LMFDB - Embedded newform 1064.2.q.n.457.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (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:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.6
Root			$0.670757 + 1.16179i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.n.305.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +O(q^{10})$	\(q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +(-2.49731 - 4.32547i) q^{11} +1.55217 q^{13} -3.90205 q^{15} +(-3.09564 - 5.36181i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.15781 - 3.35516i) q^{21} +(-3.39198 + 5.87509i) q^{23} +(-1.73024 - 2.99686i) q^{25} +5.63482 q^{27} +0.707720 q^{29} +(-4.78494 - 8.28777i) q^{31} +(3.35018 - 5.80268i) q^{33} +(5.04489 - 5.81141i) q^{35} +(-2.12203 + 3.67547i) q^{37} +(1.04113 + 1.80329i) q^{39} -2.00000 q^{41} -1.25818 q^{43} +(1.74571 + 3.02365i) q^{45} +(6.17715 - 10.6991i) q^{47} +(6.49383 + 2.61347i) q^{49} +(4.15285 - 7.19295i) q^{51} +(-0.445867 - 0.772264i) q^{53} +14.5278 q^{55} -1.34151 q^{57} +(-5.28845 - 9.15987i) q^{59} +(5.91457 - 10.2443i) q^{61} +(-2.08189 + 2.39821i) q^{63} +(-2.25739 + 3.90992i) q^{65} +(-0.994841 - 1.72312i) q^{67} -9.10079 q^{69} -12.4174 q^{71} +(3.50344 + 6.06814i) q^{73} +(2.32114 - 4.02033i) q^{75} +(4.31068 + 12.4917i) q^{77} +(-8.46797 + 14.6670i) q^{79} +(1.97908 + 3.42787i) q^{81} -0.494217 q^{83} +18.0085 q^{85} +(0.474708 + 0.822219i) q^{87} +(1.69022 - 2.92754i) q^{89} +(-4.03174 - 0.780862i) q^{91} +(6.41907 - 11.1182i) q^{93} +(-1.45434 - 2.51900i) q^{95} -10.0685 q^{97} -5.99524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	0.670757	+	1.16179i	0.387262	+	0.670757i	0.992080	−	0.125606i	$-0.0400876\pi$
$3$	0.670757	+	1.16179i	0.387262	+	0.670757i	−0.604818	+	0.796363i	$0.706754\pi$
$4$		0			0
$5$	−1.45434	+	2.51900i	−0.650403	+	1.12653i	0.332622	+	0.943060i	$0.392067\pi$
$5$	−1.45434	+	2.51900i	−0.650403	+	1.12653i	−0.983025	+	0.183471i	$0.941267\pi$
$6$		0			0
$7$	−2.59748	−	0.503078i	−0.981756	−	0.190145i
$7$	−2.59748	−	0.503078i	−0.981756	−	0.190145i
$8$		0			0
$9$	0.600170	−	1.03952i	0.200057	−	0.346508i
$10$		0			0
$11$	−2.49731	−	4.32547i	−0.752968	−	1.30418i	−0.946378	−	0.323061i	$-0.895288\pi$
$11$	−2.49731	−	4.32547i	−0.752968	−	1.30418i	0.193410	−	0.981118i	$-0.438045\pi$
$12$		0			0
$13$	1.55217			0.430495			0.215247	−	0.976560i	$-0.430944\pi$
$13$	1.55217			0.430495			0.215247	+	0.976560i	$0.430944\pi$
$14$		0			0
$15$	−3.90205			−1.00750
$16$		0			0
$17$	−3.09564	−	5.36181i	−0.750804	−	1.30043i	−0.947434	−	0.319953i	$-0.896333\pi$
$17$	−3.09564	−	5.36181i	−0.750804	−	1.30043i	0.196630	−	0.980478i	$-0.437000\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	−1.15781	−	3.35516i	−0.252655	−	0.732156i
$22$		0			0
$23$	−3.39198	+	5.87509i	−0.707278	+	1.22504i	0.258586	+	0.965988i	$0.416744\pi$
$23$	−3.39198	+	5.87509i	−0.707278	+	1.22504i	−0.965863	+	0.259052i	$0.916590\pi$
$24$		0			0
$25$	−1.73024	−	2.99686i	−0.346047	−	0.599372i
$26$		0			0
$27$	5.63482			1.08442
$28$		0			0
$29$	0.707720			0.131420			0.0657102	−	0.997839i	$-0.479069\pi$
$29$	0.707720			0.131420			0.0657102	+	0.997839i	$0.479069\pi$
$30$		0			0
$31$	−4.78494	−	8.28777i	−0.859401	−	1.48853i	−0.872501	−	0.488613i	$-0.837503\pi$
$31$	−4.78494	−	8.28777i	−0.859401	−	1.48853i	0.0130995	−	0.999914i	$-0.495830\pi$
$32$		0			0
$33$	3.35018	−	5.80268i	0.583192	−	1.01012i
$34$		0			0
$35$	5.04489	−	5.81141i	0.852741	−	0.982307i
$36$		0			0
$37$	−2.12203	+	3.67547i	−0.348860	+	0.604243i	−0.986047	−	0.166466i	$-0.946764\pi$
$37$	−2.12203	+	3.67547i	−0.348860	+	0.604243i	0.637187	+	0.770709i	$0.280098\pi$
$38$		0			0
$39$	1.04113	+	1.80329i	0.166714	+	0.288757i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−1.25818			−0.191871			−0.0959355	−	0.995388i	$-0.530584\pi$
$43$	−1.25818			−0.191871			−0.0959355	+	0.995388i	$0.530584\pi$
$44$		0			0
$45$	1.74571	+	3.02365i	0.260235	+	0.450740i
$46$		0			0
$47$	6.17715	−	10.6991i	0.901030	−	1.56063i	0.0748706	−	0.997193i	$-0.476146\pi$
$47$	6.17715	−	10.6991i	0.901030	−	1.56063i	0.826159	−	0.563436i	$-0.190521\pi$
$48$		0			0
$49$	6.49383	+	2.61347i	0.927689	+	0.373353i
$50$		0			0
$51$	4.15285	−	7.19295i	0.581515	−	1.00721i
$52$		0			0
$53$	−0.445867	−	0.772264i	−0.0612445	−	0.106079i	0.833777	−	0.552101i	$-0.186174\pi$
$53$	−0.445867	−	0.772264i	−0.0612445	−	0.106079i	−0.895022	+	0.446022i	$0.852840\pi$
$54$		0			0
$55$	14.5278			1.95893
$56$		0			0
$57$	−1.34151			−0.177688
$58$		0			0
$59$	−5.28845	−	9.15987i	−0.688498	−	1.19251i	−0.972324	−	0.233638i	$-0.924937\pi$
$59$	−5.28845	−	9.15987i	−0.688498	−	1.19251i	0.283826	−	0.958876i	$-0.408396\pi$
$60$		0			0
$61$	5.91457	−	10.2443i	0.757283	−	1.31165i	−0.186948	−	0.982370i	$-0.559860\pi$
$61$	5.91457	−	10.2443i	0.757283	−	1.31165i	0.944231	−	0.329283i	$-0.106807\pi$
$62$		0			0
$63$	−2.08189	+	2.39821i	−0.262294	+	0.302147i
$64$		0			0
$65$	−2.25739	+	3.90992i	−0.279995	+	0.484965i
$66$		0			0
$67$	−0.994841	−	1.72312i	−0.121539	−	0.210512i	0.798836	−	0.601549i	$-0.205450\pi$
$67$	−0.994841	−	1.72312i	−0.121539	−	0.210512i	−0.920375	+	0.391037i	$0.872116\pi$
$68$		0			0
$69$	−9.10079			−1.09561
$70$		0			0
$71$	−12.4174			−1.47368			−0.736839	−	0.676068i	$-0.763683\pi$
$71$	−12.4174			−1.47368			−0.736839	+	0.676068i	$0.763683\pi$
$72$		0			0
$73$	3.50344	+	6.06814i	0.410047	+	0.710222i	0.994894	−	0.100921i	$-0.0321790\pi$
$73$	3.50344	+	6.06814i	0.410047	+	0.710222i	−0.584848	+	0.811143i	$0.698846\pi$
$74$		0			0
$75$	2.32114	−	4.02033i	0.268022	−	0.464228i
$76$		0			0
$77$	4.31068	+	12.4917i	0.491247	+	1.42356i
$78$		0			0
$79$	−8.46797	+	14.6670i	−0.952721	+	1.65016i	−0.213223	+	0.977004i	$0.568396\pi$
$79$	−8.46797	+	14.6670i	−0.952721	+	1.65016i	−0.739498	+	0.673158i	$0.764937\pi$
$80$		0			0
$81$	1.97908	+	3.42787i	0.219898	+	0.380875i
$82$		0			0
$83$	−0.494217			−0.0542474			−0.0271237	−	0.999632i	$-0.508635\pi$
$83$	−0.494217			−0.0542474			−0.0271237	+	0.999632i	$0.508635\pi$
$84$		0			0
$85$	18.0085			1.95330
$86$		0			0
$87$	0.474708	+	0.822219i	0.0508941	+	0.0881511i
$88$		0			0
$89$	1.69022	−	2.92754i	0.179163	−	0.310319i	−0.762431	−	0.647069i	$-0.775995\pi$
