LMFDB - Embedded newform 1050.2.bc.g.493.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.2
Root			$2.69978 - 0.355433i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.g.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(0.942805 - 2.47207i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(0.942805 - 2.47207i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.55390 - 2.69144i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-3.40812 + 3.40812i) q^{13} +(-1.55050 + 2.14382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(5.14616 - 1.37891i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-3.61673 - 6.26436i) q^{19} +(2.63185 + 0.270861i) q^{21} +(-2.19755 + 2.19755i) q^{22} +(1.36289 - 5.08638i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.17408 - 2.40991i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.05253 - 1.66947i) q^{28} +4.49359i q^{29} +(-7.98911 - 4.61252i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(3.00191 + 0.804359i) q^{33} -5.32769 q^{34} -1.00000 q^{36} +(-3.47079 - 0.929997i) q^{37} +(1.87216 + 6.98699i) q^{38} +(-4.17408 - 2.40991i) q^{39} -2.51851i q^{41} +(-2.47207 - 0.942805i) q^{42} +(3.86848 + 3.86848i) q^{43} +(2.69144 - 1.55390i) q^{44} +(-2.63291 + 4.56033i) q^{46} +(1.05713 - 3.94526i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.22224 - 4.66135i) q^{49} +(2.66385 + 4.61392i) q^{51} +(-4.65558 + 1.24746i) q^{52} +(3.32222 - 0.890187i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.41468 + 1.08135i) q^{56} +(5.11483 - 5.11483i) q^{57} +(1.16303 - 4.34047i) q^{58} +(0.666188 - 1.15387i) q^{59} +(10.8719 - 6.27689i) q^{61} +(6.52308 + 6.52308i) q^{62} +(0.419541 + 2.61228i) q^{63} +1.00000i q^{64} +(-2.69144 - 1.55390i) q^{66} +(1.72448 + 6.43584i) q^{67} +(5.14616 + 1.37891i) q^{68} +5.26581 q^{69} +9.22738 q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.13063 - 7.95163i) q^{73} +(3.11183 + 1.79662i) q^{74} -7.23346i q^{76} +(-5.18839 - 6.37885i) q^{77} +(3.40812 + 3.40812i) q^{78} +(1.65789 - 0.957181i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.651839 + 2.43270i) q^{82} +(8.97250 - 8.97250i) q^{83} +(2.14382 + 1.55050i) q^{84} +(-2.73543 - 4.73790i) q^{86} +(-4.34047 + 1.16303i) q^{87} +(-3.00191 + 0.804359i) q^{88} +(2.03677 + 3.52779i) q^{89} +(5.21191 + 11.6383i) q^{91} +(3.72349 - 3.72349i) q^{92} +(2.38761 - 8.91070i) q^{93} +(-2.04222 + 3.53723i) q^{94} +(0.866025 - 0.500000i) q^{96} +(2.69423 + 2.69423i) q^{97} +(3.83785 + 5.85414i) q^{98} +3.10780i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	0.942805	−	2.47207i	0.356347	−	0.934354i
$7$	0.942805	−	2.47207i	0.356347	−	0.934354i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	1.55390	−	2.69144i	0.468519	−	0.811499i	−0.530833	−	0.847476i	$-0.678121\pi$
$11$	1.55390	−	2.69144i	0.468519	−	0.811499i	0.999353	+	0.0359771i	$0.0114543\pi$
$12$	−0.258819	+	0.965926i	−0.0747146	+	0.278839i
$13$	−3.40812	+	3.40812i	−0.945243	+	0.945243i	−0.998577	−	0.0533341i	$-0.983015\pi$
$13$	−3.40812	+	3.40812i	−0.945243	+	0.945243i	0.0533341	+	0.998577i	$0.483015\pi$
$14$	−1.55050	+	2.14382i	−0.414388	+	0.572960i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	5.14616	−	1.37891i	1.24813	−	0.334434i	0.426514	−	0.904481i	$-0.359742\pi$
$17$	5.14616	−	1.37891i	1.24813	−	0.334434i	0.821612	+	0.570047i	$0.193075\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−3.61673	−	6.26436i	−0.829735	−	1.43714i	−0.898246	−	0.439493i	$-0.855158\pi$
$19$	−3.61673	−	6.26436i	−0.829735	−	1.43714i	0.0685112	−	0.997650i	$-0.478175\pi$
$20$		0			0
$21$	2.63185	+	0.270861i	0.574317	+	0.0591067i
$22$	−2.19755	+	2.19755i	−0.468519	+	0.468519i
$23$	1.36289	−	5.08638i	0.284183	−	1.06058i	−0.665252	−	0.746619i	$-0.731676\pi$
$23$	1.36289	−	5.08638i	0.284183	−	1.06058i	0.949435	−	0.313965i	$-0.101657\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	4.17408	−	2.40991i	0.818604	−	0.472621i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.05253	−	1.66947i	0.387891	−	0.315500i
$29$			4.49359i			0.834438i	0.908806	+	0.417219i	$0.136995\pi$
$29$			4.49359i			0.834438i	−0.908806	+	0.417219i	$0.863005\pi$
$30$		0			0
$31$	−7.98911	−	4.61252i	−1.43489	−	0.828432i	−0.437399	−	0.899268i	$-0.644100\pi$
$31$	−7.98911	−	4.61252i	−1.43489	−	0.828432i	−0.997488	+	0.0708354i	$0.977433\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	3.00191	+	0.804359i	0.522565	+	0.140021i
$34$	−5.32769			−0.913692
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−3.47079	−	0.929997i	−0.570595	−	0.152890i	−0.0380256	−	0.999277i	$-0.512107\pi$
$37$	−3.47079	−	0.929997i	−0.570595	−	0.152890i	−0.532569	+	0.846386i	$0.678773\pi$
$38$	1.87216	+	6.98699i	0.303704	+	1.13344i
$39$	−4.17408	−	2.40991i	−0.668387	−	0.385894i
$40$		0			0
$41$		−	2.51851i		−	0.393326i	−0.980471	−	0.196663i	$-0.936990\pi$
$41$		−	2.51851i		−	0.393326i	0.980471	−	0.196663i	$-0.0630104\pi$
$42$	−2.47207	−	0.942805i	−0.381448	−	0.145478i
$43$	3.86848	+	3.86848i	0.589938	+	0.589938i	0.937615	−	0.347677i	$-0.113029\pi$
$43$	3.86848	+	3.86848i	0.589938	+	0.589938i	−0.347677	+	0.937615i	$0.613029\pi$
$44$	2.69144	−	1.55390i	0.405750	−	0.234260i
$45$		0			0
$46$	−2.63291	+	4.56033i	−0.388201	+	0.672383i
$47$	1.05713	−	3.94526i	0.154198	−	0.575476i	−0.844974	−	0.534807i	$-0.820384\pi$
$47$	1.05713	−	3.94526i	0.154198	−	0.575476i	0.999173	−	0.0406690i	$-0.0129489\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−5.22224	−	4.66135i	−0.746034	−	0.665908i
$50$		0			0
$51$	2.66385	+	4.61392i	0.373013	+	0.646078i
$52$	−4.65558	+	1.24746i	−0.645613	+	0.172991i
$53$	3.32222	−	0.890187i	0.456342	−	0.122277i	−0.0233232	−	0.999728i	$-0.507425\pi$
$53$	3.32222	−	0.890187i	0.456342	−	0.122277i	0.479665	+	0.877451i	$0.340758\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−2.41468	+	1.08135i	−0.322675	+	0.144502i
$57$	5.11483	−	5.11483i	0.677476	−	0.677476i
$58$	1.16303	−	4.34047i	0.152713	−	0.569932i
$59$	0.666188	−	1.15387i	0.0867303	−	0.150221i	−0.819397	−	0.573227i	$-0.805691\pi$
$59$	0.666188	−	1.15387i	0.0867303	−	0.150221i	0.906127	+	0.423005i	$0.139025\pi$
$60$		0			0
$61$	10.8719	−	6.27689i	1.39200	−	0.803673i	0.398466	−	0.917183i	$-0.369543\pi$
$61$	10.8719	−	6.27689i	1.39200	−	0.803673i	0.993537	+	0.113510i	$0.0362095\pi$
$62$	6.52308	+	6.52308i	0.828432	+	0.828432i
$63$	0.419541	+	2.61228i	0.0528572	+	0.329116i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.69144	−	1.55390i	−0.331293	−	0.191272i
$67$	1.72448	+	6.43584i	0.210679	+	0.786263i	0.987643	+	0.156719i	$0.0500916\pi$
$67$	1.72448	+	6.43584i	0.210679	+	0.786263i	−0.776965	+	0.629544i	$0.783242\pi$
$68$	5.14616	+	1.37891i	0.624063	+	0.167217i
$69$	5.26581			0.633929
$70$		0			0
$71$	9.22738			1.09509			0.547544	−	0.836777i	$-0.315563\pi$
$71$	9.22738			1.09509			0.547544	+	0.836777i	$0.315563\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−2.13063	−	7.95163i	−0.249372	−	0.930667i	−0.971136	−	0.238528i	$-0.923335\pi$
$73$	−2.13063	−	7.95163i	−0.249372	−	0.930667i	0.721764	−	0.692139i	$-0.243332\pi$
$74$	3.11183	+	1.79662i	0.361743	+	0.208852i
$75$		0			0
$76$		−	7.23346i		−	0.829735i
$77$	−5.18839	−	6.37885i	−0.591272	−	0.726938i
$78$	3.40812	+	3.40812i	0.385894	+	0.385894i
$79$	1.65789	−	0.957181i	0.186527	−	0.107691i	−0.403829	−	0.914835i	$-0.632321\pi$
$79$	1.65789	−	0.957181i	0.186527	−	0.107691i	0.590356	+	0.807143i	$0.298988\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.651839	+	2.43270i	−0.0719836	+	0.268646i
$83$	8.97250	−	8.97250i	0.984860	−	0.984860i	−0.0150269	−	0.999887i	$-0.504783\pi$
$83$	8.97250	−	8.97250i	0.984860	−	0.984860i	0.999887	+	0.0150269i	$0.00478339\pi$
$84$	2.14382	+	1.55050i	0.233910	+	0.169173i
$85$		0			0
$86$	−2.73543	−	4.73790i	−0.294969	−	0.510901i
$87$	−4.34047	+	1.16303i	−0.465347	+	0.124689i
$88$	−3.00191	+	0.804359i	−0.320005	+	0.0857450i
$89$	2.03677	+	3.52779i	0.215897	+	0.373945i	0.953550	−	0.301236i	$-0.0973991\pi$
