LMFDB - Embedded newform 1008.2.r.n.673.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.6095158642368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 $ x^10 - 4x^9 + 6x^8 - 7x^7 + 25x^6 - 66x^5 + 75x^4 - 63x^3 + 162x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.3
Root			$-0.902451 + 1.47837i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.n.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468714 + 1.66743i) q^{3} +(-0.553143 - 0.958072i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.56061 - 1.56309i) q^{9} +O(q^{10})$	\(q+(-0.468714 + 1.66743i) q^{3} +(-0.553143 - 0.958072i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.56061 - 1.56309i) q^{9} +(0.433737 - 0.751255i) q^{11} +(-2.70025 - 4.67696i) q^{13} +(1.85678 - 0.473263i) q^{15} +5.12123 q^{17} +5.44095 q^{19} +(-1.20968 - 1.23963i) q^{21} +(-0.967083 - 1.67504i) q^{23} +(1.88807 - 3.27023i) q^{25} +(3.80653 - 3.53699i) q^{27} +(-1.57337 + 2.72516i) q^{29} +(3.02770 + 5.24413i) q^{31} +(1.04936 + 1.07535i) q^{33} +1.10629 q^{35} +5.49687 q^{37} +(9.06413 - 2.31030i) q^{39} +(-1.71300 - 2.96700i) q^{41} +(3.41325 - 5.91192i) q^{43} +(-0.0811672 + 3.31787i) q^{45} +(-4.43384 + 7.67963i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.40039 + 8.53927i) q^{51} +0.223869 q^{53} -0.959675 q^{55} +(-2.55025 + 9.07237i) q^{57} +(-6.30905 - 10.9276i) q^{59} +(4.46891 - 7.74037i) q^{61} +(2.63398 - 1.43601i) q^{63} +(-2.98725 + 5.17406i) q^{65} +(3.17506 + 5.49937i) q^{67} +(3.24628 - 0.827426i) q^{69} -3.33466 q^{71} +16.2567 q^{73} +(4.56789 + 4.68101i) q^{75} +(0.433737 + 0.751255i) q^{77} +(-2.44616 + 4.23688i) q^{79} +(4.11349 + 8.00495i) q^{81} +(6.33675 - 10.9756i) q^{83} +(-2.83277 - 4.90651i) q^{85} +(-3.80653 - 3.90079i) q^{87} +11.1908 q^{89} +5.40049 q^{91} +(-10.1633 + 2.59046i) q^{93} +(-3.00962 - 5.21282i) q^{95} +(0.761290 - 1.31859i) q^{97} +(-2.28491 + 1.24570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 3 * q^5 - 5 * q^7	$ 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) $ 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.468714	+	1.66743i	−0.270612	+	0.962688i
$3$	−0.468714	+	1.66743i	−0.270612	+	0.962688i
$4$		0			0
$5$	−0.553143	−	0.958072i	−0.247373	−	0.428463i	0.715423	−	0.698692i	$-0.246234\pi$
$5$	−0.553143	−	0.958072i	−0.247373	−	0.428463i	−0.962796	+	0.270229i	$0.912901\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−2.56061	−	1.56309i	−0.853538	−	0.521030i
$10$		0			0
$11$	0.433737	−	0.751255i	0.130777	−	0.226512i	−0.793200	−	0.608962i	$-0.791586\pi$
$11$	0.433737	−	0.751255i	0.130777	−	0.226512i	0.923976	+	0.382450i	$0.124920\pi$
$12$		0			0
$13$	−2.70025	−	4.67696i	−0.748914	−	1.29716i	−0.948344	−	0.317244i	$-0.897242\pi$
$13$	−2.70025	−	4.67696i	−0.748914	−	1.29716i	0.199430	−	0.979912i	$-0.436091\pi$
$14$		0			0
$15$	1.85678	−	0.473263i	0.479418	−	0.122196i
$16$		0			0
$17$	5.12123			1.24208			0.621040	−	0.783779i	$-0.286710\pi$
$17$	5.12123			1.24208			0.621040	+	0.783779i	$0.286710\pi$
$18$		0			0
$19$	5.44095			1.24824			0.624119	−	0.781329i	$-0.285458\pi$
$19$	5.44095			1.24824			0.624119	+	0.781329i	$0.285458\pi$
$20$		0			0
$21$	−1.20968	−	1.23963i	−0.263973	−	0.270510i
$22$		0			0
$23$	−0.967083	−	1.67504i	−0.201651	−	0.349269i	0.747410	−	0.664363i	$-0.231297\pi$
$23$	−0.967083	−	1.67504i	−0.201651	−	0.349269i	−0.949060	+	0.315094i	$0.897964\pi$
$24$		0			0
$25$	1.88807	−	3.27023i	0.377613	−	0.654045i
$26$		0			0
$27$	3.80653	−	3.53699i	0.732568	−	0.680694i
$28$		0			0
$29$	−1.57337	+	2.72516i	−0.292167	+	0.506049i	−0.974322	−	0.225159i	$-0.927710\pi$
$29$	−1.57337	+	2.72516i	−0.292167	+	0.506049i	0.682155	+	0.731208i	$0.261043\pi$
$30$		0			0
$31$	3.02770	+	5.24413i	0.543791	+	0.941873i	0.998682	+	0.0513259i	$0.0163447\pi$
$31$	3.02770	+	5.24413i	0.543791	+	0.941873i	−0.454891	+	0.890547i	$0.650322\pi$
$32$		0			0
$33$	1.04936	+	1.07535i	0.182671	+	0.187194i
$34$		0			0
$35$	1.10629			0.186996
$36$		0			0
$37$	5.49687			0.903679			0.451840	−	0.892099i	$-0.350768\pi$
$37$	5.49687			0.903679			0.451840	+	0.892099i	$0.350768\pi$
$38$		0			0
$39$	9.06413	−	2.31030i	1.45142	−	0.369944i
$40$		0			0
$41$	−1.71300	−	2.96700i	−0.267526	−	0.463368i	0.700696	−	0.713460i	$-0.252873\pi$
$41$	−1.71300	−	2.96700i	−0.267526	−	0.463368i	−0.968222	+	0.250091i	$0.919539\pi$
$42$		0			0
$43$	3.41325	−	5.91192i	0.520515	−	0.901559i	−0.479200	−	0.877706i	$-0.659073\pi$
$43$	3.41325	−	5.91192i	0.520515	−	0.901559i	0.999715	−	0.0238534i	$-0.00759350\pi$
$44$		0			0
$45$	−0.0811672	+	3.31787i	−0.0120997	+	0.494598i
$46$		0			0
$47$	−4.43384	+	7.67963i	−0.646742	+	1.12019i	0.337154	+	0.941449i	$0.390536\pi$
$47$	−4.43384	+	7.67963i	−0.646742	+	1.12019i	−0.983896	+	0.178740i	$0.942798\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−2.40039	+	8.53927i	−0.336122	+	1.19574i
$52$		0			0
$53$	0.223869			0.0307508			0.0153754	−	0.999882i	$-0.495106\pi$
$53$	0.223869			0.0307508			0.0153754	+	0.999882i	$0.495106\pi$
$54$		0			0
$55$	−0.959675			−0.129402
$56$		0			0
$57$	−2.55025	+	9.07237i	−0.337788	+	1.20166i
$58$		0			0
$59$	−6.30905	−	10.9276i	−0.821368	−	1.42265i	−0.904664	−	0.426126i	$-0.859878\pi$
$59$	−6.30905	−	10.9276i	−0.821368	−	1.42265i	0.0832956	−	0.996525i	$-0.473455\pi$
$60$		0			0
$61$	4.46891	−	7.74037i	0.572185	−	0.991053i	−0.424156	−	0.905589i	$-0.639429\pi$
$61$	4.46891	−	7.74037i	0.572185	−	0.991053i	0.996341	−	0.0854642i	$-0.0272373\pi$
$62$		0			0
$63$	2.63398	−	1.43601i	0.331851	−	0.180920i
$64$		0			0
$65$	−2.98725	+	5.17406i	−0.370522	+	0.641763i
$66$		0			0
$67$	3.17506	+	5.49937i	0.387896	+	0.671855i	0.992166	−	0.124924i	$-0.0398687\pi$
$67$	3.17506	+	5.49937i	0.387896	+	0.671855i	−0.604270	+	0.796779i	$0.706535\pi$
$68$		0			0
$69$	3.24628	−	0.827426i	0.390807	−	0.0996103i
$70$		0			0
$71$	−3.33466			−0.395751			−0.197876	−	0.980227i	$-0.563404\pi$
$71$	−3.33466			−0.395751			−0.197876	+	0.980227i	$0.563404\pi$
$72$		0			0
$73$	16.2567			1.90270			0.951350	−	0.308113i	$-0.0996976\pi$
$73$	16.2567			1.90270			0.951350	+	0.308113i	$0.0996976\pi$
$74$		0			0
$75$	4.56789	+	4.68101i	0.527455	+	0.540516i
$76$		0			0
$77$	0.433737	+	0.751255i	0.0494289	+	0.0856134i
$78$		0			0
$79$	−2.44616	+	4.23688i	−0.275215	+	0.476686i	−0.970189	−	0.242348i	$-0.922082\pi$
$79$	−2.44616	+	4.23688i	−0.275215	+	0.476686i	0.694974	+	0.719035i	$0.255416\pi$
$80$		0			0
$81$	4.11349	+	8.00495i	0.457055	+	0.889438i
$82$		0			0
