LMFDB - Embedded newform 546.2.j.c.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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			289.3
Root			$1.26359 + 0.635098i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.c.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.611519 - 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.15207 - 2.38175i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.611519 - 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.15207 - 2.38175i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.611519 - 1.05918i) q^{10} +(-0.0702857 + 0.121738i) 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} +1.00000 q^{16} +0.186556 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.447955 - 0.775880i) q^{19} +(0.611519 - 1.05918i) q^{20} +(1.48662 + 2.18860i) q^{21} +(-0.0702857 + 0.121738i) q^{22} +0.0364808 q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.75209 + 3.03471i) q^{25} +(2.39335 - 2.69665i) q^{26} +1.00000 q^{27} +(1.15207 - 2.38175i) q^{28} +(2.99337 + 5.18466i) q^{29} +(0.611519 + 1.05918i) q^{30} +(-1.82050 - 3.15319i) q^{31} +1.00000 q^{32} +(-0.0702857 - 0.121738i) q^{33} +0.186556 q^{34} +(-1.81820 - 2.67673i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.363609 q^{37} +(-0.447955 - 0.775880i) q^{38} +(1.13869 + 3.42102i) q^{39} +(0.611519 - 1.05918i) q^{40} +(1.70480 + 2.95279i) q^{41} +(1.48662 + 2.18860i) q^{42} +(-2.06841 + 3.58258i) q^{43} +(-0.0702857 + 0.121738i) q^{44} -1.22304 q^{45} +0.0364808 q^{46} +(0.358745 - 0.621364i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.34548 - 5.48788i) q^{49} +(1.75209 + 3.03471i) q^{50} +(-0.0932782 + 0.161563i) q^{51} +(2.39335 - 2.69665i) q^{52} +(3.49556 + 6.05448i) q^{53} +1.00000 q^{54} +(0.0859621 + 0.148891i) q^{55} +(1.15207 - 2.38175i) q^{56} +0.895909 q^{57} +(2.99337 + 5.18466i) q^{58} -6.99624 q^{59} +(0.611519 + 1.05918i) q^{60} +(-0.186556 - 0.323125i) q^{61} +(-1.82050 - 3.15319i) q^{62} +(-2.63869 + 0.193156i) q^{63} +1.00000 q^{64} +(-1.39266 - 4.18404i) q^{65} +(-0.0702857 - 0.121738i) q^{66} +(2.42903 - 4.20720i) q^{67} +0.186556 q^{68} +(-0.0182404 + 0.0315933i) q^{69} +(-1.81820 - 2.67673i) q^{70} +(-5.31198 + 9.20062i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-4.80900 - 8.32943i) q^{73} -0.363609 q^{74} -3.50418 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} +(0.611519 - 1.05918i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.70480 + 2.95279i) q^{82} -9.14057 q^{83} +(1.48662 + 2.18860i) q^{84} +(0.114083 - 0.197597i) q^{85} +(-2.06841 + 3.58258i) q^{86} -5.98674 q^{87} +(-0.0702857 + 0.121738i) q^{88} -6.35472 q^{89} -1.22304 q^{90} +(-3.66544 - 8.80707i) q^{91} +0.0364808 q^{92} +3.64099 q^{93} +(0.358745 - 0.621364i) q^{94} -1.09573 q^{95} +(-0.500000 + 0.866025i) q^{96} +(3.24059 - 5.61287i) q^{97} +(-4.34548 - 5.48788i) q^{98} +0.140571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.611519	−	1.05918i	0.273479	−	0.473680i	−0.696271	−	0.717779i	$-0.745159\pi$
$5$	0.611519	−	1.05918i	0.273479	−	0.473680i	0.969750	+	0.244099i	$0.0784921\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.15207	−	2.38175i	0.435441	−	0.900217i
$7$	1.15207	−	2.38175i	0.435441	−	0.900217i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.611519	−	1.05918i	0.193379	−	0.334943i
$11$	−0.0702857	+	0.121738i	−0.0211919	+	0.0367055i	−0.876427	−	0.481535i	$-0.840079\pi$
$11$	−0.0702857	+	0.121738i	−0.0211919	+	0.0367055i	0.855235	+	0.518240i	$0.173413\pi$
$12$	−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
$16$	1.00000			0.250000
$17$	0.186556			0.0452466			0.0226233	−	0.999744i	$-0.492798\pi$
$17$	0.186556			0.0452466			0.0226233	+	0.999744i	$0.492798\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.447955	−	0.775880i	−0.102768	−	0.177999i	0.810056	−	0.586352i	$-0.199437\pi$
$19$	−0.447955	−	0.775880i	−0.102768	−	0.177999i	−0.912824	+	0.408353i	$0.866103\pi$
$20$	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
$23$	0.0364808			0.00760678			0.00380339	−	0.999993i	$-0.498789\pi$
$23$	0.0364808			0.00760678			0.00380339	+	0.999993i	$0.498789\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.75209	+	3.03471i	0.350418	+	0.606942i
$26$	2.39335	−	2.69665i	0.469374	−	0.528856i
$27$	1.00000			0.192450
$28$	1.15207	−	2.38175i	0.217720	−	0.450109i
$29$	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	$0.645725\pi$
$30$	0.611519	+	1.05918i	0.111648	+	0.193379i
$31$	−1.82050	−	3.15319i	−0.326971	−	0.566330i	0.654939	−	0.755682i	$-0.272694\pi$
$31$	−1.82050	−	3.15319i	−0.326971	−	0.566330i	−0.981909	+	0.189352i	$0.939361\pi$
$32$	1.00000			0.176777
$33$	−0.0702857	−	0.121738i	−0.0122352	−	0.0211919i
$34$	0.186556			0.0319941
$35$	−1.81820	−	2.67673i	−0.307331	−	0.452451i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.363609			−0.0597769			−0.0298884	−	0.999553i	$-0.509515\pi$
$37$	−0.363609			−0.0597769			−0.0298884	+	0.999553i	$0.509515\pi$
$38$	−0.447955	−	0.775880i	−0.0726678	−	0.125864i
$39$	1.13869	+	3.42102i	0.182337	+	0.547802i
$40$	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	$0.747550\pi$
$42$	1.48662	+	2.18860i	0.229391	+	0.337708i
$43$	−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
$45$	−1.22304			−0.182320
$46$	0.0364808			0.00537880
$47$	0.358745	−	0.621364i	0.0523283	−	0.0906353i	−0.838675	−	0.544633i	$-0.816669\pi$
$47$	0.358745	−	0.621364i	0.0523283	−	0.0906353i	0.891003	+	0.453997i	$0.150002\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−4.34548	−	5.48788i	−0.620783	−	0.783983i
$50$	1.75209	+	3.03471i	0.247783	+	0.429173i
$51$	−0.0932782	+	0.161563i	−0.0130616	+	0.0226233i
$52$	2.39335	−	2.69665i	0.331897	−	0.373957i
$53$	3.49556	+	6.05448i	0.480151	+	0.831647i	0.999741	−	0.0227694i	$-0.00724836\pi$
$53$	3.49556	+	6.05448i	0.480151	+	0.831647i	−0.519589	+	0.854416i	$0.673915\pi$
$54$	1.00000			0.136083
$55$	0.0859621	+	0.148891i	0.0115911	+	0.0200764i
$56$	1.15207	−	2.38175i	0.153952	−	0.318275i
$57$	0.895909			0.118666
$58$	2.99337	+	5.18466i	0.393048	+	0.680780i
$59$	−6.99624			−0.910833			−0.455416	−	0.890279i	$-0.650510\pi$
$59$	−6.99624			−0.910833			−0.455416	+	0.890279i	$0.650510\pi$
$60$	0.611519	+	1.05918i	0.0789467	+	0.136740i
$61$	−0.186556	−	0.323125i	−0.0238861	−	0.0413719i	0.853835	−	0.520543i	$-0.174271\pi$
$61$	−0.186556	−	0.323125i	−0.0238861	−	0.0413719i	−0.877721	+	0.479171i	$0.840937\pi$
$62$	−1.82050	−	3.15319i	−0.231203	−	0.400456i
$63$	−2.63869	+	0.193156i	−0.332444	+	0.0243353i
$64$	1.00000			0.125000
$65$	−1.39266	−	4.18404i	−0.172738	−	0.518966i
$66$	−0.0702857	−	0.121738i	−0.00865158	−	0.0149850i
$67$	2.42903	−	4.20720i	0.296753	−	0.513992i	−0.678638	−	0.734473i	$-0.737429\pi$
$67$	2.42903	−	4.20720i	0.296753	−	0.513992i	0.975391	+	0.220481i	$0.0707628\pi$
$68$	0.186556			0.0226233
$69$	−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	$0.949551\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−4.80900	−	8.32943i	−0.562851	−	0.974886i	−0.997246	−	0.0741638i	$-0.976371\pi$
$73$	−4.80900	−	8.32943i	−0.562851	−	0.974886i	0.434395	−	0.900722i	$-0.356962\pi$
$74$	−0.363609			−0.0422686
$75$	−3.50418			−0.404628
$76$	−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	−0.982849	−	0.184413i	$-0.940962\pi$
$79$	−2.94837	+	5.10673i	−0.331718	+	0.574552i	0.651131	+	0.758966i	$0.274295\pi$
