LMFDB - Embedded newform 798.2.j.l.571.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(457,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("798.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
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			571.2
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	798.571
Dual form			798.2.j.l.457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.05903 - 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 + 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.05903 - 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 + 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.05903 - 1.83430i) q^{10} +(-1.67602 + 2.90295i) q^{11} +(0.500000 + 0.866025i) q^{12} -4.23612 q^{13} +(-2.63557 + 0.231865i) q^{14} -2.11806 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.47814 + 6.02432i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +2.11806 q^{20} +(1.51859 + 2.16654i) q^{21} -3.35203 q^{22} +(3.59035 + 6.21867i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.256906 - 0.444974i) q^{25} +(-2.11806 - 3.66859i) q^{26} -1.00000 q^{27} +(-1.51859 - 2.16654i) q^{28} +7.29877 q^{29} +(-1.05903 - 1.83430i) q^{30} +(-2.27442 + 3.93940i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.67602 + 2.90295i) q^{33} -6.95628 q^{34} +(5.58231 - 0.491104i) q^{35} +1.00000 q^{36} +(0.126109 + 0.218427i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-2.11806 + 3.66859i) q^{39} +(1.05903 + 1.83430i) q^{40} -10.3359 q^{41} +(-1.11699 + 2.39840i) q^{42} +3.17133 q^{43} +(-1.67602 - 2.90295i) q^{44} +(-1.05903 + 1.83430i) q^{45} +(-3.59035 + 6.21867i) q^{46} +(-3.57762 - 6.19662i) q^{47} -1.00000 q^{48} +(-4.50469 - 5.35796i) q^{49} +0.513812 q^{50} +(3.47814 + 6.02432i) q^{51} +(2.11806 - 3.66859i) q^{52} +(-0.878666 + 1.52189i) q^{53} +(-0.500000 - 0.866025i) q^{54} +7.09982 q^{55} +(1.11699 - 2.39840i) q^{56} -1.00000 q^{57} +(3.64938 + 6.32092i) q^{58} +(-6.52327 + 11.2986i) q^{59} +(1.05903 - 1.83430i) q^{60} +(-3.45956 - 5.99213i) q^{61} -4.54883 q^{62} +(2.63557 - 0.231865i) q^{63} +1.00000 q^{64} +(4.48619 + 7.77031i) q^{65} +(-1.67602 + 2.90295i) q^{66} +(2.15308 - 3.72925i) q^{67} +(-3.47814 - 6.02432i) q^{68} +7.18070 q^{69} +(3.21646 + 4.58887i) q^{70} -10.4518 q^{71} +(0.500000 + 0.866025i) q^{72} +(6.38335 - 11.0563i) q^{73} +(-0.126109 + 0.218427i) q^{74} +(-0.256906 - 0.444974i) q^{75} +1.00000 q^{76} +(-5.09035 - 7.26231i) q^{77} -4.23612 q^{78} +(-1.13557 - 1.96687i) q^{79} +(-1.05903 + 1.83430i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.16797 - 8.95119i) q^{82} +16.5699 q^{83} +(-2.63557 + 0.231865i) q^{84} +14.7338 q^{85} +(1.58566 + 2.74645i) q^{86} +(3.64938 - 6.32092i) q^{87} +(1.67602 - 2.90295i) q^{88} +(-1.89683 - 3.28540i) q^{89} -2.11806 q^{90} +(4.73169 - 10.1599i) q^{91} -7.18070 q^{92} +(2.27442 + 3.93940i) q^{93} +(3.57762 - 6.19662i) q^{94} +(-1.05903 + 1.83430i) q^{95} +(-0.500000 - 0.866025i) q^{96} -6.18070 q^{97} +(2.38779 - 6.58016i) q^{98} +3.35203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.05903	−	1.83430i	−0.473613	−	0.820322i	0.525931	−	0.850528i	$-0.323717\pi$
$5$	−1.05903	−	1.83430i	−0.473613	−	0.820322i	−0.999544	+	0.0302055i	$0.990384\pi$
$6$	1.00000			0.408248
$7$	−1.11699	+	2.39840i	−0.422181	+	0.906512i
$7$	−1.11699	+	2.39840i	−0.422181	+	0.906512i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.05903	−	1.83430i	0.334895	−	0.580055i
$11$	−1.67602	+	2.90295i	−0.505338	+	0.875271i	0.494643	+	0.869096i	$0.335299\pi$
$11$	−1.67602	+	2.90295i	−0.505338	+	0.875271i	−0.999981	+	0.00617477i	$0.998034\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−4.23612			−1.17489			−0.587445	−	0.809264i	$-0.699866\pi$
$13$	−4.23612			−1.17489			−0.587445	+	0.809264i	$0.699866\pi$
$14$	−2.63557	+	0.231865i	−0.704386	+	0.0619684i
$15$	−2.11806			−0.546881
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.47814	+	6.02432i	−0.843573	+	1.46111i	0.0432811	+	0.999063i	$0.486219\pi$
$17$	−3.47814	+	6.02432i	−0.843573	+	1.46111i	−0.886854	+	0.462049i	$0.847114\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	2.11806			0.473613
$21$	1.51859	+	2.16654i	0.331383	+	0.472778i
$22$	−3.35203			−0.714656
$23$	3.59035	+	6.21867i	0.748640	+	1.29668i	0.948475	+	0.316853i	$0.102626\pi$
$23$	3.59035	+	6.21867i	0.748640	+	1.29668i	−0.199834	+	0.979830i	$0.564040\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	0.256906	−	0.444974i	0.0513812	−	0.0889948i
$26$	−2.11806	−	3.66859i	−0.415386	−	0.719470i
$27$	−1.00000			−0.192450
$28$	−1.51859	−	2.16654i	−0.286986	−	0.409438i
$29$	7.29877			1.35535			0.677673	−	0.735363i	$-0.262988\pi$
$29$	7.29877			1.35535			0.677673	+	0.735363i	$0.262988\pi$
$30$	−1.05903	−	1.83430i	−0.193352	−	0.334895i
$31$	−2.27442	+	3.93940i	−0.408497	+	0.707538i	−0.994722	−	0.102611i	$-0.967280\pi$
$31$	−2.27442	+	3.93940i	−0.408497	+	0.707538i	0.586225	+	0.810149i	$0.300614\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.67602	+	2.90295i	0.291757	+	0.505338i
$34$	−6.95628			−1.19299
$35$	5.58231	−	0.491104i	0.943582	−	0.0830117i
$36$	1.00000			0.166667
$37$	0.126109	+	0.218427i	0.0207322	+	0.0359092i	0.876205	−	0.481938i	$-0.160067\pi$
$37$	0.126109	+	0.218427i	0.0207322	+	0.0359092i	−0.855473	+	0.517847i	$0.826734\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$	−2.11806	+	3.66859i	−0.339161	+	0.587445i
$40$	1.05903	+	1.83430i	0.167448	+	0.290028i
$41$	−10.3359			−1.61420			−0.807101	−	0.590413i	$-0.798965\pi$
$41$	−10.3359			−1.61420			−0.807101	+	0.590413i	$0.798965\pi$
$42$	−1.11699	+	2.39840i	−0.172355	+	0.370082i
$43$	3.17133			0.483623			0.241812	−	0.970323i	$-0.422258\pi$
$43$	3.17133			0.483623			0.241812	+	0.970323i	$0.422258\pi$
$44$	−1.67602	−	2.90295i	−0.252669	−	0.437636i
$45$	−1.05903	+	1.83430i	−0.157871	+	0.273441i
$46$	−3.59035	+	6.21867i	−0.529369	+	0.916893i
$47$	−3.57762	−	6.19662i	−0.521849	−	0.903869i	−0.999677	−	0.0254158i	$-0.991909\pi$
$47$	−3.57762	−	6.19662i	−0.521849	−	0.903869i	0.477828	−	0.878454i	$-0.341424\pi$
$48$	−1.00000			−0.144338
$49$	−4.50469	−	5.35796i	−0.643527	−	0.765424i
$50$	0.513812			0.0726639
$51$	3.47814	+	6.02432i	0.487037	+	0.843573i
$52$	2.11806	−	3.66859i	0.293722	−	0.508742i
$53$	−0.878666	+	1.52189i	−0.120694	+	0.209048i	−0.920042	−	0.391821i	$-0.871845\pi$
$53$	−0.878666	+	1.52189i	−0.120694	+	0.209048i	0.799348	+	0.600869i	$0.205179\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	7.09982			0.957339
$56$	1.11699	−	2.39840i	0.149263	−	0.320500i
$57$	−1.00000			−0.132453
$58$	3.64938	+	6.32092i	0.479188	+	0.829977i
$59$	−6.52327	+	11.2986i	−0.849258	+	1.47096i	0.0326134	+	0.999468i	$0.489617\pi$
$59$	−6.52327	+	11.2986i	−0.849258	+	1.47096i	−0.881871	+	0.471490i	$0.843716\pi$
$60$	1.05903	−	1.83430i	0.136720	−	0.236807i
$61$	−3.45956	−	5.99213i	−0.442951	−	0.767213i	0.554956	−	0.831880i	$-0.312735\pi$
$61$	−3.45956	−	5.99213i	−0.442951	−	0.767213i	−0.997907	+	0.0646665i	$0.979402\pi$
$62$	−4.54883			−0.577702
$63$	2.63557	−	0.231865i	0.332051	−	0.0292122i
$64$	1.00000			0.125000
$65$	4.48619	+	7.77031i	0.556443	+	0.963788i
$66$	−1.67602	+	2.90295i	−0.206303	+	0.357328i
$67$	2.15308	−	3.72925i	0.263041	−	0.455600i	−0.704008	−	0.710192i	$-0.748608\pi$
$67$	2.15308	−	3.72925i	0.263041	−	0.455600i	0.967048	+	0.254592i	$0.0819413\pi$
$68$	−3.47814	−	6.02432i	−0.421787	−	0.730556i
$69$	7.18070			0.864455
$70$	3.21646	+	4.58887i	0.384441	+	0.548474i
$71$	−10.4518			−1.24041			−0.620203	−	0.784441i	$-0.712950\pi$
$71$	−10.4518			−1.24041			−0.620203	+	0.784441i	$0.712950\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	6.38335	−	11.0563i	0.747115	−	1.29404i	−0.202085	−	0.979368i	$-0.564772\pi$
$73$	6.38335	−	11.0563i	0.747115	−	1.29404i	0.949200	−	0.314673i	$-0.101895\pi$
$74$	−0.126109	+	0.218427i	−0.0146599	+	0.0253916i
$75$	−0.256906	−	0.444974i	−0.0296649	−	0.0513812i
$76$	1.00000			0.114708
$77$	−5.09035	−	7.26231i	−0.580099	−	0.827617i
$78$	−4.23612			−0.479647
$79$	−1.13557	−	1.96687i	−0.127762	−	0.221290i	0.795047	−	0.606547i	$-0.207446\pi$
$79$	−1.13557	−	1.96687i	−0.127762	−	0.221290i	−0.922809	+	0.385257i	$0.874113\pi$
$80$	−1.05903	+	1.83430i	−0.118403	+	0.205081i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.16797	−	8.95119i	−0.570707	−	0.988493i
