LMFDB - Embedded newform 1323.2.g.f.361.5

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.5
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.f.667.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +O(q^{10})$	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +(-0.150168 + 0.260099i) q^{10} -1.66404 q^{11} +(-0.0999454 + 0.173111i) q^{13} +(1.75890 - 3.04650i) q^{16} +(3.13555 - 5.43093i) q^{17} +(-3.45879 - 5.99080i) q^{19} +(0.162147 + 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +6.18184 q^{23} -4.97861 q^{25} +(0.205252 + 0.355508i) q^{26} +(2.46757 + 4.27396i) q^{29} +(-1.25890 - 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(-6.43931 - 11.1532i) q^{34} +(-3.50023 - 6.06257i) q^{37} -14.2062 q^{38} +0.0653107 q^{40} +(1.15895 - 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(0.905887 - 1.56904i) q^{47} +(-5.11215 + 8.85451i) q^{50} +0.443250 q^{52} +(2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +10.1350 q^{58} +(2.28549 + 3.95859i) q^{59} +(-0.339138 + 0.587404i) q^{61} -5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} -13.9059 q^{68} -1.27749 q^{71} +(0.778603 - 1.34858i) q^{73} -14.3765 q^{74} +(-7.66972 + 13.2843i) q^{76} +(-6.39787 + 11.0814i) q^{79} +(-0.257231 + 0.445537i) q^{80} +(-2.38008 - 4.12241i) q^{82} +(3.75687 + 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} -3.86493 q^{86} +0.743131 q^{88} +(4.53394 + 7.85301i) q^{89} +(-6.85398 - 11.8714i) q^{92} +(-1.86037 - 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(3.98514 + 6.90246i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8} + 7 q^{10} + 8 q^{11} + 8 q^{13} + 2 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} + 11 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} - 40 q^{38} - 6 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 27 q^{47} - 19 q^{50} - 20 q^{52} + 21 q^{53} - 4 q^{55} + 20 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 54 q^{68} + 6 q^{71} - 15 q^{73} - 72 q^{74} - 5 q^{76} - 4 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} + 28 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8 + 7 * q^10 + 8 * q^11 + 8 * q^13 + 2 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 + 11 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 - 40 * q^38 - 6 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 27 * q^47 - 19 * q^50 - 20 * q^52 + 21 * q^53 - 4 * q^55 + 20 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 54 * q^68 + 6 * q^71 - 15 * q^73 - 72 * q^74 - 5 * q^76 - 4 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 + 28 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * 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 $

$2$	1.02682	−	1.77851i	0.726073	−	1.25760i	−0.232458	−	0.972607i	$-0.574677\pi$
$2$	1.02682	−	1.77851i	0.726073	−	1.25760i	0.958531	−	0.284989i	$-0.0919900\pi$
$3$		0			0
$3$		0			0
$4$	−1.10873	−	1.92038i	−0.554365	−	0.960188i
$5$	−0.146246			−0.0654030			−0.0327015	−	0.999465i	$-0.510411\pi$
$5$	−0.146246			−0.0654030			−0.0327015	+	0.999465i	$0.510411\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.446582			−0.157891
$9$		0			0
$10$	−0.150168	+	0.260099i	−0.0474874	+	0.0822506i
$11$	−1.66404			−0.501727			−0.250864	−	0.968022i	$-0.580715\pi$
$11$	−1.66404			−0.501727			−0.250864	+	0.968022i	$0.580715\pi$
$12$		0			0
$13$	−0.0999454	+	0.173111i	−0.0277199	+	0.0480122i	−0.879553	−	0.475802i	$-0.842158\pi$
$13$	−0.0999454	+	0.173111i	−0.0277199	+	0.0480122i	0.851833	+	0.523814i	$0.175491\pi$
$14$		0			0
$15$		0			0
$16$	1.75890	−	3.04650i	0.439724	−	0.761625i
$17$	3.13555	−	5.43093i	0.760483	−	1.31720i	−0.182119	−	0.983277i	$-0.558296\pi$
$17$	3.13555	−	5.43093i	0.760483	−	1.31720i	0.942602	−	0.333919i	$-0.108371\pi$
$18$		0			0
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	−0.923787	−	0.382907i	$-0.874923\pi$
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	0.130287	−	0.991476i	$-0.458410\pi$
$20$	0.162147	+	0.280847i	0.0362571	+	0.0627992i
$21$		0			0
$22$	−1.70867	+	2.95951i	−0.364291	+	0.630970i
$23$	6.18184			1.28900			0.644501	−	0.764604i	$-0.277065\pi$
$23$	6.18184			1.28900			0.644501	+	0.764604i	$0.277065\pi$
$24$		0			0
$25$	−4.97861			−0.995722
$26$	0.205252	+	0.355508i	0.0402533	+	0.0697208i
$27$		0			0
$28$		0			0
$29$	2.46757	+	4.27396i	0.458217	+	0.793655i	0.998867	−	0.0475930i	$-0.0151551\pi$
$29$	2.46757	+	4.27396i	0.458217	+	0.793655i	−0.540650	+	0.841248i	$0.681822\pi$
$30$		0			0
$31$	−1.25890	−	2.18047i	−0.226105	−	0.391625i	0.730546	−	0.682864i	$-0.239266\pi$
$31$	−1.25890	−	2.18047i	−0.226105	−	0.391625i	−0.956650	+	0.291239i	$0.905932\pi$
$32$	−4.05873	−	7.02993i	−0.717490	−	1.24273i
$33$		0			0
$34$	−6.43931	−	11.1532i	−1.10433	−	1.91276i
$35$		0			0
$36$		0			0
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	−14.2062			−2.30456
$39$		0			0
$40$	0.0653107			0.0103265
$41$	1.15895	−	2.00736i	0.180998	−	0.313498i	−0.761223	−	0.648491i	$-0.775401\pi$
$41$	1.15895	−	2.00736i	0.180998	−	0.313498i	0.942221	+	0.334993i	$0.108734\pi$
$42$		0			0
$43$	−0.940993	−	1.62985i	−0.143500	−	0.248550i	0.785312	−	0.619100i	$-0.212502\pi$
$43$	−0.940993	−	1.62985i	−0.143500	−	0.248550i	−0.928812	+	0.370550i	$0.879169\pi$
$44$	1.84497	+	3.19558i	0.278140	+	0.481752i
$45$		0			0
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	0.905887	−	1.56904i	0.132137	−	0.228868i	−0.792363	−	0.610050i	$-0.791149\pi$
$47$	0.905887	−	1.56904i	0.132137	−	0.228868i	0.924500	+	0.381181i	$0.124483\pi$
$48$		0			0
$49$		0			0
$50$	−5.11215	+	8.85451i	−0.722967	+	1.25222i
$51$		0			0
$52$	0.443250			0.0614677
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	−0.621948	−	0.783058i	$-0.713659\pi$
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	0.989123	+	0.147094i	$0.0469920\pi$
$54$		0			0
$55$	0.243359			0.0328145
$56$		0			0
$57$		0			0
$58$	10.1350			1.33080
$59$	2.28549	+	3.95859i	0.297546	+	0.515364i	0.975574	−	0.219672i	$-0.0704986\pi$
$59$	2.28549	+	3.95859i	0.297546	+	0.515364i	−0.678028	+	0.735036i	$0.737165\pi$
$60$		0			0
$61$	−0.339138	+	0.587404i	−0.0434221	+	0.0752094i	−0.886920	−	0.461924i	$-0.847159\pi$
$61$	−0.339138	+	0.587404i	−0.0434221	+	0.0752094i	0.843498	+	0.537133i	$0.180493\pi$
$62$	−5.17066			−0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	0.0146166	−	0.0253167i	0.00181296	−	0.00314015i
$66$		0			0
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	0.990760	−	0.135630i	$-0.0433057\pi$
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	−0.612838	+	0.790208i	$0.709972\pi$
$68$	−13.9059			−1.68634
$69$		0			0
$70$		0			0
$71$	−1.27749			−0.151611			−0.0758053	−	0.997123i	$-0.524153\pi$
$71$	−1.27749			−0.151611			−0.0758053	+	0.997123i	$0.524153\pi$
$72$		0			0
$73$	0.778603	−	1.34858i	0.0911286	−	0.157839i	−0.816858	−	0.576839i	$-0.804286\pi$
