LMFDB - Embedded newform 1014.2.e.k.991.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
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			991.3
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.k.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.346011 - 0.599308i) q^{10} +(1.46950 + 2.54525i) q^{11} +1.00000 q^{12} -0.356896 q^{14} +(-0.346011 - 0.599308i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.35690 + 5.81431i) q^{17} +1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(-0.346011 + 0.599308i) q^{20} -0.356896 q^{21} +(1.46950 - 2.54525i) q^{22} +(-1.19806 - 2.07510i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.52111 q^{25} +1.00000 q^{27} +(0.178448 + 0.309081i) q^{28} +(-3.91454 - 6.78019i) q^{29} +(-0.346011 + 0.599308i) q^{30} +2.76271 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.46950 - 2.54525i) q^{33} +6.71379 q^{34} +(0.123490 - 0.213891i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.04892 + 8.74498i) q^{37} +7.20775 q^{38} +0.692021 q^{40} +(2.44504 + 4.23494i) q^{41} +(0.178448 + 0.309081i) q^{42} +(-3.29590 + 5.70866i) q^{43} -2.93900 q^{44} +(-0.346011 + 0.599308i) q^{45} +(-1.19806 + 2.07510i) q^{46} -4.98792 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.43631 + 5.95187i) q^{49} +(2.26055 + 3.91539i) q^{50} +6.71379 q^{51} -8.88769 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.01693 + 1.76137i) q^{55} +(0.178448 - 0.309081i) q^{56} +7.20775 q^{57} +(-3.91454 + 6.78019i) q^{58} +(0.821552 - 1.42297i) q^{59} +0.692021 q^{60} +(3.24698 - 5.62393i) q^{61} +(-1.38135 - 2.39258i) q^{62} +(0.178448 + 0.309081i) q^{63} +1.00000 q^{64} -2.93900 q^{66} +(6.76271 + 11.7134i) q^{67} +(-3.35690 - 5.81431i) q^{68} +(-1.19806 + 2.07510i) q^{69} -0.246980 q^{70} +(3.40581 - 5.89904i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.18598 q^{73} +(5.04892 - 8.74498i) q^{74} +(2.26055 + 3.91539i) q^{75} +(-3.60388 - 6.24210i) q^{76} +1.04892 q^{77} +15.0465 q^{79} +(-0.346011 - 0.599308i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.44504 - 4.23494i) q^{82} +14.8267 q^{83} +(0.178448 - 0.309081i) q^{84} +(-2.32304 + 4.02363i) q^{85} +6.59179 q^{86} +(-3.91454 + 6.78019i) q^{87} +(1.46950 + 2.54525i) q^{88} +(0.198062 + 0.343054i) q^{89} +0.692021 q^{90} +2.39612 q^{92} +(-1.38135 - 2.39258i) q^{93} +(2.49396 + 4.31966i) q^{94} +(-2.49396 + 4.31966i) q^{95} +1.00000 q^{96} +(-0.208947 + 0.361908i) q^{97} +(3.43631 - 5.95187i) q^{98} -2.93900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} - q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 12 q^{17} + 6 q^{18} - 4 q^{19} + 3 q^{20} + 6 q^{21} - q^{22} - 16 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{27} - 3 q^{28} - 13 q^{29} + 3 q^{30} - 18 q^{31} - 3 q^{32} - q^{33} + 24 q^{34} - 4 q^{35} - 3 q^{36} + 12 q^{37} + 8 q^{38} - 6 q^{40} + 14 q^{41} - 3 q^{42} + 8 q^{43} + 2 q^{44} + 3 q^{45} - 16 q^{46} + 8 q^{47} - 3 q^{48} + 4 q^{49} - 2 q^{50} + 24 q^{51} + 30 q^{53} - 3 q^{54} + 22 q^{55} - 3 q^{56} + 8 q^{57} - 13 q^{58} + 9 q^{59} - 6 q^{60} + 10 q^{61} + 9 q^{62} - 3 q^{63} + 6 q^{64} + 2 q^{66} + 6 q^{67} - 12 q^{68} - 16 q^{69} + 8 q^{70} - 6 q^{71} - 3 q^{72} + 10 q^{73} + 12 q^{74} - 2 q^{75} - 4 q^{76} - 12 q^{77} - 10 q^{79} + 3 q^{80} - 3 q^{81} + 14 q^{82} - 14 q^{83} - 3 q^{84} + 26 q^{85} - 16 q^{86} - 13 q^{87} - q^{88} + 10 q^{89} - 6 q^{90} + 32 q^{92} + 9 q^{93} - 4 q^{94} + 4 q^{95} + 6 q^{96} - 7 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 - q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 - 3 * q^16 - 12 * q^17 + 6 * q^18 - 4 * q^19 + 3 * q^20 + 6 * q^21 - q^22 - 16 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^27 - 3 * q^28 - 13 * q^29 + 3 * q^30 - 18 * q^31 - 3 * q^32 - q^33 + 24 * q^34 - 4 * q^35 - 3 * q^36 + 12 * q^37 + 8 * q^38 - 6 * q^40 + 14 * q^41 - 3 * q^42 + 8 * q^43 + 2 * q^44 + 3 * q^45 - 16 * q^46 + 8 * q^47 - 3 * q^48 + 4 * q^49 - 2 * q^50 + 24 * q^51 + 30 * q^53 - 3 * q^54 + 22 * q^55 - 3 * q^56 + 8 * q^57 - 13 * q^58 + 9 * q^59 - 6 * q^60 + 10 * q^61 + 9 * q^62 - 3 * q^63 + 6 * q^64 + 2 * q^66 + 6 * q^67 - 12 * q^68 - 16 * q^69 + 8 * q^70 - 6 * q^71 - 3 * q^72 + 10 * q^73 + 12 * q^74 - 2 * q^75 - 4 * q^76 - 12 * q^77 - 10 * q^79 + 3 * q^80 - 3 * q^81 + 14 * q^82 - 14 * q^83 - 3 * q^84 + 26 * q^85 - 16 * q^86 - 13 * q^87 - q^88 + 10 * q^89 - 6 * q^90 + 32 * q^92 + 9 * q^93 - 4 * q^94 + 4 * q^95 + 6 * q^96 - 7 * q^97 + 4 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.692021			0.309481			0.154741	−	0.987955i	$-0.450546\pi$
$5$	0.692021			0.309481			0.154741	+	0.987955i	$0.450546\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.178448	−	0.309081i	0.0674470	−	0.116822i	−0.830330	−	0.557272i	$-0.811848\pi$
$7$	0.178448	−	0.309081i	0.0674470	−	0.116822i	0.897777	+	0.440451i	$0.145181\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.346011	−	0.599308i	−0.109418	−	0.189518i
$11$	1.46950	+	2.54525i	0.443071	+	0.767422i	0.997916	−	0.0645324i	$-0.0205556\pi$
$11$	1.46950	+	2.54525i	0.443071	+	0.767422i	−0.554845	+	0.831954i	$0.687222\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−0.356896			−0.0953844
$15$	−0.346011	−	0.599308i	−0.0893396	−	0.154741i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.35690	+	5.81431i	−0.814167	+	1.41018i	0.0957578	+	0.995405i	$0.469473\pi$
$17$	−3.35690	+	5.81431i	−0.814167	+	1.41018i	−0.909925	+	0.414774i	$0.863861\pi$
$18$	1.00000			0.235702
$19$	−3.60388	+	6.24210i	−0.826786	+	1.43203i	0.0737611	+	0.997276i	$0.476500\pi$
$19$	−3.60388	+	6.24210i	−0.826786	+	1.43203i	−0.900547	+	0.434759i	$0.856834\pi$
$20$	−0.346011	+	0.599308i	−0.0773704	+	0.134009i
$21$	−0.356896			−0.0778811
$22$	1.46950	−	2.54525i	0.313299	−	0.542649i
$23$	−1.19806	−	2.07510i	−0.249813	−	0.432689i	0.713661	−	0.700492i	$-0.247036\pi$
$23$	−1.19806	−	2.07510i	−0.249813	−	0.432689i	−0.963474	+	0.267802i	$0.913703\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.52111			−0.904221
$26$		0			0
$27$	1.00000			0.192450
$28$	0.178448	+	0.309081i	0.0337235	+	0.0584108i
$29$	−3.91454	−	6.78019i	−0.726912	−	1.25905i	−0.958182	−	0.286159i	$-0.907621\pi$
$29$	−3.91454	−	6.78019i	−0.726912	−	1.25905i	0.231270	−	0.972890i	$-0.425712\pi$
$30$	−0.346011	+	0.599308i	−0.0631726	+	0.109418i
$31$	2.76271			0.496197			0.248099	−	0.968735i	$-0.420194\pi$
$31$	2.76271			0.496197			0.248099	+	0.968735i	$0.420194\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.46950	−	2.54525i	0.255807	−	0.443071i
$34$	6.71379			1.15141
$35$	0.123490	−	0.213891i	0.0208736	−	0.0361541i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.04892	+	8.74498i	0.830037	+	1.43767i	0.898008	+	0.439979i	$0.145014\pi$
$37$	5.04892	+	8.74498i	0.830037	+	1.43767i	−0.0679713	+	0.997687i	$0.521653\pi$
$38$	7.20775			1.16925
$39$		0			0
$40$	0.692021			0.109418
$41$	2.44504	+	4.23494i	0.381851	+	0.661386i	0.991327	−	0.131419i	$-0.0419533\pi$
$41$	2.44504	+	4.23494i	0.381851	+	0.661386i	−0.609476	+	0.792805i	$0.708620\pi$
$42$	0.178448	+	0.309081i	0.0275351	+	0.0476922i
$43$	−3.29590	+	5.70866i	−0.502620	+	0.870563i	0.497376	+	0.867535i	$0.334297\pi$
$43$	−3.29590	+	5.70866i	−0.502620	+	0.870563i	−0.999995	+	0.00302747i	$0.999036\pi$
$44$	−2.93900			−0.443071
$45$	−0.346011	+	0.599308i	−0.0515802	+	0.0893396i
$46$	−1.19806	+	2.07510i	−0.176645	+	0.305957i
$47$	−4.98792			−0.727563			−0.363781	−	0.931484i	$-0.618514\pi$
$47$	−4.98792			−0.727563			−0.363781	+	0.931484i	$0.618514\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.43631	+	5.95187i	0.490902	+	0.850267i
$50$	2.26055	+	3.91539i	0.319690	+	0.553720i
$51$	6.71379			0.940119
$52$		0			0
$53$	−8.88769			−1.22082			−0.610409	−	0.792086i	$-0.708995\pi$
$53$	−8.88769			−1.22082			−0.610409	+	0.792086i	$0.708995\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.01693	+	1.76137i	0.137122	+	0.237503i
$56$	0.178448	−	0.309081i	0.0238461	−	0.0413027i
$57$	7.20775			0.954690
$58$	−3.91454	+	6.78019i	−0.514005	+	0.890282i
$59$	0.821552	−	1.42297i	0.106957	−	0.185255i	−0.807579	−	0.589759i	$-0.799223\pi$
$59$	0.821552	−	1.42297i	0.106957	−	0.185255i	0.914536	+	0.404504i	$0.132556\pi$
$60$	0.692021			0.0893396
$61$	3.24698	−	5.62393i	0.415733	−	0.720071i	−0.579772	−	0.814779i	$-0.696858\pi$
$61$	3.24698	−	5.62393i	0.415733	−	0.720071i	0.995505	+	0.0947079i	$0.0301917\pi$
$62$	−1.38135	−	2.39258i	−0.175432	−	0.303857i
$63$	0.178448	+	0.309081i	0.0224823	+	0.0389405i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.93900			−0.361766