$83$	16.5699			1.81878			0.909392	−	0.415940i	$-0.136547\pi$
$83$	16.5699			1.81878			0.909392	+	0.415940i	$0.136547\pi$
$84$	−2.63557	+	0.231865i	−0.287564	+	0.0252985i
$85$	14.7338			1.59811
$86$	1.58566	+	2.74645i	0.170987	+	0.296157i
$87$	3.64938	−	6.32092i	0.391255	−	0.677673i
$88$	1.67602	−	2.90295i	0.178664	−	0.309455i
$89$	−1.89683	−	3.28540i	−0.201063	−	0.348252i	0.747808	−	0.663915i	$-0.231106\pi$
$89$	−1.89683	−	3.28540i	−0.201063	−	0.348252i	−0.948871	+	0.315663i	$0.897773\pi$
$90$	−2.11806			−0.223263
$91$	4.73169	−	10.1599i	0.496016	−	1.06505i
$92$	−7.18070			−0.748640
$93$	2.27442	+	3.93940i	0.235846	+	0.408497i
$94$	3.57762	−	6.19662i	0.369003	−	0.639132i
$95$	−1.05903	+	1.83430i	−0.108654	+	0.188195i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−6.18070			−0.627555			−0.313778	−	0.949496i	$-0.601595\pi$
$97$	−6.18070			−0.627555			−0.313778	+	0.949496i	$0.601595\pi$
$98$	2.38779	−	6.58016i	0.241203	−	0.664696i
$99$	3.35203			0.336892
$100$	0.256906	+	0.444974i	0.0256906	+	0.0444974i
$101$	−6.61479	+	11.4572i	−0.658196	+	1.14003i	0.322886	+	0.946438i	$0.395347\pi$
$101$	−6.61479	+	11.4572i	−0.658196	+	1.14003i	−0.981082	+	0.193592i	$0.937986\pi$
$102$	−3.47814	+	6.02432i	−0.344387	+	0.596496i
$103$	3.72700	+	6.45536i	0.367232	+	0.636065i	0.989132	−	0.147032i	$-0.0469721\pi$
$103$	3.72700	+	6.45536i	0.367232	+	0.636065i	−0.621899	+	0.783097i	$0.713639\pi$
$104$	4.23612			0.415386
$105$	2.36584	−	5.07997i	0.230883	−	0.495754i
$106$	−1.75733			−0.170687
$107$	−4.30354	−	7.45395i	−0.416039	−	0.720601i	0.579498	−	0.814974i	$-0.303249\pi$
$107$	−4.30354	−	7.45395i	−0.416039	−	0.720601i	−0.995537	+	0.0943730i	$0.969915\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−3.15373	+	5.46242i	−0.302073	+	0.523205i	−0.976605	−	0.215040i	$-0.931012\pi$
$109$	−3.15373	+	5.46242i	−0.302073	+	0.523205i	0.674533	+	0.738245i	$0.264345\pi$
$110$	3.54991	+	6.14862i	0.338470	+	0.586248i
$111$	0.252218			0.0239395
$112$	2.63557	−	0.231865i	0.249038	−	0.0219091i
$113$	1.97453			0.185748			0.0928741	−	0.995678i	$-0.470395\pi$
$113$	1.97453			0.185748			0.0928741	+	0.995678i	$0.470395\pi$
$114$	−0.500000	−	0.866025i	−0.0468293	−	0.0811107i
$115$	7.60459	−	13.1715i	0.709132	−	1.22825i
$116$	−3.64938	+	6.32092i	−0.338837	+	0.586882i
$117$	2.11806	+	3.66859i	0.195815	+	0.339161i
$118$	−13.0465			−1.20103
$119$	−10.5637	−	15.0711i	−0.968375	−	1.38156i
$120$	2.11806			0.193352
$121$	−0.118062	−	0.204490i	−0.0107329	−	0.0185900i
$122$	3.45956	−	5.99213i	0.313213	−	0.542502i
$123$	−5.16797	+	8.95119i	−0.465980	+	0.807101i
$124$	−2.27442	−	3.93940i	−0.204249	−	0.353769i
$125$	−11.6786			−1.04457
$126$	1.51859	+	2.16654i	0.135286	+	0.193011i
$127$	12.2296			1.08520			0.542600	−	0.839991i	$-0.317440\pi$
$127$	12.2296			1.08520			0.542600	+	0.839991i	$0.317440\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.58566	−	2.74645i	0.139610	−	0.241812i
$130$	−4.48619	+	7.77031i	−0.393465	+	0.681501i
$131$	0.510540	+	0.884281i	0.0446061	+	0.0772600i	0.887466	−	0.460872i	$-0.152463\pi$
$131$	0.510540	+	0.884281i	0.0446061	+	0.0772600i	−0.842860	+	0.538132i	$0.819130\pi$
$132$	−3.35203			−0.291757
$133$	2.63557	−	0.231865i	0.228533	−	0.0201052i
$134$	4.30616			0.371996
$135$	1.05903	+	1.83430i	0.0911469	+	0.157871i
$136$	3.47814	−	6.02432i	0.298248	−	0.516581i
$137$	3.06381	−	5.30667i	0.261759	−	0.453379i	−0.704951	−	0.709256i	$-0.749031\pi$
$137$	3.06381	−	5.30667i	0.261759	−	0.453379i	0.966709	+	0.255877i	$0.0823642\pi$
$138$	3.59035	+	6.21867i	0.305631	+	0.529369i
$139$	18.3476			1.55623			0.778113	−	0.628124i	$-0.216177\pi$
$139$	18.3476			1.55623			0.778113	+	0.628124i	$0.216177\pi$
$140$	−2.36584	+	5.07997i	−0.199950	+	0.429336i
$141$	−7.15524			−0.602580
$142$	−5.22592	−	9.05157i	−0.438550	−	0.759591i
$143$	7.09982	−	12.2972i	0.593716	−	1.02835i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−7.72962	−	13.3881i	−0.641910	−	1.11182i
$146$	12.7667			1.05658
$147$	−6.89248	+	1.22219i	−0.568482	+	0.100805i
$148$	−0.252218			−0.0207322
$149$	10.9551	+	18.9748i	0.897478	+	1.55448i	0.830707	+	0.556710i	$0.187936\pi$
$149$	10.9551	+	18.9748i	0.897478	+	1.55448i	0.0667713	+	0.997768i	$0.478730\pi$
$150$	0.256906	−	0.444974i	0.0209763	−	0.0363320i
$151$	−0.174600	+	0.302416i	−0.0142088	+	0.0246103i	−0.873042	−	0.487644i	$-0.837856\pi$
$151$	−0.174600	+	0.302416i	−0.0142088	+	0.0246103i	0.858834	+	0.512255i	$0.171190\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	6.95628			0.562382
$154$	3.74417	−	8.03953i	0.301714	−	0.647844i
$155$	9.63471			0.773878
$156$	−2.11806	−	3.66859i	−0.169581	−	0.293722i
$157$	−6.52435	+	11.3005i	−0.520700	+	0.901879i	0.479010	+	0.877809i	$0.340996\pi$
$157$	−6.52435	+	11.3005i	−0.520700	+	0.901879i	−0.999710	+	0.0240695i	$0.992338\pi$
$158$	1.13557	−	1.96687i	0.0903412	−	0.156476i
$159$	0.878666	+	1.52189i	0.0696827	+	0.120694i
$160$	−2.11806			−0.167448
$161$	−18.9253	+	1.66495i	−1.49152	+	0.131217i
$162$	−1.00000			−0.0785674
$163$	−7.73070	−	13.3900i	−0.605515	−	1.04878i	−0.991970	−	0.126475i	$-0.959634\pi$
$163$	−7.73070	−	13.3900i	−0.605515	−	1.04878i	0.386455	−	0.922308i	$-0.373700\pi$
$164$	5.16797	−	8.95119i	0.403551	−	0.698970i
$165$	3.54991	−	6.14862i	0.276360	−	0.478669i
$166$	8.28496	+	14.3500i	0.643037	+	1.11377i
$167$	−4.68797			−0.362766			−0.181383	−	0.983413i	$-0.558057\pi$
$167$	−4.68797			−0.362766			−0.181383	+	0.983413i	$0.558057\pi$
$168$	−1.51859	−	2.16654i	−0.117161	−	0.167152i
$169$	4.94475			0.380366
$170$	7.36692	+	12.7599i	0.565017	+	0.978638i
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	−1.58566	+	2.74645i	−0.120906	+	0.209415i
$173$	10.7642	+	18.6441i	0.818385	+	1.41748i	0.906872	+	0.421407i	$0.138464\pi$
$173$	10.7642	+	18.6441i	0.818385	+	1.41748i	−0.0884866	+	0.996077i	$0.528203\pi$
$174$	7.29877			0.553318
$175$	0.780267	+	1.11319i	0.0589827	+	0.0841495i
$176$	3.35203			0.252669
$177$	6.52327	+	11.2986i	0.490319	+	0.849258i
$178$	1.89683	−	3.28540i	0.142173	−	0.246251i
$179$	−0.919111	+	1.59195i	−0.0686976	+	0.118988i	−0.898328	−	0.439325i	$-0.855218\pi$
$179$	−0.919111	+	1.59195i	−0.0686976	+	0.118988i	0.829631	+	0.558313i	$0.188551\pi$
$180$	−1.05903	−	1.83430i	−0.0789355	−	0.136720i
$181$	20.3848			1.51519			0.757596	−	0.652724i	$-0.226374\pi$
$181$	20.3848			1.51519			0.757596	+	0.652724i	$0.226374\pi$
$182$	11.1646	−	0.982207i	0.827576	−	0.0728061i
$183$	−6.91911			−0.511475
$184$	−3.59035	−	6.21867i	−0.264684	−	0.458447i
$185$	0.267107	−	0.462642i	0.0196381	−	0.0340141i
$186$	−2.27442	+	3.93940i	−0.166768	+	0.288851i
$187$	−11.6588	−	20.1937i	−0.852579	−	1.47671i
$188$	7.15524			0.521849
$189$	1.11699	−	2.39840i	0.0812487	−	0.174458i
$190$	−2.11806			−0.153660
$191$	2.74895	+	4.76131i	0.198907	+	0.344517i	0.948174	−	0.317751i	$-0.102928\pi$
$191$	2.74895	+	4.76131i	0.198907	+	0.344517i	−0.749267	+	0.662268i	$0.769594\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−3.94935	+	6.84048i	−0.284281	+	0.492389i	−0.972435	−	0.233176i	$-0.925088\pi$
$193$	−3.94935	+	6.84048i	−0.284281	+	0.492389i	0.688154	+	0.725565i	$0.258421\pi$
$194$	−3.09035	−	5.35265i	−0.221874	−	0.384298i
$195$	8.97238			0.642525
$196$	6.89248	−	1.22219i	0.492320	−	0.0872994i
$197$	−1.93736			−0.138031			−0.0690155	−	0.997616i	$-0.521986\pi$
$197$	−1.93736			−0.138031			−0.0690155	+	0.997616i	$0.521986\pi$
$198$	1.67602	+	2.90295i	0.119109	+	0.206303i
$199$	−4.36912	+	7.56753i	−0.309718	+	0.536448i	−0.978301	−	0.207190i	$-0.933568\pi$
$199$	−4.36912	+	7.56753i	−0.309718	+	0.536448i	0.668582	+	0.743638i	$0.266901\pi$
$200$	−0.256906	+	0.444974i	−0.0181660	+	0.0314644i
$201$	−2.15308	−	3.72925i	−0.151867	−	0.263041i
$202$	−13.2296			−0.930830
$203$	−8.15261	+	17.5054i	−0.572201	+	1.22864i
$204$	−6.95628			−0.487037
$205$	10.9461	+	18.9592i	0.764508	+	1.32417i
$206$	−3.72700	+	6.45536i	−0.259672	+	0.449766i
$207$	3.59035	−	6.21867i	0.249547	−	0.432228i
$208$	2.11806	+	3.66859i	0.146861	+	0.254371i
$209$	3.35203			0.231865
$210$	5.58231	−	0.491104i	0.385216	−	0.0338894i
$211$	−23.3870			−1.61003			−0.805013	−	0.593257i	$-0.797842\pi$
$211$	−23.3870			−1.61003			−0.805013	+	0.593257i	$0.797842\pi$
$212$	−0.878666	−	1.52189i	−0.0603470	−	0.104524i
$213$	−5.22592	+	9.05157i	−0.358074	+	0.620203i
$214$	4.30354	−	7.45395i	0.294184	−	0.509542i
