0259547i
$23$	−0.0182404	+	0.0315933i	−0.00380339	+	0.00658766i	−0.867921	−	0.496703i	$-0.834544\pi$
$23$	−0.0182404	+	0.0315933i	−0.00380339	+	0.00658766i	0.864117	+	0.503290i	$0.167877\pi$
$24$	1.00000			0.204124
$25$	1.75209	−	3.03471i	0.350418	−	0.606942i
$26$	1.13869	+	3.42102i	0.223316	+	0.670917i
$27$	1.00000			0.192450
$28$	−2.63869	−	0.193156i	−0.498666	−	0.0365030i
$29$	2.99337	+	5.18466i	0.555854	+	0.962768i	0.997837	+	0.0657442i	$0.0209421\pi$
$29$	2.99337	+	5.18466i	0.555854	+	0.962768i	−0.441982	+	0.897024i	$0.645725\pi$
$30$	−1.22304			−0.223295
$31$	−1.82050	+	3.15319i	−0.326971	+	0.566330i	−0.981909	−	0.189352i	$-0.939361\pi$
$31$	−1.82050	+	3.15319i	−0.326971	+	0.566330i	0.654939	+	0.755682i	$0.272694\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.140571			0.0244704
$34$	0.186556			0.0319941
$35$	3.22722	+	0.236237i	0.545499	+	0.0399313i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.181804	−	0.314894i	0.0298884	−	0.0517683i	−0.850694	−	0.525661i	$-0.823818\pi$
$37$	0.181804	−	0.314894i	0.0298884	−	0.0517683i	0.880583	+	0.473892i	$0.157151\pi$
$38$	−0.447955	+	0.775880i	−0.0726678	+	0.125864i
$39$	2.39335	−	2.69665i	0.383242	−	0.431809i
$40$	0.611519	+	1.05918i	0.0966896	+	0.167471i
$41$	1.70480	+	2.95279i	0.266245	+	0.461149i	0.967889	−	0.251378i	$-0.0808838\pi$
$41$	1.70480	+	2.95279i	0.266245	+	0.461149i	−0.701644	+	0.712527i	$0.747550\pi$
$42$	1.15207	+	2.38175i	0.177768	+	0.367512i
$43$	−2.06841	+	3.58258i	−0.315429	+	0.546339i	−0.979529	−	0.201305i	$-0.935482\pi$
$43$	−2.06841	+	3.58258i	−0.315429	+	0.546339i	0.664100	+	0.747644i	$0.268815\pi$
$44$	−0.0702857	−	0.121738i	−0.0105960	−	0.0183528i
$45$	0.611519	+	1.05918i	0.0911598	+	0.157893i
$46$	−0.0182404	−	0.0315933i	−0.00268940	−	0.00465818i
$47$	0.358745	+	0.621364i	0.0523283	+	0.0906353i	0.891003	−	0.453997i	$-0.150002\pi$
$47$	0.358745	+	0.621364i	0.0523283	+	0.0906353i	−0.838675	+	0.544633i	$0.816669\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−2.57990	−	6.50724i	−0.368557	−	0.929605i
$50$	1.75209	+	3.03471i	0.247783	+	0.429173i
$51$	−0.0932782	−	0.161563i	−0.0130616	−	0.0226233i
$52$	−3.53204	−	0.724375i	−0.489805	−	0.100453i
$53$	3.49556	−	6.05448i	0.480151	−	0.831647i	−0.519589	−	0.854416i	$-0.673915\pi$
$53$	3.49556	−	6.05448i	0.480151	−	0.831647i	0.999741	+	0.0227694i	$0.00724836\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.0859621	+	0.148891i	0.0115911	+	0.0200764i
$56$	1.48662	−	2.18860i	0.198658	−	0.292463i
$57$	0.895909			0.118666
$58$	−5.98674			−0.786097
$59$	3.49812	+	6.05892i	0.455416	+	0.788804i	0.998712	−	0.0507371i	$-0.0161571\pi$
$59$	3.49812	+	6.05892i	0.455416	+	0.788804i	−0.543296	+	0.839541i	$0.682824\pi$
$60$	0.611519	−	1.05918i	0.0789467	−	0.136740i
$61$	0.373113			0.0477722			0.0238861	−	0.999715i	$-0.492396\pi$
$61$	0.373113			0.0477722			0.0238861	+	0.999715i	$0.492396\pi$
$62$	−1.82050	−	3.15319i	−0.231203	−	0.400456i
$63$	1.48662	−	2.18860i	0.187297	−	0.275737i
$64$	1.00000			0.125000
$65$	4.31981	+	0.885937i	0.535807	+	0.109887i
$66$	−0.0702857	+	0.121738i	−0.00865158	+	0.0149850i
$67$	−4.85806			−0.593507			−0.296753	−	0.954954i	$-0.595904\pi$
$67$	−4.85806			−0.593507			−0.296753	+	0.954954i	$0.595904\pi$
$68$	−0.0932782	+	0.161563i	−0.0113116	+	0.0195923i
$69$	−0.0182404	+	0.0315933i	−0.00219589	+	0.00380339i
$70$	−1.81820	+	2.67673i	−0.217316	+	0.319931i
$71$	−5.31198	+	9.20062i	−0.630416	+	1.09191i	0.357050	+	0.934085i	$0.383782\pi$
$71$	−5.31198	+	9.20062i	−0.630416	+	1.09191i	−0.987467	+	0.157828i	$0.949551\pi$
$72$	1.00000			0.117851
$73$	−4.80900	+	8.32943i	−0.562851	+	0.974886i	0.434395	+	0.900722i	$0.356962\pi$
$73$	−4.80900	+	8.32943i	−0.562851	+	0.974886i	−0.997246	+	0.0741638i	$0.976371\pi$
$74$	0.181804	+	0.314894i	0.0211343	+	0.0366057i
$75$	1.75209	−	3.03471i	0.202314	−	0.350418i
$76$	−0.447955	−	0.775880i	−0.0513839	−	0.0889996i
$77$	0.208977	−	0.307654i	0.0238151	−	0.0350604i
$78$	1.13869	+	3.42102i	0.128931	+	0.387354i
$79$	−2.94837	−	5.10673i	−0.331718	−	0.574552i	0.651131	−	0.758966i	$-0.274295\pi$
$79$	−2.94837	−	5.10673i	−0.331718	−	0.574552i	−0.982849	+	0.184413i	$0.940962\pi$
$80$	−1.22304			−0.136740
$81$	1.00000			0.111111
$82$	−3.40959			−0.376527
$83$	−9.14057			−1.00331			−0.501654	−	0.865068i	$-0.667275\pi$
$83$	−9.14057			−1.00331			−0.501654	+	0.865068i	$0.667275\pi$
$84$	−2.63869	−	0.193156i	−0.287905	−	0.0210750i
$85$	0.114083	−	0.197597i	0.0123740	−	0.0214324i
$86$	−2.06841	−	3.58258i	−0.223042	−	0.386320i
$87$	2.99337	+	5.18466i	0.320923	+	0.555854i
$88$	0.140571			0.0149850
$89$	3.17736	−	5.50335i	0.336799	−	0.583354i	−0.647029	−	0.762465i	$-0.723989\pi$
$89$	3.17736	−	5.50335i	0.336799	−	0.583354i	0.983829	+	0.179111i	$0.0573222\pi$
$90$	−1.22304			−0.128919
$91$	−2.34386	−	9.24696i	−0.245704	−	0.969345i
$92$	0.0364808			0.00380339
$93$	−1.82050	+	3.15319i	−0.188777	+	0.326971i
$94$	−0.717490			−0.0740034
$95$	0.547865	+	0.948930i	0.0562098	+	0.0973582i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	3.24059	−	5.61287i	0.329032	−	0.569901i	−0.653288	−	0.757110i	$-0.726611\pi$
$97$	3.24059	−	5.61287i	0.329032	−	0.569901i	0.982320	+	0.187209i	$0.0599441\pi$
$98$	6.92538	+	1.01936i	0.699569	+	0.102971i
$99$	0.140571			0.0141280
$100$	−3.50418			−0.350418
$101$	−3.00460			−0.298969			−0.149484	−	0.988764i	$-0.547761\pi$
$101$	−3.00460			−0.298969			−0.149484	+	0.988764i	$0.547761\pi$
$102$	0.186556			0.0184718
$103$	−4.12788	−	7.14970i	−0.406732	−	0.704480i	0.587789	−	0.809014i	$-0.299998\pi$
$103$	−4.12788	−	7.14970i	−0.406732	−	0.704480i	−0.994521	+	0.104534i	$0.966665\pi$
$104$	2.39335	−	2.69665i	0.234687	−	0.264428i
$105$	3.22722	+	0.236237i	0.314944	+	0.0230543i
$106$	3.49556	+	6.05448i	0.339518	+	0.588063i
$107$	2.23641	−	3.87358i	0.216202	−	0.374473i	−0.737442	−	0.675411i	$-0.763966\pi$
$107$	2.23641	−	3.87358i	0.216202	−	0.374473i	0.953644	+	0.300938i	$0.0972996\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−3.83686	+	6.64563i	−0.367504	+	0.636536i	−0.989175	−	0.146743i	$-0.953121\pi$
$109$	−3.83686	+	6.64563i	−0.367504	+	0.636536i	0.621671	+	0.783279i	$0.286454\pi$
$110$	−0.171924			−0.0163923
$111$	0.181804	−	0.314894i	0.0172561	−	0.0298884i
$112$	1.15207	+	2.38175i	0.108860	+	0.225054i
$113$	−6.18222	+	10.7079i	−0.581575	+	1.00732i	0.413718	+	0.910405i	$0.364230\pi$
$113$	−6.18222	+	10.7079i	−0.581575	+	1.00732i	−0.995293	+	0.0969119i	$0.969103\pi$
$114$	−0.447955	+	0.775880i	−0.0419548	+	0.0726678i
$115$	−0.0446174			−0.00416059
$116$	2.99337	−	5.18466i	0.277927	−	0.481384i
$117$	2.39335	−	2.69665i	0.221265	−	0.249305i
$118$	−6.99624			−0.644056
$119$	−0.492265	−	0.0360344i	−0.0451258	−	0.00330327i
$120$	0.611519	+	1.05918i	0.0558238	+	0.0966896i
$121$	−10.9802			−0.998204
$122$	−0.186556	+	0.323125i	−0.0168900	+	0.0292544i
$123$	1.70480	+	2.95279i	0.153716	+	0.266245i
$124$	3.64099			0.326971
$125$	10.4009			0.930287
$126$	1.15207	+	2.38175i	0.102634	+	0.212183i
$127$	−5.45432	−	9.44716i	−0.483993	−	0.838300i	0.515838	−	0.856686i	$-0.327481\pi$
$127$	−5.45432	−	9.44716i	−0.483993	−	0.838300i	−0.999831	+	0.0183858i	$0.994147\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.06841	+	3.58258i	−0.182113	+	0.315429i
$130$	−2.92715	+	3.29810i	−0.256728	+	0.289262i
$131$	−10.9715	−	19.0032i	−0.958583	−	1.66031i	−0.725948	−	0.687749i	$-0.758599\pi$
$131$	−10.9715	−	19.0032i	−0.958583	−	1.66031i	−0.232634	−	0.972564i	$-0.574735\pi$
$132$	−0.0702857	−	0.121738i	−0.00611759	−	0.0105960i
$133$	1.33188	−	1.96078i	0.115489	−	0.170021i
$134$	2.42903	−	4.20720i	0.209836	−	0.363447i
$135$	0.611519	+	1.05918i	0.0526311	+	0.0911598i
$136$	−0.0932782	−	0.161563i	−0.00799854	−	0.0138539i
$137$	−1.34605	−	2.33143i	−0.115001	−	0.199188i	0.802779	−	0.596276i	$-0.203354\pi$
$137$	−1.34605	−	2.33143i	−0.115001	−	0.199188i	−0.917780	+	0.397089i	$0.870020\pi$
$138$	−0.0182404	−	0.0315933i	−0.00155273	−	0.00268940i
$139$	5.28925	−	9.16126i	0.448629	−	0.777048i	−0.549668	−	0.835383i	$-0.685246\pi$
