LMFDB - Embedded newform 722.2.c.n.429.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.4
Root			$-0.951057 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.n.653.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +(-1.17229 - 2.03046i) q^{10} +5.75621 q^{11} -2.79360 q^{12} +(0.152141 + 0.263516i) q^{13} +(-0.642040 + 1.11205i) q^{14} +(-3.27491 - 5.67231i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09310 + 3.62535i) q^{17} -4.80423 q^{18} -2.34458 q^{20} +(-1.79360 + 3.10661i) q^{21} +(2.87811 - 4.98503i) q^{22} +(3.23842 + 5.60910i) q^{23} +(-1.39680 + 2.41933i) q^{24} +(-0.248520 - 0.430448i) q^{25} +0.304282 q^{26} -5.04029 q^{27} +(0.642040 + 1.11205i) q^{28} +(-1.56378 - 2.70855i) q^{29} -6.54982 q^{30} -6.44246 q^{31} +(0.500000 + 0.866025i) q^{32} +(8.04029 - 13.9262i) q^{33} +(2.09310 + 3.62535i) q^{34} +(-1.50531 + 2.60727i) q^{35} +(-2.40211 + 4.16058i) q^{36} +3.97980 q^{37} +0.850045 q^{39} +(-1.17229 + 2.03046i) q^{40} +(-2.50859 + 4.34501i) q^{41} +(1.79360 + 3.10661i) q^{42} +(0.494689 - 0.856827i) q^{43} +(-2.87811 - 4.98503i) q^{44} -11.2639 q^{45} +6.47684 q^{46} +(2.19723 + 3.80571i) q^{47} +(1.39680 + 2.41933i) q^{48} -5.35114 q^{49} -0.497039 q^{50} +(5.84728 + 10.1278i) q^{51} +(0.152141 - 0.263516i) q^{52} +(1.64532 + 2.84978i) q^{53} +(-2.52015 + 4.36502i) q^{54} +(6.74794 - 11.6878i) q^{55} +1.28408 q^{56} -3.12756 q^{58} +(1.65688 - 2.86979i) q^{59} +(-3.27491 + 5.67231i) q^{60} +(5.48073 + 9.49290i) q^{61} +(-3.22123 + 5.57934i) q^{62} +(3.08450 + 5.34252i) q^{63} +1.00000 q^{64} +0.713414 q^{65} +(-8.04029 - 13.9262i) q^{66} +(-2.19041 - 3.79390i) q^{67} +4.18619 q^{68} +18.0937 q^{69} +(1.50531 + 2.60727i) q^{70} +(-2.20785 + 3.82410i) q^{71} +(2.40211 + 4.16058i) q^{72} +(1.13345 - 1.96319i) q^{73} +(1.98990 - 3.44660i) q^{74} -1.38853 q^{75} -7.39144 q^{77} +(0.425022 - 0.736160i) q^{78} +(4.28829 - 7.42754i) q^{79} +(1.17229 + 2.03046i) q^{80} +(0.166045 - 0.287598i) q^{81} +(2.50859 + 4.34501i) q^{82} -9.76464 q^{83} +3.58721 q^{84} +(4.90742 + 8.49991i) q^{85} +(-0.494689 - 0.856827i) q^{86} -8.73716 q^{87} -5.75621 q^{88} +(-7.53827 - 13.0567i) q^{89} +(-5.63194 + 9.75480i) q^{90} +(-0.195361 - 0.338376i) q^{91} +(3.23842 - 5.60910i) q^{92} +(-8.99885 + 15.5865i) q^{93} +4.39445 q^{94} +2.79360 q^{96} +(8.67609 - 15.0274i) q^{97} +(-2.67557 + 4.63422i) q^{98} +(-13.8271 - 23.9492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 + 8 * q^27 + 2 * q^28 - 2 * q^29 + 8 * q^30 - 52 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 - 12 * q^39 - 2 * q^40 - 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 + 20 * q^46 + 12 * q^47 + 2 * q^48 - 24 * q^49 - 12 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 + 4 * q^54 + 26 * q^55 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^66 + 10 * q^67 + 12 * q^68 + 40 * q^69 + 6 * q^70 + 4 * q^72 + 14 * q^73 - 4 * q^74 - 16 * q^75 + 8 * q^77 - 6 * q^78 + 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 - 8 * q^84 + 18 * q^85 - 10 * q^86 - 52 * q^87 - 4 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 + 10 * q^92 - 8 * q^93 + 24 * q^94 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.39680	−	2.41933i	0.806444	−	1.39680i	−0.108868	−	0.994056i	$-0.534722\pi$
$3$	1.39680	−	2.41933i	0.806444	−	1.39680i	0.915312	−	0.402746i	$-0.131944\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.17229	−	2.03046i	0.524263	−	0.908051i	−0.475338	−	0.879803i	$-0.657674\pi$
$5$	1.17229	−	2.03046i	0.524263	−	0.908051i	0.999601	−	0.0282472i	$-0.00899255\pi$
$6$	−1.39680	−	2.41933i	−0.570242	−	0.987688i
$7$	−1.28408			−0.485336			−0.242668	−	0.970109i	$-0.578023\pi$
$7$	−1.28408			−0.485336			−0.242668	+	0.970109i	$0.578023\pi$
$8$	−1.00000			−0.353553
$9$	−2.40211	−	4.16058i	−0.800704	−	1.38686i
$10$	−1.17229	−	2.03046i	−0.370710	−	0.642089i
$11$	5.75621			1.73556			0.867782	−	0.496945i	$-0.165545\pi$
$11$	5.75621			1.73556			0.867782	+	0.496945i	$0.165545\pi$
$12$	−2.79360			−0.806444
$13$	0.152141	+	0.263516i	0.0421964	+	0.0730863i	0.886352	−	0.463012i	$-0.153231\pi$
$13$	0.152141	+	0.263516i	0.0421964	+	0.0730863i	−0.844156	+	0.536098i	$0.819898\pi$
$14$	−0.642040	+	1.11205i	−0.171592	+	0.297207i
$15$	−3.27491	−	5.67231i	−0.845578	−	1.46458i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.09310	+	3.62535i	−0.507650	+	0.879276i	0.492310	+	0.870420i	$0.336152\pi$
$17$	−2.09310	+	3.62535i	−0.507650	+	0.879276i	−0.999961	+	0.00885651i	$0.997181\pi$
$18$	−4.80423			−1.13237
$19$		0			0
$19$		0			0
$20$	−2.34458			−0.524263
$21$	−1.79360	+	3.10661i	−0.391397	+	0.677919i
$22$	2.87811	−	4.98503i	0.613615	−	1.06281i
$23$	3.23842	+	5.60910i	0.675257	+	1.16958i	0.976394	+	0.215998i	$0.0693005\pi$
$23$	3.23842	+	5.60910i	0.675257	+	1.16958i	−0.301137	+	0.953581i	$0.597366\pi$
$24$	−1.39680	+	2.41933i	−0.285121	+	0.493844i
$25$	−0.248520	−	0.430448i	−0.0497039	−	0.0860897i
$26$	0.304282			0.0596747
$27$	−5.04029			−0.970005
$28$	0.642040	+	1.11205i	0.121334	+	0.210157i
$29$	−1.56378	−	2.70855i	−0.290387	−	0.502964i	0.683515	−	0.729937i	$-0.260451\pi$
$29$	−1.56378	−	2.70855i	−0.290387	−	0.502964i	−0.973901	+	0.226973i	$0.927117\pi$
$30$	−6.54982			−1.19583
$31$	−6.44246			−1.15710			−0.578550	−	0.815647i	$-0.696381\pi$
$31$	−6.44246			−1.15710			−0.578550	+	0.815647i	$0.696381\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	8.04029	−	13.9262i	1.39964	−	2.42424i
$34$	2.09310	+	3.62535i	0.358963	+	0.621742i
$35$	−1.50531	+	2.60727i	−0.254444	+	0.440710i
$36$	−2.40211	+	4.16058i	−0.400352	+	0.693430i
$37$	3.97980			0.654275			0.327137	−	0.944977i	$-0.393916\pi$
$37$	3.97980			0.654275			0.327137	+	0.944977i	$0.393916\pi$
$38$		0			0
$39$	0.850045			0.136116
$40$	−1.17229	+	2.03046i	−0.185355	+	0.321044i
$41$	−2.50859	+	4.34501i	−0.391776	+	0.678577i	−0.992684	−	0.120742i	$-0.961473\pi$
$41$	−2.50859	+	4.34501i	−0.391776	+	0.678577i	0.600908	+	0.799319i	$0.294806\pi$
$42$	1.79360	+	3.10661i	0.276759	+	0.479361i
$43$	0.494689	−	0.856827i	0.0754394	−	0.130665i	−0.825838	−	0.563908i	$-0.809297\pi$
$43$	0.494689	−	0.856827i	0.0754394	−	0.130665i	0.901277	+	0.433243i	$0.142631\pi$
$44$	−2.87811	−	4.98503i	−0.433891	−	0.751521i
$45$	−11.2639			−1.67912
$46$	6.47684			0.954957
$47$	2.19723	+	3.80571i	0.320498	+	0.555119i	0.980591	−	0.196065i	$-0.0628163\pi$
$47$	2.19723	+	3.80571i	0.320498	+	0.555119i	−0.660093	+	0.751184i	$0.729483\pi$
$48$	1.39680	+	2.41933i	0.201611	+	0.349201i
$49$	−5.35114			−0.764449
$50$	−0.497039			−0.0702919
$51$	5.84728	+	10.1278i	0.818783	+	1.41817i
$52$	0.152141	−	0.263516i	0.0210982	−	0.0365431i
$53$	1.64532	+	2.84978i	0.226002	+	0.391448i	0.956620	−	0.291340i	$-0.0941010\pi$
$53$	1.64532	+	2.84978i	0.226002	+	0.391448i	−0.730617	+	0.682787i	$0.760768\pi$
$54$	−2.52015	+	4.36502i	−0.342949	+	0.594004i
$55$	6.74794	−	11.6878i	0.909892	−	1.57598i
$56$	1.28408			0.171592
$57$		0			0
$58$	−3.12756			−0.410669
$59$	1.65688	−	2.86979i	0.215707	−	0.373615i	−0.737784	−	0.675037i	$-0.764128\pi$
$59$	1.65688	−	2.86979i	0.215707	−	0.373615i	0.953491	+	0.301421i	$0.0974611\pi$
$60$	−3.27491	+	5.67231i	−0.422789	+	0.732292i
$61$	5.48073	+	9.49290i	0.701735	+	1.21544i	0.967857	+	0.251502i	$0.0809245\pi$
$61$	5.48073	+	9.49290i	0.701735	+	1.21544i	−0.266121	+	0.963940i	$0.585742\pi$
$62$	−3.22123	+	5.57934i	−0.409097	+	0.708577i
$63$	3.08450	+	5.34252i	0.388611	+	0.673094i
$64$	1.00000			0.125000
$65$	0.713414			0.0884881
$66$	−8.04029	−	13.9262i	−0.989692	−	1.71420i
$67$	−2.19041	−	3.79390i	−0.267601	−	0.463498i	0.700641	−	0.713514i	$-0.252897\pi$
$67$	−2.19041	−	3.79390i	−0.267601	−	0.463498i	−0.968242	+	0.250016i	$0.919564\pi$
$68$	4.18619			0.507650
$69$	18.0937			2.17823
$70$	1.50531	+	2.60727i	0.179919	+	0.311629i
$71$	−2.20785	+	3.82410i	−0.262023	+	0.453838i	−0.966779	−	0.255612i	$-0.917723\pi$
$71$	−2.20785	+	3.82410i	−0.262023	+	0.453838i	0.704756	+	0.709450i	$0.251056\pi$
$72$	2.40211	+	4.16058i	0.283092	+	0.490329i
$73$	1.13345	−	1.96319i	0.132660	−	0.229774i	−0.792041	−	0.610468i	$-0.790982\pi$
$73$	1.13345	−	1.96319i	0.132660	−	0.229774i	0.924701	+	0.380694i	$0.124315\pi$
$74$	1.98990	−	3.44660i	0.231321	−	0.400660i
$75$	−1.38853			−0.160334
$76$		0			0
$77$	−7.39144			−0.842332