$215$	−3.35854	−	5.81715i	−0.229050	−	0.396727i
$216$	1.00000			0.0680414
$217$	−6.90779	−	9.85522i	−0.468932	−	0.669016i
$218$	−6.30746			−0.427195
$219$	−6.38335	−	11.0563i	−0.431347	−	0.747115i
$220$	−3.54991	+	6.14862i	−0.239335	+	0.414540i
$221$	14.7338	−	25.5198i	0.991106	−	1.71665i
$222$	0.126109	+	0.218427i	0.00846388	+	0.0146599i
$223$	9.80320			0.656471			0.328236	−	0.944596i	$-0.393546\pi$
$223$	9.80320			0.656471			0.328236	+	0.944596i	$0.393546\pi$
$224$	1.51859	+	2.16654i	0.101465	+	0.144758i
$225$	−0.513812			−0.0342541
$226$	0.987266	+	1.70999i	0.0656719	+	0.113747i
$227$	9.14176	−	15.8340i	0.606760	−	1.05094i	−0.385011	−	0.922912i	$-0.625802\pi$
$227$	9.14176	−	15.8340i	0.606760	−	1.05094i	0.991771	−	0.128027i	$-0.0408645\pi$
$228$	0.500000	−	0.866025i	0.0331133	−	0.0573539i
$229$	0.722313	+	1.25108i	0.0477318	+	0.0826739i	0.888904	−	0.458093i	$-0.151467\pi$
$229$	0.722313	+	1.25108i	0.0477318	+	0.0826739i	−0.841172	+	0.540767i	$0.818134\pi$
$230$	15.2092			1.00286
$231$	−8.83452	+	0.777218i	−0.581269	+	0.0511372i
$232$	−7.29877			−0.479188
$233$	7.84038	+	13.5799i	0.513640	+	0.889651i	0.999875	+	0.0158225i	$0.00503667\pi$
$233$	7.84038	+	13.5799i	0.513640	+	0.889651i	−0.486235	+	0.873828i	$0.661630\pi$
$234$	−2.11806	+	3.66859i	−0.138462	+	0.239823i
$235$	−7.57762	+	13.1248i	−0.494309	+	0.856169i
$236$	−6.52327	−	11.2986i	−0.424629	−	0.735479i
$237$	−2.27114			−0.147527
$238$	7.77007	−	16.6840i	0.503659	−	1.08146i
$239$	3.76818			0.243744			0.121872	−	0.992546i	$-0.461110\pi$
$239$	3.76818			0.243744			0.121872	+	0.992546i	$0.461110\pi$
$240$	1.05903	+	1.83430i	0.0683602	+	0.118403i
$241$	−1.49781	+	2.59428i	−0.0964821	+	0.167112i	−0.910226	−	0.414111i	$-0.864092\pi$
$241$	−1.49781	+	2.59428i	−0.0964821	+	0.167112i	0.813744	+	0.581223i	$0.197426\pi$
$242$	0.118062	−	0.204490i	0.00758934	−	0.0131451i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	6.91911			0.442951
$245$	−5.05749	+	13.9372i	−0.323111	+	0.890414i
$246$	−10.3359			−0.658995
$247$	2.11806	+	3.66859i	0.134769	+	0.233427i
$248$	2.27442	−	3.93940i	0.144426	−	0.250152i
$249$	8.28496	−	14.3500i	0.525038	−	0.909392i
$250$	−5.83930	−	10.1140i	−0.369310	−	0.639663i
$251$	26.2922			1.65955			0.829775	−	0.558098i	$-0.188469\pi$
$251$	26.2922			1.65955			0.829775	+	0.558098i	$0.188469\pi$
$252$	−1.11699	+	2.39840i	−0.0703635	+	0.151085i
$253$	−24.0700			−1.51327
$254$	6.11479	+	10.5911i	0.383676	+	0.664547i
$255$	7.36692	−	12.7599i	0.461335	−	0.799055i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.86584	+	17.0881i	0.615414	+	1.06593i	0.990312	+	0.138863i	$0.0443447\pi$
$257$	9.86584	+	17.0881i	0.615414	+	1.06593i	−0.374897	+	0.927066i	$0.622322\pi$
$258$	3.17133			0.197438
$259$	−0.664738	+	0.0584804i	−0.0413048	+	0.00363380i
$260$	−8.97238			−0.556443
$261$	−3.64938	−	6.32092i	−0.225891	−	0.391255i
$262$	−0.510540	+	0.884281i	−0.0315413	+	0.0546311i
$263$	2.22124	−	3.84729i	0.136967	−	0.237234i	−0.789380	−	0.613905i	$-0.789598\pi$
$263$	2.22124	−	3.84729i	0.136967	−	0.237234i	0.926347	+	0.376671i	$0.122931\pi$
$264$	−1.67602	−	2.90295i	−0.103152	−	0.178664i
$265$	3.72214			0.228649
$266$	1.51859	+	2.16654i	0.0931105	+	0.132839i
$267$	−3.79365			−0.232168
$268$	2.15308	+	3.72925i	0.131520	+	0.227800i
$269$	−9.73982	+	16.8699i	−0.593847	+	1.02857i	0.399861	+	0.916576i	$0.369058\pi$
$269$	−9.73982	+	16.8699i	−0.593847	+	1.02857i	−0.993708	+	0.111998i	$0.964275\pi$
$270$	−1.05903	+	1.83430i	−0.0644506	+	0.111632i
$271$	−0.787888	−	1.36466i	−0.0478608	−	0.0828973i	0.841103	−	0.540876i	$-0.181907\pi$
$271$	−0.787888	−	1.36466i	−0.0478608	−	0.0828973i	−0.888963	+	0.457978i	$0.848574\pi$
$272$	6.95628			0.421787
$273$	−6.43292	−	9.17773i	−0.389338	−	0.555462i
$274$	6.12761			0.370183
$275$	0.861157	+	1.49157i	0.0519297	+	0.0899449i
$276$	−3.59035	+	6.21867i	−0.216114	+	0.374320i
$277$	−4.90306	+	8.49234i	−0.294596	+	0.510256i	−0.974891	−	0.222683i	$-0.928518\pi$
$277$	−4.90306	+	8.49234i	−0.294596	+	0.510256i	0.680295	+	0.732939i	$0.261852\pi$
$278$	9.17382	+	15.8895i	0.550209	+	0.952990i
$279$	4.54883			0.272331
$280$	−5.58231	+	0.491104i	−0.333607	+	0.0293491i
$281$	−3.60641			−0.215140			−0.107570	−	0.994198i	$-0.534307\pi$
$281$	−3.60641			−0.215140			−0.107570	+	0.994198i	$0.534307\pi$
$282$	−3.57762	−	6.19662i	−0.213044	−	0.369003i
$283$	10.7664	−	18.6479i	0.639994	−	1.10850i	−0.345439	−	0.938441i	$-0.612270\pi$
$283$	10.7664	−	18.6479i	0.639994	−	1.10850i	0.985433	−	0.170061i	$-0.0543966\pi$
$284$	5.22592	−	9.05157i	0.310102	−	0.537112i
$285$	1.05903	+	1.83430i	0.0627316	+	0.108654i
$286$	14.1996			0.839642
$287$	11.5451	−	24.7898i	0.681485	−	1.46329i
$288$	−1.00000			−0.0589256
$289$	−15.6949	−	27.1844i	−0.923232	−	1.59908i
$290$	7.72962	−	13.3881i	0.453899	−	0.786176i
$291$	−3.09035	+	5.35265i	−0.181160	+	0.313778i
$292$	6.38335	+	11.0563i	0.373558	+	0.647021i
$293$	−24.2946			−1.41930			−0.709651	−	0.704553i	$-0.751148\pi$
$293$	−24.2946			−1.41930			−0.709651	+	0.704553i	$0.751148\pi$
$294$	−4.50469	−	5.35796i	−0.262719	−	0.312483i
$295$	27.6334			1.60888
$296$	−0.126109	−	0.218427i	−0.00732993	−	0.0126958i
$297$	1.67602	−	2.90295i	0.0972523	−	0.168446i
$298$	−10.9551	+	18.9748i	−0.634613	+	1.09918i
$299$	−15.2092	−	26.3431i	−0.879570	−	1.52346i
$300$	0.513812			0.0296649
$301$	−3.54233	+	7.60613i	−0.204176	+	0.438410i
$302$	−0.349200			−0.0200942
$303$	6.61479	+	11.4572i	0.380010	+	0.658196i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	−7.32755	+	12.6917i	−0.419575	+	0.726724i
$306$	3.47814	+	6.02432i	0.198832	+	0.344387i
$307$	5.79365			0.330661			0.165331	−	0.986238i	$-0.447131\pi$
$307$	5.79365			0.330661			0.165331	+	0.986238i	$0.447131\pi$
$308$	8.83452	−	0.777218i	0.503394	−	0.0442861i
$309$	7.45400			0.424043
$310$	4.81735	+	8.34390i	0.273607	+	0.473902i
$311$	−9.33930	+	16.1761i	−0.529583	+	0.917265i	0.469822	+	0.882761i	$0.344318\pi$
$311$	−9.33930	+	16.1761i	−0.529583	+	0.917265i	−0.999405	+	0.0345033i	$0.989015\pi$
$312$	2.11806	−	3.66859i	0.119912	−	0.207693i
$313$	−12.8684	−	22.2888i	−0.727366	−	1.25984i	−0.957993	−	0.286793i	$-0.907411\pi$
$313$	−12.8684	−	22.2888i	−0.727366	−	1.25984i	0.230626	−	0.973042i	$-0.425923\pi$
$314$	−13.0487			−0.736381
$315$	−3.21646	−	4.58887i	−0.181227	−	0.258553i
$316$	2.27114			0.127762
$317$	10.3764	+	17.9724i	0.582796	+	1.00943i	0.995146	+	0.0984067i	$0.0313746\pi$
$317$	10.3764	+	17.9724i	0.582796	+	1.00943i	−0.412350	+	0.911025i	$0.635292\pi$
$318$	−0.878666	+	1.52189i	−0.0492731	+	0.0853436i
$319$	−12.2329	+	21.1879i	−0.684908	+	1.18630i
$320$	−1.05903	−	1.83430i	−0.0592016	−	0.102540i
$321$	−8.60708			−0.480401
$322$	−10.9045	−	15.5573i	−0.607685	−	0.866973i
$323$	6.95628			0.387058
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.08828	+	1.88496i	−0.0603672	+	0.104559i
$326$	7.73070	−	13.3900i	0.428164	−	0.741601i
$327$	3.15373	+	5.46242i	0.174402	+	0.302073i
$328$	10.3359			0.570707
$329$	18.8581	−	1.65905i	1.03968	−	0.0914662i
$330$	7.09982			0.390832
$331$	17.5018	+	30.3139i	0.961983	+	1.66620i	0.717510	+	0.696548i	$0.245282\pi$
$331$	17.5018	+	30.3139i	0.961983	+	1.66620i	0.244474	+	0.969656i	$0.421385\pi$
$332$	−8.28496	+	14.3500i	−0.454696	+	0.787557i
$333$	0.126109	−	0.218427i	0.00691073	−	0.0119697i
$334$	−2.34399	−	4.05990i	−0.128257	−	0.222148i
$335$	−9.12072			−0.498318
$336$	1.11699	−	2.39840i	0.0609365	−	0.130844i
$337$	−9.06565			−0.493837			−0.246919	−	0.969036i	$-0.579418\pi$
$337$	−9.06565			−0.493837			−0.246919	+	0.969036i	$0.579418\pi$
$338$	2.47238	+	4.28228i	0.134480	+	0.232925i
$339$	0.987266	−	1.70999i	0.0536209	−	0.0928741i
$340$	−7.36692	+	12.7599i	−0.399527	+	0.692002i
$341$	−7.62391	−	13.2050i	−0.412858	−	0.715091i
$342$	−1.00000			−0.0540738
$343$	17.8822	−	4.81930i	0.965550	−	0.260218i
$344$	−3.17133			−0.170987
$345$	−7.60459	−	13.1715i	−0.409417	−	0.709132i
$346$	−10.7642	+	18.6441i	−0.578686	+	1.00231i
$347$	8.82798	−	15.2905i	0.473911	−	0.820838i	−0.525643	−	0.850705i	$-0.676175\pi$
$347$	8.82798	−	15.2905i	0.473911	−	0.820838i	0.999554	+	0.0298676i	$0.00950857\pi$
$348$	3.64938	+	6.32092i	0.195627	+	0.338837i
$349$	19.9745			1.06921			0.534606	−	0.845101i	$-0.320460\pi$
$349$	19.9745			1.06921			0.534606	+	0.845101i	$0.320460\pi$
$350$	−0.573920	+	1.23233i	−0.0306773	+	0.0658707i
$351$	4.23612			0.226108