$139$	5.28925	−	9.16126i	0.448629	−	0.777048i	0.998297	+	0.0583352i	$0.0185792\pi$
$140$	−1.40902	−	2.91297i	−0.119084	−	0.246191i
$141$	0.358745	+	0.621364i	0.0302118	+	0.0523283i
$142$	−5.31198	−	9.20062i	−0.445772	−	0.772099i
$143$	0.336436	−	0.379071i	0.0281342	−	0.0316996i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.66100	+	6.34104i	−0.304029	+	0.526595i
$146$	−4.80900	−	8.32943i	−0.397996	−	0.689349i
$147$	−2.57990	−	6.50724i	−0.212787	−	0.536708i
$148$	−0.363609			−0.0298884
$149$	−11.9049			−0.975286			−0.487643	−	0.873043i	$-0.662143\pi$
$149$	−11.9049			−0.975286			−0.487643	+	0.873043i	$0.662143\pi$
$150$	1.75209	+	3.03471i	0.143058	+	0.247783i
$151$	−3.66774	+	6.35272i	−0.298477	+	0.516977i	−0.975788	−	0.218720i	$-0.929812\pi$
$151$	−3.66774	+	6.35272i	−0.298477	+	0.516977i	0.677311	+	0.735697i	$0.263145\pi$
$152$	0.895909			0.0726678
$153$	−0.0932782	−	0.161563i	−0.00754109	−	0.0130616i
$154$	0.161948	+	0.334806i	0.0130501	+	0.0269795i
$155$	−4.45307			−0.357679
$156$	−3.53204	−	0.724375i	−0.282789	−	0.0579964i
$157$	5.15138	−	8.92246i	0.411125	−	0.712090i	−0.583888	−	0.811834i	$-0.698469\pi$
$157$	5.15138	−	8.92246i	0.411125	−	0.712090i	0.995013	+	0.0997446i	$0.0318026\pi$
$158$	5.89675			0.469120
$159$	3.49556	−	6.05448i	0.277216	−	0.480151i
$160$	0.611519	−	1.05918i	0.0483448	−	0.0837356i
$161$	0.0420284	+	0.0868883i	0.00331230	+	0.00684775i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−10.1370			−0.793994			−0.396997	−	0.917820i	$-0.629948\pi$
$163$	−10.1370			−0.793994			−0.396997	+	0.917820i	$0.629948\pi$
$164$	1.70480	−	2.95279i	0.133122	−	0.230575i
$165$	0.0859621	+	0.148891i	0.00669214	+	0.0115911i
$166$	4.57029	−	7.91597i	0.354723	−	0.614398i
$167$	−4.28857	−	7.42802i	−0.331860	−	0.574798i	0.651017	−	0.759063i	$-0.274343\pi$
$167$	−4.28857	−	7.42802i	−0.331860	−	0.574798i	−0.982876	+	0.184266i	$0.941009\pi$
$168$	1.48662	−	2.18860i	0.114695	−	0.168854i
$169$	−1.54380	−	12.9080i	−0.118754	−	0.992924i
$170$	0.114083	+	0.197597i	0.00874974	+	0.0151550i
$171$	0.895909			0.0685119
$172$	4.13681			0.315429
$173$	−10.6788			−0.811897			−0.405949	−	0.913896i	$-0.633059\pi$
$173$	−10.6788			−0.811897			−0.405949	+	0.913896i	$0.633059\pi$
$174$	−5.98674			−0.453853
$175$	−4.03705	−	8.34609i	−0.305173	−	0.630905i
$176$	−0.0702857	+	0.121738i	−0.00529799	+	0.00917638i
$177$	3.49812	+	6.05892i	0.262935	+	0.455416i
$178$	3.17736	+	5.50335i	0.238153	+	0.412493i
$179$	−12.9792			−0.970112			−0.485056	−	0.874483i	$-0.661201\pi$
$179$	−12.9792			−0.970112			−0.485056	+	0.874483i	$0.661201\pi$
$180$	0.611519	−	1.05918i	0.0455799	−	0.0789467i
$181$	23.7327			1.76403			0.882017	−	0.471217i	$-0.156185\pi$
$181$	23.7327			1.76403			0.882017	+	0.471217i	$0.156185\pi$
$182$	9.18004	+	2.59364i	0.680470	+	0.192253i
$183$	0.373113			0.0275813
$184$	−0.0182404	+	0.0315933i	−0.00134470	+	0.00232909i
$185$	0.444707			0.0326955
$186$	−1.82050	−	3.15319i	−0.133485	−	0.231203i
$187$	−0.0131122	−	0.0227111i	−0.000958863	−	0.00166080i
$188$	0.358745	−	0.621364i	0.0261642	−	0.0453176i
$189$	1.48662	−	2.18860i	0.108136	−	0.159197i
$190$	−1.09573			−0.0794926
$191$	−19.9778			−1.44555			−0.722773	−	0.691085i	$-0.757133\pi$
$191$	−19.9778			−1.44555			−0.722773	+	0.691085i	$0.757133\pi$
$192$	1.00000			0.0721688
$193$	−6.22388			−0.448004			−0.224002	−	0.974589i	$-0.571912\pi$
$193$	−6.22388			−0.448004			−0.224002	+	0.974589i	$0.571912\pi$
$194$	3.24059	+	5.61287i	0.232661	+	0.402981i
$195$	4.31981	+	0.885937i	0.309348	+	0.0634433i
$196$	−4.34548	+	5.48788i	−0.310391	+	0.391991i
$197$	12.2503	+	21.2182i	0.872799	+	1.51173i	0.859089	+	0.511827i	$0.171031\pi$
$197$	12.2503	+	21.2182i	0.872799	+	1.51173i	0.0137105	+	0.999906i	$0.495636\pi$
$198$	−0.0702857	+	0.121738i	−0.00499499	+	0.00865158i
$199$	9.80754	+	16.9872i	0.695238	+	1.20419i	0.970100	+	0.242704i	$0.0780343\pi$
$199$	9.80754	+	16.9872i	0.695238	+	1.20419i	−0.274862	+	0.961484i	$0.588632\pi$
$200$	1.75209	−	3.03471i	0.123891	−	0.214586i
$201$	−4.85806			−0.342661
$202$	1.50230	−	2.60206i	0.105701	−	0.183080i
$203$	15.7971	+	1.15637i	1.10874	+	0.0811615i
$204$	−0.0932782	+	0.161563i	−0.00653078	+	0.0113116i
$205$	−2.08503	+	3.61138i	−0.145625	+	0.252230i
$206$	8.25576			0.575206
$207$	−0.0182404	+	0.0315933i	−0.00126780	+	0.00219589i
$208$	1.13869	+	3.42102i	0.0789540	+	0.237205i
$209$	0.125939			0.00871140
$210$	−1.81820	+	2.67673i	−0.125467	+	0.184712i
$211$	−2.99635	−	5.18983i	−0.206277	−	0.357283i	0.744262	−	0.667888i	$-0.232802\pi$
$211$	−2.99635	−	5.18983i	−0.206277	−	0.357283i	−0.950539	+	0.310605i	$0.899468\pi$
$212$	−6.99111			−0.480151
$213$	−5.31198	+	9.20062i	−0.363971	+	0.630416i
$214$	2.23641	+	3.87358i	0.152878	+	0.264793i
$215$	−5.05947			−0.345053
$216$	1.00000			0.0680414
$217$	4.19467	+	8.67194i	0.284753	+	0.588689i
$218$	−3.83686	−	6.64563i	−0.259865	−	0.450099i
$219$	−4.80900	+	8.32943i	−0.324962	+	0.562851i
$220$	0.0859621	−	0.148891i	0.00579556	−	0.0100382i
$221$	−0.658924	−	0.135137i	−0.0443240	−	0.00909028i
$222$	0.181804	+	0.314894i	0.0122019	+	0.0211343i
$223$	13.8098	+	23.9193i	0.924775	+	1.60176i	0.791922	+	0.610622i	$0.209080\pi$
$223$	13.8098	+	23.9193i	0.924775	+	1.60176i	0.132853	+	0.991136i	$0.457586\pi$
$224$	−2.63869	−	0.193156i	−0.176305	−	0.0129058i
$225$	1.75209	−	3.03471i	0.116806	−	0.202314i
$226$	−6.18222	−	10.7079i	−0.411235	−	0.712281i
$227$	0.895645	+	1.55130i	0.0594460	+	0.102964i	0.894217	−	0.447634i	$-0.147733\pi$
$227$	0.895645	+	1.55130i	0.0594460	+	0.102964i	−0.834771	+	0.550598i	$0.814400\pi$
$228$	−0.447955	−	0.775880i	−0.0296665	−	0.0513839i
$229$	12.6142	+	21.8485i	0.833572	+	1.44379i	0.895188	+	0.445690i	$0.147041\pi$
$229$	12.6142	+	21.8485i	0.833572	+	1.44379i	−0.0616153	+	0.998100i	$0.519625\pi$
$230$	0.0223087	−	0.0386398i	0.00147099	−	0.00254783i
$231$	0.208977	−	0.307654i	0.0137497	−	0.0202422i
$232$	2.99337	+	5.18466i	0.196524	+	0.340390i
$233$	14.1852	+	24.5695i	0.929304	+	1.60960i	0.784489	+	0.620143i	$0.212925\pi$
$233$	14.1852	+	24.5695i	0.929304	+	1.60960i	0.144815	+	0.989459i	$0.453741\pi$
$234$	1.13869	+	3.42102i	0.0744386	+	0.223639i
$235$	−0.438758	+	0.759952i	−0.0286214	+	0.0495738i
$236$	3.49812	−	6.05892i	0.227708	−	0.394402i
$237$	−2.94837	−	5.10673i	−0.191517	−	0.331718i
$238$	0.277339	−	0.408296i	0.0179772	−	0.0264659i
$239$	−28.9654			−1.87362			−0.936809	−	0.349842i	$-0.886235\pi$
$239$	−28.9654			−1.87362			−0.936809	+	0.349842i	$0.886235\pi$
$240$	−1.22304			−0.0789467
$241$	6.59757	+	11.4273i	0.424987	+	0.736099i	0.996419	−	0.0845504i	$-0.0269454\pi$
$241$	6.59757	+	11.4273i	0.424987	+	0.736099i	−0.571432	+	0.820649i	$0.693612\pi$
$242$	5.49012	−	9.50917i	0.352918	−	0.611272i
$243$	1.00000			0.0641500
$244$	−0.186556	−	0.323125i	−0.0119430	−	0.0206860i
$245$	5.31468	−	6.71188i	0.339543	−	0.428806i
$246$	−3.40959			−0.217388
$247$	2.14422	−	2.41595i	0.136433	−	0.153723i
$248$	−1.82050	+	3.15319i	−0.115602	+	0.200228i
$249$	−9.14057			−0.579260
$250$	−5.20046	+	9.00747i	−0.328906	+	0.569682i
$251$	4.73276	−	8.19739i	0.298729	−	0.517415i	−0.677116	−	0.735876i	$-0.736771\pi$
$251$	4.73276	−	8.19739i	0.298729	−	0.517415i	0.975846	+	0.218462i	$0.0701038\pi$
$252$	−2.63869	−	0.193156i	−0.166222	−	0.0121677i
$253$	−0.00256408	+	0.00444112i	−0.000161202	+	0.000279211i
$254$	10.9086			0.684469
$255$	0.114083	−	0.197597i	0.00714413	−	0.0123740i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.11789	−	8.86444i	0.319245	−	0.552949i	−0.661086	−	0.750310i	$-0.729904\pi$
$257$	5.11789	−	8.86444i	0.319245	−	0.552949i	0.980331	+	0.197362i	$0.0632374\pi$
$258$	−2.06841	−	3.58258i	−0.128773	−	0.223042i
$259$	−0.418902	−	0.866025i	−0.0260293	−	0.0538122i
$260$	−1.39266	−	4.18404i	−0.0863692	−	0.259483i
$261$	2.99337	+	5.18466i	0.185285	+	0.320923i
$262$	21.9430			1.35564
$263$	−4.84616			−0.298827			−0.149414	−	0.988775i	$-0.547739\pi$
$263$	−4.84616			−0.298827			−0.149414	+	0.988775i	$0.547739\pi$
$264$	0.140571			0.00865158
$265$	8.55039			0.525246
$266$	1.03215	+	2.13383i	0.0632851	+	0.130834i