$80$	0.611519	−	1.05918i	0.0683699	−	0.118420i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.70480	+	2.95279i	0.188263	+	0.326082i
$83$	−9.14057			−1.00331			−0.501654	−	0.865068i	$-0.667275\pi$
$83$	−9.14057			−1.00331			−0.501654	+	0.865068i	$0.667275\pi$
$84$	1.48662	+	2.18860i	0.162204	+	0.238795i
$85$	0.114083	−	0.197597i	0.0123740	−	0.0214324i
$86$	−2.06841	+	3.58258i	−0.223042	+	0.386320i
$87$	−5.98674			−0.641845
$88$	−0.0702857	+	0.121738i	−0.00749249	+	0.0129774i
$89$	−6.35472			−0.673599			−0.336799	−	0.941576i	$-0.609344\pi$
$89$	−6.35472			−0.673599			−0.336799	+	0.941576i	$0.609344\pi$
$90$	−1.22304			−0.128919
$91$	−3.66544	−	8.80707i	−0.384243	−	0.923232i
$92$	0.0364808			0.00380339
$93$	3.64099			0.377553
$94$	0.358745	−	0.621364i	0.0370017	−	0.0640888i
$95$	−1.09573			−0.112420
$96$	−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	$0.0599441\pi$
$98$	−4.34548	−	5.48788i	−0.438960	−	0.554359i
$99$	0.140571			0.0141280
$100$	1.75209	+	3.03471i	0.175209	+	0.303471i
$101$	1.50230	−	2.60206i	0.149484	−	0.258915i	−0.781553	−	0.623839i	$-0.785572\pi$
$101$	1.50230	−	2.60206i	0.149484	−	0.258915i	0.931037	+	0.364925i	$0.118905\pi$
$102$	−0.0932782	+	0.161563i	−0.00923591	+	0.0159971i
$103$	−4.12788	+	7.14970i	−0.406732	+	0.704480i	−0.994521	−	0.104534i	$-0.966665\pi$
$103$	−4.12788	+	7.14970i	−0.406732	+	0.704480i	0.587789	+	0.809014i	$0.299998\pi$
$104$	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
$107$	−4.47283			−0.432405			−0.216202	−	0.976349i	$-0.569367\pi$
$107$	−4.47283			−0.432405			−0.216202	+	0.976349i	$0.569367\pi$
$108$	1.00000			0.0962250
$109$	−3.83686	−	6.64563i	−0.367504	−	0.636536i	0.621671	−	0.783279i	$-0.286454\pi$
$109$	−3.83686	−	6.64563i	−0.367504	−	0.636536i	−0.989175	+	0.146743i	$0.953121\pi$
$110$	0.0859621	+	0.148891i	0.00819616	+	0.0141962i
$111$	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	$0.969103\pi$
$114$	0.895909			0.0839096
$115$	0.0223087	−	0.0386398i	0.00208030	−	0.00360318i
$116$	2.99337	+	5.18466i	0.277927	+	0.481384i
$117$	−3.53204	−	0.724375i	−0.326537	−	0.0669685i
$118$	−6.99624			−0.644056
$119$	0.214926	−	0.444331i	0.0197022	−	0.0407317i
$120$	0.611519	+	1.05918i	0.0558238	+	0.0966896i
$121$	5.49012	+	9.50917i	0.499102	+	0.864470i
$122$	−0.186556	−	0.323125i	−0.0168900	−	0.0292544i
$123$	−3.40959			−0.307433
$124$	−1.82050	−	3.15319i	−0.163485	−	0.283165i
$125$	10.4009			0.930287
$126$	−2.63869	+	0.193156i	−0.235073	+	0.0172077i
$127$	−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	$0.994147\pi$
$128$	1.00000			0.0883883
$129$	−2.06841	−	3.58258i	−0.182113	−	0.315429i
$130$	−1.39266	−	4.18404i	−0.122144	−	0.366964i
$131$	−10.9715	+	19.0032i	−0.958583	+	1.66031i	−0.232634	+	0.972564i	$0.574735\pi$
$131$	−10.9715	+	19.0032i	−0.958583	+	1.66031i	−0.725948	+	0.687749i	$0.758599\pi$
$132$	−0.0702857	−	0.121738i	−0.00611759	−	0.0105960i
$133$	−2.36403	+	0.173050i	−0.204987	+	0.0150053i
$134$	2.42903	−	4.20720i	0.209836	−	0.363447i
$135$	0.611519	−	1.05918i	0.0526311	−	0.0911598i
$136$	0.186556			0.0159971
$137$	2.69210			0.230002			0.115001	−	0.993365i	$-0.463313\pi$
$137$	2.69210			0.230002			0.115001	+	0.993365i	$0.463313\pi$
$138$	−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	$0.0185792\pi$
$140$	−1.81820	−	2.67673i	−0.153666	−	0.226225i
$141$	0.358745	+	0.621364i	0.0302118	+	0.0523283i
$142$	−5.31198	+	9.20062i	−0.445772	+	0.772099i
$143$	0.160068	+	0.480898i	0.0133855	+	0.0402147i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	7.32200			0.608059
$146$	−4.80900	−	8.32943i	−0.397996	−	0.689349i
$147$	6.92538	−	1.01936i	0.571196	−	0.0840752i
$148$	−0.363609			−0.0298884
$149$	5.95244	+	10.3099i	0.487643	+	0.844623i	0.999899	−	0.0142102i	$-0.00452341\pi$
$149$	5.95244	+	10.3099i	0.487643	+	0.844623i	−0.512256	+	0.858833i	$0.671190\pi$
$150$	−3.50418			−0.286115
$151$	−3.66774	−	6.35272i	−0.298477	−	0.516977i	0.677311	−	0.735697i	$-0.263145\pi$
$151$	−3.66774	−	6.35272i	−0.298477	−	0.516977i	−0.975788	+	0.218720i	$0.929812\pi$
$152$	−0.447955	−	0.775880i	−0.0363339	−	0.0629322i
$153$	−0.0932782	−	0.161563i	−0.00754109	−	0.0130616i
$154$	0.208977	+	0.307654i	0.0168398	+	0.0247915i
$155$	−4.45307			−0.357679
$156$	1.13869	+	3.42102i	0.0911683	+	0.273901i
$157$	5.15138	+	8.92246i	0.411125	+	0.712090i	0.995013	−	0.0997446i	$-0.0318026\pi$
$157$	5.15138	+	8.92246i	0.411125	+	0.712090i	−0.583888	+	0.811834i	$0.698469\pi$
$158$	−2.94837	+	5.10673i	−0.234560	+	0.406270i
$159$	−6.99111			−0.554431
$160$	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
$163$	5.06852	+	8.77893i	0.396997	+	0.687619i	0.993354	−	0.115101i	$-0.0367190\pi$
$163$	5.06852	+	8.77893i	0.396997	+	0.687619i	−0.596357	+	0.802719i	$0.703386\pi$
$164$	1.70480	+	2.95279i	0.133122	+	0.230575i
$165$	−0.171924			−0.0133843
$166$	−9.14057			−0.709446
$167$	−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
$171$	−0.447955	+	0.775880i	−0.0342559	+	0.0593330i
$172$	−2.06841	+	3.58258i	−0.157714	+	0.273169i
$173$	5.33942	+	9.24815i	0.405949	+	0.703124i	0.994431	−	0.105386i	$-0.0336079\pi$
$173$	5.33942	+	9.24815i	0.405949	+	0.703124i	−0.588483	+	0.808510i	$0.700275\pi$
$174$	−5.98674			−0.453853
$175$	9.24645	−	0.676853i	0.698966	−	0.0511653i
$176$	−0.0702857	+	0.121738i	−0.00529799	+	0.00917638i
$177$	3.49812	−	6.05892i	0.262935	−	0.455416i
$178$	−6.35472			−0.476306
$179$	6.48961	−	11.2403i	0.485056	−	0.840142i	−0.514797	−	0.857312i	$-0.672133\pi$
$179$	6.48961	−	11.2403i	0.485056	−	0.840142i	0.999853	+	0.0171707i	$0.00546588\pi$
$180$	−1.22304			−0.0911598
$181$	23.7327			1.76403			0.882017	−	0.471217i	$-0.156185\pi$
$181$	23.7327			1.76403			0.882017	+	0.471217i	$0.156185\pi$
$182$	−3.66544	−	8.80707i	−0.271701	−	0.652824i
$183$	0.373113			0.0275813
$184$	0.0364808			0.00268940
$185$	−0.222353	+	0.385127i	−0.0163477	+	0.0283151i
$186$	3.64099			0.266970
$187$	−0.0131122	+	0.0227111i	−0.000958863	+	0.00166080i
$188$	0.358745	−	0.621364i	0.0261642	−	0.0453176i
$189$	1.15207	−	2.38175i	0.0838006	−	0.173247i
$190$	−1.09573			−0.0794926
$191$	9.98892	+	17.3013i	0.722773	+	1.25188i	0.959884	+	0.280397i	$0.0904662\pi$
$191$	9.98892	+	17.3013i	0.722773	+	1.25188i	−0.237111	+	0.971483i	$0.576200\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	3.11194	−	5.39003i	0.224002	−	0.387983i	−0.732017	−	0.681286i	$-0.761421\pi$
$193$	3.11194	−	5.39003i	0.224002	−	0.387983i	0.956020	+	0.293303i	$0.0947544\pi$
$194$	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	$0.495636\pi$
$198$	0.140571			0.00998998
$199$	−19.6151			−1.39048			−0.695238	−	0.718780i	$-0.744701\pi$
$199$	−19.6151			−1.39048			−0.695238	+	0.718780i	$0.744701\pi$
$200$	1.75209	+	3.03471i	0.123891	+	0.214586i
$201$	2.42903	+	4.20720i	0.171331	+	0.296753i
$202$	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
$205$	4.17006			0.291250
$206$	−4.12788	+	7.14970i	−0.287603	+	0.498143i
$207$	−0.0182404	−	0.0315933i	−0.00126780	−	0.00219589i
$208$	2.39335	−	2.69665i	0.165949	−	0.186979i
$209$	0.125939			0.00871140
$210$	3.22722	−	0.236237i	0.222699	−	0.0163019i
$211$	−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	$0.899468\pi$
$212$	3.49556	+	6.05448i	0.240076	+	0.415823i
$213$	−5.31198	−	9.20062i	−0.363971	−	0.630416i
$214$	−4.47283			−0.305756
$215$	2.52974	+	4.38163i	0.172527	+	0.298825i