$352$	1.67602	+	2.90295i	0.0893320	+	0.154728i
$353$	−11.2514	+	19.4880i	−0.598851	+	1.03724i	0.394140	+	0.919051i	$0.371043\pi$
$353$	−11.2514	+	19.4880i	−0.598851	+	1.03724i	−0.992991	+	0.118190i	$0.962291\pi$
$354$	−6.52327	+	11.2986i	−0.346708	+	0.600516i
$355$	11.0688	+	19.1718i	0.587473	+	1.01753i
$356$	3.79365			0.201063
$357$	−18.3338	+	1.61292i	−0.970327	+	0.0853646i
$358$	−1.83822			−0.0971530
$359$	4.91795	+	8.51813i	0.259559	+	0.449570i	0.966124	−	0.258079i	$-0.0830894\pi$
$359$	4.91795	+	8.51813i	0.259559	+	0.449570i	−0.706565	+	0.707649i	$0.749756\pi$
$360$	1.05903	−	1.83430i	0.0558158	−	0.0966759i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	10.1924	+	17.6538i	0.535701	+	0.927862i
$363$	−0.236125			−0.0123933
$364$	6.43292	+	9.17773i	0.337177	+	0.481044i
$365$	−27.0407			−1.41537
$366$	−3.45956	−	5.99213i	−0.180834	−	0.313213i
$367$	−17.6673	+	30.6006i	−0.922224	+	1.59734i	−0.126259	+	0.991997i	$0.540297\pi$
$367$	−17.6673	+	30.6006i	−0.922224	+	1.59734i	−0.795965	+	0.605342i	$0.793036\pi$
$368$	3.59035	−	6.21867i	0.187160	−	0.324171i
$369$	5.16797	+	8.95119i	0.269034	+	0.465980i
$370$	0.534213			0.0277724
$371$	−2.66866	−	3.80733i	−0.138550	−	0.197667i
$372$	−4.54883			−0.235846
$373$	−16.9147	−	29.2972i	−0.875811	−	1.51695i	−0.855896	−	0.517148i	$-0.826994\pi$
$373$	−16.9147	−	29.2972i	−0.875811	−	1.51695i	−0.0199149	−	0.999802i	$-0.506340\pi$
$374$	11.6588	−	20.1937i	0.602865	−	1.04419i
$375$	−5.83930	+	10.1140i	−0.301540	+	0.522283i
$376$	3.57762	+	6.19662i	0.184502	+	0.319566i
$377$	−30.9185			−1.59238
$378$	2.63557	−	0.231865i	0.135559	−	0.0119258i
$379$	25.4999			1.30984			0.654920	−	0.755698i	$-0.272702\pi$
$379$	25.4999			1.30984			0.654920	+	0.755698i	$0.272702\pi$
$380$	−1.05903	−	1.83430i	−0.0543272	−	0.0940974i
$381$	6.11479	−	10.5911i	0.313270	−	0.542600i
$382$	−2.74895	+	4.76131i	−0.140648	+	0.243610i
$383$	−17.8593	−	30.9332i	−0.912568	−	1.58061i	−0.810424	−	0.585844i	$-0.800763\pi$
$383$	−17.8593	−	30.9332i	−0.912568	−	1.58061i	−0.102144	−	0.994770i	$-0.532570\pi$
$384$	1.00000			0.0510310
$385$	−7.93039	+	17.0282i	−0.404170	+	0.867839i
$386$	−7.89871			−0.402034
$387$	−1.58566	−	2.74645i	−0.0806038	−	0.139610i
$388$	3.09035	−	5.35265i	0.156889	−	0.271739i
$389$	−11.0124	+	19.0740i	−0.558350	+	0.967091i	0.439284	+	0.898348i	$0.355232\pi$
$389$	−11.0124	+	19.0740i	−0.558350	+	0.967091i	−0.997634	+	0.0687425i	$0.978101\pi$
$390$	4.48619	+	7.77031i	0.227167	+	0.393465i
$391$	−49.9510			−2.52613
$392$	4.50469	+	5.35796i	0.227521	+	0.270618i
$393$	1.02108			0.0515067
$394$	−0.968679	−	1.67780i	−0.0488013	−	0.0845264i
$395$	−2.40521	+	4.16595i	−0.121019	+	0.209612i
$396$	−1.67602	+	2.90295i	−0.0842230	+	0.145879i
$397$	−9.86584	−	17.0881i	−0.495153	−	0.857629i	0.504832	−	0.863218i	$-0.331554\pi$
$397$	−9.86584	−	17.0881i	−0.495153	−	0.857629i	−0.999984	+	0.00558835i	$0.998221\pi$
$398$	−8.73823			−0.438008
$399$	1.11699	−	2.39840i	0.0559192	−	0.120070i
$400$	−0.513812			−0.0256906
$401$	−7.42638	−	12.8629i	−0.370856	−	0.642341i	0.618842	−	0.785516i	$-0.287602\pi$
$401$	−7.42638	−	12.8629i	−0.370856	−	0.642341i	−0.989697	+	0.143175i	$0.954269\pi$
$402$	2.15308	−	3.72925i	0.107386	−	0.185998i
$403$	9.63471	−	16.6878i	0.479939	−	0.831279i
$404$	−6.61479	−	11.4572i	−0.329098	−	0.570015i
$405$	2.11806			0.105247
$406$	−19.2364	+	1.69233i	−0.954688	+	0.0839887i
$407$	−0.845443			−0.0419070
$408$	−3.47814	−	6.02432i	−0.172194	−	0.298248i
$409$	−3.01816	+	5.22761i	−0.149238	+	0.258489i	−0.930946	−	0.365156i	$-0.881016\pi$
$409$	−3.01816	+	5.22761i	−0.149238	+	0.258489i	0.781708	+	0.623645i	$0.214349\pi$
$410$	−10.9461	+	18.9592i	−0.540589	+	0.936327i
$411$	−3.06381	−	5.30667i	−0.151126	−	0.261759i
$412$	−7.45400			−0.367232
$413$	−19.8123	−	28.2659i	−0.974900	−	1.39087i
$414$	7.18070			0.352912
$415$	−17.5481	−	30.3941i	−0.861400	−	1.49199i
$416$	−2.11806	+	3.66859i	−0.103847	+	0.179868i
$417$	9.17382	−	15.8895i	0.449244	−	0.778113i
$418$	1.67602	+	2.90295i	0.0819766	+	0.141988i
$419$	14.1370			0.690637			0.345319	−	0.938486i	$-0.387771\pi$
$419$	14.1370			0.690637			0.345319	+	0.938486i	$0.387771\pi$
$420$	3.21646	+	4.58887i	0.156947	+	0.223914i
$421$	−35.7565			−1.74266			−0.871331	−	0.490695i	$-0.836743\pi$
$421$	−35.7565			−1.74266			−0.871331	+	0.490695i	$0.836743\pi$
$422$	−11.6935	−	20.2537i	−0.569230	−	0.985935i
$423$	−3.57762	+	6.19662i	−0.173950	+	0.301290i
$424$	0.878666	−	1.52189i	0.0426718	−	0.0739097i
$425$	1.78711	+	3.09536i	0.0866875	+	0.150147i
$426$	−10.4518			−0.506394
$427$	18.2358	−	1.60430i	0.882493	−	0.0776374i
$428$	8.60708			0.416039
$429$	−7.09982	−	12.2972i	−0.342782	−	0.593716i
$430$	3.35854	−	5.81715i	0.161963	−	0.280528i
$431$	−8.71211	+	15.0898i	−0.419648	+	0.726851i	−0.995904	−	0.0904180i	$-0.971180\pi$
$431$	−8.71211	+	15.0898i	−0.419648	+	0.726851i	0.576256	+	0.817269i	$0.304513\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−0.745628			−0.0358326			−0.0179163	−	0.999839i	$-0.505703\pi$
$433$	−0.745628			−0.0358326			−0.0179163	+	0.999839i	$0.505703\pi$
$434$	5.08098	−	10.9099i	0.243895	−	0.523694i
$435$	−15.4592			−0.741214
$436$	−3.15373	−	5.46242i	−0.151036	−	0.261603i
$437$	3.59035	−	6.21867i	0.171750	−	0.297479i
$438$	6.38335	−	11.0563i	0.305008	−	0.528290i
$439$	−5.86443	−	10.1575i	−0.279894	−	0.484790i	0.691464	−	0.722411i	$-0.256966\pi$
$439$	−5.86443	−	10.1575i	−0.279894	−	0.484790i	−0.971358	+	0.237620i	$0.923633\pi$
$440$	−7.09982			−0.338470
$441$	−2.38779	+	6.58016i	−0.113704	+	0.313341i
$442$	29.4677			1.40163
$443$	−3.47805	−	6.02417i	−0.165247	−	0.286217i	0.771496	−	0.636234i	$-0.219509\pi$
$443$	−3.47805	−	6.02417i	−0.165247	−	0.286217i	−0.936743	+	0.350018i	$0.886176\pi$
$444$	−0.126109	+	0.218427i	−0.00598487	+	0.0103661i
$445$	−4.01760	+	6.95868i	−0.190452	+	0.329873i
$446$	4.90160	+	8.48982i	0.232098	+	0.402005i
$447$	21.9102			1.03632
$448$	−1.11699	+	2.39840i	−0.0527726	+	0.113314i
$449$	−27.5823			−1.30169			−0.650844	−	0.759211i	$-0.725585\pi$
$449$	−27.5823			−1.30169			−0.650844	+	0.759211i	$0.725585\pi$
$450$	−0.256906	−	0.444974i	−0.0121107	−	0.0209763i
$451$	17.3232	−	30.0047i	0.815718	−	1.41286i
$452$	−0.987266	+	1.70999i	−0.0464371	+	0.0804314i
$453$	0.174600	+	0.302416i	0.00820343	+	0.0142088i
$454$	18.2835			0.858088
$455$	−23.6473	+	2.08038i	−1.10860	+	0.0975296i
$456$	1.00000			0.0468293
$457$	−10.3866	−	17.9902i	−0.485866	−	0.841544i	0.514002	−	0.857789i	$-0.328162\pi$
$457$	−10.3866	−	17.9902i	−0.485866	−	0.841544i	−0.999868	+	0.0162445i	$0.994829\pi$
$458$	−0.722313	+	1.25108i	−0.0337515	+	0.0584593i
$459$	3.47814	−	6.02432i	0.162346	−	0.281191i
$460$	7.60459	+	13.1715i	0.354566	+	0.614126i
$461$	33.6610			1.56775			0.783875	−	0.620918i	$-0.213240\pi$
$461$	33.6610			1.56775			0.783875	+	0.620918i	$0.213240\pi$
$462$	−5.09035	−	7.26231i	−0.236825	−	0.337873i
$463$	−18.4933			−0.859458			−0.429729	−	0.902958i	$-0.641391\pi$
$463$	−18.4933			−0.859458			−0.429729	+	0.902958i	$0.641391\pi$
$464$	−3.64938	−	6.32092i	−0.169418	−	0.293441i
$465$	4.81735	−	8.34390i	0.223399	−	0.386939i
$466$	−7.84038	+	13.5799i	−0.363198	+	0.629078i
$467$	6.71646	+	11.6333i	0.310801	+	0.538323i	0.978536	−	0.206076i	$-0.0660695\pi$
$467$	6.71646	+	11.6333i	0.310801	+	0.538323i	−0.667735	+	0.744399i	$0.732736\pi$
$468$	−4.23612			−0.195815
$469$	6.53928	+	9.32947i	0.301956	+	0.430795i
$470$	−15.1552			−0.699059
$471$	6.52435	+	11.3005i	0.300626	+	0.520700i
$472$	6.52327	−	11.2986i	0.300258	−	0.520062i
$473$	−5.31520	+	9.20619i	−0.244393	+	0.423301i
$474$	−1.13557	−	1.96687i	−0.0521585	−	0.0903412i
$475$	−0.513812			−0.0235753
$476$	18.3338	−	1.61292i	0.840328	−	0.0739279i
$477$	1.75733			0.0804627
$478$	1.88409	+	3.26334i	0.0861764	+	0.149262i
$479$	2.02947	−	3.51514i	0.0927287	−	0.160611i	−0.815930	−	0.578151i	$-0.803774\pi$
$479$	2.02947	−	3.51514i	0.0927287	−	0.160611i	0.908658	+	0.417540i	$0.137108\pi$
$480$	−1.05903	+	1.83430i	−0.0483379	+	0.0837238i
$481$	−0.534213	−	0.925285i	−0.0243580	−	0.0421893i
$482$	−2.99561			−0.136446
$483$	−8.02074	+	17.2222i	−0.364956	+	0.783639i
$484$	0.236125			0.0107329
$485$	6.54556	+	11.3372i	0.297219	+	0.514798i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−18.7539	+	32.4827i	−0.849820	+	1.47193i	0.0315492	+	0.999502i	$0.489956\pi$