$89$	2.03677	+	3.52779i	0.215897	+	0.373945i	−0.737653	+	0.675181i	$0.764066\pi$
$90$		0			0
$91$	5.21191	+	11.6383i	0.546357	+	1.22003i
$92$	3.72349	−	3.72349i	0.388201	−	0.388201i
$93$	2.38761	−	8.91070i	0.247584	−	0.923996i
$94$	−2.04222	+	3.53723i	−0.210639	+	0.364837i
$95$		0			0
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	2.69423	+	2.69423i	0.273558	+	0.273558i	0.830531	−	0.556973i	$-0.188037\pi$
$97$	2.69423	+	2.69423i	0.273558	+	0.273558i	−0.556973	+	0.830531i	$0.688037\pi$
$98$	3.83785	+	5.85414i	0.387681	+	0.591357i
$99$			3.10780i			0.312346i
$100$		0			0
$101$	−6.80907	−	3.93122i	−0.677528	−	0.391171i	0.121395	−	0.992604i	$-0.461263\pi$
$101$	−6.80907	−	3.93122i	−0.677528	−	0.391171i	−0.798923	+	0.601433i	$0.794597\pi$
$102$	−1.37891	−	5.14616i	−0.136532	−	0.509545i
$103$	−11.4280	−	3.06212i	−1.12603	−	0.301720i	−0.352710	−	0.935732i	$-0.614740\pi$
$103$	−11.4280	−	3.06212i	−1.12603	−	0.301720i	−0.773322	+	0.634013i	$0.781407\pi$
$104$	4.81981			0.472621
$105$		0			0
$106$	−3.43942			−0.334066
$107$	−2.08859	−	0.559635i	−0.201911	−	0.0541020i	0.156446	−	0.987687i	$-0.449996\pi$
$107$	−2.08859	−	0.559635i	−0.201911	−	0.0541020i	−0.358357	+	0.933585i	$0.616663\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	0.489782	+	0.282776i	0.0469126	+	0.0270850i	0.523273	−	0.852165i	$-0.324711\pi$
$109$	0.489782	+	0.282776i	0.0469126	+	0.0270850i	−0.476360	+	0.879250i	$0.658044\pi$
$110$		0			0
$111$		−	3.59323i		−	0.341054i
$112$	2.61228	−	0.419541i	0.246837	−	0.0396429i
$113$	−9.98231	−	9.98231i	−0.939057	−	0.939057i	0.0591899	−	0.998247i	$-0.481148\pi$
$113$	−9.98231	−	9.98231i	−0.939057	−	0.939057i	−0.998247	+	0.0591899i	$0.981148\pi$
$114$	−6.26436	+	3.61673i	−0.586711	+	0.338738i
$115$		0			0
$116$	−2.24679	+	3.89156i	−0.208610	+	0.361322i
$117$	1.24746	−	4.65558i	0.115328	−	0.430408i
$118$	−0.942132	+	0.942132i	−0.0867303	+	0.0867303i
$119$	1.44306	−	14.0217i	0.132285	−	1.28537i
$120$		0			0
$121$	0.670774	+	1.16181i	0.0609795	+	0.105620i
$122$	−12.1260	+	3.24916i	−1.09784	+	0.294165i
$123$	2.43270	−	0.651839i	0.219349	−	0.0587744i
$124$	−4.61252	−	7.98911i	−0.414216	−	0.717443i
$125$		0			0
$126$	0.270861	−	2.63185i	0.0241302	−	0.234464i
$127$	2.14534	−	2.14534i	0.190368	−	0.190368i	−0.605487	−	0.795855i	$-0.707022\pi$
$127$	2.14534	−	2.14534i	0.190368	−	0.190368i	0.795855	+	0.605487i	$0.207022\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−2.73543	+	4.73790i	−0.240841	+	0.417149i
$130$		0			0
$131$	7.59798	−	4.38669i	0.663838	−	0.383267i	−0.129900	−	0.991527i	$-0.541466\pi$
$131$	7.59798	−	4.38669i	0.663838	−	0.383267i	0.793738	+	0.608260i	$0.208132\pi$
$132$	2.19755	+	2.19755i	0.191272	+	0.191272i
$133$	−18.8958	+	3.03474i	−1.63847	+	0.263145i
$134$		−	6.66287i		−	0.575584i
$135$		0			0
$136$	−4.61392	−	2.66385i	−0.395640	−	0.228423i
$137$	3.52127	+	13.1416i	0.300843	+	1.12276i	0.936465	+	0.350760i	$0.114077\pi$
$137$	3.52127	+	13.1416i	0.300843	+	1.12276i	−0.635622	+	0.772000i	$0.719256\pi$
$138$	−5.08638	−	1.36289i	−0.432982	−	0.116017i
$139$	10.9145			0.925753			0.462876	−	0.886423i	$-0.346817\pi$
$139$	10.9145			0.925753			0.462876	+	0.886423i	$0.346817\pi$
$140$		0			0
$141$	4.08444			0.343972
$142$	−8.91296	−	2.38822i	−0.747959	−	0.200415i
$143$	3.87686	+	14.4686i	0.324199	+	1.20993i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$			8.23213i			0.681296i
$147$	3.15091	−	6.25074i	0.259882	−	0.515553i
$148$	−2.54080	−	2.54080i	−0.208852	−	0.208852i
$149$	1.81017	−	1.04510i	0.148295	−	0.0856183i	−0.424016	−	0.905655i	$-0.639380\pi$
$149$	1.81017	−	1.04510i	0.148295	−	0.0856183i	0.572312	+	0.820036i	$0.306047\pi$
$150$		0			0
$151$	−2.02118	+	3.50079i	−0.164481	+	0.284890i	−0.936471	−	0.350745i	$-0.885928\pi$
$151$	−2.02118	+	3.50079i	−0.164481	+	0.284890i	0.771990	+	0.635635i	$0.219262\pi$
$152$	−1.87216	+	6.98699i	−0.151852	+	0.566720i
$153$	−3.76725	+	3.76725i	−0.304564	+	0.304564i
$154$	3.36063	+	7.50435i	0.270807	+	0.604718i
$155$		0			0
$156$	−2.40991	−	4.17408i	−0.192947	−	0.334194i
$157$	−0.874716	+	0.234379i	−0.0698099	+	0.0187055i	−0.293555	−	0.955942i	$-0.594838\pi$
$157$	−0.874716	+	0.234379i	−0.0698099	+	0.0187055i	0.223745	+	0.974648i	$0.428172\pi$
$158$	−1.84913	+	0.495474i	−0.147109	+	0.0394178i
$159$	1.71971	+	2.97862i	0.136382	+	0.236220i
$160$		0			0
$161$	−11.2889	−	8.16463i	−0.889693	−	0.643463i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	1.91065	−	7.13062i	0.149653	−	0.558514i	−0.849851	−	0.527023i	$-0.823308\pi$
$163$	1.91065	−	7.13062i	0.149653	−	0.558514i	0.999504	−	0.0314902i	$-0.0100253\pi$
$164$	1.25926	−	2.18110i	0.0983314	−	0.170315i
$165$		0			0
$166$	−10.9890	+	6.34452i	−0.852914	+	0.492430i
$167$	−0.610646	−	0.610646i	−0.0472532	−	0.0472532i	0.683085	−	0.730339i	$-0.260638\pi$
$167$	−0.610646	−	0.610646i	−0.0472532	−	0.0472532i	−0.730339	+	0.683085i	$0.760638\pi$
$168$	−1.66947	−	2.05253i	−0.128803	−	0.158356i
$169$		−	10.2306i		−	0.786967i
$170$		0			0
$171$	6.26436	+	3.61673i	0.479048	+	0.276578i
$172$	1.41596	+	5.28444i	0.107966	+	0.402935i
$173$	3.37831	+	0.905215i	0.256848	+	0.0688222i	0.384945	−	0.922939i	$-0.374220\pi$
$173$	3.37831	+	0.905215i	0.256848	+	0.0688222i	−0.128097	+	0.991762i	$0.540887\pi$
$174$	4.49359			0.340658
$175$		0			0
$176$	3.10780			0.234260
$177$	1.28698	+	0.344844i	0.0967351	+	0.0259201i
$178$	−1.05431	−	3.93474i	−0.0790239	−	0.294921i
$179$	15.6420	+	9.03091i	1.16914	+	0.675002i	0.953477	−	0.301467i	$-0.0974762\pi$
$179$	15.6420	+	9.03091i	1.16914	+	0.675002i	0.215661	+	0.976468i	$0.430810\pi$
$180$		0			0
$181$			21.7257i			1.61486i	0.589965	+	0.807429i	$0.299142\pi$
$181$			21.7257i			1.61486i	−0.589965	+	0.807429i	$0.700858\pi$
$182$	−2.02211	−	12.5907i	−0.149889	−	0.933283i
$183$	8.87686	+	8.87686i	0.656196	+	0.656196i
$184$	−4.56033	+	2.63291i	−0.336192	+	0.194100i
$185$		0			0
$186$	−4.61252	+	7.98911i	−0.338206	+	0.585790i
$187$	4.28538	−	15.9932i	0.313378	−	1.16954i
$188$	2.88813	−	2.88813i	0.210639	−	0.210639i
$189$	−2.41468	+	1.08135i	−0.175642	+	0.0786568i
$190$		0			0
$191$	−8.29123	−	14.3608i	−0.599932	−	1.03911i	−0.992830	−	0.119531i	$-0.961861\pi$
$191$	−8.29123	−	14.3608i	−0.599932	−	1.03911i	0.392898	−	0.919582i	$-0.371473\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−2.04533	+	0.548044i	−0.147226	+	0.0394491i	−0.331679	−	0.943392i	$-0.607615\pi$
$193$	−2.04533	+	0.548044i	−0.147226	+	0.0394491i	0.184453	+	0.982841i	$0.440949\pi$
$194$	−1.90511	−	3.29975i	−0.136779	−	0.236908i
$195$		0			0
$196$	−2.19191	−	6.64797i	−0.156565	−	0.474855i
$197$	1.22531	−	1.22531i	0.0872995	−	0.0872995i	−0.662108	−	0.749408i	$-0.730338\pi$
$197$	1.22531	−	1.22531i	0.0872995	−	0.0872995i	0.749408	+	0.662108i	$0.230338\pi$
$198$	0.804359	−	3.00191i	0.0571633	−	0.213336i
$199$	−3.93901	+	6.82256i	−0.279229	+	0.483638i	−0.971193	−	0.238293i	$-0.923412\pi$
$199$	−3.93901	+	6.82256i	−0.279229	+	0.483638i	0.691964	+	0.721932i	$0.256745\pi$
$200$		0			0
$201$	−5.77022	+	3.33144i	−0.407000	+	0.234981i
$202$	5.55958	+	5.55958i	0.391171	+	0.391171i
$203$	11.1085	+	4.23657i	0.779661	+	0.297349i
$204$			5.32769i			0.373013i
$205$		0			0
$206$	10.2461	+	5.91556i	0.713876	+	0.412157i
$207$	1.36289	+	5.08638i	0.0947276	+	0.353528i
$208$	−4.65558	−	1.24746i	−0.322806	−	0.0864957i
$209$	−22.4802			−1.55499
$210$		0			0
$211$	−15.9995			−1.10145			−0.550724	−	0.834687i	$-0.685648\pi$
$211$	−15.9995			−1.10145			−0.550724	+	0.834687i	$0.685648\pi$
$212$	3.32222	+	0.890187i	0.228171	+	0.0611383i
$213$	2.38822	+	8.91296i	0.163638	+	0.610706i
$214$	1.87258	+	1.08113i	0.128007	+	0.0739047i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−18.9346	+	15.4009i	−1.28537	+	1.04548i
$218$	−0.399905	−	0.399905i	−0.0270850	−	0.0270850i
$219$	7.12923	−	4.11606i	0.481749	−	0.278138i
$220$		0			0
$221$	−12.8392	+	22.2382i	−0.863660	+	1.49590i
$222$	−0.929997	+	3.47079i	−0.0624173	+	0.232944i
$223$	−1.20707	+	1.20707i	−0.0808314	+	0.0808314i	−0.746367	−	0.665535i	$-0.768203\pi$
