LMFDB - Embedded newform 1183.2.e.d.508.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^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			508.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.d.170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 - 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} +(2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.30902 - 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} +(2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.92705 - 5.06980i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(5.42705 + 9.39993i) q^{12} +(-6.54508 - 2.26728i) q^{14} +5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-0.736068 + 1.27491i) q^{17} +(-2.61803 + 4.53457i) q^{18} +(1.50000 + 2.59808i) q^{19} -10.8541 q^{20} +(-1.11803 - 5.80948i) q^{21} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(8.35410 - 14.4697i) q^{24} +2.23607 q^{27} +(2.42705 + 12.6113i) q^{28} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(2.50000 - 4.33013i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(3.35410 + 5.80948i) q^{33} +3.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +9.70820 q^{36} +(2.35410 + 4.07742i) q^{37} +(3.92705 - 6.80185i) q^{38} +(8.35410 + 14.4697i) q^{40} +4.47214 q^{41} +(-11.7082 + 10.1396i) q^{42} -8.00000 q^{43} +(-7.28115 - 12.6113i) q^{44} +(2.23607 - 3.87298i) q^{45} +(10.7812 - 18.6735i) q^{46} +(-3.73607 - 6.47106i) q^{47} -22.0344 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.64590 + 2.85078i) q^{51} +(3.73607 - 6.47106i) q^{53} +(-2.92705 - 5.06980i) q^{54} -6.70820 q^{55} +(14.9443 - 12.9421i) q^{56} +6.70820 q^{57} +(-5.85410 - 10.1396i) q^{58} +(-0.736068 + 1.27491i) q^{59} +(-12.1353 + 21.0189i) q^{60} +(-1.50000 - 2.59808i) q^{61} -13.0902 q^{62} +(-5.00000 - 1.73205i) q^{63} +8.70820 q^{64} +(8.78115 - 15.2094i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-3.57295 - 6.18853i) q^{68} +18.4164 q^{69} +(-2.92705 - 15.2094i) q^{70} +8.94427 q^{71} +(-7.47214 - 12.9421i) q^{72} +(-1.35410 + 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} -14.5623 q^{76} +(1.50000 + 7.79423i) q^{77} +(1.35410 + 2.34537i) q^{79} +(11.0172 - 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.85410 - 10.1396i) q^{82} +(27.1353 + 9.39993i) q^{84} -3.29180 q^{85} +(10.4721 + 18.1383i) q^{86} +(5.00000 - 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(1.11803 + 1.93649i) q^{89} -11.7082 q^{90} -39.9787 q^{92} +(-5.59017 - 9.68246i) q^{93} +(-9.78115 + 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(12.1353 + 21.0189i) q^{96} -9.41641 q^{97} +(-17.0172 + 6.80185i) q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^4 - 10 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	$ 4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 5 q^{10} - 6 q^{11} + 15 q^{12} - 15 q^{14} + 20 q^{15} - 13 q^{16} + 6 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{28} - 15 q^{30} + 10 q^{31} - 15 q^{32} + 2 q^{34} + 12 q^{36} - 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} - 9 q^{44} + 23 q^{46} - 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 6 q^{53} - 5 q^{54} + 24 q^{56} - 10 q^{58} + 6 q^{59} - 15 q^{60} - 6 q^{61} - 30 q^{62} - 20 q^{63} + 8 q^{64} + 15 q^{66} - 6 q^{67} - 21 q^{68} + 20 q^{69} - 5 q^{70} - 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} + 6 q^{77} - 8 q^{79} + 15 q^{80} + 22 q^{81} - 10 q^{82} + 75 q^{84} - 40 q^{85} + 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} - 66 q^{92} - 19 q^{94} + 15 q^{96} + 16 q^{97} - 39 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^4 - 10 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 5 * q^10 - 6 * q^11 + 15 * q^12 - 15 * q^14 + 20 * q^15 - 13 * q^16 + 6 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 + 18 * q^22 + 12 * q^23 + 20 * q^24 + 3 * q^28 - 15 * q^30 + 10 * q^31 - 15 * q^32 + 2 * q^34 + 12 * q^36 - 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 - 9 * q^44 + 23 * q^46 - 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 6 * q^53 - 5 * q^54 + 24 * q^56 - 10 * q^58 + 6 * q^59 - 15 * q^60 - 6 * q^61 - 30 * q^62 - 20 * q^63 + 8 * q^64 + 15 * q^66 - 6 * q^67 - 21 * q^68 + 20 * q^69 - 5 * q^70 - 12 * q^72 + 8 * q^73 + 9 * q^74 - 18 * q^76 + 6 * q^77 - 8 * q^79 + 15 * q^80 + 22 * q^81 - 10 * q^82 + 75 * q^84 - 40 * q^85 + 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 - 66 * q^92 - 19 * q^94 + 15 * q^96 + 16 * q^97 - 39 * q^98 + 24 * 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 $

$2$	−1.30902	−	2.26728i	−0.925615	−	1.60321i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−1.30902	−	2.26728i	−0.925615	−	1.60321i	−0.135045	−	0.990839i	$-0.543118\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	0.984186	−	0.177136i	$-0.0566831\pi$
$4$	−2.42705	+	4.20378i	−1.21353	+	2.10189i
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	1.00000			$0$
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−5.85410			−2.38993
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	7.47214			2.64180
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	2.92705	−	5.06980i	0.925615	−	1.60321i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	5.42705	+	9.39993i	1.56665	+	2.71353i
$13$		0			0
$13$		0			0
$14$	−6.54508	−	2.26728i	−1.74925	−	0.605957i
$15$	5.00000			1.29099
$16$	−4.92705	−	8.53390i	−1.23176	−	2.13348i
$17$	−0.736068	+	1.27491i	−0.178523	+	0.309210i	−0.941375	−	0.337363i	$-0.890465\pi$
$17$	−0.736068	+	1.27491i	−0.178523	+	0.309210i	0.762852	+	0.646573i	$0.223798\pi$
$18$	−2.61803	+	4.53457i	−0.617077	+	1.06881i
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$	−10.8541			−2.42705
$21$	−1.11803	−	5.80948i	−0.243975	−	1.26773i
$22$	7.85410			1.67450
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	0.873199	+	0.487365i	$0.162042\pi$
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	−0.0145291	+	0.999894i	$0.504625\pi$
$24$	8.35410	−	14.4697i	1.70527	−	2.95362i
$25$		0			0
$26$		0			0
$27$	2.23607			0.430331
$28$	2.42705	+	12.6113i	0.458670	+	2.38332i
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	−6.54508	−	11.3364i	−1.19496	−	2.06974i
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$	−5.42705	+	9.39993i	−0.959376	+	1.66169i
$33$	3.35410	+	5.80948i	0.583874	+	1.01130i
$34$	3.85410			0.660973
$35$	5.59017	+	1.93649i	0.944911	+	0.327327i
$36$	9.70820			1.61803
$37$	2.35410	+	4.07742i	0.387012	+	0.670324i	0.992046	−	0.125875i	$-0.0401739\pi$
$37$	2.35410	+	4.07742i	0.387012	+	0.670324i	−0.605034	+	0.796200i	$0.706841\pi$
$38$	3.92705	−	6.80185i	0.637052	−	1.10341i
$39$		0			0
$40$	8.35410	+	14.4697i	1.32090	+	2.28787i
$41$	4.47214			0.698430			0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214			0.698430			0.349215	+	0.937043i	$0.386448\pi$
$42$	−11.7082	+	10.1396i	−1.80662	+	1.56457i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−7.28115	−	12.6113i	−1.09768	−	1.90123i
$45$	2.23607	−	3.87298i	0.333333	−	0.577350i
$46$	10.7812	−	18.6735i	1.58959	−	2.75326i
$47$	−3.73607	−	6.47106i	−0.544962	−	0.943901i	−0.998609	−	0.0527200i	$-0.983211\pi$
$47$	−3.73607	−	6.47106i	−0.544962	−	0.943901i	0.453648	−	0.891181i	$-0.350122\pi$
$48$	−22.0344			−3.18040
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	1.64590	+	2.85078i	0.230472	+	0.399189i
$52$		0			0
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	−0.486695	−	0.873572i	$-0.661798\pi$
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	0.999883	−	0.0152962i	$-0.00486912\pi$
$54$	−2.92705	−	5.06980i	−0.398321	−	0.689913i
$55$	−6.70820			−0.904534
$56$	14.9443	−	12.9421i	1.99701	−	1.72946i
$57$	6.70820			0.888523
$58$	−5.85410	−	10.1396i	−0.768681	−	1.33139i
$59$	−0.736068	+	1.27491i	−0.0958279	+	0.165979i	−0.909954	−	0.414710i	$-0.863883\pi$
$59$	−0.736068	+	1.27491i	−0.0958279	+	0.165979i	0.814126	+	0.580688i	$0.197217\pi$
$60$	−12.1353	+	21.0189i	−1.56665	+	2.71353i
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$	−13.0902			−1.66245
$63$	−5.00000	−	1.73205i	−0.629941	−	0.218218i
$64$	8.70820			1.08853
$65$		0			0