$67$	6.76271	+	11.7134i	0.826196	+	1.43101i	0.901001	+	0.433816i	$0.142833\pi$
$67$	6.76271	+	11.7134i	0.826196	+	1.43101i	−0.0748051	+	0.997198i	$0.523833\pi$
$68$	−3.35690	−	5.81431i	−0.407083	−	0.705089i
$69$	−1.19806	+	2.07510i	−0.144230	+	0.249813i
$70$	−0.246980			−0.0295197
$71$	3.40581	−	5.89904i	0.404196	−	0.700087i	−0.590032	−	0.807380i	$-0.700885\pi$
$71$	3.40581	−	5.89904i	0.404196	−	0.700087i	0.994227	+	0.107293i	$0.0342181\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−3.18598			−0.372891			−0.186445	−	0.982465i	$-0.559697\pi$
$73$	−3.18598			−0.372891			−0.186445	+	0.982465i	$0.559697\pi$
$74$	5.04892	−	8.74498i	0.586925	−	1.01658i
$75$	2.26055	+	3.91539i	0.261026	+	0.452111i
$76$	−3.60388	−	6.24210i	−0.413393	−	0.716017i
$77$	1.04892			0.119535
$78$		0			0
$79$	15.0465			1.69287			0.846433	−	0.532495i	$-0.178745\pi$
$79$	15.0465			1.69287			0.846433	+	0.532495i	$0.178745\pi$
$80$	−0.346011	−	0.599308i	−0.0386852	−	0.0670047i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.44504	−	4.23494i	0.270010	−	0.467671i
$83$	14.8267			1.62744			0.813720	−	0.581256i	$-0.197439\pi$
$83$	14.8267			1.62744			0.813720	+	0.581256i	$0.197439\pi$
$84$	0.178448	−	0.309081i	0.0194703	−	0.0337235i
$85$	−2.32304	+	4.02363i	−0.251970	+	0.436424i
$86$	6.59179			0.710811
$87$	−3.91454	+	6.78019i	−0.419683	+	0.726912i
$88$	1.46950	+	2.54525i	0.156649	+	0.271325i
$89$	0.198062	+	0.343054i	0.0209946	+	0.0363636i	0.876332	−	0.481708i	$-0.159983\pi$
$89$	0.198062	+	0.343054i	0.0209946	+	0.0363636i	−0.855337	+	0.518072i	$0.826650\pi$
$90$	0.692021			0.0729455
$91$		0			0
$92$	2.39612			0.249813
$93$	−1.38135	−	2.39258i	−0.143240	−	0.248099i
$94$	2.49396	+	4.31966i	0.257232	+	0.445539i
$95$	−2.49396	+	4.31966i	−0.255875	+	0.443188i
$96$	1.00000			0.102062
$97$	−0.208947	+	0.361908i	−0.0212154	+	0.0367461i	−0.876438	−	0.481514i	$-0.840087\pi$
$97$	−0.208947	+	0.361908i	−0.0212154	+	0.0367461i	0.855223	+	0.518261i	$0.173420\pi$
$98$	3.43631	−	5.95187i	0.347120	−	0.601229i
$99$	−2.93900			−0.295381
$100$	2.26055	−	3.91539i	0.226055	−	0.391539i
$101$	−5.00753	−	8.67330i	−0.498268	−	0.863026i	0.501730	−	0.865024i	$-0.332697\pi$
$101$	−5.00753	−	8.67330i	−0.498268	−	0.863026i	−0.999998	+	0.00199864i	$0.999364\pi$
$102$	−3.35690	−	5.81431i	−0.332382	−	0.575703i
$103$	−9.62565			−0.948443			−0.474222	−	0.880406i	$-0.657270\pi$
$103$	−9.62565			−0.948443			−0.474222	+	0.880406i	$0.657270\pi$
$104$		0			0
$105$	−0.246980			−0.0241027
$106$	4.44385	+	7.69697i	0.431624	+	0.747595i
$107$	3.31551	+	5.74263i	0.320523	+	0.555161i	0.980596	−	0.196040i	$-0.0628082\pi$
$107$	3.31551	+	5.74263i	0.320523	+	0.555161i	−0.660073	+	0.751201i	$0.729475\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−12.9879			−1.24402			−0.622008	−	0.783011i	$-0.713683\pi$
$109$	−12.9879			−1.24402			−0.622008	+	0.783011i	$0.713683\pi$
$110$	1.01693	−	1.76137i	0.0969601	−	0.167940i
$111$	5.04892	−	8.74498i	0.479222	−	0.830037i
$112$	−0.356896			−0.0337235
$113$	−0.396125	+	0.686108i	−0.0372643	+	0.0645436i	−0.884056	−	0.467381i	$-0.845198\pi$
$113$	−0.396125	+	0.686108i	−0.0372643	+	0.0645436i	0.846792	+	0.531925i	$0.178531\pi$
$114$	−3.60388	−	6.24210i	−0.337534	−	0.584626i
$115$	−0.829085	−	1.43602i	−0.0773126	−	0.133909i
$116$	7.82908			0.726912
$117$		0			0
$118$	−1.64310			−0.151260
$119$	1.19806	+	2.07510i	0.109826	+	0.190225i
$120$	−0.346011	−	0.599308i	−0.0315863	−	0.0547091i
$121$	1.18114	−	2.04579i	0.107376	−	0.185981i
$122$	−6.49396			−0.587935
$123$	2.44504	−	4.23494i	0.220462	−	0.381851i
$124$	−1.38135	+	2.39258i	−0.124049	+	0.214860i
$125$	−6.58881			−0.589321
$126$	0.178448	−	0.309081i	0.0158974	−	0.0275351i
$127$	9.10872	+	15.7768i	0.808268	+	1.39996i	0.914062	+	0.405574i	$0.132928\pi$
$127$	9.10872	+	15.7768i	0.808268	+	1.39996i	−0.105794	+	0.994388i	$0.533738\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.59179			0.580375
$130$		0			0
$131$	2.73556			0.239007			0.119504	−	0.992834i	$-0.461870\pi$
$131$	2.73556			0.239007			0.119504	+	0.992834i	$0.461870\pi$
$132$	1.46950	+	2.54525i	0.127904	+	0.221536i
$133$	1.28621	+	2.22778i	0.111528	+	0.193173i
$134$	6.76271	−	11.7134i	0.584209	−	1.01188i
$135$	0.692021			0.0595597
$136$	−3.35690	+	5.81431i	−0.287851	+	0.498573i
$137$	−3.82371	+	6.62286i	−0.326681	+	0.565829i	−0.981851	−	0.189653i	$-0.939264\pi$
$137$	−3.82371	+	6.62286i	−0.326681	+	0.565829i	0.655170	+	0.755482i	$0.272597\pi$
$138$	2.39612			0.203972
$139$	−1.69202	+	2.93067i	−0.143515	+	0.248576i	−0.928818	−	0.370536i	$-0.879174\pi$
$139$	−1.69202	+	2.93067i	−0.143515	+	0.248576i	0.785303	+	0.619112i	$0.212507\pi$
$140$	0.123490	+	0.213891i	0.0104368	+	0.0180771i
$141$	2.49396	+	4.31966i	0.210029	+	0.363781i
$142$	−6.81163			−0.571619
$143$		0			0
$144$	1.00000			0.0833333
$145$	−2.70895	−	4.69203i	−0.224966	−	0.389652i
$146$	1.59299	+	2.75914i	0.131837	+	0.228348i
$147$	3.43631	−	5.95187i	0.283422	−	0.490902i
$148$	−10.0978			−0.830037
$149$	10.4085	−	18.0281i	0.852698	−	1.47692i	−0.0260669	−	0.999660i	$-0.508298\pi$
$149$	10.4085	−	18.0281i	0.852698	−	1.47692i	0.878765	−	0.477255i	$-0.158368\pi$
$150$	2.26055	−	3.91539i	0.184573	−	0.319690i
$151$	−0.895461			−0.0728715			−0.0364358	−	0.999336i	$-0.511600\pi$
$151$	−0.895461			−0.0728715			−0.0364358	+	0.999336i	$0.511600\pi$
$152$	−3.60388	+	6.24210i	−0.292313	+	0.506301i
$153$	−3.35690	−	5.81431i	−0.271389	−	0.470059i
$154$	−0.524459	−	0.908389i	−0.0422621	−	0.0732001i
$155$	1.91185			0.153564
$156$		0			0
$157$	8.59179			0.685700			0.342850	−	0.939390i	$-0.388608\pi$
$157$	8.59179			0.685700			0.342850	+	0.939390i	$0.388608\pi$
$158$	−7.52326	−	13.0307i	−0.598519	−	1.03666i
$159$	4.44385	+	7.69697i	0.352420	+	0.610409i
$160$	−0.346011	+	0.599308i	−0.0273546	+	0.0473795i
$161$	−0.855167			−0.0673966
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−0.862937	+	1.49465i	−0.0675904	+	0.117070i	−0.897840	−	0.440322i	$-0.854864\pi$
$163$	−0.862937	+	1.49465i	−0.0675904	+	0.117070i	0.830250	+	0.557392i	$0.188198\pi$
$164$	−4.89008			−0.381851
$165$	1.01693	−	1.76137i	0.0791676	−	0.137122i
$166$	−7.41335	−	12.8403i	−0.575387	−	0.996600i
$167$	−10.5700	−	18.3078i	−0.817933	−	1.41670i	−0.907203	−	0.420694i	$-0.861787\pi$
$167$	−10.5700	−	18.3078i	−0.817933	−	1.41670i	0.0892696	−	0.996007i	$-0.471547\pi$
$168$	−0.356896			−0.0275351
$169$		0			0
$170$	4.64609			0.356339
$171$	−3.60388	−	6.24210i	−0.275595	−	0.477345i
$172$	−3.29590	−	5.70866i	−0.251310	−	0.435281i
$173$	−4.67725	+	8.10124i	−0.355605	+	0.615926i	−0.987221	−	0.159355i	$-0.949058\pi$
$173$	−4.67725	+	8.10124i	−0.355605	+	0.615926i	0.631616	+	0.775281i	$0.282392\pi$
$174$	7.82908			0.593521
$175$	−0.806782	+	1.39739i	−0.0609870	+	0.105633i
$176$	1.46950	−	2.54525i	0.110768	−	0.191855i
$177$	−1.64310			−0.123503
$178$	0.198062	−	0.343054i	0.0148454	−	0.0257130i
$179$	−1.58761	−	2.74983i	−0.118664	−	0.205532i	0.800575	−	0.599233i	$-0.204528\pi$
$179$	−1.58761	−	2.74983i	−0.118664	−	0.205532i	−0.919238	+	0.393701i	$0.871194\pi$
$180$	−0.346011	−	0.599308i	−0.0257901	−	0.0446698i
$181$	−19.7995			−1.47169			−0.735844	−	0.677151i	$-0.763214\pi$
$181$	−19.7995			−1.47169			−0.735844	+	0.677151i	$0.763214\pi$
$182$		0			0
$183$	−6.49396			−0.480047
$184$	−1.19806	−	2.07510i	−0.0883223	−	0.152979i
$185$	3.49396	+	6.05171i	0.256881	+	0.444931i
$186$	−1.38135	+	2.39258i	−0.101286	+	0.175432i
$187$	−19.7318			−1.44294
$188$	2.49396	−	4.31966i	0.181891	−	0.315044i
$189$	0.178448	−	0.309081i	0.0129802	−	0.0224823i
$190$	4.98792			0.361862
$191$	−7.63102	+	13.2173i	−0.552161	+	0.956372i	0.445957	+	0.895054i	$0.352863\pi$
$191$	−7.63102	+	13.2173i	−0.552161	+	0.956372i	−0.998118	+	0.0613172i	$0.980470\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−2.38404	−	4.12928i	−0.171607	−	0.297232i	0.767375	−	0.641199i	$-0.221563\pi$
$193$	−2.38404	−	4.12928i	−0.171607	−	0.297232i	−0.938982	+	0.343967i	$0.888229\pi$
$194$	0.417895			0.0300031
$195$		0			0
$196$	−6.87263			−0.490902
$197$	−6.11745	−	10.5957i	−0.435850	−	0.754915i	0.561514	−	0.827467i	$-0.310219\pi$
$197$	−6.11745	−	10.5957i	−0.435850	−	0.754915i	−0.997365	+	0.0725523i	$0.976886\pi$
$198$	1.46950	+	2.54525i	0.104433	+	0.180883i
$199$	5.92423	−	10.2611i	0.419958	−	0.727388i	−0.575977	−	0.817466i	$-0.695378\pi$
$199$	5.92423	−	10.2611i	0.419958	−	0.727388i	0.995935	+	0.0900779i	$0.0287116\pi$
$200$	−4.52111			−0.319690
