LMFDB - Embedded newform 1183.2.e.g.508.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.6
Root			$0.217953 - 0.377506i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.g.170.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +O(q^{10})$	\(q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(0.183365 - 0.317598i) q^{10} +(-2.09137 + 3.62236i) q^{11} +(-1.66637 - 2.88623i) q^{12} +(1.92926 + 4.52187i) q^{14} +0.452762 q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +(2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +0.286720 q^{20} +(-3.64380 + 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 + 3.56386i) q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 - 4.29639i) q^{25} -1.69131 q^{27} +(-2.30751 + 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 + 1.10912i) q^{31} +(-3.43809 + 5.95495i) q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-0.204914 - 0.480285i) q^{35} +3.28723 q^{36} +(1.52242 + 2.63692i) q^{37} +(-1.25589 + 2.17526i) q^{38} +(-0.100344 - 0.173802i) q^{40} -5.39696 q^{41} +(-11.1966 - 1.35384i) q^{42} +5.32778 q^{43} +(-3.03826 - 5.26242i) q^{44} +(-0.223290 + 0.386750i) q^{45} +(-3.82334 + 6.62223i) q^{46} +(-5.83204 - 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 + 1.66842i) q^{49} +9.21843 q^{50} +(-0.965006 - 1.67144i) q^{51} +(-2.32398 + 4.02525i) q^{53} +(-1.57136 - 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 + 0.322952i) q^{56} -3.10101 q^{57} +(-7.65434 - 13.2577i) q^{58} +(3.02905 - 5.24648i) q^{59} +(-0.328878 + 0.569634i) q^{60} +(5.68285 + 9.84298i) q^{61} -2.37975 q^{62} +(-2.34932 - 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 - 15.4412i) q^{66} +(6.69851 - 11.6022i) q^{67} +(-0.611109 - 1.05847i) q^{68} -9.44053 q^{69} +(0.582500 - 0.775973i) q^{70} +5.97040 q^{71} +(-1.15044 - 1.99263i) q^{72} +(1.94273 - 3.36491i) q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} -1.96377 q^{76} +(-6.64368 + 8.85034i) q^{77} +(5.36669 + 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(-5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(-3.46025 - 8.11027i) q^{84} +0.166042 q^{85} +(4.94994 + 8.57354i) q^{86} +(9.44997 - 16.3678i) q^{87} +(-2.12662 + 3.68341i) q^{88} +(-5.99207 - 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(-1.46901 - 2.54439i) q^{93} +(10.8369 - 18.7700i) q^{94} +(0.133392 - 0.231042i) q^{95} +(-7.88721 - 13.6611i) q^{96} -19.4727 q^{97} +(3.63129 + 12.4900i) q^{98} +9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.929081	+	1.60921i	0.656959	+	1.13789i	0.981399	+	0.191980i	$0.0614909\pi$
$2$	0.929081	+	1.60921i	0.656959	+	1.13789i	−0.324440	+	0.945906i	$0.605176\pi$
$3$	−1.14703	+	1.98672i	−0.662240	+	1.14703i	0.317785	+	0.948163i	$0.397061\pi$
$3$	−1.14703	+	1.98672i	−0.662240	+	1.14703i	−0.980026	+	0.198871i	$0.936272\pi$
$4$	−0.726381	+	1.25813i	−0.363191	+	0.629065i
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	0.843116	−	0.537732i	$-0.180719\pi$
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	−0.887247	+	0.461294i	$0.847385\pi$
$6$	−4.26275			−1.74026
$7$	2.62662	+	0.317598i	0.992769	+	0.120041i
$7$	2.62662	+	0.317598i	0.992769	+	0.120041i
$8$	1.01686			0.359513
$9$	−1.13137	−	1.95960i	−0.377125	−	0.653199i
$10$	0.183365	−	0.317598i	0.0579852	−	0.100433i
$11$	−2.09137	+	3.62236i	−0.630571	+	1.09218i	0.356864	+	0.934156i	$0.383846\pi$
$11$	−2.09137	+	3.62236i	−0.630571	+	1.09218i	−0.987435	+	0.158025i	$0.949487\pi$
$12$	−1.66637	−	2.88623i	−0.481039	−	0.833184i
$13$		0			0
$13$		0			0
$14$	1.92926	+	4.52187i	0.515616	+	1.20852i
$15$	0.452762			0.116903
$16$	2.39750	+	4.15260i	0.599376	+	1.03815i
$17$	−0.420653	+	0.728592i	−0.102023	+	0.176709i	−0.912518	−	0.409036i	$-0.865865\pi$
$17$	−0.420653	+	0.728592i	−0.102023	+	0.176709i	0.810495	+	0.585746i	$0.199198\pi$
$18$	2.10227	−	3.64125i	0.495511	−	0.858250i
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	0.933080	−	0.359670i	$-0.117111\pi$
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	−0.778023	+	0.628236i	$0.783777\pi$
$20$	0.286720			0.0641126
$21$	−3.64380	+	4.85406i	−0.795143	+	1.05924i
$22$	−7.77220			−1.65704
$23$	2.05760	+	3.56386i	0.429038	+	0.743116i	0.996788	−	0.0800850i	$-0.0255192\pi$
$23$	2.05760	+	3.56386i	0.429038	+	0.743116i	−0.567750	+	0.823201i	$0.692186\pi$
$24$	−1.16637	+	2.02021i	−0.238084	+	0.412373i
$25$	2.48052	−	4.29639i	0.496105	−	0.859279i
$26$		0			0
$27$	−1.69131			−0.325492
$28$	−2.30751	+	3.07393i	−0.436078	+	0.580918i
$29$	−8.23861			−1.52987			−0.764936	−	0.644106i	$-0.777230\pi$
$29$	−8.23861			−1.52987			−0.764936	+	0.644106i	$0.777230\pi$
$30$	0.420653	+	0.728592i	0.0768003	+	0.133022i
$31$	−0.640350	+	1.10912i	−0.115010	+	0.199203i	−0.917784	−	0.397080i	$-0.870023\pi$
$31$	−0.640350	+	1.10912i	−0.115010	+	0.199203i	0.802774	+	0.596284i	$0.203357\pi$
$32$	−3.43809	+	5.95495i	−0.607774	+	1.05270i
$33$	−4.79774	−	8.30993i	−0.835180	−	1.44657i
$34$	−1.56328			−0.268100
$35$	−0.204914	−	0.480285i	−0.0346367	−	0.0811829i
$36$	3.28723			0.547872
$37$	1.52242	+	2.63692i	0.250285	+	0.433506i	0.963604	−	0.267333i	$-0.0861423\pi$
$37$	1.52242	+	2.63692i	0.250285	+	0.433506i	−0.713319	+	0.700839i	$0.752809\pi$
$38$	−1.25589	+	2.17526i	−0.203732	+	0.352874i
$39$		0			0
$40$	−0.100344	−	0.173802i	−0.0158659	−	0.0274805i
$41$	−5.39696			−0.842863			−0.421431	−	0.906860i	$-0.638472\pi$
$41$	−5.39696			−0.842863			−0.421431	+	0.906860i	$0.638472\pi$
$42$	−11.1966	−	1.35384i	−1.72768	−	0.208902i
$43$	5.32778			0.812479			0.406239	−	0.913767i	$-0.366840\pi$
$43$	5.32778			0.812479			0.406239	+	0.913767i	$0.366840\pi$
$44$	−3.03826	−	5.26242i	−0.458035	−	0.793340i
$45$	−0.223290	+	0.386750i	−0.0332862	+	0.0576534i
$46$	−3.82334	+	6.62223i	−0.563721	+	0.976394i
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	−0.880587	−	0.473885i	$-0.842851\pi$
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	0.0298969	−	0.999553i	$-0.490482\pi$
$48$	−11.0001			−1.58772
$49$	6.79826	+	1.66842i	0.971180	+	0.238346i
$50$	9.21843			1.30368
$51$	−0.965006	−	1.67144i	−0.135128	−	0.234048i
$52$		0			0
$53$	−2.32398	+	4.02525i	−0.319223	+	0.552911i	−0.980326	−	0.197384i	$-0.936755\pi$
$53$	−2.32398	+	4.02525i	−0.319223	+	0.552911i	0.661103	+	0.750295i	$0.270089\pi$
$54$	−1.57136	−	2.72168i	−0.213835	−	0.370373i
$55$	0.825514			0.111312
$56$	2.67089	+	0.322952i	0.356913	+	0.0431562i
$57$	−3.10101			−0.410739
$58$	−7.65434	−	13.2577i	−1.00506	−	1.74082i
$59$	3.02905	−	5.24648i	0.394349	−	0.683033i	−0.598669	−	0.800997i	$-0.704303\pi$
$59$	3.02905	−	5.24648i	0.394349	−	0.683033i	0.993018	+	0.117964i	$0.0376367\pi$
$60$	−0.328878	+	0.569634i	−0.0424580	+	0.0735394i
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	0.957889	+	0.287139i	$0.0927042\pi$
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	−0.230275	+	0.973126i	$0.573962\pi$
$62$	−2.37975			−0.302228
$63$	−2.34932	−	5.50644i	−0.295987	−	0.693746i
$64$	−3.18704			−0.398380
$65$		0			0
$66$	8.91498	−	15.4412i	1.09736	−	1.90068i
$67$	6.69851	−	11.6022i	0.818354	−	1.41743i	−0.0885411	−	0.996073i	$-0.528220\pi$
$67$	6.69851	−	11.6022i	0.818354	−	1.41743i	0.906895	−	0.421357i	$-0.138446\pi$
$68$	−0.611109	−	1.05847i	−0.0741078	−	0.128358i
$69$	−9.44053			−1.13651
$70$	0.582500	−	0.775973i	0.0696221	−	0.0927465i
$71$	5.97040			0.708556			0.354278	−	0.935140i	$-0.384727\pi$
$71$	5.97040			0.708556			0.354278	+	0.935140i	$0.384727\pi$
$72$	−1.15044	−	1.99263i	−0.135581	−	0.234833i
$73$	1.94273	−	3.36491i	0.227380	−	0.393833i	−0.729651	−	0.683820i	$-0.760317\pi$
$73$	1.94273	−	3.36491i	0.227380	−	0.393833i	0.957031	+	0.289986i	$0.0936508\pi$
$74$	−2.82891	+	4.89982i	−0.328854	+	0.569592i
$75$	5.69049	+	9.85622i	0.657081	+	1.13810i
$76$	−1.96377			−0.225260
$77$	−6.64368	+	8.85034i	−0.757118	+	1.00859i
$78$		0			0
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	0.992240	+	0.124337i	$0.0396805\pi$
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	−0.388441	+	0.921474i	$0.626986\pi$
$80$	0.473177	−	0.819566i	0.0529028	−	0.0916303i
$81$	5.33411	−	9.23895i	0.592679	−	1.02655i