$89$	1.69022	−	2.92754i	0.179163	−	0.310319i	0.941594	+	0.336750i	$0.109328\pi$
$90$		0			0
$91$	−4.03174	−	0.780862i	−0.422641	−	0.0818566i
$92$		0			0
$93$	6.41907	−	11.1182i	0.665627	−	1.15290i
$94$		0			0
$95$	−1.45434	−	2.51900i	−0.149213	−	0.258444i
$96$		0			0
$97$	−10.0685			−1.02230			−0.511152	−	0.859491i	$-0.670781\pi$
$97$	−10.0685			−1.02230			−0.511152	+	0.859491i	$0.670781\pi$
$98$		0			0
$99$	−5.99524			−0.602545
$100$		0			0
$101$	−1.28615	−	2.22768i	−0.127977	−	0.221663i	0.794916	−	0.606720i	$-0.207515\pi$
$101$	−1.28615	−	2.22768i	−0.127977	−	0.221663i	−0.922893	+	0.385057i	$0.874182\pi$
$102$		0			0
$103$	−3.21853	+	5.57466i	−0.317131	+	0.549288i	−0.979888	−	0.199547i	$-0.936053\pi$
$103$	−3.21853	+	5.57466i	−0.317131	+	0.549288i	0.662757	+	0.748835i	$0.269386\pi$
$104$		0			0
$105$	10.1355	+	1.96303i	0.989124	+	0.191572i
$106$		0			0
$107$	−1.19930	+	2.07724i	−0.115940	+	0.200815i	−0.918155	−	0.396221i	$-0.870322\pi$
$107$	−1.19930	+	2.07724i	−0.115940	+	0.200815i	0.802215	+	0.597035i	$0.203655\pi$
$108$		0			0
$109$	7.12729	+	12.3448i	0.682670	+	1.18242i	0.974163	+	0.225847i	$0.0725148\pi$
$109$	7.12729	+	12.3448i	0.682670	+	1.18242i	−0.291493	+	0.956573i	$0.594152\pi$
$110$		0			0
$111$	−5.69348			−0.540401
$112$		0			0
$113$	−0.713643			−0.0671338			−0.0335669	−	0.999436i	$-0.510687\pi$
$113$	−0.713643			−0.0671338			−0.0335669	+	0.999436i	$0.510687\pi$
$114$		0			0
$115$	−9.86623	−	17.0888i	−0.920031	−	1.59354i
$116$		0			0
$117$	0.931566	−	1.61352i	0.0861233	−	0.149170i
$118$		0			0
$119$	5.34347	+	15.4846i	0.489835	+	1.41947i
$120$		0			0
$121$	−6.97314	+	12.0778i	−0.633922	+	1.09798i
$122$		0			0
$123$	−1.34151	−	2.32357i	−0.120960	−	0.209509i
$124$		0			0
$125$	−4.47800			−0.400525
$126$		0			0
$127$	−8.73364			−0.774985			−0.387493	−	0.921873i	$-0.626659\pi$
$127$	−8.73364			−0.774985			−0.387493	+	0.921873i	$0.626659\pi$
$128$		0			0
$129$	−0.843935	−	1.46174i	−0.0743043	−	0.128699i
$130$		0			0
$131$	3.10003	−	5.36941i	0.270851	−	0.469128i	−0.698229	−	0.715875i	$-0.746028\pi$
$131$	3.10003	−	5.36941i	0.270851	−	0.469128i	0.969080	+	0.246747i	$0.0793616\pi$
$132$		0			0
$133$	1.73442	−	1.99795i	0.150393	−	0.173244i
$134$		0			0
$135$	−8.19496	+	14.1941i	−0.705310	+	1.22163i
$136$		0			0
$137$	−8.91814	−	15.4467i	−0.761928	−	1.31970i	−0.941856	−	0.336018i	$-0.890920\pi$
$137$	−8.91814	−	15.4467i	−0.761928	−	1.31970i	0.179928	−	0.983680i	$-0.442414\pi$
$138$		0			0
$139$	−15.1484			−1.28487			−0.642435	−	0.766340i	$-0.722076\pi$
$139$	−15.1484			−1.28487			−0.642435	+	0.766340i	$0.722076\pi$
$140$		0			0
$141$	16.5735			1.39574
$142$		0			0
$143$	−3.87625	−	6.71387i	−0.324149	−	0.561442i
$144$		0			0
$145$	−1.02927	+	1.78275i	−0.0854762	+	0.148049i
$146$		0			0
$147$	1.31949	+	9.29744i	0.108830	+	0.766840i
$148$		0			0
$149$	−4.30586	+	7.45796i	−0.352749	+	0.610980i	−0.986730	−	0.162369i	$-0.948087\pi$
$149$	−4.30586	+	7.45796i	−0.352749	+	0.610980i	0.633981	+	0.773349i	$0.281420\pi$
$150$		0			0
$151$	−8.63199	−	14.9510i	−0.702461	−	1.21670i	−0.967600	−	0.252488i	$-0.918751\pi$
$151$	−8.63199	−	14.9510i	−0.702461	−	1.21670i	0.265139	−	0.964210i	$-0.414582\pi$
$152$		0			0
$153$	−7.43165			−0.600813
$154$		0			0
$155$	27.8358			2.23583
$156$		0			0
$157$	8.47482	+	14.6788i	0.676364	+	1.17150i	0.976068	+	0.217465i	$0.0697788\pi$
$157$	8.47482	+	14.6788i	0.676364	+	1.17150i	−0.299704	+	0.954032i	$0.596888\pi$
$158$		0			0
$159$	0.598137	−	1.03600i	0.0474353	−	0.0821604i
$160$		0			0
$161$	11.7662	−	13.5540i	0.927310	−	1.06821i
$162$		0			0
$163$	8.63399	−	14.9545i	0.676266	−	1.17133i	−0.299831	−	0.953992i	$-0.596930\pi$
$163$	8.63399	−	14.9545i	0.676266	−	1.17133i	0.976097	−	0.217335i	$-0.0697365\pi$
$164$		0			0
$165$	9.74463	+	16.8782i	0.758619	+	1.31397i
$166$		0			0
$167$	8.74790			0.676933			0.338466	−	0.940979i	$-0.390092\pi$
$167$	8.74790			0.676933			0.338466	+	0.940979i	$0.390092\pi$
$168$		0			0
$169$	−10.5908			−0.814674
$170$		0			0
$171$	0.600170	+	1.03952i	0.0458961	+	0.0794944i
$172$		0			0
$173$	−3.49691	+	6.05682i	−0.265865	+	0.460491i	−0.967790	−	0.251760i	$-0.918991\pi$
$173$	−3.49691	+	6.05682i	−0.265865	+	0.460491i	0.701925	+	0.712251i	$0.252324\pi$
$174$		0			0
$175$	2.98661	+	8.65473i	0.225766	+	0.654236i
$176$		0			0
$177$	7.09454	−	12.2881i	0.533258	−	0.923630i
$178$		0			0
$179$	−10.2213	−	17.7038i	−0.763977	−	1.32325i	−0.940785	−	0.339002i	$-0.889910\pi$
$179$	−10.2213	−	17.7038i	−0.763977	−	1.32325i	0.176808	−	0.984245i	$-0.443423\pi$
$180$		0			0
$181$	9.96247			0.740505			0.370252	−	0.928931i	$-0.379271\pi$
$181$	9.96247			0.740505			0.370252	+	0.928931i	$0.379271\pi$
$182$		0			0
$183$	15.8690			1.17307
$184$		0			0
$185$	−6.17234	−	10.6908i	−0.453799	−	0.786003i
$186$		0			0
$187$	−15.4616	+	26.7802i	−1.13066	+	1.95837i
$188$		0			0
$189$	−14.6363	−	2.83475i	−1.06464	−	0.206198i
$190$		0			0
$191$	−7.27080	+	12.5934i	−0.526097	+	0.911226i	0.473441	+	0.880826i	$0.343012\pi$
$191$	−7.27080	+	12.5934i	−0.526097	+	0.911226i	−0.999538	+	0.0304008i	$0.990322\pi$
$192$		0			0
$193$	7.85414	+	13.6038i	0.565353	+	0.979220i	0.997017	+	0.0771858i	$0.0245935\pi$
$193$	7.85414	+	13.6038i	0.565353	+	0.979220i	−0.431664	+	0.902035i	$0.642073\pi$
$194$		0			0
$195$	−6.05665			−0.433725
$196$		0			0
$197$	0.726728			0.0517772			0.0258886	−	0.999665i	$-0.491758\pi$
$197$	0.726728			0.0517772			0.0258886	+	0.999665i	$0.491758\pi$
$198$		0			0
$199$	7.19019	+	12.4538i	0.509699	+	0.882825i	0.999937	+	0.0112361i	$0.00357663\pi$
$199$	7.19019	+	12.4538i	0.509699	+	0.882825i	−0.490238	+	0.871589i	$0.663090\pi$
$200$		0			0
$201$	1.33459	−	2.31158i	0.0941350	−	0.163047i
$202$		0			0
$203$	−1.83829	−	0.356038i	−0.129023	−	0.0249890i
$204$		0			0
$205$	2.90869	−	5.03800i	0.203152	−	0.351869i
$206$		0			0
$207$	4.07153	+	7.05210i	0.282991	+	0.490155i
$208$		0			0
$209$	4.99462			0.345485
$210$		0			0
$211$	−20.8134			−1.43285			−0.716427	−	0.697662i	$-0.754224\pi$
$211$	−20.8134			−1.43285			−0.716427	+	0.697662i	$0.754224\pi$
$212$		0			0
$213$	−8.32908	−	14.4264i	−0.570699	−	0.988480i
$214$		0			0
$215$	1.82983	−	3.16936i	0.124793	−	0.216148i