$201$	6.76271	−	11.7134i	0.477005	−	0.826196i
$202$	−5.00753	+	8.67330i	−0.352329	+	0.610251i
$203$	−2.79417			−0.196112
$204$	−3.35690	+	5.81431i	−0.235030	+	0.407083i
$205$	1.69202	+	2.93067i	0.118176	+	0.204687i
$206$	4.81282	+	8.33605i	0.335325	+	0.580800i
$207$	2.39612			0.166542
$208$		0			0
$209$	−21.1836			−1.46530
$210$	0.123490	+	0.213891i	0.00852161	+	0.0147599i
$211$	8.63102	+	14.9494i	0.594184	+	1.02916i	0.993661	+	0.112414i	$0.0358583\pi$
$211$	8.63102	+	14.9494i	0.594184	+	1.02916i	−0.399477	+	0.916743i	$0.630808\pi$
$212$	4.44385	−	7.69697i	0.305205	−	0.528630i
$213$	−6.81163			−0.466725
$214$	3.31551	−	5.74263i	0.226644	−	0.392558i
$215$	−2.28083	+	3.95052i	−0.155551	+	0.269423i
$216$	1.00000			0.0680414
$217$	0.493000	−	0.853901i	0.0334670	−	0.0579665i
$218$	6.49396	+	11.2479i	0.439826	+	0.761802i
$219$	1.59299	+	2.75914i	0.107644	+	0.186445i
$220$	−2.03385			−0.137122
$221$		0			0
$222$	−10.0978			−0.677722
$223$	−3.38404	−	5.86133i	−0.226612	−	0.392504i	0.730190	−	0.683245i	$-0.239432\pi$
$223$	−3.38404	−	5.86133i	−0.226612	−	0.392504i	−0.956802	+	0.290741i	$0.906098\pi$
$224$	0.178448	+	0.309081i	0.0119231	+	0.0206513i
$225$	2.26055	−	3.91539i	0.150704	−	0.261026i
$226$	0.792249			0.0526996
$227$	−11.8400	+	20.5074i	−0.785846	+	1.36113i	0.142646	+	0.989774i	$0.454439\pi$
$227$	−11.8400	+	20.5074i	−0.785846	+	1.36113i	−0.928492	+	0.371352i	$0.878894\pi$
$228$	−3.60388	+	6.24210i	−0.238672	+	0.413393i
$229$	−8.29829			−0.548366			−0.274183	−	0.961677i	$-0.588407\pi$
$229$	−8.29829			−0.548366			−0.274183	+	0.961677i	$0.588407\pi$
$230$	−0.829085	+	1.43602i	−0.0546682	+	0.0946882i
$231$	−0.524459	−	0.908389i	−0.0345068	−	0.0597676i
$232$	−3.91454	−	6.78019i	−0.257002	−	0.445141i
$233$	−23.9651			−1.57000			−0.785002	−	0.619493i	$-0.787338\pi$
$233$	−23.9651			−1.57000			−0.785002	+	0.619493i	$0.787338\pi$
$234$		0			0
$235$	−3.45175			−0.225167
$236$	0.821552	+	1.42297i	0.0534785	+	0.0926275i
$237$	−7.52326	−	13.0307i	−0.488688	−	0.846433i
$238$	1.19806	−	2.07510i	0.0776588	−	0.134509i
$239$	12.6160			0.816058			0.408029	−	0.912969i	$-0.366216\pi$
$239$	12.6160			0.816058			0.408029	+	0.912969i	$0.366216\pi$
$240$	−0.346011	+	0.599308i	−0.0223349	+	0.0386852i
$241$	−13.1969	+	22.8576i	−0.850085	+	1.47239i	0.0310462	+	0.999518i	$0.490116\pi$
$241$	−13.1969	+	22.8576i	−0.850085	+	1.47239i	−0.881131	+	0.472872i	$0.843217\pi$
$242$	−2.36227			−0.151853
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.24698	+	5.62393i	0.207867	+	0.360035i
$245$	2.37800	+	4.11882i	0.151925	+	0.263142i
$246$	−4.89008			−0.311780
$247$		0			0
$248$	2.76271			0.175432
$249$	−7.41335	−	12.8403i	−0.469802	−	0.813720i
$250$	3.29440	+	5.70608i	0.208356	+	0.360884i
$251$	15.0172	−	26.0106i	0.947879	−	1.64177i	0.197996	−	0.980203i	$-0.436557\pi$
$251$	15.0172	−	26.0106i	0.947879	−	1.64177i	0.749882	−	0.661571i	$-0.230110\pi$
$252$	−0.356896			−0.0224823
$253$	3.52111	−	6.09873i	0.221370	−	0.383424i
$254$	9.10872	−	15.7768i	0.571532	−	0.989922i
$255$	4.64609			0.290949
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.63102	−	9.75322i	−0.351254	−	0.608389i	0.635216	−	0.772335i	$-0.280911\pi$
$257$	−5.63102	−	9.75322i	−0.351254	−	0.608389i	−0.986469	+	0.163946i	$0.947578\pi$
$258$	−3.29590	−	5.70866i	−0.205194	−	0.355406i
$259$	3.60388			0.223934
$260$		0			0
$261$	7.82908			0.484608
$262$	−1.36778	−	2.36907i	−0.0845018	−	0.146361i
$263$	2.77479	+	4.80608i	0.171101	+	0.296355i	0.938805	−	0.344449i	$-0.111934\pi$
$263$	2.77479	+	4.80608i	0.171101	+	0.296355i	−0.767704	+	0.640804i	$0.778601\pi$
$264$	1.46950	−	2.54525i	0.0904415	−	0.156649i
$265$	−6.15047			−0.377821
$266$	1.28621	−	2.22778i	0.0788625	−	0.136594i
$267$	0.198062	−	0.343054i	0.0121212	−	0.0209946i
$268$	−13.5254			−0.826196
$269$	−8.34362	+	14.4516i	−0.508719	+	0.881128i	0.491230	+	0.871030i	$0.336548\pi$
$269$	−8.34362	+	14.4516i	−0.508719	+	0.881128i	−0.999949	+	0.0100977i	$0.996786\pi$
$270$	−0.346011	−	0.599308i	−0.0210575	−	0.0364727i
$271$	3.30678	+	5.72751i	0.200873	+	0.347922i	0.948810	−	0.315848i	$-0.102289\pi$
$271$	3.30678	+	5.72751i	0.200873	+	0.347922i	−0.747937	+	0.663770i	$0.768956\pi$
$272$	6.71379			0.407083
$273$		0			0
$274$	7.64742			0.461997
$275$	−6.64377	−	11.5073i	−0.400634	−	0.693919i
$276$	−1.19806	−	2.07510i	−0.0721149	−	0.124907i
$277$	10.8998	−	18.8790i	0.654904	−	1.13433i	−0.327014	−	0.945019i	$-0.606042\pi$
$277$	10.8998	−	18.8790i	0.654904	−	1.13433i	0.981918	−	0.189307i	$-0.0606242\pi$
$278$	3.38404			0.202961
$279$	−1.38135	+	2.39258i	−0.0826995	+	0.143240i
$280$	0.123490	−	0.213891i	0.00737993	−	0.0127824i
$281$	20.5918			1.22840			0.614202	−	0.789149i	$-0.289478\pi$
$281$	20.5918			1.22840			0.614202	+	0.789149i	$0.289478\pi$
$282$	2.49396	−	4.31966i	0.148513	−	0.257232i
$283$	6.50604	+	11.2688i	0.386744	+	0.669860i	0.992009	−	0.126163i	$-0.0402664\pi$
$283$	6.50604	+	11.2688i	0.386744	+	0.669860i	−0.605265	+	0.796024i	$0.706933\pi$
$284$	3.40581	+	5.89904i	0.202098	+	0.350044i
$285$	4.98792			0.295459
$286$		0			0
$287$	1.74525			0.103019
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−14.0375	−	24.3137i	−0.825735	−	1.43022i
$290$	−2.70895	+	4.69203i	−0.159075	+	0.275526i
$291$	0.417895			0.0244974
$292$	1.59299	−	2.75914i	0.0932227	−	0.161466i
$293$	7.46950	−	12.9376i	0.436373	−	0.755820i	−0.561034	−	0.827793i	$-0.689596\pi$
$293$	7.46950	−	12.9376i	0.436373	−	0.755820i	0.997407	+	0.0719730i	$0.0229295\pi$
$294$	−6.87263			−0.400820
$295$	0.568532	−	0.984726i	0.0331012	−	0.0573329i
$296$	5.04892	+	8.74498i	0.293462	+	0.508292i
$297$	1.46950	+	2.54525i	0.0852691	+	0.147690i
$298$	−20.8170			−1.20590
$299$		0			0
$300$	−4.52111			−0.261026
$301$	1.17629	+	2.03740i	0.0678003	+	0.117434i
$302$	0.447730	+	0.775492i	0.0257640	+	0.0446245i
$303$	−5.00753	+	8.67330i	−0.287675	+	0.498268i
$304$	7.20775			0.413393
$305$	2.24698	−	3.89188i	0.128662	−	0.222849i
$306$	−3.35690	+	5.81431i	−0.191901	+	0.332382i
$307$	26.0301			1.48562			0.742809	−	0.669503i	$-0.233493\pi$
$307$	26.0301			1.48562			0.742809	+	0.669503i	$0.233493\pi$
$308$	−0.524459	+	0.908389i	−0.0298838	+	0.0517603i
$309$	4.81282	+	8.33605i	0.273792	+	0.474222i
$310$	−0.955927	−	1.65571i	−0.0542930	−	0.0940382i
$311$	−4.81163			−0.272842			−0.136421	−	0.990651i	$-0.543560\pi$
$311$	−4.81163			−0.272842			−0.136421	+	0.990651i	$0.543560\pi$
$312$		0			0
$313$	−26.0411			−1.47193			−0.735966	−	0.677018i	$-0.763272\pi$
$313$	−26.0411			−1.47193			−0.735966	+	0.677018i	$0.763272\pi$
$314$	−4.29590	−	7.44071i	−0.242431	−	0.419904i
$315$	0.123490	+	0.213891i	0.00695786	+	0.0120514i
$316$	−7.52326	+	13.0307i	−0.423217	+	0.733033i
$317$	−11.5211			−0.647090			−0.323545	−	0.946213i	$-0.604875\pi$
$317$	−11.5211			−0.647090			−0.323545	+	0.946213i	$0.604875\pi$
$318$	4.44385	−	7.69697i	0.249198	−	0.431624i
$319$	11.5048	−	19.9270i	0.644148	−	1.11570i
$320$	0.692021			0.0386852
$321$	3.31551	−	5.74263i	0.185054	−	0.320523i
$322$	0.427583	+	0.740596i	0.0238283	+	0.0412718i
$323$	−24.1957	−	41.9081i	−1.34628	−	2.33183i
$324$	1.00000			0.0555556
$325$		0			0
$326$	1.72587			0.0955873
$327$	6.49396	+	11.2479i	0.359117	+	0.622008i
$328$	2.44504	+	4.23494i	0.135005	+	0.233835i
$329$	−0.890084	+	1.54167i	−0.0490719	+	0.0849950i
$330$	−2.03385			−0.111960
$331$	−1.71917	+	2.97769i	−0.0944940	+	0.163668i	−0.909397	−	0.415928i	$-0.863457\pi$
$331$	−1.71917	+	2.97769i	−0.0944940	+	0.163668i	0.814903	+	0.579597i	$0.196790\pi$
$332$	−7.41335	+	12.8403i	−0.406860	+	0.704703i
$333$	−10.0978			−0.553358
$334$	−10.5700	+	18.3078i	−0.578366	+	1.00176i
$335$	4.67994	+	8.10589i	0.255692	+	0.442872i
$336$	0.178448	+	0.309081i	0.00973513	+	0.0168617i
$337$	8.20105			0.446739			0.223370	−	0.974734i	$-0.428294\pi$
$337$	8.20105			0.446739			0.223370	+	0.974734i	$0.428294\pi$
$338$		0			0
$339$	0.792249			0.0430291
$340$	−2.32304	−	4.02363i	−0.125985	−	0.218212i
$341$	4.05980	+	7.03178i	0.219851	+	0.380792i
$342$	−3.60388	+	6.24210i	−0.194875	+	0.337534i
$343$	4.95108			0.267333
$344$	−3.29590	+	5.70866i	−0.177703	+	0.307790i
$345$	−0.829085	+	1.43602i	−0.0446364	+	0.0773126i
$346$	9.35450			0.502901
$347$	−3.93147	+	6.80950i	−0.211052	+	0.365553i	−0.952044	−	0.305961i	$-0.901022\pi$
$347$	−3.93147	+	6.80950i	−0.211052	+	0.365553i	0.740992	+	0.671514i	$0.234356\pi$
$348$	−3.91454	−	6.78019i	−0.209841	−	0.363456i
$349$	9.36227	+	16.2159i	0.501151	+	0.868019i	0.999999	+	0.00132953i	$0.000423203\pi$