$83$	6.33675	−	10.9756i	0.695548	−	1.20472i	−0.274447	−	0.961602i	$-0.588495\pi$
$83$	6.33675	−	10.9756i	0.695548	−	1.20472i	0.969996	−	0.243123i	$-0.0781718\pi$
$84$		0			0
$85$	−2.83277	−	4.90651i	−0.307257	−	0.532185i
$86$		0			0
$87$	−3.80653	−	3.90079i	−0.408103	−	0.418209i
$88$		0			0
$89$	11.1908			1.18623			0.593113	−	0.805119i	$-0.297899\pi$
$89$	11.1908			1.18623			0.593113	+	0.805119i	$0.297899\pi$
$90$		0			0
$91$	5.40049			0.566126
$92$		0			0
$93$	−10.1633	+	2.59046i	−1.05389	+	0.268619i
$94$		0			0
$95$	−3.00962	−	5.21282i	−0.308781	−	0.534824i
$96$		0			0
$97$	0.761290	−	1.31859i	0.0772973	−	0.133883i	−0.824786	−	0.565445i	$-0.808704\pi$
$97$	0.761290	−	1.31859i	0.0772973	−	0.133883i	0.902083	+	0.431563i	$0.142038\pi$
$98$		0			0
$99$	−2.28491	+	1.24570i	−0.229642	+	0.125198i
$100$		0			0
$101$	7.98844	−	13.8364i	0.794879	−	1.37677i	−0.128036	−	0.991769i	$-0.540867\pi$
$101$	7.98844	−	13.8364i	0.794879	−	1.37677i	0.922916	−	0.385002i	$-0.125799\pi$
$102$		0			0
$103$	0.873122	+	1.51229i	0.0860313	+	0.149011i	0.905830	−	0.423641i	$-0.139248\pi$
$103$	0.873122	+	1.51229i	0.0860313	+	0.149011i	−0.819799	+	0.572652i	$0.805915\pi$
$104$		0			0
$105$	−0.518532	+	1.84465i	−0.0506035	+	0.180019i
$106$		0			0
$107$	−10.6791			−1.03239			−0.516194	−	0.856472i	$-0.672652\pi$
$107$	−10.6791			−1.03239			−0.516194	+	0.856472i	$0.672652\pi$
$108$		0			0
$109$	−3.08025			−0.295034			−0.147517	−	0.989059i	$-0.547128\pi$
$109$	−3.08025			−0.295034			−0.147517	+	0.989059i	$0.547128\pi$
$110$		0			0
$111$	−2.57646	+	9.16562i	−0.244547	+	0.869962i
$112$		0			0
$113$	3.62625	+	6.28085i	0.341129	+	0.590852i	0.984643	−	0.174582i	$-0.0558574\pi$
$113$	3.62625	+	6.28085i	0.341129	+	0.590852i	−0.643514	+	0.765434i	$0.722524\pi$
$114$		0			0
$115$	−1.06987	+	1.85307i	−0.0997659	+	0.172800i
$116$		0			0
$117$	−0.396229	+	16.1966i	−0.0366314	+	1.49738i
$118$		0			0
$119$	−2.56061	+	4.43511i	−0.234731	+	0.406566i
$120$		0			0
$121$	5.12374	+	8.87459i	0.465795	+	0.806781i
$122$		0			0
$123$	5.75017	−	1.46563i	0.518475	−	0.132151i
$124$		0			0
$125$	−9.70891			−0.868392
$126$		0			0
$127$	−7.18706			−0.637749			−0.318874	−	0.947797i	$-0.603305\pi$
$127$	−7.18706			−0.637749			−0.318874	+	0.947797i	$0.603305\pi$
$128$		0			0
$129$	8.25785	+	8.46233i	0.727063	+	0.745067i
$130$		0			0
$131$	−4.62192	−	8.00540i	−0.403819	−	0.699435i	0.590364	−	0.807137i	$-0.298984\pi$
$131$	−4.62192	−	8.00540i	−0.403819	−	0.699435i	−0.994183	+	0.107702i	$0.965651\pi$
$132$		0			0
$133$	−2.72047	+	4.71200i	−0.235895	+	0.408582i
$134$		0			0
$135$	−5.49425	−	1.69047i	−0.472870	−	0.145492i
$136$		0			0
$137$	−4.37280	+	7.57390i	−0.373593	+	0.647082i	−0.990115	−	0.140255i	$-0.955208\pi$
$137$	−4.37280	+	7.57390i	−0.373593	+	0.647082i	0.616522	+	0.787337i	$0.288541\pi$
$138$		0			0
$139$	0.0669550	+	0.115970i	0.00567905	+	0.00983641i	0.868851	−	0.495074i	$-0.164859\pi$
$139$	0.0669550	+	0.115970i	0.00567905	+	0.00983641i	−0.863172	+	0.504910i	$0.831526\pi$
$140$		0			0
$141$	−10.7270	−	10.9926i	−0.903378	−	0.925748i
$142$		0			0
$143$	−4.68479			−0.391762
$144$		0			0
$145$	3.48119			0.289097
$146$		0			0
$147$	1.67839	−	0.427795i	0.138431	−	0.0352839i
$148$		0			0
$149$	−4.80937	−	8.33008i	−0.393999	−	0.682427i	0.598974	−	0.800769i	$-0.295575\pi$
$149$	−4.80937	−	8.33008i	−0.393999	−	0.682427i	−0.992973	+	0.118342i	$0.962242\pi$
$150$		0			0
$151$	11.6156	−	20.1188i	0.945263	−	1.63724i	0.190038	−	0.981777i	$-0.439139\pi$
$151$	11.6156	−	20.1188i	0.945263	−	1.63724i	0.755225	−	0.655466i	$-0.227528\pi$
$152$		0			0
$153$	−13.1135	−	8.00495i	−1.06016	−	0.647162i
$154$		0			0
$155$	3.34950	−	5.80150i	0.269038	−	0.465988i
$156$		0			0
$157$	−5.58795	−	9.67861i	−0.445967	−	0.772437i	0.552152	−	0.833743i	$-0.313807\pi$
$157$	−5.58795	−	9.67861i	−0.445967	−	0.772437i	−0.998119	+	0.0613063i	$0.980473\pi$
$158$		0			0
$159$	−0.104931	+	0.373285i	−0.00832154	+	0.0296034i
$160$		0			0
$161$	1.93417			0.152434
$162$		0			0
$163$	−14.1873			−1.11123			−0.555616	−	0.831439i	$-0.687518\pi$
$163$	−14.1873			−1.11123			−0.555616	+	0.831439i	$0.687518\pi$
$164$		0			0
$165$	0.449813	−	1.60019i	0.0350179	−	0.124574i
$166$		0			0
$167$	−5.19208	−	8.99295i	−0.401775	−	0.695895i	0.592165	−	0.805817i	$-0.298273\pi$
$167$	−5.19208	−	8.99295i	−0.401775	−	0.695895i	−0.993940	+	0.109921i	$0.964940\pi$
$168$		0			0
$169$	−8.08266	+	13.9996i	−0.621743	+	1.07689i
$170$		0			0
$171$	−13.9322	−	8.50469i	−1.06542	−	0.650370i
$172$		0			0
$173$	−5.55999	+	9.63018i	−0.422718	+	0.732169i	−0.996204	−	0.0870462i	$-0.972257\pi$
$173$	−5.55999	+	9.63018i	−0.422718	+	0.732169i	0.573486	+	0.819215i	$0.305591\pi$
$174$		0			0
$175$	1.88807	+	3.27023i	0.142724	+	0.247206i
$176$		0			0
$177$	21.1781	−	5.39795i	1.59184	−	0.405735i
$178$		0			0
$179$	−3.27300			−0.244635			−0.122318	−	0.992491i	$-0.539033\pi$
$179$	−3.27300			−0.244635			−0.122318	+	0.992491i	$0.539033\pi$
$180$		0			0
$181$	17.4012			1.29342			0.646711	−	0.762735i	$-0.276144\pi$
$181$	17.4012			1.29342			0.646711	+	0.762735i	$0.276144\pi$
$182$		0			0
$183$	10.8119	+	11.0796i	0.799235	+	0.819027i
$184$		0			0
$185$	−3.04055	−	5.26639i	−0.223546	−	0.387193i
$186$		0			0
$187$	2.22127	−	3.84735i	0.162435	−	0.281346i
$188$		0			0
$189$	1.15986	+	5.06505i	0.0843673	+	0.368428i
$190$		0			0
$191$	−0.760759	+	1.31767i	−0.0550466	+	0.0953435i	−0.892236	−	0.451570i	$-0.850864\pi$
$191$	−0.760759	+	1.31767i	−0.0550466	+	0.0953435i	0.837189	+	0.546914i	$0.184197\pi$
$192$		0			0
$193$	−10.9211	−	18.9159i	−0.786117	−	1.36159i	−0.928330	−	0.371758i	$-0.878755\pi$
$193$	−10.9211	−	18.9159i	−0.786117	−	1.36159i	0.142213	−	0.989836i	$-0.454578\pi$
$194$		0			0
$195$	−7.22720	−	7.40616i	−0.517550	−	0.530366i
$196$		0			0
$197$	−20.1902			−1.43849			−0.719245	−	0.694756i	$-0.755512\pi$
$197$	−20.1902			−1.43849			−0.719245	+	0.694756i	$0.755512\pi$
$198$		0			0
$199$	−0.223869			−0.0158697			−0.00793483	−	0.999969i	$-0.502526\pi$
$199$	−0.223869			−0.0158697			−0.00793483	+	0.999969i	$0.502526\pi$
$200$		0			0
$201$	−10.6580	+	2.71655i	−0.751757	+	0.191611i
$202$		0			0
$203$	−1.57337	−	2.72516i	−0.110429	−	0.191268i
$204$		0			0
$205$	−1.89507	+	3.28236i	−0.132357	+	0.229250i
$206$		0			0
$207$	−0.141908	+	5.80076i	−0.00986328	+	0.403181i
$208$		0			0
$209$	2.35994	−	4.08753i	0.163240	−	0.282741i
$210$		0			0
$211$	7.78029	+	13.4759i	0.535617	+	0.927717i	0.999133	+	0.0416280i	$0.0132544\pi$
