LMFDB - Embedded newform 1638.2.y.d.827.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(827,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("1638.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.y (of order $4$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} + \cdots + 16 $ x^16 - 8x^15 + 20x^14 - 12x^13 + 40x^12 + 40x^11 + 82x^10 + 104x^9 + 537x^8 - 2528x^7 + 5494x^6 - 7284x^5 + 6002x^4 - 2984x^3 + 1000x^2 - 192*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			827.3
Root			$4.26883 - 1.76821i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.d.1331.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.40096 - 1.40096i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.40096 - 1.40096i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.98125i q^{10} +(0.369713 + 0.369713i) q^{11} +(3.37077 + 1.27981i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +0.875449 q^{17} +(-2.06942 - 2.06942i) q^{19} +(-1.40096 - 1.40096i) q^{20} -0.522853 q^{22} +5.51713 q^{23} +1.07464i q^{25} +(-3.28846 + 1.47853i) q^{26} +(0.707107 + 0.707107i) q^{28} -4.89347i q^{29} +(3.42374 + 3.42374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.619036 + 0.619036i) q^{34} +1.98125i q^{35} +(-7.52440 + 7.52440i) q^{37} +2.92660 q^{38} +1.98125 q^{40} +(3.86609 - 3.86609i) q^{41} +1.96534i q^{43} +(0.369713 - 0.369713i) q^{44} +(-3.90120 + 3.90120i) q^{46} +(2.05222 + 2.05222i) q^{47} -1.00000i q^{49} +(-0.759888 - 0.759888i) q^{50} +(1.27981 - 3.37077i) q^{52} -11.4563i q^{53} +1.03590 q^{55} -1.00000 q^{56} +(3.46021 + 3.46021i) q^{58} +(1.44249 + 1.44249i) q^{59} -2.82066 q^{61} -4.84190 q^{62} +1.00000i q^{64} +(6.51526 - 2.92934i) q^{65} +(8.98311 + 8.98311i) q^{67} -0.875449i q^{68} +(-1.40096 - 1.40096i) q^{70} +(8.80440 - 8.80440i) q^{71} +(8.70125 - 8.70125i) q^{73} -10.6411i q^{74} +(-2.06942 + 2.06942i) q^{76} -0.522853 q^{77} +8.87993 q^{79} +(-1.40096 + 1.40096i) q^{80} +5.46747i q^{82} +(2.45927 - 2.45927i) q^{83} +(1.22647 - 1.22647i) q^{85} +(-1.38970 - 1.38970i) q^{86} +0.522853i q^{88} +(-5.38066 - 5.38066i) q^{89} +(-3.28846 + 1.47853i) q^{91} -5.51713i q^{92} -2.90227 q^{94} -5.79833 q^{95} +(2.17257 + 2.17257i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^5	$ 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50} - 16 q^{55} - 16 q^{56} + 4 q^{58} - 8 q^{59} - 40 q^{61} + 24 q^{62} + 56 q^{65} - 4 q^{67} - 4 q^{70} - 24 q^{71} - 12 q^{73} + 16 q^{76} - 8 q^{77} + 16 q^{79} - 4 q^{80} + 8 q^{85} + 24 q^{86} + 16 q^{89} + 8 q^{91} - 8 q^{94} - 40 q^{95} - 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.40096	−	1.40096i	0.626527	−	0.626527i	−0.320666	−	0.947192i	$-0.603907\pi$
$5$	1.40096	−	1.40096i	0.626527	−	0.626527i	0.947192	+	0.320666i	$0.103907\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$			1.98125i			0.626527i
$11$	0.369713	+	0.369713i	0.111473	+	0.111473i	0.760643	−	0.649170i	$-0.224884\pi$
$11$	0.369713	+	0.369713i	0.111473	+	0.111473i	−0.649170	+	0.760643i	$0.724884\pi$
$12$		0			0
$13$	3.37077	+	1.27981i	0.934883	+	0.354956i
$13$	3.37077	+	1.27981i	0.934883	+	0.354956i
$14$		−	1.00000i		−	0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.875449			0.212328			0.106164	−	0.994349i	$-0.466143\pi$
$17$	0.875449			0.212328			0.106164	+	0.994349i	$0.466143\pi$
$18$		0			0
$19$	−2.06942	−	2.06942i	−0.474757	−	0.474757i	0.428693	−	0.903450i	$-0.358974\pi$
$19$	−2.06942	−	2.06942i	−0.474757	−	0.474757i	−0.903450	+	0.428693i	$0.858974\pi$
$20$	−1.40096	−	1.40096i	−0.313263	−	0.313263i
$21$		0			0
$22$	−0.522853			−0.111473
$23$	5.51713			1.15040			0.575201	−	0.818012i	$-0.304924\pi$
$23$	5.51713			1.15040			0.575201	+	0.818012i	$0.304924\pi$
$24$		0			0
$25$			1.07464i			0.214929i
$26$	−3.28846	+	1.47853i	−0.644920	+	0.289963i
$27$		0			0
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$		−	4.89347i		−	0.908695i	−0.890825	−	0.454347i	$-0.849872\pi$
$29$		−	4.89347i		−	0.908695i	0.890825	−	0.454347i	$-0.150128\pi$
$30$		0			0
$31$	3.42374	+	3.42374i	0.614921	+	0.614921i	0.944224	−	0.329303i	$-0.106814\pi$
$31$	3.42374	+	3.42374i	0.614921	+	0.614921i	−0.329303	+	0.944224i	$0.606814\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.619036	+	0.619036i	−0.106164	+	0.106164i
$35$			1.98125i			0.334893i
$36$		0			0
$37$	−7.52440	+	7.52440i	−1.23700	+	1.23700i	−0.275784	+	0.961220i	$0.588937\pi$
$37$	−7.52440	+	7.52440i	−1.23700	+	1.23700i	−0.961220	+	0.275784i	$0.911063\pi$
$38$	2.92660			0.474757
$39$		0			0
$40$	1.98125			0.313263
$41$	3.86609	−	3.86609i	0.603782	−	0.603782i	−0.337532	−	0.941314i	$-0.609592\pi$
$41$	3.86609	−	3.86609i	0.603782	−	0.603782i	0.941314	+	0.337532i	$0.109592\pi$
$42$		0			0
$43$			1.96534i			0.299711i	0.988708	+	0.149856i	$0.0478809\pi$
$43$			1.96534i			0.299711i	−0.988708	+	0.149856i	$0.952119\pi$
$44$	0.369713	−	0.369713i	0.0557363	−	0.0557363i
$45$		0			0
$46$	−3.90120	+	3.90120i	−0.575201	+	0.575201i
$47$	2.05222	+	2.05222i	0.299346	+	0.299346i	0.840758	−	0.541411i	$-0.182110\pi$
$47$	2.05222	+	2.05222i	0.299346	+	0.299346i	−0.541411	+	0.840758i	$0.682110\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−0.759888	−	0.759888i	−0.107464	−	0.107464i
$51$		0			0
$52$	1.27981	−	3.37077i	0.177478	−	0.467441i
$53$		−	11.4563i		−	1.57364i	−0.617179	−	0.786822i	$-0.711725\pi$
$53$		−	11.4563i		−	1.57364i	0.617179	−	0.786822i	$-0.288275\pi$
$54$		0			0
$55$	1.03590			0.139681
$56$	−1.00000			−0.133631
$57$		0			0
$58$	3.46021	+	3.46021i	0.454347	+	0.454347i
$59$	1.44249	+	1.44249i	0.187796	+	0.187796i	0.794742	−	0.606947i	$-0.207606\pi$
$59$	1.44249	+	1.44249i	0.187796	+	0.187796i	−0.606947	+	0.794742i	$0.707606\pi$
$60$		0			0
$61$	−2.82066			−0.361149			−0.180574	−	0.983561i	$-0.557796\pi$
$61$	−2.82066			−0.361149			−0.180574	+	0.983561i	$0.557796\pi$
$62$	−4.84190			−0.614921
$63$		0			0
$64$			1.00000i			0.125000i
$65$	6.51526	−	2.92934i	0.808118	−	0.363340i
$66$		0			0
$67$	8.98311	+	8.98311i	1.09746	+	1.09746i	0.994707	+	0.102755i	$0.0327658\pi$
$67$	8.98311	+	8.98311i	1.09746	+	1.09746i	0.102755	+	0.994707i	$0.467234\pi$
$68$		−	0.875449i		−	0.106164i
$69$		0			0
$70$	−1.40096	−	1.40096i	−0.167446	−	0.167446i
$71$	8.80440	−	8.80440i	1.04489	−	1.04489i	0.0459459	−	0.998944i	$-0.485370\pi$
$71$	8.80440	−	8.80440i	1.04489	−	1.04489i	0.998944	−	0.0459459i	$-0.0146302\pi$
$72$		0			0
$73$	8.70125	−	8.70125i	1.01840	−	1.01840i	0.0185768	−	0.999827i	$-0.494086\pi$
$73$	8.70125	−	8.70125i	1.01840	−	1.01840i	0.999827	−	0.0185768i	$-0.00591352\pi$
$74$		−	10.6411i		−	1.23700i
$75$		0			0
$76$	−2.06942	+	2.06942i	−0.237379	+	0.237379i
$77$	−0.522853			−0.0595847
$78$		0			0