$487$	−18.7539	+	32.4827i	−0.849820	+	1.47193i	−0.881369	+	0.472429i	$0.843377\pi$
$488$	3.45956	+	5.99213i	0.156607	+	0.271251i
$489$	−15.4614			−0.699189
$490$	−14.5987	+	2.58868i	−0.659502	+	0.116945i
$491$	−27.2230			−1.22856			−0.614279	−	0.789089i	$-0.710553\pi$
$491$	−27.2230			−1.22856			−0.614279	+	0.789089i	$0.710553\pi$
$492$	−5.16797	−	8.95119i	−0.232990	−	0.403551i
$493$	−25.3861	+	43.9701i	−1.14333	+	1.98031i
$494$	−2.11806	+	3.66859i	−0.0952961	+	0.165058i
$495$	−3.54991	−	6.14862i	−0.159556	−	0.276360i
$496$	4.54883			0.204249
$497$	11.6746	−	25.0678i	0.523676	−	1.12444i
$498$	16.5699			0.742515
$499$	−3.46825	−	6.00719i	−0.155260	−	0.268919i	0.777893	−	0.628396i	$-0.216288\pi$
$499$	−3.46825	−	6.00719i	−0.155260	−	0.268919i	−0.933154	+	0.359477i	$0.882955\pi$
$500$	5.83930	−	10.1140i	0.261141	−	0.452310i
$501$	−2.34399	+	4.05990i	−0.104722	+	0.181383i
$502$	13.1461	+	22.7697i	0.586740	+	1.01626i
$503$	24.0509			1.07237			0.536187	−	0.844099i	$-0.319864\pi$
$503$	24.0509			1.07237			0.536187	+	0.844099i	$0.319864\pi$
$504$	−2.63557	+	0.231865i	−0.117398	+	0.0103281i
$505$	28.0211			1.24692
$506$	−12.0350	−	20.8452i	−0.535020	−	0.926682i
$507$	2.47238	−	4.28228i	0.109802	−	0.190183i
$508$	−6.11479	+	10.5911i	−0.271300	+	0.469905i
$509$	−16.1843	−	28.0320i	−0.717355	−	1.24250i	−0.962044	−	0.272894i	$-0.912019\pi$
$509$	−16.1843	−	28.0320i	−0.717355	−	1.24250i	0.244689	−	0.969602i	$-0.421314\pi$
$510$	14.7338			0.652426
$511$	19.3874	+	27.6596i	0.857646	+	1.22359i
$512$	−1.00000			−0.0441942
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−9.86584	+	17.0881i	−0.435164	+	0.753726i
$515$	7.89402	−	13.6728i	0.347852	−	0.602498i
$516$	1.58566	+	2.74645i	0.0698050	+	0.120906i
$517$	23.9846			1.05484
$518$	−0.383015	−	0.546440i	−0.0168287	−	0.0240092i
$519$	21.5283			0.944990
$520$	−4.48619	−	7.77031i	−0.196732	−	0.340750i
$521$	−6.25728	+	10.8379i	−0.274137	+	0.474819i	−0.969917	−	0.243436i	$-0.921725\pi$
$521$	−6.25728	+	10.8379i	−0.274137	+	0.474819i	0.695780	+	0.718255i	$0.255059\pi$
$522$	3.64938	−	6.32092i	0.159729	−	0.276659i
$523$	7.98288	+	13.8267i	0.349067	+	0.604601i	0.986084	−	0.166248i	$-0.0531653\pi$
$523$	7.98288	+	13.8267i	0.349067	+	0.604601i	−0.637017	+	0.770850i	$0.719832\pi$
$524$	−1.02108			−0.0446061
$525$	1.35419	−	0.119135i	0.0591016	−	0.00519947i
$526$	4.44247			0.193701
$527$	−15.8215	−	27.4036i	−0.689194	−	1.19372i
$528$	1.67602	−	2.90295i	0.0729393	−	0.126334i
$529$	−14.2813	+	24.7359i	−0.620924	+	1.07547i
$530$	1.86107	+	3.22347i	0.0808397	+	0.140018i
$531$	13.0465			0.566172
$532$	−1.11699	+	2.39840i	−0.0484275	+	0.103984i
$533$	43.7843			1.89651
$534$	−1.89683	−	3.28540i	−0.0820837	−	0.142173i
$535$	−9.11517	+	15.7879i	−0.394083	+	0.682572i
$536$	−2.15308	+	3.72925i	−0.0929989	+	0.161079i
$537$	0.919111	+	1.59195i	0.0396626	+	0.0686976i
$538$	−19.4796			−0.839827
$539$	23.1038	−	4.09683i	0.995152	−	0.176463i
$540$	−2.11806			−0.0911469
$541$	20.1348	+	34.8745i	0.865662	+	1.49937i	0.866388	+	0.499372i	$0.166436\pi$
$541$	20.1348	+	34.8745i	0.865662	+	1.49937i	−0.000725557		1.00000i	$0.500231\pi$
$542$	0.787888	−	1.36466i	0.0338427	−	0.0586172i
$543$	10.1924	−	17.6538i	0.437398	−	0.757596i
$544$	3.47814	+	6.02432i	0.149124	+	0.258291i
$545$	13.3596			0.572263
$546$	4.73169	−	10.1599i	0.202498	−	0.434805i
$547$	7.22088			0.308743			0.154371	−	0.988013i	$-0.450665\pi$
$547$	7.22088			0.308743			0.154371	+	0.988013i	$0.450665\pi$
$548$	3.06381	+	5.30667i	0.130879	+	0.226690i
$549$	−3.45956	+	5.99213i	−0.147650	+	0.255738i
$550$	−0.861157	+	1.49157i	−0.0367198	+	0.0636006i
$551$	−3.64938	−	6.32092i	−0.155469	−	0.269280i
$552$	−7.18070			−0.305631
$553$	5.98576	−	0.526598i	0.254540	−	0.0223932i
$554$	−9.80612			−0.416622
$555$	−0.267107	−	0.462642i	−0.0113380	−	0.0196381i
$556$	−9.17382	+	15.8895i	−0.389057	+	0.673866i
$557$	−1.36266	+	2.36020i	−0.0577378	+	0.100005i	−0.893450	−	0.449164i	$-0.851722\pi$
$557$	−1.36266	+	2.36020i	−0.0577378	+	0.100005i	0.835712	+	0.549168i	$0.185055\pi$
$558$	2.27442	+	3.93940i	0.0962837	+	0.166768i
$559$	−13.4341			−0.568204
$560$	−3.21646	−	4.58887i	−0.135920	−	0.193915i
$561$	−23.3177			−0.984474
$562$	−1.80320	−	3.12324i	−0.0760635	−	0.131746i
$563$	−9.17340	+	15.8888i	−0.386613	+	0.669633i	−0.991991	−	0.126305i	$-0.959688\pi$
$563$	−9.17340	+	15.8888i	−0.386613	+	0.669633i	0.605379	+	0.795937i	$0.293022\pi$
$564$	3.57762	−	6.19662i	0.150645	−	0.260925i
$565$	−2.09109	−	3.62187i	−0.0879728	−	0.152373i
$566$	21.5327			0.905088
$567$	−1.51859	−	2.16654i	−0.0637746	−	0.0909861i
$568$	10.4518			0.438550
$569$	−18.1465	−	31.4307i	−0.760742	−	1.31764i	−0.942468	−	0.334295i	$-0.891502\pi$
$569$	−18.1465	−	31.4307i	−0.760742	−	1.31764i	0.181726	−	0.983349i	$-0.441832\pi$
$570$	−1.05903	+	1.83430i	−0.0443579	+	0.0768302i
$571$	−22.9055	+	39.6735i	−0.958566	+	1.66028i	−0.232577	+	0.972578i	$0.574716\pi$
$571$	−22.9055	+	39.6735i	−0.958566	+	1.66028i	−0.725989	+	0.687707i	$0.758617\pi$
$572$	7.09982	+	12.2972i	0.296858	+	0.514173i
$573$	5.49789			0.229678
$574$	27.2411	−	2.39654i	1.13702	−	0.100030i
$575$	3.68953			0.153864
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	7.94463	−	13.7605i	0.330739	−	0.572857i	−0.651918	−	0.758290i	$-0.726035\pi$
$577$	7.94463	−	13.7605i	0.330739	−	0.572857i	0.982657	+	0.185433i	$0.0593686\pi$
$578$	15.6949	−	27.1844i	0.652824	−	1.13072i
$579$	3.94935	+	6.84048i	0.164130	+	0.284281i
$580$	15.4592			0.641910
$581$	−18.5083	+	39.7413i	−0.767856	+	1.64875i
$582$	−6.18070			−0.256198
$583$	−2.94532	−	5.10144i	−0.121983	−	0.211280i
$584$	−6.38335	+	11.0563i	−0.264145	+	0.457513i
$585$	4.48619	−	7.77031i	0.185481	−	0.321263i
$586$	−12.1473	−	21.0397i	−0.501799	−	0.869142i
$587$	−4.19680			−0.173220			−0.0866102	−	0.996242i	$-0.527603\pi$
$587$	−4.19680			−0.173220			−0.0866102	+	0.996242i	$0.527603\pi$
$588$	2.38779	−	6.58016i	0.0984708	−	0.271361i
$589$	4.54883			0.187431
$590$	13.8167	+	23.9312i	0.568825	+	0.985233i
$591$	−0.968679	+	1.67780i	−0.0398461	+	0.0690155i
$592$	0.126109	−	0.218427i	0.00518305	−	0.00897730i
$593$	12.3647	+	21.4163i	0.507758	+	0.879464i	0.999960	+	0.00898203i	$0.00285911\pi$
$593$	12.3647	+	21.4163i	0.507758	+	0.879464i	−0.492201	+	0.870481i	$0.663808\pi$
$594$	3.35203			0.137536
$595$	−16.4575	+	35.3377i	−0.674691	+	1.44871i
$596$	−21.9102			−0.897478
$597$	4.36912	+	7.56753i	0.178816	+	0.309718i
$598$	15.2092	−	26.3431i	0.621950	−	1.07725i
$599$	2.26964	−	3.93113i	0.0927350	−	0.160622i	−0.815926	−	0.578156i	$-0.803772\pi$
$599$	2.26964	−	3.93113i	0.0927350	−	0.160622i	0.908661	+	0.417535i	$0.137106\pi$
$600$	0.256906	+	0.444974i	0.0104881	+	0.0181660i
$601$	9.37441			0.382390			0.191195	−	0.981552i	$-0.438764\pi$
$601$	9.37441			0.382390			0.191195	+	0.981552i	$0.438764\pi$
$602$	−8.35826	+	0.735319i	−0.340657	+	0.0299694i
$603$	−4.30616			−0.175360
$604$	−0.174600	−	0.302416i	−0.00710438	−	0.0123051i
$605$	−0.250064	+	0.433123i	−0.0101665	+	0.0176089i
$606$	−6.61479	+	11.4572i	−0.268708	+	0.465415i
$607$	−10.3804	−	17.9794i	−0.421327	−	0.729760i	0.574742	−	0.818334i	$-0.305102\pi$
$607$	−10.3804	−	17.9794i	−0.421327	−	0.729760i	−0.996070	+	0.0885743i	$0.971769\pi$
$608$	−1.00000			−0.0405554
$609$	11.0838	+	15.8131i	0.449139	+	0.640778i
$610$	−14.6551			−0.593368
$611$	15.1552	+	26.2496i	0.613115	+	1.06195i
$612$	−3.47814	+	6.02432i	−0.140596	+	0.243519i
$613$	−1.62869	+	2.82097i	−0.0657822	+	0.113938i	−0.897041	−	0.441948i	$-0.854288\pi$
$613$	−1.62869	+	2.82097i	−0.0657822	+	0.113938i	0.831259	+	0.555886i	$0.187621\pi$
$614$	2.89683	+	5.01745i	0.116906	+	0.202488i
$615$	21.8922			0.882777
$616$	5.09035	+	7.26231i	0.205096	+	0.292607i
$617$	−9.82446			−0.395518			−0.197759	−	0.980251i	$-0.563366\pi$
$617$	−9.82446			−0.395518			−0.197759	+	0.980251i	$0.563366\pi$
$618$	3.72700	+	6.45536i	0.149922	+	0.259672i
$619$	6.88508	−	11.9253i	0.276735	−	0.479319i	−0.693837	−	0.720133i	$-0.744081\pi$
$619$	6.88508	−	11.9253i	0.276735	−	0.479319i	0.970571	+	0.240814i	$0.0774143\pi$
$620$	−4.81735	+	8.34390i	−0.193470	+	0.335099i
$621$	−3.59035	−	6.21867i	−0.144076	−	0.249547i
$622$	−18.6786			−0.748944
$623$	9.99844	−	0.879614i	0.400579	−	0.0352410i
$624$	4.23612			0.169581
$625$	11.0835	+	19.1971i	0.443339	+	0.767885i
$626$	12.8684	−	22.2888i	0.514326	−	0.890838i