$73$	0.778603	−	1.34858i	0.0911286	−	0.157839i	0.907986	+	0.419000i	$0.137619\pi$
$74$	−14.3765			−1.67123
$75$		0			0
$76$	−7.66972	+	13.2843i	−0.879777	+	1.52382i
$77$		0			0
$78$		0			0
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	0.241255	+	0.970462i	$0.422441\pi$
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	−0.961072	+	0.276298i	$0.910892\pi$
$80$	−0.257231	+	0.445537i	−0.0287593	+	0.0498126i
$81$		0			0
$82$	−2.38008	−	4.12241i	−0.262835	−	0.455244i
$83$	3.75687	+	6.50709i	0.412370	+	0.714246i	0.995148	−	0.0983854i	$-0.0313678\pi$
$83$	3.75687	+	6.50709i	0.412370	+	0.714246i	−0.582778	+	0.812631i	$0.698034\pi$
$84$		0			0
$85$	−0.458561	+	0.794251i	−0.0497379	+	0.0861486i
$86$	−3.86493			−0.416766
$87$		0			0
$88$	0.743131			0.0792181
$89$	4.53394	+	7.85301i	0.480597	+	0.832418i	0.999752	−	0.0222619i	$-0.00708678\pi$
$89$	4.53394	+	7.85301i	0.480597	+	0.832418i	−0.519155	+	0.854680i	$0.673753\pi$
$90$		0			0
$91$		0			0
$92$	−6.85398	−	11.8714i	−0.714577	−	1.23768i
$93$		0			0
$94$	−1.86037	−	3.22226i	−0.191883	−	0.332350i
$95$	0.505833	+	0.876128i	0.0518973	+	0.0898888i
$96$		0			0
$97$	3.98514	+	6.90246i	0.404630	+	0.700839i	0.994278	−	0.106821i	$-0.0340671\pi$
$97$	3.98514	+	6.90246i	0.404630	+	0.700839i	−0.589649	+	0.807660i	$0.700734\pi$
$98$		0			0
$99$		0			0
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	14.8430			1.47693			0.738467	−	0.674290i	$-0.235550\pi$
$101$	14.8430			1.47693			0.738467	+	0.674290i	$0.235550\pi$
$102$		0			0
$103$	0.203948			0.0200956			0.0100478	−	0.999950i	$-0.496802\pi$
$103$	0.203948			0.0200956			0.0100478	+	0.999950i	$0.496802\pi$
$104$	0.0446339	−	0.0773081i	0.00437671	−	0.00758068i
$105$		0			0
$106$	−5.48953	−	9.50815i	−0.533191	−	0.923513i
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	0.646985	−	0.762503i	$-0.276030\pi$
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	−0.983839	+	0.179054i	$0.942696\pi$
$108$		0			0
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	0.249886	−	0.432816i	0.0238257	−	0.0412674i
$111$		0			0
$112$		0			0
$113$	0.0193234	−	0.0334691i	0.00181779	−	0.00314851i	−0.865115	−	0.501573i	$-0.832755\pi$
$113$	0.0193234	−	0.0334691i	0.00181779	−	0.00314851i	0.866933	+	0.498425i	$0.166088\pi$
$114$		0			0
$115$	−0.904067			−0.0843047
$116$	5.47174	−	9.47733i	0.508038	−	0.879948i
$117$		0			0
$118$	9.38718			0.864160
$119$		0			0
$120$		0			0
$121$	−8.23097			−0.748270
$122$	0.696469	+	1.20632i	0.0630553	+	0.109215i
$123$		0			0
$124$	−2.79155	+	4.83511i	−0.250689	+	0.434206i
$125$	1.45933			0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	−1.77577	+	3.07572i	−0.156957	+	0.271858i
$129$		0			0
$130$	−0.0300173	−	0.0519914i	−0.00263269	−	0.00455995i
$131$	−19.8333			−1.73284			−0.866422	−	0.499312i	$-0.833586\pi$
$131$	−19.8333			−1.73284			−0.866422	+	0.499312i	$0.833586\pi$
$132$		0			0
$133$		0			0
$134$	12.7056			1.09759
$135$		0			0
$136$	−1.40028	+	2.42536i	−0.120073	+	0.207973i
$137$	6.44509			0.550642			0.275321	−	0.961352i	$-0.411216\pi$
$137$	6.44509			0.550642			0.275321	+	0.961352i	$0.411216\pi$
$138$		0			0
$139$	−6.26527	+	10.8518i	−0.531413	+	0.920435i	0.467914	+	0.883774i	$0.345006\pi$
$139$	−6.26527	+	10.8518i	−0.531413	+	0.920435i	−0.999328	+	0.0366611i	$0.988328\pi$
$140$		0			0
$141$		0			0
$142$	−1.31176	+	2.27203i	−0.110080	+	0.190665i
$143$	0.166313	−	0.288063i	0.0139078	−	0.0240890i
$144$		0			0
$145$	−0.360872	−	0.625048i	−0.0299688	−	0.0519074i
$146$	−1.59897	−	2.76950i	−0.132332	−	0.229206i
$147$		0			0
$148$	−7.76161	+	13.4435i	−0.638000	+	1.10505i
$149$	−17.7673			−1.45555			−0.727776	−	0.685815i	$-0.759446\pi$
$149$	−17.7673			−1.45555			−0.727776	+	0.685815i	$0.759446\pi$
$150$		0			0
$151$	8.46599			0.688953			0.344476	−	0.938795i	$-0.388056\pi$
$151$	8.46599			0.688953			0.344476	+	0.938795i	$0.388056\pi$
$152$	1.54463	+	2.67538i	0.125286	+	0.217002i
$153$		0			0
$154$		0			0
$155$	0.184108	+	0.318885i	0.0147879	+	0.0256135i
$156$		0			0
$157$	2.84968	+	4.93579i	0.227429	+	0.393919i	0.957045	−	0.289938i	$-0.0936347\pi$
$157$	2.84968	+	4.93579i	0.227429	+	0.393919i	−0.729616	+	0.683857i	$0.760301\pi$
$158$	13.1390	+	22.7573i	1.04528	+	1.81048i
$159$		0			0
$160$	0.593572	+	1.02810i	0.0469260	+	0.0812782i
$161$		0			0
$162$		0			0
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	−5.13986			−0.401355
$165$		0			0
$166$	15.4306			1.19764
$167$	−5.78723	+	10.0238i	−0.447829	+	0.775663i	−0.998244	−	0.0592278i	$-0.981136\pi$
$167$	−5.78723	+	10.0238i	−0.447829	+	0.775663i	0.550415	+	0.834891i	$0.314470\pi$
$168$		0			0
$169$	6.48002	+	11.2237i	0.498463	+	0.863364i
$170$	0.941721	+	1.63111i	0.0722267	+	0.125100i
$171$		0			0
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	7.95546	−	13.7793i	0.604842	−	1.04762i	−0.387234	−	0.921981i	$-0.626570\pi$
$173$	7.95546	−	13.7793i	0.604842	−	1.04762i	0.992076	−	0.125636i	$-0.0400971\pi$
$174$		0			0
$175$		0			0
$176$	−2.92688	+	5.06950i	−0.220622	+	0.382128i
$177$		0			0
$178$	18.6222			1.39579
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	−0.973751	−	0.227615i	$-0.926907\pi$
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	0.683996	+	0.729485i	$0.260240\pi$
$180$		0			0
$181$	12.1618			0.903982			0.451991	−	0.892022i	$-0.350714\pi$
$181$	12.1618			0.903982			0.451991	+	0.892022i	$0.350714\pi$
$182$		0			0
$183$		0			0
$184$	−2.76070			−0.203521
$185$	0.511893	+	0.886625i	0.0376351	+	0.0651860i
$186$		0			0
$187$	−5.21769	+	9.03730i	−0.381555	+	0.660873i
$188$	−4.01754			−0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	−2.48383	+	4.30211i	−0.179723	+	0.311290i	−0.941786	−	0.336214i	$-0.890854\pi$
$191$	−2.48383	+	4.30211i	−0.179723	+	0.311290i	0.762062	+	0.647504i	$0.224187\pi$
$192$		0			0
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	0.999093	+	0.0425800i	$0.0135577\pi$
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	−0.462671	+	0.886530i	$0.653109\pi$
$194$	16.3681			1.17516
$195$		0			0
$196$		0			0
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	−0.259098	−	0.965851i	$-0.583425\pi$
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	0.966001	−	0.258540i	$-0.0832413\pi$
$200$	2.22336			0.157215
$201$		0			0
$202$	15.2411	−	26.3984i	1.07236	−	1.85739i
$203$		0			0
$204$		0			0
$205$	−0.169492	+	0.293568i	−0.0118378	+	0.0205037i
$206$	0.209419	−	0.362724i	0.0145909	−	0.0252722i
$207$		0			0
$208$	0.351587	+	0.608967i	0.0243782	+	0.0422243i
$209$	5.75556	+	9.96893i	0.398121	+	0.689565i
$210$		0			0
$211$	11.7569	−	20.3636i	0.809381	−	1.40189i	−0.103912	−	0.994587i	$-0.533136\pi$
$211$	11.7569	−	20.3636i	0.809381	−	1.40189i	0.913293	−	0.407303i	$-0.133531\pi$
$212$	−11.8548			−0.814193
$213$		0			0
$214$	−14.3116			−0.978323
$215$	0.137616	+	0.238358i	0.00938535	+	0.0162559i