$267$	3.17736	−	5.50335i	0.194451	−	0.336799i
$268$	2.42903	+	4.20720i	0.148377	+	0.256996i
$269$	0.448638	+	0.777064i	0.0273540	+	0.0473785i	0.879378	−	0.476124i	$-0.157959\pi$
$269$	0.448638	+	0.777064i	0.0273540	+	0.0473785i	−0.852024	+	0.523502i	$0.824625\pi$
$270$	−1.22304			−0.0744317
$271$	−6.93756	+	12.0162i	−0.421427	+	0.729933i	−0.996079	−	0.0884648i	$-0.971804\pi$
$271$	−6.93756	+	12.0162i	−0.421427	+	0.729933i	0.574652	+	0.818398i	$0.305137\pi$
$272$	0.186556			0.0113116
$273$	−2.34386	−	9.24696i	−0.141857	−	0.559652i
$274$	2.69210			0.162636
$275$	0.246294	−	0.426594i	0.0148521	−	0.0257246i
$276$	0.0364808			0.00219589
$277$	10.2369	+	17.7309i	0.615078	+	1.06535i	0.990371	+	0.138441i	$0.0442090\pi$
$277$	10.2369	+	17.7309i	0.615078	+	1.06535i	−0.375292	+	0.926907i	$0.622458\pi$
$278$	5.28925	+	9.16126i	0.317228	+	0.549456i
$279$	−1.82050	+	3.15319i	−0.108990	+	0.188777i
$280$	3.22722	+	0.236237i	0.192863	+	0.0141178i
$281$	5.11819			0.305326			0.152663	−	0.988278i	$-0.451215\pi$
$281$	5.11819			0.305326			0.152663	+	0.988278i	$0.451215\pi$
$282$	−0.717490			−0.0427259
$283$	9.08132			0.539829			0.269914	−	0.962884i	$-0.413005\pi$
$283$	9.08132			0.539829			0.269914	+	0.962884i	$0.413005\pi$
$284$	10.6240			0.630416
$285$	0.547865	+	0.948930i	0.0324527	+	0.0562098i
$286$	0.160068	+	0.480898i	0.00946499	+	0.0284361i
$287$	8.99686	+	0.658583i	0.531068	+	0.0388749i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	8.48260	−	14.6923i	0.498976	−	0.864252i
$290$	−3.66100	−	6.34104i	−0.214981	−	0.372359i
$291$	3.24059	−	5.61287i	0.189967	−	0.329032i
$292$	9.61800			0.562851
$293$	3.13195	−	5.42469i	0.182970	−	0.316914i	−0.759920	−	0.650016i	$-0.774762\pi$
$293$	3.13195	−	5.42469i	0.182970	−	0.316914i	0.942891	+	0.333102i	$0.108095\pi$
$294$	6.92538	+	1.01936i	0.403896	+	0.0594501i
$295$	−4.27833	+	7.41029i	−0.249094	+	0.431443i
$296$	0.181804	−	0.314894i	0.0105672	−	0.0183029i
$297$	0.140571			0.00815678
$298$	5.95244	−	10.3099i	0.344816	−	0.597238i
$299$	0.0415404	+	0.124802i	0.00240234	+	0.00721747i
$300$	−3.50418			−0.202314
$301$	4.76589	+	9.85286i	0.274701	+	0.567909i
$302$	−3.66774	−	6.35272i	−0.211055	−	0.365558i
$303$	−3.00460			−0.172610
$304$	−0.447955	+	0.775880i	−0.0256920	+	0.0444998i
$305$	0.228165	+	0.395194i	0.0130647	+	0.0226287i
$306$	0.186556			0.0106647
$307$	30.0806			1.71679			0.858395	−	0.512989i	$-0.171462\pi$
$307$	30.0806			1.71679			0.858395	+	0.512989i	$0.171462\pi$
$308$	−0.370925	−	0.0271522i	−0.0211354	−	0.00154714i
$309$	−4.12788	−	7.14970i	−0.234827	−	0.406732i
$310$	2.22653	−	3.85647i	0.126459	−	0.219033i
$311$	−13.8292	+	23.9528i	−0.784180	+	1.35824i	0.145308	+	0.989386i	$0.453583\pi$
$311$	−13.8292	+	23.9528i	−0.784180	+	1.35824i	−0.929488	+	0.368853i	$0.879751\pi$
$312$	2.39335	−	2.69665i	0.135496	−	0.152668i
$313$	−3.43002	−	5.94097i	−0.193876	−	0.335804i	0.752655	−	0.658415i	$-0.228773\pi$
$313$	−3.43002	−	5.94097i	−0.193876	−	0.335804i	−0.946532	+	0.322611i	$0.895439\pi$
$314$	5.15138	+	8.92246i	0.290709	+	0.503523i
$315$	3.22722	+	0.236237i	0.181833	+	0.0133104i
$316$	−2.94837	+	5.10673i	−0.165859	+	0.287276i
$317$	3.37146	+	5.83953i	0.189360	+	0.327981i	0.945037	−	0.326963i	$-0.106025\pi$
$317$	3.37146	+	5.83953i	0.189360	+	0.327981i	−0.755677	+	0.654944i	$0.772692\pi$
$318$	3.49556	+	6.05448i	0.196021	+	0.339518i
$319$	0.420782	+	0.728816i	0.0235593	+	0.0408059i
$320$	0.611519	+	1.05918i	0.0341849	+	0.0592100i
$321$	2.23641	−	3.87358i	0.124824	−	0.216202i
$322$	−0.0962616	−	0.00704648i	−0.00536445	−	0.000392685i
$323$	−0.0835688	−	0.144745i	−0.00464989	−	0.00805385i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−3.99018	−	11.9879i	−0.221335	−	0.664968i
$326$	5.06852	−	8.77893i	0.280719	−	0.486220i
$327$	−3.83686	+	6.64563i	−0.212179	+	0.367504i
$328$	1.70480	+	2.95279i	0.0941317	+	0.163041i
$329$	1.89323	+	0.138587i	0.104377	+	0.00764057i
$330$	−0.171924			−0.00946411
$331$	−11.0982			−0.610010			−0.305005	−	0.952351i	$-0.598658\pi$
$331$	−11.0982			−0.610010			−0.305005	+	0.952351i	$0.598658\pi$
$332$	4.57029	+	7.91597i	0.250827	+	0.434445i
$333$	0.181804	−	0.314894i	0.00996282	−	0.0172561i
$334$	8.57714			0.469320
$335$	−2.97079	−	5.14557i	−0.162312	−	0.281132i
$336$	1.15207	+	2.38175i	0.0628504	+	0.129935i
$337$	21.6470			1.17918			0.589592	−	0.807701i	$-0.299288\pi$
$337$	21.6470			1.17918			0.589592	+	0.807701i	$0.299288\pi$
$338$	11.9506	+	5.11704i	0.650025	+	0.278330i
$339$	−6.18222	+	10.7079i	−0.335772	+	0.581575i
$340$	−0.228165			−0.0123740
$341$	−0.255910	+	0.443249i	−0.0138583	+	0.0240033i
$342$	−0.447955	+	0.775880i	−0.0242226	+	0.0419548i
$343$	−18.0770	−	4.02745i	−0.976069	−	0.217462i
$344$	−2.06841	+	3.58258i	−0.111521	+	0.193160i
$345$	−0.0446174			−0.00240212
$346$	5.33942	−	9.24815i	0.287049	−	0.497183i
$347$	−14.9337	−	25.8660i	−0.801685	−	1.38856i	−0.918506	−	0.395407i	$-0.870604\pi$
$347$	−14.9337	−	25.8660i	−0.801685	−	1.38856i	0.116821	−	0.993153i	$-0.462730\pi$
$348$	2.99337	−	5.18466i	0.160461	−	0.277927i
$349$	−6.47690	−	11.2183i	−0.346700	−	0.600503i	0.638961	−	0.769239i	$-0.279365\pi$
$349$	−6.47690	−	11.2183i	−0.346700	−	0.600503i	−0.985661	+	0.168737i	$0.946031\pi$
$350$	9.24645	+	0.676853i	0.494243	+	0.0361793i
$351$	2.39335	−	2.69665i	0.127747	−	0.143936i
$352$	−0.0702857	−	0.121738i	−0.00374624	−	0.00648868i
$353$	6.15707			0.327708			0.163854	−	0.986485i	$-0.447607\pi$
$353$	6.15707			0.327708			0.163854	+	0.986485i	$0.447607\pi$
$354$	−6.99624			−0.371846
$355$	−12.9935			−0.689624
$356$	−6.35472			−0.336799
$357$	−0.492265	−	0.0360344i	−0.0260534	−	0.00190715i
$358$	6.48961	−	11.2403i	0.342986	−	0.594070i
$359$	12.4203	+	21.5125i	0.655516	+	1.13539i	0.981764	+	0.190103i	$0.0608821\pi$
$359$	12.4203	+	21.5125i	0.655516	+	1.13539i	−0.326248	+	0.945284i	$0.605785\pi$
$360$	0.611519	+	1.05918i	0.0322299	+	0.0558238i
$361$	−18.1973			−0.957755
$362$	−11.8663	+	20.5531i	−0.623680	+	1.08025i
$363$	−10.9802			−0.576313
$364$	−6.83617	+	6.65333i	−0.358313	+	0.348729i
$365$	−11.7632			−0.615712
$366$	−0.186556	+	0.323125i	−0.00975146	+	0.0168900i
$367$	36.0612			1.88238			0.941188	−	0.337882i	$-0.109711\pi$
$367$	36.0612			1.88238			0.941188	+	0.337882i	$0.109711\pi$
$368$	−0.0182404	−	0.0315933i	−0.000950847	−	0.00164692i
$369$	1.70480	+	2.95279i	0.0887482	+	0.153716i
$370$	−0.222353	+	0.385127i	−0.0115596	+	0.0200218i
$371$	−8.05423	−	16.6511i	−0.418155	−	0.864481i
$372$	3.64099			0.188777
$373$	−14.7418			−0.763304			−0.381652	−	0.924306i	$-0.624645\pi$
$373$	−14.7418			−0.763304			−0.381652	+	0.924306i	$0.624645\pi$
$374$	0.0262245			0.00135604
$375$	10.4009			0.537102
$376$	0.358745	+	0.621364i	0.0185009	+	0.0320444i
$377$	21.1454	+	4.33664i	1.08904	+	0.223348i
$378$	1.15207	+	2.38175i	0.0592560	+	0.122504i
$379$	5.33674	+	9.24351i	0.274130	+	0.474807i	0.969915	−	0.243443i	$-0.0782768\pi$
$379$	5.33674	+	9.24351i	0.274130	+	0.474807i	−0.695785	+	0.718250i	$0.744943\pi$
$380$	0.547865	−	0.948930i	0.0281049	−	0.0486791i
$381$	−5.45432	−	9.44716i	−0.279433	−	0.483993i
$382$	9.98892	−	17.3013i	0.511078	−	0.885213i
$383$	−20.4033			−1.04256			−0.521281	−	0.853385i	$-0.674545\pi$
$383$	−20.4033			−1.04256			−0.521281	+	0.853385i	$0.674545\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	0.453655	+	0.0332082i	0.0231204	+	0.00169244i
$386$	3.11194	−	5.39003i	0.158393	−	0.274346i
$387$	−2.06841	+	3.58258i	−0.105143	+	0.182113i
$388$	−6.48119			−0.329032
$389$	−15.8455	+	27.4453i	−0.803400	+	1.39153i	0.113966	+	0.993485i	$0.463644\pi$
$389$	−15.8455	+	27.4453i	−0.803400	+	1.39153i	−0.917366	+	0.398045i	$0.869689\pi$
$390$	−2.92715	+	3.29810i	−0.148222	+	0.167006i
$391$	0.00680573			0.000344181
$392$	−2.57990	−	6.50724i	−0.130305	−	0.328665i
$393$	−10.9715	−	19.0032i	−0.553438	−	0.958583i
$394$	−24.5006			−1.23432
$395$	3.60597	−	6.24573i	0.181436	−	0.314257i
$396$	−0.0702857	−	0.121738i	−0.00353199	−	0.00611759i
$397$	−2.61048			−0.131016			−0.0655080	−	0.997852i	$-0.520867\pi$