$216$		0			0
$217$	8.25942	+	23.9345i	0.560686	+	1.62478i
$218$		0			0
$219$	−4.69992	+	8.14050i	−0.317591	+	0.550084i
$220$		0			0
$221$	−4.80497	−	8.32245i	−0.323217	−	0.559828i
$222$		0			0
$223$	6.02432			0.403418			0.201709	−	0.979445i	$-0.435350\pi$
$223$	6.02432			0.403418			0.201709	+	0.979445i	$0.435350\pi$
$224$		0			0
$225$	−4.15374			−0.276916
$226$		0			0
$227$	−3.93313	−	6.81237i	−0.261051	−	0.452153i	0.705471	−	0.708739i	$-0.250736\pi$
$227$	−3.93313	−	6.81237i	−0.261051	−	0.452153i	−0.966521	+	0.256586i	$0.917402\pi$
$228$		0			0
$229$	14.3345	−	24.8281i	0.947252	−	1.64069i	0.196075	−	0.980589i	$-0.437180\pi$
$229$	14.3345	−	24.8281i	0.947252	−	1.64069i	0.751177	−	0.660101i	$-0.229486\pi$
$230$		0			0
$231$	−11.6212	+	13.3870i	−0.764621	+	0.880798i
$232$		0			0
$233$	−1.52152	+	2.63535i	−0.0996781	+	0.172647i	−0.911551	−	0.411186i	$-0.865115\pi$
$233$	−1.52152	+	2.63535i	−0.0996781	+	0.172647i	0.811873	+	0.583834i	$0.198448\pi$
$234$		0			0
$235$	17.9674	+	31.1205i	1.17206	+	2.03008i
$236$		0			0
$237$	−22.7198			−1.47581
$238$		0			0
$239$	9.23545			0.597392			0.298696	−	0.954348i	$-0.403448\pi$
$239$	9.23545			0.597392			0.298696	+	0.954348i	$0.403448\pi$
$240$		0			0
$241$	4.51925	+	7.82757i	0.291110	+	0.504218i	0.974073	−	0.226236i	$-0.0726420\pi$
$241$	4.51925	+	7.82757i	0.291110	+	0.504218i	−0.682962	+	0.730454i	$0.739309\pi$
$242$		0			0
$243$	5.79725	−	10.0411i	0.371894	−	0.644139i
$244$		0			0
$245$	−16.0276	+	12.5571i	−1.02397	+	0.802241i
$246$		0			0
$247$	−0.776085	+	1.34422i	−0.0493811	+	0.0855306i
$248$		0			0
$249$	−0.331500	−	0.574174i	−0.0210079	−	0.0363868i
$250$		0			0
$251$	−2.91027			−0.183695			−0.0918473	−	0.995773i	$-0.529277\pi$
$251$	−2.91027			−0.183695			−0.0918473	+	0.995773i	$0.529277\pi$
$252$		0			0
$253$	33.8834			2.13023
$254$		0			0
$255$	12.0794	+	20.9221i	0.756438	+	1.31019i
$256$		0			0
$257$	−11.4544	+	19.8396i	−0.714505	+	1.23756i	0.248646	+	0.968595i	$0.420015\pi$
$257$	−11.4544	+	19.8396i	−0.714505	+	1.23756i	−0.963150	+	0.268964i	$0.913319\pi$
$258$		0			0
$259$	7.36099	−	8.47942i	0.457390	−	0.526885i
$260$		0			0
$261$	0.424752	−	0.735692i	0.0262915	−	0.0455382i
$262$		0			0
$263$	−8.83496	−	15.3026i	−0.544787	−	0.943599i	−0.998620	−	0.0525124i	$-0.983277\pi$
$263$	−8.83496	−	15.3026i	−0.544787	−	0.943599i	0.453833	−	0.891087i	$-0.350056\pi$
$264$		0			0
$265$	2.59378			0.159334
$266$		0			0
$267$	4.53490			0.277531
$268$		0			0
$269$	5.71170	+	9.89295i	0.348248	+	0.603184i	0.985938	−	0.167109i	$-0.0534432\pi$
$269$	5.71170	+	9.89295i	0.348248	+	0.603184i	−0.637690	+	0.770293i	$0.720110\pi$
$270$		0			0
$271$	2.52461	−	4.37276i	0.153359	−	0.265626i	−0.779101	−	0.626898i	$-0.784324\pi$
$271$	2.52461	−	4.37276i	0.153359	−	0.265626i	0.932460	+	0.361272i	$0.117657\pi$
$272$		0			0
$273$	−1.79712	−	5.20778i	−0.108767	−	0.315189i
$274$		0			0
$275$	−8.64189	+	14.9682i	−0.521125	+	0.902616i
$276$		0			0
$277$	−3.22844	−	5.59182i	−0.193978	−	0.335980i	0.752587	−	0.658493i	$-0.228806\pi$
$277$	−3.22844	−	5.59182i	−0.193978	−	0.335980i	−0.946565	+	0.322513i	$0.895472\pi$
$278$		0			0
$279$	−11.4871			−0.687715
$280$		0			0
$281$	−10.2877			−0.613711			−0.306856	−	0.951756i	$-0.599277\pi$
$281$	−10.2877			−0.613711			−0.306856	+	0.951756i	$0.599277\pi$
$282$		0			0
$283$	11.0250	+	19.0959i	0.655368	+	1.13513i	0.981801	+	0.189910i	$0.0608198\pi$
$283$	11.0250	+	19.0959i	0.655368	+	1.13513i	−0.326433	+	0.945220i	$0.605847\pi$
$284$		0			0
$285$	1.95102	−	3.37927i	0.115569	−	0.200171i
$286$		0			0
$287$	5.19496	+	1.00616i	0.306649	+	0.0593915i
$288$		0			0
$289$	−10.6660	+	18.4741i	−0.627413	+	1.08671i
$290$		0			0
$291$	−6.75353	−	11.6975i	−0.395899	−	0.685717i
$292$		0			0
$293$	−20.5297			−1.19936			−0.599680	−	0.800240i	$-0.704705\pi$
$293$	−20.5297			−1.19936			−0.599680	+	0.800240i	$0.704705\pi$
$294$		0			0
$295$	30.7649			1.79120
$296$		0			0
$297$	−14.0719	−	24.3732i	−0.816534	−	1.41428i
$298$		0			0
$299$	−5.26494	+	9.11914i	−0.304479	+	0.527374i
$300$		0			0
$301$	3.26810	+	0.632963i	0.188370	+	0.0364834i
$302$		0			0
$303$	1.72539	−	2.98847i	0.0991212	−	0.171683i
$304$		0			0
$305$	17.2037	+	29.7976i	0.985078	+	1.70621i
$306$		0			0
$307$	21.5830			1.23181			0.615904	−	0.787821i	$-0.288791\pi$
$307$	21.5830			1.23181			0.615904	+	0.787821i	$0.288791\pi$
$308$		0			0
$309$	−8.63541			−0.491251
$310$		0			0
$311$	11.8255	+	20.4824i	0.670562	+	1.16145i	0.977745	+	0.209798i	$0.0672805\pi$
$311$	11.8255	+	20.4824i	0.670562	+	1.16145i	−0.307182	+	0.951651i	$0.599386\pi$
$312$		0			0
$313$	13.3560	−	23.1333i	0.754927	−	1.30757i	−0.190483	−	0.981690i	$-0.561006\pi$
$313$	13.3560	−	23.1333i	0.754927	−	1.30757i	0.945411	−	0.325882i	$-0.105661\pi$
$314$		0			0
$315$	−3.01331	−	8.73211i	−0.169781	−	0.491999i
$316$		0			0
$317$	13.5370	−	23.4468i	0.760314	−	1.31690i	−0.182374	−	0.983229i	$-0.558378\pi$
$317$	13.5370	−	23.4468i	0.760314	−	1.31690i	0.942689	−	0.333674i	$-0.108288\pi$
$318$		0			0
$319$	−1.76740	−	3.06122i	−0.0989553	−	0.171396i
$320$		0			0
$321$	−3.21775			−0.179597
$322$		0			0
$323$	6.19129			0.344492
$324$		0			0
$325$	−2.68562	−	4.65164i	−0.148972	−	0.258026i
$326$		0			0
$327$	−9.56136	+	16.5608i	−0.528744	+	0.915812i
$328$		0			0
$329$	−21.4275	+	24.6832i	−1.18134	+	1.36083i
$330$		0			0
$331$	−1.57001	+	2.71934i	−0.0862957	+	0.149469i	−0.905943	−	0.423400i	$-0.860836\pi$
$331$	−1.57001	+	2.71934i	−0.0862957	+	0.149469i	0.819647	+	0.572869i	$0.194170\pi$
$332$		0			0
$333$	2.54716	+	4.41181i	0.139583	+	0.241766i
$334$		0			0
$335$	5.78737			0.316198
$336$		0			0
$337$	21.6417			1.17890			0.589449	−	0.807805i	$-0.299345\pi$
$337$	21.6417			1.17890			0.589449	+	0.807805i	$0.299345\pi$
$338$		0			0
$339$	−0.478681	−	0.829100i	−0.0259984	−	0.0450305i
$340$		0			0
$341$	−23.8990	+	41.3943i	−1.29420	+	2.24163i
$342$		0			0
$343$	−15.5528	−	10.0553i	−0.839773	−	0.542937i
$344$		0			0
$345$	13.2357	−	22.9249i	0.712586	−	1.23423i
$346$		0			0
$347$	1.28338	+	2.22288i	0.0688955	+	0.119330i	0.898415	−	0.439147i	$-0.144719\pi$
$347$	1.28338	+	2.22288i	0.0688955	+	0.119330i	−0.829520	+	0.558477i	$0.811386\pi$
$348$		0			0