$216$		0			0
$217$		0			0
$218$	−6.83983	−	11.8469i	−0.463252	−	0.802376i
$219$		0			0
$220$	−0.269819	−	0.467340i	−0.0181912	−	0.0315081i
$221$	0.626768	+	1.08559i	0.0421610	+	0.0730250i
$222$		0			0
$223$	−2.03052	−	3.51696i	−0.135974	−	0.235513i	0.789995	−	0.613113i	$-0.210083\pi$
$223$	−2.03052	−	3.51696i	−0.135974	−	0.235513i	−0.925969	+	0.377600i	$0.876750\pi$
$224$		0			0
$225$		0			0
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	−3.85285			−0.255723			−0.127861	−	0.991792i	$-0.540811\pi$
$227$	−3.85285			−0.255723			−0.127861	+	0.991792i	$0.540811\pi$
$228$		0			0
$229$	−13.1162			−0.866746			−0.433373	−	0.901215i	$-0.642677\pi$
$229$	−13.1162			−0.866746			−0.433373	+	0.901215i	$0.642677\pi$
$230$	−0.928316	+	1.60789i	−0.0612113	+	0.106021i
$231$		0			0
$232$	−1.10197	−	1.90868i	−0.0723481	−	0.125311i
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	0.996223	+	0.0868284i	$0.0276732\pi$
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	−0.422916	+	0.906169i	$0.638993\pi$
$234$		0			0
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	5.06798	−	8.77801i	0.329898	−	0.571400i
$237$		0			0
$238$		0			0
$239$	−3.65857	+	6.33683i	−0.236653	+	0.409895i	−0.959752	−	0.280849i	$-0.909384\pi$
$239$	−3.65857	+	6.33683i	−0.236653	+	0.409895i	0.723099	+	0.690745i	$0.242717\pi$
$240$		0			0
$241$	−6.23107			−0.401378			−0.200689	−	0.979655i	$-0.564318\pi$
$241$	−6.23107			−0.401378			−0.200689	+	0.979655i	$0.564318\pi$
$242$	−8.45174	+	14.6389i	−0.543299	+	0.941021i
$243$		0			0
$244$	1.50405			0.0962868
$245$		0			0
$246$		0			0
$247$	1.38276			0.0879829
$248$	0.562201	+	0.973761i	0.0356998	+	0.0618339i
$249$		0			0
$250$	1.49847	−	2.59543i	0.0947717	−	0.164149i
$251$	5.65283			0.356803			0.178402	−	0.983958i	$-0.442907\pi$
$251$	5.65283			0.356803			0.178402	+	0.983958i	$0.442907\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	13.8404	−	23.9722i	0.868422	−	1.50415i
$255$		0			0
$256$	−5.98801	−	10.3715i	−0.374250	−	0.648221i
$257$	11.8016			0.736166			0.368083	−	0.929793i	$-0.380014\pi$
$257$	11.8016			0.736166			0.368083	+	0.929793i	$0.380014\pi$
$258$		0			0
$259$		0			0
$260$	−0.0648233			−0.00402017
$261$		0			0
$262$	−20.3653	+	35.2737i	−1.25817	+	2.17922i
$263$	22.2401			1.37138			0.685691	−	0.727893i	$-0.259500\pi$
$263$	22.2401			1.37138			0.685691	+	0.727893i	$0.259500\pi$
$264$		0			0
$265$	−0.390925	+	0.677101i	−0.0240143	+	0.0415940i
$266$		0			0
$267$		0			0
$268$	6.85953	−	11.8810i	0.419012	−	0.725750i
$269$	−1.19442	+	2.06880i	−0.0728251	+	0.126137i	−0.900138	−	0.435604i	$-0.856535\pi$
$269$	−1.19442	+	2.06880i	−0.0728251	+	0.126137i	0.827313	+	0.561741i	$0.189868\pi$
$270$		0			0
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	0.966534	+	0.256537i	$0.0825815\pi$
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	−0.261100	+	0.965312i	$0.584085\pi$
$272$	−11.0302	−	19.1049i	−0.668806	−	1.15841i
$273$		0			0
$274$	6.61797	−	11.4627i	0.399806	−	0.692484i
$275$	8.28461			0.499581
$276$		0			0
$277$	−4.61800			−0.277469			−0.138734	−	0.990330i	$-0.544303\pi$
$277$	−4.61800			−0.277469			−0.138734	+	0.990330i	$0.544303\pi$
$278$	12.8666	+	22.2857i	0.771690	+	1.33661i
$279$		0			0
$280$		0			0
$281$	−5.90841	−	10.2337i	−0.352466	−	0.610489i	0.634215	−	0.773157i	$-0.281324\pi$
$281$	−5.90841	−	10.2337i	−0.352466	−	0.610489i	−0.986681	+	0.162668i	$0.947990\pi$
$282$		0			0
$283$	7.92483	+	13.7262i	0.471082	+	0.815939i	0.999453	−	0.0330753i	$-0.0105301\pi$
$283$	7.92483	+	13.7262i	0.471082	+	0.815939i	−0.528370	+	0.849014i	$0.677197\pi$
$284$	1.41639	+	2.45327i	0.0840475	+	0.145575i
$285$		0			0
$286$	−0.341548	−	0.591579i	−0.0201962	−	0.0349808i
$287$		0			0
$288$		0			0
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	−1.48220			−0.0870381
$291$		0			0
$292$	−3.45304			−0.202074
$293$	7.04804	−	12.2076i	0.411751	−	0.713173i	−0.583330	−	0.812235i	$-0.698251\pi$
$293$	7.04804	−	12.2076i	0.411751	−	0.713173i	0.995081	+	0.0990615i	$0.0315841\pi$
$294$		0			0
$295$	−0.334243	−	0.578927i	−0.0194604	−	0.0337064i
$296$	1.56314	+	2.70744i	0.0908557	+	0.157367i
$297$		0			0
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	−0.617846	+	1.07014i	−0.0357310	+	0.0618878i
$300$		0			0
$301$		0			0
$302$	8.69307	−	15.0568i	0.500230	−	0.866424i
$303$		0			0
$304$	−24.3346			−1.39569
$305$	0.0495974	−	0.0859053i	0.00283994	−	0.00491892i
$306$		0			0
$307$	−27.3916			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$307$	−27.3916			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$308$		0			0
$309$		0			0
$310$	0.756186			0.0429485
$311$	7.02785	+	12.1726i	0.398513	+	0.690244i	0.993543	−	0.113459i	$-0.0361931\pi$
$311$	7.02785	+	12.1726i	0.398513	+	0.690244i	−0.595030	+	0.803704i	$0.702860\pi$
$312$		0			0
$313$	10.8723	−	18.8314i	0.614540	−	1.06441i	−0.375925	−	0.926650i	$-0.622675\pi$
$313$	10.8723	−	18.8314i	0.614540	−	1.06441i	0.990465	−	0.137764i	$-0.0439916\pi$
$314$	11.7045			0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	4.28148	−	7.41575i	0.240472	−	0.416510i	−0.720377	−	0.693583i	$-0.756031\pi$
$317$	4.28148	−	7.41575i	0.240472	−	0.416510i	0.960849	+	0.277073i	$0.0893644\pi$
$318$		0			0
$319$	−4.10614	−	7.11204i	−0.229900	−	0.398198i
$320$	1.40905			0.0787682
$321$		0			0
$322$		0			0
$323$	−43.3808			−2.41377
$324$		0			0
$325$	0.497589	−	0.861850i	0.0276013	−	0.0478068i
$326$	−4.36471			−0.241739
$327$		0			0
$328$	−0.517568	+	0.896453i	−0.0285779	+	0.0494984i
$329$		0			0
$330$		0			0
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	−0.975703	−	0.219097i	$-0.929689\pi$
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	0.677595	+	0.735435i	$0.263022\pi$
$332$	8.33070	−	14.4292i	0.457207	−	0.791905i
$333$		0			0
$334$	11.8849	+	20.5853i	0.650314	+	1.12638i
$335$	−0.452399	−	0.783578i	−0.0247172	−	0.0428114i
$336$		0			0
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	−0.816819	−	0.576893i	$-0.804265\pi$
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	0.908014	+	0.418940i	$0.137598\pi$
$338$	26.6153			1.44768
$339$		0			0
$340$	2.03368			0.110292
$341$	2.09486	+	3.62840i	0.113443	+	0.196489i
$342$		0			0
$343$		0			0
$344$	0.420231	+	0.727861i	0.0226573	+	0.0392437i
$345$		0			0
$346$	−16.3377	−	28.2977i	−0.878319	−	1.52129i
$347$	−5.76652	−	9.98790i	−0.309563	−	0.536178i	0.668704	−	0.743529i	$-0.266849\pi$
$347$	−5.76652	−	9.98790i	−0.309563	−	0.536178i	−0.978267	+	0.207350i	$0.933516\pi$
$348$		0			0
$349$	4.44917	+	7.70619i	0.238159	+	0.412503i	0.960186	−	0.279362i	$-0.0901228\pi$
$349$	4.44917	+	7.70619i	0.238159	+	0.412503i	−0.722027	+	0.691865i	$0.756789\pi$
$350$		0			0
$351$		0			0
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	−2.64699			−0.140885			−0.0704424	−	0.997516i	$-0.522441\pi$
