LMFDB - Embedded newform 1323.2.g.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.b.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} -2.59358 q^{5} +5.05408 q^{8} +O(q^{10})$	\(q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} -2.59358 q^{5} +5.05408 q^{8} +(3.19076 - 5.52655i) q^{10} -4.51459 q^{11} +(0.500000 - 0.866025i) q^{13} +(-2.16372 + 3.74766i) q^{16} +(0.472958 - 0.819187i) q^{17} +(-2.02704 - 3.51094i) q^{19} +(5.25729 + 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +0.273346 q^{23} +1.72665 q^{25} +(1.23025 + 2.13086i) q^{26} +(1.23025 + 2.13086i) q^{29} +(1.16372 + 2.01561i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(1.16372 + 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} +9.97509 q^{38} -13.1082 q^{40} +(3.20321 - 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-2.12422 + 3.67926i) q^{50} -4.05408 q^{52} +(-3.13667 + 5.43288i) q^{53} +11.7089 q^{55} -6.05408 q^{58} +(1.36333 + 2.36135i) q^{59} +(-1.13667 + 1.96878i) q^{61} -5.72665 q^{62} -7.32743 q^{64} +(-1.29679 + 2.24611i) q^{65} +(7.90856 + 13.6980i) q^{67} -3.83482 q^{68} -3.27335 q^{71} +(-0.753696 + 1.30544i) q^{73} +4.38151 q^{74} +(-8.21780 + 14.2336i) q^{76} +(-7.35447 + 12.7383i) q^{79} +(5.61177 - 9.71987i) q^{80} +(7.88151 + 13.6512i) q^{82} +(0.472958 + 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} -25.6768 q^{86} -22.8171 q^{88} +(7.17830 + 12.4332i) q^{89} +(-0.554084 - 0.959702i) q^{92} +(14.9626 + 25.9161i) q^{94} +(5.25729 + 9.10590i) q^{95} +(-5.74484 - 9.95036i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} - 10 q^{5} + 12 q^{8}+O(q^{10}) $ 6 * q - q^2 - 3 * q^4 - 10 * q^5 + 12 * q^8	$ 6 q - q^{2} - 3 q^{4} - 10 q^{5} + 12 q^{8} + 4 q^{11} + 3 q^{13} - 3 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} + q^{29} - 3 q^{31} - 8 q^{32} - 3 q^{34} + 3 q^{37} + 16 q^{38} - 42 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} + 9 q^{47} + 10 q^{50} - 6 q^{52} - 18 q^{53} + 12 q^{55} - 18 q^{58} + 9 q^{59} - 6 q^{61} - 36 q^{62} - 24 q^{64} - 5 q^{65} + 12 q^{68} - 18 q^{71} + 3 q^{73} - 12 q^{74} - 21 q^{76} - 15 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} - 68 q^{86} - 42 q^{88} + 2 q^{89} + 15 q^{92} + 24 q^{94} + 16 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 - 10 * q^5 + 12 * q^8 + 4 * q^11 + 3 * q^13 - 3 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 + 12 * q^25 + q^26 + q^29 - 3 * q^31 - 8 * q^32 - 3 * q^34 + 3 * q^37 + 16 * q^38 - 42 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 + 9 * q^47 + 10 * q^50 - 6 * q^52 - 18 * q^53 + 12 * q^55 - 18 * q^58 + 9 * q^59 - 6 * q^61 - 36 * q^62 - 24 * q^64 - 5 * q^65 + 12 * q^68 - 18 * q^71 + 3 * q^73 - 12 * q^74 - 21 * q^76 - 15 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 - 68 * q^86 - 42 * q^88 + 2 * q^89 + 15 * q^92 + 24 * q^94 + 16 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.00784213	+	0.999969i	$0.502496\pi$
$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.862078	+	0.506776i	$0.830837\pi$
$3$		0			0
$3$		0			0
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	−2.59358			−1.15988			−0.579942	−	0.814658i	$-0.696925\pi$
$5$	−2.59358			−1.15988			−0.579942	+	0.814658i	$0.696925\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	5.05408			1.78689
$9$		0			0
$10$	3.19076	−	5.52655i	1.00901	−	1.74765i
$11$	−4.51459			−1.36120			−0.680600	−	0.732655i	$-0.738281\pi$
$11$	−4.51459			−1.36120			−0.680600	+	0.732655i	$0.738281\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$		0			0
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	0.472958	−	0.819187i	0.114709	−	0.198682i	−0.802954	−	0.596041i	$-0.796740\pi$
$17$	0.472958	−	0.819187i	0.114709	−	0.198682i	0.917663	+	0.397359i	$0.130073\pi$
$18$		0			0
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	0.534168	−	0.845378i	$-0.320625\pi$
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	−0.999203	+	0.0399136i	$0.987292\pi$
$20$	5.25729	+	9.10590i	1.17557	+	2.03614i
$21$		0			0
$22$	5.55408	−	9.61996i	1.18413	−	2.05098i
$23$	0.273346			0.0569966			0.0284983	−	0.999594i	$-0.490927\pi$
$23$	0.273346			0.0569966			0.0284983	+	0.999594i	$0.490927\pi$
$24$		0			0
$25$	1.72665			0.345331
$26$	1.23025	+	2.13086i	0.241272	+	0.417896i
$27$		0			0
$28$		0			0
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	0.957350	−	0.288932i	$-0.0933002\pi$
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	−0.728897	+	0.684623i	$0.759967\pi$
$30$		0			0
$31$	1.16372	+	2.01561i	0.209009	+	0.362015i	0.951403	−	0.307949i	$-0.0996427\pi$
$31$	1.16372	+	2.01561i	0.209009	+	0.362015i	−0.742393	+	0.669964i	$0.766309\pi$
$32$	−0.269748	−	0.467216i	−0.0476851	−	0.0825930i
$33$		0			0
$34$	1.16372	+	2.01561i	0.199576	+	0.345675i
$35$		0			0
$36$		0			0
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	0.783510	−	0.621380i	$-0.213428\pi$
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	−0.929885	+	0.367849i	$0.880094\pi$
$38$	9.97509			1.61817
$39$		0			0
$40$	−13.1082			−2.07258
$41$	3.20321	−	5.54812i	0.500257	−	0.866471i	−0.499743	−	0.866174i	$-0.666572\pi$
$41$	3.20321	−	5.54812i	0.500257	−	0.866471i	1.00000		0.000297253i	$-9.46187e-5\pi$
$42$		0			0
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	0.922389	+	0.386262i	$0.126234\pi$
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	−0.126682	+	0.991943i	$0.540433\pi$
$44$	9.15126	+	15.8505i	1.37960	+	2.38955i
$45$		0			0
$46$	−0.336285	+	0.582462i	−0.0495825	+	0.0858794i
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.0436467	−	0.999047i	$-0.486102\pi$
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.843377	−	0.537323i	$-0.180564\pi$
$48$		0			0
$49$		0			0
$50$	−2.12422	+	3.67926i	−0.300410	+	0.520326i
$51$		0			0
$52$	−4.05408			−0.562200
$53$	−3.13667	+	5.43288i	−0.430855	+	0.746263i	−0.996947	−	0.0780790i	$-0.975121\pi$
$53$	−3.13667	+	5.43288i	−0.430855	+	0.746263i	0.566092	+	0.824342i	$0.308455\pi$
$54$		0			0
$55$	11.7089			1.57883
$56$		0			0
$57$		0			0
$58$	−6.05408			−0.794940
$59$	1.36333	+	2.36135i	0.177490	+	0.307422i	0.941020	−	0.338350i	$-0.109869\pi$
$59$	1.36333	+	2.36135i	0.177490	+	0.307422i	−0.763530	+	0.645772i	$0.776536\pi$
$60$		0			0
$61$	−1.13667	+	1.96878i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$61$	−1.13667	+	1.96878i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$62$	−5.72665			−0.727286
$63$		0			0
$64$	−7.32743			−0.915929
$65$	−1.29679	+	2.24611i	−0.160847	+	0.278595i
$66$		0			0
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.706400	+	0.707813i	$0.250318\pi$
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.259784	+	0.965667i	$0.416349\pi$
$68$	−3.83482			−0.465041
$69$		0			0
$70$		0			0
$71$	−3.27335			−0.388475			−0.194237	−	0.980955i	$-0.562223\pi$
$71$	−3.27335			−0.388475			−0.194237	+	0.980955i	$0.562223\pi$
$72$		0			0
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	−0.906756	−	0.421656i	$-0.861449\pi$