$216$	1.00000			0.0680414
$217$	−9.60745	+	0.703279i	−0.652196	+	0.0477417i
$218$	−3.83686	−	6.64563i	−0.259865	−	0.450099i
$219$	9.61800			0.649924
$220$	0.0859621	+	0.148891i	0.00579556	+	0.0100382i
$221$	0.446494	−	0.503076i	0.0300344	−	0.0338406i
$222$	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	$0.457586\pi$
$224$	1.15207	−	2.38175i	0.0769758	−	0.159137i
$225$	1.75209	−	3.03471i	0.116806	−	0.202314i
$226$	−6.18222	+	10.7079i	−0.411235	+	0.712281i
$227$	−1.79129			−0.118892			−0.0594460	−	0.998232i	$-0.518933\pi$
$227$	−1.79129			−0.118892			−0.0594460	+	0.998232i	$0.518933\pi$
$228$	0.895909			0.0593330
$229$	12.6142	−	21.8485i	0.833572	−	1.44379i	−0.0616153	−	0.998100i	$-0.519625\pi$
$229$	12.6142	−	21.8485i	0.833572	−	1.44379i	0.895188	−	0.445690i	$-0.147041\pi$
$230$	0.0223087	−	0.0386398i	0.00147099	−	0.00254783i
$231$	−0.370925	+	0.0271522i	−0.0244051	+	0.00178648i
$232$	2.99337	+	5.18466i	0.196524	+	0.340390i
$233$	14.1852	−	24.5695i	0.929304	−	1.60960i	0.144815	−	0.989459i	$-0.453741\pi$
$233$	14.1852	−	24.5695i	0.929304	−	1.60960i	0.784489	−	0.620143i	$-0.212925\pi$
$234$	−3.53204	−	0.724375i	−0.230896	−	0.0473539i
$235$	−0.438758	−	0.759952i	−0.0286214	−	0.0495738i
$236$	−6.99624			−0.455416
$237$	−2.94837	−	5.10673i	−0.191517	−	0.331718i
$238$	0.214926	−	0.444331i	0.0139316	−	0.0288017i
$239$	−28.9654			−1.87362			−0.936809	−	0.349842i	$-0.886235\pi$
$239$	−28.9654			−1.87362			−0.936809	+	0.349842i	$0.886235\pi$
$240$	0.611519	+	1.05918i	0.0394734	+	0.0683699i
$241$	−13.1951			−0.849974			−0.424987	−	0.905200i	$-0.639721\pi$
$241$	−13.1951			−0.849974			−0.424987	+	0.905200i	$0.639721\pi$
$242$	5.49012	+	9.50917i	0.352918	+	0.611272i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.186556	−	0.323125i	−0.0119430	−	0.0206860i
$245$	−8.47000	+	1.24671i	−0.541128	+	0.0796495i
$246$	−3.40959			−0.217388
$247$	−3.16438	−	0.648974i	−0.201345	−	0.0412932i
$248$	−1.82050	−	3.15319i	−0.115602	−	0.200228i
$249$	4.57029	−	7.91597i	0.289630	−	0.501654i
$250$	10.4009			0.657812
$251$	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
$254$	−5.45432	−	9.44716i	−0.342235	−	0.592768i
$255$	0.114083	+	0.197597i	0.00714413	+	0.0123740i
$256$	1.00000			0.0625000
$257$	−10.2358			−0.638490			−0.319245	−	0.947672i	$-0.603429\pi$
$257$	−10.2358			−0.638490			−0.319245	+	0.947672i	$0.603429\pi$
$258$	−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
$262$	−10.9715	+	19.0032i	−0.677820	+	1.17402i
$263$	2.42308	−	4.19690i	0.149414	−	0.258792i	−0.781597	−	0.623783i	$-0.785595\pi$
$263$	2.42308	−	4.19690i	0.149414	−	0.258792i	0.931011	+	0.364991i	$0.118928\pi$
$264$	−0.0702857	−	0.121738i	−0.00432579	−	0.00749249i
$265$	8.55039			0.525246
$266$	−2.36403	+	0.173050i	−0.144948	+	0.0106104i
$267$	3.17736	−	5.50335i	0.194451	−	0.336799i
$268$	2.42903	−	4.20720i	0.148377	−	0.256996i
$269$	−0.897277			−0.0547079			−0.0273540	−	0.999626i	$-0.508708\pi$
$269$	−0.897277			−0.0547079			−0.0273540	+	0.999626i	$0.508708\pi$
$270$	0.611519	−	1.05918i	0.0372158	−	0.0644597i
$271$	13.8751			0.842854			0.421427	−	0.906862i	$-0.361529\pi$
$271$	13.8751			0.842854			0.421427	+	0.906862i	$0.361529\pi$
$272$	0.186556			0.0113116
$273$	9.45987	+	1.22917i	0.572537	+	0.0743926i
$274$	2.69210			0.162636
$275$	−0.492588			−0.0297042
$276$	−0.0182404	+	0.0315933i	−0.00109794	+	0.00190169i
$277$	−20.4739			−1.23016			−0.615078	−	0.788466i	$-0.710876\pi$
$277$	−20.4739			−1.23016			−0.615078	+	0.788466i	$0.710876\pi$
$278$	5.28925	−	9.16126i	0.317228	−	0.549456i
$279$	−1.82050	+	3.15319i	−0.108990	+	0.188777i
$280$	−1.81820	−	2.67673i	−0.108658	−	0.159965i
$281$	5.11819			0.305326			0.152663	−	0.988278i	$-0.451215\pi$
$281$	5.11819			0.305326			0.152663	+	0.988278i	$0.451215\pi$
$282$	0.358745	+	0.621364i	0.0213629	+	0.0370017i
$283$	−4.54066	+	7.86466i	−0.269914	+	0.467505i	−0.968839	−	0.247690i	$-0.920329\pi$
$283$	−4.54066	+	7.86466i	−0.269914	+	0.467505i	0.698925	+	0.715195i	$0.253662\pi$
$284$	−5.31198	+	9.20062i	−0.315208	+	0.545957i
$285$	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
$289$	−16.9652			−0.997953
$290$	7.32200			0.429963
$291$	3.24059	+	5.61287i	0.189967	+	0.329032i
$292$	−4.80900	−	8.32943i	−0.281425	−	0.487443i
$293$	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
$296$	−0.363609			−0.0211343
$297$	−0.0702857	+	0.121738i	−0.00407839	+	0.00706398i
$298$	5.95244	+	10.3099i	0.344816	+	0.597238i
$299$	0.0873112	−	0.0983759i	0.00504934	−	0.00568922i
$300$	−3.50418			−0.202314
$301$	6.14988	+	9.05381i	0.354473	+	0.521853i
$302$	−3.66774	−	6.35272i	−0.211055	−	0.365558i
$303$	1.50230	+	2.60206i	0.0863049	+	0.149484i
$304$	−0.447955	−	0.775880i	−0.0256920	−	0.0444998i
$305$	−0.456331			−0.0261294
$306$	−0.0932782	−	0.161563i	−0.00533236	−	0.00923591i
$307$	30.0806			1.71679			0.858395	−	0.512989i	$-0.171462\pi$
$307$	30.0806			1.71679			0.858395	+	0.512989i	$0.171462\pi$
$308$	0.208977	+	0.307654i	0.0119076	+	0.0175302i
$309$	−4.12788	−	7.14970i	−0.234827	−	0.406732i
$310$	−4.45307			−0.252917
$311$	−13.8292	−	23.9528i	−0.784180	−	1.35824i	−0.929488	−	0.368853i	$-0.879751\pi$
$311$	−13.8292	−	23.9528i	−0.784180	−	1.35824i	0.145308	−	0.989386i	$-0.453583\pi$
$312$	1.13869	+	3.42102i	0.0644657	+	0.193677i
$313$	−3.43002	+	5.94097i	−0.193876	+	0.335804i	−0.946532	−	0.322611i	$-0.895439\pi$
$313$	−3.43002	+	5.94097i	−0.193876	+	0.335804i	0.752655	+	0.658415i	$0.228773\pi$
$314$	5.15138	+	8.92246i	0.290709	+	0.503523i
$315$	−1.40902	+	2.91297i	−0.0793894	+	0.164127i
$316$	−2.94837	+	5.10673i	−0.165859	+	0.287276i
$317$	3.37146	−	5.83953i	0.189360	−	0.327981i	−0.755677	−	0.654944i	$-0.772692\pi$
$317$	3.37146	−	5.83953i	0.189360	−	0.327981i	0.945037	+	0.326963i	$0.106025\pi$
$318$	−6.99111			−0.392042
$319$	−0.841564			−0.0471186
$320$	0.611519	−	1.05918i	0.0341849	−	0.0592100i
$321$	2.23641	−	3.87358i	0.124824	−	0.216202i
$322$	0.0420284	−	0.0868883i	0.00234215	−	0.00484209i
$323$	−0.0835688	−	0.144745i	−0.00464989	−	0.00805385i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	12.3769	+	2.53834i	0.686546	+	0.140802i
$326$	5.06852	+	8.77893i	0.280719	+	0.486220i
$327$	7.67371			0.424357
$328$	1.70480	+	2.95279i	0.0941317	+	0.163041i
$329$	−1.06664	−	1.57029i	−0.0588056	−	0.0865731i
$330$	−0.171924			−0.00946411
$331$	5.54908	+	9.61129i	0.305005	+	0.528284i	0.977262	−	0.212033i	$-0.0680085\pi$
$331$	5.54908	+	9.61129i	0.305005	+	0.528284i	−0.672257	+	0.740317i	$0.734675\pi$
$332$	−9.14057			−0.501654
$333$	0.181804	+	0.314894i	0.00996282	+	0.0172561i
$334$	−4.28857	−	7.42802i	−0.234660	−	0.406443i
$335$	−2.97079	−	5.14557i	−0.162312	−	0.281132i
$336$	1.48662	+	2.18860i	0.0811020	+	0.119398i
$337$	21.6470			1.17918			0.589592	−	0.807701i	$-0.299288\pi$
$337$	21.6470			1.17918			0.589592	+	0.807701i	$0.299288\pi$
$338$	−1.54380	−	12.9080i	−0.0839715	−	0.702103i
$339$	−6.18222	−	10.7079i	−0.335772	−	0.581575i
$340$	0.114083	−	0.197597i	0.00618700	−	0.0107162i
$341$	0.511819			0.0277166
$342$	−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
$345$	0.0223087	+	0.0386398i	0.00120106	+	0.00208030i
$346$	5.33942	+	9.24815i	0.287049	+	0.497183i
$347$	29.8675			1.60337			0.801685	−	0.597746i	$-0.203937\pi$
$347$	29.8675			1.60337			0.801685	+	0.597746i	$0.203937\pi$
$348$	−5.98674			−0.320923