$397$	−2.61048			−0.131016			−0.0655080	+	0.997852i	$0.520867\pi$
$398$	−19.6151			−0.983215
$399$	1.33188	−	1.96078i	0.0666774	−	0.0981619i
$400$	1.75209	+	3.03471i	0.0876045	+	0.151735i
$401$	8.18479	−	14.1765i	0.408729	−	0.707939i	−0.586019	−	0.810297i	$-0.699306\pi$
$401$	8.18479	−	14.1765i	0.408729	−	0.707939i	0.994748	+	0.102358i	$0.0326389\pi$
$402$	2.42903	−	4.20720i	0.121149	−	0.209836i
$403$	4.14596	+	12.4559i	0.206525	+	0.620473i
$404$	1.50230	+	2.60206i	0.0747422	+	0.129457i
$405$	0.611519	+	1.05918i	0.0303866	+	0.0526311i
$406$	−8.90002	+	13.1025i	−0.441701	+	0.650268i
$407$	0.0255565	−	0.0442652i	0.00126679	−	0.00219414i
$408$	−0.0932782	−	0.161563i	−0.00461796	−	0.00799854i
$409$	−11.3653	−	19.6853i	−0.561980	−	0.973377i	−0.997324	−	0.0731132i	$-0.976707\pi$
$409$	−11.3653	−	19.6853i	−0.561980	−	0.973377i	0.435344	−	0.900264i	$-0.356627\pi$
$410$	−2.08503	−	3.61138i	−0.102972	−	0.178353i
$411$	−1.34605	−	2.33143i	−0.0663958	−	0.115001i
$412$	−4.12788	+	7.14970i	−0.203366	+	0.352240i
$413$	18.4609	+	1.35136i	0.908402	+	0.0664963i
$414$	−0.0182404	−	0.0315933i	−0.000896467	−	0.00155273i
$415$	−5.58963	−	9.68152i	−0.274384	−	0.475247i
$416$	−3.53204	−	0.724375i	−0.173172	−	0.0355154i
$417$	5.28925	−	9.16126i	0.259016	−	0.448629i
$418$	−0.0629697	+	0.109067i	−0.00307995	+	0.00533462i
$419$	−11.4491	−	19.8303i	−0.559323	−	0.968776i	−0.997553	−	0.0699131i	$-0.977728\pi$
$419$	−11.4491	−	19.8303i	−0.559323	−	0.968776i	0.438230	−	0.898863i	$-0.355606\pi$
$420$	−1.40902	−	2.91297i	−0.0687532	−	0.142138i
$421$	8.33173			0.406064			0.203032	−	0.979172i	$-0.434921\pi$
$421$	8.33173			0.406064			0.203032	+	0.979172i	$0.434921\pi$
$422$	5.99270			0.291720
$423$	0.358745	+	0.621364i	0.0174428	+	0.0302118i
$424$	3.49556	−	6.05448i	0.169759	−	0.294032i
$425$	−0.653727			−0.0317104
$426$	−5.31198	−	9.20062i	−0.257366	−	0.445772i
$427$	0.554678	−	0.816593i	0.0268428	−	0.0395177i
$428$	−4.47283			−0.216202
$429$	0.336436	−	0.379071i	0.0162433	−	0.0183017i
$430$	2.52974	−	4.38163i	0.121995	−	0.211301i
$431$	−27.5866			−1.32880			−0.664401	−	0.747376i	$-0.731313\pi$
$431$	−27.5866			−1.32880			−0.664401	+	0.747376i	$0.731313\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−15.7254	+	27.2372i	−0.755714	+	1.30893i	0.189305	+	0.981918i	$0.439376\pi$
$433$	−15.7254	+	27.2372i	−0.755714	+	1.30893i	−0.945019	+	0.327016i	$0.893957\pi$
$434$	−9.60745	−	0.703279i	−0.461172	−	0.0337585i
$435$	−3.66100	+	6.34104i	−0.175532	+	0.304029i
$436$	7.67371			0.367504
$437$	−0.0163418	+	0.0283048i	−0.000781732	+	0.00135400i
$438$	−4.80900	−	8.32943i	−0.229783	−	0.397996i
$439$	7.62301	−	13.2034i	0.363827	−	0.630166i	−0.624760	−	0.780816i	$-0.714803\pi$
$439$	7.62301	−	13.2034i	0.363827	−	0.630166i	0.988587	+	0.150650i	$0.0481367\pi$
$440$	0.0859621	+	0.148891i	0.00409808	+	0.00709808i
$441$	−2.57990	−	6.50724i	−0.122852	−	0.309868i
$442$	0.446494	−	0.503076i	0.0212375	−	0.0239289i
$443$	10.7666	+	18.6482i	0.511535	+	0.886005i	0.999911	+	0.0133713i	$0.00425634\pi$
$443$	10.7666	+	18.6482i	0.511535	+	0.886005i	−0.488375	+	0.872634i	$0.662410\pi$
$444$	−0.363609			−0.0172561
$445$	7.77206			0.368431
$446$	−27.6197			−1.30783
$447$	−11.9049			−0.563082
$448$	1.48662	−	2.18860i	0.0702364	−	0.103401i
$449$	2.76290	−	4.78549i	0.130389	−	0.225841i	−0.793437	−	0.608652i	$-0.791711\pi$
$449$	2.76290	−	4.78549i	0.130389	−	0.225841i	0.923827	+	0.382811i	$0.125044\pi$
$450$	1.75209	+	3.03471i	0.0825943	+	0.143058i
$451$	0.239646	+	0.415079i	0.0112845	+	0.0195453i
$452$	12.3644			0.581575
$453$	−3.66774	+	6.35272i	−0.172326	+	0.298477i
$454$	−1.79129			−0.0840694
$455$	8.36089	−	8.13727i	0.391965	−	0.381481i
$456$	0.895909			0.0419548
$457$	16.0187	−	27.7451i	0.749321	−	1.29786i	−0.198827	−	0.980035i	$-0.563713\pi$
$457$	16.0187	−	27.7451i	0.749321	−	1.29786i	0.948148	−	0.317828i	$-0.102953\pi$
$458$	−25.2285			−1.17885
$459$	−0.0932782	−	0.161563i	−0.00435385	−	0.00754109i
$460$	0.0223087	+	0.0386398i	0.00104015	+	0.00180159i
$461$	−6.48516	+	11.2326i	−0.302044	+	0.523156i	−0.976599	−	0.215069i	$-0.931002\pi$
$461$	−6.48516	+	11.2326i	−0.302044	+	0.523156i	0.674555	+	0.738225i	$0.264336\pi$
$462$	0.161948	+	0.334806i	0.00753450	+	0.0155766i
$463$	−11.6453			−0.541202			−0.270601	−	0.962692i	$-0.587222\pi$
$463$	−11.6453			−0.541202			−0.270601	+	0.962692i	$0.587222\pi$
$464$	−5.98674			−0.277927
$465$	−4.45307			−0.206506
$466$	−28.3704			−1.31423
$467$	2.99029	+	5.17934i	0.138374	+	0.239671i	0.926881	−	0.375354i	$-0.122479\pi$
$467$	2.99029	+	5.17934i	0.138374	+	0.239671i	−0.788507	+	0.615026i	$0.789146\pi$
$468$	−3.53204	−	0.724375i	−0.163268	−	0.0334842i
$469$	−7.22211	+	10.6323i	−0.333486	+	0.490955i
$470$	−0.438758	−	0.759952i	−0.0202384	−	0.0350539i
$471$	5.15138	−	8.92246i	0.237363	−	0.411125i
$472$	3.49812	+	6.05892i	0.161014	+	0.278884i
$473$	−0.290759	+	0.503609i	−0.0133691	+	0.0231560i
$474$	5.89675			0.270847
$475$	1.56971	−	2.71882i	0.0720234	−	0.124748i
$476$	0.214926	+	0.444331i	0.00985109	+	0.0203659i
$477$	3.49556	−	6.05448i	0.160050	−	0.277216i
$478$	14.4827	−	25.0848i	0.662424	−	1.14735i
$479$	6.66159			0.304376			0.152188	−	0.988352i	$-0.451368\pi$
$479$	6.66159			0.304376			0.152188	+	0.988352i	$0.451368\pi$
$480$	0.611519	−	1.05918i	0.0279119	−	0.0483448i
$481$	−0.414038	−	1.24391i	−0.0188785	−	0.0567175i
$482$	−13.1951			−0.601022
$483$	0.0420284	+	0.0868883i	0.00191236	+	0.00395355i
$484$	5.49012	+	9.50917i	0.249551	+	0.432235i
$485$	7.92673			0.359934
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	9.46808	+	16.3992i	0.429039	+	0.743118i	0.996788	−	0.0800838i	$-0.0255188\pi$
$487$	9.46808	+	16.3992i	0.429039	+	0.743118i	−0.567749	+	0.823202i	$0.692185\pi$
$488$	0.373113			0.0168900
$489$	−10.1370			−0.458413
$490$	3.15532	+	7.95859i	0.142543	+	0.359532i
$491$	−19.5234	−	33.8155i	−0.881079	−	1.52607i	−0.850143	−	0.526553i	$-0.823484\pi$
$491$	−19.5234	−	33.8155i	−0.881079	−	1.52607i	−0.0309367	−	0.999521i	$-0.509849\pi$
$492$	1.70480	−	2.95279i	0.0768582	−	0.133122i
$493$	0.558432	−	0.967232i	0.0251505	−	0.0435619i
$494$	1.02016	+	3.06492i	0.0458993	+	0.137897i
$495$	0.0859621	+	0.148891i	0.00386371	+	0.00669214i
$496$	−1.82050	−	3.15319i	−0.0817427	−	0.141582i
$497$	12.2395	+	25.3036i	0.549018	+	1.13502i
$498$	4.57029	−	7.91597i	0.204799	−	0.354723i
$499$	−16.6602	−	28.8563i	−0.745812	−	1.29178i	−0.949814	−	0.312814i	$-0.898728\pi$
$499$	−16.6602	−	28.8563i	−0.745812	−	1.29178i	0.204002	−	0.978970i	$-0.434605\pi$
$500$	−5.20046	−	9.00747i	−0.232572	−	0.402826i
$501$	−4.28857	−	7.42802i	−0.191599	−	0.331860i
$502$	4.73276	+	8.19739i	0.211234	+	0.365867i
$503$	5.86768	−	10.1631i	0.261627	−	0.453151i	−0.705048	−	0.709160i	$-0.749074\pi$
$503$	5.86768	−	10.1631i	0.261627	−	0.453151i	0.966674	+	0.256009i	$0.0824077\pi$
$504$	1.48662	−	2.18860i	0.0662195	−	0.0974878i
$505$	−1.83737	−	3.18242i	−0.0817618	−	0.141616i
$506$	−0.00256408	−	0.00444112i	−0.000113987	−	0.000197432i
$507$	−1.54380	−	12.9080i	−0.0685624	−	0.573265i
$508$	−5.45432	+	9.44716i	−0.241996	+	0.419150i
$509$	17.3265	−	30.0103i	0.767982	−	1.33018i	−0.170674	−	0.985328i	$-0.554594\pi$
$509$	17.3265	−	30.0103i	0.767982	−	1.33018i	0.938656	−	0.344856i	$-0.112072\pi$
$510$	0.114083	+	0.197597i	0.00505167	+	0.00874974i
$511$	11.0806	+	22.9077i	0.490176	+	1.01338i
$512$	1.00000			0.0441942
$513$	0.895909			0.0395554
$514$	5.11789	+	8.86444i	0.225740	+	0.390994i
$515$	5.04855	−	8.74434i	0.222466	−	0.385322i
$516$	4.13681			0.182113
$517$	0.0504293	+	0.0873461i	0.00221788	+	0.00384148i
$518$	0.959451	+	0.0702331i	0.0421559	+	0.00308587i
$519$	−10.6788			−0.468749
$520$	4.31981	+	0.885937i	0.189436	+	0.0388509i
$521$	2.62165	−	4.54083i	0.114856	−	0.198937i	−0.802866	−	0.596160i	$-0.796693\pi$
$521$	2.62165	−	4.54083i	0.114856	−	0.198937i	0.917722	+	0.397222i	$0.130026\pi$
$522$	−5.98674			−0.262032
$523$	7.99001	−	13.8391i	0.349379	−	0.605142i	−0.636761	−	0.771062i	$-0.719726\pi$
$523$	7.99001	−	13.8391i	0.349379	−	0.605142i	0.986139	+	0.165920i	$0.0530594\pi$