$211$	7.78029	+	13.4759i	0.535617	+	0.927717i	−0.463516	+	0.886089i	$0.653412\pi$
$212$		0			0
$213$	1.56300	−	5.56029i	0.107095	−	0.380985i
$214$		0			0
$215$	−7.55206			−0.515046
$216$		0			0
$217$	−6.05539			−0.411067
$218$		0			0
$219$	−7.61973	+	27.1068i	−0.514893	+	1.83171i
$220$		0			0
$221$	−13.8286	−	23.9518i	−0.930211	−	1.61117i
$222$		0			0
$223$	10.2226	−	17.7061i	0.684557	−	1.18569i	−0.289018	−	0.957324i	$-0.593329\pi$
$223$	10.2226	−	17.7061i	0.684557	−	1.18569i	0.973576	−	0.228365i	$-0.0733378\pi$
$224$		0			0
$225$	−9.94627	+	5.42257i	−0.663084	+	0.361505i
$226$		0			0
$227$	−11.7673	+	20.3815i	−0.781021	+	1.35277i	0.150326	+	0.988637i	$0.451968\pi$
$227$	−11.7673	+	20.3815i	−0.781021	+	1.35277i	−0.931347	+	0.364132i	$0.881366\pi$
$228$		0			0
$229$	−4.50999	−	7.81153i	−0.298028	−	0.516200i	0.677656	−	0.735379i	$-0.262996\pi$
$229$	−4.50999	−	7.81153i	−0.298028	−	0.516200i	−0.975685	+	0.219178i	$0.929662\pi$
$230$		0			0
$231$	−1.45596	+	0.371101i	−0.0957951	+	0.0244166i
$232$		0			0
$233$	−29.4795			−1.93127			−0.965633	−	0.259908i	$-0.916308\pi$
$233$	−29.4795			−1.93127			−0.965633	+	0.259908i	$0.916308\pi$
$234$		0			0
$235$	9.81019			0.639946
$236$		0			0
$237$	−5.91813	−	6.06468i	−0.384424	−	0.393943i
$238$		0			0
$239$	8.82336	+	15.2825i	0.570736	+	0.988543i	0.996491	+	0.0837049i	$0.0266753\pi$
$239$	8.82336	+	15.2825i	0.570736	+	0.988543i	−0.425755	+	0.904839i	$0.639991\pi$
$240$		0			0
$241$	−0.899362	+	1.55774i	−0.0579330	+	0.100343i	−0.893537	−	0.448989i	$-0.851784\pi$
$241$	−0.899362	+	1.55774i	−0.0579330	+	0.100343i	0.835604	+	0.549332i	$0.185118\pi$
$242$		0			0
$243$	−15.2757	+	3.10692i	−0.979937	+	0.199309i
$244$		0			0
$245$	−0.553143	+	0.958072i	−0.0353390	+	0.0612090i
$246$		0			0
$247$	−14.6919	−	25.4471i	−0.934823	−	1.61916i
$248$		0			0
$249$	15.3308	+	15.7104i	0.971551	+	0.995609i
$250$		0			0
$251$	26.7181			1.68643			0.843216	−	0.537574i	$-0.180659\pi$
$251$	26.7181			1.68643			0.843216	+	0.537574i	$0.180659\pi$
$252$		0			0
$253$	−1.67784			−0.105485
$254$		0			0
$255$	9.50899	−	2.42369i	0.595476	−	0.151777i
$256$		0			0
$257$	−2.72074	−	4.71245i	−0.169715	−	0.293955i	0.768605	−	0.639724i	$-0.220951\pi$
$257$	−2.72074	−	4.71245i	−0.169715	−	0.293955i	−0.938320	+	0.345769i	$0.887618\pi$
$258$		0			0
$259$	−2.74843	+	4.76043i	−0.170779	+	0.295798i
$260$		0			0
$261$	8.28846	−	4.51875i	0.513043	−	0.279704i
$262$		0			0
$263$	−10.7972	+	18.7012i	−0.665781	+	1.15317i	0.313292	+	0.949657i	$0.398568\pi$
$263$	−10.7972	+	18.7012i	−0.665781	+	1.15317i	−0.979073	+	0.203509i	$0.934765\pi$
$264$		0			0
$265$	−0.123832	−	0.214483i	−0.00760692	−	0.0131756i
$266$		0			0
$267$	−5.24530	+	18.6599i	−0.321007	+	1.14197i
$268$		0			0
$269$	28.8770			1.76066			0.880331	−	0.474360i	$-0.157320\pi$
$269$	28.8770			1.76066			0.880331	+	0.474360i	$0.157320\pi$
$270$		0			0
$271$	−5.85261			−0.355521			−0.177760	−	0.984074i	$-0.556885\pi$
$271$	−5.85261			−0.355521			−0.177760	+	0.984074i	$0.556885\pi$
$272$		0			0
$273$	−2.53129	+	9.00492i	−0.153200	+	0.545003i
$274$		0			0
$275$	−1.63785	−	2.83684i	−0.0987659	−	0.171068i
$276$		0			0
$277$	3.10837	−	5.38386i	0.186764	−	0.323485i	−0.757406	−	0.652945i	$-0.773533\pi$
$277$	3.10837	−	5.38386i	0.186764	−	0.323485i	0.944170	+	0.329460i	$0.106867\pi$
$278$		0			0
$279$	0.444278	−	18.1608i	0.0265983	−	1.08726i
$280$		0			0
$281$	3.40082	−	5.89039i	0.202876	−	0.351391i	−0.746578	−	0.665298i	$-0.768305\pi$
$281$	3.40082	−	5.89039i	0.202876	−	0.351391i	0.949454	+	0.313907i	$0.101638\pi$
$282$		0			0
$283$	5.20804	+	9.02060i	0.309586	+	0.536219i	0.978272	−	0.207326i	$-0.0664762\pi$
$283$	5.20804	+	9.02060i	0.309586	+	0.536219i	−0.668686	+	0.743545i	$0.733143\pi$
$284$		0			0
$285$	10.1026	−	2.57500i	0.598428	−	0.152530i
$286$		0			0
$287$	3.42600			0.202231
$288$		0			0
$289$	9.22699			0.542764
$290$		0			0
$291$	1.84183	+	1.88744i	0.107970	+	0.110644i
$292$		0			0
$293$	−4.11879	−	7.13395i	−0.240622	−	0.416770i	0.720270	−	0.693694i	$-0.244018\pi$
$293$	−4.11879	−	7.13395i	−0.240622	−	0.416770i	−0.960892	+	0.276925i	$0.910685\pi$
$294$		0			0
$295$	−6.97961	+	12.0890i	−0.406369	+	0.703851i
$296$		0			0
$297$	−1.00615	−	4.39380i	−0.0583826	−	0.254954i
$298$		0			0
$299$	−5.22272	+	9.04602i	−0.302038	+	0.523145i
$300$		0			0
$301$	3.41325	+	5.91192i	0.196736	+	0.340757i
$302$		0			0
$303$	19.3268	+	19.8054i	1.11030	+	1.13779i
$304$		0			0
$305$	−9.88778			−0.566173
$306$		0			0
$307$	−3.40102			−0.194106			−0.0970532	−	0.995279i	$-0.530942\pi$
$307$	−3.40102			−0.194106			−0.0970532	+	0.995279i	$0.530942\pi$
$308$		0			0
$309$	−2.93088	+	0.747034i	−0.166732	+	0.0424973i
$310$		0			0
$311$	2.23611	+	3.87305i	0.126798	+	0.219621i	0.922434	−	0.386154i	$-0.126197\pi$
$311$	2.23611	+	3.87305i	0.126798	+	0.219621i	−0.795636	+	0.605775i	$0.792863\pi$
$312$		0			0
$313$	−6.90717	+	11.9636i	−0.390416	+	0.676221i	−0.992504	−	0.122209i	$-0.961002\pi$
$313$	−6.90717	+	11.9636i	−0.390416	+	0.676221i	0.602088	+	0.798430i	$0.294336\pi$
$314$		0			0
$315$	−2.83277	−	1.72923i	−0.159609	−	0.0974308i
$316$		0			0
$317$	−16.5956	+	28.7445i	−0.932103	+	1.61445i	−0.152383	+	0.988322i	$0.548695\pi$
$317$	−16.5956	+	28.7445i	−0.932103	+	1.61445i	−0.779720	+	0.626128i	$0.784639\pi$
$318$		0			0
$319$	1.36486	+	2.36400i	0.0764173	+	0.132359i
$320$		0			0
$321$	5.00544	−	17.8066i	0.279377	−	0.993868i
$322$		0			0
$323$	27.8643			1.55041
$324$		0			0
$325$	−20.3930			−1.13120
$326$		0			0
$327$	1.44376	−	5.13609i	0.0798399	−	0.284026i
$328$		0			0
$329$	−4.43384	−	7.67963i	−0.244445	−	0.423392i
$330$		0			0
$331$	−1.50469	+	2.60620i	−0.0827054	+	0.143250i	−0.904411	−	0.426662i	$-0.859689\pi$
$331$	−1.50469	+	2.60620i	−0.0827054	+	0.143250i	0.821706	+	0.569912i	$0.193023\pi$
$332$		0			0
$333$	−14.0754	−	8.59210i	−0.771325	−	0.470844i
$334$		0			0
$335$	3.51253	−	6.08388i	0.191910	−	0.332398i
$336$		0			0
$337$	17.3481	+	30.0478i	0.945012	+	1.63681i	0.755727	+	0.654887i	$0.227284\pi$
$337$	17.3481	+	30.0478i	0.945012	+	1.63681i	0.189285	+	0.981922i	$0.439383\pi$
$338$		0			0
$339$	−12.1725	+	3.10258i	−0.661120	+	0.168509i
$340$		0			0
$341$	5.25290			0.284460
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−2.58839	−	2.65249i	−0.139354	−	0.142805i
$346$		0			0
$347$	−6.83499	−	11.8385i	−0.366921	−	0.635526i	0.622161	−	0.782889i	$-0.286255\pi$
$347$	−6.83499	−	11.8385i	−0.366921	−	0.635526i	−0.989082	+	0.147363i	$0.952921\pi$
$348$		0			0