$349$	9.36227	+	16.2159i	0.501151	+	0.868019i	−0.498848	+	0.866689i	$0.666243\pi$
$350$	1.61356			0.0862486
$351$		0			0
$352$	−2.93900			−0.156649
$353$	15.7724	+	27.3186i	0.839480	+	1.45402i	0.890330	+	0.455316i	$0.150474\pi$
$353$	15.7724	+	27.3186i	0.839480	+	1.45402i	−0.0508500	+	0.998706i	$0.516193\pi$
$354$	0.821552	+	1.42297i	0.0436650	+	0.0756300i
$355$	2.35690	−	4.08226i	0.125091	−	0.216664i
$356$	−0.396125			−0.0209946
$357$	1.19806	−	2.07510i	0.0634082	−	0.109826i
$358$	−1.58761	+	2.74983i	−0.0839080	+	0.145333i
$359$	2.39612			0.126463			0.0632313	−	0.997999i	$-0.479859\pi$
$359$	2.39612			0.126463			0.0632313	+	0.997999i	$0.479859\pi$
$360$	−0.346011	+	0.599308i	−0.0182364	+	0.0315863i
$361$	−16.4758	−	28.5370i	−0.867149	−	1.50195i
$362$	9.89977	+	17.1469i	0.520320	+	0.901222i
$363$	−2.36227			−0.123987
$364$		0			0
$365$	−2.20477			−0.115403
$366$	3.24698	+	5.62393i	0.169722	+	0.293968i
$367$	0.00215593	+	0.00373419i	0.000112539	+	0.000194923i	0.866082	−	0.499903i	$-0.166631\pi$
$367$	0.00215593	+	0.00373419i	0.000112539	+	0.000194923i	−0.865969	+	0.500097i	$0.833298\pi$
$368$	−1.19806	+	2.07510i	−0.0624533	+	0.108172i
$369$	−4.89008			−0.254568
$370$	3.49396	−	6.05171i	0.181642	−	0.314614i
$371$	−1.58599	+	2.74702i	−0.0823405	+	0.142618i
$372$	2.76271			0.143240
$373$	16.1564	−	27.9838i	0.836549	−	1.44895i	−0.0562144	−	0.998419i	$-0.517903\pi$
$373$	16.1564	−	27.9838i	0.836549	−	1.44895i	0.892763	−	0.450526i	$-0.148764\pi$
$374$	9.86592	+	17.0883i	0.510155	+	0.883614i
$375$	3.29440	+	5.70608i	0.170122	+	0.294661i
$376$	−4.98792			−0.257232
$377$		0			0
$378$	−0.356896			−0.0183567
$379$	−9.87800	−	17.1092i	−0.507399	−	0.878841i	−0.999963	−	0.00856468i	$-0.997274\pi$
$379$	−9.87800	−	17.1092i	−0.507399	−	0.878841i	0.492564	−	0.870276i	$-0.336060\pi$
$380$	−2.49396	−	4.31966i	−0.127937	−	0.221594i
$381$	9.10872	−	15.7768i	0.466654	−	0.808268i
$382$	15.2620			0.780874
$383$	−14.4058	+	24.9516i	−0.736103	+	1.27497i	0.218135	+	0.975919i	$0.430003\pi$
$383$	−14.4058	+	24.9516i	−0.736103	+	1.27497i	−0.954238	+	0.299049i	$0.903331\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	0.725873			0.0369939
$386$	−2.38404	+	4.12928i	−0.121345	+	0.210175i
$387$	−3.29590	−	5.70866i	−0.167540	−	0.290188i
$388$	−0.208947	−	0.361908i	−0.0106077	−	0.0183731i
$389$	34.7821			1.76352			0.881761	−	0.471697i	$-0.156358\pi$
$389$	34.7821			1.76352			0.881761	+	0.471697i	$0.156358\pi$
$390$		0			0
$391$	16.0871			0.813559
$392$	3.43631	+	5.95187i	0.173560	+	0.300615i
$393$	−1.36778	−	2.36907i	−0.0689954	−	0.119504i
$394$	−6.11745	+	10.5957i	−0.308193	+	0.533805i
$395$	10.4125			0.523911
$396$	1.46950	−	2.54525i	0.0738452	−	0.127904i
$397$	2.57673	−	4.46302i	0.129322	−	0.223993i	−0.794092	−	0.607798i	$-0.792053\pi$
$397$	2.57673	−	4.46302i	0.129322	−	0.223993i	0.923414	+	0.383805i	$0.125386\pi$
$398$	−11.8485			−0.593910
$399$	1.28621	−	2.22778i	0.0643910	−	0.111528i
$400$	2.26055	+	3.91539i	0.113028	+	0.195770i
$401$	−6.66248	−	11.5398i	−0.332708	−	0.576268i	0.650333	−	0.759649i	$-0.274629\pi$
$401$	−6.66248	−	11.5398i	−0.332708	−	0.576268i	−0.983042	+	0.183381i	$0.941296\pi$
$402$	−13.5254			−0.674587
$403$		0			0
$404$	10.0151			0.498268
$405$	−0.346011	−	0.599308i	−0.0171934	−	0.0297799i
$406$	1.39708	+	2.41982i	0.0693361	+	0.120094i
$407$	−14.8388	+	25.7015i	−0.735531	+	1.27398i
$408$	6.71379			0.332382
$409$	12.0118	−	20.8051i	0.593947	−	1.02875i	−0.399747	−	0.916626i	$-0.630902\pi$
$409$	12.0118	−	20.8051i	0.593947	−	1.02875i	0.993694	−	0.112122i	$-0.0357647\pi$
$410$	1.69202	−	2.93067i	0.0835630	−	0.144735i
$411$	7.64742			0.377219
$412$	4.81282	−	8.33605i	0.237111	−	0.410688i
$413$	−0.293209	−	0.507852i	−0.0144278	−	0.0249898i
$414$	−1.19806	−	2.07510i	−0.0588815	−	0.101986i
$415$	10.2604			0.503663
$416$		0			0
$417$	3.38404			0.165717
$418$	10.5918	+	18.3455i	0.518062	+	0.897309i
$419$	−6.90246	−	11.9554i	−0.337207	−	0.584060i	0.646699	−	0.762745i	$-0.276149\pi$
$419$	−6.90246	−	11.9554i	−0.337207	−	0.584060i	−0.983906	+	0.178685i	$0.942816\pi$
$420$	0.123490	−	0.213891i	0.00602569	−	0.0104368i
$421$	7.72587			0.376536			0.188268	−	0.982118i	$-0.439713\pi$
$421$	7.72587			0.376536			0.188268	+	0.982118i	$0.439713\pi$
$422$	8.63102	−	14.9494i	0.420152	−	0.727724i
$423$	2.49396	−	4.31966i	0.121260	−	0.210029i
$424$	−8.88769			−0.431624
$425$	15.1769	−	26.2871i	0.736187	−	1.27511i
$426$	3.40581	+	5.89904i	0.165012	+	0.285809i
$427$	−1.15883	−	2.00716i	−0.0560799	−	0.0971332i
$428$	−6.63102			−0.320523
$429$		0			0
$430$	4.56166			0.219983
$431$	−0.320060	−	0.554360i	−0.0154168	−	0.0267026i	0.858214	−	0.513292i	$-0.171574\pi$
$431$	−0.320060	−	0.554360i	−0.0154168	−	0.0267026i	−0.873631	+	0.486589i	$0.838241\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−10.6380	+	18.4256i	−0.511231	+	0.885478i	0.488685	+	0.872461i	$0.337477\pi$
$433$	−10.6380	+	18.4256i	−0.511231	+	0.885478i	−0.999915	+	0.0130171i	$0.995856\pi$
$434$	−0.985999			−0.0473295
$435$	−2.70895	+	4.69203i	−0.129884	+	0.224966i
$436$	6.49396	−	11.2479i	0.311004	−	0.538675i
$437$	17.2707			0.826168
$438$	1.59299	−	2.75914i	0.0761160	−	0.131837i
$439$	−6.35905	−	11.0142i	−0.303501	−	0.525679i	0.673425	−	0.739255i	$-0.264822\pi$
$439$	−6.35905	−	11.0142i	−0.303501	−	0.525679i	−0.976926	+	0.213576i	$0.931489\pi$
$440$	1.01693	+	1.76137i	0.0484800	+	0.0839699i
$441$	−6.87263			−0.327268
$442$		0			0
$443$	22.5972			1.07362			0.536812	−	0.843702i	$-0.319628\pi$
$443$	22.5972			1.07362			0.536812	+	0.843702i	$0.319628\pi$
$444$	5.04892	+	8.74498i	0.239611	+	0.415018i
$445$	0.137063	+	0.237401i	0.00649743	+	0.0112539i
$446$	−3.38404	+	5.86133i	−0.160239	+	0.277542i
$447$	−20.8170			−0.984610
$448$	0.178448	−	0.309081i	0.00843087	−	0.0146027i
$449$	−5.82371	+	10.0870i	−0.274838	+	0.476033i	−0.970094	−	0.242729i	$-0.921957\pi$
$449$	−5.82371	+	10.0870i	−0.274838	+	0.476033i	0.695256	+	0.718762i	$0.255291\pi$
$450$	−4.52111			−0.213127
$451$	−7.18598	+	12.4465i	−0.338375	+	0.586082i
$452$	−0.396125	−	0.686108i	−0.0186321	−	0.0322718i
$453$	0.447730	+	0.775492i	0.0210362	+	0.0364358i
$454$	23.6799			1.11135
$455$		0			0
$456$	7.20775			0.337534
$457$	10.5945	+	18.3502i	0.495589	+	0.858385i	0.999987	−	0.00508594i	$-0.00161891\pi$
$457$	10.5945	+	18.3502i	0.495589	+	0.858385i	−0.504398	+	0.863471i	$0.668286\pi$
$458$	4.14914	+	7.18653i	0.193877	+	0.335804i
$459$	−3.35690	+	5.81431i	−0.156686	+	0.271389i
$460$	1.65817			0.0773126
$461$	−12.0347	+	20.8447i	−0.560511	+	0.970833i	0.436941	+	0.899490i	$0.356062\pi$
$461$	−12.0347	+	20.8447i	−0.560511	+	0.970833i	−0.997452	+	0.0713432i	$0.977271\pi$
$462$	−0.524459	+	0.908389i	−0.0244000	+	0.0422621i
$463$	−18.1715			−0.844502			−0.422251	−	0.906479i	$-0.638760\pi$
$463$	−18.1715			−0.844502			−0.422251	+	0.906479i	$0.638760\pi$
$464$	−3.91454	+	6.78019i	−0.181728	+	0.314762i
$465$	−0.955927	−	1.65571i	−0.0443301	−	0.0767819i
$466$	11.9825	+	20.7544i	0.555081	+	0.961428i
$467$	−2.93123			−0.135641			−0.0678206	−	0.997698i	$-0.521605\pi$
$467$	−2.93123			−0.135641			−0.0678206	+	0.997698i	$0.521605\pi$
$468$		0			0
$469$	4.82717			0.222898
$470$	1.72587	+	2.98930i	0.0796086	+	0.137886i
$471$	−4.29590	−	7.44071i	−0.197944	−	0.342850i
$472$	0.821552	−	1.42297i	0.0378150	−	0.0654975i
$473$	−19.3733			−0.890785
$474$	−7.52326	+	13.0307i	−0.345555	+	0.598519i
$475$	16.2935	−	28.2212i	0.747597	−	1.29488i
$476$	−2.39612			−0.109826
$477$	4.44385	−	7.69697i	0.203470	−	0.352420i
$478$	−6.30798	−	10.9257i	−0.288520	−	0.499732i
$479$	15.3545	+	26.5948i	0.701565	+	1.21515i	0.967917	+	0.251271i	$0.0808484\pi$
$479$	15.3545	+	26.5948i	0.701565	+	1.21515i	−0.266352	+	0.963876i	$0.585818\pi$
$480$	0.692021			0.0315863
$481$		0			0
$482$	26.3937			1.20220
$483$	0.427583	+	0.740596i	0.0194557	+	0.0336983i
$484$	1.18114	+	2.04579i	0.0536880	+	0.0929904i
$485$	−0.144596	+	0.250448i	−0.00656577	+	0.0113722i
$486$	1.00000			0.0453609
$487$	−12.0749	+	20.9143i	−0.547164	+	0.947717i	0.451303	+	0.892371i	$0.350959\pi$
$487$	−12.0749	+	20.9143i	−0.547164	+	0.947717i	−0.998467	+	0.0553458i	$0.982374\pi$
$488$	3.24698	−	5.62393i	0.146984	−	0.254584i
$489$	1.72587			0.0780467
$490$	2.37800	−	4.11882i	0.107427	−	0.186069i
$491$	−7.29859	−	12.6415i	−0.329381	−	0.570504i	0.653009	−	0.757351i	$-0.273507\pi$
$491$	−7.29859	−	12.6415i	−0.329381	−	0.570504i	−0.982389	+	0.186847i	$0.940173\pi$
$492$	2.44504	+	4.23494i	0.110231	+	0.190926i
$493$	52.5628			2.36731