$524$	−10.9715	+	19.0032i	−0.479291	+	0.830157i
$525$	−4.03705	−	8.34609i	−0.176191	−	0.364253i
$526$	2.42308	−	4.19690i	0.105651	−	0.182994i
$527$	0.679250			0.0295886
$528$	−0.0702857	+	0.121738i	−0.00305879	+	0.00529799i
$529$	11.4993	+	19.9174i	0.499971	+	0.865975i
$530$	−4.27519	+	7.40485i	−0.185703	+	0.321646i
$531$	3.49812	+	6.05892i	0.151805	+	0.262935i
$532$	−2.36403	−	0.173050i	−0.102494	−	0.00750267i
$533$	12.0428	+	2.46982i	0.521632	+	0.106980i
$534$	3.17736	+	5.50335i	0.137498	+	0.238153i
$535$	5.47043			0.236507
$536$	−4.85806			−0.209836
$537$	−12.9792			−0.560094
$538$	−0.897277			−0.0386843
$539$	−0.362661	−	0.914732i	−0.0156209	−	0.0394003i
$540$	0.611519	−	1.05918i	0.0263156	−	0.0455799i
$541$	−0.886405	−	1.53530i	−0.0381095	−	0.0660077i	0.846342	−	0.532641i	$-0.178800\pi$
$541$	−0.886405	−	1.53530i	−0.0381095	−	0.0660077i	−0.884451	+	0.466633i	$0.845467\pi$
$542$	−6.93756	−	12.0162i	−0.297994	−	0.516140i
$543$	23.7327			1.01847
$544$	−0.0932782	+	0.161563i	−0.00399927	+	0.00692694i
$545$	−9.38523			−0.402019
$546$	9.18004	+	2.59364i	0.392869	+	0.110997i
$547$	9.88287			0.422561			0.211280	−	0.977425i	$-0.432237\pi$
$547$	9.88287			0.422561			0.211280	+	0.977425i	$0.432237\pi$
$548$	−1.34605	+	2.33143i	−0.0575005	+	0.0995938i
$549$	0.373113			0.0159241
$550$	0.246294	+	0.426594i	0.0105020	+	0.0181900i
$551$	2.68179	+	4.64499i	0.114248	+	0.197883i
$552$	−0.0182404	+	0.0315933i	−0.000776364	+	0.00134470i
$553$	−15.5597	−	1.13899i	−0.661666	−	0.0484348i
$554$	−20.4739			−0.869852
$555$	0.444707			0.0188768
$556$	−10.5785			−0.448629
$557$	20.1731			0.854760			0.427380	−	0.904072i	$-0.359437\pi$
$557$	20.1731			0.854760			0.427380	+	0.904072i	$0.359437\pi$
$558$	−1.82050	−	3.15319i	−0.0770677	−	0.133485i
$559$	4.71055	+	14.1521i	0.199235	+	0.598571i
$560$	−1.81820	+	2.67673i	−0.0768328	+	0.113113i
$561$	−0.0131122	−	0.0227111i	−0.000553600	−	0.000958863i
$562$	−2.55910	+	4.43249i	−0.107949	+	0.186973i
$563$	0.0531484	+	0.0920558i	0.00223994	+	0.00387969i	0.867143	−	0.498059i	$-0.165954\pi$
$563$	0.0531484	+	0.0920558i	0.00223994	+	0.00387969i	−0.864903	+	0.501939i	$0.832620\pi$
$564$	0.358745	−	0.621364i	0.0151059	−	0.0261642i
$565$	−15.1222			−0.636195
$566$	−4.54066	+	7.86466i	−0.190858	+	0.330576i
$567$	1.48662	−	2.18860i	0.0624323	−	0.0919124i
$568$	−5.31198	+	9.20062i	−0.222886	+	0.386050i
$569$	3.83091	−	6.63533i	0.160600	−	0.278167i	−0.774484	−	0.632593i	$-0.781990\pi$
$569$	3.83091	−	6.63533i	0.160600	−	0.278167i	0.935084	+	0.354426i	$0.115324\pi$
$570$	−1.09573			−0.0458951
$571$	−1.44075	+	2.49545i	−0.0602935	+	0.104431i	−0.894597	−	0.446875i	$-0.852537\pi$
$571$	−1.44075	+	2.49545i	−0.0602935	+	0.104431i	0.834303	+	0.551306i	$0.185870\pi$
$572$	−0.496504	−	0.101826i	−0.0207599	−	0.00425758i
$573$	−19.9778			−0.834587
$574$	−5.06878	+	7.46222i	−0.211567	+	0.311467i
$575$	0.0639177	+	0.110709i	0.00266555	+	0.00461687i
$576$	1.00000			0.0416667
$577$	17.3055	−	29.9740i	0.720438	−	1.24783i	−0.240387	−	0.970677i	$-0.577274\pi$
$577$	17.3055	−	29.9740i	0.720438	−	1.24783i	0.960825	−	0.277157i	$-0.0893923\pi$
$578$	8.48260	+	14.6923i	0.352830	+	0.611119i
$579$	−6.22388			−0.258655
$580$	7.32200			0.304029
$581$	−13.5886	+	20.0050i	−0.563750	+	0.829948i
$582$	3.24059	+	5.61287i	0.134327	+	0.232661i
$583$	0.491375	−	0.851087i	0.0203507	−	0.0352484i
$584$	−4.80900	+	8.32943i	−0.198998	+	0.344674i
$585$	4.31981	+	0.885937i	0.178602	+	0.0366290i
$586$	3.13195	+	5.42469i	0.129380	+	0.224092i
$587$	−5.21346	−	9.02999i	−0.215183	−	0.372707i	0.738146	−	0.674641i	$-0.235701\pi$
$587$	−5.21346	−	9.02999i	−0.215183	−	0.372707i	−0.953329	+	0.301933i	$0.902368\pi$
$588$	−4.34548	+	5.48788i	−0.179205	+	0.226316i
$589$	−1.63100	+	2.82497i	−0.0672041	+	0.116401i
$590$	−4.27833	−	7.41029i	−0.176136	−	0.305077i
$591$	12.2503	+	21.2182i	0.503911	+	0.872799i
$592$	0.181804	+	0.314894i	0.00747211	+	0.0129421i
$593$	10.9551	+	18.9748i	0.449873	+	0.779203i	0.998377	−	0.0569451i	$-0.0181360\pi$
$593$	10.9551	+	18.9748i	0.449873	+	0.779203i	−0.548505	+	0.836148i	$0.684803\pi$
$594$	−0.0702857	+	0.121738i	−0.00288386	+	0.00499499i
$595$	−0.262862	−	0.543433i	−0.0107763	−	0.0222786i
$596$	5.95244	+	10.3099i	0.243822	+	0.422311i
$597$	9.80754	+	16.9872i	0.401396	+	0.695238i
$598$	−0.128852	−	0.0264258i	−0.00526913	−	0.00108063i
$599$	−7.67924	+	13.3008i	−0.313765	+	0.543457i	−0.979174	−	0.203022i	$-0.934924\pi$
$599$	−7.67924	+	13.3008i	−0.313765	+	0.543457i	0.665409	+	0.746479i	$0.268257\pi$
$600$	1.75209	−	3.03471i	0.0715288	−	0.123891i
$601$	1.63801	+	2.83711i	0.0668157	+	0.115728i	0.897498	−	0.441019i	$-0.145383\pi$
$601$	1.63801	+	2.83711i	0.0668157	+	0.115728i	−0.830682	+	0.556747i	$0.812049\pi$
$602$	−10.9158	−	0.799049i	−0.444893	−	0.0325668i
$603$	−4.85806			−0.197836
$604$	7.33549			0.298477
$605$	−6.71462	−	11.6301i	−0.272988	−	0.472829i
$606$	1.50230	−	2.60206i	0.0610268	−	0.105701i
$607$	33.1535			1.34566			0.672830	−	0.739797i	$-0.265078\pi$
$607$	33.1535			1.34566			0.672830	+	0.739797i	$0.265078\pi$
$608$	−0.447955	−	0.775880i	−0.0181670	−	0.0314661i
$609$	15.7971	+	1.15637i	0.640133	+	0.0468586i
$610$	−0.456331			−0.0184763
$611$	2.53420	+	0.519731i	0.102523	+	0.0210261i
$612$	−0.0932782	+	0.161563i	−0.00377055	+	0.00653078i
$613$	−34.3585			−1.38773			−0.693863	−	0.720107i	$-0.744093\pi$
$613$	−34.3585			−1.38773			−0.693863	+	0.720107i	$0.744093\pi$
$614$	−15.0403	+	26.0506i	−0.606977	+	1.05132i
$615$	−2.08503	+	3.61138i	−0.0840765	+	0.145625i
$616$	0.208977	−	0.307654i	0.00841992	−	0.0123957i
$617$	−10.2155	+	17.6938i	−0.411261	+	0.712325i	−0.995028	−	0.0995961i	$-0.968245\pi$
$617$	−10.2155	+	17.6938i	−0.411261	+	0.712325i	0.583767	+	0.811921i	$0.301578\pi$
$618$	8.25576			0.332095
$619$	−6.14114	+	10.6368i	−0.246833	+	0.427528i	−0.962645	−	0.270765i	$-0.912723\pi$
$619$	−6.14114	+	10.6368i	−0.246833	+	0.427528i	0.715812	+	0.698293i	$0.246057\pi$
$620$	2.22653	+	3.85647i	0.0894197	+	0.154880i
$621$	−0.0182404	+	0.0315933i	−0.000731963	+	0.00126780i
$622$	−13.8292	−	23.9528i	−0.554499	−	0.960420i
$623$	−7.32107	−	15.1354i	−0.293312	−	0.606386i
$624$	1.13869	+	3.42102i	0.0455841	+	0.136950i
$625$	−2.40009	−	4.15708i	−0.0960036	−	0.166283i
$626$	6.86004			0.274182
$627$	0.125939			0.00502953
$628$	−10.3028			−0.411125
$629$	−0.0678335			−0.00270470
$630$	−1.81820	+	2.67673i	−0.0724386	+	0.106644i
$631$	−0.272895	+	0.472667i	−0.0108638	+	0.0188166i	−0.871406	−	0.490562i	$-0.836791\pi$
$631$	−0.272895	+	0.472667i	−0.0108638	+	0.0188166i	0.860542	+	0.509379i	$0.170125\pi$
$632$	−2.94837	−	5.10673i	−0.117280	−	0.203135i
$633$	−2.99635	−	5.18983i	−0.119094	−	0.206277i
$634$	−6.74291			−0.267795
$635$	6.67084	−	11.5542i	0.264724	−	0.458516i
$636$	−6.99111			−0.277216
$637$	−23.7223	−	8.61698i	−0.939912	−	0.341417i
$638$	−0.841564			−0.0333178
$639$	−5.31198	+	9.20062i	−0.210139	+	0.363971i
$640$	−1.22304			−0.0483448
$641$	18.0298	+	31.2286i	0.712136	+	1.23346i	0.964054	+	0.265707i	$0.0856055\pi$
$641$	18.0298	+	31.2286i	0.712136	+	1.23346i	−0.251918	+	0.967749i	$0.581061\pi$
$642$	2.23641	+	3.87358i	0.0882642	+	0.152878i
$643$	13.7343	−	23.7885i	0.541627	−	0.938125i	−0.457184	−	0.889372i	$-0.651142\pi$
$643$	13.7343	−	23.7885i	0.541627	−	0.938125i	0.998811	−	0.0487529i	$-0.0155247\pi$
$644$	0.0542333	−	0.0798418i	0.00213709	−	0.00314621i
$645$	−5.05947			−0.199217
$646$	0.167138			0.00657594
$647$	6.14160			0.241451			0.120726	−	0.992686i	$-0.461478\pi$
$647$	6.14160			0.241451			0.120726	+	0.992686i	$0.461478\pi$
$648$	1.00000			0.0392837
$649$	0.491736	+	0.851712i	0.0193023	+	0.0334326i
$650$	12.3769	+	2.53834i	0.485462	+	0.0995619i
$651$	4.19467	+	8.67194i	0.164402	+	0.339880i
$652$	5.06852	+	8.77893i	0.198498	+	0.343809i
$653$	12.1803	−	21.0969i	0.476652	−	0.825585i	−0.522990	−	0.852339i	$-0.675184\pi$
$653$	12.1803	−	21.0969i	0.476652	−	0.825585i	0.999642	+	0.0267533i	$0.00851686\pi$
$654$	−3.83686	−	6.64563i	−0.150033	−	0.259865i
$655$	13.4185	−	23.2416i	0.524305	−	0.908123i