$66$	8.78115	−	15.2094i	1.08089	−	1.87215i
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	−3.57295	−	6.18853i	−0.433284	−	0.750469i
$69$	18.4164			2.21707
$70$	−2.92705	−	15.2094i	−0.349850	−	1.81787i
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$	−7.47214	−	12.9421i	−0.880600	−	1.52524i
$73$	−1.35410	+	2.34537i	−0.158486	+	0.274505i	−0.934323	−	0.356428i	$-0.883994\pi$
$73$	−1.35410	+	2.34537i	−0.158486	+	0.274505i	0.775837	+	0.630933i	$0.217328\pi$
$74$	6.16312	−	10.6748i	0.716448	−	1.24092i
$75$		0			0
$76$	−14.5623			−1.67041
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$		0			0
$79$	1.35410	+	2.34537i	0.152348	+	0.263875i	0.932090	−	0.362226i	$-0.117983\pi$
$79$	1.35410	+	2.34537i	0.152348	+	0.263875i	−0.779742	+	0.626101i	$0.784650\pi$
$80$	11.0172	−	19.0824i	1.23176	−	2.13348i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−5.85410	−	10.1396i	−0.646477	−	1.11973i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	27.1353	+	9.39993i	2.96070	+	1.02562i
$85$	−3.29180			−0.357045
$86$	10.4721	+	18.1383i	1.12924	+	1.95590i
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$	−11.2082	+	19.4132i	−1.19480	+	2.06945i
$89$	1.11803	+	1.93649i	0.118511	+	0.205268i	0.919178	−	0.393842i	$-0.128854\pi$
$89$	1.11803	+	1.93649i	0.118511	+	0.205268i	−0.800667	+	0.599110i	$0.795521\pi$
$90$	−11.7082			−1.23415
$91$		0			0
$92$	−39.9787			−4.16807
$93$	−5.59017	−	9.68246i	−0.579674	−	1.00402i
$94$	−9.78115	+	16.9415i	−1.00885	+	1.74738i
$95$	−3.35410	+	5.80948i	−0.344124	+	0.596040i
$96$	12.1353	+	21.0189i	1.23855	+	2.14523i
$97$	−9.41641			−0.956091			−0.478046	−	0.878335i	$-0.658655\pi$
$97$	−9.41641			−0.956091			−0.478046	+	0.878335i	$0.658655\pi$
$98$	−17.0172	+	6.80185i	−1.71900	+	0.687091i
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	4.30902	−	7.46344i	0.426656	−	0.738990i
$103$	1.35410	+	2.34537i	0.133424	+	0.231097i	0.924994	−	0.379981i	$-0.124070\pi$
$103$	1.35410	+	2.34537i	0.133424	+	0.231097i	−0.791571	+	0.611078i	$0.790736\pi$
$104$		0			0
$105$	10.0000	−	8.66025i	0.975900	−	0.845154i
$106$	−19.5623			−1.90006
$107$	4.88197	+	8.45581i	0.471957	+	0.817454i	0.999485	−	0.0320835i	$-0.0102142\pi$
$107$	4.88197	+	8.45581i	0.471957	+	0.817454i	−0.527528	+	0.849538i	$0.676881\pi$
$108$	−5.42705	+	9.39993i	−0.522218	+	0.904508i
$109$	−1.35410	+	2.34537i	−0.129699	+	0.224646i	−0.923560	−	0.383454i	$-0.874735\pi$
$109$	−1.35410	+	2.34537i	−0.129699	+	0.224646i	0.793861	+	0.608100i	$0.208068\pi$
$110$	8.78115	+	15.2094i	0.837250	+	1.45016i
$111$	10.5279			0.999261
$112$	−24.6353	−	8.53390i	−2.32781	−	0.806378i
$113$	2.94427			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$113$	2.94427			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$114$	−8.78115	−	15.2094i	−0.822430	−	1.42449i
$115$	−9.20820	+	15.9491i	−0.858669	+	1.48726i
$116$	−10.8541	+	18.7999i	−1.00778	+	1.74552i
$117$		0			0
$118$	3.85410			0.354799
$119$	0.736068	+	3.82472i	0.0674752	+	0.350612i
$120$	37.3607			3.41055
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−3.92705	+	6.80185i	−0.355538	+	0.615811i
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	12.1353	+	21.0189i	1.08978	+	1.88755i
$125$	11.1803			1.00000
$126$	2.61803	+	13.6037i	0.233233	+	1.21191i
$127$	−11.4164			−1.01304			−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164			−1.01304			−0.506521	+	0.862228i	$0.669069\pi$
$128$	−0.545085	−	0.944115i	−0.0481792	−	0.0834488i
$129$	−8.94427	+	15.4919i	−0.787499	+	1.36399i
$130$		0			0
$131$	4.11803	+	7.13264i	0.359794	+	0.623182i	0.987926	−	0.154925i	$-0.0495135\pi$
$131$	4.11803	+	7.13264i	0.359794	+	0.623182i	−0.628132	+	0.778107i	$0.716180\pi$
$132$	−32.5623			−2.83418
$133$	7.50000	+	2.59808i	0.650332	+	0.225282i
$134$	7.85410			0.678491
$135$	2.50000	+	4.33013i	0.215166	+	0.372678i
$136$	−5.50000	+	9.52628i	−0.471621	+	0.816872i
$137$	−4.11803	+	7.13264i	−0.351827	+	0.609383i	−0.986570	−	0.163341i	$-0.947773\pi$
$137$	−4.11803	+	7.13264i	−0.351827	+	0.609383i	0.634742	+	0.772724i	$0.281106\pi$
$138$	−24.1074	−	41.7552i	−2.05216	−	3.55444i
$139$	−23.4164			−1.98615			−0.993077	−	0.117466i	$-0.962523\pi$
$139$	−23.4164			−1.98615			−0.993077	+	0.117466i	$0.962523\pi$
$140$	−21.7082	+	18.7999i	−1.83468	+	1.58888i
$141$	−16.7082			−1.40708
$142$	−11.7082	−	20.2792i	−0.982531	−	1.70179i
$143$		0			0
$144$	−9.85410	+	17.0678i	−0.821175	+	1.42232i
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	7.09017			0.586787
$147$	−12.2984	−	9.68246i	−1.01435	−	0.798596i
$148$	−22.8541			−1.87860
$149$	0.354102	+	0.613323i	0.0290092	+	0.0502453i	0.880166	−	0.474667i	$-0.157431\pi$
$149$	0.354102	+	0.613323i	0.0290092	+	0.0502453i	−0.851156	+	0.524912i	$0.824098\pi$
$150$		0			0
$151$	10.2082	−	17.6811i	0.830732	−	1.43887i	−0.0667268	−	0.997771i	$-0.521256\pi$
$151$	10.2082	−	17.6811i	0.830732	−	1.43887i	0.897459	−	0.441098i	$-0.145411\pi$
$152$	11.2082	+	19.4132i	0.909105	+	1.57462i
$153$	2.94427			0.238030
$154$	15.7082	−	13.6037i	1.26580	−	1.09622i
$155$	11.1803			0.898027
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	3.54508	−	6.14027i	0.282032	−	0.488493i
$159$	−8.35410	−	14.4697i	−0.662523	−	1.14752i
$160$	−24.2705			−1.91875
$161$	20.5902	+	7.13264i	1.62273	+	0.562131i
$162$	−28.7984			−2.26261
$163$	−8.20820	−	14.2170i	−0.642916	−	1.11356i	−0.984779	−	0.173813i	$-0.944391\pi$
$163$	−8.20820	−	14.2170i	−0.642916	−	1.11356i	0.341862	−	0.939750i	$-0.388942\pi$
$164$	−10.8541	+	18.7999i	−0.847563	+	1.46802i
$165$	−7.50000	+	12.9904i	−0.583874	+	1.01130i
$166$		0			0
$167$	−22.4721			−1.73895			−0.869473	−	0.493980i	$-0.835541\pi$
$167$	−22.4721			−1.73895			−0.869473	+	0.493980i	$0.835541\pi$
$168$	−8.35410	−	43.4092i	−0.644533	−	3.34909i
$169$		0			0
$170$	4.30902	+	7.46344i	0.330487	+	0.572419i
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	19.4164	−	33.6302i	1.48049	−	2.56428i
$173$	8.20820	+	14.2170i	0.624058	+	1.08090i	0.988722	+	0.149761i	$0.0478505\pi$
$173$	8.20820	+	14.2170i	0.624058	+	1.08090i	−0.364664	+	0.931139i	$0.618816\pi$
$174$	−26.1803			−1.98473
$175$		0			0
$176$	29.5623			2.22834
$177$	1.64590	+	2.85078i	0.123713	+	0.214278i
$178$	2.92705	−	5.06980i	0.219392	−	0.379998i
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	−0.194715	−	0.980860i	$-0.562378\pi$
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	0.946807	−	0.321802i	$-0.104288\pi$
$180$	10.8541	+	18.7999i	0.809017	+	1.40126i
$181$	−25.4164			−1.88919			−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164			−1.88919			−0.944593	+	0.328243i	$0.893544\pi$
$182$		0			0
$183$	−6.70820			−0.495885
$184$	30.7705	+	53.2961i	2.26843	+	3.92904i
$185$	−5.26393	+	9.11740i	−0.387012	+	0.670324i
$186$	−14.6353	+	25.3490i	−1.07311	+	1.85868i
$187$	−2.20820	−	3.82472i	−0.161480	−	0.279691i
$188$	36.2705			2.64530
$189$	4.47214	−	3.87298i	0.325300	−	0.281718i
$190$	17.5623			1.27410
$191$	−5.59017	−	9.68246i	−0.404491	−	0.700598i	0.589772	−	0.807570i	$-0.299218\pi$
$191$	−5.59017	−	9.68246i	−0.404491	−	0.700598i	−0.994262	+	0.106972i	$0.965884\pi$
$192$	9.73607	−	16.8634i	0.702640	−	1.21701i
$193$	0.354102	−	0.613323i	0.0254888	−	0.0441479i	−0.853000	−	0.521912i	$-0.825219\pi$
$193$	0.354102	−	0.613323i	0.0254888	−	0.0441479i	0.878488	+	0.477764i	$0.158552\pi$
$194$	12.3262	+	21.3497i	0.884972	+	1.53282i
$195$		0			0
$196$	26.6976	+	21.0189i	1.90697	+	1.50135i
$197$	9.05573			0.645194			0.322597	−	0.946536i	$-0.395444\pi$
$197$	9.05573			0.645194			0.322597	+	0.946536i	$0.395444\pi$
$198$	−7.85410	−	13.6037i	−0.558167	−	0.966773i
$199$	10.3541	−	17.9338i	0.733983	−	1.27130i	−0.221185	−	0.975232i	$-0.570993\pi$
$199$	10.3541	−	17.9338i	0.733983	−	1.27130i	0.955168	−	0.296064i	$-0.0956741\pi$
$200$		0			0
$201$	3.35410	+	5.80948i	0.236580	+	0.409769i
$202$	−23.5623			−1.65784
$203$	8.94427	−	7.74597i	0.627765	−	0.543660i
$204$	−15.9787			−1.11873
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	3.54508	−	6.14027i	0.246998	−	0.427813i
$207$	8.23607	−	14.2653i	0.572446	−	0.991506i
$208$		0			0
$209$	−9.00000			−0.622543