$82$	−5.01421	−	8.68486i	−0.553726	−	0.959082i
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$	−3.46025	−	8.11027i	−0.377544	−	0.884903i
$85$	0.166042			0.0180098
$86$	4.94994	+	8.57354i	0.533765	+	0.924509i
$87$	9.44997	−	16.3678i	1.01314	−	1.75482i
$88$	−2.12662	+	3.68341i	−0.226698	+	0.392653i
$89$	−5.99207	−	10.3786i	−0.635159	−	1.10013i	−0.986482	−	0.163873i	$-0.947601\pi$
$89$	−5.99207	−	10.3786i	−0.635159	−	1.10013i	0.351323	−	0.936254i	$-0.385732\pi$
$90$	−0.829819			−0.0874706
$91$		0			0
$92$	−5.97840			−0.623291
$93$	−1.46901	−	2.54439i	−0.152329	−	0.263841i
$94$	10.8369	−	18.7700i	1.11774	−	1.93598i
$95$	0.133392	−	0.231042i	0.0136858	−	0.0237045i
$96$	−7.88721	−	13.6611i	−0.804986	−	1.39428i
$97$	−19.4727			−1.97716			−0.988578	−	0.150709i	$-0.951844\pi$
$97$	−19.4727			−1.97716			−0.988578	+	0.150709i	$0.951844\pi$
$98$	3.63129	+	12.4900i	0.366815	+	1.26168i
$99$	9.46448			0.951216
$100$	3.60361	+	6.24164i	0.360361	+	0.624164i
$101$	8.46697	−	14.6652i	0.842495	−	1.45924i	−0.0452843	−	0.998974i	$-0.514419\pi$
$101$	8.46697	−	14.6652i	0.842495	−	1.45924i	0.887779	−	0.460270i	$-0.152247\pi$
$102$	1.79314	−	3.10580i	0.177547	−	0.307520i
$103$	3.61712	+	6.26504i	0.356406	+	0.617313i	0.987357	−	0.158509i	$-0.0506688\pi$
$103$	3.61712	+	6.26504i	0.356406	+	0.617313i	−0.630952	+	0.775822i	$0.717335\pi$
$104$		0			0
$105$	1.18923	+	0.143797i	0.116057	+	0.0140331i
$106$	−8.63667			−0.838867
$107$	4.92625	+	8.53251i	0.476238	+	0.824869i	0.999629	−	0.0272237i	$-0.00866664\pi$
$107$	4.92625	+	8.53251i	0.476238	+	0.824869i	−0.523391	+	0.852093i	$0.675333\pi$
$108$	1.22853	−	2.12788i	0.118216	−	0.204756i
$109$	−6.90796	+	11.9649i	−0.661662	+	1.14603i	0.318516	+	0.947917i	$0.396815\pi$
$109$	−6.90796	+	11.9649i	−0.661662	+	1.14603i	−0.980179	+	0.198115i	$0.936518\pi$
$110$	0.766969	+	1.32843i	0.0731277	+	0.126661i
$111$	−6.98509			−0.662995
$112$	4.97847	+	11.6687i	0.470421	+	1.10259i
$113$	−4.26864			−0.401560			−0.200780	−	0.979636i	$-0.564348\pi$
$113$	−4.26864			−0.401560			−0.200780	+	0.979636i	$0.564348\pi$
$114$	−2.88109	−	4.99019i	−0.269839	−	0.467374i
$115$	0.406092	−	0.703371i	0.0378682	−	0.0655897i
$116$	5.98437	−	10.3652i	0.555635	−	0.962388i
$117$		0			0
$118$	11.2569			1.03629
$119$	−1.33629	+	1.78014i	−0.122498	+	0.163185i
$120$	0.460394			0.0420280
$121$	−3.24765	−	5.62509i	−0.295240	−	0.511372i
$122$	−10.5596	+	18.2898i	−0.956026	+	1.65589i
$123$	6.19049	−	10.7222i	0.558178	−	0.966792i
$124$	−0.930276	−	1.61129i	−0.0835412	−	0.144698i
$125$	−1.96593			−0.175839
$126$	6.67833	−	8.89649i	0.594953	−	0.792562i
$127$	−2.19024			−0.194352			−0.0971761	−	0.995267i	$-0.530981\pi$
$127$	−2.19024			−0.194352			−0.0971761	+	0.995267i	$0.530981\pi$
$128$	3.91516	+	6.78126i	0.346055	+	0.599385i
$129$	−6.11114	+	10.5848i	−0.538056	+	0.931941i
$130$		0			0
$131$	−1.13806	−	1.97117i	−0.0994326	−	0.172222i	0.812017	−	0.583633i	$-0.198369\pi$
$131$	−1.13806	−	1.97117i	−0.0994326	−	0.172222i	−0.911450	+	0.411411i	$0.865036\pi$
$132$	13.9400			1.21332
$133$	1.40347	+	3.28951i	0.121696	+	0.285237i
$134$	24.8938			2.15050
$135$	0.166900	+	0.289079i	0.0143645	+	0.0248800i
$136$	−0.427743	+	0.740873i	−0.0366787	+	0.0635293i
$137$	6.72399	−	11.6463i	0.574469	−	0.995010i	−0.421630	−	0.906768i	$-0.638542\pi$
$137$	6.72399	−	11.6463i	0.574469	−	0.995010i	0.996099	−	0.0882417i	$-0.0281248\pi$
$138$	−8.77101	−	15.1918i	−0.746638	−	1.29321i
$139$	4.04540			0.343126			0.171563	−	0.985173i	$-0.445118\pi$
$139$	4.04540			0.343126			0.171563	+	0.985173i	$0.445118\pi$
$140$	0.753106	+	0.0910619i	0.0636490	+	0.00769614i
$141$	26.7582			2.25344
$142$	5.54698	+	9.60765i	0.465492	+	0.806256i
$143$		0			0
$144$	5.42494	−	9.39628i	0.452079	−	0.783023i
$145$	0.812996	+	1.40815i	0.0675156	+	0.116940i
$146$	7.21982			0.597517
$147$	−11.1125	+	11.5925i	−0.916545	+	0.956135i
$148$	−4.42344			−0.363605
$149$	7.67596	+	13.2952i	0.628840	+	1.08918i	0.987785	+	0.155823i	$0.0498031\pi$
$149$	7.67596	+	13.2952i	0.628840	+	1.08918i	−0.358945	+	0.933359i	$0.616864\pi$
$150$	−10.5738	+	18.3144i	−0.863351	+	1.49537i
$151$	3.06054	−	5.30101i	0.249063	−	0.431390i	−0.714203	−	0.699939i	$-0.753211\pi$
$151$	3.06054	−	5.30101i	0.249063	−	0.431390i	0.963266	+	0.268548i	$0.0865439\pi$
$152$	0.687268	+	1.19038i	0.0557448	+	0.0965528i
$153$	1.90366			0.153902
$154$	−20.4146	−	2.46844i	−1.64506	−	0.198912i
$155$	0.252762			0.0203023
$156$		0			0
$157$	−2.26834	+	3.92888i	−0.181033	+	0.313559i	−0.942233	−	0.334959i	$-0.891278\pi$
$157$	−2.26834	+	3.92888i	−0.181033	+	0.313559i	0.761199	+	0.648518i	$0.224611\pi$
$158$	−9.97217	+	17.2723i	−0.793343	+	1.37411i
$159$	−5.33137	−	9.23421i	−0.422805	−	0.732320i
$160$	1.35710			0.107288
$161$	4.27265	+	10.0144i	0.336732	+	0.789245i
$162$	19.8233			1.55746
$163$	0.911271	+	1.57837i	0.0713762	+	0.123627i	0.899505	−	0.436911i	$-0.143928\pi$
$163$	0.911271	+	1.57837i	0.0713762	+	0.123627i	−0.828128	+	0.560538i	$0.810594\pi$
$164$	3.92025	−	6.79007i	0.306120	−	0.530215i
$165$	−0.946893	+	1.64007i	−0.0737155	+	0.127679i
$166$	−2.85590	−	4.94656i	−0.221661	−	0.383928i
$167$	10.7079			0.828606			0.414303	−	0.910139i	$-0.364025\pi$
$167$	10.7079			0.828606			0.414303	+	0.910139i	$0.364025\pi$
$168$	−3.70522	+	4.93588i	−0.285864	+	0.380812i
$169$		0			0
$170$	0.154266	+	0.267197i	0.0118317	+	0.0204931i
$171$	1.52934	−	2.64889i	0.116951	−	0.202566i
$172$	−3.87000	+	6.70303i	−0.295085	+	0.511102i
$173$	6.74634	+	11.6850i	0.512915	+	0.888395i	0.999888	+	0.0149778i	$0.00476775\pi$
$173$	6.74634	+	11.6850i	0.512915	+	0.888395i	−0.486973	+	0.873417i	$0.661899\pi$
$174$	35.1191			2.66237
$175$	7.87992	−	10.4972i	0.595666	−	0.793512i
$176$	−20.0563			−1.51180
$177$	6.94886	+	12.0358i	0.522308	+	0.904664i
$178$	11.1342	−	19.2851i	0.834547	−	1.44548i
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	−0.992615	−	0.121309i	$-0.961291\pi$
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	0.601364	+	0.798975i	$0.294624\pi$
$180$	−0.324388	−	0.561857i	−0.0241785	−	0.0418783i
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$		0			0
$183$	−26.0737			−1.92742
$184$	2.09228	+	3.62393i	0.154245	+	0.267160i
$185$	0.300469	−	0.520428i	0.0220909	−	0.0382626i
$186$	2.72965	−	4.72789i	0.200148	−	0.346666i
$187$	−1.75948	−	3.04751i	−0.128666	−	0.222856i
$188$	16.9451			1.23585
$189$	−4.44242	−	0.537156i	−0.323139	−	0.0390724i
$190$	0.495729			0.0359640
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	0.525135	−	0.851019i	$-0.324015\pi$
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	−0.999572	+	0.0292704i	$0.990682\pi$
$192$	3.65565	−	6.33176i	0.263823	−	0.456956i
$193$	0.520786	−	0.902028i	0.0374870	−	0.0649294i	−0.846673	−	0.532113i	$-0.821398\pi$
$193$	0.520786	−	0.902028i	0.0374870	−	0.0649294i	0.884160	+	0.467184i	$0.154731\pi$
$194$	−18.0917	−	31.3358i	−1.29891	−	2.24978i
$195$		0			0
$196$	−7.03722	+	7.34118i	−0.502658	+	0.524370i
$197$	−1.47833			−0.105327			−0.0526635	−	0.998612i	$-0.516771\pi$
$197$	−1.47833			−0.105327			−0.0526635	+	0.998612i	$0.516771\pi$
$198$	8.79326	+	15.2304i	0.624910	+	1.08238i
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	−1.00000		0.000281618i	$-0.999910\pi$
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	0.500244	+	0.865885i	$0.333244\pi$
$200$	2.52233	−	4.36881i	0.178356	−	0.308922i
$201$	15.3668	+	26.6162i	1.08389	+	1.87736i
$202$	31.4660			2.21394
$203$	−21.6397	−	2.61657i	−1.51881	−	0.183647i
$204$	2.80385			0.196309
$205$	0.532578	+	0.922451i	0.0371968	+	0.0644268i
$206$	−6.72120	+	11.6415i	−0.468288	+	0.811099i
$207$	4.65582	−	8.06412i	0.323602	−	0.560495i
$208$		0			0
$209$	−5.65402			−0.391097
$210$	0.873495	+	2.04733i	0.0602769	+	0.141279i
$211$	26.4692			1.82222			0.911108	−	0.412167i	$-0.135228\pi$
$211$	26.4692			1.82222			0.911108	+	0.412167i	$0.135228\pi$
$212$	−3.37619	−	5.84774i	−0.231878	−	0.401624i
$213$	−6.84825	+	11.8615i	−0.469234	+	0.812737i
$214$	−9.15376	+	15.8548i	−0.625738	+	1.08381i
$215$	−0.525751	−	0.910628i	−0.0358559	−	0.0621043i
$216$	−1.71981			−0.117019
$217$	−2.03421	+	2.70986i	−0.138091	+	0.183957i