$223$	−1.20707	+	1.20707i	−0.0808314	+	0.0808314i	0.665535	+	0.746367i	$0.268203\pi$
$224$	−2.63185	−	0.270861i	−0.175848	−	0.0180977i
$225$		0			0
$226$	7.05856	+	12.2258i	0.469528	+	0.813247i
$227$	−6.58082	+	1.76332i	−0.436784	+	0.117036i	−0.470509	−	0.882395i	$-0.655930\pi$
$227$	−6.58082	+	1.76332i	−0.436784	+	0.117036i	0.0337248	+	0.999431i	$0.489263\pi$
$228$	6.98699	−	1.87216i	0.462725	−	0.123987i
$229$	−9.90714	−	17.1597i	−0.654682	−	1.13394i	−0.981973	−	0.189019i	$-0.939469\pi$
$229$	−9.90714	−	17.1597i	−0.654682	−	1.13394i	0.327291	−	0.944924i	$-0.393864\pi$
$230$		0			0
$231$	4.81864	−	6.66257i	0.317043	−	0.438365i
$232$	3.17745	−	3.17745i	0.208610	−	0.208610i
$233$	−4.65807	+	17.3842i	−0.305161	+	1.13887i	0.627647	+	0.778498i	$0.284018\pi$
$233$	−4.65807	+	17.3842i	−0.305161	+	1.13887i	−0.932807	+	0.360376i	$0.882648\pi$
$234$	−2.40991	+	4.17408i	−0.157540	+	0.272868i
$235$		0			0
$236$	1.15387	−	0.666188i	0.0751107	−	0.0433652i
$237$	1.35366	+	1.35366i	0.0879296	+	0.0879296i
$238$	−5.02297	+	13.1704i	−0.325591	+	0.853711i
$239$			26.6409i			1.72325i	0.507542	+	0.861627i	$0.330554\pi$
$239$			26.6409i			1.72325i	−0.507542	+	0.861627i	$0.669446\pi$
$240$		0			0
$241$	−12.4923	−	7.21241i	−0.804697	−	0.464592i	0.0404137	−	0.999183i	$-0.487132\pi$
$241$	−12.4923	−	7.21241i	−0.804697	−	0.464592i	−0.845111	+	0.534591i	$0.820466\pi$
$242$	−0.347218	−	1.29584i	−0.0223200	−	0.0832995i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	12.5538			0.803673
$245$		0			0
$246$	−2.51851			−0.160575
$247$	33.6760	+	9.02344i	2.14275	+	0.574148i
$248$	2.38761	+	8.91070i	0.151614	+	0.565830i
$249$	10.9890	+	6.34452i	0.696401	+	0.402067i
$250$		0			0
$251$			26.4573i			1.66997i	0.550271	+	0.834986i	$0.314524\pi$
$251$			26.4573i			1.66997i	−0.550271	+	0.834986i	$0.685476\pi$
$252$	−0.942805	+	2.47207i	−0.0593911	+	0.155726i
$253$	−11.5719	−	11.5719i	−0.727518	−	0.727518i
$254$	−2.62750	+	1.51699i	−0.164864	+	0.0951842i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.90266	−	10.8329i	0.181063	−	0.675736i	−0.814376	−	0.580337i	$-0.802921\pi$
$257$	2.90266	−	10.8329i	0.181063	−	0.675736i	0.995439	−	0.0953987i	$-0.0304126\pi$
$258$	3.86848	−	3.86848i	0.240841	−	0.240841i
$259$	−5.57130	+	7.70323i	−0.346183	+	0.478656i
$260$		0			0
$261$	−2.24679	−	3.89156i	−0.139073	−	0.240882i
$262$	−8.47444	+	2.27072i	−0.523553	+	0.140286i
$263$	−6.62539	+	1.77527i	−0.408539	+	0.109468i	−0.457235	−	0.889346i	$-0.651160\pi$
$263$	−6.62539	+	1.77527i	−0.408539	+	0.109468i	0.0486959	+	0.998814i	$0.484493\pi$
$264$	−1.55390	−	2.69144i	−0.0956361	−	0.165647i
$265$		0			0
$266$	19.0374	+	1.95926i	1.16726	+	0.120130i
$267$	−2.88043	+	2.88043i	−0.176279	+	0.176279i
$268$	−1.72448	+	6.43584i	−0.105339	+	0.393131i
$269$	−4.49032	+	7.77746i	−0.273780	+	0.474200i	−0.969827	−	0.243796i	$-0.921607\pi$
$269$	−4.49032	+	7.77746i	−0.273780	+	0.474200i	0.696047	+	0.717996i	$0.254941\pi$
$270$		0			0
$271$	7.76980	−	4.48590i	0.471982	−	0.272499i	−0.245087	−	0.969501i	$-0.578817\pi$
$271$	7.76980	−	4.48590i	0.471982	−	0.272499i	0.717069	+	0.697002i	$0.245483\pi$
$272$	3.76725	+	3.76725i	0.228423	+	0.228423i
$273$	−9.89279	+	8.04653i	−0.598739	+	0.486998i
$274$		−	13.6052i		−	0.821918i
$275$		0			0
$276$	4.56033	+	2.63291i	0.274499	+	0.158482i
$277$	6.39571	+	23.8691i	0.384281	+	1.43416i	0.839297	+	0.543673i	$0.182967\pi$
$277$	6.39571	+	23.8691i	0.384281	+	1.43416i	−0.455016	+	0.890483i	$0.650367\pi$
$278$	−10.5426	−	2.82487i	−0.632301	−	0.169424i
$279$	9.22503			0.552288
$280$		0			0
$281$	18.4916			1.10312			0.551558	−	0.834137i	$-0.314034\pi$
$281$	18.4916			1.10312			0.551558	+	0.834137i	$0.314034\pi$
$282$	−3.94526	−	1.05713i	−0.234937	−	0.0629512i
$283$	−1.44208	−	5.38190i	−0.0857226	−	0.319921i	0.909727	−	0.415206i	$-0.136290\pi$
$283$	−1.44208	−	5.38190i	−0.0857226	−	0.319921i	−0.995450	+	0.0952849i	$0.969624\pi$
$284$	7.99114	+	4.61369i	0.474187	+	0.273772i
$285$		0			0
$286$		−	14.9790i		−	0.885729i
$287$	−6.22594	−	2.37447i	−0.367505	−	0.140160i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	9.85909	−	5.69215i	0.579947	−	0.334832i
$290$		0			0
$291$	−1.90511	+	3.29975i	−0.111679	+	0.193434i
$292$	2.13063	−	7.95163i	0.124686	−	0.465334i
$293$	−17.6465	+	17.6465i	−1.03092	+	1.03092i	−0.0314115	+	0.999507i	$0.510000\pi$
$293$	−17.6465	+	17.6465i	−1.03092	+	1.03092i	−0.999507	+	0.0314115i	$0.990000\pi$
$294$	−4.66135	+	5.22224i	−0.271856	+	0.304567i
$295$		0			0
$296$	1.79662	+	3.11183i	0.104426	+	0.180871i
$297$	−3.00191	+	0.804359i	−0.174188	+	0.0466736i
$298$	−2.01899	+	0.540986i	−0.116957	+	0.0313385i
$299$	12.6901	+	21.9799i	0.733888	+	1.27113i
$300$		0			0
$301$	13.2104	−	5.91593i	0.761433	−	0.340988i
$302$	2.85838	−	2.85838i	0.164481	−	0.164481i
$303$	2.03495	−	7.59453i	0.116905	−	0.436295i
$304$	3.61673	−	6.26436i	0.207434	−	0.359286i
$305$		0			0
$306$	4.61392	−	2.66385i	0.263760	−	0.152282i
$307$	−11.4807	−	11.4807i	−0.655239	−	0.655239i	0.299011	−	0.954250i	$-0.403343\pi$
$307$	−11.4807	−	11.4807i	−0.655239	−	0.655239i	−0.954250	+	0.299011i	$0.903343\pi$
$308$	−1.30385	−	8.11844i	−0.0742939	−	0.462591i
$309$		−	11.8311i		−	0.673049i
$310$		0			0
$311$	−11.3751	−	6.56743i	−0.645024	−	0.372405i	0.141523	−	0.989935i	$-0.454800\pi$
$311$	−11.3751	−	6.56743i	−0.645024	−	0.372405i	−0.786547	+	0.617530i	$0.788133\pi$
$312$	1.24746	+	4.65558i	0.0706234	+	0.263570i
$313$	24.5811	+	6.58648i	1.38940	+	0.372290i	0.874528	−	0.484974i	$-0.161171\pi$
$313$	24.5811	+	6.58648i	1.38940	+	0.372290i	0.514877	+	0.857264i	$0.327838\pi$
$314$	0.905573			0.0511044
$315$		0			0
$316$	1.91436			0.107691
$317$	18.3779	+	4.92434i	1.03220	+	0.276578i	0.734879	−	0.678198i	$-0.237239\pi$
$317$	18.3779	+	4.92434i	1.03220	+	0.276578i	0.297325	+	0.954776i	$0.403906\pi$
$318$	−0.890187	−	3.32222i	−0.0499192	−	0.186301i
$319$	12.0942	+	6.98260i	0.677146	+	0.390950i
$320$		0			0
$321$		−	2.16226i		−	0.120686i
$322$	8.79112	+	10.8082i	0.489910	+	0.602318i
$323$	−27.2502	−	27.2502i	−1.51624	−	1.51624i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$		0			0
$326$	−3.69108	+	6.39314i	−0.204430	+	0.354083i
$327$	−0.146375	+	0.546281i	−0.00809458	+	0.0302094i
$328$	−1.78086	+	1.78086i	−0.0983314	+	0.0983314i
$329$	−8.75629	−	6.33291i	−0.482750	−	0.349145i
$330$		0			0
$331$	10.4690	+	18.1329i	0.575430	+	0.996674i	0.995995	+	0.0894115i	$0.0284986\pi$
$331$	10.4690	+	18.1329i	0.575430	+	0.996674i	−0.420565	+	0.907263i	$0.638168\pi$
$332$	12.2567	−	3.28416i	0.672672	−	0.180242i
$333$	3.47079	−	0.929997i	0.190198	−	0.0509635i
$334$	0.431792	+	0.747886i	0.0236266	+	0.0409225i
$335$		0			0
$336$	1.08135	+	2.41468i	0.0589926	+	0.131732i
$337$	−0.272770	+	0.272770i	−0.0148587	+	0.0148587i	−0.714497	−	0.699638i	$-0.753344\pi$
$337$	−0.272770	+	0.272770i	−0.0148587	+	0.0148587i	0.699638	+	0.714497i	$0.253344\pi$
$338$	−2.64787	+	9.88197i	−0.144025	+	0.537508i
$339$	7.05856	−	12.2258i	0.383368	−	0.664013i
$340$		0			0
$341$	−24.8286	+	14.3348i	−1.34454	+	0.776273i
$342$	−5.11483	−	5.11483i	−0.276578	−	0.276578i
$343$	−16.4467	+	8.51498i	−0.888040	+	0.459766i
$344$		−	5.47086i		−	0.294969i
$345$		0			0
$346$	−3.02891	−	1.74874i	−0.162835	−	0.0940129i
$347$	3.91516	+	14.6116i	0.210177	+	0.784391i	0.987809	+	0.155671i	$0.0497540\pi$
$347$	3.91516	+	14.6116i	0.210177	+	0.784391i	−0.777632	+	0.628720i	$0.783579\pi$
$348$	−4.34047	−	1.16303i	−0.232674	−	0.0623447i
$349$	−15.2733			−0.817563			−0.408781	−	0.912632i	$-0.634046\pi$
$349$	−15.2733			−0.817563			−0.408781	+	0.912632i	$0.634046\pi$
$350$		0			0
$351$	4.81981			0.257262
$352$	−3.00191	−	0.804359i	−0.160002	−	0.0428725i
$353$	−7.77147	−	29.0035i	−0.413634	−	1.54370i	−0.787557	−	0.616242i	$-0.788654\pi$
$353$	−7.77147	−	29.0035i	−0.413634	−	1.54370i	0.373923	−	0.927460i	$-0.378012\pi$
$354$	−1.15387	−	0.666188i	−0.0613276	−	0.0354075i
$355$		0			0
$356$			4.07354i			0.215897i
$357$	13.9174	−	2.23519i	0.736587	−	0.118299i
$358$	−12.7716	−	12.7716i	−0.675002	−	0.675002i