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	0.818543	+	0.574446i	$0.194782\pi$
$74$	4.38151			0.509341
$75$		0			0
$76$	−8.21780	+	14.2336i	−0.942646	+	1.63271i
$77$		0			0
$78$		0			0
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	0.0725952	+	0.997361i	$0.476872\pi$
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	−0.900038	+	0.435811i	$0.856461\pi$
$80$	5.61177	−	9.71987i	0.627415	−	1.08671i
$81$		0			0
$82$	7.88151	+	13.6512i	0.870368	+	1.50752i
$83$	0.472958	+	0.819187i	0.0519139	+	0.0899175i	0.890815	−	0.454367i	$-0.150135\pi$
$83$	0.472958	+	0.819187i	0.0519139	+	0.0899175i	−0.838901	+	0.544285i	$0.816801\pi$
$84$		0			0
$85$	−1.22665	+	2.12463i	−0.133049	+	0.230448i
$86$	−25.6768			−2.76881
$87$		0			0
$88$	−22.8171			−2.43231
$89$	7.17830	+	12.4332i	0.760899	+	1.31792i	0.942388	+	0.334522i	$0.108575\pi$
$89$	7.17830	+	12.4332i	0.760899	+	1.31792i	−0.181489	+	0.983393i	$0.558092\pi$
$90$		0			0
$91$		0			0
$92$	−0.554084	−	0.959702i	−0.0577673	−	0.100056i
$93$		0			0
$94$	14.9626	+	25.9161i	1.54328	+	2.67304i
$95$	5.25729	+	9.10590i	0.539387	+	0.934246i
$96$		0			0
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	−0.995085	−	0.0990246i	$-0.968428\pi$
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	0.411785	−	0.911281i	$-0.364906\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	−3.67977			−0.366150			−0.183075	−	0.983099i	$-0.558605\pi$
$101$	−3.67977			−0.366150			−0.183075	+	0.983099i	$0.558605\pi$
$102$		0			0
$103$	9.72665			0.958396			0.479198	−	0.877707i	$-0.340928\pi$
$103$	9.72665			0.958396			0.479198	+	0.877707i	$0.340928\pi$
$104$	2.52704	−	4.37697i	0.247797	−	0.429197i
$105$		0			0
$106$	−7.71780	−	13.3676i	−0.749619	−	1.29838i
$107$	−0.687159	−	1.19019i	−0.0664301	−	0.115060i	0.830897	−	0.556426i	$-0.187828\pi$
$107$	−0.687159	−	1.19019i	−0.0664301	−	0.115060i	−0.897327	+	0.441365i	$0.854494\pi$
$108$		0			0
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	−0.773076	−	0.634313i	$-0.781283\pi$
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	0.935869	+	0.352347i	$0.114616\pi$
$110$	−14.4050	+	24.9501i	−1.37346	+	2.37890i
$111$		0			0
$112$		0			0
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	−0.511271	−	0.859420i	$-0.670825\pi$
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	0.999915	+	0.0130636i	$0.00415840\pi$
$114$		0			0
$115$	−0.708945			−0.0661095
$116$	4.98755	−	8.63868i	0.463082	−	0.802082i
$117$		0			0
$118$	−6.70895			−0.617608
$119$		0			0
$120$		0			0
$121$	9.38151			0.852865
$122$	−2.79679	−	4.84418i	−0.253209	−	0.438572i
$123$		0			0
$124$	4.71780	−	8.17147i	0.423671	−	0.733820i
$125$	8.48968			0.759340
$126$		0			0
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	9.55408	−	16.5482i	0.844470	−	1.46266i
$129$		0			0
$130$	−3.19076	−	5.52655i	−0.279848	−	0.484711i
$131$	7.91381			0.691433			0.345717	−	0.938339i	$-0.387636\pi$
$131$	7.91381			0.691433			0.345717	+	0.938339i	$0.387636\pi$
$132$		0			0
$133$		0			0
$134$	−38.9181			−3.36201
$135$		0			0
$136$	2.39037	−	4.14024i	0.204972	−	0.355023i
$137$	3.67257			0.313769			0.156884	−	0.987617i	$-0.449855\pi$
$137$	3.67257			0.313769			0.156884	+	0.987617i	$0.449855\pi$
$138$		0			0
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	−0.906289	−	0.422658i	$-0.861097\pi$
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	0.819177	+	0.573541i	$0.194431\pi$
$140$		0			0
$141$		0			0
$142$	4.02704	−	6.97504i	0.337942	−	0.585332i
$143$	−2.25729	+	3.90975i	−0.188764	+	0.326950i
$144$		0			0
$145$	−3.19076	−	5.52655i	−0.264978	−	0.458955i
$146$	−1.85447	−	3.21204i	−0.153477	−	0.265830i
$147$		0			0
$148$	−3.60963	+	6.25206i	−0.296710	+	0.513917i
$149$	13.5438			1.10955			0.554774	−	0.832001i	$-0.312805\pi$
$149$	13.5438			1.10955			0.554774	+	0.832001i	$0.312805\pi$
$150$		0			0
$151$	9.92821			0.807946			0.403973	−	0.914771i	$-0.367629\pi$
$151$	9.92821			0.807946			0.403973	+	0.914771i	$0.367629\pi$
$152$	−10.2448	−	17.7446i	−0.830966	−	1.43928i
$153$		0			0
$154$		0			0
$155$	−3.01819	−	5.22765i	−0.242427	−	0.419895i
$156$		0			0
$157$	3.02704	+	5.24299i	0.241584	+	0.418436i	0.961166	−	0.275972i	$-0.0889996\pi$
$157$	3.02704	+	5.24299i	0.241584	+	0.418436i	−0.719581	+	0.694408i	$0.755666\pi$
$158$	−18.0957	−	31.3427i	−1.43962	−	2.49349i
$159$		0			0
$160$	0.699612	+	1.21176i	0.0553092	+	0.0957983i
$161$		0			0
$162$		0			0
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	−0.969237	−	0.246128i	$-0.920842\pi$
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	0.271465	−	0.962448i	$-0.412492\pi$
$164$	−25.9722			−2.02809
$165$		0			0
$166$	−2.32743			−0.180644
$167$	4.23385	−	7.33325i	0.327625	−	0.567464i	−0.654415	−	0.756136i	$-0.727085\pi$
$167$	4.23385	−	7.33325i	0.327625	−	0.567464i	0.982040	+	0.188672i	$0.0604183\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−3.01819	−	5.22765i	−0.231484	−	0.400943i
$171$		0			0
$172$	21.1534	−	36.6388i	1.61293	−	2.79368i
$173$	−8.67830	+	15.0313i	−0.659799	+	1.14281i	0.320868	+	0.947124i	$0.396025\pi$
$173$	−8.67830	+	15.0313i	−0.659799	+	1.14281i	−0.980667	+	0.195682i	$0.937308\pi$
$174$		0			0
$175$		0			0
$176$	9.76829	−	16.9192i	0.736312	−	1.27533i
$177$		0			0
$178$	−35.3245			−2.64768
$179$	−5.67471	+	9.82888i	−0.424147	+	0.734645i	−0.996340	−	0.0854741i	$-0.972759\pi$
$179$	−5.67471	+	9.82888i	−0.424147	+	0.734645i	0.572193	+	0.820119i	$0.306093\pi$
$180$		0			0
$181$	−21.8889			−1.62699			−0.813495	−	0.581572i	$-0.802438\pi$
$181$	−21.8889			−1.62699			−0.813495	+	0.581572i	$0.802438\pi$
$182$		0			0
$183$		0			0
$184$	1.38151			0.101847
$185$	2.30924	+	3.99973i	0.169779	+	0.294066i
$186$		0			0
$187$	−2.13521	+	3.69829i	−0.156142	+	0.270446i
$188$	−49.3068			−3.59607
$189$		0			0
$190$	−25.8712			−1.87689
$191$	−0.350874	+	0.607731i	−0.0253883	+	0.0439739i	−0.878440	−	0.477852i	$-0.841416\pi$
$191$	−0.350874	+	0.607731i	−0.0253883	+	0.0439739i	0.853052	+	0.521826i	$0.174749\pi$
$192$		0			0
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	0.560372	−	0.828241i	$-0.310658\pi$
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	−0.997464	+	0.0711760i	$0.977325\pi$
$194$	28.2704			2.02970
$195$		0			0
$196$		0			0
$197$	16.4107			1.16921			0.584607	−	0.811317i	$-0.301249\pi$
$197$	16.4107			1.16921			0.584607	+	0.811317i	$0.301249\pi$
$198$		0			0
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	−0.111637	−	0.993749i	$-0.535609\pi$
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	0.916430	−	0.400194i	$-0.131057\pi$
$200$	8.72665			0.617068
$201$		0			0
$202$	4.52704	−	7.84107i	0.318522	−	0.551696i
$203$		0			0
$204$		0			0
$205$	−8.30778	+	14.3895i	−0.580241	+	1.00501i
$206$	−11.9662	+	20.7261i	−0.833727	+	1.44406i
$207$		0			0
$208$	2.16372	+	3.74766i	0.150027	+	0.259854i
$209$	9.15126	+	15.8505i	0.633006	+	1.09640i
$210$		0			0
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	−0.933790	−	0.357822i	$-0.883520\pi$