$353$	−2.64699			−0.140885			−0.0704424	+	0.997516i	$0.522441\pi$
$354$		0			0
$355$	0.186828			0.00991579
$356$	10.0538	−	17.4137i	0.532852	−	0.922926i
$357$		0			0
$358$	7.96127	+	13.7893i	0.420766	+	0.728789i
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	0.973360	+	0.229284i	$0.0736384\pi$
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	−0.288114	+	0.957596i	$0.593028\pi$
$360$		0			0
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	12.4880	−	21.6299i	0.656357	−	1.13684i
$363$		0			0
$364$		0			0
$365$	−0.113867	+	0.197224i	−0.00596009	+	0.0103232i
$366$		0			0
$367$	−17.5874			−0.918056			−0.459028	−	0.888422i	$-0.651802\pi$
$367$	−17.5874			−0.918056			−0.459028	+	0.888422i	$0.651802\pi$
$368$	10.8732	−	18.8330i	0.566806	−	0.981736i
$369$		0			0
$370$	2.10249			0.109303
$371$		0			0
$372$		0			0
$373$	0.815075			0.0422030			0.0211015	−	0.999777i	$-0.493283\pi$
$373$	0.815075			0.0422030			0.0211015	+	0.999777i	$0.493283\pi$
$374$	10.7153	+	18.5594i	0.554074	+	0.959684i
$375$		0			0
$376$	−0.404553	+	0.700707i	−0.0208632	+	0.0361362i
$377$	−0.986490			−0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	1.12166	−	1.94278i	0.0575401	−	0.0996624i
$381$		0			0
$382$	5.10090	+	8.83501i	0.260985	+	0.452039i
$383$	17.8928			0.914278			0.457139	−	0.889395i	$-0.348874\pi$
$383$	17.8928			0.914278			0.457139	+	0.889395i	$0.348874\pi$
$384$		0			0
$385$		0			0
$386$	30.6084			1.55793
$387$		0			0
$388$	8.83688	−	15.3059i	0.448625	−	0.777041i
$389$	−15.6278			−0.792363			−0.396181	−	0.918172i	$-0.629665\pi$
$389$	−15.6278			−0.792363			−0.396181	+	0.918172i	$0.629665\pi$
$390$		0			0
$391$	19.3835	−	33.5731i	0.980264	−	1.69787i
$392$		0			0
$393$		0			0
$394$	21.8311	−	37.8126i	1.09984	−	1.90497i
$395$	0.935661	−	1.62061i	0.0470782	−	0.0815419i
$396$		0			0
$397$	−9.63064	−	16.6808i	−0.483348	−	0.837183i	0.516469	−	0.856306i	$-0.327246\pi$
$397$	−9.63064	−	16.6808i	−0.483348	−	0.837183i	−0.999817	+	0.0191225i	$0.993913\pi$
$398$	−20.4791	−	35.4709i	−1.02653	−	1.77799i
$399$		0			0
$400$	−8.75687	+	15.1673i	−0.437843	+	0.758367i
$401$	−14.3013			−0.714172			−0.357086	−	0.934072i	$-0.616230\pi$
$401$	−14.3013			−0.714172			−0.357086	+	0.934072i	$0.616230\pi$
$402$		0			0
$403$	0.503284			0.0250704
$404$	−16.4569	−	28.5041i	−0.818760	−	1.41813i
$405$		0			0
$406$		0			0
$407$	5.82452	+	10.0884i	0.288711	+	0.500062i
$408$		0			0
$409$	15.9305	+	27.5924i	0.787712	+	1.36436i	0.927366	+	0.374156i	$0.122068\pi$
$409$	15.9305	+	27.5924i	0.787712	+	1.36436i	−0.139654	+	0.990200i	$0.544599\pi$
$410$	0.348076	+	0.602885i	0.0171902	+	0.0297744i
$411$		0			0
$412$	−0.226124	−	0.391657i	−0.0111403	−	0.0192956i
$413$		0			0
$414$		0			0
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	1.62261			0.0795549
$417$		0			0
$418$	23.6398			1.15626
$419$	11.9480	−	20.6945i	0.583697	−	1.01099i	−0.411339	−	0.911482i	$-0.634939\pi$
$419$	11.9480	−	20.6945i	0.583697	−	1.01099i	0.995036	−	0.0995110i	$-0.0317278\pi$
$420$		0			0
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	0.834696	−	0.550711i	$-0.185643\pi$
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	−0.894278	+	0.447513i	$0.852310\pi$
$422$	−24.1446	−	41.8197i	−1.17534	−	2.03575i
$423$		0			0
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	−15.6107	+	27.0385i	−0.757230	+	1.31156i
$426$		0			0
$427$		0			0
$428$	−7.72661	+	13.3829i	−0.373480	+	0.646886i
$429$		0			0
$430$	0.565230			0.0272578
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	−0.919244	−	0.393688i	$-0.871199\pi$
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	0.800566	+	0.599244i	$0.204532\pi$
$432$		0			0
$433$	−30.8539			−1.48274			−0.741371	−	0.671095i	$-0.765824\pi$
$433$	−30.8539			−1.48274			−0.741371	+	0.671095i	$0.765824\pi$
$434$		0			0
$435$		0			0
$436$	−14.7709			−0.707395
$437$	−21.3817	−	37.0341i	−1.02282	−	1.77158i
$438$		0			0
$439$	1.22411	−	2.12022i	0.0584235	−	0.101192i	−0.835334	−	0.549742i	$-0.814726\pi$
$439$	1.22411	−	2.12022i	0.0584235	−	0.101192i	0.893758	+	0.448550i	$0.148059\pi$
$440$	−0.108680			−0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	−13.1475	+	22.7722i	−0.624657	+	1.08194i	0.363950	+	0.931419i	$0.381428\pi$
$443$	−13.1475	+	22.7722i	−0.624657	+	1.08194i	−0.988607	+	0.150520i	$0.951905\pi$
$444$		0			0
$445$	−0.663069	−	1.14847i	−0.0314325	−	0.0544427i
$446$	−8.33993			−0.394907
$447$		0			0
$448$		0			0
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	−1.92854	+	3.34034i	−0.0908116	+	0.157290i
$452$	−0.0856976			−0.00403087
$453$		0			0
$454$	−3.95620	+	6.85233i	−0.185673	+	0.321596i
$455$		0			0
$456$		0			0
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	−0.738874	−	0.673844i	$-0.764642\pi$
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	0.953003	+	0.302961i	$0.0979754\pi$
$458$	−13.4681	+	23.3274i	−0.629321	+	1.09002i
$459$		0			0
$460$	1.00237	+	1.73615i	0.0467355	+	0.0809483i
$461$	14.6152	+	25.3143i	0.680698	+	1.17900i	0.974768	+	0.223220i	$0.0716568\pi$
$461$	14.6152	+	25.3143i	0.680698	+	1.17900i	−0.294070	+	0.955784i	$0.595010\pi$
$462$		0			0
$463$	−8.21031	+	14.2207i	−0.381565	+	0.660891i	−0.991286	−	0.131726i	$-0.957948\pi$
$463$	−8.21031	+	14.2207i	−0.381565	+	0.660891i	0.609721	+	0.792616i	$0.291282\pi$
$464$	17.3608			0.805956
$465$		0			0
$466$	35.9435			1.66505
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	0.987234	−	0.159276i	$-0.0509158\pi$
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	−0.631554	+	0.775332i	$0.717582\pi$
$468$		0			0
$469$		0			0
$470$	0.272071	+	0.471241i	0.0125497	+	0.0217367i
$471$		0			0
$472$	−1.02066	−	1.76784i	−0.0469797	−	0.0813713i
$473$	1.56585	+	2.71213i	0.0719979	+	0.124704i
$474$		0			0
$475$	17.2200	+	29.8259i	0.790106	+	1.36850i
$476$		0			0
$477$		0			0
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	−37.9291			−1.73303			−0.866513	−	0.499155i	$-0.833644\pi$
$479$	−37.9291			−1.73303			−0.866513	+	0.499155i	$0.833644\pi$
$480$		0			0
$481$	1.39933			0.0638038
$482$	−6.39820	+	11.0820i	−0.291430	+	0.504772i
$483$		0			0
$484$	9.12591	+	15.8065i	0.414814	+	0.718479i
$485$	−0.582809	−	1.00946i	−0.0264640	−	0.0458370i
$486$		0			0
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	0.151453	−	0.262324i	0.00685595	−	0.0118749i
$489$		0			0
$490$		0			0
$491$	15.1876	−	26.3056i	0.685405	−	1.18716i	−0.287904	−	0.957659i	$-0.592958\pi$
$491$	15.1876	−	26.3056i	0.685405	−	1.18716i	0.973309	−	0.229497i	$-0.0737082\pi$
$492$		0			0
$493$	30.9488			1.39386
$494$	1.41985	−	2.45925i	0.0638820	−	0.110647i
$495$		0			0
$496$	−8.85709			−0.397695
$497$		0			0
$498$		0			0
$499$	9.26871			0.414925			0.207462	−	0.978243i	$-0.433480\pi$
$499$	9.26871			0.414925			0.207462	+	0.978243i	$0.433480\pi$
$500$	−1.61800	−	2.80246i	−0.0723592	−	0.125330i
$501$		0			0