$218$	−25.6722			−1.73874
$219$	4.45676	+	7.71934i	0.301160	+	0.521625i
$220$	−0.599638	+	1.03860i	−0.0404276	+	0.0700227i
$221$		0			0
$222$	−6.48971	−	11.2405i	−0.435561	−	0.754414i
$223$	0.728048			0.0487537			0.0243769	−	0.999703i	$-0.492240\pi$
$223$	0.728048			0.0487537			0.0243769	+	0.999703i	$0.492240\pi$
$224$	−10.9218	+	14.5495i	−0.729746	+	0.972126i
$225$	−11.2256			−0.748373
$226$	−3.96591	−	6.86916i	−0.263808	−	0.456929i
$227$	−1.42598	+	2.46986i	−0.0946454	+	0.163931i	−0.909461	−	0.415790i	$-0.863505\pi$
$227$	−1.42598	+	2.46986i	−0.0946454	+	0.163931i	0.814815	+	0.579721i	$0.196838\pi$
$228$	2.25252	−	3.90147i	0.149177	−	0.258381i
$229$	1.58676	+	2.74835i	0.104856	+	0.181616i	0.913679	−	0.406436i	$-0.133228\pi$
$229$	1.58676	+	2.74835i	0.104856	+	0.181616i	−0.808823	+	0.588052i	$0.799895\pi$
$230$	1.50917			0.0995116
$231$	−9.96262	−	23.3508i	−0.655492	−	1.53637i
$232$	−8.37748			−0.550009
$233$	−6.70354	−	11.6109i	−0.439163	−	0.760653i	0.558462	−	0.829530i	$-0.311392\pi$
$233$	−6.70354	−	11.6109i	−0.439163	−	0.760653i	−0.997625	+	0.0688769i	$0.978058\pi$
$234$		0			0
$235$	−1.15102	+	1.99363i	−0.0750845	+	0.130050i
$236$	4.40050	+	7.62188i	0.286448	+	0.496142i
$237$	−24.6231			−1.59944
$238$	−4.10614	−	0.496495i	−0.266162	−	0.0321830i
$239$	15.5538			1.00609			0.503046	−	0.864259i	$-0.332212\pi$
$239$	15.5538			1.00609			0.503046	+	0.864259i	$0.332212\pi$
$240$	1.08550	+	1.88014i	0.0700687	+	0.121363i
$241$	−3.78787	+	6.56078i	−0.243998	+	0.422617i	−0.961849	−	0.273579i	$-0.911792\pi$
$241$	−3.78787	+	6.56078i	−0.243998	+	0.422617i	0.717851	+	0.696196i	$0.245126\pi$
$242$	6.03465	−	10.4523i	0.387922	−	0.671900i
$243$	9.69985	+	16.8006i	0.622245	+	1.07776i
$244$	−16.5117			−1.05705
$245$	−0.385693	−	1.32661i	−0.0246410	−	0.0847537i
$246$	23.0059			1.46680
$247$		0			0
$248$	−0.651143	+	1.12781i	−0.0413476	+	0.0716162i
$249$	3.52587	−	6.10698i	0.223443	−	0.387014i
$250$	−1.82651	−	3.16361i	−0.115519	−	0.200084i
$251$	1.27476			0.0804624			0.0402312	−	0.999190i	$-0.487191\pi$
$251$	1.27476			0.0804624			0.0402312	+	0.999190i	$0.487191\pi$
$252$	8.63432	+	1.04402i	0.543911	+	0.0657671i
$253$	−17.2128			−1.08216
$254$	−2.03491	−	3.52456i	−0.127682	−	0.221151i
$255$	−0.190456	+	0.329879i	−0.0119268	+	0.0206578i
$256$	−10.4620	+	18.1208i	−0.653878	+	1.13255i
$257$	4.24010	+	7.34406i	0.264490	+	0.458110i	0.967430	−	0.253139i	$-0.0814631\pi$
$257$	4.24010	+	7.34406i	0.264490	+	0.458110i	−0.702940	+	0.711249i	$0.748130\pi$
$258$	−22.7110			−1.41392
$259$	3.16135	+	7.40970i	0.196437	+	0.460416i
$260$		0			0
$261$	9.32095	+	16.1444i	0.576952	+	0.999311i
$262$	2.11470	−	3.66276i	0.130646	−	0.226286i
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	−0.993009	−	0.118038i	$-0.962339\pi$
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	0.598729	+	0.800952i	$0.295673\pi$
$264$	−4.87861	−	8.45000i	−0.300258	−	0.520062i
$265$	0.917333			0.0563513
$266$	−3.98959	+	5.31471i	−0.244618	+	0.325866i
$267$	27.4925			1.68251
$268$	9.73135	+	16.8552i	0.594437	+	1.02959i
$269$	2.35586	−	4.08047i	0.143639	−	0.248790i	−0.785225	−	0.619210i	$-0.787453\pi$
$269$	2.35586	−	4.08047i	0.143639	−	0.248790i	0.928864	+	0.370420i	$0.120786\pi$
$270$	−0.310127	+	0.537156i	−0.0188737	+	0.0326903i
$271$	−9.00562	−	15.5982i	−0.547052	−	0.947522i	−0.998475	−	0.0552119i	$-0.982417\pi$
$271$	−9.00562	−	15.5982i	−0.547052	−	0.947522i	0.451422	−	0.892310i	$-0.350917\pi$
$272$	−4.03407			−0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	10.3754	+	17.9707i	0.625659	+	1.08367i
$276$	6.85742	−	11.8774i	0.412768	−	0.714936i
$277$	13.0604	−	22.6213i	0.784725	−	1.35918i	−0.144438	−	0.989514i	$-0.546137\pi$
$277$	13.0604	−	22.6213i	0.784725	−	1.35918i	0.929163	−	0.369670i	$-0.120529\pi$
$278$	3.75850	+	6.50991i	0.225420	+	0.390439i
$279$	2.89790			0.173493
$280$	−0.208368	−	0.488380i	−0.0124523	−	0.0291863i
$281$	3.66197			0.218455			0.109227	−	0.994017i	$-0.465162\pi$
$281$	3.66197			0.218455			0.109227	+	0.994017i	$0.465162\pi$
$282$	24.8605	+	43.0596i	1.48042	+	2.56416i
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	−0.956987	−	0.290132i	$-0.906301\pi$
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	0.729755	+	0.683709i	$0.239634\pi$
$284$	−4.33678	+	7.51153i	−0.257341	+	0.445727i
$285$	0.306011	+	0.530027i	0.0181265	+	0.0313961i
$286$		0			0
$287$	−14.1757	−	1.71406i	−0.836768	−	0.101178i
$288$	15.5591			0.916827
$289$	8.14610	+	14.1095i	0.479183	+	0.829968i
$290$	−1.51068	+	2.61657i	−0.0887100	+	0.153650i
$291$	22.3359	−	38.6869i	1.30935	−	2.26787i
$292$	2.82233	+	4.88842i	0.165164	+	0.286073i
$293$	17.1534			1.00211			0.501056	−	0.865415i	$-0.332945\pi$
$293$	17.1534			1.00211			0.501056	+	0.865415i	$0.332945\pi$
$294$	−28.9793	−	7.11205i	−1.69011	−	0.414783i
$295$	−1.19564			−0.0696130
$296$	1.54809	+	2.68136i	0.0899807	+	0.155851i
$297$	3.53715	−	6.12652i	0.205246	−	0.355497i
$298$	−14.2632	+	24.7045i	−0.826244	+	1.43110i
$299$		0			0
$300$	−16.5339			−0.954583
$301$	13.9940	+	1.69209i	0.806604	+	0.0975306i
$302$	11.3740			0.654498
$303$	19.4238	+	33.6430i	1.11587	+	1.93274i
$304$	−3.24083	+	5.61328i	−0.185874	+	0.321944i
$305$	1.12158	−	1.94263i	0.0642215	−	0.111235i
$306$	1.76866	+	3.06340i	0.101107	+	0.175123i
$307$	28.0696			1.60201			0.801007	−	0.598655i	$-0.204298\pi$
$307$	28.0696			1.60201			0.801007	+	0.598655i	$0.204298\pi$
$308$	−6.30902	−	14.7873i	−0.359490	−	0.842586i
$309$	−16.5959			−0.944105
$310$	0.234836	+	0.406748i	0.0133378	+	0.0231017i
$311$	11.7670	−	20.3811i	0.667248	−	1.15571i	−0.311423	−	0.950271i	$-0.600806\pi$
$311$	11.7670	−	20.3811i	0.667248	−	1.15571i	0.978671	−	0.205436i	$-0.0658611\pi$
$312$		0			0
$313$	1.67430	+	2.89997i	0.0946370	+	0.163916i	0.909457	−	0.415798i	$-0.136498\pi$
$313$	1.67430	+	2.89997i	0.0946370	+	0.163916i	−0.814820	+	0.579714i	$0.803164\pi$
$314$	−8.42989			−0.475726
$315$	−0.709330	+	0.944930i	−0.0399662	+	0.0532408i
$316$	−15.5930			−0.877177
$317$	−3.63917	−	6.30323i	−0.204396	−	0.354025i	0.745544	−	0.666456i	$-0.232190\pi$
$317$	−3.63917	−	6.30323i	−0.204396	−	0.354025i	−0.949940	+	0.312432i	$0.898856\pi$
$318$	9.90655	−	17.1586i	0.555532	−	0.962209i
$319$	17.2300	−	29.8432i	0.964694	−	1.67090i
$320$	0.314501	+	0.544732i	0.0175811	+	0.0304514i
$321$	−22.6023			−1.26154
$322$	−12.1457	+	16.1798i	−0.676852	+	0.901664i
$323$	−1.13724			−0.0632775
$324$	7.74919	+	13.4220i	0.430511	+	0.745666i
$325$		0			0
$326$	−1.69329	+	2.93286i	−0.0937826	+	0.162436i
$327$	−15.8473	−	27.4484i	−0.876359	−	1.51790i
$328$	−5.48792			−0.303020
$329$	−12.1104	−	28.3847i	−0.667666	−	1.56490i
$330$	−3.51896			−0.193712
$331$	−7.16168	−	12.4044i	−0.393642	−	0.681807i	0.599285	−	0.800536i	$-0.295452\pi$
$331$	−7.16168	−	12.4044i	−0.393642	−	0.681807i	−0.992927	+	0.118728i	$0.962118\pi$
$332$	2.23282	−	3.86736i	0.122542	−	0.212249i
$333$	3.44486	−	5.96668i	0.188777	−	0.326972i
$334$	9.94855	+	17.2314i	0.544360	+	0.942860i
$335$	−2.64407			−0.144461
$336$	−28.8930	−	3.49360i	−1.57624	−	0.190592i
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$		0			0
$339$	4.89627	−	8.48060i	0.265929	−	0.460603i
$340$	−0.120610	+	0.208902i	−0.00654098	+	0.0113293i
$341$	−2.67841	−	4.63915i	−0.145044	−	0.251224i
$342$	5.68351			0.307329
$343$	17.3266	+	6.54142i	0.935547	+	0.353203i
$344$	5.41758			0.292096
$345$	0.931602	+	1.61358i	0.0501558	+	0.0868723i
$346$	−12.5358	+	21.7126i	−0.673928	+	1.16728i
$347$	3.85139	−	6.67080i	0.206753	−	0.358107i	−0.743937	−	0.668250i	$-0.767044\pi$
$347$	3.85139	−	6.67080i	0.206753	−	0.358107i	0.950690	+	0.310143i	$0.100377\pi$
$348$	13.7286	+	23.7786i	0.735928	+	1.27466i
$349$	−22.3701			−1.19744			−0.598721	−	0.800958i	$-0.704324\pi$
$349$	−22.3701			−1.19744			−0.598721	+	0.800958i	$0.704324\pi$
$350$	24.2133	+	2.92776i	1.29426	+	0.156495i
$351$		0			0
$352$	−14.3806	−	24.9080i	−0.766490	−	1.32760i
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	0.401450	+	0.915881i	$0.368506\pi$
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	−0.993901	+	0.110275i	$0.964827\pi$