$210$	−32.7254	−	11.3364i	−2.25827	−	0.782287i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	18.1353	+	31.4112i	1.24553	+	2.15733i
$213$	10.0000	−	17.3205i	0.685189	−	1.18678i
$214$	12.7812	−	22.1376i	0.873702	−	1.51330i
$215$	−8.94427	−	15.4919i	−0.609994	−	1.05654i
$216$	16.7082			1.13685
$217$	−2.50000	−	12.9904i	−0.169711	−	0.881845i
$218$	7.09017			0.480207
$219$	3.02786	+	5.24441i	0.204604	+	0.354385i
$220$	16.2812	−	28.1998i	1.09768	−	1.90123i
$221$		0			0
$222$	−13.7812	−	23.8697i	−0.924930	−	1.60203i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	5.42705	+	28.1998i	0.362610	+	1.88418i
$225$		0			0
$226$	−3.85410	−	6.67550i	−0.256371	−	0.444048i
$227$	2.97214	−	5.14789i	0.197268	−	0.341677i	−0.750374	−	0.661014i	$-0.770127\pi$
$227$	2.97214	−	5.14789i	0.197268	−	0.341677i	0.947642	+	0.319336i	$0.103460\pi$
$228$	−16.2812	+	28.1998i	−1.07825	+	1.86758i
$229$	12.0623	+	20.8925i	0.797100	+	1.38062i	0.921497	+	0.388385i	$0.126967\pi$
$229$	12.0623	+	20.8925i	0.797100	+	1.38062i	−0.124398	+	0.992232i	$0.539700\pi$
$230$	48.2148			3.17919
$231$	16.7705	+	5.80948i	1.10342	+	0.382235i
$232$	33.4164			2.19389
$233$	−5.97214	−	10.3440i	−0.391248	−	0.677661i	0.601367	−	0.798973i	$-0.294623\pi$
$233$	−5.97214	−	10.3440i	−0.391248	−	0.677661i	−0.992614	+	0.121312i	$0.961290\pi$
$234$		0			0
$235$	8.35410	−	14.4697i	0.544962	−	0.943901i
$236$	−3.57295	−	6.18853i	−0.232579	−	0.402839i
$237$	6.05573			0.393362
$238$	7.70820	−	6.67550i	0.499649	−	0.432708i
$239$	−19.4164			−1.25594			−0.627972	−	0.778236i	$-0.716115\pi$
$239$	−19.4164			−1.25594			−0.627972	+	0.778236i	$0.716115\pi$
$240$	−24.6353	−	42.6695i	−1.59020	−	2.75431i
$241$	2.35410	−	4.07742i	0.151641	−	0.262650i	−0.780190	−	0.625543i	$-0.784878\pi$
$241$	2.35410	−	4.07742i	0.151641	−	0.262650i	0.931831	+	0.362893i	$0.118211\pi$
$242$	2.61803	−	4.53457i	0.168294	−	0.291493i
$243$	−8.94427	−	15.4919i	−0.573775	−	0.993808i
$244$	14.5623			0.932256
$245$	14.5344	−	5.80948i	0.928571	−	0.371154i
$246$	−26.1803			−1.66920
$247$		0			0
$248$	18.6803	−	32.3553i	1.18620	−	2.05456i
$249$		0			0
$250$	−14.6353	−	25.3490i	−0.925615	−	1.60321i
$251$	1.52786			0.0964379			0.0482190	−	0.998837i	$-0.484645\pi$
$251$	1.52786			0.0964379			0.0482190	+	0.998837i	$0.484645\pi$
$252$	19.4164	−	16.8151i	1.22312	−	1.05925i
$253$	−24.7082			−1.55339
$254$	14.9443	+	25.8842i	0.937687	+	1.62412i
$255$	−3.68034	+	6.37454i	−0.230472	+	0.399189i
$256$	7.28115	−	12.6113i	0.455072	−	0.788208i
$257$	0.0278640	+	0.0482619i	0.00173811	+	0.00301050i	0.866893	−	0.498494i	$-0.166113\pi$
$257$	0.0278640	+	0.0482619i	0.00173811	+	0.00301050i	−0.865155	+	0.501504i	$0.832780\pi$
$258$	46.8328			2.91568
$259$	11.7705	+	4.07742i	0.731384	+	0.253359i
$260$		0			0
$261$	−4.47214	−	7.74597i	−0.276818	−	0.479463i
$262$	10.7812	−	18.6735i	0.666062	−	1.15365i
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	0.110526	+	0.993873i	$0.464746\pi$
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	−0.915983	+	0.401218i	$0.868587\pi$
$264$	25.0623	+	43.4092i	1.54248	+	2.67165i
$265$	16.7082			1.02638
$266$	−3.92705	−	20.4056i	−0.240783	−	1.25114i
$267$	5.00000			0.305995
$268$	−7.28115	−	12.6113i	−0.444767	−	0.770359i
$269$	−6.73607	+	11.6672i	−0.410705	+	0.711362i	−0.994967	−	0.100203i	$-0.968051\pi$
$269$	−6.73607	+	11.6672i	−0.410705	+	0.711362i	0.584262	+	0.811565i	$0.301384\pi$
$270$	6.54508	−	11.3364i	0.398321	−	0.689913i
$271$	−10.2082	−	17.6811i	−0.620104	−	1.07405i	−0.989466	−	0.144766i	$-0.953757\pi$
$271$	−10.2082	−	17.6811i	−0.620104	−	1.07405i	0.369362	−	0.929286i	$-0.379576\pi$
$272$	14.5066			0.879590
$273$		0			0
$274$	21.5623			1.30263
$275$		0			0
$276$	−44.6976	+	77.4184i	−2.69048	+	4.66004i
$277$	0.208204	−	0.360620i	0.0125098	−	0.0216675i	−0.859703	−	0.510795i	$-0.829351\pi$
$277$	0.208204	−	0.360620i	0.0125098	−	0.0216675i	0.872213	+	0.489127i	$0.162685\pi$
$278$	30.6525	+	53.0916i	1.83841	+	3.18423i
$279$	−10.0000			−0.598684
$280$	41.7705	+	14.4697i	2.49627	+	0.864732i
$281$	−26.9443			−1.60736			−0.803680	−	0.595061i	$-0.797128\pi$
$281$	−26.9443			−1.60736			−0.803680	+	0.595061i	$0.797128\pi$
$282$	21.8713	+	37.8822i	1.30242	+	2.25585i
$283$	−13.0623	+	22.6246i	−0.776473	+	1.34489i	0.157489	+	0.987521i	$0.449660\pi$
$283$	−13.0623	+	22.6246i	−0.776473	+	1.34489i	−0.933963	+	0.357371i	$0.883673\pi$
$284$	−21.7082	+	37.5997i	−1.28814	+	2.23113i
$285$	7.50000	+	12.9904i	0.444262	+	0.769484i
$286$		0			0
$287$	8.94427	−	7.74597i	0.527964	−	0.457230i
$288$	21.7082			1.27917
$289$	7.41641	+	12.8456i	0.436259	+	0.755623i
$290$	13.0902	−	22.6728i	0.768681	−	1.33139i
$291$	−10.5279	+	18.2348i	−0.617154	+	1.06894i
$292$	−6.57295	−	11.3847i	−0.384653	−	0.666238i
$293$	14.9443			0.873054			0.436527	−	0.899691i	$-0.356208\pi$
$293$	14.9443			0.873054			0.436527	+	0.899691i	$0.356208\pi$
$294$	−5.85410	+	40.5584i	−0.341418	+	2.36541i
$295$	−3.29180			−0.191656
$296$	17.5902	+	30.4671i	1.02241	+	1.77086i
$297$	−3.35410	+	5.80948i	−0.194625	+	0.337100i
$298$	0.927051	−	1.60570i	0.0537026	−	0.0930157i
$299$		0			0
$300$		0			0
$301$	−16.0000	+	13.8564i	−0.922225	+	0.798670i
$302$	−53.4508			−3.07575
$303$	−10.0623	−	17.4284i	−0.578064	−	1.00124i
$304$	14.7812	−	25.6017i	0.847757	−	1.46836i
$305$	3.35410	−	5.80948i	0.192055	−	0.332650i
$306$	−3.85410	−	6.67550i	−0.220324	−	0.381613i
$307$	−19.4164			−1.10815			−0.554076	−	0.832466i	$-0.686928\pi$
$307$	−19.4164			−1.10815			−0.554076	+	0.832466i	$0.686928\pi$
$308$	−36.4058	−	12.6113i	−2.07441	−	0.718597i
$309$	6.05573			0.344498
$310$	−14.6353	−	25.3490i	−0.831227	−	1.43973i
$311$	13.8820	−	24.0443i	0.787174	−	1.36343i	−0.140518	−	0.990078i	$-0.544877\pi$
$311$	13.8820	−	24.0443i	0.787174	−	1.36343i	0.927692	−	0.373347i	$-0.121790\pi$
$312$		0			0
$313$	2.79180	+	4.83553i	0.157802	+	0.273320i	0.934076	−	0.357075i	$-0.116226\pi$
$313$	2.79180	+	4.83553i	0.157802	+	0.273320i	−0.776274	+	0.630396i	$0.782893\pi$
$314$	18.3262			1.03421
$315$	−2.23607	−	11.6190i	−0.125988	−	0.654654i
$316$	−13.1459			−0.739515
$317$	−4.11803	−	7.13264i	−0.231292	−	0.400609i	0.726897	−	0.686747i	$-0.240962\pi$
$317$	−4.11803	−	7.13264i	−0.231292	−	0.400609i	−0.958189	+	0.286138i	$0.907629\pi$
$318$	−21.8713	+	37.8822i	−1.22648	+	2.12433i
$319$	−6.70820	+	11.6190i	−0.375587	+	0.650536i
$320$	9.73607	+	16.8634i	0.544263	+	0.942691i
$321$	21.8328			1.21859
$322$	−10.7812	−	56.0205i	−0.600810	−	3.12190i
$323$	−4.41641			−0.245736
$324$	26.6976	+	46.2415i	1.48320	+	2.56897i
$325$		0			0
$326$	−21.4894	+	37.2207i	−1.19019	+	2.06146i
$327$	3.02786	+	5.24441i	0.167441	+	0.290017i
$328$	33.4164			1.84511
$329$	−18.6803	−	6.47106i	−1.02988	−	0.356761i
$330$	39.2705			2.16177
$331$	−0.791796	−	1.37143i	−0.0435210	−	0.0753807i	0.843444	−	0.537217i	$-0.180524\pi$
$331$	−0.791796	−	1.37143i	−0.0435210	−	0.0753807i	−0.886965	+	0.461836i	$0.847191\pi$
$332$		0			0
$333$	4.70820	−	8.15485i	0.258008	−	0.446883i
$334$	29.4164	+	50.9507i	1.60959	+	2.78790i
$335$	−6.70820			−0.366508
$336$	−44.0689	+	38.1648i	−2.40415	+	2.08206i
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	3.29180	−	5.70156i	0.178786	−	0.309666i
$340$	7.98936	−	13.8380i	0.433284	−	0.750469i
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$	−15.7082			−0.849402
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−59.7771			−3.22296
$345$	20.5902	+	35.6632i	1.10854	+	1.92004i
$346$	21.4894	−	37.2207i	1.15527	−	2.00099i
$347$	−11.5344	+	19.9782i	−0.619201	+	1.07249i	0.370430	+	0.928860i	$0.379210\pi$
$347$	−11.5344	+	19.9782i	−0.619201	+	1.07249i	−0.989632	+	0.143628i	$0.954123\pi$
$348$	24.2705	+	42.0378i	1.30104	+	2.25346i
$349$	29.4164			1.57462			0.787312	−	0.616555i	$-0.211472\pi$
$349$	29.4164			1.57462			0.787312	+	0.616555i	$0.211472\pi$
$350$		0			0
$351$		0			0
$352$	−16.2812	−	28.1998i	−0.867788	−	1.50305i
$353$	8.64590	−	14.9751i	0.460175	−	0.797046i	−0.538795	−	0.842437i	$-0.681120\pi$
$353$	8.64590	−	14.9751i	0.460175	−	0.797046i	0.998969	+	0.0453912i	$0.0144534\pi$
$354$	4.30902	−	7.46344i	0.229022	−	0.396677i