$78$	0.425022	−	0.736160i	0.0481243	−	0.0833538i
$79$	4.28829	−	7.42754i	0.482471	−	0.835664i	−0.517327	−	0.855788i	$-0.673073\pi$
$79$	4.28829	−	7.42754i	0.482471	−	0.835664i	0.999797	+	0.0201241i	$0.00640614\pi$
$80$	1.17229	+	2.03046i	0.131066	+	0.227013i
$81$	0.166045	−	0.287598i	0.0184495	−	0.0319554i
$82$	2.50859	+	4.34501i	0.277028	+	0.479826i
$83$	−9.76464			−1.07181			−0.535904	−	0.844279i	$-0.680029\pi$
$83$	−9.76464			−1.07181			−0.535904	+	0.844279i	$0.680029\pi$
$84$	3.58721			0.391397
$85$	4.90742	+	8.49991i	0.532285	+	0.921944i
$86$	−0.494689	−	0.856827i	−0.0533437	−	0.0923940i
$87$	−8.73716			−0.936722
$88$	−5.75621			−0.613615
$89$	−7.53827	−	13.0567i	−0.799055	−	1.38400i	−0.920232	−	0.391372i	$-0.872000\pi$
$89$	−7.53827	−	13.0567i	−0.799055	−	1.38400i	0.121178	−	0.992631i	$-0.461333\pi$
$90$	−5.63194	+	9.75480i	−0.593658	+	1.02825i
$91$	−0.195361	−	0.338376i	−0.0204794	−	0.0354714i
$92$	3.23842	−	5.60910i	0.337628	−	0.584790i
$93$	−8.99885	+	15.5865i	−0.933137	+	1.61624i
$94$	4.39445			0.453253
$95$		0			0
$96$	2.79360			0.285121
$97$	8.67609	−	15.0274i	0.880924	−	1.52580i	0.0306077	−	0.999531i	$-0.490256\pi$
$97$	8.67609	−	15.0274i	0.880924	−	1.52580i	0.850316	−	0.526273i	$-0.176411\pi$
$98$	−2.67557	+	4.63422i	−0.270273	+	0.468127i
$99$	−13.8271	−	23.9492i	−1.38967	−	2.40699i
$100$	−0.248520	+	0.430448i	−0.0248520	+	0.0430448i
$101$	−1.83833	−	3.18409i	−0.182921	−	0.316828i	0.759953	−	0.649978i	$-0.225222\pi$
$101$	−1.83833	−	3.18409i	−0.182921	−	0.316828i	−0.942874	+	0.333150i	$0.891889\pi$
$102$	11.6946			1.15793
$103$	−19.0135			−1.87346			−0.936729	−	0.350055i	$-0.886163\pi$
$103$	−19.0135			−1.87346			−0.936729	+	0.350055i	$0.886163\pi$
$104$	−0.152141	−	0.263516i	−0.0149187	−	0.0258399i
$105$	4.20524	+	7.28369i	0.410390	+	0.710816i
$106$	3.29064			0.319616
$107$	−10.0373			−0.970340			−0.485170	−	0.874420i	$-0.661242\pi$
$107$	−10.0373			−0.970340			−0.485170	+	0.874420i	$0.661242\pi$
$108$	2.52015	+	4.36502i	0.242501	+	0.420025i
$109$	−4.42174	+	7.65868i	−0.423526	+	0.733568i	−0.996282	−	0.0861578i	$-0.972541\pi$
$109$	−4.42174	+	7.65868i	−0.423526	+	0.733568i	0.572756	+	0.819726i	$0.305874\pi$
$110$	−6.74794	−	11.6878i	−0.643391	−	1.11439i
$111$	5.55899	−	9.62845i	0.527636	−	0.913892i
$112$	0.642040	−	1.11205i	0.0606670	−	0.105078i
$113$	14.2502			1.34055			0.670275	−	0.742113i	$-0.266176\pi$
$113$	14.2502			1.34055			0.670275	+	0.742113i	$0.266176\pi$
$114$		0			0
$115$	15.1854			1.41605
$116$	−1.56378	+	2.70855i	−0.145193	+	0.251482i
$117$	0.730921	−	1.26599i	0.0675737	−	0.117041i
$118$	−1.65688	−	2.86979i	−0.152528	−	0.264186i
$119$	2.68770	−	4.65523i	0.246381	−	0.426745i
$120$	3.27491	+	5.67231i	0.298957	+	0.517809i
$121$	22.1340			2.01218
$122$	10.9615			0.992404
$123$	7.00802	+	12.1382i	0.631892	+	1.09447i
$124$	3.22123	+	5.57934i	0.289275	+	0.501039i
$125$	10.5575			0.944295
$126$	6.16901			0.549579
$127$	1.11507	+	1.93136i	0.0989467	+	0.171381i	0.911249	−	0.411856i	$-0.135119\pi$
$127$	1.11507	+	1.93136i	0.0989467	+	0.171381i	−0.812302	+	0.583237i	$0.801786\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.38197	−	2.39364i	−0.121675	−	0.210748i
$130$	0.356707	−	0.617834i	0.0312853	−	0.0541876i
$131$	−0.761327	+	1.31866i	−0.0665175	+	0.115212i	−0.897366	−	0.441287i	$-0.854522\pi$
$131$	−0.761327	+	1.31866i	−0.0665175	+	0.115212i	0.830849	+	0.556498i	$0.187855\pi$
$132$	−16.0806			−1.39964
$133$		0			0
$134$	−4.38081			−0.378445
$135$	−5.90868	+	10.2341i	−0.508538	+	0.880814i
$136$	2.09310	−	3.62535i	0.179482	−	0.310871i
$137$	−5.35588	−	9.27665i	−0.457583	−	0.792558i	0.541249	−	0.840862i	$-0.317952\pi$
$137$	−5.35588	−	9.27665i	−0.457583	−	0.792558i	−0.998833	+	0.0483046i	$0.984618\pi$
$138$	9.04686	−	15.6696i	0.770120	−	1.33389i
$139$	5.40717	+	9.36549i	0.458630	+	0.794371i	0.998889	−	0.0471283i	$-0.0150070\pi$
$139$	5.40717	+	9.36549i	0.458630	+	0.794371i	−0.540259	+	0.841499i	$0.681674\pi$
$140$	3.01062			0.254444
$141$	12.2764			1.03386
$142$	2.20785	+	3.82410i	0.185278	+	0.320912i
$143$	0.875758	+	1.51686i	0.0732345	+	0.126846i
$144$	4.80423			0.400352
$145$	−7.33280			−0.608956
$146$	−1.13345	−	1.96319i	−0.0938047	−	0.162475i
$147$	−7.47449	+	12.9462i	−0.616485	+	1.06778i
$148$	−1.98990	−	3.44660i	−0.163569	−	0.283309i
$149$	4.66692	−	8.08334i	0.382329	−	0.662213i	−0.609066	−	0.793120i	$-0.708455\pi$
$149$	4.66692	−	8.08334i	0.382329	−	0.662213i	0.991395	+	0.130906i	$0.0417887\pi$
$150$	−0.694265	+	1.20250i	−0.0566865	+	0.0981839i
$151$	−19.8232			−1.61319			−0.806593	−	0.591107i	$-0.798691\pi$
$151$	−19.8232			−1.61319			−0.806593	+	0.591107i	$0.798691\pi$
$152$		0			0
$153$	20.1114			1.62591
$154$	−3.69572	+	6.40117i	−0.297809	+	0.515821i
$155$	−7.55242	+	13.0812i	−0.606625	+	1.05071i
$156$	−0.425022	−	0.736160i	−0.0340290	−	0.0589400i
$157$	−6.93381	+	12.0097i	−0.553379	+	0.958480i	0.444649	+	0.895705i	$0.353328\pi$
$157$	−6.93381	+	12.0097i	−0.553379	+	0.958480i	−0.998028	+	0.0627750i	$0.980005\pi$
$158$	−4.28829	−	7.42754i	−0.341158	−	0.590904i
$159$	9.19276			0.729033
$160$	2.34458			0.185355
$161$	−4.15838	−	7.20253i	−0.327727	−	0.567639i
$162$	−0.166045	−	0.287598i	−0.0130457	−	0.0225959i
$163$	14.2496			1.11611			0.558057	−	0.829803i	$-0.311547\pi$
$163$	14.2496			1.11611			0.558057	+	0.829803i	$0.311547\pi$
$164$	5.01719			0.391776
$165$	−18.8511	−	32.6510i	−1.46755	−	2.54188i
$166$	−4.88232	+	8.45643i	−0.378942	+	0.656346i
$167$	5.79506	+	10.0373i	0.448435	+	0.776712i	0.998284	−	0.0585517i	$-0.0186482\pi$
$167$	5.79506	+	10.0373i	0.448435	+	0.776712i	−0.549849	+	0.835264i	$0.685315\pi$
$168$	1.79360	−	3.10661i	0.138380	−	0.239680i
$169$	6.45371	−	11.1781i	0.496439	−	0.859857i
$170$	9.81485			0.752764
$171$		0			0
$172$	−0.989378			−0.0754394
$173$	1.99176	−	3.44983i	0.151431	−	0.262286i	−0.780323	−	0.625377i	$-0.784945\pi$
$173$	1.99176	−	3.44983i	0.151431	−	0.262286i	0.931754	+	0.363091i	$0.118279\pi$
$174$	−4.36858	+	7.56661i	−0.331181	+	0.573623i
$175$	0.319119	+	0.552730i	0.0241231	+	0.0417824i
$176$	−2.87811	+	4.98503i	−0.216946	+	0.375761i
$177$	−4.62866	−	8.01707i	−0.347911	−	0.602600i
$178$	−15.0765			−1.13003
$179$	8.45089			0.631649			0.315825	−	0.948818i	$-0.397719\pi$
$179$	8.45089			0.631649			0.315825	+	0.948818i	$0.397719\pi$
$180$	5.63194	+	9.75480i	0.419780	+	0.727080i
$181$	4.24263	+	7.34845i	0.315352	+	0.546206i	0.979512	−	0.201384i	$-0.0645440\pi$
$181$	4.24263	+	7.34845i	0.315352	+	0.546206i	−0.664160	+	0.747591i	$0.731211\pi$
$182$	−0.390723			−0.0289623
$183$	30.6220			2.26364
$184$	−3.23842	−	5.60910i	−0.238739	−	0.413509i
$185$	4.66547	−	8.08083i	0.343012	−	0.594114i
$186$	8.99885	+	15.5865i	0.659828	+	1.14285i
$187$	−12.0483	+	20.8683i	−0.881060	+	1.52604i
$188$	2.19723	−	3.80571i	0.160249	−	0.277560i
$189$	6.47214			0.470779
$190$		0			0
$191$	−22.3790			−1.61929			−0.809644	−	0.586921i	$-0.800340\pi$
$191$	−22.3790			−1.61929			−0.809644	+	0.586921i	$0.800340\pi$
$192$	1.39680	−	2.41933i	0.100806	−	0.174600i
$193$	3.71406	−	6.43293i	0.267344	−	0.463053i	−0.700831	−	0.713327i	$-0.747187\pi$
$193$	3.71406	−	6.43293i	0.267344	−	0.463053i	0.968175	+	0.250274i	$0.0805208\pi$
$194$	−8.67609	−	15.0274i	−0.622907	−	1.07891i
$195$	0.996498	−	1.72598i	0.0713607	−	0.123600i
$196$	2.67557	+	4.63422i	0.191112	+	0.331016i
$197$	8.53554			0.608132			0.304066	−	0.952651i	$-0.401656\pi$
$197$	8.53554			0.608132			0.304066	+	0.952651i	$0.401656\pi$
$198$	−27.6542			−1.96530
$199$	3.17963	+	5.50728i	0.225398	+	0.390400i	0.956439	−	0.291933i	$-0.0942985\pi$
$199$	3.17963	+	5.50728i	0.225398	+	0.390400i	−0.731041	+	0.682334i	$0.760965\pi$
$200$	0.248520	+	0.430448i	0.0175730	+	0.0304373i
$201$	−12.2383			−0.863220
$202$	−3.67667			−0.258689
$203$	2.00802	+	3.47799i	0.140935	+	0.244107i
$204$	5.84728	−	10.1278i	0.409392	−	0.709087i
$205$	5.88159	+	10.1872i	0.410788	+	0.711506i
$206$	−9.50676	+	16.4662i	−0.662368	+	1.14725i
$207$	15.5581	−	26.9474i	1.08136	−	1.87297i
$208$	−0.304282			−0.0210982
$209$		0			0
$210$	8.41049			0.580379
$211$	−6.97890	+	12.0878i	−0.480447	+	0.832159i	−0.999748	−	0.0224323i	$-0.992859\pi$
$211$	−6.97890	+	12.0878i	−0.480447	+	0.832159i	0.519301	+	0.854591i	$0.326192\pi$
$212$	1.64532	−	2.84978i	0.113001	−	0.195724i