$354$	−12.9121	+	22.3644i	−0.686270	+	1.18865i
$355$	−0.589165	−	1.02046i	−0.0312697	−	0.0541606i
$356$	17.4101			0.922735
$357$	−2.00386	−	4.69672i	−0.106055	−	0.248577i
$358$	−19.4534			−1.02814
$359$	−1.37921	−	2.38887i	−0.0727920	−	0.126079i	0.827332	−	0.561713i	$-0.189858\pi$
$359$	−1.37921	−	2.38887i	−0.0727920	−	0.126079i	−0.900124	+	0.435634i	$0.856524\pi$
$360$	−0.227054	+	0.393269i	−0.0119668	+	0.0207271i
$361$	8.58638	−	14.8721i	0.451915	−	0.782740i
$362$	11.6330	+	20.1489i	0.611415	+	1.05900i
$363$	14.9006			0.782081
$364$		0			0
$365$	−0.766844			−0.0401385
$366$	−24.2246	−	41.9582i	−1.26624	−	2.19319i
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	−0.620153	−	0.784481i	$-0.712929\pi$
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	0.989457	+	0.144827i	$0.0462626\pi$
$368$	−9.86618	+	17.0887i	−0.514310	+	0.890812i
$369$	6.10597	+	10.5759i	0.317864	+	0.550557i
$370$	1.11664			0.0580514
$371$	−7.38263	+	9.83472i	−0.383287	+	0.510593i
$372$	4.26823			0.221298
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	0.923890	−	0.382657i	$-0.124991\pi$
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	−0.793336	+	0.608784i	$0.791658\pi$
$374$	3.26940	−	5.66276i	0.169056	−	0.292814i
$375$	2.25499	−	3.90576i	0.116447	−	0.201693i
$376$	−5.93034	−	10.2716i	−0.305834	−	0.529720i
$377$		0			0
$378$	−3.26297	−	7.64787i	−0.167829	−	0.393364i
$379$	6.05964			0.311263			0.155631	−	0.987815i	$-0.450259\pi$
$379$	6.05964			0.311263			0.155631	+	0.987815i	$0.450259\pi$
$380$	0.193787	+	0.335650i	0.00994109	+	0.0172185i
$381$	2.51228	−	4.35139i	0.128708	−	0.222929i
$382$	12.1837	−	21.1028i	0.623371	−	1.07971i
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	0.802168	−	0.597098i	$-0.203680\pi$
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	−0.918186	+	0.396149i	$0.870346\pi$
$384$	−17.9633			−0.916686
$385$	2.16831	+	0.262182i	0.110507	+	0.0133620i
$386$	1.93541			0.0985098
$387$	−6.02771	−	10.4403i	−0.306406	−	0.530710i
$388$	14.1446	−	24.4992i	0.718085	−	1.24376i
$389$	−2.25383	+	3.90374i	−0.114273	+	0.197927i	−0.917489	−	0.397761i	$-0.869787\pi$
$389$	−2.25383	+	3.90374i	−0.114273	+	0.197927i	0.803216	+	0.595688i	$0.203121\pi$
$390$		0			0
$391$	−3.46213			−0.175088
$392$	6.91285	+	1.69654i	0.349152	+	0.0856883i
$393$	5.22157			0.263393
$394$	−1.37349	−	2.37896i	−0.0691955	−	0.119850i
$395$	1.05918	−	1.83456i	0.0532932	−	0.0923065i
$396$	−6.87482	+	11.9075i	−0.345473	+	0.598376i
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	0.911876	−	0.410465i	$-0.134634\pi$
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	−0.811412	+	0.584475i	$0.801300\pi$
$398$	−26.1998			−1.31328
$399$	−8.14518	−	0.984875i	−0.407769	−	0.0493054i
$400$	23.7883			1.18941
$401$	6.30674	+	10.9236i	0.314944	+	0.545498i	0.979426	−	0.201806i	$-0.0646810\pi$
$401$	6.30674	+	10.9236i	0.314944	+	0.545498i	−0.664482	+	0.747304i	$0.731348\pi$
$402$	−28.5541	+	49.4571i	−1.42415	+	2.46670i
$403$		0			0
$404$	12.3005	+	21.3051i	0.611972	+	1.05997i
$405$	−2.10550			−0.104623
$406$	−15.8944	−	37.2539i	−0.788826	−	1.84888i
$407$	−12.7358			−0.631290
$408$	−0.981272	−	1.69961i	−0.0485802	−	0.0841434i
$409$	10.3476	−	17.9226i	0.511657	−	0.886216i	−0.488252	−	0.872703i	$-0.662365\pi$
$409$	10.3476	−	17.9226i	0.511657	−	0.886216i	0.999909	−	0.0135128i	$-0.00430140\pi$
$410$	−0.989615	+	1.71406i	−0.0488736	+	0.0846516i
$411$	15.4253	+	26.7174i	0.760873	+	1.31787i
$412$	−10.5096			−0.517773
$413$	9.62244	−	12.8185i	0.473490	−	0.630756i
$414$	17.3025			0.850373
$415$	0.303336	+	0.525393i	0.0148902	+	0.0257905i
$416$		0			0
$417$	−4.64021	+	8.03708i	−0.227232	+	0.393577i
$418$	−5.25304	−	9.09854i	−0.256935	−	0.445024i
$419$	−21.8175			−1.06586			−0.532928	−	0.846161i	$-0.678908\pi$
$419$	−21.8175			−1.06586			−0.532928	+	0.846161i	$0.678908\pi$
$420$	−1.04475	+	1.39176i	−0.0509787	+	0.0679109i
$421$	−9.42727			−0.459457			−0.229728	−	0.973255i	$-0.573784\pi$
$421$	−9.42727			−0.459457			−0.229728	+	0.973255i	$0.573784\pi$
$422$	24.5920	+	42.5947i	1.19712	+	2.07348i
$423$	−13.1964	+	22.8569i	−0.641632	+	1.11134i
$424$	−2.36315	+	4.09310i	−0.114765	+	0.198779i
$425$	2.08688	+	3.61458i	0.101228	+	0.175333i
$426$	−25.4503			−1.23307
$427$	11.8006	+	27.6586i	0.571070	+	1.33850i
$428$	−14.3133			−0.691861
$429$		0			0
$430$	0.976930	−	1.69209i	0.0471118	−	0.0816000i
$431$	10.2138	−	17.6908i	0.491980	−	0.852134i	−0.507977	−	0.861370i	$-0.669607\pi$
$431$	10.2138	−	17.6908i	0.491980	−	0.852134i	0.999957	+	0.00923613i	$0.00293999\pi$
$432$	−4.05491	−	7.02332i	−0.195092	−	0.337909i
$433$	26.3486			1.26623			0.633117	−	0.774056i	$-0.281775\pi$
$433$	26.3486			1.26623			0.633117	+	0.774056i	$0.281775\pi$
$434$	−6.25069	−	0.755803i	−0.300043	−	0.0362797i
$435$	−3.73014			−0.178846
$436$	−10.0356	−	17.3822i	−0.480619	−	0.832457i
$437$	−2.78136	+	4.81745i	−0.133050	+	0.230450i
$438$	−8.28138	+	14.3438i	−0.395700	+	0.685372i
$439$	−12.5655	−	21.7641i	−0.599720	−	1.03875i	−0.992862	−	0.119267i	$-0.961945\pi$
$439$	−12.5655	−	21.7641i	−0.599720	−	1.03875i	0.393142	−	0.919478i	$-0.371388\pi$
$440$	0.839429			0.0400182
$441$	−4.42195	−	15.2095i	−0.210569	−	0.724260i
$442$		0			0
$443$	−9.25995	−	16.0387i	−0.439953	−	0.762022i	0.557732	−	0.830021i	$-0.311672\pi$
$443$	−9.25995	−	16.0387i	−0.439953	−	0.762022i	−0.997685	+	0.0679994i	$0.978338\pi$
$444$	5.07384	−	8.78815i	0.240794	−	0.417067i
$445$	−1.18261	+	2.04834i	−0.0560611	+	0.0971006i
$446$	0.676415	+	1.17159i	0.0320292	+	0.0554762i
$447$	−35.2184			−1.66577
$448$	−8.37115	−	1.01220i	−0.395500	−	0.0478219i
$449$	−11.6431			−0.549471			−0.274736	−	0.961520i	$-0.588590\pi$
$449$	−11.6431			−0.549471			−0.274736	+	0.961520i	$0.588590\pi$
$450$	−10.4295	−	18.0644i	−0.491651	−	0.851564i
$451$	11.2870	−	19.5497i	0.531485	−	0.920559i
$452$	3.10066	−	5.37050i	0.145843	−	0.252607i
$453$	7.02109	+	12.1609i	0.329880	+	0.571368i
$454$	−5.29939			−0.248713
$455$		0			0
$456$	−3.15328			−0.147666
$457$	10.2592	+	17.7695i	0.479906	+	0.831222i	0.999734	−	0.0230490i	$-0.00733739\pi$
$457$	10.2592	+	17.7695i	0.479906	+	0.831222i	−0.519828	+	0.854271i	$0.674004\pi$
$458$	−2.94845	+	5.10687i	−0.137772	+	0.238629i
$459$	0.711453	−	1.23227i	0.0332078	−	0.0575176i
$460$	0.589955	+	1.02183i	0.0275068	+	0.0476431i
$461$	−2.04075			−0.0950473			−0.0475236	−	0.998870i	$-0.515133\pi$
$461$	−2.04075			−0.0950473			−0.0475236	+	0.998870i	$0.515133\pi$
$462$	28.3203	−	37.7268i	1.31758	−	1.75521i
$463$	−3.03155			−0.140888			−0.0704441	−	0.997516i	$-0.522442\pi$
$463$	−3.03155			−0.140888			−0.0704441	+	0.997516i	$0.522442\pi$
$464$	−19.7521	−	34.2116i	−0.916968	−	1.58824i
$465$	−0.289926	+	0.502167i	−0.0134450	+	0.0232874i
$466$	12.4563	−	21.5749i	0.577025	−	0.999436i
$467$	6.46371	+	11.1955i	0.299105	+	0.518065i	0.975931	−	0.218078i	$-0.0699787\pi$
$467$	6.46371	+	11.1955i	0.299105	+	0.518065i	−0.676827	+	0.736142i	$0.736645\pi$
$468$		0			0
$469$	21.2793	−	28.3470i	0.982585	−	1.30894i
$470$	−4.27757			−0.197310
$471$	−5.20373	−	9.01312i	−0.239775	−	0.415303i
$472$	3.08011	−	5.33491i	0.141774	−	0.245559i
$473$	−11.1423	+	19.2991i	−0.512326	+	0.887374i
$474$	−22.8768	−	39.6238i	−1.05077	−	1.81998i
$475$	6.70611			0.307697
$476$	−1.26898	−	2.97429i	−0.0581637	−	0.136326i
$477$	10.5172			0.481548
$478$	14.4507	+	25.0294i	0.660962	+	1.14482i
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	−0.0576873	−	0.998335i	$-0.518373\pi$
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	0.893427	−	0.449209i	$-0.148294\pi$
$480$	−1.55664	+	2.69618i	−0.0710505	+	0.123063i
$481$		0			0
$482$	−14.0769			−0.641187
$483$	−24.7967	−	2.99830i	−1.12829	−	0.136427i
$484$	9.43611			0.428914
$485$	1.92159	+	3.32829i	0.0872550	+	0.151130i
$486$	−18.0239	+	31.2183i	−0.817580	+	1.41609i
$487$	18.3748	−	31.8261i	0.832642	−	1.44218i	−0.0632939	−	0.997995i	$-0.520161\pi$
$487$	18.3748	−	31.8261i	0.832642	−	1.44218i	0.895936	−	0.444183i	$-0.146506\pi$
$488$	5.77864	+	10.0089i	0.261587	+	0.453081i
$489$	−4.18103			−0.189073
$490$	1.77645	−	1.85319i	0.0802520	−	0.0837184i