$79$	8.87993			0.999070			0.499535	−	0.866294i	$-0.333504\pi$
$79$	8.87993			0.999070			0.499535	+	0.866294i	$0.333504\pi$
$80$	−1.40096	+	1.40096i	−0.156632	+	0.156632i
$81$		0			0
$82$			5.46747i			0.603782i
$83$	2.45927	−	2.45927i	0.269940	−	0.269940i	−0.559136	−	0.829076i	$-0.688867\pi$
$83$	2.45927	−	2.45927i	0.269940	−	0.269940i	0.829076	+	0.559136i	$0.188867\pi$
$84$		0			0
$85$	1.22647	−	1.22647i	0.133029	−	0.133029i
$86$	−1.38970	−	1.38970i	−0.149856	−	0.149856i
$87$		0			0
$88$			0.522853i			0.0557363i
$89$	−5.38066	−	5.38066i	−0.570349	−	0.570349i	0.361877	−	0.932226i	$-0.382136\pi$
$89$	−5.38066	−	5.38066i	−0.570349	−	0.570349i	−0.932226	+	0.361877i	$0.882136\pi$
$90$		0			0
$91$	−3.28846	+	1.47853i	−0.344724	+	0.154992i
$92$		−	5.51713i		−	0.575201i
$93$		0			0
$94$	−2.90227			−0.299346
$95$	−5.79833			−0.594896
$96$		0			0
$97$	2.17257	+	2.17257i	0.220591	+	0.220591i	0.808747	−	0.588156i	$-0.200146\pi$
$97$	2.17257	+	2.17257i	0.220591	+	0.220591i	−0.588156	+	0.808747i	$0.700146\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	1.07464			0.107464
$101$	16.7323			1.66493			0.832464	−	0.554080i	$-0.186930\pi$
$101$	16.7323			1.66493			0.832464	+	0.554080i	$0.186930\pi$
$102$		0			0
$103$			1.86637i			0.183899i	0.995764	+	0.0919493i	$0.0293098\pi$
$103$			1.86637i			0.183899i	−0.995764	+	0.0919493i	$0.970690\pi$
$104$	1.47853	+	3.28846i	0.144982	+	0.322460i
$105$		0			0
$106$	8.10083	+	8.10083i	0.786822	+	0.786822i
$107$			13.7497i			1.32924i	0.747182	+	0.664619i	$0.231406\pi$
$107$			13.7497i			1.32924i	−0.747182	+	0.664619i	$0.768594\pi$
$108$		0			0
$109$	−6.08191	−	6.08191i	−0.582542	−	0.582542i	0.353059	−	0.935601i	$-0.385141\pi$
$109$	−6.08191	−	6.08191i	−0.582542	−	0.582542i	−0.935601	+	0.353059i	$0.885141\pi$
$110$	−0.732494	+	0.732494i	−0.0698406	+	0.0698406i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$		−	0.0237301i		−	0.00223234i	−0.999999	−	0.00111617i	$-0.999645\pi$
$113$		−	0.0237301i		−	0.00223234i	0.999999	−	0.00111617i	$-0.000355288\pi$
$114$		0			0
$115$	7.72926	−	7.72926i	0.720757	−	0.720757i
$116$	−4.89347			−0.454347
$117$		0			0
$118$	−2.03998			−0.187796
$119$	−0.619036	+	0.619036i	−0.0567469	+	0.0567469i
$120$		0			0
$121$		−	10.7266i		−	0.975148i
$122$	1.99451	−	1.99451i	0.180574	−	0.180574i
$123$		0			0
$124$	3.42374	−	3.42374i	0.307461	−	0.307461i
$125$	8.51031	+	8.51031i	0.761185	+	0.761185i
$126$		0			0
$127$		−	6.04749i		−	0.536628i	−0.963332	−	0.268314i	$-0.913534\pi$
$127$		−	6.04749i		−	0.536628i	0.963332	−	0.268314i	$-0.0864665\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−2.53563	+	6.67834i	−0.222389	+	0.585729i
$131$			12.3826i			1.08188i	0.841063	+	0.540938i	$0.181930\pi$
$131$			12.3826i			1.08188i	−0.841063	+	0.540938i	$0.818070\pi$
$132$		0			0
$133$	2.92660			0.253768
$134$	−12.7040			−1.09746
$135$		0			0
$136$	0.619036	+	0.619036i	0.0530819	+	0.0530819i
$137$	−7.15255	−	7.15255i	−0.611084	−	0.611084i	0.332145	−	0.943228i	$-0.392228\pi$
$137$	−7.15255	−	7.15255i	−0.611084	−	0.611084i	−0.943228	+	0.332145i	$0.892228\pi$
$138$		0			0
$139$	−6.65697			−0.564637			−0.282318	−	0.959321i	$-0.591103\pi$
$139$	−6.65697			−0.564637			−0.282318	+	0.959321i	$0.591103\pi$
$140$	1.98125			0.167446
$141$		0			0
$142$			12.4513i			1.04489i
$143$	0.773054	+	1.71938i	0.0646460	+	0.143782i
$144$		0			0
$145$	−6.85554	−	6.85554i	−0.569321	−	0.569321i
$146$			12.3054i			1.01840i
$147$		0			0
$148$	7.52440	+	7.52440i	0.618502	+	0.618502i
$149$	0.562645	−	0.562645i	0.0460937	−	0.0460937i	−0.683684	−	0.729778i	$-0.739623\pi$
$149$	0.562645	−	0.562645i	0.0460937	−	0.0460937i	0.729778	+	0.683684i	$0.239623\pi$
$150$		0			0
$151$	−6.90603	+	6.90603i	−0.562005	+	0.562005i	−0.929877	−	0.367871i	$-0.880087\pi$
$151$	−6.90603	+	6.90603i	−0.562005	+	0.562005i	0.367871	+	0.929877i	$0.380087\pi$
$152$		−	2.92660i		−	0.237379i
$153$		0			0
$154$	0.369713	−	0.369713i	0.0297923	−	0.0297923i
$155$	9.59301			0.770529
$156$		0			0
$157$	24.7167			1.97261			0.986303	−	0.164944i	$-0.0527444\pi$
$157$	24.7167			1.97261			0.986303	+	0.164944i	$0.0527444\pi$
$158$	−6.27906	+	6.27906i	−0.499535	+	0.499535i
$159$		0			0
$160$		−	1.98125i		−	0.156632i
$161$	−3.90120	+	3.90120i	−0.307458	+	0.307458i
$162$		0			0
$163$	−11.3527	+	11.3527i	−0.889212	+	0.889212i	−0.994447	−	0.105235i	$-0.966440\pi$
$163$	−11.3527	+	11.3527i	−0.889212	+	0.889212i	0.105235	+	0.994447i	$0.466440\pi$
$164$	−3.86609	−	3.86609i	−0.301891	−	0.301891i
$165$		0			0
$166$			3.47793i			0.269940i
$167$	11.3148	+	11.3148i	0.875563	+	0.875563i	0.993072	−	0.117508i	$-0.0374907\pi$
$167$	11.3148	+	11.3148i	0.875563	+	0.875563i	−0.117508	+	0.993072i	$0.537491\pi$
$168$		0			0
$169$	9.72416	+	8.62790i	0.748012	+	0.663685i
$170$			1.73448i			0.133029i
$171$		0			0
$172$	1.96534			0.149856
$173$	−7.53167			−0.572622			−0.286311	−	0.958137i	$-0.592429\pi$
$173$	−7.53167			−0.572622			−0.286311	+	0.958137i	$0.592429\pi$
$174$		0			0
$175$	−0.759888	−	0.759888i	−0.0574421	−	0.0574421i
$176$	−0.369713	−	0.369713i	−0.0278682	−	0.0278682i
$177$		0			0
$178$	7.60940			0.570349
$179$	0.794222			0.0593630			0.0296815	−	0.999559i	$-0.490551\pi$
$179$	0.794222			0.0593630			0.0296815	+	0.999559i	$0.490551\pi$
$180$		0			0
$181$		−	1.75554i		−	0.130489i	−0.997869	−	0.0652443i	$-0.979217\pi$
$181$		−	1.75554i		−	0.130489i	0.997869	−	0.0652443i	$-0.0207827\pi$
$182$	1.27981	−	3.37077i	0.0948660	−	0.249858i
$183$		0			0
$184$	3.90120	+	3.90120i	0.287600	+	0.287600i
$185$			21.0827i			1.55003i
$186$		0			0
$187$	0.323665	+	0.323665i	0.0236687	+	0.0236687i
$188$	2.05222	−	2.05222i	0.149673	−	0.149673i
$189$		0			0
$190$	4.10004	−	4.10004i	0.297448	−	0.297448i
$191$		−	2.86032i		−	0.206966i	−0.994631	−	0.103483i	$-0.967001\pi$
$191$		−	2.86032i		−	0.206966i	0.994631	−	0.103483i	$-0.0329987\pi$
$192$		0			0
$193$	1.49865	−	1.49865i	0.107875	−	0.107875i	−0.651109	−	0.758984i	$-0.725696\pi$
$193$	1.49865	−	1.49865i	0.107875	−	0.107875i	0.758984	+	0.651109i	$0.225696\pi$
$194$	−3.07247			−0.220591
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	3.73628	−	3.73628i	0.266199	−	0.266199i	−0.561368	−	0.827566i	$-0.689725\pi$
$197$	3.73628	−	3.73628i	0.266199	−	0.266199i	0.827566	+	0.561368i	$0.189725\pi$
$198$		0			0
$199$		−	3.12917i		−	0.221821i	−0.993830	−	0.110911i	$-0.964623\pi$
$199$		−	3.12917i		−	0.221821i	0.993830	−	0.110911i	$-0.0353767\pi$
$200$	−0.759888	+	0.759888i	−0.0537322	+	0.0537322i
$201$		0			0
$202$	−11.8315	+	11.8315i	−0.832464	+	0.832464i
$203$	3.46021	+	3.46021i	0.242859	+	0.242859i
$204$		0			0
$205$		−	10.8324i		−	0.756570i
$206$	−1.31972	−	1.31972i	−0.0919493	−	0.0919493i
$207$		0			0
$208$	−3.37077	−	1.27981i	−0.233721	−	0.0887390i