$349$	−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
$353$	−3.07853	+	5.33218i	−0.163854	+	0.283803i	−0.936248	−	0.351341i	$-0.885726\pi$
$353$	−3.07853	+	5.33218i	−0.163854	+	0.283803i	0.772394	+	0.635144i	$0.219059\pi$
$354$	3.49812	−	6.05892i	0.185923	−	0.322028i
$355$	6.49675	+	11.2527i	0.344812	+	0.597232i
$356$	−6.35472			−0.336799
$357$	0.277339	+	0.408296i	0.0146783	+	0.0216093i
$358$	6.48961	−	11.2403i	0.342986	−	0.594070i
$359$	12.4203	−	21.5125i	0.655516	−	1.13539i	−0.326248	−	0.945284i	$-0.605785\pi$
$359$	12.4203	−	21.5125i	0.655516	−	1.13539i	0.981764	−	0.190103i	$-0.0608821\pi$
$360$	−1.22304			−0.0644597
$361$	9.09867	−	15.7594i	0.478878	−	0.829440i
$362$	23.7327			1.24736
$363$	−10.9802			−0.576313
$364$	−3.66544	−	8.80707i	−0.192121	−	0.461616i
$365$	−11.7632			−0.615712
$366$	0.373113			0.0195029
$367$	−18.0306	+	31.2299i	−0.941188	+	1.63019i	−0.177980	+	0.984034i	$0.556956\pi$
$367$	−18.0306	+	31.2299i	−0.941188	+	1.63019i	−0.763209	+	0.646152i	$0.776377\pi$
$368$	0.0364808			0.00190169
$369$	1.70480	−	2.95279i	0.0887482	−	0.153716i
$370$	−0.222353	+	0.385127i	−0.0115596	+	0.0200218i
$371$	18.4474	−	1.35037i	0.957740	−	0.0701079i
$372$	3.64099			0.188777
$373$	7.37092	+	12.7668i	0.381652	+	0.661041i	0.991299	−	0.131633i	$-0.0420219\pi$
$373$	7.37092	+	12.7668i	0.381652	+	0.661041i	−0.609647	+	0.792673i	$0.708689\pi$
$374$	−0.0131122	+	0.0227111i	−0.000678018	+	0.00117436i
$375$	−5.20046	+	9.00747i	−0.268551	+	0.465144i
$376$	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	$0.744943\pi$
$380$	−1.09573			−0.0562098
$381$	10.9086			0.558867
$382$	9.98892	+	17.3013i	0.511078	+	0.885213i
$383$	10.2017	+	17.6698i	0.521281	+	0.902884i	0.999694	+	0.0247495i	$0.00787881\pi$
$383$	10.2017	+	17.6698i	0.521281	+	0.902884i	−0.478413	+	0.878135i	$0.658788\pi$
$384$	−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
$387$	4.13681			0.210286
$388$	3.24059	−	5.61287i	0.164516	−	0.284950i
$389$	−15.8455	−	27.4453i	−0.803400	−	1.39153i	−0.917366	−	0.398045i	$-0.869689\pi$
$389$	−15.8455	−	27.4453i	−0.803400	−	1.39153i	0.113966	−	0.993485i	$-0.463644\pi$
$390$	4.31981	+	0.885937i	0.218742	+	0.0448612i
$391$	0.00680573			0.000344181
$392$	−4.34548	−	5.48788i	−0.219480	−	0.277180i
$393$	−10.9715	−	19.0032i	−0.553438	−	0.958583i
$394$	12.2503	+	21.2182i	0.617162	+	1.06896i
$395$	3.60597	+	6.24573i	0.181436	+	0.314257i
$396$	0.140571			0.00706398
$397$	1.30524	+	2.26074i	0.0655080	+	0.113463i	0.896919	−	0.442194i	$-0.145800\pi$
$397$	1.30524	+	2.26074i	0.0655080	+	0.113463i	−0.831411	+	0.555658i	$0.812467\pi$
$398$	−19.6151			−0.983215
$399$	1.03215	−	2.13383i	0.0516720	−	0.106825i
$400$	1.75209	+	3.03471i	0.0876045	+	0.151735i
$401$	−16.3696			−0.817458			−0.408729	−	0.912656i	$-0.634028\pi$
$401$	−16.3696			−0.817458			−0.408729	+	0.912656i	$0.634028\pi$
$402$	2.42903	+	4.20720i	0.121149	+	0.209836i
$403$	−12.8601	−	2.63744i	−0.640608	−	0.131380i
$404$	1.50230	−	2.60206i	0.0747422	−	0.129457i
$405$	0.611519	+	1.05918i	0.0303866	+	0.0526311i
$406$	15.7971	−	1.15637i	0.783999	−	0.0573898i
$407$	0.0255565	−	0.0442652i	0.00126679	−	0.00219414i
$408$	−0.0932782	+	0.161563i	−0.00461796	+	0.00799854i
$409$	22.7307			1.12396			0.561980	−	0.827151i	$-0.310040\pi$
$409$	22.7307			1.12396			0.561980	+	0.827151i	$0.310040\pi$
$410$	4.17006			0.205945
$411$	−1.34605	+	2.33143i	−0.0663958	+	0.115001i
$412$	−4.12788	+	7.14970i	−0.203366	+	0.352240i
$413$	−8.06014	+	16.6633i	−0.396614	+	0.819948i
$414$	−0.0182404	−	0.0315933i	−0.000896467	−	0.00155273i
$415$	−5.58963	+	9.68152i	−0.274384	+	0.475247i
$416$	2.39335	−	2.69665i	0.117343	−	0.132214i
$417$	5.28925	+	9.16126i	0.259016	+	0.448629i
$418$	0.125939			0.00615989
$419$	−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	$-0.355606\pi$
$420$	3.22722	−	0.236237i	0.157472	−	0.0115272i
$421$	8.33173			0.406064			0.203032	−	0.979172i	$-0.434921\pi$
$421$	8.33173			0.406064			0.203032	+	0.979172i	$0.434921\pi$
$422$	−2.99635	−	5.18983i	−0.145860	−	0.252637i
$423$	−0.717490			−0.0348855
$424$	3.49556	+	6.05448i	0.169759	+	0.294032i
$425$	0.326863	+	0.566144i	0.0158552	+	0.0274620i
$426$	−5.31198	−	9.20062i	−0.257366	−	0.445772i
$427$	−0.984529	+	0.0720689i	−0.0476447	+	0.00348766i
$428$	−4.47283			−0.216202
$429$	−0.496504	−	0.101826i	−0.0239714	−	0.00491623i
$430$	2.52974	+	4.38163i	0.121995	+	0.211301i
$431$	13.7933	−	23.8907i	0.664401	−	1.15078i	−0.315046	−	0.949076i	$-0.602020\pi$
$431$	13.7933	−	23.8907i	0.664401	−	1.15078i	0.979447	−	0.201700i	$-0.0646466\pi$
$432$	1.00000			0.0481125
$433$	−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
$436$	−3.83686	−	6.64563i	−0.183752	−	0.318268i
$437$	−0.0163418	−	0.0283048i	−0.000781732	−	0.00135400i
$438$	9.61800			0.459566
$439$	−15.2460			−0.727653			−0.363827	−	0.931467i	$-0.618530\pi$
$439$	−15.2460			−0.727653			−0.363827	+	0.931467i	$0.618530\pi$
$440$	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	−0.488375	−	0.872634i	$-0.662410\pi$
$443$	10.7666	−	18.6482i	0.511535	−	0.886005i	0.999911	−	0.0133713i	$-0.00425634\pi$
$444$	0.181804	−	0.314894i	0.00862805	−	0.0149442i
$445$	−3.88603	+	6.73080i	−0.184215	+	0.319071i
$446$	13.8098	+	23.9193i	0.653915	+	1.13261i
$447$	−11.9049			−0.563082
$448$	1.15207	−	2.38175i	0.0544301	−	0.112527i
$449$	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
$451$	−0.479292			−0.0225690
$452$	−6.18222	+	10.7079i	−0.290787	+	0.503658i
$453$	7.33549			0.344651
$454$	−1.79129			−0.0840694
$455$	−11.5698	−	1.50332i	−0.542399	−	0.0704767i
$456$	0.895909			0.0419548
$457$	−32.0373			−1.49864			−0.749321	−	0.662207i	$-0.769620\pi$
$457$	−32.0373			−1.49864			−0.749321	+	0.662207i	$0.769620\pi$
$458$	12.6142	−	21.8485i	0.589425	−	1.02091i
$459$	0.186556			0.00870770
$460$	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	$0.264336\pi$
$462$	−0.370925	+	0.0271522i	−0.0172570	+	0.00126323i
$463$	−11.6453			−0.541202			−0.270601	−	0.962692i	$-0.587222\pi$
$463$	−11.6453			−0.541202			−0.270601	+	0.962692i	$0.587222\pi$
$464$	2.99337	+	5.18466i	0.138964	+	0.240692i
$465$	2.22653	−	3.85647i	0.103253	−	0.178839i
$466$	14.1852	−	24.5695i	0.657117	−	1.13816i
$467$	2.99029	−	5.17934i	0.138374	−	0.239671i	−0.788507	−	0.615026i	$-0.789146\pi$
$467$	2.99029	−	5.17934i	0.138374	−	0.239671i	0.926881	+	0.375354i	$0.122479\pi$
$468$	−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
$471$	−10.3028			−0.474726
$472$	−6.99624			−0.322028
$473$	−0.290759	−	0.503609i	−0.0133691	−	0.0231560i
$474$	−2.94837	−	5.10673i	−0.135423	−	0.234560i
$475$	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
$478$	−28.9654			−1.32485
$479$	−3.33079	+	5.76911i	−0.152188	+	0.263597i	−0.932032	−	0.362377i	$-0.881965\pi$
$479$	−3.33079	+	5.76911i	−0.152188	+	0.263597i	0.779844	+	0.625974i	$0.215299\pi$
$480$	0.611519	+	1.05918i	0.0279119	+	0.0483448i
$481$	−0.870241	+	0.980524i	−0.0396796	+	0.0447080i
$482$	−13.1951			−0.601022
$483$	0.0542333	+	0.0798418i	0.00246770	+	0.00363293i
$484$	5.49012	+	9.50917i	0.249551	+	0.432235i
$485$	−3.96337	−	6.86475i	−0.179967	−	0.311712i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−18.9362			−0.858079			−0.429039	−	0.903286i	$-0.641148\pi$
$487$	−18.9362			−0.858079			−0.429039	+	0.903286i	$0.641148\pi$
$488$	−0.186556	−	0.323125i	−0.00844501	−	0.0146272i
$489$	−10.1370			−0.458413