$502$	5.80445	−	10.0536i	0.259065	−	0.448715i
$503$	−22.4230			−0.999791			−0.499896	−	0.866086i	$-0.666628\pi$
$503$	−22.4230			−0.999791			−0.499896	+	0.866086i	$0.666628\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	−10.5627	+	18.2952i	−0.469571	+	0.813321i
$507$		0			0
$508$	−14.9444	−	25.8844i	−0.663050	−	1.14844i
$509$	−37.6414			−1.66843			−0.834213	−	0.551443i	$-0.814077\pi$
$509$	−37.6414			−1.66843			−0.834213	+	0.551443i	$0.814077\pi$
$510$		0			0
$511$		0			0
$512$	−31.6976			−1.40085
$513$		0			0
$514$	12.1182	−	20.9893i	0.534511	−	0.925800i
$515$	−0.0298266			−0.00131432
$516$		0			0
$517$	−1.50743	+	2.61095i	−0.0662969	+	0.114830i
$518$		0			0
$519$		0			0
$520$	−0.00652751	+	0.0113060i	−0.000286250	+	0.000495800i
$521$	17.4641	−	30.2488i	0.765117	−	1.32522i	−0.175067	−	0.984556i	$-0.556014\pi$
$521$	17.4641	−	30.2488i	0.765117	−	1.32522i	0.940185	−	0.340666i	$-0.110652\pi$
$522$		0			0
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	0.999751	+	0.0223069i	$0.00710109\pi$
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	−0.480557	+	0.876963i	$0.659566\pi$
$524$	21.9898	+	38.0874i	0.960628	+	1.66386i
$525$		0			0
$526$	22.8366	−	39.5542i	0.995723	−	1.72464i
$527$	−15.7894			−0.687795
$528$		0			0
$529$	15.2151			0.661526
$530$	0.802820	+	1.39053i	0.0348723	+	0.0604006i
$531$		0			0
$532$		0			0
$533$	0.231664	+	0.401254i	0.0100345	+	0.0173802i
$534$		0			0
$535$	0.509585	+	0.882627i	0.0220313	+	0.0381593i
$536$	−1.38147	−	2.39277i	−0.0596702	−	0.103352i
$537$		0			0
$538$	2.45292	+	4.24857i	0.105753	+	0.183169i
$539$		0			0
$540$		0			0
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	47.6976			2.04879
$543$		0			0
$544$	−50.9055			−2.18255
$545$	−0.487083	+	0.843653i	−0.0208643	+	0.0361381i
$546$		0			0
$547$	−10.0046	−	17.3284i	−0.427765	−	0.740910i	0.568910	−	0.822400i	$-0.307365\pi$
$547$	−10.0046	−	17.3284i	−0.427765	−	0.740910i	−0.996674	+	0.0814901i	$0.974032\pi$
$548$	−7.14586	−	12.3770i	−0.305256	−	0.528719i
$549$		0			0
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	17.0696	−	29.5654i	0.727190	−	1.25953i
$552$		0			0
$553$		0			0
$554$	−4.74187	+	8.21316i	−0.201463	+	0.348944i
$555$		0			0
$556$	27.7860			1.17839
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	−0.863413	−	0.504497i	$-0.831678\pi$
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	0.868614	+	0.495489i	$0.165011\pi$
$558$		0			0
$559$	0.376192			0.0159112
$560$		0			0
$561$		0			0
$562$	−24.2676			−1.02367
$563$	22.1255	+	38.3224i	0.932477	+	1.61510i	0.779073	+	0.626934i	$0.215690\pi$
$563$	22.1255	+	38.3224i	0.932477	+	1.61510i	0.153404	+	0.988164i	$0.450976\pi$
$564$		0			0
$565$	−0.00282596	+	0.00489471i	−0.000118889	+	0.000205922i
$566$	32.5496			1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	−2.76767	+	4.79374i	−0.116027	+	0.200964i	−0.918190	−	0.396141i	$-0.870349\pi$
$569$	−2.76767	+	4.79374i	−0.116027	+	0.200964i	0.802163	+	0.597105i	$0.203682\pi$
$570$		0			0
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	0.905761	−	0.423788i	$-0.139300\pi$
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	−0.819892	+	0.572518i	$0.805966\pi$
$572$	−0.737585			−0.0308400
$573$		0			0
$574$		0			0
$575$	−30.7770			−1.28349
$576$		0			0
$577$	2.82275	−	4.88915i	0.117513	−	0.203538i	−0.801269	−	0.598305i	$-0.795841\pi$
$577$	2.82275	−	4.88915i	0.117513	−	0.203538i	0.918781	+	0.394767i	$0.129175\pi$
$578$	−45.8512			−1.90716
$579$		0			0
$580$	−0.800218	+	1.38602i	−0.0332272	+	0.0575513i
$581$		0			0
$582$		0			0
$583$	−4.44809	+	7.70433i	−0.184221	+	0.319081i
$584$	−0.347710	+	0.602252i	−0.0143884	+	0.0249214i
$585$		0			0
$586$	−14.4742	−	25.0700i	−0.597923	−	1.03563i
$587$	9.36644	+	16.2232i	0.386595	+	0.669601i	0.991989	−	0.126324i	$-0.0403180\pi$
$587$	9.36644	+	16.2232i	0.386595	+	0.669601i	−0.605394	+	0.795926i	$0.706985\pi$
$588$		0			0
$589$	−8.70852	+	15.0836i	−0.358828	+	0.621509i
$590$	−1.37283			−0.0565187
$591$		0			0
$592$	−24.6262			−1.01213
$593$	−9.43516	−	16.3422i	−0.387456	−	0.671093i	0.604651	−	0.796491i	$-0.293313\pi$
$593$	−9.43516	−	16.3422i	−0.387456	−	0.671093i	−0.992107	+	0.125398i	$0.959979\pi$
$594$		0			0
$595$		0			0
$596$	19.6991	+	34.1198i	0.806906	+	1.39760i
$597$		0			0
$598$	1.26884	+	2.19769i	0.0518866	+	0.0898702i
$599$	1.33726	+	2.31620i	0.0546388	+	0.0946372i	0.892051	−	0.451934i	$-0.149266\pi$
$599$	1.33726	+	2.31620i	0.0546388	+	0.0946372i	−0.837412	+	0.546572i	$0.815933\pi$
$600$		0			0
$601$	6.60716	+	11.4439i	0.269511	+	0.466808i	0.968736	−	0.248095i	$-0.0798044\pi$
$601$	6.60716	+	11.4439i	0.269511	+	0.466808i	−0.699224	+	0.714902i	$0.746471\pi$
$602$		0			0
$603$		0			0
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	1.20374			0.0489391
$606$		0			0
$607$	−25.8052			−1.04740			−0.523701	−	0.851902i	$-0.675449\pi$
$607$	−25.8052			−1.04740			−0.523701	+	0.851902i	$0.675449\pi$
$608$	−28.0766	+	48.6301i	−1.13866	+	1.97221i
$609$		0			0
$610$	−0.101856	−	0.176419i	−0.00412401	−	0.00714299i
$611$	0.181079	+	0.313637i	0.00732565	+	0.0126884i
$612$		0			0
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	−28.1263	+	48.7162i	−1.13509	+	1.96603i
$615$		0			0
$616$		0			0
$617$	4.76588	−	8.25474i	0.191867	−	0.332323i	−0.754002	−	0.656872i	$-0.771879\pi$
$617$	4.76588	−	8.25474i	0.191867	−	0.332323i	0.945869	+	0.324549i	$0.105212\pi$
$618$		0			0
$619$	−34.7071			−1.39500			−0.697499	−	0.716586i	$-0.745704\pi$
$619$	−34.7071			−1.39500			−0.697499	+	0.716586i	$0.745704\pi$
$620$	0.408253	−	0.707114i	0.0163958	−	0.0283984i
$621$		0			0
$622$	28.8654			1.15740
$623$		0			0
$624$		0			0
$625$	24.6796			0.987186
$626$	−22.3279	−	38.6730i	−0.892402	−	1.54568i
$627$		0			0
$628$	6.31904	−	10.9449i	0.252157	−	0.436749i
$629$	−43.9006			−1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	2.85718	−	4.94877i	0.113652	−	0.196852i
$633$		0			0
$634$	−8.79265	−	15.2293i	−0.349201	−	0.604833i
$635$	−1.97122			−0.0782256
$636$		0			0
$637$		0			0
$638$	−16.8651			−0.667696
$639$		0			0
$640$	0.259699	−	0.449811i	0.0102655	−	0.0177804i
$641$	44.1844			1.74518			0.872590	−	0.488454i	$-0.162439\pi$
$641$	44.1844			1.74518			0.872590	+	0.488454i	$0.162439\pi$
$642$		0			0
$643$	−7.24065	+	12.5412i	−0.285543	+	0.494575i	−0.972741	−	0.231895i	$-0.925507\pi$
$643$	−7.24065	+	12.5412i	−0.285543	+	0.494575i	0.687197	+	0.726471i	$0.258841\pi$
$644$		0			0
$645$		0			0
$646$	−44.5444	+	77.1532i	−1.75258	+	3.03555i
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	0.327245	+	0.944940i	$0.393880\pi$
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	−0.981964	+	0.189068i	$0.939453\pi$
$648$		0			0
$649$	−3.80315	−	6.58725i	−0.149287	−	0.258572i
$650$	−1.02187	−	1.76993i	−0.0400811	−	0.0694225i
$651$		0			0
$652$	−2.35643	+	4.08146i	−0.0922850	+	0.159842i