$359$	−10.1537	+	5.86222i	−0.535890	+	0.309396i	−0.743411	−	0.668834i	$-0.766794\pi$
$359$	−10.1537	+	5.86222i	−0.535890	+	0.309396i	0.207522	+	0.978230i	$0.433460\pi$
$360$		0			0
$361$	−16.6615	+	28.8585i	−0.876920	+	1.51887i
$362$	5.62302	−	20.9854i	0.295540	−	1.10297i
$363$	−0.948618	+	0.948618i	−0.0497895	+	0.0497895i
$364$	−1.30550	+	12.6850i	−0.0684267	+	0.664876i
$365$		0			0
$366$	−6.27689	−	10.8719i	−0.328098	−	0.568283i
$367$	−29.3629	+	7.86775i	−1.53273	+	0.410693i	−0.923908	−	0.382615i	$-0.875024\pi$
$367$	−29.3629	+	7.86775i	−1.53273	+	0.410693i	−0.608821	+	0.793308i	$0.708357\pi$
$368$	5.08638	−	1.36289i	0.265146	−	0.0710457i
$369$	1.25926	+	2.18110i	0.0655543	+	0.113543i
$370$		0			0
$371$	0.931604	−	9.05203i	0.0483665	−	0.469958i
$372$	6.52308	−	6.52308i	0.338206	−	0.338206i
$373$	−7.80742	+	29.1377i	−0.404253	+	1.50869i	0.401176	+	0.916001i	$0.368601\pi$
$373$	−7.80742	+	29.1377i	−0.404253	+	1.50869i	−0.805429	+	0.592692i	$0.798065\pi$
$374$	−8.27871	+	14.3392i	−0.428082	+	0.741460i
$375$		0			0
$376$	−3.53723	+	2.04222i	−0.182419	+	0.105319i
$377$	−15.3147	−	15.3147i	−0.788746	−	0.788746i
$378$	2.61228	−	0.419541i	0.134361	−	0.0215789i
$379$			4.44115i			0.228127i	0.993473	+	0.114063i	$0.0363867\pi$
$379$			4.44115i			0.228127i	−0.993473	+	0.114063i	$0.963613\pi$
$380$		0			0
$381$	2.62750	+	1.51699i	0.134611	+	0.0777176i
$382$	4.29186	+	16.0174i	0.219590	+	0.819523i
$383$	21.5032	+	5.76177i	1.09876	+	0.294413i	0.762261	−	0.647270i	$-0.224089\pi$
$383$	21.5032	+	5.76177i	1.09876	+	0.294413i	0.336502	+	0.941683i	$0.390756\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	2.11748			0.107777
$387$	−5.28444	−	1.41596i	−0.268623	−	0.0719774i
$388$	0.986157	+	3.68039i	0.0500645	+	0.186843i
$389$	−10.9881	−	6.34400i	−0.557120	−	0.321653i	0.194869	−	0.980829i	$-0.437572\pi$
$389$	−10.9881	−	6.34400i	−0.557120	−	0.321653i	−0.751989	+	0.659176i	$0.770905\pi$
$390$		0			0
$391$		−	28.0546i		−	1.41878i
$392$	0.396606	+	6.98876i	0.0200316	+	0.352985i
$393$	6.20372	+	6.20372i	0.312936	+	0.312936i
$394$	−1.50069	+	0.866423i	−0.0756036	+	0.0436498i
$395$		0			0
$396$	−1.55390	+	2.69144i	−0.0780865	+	0.135250i
$397$	−5.63565	+	21.0326i	−0.282845	+	1.05559i	0.667554	+	0.744561i	$0.267341\pi$
$397$	−5.63565	+	21.0326i	−0.282845	+	1.05559i	−0.950399	+	0.311032i	$0.899325\pi$
$398$	5.57060	−	5.57060i	0.279229	−	0.279229i
$399$	−7.82192	−	17.4665i	−0.391586	−	0.874418i
$400$		0			0
$401$	−13.1539	−	22.7832i	−0.656872	−	1.13774i	−0.981421	−	0.191867i	$-0.938546\pi$
$401$	−13.1539	−	22.7832i	−0.656872	−	1.13774i	0.324549	−	0.945869i	$-0.394788\pi$
$402$	6.43584	−	1.72448i	0.320990	−	0.0860091i
$403$	42.9479	−	11.5078i	2.13939	−	0.573247i
$404$	−3.93122	−	6.80907i	−0.195585	−	0.338764i
$405$		0			0
$406$	−9.63343	−	6.96730i	−0.478099	−	0.345781i
$407$	−7.89630	+	7.89630i	−0.391405	+	0.391405i
$408$	1.37891	−	5.14616i	0.0682661	−	0.254773i
$409$	1.17325	−	2.03214i	0.0580137	−	0.100483i	−0.835560	−	0.549399i	$-0.814857\pi$
$409$	1.17325	−	2.03214i	0.0580137	−	0.100483i	0.893574	+	0.448917i	$0.148190\pi$
$410$		0			0
$411$	−11.7824	+	6.80258i	−0.581184	+	0.335547i
$412$	−8.36587	−	8.36587i	−0.412157	−	0.412157i
$413$	−2.22436	−	2.73474i	−0.109454	−	0.134568i
$414$		−	5.26581i		−	0.258800i
$415$		0			0
$416$	4.17408	+	2.40991i	0.204651	+	0.118155i
$417$	2.82487	+	10.5426i	0.138335	+	0.516271i
$418$	21.7142	+	5.81830i	1.06208	+	0.284582i
$419$	1.03087			0.0503614			0.0251807	−	0.999683i	$-0.491984\pi$
$419$	1.03087			0.0503614			0.0251807	+	0.999683i	$0.491984\pi$
$420$		0			0
$421$	28.6945			1.39849			0.699243	−	0.714884i	$-0.253521\pi$
$421$	28.6945			1.39849			0.699243	+	0.714884i	$0.253521\pi$
$422$	15.4543	+	4.14097i	0.752304	+	0.201579i
$423$	1.05713	+	3.94526i	0.0513994	+	0.191825i
$424$	−2.97862	−	1.71971i	−0.144655	−	0.0835164i
$425$		0			0
$426$		−	9.22738i		−	0.447068i
$427$	−5.26683	−	32.7939i	−0.254880	−	1.58701i
$428$	−1.52895	−	1.52895i	−0.0739047	−	0.0739047i
$429$	−12.9722	+	7.48952i	−0.626305	+	0.361597i
$430$		0			0
$431$	12.1388	−	21.0250i	0.584704	−	1.01274i	−0.410208	−	0.911992i	$-0.634544\pi$
$431$	12.1388	−	21.0250i	0.584704	−	1.01274i	0.994912	−	0.100745i	$-0.0321227\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	19.1704	−	19.1704i	0.921271	−	0.921271i	−0.0758481	−	0.997119i	$-0.524166\pi$
$433$	19.1704	−	19.1704i	0.921271	−	0.921271i	0.997119	+	0.0758481i	$0.0241664\pi$
$434$	22.2755	−	9.97551i	1.06926	−	0.478840i
$435$		0			0
$436$	0.282776	+	0.489782i	0.0135425	+	0.0234563i
$437$	−36.7922	+	9.85843i	−1.76001	+	0.471593i
$438$	−7.95163	+	2.13063i	−0.379943	+	0.101806i
$439$	7.29947	+	12.6431i	0.348385	+	0.603420i	0.985963	−	0.166966i	$-0.0533969\pi$
$439$	7.29947	+	12.6431i	0.348385	+	0.603420i	−0.637578	+	0.770386i	$0.720064\pi$
$440$		0			0
$441$	6.85327	+	1.42573i	0.326346	+	0.0678920i
$442$	18.1574	−	18.1574i	0.863660	−	0.863660i
$443$	5.88534	−	21.9644i	0.279621	−	1.04356i	−0.673060	−	0.739587i	$-0.735021\pi$
$443$	5.88534	−	21.9644i	0.279621	−	1.04356i	0.952681	−	0.303971i	$-0.0983127\pi$
$444$	1.79662	−	3.11183i	0.0852636	−	0.147681i
$445$		0			0
$446$	1.47835	−	0.853528i	0.0700021	−	0.0404157i
$447$	1.47800	+	1.47800i	0.0699071	+	0.0699071i
$448$	2.47207	+	0.942805i	0.116794	+	0.0445433i
$449$		−	41.8564i		−	1.97532i	−0.156600	−	0.987662i	$-0.550053\pi$
$449$		−	41.8564i		−	1.97532i	0.156600	−	0.987662i	$-0.449947\pi$
$450$		0			0
$451$	−6.77842	−	3.91352i	−0.319183	−	0.184281i
$452$	−3.65378	−	13.6361i	−0.171859	−	0.641388i
$453$	−3.90462	−	1.04624i	−0.183455	−	0.0491566i
$454$	6.81296			0.319748
$455$		0			0
$456$	−7.23346			−0.338738
$457$	25.6536	+	6.87387i	1.20003	+	0.321546i	0.802841	−	0.596193i	$-0.203321\pi$
$457$	25.6536	+	6.87387i	1.20003	+	0.321546i	0.397185	+	0.917739i	$0.369987\pi$
$458$	5.12831	+	19.1391i	0.239630	+	0.894313i
$459$	−4.61392	−	2.66385i	−0.215359	−	0.124338i
$460$		0			0
$461$			16.5608i			0.771313i	0.922642	+	0.385656i	$0.126025\pi$
$461$			16.5608i			0.771313i	−0.922642	+	0.385656i	$0.873975\pi$
$462$	−6.37885	+	5.18839i	−0.296771	+	0.241386i
$463$	19.0305	+	19.0305i	0.884424	+	0.884424i	0.993981	−	0.109557i	$-0.0349431\pi$
$463$	19.0305	+	19.0305i	0.884424	+	0.884424i	−0.109557	+	0.993981i	$0.534943\pi$
$464$	−3.89156	+	2.24679i	−0.180661	+	0.104305i
$465$		0			0
$466$	8.99871	−	15.5862i	0.416857	−	0.722018i
$467$	3.52162	−	13.1429i	0.162961	−	0.608179i	−0.835330	−	0.549748i	$-0.814724\pi$
$467$	3.52162	−	13.1429i	0.162961	−	0.608179i	0.998291	−	0.0584309i	$-0.0186097\pi$
$468$	3.40812	−	3.40812i	0.157540	−	0.157540i
$469$	17.5357	+	1.80471i	0.809722	+	0.0833339i
$470$		0			0
$471$	−0.452786	−	0.784249i	−0.0208633	−	0.0361363i
$472$	−1.28698	+	0.344844i	−0.0592379	+	0.0158727i
$473$	16.4230	−	4.40054i	0.755131	−	0.202337i
$474$	−0.957181	−	1.65789i	−0.0439648	−	0.0761493i
$475$		0			0
$476$	8.26057	−	11.4216i	0.378623	−	0.523508i
$477$	−2.43203	+	2.43203i	−0.111355	+	0.111355i
$478$	6.89516	−	25.7331i	0.315377	−	1.17700i
$479$	0.662643	−	1.14773i	0.0302769	−	0.0524412i	−0.850490	−	0.525991i	$-0.823694\pi$
$479$	0.662643	−	1.14773i	0.0302769	−	0.0524412i	0.880767	+	0.473550i	$0.157028\pi$
$480$		0			0
$481$	14.9984	−	8.65935i	0.683869	−	0.394832i
$482$	10.1999	+	10.1999i	0.464592	+	0.464592i
$483$	4.96463	−	13.0174i	0.225899	−	0.592314i
$484$			1.34155i			0.0609795i
$485$		0			0
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−8.29304	−	30.9501i	−0.375794	−	1.40248i	−0.852182	−	0.523246i	$-0.824721\pi$
$487$	−8.29304	−	30.9501i	−0.375794	−	1.40248i	0.476388	−	0.879235i	$-0.341946\pi$
$488$	−12.1260	−	3.24916i	−0.548919	−	0.147082i
$489$	7.38217			0.333833
$490$		0			0
$491$	−22.3460			−1.00846			−0.504231	−	0.863569i	$-0.668224\pi$
$491$	−22.3460			−1.00846			−0.504231	+	0.863569i	$0.668224\pi$
$492$	2.43270	+	0.651839i	0.109674	+	0.0293872i
$493$	6.19624	+	23.1247i	0.279065	+	1.04148i
$494$	−30.1930	−	17.4320i	−1.35845	−	0.784301i
$495$		0			0
$496$		−	9.22503i		−	0.414216i