$355$	10.0000	+	17.3205i	0.530745	+	0.919277i
$356$	−10.8541			−0.575266
$357$	8.22949	+	2.85078i	0.435551	+	0.150879i
$358$	−52.6869			−2.78459
$359$	5.97214	+	10.3440i	0.315197	+	0.545938i	0.979479	−	0.201544i	$-0.0645960\pi$
$359$	5.97214	+	10.3440i	0.315197	+	0.545938i	−0.664282	+	0.747482i	$0.731263\pi$
$360$	16.7082	−	28.9395i	0.880600	−	1.52524i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	33.2705	+	57.6262i	1.74866	+	3.02877i
$363$	4.47214			0.234726
$364$		0			0
$365$	−6.05573			−0.316971
$366$	8.78115	+	15.2094i	0.458998	+	0.795008i
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	−0.651160	−	0.758940i	$-0.725717\pi$
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	0.982842	+	0.184451i	$0.0590508\pi$
$368$	40.5795	−	70.2858i	2.11535	−	3.66390i
$369$	−4.47214	−	7.74597i	−0.232810	−	0.403239i
$370$	27.5623			1.43290
$371$	−3.73607	−	19.4132i	−0.193967	−	1.00788i
$372$	54.2705			2.81379
$373$	0.791796	+	1.37143i	0.0409976	+	0.0710100i	0.885796	−	0.464075i	$-0.153613\pi$
$373$	0.791796	+	1.37143i	0.0409976	+	0.0710100i	−0.844798	+	0.535085i	$0.820280\pi$
$374$	−5.78115	+	10.0133i	−0.298936	+	0.517773i
$375$	12.5000	−	21.6506i	0.645497	−	1.11803i
$376$	−27.9164	−	48.3526i	−1.43968	−	2.49360i
$377$		0			0
$378$	−14.6353	−	5.06980i	−0.752756	−	0.260762i
$379$	15.4164			0.791888			0.395944	−	0.918275i	$-0.370417\pi$
$379$	15.4164			0.791888			0.395944	+	0.918275i	$0.370417\pi$
$380$	−16.2812	−	28.1998i	−0.835206	−	1.44662i
$381$	−12.7639	+	22.1078i	−0.653916	+	1.13262i
$382$	−14.6353	+	25.3490i	−0.748805	+	1.29697i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	−2.43769			−0.124398
$385$	−13.4164	+	11.6190i	−0.683763	+	0.592157i
$386$	−1.85410			−0.0943713
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	22.8541	−	39.5845i	1.16024	−	2.00960i
$389$	−0.736068	+	1.27491i	−0.0373201	+	0.0646404i	−0.884082	−	0.467332i	$-0.845215\pi$
$389$	−0.736068	+	1.27491i	−0.0373201	+	0.0646404i	0.846762	+	0.531972i	$0.178549\pi$
$390$		0			0
$391$	−12.1246			−0.613168
$392$	7.47214	−	51.7685i	0.377400	−	2.61470i
$393$	18.4164			0.928985
$394$	−11.8541	−	20.5319i	−0.597201	−	1.03438i
$395$	−3.02786	+	5.24441i	−0.152348	+	0.263875i
$396$	−14.5623	+	25.2227i	−0.731783	+	1.26749i
$397$	−13.0623	−	22.6246i	−0.655578	−	1.13549i	−0.981748	−	0.190184i	$-0.939092\pi$
$397$	−13.0623	−	22.6246i	−0.655578	−	1.13549i	0.326170	−	0.945311i	$-0.394242\pi$
$398$	−54.2148			−2.71754
$399$	13.4164	−	11.6190i	0.671660	−	0.581675i
$400$		0			0
$401$	7.11803	+	12.3288i	0.355458	+	0.615671i	0.987196	−	0.159511i	$-0.0509917\pi$
$401$	7.11803	+	12.3288i	0.355458	+	0.615671i	−0.631739	+	0.775182i	$0.717658\pi$
$402$	8.78115	−	15.2094i	0.437964	−	0.758576i
$403$		0			0
$404$	21.8435	+	37.8340i	1.08675	+	1.88231i
$405$	24.5967			1.22222
$406$	−29.2705	−	10.1396i	−1.45267	−	0.503220i
$407$	−14.1246			−0.700131
$408$	12.2984	+	21.3014i	0.608860	+	1.05458i
$409$	4.35410	−	7.54153i	0.215296	−	0.372904i	−0.738068	−	0.674727i	$-0.764262\pi$
$409$	4.35410	−	7.54153i	0.215296	−	0.372904i	0.953364	+	0.301822i	$0.0975949\pi$
$410$	13.0902	−	22.6728i	0.646477	−	1.11973i
$411$	9.20820	+	15.9491i	0.454207	+	0.786710i
$412$	−13.1459			−0.647652
$413$	0.736068	+	3.82472i	0.0362195	+	0.188202i
$414$	−43.1246			−2.11946
$415$		0			0
$416$		0			0
$417$	−26.1803	+	45.3457i	−1.28206	+	2.22059i
$418$	11.7812	+	20.4056i	0.576235	+	0.998068i
$419$	32.9443			1.60943			0.804717	−	0.593659i	$-0.202317\pi$
$419$	32.9443			1.60943			0.804717	+	0.593659i	$0.202317\pi$
$420$	12.1353	+	63.0566i	0.592140	+	3.07685i
$421$	−13.4164			−0.653876			−0.326938	−	0.945046i	$-0.606017\pi$
$421$	−13.4164			−0.653876			−0.326938	+	0.945046i	$0.606017\pi$
$422$	−5.23607	−	9.06914i	−0.254888	−	0.441479i
$423$	−7.47214	+	12.9421i	−0.363308	+	0.629267i
$424$	27.9164	−	48.3526i	1.35574	−	2.34821i
$425$		0			0
$426$	−52.3607			−2.53688
$427$	−7.50000	−	2.59808i	−0.362950	−	0.125730i
$428$	−47.3951			−2.29093
$429$		0			0
$430$	−23.4164	+	40.5584i	−1.12924	+	1.95590i
$431$	−15.6803	+	27.1591i	−0.755295	+	1.30821i	0.189932	+	0.981797i	$0.439173\pi$
$431$	−15.6803	+	27.1591i	−0.755295	+	1.30821i	−0.945227	+	0.326413i	$0.894160\pi$
$432$	−11.0172	−	19.0824i	−0.530066	−	0.918102i
$433$	29.4164			1.41366			0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164			1.41366			0.706831	+	0.707382i	$0.250124\pi$
$434$	−26.1803	+	22.6728i	−1.25670	+	1.08833i
$435$	22.3607			1.07211
$436$	−6.57295	−	11.3847i	−0.314787	−	0.545227i
$437$	−12.3541	+	21.3979i	−0.590977	+	1.02360i
$438$	7.92705	−	13.7301i	0.378769	−	0.656047i
$439$	−12.0623	−	20.8925i	−0.575702	−	0.997146i	−0.995965	−	0.0897433i	$-0.971395\pi$
$439$	−12.0623	−	20.8925i	−0.575702	−	0.997146i	0.420262	−	0.907403i	$-0.361938\pi$
$440$	−50.1246			−2.38960
$441$	−13.0000	+	5.19615i	−0.619048	+	0.247436i
$442$		0			0
$443$	−1.11803	−	1.93649i	−0.0531194	−	0.0920055i	0.838243	−	0.545297i	$-0.183583\pi$
$443$	−1.11803	−	1.93649i	−0.0531194	−	0.0920055i	−0.891362	+	0.453291i	$0.850250\pi$
$444$	−25.5517	+	44.2568i	−1.21263	+	2.10033i
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$	−5.23607	−	9.06914i	−0.247935	−	0.429436i
$447$	1.58359			0.0749013
$448$	17.4164	−	15.0831i	0.822848	−	0.712607i
$449$	34.3607			1.62158			0.810790	−	0.585337i	$-0.199038\pi$
$449$	34.3607			1.62158			0.810790	+	0.585337i	$0.199038\pi$
$450$		0			0
$451$	−6.70820	+	11.6190i	−0.315877	+	0.547115i
$452$	−7.14590	+	12.3771i	−0.336115	+	0.582168i
$453$	−22.8262	−	39.5362i	−1.07247	−	1.85757i
$454$	−15.5623			−0.730375
$455$		0			0
$456$	50.1246			2.34730
$457$	−3.06231	−	5.30407i	−0.143249	−	0.248114i	0.785470	−	0.618900i	$-0.212422\pi$
$457$	−3.06231	−	5.30407i	−0.143249	−	0.248114i	−0.928718	+	0.370786i	$0.879088\pi$
$458$	31.5795	−	54.6973i	1.47561	−	2.55584i
$459$	−1.64590	+	2.85078i	−0.0768239	+	0.133063i
$460$	−44.6976	−	77.4184i	−2.08403	−	3.60965i
$461$	−34.3607			−1.60034			−0.800168	−	0.599776i	$-0.795256\pi$
$461$	−34.3607			−1.60034			−0.800168	+	0.599776i	$0.795256\pi$
$462$	−8.78115	−	45.6282i	−0.408536	−	2.12282i
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	−22.0344	−	38.1648i	−1.02292	−	1.77176i
$465$	12.5000	−	21.6506i	0.579674	−	1.00402i
$466$	−15.6353	+	27.0811i	−0.724289	+	1.25451i
$467$	−4.82624	−	8.35929i	−0.223332	−	0.386822i	0.732486	−	0.680782i	$-0.238360\pi$
$467$	−4.82624	−	8.35929i	−0.223332	−	0.386822i	−0.955818	+	0.293960i	$0.905027\pi$
$468$		0			0
$469$	1.50000	+	7.79423i	0.0692636	+	0.359904i
$470$	−43.7426			−2.01770
$471$	7.82624	+	13.5554i	0.360614	+	0.624602i
$472$	−5.50000	+	9.52628i	−0.253158	+	0.438483i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$	−7.92705	−	13.7301i	−0.364102	−	0.630642i
$475$		0			0
$476$	−17.8647	−	6.18853i	−0.818829	−	0.283651i
$477$	−14.9443			−0.684251
$478$	25.4164	+	44.0225i	1.16252	+	2.01354i
$479$	11.9164	−	20.6398i	0.544475	−	0.943058i	−0.454165	−	0.890917i	$-0.650062\pi$
$479$	11.9164	−	20.6398i	0.544475	−	0.943058i	0.998640	−	0.0521401i	$-0.0166043\pi$
$480$	−27.1353	+	46.9996i	−1.23855	+	2.14523i
$481$		0			0
$482$	−12.3262			−0.561445
$483$	36.8328	−	31.8982i	1.67595	−	1.45142i
$484$	−9.70820			−0.441282
$485$	−10.5279	−	18.2348i	−0.478046	−	0.827999i
$486$	−23.4164	+	40.5584i	−1.06219	+	1.83977i
$487$	−10.9164	+	18.9078i	−0.494670	+	0.856793i	−0.999981	−	0.00614405i	$-0.998044\pi$
$487$	−10.9164	+	18.9078i	−0.494670	+	0.856793i	0.505311	+	0.862937i	$0.331378\pi$
$488$	−11.2082	−	19.4132i	−0.507372	−	0.878793i
$489$	−36.7082			−1.66000
$490$	−32.1976	−	25.3490i	−1.45454	−	1.14515i
$491$	−25.5279			−1.15206			−0.576028	−	0.817430i	$-0.695398\pi$
$491$	−25.5279			−1.15206			−0.576028	+	0.817430i	$0.695398\pi$
$492$	24.2705	+	42.0378i	1.09420	+	1.89521i
$493$	−3.29180	+	5.70156i	−0.148255	+	0.256785i
$494$		0			0
$495$	6.70820	+	11.6190i	0.301511	+	0.522233i
$496$	−49.2705			−2.21231
$497$	17.8885	−	15.4919i	0.802411	−	0.694908i
$498$		0			0
$499$	13.2082	+	22.8773i	0.591280	+	1.02413i	0.994060	+	0.108831i	$0.0347107\pi$
$499$	13.2082	+	22.8773i	0.591280	+	1.02413i	−0.402780	+	0.915297i	$0.631956\pi$