$491$	−8.19797			−0.369969			−0.184985	−	0.982741i	$-0.559224\pi$
$491$	−8.19797			−0.369969			−0.184985	+	0.982741i	$0.559224\pi$
$492$	8.99331	+	15.5769i	0.405450	+	0.702260i
$493$	3.46560	−	6.00259i	0.156083	−	0.270343i
$494$		0			0
$495$	−0.933965	−	1.61768i	−0.0419786	−	0.0727091i
$496$	−6.14096			−0.275737
$497$	15.6820	+	1.89619i	0.703432	+	0.0850556i
$498$	13.1033			0.587171
$499$	−21.6266	−	37.4584i	−0.968141	−	1.67687i	−0.700929	−	0.713231i	$-0.747231\pi$
$499$	−21.6266	−	37.4584i	−0.968141	−	1.67687i	−0.267211	−	0.963638i	$-0.586102\pi$
$500$	1.42802	−	2.47340i	0.0638629	−	0.110614i
$501$	−12.2824	+	21.2737i	−0.548736	+	0.950439i
$502$	1.18436	+	2.05137i	0.0528605	+	0.0915571i
$503$	0.0181922			0.000811149			0.000405575	−	1.00000i	$-0.499871\pi$
$503$	0.0181922			0.000811149			0.000405575		1.00000i	$0.499871\pi$
$504$	−2.38892	−	5.59925i	−0.106411	−	0.249411i
$505$	−3.34212			−0.148722
$506$	−15.9920	−	27.6990i	−0.710933	−	1.23137i
$507$		0			0
$508$	1.59095	−	2.75560i	0.0705869	−	0.122260i
$509$	21.5503	+	37.3262i	0.955200	+	1.65446i	0.733909	+	0.679248i	$0.237694\pi$
$509$	21.5503	+	37.3262i	0.955200	+	1.65446i	0.221292	+	0.975208i	$0.428973\pi$
$510$	−0.707795			−0.0313417
$511$	6.17151	−	8.22134i	0.273012	−	0.363691i
$512$	−23.2197			−1.02617
$513$	−1.14311	−	1.97993i	−0.0504697	−	0.0874161i
$514$	−7.87878	+	13.6464i	−0.347518	+	0.601919i
$515$	0.713884	−	1.23648i	0.0314575	−	0.0544859i
$516$	−8.87804	−	15.3772i	−0.390834	−	0.676944i
$517$	48.7877			2.14568
$518$	−8.98664	+	11.9715i	−0.394850	+	0.525997i
$519$	−30.9531			−1.35869
$520$		0			0
$521$	−10.4770	+	18.1467i	−0.459006	+	0.795022i	−0.998909	−	0.0467056i	$-0.985128\pi$
$521$	−10.4770	+	18.1467i	−0.459006	+	0.795022i	0.539903	+	0.841727i	$0.318461\pi$
$522$	−17.3198	+	29.9988i	−0.758068	+	1.31301i
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	0.943084	+	0.332555i	$0.107911\pi$
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	−0.183541	+	0.983012i	$0.558756\pi$
$524$	3.30666			0.144452
$525$	11.8164	+	27.6958i	0.515712	+	1.20875i
$526$	−23.7627			−1.03610
$527$	−0.538730	−	0.933107i	−0.0234674	−	0.0406468i
$528$	23.0052	−	39.8462i	1.00117	−	1.73408i
$529$	3.03260	−	5.25262i	0.131852	−	0.228375i
$530$	0.852276	+	1.47619i	0.0370205	+	0.0641214i
$531$	−13.7080			−0.594875
$532$	−5.15809	−	0.623691i	−0.223631	−	0.0270404i
$533$		0			0
$534$	25.5427	+	44.2413i	1.10534	+	1.91451i
$535$	0.972255	−	1.68400i	0.0420343	−	0.0728055i
$536$	6.81142	−	11.7977i	0.294209	−	0.509584i
$537$	−12.0085	−	20.7993i	−0.518205	−	0.897557i
$538$	8.75513			0.377460
$539$	−20.2613	+	21.1365i	−0.872715	+	0.910411i
$540$	−0.484932			−0.0208682
$541$	−1.64923	−	2.85655i	−0.0709059	−	0.122813i	0.828393	−	0.560148i	$-0.189256\pi$
$541$	−1.64923	−	2.85655i	−0.0709059	−	0.122813i	−0.899299	+	0.437335i	$0.855922\pi$
$542$	16.7339	−	28.9839i	0.718782	−	1.24497i
$543$	−14.3619	+	24.8756i	−0.616330	+	1.06752i
$544$	−2.89249	−	5.00993i	−0.124014	−	0.214799i
$545$	2.72674			0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	9.76836	+	16.9193i	0.417284	+	0.722756i
$549$	12.8589	−	22.2722i	0.548803	−	0.950554i
$550$	−19.2791	+	33.3924i	−0.822065	+	1.42386i
$551$	−5.56828	−	9.64455i	−0.237217	−	0.410871i
$552$	−9.59965			−0.408588
$553$	11.1440	+	26.1199i	0.473893	+	1.11073i
$554$	48.5368			2.06213
$555$	0.689297	+	1.19390i	0.0292590	+	0.0506781i
$556$	−2.93850	+	5.08963i	−0.124620	+	0.215848i
$557$	−7.14329	+	12.3725i	−0.302671	+	0.524241i	−0.976740	−	0.214427i	$-0.931212\pi$
$557$	−7.14329	+	12.3725i	−0.302671	+	0.524241i	0.674069	+	0.738668i	$0.264545\pi$
$558$	2.69238	+	4.66334i	0.113978	+	0.197415i
$559$		0			0
$560$	1.50315	−	2.00241i	0.0635196	−	0.0846172i
$561$	8.07273			0.340831
$562$	3.40226	+	5.89289i	0.143516	+	0.248577i
$563$	−3.39392	+	5.87844i	−0.143037	+	0.247747i	−0.928639	−	0.370985i	$-0.879020\pi$
$563$	−3.39392	+	5.87844i	−0.143037	+	0.247747i	0.785602	+	0.618732i	$0.212353\pi$
$564$	−19.4366	+	33.6652i	−0.818430	+	1.41756i
$565$	0.421234	+	0.729599i	0.0177215	+	0.0306945i
$566$	−14.2061			−0.597128
$567$	16.9449	−	22.5731i	0.711621	−	0.947981i
$568$	6.07103			0.254735
$569$	8.66061	+	15.0006i	0.363072	+	0.628859i	0.988465	−	0.151451i	$-0.0483947\pi$
$569$	8.66061	+	15.0006i	0.363072	+	0.628859i	−0.625393	+	0.780310i	$0.715061\pi$
$570$	−0.568618	+	0.984875i	−0.0238168	+	0.0412519i
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	−0.697180	−	0.716896i	$-0.745562\pi$
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	0.969440	+	0.245328i	$0.0788957\pi$
$572$		0			0
$573$	30.0837			1.25676
$574$	−10.4121	−	24.4043i	−0.434593	−	1.01862i
$575$	20.4157			0.851392
$576$	3.60574	+	6.24532i	0.150239	+	0.260222i
$577$	−0.365767	+	0.633528i	−0.0152271	+	0.0263741i	−0.873539	−	0.486755i	$-0.838180\pi$
$577$	−0.365767	+	0.633528i	−0.0152271	+	0.0263741i	0.858311	+	0.513129i	$0.171514\pi$
$578$	−15.1368	+	26.2177i	−0.629607	+	1.09051i
$579$	1.19472	+	2.06931i	0.0496508	+	0.0859978i
$580$	−2.36218			−0.0980842
$581$	−8.07396	−	0.976265i	−0.334964	−	0.0405023i
$582$	83.0073			3.44076
$583$	−9.72061	−	16.8366i	−0.402586	−	0.697300i
$584$	1.97548	−	3.42163i	0.0817459	−	0.141588i
$585$		0			0
$586$	15.9369	+	27.6035i	0.658347	+	1.14029i
$587$	8.52284			0.351775			0.175888	−	0.984410i	$-0.443720\pi$
$587$	8.52284			0.351775			0.175888	+	0.984410i	$0.443720\pi$
$588$	−6.51296	−	22.4016i	−0.268590	−	0.923825i
$589$	−1.73119			−0.0713323
$590$	−1.11085	−	1.92404i	−0.0457329	−	0.0792117i
$591$	1.69570	−	2.93704i	0.0697517	−	0.120814i
$592$	−7.30004	+	12.6440i	−0.300030	+	0.519667i
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	−0.984791	−	0.173741i	$-0.944415\pi$
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	0.341932	−	0.939725i	$-0.388919\pi$
$594$	13.1452			0.539353
$595$	0.436129	+	0.0527346i	0.0178795	+	0.00216191i
$596$	−22.3027			−0.913554
$597$	−16.1730	−	28.0125i	−0.661917	−	1.14647i
$598$		0			0
$599$	0.375116	−	0.649720i	0.0153268	−	0.0265468i	−0.858260	−	0.513215i	$-0.828454\pi$
$599$	0.375116	−	0.649720i	0.0153268	−	0.0265468i	0.873587	+	0.486668i	$0.161788\pi$
$600$	5.78641	+	10.0224i	0.236229	+	0.409161i
$601$	−9.55305			−0.389677			−0.194838	−	0.980835i	$-0.562418\pi$
$601$	−9.55305			−0.389677			−0.194838	+	0.980835i	$0.562418\pi$
$602$	10.2787	+	24.0915i	0.418927	+	0.981897i
$603$	−30.3141			−1.23449
$604$	4.44624	+	7.70111i	0.180915	+	0.313354i
$605$	−0.640963	+	1.11018i	−0.0260588	+	0.0451352i
$606$	−36.0925	+	62.5141i	−1.46616	+	2.53946i
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	0.547133	−	0.837045i	$-0.315719\pi$
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	−0.998469	+	0.0553087i	$0.982386\pi$
$608$	−9.29489			−0.376958
$609$	30.0199	−	39.9908i	1.21647	−	1.62051i
$610$	4.16815			0.168764
$611$		0			0
$612$	−1.38278	+	2.39505i	−0.0558957	+	0.0968143i
$613$	−4.13993	+	7.17057i	−0.167210	+	0.289617i	−0.937438	−	0.348152i	$-0.886809\pi$
$613$	−4.13993	+	7.17057i	−0.167210	+	0.289617i	0.770228	+	0.637769i	$0.220143\pi$
$614$	26.0789	+	45.1699i	1.05246	+	1.82291i
$615$	−2.44354			−0.0985330
$616$	−6.75567	+	8.99952i	−0.272194	+	0.362601i
$617$	−20.3312			−0.818503			−0.409252	−	0.912422i	$-0.634210\pi$
$617$	−20.3312			−0.818503			−0.409252	+	0.912422i	$0.634210\pi$
$618$	−15.4189	−	26.7063i	−0.620238	−	1.07428i
$619$	2.67049	−	4.62542i	0.107336	−	0.185911i	−0.807354	−	0.590067i	$-0.799101\pi$
$619$	2.67049	−	4.62542i	0.107336	−	0.185911i	0.914690	+	0.404156i	$0.132435\pi$
$620$	−0.183601	+	0.318007i	−0.00737361	+	0.0127715i
$621$	−3.48003	−	6.02758i	−0.139649	−	0.241879i
$622$	43.7301			1.75342
$623$	−12.4427	−	29.1636i	−0.498506	−	1.16842i
$624$		0			0
$625$	−12.2086	−	21.1459i	−0.488345	−	0.845838i
$626$	−3.11112	+	5.38862i	−0.124345	+	0.215372i
$627$	6.48536	−	11.2330i	0.259000	−	0.448601i
$628$	−3.29536	−	5.70773i	−0.131499	−	0.227763i
$629$	−2.56165			−0.102140
$630$	−2.17962	−	0.263549i	−0.0868381	−	0.0105001i
$631$	−6.46662			−0.257432			−0.128716	−	0.991681i	$-0.541086\pi$
$631$	−6.46662			−0.257432			−0.128716	+	0.991681i	$0.541086\pi$
$632$	5.45714	+	9.45205i	0.217074	+	0.375982i