$494$		0			0
$495$	−2.03385			−0.0914148
$496$	−1.38135	−	2.39258i	−0.0620246	−	0.107430i
$497$	−1.21552	−	2.10534i	−0.0545236	−	0.0944376i
$498$	−7.41335	+	12.8403i	−0.332200	+	0.575387i
$499$	6.85517			0.306879			0.153440	−	0.988158i	$-0.450965\pi$
$499$	6.85517			0.306879			0.153440	+	0.988158i	$0.450965\pi$
$500$	3.29440	−	5.70608i	0.147330	−	0.255184i
$501$	−10.5700	+	18.3078i	−0.472234	+	0.817933i
$502$	−30.0344			−1.34050
$503$	13.3666	−	23.1516i	0.595987	−	1.03228i	−0.397420	−	0.917637i	$-0.630094\pi$
$503$	13.3666	−	23.1516i	0.595987	−	1.03228i	0.993407	−	0.114642i	$-0.0365722\pi$
$504$	0.178448	+	0.309081i	0.00794870	+	0.0137676i
$505$	−3.46532	−	6.00211i	−0.154205	−	0.267090i
$506$	−7.04221			−0.313065
$507$		0			0
$508$	−18.2174			−0.808268
$509$	10.3297	+	17.8916i	0.457858	+	0.793033i	0.998848	−	0.0479959i	$-0.0152835\pi$
$509$	10.3297	+	17.8916i	0.457858	+	0.793033i	−0.540989	+	0.841029i	$0.681950\pi$
$510$	−2.32304	−	4.02363i	−0.102866	−	0.178169i
$511$	−0.568532	+	0.984726i	−0.0251504	+	0.0435617i
$512$	1.00000			0.0441942
$513$	−3.60388	+	6.24210i	−0.159115	+	0.275595i
$514$	−5.63102	+	9.75322i	−0.248374	+	0.430196i
$515$	−6.66115			−0.293525
$516$	−3.29590	+	5.70866i	−0.145094	+	0.251310i
$517$	−7.32975	−	12.6955i	−0.322362	−	0.558347i
$518$	−1.80194	−	3.12105i	−0.0791726	−	0.137131i
$519$	9.35450			0.410617
$520$		0			0
$521$	−15.0965			−0.661390			−0.330695	−	0.943738i	$-0.607283\pi$
$521$	−15.0965			−0.661390			−0.330695	+	0.943738i	$0.607283\pi$
$522$	−3.91454	−	6.78019i	−0.171335	−	0.296761i
$523$	−0.0174584	−	0.0302388i	−0.000763402	−	0.00132225i	0.865643	−	0.500661i	$-0.166910\pi$
$523$	−0.0174584	−	0.0302388i	−0.000763402	−	0.00132225i	−0.866407	+	0.499339i	$0.833576\pi$
$524$	−1.36778	+	2.36907i	−0.0597518	+	0.103493i
$525$	1.61356			0.0704217
$526$	2.77479	−	4.80608i	0.120987	−	0.209555i
$527$	−9.27413	+	16.0633i	−0.403987	+	0.699727i
$528$	−2.93900			−0.127904
$529$	8.62929	−	14.9464i	0.375187	−	0.649842i
$530$	3.07524	+	5.32647i	0.133580	+	0.231367i
$531$	0.821552	+	1.42297i	0.0356523	+	0.0617516i
$532$	−2.57242			−0.111528
$533$		0			0
$534$	−0.396125			−0.0171420
$535$	2.29440	+	3.97403i	0.0991958	+	0.171812i
$536$	6.76271	+	11.7134i	0.292105	+	0.505940i
$537$	−1.58761	+	2.74983i	−0.0685106	+	0.118664i
$538$	16.6872			0.719438
$539$	−10.0993	+	17.4925i	−0.435009	+	0.753457i
$540$	−0.346011	+	0.599308i	−0.0148899	+	0.0257901i
$541$	13.0858			0.562600			0.281300	−	0.959620i	$-0.409234\pi$
$541$	13.0858			0.562600			0.281300	+	0.959620i	$0.409234\pi$
$542$	3.30678	−	5.72751i	0.142038	−	0.246018i
$543$	9.89977	+	17.1469i	0.424840	+	0.735844i
$544$	−3.35690	−	5.81431i	−0.143926	−	0.249287i
$545$	−8.98792			−0.385000
$546$		0			0
$547$	−5.97584			−0.255508			−0.127754	−	0.991806i	$-0.540777\pi$
$547$	−5.97584			−0.255508			−0.127754	+	0.991806i	$0.540777\pi$
$548$	−3.82371	−	6.62286i	−0.163341	−	0.282914i
$549$	3.24698	+	5.62393i	0.138578	+	0.240024i
$550$	−6.64377	+	11.5073i	−0.283291	+	0.490675i
$551$	56.4301			2.40400
$552$	−1.19806	+	2.07510i	−0.0509929	+	0.0883223i
$553$	2.68502	−	4.65059i	0.114179	−	0.197763i
$554$	−21.7995			−0.926174
$555$	3.49396	−	6.05171i	0.148310	−	0.256881i
$556$	−1.69202	−	2.93067i	−0.0717577	−	0.124288i
$557$	5.21983	+	9.04102i	0.221171	+	0.383080i	0.955164	−	0.296077i	$-0.0956786\pi$
$557$	5.21983	+	9.04102i	0.221171	+	0.383080i	−0.733993	+	0.679158i	$0.762345\pi$
$558$	2.76271			0.116955
$559$		0			0
$560$	−0.246980			−0.0104368
$561$	9.86592	+	17.0883i	0.416539	+	0.721468i
$562$	−10.2959	−	17.8330i	−0.434306	−	0.752240i
$563$	2.83028	−	4.90219i	0.119282	−	0.206603i	−0.800201	−	0.599732i	$-0.795274\pi$
$563$	2.83028	−	4.90219i	0.119282	−	0.206603i	0.919483	+	0.393129i	$0.128607\pi$
$564$	−4.98792			−0.210029
$565$	−0.274127	+	0.474801i	−0.0115326	+	0.0199750i
$566$	6.50604	−	11.2688i	0.273469	−	0.473663i
$567$	−0.356896			−0.0149882
$568$	3.40581	−	5.89904i	0.142905	−	0.247518i
$569$	−10.3284	−	17.8893i	−0.432990	−	0.749961i	0.564139	−	0.825680i	$-0.309208\pi$
$569$	−10.3284	−	17.8893i	−0.432990	−	0.749961i	−0.997129	+	0.0757191i	$0.975875\pi$
$570$	−2.49396	−	4.31966i	−0.104460	−	0.180931i
$571$	44.3672			1.85671			0.928354	−	0.371697i	$-0.121224\pi$
$571$	44.3672			1.85671			0.928354	+	0.371697i	$0.121224\pi$
$572$		0			0
$573$	15.2620			0.637581
$574$	−0.872625	−	1.51143i	−0.0364227	−	0.0630859i
$575$	5.41657	+	9.38177i	0.225886	+	0.391247i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	29.4426			1.22571			0.612857	−	0.790194i	$-0.290020\pi$
$577$	29.4426			1.22571			0.612857	+	0.790194i	$0.290020\pi$
$578$	−14.0375	+	24.3137i	−0.583883	+	1.01132i
$579$	−2.38404	+	4.12928i	−0.0990774	+	0.171607i
$580$	5.41789			0.224966
$581$	2.64579	−	4.58265i	0.109766	−	0.190120i
$582$	−0.208947	−	0.361908i	−0.00866115	−	0.0150015i
$583$	−13.0605	−	22.6214i	−0.540909	−	0.936882i
$584$	−3.18598			−0.131837
$585$		0			0
$586$	−14.9390			−0.617124
$587$	9.78179	+	16.9426i	0.403738	+	0.699294i	0.994174	−	0.107790i	$-0.0343775\pi$
$587$	9.78179	+	16.9426i	0.403738	+	0.699294i	−0.590436	+	0.807085i	$0.701044\pi$
$588$	3.43631	+	5.95187i	0.141711	+	0.245451i
$589$	−9.95646	+	17.2451i	−0.410249	+	0.710572i
$590$	−1.13706			−0.0468122
$591$	−6.11745	+	10.5957i	−0.251638	+	0.435850i
$592$	5.04892	−	8.74498i	0.207509	−	0.359417i
$593$	−10.8793			−0.446761			−0.223380	−	0.974731i	$-0.571709\pi$
$593$	−10.8793			−0.446761			−0.223380	+	0.974731i	$0.571709\pi$
$594$	1.46950	−	2.54525i	0.0602943	−	0.104433i
$595$	0.829085	+	1.43602i	0.0339892	+	0.0588710i
$596$	10.4085	+	18.0281i	0.426349	+	0.738458i
$597$	−11.8485			−0.484925
$598$		0			0
$599$	16.0543			0.655961			0.327980	−	0.944685i	$-0.393632\pi$
$599$	16.0543			0.655961			0.327980	+	0.944685i	$0.393632\pi$
$600$	2.26055	+	3.91539i	0.0922867	+	0.159845i
$601$	−6.44773	−	11.1678i	−0.263008	−	0.455544i	0.704032	−	0.710169i	$-0.251381\pi$
$601$	−6.44773	−	11.1678i	−0.263008	−	0.455544i	−0.967040	+	0.254625i	$0.918048\pi$
$602$	1.17629	−	2.03740i	0.0479421	−	0.0830381i
$603$	−13.5254			−0.550798
$604$	0.447730	−	0.775492i	0.0182179	−	0.0315543i
$605$	0.817372	−	1.41573i	0.0332309	−	0.0575576i
$606$	10.0151			0.406834
$607$	−22.2371	+	38.5157i	−0.902574	+	1.56330i	−0.0784334	+	0.996919i	$0.524992\pi$
$607$	−22.2371	+	38.5157i	−0.902574	+	1.56330i	−0.824141	+	0.566385i	$0.808342\pi$
$608$	−3.60388	−	6.24210i	−0.146156	−	0.253150i
$609$	1.39708	+	2.41982i	0.0566127	+	0.0980561i
$610$	−4.49396			−0.181955
$611$		0			0
$612$	6.71379			0.271389
$613$	−21.0127	−	36.3950i	−0.848694	−	1.46998i	−0.882374	−	0.470548i	$-0.844056\pi$
$613$	−21.0127	−	36.3950i	−0.848694	−	1.46998i	0.0336804	−	0.999433i	$-0.489277\pi$
$614$	−13.0151	−	22.5428i	−0.525245	−	0.909752i
$615$	1.69202	−	2.93067i	0.0682289	−	0.118176i
$616$	1.04892			0.0422621
$617$	8.33273	−	14.4327i	0.335463	−	0.581039i	−0.648111	−	0.761546i	$-0.724441\pi$
$617$	8.33273	−	14.4327i	0.335463	−	0.581039i	0.983574	+	0.180507i	$0.0577739\pi$
$618$	4.81282	−	8.33605i	0.193600	−	0.335325i
$619$	39.7512			1.59774			0.798868	−	0.601506i	$-0.205432\pi$
$619$	39.7512			1.59774			0.798868	+	0.601506i	$0.205432\pi$
$620$	−0.955927	+	1.65571i	−0.0383910	+	0.0664951i
$621$	−1.19806	−	2.07510i	−0.0480766	−	0.0832711i
$622$	2.40581	+	4.16699i	0.0964643	+	0.167081i
$623$	0.141375			0.00566408
$624$		0			0
$625$	18.0459			0.721837
$626$	13.0206	+	22.5523i	0.520407	+	0.901371i
$627$	10.5918	+	18.3455i	0.422996	+	0.732650i
$628$	−4.29590	+	7.44071i	−0.171425	+	0.296917i
$629$	−67.7948			−2.70315
$630$	0.123490	−	0.213891i	0.00491995	−	0.00852161i
$631$	−7.28836	+	12.6238i	−0.290145	+	0.502546i	−0.973844	−	0.227218i	$-0.927037\pi$
$631$	−7.28836	+	12.6238i	−0.290145	+	0.502546i	0.683699	+	0.729764i	$0.260370\pi$
$632$	15.0465			0.598519
$633$	8.63102	−	14.9494i	0.343052	−	0.594184i
$634$	5.76055	+	9.97757i	0.228781	+	0.396260i
$635$	6.30343	+	10.9179i	0.250144	+	0.433262i
$636$	−8.88769			−0.352420
$637$		0			0
$638$	−23.0097			−0.910962
$639$	3.40581	+	5.89904i	0.134732	+	0.233362i
$640$	−0.346011	−	0.599308i	−0.0136773	−	0.0236897i
$641$	−19.2174	+	33.2856i	−0.759043	+	1.31470i	0.184296	+	0.982871i	$0.441000\pi$
$641$	−19.2174	+	33.2856i	−0.759043	+	1.31470i	−0.943339	+	0.331831i	$0.892334\pi$
$642$	−6.63102			−0.261706
$643$	0.521106	−	0.902583i	0.0205504	−	0.0355944i	−0.855567	−	0.517692i	$-0.826791\pi$
$643$	0.521106	−	0.902583i	0.0205504	−	0.0355944i	0.876118	+	0.482097i	$0.160125\pi$