$656$	−3.40959			−0.133122
$657$	−4.80900	+	8.32943i	−0.187617	+	0.324962i
$658$	−1.06664	+	1.57029i	−0.0415818	+	0.0612165i
$659$	5.44539	−	9.43169i	0.212122	−	0.367407i	−0.740256	−	0.672325i	$-0.765296\pi$
$659$	5.44539	−	9.43169i	0.212122	−	0.367407i	0.952379	+	0.304918i	$0.0986291\pi$
$660$	0.0859621	−	0.148891i	0.00334607	−	0.00579556i
$661$	−37.2725			−1.44973			−0.724866	−	0.688889i	$-0.758099\pi$
$661$	−37.2725			−1.44973			−0.724866	+	0.688889i	$0.758099\pi$
$662$	5.54908	−	9.61129i	0.215671	−	0.373553i
$663$	−0.658924	−	0.135137i	−0.0255905	−	0.00524828i
$664$	−9.14057			−0.354723
$665$	2.89129	+	0.211647i	0.112120	+	0.00820731i
$666$	0.181804	+	0.314894i	0.00704477	+	0.0122019i
$667$	−0.218401			−0.00845652
$668$	−4.28857	+	7.42802i	−0.165930	+	0.287399i
$669$	13.8098	+	23.9193i	0.533919	+	0.924775i
$670$	5.94159			0.229544
$671$	0.0524490			0.00202477
$672$	−2.63869	−	0.193156i	−0.101790	−	0.00745115i
$673$	−21.9417	−	38.0042i	−0.845792	−	1.46495i	−0.884932	−	0.465721i	$-0.845795\pi$
$673$	−21.9417	−	38.0042i	−0.845792	−	1.46495i	0.0391397	−	0.999234i	$-0.487538\pi$
$674$	−10.8235	+	18.7468i	−0.416905	+	0.722100i
$675$	1.75209	−	3.03471i	0.0674380	−	0.116806i
$676$	−10.4068	+	7.79097i	−0.400260	+	0.299653i
$677$	−20.6518	−	35.7700i	−0.793713	−	1.37475i	−0.923653	−	0.383230i	$-0.874812\pi$
$677$	−20.6518	−	35.7700i	−0.793713	−	1.37475i	0.129940	−	0.991522i	$-0.458522\pi$
$678$	−6.18222	−	10.7079i	−0.237427	−	0.411235i
$679$	−7.46677	−	15.4366i	−0.286548	−	0.592402i
$680$	0.114083	−	0.197597i	0.00437487	−	0.00757750i
$681$	0.895645	+	1.55130i	0.0343212	+	0.0594460i
$682$	−0.255910	−	0.443249i	−0.00979929	−	0.0169729i
$683$	−13.7908	−	23.8864i	−0.527690	−	0.913987i	−0.999479	−	0.0322749i	$-0.989725\pi$
$683$	−13.7908	−	23.8864i	−0.527690	−	0.913987i	0.471789	−	0.881712i	$-0.343609\pi$
$684$	−0.447955	−	0.775880i	−0.0171280	−	0.0296665i
$685$	1.64627	−	2.85143i	0.0629008	−	0.108947i
$686$	12.5264	−	13.6415i	0.478260	−	0.520833i
$687$	12.6142	+	21.8485i	0.481263	+	0.833572i
$688$	−2.06841	−	3.58258i	−0.0788572	−	0.136585i
$689$	−7.96072	−	23.9167i	−0.303279	−	0.911155i
$690$	0.0223087	−	0.0386398i	0.000849278	−	0.00147099i
$691$	−14.6997	+	25.4606i	−0.559202	+	0.968566i	0.438362	+	0.898799i	$0.355559\pi$
$691$	−14.6997	+	25.4606i	−0.559202	+	0.968566i	−0.997563	+	0.0697671i	$0.977774\pi$
$692$	5.33942	+	9.24815i	0.202974	+	0.351562i
$693$	0.208977	−	0.307654i	0.00793837	−	0.0116868i
$694$	29.8675			1.13375
$695$	12.9379			0.490763
$696$	2.99337	+	5.18466i	0.113463	+	0.196524i
$697$	0.318041	−	0.550863i	0.0120466	−	0.0208654i
$698$	12.9538			0.490308
$699$	14.1852	+	24.5695i	0.536534	+	0.929304i
$700$	−5.20940	+	7.66923i	−0.196897	+	0.289870i
$701$	19.0498			0.719500			0.359750	−	0.933049i	$-0.382862\pi$
$701$	19.0498			0.719500			0.359750	+	0.933049i	$0.382862\pi$
$702$	1.13869	+	3.42102i	0.0429771	+	0.129118i
$703$	0.162880	−	0.282117i	0.00614314	−	0.0106402i
$704$	0.140571			0.00529799
$705$	−0.438758	+	0.759952i	−0.0165246	+	0.0286214i
$706$	−3.07853	+	5.33218i	−0.115862	+	0.200679i
$707$	−4.46671	+	6.57585i	−0.167988	+	0.247310i
$708$	3.49812	−	6.05892i	0.131467	−	0.227708i
$709$	17.9056			0.672460			0.336230	−	0.941780i	$-0.390848\pi$
$709$	17.9056			0.672460			0.336230	+	0.941780i	$0.390848\pi$
$710$	6.49675	−	11.2527i	0.243819	−	0.422306i
$711$	−2.94837	−	5.10673i	−0.110573	−	0.191517i
$712$	3.17736	−	5.50335i	0.119077	−	0.206247i
$713$	−0.0664132	−	0.115031i	−0.00248719	−	0.00430794i
$714$	0.277339	−	0.408296i	0.0103792	−	0.0152801i
$715$	0.607242	+	0.124538i	0.0227096	+	0.00465744i
$716$	6.48961	+	11.2403i	0.242528	+	0.420071i
$717$	−28.9654			−1.08173
$718$	−24.8405			−0.927039
$719$	34.3166			1.27979			0.639897	−	0.768461i	$-0.278977\pi$
$719$	34.3166			1.27979			0.639897	+	0.768461i	$0.278977\pi$
$720$	−1.22304			−0.0455799
$721$	−21.7844	−	1.59465i	−0.811293	−	0.0593878i
$722$	9.09867	−	15.7594i	0.338618	−	0.586503i
$723$	6.59757	+	11.4273i	0.245366	+	0.424987i
$724$	−11.8663	−	20.5531i	−0.441009	−	0.763849i
$725$	20.9786			0.779126
$726$	5.49012	−	9.50917i	0.203757	−	0.352918i
$727$	20.6482			0.765800			0.382900	−	0.923790i	$-0.374925\pi$
$727$	20.6482			0.765800			0.382900	+	0.923790i	$0.374925\pi$
$728$	−2.34386	−	9.24696i	−0.0868694	−	0.342715i
$729$	1.00000			0.0370370
$730$	5.88158	−	10.1872i	0.217687	−	0.377045i
$731$	0.771748			0.0285441
$732$	−0.186556	−	0.323125i	−0.00689532	−	0.0119430i
$733$	14.5834	+	25.2592i	0.538650	+	0.932969i	0.998977	+	0.0452199i	$0.0143988\pi$
$733$	14.5834	+	25.2592i	0.538650	+	0.932969i	−0.460327	+	0.887749i	$0.652268\pi$
$734$	−18.0306	+	31.2299i	−0.665521	+	1.15272i
$735$	5.31468	−	6.71188i	0.196035	−	0.247571i
$736$	0.0364808			0.00134470
$737$	−0.682905			−0.0251551
$738$	−3.40959			−0.125509
$739$	−42.2160			−1.55294			−0.776471	−	0.630153i	$-0.782992\pi$
$739$	−42.2160			−1.55294			−0.776471	+	0.630153i	$0.782992\pi$
$740$	−0.222353	−	0.385127i	−0.00817387	−	0.0141576i
$741$	2.14422	−	2.41595i	0.0787699	−	0.0887521i
$742$	18.4474	+	1.35037i	0.677225	+	0.0495738i
$743$	8.87311	+	15.3687i	0.325523	+	0.563822i	0.981618	−	0.190856i	$-0.0611263\pi$
$743$	8.87311	+	15.3687i	0.325523	+	0.563822i	−0.656095	+	0.754678i	$0.727793\pi$
$744$	−1.82050	+	3.15319i	−0.0667426	+	0.115602i
$745$	−7.28006	−	12.6094i	−0.266721	−	0.461974i
$746$	7.37092	−	12.7668i	0.269869	−	0.467426i
$747$	−9.14057			−0.334436
$748$	−0.0131122	+	0.0227111i	−0.000479431	+	0.000830399i
$749$	−5.15300	−	10.6532i	−0.188287	−	0.389258i
$750$	−5.20046	+	9.00747i	−0.189894	+	0.328906i
$751$	−15.6637	+	27.1303i	−0.571576	+	0.989998i	0.424829	+	0.905274i	$0.360334\pi$
$751$	−15.6637	+	27.1303i	−0.571576	+	0.989998i	−0.996404	+	0.0847243i	$0.972999\pi$
$752$	−0.717490			−0.0261642
$753$	4.73276	−	8.19739i	0.172472	−	0.298729i
$754$	−14.3283	+	16.1441i	−0.521807	+	0.587934i
$755$	−8.97157			−0.326509
$756$	−2.63869	−	0.193156i	−0.0959683	−	0.00702501i
$757$	12.9370	+	22.4076i	0.470204	+	0.814417i	0.999419	−	0.0340705i	$-0.0108471\pi$
$757$	12.9370	+	22.4076i	0.470204	+	0.814417i	−0.529216	+	0.848487i	$0.677514\pi$
$758$	−10.6735			−0.387679
$759$	−0.00256408	+	0.00444112i	−9.30703e−5	+	0.000161202i
$760$	0.547865	+	0.948930i	0.0198732	+	0.0344213i
$761$	−0.955383			−0.0346326			−0.0173163	−	0.999850i	$-0.505512\pi$
$761$	−0.955383			−0.0346326			−0.0173163	+	0.999850i	$0.505512\pi$
$762$	10.9086			0.395179
$763$	8.84063	+	18.2769i	0.320052	+	0.661667i
$764$	9.98892	+	17.3013i	0.361387	+	0.625940i
$765$	0.114083	−	0.197597i	0.00412467	−	0.00714413i
$766$	10.2017	−	17.6698i	0.368601	−	0.638436i
$767$	24.7110	+	5.06790i	0.892261	+	0.182991i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	0.0702857	+	0.121738i	0.00253457	+	0.00439000i	0.867290	−	0.497803i	$-0.165860\pi$
$769$	0.0702857	+	0.121738i	0.00253457	+	0.00439000i	−0.864755	+	0.502193i	$0.832527\pi$
$770$	−0.255586	+	0.376272i	−0.00921070	+	0.0135599i
$771$	5.11789	−	8.86444i	0.184316	−	0.319245i
$772$	3.11194	+	5.39003i	0.112001	+	0.193992i
$773$	−8.17360	−	14.1571i	−0.293984	−	0.509195i	0.680764	−	0.732503i	$-0.261648\pi$
$773$	−8.17360	−	14.1571i	−0.293984	−	0.509195i	−0.974748	+	0.223308i	$0.928315\pi$
$774$	−2.06841	−	3.58258i	−0.0743473	−	0.128773i
$775$	6.37934	+	11.0493i	0.229153	+	0.396904i
$776$	3.24059	−	5.61287i	0.116331	−	0.201490i
$777$	−0.418902	−	0.866025i	−0.0150280	−	0.0310685i
$778$	−15.8455	−	27.4453i	−0.568090	−	0.983960i
$779$	1.52734	+	2.64544i	0.0547228	+	0.0947826i
$780$	−1.39266	−	4.18404i	−0.0498653	−	0.149812i
$781$	−0.746713	+	1.29335i	−0.0267195	+	0.0462795i
$782$	−0.00340286	+	0.00589393i	−0.000121686	+	0.000210767i
$783$	2.99337	+	5.18466i	0.106974	+	0.185285i
$784$	6.92538	+	1.01936i	0.247335	+	0.0364056i
$785$	12.6007			0.449737
$786$	21.9430			0.782679
$787$	−17.8553	−	30.9262i	−0.636471	−	1.10240i	−0.986201	−	0.165550i	$-0.947060\pi$
$787$	−17.8553	−	30.9262i	−0.636471	−	1.10240i	0.349730	−	0.936850i	$-0.386273\pi$
$788$	12.2503	−	21.2182i	0.436400	−	0.755866i
$789$	−4.84616			−0.172528