$209$		−	1.53018i		−	0.105845i
$210$		0			0
$211$	23.1615			1.59451			0.797253	−	0.603645i	$-0.206286\pi$
$211$	23.1615			1.59451			0.797253	+	0.603645i	$0.206286\pi$
$212$	−11.4563			−0.786822
$213$		0			0
$214$	−9.72254	−	9.72254i	−0.664619	−	0.664619i
$215$	2.75335	+	2.75335i	0.187777	+	0.187777i
$216$		0			0
$217$	−4.84190			−0.328689
$218$	8.60112			0.582542
$219$		0			0
$220$		−	1.03590i		−	0.0698406i
$221$	2.95094	+	1.12041i	0.198501	+	0.0753669i
$222$		0			0
$223$	−4.16221	−	4.16221i	−0.278722	−	0.278722i	0.553876	−	0.832599i	$-0.313148\pi$
$223$	−4.16221	−	4.16221i	−0.278722	−	0.278722i	−0.832599	+	0.553876i	$0.813148\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	0.0167797	+	0.0167797i	0.00111617	+	0.00111617i
$227$	−7.85281	+	7.85281i	−0.521209	+	0.521209i	−0.917937	−	0.396727i	$-0.870146\pi$
$227$	−7.85281	+	7.85281i	−0.521209	+	0.521209i	0.396727	+	0.917937i	$0.370146\pi$
$228$		0			0
$229$	−0.120762	+	0.120762i	−0.00798018	+	0.00798018i	−0.711086	−	0.703105i	$-0.751796\pi$
$229$	−0.120762	+	0.120762i	−0.00798018	+	0.00798018i	0.703105	+	0.711086i	$0.251796\pi$
$230$			10.9308i			0.720757i
$231$		0			0
$232$	3.46021	−	3.46021i	0.227174	−	0.227174i
$233$	7.61641			0.498968			0.249484	−	0.968379i	$-0.419739\pi$
$233$	7.61641			0.498968			0.249484	+	0.968379i	$0.419739\pi$
$234$		0			0
$235$	5.75013			0.375097
$236$	1.44249	−	1.44249i	0.0938979	−	0.0938979i
$237$		0			0
$238$		−	0.875449i		−	0.0567469i
$239$	−8.09946	+	8.09946i	−0.523910	+	0.523910i	−0.918750	−	0.394840i	$-0.870800\pi$
$239$	−8.09946	+	8.09946i	−0.523910	+	0.523910i	0.394840	+	0.918750i	$0.370800\pi$
$240$		0			0
$241$	−18.2938	+	18.2938i	−1.17841	+	1.17841i	−0.198254	+	0.980151i	$0.563527\pi$
$241$	−18.2938	+	18.2938i	−1.17841	+	1.17841i	−0.980151	+	0.198254i	$0.936473\pi$
$242$	7.58487	+	7.58487i	0.487574	+	0.487574i
$243$		0			0
$244$			2.82066i			0.180574i
$245$	−1.40096	−	1.40096i	−0.0895038	−	0.0895038i
$246$		0			0
$247$	−4.32706	−	9.62399i	−0.275324	−	0.612360i
$248$			4.84190i			0.307461i
$249$		0			0
$250$	−12.0354			−0.761185
$251$	−24.8882			−1.57093			−0.785464	−	0.618908i	$-0.787575\pi$
$251$	−24.8882			−1.57093			−0.785464	+	0.618908i	$0.787575\pi$
$252$		0			0
$253$	2.03976	+	2.03976i	0.128238	+	0.128238i
$254$	4.27622	+	4.27622i	0.268314	+	0.268314i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.80357			−0.362017			−0.181008	−	0.983482i	$-0.557936\pi$
$257$	−5.80357			−0.362017			−0.181008	+	0.983482i	$0.557936\pi$
$258$		0			0
$259$		−	10.6411i		−	0.661206i
$260$	−2.92934	−	6.51526i	−0.181670	−	0.404059i
$261$		0			0
$262$	−8.75584	−	8.75584i	−0.540938	−	0.540938i
$263$		−	14.7795i		−	0.911341i	−0.890148	−	0.455671i	$-0.849399\pi$
$263$		−	14.7795i		−	0.911341i	0.890148	−	0.455671i	$-0.150601\pi$
$264$		0			0
$265$	−16.0498	−	16.0498i	−0.985930	−	0.985930i
$266$	−2.06942	+	2.06942i	−0.126884	+	0.126884i
$267$		0			0
$268$	8.98311	−	8.98311i	0.548731	−	0.548731i
$269$		−	15.4702i		−	0.943233i	−0.881804	−	0.471617i	$-0.843671\pi$
$269$		−	15.4702i		−	0.943233i	0.881804	−	0.471617i	$-0.156329\pi$
$270$		0			0
$271$	−12.6923	+	12.6923i	−0.771001	+	0.771001i	−0.978282	−	0.207281i	$-0.933539\pi$
$271$	−12.6923	+	12.6923i	−0.771001	+	0.771001i	0.207281	+	0.978282i	$0.433539\pi$
$272$	−0.875449			−0.0530819
$273$		0			0
$274$	10.1152			0.611084
$275$	−0.397310	+	0.397310i	−0.0239587	+	0.0239587i
$276$		0			0
$277$		−	2.67811i		−	0.160912i	−0.996758	−	0.0804560i	$-0.974362\pi$
$277$		−	2.67811i		−	0.160912i	0.996758	−	0.0804560i	$-0.0256376\pi$
$278$	4.70719	−	4.70719i	0.282318	−	0.282318i
$279$		0			0
$280$	−1.40096	+	1.40096i	−0.0837231	+	0.0837231i
$281$	2.06615	+	2.06615i	0.123256	+	0.123256i	0.766044	−	0.642788i	$-0.222222\pi$
$281$	2.06615	+	2.06615i	0.123256	+	0.123256i	−0.642788	+	0.766044i	$0.722222\pi$
$282$		0			0
$283$		−	13.8604i		−	0.823918i	−0.911202	−	0.411959i	$-0.864845\pi$
$283$		−	13.8604i		−	0.823918i	0.911202	−	0.411959i	$-0.135155\pi$
$284$	−8.80440	−	8.80440i	−0.522445	−	0.522445i
$285$		0			0
$286$	−1.76242	−	0.669154i	−0.104214	−	0.0395679i
$287$			5.46747i			0.322735i
$288$		0			0
$289$	−16.2336			−0.954917
$290$	9.69520			0.569321
$291$		0			0
$292$	−8.70125	−	8.70125i	−0.509202	−	0.509202i
$293$	4.90678	+	4.90678i	0.286657	+	0.286657i	0.835757	−	0.549100i	$-0.185029\pi$
$293$	4.90678	+	4.90678i	0.286657	+	0.286657i	−0.549100	+	0.835757i	$0.685029\pi$
$294$		0			0
$295$	4.04172			0.235318
$296$	−10.6411			−0.618502
$297$		0			0
$298$			0.795701i			0.0460937i
$299$	18.5970	+	7.06089i	1.07549	+	0.408342i
$300$		0			0
$301$	−1.38970	−	1.38970i	−0.0801013	−	0.0801013i
$302$		−	9.76661i		−	0.562005i
$303$		0			0
$304$	2.06942	+	2.06942i	0.118689	+	0.118689i
$305$	−3.95162	+	3.95162i	−0.226269	+	0.226269i
$306$		0			0
$307$	−0.885664	+	0.885664i	−0.0505475	+	0.0505475i	−0.731929	−	0.681381i	$-0.761380\pi$
$307$	−0.885664	+	0.885664i	−0.0505475	+	0.0505475i	0.681381	+	0.731929i	$0.261380\pi$
$308$			0.522853i			0.0297923i
$309$		0			0
$310$	−6.78328	+	6.78328i	−0.385265	+	0.385265i
$311$	−34.1323			−1.93547			−0.967734	−	0.251975i	$-0.918920\pi$
$311$	−34.1323			−1.93547			−0.967734	+	0.251975i	$0.918920\pi$
$312$		0			0
$313$	−11.2654			−0.636759			−0.318379	−	0.947963i	$-0.603139\pi$
$313$	−11.2654			−0.636759			−0.318379	+	0.947963i	$0.603139\pi$
$314$	−17.4773	+	17.4773i	−0.986303	+	0.986303i
$315$		0			0
$316$		−	8.87993i		−	0.499535i
$317$	2.06783	−	2.06783i	0.116141	−	0.116141i	−0.646648	−	0.762789i	$-0.723830\pi$
$317$	2.06783	−	2.06783i	0.116141	−	0.116141i	0.762789	+	0.646648i	$0.223830\pi$
$318$		0			0
$319$	1.80918	−	1.80918i	0.101295	−	0.101295i
$320$	1.40096	+	1.40096i	0.0783158	+	0.0783158i
$321$		0			0
$322$		−	5.51713i		−	0.307458i
$323$	−1.81167	−	1.81167i	−0.100804	−	0.100804i
$324$		0			0
$325$	−1.37534	+	3.62238i	−0.0762903	+	0.200933i
$326$		−	16.0551i		−	0.889212i
$327$		0			0
$328$	5.46747			0.301891
$329$	−2.90227			−0.160007
$330$		0			0
$331$	−13.5841	−	13.5841i	−0.746647	−	0.746647i	0.227201	−	0.973848i	$-0.427043\pi$
$331$	−13.5841	−	13.5841i	−0.746647	−	0.746647i	−0.973848	+	0.227201i	$0.927043\pi$
$332$	−2.45927	−	2.45927i	−0.134970	−	0.134970i
$333$		0			0
$334$	−16.0015			−0.875563
$335$	25.1699			1.37518
$336$		0			0
$337$		−	16.6356i		−	0.906197i	−0.891461	−	0.453098i	$-0.850319\pi$
$337$		−	16.6356i		−	0.906197i	0.891461	−	0.453098i	$-0.149681\pi$
$338$	−12.9769	+	0.775172i	−0.705849	+	0.0421638i
$339$		0			0
$340$	−1.22647	−	1.22647i	−0.0665144	−	0.0665144i
$341$			2.53160i			0.137094i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−1.38970	+	1.38970i	−0.0749279	+	0.0749279i
$345$		0			0
$346$	5.32570	−	5.32570i	0.286311	−	0.286311i