$644$	0.427583	−	0.740596i	0.0168491	−	0.0291836i
$645$	4.56166			0.179615
$646$	−24.1957	+	41.9081i	−0.951966	+	1.64885i
$647$	14.0804	+	24.3879i	0.553557	+	0.958788i	0.998014	+	0.0629884i	$0.0200631\pi$
$647$	14.0804	+	24.3879i	0.553557	+	0.958788i	−0.444458	+	0.895800i	$0.646604\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	4.82908			0.189558
$650$		0			0
$651$	−0.985999			−0.0386444
$652$	−0.862937	−	1.49465i	−0.0337952	−	0.0585350i
$653$	−5.31013	−	9.19742i	−0.207802	−	0.359923i	0.743220	−	0.669047i	$-0.233298\pi$
$653$	−5.31013	−	9.19742i	−0.207802	−	0.359923i	−0.951022	+	0.309124i	$0.899964\pi$
$654$	6.49396	−	11.2479i	0.253934	−	0.439826i
$655$	1.89307			0.0739683
$656$	2.44504	−	4.23494i	0.0954628	−	0.165347i
$657$	1.59299	−	2.75914i	0.0621485	−	0.107644i
$658$	1.78017			0.0693982
$659$	20.1814	−	34.9553i	0.786157	−	1.36166i	−0.142148	−	0.989845i	$-0.545401\pi$
$659$	20.1814	−	34.9553i	0.786157	−	1.36166i	0.928305	−	0.371818i	$-0.121266\pi$
$660$	1.01693	+	1.76137i	0.0395838	+	0.0685611i
$661$	15.9584	+	27.6407i	0.620709	+	1.07510i	0.989354	+	0.145529i	$0.0464885\pi$
$661$	15.9584	+	27.6407i	0.620709	+	1.07510i	−0.368645	+	0.929570i	$0.620178\pi$
$662$	3.43834			0.133635
$663$		0			0
$664$	14.8267			0.575387
$665$	0.890084	+	1.54167i	0.0345160	+	0.0597834i
$666$	5.04892	+	8.74498i	0.195642	+	0.338861i
$667$	−9.37973	+	16.2462i	−0.363185	+	0.629054i
$668$	21.1400			0.817933
$669$	−3.38404	+	5.86133i	−0.130835	+	0.226612i
$670$	4.67994	−	8.10589i	0.180802	−	0.313158i
$671$	19.0858			0.736797
$672$	0.178448	−	0.309081i	0.00688378	−	0.0119231i
$673$	−1.91401	−	3.31516i	−0.0737797	−	0.127790i	0.826775	−	0.562532i	$-0.190173\pi$
$673$	−1.91401	−	3.31516i	−0.0737797	−	0.127790i	−0.900555	+	0.434742i	$0.856839\pi$
$674$	−4.10052	−	7.10231i	−0.157946	−	0.273571i
$675$	−4.52111			−0.174017
$676$		0			0
$677$	1.78927			0.0687670			0.0343835	−	0.999409i	$-0.489053\pi$
$677$	1.78927			0.0687670			0.0343835	+	0.999409i	$0.489053\pi$
$678$	−0.396125	−	0.686108i	−0.0152131	−	0.0263498i
$679$	0.0745725	+	0.129163i	0.00286183	+	0.00495683i
$680$	−2.32304	+	4.02363i	−0.0890847	+	0.154299i
$681$	23.6799			0.907417
$682$	4.05980	−	7.03178i	0.155458	−	0.269261i
$683$	−0.379863	+	0.657941i	−0.0145350	+	0.0251754i	−0.873201	−	0.487359i	$-0.837960\pi$
$683$	−0.379863	+	0.657941i	−0.0145350	+	0.0251754i	0.858666	+	0.512535i	$0.171293\pi$
$684$	7.20775			0.275595
$685$	−2.64609	+	4.58316i	−0.101102	+	0.175114i
$686$	−2.47554	−	4.28776i	−0.0945166	−	0.163708i
$687$	4.14914	+	7.18653i	0.158300	+	0.274183i
$688$	6.59179			0.251310
$689$		0			0
$690$	1.65817			0.0631254
$691$	−2.32975	−	4.03524i	−0.0886278	−	0.153508i	0.818304	−	0.574786i	$-0.194915\pi$
$691$	−2.32975	−	4.03524i	−0.0886278	−	0.153508i	−0.906931	+	0.421278i	$0.861582\pi$
$692$	−4.67725	−	8.10124i	−0.177802	−	0.307963i
$693$	−0.524459	+	0.908389i	−0.0199225	+	0.0345068i
$694$	7.86294			0.298473
$695$	−1.17092	+	2.02808i	−0.0444153	+	0.0769296i
$696$	−3.91454	+	6.78019i	−0.148380	+	0.257002i
$697$	−32.8310			−1.24356
$698$	9.36227	−	16.2159i	0.354367	−	0.613782i
$699$	11.9825	+	20.7544i	0.453221	+	0.785002i
$700$	−0.806782	−	1.39739i	−0.0304935	−	0.0528163i
$701$	−24.3284			−0.918872			−0.459436	−	0.888211i	$-0.651948\pi$
$701$	−24.3284			−0.918872			−0.459436	+	0.888211i	$0.651948\pi$
$702$		0			0
$703$	−72.7827			−2.74505
$704$	1.46950	+	2.54525i	0.0553839	+	0.0959277i
$705$	1.72587	+	2.98930i	0.0650001	+	0.112584i
$706$	15.7724	−	27.3186i	0.593602	−	1.02815i
$707$	−3.57434			−0.134427
$708$	0.821552	−	1.42297i	0.0308758	−	0.0534785i
$709$	14.6963	−	25.4548i	0.551932	−	0.955975i	−0.446203	−	0.894932i	$-0.647224\pi$
$709$	14.6963	−	25.4548i	0.551932	−	0.955975i	0.998135	−	0.0610430i	$-0.0194427\pi$
$710$	−4.71379			−0.176905
$711$	−7.52326	+	13.0307i	−0.282144	+	0.488688i
$712$	0.198062	+	0.343054i	0.00742270	+	0.0128565i
$713$	−3.30990	−	5.73291i	−0.123957	−	0.214699i
$714$	−2.39612			−0.0896727
$715$		0			0
$716$	3.17523			0.118664
$717$	−6.30798	−	10.9257i	−0.235576	−	0.408029i
$718$	−1.19806	−	2.07510i	−0.0447113	−	0.0774422i
$719$	25.7439	−	44.5898i	0.960086	−	1.66292i	0.237812	−	0.971311i	$-0.423570\pi$
$719$	25.7439	−	44.5898i	0.960086	−	1.66292i	0.722274	−	0.691607i	$-0.243097\pi$
$720$	0.692021			0.0257901
$721$	−1.71768	+	2.97510i	−0.0639696	+	0.110799i
$722$	−16.4758	+	28.5370i	−0.613167	+	1.06204i
$723$	26.3937			0.981593
$724$	9.89977	−	17.1469i	0.367922	−	0.637260i
$725$	17.6981	+	30.6539i	0.657290	+	1.13846i
$726$	1.18114	+	2.04579i	0.0438361	+	0.0759263i
$727$	−3.67324			−0.136233			−0.0681164	−	0.997677i	$-0.521699\pi$
$727$	−3.67324			−0.136233			−0.0681164	+	0.997677i	$0.521699\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.10238	+	1.90938i	0.0408010	+	0.0706695i
$731$	−22.1280	−	38.3268i	−0.818432	−	1.41757i
$732$	3.24698	−	5.62393i	0.120012	−	0.207867i
$733$	18.3612			0.678187			0.339093	−	0.940753i	$-0.389880\pi$
$733$	18.3612			0.678187			0.339093	+	0.940753i	$0.389880\pi$
$734$	0.00215593	−	0.00373419i	7.95770e−5	−	0.000137831i
$735$	2.37800	−	4.11882i	0.0877139	−	0.151925i
$736$	2.39612			0.0883223
$737$	−19.8756	+	34.4256i	−0.732127	+	1.26808i
$738$	2.44504	+	4.23494i	0.0900032	+	0.155890i
$739$	−0.841166	−	1.45694i	−0.0309428	−	0.0535945i	0.850139	−	0.526558i	$-0.176518\pi$
$739$	−0.841166	−	1.45694i	−0.0309428	−	0.0535945i	−0.881082	+	0.472963i	$0.843184\pi$
$740$	−6.98792			−0.256881
$741$		0			0
$742$	3.17198			0.116447
$743$	−24.1468	−	41.8234i	−0.885858	−	1.53435i	−0.844727	−	0.535198i	$-0.820237\pi$
$743$	−24.1468	−	41.8234i	−0.885858	−	1.53435i	−0.0411318	−	0.999154i	$-0.513096\pi$
$744$	−1.38135	−	2.39258i	−0.0506429	−	0.0877161i
$745$	7.20291	−	12.4758i	0.263894	−	0.457078i
$746$	−32.3129			−1.18306
$747$	−7.41335	+	12.8403i	−0.271240	+	0.469802i
$748$	9.86592	−	17.0883i	0.360734	−	0.624809i
$749$	2.36658			0.0864731
$750$	3.29440	−	5.70608i	0.120295	−	0.208356i
$751$	−5.85056	−	10.1335i	−0.213490	−	0.369775i	0.739314	−	0.673360i	$-0.235150\pi$
$751$	−5.85056	−	10.1335i	−0.213490	−	0.369775i	−0.952804	+	0.303585i	$0.901816\pi$
$752$	2.49396	+	4.31966i	0.0909453	+	0.157522i
$753$	−30.0344			−1.09452
$754$		0			0
$755$	−0.619678			−0.0225524
$756$	0.178448	+	0.309081i	0.00649009	+	0.0112412i
$757$	−12.5918	−	21.8096i	−0.457657	−	0.792684i	0.541180	−	0.840907i	$-0.317978\pi$
$757$	−12.5918	−	21.8096i	−0.457657	−	0.792684i	−0.998837	+	0.0482223i	$0.984644\pi$
$758$	−9.87800	+	17.1092i	−0.358785	+	0.621434i
$759$	−7.04221			−0.255616
$760$	−2.49396	+	4.31966i	−0.0904654	+	0.156691i
$761$	−11.2078	+	19.4124i	−0.406281	+	0.703699i	−0.994470	−	0.105025i	$-0.966508\pi$
$761$	−11.2078	+	19.4124i	−0.406281	+	0.703699i	0.588189	+	0.808724i	$0.299841\pi$
$762$	−18.2174			−0.659948
$763$	−2.31767	+	4.01432i	−0.0839052	+	0.145328i
$764$	−7.63102	−	13.2173i	−0.276081	−	0.478186i
$765$	−2.32304	−	4.02363i	−0.0839898	−	0.145475i
$766$	28.8116			1.04101
$767$		0			0
$768$	1.00000			0.0360844
$769$	0.0663757	+	0.114966i	0.00239357	+	0.00414579i	0.867220	−	0.497926i	$-0.165905\pi$
$769$	0.0663757	+	0.114966i	0.00239357	+	0.00414579i	−0.864826	+	0.502071i	$0.832571\pi$
$770$	−0.362937	−	0.628625i	−0.0130793	−	0.0226541i
$771$	−5.63102	+	9.75322i	−0.202796	+	0.351254i
$772$	4.76809			0.171607
$773$	24.0347	−	41.6293i	0.864467	−	1.49730i	−0.00310775	−	0.999995i	$-0.500989\pi$
$773$	24.0347	−	41.6293i	0.864467	−	1.49730i	0.867575	−	0.497306i	$-0.165677\pi$
$774$	−3.29590	+	5.70866i	−0.118469	+	0.205194i
$775$	−12.4905			−0.448672
$776$	−0.208947	+	0.361908i	−0.00750077	+	0.0129917i
$777$	−1.80194	−	3.12105i	−0.0646442	−	0.111967i
$778$	−17.3910	−	30.1222i	−0.623499	−	1.07993i
$779$	−35.2465			−1.26284
$780$		0			0
$781$	20.0194			0.716350
$782$	−8.04354	−	13.9318i	−0.287636	−	0.498201i
$783$	−3.91454	−	6.78019i	−0.139894	−	0.242304i
$784$	3.43631	−	5.95187i	0.122725	−	0.212567i
$785$	5.94571			0.212211
$786$	−1.36778	+	2.36907i	−0.0487871	+	0.0845018i
$787$	−3.10454	+	5.37722i	−0.110665	+	0.191677i	−0.916039	−	0.401090i	$-0.868631\pi$
$787$	−3.10454	+	5.37722i	−0.110665	+	0.191677i	0.805374	+	0.592767i	$0.201965\pi$
$788$	12.2349			0.435850
$789$	2.77479	−	4.80608i	0.0987852	−	0.171101i
$790$	−5.20626	−	9.01751i	−0.185230	−	0.320828i
$791$	0.141375	+	0.244869i	0.00502672	+	0.00870654i
$792$	−2.93900			−0.104433
$793$		0			0
$794$	−5.15346			−0.182889
$795$	3.07524	+	5.32647i	0.109067	+	0.188910i
$796$	5.92423	+	10.2611i	0.209979	+	0.363694i