$627$	1.67602	−	2.90295i	0.0669337	−	0.115932i
$628$	−6.52435	−	11.3005i	−0.260350	−	0.450939i
$629$	−1.75450			−0.0699565
$630$	2.36584	−	5.07997i	0.0942575	−	0.202391i
$631$	45.3832			1.80668			0.903338	−	0.428930i	$-0.141109\pi$
$631$	45.3832			1.80668			0.903338	+	0.428930i	$0.141109\pi$
$632$	1.13557	+	1.96687i	0.0451706	+	0.0782378i
$633$	−11.6935	+	20.2537i	−0.464774	+	0.805013i
$634$	−10.3764	+	17.9724i	−0.412099	+	0.713776i
$635$	−12.9515	−	22.4327i	−0.513965	−	0.890213i
$636$	−1.75733			−0.0696827
$637$	19.0824	+	22.6970i	0.756073	+	0.899288i
$638$	−24.4657			−0.968607
$639$	5.22592	+	9.05157i	0.206734	+	0.358074i
$640$	1.05903	−	1.83430i	0.0418619	−	0.0725069i
$641$	10.5389	−	18.2540i	0.416263	−	0.720988i	−0.579297	−	0.815116i	$-0.696673\pi$
$641$	10.5389	−	18.2540i	0.416263	−	0.720988i	0.995560	+	0.0941282i	$0.0300064\pi$
$642$	−4.30354	−	7.45395i	−0.169847	−	0.294184i
$643$	28.6923			1.13151			0.565757	−	0.824572i	$-0.308584\pi$
$643$	28.6923			1.13151			0.565757	+	0.824572i	$0.308584\pi$
$644$	8.02074	−	17.2222i	0.316061	−	0.678651i
$645$	−6.71707			−0.264484
$646$	3.47814	+	6.02432i	0.136846	+	0.237024i
$647$	−0.425741	+	0.737405i	−0.0167376	+	0.0289904i	−0.874273	−	0.485435i	$-0.838661\pi$
$647$	−0.425741	+	0.737405i	−0.0167376	+	0.0289904i	0.857535	+	0.514425i	$0.171995\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−21.8662	−	37.8734i	−0.858325	−	1.48666i
$650$	−2.17657			−0.0853721
$651$	−11.9888	+	1.05471i	−0.469877	+	0.0413375i
$652$	15.4614			0.605515
$653$	0.507356	+	0.878766i	0.0198544	+	0.0343888i	0.875782	−	0.482707i	$-0.160346\pi$
$653$	0.507356	+	0.878766i	0.0198544	+	0.0343888i	−0.855928	+	0.517096i	$0.827013\pi$
$654$	−3.15373	+	5.46242i	−0.123321	+	0.213598i
$655$	1.08136	−	1.87296i	0.0422521	−	0.0731827i
$656$	5.16797	+	8.95119i	0.201775	+	0.349485i
$657$	−12.7667			−0.498077
$658$	10.8658	+	15.5021i	0.423595	+	0.604335i
$659$	10.9687			0.427279			0.213639	−	0.976913i	$-0.431468\pi$
$659$	10.9687			0.427279			0.213639	+	0.976913i	$0.431468\pi$
$660$	3.54991	+	6.14862i	0.138180	+	0.239335i
$661$	10.1333	−	17.5514i	0.394141	−	0.682672i	−0.598850	−	0.800861i	$-0.704376\pi$
$661$	10.1333	−	17.5514i	0.394141	−	0.682672i	0.992991	+	0.118189i	$0.0377089\pi$
$662$	−17.5018	+	30.3139i	−0.680225	+	1.17818i
$663$	−14.7338	−	25.5198i	−0.572215	−	0.991106i
$664$	−16.5699			−0.643037
$665$	−3.21646	−	4.58887i	−0.124729	−	0.177949i
$666$	0.252218			0.00977325
$667$	26.2051	+	45.3886i	1.01467	+	1.75746i
$668$	2.34399	−	4.05990i	0.0906916	−	0.157082i
$669$	4.90160	−	8.48982i	0.189507	−	0.328236i
$670$	−4.56036	−	7.89878i	−0.176182	−	0.305156i
$671$	23.1931			0.895359
$672$	2.63557	−	0.231865i	0.101669	−	0.00894437i
$673$	40.5792			1.56421			0.782107	−	0.623145i	$-0.214145\pi$
$673$	40.5792			1.56421			0.782107	+	0.623145i	$0.214145\pi$
$674$	−4.53282	−	7.85108i	−0.174598	−	0.302412i
$675$	−0.256906	+	0.444974i	−0.00988831	+	0.0171271i
$676$	−2.47238	+	4.28228i	−0.0950914	+	0.164703i
$677$	4.55641	+	7.89193i	0.175117	+	0.303312i	0.940202	−	0.340618i	$-0.110636\pi$
$677$	4.55641	+	7.89193i	0.175117	+	0.303312i	−0.765085	+	0.643930i	$0.777303\pi$
$678$	1.97453			0.0758314
$679$	6.90376	−	14.8238i	0.264942	−	0.568886i
$680$	−14.7338			−0.565017
$681$	−9.14176	−	15.8340i	−0.350313	−	0.606760i
$682$	7.62391	−	13.2050i	0.291935	−	0.505646i
$683$	2.03979	−	3.53303i	0.0780505	−	0.135188i	−0.824358	−	0.566068i	$-0.808464\pi$
$683$	2.03979	−	3.53303i	0.0780505	−	0.135188i	0.902409	+	0.430881i	$0.141797\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$	−12.9787			−0.495889
$686$	13.1148	+	13.0768i	0.500724	+	0.499275i
$687$	1.44463			0.0551159
$688$	−1.58566	−	2.74645i	−0.0604529	−	0.104707i
$689$	3.72214	−	6.44693i	0.141802	−	0.245609i
$690$	7.60459	−	13.1715i	0.289502	−	0.501432i
$691$	0.733192	+	1.26993i	0.0278920	+	0.0483103i	0.879634	−	0.475650i	$-0.157787\pi$
$691$	0.733192	+	1.26993i	0.0278920	+	0.0483103i	−0.851742	+	0.523961i	$0.824454\pi$
$692$	−21.5283			−0.818385
$693$	−3.74417	+	8.03953i	−0.142229	+	0.305397i
$694$	17.6560			0.670211
$695$	−19.4307	−	33.6550i	−0.737050	−	1.27661i
$696$	−3.64938	+	6.32092i	−0.138330	+	0.239594i
$697$	35.9499	−	62.2670i	1.36170	−	2.35853i
$698$	9.98727	+	17.2985i	0.378024	+	0.654756i
$699$	15.6808			0.593100
$700$	−1.35419	+	0.119135i	−0.0511835	+	0.00450287i
$701$	18.9890			0.717204			0.358602	−	0.933491i	$-0.383254\pi$
$701$	18.9890			0.717204			0.358602	+	0.933491i	$0.383254\pi$
$702$	2.11806	+	3.66859i	0.0799411	+	0.138462i
$703$	0.126109	−	0.218427i	0.00475629	−	0.00823814i
$704$	−1.67602	+	2.90295i	−0.0631672	+	0.109409i
$705$	7.57762	+	13.1248i	0.285390	+	0.494309i
$706$	−22.5028			−0.846904
$707$	−20.0903	−	28.6624i	−0.755572	−	1.07796i
$708$	−13.0465			−0.490319
$709$	10.3040	+	17.8470i	0.386974	+	0.670258i	0.992041	−	0.125916i	$-0.0401871\pi$
$709$	10.3040	+	17.8470i	0.386974	+	0.670258i	−0.605067	+	0.796174i	$0.706854\pi$
$710$	−11.0688	+	19.1718i	−0.415406	+	0.719504i
$711$	−1.13557	+	1.96687i	−0.0425873	+	0.0737633i
$712$	1.89683	+	3.28540i	0.0710866	+	0.123126i
$713$	−32.6638			−1.22327
$714$	−10.5637	−	15.0711i	−0.395337	−	0.564020i
$715$	−30.0757			−1.12477
$716$	−0.919111	−	1.59195i	−0.0343488	−	0.0594938i
$717$	1.88409	−	3.26334i	0.0703627	−	0.121872i
$718$	−4.91795	+	8.51813i	−0.183536	+	0.317894i
$719$	−2.51399	−	4.35435i	−0.0937559	−	0.162390i	0.815333	−	0.578993i	$-0.196554\pi$
$719$	−2.51399	−	4.35435i	−0.0937559	−	0.162390i	−0.909089	+	0.416603i	$0.863221\pi$
$720$	2.11806			0.0789355
$721$	−19.6456	+	1.72832i	−0.731639	+	0.0643660i
$722$	−1.00000			−0.0372161
$723$	1.49781	+	2.59428i	0.0557040	+	0.0964821i
$724$	−10.1924	+	17.6538i	−0.378798	+	0.656097i
$725$	1.87510	−	3.24776i	0.0696393	−	0.120619i
$726$	−0.118062	−	0.204490i	−0.00438171	−	0.00758934i
$727$	−12.6690			−0.469866			−0.234933	−	0.972012i	$-0.575487\pi$
$727$	−12.6690			−0.469866			−0.234933	+	0.972012i	$0.575487\pi$
$728$	−4.73169	+	10.1599i	−0.175368	+	0.376552i
$729$	1.00000			0.0370370
$730$	−13.5203	−	23.4179i	−0.500410	−	0.866736i
$731$	−11.0303	+	19.1051i	−0.407972	+	0.706627i
$732$	3.45956	−	5.99213i	0.127869	−	0.221475i
$733$	−1.65416	−	2.86509i	−0.0610977	−	0.105824i	0.833859	−	0.551978i	$-0.186127\pi$
$733$	−1.65416	−	2.86509i	−0.0610977	−	0.105824i	−0.894956	+	0.446154i	$0.852793\pi$
$734$	−35.3346			−1.30422
$735$	9.54121	+	11.3485i	0.351933	+	0.418596i
$736$	7.18070			0.264684
$737$	7.21720	+	12.5006i	0.265849	+	0.460464i
$738$	−5.16797	+	8.95119i	−0.190236	+	0.329498i
$739$	10.2448	−	17.7446i	0.376863	−	0.652746i	−0.613741	−	0.789507i	$-0.710336\pi$
$739$	10.2448	−	17.7446i	0.376863	−	0.652746i	0.990604	+	0.136762i	$0.0436695\pi$
$740$	0.267107	+	0.462642i	0.00981904	+	0.0170071i
$741$	4.23612			0.155618
$742$	1.96291	−	4.21479i	0.0720608	−	0.154730i
$743$	13.7973			0.506172			0.253086	−	0.967444i	$-0.418554\pi$
$743$	13.7973			0.506172			0.253086	+	0.967444i	$0.418554\pi$
$744$	−2.27442	−	3.93940i	−0.0833841	−	0.144426i
$745$	23.2036	−	40.1899i	0.850115	−	1.47244i
$746$	16.9147	−	29.2972i	0.619292	−	1.07265i
$747$	−8.28496	−	14.3500i	−0.303131	−	0.525038i
$748$	23.3177			0.852579
$749$	22.6846	−	1.99568i	0.828877	−	0.0729205i
$750$	−11.6786			−0.426442
$751$	4.40672	+	7.63266i	0.160803	+	0.278520i	0.935157	−	0.354233i	$-0.115258\pi$
$751$	4.40672	+	7.63266i	0.160803	+	0.278520i	−0.774354	+	0.632753i	$0.781925\pi$
$752$	−3.57762	+	6.19662i	−0.130462	+	0.225967i
$753$	13.1461	−	22.7697i	0.479071	−	0.829775i
$754$	−15.4592	−	26.7762i	−0.562992	−	0.975132i
$755$	0.739628			0.0269178
$756$	1.51859	+	2.16654i	0.0552305	+	0.0787963i
$757$	−16.4445			−0.597684			−0.298842	−	0.954303i	$-0.596600\pi$
$757$	−16.4445			−0.597684			−0.298842	+	0.954303i	$0.596600\pi$
$758$	12.7499	+	22.0835i	0.463099	+	0.802110i
$759$	−12.0350	+	20.8452i	−0.436842	+	0.756633i
$760$	1.05903	−	1.83430i	0.0384151	−	0.0665369i
$761$	13.8327	+	23.9589i	0.501434	+	0.868509i	0.999999	+	0.00165644i	$0.000527262\pi$
$761$	13.8327	+	23.9589i	0.501434	+	0.868509i	−0.498565	+	0.866852i	$0.666139\pi$
$762$	12.2296			0.443031
$763$	−9.57843	−	13.6654i	−0.346762	−	0.494720i
$764$	−5.49789			−0.198907
$765$	−7.36692	−	12.7599i	−0.266352	−	0.461335i
$766$	17.8593	−	30.9332i	0.645283	−	1.11766i