$500$	−27.1353	+	46.9996i	−1.21353	+	2.10189i
$501$	−25.1246	+	43.5171i	−1.12248	+	1.94420i
$502$	−2.00000	−	3.46410i	−0.0892644	−	0.154610i
$503$	20.9443			0.933859			0.466929	−	0.884295i	$-0.345360\pi$
$503$	20.9443			0.933859			0.466929	+	0.884295i	$0.345360\pi$
$504$	−37.3607	−	12.9421i	−1.66418	−	0.576488i
$505$	20.1246			0.895533
$506$	32.3435	+	56.0205i	1.43784	+	2.49042i
$507$		0			0
$508$	27.7082	−	47.9920i	1.22935	−	2.12930i
$509$	−10.1180	−	17.5249i	−0.448474	−	0.776780i	0.549813	−	0.835288i	$-0.314699\pi$
$509$	−10.1180	−	17.5249i	−0.448474	−	0.776780i	−0.998287	+	0.0585081i	$0.981366\pi$
$510$	19.2705			0.853313
$511$	1.35410	+	7.03612i	0.0599019	+	0.311260i
$512$	−40.3050			−1.78124
$513$	3.35410	+	5.80948i	0.148087	+	0.256495i
$514$	0.0729490	−	0.126351i	0.00321764	−	0.00557312i
$515$	−3.02786	+	5.24441i	−0.133424	+	0.231097i
$516$	−43.4164	−	75.1994i	−1.91130	−	3.31047i
$517$	22.4164			0.985872
$518$	−6.16312	−	32.0245i	−0.270792	−	1.40708i
$519$	36.7082			1.61131
$520$		0			0
$521$	8.97214	−	15.5402i	0.393076	−	0.680828i	−0.599777	−	0.800167i	$-0.704744\pi$
$521$	8.97214	−	15.5402i	0.393076	−	0.680828i	0.992854	+	0.119339i	$0.0380775\pi$
$522$	−11.7082	+	20.2792i	−0.512454	+	0.887597i
$523$	−16.3541	−	28.3261i	−0.715115	−	1.23862i	−0.962915	−	0.269804i	$-0.913041\pi$
$523$	−16.3541	−	28.3261i	−0.715115	−	1.23862i	0.247800	−	0.968811i	$-0.420292\pi$
$524$	−39.9787			−1.74648
$525$		0			0
$526$	68.3951			2.98217
$527$	3.68034	+	6.37454i	0.160318	+	0.277679i
$528$	33.0517	−	57.2472i	1.43839	−	2.49136i
$529$	−22.4164	+	38.8264i	−0.974626	+	1.68810i
$530$	−21.8713	−	37.8822i	−0.950030	−	1.64550i
$531$	2.94427			0.127771
$532$	−29.1246	+	25.2227i	−1.26271	+	1.09354i
$533$		0			0
$534$	−6.54508	−	11.3364i	−0.283234	−	0.490575i
$535$	−10.9164	+	18.9078i	−0.471957	+	0.817454i
$536$	−11.2082	+	19.4132i	−0.484121	+	0.838522i
$537$	−22.5000	−	38.9711i	−0.970947	−	1.68173i
$538$	35.2705			1.52062
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$	−24.2705			−1.04444
$541$	0.645898	+	1.11873i	0.0277693	+	0.0480979i	0.879576	−	0.475758i	$-0.157826\pi$
$541$	0.645898	+	1.11873i	0.0277693	+	0.0480979i	−0.851807	+	0.523856i	$0.824493\pi$
$542$	−26.7254	+	46.2898i	−1.14796	+	1.98832i
$543$	−28.4164	+	49.2187i	−1.21946	+	2.11217i
$544$	−7.98936	−	13.8380i	−0.342541	−	0.593298i
$545$	−6.05573			−0.259399
$546$		0			0
$547$	−4.58359			−0.195980			−0.0979901	−	0.995187i	$-0.531241\pi$
$547$	−4.58359			−0.195980			−0.0979901	+	0.995187i	$0.531241\pi$
$548$	−19.9894	−	34.6226i	−0.853903	−	1.47900i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	6.70820	+	11.6190i	0.285779	+	0.494984i
$552$	137.610			5.85707
$553$	6.77051	+	2.34537i	0.287911	+	0.0997354i
$554$	−1.09017			−0.0463169
$555$	11.7705	+	20.3871i	0.499630	+	0.865385i
$556$	56.8328	−	98.4373i	2.41025	−	4.17467i
$557$	−9.35410	+	16.2018i	−0.396346	+	0.686491i	−0.993272	−	0.115805i	$-0.963055\pi$
$557$	−9.35410	+	16.2018i	−0.396346	+	0.686491i	0.596926	+	0.802296i	$0.296389\pi$
$558$	13.0902	+	22.6728i	0.554151	+	0.959818i
$559$		0			0
$560$	−11.0172	−	57.2472i	−0.465563	−	2.41913i
$561$	−9.87539			−0.416939
$562$	35.2705	+	61.0903i	1.48780	+	2.57694i
$563$	−6.29837	+	10.9091i	−0.265445	+	0.459764i	−0.967680	−	0.252181i	$-0.918852\pi$
$563$	−6.29837	+	10.9091i	−0.265445	+	0.459764i	0.702235	+	0.711945i	$0.252185\pi$
$564$	40.5517	−	70.2375i	1.70753	−	2.95753i
$565$	3.29180	+	5.70156i	0.138487	+	0.239866i
$566$	68.3951			2.87486
$567$	−5.50000	−	28.5788i	−0.230978	−	1.20020i
$568$	66.8328			2.80424
$569$	−12.7361	−	22.0595i	−0.533924	−	0.924783i	−0.999215	−	0.0396252i	$-0.987384\pi$
$569$	−12.7361	−	22.0595i	−0.533924	−	0.924783i	0.465291	−	0.885158i	$-0.345950\pi$
$570$	19.6353	−	34.0093i	0.822430	−	1.42449i
$571$	18.0623	−	31.2848i	0.755884	−	1.30923i	−0.189050	−	0.981968i	$-0.560541\pi$
$571$	18.0623	−	31.2848i	0.755884	−	1.30923i	0.944934	−	0.327262i	$-0.106126\pi$
$572$		0			0
$573$	−25.0000			−1.04439
$574$	−29.2705	−	10.1396i	−1.22173	−	0.423219i
$575$		0			0
$576$	−8.70820	−	15.0831i	−0.362842	−	0.628460i
$577$	−9.64590	+	16.7072i	−0.401564	+	0.695529i	−0.993915	−	0.110151i	$-0.964867\pi$
$577$	−9.64590	+	16.7072i	−0.401564	+	0.695529i	0.592351	+	0.805680i	$0.298200\pi$
$578$	19.4164	−	33.6302i	0.807616	−	1.39883i
$579$	−0.791796	−	1.37143i	−0.0329059	−	0.0569947i
$580$	−48.5410			−2.01556
$581$		0			0
$582$	55.1246			2.28499
$583$	11.2082	+	19.4132i	0.464196	+	0.804012i
$584$	−10.1180	+	17.5249i	−0.418687	+	0.725188i
$585$		0			0
$586$	−19.5623	−	33.8829i	−0.808111	−	1.39969i
$587$	6.11146			0.252247			0.126123	−	0.992015i	$-0.459746\pi$
$587$	6.11146			0.252247			0.126123	+	0.992015i	$0.459746\pi$
$588$	70.5517	−	28.1998i	2.90950	−	1.16294i
$589$	15.0000			0.618064
$590$	4.30902	+	7.46344i	0.177399	+	0.307265i
$591$	10.1246	−	17.5363i	0.416471	−	0.721349i
$592$	23.1976	−	40.1794i	0.953414	−	1.65136i
$593$	13.8820	+	24.0443i	0.570064	+	0.987380i	0.996559	+	0.0828898i	$0.0264149\pi$
$593$	13.8820	+	24.0443i	0.570064	+	0.987380i	−0.426495	+	0.904490i	$0.640252\pi$
$594$	17.5623			0.720590
$595$	−6.58359	+	5.70156i	−0.269901	+	0.233741i
$596$	−3.43769			−0.140813
$597$	−23.1525	−	40.1013i	−0.947568	−	1.64124i
$598$		0			0
$599$	8.53444	−	14.7821i	0.348708	−	0.603980i	−0.637312	−	0.770606i	$-0.719954\pi$
$599$	8.53444	−	14.7821i	0.348708	−	0.603980i	0.986020	+	0.166626i	$0.0532872\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	52.3607	+	18.1383i	2.13406	+	0.739261i
$603$	6.00000			0.244339
$604$	49.5517	+	85.8260i	2.01623	+	3.49221i
$605$	−2.23607	+	3.87298i	−0.0909091	+	0.157459i
$606$	−26.3435	+	45.6282i	−1.07013	+	1.85352i
$607$	−12.0623	−	20.8925i	−0.489594	−	0.848001i	0.510334	−	0.859976i	$-0.329522\pi$
$607$	−12.0623	−	20.8925i	−0.489594	−	0.848001i	−0.999928	+	0.0119745i	$0.996188\pi$
$608$	−32.5623			−1.32058
$609$	−5.00000	−	25.9808i	−0.202610	−	1.05279i
$610$	−17.5623			−0.711077
$611$		0			0
$612$	−7.14590	+	12.3771i	−0.288856	+	0.500313i
$613$	−9.06231	+	15.6964i	−0.366023	+	0.633971i	−0.988940	−	0.148318i	$-0.952614\pi$
$613$	−9.06231	+	15.6964i	−0.366023	+	0.633971i	0.622917	+	0.782288i	$0.285948\pi$
$614$	25.4164	+	44.0225i	1.02572	+	1.77660i
$615$	22.3607			0.901670
$616$	11.2082	+	58.2395i	0.451591	+	2.34654i
$617$	4.47214			0.180041			0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214			0.180041			0.0900207	+	0.995940i	$0.471307\pi$
$618$	−7.92705	−	13.7301i	−0.318873	−	0.552304i
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	0.984738	+	0.174042i	$0.0556830\pi$
$620$	−27.1353	+	46.9996i	−1.08978	+	1.88755i
$621$	9.20820	+	15.9491i	0.369512	+	0.640014i
$622$	−72.6869			−2.91448
$623$	5.59017	+	1.93649i	0.223965	+	0.0775839i
$624$		0			0
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	7.30902	−	12.6596i	0.292127	−	0.505979i
$627$	−10.0623	+	17.4284i	−0.401850	+	0.696024i
$628$	−16.9894	−	29.4264i	−0.677949	−	1.17424i
$629$	−6.93112			−0.276362
$630$	−23.4164	+	20.2792i	−0.932932	+	0.807943i
$631$	−22.8328			−0.908960			−0.454480	−	0.890757i	$-0.650175\pi$
$631$	−22.8328			−0.908960			−0.454480	+	0.890757i	$0.650175\pi$
$632$	10.1180	+	17.5249i	0.402474	+	0.697105i
$633$	4.47214	−	7.74597i	0.177751	−	0.307875i
$634$	−10.7812	+	18.6735i	−0.428174	+	0.741620i
$635$	−12.7639	−	22.1078i	−0.506521	−	0.877320i
$636$	81.1033			3.21596
$637$		0			0
$638$	35.1246			1.39060
$639$	−8.94427	−	15.4919i	−0.353830	−	0.612851i
$640$	1.21885	−	2.11111i	0.0481792	−	0.0834488i
$641$	−5.97214	+	10.3440i	−0.235885	+	0.408565i	−0.959530	−	0.281608i	$-0.909132\pi$
$641$	−5.97214	+	10.3440i	−0.235885	+	0.408565i	0.723644	+	0.690173i	$0.242466\pi$
$642$	−28.5795	−	49.5012i	−1.12794	−	1.95366i
$643$	−34.8328			−1.37367			−0.686836	−	0.726812i	$-0.741001\pi$
$643$	−34.8328			−1.37367			−0.686836	+	0.726812i	$0.741001\pi$
$644$	−79.9574	+	69.2452i	−3.15076	+	2.72864i
$645$	−40.0000			−1.57500
$646$	5.78115	+	10.0133i	0.227456	+	0.393966i
$647$	−10.1180	+	17.5249i	−0.397781	+	0.688977i	−0.993452	−	0.114252i	$-0.963553\pi$