$653$	9.06643			0.354797			0.177398	−	0.984139i	$-0.443232\pi$
$653$	9.06643			0.354797			0.177398	+	0.984139i	$0.443232\pi$
$654$		0			0
$655$	2.90054			0.113333
$656$	−4.07696	−	7.06150i	−0.159178	−	0.275705i
$657$		0			0
$658$		0			0
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	−0.987489	−	0.157686i	$-0.949596\pi$
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	0.357184	−	0.934034i	$-0.383737\pi$
$660$		0			0
$661$	−4.32958	−	7.49905i	−0.168401	−	0.291679i	0.769457	−	0.638699i	$-0.220527\pi$
$661$	−4.32958	−	7.49905i	−0.168401	−	0.291679i	−0.937858	+	0.347020i	$0.887194\pi$
$662$	11.1382	+	19.2919i	0.432897	+	0.749799i
$663$		0			0
$664$	−1.67775	−	2.90595i	−0.0651094	−	0.112773i
$665$		0			0
$666$		0			0
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	25.6659			0.993043
$669$		0			0
$670$	−1.85813			−0.0717860
$671$	0.564339	−	0.977464i	0.0217861	−	0.0377346i
$672$		0			0
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	0.971237	−	0.238114i	$-0.0765291\pi$
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	−0.691831	+	0.722059i	$0.743196\pi$
$674$	−3.43803	−	5.95484i	−0.132428	−	0.229372i
$675$		0			0
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	−19.1657	+	33.1960i	−0.736600	+	1.27583i	0.217418	+	0.976078i	$0.430236\pi$
$677$	−19.1657	+	33.1960i	−0.736600	+	1.27583i	−0.954018	+	0.299749i	$0.903097\pi$
$678$		0			0
$679$		0			0
$680$	0.204785	−	0.354698i	0.00785315	−	0.0136021i
$681$		0			0
$682$	8.60418			0.329471
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	−0.795570	−	0.605861i	$-0.792829\pi$
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	0.922476	+	0.386054i	$0.126162\pi$
$684$		0			0
$685$	−0.942567			−0.0360136
$686$		0			0
$687$		0			0
$688$	−6.62044			−0.252402
$689$	0.534322	+	0.925472i	0.0203560	+	0.0352577i
$690$		0			0
$691$	−11.6938	+	20.2542i	−0.444852	+	0.770506i	−0.998042	−	0.0625490i	$-0.980077\pi$
$691$	−11.6938	+	20.2542i	−0.444852	+	0.770506i	0.553190	+	0.833055i	$0.313410\pi$
$692$	−35.2818			−1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	0.916269	−	1.58702i	0.0347561	−	0.0601992i
$696$		0			0
$697$	−7.26791	−	12.5884i	−0.275292	−	0.476819i
$698$	18.2740			0.691683
$699$		0			0
$700$		0			0
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	−24.2131	+	41.9383i	−0.913214	+	1.58173i
$704$	16.0327			0.604256
$705$		0			0
$706$	−2.71799	+	4.70769i	−0.102293	+	0.177176i
$707$		0			0
$708$		0			0
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	−0.968167	−	0.250305i	$-0.919469\pi$
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	0.700854	+	0.713305i	$0.252802\pi$
$710$	0.191839	−	0.332275i	0.00719959	−	0.0124701i
$711$		0			0
$712$	−2.02478	−	3.50702i	−0.0758817	−	0.131431i
$713$	−7.78230	−	13.4793i	−0.291449	−	0.504805i
$714$		0			0
$715$	−0.0243226	+	0.0421280i	−0.000909613	+	0.00157550i
$716$	17.1926			0.642519
$717$		0			0
$718$	53.3272			1.99015
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	0.965810	−	0.259249i	$-0.0834752\pi$
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	−0.707422	+	0.706792i	$0.750142\pi$
$720$		0			0
$721$		0			0
$722$	29.6268	+	51.3151i	1.10259	+	1.90975i
$723$		0			0
$724$	−13.4842	−	23.3553i	−0.501136	−	0.867993i
$725$	−12.2851	−	21.2784i	−0.456257	−	0.790260i
$726$		0			0
$727$	−15.7000	−	27.1932i	−0.582280	−	1.00854i	−0.995208	−	0.0977755i	$-0.968827\pi$
$727$	−15.7000	−	27.1932i	−0.582280	−	1.00854i	0.412928	−	0.910764i	$-0.364506\pi$
$728$		0			0
$729$		0			0
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	−11.8021			−0.436518
$732$		0			0
$733$	26.6006			0.982515			0.491257	−	0.871014i	$-0.336537\pi$
$733$	26.6006			0.982515			0.491257	+	0.871014i	$0.336537\pi$
$734$	−18.0592	+	31.2794i	−0.666576	+	1.15454i
$735$		0			0
$736$	−25.0904	−	43.4579i	−0.924845	−	1.60188i
$737$	−5.14757	−	8.91586i	−0.189613	−	0.328420i
$738$		0			0
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	1.13510	−	1.96605i	0.0417272	−	0.0722736i
$741$		0			0
$742$		0			0
$743$	−19.3008	+	33.4299i	−0.708076	+	1.22642i	0.257493	+	0.966280i	$0.417103\pi$
$743$	−19.3008	+	33.4299i	−0.708076	+	1.22642i	−0.965570	+	0.260144i	$0.916230\pi$
$744$		0			0
$745$	2.59839			0.0951975
$746$	0.836938	−	1.44962i	0.0306425	−	0.0530743i
$747$		0			0
$748$	23.1400			0.846082
$749$		0			0
$750$		0			0
$751$	−37.8996			−1.38297			−0.691487	−	0.722389i	$-0.743044\pi$
$751$	−37.8996			−1.38297			−0.691487	+	0.722389i	$0.743044\pi$
$752$	−3.18673	−	5.51957i	−0.116208	−	0.201278i
$753$		0			0
$754$	−1.01295	+	1.75448i	−0.0368895	+	0.0638944i
$755$	−1.23811			−0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	−20.9793	+	36.3371i	−0.762001	+	1.31982i
$759$		0			0
$760$	−0.225896	−	0.391263i	−0.00819411	−	0.0141926i
$761$	27.7470			1.00583			0.502913	−	0.864337i	$-0.332261\pi$
$761$	27.7470			1.00583			0.502913	+	0.864337i	$0.332261\pi$
$762$		0			0
$763$		0			0
$764$	11.0156			0.398529
$765$		0			0
$766$	18.3727	−	31.8224i	0.663832	−	1.14979i
$767$	−0.913698			−0.0329917
$768$		0			0
$769$	6.07668	−	10.5251i	0.219131	−	0.379546i	−0.735412	−	0.677621i	$-0.763011\pi$
$769$	6.07668	−	10.5251i	0.219131	−	0.379546i	0.954542	+	0.298075i	$0.0963445\pi$
$770$		0			0
$771$		0			0
$772$	16.5250	−	28.6221i	0.594747	−	1.03013i
$773$	−20.7795	+	35.9912i	−0.747388	+	1.29451i	0.201682	+	0.979451i	$0.435359\pi$
$773$	−20.7795	+	35.9912i	−0.747388	+	1.29451i	−0.949071	+	0.315063i	$0.897974\pi$
$774$		0			0
$775$	6.26756	+	10.8557i	0.225137	+	0.389950i
$776$	−1.77969	−	3.08252i	−0.0638873	−	0.110656i
$777$		0			0
$778$	−16.0470	+	27.7942i	−0.575313	+	0.996472i
$779$	−16.0343			−0.574488
$780$		0			0
$781$	2.12580			0.0760671
$782$	−39.8068	−	68.9473i	−1.42349	−	2.46555i
$783$		0			0
$784$		0			0
$785$	−0.416753	−	0.721837i	−0.0148746	−	0.0257635i
$786$		0			0
$787$	−10.4484	−	18.0972i	−0.372446	−	0.645096i	0.617495	−	0.786575i	$-0.288148\pi$
$787$	−10.4484	−	18.0972i	−0.372446	−	0.645096i	−0.989941	+	0.141479i	$0.954814\pi$
$788$	−23.5725	−	40.8288i	−0.839736	−	1.45447i
$789$		0			0
$790$	−1.92152	−	3.32816i	−0.0683645	−	0.118411i
$791$		0			0
$792$		0			0
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	−39.5558			−1.40378
$795$		0			0
$796$	−44.2254			−1.56753
$797$	−0.319383	+	0.553188i	−0.0113131	+	0.0195949i	−0.871627	−	0.490171i	$-0.836934\pi$
$797$	−0.319383	+	0.553188i	−0.0113131	+	0.0195949i	0.860313	+	0.509765i	$0.170268\pi$
$798$		0			0
$799$	−5.68091	−	9.83963i	−0.200976	−	0.348101i
$800$	20.2069	+	34.9993i	0.714420	+	1.23741i
$801$		0			0
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	−1.29563	+	2.24409i	−0.0457217	+	0.0791923i
$804$		0			0
$805$		0			0
$806$	0.516783	−	0.895095i	0.0182029	−	0.0315284i
$807$		0			0
$808$	−6.62862			−0.233194