$490$	−8.47000	+	1.24671i	−0.382636	+	0.0563207i
$491$	−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	$-0.509849\pi$
$492$	−3.40959			−0.153716
$493$	0.558432	+	0.967232i	0.0251505	+	0.0435619i
$494$	−3.16438	−	0.648974i	−0.142372	−	0.0291987i
$495$	0.0859621	−	0.148891i	0.00386371	−	0.00669214i
$496$	−1.82050	−	3.15319i	−0.0817427	−	0.141582i
$497$	15.7938	+	23.2516i	0.708450	+	1.04298i
$498$	4.57029	−	7.91597i	0.204799	−	0.354723i
$499$	−16.6602	+	28.8563i	−0.745812	+	1.29178i	0.204002	+	0.978970i	$0.434605\pi$
$499$	−16.6602	+	28.8563i	−0.745812	+	1.29178i	−0.949814	+	0.312814i	$0.898728\pi$
$500$	10.4009			0.465144
$501$	8.57714			0.383198
$502$	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	$0.0824077\pi$
$504$	−2.63869	+	0.193156i	−0.117537	+	0.00860384i
$505$	−1.83737	−	3.18242i	−0.0817618	−	0.141616i
$506$	−0.00256408	+	0.00444112i	−0.000113987	+	0.000197432i
$507$	11.9506	+	5.11704i	0.530743	+	0.227256i
$508$	−5.45432	−	9.44716i	−0.241996	−	0.419150i
$509$	−34.6529			−1.53596			−0.767982	−	0.640471i	$-0.778739\pi$
$509$	−34.6529			−1.53596			−0.767982	+	0.640471i	$0.778739\pi$
$510$	0.114083	+	0.197597i	0.00505167	+	0.00874974i
$511$	−25.3789	+	1.85777i	−1.12270	+	0.0821830i
$512$	1.00000			0.0441942
$513$	−0.447955	−	0.775880i	−0.0197777	−	0.0342559i
$514$	−10.2358			−0.451481
$515$	5.04855	+	8.74434i	0.222466	+	0.385322i
$516$	−2.06841	−	3.58258i	−0.0910565	−	0.157714i
$517$	0.0504293	+	0.0873461i	0.00221788	+	0.00384148i
$518$	−0.418902	+	0.866025i	−0.0184055	+	0.0380510i
$519$	−10.6788			−0.468749
$520$	−1.39266	−	4.18404i	−0.0610722	−	0.183482i
$521$	2.62165	+	4.54083i	0.114856	+	0.198937i	0.917722	−	0.397222i	$-0.130026\pi$
$521$	2.62165	+	4.54083i	0.114856	+	0.198937i	−0.802866	+	0.596160i	$0.796693\pi$
$522$	2.99337	−	5.18466i	0.131016	−	0.226927i
$523$	−15.9800			−0.698757			−0.349379	−	0.936982i	$-0.613607\pi$
$523$	−15.9800			−0.698757			−0.349379	+	0.936982i	$0.613607\pi$
$524$	−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
$527$	−0.339625	−	0.588248i	−0.0147943	−	0.0256245i
$528$	−0.0702857	−	0.121738i	−0.00305879	−	0.00529799i
$529$	−22.9987			−0.999942
$530$	8.55039			0.371405
$531$	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
$535$	−2.73522	+	4.73753i	−0.118254	+	0.204821i
$536$	2.42903	−	4.20720i	0.104918	−	0.181724i
$537$	6.48961	+	11.2403i	0.280047	+	0.485056i
$538$	−0.897277			−0.0386843
$539$	0.973511	−	0.143293i	0.0419321	−	0.00617205i
$540$	0.611519	−	1.05918i	0.0263156	−	0.0455799i
$541$	−0.886405	+	1.53530i	−0.0381095	+	0.0660077i	−0.884451	−	0.466633i	$-0.845467\pi$
$541$	−0.886405	+	1.53530i	−0.0381095	+	0.0660077i	0.846342	+	0.532641i	$0.178800\pi$
$542$	13.8751			0.595988
$543$	−11.8663	+	20.5531i	−0.509233	+	0.882017i
$544$	0.186556			0.00799854
$545$	−9.38523			−0.402019
$546$	9.45987	+	1.22917i	0.404845	+	0.0526035i
$547$	9.88287			0.422561			0.211280	−	0.977425i	$-0.432237\pi$
$547$	9.88287			0.422561			0.211280	+	0.977425i	$0.432237\pi$
$548$	2.69210			0.115001
$549$	−0.186556	+	0.323125i	−0.00796203	+	0.0137906i
$550$	−0.492588			−0.0210040
$551$	2.68179	−	4.64499i	0.114248	−	0.197883i
$552$	−0.0182404	+	0.0315933i	−0.000776364	+	0.00134470i
$553$	8.76624	+	12.9056i	0.372779	+	0.548802i
$554$	−20.4739			−0.869852
$555$	−0.222353	−	0.385127i	−0.00943838	−	0.0163477i
$556$	5.28925	−	9.16126i	0.224314	−	0.388524i
$557$	−10.0865	+	17.4704i	−0.427380	+	0.740244i	−0.996639	−	0.0819139i	$-0.973897\pi$
$557$	−10.0865	+	17.4704i	−0.427380	+	0.740244i	0.569259	+	0.822158i	$0.307230\pi$
$558$	−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
$562$	5.11819			0.215898
$563$	−0.106297			−0.00447988			−0.00223994	−	0.999997i	$-0.500713\pi$
$563$	−0.106297			−0.00447988			−0.00223994	+	0.999997i	$0.500713\pi$
$564$	0.358745	+	0.621364i	0.0151059	+	0.0261642i
$565$	7.56109	+	13.0962i	0.318097	+	0.550961i
$566$	−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
$569$	−7.66181			−0.321200			−0.160600	−	0.987020i	$-0.551343\pi$
$569$	−7.66181			−0.321200			−0.160600	+	0.987020i	$0.551343\pi$
$570$	0.547865	−	0.948930i	0.0229475	−	0.0397463i
$571$	−1.44075	−	2.49545i	−0.0602935	−	0.104431i	0.834303	−	0.551306i	$-0.185870\pi$
$571$	−1.44075	−	2.49545i	−0.0602935	−	0.104431i	−0.894597	+	0.446875i	$0.852537\pi$
$572$	0.160068	+	0.480898i	0.00669276	+	0.0201074i
$573$	−19.9778			−0.834587
$574$	8.99686	−	0.658583i	0.375522	−	0.0274887i
$575$	0.0639177	+	0.110709i	0.00266555	+	0.00461687i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	17.3055	+	29.9740i	0.720438	+	1.24783i	0.960825	+	0.277157i	$0.0893923\pi$
$577$	17.3055	+	29.9740i	0.720438	+	1.24783i	−0.240387	+	0.970677i	$0.577274\pi$
$578$	−16.9652			−0.705659
$579$	3.11194	+	5.39003i	0.129328	+	0.224002i
$580$	7.32200			0.304029
$581$	−10.5306	+	21.7706i	−0.436881	+	0.903195i
$582$	3.24059	+	5.61287i	0.134327	+	0.232661i
$583$	−0.982751			−0.0407014
$584$	−4.80900	−	8.32943i	−0.198998	−	0.344674i
$585$	−2.92715	+	3.29810i	−0.121023	+	0.136360i
$586$	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	$0.902368\pi$
$588$	6.92538	−	1.01936i	0.285598	−	0.0420376i
$589$	−1.63100	+	2.82497i	−0.0672041	+	0.116401i
$590$	−4.27833	+	7.41029i	−0.176136	+	0.305077i
$591$	−24.5006			−1.00782
$592$	−0.363609			−0.0149442
$593$	10.9551	−	18.9748i	0.449873	−	0.779203i	−0.548505	−	0.836148i	$-0.684803\pi$
$593$	10.9551	−	18.9748i	0.449873	−	0.779203i	0.998377	+	0.0569451i	$0.0181360\pi$
$594$	−0.0702857	+	0.121738i	−0.00288386	+	0.00499499i
$595$	−0.339196	−	0.499362i	−0.0139057	−	0.0204718i
$596$	5.95244	+	10.3099i	0.243822	+	0.422311i
$597$	9.80754	−	16.9872i	0.401396	−	0.695238i
$598$	0.0873112	−	0.0983759i	0.00357042	−	0.00402289i
$599$	−7.67924	−	13.3008i	−0.313765	−	0.543457i	0.665409	−	0.746479i	$-0.268257\pi$
$599$	−7.67924	−	13.3008i	−0.313765	−	0.543457i	−0.979174	+	0.203022i	$0.934924\pi$
$600$	−3.50418			−0.143058
$601$	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	$0.812049\pi$
$602$	6.14988	+	9.05381i	0.250650	+	0.369006i
$603$	−4.85806			−0.197836
$604$	−3.66774	−	6.35272i	−0.149238	−	0.258488i
$605$	13.4292			0.545976
$606$	1.50230	+	2.60206i	0.0610268	+	0.105701i
$607$	−16.5768	−	28.7118i	−0.672830	−	1.16538i	−0.977098	−	0.212790i	$-0.931745\pi$
$607$	−16.5768	−	28.7118i	−0.672830	−	1.16538i	0.304268	−	0.952587i	$-0.401588\pi$
$608$	−0.447955	−	0.775880i	−0.0181670	−	0.0314661i
$609$	−6.89712	+	14.2589i	−0.279486	+	0.577800i
$610$	−0.456331			−0.0184763
$611$	−0.816999	−	2.45455i	−0.0330522	−	0.0993003i
$612$	−0.0932782	−	0.161563i	−0.00377055	−	0.00653078i
$613$	17.1792	−	29.7553i	0.693863	−	1.20181i	−0.276700	−	0.960956i	$-0.589241\pi$
$613$	17.1792	−	29.7553i	0.693863	−	1.20181i	0.970562	−	0.240849i	$-0.0774260\pi$
$614$	30.0806			1.21395
$615$	−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	$0.301578\pi$
$618$	−4.12788	−	7.14970i	−0.166048	−	0.287603i
$619$	−6.14114	−	10.6368i	−0.246833	−	0.427528i	0.715812	−	0.698293i	$-0.246057\pi$
$619$	−6.14114	−	10.6368i	−0.246833	−	0.427528i	−0.962645	+	0.270765i	$0.912723\pi$
$620$	−4.45307			−0.178839
$621$	0.0364808			0.00146393
$622$	−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
$626$	−3.43002	+	5.94097i	−0.137091	+	0.237449i
$627$	−0.0629697	+	0.109067i	−0.00251477	+	0.00435570i
$628$	5.15138	+	8.92246i	0.205563	+	0.356045i
$629$	−0.0678335			−0.00270470