$633$	−30.3611	+	52.5870i	−1.20675	+	2.09014i
$634$	6.76217	−	11.7124i	0.268560	−	0.465160i
$635$	0.216135	+	0.374357i	0.00857707	+	0.0148559i
$636$	15.4904			0.614236
$637$		0			0
$638$	64.0322			2.53506
$639$	−6.75475	−	11.6996i	−0.267214	−	0.462828i
$640$	0.772706	−	1.33837i	0.0305439	−	0.0529035i
$641$	−11.6644	+	20.2034i	−0.460717	+	0.797985i	−0.998997	−	0.0447808i	$-0.985741\pi$
$641$	−11.6644	+	20.2034i	−0.460717	+	0.797985i	0.538280	+	0.842766i	$0.319074\pi$
$642$	−20.9993	−	36.3719i	−0.828778	−	1.43549i
$643$	3.58878			0.141527			0.0707637	−	0.997493i	$-0.477456\pi$
$643$	3.58878			0.141527			0.0707637	+	0.997493i	$0.477456\pi$
$644$	−15.7030	−	1.89873i	−0.618784	−	0.0748204i
$645$	2.41222			0.0949810
$646$	−1.05658	−	1.83006i	−0.0415707	−	0.0720026i
$647$	19.8262	−	34.3400i	0.779448	−	1.35004i	−0.152812	−	0.988255i	$-0.548833\pi$
$647$	19.8262	−	34.3400i	0.779448	−	1.35004i	0.932260	−	0.361788i	$-0.117834\pi$
$648$	5.42402	−	9.39467i	0.213076	−	0.369058i
$649$	12.6697	+	21.9446i	0.497331	+	0.861402i
$650$		0			0
$651$	−3.05042	−	7.14970i	−0.119556	−	0.280219i
$652$	−2.64772			−0.103693
$653$	−9.06777	−	15.7058i	−0.354849	−	0.614617i	0.632243	−	0.774770i	$-0.282135\pi$
$653$	−9.06777	−	15.7058i	−0.354849	−	0.614617i	−0.987092	+	0.160153i	$0.948801\pi$
$654$	29.4469	−	51.0035i	1.15146	−	1.99439i
$655$	−0.224610	+	0.389035i	−0.00877623	+	0.0152009i
$656$	−12.9392	−	22.4114i	−0.505192	−	0.875017i
$657$	−8.79183			−0.343002
$658$	34.4256	−	45.8599i	1.34205	−	1.78780i
$659$	13.4810			0.525147			0.262573	−	0.964912i	$-0.415429\pi$
$659$	13.4810			0.525147			0.262573	+	0.964912i	$0.415429\pi$
$660$	−1.37561	−	2.38263i	−0.0535456	−	0.0927437i
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	−0.748156	−	0.663523i	$-0.769061\pi$
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	0.948706	+	0.316161i	$0.102394\pi$
$662$	13.3076	−	23.0494i	0.517213	−	0.895839i
$663$		0			0
$664$	−3.12571			−0.121301
$665$	0.423750	−	0.564495i	0.0164323	−	0.0218902i
$666$	12.8022			0.496076
$667$	−16.9517	−	29.3613i	−0.656374	−	1.13687i
$668$	−7.77805	+	13.4720i	−0.300942	+	0.521247i
$669$	−0.835096	+	1.44643i	−0.0322867	+	0.0559222i
$670$	−2.45655	−	4.25487i	−0.0949049	−	0.164380i
$671$	−47.5397			−1.83525
$672$	−16.3780	−	38.3874i	−0.631795	−	1.48082i
$673$	−9.23056			−0.355812			−0.177906	−	0.984048i	$-0.556932\pi$
$673$	−9.23056			−0.355812			−0.177906	+	0.984048i	$0.556932\pi$
$674$	15.9618	+	27.6467i	0.614827	+	1.06491i
$675$	−4.19533	+	7.26652i	−0.161478	+	0.279689i
$676$		0			0
$677$	10.5467	+	18.2674i	0.405343	+	0.702075i	0.994361	−	0.106045i	$-0.0338187\pi$
$677$	10.5467	+	18.2674i	0.405343	+	0.702075i	−0.589018	+	0.808120i	$0.700485\pi$
$678$	18.1961			0.698818
$679$	−51.1475	−	6.18450i	−1.96286	−	0.237340i
$680$	0.168841			0.00647474
$681$	−3.27129	−	5.66604i	−0.125356	−	0.217123i
$682$	4.97693	−	8.62029i	0.190576	−	0.330088i
$683$	−19.1106	+	33.1005i	−0.731246	+	1.26656i	0.225104	+	0.974335i	$0.427728\pi$
$683$	−19.1106	+	33.1005i	−0.731246	+	1.26656i	−0.956351	+	0.292221i	$0.905606\pi$
$684$	2.22176	+	3.84821i	0.0849512	+	0.147140i
$685$	−2.65412			−0.101409
$686$	5.57122	+	33.9597i	0.212710	+	1.29659i
$687$	−7.28027			−0.277760
$688$	12.7734	+	22.1241i	0.486980	+	0.843474i
$689$		0			0
$690$	−1.73107	+	2.99830i	−0.0659006	+	0.114143i
$691$	−13.1161	−	22.7178i	−0.498960	−	0.864224i	0.501039	−	0.865425i	$-0.332951\pi$
$691$	−13.1161	−	22.7178i	−0.498960	−	0.864224i	−0.999999	+	0.00120019i	$0.999618\pi$
$692$	−19.6017			−0.745144
$693$	24.8596	+	3.00590i	0.944338	+	0.114185i
$694$	14.3130			0.543314
$695$	−0.399204	−	0.691442i	−0.0151427	−	0.0262279i
$696$	9.60925	−	16.6437i	0.364238	−	0.630878i
$697$	2.27024	−	3.93218i	0.0859916	−	0.148942i
$698$	−20.7836	−	35.9982i	−0.786670	−	1.36255i
$699$	30.7567			1.16333
$700$	7.48299	+	17.5389i	0.282830	+	0.662909i
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$		0			0
$703$	−2.05794	+	3.56446i	−0.0776167	+	0.134436i
$704$	6.66528	−	11.5446i	0.251207	−	0.435104i
$705$	−2.64053	−	4.57353i	−0.0994480	−	0.172249i
$706$	−41.3669			−1.55687
$707$	26.8972	−	35.8309i	1.01157	−	1.34756i
$708$	−20.1901			−0.758789
$709$	−23.7232	−	41.0898i	−0.890944	−	1.54316i	−0.838745	−	0.544524i	$-0.816710\pi$
$709$	−23.7232	−	41.0898i	−0.890944	−	1.54316i	−0.0521988	−	0.998637i	$-0.516623\pi$
$710$	1.09476	−	1.89619i	0.0410858	−	0.0711626i
$711$	12.1435	−	21.0331i	0.455415	−	0.788802i
$712$	−6.09307	−	10.5535i	−0.228348	−	0.395510i
$713$	−5.27032			−0.197375
$714$	5.69629	−	7.58827i	0.213178	−	0.283984i
$715$		0			0
$716$	−7.60461	−	13.1716i	−0.284197	−	0.492244i
$717$	−17.8408	+	30.9011i	−0.666275	+	1.15402i
$718$	2.56280	−	4.43890i	0.0956428	−	0.165658i
$719$	24.6190	+	42.6413i	0.918133	+	1.59025i	0.802249	+	0.596990i	$0.203637\pi$
$719$	24.6190	+	42.6413i	0.918133	+	1.59025i	0.115884	+	0.993263i	$0.463030\pi$
$720$	−2.14136			−0.0798037
$721$	7.51104	+	17.6047i	0.279726	+	0.655632i
$722$	31.9098			1.18756
$723$	−8.68963	−	15.0509i	−0.323171	−	0.559748i
$724$	−9.09498	+	15.7530i	−0.338012	+	0.585454i
$725$	−20.4361	+	35.3963i	−0.758977	+	1.31459i
$726$	13.8439	+	23.9783i	0.513795	+	0.889919i
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$		0			0
$729$	−12.4996			−0.462947
$730$	−0.712460	−	1.23402i	−0.0263693	−	0.0456730i
$731$	−2.24114	+	3.88178i	−0.0828917	+	0.143573i
$732$	18.9394	−	32.8041i	0.700022	−	1.21247i
$733$	14.1005	+	24.4228i	0.520813	+	0.902075i	0.999707	+	0.0242025i	$0.00770464\pi$
$733$	14.1005	+	24.4228i	0.520813	+	0.902075i	−0.478894	+	0.877873i	$0.658962\pi$
$734$	26.2924			0.970472
$735$	3.07800	+	0.755398i	0.113534	+	0.0278633i
$736$	−28.2968			−1.04303
$737$	28.0181	+	48.5288i	1.03206	+	1.78758i
$738$	−11.3459	+	19.6516i	−0.417648	+	0.723387i
$739$	−21.2685	+	36.8381i	−0.782375	+	1.35511i	0.148180	+	0.988960i	$0.452658\pi$
$739$	−21.2685	+	36.8381i	−0.782375	+	1.35511i	−0.930555	+	0.366153i	$0.880675\pi$
$740$	0.436510	+	0.756058i	0.0160464	+	0.0277932i
$741$		0			0
$742$	−22.6852	−	2.74299i	−0.832801	−	0.100698i
$743$	−15.9142			−0.583836			−0.291918	−	0.956443i	$-0.594294\pi$
$743$	−15.9142			−0.583836			−0.291918	+	0.956443i	$0.594294\pi$
$744$	−1.49377	−	2.58728i	−0.0547641	−	0.0948543i
$745$	1.51495	−	2.62396i	0.0555033	−	0.0961346i
$746$	−4.68521	+	8.11502i	−0.171538	+	0.297112i
$747$	3.47773	+	6.02360i	0.127243	+	0.220392i
$748$	5.11221			0.186921
$749$	10.2295	+	23.9762i	0.373777	+	0.876072i
$750$	8.38028			0.306005
$751$	−9.09981	−	15.7613i	−0.332057	−	0.575139i	0.650858	−	0.759199i	$-0.274409\pi$
$751$	−9.09981	−	15.7613i	−0.332057	−	0.575139i	−0.982915	+	0.184060i	$0.941076\pi$
$752$	27.9646	−	48.4362i	1.01977	−	1.76629i
$753$	−1.46220	+	2.53260i	−0.0532855	+	0.0922931i
$754$		0			0
$755$	−1.20807			−0.0439662
$756$	3.90270	−	5.19896i	0.141940	−	0.189084i
$757$	−44.9004			−1.63193			−0.815967	−	0.578099i	$-0.803795\pi$
$757$	−44.9004			−1.63193			−0.815967	+	0.578099i	$0.803795\pi$
$758$	5.62989	+	9.75126i	0.204487	+	0.354182i
$759$	19.7436	−	34.1970i	0.716648	−	1.24127i
$760$	0.135641	−	0.234937i	0.00492021	−	0.00852205i
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	0.519631	−	0.854391i	$-0.326069\pi$
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	−0.999740	+	0.0228184i	$0.992736\pi$
$762$	9.33644			0.338223
$763$	−21.9446	+	29.2334i	−0.794449	+	1.05832i
$764$	19.0511			0.689244
$765$	−0.187856	−	0.325375i	−0.00679193	−	0.0117640i
$766$	4.21900	−	7.30752i	0.152439	−	0.264031i
$767$		0			0
$768$	−24.0006	−	41.5703i	−0.866049	−	1.50004i
$769$	−13.9625			−0.503502			−0.251751	−	0.967792i	$-0.581006\pi$
$769$	−13.9625			−0.503502			−0.251751	+	0.967792i	$0.581006\pi$
$770$	1.59263	+	3.73287i	0.0573944	+	0.134523i
$771$	−19.4541			−0.700623
$772$	0.756579	+	1.31043i	0.0272299	+	0.0471635i
$773$	6.40564	−	11.0949i	0.230395	−	0.399056i	−0.727529	−	0.686077i	$-0.759332\pi$
$773$	6.40564	−	11.0949i	0.230395	−	0.399056i	0.957924	+	0.287021i	$0.0926648\pi$
$774$	11.2005	−	19.3998i	0.402592	−	0.697310i
$775$	3.17681	+	5.50239i	0.114114	+	0.197652i
$776$	−19.8010			−0.710813