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.0474686	+	0.998873i	$0.515115\pi$
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.841315	+	0.540545i	$0.818218\pi$
$810$		0			0
$811$	0.784071			0.0275325			0.0137662	−	0.999905i	$-0.495618\pi$
$811$	0.784071			0.0275325			0.0137662	+	0.999905i	$0.495618\pi$
$812$		0			0
$813$		0			0
$814$	23.9230			0.838501
$815$	0.155411	+	0.269180i	0.00544382	+	0.00942897i
$816$		0			0
$817$	−6.50939	+	11.2746i	−0.227735	+	0.394448i
$818$	65.4311			2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	21.7207	−	37.6213i	0.758056	−	1.31299i	−0.185784	−	0.982591i	$-0.559483\pi$
$821$	21.7207	−	37.6213i	0.758056	−	1.31299i	0.943841	−	0.330401i	$-0.107184\pi$
$822$		0			0
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	0.829398	−	0.558659i	$-0.188684\pi$
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	−0.898511	+	0.438950i	$0.855350\pi$
$824$	−0.0910797			−0.00317291
$825$		0			0
$826$		0			0
$827$	−29.3159			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$827$	−29.3159			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$828$		0			0
$829$	17.5213	−	30.3478i	0.608541	−	1.05402i	−0.382940	−	0.923773i	$-0.625088\pi$
$829$	17.5213	−	30.3478i	0.608541	−	1.05402i	0.991481	−	0.130251i	$-0.0415782\pi$
$830$	−2.25665			−0.0783295
$831$		0			0
$832$	0.962955	−	1.66789i	0.0333844	−	0.0578236i
$833$		0			0
$834$		0			0
$835$	0.846358	−	1.46593i	0.0292894	−	0.0507308i
$836$	12.7627	−	22.1057i	0.441408	−	0.764541i
$837$		0			0
$838$	−24.5369	−	42.4992i	−0.847614	−	1.46811i
$839$	−18.7921	−	32.5489i	−0.648777	−	1.12371i	−0.983415	−	0.181368i	$-0.941948\pi$
$839$	−18.7921	−	32.5489i	−0.648777	−	1.12371i	0.334639	−	0.942347i	$-0.391386\pi$
$840$		0			0
$841$	2.32218	−	4.02213i	0.0800750	−	0.138694i
$842$	−5.02119			−0.173042
$843$		0			0
$844$	−52.1411			−1.79477
$845$	−0.947675	−	1.64142i	−0.0326010	−	0.0564666i
$846$		0			0
$847$		0			0
$848$	−9.40331	−	16.2870i	−0.322911	−	0.559298i
$849$		0			0
$850$	32.0588	+	55.5275i	1.09961	+	1.90458i
$851$	−21.6378	−	37.4778i	−0.741735	−	1.28472i
$852$		0			0
$853$	−16.3849	−	28.3795i	−0.561009	−	0.971696i	−0.997409	−	0.0719434i	$-0.977080\pi$
$853$	−16.3849	−	28.3795i	−0.561009	−	0.971696i	0.436400	−	0.899753i	$-0.356253\pi$
$854$		0			0
$855$		0			0
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	27.5347			0.940566			0.470283	−	0.882516i	$-0.344152\pi$
$857$	27.5347			0.940566			0.470283	+	0.882516i	$0.344152\pi$
$858$		0			0
$859$	46.5101			1.58690			0.793451	−	0.608634i	$-0.208282\pi$
$859$	46.5101			1.58690			0.793451	+	0.608634i	$0.208282\pi$
$860$	0.305158	−	0.528549i	0.0104058	−	0.0180234i
$861$		0			0
$862$	5.05981	+	8.76384i	0.172338	+	0.298498i
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	0.821502	−	0.570205i	$-0.193136\pi$
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	−0.904563	+	0.426339i	$0.859803\pi$
$864$		0			0
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	−31.6814	+	54.8739i	−1.07658	+	1.86469i
$867$		0			0
$868$		0			0
$869$	10.6463	−	18.4400i	0.361152	−	0.625533i
$870$		0			0
$871$	−1.23669			−0.0419037
$872$	−1.48738	+	2.57622i	−0.0503690	+	0.0872417i
$873$		0			0
$874$	−87.8207			−2.97058
$875$		0			0
$876$		0			0
$877$	39.2892			1.32670			0.663352	−	0.748308i	$-0.269133\pi$
$877$	39.2892			1.32670			0.663352	+	0.748308i	$0.269133\pi$
$878$	−2.51388	−	4.35418i	−0.0848395	−	0.146946i
$879$		0			0
$880$	0.428043	−	0.741392i	0.0144293	−	0.0249923i
$881$	47.3713			1.59598			0.797990	−	0.602670i	$-0.205897\pi$
$881$	47.3713			1.59598			0.797990	+	0.602670i	$0.205897\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	1.38983	−	2.40726i	0.0467451	−	0.0809649i
$885$		0			0
$886$	27.0003	+	46.7659i	0.907094	+	1.57113i
$887$	−22.9600			−0.770922			−0.385461	−	0.922724i	$-0.625958\pi$
$887$	−22.9600			−0.770922			−0.385461	+	0.922724i	$0.625958\pi$
$888$		0			0
$889$		0			0
$890$	−2.72342			−0.0912891
$891$		0			0
$892$	−4.50259	+	7.79871i	−0.150758	+	0.261120i
$893$	−12.5331			−0.419404
$894$		0			0
$895$	0.566944	−	0.981976i	0.0189508	−	0.0328238i
$896$		0			0
$897$		0			0
$898$	39.7460	−	68.8420i	1.32634	−	2.29729i
$899$	6.21284	−	10.7610i	0.207210	−	0.358898i
$900$		0			0
$901$	−16.7631	−	29.0345i	−0.558459	−	0.967280i
$902$	3.96054	+	6.85986i	0.131872	+	0.228408i
$903$		0			0
$904$	−0.00862948	+	0.0149467i	−0.000287012	+	0.000497120i
$905$	−1.77862			−0.0591232
$906$		0			0
$907$	−27.8982			−0.926345			−0.463173	−	0.886268i	$-0.653289\pi$
$907$	−27.8982			−0.926345			−0.463173	+	0.886268i	$0.653289\pi$
$908$	4.27177	+	7.39892i	0.141764	+	0.245542i
$909$		0			0
$910$		0			0
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	0.989333	+	0.145670i	$0.0465337\pi$
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	−0.368513	+	0.929623i	$0.620133\pi$
$912$		0			0
$913$	−6.25158	−	10.8281i	−0.206897	−	0.358356i
$914$	−9.40068	−	16.2825i	−0.310947	−	0.538576i
$915$		0			0
$916$	14.5424	+	25.1881i	0.480493	+	0.832239i
$917$		0			0
$918$		0			0
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	0.403740			0.0133109
$921$		0			0
$922$	60.0289			1.97695
$923$	0.127680	−	0.221147i	0.00420262	−	0.00727916i
$924$		0			0
$925$	17.4263	+	30.1832i	0.572972	+	0.992417i
$926$	16.8611	+	29.2042i	0.554089	+	0.959710i
$927$		0			0
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	22.9675	−	39.7809i	0.753540	−	1.30517i	−0.192556	−	0.981286i	$-0.561678\pi$
$929$	22.9675	−	39.7809i	0.753540	−	1.30517i	0.946097	−	0.323884i	$-0.104989\pi$
$930$		0			0
$931$		0			0
$932$	19.4053	−	33.6110i	0.635642	−	1.10096i
$933$		0			0
$934$	31.5699			1.03300
$935$	0.763064	−	1.32167i	0.0249549	−	0.0432231i
$936$		0			0
$937$	45.3797			1.48249			0.741245	−	0.671235i	$-0.234236\pi$
$937$	45.3797			1.48249			0.741245	+	0.671235i	$0.234236\pi$
$938$		0			0
$939$		0			0
$940$	0.587547			0.0191637
$941$	−24.7002	−	42.7819i	−0.805202	−	1.39465i	−0.916154	−	0.400825i	$-0.868723\pi$
$941$	−24.7002	−	42.7819i	−0.805202	−	1.39465i	0.110952	−	0.993826i	$-0.464610\pi$
$942$		0			0
$943$	7.16445	−	12.4092i	0.233307	−	0.404099i
$944$	16.0798			0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	15.8253	−	27.4102i	0.514252	−	0.890711i	−0.485611	−	0.874175i	$-0.661403\pi$
$947$	15.8253	−	27.4102i	0.514252	−	0.890711i	0.999863	−	0.0165357i	$-0.00526371\pi$
$948$		0			0
$949$	0.155636	+	0.269569i	0.00505214	+	0.00875057i
$950$	70.7274			2.29470
$951$		0			0
$952$		0			0
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	0.363249	−	0.629165i	0.0117545	−	0.0203593i
$956$	16.2255			0.524769
$957$		0			0
$958$	−38.9465	+	67.4573i	−1.25830	+	2.17945i
$959$		0			0
$960$		0			0
$961$	12.3304	−	21.3568i	0.397753	−	0.688929i
$962$	1.43686	−	2.48871i	0.0463262	−	0.0802394i
$963$		0			0
$964$	6.90857	+	11.9660i	0.222510	+	0.385399i