$213$	6.16785	+	10.6830i	0.422614	+	0.731990i
$214$	−5.01864	+	8.69254i	−0.343067	+	0.594210i
$215$	−1.15984	−	2.00890i	−0.0791002	−	0.137006i
$216$	5.04029			0.342949
$217$	8.27263			0.561583
$218$	4.42174	+	7.65868i	0.299478	+	0.518711i
$219$	−3.16640	−	5.48437i	−0.213966	−	0.370599i
$220$	−13.4959			−0.909892
$221$	−1.27378			−0.0856840
$222$	−5.55899	−	9.62845i	−0.373095	−	0.646219i
$223$	4.46200	−	7.72841i	0.298798	−	0.517533i	−0.677064	−	0.735925i	$-0.736748\pi$
$223$	4.46200	−	7.72841i	0.298798	−	0.517533i	0.975861	+	0.218392i	$0.0700811\pi$
$224$	−0.642040	−	1.11205i	−0.0428981	−	0.0743016i
$225$	−1.19394	+	2.06797i	−0.0795963	+	0.137865i
$226$	7.12512	−	12.3411i	0.473956	−	0.820916i
$227$	0.659796			0.0437922			0.0218961	−	0.999760i	$-0.493030\pi$
$227$	0.659796			0.0437922			0.0218961	+	0.999760i	$0.493030\pi$
$228$		0			0
$229$	−6.97208			−0.460728			−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208			−0.460728			−0.230364	+	0.973105i	$0.573992\pi$
$230$	7.59272	−	13.1510i	0.500649	−	0.867150i
$231$	−10.3244	+	17.8823i	−0.679294	+	1.17657i
$232$	1.56378	+	2.70855i	0.102667	+	0.177825i
$233$	14.8048	−	25.6427i	0.969898	−	1.67991i	0.274061	−	0.961712i	$-0.411633\pi$
$233$	14.8048	−	25.6427i	0.969898	−	1.67991i	0.695837	−	0.718200i	$-0.255034\pi$
$234$	−0.730921	−	1.26599i	−0.0477818	−	0.0827605i
$235$	10.3031			0.672102
$236$	−3.31375			−0.215707
$237$	−11.9798	−	20.7496i	−0.778171	−	1.34783i
$238$	−2.68770	−	4.65523i	−0.174218	−	0.301754i
$239$	−24.7034			−1.59793			−0.798965	−	0.601378i	$-0.794619\pi$
$239$	−24.7034			−1.59793			−0.798965	+	0.601378i	$0.794619\pi$
$240$	6.54982			0.422789
$241$	13.7793	+	23.8665i	0.887604	+	1.53738i	0.842699	+	0.538384i	$0.180965\pi$
$241$	13.7793	+	23.8665i	0.887604	+	1.53738i	0.0449048	+	0.998991i	$0.485702\pi$
$242$	11.0670	−	19.1686i	0.711414	−	1.23221i
$243$	−8.02431	−	13.8985i	−0.514759	−	0.891589i
$244$	5.48073	−	9.49290i	0.350868	−	0.607721i
$245$	−6.27308	+	10.8653i	−0.400772	+	0.694158i
$246$	14.0160			0.893630
$247$		0			0
$248$	6.44246			0.409097
$249$	−13.6393	+	23.6239i	−0.864354	+	1.49711i
$250$	5.27877	−	9.14309i	0.333859	−	0.578260i
$251$	1.49428	+	2.58816i	0.0943179	+	0.163363i	0.909324	−	0.416089i	$-0.136600\pi$
$251$	1.49428	+	2.58816i	0.0943179	+	0.163363i	−0.815006	+	0.579453i	$0.803266\pi$
$252$	3.08450	−	5.34252i	0.194305	−	0.336547i
$253$	18.6410	+	32.2872i	1.17195	+	2.02988i
$254$	2.23015			0.139932
$255$	27.4188			1.71703
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.06613	+	12.2389i	0.440773	+	0.763441i	0.997747	−	0.0670886i	$-0.0213710\pi$
$257$	7.06613	+	12.2389i	0.440773	+	0.763441i	−0.556974	+	0.830530i	$0.688038\pi$
$258$	−2.76393			−0.172075
$259$	−5.11037			−0.317543
$260$	−0.356707	−	0.617834i	−0.0221220	−	0.0383165i
$261$	−7.51275	+	13.0125i	−0.465028	+	0.805451i
$262$	0.761327	+	1.31866i	0.0470350	+	0.0814669i
$263$	−3.78444	+	6.55483i	−0.233358	+	0.404188i	−0.958794	−	0.284101i	$-0.908305\pi$
$263$	−3.78444	+	6.55483i	−0.233358	+	0.404188i	0.725436	+	0.688290i	$0.241638\pi$
$264$	−8.04029	+	13.9262i	−0.494846	+	0.857098i
$265$	7.71517			0.473939
$266$		0			0
$267$	−42.1179			−2.57757
$268$	−2.19041	+	3.79390i	−0.133800	+	0.231749i
$269$	−3.83537	+	6.64306i	−0.233847	+	0.405035i	−0.958937	−	0.283619i	$-0.908465\pi$
$269$	−3.83537	+	6.64306i	−0.233847	+	0.405035i	0.725090	+	0.688654i	$0.241798\pi$
$270$	5.90868	+	10.2341i	0.359591	+	0.622829i
$271$	−5.83245	+	10.1021i	−0.354296	+	0.613658i	−0.986997	−	0.160737i	$-0.948613\pi$
$271$	−5.83245	+	10.1021i	−0.354296	+	0.613658i	0.632701	+	0.774396i	$0.281946\pi$
$272$	−2.09310	−	3.62535i	−0.126913	−	0.219819i
$273$	−1.09152			−0.0660621
$274$	−10.7118			−0.647121
$275$	−1.43053	−	2.47775i	−0.0862643	−	0.149414i
$276$	−9.04686	−	15.6696i	−0.544557	−	0.943200i
$277$	27.4405			1.64874			0.824370	−	0.566052i	$-0.191530\pi$
$277$	27.4405			1.64874			0.824370	+	0.566052i	$0.191530\pi$
$278$	10.8143			0.648601
$279$	15.4755	+	26.8044i	0.926495	+	1.60474i
$280$	1.50531	−	2.60727i	0.0899595	−	0.155814i
$281$	8.13574	+	14.0915i	0.485338	+	0.840629i	0.999858	−	0.0168488i	$-0.00536339\pi$
$281$	8.13574	+	14.0915i	0.485338	+	0.840629i	−0.514520	+	0.857478i	$0.672030\pi$
$282$	6.13818	−	10.6316i	0.365523	−	0.633105i
$283$	−1.69687	+	2.93907i	−0.100868	+	0.174709i	−0.912043	−	0.410095i	$-0.865495\pi$
$283$	−1.69687	+	2.93907i	−0.100868	+	0.174709i	0.811174	+	0.584805i	$0.198829\pi$
$284$	4.41570			0.262023
$285$		0			0
$286$	1.75152			0.103569
$287$	3.22123	−	5.57934i	0.190143	−	0.329338i
$288$	2.40211	−	4.16058i	0.141546	−	0.245165i
$289$	−0.262102	−	0.453974i	−0.0154178	−	0.0267044i
$290$	−3.66640	+	6.35039i	−0.215298	+	0.372908i
$291$	−24.2376	−	41.9807i	−1.42083	−	2.46095i
$292$	−2.26689			−0.132660
$293$	−23.3783			−1.36578			−0.682888	−	0.730523i	$-0.739276\pi$
$293$	−23.3783			−1.36578			−0.682888	+	0.730523i	$0.739276\pi$
$294$	7.47449	+	12.9462i	0.435921	+	0.755037i
$295$	−3.88467	−	6.72845i	−0.226174	−	0.391745i
$296$	−3.97980			−0.231321
$297$	−29.0130			−1.68351
$298$	−4.66692	−	8.08334i	−0.270347	−	0.468256i
$299$	−0.985394	+	1.70675i	−0.0569868	+	0.0987040i
$300$	0.694265	+	1.20250i	0.0400834	+	0.0694265i
$301$	−0.635220	+	1.10023i	−0.0366135	+	0.0634164i
$302$	−9.91158	+	17.1674i	−0.570347	+	0.987871i
$303$	−10.2712			−0.590062
$304$		0			0
$305$	25.7000			1.47158
$306$	10.0557	−	17.4170i	0.574846	−	0.995663i
$307$	−0.694010	+	1.20206i	−0.0396093	+	0.0686052i	−0.885150	−	0.465305i	$-0.845945\pi$
$307$	−0.694010	+	1.20206i	−0.0396093	+	0.0686052i	0.845541	+	0.533910i	$0.179278\pi$
$308$	3.69572	+	6.40117i	0.210583	+	0.364741i
$309$	−26.5581	+	46.0000i	−1.51084	+	2.61685i
$310$	7.55242	+	13.0812i	0.428949	+	0.742961i
$311$	−12.1902			−0.691246			−0.345623	−	0.938374i	$-0.612332\pi$
$311$	−12.1902			−0.691246			−0.345623	+	0.938374i	$0.612332\pi$
$312$	−0.850045			−0.0481243
$313$	−8.26571	−	14.3166i	−0.467205	−	0.809223i	0.532093	−	0.846686i	$-0.321406\pi$
$313$	−8.26571	−	14.3166i	−0.467205	−	0.809223i	−0.999298	+	0.0374628i	$0.988072\pi$
$314$	6.93381	+	12.0097i	0.391298	+	0.677748i
$315$	14.4637			0.814938
$316$	−8.57659			−0.482471
$317$	1.34406	+	2.32797i	0.0754897	+	0.130752i	0.901299	−	0.433197i	$-0.142615\pi$
$317$	1.34406	+	2.32797i	0.0754897	+	0.130752i	−0.825809	+	0.563949i	$0.809281\pi$
$318$	4.59638	−	7.96116i	0.257752	−	0.446440i
$319$	−9.00145	−	15.5910i	−0.503985	−	0.872927i
$320$	1.17229	−	2.03046i	0.0655329	−	0.113506i
$321$	−14.0201	+	24.2835i	−0.782525	+	1.35537i
$322$	−8.31677			−0.463475
$323$		0			0
$324$	−0.332090			−0.0184495
$325$	0.0756201	−	0.130978i	0.00419465	−	0.00726535i
$326$	7.12480	−	12.3405i	0.394606	−	0.683478i
$327$	12.3526	+	21.3953i	0.683100	+	1.18316i
$328$	2.50859	−	4.34501i	0.138514	−	0.239913i
$329$	−2.82141	−	4.88683i	−0.155549	−	0.269420i
$330$	−37.7022			−2.07544
$331$	−5.21303			−0.286534			−0.143267	−	0.989684i	$-0.545761\pi$
$331$	−5.21303			−0.286534			−0.143267	+	0.989684i	$0.545761\pi$
$332$	4.88232	+	8.45643i	0.267952	+	0.464107i
$333$	−9.55992	−	16.5583i	−0.523880	−	0.907388i
$334$	11.5901			0.634183
$335$	−10.2712			−0.561173
$336$	−1.79360	−	3.10661i	−0.0978491	−	0.169480i
$337$	−13.3637	+	23.1467i	−0.727969	+	1.26088i	0.229771	+	0.973245i	$0.426202\pi$
$337$	−13.3637	+	23.1467i	−0.727969	+	1.26088i	−0.957740	+	0.287635i	$0.907131\pi$
$338$	−6.45371	−	11.1781i	−0.351035	−	0.608011i
$339$	19.9048	−	34.4761i	1.08108	−	1.87248i
$340$	4.90742	−	8.49991i	0.266142	−	0.460972i
$341$	−37.0842			−2.00822
$342$		0			0
$343$	15.8598			0.856351
$344$	−0.494689	+	0.856827i	−0.0266719	+	0.0461970i
$345$	21.2111	−	36.7386i	1.14196	−	1.97794i
$346$	−1.99176	−	3.44983i	−0.107078	−	0.185464i
$347$	16.3341	−	28.2915i	0.876860	−	1.51877i	0.0220925	−	0.999756i	$-0.492967\pi$
$347$	16.3341	−	28.2915i	0.876860	−	1.51877i	0.854768	−	0.519011i	$-0.173699\pi$
$348$	4.36858	+	7.56661i	0.234181	+	0.405613i
$349$	−29.1058			−1.55800			−0.778998	−	0.627026i	$-0.784272\pi$
$349$	−29.1058			−1.55800			−0.778998	+	0.627026i	$0.784272\pi$
$350$	0.638237			0.0341152
$351$	−0.766837	−	1.32820i	−0.0409307	−	0.0708941i
$352$	2.87811	+	4.98503i	0.153404	+	0.265703i
$353$	−14.3049			−0.761372			−0.380686	−	0.924704i	$-0.624312\pi$