$349$	1.91567			0.102543			0.0512716	−	0.998685i	$-0.483673\pi$
$349$	1.91567			0.102543			0.0512716	+	0.998685i	$0.483673\pi$
$350$		0			0
$351$	8.74619			0.466837
$352$		0			0
$353$	7.93887	+	13.7505i	0.422543	+	0.731867i	0.996188	−	0.0872380i	$-0.0278040\pi$
$353$	7.93887	+	13.7505i	0.422543	+	0.731867i	−0.573644	+	0.819105i	$0.694471\pi$
$354$		0			0
$355$	18.0592	−	31.2795i	0.958485	−	1.66014i
$356$		0			0
$357$	−14.4056	+	16.5943i	−0.762423	+	0.878266i
$358$		0			0
$359$	−10.0397	+	17.3893i	−0.529875	+	0.917771i	0.469517	+	0.882923i	$0.344428\pi$
$359$	−10.0397	+	17.3893i	−0.529875	+	0.917771i	−0.999393	+	0.0348477i	$0.988905\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−18.7091			−0.981975
$364$		0			0
$365$	−20.3808			−1.06678
$366$		0			0
$367$	−1.79240	−	3.10453i	−0.0935626	−	0.162055i	0.815445	−	0.578834i	$-0.196492\pi$
$367$	−1.79240	−	3.10453i	−0.0935626	−	0.162055i	−0.909008	+	0.416779i	$0.863159\pi$
$368$		0			0
$369$	−1.20034	+	2.07905i	−0.0624872	+	0.108231i
$370$		0			0
$371$	0.769622	+	2.23025i	0.0399568	+	0.115789i
$372$		0			0
$373$	−13.3372	+	23.1008i	−0.690576	+	1.19611i	0.281073	+	0.959686i	$0.409310\pi$
$373$	−13.3372	+	23.1008i	−0.690576	+	1.19611i	−0.971649	+	0.236427i	$0.924024\pi$
$374$		0			0
$375$	−3.00365	−	5.20248i	−0.155108	−	0.268655i
$376$		0			0
$377$	1.09850			0.0565758
$378$		0			0
$379$	18.9451			0.973146			0.486573	−	0.873640i	$-0.338247\pi$
$379$	18.9451			0.973146			0.486573	+	0.873640i	$0.338247\pi$
$380$		0			0
$381$	−5.85815	−	10.1466i	−0.300122	−	0.519827i
$382$		0			0
$383$	7.47577	−	12.9484i	0.381994	−	0.661633i	−0.609353	−	0.792899i	$-0.708571\pi$
$383$	7.47577	−	12.9484i	0.381994	−	0.661633i	0.991347	+	0.131266i	$0.0419042\pi$
$384$		0			0
$385$	−37.7357	−	7.30862i	−1.92319	−	0.372482i
$386$		0			0
$387$	−0.755123	+	1.30791i	−0.0383850	+	0.0664848i
$388$		0			0
$389$	−18.3084	−	31.7111i	−0.928273	−	1.60782i	−0.786211	−	0.617958i	$-0.787960\pi$
$389$	−18.3084	−	31.7111i	−0.928273	−	1.60782i	−0.142061	−	0.989858i	$-0.545373\pi$
$390$		0			0
$391$	42.0015			2.12411
$392$		0			0
$393$	8.31748			0.419561
$394$		0			0
$395$	−24.6307	−	42.6616i	−1.23931	−	2.14654i
$396$		0			0
$397$	9.92602	−	17.1924i	0.498173	−	0.862861i	−0.501825	−	0.864969i	$-0.667338\pi$
$397$	9.92602	−	17.1924i	0.498173	−	0.862861i	0.999998	+	0.00210848i	$0.000671150\pi$
$398$		0			0
$399$	3.48456	+	0.674886i	0.174446	+	0.0337866i
$400$		0			0
$401$	−2.31504	+	4.00977i	−0.115608	+	0.200238i	−0.918023	−	0.396528i	$-0.870215\pi$
$401$	−2.31504	+	4.00977i	−0.115608	+	0.200238i	0.802415	+	0.596767i	$0.203548\pi$
$402$		0			0
$403$	−7.42705	−	12.8640i	−0.369968	−	0.640803i
$404$		0			0
$405$	−11.5131			−0.572090
$406$		0			0
$407$	21.1975			1.05072
$408$		0			0
$409$	−2.20637	−	3.82155i	−0.109098	−	0.188963i	0.806307	−	0.591497i	$-0.201463\pi$
$409$	−2.20637	−	3.82155i	−0.109098	−	0.188963i	−0.915405	+	0.402534i	$0.868130\pi$
$410$		0			0
$411$	11.9638	−	20.7219i	0.590131	−	1.02214i
$412$		0			0
$413$	9.12854	+	26.4531i	0.449186	+	1.30167i
$414$		0			0
$415$	0.718762	−	1.24493i	0.0352826	−	0.0611113i
$416$		0			0
$417$	−10.1609	−	17.5992i	−0.497581	−	0.861836i
$418$		0			0
$419$	32.8148			1.60311			0.801554	−	0.597922i	$-0.204007\pi$
$419$	32.8148			1.60311			0.801554	+	0.597922i	$0.204007\pi$
$420$		0			0
$421$	10.3765			0.505721			0.252861	−	0.967503i	$-0.418629\pi$
$421$	10.3765			0.505721			0.252861	+	0.967503i	$0.418629\pi$
$422$		0			0
$423$	−7.41468	−	12.8426i	−0.360514	−	0.624428i
$424$		0			0
$425$	−10.7124	+	18.5544i	−0.519628	+	0.900021i
$426$		0			0
$427$	−20.5167	+	23.6340i	−0.992872	+	1.14373i
$428$		0			0
$429$	5.20005	−	9.00675i	0.251061	−	0.434850i
$430$		0			0
$431$	1.05984	+	1.83569i	0.0510505	+	0.0884220i	0.890421	−	0.455137i	$-0.150410\pi$
$431$	1.05984	+	1.83569i	0.0510505	+	0.0884220i	−0.839371	+	0.543559i	$0.817076\pi$
$432$		0			0
$433$	−4.23274			−0.203413			−0.101706	−	0.994814i	$-0.532430\pi$
$433$	−4.23274			−0.203413			−0.101706	+	0.994814i	$0.532430\pi$
$434$		0			0
$435$	−2.76156			−0.132407
$436$		0			0
$437$	−3.39198	−	5.87509i	−0.162261	−	0.281044i
$438$		0			0
$439$	11.8690	−	20.5577i	0.566476	−	0.981166i	−0.430434	−	0.902622i	$-0.641640\pi$
$439$	11.8690	−	20.5577i	0.566476	−	0.981166i	0.996911	−	0.0785439i	$-0.0250271\pi$
$440$		0			0
$441$	6.61416	−	5.18196i	0.314960	−	0.246760i
$442$		0			0
$443$	5.32007	−	9.21464i	0.252764	−	0.437801i	−0.711522	−	0.702664i	$-0.751994\pi$
$443$	5.32007	−	9.21464i	0.252764	−	0.437801i	0.964286	+	0.264864i	$0.0853269\pi$
$444$		0			0
$445$	4.91631	+	8.51530i	0.233056	+	0.403664i
$446$		0			0
$447$	−11.5527			−0.546426
$448$		0			0
$449$	18.4650			0.871418			0.435709	−	0.900088i	$-0.356498\pi$
$449$	18.4650			0.871418			0.435709	+	0.900088i	$0.356498\pi$
$450$		0			0
$451$	4.99462	+	8.65094i	0.235188	+	0.407357i
$452$		0			0
$453$	11.5799	−	20.0570i	0.544073	−	0.942362i
$454$		0			0
$455$	7.83052	−	9.02029i	0.367101	−	0.422878i
$456$		0			0
$457$	4.21897	−	7.30748i	0.197355	−	0.341829i	−0.750315	−	0.661081i	$-0.770098\pi$
$457$	4.21897	−	7.30748i	0.197355	−	0.341829i	0.947670	+	0.319251i	$0.103431\pi$
$458$		0			0
$459$	−17.4434	−	30.2128i	−0.814187	−	1.41021i
$460$		0			0
$461$	−18.8951			−0.880034			−0.440017	−	0.897990i	$-0.645028\pi$
$461$	−18.8951			−0.880034			−0.440017	+	0.897990i	$0.645028\pi$
$462$		0			0
$463$	27.5602			1.28083			0.640415	−	0.768029i	$-0.278762\pi$
$463$	27.5602			1.28083			0.640415	+	0.768029i	$0.278762\pi$
$464$		0			0
$465$	18.6711	+	32.3393i	0.865851	+	1.49970i
$466$		0			0
$467$	−11.6370	+	20.1560i	−0.538498	+	0.932706i	0.460487	+	0.887666i	$0.347675\pi$
$467$	−11.6370	+	20.1560i	−0.538498	+	0.932706i	−0.998985	+	0.0450398i	$0.985659\pi$
$468$		0			0
$469$	1.71722	+	4.97625i	0.0792939	+	0.229782i
$470$		0			0
$471$	−11.3691	+	19.6918i	−0.523860	+	0.907352i
$472$		0			0
$473$	3.14207	+	5.44223i	0.144473	+	0.250234i
$474$		0			0
$475$	3.46047			0.158777
$476$		0			0
$477$	−1.07038			−0.0490095
$478$		0			0
$479$	−2.20147	−	3.81305i	−0.100588	−	0.174223i	0.811339	−	0.584576i	$-0.198739\pi$
$479$	−2.20147	−	3.81305i	−0.100588	−	0.174223i	−0.911927	+	0.410353i	$0.865406\pi$
$480$		0			0