$497$	8.69961	−	22.8107i	0.390231	−	1.02320i
$498$	−8.97250	−	8.97250i	−0.402067	−	0.402067i
$499$	9.39838	−	5.42616i	0.420729	−	0.242908i	−0.274660	−	0.961541i	$-0.588565\pi$
$499$	9.39838	−	5.42616i	0.420729	−	0.242908i	0.695389	+	0.718633i	$0.255232\pi$
$500$		0			0
$501$	0.431792	−	0.747886i	0.0192910	−	0.0334131i
$502$	6.84766	−	25.5558i	0.305626	−	1.14061i
$503$	2.64043	−	2.64043i	0.117731	−	0.117731i	−0.645787	−	0.763518i	$-0.723471\pi$
$503$	2.64043	−	2.64043i	0.117731	−	0.117731i	0.763518	+	0.645787i	$0.223471\pi$
$504$	1.55050	−	2.14382i	0.0690647	−	0.0954933i
$505$		0			0
$506$	8.18256	+	14.1726i	0.363759	+	0.630049i
$507$	9.88197	−	2.64787i	0.438874	−	0.117596i
$508$	2.93059	−	0.785250i	0.130024	−	0.0348398i
$509$	−8.70464	−	15.0769i	−0.385827	−	0.668271i	0.606057	−	0.795421i	$-0.292750\pi$
$509$	−8.70464	−	15.0769i	−0.385827	−	0.668271i	−0.991883	+	0.127150i	$0.959417\pi$
$510$		0			0
$511$	−21.6657	−	2.22976i	−0.958435	−	0.0986389i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.87216	+	6.98699i	−0.0826578	+	0.308483i
$514$	−5.60751	+	9.71249i	−0.247337	+	0.428399i
$515$		0			0
$516$	−4.73790	+	2.73543i	−0.208575	+	0.120421i
$517$	−8.97575	−	8.97575i	−0.394753	−	0.394753i
$518$	7.37520	−	5.99880i	0.324048	−	0.263572i
$519$			3.49748i			0.153522i
$520$		0			0
$521$	6.14512	+	3.54789i	0.269223	+	0.155436i	0.628534	−	0.777782i	$-0.283655\pi$
$521$	6.14512	+	3.54789i	0.269223	+	0.155436i	−0.359312	+	0.933218i	$0.616989\pi$
$522$	1.16303	+	4.34047i	0.0509043	+	0.189977i
$523$	−3.40450	−	0.912232i	−0.148868	−	0.0398891i	0.183615	−	0.982998i	$-0.441220\pi$
$523$	−3.40450	−	0.912232i	−0.148868	−	0.0398891i	−0.332484	+	0.943109i	$0.607887\pi$
$524$	8.77339			0.383267
$525$		0			0
$526$	6.85911			0.299071
$527$	−47.4734	−	12.7205i	−2.06798	−	0.554112i
$528$	0.804359	+	3.00191i	0.0350052	+	0.130641i
$529$	−4.09523	−	2.36438i	−0.178053	−	0.102799i
$530$		0			0
$531$			1.33238i			0.0578202i
$532$	−17.8816	−	6.81974i	−0.775266	−	0.295673i
$533$	8.58340	+	8.58340i	0.371788	+	0.371788i
$534$	3.52779	−	2.03677i	0.152662	−	0.0881397i
$535$		0			0
$536$	3.33144	−	5.77022i	0.143896	−	0.249235i
$537$	−4.67474	+	17.4464i	−0.201730	+	0.752867i
$538$	6.35027	−	6.35027i	0.273780	−	0.273780i
$539$	−20.6606	+	6.81204i	−0.889915	+	0.293415i
$540$		0			0
$541$	−10.1975	−	17.6627i	−0.438426	−	0.759377i	0.559142	−	0.829072i	$-0.311131\pi$
$541$	−10.1975	−	17.6627i	−0.438426	−	0.759377i	−0.997568	+	0.0696952i	$0.977797\pi$
$542$	−8.66609	+	2.32207i	−0.372240	+	0.0997415i
$543$	−20.9854	+	5.62302i	−0.900570	+	0.241307i
$544$	−2.66385	−	4.61392i	−0.114211	−	0.197820i
$545$		0			0
$546$	11.6383	−	5.21191i	0.498073	−	0.223049i
$547$	8.79499	−	8.79499i	0.376047	−	0.376047i	−0.493627	−	0.869674i	$-0.664329\pi$
$547$	8.79499	−	8.79499i	0.376047	−	0.376047i	0.869674	+	0.493627i	$0.164329\pi$
$548$	−3.52127	+	13.1416i	−0.150421	+	0.561380i
$549$	−6.27689	+	10.8719i	−0.267891	+	0.464001i
$550$		0			0
$551$	28.1495	−	16.2521i	1.19921	−	0.692363i
$552$	−3.72349	−	3.72349i	−0.158482	−	0.158482i
$553$	−0.803154	−	5.00084i	−0.0341536	−	0.212658i
$554$		−	24.7111i		−	1.04988i
$555$		0			0
$556$	9.45220	+	5.45723i	0.400863	+	0.231438i
$557$	4.64933	+	17.3515i	0.196999	+	0.735208i	0.991740	+	0.128261i	$0.0409395\pi$
$557$	4.64933	+	17.3515i	0.196999	+	0.735208i	−0.794742	+	0.606947i	$0.792394\pi$
$558$	−8.91070	−	2.38761i	−0.377220	−	0.101076i
$559$	−26.3685			−1.11527
$560$		0			0
$561$	16.5574			0.699055
$562$	−17.8615	−	4.78598i	−0.753442	−	0.201884i
$563$	11.2652	+	42.0423i	0.474771	+	1.77187i	0.622264	+	0.782807i	$0.286213\pi$
$563$	11.2652	+	42.0423i	0.474771	+	1.77187i	−0.147493	+	0.989063i	$0.547120\pi$
$564$	3.53723	+	2.04222i	0.148944	+	0.0859929i
$565$		0			0
$566$			5.57176i			0.234198i
$567$	−1.66947	−	2.05253i	−0.0701112	−	0.0861980i
$568$	−6.52474	−	6.52474i	−0.273772	−	0.273772i
$569$	15.7466	−	9.09131i	0.660132	−	0.381128i	−0.132195	−	0.991224i	$-0.542203\pi$
$569$	15.7466	−	9.09131i	0.660132	−	0.381128i	0.792327	+	0.610096i	$0.208869\pi$
$570$		0			0
$571$	13.6567	−	23.6541i	0.571516	−	0.989894i	−0.424895	−	0.905243i	$-0.639689\pi$
$571$	13.6567	−	23.6541i	0.571516	−	0.989894i	0.996411	−	0.0846515i	$-0.0269777\pi$
$572$	−3.87686	+	14.4686i	−0.162100	+	0.604964i
$573$	11.7256	−	11.7256i	0.489843	−	0.489843i
$574$	5.39923	+	3.90495i	0.225360	+	0.162989i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−23.9084	+	6.40624i	−0.995320	+	0.266695i	−0.719484	−	0.694509i	$-0.755621\pi$
$577$	−23.9084	+	6.40624i	−0.995320	+	0.266695i	−0.275836	+	0.961205i	$0.588955\pi$
$578$	−10.9964	+	2.94647i	−0.457390	+	0.122557i
$579$	−1.05874	−	1.83379i	−0.0439997	−	0.0762098i
$580$		0			0
$581$	−13.7213	−	30.6400i	−0.569256	−	1.27116i
$582$	2.69423	−	2.69423i	0.111679	−	0.111679i
$583$	2.76653	−	10.3248i	0.114578	−	0.427610i
$584$	−4.11606	+	7.12923i	−0.170324	+	0.295010i
$585$		0			0
$586$	21.6124	−	12.4779i	0.892801	−	0.515459i
$587$	25.7187	+	25.7187i	1.06153	+	1.06153i	0.997979	+	0.0635463i	$0.0202411\pi$
$587$	25.7187	+	25.7187i	1.06153	+	1.06153i	0.0635463	+	0.997979i	$0.479759\pi$
$588$	5.85414	−	3.83785i	0.241421	−	0.158270i
$589$			66.7289i			2.74952i
$590$		0			0
$591$	1.50069	+	0.866423i	0.0617301	+	0.0356399i
$592$	−0.929997	−	3.47079i	−0.0382226	−	0.142649i
$593$	−26.7446	−	7.16619i	−1.09827	−	0.294280i	−0.336209	−	0.941787i	$-0.609145\pi$
$593$	−26.7446	−	7.16619i	−1.09827	−	0.294280i	−0.762059	+	0.647507i	$0.775812\pi$
$594$	3.10780			0.127515
$595$		0			0
$596$	2.09021			0.0856183
$597$	−7.60958	−	2.03898i	−0.311439	−	0.0834499i
$598$	−6.56888	−	24.5154i	−0.268622	−	1.00251i
$599$	19.0168	+	10.9793i	0.777004	+	0.448603i	0.835367	−	0.549692i	$-0.185255\pi$
$599$	19.0168	+	10.9793i	0.777004	+	0.448603i	−0.0583635	+	0.998295i	$0.518588\pi$
$600$		0			0
$601$		−	7.04092i		−	0.287205i	−0.989635	−	0.143603i	$-0.954131\pi$
$601$		−	7.04092i		−	0.287205i	0.989635	−	0.143603i	$-0.0458687\pi$
$602$	−14.2914	+	2.29525i	−0.582474	+	0.0935475i
$603$	−4.71136	−	4.71136i	−0.191861	−	0.191861i
$604$	−3.50079	+	2.02118i	−0.142445	+	0.0822407i
$605$		0			0
$606$	−3.93122	+	6.80907i	−0.159695	+	0.276600i
$607$	−6.10130	+	22.7704i	−0.247644	+	0.924221i	0.724392	+	0.689388i	$0.242121\pi$
$607$	−6.10130	+	22.7704i	−0.247644	+	0.924221i	−0.972036	+	0.234832i	$0.924546\pi$
$608$	−5.11483	+	5.11483i	−0.207434	+	0.207434i
$609$	−1.21714	+	11.8264i	−0.0493209	+	0.479232i
$610$		0			0
$611$	9.84311	+	17.0488i	0.398209	+	0.689719i
$612$	−5.14616	+	1.37891i	−0.208021	+	0.0557391i
$613$	−13.4583	+	3.60613i	−0.543574	+	0.145650i	−0.520149	−	0.854075i	$-0.674124\pi$
$613$	−13.4583	+	3.60613i	−0.543574	+	0.145650i	−0.0234247	+	0.999726i	$0.507457\pi$
$614$	8.11809	+	14.0609i	0.327620	+	0.567454i
$615$		0			0
$616$	−0.841783	+	8.17928i	−0.0339164	+	0.329552i
$617$	−9.68360	+	9.68360i	−0.389847	+	0.389847i	−0.874633	−	0.484786i	$-0.838898\pi$
$617$	−9.68360	+	9.68360i	−0.389847	+	0.389847i	0.484786	+	0.874633i	$0.338898\pi$
$618$	−3.06212	+	11.4280i	−0.123177	+	0.459701i
$619$	6.20950	−	10.7552i	0.249581	−	0.432287i	−0.713829	−	0.700320i	$-0.753040\pi$
$619$	6.20950	−	10.7552i	0.249581	−	0.432287i	0.963410	+	0.268033i	$0.0863738\pi$
$620$		0			0
$621$	−4.56033	+	2.63291i	−0.183000	+	0.105655i
$622$	9.28775	+	9.28775i	0.372405	+	0.372405i
$623$	10.6412	−	1.70902i	0.426331	−	0.0684704i
$624$		−	4.81981i		−	0.192947i
$625$		0			0
$626$	−22.0388	−	12.7241i	−0.880847	−	0.508557i
$627$	−5.81830	−	21.7142i	−0.232361	−	0.867181i
$628$	−0.874716	−	0.234379i	−0.0349050	−	0.00935276i
$629$	−19.1436			−0.763306
$630$		0			0
$631$	−0.546516			−0.0217565			−0.0108782	−	0.999941i	$-0.503463\pi$
$631$	−0.546516			−0.0217565			−0.0108782	+	0.999941i	$0.503463\pi$
$632$	−1.84913	−	0.495474i	−0.0735545	−	0.0197089i
$633$	−4.14097	−	15.4543i	−0.164589	−	0.614253i
$634$	−16.4772	−	9.51309i	−0.654391	−	0.377813i
$635$		0			0
$636$			3.43942i			0.136382i
$637$	33.6845	−	1.91156i	1.33463	−	0.0757389i