$347$		−	19.7949i		−	1.06265i	−0.847169	−	0.531323i	$-0.821695\pi$
$347$		−	19.7949i		−	1.06265i	0.847169	−	0.531323i	$-0.178305\pi$
$348$		0			0
$349$	6.97237	−	6.97237i	0.373222	−	0.373222i	−0.495427	−	0.868649i	$-0.664988\pi$
$349$	6.97237	−	6.97237i	0.373222	−	0.373222i	0.868649	+	0.495427i	$0.164988\pi$
$350$	1.07464			0.0574421
$351$		0			0
$352$	0.522853			0.0278682
$353$	18.0332	−	18.0332i	0.959809	−	0.959809i	−0.0394139	−	0.999223i	$-0.512549\pi$
$353$	18.0332	−	18.0332i	0.959809	−	0.959809i	0.999223	+	0.0394139i	$0.0125491\pi$
$354$		0			0
$355$		−	24.6691i		−	1.30930i
$356$	−5.38066	+	5.38066i	−0.285174	+	0.285174i
$357$		0			0
$358$	−0.561600	+	0.561600i	−0.0296815	+	0.0296815i
$359$	10.6075	+	10.6075i	0.559842	+	0.559842i	0.929262	−	0.369420i	$-0.120444\pi$
$359$	10.6075	+	10.6075i	0.559842	+	0.559842i	−0.369420	+	0.929262i	$0.620444\pi$
$360$		0			0
$361$		−	10.4350i		−	0.549212i
$362$	1.24136	+	1.24136i	0.0652443	+	0.0652443i
$363$		0			0
$364$	1.47853	+	3.28846i	0.0774960	+	0.172362i
$365$		−	24.3801i		−	1.27611i
$366$		0			0
$367$	16.7597			0.874849			0.437424	−	0.899255i	$-0.355891\pi$
$367$	16.7597			0.874849			0.437424	+	0.899255i	$0.355891\pi$
$368$	−5.51713			−0.287600
$369$		0			0
$370$	−14.9077	−	14.9077i	−0.775016	−	0.775016i
$371$	8.10083	+	8.10083i	0.420574	+	0.420574i
$372$		0			0
$373$	−27.4568			−1.42166			−0.710830	−	0.703364i	$-0.751680\pi$
$373$	−27.4568			−1.42166			−0.710830	+	0.703364i	$0.751680\pi$
$374$	−0.457731			−0.0236687
$375$		0			0
$376$			2.90227i			0.149673i
$377$	6.26273	−	16.4948i	0.322547	−	0.849523i
$378$		0			0
$379$	7.45659	+	7.45659i	0.383019	+	0.383019i	0.872189	−	0.489169i	$-0.162700\pi$
$379$	7.45659	+	7.45659i	0.383019	+	0.383019i	−0.489169	+	0.872189i	$0.662700\pi$
$380$			5.79833i			0.297448i
$381$		0			0
$382$	2.02255	+	2.02255i	0.103483	+	0.103483i
$383$	−26.2137	+	26.2137i	−1.33946	+	1.33946i	−0.442871	+	0.896585i	$0.646040\pi$
$383$	−26.2137	+	26.2137i	−1.33946	+	1.33946i	−0.896585	+	0.442871i	$0.853960\pi$
$384$		0			0
$385$	−0.732494	+	0.732494i	−0.0373314	+	0.0373314i
$386$			2.11940i			0.107875i
$387$		0			0
$388$	2.17257	−	2.17257i	0.110295	−	0.110295i
$389$	−28.0079			−1.42005			−0.710027	−	0.704174i	$-0.751317\pi$
$389$	−28.0079			−1.42005			−0.710027	+	0.704174i	$0.751317\pi$
$390$		0			0
$391$	4.82996			0.244262
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			5.28389i			0.266199i
$395$	12.4404	−	12.4404i	0.625944	−	0.625944i
$396$		0			0
$397$	−22.5495	+	22.5495i	−1.13173	+	1.13173i	−0.141836	+	0.989890i	$0.545300\pi$
$397$	−22.5495	+	22.5495i	−1.13173	+	1.13173i	−0.989890	+	0.141836i	$0.954700\pi$
$398$	2.21266	+	2.21266i	0.110911	+	0.110911i
$399$		0			0
$400$		−	1.07464i		−	0.0537322i
$401$	−18.1238	−	18.1238i	−0.905060	−	0.905060i	0.0908085	−	0.995868i	$-0.471055\pi$
$401$	−18.1238	−	18.1238i	−0.905060	−	0.905060i	−0.995868	+	0.0908085i	$0.971055\pi$
$402$		0			0
$403$	7.15888	+	15.9224i	0.356609	+	0.793150i
$404$		−	16.7323i		−	0.832464i
$405$		0			0
$406$	−4.89347			−0.242859
$407$	−5.56374			−0.275784
$408$		0			0
$409$	3.09451	+	3.09451i	0.153014	+	0.153014i	0.779462	−	0.626449i	$-0.215492\pi$
$409$	3.09451	+	3.09451i	0.153014	+	0.153014i	−0.626449	+	0.779462i	$0.715492\pi$
$410$	7.65969	+	7.65969i	0.378285	+	0.378285i
$411$		0			0
$412$	1.86637			0.0919493
$413$	−2.03998			−0.100381
$414$		0			0
$415$		−	6.89065i		−	0.338249i
$416$	3.28846	−	1.47853i	0.161230	−	0.0724909i
$417$		0			0
$418$	1.08200	+	1.08200i	0.0529224	+	0.0529224i
$419$			35.6321i			1.74074i	0.492394	+	0.870372i	$0.336122\pi$
$419$			35.6321i			1.74074i	−0.492394	+	0.870372i	$0.663878\pi$
$420$		0			0
$421$	14.4576	+	14.4576i	0.704622	+	0.704622i	0.965399	−	0.260777i	$-0.0839788\pi$
$421$	14.4576	+	14.4576i	0.704622	+	0.704622i	−0.260777	+	0.965399i	$0.583979\pi$
$422$	−16.3777	+	16.3777i	−0.797253	+	0.797253i
$423$		0			0
$424$	8.10083	−	8.10083i	0.393411	−	0.393411i
$425$			0.940796i			0.0456353i
$426$		0			0
$427$	1.99451	−	1.99451i	0.0965210	−	0.0965210i
$428$	13.7497			0.664619
$429$		0			0
$430$	−3.89383			−0.187777
$431$	−10.0564	+	10.0564i	−0.484399	+	0.484399i	−0.906533	−	0.422134i	$-0.861281\pi$
$431$	−10.0564	+	10.0564i	−0.484399	+	0.484399i	0.422134	+	0.906533i	$0.361281\pi$
$432$		0			0
$433$		−	21.8337i		−	1.04926i	−0.851331	−	0.524629i	$-0.824204\pi$
$433$		−	21.8337i		−	1.04926i	0.851331	−	0.524629i	$-0.175796\pi$
$434$	3.42374	−	3.42374i	0.164345	−	0.164345i
$435$		0			0
$436$	−6.08191	+	6.08191i	−0.291271	+	0.291271i
$437$	−11.4172	−	11.4172i	−0.546161	−	0.546161i
$438$		0			0
$439$		−	8.36981i		−	0.399469i	−0.979850	−	0.199735i	$-0.935992\pi$
$439$		−	8.36981i		−	0.399469i	0.979850	−	0.199735i	$-0.0640080\pi$
$440$	0.732494	+	0.732494i	0.0349203	+	0.0349203i
$441$		0			0
$442$	−2.87888	+	1.29438i	−0.136934	+	0.0615672i
$443$		−	19.3324i		−	0.918508i	−0.888305	−	0.459254i	$-0.848117\pi$
$443$		−	19.3324i		−	0.918508i	0.888305	−	0.459254i	$-0.151883\pi$
$444$		0			0
$445$	−15.0761			−0.714677
$446$	5.88626			0.278722
$447$		0			0
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−6.51223	−	6.51223i	−0.307331	−	0.307331i	0.536542	−	0.843873i	$-0.319730\pi$
$449$	−6.51223	−	6.51223i	−0.307331	−	0.307331i	−0.843873	+	0.536542i	$0.819730\pi$
$450$		0			0
$451$	2.85869			0.134610
$452$	−0.0237301			−0.00111617
$453$		0			0
$454$		−	11.1056i		−	0.521209i
$455$	−2.53563	+	6.67834i	−0.118872	+	0.313085i
$456$		0			0
$457$	−8.39343	−	8.39343i	−0.392628	−	0.392628i	0.482995	−	0.875623i	$-0.339549\pi$
$457$	−8.39343	−	8.39343i	−0.392628	−	0.392628i	−0.875623	+	0.482995i	$0.839549\pi$
$458$		−	0.170783i		−	0.00798018i
$459$		0			0
$460$	−7.72926	−	7.72926i	−0.360378	−	0.360378i
$461$	3.34156	−	3.34156i	0.155632	−	0.155632i	−0.624996	−	0.780628i	$-0.714899\pi$
$461$	3.34156	−	3.34156i	0.155632	−	0.155632i	0.780628	+	0.624996i	$0.214899\pi$
$462$		0			0
$463$	14.2239	−	14.2239i	0.661039	−	0.661039i	−0.294586	−	0.955625i	$-0.595182\pi$
$463$	14.2239	−	14.2239i	0.661039	−	0.661039i	0.955625	+	0.294586i	$0.0951818\pi$
$464$			4.89347i			0.227174i
$465$		0			0
$466$	−5.38562	+	5.38562i	−0.249484	+	0.249484i
$467$	−25.2574			−1.16877			−0.584386	−	0.811476i	$-0.698665\pi$
$467$	−25.2574			−1.16877			−0.584386	+	0.811476i	$0.698665\pi$
$468$		0			0
$469$	−12.7040			−0.586618
$470$	−4.06595	+	4.06595i	−0.187548	+	0.187548i
$471$		0			0
$472$			2.03998i			0.0938979i
$473$	−0.726612	+	0.726612i	−0.0334096	+	0.0334096i
$474$		0			0
$475$	2.22389	−	2.22389i	0.102039	−	0.102039i
$476$	0.619036	+	0.619036i	0.0283735	+	0.0283735i
$477$		0			0
$478$		−	11.4544i		−	0.523910i
$479$	−4.25790	−	4.25790i	−0.194549	−	0.194549i	0.603110	−	0.797658i	$-0.293928\pi$