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	0.776778	+	0.629775i	$0.216853\pi$
$212$	25.4327			1.74672
$213$		0			0
$214$	3.38151			0.231156
$215$	−13.5328	−	23.4395i	−0.922928	−	1.59856i
$216$		0			0
$217$		0			0
$218$	4.18190	+	7.24327i	0.283234	+	0.490576i
$219$		0			0
$220$	−23.7345	−	41.1094i	−1.60018	−	2.77160i
$221$	−0.472958	−	0.819187i	−0.0318146	−	0.0551045i
$222$		0			0
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	0.998131	−	0.0611159i	$-0.0194659\pi$
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	−0.551993	+	0.833849i	$0.686133\pi$
$224$		0			0
$225$		0			0
$226$	12.7807	+	22.1369i	0.850162	+	1.47252i
$227$	1.38151			0.0916943			0.0458472	−	0.998948i	$-0.485401\pi$
$227$	1.38151			0.0916943			0.0458472	+	0.998948i	$0.485401\pi$
$228$		0			0
$229$	17.9794			1.18811			0.594055	−	0.804424i	$-0.297526\pi$
$229$	17.9794			1.18811			0.594055	+	0.804424i	$0.297526\pi$
$230$	0.872181	−	1.51066i	0.0575099	−	0.0996101i
$231$		0			0
$232$	6.21780	+	10.7695i	0.408219	+	0.707055i
$233$	−9.49115	−	16.4391i	−0.621786	−	1.07696i	−0.989153	−	0.146888i	$-0.953074\pi$
$233$	−9.49115	−	16.4391i	−0.621786	−	1.07696i	0.367367	−	0.930076i	$-0.380259\pi$
$234$		0			0
$235$	−15.7719	+	27.3177i	−1.02884	+	1.78201i
$236$	5.52704	−	9.57312i	0.359780	−	0.623157i
$237$		0			0
$238$		0			0
$239$	2.44592	−	4.23645i	0.158213	−	0.274033i	−0.776011	−	0.630719i	$-0.782760\pi$
$239$	2.44592	−	4.23645i	0.158213	−	0.274033i	0.934224	+	0.356686i	$0.116093\pi$
$240$		0			0
$241$	26.1593			1.68507			0.842535	−	0.538641i	$-0.181062\pi$
$241$	26.1593			1.68507			0.842535	+	0.538641i	$0.181062\pi$
$242$	−11.5416	+	19.9907i	−0.741924	+	1.28505i
$243$		0			0
$244$	9.21634			0.590016
$245$		0			0
$246$		0			0
$247$	−4.05408			−0.257955
$248$	5.88151	+	10.1871i	0.373477	+	0.646880i
$249$		0			0
$250$	−10.4445	+	18.0903i	−0.660565	+	1.14413i
$251$	18.4576			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$251$	18.4576			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$	−0.827430	+	1.43315i	−0.0519176	+	0.0899239i
$255$		0			0
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	−11.7339			−0.731938			−0.365969	−	0.930627i	$-0.619262\pi$
$257$	−11.7339			−0.731938			−0.365969	+	0.930627i	$0.619262\pi$
$258$		0			0
$259$		0			0
$260$	10.5146			0.652087
$261$		0			0
$262$	−9.73599	+	16.8632i	−0.601491	+	1.04181i
$263$	7.52179			0.463813			0.231907	−	0.972738i	$-0.425504\pi$
$263$	7.52179			0.463813			0.231907	+	0.972738i	$0.425504\pi$
$264$		0			0
$265$	8.13521	−	14.0906i	0.499742	−	0.865579i
$266$		0			0
$267$		0			0
$268$	32.0620	−	55.5329i	1.95850	−	3.39221i
$269$	9.41741	−	16.3114i	0.574190	−	0.994526i	−0.421939	−	0.906624i	$-0.638651\pi$
$269$	9.41741	−	16.3114i	0.574190	−	0.994526i	0.996129	−	0.0879017i	$-0.0280161\pi$
$270$		0			0
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	−0.957555	−	0.288251i	$-0.906926\pi$
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	0.229145	−	0.973392i	$-0.426407\pi$
$272$	2.04669	+	3.54498i	0.124099	+	0.214946i
$273$		0			0
$274$	−4.51819	+	7.82573i	−0.272954	+	0.472770i
$275$	−7.79513			−0.470064
$276$		0			0
$277$	7.16225			0.430338			0.215169	−	0.976577i	$-0.430970\pi$
$277$	7.16225			0.430338			0.215169	+	0.976577i	$0.430970\pi$
$278$	−2.52704	−	4.37697i	−0.151562	−	0.262513i
$279$		0			0
$280$		0			0
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	0.997974	−	0.0636271i	$-0.0202668\pi$
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	−0.554090	+	0.832457i	$0.686933\pi$
$282$		0			0
$283$	9.99854	+	17.3180i	0.594351	+	1.02945i	0.993638	+	0.112621i	$0.0359245\pi$
$283$	9.99854	+	17.3180i	0.594351	+	1.02945i	−0.399287	+	0.916826i	$0.630742\pi$
$284$	6.63521	+	11.4925i	0.393727	+	0.681956i
$285$		0			0
$286$	−5.55408	−	9.61996i	−0.328420	−	0.568840i
$287$		0			0
$288$		0			0
$289$	8.05262	+	13.9475i	0.473684	+	0.820444i
$290$	15.7017			0.922038
$291$		0			0
$292$	6.11109			0.357625
$293$	−7.53278	+	13.0472i	−0.440070	+	0.762223i	−0.997694	−	0.0678705i	$-0.978380\pi$
$293$	−7.53278	+	13.0472i	−0.440070	+	0.762223i	0.557625	+	0.830093i	$0.311713\pi$
$294$		0			0
$295$	−3.53590	−	6.12435i	−0.205868	−	0.356574i
$296$	−4.50000	−	7.79423i	−0.261557	−	0.453030i
$297$		0			0
$298$	−16.6623	+	28.8599i	−0.965218	+	1.67181i
$299$	0.136673	−	0.236725i	0.00790401	−	0.0136901i
$300$		0			0
$301$		0			0
$302$	−12.2142	+	21.1556i	−0.702848	+	1.21737i
$303$		0			0
$304$	17.5438			1.00620
$305$	2.94805	−	5.10618i	0.168805	−	0.292379i
$306$		0			0
$307$	27.2704			1.55641			0.778203	−	0.628013i	$-0.216132\pi$
$307$	27.2704			1.55641			0.778203	+	0.628013i	$0.216132\pi$
$308$		0			0
$309$		0			0
$310$	14.8525			0.843567
$311$	7.99115	+	13.8411i	0.453136	+	0.784855i	0.998579	−	0.0532931i	$-0.0169718\pi$
$311$	7.99115	+	13.8411i	0.453136	+	0.784855i	−0.545443	+	0.838148i	$0.683638\pi$
$312$		0			0
$313$	5.79893	−	10.0440i	0.327775	−	0.567722i	−0.654295	−	0.756239i	$-0.727035\pi$
$313$	5.79893	−	10.0440i	0.327775	−	0.567722i	0.982070	+	0.188517i	$0.0603680\pi$
$314$	−14.8961			−0.840636
$315$		0			0
$316$	59.6313			3.35452
$317$	−1.00885	+	1.74739i	−0.0566629	+	0.0981430i	−0.892965	−	0.450125i	$-0.851379\pi$
$317$	−1.00885	+	1.74739i	−0.0566629	+	0.0981430i	0.836303	+	0.548268i	$0.184713\pi$
$318$		0			0
$319$	−5.55408	−	9.61996i	−0.310969	−	0.538614i
$320$	19.0043			1.06237
$321$		0			0
$322$		0			0
$323$	−3.83482			−0.213375
$324$		0			0
$325$	0.863327	−	1.49533i	0.0478888	−	0.0829458i
$326$	43.8391			2.42802
$327$		0			0
$328$	16.1893	−	28.0407i	0.893904	−	1.54829i
$329$		0			0
$330$		0			0
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	−0.457159	−	0.889385i	$-0.651133\pi$
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	0.998809	−	0.0487815i	$-0.0155338\pi$
$332$	1.91741	−	3.32105i	0.105232	−	0.182266i
$333$		0			0
$334$	10.4174	+	18.0435i	0.570015	+	0.987296i
$335$	−20.5115	−	35.5269i	−1.12066	−	1.94104i
$336$		0			0
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	−0.133929	−	0.990991i	$-0.542759\pi$
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	0.925188	−	0.379509i	$-0.123907\pi$
$338$	−29.5261			−1.60601
$339$		0			0
$340$	9.94592			0.539393
$341$	−5.25370	−	9.09967i	−0.284504	−	0.492775i
$342$		0			0
$343$		0			0
$344$	26.3712	+	45.6763i	1.42184	+	2.46270i
$345$		0			0
$346$	−21.3530	−	36.9845i	−1.14794	−	1.98830i
$347$	14.5416	+	25.1868i	0.780636	+	1.35210i	0.931572	+	0.363557i	$0.118438\pi$
$347$	14.5416	+	25.1868i	0.780636	+	1.35210i	−0.150936	+	0.988544i	$0.548229\pi$
$348$		0			0
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	0.979885	+	0.199561i	$0.0639515\pi$
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	−0.317118	+	0.948386i	$0.602715\pi$
$350$		0			0
$351$		0			0
$352$	1.21780	+	2.10929i	0.0649089	+	0.112426i
$353$	−33.3025			−1.77251			−0.886257	−	0.463193i	$-0.846704\pi$