$353$	−14.3049			−0.761372			−0.380686	+	0.924704i	$0.624312\pi$
$354$	−9.25731			−0.492021
$355$	5.17647	+	8.96591i	0.274738	+	0.475861i
$356$	−7.53827	+	13.0567i	−0.399527	+	0.692002i
$357$	−7.50837	−	13.0049i	−0.397385	−	0.688291i
$358$	4.22545	−	7.31869i	0.223322	−	0.386805i
$359$	−9.83535	+	17.0353i	−0.519090	+	0.899090i	0.480664	+	0.876905i	$0.340396\pi$
$359$	−9.83535	+	17.0353i	−0.519090	+	0.899090i	−0.999754	+	0.0221853i	$0.992938\pi$
$360$	11.2639			0.593658
$361$		0			0
$362$	8.48526			0.445976
$363$	30.9168	−	53.5495i	1.62271	−	2.81062i
$364$	−0.195361	+	0.338376i	−0.0102397	+	0.0177357i
$365$	−2.65745	−	4.60284i	−0.139097	−	0.240924i
$366$	15.3110	−	26.5194i	0.800318	−	1.38619i
$367$	−4.77527	−	8.27100i	−0.249267	−	0.431743i	0.714056	−	0.700089i	$-0.246856\pi$
$367$	−4.77527	−	8.27100i	−0.249267	−	0.431743i	−0.963323	+	0.268346i	$0.913523\pi$
$368$	−6.47684			−0.337628
$369$	24.1037			1.25479
$370$	−4.66547	−	8.08083i	−0.242546	−	0.420102i
$371$	−2.11272	−	3.65934i	−0.109687	−	0.189984i
$372$	17.9977			0.933137
$373$	−3.64010			−0.188477			−0.0942387	−	0.995550i	$-0.530042\pi$
$373$	−3.64010			−0.188477			−0.0942387	+	0.995550i	$0.530042\pi$
$374$	12.0483	+	20.8683i	0.623003	+	1.07907i
$375$	14.7468	−	25.5422i	0.761521	−	1.31899i
$376$	−2.19723	−	3.80571i	−0.113313	−	0.196264i
$377$	0.475831	−	0.824163i	0.0245065	−	0.0424466i
$378$	3.23607	−	5.60503i	0.166445	−	0.288292i
$379$	−8.34741			−0.428778			−0.214389	−	0.976748i	$-0.568776\pi$
$379$	−8.34741			−0.428778			−0.214389	+	0.976748i	$0.568776\pi$
$380$		0			0
$381$	6.23015			0.319180
$382$	−11.1895	+	19.3808i	−0.572505	+	0.991608i
$383$	−4.74283	+	8.21482i	−0.242347	+	0.419758i	−0.961382	−	0.275216i	$-0.911251\pi$
$383$	−4.74283	+	8.21482i	−0.242347	+	0.419758i	0.719035	+	0.694974i	$0.244584\pi$
$384$	−1.39680	−	2.41933i	−0.0712803	−	0.123461i
$385$	−8.66489	+	15.0080i	−0.441604	+	0.764880i
$386$	−3.71406	−	6.43293i	−0.189040	−	0.327428i
$387$	−4.75320			−0.241619
$388$	−17.3522			−0.880924
$389$	−18.0240	−	31.2185i	−0.913852	−	1.58284i	−0.808573	−	0.588396i	$-0.799760\pi$
$389$	−18.0240	−	31.2185i	−0.913852	−	1.58284i	−0.105279	−	0.994443i	$-0.533574\pi$
$390$	−0.996498	−	1.72598i	−0.0504596	−	0.0873986i
$391$	−27.1133			−1.37118
$392$	5.35114			0.270273
$393$	2.12685	+	3.68381i	0.107285	+	0.185823i
$394$	4.26777	−	7.39199i	0.215007	−	0.372403i
$395$	−10.0542	−	17.4144i	−0.505883	−	0.876216i
$396$	−13.8271	+	23.9492i	−0.694837	+	1.20349i
$397$	3.20453	−	5.55041i	0.160831	−	0.278567i	−0.774336	−	0.632775i	$-0.781916\pi$
$397$	3.20453	−	5.55041i	0.160831	−	0.278567i	0.935167	+	0.354207i	$0.115249\pi$
$398$	6.35926			0.318761
$399$		0			0
$400$	0.497039			0.0248520
$401$	0.0938299	−	0.162518i	0.00468564	−	0.00811577i	−0.863673	−	0.504052i	$-0.831842\pi$
$401$	0.0938299	−	0.162518i	0.00468564	−	0.00811577i	0.868359	+	0.495937i	$0.165175\pi$
$402$	−6.11913	+	10.5986i	−0.305194	+	0.528612i
$403$	−0.980164	−	1.69769i	−0.0488255	−	0.0845682i
$404$	−1.83833	+	3.18409i	−0.0914605	+	0.158414i
$405$	−0.389305	−	0.674297i	−0.0193447	−	0.0335061i
$406$	4.01603			0.199312
$407$	22.9086			1.13554
$408$	−5.84728	−	10.1278i	−0.289484	−	0.501400i
$409$	8.63314	+	14.9530i	0.426881	+	0.739380i	0.996594	−	0.0824641i	$-0.0262790\pi$
$409$	8.63314	+	14.9530i	0.426881	+	0.739380i	−0.569713	+	0.821844i	$0.692946\pi$
$410$	11.7632			0.580942
$411$	−29.9244			−1.47606
$412$	9.50676	+	16.4662i	0.468365	+	0.811231i
$413$	−2.12756	+	3.68504i	−0.104690	+	0.181329i
$414$	−15.5581	−	26.9474i	−0.764638	−	1.32439i
$415$	−11.4470	+	19.8267i	−0.561910	+	0.973257i
$416$	−0.152141	+	0.263516i	−0.00745934	+	0.0129200i
$417$	30.2110			1.47944
$418$		0			0
$419$	−1.72572			−0.0843068			−0.0421534	−	0.999111i	$-0.513422\pi$
$419$	−1.72572			−0.0843068			−0.0421534	+	0.999111i	$0.513422\pi$
$420$	4.20524	−	7.28369i	0.205195	−	0.355408i
$421$	16.3773	−	28.3663i	0.798180	−	1.38249i	−0.122621	−	0.992454i	$-0.539130\pi$
$421$	16.3773	−	28.3663i	0.798180	−	1.38249i	0.920800	−	0.390034i	$-0.127537\pi$
$422$	6.97890	+	12.0878i	0.339727	+	0.588425i
$423$	10.5560	−	18.2835i	0.513249	−	0.888973i
$424$	−1.64532	−	2.84978i	−0.0799039	−	0.138398i
$425$	2.08070			0.100929
$426$	12.3357			0.597667
$427$	−7.03769	−	12.1896i	−0.340578	−	0.589898i
$428$	5.01864	+	8.69254i	0.242585	+	0.420170i
$429$	4.89304			0.236238
$430$	−2.31967			−0.111865
$431$	−12.7560	−	22.0940i	−0.614433	−	1.06423i	−0.990484	−	0.137630i	$-0.956051\pi$
$431$	−12.7560	−	22.0940i	−0.614433	−	1.06423i	0.376051	−	0.926599i	$-0.377282\pi$
$432$	2.52015	−	4.36502i	0.121251	−	0.210012i
$433$	12.2417	+	21.2032i	0.588299	+	1.01896i	0.994455	+	0.105160i	$0.0335353\pi$
$433$	12.2417	+	21.2032i	0.588299	+	1.01896i	−0.406157	+	0.913803i	$0.633131\pi$
$434$	4.13632	−	7.16431i	0.198550	−	0.343898i
$435$	−10.2425	+	17.7405i	−0.491089	+	0.850591i
$436$	8.84348			0.423526
$437$		0			0
$438$	−6.33280			−0.302593
$439$	−15.4194	+	26.7072i	−0.735928	+	1.27466i	0.218387	+	0.975862i	$0.429920\pi$
$439$	−15.4194	+	26.7072i	−0.735928	+	1.27466i	−0.954315	+	0.298802i	$0.903413\pi$
$440$	−6.74794	+	11.6878i	−0.321696	+	0.557193i
$441$	12.8540	+	22.2639i	0.612097	+	1.06018i
$442$	−0.636892	+	1.10313i	−0.0302939	+	0.0524705i
$443$	−5.35234	−	9.27052i	−0.254297	−	0.440456i	0.710407	−	0.703791i	$-0.248511\pi$
$443$	−5.35234	−	9.27052i	−0.254297	−	0.440456i	−0.964704	+	0.263335i	$0.915177\pi$
$444$	−11.1180			−0.527636
$445$	−35.3481			−1.67566
$446$	−4.46200	−	7.72841i	−0.211282	−	0.365951i
$447$	−13.0375	−	22.5817i	−0.616654	−	1.06808i
$448$	−1.28408			−0.0606670
$449$	−2.31562			−0.109281			−0.0546403	−	0.998506i	$-0.517401\pi$
$449$	−2.31562			−0.109281			−0.0546403	+	0.998506i	$0.517401\pi$
$450$	1.19394	+	2.06797i	0.0562831	+	0.0974851i
$451$	−14.4400	+	25.0108i	−0.679953	+	1.17771i
$452$	−7.12512	−	12.3411i	−0.335137	−	0.580475i
$453$	−27.6890	+	47.9588i	−1.30094	+	2.25330i
$454$	0.329898	−	0.571400i	0.0154829	−	0.0268171i
$455$	−0.916079			−0.0429465
$456$		0			0
$457$	−0.0521810			−0.00244092			−0.00122046	−	0.999999i	$-0.500388\pi$
$457$	−0.0521810			−0.00244092			−0.00122046	+	0.999999i	$0.500388\pi$
$458$	−3.48604	+	6.03800i	−0.162892	+	0.282137i
$459$	10.5498	−	18.2728i	0.492423	−	0.852902i
$460$	−7.59272	−	13.1510i	−0.354012	−	0.613167i
$461$	−19.7360	+	34.1838i	−0.919198	+	1.59210i	−0.118561	+	0.992947i	$0.537828\pi$
$461$	−19.7360	+	34.1838i	−0.919198	+	1.59210i	−0.800637	+	0.599150i	$0.795505\pi$
$462$	10.3244	+	17.8823i	0.480333	+	0.831962i
$463$	−6.19056			−0.287700			−0.143850	−	0.989600i	$-0.545948\pi$
$463$	−6.19056			−0.287700			−0.143850	+	0.989600i	$0.545948\pi$
$464$	3.12756			0.145193
$465$	21.0985	+	36.5437i	0.978419	+	1.69467i
$466$	−14.8048	−	25.6427i	−0.685821	−	1.18788i
$467$	−20.9962			−0.971586			−0.485793	−	0.874074i	$-0.661469\pi$
$467$	−20.9962			−0.971586			−0.485793	+	0.874074i	$0.661469\pi$
$468$	−1.46184			−0.0675737
$469$	2.81266	+	4.87166i	0.129876	+	0.224952i
$470$	5.15156	−	8.92277i	0.237624	−	0.411577i
$471$	19.3703	+	33.5504i	0.892538	+	1.54592i
$472$	−1.65688	+	2.86979i	−0.0762639	+	0.132093i
$473$	2.84754	−	4.93208i	0.130930	−	0.226777i
$474$	−23.9596			−1.10050
$475$		0			0
$476$	−5.37540			−0.246381
$477$	7.90450	−	13.6910i	0.361922	−	0.626867i
$478$	−12.3517	+	21.3938i	−0.564953	+	0.978528i
$479$	−7.76147	−	13.4433i	−0.354631	−	0.614238i	0.632424	−	0.774622i	$-0.282060\pi$
$479$	−7.76147	−	13.4433i	−0.354631	−	0.614238i	−0.987055	+	0.160384i	$0.948727\pi$
$480$	3.27491	−	5.67231i	0.149478	−	0.258904i
$481$	0.605491	+	1.04874i	0.0276080	+	0.0478185i
$482$	27.5586			1.25526
$483$	−23.2338			−1.05717
$484$	−11.0670	−	19.1686i	−0.503046	−	0.871301i
$485$	−20.3418	−	35.2330i	−0.923672	−	1.59985i
$486$	−16.0486			−0.727980
$487$	28.6065			1.29629			0.648143	−	0.761519i	$-0.275546\pi$
$487$	28.6065			1.29629			0.648143	+	0.761519i	$0.275546\pi$
$488$	−5.48073	−	9.49290i	−0.248101	−	0.429723i
$489$	19.9039	−	34.4745i	0.900084	−	1.55899i
$490$	6.27308	+	10.8653i	0.283389	+	0.490844i
$491$	15.1744	−	26.2829i	0.684812	−	1.18613i	−0.288684	−	0.957424i	$-0.593218\pi$
$491$	15.1744	−	26.2829i	0.684812	−	1.18613i	0.973496	−	0.228705i	$-0.0734490\pi$
$492$	7.00802	−	12.1382i	0.315946	−	0.547234i
$493$	13.0926			0.589659