$481$	−3.29376	+	5.70496i	−0.150182	+	0.260124i
$482$		0			0
$483$	23.6391	+	4.57840i	1.07562	+	0.208325i
$484$		0			0
$485$	14.6431	−	25.3626i	0.664909	−	1.15166i
$486$		0			0
$487$	12.1248	+	21.0008i	0.549429	+	0.951638i	0.998314	+	0.0580489i	$0.0184879\pi$
$487$	12.1248	+	21.0008i	0.549429	+	0.951638i	−0.448885	+	0.893590i	$0.648179\pi$
$488$		0			0
$489$	23.1652			1.04757
$490$		0			0
$491$	−27.0129			−1.21908			−0.609538	−	0.792757i	$-0.708645\pi$
$491$	−27.0129			−1.21908			−0.609538	+	0.792757i	$0.708645\pi$
$492$		0			0
$493$	−2.19085	−	3.79466i	−0.0986709	−	0.170903i
$494$		0			0
$495$	8.71915	−	15.1020i	0.391897	−	0.678785i
$496$		0			0
$497$	32.2541	+	6.24693i	1.44679	+	0.280213i
$498$		0			0
$499$	−9.84696	+	17.0554i	−0.440810	+	0.763506i	−0.997750	−	0.0670472i	$-0.978642\pi$
$499$	−9.84696	+	17.0554i	−0.440810	+	0.763506i	0.556940	+	0.830553i	$0.311976\pi$
$500$		0			0
$501$	5.86772	+	10.1632i	0.262150	+	0.454057i
$502$		0			0
$503$	0.561980			0.0250574			0.0125287	−	0.999922i	$-0.496012\pi$
$503$	0.561980			0.0250574			0.0125287	+	0.999922i	$0.496012\pi$
$504$		0			0
$505$	7.48204			0.332946
$506$		0			0
$507$	−7.10383	−	12.3042i	−0.315492	−	0.546449i
$508$		0			0
$509$	8.84945	−	15.3277i	0.392245	−	0.679388i	−0.600500	−	0.799625i	$-0.705032\pi$
$509$	8.84945	−	15.3277i	0.392245	−	0.679388i	0.992745	+	0.120236i	$0.0383652\pi$
$510$		0			0
$511$	−6.04738	−	17.5244i	−0.267520	−	0.775233i
$512$		0			0
$513$	−2.81741	+	4.87989i	−0.124392	+	0.215453i
$514$		0			0
$515$	−9.36171	−	16.2150i	−0.412526	−	0.714516i
$516$		0			0
$517$	−61.7051			−2.71379
$518$		0			0
$519$	−9.38230			−0.411837
$520$		0			0
$521$	−20.1517	−	34.9038i	−0.882863	−	1.52916i	−0.848143	−	0.529767i	$-0.822279\pi$
$521$	−20.1517	−	34.9038i	−0.882863	−	1.52916i	−0.0347205	−	0.999397i	$-0.511054\pi$
$522$		0			0
$523$	−0.978350	+	1.69455i	−0.0427803	+	0.0740976i	−0.886623	−	0.462493i	$-0.846955\pi$
$523$	−0.978350	+	1.69455i	−0.0427803	+	0.0740976i	0.843842	+	0.536591i	$0.180288\pi$
$524$		0			0
$525$	−8.05165	+	9.27502i	−0.351403	+	0.404795i
$526$		0			0
$527$	−29.6250	+	51.3119i	−1.29048	+	2.23518i
$528$		0			0
$529$	−11.5111	−	19.9378i	−0.500483	−	0.866862i
$530$		0			0
$531$	−12.6959			−0.550954
$532$		0			0
$533$	−3.10434			−0.134464
$534$		0			0
$535$	−3.48838	−	6.04206i	−0.150816	−	0.261221i
$536$		0			0
$537$	13.7121	−	23.7500i	0.591719	−	1.02489i
$538$		0			0
$539$	−4.91262	−	34.6155i	−0.211601	−	1.49100i
$540$		0			0
$541$	15.5344	−	26.9064i	0.667877	−	1.15680i	−0.310620	−	0.950534i	$-0.600537\pi$
$541$	15.5344	−	26.9064i	0.667877	−	1.15680i	0.978497	−	0.206263i	$-0.0661301\pi$
$542$		0			0
$543$	6.68240	+	11.5743i	0.286769	+	0.496699i
$544$		0			0
$545$	−41.4621			−1.77604
$546$		0			0
$547$	36.8556			1.57583			0.787917	−	0.615782i	$-0.211160\pi$
$547$	36.8556			1.57583			0.787917	+	0.615782i	$0.211160\pi$
$548$		0			0
$549$	−7.09949	−	12.2967i	−0.302999	−	0.524810i
$550$		0			0
$551$	−0.353860	+	0.612904i	−0.0150749	+	0.0261106i
$552$		0			0
$553$	29.3740	−	33.8371i	1.24911	−	1.43890i
$554$		0			0
$555$	8.28028	−	14.3419i	0.351478	−	0.608778i
$556$		0			0
$557$	−11.6136	−	20.1153i	−0.492083	−	0.852313i	0.507875	−	0.861431i	$-0.330431\pi$
$557$	−11.6136	−	20.1153i	−0.492083	−	0.852313i	−0.999958	+	0.00911734i	$0.997098\pi$
$558$		0			0
$559$	−1.95291			−0.0825994
$560$		0			0
$561$	−41.4839			−1.75145
$562$		0			0
$563$	−12.0273	−	20.8319i	−0.506891	−	0.877962i	−0.999968	−	0.00797592i	$-0.997461\pi$
$563$	−12.0273	−	20.8319i	−0.506891	−	0.877962i	0.493077	−	0.869986i	$-0.335872\pi$
$564$		0			0
$565$	1.03788	−	1.79766i	0.0436640	−	0.0756283i
$566$		0			0
$567$	−3.41615	−	9.89948i	−0.143465	−	0.415739i
$568$		0			0
$569$	14.7880	−	25.6136i	0.619946	−	1.07378i	−0.369548	−	0.929211i	$-0.620488\pi$
$569$	14.7880	−	25.6136i	0.619946	−	1.07378i	0.989495	−	0.144567i	$-0.0461790\pi$
$570$		0			0
$571$	13.2462	+	22.9431i	0.554337	+	0.960141i	0.997955	+	0.0639243i	$0.0203616\pi$
$571$	13.2462	+	22.9431i	0.554337	+	0.960141i	−0.443617	+	0.896216i	$0.646305\pi$
$572$		0			0
$573$	−19.5078			−0.814949
$574$		0			0
$575$	23.4757			0.979006
$576$		0			0
$577$	−12.7908	−	22.1543i	−0.532487	−	0.922295i	−0.999280	−	0.0379287i	$-0.987924\pi$
$577$	−12.7908	−	22.1543i	−0.532487	−	0.922295i	0.466793	−	0.884367i	$-0.345409\pi$
$578$		0			0
$579$	−10.5364	+	18.2496i	−0.437879	+	0.758429i
$580$		0			0
$581$	1.28372	+	0.248630i	0.0532577	+	0.0103149i
$582$		0			0
$583$	−2.22694	+	3.85717i	−0.0922303	+	0.159748i
$584$		0			0
$585$	2.70963	+	4.69323i	0.112030	+	0.194041i
$586$		0			0
$587$	27.2213			1.12354			0.561771	−	0.827293i	$-0.310120\pi$
$587$	27.2213			1.12354			0.561771	+	0.827293i	$0.310120\pi$
$588$		0			0
$589$	9.56989			0.394320
$590$		0			0
$591$	0.487458	+	0.844302i	0.0200514	+	0.0347300i
$592$		0			0
$593$	−0.952988	+	1.65062i	−0.0391345	+	0.0677830i	−0.884929	−	0.465725i	$-0.845793\pi$
$593$	−0.952988	+	1.65062i	−0.0391345	+	0.0677830i	0.845795	+	0.533508i	$0.179127\pi$
$594$		0			0
$595$	−46.7768	−	9.05969i	−1.91766	−	0.371411i
$596$		0			0
$597$	−9.64575	+	16.7069i	−0.394774	+	0.683769i
$598$		0			0
$599$	10.0250	+	17.3638i	0.409610	+	0.709466i	0.994846	−	0.101397i	$-0.0323313\pi$
$599$	10.0250	+	17.3638i	0.409610	+	0.709466i	−0.585236	+	0.810863i	$0.698998\pi$
$600$		0			0
$601$	−14.6961			−0.599466			−0.299733	−	0.954023i	$-0.596898\pi$
$601$	−14.6961			−0.599466			−0.299733	+	0.954023i	$0.596898\pi$
$602$		0			0
$603$	−2.38829			−0.0972589
$604$		0			0
$605$	−20.2827	−	35.1307i	−0.824609	−	1.42826i
$606$		0			0
$607$	−11.7400	+	20.3343i	−0.476512	+	0.825344i	−0.999638	−	0.0269121i	$-0.991433\pi$
$607$	−11.7400	+	20.3343i	−0.476512	+	0.825344i	0.523125	+	0.852256i	$0.324766\pi$
$608$		0			0
$609$	−0.819407	−	2.37451i	−0.0332040	−	0.0962202i
$610$		0			0
$611$	9.58799	−	16.6069i	0.387889	−	0.671843i
$612$		0			0
$613$	−13.6639	−	23.6666i	−0.551880	−	0.955884i	−0.998139	−	0.0609799i	$-0.980577\pi$
$613$	−13.6639	−	23.6666i	−0.551880	−	0.955884i	0.446259	−	0.894904i	$-0.352756\pi$
$614$		0			0
$615$	7.80410			0.314692
$616$		0			0
$617$	−25.5796			−1.02980			−0.514898	−	0.857252i	$-0.672170\pi$