$638$	−9.87488	−	9.87488i	−0.390950	−	0.390950i
$639$	−7.99114	+	4.61369i	−0.316125	+	0.182515i
$640$		0			0
$641$	−4.37559	+	7.57874i	−0.172825	+	0.299342i	−0.939407	−	0.342805i	$-0.888623\pi$
$641$	−4.37559	+	7.57874i	−0.172825	+	0.299342i	0.766581	+	0.642147i	$0.221956\pi$
$642$	−0.559635	+	2.08859i	−0.0220870	+	0.0824300i
$643$	10.2080	−	10.2080i	0.402565	−	0.402565i	−0.476571	−	0.879136i	$-0.658121\pi$
$643$	10.2080	−	10.2080i	0.402565	−	0.402565i	0.879136	+	0.476571i	$0.158121\pi$
$644$	−5.69420	−	12.7152i	−0.224383	−	0.501051i
$645$		0			0
$646$	19.2688	+	33.3746i	0.758122	+	1.31311i
$647$	23.1835	−	6.21201i	0.911438	−	0.244219i	0.227516	−	0.973774i	$-0.426940\pi$
$647$	23.1835	−	6.21201i	0.911438	−	0.244219i	0.683922	+	0.729555i	$0.260273\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−2.07038	−	3.58601i	−0.0812696	−	0.140763i
$650$		0			0
$651$	−19.7768	−	14.3034i	−0.775114	−	0.560594i
$652$	5.21998	−	5.21998i	0.204430	−	0.204430i
$653$	9.71382	−	36.2525i	0.380131	−	1.41867i	−0.465570	−	0.885011i	$-0.654151\pi$
$653$	9.71382	−	36.2525i	0.380131	−	1.41867i	0.845701	−	0.533657i	$-0.179183\pi$
$654$	0.282776	−	0.489782i	0.0110574	−	0.0191520i
$655$		0			0
$656$	2.18110	−	1.25926i	0.0851575	−	0.0491657i
$657$	5.82099	+	5.82099i	0.227099	+	0.227099i
$658$	6.81885	+	8.38342i	0.265826	+	0.326820i
$659$		−	30.4591i		−	1.18652i	−0.805011	−	0.593259i	$-0.797841\pi$
$659$		−	30.4591i		−	1.18652i	0.805011	−	0.593259i	$-0.202159\pi$
$660$		0			0
$661$	−23.8795	−	13.7868i	−0.928805	−	0.536246i	−0.0423719	−	0.999102i	$-0.513491\pi$
$661$	−23.8795	−	13.7868i	−0.928805	−	0.536246i	−0.886434	+	0.462856i	$0.846825\pi$
$662$	−5.41917	−	20.2246i	−0.210622	−	0.786052i
$663$	−24.8035	−	6.64608i	−0.963288	−	0.258112i
$664$	−12.6890			−0.492430
$665$		0			0
$666$	−3.59323			−0.139235
$667$	22.8561	+	6.12427i	0.884992	+	0.237133i
$668$	−0.223512	−	0.834158i	−0.00864794	−	0.0322746i
$669$	−1.47835	−	0.853528i	−0.0571565	−	0.0329993i
$670$		0			0
$671$		−	39.0147i		−	1.50615i
$672$	−0.419541	−	2.61228i	−0.0161842	−	0.100771i
$673$	8.77420	+	8.77420i	0.338221	+	0.338221i	0.855697	−	0.517477i	$-0.173129\pi$
$673$	8.77420	+	8.77420i	0.338221	+	0.338221i	−0.517477	+	0.855697i	$0.673129\pi$
$674$	0.334073	−	0.192877i	0.0128680	−	0.00742935i
$675$		0			0
$676$	5.11529	−	8.85994i	0.196742	−	0.340767i
$677$	−7.68002	+	28.6622i	−0.295167	+	1.10158i	0.645917	+	0.763407i	$0.276475\pi$
$677$	−7.68002	+	28.6622i	−0.295167	+	1.10158i	−0.941085	+	0.338171i	$0.890192\pi$
$678$	−9.98231	+	9.98231i	−0.383368	+	0.383368i
$679$	9.20045	−	4.12019i	0.353081	−	0.158118i
$680$		0			0
$681$	−3.40648	−	5.90020i	−0.130537	−	0.226096i
$682$	27.6927	−	7.42024i	1.06041	−	0.284136i
$683$	40.3297	−	10.8063i	1.54317	−	0.413492i	0.615882	−	0.787838i	$-0.288800\pi$
$683$	40.3297	−	10.8063i	1.54317	−	0.413492i	0.927289	+	0.374346i	$0.122133\pi$
$684$	3.61673	+	6.26436i	0.138289	+	0.239524i
$685$		0			0
$686$	18.0902	−	3.96811i	0.690686	−	0.151503i
$687$	14.0108	−	14.0108i	0.534546	−	0.534546i
$688$	−1.41596	+	5.28444i	−0.0539831	+	0.201468i
$689$	−8.28867	+	14.3564i	−0.315773	+	0.546935i
$690$		0			0
$691$	39.0636	−	22.5534i	1.48605	−	0.857972i	0.486177	−	0.873860i	$-0.338391\pi$
$691$	39.0636	−	22.5534i	1.48605	−	0.857972i	0.999874	+	0.0158887i	$0.00505775\pi$
$692$	2.47309	+	2.47309i	0.0940129	+	0.0940129i
$693$	7.68270	+	2.93005i	0.291842	+	0.111304i
$694$		−	15.1270i		−	0.574214i
$695$		0			0
$696$	3.89156	+	2.24679i	0.147509	+	0.0851645i
$697$	−3.47280	−	12.9607i	−0.131542	−	0.490920i
$698$	14.7529	+	3.95303i	0.558406	+	0.149624i
$699$	−17.9974			−0.680725
$700$		0			0
$701$	−2.29359			−0.0866278			−0.0433139	−	0.999062i	$-0.513792\pi$
$701$	−2.29359			−0.0866278			−0.0433139	+	0.999062i	$0.513792\pi$
$702$	−4.65558	−	1.24746i	−0.175714	−	0.0470823i
$703$	6.72709	+	25.1059i	0.253717	+	0.946885i
$704$	2.69144	+	1.55390i	0.101437	+	0.0585649i
$705$		0			0
$706$			30.0267i			1.13007i
$707$	−16.1379	+	13.1261i	−0.606927	+	0.493658i
$708$	0.942132	+	0.942132i	0.0354075	+	0.0354075i
$709$	41.7942	−	24.1299i	1.56961	−	0.906217i	0.573401	−	0.819275i	$-0.305624\pi$
$709$	41.7942	−	24.1299i	1.56961	−	0.906217i	0.996213	−	0.0869427i	$-0.0277097\pi$
$710$		0			0
$711$	−0.957181	+	1.65789i	−0.0358971	+	0.0621756i
$712$	1.05431	−	3.93474i	0.0395119	−	0.147461i
$713$	−34.3493	+	34.3493i	−1.28639	+	1.28639i
$714$	−14.0217	−	1.44306i	−0.524748	−	0.0540053i
$715$		0			0
$716$	9.03091	+	15.6420i	0.337501	+	0.584569i
$717$	−25.7331	+	6.89516i	−0.961020	+	0.257505i
$718$	11.3249	−	3.03451i	0.422643	−	0.113247i
$719$	12.5235	+	21.6914i	0.467048	+	0.808951i	0.999291	−	0.0376405i	$-0.0119842\pi$
$719$	12.5235	+	21.6914i	0.467048	+	0.808951i	−0.532243	+	0.846591i	$0.678651\pi$
$720$		0			0
$721$	−18.3441	+	25.3638i	−0.683171	+	0.944596i
$722$	23.5629	−	23.5629i	0.876920	−	0.876920i
$723$	3.73342	−	13.9333i	0.138847	−	0.518185i
$724$	−10.8628	+	18.8150i	−0.403714	+	0.699254i
$725$		0			0
$726$	1.16181	−	0.670774i	0.0431190	−	0.0248948i
$727$	−17.1495	−	17.1495i	−0.636039	−	0.636039i	0.313537	−	0.949576i	$-0.398486\pi$
$727$	−17.1495	−	17.1495i	−0.636039	−	0.636039i	−0.949576	+	0.313537i	$0.898486\pi$
$728$	4.54414	−	11.9149i	0.168417	−	0.441596i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	25.2421	+	14.5735i	0.933612	+	0.539021i
$732$	3.24916	+	12.1260i	0.120092	+	0.448190i
$733$	7.18102	+	1.92415i	0.265237	+	0.0710700i	0.388986	−	0.921243i	$-0.372825\pi$
$733$	7.18102	+	1.92415i	0.265237	+	0.0710700i	−0.123750	+	0.992313i	$0.539492\pi$
$734$	30.3987			1.12204
$735$		0			0
$736$	−5.26581			−0.194100
$737$	20.0013	+	5.35934i	0.736759	+	0.197414i
$738$	−0.651839	−	2.43270i	−0.0239945	−	0.0895488i
$739$	7.23527	+	4.17729i	0.266154	+	0.153664i	0.627139	−	0.778908i	$-0.284226\pi$
$739$	7.23527	+	4.17729i	0.266154	+	0.153664i	−0.360985	+	0.932572i	$0.617559\pi$
$740$		0			0
$741$			34.8639i			1.28076i
$742$	−3.24270	+	8.50247i	−0.119043	+	0.312136i
$743$	20.5565	+	20.5565i	0.754146	+	0.754146i	0.975250	−	0.221104i	$-0.0709661\pi$
$743$	20.5565	+	20.5565i	0.754146	+	0.754146i	−0.221104	+	0.975250i	$0.570966\pi$
$744$	−7.98911	+	4.61252i	−0.292895	+	0.169103i
$745$		0			0
$746$	15.0828	−	26.1241i	0.552220	−	0.956473i
$747$	−3.28416	+	12.2567i	−0.120161	+	0.448448i
$748$	11.7079	−	11.7079i	0.428082	−	0.428082i
$749$	−3.35259	+	4.63550i	−0.122501	+	0.169378i
$750$		0			0
$751$	17.3148	+	29.9902i	0.631828	+	1.09436i	0.987178	+	0.159625i	$0.0510283\pi$
$751$	17.3148	+	29.9902i	0.631828	+	1.09436i	−0.355350	+	0.934733i	$0.615638\pi$
$752$	3.94526	−	1.05713i	0.143869	−	0.0385496i
$753$	−25.5558	+	6.84766i	−0.931306	+	0.249543i
$754$	10.8291	+	18.7566i	0.394373	+	0.683075i
$755$		0			0
$756$	−2.63185	−	0.270861i	−0.0957195	−	0.00985112i
$757$	24.7332	−	24.7332i	0.898945	−	0.898945i	−0.0963983	−	0.995343i	$-0.530732\pi$
$757$	24.7332	−	24.7332i	0.898945	−	0.898945i	0.995343	+	0.0963983i	$0.0307323\pi$
$758$	1.14946	−	4.28983i	0.0417501	−	0.155813i
$759$	8.18256	−	14.1726i	0.297008	−	0.514433i
$760$		0			0
$761$	−32.5612	+	18.7992i	−1.18034	+	0.681471i	−0.956094	−	0.293061i	$-0.905326\pi$
$761$	−32.5612	+	18.7992i	−1.18034	+	0.681471i	−0.224248	+	0.974532i	$0.571993\pi$
$762$	−2.14534	−	2.14534i	−0.0777176	−	0.0777176i
$763$	1.16081	−	0.944172i	0.0420241	−	0.0341813i
$764$		−	16.5825i		−	0.599932i
$765$		0			0
$766$	−19.2793	−	11.1309i	−0.696588	−	0.402175i
$767$	1.66208	+	6.20298i	0.0600144	+	0.223977i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−23.9494			−0.863638			−0.431819	−	0.901960i	$-0.642128\pi$
$769$	−23.9494			−0.863638			−0.431819	+	0.901960i	$0.642128\pi$
$770$		0			0
$771$	11.2150			0.403899
$772$	−2.04533	−	0.548044i	−0.0736130	−	0.0197245i
$773$	0.00969506	+	0.0361824i	0.000348707	+	0.00130139i	0.966100	−	0.258168i	$-0.0831189\pi$
$773$	0.00969506	+	0.0361824i	0.000348707	+	0.00130139i	−0.965751	+	0.259470i	$0.916452\pi$
$774$	4.73790	+	2.73543i	0.170300	+	0.0983230i
$775$		0			0
$776$		−	3.81022i		−	0.136779i