$777$	−18.3472	−	2.21845i	−0.658201	−	0.0795865i
$778$	−8.37594			−0.300292
$779$	−3.64767	−	6.31795i	−0.130691	−	0.226364i
$780$		0			0
$781$	−12.4863	+	21.6269i	−0.446795	+	0.773871i
$782$	−3.21660	−	5.57132i	−0.115025	−	0.199230i
$783$	13.9340			0.497961
$784$	9.37058	+	32.2305i	0.334664	+	1.15109i
$785$	0.895370			0.0319571
$786$	4.85125	+	8.40262i	0.173039	+	0.299712i
$787$	−13.6599	+	23.6597i	−0.486924	+	0.843377i	−0.999887	−	0.0150334i	$-0.995215\pi$
$787$	−13.6599	+	23.6597i	−0.486924	+	0.843377i	0.512963	+	0.858411i	$0.328548\pi$
$788$	1.07383	−	1.85993i	0.0382537	−	0.0662574i
$789$	−14.6686	−	25.4068i	−0.522217	−	0.904506i
$790$	3.93626			0.140046
$791$	−11.2121	−	1.35571i	−0.398656	−	0.0482036i
$792$	9.62401			0.341974
$793$		0			0
$794$	−3.71956	+	6.44247i	−0.132002	+	0.228635i
$795$	−1.05221	+	1.82248i	−0.0373181	+	0.0646369i
$796$	−10.2419	−	17.7394i	−0.363013	−	0.628758i
$797$	−29.4003			−1.04141			−0.520707	−	0.853736i	$-0.674332\pi$
$797$	−29.4003			−1.04141			−0.520707	+	0.853736i	$0.674332\pi$
$798$	−5.98265	−	14.0224i	−0.211783	−	0.496386i
$799$	9.81305			0.347161
$800$	17.0565	+	29.5428i	0.603040	+	1.04450i
$801$	−13.5586	+	23.4841i	−0.479068	+	0.829770i
$802$	−11.7189	+	20.2978i	−0.413810	+	0.716740i
$803$	8.12594	+	14.0745i	0.286758	+	0.496680i
$804$	−44.6487			−1.57464
$805$	1.29004	−	1.71852i	0.0454679	−	0.0605697i
$806$		0			0
$807$	5.40450	+	9.36087i	0.190247	+	0.329518i
$808$	8.60968	−	14.9124i	0.302888	−	0.524617i
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	−0.808329	−	0.588731i	$-0.799628\pi$
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	0.914020	+	0.405668i	$0.132961\pi$
$810$	−1.95618	−	3.38821i	−0.0687332	−	0.119049i
$811$	−8.44807			−0.296652			−0.148326	−	0.988939i	$-0.547388\pi$
$811$	−8.44807			−0.296652			−0.148326	+	0.988939i	$0.547388\pi$
$812$	19.0107	−	25.3249i	0.667143	−	0.888730i
$813$	41.3190			1.44912
$814$	−11.8326	−	20.4946i	−0.414732	−	0.718337i
$815$	0.179850	−	0.311510i	0.00629989	−	0.0109117i
$816$	4.62721	−	8.01456i	0.161985	−	0.280566i
$817$	3.60092	+	6.23697i	0.125980	+	0.218204i
$818$	38.4551			1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	−17.1318	−	29.6731i	−0.597903	−	1.03560i	−0.993130	−	0.117014i	$-0.962668\pi$
$821$	−17.1318	−	29.6731i	−0.597903	−	1.03560i	0.395228	−	0.918583i	$-0.370666\pi$
$822$	−28.6627	+	49.6452i	−0.999725	+	1.73157i
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	−0.806538	−	0.591182i	$-0.798661\pi$
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	0.915248	+	0.402891i	$0.131995\pi$
$824$	3.67809	+	6.37064i	0.128132	+	0.221932i
$825$	−47.6037			−1.65735
$826$	29.5677	+	3.57518i	1.02879	+	0.124397i
$827$	−19.5232			−0.678889			−0.339445	−	0.940626i	$-0.610239\pi$
$827$	−19.5232			−0.678889			−0.339445	+	0.940626i	$0.610239\pi$
$828$	6.76380	+	11.7152i	0.235058	+	0.407133i
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	0.429364	+	0.903131i	$0.358738\pi$
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	−0.996817	+	0.0797254i	$0.974596\pi$
$830$	−0.563647	+	0.976265i	−0.0195645	+	0.0338866i
$831$	29.9615	+	51.8949i	1.03935	+	1.80021i
$832$		0			0
$833$	−4.07530	+	4.25133i	−0.141201	+	0.147300i
$834$	−17.2445			−0.597128
$835$	−1.05667	−	1.83021i	−0.0365677	−	0.0633370i
$836$	4.10698	−	7.11349i	0.142043	−	0.246025i
$837$	1.08303	−	1.87586i	0.0374349	−	0.0648392i
$838$	−20.2702	−	35.1091i	−0.700223	−	1.21282i
$839$	−24.7427			−0.854212			−0.427106	−	0.904202i	$-0.640467\pi$
$839$	−24.7427			−0.854212			−0.427106	+	0.904202i	$0.640467\pi$
$840$	1.20928	+	0.146220i	0.0417241	+	0.00504508i
$841$	38.8748			1.34051
$842$	−8.75869	−	15.1705i	−0.301844	−	0.522810i
$843$	−4.20040	+	7.27531i	−0.144669	+	0.250575i
$844$	−19.2267	+	33.3017i	−0.661812	+	1.14629i
$845$		0			0
$846$	−49.0422			−1.68610
$847$	−6.74381	−	15.8064i	−0.231720	−	0.543115i
$848$	−22.2870			−0.765339
$849$	−8.76938	−	15.1890i	−0.300964	−	0.521285i
$850$	−3.87776	+	6.71647i	−0.133006	+	0.230373i
$851$	−6.26507	+	10.8514i	−0.214764	+	0.371982i
$852$	−9.94888	−	17.2320i	−0.340843	−	0.590357i
$853$	−18.2245			−0.623994			−0.311997	−	0.950083i	$-0.600998\pi$
$853$	−18.2245			−0.623994			−0.311997	+	0.950083i	$0.600998\pi$
$854$	−33.5450	+	44.6868i	−1.14789	+	1.52915i
$855$	−0.603667			−0.0206450
$856$	5.00928	+	8.67633i	0.171214	+	0.296551i
$857$	−1.27340	+	2.20559i	−0.0434984	+	0.0753414i	−0.886955	−	0.461856i	$-0.847184\pi$
$857$	−1.27340	+	2.20559i	−0.0434984	+	0.0753414i	0.843457	+	0.537197i	$0.180517\pi$
$858$		0			0
$859$	−27.0045	−	46.7732i	−0.921382	−	1.59588i	−0.797278	−	0.603612i	$-0.793728\pi$
$859$	−27.0045	−	46.7732i	−0.921382	−	1.59588i	−0.124104	−	0.992269i	$-0.539606\pi$
$860$	1.52758			0.0520902
$861$	19.6654	−	26.1972i	0.670196	−	0.892797i
$862$	37.9577			1.29284
$863$	0.621545	+	1.07655i	0.0211576	+	0.0366461i	0.876410	−	0.481565i	$-0.159931\pi$
$863$	0.621545	+	1.07655i	0.0211576	+	0.0366461i	−0.855253	+	0.518211i	$0.826598\pi$
$864$	5.81487	−	10.0716i	0.197826	−	0.342644i
$865$	1.33147	−	2.30618i	0.0452715	−	0.0784125i
$866$	24.4800	+	42.4006i	0.831864	+	1.44083i
$867$	−37.3754			−1.26934
$868$	−1.93174	−	4.52769i	−0.0655675	−	0.153680i
$869$	−44.8949			−1.52295
$870$	−3.46560	−	6.00259i	−0.117495	−	0.203507i
$871$		0			0
$872$	−7.02440	+	12.1666i	−0.237876	+	0.412013i
$873$	22.0309	+	38.1587i	0.745634	+	1.29148i
$874$	−10.3364			−0.349635
$875$	−5.16376	−	0.624377i	−0.174567	−	0.0211078i
$876$	−12.9492			−0.437514
$877$	0.401330	+	0.695125i	0.0135520	+	0.0234727i	0.872722	−	0.488218i	$-0.162353\pi$
$877$	0.401330	+	0.695125i	0.0135520	+	0.0234727i	−0.859170	+	0.511690i	$0.829019\pi$
$878$	23.3488	−	40.4412i	0.787983	−	1.36483i
$879$	−19.6755	+	34.0790i	−0.663639	+	1.14946i
$880$	1.97917	+	3.42803i	0.0667179	+	0.115559i
$881$	−37.0636			−1.24870			−0.624352	−	0.781143i	$-0.714637\pi$
$881$	−37.0636			−1.24870			−0.624352	+	0.781143i	$0.714637\pi$
$882$	20.3669	−	21.2467i	0.685791	−	0.715413i
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$		0			0
$885$	1.37144	−	2.37541i	0.0461005	−	0.0798484i
$886$	17.2065	−	29.8025i	0.578063	−	1.00123i
$887$	24.6287	+	42.6581i	0.826950	+	1.43232i	0.900420	+	0.435022i	$0.143259\pi$
$887$	24.6287	+	42.6581i	0.826950	+	1.43232i	−0.0734699	+	0.997297i	$0.523407\pi$
$888$	−7.10283			−0.238355
$889$	−5.75292	−	0.695616i	−0.192947	−	0.0233302i
$890$	−4.39496			−0.147319
$891$	22.3112	+	38.6441i	0.747452	+	1.29463i
$892$	−0.528840	+	0.915978i	−0.0177069	+	0.0306692i
$893$	7.88347	−	13.6546i	0.263810	−	0.456932i
$894$	−32.7207	−	56.6739i	−1.09434	−	1.89546i
$895$	2.06622			0.0690661
$896$	8.12993	+	19.0552i	0.271602	+	0.636591i
$897$		0			0
$898$	−10.8174	−	18.7362i	−0.360980	−	0.625236i
$899$	5.27559	−	9.13760i	0.175951	−	0.304756i
$900$	8.15406	−	14.1233i	0.271802	−	0.470775i
$901$	−1.95518	−	3.38647i	−0.0651365	−	0.112820i
$902$	41.9462			1.39666
$903$	−19.4134	+	25.8614i	−0.646036	+	0.860613i
$904$	−4.34059			−0.144366
$905$	−1.23558	−	2.14009i	−0.0410721	−	0.0711390i
$906$	−13.0463	+	22.5969i	−0.433435	+	0.750731i
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	−0.821488	−	0.570226i	$-0.806855\pi$
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	0.904574	+	0.426316i	$0.140189\pi$
$908$	−2.07161	−	3.58813i	−0.0687487	−	0.119076i
$909$	−38.3172			−1.27090
$910$		0			0
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	−7.43468	−	12.8772i	−0.246187	−	0.426408i
$913$	6.42866	−	11.1348i	0.212757	−	0.368507i
$914$	−19.0633	+	33.0186i	−0.630557	+	1.09216i
$915$	2.57298	+	4.45653i	0.0850601	+	0.147328i
$916$	−4.61037			−0.152331
$917$	−2.36320	−	5.53897i	−0.0780399	−	0.182913i
$918$	2.64399			0.0872646
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	−0.999909	+	0.0134590i	$0.995716\pi$
$920$	0.412937	−	0.715227i	0.0136141	−	0.0235803i
$921$	−32.1967	+	55.7664i	−1.06092	+	1.83756i
$922$	−1.89602	−	3.28401i	−0.0624422	−	0.108153i
$923$		0			0
$924$	36.6150	+	4.42731i	1.20454	+	0.145648i
$925$	15.1056			0.496670
$926$	−2.81656	−	4.87842i	−0.0925578	−	0.160315i
$927$	8.18464	−	14.1762i	0.268819	−	0.465608i