$349$	−10.3247	+	17.8830i	−0.552671	+	0.957254i	0.445410	+	0.895327i	$0.353058\pi$
$349$	−10.3247	+	17.8830i	−0.552671	+	0.957254i	−0.998081	+	0.0619274i	$0.980275\pi$
$350$		0			0
$351$	−26.8210	−	8.25227i	−1.43160	−	0.440474i
$352$		0			0
$353$	−6.55288	+	11.3499i	−0.348775	+	0.604095i	−0.986032	−	0.166556i	$-0.946735\pi$
$353$	−6.55288	+	11.3499i	−0.348775	+	0.604095i	0.637257	+	0.770651i	$0.280069\pi$
$354$		0			0
$355$	1.84454	+	3.19484i	0.0978982	+	0.169565i
$356$		0			0
$357$	−6.19503	−	6.34843i	−0.327876	−	0.335995i
$358$		0			0
$359$	34.2209			1.80611			0.903056	−	0.429523i	$-0.141318\pi$
$359$	34.2209			1.80611			0.903056	+	0.429523i	$0.141318\pi$
$360$		0			0
$361$	10.6039			0.558099
$362$		0			0
$363$	−17.1993	+	4.38382i	−0.902728	+	0.230091i
$364$		0			0
$365$	−8.99227	−	15.5751i	−0.470677	−	0.815236i
$366$		0			0
$367$	2.24027	−	3.88026i	0.116941	−	0.202548i	−0.801613	−	0.597843i	$-0.796024\pi$
$367$	2.24027	−	3.88026i	0.116941	−	0.202548i	0.918554	+	0.395295i	$0.129358\pi$
$368$		0			0
$369$	−0.251362	+	10.2749i	−0.0130854	+	0.534892i
$370$		0			0
$371$	−0.111935	+	0.193876i	−0.00581135	+	0.0100656i
$372$		0			0
$373$	14.7118	+	25.4815i	0.761746	+	1.31938i	0.941950	+	0.335753i	$0.108991\pi$
$373$	14.7118	+	25.4815i	0.761746	+	1.31938i	−0.180204	+	0.983629i	$0.557676\pi$
$374$		0			0
$375$	4.55070	−	16.1889i	0.234997	−	0.835991i
$376$		0			0
$377$	16.9939			0.875232
$378$		0			0
$379$	18.0301			0.926144			0.463072	−	0.886321i	$-0.346747\pi$
$379$	18.0301			0.926144			0.463072	+	0.886321i	$0.346747\pi$
$380$		0			0
$381$	3.36868	−	11.9839i	0.172583	−	0.613953i
$382$		0			0
$383$	14.0017	+	24.2516i	0.715451	+	1.23920i	0.962785	+	0.270268i	$0.0871123\pi$
$383$	14.0017	+	24.2516i	0.715451	+	1.23920i	−0.247334	+	0.968930i	$0.579554\pi$
$384$		0			0
$385$	0.479837	−	0.831103i	0.0244548	−	0.0423569i
$386$		0			0
$387$	−17.9809	+	9.80293i	−0.914019	+	0.498311i
$388$		0			0
$389$	−7.07294	+	12.2507i	−0.358612	+	0.621135i	−0.987729	−	0.156176i	$-0.950083\pi$
$389$	−7.07294	+	12.2507i	−0.358612	+	0.621135i	0.629117	+	0.777311i	$0.283417\pi$
$390$		0			0
$391$	−4.95265	−	8.57825i	−0.250466	−	0.433821i
$392$		0			0
$393$	15.5148	−	3.95447i	0.782617	−	0.199476i
$394$		0			0
$395$	5.41232			0.272323
$396$		0			0
$397$	−21.5268			−1.08040			−0.540198	−	0.841538i	$-0.681651\pi$
$397$	−21.5268			−1.08040			−0.540198	+	0.841538i	$0.681651\pi$
$398$		0			0
$399$	−6.58178	−	6.74476i	−0.329501	−	0.337660i
$400$		0			0
$401$	11.8468	+	20.5192i	0.591599	+	1.02468i	0.994017	+	0.109224i	$0.0348364\pi$
$401$	11.8468	+	20.5192i	0.591599	+	1.02468i	−0.402418	+	0.915456i	$0.631830\pi$
$402$		0			0
$403$	16.3511	−	28.3209i	0.814504	−	1.41076i
$404$		0			0
$405$	5.39396	−	8.36890i	0.268028	−	0.415854i
$406$		0			0
$407$	2.38419	−	4.12955i	0.118180	−	0.204694i
$408$		0			0
$409$	0.157382	+	0.272593i	0.00778202	+	0.0134789i	0.869890	−	0.493245i	$-0.164190\pi$
$409$	0.157382	+	0.272593i	0.00778202	+	0.0134789i	−0.862108	+	0.506724i	$0.830856\pi$
$410$		0			0
$411$	−10.5793	−	10.8413i	−0.521840	−	0.534762i
$412$		0			0
$413$	12.6181			0.620896
$414$		0			0
$415$	−14.0205			−0.688240
$416$		0			0
$417$	−0.224753	+	0.0572860i	−0.0110062	+	0.00280531i
$418$		0			0
$419$	−0.412984	−	0.715310i	−0.0201756	−	0.0349452i	0.855761	−	0.517371i	$-0.173089\pi$
$419$	−0.412984	−	0.715310i	−0.0201756	−	0.0349452i	−0.875937	+	0.482426i	$0.839756\pi$
$420$		0			0
$421$	9.11201	−	15.7825i	0.444092	−	0.769190i	−0.553896	−	0.832586i	$-0.686860\pi$
$421$	9.11201	−	15.7825i	0.444092	−	0.769190i	0.997988	+	0.0633955i	$0.0201930\pi$
$422$		0			0
$423$	23.3573	−	12.7341i	1.13567	−	0.619153i
$424$		0			0
$425$	9.66922	−	16.7476i	0.469026	−	0.812377i
$426$		0			0
$427$	4.46891	+	7.74037i	0.216266	+	0.374583i
$428$		0			0
$429$	2.19582	−	7.81153i	0.106015	−	0.377144i
$430$		0			0
$431$	−24.3815			−1.17441			−0.587207	−	0.809437i	$-0.699773\pi$
$431$	−24.3815			−1.17441			−0.587207	+	0.809437i	$0.699773\pi$
$432$		0			0
$433$	29.2376			1.40507			0.702535	−	0.711649i	$-0.252051\pi$
$433$	29.2376			1.40507			0.702535	+	0.711649i	$0.252051\pi$
$434$		0			0
$435$	−1.63168	+	5.80463i	−0.0782332	+	0.278311i
$436$		0			0
$437$	−5.26184	−	9.11378i	−0.251708	−	0.435971i
$438$		0			0
$439$	5.86758	−	10.1629i	0.280044	−	0.485051i	−0.691351	−	0.722519i	$-0.742984\pi$
$439$	5.86758	−	10.1629i	0.280044	−	0.485051i	0.971395	+	0.237468i	$0.0763176\pi$
$440$		0			0
$441$	−0.0733690	+	2.99910i	−0.00349376	+	0.142814i
$442$		0			0
$443$	7.47083	−	12.9399i	0.354950	−	0.614791i	−0.632159	−	0.774838i	$-0.717831\pi$
$443$	7.47083	−	12.9399i	0.354950	−	0.614791i	0.987109	+	0.160047i	$0.0511646\pi$
$444$		0			0
$445$	−6.19013	−	10.7216i	−0.293440	−	0.508254i
$446$		0			0
$447$	16.1440	−	4.11485i	0.763585	−	0.194626i
$448$		0			0
$449$	16.1386			0.761626			0.380813	−	0.924652i	$-0.375644\pi$
$449$	16.1386			0.761626			0.380813	+	0.924652i	$0.375644\pi$
$450$		0			0
$451$	−2.97197			−0.139945
$452$		0			0
$453$	28.1022	+	28.7981i	1.32036	+	1.35305i
$454$		0			0
$455$	−2.98725	−	5.17406i	−0.140044	−	0.242564i
$456$		0			0
$457$	−4.17193	+	7.22600i	−0.195155	+	0.338018i	−0.946951	−	0.321377i	$-0.895854\pi$
$457$	−4.17193	+	7.22600i	−0.195155	+	0.338018i	0.751797	+	0.659395i	$0.229188\pi$
$458$		0			0
$459$	19.4941	−	18.1137i	0.909908	−	0.845477i
$460$		0			0
$461$	10.8653	−	18.8193i	0.506048	−	0.876501i	−0.493928	−	0.869503i	$-0.664439\pi$
$461$	10.8653	−	18.8193i	0.506048	−	0.876501i	0.999976	−	0.00699772i	$-0.00222746\pi$
$462$		0			0
$463$	−11.3577	−	19.6721i	−0.527835	−	0.914238i	−0.999474	−	0.0324455i	$-0.989670\pi$
$463$	−11.3577	−	19.6721i	−0.527835	−	0.914238i	0.471638	−	0.881792i	$-0.343663\pi$
$464$		0			0
$465$	8.10362	+	8.30429i	0.375796	+	0.385102i
$466$		0			0
$467$	−31.0988			−1.43908			−0.719541	−	0.694450i	$-0.755648\pi$
$467$	−31.0988			−1.43908			−0.719541	+	0.694450i	$0.755648\pi$
$468$		0			0
$469$	−6.35013			−0.293222
$470$		0			0
$471$	18.7575	−	4.78099i	0.864300	−	0.220296i
$472$		0			0
$473$	−2.96090	−	5.12844i	−0.136142	−	0.235806i
$474$		0			0
$475$	10.2729	−	17.7931i	0.471351	−	0.816404i
$476$		0			0
$477$	−0.573243	−	0.349928i	−0.0262470	−	0.0160221i
$478$		0			0
$479$	−2.11551	+	3.66417i	−0.0966600	+	0.167420i	−0.910300	−	0.413949i	$-0.864149\pi$
$479$	−2.11551	+	3.66417i	−0.0966600	+	0.167420i	0.813640	+	0.581369i	$0.197483\pi$
$480$		0			0
$481$	−14.8429	−	25.7087i	−0.676778	−	1.17221i
$482$		0			0
$483$	−0.906570	+	3.22508i	−0.0412504	+	0.146746i