$777$	−8.88271	−	3.38771i	−0.318665	−	0.121534i
$778$	8.97176	+	8.97176i	0.321653	+	0.321653i
$779$	−15.7769	+	9.10878i	−0.565265	+	0.326356i
$780$		0			0
$781$	14.3384	−	24.8349i	0.513070	−	0.888663i
$782$	−7.26107	+	27.0987i	−0.259655	+	0.969047i
$783$	3.17745	−	3.17745i	0.113553	−	0.113553i
$784$	1.42573	−	6.85327i	0.0509190	−	0.244760i
$785$		0			0
$786$	−4.38669	−	7.59798i	−0.156468	−	0.271011i
$787$	25.2135	−	6.75595i	0.898766	−	0.240824i	0.220280	−	0.975437i	$-0.429303\pi$
$787$	25.2135	−	6.75595i	0.898766	−	0.240824i	0.678486	+	0.734613i	$0.262636\pi$
$788$	1.67380	−	0.448494i	0.0596267	−	0.0159769i
$789$	−3.42955	−	5.94016i	−0.122095	−	0.211475i
$790$		0			0
$791$	−34.0883	+	15.2656i	−1.21204	+	0.542782i
$792$	2.19755	−	2.19755i	0.0780865	−	0.0780865i
$793$	−15.6603	+	58.4451i	−0.556114	+	2.07545i
$794$	10.8872	−	18.8573i	0.386374	−	0.669219i
$795$		0			0
$796$	−6.82256	+	3.93901i	−0.241819	+	0.139614i
$797$	−0.973551	−	0.973551i	−0.0344850	−	0.0344850i	0.689654	−	0.724139i	$-0.257763\pi$
$797$	−0.973551	−	0.973551i	−0.0344850	−	0.0344850i	−0.724139	+	0.689654i	$0.757763\pi$
$798$	3.03474	+	18.8958i	0.107428	+	0.668904i
$799$		−	21.7606i		−	0.769835i
$800$		0			0
$801$	−3.52779	−	2.03677i	−0.124648	−	0.0719657i
$802$	6.80894	+	25.4113i	0.240432	+	0.897304i
$803$	−24.7121	−	6.62159i	−0.872071	−	0.233671i
$804$	−6.66287			−0.234981
$805$		0			0
$806$	−44.4629			−1.56614
$807$	−8.67463	−	2.32436i	−0.305361	−	0.0818214i
$808$	2.03495	+	7.59453i	0.0715893	+	0.267175i
$809$	34.7908	+	20.0865i	1.22318	+	0.706203i	0.965595	−	0.260052i	$-0.0837398\pi$
$809$	34.7908	+	20.0865i	1.22318	+	0.706203i	0.257585	+	0.966256i	$0.417073\pi$
$810$		0			0
$811$			24.5727i			0.862866i	0.902145	+	0.431433i	$0.141992\pi$
$811$			24.5727i			0.862866i	−0.902145	+	0.431433i	$0.858008\pi$
$812$	7.50191	+	9.22321i	0.263266	+	0.323671i
$813$	6.34402	+	6.34402i	0.222494	+	0.222494i
$814$	9.67096	−	5.58353i	0.338967	−	0.195703i
$815$		0			0
$816$	−2.66385	+	4.61392i	−0.0932533	+	0.161519i
$817$	10.2423	−	38.2248i	0.358333	−	1.33732i
$818$	−1.65923	+	1.65923i	−0.0580137	+	0.0580137i
$819$	−10.3328	−	7.47310i	−0.361057	−	0.261131i
$820$		0			0
$821$	24.5409	+	42.5060i	0.856482	+	1.48347i	0.875263	+	0.483647i	$0.160688\pi$
$821$	24.5409	+	42.5060i	0.856482	+	1.48347i	−0.0187814	+	0.999824i	$0.505979\pi$
$822$	13.1416	−	3.52127i	0.458365	−	0.122819i
$823$	28.2946	−	7.58153i	0.986289	−	0.264275i	0.270598	−	0.962692i	$-0.412779\pi$
$823$	28.2946	−	7.58153i	0.986289	−	0.264275i	0.715691	+	0.698417i	$0.246112\pi$
$824$	5.91556	+	10.2461i	0.206078	+	0.356938i
$825$		0			0
$826$	1.44077	+	3.21726i	0.0501307	+	0.111943i
$827$	−14.8882	+	14.8882i	−0.517712	+	0.517712i	−0.916879	−	0.399166i	$-0.869300\pi$
$827$	−14.8882	+	14.8882i	−0.517712	+	0.517712i	0.399166	+	0.916879i	$0.369300\pi$
$828$	−1.36289	+	5.08638i	−0.0473638	+	0.176764i
$829$	−18.3844	+	31.8427i	−0.638516	+	1.10594i	0.347243	+	0.937775i	$0.387118\pi$
$829$	−18.3844	+	31.8427i	−0.638516	+	1.10594i	−0.985759	+	0.168167i	$0.946215\pi$
$830$		0			0
$831$	−21.4005	+	12.3556i	−0.742374	+	0.428610i
$832$	−3.40812	−	3.40812i	−0.118155	−	0.118155i
$833$	−33.3020	−	16.7871i	−1.15385	−	0.581637i
$834$		−	10.9145i		−	0.377937i
$835$		0			0
$836$	−19.4684	−	11.2401i	−0.673329	−	0.388747i
$837$	2.38761	+	8.91070i	0.0825280	+	0.307999i
$838$	−0.995746	−	0.266809i	−0.0343975	−	0.00921678i
$839$	−11.6715			−0.402944			−0.201472	−	0.979494i	$-0.564573\pi$
$839$	−11.6715			−0.402944			−0.201472	+	0.979494i	$0.564573\pi$
$840$		0			0
$841$	8.80767			0.303713
$842$	−27.7168	−	7.42669i	−0.955183	−	0.255941i
$843$	4.78598	+	17.8615i	0.164838	+	0.615183i
$844$	−13.8559	−	7.99974i	−0.476941	−	0.275362i
$845$		0			0
$846$		−	4.08444i		−	0.140426i
$847$	3.50449	−	0.562835i	0.120416	−	0.0193392i
$848$	2.43203	+	2.43203i	0.0835164	+	0.0835164i
$849$	4.82528	−	2.78588i	0.165603	−	0.0956111i
$850$		0			0
$851$	−9.46064	+	16.3863i	−0.324306	+	0.561715i
$852$	−2.38822	+	8.91296i	−0.0818191	+	0.305353i
$853$	19.6499	−	19.6499i	0.672801	−	0.672801i	−0.285560	−	0.958361i	$-0.592179\pi$
$853$	19.6499	−	19.6499i	0.672801	−	0.672801i	0.958361	+	0.285560i	$0.0921795\pi$
$854$	−3.40033	+	33.0397i	−0.116357	+	1.13059i
$855$		0			0
$856$	1.08113	+	1.87258i	0.0369523	+	0.0640033i
$857$	54.1966	−	14.5219i	1.85132	−	0.496059i	0.851710	−	0.524014i	$-0.175566\pi$
$857$	54.1966	−	14.5219i	1.85132	−	0.496059i	0.999609	+	0.0279541i	$0.00889924\pi$
$858$	14.4686	−	3.87686i	0.493951	−	0.132354i
$859$	−9.51449	−	16.4796i	−0.324630	−	0.562276i	0.656807	−	0.754059i	$-0.271907\pi$
$859$	−9.51449	−	16.4796i	−0.324630	−	0.562276i	−0.981437	+	0.191782i	$0.938573\pi$
$860$		0			0
$861$	0.682167	−	6.62835i	0.0232482	−	0.225894i
$862$	−17.1668	+	17.1668i	−0.584704	+	0.584704i
$863$	5.33865	−	19.9241i	0.181730	−	0.678224i	−0.813577	−	0.581457i	$-0.802483\pi$
$863$	5.33865	−	19.9241i	0.181730	−	0.678224i	0.995307	−	0.0967676i	$-0.0308504\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−23.4789	+	13.5555i	−0.797844	+	0.460636i
$867$	8.04992	+	8.04992i	0.273389	+	0.273389i
$868$	−24.0983	+	3.87028i	−0.817951	+	0.131366i
$869$		−	5.94947i		−	0.201822i
$870$		0			0
$871$	−27.8113	−	16.0569i	−0.942351	−	0.544067i
$872$	−0.146375	−	0.546281i	−0.00495690	−	0.0184994i
$873$	−3.68039	−	0.986157i	−0.124562	−	0.0333764i
$874$	38.0900			1.28841
$875$		0			0
$876$	8.23213			0.278138
$877$	−27.4780	−	7.36270i	−0.927866	−	0.248621i	−0.236921	−	0.971529i	$-0.576138\pi$
$877$	−27.4780	−	7.36270i	−0.927866	−	0.248621i	−0.690944	+	0.722908i	$0.742805\pi$
$878$	−3.77848	−	14.1015i	−0.127518	−	0.475902i
$879$	−21.6124	−	12.4779i	−0.728969	−	0.420871i
$880$		0			0
$881$		−	17.6227i		−	0.593724i	−0.954920	−	0.296862i	$-0.904060\pi$
$881$		−	17.6227i		−	0.593724i	0.954920	−	0.296862i	$-0.0959401\pi$
$882$	−6.25074	−	3.15091i	−0.210473	−	0.106097i
$883$	4.03577	+	4.03577i	0.135814	+	0.135814i	0.771746	−	0.635931i	$-0.219384\pi$
$883$	4.03577	+	4.03577i	0.135814	+	0.135814i	−0.635931	+	0.771746i	$0.719384\pi$
$884$	−22.2382	+	12.8392i	−0.747952	+	0.431830i
$885$		0			0
$886$	−11.3696	+	19.6927i	−0.381969	+	0.661590i
$887$	−3.87133	+	14.4480i	−0.129986	+	0.485116i	−0.999968	−	0.00796774i	$-0.997464\pi$
$887$	−3.87133	+	14.4480i	−0.129986	+	0.485116i	0.869982	+	0.493084i	$0.164130\pi$
$888$	−2.54080	+	2.54080i	−0.0852636	+	0.0852636i
$889$	−3.28080	−	7.32608i	−0.110034	−	0.245709i
$890$		0			0
$891$	−1.55390	−	2.69144i	−0.0520577	−	0.0901666i
$892$	−1.64889	+	0.441819i	−0.0552089	+	0.0147932i
$893$	−28.5379	+	7.64671i	−0.954985	+	0.255887i
$894$	−1.04510	−	1.81017i	−0.0349535	−	0.0605413i
$895$		0			0
$896$	−2.14382	−	1.55050i	−0.0716199	−	0.0517985i
$897$	−17.9465	+	17.9465i	−0.599217	+	0.599217i
$898$	−10.8332	+	40.4301i	−0.361509	+	1.34917i
$899$	20.7267	−	35.8998i	0.691276	−	1.19732i
$900$		0			0
$901$	15.8692	−	9.16208i	0.528679	−	0.305233i
$902$	5.53456	+	5.53456i	0.184281	+	0.184281i
$903$	9.13344	+	11.2291i	0.303942	+	0.373681i
$904$			14.1171i			0.469528i
$905$		0			0
$906$	3.50079	+	2.02118i	0.116306	+	0.0671492i
$907$	4.50593	+	16.8164i	0.149617	+	0.558378i	0.999506	+	0.0314169i	$0.0100020\pi$
$907$	4.50593	+	16.8164i	0.149617	+	0.558378i	−0.849889	+	0.526961i	$0.823331\pi$
$908$	−6.58082	−	1.76332i	−0.218392	−	0.0585180i
$909$	7.86244			0.260781
$910$		0			0
$911$	9.74129			0.322743			0.161372	−	0.986894i	$-0.448408\pi$
$911$	9.74129			0.322743			0.161372	+	0.986894i	$0.448408\pi$
$912$	6.98699	+	1.87216i	0.231362	+	0.0619933i
$913$	−10.2065	−	38.0913i	−0.337787	−	1.26064i
$914$	−23.0004	−	13.2793i	−0.760786	−	0.439240i
$915$		0			0
$916$		−	19.8143i		−	0.654682i
$917$	−3.68080	−	22.9185i	−0.121551	−	0.756836i
$918$	3.76725	+	3.76725i	0.124338	+	0.124338i
$919$	−20.0203	+	11.5587i	−0.660410	+	0.381288i	−0.792433	−	0.609959i	$-0.791186\pi$
$919$	−20.0203	+	11.5587i	−0.660410	+	0.381288i	0.132023	+	0.991247i	$0.457853\pi$
$920$		0			0
$921$	8.11809	−	14.0609i	0.267500	−	0.463324i