$494$		0			0
$495$	−64.8373			−2.91422
$496$	3.22123	−	5.57934i	0.144638	−	0.250520i
$497$	2.83505	−	4.91045i	0.127169	−	0.220264i
$498$	13.6393	+	23.6239i	0.611191	+	1.05861i
$499$	−4.38812	+	7.60044i	−0.196439	+	0.340243i	−0.947371	−	0.320137i	$-0.896271\pi$
$499$	−4.38812	+	7.60044i	−0.196439	+	0.340243i	0.750932	+	0.660379i	$0.229604\pi$
$500$	−5.27877	−	9.14309i	−0.236074	−	0.408892i
$501$	32.3782			1.44655
$502$	2.98855			0.133386
$503$	10.5522	+	18.2769i	0.470498	+	0.814926i	0.999431	−	0.0337373i	$-0.0107410\pi$
$503$	10.5522	+	18.2769i	0.470498	+	0.814926i	−0.528933	+	0.848664i	$0.677408\pi$
$504$	−3.08450	−	5.34252i	−0.137395	−	0.237975i
$505$	−8.62023			−0.383595
$506$	37.2821			1.65739
$507$	−18.0291	−	31.2273i	−0.800701	−	1.38685i
$508$	1.11507	−	1.93136i	0.0494734	−	0.0856904i
$509$	11.1106	+	19.2441i	0.492468	+	0.852979i	0.999962	−	0.00867561i	$-0.00276157\pi$
$509$	11.1106	+	19.2441i	0.492468	+	0.852979i	−0.507494	+	0.861655i	$0.669428\pi$
$510$	13.7094	−	23.7454i	0.607062	−	1.05146i
$511$	−1.45543	+	2.52089i	−0.0643846	+	0.111517i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	14.1323			0.623347
$515$	−22.2893	+	38.6063i	−0.982185	+	1.70119i
$516$	−1.38197	+	2.39364i	−0.0608377	+	0.105374i
$517$	12.6477	+	21.9065i	0.556245	+	0.963445i
$518$	−2.55519	+	4.42571i	−0.112268	+	0.194455i
$519$	−5.56420	−	9.63747i	−0.244241	−	0.423038i
$520$	−0.713414			−0.0312853
$521$	−10.0332			−0.439563			−0.219782	−	0.975549i	$-0.570534\pi$
$521$	−10.0332			−0.439563			−0.219782	+	0.975549i	$0.570534\pi$
$522$	7.51275	+	13.0125i	0.328824	+	0.569540i
$523$	14.6411	+	25.3592i	0.640212	+	1.10888i	0.985385	+	0.170341i	$0.0544870\pi$
$523$	14.6411	+	25.3592i	0.640212	+	1.10888i	−0.345173	+	0.938539i	$0.612180\pi$
$524$	1.52265			0.0665175
$525$	1.78298			0.0778158
$526$	3.78444	+	6.55483i	0.165009	+	0.285804i
$527$	13.4847	−	23.3562i	0.587403	−	1.01741i
$528$	8.04029	+	13.9262i	0.349909	+	0.606060i
$529$	−9.47470	+	16.4107i	−0.411943	+	0.713507i
$530$	3.85758	−	6.68153i	0.167563	−	0.290227i
$531$	−15.9200			−0.690870
$532$		0			0
$533$	−1.52664			−0.0661262
$534$	−21.0589	+	36.4751i	−0.911309	+	1.57843i
$535$	−11.7666	+	20.3803i	−0.508714	+	0.881118i
$536$	2.19041	+	3.79390i	0.0946112	+	0.163871i
$537$	11.8042	−	20.4455i	0.509390	−	0.882289i
$538$	3.83537	+	6.64306i	0.165355	+	0.286403i
$539$	−30.8023			−1.32675
$540$	11.8174			0.508538
$541$	18.9202	+	32.7707i	0.813442	+	1.40892i	0.910441	+	0.413638i	$0.135742\pi$
$541$	18.9202	+	32.7707i	0.813442	+	1.40892i	−0.0969995	+	0.995284i	$0.530925\pi$
$542$	5.83245	+	10.1021i	0.250525	+	0.433922i
$543$	23.7045			1.01726
$544$	−4.18619			−0.179482
$545$	10.3671	+	17.9564i	0.444078	+	0.769166i
$546$	−0.545762	+	0.945288i	−0.0233565	+	0.0404546i
$547$	−7.24878	−	12.5553i	−0.309936	−	0.536824i	0.668412	−	0.743791i	$-0.266974\pi$
$547$	−7.24878	−	12.5553i	−0.309936	−	0.536824i	−0.978348	+	0.206967i	$0.933641\pi$
$548$	−5.35588	+	9.27665i	−0.228792	+	0.396279i
$549$	26.3307	−	45.6060i	1.12377	−	1.94642i
$550$	−2.86106			−0.121996
$551$		0			0
$552$	−18.0937			−0.770120
$553$	−5.50651	+	9.53755i	−0.234161	+	0.405578i
$554$	13.7202	−	23.7642i	0.582917	−	1.00964i
$555$	−13.0335	−	22.5746i	−0.553240	−	0.958240i
$556$	5.40717	−	9.36549i	0.229315	−	0.397185i
$557$	2.16901	+	3.75683i	0.0919037	+	0.159182i	0.908312	−	0.418293i	$-0.137371\pi$
$557$	2.16901	+	3.75683i	0.0919037	+	0.159182i	−0.816408	+	0.577475i	$0.804038\pi$
$558$	30.9511			1.31026
$559$	0.301051			0.0127331
$560$	−1.50531	−	2.60727i	−0.0636110	−	0.110177i
$561$	33.6582	+	58.2977i	1.42105	+	2.46133i
$562$	16.2715			0.686371
$563$	27.2936			1.15029			0.575144	−	0.818052i	$-0.304946\pi$
$563$	27.2936			1.15029			0.575144	+	0.818052i	$0.304946\pi$
$564$	−6.13818	−	10.6316i	−0.258464	−	0.447673i
$565$	16.7054	−	28.9346i	0.702801	−	1.21729i
$566$	1.69687	+	2.93907i	0.0713248	+	0.123538i
$567$	−0.213215	+	0.369299i	−0.00895419	+	0.0155091i
$568$	2.20785	−	3.82410i	0.0926392	−	0.160456i
$569$	7.19043			0.301439			0.150719	−	0.988577i	$-0.451841\pi$
$569$	7.19043			0.301439			0.150719	+	0.988577i	$0.451841\pi$
$570$		0			0
$571$	42.0134			1.75821			0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134			1.75821			0.879103	+	0.476631i	$0.158142\pi$
$572$	0.875758	−	1.51686i	0.0366173	−	0.0634230i
$573$	−31.2591	+	54.1423i	−1.30587	+	2.26183i
$574$	−3.22123	−	5.57934i	−0.134452	−	0.232877i
$575$	1.60962	−	2.78794i	0.0671258	−	0.116265i
$576$	−2.40211	−	4.16058i	−0.100088	−	0.173358i
$577$	21.6713			0.902190			0.451095	−	0.892476i	$-0.351034\pi$
$577$	21.6713			0.902190			0.451095	+	0.892476i	$0.351034\pi$
$578$	−0.524204			−0.0218040
$579$	−10.3756	−	17.9711i	−0.431195	−	0.746852i
$580$	3.66640	+	6.35039i	0.152239	+	0.263686i
$581$	12.5386			0.520188
$582$	−48.4751			−2.00936
$583$	9.47083	+	16.4040i	0.392242	+	0.679382i
$584$	−1.13345	+	1.96319i	−0.0469023	+	0.0812373i
$585$	−1.71370	−	2.96822i	−0.0708528	−	0.122721i
$586$	−11.6892	+	20.2462i	−0.482874	+	0.836363i
$587$	0.634322	−	1.09868i	0.0261813	−	0.0453473i	−0.852638	−	0.522502i	$-0.824999\pi$
$587$	0.634322	−	1.09868i	0.0261813	−	0.0453473i	0.878819	+	0.477155i	$0.158332\pi$
$588$	14.9490			0.616485
$589$		0			0
$590$	−7.76934			−0.319859
$591$	11.9225	−	20.6503i	0.490424	−	0.849440i
$592$	−1.98990	+	3.44660i	−0.0817843	+	0.141655i
$593$	−10.7800	−	18.6715i	−0.442682	−	0.766747i	0.555206	−	0.831713i	$-0.312639\pi$
$593$	−10.7800	−	18.6715i	−0.442682	−	0.766747i	−0.997887	+	0.0649660i	$0.979306\pi$
$594$	−14.5065	+	25.1260i	−0.595209	+	1.03093i
$595$	−6.30152	−	10.9146i	−0.258337	−	0.447453i
$596$	−9.33384			−0.382329
$597$	17.7652			0.727083
$598$	0.985394	+	1.70675i	0.0402957	+	0.0697943i
$599$	−14.3209	−	24.8045i	−0.585135	−	1.01348i	−0.994859	−	0.101274i	$-0.967708\pi$
$599$	−14.3209	−	24.8045i	−0.585135	−	1.01348i	0.409724	−	0.912210i	$-0.365625\pi$
$600$	1.38853			0.0566865
$601$	−7.55865			−0.308324			−0.154162	−	0.988046i	$-0.549268\pi$
$601$	−7.55865			−0.308324			−0.154162	+	0.988046i	$0.549268\pi$
$602$	0.635220	+	1.10023i	0.0258896	+	0.0448422i
$603$	−10.5232	+	18.2267i	−0.428538	+	0.742250i
$604$	9.91158	+	17.1674i	0.403297	+	0.698530i
$605$	25.9474	−	44.9423i	1.05491	−	1.82716i
$606$	−5.13558	+	8.89508i	−0.208619	+	0.361338i
$607$	−1.72737			−0.0701117			−0.0350558	−	0.999385i	$-0.511161\pi$
$607$	−1.72737			−0.0701117			−0.0350558	+	0.999385i	$0.511161\pi$
$608$		0			0
$609$	11.2192			0.454625
$610$	12.8500	−	22.2568i	0.520281	−	0.901153i
$611$	−0.668577	+	1.15801i	−0.0270477	+	0.0468481i
$612$	−10.0557	−	17.4170i	−0.406478	−	0.704040i
$613$	13.7085	−	23.7438i	0.553680	−	0.959002i	−0.444325	−	0.895866i	$-0.646556\pi$
$613$	13.7085	−	23.7438i	0.553680	−	0.959002i	0.998005	−	0.0631360i	$-0.0201102\pi$
$614$	0.694010	+	1.20206i	0.0280080	+	0.0485112i
$615$	32.8617			1.32511
$616$	7.39144			0.297809
$617$	−5.31375	−	9.20369i	−0.213924	−	0.370527i	0.739015	−	0.673688i	$-0.235291\pi$
$617$	−5.31375	−	9.20369i	−0.213924	−	0.370527i	−0.952939	+	0.303162i	$0.901958\pi$
$618$	26.5581	+	46.0000i	1.06832	+	1.85039i
$619$	8.36008			0.336020			0.168010	−	0.985785i	$-0.446266\pi$
$619$	8.36008			0.336020			0.168010	+	0.985785i	$0.446266\pi$
$620$	15.1048			0.606625
$621$	−16.3226	−	28.2715i	−0.655002	−	1.13450i
$622$	−6.09512	+	10.5571i	−0.244392	+	0.423300i
$623$	9.67973	+	16.7658i	0.387810	+	0.671707i
$624$	−0.425022	+	0.736160i	−0.0170145	+	0.0294700i
$625$	13.6191	−	23.5889i	0.544763	−	0.943557i
$626$	−16.5314			−0.660728
$627$		0			0
$628$	13.8676			0.553379
$629$	−8.33010	+	14.4282i	−0.332143	+	0.575288i
$630$	7.23185	−	12.5259i	0.288124	−	0.499045i
$631$	−12.2651	−	21.2437i	−0.488265	−	0.845700i	0.511644	−	0.859198i	$-0.329037\pi$
$631$	−12.2651	−	21.2437i	−0.488265	−	0.845700i	−0.999909	+	0.0134980i	$0.995703\pi$
$632$	−4.28829	+	7.42754i	−0.170579	+	0.295452i
$633$	19.4963	+	33.7686i	0.774908	+	1.34218i
$634$	2.68811			0.106759
$635$	5.22875			0.207497
$636$	−4.59638	−	7.96116i	−0.182258	−	0.315681i
$637$	−0.814129	−	1.41011i	−0.0322570	−	0.0558707i
$638$	−18.0029			−0.712742
$639$	21.2140			0.839213
$640$	−1.17229	−	2.03046i	−0.0463388	−	0.0802611i
$641$	−3.48635	+	6.03854i	−0.137703	+	0.238508i	−0.926627	−	0.375983i	$-0.877305\pi$