$484$		0			0
$485$	−1.68441			−0.0764851
$486$		0			0
$487$	−35.2583			−1.59771			−0.798853	−	0.601527i	$-0.794559\pi$
$487$	−35.2583			−1.59771			−0.798853	+	0.601527i	$0.794559\pi$
$488$		0			0
$489$	6.64977	−	23.6562i	0.300713	−	1.06977i
$490$		0			0
$491$	−13.7323	−	23.7851i	−0.619730	−	1.07340i	−0.989535	−	0.144295i	$-0.953909\pi$
$491$	−13.7323	−	23.7851i	−0.619730	−	1.07340i	0.369804	−	0.929110i	$-0.379425\pi$
$492$		0			0
$493$	−8.05758	+	13.9561i	−0.362895	+	0.628553i
$494$		0			0
$495$	2.45736	+	1.50006i	0.110450	+	0.0674226i
$496$		0			0
$497$	1.66733	−	2.88790i	0.0747899	−	0.129540i
$498$		0			0
$499$	2.82650	+	4.89563i	0.126531	+	0.219159i	0.922330	−	0.386402i	$-0.126282\pi$
$499$	2.82650	+	4.89563i	0.126531	+	0.219159i	−0.795799	+	0.605561i	$0.792949\pi$
$500$		0			0
$501$	17.4287	−	4.44229i	0.778656	−	0.198467i
$502$		0			0
$503$	37.4049			1.66780			0.833900	−	0.551915i	$-0.186103\pi$
$503$	37.4049			1.66780			0.833900	+	0.551915i	$0.186103\pi$
$504$		0			0
$505$	−17.6750			−0.786527
$506$		0			0
$507$	−19.5548	−	20.0390i	−0.868459	−	0.889965i
$508$		0			0
$509$	8.13118	+	14.0836i	0.360408	+	0.624245i	0.988028	−	0.154275i	$-0.0493041\pi$
$509$	8.13118	+	14.0836i	0.360408	+	0.624245i	−0.627620	+	0.778520i	$0.715971\pi$
$510$		0			0
$511$	−8.12834	+	14.0787i	−0.359576	+	0.622805i
$512$		0			0
$513$	20.7111	−	19.2446i	0.914419	−	0.849669i
$514$		0			0
$515$	0.965923	−	1.67303i	0.0425637	−	0.0737224i
$516$		0			0
$517$	3.84624	+	6.66188i	0.169157	+	0.292989i
$518$		0			0
$519$	−13.4516	−	13.7847i	−0.590458	−	0.605079i
$520$		0			0
$521$	17.1455			0.751158			0.375579	−	0.926790i	$-0.377444\pi$
$521$	17.1455			0.751158			0.375579	+	0.926790i	$0.377444\pi$
$522$		0			0
$523$	19.9114			0.870667			0.435333	−	0.900269i	$-0.356631\pi$
$523$	19.9114			0.870667			0.435333	+	0.900269i	$0.356631\pi$
$524$		0			0
$525$	−6.33782	+	1.61541i	−0.276605	+	0.0705022i
$526$		0			0
$527$	15.5055	+	26.8564i	0.675432	+	1.16988i
$528$		0			0
$529$	9.62950	−	16.6788i	0.418674	−	0.725165i
$530$		0			0
$531$	−0.925778	+	37.8430i	−0.0401753	+	1.64224i
$532$		0			0
$533$	−9.25105	+	16.0233i	−0.400707	+	0.694046i
$534$		0			0
$535$	5.90707	+	10.2314i	0.255385	+	0.442340i
$536$		0			0
$537$	1.53410	−	5.45748i	0.0662013	−	0.235508i
$538$		0			0
$539$	−0.867474			−0.0373648
$540$		0			0
$541$	28.7165			1.23462			0.617310	−	0.786720i	$-0.288222\pi$
$541$	28.7165			1.23462			0.617310	+	0.786720i	$0.288222\pi$
$542$		0			0
$543$	−8.15620	+	29.0152i	−0.350016	+	1.24516i
$544$		0			0
$545$	1.70382	+	2.95110i	0.0729836	+	0.126411i
$546$		0			0
$547$	−7.75713	+	13.4357i	−0.331671	+	0.574471i	−0.982840	−	0.184462i	$-0.940946\pi$
$547$	−7.75713	+	13.4357i	−0.331671	+	0.574471i	0.651169	+	0.758933i	$0.274279\pi$
$548$		0			0
$549$	−23.5421	+	12.8348i	−1.00475	+	0.547776i
$550$		0			0
$551$	−8.56061	+	14.8274i	−0.364694	+	0.631669i
$552$		0			0
$553$	−2.44616	−	4.23688i	−0.104022	−	0.180171i
$554$		0			0
$555$	10.2065	−	2.60146i	0.433240	−	0.110426i
$556$		0			0
$557$	41.7115			1.76737			0.883687	−	0.468079i	$-0.155054\pi$
$557$	41.7115			1.76737			0.883687	+	0.468079i	$0.155054\pi$
$558$		0			0
$559$	−36.8664			−1.55928
$560$		0			0
$561$	5.37402	+	5.50710i	0.226892	+	0.232510i
$562$		0			0
$563$	−9.70563	−	16.8106i	−0.409044	−	0.708484i	0.585739	−	0.810500i	$-0.300804\pi$
$563$	−9.70563	−	16.8106i	−0.409044	−	0.708484i	−0.994783	+	0.102015i	$0.967471\pi$
$564$		0			0
$565$	4.01167	−	6.94841i	0.168772	−	0.292322i
$566$		0			0
$567$	−8.98923	−	0.440083i	−0.377512	−	0.0184817i
$568$		0			0
$569$	−3.09062	+	5.35312i	−0.129566	+	0.224414i	−0.923508	−	0.383578i	$-0.874692\pi$
$569$	−3.09062	+	5.35312i	−0.129566	+	0.224414i	0.793943	+	0.607993i	$0.208025\pi$
$570$		0			0
$571$	−6.35941	−	11.0148i	−0.266133	−	0.460956i	0.701727	−	0.712446i	$-0.252413\pi$
$571$	−6.35941	−	11.0148i	−0.266133	−	0.460956i	−0.967860	+	0.251490i	$0.919079\pi$
$572$		0			0
$573$	−1.84054	−	1.88612i	−0.0768898	−	0.0787938i
$574$		0			0
$575$	−7.30366			−0.304584
$576$		0			0
$577$	−31.4573			−1.30958			−0.654792	−	0.755809i	$-0.727244\pi$
$577$	−31.4573			−1.30958			−0.654792	+	0.755809i	$0.727244\pi$
$578$		0			0
$579$	36.6597	−	9.34396i	1.52352	−	0.388322i
$580$		0			0
$581$	6.33675	+	10.9756i	0.262892	+	0.455343i
$582$		0			0
$583$	0.0971003	−	0.168183i	0.00402149	−	0.00696542i
$584$		0			0
$585$	15.7367	−	8.57944i	0.650633	−	0.354716i
$586$		0			0
$587$	19.0035	−	32.9150i	0.784358	−	1.35855i	−0.145024	−	0.989428i	$-0.546326\pi$
$587$	19.0035	−	32.9150i	0.784358	−	1.35855i	0.929382	−	0.369119i	$-0.120341\pi$
$588$		0			0
$589$	16.4735	+	28.5330i	0.678780	+	1.17568i
$590$		0			0
$591$	9.46342	−	33.6656i	0.389273	−	1.38482i
$592$		0			0
$593$	−41.0351			−1.68511			−0.842554	−	0.538612i	$-0.818949\pi$
$593$	−41.0351			−1.68511			−0.842554	+	0.538612i	$0.818949\pi$
$594$		0			0
$595$	5.66555			0.232265
$596$		0			0
$597$	0.104931	−	0.373285i	0.00429452	−	0.0152775i
$598$		0			0
$599$	2.77130	+	4.80004i	0.113232	+	0.196124i	0.917072	−	0.398722i	$-0.130546\pi$
$599$	2.77130	+	4.80004i	0.113232	+	0.196124i	−0.803839	+	0.594846i	$0.797213\pi$
$600$		0			0
$601$	−13.9052	+	24.0845i	−0.567206	+	0.982429i	0.429635	+	0.903003i	$0.358642\pi$
$601$	−13.9052	+	24.0845i	−0.567206	+	0.982429i	−0.996841	+	0.0794266i	$0.974691\pi$
$602$		0			0
$603$	0.465903	−	19.0447i	0.0189730	−	0.775560i
$604$		0			0
$605$	5.66833	−	9.81783i	0.230450	−	0.399152i
$606$		0			0
$607$	−4.10139	−	7.10382i	−0.166470	−	0.288335i	0.770706	−	0.637191i	$-0.219904\pi$
$607$	−4.10139	−	7.10382i	−0.166470	−	0.288335i	−0.937176	+	0.348856i	$0.886570\pi$
$608$		0			0
$609$	5.28145	−	1.34616i	0.214015	−	0.0545491i
$610$		0			0
$611$	47.8898			1.93742
$612$		0			0
$613$	−18.3846			−0.742546			−0.371273	−	0.928524i	$-0.621079\pi$
$613$	−18.3846			−0.742546			−0.371273	+	0.928524i	$0.621079\pi$
$614$		0			0
$615$	−4.58484	−	4.69837i	−0.184879	−	0.189457i
$616$		0			0
$617$	19.2090	+	33.2710i	0.773326	+	1.33944i	0.935731	+	0.352715i	$0.114742\pi$
$617$	19.2090	+	33.2710i	0.773326	+	1.33944i	−0.162405	+	0.986724i	$0.551925\pi$
$618$		0			0
$619$	−14.0621	+	24.3564i	−0.565205	+	0.978964i	0.431825	+	0.901957i	$0.357870\pi$
$619$	−14.0621	+	24.3564i	−0.565205	+	0.978964i	−0.997031	+	0.0770071i	$0.975464\pi$
$620$		0			0
$621$	−9.60582	−	2.95552i	−0.385468	−	0.118601i
$622$		0			0
$623$	−5.59542	+	9.69155i	−0.224176	+	0.388284i
$624$		0			0