$353$	−33.3025			−1.77251			−0.886257	+	0.463193i	$0.846704\pi$
$354$		0			0
$355$	8.48968			0.450586
$356$	29.1015	−	50.4052i	1.54237	−	2.67147i
$357$		0			0
$358$	−13.9626	−	24.1840i	−0.737949	−	1.27816i
$359$	12.7683	+	22.1153i	0.673884	+	1.16720i	0.976794	+	0.214182i	$0.0687087\pi$
$359$	12.7683	+	22.1153i	0.673884	+	1.16720i	−0.302909	+	0.953019i	$0.597958\pi$
$360$		0			0
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$	26.9289	−	46.6422i	1.41535	−	2.45146i
$363$		0			0
$364$		0			0
$365$	1.95477	−	3.38576i	0.102317	−	0.177219i
$366$		0			0
$367$	−27.4504			−1.43290			−0.716449	−	0.697639i	$-0.754234\pi$
$367$	−27.4504			−1.43290			−0.716449	+	0.697639i	$0.754234\pi$
$368$	−0.591443	+	1.02441i	−0.0308311	+	0.0534011i
$369$		0			0
$370$	−11.3638			−0.590776
$371$		0			0
$372$		0			0
$373$	16.3274			0.845402			0.422701	−	0.906269i	$-0.361082\pi$
$373$	16.3274			0.845402			0.422701	+	0.906269i	$0.361082\pi$
$374$	−5.25370	−	9.09967i	−0.271662	−	0.470533i
$375$		0			0
$376$	30.7345	−	53.2338i	1.58501	−	2.74532i
$377$	2.46050			0.126722
$378$		0			0
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	21.3135	−	36.9161i	1.09336	−	1.89376i
$381$		0			0
$382$	−0.863327	−	1.49533i	−0.0441716	−	0.0765075i
$383$	−12.4356			−0.635429			−0.317715	−	0.948186i	$-0.602915\pi$
$383$	−12.4356			−0.635429			−0.317715	+	0.948186i	$0.602915\pi$
$384$		0			0
$385$		0			0
$386$	29.8817			1.52094
$387$		0			0
$388$	−23.2901	+	40.3396i	−1.18237	+	2.04793i
$389$	−20.6008			−1.04450			−0.522250	−	0.852792i	$-0.674907\pi$
$389$	−20.6008			−1.04450			−0.522250	+	0.852792i	$0.674907\pi$
$390$		0			0
$391$	0.129281	−	0.223922i	0.00653803	−	0.0113242i
$392$		0			0
$393$		0			0
$394$	−20.1893	+	34.9689i	−1.01712	+	1.76171i
$395$	19.0744	−	33.0378i	0.959738	−	1.66231i
$396$		0			0
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	−0.993804	−	0.111146i	$-0.964548\pi$
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	0.400647	−	0.916233i	$-0.368785\pi$
$398$	27.9341	+	48.3833i	1.40021	+	2.42524i
$399$		0			0
$400$	−3.73599	+	6.47092i	−0.186799	+	0.323546i
$401$	2.56440			0.128060			0.0640300	−	0.997948i	$-0.479605\pi$
$401$	2.56440			0.128060			0.0640300	+	0.997948i	$0.479605\pi$
$402$		0			0
$403$	2.32743			0.115938
$404$	7.45904	+	12.9194i	0.371101	+	0.642766i
$405$		0			0
$406$		0			0
$407$	4.01965	+	6.96224i	0.199247	+	0.345105i
$408$		0			0
$409$	−17.1623	−	29.7259i	−0.848619	−	1.46985i	−0.882441	−	0.470423i	$-0.844101\pi$
$409$	−17.1623	−	29.7259i	−0.848619	−	1.46985i	0.0338223	−	0.999428i	$-0.489232\pi$
$410$	−20.4413	−	35.4054i	−1.00953	−	1.74855i
$411$		0			0
$412$	−19.7163	−	34.1497i	−0.971354	−	1.68243i
$413$		0			0
$414$		0			0
$415$	−1.22665	−	2.12463i	−0.0602141	−	0.104294i
$416$	−0.539495			−0.0264509
$417$		0			0
$418$	−45.0335			−2.20266
$419$	−2.02850	+	3.51347i	−0.0990989	+	0.171644i	−0.911312	−	0.411717i	$-0.864929\pi$
$419$	−2.02850	+	3.51347i	−0.0990989	+	0.171644i	0.812213	+	0.583361i	$0.198263\pi$
$420$		0			0
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	0.999879	+	0.0155624i	$0.00495387\pi$
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	−0.486462	+	0.873702i	$0.661713\pi$
$422$	−5.61177	−	9.71987i	−0.273177	−	0.473156i
$423$		0			0
$424$	−15.8530	+	27.4582i	−0.769890	+	1.33349i
$425$	0.816635	−	1.41445i	0.0396126	−	0.0686110i
$426$		0			0
$427$		0			0
$428$	−2.78580	+	4.82515i	−0.134657	+	0.233232i
$429$		0			0
$430$	66.5949			3.21149
$431$	11.3092	−	19.5882i	0.544747	−	0.943530i	−0.453876	−	0.891065i	$-0.649959\pi$
$431$	11.3092	−	19.5882i	0.544747	−	0.943530i	0.998623	−	0.0524646i	$-0.0167077\pi$
$432$		0			0
$433$	−2.41789			−0.116196			−0.0580982	−	0.998311i	$-0.518504\pi$
$433$	−2.41789			−0.116196			−0.0580982	+	0.998311i	$0.518504\pi$
$434$		0			0
$435$		0			0
$436$	−13.7807			−0.659978
$437$	−0.554084	−	0.959702i	−0.0265054	−	0.0459088i
$438$		0			0
$439$	−11.7448	+	20.3427i	−0.560551	+	0.970902i	0.436898	+	0.899511i	$0.356077\pi$
$439$	−11.7448	+	20.3427i	−0.560551	+	0.970902i	−0.997448	+	0.0713911i	$0.977256\pi$
$440$	59.1780			2.82120
$441$		0			0
$442$	2.32743			0.110705
$443$	−6.70895	+	11.6202i	−0.318752	+	0.552094i	−0.980228	−	0.197872i	$-0.936597\pi$
$443$	−6.70895	+	11.6202i	−0.318752	+	0.552094i	0.661476	+	0.749966i	$0.269930\pi$
$444$		0			0
$445$	−18.6175	−	32.2465i	−0.882554	−	1.52863i
$446$	−32.7850			−1.55242
$447$		0			0
$448$		0			0
$449$	9.16225			0.432393			0.216197	−	0.976350i	$-0.430635\pi$
$449$	9.16225			0.432393			0.216197	+	0.976350i	$0.430635\pi$
$450$		0			0
$451$	−14.4612	+	25.0475i	−0.680950	+	1.17944i
$452$	−42.1167			−1.98100
$453$		0			0
$454$	−1.69961	+	2.94381i	−0.0797667	+	0.138160i
$455$		0			0
$456$		0			0
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	−0.950522	−	0.310658i	$-0.899451\pi$
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	0.744298	+	0.667847i	$0.232784\pi$
$458$	−22.1192	+	38.3115i	−1.03356	+	1.79018i
$459$		0			0
$460$	1.43706	+	2.48906i	0.0670033	+	0.116053i
$461$	2.82957	+	4.90095i	0.131786	+	0.228260i	0.924365	−	0.381509i	$-0.124595\pi$
$461$	2.82957	+	4.90095i	0.131786	+	0.228260i	−0.792579	+	0.609769i	$0.791262\pi$
$462$		0			0
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	−0.988847	−	0.148937i	$-0.952415\pi$
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	0.623407	+	0.781898i	$0.285748\pi$
$464$	−10.6477			−0.494305
$465$		0			0
$466$	46.7060			2.16361
$467$	10.9985	+	19.0500i	0.508952	+	0.881530i	0.999946	+	0.0103675i	$0.00330013\pi$
$467$	10.9985	+	19.0500i	0.508952	+	0.881530i	−0.490995	+	0.871163i	$0.663367\pi$
$468$		0			0
$469$		0			0
$470$	−38.8068	−	67.2153i	−1.79002	−	3.10041i
$471$		0			0
$472$	6.89037	+	11.9345i	0.317155	+	0.549328i
$473$	−23.5562	−	40.8006i	−1.08312	−	1.87601i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$	6.01819	+	10.4238i	0.275265	+	0.476774i
$479$	24.9751			1.14114			0.570571	−	0.821249i	$-0.306722\pi$
$479$	24.9751			1.14114			0.570571	+	0.821249i	$0.306722\pi$
$480$		0			0
$481$	−1.78074			−0.0811947
$482$	−32.1826	+	55.7419i	−1.46588	+	2.53897i
$483$		0			0
$484$	−19.0167	−	32.9379i	−0.864397	−	1.49718i
$485$	14.8997	+	25.8070i	0.676561	+	1.17184i
$486$		0			0
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	−0.594851	−	0.803836i	$-0.702789\pi$
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	0.993568	+	0.113238i	$0.0361221\pi$
$488$	−5.74484	+	9.95036i	−0.260057	+	0.450432i
$489$		0			0
$490$		0			0
$491$	6.89757	−	11.9469i	0.311283	−	0.539158i	−0.667358	−	0.744737i	$-0.732575\pi$
$491$	6.89757	−	11.9469i	0.311283	−	0.539158i	0.978640	+	0.205580i	$0.0659080\pi$
$492$		0			0
$493$	2.32743			0.104822
$494$	4.98755	−	8.63868i	0.224400	−	0.388673i
$495$		0			0
$496$	−10.0718			−0.452237
$497$		0			0
$498$		0			0
$499$	13.0875			0.585879			0.292939	−	0.956131i	$-0.405367\pi$
$499$	13.0875			0.585879			0.292939	+	0.956131i	$0.405367\pi$
$500$	−17.2089	−	29.8068i	−0.769607	−	1.33300i