$928$	28.3251	−	49.0605i	0.929817	−	1.61049i
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	0.970411	−	0.241460i	$-0.0776261\pi$
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	−0.694316	+	0.719671i	$0.744293\pi$
$930$	−1.07746			−0.0353313
$931$	2.64164	+	9.08604i	0.0865764	+	0.297783i
$932$	19.4773			0.638000
$933$	26.9944	+	46.7557i	0.883757	+	1.53071i
$934$	−12.0106	+	20.8030i	−0.392999	+	0.680695i
$935$	−0.347255	+	0.601463i	−0.0113565	+	0.0196699i
$936$		0			0
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	65.3866	+	7.90624i	2.13495	+	0.258148i
$939$	−7.68191			−0.250690
$940$	−1.67216	−	2.89627i	−0.0545400	−	0.0944660i
$941$	26.5338	−	45.9578i	0.864976	−	1.49818i	−0.00209573	−	0.999998i	$-0.500667\pi$
$941$	26.5338	−	45.9578i	0.864976	−	1.49818i	0.867071	−	0.498184i	$-0.166000\pi$
$942$	9.66937	−	16.7478i	0.315045	−	0.545674i
$943$	−11.1048	−	19.2340i	−0.361620	−	0.626345i
$944$	29.0487			0.945453
$945$	0.346572	+	0.812309i	0.0112740	+	0.0264244i
$946$	−41.4086			−1.34631
$947$	−13.9409	−	24.1463i	−0.453017	−	0.784649i	0.545555	−	0.838075i	$-0.316319\pi$
$947$	−13.9409	−	24.1463i	−0.453017	−	0.784649i	−0.998572	+	0.0534265i	$0.982986\pi$
$948$	17.8857	−	30.9790i	0.580902	−	1.00615i
$949$		0			0
$950$	6.23051	+	10.7916i	0.202145	+	0.350125i
$951$	16.6970			0.541438
$952$	−1.35882	+	1.81014i	−0.0440396	+	0.0586670i
$953$	−36.3568			−1.17771			−0.588856	−	0.808238i	$-0.700421\pi$
$953$	−36.3568			−1.17771			−0.588856	+	0.808238i	$0.700421\pi$
$954$	9.77130	+	16.9244i	0.316357	+	0.547947i
$955$	−1.29407	+	2.24140i	−0.0418753	+	0.0725301i
$956$	−11.2980	+	19.5687i	−0.365403	+	0.632897i
$957$	39.5267	+	68.4623i	1.27772	+	2.21307i
$958$	67.9754			2.19619
$959$	21.3602	−	28.4548i	0.689757	−	0.918855i
$960$	−1.44297			−0.0465718
$961$	14.6799	+	25.4263i	0.473545	+	0.820205i
$962$		0			0
$963$	11.1469	−	19.3069i	0.359202	−	0.622157i
$964$	−5.50287	−	9.53126i	−0.177236	−	0.306981i
$965$	−0.205567			−0.00661744
$966$	−18.2132	−	42.6888i	−0.586000	−	1.37349i
$967$	15.2681			0.490988			0.245494	−	0.969398i	$-0.421050\pi$
$967$	15.2681			0.490988			0.245494	+	0.969398i	$0.421050\pi$
$968$	−3.30239	−	5.71990i	−0.106143	−	0.183845i
$969$	1.30445	−	2.25937i	0.0419049	−	0.0725815i
$970$	−3.57063	+	6.18450i	−0.114646	+	0.198572i
$971$	18.4460	+	31.9494i	0.591961	+	1.02531i	0.993968	+	0.109669i	$0.0349792\pi$
$971$	18.4460	+	31.9494i	0.591961	+	1.02531i	−0.402008	+	0.915636i	$0.631687\pi$
$972$	−28.1831			−0.903975
$973$	10.6257	+	1.28481i	0.340645	+	0.0411891i
$974$	68.2867			2.18805
$975$		0			0
$976$	−27.2493	+	47.1972i	−0.872229	+	1.51074i
$977$	−0.221957	+	0.384441i	−0.00710104	+	0.0122994i	−0.869554	−	0.493838i	$-0.835594\pi$
$977$	−0.221957	+	0.384441i	−0.00710104	+	0.0122994i	0.862453	+	0.506137i	$0.168927\pi$
$978$	−3.88452	−	6.72818i	−0.124213	−	0.215144i
$979$	50.1265			1.60205
$980$	1.94920	+	0.478370i	0.0622649	+	0.0152810i
$981$	31.2619			0.998117
$982$	−7.61658	−	13.1923i	−0.243055	−	0.420983i
$983$	22.7802	−	39.4564i	0.726575	−	1.25846i	−0.231748	−	0.972776i	$-0.574444\pi$
$983$	22.7802	−	39.4564i	0.726575	−	1.25846i	0.958323	−	0.285688i	$-0.0922222\pi$
$984$	6.29483	−	10.9030i	0.200672	−	0.347574i
$985$	0.145884	+	0.252678i	0.00464824	+	0.00805099i
$986$	12.8793			0.410160
$987$	70.2835	+	8.49835i	2.23715	+	0.270505i
$988$		0			0
$989$	10.9624	+	18.9875i	0.348585	+	0.603766i
$990$	1.73546	−	3.00590i	0.0551565	−	0.0955338i
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	0.0277842	+	0.999614i	$0.491155\pi$
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	−0.879583	+	0.475745i	$0.842178\pi$
$992$	−4.40316	−	7.62650i	−0.139801	−	0.242142i
$993$	32.8588			1.04274
$994$	11.5184	+	26.9974i	0.365342	+	0.856304i
$995$	2.78278			0.0882200
$996$	5.12225	+	8.87199i	0.162305	+	0.281120i
$997$	−14.5426	+	25.1886i	−0.460569	+	0.797730i	−0.998989	−	0.0449470i	$-0.985688\pi$
$997$	−14.5426	+	25.1886i	−0.460569	+	0.797730i	0.538420	+	0.842677i	$0.319021\pi$
$998$	40.1857	−	69.6038i	1.27206	−	2.20327i
$999$	−2.57489	−	4.45984i	−0.0814658	−	0.141103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.g.508.6		12
7.2	even	3	inner	1183.2.e.g.170.6		12
7.3	odd	6		8281.2.a.cf.1.1		6
7.4	even	3		8281.2.a.ce.1.1		6
13.4	even	6		91.2.g.b.81.1	yes	12
13.10	even	6		91.2.h.b.74.6	yes	12
13.12	even	2		1183.2.e.h.508.1		12
39.17	odd	6		819.2.n.d.172.6		12
39.23	odd	6		819.2.s.d.802.1		12
91.4	even	6		637.2.f.k.393.1		12
91.10	odd	6		637.2.f.j.295.1		12
91.17	odd	6		637.2.f.j.393.1		12
91.23	even	6		91.2.g.b.9.1	✓	12
91.25	even	6		8281.2.a.bz.1.6		6
91.30	even	6		91.2.h.b.16.6	yes	12
91.38	odd	6		8281.2.a.ca.1.6		6
91.51	even	6		1183.2.e.h.170.1		12
91.62	odd	6		637.2.h.l.165.6		12
91.69	odd	6		637.2.g.l.263.1		12
91.75	odd	6		637.2.g.l.373.1		12
91.82	odd	6		637.2.h.l.471.6		12
91.88	even	6		637.2.f.k.295.1		12
273.23	odd	6		819.2.n.d.100.6		12
273.212	odd	6		819.2.s.d.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	91.23	even	6
91.2.g.b.81.1	yes	12	13.4	even	6
91.2.h.b.16.6	yes	12	91.30	even	6
91.2.h.b.74.6	yes	12	13.10	even	6
637.2.f.j.295.1		12	91.10	odd	6
637.2.f.j.393.1		12	91.17	odd	6
637.2.f.k.295.1		12	91.88	even	6
637.2.f.k.393.1		12	91.4	even	6
637.2.g.l.263.1		12	91.69	odd	6
637.2.g.l.373.1		12	91.75	odd	6
637.2.h.l.165.6		12	91.62	odd	6
637.2.h.l.471.6		12	91.82	odd	6
819.2.n.d.100.6		12	273.23	odd	6
819.2.n.d.172.6		12	39.17	odd	6
819.2.s.d.289.1		12	273.212	odd	6
819.2.s.d.802.1		12	39.23	odd	6
1183.2.e.g.170.6		12	7.2	even	3	inner
1183.2.e.g.508.6		12	1.1	even	1	trivial
1183.2.e.h.170.1		12	91.51	even	6
1183.2.e.h.508.1		12	13.12	even	2
8281.2.a.bz.1.6		6	91.25	even	6
8281.2.a.ca.1.6		6	91.38	odd	6
8281.2.a.ce.1.1		6	7.4	even	3
8281.2.a.cf.1.1		6	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +O(q^{10})\)	\(q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(0.183365 - 0.317598i) q^{10} +(-2.09137 + 3.62236i) q^{11} +(-1.66637 - 2.88623i) q^{12} +(1.92926 + 4.52187i) q^{14} +0.452762 q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +(2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +0.286720 q^{20} +(-3.64380 + 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 + 3.56386i) q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 - 4.29639i) q^{25} -1.69131 q^{27} +(-2.30751 + 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 + 1.10912i) q^{31} +(-3.43809 + 5.95495i) q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-0.204914 - 0.480285i) q^{35} +3.28723 q^{36} +(1.52242 + 2.63692i) q^{37} +(-1.25589 + 2.17526i) q^{38} +(-0.100344 - 0.173802i) q^{40} -5.39696 q^{41} +(-11.1966 - 1.35384i) q^{42} +5.32778 q^{43} +(-3.03826 - 5.26242i) q^{44} +(-0.223290 + 0.386750i) q^{45} +(-3.82334 + 6.62223i) q^{46} +(-5.83204 - 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 + 1.66842i) q^{49} +9.21843 q^{50} +(-0.965006 - 1.67144i) q^{51} +(-2.32398 + 4.02525i) q^{53} +(-1.57136 - 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 + 0.322952i) q^{56} -3.10101 q^{57} +(-7.65434 - 13.2577i) q^{58} +(3.02905 - 5.24648i) q^{59} +(-0.328878 + 0.569634i) q^{60} +(5.68285 + 9.84298i) q^{61} -2.37975 q^{62} +(-2.34932 - 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 - 15.4412i) q^{66} +(6.69851 - 11.6022i) q^{67} +(-0.611109 - 1.05847i) q^{68} -9.44053 q^{69} +(0.582500 - 0.775973i) q^{70} +5.97040 q^{71} +(-1.15044 - 1.99263i) q^{72} +(1.94273 - 3.36491i) q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} -1.96377 q^{76} +(-6.64368 + 8.85034i) q^{77} +(5.36669 + 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(-5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(-3.46025 - 8.11027i) q^{84} +0.166042 q^{85} +(4.94994 + 8.57354i) q^{86} +(9.44997 - 16.3678i) q^{87} +(-2.12662 + 3.68341i) q^{88} +(-5.99207 - 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(-1.46901 - 2.54439i) q^{93} +(10.8369 - 18.7700i) q^{94} +(0.133392 - 0.231042i) q^{95} +(-7.88721 - 13.6611i) q^{96} -19.4727 q^{97} +(3.63129 + 12.4900i) q^{98} +9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more