$479$	−4.25790	−	4.25790i	−0.194549	−	0.194549i	−0.797658	+	0.603110i	$0.793928\pi$
$480$		0			0
$481$	−34.9928	+	15.7332i	−1.59554	+	0.717372i
$482$		−	25.8713i		−	1.17841i
$483$		0			0
$484$	−10.7266			−0.487574
$485$	6.08734			0.276412
$486$		0			0
$487$	−8.25073	−	8.25073i	−0.373876	−	0.373876i	0.495011	−	0.868887i	$-0.335164\pi$
$487$	−8.25073	−	8.25073i	−0.373876	−	0.373876i	−0.868887	+	0.495011i	$0.835164\pi$
$488$	−1.99451	−	1.99451i	−0.0902872	−	0.0902872i
$489$		0			0
$490$	1.98125			0.0895038
$491$	16.1847			0.730405			0.365202	−	0.930928i	$-0.381000\pi$
$491$	16.1847			0.730405			0.365202	+	0.930928i	$0.381000\pi$
$492$		0			0
$493$		−	4.28398i		−	0.192941i
$494$	9.86489	+	3.74550i	0.443842	+	0.168518i
$495$		0			0
$496$	−3.42374	−	3.42374i	−0.153730	−	0.153730i
$497$			12.4513i			0.558517i
$498$		0			0
$499$	−8.18081	−	8.18081i	−0.366223	−	0.366223i	0.499874	−	0.866098i	$-0.333379\pi$
$499$	−8.18081	−	8.18081i	−0.366223	−	0.366223i	−0.866098	+	0.499874i	$0.833379\pi$
$500$	8.51031	−	8.51031i	0.380593	−	0.380593i
$501$		0			0
$502$	17.5986	−	17.5986i	0.785464	−	0.785464i
$503$			0.775560i			0.0345805i	0.999851	+	0.0172903i	$0.00550393\pi$
$503$			0.775560i			0.0345805i	−0.999851	+	0.0172903i	$0.994496\pi$
$504$		0			0
$505$	23.4412	−	23.4412i	1.04312	−	1.04312i
$506$	−2.88465			−0.128238
$507$		0			0
$508$	−6.04749			−0.268314
$509$	−18.5944	+	18.5944i	−0.824181	+	0.824181i	−0.986705	−	0.162524i	$-0.948037\pi$
$509$	−18.5944	+	18.5944i	−0.824181	+	0.824181i	0.162524	+	0.986705i	$0.448037\pi$
$510$		0			0
$511$			12.3054i			0.544360i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	4.10374	−	4.10374i	0.181008	−	0.181008i
$515$	2.61470	+	2.61470i	0.115217	+	0.115217i
$516$		0			0
$517$			1.51746i			0.0667379i
$518$	7.52440	+	7.52440i	0.330603	+	0.330603i
$519$		0			0
$520$	6.67834	+	2.53563i	0.292865	+	0.111195i
$521$			26.4481i			1.15871i	0.815074	+	0.579356i	$0.196696\pi$
$521$			26.4481i			1.15871i	−0.815074	+	0.579356i	$0.803304\pi$
$522$		0			0
$523$	2.76680			0.120984			0.0604919	−	0.998169i	$-0.480733\pi$
$523$	2.76680			0.120984			0.0604919	+	0.998169i	$0.480733\pi$
$524$	12.3826			0.540938
$525$		0			0
$526$	10.4507	+	10.4507i	0.455671	+	0.455671i
$527$	2.99731	+	2.99731i	0.130565	+	0.130565i
$528$		0			0
$529$	7.43873			0.323423
$530$	22.6978			0.985930
$531$		0			0
$532$		−	2.92660i		−	0.126884i
$533$	17.9796	−	8.08382i	0.778781	−	0.350149i
$534$		0			0
$535$	19.2628	+	19.2628i	0.832803	+	0.832803i
$536$			12.7040i			0.548731i
$537$		0			0
$538$	10.9391	+	10.9391i	0.471617	+	0.471617i
$539$	0.369713	−	0.369713i	0.0159247	−	0.0159247i
$540$		0			0
$541$	−28.2316	+	28.2316i	−1.21377	+	1.21377i	−0.243995	+	0.969776i	$0.578458\pi$
$541$	−28.2316	+	28.2316i	−1.21377	+	1.21377i	−0.969776	+	0.243995i	$0.921542\pi$
$542$		−	17.9496i		−	0.771001i
$543$		0			0
$544$	0.619036	−	0.619036i	0.0265409	−	0.0265409i
$545$	−17.0410			−0.729956
$546$		0			0
$547$	41.9792			1.79490			0.897449	−	0.441117i	$-0.145418\pi$
$547$	41.9792			1.79490			0.897449	+	0.441117i	$0.145418\pi$
$548$	−7.15255	+	7.15255i	−0.305542	+	0.305542i
$549$		0			0
$550$		−	0.561881i		−	0.0239587i
$551$	−10.1266	+	10.1266i	−0.431409	+	0.431409i
$552$		0			0
$553$	−6.27906	+	6.27906i	−0.267013	+	0.267013i
$554$	1.89371	+	1.89371i	0.0804560	+	0.0804560i
$555$		0			0
$556$			6.65697i			0.282318i
$557$	−6.06123	−	6.06123i	−0.256823	−	0.256823i	0.566938	−	0.823761i	$-0.308128\pi$
$557$	−6.06123	−	6.06123i	−0.256823	−	0.256823i	−0.823761	+	0.566938i	$0.808128\pi$
$558$		0			0
$559$	−2.51527	+	6.62470i	−0.106384	+	0.280195i
$560$		−	1.98125i		−	0.0837231i
$561$		0			0
$562$	−2.92197			−0.123256
$563$	−8.67668			−0.365679			−0.182839	−	0.983143i	$-0.558529\pi$
$563$	−8.67668			−0.365679			−0.182839	+	0.983143i	$0.558529\pi$
$564$		0			0
$565$	−0.0332448	−	0.0332448i	−0.00139862	−	0.00139862i
$566$	9.80082	+	9.80082i	0.411959	+	0.411959i
$567$		0			0
$568$	12.4513			0.522445
$569$	−1.05049			−0.0440390			−0.0220195	−	0.999758i	$-0.507010\pi$
$569$	−1.05049			−0.0440390			−0.0220195	+	0.999758i	$0.507010\pi$
$570$		0			0
$571$			16.9269i			0.708369i	0.935176	+	0.354185i	$0.115242\pi$
$571$			16.9269i			0.708369i	−0.935176	+	0.354185i	$0.884758\pi$
$572$	1.71938	−	0.773054i	0.0718909	−	0.0323230i
$573$		0			0
$574$	−3.86609	−	3.86609i	−0.161367	−	0.161367i
$575$			5.92895i			0.247254i
$576$		0			0
$577$	10.1650	+	10.1650i	0.423172	+	0.423172i	0.886295	−	0.463122i	$-0.153271\pi$
$577$	10.1650	+	10.1650i	0.423172	+	0.423172i	−0.463122	+	0.886295i	$0.653271\pi$
$578$	11.4789	−	11.4789i	0.477459	−	0.477459i
$579$		0			0
$580$	−6.85554	+	6.85554i	−0.284661	+	0.284661i
$581$			3.47793i			0.144289i
$582$		0			0
$583$	4.23555	−	4.23555i	0.175418	−	0.175418i
$584$	12.3054			0.509202
$585$		0			0
$586$	−6.93924			−0.286657
$587$	−5.47838	+	5.47838i	−0.226117	+	0.226117i	−0.811068	−	0.584951i	$-0.801114\pi$
$587$	−5.47838	+	5.47838i	−0.226117	+	0.226117i	0.584951	+	0.811068i	$0.301114\pi$
$588$		0			0
$589$		−	14.1703i		−	0.583876i
$590$	−2.85793	+	2.85793i	−0.117659	+	0.117659i
$591$		0			0
$592$	7.52440	−	7.52440i	0.309251	−	0.309251i
$593$	4.15790	+	4.15790i	0.170745	+	0.170745i	0.787306	−	0.616562i	$-0.211475\pi$
$593$	4.15790	+	4.15790i	0.170745	+	0.170745i	−0.616562	+	0.787306i	$0.711475\pi$
$594$		0			0
$595$			1.73448i			0.0711069i
$596$	−0.562645	−	0.562645i	−0.0230469	−	0.0230469i
$597$		0			0
$598$	−18.1428	+	8.15724i	−0.741916	+	0.333574i
$599$		−	5.28862i		−	0.216087i	−0.994146	−	0.108044i	$-0.965541\pi$
$599$		−	5.28862i		−	0.216087i	0.994146	−	0.108044i	$-0.0344586\pi$
$600$		0			0
$601$	−46.9268			−1.91418			−0.957092	−	0.289783i	$-0.906417\pi$
$601$	−46.9268			−1.91418			−0.957092	+	0.289783i	$0.906417\pi$
$602$	1.96534			0.0801013
$603$		0			0
$604$	6.90603	+	6.90603i	0.281003	+	0.281003i
$605$	−15.0275	−	15.0275i	−0.610956	−	0.610956i
$606$		0			0
$607$	−17.9237			−0.727499			−0.363749	−	0.931497i	$-0.618504\pi$
$607$	−17.9237			−0.727499			−0.363749	+	0.931497i	$0.618504\pi$
$608$	−2.92660			−0.118689
$609$		0			0
$610$		−	5.58844i		−	0.226269i
$611$	4.29109	+	9.54399i	0.173599	+	0.386109i
$612$		0			0
$613$	31.1368	+	31.1368i	1.25760	+	1.25760i	0.952233	+	0.305371i	$0.0987805\pi$
$613$	31.1368	+	31.1368i	1.25760	+	1.25760i	0.305371	+	0.952233i	$0.401220\pi$
$614$		−	1.25252i		−	0.0505475i
$615$		0			0
$616$	−0.369713	−	0.369713i	−0.0148962	−	0.0148962i
$617$	−1.79924	+	1.79924i	−0.0724346	+	0.0724346i	−0.742396	−	0.669961i	$-0.766311\pi$
$617$	−1.79924	+	1.79924i	−0.0724346	+	0.0724346i	0.669961	+	0.742396i	$0.266311\pi$
$618$		0			0
$619$	−16.1002	+	16.1002i	−0.647121	+	0.647121i	−0.952296	−	0.305175i	$-0.901285\pi$