$647$	−10.1180	+	17.5249i	−0.397781	+	0.688977i	0.595671	+	0.803229i	$0.296886\pi$
$648$	41.0967	−	71.1817i	1.61443	−	2.79628i
$649$	−2.20820	−	3.82472i	−0.0866796	−	0.150133i
$650$		0			0
$651$	−27.9508	−	9.68246i	−1.09548	−	0.379485i
$652$	79.6869			3.12078
$653$	−2.26393	−	3.92125i	−0.0885945	−	0.153450i	0.818323	−	0.574759i	$-0.194904\pi$
$653$	−2.26393	−	3.92125i	−0.0885945	−	0.153450i	−0.906917	+	0.421309i	$0.861571\pi$
$654$	7.92705	−	13.7301i	0.309972	−	0.536888i
$655$	−9.20820	+	15.9491i	−0.359794	+	0.623182i
$656$	−22.0344	−	38.1648i	−0.860300	−	1.49008i
$657$	5.41641			0.211314
$658$	9.78115	+	50.8244i	0.381309	+	1.98134i
$659$	−8.94427			−0.348419			−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427			−0.348419			−0.174210	+	0.984709i	$0.555737\pi$
$660$	−36.4058	−	63.0566i	−1.41709	−	2.45448i
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	−0.923854	−	0.382746i	$-0.874979\pi$
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	0.793394	+	0.608708i	$0.208312\pi$
$662$	−2.07295	+	3.59045i	−0.0805675	+	0.139547i
$663$		0			0
$664$		0			0
$665$	3.35410	+	17.4284i	0.130066	+	0.675845i
$666$	−24.6525			−0.955264
$667$	18.4164	+	31.8982i	0.713086	+	1.23510i
$668$	54.5410	−	94.4678i	2.11026	−	3.65507i
$669$	4.47214	−	7.74597i	0.172903	−	0.299476i
$670$	8.78115	+	15.2094i	0.339246	+	0.587591i
$671$	9.00000			0.347441
$672$	60.6763	+	21.0189i	2.34064	+	0.810821i
$673$	−9.41641			−0.362976			−0.181488	−	0.983393i	$-0.558091\pi$
$673$	−9.41641			−0.362976			−0.181488	+	0.983393i	$0.558091\pi$
$674$	−23.5623	−	40.8111i	−0.907586	−	1.57199i
$675$		0			0
$676$		0			0
$677$	1.44427	+	2.50155i	0.0555079	+	0.0961425i	0.892444	−	0.451158i	$-0.148989\pi$
$677$	1.44427	+	2.50155i	0.0555079	+	0.0961425i	−0.836936	+	0.547300i	$0.815656\pi$
$678$	−17.2361			−0.661947
$679$	−18.8328	+	16.3097i	−0.722737	+	0.625909i
$680$	−24.5967			−0.943242
$681$	−6.64590	−	11.5110i	−0.254671	−	0.441104i
$682$	19.6353	−	34.0093i	0.751873	−	1.30228i
$683$	−6.73607	+	11.6672i	−0.257748	+	0.446433i	−0.965638	−	0.259889i	$-0.916314\pi$
$683$	−6.73607	+	11.6672i	−0.257748	+	0.446433i	0.707890	+	0.706323i	$0.249647\pi$
$684$	14.5623	+	25.2227i	0.556804	+	0.964412i
$685$	−18.4164			−0.703655
$686$	−22.2533	+	43.0784i	−0.849635	+	1.64474i
$687$	53.9443			2.05810
$688$	39.4164	+	68.2712i	1.50274	+	2.60282i
$689$		0			0
$690$	53.9058	−	93.3675i	2.05216	−	3.55444i
$691$	−25.9164	−	44.8885i	−0.985907	−	1.70764i	−0.637836	−	0.770172i	$-0.720170\pi$
$691$	−25.9164	−	44.8885i	−0.985907	−	1.70764i	−0.348070	−	0.937468i	$-0.613163\pi$
$692$	−79.6869			−3.02924
$693$	12.0000	−	10.3923i	0.455842	−	0.394771i
$694$	60.3951			2.29257
$695$	−26.1803	−	45.3457i	−0.993077	−	1.72006i
$696$	37.3607	−	64.7106i	1.41615	−	2.45285i
$697$	−3.29180	+	5.70156i	−0.124686	+	0.215962i
$698$	−38.5066	−	66.6953i	−1.45750	−	2.52446i
$699$	−26.7082			−1.01020
$700$		0			0
$701$	−22.3607			−0.844551			−0.422276	−	0.906467i	$-0.638769\pi$
$701$	−22.3607			−0.844551			−0.422276	+	0.906467i	$0.638769\pi$
$702$		0			0
$703$	−7.06231	+	12.2323i	−0.266360	+	0.461349i
$704$	−13.0623	+	22.6246i	−0.492304	+	0.852696i
$705$	−18.6803	−	32.3553i	−0.703542	−	1.21857i
$706$	−45.2705			−1.70378
$707$	−4.50000	−	23.3827i	−0.169240	−	0.879396i
$708$	−15.9787			−0.600517
$709$	−25.0623	−	43.4092i	−0.941235	−	1.63027i	−0.763120	−	0.646256i	$-0.776334\pi$
$709$	−25.0623	−	43.4092i	−0.941235	−	1.63027i	−0.178114	−	0.984010i	$-0.557000\pi$
$710$	26.1803	−	45.3457i	0.982531	−	1.70179i
$711$	2.70820	−	4.69075i	0.101566	−	0.175917i
$712$	8.35410	+	14.4697i	0.313083	+	0.542276i
$713$	41.1803			1.54222
$714$	−4.30902	−	22.3903i	−0.161261	−	0.837936i
$715$		0			0
$716$	48.8435	+	84.5994i	1.82537	+	3.16163i
$717$	−21.7082	+	37.5997i	−0.810708	+	1.40419i
$718$	15.6353	−	27.0811i	0.583503	−	1.01066i
$719$	−12.3541	−	21.3979i	−0.460730	−	0.798008i	0.538267	−	0.842774i	$-0.319079\pi$
$719$	−12.3541	−	21.3979i	−0.460730	−	0.798008i	−0.998998	+	0.0447660i	$0.985746\pi$
$720$	−44.0689			−1.64235
$721$	6.77051	+	2.34537i	0.252147	+	0.0873463i
$722$	−26.1803			−0.974331
$723$	−5.26393	−	9.11740i	−0.195768	−	0.339080i
$724$	61.6869	−	106.845i	2.29258	−	3.97086i
$725$		0			0
$726$	−5.85410	−	10.1396i	−0.217266	−	0.376316i
$727$	−38.8328			−1.44023			−0.720115	−	0.693855i	$-0.755911\pi$
$727$	−38.8328			−1.44023			−0.720115	+	0.693855i	$0.755911\pi$
$728$		0			0
$729$	−7.00000			−0.259259
$730$	7.92705	+	13.7301i	0.293393	+	0.508172i
$731$	5.88854	−	10.1993i	0.217796	−	0.377233i
$732$	16.2812	−	28.1998i	0.601769	−	1.04229i
$733$	14.3541	+	24.8620i	0.530181	+	0.918300i	0.999380	+	0.0352078i	$0.0112093\pi$
$733$	14.3541	+	24.8620i	0.530181	+	0.918300i	−0.469199	+	0.883092i	$0.655457\pi$
$734$	−33.2705			−1.22804
$735$	5.00000	−	34.6410i	0.184428	−	1.27775i
$736$	−89.3951			−3.29515
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	−11.7082	+	20.2792i	−0.430985	+	0.746488i
$739$	−8.91641	+	15.4437i	−0.327995	+	0.568105i	−0.982114	−	0.188287i	$-0.939706\pi$
$739$	−8.91641	+	15.4437i	−0.327995	+	0.568105i	0.654119	+	0.756392i	$0.273040\pi$
$740$	−25.5517	−	44.2568i	−0.939298	−	1.62691i
$741$		0			0
$742$	−39.1246	+	33.8829i	−1.43631	+	1.24388i
$743$	−32.9443			−1.20861			−0.604304	−	0.796754i	$-0.706549\pi$
$743$	−32.9443			−1.20861			−0.604304	+	0.796754i	$0.706549\pi$
$744$	−41.7705	−	72.3486i	−1.53138	−	2.65243i
$745$	−0.791796	+	1.37143i	−0.0290092	+	0.0502453i
$746$	2.07295	−	3.59045i	0.0758961	−	0.131456i
$747$		0			0
$748$	21.4377			0.783840
$749$	24.4098	+	8.45581i	0.891916	+	0.308969i
$750$	−65.4508			−2.38993
$751$	5.06231	+	8.76817i	0.184726	+	0.319955i	0.943484	−	0.331417i	$-0.107527\pi$
$751$	5.06231	+	8.76817i	0.184726	+	0.319955i	−0.758758	+	0.651373i	$0.774194\pi$
$752$	−36.8156	+	63.7665i	−1.34253	+	2.32532i
$753$	1.70820	−	2.95870i	0.0622504	−	0.107821i
$754$		0			0
$755$	45.6525			1.66146
$756$	5.42705	+	28.1998i	0.197380	+	1.02562i
$757$	−52.8328			−1.92024			−0.960121	−	0.279586i	$-0.909803\pi$
$757$	−52.8328			−1.92024			−0.960121	+	0.279586i	$0.909803\pi$
$758$	−20.1803	−	34.9534i	−0.732983	−	1.26956i
$759$	−27.6246	+	47.8472i	−1.00271	+	1.73674i
$760$	−25.0623	+	43.4092i	−0.909105	+	1.57462i
$761$	−16.7705	−	29.0474i	−0.607931	−	1.05297i	−0.991581	−	0.129488i	$-0.958667\pi$
$761$	−16.7705	−	29.0474i	−0.607931	−	1.05297i	0.383650	−	0.923478i	$-0.374667\pi$
$762$	66.8328			2.42110
$763$	1.35410	+	7.03612i	0.0490218	+	0.254725i
$764$	54.2705			1.96344
$765$	3.29180	+	5.70156i	0.119015	+	0.206140i
$766$	19.6353	−	34.0093i	0.709451	−	1.22880i
$767$		0			0
$768$	−16.2812	−	28.1998i	−0.587496	−	1.01757i
$769$	−46.0000			−1.65880			−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000			−1.65880			−0.829401	+	0.558653i	$0.811318\pi$
$770$	43.9058	+	15.2094i	1.58225	+	0.548109i
$771$	0.124612			0.00448778
$772$	1.71885	+	2.97713i	0.0618627	+	0.107149i
$773$	−23.5344	+	40.7628i	−0.846475	+	1.46614i	0.0378590	+	0.999283i	$0.487946\pi$
$773$	−23.5344	+	40.7628i	−0.846475	+	1.46614i	−0.884334	+	0.466855i	$0.845387\pi$
$774$	20.9443	−	36.2765i	0.752826	−	1.30393i
$775$		0			0
$776$	−70.3607			−2.52580
$777$	21.0557	−	18.2348i	0.755370	−	0.654170i
$778$	3.85410			0.138176
$779$	6.70820	+	11.6190i	0.240346	+	0.416292i
$780$		0			0
$781$	−13.4164	+	23.2379i	−0.480077	+	0.831517i
$782$	15.8713	+	27.4899i	0.567557	+	0.983038i
$783$	10.0000			0.357371
$784$	−64.0517	+	25.6017i	−2.28756	+	0.914347i
$785$	−15.6525			−0.558661
$786$	−24.1074	−	41.7552i	−0.859882	−	1.48936i
$787$	10.2082	−	17.6811i	0.363883	−	0.630264i	−0.624713	−	0.780854i	$-0.714784\pi$
$787$	10.2082	−	17.6811i	0.363883	−	0.630264i	0.988596	+	0.150590i	$0.0481174\pi$
$788$	−21.9787	+	38.0682i	−0.782959	+	1.35613i
$789$	29.2082	+	50.5901i	1.03984	+	1.80106i
$790$	15.8541			0.564064
$791$	5.88854	−	5.09963i	0.209373	−	0.181322i
$792$	44.8328			1.59306
$793$		0			0
$794$	−34.1976	+	59.2319i	−1.21363	+	2.10206i
$795$	18.6803	−	32.3553i	0.662523	−	1.14752i
$796$	50.2599	+	87.0526i	1.78141	+	3.08550i
$797$	9.05573			0.320770			0.160385	−	0.987055i	$-0.448726\pi$
$797$	9.05573			0.320770			0.160385	+	0.987055i	$0.448726\pi$