$617$	−25.5796			−1.02980			−0.514898	+	0.857252i	$0.672170\pi$
$618$		0			0
$619$	−0.745582	−	1.29139i	−0.0299675	−	0.0519052i	0.850653	−	0.525728i	$-0.176207\pi$
$619$	−0.745582	−	1.29139i	−0.0299675	−	0.0519052i	−0.880620	+	0.473823i	$0.842874\pi$
$620$		0			0
$621$	−19.1132	+	33.1050i	−0.766987	+	1.32846i
$622$		0			0
$623$	−5.86309	+	6.75392i	−0.234900	+	0.270590i
$624$		0			0
$625$	15.1637	−	26.2644i	0.606550	−	1.05058i
$626$		0			0
$627$	3.35018	+	5.80268i	0.133793	+	0.231737i
$628$		0			0
$629$	26.2762			1.04770
$630$		0			0
$631$	−22.0819			−0.879066			−0.439533	−	0.898226i	$-0.644856\pi$
$631$	−22.0819			−0.879066			−0.439533	+	0.898226i	$0.644856\pi$
$632$		0			0
$633$	−13.9607	−	24.1807i	−0.554890	−	0.961097i
$634$		0			0
$635$	12.7017	−	22.0000i	0.504052	−	0.873045i
$636$		0			0
$637$	10.0795	+	4.05655i	0.399365	+	0.160726i
$638$		0			0
$639$	−7.45257	+	12.9082i	−0.294819	+	0.510641i
$640$		0			0
$641$	1.40167	+	2.42777i	0.0553627	+	0.0958910i	0.892379	−	0.451288i	$-0.149035\pi$
$641$	1.40167	+	2.42777i	0.0553627	+	0.0958910i	−0.837016	+	0.547179i	$0.815702\pi$
$642$		0			0
$643$	−27.0640			−1.06730			−0.533649	−	0.845706i	$-0.679180\pi$
$643$	−27.0640			−1.06730			−0.533649	+	0.845706i	$0.679180\pi$
$644$		0			0
$645$	4.90949			0.193311
$646$		0			0
$647$	−2.68786	−	4.65551i	−0.105671	−	0.183027i	0.808341	−	0.588714i	$-0.200366\pi$
$647$	−2.68786	−	4.65551i	−0.105671	−	0.183027i	−0.914012	+	0.405687i	$0.867032\pi$
$648$		0			0
$649$	−26.4138	+	45.7501i	−1.03683	+	1.79585i
$650$		0			0
$651$	−22.2667	+	25.6499i	−0.872702	+	1.00530i
$652$		0			0
$653$	14.0625	−	24.3570i	0.550308	−	0.953162i	−0.447944	−	0.894062i	$-0.647844\pi$
$653$	14.0625	−	24.3570i	0.550308	−	0.953162i	0.998252	−	0.0590999i	$-0.0188231\pi$
$654$		0			0
$655$	9.01703	+	15.6180i	0.352325	+	0.610244i
$656$		0			0
$657$	8.41064			0.328130
$658$		0			0
$659$	35.3753			1.37802			0.689012	−	0.724750i	$-0.258045\pi$
$659$	35.3753			1.37802			0.689012	+	0.724750i	$0.258045\pi$
$660$		0			0
$661$	−21.7358	−	37.6476i	−0.845426	−	1.46432i	−0.885251	−	0.465114i	$-0.846013\pi$
$661$	−21.7358	−	37.6476i	−0.845426	−	1.46432i	0.0398248	−	0.999207i	$-0.487320\pi$
$662$		0			0
$663$	6.44593	−	11.1647i	0.250339	−	0.433600i
$664$		0			0
$665$	2.51038	+	7.27470i	0.0973484	+	0.282101i
$666$		0			0
$667$	−2.40058	+	4.15792i	−0.0929507	+	0.160995i
$668$		0			0
$669$	4.04085	+	6.99896i	0.156228	+	0.270596i
$670$		0			0
$671$	−59.0821			−2.28084
$672$		0			0
$673$	17.7175			0.682961			0.341481	−	0.939889i	$-0.389072\pi$
$673$	17.7175			0.682961			0.341481	+	0.939889i	$0.389072\pi$
$674$		0			0
$675$	−9.74957	−	16.8867i	−0.375261	−	0.649971i
$676$		0			0
$677$	−22.4224	+	38.8367i	−0.861761	+	1.49261i	0.00846617	+	0.999964i	$0.497305\pi$
$677$	−22.4224	+	38.8367i	−0.861761	+	1.49261i	−0.870227	+	0.492650i	$0.836028\pi$
$678$		0			0
$679$	26.1528	+	5.06525i	1.00365	+	0.194386i
$680$		0			0
$681$	5.27635	−	9.13890i	0.202190	−	0.350203i
$682$		0			0
$683$	15.0236	+	26.0216i	0.574861	+	0.995688i	0.996057	+	0.0887184i	$0.0282771\pi$
$683$	15.0236	+	26.0216i	0.574861	+	0.995688i	−0.421196	+	0.906970i	$0.638390\pi$
$684$		0			0
$685$	51.8802			1.98224
$686$		0			0
$687$	38.4600			1.46734
$688$		0			0
$689$	−0.692061	−	1.19869i	−0.0263654	−	0.0456663i
$690$		0			0
$691$	9.24652	−	16.0154i	0.351754	−	0.609256i	−0.634803	−	0.772674i	$-0.718919\pi$
$691$	9.24652	−	16.0154i	0.351754	−	0.609256i	0.986557	+	0.163418i	$0.0522520\pi$
$692$		0			0
$693$	15.5725	+	3.01607i	0.591552	+	0.114571i
$694$		0			0
$695$	22.0310	−	38.1588i	0.835683	−	1.44745i
$696$		0			0
$697$	6.19129	+	10.7236i	0.234512	+	0.406186i
$698$		0			0
$699$	−4.08228			−0.154406
$700$		0			0
$701$	−26.5282			−1.00196			−0.500978	−	0.865460i	$-0.667026\pi$
$701$	−26.5282			−1.00196			−0.500978	+	0.865460i	$0.667026\pi$
$702$		0			0
$703$	−2.12203	−	3.67547i	−0.0800340	−	0.138623i
$704$		0			0
$705$	−24.1035	+	41.7486i	−0.907792	+	1.57234i
$706$		0			0
$707$	2.22006	+	6.43340i	0.0834940	+	0.241953i
$708$		0			0
$709$	−18.9660	+	32.8500i	−0.712281	+	1.23371i	0.251718	+	0.967801i	$0.419005\pi$
$709$	−18.9660	+	32.8500i	−0.712281	+	1.23371i	−0.963999	+	0.265907i	$0.914329\pi$
$710$		0			0
$711$	10.1644	+	17.6053i	0.381196	+	0.660251i
$712$		0			0
$713$	64.9218			2.43134
$714$		0			0
$715$	22.5496			0.843309
$716$		0			0
$717$	6.19475	+	10.7296i	0.231347	+	0.400705i
$718$		0			0
$719$	0.215748	−	0.373686i	0.00804603	−	0.0139361i	−0.861974	−	0.506952i	$-0.830772\pi$
$719$	0.215748	−	0.373686i	0.00804603	−	0.0139361i	0.870020	+	0.493016i	$0.164106\pi$
$720$		0			0
$721$	11.1646	−	12.8609i	0.415790	−	0.478965i
$722$		0			0
$723$	−6.06264	+	10.5008i	−0.225472	+	0.390529i
$724$		0			0
$725$	−1.22452	−	2.12094i	−0.0454777	−	0.0787696i
$726$		0			0
$727$	−3.14690			−0.116712			−0.0583560	−	0.998296i	$-0.518586\pi$
$727$	−3.14690			−0.116712			−0.0583560	+	0.998296i	$0.518586\pi$
$728$		0			0
$729$	27.4287			1.01588
$730$		0			0
$731$	3.89488	+	6.74614i	0.144057	+	0.249515i
$732$		0			0
$733$	7.35219	−	12.7344i	0.271559	−	0.470355i	−0.697702	−	0.716388i	$-0.745794\pi$
$733$	7.35219	−	12.7344i	0.271559	−	0.470355i	0.969261	+	0.246033i	$0.0791273\pi$
$734$		0			0
$735$	−25.3392	−	10.1979i	−0.934651	−	0.376155i
$736$		0			0
$737$	−4.96886	+	8.60632i	−0.183030	+	0.317018i
$738$		0			0
$739$	7.49950	+	12.9895i	0.275873	+	0.477827i	0.970355	−	0.241684i	$-0.0776996\pi$
$739$	7.49950	+	12.9895i	0.275873	+	0.477827i	−0.694482	+	0.719510i	$0.744366\pi$
$740$		0			0
$741$	−2.08226			−0.0764937
$742$		0			0
$743$	−31.3454			−1.14995			−0.574975	−	0.818171i	$-0.694988\pi$
$743$	−31.3454			−1.14995			−0.574975	+	0.818171i	$0.694988\pi$
$744$		0			0
$745$	−12.5244	−	21.6929i	−0.458858	−	0.794766i
$746$		0			0
$747$	−0.296614	+	0.513751i	−0.0108525	+	0.0187972i
$748$		0			0
$749$	4.16017	−	4.79226i	0.152009	−	0.175106i
$750$		0			0
$751$	−2.21954	+	3.84436i	−0.0809923	+	0.140283i	−0.903676	−	0.428216i	$-0.859142\pi$
$751$	−2.21954	+	3.84436i	−0.0809923	+	0.140283i	0.822684	+	0.568499i	$0.192476\pi$
$752$		0			0
$753$	−1.95209	−	3.38111i	−0.0711379	−	0.123215i
$754$		0			0
$755$	50.2155			1.82753
$756$		0			0