$625$	−4.06991	−	7.04929i	−0.162796	−	0.281972i
$626$		0			0
$627$	5.70952	+	5.85091i	0.228016	+	0.233663i
$628$		0			0
$629$	28.1507			1.12244
$630$		0			0
$631$	−18.9310			−0.753632			−0.376816	−	0.926288i	$-0.622981\pi$
$631$	−18.9310			−0.753632			−0.376816	+	0.926288i	$0.622981\pi$
$632$		0			0
$633$	−26.1167	+	6.65673i	−1.03805	+	0.264581i
$634$		0			0
$635$	3.97547	+	6.88572i	0.157762	+	0.273252i
$636$		0			0
$637$	−2.70025	+	4.67696i	−0.106988	+	0.185308i
$638$		0			0
$639$	8.53878	+	5.21237i	0.337789	+	0.206198i
$640$		0			0
$641$	0.484302	−	0.838835i	0.0191288	−	0.0331320i	−0.856303	−	0.516475i	$-0.827244\pi$
$641$	0.484302	−	0.838835i	0.0191288	−	0.0331320i	0.875431	+	0.483343i	$0.160577\pi$
$642$		0			0
$643$	20.4551	+	35.4293i	0.806672	+	1.39720i	0.915157	+	0.403098i	$0.132067\pi$
$643$	20.4551	+	35.4293i	0.806672	+	1.39720i	−0.108485	+	0.994098i	$0.534600\pi$
$644$		0			0
$645$	3.53975	−	12.5925i	0.139378	−	0.495829i
$646$		0			0
$647$	38.2345			1.50315			0.751576	−	0.659646i	$-0.229294\pi$
$647$	38.2345			1.50315			0.751576	+	0.659646i	$0.229294\pi$
$648$		0			0
$649$	−10.9459			−0.429663
$650$		0			0
$651$	2.83825	−	10.0969i	0.111240	−	0.395729i
$652$		0			0
$653$	−7.34784	−	12.7268i	−0.287543	−	0.498039i	0.685680	−	0.727903i	$-0.259505\pi$
$653$	−7.34784	−	12.7268i	−0.287543	−	0.498039i	−0.973223	+	0.229864i	$0.926172\pi$
$654$		0			0
$655$	−5.11317	+	8.85627i	−0.199788	+	0.346043i
$656$		0			0
$657$	−41.6271	−	25.4107i	−1.62403	−	0.991364i
$658$		0			0
$659$	−13.8081	+	23.9163i	−0.537887	+	0.931647i	0.461131	+	0.887332i	$0.347444\pi$
$659$	−13.8081	+	23.9163i	−0.537887	+	0.931647i	−0.999018	+	0.0443152i	$0.985889\pi$
$660$		0			0
$661$	1.28171	+	2.21998i	0.0498526	+	0.0863472i	0.889875	−	0.456205i	$-0.150792\pi$
$661$	1.28171	+	2.21998i	0.0498526	+	0.0863472i	−0.840022	+	0.542552i	$0.817458\pi$
$662$		0			0
$663$	46.4195	−	11.8316i	1.80278	−	0.459501i
$664$		0			0
$665$	6.01924			0.233416
$666$		0			0
$667$	6.08631			0.235663
$668$		0			0
$669$	24.7321	+	25.3446i	0.956199	+	0.979877i
$670$		0			0
$671$	−3.87666	−	6.71457i	−0.149657	−	0.259213i
$672$		0			0
$673$	6.72606	−	11.6499i	0.259270	−	0.449070i	−0.706776	−	0.707437i	$-0.749851\pi$
$673$	6.72606	−	11.6499i	0.259270	−	0.449070i	0.966047	+	0.258368i	$0.0831846\pi$
$674$		0			0
$675$	−4.37978	−	19.1263i	−0.168578	−	0.736171i
$676$		0			0
$677$	−14.0447	+	24.3262i	−0.539783	+	0.934931i	0.459133	+	0.888368i	$0.348160\pi$
$677$	−14.0447	+	24.3262i	−0.539783	+	0.934931i	−0.998915	+	0.0465633i	$0.985173\pi$
$678$		0			0
$679$	0.761290	+	1.31859i	0.0292156	+	0.0506029i
$680$		0			0
$681$	−28.4692	−	29.1742i	−1.09094	−	1.11796i
$682$		0			0
$683$	−13.6631			−0.522802			−0.261401	−	0.965230i	$-0.584185\pi$
$683$	−13.6631			−0.522802			−0.261401	+	0.965230i	$0.584185\pi$
$684$		0			0
$685$	9.67513			0.369668
$686$		0			0
$687$	15.1390	−	3.85870i	0.577590	−	0.147218i
$688$		0			0
$689$	−0.604502	−	1.04703i	−0.0230297	−	0.0398886i
$690$		0			0
$691$	−24.2466	+	41.9963i	−0.922384	+	1.59762i	−0.126669	+	0.991945i	$0.540429\pi$
$691$	−24.2466	+	41.9963i	−0.922384	+	1.59762i	−0.795715	+	0.605671i	$0.792905\pi$
$692$		0			0
$693$	0.0636457	−	2.60164i	0.00241770	−	0.0988283i
$694$		0			0
$695$	0.0740714	−	0.128295i	0.00280969	−	0.00486653i
$696$		0			0
$697$	−8.77267	−	15.1947i	−0.332289	−	0.575541i
$698$		0			0
$699$	13.8175	−	49.1549i	0.522624	−	1.85921i
$700$		0			0
$701$	40.3022			1.52219			0.761097	−	0.648638i	$-0.224661\pi$
$701$	40.3022			1.52219			0.761097	+	0.648638i	$0.224661\pi$
$702$		0			0
$703$	29.9082			1.12801
$704$		0			0
$705$	−4.59817	+	16.3578i	−0.173177	+	0.616069i
$706$		0			0
$707$	7.98844	+	13.8364i	0.300436	+	0.520371i
$708$		0			0
$709$	18.7515	−	32.4785i	0.704227	−	1.21976i	−0.262743	−	0.964866i	$-0.584627\pi$
$709$	18.7515	−	32.4785i	0.704227	−	1.21976i	0.966970	−	0.254890i	$-0.0820394\pi$
$710$		0			0
$711$	12.8863	−	7.02544i	0.483275	−	0.263475i
$712$		0			0
$713$	5.85607	−	10.1430i	0.219311	−	0.379859i
$714$		0			0
$715$	2.59136	+	4.48836i	0.0969113	+	0.167855i
$716$		0			0
$717$	−29.6181	+	7.54917i	−1.10611	+	0.281929i
$718$		0			0
$719$	−14.5191			−0.541470			−0.270735	−	0.962654i	$-0.587267\pi$
$719$	−14.5191			−0.541470			−0.270735	+	0.962654i	$0.587267\pi$
$720$		0			0
$721$	−1.74624			−0.0650336
$722$		0			0
$723$	−2.17587	−	2.22975i	−0.0809216	−	0.0829254i
$724$		0			0
$725$	5.94125	+	10.2905i	0.220652	+	0.382181i
$726$		0			0
$727$	−26.1258	+	45.2512i	−0.968953	+	1.67828i	−0.270354	+	0.962761i	$0.587141\pi$
$727$	−26.1258	+	45.2512i	−0.968953	+	1.67828i	−0.698598	+	0.715514i	$0.746193\pi$
$728$		0			0
$729$	1.97938	−	26.9273i	0.0733105	−	0.997309i
$730$		0			0
$731$	17.4800	−	30.2763i	0.646522	−	1.11981i
$732$		0			0
$733$	−4.81463	−	8.33919i	−0.177833	−	0.308015i	0.763305	−	0.646038i	$-0.223575\pi$
$733$	−4.81463	−	8.33919i	−0.177833	−	0.308015i	−0.941138	+	0.338023i	$0.890242\pi$
$734$		0			0
$735$	−1.33825	−	1.37139i	−0.0493620	−	0.0505844i
$736$		0			0
$737$	5.50857			0.202911
$738$		0			0
$739$	41.1005			1.51191			0.755953	−	0.654626i	$-0.227174\pi$
$739$	41.1005			1.51191			0.755953	+	0.654626i	$0.227174\pi$
$740$		0			0
$741$	49.3174	−	12.5702i	1.81172	−	0.461779i
$742$		0			0
$743$	4.43939	+	7.68924i	0.162865	+	0.282091i	0.935895	−	0.352279i	$-0.114593\pi$
$743$	4.43939	+	7.68924i	0.162865	+	0.282091i	−0.773030	+	0.634370i	$0.781260\pi$
$744$		0			0
$745$	−5.32054	+	9.21545i	−0.194930	+	0.337628i
$746$		0			0
$747$	−33.3818	+	18.1993i	−1.22138	+	0.665877i
$748$		0			0
$749$	5.33955	−	9.24838i	0.195103	−	0.337928i
$750$		0			0
$751$	−13.7339	−	23.7878i	−0.501157	−	0.868030i	−0.999999	−	0.00133671i	$-0.999575\pi$
$751$	−13.7339	−	23.7878i	−0.501157	−	0.868030i	0.498842	−	0.866693i	$-0.333759\pi$
$752$		0			0
$753$	−12.5232	+	44.5505i	−0.456369	+	1.62351i
$754$		0			0
$755$	−25.7003			−0.935330
$756$		0			0
$757$	−5.45818			−0.198381			−0.0991904	−	0.995068i	$-0.531625\pi$
$757$	−5.45818			−0.198381			−0.0991904	+	0.995068i	$0.531625\pi$
$758$		0			0
$759$	0.786426	−	2.79767i	0.0285455	−	0.101549i
$760$		0			0
$761$	6.18772	+	10.7174i	0.224305	+	0.388507i	0.956111	−	0.293006i	$-0.0946556\pi$
$761$	6.18772	+	10.7174i	0.224305	+	0.388507i	−0.731806	+	0.681513i	$0.761322\pi$
$762$		0			0
$763$	1.54013	−	2.66758i	0.0557563	−	0.0965727i
$764$		0			0
$765$	−0.415676	+	16.9916i	−0.0150288	+	0.614331i
$766$		0			0
$767$	−34.0720	+	59.0144i	−1.23027	+	2.13089i
$768$		0			0