$501$		0			0
$502$	−22.7075	+	39.3305i	−1.01348	+	1.75541i
$503$	−22.3068			−0.994611			−0.497305	−	0.867576i	$-0.665677\pi$
$503$	−22.3068			−0.994611			−0.497305	+	0.867576i	$0.665677\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$	1.51819	−	2.62958i	0.0674917	−	0.116899i
$507$		0			0
$508$	−1.36333	−	2.36135i	−0.0604879	−	0.104768i
$509$	−15.8932			−0.704453			−0.352226	−	0.935915i	$-0.614575\pi$
$509$	−15.8932			−0.704453			−0.352226	+	0.935915i	$0.614575\pi$
$510$		0			0
$511$		0			0
$512$	−41.4078			−1.82998
$513$		0			0
$514$	14.4356	−	25.0032i	0.636727	−	1.10284i
$515$	−25.2268			−1.11163
$516$		0			0
$517$	−27.4538	+	47.5514i	−1.20742	+	2.09131i
$518$		0			0
$519$		0			0
$520$	−6.55408	+	11.3520i	−0.287416	+	0.497818i
$521$	−2.20895	+	3.82600i	−0.0967756	+	0.167620i	−0.910348	−	0.413843i	$-0.864186\pi$
$521$	−2.20895	+	3.82600i	−0.0967756	+	0.167620i	0.813573	+	0.581463i	$0.197520\pi$
$522$		0			0
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	0.998089	+	0.0617982i	$0.0196835\pi$
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	−0.445526	+	0.895269i	$0.646983\pi$
$524$	−16.0416	−	27.7849i	−0.700782	−	1.21379i
$525$		0			0
$526$	−9.25370	+	16.0279i	−0.403480	+	0.698848i
$527$	2.20155			0.0959012
$528$		0			0
$529$	−22.9253			−0.996751
$530$	20.0167	+	34.6700i	0.869471	+	1.50597i
$531$		0			0
$532$		0			0
$533$	−3.20321	−	5.54812i	−0.138746	−	0.240316i
$534$		0			0
$535$	1.78220	+	3.08686i	0.0770513	+	0.133457i
$536$	39.9705	+	69.2310i	1.72646	+	2.99032i
$537$		0			0
$538$	23.1716	+	40.1344i	0.998998	+	1.73032i
$539$		0			0
$540$		0			0
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	0.900615	−	0.434618i	$-0.143117\pi$
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	−0.826698	+	0.562646i	$0.809783\pi$
$542$	59.0085			2.53463
$543$		0			0
$544$	−0.510317			−0.0218797
$545$	−4.40808	+	7.63501i	−0.188821	+	0.327048i
$546$		0			0
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	0.930531	−	0.366214i	$-0.119346\pi$
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	−0.782416	+	0.622756i	$0.786013\pi$
$548$	−7.44445	−	12.8942i	−0.318011	−	0.550812i
$549$		0			0
$550$	9.58998	−	16.6103i	0.408918	−	0.708267i
$551$	4.98755	−	8.63868i	0.212477	−	0.368020i
$552$		0			0
$553$		0			0
$554$	−8.81138	+	15.2618i	−0.374360	+	0.648410i
$555$		0			0
$556$	8.32743			0.353162
$557$	16.7917	−	29.0841i	0.711488	−	1.23233i	−0.252810	−	0.967516i	$-0.581355\pi$
$557$	16.7917	−	29.0841i	0.711488	−	1.23233i	0.964298	−	0.264818i	$-0.0853119\pi$
$558$		0			0
$559$	10.4356			0.441379
$560$		0			0
$561$		0			0
$562$	−36.6165			−1.54457
$563$	−21.2396	−	36.7880i	−0.895142	−	1.55043i	−0.833629	−	0.552325i	$-0.813741\pi$
$563$	−21.2396	−	36.7880i	−0.895142	−	1.55043i	−0.0615128	−	0.998106i	$-0.519593\pi$
$564$		0			0
$565$	−13.4720	+	23.3341i	−0.566770	+	0.981675i
$566$	−49.2029			−2.06815
$567$		0			0
$568$	−16.5438			−0.694161
$569$	5.20175	−	9.00969i	0.218069	−	0.377706i	−0.736149	−	0.676820i	$-0.763358\pi$
$569$	5.20175	−	9.00969i	0.218069	−	0.377706i	0.954217	+	0.299114i	$0.0966910\pi$
$570$		0			0
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	0.616609	−	0.787270i	$-0.288506\pi$
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	−0.990100	+	0.140364i	$0.955173\pi$
$572$	18.3025			0.765267
$573$		0			0
$574$		0			0
$575$	0.471974			0.0196827
$576$		0			0
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	−0.714540	−	0.699595i	$-0.753364\pi$
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	0.963137	+	0.269013i	$0.0866973\pi$
$578$	−39.6270			−1.64827
$579$		0			0
$580$	−12.9356	+	22.4051i	−0.537122	+	0.930322i
$581$		0			0
$582$		0			0
$583$	14.1608	−	24.5272i	0.586480	−	1.01581i
$584$	−3.80924	+	6.59780i	−0.157628	+	0.273019i
$585$		0			0
$586$	−18.5344	−	32.1026i	−0.765650	−	1.32615i
$587$	−11.9299	−	20.6631i	−0.492398	−	0.852859i	0.507563	−	0.861614i	$-0.330546\pi$
$587$	−11.9299	−	20.6631i	−0.492398	−	0.852859i	−0.999962	+	0.00875568i	$0.997213\pi$
$588$		0			0
$589$	4.71780	−	8.17147i	0.194394	−	0.336699i
$590$	17.4002			0.716354
$591$		0			0
$592$	7.70602			0.316715
$593$	−9.79007	−	16.9569i	−0.402030	−	0.696336i	0.591941	−	0.805981i	$-0.298362\pi$
$593$	−9.79007	−	16.9569i	−0.402030	−	0.696336i	−0.993971	+	0.109645i	$0.965029\pi$
$594$		0			0
$595$		0			0
$596$	−27.4538	−	47.5514i	−1.12455	−	1.94778i
$597$		0			0
$598$	0.336285	+	0.582462i	0.0137517	+	0.0238187i
$599$	9.27335	+	16.0619i	0.378899	+	0.656272i	0.990902	−	0.134583i	$-0.0429696\pi$
$599$	9.27335	+	16.0619i	0.378899	+	0.656272i	−0.612004	+	0.790855i	$0.709636\pi$
$600$		0			0
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	0.618577	−	0.785724i	$-0.287710\pi$
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	−0.989746	+	0.142841i	$0.954376\pi$
$602$		0			0
$603$		0			0
$604$	−20.1249	−	34.8573i	−0.818870	−	1.41832i
$605$	−24.3317			−0.989224
$606$		0			0
$607$	22.3097			0.905524			0.452762	−	0.891631i	$-0.350439\pi$
$607$	22.3097			0.905524			0.452762	+	0.891631i	$0.350439\pi$
$608$	−1.09358	+	1.89413i	−0.0443505	+	0.0768173i
$609$		0			0
$610$	7.25370	+	12.5638i	0.293694	+	0.508692i
$611$	−6.08113	−	10.5328i	−0.246016	−	0.426112i
$612$		0			0
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	−0.950684	−	0.310162i	$-0.899617\pi$
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	0.743950	+	0.668235i	$0.232950\pi$
$614$	−33.5495	+	58.1094i	−1.35395	+	2.34511i
$615$		0			0
$616$		0			0
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	−0.957219	−	0.289364i	$-0.906556\pi$
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	0.729206	+	0.684294i	$0.239889\pi$
$618$		0			0
$619$	−8.63327			−0.347000			−0.173500	−	0.984834i	$-0.555508\pi$
$619$	−8.63327			−0.347000			−0.173500	+	0.984834i	$0.555508\pi$
$620$	−12.2360	+	21.1934i	−0.491409	+	0.851145i
$621$		0			0
$622$	−39.3245			−1.57677
$623$		0			0
$624$		0			0
$625$	−30.6519			−1.22608
$626$	14.2683	+	24.7134i	0.570275	+	0.987746i
$627$		0			0
$628$	12.2719	−	21.2555i	0.489701	−	0.848188i
$629$	−1.68443			−0.0671626
$630$		0			0
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	−37.1701	+	64.3805i	−1.47855	+	2.56092i
$633$		0			0
$634$	−2.48229	−	4.29945i	−0.0985844	−	0.170753i
$635$	−1.74436			−0.0692229
$636$		0			0
$637$		0			0
$638$	27.3317			1.08207
$639$		0			0
$640$	−24.7793	+	42.9190i	−0.979487	+	1.69652i
$641$	34.1593			1.34921			0.674606	−	0.738178i	$-0.264313\pi$
$641$	34.1593			1.34921			0.674606	+	0.738178i	$0.264313\pi$
$642$		0			0
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	−0.952852	−	0.303437i	$-0.901866\pi$
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	0.739210	+	0.673475i	$0.235199\pi$
$644$		0			0
$645$		0			0
$646$	4.71780	−	8.17147i	0.185619	−	0.321502i
$647$	−16.4846	+	28.5522i	−0.648077	+	1.12250i	0.335504	+	0.942039i	$0.391093\pi$
$647$	−16.4846	+	28.5522i	−0.648077	+	1.12250i	−0.983582	+	0.180464i	$0.942240\pi$