$641$	−3.48635	+	6.03854i	−0.137703	+	0.238508i	0.788924	+	0.614491i	$0.210638\pi$
$642$	14.0201	+	24.2835i	0.553329	+	0.958394i
$643$	4.54512	−	7.87238i	0.179242	−	0.310456i	−0.762379	−	0.647131i	$-0.775969\pi$
$643$	4.54512	−	7.87238i	0.179242	−	0.310456i	0.941621	+	0.336674i	$0.109302\pi$
$644$	−4.15838	+	7.20253i	−0.163863	+	0.283820i
$645$	−6.48025			−0.255160
$646$		0			0
$647$	30.0074			1.17971			0.589856	−	0.807509i	$-0.299185\pi$
$647$	30.0074			1.17971			0.589856	+	0.807509i	$0.299185\pi$
$648$	−0.166045	+	0.287598i	−0.00652287	+	0.0112979i
$649$	9.53733	−	16.5191i	0.374373	−	0.648433i
$650$	−0.0756201	−	0.130978i	−0.00296607	−	0.00513738i
$651$	11.5552	−	20.0142i	0.452885	−	0.784420i
$652$	−7.12480	−	12.3405i	−0.279029	−	0.483292i
$653$	10.4191			0.407732			0.203866	−	0.978999i	$-0.434649\pi$
$653$	10.4191			0.407732			0.203866	+	0.978999i	$0.434649\pi$
$654$	24.7052			0.966049
$655$	1.78499	+	3.09169i	0.0697453	+	0.120802i
$656$	−2.50859	−	4.34501i	−0.0979441	−	0.169644i
$657$	−10.8907			−0.424885
$658$	−5.64282			−0.219980
$659$	−13.1878	−	22.8419i	−0.513724	−	0.889796i	−0.999873	−	0.0159201i	$-0.994932\pi$
$659$	−13.1878	−	22.8419i	−0.513724	−	0.889796i	0.486149	−	0.873876i	$-0.338401\pi$
$660$	−18.8511	+	32.6510i	−0.733777	+	1.27094i
$661$	−12.3470	−	21.3856i	−0.480242	−	0.831803i	0.519502	−	0.854470i	$-0.326118\pi$
$661$	−12.3470	−	21.3856i	−0.480242	−	0.831803i	−0.999743	+	0.0226668i	$0.992784\pi$
$662$	−2.60651	+	4.51462i	−0.101305	+	0.175466i
$663$	−1.77923	+	3.08171i	−0.0690994	+	0.119684i
$664$	9.76464			0.378942
$665$		0			0
$666$	−19.1198			−0.740879
$667$	10.1283	−	17.5428i	0.392171	−	0.679260i
$668$	5.79506	−	10.0373i	0.224217	−	0.388356i
$669$	−12.4651	−	21.5901i	−0.481927	−	0.834722i
$670$	−5.13558	+	8.89508i	−0.198405	+	0.343647i
$671$	31.5483	+	54.6432i	1.21791	+	2.10948i
$672$	−3.58721			−0.138380
$673$	9.77380			0.376752			0.188376	−	0.982097i	$-0.439678\pi$
$673$	9.77380			0.376752			0.188376	+	0.982097i	$0.439678\pi$
$674$	13.3637	+	23.1467i	0.514752	+	0.891576i
$675$	1.25261	+	2.16959i	0.0482130	+	0.0835074i
$676$	−12.9074			−0.496439
$677$	21.5747			0.829184			0.414592	−	0.910007i	$-0.363924\pi$
$677$	21.5747			0.829184			0.414592	+	0.910007i	$0.363924\pi$
$678$	−19.9048	−	34.4761i	−0.764438	−	1.32405i
$679$	−11.1408	+	19.2964i	−0.427544	+	0.740528i
$680$	−4.90742	−	8.49991i	−0.188191	−	0.325957i
$681$	0.921604	−	1.59627i	0.0353159	−	0.0611690i
$682$	−18.5421	+	32.1159i	−0.710014	+	1.22978i
$683$	−33.2509			−1.27231			−0.636155	−	0.771561i	$-0.719476\pi$
$683$	−33.2509			−1.27231			−0.636155	+	0.771561i	$0.719476\pi$
$684$		0			0
$685$	−25.1145			−0.959576
$686$	7.92992	−	13.7350i	0.302766	−	0.524406i
$687$	−9.73862	+	16.8678i	−0.371551	+	0.643546i
$688$	0.494689	+	0.856827i	0.0188598	+	0.0326662i
$689$	−0.500643	+	0.867138i	−0.0190730	+	0.0330353i
$690$	−21.2111	−	36.7386i	−0.807491	−	1.39862i
$691$	4.80932			0.182955			0.0914776	−	0.995807i	$-0.470841\pi$
$691$	4.80932			0.182955			0.0914776	+	0.995807i	$0.470841\pi$
$692$	−3.98353			−0.151431
$693$	17.7551	+	30.7527i	0.674459	+	1.16820i
$694$	−16.3341	−	28.2915i	−0.620034	−	1.07393i
$695$	25.3550			0.961772
$696$	8.73716			0.331181
$697$	−10.5015	−	18.1890i	−0.397771	−	0.688959i
$698$	−14.5529	+	25.2063i	−0.550835	+	0.954074i
$699$	−41.3589	−	71.6357i	−1.56434	−	2.70951i
$700$	0.319119	−	0.552730i	0.0120616	−	0.0208912i
$701$	−1.73233	+	3.00049i	−0.0654293	+	0.113327i	−0.896884	−	0.442265i	$-0.854175\pi$
$701$	−1.73233	+	3.00049i	−0.0654293	+	0.113327i	0.831455	+	0.555592i	$0.187508\pi$
$702$	−1.53367			−0.0578848
$703$		0			0
$704$	5.75621			0.216946
$705$	14.3914	−	24.9267i	0.542013	−	0.938794i
$706$	−7.15244	+	12.3884i	−0.269186	+	0.466243i
$707$	2.36057	+	4.08862i	0.0887782	+	0.153768i
$708$	−4.62866	+	8.01707i	−0.173956	+	0.301300i
$709$	−10.2871	−	17.8179i	−0.386342	−	0.669164i	0.605612	−	0.795760i	$-0.292928\pi$
$709$	−10.2871	−	17.8179i	−0.386342	−	0.669164i	−0.991954	+	0.126596i	$0.959595\pi$
$710$	10.3529			0.388539
$711$	−41.2039			−1.54527
$712$	7.53827	+	13.0567i	0.282508	+	0.489319i
$713$	−20.8634	−	36.1364i	−0.781340	−	1.35332i
$714$	−15.0167			−0.561988
$715$	4.10656			0.153577
$716$	−4.22545	−	7.31869i	−0.157912	−	0.273512i
$717$	−34.5058	+	59.7657i	−1.28864	+	2.23199i
$718$	9.83535	+	17.0353i	0.367052	+	0.635753i
$719$	−12.0943	+	20.9479i	−0.451040	+	0.781225i	−0.998451	−	0.0556395i	$-0.982280\pi$
$719$	−12.0943	+	20.9479i	−0.451040	+	0.781225i	0.547411	+	0.836864i	$0.315614\pi$
$720$	5.63194	−	9.75480i	0.209890	−	0.363540i
$721$	24.4149			0.909257
$722$		0			0
$723$	76.9880			2.86321
$724$	4.24263	−	7.34845i	0.157676	−	0.273103i
$725$	−0.777260	+	1.34625i	−0.0288667	+	0.0499986i
$726$	−30.9168	−	53.5495i	−1.14743	−	1.98741i
$727$	−9.06381	+	15.6990i	−0.336158	+	0.582243i	−0.983707	−	0.179781i	$-0.942461\pi$
$727$	−9.06381	+	15.6990i	−0.336158	+	0.582243i	0.647548	+	0.762024i	$0.275794\pi$
$728$	0.195361	+	0.338376i	0.00724057	+	0.0125410i
$729$	−43.8372			−1.62360
$730$	−5.31490			−0.196713
$731$	2.07086	+	3.58684i	0.0765937	+	0.132664i
$732$	−15.3110	−	26.5194i	−0.565910	−	0.980186i
$733$	22.7363			0.839785			0.419893	−	0.907574i	$-0.362068\pi$
$733$	22.7363			0.839785			0.419893	+	0.907574i	$0.362068\pi$
$734$	−9.55053			−0.352517
$735$	17.5245	+	30.3533i	0.646401	+	1.11960i
$736$	−3.23842	+	5.60910i	−0.119370	+	0.206754i
$737$	−12.6085	−	21.8385i	−0.464438	−	0.804431i
$738$	12.0518	−	20.8744i	0.443635	−	0.768398i
$739$	−7.58933	+	13.1451i	−0.279178	+	0.483550i	−0.971181	−	0.238344i	$-0.923395\pi$
$739$	−7.58933	+	13.1451i	−0.279178	+	0.483550i	0.692003	+	0.721895i	$0.256729\pi$
$740$	−9.33094			−0.343012
$741$		0			0
$742$	−4.22545			−0.155121
$743$	−1.63812	+	2.83732i	−0.0600970	+	0.104091i	−0.894509	−	0.447051i	$-0.852474\pi$
$743$	−1.63812	+	2.83732i	−0.0600970	+	0.104091i	0.834412	+	0.551142i	$0.185808\pi$
$744$	8.99885	−	15.5865i	0.329914	−	0.571427i
$745$	−10.9420	−	18.9520i	−0.400882	−	0.694348i
$746$	−1.82005	+	3.15242i	−0.0666368	+	0.115418i
$747$	23.4558	+	40.6266i	0.858202	+	1.48645i
$748$	24.0966			0.881060
$749$	12.8887			0.470941
$750$	−14.7468	−	25.5422i	−0.538477	−	0.932669i
$751$	26.1162	+	45.2345i	0.952992	+	1.65063i	0.738897	+	0.673818i	$0.235347\pi$
$751$	26.1162	+	45.2345i	0.952992	+	1.65063i	0.214095	+	0.976813i	$0.431320\pi$
$752$	−4.39445			−0.160249
$753$	8.34884			0.304248
$754$	−0.475831	−	0.824163i	−0.0173287	−	0.0300142i
$755$	−23.2385	+	40.2502i	−0.845734	+	1.46485i
$756$	−3.23607	−	5.60503i	−0.117695	−	0.203853i
$757$	12.1171	−	20.9874i	0.440404	−	0.762801i	−0.557316	−	0.830301i	$-0.688169\pi$
$757$	12.1171	−	20.9874i	0.440404	−	0.762801i	0.997719	+	0.0674993i	$0.0215020\pi$
$758$	−4.17371	+	7.22907i	−0.151596	+	0.262572i
$759$	104.151			3.78045
$760$		0			0
$761$	−24.8054			−0.899195			−0.449597	−	0.893231i	$-0.648433\pi$
$761$	−24.8054			−0.899195			−0.449597	+	0.893231i	$0.648433\pi$
$762$	3.11507	−	5.39546i	0.112847	−	0.195457i
$763$	5.67786	−	9.83435i	0.205552	−	0.356027i
$764$	11.1895	+	19.3808i	0.404822	+	0.701173i
$765$	23.5764	−	40.8355i	0.852406	−	1.47641i
$766$	4.74283	+	8.21482i	0.171365	+	0.296814i
$767$	1.00832			0.0364082
$768$	−2.79360			−0.100806
$769$	−4.82145	−	8.35099i	−0.173866	−	0.301144i	0.765902	−	0.642957i	$-0.222293\pi$
$769$	−4.82145	−	8.35099i	−0.173866	−	0.301144i	−0.939768	+	0.341812i	$0.888959\pi$
$770$	8.66489	+	15.0080i	0.312261	+	0.540852i
$771$	39.4799			1.42184
$772$	−7.42811			−0.267344
$773$	0.643656	+	1.11484i	0.0231507	+	0.0400982i	0.877369	−	0.479817i	$-0.159297\pi$
$773$	0.643656	+	1.11484i	0.0231507	+	0.0400982i	−0.854218	+	0.519915i	$0.825964\pi$
$774$	−2.37660	+	4.11639i	−0.0854251	+	0.147961i
$775$	1.60108	+	2.77315i	0.0575124	+	0.0996144i
$776$	−8.67609	+	15.0274i	−0.311453	+	0.539453i
$777$	−7.13818	+	12.3637i	−0.256081	+	0.443545i
$778$	−36.0480			−1.29238
$779$		0			0
$780$	−1.99300			−0.0713607
$781$	−12.7088	+	22.0124i	−0.454758	+	0.787664i
$782$	−13.5566	+	23.4808i	−0.484784	+	0.839671i
$783$	7.88191	+	13.6519i	0.281676	+	0.487878i
$784$	2.67557	−	4.63422i	0.0955561	−	0.165508i
$785$	16.2569	+	28.1577i	0.580232	+	1.00499i
$786$	4.25369			0.151724
$787$	16.3446			0.582624			0.291312	−	0.956628i	$-0.405908\pi$