$767$	27.6334	−	47.8625i	0.997784	−	1.72821i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−6.46278			−0.233054			−0.116527	−	0.993188i	$-0.537176\pi$
$769$	−6.46278			−0.233054			−0.116527	+	0.993188i	$0.537176\pi$
$770$	−18.7121	+	1.64620i	−0.674336	+	0.0593248i
$771$	19.7317			0.710619
$772$	−3.94935	−	6.84048i	−0.142140	−	0.246194i
$773$	12.2665	−	21.2461i	0.441194	−	0.764170i	−0.556585	−	0.830791i	$-0.687888\pi$
$773$	12.2665	−	21.2461i	0.441194	−	0.764170i	0.997778	+	0.0666209i	$0.0212218\pi$
$774$	1.58566	−	2.74645i	0.0569955	−	0.0987191i
$775$	1.16862	+	2.02411i	0.0419781	+	0.0727082i
$776$	6.18070			0.221874
$777$	−0.281724	+	0.604921i	−0.0101068	+	0.0217014i
$778$	−22.0248			−0.789626
$779$	5.16797	+	8.95119i	0.185162	+	0.320710i
$780$	−4.48619	+	7.77031i	−0.160631	+	0.278222i
$781$	17.5175	−	30.3411i	0.626824	−	1.08569i
$782$	−24.9755	−	43.2588i	−0.893122	−	1.54693i
$783$	−7.29877			−0.260837
$784$	−2.38779	+	6.58016i	−0.0852782	+	0.235006i
$785$	27.6380			0.986441
$786$	0.510540	+	0.884281i	0.0182104	+	0.0315413i
$787$	−0.606405	+	1.05032i	−0.0216160	+	0.0374400i	−0.876631	−	0.481163i	$-0.840214\pi$
$787$	−0.606405	+	1.05032i	−0.0216160	+	0.0374400i	0.855015	+	0.518603i	$0.173548\pi$
$788$	0.968679	−	1.67780i	0.0345078	−	0.0597692i
$789$	−2.22124	−	3.84729i	−0.0790781	−	0.136967i
$790$	−4.81042			−0.171147
$791$	−2.20552	+	4.73572i	−0.0784193	+	0.168383i
$792$	−3.35203			−0.119109
$793$	14.6551	+	25.3834i	0.520418	+	0.901391i
$794$	9.86584	−	17.0881i	0.350126	−	0.606436i
$795$	1.86107	−	3.22347i	0.0660053	−	0.114325i
$796$	−4.36912	−	7.56753i	−0.154859	−	0.268224i
$797$	3.35867			0.118970			0.0594851	−	0.998229i	$-0.481054\pi$
$797$	3.35867			0.118970			0.0594851	+	0.998229i	$0.481054\pi$
$798$	2.63557	−	0.231865i	0.0932982	−	0.00820792i
$799$	49.7738			1.76087
$800$	−0.256906	−	0.444974i	−0.00908299	−	0.0157322i
$801$	−1.89683	+	3.28540i	−0.0670211	+	0.116084i
$802$	7.42638	−	12.8629i	0.262235	−	0.454204i
$803$	21.3972	+	37.0611i	0.755091	+	1.30786i
$804$	4.30616			0.151867
$805$	23.0965	+	32.9513i	0.814043	+	1.16138i
$806$	19.2694			0.678736
$807$	9.73982	+	16.8699i	0.342858	+	0.593847i
$808$	6.61479	−	11.4572i	0.232708	−	0.403061i
$809$	5.94424	−	10.2957i	0.208988	−	0.361978i	−0.742408	−	0.669948i	$-0.766316\pi$
$809$	5.94424	−	10.2957i	0.208988	−	0.361978i	0.951396	+	0.307970i	$0.0996496\pi$
$810$	1.05903	+	1.83430i	0.0372106	+	0.0644506i
$811$	−27.5357			−0.966908			−0.483454	−	0.875370i	$-0.660618\pi$
$811$	−27.5357			−0.966908			−0.483454	+	0.875370i	$0.660618\pi$
$812$	−11.0838	−	15.8131i	−0.388965	−	0.554930i
$813$	−1.57578			−0.0552648
$814$	−0.422721	−	0.732175i	−0.0148164	−	0.0256627i
$815$	−16.3741	+	28.3608i	−0.573560	+	0.993435i
$816$	3.47814	−	6.02432i	0.121759	−	0.210893i
$817$	−1.58566	−	2.74645i	−0.0554754	−	0.0960862i
$818$	−6.03632			−0.211055
$819$	−11.1646	+	0.982207i	−0.390123	+	0.0343211i
$820$	−21.8922			−0.764508
$821$	−19.3370	−	33.4927i	−0.674867	−	1.16890i	−0.976508	−	0.215482i	$-0.930868\pi$
$821$	−19.3370	−	33.4927i	−0.674867	−	1.16890i	0.301641	−	0.953421i	$-0.402465\pi$
$822$	3.06381	−	5.30667i	0.106863	−	0.185091i
$823$	−17.5783	+	30.4465i	−0.612741	+	1.06130i	0.378035	+	0.925791i	$0.376600\pi$
$823$	−17.5783	+	30.4465i	−0.612741	+	1.06130i	−0.990776	+	0.135507i	$0.956734\pi$
$824$	−3.72700	−	6.45536i	−0.129836	−	0.224883i
$825$	1.72231			0.0599633
$826$	14.5728	−	31.2909i	0.507053	−	1.08875i
$827$	0.861710			0.0299646			0.0149823	−	0.999888i	$-0.495231\pi$
$827$	0.861710			0.0299646			0.0149823	+	0.999888i	$0.495231\pi$
$828$	3.59035	+	6.21867i	0.124773	+	0.216114i
$829$	−1.92565	+	3.33533i	−0.0668807	+	0.115841i	−0.897527	−	0.440960i	$-0.854638\pi$
$829$	−1.92565	+	3.33533i	−0.0668807	+	0.115841i	0.830646	+	0.556801i	$0.187971\pi$
$830$	17.5481	−	30.3941i	0.609102	−	1.05500i
$831$	4.90306	+	8.49234i	0.170085	+	0.294596i
$832$	−4.23612			−0.146861
$833$	47.9460	−	8.50191i	1.66123	−	0.294574i
$834$	18.3476			0.635327
$835$	4.96471	+	8.59913i	0.171811	+	0.297585i
$836$	−1.67602	+	2.90295i	−0.0579662	+	0.100400i
$837$	2.27442	−	3.93940i	0.0786153	−	0.136166i
$838$	7.06849	+	12.2430i	0.244177	+	0.422927i
$839$	−14.4709			−0.499593			−0.249796	−	0.968298i	$-0.580364\pi$
$839$	−14.4709			−0.499593			−0.249796	+	0.968298i	$0.580364\pi$
$840$	−2.36584	+	5.07997i	−0.0816294	+	0.175276i
$841$	24.2720			0.836965
$842$	−17.8782	−	30.9660i	−0.616124	−	1.06716i
$843$	−1.80320	+	3.12324i	−0.0621056	+	0.107570i
$844$	11.6935	−	20.2537i	0.402506	−	0.697162i
$845$	−5.23665	−	9.07014i	−0.180146	−	0.312022i
$846$	−7.15524			−0.246002
$847$	0.622324	−	0.0547490i	0.0213833	−	0.00188120i
$848$	1.75733			0.0603470
$849$	−10.7664	−	18.6479i	−0.369501	−	0.639994i
$850$	−1.78711	+	3.09536i	−0.0612974	+	0.106170i
$851$	−0.905551	+	1.56846i	−0.0310419	+	0.0537661i
$852$	−5.22592	−	9.05157i	−0.179037	−	0.310102i
$853$	−22.3323			−0.764642			−0.382321	−	0.924030i	$-0.624875\pi$
$853$	−22.3323			−0.764642			−0.382321	+	0.924030i	$0.624875\pi$
$854$	10.5073	+	14.9905i	0.359551	+	0.512965i
$855$	2.11806			0.0724362
$856$	4.30354	+	7.45395i	0.147092	+	0.254771i
$857$	15.8047	−	27.3746i	0.539879	−	0.935099i	−0.459031	−	0.888420i	$-0.651803\pi$
$857$	15.8047	−	27.3746i	0.539879	−	0.935099i	0.998910	−	0.0466781i	$-0.0148635\pi$
$858$	7.09982	−	12.2972i	0.242384	−	0.419821i
$859$	−11.8560	−	20.5352i	−0.404521	−	0.700651i	0.589745	−	0.807590i	$-0.299228\pi$
$859$	−11.8560	−	20.5352i	−0.404521	−	0.700651i	−0.994266	+	0.106939i	$0.965895\pi$
$860$	6.71707			0.229050
$861$	−15.6960	−	22.3932i	−0.534919	−	0.763159i
$862$	−17.4242			−0.593471
$863$	13.9643	+	24.1869i	0.475351	+	0.823333i	0.999601	−	0.0282317i	$-0.00898762\pi$
$863$	13.9643	+	24.1869i	0.475351	+	0.823333i	−0.524250	+	0.851564i	$0.675654\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	22.7992	−	39.4894i	0.775196	−	1.34268i
$866$	−0.372814	−	0.645733i	−0.0126687	−	0.0219429i
$867$	−31.3899			−1.06606
$868$	11.9888	−	1.05471i	0.406925	−	0.0357993i
$869$	7.61295			0.258252
$870$	−7.72962	−	13.3881i	−0.262059	−	0.453899i
$871$	−9.12072	+	15.7976i	−0.309044	+	0.535280i
$872$	3.15373	−	5.46242i	0.106799	−	0.184981i
$873$	3.09035	+	5.35265i	0.104593	+	0.181160i
$874$	7.18070			0.242891
$875$	13.0448	−	28.0100i	0.440995	−	0.946911i
$876$	12.7667			0.431347
$877$	6.14418	+	10.6420i	0.207474	+	0.359356i	0.950918	−	0.309442i	$-0.100142\pi$
$877$	6.14418	+	10.6420i	0.207474	+	0.359356i	−0.743444	+	0.668798i	$0.766809\pi$
$878$	5.86443	−	10.1575i	0.197915	−	0.342799i
$879$	−12.1473	+	21.0397i	−0.409717	+	0.709651i
$880$	−3.54991	−	6.14862i	−0.119667	−	0.207270i
$881$	−20.8380			−0.702049			−0.351024	−	0.936366i	$-0.614167\pi$
$881$	−20.8380			−0.702049			−0.351024	+	0.936366i	$0.614167\pi$
$882$	−6.89248	+	1.22219i	−0.232082	+	0.0411533i
$883$	−43.9662			−1.47958			−0.739790	−	0.672838i	$-0.765075\pi$
$883$	−43.9662			−1.47958			−0.739790	+	0.672838i	$0.765075\pi$
$884$	14.7338	+	25.5198i	0.495553	+	0.858323i
$885$	13.8167	−	23.9312i	0.464443	−	0.804440i
$886$	3.47805	−	6.02417i	0.116848	−	0.202386i
$887$	−0.105707	−	0.183090i	−0.00354930	−	0.00614757i	0.864245	−	0.503071i	$-0.167796\pi$
$887$	−0.105707	−	0.183090i	−0.00354930	−	0.00614757i	−0.867795	+	0.496923i	$0.834463\pi$
$888$	−0.252218			−0.00846388
$889$	−13.6603	+	29.3315i	−0.458151	+	0.983746i
$890$	−8.03519			−0.269340
$891$	−1.67602	−	2.90295i	−0.0561487	−	0.0972523i
$892$	−4.90160	+	8.48982i	−0.164118	+	0.284260i
$893$	−3.57762	+	6.19662i	−0.119720	+	0.207362i
$894$	10.9551	+	18.9748i	0.366394	+	0.634613i
$895$	3.89347			0.130144
$896$	−2.63557	+	0.231865i	−0.0880483	+	0.00774605i
$897$	−30.4184			−1.01564
$898$	−13.7911	−	23.8870i	−0.460217	−	0.797118i
$899$	−16.6004	+	28.7528i	−0.553655	+	0.958959i
$900$	0.256906	−	0.444974i	0.00856353	−	0.0148325i
$901$	−6.11225	−	10.5867i	−0.203629	−	0.352695i
$902$	34.6464			1.15360
$903$	4.81594	+	6.87081i	0.160264	+	0.228646i
$904$	−1.97453			−0.0656719
$905$	−21.5882	−	37.3918i	−0.717615	−	1.24295i
$906$	−0.174600	+	0.302416i	−0.00580070	+	0.0100471i
$907$	−14.9938	+	25.9700i	−0.497861	+	0.862321i	−0.999997	−	0.00246786i	$-0.999214\pi$
$907$	−14.9938	+	25.9700i	−0.497861	+	0.862321i	0.502136	+	0.864789i	$0.332548\pi$
$908$	9.14176	+	15.8340i	0.303380	+	0.525470i
$909$	13.2296			0.438798
$910$	−13.6253	−	19.4390i	−0.451675	−	0.644397i
$911$	36.8337			1.22035			0.610177	−	0.792265i	$-0.291098\pi$