$798$	−43.9058	−	15.2094i	−1.55425	−	0.538407i
$799$	11.0000			0.389152
$800$		0			0
$801$	2.23607	−	3.87298i	0.0790076	−	0.136845i
$802$	18.6353	−	32.2772i	0.658034	−	1.13975i
$803$	−4.06231	−	7.03612i	−0.143356	−	0.248299i
$804$	−32.5623			−1.14838
$805$	9.20820	+	47.8472i	0.324547	+	1.68639i
$806$		0			0
$807$	15.0623	+	26.0887i	0.530218	+	0.918365i
$808$	33.6246	−	58.2395i	1.18291	−	2.04886i
$809$	−11.2082	+	19.4132i	−0.394059	+	0.682531i	−0.992981	−	0.118277i	$-0.962263\pi$
$809$	−11.2082	+	19.4132i	−0.394059	+	0.682531i	0.598921	+	0.800808i	$0.295596\pi$
$810$	−32.1976	−	55.7678i	−1.13131	−	1.95948i
$811$	14.8328			0.520851			0.260425	−	0.965494i	$-0.416137\pi$
$811$	14.8328			0.520851			0.260425	+	0.965494i	$0.416137\pi$
$812$	10.8541	+	56.3996i	0.380904	+	1.97924i
$813$	−45.6525			−1.60110
$814$	18.4894	+	32.0245i	0.648052	+	1.12246i
$815$	18.3541	−	31.7902i	0.642916	−	1.11356i
$816$	16.2188	−	28.0919i	0.567773	−	0.983412i
$817$	−12.0000	−	20.7846i	−0.419827	−	0.727161i
$818$	−22.7984			−0.797126
$819$		0			0
$820$	−48.5410			−1.69513
$821$	19.1180	+	33.1134i	0.667224	+	1.15567i	0.978677	+	0.205404i	$0.0658509\pi$
$821$	19.1180	+	33.1134i	0.667224	+	1.15567i	−0.311453	+	0.950261i	$0.600816\pi$
$822$	24.1074	−	41.7552i	0.840842	−	1.45638i
$823$	−17.0623	+	29.5528i	−0.594755	+	1.03015i	0.398827	+	0.917026i	$0.369417\pi$
$823$	−17.0623	+	29.5528i	−0.594755	+	1.03015i	−0.993581	+	0.113119i	$0.963916\pi$
$824$	10.1180	+	17.5249i	0.352478	+	0.610511i
$825$		0			0
$826$	7.70820	−	6.67550i	0.268203	−	0.232270i
$827$	−26.8328			−0.933068			−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328			−0.933068			−0.466534	+	0.884503i	$0.654498\pi$
$828$	39.9787	+	69.2452i	1.38936	+	2.40644i
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$	−0.465558	−	0.806370i	−0.0161500	−	0.0279727i
$832$		0			0
$833$	8.09675	+	6.37454i	0.280536	+	0.220865i
$834$	137.082			4.74676
$835$	−25.1246	−	43.5171i	−0.869473	−	1.50597i
$836$	21.8435	−	37.8340i	0.755472	−	1.30852i
$837$	5.59017	−	9.68246i	0.193225	−	0.334675i
$838$	−43.1246	−	74.6940i	−1.48971	−	2.58026i
$839$	5.88854			0.203295			0.101648	−	0.994820i	$-0.467589\pi$
$839$	5.88854			0.203295			0.101648	+	0.994820i	$0.467589\pi$
$840$	74.7214	−	64.7106i	2.57813	−	2.23273i
$841$	−9.00000			−0.310345
$842$	17.5623	+	30.4188i	0.605237	+	1.04830i
$843$	−30.1246	+	52.1774i	−1.03755	+	1.79708i
$844$	−9.70820	+	16.8151i	−0.334170	+	0.578800i
$845$		0			0
$846$	39.1246			1.34513
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$	−73.6312			−2.52851
$849$	29.2082	+	50.5901i	1.00242	+	1.73625i
$850$		0			0
$851$	−19.3885	+	33.5819i	−0.664631	+	1.15117i
$852$	48.5410	+	84.0755i	1.66299	+	2.88038i
$853$	52.2492			1.78898			0.894490	−	0.447089i	$-0.147539\pi$
$853$	52.2492			1.78898			0.894490	+	0.447089i	$0.147539\pi$
$854$	3.92705	+	20.4056i	0.134381	+	0.698264i
$855$	13.4164			0.458831
$856$	36.4787	+	63.1830i	1.24682	+	2.15955i
$857$	0.680340	−	1.17838i	0.0232400	−	0.0402528i	−0.854172	−	0.519991i	$-0.825935\pi$
$857$	0.680340	−	1.17838i	0.0232400	−	0.0402528i	0.877411	+	0.479739i	$0.159268\pi$
$858$		0			0
$859$	−10.3541	−	17.9338i	−0.353277	−	0.611894i	0.633544	−	0.773707i	$-0.281599\pi$
$859$	−10.3541	−	17.9338i	−0.353277	−	0.611894i	−0.986822	+	0.161812i	$0.948266\pi$
$860$	86.8328			2.96097
$861$	−5.00000	−	25.9808i	−0.170400	−	0.885422i
$862$	82.1033			2.79645
$863$	11.9721	+	20.7363i	0.407536	+	0.705873i	0.994613	−	0.103658i	$-0.0330547\pi$
$863$	11.9721	+	20.7363i	0.407536	+	0.705873i	−0.587077	+	0.809531i	$0.699721\pi$
$864$	−12.1353	+	21.0189i	−0.412850	+	0.715077i
$865$	−18.3541	+	31.7902i	−0.624058	+	1.08090i
$866$	−38.5066	−	66.6953i	−1.30851	−	2.26640i
$867$	33.1672			1.12642
$868$	60.6763	+	21.0189i	2.05949	+	0.713427i
$869$	−8.12461			−0.275609
$870$	−29.2705	−	50.6980i	−0.992363	−	1.71882i
$871$		0			0
$872$	−10.1180	+	17.5249i	−0.342640	+	0.593470i
$873$	9.41641	+	16.3097i	0.318697	+	0.552000i
$874$	64.6869			2.18807
$875$	22.3607	−	19.3649i	0.755929	−	0.654654i
$876$	−29.3951			−0.993169
$877$	16.0623	+	27.8207i	0.542386	+	0.939439i	0.998766	+	0.0496548i	$0.0158121\pi$
$877$	16.0623	+	27.8207i	0.542386	+	0.939439i	−0.456381	+	0.889785i	$0.650855\pi$
$878$	−31.5795	+	54.6973i	−1.06576	+	1.84595i
$879$	16.7082	−	28.9395i	0.563554	−	0.976104i
$880$	33.0517	+	57.2472i	1.11417	+	1.92980i
$881$	43.3050			1.45898			0.729490	−	0.683991i	$-0.239757\pi$
$881$	43.3050			1.45898			0.729490	+	0.683991i	$0.239757\pi$
$882$	28.7984	+	22.6728i	0.969692	+	0.763434i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−3.68034	+	6.37454i	−0.123713	+	0.214278i
$886$	−2.92705	+	5.06980i	−0.0983362	+	0.170323i
$887$	10.1180	+	17.5249i	0.339730	+	0.588430i	0.984382	−	0.176046i	$-0.0563309\pi$
$887$	10.1180	+	17.5249i	0.339730	+	0.588430i	−0.644652	+	0.764477i	$0.722998\pi$
$888$	78.6656			2.63985
$889$	−22.8328	+	19.7738i	−0.765788	+	0.663192i
$890$	13.0902			0.438783
$891$	16.5000	+	28.5788i	0.552771	+	0.957427i
$892$	−9.70820	+	16.8151i	−0.325055	+	0.563011i
$893$	11.2082	−	19.4132i	0.375068	−	0.649637i
$894$	−2.07295	−	3.59045i	−0.0693298	−	0.120083i
$895$	45.0000			1.50418
$896$	−2.72542	−	0.944115i	−0.0910501	−	0.0315407i
$897$		0			0
$898$	−44.9787	−	77.9054i	−1.50096	−	2.59974i
$899$	11.1803	−	19.3649i	0.372885	−	0.645856i
$900$		0			0
$901$	5.50000	+	9.52628i	0.183232	+	0.317366i
$902$	35.1246			1.16952
$903$	8.94427	+	46.4758i	0.297647	+	1.54662i
$904$	22.0000			0.731709
$905$	−28.4164	−	49.2187i	−0.944593	−	1.63608i
$906$	−59.7599	+	103.507i	−1.98539	+	3.43879i
$907$	−9.35410	+	16.2018i	−0.310598	+	0.537971i	−0.978492	−	0.206285i	$-0.933863\pi$
$907$	−9.35410	+	16.2018i	−0.310598	+	0.537971i	0.667894	+	0.744256i	$0.267196\pi$
$908$	14.4271	+	24.9884i	0.478779	+	0.829269i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−34.2492			−1.13473			−0.567364	−	0.823467i	$-0.692037\pi$
$911$	−34.2492			−1.13473			−0.567364	+	0.823467i	$0.692037\pi$
$912$	−33.0517	−	57.2472i	−1.09445	−	1.89564i
$913$		0			0
$914$	−8.01722	+	13.8862i	−0.265186	+	0.459316i
$915$	−7.50000	−	12.9904i	−0.247942	−	0.429449i
$916$	−117.103			−3.86920
$917$	20.5902	+	7.13264i	0.679947	+	0.235541i
$918$	8.61803			0.284438
$919$	−10.0623	−	17.4284i	−0.331925	−	0.574911i	0.650964	−	0.759108i	$-0.274365\pi$
$919$	−10.0623	−	17.4284i	−0.331925	−	0.574911i	−0.982889	+	0.184198i	$0.941031\pi$
$920$	−68.8050	+	119.174i	−2.26843	+	3.92904i
$921$	−21.7082	+	37.5997i	−0.715310	+	1.23895i
$922$	44.9787	+	77.9054i	1.48130	+	2.56568i
$923$		0			0
$924$	−65.1246	+	56.3996i	−2.14244	+	1.85541i
$925$		0			0
$926$	−31.4164	−	54.4148i	−1.03241	−	1.78818i
$927$	2.70820	−	4.69075i	0.0889491	−	0.154064i
$928$	−24.2705	+	42.0378i	−0.796719	+	1.37996i
$929$	−12.4098	−	21.4945i	−0.407153	−	0.705210i	0.587416	−	0.809285i	$-0.300145\pi$
$929$	−12.4098	−	21.4945i	−0.407153	−	0.705210i	−0.994569	+	0.104075i	$0.966812\pi$
$930$	−65.4508			−2.14622
$931$	19.5000	−	7.79423i	0.639087	−	0.255446i
$932$	57.9787			1.89916
$933$	−31.0410	−	53.7646i	−1.01624	−	1.76017i
$934$	−12.6353	+	21.8849i	−0.413438	+	0.716096i
$935$	4.93769	−	8.55234i	0.161480	−	0.279691i
$936$		0			0
$937$	25.4164			0.830318			0.415159	−	0.909749i	$-0.363726\pi$
$937$	25.4164			0.830318			0.415159	+	0.909749i	$0.363726\pi$
$938$	15.7082	−	13.6037i	0.512891	−	0.444177i
$939$	12.4853			0.407442
$940$	40.5517	+	70.2375i	1.32265	+	2.29090i
$941$	25.1180	−	43.5057i	0.818825	−	1.41825i	−0.0877244	−	0.996145i	$-0.527959\pi$
$941$	25.1180	−	43.5057i	0.818825	−	1.41825i	0.906549	−	0.422101i	$-0.138707\pi$
$942$	20.4894	−	35.4886i	0.667579	−	1.15628i
$943$	18.4164	+	31.8982i	0.599721	+	1.03875i
$944$	14.5066			0.472149
$945$	12.5000	+	4.33013i	0.406625	+	0.140859i
$946$	−62.8328			−2.04287
$947$	−11.2639	−	19.5097i	−0.366029	−	0.633980i	0.622912	−	0.782292i	$-0.285949\pi$
$947$	−11.2639	−	19.5097i	−0.366029	−	0.633980i	−0.988941	+	0.148312i	$0.952616\pi$
$948$	−14.6976	+	25.4569i	−0.477355	+	0.826802i
$949$		0			0
$950$		0			0
$951$	−18.4164			−0.597193
$952$	5.50000	+	28.5788i	0.178256	+	0.926245i