$790$	3.60597	+	6.24573i	0.128295	+	0.222213i
$791$	14.2447	+	29.4490i	0.506483	+	1.04709i
$792$	0.140571			0.00499499
$793$	0.892987	−	1.00615i	0.0317109	−	0.0357295i
$794$	1.30524	−	2.26074i	0.0463212	−	0.0802306i
$795$	8.55039			0.303251
$796$	9.80754	−	16.9872i	0.347619	−	0.602094i
$797$	2.01756	−	3.49451i	0.0714655	−	0.123782i	−0.828078	−	0.560612i	$-0.810566\pi$
$797$	2.01756	−	3.49451i	0.0714655	−	0.123782i	0.899544	+	0.436831i	$0.143899\pi$
$798$	1.03215	+	2.13383i	0.0365377	+	0.0755369i
$799$	0.0669261	−	0.115919i	0.00236768	−	0.00410093i
$800$	−3.50418			−0.123891
$801$	3.17736	−	5.50335i	0.112266	−	0.194451i
$802$	8.18479	+	14.1765i	0.289015	+	0.500588i
$803$	−0.676008	+	1.17088i	−0.0238558	+	0.0413195i
$804$	2.42903	+	4.20720i	0.0856653	+	0.148377i
$805$	−0.0663293	+	0.0976495i	−0.00233780	+	0.00344169i
$806$	−12.8601	−	2.63744i	−0.452978	−	0.0928999i
$807$	0.448638	+	0.777064i	0.0157928	+	0.0273540i
$808$	−3.00460			−0.105701
$809$	−27.9567			−0.982904			−0.491452	−	0.870905i	$-0.663534\pi$
$809$	−27.9567			−0.982904			−0.491452	+	0.870905i	$0.663534\pi$
$810$	−1.22304			−0.0429731
$811$	49.6578			1.74372			0.871861	−	0.489754i	$-0.162913\pi$
$811$	49.6578			1.74372			0.871861	+	0.489754i	$0.162913\pi$
$812$	−6.89712	−	14.2589i	−0.242042	−	0.500390i
$813$	−6.93756	+	12.0162i	−0.243311	+	0.421427i
$814$	0.0255565	+	0.0442652i	0.000895755	+	0.00155149i
$815$	−6.19898	−	10.7370i	−0.217141	−	0.376099i
$816$	0.186556			0.00653078
$817$	−1.85310	+	3.20967i	−0.0648319	+	0.112292i
$818$	22.7307			0.794759
$819$	−2.34386	−	9.24696i	−0.0819012	−	0.323115i
$820$	4.17006			0.145625
$821$	20.3635	−	35.2705i	0.710690	−	1.23095i	−0.253909	−	0.967228i	$-0.581716\pi$
$821$	20.3635	−	35.2705i	0.710690	−	1.23095i	0.964599	−	0.263722i	$-0.0849502\pi$
$822$	2.69210			0.0938979
$823$	26.8315	+	46.4735i	0.935288	+	1.61997i	0.774120	+	0.633038i	$0.218192\pi$
$823$	26.8315	+	46.4735i	0.935288	+	1.61997i	0.161167	+	0.986927i	$0.448474\pi$
$824$	−4.12788	−	7.14970i	−0.143801	−	0.249071i
$825$	0.246294	−	0.426594i	0.00857485	−	0.0148521i
$826$	−10.4008	+	15.3119i	−0.361889	+	0.532770i
$827$	55.5393			1.93129			0.965646	−	0.259862i	$-0.0836769\pi$
$827$	55.5393			1.93129			0.965646	+	0.259862i	$0.0836769\pi$
$828$	0.0364808			0.00126780
$829$	−33.2943			−1.15636			−0.578180	−	0.815909i	$-0.696237\pi$
$829$	−33.2943			−1.15636			−0.578180	+	0.815909i	$0.696237\pi$
$830$	11.1793			0.388038
$831$	10.2369	+	17.7309i	0.355116	+	0.615078i
$832$	2.39335	−	2.69665i	0.0829743	−	0.0934894i
$833$	−0.810677	+	1.02380i	−0.0280883	+	0.0354725i
$834$	5.28925	+	9.16126i	0.183152	+	0.317228i
$835$	5.24508	−	9.08475i	0.181514	−	0.314391i
$836$	−0.0629697	−	0.109067i	−0.00217785	−	0.00377215i
$837$	−1.82050	+	3.15319i	−0.0629255	+	0.108990i
$838$	22.8981			0.791002
$839$	2.98552	−	5.17107i	0.103072	−	0.178525i	−0.809877	−	0.586600i	$-0.800466\pi$
$839$	2.98552	−	5.17107i	0.103072	−	0.178525i	0.912949	+	0.408074i	$0.133800\pi$
$840$	3.22722	+	0.236237i	0.111350	+	0.00815094i
$841$	−3.42050	+	5.92448i	−0.117948	+	0.204292i
$842$	−4.16586	+	7.21549i	−0.143565	+	0.248662i
$843$	5.11819			0.176280
$844$	−2.99635	+	5.18983i	−0.103139	+	0.178641i
$845$	12.7279	−	9.52865i	0.437852	−	0.327795i
$846$	−0.717490			−0.0246678
$847$	−16.3235	+	24.0313i	−0.560881	+	0.825725i
$848$	3.49556	+	6.05448i	0.120038	+	0.207912i
$849$	9.08132			0.311670
$850$	0.326863	−	0.566144i	0.0112113	−	0.0194186i
$851$	0.00663237	+	0.0114876i	0.000227355	+	0.000393790i
$852$	10.6240			0.363971
$853$	−24.0993			−0.825143			−0.412572	−	0.910925i	$-0.635369\pi$
$853$	−24.0993			−0.825143			−0.412572	+	0.910925i	$0.635369\pi$
$854$	0.429851	+	0.888662i	0.0147092	+	0.0304094i
$855$	0.547865	+	0.948930i	0.0187366	+	0.0324527i
$856$	2.23641	−	3.87358i	0.0764390	−	0.132396i
$857$	0.639263	−	1.10724i	0.0218368	−	0.0378225i	−0.854900	−	0.518792i	$-0.826382\pi$
$857$	0.639263	−	1.10724i	0.0218368	−	0.0378225i	0.876737	+	0.480970i	$0.159715\pi$
$858$	0.160068	+	0.480898i	0.00546461	+	0.0164176i
$859$	−3.92591	−	6.79988i	−0.133950	−	0.232009i	0.791246	−	0.611498i	$-0.209433\pi$
$859$	−3.92591	−	6.79988i	−0.133950	−	0.232009i	−0.925196	+	0.379490i	$0.876100\pi$
$860$	2.52974	+	4.38163i	0.0862633	+	0.149412i
$861$	8.99686	+	0.658583i	0.306612	+	0.0224444i
$862$	13.7933	−	23.8907i	0.469802	−	0.813722i
$863$	19.2024	+	33.2595i	0.653656	+	1.13217i	0.982229	+	0.187687i	$0.0600990\pi$
$863$	19.2024	+	33.2595i	0.653656	+	1.13217i	−0.328573	+	0.944479i	$0.606568\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−6.53031	−	11.3108i	−0.222037	−	0.384580i
$866$	−15.7254	−	27.2372i	−0.534370	−	0.925556i
$867$	8.48260	−	14.6923i	0.288084	−	0.498976i
$868$	5.41278	−	7.96866i	0.183722	−	0.270474i
$869$	−0.414457	−	0.717861i	−0.0140595	−	0.0243518i
$870$	−3.66100	−	6.34104i	−0.124120	−	0.214981i
$871$	−11.6270	+	13.1005i	−0.393966	+	0.443892i
$872$	−3.83686	+	6.64563i	−0.129932	+	0.225049i
$873$	3.24059	−	5.61287i	0.109677	−	0.189967i
$874$	−0.0163418	−	0.0283048i	−0.000552768	−	0.000957423i
$875$	15.4623	−	22.7634i	0.522720	−	0.769544i
$876$	9.61800			0.324962
$877$	19.1059			0.645161			0.322580	−	0.946542i	$-0.395450\pi$
$877$	19.1059			0.645161			0.322580	+	0.946542i	$0.395450\pi$
$878$	7.62301	+	13.2034i	0.257264	+	0.445595i
$879$	3.13195	−	5.42469i	0.105638	−	0.182970i
$880$	−0.171924			−0.00579556
$881$	13.6438	+	23.6317i	0.459671	+	0.796173i	0.998943	−	0.0459583i	$-0.0146342\pi$
$881$	13.6438	+	23.6317i	0.459671	+	0.796173i	−0.539273	+	0.842131i	$0.681301\pi$
$882$	6.92538	+	1.01936i	0.233190	+	0.0343235i
$883$	35.8526			1.20654			0.603268	−	0.797538i	$-0.293865\pi$
$883$	35.8526			1.20654			0.603268	+	0.797538i	$0.293865\pi$
$884$	0.212430	+	0.638213i	0.00714480	+	0.0214654i
$885$	−4.27833	+	7.41029i	−0.143814	+	0.249094i
$886$	−21.5331			−0.723420
$887$	3.71928	−	6.44198i	0.124881	−	0.216300i	−0.796805	−	0.604236i	$-0.793478\pi$
$887$	3.71928	−	6.44198i	0.124881	−	0.216300i	0.921686	+	0.387936i	$0.126812\pi$
$888$	0.181804	−	0.314894i	0.00610095	−	0.0105672i
$889$	−28.7845	−	2.10707i	−0.965403	−	0.0706688i
$890$	−3.88603	+	6.73080i	−0.130260	+	0.225617i
$891$	0.140571			0.00470932
$892$	13.8098	−	23.9193i	0.462388	−	0.800879i
$893$	0.321403	+	0.556686i	0.0107553	+	0.0186288i
$894$	5.95244	−	10.3099i	0.199079	−	0.344816i
$895$	−7.93703	−	13.7473i	−0.265306	−	0.459523i
$896$	1.15207	+	2.38175i	0.0384879	+	0.0795687i
$897$	0.0415404	+	0.124802i	0.00138699	+	0.00416701i
$898$	2.76290	+	4.78549i	0.0921993	+	0.159694i
$899$	−21.7976			−0.726992
$900$	−3.50418			−0.116806
$901$	−1.30424			−0.0434504
$902$	−0.479292			−0.0159587
$903$	4.76589	+	9.85286i	0.158599	+	0.327882i
$904$	−6.18222	+	10.7079i	−0.205618	+	0.356140i
$905$	14.5130	+	25.1372i	0.482427	+	0.835588i
$906$	−3.66774	−	6.35272i	−0.121853	−	0.211055i
$907$	7.29048			0.242076			0.121038	−	0.992648i	$-0.461378\pi$
$907$	7.29048			0.242076			0.121038	+	0.992648i	$0.461378\pi$
$908$	0.895645	−	1.55130i	0.0297230	−	0.0514818i
$909$	−3.00460			−0.0996563
$910$	2.86663	+	11.3094i	0.0950280	+	0.374902i
$911$	8.89914			0.294842			0.147421	−	0.989074i	$-0.452903\pi$
$911$	8.89914			0.294842			0.147421	+	0.989074i	$0.452903\pi$
$912$	−0.447955	+	0.775880i	−0.0148333	+	0.0256920i
$913$	−1.28490			−0.0425241
$914$	16.0187	+	27.7451i	0.529850	+	0.917727i
$915$	0.228165	+	0.395194i	0.00754291	+	0.0130647i
$916$	12.6142	−	21.8485i	0.416786	−	0.721895i
$917$	−57.9007	−	4.23841i	−1.91205	−	0.139965i
$918$	0.186556			0.00615728
$919$	−7.26977			−0.239808			−0.119904	−	0.992786i	$-0.538259\pi$
$919$	−7.26977			−0.239808			−0.119904	+	0.992786i	$0.538259\pi$
$920$	−0.0446174			−0.00147099
$921$	30.0806			0.991190
$922$	−6.48516	−	11.2326i	−0.213577	−	0.369927i
$923$	12.0974	+	36.3448i	0.398191	+	1.19630i
$924$	−0.370925	−	0.0271522i	−0.0122025	−	0.000893242i
$925$	−0.637075	−	1.10345i	−0.0209469	−	0.0362811i
$926$	5.82264	−	10.0851i	0.191344	−	0.331417i
$927$	−4.12788	−	7.14970i	−0.135577	−	0.234827i
$928$	2.99337	−	5.18466i	0.0982621	−	0.170195i