$630$	−1.40902	+	2.91297i	−0.0561368	+	0.116056i
$631$	−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
$633$	5.99270			0.238189
$634$	3.37146	−	5.83953i	0.133898	−	0.231917i
$635$	−13.3417			−0.529448
$636$	−6.99111			−0.277216
$637$	−25.1991	−	1.41617i	−0.998425	−	0.0561105i
$638$	−0.841564			−0.0333178
$639$	10.6240			0.420278
$640$	0.611519	−	1.05918i	0.0241724	−	0.0418678i
$641$	−36.0597			−1.42427			−0.712136	−	0.702041i	$-0.752272\pi$
$641$	−36.0597			−1.42427			−0.712136	+	0.702041i	$0.752272\pi$
$642$	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	$-0.0155247\pi$
$644$	0.0420284	−	0.0868883i	0.00165615	−	0.00342388i
$645$	−5.05947			−0.199217
$646$	−0.0835688	−	0.144745i	−0.00328797	−	0.00569493i
$647$	−3.07080	+	5.31878i	−0.120726	+	0.209103i	−0.920054	−	0.391792i	$-0.871855\pi$
$647$	−3.07080	+	5.31878i	−0.120726	+	0.209103i	0.799328	+	0.600894i	$0.205189\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	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
$653$	−24.3606			−0.953304			−0.476652	−	0.879092i	$-0.658150\pi$
$653$	−24.3606			−0.953304			−0.476652	+	0.879092i	$0.658150\pi$
$654$	7.67371			0.300066
$655$	13.4185	+	23.2416i	0.524305	+	0.908123i
$656$	1.70480	+	2.95279i	0.0665611	+	0.115287i
$657$	−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	$0.0986291\pi$
$660$	−0.171924			−0.00669214
$661$	18.6363	−	32.2789i	0.724866	−	1.25551i	−0.234163	−	0.972197i	$-0.575235\pi$
$661$	18.6363	−	32.2789i	0.724866	−	1.25551i	0.959029	−	0.283308i	$-0.0914319\pi$
$662$	5.54908	+	9.61129i	0.215671	+	0.373553i
$663$	0.212430	+	0.638213i	0.00825010	+	0.0247861i
$664$	−9.14057			−0.354723
$665$	−1.26236	+	2.60976i	−0.0489521	+	0.101202i
$666$	0.181804	+	0.314894i	0.00704477	+	0.0122019i
$667$	0.109201	+	0.189141i	0.00422826	+	0.00732356i
$668$	−4.28857	−	7.42802i	−0.165930	−	0.287399i
$669$	−27.6197			−1.06784
$670$	−2.97079	−	5.14557i	−0.114772	−	0.198791i
$671$	0.0524490			0.00202477
$672$	1.48662	+	2.18860i	0.0573477	+	0.0844269i
$673$	−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	$-0.487538\pi$
$674$	21.6470			0.833810
$675$	1.75209	+	3.03471i	0.0674380	+	0.116806i
$676$	−1.54380	−	12.9080i	−0.0593768	−	0.496462i
$677$	−20.6518	+	35.7700i	−0.793713	+	1.37475i	0.129940	+	0.991522i	$0.458522\pi$
$677$	−20.6518	+	35.7700i	−0.793713	+	1.37475i	−0.923653	+	0.383230i	$0.874812\pi$
$678$	−6.18222	−	10.7079i	−0.237427	−	0.411235i
$679$	−9.63509	−	14.1847i	−0.369761	−	0.544359i
$680$	0.114083	−	0.197597i	0.00437487	−	0.00757750i
$681$	0.895645	−	1.55130i	0.0343212	−	0.0594460i
$682$	0.511819			0.0195986
$683$	27.5816			1.05538			0.527690	−	0.849437i	$-0.323058\pi$
$683$	27.5816			1.05538			0.527690	+	0.849437i	$0.323058\pi$
$684$	−0.447955	+	0.775880i	−0.0171280	+	0.0296665i
$685$	1.64627	−	2.85143i	0.0629008	−	0.108947i
$686$	−18.0770	+	4.02745i	−0.690185	+	0.153769i
$687$	12.6142	+	21.8485i	0.481263	+	0.833572i
$688$	−2.06841	+	3.58258i	−0.0788572	+	0.136585i
$689$	24.6929	+	5.06419i	0.940723	+	0.192930i
$690$	0.0223087	+	0.0386398i	0.000849278	+	0.00147099i
$691$	29.3993			1.11840			0.559202	−	0.829032i	$-0.311108\pi$
$691$	29.3993			1.11840			0.559202	+	0.829032i	$0.311108\pi$
$692$	5.33942	+	9.24815i	0.202974	+	0.351562i
$693$	0.161948	−	0.334806i	0.00615189	−	0.0127182i
$694$	29.8675			1.13375
$695$	−6.46895	−	11.2046i	−0.245381	−	0.425013i
$696$	−5.98674			−0.226927
$697$	0.318041	+	0.550863i	0.0120466	+	0.0208654i
$698$	−6.47690	−	11.2183i	−0.245154	−	0.424619i
$699$	14.1852	+	24.5695i	0.536534	+	0.929304i
$700$	9.24645	−	0.676853i	0.349483	−	0.0255826i
$701$	19.0498			0.719500			0.359750	−	0.933049i	$-0.382862\pi$
$701$	19.0498			0.719500			0.359750	+	0.933049i	$0.382862\pi$
$702$	2.39335	−	2.69665i	0.0903310	−	0.101778i
$703$	0.162880	+	0.282117i	0.00614314	+	0.0106402i
$704$	−0.0702857	+	0.121738i	−0.00264899	+	0.00458819i
$705$	0.877516			0.0330492
$706$	−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
$709$	−8.95282	−	15.5067i	−0.336230	−	0.582368i	0.647490	−	0.762074i	$-0.275819\pi$
$709$	−8.95282	−	15.5067i	−0.336230	−	0.582368i	−0.983720	+	0.179706i	$0.942485\pi$
$710$	6.49675	+	11.2527i	0.243819	+	0.422306i
$711$	5.89675			0.221145
$712$	−6.35472			−0.238153
$713$	−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
$717$	14.4827	−	25.0848i	0.540867	−	0.936809i
$718$	12.4203	−	21.5125i	0.463520	−	0.802840i
$719$	−17.1583	−	29.7191i	−0.639897	−	1.10833i	−0.985455	−	0.169936i	$-0.945644\pi$
$719$	−17.1583	−	29.7191i	−0.639897	−	1.10833i	0.345558	−	0.938397i	$-0.387690\pi$
$720$	−1.22304			−0.0455799
$721$	12.2732	+	18.0685i	0.457078	+	0.672907i
$722$	9.09867	−	15.7594i	0.338618	−	0.586503i
$723$	6.59757	−	11.4273i	0.245366	−	0.424987i
$724$	23.7327			0.882017
$725$	−10.4893	+	18.1680i	−0.389563	+	0.674743i
$726$	−10.9802			−0.407515
$727$	20.6482			0.765800			0.382900	−	0.923790i	$-0.374925\pi$
$727$	20.6482			0.765800			0.382900	+	0.923790i	$0.374925\pi$
$728$	−3.66544	−	8.80707i	−0.135850	−	0.326412i
$729$	1.00000			0.0370370
$730$	−11.7632			−0.435374
$731$	−0.385874	+	0.668354i	−0.0142721	+	0.0247199i
$732$	0.373113			0.0137906
$733$	14.5834	−	25.2592i	0.538650	−	0.932969i	−0.460327	−	0.887749i	$-0.652268\pi$
$733$	14.5834	−	25.2592i	0.538650	−	0.932969i	0.998977	−	0.0452199i	$-0.0143988\pi$
$734$	−18.0306	+	31.2299i	−0.665521	+	1.15272i
$735$	3.15532	−	7.95859i	0.116386	−	0.293557i
$736$	0.0364808			0.00134470
$737$	0.341452	+	0.591413i	0.0125776	+	0.0217850i
$738$	1.70480	−	2.95279i	0.0627544	−	0.108694i
$739$	21.1080	−	36.5602i	0.776471	−	1.34489i	−0.157493	−	0.987520i	$-0.550341\pi$
$739$	21.1080	−	36.5602i	0.776471	−	1.34489i	0.933964	−	0.357367i	$-0.116326\pi$
$740$	−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	$0.727793\pi$
$744$	3.64099			0.133485
$745$	14.5601			0.533441
$746$	7.37092	+	12.7668i	0.269869	+	0.467426i
$747$	4.57029	+	7.91597i	0.167218	+	0.289630i
$748$	−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
$751$	31.3274			1.14315			0.571576	−	0.820549i	$-0.306332\pi$
$751$	31.3274			1.14315			0.571576	+	0.820549i	$0.306332\pi$
$752$	0.358745	−	0.621364i	0.0130821	−	0.0226588i
$753$	4.73276	+	8.19739i	0.172472	+	0.298729i
$754$	21.1454	+	4.33664i	0.770069	+	0.157931i
$755$	−8.97157			−0.326509
$756$	1.15207	−	2.38175i	0.0419003	−	0.0866235i
$757$	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	$0.677514\pi$
$758$	5.33674	+	9.24351i	0.193839	+	0.335739i
$759$	−0.00256408	−	0.00444112i	−9.30703e−5	−	0.000161202i
$760$	−1.09573			−0.0397463
$761$	0.477691	+	0.827386i	0.0173163	+	0.0299927i	0.874554	−	0.484929i	$-0.161154\pi$
$761$	0.477691	+	0.827386i	0.0173163	+	0.0299927i	−0.857237	+	0.514921i	$0.827821\pi$
$762$	10.9086			0.395179
$763$	−20.2486	+	1.48222i	−0.733047	+	0.0536600i
$764$	9.98892	+	17.3013i	0.361387	+	0.625940i
$765$	−0.228165			−0.00824933
$766$	10.2017	+	17.6698i	0.368601	+	0.638436i
$767$	−16.7444	+	18.8664i	−0.604606	+	0.681225i
$768$	−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	$0.832527\pi$
$770$	0.453655	−	0.0332082i	0.0163486	−	0.00119674i
$771$	5.11789	−	8.86444i	0.184316	−	0.319245i
$772$	3.11194	−	5.39003i	0.112001	−	0.193992i
$773$	16.3472			0.587968			0.293984	−	0.955810i	$-0.405019\pi$
$773$	16.3472			0.587968			0.293984	+	0.955810i	$0.405019\pi$
$774$	4.13681			0.148695