$619$	−16.1002	+	16.1002i	−0.647121	+	0.647121i	0.305175	+	0.952296i	$0.401285\pi$
$620$		−	9.59301i		−	0.385265i
$621$		0			0
$622$	24.1352	−	24.1352i	0.967734	−	0.967734i
$623$	7.60940			0.304864
$624$		0			0
$625$	18.4719			0.738877
$626$	7.96585	−	7.96585i	0.318379	−	0.318379i
$627$		0			0
$628$		−	24.7167i		−	0.986303i
$629$	−6.58722	+	6.58722i	−0.262650	+	0.262650i
$630$		0			0
$631$	−31.7853	+	31.7853i	−1.26535	+	1.26535i	−0.316891	+	0.948462i	$0.602639\pi$
$631$	−31.7853	+	31.7853i	−1.26535	+	1.26535i	−0.948462	+	0.316891i	$0.897361\pi$
$632$	6.27906	+	6.27906i	0.249768	+	0.249768i
$633$		0			0
$634$			2.92435i			0.116141i
$635$	−8.47227	−	8.47227i	−0.336212	−	0.336212i
$636$		0			0
$637$	1.27981	−	3.37077i	0.0507080	−	0.133555i
$638$			2.55857i			0.101295i
$639$		0			0
$640$	−1.98125			−0.0783158
$641$	40.5881			1.60313			0.801567	−	0.597906i	$-0.204000\pi$
$641$	40.5881			1.60313			0.801567	+	0.597906i	$0.204000\pi$
$642$		0			0
$643$	−12.2661	−	12.2661i	−0.483728	−	0.483728i	0.422592	−	0.906320i	$-0.361120\pi$
$643$	−12.2661	−	12.2661i	−0.483728	−	0.483728i	−0.906320	+	0.422592i	$0.861120\pi$
$644$	3.90120	+	3.90120i	0.153729	+	0.153729i
$645$		0			0
$646$	2.56209			0.100804
$647$	−34.9084			−1.37239			−0.686194	−	0.727418i	$-0.740720\pi$
$647$	−34.9084			−1.37239			−0.686194	+	0.727418i	$0.740720\pi$
$648$		0			0
$649$			1.06661i			0.0418682i
$650$	−1.58889	−	3.53392i	−0.0623215	−	0.138612i
$651$		0			0
$652$	11.3527	+	11.3527i	0.444606	+	0.444606i
$653$		−	30.5925i		−	1.19718i	−0.801057	−	0.598588i	$-0.795728\pi$
$653$		−	30.5925i		−	1.19718i	0.801057	−	0.598588i	$-0.204272\pi$
$654$		0			0
$655$	17.3475	+	17.3475i	0.677824	+	0.677824i
$656$	−3.86609	+	3.86609i	−0.150945	+	0.150945i
$657$		0			0
$658$	2.05222	−	2.05222i	0.0800037	−	0.0800037i
$659$		−	19.1998i		−	0.747919i	−0.927445	−	0.373960i	$-0.878000\pi$
$659$		−	19.1998i		−	0.747919i	0.927445	−	0.373960i	$-0.122000\pi$
$660$		0			0
$661$	−10.6127	+	10.6127i	−0.412785	+	0.412785i	−0.882708	−	0.469923i	$-0.844282\pi$
$661$	−10.6127	+	10.6127i	−0.412785	+	0.412785i	0.469923	+	0.882708i	$0.344282\pi$
$662$	19.2107			0.746647
$663$		0			0
$664$	3.47793			0.134970
$665$	4.10004	−	4.10004i	0.158993	−	0.158993i
$666$		0			0
$667$		−	26.9979i		−	1.04536i
$668$	11.3148	−	11.3148i	0.437782	−	0.437782i
$669$		0			0
$670$	−17.7978	+	17.7978i	−0.687589	+	0.687589i
$671$	−1.04284	−	1.04284i	−0.0402582	−	0.0402582i
$672$		0			0
$673$		−	16.5781i		−	0.639039i	−0.947580	−	0.319520i	$-0.896478\pi$
$673$		−	16.5781i		−	0.639039i	0.947580	−	0.319520i	$-0.103522\pi$
$674$	11.7631	+	11.7631i	0.453098	+	0.453098i
$675$		0			0
$676$	8.62790	−	9.72416i	0.331842	−	0.374006i
$677$		−	24.7005i		−	0.949318i	−0.880170	−	0.474659i	$-0.842571\pi$
$677$		−	24.7005i		−	0.949318i	0.880170	−	0.474659i	$-0.157429\pi$
$678$		0			0
$679$	−3.07247			−0.117911
$680$	1.73448			0.0665144
$681$		0			0
$682$	−1.79011	−	1.79011i	−0.0685469	−	0.0685469i
$683$	21.6195	+	21.6195i	0.827246	+	0.827246i	0.987135	−	0.159889i	$-0.0511138\pi$
$683$	21.6195	+	21.6195i	0.827246	+	0.827246i	−0.159889	+	0.987135i	$0.551114\pi$
$684$		0			0
$685$	−20.0408			−0.765720
$686$	−1.00000			−0.0381802
$687$		0			0
$688$		−	1.96534i		−	0.0749279i
$689$	14.6619	−	38.6166i	0.558575	−	1.47117i
$690$		0			0
$691$	22.2311	+	22.2311i	0.845711	+	0.845711i	0.989595	−	0.143884i	$-0.0459591\pi$
$691$	22.2311	+	22.2311i	0.845711	+	0.845711i	−0.143884	+	0.989595i	$0.545959\pi$
$692$			7.53167i			0.286311i
$693$		0			0
$694$	13.9971	+	13.9971i	0.531323	+	0.531323i
$695$	−9.32612	+	9.32612i	−0.353760	+	0.353760i
$696$		0			0
$697$	3.38456	−	3.38456i	0.128199	−	0.128199i
$698$			9.86042i			0.373222i
$699$		0			0
$700$	−0.759888	+	0.759888i	−0.0287211	+	0.0287211i
$701$	−28.1742			−1.06412			−0.532062	−	0.846706i	$-0.678583\pi$
$701$	−28.1742			−1.06412			−0.532062	+	0.846706i	$0.678583\pi$
$702$		0			0
$703$	31.1422			1.17455
$704$	−0.369713	+	0.369713i	−0.0139341	+	0.0139341i
$705$		0			0
$706$			25.5028i			0.959809i
$707$	−11.8315	+	11.8315i	−0.444971	+	0.444971i
$708$		0			0
$709$	−19.2695	+	19.2695i	−0.723682	+	0.723682i	−0.969353	−	0.245671i	$-0.920992\pi$
$709$	−19.2695	+	19.2695i	−0.723682	+	0.723682i	0.245671	+	0.969353i	$0.420992\pi$
$710$	17.4437	+	17.4437i	0.654651	+	0.654651i
$711$		0			0
$712$		−	7.60940i		−	0.285174i
$713$	18.8892	+	18.8892i	0.707406	+	0.707406i
$714$		0			0
$715$	3.49179	+	1.32576i	0.130586	+	0.0495807i
$716$		−	0.794222i		−	0.0296815i
$717$		0			0
$718$	−15.0013			−0.559842
$719$	−6.48318			−0.241782			−0.120891	−	0.992666i	$-0.538575\pi$
$719$	−6.48318			−0.241782			−0.120891	+	0.992666i	$0.538575\pi$
$720$		0			0
$721$	−1.31972	−	1.31972i	−0.0491490	−	0.0491490i
$722$	7.37867	+	7.37867i	0.274606	+	0.274606i
$723$		0			0
$724$	−1.75554			−0.0652443
$725$	5.25874			0.195305
$726$		0			0
$727$		−	2.29484i		−	0.0851108i	−0.999094	−	0.0425554i	$-0.986450\pi$
$727$		−	2.29484i		−	0.0851108i	0.999094	−	0.0425554i	$-0.0135499\pi$
$728$	−3.37077	−	1.27981i	−0.124929	−	0.0474330i
$729$		0			0
$730$	17.2394	+	17.2394i	0.638057	+	0.638057i
$731$			1.72055i			0.0636370i
$732$		0			0
$733$	34.3990	+	34.3990i	1.27056	+	1.27056i	0.945797	+	0.324758i	$0.105283\pi$
$733$	34.3990	+	34.3990i	1.27056	+	1.27056i	0.324758	+	0.945797i	$0.394717\pi$
$734$	−11.8509	+	11.8509i	−0.437424	+	0.437424i
$735$		0			0
$736$	3.90120	−	3.90120i	0.143800	−	0.143800i
$737$			6.64235i			0.244674i
$738$		0			0
$739$	7.43068	−	7.43068i	0.273342	−	0.273342i	−0.557102	−	0.830444i	$-0.688087\pi$
$739$	7.43068	−	7.43068i	0.273342	−	0.273342i	0.830444	+	0.557102i	$0.188087\pi$
$740$	21.0827			0.775016
$741$		0			0
$742$	−11.4563			−0.420574
$743$	19.7108	−	19.7108i	0.723118	−	0.723118i	−0.246121	−	0.969239i	$-0.579156\pi$
$743$	19.7108	−	19.7108i	0.723118	−	0.723118i	0.969239	+	0.246121i	$0.0791561\pi$
$744$		0			0
$745$		−	1.57648i		−	0.0577579i
$746$	19.4149	−	19.4149i	0.710830	−	0.710830i
$747$		0			0
$748$	0.323665	−	0.323665i	0.0118344	−	0.0118344i
$749$	−9.72254	−	9.72254i	−0.355254	−	0.355254i
$750$		0			0
$751$		−	39.5565i		−	1.44344i	−0.692186	−	0.721719i	$-0.743352\pi$
$751$		−	39.5565i		−	1.44344i	0.692186	−	0.721719i	$-0.256648\pi$
$752$	−2.05222	−	2.05222i	−0.0748366	−	0.0748366i
$753$		0			0
$754$	7.23514	+	16.0920i	0.263488	+	0.586035i
$755$			19.3501i			0.704222i
$756$		0			0
$757$	38.8838			1.41326			0.706629	−	0.707585i	$-0.250215\pi$
$757$	38.8838			1.41326			0.706629	+	0.707585i	$0.250215\pi$
$758$	−10.5452			−0.383019
$759$		0			0
$760$	−4.10004	−	4.10004i	−0.148724	−	0.148724i
$761$	14.6066	+	14.6066i	0.529487	+	0.529487i	0.920419	−	0.390932i	$-0.127847\pi$