$787$	16.3446			0.582624			0.291312	+	0.956628i	$0.405908\pi$
$788$	−4.26777	−	7.39199i	−0.152033	−	0.263329i
$789$	10.5722	+	18.3116i	0.376381	+	0.651911i
$790$	−20.1085			−0.715427
$791$	−18.2984			−0.650617
$792$	13.8271	+	23.9492i	0.491324	+	0.850998i
$793$	−1.66769	+	2.88852i	−0.0592214	+	0.102574i
$794$	−3.20453	−	5.55041i	−0.113725	−	0.196977i
$795$	10.7766	−	18.6656i	0.382205	−	0.661999i
$796$	3.17963	−	5.50728i	0.112699	−	0.195200i
$797$	15.6884			0.555712			0.277856	−	0.960623i	$-0.410376\pi$
$797$	15.6884			0.555712			0.277856	+	0.960623i	$0.410376\pi$
$798$		0			0
$799$	−18.3960			−0.650804
$800$	0.248520	−	0.430448i	0.00878649	−	0.0152187i
$801$	−36.2155	+	62.7271i	−1.27961	+	2.21635i
$802$	−0.0938299	−	0.162518i	−0.00331325	−	0.00573871i
$803$	6.52436	−	11.3005i	0.230240	−	0.398787i
$804$	6.11913	+	10.5986i	0.215805	+	0.373785i
$805$	−19.4993			−0.687260
$806$	−1.96033			−0.0690496
$807$	10.7145	+	18.5581i	0.377169	+	0.653275i
$808$	1.83833	+	3.18409i	0.0646723	+	0.112016i
$809$	−11.5248			−0.405192			−0.202596	−	0.979262i	$-0.564938\pi$
$809$	−11.5248			−0.405192			−0.202596	+	0.979262i	$0.564938\pi$
$810$	−0.778611			−0.0273576
$811$	−4.15051	−	7.18889i	−0.145744	−	0.252436i	0.783906	−	0.620879i	$-0.213224\pi$
$811$	−4.15051	−	7.18889i	−0.145744	−	0.252436i	−0.929650	+	0.368443i	$0.879891\pi$
$812$	2.00802	−	3.47799i	0.0704676	−	0.122053i
$813$	16.2935	+	28.2213i	0.571440	+	0.989763i
$814$	11.4543	−	19.8394i	0.401472	−	0.695371i
$815$	16.7046	−	28.9333i	0.585138	−	1.01349i
$816$	−11.6946			−0.409392
$817$		0			0
$818$	17.2663			0.603701
$819$	−0.938560	+	1.62563i	−0.0327959	+	0.0568042i
$820$	5.88159	−	10.1872i	0.205394	−	0.355753i
$821$	16.8556	+	29.1948i	0.588265	+	1.01891i	0.994460	+	0.105119i	$0.0335222\pi$
$821$	16.8556	+	29.1948i	0.588265	+	1.01891i	−0.406194	+	0.913787i	$0.633144\pi$
$822$	−14.9622	+	25.9153i	−0.521867	+	0.903899i
$823$	−10.9339	−	18.9380i	−0.381131	−	0.660138i	0.610093	−	0.792330i	$-0.291132\pi$
$823$	−10.9339	−	18.9380i	−0.381131	−	0.660138i	−0.991224	+	0.132191i	$0.957799\pi$
$824$	19.0135			0.662368
$825$	−7.99268			−0.278269
$826$	2.12756	+	3.68504i	0.0740273	+	0.128219i
$827$	19.5847	+	33.9218i	0.681028	+	1.17958i	0.974667	+	0.223659i	$0.0718003\pi$
$827$	19.5847	+	33.9218i	0.681028	+	1.17958i	−0.293639	+	0.955916i	$0.594866\pi$
$828$	−31.1162			−1.08136
$829$	14.4176			0.500743			0.250371	−	0.968150i	$-0.419447\pi$
$829$	14.4176			0.500743			0.250371	+	0.968150i	$0.419447\pi$
$830$	11.4470	+	19.8267i	0.397330	+	0.688196i
$831$	38.3289	−	66.3877i	1.32962	−	2.30296i
$832$	0.152141	+	0.263516i	0.00527455	+	0.00913579i
$833$	11.2005	−	19.3998i	0.388073	−	0.672162i
$834$	15.1055	−	26.1635i	0.523060	−	0.905967i
$835$	27.1739			0.940392
$836$		0			0
$837$	32.4719			1.12239
$838$	−0.862859	+	1.49452i	−0.0298070	+	0.0516272i
$839$	10.4766	−	18.1460i	0.361693	−	0.626470i	−0.626547	−	0.779384i	$-0.715532\pi$
$839$	10.4766	−	18.1460i	0.361693	−	0.626470i	0.988240	+	0.152914i	$0.0488657\pi$
$840$	−4.20524	−	7.28369i	−0.145095	−	0.251311i
$841$	9.60919	−	16.6436i	0.331351	−	0.573917i
$842$	−16.3773	−	28.3663i	−0.564398	−	0.977566i
$843$	45.4561			1.56559
$844$	13.9578			0.480447
$845$	−15.1312	−	26.2080i	−0.520529	−	0.901583i
$846$	−10.5560	−	18.2835i	−0.362922	−	0.628599i
$847$	−28.4218			−0.976585
$848$	−3.29064			−0.113001
$849$	4.74038	+	8.21059i	0.162690	+	0.281787i
$850$	1.04035	−	1.80194i	0.0356837	−	0.0618060i
$851$	12.8882	+	22.3231i	0.441803	+	0.765226i
$852$	6.16785	−	10.6830i	0.211307	−	0.365995i
$853$	−25.9777	+	44.9946i	−0.889458	+	1.54059i	−0.0489407	+	0.998802i	$0.515585\pi$
$853$	−25.9777	+	44.9946i	−0.889458	+	1.54059i	−0.840517	+	0.541785i	$0.817749\pi$
$854$	−14.0754			−0.481650
$855$		0			0
$856$	10.0373			0.343067
$857$	14.5917	−	25.2736i	0.498444	−	0.863330i	−0.501554	−	0.865126i	$-0.667238\pi$
$857$	14.5917	−	25.2736i	0.498444	−	0.863330i	0.999998	+	0.00179580i	$0.000571621\pi$
$858$	2.44652	−	4.23750i	0.0835228	−	0.144666i
$859$	−10.9957	−	19.0451i	−0.375168	−	0.649809i	0.615185	−	0.788383i	$-0.289081\pi$
$859$	−10.9957	−	19.0451i	−0.375168	−	0.649809i	−0.990352	+	0.138574i	$0.955748\pi$
$860$	−1.15984	+	2.00890i	−0.0395501	+	0.0685028i
$861$	−8.99885	−	15.5865i	−0.306680	−	0.531185i
$862$	−25.5119			−0.868939
$863$	35.8157			1.21918			0.609590	−	0.792717i	$-0.291334\pi$
$863$	35.8157			1.21918			0.609590	+	0.792717i	$0.291334\pi$
$864$	−2.52015	−	4.36502i	−0.0857371	−	0.148501i
$865$	−4.66984	−	8.08840i	−0.158779	−	0.275014i
$866$	24.4834			0.831980
$867$	−1.46442			−0.0497343
$868$	−4.13632	−	7.16431i	−0.140396	−	0.243173i
$869$	24.6843	−	42.7545i	0.837359	−	1.45035i
$870$	10.2425	+	17.7405i	0.347252	+	0.601459i
$871$	0.666502	−	1.15442i	0.0225836	−	0.0391159i
$872$	4.42174	−	7.65868i	0.149739	−	0.259356i
$873$	−83.3638			−2.82144
$874$		0			0
$875$	−13.5567			−0.458300
$876$	−3.16640	+	5.48437i	−0.106983	+	0.185300i
$877$	3.91241	−	6.77650i	0.132113	−	0.228826i	−0.792378	−	0.610030i	$-0.791157\pi$
$877$	3.91241	−	6.77650i	0.132113	−	0.228826i	0.924491	+	0.381204i	$0.124491\pi$
$878$	15.4194	+	26.7072i	0.520380	+	0.901324i
$879$	−32.6549	+	56.5599i	−1.10142	+	1.90772i
$880$	6.74794	+	11.6878i	0.227473	+	0.393995i
$881$	−14.4829			−0.487941			−0.243970	−	0.969783i	$-0.578450\pi$
$881$	−14.4829			−0.487941			−0.243970	+	0.969783i	$0.578450\pi$
$882$	25.7081			0.865636
$883$	11.7765	+	20.3974i	0.396310	+	0.686428i	0.993267	−	0.115844i	$-0.0369574\pi$
$883$	11.7765	+	20.3974i	0.396310	+	0.686428i	−0.596958	+	0.802273i	$0.703624\pi$
$884$	0.636892	+	1.10313i	0.0214210	+	0.0371023i
$885$	−21.7045			−0.729588
$886$	−10.7047			−0.359631
$887$	−7.93678	−	13.7469i	−0.266491	−	0.461576i	0.701462	−	0.712707i	$-0.252531\pi$
$887$	−7.93678	−	13.7469i	−0.266491	−	0.461576i	−0.967953	+	0.251131i	$0.919198\pi$
$888$	−5.55899	+	9.62845i	−0.186547	+	0.323110i
$889$	−1.43184	−	2.48002i	−0.0480224	−	0.0831773i
$890$	−17.6740	+	30.6123i	−0.592435	+	1.02613i
$891$	0.955791	−	1.65548i	0.0320202	−	0.0554606i
$892$	−8.92400			−0.298798
$893$		0			0
$894$	−26.0751			−0.872081
$895$	9.90688	−	17.1592i	0.331151	−	0.573570i
$896$	−0.642040	+	1.11205i	−0.0214490	+	0.0371508i
$897$	2.75280	+	4.76799i	0.0919133	+	0.159199i
$898$	−1.15781	+	2.00538i	−0.0386366	+	0.0669205i
$899$	10.0746	+	17.4497i	0.336007	+	0.581980i
$900$	2.38789			0.0795963
$901$	−13.7753			−0.458921
$902$	14.4400	+	25.0108i	0.480799	+	0.832769i
$903$	1.77455	+	3.07362i	0.0590534	+	0.102284i
$904$	−14.2502			−0.473956
$905$	19.8944			0.661311
$906$	27.6890	+	47.9588i	0.919907	+	1.59333i
$907$	22.5064	−	38.9821i	0.747311	−	1.29438i	−0.201796	−	0.979428i	$-0.564678\pi$
$907$	22.5064	−	38.9821i	0.747311	−	1.29438i	0.949107	−	0.314953i	$-0.101989\pi$
$908$	−0.329898	−	0.571400i	−0.0109480	−	0.0189626i
$909$	−8.83177	+	15.2971i	−0.292931	+	0.507372i
$910$	−0.458040	+	0.793348i	−0.0151839	+	0.0262992i
$911$	2.75901			0.0914100			0.0457050	−	0.998955i	$-0.485447\pi$
$911$	2.75901			0.0914100			0.0457050	+	0.998955i	$0.485447\pi$
$912$		0			0
$913$	−56.2074			−1.86019
$914$	−0.0260905	+	0.0451900i	−0.000862996	+	0.00149475i
$915$	35.8978	−	62.1768i	1.18674	−	2.05550i
$916$	3.48604	+	6.03800i	0.115182	+	0.199501i
$917$	0.977604	−	1.69326i	0.0322833	−	0.0559164i
$918$	−10.5498	−	18.2728i	−0.348196	−	0.603093i
$919$	−39.3083			−1.29666			−0.648331	−	0.761359i	$-0.724533\pi$
$919$	−39.3083			−1.29666			−0.648331	+	0.761359i	$0.724533\pi$
$920$	−15.1854			−0.500649
$921$	1.93879	+	3.35808i	0.0638853	+	0.110653i
$922$	19.7360	+	34.1838i	0.649971	+	1.12578i
$923$	−1.34362			−0.0442258
$924$	20.6487			0.679294
$925$	−0.989057	−	1.71310i	−0.0325200	−	0.0563263i
$926$	−3.09528	+	5.36119i	−0.101717	+	0.176180i
$927$	45.6726	+	79.1073i	1.50009	+	2.59823i
$928$	1.56378	−	2.70855i	0.0513336	−	0.0889124i
$929$	14.8709	−	25.7571i	0.487897	−	0.845063i	−0.512006	−	0.858982i	$-0.671097\pi$
$929$	14.8709	−	25.7571i	0.487897	−	0.845063i	0.999903	+	0.0139190i	$0.00443068\pi$
$930$	42.1970			1.38369
$931$		0			0
$932$	−29.6097			−0.969898
$933$	−17.0274	+	29.4923i	−0.557451	+	0.965533i
$934$	−10.4981	+	18.1832i	−0.343508	+	0.594973i
$935$	28.2482	+	48.9273i	0.923814	+	1.60009i
$936$	−0.730921	+	1.26599i	−0.0238909	+	0.0413802i