$775$	6.37934	−	11.0493i	0.229153	−	0.396904i
$776$	3.24059	−	5.61287i	0.116331	−	0.201490i
$777$	−0.540549	−	0.795792i	−0.0193921	−	0.0285489i
$778$	−15.8455	−	27.4453i	−0.568090	−	0.983960i
$779$	1.52734	−	2.64544i	0.0547228	−	0.0947826i
$780$	4.31981	+	0.885937i	0.154674	+	0.0317216i
$781$	−0.746713	−	1.29335i	−0.0267195	−	0.0462795i
$782$	0.00680573			0.000243372
$783$	2.99337	+	5.18466i	0.106974	+	0.185285i
$784$	−4.34548	−	5.48788i	−0.155196	−	0.195996i
$785$	12.6007			0.449737
$786$	−10.9715	−	19.0032i	−0.391340	−	0.677820i
$787$	35.7105			1.27294			0.636471	−	0.771301i	$-0.280394\pi$
$787$	35.7105			1.27294			0.636471	+	0.771301i	$0.280394\pi$
$788$	12.2503	+	21.2182i	0.436400	+	0.755866i
$789$	2.42308	+	4.19690i	0.0862640	+	0.149414i
$790$	3.60597	+	6.24573i	0.128295	+	0.222213i
$791$	18.3813	+	27.0608i	0.653563	+	0.962170i
$792$	0.140571			0.00499499
$793$	−1.31785	−	0.270273i	−0.0467981	−	0.00959769i
$794$	1.30524	+	2.26074i	0.0463212	+	0.0802306i
$795$	−4.27519	+	7.40485i	−0.151626	+	0.262623i
$796$	−19.6151			−0.695238
$797$	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
$800$	1.75209	+	3.03471i	0.0619457	+	0.107293i
$801$	3.17736	+	5.50335i	0.112266	+	0.194451i
$802$	−16.3696			−0.578030
$803$	1.35202			0.0477116
$804$	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
$808$	1.50230	−	2.60206i	0.0528507	−	0.0915401i
$809$	13.9783	−	24.2112i	0.491452	−	0.851220i	−0.508499	−	0.861062i	$-0.669800\pi$
$809$	13.9783	−	24.2112i	0.491452	−	0.851220i	0.999952	+	0.00984234i	$0.00313297\pi$
$810$	0.611519	+	1.05918i	0.0214866	+	0.0372158i
$811$	49.6578			1.74372			0.871861	−	0.489754i	$-0.162913\pi$
$811$	49.6578			1.74372			0.871861	+	0.489754i	$0.162913\pi$
$812$	15.7971	−	1.15637i	0.554371	−	0.0405807i
$813$	−6.93756	+	12.0162i	−0.243311	+	0.421427i
$814$	0.0255565	−	0.0442652i	0.000895755	−	0.00155149i
$815$	12.3980			0.434282
$816$	−0.0932782	+	0.161563i	−0.00326539	+	0.00565582i
$817$	3.70621			0.129664
$818$	22.7307			0.794759
$819$	−5.79443	+	7.57790i	−0.202474	+	0.264793i
$820$	4.17006			0.145625
$821$	−40.7269			−1.42138			−0.710690	−	0.703506i	$-0.751617\pi$
$821$	−40.7269			−1.42138			−0.710690	+	0.703506i	$0.751617\pi$
$822$	−1.34605	+	2.33143i	−0.0469490	+	0.0813180i
$823$	−53.6630			−1.87058			−0.935288	−	0.353889i	$-0.884859\pi$
$823$	−53.6630			−1.87058			−0.935288	+	0.353889i	$0.884859\pi$
$824$	−4.12788	+	7.14970i	−0.143801	+	0.249071i
$825$	0.246294	−	0.426594i	0.00857485	−	0.0148521i
$826$	−8.06014	+	16.6633i	−0.280448	+	0.579790i
$827$	55.5393			1.93129			0.965646	−	0.259862i	$-0.0836769\pi$
$827$	55.5393			1.93129			0.965646	+	0.259862i	$0.0836769\pi$
$828$	−0.0182404	−	0.0315933i	−0.000633898	−	0.00109794i
$829$	16.6472	−	28.8337i	0.578180	−	1.00144i	−0.417508	−	0.908673i	$-0.637097\pi$
$829$	16.6472	−	28.8337i	0.578180	−	1.00144i	0.995688	−	0.0927638i	$-0.0295701\pi$
$830$	−5.58963	+	9.68152i	−0.194019	+	0.336051i
$831$	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
$835$	−10.4902			−0.363027
$836$	0.125939			0.00435570
$837$	−1.82050	−	3.15319i	−0.0629255	−	0.108990i
$838$	−11.4491	−	19.8303i	−0.395501	−	0.685028i
$839$	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
$842$	8.33173			0.287130
$843$	−2.55910	+	4.43249i	−0.0881400	+	0.152663i
$844$	−2.99635	−	5.18983i	−0.103139	−	0.178641i
$845$	−14.6160	−	6.25833i	−0.502805	−	0.215293i
$846$	−0.717490			−0.0246678
$847$	28.9735	−	2.12090i	0.995540	−	0.0728749i
$848$	3.49556	+	6.05448i	0.120038	+	0.207912i
$849$	−4.54066	−	7.86466i	−0.155835	−	0.269914i
$850$	0.326863	+	0.566144i	0.0112113	+	0.0194186i
$851$	−0.0132647			−0.000454710
$852$	−5.31198	−	9.20062i	−0.181986	−	0.315208i
$853$	−24.0993			−0.825143			−0.412572	−	0.910925i	$-0.635369\pi$
$853$	−24.0993			−0.825143			−0.412572	+	0.910925i	$0.635369\pi$
$854$	−0.984529	+	0.0720689i	−0.0336899	+	0.00246615i
$855$	0.547865	+	0.948930i	0.0187366	+	0.0324527i
$856$	−4.47283			−0.152878
$857$	0.639263	+	1.10724i	0.0218368	+	0.0378225i	0.876737	−	0.480970i	$-0.159715\pi$
$857$	0.639263	+	1.10724i	0.0218368	+	0.0378225i	−0.854900	+	0.518792i	$0.826382\pi$
$858$	−0.496504	−	0.101826i	−0.0169504	−	0.00347630i
$859$	−3.92591	+	6.79988i	−0.133950	+	0.232009i	−0.925196	−	0.379490i	$-0.876100\pi$
$859$	−3.92591	+	6.79988i	−0.133950	+	0.232009i	0.791246	+	0.611498i	$0.209433\pi$
$860$	2.52974	+	4.38163i	0.0862633	+	0.149412i
$861$	−3.92808	+	8.12080i	−0.133869	+	0.276756i
$862$	13.7933	−	23.8907i	0.469802	−	0.813722i
$863$	19.2024	−	33.2595i	0.653656	−	1.13217i	−0.328573	−	0.944479i	$-0.606568\pi$
$863$	19.2024	−	33.2595i	0.653656	−	1.13217i	0.982229	−	0.187687i	$-0.0600990\pi$
$864$	1.00000			0.0340207
$865$	13.0606			0.444074
$866$	−15.7254	+	27.2372i	−0.534370	+	0.925556i
$867$	8.48260	−	14.6923i	0.288084	−	0.498976i
$868$	−9.60745	+	0.703279i	−0.326098	+	0.0238708i
$869$	−0.414457	−	0.717861i	−0.0140595	−	0.0243518i
$870$	−3.66100	+	6.34104i	−0.124120	+	0.214981i
$871$	−5.53183	−	16.6195i	−0.187439	−	0.563131i
$872$	−3.83686	−	6.64563i	−0.129932	−	0.225049i
$873$	−6.48119			−0.219355
$874$	−0.0163418	−	0.0283048i	−0.000552768	−	0.000957423i
$875$	11.9826	−	24.7724i	0.405085	−	0.837461i
$876$	9.61800			0.324962
$877$	−9.55295	−	16.5462i	−0.322580	−	0.558725i	0.658439	−	0.752634i	$-0.271217\pi$
$877$	−9.55295	−	16.5462i	−0.322580	−	0.558725i	−0.981020	+	0.193908i	$0.937884\pi$
$878$	−15.2460			−0.514529
$879$	3.13195	+	5.42469i	0.105638	+	0.182970i
$880$	0.0859621	+	0.148891i	0.00289778	+	0.00501910i
$881$	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	$0.681301\pi$
$882$	−2.57990	+	6.50724i	−0.0868698	+	0.219110i
$883$	35.8526			1.20654			0.603268	−	0.797538i	$-0.293865\pi$
$883$	35.8526			1.20654			0.603268	+	0.797538i	$0.293865\pi$
$884$	0.446494	−	0.503076i	0.0150172	−	0.0169203i
$885$	−4.27833	−	7.41029i	−0.143814	−	0.249094i
$886$	10.7666	−	18.6482i	0.361710	−	0.626500i
$887$	−7.43855			−0.249762			−0.124881	−	0.992172i	$-0.539855\pi$
$887$	−7.43855			−0.249762			−0.124881	+	0.992172i	$0.539855\pi$
$888$	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
$891$	−0.0702857	−	0.121738i	−0.00235466	−	0.00407839i
$892$	13.8098	+	23.9193i	0.462388	+	0.800879i
$893$	−0.642806			−0.0215107
$894$	−11.9049			−0.398159
$895$	−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
$899$	10.8988	−	18.8773i	0.363496	−	0.629594i
$900$	1.75209	−	3.03471i	0.0584030	−	0.101157i
$901$	0.652118	+	1.12950i	0.0217252	+	0.0376292i
$902$	−0.479292			−0.0159587
$903$	−10.9158	+	0.799049i	−0.363254	+	0.0265907i
$904$	−6.18222	+	10.7079i	−0.205618	+	0.356140i
$905$	14.5130	−	25.1372i	0.482427	−	0.835588i
$906$	7.33549			0.243705
$907$	−3.64524	+	6.31374i	−0.121038	+	0.209644i	−0.920177	−	0.391502i	$-0.871956\pi$
$907$	−3.64524	+	6.31374i	−0.121038	+	0.209644i	0.799139	+	0.601146i	$0.205289\pi$
$908$	−1.79129			−0.0594460
$909$	−3.00460			−0.0996563
$910$	−11.5698	−	1.50332i	−0.383534	−	0.0498345i
$911$	8.89914			0.294842			0.147421	−	0.989074i	$-0.452903\pi$
$911$	8.89914			0.294842			0.147421	+	0.989074i	$0.452903\pi$
$912$	0.895909			0.0296665
$913$	0.642452	−	1.11276i	0.0212621	−	0.0368270i
$914$	−32.0373			−1.05970
$915$	0.228165	−	0.395194i	0.00754291	−	0.0130647i
$916$	12.6142	−	21.8485i	0.416786	−	0.721895i
$917$	32.6209	+	48.0243i	1.07724	+	1.58590i
$918$	0.186556			0.00615728