$648$		0			0
$649$	−6.15486	−	10.6605i	−0.241599	−	0.418462i
$650$	2.12422	+	3.67926i	0.0833188	+	0.144312i
$651$		0			0
$652$	−36.1160	+	62.5548i	−1.41441	+	2.44984i
$653$	3.93113			0.153837			0.0769185	−	0.997037i	$-0.475492\pi$
$653$	3.93113			0.153837			0.0769185	+	0.997037i	$0.475492\pi$
$654$		0			0
$655$	−20.5251			−0.801982
$656$	13.8617	+	24.0091i	0.541207	+	0.937399i
$657$		0			0
$658$		0			0
$659$	8.40856	+	14.5640i	0.327551	+	0.567335i	0.982025	−	0.188749i	$-0.0604434\pi$
$659$	8.40856	+	14.5640i	0.327551	+	0.567335i	−0.654474	+	0.756084i	$0.727110\pi$
$660$		0			0
$661$	−8.51080	−	14.7411i	−0.331032	−	0.573364i	0.651683	−	0.758492i	$-0.274063\pi$
$661$	−8.51080	−	14.7411i	−0.331032	−	0.573364i	−0.982714	+	0.185128i	$0.940730\pi$
$662$	24.2470	+	41.9970i	0.942386	+	1.63226i
$663$		0			0
$664$	2.39037	+	4.14024i	0.0927643	+	0.160672i
$665$		0			0
$666$		0			0
$667$	0.336285	+	0.582462i	0.0130210	+	0.0225530i
$668$	−34.3288			−1.32822
$669$		0			0
$670$	100.937			3.89954
$671$	5.13161	−	8.88821i	0.198104	−	0.343126i
$672$		0			0
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	−0.997979	−	0.0635501i	$-0.979758\pi$
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	0.443953	−	0.896050i	$-0.353576\pi$
$674$	35.7403	+	61.9039i	1.37666	+	2.38445i
$675$		0			0
$676$	24.3245	−	42.1313i	0.935558	−	1.62043i
$677$	3.01819	−	5.22765i	0.115998	−	0.200915i	−0.802180	−	0.597082i	$-0.796327\pi$
$677$	3.01819	−	5.22765i	0.115998	−	0.200915i	0.918178	+	0.396167i	$0.129660\pi$
$678$		0			0
$679$		0			0
$680$	−6.19961	+	10.7380i	−0.237744	+	0.411785i
$681$		0			0
$682$	25.8535			0.989981
$683$	10.2556	−	17.7633i	0.392421	−	0.679693i	−0.600347	−	0.799739i	$-0.704971\pi$
$683$	10.2556	−	17.7633i	0.392421	−	0.679693i	0.992768	+	0.120046i	$0.0383043\pi$
$684$		0			0
$685$	−9.52510			−0.363935
$686$		0			0
$687$		0			0
$688$	−45.1593			−1.72168
$689$	3.13667	+	5.43288i	0.119498	+	0.206976i
$690$		0			0
$691$	−7.50146	+	12.9929i	−0.285369	+	0.494274i	−0.972699	−	0.232072i	$-0.925450\pi$
$691$	−7.50146	+	12.9929i	−0.285369	+	0.494274i	0.687330	+	0.726346i	$0.258783\pi$
$692$	70.3652			2.67488
$693$		0			0
$694$	−71.5595			−2.71636
$695$	2.66372	−	4.61369i	0.101040	−	0.175007i
$696$		0			0
$697$	−3.02997	−	5.24806i	−0.114768	−	0.198784i
$698$	−60.9296			−2.30622
$699$		0			0
$700$		0			0
$701$	−38.5113			−1.45455			−0.727275	−	0.686346i	$-0.759214\pi$
$701$	−38.5113			−1.45455			−0.727275	+	0.686346i	$0.759214\pi$
$702$		0			0
$703$	−3.60963	+	6.25206i	−0.136140	+	0.235801i
$704$	33.0803			1.24676
$705$		0			0
$706$	40.9705	−	70.9630i	1.54195	−	2.67073i
$707$		0			0
$708$		0			0
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	−0.928799	−	0.370584i	$-0.879158\pi$
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	0.785334	+	0.619072i	$0.212491\pi$
$710$	−10.4445	+	18.0903i	−0.391973	+	0.678918i
$711$		0			0
$712$	36.2798	+	62.8384i	1.35964	+	2.35497i
$713$	0.318097	+	0.550960i	0.0119128	+	0.0206336i
$714$		0			0
$715$	5.85447	−	10.1402i	0.218945	−	0.379224i
$716$	46.0115			1.71953
$717$		0			0
$718$	−62.8329			−2.34490
$719$	15.0182	+	26.0123i	0.560084	+	0.970094i	0.997488	+	0.0708289i	$0.0225644\pi$
$719$	15.0182	+	26.0123i	0.560084	+	0.970094i	−0.437405	+	0.899265i	$0.644102\pi$
$720$		0			0
$721$		0			0
$722$	3.15486	+	5.46438i	0.117412	+	0.203363i
$723$		0			0
$724$	44.3697	+	76.8506i	1.64899	+	2.85613i
$725$	2.12422	+	3.67926i	0.0788916	+	0.136644i
$726$		0			0
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	0.896291	−	0.443466i	$-0.146251\pi$
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	−0.832199	+	0.554478i	$0.812918\pi$
$728$		0			0
$729$		0			0
$730$	4.80972	+	8.33068i	0.178016	+	0.308332i
$731$	9.87120			0.365099
$732$		0			0
$733$	−38.5261			−1.42299			−0.711496	−	0.702690i	$-0.751982\pi$
$733$	−38.5261			−1.42299			−0.711496	+	0.702690i	$0.751982\pi$
$734$	33.7709	−	58.4929i	1.24651	−	2.15901i
$735$		0			0
$736$	−0.0737345	−	0.127712i	−0.00271789	−	0.00470752i
$737$	−35.7039	−	61.8409i	−1.31517	−	2.27794i
$738$		0			0
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	0.0681179	+	0.997677i	$0.478301\pi$
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	−0.898073	+	0.439847i	$0.855033\pi$
$740$	9.36186	−	16.2152i	0.344149	−	0.596084i
$741$		0			0
$742$		0			0
$743$	4.74338	−	8.21577i	0.174018	−	0.301407i	−0.765803	−	0.643075i	$-0.777658\pi$
$743$	4.74338	−	8.21577i	0.174018	−	0.301407i	0.939821	+	0.341668i	$0.110992\pi$
$744$		0			0
$745$	−35.1268			−1.28695
$746$	−20.0869	+	34.7915i	−0.735432	+	1.27381i
$747$		0			0
$748$	17.3126			0.633013
$749$		0			0
$750$		0			0
$751$	−9.83190			−0.358771			−0.179386	−	0.983779i	$-0.557411\pi$
$751$	−9.83190			−0.358771			−0.179386	+	0.983779i	$0.557411\pi$
$752$	26.3157	+	45.5800i	0.959633	+	1.66213i
$753$		0			0
$754$	−3.02704	+	5.24299i	−0.110238	+	0.190938i
$755$	−25.7496			−0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	−14.8078	+	25.6478i	−0.537843	+	0.931571i
$759$		0			0
$760$	26.5708	+	46.0220i	0.963825	+	1.66939i
$761$	22.9794			0.833001			0.416501	−	0.909135i	$-0.363256\pi$
$761$	22.9794			0.833001			0.416501	+	0.909135i	$0.363256\pi$
$762$		0			0
$763$		0			0
$764$	2.84494			0.102926
$765$		0			0
$766$	15.2989	−	26.4985i	0.552773	−	0.957430i
$767$	2.72665			0.0984538
$768$		0			0
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	−0.805923	−	0.592021i	$-0.798330\pi$
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	0.915666	+	0.401939i	$0.131664\pi$
$770$		0			0
$771$		0			0
$772$	−24.6175	+	42.6388i	−0.886003	+	1.53460i
$773$	20.9107	−	36.2184i	0.752105	−	1.30268i	−0.194695	−	0.980864i	$-0.562372\pi$
$773$	20.9107	−	36.2184i	0.752105	−	1.30268i	0.946801	−	0.321821i	$-0.104295\pi$
$774$		0			0
$775$	2.00933	+	3.48027i	0.0721774	+	0.125015i
$776$	−29.0349	−	50.2899i	−1.04229	−	1.80530i
$777$		0			0
$778$	25.3442	−	43.8974i	0.908632	−	1.57380i
$779$	−25.9722			−0.930550
$780$		0			0
$781$	14.7778			0.528792
$782$	0.318097	+	0.550960i	0.0113751	+	0.0197023i
$783$		0			0
$784$		0			0
$785$	−7.85087	−	13.5981i	−0.280210	−	0.485337i
$786$		0			0
$787$	16.1460	+	27.9657i	0.575543	+	0.996870i	0.995982	+	0.0895491i	$0.0285426\pi$
$787$	16.1460	+	27.9657i	0.575543	+	0.996870i	−0.420439	+	0.907321i	$0.638124\pi$
$788$	−33.2652	−	57.6170i	−1.18502	−	2.05252i
$789$		0			0
$790$	46.9327	+	81.2898i	1.66979	+	2.89216i
$791$		0			0
$792$		0			0
$793$	1.13667	+	1.96878i	0.0403644	+	0.0699133i
$794$	58.1593			2.06400
$795$		0			0
$796$	−92.0521			−3.26270
$797$	−23.2829	+	40.3271i	−0.824722	+	1.42846i	0.0774101	+	0.996999i	$0.475335\pi$
$797$	−23.2829	+	40.3271i	−0.824722	+	1.42846i	−0.902132	+	0.431461i	$0.857998\pi$
$798$		0			0
$799$	−5.75223	−	9.96316i	−0.203499	−	0.352471i
$800$	−0.465761	−	0.806721i	−0.0164671	−	0.0285219i
$801$		0			0
$802$	−3.15486	+	5.46438i	−0.111402	+	0.192954i
$803$	3.40263	−	5.89352i	0.120076	−	0.207978i