$797$	−0.163915	+	0.283909i	−0.00580616	+	0.0100566i	−0.868914	−	0.494963i	$-0.835182\pi$
$797$	−0.163915	+	0.283909i	−0.00580616	+	0.0100566i	0.863108	+	0.505020i	$0.168515\pi$
$798$	−2.57242			−0.0910626
$799$	16.7439	−	29.0013i	0.592357	−	1.02599i
$800$	2.26055	−	3.91539i	0.0799226	−	0.138430i
$801$	−0.396125			−0.0139964
$802$	−6.66248	+	11.5398i	−0.235260	+	0.407483i
$803$	−4.68180	−	8.10912i	−0.165217	−	0.286164i
$804$	6.76271	+	11.7134i	0.238502	+	0.413098i
$805$	−0.591794			−0.0208580
$806$		0			0
$807$	16.6872			0.587419
$808$	−5.00753	−	8.67330i	−0.176164	−	0.305126i
$809$	18.7192	+	32.4226i	0.658131	+	1.13992i	0.981099	+	0.193506i	$0.0619860\pi$
$809$	18.7192	+	32.4226i	0.658131	+	1.13992i	−0.322968	+	0.946410i	$0.604681\pi$
$810$	−0.346011	+	0.599308i	−0.0121576	+	0.0210575i
$811$	17.1448			0.602037			0.301018	−	0.953618i	$-0.402673\pi$
$811$	17.1448			0.602037			0.301018	+	0.953618i	$0.402673\pi$
$812$	1.39708	−	2.41982i	0.0490280	−	0.0849191i
$813$	3.30678	−	5.72751i	0.115974	−	0.200873i
$814$	29.6775			1.04020
$815$	−0.597171	+	1.03433i	−0.0209180	+	0.0362310i
$816$	−3.35690	−	5.81431i	−0.117515	−	0.203542i
$817$	−23.7560	−	41.1466i	−0.831117	−	1.43954i
$818$	−24.0237			−0.839969
$819$		0			0
$820$	−3.38404			−0.118176
$821$	8.89426	+	15.4053i	0.310412	+	0.537649i	0.978452	−	0.206476i	$-0.0661997\pi$
$821$	8.89426	+	15.4053i	0.310412	+	0.537649i	−0.668040	+	0.744126i	$0.732866\pi$
$822$	−3.82371	−	6.62286i	−0.133367	−	0.230999i
$823$	−6.11506	+	10.5916i	−0.213157	+	0.369200i	−0.952701	−	0.303909i	$-0.901708\pi$
$823$	−6.11506	+	10.5916i	−0.213157	+	0.369200i	0.739544	+	0.673109i	$0.235041\pi$
$824$	−9.62565			−0.335325
$825$	−6.64377	+	11.5073i	−0.231306	+	0.400634i
$826$	−0.293209	+	0.507852i	−0.0102020	+	0.0176704i
$827$	20.5623			0.715020			0.357510	−	0.933909i	$-0.383626\pi$
$827$	20.5623			0.715020			0.357510	+	0.933909i	$0.383626\pi$
$828$	−1.19806	+	2.07510i	−0.0416355	+	0.0721149i
$829$	12.7235	+	22.0377i	0.441905	+	0.765401i	0.997831	−	0.0658303i	$-0.0209696\pi$
$829$	12.7235	+	22.0377i	0.441905	+	0.765401i	−0.555926	+	0.831232i	$0.687636\pi$
$830$	−5.13019	−	8.88576i	−0.178072	−	0.308429i
$831$	−21.7995			−0.756218
$832$		0			0
$833$	−46.1414			−1.59870
$834$	−1.69202	−	2.93067i	−0.0585899	−	0.101481i
$835$	−7.31468	−	12.6694i	−0.253135	−	0.438443i
$836$	10.5918	−	18.3455i	0.366325	−	0.634493i
$837$	2.76271			0.0954932
$838$	−6.90246	+	11.9554i	−0.238442	+	0.412993i
$839$	−2.88338	+	4.99416i	−0.0995453	+	0.172418i	−0.911497	−	0.411308i	$-0.865072\pi$
$839$	−2.88338	+	4.99416i	−0.0995453	+	0.172418i	0.811951	+	0.583725i	$0.198405\pi$
$840$	−0.246980			−0.00852161
$841$	−16.1473	+	27.9679i	−0.556803	+	0.964411i
$842$	−3.86294	−	6.69080i	−0.133126	−	0.230580i
$843$	−10.2959	−	17.8330i	−0.354610	−	0.614202i
$844$	−17.2620			−0.594184
$845$		0			0
$846$	−4.98792			−0.171488
$847$	−0.421543	−	0.730133i	−0.0144844	−	0.0250877i
$848$	4.44385	+	7.69697i	0.152602	+	0.264315i
$849$	6.50604	−	11.2688i	0.223287	−	0.386744i
$850$	−30.3538			−1.04113
$851$	12.0978	−	20.9541i	0.414708	−	0.718296i
$852$	3.40581	−	5.89904i	0.116681	−	0.202098i
$853$	−21.1728			−0.724944			−0.362472	−	0.931995i	$-0.618067\pi$
$853$	−21.1728			−0.724944			−0.362472	+	0.931995i	$0.618067\pi$
$854$	−1.15883	+	2.00716i	−0.0396545	+	0.0686836i
$855$	−2.49396	−	4.31966i	−0.0852916	−	0.147729i
$856$	3.31551	+	5.74263i	0.113322	+	0.196279i
$857$	12.0086			0.410207			0.205103	−	0.978740i	$-0.434247\pi$
$857$	12.0086			0.410207			0.205103	+	0.978740i	$0.434247\pi$
$858$		0			0
$859$	−1.66296			−0.0567393			−0.0283697	−	0.999598i	$-0.509032\pi$
$859$	−1.66296			−0.0567393			−0.0283697	+	0.999598i	$0.509032\pi$
$860$	−2.28083	−	3.95052i	−0.0777757	−	0.134711i
$861$	−0.872625	−	1.51143i	−0.0297390	−	0.0515094i
$862$	−0.320060	+	0.554360i	−0.0109013	+	0.0188816i
$863$	−23.8323			−0.811262			−0.405631	−	0.914037i	$-0.632948\pi$
$863$	−23.8323			−0.811262			−0.405631	+	0.914037i	$0.632948\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−3.23676	+	5.60623i	−0.110053	+	0.190618i
$866$	21.2760			0.722989
$867$	−14.0375	+	24.3137i	−0.476738	+	0.825735i
$868$	0.493000	+	0.853901i	0.0167335	+	0.0289833i
$869$	22.1109	+	38.2972i	0.750060	+	1.29914i
$870$	5.41789			0.183684
$871$		0			0
$872$	−12.9879			−0.439826
$873$	−0.208947	−	0.361908i	−0.00707180	−	0.0122487i
$874$	−8.63533	−	14.9568i	−0.292095	−	0.505923i
$875$	−1.17576	+	2.03648i	−0.0397479	+	0.0688454i
$876$	−3.18598			−0.107644
$877$	21.1588	−	36.6482i	0.714483	−	1.23752i	−0.248676	−	0.968587i	$-0.579995\pi$
$877$	21.1588	−	36.6482i	0.714483	−	1.23752i	0.963159	−	0.268934i	$-0.0866714\pi$
$878$	−6.35905	+	11.0142i	−0.214608	+	0.371711i
$879$	−14.9390			−0.503880
$880$	1.01693	−	1.76137i	0.0342806	−	0.0593757i
$881$	−11.1371	−	19.2900i	−0.375217	−	0.649895i	0.615142	−	0.788416i	$-0.289099\pi$
$881$	−11.1371	−	19.2900i	−0.375217	−	0.649895i	−0.990360	+	0.138521i	$0.955765\pi$
$882$	3.43631	+	5.95187i	0.115707	+	0.200410i
$883$	−8.54229			−0.287471			−0.143735	−	0.989616i	$-0.545911\pi$
$883$	−8.54229			−0.287471			−0.143735	+	0.989616i	$0.545911\pi$
$884$		0			0
$885$	−1.13706			−0.0382220
$886$	−11.2986	−	19.5697i	−0.379583	−	0.657458i
$887$	9.45712	+	16.3802i	0.317539	+	0.549994i	0.979974	−	0.199126i	$-0.0638102\pi$
$887$	9.45712	+	16.3802i	0.317539	+	0.549994i	−0.662435	+	0.749120i	$0.730477\pi$
$888$	5.04892	−	8.74498i	0.169431	−	0.293462i
$889$	6.50173			0.218061
$890$	0.137063	−	0.237401i	0.00459437	−	0.00795769i
$891$	1.46950	−	2.54525i	0.0492301	−	0.0852691i
$892$	6.76809			0.226612
$893$	17.9758	−	31.1351i	0.601538	−	1.04190i
$894$	10.4085	+	18.0281i	0.348112	+	0.602948i
$895$	−1.09866	−	1.90294i	−0.0367242	−	0.0636083i
$896$	−0.356896			−0.0119231
$897$		0			0
$898$	11.6474			0.388679
$899$	−10.8147	−	18.7317i	−0.360692	−	0.624737i
$900$	2.26055	+	3.91539i	0.0753518	+	0.130513i
$901$	29.8351	−	51.6758i	0.993950	−	1.72157i
$902$	14.3720			0.478534
$903$	1.17629	−	2.03740i	0.0391445	−	0.0678003i
$904$	−0.396125	+	0.686108i	−0.0131749	+	0.0228196i
$905$	−13.7017			−0.455460
$906$	0.447730	−	0.775492i	0.0148748	−	0.0257640i
$907$	−6.97584	−	12.0825i	−0.231629	−	0.401193i	0.726659	−	0.686999i	$-0.241072\pi$
$907$	−6.97584	−	12.0825i	−0.231629	−	0.401193i	−0.958288	+	0.285806i	$0.907739\pi$
$908$	−11.8400	−	20.5074i	−0.392923	−	0.680563i
$909$	10.0151			0.332179
$910$		0			0
$911$	45.0422			1.49232			0.746158	−	0.665769i	$-0.231897\pi$
$911$	45.0422			1.49232			0.746158	+	0.665769i	$0.231897\pi$
$912$	−3.60388	−	6.24210i	−0.119336	−	0.206696i
$913$	21.7878	+	37.7376i	0.721072	+	1.24893i
$914$	10.5945	−	18.3502i	0.350434	−	0.606970i
$915$	−4.49396			−0.148566
$916$	4.14914	−	7.18653i	0.137092	−	0.237450i
$917$	0.488155	−	0.845510i	0.0161203	−	0.0279212i
$918$	6.71379			0.221588
$919$	−19.9988	+	34.6389i	−0.659700	+	1.14263i	0.320994	+	0.947081i	$0.395983\pi$
$919$	−19.9988	+	34.6389i	−0.659700	+	1.14263i	−0.980693	+	0.195552i	$0.937350\pi$
$920$	−0.829085	−	1.43602i	−0.0273341	−	0.0473441i
$921$	−13.0151	−	22.5428i	−0.428861	−	0.742809i
$922$	24.0694			0.792682
$923$		0			0
$924$	1.04892			0.0345068
$925$	−22.8267	−	39.5370i	−0.750537	−	1.29997i
$926$	9.08575	+	15.7370i	0.298576	+	0.517149i
$927$	4.81282	−	8.33605i	0.158074	−	0.273792i
$928$	7.82908			0.257002
$929$	−17.3424	+	30.0380i	−0.568986	+	0.985513i	0.427680	+	0.903930i	$0.359331\pi$
$929$	−17.3424	+	30.0380i	−0.568986	+	0.985513i	−0.996667	+	0.0815832i	$0.974002\pi$
$930$	−0.955927	+	1.65571i	−0.0313461	+	0.0542930i
$931$	−49.5362			−1.62348
$932$	11.9825	−	20.7544i	0.392501	−	0.679832i
$933$	2.40581	+	4.16699i	0.0787628	+	0.136421i
$934$	1.46562	+	2.53852i	0.0479564	+	0.0830629i
$935$	−13.6549			−0.446562
$936$		0			0
$937$	−19.1260			−0.624821			−0.312410	−	0.949947i	$-0.601136\pi$
$937$	−19.1260			−0.624821			−0.312410	+	0.949947i	$0.601136\pi$
$938$	−2.41358	−	4.18045i	−0.0788063	−	0.136496i
$939$	13.0206	+	22.5523i	0.424910	+	0.735966i
$940$	1.72587	−	2.98930i	0.0562918	−	0.0975002i
$941$	−22.5972			−0.736647			−0.368323	−	0.929698i	$-0.620068\pi$
$941$	−22.5972			−0.736647			−0.368323	+	0.929698i	$0.620068\pi$
$942$	−4.29590	+	7.44071i	−0.139968	+	0.242431i
$943$	5.85862	−	10.1474i	0.190783	−	0.330446i
$944$	−1.64310			−0.0534785
$945$	0.123490	−	0.213891i	0.00401712	−	0.00695786i
$946$	9.68664	+	16.7778i	0.314940	+	0.545492i
$947$	13.7180	+	23.7602i	0.445774	+	0.772104i	0.998106	−	0.0615209i	$-0.0195951\pi$