$769$	−15.5308	−	26.9002i	−0.560055	−	0.970044i	−0.997491	−	0.0707947i	$-0.977446\pi$
$769$	−15.5308	−	26.9002i	−0.560055	−	0.970044i	0.437435	−	0.899250i	$-0.355887\pi$
$770$		0			0
$771$	9.13291	−	2.32783i	0.328914	−	0.0838348i
$772$		0			0
$773$	6.61465			0.237913			0.118956	−	0.992899i	$-0.462045\pi$
$773$	6.61465			0.237913			0.118956	+	0.992899i	$0.462045\pi$
$774$		0			0
$775$	22.8660			0.821370
$776$		0			0
$777$	−6.64943	−	6.81409i	−0.238547	−	0.244454i
$778$		0			0
$779$	−9.32034	−	16.1433i	−0.333936	−	0.578394i
$780$		0			0
$781$	−1.44637	+	2.50518i	−0.0517550	+	0.0896423i
$782$		0			0
$783$	3.64977	+	15.9384i	0.130432	+	0.569591i
$784$		0			0
$785$	−6.18187	+	10.7073i	−0.220640	+	0.382160i
$786$		0			0
$787$	17.9125	+	31.0254i	0.638512	+	1.10593i	0.985759	+	0.168161i	$0.0537830\pi$
$787$	17.9125	+	31.0254i	0.638512	+	1.10593i	−0.347248	+	0.937773i	$0.612884\pi$
$788$		0			0
$789$	−26.1221	−	26.7690i	−0.929972	−	0.953000i
$790$		0			0
$791$	−7.25250			−0.257869
$792$		0			0
$793$	−48.2686			−1.71407
$794$		0			0
$795$	0.415676	−	0.105949i	0.0147425	−	0.00375762i
$796$		0			0
$797$	−2.80335	−	4.85555i	−0.0992999	−	0.171992i	0.812095	−	0.583525i	$-0.198327\pi$
$797$	−2.80335	−	4.85555i	−0.0992999	−	0.171992i	−0.911395	+	0.411533i	$0.864994\pi$
$798$		0			0
$799$	−22.7067	+	39.3292i	−0.803306	+	1.39137i
$800$		0			0
$801$	−28.6554	−	17.4923i	−1.01249	−	0.618060i
$802$		0			0
$803$	7.05112	−	12.2129i	0.248829	−	0.430984i
$804$		0			0
$805$	−1.06987	−	1.85307i	−0.0377080	−	0.0653121i
$806$		0			0
$807$	−13.5351	+	48.1503i	−0.476456	+	1.69497i
$808$		0			0
$809$	−11.2504			−0.395542			−0.197771	−	0.980248i	$-0.563370\pi$
$809$	−11.2504			−0.395542			−0.197771	+	0.980248i	$0.563370\pi$
$810$		0			0
$811$	−21.5197			−0.755658			−0.377829	−	0.925875i	$-0.623329\pi$
$811$	−21.5197			−0.755658			−0.377829	+	0.925875i	$0.623329\pi$
$812$		0			0
$813$	2.74320	−	9.75879i	0.0962082	−	0.342256i
$814$		0			0
$815$	7.84759	+	13.5924i	0.274889	+	0.476122i
$816$		0			0
$817$	18.5713	−	32.1664i	0.649727	−	1.12536i
$818$		0			0
$819$	−13.8286	−	8.44146i	−0.483210	−	0.294969i
$820$		0			0
$821$	−24.5037	+	42.4416i	−0.855183	+	1.48122i	0.0212916	+	0.999773i	$0.493222\pi$
$821$	−24.5037	+	42.4416i	−0.855183	+	1.48122i	−0.876475	+	0.481448i	$0.840111\pi$
$822$		0			0
$823$	−17.5821	−	30.4532i	−0.612875	−	1.06153i	−0.990753	−	0.135676i	$-0.956680\pi$
$823$	−17.5821	−	30.4532i	−0.612875	−	1.06153i	0.377878	−	0.925855i	$-0.376654\pi$
$824$		0			0
$825$	5.49789	−	1.40132i	0.191412	−	0.0487879i
$826$		0			0
$827$	36.9397			1.28452			0.642260	−	0.766487i	$-0.277997\pi$
$827$	36.9397			1.28452			0.642260	+	0.766487i	$0.277997\pi$
$828$		0			0
$829$	−26.6141			−0.924348			−0.462174	−	0.886789i	$-0.652930\pi$
$829$	−26.6141			−0.924348			−0.462174	+	0.886789i	$0.652930\pi$
$830$		0			0
$831$	7.52025	+	7.70647i	0.260874	+	0.267334i
$832$		0			0
$833$	−2.56061	−	4.43511i	−0.0887200	−	0.153668i
$834$		0			0
$835$	−5.74393	+	9.94878i	−0.198777	+	0.344292i
$836$		0			0
$837$	30.0735	+	9.25300i	1.03949	+	0.319830i
$838$		0			0
$839$	−12.8605	+	22.2751i	−0.443995	+	0.769022i	−0.997982	−	0.0635034i	$-0.979773\pi$
$839$	−12.8605	+	22.2751i	−0.443995	+	0.769022i	0.553986	+	0.832526i	$0.313106\pi$
$840$		0			0
$841$	9.54902	+	16.5394i	0.329277	+	0.570324i
$842$		0			0
$843$	8.22778	+	8.43152i	0.283380	+	0.290397i
$844$		0			0
$845$	17.8835			0.615210
$846$		0			0
$847$	−10.2475			−0.352108
$848$		0			0
$849$	−17.4823	+	4.45595i	−0.599989	+	0.152928i
$850$		0			0
$851$	−5.31593	−	9.20745i	−0.182228	−	0.315627i
$852$		0			0
$853$	−6.45165	+	11.1746i	−0.220900	+	0.382610i	−0.955082	−	0.296343i	$-0.904233\pi$
$853$	−6.45165	+	11.1746i	−0.220900	+	0.382610i	0.734181	+	0.678953i	$0.237566\pi$
$854$		0			0
$855$	−0.441626	+	18.0523i	−0.0151033	+	0.617377i
$856$		0			0
$857$	23.5168	−	40.7323i	0.803319	−	1.39139i	−0.114101	−	0.993469i	$-0.536399\pi$
$857$	23.5168	−	40.7323i	0.803319	−	1.39139i	0.917420	−	0.397920i	$-0.130268\pi$
$858$		0			0
$859$	−8.23168	−	14.2577i	−0.280861	−	0.486466i	0.690736	−	0.723107i	$-0.257287\pi$
$859$	−8.23168	−	14.2577i	−0.280861	−	0.486466i	−0.971597	+	0.236641i	$0.923953\pi$
$860$		0			0
$861$	−1.60581	+	5.71260i	−0.0547260	+	0.194685i
$862$		0			0
$863$	−11.7061			−0.398481			−0.199241	−	0.979951i	$-0.563848\pi$
$863$	−11.7061			−0.398481			−0.199241	+	0.979951i	$0.563848\pi$
$864$		0			0
$865$	12.3019			0.418276
$866$		0			0
$867$	−4.32482	+	15.3853i	−0.146879	+	0.522513i
$868$		0			0
$869$	2.12198	+	3.67538i	0.0719834	+	0.124679i
$870$		0			0
$871$	17.1469	−	29.6993i	0.581001	−	1.00632i
$872$		0			0
$873$	−4.01045	+	2.18644i	−0.135733	+	0.0739999i
$874$		0			0
$875$	4.85446	−	8.40816i	0.164111	−	0.284248i
$876$		0			0
$877$	16.9109	+	29.2905i	0.571039	+	0.989069i	0.996460	+	0.0840734i	$0.0267930\pi$
$877$	16.9109	+	29.2905i	0.571039	+	0.989069i	−0.425420	+	0.904996i	$0.639874\pi$
$878$		0			0
$879$	13.8259	−	3.52399i	0.466335	−	0.118861i
$880$		0			0
$881$	−16.2682			−0.548090			−0.274045	−	0.961717i	$-0.588362\pi$
$881$	−16.2682			−0.548090			−0.274045	+	0.961717i	$0.588362\pi$
$882$		0			0
$883$	−38.9429			−1.31053			−0.655266	−	0.755398i	$-0.727443\pi$
$883$	−38.9429			−1.31053			−0.655266	+	0.755398i	$0.727443\pi$
$884$		0			0
$885$	−16.8861	−	17.3043i	−0.567621	−	0.581677i
$886$		0			0
$887$	−19.6112	−	33.9676i	−0.658479	−	1.14052i	−0.981009	−	0.193960i	$-0.937867\pi$
$887$	−19.6112	−	33.9676i	−0.658479	−	1.14052i	0.322530	−	0.946559i	$-0.395467\pi$
$888$		0			0
$889$	3.59353	−	6.22418i	0.120523	−	0.208752i
$890$		0			0
$891$	7.79793	+	0.381760i	0.261240	+	0.0127894i
$892$		0			0
$893$	−24.1243	+	41.7845i	−0.807288	+	1.39826i
$894$		0			0
$895$	1.81044	+	3.13577i	0.0605162	+	0.104817i
$896$		0			0
$897$	−12.6356	−	12.9485i	−0.421891	−	0.432338i
$898$		0			0
$899$	−19.0547			−0.635511
$900$		0			0
$901$	1.14649			0.0381950
$902$		0			0
$903$	−11.4575	+	2.92034i	−0.381282	+	0.0971827i
$904$		0			0
$905$	−9.62537	−	16.6716i	−0.319958	−	0.554184i
$906$		0			0
$907$	−14.7640	+	25.5719i	−0.490229	+	0.849102i	−0.999937	−	0.0112456i	$-0.996420\pi$
$907$	−14.7640	+	25.5719i	−0.490229	+	0.849102i	0.509707	+	0.860348i	$0.329754\pi$
$908$		0			0
$909$	−42.0828	+	22.9430i	−1.39580	+	0.760971i
$910$		0			0
$911$	5.61267	−	9.72142i	0.185956	−	0.322085i	−0.757942	−	0.652322i	$-0.773795\pi$
$911$	5.61267	−	9.72142i	0.185956	−	0.322085i	0.943898	+	0.330237i	$0.107129\pi$
$912$		0			0