$761$	14.6066	+	14.6066i	0.529487	+	0.529487i	−0.390932	+	0.920419i	$0.627847\pi$
$762$		0			0
$763$	8.60112			0.311382
$764$	−2.86032			−0.103483
$765$		0			0
$766$		−	37.0717i		−	1.33946i
$767$	3.01618	+	6.70840i	0.108908	+	0.242226i
$768$		0			0
$769$	−18.7539	−	18.7539i	−0.676283	−	0.676283i	0.282874	−	0.959157i	$-0.408712\pi$
$769$	−18.7539	−	18.7539i	−0.676283	−	0.676283i	−0.959157	+	0.282874i	$0.908712\pi$
$770$		−	1.03590i		−	0.0373314i
$771$		0			0
$772$	−1.49865	−	1.49865i	−0.0539374	−	0.0539374i
$773$	−13.4430	+	13.4430i	−0.483511	+	0.483511i	−0.906251	−	0.422740i	$-0.861068\pi$
$773$	−13.4430	+	13.4430i	−0.483511	+	0.483511i	0.422740	+	0.906251i	$0.361068\pi$
$774$		0			0
$775$	−3.67930	+	3.67930i	−0.132164	+	0.132164i
$776$			3.07247i			0.110295i
$777$		0			0
$778$	19.8045	−	19.8045i	0.710027	−	0.710027i
$779$	−16.0011			−0.573299
$780$		0			0
$781$	6.51020			0.232953
$782$	−3.41530	+	3.41530i	−0.122131	+	0.122131i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	34.6270	−	34.6270i	1.23589	−	1.23589i
$786$		0			0
$787$	3.86031	−	3.86031i	0.137605	−	0.137605i	−0.634949	−	0.772554i	$-0.718979\pi$
$787$	3.86031	−	3.86031i	0.137605	−	0.137605i	0.772554	+	0.634949i	$0.218979\pi$
$788$	−3.73628	−	3.73628i	−0.133099	−	0.133099i
$789$		0			0
$790$			17.5934i			0.625944i
$791$	0.0167797	+	0.0167797i	0.000596617	+	0.000596617i
$792$		0			0
$793$	−9.50780	−	3.60992i	−0.337632	−	0.128192i
$794$		−	31.8898i		−	1.13173i
$795$		0			0
$796$	−3.12917			−0.110911
$797$	−41.0398			−1.45370			−0.726851	−	0.686795i	$-0.759017\pi$
$797$	−41.0398			−1.45370			−0.726851	+	0.686795i	$0.759017\pi$
$798$		0			0
$799$	1.79661	+	1.79661i	0.0635595	+	0.0635595i
$800$	0.759888	+	0.759888i	0.0268661	+	0.0268661i
$801$		0			0
$802$	25.6309			0.905060
$803$	6.43393			0.227048
$804$		0			0
$805$			10.9308i			0.385261i
$806$	−16.3209	−	6.19672i	−0.574880	−	0.218270i
$807$		0			0
$808$	11.8315	+	11.8315i	0.416232	+	0.416232i
$809$			4.21548i			0.148208i	0.997251	+	0.0741041i	$0.0236097\pi$
$809$			4.21548i			0.148208i	−0.997251	+	0.0741041i	$0.976390\pi$
$810$		0			0
$811$	28.4647	+	28.4647i	0.999529	+	0.999529i	1.00000		0.000470560i	$-0.000149784\pi$
$811$	28.4647	+	28.4647i	0.999529	+	0.999529i	−0.000470560		1.00000i	$0.500150\pi$
$812$	3.46021	−	3.46021i	0.121429	−	0.121429i
$813$		0			0
$814$	3.93416	−	3.93416i	0.137892	−	0.137892i
$815$			31.8093i			1.11423i
$816$		0			0
$817$	4.06711	−	4.06711i	0.142290	−	0.142290i
$818$	−4.37629			−0.153014
$819$		0			0
$820$	−10.8324			−0.378285
$821$	24.5629	−	24.5629i	0.857252	−	0.857252i	−0.133762	−	0.991014i	$-0.542706\pi$
$821$	24.5629	−	24.5629i	0.857252	−	0.857252i	0.991014	+	0.133762i	$0.0427057\pi$
$822$		0			0
$823$		−	15.0153i		−	0.523400i	−0.965149	−	0.261700i	$-0.915717\pi$
$823$		−	15.0153i		−	0.523400i	0.965149	−	0.261700i	$-0.0842831\pi$
$824$	−1.31972	+	1.31972i	−0.0459747	+	0.0459747i
$825$		0			0
$826$	1.44249	−	1.44249i	0.0501905	−	0.0501905i
$827$	−34.7791	−	34.7791i	−1.20939	−	1.20939i	−0.971226	−	0.238161i	$-0.923455\pi$
$827$	−34.7791	−	34.7791i	−1.20939	−	1.20939i	−0.238161	−	0.971226i	$-0.576545\pi$
$828$		0			0
$829$			55.6937i			1.93432i	0.254161	+	0.967162i	$0.418201\pi$
$829$			55.6937i			1.93432i	−0.254161	+	0.967162i	$0.581799\pi$
$830$	4.87242	+	4.87242i	0.169124	+	0.169124i
$831$		0			0
$832$	−1.27981	+	3.37077i	−0.0443695	+	0.116860i
$833$		−	0.875449i		−	0.0303325i
$834$		0			0
$835$	31.7030			1.09713
$836$	−1.53018			−0.0529224
$837$		0			0
$838$	−25.1957	−	25.1957i	−0.870372	−	0.870372i
$839$	−19.9624	−	19.9624i	−0.689179	−	0.689179i	0.272871	−	0.962051i	$-0.412027\pi$
$839$	−19.9624	−	19.9624i	−0.689179	−	0.689179i	−0.962051	+	0.272871i	$0.912027\pi$
$840$		0			0
$841$	5.05394			0.174274
$842$	−20.4462			−0.704622
$843$		0			0
$844$		−	23.1615i		−	0.797253i
$845$	25.7104	−	1.53581i	0.884466	−	0.0528335i
$846$		0			0
$847$	7.58487	+	7.58487i	0.260619	+	0.260619i
$848$			11.4563i			0.393411i
$849$		0			0
$850$	−0.665243	−	0.665243i	−0.0228177	−	0.0228177i
$851$	−41.5131	+	41.5131i	−1.42305	+	1.42305i
$852$		0			0
$853$	−34.5290	+	34.5290i	−1.18225	+	1.18225i	−0.203091	+	0.979160i	$0.565099\pi$
$853$	−34.5290	+	34.5290i	−1.18225	+	1.18225i	−0.979160	+	0.203091i	$0.934901\pi$
$854$			2.82066i			0.0965210i
$855$		0			0
$856$	−9.72254	+	9.72254i	−0.332310	+	0.332310i
$857$	15.7993			0.539694			0.269847	−	0.962903i	$-0.413027\pi$
$857$	15.7993			0.539694			0.269847	+	0.962903i	$0.413027\pi$
$858$		0			0
$859$	−3.27576			−0.111767			−0.0558837	−	0.998437i	$-0.517798\pi$
$859$	−3.27576			−0.111767			−0.0558837	+	0.998437i	$0.517798\pi$
$860$	2.75335	−	2.75335i	0.0938886	−	0.0938886i
$861$		0			0
$862$		−	14.2219i		−	0.484399i
$863$	12.1192	−	12.1192i	0.412543	−	0.412543i	−0.470081	−	0.882623i	$-0.655775\pi$
$863$	12.1192	−	12.1192i	0.412543	−	0.412543i	0.882623	+	0.470081i	$0.155775\pi$
$864$		0			0
$865$	−10.5515	+	10.5515i	−0.358763	+	0.358763i
$866$	15.4387	+	15.4387i	0.524629	+	0.524629i
$867$		0			0
$868$			4.84190i			0.164345i
$869$	3.28303	+	3.28303i	0.111369	+	0.111369i
$870$		0			0
$871$	18.7833	+	41.7767i	0.636448	+	1.41555i
$872$		−	8.60112i		−	0.291271i
$873$		0			0
$874$	16.1464			0.546161
$875$	−12.0354			−0.406871
$876$		0			0
$877$	19.1024	+	19.1024i	0.645041	+	0.645041i	0.951790	−	0.306749i	$-0.0992413\pi$
$877$	19.1024	+	19.1024i	0.645041	+	0.645041i	−0.306749	+	0.951790i	$0.599241\pi$
$878$	5.91835	+	5.91835i	0.199735	+	0.199735i
$879$		0			0
$880$	−1.03590			−0.0349203
$881$	16.5191			0.556543			0.278271	−	0.960502i	$-0.410239\pi$
$881$	16.5191			0.556543			0.278271	+	0.960502i	$0.410239\pi$
$882$		0			0
$883$			52.6966i			1.77338i	0.462362	+	0.886691i	$0.347002\pi$
$883$			52.6966i			1.77338i	−0.462362	+	0.886691i	$0.652998\pi$
$884$	1.12041	−	2.95094i	0.0376835	−	0.0992507i
$885$		0			0
$886$	13.6700	+	13.6700i	0.459254	+	0.459254i
$887$			36.1117i			1.21251i	0.795269	+	0.606256i	$0.207329\pi$
$887$			36.1117i			1.21251i	−0.795269	+	0.606256i	$0.792671\pi$
$888$		0			0
$889$	4.27622	+	4.27622i	0.143420	+	0.143420i
$890$	10.6604	−	10.6604i	0.357339	−	0.357339i
$891$		0			0
$892$	−4.16221	+	4.16221i	−0.139361	+	0.139361i
$893$		−	8.49378i		−	0.284234i
$894$		0			0
$895$	1.11267	−	1.11267i	0.0371925	−	0.0371925i
$896$	1.00000			0.0334077
$897$		0			0
$898$	9.20968			0.307331
$899$	16.7540	−	16.7540i	0.558776	−	0.558776i
$900$		0			0
$901$		−	10.0294i		−	0.334128i
$902$	−2.02140	+	2.02140i	−0.0673051	+	0.0673051i
$903$		0			0
$904$	0.0167797	−	0.0167797i	0.000558084	−	0.000558084i
$905$	−2.45944	−	2.45944i	−0.0817546	−	0.0817546i
$906$		0			0
$907$			16.6847i			0.554007i	0.960869	+	0.277004i	$0.0893414\pi$