$922$	4.28625	−	15.9965i	0.141160	−	0.526816i
$923$	−31.4480	+	31.4480i	−1.03512	+	1.03512i
$924$	7.50435	−	3.36063i	0.246875	−	0.110557i
$925$		0			0
$926$	−13.4566	−	23.3075i	−0.442212	−	0.765934i
$927$	11.4280	−	3.06212i	0.375344	−	0.100573i
$928$	4.34047	−	1.16303i	0.142483	−	0.0381782i
$929$	−9.18893	−	15.9157i	−0.301479	−	0.522177i	0.674992	−	0.737825i	$-0.264147\pi$
$929$	−9.18893	−	15.9157i	−0.301479	−	0.522177i	−0.976471	+	0.215648i	$0.930814\pi$
$930$		0			0
$931$	−10.3130	+	49.5729i	−0.337994	+	1.62468i
$932$	−12.7261	+	12.7261i	−0.416857	+	0.416857i
$933$	3.39955	−	12.6873i	0.111296	−	0.415363i
$934$	−6.80325	+	11.7836i	−0.222609	+	0.385570i
$935$		0			0
$936$	−4.17408	+	2.40991i	−0.136434	+	0.0787702i
$937$	12.6455	+	12.6455i	0.413111	+	0.413111i	0.882821	−	0.469710i	$-0.155642\pi$
$937$	12.6455	+	12.6455i	0.413111	+	0.413111i	−0.469710	+	0.882821i	$0.655642\pi$
$938$	−16.4711	−	6.28179i	−0.537799	−	0.205108i
$939$			25.4482i			0.830471i
$940$		0			0
$941$	44.7044	+	25.8101i	1.45732	+	0.841385i	0.998879	−	0.0473392i	$-0.0150742\pi$
$941$	44.7044	+	25.8101i	1.45732	+	0.841385i	0.458442	+	0.888724i	$0.348407\pi$
$942$	0.234379	+	0.874716i	0.00763650	+	0.0284998i
$943$	−12.8101	−	3.43246i	−0.417155	−	0.111776i
$944$	1.33238			0.0433652
$945$		0			0
$946$	−17.0024			−0.552795
$947$	50.4273	+	13.5119i	1.63867	+	0.439079i	0.956408	−	0.292032i	$-0.0943315\pi$
$947$	50.4273	+	13.5119i	1.63867	+	0.439079i	0.682258	+	0.731112i	$0.260998\pi$
$948$	0.495474	+	1.84913i	0.0160922	+	0.0600570i
$949$	34.3616	+	19.8387i	1.11542	+	0.643990i
$950$		0			0
$951$			19.0262i			0.616966i
$952$	−10.9352	+	8.89443i	−0.354413	+	0.288270i
$953$	−0.900242	−	0.900242i	−0.0291617	−	0.0291617i	0.692376	−	0.721537i	$-0.256564\pi$
$953$	−0.900242	−	0.900242i	−0.0291617	−	0.0291617i	−0.721537	+	0.692376i	$0.756564\pi$
$954$	2.97862	−	1.71971i	0.0964365	−	0.0556776i
$955$		0			0
$956$	−13.3204	+	23.0717i	−0.430814	+	0.746191i
$957$	−3.61446	+	13.4893i	−0.116839	+	0.436048i
$958$	−0.937119	+	0.937119i	−0.0302769	+	0.0302769i
$959$	35.8067	+	3.68511i	1.15626	+	0.118998i
$960$		0			0
$961$	27.0506	+	46.8530i	0.872600	+	1.51139i
$962$	−16.7286	+	4.48241i	−0.539351	+	0.144519i
$963$	2.08859	−	0.559635i	0.0673038	−	0.0180340i
$964$	−7.21241	−	12.4923i	−0.232296	−	0.402349i
$965$		0			0
$966$	−8.16463	+	11.2889i	−0.262693	+	0.363216i
$967$	−39.5119	+	39.5119i	−1.27062	+	1.27062i	−0.324852	+	0.945765i	$0.605314\pi$
$967$	−39.5119	+	39.5119i	−1.27062	+	1.27062i	−0.945765	+	0.324852i	$0.894686\pi$
$968$	0.347218	−	1.29584i	0.0111600	−	0.0416497i
$969$	19.2688	−	33.3746i	0.619004	−	1.07215i
$970$		0			0
$971$	−0.0958100	+	0.0553159i	−0.00307469	+	0.00177517i	−0.501537	−	0.865136i	$-0.667232\pi$
$971$	−0.0958100	+	0.0553159i	−0.00307469	+	0.00177517i	0.498462	+	0.866912i	$0.333898\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	10.2902	−	26.9813i	0.329889	−	0.864981i
$974$			32.0419i			1.02669i
$975$		0			0
$976$	10.8719	+	6.27689i	0.348001	+	0.200918i
$977$	−2.05352	−	7.66383i	−0.0656978	−	0.245188i	0.925266	−	0.379320i	$-0.123842\pi$
$977$	−2.05352	−	7.66383i	−0.0656978	−	0.245188i	−0.990963	+	0.134132i	$0.957175\pi$
$978$	−7.13062	−	1.91065i	−0.228012	−	0.0610957i
$979$	12.6598			0.404608
$980$		0			0
$981$	−0.565551			−0.0180567
$982$	21.5846	+	5.78357i	0.688792	+	0.184561i
$983$	−8.60664	−	32.1204i	−0.274509	−	1.02448i	−0.956170	−	0.292814i	$-0.905408\pi$
$983$	−8.60664	−	32.1204i	−0.274509	−	1.02448i	0.681660	−	0.731669i	$-0.261258\pi$
$984$	−2.18110	−	1.25926i	−0.0695308	−	0.0401436i
$985$		0			0
$986$		−	23.9404i		−	0.762419i
$987$	3.85083	−	10.0970i	0.122573	−	0.321391i
$988$	24.6525	+	24.6525i	0.784301	+	0.784301i
$989$	24.9489	−	14.4043i	0.793329	−	0.458029i
$990$		0			0
$991$	7.16865	−	12.4165i	0.227720	−	0.394422i	−0.729412	−	0.684074i	$-0.760206\pi$
$991$	7.16865	−	12.4165i	0.227720	−	0.394422i	0.957132	+	0.289652i	$0.0935397\pi$
$992$	−2.38761	+	8.91070i	−0.0758068	+	0.282915i
$993$	−14.8054	+	14.8054i	−0.469837	+	0.469837i
$994$	−14.3070	+	19.7818i	−0.453791	+	0.627441i
$995$		0			0
$996$	6.34452	+	10.9890i	0.201034	+	0.348201i
$997$	−29.3837	+	7.87333i	−0.930590	+	0.249351i	−0.692106	−	0.721796i	$-0.743317\pi$
$997$	−29.3837	+	7.87333i	−0.930590	+	0.249351i	−0.238484	+	0.971146i	$0.576650\pi$
$998$	−10.4825	+	2.80879i	−0.331819	+	0.0889106i
$999$	1.79662	+	3.11183i	0.0568424	+	0.0984539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.g.493.2		16
5.2	odd	4		1050.2.bc.h.157.4		16
5.3	odd	4		210.2.u.a.157.1	yes	16
5.4	even	2		210.2.u.b.73.4	yes	16
7.5	odd	6		1050.2.bc.h.943.4		16
15.8	even	4		630.2.bv.a.577.4		16
15.14	odd	2		630.2.bv.b.73.1		16
35.3	even	12		1470.2.m.e.97.1		16
35.4	even	6		1470.2.m.e.1273.1		16
35.12	even	12	inner	1050.2.bc.g.607.2		16
35.18	odd	12		1470.2.m.d.97.4		16
35.19	odd	6		210.2.u.a.103.1	✓	16
35.24	odd	6		1470.2.m.d.1273.4		16
35.33	even	12		210.2.u.b.187.4	yes	16
105.68	odd	12		630.2.bv.b.397.1		16
105.89	even	6		630.2.bv.a.523.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.1	✓	16	35.19	odd	6
210.2.u.a.157.1	yes	16	5.3	odd	4
210.2.u.b.73.4	yes	16	5.4	even	2
210.2.u.b.187.4	yes	16	35.33	even	12
630.2.bv.a.523.4		16	105.89	even	6
630.2.bv.a.577.4		16	15.8	even	4
630.2.bv.b.73.1		16	15.14	odd	2
630.2.bv.b.397.1		16	105.68	odd	12
1050.2.bc.g.493.2		16	1.1	even	1	trivial
1050.2.bc.g.607.2		16	35.12	even	12	inner
1050.2.bc.h.157.4		16	5.2	odd	4
1050.2.bc.h.943.4		16	7.5	odd	6
1470.2.m.d.97.4		16	35.18	odd	12
1470.2.m.d.1273.4		16	35.24	odd	6
1470.2.m.e.97.1		16	35.3	even	12
1470.2.m.e.1273.1		16	35.4	even	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(0.942805 - 2.47207i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(0.942805 - 2.47207i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.55390 - 2.69144i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-3.40812 + 3.40812i) q^{13} +(-1.55050 + 2.14382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(5.14616 - 1.37891i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-3.61673 - 6.26436i) q^{19} +(2.63185 + 0.270861i) q^{21} +(-2.19755 + 2.19755i) q^{22} +(1.36289 - 5.08638i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.17408 - 2.40991i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.05253 - 1.66947i) q^{28} +4.49359i q^{29} +(-7.98911 - 4.61252i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(3.00191 + 0.804359i) q^{33} -5.32769 q^{34} -1.00000 q^{36} +(-3.47079 - 0.929997i) q^{37} +(1.87216 + 6.98699i) q^{38} +(-4.17408 - 2.40991i) q^{39} -2.51851i q^{41} +(-2.47207 - 0.942805i) q^{42} +(3.86848 + 3.86848i) q^{43} +(2.69144 - 1.55390i) q^{44} +(-2.63291 + 4.56033i) q^{46} +(1.05713 - 3.94526i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.22224 - 4.66135i) q^{49} +(2.66385 + 4.61392i) q^{51} +(-4.65558 + 1.24746i) q^{52} +(3.32222 - 0.890187i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.41468 + 1.08135i) q^{56} +(5.11483 - 5.11483i) q^{57} +(1.16303 - 4.34047i) q^{58} +(0.666188 - 1.15387i) q^{59} +(10.8719 - 6.27689i) q^{61} +(6.52308 + 6.52308i) q^{62} +(0.419541 + 2.61228i) q^{63} +1.00000i q^{64} +(-2.69144 - 1.55390i) q^{66} +(1.72448 + 6.43584i) q^{67} +(5.14616 + 1.37891i) q^{68} +5.26581 q^{69} +9.22738 q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.13063 - 7.95163i) q^{73} +(3.11183 + 1.79662i) q^{74} -7.23346i q^{76} +(-5.18839 - 6.37885i) q^{77} +(3.40812 + 3.40812i) q^{78} +(1.65789 - 0.957181i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.651839 + 2.43270i) q^{82} +(8.97250 - 8.97250i) q^{83} +(2.14382 + 1.55050i) q^{84} +(-2.73543 - 4.73790i) q^{86} +(-4.34047 + 1.16303i) q^{87} +(-3.00191 + 0.804359i) q^{88} +(2.03677 + 3.52779i) q^{89} +(5.21191 + 11.6383i) q^{91} +(3.72349 - 3.72349i) q^{92} +(2.38761 - 8.91070i) q^{93} +(-2.04222 + 3.53723i) q^{94} +(0.866025 - 0.500000i) q^{96} +(2.69423 + 2.69423i) q^{97} +(3.83785 + 5.85414i) q^{98} +3.10780i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more