$913$	−5.49696	−	9.52102i	−0.181923	−	0.315100i
$914$		0			0
$915$	4.63454	−	16.4871i	0.153213	−	0.545048i
$916$		0			0
$917$	9.24384			0.305259
$918$		0			0
$919$	56.5840			1.86653			0.933267	−	0.359183i	$-0.116945\pi$
$919$	56.5840			1.86653			0.933267	+	0.359183i	$0.116945\pi$
$920$		0			0
$921$	1.59411	−	5.67095i	0.0525276	−	0.186864i
$922$		0			0
$923$	9.00440	+	15.5961i	0.296383	+	0.513351i
$924$		0			0
$925$	10.3784	−	17.9760i	0.341241	−	0.591047i
$926$		0			0
$927$	0.128120	−	5.23717i	0.00420802	−	0.172011i
$928$		0			0
$929$	23.9739	−	41.5239i	0.786557	−	1.36236i	−0.141508	−	0.989937i	$-0.545195\pi$
$929$	23.9739	−	41.5239i	0.786557	−	1.36236i	0.928065	−	0.372419i	$-0.121472\pi$
$930$		0			0
$931$	−2.72047	−	4.71200i	−0.0891599	−	0.154429i
$932$		0			0
$933$	−7.50612	+	1.91319i	−0.245739	+	0.0626350i
$934$		0			0
$935$	−4.91471			−0.160728
$936$		0			0
$937$	1.33446			0.0435950			0.0217975	−	0.999762i	$-0.493061\pi$
$937$	1.33446			0.0435950			0.0217975	+	0.999762i	$0.493061\pi$
$938$		0			0
$939$	−16.7109	−	17.1247i	−0.545339	−	0.558843i
$940$		0			0
$941$	12.7341	+	22.0561i	0.415119	+	0.719007i	0.995441	−	0.0953803i	$-0.0304067\pi$
$941$	12.7341	+	22.0561i	0.415119	+	0.719007i	−0.580322	+	0.814387i	$0.697073\pi$
$942$		0			0
$943$	−3.31323	+	5.73868i	−0.107894	+	0.186877i
$944$		0			0
$945$	4.21111	−	3.91292i	0.136988	−	0.127287i
$946$		0			0
$947$	−8.39346	+	14.5379i	−0.272751	+	0.472418i	−0.969565	−	0.244833i	$-0.921267\pi$
$947$	−8.39346	+	14.5379i	−0.272751	+	0.472418i	0.696814	+	0.717251i	$0.254600\pi$
$948$		0			0
$949$	−43.8970	−	76.0319i	−1.42496	−	2.46810i
$950$		0			0
$951$	−40.1506	−	41.1449i	−1.30197	−	1.33421i
$952$		0			0
$953$	−4.19103			−0.135761			−0.0678804	−	0.997693i	$-0.521624\pi$
$953$	−4.19103			−0.135761			−0.0678804	+	0.997693i	$0.521624\pi$
$954$		0			0
$955$	1.68323			0.0544682
$956$		0			0
$957$	−4.58152	+	1.16776i	−0.148100	+	0.0377482i
$958$		0			0
$959$	−4.37280	−	7.57390i	−0.141205	−	0.244574i
$960$		0			0
$961$	−2.83390	+	4.90847i	−0.0914162	+	0.158338i
$962$		0			0
$963$	27.3451	+	16.6924i	0.881183	+	0.537905i
$964$		0			0
$965$	−12.0818	+	20.9264i	−0.388928	+	0.673644i
$966$		0			0
$967$	−3.68134	−	6.37627i	−0.118384	−	0.205047i	0.800743	−	0.599007i	$-0.204438\pi$
$967$	−3.68134	−	6.37627i	−0.118384	−	0.205047i	−0.919127	+	0.393960i	$0.871105\pi$
$968$		0			0
$969$	−13.0604	+	46.4617i	−0.419560	+	1.49256i
$970$		0			0
$971$	−20.7904			−0.667196			−0.333598	−	0.942715i	$-0.608263\pi$
$971$	−20.7904			−0.667196			−0.333598	+	0.942715i	$0.608263\pi$
$972$		0			0
$973$	−0.133910			−0.00429296
$974$		0			0
$975$	9.55847	−	34.0038i	0.306116	−	1.08899i
$976$		0			0
$977$	13.6324	+	23.6120i	0.436138	+	0.755414i	0.997388	−	0.0722330i	$-0.0230125\pi$
$977$	13.6324	+	23.6120i	0.436138	+	0.755414i	−0.561249	+	0.827647i	$0.689679\pi$
$978$		0			0
$979$	4.85388	−	8.40717i	0.155131	−	0.268694i
$980$		0			0
$981$	7.88733	+	4.81471i	0.251823	+	0.153722i
$982$		0			0
$983$	6.85073	−	11.8658i	0.218504	−	0.378461i	−0.735847	−	0.677148i	$-0.763216\pi$
$983$	6.85073	−	11.8658i	0.218504	−	0.378461i	0.954351	+	0.298688i	$0.0965488\pi$
$984$		0			0
$985$	11.1681	+	19.3436i	0.355844	+	0.616340i
$986$		0			0
$987$	14.8834	−	3.79354i	0.473744	−	0.120750i
$988$		0			0
$989$	−13.2036			−0.419849
$990$		0			0
$991$	−23.3651			−0.742218			−0.371109	−	0.928589i	$-0.621022\pi$
$991$	−23.3651			−0.742218			−0.371109	+	0.928589i	$0.621022\pi$
$992$		0			0
$993$	−3.64038	−	3.73053i	−0.115524	−	0.118385i
$994$		0			0
$995$	0.123832	+	0.214483i	0.00392573	+	0.00679956i
$996$		0			0
$997$	−13.2351	+	22.9238i	−0.419159	+	0.726006i	−0.995855	−	0.0909536i	$-0.971009\pi$
$997$	−13.2351	+	22.9238i	−0.419159	+	0.726006i	0.576696	+	0.816959i	$0.304342\pi$
$998$		0			0
$999$	20.9240	−	19.4424i	0.662006	−	0.615129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.n.673.3		10
3.2	odd	2		3024.2.r.n.2017.3		10
4.3	odd	2		504.2.r.f.169.3	✓	10
9.2	odd	6		9072.2.a.cm.1.3		5
9.4	even	3	inner	1008.2.r.n.337.3		10
9.5	odd	6		3024.2.r.n.1009.3		10
9.7	even	3		9072.2.a.cn.1.3		5
12.11	even	2		1512.2.r.f.505.3		10
36.7	odd	6		4536.2.a.bd.1.3		5
36.11	even	6		4536.2.a.bc.1.3		5
36.23	even	6		1512.2.r.f.1009.3		10
36.31	odd	6		504.2.r.f.337.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.f.169.3	✓	10	4.3	odd	2
504.2.r.f.337.3	yes	10	36.31	odd	6
1008.2.r.n.337.3		10	9.4	even	3	inner
1008.2.r.n.673.3		10	1.1	even	1	trivial
1512.2.r.f.505.3		10	12.11	even	2
1512.2.r.f.1009.3		10	36.23	even	6
3024.2.r.n.1009.3		10	9.5	odd	6
3024.2.r.n.2017.3		10	3.2	odd	2
4536.2.a.bc.1.3		5	36.11	even	6
4536.2.a.bd.1.3		5	36.7	odd	6
9072.2.a.cm.1.3		5	9.2	odd	6
9072.2.a.cn.1.3		5	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.468714 + 1.66743i) q^{3} +(-0.553143 - 0.958072i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.56061 - 1.56309i) q^{9} +O(q^{10})\)	\(q+(-0.468714 + 1.66743i) q^{3} +(-0.553143 - 0.958072i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.56061 - 1.56309i) q^{9} +(0.433737 - 0.751255i) q^{11} +(-2.70025 - 4.67696i) q^{13} +(1.85678 - 0.473263i) q^{15} +5.12123 q^{17} +5.44095 q^{19} +(-1.20968 - 1.23963i) q^{21} +(-0.967083 - 1.67504i) q^{23} +(1.88807 - 3.27023i) q^{25} +(3.80653 - 3.53699i) q^{27} +(-1.57337 + 2.72516i) q^{29} +(3.02770 + 5.24413i) q^{31} +(1.04936 + 1.07535i) q^{33} +1.10629 q^{35} +5.49687 q^{37} +(9.06413 - 2.31030i) q^{39} +(-1.71300 - 2.96700i) q^{41} +(3.41325 - 5.91192i) q^{43} +(-0.0811672 + 3.31787i) q^{45} +(-4.43384 + 7.67963i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.40039 + 8.53927i) q^{51} +0.223869 q^{53} -0.959675 q^{55} +(-2.55025 + 9.07237i) q^{57} +(-6.30905 - 10.9276i) q^{59} +(4.46891 - 7.74037i) q^{61} +(2.63398 - 1.43601i) q^{63} +(-2.98725 + 5.17406i) q^{65} +(3.17506 + 5.49937i) q^{67} +(3.24628 - 0.827426i) q^{69} -3.33466 q^{71} +16.2567 q^{73} +(4.56789 + 4.68101i) q^{75} +(0.433737 + 0.751255i) q^{77} +(-2.44616 + 4.23688i) q^{79} +(4.11349 + 8.00495i) q^{81} +(6.33675 - 10.9756i) q^{83} +(-2.83277 - 4.90651i) q^{85} +(-3.80653 - 3.90079i) q^{87} +11.1908 q^{89} +5.40049 q^{91} +(-10.1633 + 2.59046i) q^{93} +(-3.00962 - 5.21282i) q^{95} +(0.761290 - 1.31859i) q^{97} +(-2.28491 + 1.24570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 3 * q^5 - 5 * q^7	\( 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) \) 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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