$947$	13.7180	+	23.7602i	0.445774	+	0.772104i	−0.552332	+	0.833625i	$0.686262\pi$
$948$	15.0465			0.488688
$949$		0			0
$950$	−32.5870			−1.05726
$951$	5.76055	+	9.97757i	0.186799	+	0.323545i
$952$	1.19806	+	2.07510i	0.0388294	+	0.0672545i
$953$	0.923936	−	1.60030i	0.0299292	−	0.0518389i	−0.850673	−	0.525695i	$-0.823805\pi$
$953$	0.923936	−	1.60030i	0.0299292	−	0.0518389i	0.880602	+	0.473857i	$0.157138\pi$
$954$	−8.88769			−0.287750
$955$	−5.28083	+	9.14667i	−0.170884	+	0.295979i
$956$	−6.30798	+	10.9257i	−0.204015	+	0.353364i
$957$	−23.0097			−0.743798
$958$	15.3545	−	26.5948i	0.496081	−	0.859238i
$959$	1.36467	+	2.36367i	0.0440674	+	0.0763269i
$960$	−0.346011	−	0.599308i	−0.0111674	−	0.0193426i
$961$	−23.3674			−0.753788
$962$		0			0
$963$	−6.63102			−0.213682
$964$	−13.1969	−	22.8576i	−0.425042	−	0.736195i
$965$	−1.64981	−	2.85755i	−0.0531092	−	0.0919879i
$966$	0.427583	−	0.740596i	0.0137573	−	0.0238283i
$967$	−8.88471			−0.285713			−0.142856	−	0.989743i	$-0.545629\pi$
$967$	−8.88471			−0.285713			−0.142856	+	0.989743i	$0.545629\pi$
$968$	1.18114	−	2.04579i	0.0379632	−	0.0657541i
$969$	−24.1957	+	41.9081i	−0.777277	+	1.34628i
$970$	0.289192			0.00928540
$971$	−17.5432	+	30.3857i	−0.562987	+	0.975122i	0.434247	+	0.900794i	$0.357015\pi$
$971$	−17.5432	+	30.3857i	−0.562987	+	0.975122i	−0.997234	+	0.0743284i	$0.976319\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	0.603875	+	1.04594i	0.0193594	+	0.0335314i
$974$	24.1497			0.773807
$975$		0			0
$976$	−6.49396			−0.207867
$977$	4.16852	+	7.22009i	0.133363	+	0.230991i	0.924971	−	0.380038i	$-0.124089\pi$
$977$	4.16852	+	7.22009i	0.133363	+	0.230991i	−0.791608	+	0.611029i	$0.790756\pi$
$978$	−0.862937	−	1.49465i	−0.0275937	−	0.0477936i
$979$	−0.582105	+	1.00824i	−0.0186042	+	0.0322234i
$980$	−4.75600			−0.151925
$981$	6.49396	−	11.2479i	0.207336	−	0.359117i
$982$	−7.29859	+	12.6415i	−0.232907	+	0.403407i
$983$	−55.6051			−1.77353			−0.886763	−	0.462224i	$-0.847051\pi$
$983$	−55.6051			−1.77353			−0.886763	+	0.462224i	$0.847051\pi$
$984$	2.44504	−	4.23494i	0.0779451	−	0.135005i
$985$	−4.23341	−	7.33247i	−0.134888	−	0.233632i
$986$	−26.2814	−	45.5208i	−0.836971	−	1.44968i
$987$	1.78017			0.0566634
$988$		0			0
$989$	15.7948			0.502244
$990$	1.01693	+	1.76137i	0.0323200	+	0.0559799i
$991$	21.7983	+	37.7558i	0.692447	+	1.19935i	0.971034	+	0.238943i	$0.0768008\pi$
$991$	21.7983	+	37.7558i	0.692447	+	1.19935i	−0.278586	+	0.960411i	$0.589866\pi$
$992$	−1.38135	+	2.39258i	−0.0438581	+	0.0759644i
$993$	3.43834			0.109112
$994$	−1.21552	+	2.10534i	−0.0385540	+	0.0667774i
$995$	4.09970	−	7.10088i	0.129969	−	0.225113i
$996$	14.8267			0.469802
$997$	−11.2295	+	19.4501i	−0.355643	+	0.615991i	−0.987228	−	0.159316i	$-0.949071\pi$
$997$	−11.2295	+	19.4501i	−0.355643	+	0.615991i	0.631585	+	0.775306i	$0.282405\pi$
$998$	−3.42758	−	5.93675i	−0.108498	−	0.187924i
$999$	5.04892	+	8.74498i	0.159741	+	0.276679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.k.991.3		6
13.2	odd	12		1014.2.b.g.337.1		6
13.3	even	3		1014.2.a.o.1.3	yes	3
13.4	even	6		1014.2.e.m.529.1		6
13.5	odd	4		1014.2.i.g.361.1		12
13.6	odd	12		1014.2.i.g.823.4		12
13.7	odd	12		1014.2.i.g.823.3		12
13.8	odd	4		1014.2.i.g.361.6		12
13.9	even	3	inner	1014.2.e.k.529.3		6
13.10	even	6		1014.2.a.m.1.1	✓	3
13.11	odd	12		1014.2.b.g.337.6		6
13.12	even	2		1014.2.e.m.991.1		6
39.2	even	12		3042.2.b.r.1351.6		6
39.11	even	12		3042.2.b.r.1351.1		6
39.23	odd	6		3042.2.a.be.1.3		3
39.29	odd	6		3042.2.a.bd.1.1		3
52.3	odd	6		8112.2.a.bz.1.3		3
52.23	odd	6		8112.2.a.ce.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.1	✓	3	13.10	even	6
1014.2.a.o.1.3	yes	3	13.3	even	3
1014.2.b.g.337.1		6	13.2	odd	12
1014.2.b.g.337.6		6	13.11	odd	12
1014.2.e.k.529.3		6	13.9	even	3	inner
1014.2.e.k.991.3		6	1.1	even	1	trivial
1014.2.e.m.529.1		6	13.4	even	6
1014.2.e.m.991.1		6	13.12	even	2
1014.2.i.g.361.1		12	13.5	odd	4
1014.2.i.g.361.6		12	13.8	odd	4
1014.2.i.g.823.3		12	13.7	odd	12
1014.2.i.g.823.4		12	13.6	odd	12
3042.2.a.bd.1.1		3	39.29	odd	6
3042.2.a.be.1.3		3	39.23	odd	6
3042.2.b.r.1351.1		6	39.11	even	12
3042.2.b.r.1351.6		6	39.2	even	12
8112.2.a.bz.1.3		3	52.3	odd	6
8112.2.a.ce.1.1		3	52.23	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.346011 - 0.599308i) q^{10} +(1.46950 + 2.54525i) q^{11} +1.00000 q^{12} -0.356896 q^{14} +(-0.346011 - 0.599308i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.35690 + 5.81431i) q^{17} +1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(-0.346011 + 0.599308i) q^{20} -0.356896 q^{21} +(1.46950 - 2.54525i) q^{22} +(-1.19806 - 2.07510i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.52111 q^{25} +1.00000 q^{27} +(0.178448 + 0.309081i) q^{28} +(-3.91454 - 6.78019i) q^{29} +(-0.346011 + 0.599308i) q^{30} +2.76271 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.46950 - 2.54525i) q^{33} +6.71379 q^{34} +(0.123490 - 0.213891i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.04892 + 8.74498i) q^{37} +7.20775 q^{38} +0.692021 q^{40} +(2.44504 + 4.23494i) q^{41} +(0.178448 + 0.309081i) q^{42} +(-3.29590 + 5.70866i) q^{43} -2.93900 q^{44} +(-0.346011 + 0.599308i) q^{45} +(-1.19806 + 2.07510i) q^{46} -4.98792 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.43631 + 5.95187i) q^{49} +(2.26055 + 3.91539i) q^{50} +6.71379 q^{51} -8.88769 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.01693 + 1.76137i) q^{55} +(0.178448 - 0.309081i) q^{56} +7.20775 q^{57} +(-3.91454 + 6.78019i) q^{58} +(0.821552 - 1.42297i) q^{59} +0.692021 q^{60} +(3.24698 - 5.62393i) q^{61} +(-1.38135 - 2.39258i) q^{62} +(0.178448 + 0.309081i) q^{63} +1.00000 q^{64} -2.93900 q^{66} +(6.76271 + 11.7134i) q^{67} +(-3.35690 - 5.81431i) q^{68} +(-1.19806 + 2.07510i) q^{69} -0.246980 q^{70} +(3.40581 - 5.89904i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.18598 q^{73} +(5.04892 - 8.74498i) q^{74} +(2.26055 + 3.91539i) q^{75} +(-3.60388 - 6.24210i) q^{76} +1.04892 q^{77} +15.0465 q^{79} +(-0.346011 - 0.599308i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.44504 - 4.23494i) q^{82} +14.8267 q^{83} +(0.178448 - 0.309081i) q^{84} +(-2.32304 + 4.02363i) q^{85} +6.59179 q^{86} +(-3.91454 + 6.78019i) q^{87} +(1.46950 + 2.54525i) q^{88} +(0.198062 + 0.343054i) q^{89} +0.692021 q^{90} +2.39612 q^{92} +(-1.38135 - 2.39258i) q^{93} +(2.49396 + 4.31966i) q^{94} +(-2.49396 + 4.31966i) q^{95} +1.00000 q^{96} +(-0.208947 + 0.361908i) q^{97} +(3.43631 - 5.95187i) q^{98} -2.93900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} - q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 12 q^{17} + 6 q^{18} - 4 q^{19} + 3 q^{20} + 6 q^{21} - q^{22} - 16 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{27} - 3 q^{28} - 13 q^{29} + 3 q^{30} - 18 q^{31} - 3 q^{32} - q^{33} + 24 q^{34} - 4 q^{35} - 3 q^{36} + 12 q^{37} + 8 q^{38} - 6 q^{40} + 14 q^{41} - 3 q^{42} + 8 q^{43} + 2 q^{44} + 3 q^{45} - 16 q^{46} + 8 q^{47} - 3 q^{48} + 4 q^{49} - 2 q^{50} + 24 q^{51} + 30 q^{53} - 3 q^{54} + 22 q^{55} - 3 q^{56} + 8 q^{57} - 13 q^{58} + 9 q^{59} - 6 q^{60} + 10 q^{61} + 9 q^{62} - 3 q^{63} + 6 q^{64} + 2 q^{66} + 6 q^{67} - 12 q^{68} - 16 q^{69} + 8 q^{70} - 6 q^{71} - 3 q^{72} + 10 q^{73} + 12 q^{74} - 2 q^{75} - 4 q^{76} - 12 q^{77} - 10 q^{79} + 3 q^{80} - 3 q^{81} + 14 q^{82} - 14 q^{83} - 3 q^{84} + 26 q^{85} - 16 q^{86} - 13 q^{87} - q^{88} + 10 q^{89} - 6 q^{90} + 32 q^{92} + 9 q^{93} - 4 q^{94} + 4 q^{95} + 6 q^{96} - 7 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 - q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 - 3 * q^16 - 12 * q^17 + 6 * q^18 - 4 * q^19 + 3 * q^20 + 6 * q^21 - q^22 - 16 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^27 - 3 * q^28 - 13 * q^29 + 3 * q^30 - 18 * q^31 - 3 * q^32 - q^33 + 24 * q^34 - 4 * q^35 - 3 * q^36 + 12 * q^37 + 8 * q^38 - 6 * q^40 + 14 * q^41 - 3 * q^42 + 8 * q^43 + 2 * q^44 + 3 * q^45 - 16 * q^46 + 8 * q^47 - 3 * q^48 + 4 * q^49 - 2 * q^50 + 24 * q^51 + 30 * q^53 - 3 * q^54 + 22 * q^55 - 3 * q^56 + 8 * q^57 - 13 * q^58 + 9 * q^59 - 6 * q^60 + 10 * q^61 + 9 * q^62 - 3 * q^63 + 6 * q^64 + 2 * q^66 + 6 * q^67 - 12 * q^68 - 16 * q^69 + 8 * q^70 - 6 * q^71 - 3 * q^72 + 10 * q^73 + 12 * q^74 - 2 * q^75 - 4 * q^76 - 12 * q^77 - 10 * q^79 + 3 * q^80 - 3 * q^81 + 14 * q^82 - 14 * q^83 - 3 * q^84 + 26 * q^85 - 16 * q^86 - 13 * q^87 - q^88 + 10 * q^89 - 6 * q^90 + 32 * q^92 + 9 * q^93 - 4 * q^94 + 4 * q^95 + 6 * q^96 - 7 * q^97 + 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more