$804$		0			0
$805$		0			0
$806$	−2.86333	+	4.95943i	−0.100856	+	0.174688i
$807$		0			0
$808$	−18.5979			−0.654270
$809$	−5.40116	+	9.35509i	−0.189895	+	0.328908i	−0.945215	−	0.326448i	$-0.894148\pi$
$809$	−5.40116	+	9.35509i	−0.189895	+	0.328908i	0.755320	+	0.655356i	$0.227481\pi$
$810$		0			0
$811$	−5.58307			−0.196048			−0.0980240	−	0.995184i	$-0.531252\pi$
$811$	−5.58307			−0.196048			−0.0980240	+	0.995184i	$0.531252\pi$
$812$		0			0
$813$		0			0
$814$	−19.7807			−0.693315
$815$	23.1050	+	40.0191i	0.809335	+	1.40181i
$816$		0			0
$817$	21.1534	−	36.6388i	0.740064	−	1.28183i
$818$	84.4556			2.95292
$819$		0			0
$820$	67.3609			2.35234
$821$	−15.8940	+	27.5292i	−0.554703	+	0.960774i	0.443223	+	0.896411i	$0.353835\pi$
$821$	−15.8940	+	27.5292i	−0.554703	+	0.960774i	−0.997927	+	0.0643630i	$0.979498\pi$
$822$		0			0
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	49.1593			1.71255
$825$		0			0
$826$		0			0
$827$	−15.9224			−0.553675			−0.276837	−	0.960917i	$-0.589286\pi$
$827$	−15.9224			−0.553675			−0.276837	+	0.960917i	$0.589286\pi$
$828$		0			0
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	−0.374213	−	0.927343i	$-0.622087\pi$
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	0.990209	−	0.139594i	$-0.0445797\pi$
$830$	6.03638			0.209526
$831$		0			0
$832$	−3.66372	+	6.34574i	−0.127016	+	0.219999i
$833$		0			0
$834$		0			0
$835$	−10.9808	+	19.0194i	−0.380007	+	0.658192i
$836$	37.1000	−	64.2591i	1.28313	−	2.22245i
$837$		0			0
$838$	−4.99115	−	8.64492i	−0.172416	−	0.298634i
$839$	27.3391	+	47.3527i	0.943850	+	1.63480i	0.758037	+	0.652212i	$0.226159\pi$
$839$	27.3391	+	47.3527i	0.943850	+	1.63480i	0.185814	+	0.982585i	$0.440508\pi$
$840$		0			0
$841$	11.4730	−	19.8717i	0.395619	−	0.685233i
$842$	−51.8401			−1.78653
$843$		0			0
$844$	18.4926			0.636542
$845$	−15.5615	−	26.9533i	−0.535331	−	0.927221i
$846$		0			0
$847$		0			0
$848$	−13.5737	−	23.5104i	−0.466124	−	0.807350i
$849$		0			0
$850$	2.00933	+	3.48027i	0.0689196	+	0.119372i
$851$	−0.243379	−	0.421545i	−0.00834292	−	0.0144504i
$852$		0			0
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	0.846601	−	0.532229i	$-0.178645\pi$
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	−0.884224	+	0.467063i	$0.845312\pi$
$854$		0			0
$855$		0			0
$856$	−3.47296	−	6.01534i	−0.118703	−	0.205600i
$857$	−15.7765			−0.538914			−0.269457	−	0.963012i	$-0.586844\pi$
$857$	−15.7765			−0.538914			−0.269457	+	0.963012i	$0.586844\pi$
$858$		0			0
$859$	−5.57626			−0.190260			−0.0951298	−	0.995465i	$-0.530327\pi$
$859$	−5.57626			−0.190260			−0.0951298	+	0.995465i	$0.530327\pi$
$860$	−54.8630	+	95.0255i	−1.87081	+	3.24034i
$861$		0			0
$862$	27.8264	+	48.1968i	0.947773	+	1.64159i
$863$	11.5634	+	20.0284i	0.393623	+	0.681776i	0.992924	−	0.118748i	$-0.0378881\pi$
$863$	11.5634	+	20.0284i	0.393623	+	0.681776i	−0.599301	+	0.800524i	$0.704555\pi$
$864$		0			0
$865$	22.5079	−	38.9848i	0.765291	−	1.32552i
$866$	2.97462	−	5.15218i	0.101082	−	0.175078i
$867$		0			0
$868$		0			0
$869$	33.2024	−	57.5083i	1.12631	−	1.95083i
$870$		0			0
$871$	15.8171			0.535942
$872$	8.58998	−	14.8783i	0.290893	−	0.503842i
$873$		0			0
$874$	2.72665			0.0922304
$875$		0			0
$876$		0			0
$877$	3.92528			0.132547			0.0662737	−	0.997801i	$-0.478889\pi$
$877$	3.92528			0.132547			0.0662737	+	0.997801i	$0.478889\pi$
$878$	−28.8982	−	50.0532i	−0.975268	−	1.68921i
$879$		0			0
$880$	−25.3348	+	43.8812i	−0.854037	+	1.47923i
$881$	27.1986			0.916345			0.458173	−	0.888863i	$-0.348504\pi$
$881$	27.1986			0.916345			0.458173	+	0.888863i	$0.348504\pi$
$882$		0			0
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	−1.91741	+	3.32105i	−0.0644895	+	0.111699i
$885$		0			0
$886$	−16.5074	−	28.5916i	−0.554577	−	0.960555i
$887$	−6.48114			−0.217615			−0.108808	−	0.994063i	$-0.534703\pi$
$887$	−6.48114			−0.217615			−0.108808	+	0.994063i	$0.534703\pi$
$888$		0			0
$889$		0			0
$890$	91.6169			3.07101
$891$		0			0
$892$	27.0093	−	46.7815i	0.904339	−	1.56636i
$893$	−49.3068			−1.64999
$894$		0			0
$895$	14.7178	−	25.4920i	0.491962	−	0.852103i
$896$		0			0
$897$		0			0
$898$	−11.2719	+	19.5235i	−0.376148	+	0.651507i
$899$	−2.86333	+	4.95943i	−0.0954973	+	0.165406i
$900$		0			0
$901$	2.96703	+	5.13904i	0.0988461	+	0.171206i
$902$	−35.5818	−	61.6295i	−1.18474	−	2.05204i
$903$		0			0
$904$	26.2527	−	45.4710i	0.873152	−	1.51234i
$905$	56.7706			1.88712
$906$		0			0
$907$	10.1288			0.336321			0.168161	−	0.985760i	$-0.446217\pi$
$907$	10.1288			0.336321			0.168161	+	0.985760i	$0.446217\pi$
$908$	−2.80039	−	4.85041i	−0.0929341	−	0.160967i
$909$		0			0
$910$		0			0
$911$	22.9612	+	39.7699i	0.760738	+	1.31764i	0.942471	+	0.334289i	$0.108496\pi$
$911$	22.9612	+	39.7699i	0.760738	+	1.31764i	−0.181733	+	0.983348i	$0.558171\pi$
$912$		0			0
$913$	−2.13521	−	3.69829i	−0.0706652	−	0.122396i
$914$	−10.8473	−	18.7880i	−0.358796	−	0.621453i
$915$		0			0
$916$	−36.4449	−	63.1245i	−1.20417	−	2.08569i
$917$		0			0
$918$		0			0
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	0.903774	−	0.428010i	$-0.140785\pi$
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	−0.822555	+	0.568686i	$0.807452\pi$
$920$	−3.58307			−0.118130
$921$		0			0
$922$	−13.9243			−0.458573
$923$	−1.63667	+	2.83480i	−0.0538718	+	0.0933086i
$924$		0			0
$925$	−1.53736	−	2.66278i	−0.0505481	−	0.0875518i
$926$	−19.3478	−	33.5113i	−0.635807	−	1.10125i
$927$		0			0
$928$	0.663715	−	1.14959i	0.0217875	−	0.0377371i
$929$	−0.00379324	+	0.00657009i	−0.000124452	+	0.000215558i	−0.866088	−	0.499892i	$-0.833373\pi$
$929$	−0.00379324	+	0.00657009i	−0.000124452	+	0.000215558i	0.865963	+	0.500108i	$0.166706\pi$
$930$		0			0
$931$		0			0
$932$	−38.4779	+	66.6457i	−1.26039	+	2.18305i
$933$		0			0
$934$	−54.1239			−1.77099
$935$	5.53784	−	9.59182i	0.181107	−	0.313686i
$936$		0			0
$937$	−21.1623			−0.691341			−0.345670	−	0.938356i	$-0.612348\pi$
$937$	−21.1623			−0.691341			−0.345670	+	0.938356i	$0.612348\pi$
$938$		0			0
$939$		0			0
$940$	127.881			4.17102
$941$	−2.27908	−	3.94748i	−0.0742959	−	0.128684i	0.826484	−	0.562960i	$-0.190338\pi$
$941$	−2.27908	−	3.94748i	−0.0742959	−	0.128684i	−0.900780	+	0.434276i	$0.857004\pi$
$942$		0			0
$943$	0.875585	−	1.51656i	0.0285130	−	0.0493859i
$944$	−11.7994			−0.384038
$945$		0			0
$946$	115.920			3.76890
$947$	6.86760	−	11.8950i	0.223167	−	0.386537i	−0.732601	−	0.680658i	$-0.761694\pi$
$947$	6.86760	−	11.8950i	0.223167	−	0.386537i	0.955768	+	0.294122i	$0.0950271\pi$
$948$		0			0
$949$	0.753696	+	1.30544i	0.0244660	+	0.0423764i
$950$	17.2235			0.558805
$951$		0			0
$952$		0			0
$953$	−8.80699			−0.285286			−0.142643	−	0.989774i	$-0.545560\pi$
$953$	−8.80699			−0.285286			−0.142643	+	0.989774i	$0.545560\pi$
$954$		0			0
$955$	0.910019	−	1.57620i	0.0294475	−	0.0510046i
$956$	−19.8319			−0.641409
$957$		0			0
$958$	−30.7257	+	53.2184i	−0.992701	+	1.71941i
$959$		0			0
$960$		0			0
$961$	12.7915	−	22.1556i	0.412630	−	0.714696i