$757$	7.60936			0.276567			0.138283	−	0.990393i	$-0.455841\pi$
$757$	7.60936			0.276567			0.138283	+	0.990393i	$0.455841\pi$
$758$		0			0
$759$	22.7275	+	39.3652i	0.824957	+	1.42887i
$760$		0			0
$761$	−6.74146	+	11.6765i	−0.244378	+	0.423274i	−0.961956	−	0.273203i	$-0.911917\pi$
$761$	−6.74146	+	11.6765i	−0.244378	+	0.423274i	0.717579	+	0.696477i	$0.245250\pi$
$762$		0			0
$763$	−12.3026	−	35.6510i	−0.445384	−	1.29065i
$764$		0			0
$765$	10.8082	−	18.7203i	0.390770	−	0.676834i
$766$		0			0
$767$	−8.20858	−	14.2177i	−0.296395	−	0.513371i
$768$		0			0
$769$	21.3561			0.770121			0.385061	−	0.922891i	$-0.374181\pi$
$769$	21.3561			0.770121			0.385061	+	0.922891i	$0.374181\pi$
$770$		0			0
$771$	−30.7324			−1.10680
$772$		0			0
$773$	20.7104	+	35.8714i	0.744900	+	1.29020i	0.950241	+	0.311514i	$0.100836\pi$
$773$	20.7104	+	35.8714i	0.744900	+	1.29020i	−0.205341	+	0.978690i	$0.565830\pi$
$774$		0			0
$775$	−16.5582	+	28.6796i	−0.594787	+	1.03020i
$776$		0			0
$777$	14.7887	+	2.86426i	0.530542	+	0.102755i
$778$		0			0
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	31.0102	+	53.7113i	1.10963	+	1.92194i
$782$		0			0
$783$	3.98787			0.142515
$784$		0			0
$785$	−49.3012			−1.75964
$786$		0			0
$787$	18.1780	+	31.4851i	0.647974	+	1.12232i	0.983606	+	0.180331i	$0.0577169\pi$
$787$	18.1780	+	31.4851i	0.647974	+	1.12232i	−0.335632	+	0.941993i	$0.608950\pi$
$788$		0			0
$789$	11.8522	−	20.5287i	0.421951	−	0.730840i
$790$		0			0
$791$	1.85367	+	0.359018i	0.0659090	+	0.0127652i
$792$		0			0
$793$	9.18042	−	15.9010i	0.326006	−	0.564660i
$794$		0			0
$795$	1.73979	+	3.01341i	0.0617041	+	0.106875i
$796$		0			0
$797$	8.65901			0.306718			0.153359	−	0.988171i	$-0.450991\pi$
$797$	8.65901			0.306718			0.153359	+	0.988171i	$0.450991\pi$
$798$		0			0
$799$	−76.4890			−2.70599
$800$		0			0
$801$	−2.02883	−	3.51404i	−0.0716853	−	0.124163i
$802$		0			0
$803$	17.4984	−	30.3081i	0.617504	−	1.06955i
$804$		0			0
$805$	17.0304	+	49.3514i	0.600241	+	1.73941i
$806$		0			0
$807$	−7.66233	+	13.2715i	−0.269727	+	0.467180i
$808$		0			0
$809$	18.0653	+	31.2900i	0.635142	+	1.10010i	0.986485	+	0.163852i	$0.0523920\pi$
$809$	18.0653	+	31.2900i	0.635142	+	1.10010i	−0.351342	+	0.936247i	$0.614275\pi$
$810$		0			0
$811$	30.7940			1.08133			0.540663	−	0.841240i	$-0.318174\pi$
$811$	30.7940			1.08133			0.540663	+	0.841240i	$0.318174\pi$
$812$		0			0
$813$	6.77361			0.237561
$814$		0			0
$815$	25.1136	+	43.4980i	0.879691	+	1.52367i
$816$		0			0
$817$	0.629091	−	1.08962i	0.0220091	−	0.0381209i
$818$		0			0
$819$	−3.23145	+	3.72244i	−0.112916	+	0.130072i
$820$		0			0
$821$	−6.19384	+	10.7280i	−0.216166	+	0.374411i	−0.953633	−	0.300973i	$-0.902689\pi$
$821$	−6.19384	+	10.7280i	−0.216166	+	0.374411i	0.737466	+	0.675384i	$0.236022\pi$
$822$		0			0
$823$	0.237727	+	0.411756i	0.00828665	+	0.0143529i	0.870139	−	0.492806i	$-0.164029\pi$
$823$	0.237727	+	0.411756i	0.00828665	+	0.0143529i	−0.861852	+	0.507159i	$0.830696\pi$
$824$		0			0
$825$	−23.1864			−0.807248
$826$		0			0
$827$	29.8510			1.03802			0.519010	−	0.854768i	$-0.326301\pi$
$827$	29.8510			1.03802			0.519010	+	0.854768i	$0.326301\pi$
$828$		0			0
$829$	−15.0065	−	25.9919i	−0.521196	−	0.902737i	−0.999696	−	0.0246500i	$-0.992153\pi$
$829$	−15.0065	−	25.9919i	−0.521196	−	0.902737i	0.478501	−	0.878087i	$-0.341180\pi$
$830$		0			0
$831$	4.33099	−	7.50150i	0.150241	−	0.260224i
$832$		0			0
$833$	−6.08963	−	42.9090i	−0.210993	−	1.48671i
$834$		0			0
$835$	−12.7225	+	22.0359i	−0.440279	+	0.762585i
$836$		0			0
$837$	−26.9623	−	46.7000i	−0.931953	−	1.61419i
$838$		0			0
$839$	−34.3155			−1.18470			−0.592351	−	0.805680i	$-0.701800\pi$
$839$	−34.3155			−1.18470			−0.592351	+	0.805680i	$0.701800\pi$
$840$		0			0
$841$	−28.4991			−0.982729
$842$		0			0
$843$	−6.90053	−	11.9521i	−0.237667	−	0.411651i
$844$		0			0
$845$	15.4026	−	26.6781i	0.529866	−	0.917756i
$846$		0			0
$847$	24.1887	−	27.8639i	0.831133	−	0.957416i
$848$		0			0
$849$	−14.7902	+	25.6174i	−0.507598	+	0.879186i
$850$		0			0
$851$	−14.3958	−	24.9343i	−0.493482	−	0.854736i
$852$		0			0
$853$	−6.59556			−0.225828			−0.112914	−	0.993605i	$-0.536018\pi$
$853$	−6.59556			−0.225828			−0.112914	+	0.993605i	$0.536018\pi$
$854$		0			0
$855$	−3.49141			−0.119404
$856$		0			0
$857$	−22.3519	−	38.7145i	−0.763525	−	1.32246i	−0.941023	−	0.338343i	$-0.890134\pi$
$857$	−22.3519	−	38.7145i	−0.763525	−	1.32246i	0.177498	−	0.984121i	$-0.443200\pi$
$858$		0			0
$859$	26.5348	−	45.9596i	0.905356	−	1.56812i	0.0849179	−	0.996388i	$-0.472937\pi$
$859$	26.5348	−	45.9596i	0.905356	−	1.56812i	0.820438	−	0.571735i	$-0.193729\pi$
$860$		0			0
$861$	2.31562	+	6.71032i	0.0789162	+	0.228687i
$862$		0			0
$863$	19.2025	−	33.2597i	0.653661	−	1.13217i	−0.328567	−	0.944481i	$-0.606566\pi$
$863$	19.2025	−	33.2597i	0.653661	−	1.13217i	0.982228	−	0.187693i	$-0.0601011\pi$
$864$		0			0
$865$	−10.1714	−	17.6174i	−0.345838	−	0.599010i
$866$		0			0
$867$	−28.6172			−0.971893
$868$		0			0
$869$	84.5887			2.86948
$870$		0			0
$871$	−1.54416	−	2.67457i	−0.0523220	−	0.0906243i
$872$		0			0
$873$	−6.04282	+	10.4665i	−0.204518	+	0.354236i
$874$		0			0
$875$	11.6315	+	2.25278i	0.393217	+	0.0761580i
$876$		0			0
$877$	−10.3664	+	17.9552i	−0.350050	+	0.606304i	−0.986258	−	0.165214i	$-0.947169\pi$
$877$	−10.3664	+	17.9552i	−0.350050	+	0.606304i	0.636208	+	0.771517i	$0.280502\pi$
$878$		0			0
$879$	−13.7705	−	23.8512i	−0.464466	−	0.804479i
$880$		0			0
$881$	39.3452			1.32557			0.662786	−	0.748809i	$-0.269374\pi$
$881$	39.3452			1.32557			0.662786	+	0.748809i	$0.269374\pi$
$882$		0			0
$883$	26.7816			0.901272			0.450636	−	0.892708i	$-0.351197\pi$
$883$	26.7816			0.901272			0.450636	+	0.892708i	$0.351197\pi$
$884$		0			0
$885$	20.6358	+	35.7423i	0.693665	+	1.20146i
$886$		0			0
$887$	−4.96709	+	8.60325i	−0.166779	+	0.288869i	−0.937285	−	0.348563i	$-0.886670\pi$
$887$	−4.96709	+	8.60325i	−0.166779	+	0.288869i	0.770507	+	0.637432i	$0.220003\pi$
$888$		0			0
$889$	22.6855	+	4.39370i	0.760846	+	0.147360i
$890$		0			0
$891$	9.88478	−	17.1209i	0.331153	−	0.573573i
$892$		0			0
$893$	6.17715	+	10.6991i	0.206710	+	0.358033i
$894$		0			0
$895$	59.4613			1.98757
$896$		0			0
$897$	−14.1260			−0.471653
$898$		0			0