$965$	−1.08985	−	1.88768i	−0.0350836	−	0.0607666i
$966$		0			0
$967$	4.98525	−	8.63470i	0.160315	−	0.277673i	−0.774667	−	0.632370i	$-0.782082\pi$
$967$	4.98525	−	8.63470i	0.160315	−	0.277673i	0.934982	+	0.354696i	$0.115416\pi$
$968$	3.67581			0.118145
$969$		0			0
$970$	−2.39377			−0.0768592
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	0.874288	−	0.485407i	$-0.161329\pi$
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	−0.857519	+	0.514453i	$0.827995\pi$
$972$		0			0
$973$		0			0
$974$	−4.72847	−	8.18994i	−0.151510	−	0.262423i
$975$		0			0
$976$	1.19302	+	2.06637i	0.0381875	+	0.0661428i
$977$	−9.44308	−	16.3559i	−0.302111	−	0.523272i	0.674503	−	0.738272i	$-0.264358\pi$
$977$	−9.44308	−	16.3559i	−0.302111	−	0.523272i	−0.976614	+	0.215001i	$0.931025\pi$
$978$		0			0
$979$	−7.54466	−	13.0677i	−0.241128	−	0.417647i
$980$		0			0
$981$		0			0
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	2.28891			0.0730050			0.0365025	−	0.999334i	$-0.488378\pi$
$983$	2.28891			0.0730050			0.0365025	+	0.999334i	$0.488378\pi$
$984$		0			0
$985$	−3.10930			−0.0990707
$986$	31.7789	−	55.0427i	1.01205	−	1.75292i
$987$		0			0
$988$	−1.53311	−	2.65542i	−0.0487746	−	0.0844801i
$989$	−5.81707	−	10.0755i	−0.184972	−	0.320381i
$990$		0			0
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	−10.2191	+	17.6999i	−0.324455	+	0.561973i
$993$		0			0
$994$		0			0
$995$	−1.45837	+	2.52598i	−0.0462336	+	0.0800789i
$996$		0			0
$997$	−37.0151			−1.17228			−0.586139	−	0.810210i	$-0.699353\pi$
$997$	−37.0151			−1.17228			−0.586139	+	0.810210i	$0.699353\pi$
$998$	9.51732	−	16.4845i	0.301266	−	0.521807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.f.361.5		10
3.2	odd	2		441.2.g.f.67.1		10
7.2	even	3		1323.2.h.f.226.1		10
7.3	odd	6		1323.2.f.e.442.5		10
7.4	even	3		1323.2.f.f.442.5		10
7.5	odd	6		189.2.h.b.37.1		10
7.6	odd	2		189.2.g.b.172.5		10
9.2	odd	6		441.2.h.f.214.5		10
9.7	even	3		1323.2.h.f.802.1		10
21.2	odd	6		441.2.h.f.373.5		10
21.5	even	6		63.2.h.b.58.5	yes	10
21.11	odd	6		441.2.f.f.148.1		10
21.17	even	6		441.2.f.e.148.1		10
21.20	even	2		63.2.g.b.4.1	✓	10
28.19	even	6		3024.2.q.i.2305.3		10
28.27	even	2		3024.2.t.i.1873.3		10
63.2	odd	6		441.2.g.f.79.1		10
63.4	even	3		3969.2.a.bb.1.1		5
63.5	even	6		567.2.e.f.163.1		10
63.11	odd	6		441.2.f.f.295.1		10
63.13	odd	6		567.2.e.e.487.5		10
63.16	even	3	inner	1323.2.g.f.667.5		10
63.20	even	6		63.2.h.b.25.5	yes	10
63.25	even	3		1323.2.f.f.883.5		10
63.31	odd	6		3969.2.a.bc.1.1		5
63.32	odd	6		3969.2.a.ba.1.5		5
63.34	odd	6		189.2.h.b.46.1		10
63.38	even	6		441.2.f.e.295.1		10
63.40	odd	6		567.2.e.e.163.5		10
63.41	even	6		567.2.e.f.487.1		10
63.47	even	6		63.2.g.b.16.1	yes	10
63.52	odd	6		1323.2.f.e.883.5		10
63.59	even	6		3969.2.a.z.1.5		5
63.61	odd	6		189.2.g.b.100.5		10
84.47	odd	6		1008.2.q.i.625.5		10
84.83	odd	2		1008.2.t.i.193.2		10
252.47	odd	6		1008.2.t.i.961.2		10
252.83	odd	6		1008.2.q.i.529.5		10
252.187	even	6		3024.2.t.i.289.3		10
252.223	even	6		3024.2.q.i.2881.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	21.20	even	2
63.2.g.b.16.1	yes	10	63.47	even	6
63.2.h.b.25.5	yes	10	63.20	even	6
63.2.h.b.58.5	yes	10	21.5	even	6
189.2.g.b.100.5		10	63.61	odd	6
189.2.g.b.172.5		10	7.6	odd	2
189.2.h.b.37.1		10	7.5	odd	6
189.2.h.b.46.1		10	63.34	odd	6
441.2.f.e.148.1		10	21.17	even	6
441.2.f.e.295.1		10	63.38	even	6
441.2.f.f.148.1		10	21.11	odd	6
441.2.f.f.295.1		10	63.11	odd	6
441.2.g.f.67.1		10	3.2	odd	2
441.2.g.f.79.1		10	63.2	odd	6
441.2.h.f.214.5		10	9.2	odd	6
441.2.h.f.373.5		10	21.2	odd	6
567.2.e.e.163.5		10	63.40	odd	6
567.2.e.e.487.5		10	63.13	odd	6
567.2.e.f.163.1		10	63.5	even	6
567.2.e.f.487.1		10	63.41	even	6
1008.2.q.i.529.5		10	252.83	odd	6
1008.2.q.i.625.5		10	84.47	odd	6
1008.2.t.i.193.2		10	84.83	odd	2
1008.2.t.i.961.2		10	252.47	odd	6
1323.2.f.e.442.5		10	7.3	odd	6
1323.2.f.e.883.5		10	63.52	odd	6
1323.2.f.f.442.5		10	7.4	even	3
1323.2.f.f.883.5		10	63.25	even	3
1323.2.g.f.361.5		10	1.1	even	1	trivial
1323.2.g.f.667.5		10	63.16	even	3	inner
1323.2.h.f.226.1		10	7.2	even	3
1323.2.h.f.802.1		10	9.7	even	3
3024.2.q.i.2305.3		10	28.19	even	6
3024.2.q.i.2881.3		10	252.223	even	6
3024.2.t.i.289.3		10	252.187	even	6
3024.2.t.i.1873.3		10	28.27	even	2
3969.2.a.z.1.5		5	63.59	even	6
3969.2.a.ba.1.5		5	63.32	odd	6
3969.2.a.bb.1.1		5	63.4	even	3
3969.2.a.bc.1.1		5	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +O(q^{10})\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +(-0.150168 + 0.260099i) q^{10} -1.66404 q^{11} +(-0.0999454 + 0.173111i) q^{13} +(1.75890 - 3.04650i) q^{16} +(3.13555 - 5.43093i) q^{17} +(-3.45879 - 5.99080i) q^{19} +(0.162147 + 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +6.18184 q^{23} -4.97861 q^{25} +(0.205252 + 0.355508i) q^{26} +(2.46757 + 4.27396i) q^{29} +(-1.25890 - 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(-6.43931 - 11.1532i) q^{34} +(-3.50023 - 6.06257i) q^{37} -14.2062 q^{38} +0.0653107 q^{40} +(1.15895 - 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(0.905887 - 1.56904i) q^{47} +(-5.11215 + 8.85451i) q^{50} +0.443250 q^{52} +(2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +10.1350 q^{58} +(2.28549 + 3.95859i) q^{59} +(-0.339138 + 0.587404i) q^{61} -5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} -13.9059 q^{68} -1.27749 q^{71} +(0.778603 - 1.34858i) q^{73} -14.3765 q^{74} +(-7.66972 + 13.2843i) q^{76} +(-6.39787 + 11.0814i) q^{79} +(-0.257231 + 0.445537i) q^{80} +(-2.38008 - 4.12241i) q^{82} +(3.75687 + 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} -3.86493 q^{86} +0.743131 q^{88} +(4.53394 + 7.85301i) q^{89} +(-6.85398 - 11.8714i) q^{92} +(-1.86037 - 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(3.98514 + 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8} + 7 q^{10} + 8 q^{11} + 8 q^{13} + 2 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} + 11 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} - 40 q^{38} - 6 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 27 q^{47} - 19 q^{50} - 20 q^{52} + 21 q^{53} - 4 q^{55} + 20 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 54 q^{68} + 6 q^{71} - 15 q^{73} - 72 q^{74} - 5 q^{76} - 4 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} + 28 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8 + 7 * q^10 + 8 * q^11 + 8 * q^13 + 2 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 + 11 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 - 40 * q^38 - 6 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 27 * q^47 - 19 * q^50 - 20 * q^52 + 21 * q^53 - 4 * q^55 + 20 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 54 * q^68 + 6 * q^71 - 15 * q^73 - 72 * q^74 - 5 * q^76 - 4 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 + 28 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more