$929$	6.60933			0.216845			0.108423	−	0.994105i	$-0.465420\pi$
$929$	6.60933			0.216845			0.108423	+	0.994105i	$0.465420\pi$
$930$	2.22653	−	3.85647i	0.0730109	−	0.126459i
$931$	−2.31136	−	5.82989i	−0.0757517	−	0.191067i
$932$	14.1852	−	24.5695i	0.464652	−	0.804801i
$933$	−13.8292	+	23.9528i	−0.452746	+	0.784180i
$934$	−5.98058			−0.195691
$935$	0.0160368	−	0.0277765i	0.000524458	−	0.000908389i
$936$	2.39335	−	2.69665i	0.0782289	−	0.0881426i
$937$	−44.3217			−1.44793			−0.723963	−	0.689838i	$-0.757682\pi$
$937$	−44.3217			−1.44793			−0.723963	+	0.689838i	$0.757682\pi$
$938$	−5.59682	−	11.5707i	−0.182742	−	0.377797i
$939$	−3.43002	−	5.94097i	−0.111935	−	0.193876i
$940$	0.877516			0.0286214
$941$	8.06612	−	13.9709i	0.262948	−	0.455440i	−0.704076	−	0.710125i	$-0.748639\pi$
$941$	8.06612	−	13.9709i	0.262948	−	0.455440i	0.967024	+	0.254685i	$0.0819719\pi$
$942$	5.15138	+	8.92246i	0.167841	+	0.290709i
$943$	−0.124385			−0.00405053
$944$	−6.99624			−0.227708
$945$	3.22722	+	0.236237i	0.104981	+	0.00768478i
$946$	−0.290759	−	0.503609i	−0.00945338	−	0.0163737i
$947$	−3.98244	+	6.89779i	−0.129412	+	0.224148i	−0.923449	−	0.383721i	$-0.874642\pi$
$947$	−3.98244	+	6.89779i	−0.129412	+	0.224148i	0.794037	+	0.607870i	$0.207976\pi$
$948$	−2.94837	+	5.10673i	−0.0957587	+	0.165859i
$949$	10.9519	+	32.9034i	0.355515	+	1.06809i
$950$	1.56971	+	2.71882i	0.0509282	+	0.0882103i
$951$	3.37146	+	5.83953i	0.109327	+	0.189360i
$952$	−0.492265	−	0.0360344i	−0.0159544	−	0.00116788i
$953$	21.7224	−	37.6243i	0.703658	−	1.21877i	−0.263516	−	0.964655i	$-0.584882\pi$
$953$	21.7224	−	37.6243i	0.703658	−	1.21877i	0.967174	−	0.254116i	$-0.0817846\pi$
$954$	3.49556	+	6.05448i	0.113173	+	0.196021i
$955$	−12.2168	−	21.1602i	−0.395327	−	0.684727i
$956$	14.4827	+	25.0848i	0.468404	+	0.811300i
$957$	0.420782	+	0.728816i	0.0136020	+	0.0235593i
$958$	−3.33079	+	5.76911i	−0.107613	+	0.186391i
$959$	−7.10363	−	0.519996i	−0.229388	−	0.0167915i
$960$	0.611519	+	1.05918i	0.0197367	+	0.0341849i
$961$	8.87159	+	15.3660i	0.286180	+	0.495679i
$962$	1.28428	+	0.263389i	0.0414068	+	0.00849200i
$963$	2.23641	−	3.87358i	0.0720674	−	0.124824i
$964$	6.59757	−	11.4273i	0.212493	−	0.368049i
$965$	−3.80602	−	6.59221i	−0.122520	−	0.212211i
$966$	−0.0962616	−	0.00704648i	−0.00309717	−	0.000226717i
$967$	−8.68636			−0.279335			−0.139667	−	0.990198i	$-0.544603\pi$
$967$	−8.68636			−0.279335			−0.139667	+	0.990198i	$0.544603\pi$
$968$	−10.9802			−0.352918
$969$	−0.0835688	−	0.144745i	−0.00268462	−	0.00464989i
$970$	−3.96337	+	6.86475i	−0.127256	+	0.220414i
$971$	27.8030			0.892241			0.446120	−	0.894973i	$-0.352805\pi$
$971$	27.8030			0.892241			0.446120	+	0.894973i	$0.352805\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−12.1872	−	25.1954i	−0.390702	−	0.807727i
$974$	−18.9362			−0.606753
$975$	−3.99018	−	11.9879i	−0.127788	−	0.383919i
$976$	−0.186556	+	0.323125i	−0.00597152	+	0.0103430i
$977$	−42.2796			−1.35264			−0.676322	−	0.736606i	$-0.736427\pi$
$977$	−42.2796			−1.35264			−0.676322	+	0.736606i	$0.736427\pi$
$978$	5.06852	−	8.77893i	0.162073	−	0.280719i
$979$	0.446646	−	0.773614i	0.0142749	−	0.0247248i
$980$	−8.47000	−	1.24671i	−0.270564	−	0.0398247i
$981$	−3.83686	+	6.64563i	−0.122501	+	0.212179i
$982$	39.0468			1.24603
$983$	−20.5285	+	35.5564i	−0.654757	+	1.13407i	0.327197	+	0.944956i	$0.393896\pi$
$983$	−20.5285	+	35.5564i	−0.654757	+	1.13407i	−0.981955	+	0.189117i	$0.939437\pi$
$984$	1.70480	+	2.95279i	0.0543469	+	0.0941317i
$985$	−14.9826	+	25.9506i	−0.477385	+	0.826856i
$986$	0.558432	+	0.967232i	0.0177841	+	0.0308029i
$987$	1.89323	+	0.138587i	0.0602623	+	0.00441128i
$988$	−3.16438	−	0.648974i	−0.100672	−	0.0206466i
$989$	−0.0754571	−	0.130696i	−0.00239940	−	0.00415588i
$990$	−0.171924			−0.00546411
$991$	−27.5175			−0.874122			−0.437061	−	0.899432i	$-0.643981\pi$
$991$	−27.5175			−0.874122			−0.437061	+	0.899432i	$0.643981\pi$
$992$	3.64099			0.115602
$993$	−11.0982			−0.352189
$994$	−28.0334	−	2.05208i	−0.889164	−	0.0650881i
$995$	−11.9950	+	20.7759i	−0.380267	+	0.658641i
$996$	4.57029	+	7.91597i	0.144815	+	0.250827i
$997$	−18.4340	−	31.9286i	−0.583810	−	1.01119i	−0.995023	−	0.0996486i	$-0.968228\pi$
$997$	−18.4340	−	31.9286i	−0.583810	−	1.01119i	0.411213	−	0.911539i	$-0.365105\pi$
$998$	33.3204			1.05474
$999$	0.181804	−	0.314894i	0.00575203	−	0.00996282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.c.445.3	yes	8
3.2	odd	2		1638.2.p.h.991.2		8
7.2	even	3		546.2.j.c.289.3	✓	8
13.9	even	3		546.2.j.c.529.3	yes	8
21.2	odd	6		1638.2.m.h.289.2		8
39.35	odd	6		1638.2.m.h.1621.2		8
91.9	even	3	inner	546.2.k.c.373.3	yes	8
273.191	odd	6		1638.2.p.h.919.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.3	✓	8	7.2	even	3
546.2.j.c.529.3	yes	8	13.9	even	3
546.2.k.c.373.3	yes	8	91.9	even	3	inner
546.2.k.c.445.3	yes	8	1.1	even	1	trivial
1638.2.m.h.289.2		8	21.2	odd	6
1638.2.m.h.1621.2		8	39.35	odd	6
1638.2.p.h.919.2		8	273.191	odd	6
1638.2.p.h.991.2		8	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.611519 + 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.48662 - 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.611519 + 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.48662 - 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.22304 q^{10} +0.140571 q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.39335 - 2.69665i) q^{13} +(1.15207 + 2.38175i) q^{14} +(0.611519 + 1.05918i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0932782 - 0.161563i) q^{17} +(-0.500000 + 0.866025i) q^{18} +0.895909 q^{19} +(0.611519 - 1.05918i) q^{20} +(1.48662 - 2.18860i) q^{21} +(-0.0702857 + 0.121738i) q^{22} +(-0.0182404 + 0.0315933i) q^{23} +1.00000 q^{24} +(1.75209 - 3.03471i) q^{25} +(1.13869 + 3.42102i) q^{26} +1.00000 q^{27} +(-2.63869 - 0.193156i) q^{28} +(2.99337 + 5.18466i) q^{29} -1.22304 q^{30} +(-1.82050 + 3.15319i) q^{31} +(-0.500000 - 0.866025i) q^{32} +0.140571 q^{33} +0.186556 q^{34} +(3.22722 + 0.236237i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.181804 - 0.314894i) q^{37} +(-0.447955 + 0.775880i) q^{38} +(2.39335 - 2.69665i) q^{39} +(0.611519 + 1.05918i) q^{40} +(1.70480 + 2.95279i) q^{41} +(1.15207 + 2.38175i) q^{42} +(-2.06841 + 3.58258i) q^{43} +(-0.0702857 - 0.121738i) q^{44} +(0.611519 + 1.05918i) q^{45} +(-0.0182404 - 0.0315933i) q^{46} +(0.358745 + 0.621364i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.57990 - 6.50724i) q^{49} +(1.75209 + 3.03471i) q^{50} +(-0.0932782 - 0.161563i) q^{51} +(-3.53204 - 0.724375i) q^{52} +(3.49556 - 6.05448i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.0859621 + 0.148891i) q^{55} +(1.48662 - 2.18860i) q^{56} +0.895909 q^{57} -5.98674 q^{58} +(3.49812 + 6.05892i) q^{59} +(0.611519 - 1.05918i) q^{60} +0.373113 q^{61} +(-1.82050 - 3.15319i) q^{62} +(1.48662 - 2.18860i) q^{63} +1.00000 q^{64} +(4.31981 + 0.885937i) q^{65} +(-0.0702857 + 0.121738i) q^{66} -4.85806 q^{67} +(-0.0932782 + 0.161563i) q^{68} +(-0.0182404 + 0.0315933i) q^{69} +(-1.81820 + 2.67673i) q^{70} +(-5.31198 + 9.20062i) q^{71} +1.00000 q^{72} +(-4.80900 + 8.32943i) q^{73} +(0.181804 + 0.314894i) q^{74} +(1.75209 - 3.03471i) q^{75} +(-0.447955 - 0.775880i) q^{76} +(0.208977 - 0.307654i) q^{77} +(1.13869 + 3.42102i) q^{78} +(-2.94837 - 5.10673i) q^{79} -1.22304 q^{80} +1.00000 q^{81} -3.40959 q^{82} -9.14057 q^{83} +(-2.63869 - 0.193156i) q^{84} +(0.114083 - 0.197597i) q^{85} +(-2.06841 - 3.58258i) q^{86} +(2.99337 + 5.18466i) q^{87} +0.140571 q^{88} +(3.17736 - 5.50335i) q^{89} -1.22304 q^{90} +(-2.34386 - 9.24696i) q^{91} +0.0364808 q^{92} +(-1.82050 + 3.15319i) q^{93} -0.717490 q^{94} +(0.547865 + 0.948930i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(3.24059 - 5.61287i) q^{97} +(6.92538 + 1.01936i) q^{98} +0.140571 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	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 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 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

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