$899$	−3.38640	−	5.86542i	−0.112943	−	0.195623i
$900$		0			0
$901$	−2.76049	+	4.78131i	−0.0919653	+	0.159289i
$902$		0			0
$903$	1.45674	+	4.22140i	0.0484772	+	0.140479i
$904$		0			0
$905$	−14.4889	+	25.0954i	−0.481626	+	0.834201i
$906$		0			0
$907$	−9.57946	−	16.5921i	−0.318081	−	0.550932i	0.662007	−	0.749498i	$-0.269705\pi$
$907$	−9.57946	−	16.5921i	−0.318081	−	0.550932i	−0.980088	+	0.198566i	$0.936372\pi$
$908$		0			0
$909$	−3.08764			−0.102411
$910$		0			0
$911$	−53.0363			−1.75717			−0.878586	−	0.477584i	$-0.841513\pi$
$911$	−53.0363			−1.75717			−0.878586	+	0.477584i	$0.841513\pi$
$912$		0			0
$913$	1.23421	+	2.13772i	0.0408465	+	0.0707483i
$914$		0			0
$915$	−23.0789	+	39.9739i	−0.762966	+	1.32150i
$916$		0			0
$917$	−10.7535	+	12.3874i	−0.355112	+	0.409068i
$918$		0			0
$919$	−21.3987	+	37.0636i	−0.705878	+	1.22262i	0.260496	+	0.965475i	$0.416114\pi$
$919$	−21.3987	+	37.0636i	−0.705878	+	1.22262i	−0.966374	+	0.257141i	$0.917219\pi$
$920$		0			0
$921$	14.4770	+	25.0748i	0.477032	+	0.826244i
$922$		0			0
$923$	−19.2740			−0.634411
$924$		0			0
$925$	14.6865			0.482889
$926$		0			0
$927$	3.86333	+	6.69148i	0.126888	+	0.219777i
$928$		0			0
$929$	−10.1792	+	17.6309i	−0.333969	+	0.578451i	−0.983286	−	0.182066i	$-0.941721\pi$
$929$	−10.1792	+	17.6309i	−0.333969	+	0.578451i	0.649317	+	0.760518i	$0.275055\pi$
$930$		0			0
$931$	−5.51024	+	4.31708i	−0.180591	+	0.141487i
$932$		0			0
$933$	−15.8641	+	27.4774i	−0.519367	+	0.899569i
$934$		0			0
$935$	−44.9729	−	77.8954i	−1.47077	−	2.54745i
$936$		0			0
$937$	46.5032			1.51919			0.759596	−	0.650395i	$-0.225396\pi$
$937$	46.5032			1.51919			0.759596	+	0.650395i	$0.225396\pi$
$938$		0			0
$939$	35.8346			1.16942
$940$		0			0
$941$	19.9150	+	34.4938i	0.649211	+	1.12447i	0.983312	+	0.181928i	$0.0582339\pi$
$941$	19.9150	+	34.4938i	0.649211	+	1.12447i	−0.334101	+	0.942537i	$0.608433\pi$
$942$		0			0
$943$	6.78397	−	11.7502i	0.220916	−	0.382638i
$944$		0			0
$945$	28.4270	−	32.7462i	0.924730	−	1.06523i
$946$		0			0
$947$	3.67423	−	6.36396i	0.119397	−	0.206801i	−0.800132	−	0.599824i	$-0.795237\pi$
$947$	3.67423	−	6.36396i	0.119397	−	0.206801i	0.919529	+	0.393023i	$0.128571\pi$
$948$		0			0
$949$	5.43794	+	9.41879i	0.176523	+	0.305747i
$950$		0			0
$951$	36.3202			1.17776
$952$		0			0
$953$	27.7557			0.899094			0.449547	−	0.893257i	$-0.351585\pi$
$953$	27.7557			0.899094			0.449547	+	0.893257i	$0.351585\pi$
$954$		0			0
$955$	−21.1485	−	36.6303i	−0.684350	−	1.18533i
$956$		0			0
$957$	2.37099	−	4.10668i	0.0766432	−	0.132750i
$958$		0			0
$959$	15.3938	+	44.6090i	0.497093	+	1.44050i
$960$		0			0
$961$	−30.2914	+	52.4662i	−0.977141	+	1.69246i
$962$		0			0
$963$	1.43956	+	2.49340i	0.0463893	+	0.0803486i
$964$		0			0
$965$	−45.6905			−1.47083
$966$		0			0
$967$	−42.6002			−1.36993			−0.684965	−	0.728576i	$-0.740183\pi$
$967$	−42.6002			−1.36993			−0.684965	+	0.728576i	$0.740183\pi$
$968$		0			0
$969$	4.15285	+	7.19295i	0.133409	+	0.231071i
$970$		0			0
$971$	−21.7347	+	37.6457i	−0.697501	+	1.20811i	0.271829	+	0.962346i	$0.412372\pi$
$971$	−21.7347	+	37.6457i	−0.697501	+	1.20811i	−0.969330	+	0.245762i	$0.920962\pi$
$972$		0			0
$973$	39.3477	+	7.62082i	1.26143	+	0.244312i
$974$		0			0
$975$	3.60280	−	6.24024i	0.115382	−	0.199848i
$976$		0			0
$977$	12.5852	+	21.7983i	0.402637	+	0.697389i	0.994043	−	0.108985i	$-0.0347602\pi$
$977$	12.5852	+	21.7983i	0.402637	+	0.697389i	−0.591406	+	0.806374i	$0.701427\pi$
$978$		0			0
$979$	−16.8840			−0.539615
$980$		0			0
$981$	17.1103			0.546291
$982$		0			0
$983$	16.4929	+	28.5665i	0.526041	+	0.911129i	0.999540	+	0.0303348i	$0.00965734\pi$
$983$	16.4929	+	28.5665i	0.526041	+	0.911129i	−0.473499	+	0.880794i	$0.657009\pi$
$984$		0			0
$985$	−1.05691	+	1.83063i	−0.0336761	+	0.0583286i
$986$		0			0
$987$	−43.0493	−	8.33774i	−1.37027	−	0.265393i
$988$		0			0
$989$	4.26773	−	7.39193i	0.135706	−	0.235050i
$990$		0			0
$991$	−20.6446	−	35.7574i	−0.655796	−	1.13587i	−0.981694	−	0.190467i	$-0.939000\pi$
$991$	−20.6446	−	35.7574i	−0.655796	−	1.13587i	0.325897	−	0.945405i	$-0.394334\pi$
$992$		0			0
$993$	−4.21239			−0.133676
$994$		0			0
$995$	−41.8281			−1.32604
$996$		0			0
$997$	5.25921	+	9.10923i	0.166561	+	0.288492i	0.937209	−	0.348770i	$-0.113400\pi$
$997$	5.25921	+	9.10923i	0.166561	+	0.288492i	−0.770648	+	0.637262i	$0.780067\pi$
$998$		0			0
$999$	−11.9573	+	20.7106i	−0.378311	+	0.655254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.457.6	yes	16
7.2	even	3		7448.2.a.bq.1.3		8
7.4	even	3	inner	1064.2.q.n.305.6	✓	16
7.5	odd	6		7448.2.a.br.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.6	✓	16	7.4	even	3	inner
1064.2.q.n.457.6	yes	16	1.1	even	1	trivial
7448.2.a.bq.1.3		8	7.2	even	3
7448.2.a.br.1.6		8	7.5	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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +O(q^{10})\)	\(q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +(-2.49731 - 4.32547i) q^{11} +1.55217 q^{13} -3.90205 q^{15} +(-3.09564 - 5.36181i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.15781 - 3.35516i) q^{21} +(-3.39198 + 5.87509i) q^{23} +(-1.73024 - 2.99686i) q^{25} +5.63482 q^{27} +0.707720 q^{29} +(-4.78494 - 8.28777i) q^{31} +(3.35018 - 5.80268i) q^{33} +(5.04489 - 5.81141i) q^{35} +(-2.12203 + 3.67547i) q^{37} +(1.04113 + 1.80329i) q^{39} -2.00000 q^{41} -1.25818 q^{43} +(1.74571 + 3.02365i) q^{45} +(6.17715 - 10.6991i) q^{47} +(6.49383 + 2.61347i) q^{49} +(4.15285 - 7.19295i) q^{51} +(-0.445867 - 0.772264i) q^{53} +14.5278 q^{55} -1.34151 q^{57} +(-5.28845 - 9.15987i) q^{59} +(5.91457 - 10.2443i) q^{61} +(-2.08189 + 2.39821i) q^{63} +(-2.25739 + 3.90992i) q^{65} +(-0.994841 - 1.72312i) q^{67} -9.10079 q^{69} -12.4174 q^{71} +(3.50344 + 6.06814i) q^{73} +(2.32114 - 4.02033i) q^{75} +(4.31068 + 12.4917i) q^{77} +(-8.46797 + 14.6670i) q^{79} +(1.97908 + 3.42787i) q^{81} -0.494217 q^{83} +18.0085 q^{85} +(0.474708 + 0.822219i) q^{87} +(1.69022 - 2.92754i) q^{89} +(-4.03174 - 0.780862i) q^{91} +(6.41907 - 11.1182i) q^{93} +(-1.45434 - 2.51900i) q^{95} -10.0685 q^{97} -5.99524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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