$953$	−41.7771			−1.35329			−0.676646	−	0.736308i	$-0.736567\pi$
$953$	−41.7771			−1.35329			−0.676646	+	0.736308i	$0.736567\pi$
$954$	19.5623	+	33.8829i	0.633353	+	1.09700i
$955$	12.5000	−	21.6506i	0.404491	−	0.700598i
$956$	47.1246	−	81.6222i	1.52412	−	2.63985i
$957$	15.0000	+	25.9808i	0.484881	+	0.839839i
$958$	−62.3951			−2.01589
$959$	4.11803	+	21.3979i	0.132978	+	0.690975i
$960$	43.5410			1.40528
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	9.76393	−	16.9116i	0.314638	−	0.544970i
$964$	11.4271	+	19.7922i	0.368041	+	0.637465i
$965$	1.58359			0.0509776
$966$	−120.537	−	41.7552i	−3.87821	−	1.34345i
$967$	−16.5836			−0.533292			−0.266646	−	0.963794i	$-0.585916\pi$
$967$	−16.5836			−0.533292			−0.266646	+	0.963794i	$0.585916\pi$
$968$	7.47214	+	12.9421i	0.240164	+	0.415975i
$969$	−4.93769	+	8.55234i	−0.158622	+	0.274741i
$970$	−27.5623	+	47.7393i	−0.884972	+	1.53282i
$971$	5.64590	+	9.77898i	0.181185	+	0.313822i	0.942285	−	0.334813i	$-0.108673\pi$
$971$	5.64590	+	9.77898i	0.181185	+	0.313822i	−0.761099	+	0.648636i	$0.775340\pi$
$972$	86.8328			2.78516
$973$	−46.8328	+	40.5584i	−1.50139	+	1.30024i
$974$	57.1591			1.83149
$975$		0			0
$976$	−14.7812	+	25.6017i	−0.473133	+	0.819491i
$977$	−1.17376	+	2.03302i	−0.0375520	+	0.0650419i	−0.884191	−	0.467126i	$-0.845289\pi$
$977$	−1.17376	+	2.03302i	−0.0375520	+	0.0650419i	0.846639	+	0.532168i	$0.178623\pi$
$978$	48.0517	+	83.2279i	1.53652	+	2.66134i
$979$	−6.70820			−0.214395
$980$	−10.8541	+	75.1994i	−0.346722	+	2.40216i
$981$	5.41641			0.172933
$982$	33.4164	+	57.8789i	1.06636	+	1.84699i
$983$	3.73607	−	6.47106i	0.119162	−	0.206395i	−0.800274	−	0.599635i	$-0.795313\pi$
$983$	3.73607	−	6.47106i	0.119162	−	0.206395i	0.919436	+	0.393240i	$0.128646\pi$
$984$	37.3607	−	64.7106i	1.19101	−	2.06290i
$985$	10.1246	+	17.5363i	0.322597	+	0.558754i
$986$	17.2361			0.548908
$987$	−33.4164	+	28.9395i	−1.06366	+	0.921153i
$988$		0			0
$989$	−32.9443	−	57.0612i	−1.04757	−	1.81444i
$990$	17.5623	−	30.4188i	0.558167	−	0.966773i
$991$	−15.3541	+	26.5941i	−0.487739	+	0.844789i	−0.999901	−	0.0141002i	$-0.995512\pi$
$991$	−15.3541	+	26.5941i	−0.487739	+	0.844789i	0.512161	+	0.858889i	$0.328845\pi$
$992$	27.1353	+	46.9996i	0.861545	+	1.49224i
$993$	−3.54102			−0.112371
$994$	−58.5410	−	20.2792i	−1.85681	−	0.643217i
$995$	46.3050			1.46797
$996$		0			0
$997$	−13.2082	+	22.8773i	−0.418308	+	0.724531i	−0.995769	−	0.0918873i	$-0.970710\pi$
$997$	−13.2082	+	22.8773i	−0.418308	+	0.724531i	0.577461	+	0.816418i	$0.304043\pi$
$998$	34.5795	−	59.8935i	1.09460	−	1.89590i
$999$	5.26393	+	9.11740i	0.166543	+	0.288462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.d.508.1		4
7.2	even	3	inner	1183.2.e.d.170.1		4
7.3	odd	6		8281.2.a.ba.1.2		2
7.4	even	3		8281.2.a.z.1.2		2
13.12	even	2		91.2.e.b.53.2	✓	4
39.38	odd	2		819.2.j.c.235.1		4
52.51	odd	2		1456.2.r.j.417.1		4
91.12	odd	6		637.2.e.h.79.2		4
91.25	even	6		637.2.a.f.1.1		2
91.38	odd	6		637.2.a.e.1.1		2
91.51	even	6		91.2.e.b.79.2	yes	4
91.90	odd	2		637.2.e.h.508.2		4
273.38	even	6		5733.2.a.w.1.2		2
273.116	odd	6		5733.2.a.v.1.2		2
273.233	odd	6		819.2.j.c.352.1		4
364.51	odd	6		1456.2.r.j.625.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.2	✓	4	13.12	even	2
91.2.e.b.79.2	yes	4	91.51	even	6
637.2.a.e.1.1		2	91.38	odd	6
637.2.a.f.1.1		2	91.25	even	6
637.2.e.h.79.2		4	91.12	odd	6
637.2.e.h.508.2		4	91.90	odd	2
819.2.j.c.235.1		4	39.38	odd	2
819.2.j.c.352.1		4	273.233	odd	6
1183.2.e.d.170.1		4	7.2	even	3	inner
1183.2.e.d.508.1		4	1.1	even	1	trivial
1456.2.r.j.417.1		4	52.51	odd	2
1456.2.r.j.625.1		4	364.51	odd	6
5733.2.a.v.1.2		2	273.116	odd	6
5733.2.a.w.1.2		2	273.38	even	6
8281.2.a.z.1.2		2	7.4	even	3
8281.2.a.ba.1.2		2	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)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} +(2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.30902 - 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} +(2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.92705 - 5.06980i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(5.42705 + 9.39993i) q^{12} +(-6.54508 - 2.26728i) q^{14} +5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-0.736068 + 1.27491i) q^{17} +(-2.61803 + 4.53457i) q^{18} +(1.50000 + 2.59808i) q^{19} -10.8541 q^{20} +(-1.11803 - 5.80948i) q^{21} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(8.35410 - 14.4697i) q^{24} +2.23607 q^{27} +(2.42705 + 12.6113i) q^{28} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(2.50000 - 4.33013i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(3.35410 + 5.80948i) q^{33} +3.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +9.70820 q^{36} +(2.35410 + 4.07742i) q^{37} +(3.92705 - 6.80185i) q^{38} +(8.35410 + 14.4697i) q^{40} +4.47214 q^{41} +(-11.7082 + 10.1396i) q^{42} -8.00000 q^{43} +(-7.28115 - 12.6113i) q^{44} +(2.23607 - 3.87298i) q^{45} +(10.7812 - 18.6735i) q^{46} +(-3.73607 - 6.47106i) q^{47} -22.0344 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.64590 + 2.85078i) q^{51} +(3.73607 - 6.47106i) q^{53} +(-2.92705 - 5.06980i) q^{54} -6.70820 q^{55} +(14.9443 - 12.9421i) q^{56} +6.70820 q^{57} +(-5.85410 - 10.1396i) q^{58} +(-0.736068 + 1.27491i) q^{59} +(-12.1353 + 21.0189i) q^{60} +(-1.50000 - 2.59808i) q^{61} -13.0902 q^{62} +(-5.00000 - 1.73205i) q^{63} +8.70820 q^{64} +(8.78115 - 15.2094i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-3.57295 - 6.18853i) q^{68} +18.4164 q^{69} +(-2.92705 - 15.2094i) q^{70} +8.94427 q^{71} +(-7.47214 - 12.9421i) q^{72} +(-1.35410 + 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} -14.5623 q^{76} +(1.50000 + 7.79423i) q^{77} +(1.35410 + 2.34537i) q^{79} +(11.0172 - 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.85410 - 10.1396i) q^{82} +(27.1353 + 9.39993i) q^{84} -3.29180 q^{85} +(10.4721 + 18.1383i) q^{86} +(5.00000 - 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(1.11803 + 1.93649i) q^{89} -11.7082 q^{90} -39.9787 q^{92} +(-5.59017 - 9.68246i) q^{93} +(-9.78115 + 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(12.1353 + 21.0189i) q^{96} -9.41641 q^{97} +(-17.0172 + 6.80185i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^4 - 10 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 4 q - 3 q^{2} - 3 q^{4} - 10 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 5 q^{10} - 6 q^{11} + 15 q^{12} - 15 q^{14} + 20 q^{15} - 13 q^{16} + 6 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{28} - 15 q^{30} + 10 q^{31} - 15 q^{32} + 2 q^{34} + 12 q^{36} - 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} - 9 q^{44} + 23 q^{46} - 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 6 q^{53} - 5 q^{54} + 24 q^{56} - 10 q^{58} + 6 q^{59} - 15 q^{60} - 6 q^{61} - 30 q^{62} - 20 q^{63} + 8 q^{64} + 15 q^{66} - 6 q^{67} - 21 q^{68} + 20 q^{69} - 5 q^{70} - 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} + 6 q^{77} - 8 q^{79} + 15 q^{80} + 22 q^{81} - 10 q^{82} + 75 q^{84} - 40 q^{85} + 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} - 66 q^{92} - 19 q^{94} + 15 q^{96} + 16 q^{97} - 39 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^4 - 10 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 5 * q^10 - 6 * q^11 + 15 * q^12 - 15 * q^14 + 20 * q^15 - 13 * q^16 + 6 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 + 18 * q^22 + 12 * q^23 + 20 * q^24 + 3 * q^28 - 15 * q^30 + 10 * q^31 - 15 * q^32 + 2 * q^34 + 12 * q^36 - 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 - 9 * q^44 + 23 * q^46 - 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 6 * q^53 - 5 * q^54 + 24 * q^56 - 10 * q^58 + 6 * q^59 - 15 * q^60 - 6 * q^61 - 30 * q^62 - 20 * q^63 + 8 * q^64 + 15 * q^66 - 6 * q^67 - 21 * q^68 + 20 * q^69 - 5 * q^70 - 12 * q^72 + 8 * q^73 + 9 * q^74 - 18 * q^76 + 6 * q^77 - 8 * q^79 + 15 * q^80 + 22 * q^81 - 10 * q^82 + 75 * q^84 - 40 * q^85 + 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 - 66 * q^92 - 19 * q^94 + 15 * q^96 + 16 * q^97 - 39 * q^98 + 24 * q^99

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