$919$	3.63489	+	6.29581i	0.119904	+	0.207680i	0.919729	−	0.392553i	$-0.128408\pi$
$919$	3.63489	+	6.29581i	0.119904	+	0.207680i	−0.799826	+	0.600233i	$0.795075\pi$
$920$	0.0223087	−	0.0386398i	0.000735496	−	0.00127392i
$921$	−15.0403	+	26.0506i	−0.495595	+	0.858395i
$922$	−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
$926$	−11.6453			−0.382688
$927$	8.25576			0.271155
$928$	2.99337	+	5.18466i	0.0982621	+	0.170195i
$929$	−3.30467	−	5.72385i	−0.108423	−	0.187793i	0.806709	−	0.590949i	$-0.201247\pi$
$929$	−3.30467	−	5.72385i	−0.108423	−	0.187793i	−0.915131	+	0.403156i	$0.867913\pi$
$930$	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
$933$	27.6583			0.905493
$934$	2.99029	−	5.17934i	0.0978453	−	0.169473i
$935$	0.0160368	+	0.0277765i	0.000524458	+	0.000908389i
$936$	−3.53204	−	0.724375i	−0.115448	−	0.0236769i
$937$	−44.3217			−1.44793			−0.723963	−	0.689838i	$-0.757682\pi$
$937$	−44.3217			−1.44793			−0.723963	+	0.689838i	$0.757682\pi$
$938$	−7.22211	−	10.6323i	−0.235810	−	0.347158i
$939$	−3.43002	−	5.94097i	−0.111935	−	0.193876i
$940$	−0.438758	−	0.759952i	−0.0143107	−	0.0247869i
$941$	8.06612	+	13.9709i	0.262948	+	0.455440i	0.967024	−	0.254685i	$-0.0819719\pi$
$941$	8.06612	+	13.9709i	0.262948	+	0.455440i	−0.704076	+	0.710125i	$0.748639\pi$
$942$	−10.3028			−0.335682
$943$	0.0621924	+	0.107720i	0.00202526	+	0.00350786i
$944$	−6.99624			−0.227708
$945$	−1.81820	−	2.67673i	−0.0591459	−	0.0870742i
$946$	−0.290759	−	0.503609i	−0.00945338	−	0.0163737i
$947$	7.96489			0.258824			0.129412	−	0.991591i	$-0.458691\pi$
$947$	7.96489			0.258824			0.129412	+	0.991591i	$0.458691\pi$
$948$	−2.94837	−	5.10673i	−0.0957587	−	0.165859i
$949$	−33.9711	−	6.96704i	−1.10275	−	0.226160i
$950$	1.56971	−	2.71882i	0.0509282	−	0.0882103i
$951$	3.37146	+	5.83953i	0.109327	+	0.189360i
$952$	0.214926	−	0.444331i	0.00696578	−	0.0144008i
$953$	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
$955$	24.4336			0.790654
$956$	−28.9654			−0.936809
$957$	0.420782	−	0.728816i	0.0136020	−	0.0235593i
$958$	−3.33079	+	5.76911i	−0.107613	+	0.186391i
$959$	3.10149	−	6.41192i	0.100152	−	0.207052i
$960$	0.611519	+	1.05918i	0.0197367	+	0.0341849i
$961$	8.87159	−	15.3660i	0.286180	−	0.495679i
$962$	−0.870241	+	0.980524i	−0.0280577	+	0.0316134i
$963$	2.23641	+	3.87358i	0.0720674	+	0.124824i
$964$	−13.1951			−0.424987
$965$	−3.80602	−	6.59221i	−0.122520	−	0.212211i
$966$	0.0542333	+	0.0798418i	0.00174493	+	0.00256887i
$967$	−8.68636			−0.279335			−0.139667	−	0.990198i	$-0.544603\pi$
$967$	−8.68636			−0.279335			−0.139667	+	0.990198i	$0.544603\pi$
$968$	5.49012	+	9.50917i	0.176459	+	0.305636i
$969$	0.167138			0.00536923
$970$	−3.96337	−	6.86475i	−0.127256	−	0.220414i
$971$	−13.9015	−	24.0781i	−0.446120	−	0.772703i	0.552009	−	0.833838i	$-0.313861\pi$
$971$	−13.9015	−	24.0781i	−0.446120	−	0.772703i	−0.998130	+	0.0611349i	$0.980528\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−15.7263	−	23.1521i	−0.504161	−	0.742222i
$974$	−18.9362			−0.606753
$975$	−8.38671	+	9.44953i	−0.268590	+	0.302627i
$976$	−0.186556	−	0.323125i	−0.00597152	−	0.0103430i
$977$	21.1398	−	36.6152i	0.676322	−	1.17142i	−0.299759	−	0.954015i	$-0.596906\pi$
$977$	21.1398	−	36.6152i	0.676322	−	1.17142i	0.976081	−	0.217409i	$-0.0697605\pi$
$978$	−10.1370			−0.324147
$979$	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
$982$	−19.5234	−	33.8155i	−0.623017	−	1.07910i
$983$	−20.5285	−	35.5564i	−0.654757	−	1.13407i	−0.981955	−	0.189117i	$-0.939437\pi$
$983$	−20.5285	−	35.5564i	−0.654757	−	1.13407i	0.327197	−	0.944956i	$-0.393896\pi$
$984$	−3.40959			−0.108694
$985$	29.9652			0.954771
$986$	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
$990$	0.0859621	−	0.148891i	0.00273205	−	0.00473206i
$991$	13.7587	−	23.8308i	0.437061	−	0.757012i	−0.560401	−	0.828222i	$-0.689353\pi$
$991$	13.7587	−	23.8308i	0.437061	−	0.757012i	0.997461	+	0.0712102i	$0.0226861\pi$
$992$	−1.82050	−	3.15319i	−0.0578008	−	0.100114i
$993$	−11.0982			−0.352189
$994$	15.7938	+	23.2516i	0.500950	+	0.737495i
$995$	−11.9950	+	20.7759i	−0.380267	+	0.658641i
$996$	4.57029	−	7.91597i	0.144815	−	0.250827i
$997$	36.8679			1.16762			0.583810	−	0.811891i	$-0.301561\pi$
$997$	36.8679			1.16762			0.583810	+	0.811891i	$0.301561\pi$
$998$	−16.6602	+	28.8563i	−0.527369	+	0.913430i
$999$	−0.363609			−0.0115041

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.3	✓	8	1.1	even	1	trivial
546.2.j.c.529.3	yes	8	91.74	even	3	inner
546.2.k.c.373.3	yes	8	13.9	even	3
546.2.k.c.445.3	yes	8	7.4	even	3
1638.2.m.h.289.2		8	3.2	odd	2
1638.2.m.h.1621.2		8	273.74	odd	6
1638.2.p.h.919.2		8	39.35	odd	6
1638.2.p.h.991.2		8	21.11	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.611519 - 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.15207 - 2.38175i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.611519 - 1.05918i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.15207 - 2.38175i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.611519 - 1.05918i) q^{10} +(-0.0702857 + 0.121738i) 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} +1.00000 q^{16} +0.186556 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.447955 - 0.775880i) q^{19} +(0.611519 - 1.05918i) q^{20} +(1.48662 + 2.18860i) q^{21} +(-0.0702857 + 0.121738i) q^{22} +0.0364808 q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.75209 + 3.03471i) q^{25} +(2.39335 - 2.69665i) q^{26} +1.00000 q^{27} +(1.15207 - 2.38175i) q^{28} +(2.99337 + 5.18466i) q^{29} +(0.611519 + 1.05918i) q^{30} +(-1.82050 - 3.15319i) q^{31} +1.00000 q^{32} +(-0.0702857 - 0.121738i) q^{33} +0.186556 q^{34} +(-1.81820 - 2.67673i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.363609 q^{37} +(-0.447955 - 0.775880i) q^{38} +(1.13869 + 3.42102i) q^{39} +(0.611519 - 1.05918i) q^{40} +(1.70480 + 2.95279i) q^{41} +(1.48662 + 2.18860i) q^{42} +(-2.06841 + 3.58258i) q^{43} +(-0.0702857 + 0.121738i) q^{44} -1.22304 q^{45} +0.0364808 q^{46} +(0.358745 - 0.621364i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.34548 - 5.48788i) q^{49} +(1.75209 + 3.03471i) q^{50} +(-0.0932782 + 0.161563i) q^{51} +(2.39335 - 2.69665i) q^{52} +(3.49556 + 6.05448i) q^{53} +1.00000 q^{54} +(0.0859621 + 0.148891i) q^{55} +(1.15207 - 2.38175i) q^{56} +0.895909 q^{57} +(2.99337 + 5.18466i) q^{58} -6.99624 q^{59} +(0.611519 + 1.05918i) q^{60} +(-0.186556 - 0.323125i) q^{61} +(-1.82050 - 3.15319i) q^{62} +(-2.63869 + 0.193156i) q^{63} +1.00000 q^{64} +(-1.39266 - 4.18404i) q^{65} +(-0.0702857 - 0.121738i) q^{66} +(2.42903 - 4.20720i) q^{67} +0.186556 q^{68} +(-0.0182404 + 0.0315933i) q^{69} +(-1.81820 - 2.67673i) q^{70} +(-5.31198 + 9.20062i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-4.80900 - 8.32943i) q^{73} -0.363609 q^{74} -3.50418 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} +(0.611519 - 1.05918i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.70480 + 2.95279i) q^{82} -9.14057 q^{83} +(1.48662 + 2.18860i) q^{84} +(0.114083 - 0.197597i) q^{85} +(-2.06841 + 3.58258i) q^{86} -5.98674 q^{87} +(-0.0702857 + 0.121738i) q^{88} -6.35472 q^{89} -1.22304 q^{90} +(-3.66544 - 8.80707i) q^{91} +0.0364808 q^{92} +3.64099 q^{93} +(0.358745 - 0.621364i) q^{94} -1.09573 q^{95} +(-0.500000 + 0.866025i) q^{96} +(3.24059 - 5.61287i) q^{97} +(-4.34548 - 5.48788i) q^{98} +0.140571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more