$962$	2.19076	−	3.79450i	0.0706329	−	0.122340i
$963$		0			0
$964$	−53.0261	−	91.8438i	−1.70785	−	2.95809i
$965$	15.7489	+	27.2779i	0.506976	+	0.878108i
$966$		0			0
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	0.373880	+	0.927477i	$0.378027\pi$
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	−0.990159	+	0.139949i	$0.955306\pi$
$968$	47.4150			1.52397
$969$		0			0
$970$	−73.3216			−2.35421
$971$	15.5093	+	26.8630i	0.497718	+	0.862073i	0.999997	−	0.00263281i	$-0.000838049\pi$
$971$	15.5093	+	26.8630i	0.497718	+	0.862073i	−0.502278	+	0.864706i	$0.667505\pi$
$972$		0			0
$973$		0			0
$974$	21.6498	+	37.4986i	0.693704	+	1.20153i
$975$		0			0
$976$	−4.91887	−	8.51974i	−0.157449	−	0.272710i
$977$	−26.3712	−	45.6763i	−0.843689	−	1.46131i	−0.886755	−	0.462241i	$-0.847046\pi$
$977$	−26.3712	−	45.6763i	−0.843689	−	1.46131i	0.0430652	−	0.999072i	$-0.486288\pi$
$978$		0			0
$979$	−32.4071	−	56.1307i	−1.03574	−	1.79395i
$980$		0			0
$981$		0			0
$982$	16.9715	+	29.3955i	0.541582	+	0.938048i
$983$	−18.3029			−0.583772			−0.291886	−	0.956453i	$-0.594283\pi$
$983$	−18.3029			−0.583772			−0.291886	+	0.956453i	$0.594283\pi$
$984$		0			0
$985$	−42.5624			−1.35615
$986$	−2.86333	+	4.95943i	−0.0911869	+	0.157940i
$987$		0			0
$988$	8.21780	+	14.2336i	0.261443	+	0.452833i
$989$	1.42627	+	2.47036i	0.0453526	+	0.0785530i
$990$		0			0
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	−0.748434	−	0.663209i	$-0.769194\pi$
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	0.948573	+	0.316559i	$0.102527\pi$
$992$	0.627819	−	1.08741i	0.0199333	−	0.0345254i
$993$		0			0
$994$		0			0
$995$	−29.4449	+	51.0001i	−0.933467	+	1.61681i
$996$		0			0
$997$	−11.7424			−0.371885			−0.185943	−	0.982561i	$-0.559534\pi$
$997$	−11.7424			−0.371885			−0.185943	+	0.982561i	$0.559534\pi$
$998$	−16.1010	+	27.8877i	−0.509667	+	0.882770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.b.361.1		6
3.2	odd	2		441.2.g.d.67.3		6
7.2	even	3		1323.2.h.e.226.3		6
7.3	odd	6		189.2.f.a.64.1		6
7.4	even	3		1323.2.f.c.442.1		6
7.5	odd	6		1323.2.h.d.226.3		6
7.6	odd	2		1323.2.g.c.361.1		6
9.2	odd	6		441.2.h.b.214.1		6
9.7	even	3		1323.2.h.e.802.3		6
21.2	odd	6		441.2.h.b.373.1		6
21.5	even	6		441.2.h.c.373.1		6
21.11	odd	6		441.2.f.d.148.3		6
21.17	even	6		63.2.f.b.22.3	✓	6
21.20	even	2		441.2.g.e.67.3		6
28.3	even	6		3024.2.r.g.1009.2		6
63.2	odd	6		441.2.g.d.79.3		6
63.4	even	3		3969.2.a.p.1.3		3
63.11	odd	6		441.2.f.d.295.3		6
63.16	even	3	inner	1323.2.g.b.667.1		6
63.20	even	6		441.2.h.c.214.1		6
63.25	even	3		1323.2.f.c.883.1		6
63.31	odd	6		567.2.a.g.1.3		3
63.32	odd	6		3969.2.a.m.1.1		3
63.34	odd	6		1323.2.h.d.802.3		6
63.38	even	6		63.2.f.b.43.3	yes	6
63.47	even	6		441.2.g.e.79.3		6
63.52	odd	6		189.2.f.a.127.1		6
63.59	even	6		567.2.a.d.1.1		3
63.61	odd	6		1323.2.g.c.667.1		6
84.59	odd	6		1008.2.r.k.337.3		6
252.31	even	6		9072.2.a.cd.1.2		3
252.59	odd	6		9072.2.a.bq.1.2		3
252.115	even	6		3024.2.r.g.2017.2		6
252.227	odd	6		1008.2.r.k.673.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	21.17	even	6
63.2.f.b.43.3	yes	6	63.38	even	6
189.2.f.a.64.1		6	7.3	odd	6
189.2.f.a.127.1		6	63.52	odd	6
441.2.f.d.148.3		6	21.11	odd	6
441.2.f.d.295.3		6	63.11	odd	6
441.2.g.d.67.3		6	3.2	odd	2
441.2.g.d.79.3		6	63.2	odd	6
441.2.g.e.67.3		6	21.20	even	2
441.2.g.e.79.3		6	63.47	even	6
441.2.h.b.214.1		6	9.2	odd	6
441.2.h.b.373.1		6	21.2	odd	6
441.2.h.c.214.1		6	63.20	even	6
441.2.h.c.373.1		6	21.5	even	6
567.2.a.d.1.1		3	63.59	even	6
567.2.a.g.1.3		3	63.31	odd	6
1008.2.r.k.337.3		6	84.59	odd	6
1008.2.r.k.673.3		6	252.227	odd	6
1323.2.f.c.442.1		6	7.4	even	3
1323.2.f.c.883.1		6	63.25	even	3
1323.2.g.b.361.1		6	1.1	even	1	trivial
1323.2.g.b.667.1		6	63.16	even	3	inner
1323.2.g.c.361.1		6	7.6	odd	2
1323.2.g.c.667.1		6	63.61	odd	6
1323.2.h.d.226.3		6	7.5	odd	6
1323.2.h.d.802.3		6	63.34	odd	6
1323.2.h.e.226.3		6	7.2	even	3
1323.2.h.e.802.3		6	9.7	even	3
3024.2.r.g.1009.2		6	28.3	even	6
3024.2.r.g.2017.2		6	252.115	even	6
3969.2.a.m.1.1		3	63.32	odd	6
3969.2.a.p.1.3		3	63.4	even	3
9072.2.a.bq.1.2		3	252.59	odd	6
9072.2.a.cd.1.2		3	252.31	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} -2.59358 q^{5} +5.05408 q^{8} +O(q^{10})\)	\(q+(-1.23025 + 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} -2.59358 q^{5} +5.05408 q^{8} +(3.19076 - 5.52655i) q^{10} -4.51459 q^{11} +(0.500000 - 0.866025i) q^{13} +(-2.16372 + 3.74766i) q^{16} +(0.472958 - 0.819187i) q^{17} +(-2.02704 - 3.51094i) q^{19} +(5.25729 + 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +0.273346 q^{23} +1.72665 q^{25} +(1.23025 + 2.13086i) q^{26} +(1.23025 + 2.13086i) q^{29} +(1.16372 + 2.01561i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(1.16372 + 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} +9.97509 q^{38} -13.1082 q^{40} +(3.20321 - 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-2.12422 + 3.67926i) q^{50} -4.05408 q^{52} +(-3.13667 + 5.43288i) q^{53} +11.7089 q^{55} -6.05408 q^{58} +(1.36333 + 2.36135i) q^{59} +(-1.13667 + 1.96878i) q^{61} -5.72665 q^{62} -7.32743 q^{64} +(-1.29679 + 2.24611i) q^{65} +(7.90856 + 13.6980i) q^{67} -3.83482 q^{68} -3.27335 q^{71} +(-0.753696 + 1.30544i) q^{73} +4.38151 q^{74} +(-8.21780 + 14.2336i) q^{76} +(-7.35447 + 12.7383i) q^{79} +(5.61177 - 9.71987i) q^{80} +(7.88151 + 13.6512i) q^{82} +(0.472958 + 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} -25.6768 q^{86} -22.8171 q^{88} +(7.17830 + 12.4332i) q^{89} +(-0.554084 - 0.959702i) q^{92} +(14.9626 + 25.9161i) q^{94} +(5.25729 + 9.10590i) q^{95} +(-5.74484 - 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} - 10 q^{5} + 12 q^{8}+O(q^{10}) \) 6 * q - q^2 - 3 * q^4 - 10 * q^5 + 12 * q^8	\( 6 q - q^{2} - 3 q^{4} - 10 q^{5} + 12 q^{8} + 4 q^{11} + 3 q^{13} - 3 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} + q^{29} - 3 q^{31} - 8 q^{32} - 3 q^{34} + 3 q^{37} + 16 q^{38} - 42 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} + 9 q^{47} + 10 q^{50} - 6 q^{52} - 18 q^{53} + 12 q^{55} - 18 q^{58} + 9 q^{59} - 6 q^{61} - 36 q^{62} - 24 q^{64} - 5 q^{65} + 12 q^{68} - 18 q^{71} + 3 q^{73} - 12 q^{74} - 21 q^{76} - 15 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} - 68 q^{86} - 42 q^{88} + 2 q^{89} + 15 q^{92} + 24 q^{94} + 16 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 - 10 * q^5 + 12 * q^8 + 4 * q^11 + 3 * q^13 - 3 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 + 12 * q^25 + q^26 + q^29 - 3 * q^31 - 8 * q^32 - 3 * q^34 + 3 * q^37 + 16 * q^38 - 42 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 + 9 * q^47 + 10 * q^50 - 6 * q^52 - 18 * q^53 + 12 * q^55 - 18 * q^58 + 9 * q^59 - 6 * q^61 - 36 * q^62 - 24 * q^64 - 5 * q^65 + 12 * q^68 - 18 * q^71 + 3 * q^73 - 12 * q^74 - 21 * q^76 - 15 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 - 68 * q^86 - 42 * q^88 + 2 * q^89 + 15 * q^92 + 24 * q^94 + 16 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more