$907$			16.6847i			0.554007i	−0.960869	+	0.277004i	$0.910659\pi$
$908$	7.85281	+	7.85281i	0.260605	+	0.260605i
$909$		0			0
$910$	−2.92934	−	6.51526i	−0.0971066	−	0.215979i
$911$		−	45.6144i		−	1.51127i	−0.654991	−	0.755637i	$-0.727328\pi$
$911$		−	45.6144i		−	1.51127i	0.654991	−	0.755637i	$-0.272672\pi$
$912$		0			0
$913$	1.81845			0.0601818
$914$	11.8701			0.392628
$915$		0			0
$916$	0.120762	+	0.120762i	0.00399009	+	0.00399009i
$917$	−8.75584	−	8.75584i	−0.289143	−	0.289143i
$918$		0			0
$919$	26.5899			0.877120			0.438560	−	0.898702i	$-0.355489\pi$
$919$	26.5899			0.877120			0.438560	+	0.898702i	$0.355489\pi$
$920$	10.9308			0.360378
$921$		0			0
$922$			4.72568i			0.155632i
$923$	40.9456	−	18.4096i	1.34774	−	0.605960i
$924$		0			0
$925$	−8.08605	−	8.08605i	−0.265868	−	0.265868i
$926$			20.1156i			0.661039i
$927$		0			0
$928$	−3.46021	−	3.46021i	−0.113587	−	0.113587i
$929$	−9.54943	+	9.54943i	−0.313307	+	0.313307i	−0.846189	−	0.532883i	$-0.821109\pi$
$929$	−9.54943	+	9.54943i	−0.313307	+	0.313307i	0.532883	+	0.846189i	$0.321109\pi$
$930$		0			0
$931$	−2.06942	+	2.06942i	−0.0678224	+	0.0678224i
$932$		−	7.61641i		−	0.249484i
$933$		0			0
$934$	17.8597	−	17.8597i	0.584386	−	0.584386i
$935$	0.906880			0.0296582
$936$		0			0
$937$	24.9477			0.815004			0.407502	−	0.913204i	$-0.366400\pi$
$937$	24.9477			0.815004			0.407502	+	0.913204i	$0.366400\pi$
$938$	8.98311	−	8.98311i	0.293309	−	0.293309i
$939$		0			0
$940$		−	5.75013i		−	0.187548i
$941$	−21.3592	+	21.3592i	−0.696290	+	0.696290i	−0.963608	−	0.267318i	$-0.913863\pi$
$941$	−21.3592	+	21.3592i	−0.696290	+	0.696290i	0.267318	+	0.963608i	$0.413863\pi$
$942$		0			0
$943$	21.3297	−	21.3297i	0.694591	−	0.694591i
$944$	−1.44249	−	1.44249i	−0.0469489	−	0.0469489i
$945$		0			0
$946$		−	1.02758i		−	0.0334096i
$947$	−0.393942	−	0.393942i	−0.0128014	−	0.0128014i	0.700677	−	0.713479i	$-0.252881\pi$
$947$	−0.393942	−	0.393942i	−0.0128014	−	0.0128014i	−0.713479	+	0.700677i	$0.752881\pi$
$948$		0			0
$949$	40.4659	−	18.1939i	1.31358	−	0.590600i
$950$			3.14505i			0.102039i
$951$		0			0
$952$	−0.875449			−0.0283735
$953$	9.23561			0.299171			0.149585	−	0.988749i	$-0.452206\pi$
$953$	9.23561			0.299171			0.149585	+	0.988749i	$0.452206\pi$
$954$		0			0
$955$	−4.00719	−	4.00719i	−0.129670	−	0.129670i
$956$	8.09946	+	8.09946i	0.261955	+	0.261955i
$957$		0			0
$958$	6.02159			0.194549
$959$	10.1152			0.326638
$960$		0			0
$961$		−	7.55605i		−	0.243743i
$962$	13.6186	−	35.8687i	0.439082	−	1.15645i
$963$		0			0
$964$	18.2938	+	18.2938i	0.589203	+	0.589203i
$965$		−	4.19907i		−	0.135173i
$966$		0			0
$967$	38.3784	+	38.3784i	1.23417	+	1.23417i	0.962348	+	0.271819i	$0.0876252\pi$
$967$	38.3784	+	38.3784i	1.23417	+	1.23417i	0.271819	+	0.962348i	$0.412375\pi$
$968$	7.58487	−	7.58487i	0.243787	−	0.243787i
$969$		0			0
$970$	−4.30440	+	4.30440i	−0.138206	+	0.138206i
$971$			21.3719i			0.685858i	0.939361	+	0.342929i	$0.111419\pi$
$971$			21.3719i			0.685858i	−0.939361	+	0.342929i	$0.888581\pi$
$972$		0			0
$973$	4.70719	−	4.70719i	0.150906	−	0.150906i
$974$	11.6683			0.373876
$975$		0			0
$976$	2.82066			0.0902872
$977$	−11.1583	+	11.1583i	−0.356985	+	0.356985i	−0.862700	−	0.505716i	$-0.831229\pi$
$977$	−11.1583	+	11.1583i	−0.356985	+	0.356985i	0.505716	+	0.862700i	$0.331229\pi$
$978$		0			0
$979$		−	3.97860i		−	0.127157i
$980$	−1.40096	+	1.40096i	−0.0447519	+	0.0447519i
$981$		0			0
$982$	−11.4443	+	11.4443i	−0.365202	+	0.365202i
$983$	16.9173	+	16.9173i	0.539579	+	0.539579i	0.923405	−	0.383827i	$-0.125394\pi$
$983$	16.9173	+	16.9173i	0.539579	+	0.539579i	−0.383827	+	0.923405i	$0.625394\pi$
$984$		0			0
$985$		−	10.4687i		−	0.333561i
$986$	3.02923	+	3.02923i	0.0964705	+	0.0964705i
$987$		0			0
$988$	−9.62399	+	4.32706i	−0.306180	+	0.137662i
$989$			10.8430i			0.344788i
$990$		0			0
$991$	−34.3799			−1.09212			−0.546058	−	0.837748i	$-0.683872\pi$
$991$	−34.3799			−1.09212			−0.546058	+	0.837748i	$0.683872\pi$
$992$	4.84190			0.153730
$993$		0			0
$994$	−8.80440	−	8.80440i	−0.279259	−	0.279259i
$995$	−4.38384	−	4.38384i	−0.138977	−	0.138977i
$996$		0			0
$997$	20.4514			0.647703			0.323852	−	0.946108i	$-0.395022\pi$
$997$	20.4514			0.647703			0.323852	+	0.946108i	$0.395022\pi$
$998$	11.5694			0.366223
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.d.827.3	yes	16
3.2	odd	2		1638.2.y.c.827.6	✓	16
13.5	odd	4		1638.2.y.c.1331.6	yes	16
39.5	even	4	inner	1638.2.y.d.1331.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.6	✓	16	3.2	odd	2
1638.2.y.c.1331.6	yes	16	13.5	odd	4
1638.2.y.d.827.3	yes	16	1.1	even	1	trivial
1638.2.y.d.1331.3	yes	16	39.5	even	4	inner

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.40096 - 1.40096i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.40096 - 1.40096i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.98125i q^{10} +(0.369713 + 0.369713i) q^{11} +(3.37077 + 1.27981i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +0.875449 q^{17} +(-2.06942 - 2.06942i) q^{19} +(-1.40096 - 1.40096i) q^{20} -0.522853 q^{22} +5.51713 q^{23} +1.07464i q^{25} +(-3.28846 + 1.47853i) q^{26} +(0.707107 + 0.707107i) q^{28} -4.89347i q^{29} +(3.42374 + 3.42374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.619036 + 0.619036i) q^{34} +1.98125i q^{35} +(-7.52440 + 7.52440i) q^{37} +2.92660 q^{38} +1.98125 q^{40} +(3.86609 - 3.86609i) q^{41} +1.96534i q^{43} +(0.369713 - 0.369713i) q^{44} +(-3.90120 + 3.90120i) q^{46} +(2.05222 + 2.05222i) q^{47} -1.00000i q^{49} +(-0.759888 - 0.759888i) q^{50} +(1.27981 - 3.37077i) q^{52} -11.4563i q^{53} +1.03590 q^{55} -1.00000 q^{56} +(3.46021 + 3.46021i) q^{58} +(1.44249 + 1.44249i) q^{59} -2.82066 q^{61} -4.84190 q^{62} +1.00000i q^{64} +(6.51526 - 2.92934i) q^{65} +(8.98311 + 8.98311i) q^{67} -0.875449i q^{68} +(-1.40096 - 1.40096i) q^{70} +(8.80440 - 8.80440i) q^{71} +(8.70125 - 8.70125i) q^{73} -10.6411i q^{74} +(-2.06942 + 2.06942i) q^{76} -0.522853 q^{77} +8.87993 q^{79} +(-1.40096 + 1.40096i) q^{80} +5.46747i q^{82} +(2.45927 - 2.45927i) q^{83} +(1.22647 - 1.22647i) q^{85} +(-1.38970 - 1.38970i) q^{86} +0.522853i q^{88} +(-5.38066 - 5.38066i) q^{89} +(-3.28846 + 1.47853i) q^{91} -5.51713i q^{92} -2.90227 q^{94} -5.79833 q^{95} +(2.17257 + 2.17257i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^5	\( 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50} - 16 q^{55} - 16 q^{56} + 4 q^{58} - 8 q^{59} - 40 q^{61} + 24 q^{62} + 56 q^{65} - 4 q^{67} - 4 q^{70} - 24 q^{71} - 12 q^{73} + 16 q^{76} - 8 q^{77} + 16 q^{79} - 4 q^{80} + 8 q^{85} + 24 q^{86} + 16 q^{89} + 8 q^{91} - 8 q^{94} - 40 q^{95} - 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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