$911$	36.8337			1.22035			0.610177	+	0.792265i	$0.291098\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$	−27.7714	+	48.1015i	−0.919101	+	1.59193i
$914$	10.3866	−	17.9902i	0.343559	−	0.595062i
$915$	7.32755	+	12.6917i	0.242241	+	0.419575i
$916$	−1.44463			−0.0477318
$917$	−2.69113	+	0.236752i	−0.0888689	+	0.00781825i
$918$	6.95628			0.229592
$919$	−10.3368	−	17.9039i	−0.340980	−	0.590594i	0.643635	−	0.765332i	$-0.277425\pi$
$919$	−10.3368	−	17.9039i	−0.340980	−	0.590594i	−0.984615	+	0.174738i	$0.944092\pi$
$920$	−7.60459	+	13.1715i	−0.250716	+	0.434253i
$921$	2.89683	−	5.01745i	0.0954537	−	0.165331i
$922$	16.8305	+	29.1513i	0.554283	+	0.960047i
$923$	44.2753			1.45734
$924$	3.74417	−	8.03953i	0.123174	−	0.264481i
$925$	0.129592			0.00426097
$926$	−9.24666	−	16.0157i	−0.303864	−	0.526308i
$927$	3.72700	−	6.45536i	0.122411	−	0.212022i
$928$	3.64938	−	6.32092i	0.119797	−	0.207494i
$929$	26.2416	+	45.4518i	0.860960	+	1.49123i	0.871004	+	0.491277i	$0.163470\pi$
$929$	26.2416	+	45.4518i	0.860960	+	1.49123i	−0.0100438	+	0.999950i	$0.503197\pi$
$930$	9.63471			0.315934
$931$	−2.38779	+	6.58016i	−0.0782566	+	0.215656i
$932$	−15.6808			−0.513640
$933$	9.33930	+	16.1761i	0.305755	+	0.529583i
$934$	−6.71646	+	11.6333i	−0.219769	+	0.380652i
$935$	−24.6942	+	42.7715i	−0.807586	+	1.39878i
$936$	−2.11806	−	3.66859i	−0.0692310	−	0.119912i
$937$	8.21848			0.268486			0.134243	−	0.990948i	$-0.457140\pi$
$937$	8.21848			0.268486			0.134243	+	0.990948i	$0.457140\pi$
$938$	−4.80992	+	10.3279i	−0.157049	+	0.337219i
$939$	−25.7369			−0.839890
$940$	−7.57762	−	13.1248i	−0.247155	−	0.428084i
$941$	−10.5412	+	18.2578i	−0.343632	+	0.595189i	−0.985104	−	0.171958i	$-0.944991\pi$
$941$	−10.5412	+	18.2578i	−0.343632	+	0.595189i	0.641472	+	0.767146i	$0.278324\pi$
$942$	−6.52435	+	11.3005i	−0.212575	+	0.368190i
$943$	−37.1097	−	64.2758i	−1.20846	−	2.09311i
$944$	13.0465			0.424629
$945$	−5.58231	+	0.491104i	−0.181592	+	0.0159756i
$946$	−10.6304			−0.345624
$947$	−27.0863	−	46.9148i	−0.880185	−	1.52453i	−0.851135	−	0.524947i	$-0.824085\pi$
$947$	−27.0863	−	46.9148i	−0.880185	−	1.52453i	−0.0290503	−	0.999578i	$-0.509248\pi$
$948$	1.13557	−	1.96687i	0.0368817	−	0.0638809i
$949$	−27.0407	+	46.8358i	−0.877778	+	1.52036i
$950$	−0.256906	−	0.444974i	−0.00833512	−	0.0144369i
$951$	20.7528			0.672955
$952$	10.5637	+	15.0711i	0.342372	+	0.488456i
$953$	21.4081			0.693477			0.346739	−	0.937962i	$-0.387289\pi$
$953$	21.4081			0.693477			0.346739	+	0.937962i	$0.387289\pi$
$954$	0.878666	+	1.52189i	0.0284479	+	0.0492731i
$955$	5.82244	−	10.0848i	0.188410	−	0.326335i
$956$	−1.88409	+	3.26334i	−0.0609359	+	0.105544i
$957$	12.2329	+	21.1879i	0.395432	+	0.684908i
$958$	4.05893			0.131138
$959$	9.30531	+	13.2757i	0.300484	+	0.428695i
$960$	−2.11806			−0.0683602
$961$	5.15407	+	8.92711i	0.166260	+	0.287971i
$962$	0.534213	−	0.925285i	0.0172237	−	0.0298324i
$963$	−4.30354	+	7.45395i	−0.138680	+	0.240200i
$964$	−1.49781	−	2.59428i	−0.0482411	−	0.0835560i
$965$	16.7300			0.538556
$966$	−18.9253	+	1.66495i	−0.608910	+	0.0535689i
$967$	41.4314			1.33234			0.666171	−	0.745799i	$-0.267932\pi$
$967$	41.4314			1.33234			0.666171	+	0.745799i	$0.267932\pi$
$968$	0.118062	+	0.204490i	0.00379467	+	0.00657256i
$969$	3.47814	−	6.02432i	0.111734	−	0.193529i
$970$	−6.54556	+	11.3372i	−0.210165	+	0.364017i
$971$	−8.87315	−	15.3688i	−0.284753	−	0.493207i	0.687796	−	0.725904i	$-0.258578\pi$
$971$	−8.87315	−	15.3688i	−0.284753	−	0.493207i	−0.972549	+	0.232697i	$0.925245\pi$
$972$	−1.00000			−0.0320750
$973$	−20.4940	+	44.0051i	−0.657009	+	1.41074i
$974$	−37.5078			−1.20183
$975$	1.08828	+	1.88496i	0.0348530	+	0.0603672i
$976$	−3.45956	+	5.99213i	−0.110738	+	0.191803i
$977$	16.3988	−	28.4035i	0.524643	−	0.908708i	−0.474946	−	0.880015i	$-0.657532\pi$
$977$	16.3988	−	28.4035i	0.524643	−	0.908708i	0.999588	−	0.0286926i	$-0.00913440\pi$
$978$	−7.73070	−	13.3900i	−0.247200	−	0.428164i
$979$	12.7164			0.406419
$980$	−9.54121	−	11.3485i	−0.304783	−	0.362515i
$981$	6.30746			0.201382
$982$	−13.6115	−	23.5758i	−0.434361	−	0.752335i
$983$	10.0285	−	17.3698i	0.319859	−	0.554012i	−0.660600	−	0.750738i	$-0.729698\pi$
$983$	10.0285	−	17.3698i	0.319859	−	0.554012i	0.980458	+	0.196727i	$0.0630312\pi$
$984$	5.16797	−	8.95119i	0.164749	−	0.285353i
$985$	2.05172	+	3.55369i	0.0653733	+	0.113230i
$986$	−50.7723			−1.61692
$987$	7.99229	−	17.1611i	0.254397	−	0.546245i
$988$	−4.23612			−0.134769
$989$	11.3862	+	19.7215i	0.362060	+	0.627106i
$990$	3.54991	−	6.14862i	0.112823	−	0.195416i
$991$	−10.1783	+	17.6293i	−0.323324	+	0.560013i	−0.981172	−	0.193137i	$-0.938134\pi$
$991$	−10.1783	+	17.6293i	−0.323324	+	0.560013i	0.657848	+	0.753151i	$0.271467\pi$
$992$	2.27442	+	3.93940i	0.0722128	+	0.125076i
$993$	35.0035			1.11080
$994$	27.5466	−	2.42341i	0.873725	−	0.0768660i
$995$	18.5081			0.586747
$996$	8.28496	+	14.3500i	0.262519	+	0.454696i
$997$	−0.131921	+	0.228494i	−0.00417798	+	0.00723648i	−0.868107	−	0.496377i	$-0.834663\pi$
$997$	−0.131921	+	0.228494i	−0.00417798	+	0.00723648i	0.863929	+	0.503614i	$0.167997\pi$
$998$	3.46825	−	6.00719i	0.109786	−	0.190154i
$999$	−0.126109	−	0.218427i	−0.00398991	−	0.00691073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.j.l.571.2	yes	8
7.2	even	3	inner	798.2.j.l.457.2	✓	8
7.3	odd	6		5586.2.a.bz.1.2		4
7.4	even	3		5586.2.a.bw.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.2	✓	8	7.2	even	3	inner
798.2.j.l.571.2	yes	8	1.1	even	1	trivial
5586.2.a.bw.1.3		4	7.4	even	3
5586.2.a.bz.1.2		4	7.3	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.05903 - 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 + 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.05903 - 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 + 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.05903 - 1.83430i) q^{10} +(-1.67602 + 2.90295i) q^{11} +(0.500000 + 0.866025i) q^{12} -4.23612 q^{13} +(-2.63557 + 0.231865i) q^{14} -2.11806 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.47814 + 6.02432i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +2.11806 q^{20} +(1.51859 + 2.16654i) q^{21} -3.35203 q^{22} +(3.59035 + 6.21867i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.256906 - 0.444974i) q^{25} +(-2.11806 - 3.66859i) q^{26} -1.00000 q^{27} +(-1.51859 - 2.16654i) q^{28} +7.29877 q^{29} +(-1.05903 - 1.83430i) q^{30} +(-2.27442 + 3.93940i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.67602 + 2.90295i) q^{33} -6.95628 q^{34} +(5.58231 - 0.491104i) q^{35} +1.00000 q^{36} +(0.126109 + 0.218427i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-2.11806 + 3.66859i) q^{39} +(1.05903 + 1.83430i) q^{40} -10.3359 q^{41} +(-1.11699 + 2.39840i) q^{42} +3.17133 q^{43} +(-1.67602 - 2.90295i) q^{44} +(-1.05903 + 1.83430i) q^{45} +(-3.59035 + 6.21867i) q^{46} +(-3.57762 - 6.19662i) q^{47} -1.00000 q^{48} +(-4.50469 - 5.35796i) q^{49} +0.513812 q^{50} +(3.47814 + 6.02432i) q^{51} +(2.11806 - 3.66859i) q^{52} +(-0.878666 + 1.52189i) q^{53} +(-0.500000 - 0.866025i) q^{54} +7.09982 q^{55} +(1.11699 - 2.39840i) q^{56} -1.00000 q^{57} +(3.64938 + 6.32092i) q^{58} +(-6.52327 + 11.2986i) q^{59} +(1.05903 - 1.83430i) q^{60} +(-3.45956 - 5.99213i) q^{61} -4.54883 q^{62} +(2.63557 - 0.231865i) q^{63} +1.00000 q^{64} +(4.48619 + 7.77031i) q^{65} +(-1.67602 + 2.90295i) q^{66} +(2.15308 - 3.72925i) q^{67} +(-3.47814 - 6.02432i) q^{68} +7.18070 q^{69} +(3.21646 + 4.58887i) q^{70} -10.4518 q^{71} +(0.500000 + 0.866025i) q^{72} +(6.38335 - 11.0563i) q^{73} +(-0.126109 + 0.218427i) q^{74} +(-0.256906 - 0.444974i) q^{75} +1.00000 q^{76} +(-5.09035 - 7.26231i) q^{77} -4.23612 q^{78} +(-1.13557 - 1.96687i) q^{79} +(-1.05903 + 1.83430i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.16797 - 8.95119i) q^{82} +16.5699 q^{83} +(-2.63557 + 0.231865i) q^{84} +14.7338 q^{85} +(1.58566 + 2.74645i) q^{86} +(3.64938 - 6.32092i) q^{87} +(1.67602 - 2.90295i) q^{88} +(-1.89683 - 3.28540i) q^{89} -2.11806 q^{90} +(4.73169 - 10.1599i) q^{91} -7.18070 q^{92} +(2.27442 + 3.93940i) q^{93} +(3.57762 - 6.19662i) q^{94} +(-1.05903 + 1.83430i) q^{95} +(-0.500000 - 0.866025i) q^{96} -6.18070 q^{97} +(2.38779 - 6.58016i) q^{98} +3.35203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

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