$937$	−18.8606	−	32.6674i	−0.616147	−	1.06720i	−0.990182	−	0.139784i	$-0.955359\pi$
$937$	−18.8606	−	32.6674i	−0.616147	−	1.06720i	0.374035	−	0.927415i	$-0.377974\pi$
$938$	5.62531			0.183673
$939$	−46.1822			−1.50710
$940$	−5.15156	−	8.92277i	−0.168026	−	0.291029i
$941$	−3.23826	−	5.60883i	−0.105564	−	0.182843i	0.808404	−	0.588628i	$-0.200332\pi$
$941$	−3.23826	−	5.60883i	−0.105564	−	0.182843i	−0.913969	+	0.405785i	$0.866998\pi$
$942$	38.7407			1.26224
$943$	−32.4955			−1.05820
$944$	1.65688	+	2.86979i	0.0539267	+	0.0934038i
$945$	7.58721	−	13.1414i	0.246812	−	0.427491i
$946$	−2.84754	−	4.93208i	−0.0925814	−	0.160356i
$947$	−8.14564	+	14.1087i	−0.264698	+	0.458470i	−0.967484	−	0.252931i	$-0.918606\pi$
$947$	−8.14564	+	14.1087i	−0.264698	+	0.458470i	0.702787	+	0.711401i	$0.251939\pi$
$948$	−11.9798	+	20.7496i	−0.389086	+	0.673916i
$949$	0.689776			0.0223911
$950$		0			0
$951$	7.50953			0.243513
$952$	−2.68770	+	4.65523i	−0.0871089	+	0.150877i
$953$	−17.3107	+	29.9830i	−0.560748	+	0.971243i	0.436684	+	0.899615i	$0.356153\pi$
$953$	−17.3107	+	29.9830i	−0.560748	+	0.971243i	−0.997431	+	0.0716282i	$0.977180\pi$
$954$	−7.90450	−	13.6910i	−0.255918	−	0.443262i
$955$	−26.2347	+	45.4398i	−0.848934	+	1.47040i
$956$	12.3517	+	21.3938i	0.399482	+	0.691924i
$957$	−50.2930			−1.62574
$958$	−15.5229			−0.501523
$959$	6.87737	+	11.9119i	0.222082	+	0.384657i
$960$	−3.27491	−	5.67231i	−0.105697	−	0.183073i
$961$	10.5053			0.338882
$962$	1.21098			0.0390436
$963$	24.1107	+	41.7609i	0.776956	+	1.34573i
$964$	13.7793	−	23.8665i	0.443802	−	0.768688i
$965$	−8.70789	−	15.0825i	−0.280317	−	0.485523i
$966$	−11.6169	+	20.1210i	−0.373767	+	0.647383i
$967$	24.4552	−	42.3577i	0.786428	−	1.36213i	−0.141715	−	0.989908i	$-0.545262\pi$
$967$	24.4552	−	42.3577i	0.786428	−	1.36213i	0.928142	−	0.372225i	$-0.121405\pi$
$968$	−22.1340			−0.711414
$969$		0			0
$970$	−40.6835			−1.30627
$971$	3.03796	−	5.26190i	0.0974928	−	0.168862i	−0.813153	−	0.582049i	$-0.802251\pi$
$971$	3.03796	−	5.26190i	0.0974928	−	0.168862i	0.910646	+	0.413187i	$0.135584\pi$
$972$	−8.02431	+	13.8985i	−0.257380	+	0.445795i
$973$	−6.94323	−	12.0260i	−0.222590	−	0.385537i
$974$	14.3033	−	24.7740i	0.458306	−	0.793810i
$975$	−0.211253	−	0.365900i	−0.00676550	−	0.0117182i
$976$	−10.9615			−0.350868
$977$	−57.0477			−1.82512			−0.912559	−	0.408944i	$-0.865897\pi$
$977$	−57.0477			−1.82512			−0.912559	+	0.408944i	$0.865897\pi$
$978$	−19.9039	−	34.4745i	−0.636455	−	1.10237i
$979$	−43.3919	−	75.1569i	−1.38681	−	2.40203i
$980$	12.5462			0.400772
$981$	42.4861			1.35648
$982$	−15.1744	−	26.2829i	−0.484235	−	0.838720i
$983$	0.0932597	−	0.161531i	0.00297452	−	0.00515203i	−0.864534	−	0.502574i	$-0.832387\pi$
$983$	0.0932597	−	0.161531i	0.00297452	−	0.00515203i	0.867509	+	0.497422i	$0.165720\pi$
$984$	−7.00802	−	12.1382i	−0.223407	−	0.386953i
$985$	10.0061	−	17.3311i	0.318821	−	0.552215i
$986$	6.54628	−	11.3385i	0.208476	−	0.361091i
$987$	−15.7638			−0.501768
$988$		0			0
$989$	6.40804			0.203764
$990$	−32.4186	+	56.1507i	−1.03033	+	1.78459i
$991$	−23.1199	+	40.0449i	−0.734428	+	1.27207i	0.220545	+	0.975377i	$0.429216\pi$
$991$	−23.1199	+	40.0449i	−0.734428	+	1.27207i	−0.954974	+	0.296690i	$0.904117\pi$
$992$	−3.22123	−	5.57934i	−0.102274	−	0.177144i
$993$	−7.28157	+	12.6121i	−0.231074	+	0.400231i
$994$	−2.83505	−	4.91045i	−0.0899224	−	0.155750i
$995$	14.9098			0.472671
$996$	27.2786			0.864354
$997$	10.4245	+	18.0558i	0.330147	+	0.571832i	0.982541	−	0.186049i	$-0.0595682\pi$
$997$	10.4245	+	18.0558i	0.330147	+	0.571832i	−0.652393	+	0.757881i	$0.726235\pi$
$998$	4.38812	+	7.60044i	0.138903	+	0.240588i
$999$	−20.0593			−0.634650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.n.429.4		8
19.2	odd	18		722.2.e.r.595.1		24
19.3	odd	18		722.2.e.r.99.4		24
19.4	even	9		722.2.e.s.423.1		24
19.5	even	9		722.2.e.s.389.1		24
19.6	even	9		722.2.e.s.415.4		24
19.7	even	3	inner	722.2.c.n.653.4		8
19.8	odd	6		722.2.a.n.1.4	yes	4
19.9	even	9		722.2.e.s.245.1		24
19.10	odd	18		722.2.e.r.245.4		24
19.11	even	3		722.2.a.m.1.1	✓	4
19.12	odd	6		722.2.c.m.653.1		8
19.13	odd	18		722.2.e.r.415.1		24
19.14	odd	18		722.2.e.r.389.4		24
19.15	odd	18		722.2.e.r.423.4		24
19.16	even	9		722.2.e.s.99.1		24
19.17	even	9		722.2.e.s.595.4		24
19.18	odd	2		722.2.c.m.429.1		8
57.8	even	6		6498.2.a.bx.1.3		4
57.11	odd	6		6498.2.a.ca.1.3		4
76.11	odd	6		5776.2.a.bv.1.4		4
76.27	even	6		5776.2.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.1	✓	4	19.11	even	3
722.2.a.n.1.4	yes	4	19.8	odd	6
722.2.c.m.429.1		8	19.18	odd	2
722.2.c.m.653.1		8	19.12	odd	6
722.2.c.n.429.4		8	1.1	even	1	trivial
722.2.c.n.653.4		8	19.7	even	3	inner
722.2.e.r.99.4		24	19.3	odd	18
722.2.e.r.245.4		24	19.10	odd	18
722.2.e.r.389.4		24	19.14	odd	18
722.2.e.r.415.1		24	19.13	odd	18
722.2.e.r.423.4		24	19.15	odd	18
722.2.e.r.595.1		24	19.2	odd	18
722.2.e.s.99.1		24	19.16	even	9
722.2.e.s.245.1		24	19.9	even	9
722.2.e.s.389.1		24	19.5	even	9
722.2.e.s.415.4		24	19.6	even	9
722.2.e.s.423.1		24	19.4	even	9
722.2.e.s.595.4		24	19.17	even	9
5776.2.a.bt.1.1		4	76.27	even	6
5776.2.a.bv.1.4		4	76.11	odd	6
6498.2.a.bx.1.3		4	57.8	even	6
6498.2.a.ca.1.3		4	57.11	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +(-1.17229 - 2.03046i) q^{10} +5.75621 q^{11} -2.79360 q^{12} +(0.152141 + 0.263516i) q^{13} +(-0.642040 + 1.11205i) q^{14} +(-3.27491 - 5.67231i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09310 + 3.62535i) q^{17} -4.80423 q^{18} -2.34458 q^{20} +(-1.79360 + 3.10661i) q^{21} +(2.87811 - 4.98503i) q^{22} +(3.23842 + 5.60910i) q^{23} +(-1.39680 + 2.41933i) q^{24} +(-0.248520 - 0.430448i) q^{25} +0.304282 q^{26} -5.04029 q^{27} +(0.642040 + 1.11205i) q^{28} +(-1.56378 - 2.70855i) q^{29} -6.54982 q^{30} -6.44246 q^{31} +(0.500000 + 0.866025i) q^{32} +(8.04029 - 13.9262i) q^{33} +(2.09310 + 3.62535i) q^{34} +(-1.50531 + 2.60727i) q^{35} +(-2.40211 + 4.16058i) q^{36} +3.97980 q^{37} +0.850045 q^{39} +(-1.17229 + 2.03046i) q^{40} +(-2.50859 + 4.34501i) q^{41} +(1.79360 + 3.10661i) q^{42} +(0.494689 - 0.856827i) q^{43} +(-2.87811 - 4.98503i) q^{44} -11.2639 q^{45} +6.47684 q^{46} +(2.19723 + 3.80571i) q^{47} +(1.39680 + 2.41933i) q^{48} -5.35114 q^{49} -0.497039 q^{50} +(5.84728 + 10.1278i) q^{51} +(0.152141 - 0.263516i) q^{52} +(1.64532 + 2.84978i) q^{53} +(-2.52015 + 4.36502i) q^{54} +(6.74794 - 11.6878i) q^{55} +1.28408 q^{56} -3.12756 q^{58} +(1.65688 - 2.86979i) q^{59} +(-3.27491 + 5.67231i) q^{60} +(5.48073 + 9.49290i) q^{61} +(-3.22123 + 5.57934i) q^{62} +(3.08450 + 5.34252i) q^{63} +1.00000 q^{64} +0.713414 q^{65} +(-8.04029 - 13.9262i) q^{66} +(-2.19041 - 3.79390i) q^{67} +4.18619 q^{68} +18.0937 q^{69} +(1.50531 + 2.60727i) q^{70} +(-2.20785 + 3.82410i) q^{71} +(2.40211 + 4.16058i) q^{72} +(1.13345 - 1.96319i) q^{73} +(1.98990 - 3.44660i) q^{74} -1.38853 q^{75} -7.39144 q^{77} +(0.425022 - 0.736160i) q^{78} +(4.28829 - 7.42754i) q^{79} +(1.17229 + 2.03046i) q^{80} +(0.166045 - 0.287598i) q^{81} +(2.50859 + 4.34501i) q^{82} -9.76464 q^{83} +3.58721 q^{84} +(4.90742 + 8.49991i) q^{85} +(-0.494689 - 0.856827i) q^{86} -8.73716 q^{87} -5.75621 q^{88} +(-7.53827 - 13.0567i) q^{89} +(-5.63194 + 9.75480i) q^{90} +(-0.195361 - 0.338376i) q^{91} +(3.23842 - 5.60910i) q^{92} +(-8.99885 + 15.5865i) q^{93} +4.39445 q^{94} +2.79360 q^{96} +(8.67609 - 15.0274i) q^{97} +(-2.67557 + 4.63422i) q^{98} +(-13.8271 - 23.9492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 + 8 * q^27 + 2 * q^28 - 2 * q^29 + 8 * q^30 - 52 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 - 12 * q^39 - 2 * q^40 - 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 + 20 * q^46 + 12 * q^47 + 2 * q^48 - 24 * q^49 - 12 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 + 4 * q^54 + 26 * q^55 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^66 + 10 * q^67 + 12 * q^68 + 40 * q^69 + 6 * q^70 + 4 * q^72 + 14 * q^73 - 4 * q^74 - 16 * q^75 + 8 * q^77 - 6 * q^78 + 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 - 8 * q^84 + 18 * q^85 - 10 * q^86 - 52 * q^87 - 4 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 + 10 * q^92 - 8 * q^93 + 24 * q^94 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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